𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, February 09, 2022

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Generated Thu 10 Feb 02:41:12 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/2022/02/09/

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

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

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Qma88nEdV64rLJsqR8uVd62B8zwrDvuX6Etg42wsovLPUQ

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

⦿ [Meme] Team UPC and Team Battistelli Above the Law, Ignore the Law, Break the Law | Techrights

⦿ The EPO’s Overseer/Overseen Collusion — Part XXXXVI: An Erosion of Fundamental Rights Protection? | Techrights

⦿ Response to Gemini Misconceptions and Mythology (It’s Not Ugly or Just for Geeks) | Techrights

⦿ Despite Occasional Shutdowns, Geminispace Has a Net Gain of About 100 Working Capsules Per Month (It Has Accelerated Further in 2022) | Techrights

⦿ Staff Holding Management at the EPO Accountable | Techrights

⦿ [Meme] Drunk Driving, Like Son of António Campinos | Techrights

⦿ IRC Proceedings: Tuesday, February 08, 2022 | Techrights

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

	http://techrights.org/2022/02/09/breaking-the-law-in-nl/#comments

	http://techrights.org/2022/02/09/fundamental-rights-epo/#comments

	http://techrights.org/2022/02/09/gemini-not-ugly/#comments

	http://techrights.org/2022/02/09/geminispace-1705-working-capsules/#comments

	http://techrights.org/2022/02/09/holding-management-accountable/#comments

	http://techrights.org/2022/02/09/iloat-ruling-no-4430-and-iloat-ruling-no-4482/#comments

	http://techrights.org/2022/02/09/irc-log-080222/#comments

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

	http://techrights.org/2022/02/09/epic-wants-rootkits-in-linux/#comments

	http://techrights.org/2022/02/09/gulag-stadia-failing/#comments

                ䷩ 𝚕𝚒𝚗𝚎 66

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/breaking-the-law-in-nl/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/09/breaking-the-law-in-nl/

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Gemini_version_available_♊︎

✐ [Meme]_Team_UPC_and_Team_Battistelli_Above_the_Law,_Ignore_the_Law,_Break_the

Law⠀✐

Posted in Europe, Patents at 8:52 am by Dr. Roy Schestowitz

Much can be said about how Team UPC too flagrantly breaks_the_law with the

EPO's_complicity

        🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Law? Sorry, not applicable to us.⦈

Summary: In the_Netherlands, EPO management is effectively above the law, so

Benoît_Battistelli and António_Campinos can ignore court rulings, gaslight an

International_Criminal_Court_(ICC)_judge_looking_to_rectify_things_at_the_EPO,

and bribe_Dutch_media to defame actual judges with integrity

      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇António Campinos fronting for Team UPC⦈

Tony fronting for ‘Team UPC’ only 3 days after he became EPO President.

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⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡆⠀⠀⠀⠀⢡⣴⣿⣼⣿⣿⠏⠀⠀⣸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠩⢹⣿⡍⠈⡿⢿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⢀⡀⠀⢰⣾⣿⠉⠉⠉⠁⠀⠀⣰⣿⣿⣿⣿⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⠀⠐⢪⣆⠷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣷⣾⣟⣿⣿⣿⣿⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣿⣿⣷⣾⣿⣿⣦⣤⣤⣴⣶⣤⣿⣿⡏⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⣾⣿⣿⣿⡿⠋⠛⠉⠈⠛⠿⡇⠀⠈⢿⡉⣭⣝⣿⡿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢰⣿⣯⣿⡿⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿

⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣿⣿⡏⣉⣹⣿⣟⣿⣟⠛⠃⠀⠀⠀⣀⣤⣴⣶⣄⠀⠈⠑⠿⠿⠿⣶⣿⣷⣦⣀⠀⠀⠀⠀⢠⣿⡿⣿⣿⠇⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣶⣬⣿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡷⠀⠀⢀⣘⠛⠙⠋⠙⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣄⠀⣰⣿⠟⠹⣿⡯⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢻⣿⣿⣿⣿⡟⠀⠀⠉⠉⠁⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣛⣷⣶⣶⣷⣤⣦⣤⣶⣦⣶⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠘⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣧⣰⣶⡖⠉⠛⠛⠛⠉⠙⢿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⡿⠀⠙⠟⠻⢿⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠟⠋⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣄⣄⣀⣀⣀⣀⣼⠉⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣷⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠋⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⠛⣿⡿⠟⠃⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⢿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏⢠⡆⠁⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀⡀⠀⠀⠐

⠀⠀⠉⠉⠉⠉⢉⣭⣭⣭⣭⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣤⣄⣼⣿⣿⣿⣿⣿⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣷⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⠻⣿⣿⣿⣿⠇⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠾⠀⠰⠆⢀⠙⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⡁⠀⠀⠀⢠⣴⣿⣴⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⡿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⢾⣿⠋⠉⠉⠉⠀⠀⠀⠈⢿⣿⣿⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠐⠪⣏⠳⠀⠈⢻⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣤⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣦⣄⣄⣠⣀⣀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⣿⣷⣶⣾⣟⣶⣶⣶⣿⣿⣿⡏⢀⡴⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⣿⣿⣼⣿⣿⠿⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣟

⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⡏⣉⣹⣿⢏⣿⣿⣿⣷⡏⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⠀⡃⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⠉⠛⢿⣿⣦⣄⡈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⠟⢻⣿⣿⠃⠀⠃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⠈⠛⠛⢿⡿⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢺⣿⡟⠀⠀⠀⠈⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧⡀⠀⠘⠚⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⠇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡇⠀⠘⠛⠛⠻⣿⠷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣰⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⠋⠘⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠰⠚⠫⠁⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠐⠒⠒⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣰⣶⣶⠶⠶⠒

⠀⠀⠀⢀⡴⠉⣉⣭⣭⣿⣽⣿⣿⣿⣿⠏⠉⢉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠁⠙⢛⣻⣵⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣄⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⣟⠋⢉⠋⠹⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠙⠀⡜⢃⣼⣈⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠿⣿⣿⣿⣿⡇⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⣷⣿⣿⡿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢸⣆⠓⠀⠀⣿⣿⣿⣿⡿⢁⣸⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣿⠧⣠⣾⣿⣿⡃⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⢀⣀⡀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣾⣿⣯⣿⣶⣿⣿⣿⣿⣿⣿⡿⢓⣀⣬⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣾⠂⠉⠻⣿⣷⣴⣿⣿⣿⣿⣿⣶⣶⣤⣶⣤⡀⠀⠀⠙⢿⣿⣿⣿

⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡉⣁⣹⣿⢉⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠙⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⣿⣿⣦⡀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⠋⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠙⢿⣷⡄⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⡿⢿⣿⣧⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣫⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠛⠀⠀⠀⠀⠀⠀⢀⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶

⠀⠀⠀⠙⣫⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⡏⢉⣩⣭⣍⡉⠉⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣶⣶⣆⣀⣈⠉⠉⠉⠉⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠾⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠁⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡼⢿⣿⣿⡿⣫⡾⠏⠁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⢹⣿⣿⠟⣿⣯⠁⢹⡄⠈⠿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⣿⡿⠿⠿⣿⣿⣿⡿⠁⠈⢿⣿⣾⠋⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣦⣤⡏⠀⠀⣋⣡⣾⣆⣿⣿⣿⣷⠀⠈⢿⣿⣷⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⢉⣇⠉⠀⢀⣼⣿⣿⣿⢀⣴⠟⠉⡵⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢋⢡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣤⢄⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⣿

⠀⢘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣭⣥⣼⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣷⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⢿⣿⣦⡀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡿⠛⠁⡽⢿⣿⣿⡿⣿⣿⣿⣿⠀⠒⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⠻⣷⣤⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⢿⣷⣦⣤⣤⣿⠁⠀⠀⠻⢿⠿⠿⠛⠋⠀⠙⠛⠛⢿⣿⣆⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⡿⠿⠟⠋⠛⠛⠿⠋⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠖

⠀⠀⢀⣭⡿⠉⣉⣭⣭⣭⣽⣿⣿⣿⣿⣏⡉⢉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣤⣬⣉⠉⠉⠉⠁⢀⣠⣴⣶⣶

⠀⠀⠈⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠿⠏⢹⣿⠀⢰⡆⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢶⣾⣄⣘⣧⣶⣿⣿⣿⣿⠟⠁⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣏⠁⠈⠋⢛⠛⠋⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣭⡉⠉⠀⠀⡼⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠏⢹⣦⣤⣤⣿⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⠀⠀⠀⠙⢿⣿⣿⣟

⠀⢐⣒⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣿⡿⣿⣿⣋⡙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢰⣿⣯⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣷⣄⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣟⠷⠀⠀⠈⠉⢿⣿⣧⡀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠈⠛⣿⣦⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠹⣿⣿⣿⠟⠀⠉⠛⠛⢿⠿⡦⠀⠀⠀⠐⢿⣿⣿⠟⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⡿⠟⠉⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢘⡿⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠘⠛⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠃⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠰⠶⠶

⠀⠀⠀⡹⠟⠍⢉⣭⣭⣭⣽⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⢉⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⡅⠙⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢯⣭⣀⣿⣷⡞⢇⣶⡏⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣏⣿⣀⣁⣼⣿⣆⣀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠈⢿⣿⣿⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠿⢿⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡧⢶⣤⣤⣄⠀⠀⠙⣿⣿⣿⣿

⠀⢠⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⢁⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⣰⣾⣸⠁⠉⢿⣿⣷⡄⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⠝⣿⣿⠏⠀⠀⠀⢀⣀⣼⣿⢃⢛⠆⠀⠀⠹⣿⣿⣆⠀⠀⠀⠸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢁⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⠃⠀⠀⡝⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇⠀⢩⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣷⡄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠈⠙⢫⠉⠀⠀⢸⣿⣿⣿⣿⣿⠛⠃⠀⢸⣿⣿⣿⣿⣿⣷⣤⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⣀⣀⣾⣿⠿⠿⠻⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣤⣶⣮⣷⣦⣄⣤⣶⣭⣿⢟⠹⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠖⠒⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⢀⡶⠖

⠀⠀⠀⠉⠉⠉⢉⣭⡭⣿⣿⣿⣿⣿⣿⣿⣿⠉⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⣡⣿⣿⣿⣿⣿⣶⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢋⣠⣾⣶⣶

⠀⠀⠘⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⣿

⠀⠀⠁⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡴⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣴⡟⠀⠘⡊⢠⣿⣧⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠞⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⡿⠛⢻⣿⣟⡛⠛⡿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢿⣿⣇⠀⠀⣭⣽⡟⠻⠛⠿⠃⠀⠀⠈⢿⣿⣿⣩⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣷⣤⣼⣿⣿⣧⣶⣷⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣶⡆⠀⠀⣽⣿⠁⣀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⢹⣿⣿⣿⡇⠀⠀⠈⠿⣿⡟⠻⣿⡿⠿⠿⣿⣿⠛⠙⣿⠏⠁⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠠⠟⢀⣿⣟⣿⣷⣶⣦⡄⠀⠙⣿⣿⣿⣿

⠀⢀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡿⣿⣿⣿⠀⠀⢀⣠⣴⣾⣷⣦⠹⡷⣄⡤⣽⢇⣠⣴⣤⣄⡀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⣸⡇⠈⢹⣿⣿⣆⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⢀⣼⣿⣿⣿⣿⣿⣿⣄⠈⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⠁⠀⠀⠀⣿⣿⣇⠀⠀⢸⡘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠸⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣿⠀⠀⠀⠀⠀⠹⢻⣿⡀⠀⠀⢠

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⡿⠿⠇⠘⠋⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢻

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⡟⠉⢿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠀⣲⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠺⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⢿⣿⠇⠋⢻⣿⣿⡿⠛⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠐⣶⣶⣶⠆

⠀⠀⠀⡍⠉⠉⣽⣯⣭⣽⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⣨⣶⣶⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣸⣿⣿⣷

⠀⠀⢠⠁⢀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿

⠀⠀⡌⣠⡾⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠻⢻⠟⠻⠿⠟⡿⠿⣿⣿⣿⡿⠟⢫⣿⣿⣿⣿⣿⣿

⠀⠀⠙⠟⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⡿⠀⠀⠀⠐⠀⢰⣷⣠⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⣭⣾⡟⠛⠛⠿⠁⠀⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀⢃⣿⣿⠀⢈⣟⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⣠⣸⣿⣛⡄⠀⠀⠀⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⠃⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠟⠀⣿⡟⡿⣷⣶⣤⡀⠀⠙⣿⣿⣿⣿

⠀⢀⣀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣇⢀⣀⣹⡏⣨⣿⠟⠉⠀⠀⠀⠀⠀⢠⣿⣇⣻⣿⣿⣿⣿⣷⣄⡀⣠⣴⣾⣿⣷⣿⣙⢻⣿⣿⣆⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠨⣿⡿⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠸⠃⣿⣿⡀⠀⠀⠀⠸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣿⣾⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⢻⣿⡇⠀⠀⢠⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣸⣿⡏⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠻⢿⣿⣿⠿⣿⣿⡿⠛⠿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠹⡇⠀⠀⠈⣀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢸⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠇⠀⠀⠨⣿⣿⣿⣿⡿⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⣤⣤⣾⣾⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠒

⠀⠀⠀⡍⠉⣽⢫⣭⣭⣿⣿⣿⣿⣿⣭⣭⣈⠁⣠⣼⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⣠⣶⣶⣦⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠀⢀⣠⣴⣶⣶

⠀⠀⢴⣠⡾⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠙⠃⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢹⣿⣿⣿⣿⠟⢠⣄⢈⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠿⠛⠁⠀⠢⣻⣿⡾⣿⣿⠇⠀⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣾⣿⣁⣀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣄⣀⡟⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢀⣴⠦⣿⣿⣷⡀⠀⠀⠀⢻⣿⣀⣶⣶⣤⣤⣀⡀⠀⠀⠙⢿⣿⣿⣟

⠀⢀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣖⢶⣾⣿⣴⣿⣋⡀⠀⠀⠀⠀⠀⠀⣼⣿⣤⠙⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⢿⣿⣦⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠻⣿⣿⣿⠉⠉⠉⠀⢠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⡟⠛⠏⣿⣟⣿⣷⣤⣤⣴⣿⣿⣿⣿⠿⠀⠟⣿⣿⣧⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⢀⣼⣿⣿⣿⣷⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠻⠃⠀⠀⡿⢻⢿⣿⣿⣿⣿⣿⣿⡿⠹⠀⠀⠀⠈⣿⣿⣦⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠣⠘⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⢿⣿⣿⣷⠤⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠋⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⡿⢿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠙⣿⡟⠛⠀⠀⠀⢠⡿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠖

⠀⠀⠀⡍⢉⣽⢋⣭⣭⣿⣿⣿⣿⣿⣭⣍⣈⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣧⣤⣌⡉⠉⠉⠉⠀⢁⣠⣴⣶⣶

⠀⠀⢺⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣾⣿⣿⣿⣿⣉⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⣆⣼⠋⠉⢻⣉⣿⣿⣿⣿⣿⡏⠀⠀⠈⢿⣿⣷⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⠀⠀⠙⠉⠙⠛⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⠿⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣤⣾⣷⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟

⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣾⣿⠛⠛⢿⣿⡿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⣸⣿⠿⣿⣿⣿⣿⣧⠀⠈⠛⠿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿⡗⠀⠘⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠋⠉⣿⣿⣿⡄⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢻⠏⠀⢰⣿⣿⣿⣿⣿⣶⣴⣶⣤⣿⠟⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⢿⣿⣦⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠀⠙⠉⠙⢿⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢿⡿⠿⠷⠒⠀⠀⠀⠶⣴⣠⣤⣾⣷⣶⣾⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣤⣴⣶

⠀⠀⠀⠉⡉⠉⢉⣭⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠁⠈⢻⣿⣿⣿⣿

⠀⠀⠀⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣴⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⢹⡿⣻⣻⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠻⣿⣿⣿⣀⣀⣹⣿⣉⠉⣹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⡀⣾⣾⣷⣿⣶⣿⣿⣿⣿⣿⡟⠀⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠃⠉⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⢹⣧⡀⠀⢀⣀⠀⠀⠀⢹⣿⣿⣿⣇⣠⣶⣶⣶⣿⣶⠹⢿⣿⣿⣿⣿⣵⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢻⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⡟⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿

⠀⢀⣀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣷⣦⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⡀⠘⣿⣶⣄⠀⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢿⣿⠇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣇⡀⢸⢿⣿⣆⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣐⡛⠊⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⠏⢸⣿⣿⣿⠛⠛⠿⣿⣿⣿⣿⢣⢿⣿⠇⠀⠸⢿⣿⣇⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⠿⠟⠀⠈⢿⠿⢿⣿⡁⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠈⣿⡿⢋⡟⠀⠉⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⠟⠀⠀⠀⠀⠀⢙⠙⠀⣿⣄⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣴⣶⣿⣿⣿⣿⣿⣴⣆⠀⠀⠀⠀⠀⠀⢀⡐⣶⡿⠿⡿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠽⢿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠾⠀⡉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠂⠀⠈⠀⠀⠻⠿⠿⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⢰⣶⣶⡶⠶⠖

⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢛⣻⣷⣶⣶

⠀⠀⠀⠀⠀⠁⠀⣨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣻⡿⢙⠉⠙⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⣛⢳⡟⢀⡸⢂⣤⣽⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣧⣹⣧⣀⣠⣿⣧⣀⣨⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣹⣭⣽⣿⣿⣿⣷⣿⣿⣿⣿⠀⠉⢀⡀⠈⢿⣿⣷⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠙⠻⣿⣍⡉⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣠⣴⣶⣶⣶⡄⠹⣿⣿⣿⢿⢿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⣿⣿⣿⣿

⠀⢀⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣁⣀⣀⣿⣿⣧⣀⣀⣠⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⢀⣰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣼⣿⡷⠀⢸⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡗⢀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣿⣿⠃⠀⠀⡿⠋⠁⠳⣦⣀⡀⠹⣿⣿⣿⣿⣿⢿⣿⣷⡀⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢷⠄⢄⢀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⡿⠋⠀⠀⠀⠇⠀⠀⠀⠹⣿⣿⡶⣾⣿⣿⠟⠁⠈⢻⣿⣷⡄⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣼⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⢿⣿⣿⡿⠋⠻⠿⢿⣿⣧⡄⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⡿⢡⡿⠛⠁⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⢿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣸⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢿⠿⠛⡿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⢲⣶⣤⡶⠖

⠀⠀⠀⠉⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣴⣶⣄⣿⣿⣷⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⢫⡟⠉⢩⠠⢀⣰⣾⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡞⠉⢠⠈⠀⣿⡄⣼⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⠋⢉⣿⡉⠉⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢩⢭⡍⠐⠀⠀⢐⠀⣿⠿⠻⠿⠃⠀⠀⠈⢿⣿⣷⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⡿⠿⣷⣿⣷⣶⣾⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⢀⡀⢼⣗⠂⠈⠁⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⡉⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⠁⠀⠀⣈⣀⡀⠈⠘⢛⣿⡉⠉⢩⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠻⡦⠀⠀⠀⠀⢘⣿⣇⣿⣷⣶⣶⣤⣄⡀⠀⠙⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣄⠀⢀⣠⠀⠀⠀⣼⣿⣯⣴⣾⣿⣿⣿⣿⣷⡀⠈⠛⠻⠋⢋⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣾⣿⡂⠀⢨⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣟⣿⣷⡄⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⠿⠂⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣿⡿⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⡾⢻⣿⣿⡄⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡃⠀⠀⢠⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⡿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⠈⢻⢿⣷⡄⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣾⣶⣿⣿⡿⠿⠟⣻⣿⣿⠟⠀⠀⠀⠀⠈⠘⣿⣿⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠉⠀⠻⣿⣿⣀⡀⠀⠘⠟⠛⠋⢹⣀⣀⣠⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⢿⠟⠋⠀⠈⠉⠉⠀⠀⠀⠀⠹⠧⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⢀⣹⢿⣿⣿⣿⣿⣗⠀⠀⠀⢀⣀⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠛⠉⠉⡀⠀⠀⠀⠀⠚⠛⠋⠁⠉⠙⠛⠃⣠⣶⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣍⠉⠁⠉⠀⢉⣻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠐⠶⣦⡄⠒

⣤⣾⣿⡟⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣤⣤⣤⣶⣿⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣉⠄⠀⢀⣠⣼⣷⣶

⢿⡿⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⢟⡛⠋⣛⠛⠻⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣯⣵⠏⠈⠁⢀⠐⢀⣤⠀⣽⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣾⣿⣿⣿⣿⠟⢻⣿⡿⡿⠿⣿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⡄⠀⠀⠀⠔⢘⣿⢾⠻⡿⠃⠀⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣷⣄⣤⣿⣿⣅⣤⣧⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⣾⠀⠀⠀⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⣷⡄⠀⠀⠉⠉⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠘⠻⠿⠏⠛⢿⣿⠿⠿⣿⣿⠿⠙⠟⠁⠀⠀⠀⠀⠀⠀⢠⣾⡟⢿⣿⣯⣏⡀⠀⠀⢻⣿⠇⢶⣦⣤⣀⣀⠀⠀⠀⠙⢿⣿⣿⣿

⠀⢀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣀⣸⣿⣶⣶⢾⢷⣦⣤⠀⠛⠿⢿⠀⠀⠀⣠⣤⣶⣶⣶⡄⠘⣷⡠⣤⢼⢇⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣼⣿⣿⣿⣷⣶⣦⣬⣅⣤⣿⣿⣿⣿⡿⣿⣦⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢹⣷⣶⣶⣤⡀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠢⠔⠀⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣧⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⠐⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢯⡟⠁⠊⢸⢿⣿⣆⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠁⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠚⢿⣿⣧⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡟⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⡄⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠈⠛⣿⡇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⣟⠀⠀⠀⣿⣿⣿⠿⠋⠀⠀⠛⠛⠉⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⡛⣭⣤⠠⠶⠀⠀⠀⠀⠀⠄⠀⠀⠈⠙⠀⠀⠀⠭⠝⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠀⠀⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠖

⠀⠀⠀⠈⠉⠉⠉⣩⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣍⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣨⣶⣾⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣬⡉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠉⢺⠄⡈⠛⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠛⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠛⠁⣿⠏⠀⠘⣀⢰⣿⣤⣿⣿⠏⠀⠀⠈⢿⣿⣷⣸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⠟⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⣠⣼⣿⣌⣀⣽⣭⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠰⣿⣷⣾⡏⠀⠀⠈⣽⣼⡟⠙⠀⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣆⣀⣀⣸⣄⣀⣀⣸⡿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⢹⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⠟⠀⠀⠀⠀⠀⣠⡄⠘⢿⣿⣿⠀⠀⠀⣼⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿

⠀⢀⣀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣥⣿⣿⢿⠿⠿⣿⣷⣤⣤⣀⡀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡜⠷⠲⣷⣾⡿⠋⣀⣈⣛⠉⠁⠀⠀⠀⠀⠀⠀⢿⠿⢧⡬⣿⣣⠄⠀⠀⢸⡿⢃⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠈⢿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢤⣦⣜⢿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⣿⣿⣿⣿⣧⡀⠀⠉⠉⣠⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⣽⣅⣀⣹⣿⣿⡮⣦⣀⡈⣿⣿⣿⣿⣿⡏⣿⣿⣷⡄⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣴⣿⣿⡿⠛⣿⣿⣿⣿⣷⣄⣀⣄⣴⣿⣿⣿⣿⣿⣿⠁⠀⠻⠻⢿⣿⣿⢻⠟⠀⠀⢿⣿⣿⡀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡻⡄⠸⣿⣿⣿⣍⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⠋⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠈⠫⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⣴⣤⣤⡃⠀⠀⠀⠉⠛⠋⠉⠻⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⢀⡀⠀⠈⠀⠁⠀⠀⠀⠈⠓⠁⠀⠀⠈⠛⠛⠫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀

⠶⢶⣶⣶⠖⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠖

⠀⠀⠀⠁⠀⠈⢩⣭⣽⣿⣿⣿⣿⣿⣿⣯⣭⣿⣭⣭⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣶⣤⣀⣈⠉⠉⠉⠉⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⣿⠍⢹⡄⠈⠻⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⡿⡟⠉⠹⣿⣿⡻⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠐⢊⠀⣿⣆⣿⣿⡟⠀⠀⠈⢿⣿⣿⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣏⠉⠉⠛⠛⠛⠉⠉⢙⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠻⣿⢿⣿⣶⣶⣿⣿⣦⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⣿⣿⡇⠀⠀⢩⣴⣿⠛⠋⠛⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣆⣀⣤⣾⣦⣤⣤⡼⠟⠛⠛⠷⠀⠀⠀⠀⠀⠀⠀⢉⢨⣷⣦⠉⣿⣿⣿⡿⢻⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⣻⡿⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿

⣂⣤⣴⣶⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣶⣿⡿⠶⠞⢿⣿⣷⣦⣤⣄⡀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣾⣿⠻⣷⣾⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⣿⠇⠈⢻⣿⣷⡀⠀⠀⠸⣿⡿⢸⣿⣶⣤⣤⣄⡀⠀⠀⠀⠈⢿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣧⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣷⠀⢀⣾⣿⣿⣿⣶⣿⣿⣿⣴⣿⣿⡟⡟⢻⣿⣷⡄⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠋⠀⠀⢹⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⡗⠁⠉⢻⣿⣿⡀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⢻⣿⣿⣿⣿⣿⣤⠊⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⡿⠛⠉⢿⣿⣿⣿⠃⠀⠀⠀⠀⠛⢿⣿⣦⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠀⠀⠀⠙⢛⠿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠘⠛⠛⣿⣿⡤⠀⠀⠀⠀⠈⢻⡏⢄⡀⠀⠀⠻⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⡷⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣴⣶⠶⠾⠀⠀⠐⠲⠯⡄⠀⠀⢼⣿⣿⢿⢯⠃⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⢼⢭⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠀⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⢩⣍⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡯⠁⠍⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠁⠀

⠆⠰⣶⣶⠖⠂⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⣿⣭⣭⣿⣿⣿⣿⣿⣏⣩⣭⣭⣭⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣶⣬⣍⠉⠉⠁⠸⢟⣧⣾⣶⣶

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠿⠿⠏⠻⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⠀⠽⠄⡨⠇⢠⡙⢻⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣯⣿⠉⠉⣹⣿⠃⠉⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⣹⠀⠀⠀⢡⠄⣿⣧⣿⣿⡏⠀⠀⠈⢿⣿⣿⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣟⠣⡛⠀⠀⠀⢰⣷⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⣿⣄⡀⣀⣠⣆⠀⠀⠀⠹⠿⡇⠀⠀⠀⢀⣴⣿⣿⣿⠃⠸⣿⣿⣿⡿⢻⣾⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣻⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⣹⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⡿⠇⢸⣿⣿⣾⣤⠀⠀⠸⠋⢹⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇⢀⣤⠄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⡷⠀⣾⣿⣿⣿⡟⠧⣴⡇⠀⢸⣿⣿⣿⣿⣻⣿⣿⣷⡀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⢸⣡⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⣶⣿⣷⠀⠀⣿⣿⣿⡿⠀⠀⢿⣿⣷⡀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣠⣶⣿⡇⠀⢸⣿⣿⣿⣿⣿⡟⠙⠿⠿⣿⣿⣤⡀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡧⣠⣾⣿⡿⠏⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⠛⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⢃⡸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠰⠦⣴⣶⣶⣶⣶⣶⠖

⠀⠘⠀⠀⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠙⠻⢿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⢭⠉⢉⡇⠀⢿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠀⠀⠈⠁⡄⠉⣰⡄⢸⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣏⣿⠁⠁⣸⣿⡀⠀⣹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣶⣿⣗⢶⠁⠀⠀⠀⠐⣂⣽⡿⠿⢿⣿⣶⣆⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠙⠟⠃⠻⢿⣿⣿⣿⣿⣿⡿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣌⡋⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⣿⣿⣀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡟⠿⣿⣿⣏⡛⠛⠛⠿⠿⠿⠿⢿⣿⡗⠀⣀⣤⣴⣶⣦⠈⠻⣿⣿⣿⣿⢿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣮⣿⣧⡀⠀⠀⠀⠐⣿⣿⢰⣶⣾⣿⣿⣿⣿⣧⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣷⣄⠀⣀⣄⠀⠀⣸⣿⣴⣾⣿⣿⣿⣿⣿⣧⡀⠀⠉⠉⣱⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣎⢸⣿⣿⣿⣿⣦⡀⠀⠀⢉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠁⣿⣿⣿⣿⡏⡇⠈⢷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⣿⣿⣿⣿⡇⢿⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⣿⣿⣿⣿⣿⠁⠈⠛⠻⣿⣿⣦⣀⠀⠀⡺⡿⡟⢘⡃⢸⣆⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠉⠙⠻⠿⠿⠏⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠙⢿⣿⠛⠀⠀⠠⠀⠀⠀⠀⠈⣿⠂⠀⠀⠉⠙⠛⠻⠿⠟⠉⠈⠉⠀⠉⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣶⣾⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⠚⠛⠛⠉⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⣤⣤⣤⣤⣦⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣦⣤⣤⣤⡒

⠀⠀⠀⠉⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⠈⠹⢿⣿⣿⣿⣿⣷

⠀⠀⢀⣤⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣶⡆⠀⠀⢰⣿⣿⣿⣿⣿

⢠⣾⣿⣿⣿⡆⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣴⣶⣷⣶⣶⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠛⢭⡉⠉⠄⠀⠻⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠓⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠨⣽⣿⡉⠁⠀⠈⠁⠄⠉⢰⡦⣸⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿

⣿⡿⠛⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢙⣿⡟⠋⢹⣏⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣶⣷⣬⡇⠀⠀⠀⠀⢐⣆⣾⠿⠿⠿⠃⠀⠀⠈⢿⣿⣷⣠⣿⣿

⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠟⠳⣶⣿⣿⣿⣿⣿⢿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣨⡁⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⣶⣶⡄⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣀⡀⢹⡿⣿⣿⣿⡟⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⡀⠀⠀⠀⠈⢿⡷⢸⣶⡆⠘⢻⣿⣦⣀⣙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠉⠉⠙⢻⣭⣭⣍⡉⠉⠉⠛⠋⠉⢻⣋⣤⣶⣿⣿⣿⣿⡄⠈⠛⠛⠉⣸⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣄⠀⠀⠀⢀⣤⣾⣿⡅⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿

⣴⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣼⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⡯⡇⠀⢲⣦⣼⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣳⡝⠛⠀⣠⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠐⢿⣿⣿⢹⡇⢱⠀⠈⢻⣿⣿⣭⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣉⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⡟⠙⠿⣿⣿⣿⣇⡀⠀⠀⠙⣿⡏⢸⡇⠸⡆⠀⠀⠙⠛⢿⠇⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠛⢿⠿⠀⠀⠀⠛⠀⢸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠟⠁⠀⠀⠀⠉⢁⣀⠀⡸⠿⡿⠻⠋⠀⠀⠀⠀⠀⠀⠀⢨⣾⣶⣀⠀⠀⠀⠈⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠟⠋⢛⠛⠉⠉

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠐⠐⠂⠀⠀⣄⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⢸⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠖

⠀⠀⠀⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⣉⣠⣾⣿⣿⣿⣿⣿⣯⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠉⠉⠈⢙⣦⣶⣶⣶

⠀⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⣴⣿⣿⣿⣿⣿

⠀⠀⠀⣼⣦⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣴⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠛⠟⠋⠙⣿⣿⣿⣿⠘⠿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡰⠿⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣤⣤⣾⣹⠿⠋⠀⠹⠆⠈⠇⢠⡈⢹⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠿⠏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⡟⠛⢻⣿⠛⡛⢻⡿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢡⡄⣾⣧⣾⣿⠏⠀⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⢿⣿⣧⣤⣼⣿⣦⣴⣾⣧⣶⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⣷⡿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠃⠸⡿⠻⣿⣿⣿⠋⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣗⡦⠀⠀⠀⠀⢰⣿⣇⢠⣄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠉⣉⣹⣿⣿⣤⡀⠀⢀⣄⠀⠀⠻⠇⠀⢀⣀⣤⣴⣶⡄⠀⢸⡿⠟⠉⢠⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣧⢀⠀⠀⠀⠙⠁⣸⣿⣿⢿⣿⣶⣄⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣠⣀⠀⠀⣴⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡝⡇⠐⣄⡀⣼⣿⣿⣿⣶⠦⠘⠿⣷⣶⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡈⠉⠠⠀⢀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢿⣿⣿⣿⡇⣷⠀⠻⣿⣿⣿⣧⢂⣯⣶⣶⡶⣾⣿⣇⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠴⠆⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⠇⢸⡇⢹⡀⠀⠙⠿⣿⢿⣿⡿⠋⠁⠀⠘⠻⣿⣷⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡧⠀⠀⢿⣿⣿⣿⣿⣿⠃⠀⠈⠻⠟⢿⣿⣷⡄⠀⠀⢹⠀⢸⡇⠸⣧⠀⠀⠀⠋⠀⠈⠁⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠁⠈⠉⠉⠻⠃⠀⠀⢼⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣠⣾⣿⣷⡄⠀⠃⠀⠸⠃⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠛⢿⣶⡦⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣹⠁⠀

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠖

⣿⣿⡟⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢠⣼⣿⣿⣿⣷⣬⣁⡀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣶⣿⣷⣦⣤⣤⠀⠉⠉⠉⠉⠉⠈⢁⣠⣴⣶⣶

⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⢀⠃⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠂⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡛⢋⡏⠈⢿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⣿⡿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢶⣶⣤⣿⡋⠛⠀⠈⠁⠆⠉⣰⡆⣽⣿⣿⠃⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠛⠿⠻⠛⠟⠛⠻⣿⣿⣿⣿⠀⠀⠀⠹⢿⣿⣿⣧⣀⣸⣿⣯⣀⣼⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⢘⣇⣿⠿⠛⠛⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⠻⣧⣀⣀⣤⣴⣄⣀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠈⠻⠏⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⠀⠀⠀⠀⢈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣏⣁⠉⠉⠉⠀⠀⠀⢀⣀⣤⣤⡄⠹⠿⣿⡿⠿⠋⣠⣼⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣾⣦⠀⠀⠀⠸⣿⠿⣹⣷⣶⣤⣤⣀⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣄⠀⣰⣾⣿⣿⣿⣿⣧⠀⠀⠁⠀⢀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⣄⠀⠐⣦⣴⣿⣿⣏⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⣷⠊⣿⣾⣿⣿⣏⣿⣿⡟⣿⢹⣿⣿⣄⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢹⡇⣿⠇⢯⠀⠘⢿⣿⣿⣿⡏⠀⠻⠿⠏⠻⢿⣿⣧⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣧⡀⠀⠀⠀⠸⠀⣼⠁⢸⡀⠀⠈⠉⠙⠛⠁⣶⠟⠀⠀⠀⠀⠙⢻⣿⡆⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠛⠿⠟⠋⠀⠀⠀⠈⠉⠛⢿⠁⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠙⢿⢿⠂⠀⠀⠀⠀⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⠏⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢂⠀⠘⠀⠀⡿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠀⠀⠀⠀⠉⠛⠛⠛⢿⣧⣀⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀

⣲⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⣶

⠿⢿⣿⣿⠇⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣯⣉⣉⣉⣩⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⣽⣿⣿⣿⣿⣿⣆⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣤⣤⣄⠈⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⠟⢹⡏⠉⢥⠀⠘⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⡛⠻⣿⡟⠛⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣫⣡⠀⠀⠀⠰⠁⢠⣆⢸⣿⣿⠃⠀⠈⢿⣿⣷⣠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⢀⣄⡀⠈⠁⣤⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣤⣿⣧⣤⣼⣿⣧⣤⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⢛⣽⣏⠀⠀⠀⠀⠀⣯⣼⠟⠛⠛⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⡏⠀⠀⠀⠀⠙⠿⠿⠀⠛⠹⣿⣿⣿⣿⣿⠿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⢀⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⢣⣤⣤⣀⣀⠀⠀⠀⠀⢀⣀⣤⣴⣤⣄⠀⠈⠛⠛⠛⠉⢰⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠈⠻⠿⢸⣿⡶⣦⣤⣄⡀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠋⣡⣾⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠄⠀⠀⢀⣴⣾⣟⡇⠙⠻⣿⣿⣄⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠇⠀⢳⣶⣿⣿⢏⣿⠁⢀⣠⣴⣿⣿⣇⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡵⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠻⣿⡷⠘⠿⠿⠿⣿⣿⢻⣿⣿⣿⣿⡆⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⡇⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠻⠃⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣭⢉⣥⣨⣍⣭⣭⣡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣠⣬⣠⣤⡍⢡⣭⢡⣤⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠁⠀⣿⢸⣿⣿⣿⣿⣿⢽⣼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⡁⡀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠂⠀⢀⡀⠀⠀⠀⠲⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣰⣶⡔⠀⠲⢶⣶⣶⣶⣶

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣏⣭⣭⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⠀⠀⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠛⠛⠛⠁⠈⢿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠦⣘⠁⠀⠙⠀⡐⠂⣀⠈⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠉⢹⣿⠁⠉⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⠂⠸⠀⠀⠀⠀⢠⢄⣿⣼⣿⡿⠁⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡀⠀⣨⣄⠈⠁⢀⣈⣿⣿⣿⣿⠇⠀⠀⢻⣿⣿⣿⡿⣿⣽⣿⣷⣶⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠇⠀⠀⠀⠀⢸⡾⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠙⠛⠀⠈⠁⠹⣿⣿⣋⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣺⣿⠀⠀⠀⠀⠀⢿⣧⢰⣦⣴⣷⣶⣤⣄⠀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⣿⣿⣏⣠⣀⣈⣙⠁⠀⠀⠀⣠⣶⣾⣿⣿⣶⡀⠀⠈⠙⠋⠀⢨⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⡀⠀⠀⠀⠀⣠⣼⠿⣿⣿⣿⣿⣿⣷⣆⡀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠨⢿⣟⢃⢡⠀⢢⣀⣼⡿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣶⣶⡄⠸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠨⡏⠈⢐⠀⠈⢿⣿⡃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠃⢸⠟⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠿⣷⡆⠀⢀⣦⠉⢿⣿⣿⣿⣿⣿⣷⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠙⠛⠛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠐⣿⢃⠀⣀⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣤⢀⣤⣠⣄⣤⣤⣨⣭⡙⣩⣭⣉⣭⡍⣭⣍⣡⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣨⣭⡙⣿⡿

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠈⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⠀⠀⠉⠉⠉⠉⣉⣈⣉⣉⣡⣦⣌⣋⣉⣛⣁⣉⣉⡉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⠉⠁⠙⢋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⡶⠒⠒⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣀⡀⣀⣠⣶⣶⣶⣶⣶

⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣏⣉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠿⠟⠻⠻⠿⡿⠿⢛⣫⣵⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⡟⠛⠀⣠⠀⢀⡀⠀⠰⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⠓⠦⣼⠀⠀⠀⠀⠈⠀⣴⢀⣾⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⡿⣿⡁⣁⣼⣿⣄⣀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠒⠸⠀⠀⠀⠀⢨⣥⡿⠛⠿⠏⠀⠀⣸⣿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠟⠿⢿⣿⡿⣿⣿⣿⣿⡟⠀⠙⣿⣿⣿⡟⢿⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣿⠃⠀⠀⠀⠀⢸⡏⢀⡀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⣿⣧⣄⠀⢀⣀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⣈⣭⣄⡀⠀⢻⣿⣧⡄⣨⣿⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢘⣿⣿⠀⠀⠀⠀⠀⠘⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣷⣄⢰⣿⣿⡟⠀⢠⣶⣿⣿⣿⣿⣿⣄⠀⠈⠉⠗⢓⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⡟⠀⢸⣿⡿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡉⠉⠉⣰⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠃⠀⢘⣿⡏⠀⠀⠀⠘⣧⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⢿⡿⠿⢿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢒⣿⠇⠀⢸⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢻

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠉⠻⡿⢿⣿⣧⣄⠀⠀⠀⠀⠈⠀⠀⠐⡆⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠠⣤⣾⣷⣷⠀⠀⠀⠀⠀⠙⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⣩⣭⡙⣩⣭⣉⣥⡅⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢩⣭⣭⣡⣍⠉⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠋⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⣿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠁⢀⣈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣉⡁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠒⠲⠶⠶⣶⣶⣤

⠀⠀⠀⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡄⠀⢀⣠⣼⣿⣿⣿

⠀⠀⠀⣠⣴⣿⠟⠛⠁⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⡿⠿⢿⠗⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠸⠿⠋⠀⡀⢀⣸⣿⣿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣱⡟⠀⠀⣀⠀⢀⡀⠀⠘⠛⠛⠉⠉⢙⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣿⣿⣿⣿⣿⠿⢿⣿⣿⠟⠛⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⡛⠿⠄⠀⠀⠀⠀⠀⠀⣴⠀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣻⣀⣀⣽⣿⣅⣀⣦⡄⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣝⡂⠄⠀⠀⠀⠀⢨⣠⡿⠊⠛⠃⠀⠀⠈⣿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠻⢿⡏⠋⢿⣿⣿⣿⣿⣿⡟⠃⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣀⠀⠀⠀⠀⠀⢰⡏⢀⡀⠀⢀⣤⣤⣴⣻⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣤⣶⣄⠘⠻⢾⡿⣿⡿⣡⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⡼⠀⢠⣼⡟⠀⠀⠀⠀⠀⠈⠋⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⣀⣿⣿⣷⣄⠀⠀⠉⠉⠉⠀⢹⡟⢁⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡇⠀⢸⣿⠧⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣴⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣠⡦⠀⢀⡸⢁⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠐⠃⠀⠰⣿⠀⠀⢀⠀⠈⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠈⠛⠉⠉⠉⠀⣰⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⢦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠠⣿⠀⠃⢸⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢡

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⡟⠀⠈⠛⠋⢻⣿⣷⡄⠀⠀⠀⠐⠀⠀⠈⡆⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠟⠛⠉⠉⠙⠟⠋⠋⠻⠿⢿⡇⠀⠀⠹⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡘⠻⣿⣿⣿⡿⠟⠋⠀⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣌⠁⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠟⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⢁⣀⣉⣉⡉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖

⠀⠀⠀⠉⠉⠉⠉⣭⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠁⠈⢿⣷⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣠⣴⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣿⡿⠛⠉⠙⠀⠀⠈⣿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢿⣿⣿⣿⡿⠿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠃⠀⠃⠀⠐⠀⢀⠈⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢻⣿⣿⣇⣀⣸⣿⣦⣃⣸⡏⡙⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡏⠀⠀⠀⠀⢠⢰⣿⡼⠿⠏⠀⠀⠈⢿⣿⣶⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠛⠟⠸⣿⣿⣿⣿⣿⣿⠻⠇⢸⣿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢺⡞⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣠⣤⣄⠻⠷⣶⣾⣿⠏⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡤⡄⠀⠀⠀⠀⠀⢸⡷⢰⣦⣤⣀⣀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠿⠿⢿⡿⠋⠉⠉⠛⠛⢿⣿⣿⠋⠀⣠⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣚⠀⢠⣶⣿⣿⣿⣴⣄⠀⣀⣠⣼⣿⣿⣿⡿⣿⣦⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⠿⣧⣤⠀⠀⠀⣴⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣴⣿⣾⣿⣿⣿⣿⣿⠿⣿⣷⣾⣿⣿⣿⣿⣿⠀⡿⣿⣧⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠈⠀⠀⠀⠀⠀⢀⣿⣆⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⢿⡻⡿⠿⢶⣜⢿⣿⣿⣿⣿⣿⡏⡜⢀⣿⣿⣆⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⣿⣿⣿⣿⣿⡿⠉⠙⠿⠿⠻⠟⠋⠛⠋⠁⠀⠀⠁⣄⣾⣿⣟⠛⠿⢿⣿⣿⣿⡟⠀⠙⣿⣿⣿⡄⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣤⣤⣼⣿⣿⣿⠿⠿⣿⡿⠋⠙⠿⠻⠿⠃⠀⠀⢺⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠃⠀⠀⠈⢹⣿⠟⠁⠀⠄⠀⠘⢿⡇⠀⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣭⣥⢠⣤⡉⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣥⣍⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⢹

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣶⣷⣀⣉⣉⣉⡉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⡉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠖

⠀⠀⠀⠉⠉⠉⢉⣹⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⢉⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣦⣤⣤⠀⠈⠉⠉⠉⠉⠈⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⡿⡏⠀⢮⣿⣧⠉⢹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿⣿⣿⠏⢠⡆⢸⣿⣿⠃⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⢧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠿⠟⠋⠁⠓⣼⠿⠛⠛⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⠿⠛⠛⠻⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁⠈⠙⣿⡏⠉⠙⣿⡟⠁⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⣤⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⢀⣄⠀⠀⠀⠉⠀⠀⠀⠀⣀⣤⣴⣶⣶⡀⠈⠓⠉⠈⠛⢠⣴⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠉⠙⠀⠀⠀⠀⣾⠟⣸⣿⣶⣤⣤⣀⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠖⠴⠀⠀⣠⣶⣤⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠃⠀⠀⠀⢠⣤⠀⠀⡀⠀⢠⣶⣿⣿⣿⡿⢻⣿⣧⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡀⠀⠀⡾⠸⡇⡆⠀⢻⣶⣿⣿⣿⣿⣿⠇⠈⢹⣿⣧⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠅⢠⠇⣇⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠈⠿⣿⣦⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⣿⣿⠄⠀⠀⣿⣿⣿⣿⠟⠋⠛⠛⠛⠛⠉⠉⠀⣸⣿⣷⡄⠀⢸⠀⢸⡄⠀⠀⠙⢿⣿⣿⡟⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣭⢉⣤⣠⣌⣭⣭⣠⣤⡉⣡⣤⣀⣤⡄⣤⣄⢠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⡀⣤⢩⣍⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢨⣤⣤⣠⣄⠀⣤⣤⣠⣭⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⢻⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⠏⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣷⣀⣉⣉⣉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠈⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠀⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖

⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡏⠉⣉⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠁⣠⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣧⣄⣀⠀⠈⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⣶⣾⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡄⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠈⢿⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠛⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡍⠉⢹⣿⣿⣿⡏⢁⣄⢹⣿⣿⠇⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠉⠛⠛⠛⠛⠟⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⢹⣧⣈⣠⣿⣷⣀⣠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⠸⠿⠛⠛⠶⣸⡿⠞⠻⠋⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⢀⣀⣤⣦⣀⣀⣸⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⢿⣿⡿⠹⡇⣿⣿⣿⠿⠿⣿⡿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠸⢯⡀⠀⠀⠀⠀⠀⠀⢿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣿⣿⠿⢿⣿⣿⣿⢋⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⡀⠀⠈⢿⣇⣰⣀⡼⢀⣻⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠀⠀⠀⣸⡿⢸⣿⣶⣤⣤⣀⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣴⣶⣶⣿⠟⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⣠⣶⣿⣿⣿⣿⣇⠀⠀⠈⠀⠀⢡⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣶⣦⣤⡀⣤⣴⣾⣿⣿⣿⠟⣿⣷⡀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⢿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠉⣿⣷⡀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⠊⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠻⢿⣿⣆⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠿⠿⢻⣿⣿⣿⣿⡇⠉⠀⣼⣿⣿⣿⣿⣿⡟⠿⣿⣟⠛⠡⣤⠄⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⣡⣤⡀⣩⣤⣀⣤⡄⣤⣄⢠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡍⢠⣬⢩⣥⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣨⡅⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣾⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢟⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⣿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠀⠀⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠂⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣭⣅⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣶⣦⣬⣍⡉⠉⠁⠀⢀⣠⣴⣶⣶

⠉⠉⠙⠛⠛⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡟⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⢸⡿⠇⠀⠈⢿⣿⡿⠀⠀⠻⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠨⠀⠀⠀⠈⣁⢠⣿⣰⣿⡿⠃⠀⠈⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⡀⠀⠈⠉⣉⣹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⡟⢹⣇⠈⣸⣿⣇⠀⠀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⢨⣼⠏⠁⠈⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣾⣿⣶⣦⣶⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⠻⠂⢻⣿⣿⣯⠿⣿⡟⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠦⣼⠃⠀⠀⠀⠀⠀⠘⣿⢠⣤⣀⡀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢉⣻⣿⣿⣿⠇⢀⣭⣉⣁⣀⣠⣤⣤⣤⠀⠀⠀⢈⣙⣏⣀⠀⠈⠻⡁⠤⠄⡺⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠀⠀⠀⠀⠀⠀⠐⢋⣸⣿⢹⠹⢿⣿⣦⡀⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟⣀⣴⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣠⢽⣷⠄⠀⠀⠀⢄⣀⣠⣿⣿⣏⡾⠀⠀⠘⢹⣿⡄⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠐⠾⠼⡇⠀⠀⠆⠀⠈⢿⣿⣿⣟⡅⠀⠀⠀⠀⠈⣿⣿⣦⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⢴⣿⣿⣿⡿⠛⠋⠉⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣶⡶⠀⡠⠄⠀⠙⢿⣿⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠛⠿⣿⣿⡿⠛⠉⠉⠙⠙⢻⢿⣿⡇⠁⠀⢸⣿⣿⣿⠁⣠⣀⣴⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢏⡀⢼⠦⠀⠀⠀⠀⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⢉⣥⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣬⡝⢩⣤⢩⣭⣩⣭⣉⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠛⠁⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⣀⣲⣶⠀

⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣏⣉⣉⣁⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣾⣿⣿⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠐⣿⣭⣿⣷⣶

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡟⠟⠛⠛⠿⠛⠀⠙⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⢢⣨⠀⠈⠀⢀⠀⠀⣤⢈⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠂⠀⠀⠀⠀⠤⢸⡿⡾⢿⠟⠀⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁⠉⠛⠛⠿⠿⠻⠿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡁⣀⣀⣿⣧⣀⣠⣧⣤⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣌⣿⡿⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣤⣠⣤⣤⣀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⡿⠀⢽⣿⣿⣿⣿⣿⡏⠃⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠈⠿⢸⣶⢶⢤⣤⢄⡀⠀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠀⢛⣛⠛⠿⠇⠀⣰⣶⣾⣿⣿⣶⣷⣦⠈⠛⠉⠉⠛⠛⣠⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢤⠀⠀⠀⠀⠀⠀⣴⣾⡿⣸⣮⣞⣾⣿⣦⣀⡀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣿⣿⣿⣿⣶⣄⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠱⣤⡴⠟⠛⠁⢻⣿⠿⣿⣿⣿⣿⣿⣄⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⡻⣽⡏⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⡋⣠⣿⣿⣿⣿⣿⣿⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠉⠉⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠃⠀⠉⠋⠛⠿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠻⠿⠿⢿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣭⢛⣭⣩⣍⣭⣭⣠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣤⡍⢡⣤⢠⣤⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣮⣉⡉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠖⠀⣠⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⣰⡶⠶⠒⣶⡶⠖⠀⠀

⠀⣠⣴⣿⣿⣿⡿⠛⠁⠀⣸⣿⣿⣿⣿⠏⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⢀⣠⣴⣶⣶

⠀⠿⠛⠛⠉⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡷⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠋⢉⠈⢻⣟⠀⠘⣿⣿⣿⡧⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠻⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⣠⡶⢬⠉⠀⠀⠀⠈⠁⢠⡆⢰⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⠉⠙⢻⡟⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣯⡍⠀⠉⠀⠀⠀⠀⠀⣸⠟⠋⠛⠃⠀⠀⠈⢿⣿⣷⣠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⠏⠤⣴⣿⣿⣶⣶⣾⢠⡏⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣘⢛⣦⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡏⢻⣏⠙⠛⠻⠿⣿⣿⡿⠿⣿⣿⣿⠃⠀⠀⠀⢀⣀⢀⣟⢉⣛⣿⣿⡿⠈⢀⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠟⢀⣿⣱⣶⣶⣶⣦⡀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣀⣸⣿⣧⡀⠀⠀⡀⠀⠀⠀⣿⣿⡏⠀⣠⣴⣾⣿⣿⣿⠀⠀⠼⠙⠉⢠⣶⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⡿⣿⢠⠀⠀⠀⠀⠀⠀⣴⠋⠁⠉⢻⣿⣿⣿⡿⢀⡈⠙⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣴⣿⣦⣤⣤⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠐⢊⣿⠈⠀⠀⠀⠰⣤⡾⠃⠀⠀⠀⠀⠙⢿⣿⣦⣿⣟⠀⠀⢸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠑⠟⠀⠀⠀⠀⠀⠙⠳⠈⠀⠀⠀⠀⠀⠈⣿⣿⠿⣿⡇⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠛⢸⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠈⠉⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣭⢋⣭⣩⣍⣤⣤⢠⣭⡙⣩⣭⣉⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣡⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⠉⣉⣉⣉⣉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠠⢀⢠⣤⡶⠖

⠀⠀⠀⠉⠉⠉⢩⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣷⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⠛⢱⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣠⣤⣶⣶⣶⣶⣄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⠟⠛⢿⣿⣿⣿⠿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡏⠀⠁⢸⣿⣿⣿⡄⢸⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠘⢿⣿⣟⠋⠀⠈⣿⣏⠋⠉⡻⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠸⠟⠋⣿⠟⠋⠛⠁⠀⠀⠈⢿⣿⣶⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠛⠋⠆⣾⣿⣟⣿⣿⣿⡿⠻⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⣼⣏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣀⡀⠿⠿⠿⡿⣿⠿⠀⣠⣄⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡄⠀⠀⠀⠀⠀⠀⠿⠀⣷⡆⣦⣤⣀⠀⠀⠘⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠋⠛⠻⢿⡿⠛⠻⠿⣿⣿⣿⣿⡿⢿⣟⣡⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡋⠙⠹⣿⣦⣴⣶⡘⢿⣿

⣤⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢽⡔⡀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⢣⡀⣴⣿⣿⣿⣿⠁⠀⠀⠸⣿⣿⣿⠇⠀⠸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠀⠀⠀⠀⠈⠂⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⢳⠉⢿⣿⣿⣽⠀⠀⠀⠀⠸⡿⠁⢀⣤⡄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢸⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⡿⠃⣸⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠹⠻⣿⡟⠟⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠈⠉⠉⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⢩⣬⡉⣡⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡈⠙⠟

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⠀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠖

⠀⠀⠀⠉⠉⠉⢩⣽⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣴⣾⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠋⢹⣿⣿⣿⡛⢻⠏⠙⢻⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠫⠉⣿⣏⠉⢹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠉⢣⠈⣿⣤⠾⠿⠁⠀⠀⠈⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠛⣶⠘⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠉⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠘⢿⣟⠋⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣳⡆⠀⠀⠀⠀⠀⠹⣧⠀⣄⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠛⠛⠛⠻⠿⠿⠻⢿⡇⠀⢀⣤⣶⣿⣿⣶⠀⠀⠀⠈⠁⠂⢸⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠋⣠⣿⣷⢿⣶⣤⣀⠀⠀⠀⠘⢿⣿

⣤⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣶⣶⣶⠎⠑⡄⡀⠀⠀⠂⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡀⠀⢠⣿⣿⣿⣿⡄⣟⣿⣿⡄⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⡄⠀⢳⡐⠯⣿⣿⣿⡿⠁⠈⠁⣿⣧⡀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠛⢸⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣷⠀⠀⠀⠀⢸⠁⠀⠀⠁⠀⠀⠷⠀⠹⣿⡟⠁⠀⠀⠀⠀⣿⣧⠀⢀⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⡿⠿⠟⠋⠙⠙⠻⢿⣿⠟⠂⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠙⠛⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠿⣶⣶⡆⠀⣤⢾⣿⣯⣷⣟⠉⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣬⣭⢠⣤⡉⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠈⣤⣤⣠⣤⡈⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⢿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⣉⣉⣉⣉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⣉⣁⣈⣁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⢉⣉⣀⣉⣁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠖

⠀⠀⠀⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⣀⣬⣥⣠⣽⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⡀⠈⠉⠉⠉⠉⠈⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠂⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣾⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠸⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⡟⠛⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢿⣿⣷⣠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⡛⢻⣿⣄⣀⣼⣿⣴⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠉⠙⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠂⠀⠀⠹⣿⣿⣿⠏⠙⢿⠘⠿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠂⠀⠙⠛⠉⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠶⣶⡾⠓⠶⠄⠀⠉⠛⠛⠀⠀⠀⠀⠀⣈⣭⣀⠀⠀⠀⠀⠉⠻⠴⠤⢸⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠻⡿⡇⠀⠀⠀⠀⠈⢻⣿⢠⣷⣦⣤⣀⠀⠀⠀⠀⠻⠿⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢠⣾⣷⣦⣄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⣠⣾⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢠⣷⡆⠄⢀⠀⢸⣶⣤⣾⣿⣿⣿⣿⠀⣿⣿⣴⡀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣿⡿⠀⠘⢸⡀⠀⢿⡟⢿⣿⣿⢿⡇⠀⠉⣼⡟⠃⠀⢀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠹⠿⢿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣿⣿⣦⣾⡁⣻⠁⠀⣺⡟⢿⡿⣿⡿⣿⢿⣿⣿⠇⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣭⢉⣭⣩⣍⣭⣭⢡⣤⡉⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣩⣥⡄⢠⣤⢠⣭⣩⣭⣄⣤⢠⣄⣤⣄⣩⣍⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⣉⣉⣉⡉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⣉⣉⣉⣉⣉⣄⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠖

⠀⠀⠀⠉⢉⣽⢏⣭⣯⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢀⣨⣴⣤⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣷⣤⣄⠉⠉⠉⠉⠁⠈⢀⣠⣴⣶⣶

⠀⠀⠀⢴⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⡼⠁⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣶⣦⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⡇⢹⠉⠀⠀⠀⣿⣿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⢀⡀⠀⠉⢡⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⠉⢀⣼⣷⣀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢿⡟⡇⠀⠀⢹⣿⣿⣧⣿⠛⠁⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣶⣿⣿⣷⣶⣾⣿⣿⢿⣿⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⢿⠆⠻⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠑⣽⠁⠀⠀⠀⠉⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡇⠙⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣏⣉⣉⣹⣿⣿⡃⣠⣀⣀⣁⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠀⠀⠀⠘⠿⠵⠶⠒⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⢀⠀⠀⠀⠘⣿⣿⢦⣿⣦⣤⣀⠀⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣼⣿⣿⣿⣿⣿⣶⣄⠀⢀⣴⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠁⢰⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣾⣿⠀⡀⠀⠀⠋⣡⣾⣿⣿⠻⣿⡗⠀⠀⣠⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠈⢹⡲⣴⣾⣿⣿⣿⣿⠇⣿⠇⠀⠀⠻⡆⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⡟⣿⣿⣿⡿⢱⠀⠀⡇⠈⢿⣿⣿⠋⡇⠀⠉⡀⠀⠀⠀⠃⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠛⠉⠀⠀⠙⠛⢿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⡟⠻⣿⣿⣵⠃⠀⡀⠀⢿⡀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣤⣩⣍⣭⣭⣡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡍⢠⣤⢠⣬⣩⣭⡍⣭⢩⣍⣥⣄⣠⣄⣠⣤⣨⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⣼⠇⣙⣿⣽⣿⡇⣿⣿⢾⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⠏⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⣿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣌⡉⠉⠉⠉⠉⠈⠉⠉⣠⣤⡈⠋⠉⠛⠁⠉⠉⠈⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⡈⠁⠀⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⠶⠶⠶⠖

⠀⠀⠀⠛⣿⣯⠹⣿⣽⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣶⠦⣴⠀⠀⡅⠀⢀⣠⣴⣶⣶

⠀⠀⠀⡰⣿⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⡿⢿⣿⣯⣴⣾⣿⣿⣿⣿

⠀⠀⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠛⠛⠉⠁⠀⠀⠉⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠅⢠⡀⠀⠀⠀⠀⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠛⠻⡿⠿⢿⣿⡿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠰⣿⣿⣿⣿⡟⠛⢻⣿⣟⡛⠻⡿⠿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢀⣴⡓⣎⡇⠀⠀⢀⣸⠀⠀⣾⣆⣼⣿⡟⠀⠀⠘⢿⣿⣷⣠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⢱⣀⣦⡀⠈⠁⢰⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⢧⣤⣴⣿⣷⣤⣴⣷⡆⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢸⣯⡟⠠⡇⠀⠀⣼⣿⡇⣴⡟⠀⠀⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⠿⠏⠀⢿⣿⣿⣿⣿⣿⠛⠁⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⡆⠀⠀⢰⣿⣿⡿⣿⣧⢠⣄⡀⠀⠀⠀⠀⠀⣙⢿⣿⣿⣟

⠀⢀⣀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣤⣄⣀⣿⣇⠀⠀⠀⠀⠀⣠⣤⣶⣷⣄⠀⠉⠀⠟⠛⠃⣠⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡀⠀⠀⣼⣿⣿⠇⠟⠛⣸⣿⣿⢿⣶⡆⠀⠀⢿⡄⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⣿⣿⣿⣿⣷⣄⡀⣠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⢀⣿⣿⣇⢀⠂⠀⠿⠛⣿⠀⢠⣾⣿⣿⣿⡀⠟⡇⠀⠀⠀⠃⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣼⣿⣿⣷⢸⠀⠀⠀⠀⡿⠰⣿⣿⣿⡟⡿⠁⠘⠁⡀⠀⢰⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉⢉⣛⣛⣛⣛⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠿⠄⠘⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⢀⣠⡾⠃⠀⢻⣿⣿⠿⠃⠀⠀⠘⡅⠀⠘⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠁⠀⠀⠀⠀⠀⠛⠛⢻⡄⠀⠀⣿⣿⡍⡁⠀⠀⠀⠉⠛⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⠀⠐⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣭⢩⣭⡁⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣨⣭⣍⣭⢩⣍⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡙⡆⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠁⠀

⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⢉⣉⣋⣀⣉⣄⣉⣉⣉⣁⣈⣁⣌⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⠒⢲⣶⣶⠶⠶⠶⠖

⠀⠀⠀⠈⣿⡍⢻⣯⣭⣽⣿⣿⣿⣿⣿⣏⣭⣭⣅⣈⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣠⣤⣀⣀⠀⢀⣠⣴⣶⣶

⠀⠀⠀⣼⣿⣿⣎⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠿⠟⠉⠉⠙⠋⠈⠉⠹⢿⣿⣾⣿⣿⣿⣿⣿

⠀⠀⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠉⠁⠀⠀⢀⣰⡁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠈⡿⣿⠁⠀⠀⠁⢸⣿⣿⣿⡄⢸⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣇⣀⣸⣿⡉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣴⡲⡌⡄⠀⠀⢀⣿⣯⣭⣿⠷⠿⠿⠃⠀⠀⠈⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⡙⠠⠃⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣤⣶⣾⠁⣿⣿⣿⡧⢰⣶⣤⣄⣀⠀⠀⠀⢹⣿⣿⣿⣟

⠀⢀⣤⣄⣀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣇⠀⠙⢿⣇⣠⣾⣿⣿⠙⡿⣿⠃⠀⠘⢿⡈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣿⣿⣿⡀⢡⡇⠀⠀⠀⠀⠁⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⡉⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⠀⠀⣾⣿⣿⣿⣿⠁⠀⢀⠀⠀⢠⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣇⡜⠁⠀⠈⠙⢿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⣿⣿⣿⢟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠠⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣤⢀⣤⣠⣍⣥⣤⢠⣬⡉⣩⣭⣉⣭⡍⣭⣅⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣬⢩⣭⣩⣭⣉⣄⢠⣄⣤⣄⣠⡄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡙⡆⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠁⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠛⠧⠀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⢂⣴⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⠶⠶⠶⠒

⠀⣷⣿⣿⣧⣿⠉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁⠀⠀⢀⣠⣴⣶⣶

⠀⠈⢿⣿⣿⣏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣄⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣀⣀⣰⣾⣿⣿⣿⣿

⠀⠀⠈⠹⠛⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠻⠟⠋⠉⠛⢟⡛⢟⡶⠿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⠏⠀⢹⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣀⣠⣿⣇⣉⣉⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣶⣾⠁⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢿⣿⢶⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠸⡿⣿⣿⣿⣿⠏⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡀⢞⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⣀⣠⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣀⣤⣤⡀⢀⢈⠛⠟⠋⠀⠀⣉⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢂⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣤⣀⡀⠀⠀⠙⣿⣿⣿⣟

⣿⣿⣿⣿⣶⣄⡀⢠⣿⣿⣿⣿⣿⠿⠋⠉⠉⠁⠀⠀⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠙⡟⣿⣆⠀⠀⠀⠈⢿⣿

⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⡿⠀⢰⠋⣿⠄⠀⢰⡄⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠘⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⠿⡿⢿⠋⠹⣿⣿⣿⣽⡷⠀⠀⠰⠉⠀⠀⢸⡇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢌⠉⠛⠻⠿⠿⠿⠿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠈⠛⠁⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⡇⠈⠀⡄⠉⠻⢿⡟⠇⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠁⠀⠀⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣷⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣭⢉⣤⣡⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣬⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣭⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⣉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠁⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠖

⠀⠀⠀⠉⠉⠉⣉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠟⡋⠙⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢸⣿⣿⣿⣿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡈⠃⢀⢈⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⡿⣠⣀⣠⣿⣿⣁⣀⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠙⠃⠀⣾⣿⣿⣿⣿⡆⡀⠀⢘⣿⣿⣷⣠⣼⣿

⣴⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣴⡏⠈⣿⣿⣿⣿⣿

⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣀⣀⣀⠈⠋⣍⡿⠿⠋⠀⣠⣹⣏⠁⠀⠀⠀⠀⠀⠀⠀⢸⣶⣦⠀⠙⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣟

⠀⢀⣀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⢹⣿⣿⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠸⠿⠿⠆⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⠄⠀⠈⠙⠻⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣤⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠐⠂⢀⠀⠁⠀⡀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⡇⠀⠀⢃⠘⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⡟⠉⠉⠻⠛⠻⣿⣆⠀⠀⠿⠃⠀⠀⢸⡀⢹⠀⠘⣿⣿⣿⣿⣿⠋⢺⣿⣿⡆⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠹⢿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠃⢸⣿⣿⣿⡿⠀⠀⠈⣽⠿⠁⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠉⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣛⢣⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠖

⠀⠀⠀⠉⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢉⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣄⣀⠈⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⠿⣿⣿⣿⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡏⠏⣸⣿⡁⠈⠙⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⡿⠿⠛⠏⠁⣠⡀⣸⣿⡿⠀⠀⠀⠈⢿⣿⣦⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢦⣿⠓⠉⠉⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠁⠀⠈⠈⠙⣿⡿⠅⠹⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣇⠀⠀⠀⠀⢾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠉⣙⣻⣿⣃⠀⠀⠉⠛⠿⠋⠉⢿⠋⢀⣠⣤⣶⣶⣶⠀⠀⠀⠀⠀⠀⣰⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠨⡆⠀⠀⠘⠀⠀⠀⠀⠘⠟⢸⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠈⢿⣿

⣤⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢟⠸⡇⠀⠀⠛⠀⢀⡀⠈⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠘⢣⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢋⡟⢿⣧⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⡌⠀⢰⠀⡄⠀⢰⣾⣿⣿⡏⠋⢀⣤⣎⣿⣇⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⣀⠀⠀⢸⠃⠀⠀⡇⠸⡄⠀⢹⣿⣿⠀⢀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠿⡿⠛⠋⠀⠉⠉⠛⠻⣿⣿⣝⡀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠙⠋⠙⠛⠿⠀⠀⠘⠀⠀⠀⢹⠀⠳⠀⢀⣿⡿⠀⠲⠿⠏⠸⣿⠁⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣠⣄⣤⣭⢡⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣡⣤⣡⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣌⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠁⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⡉⣉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⢉⣉⣉⣉⣉⣀⣉⣁⣙⣋⣀⡙⢋⡈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠖

⠀⠀⠀⠉⠉⠉⣩⣽⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢀⣈⡁⢀⣭⣿⣿⣿⣦⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣥⣀⣀⠀⠀⠉⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣶⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⣰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠻⠉⠉⠁⠀⢹⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣿⠋⠙⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠈⠁⠀⠚⢀⡈⢹⣿⣿⠇⠀⠀⠈⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⠿⢿⠿⠿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣯⡙⣿⣧⣤⣴⣿⣷⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣎⢃⡏⠀⠀⠀⠀⣦⣼⣧⠾⠿⠛⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⢹⣦⡀⠀⠀⣀⡀⠀⠀⣸⣿⣿⡇⠀⠘⣿⣿⣿⡏⠙⠯⢹⣿⣿⣿⡟⢻⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣦⡀⠇⠀⠀⠀⠀⢽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣀⣨⣿⣿⣿⣿⠋⠋⣤⠀⠉⠛⠻⠃⠀⠀⠈⢉⣛⣁⡀⠀⠀⠈⠛⠛⠉⠉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡟⠀⠀⠀⠀⠀⢸⡷⢸⣿⢶⣤⣄⣀⠀⠀⠀⠀⠀⡎⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠟⠫⠉⣼⣿⣷⣦⡀⢀⣴⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠆⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠹⣿⣿⣧⡀⠀⠀⠘⢧⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠐⣿⡇⠀⠀⠐⡰⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⡅⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣀⣿⠃⠀⠰⠀⠱⠀⠈⢿⣿⣿⣿⣿⠘⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠃⠀⠀⠀⠉⠻⠿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⠋⠙⢿⣿⣿⣏⣿⣾⣿⡏⠀⠀⠀⡆⠀⠀⠀⠈⢿⣿⣿⣿⣦⠁⠿⠙⠁⠀⠀⢀⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣭⢉⣭⣩⣍⣭⣭⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣭⣩⣥⡄⢠⣤⢩⣭⣩⣭⣅⣭⢡⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣬⢩⣭⣭⣠⣄⠀⣤⣤⣠⣤⡁⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⠶⠖⠒⠒

⠀⠀⠀⠉⠉⠉⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣯⣭⣅⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣴⣾⣾⣷⣦⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣄⠀⠉⠛⠛⠋⠈⢉⣠⣴⣶⣶

⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢰⣿⣿⣿⣿⣿

⣿⠟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠿⠿⠿⠿⢻⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣛⡿⣇⠉⠀⠴⠄⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢟⠋⠻⣿⠉⠙⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣶⢯⣑⡆⠀⠀⠀⠀⢐⡀⣰⣾⣿⣿⡿⠀⠀⠈⢿⣿⣷⣠⣾⣿

⠀⠀⢀⣀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣇⠀⠀⢡⡀⠈⠀⢀⣹⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣯⡘⣿⣦⣤⣾⠿⣦⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡈⠃⠀⠀⠀⠀⠀⣿⣿⣾⣿⣟⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⢠⣿⣿⣷⣤⣄⢠⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣶⣾⣿⢿⣿⣿⠁⠀⠀⠀⢿⣿⣿⡿⠙⠇⠸⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡗⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⡆⠀⠀⠀⠀⠙⣿⣿⣿⣟

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢁⣄⣀⣄⣉⠀⠀⠀⠀⠀⣉⣿⣇⣀⠀⠀⠈⠛⠛⠉⠹⣡⣤⣀⡀⠀⠀⠀⠀⠀⠀⡄⣼⣿⡿⠀⠀⠀⠀⠀⠀⡈⠹⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢠⠉⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⣠⣾⣿⣿⣿⣿⣷⣄⣠⣶⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⢀⣀⡇⠀⠈⣿⣿⡏⠀⠻⣿⣷⡄⠀⠈⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣼⣿⣿⡇⠀⠀⠀⣷⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⢻⣿⣿⡄⠀⢰⣧⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢿⣿⣿⣿⣿⣿⡅⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⢟⠟⠛⠁⢀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠈⣿⣧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡇⠀⠀⢸⡟⠛⠛⠻⠿⠿⠛⢻⠟⢛⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣤⢀⣤⣨⣍⣭⣭⣡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣍⣩⣍⣡⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠻

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡆⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣧⣀⠉⠉⠉⠉⠉⠈⢉⣉⣀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⣙⡉⢉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡐⢶⡶⠖⠒⡆⠀⢶⠶⠖⠒

⠀⠹⣿⣿⣿⢋⣭⣭⣭⣿⣿⣿⣿⣿⣿⣏⣭⣍⣁⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣤⣶⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠠⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣾⣿⣿⣿⣿

⡄⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡏⠿⠟⠁⡀⠈⠉⠻⠯⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿

⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡐⢯⡑⠀⠀⠀⠉⠀⠀⠀⠀⢹⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠿⡿⠛⠟⣿⣿⠉⠙⡟⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⣏⠂⡇⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⡿⠟⠁⠈⢿⣿⣷⣠⣼⣿

⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣦⠃⣤⣴⣿⣿⣦⣴⣷⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣼⣿⡧⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠛⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠙⠻⠋⠈⠀⠙⡿⠓⠛⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⡤⣤⣀⠀⠀⠙⣿⣿⣿⣟

⠙⢙⣛⡛⢀⣈⠛⣇⣸⣿⣿⣾⣦⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣤⣴⣶⣿⣶⡄⠀⠀⠈⠁⠘⢵⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠃⣻⣿⡏⠀⠀⠀⠀⠀⣴⣿⣿⣧⡄⠀⠀⠀⠻⣿⣷⡄⠀⠀⠈⣿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣔⣶⣾⣿⣿⣿⣿⣿⣿⣶⣄⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢀⣼⣿⡿⢻⣿⠃⠀⠀⠀⠀⠸⢿⣿⣆⠀⠀⢻⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠠⢼⣿⡟⠃⠀⠀⠀⠸⢿⠉⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⢿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠉⠙⠛⠛⠻⣿⣿⡍⠉⠉⠉⠉⠉⠙⢿⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠒⠒⣤⡀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠉⠙⠛⣻⣿⡿⠀⠀⠘⠉⠈⠻⠿⠇⠀⠀⠀⠀⠀⠔⠖⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣨⣍⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣄⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⡉⠉⠉⢉⣉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀⣰⣦⡀⠀⠒⠲⠶⠲⣶⡀⠰⠶⠶⠒

⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣩⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⢀⣤⣴⣶⣶

⡔⠿⠛⠛⠻⠛⣻⣿⢿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠽⠟⠋⡉⠙⠛⠿⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⡠⢭⣓⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⢿⣿⣿⠟⠙⠻⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⠣⢸⠀⠀⠀⠀⠀⢠⣄⣿⣴⣾⣿⣿⣿⣿⣿⣿⣷⣠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⢠⠀⠈⢛⠋⠀⢻⣿⣿⠀⠀⠀⠀⠀⠙⠛⠀⣤⣼⣿⣤⣤⣼⡧⡦⠘⢿⡿⠿⠟⠀⠀⠀⠀⠀⠀⢨⣿⣧⠈⠀⠀⠀⠀⠀⢸⡟⢻⣿⣿⣿⣿⠟⠁⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠙⢿⡀⠀⢸⠀⢠⠃⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣀⡀⠘⠛⠛⠿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢸⣿⡟⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣤⡀⠀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⣤⣷⣤⣿⣄⡞⠀⠀⢀⡈⠙⠃⠀⠀⣠⣶⣿⣿⣿⣿⡀⠀⠉⠉⠛⢁⣶⣿⣿⣿⣷⣦⣀⠀⠀⠀⢀⣿⠇⣼⣿⠁⠀⠀⠀⠀⠀⢀⣶⣿⠏⣿⡃⠀⠛⢿⣷⣄⠀⠀⠈⣿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣷⣄⣀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠸⠛⣾⣿⣿⠀⠀⠀⠀⡀⢰⣿⡿⢃⣼⡏⠀⠀⠀⠙⠿⣿⣦⠀⠀⢿⣾

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⡇⠀⠀⠀⠀⠙⠾⡍⠀⣺⠏⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠸⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⠿⣿⣿⠛⠛⠛⠛⠛⠻⣿⣿⣿⡿⠛⠻⠏⠉⠀⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⡿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⣶⣄⠀⠉⠈⠀⠀⠀⠀⠀⠘⢿⡿⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠻⠛⠁⠀⠀⠀⠀⠠⠚⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣨⣍⣭⣤⣠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣩⣭⣡⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⣿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣮⣉⡉⠉⣉⡉⠈⠉⠉⠁⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⢉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠖⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠆⠒⠲⣶⣶⣄⡀⠀⠀⠰⠶⠶⠖

⠀⠸⠟⠋⠉⠈⠈⣩⣭⣿⣿⣿⡿⠉⠙⠻⣿⣿⣯⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠉⠻⠇⠀⢀⣠⣴⣶⣶

⠀⠀⠀⢰⣶⠀⢲⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠟⠀⠀⠻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⢏⣿⠿⠛⠛⠻⠿⠟⢻⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣯⣸⠋⠀⠐⠃⠀⠀⠀⢸⣿⣿⣿⣏⣠⣼⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠿⠋⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣀⢸⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣤⣿⣆⣀⣈⣿⠛⠻⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⣾⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇⢹⣿⡇⠀⠀⡉⠀⢻⡿⠋⠉⢻⠇⠀⠀⠀⠀⢀⣀⡀⠙⠐⠻⣿⣿⡿⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⢀⡆⠀⠙⣷⡄⠀⠀⠀⠀⠀⠌⠀⠘⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⣤⣿⣷⣀⣶⢧⣤⠄⠀⠀⠀⢾⠀⠀⣠⣴⣿⣿⣿⣧⠀⠀⠈⠉⠉⢀⣶⣾⣿⣿⣷⣦⣀⠀⠀⠀⠀⣾⠇⠀⢀⣻⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⡓⠀⢠⠛⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠙⠀⢀⣤⣄⡀⠀⣼⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⡟⠀⠀⠈⠆⠀⠀⠠⡀⢀⣴⠃⠀⠀⣼⣿⡿⠻⣿⣿⡇⠀⠸⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡿⣯⣴⣾⣿⡟⠁⠀⠘⣿⣷⠀⠀⣴⡄⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠻⢿⡟⠀⠘⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠈⠉⢸⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⡿⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠋⠀⠀⠀⠀⠀⠿⠀⠀⢻⣷⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣩⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠸⡇

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠁

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣆⣉⣉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡆⣲⣶⢲⠶⠶⠶⠖

⠀⠀⠀⠉⠉⠉⣩⣭⣭⣿⣿⣿⣿⣿⣿⠏⢉⣩⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣶⣦⣩⣿⣿⣷⣧⡀⣀⣤⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣄⡀⠀⠀⢨⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠟⠛⠻⣿⣿⠉⠀⠀⠀⠘⢿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠻⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⣴⡀⣼⣿⡟⠀⠀⠈⢿⣿⣲⣠⣼⣿

⠀⢠⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠁⢀⣀⣼⣯⣀⣉⡛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡿⠋⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠘⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠿⠭⠿⣿⡿⠅⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣿⡄⣄⣀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠙⣿⣿⣿⡟⠛⣿⣿⠟⠁⣠⣴⣶⣿⣷⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⢠⡌⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢸⣿⣿⠀⢠⣿⡏⣠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⢀⣺⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⡇⠀⠀⠸⣿⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⢒⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢰⠿⣿⣷⠀⠀⠀⠙⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠼⠸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢻⣿⣿⣷⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⣀⣤⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠈⠉⠛⣯⣿⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⣿⡟⠁⠀⠀⠘⠃⠀⠀⢀⡄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣤⣠⣄⣤⣬⢠⣤⡁⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡁⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖

⠀⠀⠀⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠀⠉⠁⠈⠉⠁⢈⣩⣬⣭⣥⣽⣿⣯⣿⡅⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⡀⠈⠉⠉⠉⠉⠉⠉⢁⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣤⣴⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠉⠈⢀⣿⣿⣿⣿⣿⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣏⡉⢻⣏⣁⣠⣿⣄⡀⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠶⠛⠛⠀⠹⣿⣿⡿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⠋⠁⠈⠏⠰⢿⣿⣿⠟⠻⠋⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠘⠿⠛⠡⣿⠃⠀⠀⠀⠀⠀⠈⠉⠁⠙⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⡄⠀⠀⢈⠿⠋⠉⠙⣿⡏⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠙⠁⠀⠀⢀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⡇⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⡟⣿⣷⠀⠄⠘⠀⠀⠀⣼⡿⠀⢀⣤⣶⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠩⠀⠀⠀⠀⢠⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⣤⣿⣿⣿⣿⣿⢸⣿⣿⣧⠀⠀⠀⠠⣤⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣟⣁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠀⡇⠀⢀⠔⣿⣿⣿⣿⣿⡇⠘⠙⣿⣿⡆⠀⠀⠈⠿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣶⣴⣿⠟⠿⠿⠟⠁⠀⠀⠀⠙⠛⠿⠿⢿⠋⠈⠀⢸⣿⣿⣿⣿⣿⠏⠉⠻⣿⣿⢿⣏⠀⠀⠀⠀⠀⠀⢹⡀⠀⠑⢸⣿⣿⣿⣿⡇⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣤⣠⣌⣭⣭⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡄⢠⣤⢠⣤⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢩⣥⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣶⣧⡀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠒

⠀⠀⠀⠉⠉⠉⣉⣯⣽⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠉⠀⠈⠉⠀⣈⣁⣈⠉⣁⣭⣭⣬⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣧⣤⣀⡀⠉⠉⠉⠉⠉⠈⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣾⣷⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⡿⣿⣿⡿⢯⡀⠈⠿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⠛⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⠀⢹⣿⠛⠀⢀⣦⠀⣿⣿⡟⠀⠀⠈⢿⣿⣲⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⡛⢻⣿⣧⣀⣠⡿⣦⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠘⡏⠀⠐⣼⡿⠚⠛⠛⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⢻⣷⣄⠀⠀⢀⡀⠀⠀⠈⣿⣿⡿⠀⠀⠸⣿⣿⣿⡿⠛⠻⠀⠻⣿⣿⣿⡿⢟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠃⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟

⠀⢀⣀⡀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣀⣹⣿⣿⣿⡿⠗⠂⠀⠘⠿⢿⠇⠀⠀⠀⠈⠙⣻⡁⠀⠀⠀⠀⠉⠻⠛⠛⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⣴⣶⠘⠀⠀⠀⠀⠀⣿⠷⣼⣷⣦⣤⣀⡀⠀⠀⠀⠀⢸⣿⣿

⣴⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠏⠘⠄⠚⣰⣿⣶⣤⡀⠀⢀⣤⣶⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣤⡀⠀⠀⠀⣰⣿⣿⣿⣿⣦⣴⡄⠀⠀⠀⢀⣴⣿⡯⣏⢻⣿⣿⣆⠀⠀⠀⠘⢿⠟

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⡿⠁⠠⠀⣴⣿⣿⣿⣻⡿⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⣿⠇⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠁⠻⣿⣿⠀⠀⠆⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠛⠁⠀⠀⠀⠙⠛⠿⠿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⠏⠉⠛⠿⣿⣿⣿⡿⠟⠉⠁⠀⠀⢸⡀⠀⠀⠀⠹⣿⣿⠁⠀⠀⠀⠈⠻⣿⠀⠀⢀⡆⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣍⣭⣭⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡄⢠⣤⢠⣤⣨⣭⣁⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡈⢿⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠘⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣧⣀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⣁⣈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣤⣴⠲⠖⠀⠀

⠀⠀⠀⠉⠉⠉⣩⣭⣽⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣤⣤⣵⣾⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⣍⠉⠉⠙⢿⠍⢃⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠻⠛⠃⠀⠀⢻⣿⣿⣿⣧⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠁⠨⠆⠀⠀⠀⠀⠉⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⡁⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⢣⠀⠀⠀⠀⢀⣸⣶⣾⣿⣿⠃⠀⠀⠈⢿⣿⣷⣠⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⢨⠙⠃⠉⠙⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡙⣿⣿⣤⣶⣟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣕⣤⣤⣴⣶⣀⣴⣿⣿⣿⠃⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢿⣷⣶⣶⡿⢷⣤⢀⣼⣿⣿⣿⠁⠀⠀⠻⣿⣿⣿⡟⠙⠿⠙⣿⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣯⣻⣿⠃⣈⣉⠛⠓⠀⠀⠀⠀⠈⣩⣿⣅⣀⠀⠀⠀⠉⠛⠛⠋⢡⣶⣶⣤⣀⠀⠀⠀⠀⠀⢰⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣷⣄⠀⠀⠀⢸⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⠿⠛⠃⣴⣿⣿⣿⣦⣄⠀⣠⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⡀⠀⠀⠈⠀⠈⠉⠛⠙⠛⠛⢛⣿⣿⣧⣿⠄⢹⣿⣿⣧⠀⠀⠸⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠈⣿⣿⣧⠀⠀⣴⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠻⢿⣿⣿⣿⣿⣿⠣⠀⠘⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢠⣿⣿⡟⠀⠀⠀⢀⠀⠀⠀⠻⣿⡟⠁⠀⠀⠀⠀⠘⢻⣿⠀⠀⢻⣧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⠛⠁⠀⠀⠀⠀⠉⠿⠟⠿⣿⢿⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⣈⣿⠃⠀⣠⣿⣿⡿⠇⠀⠀⠀⡎⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢀⣤⣠⣍⣥⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣥⡄⢨⣭⢩⣤⣠⣤⣌⣭⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⢻

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡟⢿⡀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⢉⣡⡈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⠀⠀⠀⠀⢀⢶⠶⠖⠒

⡿⠋⠀⠉⠉⠉⣩⣭⣭⣿⣿⣿⣿⣿⣿⠋⢉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠀⠀⠀⠀⢛⣠⣴⣶⣶

⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠙⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠉⠁⠀⢀⠀⢸⣿⣿⣿⣗⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⡛⠣⣰⣶⡄⠉⠁⣿⣿⣿⣿⣷⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⡟⠻⠉⣿⣇⠀⢈⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠦⣹⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣶⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠀⡉⠛⠉⠉⢻⣿⣿⡿⠀⠀⣿⣿⣿⣿⣷⡌⢿⣶⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠙⠻⣿⣿⣿⠁⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠻⢿⣷⣶⣞⣿⣦⡄⢀⣾⣿⣿⠇⠀⠀⠙⠿⣿⡟⠀⠁⠈⢿⣿⡋⣉⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡷⠀⠠⠀⠀⠀⠀⠀⠘⠿⣦⡄⠀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣤⣾⣿⣏⣙⠉⣿⡏⢉⣉⠛⠛⠀⠀⠀⠀⣀⣤⣾⣦⣤⠀⠀⠈⠉⠀⠀⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣤⣄⠀⡀⠀⠀⣿⣿⣦⠀⠀⠿⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⣛⡛⠍⣠⣿⣿⣿⣦⣄⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣹⣿⣿⣿⣿⣿⡟⠀⠀⠀⣤⣼⣿⠟⣴⠁⠀⠀⠉⣿⣿⣄⠀⠀⣤⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠋⡾⠃⠀⠀⠀⠀⠐⠿⣿⠀⠀⢻⣧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⠓⠀⠘⠁⠙⢿⣿⣿⣿⡛⠛⠻⠛⠉⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⡿⢛⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣄⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⠉⣭⢁⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡌⢩⣭⢩⣥⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣷⡀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣦⣤⡄⠐⠀⠀⢠⣴⠶⠶⠖⠒

⠀⠋⠀⠉⠉⠉⣩⣭⣭⣿⣿⣿⣿⣿⣿⣏⣉⣭⣉⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡆⠀⠘⢃⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⡁⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣹⠋⠉⡀⠉⠹⡿⣿⣿⡟⠋⢿⣿⡿⠁⢀⣿⣿⣿⣿⣿⣿

⣇⣀⡀⠀⠀⡀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠸⠿⣿⣷⡟⠀⠀⠀⠁⠀⢾⡹⠿⠏⢀⢎⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⣆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⢿⣿⣿⡿⠉⠀⢹⣿⡙⠀⢹⡉⠙⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢼⠁⠀⠀⠀⠀⠀⣸⡁⠀⠀⠈⠟⠀⠀⠀⠈⢿⣿⣶⣠⣼⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡉⠛⠛⠻⢿⣿⠿⢿⣿⣿⣿⠇⠀⠘⢿⣿⠟⢱⣶⣿⣿⣿⣶⣿⢻⠁⠿⠛⣿⠁⠀⠀⠀⠀⠀⠀⠸⢛⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢀⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣧⣀⡀⢠⡄⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣉⣉⣙⣿⣟⢀⣀⣀⣠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠺⢆⠀⠀⠀⠀⠀⠀⠈⠋⠀⣸⡇⢀⠈⠳⢳⣦⡀⠙⣿⣿⣿⣟

⣿⣿⣿⣿⣿⠿⠻⣽⣿⣿⣿⣿⣿⣿⣷⣦⡾⣿⣿⢿⠿⠛⠂⠀⢸⠿⣿⠀⠀⢀⣠⣴⣾⣿⣦⠀⠈⠋⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡄⡈⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠍⡼⠀⠀⣿⢿⣷⠀⠀⣿⢿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⠁⠤⠀⠀⠀⣼⣿⣷⣄⠀⣴⣿⣿⣿⣿⣿⣿⣇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠜⠙⢧⣴⠃⠀⠀⠀⠸⣿⡀⠀⠀⣀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠋⢳⣆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⢧⠀⠀⢻⣧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠠⠟⠙⠓⠠⣶⡀⠉⠙⠛⠻⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠩⠟⢻⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠖⠀⣤⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡇⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⣶⣶⣐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡠⣶⣶⡆⠀⠀⠀⠀⢰⠶⠶⠒

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠉⠀⠈⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣆⠀⠐⠻⠿⠿⣧⠀⠀⢰⣿⣦⣴⣶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣴⣿⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣤⣶⣾⣤⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⡟⠹⣿⡿⠿⢿⣿⣿⠛⢿⡿⠆⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠉⠉⢹⣟⠹⠟⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠙⠀⢀⠇⠀⠀⠀⠁⢹⡆⠀⠀⠀⢠⣿⣿⡟⠈⠘⢿⣿⢲⣠⣼⣿

⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠏⢰⣶⣿⣿⣶⣶⡿⣪⠙⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡤⡼⠀⠀⠀⠀⢠⣾⣧⠀⠀⠀⠀⢿⠏⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠻⢿⣿⣿⡿⣿⣿⣿⡿⠁⠀⠀⠀⠐⣿⢸⣿⣿⣿⠁⠈⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠻⠗⠀⠇⠀⠃⠀⠀⣲⣄⠀⠙⣿⣿⣿⣟

⣾⣿⣿⡿⠿⠛⠁⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⣀⣤⣶⣶⣆⠀⠉⣿⣿⠏⠀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠂⡀⠀⠀⣿⣿⡇⠀⠀⠘⢿⣿

⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⠂⠀⠀⣸⣏⣤⣾⣿⣿⣿⣿⣿⡀⠀⢠⣿⡀⣸⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠃⣰⠃⠀⠀⠋⢻⣧⠀⠀⢀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠽⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠏⣰⣇⠀⠀⠀⠀⢩⣿⠀⠀⠸⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠓⠗⠀⣹⣿⣿⣿⣿⠿⠛⢿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢿⡿⠁⠀⠀⠀⠀⠀⡄⠀⠀⢸⣧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠛⠛⠿⠯⠅⠀⠀⠘⠀⣿⣿⣿⣿⠟⠀⠀⠀⠉⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣤⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⣉⡉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠲⣶⣶⣶⡆⠀⠰⠶⠶⠒

⠀⠀⠀⠉⠉⠉⣭⣭⣭⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⣠⣬⣷⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣄⠀⠀⠀⠀⠀⠈⠹⣿⣿⣟⠁⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⣰⣦⣍⣿⡿⣰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣤⣤⣤⣶⣶⣶⣶⣤⣄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢻⣿⣿⡀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⣟⣿⣟⠛⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⠏⠐⢶⡀⠛⠛⠁⠀⠀⠀⠀⠀⠈⢿⣿⣶⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣜⢷⣤⣴⣿⣿⣤⣤⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠘⡿⠻⠛⠻⣿⡟⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠐⣿⣿⣄⠀⣄⠀⣀⡞⠀⠀⠀⠀⠘⢿⣿⣿⣟

⣴⢆⣀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀⣾⣿⣾⣦⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠂⠀⠀⠃⢀⣤⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡤⠀⠀⠀⠀⠀⠀⠙⠁⢠⣣⣾⠏⠻⡿⣿⣦⡀⠀⠀⠈⢿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⡀⠀⠀⠈⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠙⠓⠄⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠈⠉⢹⣷⡄⠀⠀⠀⣾

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠁⢀⣰⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⣤⡄⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠿⡟⣥⣄⣀⠀⠋⡿⠋⠉⠈⠉⠉⠿⠿⣿⠿⠇⠀⠀⢸⣻⣿⣿⣿⣿⣿⣡⠀⠻⠿⠟⠋⠃⠀⠀⠈⠿⠀⠀⠀⣠⣿⣿⡿⠟⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣬⣡⣄⣭⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣡⣤⡝⢩⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠘

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠚⢷⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠖

⠀⠀⠀⠉⠉⠉⣩⣭⣽⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣅⣠⣈⣠⣶⣿⣦⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣤⣶⣶⣶⣾⣿⣿⣷⣦⣄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⣈⠛⠛⢿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⠻⣿⠛⠛⣿⣿⣿⣿⠁⠀⠀⢠⣾⣤⣿⣿⣿⣿⣿⡏⠁⠘⠀⣤⠀⢿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠹⣿⣎⣀⣴⢿⣤⣤⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡇⠀⠈⠙⣻⣟⣹⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠙⠇⠙⠿⢿⠿⠟⠻⠿⣿⣿⡿⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠈⠉⠙⢿⡟⠁⠀⣀⣀⠀⠀⠀⠀⠀⠦⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠿⠃⣸⣿⢘⠳⣶⣶⣄⠀⠀⠀⠈⢿⣿

⣤⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠋⠒⠀⠐⠂⠀⠀⠀⣠⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⣀⠀⠀⠀⠘⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢨⠀⠀⠸⢿⣷⣄⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢛⣠⣶⣴⠯⡿⢧⡇⠀⠀⠀⠸⢿⣿⡆⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢸⡄⣮⣯⣽⠉⠉⠉⠀⢰⡇⢼⠇⠀⠀⠀⠀⠀⠻⠧⠀⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠿⣿⡿⠏⠉⠉⠉⢻⣿⠿⡿⠟⠃⠉⠀⢸⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣹⠃⠿⠿⠃⠀⠀⠀⠀⠀⠇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣤⣭⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢨⣭⢩⣭⣩⣥⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⢿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣷⣀⣉⣉⣉⡉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⢁⣌⣉⣉⣉⡙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢐⠒⠶⢦⣤⠐⠒

⠀⠀⠈⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠈⠁⠀⠉⠀⠈⢉⣀⣈⣁⣨⣽⣷⣿⣭⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠉⠉⠉⠁⣧⣀⣀⣨⣿⣶⣶

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣷⡆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠁⠀⢤⠈⠉⢻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠛⠛⣿⣿⣿⡏⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣶⣶⢸⣿⣿⠇⠀⠀⠀⠈⢿⣿⣦⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⠛⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⣍⢁⣸⣿⣤⣠⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣹⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣇⡀⠀⠀⠀⠈⠁⠈⢿⣿⣿⠛⠛⣿⣿⡏⠙⠇⠀⠿⢿⡿⢿⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⢠⣾⣿⣿⣧⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣀⣀⣈⣿⣿⣿⡛⠓⠀⠀⢀⣾⣿⠇⠀⠀⠀⢉⣁⡀⠀⠀⠀⠀⠒⠀⠀⣆⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣷⣿⣿⣿⣿⠟⠁⣿⡇⠈⠛⠿⣷⣦⡀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⠘⠈⠀⠀⠀⠀⣠⣼⣿⡛⠀⢀⣴⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣾⣿⡇⡇⠀⠀⠿⢻⣷⣄⠀⠀⠀⣸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡵⠁⠀⠀⠀⠘⢻⣿⣦⠀⠀⠙

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠙⢑⠼⠁⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠟⠉⠀⠀⠈⢻⣿⣿⢿⡿⠅⠁⠀⣽⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠿⢿⠿⠿⡟⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣠⣌⣭⣭⢡⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡍⢩⣭⢩⣭⣩⣭⣉⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⢾⣿⣿⣾⣷⣀⡉⠉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀

⠒⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⢠⣠⠒⠀

⠀⠀⠀⠀⠀⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⡉⠉⠉⠹⠛⢡⣤⣽⣷⣶

⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠃⠈⢻⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿

⣿⣶⣦⣄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠉⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⣛⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡿⠿⣿⣿⣿⡛⠻⡏⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣄⢰⣿⣤⣿⣿⠏⠀⠀⠈⢿⣿⣶⣠⣾⣿

⣿⣿⣿⡿⠿⠛⠁⣾⣿⣿⣿⣿⣿⣿⡇⠀⠈⢁⠉⠙⠋⠉⠻⣿⣿⣿⣿⠀⠀⢾⣿⣿⣿⣏⠀⣀⣠⣿⣧⣤⣴⣷⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠛⠉⠀⠂⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠿⣷⣶⣿⣷⣤⣄⣴⣾⣿⣿⣿⡏⠀⠀⠈⠻⠿⣿⠁⠀⠘⠿⢭⣟⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣤⢠⣀⣀⣀⠀⠀⠘⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣤⣿⠉⢉⠉⠻⠏⠉⣉⣉⡛⠛⠀⠀⠀⠀⢀⣠⣴⣦⡄⠀⠀⠈⠉⠙⠋⣴⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠛⢿⣿⣿⣿⣿⣿⣥⣾⡟⣮⠈⠛⣿⣷⣄⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡂⠌⠀⠀⠀⣼⣿⣿⣿⣷⣄⡀⣠⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢿⠛⠀⠀⠀⠽⠿⣿⣿⣿⣿⢧⠇⠀⠀⠙⢿⣿⣧⡀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢹⠀⢀⡷⠀⠀⠀⠘⢿⠟⣡⠞⠀⠀⠀⠀⠈⠹⢿⣷⣄⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⡏⠆⠀⠙⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠀⠀⠀⠀⠘⠟⠛⠿⠿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣭⢁⣤⣠⣌⣭⣤⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢨⣭⢩⣥⣠⣤⣀⣤⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⢿⣷⡀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⣀⠀⠀⠀⠀⠀

⠀⢠⠀⠀⠉⠉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣏⣈⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠸⢗⣶⣶⣶⣶

⠀⣿⣷⣄⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣷⠀⢰⣾⣿⣿⣿⣿

⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢻⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠿⠛⠋⠁⣾⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠈⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⡟⠛⠻⣿⠟⠻⠿⣿⠿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⢰⣿⣠⣾⣿⠟⠀⠈⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠘⣿⠟⠋⠹⣿⣿⣿⣿⣿⠀⠀⢈⣀⠀⠛⠈⠉⢻⣿⣿⣿⡿⠀⠀⠀⠈⢻⣿⣧⣀⣴⣿⣦⣀⣴⣿⣰⠂⠹⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣶⠟⠁⠀⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⢿⣷⣟⣛⣶⣤⣤⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠸⠀⣰⡆⠠⣤⣄⣀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣾⠏⢉⡉⠈⠛⠉⢈⣉⣉⣛⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣶⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⠀⠀⢀⣴⣿⡇⡯⠈⠉⣿⣷⣄⠀⠀⠘⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣟⠒⠂⠀⠀⣠⣾⣿⣿⣿⣷⣦⡀⣠⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢀⣼⣿⠟⣴⠋⠀⠀⠋⣿⣿⣧⠀⠀⠀⠸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣿⠧⠒⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠟⠉⠻⣿⠟⠻⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣬⢉⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠋⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣾⣄⡀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⣶⣦⣶⣶⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠒

⠀⠀⢸⣿⣿⠝⣛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣉⣉⠉⠉⠈⠀⠀⠈⠁⠀⠉⠀⢈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⣄⠀⢀⣠⣴⣶⣶

⠄⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢰⣿⣿⣿⣿⣿

⠀⠀⠈⠙⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣻⣄⢻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿

⠀⡴⣆⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠈⠛⢿⠟⠛⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⡁⢨⣿⣿⠏⠈⢿⣿⣢⣠⣼⣿

⣶⣿⣿⣷⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠀⠀⠙⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢰⢠⣼⣿⣄⣀⣽⡝⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢡⠟⠓⠿⠟⠋⠀⠀⠈⣿⣿⣿⣿⣿

⣽⣿⣿⣿⣿⣿⠟⠁⡲⢻⣿⣿⣿⣿⠿⣧⣤⣤⣶⣀⠀⠀⠀⣸⣿⣿⡿⠻⣿⣧⠀⠀⠀⠀⠹⠋⠿⢿⣿⡿⠃⠃⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡘⠀⠸⠀⣤⡀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⣿⣿⣿⡟⠋⠁⠀⠠⣶⣾⣿⣿⣿⣿⣤⣿⠛⠷⠷⠉⠛⠀⠘⢻⣿⣿⠁⠀⠹⣿⠆⠀⣶⣶⡀⠀⠉⠙⠏⠁⢀⣴⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃⠀⢀⣠⣿⡇⡏⠿⣿⣶⡀⠀⠀⠀⠈⢿⣿

⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠒⠀⠀⠀⢀⣾⣿⣿⣶⣄⠀⣠⡿⠇⠀⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⢀⣾⣿⡿⣸⠇⠀⣸⣿⣿⣄⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⢈⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣾⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⣿⣿⣿⡏⡀⠀⠈⢹⣿⣿⡄⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉⠉⠂⠺⣿⣿⣿⣿⠐⠛⠘⣿⣿⣿⣿⣿⣿⠏⠉⠻⠿⠛⠛⠊⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠃⠀⠀⠈⣿⣿⣿⡆⠀⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠋⠙⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠻⠿⠂⠀⠘⣿⣿⣏⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⠀⠀⣾

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣡⣬⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⡄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠸

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣺⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒

⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠏⠈⣡⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣍⡉⠉⠁⠀⢀⣠⣴⣶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣰⣾⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⠉⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⣿⠟⠛⢻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⣤⣼⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠟⡋⣹⣿⣿⣿⣿⣿⡿⠃⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢿⣯⣿⣿⣿⡟⠙⠉⠿⢿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⢸⠃⢠⠀⢺⠋⣀⠀⠀⠁⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣼⣿⡟⠀⠀⣠⣴⣾⣿⣦⠀⢻⣿⣿⣿⣀⣴⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠔⣂⠀⠀⠀⠀⠀⡘⠀⡆⠀⠈⢀⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣶⣶⣿⣆⡀⣳⣸⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣴⣿⣿⡀⣠⣾⣿⣿⣿⣿⣿⡄⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⠀⠀⠀⢠⠀⡧⣰⠀⠀⣾⣿⣿⣿⣟⢿⣿⣿⡄⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠨⡄⠀⠟⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠛⢿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⠁⠙⠀⠀⠀⠀⠈⠙⢿⠋⠉⠻⣿⠿⠿⢿⡆⠀⠀⠀⠀⠀⠛⠀⠀⠀⠙⢻⣿⣿⣿⣿⠎⠉⣿⣿⣧⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠇⠀⠀⠀⢀⣀⡀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠁⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⢀⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠈⣭⣭⣡⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣷⣄⡉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠒

⠀⠀⠀⠉⠉⢉⣭⣭⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣤⣵⣶⣿⣿⣿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣦⣈⠉⠉⠉⠁⠈⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣶⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣟⠁⣾⣽⣿⡿⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⡏⠀⠀⢹⣿⣿⡿⠉⢿⣿⣶⣠⣾⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⡿⠀⢁⣸⣿⣀⣀⡽⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⢹⣿⣿⣿⣷⣿⣆⣼⣿⡿⠃⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠹⠈⢿⣿⡿⠿⣿⣿⠇⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⣠⣤⣤⠠⢾⡟⠀⢸⣿⣿⣿⣿⣿⡏⠛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠁⠀⣀⣾⣿⡆⠉⠛⠻⠿⢿⠿⠛⢻⣿⡟⠉⢀⣠⣤⣀⠀⠀⠱⠀⠀⠐⢃⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣶⢃⠈⣽⣷⡎⠀⢀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠁⠀⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⡀⠀⠀⠀⠀⠀⠀⣸⠛⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠟⠷⠀⠀⠁⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠙⠁⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣰⣿⣿⠿⠟⠛⠻⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⢸⣈⠿⣿⠟⢻⣿⣿⣿⣿⡆⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢠⣼⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣥⠀⠰⠟⠉⠀⠀⠀⠀⠀⣹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⡄⠀⢸⣦⠸⣿⣿⣿⣿⡇⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢛⡃⣀⣀⣀⠈⠉⠉⠀⠀⠀⠀⠉⠉⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⠙⠿⠿⠛⠯⠀⠀⠀⠀⠀⠀⣧⠀⠀⠁⠄⢿⣿⣿⣿⠇⠈⣾⣿⣿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣤⢁⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⢠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢩⣤⣤⣠⣌⠉⣭⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⡇⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣹⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢯⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠚⠃⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠒

⠀⠀⠀⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠁⠀⠈⠁⠈⠉⠀⠈⠉⠀⢉⣵⣯⣭⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣄⠀⠉⠉⠉⠉⠁⠉⢁⣠⣴⣶⣶

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣶⣦⣤⣶⣾⣿⣷⣶⣤⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠋⠁⠘⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡻⡿⠉⠀⠐⠀⠀⠘⣿⣿⣿⠀⠈⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡟⠑⠀⣹⣧⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠞⠀⠀⠀⠀⡄⢸⣇⣸⣿⡿⠃⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠛⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢶⡈⠻⣶⣾⣯⣻⣿⡿⡿⠛⠛⠁⠀⠀⠀⠀⠀⢀⣠⣄⠀⢝⢿⠀⠀⠀⠀⢰⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣇⠀⠀⠀⠉⢻⡿⠿⢿⡿⠋⠉⠻⠿⠀⠀⠁⠀⠈⠛⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⠿⠆⠀⠀⠆⠀⠀⣠⡟⠀⢀⣠⣴⣿⣶⣤⡀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣶⣄⠀⠀⠀⠀⢸⡇⠀⠀⢲⡆⠀⢀⠀⣀⣴⣿⣤⣼⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⢀⣶⣿⣧⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠸⠁⠀⠀⡄⠁⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⠿⠛⠉⠙⠻⠿⣿⣿⣿⡟⠇⠃⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⡇⠀⠘⣿⣿⣿⣿⡇⠻⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣠⣄⣤⣥⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣭⡝⢩⣤⢨⣭⣡⣤⣀⣤⢠⣄⣤⣄⣠⣌⣠⣤⣠⡄⣠⣤⢡⣤⣤⣠⣌⠙⣥⣤⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣼⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠲⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒

⠀⠀⠀⠀⠈⢉⣭⣽⣿⣿⣿⣿⣿⣿⣿⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣄⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣾⣿⣿⣿⣿⣆⡀⠉⠉⠉⠀⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣶⣶⣾⣿⣶⣶⣦⡀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢋⡿⢋⣉⠁⠀⠀⠘⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠁⠀⠀⠀⠀⢠⡄⢈⣿⣿⡟⠀⠀⠈⢿⣿⣦⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢻⡋⠂⢀⣿⣆⠀⢘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡈⠀⠀⠀⠀⠂⣸⠟⠊⠋⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡄⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⠋⢹⣿⣿⣿⠟⢦⠈⢳⣶⣾⣍⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠀⠀⠀⠀⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⢀⣴⣶⣄⡀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣁⣠⣽⣿⣿⡖⠛⠂⠀⠀⢰⣿⣿⠃⠀⠀⠙⠿⢿⠀⠀⠀⠀⠙⠇⠠⠥⠸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣽⡇⠀⠀⠀⠀⠀⠀⠛⢸⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠈⢿⣿

⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠀⠀⠀⠀⠀⣠⣶⣿⣝⠀⠀⣠⣴⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣦⣀⠀⠀⠀⢸⠇⠀⢸⣿⠀⡀⢀⢀⠀⠀⢠⣴⣿⣿⣿⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣴⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠀⠀⢸⡏⠀⢡⠈⠘⠀⣾⣿⣿⣿⣿⣿⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢐⡇⠀⢘⣄⣀⣀⡘⣿⣿⣿⣟⢁⠠⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠟⠉⠉⠙⠻⠿⣿⣿⡿⡇⠙⠀⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣆⠀⢠⣷⣶⣿⣿⣿⣿⠇⠉⢻⣿⣿⣾⠀⠢⠛⣿⣿⡆⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣥⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣡⣤⣠⣤⡄⢠⣄⣤⣠⣤⣩⣭⡍⢠⣤⢨⣭⣩⣤⣀⣤⢠⣌⣭⣍⣩⣍⣩⣤⣠⡄⣠⣤⢩⣭⣤⣠⣄⠀⣤⣭⣠⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⣉⣉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⢉⡉⣉⡉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒

⠀⠀⠀⠈⠉⠉⣭⣭⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣀⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣧⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⡿⠙⢻⡄⠀⠉⠉⠉⠀⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⣠⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠙⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠿⣟⣯⡏⠤⠀⠀⠀⠀⠙⢿⣿⣿⡗⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠠⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡉⠂⠀⠀⠀⠀⣰⣆⠸⠿⠿⠋⠀⠀⠀⠈⢿⣿⢶⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠀⠉⠙⠛⠛⠛⠛⠿⣿⣿⣿⣿⠃⠀⠸⣿⣿⣿⡟⠛⠉⠉⢹⣿⡙⠀⢸⡅⣹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣒⠠⠈⠇⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠙⣦⣤⣤⣦⣀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠹⣿⣿⡏⠀⠀⢶⡾⠿⢻⣶⡿⠁⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠘⢿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣤⣼⡟⠷⠆⠁⠰⠀⠈⠙⠛⠻⠁⠀⠀⠀⠀⢀⣨⣄⡀⠀⠀⠁⠤⠍⠙⢃⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⠆⠀⣤⣿⠁⠀⠀⠀⠀⠀⠈⠁⣼⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠈⢿⣿

⣤⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣻⢛⣃⡠⠀⢀⣾⣿⣿⣶⣄⠀⢀⣴⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠸⠀⠀⢹⡇⠀⡄⠀⣤⠀⢀⣰⣿⣿⣿⢙⣋⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣁⣀⣴⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢼⡇⠀⢃⠀⠘⠀⢾⣿⣿⣿⡏⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢸⠀⠀⠘⡀⠀⠀⠈⠻⣿⣿⣿⣯⡗⠙⠻⣿⣿⣇⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⠿⡿⠛⠉⠀⠀⠀⢹⣿⣿⣿⡻⠃⠈⠀⣸⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣷⣀⡈⠀⠀⠀⠰⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠙⢻⣿⣿⡆⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢁⣤⣠⣌⣭⣭⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡍⢡⣤⢠⣤⣠⣤⣀⣭⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣭⢩⣭⣭⣠⣄⠀⣤⣭⣡⣤⡀⠀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⣉⡉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⢁⣈⣉⣉⣉⣙⣉⣉⣉⠉⠉⠉⠉⠉⠉⠀⠉⢁⣙⣋⣄⠙⠋⠈⢻⣹⠁⠀

⠶⠒⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒

⠀⣀⣀⠀⣴⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣏⣩⣭⣤⣍⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠙⣿⣆⠀⠀⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿

⠉⠸⠟⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠻⣿⣿⣿⡽⡁⠀⠨⠭⠀⡀⢹⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣈⣙⠃⠀⠀⠀⠀⢾⡷⠜⠛⠓⠀⠀⠀⠀⠀⠈⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣿⣿⣿⡇⠀⠉⠙⠛⠛⠛⠛⠿⣿⣿⣿⣿⠀⠀⠀⠀⠹⢿⡿⠀⠀⣸⣯⠀⠁⢹⡟⠛⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡼⠒⠌⢲⠀⠀⠀⢠⣿⡇⢸⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⣿⠳⣤⣤⣴⣧⣀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⢛⣿⣿⣿⠇⠃⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⢿⣦⠀⠀⠀⠀⠈⢻⣷⣾⣿⣧⣤⣶⡀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⡀⢀⡀⣰⣶⣼⣿⣿⣿⣿⣿⣤⣾⣛⣲⠂⠉⠂⠀⢉⣙⡛⠻⠀⠀⠀⠀⣀⣤⣶⣶⣆⠀⠀⠤⣬⣯⢁⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⢰⠀⢠⣼⡿⠀⠀⢀⣤⡄⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣽⣧⠔⠀⣰⣿⣿⣿⣷⣄⠀⣠⣾⣿⣿⣿⣿⣿⣆⠀⣤⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠸⠀⠐⣿⡇⢀⣾⣿⣿⣇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢹⣷⣾⣿⣿⣿⣿⡀⠀⠀⠸⣿⣿⣿⣟⢿⣿⣿⡆⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⡿⠿⡿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠹⣿⣿⣿⡄⠙⣿⣿⡄⠀⠀⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠋⠙⠛⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⠃⠀⠘⠻⠟⠛⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⢿⣿⠃⠀⠹⢿⡇⠀⠀⢀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢀⣤⣠⣍⣭⣭⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣤⡄⢠⣤⢠⣤⣠⣤⣀⣤⢨⣍⣭⣍⣩⣍⣩⣭⣩⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣡⣤⡀⢸⡆

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣼⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠈⠀

⠿⢿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠟⠛⠀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⣉⣙⣉⣉⣉⣉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠠⠦⢤⠆⠀⢠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⠶⠶⠖⠒

⣶⣶⣶⣶⣶⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠉⠉⠈⠀⠀⢀⣠⣴⣶⣶

⠿⠿⠿⢿⣿⣻⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣤⣦⣤⣤⣿⣿⣿⣿⣿⣿

⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⡿⢛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿

⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠙⠻⢋⡸⠁⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⢿⣿⢢⣠⣼⣿

⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠁⠀⣠⣿⣄⠈⢉⡟⠻⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢙⡇⣠⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⠏⠀⠀⠈⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠇⠀⠀⢀⡄⠀⠀⠀⢈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⣿⣿⠟⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⢿⣃⡀⠀⠀⠀⠙⢿⣿⣿⣟

⣿⣿⣿⣿⣿⣿⣿⠟⠁⠙⢿⣿⣿⣿⣤⡄⠀⠈⠉⠉⠒⠀⢐⣻⣿⣿⣿⣦⣴⣶⣴⣶⣿⣿⡆⠀⠀⠂⠙⠃⠀⣴⣾⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⢘⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⢨⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⠟⣿⣿⣿⣶⣶⢰⠀⢾⡟⣿⣧⠀⠀⠀⢸⣷⡘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠱⠀⢡⣤⡀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⢸⣿⣿⣿⡶⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⢏⣿⣿⣿⣼⠀⠈⠀⣿⣿⡇⠀⠀⠀⠙⠇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⢦⣶⣿⣦⣴⣿⣟⣻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠻⣿⣿⣿⠇⠘⠸⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⢰⠀⠀⠀⡘⠀⢹⣿⣱⡇⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠟⠉⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⠆⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠈⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢿⡿⠃⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠛⠉⣭⢉⣤⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣬⣡⣤⣠⣤⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⢲⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⡇⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣼⣿⣽⡇⣹⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠈⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠒

⠀⠀⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⢀⣀⣀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣷⣶⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⣰⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⣆⠀⢀⣿⣿⣿⣿⣿⣿

⠀⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣴⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿

⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠹⣿⣿⠟⠛⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⠏⠉⠉⢻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢹⡿⠀⠀⠘⣿⣿⢢⣠⣼⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠀⢀⣰⣿⣄⣀⣸⡟⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣦⣶⣿⠇⠀⠀⠀⠈⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠿⠿⠿⠿⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠋⠹⠿⣿⡟⠁⠀⠛⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⣿⣿⣿⣿⣤⠈⠉⠹⠏⡀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⣿⣿⣿⡿⣿⠿⠿⠿⢿⣿⠏⠉⠉⠁⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⣠⣤⣾⣿⣦⠀⠀⠐⠂⠊⠀⣰⣾⣿⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⢸⢿⣷⡄⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⣠⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡅⡀⠠⠀⠀⢻⠟⣿⣆⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢆⠀⡏⢹⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⡟⡇⡇⠀⡆⠀⠈⠀⣿⣿⣆⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢨⣦⣷⣾⣆⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⠿⠛⠛⠿⠿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢢⠀⠀⡂⡜⠀⠃⣷⡀⡃⠀⠀⠀⠸⢿⣿⠀⠀⢀⣧⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣿⣿⣿⣿⣿⡆⠀⠀⠘⠏⠙⠛⠛⠁⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⠇⠀⠀⠛⠉⠀⠉⠀⠀⠀⠂⠀⠀⠀⠐⡐⠀⠀⠀⢹⠟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣥⡄⢠⣤⢠⣤⣠⣤⣀⣄⢠⣄⣤⣄⣠⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⢀⠀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣽⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠈⠁

⠿⠿⣿⣿⣿⣿⣿⣿⡿⢾⣿⣿⣿⣿⣄⡉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣩⠁⠀

⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠒

⠀⠀⠀⠉⠉⠉⣭⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣾⣷⣶⣿⣿⣿⣿⣶⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⡟⠻⣿⣿⣿⣿⣿⣶⡄⠀⠸⢿⣿⡿⠛⠋⠉⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣢⣠⣼⣿

⠀⠀⠀⠀⠀⠰⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⠿⣀⣀⣼⣿⣧⣤⡜⣿⣿⣿⣿⠟⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠘⠀⠻⢿⠟⠻⢿⣿⠇⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟

⠀⢀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣿⣿⡋⠙⠿⣿⣿⣿⣿⠿⢿⣿⠟⠋⢀⣠⣤⣤⠀⠀⠙⠀⠀⠐⢃⣴⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⣿⣿⣿⣿⡟⠃⠍⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⠈⠙⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠥⠀⠀⠀⠀⠀⠀⠀⠘⠁⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣤⡀⠀⠰⠎⠙⢻⣶⣞⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠙

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⡏⠀⡀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣨⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⠃⠋⠀⠀⢧⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣤⣀⣤⠊⠙⠛⠁⠀⠀⠀⠀⠙⠿⢿⡿⠿⠇⠀⠀⢸⣿⣿⣿⣿⣿⠟⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠘⡄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣬⢉⣥⣠⣄⣤⣤⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣤⣨⣥⡄⢠⣤⢠⣤⣠⣤⣀⣤⢨⣍⣭⣍⣡⣄⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⢀

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠸

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⢀⠉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠒

⠀⠀⠀⠉⠉⢉⣭⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣦⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣤⣤⣤⣶⣶⣤⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⡛⠛⢻⣿⣿⡟⠁⠀⠀⠀⠻⣿⡿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠐⠀⠈⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⣿⣿⣄⣤⣿⣷⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡇⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢷⠘⢿⣿⡿⠿⠟⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢼⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣸⣿⣿⡟⠋⠉⠛⢿⣿⣿⣿⣿⠟⠛⠛⢛⡁⠀⠀⠀⠀⠈⠑⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢸⣿⣿⣿⣿⣿⢿⣿⣿⠀⠙⢷⣶⣦⡀⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⠿⠇⠀⠀⢀⠀⠙⠋⠉⠁⢀⣴⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠄⠀⠀⠸⣿⣿⣿⠋⠀⣸⣿⣻⠀⠀⠀⠛⠻⣿⣦⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣧⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣂⢺⡭⡇⡇⠀⠀⠀⠀⠀⠿⣿⡇⠀⠀⢂⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠋⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣤⣤⣴⡘⠛⢻⠟⠁⠀⠉⠉⠛⣿⣿⣿⣿⣿⠈⠀⠀⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣯⣤⣴⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣥⣠⣄⣭⣤⢠⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣬⣩⣭⡍⢠⣤⢠⣬⣩⣭⣉⣭⢩⣍⣭⣍⣩⣅⣠⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⣿

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠈

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⡀⣉⣉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⣤⣉⣉⠉⠁⢈⣁⣈⣉⣉⣉⡙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠒

⠀⠀⠀⠉⠉⢉⣭⣭⣭⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣴⣶⣾⣶⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣷⣦⣴⣶⣄⠀⠀⠀⠀⠉⣩⣿⣯⡉⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣤⣤⣴⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢹⣿⠁⢉⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠉⡝⣿⣿⣿⣿⠏⠉⣤⡀⠸⠿⠆⠀⠀⠀⠀⠀⠈⢿⣿⣶⣠⣼⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⡟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡙⣿⣷⣴⣾⣿⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⠉⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⡂⠀⠀⠀⠉⠙⠛⢻⣿⣿⡿⠻⣿⣿⣿⡉⠙⠇⠙⢿⣿⡟⠛⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⡏⠀⠀⠀⠀⢿⣆⢀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟

⠀⢀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣠⣤⣿⣿⡦⠀⠰⠂⠀⠀⣸⣿⡏⠀⠀⠀⠙⣻⣀⡀⠀⠀⠀⠉⠙⠙⠒⣥⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⠀⠀⠀⠀⠀⠈⠉⣾⣿⠃⠈⠻⢿⣷⣄⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⣠⣿⡿⠸⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠀⠀⠀⢀⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣴⣿⣧⣶⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⡀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⣀⣸⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣾⣿⣿⡿⠿⣿⠟⠋⠀⠀⠀⠙⣿⠿⠿⣿⣿⠈⠀⠀⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣭⣩⣍⣭⣥⢠⣤⡀⣠⣤⣀⣤⡀⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣨⣬⣠⣥⡍⢠⣤⢠⣭⣩⣭⣉⣭⢩⣍⣭⣌⣨⣍⣩⣭⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠉

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢹⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⠿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣀⣉⣉⡉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⢀⣉⣉⣉⣁⣌⣁⣌⣉⣉⣉⣙⡉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⣦⠄⠰⣶⣶⣶⣶⣴⣶⣶⣶⠶⠶⠶⠒

⠀⠀⠀⠈⠉⢉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣯⠄⠐⠛⠻⢿⣿⣿⡍⠀⠀⢀⣠⣴⣶⣶

⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠉⠀⠀⢰⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠛⢿⠟⢿⣿⣿⣿⣿⣿⣿⢶⣶⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢺⣿⣿⣿⣿⠛⣇⠈⣺⣿⣇⣀⣨⡉⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣴⣿⣿⣿⣿⣿⣿⣸⣿⠏⠁⠀⠀⠀⠘⢿⣿⣷⣠⣼⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⣄⠈⠃⠀⠙⣿⣿⣿⡏⠀⠀⣿⣿⣿⡿⠇⢻⣿⣿⣿⣿⣿⡿⠳⠿⠋⠁⠀⠀⠀⠀⠀⠀⢰⣿⣼⣙⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⠇⠙⣿⣿⣿⡛⢷⣦⣀⣾⣿⣿⡿⠁⠀⠀⠈⠻⠿⠃⠀⠀⠻⣿⡿⣿⣿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣤⡄⣀⣀⣀⠀⠀⠀⠀⠙⣿⣿⣿⣟

⠀⢀⣀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣧⣽⡁⢰⡟⢀⣀⣉⠙⠃⠀⠀⢀⣠⣴⣾⣷⣶⡄⠀⠈⠀⠀⢀⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⣿⠀⣿⡇⠀⠙⢻⣿⣦⠀⠀⠀⠀⠈⢿⣿

⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⢀⣾⣿⣿⣿⣦⡀⣠⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢱⠡⠹⠀⠀⠀⠀⠀⣿⣧⠀⠀⢸⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠁⠀⠈⠁⡀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⠿⢯⣿⣤⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠿⢿⣿⣿⣿⠿⠿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⢉⣤⣠⣌⣥⣬⢡⣤⡀⣠⣤⣀⣤⡄⣤⣄⣠⣤⣠⣤⡄⢠⣄⣤⣠⣭⣠⣤⡄⢠⣤⢠⣤⣠⣤⣈⣭⢩⣍⣭⣍⣩⣍⣩⣤⣠⡄⣠⣤⢠⣤⣤⣠⣄⠀⣤⣤⣠⣤⡀⠀⠈

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡿⣿⣿⣿⢽⢼⠇⣙⣿⣽⣿⡇⣿⣿⣿⣿⡍⣿⠁⢸⣿⣿⣿⣿⡇⣿⠀⣾⣿⣸⡿⢻⡿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣽⡇⣿⡷⠀⣿⡇⣿⣿⠀⣿⣿⣙⣿⡅⠀⠀

⡿⠿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣄⡉⠉⠉⠉⠉⠈⠉⠈⠀⠀⠈⠋⠉⠛⠁⠉⠉⠉⠉⠁⠉⠛⠈⠉⠉⠉⠋⠀⠉⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⣉⡙⣉⡉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠙⠋⠀⠙⠋⠈⢻⣹⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣀⡀⢀⠀

⠀⢸⣷⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣶⣶⣶⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⢸⡇

⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢰⣿⣿⣿⣿⣿⣿⢸⣧

⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⢸⣿⣿⣿⣿⣿⣼⣿

⠀⢸⣿⣿⣿⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⡏⠛⠭⠿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⣿⣿⣿⣿⢸⡿

⠀⢸⣿⣿⣿⠀⠀⠀⣶⣶⣮⣭⣭⣭⣭⣭⣽⣗⣶⣚⣚⣻⣿⣧⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠒⠘⠒⠇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⢀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠘⡇

⠀⠸⠿⠿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣯⣭⣭⣿⣿⣿⠀⠀⠀⠀⠀⠿⠿⠟⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⣾⣿⣛⣋⡁⣁

⠀⢰⣶⢠⣶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⢿⣿⣿⡇⣿

⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⣿

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

⠀⢸⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠂⣒⠤⠤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣦⣤⣤⠤⠤⠤⠤⠤⣿⣿⡇⢸

⠀⢸⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⢠⡿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⡇⢸

⠀⢸⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣟⡟⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⠠⠤⠐⠒⠨⠉⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⣤⣤⠀⠀⢹⣿⡇⠸

⠀⢸⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⠀⠀⢸⡿⡇⠘

⠀⢸⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣶⣧⠀

⠀⢸⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⠀

⠀⢸⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⡇⠀⢈⣁⢈⠀

⠀⢠⣤⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣘⣿⢿⠀

⠀⢸⣿⢸⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣏⣭⣉⣩⣉⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀

⠀⢸⣿⢸⣯⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡇

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

⠀⢸⣿⢸⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠭⠭⠥⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⣀⣀⢻⣿⣇

⠀⢸⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿

⠀⠿⠟⠘⠛⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠴⠶⠤⠒⠒⠒⠂⠚⠋⠙⠛⠉⠉⠁⠀⢀⣀⣀⣀⣀⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤

⠀⠀⠀⠀⠠⠤⠤⣄⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣾⣿⡿⠿⠿⠿⢿⣿⣟⣛⣛⣻⣿⣿⣶⣶⣶⣶⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠰⣶⣤⡀⠿⠿⠿⠿⢿⣟⣛⣛⣛⣛⣿⣯⣭⣭⣭⣽⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠐⠠⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⢾⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 1269

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✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXVI:_An_Erosion_of

Fundamental_Rights_Protection?⠀✐

Posted in Courtroom, Europe, Law, Patents at 8:40 am by Dr. Roy Schestowitz

Series parts:

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In!

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:A“Unanimous”

  Endorsement?

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:Germany_Says“Ja”

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch

  Courage

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and

  Pusillanimous_Hibernia

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss

  Cheese

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the

  Controversial_Christian_Bock

  1. The_EPO’s_Overseer/Overseen_Collusion_—Part_XI:“General_Bock”_–

  Battistelli’s_Swiss_Apprentice?

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian

  Facilitators_–_Spain

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian

  Facilitators_–_Portugal

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XV:_Et_Tu_Felix_Austria…

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVI:_The_Demise_of_the

  Austrian_Double-Dipper

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVII:_The_Non-Monolithic

  Nordic_Bloc

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVIII:_Helsinki’s_Accord

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXX:_The_Baltic_States

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XX:_The_Visegrád_Group

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXI:The_Balkan_League–_The

  Doyen_and_His_“Protégée”

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXII:The_Balkan_League

  North_Macedonia_and_Albania

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIII:The_Balkan_League

  Bulgaria

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIV:The_Balkan_League

  Romania

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXV:The_Balkan_League

  Fresh_Blood_or_Same_Old,_Same_Old?

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVI:_A_Trojan_Horse_on_the

  Budget_and_Finance_Committee

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVII:_Cypriot_Complicity

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVIII:_Benoît_and_António’s

  Loyal_“Habibi”

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXXX:_The_EPOnian_Micro-

  States_–_Monaco_and_Malta

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXX:_San_Marino_and_the

  Perfidious_Betrayal_of_Liberty

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXI:_The_Abstentionists

  1. The_EPO’s_Overseer/Overseen_Collusion_—Part_XXXII:“Plucky_Little

  Belgium”?

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIII:_Swedish_Scepticism

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIV:An“Extremely

  Dubious”_Proposal

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXV:_Slovakian_Scruples

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVI:_Serbian_Sour_Grapes

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVII:_Stubbornly

  Independent_Slovenia

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVIII:_Ensnared_in_the

  Tentacles_of_the_SAZAS_Octopus

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIX:_On_the_Slippery_Slope

  to_Capture

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXX:_The_Idiosyncratic

  Italians

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXI:_Public_Service_or

  Self-Service?

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXII:_A_Parcel_of_Rogues?

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXIII:_A_Legal_No-Man’s

  Land

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXIV:Immunity=_Impunity?

  1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXV:_In_the_Shadow_of

  “Waite_and_Kennedy”

  1. YOU ARE HERE ☞ An Erosion of Fundamental Rights Protection?

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

Recent judgments of the European Court of Human Rights appear to have eroded

the obligation of ECHR states to protect fundamental rights in cases where the

       alleged violations involve an international organisation.

Summary: What the European Court of Human Rights means to EPO workers in light

of more recent developments, especially 5 years ago (Supreme Court of the

Netherlands)

In the last part we saw how the European Court of Human Rights (ECtHR) has

ruled that states which are signatories of the European Convention on Human

Rights (ECHR) have a responsibility to ensure that their membership of

international organisations does not lead to a breach of their ECHR

obligations.

“…it has become evident that the overriding priority of the Court is to protect

the autonomy of international organisations at the expense of the fundamental

rights of their staff (and other individuals adversely affected by the acts of

such organisations).”In other words, ECHR signatory states must ensure that

adequate provision is made for an “equivalent protection” of fundamental rights

inside any international organisation which they join.

This has implications for the internal justice systems of international

organisations on which staff are obliged to rely for legal redress, because of

their lack of access to national courts.

According to the “Waite_and_Kennedy_v._Germany” judgment, such internal justice

systems must provide staff of an international organisation with “reasonable

alternative means to protect effectively their rights under the [European]

Convention [on Human Rights]“.

However, following the delivery of ECtHR judgments in the cases of Klausecker

v. Germany (application_no._415/07) and Perez_v._Germany [PDF] (no._15521/08)

in January 2015, it has become evident that the overriding priority of the

Court is to protect the autonomy of international organisations at the expense

of the fundamental rights of their staff (and other individuals adversely

affected by the acts of such organisations).

“There was now a distinct possibility that international organisations and

their member states could get away with applying a different and less rigorous

standard of human rights protection to the acts and omissions of an

international organisation.”The Klausecker and Perez judgments prompted the

legal scholar Anne-Marie Thévenot-Werner to express concern about an_erosion_of

the_obligation_of_states_to_protect_the_fundamental_rights_enshrined_in_the

ECHR.

In an article published in the legal journal Revue de droit allemande in 2015

Thévenot-Werner acknowledged that the ECtHR had formally reaffirmed its case

law requiring the provision of “reasonable alternative means” for the

protection of fundamental rights inside international organisations.

However, at the same time the Court signalled that it would not hold a state to

account for a breach of the ECHR involving an international organisation unless

the protection available via the organisation’s internal justice system was

shown to be “manifestly deficient”.

Thévenot-Werner warned that the approach taken by the Court in these cases

risked creating a loophole with respect to the protection of fundamental rights

enshrined in the ECHR.

“It deserves to be emphasised at this point that these are matters which are

not merely of academic and theoretical interest.”There was now a distinct

possibility that international organisations and their member states could get

away with applying a different and less rigorous standard of human rights

protection to the acts and omissions of an international organisation. In such

situations, states would only be called to account if it could be established

to the satisfaction of the Court that the level of protection available was

“manifestly deficient”.

The risk of such an erosion of legal protection exists even in the case of

organisations where all participating states are signatories to the ECHR (which

is the case for the EPO).

It deserves to be emphasised at this point that these are matters which are not

merely of academic and theoretical interest.

The saga of Benoît_Battistelli‘s “Strike Regulations” at the EPO provides a

striking illustration of their practical significance for the staff of

international organisations.

“The Gerechtshof judgment showed that at least some judges in the Netherlands

were serious about setting limits to the “immunity” enjoyed by an international

organisation in order to prevent abuses involving clear-cut violations of

fundamental rights.”As noted in an_earlier_part_of_this_series, Battistelli’s

controversial “Strike Regulations” were one of a long litany of grievances

which the EPO staff union SUEPO attempted to litigate before the national

justice system in the Netherlands.

During the litigation procedure, the Gerechtshof den Haag (Appeal Court of The

Hague) decided that breaches of fundamental rights by EPO management were so

severe that they justified lifting the organisation’s immunity from

jurisdiction.

This lead to a judgment, delivered on 17_February_2015, in which the

Gerechtshof ordered_the_EPO [PDF] to rescind several amendments to the

organisation’s staff regulations, including the undue restrictions on

industrial actions imposed by the impugned “Strike Regulations”.

In addition to this, the EPO was ordered by the court to uphold the rule-of-law

and social dialogue standards in_line_with_the_European_Convention_on_Human

Rights_and_ILO_Conventions_No._87,_on_the_right_to_organise_in_trade_unions,

and_No._98_on_the_right_to_collective_bargaining. [PDF]

The Gerechtshof judgment showed that at least some judges in the Netherlands

were serious about setting limits to the “immunity” enjoyed by an international

organisation in order to prevent abuses involving clear-cut violations of

fundamental rights.

The European Public Service Union (EPSU) reported on the judgment under the

headline “European_Patent_Office_does_not_live_in_a_Dutch_no_man’s_land”.

“The problem with the Gerechtshof judgment was that it set a worrying precedent

which had political ramifications going far beyond the EPO.”Unfortunately, both

SUEPO’s legal victory and EPSU’s optimism turned out to be short-lived.

Less than two years later, the Gerechtshof judgment was set aside, thereby

confirming what many had long suspected: the European Patent Office does indeed

live in a Dutch no man’s land!

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

An independent judicial review of violations of fundamental rights by the EPO

carried out by the Gerechtshof den Haag led to a short-lived lifting of the

organisation’s immunity in February 2015. This was overruled in January 2017

when the Supreme Court proclaimed that Dutch courts had “no jurisdiction in the

                             EPO dispute”.

The problem with the Gerechtshof judgment was that it set a worrying precedent

which had political ramifications going far beyond the EPO.

“The Hoge Raad attempted to justify its findings on the basis that the

fundamental rights of EPO staff “were sufficiently protected by the internal

dispute settlement procedure provided for by EPOrg”.”It was a veritable thorn

in the flesh not only for Battistelli and his clique at the EPO, but also for

the Dutch government which reaps significant economic benefits from the

country’s status as a host to a large number of international organisations.

This led to the Dutch government joining forces with Team Battistelli in

support of an application for “cassation” of the judgment.

Finally, on January 2017, the Hoge Raad (Supreme Court of the Netherlands)

issued a ruling to the effect that Dutch courts had no_jurisdiction_in_the_EPO

dispute:

 “According to the European Court of Human Rights (ECtHR), granting

 jurisdictional immunity to an international organisation constitutes

 a limitation of the right of access to a court as referred to in

 article 6 of the Convention for the Protection of Human Rights and

 Fundamental Freedom Rights (ECHR). This limitation is acceptable

 provided that litigants have a reasonable alternative means of

 protecting their rights effectively.

 The Supreme Court found that such alternative means exist. The rights

 of VEOB [the Netherlands branch of SUEPO] and SUEPO are sufficiently

 protected by the internal dispute settlement procedure provided for

 by EPOrg, under which individual employees and staff representatives

 can ultimately take their complaint to the Administrative Tribunal of

 the International Labour Organization in Geneva. According to the

 Supreme Court, this means that the essence of their right of access

 to a court has not been impaired.”

The Hoge Raad attempted to justify its findings on the basis that the

fundamental rights of EPO staff “were sufficiently protected by the internal

dispute settlement procedure provided for by EPOrg”.

But is this really the case?

“In the upcoming parts, we will take a closer look at the EPO’s internal

justice system and the role which it played in “Strike Regulations” affair.”Not

everybody would agree. Indeed, many would argue that the facts tell a very

different story and that the judgment delivered by the Hoge Raad in January

2017 was driven by political expediency and a misplaced desire to tell the

Dutch government and the EPO what they wanted to hear rather than what they

needed to hear.

In the upcoming parts, we will take a closer look at the EPO’s internal justice

system and the role which it played in “Strike Regulations” affair.

In particular, we will see how a former judge of the European Court of Human

Rights played a bizarre and incongruous role in prolonging the suppression of

the fundamental right to “freedom of association” at the EPO. █

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

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠋⠛⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠚⠓⠛⠛⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠀⠘⠙⠿⡤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠐⠤⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠛⠛⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢤⡂⠸⠦⣠⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣯⠆⠀⠀⠀⠀⠀⠀⣨⣧⣶⣿⣿⣿⣿⣵⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⡛⠈⠀⠀⠀⠀⠀⠀⠀⠐⠹⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢹⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⣠⣿⣿⣿⣿⣿⣿⣿⣟⠿⠃⠈⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⢀⡇⢸⣽⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣽⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⡏⠽⠟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣿⠁⣔⠀⣼⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣴⡠⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣔⣶⣟⡀⢛⣿⣿⣿⣿⣿⡅⣰⣿⠀⣿⣿⣿⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢱⣿⣿⣿⡿⡿⠿⠟⠛⠁⠀⣀⣀⣤⣶⣯⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠁⠈⠉⠉⠙⠃⠈⢿⣿⣿⡟⠛⠀⠙⠉⠈⠉⠉⠉⠙⠂⠙⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣯⡉⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢴⣾⠗⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣤⡄⡀⠀⠀⠀⠀⠀⣀⢠⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⠐⠳⠧⠀⠀⠙⠁⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣀⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣶⣿⣿⣿⣿⣿⣿⠿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠛⠛⠀⠸⡿⠛⠙⠻⣿⣿⣿⡇⠀⢄⠀⢀⠽⠋⠛⠟⡻⡻⠛⠛⢟⠀⠘⠙⢯⠟⠉⠙⢿⠏⠙⠫⢿⠛⠛⠛⠻⢯⠙⠙⠙⡟⠛⠛⠏⡽⠉⠉⠻⢏⡇⢘⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢐⡠⠀⠰⠀⠀⠁⠀⣿⣿⣿⡇⠀⡀⠀⣼⠀⠀⠀⠀⠂⠀⠤⡄⣞⠀⢠⡂⢨⣠⠀⠰⣾⡀⠈⠐⢾⠀⠠⡤⠀⢹⠀⢰⣤⠆⠈⠀⠀⡵⠀⠈⠀⢸⡇⠀⠀⢼⢻⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣠⣼⣧⣄⣀⣴⣿⣿⣿⣇⣤⣷⣄⣸⣦⣄⣀⣤⣴⣦⣀⣠⣴⣤⣜⣇⣸⣿⣄⣀⣼⣄⣀⣤⡼⠀⢠⣀⣠⣝⣤⣜⣧⣤⣀⣀⣤⣧⣄⣀⣤⣼⣇⣸⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿

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

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⡟⢛⣿⣿⢿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣟⡎⢛⣻⣿⠛⠛⠟⢿⢿⣿⣿⣿⣿⣿⣿⣟⡟⢻⣿⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣟⠓⠺⠍⠉⠉⠍⢉⠍⠩⠉⠟⢉⣉⠁⢈⡉⣫⠀⡍⠉⠁⠇⢈⠉⡋⠉⠍⠹⠄⢨⣽⣷⠀⣿⡄⢨⠋⠍⠉⠍⢡⠙⣿⣿⡇⢘⡛⢸⡍⠩⠙⠏⠩⠉⡟⢩⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣄⣉⣁⣸⡂⢀⢠⣇⣨⣤⣀⣀⡃⡈⡉⣁⣸⣂⣙⣀⡡⣀⣀⣁⣨⣀⡧⣀⠁⢸⣂⣾⣿⣿⣀⣉⣠⢾⣀⣀⣴⣂⣊⣀⣿⣿⣃⣸⣟⢈⢁⣀⣀⣇⣈⣀⡆⢈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿

                ䷩ 𝚕𝚒𝚗𝚎 1632

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/gemini-not-ugly/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/09/gemini-not-ugly/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Response_to_Gemini_Misconceptions_and_Mythology_(It’s_Not_Ugly_or_Just_for

Geeks)⠀✐

Posted in Deception, Free/Libre_Software, FUD, Protocol, Standard at 7:54 am by

Dr. Roy Schestowitz

Video_download_link | md5sum 420621d8ea77533494fdde5e187ca23a

Gemini Misconceptions

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/gemini-myths.webm

Summary: Another gemini:// FUD response; this time we deal with this_new

article, a polite article, which nevertheless makes Gemini as a whole seem

crude and ugly; in reality, depending how it’s presented, Gemini can be

beautiful, expressive, and feature-rich (depending on the creativity of

pertinent capsules)

THE RISE of Gemini isn’t a subjective thing. It is measurable. It’s objective.

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇1700 Gemini capsules approached⦈ As shown in the image to

the right, Gemini is growing fast. On January 16th we_wrote_about_1,600_active

capsule and now we’re flirting with 1,700. Almost 100 active capsules in net

gain in 3.5 weeks is nothing to sneeze at (not the same as 100 new capsules as

it’s possible that 10 of the existing ones shut down while 110 new ones

emerged).

“Almost 100 active capsules in net gain in 3.5 weeks is nothing to sneeze at

(not the same as 100 new capsules as it’s possible that 10 of the existing ones

shut down while 110 new ones emerged).”Over the past few months I’ve seen a

number of Gemini-bashing posts that were mostly based on misunderstandings.

Sometimes there’s almost outdated information or misinformation. “I had a

discussion with someone about Gemini,” one person told me this morning, “a

couple of years ago.” That’s like the time Gemini was only months old. A lot

has changed since then. The number of capsules grew from a couple hundred to

over 2,000, with probably around a million pages in them (Lupa alone has

retrieved and analysed almost half a million pages).

That same person then asked me and another Gemini proponent: “What are the

advantages you two see in Gemini?”

“The number of capsules grew from a couple hundred to over 2,000, with probably

around a million pages in them (Lupa alone has retrieved and analysed almost

half a million pages).”“Speaking for myself,” I replied, “self-hosting is one.

The Web became far too bloated, so it’s difficult to host from one’s

residential perimeter, hence people move to centralised platforms and

datacentres.”

“But people’s connections have gotten faster, it’s just the Web that changed.

Why can’t people take back control of the Internet? In his talks about

Freedombox, Eben Moglen raised this point.”

The person then asked: “Does Gemini use HTML? Could we post the same pages HTML

pages we have now on a gemini server, or would they need to be modified and

adapted?”

Some people wrongly believe that Gemini Protocol is only for transmission or

only for ‘markup’. It’s actually both. HTML is very complicated for a lot of

people. Setting up a Web server is also hard compared to Gemini. So lesser

technical people cannot easily participate, unless they create some accounts in

Blogspot (Gulag) or Facebook…

“There are already dozens of Gemini clients (like Web browsers) and over a

dozen Gemini server implementations.”Gemini uses GemText, which is simple

enough to teach to 6 year olds. It’s also a lot simpler to program with, owing

to this simplicity.

There are many good HTML→GemText (and vice verse) converters. Anyone with basic

coding skills can write one in a few hours, as many people have. “XSLT might

also be an option for HTML→GemText,” an associate of ours notes.

There are already dozens_of_Gemini_clients_(like_Web_browsers)_and_over_a_dozen

Gemini_server_implementations.

Our hope is that better understanding of Gemini, owing to media coverage (the

mainstream media is paid to push ads and lies, so it won’t help Gemini grow),

can help without it resembling “advocacy”/”evangelism” (religious term) or

“marketing”. As it turns out, some mainstream media already_embraces_Gemini and

it has become big enough for Microsoft_to_attempt_to_hijack/undermine_it. █

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

⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣇⢿⣿⡟⡇⡇⡷⣹⡜⡇⢿⢸⢸⡱⣼⢬⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

⣿⣿⣿⣿⣿⣿⣷⣾⣀⣇⣾⣈⣿⣟⣼⣷⣇⣸⣿⣏⣾⣃⣿⣸⣽⣿⣯⣺⣢⣗⣺⣐⣟⣸⣻⣧⣽⣼⣟⣿⣿⣉⣇⣸⣿⣧⣻⣇⣵⣯⣾⣠⣗⣺⣐⣇⣿⣃⣇⣿⣸⣞⣿⣿⣒⣗⣺⣇⣿⣸⣬⣵⣷⣺⣡⣗⣿⣿

⣿⣿⣿⣿⣿⢿⡿⣿⡿⣿⢿⡿⡿⣿⢻⢿⣿⣿⣿⣿⢿⣿⣟⣿⢻⢿⣿⢿⣿⡿⣿⢿⣿⣿⢻⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣾⣷⣿⣿⣯⣿⣷⣷⣿⣼⣧⣿⣿⣯⣿⣿⣿⣿⣿⣵⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣶⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

                ䷩ 𝚕𝚒𝚗𝚎 1753

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/geminispace-1705-working-capsules/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/09/geminispace-1705-working-capsules/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Despite_Occasional_Shutdowns,_Geminispace_Has_a_Net_Gain_of_About_100_Working

Capsules_Per_Month_(It_Has_Accelerated_Further_in_2022)⠀✐

Posted in Site_News at 9:37 am by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇January 2021: ~400; June 2021: 1000; December 2021: 1500;

           January 2022: 1600; Today (Feb. 9th): Over 1700⦈

                  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇1705_capsules⦈_

Summary: With almost 2,100 known Gemini capsules, about 82% of which are online

and accessible, the_growth_continues_unabated (net gain of about 100 in just 3

weeks or roughly 5 per day, on average)

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

⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣍⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿

⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⢛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⡇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⣿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⣿⣆⠀⠀⠀⢀⣰⣾⣿⣿⣿⡆⠀⠀⠀⠀⢰⣟⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣶⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀

⠀⠠⠠⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣄⣀⣀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠄⠀

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⠶⠶⠶⠒⣲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠍⠀⠀⠀⠈⠉⠉⠐⠶⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠛⠙⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⠋⠙⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣶⣶⡒⠲⠤⠤⠤⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣿⠷⢿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀

⠄⠠⠒⠒⠚⠛⡛⠋⢹⣟⠁⠀⣻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣿⣿⣿⣿⣿⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⢀⠠⠤⣶⣾⣿⣿⣿⣿⣿⡿⠋⡌⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⠶⣆⡹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠉⠀⠀

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

⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣍⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿

⠻⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣹⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢰⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⡇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡌⠁⣿⣿⢰⣶⡏⢿⣿⣿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⣿⣆⠀⠀⠀⢀⣰⣾⣿⣿⣿⡄⠀⠀⠀⠀⢰⣞⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣶⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀

⠀⠄⠠⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣀⣀⣀⠀⠀⠀⠠⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠴⠶⠶⠖⣲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠀⠀⠀⠈⠉⠉⠒⠶⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠂⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠋⠉⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣶⣶⡒⠦⠤⠤⠤⢤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⣿⡷⢶⣿⣿⣿⣿⣿⡿⠟⠉⠉⠛⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀

⠄⠠⠒⠒⠚⠛⠛⠋⢽⡿⠁⠁⣿⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣿⣿⣿⡿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⢀⠠⠤⣶⣾⣿⣿⣿⣿⣿⡿⠋⡀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀

⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⣆⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠿⠛⠀⠀

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

⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿

⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠟⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠁

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⣿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠠⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⢿⣿⣄⠀⠀⠀⢀⣲⣿⣿⣿⣿⡄⠀⠀⠀⠀⢰⣾⣧⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣠⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣁⣀⣀⣀⠀⠀⠠⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠴⠶⠶⠖⣲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠀⠀⠀⠈⠉⠉⠒⠶⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠋⠉⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣶⣶⡒⠦⠤⠤⠤⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣾⡶⢾⣿⣿⣿⣿⣿⡿⠏⠉⠈⠛⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀

⠤⠠⠔⠒⠚⠛⠛⠋⢹⡏⠁⠁⣲⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⡿⣋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⢀⠠⠤⣶⣶⣿⣿⣿⣿⣿⡿⠋⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣆⡹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠁⠀⠀

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

⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⢛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣬⠻⣿

⠻⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢰⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣷⡄⠀⠀⠀⢐⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣲⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀

⠀⠀⠀⢄⣤⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣀⣀⣀⣀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠶⠶⠖⣲⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⠉⠀⠀⠀⠈⠉⠉⠒⠶⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠂⠘⠛⠋⠙⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠙⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⣶⣶⡒⠦⠤⠤⢤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣦⣶⡶⢶⣿⣿⣿⣿⣿⡿⠟⠉⠙⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀

⠀⠠⠰⠒⠚⠛⠛⠋⠻⠏⠉⠀⣩⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⣿⣿⣿⣿⣏⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃

⠀⠀⠀⠀⠀⠤⣶⣶⣿⣿⣿⣿⣿⡿⠋⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣆⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠉⠀⠀

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

⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣽⣶⣶⣭⠛⣽⣶⣶⣬⠻⣿

⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⢃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣧⡀⠀⠀⠀⢐⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣰⣲⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣤⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀

⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣀⣀⣀⠀⠄⠀⠄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠶⠶⠖⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠋⠀⠀⠀⠈⠉⠉⠒⠶⣤⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠐⠚⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠙⠛⠋⠋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⣶⣶⡒⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣴⣷⡾⢿⣿⣿⣿⣿⣿⡿⠟⠉⠛⠛⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀

⠀⠤⠔⠒⠒⠛⠟⠛⢻⡛⠉⠁⣵⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣿⣿⣿⣿⣏⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⢀⠠⠤⣶⣶⣿⣿⣿⣿⣿⡿⠋⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀

⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⣖⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠋⠁⠀

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

⣿⡿⢰⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⢛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣵⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿

⠻⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣾⣄⠀⠀⠀⠀⢺⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣔⣲⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣦⣠⣴⣾⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀⣠⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀

⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠒⠒⠂⠂⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣀⣀⣀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠄⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠃⠀⠀⠀⠉⠉⠉⠒⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠘⠋⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣶⣶⡤⠤⠤⠤⢤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⡶⢶⣾⣿⣿⣿⣿⡿⠛⠉⠉⠛⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀

⠠⠤⠔⠒⠚⠛⠛⠛⢻⡋⠉⠉⣬⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣀⣠⣿⣿⣿⡿⣋⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠤⣴⣶⣿⣿⣿⣿⣿⡿⠋⠩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀

⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⣆⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠓⠀⠀

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

⣿⡿⢱⣶⡆⢰⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣵⣶⣶⣭⠛⣽⣶⣶⣬⠻⣿

⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣹⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡎⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣯⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣔⢶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣄⡀⢀⣤⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀

⠀⠀⠀⣀⣀⣀⣠⣤⣄⣄⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⣀⣀⣀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠤⠶⠶⣲⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠋⠀⠀⠀⠉⠉⠉⠒⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠂⠚⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣶⣶⣖⡠⠤⠤⠤⢤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶⡶⣶⣶⣿⣿⣿⣿⡿⠟⠉⠙⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀

⠀⠤⠤⠖⠒⠛⠛⠛⢛⡉⠉⠠⣤⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣰⣿⣿⣿⣿⣏⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁

⠀⠀⠀⠀⠀⠤⣴⣶⣾⣿⣿⣿⣿⡿⠋⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣖⡹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠟⠁⠀⠀

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

⣿⡿⢱⣶⡆⢱⣶⣶⡏⠉⣷⣦⢰⣶⡆⣶⣶⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣬⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣵⣶⣶⣭⠛⣽⣶⣶⣬⠻⣿

⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣹⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡇⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠁⣿⣿⢰⣶⡏⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢻⣿⣦⣄⣀⣠⣴⣿⣿⣿⣿⣿⣿⣦⣄⠀⢀⣠⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠴⠶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⠋⠀⠀⠀⠉⠉⠉⠒⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠒⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣤⡤⠤⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣶⡶⢶⣶⣿⣿⣿⣿⣿⠟⠉⠙⠛⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀

⠀⠤⠤⠖⠲⠛⠛⠛⣿⠋⠉⠡⣦⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⣰⣿⣿⣿⣿⣋⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠤⣤⣶⣾⣿⣿⣿⣿⡿⠋⡈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣖⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠇⠀⠀

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

⣿⡿⢱⣶⡆⢰⣶⣶⡎⠉⣷⣦⢰⣶⡎⣷⣾⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣵⣶⣶⣭⠛⣽⣶⣶⣌⠻⣿

⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢰⡆⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⢃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⡟⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠀⣿⣿⢰⣶⡎⢿⣿⡿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣲⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⢿⣿⣤⡀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣠⣿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀

⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠤⠶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⠏⠀⠀⠀⠉⠉⠙⠒⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠻⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⣤⣴⡤⠤⠤⢤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣦⣶⢶⣶⣿⣿⣿⣿⡿⠟⠉⠹⠟⠛⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀

⠀⠤⠤⠶⠞⠟⠛⠛⢿⠍⠉⢻⣧⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣸⣿⣿⣿⡿⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅

⠀⠀⠀⠀⠀⠤⣴⣶⣾⣿⣿⣿⣿⡿⠋⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⣖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⢿⡅⠀⠀

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

⣿⡿⢱⣶⡆⢱⣶⣶⡎⠋⣷⣦⢰⣶⡎⣷⣾⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣴⣶⣶⣬⠛⣵⣶⣶⣌⠻⣿

⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢠⡆⣿⣿⠘⣛⣿⣷⣟⣉⡛⠛⢃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠙⠿⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠀⣿⣿⢰⣶⡎⢿⣿⡿⠿⠛⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⢽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣷⣶⣷⡀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⣠⣿⣶⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠒⠒⠒⠂⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠤⠴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠟⠃⠀⠀⠉⠉⠙⠒⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠒⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣶⣤⣤⡤⠤⠤⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣦⣴⣶⣶⣾⣿⣿⣿⡿⠟⠉⠙⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀

⠀⠠⠤⠴⠶⠟⠛⠛⣻⠉⠉⢉⣥⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣸⣿⣿⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠠⣤⣴⣶⣿⣿⣿⣿⡿⠉⠑⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀

⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⣆⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠋⠀⠀

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

⣿⡿⢱⣶⡎⢰⣶⣶⡎⠉⣷⣦⢰⣶⡎⣷⣾⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡄⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣴⣶⣶⣭⠛⣵⣶⣶⣌⠻⣿

⠿⡇⢸⣿⡇⣸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢰⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢠⡆⣿⣿⠘⢛⣿⣷⣟⣉⡛⠛⠃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠙⠟⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠀⣿⣿⢰⣶⡊⢿⣿⠿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢷⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⢿⣿⣦⡀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⣠⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣤⠤⠤⠤⠤⠤⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠋⠁⠀⠀⠉⠉⠓⠒⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠒⠒⠚⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣤⣤⡤⠤⠤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⠟⠋⠙⠛⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀

⡀⠠⠤⠴⠖⠿⠛⠛⡛⠉⠉⢉⣥⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅

⠀⠀⠀⠀⠀⢠⣤⣴⣶⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⡆⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⠿⠁⠀⠀

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

⣿⡿⢱⣶⡆⢱⣶⣶⡎⠋⣷⣦⢰⣶⡎⣷⣾⢱⣶⡏⢹⣶⣶⡏⢻⣶⣶⣶⣭⢱⣶⡌⣶⡾⢻⡟⣵⣶⣶⣍⢋⣵⣶⣶⣝⢫⣴⣶⣦⡙⣛⣩⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣶⣶⠈⣴⣶⣶⣬⠛⣵⣶⣶⣌⠻⣿

⠿⡇⢸⣿⡇⢸⣿⣿⣿⠀⣿⣿⣾⣿⡇⣿⣿⢸⣿⡇⣼⣿⣿⣷⢸⣿⣿⣽⣿⠀⣿⣷⣿⢇⣿⣾⠿⢇⣿⣿⢸⣿⡇⣿⣿⠸⠿⢠⣿⡇⠛⣿⣿⢈⣿⣿⣿⢟⣛⡛⠛⡛⢱⡿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠉

⠀⠀⢸⣿⡇⣿⣿⣸⣿⡄⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣹⣿⢸⣿⣿⢿⣷⠀⢸⣿⡟⣸⣿⣿⢃⣾⡿⠃⢸⣿⡇⣿⣿⠀⣠⣿⡟⢠⡆⣿⣿⠘⢛⣿⣷⣟⣉⣛⠛⢃⣿⣇⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀

⠀⢠⣼⣿⣇⣿⣿⢻⣿⡇⣿⡇⢿⣿⡇⢿⣿⣼⣿⢧⣿⡿⢻⣿⣿⣿⣿⢸⣿⠀⢸⣿⡇⠹⠟⢡⣿⣿⣥⣤⠸⣿⣧⣿⡟⢰⣿⣯⣤⡄⠀⣿⣿⢰⣶⡎⢿⣿⠿⠿⠟⠘⠛⠛⣿⣿⠋⢿⣧⣿⡿⠘⣿⣧⣿⡿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠻⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡆⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣇⠀⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⣦⡀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣠⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠒⠒⠒⠂⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣥⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⣀⣀⣀⣤⣠⣄⣀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⡛⠋⠀⠀⠈⠉⠉⠓⠲⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠒⠒⠚⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣶⣤⣤⡤⠤⢤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣤⡀⠀⠀⠀⠉⠉⠉⠉⠉⠑⠐⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣤⣤⣶⣶⣿⣿⣿⣿⣿⠟⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀

⠀⡀⠤⠴⠶⠿⠛⢻⠛⠋⠉⢹⣥⣶⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣼⣿⣿⣿⡿⢋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⢠⣤⣴⣶⣾⣿⣿⣿⡿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀

⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⡆⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠟⠁⠀

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

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

⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛

⠀⠈⠁⠈⠉⠛⠛⠛⠿⠿⠟⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠉⠈⠉⠛⠛⠿⠿⢿⢿⣿⠿⠿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣻⡀⠀⠀⠀⠀⢀⣴⣤⣿⣿⣷⠀⠀⠀⠀⠀⢠⠴⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣷⣤⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷⣤⣀⣀⣤⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠒⠂⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⣩⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠤⠤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠀⠉⠉⠓⠒⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠒⠒⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠉⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣤⣤⡤⠤⢄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣾⣿⣿⣿⡿⠛⠋⠛⠟⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠠⠤⠶⠾⠟⠛⠛⠉⠉⠉⣁⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀

⠀⠖⠲⣶⠏⢶⠄⠱⠶⢶⠖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⠃⠄⠀⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠻⠟⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⢿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⣛⠿⢿⣿⡿⠛⡛⠛⢿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⡏⣾⣿⢻⣿⣆⢰⣿⡿⢿⣷⡌⣴⣿⠿⣿⣧⣩⣴⣾⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣆⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⣛⡛⣰⣿⡿⣉⢹⣿⣿⢠⣬⡝⣿⣮⡉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠹⣿⠿⠿⠋

⠀⠈⠁⠉⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣱⣿⢸⣿⣿⠘⠛⢣⣿⣿⡇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠻⢁⣾⣿⣯⣤⡄⢸⣿⣇⣼⣿⠇⣼⣿⣯⣤⣭⠉⢸⣿⣿⢠⣤⡄⠙⠛⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣻⠀⠀⠀⠀⠀⢀⣴⣤⣿⣿⣷⠀⠀⠀⠀⠀⣠⠴⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣷⣤⣀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣤⣀⣀⣤⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠒⠒⠂⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠉⠁⠈⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠁⠈⠀⠀⣩⣥⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠈⠉⠉⠓⠒⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠉⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣶⣤⣤⡤⠤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠐⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣤⣤⣤⣶⣾⣿⣿⣿⣿⠟⠛⠛⠿⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀

⡀⠠⠤⠤⠶⠿⠟⠛⠛⠛⠉⢩⣥⣶⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃

⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡯⡋⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⣶⡖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⠛⠀⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠟⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⠿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⣛⠿⢿⣿⡿⠟⡛⠛⢿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⢿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⣉⢹⣿⣿⢠⣬⡝⣿⣮⡉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠹⣿⠿⠟⠋

⠀⠈⠁⠉⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣡⣿⢸⣿⣿⠈⠛⢣⣿⣿⡇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠛⢁⣾⣿⣯⣤⡄⢸⣿⣇⣾⣿⠇⣼⣿⣯⣤⣭⠉⢸⣿⣿⢠⣤⡆⠙⠛⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠉⠀⢉⣉⣉⠉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠸⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣇⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⡀⠀⠀⠀⠀⢠⣚⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣴⣾⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠐⠒⠒⠒⠒⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠈⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣩⣭⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⢀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠛⠁⠀⠈⠉⠙⠓⠂⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠒⠒⠶⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠟⠉⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣤⣤⡤⢄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣤⡀⠀⠈⠉⠉⠉⠉⠉⠛⠐⠒⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⣾⣿⣿⣿⡿⠟⠛⠻⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀

⢀⣀⣤⡤⠶⠶⠾⠟⠛⠛⠋⢉⣍⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣿⣿⣿⡟⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁

⠀⠖⠲⣶⠏⢶⠄⠱⠶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⡿⡿⠍⠀⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠟⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⠿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠟⣛⠿⢿⣿⡿⠟⡛⠛⢿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⡛⣰⣿⡿⣉⢹⣿⣿⢠⣤⡝⣿⣮⡉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠹⣿⠿⠟⠋

⠀⠈⠁⠈⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣱⣿⢸⣿⣿⠈⠛⢣⣿⣿⠇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠛⢁⣾⣿⣯⣤⡄⢸⣿⣇⣼⣿⠇⣼⣿⣯⣤⣭⠉⢸⣿⣿⢠⣤⡆⠙⠛⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠁⠀⠉⣉⣉⡉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡿⣧⠀⠀⠀⠀⠀⠀⠿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⢿⣷⡀⠀⠀⠀⢀⣀⣀⣿⣿⣿⡀⠀⠀⠀⠀⣴⣌⣧⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣤⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠒⠒⠒⠒⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣁⣬⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠈⠉⠙⠒⠢⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠲⠲⠶⠒⠒⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠟⠿⠟⠛⠉⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣶⣤⡀⠀⠈⠉⠉⠉⠉⠉⠒⠒⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣴⣿⣿⣿⣿⡿⠟⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⢀⣤⡤⢶⠶⠾⠿⠛⠛⠛⢩⣭⣷⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠅

⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⠟⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣯⠏⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡿⠿⠋⠁⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⠿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⣛⠿⢿⣿⡿⠟⡛⠛⢿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⣉⢹⣿⣿⢠⣤⡝⣿⣯⡉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠹⣿⡿⠟⠋

⠀⠈⠁⠉⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣡⣿⢸⣿⣿⠈⠛⢣⣿⣿⠇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠛⢁⣾⣿⣯⣤⡄⢸⣿⣇⣼⣿⠇⣼⣿⣯⣤⣭⠉⢸⣿⣿⢠⣤⡄⠙⠛⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡻⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⢿⣿⡄⠀⠀⠀⢀⣀⡀⣼⣿⣿⡄⠀⠀⠀⠀⢴⣭⣧⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠒⠒⠒⠂⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⣩⣬⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠈⠉⠙⠒⠢⢤⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠖⠖⠒⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠛⠿⠻⠟⠉⠙⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠀⠉⠉⠉⠉⠉⠉⠐⠒⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⣤⣤⣴⣾⣿⣿⣿⡿⠟⠛⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⠠⠤⠶⠶⠾⠿⠛⠛⠛⣯⣅⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⠟⠋⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠟⠀⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢿⡿⠿⣿⡿⠿⣻⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⣛⠿⢿⣿⡿⠟⡛⠛⠿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⡏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠸⣿⣿⣿⢯⣥⣾⣿⠁⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣆⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⣉⢹⣿⣿⢠⣬⡝⣿⣯⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠸⣿⠿⠟⠋

⠀⠈⠁⠉⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣱⣿⢸⣿⣿⠈⠛⠃⣿⣿⠇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠛⢁⣾⣿⣯⣤⡄⢸⣿⣇⣾⣿⠇⣼⣿⣯⣤⣬⠉⢸⣿⣿⢠⣤⡄⠉⠋⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠁⠀⠉⢉⣉⣉⡉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣔⣄⠀⠀⠀⠀⠀⠀⢰⣟⡻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣽⡄⠀⠀⠀⠀⠀⠚⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠛⣿⣷⡀⠀⠀⢀⡀⠀⠀⣿⣿⡇⢀⠀⠀⠀⣴⣛⣿⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣦⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠄⠀⠐⠒⠒⠒⠒⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⢀⣠⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠁⠀⠈⠉⠙⠒⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠴⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠏⠉⠛⠛⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣦⣤⣤⢤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣶⣤⡀⠀⠈⠉⠉⠉⠙⠓⠒⠒⠒⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣾⣿⣿⣿⡿⠟⠛⠻⠟⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣠⣤⣴⠶⠶⠿⠟⠛⠋⢋⣉⣽⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢐⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⠟⠉⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠿⡉⠀⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢟⡿⠿⣿⡿⠿⣛⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⣛⠿⢿⣿⡿⠟⡛⠛⠿⣿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⢿⣷⡌⣴⣿⠿⣿⣧⣩⣴⣾⣿⠸⣿⣿⣿⢯⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⣿⣿⣿⣿⣿

⠿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⣉⢹⣿⣿⢠⣤⡝⣿⣯⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡗⠸⣿⠿⠟⠋

⠀⠈⠁⠈⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢏⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣱⣿⢸⣿⣿⠘⠛⠃⣿⣿⠇⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠙⢁⣾⣿⣯⣤⡄⢸⣿⣇⣾⣿⠇⣼⣿⣯⣤⣬⠁⢸⣿⣿⢠⣤⡄⠉⠋⠀⣿⣿⠀⢿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠛⠛⠁⠀⠉⢉⣉⣉⡉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⡤⠀⠀⠀⠀⠀⠀⣰⣟⠒⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠻⣿⣦⡀⠀⠀⣀⣀⣂⣸⣿⣿⡇⣀⡄⠀⠀⢰⣎⣿⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠀⠀⠀⠒⠒⠒⠒⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣤⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠈⠉⠙⠒⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠴⠶⠶⠶⠶⠾⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠛⠻⠛⠋⠈⠙⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣤⡀⠀⠉⠉⠉⠉⠙⠓⠒⠒⠒⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣾⣿⣿⣿⡿⠟⠛⠻⠟⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣀⣀⣤⣴⠶⠶⠿⠟⠛⠋⠋⢉⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⠟⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀

⠀⠖⠶⣶⠏⢶⠄⠱⠶⢶⠆⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠇⠀⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢟⡛⠿⣿⡿⠿⣛⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠟⣛⠿⢿⣿⡿⠟⡛⠛⠻⡿⠿⢿⡻⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣾⣿⠘⣿⣿⣿⢯⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣆⢠⣾⣿⢻⣿⡎⢿⣿⣿⣿⣿

⠻⣿⣿⣿⣷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡝⣿⣯⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠸⠿⠟⠛⠉

⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠛⣴⣿⡿⣡⣿⢸⣿⣿⠈⠛⠃⣿⣿⠆⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠙⢁⣾⣿⣯⣤⡄⢸⣿⣧⣾⣿⠇⣼⣿⣿⣤⣬⠁⢸⣿⣿⢠⣤⡄⠈⠉⠀⣿⣿⠀⢿⣿⣤⣿⡿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⣀⠉⠛⠛⠉⠀⠉⣉⣉⣉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣰⣛⣳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⣽⣾⣿⣿⠀⢠⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡾⢛⠀⠀⠀⣤⣾⣿⣿⣿⣷⣾⣿⣄⡀⢠⣶⣻⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠁⠘⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⡀⠀⣀⣀⣀⡀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠄⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⠁⠈⠉⠛⠒⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠒⠒⠒⠒⠒⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠛⠛⠟⠋⠈⠙⠛⠿⠿⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣦⣀⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣶⣄⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣾⣿⣿⣿⡿⠟⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠠⠴⠖⠒⠛⠋⠉⢉⣴⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⢶⣶⠖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⡿⠿⠁⠀⠀⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢟⡛⠿⣿⡿⠟⣛⠿⢿⣿⣿⠿⠟⢿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠟⣛⠿⢿⣿⡿⠟⡛⠛⠻⠿⠿⢿⡛⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣴⣿⠿⣿⣧⣩⣴⣿⣿⠈⣿⣿⣿⢯⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⢿⣿⣿⣿⣿

⠛⣿⡿⣿⡷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡝⣿⣮⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠘⠟⠛⠋⠁

⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠊⣴⣿⡿⣡⣿⢸⣿⣿⠈⠛⠃⣿⣿⠆⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠙⢁⣾⣿⣯⣤⡄⢸⣿⣧⣾⣿⠇⣼⣿⣿⣤⣬⠁⢸⣿⣿⢠⣤⡄⠈⠁⠀⣿⣿⠀⣿⣿⣤⣿⡿⠈⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠙⠛⠉⠀⠈⠉⢁⡈⠉⡉⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⣀⠉⠛⠛⠉⠀⠉⣉⣉⣉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⠻⣿⡟⡯⠈⠁⠀⣒⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣰⣛⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡐⠠⠀⠀⠀⢺⣿⣿⣿⣿⣿⡿⣿⣿⡧⠀⠀⠀⣽⣾⣿⣿⢠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣷⡿⣿⢡⡀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣄⢠⣶⣻⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠻⠝⠚⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠏⠁⠈⠉⠓⠒⠠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⠋⠉⠙⠛⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⠿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⠿⠻⠿⠟⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠠⠀⠒⠒⠚⠉⠉⢁⣴⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⠟⠋⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⢶⣶⡖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠿⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢛⡛⠿⣿⡿⠟⣛⠿⢿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠟⣛⠻⢿⣿⡿⠟⡛⠉⠀⠿⠻⢿⡛⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⣿⣿⣿⢫⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⢻⣿⣿⣿⣿

⠛⣿⡿⣿⡷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⣛⠛⣼⣿⡏⢸⣿⡇⢸⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡌⣿⣮⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠘⠛⠋⠉⠀

⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⢸⣿⡇⠊⣴⣿⡿⣡⣿⢸⣿⣿⠘⠛⠃⣾⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠙⢁⣾⣿⣯⣤⡄⢸⣿⣧⣾⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣤⡆⠀⠀⠀⣿⣿⠀⣿⣿⣤⣿⡿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠙⠛⠋⣀⣈⠉⣁⣈⣉⣉⣈⣉⠉⠉⢁⣤⣈⣉⣉⣉⣉⣁⣀⡉⠛⠛⠉⢀⣩⣉⣉⣉⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠝⠊⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣾⢻⡻⣿⣿⠄⣶⡤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⣟⢿⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣀⣽⣿⣿⣿⣿⣾⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⠋⡈⠫⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⢖⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠉⠙⠓⠒⠠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠐⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠛⠿⠿⠿⠿⠿⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⠿⠿⠿⠟⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⠋⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⢶⣶⡖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡇⠁⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠿⢛⡛⠿⣿⡿⠟⣛⠿⢿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠟⣛⠻⢿⣿⡿⠟⡋⠁⠀⠘⠛⢿⡛⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⣿⣿⣿⢫⣥⣾⣿⠃⣾⣿⠿⣿⣦⠉⣾⣿⢻⣿⣦⢠⣾⣿⢻⣿⡎⢻⣿⣿⣿⡿

⠛⣿⡿⣿⡧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⣿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣾⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡌⢿⣮⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠘⠛⠉⠁⠀

⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠈⣴⣿⡿⣡⣿⢸⣿⣿⠘⠛⠃⢾⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠹⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣤⡆⠀⠀⠀⣿⣿⡀⣿⣿⣤⣿⡿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠉⠉⠁⢀⠈⠙⠛⠋⣀⣈⣉⣁⣈⣉⣉⣈⣉⡉⣉⣁⣴⣈⣉⣉⣉⣉⣁⣄⣉⠛⠛⢉⣀⣍⣉⣉⢉⠉⢠⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠻⠻⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠎⣿⢿⣿⣿⣿⣷⣿⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢘⢏⣟⡛⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡍⠈⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⠿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⠀⠉⠙⠓⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠙⠻⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠿⡿⠿⢿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿⢋⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠽⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⢶⣶⡖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠟⢛⡛⠿⣿⡿⠟⣛⠻⢿⣿⡿⠿⠛⠳⣤⣼⣿⣿⣿⠿⠿⢿⡿⠟⣛⠻⢿⣿⡿⠟⡁⠀⠀⠀⠘⢛⡛⠿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡈⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢱⣿⡿⣿⣷⡌⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⢿⣿⣿⢫⣥⣾⣿⠇⣾⣿⠿⣿⣧⠉⣾⣿⢿⣿⣦⢠⣾⣿⢻⣿⡎⢻⣿⣿⣿⠿

⠙⣿⡿⣿⡧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣿⣿⡇⢛⠛⣰⣿⡿⢉⢹⣿⣿⢠⣤⡌⢿⣮⠉⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠘⠛⠉⠀⠀

⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠈⣴⣿⡿⢡⣾⢸⣿⣿⠘⠛⠃⢸⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⠹⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡀⣿⣿⣤⣿⡿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠉⠉⠁⣀⣈⠙⠛⢋⣠⣌⣉⣁⣈⣉⣉⣈⣉⣉⣉⣁⣴⣌⣉⣉⣉⣉⣁⣤⣉⠛⠛⢉⣠⣍⣉⣉⣉⠉⣠⡈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣗⠄⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢫⢛⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⢉⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠈⠩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠹⠛⠿⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠉⠚⠒⠲⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠛⠿⢿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⢛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿⡛⠴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⣖⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡄⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠟⠛⠻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠟⢛⡛⠿⣿⡿⠟⣛⠻⢿⣿⡿⠟⠃⠀⢀⣠⣾⣿⣿⠿⠻⢿⡿⠟⣛⠻⢿⣿⡿⠟⡀⠀⠀⠀⠀⢛⡛⠻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡘⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⣿⣷⡄⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⠻⣿⣿⢫⣥⣾⣿⡇⣾⣿⢿⣿⣧⠉⣾⣿⢿⣿⣦⢠⣾⣿⢿⣿⡎⢹⣿⣿⣿⠟

⠙⣿⡿⣿⡧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣾⣿⡇⢛⠛⣰⣿⡿⠉⢹⣿⣿⢠⣤⡌⢿⣮⠉⣿⣿⠁⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠈⠋⠁⠀⠀

⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣷⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠀⣴⣿⡿⢡⣾⢸⣿⣿⠘⠛⠃⢸⣿⠀⣿⣿⠀⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⢻⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡆⣿⣿⣼⣿⣿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠉⠉⢁⣤⣈⡙⠛⣋⣠⣌⣉⣁⣌⣉⣉⣈⣉⣉⣉⣡⣾⣌⣉⣉⣉⣉⣁⣤⣉⠛⠛⢉⣤⣍⣉⣉⣉⢉⣠⠌⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠋⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠿⡛⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠘⠉⠟⢯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠣⠒⡊⡟⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠁⢁⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠉⠛⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠻⠿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⡿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⡖⠹⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡄⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠟⢛⡛⠿⣿⡿⠟⣛⠛⢿⣿⡿⠟⠃⠀⠀⢠⣼⣿⣿⠿⠻⢿⡿⠟⣛⠻⢿⣿⡿⠛⡀⠀⠀⠀⠀⢛⡛⠻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡸⣿⣿⢸⣿⣿⣿⣏⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⣿⣷⡄⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⠀⣿⣿⢫⣥⣾⣿⡇⣾⣿⢿⣿⣦⢉⣾⣿⢿⣿⣦⢠⣾⣿⢿⣿⡎⢹⣿⣿⣿⠟

⠉⣿⡟⣿⠧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣿⣿⡇⠛⠛⣰⣿⡿⠉⢹⣿⣿⢠⣤⡌⢿⣮⠉⣿⣿⠀⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠈⠋⠁⠀⠀

⠀⠈⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢇⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠀⣴⣿⡿⢡⣾⢸⣿⣿⠘⠛⠃⠸⣿⠀⣿⣿⠆⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⢻⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡆⣿⣿⣼⣿⣿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠉⠉⢁⣤⣈⡙⠛⣋⣠⣌⣉⣁⣌⣉⣉⣈⣉⣉⣉⣡⣾⣌⣉⣉⣉⣉⣡⣤⣉⠛⠛⣉⣤⣍⣉⣉⣉⢉⣠⠈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠉⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠨⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠟⠻⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢙⠿⠻⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠙⠛⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠻⠿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠛⠋⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⡖⠙⠋⠀⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡆⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠿⠛⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⢛⡛⠻⢿⣿⠟⢛⡛⠿⣿⡿⠛⣛⠛⢿⣿⡿⠟⠃⠀⠀⠀⣤⣿⣿⠿⠛⢿⠿⠛⣛⠻⢿⣿⡿⠛⡀⠀⠀⠀⠀⢘⡛⠛⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡘⣿⣿⢸⣿⣿⣿⣇⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⣿⣷⡄⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⠀⠐⣿⢫⣤⣾⣿⡇⣾⣿⢿⣿⣧⢁⣾⣿⢿⣿⣦⢠⣾⣿⢿⣿⡎⢹⣿⣿⣿⠟

⠙⣿⡿⠿⡧⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣠⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣿⣿⡇⠛⠛⣰⣿⡿⠉⢹⣿⣿⢠⣤⡄⢻⣎⠉⣿⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣷⠈⠉⠁⠀⠀

⠀⠈⠁⠀⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢃⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠀⣴⣿⡿⢡⠶⢸⣿⣿⠘⠛⠃⠸⡿⠀⣿⣿⡁⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⢿⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡇⣿⣿⣼⣿⣿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠉⢉⣁⣤⣌⣙⢛⣋⣤⣬⣉⣡⣌⣉⣉⣈⣉⣉⣉⣡⣾⣮⣉⣉⣉⣉⣡⣤⣉⡛⠛⣉⣴⣍⣉⣉⣉⢉⣤⡈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠋⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠨⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠩⠂⠓⠐⠋⠊⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠽⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠐⠒⠲⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⢿⣿⣿⣿⣿⡿⠟⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠟⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⣖⠙⠃⠘⠉⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠿⠟⠿⠿⠛⠛⠿⠛⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛⡛⠻⢿⣿⠟⢛⡛⠻⣿⡿⠛⣛⠛⢿⣿⡿⠛⠁⠀⠀⠀⣠⣿⣿⠟⠛⢿⠿⠛⣛⠻⢿⣿⠟⠛⡀⠀⠀⠀⠀⢘⡛⠛⢿⣿⣿⣿⣿⣿

⣿⡿⢿⣿⣷⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡘⣿⣿⢸⣿⣿⣿⣇⣿⠏⣾⣿⢻⣿⣆⢰⣿⡿⣿⣷⡄⣼⣿⠿⣿⣧⣩⣴⣿⣿⠀⠀⠀⡛⢫⣤⣾⣿⡇⣾⣿⢿⣿⣧⢀⣾⣿⢿⣿⣦⢠⣾⣿⢿⣿⡎⢉⣿⣿⡿⠟

⠉⣿⡿⠿⡦⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣧⣿⣿⢸⣿⣿⣤⡿⣿⣾⡛⠛⣼⣿⡏⢸⣿⡇⣿⣿⡇⠛⠛⣰⣿⡿⠉⢹⣿⣿⢠⣤⡄⠻⣎⠉⣿⣿⡇⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠉⠀⠀⠀

⠀⠈⠁⢐⠇⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⡿⣿⣿⣿⢸⣿⣿⠛⣳⣿⣿⢃⣼⣿⠟⠀⢸⣿⡇⣿⣿⡇⠀⣴⣿⡿⠡⠶⢸⣿⣿⠘⠛⠃⠸⠿⠀⣿⣿⡁⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⣼⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿⡇⢻⣿⣿⢸⣿⣿⣤⡌⢻⢁⣾⣿⣯⣤⡄⢸⣿⣧⣿⣿⠇⣼⣿⣿⣤⣤⠀⢸⣿⣿⢠⣶⡆⠀⠀⠀⣿⣿⡇⣿⣿⣼⣿⣿⠘⣿⣿⣸⣿⡿⠸⣿⣿⣸⣿⡏⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠉⠉⣁⣤⣌⣙⢛⣋⣤⣬⣉⣡⣌⣉⣉⣌⣉⣉⣉⣡⣿⣮⣉⣉⣉⣉⣡⣤⣉⡛⢛⣉⣤⣍⣉⣉⣉⢉⣤⡈⠉⠉⠈⠉⠁⠀⠀⠀⠉⠉⠁⠈⠙⠛⠋⠁⠀⠈⠙⠛⠋⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣷⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠍⠛⠉⠫⠿⡺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠌⠿⢷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⠐⠒⠲⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠿⠿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣯⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⣶⣶⣖⠹⠋⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣦⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿

⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢰⣿⠾⢿⣋⣿⡿⠿⠟

⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡀⠀⠀⠀⠈⣷⡶⠿⠋⠉⠁⠀⠀

⠀⠈⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠻⠟⠛⠟⠛⠛⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡝⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢚⡿⠿⠿⡻⡟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠠⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠓⠲⠶⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⢿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠬⠛⣛⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⡿⠟⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣧⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠖⢰⣶⣶⣶⠹⢿⣿⡿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀

⣿⣿⡿⠛⠻⠿⠿⡿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠟⠛⠻⣿⠛⠛⠁⠀⠀⠀⠀⠸⢿⡿⠛⢿⣿⣿⣿⣿⠎⠷⠆⠰⠄⠀⠀⠀⠀⠰⠿⠟⠛⠉⠻⣿⣿⣿

⣽⡿⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⣿⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡎⠛⢰⣿⢿⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠿⢿⢩⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠿⠟

⠙⣥⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⣹⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢾⡎⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⡷⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠈⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣯⣀⢻⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠘⢁⣾⣿⣁⡸⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠸⠟⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀

⠀⠀⠀⠛⠛⠛⢋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣙⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣋⡛⣃⣤⣜⡛⠛⠛⢃⠙⠛⠛⠁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⠀⠐⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠓⢛⢟⣛⠿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠈⠈⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣋⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠓⠲⠶⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠬⠛⠛⠶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⡿⡟⠋⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠟⢷⠖⢰⣶⣶⣶⠹⢟⣿⡿⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀

⣿⣿⡿⠛⠻⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠛⠟⠙⠛⠀⠀⠀⠀⠀⠘⢻⡭⠙⢥⣭⣵⣬⣤⠄⠰⠄⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠁⠰⢿⠟⠛

⣽⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢻⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠻⠟⢡⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠸⠏

⠉⣥⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢺⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⡀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠈⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣯⣀⢺⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡇⣿⡇⠘⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠘⠟⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀

⠀⠀⠀⠛⠛⠛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣙⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣋⡛⢃⣤⣘⣛⠛⠛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠒⠲⠶⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⣻⣷⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠟⠙⠛⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣯⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠿⢶⠄⢰⣶⣶⣶⠹⢛⠛⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀

⣿⣿⡿⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠛⠟⠙⠛⠀⠀⠀⠀⠀⠈⠙⠭⠉⢠⣬⣤⣤⡤⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉⠁⠐⠿⠂⠋

⣥⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢹⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠙⠟⢡⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠰⠋

⠉⣥⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢸⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠈⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣧⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠘⠟⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀

⠀⠀⠀⠛⠛⠛⢋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⡛⣃⢛⣃⣤⣘⣛⡛⠛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⢹⢿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠁⠀⠘⠙⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣄⣤⣂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠻⢛⣛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⠒⠲⠶⠤⣄⣀⣿⣿⣿⣯⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠛⠿⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠯⠛⠛⠉⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠕⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠟⢶⠄⢰⣶⣶⣶⠹⢋⠛⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀

⣿⣿⡿⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠛⠏⠈⠉⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⣀⣠⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠉⠀⠀⠶⠀⠈

⣴⡷⠀⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣆⢰⣿⢻⣷⣤⣴⣿⡇⠈⠉⢡⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀

⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢰⡌⢉⣼⡿⢣⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠈⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣧⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠘⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠐⠛⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀

⠀⠀⠀⠛⠛⠛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣃⡛⣃⣤⣘⣛⣛⠛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠚⠛⠉⠩⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠒⠶⠶⠤⣄⣀⣿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠟⢶⠄⢰⣶⣶⣖⠙⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀

⡿⣿⡿⠛⠛⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠟⠿⠿⢿⣿⡿⠟⠋⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀

⣤⡷⠀⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠋⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀

⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢰⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠋⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣧⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠘⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠃⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀

⠀⠀⠀⠛⠛⠛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣃⣛⣃⣤⣘⣛⣛⡛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠟⠿⠿⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠶⠶⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠘⠟⠳⢶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡅⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠿⢶⠄⢰⣶⣶⡶⠙⠙⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀

⣼⣿⡿⠛⠛⠿⠿⡿⠿⠿⠿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀

⣤⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠋⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀

⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠉⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣯⣀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀

⠀⢠⡀⠛⠛⢛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣤⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣃⣛⣃⣤⣘⣛⣛⣛⡃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

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

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠂⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⠶⠶⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠩⠟⠳⢶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠟⠛⠋⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠣⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠔⢰⣶⣶⣶⠹⠋⠛⠟⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀

⢽⣿⡿⠛⠛⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⡿⠀⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀

⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀

⢈⡯⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣯⣀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢸⣿⢸⣿⠇⠀⠀

⠀⣿⣀⠛⠛⢛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣤⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣃⣴⣘⣛⣛⡛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⠉⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⣠⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠶⠶⢦⣤⣄⣀⣿⡾⣿⣿⣽⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠉⢿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠻⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠓⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠿⢶⠆⢰⣶⣶⣶⠹⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀

⣿⣿⡿⠛⠛⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣵⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀

⠉⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠈⡟⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣷⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢻⣿⢸⣿⠇⠀⠀

⠀⣳⣀⠛⠛⢛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣤⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣓⣛⣃⣶⣘⣛⣛⢛⠃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠉⠉⠋⠉⠉⠯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠶⠶⢦⣤⣄⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠁⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠿⠛⠍⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠛⣛⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠿⢶⠆⢰⣶⣶⣶⠹⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀

⣿⣿⠿⠛⠻⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣴⡷⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠛⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀

⢙⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢳⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠘⣏⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣧⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡘⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢻⣿⢸⣿⠇⠀⠀

⠀⣷⣀⠛⠛⢛⣋⣘⣛⣛⣛⣌⣛⣛⣋⣤⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣃⣛⣃⣶⣘⣛⣛⠛⢃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠚⠛⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠦⢤⣤⣀⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢉⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠿⠋⠉⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⣝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠟⢶⠄⢰⣶⣶⣶⠙⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣦⠀⠀⠀⠀⠀⠀

⣼⣿⡿⠛⠛⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢔⡿⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⡿⠿⢹⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠙⢰⣿⢻⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀

⢘⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣷⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣷⣿⡃⢴⡌⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠈⣟⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⢸⣿⢿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⡏⣿⡇⠸⢁⣾⣿⣁⡸⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀

⠀⢻⡀⠛⠛⢛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣋⣛⣃⣶⣘⣛⡛⠛⢃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠊⠙⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠦⢤⣤⣀⣀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠫⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢻⣿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠟⢷⠖⣰⣶⣶⣶⠙⠋⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀

⣻⣿⠿⠛⠻⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢹⡿⠆⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⣿⠿⢹⣿⣷⣼⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⡿⣿⡆⠙⢰⣿⢿⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀

⢈⣷⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢰⡌⢉⣼⡿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⣟⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣏⣿⡇⠸⢁⣾⣿⣁⡸⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢻⣿⢸⣿⠇⠀⠀

⠀⢻⣀⠛⠛⠛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣃⣴⣼⣛⡛⡛⢃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣅⣄⣐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠻⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢘⢽⡻⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢶⣾⣧⣼⣧⣢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠹⠿⣿⠿⣿⣿⠷⢦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠋⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠻⠛⠿⠻⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡝⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⣰⣶⣾⣶⠹⡻⣿⢿⠿⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀

⠸⣿⠿⠛⠛⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⡿⠂⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡀⣿⣿⠿⢸⣿⣷⣸⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⣿⣿⡆⠉⢰⣿⢿⣷⡄⣾⡟⣿⣦⢰⣿⢻⣷⣤⣴⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⢰⣿⢻⣷⡀⠀⠀

⠀⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢰⡌⢉⣼⣿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠟⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠸⢁⣾⣿⣁⡸⣿⡇⣿⣿⢠⣿⣟⣀⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢻⣿⢸⣿⠇⠀⠀

⠀⢠⣀⠛⠛⢛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣘⣛⣘⣋⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣃⣶⣜⡛⡛⠛⣃⠙⠛⠛⠁⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠘⠛⡛⡿⠻⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣽⠝⣍⢆⡄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣶⣾⣷⣿⣿⣁⣿⠇⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⠿⠿⠻⡟⠿⠷⣦⣤⣤⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠠⠁⠐⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠿⠛⠿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⣰⣶⣾⣶⠹⢿⣿⡿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀

⠼⣿⡿⠛⠛⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢴⡿⠆⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢻⣷⡈⣿⣿⠿⣿⣿⣷⣼⣿⣿⢸⣿⣿⣷⡄⣿⣿⠿⢸⣿⣿⣿⡆⠉⢰⣿⢿⣿⣄⣾⡟⣿⣦⣰⣿⢻⣷⣤⣶⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀

⠚⣶⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⣴⡌⢉⣼⣿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠘⣛⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠸⢁⣾⣿⣁⡸⣿⣇⣿⣿⢠⣿⣟⣁⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⠇⠀⠀

⠀⣶⡀⠛⠛⢛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣙⣛⣘⣛⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣃⣾⣞⣛⣛⡛⣃⡙⠛⠛⣁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠛⢛⡻⣻⡻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠁⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠄⠀⠉⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡛⠭⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⡿⣿⠟⣻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢭⠛⠛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠟⠛⠿⢿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⡷⠆⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢿⣷⡀⣿⣿⠿⣿⣿⣷⣼⣿⣿⢸⣿⣿⣿⡄⣿⣿⠿⢸⣿⣿⣿⡆⠈⢰⣿⢿⣿⣄⣾⡟⣿⣦⣰⣿⢻⣷⣤⣶⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡀⠀⠀

⠀⣶⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢰⡌⢉⣼⣿⢻⣿⡇⣿⣿⠈⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠛⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠸⢁⣾⣿⣁⡸⣿⣇⣿⣿⢠⣿⣟⣁⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⡇⠀⠀

⠀⢠⣀⠛⠛⣛⣋⣘⣛⣛⣛⣈⣛⣛⣋⣄⣛⣛⣛⣛⣛⣘⣛⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣣⣶⣜⣛⣛⢛⣃⠙⠛⠛⢁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠁⠒⠹⠚⡫⠈⠉⠟⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠆⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠂⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠐⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠉⠀⠛⠛⠙⠛⢋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠙⠛⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠛⠿⠿⠟⠛⠻⠿⣯⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡷⠆⣿⣿⣿⣷⢸⣿⡿⠇⣴⣿⢿⣷⡈⣿⣿⠿⣿⣿⣷⣼⣿⣿⢸⣿⣿⣿⡄⣿⣿⠿⢸⣿⣿⣿⡆⠁⢰⣿⢿⣿⣄⣾⡟⣿⣦⣰⣿⢻⣷⣤⣶⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡄⠀⠀

⠀⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢠⡈⢉⣼⣿⢻⣿⡇⣿⣿⠉⢉⣾⡿⠀⢸⣿⣷⣶⠀⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠋⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠸⢁⣾⣿⣁⡸⣿⣇⣿⣿⢠⣿⣟⣁⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⣸⣿⣿⣿⡇⣿⡿⢿⣿⢸⣿⡇⠀⠀

⠀⢰⣀⠛⠛⣛⣋⣘⣛⣛⣛⣈⣛⢛⣋⣔⣛⣛⣛⣛⣛⣘⣛⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣣⣾⣾⣛⣛⠛⣃⡙⠛⠛⠁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠫⠅⠐⠊⠛⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⡀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠰⠒⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⠶⠺⠳⠄⠀⠈⠻⠿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⠟⠛⠋⠉⠉⠉⠉⠉⠛⠻⠿⣿⠛⠉⠁⠚⠈⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠚⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠻⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠛⠻⠿⠛⠛⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠷⠆⣿⣿⣿⣷⢸⣿⡿⠇⣼⣿⢿⣷⡈⣿⣿⠿⣿⣿⣷⣼⣿⣿⢸⣿⣿⣿⡄⣿⣿⠿⢸⣿⣿⣿⡆⠀⢰⣿⢿⣿⣄⣾⡿⣿⣦⣰⣿⢻⣷⣤⣶⣿⡇⠀⠀⢠⣴⣾⡇⣿⣿⠿⠿⢠⣾⡟⣿⣆⣰⣿⢻⣷⡄⠀⠀

⠀⣤⠀⣿⣿⣿⣿⢸⣿⣷⡆⣿⣿⠘⠛⠃⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⣶⢸⣿⣿⣿⡃⢠⠈⢉⣼⣿⢻⣿⡇⣿⣿⠉⢉⣾⡿⠀⢸⣿⣷⣶⠂⠀⠈⣿⡇⠿⠿⢻⣿⣼⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠀

⠀⠋⠀⣿⣿⣿⣿⢸⣿⣇⣀⣿⣿⣸⣿⠇⣿⣿⣀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣀⢸⣿⣿⣿⡇⠈⢀⣾⣿⣁⡸⣿⣇⣿⣿⢠⣿⣟⣁⠀⢸⣿⣇⣀⠀⠀⠀⣿⡇⣿⣿⣸⣿⣿⣿⣇⣿⡿⢿⣿⢸⣿⡇⠀⠀

⠀⢳⣀⠛⠛⣛⣋⣜⣛⣛⣛⣈⡛⠛⣋⣀⣛⣛⣛⣛⣛⣘⣛⣛⣛⣘⣛⣛⣛⣁⣛⣛⣛⣘⣛⣛⣛⣣⣶⣾⣛⡛⠛⣃⡙⠛⠛⠁⠙⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠛⠃⠈⠛⠛⠋⠀⠙⠛⠛⠁⠈⠛⠛⠋⠀⠀⠀

⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣼⣧⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢩⣝⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡻⡿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⠿⠿⠿⠿⠋⠁⠀⠀⠀⠸⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣍⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⢝⡿⡿⡻⠛⠀⠝⠻⠻⣿⣿⣿⠿⠿⢛⠉⠈⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢰⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢄⠰⠙⠩⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⢉⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠙⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣼⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣴⣦⢉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡲⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡂⠙⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⠀⠀⠄⠹⠝⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⢪⣜⡯⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠍⡋⠇⠪⡥⣿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⣊⡥⠫⠯⠁⣩⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡝⢯⣿⢣⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣽⣹⣿⢿⣫⣻⡉⣛⢷⣶⡿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣻⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣻⡻⠀⠼⣿⢡⡰⣩⠿⠙⢫⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠰⠿⠷⣶⠿⢿⠶⡾⠾⠿⡿⠚⠻⠿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠳⢃⣘⠗⠑⠭⠂⠈⠰⠝⠽⣯⣿⠿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢷⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠷⢶⢠⣤⡄⢠⣤⣤⡌⢩⣤⡍⣭⣭⢩⣥⡌⣭⣬⠉⣥⣤⣤⠉⣥⣤⣤⣭⡡⣤⡄⣡⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀

⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀

⠀⠈⠁⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⣼⡦⢀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠿⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⢠⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⠁⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀

⠀⠀⠀⣉⣉⣬⣭⣭⣬⣭⣍⣉⣡⣉⣉⣤⣈⣉⣉⣁⣉⣉⣥⣭⣭⣭⣭⣭⣭⣥⣶⣭⣭⣾⣿⣮⣭⣭⣭⣽⣶⣬⣉⣉⣤⣈⢉⣉⣉⡁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⡱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣵⣿⣗⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠉⢯⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⡯⠓⠶⡳⢭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⠹⠉⡉⠛⢙⠁⠉⠀⠬⠒⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⢀⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠠⠀⠀⠀⠈⠙⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠹⣿⡟⢻⠉⠋⠛⠛⠻⣿⠿⠿⢟⠟⠋⠉⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡮⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠃⠻⢇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠽⢟⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⢶⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠈⣤⣤⣤⠉⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀

⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀

⠀⠈⠁⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⣀⠂⢀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠻⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⢀⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀

⠀⠀⠈⣉⣉⣬⣭⣭⣬⣍⣉⣉⠁⠉⠉⠀⡈⠉⠉⢁⣉⣉⣁⣉⣉⣍⣭⣭⣭⣥⣦⣭⣭⣴⣿⣮⣭⣭⣭⣽⣶⣬⣉⣩⣤⣉⢉⢉⣉⡁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⣂⠀⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣼⣿⣷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠿⠯⠽⠻⣻⣿⣿⠩⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠂⠀⠊⠩⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⢠⣴⣾⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⠎⠀⠀⠀⠀⠈⠙⠿⠿⠿⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣟⠵⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠿⠿⠿⠛⠟⠻⣿⡿⠟⠻⠟⠏⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠗⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠁⢋⢳⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠶⢶⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀

⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀

⠀⠈⠁⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⢀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠿⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀

⠀⠀⠈⣉⢉⣨⣍⣩⣌⣉⡉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⣉⣁⣉⣉⣉⣩⣭⣉⣡⣤⣍⣉⣴⣿⣮⣭⣉⣭⣽⣶⣮⣉⣩⣄⠈⡉⢉⡉⠁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠉⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢆⣤⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⡺⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⠍⠁⠀⠈⠙⠛⠛⠛⠋⠛⠍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠽⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠽⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠿⠛⠛⠙⠛⠛⠟⣿⡿⡿⠿⡛⠟⠛⠉⠉⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢩⣗⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢼⢙⡷⣧⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢆⢒⠌⠉⠉⠋⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠲⢦⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀

⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀

⠀⠈⠁⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⢀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠿⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⢀⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣄⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀

⠀⠀⠀⢉⣉⣨⣉⣩⣈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⣁⣉⣉⣉⣉⣉⣉⣁⢀⣍⣩⣼⣿⣾⣭⣉⣭⣽⣶⣮⣉⣩⣄⣈⠉⠉⠉⠁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠘⢟⠛⡿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣠⡤⡂⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠘⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⠛⠋⠉⠀⠁⠈⠙⠛⠛⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠿⠿⠿⠛⠛⠛⠿⢿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠋⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢥⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠄⡁⠆⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠌⢉⡻⣄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠣⠂⠀⠋⠀⠀⠀⠀⠀⠀⣰⣶⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢁⠂⠈⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠲⢦⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀

⠀⣤⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣷⣾⣿⣿⣿⡇⠀⠀

⠀⠈⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠿⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⢀⣼⣿⣧⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⣄⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀

⠀⠀⠈⠉⠉⣌⡉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠁⠉⣉⣉⣉⢉⢉⢁⣤⣭⣭⣾⣿⣯⣍⣉⣭⣽⣶⣮⣍⣉⣀⡈⠉⠉⠉⠁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣷⣿⣿⣿⣬⣢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣶⢒⣤⣄⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠉⠀⠀⠀⠉⠉⠛⠻⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⢛⠛⠋⠻⠿⠿⢿⣿⡿⡿⠟⠿⠟⠛⠛⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⡠⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠀⠙⢞⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠈⠊⠈⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠲⠆⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀

⠀⣠⡄⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣿⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣧⣼⣿⣿⣿⡇⠀⠀

⠀⠈⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠏⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠻⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣾⣿⡟⣿⣿⠸⣿⣧⣿⣿⣸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣿⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⢸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢻⣿⣿⣿⡇⠀⠀

⠀⠀⠀⠉⢉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠁⠉⢉⣉⣉⣉⣉⣁⣄⠉⠉⢀⣴⣆⣉⣭⣭⣽⣶⣮⣍⣉⣀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠟⠍⠙⠻⠿⠛⠛⠛⠛⠋⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠒⠆⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣤⡠⣤⡄⣠⣤⠄⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⢀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀

⠀⣤⡀⢸⣿⡇⣼⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣿⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠘⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣧⣼⣿⣿⣿⡇⠀⠀

⠀⠈⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⣠⣿⡿⠁⠀⣼⣿⠏⠘⠻⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡟⣿⣿⠸⣿⣧⣿⡿⣸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣧⣿⡿⢸⣿⣧⣿⡟⢹⣿⣿⣿⡇⠀⠀

⠀⠀⠀⠉⡉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠉⠉⠁⠉⢉⣉⣉⣉⣉⣁⡀⠉⠉⢀⣼⣄⣉⣩⣭⣽⣶⣮⣉⣉⣀⠉⠉⠉⠉⢁⠉⠉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⡿⠃⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆⣀⣿⣧⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⡨⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢸⡚⢀⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡾⢹⡑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡧⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠋⠛⠛⠛⠛⠛⠋⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠒⠆⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣄⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣤⡀⠀⠀

⠀⣠⡀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡏⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣏⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀

⠀⠈⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣟⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⣠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣿⢸⣿⡇⣿⣿⢽⣿⢸⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣧⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣧⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀

⠀⠀⠀⠉⠉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⢀⣄⢀⣉⣉⣩⣽⣶⣮⣉⣉⣠⣌⣉⣉⣉⣡⣍⣉⠉⠉⠈⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠠⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠐⣠⡄⠀⡀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡆⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠁⠠⠅⠘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠯⠀⠀⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣧⡦⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠿⣿⣿⣿⣿⣿⣿⣔⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⠉⠉⠉⠁⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠋⠂⠉⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⡀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠿⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠒⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀

⠀⠠⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀

⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣧⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀

⠀⠀⠀⠉⠉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⢉⡁⡀⠉⣉⣠⣦⠀⣉⣉⣭⣭⣶⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⡉⠈⠉⠐⠂⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣸⣹⣄⢀⠀⢄⡖⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣼⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣤⡔⠚⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠩⠨⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠅⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠏⠉⠀⠀⠀⠀⠀⠈⠫⠙⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⠿⣿⣿⣿⣿⣿⡿⣿⢿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣄⠀⠀⠀⠀⣄⡀⢴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠁⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀

⠀⢠⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀

⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀

⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⢁⢀⣉⣉⣤⡄⢀⣉⣭⣭⣭⣦⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠐⠂⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣸⣻⣆⠀⠀⣠⡆⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣽⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⠿⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣷⣦⣄⠚⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢉⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠅⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠉⠀⠀⠀⠀⠀⠉⠉⠉⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⡀⠀⣄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠊⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⡀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀

⠀⠠⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀

⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⢿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀

⠀⠀⠀⠉⠉⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⢀⣠⣀⣉⣭⣭⣭⣦⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠐⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣜⣹⣆⠀⠀⣤⡆⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠴⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣦⣾⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⠟⠛⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣤⣄⠘⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢉⠀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣯⢿⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠍⠀⠀⠀⠈⠉⠉⠉⠉⠉⠽⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢝⡿⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠋⠉⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠂⠀⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀

⠀⠀⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀

⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⢿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣾⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀

⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠀⣸⣤⣩⣭⣭⣭⣦⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣰⣀⠀⠀⢠⡄⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣧⡤⣠⢤⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢷⡞⠯⠘⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣤⡄⠘⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠆⢈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠕⢁⠄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣾⣿⣿⣦⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠟⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⢿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠃⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀

⠀⠀⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀

⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⢿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀

⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠀⣾⣦⣩⣭⣭⣭⣦⣌⣉⣉⣠⣬⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⢉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢀⣱⣀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⠤⣠⢀⣽⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢷⡿⠟⠛⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣤⣄⠈⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⢌⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠕⢀⠄⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣿⣿⣦⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡾⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠻⢿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠒⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠒⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀

⠀⠀⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀

⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⢿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣾⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀

⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⠉⢉⡁⣀⣉⣉⣤⢰⣄⣭⣭⣭⣭⣦⣌⣉⣉⣠⣌⣉⣉⣉⣥⣍⣉⣉⠉⠈⢉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⢉⠉⠉⠀⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣀⣰⣀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣿⡤⣠⣄⣷⣶⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠓⡟⠿⠙⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣤⡤⠘⠁⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠕⢀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠩⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠆⠖⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠂⠄⢠⣤⡄⢠⣤⣤⡄⢠⣤⡄⢠⣤⢠⣤⡄⣤⣤⠀⣤⣤⣤⠀⣤⣤⣤⣄⡠⣤⡄⣠⣤⠀⠀⣠⣤⣤⣀⠀⣠⣤⣤⡀⢀⣤⣤⣄⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⣤⡀⢀⣤⣤⣤⡀⢀⣤⣤⣄⡀⠀⠀

⠀⠀⠀⢸⣿⡇⣸⣿⣿⣧⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⠀⣿⣿⣿⡆⣿⣿⣹⣿⡇⢻⣷⣿⡟⠀⠀⠿⠏⣽⣿⢸⣿⡇⣿⣿⠸⠿⢹⣿⡇⠿⠏⣽⣿⢀⣀⠀⠐⠻⣿⣿⢸⣿⣇⣛⡛⢸⣿⡏⣿⣧⢸⣿⢹⣿⡇⠀⠀

⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢰⣿⣟⣿⡇⣿⣿⣿⣿⡅⠘⣿⣿⠁⠀⠀⠀⣼⣿⠋⢸⣿⡇⣿⣿⠀⢠⣿⡟⠁⠀⣼⣿⠏⠘⠛⠀⠀⠀⣿⣿⢸⣿⡏⣿⣷⢸⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠀

⠀⠀⠀⣼⣿⣇⣿⣿⢻⣿⣼⣿⡏⣿⣿⠸⣿⣧⣿⡿⢸⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⣧⣤⠸⣿⣇⣿⡿⢰⣿⣯⣤⡄⣾⣿⣧⣤⢠⣤⠀⠀⠀⣿⣿⠸⣿⣇⣿⡿⢸⣿⣧⣿⡏⢸⣿⣼⣿⡇⠀⠀

⠀⠀⠀⠉⠉⠈⠉⠁⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠀⠉⠉⠁⠉⠉⠉⠉⢉⣉⣁⣄⣉⣉⣤⢶⣄⣩⣭⣭⣭⣦⣌⣉⣉⣤⣌⣉⣉⣉⣥⣉⣉⣉⠉⠈⢉⡀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣺⣂⠀⠀⢰⡏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⠴⣦⣤⣿⣷⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣷⡾⠿⠛⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣦⡦⠘⠁⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠄⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⡐⠥⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠩⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡒⠤⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⣹⣧⣌⣵⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠲⣾⣷⣶⠶⢄⣰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⣀⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣤⡄⠠⠀⠀⢐⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀

⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⡿⠋⠋⠁⢀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣐⣹⣿⣿⣷⣶⣤⣤⣤⣦⣦⣀⠀⡀⣬⣢⣿⢰⠇⠋⡝⠈⠀⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣬⡿⠃⠄⠀⠀⠀⣸⡿⠋⠀⠀⣴⣮⠇⠃⢐⣦⣤⣴⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡺⣿⣽⣿⣗⡋⠴⢀⠀⡀⠀⣀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⢽⡿⡋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⠌⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣜⣿⣯⢝⣿⣾⡄⠁⠀⠅⠀

⠀⠀⠀⠀⠀⠀⠠⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⠋⡀⠀⠓⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢯⢧⠀⣠⠀⢠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣯⠙⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡗⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣄⣦⣥⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣵⡿⣷⣘⣾⠆⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⡿⠃⠀⡁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠿⣟⣟⣿⣟⠛⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠫⣟⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠪⢙⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣲⣶⣖⣆⣴⣶⣂⣾⣞⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠾⢭⢶⣿⣿⣿⣿⣿⣿⣿⡿⢙⠂⡙⠛⢫⣿⣿⣿⣟⡟⠝⣙⣛⢿⢿⣿⣿⣿⣿⠿⠿⠿⡿⣿⣿⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠲⢾⣶⣶⠾⠄⠠⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣤⡄⠠⠀⠄⠀⠻⠻⢿⣿⢿⣿⣿⣿⣿⡻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀

⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⠿⠟⠋⠀⠀⣠⡤⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⣹⢿⣿⣷⣤⣤⣦⣠⣤⣠⣤⡀⣐⣨⣕⣿⠰⠗⢊⡍⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡷⠃⠔⠂⠀⠀⢾⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⣰⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡺⣿⣺⣾⣗⣹⠐⠂⠀⠀⠀⣀⠀

⠀⠀⠀⠀⠀⠀⠀⣰⡿⡛⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠙⣺⣷⣻⢺⢶⡄⡀⠀⠄⠀

⠀⠀⠀⠀⠀⠀⠀⡾⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠟⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠻⣏⠉⡄⠀⠛⠀⠀⠀

⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⠦⠀⣀⠀⠠⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⠙⠁⠀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⠩⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡮⢥⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣲⣿⢔⡀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⡿⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⣤⣫⡻⠙⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠈⠸⠻⠟⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡊⣙⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣶⣼⣛⣦⣄⣬⣹⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⡟⢹⣿⣯⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣟⠏⠍⠁⠈⠘⠭⡇⠋⣛⣿⣿⣿⣿⣿⣿⣿⡿⠫⠃⠑⣋⣻⣿⣿⣿⣿⣿⢿⠹⠛⢻⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⣐⣿⣅⣩⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠲⢾⣶⣶⡾⢄⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣤⡄⠠⠀⠄⠔⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣦⣅⠀⠀⠀⢠⣄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⢠⡀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀

⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⠏⠁⠀⢀⣦⣴⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠈⣀⣿⣿⣿⣷⣶⣴⣦⣴⣦⣤⢤⣀⣐⣬⣓⣿⢰⡇⣃⡌⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣈⣎⣿⡟⠂⠄⠀⠀⢸⣿⠟⠀⠀⢠⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣼⡿⣓⣻⡘⢂⠀⡀⠀⣀⠀

⠀⠀⠀⠀⠀⠀⠀⣔⣿⠟⠁⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡲⣿⠞⡿⢷⡄⠀⠀⠆⠀

⠀⠀⠀⠀⠀⠀⠀⣥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⡂⠀⠛⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡅⠀⣠⠀⠠⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⢝⠙⠡⠀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢷⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⠔⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⠦⠈⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣷⣽⣷⣶⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⠟⠌⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣝⣻⣿⠟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠛⢿⠯⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠗⢛⠏⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣷⣿⣤⣡⣲⣗⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠯⡿⢿⣿⡿⠏⡻⡿⣟⣿⣿⣿⣿⣿⣿⣿⡯⠓⠑⠐⠚⡿⣿⣿⣿⣿⣿⡿⠷⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠆⠀⠠⠲⠄⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡟⣿⣼⡟⠀⣼⡟⢸⣿⠿⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠗⣿⡿⣷⡀⢠⣶⣿⠛⢻⣿⣾⡟⣷⣰⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡿⢸⣿⠇⣿⡿⣿⡀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⢇⡸⠿⠼⠿⠴⠿⠰⠆⣀⠻⢷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠇⡀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠠⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⡖⠀⠀⠀⣄⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡶⢿⣿⣉⣖⢘⣀⡀⠰⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⠟⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠊⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣒⠛⠀⠸⣿⣿⣿⣿⣿⡟⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠍⠀⠀⠀⠀⠉⠩⠋⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠿⢷⠖⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣡⣠⣶⣿⣾⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠆⠀⠠⠲⠄⠀⠀⠀⠀⠛⠛⠛⠛⠛⠊⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠗⣿⡿⣷⡀⢠⣶⣿⠛⢻⣿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡿⢸⣿⠇⣿⡿⣿⡀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠿⠿⠿⠁⠿⢇⡸⠿⠼⠿⠴⠿⠰⠆⣀⠻⢷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠇⡀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠠⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣿⣿⣷⣶⣶⣾⣶⣴⣦⣴⣖⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣖⢿⣿⣌⣒⣘⣀⠂⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁⠒⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⢿⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⠂⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠼⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⠻⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢄⠑⠂⠀⢨⣿⣿⣿⣿⣿⣿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠋⠉⠝⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠡⠙⠛⣿⣟⠟⠿⡿⢿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠿⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣁⣠⣶⣿⣾⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠆⠀⠠⠲⠄⠀⠀⠀⠀⠉⠛⠛⠛⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡿⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⢇⡸⠿⠸⠿⠴⠿⠰⠆⣀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⡀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠠⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⢤⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣶⣶⣶⣶⣷⣿⣿⣿⣶⣶⣶⣶⡐⣦⣦⣖⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣤⠆⣺⣿⣌⣒⡈⡀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠒⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣉⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣽⠺⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠉⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠉⠁⠈⣹⣿⣻⣋⣛⣾⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⠂⠀⠀⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠛⠿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢂⠀⣤⣶⡔⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠆⠀⠀⠲⠀⠀⠀⠀⠀⠚⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⠇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⡀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠢⠰⠔⠀⠀⠀⠀⠀⢀⣼⣷⣶⣾⣿⣷⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⡶⠀⢴⣤⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣥⣅⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⢹⣿⣈⡐⣈⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡷⣍⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠤⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣙⠪⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠉⠓⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠀⠀⠀⠀⠀⠙⠟⢛⠁⣀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠋⠃⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⡷⠿⠿⠿⠿⠿⠿⠿⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⠻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠂⠀⠠⠲⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⠇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣾⣿⣷⣿⣿⣿⣿⣶⣶⣶⣾⣾⣿⣷⣶⣶⣶⣦⠀⢶⣦⡀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣥⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣤⣂⢸⣿⣄⣀⣈⣀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣅⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣙⠪⠆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⠋⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠹⠛⠛⠁⣀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠝⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠟⡿⡿⠿⠿⠿⠿⢿⠿⡳⢟⠯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢦⡶⣦⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠆⠀⠠⠲⠀⠀⠀⠀⠚⠛⠛⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠿⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠗⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡿⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠿⠿⠿⠁⠿⢇⡸⠿⠼⠿⠴⠿⠰⠆⡀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠄⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣾⣶⣶⣶⣿⣶⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⠴⣦⣦⡄⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠑⢂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣦⣺⣿⣤⣜⣈⣀⣀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣹⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠲⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠢⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣙⡒⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡟⢛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠁⠸⢿⠿⡓⣊⣱⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⣻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠟⢷⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠆⠀⠠⠲⠄⠀⠀⠀⠈⠛⠛⠛⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠗⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠃⠀⣿⡇⢸⣿⠗⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⢇⡸⠿⠸⠿⠴⠿⠰⠆⡀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠄⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣠⣶⣶⣶⣶⣿⣶⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣦⠤⣶⣦⡄⠀⠀⢀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠙⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣽⣿⣤⣌⣌⡄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠉⡀⠀⠀⠀⠀⠂⠀⠈⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡋⣹⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡲⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⠓⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠁⢸⢿⣿⠿⠊⣰⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠈⠀⠉⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠟⢷⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠝⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠂⠀⠀⠲⠀⠀⠀⠀⠀⠛⠛⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⢇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠃⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣲⣆⣰⣾⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣦⠀⣶⣦⠀⠀⠀⢀⣢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠛⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡔⣂⣸⣿⣦⣌⣄⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣋⢉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠡⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡢⠾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡒⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡛⢿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠁⠘⠿⠷⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠊⠉⠉⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣰⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⡗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠆⠀⠠⠲⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣸⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣻⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡟⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⠁⠿⠇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣆⠀⣴⣦⡀⠀⠀⠀⣠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⡄⡀⣸⣿⣦⣬⣄⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⡋⡈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠩⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡆⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⡒⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢿⣿⣿⠟⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⠁⠀⠀⠀⠁⠘⠿⠗⠂⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣴⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠂⠀⠠⠲⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣸⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣷⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣻⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡟⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⢁⠿⠇⡸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠰⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⢂⠀⣶⣤⡀⠀⠀⢀⣤⢀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⡆⣀⣸⣿⣤⣬⣄⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣟⠃⠈⢽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡷⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡂⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣀⡚⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣗⣿⣿⣿⣿⠄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⠿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢻⡿⣿⠍⠁⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠁⠘⠻⠒⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣳⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠂⠀⠀⠲⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣸⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣷⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣻⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡟⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⣁⠿⠇⠸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠰⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⡀⠀⣴⣤⡀⠀⠀⢀⣤⠄⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡆⣀⡸⣿⣦⣬⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣟⠋⠀⢽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡂⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣃⡚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢻⣿⣿⠟⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⠉⠀⠀⠀⠁⠈⠻⠲⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠉⠙⠛⠋⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣾⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠒⠆⠀⠀⠲⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣸⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣷⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣻⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣾⡟⢸⣿⠇⣿⡟⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⢀

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⣁⠿⠇⠸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠰⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣶⣾⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣂⠀⠴⣦⡀⠀⠀⢀⣤⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡆⣠⣘⣿⣦⣤⣀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⢿⣟⣋⡀⢽⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠡⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡆⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣃⡚⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢿⣿⣿⡟⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⠀⠁⠈⠻⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠉⠙⠛⠻⢿⠿⠟⠻⠿⠟⠟⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠒⠆⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⢠

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⣁⡿⢇⠸⠿⠸⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⡂⠀⢶⣤⡀⠀⠀⢀⣠⠄⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡄⣀⠐⣿⣦⣤⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣛⣇⡀⢹⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣒⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣂⡘⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡿⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠈⠿⠷⠖⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠁⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀⠙⠟⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠿⠅⠀⠀⠀⠀⠀⠀⠸⠽⢟⢻⣿⣴⣦⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠁⠩⠋⠉⠀⠈⠉⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⠠⢷⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠠⠉⠘⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠒⠆⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠿⣿⡿⢳⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠠

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⣁⡿⢇⠸⠿⠼⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣾⣿⣷⣶⣶⣶⣀⠀⢶⣦⡀⠀⠀⠀⣴⠂⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡆⣀⣐⣿⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⢿⣿⡷⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣏⣅⡀⢹⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢐⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣂⡘⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠟⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠈⠻⠷⠆⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠸⠀⢀⠁⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠈⢼⠺⢛⠿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠶⠙⠏⠻⡅⠉⠁⠊⠠⢠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠝⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠛⠙⠓⠟⠚⠔⡺⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⠀⠀⠀⠀⠀⠐⠂⠊⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠿⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠻⠿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠒⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠻⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⢠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠠

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠻⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠿⠿⠿⢁⡿⢇⡸⠿⠼⠿⠴⠿⠰⠆⡀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡀⠀⣶⣦⠀⠀⠀⠀⣰⠢⢀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣿⣷⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⡯⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣏⣍⣀⢸⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠆⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⠚⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢂⣐⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡟⠋⠛⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠈⠻⡧⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠫⢀⠀⠁⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣔⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⢼⢽⣿⣷⣾⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⣾⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⡄⠈⠐⠺⢿⢛⣿⢟⣟⠙⠯⠯⢴⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠸⠯⠛⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠈⠍⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠟⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠙⠛⠋⠛⠟⠉⠙⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠡⠊⠉⠉⠛⠛⠿⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠒⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠿⣿⡿⢷⣿⢻⣦⣿⡟⣿⡆⣿⣿⡏⣿⣼⡟⠀⣼⡟⢸⣿⠟⣿⡿⠇⣿⣿⣷⠀⠀⠀⣾⣿⣷⡼⣿⡿⢿⣿⢸⣿⠛⣿⠀⠀⠀⣾⡟⣿⣼⣿⢸⣿⢸⣿⠇⣿⡟⣷⠀⠠⣶⣿⠛⢻⡿⣾⡟⣷⣠⣿⢻⣧⠀⠀

⠀⠀⠀⣿⡇⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣷⢹⣿⠁⠀⣿⡇⢸⣿⠇⣿⡿⠇⣿⣿⣿⠀⠀⠀⢿⣿⣿⡇⣿⡇⢸⣿⢿⣿⠀⣿⠘⠃⠀⣿⡇⣿⡏⣿⣿⡟⢸⣿⠇⣿⡿⣿⠀⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⢸⣿⠀⠠

⠀⠀⠀⠿⠇⠘⠿⠾⠏⠿⠷⠿⠻⠿⠹⠿⠸⠿⠀⠀⠹⠷⠸⠿⠀⠿⠷⠆⠿⠿⠿⠰⠆⠀⠻⠿⠿⢁⡿⢇⡸⠿⠼⠿⠴⠿⠰⠆⠀⠻⠷⠿⠁⠿⠿⠇⠸⠿⠶⠿⠇⠿⠀⠀⠸⠿⠸⠿⠁⠻⠷⠿⠙⠿⠾⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡀⠀⢶⣦⠀⠀⠀⠀⣰⠂⢄⠀⠄⠀⠀⡤⠀⠀⠀⠀⠀⠀⠈⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡄⣀⣀⣿⣷⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⡯⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣏⡅⡀⢸⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠆⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⠒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣊⣐⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠋⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠈⠻⡧⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠣⣀⠀⠈⠢⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣼⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠯⢻⣿⣷⣶⣶⣤⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⠀⠈⠐⠿⠿⡿⡟⠻⡟⢻⢛⡜⣛⡥⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠽⢟⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠹⠞⠛⠙⠉⠀⠀⠀⠀⠀⢡⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠠⠐⠛⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠑⠛⢿⠿⣽⠟⠃⠉⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠔⠀⠀⠉⠛⠛⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠀⢀⡖⠀⠂⠀⢀⢀⡀⣀⢀⢀⢀⠀⡀⣿⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⠧⠀⠄⠶⠸⢸⡇⠟⠈⠳⠸⠠⠇⠿⠸⠌⠨⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

⠀⠀⠀⠀⠀⠀⠀⢹⢰⢠⠀⠄⡄⢠⠠⠀⠀⠀⢠⠀⡄⠄⠀⢈⠅⡮⣆⢕⠨⠅⠀⢠⠠⠀⡄⠀⠠⠀⡄⡄⠁⢠⠀⠄⡀⠀⠀⠀⡤⢣⠠⠀⠀⠄⢠⢠⠀⠄⠀⢠⠀⠄⡀⢀⠀⠁⡄⡄⡇⠈⠀⢄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠁⠀⠀⠁⠀⠀⠈⠀⠀⠈⠁⠈⠀⠁⠈⠁⠀⠀⠁⠈⠀⠈⠀⠁⠈⠁⠉⠀⠁⠈⠀⠁⠀⠀⠀⠀⠁⠀⠀⠉⠀⠁⠈⠀⠉⠀⠁⠈⠀⠉⠀⠀⠈⠀⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡔⢠⢢⠐⠂⠐⢠⠢⠔⡀⡗⢰⠂⡔⡇⠀⢰⠂⡔⢤⢂⠐⠂⡖⠐⣂⠈⠀⢤⠀⠀⢺⠀⠒⠀⠀⢸⠀⡙⠨⠁⡏⠀⠀⠐⠂⠚⠀⠀⢸⠂⠒⢠⠢⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

⠀⠀⠈⢃⠠⡇⡄⠄⣄⢠⠀⢀⠄⢠⠠⢠⢠⢠⢠⢠⠠⢀⠠⣠⠠⠀⢀⠀⠠⡀⠄⢄⣄⢠⠀⠀⢀⣠⢠⠀⠀⡇⠄⠄⡀⠀⡄⡄⡄⡄⡄⡄⠄⡇⠄⣄⡄⡤⠀⡀⢄⠨⠁⢠⢠⠠⠠⢠⠠⠌⡠⠀⠀⠠⠀⠠⠀⠀

⠀⠀⠐⠊⠁⠃⠑⠂⠒⠉⠂⠈⠒⠈⠒⠘⠘⠘⠘⠘⠐⠊⠒⠘⠐⠀⠈⠒⠐⠐⠐⠊⠒⠉⠂⠐⠊⠒⠐⠂⠀⠑⠂⠸⠀⠀⠃⠃⠑⠃⠃⠃⠂⠓⠂⠑⠂⠃⠀⠑⠂⠐⠀⠀⠃⠃⠐⠊⠐⠐⠘⠒⠒⠂⠢⠒⠆⠀

⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⡸⢸⠒⡁⢀⢀⢘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

⠀⠀⠀⠀⠀⠀⠀⡴⢡⢦⠀⠀⠒⢐⢦⢂⠆⠶⠀⠀⡰⡄⠀⠀⠀⢺⢰⣶⠐⠀⠒⡀⠀⠐⡂⠒⠀⠀⠈⠀⢝⢨⠀⡇⡇⢼⠀⠀⡇⢸⢜⠀⠀⠖⠀⠀⠐⡆⠶⢰⠂⠀⠀⢒⢐⠆⡖⡄⢖⠀⡀⢸⢠⢦⠀⠀⠀⠀

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⡀⢀⠀⡀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢎⠲⠿⠈⠀⠎⠀⡇⠀⠀⢉⠰⡑⢎⠄⠀⠰⠀⢸⠀⣱⠀⠁⠉⠄⡡⠀⠀⠈⠀⠀⢈⡆⠀⠀⠀⠀⠀⠂⠐⠀⢗⠟⡺⠀⠀⢇⠸⠊⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

                ䷩ 𝚕𝚒𝚗𝚎 3574

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/holding-management-accountable/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/09/holding-management-accountable/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Staff_Holding_Management_at_the_EPO_Accountable⠀✐

Posted in Europe, Patents at 2:37 pm by Dr. Roy Schestowitz

Video_download_link | md5sum 3e57c063cb4318309a3e810ef7b45ce7

Consequences for Rogues at the EPO

Creative Commons Attribution-No Derivative Works 4.0

http://techrights.org/videos/epo-action-and-impunity.webm

Summary: It seems possible that in months to come the administrative body of

the EPO will finally acknowledge that “breaking point” has been reached and

it’s time to reboot the Office

THE immunity and impunity of EPO management has been a theme of recent coverage

here. We last wrote about it earlier_today, focusing on what Benoît_Battistelli

had done in the Netherlands. After 3 years at the Office António_Campinos is

starting to see it all crumbling or falling down, starting with last summer’s

ILOAT ruling no. 4430 and then ILOAT ruling no. 4482, which is still very

fresh. But why did it take so long? As noted in the video above, many of the

people wronged are already dead, unable to claim_or_collect_compensation_from

the_Office.

The EPO got infiltrated by white-collar criminals, who in effect fronted for

international (non-European) or multinational corporations with their patent

litigation staff (in-house) and/or outside law firms. The solution to such a

dire crisis must come from the outside, but the_EU_too_is_infiltrated. The EPO

conflict has exposed a rotting unregulated system, which extends_to_EUIPO and

even some courts. It won’t be pretty, but “ordinary” EPO staff (such as patent

examiners) are on the right side of history. █

                ䷩ 𝚕𝚒𝚗𝚎 3626

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/iloat-ruling-no-4430-and-iloat-ruling-no-4482/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/09/iloat-ruling-no-4430-and-iloat-ruling-no-4482/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ [Meme]_Drunk_Driving,_Like_Son_of_António_Campinos⠀✐

Posted in Europe, Patents at 2:47 pm by Dr. Roy Schestowitz

Benoît_Battistelli is notorious for misusing EPO funds to build himself a_pub;

António_Campinos received a lot of negative press after his son had_gotten

drunk,_crashed_the_car,_and_wanted_to_borrow_dad's_diplomatic_immunity (his

grandpa Jorge did not live long enough to see such a disgrace; he died_in_a_car

accident_in_1993)

 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇ILOAT ruling no. 4430 and ILOAT ruling no. 4482⦈

Summary: In the Netherlands, the drunk-on-power EPO may have gotten its way (an

above-the-law status), but ILOAT keeps delivering much-belated rulings (4430,

4482, maybe more to come) which curtail the illegal actions of the EPO albeit

without any consequences for the perpetrators

⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠨⣲⣍⡩⣿⡯⠻⠿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠉⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⡀⠄⣤⣆⡰⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡝⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣜⣍⢿⢿⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⣻⢾⣿⣿⡿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠝⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢧⣿⣾⠃⣠⣿⣾⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠇⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠉⢋⣛⢹⡿⣸⣿⣾⣧⡟⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡝⠈⠅⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣰⠀⡏⠀⠗⠀⣢⠉⠘⠁⠗⠛⡿⠀⣿⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣿⣿⣿⣿⣿⣸⠽⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣤⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢸⣽⣿⣹⠃⠐⠛⠀⠀⠀⠉⠀⠸⣿⠿⡿⠿⠦⢴⣇⣸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠓⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⣿⢳⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠛⣿⢿⡇⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠯⠿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠀⠀⠀⠀⠀⢸⣇⣿⠏⠀⠀⠀⠀⠀⠀⠏⠀⢐⢀⡀⠙⢼⠃⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣈⣃⠈⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠉⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀

⢀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠐⠀⠂

⠂⠄⠰⢠⠀⠀⠀⡠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⢉⣓⣍⡹⣿⡮⠟⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢄⢰⣄⡤⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣿⣿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢧⣿⣾⠃⣠⣿⣾⠩⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣷⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠆⣼⣿⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠈⢉⣛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠓⠈⡁⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠂⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡋⠀⠗⠀⣂⠉⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⠑⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣾⣿⣿⣿⣿⣸⠽⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣿⣹⠃⠐⠛⠀⠀⠀⠁⠀⠸⣿⣿⡿⠿⠦⠴⣧⣼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠛⣿⢿⡇⢸⣿⡟⠁⠀⠀⠐⠀⠀⠀⠀⠀⠂⣿⡿⠻⠃⠀⠀⠀⠀⠀⠉⡍⠉⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠁⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⢐⢀⡀⠙⢼⠃⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣈⣃⠈⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⡀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⠄⠈⠀⠉⠀⠀⠈⠑⠂⠂⠀⠀⠀⠀

⢀⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠂

⠃⠄⠰⢠⠀⠀⠀⡠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣈⢉⣡⣍⡹⣿⡿⠛⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⡀⡄⣔⣄⡤⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢧⣿⣾⠃⣠⣿⣾⠩⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠃⣸⣿⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠁⢉⣛⢹⡿⣸⣿⣾⣧⡟⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠝⠀⡅⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢘⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡋⠀⠓⠀⣢⠉⠘⠁⠗⠛⡿⠀⣿⣿⠀⢿⡟⠐⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣾⣿⣿⣿⣿⣘⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣤⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢸⣯⣿⣹⠃⠐⠛⠀⠀⠀⠉⠀⠸⣿⣿⣿⡽⠧⠴⣧⣼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠻⣿⢿⡇⢸⣿⡏⠁⠀⠀⠐⠀⠀⠀⠀⠀⠂⣿⣿⡿⠀⠖⠀⠀⠀⠀⠀⠉⠉⠉⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⢐⢀⡀⠙⢾⠃⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡅⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠉⠀⠀⠈⠑⠂⠂⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠂

⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠉⣪⣭⣉⣓⣭⡻⣿⡿⠻⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡝⠋⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⡄⣤⣴⣄⡶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠬⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠫⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣾⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠃⣼⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠁⠛⣛⢹⡿⣸⣿⣾⣧⡟⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠝⠈⠅⢈⣋⣻⢹⣠⡌⣽⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⠀⡇⠀⠗⠀⣢⠉⠘⠁⡗⠛⣿⠀⣻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣾⣿⣿⣿⣿⣸⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣭⣿⣹⠃⠐⠋⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⡴⠧⣼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠻⣿⣿⡇⠸⣿⡟⠁⠀⠀⠄⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⠃⠰⠀⠀⠀⠀⠉⠉⠉⠘⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣗⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⢐⢀⡀⠙⢿⠃⠃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⡱⠢⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⡀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡄⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠁⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠂

⠃⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⡪⣨⢉⣓⣭⡫⣿⡿⠿⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡐⡙⠏⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠰⠐⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⡀⠤⢄⣄⡤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢤⣿⣾⠃⣠⣿⣾⠩⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣯⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠃⣸⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠈⠛⣛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠝⠈⠅⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠂⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡋⠀⠓⠀⣂⠈⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⠐⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣾⣿⣿⣿⣿⣸⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣤⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣭⣽⣹⠃⠐⠛⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⣿⣰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠻⣿⣿⡇⠸⣿⡟⠁⠀⠂⠄⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⠏⠆⠀⠀⠀⠈⠉⠉⠘⠒⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣗⣿⠇⠀⠀⠀⠀⠀⠀⠯⠀⢐⢀⡀⠙⢿⠃⠃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣝⡧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⡀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠈⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂

⠁⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⣊⣉⣑⣍⡩⢿⡻⠛⠟⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠏⠋⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠙⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠤⣄⣀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣗⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣯⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣸⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡾⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⣼⣿⣼⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠀⠛⣛⢹⡿⣸⣿⣶⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠐⠀⠁⢈⣋⣛⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡇⠀⠓⠀⣂⠈⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⡑⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣾⣿⣿⣿⣿⣜⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠋⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣇⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⣿⣰⣿⠁⠀⠀⠀⠀⠈⣿⠀⢸⠈⠻⣿⢿⡇⠸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠖⠀⠀⠀⠉⠉⠘⠒⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣷⣿⠇⠀⠀⠀⠀⠀⠀⠛⠀⠼⢀⡀⠙⢿⠃⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⢾⡏⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠁⢀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡧⠤⠤⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⡀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠂

⠂⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠚⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⣉⣑⣩⡹⣿⡯⠿⠿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡡⡱⠟⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠄⣄⣐⠤⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣟⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡾⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠃⣼⣿⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠈⢛⣛⢹⡿⣸⣿⣾⣧⡟⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠟⠈⠅⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⠀⡏⠀⠷⠀⣂⠈⠘⠁⠗⠋⣿⠀⣿⣿⠀⢿⡟⠑⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣾⣿⣿⣿⣿⣼⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣿⣹⠃⠐⠙⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡼⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⡿⣳⣿⠁⠀⠀⠀⠀⠀⣿⠀⢸⠈⠻⣿⢿⡇⠸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠯⠭⠠⠀⠀⠈⠉⠈⠒⠂⠠⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠋⠀⠸⢢⡀⠙⢿⠃⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡍⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⡀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡧⠤⠤⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠂

⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠰⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣌⣉⣁⣍⡹⣿⡯⠟⠟⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠈⡙⠋⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠤⢄⣀⡱⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡾⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣟⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⣼⣟⣼⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠚⠈⠋⢛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠙⠈⡁⢈⣋⣻⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢹⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡇⠀⠗⠀⣂⠈⠘⠁⠗⠉⣿⠀⣿⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⣟⠃⣿⣾⣿⣿⣿⣿⣸⠹⠻⠻⠍⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⣇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠀⣿⠀⢸⡈⠻⣿⢿⡇⠸⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠯⠭⣀⢠⠁⠈⠉⠉⠒⠂⠀⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⠘⢂⡀⠘⢿⠃⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠍⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢁⡀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⡧⠤⠤⠄⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤⠤⠤⠀⠈⠀⠀⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠒

⠁⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡪⢉⣑⣉⡹⣿⡻⠻⠟⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡠⡙⠊⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⣄⡂⠨⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣟⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠙⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣟⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⣼⣷⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠀⢋⣙⢹⡿⣸⣿⣾⣧⡏⢟⣻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠚⠀⡁⢈⣋⣛⢸⣠⡌⣽⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡏⠀⠧⠀⣢⠀⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⣟⠃⣿⣿⣿⣿⣿⣿⣸⠹⠻⠻⠍⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⠇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠀⣿⠀⢸⠈⠻⣿⣻⡇⢸⣿⡟⠁⠀⠀⠐⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠯⠭⣀⣀⢫⠍⠉⠉⠒⠂⠀⠤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⡀⠘⢿⠇⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠍⠙⠋⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⢂⡀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠚⠓⢠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⡧⠤⠤⠄⠀⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠤⠤⠀⠉⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠂

⠁⠄⠰⢠⠀⠀⠀⡠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣎⢉⣡⣉⡹⣿⡫⠛⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⡝⠏⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣄⣂⠄⠝⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣮⣶⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡯⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⣸⣿⣼⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠀⢋⡋⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠙⠈⠁⢈⣋⣛⢸⢠⡌⣽⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡇⠀⠷⠀⣢⠀⠘⠁⠗⠛⣿⠀⣿⣿⠀⢿⡏⠐⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣿⣿⣿⣿⣿⣸⠹⠻⠻⠍⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⠇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠀⣾⠀⢰⠈⠛⣿⣿⡇⢸⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠯⠭⣀⣀⣿⡋⠉⠉⠀⠂⠀⠤⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠏⠀⠼⢡⡀⠈⢿⠁⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠍⠙⠋⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠚⠸⡰⣃⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠗⠠⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡧⠤⠤⠀⠀⢈⣀⣀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠤⠤⠀⠉⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂

⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢈⢉⣑⣍⡩⣿⡿⠟⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡂⡑⠓⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠐⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⣀⣀⠠⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠬⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣾⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢟⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠫⠠⢼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣮⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣟⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⣼⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠚⠀⠋⣛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠚⠈⠁⢈⣋⣛⢸⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢘⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡃⠀⠇⠀⣂⠀⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⡁⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣿⣿⣿⣿⣿⣼⠹⠻⠻⠍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⢠⣷⡇⠀⠀⠛⠀⢸⠇⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠛⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⡿⢰⣿⠁⠀⠀⠀⠀⠀⣿⠀⢰⠈⠛⠿⢿⡇⠸⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⣀⣿⣛⡛⠈⠀⠀⠀⠤⠤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⠀⠀⠀⠋⠀⢬⢅⡀⠙⢿⠁⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠉⠙⠋⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⡹⣁⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⡧⠤⠤⣀⠀⢈⣀⣈⠹⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠤⠤⠀⠉⠀⠁⠐⠀⠈⠑⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂

⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⣈⢄⣍⡩⢿⡮⠻⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠎⠋⠛⠉⠁⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣐⠴⠊⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣔⣾⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⡿⠀⣿⣿⢀⣨⣿⣸⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣧⣬⠙⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢶⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⣿⠷⠋⢠⣼⢿⡮⣬⣽⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣾⣿⣔⣇⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠃⣼⣟⣼⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡏⢽⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠓⠀⠉⣛⢹⡿⣸⣿⣾⣧⡏⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠝⠀⠁⢈⣋⣛⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢘⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡇⠀⠗⠀⣂⠀⠘⠁⠗⠋⣿⠀⣻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣾⣿⣿⣿⣿⣸⠹⠻⠻⠅⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢘⠃⠀⠸⢷⣷⣾⣿⡇⢨⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⠻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⣿⣷⣿⠁⠀⠀⠀⠀⠀⣾⠀⢰⠈⠛⡆⣻⡇⠐⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⢀⣿⣛⡛⠉⠀⠀⠀⠀⠠⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣷⣿⠇⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠹⠁⡀⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠍⠙⠋⠀⠀⠀⠀⠻⠿⡿⣷⣦⠀⠀⠀⠀⠀⠂⠑⡠⠟⣽⡙⠐⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡧⠤⠀⢀⠀⠀⣀⡸⢿⡿⣇⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠒⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠤⠤⠀⠉⠀⠁⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠐⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢈⡈⣉⡩⢿⡾⠛⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠌⠋⠛⠉⠁⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⡄⣀⠴⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣆⣾⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣾⣿⣿⠀⣿⣿⢀⣨⣿⣸⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣧⣬⠙⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢶⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⠷⠋⢠⣼⢿⡮⣬⣽⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠤⣼⣿⣴⢆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⣯⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡼⣟⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠃⠈⠉⢙⢹⡿⣨⣿⣶⣧⡏⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠑⠀⠁⢈⣋⣛⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⡏⠀⠗⠀⣂⠀⠘⠁⠗⠛⣿⠀⢿⣿⠀⢿⡏⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣾⣿⣿⣿⣿⣼⠹⠻⠻⠅⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢘⠃⠀⠸⢲⣷⠾⢾⡇⠸⣯⣽⣹⠃⠐⠉⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⣿⣷⣿⠁⠀⠀⠀⠀⠀⣾⠀⢰⠈⠙⡀⠘⡇⠀⡿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⣀⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣧⣿⡏⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠍⠙⠋⠀⠀⠀⠀⠻⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠴⢑⣠⣏⣽⡳⢦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⡧⠄⠀⣀⠀⢀⣀⡹⢿⡿⣇⣛⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠠⠤⠀⠉⠀⠁⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂

⠁⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠐⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣈⣙⣂⣍⣋⢽⡿⠿⠿⠿⠿⠿⡿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⢀⠤⠈⠃⠛⠉⠉⠀⠀⠈⠀⠀⠀⠰⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣗⣾⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⡻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣻⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⡷⠋⢠⣼⢿⡮⣬⣽⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣾⡿⣴⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⣼⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⠀⠉⡛⢹⡿⣸⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠑⠀⠁⢈⣋⣛⢹⢠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣀⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⠀⡏⠀⠣⠀⣂⠈⠘⠁⠗⠋⣿⠀⢻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⢀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣾⣿⣿⣿⣿⣜⠹⠻⠻⠅⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⡇⠀⠸⢳⣷⠚⠛⡇⠈⠭⠽⢹⠃⠐⠉⠀⠀⠀⠁⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⣿⣳⣿⠁⠀⠀⠀⠀⠀⣾⠀⢠⠈⠙⡀⠀⡇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⢀⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣧⣿⡏⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠉⠙⠋⠀⠀⠀⠀⠻⣿⢿⣷⣦⣄⢀⠀⠀⠀⠀⠀⢰⣛⣛⣛⣟⡆⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡧⠄⠀⣀⠀⣀⣀⠿⣿⢿⣃⣛⣃⣈⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠄⠠⠠⠄⠉⠀⠁⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂

⠁⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠐⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠁⠉⢀⢈⣈⣀⣥⡿⣿⣿⠿⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⢀⡵⠅⠃⠋⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠁⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢄⡡⡼⠎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡶⣼⣺⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⣻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣌⢿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⢠⣿⣾⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣯⢻⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⣽⢷⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣾⣿⣴⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⣼⣿⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠈⢛⣛⢹⡿⣨⣿⣾⣧⡟⢟⢻⣿⡟⣿⣿⠛⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠙⠀⡁⢈⣋⣛⢹⣠⡌⣿⣿⠀⣿⣿⠃⣿⣿⢸⣿⣿⡇⣿⣾⣿⣿⣿⣿⠆⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⠀⡋⠀⠗⠀⣂⠈⠘⠁⠗⠛⣿⠀⣻⣿⠀⢿⡟⠀⣿⣿⡇⢻⣽⣿⣿⣿⠃⠀⠀⠙⠿⣿⠀⢻⣿⣿⣿⣿⣿⣟⡷⢾⡟⠃⣿⣿⣿⣿⣿⣿⣘⠹⠻⠻⠅⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡟⠀⠀⠀⠀⢰⡦⣠⣷⡇⠀⠀⠛⠀⢸⣇⠀⢸⢶⣷⠞⠛⡇⠈⠛⠛⢹⠃⠈⠋⠀⠀⠀⠉⠀⠸⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⠀⠀⠀⠀⢸⣿⣷⣿⠁⠀⠀⠀⠀⠈⣿⠀⢰⠈⠙⡀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣼⣿⡿⠭⠭⣀⣀⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣧⣿⡏⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⡀⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠯⡉⠙⠋⠀⠀⠀⠀⠻⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣛⣋⣛⣛⣖⡂⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣉⡁⢀⣀⠀⣀⣘⣿⡿⣿⣃⣛⣃⣈⣃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢩⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠍⠅⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠠⠄⠠⠄⠉⠀⠁⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀

⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂

⠂⠄⠰⢠⠀⠀⠀⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠒⠙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⢀⠩⡉⣻⣻⣿⣿⣿⡿⣿⡿⠿⡿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠀⠀⠀⠀⣤⣭⣶⣿⡿⠟⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡔⣧⣾⣞⣿⡽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⢾⣿⣿⣿⠀⣿⣿⢀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢶⣿⣾⠃⣴⣿⣾⠹⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡋⣿⣷⠋⢠⣼⢿⡿⣭⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣺⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢓⡏⣿⡇⣾⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠻⠿⠃⠀⠀⠀⢤⣟⣻⣿⣿⣿⣏⣀⠿⠟⠉⠼⣿⢸⢳⣿⢱⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡗⠀⣀⡿⣿⢘⡽⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣒⣔⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠻⠻⠻⠅⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⡭⠿⠟⠛⠛⠛⠛⠣⠭⠼⠙⣿⣿⣿⣽⣧⣴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⣴⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣵⣿⣼⣿⡿⠯⠭⣄⣐⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣍⣷⠒⡂⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠓⠢⡈⢛⣃⣛⣃⣈⣃⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠂⠧⠀⠀⠀⠀⡀⠉⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠄⠠⠀⠀⠁⠐⠀⠈⠑⠂⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠉⠀⠀⠈⠈⠀⠂⠂⠒

⠀⠀⠲⢶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠁⠁⠉⠈⣸⣝⣫⢝⣯⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣄⠢⡯⠖⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠠⢄⢄⣶⠼⠞⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⣻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢛⣟⣿⣶⣯⣽⣿⡷⢶⣿⣾⠃⣠⣿⣾⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣽⣷⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣾⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢀⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣺⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⠹⣿⢳⡏⣿⡇⣾⣿⣿⣿⢿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠛⠿⠃⠀⠀⠀⢠⣟⣻⣿⣿⣿⣏⡀⠿⠟⠉⠼⣿⢸⢡⣿⢱⣿⣿⣽⣿⣿⣿⢻⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⢻⣿⡗⠀⣀⡿⣿⢘⡽⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣒⣅⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣾⣿⣿⣿⣿⣿⣼⠻⠻⠻⠍⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣛⡛⠿⠿⠣⠍⠼⠽⠿⠯⠿⣽⣧⣴⣧⡸⢳⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⠔⠐⠚⢛⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢼⣿⣭⣭⣀⣐⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠿⠿⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⢑⡒⡒⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣄⠈⣽⡶⣦⡌⠉

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⠀⠛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⠀⣿⡇⣿⣿⠀⢿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡻⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠃⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠋⠀⠛⠷⠟⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣻⣻⣯⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠀⠀⠀⠀⠀⠀⢤⢸⡽⠝⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠰⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠠⣤⣤⣿⠼⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⠠⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢛⣟⣿⣶⣯⣽⣻⡷⢶⣿⣾⠃⣠⣿⣾⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⠋⣿⣷⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣺⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣾⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠛⠿⠃⠀⠀⠀⢦⣟⣻⣿⣿⣿⣏⣀⠿⠟⠉⠸⣿⠸⢣⣿⢱⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡗⠀⣀⡿⣿⢘⡽⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣐⣅⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣼⠹⠻⠻⠍⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⠃⠉⠸⠽⠿⠯⠿⠽⠧⢴⣧⡸⢻⠄⣿⣼⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠙⠋⠁⠀⠘⠒⠚⠚⠛⢿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢑⢢⢿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠢⠤⠤⡀⠀⠀⠀⠀⠀⠀⢘⠓⢒⢒⠄⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢩⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠁⣶⣶⡆⢠⣶⢶⣄⠈⣽⡶⣦⡌⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⢛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠂⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡻⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠃⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀

⠀⠀⠀⠀⠀⠈⠀⠉⠉⠙⢻⣟⣯⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⢀⢸⡽⠝⠻⠋⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠋⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⢤⣤⣄⣶⠼⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣍⢿⢷⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⢾⣿⣿⣿⠀⣿⣿⠀⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢶⣿⣾⠃⣰⣿⣾⠩⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⣷⠋⢠⣼⢿⡯⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣺⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣾⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠛⠿⠃⠀⠀⠀⢦⣟⣻⣿⣿⣿⣏⣀⠿⠟⠉⠼⣿⢸⢣⣿⢱⣿⣿⣽⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⢻⣿⡟⠀⣀⡿⡻⠘⡿⣼⣿⣻⣿⣿⣿⣿⢸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣒⣅⣀⣹⣧⡏⣾⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣼⠹⠿⠿⠅⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣏⣿⣽⡧⠴⠧⠼⠿⠄⠿⠼⠿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠘⠉⠁⠀⠘⠒⠚⣿⢻⡟⣿⣿⣿⣿⣿⣿⠆⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠉⠈⠓⠶⠤⠀⠀⢀⣄⣀⣀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠗⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠴⠬⢥⠀⠲⠒⠢⠤⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠁⣶⣶⡆⢠⣶⢶⣄⠈⣽⡶⣦⡌⠉

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⢛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⠀⣿⡇⣿⣿⠀⢿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡻⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠃⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠀⠛⠃⠘⠻⠾⠋⠀⠛⠷⠟⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⣿⣯⣽⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⢀⢰⡍⠝⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠠⣤⣠⣶⡽⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣏⢿⢿⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢦⣿⣾⠃⣠⣿⣾⠩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⣷⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢠⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣗⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣞⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣾⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠛⠻⠿⠃⠀⠀⠀⢦⣏⣻⣿⣿⣿⣏⣀⠿⠿⠩⠸⣿⢸⢧⣿⢱⣿⣿⣽⣿⣿⣿⢿⠟⣷⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡟⠀⣀⡿⣻⢘⡹⣼⣿⣻⣿⣿⣿⣿⢸⢿⣶⠈⣈⡷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣓⣅⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⡟⠓⣿⣿⣿⣿⣿⣿⣼⠻⠿⠿⠅⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣏⣿⣽⣧⣴⠧⠼⠛⠐⠛⢚⠛⠛⠃⠯⢄⣀⡀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠉⠁⠀⠘⠒⡚⣿⢻⡿⣿⣿⣿⣿⣿⣿⣖⠸⠀⠀⠁⠉⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⣒⣀⢤⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠸⠼⠿⠿⠿⠿⠛⢛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠑⠢⠤⠜⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠈⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉

⠀⠀⢠⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⠀⡛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢈⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠈⠛⠃⠘⠻⠾⠋⠀⠛⠷⠟⠁⠀

⠀⠀⠠⠀⠀⠉⠉⣉⣉⣿⣻⣿⣯⣿⣿⣿⣿⠿⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⢤⢤⣶⣺⡿⠟⠛⠋⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣳⣶⣾⣾⣿⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣍⢿⢿⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣹⣿⣿⣿⣿⡗⠾⣭⣟⡛⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢦⣿⣾⠃⣠⣿⣾⠹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⣿⣷⠋⢤⣼⢿⡿⣭⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣆⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⡿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣻⣿⣻⣤⣾⣿⠈⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠙⠛⠻⠿⠃⠀⠀⠀⢤⣏⣿⣿⣿⣿⣏⡀⠿⠿⠉⠸⣛⢸⢣⢿⢱⣿⣿⣽⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⢻⣿⡟⠀⣀⡿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⠈⣈⡷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣼⠽⠿⠿⠅⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣏⣿⣽⣧⣴⣧⠼⠟⠐⠋⠈⠉⠭⣥⠍⠉⠒⠒⠂⠠⠄⠠⠤⠉⠙⣛⣓⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠉⠉⠁⠀⠘⣴⠚⣿⢻⢿⣿⣿⣿⣿⣿⣿⣖⢸⠐⣆⠁⠋⠁⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡬⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠸⠸⠿⠿⠿⠿⠛⢛⠿⠸⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠜⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⢛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠂⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀

⠀⠀⠀⠀⠈⠈⢈⣩⣝⢿⣛⣻⣯⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢄⠀⣠⣤⣿⣾⡿⠟⠛⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⢿⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⠭⡍⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣤⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣻⡷⢦⣿⣾⠃⣰⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡉⣿⣷⠋⢤⣼⢿⡿⣮⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⡆⣀⣿⣇⣿⢸⣿⢹⣿⣿⣿⣯⣿⡿⣿⢸⣿⠿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢙⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠛⠿⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣏⣁⠿⠿⠡⠼⣿⢸⢳⣶⢳⣿⣿⣽⣿⣿⣿⢿⠟⣿⣆⣀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⢻⣿⡿⠀⣀⡿⣿⢘⡿⣼⣿⣻⣿⣿⣷⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣾⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⡿⠿⠿⠼⠿⢿⣿⣁⣛⠟⣿⠿⠿⠿⢛⣛⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣏⣿⣿⣧⣴⣧⡸⠿⠀⠉⠀⠀⠰⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠉⠉⠁⢠⠘⣴⠚⣿⢻⢻⣿⣿⣿⣿⣿⣿⣆⢸⠐⣆⣅⣿⠷⠋⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠋⠸⠺⠿⠿⠿⠿⠛⢛⠿⠸⡀⢹⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠼⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠐⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀

⠀⠀⠀⠢⠉⢉⢫⣭⣝⣿⣿⣿⣯⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⡀⠔⣴⣖⣥⣦⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠋⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⢿⣷⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠃⣰⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢤⣼⢿⡿⣮⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⠀⢾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢸⣿⢳⡇⣶⡆⣿⣿⣿⣿⣿⣿⡟⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠛⠿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢣⣿⢱⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣛⣯⠭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡿⠀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣷⣿⣸⢿⣶⠈⣈⣷⣿⣿⠿⠿⠛⠛⠛⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⡇⣿⡿⣿⣿⣿⣿⣟⡷⢾⣟⠓⠿⠋⠁⢠⣶⠞⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣯⣴⣧⡼⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠙⠏⠁⠀⠘⣜⠚⣿⢻⢻⣿⣿⣿⣿⣿⣿⣶⢸⡐⣆⣅⣿⣷⣿⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠘⠛⠸⠺⠿⠿⠿⠿⠛⢛⠿⢸⡃⢹⢟⢹⠏⠉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠐⠤⠼⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡇⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⢻⣪⠀⢢⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀

⠀⠀⠠⠒⢛⢉⢩⣿⣟⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⡀⡑⣶⣏⣌⣢⣿⣿⡿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣥⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠃⣰⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢤⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡟⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⢀⣛⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠭⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠛⠿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢣⣿⢱⣿⣿⣽⣿⣿⣿⢿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡿⠀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⡷⠟⠋⣉⣤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⡷⢾⡟⠃⠉⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣽⣯⣴⣧⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠟⠋⠁⠀⠘⠾⠚⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣅⣿⣷⣿⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠘⠛⠰⠻⠿⠿⠿⠿⠛⢛⠿⢸⠇⢹⠏⠻⠏⢉⣉⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠂⡦⠀⠀⠀⠠⠼⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢸⡎⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠈⠻⢠⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠠⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⠈⢀⠩⢿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣅⣤⣽⣿⣷⣾⣿⣿⣿⡿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣥⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣯⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠃⣱⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢤⣼⢿⡿⣯⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⣨⣹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠓⢸⣿⡆⣀⣿⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠫⠭⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢻⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⠿⠟⢋⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⠈⠈⠃⣡⡔⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⡷⢺⠟⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣯⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠉⠉⠉⠉⠍⠛⠋⠁⠀⠸⠿⠺⣿⠟⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⣿⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠠⠀⠀⠘⠸⠘⠛⠠⠿⠿⠿⠿⠿⠛⢛⠿⢸⡇⢹⡏⠻⢏⣉⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠀⠀⠒⣦⡀⠀⠐⠀⠼⢛⡛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡎⢱⡏⢁⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣷⣶⠂⠀⣶⣶⡆⣠⣶⢶⣤⠈⣽⡶⣦⡌⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠠⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⠀⠀⠡⢾⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣠⣽⣾⣾⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣥⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣯⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠇⣰⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢤⣼⢿⡿⣯⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⡿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⣹⣿⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡫⠭⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣯⣿⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢻⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢽⡿⣇⣿⣮⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢷⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⡿⠉⣡⡤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⠄⠈⢄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⡷⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣯⣴⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠉⠩⡍⠉⠛⠋⠁⠀⠘⣾⠻⣿⠟⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⣿⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠄⠀⠠⠀⠀⠈⠸⠘⠛⠐⠿⠿⠿⠿⠿⠛⢛⠿⢸⡇⢻⠏⠿⣏⣩⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠦⠀⠀⠒⣦⣀⠀⠐⠀⠸⠟⣛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡇⢹⡟⢁⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣾⠐⠂⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡌⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⢰⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢶⣦⢹⣿⠈⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⠈⠀⢩⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣶⣽⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣜⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣽⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣯⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠇⣱⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢠⣼⢿⡿⣯⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢴⡿⣿⣿⣿⣿⣿⣿⠟⠋⠐⠖⠀⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⣗⢺⣿⣽⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⠯⠑⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠃⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⡆⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣨⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣧⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡩⠉⠉⠉⠉⠛⠋⠁⠀⠘⢿⢛⣿⠟⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⣿⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠄⠀⠀⠀⠈⠸⠘⠛⠸⠿⠿⠿⠿⠿⠛⢛⠿⢸⡇⠻⢯⣛⣉⣽⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⢦⣀⠀⠀⠀⠘⠛⣛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠈⣶⡏⢻⡏⢁⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢠⣶⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⣠⣶⢶⣤⠈⣽⡶⣦⡍⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⢰⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⣴⣦⢹⣿⠘⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⠀⢉⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣇⣰⣽⣿⣿⣿⣿⣿⣿⡿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡟⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣨⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢛⣟⣿⣶⣯⣽⣿⡷⢷⣿⣿⠇⣱⣿⣾⠹⣸⣿⣿⣿⣿⣿⣿⠿⢛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢠⣼⢿⡿⣮⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢵⡿⣿⣿⣿⣿⠏⠁⠀⠉⠀⠐⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⢺⣿⣽⣿⠏⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⢯⠭⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⠃⠛⠁⠀⠀⠂⠀⠀⠀⠀⠠⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⡏⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⣸⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⠏⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⣧⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⢿⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠀⠀⠄⠠⠀⠀⠀⠸⠘⠛⠰⠿⠿⠿⠿⠿⠛⢛⠿⠸⠇⢽⣏⣩⣭⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢒⢄⡀⠀⠘⠛⣛⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣾⠀⣷⡏⢻⡏⢁⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡍⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⢰⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣯⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⣴⣦⢹⣿⠈⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⡈⢉⢡⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣥⣶⣽⣿⣿⣿⣿⣿⣿⡿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣘⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⠠⣨⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣯⣬⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣾⠇⣱⣿⣾⠻⣸⣿⣿⣿⣿⠟⠋⢭⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢤⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢵⡿⣿⣿⠟⠁⠀⠀⠀⠀⠐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⣗⢺⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⠹⠫⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⣢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⠏⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣿⣿⣿⡇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⣿⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⡆⣇⣿⣷⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠀⠀⠀⠄⠠⠀⠀⠀⠹⠘⠛⠰⠿⠿⠿⠿⠿⠛⢛⠿⠸⢇⣗⣯⣯⣯⣽⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠘⠛⢛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠈⣶⡏⢳⡎⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢡⣶⢶⣤⠈⣽⡶⣦⡍⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠈⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⠀⠀⠩⣿⣿⣻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣅⡴⣽⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣷⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢳⣟⣶⣶⣮⣽⣿⡷⢷⣿⣾⠇⣱⣿⣾⠹⣸⣿⣿⡿⠋⠩⠏⠙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢵⡿⡟⠁⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⣿⡗⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⠆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⡿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⣿⣿⣿⣿⡿⡟⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣦⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⣿⣿⡏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⠿⠻⠏⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⣿⣿⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⣽⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⡆⣅⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠄⠄⠀⠀⠀⠄⠠⠀⠀⠀⠹⠘⠛⠰⠿⠿⠿⠿⠿⠛⢛⠿⢘⣃⣧⣮⣽⣭⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠺⢛⠛⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢱⣾⠉⣶⡏⢺⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠀⠀⢀⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡍⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠠⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⠀⠌⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣴⣽⣿⣿⣿⣿⣿⣿⡿⠿⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣿⣾⣿⣿⣿⠀⣿⣿⠠⣨⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⢟⠃⠀⢺⣟⣿⣶⣮⣽⣿⡷⢷⣿⣾⠇⣠⣿⣾⠙⠜⠋⠀⠒⠂⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠋⢤⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⣿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⠆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⡟⠈⠈⠀⠀⡀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡏⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢦⣯⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣶⣛⣗⣂⣹⣧⡏⣿⣇⣿⡿⣿⣿⢳⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠻⠿⠿⠍⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣽⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⣽⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠄⠀⠀⠄⠀⠀⠀⠀⠹⠘⠛⠲⠿⠿⠿⠿⠿⠛⠛⣻⣼⣦⣥⣯⣽⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠉⠀⠁⠈⠉⠙⡛⢿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢹⣶⠉⣶⡎⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠠⢀⢢⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠀⣼⡶⣦⡌⣉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⠈⢍⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣦⣶⣽⣿⣿⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡿⠁⣭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣿⣾⣿⣿⣿⢀⣿⣿⢠⣨⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢛⣟⢿⣦⣯⣽⣿⡿⢷⣿⣾⠇⣡⣿⣾⠉⠁⠀⠉⠂⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠫⢤⣼⢿⡿⣮⣿⣿⣿⣿⣿⣿⣿⢄⣼⠟⠁⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⣿⣾⣶⣶⣤⡌⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⠆⣀⣾⣧⣿⢸⣿⢹⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢿⡏⣿⡏⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢦⣯⣿⣿⣿⣿⣏⣁⠿⠿⠩⢼⣿⢸⢳⣿⢳⣿⣿⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣦⣛⣗⣂⣹⣧⡏⣿⣇⣿⡿⣿⡏⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⠻⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⣷⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠄⠀⠀⠄⠀⠀⠀⠀⠈⠘⠋⠂⠿⠿⠿⠿⠿⠛⢻⢿⣴⣥⣯⣭⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⠀⠀⠀⠀⠈⠉⠙⠛⢛⠻⢿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠉⢹⣾⠁⣾⡇⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣶⡆⢨⣷⢶⣤⠀⠀⠨⠀⢢⣶⣶⠀⠀⣶⣶⡆⢠⣶⢶⣤⠀⣵⡶⣦⡍⠉

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣿⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣿⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠿⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⠀⠈⠩⣿⣭⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣄⡠⣽⣯⣽⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡍⠟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⡯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡋⡿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣖⣯⣽⣿⡷⢷⣿⣿⠃⣠⡿⠊⠁⠀⠉⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢤⣼⢿⡶⣮⣿⣿⣿⣿⣿⣿⣿⢄⠈⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⡿⣾⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⢆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢷⡏⣿⡇⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢤⣯⣿⣿⣿⣿⣏⣁⠿⠿⠩⠼⣿⢸⢳⣿⢳⣿⣿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣦⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⠻⠿⠿⠏⠝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⣿⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⢇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠤⠁⠀⠀⠈⠀⠀⠀⠀⠀⠤⠄⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⠘⠋⠂⠿⠿⠿⠿⠛⢻⠿⣧⣤⣼⣭⣾⡟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣾⠉⢹⣶⠀⣷⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣷⡆⢨⣷⢶⣤⠀⠀⠬⠀⢢⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣤⠀⣴⡶⣦⡌⠫

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢠⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠃⠀

⠀⠀⠡⡭⢉⠯⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣴⣵⣆⣼⣿⣿⣿⣿⡿⠟⡫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣯⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⠠⣸⣿⣽⣿⣿⣿⣿⣗⠾⣭⣟⡛⡽⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣿⠇⠀⠃⠀⠀⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⠋⣿⣿⠫⢤⣼⢿⡿⣬⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢐⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⡿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⡯⠈⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠸⣿⢸⢳⣿⢳⣿⣿⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣿⣻⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣦⣛⣗⣀⣹⣧⡏⣿⣇⣿⡿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⣿⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠤⠁⠀⠈⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⠘⠃⠇⠿⠿⠿⠛⢛⠿⣯⣥⣼⣬⣽⣼⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠿⢿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣾⠉⢱⣶⠉⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡈⣶⡆⢨⣷⢶⣤⠀⠀⠬⢀⢢⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣴⡶⣦⡄⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠀⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢰⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⣏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀

⠀⠀⠡⠉⢩⣫⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⡿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡄⣄⣥⣤⣾⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠱⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣯⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣴⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡗⠾⣭⣟⡟⡿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⠟⠁⠀⠈⠈⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢠⣼⢿⡿⣬⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠂⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⠐⣿⡿⠤⣾⣿⣶⣆⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠉⠸⣿⢸⢳⣿⢳⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⡿⡀⣀⣿⣿⢘⡿⣼⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⣹⣧⡏⣿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⢿⢛⡿⠻⣿⣿⣿⣿⣿⣿⣿⣞⢸⡐⣆⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⠘⠃⠃⠿⠟⠛⠿⢭⣥⣤⣧⣬⣧⡟⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠻⢿⡿⠿⠿⠿⠿⠿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣾⠈⢸⣷⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡉⣷⡆⢨⣷⢶⣤⠀⠀⠬⢀⢂⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣴⡶⣦⡄⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠀⠐⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢸⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀

⠀⠀⠡⠉⠉⢫⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⣠⣥⣤⣾⣿⣿⣿⣿⡿⠟⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣥⡄⠀⣸⣿⣷⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡗⠾⣭⣟⠛⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⠟⠀⠀⠈⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢠⣼⢿⡿⣬⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠮⣿⣿⣶⢆⣿⣿⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢧⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⡁⠿⠿⠉⠸⣿⢸⢳⣿⢱⡟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡽⣼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣛⣗⣀⣹⣧⡏⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣽⠿⠻⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠚⢿⢛⡿⠻⣿⣿⣿⣿⣿⣿⣿⣾⢸⡐⣆⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⠘⠃⠃⠟⠛⠿⢭⢭⣤⣧⣬⣿⡇⡛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⡿⠿⠿⠿

⠀⠀⠰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠈⢱⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡉⣷⡆⢨⣷⢶⣤⠀⠀⠬⢀⢂⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣵⡶⣦⡄⠀

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⠀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠐⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠛⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀

⠀⠀⠡⣉⠩⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡄⣠⣥⣦⣼⣿⣿⣿⣿⡿⠟⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⡗⠾⣭⡟⢛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⠇⠁⠀⠐⠁⠀⠈⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⠋⣿⣷⠫⢠⣼⢿⡿⣮⣿⣿⡿⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢐⣿⡿⠬⢿⣿⣶⣆⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⡁⠿⠿⠉⠸⣿⢸⢳⣿⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⣹⣧⡏⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠚⢿⢛⡿⠻⣿⣿⣿⣿⣿⣿⣿⣞⢸⡐⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠨⠘⠃⠇⠛⠿⠯⠽⠷⠷⢤⢿⣼⡇⡋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⠿⠿

⠀⠀⠰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠉⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣾⡈⣶⡇⢨⣷⢶⣤⠀⠀⠬⢀⢢⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣽⡶⣦⡄⠀

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠒⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠓⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀

⠀⠀⠀⠉⢩⣫⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⢠⣤⣤⣾⣿⣿⣿⣿⡿⠟⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⢟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣯⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣨⣿⣽⣿⣿⣿⣿⡗⢾⡝⢟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⠛⠃⠀⢻⣟⣿⣶⣯⣽⣿⠏⠇⠀⠑⠀⠀⠀⠾⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠫⢠⣼⢿⡿⣬⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢑⣿⡿⠬⣿⣿⣶⣇⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠆⣀⣾⣇⣿⢸⣿⠹⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣤⣾⣿⠉⢹⣿⢳⡏⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠉⠸⣿⢸⢳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⡀⣀⣿⣿⢘⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣆⣚⣗⣀⣹⣧⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠚⢻⠛⡿⠻⢿⣿⣿⢿⣿⣿⣿⣞⢸⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣚⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠨⠘⠃⠃⠿⠽⠽⠷⠶⢶⠿⣿⢸⡇⡋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣾⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡉⣶⡆⢨⣷⢶⣤⠀⠀⠨⢀⢢⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣄⠀⣽⡶⣦⡌⠁

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⣛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠒⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⠀⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠰⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠈⠛⠃⠘⠻⠾⠋⠀⠛⠷⠟⠁⠀

⠀⠀⠀⠉⢉⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣠⣤⣤⣾⣿⣿⣿⣿⡿⠟⠫⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⢟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣿⣿⣯⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⡭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⡿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⣶⣯⠝⠁⠈⠃⠀⠀⠁⢴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⣿⣿⣿⣿⣿⣿⡏⣿⣷⠋⢠⣼⢿⡿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣯⣽⣿⣿⣿⡟⠑⣿⡿⠬⣿⡿⣶⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⣆⣀⣿⣇⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠩⠸⣿⢸⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⣀⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣚⣗⣀⣹⣧⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠛⠋⠁⠀⠘⢺⠚⡿⠻⢿⠿⠿⢿⣿⣿⣿⣮⢸⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠈⠘⠁⠳⠾⠿⠾⠶⠾⣿⡟⠿⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣶⡆⣶⣶⠀⢠⣶⢶⣤⠀⢰⣶⣶⢰⣶⣶⣶⠀⠀⣶⣶⣶⣄⢰⣶⡆⣶⡆⢰⣶⠀⢰⣶⠀⣶⡆⢰⡆⢀⣴⢶⣦⡀⠀⢰⣶⡀⣾⡆⢨⣷⢶⣤⠀⠀⠨⢀⢂⣶⣶⠂⠈⣶⣶⡆⢠⣶⢶⣤⠈⣽⡶⣦⡍⠉

⠀⠀⠸⣿⡇⣿⣿⠀⣿⣿⢸⣿⠀⣿⡟⣿⡀⢸⣿⠀⠀⠀⣿⣧⣼⡿⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⣷⣼⡇⢸⣿⢀⢛⡃⠀⢸⣿⣧⣿⡇⣿⣿⢸⣿⠀⠐⠒⠀⣼⢻⣿⠀⣸⡟⣿⡇⠉⢉⣼⡟⠀⣿⡇⣿⡇⠀

⠀⠀⢠⣿⡇⣿⣿⠀⣿⣿⢸⣿⢀⣿⣧⣿⡇⢸⣿⠀⠀⠀⣿⡏⢹⣷⢸⣿⡇⣿⡇⢸⣿⠀⢸⣿⠀⣿⡿⣿⡇⢸⣿⠈⣿⡇⠀⢸⣿⢻⣿⡇⣿⣿⢸⣿⠀⠀⠀⢰⣿⣼⣿⣤⣿⣤⣿⣧⢴⣦⢹⣿⠀⣿⡇⣿⡇⠀

⠀⠀⠸⢿⠇⠿⠟⠻⠸⠿⠾⠋⠘⠛⠁⠛⠃⠘⠛⠀⠀⠀⠛⠓⠘⠛⠈⠛⠷⠟⠁⠘⠛⠛⠘⠛⠀⠛⠃⠛⠃⠈⠻⠟⠛⠃⠀⠘⠛⠈⠛⠃⠘⠻⠾⠋⠘⠛⠀⠀⠀⠘⠛⠀⠀⠘⠛⠃⠘⠻⠾⠛⠀⠛⠷⠟⠁⠀

⠀⠀⠡⣩⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⣴⣥⣦⣾⣿⣿⣿⣿⣿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⢟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡍⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣜⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⡷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠛⠃⠀⢻⣟⣿⡶⠋⠁⠢⠀⠀⠉⢿⠇⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠫⢠⣼⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⠑⣿⡿⠬⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢸⣿⡇⣀⣾⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣅⠿⠿⠩⠸⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡟⠀⣀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣂⣹⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣻⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⢻⢛⡿⠻⠿⠿⠿⣿⣿⣿⣿⣞⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⣶⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠄⠀⠀⠠⠤⠀⠀⠀⢀⣀⠄⠠⠀⣀⠀⠈⠈⠓⠶⠾⠾⠶⠾⢿⣟⣛⠿⢸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣣⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⡛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣬⡌⣤⡤⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡄⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢨⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠀⠀⢰⢿⣿⠀⢰⡟⣿⡇⠸⣧⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣼⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢐⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒

⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠨⠽⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣴⣅⣤⣾⣿⣿⣿⣿⣿⠟⠿⠛⠋⠉⠀⠀⠈⠀⠀⠀⠘⠹⠏⠱⠛⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⡀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣔⣏⢿⢿⣿⣷⠿⢻⣵⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣿⣾⣿⣿⣿⠀⣿⣿⢠⣨⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣧⣬⠟⠃⠀⢻⣟⡿⠂⠙⠆⠀⠀⠰⠿⣾⠇⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠫⣰⣼⠟⠀⠀⠀⠀⠀⠁⠀⠀⠈⣄⣼⣿⡏⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⠑⣿⡿⠤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⢹⣿⣗⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠉⢸⣿⣆⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⢹⣿⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢏⢹⡟⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣅⠿⠿⠩⢸⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡗⠀⣀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠚⢻⢻⡿⠻⠿⠿⢿⣿⣿⣿⣿⣮⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⣀⠄⠀⢀⢀⠀⠈⠚⠖⠾⠶⢶⠶⢿⣿⠛⣛⠿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣫⣶⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠈⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣠⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠋⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢨⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢰⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢐⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒

⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠨⠽⢩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣠⣦⣕⣴⣾⣿⣿⣿⣿⣿⠟⠿⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⡀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣏⢿⢿⣿⣷⠿⢻⣴⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠟⠃⠁⠛⢛⡏⠁⠉⢽⣿⡷⢷⣿⣾⠇⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠋⠀⠀⠀⠀⠀⠂⠀⠀⠈⢿⣿⣿⢄⣼⣿⡏⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢑⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⢨⢹⣿⣗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠉⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢤⣿⣿⣿⣿⣿⣏⣁⠿⠿⠉⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣻⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠚⢻⠻⠿⠻⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡿⣸⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⣀⠄⠀⠀⠀⠐⠒⠒⠒⠳⠶⠿⣿⠿⠿⠛⣛⠿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢨⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠘⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⠿⣿⠀⢠⡟⣿⡇⠸⣧⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠰⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣠⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒

⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠿⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠨⢽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣂⣤⣔⣶⣿⣿⣿⣿⣿⣿⠟⡿⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠻⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⢿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⠿⠃⢀⣛⠛⠛⠲⣯⣿⣿⡷⢷⣿⣿⠇⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠋⠀⠁⠀⠐⠀⠠⠈⠹⣿⣿⣿⣿⢄⣼⣿⡏⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡟⢑⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⢨⢹⣿⣗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⡏⢽⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣅⠿⠿⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢿⣶⠈⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣦⡻⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⢚⠻⠛⠿⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣣⣟⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣀⠄⠀⠀⠐⠒⠒⠂⠓⠶⠺⣿⡿⠿⠿⠛⣛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠀⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣬⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠐⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠰⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒

⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠀⠀⠉⢩⣽⣽⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡦⣠⣄⣤⣼⣾⣿⣿⣿⣿⠟⡯⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣷⠷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣐⣏⢿⢿⣿⣷⠿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣬⢛⠃⠀⠿⠟⣿⣶⣯⣽⣿⡷⢷⣿⣿⠃⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⠉⠑⠀⠀⠀⠈⠈⠙⣿⣿⣿⣿⣿⣿⢄⣼⣿⡏⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡟⢑⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⢨⢹⣿⣗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣯⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⡏⢽⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠿⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠻⠻⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣦⢿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⡘⠳⠺⠿⡻⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣋⣾⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢀⣀⠄⠀⠐⠂⠒⠂⠒⠒⠺⣿⡿⠿⠿⠿⠛⣛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⢛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢀⣤⣤⠀⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣬⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠠⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⠿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢠⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣠⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒

⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠨⢙⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣢⣤⣌⣶⣿⣿⣿⣿⣿⣿⠟⡻⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠡⠛⢏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⡀⠀⣾⣿⡟⠁⣭⡝⠟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣏⢿⢿⣿⣷⠿⢻⣤⡆⢀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣿⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢛⠃⠀⢻⡟⠿⣶⣯⣽⣿⡷⢷⣿⣿⠃⣴⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⢟⡋⠁⠀⠘⠛⠻⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣯⣽⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⢩⣹⣿⣗⢺⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣯⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡟⡏⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠇⠀⠀⠀⢦⣿⣿⣿⣿⣿⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣽⣷⣖⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡾⠟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠀⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⠳⠺⣿⠻⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣈⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⢀⡀⠀⠀⠂⠂⠂⠒⠒⠘⢿⡿⠿⠿⠿⠿⠛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠀⠀⢰⢿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠨⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒

⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠠⢝⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣦⣢⣅⣶⣽⣿⣿⣿⣿⣿⠟⡻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⢟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⣀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣘⣍⢿⢿⣿⣷⢿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠂⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡿⢷⣿⣾⠇⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣿⠋⢠⣼⢿⡶⣮⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣿⣽⣿⢿⣟⠉⠀⠉⠉⠈⠻⣿⣶⣧⣿⣿⣿⣿⣿⣿⣿⣯⢩⢻⣿⣗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢦⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣸⢿⣶⢌⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⢫⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣍⣟⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠟⠃⢿⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠘⠿⡚⣿⠻⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⣈⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈⠀⠘⠻⠿⠾⡸⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠀⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⠿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣠⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒

⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠠⠝⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣦⣶⣅⣶⣿⣿⣿⣿⣿⣿⠟⠻⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⣀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣘⣍⢿⢿⣿⣷⢿⢻⣥⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⠟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡿⢷⣿⣾⠇⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡋⣿⣷⠋⢠⣼⢿⡷⣬⣽⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⡿⠿⠿⠑⠿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢩⣹⣿⣗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⡻⠫⠀⠀⠀⠀⠀⠀⢂⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⢸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡏⣿⡇⣿⣿⣿⣿⣿⣿⣟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠇⠀⠀⠀⢤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣸⢿⣶⢌⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣯⣍⡳⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠡⡼⢻⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⠺⣿⠛⣿⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣄⣈⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠛⠻⠟⠾⡸⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⢈⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠈⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢰⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠲

⠀⠀⠺⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠿⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠨⠙⢩⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣠⣠⣅⣦⣿⣿⣿⣿⣿⣿⠟⡻⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠱⠛⢟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⡀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⣍⢿⢿⣿⣷⠿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣹⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡿⢷⣿⣾⠇⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠋⢤⣼⢿⡯⣬⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⡿⠑⣿⡿⠬⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣯⢨⣹⣿⣗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⠟⠛⠿⠛⠃⠸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠀⠀⠹⠈⢹⣿⢻⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠺⢿⣻⣿⣿⣿⣿⣸⢿⣶⢌⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢮⡯⠙⣿⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠘⢷⡼⢻⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠋⠁⠀⢼⢻⠛⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡼⠭⣄⣈⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠘⠟⠏⠛⠾⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⢛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠀⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠈⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣍⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠈⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠒

⠀⠀⠸⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠈⠝⣫⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⣿⠿⠿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣦⣢⣥⣶⣻⣿⣿⣿⣿⣿⠿⡻⠛⠋⠉⠀⠀⠈⠀⠀⠀⠸⠹⠏⠹⠛⢏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠠⣤⡀⠀⣾⣿⡟⢁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣜⣏⢿⢿⣿⣷⠿⢻⣥⡆⢀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⢠⣸⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⢟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡿⢷⣿⣿⠇⣵⣿⣾⠻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⣿⣿⣿⡏⣿⣿⠋⢠⣼⢿⡟⣭⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣾⣿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣯⣽⣿⣿⣿⡿⢑⣿⡿⠬⣿⣿⣶⣧⣿⣿⣿⣿⣿⣿⣿⣯⢨⣻⣿⣗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠟⠛⠛⠋⠉⠛⢦⣾⣿⠉⢸⣿⢷⡏⣿⡇⣿⣿⣿⣿⣿⣿⡟⡟⢹⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠩⠸⣿⢸⢳⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⠿⣼⢿⣻⣿⣿⣿⣿⣸⢿⣶⢌⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠦⡖⡮⢻⣟⡿⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠿⠿⠏⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⣷⡼⢻⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠛⠛⠁⠠⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠫⠭⣄⣘⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈⠻⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠁⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⢛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣬⣤⡀⠈⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣢⣬⡍⢃⣤⣤⡄⠀⣠⣬⣝⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⠿⣿⠀⢠⡟⣿⡇⠸⣇⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣠⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣰⡿⠃⠀⠒⠒⠲

⠀⠀⠺⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠟⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠾⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

⠀⠀⠩⠙⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⣤⣥⣶⢻⣿⣿⣿⣿⡿⠟⠻⠛⠉⠉⠀⠀⠈⠀⠀⠀⠸⠸⠏⠱⠻⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣾⢿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠀⣤⣀⠀⣾⣿⡟⠁⣭⡝⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣔⣏⢿⢿⣿⣷⠿⢻⣤⡆⠀⣸⣿⣷⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣻⣾⣿⣿⣿⠀⣿⣿⣨⣸⣿⣽⣿⣿⣿⣿⣷⠾⣭⣟⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧⣼⣟⠃⠀⢻⣟⣿⣶⣯⣽⣿⡷⢷⣿⣿⠃⣴⣿⣾⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣿⣿⣿⣿⣿⣿⡏⣿⣷⠋⠤⣼⢿⡿⣯⣿⣿⣿⣿⣿⣿⣿⢄⣼⣿⡯⢵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠀⣼⡿⣼⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣿⣿⣿⡿⢑⣿⡿⠬⣿⣿⣾⣆⣿⣿⣿⣿⣿⣿⣿⣯⢨⢻⣿⡗⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⢷⢸⣿⣿⣶⣦⣤⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠁⢸⣿⡆⣀⣾⣇⣿⢸⣿⢹⣿⣿⣿⣿⣿⡿⣿⣸⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠸⠿⢿⣷⣿⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣾⣿⠉⠹⣿⣳⡏⣿⡇⣾⣿⣿⣿⣿⣿⡟⡟⢽⡿⣇⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠙⠛⠻⠿⠃⠀⠀⠀⢤⣯⣿⣯⣿⣿⣏⣁⠿⠟⠉⠹⣿⢹⢣⣿⢳⣿⣿⣽⣿⣿⣿⣿⠟⣿⣆⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⣿⣿⡿⢻⣿⡗⠀⣀⣿⣿⢘⡽⣼⣿⣻⣿⣿⣿⣿⣸⢿⣶⢈⣈⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠁⠈⠁⠀⠙⠃⠋⠛⠁⠡⠈⠹⣿⣿⣿⣟⡷⢾⣟⠓⣿⣿⣿⣿⣿⣿⣽⠿⠻⠻⠏⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣶⣧⡼⢻⢄⣿⣼⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠿⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢹⡿⠭⠭⣀⣘⣿⣛⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⢠⠀⠿⢿⣿⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⠀⠀⠀⠘⢛⠛⢿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⠀⣤⡄⠀⣠⣤⣤⡀⢠⣤⣤⠠⣤⣤⣤⡄⠀⢠⣤⣤⡀⢠⣤⠀⣤⡄⣤⡄⠀⢠⣤⢠⣤⠀⣤⡄⢀⣤⣤⡀⠈⠀⣤⡌⢩⣥⠛⣡⣬⣅⠈⠀⠀⠀⠀⣤⣤⠀⠀⣠⣬⡍⢃⣤⣤⡄⠀⣠⣬⣝⠉⠉⠉⠉

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⢸⡿⣿⡇⠉⣿⡏⠁⠀⢸⣿⣸⡿⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⠀⣿⣇⣿⡇⣿⡇⠸⠿⠀⠀⣿⣿⣸⣿⢸⣿⠀⣿⡇⠀⠐⠀⢰⢿⣿⠀⢠⡟⣿⡇⠸⣧⣸⡿⠘⠛⢰⣿⠀⠀⠀⠀

⠀⠀⢸⣿⠀⣿⡇⠀⣿⡇⣿⡇⣸⣧⣼⣇⠀⣿⡇⠀⠀⢸⣿⢹⣶⢸⣿⠀⣿⡇⣿⡇⠀⢸⣿⢀⣿⢻⣿⡇⣿⡇⢻⣿⠀⠀⣿⡟⣿⣿⢸⣿⠀⣿⡇⠀⠀⠀⣿⣸⣿⣄⣾⣀⣿⣇⢸⡏⢹⣷⠀⣠⡿⠃⠀⠒⠂⠲

⠀⠀⠺⢿⠀⠿⠷⠦⠻⠷⠿⠃⠿⠏⠹⠿⠀⠿⠇⠀⠀⠸⠿⠸⠿⠈⠻⠶⠿⠁⠿⠿⠶⠸⠿⠰⠿⠈⠿⠇⠙⠷⠞⠿⠀⠀⠿⠇⠹⠿⠈⠻⠶⠟⠁⠿⠀⠀⠉⠹⠿⠁⠉⠉⠿⠇⠘⠷⠾⠟⠰⠿⠷⠶⠀⠀⠀⠀

                ䷩ 𝚕𝚒𝚗𝚎 4662

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/09/irc-log-080222/#comments

Gemini version at gemini://gemini.techrights.org/2022/02/09/irc-log-080222/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ IRC_Proceedings:_Tuesday,_February_08,_2022⠀✐

Posted in IRC_Logs at 2:05 am by Needs Sunlight

Also available via the Gemini protocol at:

* gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-080222.gmi

* gemini://gemini.techrights.org/irc-gmi/irc-log-080222.gmi

* gemini://gemini.techrights.org/irc-gmi/irc-log-social-080222.gmi

* gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-080222.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

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                                             (full IRC log

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 QmZ1bdTSeqAGWrkhHaAgv4xRVVfsmxscv5gLnSfRfN71gs #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

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                                             #techbytes

 QmfUrmap41BA4T33JqUekFtEoo9ELRmrFCQrfgsgZ5WmQ9 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈

                                             as plain/ASCII

                                             text)

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 QmSpmWXjBZoyq7JvUVZzbbF5nUig5NwMPdN7FXiswiNmxQ #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈

                                             (full IRC log

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                                             #techrights

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                                             as plain/ASCII

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§ Bulletin for Yesterday⠀➾

Local_copy | CID (IPFS): QmYBkNNgDtvjiZGy3f7RwY487FEsQEUQkXJN3yYkKnMGUa

                ䷩ 𝚕𝚒𝚗𝚎 4789

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Links_10/2/2022:_Epic_Wants_Rootkits_in_Linux_and_Serial_GPL_Violator_VMware

Launches_Vicious_FUD_Attack_on_Linux⠀✐

Posted in News_Roundup at 8:27 pm by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Distributions

      o Devices/Embedded

* Free_Software/Open_Source

* Leftovers

* § GNU/Linux⠀➾

      o ⚓ Chrome_OS_98_Stable_Channel_arrives:_What_you_need_to_know⠀⇛

             According to the official Chrome Release blog, the Chrome

             OS 98 Stable Channel was released on Monday night. All

             supported Chromebooks, Chromeboxes and Chrome OS tablets

             should see the update now, or in the coming days.

             As of Tuesday morning, the main Google site did not have

             any information as to what’s in this update. So here’s a

             rundown on the new features and functions found so far in

             the Chrome OS 98 Stable Channel. Many are experimental

             features.

      o § Desktop/Laptop⠀➾

            # ⚓ Compulab’s_Fitlet3_mini-PC_offers_Elkhart_Lake_and_triple

              M.2⠀⇛

                   Compulab has launched a highly customizable

                   “Fitlet3” industrial mini-PC that starts at about

                   $260 and runs Linux or Windows on Elkhart Lake.

                   Standard features include 2x GbE, 6x USB, HDMI,

                   mini-DP, FACET expansion, and M.2 M-, B- and E-key

                   slots.

                   Compulab has updated its five-year old, Apollo Lake

                   based Fitlet2 mini-PC. The Fitlet3 advances to

                   Intel’s 10nm Elkhart Lake. Aside from the much

                   faster Atom x6000 processor, the Fitlet3 ships with

                   up to 32GB, 3200MT/s DDR4. That is is twice the RAM

                   of the Fitlet2, which is also available as the

                   Linux Mint optimized MintBox Mini 2.

            # ⚓ Fitlet3_is_a_compact,_fanless_Elkhart_Lake_mini_PC_for_IoT

              and_industrial_applications⠀⇛

                   Fitlet3 fanless mini PC based on a choice of three

                   Atom or Celeron Elkhart Lake processors is an

                   upgrade to the Compulab Fitlet2 mini PC introduced

                   in 2017 with Apollo Lake processors.

                   Designed to be used as a fanless industrial mini PC

                   or an IoT gateway, Fitlet3 comes with up to 32GB

                   RAM, supports SATA and NVMe storage, offers two 4K

                   video outputs, up to four Gigabit Ethernet ports,

                   optional WiFi 6E, Bluetooth 5.2, and/or 4G/5G

                   cellular connectivity, as well as a wide range 7V

                   to 42V power input.

            # ⚓ Windows,_macOS,_Chrome_OS,_or_Linux:_Which_Operating_System

              Is_Best?⠀⇛

                   You don’t have a great many choices when it comes

                   to your computer’s operating system, but the choice

                   that you make can have wide-ranging consequences.

                   The five OSes included here are your most viable

                   options. That’s not a huge number, but these

                   operating systems differ distinctly in strengths

                   and weaknesses. Four come from gargantuan

                   commercial tech giants, while one, the Linux-based

                   Ubuntu, is a free, open-source option. Windows and

                   macOS are generally the most powerful in terms of

                   hardware and software selection as well as

                   interface conveniences and utilities, while Chrome

                   OS is more lightweight and runs on inexpensive

                   hardware.

            # ⚓ Best_desktop_Linux_for_pros_2022:_Our_top_5_choices_|

              ZDNet⠀⇛

                   You knew Fedora, Red Hat’s community Linux

                   distribution, would be first on my list. It’s the

                   mainstream distro that pushes Linux’s limits. It

                   comes powered by the newest Linux kernel and with

                   the latest open-source software.

                   In particular, Fedora is the Linux of choice for

                   programmers. No less a figure than Linus Torvalds

                   uses Fedora for his development work. Need I say

                   more?

                   Sometimes, however, when you’re running a leading-

                   edge distro, you can cut yourself. There’s a reason

                   why Fedora’s also known as a bleeding-edge Linux.

                   On the other hand, Fedora is easy to install and

                   set up. You don’t need to be a Linux expert to get

                   up and running with it.

                   For programmers, Fedora also boasts an excellent

                   Developer Portal. It features dedicated guides on

                   developing command line, desktop, mobile, and web

                   apps.

                   The Fedora Developer Portal also comes with an

                   excellent guide for developing hardware devices

                   such as Arduino and Raspberry Pi. Last but not

                   least, it comes with such development tools as the

                   top-notch integrated development environment (IDE)

                   Eclipse for Java, C/C++, and PHP and Vagrant, a

                   tool for creating reproducible, portable container

                   or virtual machine (VM)-based development

                   environments.

                   Unless you’re working on the Debian/Ubuntu family

                   programs, Fedora should be your first choice for a

                   development operating system. For developers in

                   that group, I recommend the newest version of

                   Ubuntu.

            # ⚓ Best_Linux_distros_for_beginners_in_2022:_You_can_do_this!

              |_ZDNet⠀⇛

                   Some people still insist that using Linux is hard.

                   Sure, it was difficult — when I started with the

                   Linux desktop back in the 1990s. But that was a

                   long time ago. Today, the easiest desktop of all,

                   Chrome OS, is simply Linux with the Chrome web

                   browser on top of it. The more full-featured Linux

                   desktop distributions are as easy to use in 2021 as

                   Windows or macOS.

                   Yes, you can get a lot more from Linux if you know

                   how to do shell programming and the like. But

                   that’s also true of Windows and PowerShell. With

                   both operating systems, you don’t need to know the

                   deep ins and outs of either one to get your work

                   done.

      o § Kernel Space⠀➾

            # ⚓ From_Prototype_to_Post_Deployment:_Linux_Decision_Points⠀⇛

                   There were four options given:

                   1) Choose roll-your-own based on Yocto Project

                   Linux, Debian, or something similar: 27 %

                   2) Choose Linux provided through a semiconductor or

                   board vendor: 17 %

                   3) Choose Linux from a commercial open source

                   provider: 10 %

                   4) Continue evaluating whether you want to use

                   Linux: 45 %

                   It is interesting that the number of respondents

                   choosing Linux from a commercial OS provider is not

                   higher than 10%. Additionally, given recent trends

                   around the migration to Linux for embedded

                   development, it is surprising that 45% of the

                   audience was still evaluating whether to use Linux

                   at all.

            # § Graphics Stack⠀➾

                  # ⚓ AMD_looking_for_more_Linux_help_to_reach_client-

                    stages_on_the_open-source_platform⠀⇛

                  # ⚓ Intel’s_Open-Source_Linux_Driver_now_offers_Vulkan

                    “ANV”_ray-tracing_support⠀⇛

                         With the impending launch of Intel Arc GPUs

                         with new ray-tracing technology approaching

                         soon, the company has introduced further

                         open-source “ANV” Vulkan support for the

                         Linux operating system. In the latest driver

                         update, this new support is filed under

                         “VK_KHR_ray_query.”

      o § Applications⠀➾

            # ⚓ DeskCut_Helps_You_to_Create_Linux_Desktop_Shortcuts_with

              Ease⠀⇛

                   This article explains briefly how to create useful

                   and standard-compliant desktop entries on Linux by

                   using the DeskCut app.

                   Have you ever installed a program in Linux from an

                   outside source and wished that it had a convenient

                   entry in your desktop environment’s menu? While

                   most GUI programs automatically create their

                   desktop shortcut during installation, some

                   applications may require you to set up associated

                   shortcuts manually.

                   And this is where DeskCut comes on the scene. But

                   before that, let’s explain what Linux shortcuts

                   actually are.

      o § Instructionals/Technical⠀➾

            # ⚓ How_To_Install_Plex_Media_Server_on_Fedora_35_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   Plex Media Server on Fedora 35. For those of you

                   who didn’t know, Plex Media Server is a self-hosted

                   media player system for storing your movies, shows,

                   music, and photos. Over time Plex Media Server has

                   grown much and now supports many platforms.

                   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 Plex Media Server on a Fedora

                   35.

            # ⚓ How_to_Install_Nginx_on_WHM/cPanel_With_Engintron_–

              RoseHosting⠀⇛

                   In this tutorial, we are going to explain how to

                   Install Nginx with Engintron on a server with WHM/

                   cPanel control panel installed.

                   Engintron is a free WHM/cPanel plugin that can be

                   used for installing the Nginx web server as a

                   reverse proxy of the default Apache webserver. The

                   reason for using the Nginx as a reverse proxy of

                   Apache on our WHM/cPanel server is that the Apache

                   will server the dynamic content such as PHP, Perl

                   and etc, and the Nginx will be responsible for

                   serving the static content like CSS, Javascript,

                   and images.

                   Installing Nginx with Engintron to your cPanel

                   server can take a few minutes and is a very easy

                   process. Let’s get to work!

            # ⚓ How_to_install_InfluxDB_2_on_Debian_11_–_NextGenTips⠀⇛

                   InfluxDB is an open-source time-series database. It

                   is used for storage and retrieval of time series

                   data in fields such as operation monitoring,

                   operations metrics, internet of things sensor data,

                   and real-time analytics. In this tutorial, we are

                   going to learn how to install InfluxDB on Debian

                   11.

                   By default, InfluxDB uses the following network

                   ports for communication.

            # ⚓ How_to_install_Google_PageSpeed_to_improve_NGINX

              performance_–_News_Update⠀⇛

                   Google PageSpeed is an open-source module, created

                   by Google, to help make web pages load faster. This

                   added speed is achieved by rewriting them for

                   better latency and decreasing bandwidth. Although

                   PageSpeed has been around for some time, it’s not

                   often used. However, by adding it to your NGINX or

                   Apache websites, you’ll find they perform

                   considerably better.

                   I’m going to show you how to install both NGINX and

                   PageSpeed, so your users can enjoy a much-improved

                   experience with your web pages. We are going to

                   install everything from scratch, so you’ll want to

                   do this on a non-production machine first. Once

                   you’ve mastered this, move it to production and

                   then migrate your sites to the new web server.

            # ⚓ How_to_easily_install_minix_3.3.0⠀⇛

                   This is an screen by screen guide on how to install

                   minix 3.3.0.

            # ⚓ Install_and_use_WPscan_(WordPress_security_scanner)_in

              Linux⠀⇛

                   WPScan is a free, for non-commercial use, black box

                   WordPress security scanner written for security

                   professionals and blog maintainers to test the

                   security of their sites.

            # ⚓ Install_Metasploit_Framework_on_Ubuntu_22.04/Ubuntu_20.04_–

              kifarunix.com⠀⇛

                   In this tutorial, you will learn how to install

                   Metasploit Framework on Ubuntu 22.04/Ubuntu 20.04

                   LTS. Metasploit Framework provides a platform and

                   tools for performing deep system security auditing

                   as well as penetration testing to unearth, exploit

                   and validate every other would-be vulnerability.

            # ⚓ How_to_install_Peppermint_OS_2022-02-02_–_Invidious⠀⇛

            # ⚓ How_to_install_OpenVPN_Client_on_Debian_11_Bullseye_–_Linux

              Shout⠀⇛

                   Learn the steps to install OpenVPN client on Debian

                   11 Bullseye Linux to connect VPN server for

                   establishing a secure connection. It was programmed

                   by James Yonan and was first released in 2001 under

                   the open-source license.

                   OpenVPN is a popular open-source software freely

                   available. It is available in a client-server

                   architecture and can be installed on computers,

                   servers, or network devices such as routers and

                   supports operating systems such as Windows, Linux,

                   macOS, Solaris, OpenBSD, Android, and many more.

                   It can be used to implement encrypted private

                   networks between individual clients or entire

                   networks. For the connection to be established, the

                   OpenVPN software must be available and suitably

                   configured on both sides. The software transmits

                   the user data via TCP or UDP packets. The VPN

                   software can also be used across NAT borders (NAT –

                   Network Address Translation). The data exchanged in

                   the VPN is via SSL/ TLSencrypted. The OpenSSL

                   library is used for encryption.

            # ⚓ Ubuntu_Linux_PC_Won’t_Boot?_5_Common_Issues_and_Fixes⠀⇛

                   You’ve switched on your computer, preparing to do

                   some work, edit a document, mix a composition, or

                   just play a game… but something goes wrong.

                   Ubuntu won’t boot.

                   Sadly, as reliable as Linux is in general, and as

                   popular as Ubuntu is, sometimes it runs into

                   problems, just like Windows 10 or macOS. In most

                   cases, you’ll be able to work around this.

                   Whether you’re using Ubuntu desktop or Ubuntu

                   Server, here’s what to do if Ubuntu doesn’t boot.

            # ⚓ What_Is_Log4Shell_and_How_to_Protect_Your_Linux_System

              Against_It⠀⇛

                   The Log4Shell (CVE-2021-44228) vulnerability is

                   described by many cybersecurity researchers and

                   experts to be the most critical zero-day

                   vulnerability of all time. It affects a widely-used

                   Java utility by the name of Log4j, which has been

                   around since 2001 for logging and communicating

                   events, such as routine system operations and

                   software errors. Here we show you how to protect

                   your Linux system against it.

            # ⚓ 100%_easy_Open-source_VPN_and_Proxy_with_podman⠀⇛

                   OpenConnect VPN is not officially supported by or

                   associated in any way with Cisco Systems, Juniper

                   Networks, Pulse Secure, Palo Alto Networks, F5,

                   Fortinet, or any of the companies whose protocols

                   we may support in the future. It just happens to

                   interoperate with their equipment. Trademarks

                   belong to their owners in a somewhat tautological

                   and obvious fashion.

                   An openconnect VPN server (ocserv), which

                   implements an improved version of the Cisco

                   AnyConnect protocol, was also written.

                   OpenConnect VPN server is an SSL VPN server that is

                   secure, small, fast, and configurable. It

                   implements the OpenConnect SSL VPN protocol and has

                   also (currently experimental) compatibility with

                   clients using the AnyConnect SSL VPN protocol. The

                   OpenConnect protocol provides a dual TCP/UDP VPN

                   channel and uses the standard IETF security

                   protocols to secure it. The OpenConnect client is

                   multi-platform and available here. Alternatively,

                   you can try connecting using the official Cisco

                   AnyConnect client (Confirmed working on Android).

                   For the HAproxy tutorial, you can try the link.

            # ⚓ Failed_to_download_metadata_for_repo⠀⇛

            # ⚓ Bash_Scripting:_Check_if_file_exists⠀⇛

            # ⚓ Bash_Scripting:_Check_if_directory_exists⠀⇛

                   When writing a Bash script, it is common that

                   you’ll run into the need to check for the existence

                   of a directory. Based on the result, your Bash

                   script can proceed with the appropriate action.

                   This functionality can be written into a Bash

                   script or used directly from the command line,

                   without writing a script for it. In this tutorial,

                   you will see how to check if a directory exists in

                   Bash on Linux systems.

            # ⚓ MySQL:_Allow_user_access_to_database⠀⇛

                   After installing MySQL on your Linux system and

                   creating a new database, you will need to setup a

                   new user to access that database, granting it

                   permissions to read and/or write data to it.

                   It is not recommended to use the root account, but

                   rather create a new account and grant privileges as

                   needed. In this tutorial, you will see how to allow

                   a user to access a MySQL database on Linux.

            # ⚓ MySQL:_Allow_access_from_specific_IP_address⠀⇛

                   If you need to allow remote access to your MySQL

                   server, a good security practice is to only allow

                   access from one or more specific IP addresses. This

                   way, you are not needlessly exposing an attack

                   vector to the entire internet.

                   In this tutorial, we will take you through the step

                   by step instructions to allow remote connections to

                   a MySQL server from a specific IP address on a

                   Linux system. These instructions should work

                   independently of whichever Linux distro you are

                   using.

            # ⚓ MySQL:_Allow_remote_connections⠀⇛

                   After installing a MySQL server on a Linux system,

                   by default it will only accept incoming connections

                   from itself (i.e. the loopback address 127.0.0.1).

                   This default configuration works perfectly fine if

                   you are only trying to read or write information

                   from the database on the same server. So users that

                   host their website and MySQL server on the same box

                   won’t need to do any extra configuration to allow

                   remote connections.

                   If you want to allow remote connections to your

                   MySQL server, because you have other computers and/

                   or users that need to access that data, you will

                   need to bind the MySQL service to a public IP

                   address on your server, and perhaps allow incoming

                   MySQL connections through your system firewall.

                   In this tutorial, we will take you through the step

                   by step instructions to allow remote connections to

                   a MySQL server on a Linux system. These

                   instructions should work independently of whichever

                   Linux distro you are using.

            # ⚓ Building_a_Docker_image_in_Jenkinsfile_and_publishing_to

              ECR_–_Octopus_Deploy⠀⇛

                   In this post, you learn how to build and push the

                   Octopus Deploy underwater app to Amazon Elastic

                   Container Registry (ECR) using Jenkins.

      o § Games⠀➾

            # ⚓ Lilbits:_Fortnite_for_Linux_isn’t_happening,_Vivo_NEX_5

              specs_leaked,_MAME_turns_25_–_Liliputing⠀⇛

                   While Valve’s game client has been able to run on

                   Linux for years, as of last month just over 1% of

                   Steam users were running Linux (and fewer than 3%

                   were using macOS, with Windows holding a 96%

                   share). It’ll be interesting to see if that starts

                   to change once the Steam Deck hits the streets. And

                   if it does, maybe we’ll see more game makers add

                   support for Linux… but one of the most popular

                   games around isn’t going to add Linux support

                   anytime soon: Epic CEO Tim Sweeney says the company

                   has no plans to port Fortnite to Linux.

                   He says it’s because Epic doesn’t “have confidence

                   that we’d be able to combat cheating at scale under

                   a wide array of kernel configurations including

                   custom ones,” but it’s an interesting take since

                   Epic has already ported its anti-cheat software to

                   support Mac and Linux devices including the Steam

                   Deck.

                   That means third-party games that use Epic’s Easy

                   Anti-Cheat software should be compatible with the

                   Steam Deck. But Epic’s own Fortnite won’t be one of

                   those games.

                   Then again, Fortnite also isn’t available in the

                   Steam Store, so it’s not like it’s a huge surprise

                   that the company doesn’t want to make it too easy

                   for you to play its massively popular game on a

                   device that may lock you into a rival’s ecosystem.

                   But the Steam Deck is basically a PC, and while it

                   will ship with Steam OS, it’s also capable of

                   running Windows. And that could provide folks

                   willing to install an alternate operating system a

                   way to play Fortnite or any other games that may

                   not be available or play well under Linux.

            # ⚓ Fortnite_Is_Never_Coming_To_The_Steam_Deck_–_Invidious⠀⇛

                   With EAC and Battleye now being supported on Linux

                   and by extension the Steam Deck someone asked Tim

                   Sweeney if Fortnite is coming to the Steam Deck and

                   he had a simple answer no, but his reasoning is

                   interesting

            # ⚓ Epic_Is_Worried_About_Fortnite_Cheaters_on_Linux [Ed:

              Worried about the freedom of the platform, Epic wants to put

              rootkits in Linux]⠀⇛

                   Epic Games makes Fortnite, which is one of the

                   biggest video game phenomenons in recent history.

                   Because the game is so popular, fans wondered

                   whether it would make its way to Valve’s Steam

                   Deck, but it appears Epic is too worried about

                   cheaters on Linux to make it happen.

            # ⚓ Tim_Sweeney_has_a_point_about_Fortnite_EAC_support_|

              GamingOnLinux⠀⇛

                   One of the big topics of discourse in the Linux

                   gaming sphere recently has been Tim Sweeney’s

                   statement on porting Fortnite to the Steam Deck,

                   where Sweeney argues that Linux would be too

                   difficult of a target and the market not big enough

                   to warrant the amount of resources it would take to

                   bring all of Fortnite on the platform.

                   The central crux of the issue, from Sweeney’s point

                   of view, is that making Easy Anti-Cheat, with all

                   of its capabilities, run on Steam Deck (and thus on

                   Linux) would be extremely difficult. He argues,

                   that for a game of Fortnite’s size this would open

                   the flood-gates to significant influx of cheaters.

                   There have been some responses to this from the

                   Linux side, with some accusing Sweeney of

                   exaggerating the difficulty of such a port or that

                   his statements are conflicting, because he

                   simultaneously believes the Linux market is too

                   small to be worthwhile but also would provide a way

                   for too many cheaters. I will address some of these

                   aspects a bit later, but for now let’s focus on the

                   main technical blocker, which is Easy Anti-Cheat.

            # ⚓ Proton_vs_Native:_Is_There_Really_A_Difference?_–_Boiling

              Steam⠀⇛

                   The debate over emulation or translation and native

                   games is at least as old as projects like Wine for

                   Linux, and more generally as old as gaming

                   platforms. More recently Proton and DXVK are the

                   stars, but there have been other tools in the past,

                   like VOGL (to translate DirectX 9 to OpenGL, used

                   in CS:Go, for example). Rather than rehash the same

                   debate here, what I would like to do is explore and

                   pose some questions. Not questions like which is

                   “better” (for whatever your definition of

                   “better”), but to think a bit more deeply about

                   another aspect of this debate. To me, much of the

                   endless back and forth comes down to this: is there

                   really a difference between native and tools like

                   Proton?

                   Hold your flames and passioned arguments please!

                   I’m not here to make the case for one side or the

                   other or throw my hands up to say “it doesn’t

                   matter,” but to attempt to go beyond our surface

                   arguments and see where that may lead us.

            # ⚓ Valheim_developers_have_another_fireside_chat_filled_with

              teasers_|_GamingOnLinux⠀⇛

                   Ready for even more content to come to Valheim?

                   Well, there’s still a bit of a wait and the

                   developers teased biome updates previously but

                   there’s more to see – and hear.

                   In a fresh fireside chat, with a much upgraded

                   seating area that’s no longer just a fire in a

                   forest, three members of Iron Gate had a talk about

                   the game now it’s one year on from the Early Access

                   release. The fun thing is that this is clearly an

                   unreleased build, as there’s multiple sneaky new

                   things surrounding them. Their official Twitter

                   account even teased “How many sneak peeks can you

                   spot?”.

            # ⚓ Godot_Engine_–_Dev_snapshot:_Godot_4.0_alpha_2⠀⇛

                   Two weeks ago we finally released Godot 4.0 alpha 1

                   ― the first official alpha build of our upcoming

                   major milestone, enabling all interested users to

                   try it out and report bugs, as well as provide

                   feedback on the new features.

                   We got lots of bug reports and many have been fixed

                   already in these two weeks! To keep iterating on

                   stabilizing the 4.0 branch, we’re going to release

                   new alpha builds every other week, so that testers

                   can always have a recent version to test the latest

                   changes.

                   So here’s Godot 4.0 alpha 2 with a great deal of

                   fixes and new features!

                   Be aware that during the alpha stage the engine is

                   still not feature-complete or stable. There will

                   likely be breaking changes between this release and

                   the first beta release. Only the beta will mark the

                   so-called “feature freeze”.

                   As such, we do not recommend porting existing

                   projects to this and other upcoming alpha releases

                   unless you are prepared to do it again to fix

                   future incompatibilities. However, if you can port

                   some existing projects and demos to the new

                   version, that may provide a lot of useful

                   information about critical issues still left to

                   fix.

                   Most importantly: Make backups before opening any

                   existing project in Godot 4.0 alpha builds. There

                   is no easy way back once a project has been

                   (partially) converted.

            # ⚓ Wordle_Reverse-Engineering_And_Automated_Solving_|

              Hackaday⠀⇛

                   We don’t know about you, but we have mixed feelings

                   about online puzzle fads. On one hand, they are

                   great tool to help keep one sharp, but they’re just

                   everywhere. The latest social-media driven fad,

                   Wordle, may be a little bit too prevalent for our

                   liking, with social media timelines stuffed with

                   updates about the thing. [Ed Locard] was getting a

                   bit miffed with friends’ constant posts about

                   ‘Today’s Wordle’, and was hoping they’d get back to

                   posting pictures of their dogs instead, so did what

                   any self-respecting hacker would do, and wrote a

                   python script to automate solving Wordle puzzles,

                   in a likely futile attempt to get them to stop

                   posting.

      o § Desktop Environments/WMs⠀➾

            # ⚓ Give_Your_Linux_Mint_and_Xubuntu_a_Visual_Uplift_Using

              Twister_UI⠀⇛

                   Twister UI is the easiest way to give your Linxu

                   Mint and XUbuntu a visual uplift using pre-loaded

                   themes. Here’s how.

            # § K Desktop Environment/KDE SC/Qt⠀➾

                  # ⚓ KDE_Community_releases_Plasma_5.24:_It’s_eccentric,

                    just_like_many_old-timers⠀⇛

                         The new release of KDE’s Plasma desktop

                         brings a GNOME Shell-like instant overview

                         and other improvements.

                         KDE is fairly mature now. The FOSS community

                         was founded in 1996, allowing it to call last

                         year’s Plasma release, 5.23, the 25th

                         Anniversary Edition. KDE 1.0 came out in

                         1998, making it the first FOSS desktop for

                         Linux. It does also support FreeBSD, although

                         not always the latest version.

                  # ⚓ Plasma_Mobile_Gear_22.02_is_Out⠀⇛

                         The Plasma Mobile team is happy to announce

                         the Plasma Mobile updates for January to

                         February 2022.

                         Plasma 5.24 was released on February 8th,

                         with many changes to the Plasma Mobile shell.

                         The primary shell repository (and

                         corresponding package name for distributions)

                         has been renamed from plasma-phone-components

                         to plasma-mobile. Devin Lin did a lot of work

                         on the shell for this release.

                  # ⚓ KDE_Neon_vs_Kubuntu_vs_KDE_Plasma⠀⇛

                         One of the best aspects of using a Linux

                         system is that there are many popular desktop

                         environments to choose from. If you do not

                         like the style or behavior of yours, it is

                         simple enough to install a different one.

                         When it comes to the KDE Plasma desktop

                         environment, there are a few different ways

                         to experience it. KDE Plasma comes not only

                         as a graphical user interface, but also

                         includes a slew of applications (over 200;

                         some installed by default and some not) that

                         integrate into the desktop environment and

                         give the user a more unified experience that

                         flows together.

                         If you are ready to try out KDE Plasma, you

                         have a few choices. First of all, you can

                         install it the same way you would any other

                         desktop environment – right from your

                         system’s package manager. But you can also

                         choose from the KDE Neon and Kubuntu Linux

                         distributions.

                         So, which one should you choose? We will go

                         over all the details in this article and help

                         you make an informed decision.

                  # ⚓ More_wlroots_with_KWinFT_5.24_–_subdiff.org⠀⇛

                         In the last year our development focus for

                         KWinFT was on the integration with the

                         wlroots library. In a single sentence our

                         goal with this is to share underlying

                         architecture, patterns and ideas across the

                         Wayland ecosystem, instead of reimplementing

                         things again and again for each and every big

                         project while leaving smaller ones behind.

                         Only a few months ago in October a first

                         iteration of this integration was released

                         with KWinFT 5.23. I talked about it here on

                         this blog and at X.Org Developer Conference

                         (XDC) 2021 in a talk including a primer on

                         wlroots itself.

                         If you’re interested in that first part of

                         integration specifically or a wlroots primer

                         in general check out my talk on YouTube.

            # § GNOME Desktop/GTK⠀➾

                  # ⚓ GNOME_42_Adds_’Dark_Wallpaper’_Support⠀⇛

                         Simply put: when the new standardised dark

                         mode setting is enabled in GNOME 42 a ‘dark’

                         version of the default wallpaper is applied.

                         When light mode is enabled, a ‘light’ version

                         of the wallpaper is applied. If this all

                         sounds a bit familiar it’s probably because I

                         mentioned this was on the way last month when

                         I wrote about the streamlining of wallpaper

                         options in GNOME 42.

                         Naturally, you are free to override this

                         behaviour and set any image you like as the

                         desktop background, regardless of whatever

                         dark mode preference is active.

                  # ⚓ Turbocharging_GNOME_Nightly_and_GNOME_OS

                    infrastructure⠀⇛

                         Mistakes were made¹, and after recent

                         maintenance, Jordan asked Infrastructure Team

                         if there is a chance GNOME Nightly (and its

                         younger sibling GNOME OS) could be moved

                         somewhere with faster network and more

                         storage. After short discussion, we decided

                         to move it to AWS (thanks to promotional

                         credits for open source projects). The new

                         server has three times more space, uses SSD

                         instead of HDD, and should offer up to 10

                         Gbps of network bandwidth.

                         It quickly became apparent we underestimated

                         GNOME Nightly popularity by a large margin.

                         On the second day, the new server transmitted

                         almost 500 GB of data. As we wanted to limit

                         potential egress costs, we reached out to

                         CDN77, and they quickly agreed to help us.

                         CDN77 team aren’t stranger to the open source

                         world, helping other projects like KDE,

                         Gentoo and Manjaro.

                  # ⚓ 7_New_Features_That_Make_GNOME_42_an_Awesome_Release

                    –_It’s_FOSS_News⠀⇛

                         GNOME 42 will be an interesting release.

                         It includes noticeable visual changes and

                         improvements to the desktop experience. Of

                         course, the changes in GNOME 41 compliments

                         the new release as well.

                         GNOME 42 is due on March 23, 2022, but it has

                         almost reached beta (scheduled for February

                         12, 2022).

      o § Distributions⠀➾

            # ⚓ Theme_in_EasyOS_3.3⠀⇛

                   The snapshot was taken on a 1024×768 monitor, which

                   is the smallest resolution that is practical to use

                   with EasyOS. You can see the icons along the top,

                   anything less than 1024 pixels, say 800 pixels, is

                   going to be a problem.

                   In a running Easy, you will see there is a file /

                   root/.packages/default-theme. This is used in woofQ

                   to set the theme, and is included in the release

                   build so that users can see the choices made. Here

                   is the file for Easy 3.3…

            # ⚓ Icon-free_desktop_peach_theme⠀⇛

                   By using the ‘xdotool’ utility, the “Drives” menu

                   will now automatically popup whenever a drive is

                   plugged in.

                   On a screen that is smaller than 1920 pixels wide,

                   the app labels automatically do not display. Here

                   is a snapshot on a 1024×768 screen…

            # ⚓ Experimental_icon-free_desktop⠀⇛

                   I have wanted to try this for a long time, a

                   desktop completely free of icons. You could then

                   have, say, a beautiful nature scene filling almost

                   the entire screen, unmarred by icons. Also, you

                   will no longer have to shove windows aside to get

                   at underlying icons.

                   ROX-Filer is not just a file manager, it also

                   manages the desktop icons and wallpaper. However,

                   it is possible for JWM window manager to display

                   all of the icons, in one or more trays, and also be

                   responsible for the wallpaper.

                   One big problem is the drive partition icons, that

                   will dynamically change as partitions are mounted

                   and unmounted, and drives plugged in and removed.

                   Implementing dynamic drive icons in a JWM tray is

                   not feasible; however, it can be done as a menu.

            # § BSD⠀➾

                  # ⚓ Why_you_should_read_Section_8_of_the_Unix_User’s

                    Manual_•_The_Register⠀⇛

                         If, like me, you were a computer-science

                         graduate student who cut your teeth on

                         Berkeley Unix – complete with the first open-

                         source implementation of TCP/IP – you know

                         Section 8 as the cryptic System Maintenance

                         Commands section of the Unix User’s Manual.

                         It was obvious, to me, that this concluding

                         section warranted a closer look because the

                         introduction warned: “Information in this

                         section is not of great interest to most

                         users.” Judging by my taste in research

                         problems over the years, reading Section 8

                         turned out to be a pretty good investment.

                         But before getting to Section 8, you first

                         learned about the rest of Unix, where you

                         discovered how empowering it is to be able to

                         build new internet applications. Anyone

                         interested in how targeted investments in

                         open-source software, coupled with affordable

                         hardware, can spur innovation should study

                         the role of the Berkeley Software

                         Distribution (BSD) in the success of the

                         internet.

            # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾

                  # ⚓ Mozilla_Thunderbird_update_»_PCLinuxOS⠀⇛

                         Thunderbird, the email client from Mozilla

                         has been updated to 91.6.0 and shipped to the

                         PCLinuxOS Software Repository.

                  # ⚓ Firefox_browser_update_»_PCLinuxOS⠀⇛

                         Firefox, the web browser from Mozilla has

                         been updated to 97.0 and sent to the software

                         repository.

                  # ⚓ Kernel_updates_available_»_PCLinuxOS⠀⇛

                         Current kernels:

                         kernel-5.4.178-pclos1-1-1pclos2022.x86_64.rpm

                         kernel-5.10.99-pclos1-1-1pclos2022.x86_64.rpm

                         kernel-5.15.22-pclos1-1-1pclos2022.x86_64.rpm

                         kernel-5.16.8-pclos1-1-1pclos2022.x86_64.rpm

            # § IBM/Red Hat/Fedora⠀➾

                  # ⚓ 3_ideas_for_bringing_innersource_to_your_company_|

                    Opensource.com⠀⇛

                         As workforces become more distributed and new

                         tools and processes enable more effective

                         asynchronous communication, innersource is

                         very likely to keep changing the work culture

                         as we know it.

                  # ⚓ Comparison_of_Fedora_Flatpaks_and_Flathub_remotes_–

                    Fedora_Magazine⠀⇛

                         In the previous article in this series, we

                         looked at how to get started with Fedora

                         Flatpaks and how to use it. This article

                         compares and contrasts between the Fedora

                         Flatpaks remote and the Flathub remote.

                         Flathub is the de-facto standard Flatpak

                         remote, whereas Fedora Flatpaks is the Fedora

                         Project’s Flatpak remote. The things that

                         differ between the remotes include but are

                         not limited to their policies, their ways of

                         distribution, and their implementation.

                  # ⚓ GitOps_using_Red_Hat_OpenShift_console_4.9_and_4.10_|

                    Red_Hat_Developer⠀⇛

                         This article introduces new Red Hat OpenShift

                         developer console features supporting GitOps

                         processes for applications running in the

                         cloud. Learn about improvements and updates

                         to the OpenShift GitOps Operator, then watch

                         a video showing how to manage cluster

                         configurations and deliver cloud-native

                         applications using Red Hat OpenShift GitOps

                         in the developer console.

                         [...]

                         OpenShift GitOps supports GitOps processes

                         for cloud-native applications. It is built on

                         top of Argo CD, a declarative GitOps

                         continuous delivery tool for Kubernetes, and

                         includes OpenShift’s GitOps Operator and

                         Pipelines Operator, both available from the

                         OpenShift OperatorHub. Figure 1 shows the

                         development flow and tools OpenShift GitOps

                         provides.

                  # ⚓ The_State_of_Customer_Experience_at_Red_Hat:_Where

                    we’ve_been_and_where_we_are_going⠀⇛

                         In the final part of our three-part blog

                         series on the state of customer experience at

                         Red Hat, we will cover enhancements that our

                         marketing teams made in 2021 based on

                         customer feedback. In addition, we will recap

                         where we have been and will look ahead at the

                         plans we have as an organization in 2022 to

                         continue to advance and improve the customer

                         experience.

                  # ⚓ Automating_Content_Management_in_Satellite_6.9_with

                    Ansible_Automation_Platform:_Part_2⠀⇛

                         If you recall from part one of the Automating

                         Content Management series, we are working to

                         minimize the management effort of maintaining

                         the Red Hat Satellite managed content for a

                         large fleet of servers. We developed a simple

                         plan that aligns with the guide to Building a

                         Red Hat Enterprise Linux Standard Operating

                         Environment (SOE) and allows us to automate

                         our process.

                         The simple model is: update the content,

                         publish the content, validate the content,

                         promote the content to the next life cycle

                         environment, rinse and repeat.

                  # ⚓ Agile_adoption:_6_strategic_steps_for_IT_leaders_|

                    The_Enterprisers_Project⠀⇛

                         At Thales Group, our IT organization has been

                         working on a transformation known as NextGen

                         IT for a couple years. One of the key

                         elements is to change from a waterfall

                         delivery model to an agile one.

                         As part of this enterprise initiative, my

                         North America leadership team and I took on

                         the challenge of reworking our entire

                         operation to adopt agile principles for both

                         product and service delivery. We knew what we

                         wanted to achieve: squads, operating using

                         agile methods, driven by user stories, and

                         ultimately delivering incremental value.

                         As we embarked on this journey, something

                         dawned on us early on: The only way we could

                         truly be effective in leading the

                         organization through an agile transformation

                         is if we transformed our leadership team

                         first.

                         We did this by adopting agile principles and

                         adapting the agile process to our leadership

                         team. Here’s what we learned.

            # § Debian Family⠀➾

                  # ⚓ Writing_Debian_New_Contributor_Guide_–_ひとりしずかに。⠀⇛

                         Recently, I’ve wrote Debian New Cotributor

                         Guide in Japanese.

                         Here is the photo of on-demand printed

                         version.

                         This book (JIS-B5 128p) was published for

                         online event – Techbookfest 12th. It covers

                         how to package a new software in Debian.

            # § Canonical/Ubuntu Family⠀➾

                  # ⚓ Ubuntu_Blog:_Canonical_and_CoreSpace_Announce

                    Partnership_To_Offer_Organizations_‘One-Stop_Shopping’

                    for_Private_Clouds⠀⇛

                         Canonical, the publisher of Ubuntu, and

                         CoreSpace, a leading Infrastructure-as-a-

                         Service provider, announced a partnership

                         today that makes it easier and more

                         economical for organizations to set up,

                         customize, and manage private clouds.

                         Hybrid or multi-cloud environments that allow

                         organizations to run workloads where it makes

                         the most sense have become common in the

                         modern enterprise. Because private workloads

                         remain essential for most companies, high-

                         performing private clouds are playing a

                         critical role in their containerisation,

                         cloud, and digital transformation strategies.

                         The Canonical-CoreSpace alliance enables

                         organizations to adopt and get the most out

                         of private clouds. It does this through an

                         end-to-end solution that combines Canonical’s

                         leadership in designing, building, operating,

                         and supporting private clouds with

                         CoreSpace’s infrastructure technology and

                         expertise. With the announcement, CoreSpace

                         becomes Canonical’s first cloud delivery

                         partner in the United States.

      o § Devices/Embedded⠀➾

            # ⚓ Vestel_puts_TikTok_on_Linux-based_TVs_|_Light_Reading⠀⇛

                   Vestel, the largest TV manufacturer in Europe, is

                   today announcing the arrival of TikTok on its vast

                   range of Smart TVs. The app collaboration will see

                   Vestel now bring the video sharing phenomenon to

                   more than twenty high-profile and premium TV

                   brands, including its own portfolio of brand

                   licences.

                   Especially designed for TV, the TikTok app is

                   already available on all Vestel-designed Android

                   Smart TV ranges for brands in the UK, Germany and

                   France. The roll out of TikTok for Vestel Linux-

                   based Smart TVs started on the 20th, January, with

                   the app set to launch on Vestel 2021 UHD TV ranges

                   in early February, and on Vestel 2020 UHD TVs by

                   the end of March.

                   Supporting the display of high definition TikTok

                   content, the Vestel-manufactured Smart TVs bring

                   more detail, vibrancy, and colour to the screen for

                   a larger-than-life home viewing experience.

            # § Open Hardware/Modding⠀➾

                  # ⚓ Intel_Makes_Massive_Investment_in_RISC-V⠀⇛

                         Intel has joined RISC-V International, the

                         global open hardware standards organization,

                         and has announced creation of a billion-

                         dollar fund that aims to speed innovation and

                         development of RISC-V.

                         Intel’s Nios® V processors are already based

                         on RISC-V, but according to the announcement,

                         the company’s investment “will strengthen the

                         overall ecosystem and drive commercialization

                         of RISC-V.”

            # § Mobile Systems/Mobile Applications⠀➾

                  # ⚓ 6_secret_settings_for_better_browsing_in_Chrome_on

                    Android_|_Computerworld⠀⇛

                  # ⚓ OnePlus_&_Oppo_tipped_to_merge_designs_in_Android_13

                    –_9to5Google⠀⇛

                  # ⚓ Google_patched_a_critical_Android_12_security_flaw

                    today_–_PhoneArena⠀⇛

                  # ⚓ Android_12L_is_coming_to_Samsung_tablets_–

                    9to5Google⠀⇛

                  # ⚓ OnePlus’s_first_tablet_may_come_with_Android_12L_OS_–

                    PhoneArena⠀⇛

                  # ⚓ Android_12L_Beta_3_rolling_out,_including_for_Pixel_6

                    and_6_Pro_–_9to5Google⠀⇛

                  # ⚓ Android_12L_Beta_3_now_available,_adds_support_for

                    Pixel_6_series⠀⇛

                  # ⚓ Google_releases_Android_12L_Beta_3_with_support_for

                    the_Pixel_6_series_|_Android_Central⠀⇛

                  # ⚓ Galaxy_S22_gets_Android_12′s_Material_You_design,_so

                    you_can_change_all_the_colors_–_CNET⠀⇛

                  # ⚓ How_to_install_Android_12L_Beta_on_Google_Pixel_–

                    9to5Google⠀⇛

                  # ⚓ Android_12L_beta_3_now_available_on_Pixel_phones_—

                    here’s_how_to_get_it⠀⇛

                  # ⚓ Here’s_everything_new_in_Android_12L_Beta_3_[Gallery]

                    –_9to5Google⠀⇛

                  # ⚓ Wallpaper_Wednesday:_Android_wallpapers_2022-02-09_–

                    Android_Authority⠀⇛

                  # ⚓ Google_just_added_the_Pixel_6_and_Pixel_6_Pro_to_its

                    Android_beta_program⠀⇛

                  # ⚓ Samsung_phones_will_get_an_extra_year_of_Android

                    updates_versus_Google’s_Pixel_–_The_Verge⠀⇛

                  # ⚓ Samsung_Galaxy_S22_Ultra:_stylus-equipped_Android

                    superphone_launched_|_Samsung_|_The_Guardian⠀⇛

                  # ⚓ Samsung_promises_“up_to”_four_major_Android_updates

                    for_some_devices_(and_five_years_of_security_updates)_–

                    Liliputing⠀⇛

                  # ⚓ The_best_mobile_video_editing_app_is_coming_to

                    Android,_with_a_little_help_from_Samsung⠀⇛

                  # ⚓ Samsung_leapfrogs_Google_by_announcing_4-year_Android

                    OS_upgrade_commitment⠀⇛

      o § Free, Libre, and Open Source Software⠀➾

            # ⚓ syslog-ng-future.blog?_Is_this_a_fork_or_what?_–_syslog-ng-

              future.blog⠀⇛

                   I mentioned in the previous post that I would like

                   to focus on syslog-ng and put it more into the

                   spotlight. I also mentioned that Balabit, the

                   company I was a founder of and the commercial

                   sponsor behind syslog-ng, was acquired by One

                   Identity ~4 years ago. How does this add up? Who

                   owns the Intellectual Property (IP) for syslog-ng?

                   Who am I or this blog affiliated with?

                   I felt this post was important to set things

                   straight and make it easier to understand my

                   motivation. If you are not much into Free Software

                   and Open Source licenses or not interested too much

                   in administrative nuisances of FLOSS projects, feel

                   free to skip this post.

            # § Web Browsers⠀➾

                  # § Mozilla⠀➾

                        # ⚓ Firefox_97.0_Released!_Support_New_Overlay

                          Scrollbars_in_Windows_11⠀⇛

                               Mozilla Firefox web browser 97.0 was

                               released a day ago with few new

                               features and various bug-fixes.

                               The release does not include any

                               exciting new features for Linux, but

                               only adds new minimal overlay scrollbar

                               support for Windows 11. As well, system

                               font loading on macOS has been improved

                               to make opening and switching to new

                               tabs faster in certain situations.

                        # ⚓ This_Week_in_Glean:_Migrating_Legacy_Telemetry

                          Collections_to_Glean⠀⇛

                               One of the things I’ve spent a fair

                               amount of time helping with on the

                               Glean Team are the migrations from

                               legacy telemetry to Glean being

                               performed by different Mozilla

                               products. This includes everything from

                               internal tools and libraries to the

                               mobile browsers and even desktop

                               Firefox. As it turns out, there were

                               quite a few projects and products that

                               needed to be migrated. While we have

                               started migrating all of our active

                               products, each of them are at different

                               stages and have different timelines for

                               completion. I thought it might be

                               helpful to take a little narrative look

                               through what the migration process

                               looks like, and so here we go!

            # § FSF⠀➾

                  # § GNU Projects⠀➾

                        # ⚓ GNU_Binutils_2.38_released⠀⇛

                               Version 2.38 of the GNU Binutils tool

                               set has been released. Changes include

                               new hardware support (including for the

                               LoongArch architecture), various

                               Unicode-handling improvements, a new

                               –thin option to ar for the creation of

                               thin archives, and more.

            # § Programming/Development⠀➾

                  # ⚓ QtQuick3D_Realtime_Reflections⠀⇛

                         Reflections enhance the realism of a rendered

                         3D scene and without it we can not have

                         objects like mirrors or puddles of water that

                         reflect the surrounding environment. Raster

                         rendering pipelines like QtQuick3D can

                         approximately calculate reflections using

                         different methods to get good results, as

                         opposed to Ray Tracing where reflections can

                         be calculated accurately by following the

                         light rays and checking where they bounce

                         from. In this blog post, we are going to

                         discuss two different techniques to do

                         reflections in QtQuick3D.

                  # ⚓ Qt_for_MCUs_2.0.1_Released⠀⇛

                         Qt for MCUs 2.0.1 has been released and is

                         available for download. This is the first

                         patch release made on top of the new Qt for

                         MCUs 2.0 series. As a patch release, Qt for

                         MCUs 2.0.1 provides bug fixes and other

                         improvements, and maintains source

                         compatibility with Qt for MCUs 2.0.0. It does

                         not add any new functionality.

                  # ⚓ Qt_for_Android_Automotive_6.2.3_released⠀⇛

                         We are happy to announce the release of Qt

                         for Android Automotive 6.2.3!

                         This release comes with several fixes that

                         improve the stability and developer

                         experience of QAA. Big thanks to our

                         technology preview users for reporting the

                         issues!

                  # ⚓ Raspberry_Pi:_This_new_feature_could_help_you_get

                    started_more_easily⠀⇛

                         The makers of Raspberry Pi computers have

                         released a new boot loader that lets users

                         install an operating system like the official

                         OS directly on the compute board rather than

                         via a separate computer.

                         Until now, Raspberry Pi owners needed the

                         imager on a macOS, Windows or Ubuntu desktop

                         to install the OS on a Pi device. It could

                         also be done via another Pi device by

                         connecting SD card readers on each of them.

                         The new Raspberry Pi bootloader delivers

                         network installation, cutting out the need

                         for a second computer to install the OS.

                  # ⚓ Getting_Started_with_C++_and_InfluxDB [Ed:

                    "InfluxData sponsored this post." The so-called 'media'

                    or so-called 'news' sites on the Web have become

                    nothing short of webspam]⠀⇛

                  # § Perl/Raku⠀➾

                        # ⚓ gfldex:_Fuzzy_commands⠀⇛

                               Reading can make one learned. Today I

                               had a peak into lizmat´s new module

                               shorten-sub-commands and learned about

                               Parameter.constraint_list. We need this

                               method to introspect a routines literal

                               parameters.

                  # § Shell/Bash/Zsh/Ksh⠀➾

                        # ⚓ how_to_use_vim’s_build_in_history_(re_run_re

                          play_commands)_by_line_number

                          ⠀⇛

                        # ⚓ Using_the_Linux_fold_command_to_make_text_more

                          readable_|_Network_World⠀⇛

                               The Linux fold takes lines of text and

                               breaks them into chunks based on the

                               arguments that you provide. With no

                               arguments, fold will break lines at 80

                               characters.

                               The first example below uses a single-

                               line text file that includes

                               indications of character positions.

                               First, we count the number of

                               characters and lines in the file using

                               the wc -l and wc -l command…

                  # § Rust⠀➾

                        # ⚓ Dare_to_ask_for_more_#rust2024⠀⇛

                               Last year, we shipped Rust 2021 and I

                               have found the changes to be a real

                               improvement in usability. Even though

                               the actual changes themselves were

                               quite modest, the combination of

                               precise capture closure and simpler

                               formatting strings (println!(“{x:?}”)

                               instead of println!(“{:?}”, x)) is

                               making a real difference in my “day to

                               day” life.1 Just like NLL and the new

                               module system from Rust 2018, I’ve

                               quickly adapted to these new

                               conventions. When I go back to older

                               code, with its clunky borrow checker

                               workarounds and format strings, I die a

                               little inside.2

                               As we enter 2022, I am finding my

                               thoughts turning more and more to the

                               next Rust edition. What do I want from

                               Rust, and the Rust community, over the

                               next few years? To me, the theme that

                               keeps coming to mind is dare to ask for

                               more. Rust has gotten quite a bit nicer

                               to use over the last few years, but I

                               am not satisfied. I believe that there

                               is room for Rust to be 22x more

                               productive3 and easy to use than it is

                               today, and I think we can do it without

                               meaningfully sacrificing reliability,

                               performance, or versatility.

                  # § Java⠀➾

                        # ⚓ Java_break_and_continue_Statements⠀⇛

                               The continue statement is used in the

                               body of a while, do and for loop. The

                               break statement is used in these loops,

                               as well as in the switch statement.

                               Iteration can be considered the

                               execution of a loop’s body, over and

                               over. The break statement stops the

                               iteration. The continue statement skips

                               one execution (rest of the statements

                               below) of the body. This article

                               explains the employment of the continue

                               and break statements in Java. The

                               while-loop compound statement will be

                               used. For the break statement, the

                               switch compound statement will also be

                               used.

      o § Standards/Consortia⠀➾

            # ⚓ MIPI_CSI-2_v4.0_adds_features_for_always-on,_low_power

              machine_vision_applications_–_CNX_Software⠀⇛

                   While MIPI CSI-2 standard was first introduced in

                   2005 as a high-speed protocol for the transmission

                   of still and video images from image sensors to

                   application processors, the standard has evolved

                   over the years, and the latest MIPI CSI-2 v4.0

                   introduces features to better support always-on,

                   low power machine vision applications, high-

                   resolution sensors, and high-dynamic-range

                   automotive image sensors.

                   The main changes for v4.0 include support for a

                   two-wire interface (MIPI I3C) to lower cost and

                   complexity, multi-pixel compression for the latest

                   generation of advanced image sensors, and RAW28

                   color depth for better image quality and an

                   improved signal-to-noise (SNR) ratio.

* § Leftovers⠀➾

      o ⚓ Heart-Shaped_Pizza_History:_Less_Pizza_for_the_Same_Price⠀⇛

             It doesn’t matter that the heart symbol doesn’t look like

             an actual human heart, and never has. It nonetheless has

             become our general symbol for what we think of as love.

             The symbol is everywhere—on greeting cards, in emoji. But

             there’s one particular heart-shaped thing that I can’t

             stop thinking about right now: The heart-shaped pizza. It

             seems like the most crass of romantic gestures, to put

             tomato sauce and cheese on bread, but in a way, it’s

             genius. And seemingly every major chain that’s not

             Domino’s is offering a heart-shaped pizza. (Hey, if two

             people are sharing, it makes splitting it kind of easy, I

             guess.) I can’t stop thinking about the fact that lots of

             people are expected to buy cheap, rubbery Papa John’s

             pizza as a way to show off their love. (Papa John’s

             doesn’t even use heart-shaped pepperonis!) Today’s

             Tedium, in our first Valentine’s-themed post in our

             seven-year history, talks about our cultural tendency to

             make heart-shaped food. Especially pizza.

      o § Hardware⠀➾

            # ⚓ China_Loves_Battery_Swapping_EVs,_But_Will_They_Ever_Make

              It_Here?_|_Hackaday⠀⇛

                   Electric vehicles promise efficiency gains over

                   their gas-fuelled predecessors, but the issue of

                   recharging remains a hurdle for many eager to jump

                   on board with the technology. The problem is only

                   magnified for those that regularly street park

                   their vehicles or live in apartments, without

                   provision to charge a vehicle overnight at home.

                   Battery swapping promises to solve that issue,

                   letting drivers of EVs change out their empty

                   battery for a freshly charged one in a matter of

                   minutes. The technology has been widely panned and

                   failed to gain traction in the US.

                   However, as it turns out, battery swapping for EVs

                   is actually thing in China, and it’s catching on at

                   a rapid rate.

            # ⚓ Build_Your_Own_CRT_TV_|_Hackaday⠀⇛

                   There was a time following the Second World War

                   when TV sets for the nascent broadcast medium were

                   still very expensive, but there was an ample supply

                   of war-surplus electronic parts including ex-radar

                   CRTs. Thus it wasn’t uncommon at all for

                   electronics enthusiasts of the day to build their

                   own TV set, and magazines would publish designs to

                   enable them. With a burgeoning consumer electronics

                   industry the price of a new TV quickly dropped to

                   the point of affordability so nobody would consider

                   building one themselves today. Perhaps that should

                   be amended to almost nobody, because [Retro Tech or

                   Die] has assembled a small black-and-white CRT TV

                   from a kit he found on AliExpress.

            # ⚓ That_Clock_On_The_Wall_Is_Actually_A_Network_Ping_Display_|

              Hackaday⠀⇛

                   We’ve all been online from home a bit more than

                   usual lately, in ways that often stretch the limits

                   of what our ISP can muster. You know the signs —

                   audio that drops out, video sessions that make you

                   look like [Max Headroom], and during the off-hours,

                   getting owned in CS:GO by pretty much everyone. All

                   the bandwidth in the world won’t make up for high

                   latency, and knowing where you stand on that score

                   is the point of this ping-tracking clock.

            # ⚓ It’s_Always_Floppy_Time!_|_Hackaday⠀⇛

                   On [Jan Derogee]’s desk is something that wouldn’t

                   look out of place for many of us, a pile of

                   computer magazines with a case of 3.5″ floppy disks

                   on top of it. The causal observer would see nothing

                   more than the detritus of a retrocomputer

                   enthusiast’s existence, but stick around. In fact

                   it’s a clock, and one of the most unusual ones

                   we’ve seen in a long time.

            # ⚓ A_Guide_To_Milling_PCBs_At_Home_|_Hackaday⠀⇛

                   If you keep up with various retro vacuum tube

                   projects, you probably have run across

                   [UsagiElectric] aka [David]’s various PCBs that he

                   makes on his own Bridgeport EZ-Track 3-axis milling

                   machine — massively oversized for the job, as he

                   puts it. In a recent video, [David] walks us

                   through the steps of making a sample PCB,

                   introducing the various tools and procedures of his

                   workflow. He points out that these are the tools he

                   uses, but the overall process should be similar no

                   matter what tools you use.

            # ⚓ Mystery_Effect_Causing_LEDs_To_Glow_During_Reflow_|

              Hackaday⠀⇛

                   Sometimes you notice something small that

                   nevertheless you can’t explain. [Greg Davill] found

                   himself in just such a situation this week when he

                   noticed some green LEDs glowing dimly when

                   reflowing some boards. Naturally, [Greg] set out to

                   investigate.

                   The green LEDs were wired up as power indicators,

                   and [Greg] suspected that the polymer caps on the

                   board might be generating a small current somehow

                   that was causing the LEDs to light up ever so

                   slightly. A simple test hooked a polymer cap

                   directly up to a multimeter. When warmed with a

                   heat gun, the meter showed a small current “in the

                   5-10 uA range.”

                   [...]

                   It’s a curious case, and has many speculating as to

                   the causative mechanism on Twitter. Explanations

                   from thermoelectric effects to chemical reactions

                   inside the capacitor. If you’ve got the inside

                   scoop on what’s going on here, don’t hesitate to

                   let us know in the comments. Meanwhile, check out

                   some of [Greg]’s best work – a glowing D20 dice

                   featuring a whopping 2400 LEDs.

            # ⚓ Working_Model_Reveals_Amazing_Engineering_Of_Webb’s_Mirror

              Actuators_|_Hackaday⠀⇛

                   We end up covering a lot of space topics here on

                   Hackaday, not because we’re huge space nerds —

                   spoiler alert: we are — but because when you’ve got

                   an effectively unlimited budget and a remit to make

                   something that cannot fail, awe-inspiring

                   engineering is often the result. The mirror

                   actuators on the James Webb Space Telescope are a

                   perfect example of this extreme engineering, and to

                   understand how they work a little better, [Zachary

                   Tong] built a working model of these amazing

                   machines.

                   The main mirror of the JWST is made of 18 separate

                   hexagonal sections, the position of each which must

                   be finely tuned to make a perfect reflector. Each

                   mirror has seven actuators that move it through

                   seven degrees of freedom — the usual six that a

                   Stewart platform mechanism provides, plus the

                   ability to deform the mirror’s curvature slightly.

                   [Zach]’s model actuator is reverse-engineered from

                   public information (PDF) made available by the

                   mirror contractor, Ball Aerospace. While the OEM

                   part is made from the usual space-rated alloys and

                   materials, the model is 3D printed and powered by a

                   cheap stepper motor.

            # ⚓ A_Tuning_Fork_Clock,_With_Discrete_Logic_|_Hackaday⠀⇛

                   [Willem Koopman aka Secretbatcave] was looking at a

                   master clock he has in his collection which was

                   quite a noisy device, but wanted to use the

                   matching solenoid slave clock mechanism he had to

                   hand. Willem is a fan of old-school ‘sector’

                   clocks, so proceeded to build his ideal time piece

                   — Vibrmatic — exactly the way he wanted. Now, since

                   most time keeping devices utilise a crystal

                   oscillator — which is little more than a lump of

                   vibrating quartz — why not scale it up a bit and

                   use the same principle, except with a metal tuning

                   fork? (some profanity, just to warn you!)

      o § Integrity/Availability⠀➾

            # § Proprietary⠀➾

                  # ⚓ Microsoft_Teams_will_soon_have_LinkedIn_and_OneDrive

                    integration [Ed: While Microsoft keeps antitrust

                    regulators busy with “GAFA” or “Big Tech” [1, 2]]⠀⇛

                  # ⚓ Microsoft_February_2022_Patch_Tuesday:_48_bugs

                    squashed,_one_zero-day_resolved [Ed: Charlie Osborne of

                    Microsoft_ZDNet failing to mention that Microsoft

                    intentionally_leaves_holes_for_the_NSA]⠀⇛

                  # ⚓ Microsoft_365_will_tell_your_boss_almost_immediately

                    if_you_send_an_inappropriate_message_|_TechRadar [Ed:

                    TechRadar is posting promotional ‘articles’ (ads) that

                    are painting spyware as “protection”]⠀⇛

                         Microsoft will soon roll out a new system

                         that will help businesses identify

                         inappropriate messages sent by employees over

                         its productivity and collaboration software.

                  # § Security⠀➾

                        # ⚓ Linux_kernel_developer_Alan_Cox_on_Microsoft

                          security_practices._“I_pointed_out_that_they_ship

                          an_OpenSSL_from_2017_and_they_won’t_even

                          respond.”._–_BaronHK’s_Rants⠀⇛

                               Linux kernel developer Alan Cox on

                               Microsoft security practices. “I

                               pointed out that they ship an OpenSSL

                               from 2017 and they won’t even

                               respond.”.

                               OpenSSL is a deeply troubled project

                               that Big Tech uses extensively. It has

                               a long history of disastrous security

                               flaws, thousands, some of which have

                               THEIR OWN Wikipedia articles, which

                               routinely compromise the security of

                               the connection between your computer

                               and a Web server. So it’s not like

                               shipping a recent version is important

                               or anything.

                               Shipping it in the first place is

                               stupid when it has a community fork

                               that removes poorly written and little-

                               used code and audits and fixes the

                               rest. But that’s Microsoft/Big Tech/

                               what most “Linux” distributions have

                               become under their guiding hand.

                        # ⚓ Breaking_256-bit_Elliptic_Curve_Encryption_with

                          a_Quantum_Computer_–_Schneier_on_Security⠀⇛

                               In other words: no time soon. Not even

                               remotely soon. IBM’s largest ever

                               superconducting quantum computer is 127

                               physical qubits.

                        # ⚓ The_impact_of_hardware_specifications_on

                          reaching_quantum_advantage_in_the_fault_tolerant

                          regime⠀⇛

                        # ⚓ 2021_Trends_Show_Increased_Globalized_Threat_of

                          Ransomware [Ed: Could they they type this with a

                          straight face without_mentioning_Microsoft_or

                          Windows?]⠀⇛

                               CISA, the Federal Bureau of

                               Investigation (FBI), the National

                               Security Agency (NSA), the Australian

                               Cyber Security Centre (ACSC), and the

                               United Kingdom’s National Cyber

                               Security Centre (NCSC-UK) have released

                               a joint Cybersecurity Advisory (CSA)

                               highlighting a global increase in

                               sophisticated, high-impact, ransomware

                               incidents against critical

                               infrastructure organizations in 2021.

                               This CSA provides observed behaviors

                               and trends as well as mitigation

                               recommendations to help network

                               defenders reduce their risk of

                               compromise by ransomware.

                        # § Fear, Uncertainty, Doubt/Fear-mongering/

                          Dramatisation⠀➾

                              # ⚓ Deterrence,_diplomacy,_in_hybrid_war._UK

                                Foreign_Office_hacked._Threats_to_Linux-

                                based_multi-cloud_environments._Patch

                                Tuesday. [Ed: They're calling everything

                                "Linux", even things that have nothing to

                                do with Linux]⠀⇛

                                     Russia stages more general

                                     purpose forces near Ukraine

                                     (notably moving amphibious

                                     assault ships from the

                                     Mediterranean through the

                                     Dardanelles and toward Ukraine’s

                                     Black Sea coast) while diplomatic

                                     efforts to reduce tension

                                     continue. Belarus continues to

                                     emerge as an important staging

                                     point for Russian conventional

                                     forces. No fresh, large-scale

                                     cyber activity, however, is being

                                     reported. The New York Times

                                     reviews the current state of

                                     multilateral negotiations and

                                     sees, if not stalemate, at least

                                     stasis. Its analysis foresees “a

                                     drawn-out and dangerous

                                     diplomatic slog toward a

                                     difficult settlement.”

                              # ⚓ Threat_actors_view_Linux_servers_as_their

                                ticket_to_accessing_multi-cloud

                                environments [Ed: Only weeks after Dirk

                                left VMware the company has launched an

                                anti-Linux FUD campaign in the media, maybe

                                in order to distract from the back doors in

                                its own products and blame Linux itself

                                (while violating GPL, too)]⠀⇛

                              # ⚓ How_cybercriminals_are_using_malware_to

                                target_Linux-based_operating_systems [Ed:

                                Ransomware is a Windows issue (more than

                                90% of the time, but VMware now pays the

                                media to shift attention to Linux]⠀⇛

                                     As the most common cloud

                                     operating system, Linux is a core

                                     part of digital infrastructure

                                     and is quickly becoming an

                                     attacker’s ticket into a multi-

                                     cloud environment. Current

                                     malware countermeasures are

                                     mostly focused on addressing

                                     Windows-based threats, leaving

                                     many public and private cloud

                                     deployments vulnerable to attacks

                                     that target Linux-based

                                     workloads, VMware reveals.

                              # ⚓ Cybercriminals_Are_Using_Malware_To

                                Target_Linux-Based_Systems [Ed: Microsoft-

                                connected sites are at it, too]⠀⇛

                              # ⚓ Cybercriminals_Target_Linux‑based_Systems

                                with_Ransomware_and_Cryptojacking_Attacks_–

                                VMware_News⠀⇛

                              # ⚓ Cybercriminals_Target_Linux-based_Systems

                                With_Ransomware_and_Cryptojacking_Attacks

                                [Ed: VMware is attacking Linux again with

                                FUD as paid press releases, adding to its

                                GPL_violations etc.]⠀⇛

                              # ⚓ Linux_Malware_on_the_Rise [Ed: Blindly

                                repeating the talking points]⠀⇛

      o § Environment⠀➾

            # § Energy⠀➾

                  # ⚓ The_Environmental_Costs_of_Cryptocurrency⠀⇛

                         New Scientist defines Bitcoin as a digital

                         currency that relies on peer-to-peer software

                         and cryptography. A public ledger (or

                         blockchain) records all Bitcoin transactions,

                         and copies of those transactions are held on

                         servers (or nodes) around the world.

                         “Consensus on who owns which coins is reached

                         cryptographically across these nodes rather

                         than relying on a central source of trust

                         like a bank.”

                         To acquire Bitcoin, you can buy it, you can

                         sell something and be paid in Bitcoin, or you

                         can mine it. Each cryptocurrency transaction,

                         however, involves an immense amount of

                         processing power, with this article

                         estimating that each Bitcoin transaction

                         consumes more than $100 worth of electricity.

      o § Internet Policy/Net Neutrality⠀➾

            # ⚓ #SocialMediaComplianceWatch:_analysis_of_Social_Media

              Compliance_Reports_of_November,_2021⠀⇛

                   Google (including YouTube), Facebook, Instagram,

                   ShareChat, Snap, Twitter and WhatsApp released

                   their reports in compliance with Rule 4(1)(d) of

                   the IT Rules 2021 for the month of November, 2021.

                   The reports were made available in January 2022 and

                   they exhibit similar shortcomings. This outlines

                   lack of effort on the part of the SSMIs and the

                   government to further transparency and

                   accountability in platform governance. The SSMIs

                   have continued to not report on government

                   requests, used misleading metrics, and not

                   disclosed how they use algorithms for proactive

                   monitoring. You can read our analysis of the

                   previous reports here.

      o § Monopolies⠀➾

            # § Copyrights⠀➾

                  # ⚓ A_Paper_Archaeology:_Piranesi’s_Ruinous_Fantasias_–

                    The_Public_Domain_Review⠀⇛

                         From the vast confines of his imaginary

                         prisons to the billowy scenes that comprise

                         his grotteschi, the early works of Giovanni

                         Battista Piranesi wed the exacting details of

                         first-hand observation with the farthest

                         reaches of artistic imagination. Susan

                         Stewart journeys through this 18th-century

                         engraver-architect’s paper worlds.

                ䷩ 𝚕𝚒𝚗𝚎 6972

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧

Gemini_version_available_♊︎

✐ Links_9/2/2022:_GNU_Binutils_2.38_and_Google_Stadia_Failing⠀✐

Posted in News_Roundup at 2:01 pm by Dr. Roy Schestowitz

🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈

§ Contents⠀➾

* GNU/Linux

      o Distributions

      o Devices/Embedded

* Free_Software/Open_Source

* Leftovers

* § GNU/Linux⠀➾

      o § Audiocasts/Shows⠀➾

            # ⚓ Shockingly_Pragmatic_|_Coder_Radio_452_|_Jupiter

              Broadcasting⠀⇛

                   Mike makes a shocking admission, and Chris wishes

                   he had a time machine.

      o § Applications⠀➾

            # ⚓ Best_Free_and_Open_Source_Alternatives_to_Atlassian

              Trello⠀⇛

                   Atlassian Corporation Plc is a software company

                   founded in 2002 that develops products for software

                   developers, project managers and other software

                   development teams. It employs over 7,000 people and

                   is headquartered in Sydney, Australia.

                   Atlassian’s range of proprietary software includes

                   software for collaboration, development, and issue

                   tracking software for teams. Atlassian dominates

                   several markets where it still has intense

                   competition.

      o § Instructionals/Technical⠀➾

            # ⚓ Checking_out_a_Git_branch_further_back_than_the_head⠀⇛

                   It’s possible to move a branch (including ‘main’)

                   back to an older commit while staying on the

                   branch. This avoids Git complaints about being in a

                   detached HEAD state and makes ‘git status’ do

                   useful things like report how many commits you are

                   behind the upstream tip. As far as I know so far,

                   the way you do this is: [...]

            # ⚓ Ignore_A_Package_From_Being_Upgraded_In_Arch_Linux_–

              OSTechNix [Ed: Updated after 5 years]⠀⇛

                   Sometimes, you may want to ignore a package from

                   being upgraded in your Arch Linux system. It is

                   true that the outdated packages might be vulnerable

                   and not safe to our system. Yes! We need to update

                   the Arch Linux system regularly to get latest

                   packages and make our system more secure. However,

                   we need to hold a package or group of packages from

                   being upgraded for certain reasons.

            # ⚓ How_to_install_WhatsApp_on_Linux⠀⇛

                   WhatsApp is a telecommunications application to

                   provide video, chat and voice communication between

                   computers, tablets, and mobile devices over the

                   Internet connection. All you need is a phone number

                   to sign up, and then you can send messages from

                   your Linux system.

                   There is no official Linux client for WhatsApp,

                   unfortunately. The good news is that it is still

                   possible to download WhatsApp clients made by

                   users, which will use WhatApp’s web interface to

                   create a seamless experience. Using this method, we

                   are able to have WhatsApp on Linux and have it

                   resemble the same client you would get on a Windows

                   PC.

            # ⚓ How_to_install_PHP_on_Ubuntu_Linux⠀⇛

                   PHP is one of the most used languages when it comes

                   to programming dynamic web sites. If you are a web

                   developer, or just hosting a website that requires

                   PHP, you will need to install the software on your

                   server in order for your website to make use of its

                   PHP code.

                   PHP is also required by various content management

                   systems, including the most popular one in the

                   world, WordPress. In this tutorial, we will take

                   you through the step by step instructions to

                   install PHP on Ubuntu Linux.

            # ⚓ How_to_install_Grub_Customizer_on_Linux_(all_major

              distros)⠀⇛

                   Grub Customizer is a software package that does

                   exactly as the name would imply. It allows the user

                   to customize different aspects of the grub boot

                   menu – such as the order that entries appear in the

                   list, how long grub waits before selecting a

                   default system to boot to, etc.

                   The good news is that you can use this application

                   on all major Linux distros. In this tutorial, we

                   will show you how to install the Grub Customizer

                   package on all Linux systems.

            # ⚓ How_to_fix_Kubernetes_namespaces_stuck_in_the_terminating

              state_|_Enable_Sysadmin⠀⇛

                   A Kubernetes namespace isolates specific system

                   resources usually visible to all processes. Each

                   namespace has its own services, pods, and

                   deployments in the cluster. A namespace in

                   Kubernetes is essentially the same as a project in

                   OpenShift.

                   These days, most products are containerized and can

                   easily be deployed on Kubernetes or OpenShift. This

                   requires continuous application deployment and

                   testing. I recently worked on test automation that

                   involves the creation of namespaces, resources, and

                   data in the namespace, followed by running the test

                   suite, and then removing the data and namespace

                   once the tests are complete.

                   While frequently creating and deleting namespaces

                   in Kubernetes, I stumbled upon an issue where a

                   namespace got stuck in the Terminating state and

                   just refused to delete.

                   I use minikube to run Kubernetes locally, but you

                   can use the following steps and commands in any

                   Kubernetes or OpenShift environment.

            # ⚓ How_to_Fix_“Unacceptable_TLS_certificate”_Error_in_Linux?⠀⇛

                   When it comes to SSL/TLS certificates, you may come

                   across a variety of issues, some related to the

                   browser or a problem in a website’s back-end.

                   One such error is “Unacceptable TLS certificate” in

                   Linux.

                   Unfortunately, there’s no “one-solves-it-all’

                   answer to this. However, there are some potential

                   solutions that you can try, and here, I plan to

                   highlight those for you.

            # ⚓ How_to_Add_Linux_Host_to_Nagios_Ubuntu_Server_–_Part_2⠀⇛

                   This article assumes that you already have Nagios

                   installed on your Ubuntu system. If not, follow the

                   Part 1 tutorial guide article which is succeeded by

                   this one.

            # ⚓ How_To_Install_Podman_on_Linux_Mint_20_–_idroot⠀⇛

                   In this tutorial, we will show you how to install

                   Podman on Linux Mint 20. For those of you who

                   didn’t know, Podman (POD Manager) is a tool for

                   managing OCI containers and pods. It’s an open-

                   source project that can be used in most of the

                   Linux distributions that use Demon-less container

                   Engines. It exposes the same command-line interface

                   as Docker but runs containers unprivileged by

                   default.

                   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 a PHP 8.1 on a Linux Mint 20

                   (Ulyana).

            # ⚓ Create_a_data_stream_with_Amazon_Kinesis_|_Red_Hat

              Developer⠀⇛

                   Streaming data is key to many modern applications.

                   This tutorial walks you through setting up a data

                   stream using Amazon Kinesis and Node.js.

            # ⚓ Getting_started_with_Arduino⠀⇛

                   The Arduino is an advanced form of a

                   microcontroller which is comparatively easier to

                   work on. Similarly, it is a kind of plug and play

                   device and is much easier for the beginners to

                   learn how to make different projects related to

                   embedded systems. Arduino has different types of

                   microcontroller boards having different

                   specifications and the most common Arduino board is

                   the Arduino Uno board. All the Arduino boards can

                   be configured using the Arduino IDE software. This

                   discourse explains how to use the Arduino Uno board

            # ⚓ seife’s_assorted_rants:_dracut:_fix_hibernate_after_fresh

              install⠀⇛

                   Just for fun, I finally installed a fresh

                   Tumbleweed on one of my machines to actually find

                   out if I’m missing out on new features that are

                   masked by just always updating the old

                   installation.

                   One feature that I had missed was, that hibernation

                   was no longer working. Or, to be more exact,

                   hibernation was working, but resume was not.

                   Investigating the issue, I found that dracut’s

                   “resume” module was not included in the initramfs,

                   which in turn lead to initramfs not even trying to

                   resume.

                   The dracut mechanism has some logic to actually

                   find out if suspend and resume is configured, and

                   when it decides it is not, it will just skip adding

                   the “useless” resume module.

                   Unfortunately, the check is faulty IMHO. It checks,

                   if the resume device is configured in the kernel,

                   and if it is, it adds the module to dracut. The

                   problem is, that this kernel config is written by

                   the resume code in the initrd… so during

                   installation this is not the case, and as a result

                   the module is not added to initrd, which leads to

                   the config not being set on next reboot…

            # ⚓ Install/Upgrade_XanMod_Kernel_LTS_on_Rocky_Linux_8_–

              LinuxCapable⠀⇛

                   XanMod is a free, open-source general-purpose Linux

                   Kernel alternative to the stock kernel that is on

                   Rocky Linux. It features custom settings and new

                   features and is built to provide a responsive and

                   smooth desktop experience, especially for new

                   hardware.

                   Installing a third-party kernel may be for you for

                   users seeking to have their system kernel up to

                   date and not wanting to install kernels or use the

                   testing/unstable repositories manually.

                   Currently, the XanMod LTS kernel is supported and

                   not the latest bleeding-edge using the rmnscnce/

                   kernel-xanmod.

            # ⚓ Install/Upgrade_MakeMKV_on_Debian_11_Bullseye_–

              LinuxCapable⠀⇛

                   MakeMKV is a free, open-source tool that can

                   convert video clips from DVDs and Blu-rays, which

                   are usually encrypted. The output will have most

                   information preserved but not changed in any way;

                   it’s perfect for people who want their media

                   without hassle or headache caused by software

                   limitations like those found with some other

                   transcoder apps.

                   In the following tutorial, you will learn how to

                   install or upgrade to the latest version of MakeMKV

                   on Debian 11 Bullseye using a recommended

                   repository by the MakeMKV team to provide the most

                   up-to-date version.

            # ⚓ Install_Podman_on_Debian_11_–_Unix_/_Linux_the_admins

              Tutorials⠀⇛

                   Podman is an alternative to Docker that is backed

                   by Red Hat and IBM. The open-source project has a

                   great ease of use, which is a big draw among

                   developers.

                   Well, one of the differences is that it is not

                   based on daemons (services in the *nix world). One

                   of the advantages is that Docker has a single

                   daemon that when it handles many containers grows

                   and grows, becoming much heavier.

                   This last point is where Podman wants to be a solid

                   alternative to Docker and is where Podman bases its

                   reason.

                   As you would expect, Podman has great support for

                   all the Linux distributions out there. This is also

                   the case for Debian 11 where the installation is

                   effortless.

            # ⚓ Install_Htop_on_Debian_11_Bullseye_–_LinuxCapable⠀⇛

                   Htop is a free, open-source, cross-platform

                   interactive process viewer. It is a text-mode

                   application (for console or X terminals) and

                   requires ncurses. The terminal UI is a great way to

                   see what your system looks like inside, both in

                   terms of processes and other info. It’s also

                   completely customizable, so you can change colors

                   or add different widgets for more visual

                   representation!

                   In the following tutorial, you will learn how to

                   install Htop Interactive Process Viewer on Debian

                   11 Bullseye desktop or server.

            # ⚓ 6_Linux_metacharacters_I_love_to_use_on_the_command_line_|

              Opensource.com⠀⇛

                   Early in my Linux journey, I learned how to use the

                   command line. It’s what sets Linux apart. I could

                   lose the graphical user interface (GUI), but it was

                   unnecessary to rebuild the machine completely. Many

                   Linux computers run headless, and you can

                   accomplish all the administrative tasks on the

                   command line. It uses many basic commands that all

                   are familiar with—like ls, ls-l, ls-l, cd, pwd,

                   top, and many more.

      o § Games⠀➾

            # ⚓ Google_Stadia’s_Failure_Is_Almost_Complete⠀⇛

                   While Google’s Stadia game streaming service

                   arrived with a lot of promise, it generally landed

                   with a disappointing thud. A limited catalog,

                   deployment issues, and a quality that couldn’t

                   match current gen game consoles meant the service

                   just never saw the kind of traction Google (or a

                   lot of other people) originally envisioned. In the

                   years since, developers have been consistently

                   abandoning the platform, and Google has

                   consistently sidelined the service, even shutting

                   down its own development efforts as a parade of

                   executives headed for the exists.

            # ⚓ How_to_Connect_Xbox_Controller_with_Raspberry_Pi⠀⇛

                   For those who want to enjoy a better gaming

                   experience, they certainly need an Xbox controller

                   in order to play games with great control. Getting

                   a wireless Xbox controller is a bit expensive so

                   most people stick with buying an affordable wired

                   Xbox controller. So, if you are one of those people

                   who have a wired Xbox USB controller and you want

                   to play games with it on your Raspberry Pi OS then

                   you certainly need help in configuring it on the

                   device.

            # ⚓ Wadjet_Eye_Games_brings_Shardlight_over_to_Linux_|

              GamingOnLinux⠀⇛

                   Is there no stopping Wadjet Eye Games? Shardlight,

                   another quality point and click adventure from 2016

                   has now been ported over to Linux. This adds to the

                   list of titles that Wadjet Eye Games has recently

                   upgraded and ported (or re-ported) to Linux

                   including Resonance, Technobabylon, Unavowed,

                   Gemini Rue, The Blackwell Bundle.

            # ⚓ ChimeraOS_30_is_out_with_big_OneXPlayer_improvements⠀⇛

                   ChimeraOS continues to provide a full-screen

                   console-like Linux experience for those that want

                   it, and ChimeraOS 30 is now live with some great

                   upgrades.

                   First, the usual upgrades to the major parts like

                   Linux Kernel 5.16.5, Mesa drivers 21.3.5, NVIDIA

                   drivers 510.47.03 and upgrades to their own special

                   compositor and Chimera software. Plus, a bump for

                   RetroArch to version 1.10.0. The bigger changes

                   come for those who have a OneXPlayer handheld

                   device as it should work vastly better with

                   ChimeraOS now thanks to controller detection fixes,

                   screen orientation fixes, a fix for custom

                   resolution support and a default resolution set

                   properly to 1280×800. So out of the box, OneXPlayer

                   devices should work nicely.

            # ⚓ SimAirport_getting_some_great_upgrades_ready_for_the_Steam

              Deck_|_GamingOnLinux⠀⇛

                   A little building and management on the go?

                   SimAirport from LVGameDev LLC sounds like it might

                   be a good choice, with the developer highlighting

                   upcoming changes and improvements for the Steam

                   Deck and it will help all platforms.

                   You probably don’t need a big explanation to begin

                   with on this one, the name SimAirport speaks for

                   itself really. You construct and manage an Airport

                   from a single plane to a massive international

                   terminal filled to the brim with passengers, staff

                   and it’s your job to keep everything flying

                   smoothly.

            # ⚓ WRAEK_think_they_can_change_PC_gaming_with_the_Tactonic_Pro

              |_GamingOnLinux [Ed: Looks to me like paid-for spam; is Liam

              Dawe selling itself out like Phoronix?]⠀⇛

                   What’s really great to see though, is how Linux has

                   clearly been making more waves – enough for this

                   hardware vendor to target it too. They said their

                   software is fully compatible with Linux!

            # ⚓ With_You_looks_like_a_sweet_co-op_experience_and_it’s_free

              |_GamingOnLinux⠀⇛

                   Need a new casual co-op game to play with a

                   partner? With You recently released on Steam and

                   itch.io and it looks adorable. It’s free to, so

                   you’ve got nothing to lose but a few moments of

                   your time, and perhaps a fun memory to gain from

                   it.

      o § Desktop Environments/WMs⠀➾

            # § K Desktop Environment/KDE SC/Qt⠀➾

                  # ⚓ KDE_Plasma_5.24_LTS_Releases_with_Updated_Breeze

                    Theme_and_New_Overview_Effect⠀⇛

                         We have been keeping an eye on KDE Plasma

                         5.24 for a while.

                         From spotting the GNOME-Style overview effect

                         to the addition of fingerprint support. If

                         you have been following our coverages, you

                         already know about the changes introduced

                         with KDE Plasma 5.24.

                         Now that KDE Plasma 5.24 stable release is

                         finally here, let me highlight the key

                         additions and improvements below.

                         [...]

                         KDE Plasma 5.24 is a long-term support

                         release that will receive updates until the

                         final Plasma 5 release (and the transition to

                         Plasma 6).

                         With this release, you do not get to see

                         massive visual changes, but you can find

                         various functional improvements and subtle

                         visual refinements.

                  # ⚓ KDE/Plasma_5.24_for_Debian⠀⇛

                         Yesterday, KDE released version 5.24 of the

                         Plasma desktop with the usual long list of

                         updates and improvements. This release will

                         be considered a LTS release. And Plasma 5.24

                         is now available for all Debian releases.

                         (And don’t forget KDE Gears/Apps 21.12!)

                  # ⚓ KDE_Plasma_5.24_LTS_desktop_environment_brings

                    fingerprint_support,_performance_and_user_interface

                    improvements_and_more⠀⇛

                         The developers of the open source KDE Plasma

                         desktop environment for Linux distributions

                         have released Plasma 5.24, which brings a

                         number of performance improvements, visual

                         tweaks, and new features.

                         It’s also a long term support (LTS) release,

                         which means it will continue to receive bug

                         fixes and other updates until the next major

                         update, which will be Plasma 6.

                  # ⚓ Plasma_5.24_available_on_Kubuntu_21.10⠀⇛

                         We are pleased to announce that Plasma 5.24

                         is now available in our backports PPA for

                         Kubuntu 21.10 (Impish Indri).

                         The release announcement detailing the new

                         features and improvements in Plasma 5.24 can

                         be found here.

                  # ⚓ Plasma_Mobile_Gear_22.02_Is_Out_with_Many_Changes_to

                    the_Plasma_Mobile_Shell_and_Apps⠀⇛

                         Coming hot on the heels of the KDE Plasma

                         5.24 desktop environment, which is also

                         available for mobile devices as Plasma

                         Mobile, the Plasma Mobile Gear 22.02 software

                         suite is here to update some of your favorite

                         mobile apps, as well as the Plasma Mobile

                         shell.

                         In fact, Plasma Mobile Gear 22.02 is packed

                         with great improvements for the Plasma Mobile

                         shell, including a revamped Quick Settings

                         panel with support for media and

                         notifications widgets, as well as a new

                         landscape format for tablets, a smoother

                         gesture experience, a revamped task switcher

                         to use a single row of thumbnails with

                         gesture support, and a revamped app drawer

                         open/close gesture.

            # § GNOME Desktop/GTK⠀➾

                  # ⚓ Best_Audio_and_Video_Players_for_Gnome_Desktop⠀⇛

                         To take a break from our everyday routines,

                         most unwind by watching movies, TV shows,

                         listening to music, and indulging in other

                         forms of entertainment. Aside from that,

                         videos can be utilized for business

                         information sharing, product advertisements,

                         and a variety of other tasks in which digital

                         media is at the center of business marketing.

                         There are quite a number of video and audio

                         players. They provide features like subtitle

                         synchronization, support for a variety of

                         video formats, and the ability to play

                         YouTube videos directly without

                         advertisements.

      o § Distributions⠀➾

            # ⚓ VA_Linux⠀⇛

                   In 1999, one of the hottest IPOs was an open source

                   company named VA Linux ($LNUX). The stock opened

                   10x in its first day of trading. The stock was

                   offered at $30, opened at $300, and was $8.50 a

                   year later. The company later launched SourceForge.

                   In 2015, it become a subsidiary of Gamestop.

                   VA Linux was the largest vendor of pre-installed

                   Linux computers. Red Hat had just gone public

                   earlier that year. The company had Intel and

                   Sequoia as investors in its seed round, and the

                   founder was classmates at Stanford with Yahoo

                   founders Jerry Yang and David Filo.

            # § IBM/Red Hat/Fedora⠀➾

                  # ⚓ Comparison_of_Fedora_Flatpaks_and_Flathub_remotes⠀⇛

                         In the previous article in this series, we

                         looked at how to get started with Fedora

                         Flatpaks and how to use it. This article

                         compares and contrasts between the Fedora

                         Flatpaks remote and the Flathub remote.

                         Flathub is the de-facto standard Flatpak

                         remote, whereas Fedora Flatpaks is the Fedora

                         Project’s Flatpak remote. The things that

                         differ between the remotes include but are

                         not limited to their policies, their ways of

                         distribution, and their implementatio

            # § Debian Family⠀➾

                  # ⚓ Testing_Slax_11.2_based_on_Debian_Bullseye_–_Slax

                    Linux⠀⇛

                         I made my first attempt to build Slax based

                         on Debian Bullseye (version 11.2). Here is a

                         work in progress (well, it is mostly finished

                         I guess so lets call it RC1). Some of the

                         applications are no longer available, such as

                         leafpad, wicd, and I replaced pcmanfm with

                         tuxCommander.

                         Please feel free to suggest a small simple

                         GUI app (GTK-based) for network

                         configuration.

                         This version does not include chromium

                         browser due to its size, but if you click the

                         icon, it will install automatically before

                         first use.

                         Debian also no longer supports aufs, so it

                         has been replaced by overlayfs in Slax. This

                         is internal change which affects the use of

                         ‘slax activate’ command (it will no longer

                         work). I am investigating possibilities to

                         make it work again but as far as I can see,

                         there is no way to modify the existing

                         overlay filesystem on the fly as it was

                         possible with AUFS, this means it is no

                         longer possible to add new modules on the fly

                         while running Slax. You can of course still

                         add modules to your ISO (or USB directory

                         tree). Suggestions welcome.

      o § Devices/Embedded⠀➾

            # ⚓ Raspberry_Pi_4_GPIO_Pinout⠀⇛

                   Raspberry Pi 4 has come up with more advanced

                   features as compared to the previous model of the

                   Raspberry Pi. It was launched in June 2019 and has

                   come up with a much-improved processing speed of

                   about 90% as compared to previous version due to

                   the inclusion of 4GB and 8GB RAM memory. Its

                   General-Purpose Input Output (GPIO) pins have also

                   maintained the previous standard set by the

                   Raspberry Pi models, and are now more functional

                   and performing flawlessly.

                   The Raspberry Pi 4 has 40 GPIO pins that can be

                   easily configured to read inputs or write outputs.

                   If you are unfamiliar with the operation of these

                   GPIO pins, this article will assist you in

                   understanding the operation of each pin.

            # ⚓ Raspberry_Pi_4_to_support_Network_install_to_a_blank

              MicroSD_card⠀⇛

                   The Raspberry Pi 4 will soon be able to install

                   Raspberry Pi OS without the need for external

                   hardware to flash the image. Raspberry Pi Network

                   install will allow users to install a blank MicroSD

                   card into their board, which will trigger the

                   launch of Raspberry Pi Imager on the Raspberry Pi,

                   and flash the image downloaded from the Raspberry

                   Pi website.

                   So far in order to install Raspberry Pi OS, you had

                   to download Raspberry Pi Imager on a computer or a

                   working Raspberry Pi, insert the MicroSD card into

                   the host, and flash the image, before moving the

                   MicroSD card into the Raspberry Pi board. This

                   works just fine for most people, but if the

                   Raspberry Pi is your only computing device, as may

                   be the case in developing countries, that does not

                   work. Network Installs may also speed up the

                   installation process in the classroom where

                   multiple boards may need to be set up.

            # ⚓ How_to_List_Installed_Packages_in_Raspberry_Pi_OS⠀⇛

                   You already know that your Raspberry Pi OS has so

                   many different packages installed in it. However,

                   you don’t know what packages are installed on the

                   Raspberry Pi OS. Finding those packages used to be

                   a difficult task as it requires your time in

                   searching for those packages. As it becomes

                   necessary for you to look for those packages, there

                   should be a solution that can help you in finding

                   those packages on your Raspberry Pi OS. If you are

                   still searching for the right solution then this

                   article will provide you with the solution so that

                   you can easily list the pre-installed packages in

                   Raspberry Pi OS.

            # ⚓ How_to_Mine_Crypto_on_Raspberry_Pi⠀⇛

                   Nowadays, cryptocurrency is becoming much popular

                   among the young generation and the reason is it

                   provides them the opportunity to earn a lot of

                   money. Cryptocurrency can be obtained by two

                   methods which are purchasing and mining. The

                   purchasing method of Cryptocurrency is hard for

                   most of the people because they don’t have enough

                   money in their pockets. The second method is a

                   better one to start with but it requires some

                   effort and hard work.

                   Cryptocurrency mining has long affected the passion

                   of technology addicts, pushing them to design new

                   algorithms to defend networks, mining pools, and

                   innovative ways to build mining systems. If you are

                   among the Raspberry Pi users and you want to start

                   your Cryptocurrency mining journey, you can do it

                   on your Raspberry Pi operating system. This

                   requires your efforts and some time so that you can

                   begin mining Cryptocurrency on Raspberry Pi.

            # § Mobile Systems/Mobile Applications⠀➾

                  # ⚓ Android_vs._iOS:_Is_iPhone_Better_Than_Android_or

                    Vice_Versa?⠀⇛

                  # ⚓ Exclusive:_Material_You-style_theming_will_soon_be

                    required_for_phones_getting_Android_12⠀⇛

                  # ⚓ OnePlus_Pad_tablet_tipped_to_ship_with_Android_12L⠀⇛

                  # ⚓ Google_fixes_“critical”_Android_12_security_flaw_|

                    TechRadar⠀⇛

                  # ⚓ Which_phones_and_cars_can_use_Android_digital_car

                    key?_|_Android_Central⠀⇛

                  # ⚓ How_to_forward_calls_on_Android_–_Phandroid⠀⇛

                  # ⚓ Vivaldi_5.1_arrives_for_desktop_and_Android_–_gHacks

                    Tech_News⠀⇛

                  # ⚓ Top_10_Android_MMORPGs_of_2022:_RuneScape,_Albion,

                    Adventure_Quest_3D,_and_More_|_Tech_Times⠀⇛

                  # ⚓ Top_10_Best_Third-Party_Android_App_Stores_–_2022⠀⇛

                  # ⚓ OnePlus_Pad_rumored_to_get_Android_12L._Would_you_buy

                    it?⠀⇛

                  # ⚓ Motorola’s_first_smartphone_receiving_Android_12

                    stable_update_was_launched_in_2020_–_GSMArena.com

                    news⠀⇛

                  # ⚓ Critical_Android_12_bug_fixed_in_February_security

                    patches_•_The_Register⠀⇛

                  # ⚓ OnePlus_Unified_OS_to_Debut_in_Second_Half_of_2022,

                    OnePlus_Pad_to_Run_Android_12L:_Reports_|_Technology

                    News⠀⇛

                  # ⚓ Smartphone_Lifespan:_How_Long_Android_Phones_From

                    Samsung,_Xiaomi,_Realme_And_Others_Will_Last

                    ‘Officially’⠀⇛

                  # ⚓ YouTube_Music_For_Android_Gets_A_New_Playback

                    Shortcut⠀⇛

                  # ⚓ 6_secret_settings_for_better_browsing_in_Chrome_on

                    Android_|_Computerworld⠀⇛

      o § Free, Libre, and Open Source Software⠀➾

            # § FSF⠀➾

                  # § GNU Projects⠀➾

                        # ⚓ GNU_Binutils_2.38_has_been_released⠀⇛

                               Hi Everyone,

                               We are pleased to announce that version

                               2.38 of the GNU Binutils project

                               sources have been released and are now

                               available for download at:

                               https://ftp.gnu.org/gnu/binutils

                               https://sourceware.org/pub/binutils/

                               releases/

                               The SHA256 checksums are as follows:

                               070ec71cf077a6a58e0b959f05a09a35015378c2d8a51e90f3aeabfe30590ef8

                               binutils-2.38.tar.bz2

                               6e54170356709d401f1cb781f86bb59656b99b398412047f5c44f0fbc633fa4d

                               binutils-2.38.tar.bz2.sig

                               b3f1dc5b17e75328f19bd88250bee2ef9f91fc8cbb7bd48bdb31390338636052

                               binutils-2.38.tar.gz

                               864d330b71f2b40120d96e68ebed43a07c5286d9c28f3a3893ae4ae7ec25ede9

                               binutils-2.38.tar.gz.sig

                               807ccfa77ccfc3e09b1f760cd73e13839180c6950a37843df1c1e7a58c777dc9

                               binutils-2.38.tar.lz

                               49ee3c3b5803dea2acb15a3fa4c8ad0daebf142ba284a8b3d3524a52823a0ceb

                               binutils-2.38.tar.lz.sig

                               e316477a914f567eccc34d5d29785b8b0f5a10208d36bbacedcc39048ecfe024

                               binutils-2.38.tar.xz

                               41301d67da78df1ad6df04aefe9e7bea8235484b0323cee52caa8f7435385014

                               binutils-2.38.tar.xz.sig

                               This release contains numerous bug

                               fixes and improvements, along with

                               the following new features:

                                 Assembler:

                                   General:

                                     * Add support for the LoongArch

                               architecture.

                                     * Add an option to control how

                               multibyte characters are handled in

                                       the assembler.  Using the

                               option warnings can be generated when

                                       such characters are encountered

                               in symbol names, or anywhere in

                                       the input source file(s).

                                   AArch64 and ARM:

                                     * Add support for more system

                               registers.

                                     * Add support for Scalable Matrix

                               Extension.

                                     * Add support for Cortex-R52+,

                               Cortex-A510, Cortex-A710,

                                       Cortex-X2, Cortex-A710 cores.

                                     * Add support for 'v8.7-a',

                               'v8.8-a', 'v9-a', 'v9.1-a',

                                       'armv9.2-a' and 'armv9.3-a'

                               architecture extensions.

                                   X86:

                                     * Add a command-line option to

                               encode aligned vector move as

                                       unaligned vector move.

                                     * Add support for Intel

                               AVX512_FP16 instructions.

                                     * The outputs of .ds.x directive

                               and .tfloat directive with hex

                                       input have been reduced from 12

                               bytes to 10 bytes to match the

                                       output of .tfloat directive.

                                 Linker:

                                   * Add support for the LoongArch

                               architecture.

                                   * Add -z pack-relative-relocs/-z no

                               pack-relative-relocs to x86 ELF

                                    linker to pack relative

                               relocations in the DT_RELR section.

                                   * Add -z indirect-extern-access/-

                               z noindirect-extern-access to x86

                                     ELF linker to control canonical

                               function pointers and copy

                                     relocation.

                                 Other Binary Tools:

                                   * elfedit: Add --output-abiversion

                               option to update ABIVERSION.

                                   * Tools which display symbols or

                               strings (readelf, strings, nm,

                                     objdump) have a new command line

                               option which controls how unicode

                                     characters are handled.  By

                               default they are treated as normal for

                                     the tool.  Using --unicode=locale

                               will display them according to

                                     the current locale.  Using --

                               unicode=hex will display them as hex

                                     byte values, whilst --

                               unicode=escape will display them as

                               escape

                                     sequences.  In addition using --

                               unicode=highlight will display

                                     them as unicode escape sequences

                               highlighted in red (if supported

                                     by the output device).

                                   * readelf -r dumps RELR relative

                               relocations now.

                                   * Support for efi-app-aarch64, efi-

                               rtdrv-aarch64 and

                                     efi-bsdrv-aarch64 has been added

                               to objcopy in order to enable

                                     UEFI development using binutils.

                                   * ar: Add --thin for creating thin

                               archives. -T is a deprecated

                                     alias without diagnostics. In

                               many ar implementations -T has a

                                     different meaning, as specified

                               by X/Open System Interface.

                               Our thanks go out to all of the

                               binutils contributors, past and

                               present, for helping to make this

                               release possible.

                               Cheers

                                 Nick Clifton

                                 GNU Binutils Chief Maintainer

            # § Programming/Development⠀➾

                  # ⚓ Sunsetting_gzip_substitutes_availability⠀⇛

                         Starting next month (2022/03/01), the build

                         farm known as ci.guix.gnu.org will no longer

                         offer gzip-compressed binary substitutes. The

                         Guix daemon has known to use lzip for

                         substitutes since 2019; unless you are

                         running a very outdated daemon, you have no

                         need to worry about this change.

                         This idea was first discussed about a year

                         ago, when it was found that gzip-compressed

                         substitutes accounted for about only 1% of

                         the downloaded substitutes. Since then, the

                         daemon has gained support for zstd on top of

                         gzip and lzip, and the build farm has happily

                         generated compressed substitutes for all of

                         these compression schemes.

                  # ⚓ I_would_like_a_job_writing_Haskell⠀⇛

                         Perhaps someone out there wants to take a

                         chance on a senior programmer with thirty

                         years of experience who wants to make a move

                         into Haskell.

                  # § Java⠀➾

                        # ⚓ Hashset_vs_Hashmap_in_Java⠀⇛

                               The Java programming language has two

                               distinct yet similar types of data

                               containers, HashMap and HashSet . Both

                               use a hash table to store data. A table

                               is a table of values ​​that uses a hash

                               function to determine where to look and

                               store data. This allowsquick access to

                               data because a value does not have to

                               be searched. Instead, the hash function

                               can provide the exact location of the

                               value. Despite so much use of hash

                               tables, HashMap and HashSet are quite

                               different from each other.

                        # ⚓ Java_assert⠀⇛

                               Assertion in Java is a statement based

                               on the reserved word, assert, having a

                               boolean expression and ending with a

                               semicolon. It happens that certain

                               conditions in a program may prevent it

                               from working properly. The assert

                               statement checks if such conditions

                               exist in a program. Java assert is

                               explained in this article.

                        # ⚓ How_do_You_write_Comparable_in_Java?⠀⇛

                               Examples of Java lists are; Vector,

                               Stack, AttributeList, ArrayList, and

                               LinkedList. The Java Collections class

                               has overloaded methods to sort a list

                               of predefined objects. The Java Arrays

                               class has overloaded methods to sort an

                               array of predefined objects.

                               The predefined sort() methods are to

                               sort predefined objects. What about

                               user-defined objects? Java has an

                               interface called Comparable. An

                               interface is a kind of class whose

                               methods are declarations without

                               definitions (bodies). So, a class must

                               be implemented from an interface for

                               the methods to be defined (given

                               bodies). From the implemented class,

                               objects can be instantiated from a name

                               given by the programmer.

                               Java has a predefined Comparable class.

                               The sort() methods in Collections and

                               Arrays use the predefined comparable

                               class to sort predefined objects.

                               However, in order to sort a list or

                               array of user-defined objects, the

                               programmer has to implement (define) a

                               user Comparable class from the

                               Comparable interface. This user

                               implemented (defined) class enables the

                               sorting of user-defined objects in a

                               list or array. So, a predefined

                               Comparable class enables sorting of

                               predefined objects, while a user-

                               defined Comparable class enables

                               sorting of user-defined objects. User-

                               defined objects are not literals, so a

                               class of user-defined objects needs its

                               own user-defined Comparable

                               implementation.

                               This article illustrates how to write

                               Comparable in Java.

                        # ⚓ Hashtable_in_Java⠀⇛

                               A hash table is for key/value pairs.

                               Internally, the values are stored in an

                               array. Each key is converted into an

                               index of the array. This conversion is

                               known as hashing. It is done by a hash

                               function internally. In other words,

                               the keys do not have to be stored. All

                               that is the hash-table, in java and in

                               other computer languages. This article

                               explains two constructors of the Java

                               hastable and its commonly used methods.

                        # ⚓ How_AJAX_works⠀⇛

                               AJAX comprises a set of useful web

                               development techniques utilized to

                               develop dynamic and speedy web pages.

                               Behind the scenes, it shares small

                               chunks of the data, permitting the web

                               pages to be updated asynchronously.

                               This states that by using AJAX, HTML

                               page elements will be updated without

                               reloading.

                               This write-up will discuss the

                               components of AJAX and how AJAX works.

                               We will talk about the working of AJAX

                               in some top web-based applications.

                               Moreover, a comparison between the

                               conventional and AJAX model will be

                               provided. So, let’s start!

      o § Standards/Consortia⠀➾

            # ⚓ Gemini_Isn’t_The_Solution_To_The_Broken_Web⠀⇛

                   I’m not sure if you heard, but The Web Is F*cked

                   and techies everywhere are touting the Gemini

                   protocol as its saviour. I disagree. A lot.

                   When I wrote The Web Is F*cked, I had a number of

                   people reach out asking why I didn’t mention

                   Gemini, as it’s the saviour of the web…apparently.

                   Well, I didn’t mention Gemini because I think it

                   actually does more harm than good when it comes to

                   the web. Let me explain…

* § Leftovers⠀➾

      o ⚓ Todd_Gitlin_Told_His_Truth_Everywhere_He_Went⠀⇛

             I met Todd Gitlin on October 23, 1987. It was the

             beginning of what would become a decades-long “beautiful

             friendship.” (We shared a favorite movie in Casablanca.)

             I can pin down the date because our meeting took place at

             the ridiculous Second Thoughts conference in which

             apostate liberals and New Leftists were gathered to

             denounce their former selves and embrace the new right.

             It took place at the Grand Hyatt hotel in Washington,

             D.C., and was organized by left-wing Stalinists turned

             right-wing Stalinists David Horowitz and Peter Collier,

             with funding from a Christian conservative foundation led

             by the son of the far-right Alabama Senator Jeremiah

             Denton, together with the Bradley and Olin foundations.

             Funnily enough, it took place just days after Ronald

             Reagan’s Iran/Contra plot was revealed and the largest

             single drop in the stock market since 1929. These week’s

             events signaled the long-awaited end to the Reaganite

             hegemony these folks had gathered to celebrate.

      o ⚓ Everyday_Specters⠀⇛

             Last fall, I was in the English countryside on a research

             trip and decided to visit Blo’ Norton Hall, the moated,

             16th-century manor house in Norfolk where a prince I was

             writing about had once lived. It was almost dusk when I

             arrived, but there were several people my age walking the

             grounds: guests, I assumed, of the bed-and-breakfast to

             which the house had been converted after the prince’s

             death. I tried to maintain a friendly distance.

             As I walked around the house’s rear, the four young men,

             holding glasses of beer, strolled directly past me, and I

             smiled at them—but none appeared to see me. Moments

             later, I realized that this was not, in fact, a bed-and-

             breakfast through which I was welcome to perambulate but

             a single, large holiday home, and I was trespassing on

             some friends’ private vacation. Mortified, I ran back to

             my car, reversed for several minutes down the long gravel

             driveway, and hightailed it home. It felt like a close

             call. The occupants could have interrogated me or even

             called the police. But one more chilling possibility also

             struck me: Had those men seen me at all? Or had I been

             somehow invisible to them—perhaps as an interloper from

             another realm, or perceived as the type of grounds staff

             some are trained not to see? Was I, in other words, a

             sort of ghost passing through their domain?

      o ⚓ Anatomy_of_a_Cancellation⠀⇛

             Again with no ill will towards anyone in the DSA, I’m

             hoping this might be a teachable moment.  In order for it

             to be one, we need to do some unpacking.  There is a

             diverse cast of characters involved.

             I’ll just assume everyone knows who the Democratic

             Socialists of America are.  If not, you can look them up

             easily enough, but they probably represent the biggest

             organized political group to the left of the Democratic

             Party today (or on the left of the Democratic Party,

             depending).  As any sensible democratic socialist

             organization would do, they are actively supporting the

             Portland city workers in their contract negotiations with

             the city, and their plan for an imminent strike.

      o ⚓ CNN_Could_Face_a_Reset_Once_Under_Discovery_Control⠀⇛

             One prominent Discovery shareholder, John Malone, has

             already been vocal. “I would like to see CNN evolve back

             to the kind of journalism that it started with, and

             actually have journalists, which would be unique and

             refreshing,” the entrepreneurial media investor told CNBC

             in November. Malone will serve on the Discovery board,

             but no longer has a commanding block of super-voting

             shares as he once did, leaving Zaslav at the helm.

      o ⚓ Joe_Rogan_Calls_Backlash_Over_His_Use_of_N-Word_a_‘Political_Hit

        Job’⠀⇛

             “That video had always been out there. It’s like, this is

             a political hit job,” Rogan said. He continued, “And so

             they’re taking all this stuff I’ve ever said that’s wrong

             and smushing it all together.”

      o ⚓ ViacomCBS_Elevates_Alex_Berkett_to_Chief_Corporate_Development

        and_Strategy_Officer_Role⠀⇛

             ViacomCBS has promoted veteran dealmaker Alex Berkett to

             the role of chief corporate development and strategy

             officer.

             His previous title was executive vp, corporate

             development & strategy. Berkett will continue to report

             to ViacomCBS CFO Naveen Chopra and to serve on the

             company’s senior leadership team and global inclusion

             advisory committee.

      o § Education⠀➾

            # ⚓ Hunger-Striking_Teachers_Say_School_Closures_Will_Hurt

              Black_and_Brown_Kids⠀⇛

      o § Hardware⠀➾

            # ⚓ CR+LF_has_a_long_history…⠀⇛

                   There is one exception: carriage return [CR]. The

                   carriage is released within the 100ms time, but the

                   carriage is on a spring, and does not get back to

                   the left within 100ms if it is too far over to the

                   right. The usual fix is to send another non

                   printing character, such as a line feed [LF], as

                   the next character, where CR and LF are used for

                   each new line. The paper advances whilst the

                   carriage is returning so giving the carriage a

                   whole 200ms to complete the return. This allows

                   enough time to get to the left, but can leave the

                   carriage still bouncing and mean the first

                   printable character is not well aligned. The fact

                   that 200ms is enough is usually fine, unless you

                   are particularly fussy. The fix to this is to send

                   another non printing character, such as a NULL,

                   another CR, or even a rub out [RO]. The standard

                   HEREIS drum coding even specifies CR, LF and RO at

                   the start.

            # ⚓ Nvidia_Deal_to_Buy_Arm_From_SoftBank_Is_Off_After

              Setbacks⠀⇛

                   Nvidia, a fast-growing company whose chips are best

                   known for rendering images in video games, in

                   September 2020 offered cash and stock then valued

                   at $40 billion for Arm, making it the most

                   expensive deal ever among chip companies. Nvidia

                   made the offer to buy Arm from SoftBank, the

                   Japanese conglomerate that has owned the British

                   company since 2016. Nvidia’s rising stock price

                   later sent the transaction’s value much higher,

                   settling at about $60 billion on Monday.

                   But the blockbuster deal encountered setbacks that

                   included a Federal Trade Commission lawsuit in

                   December to block the acquisition, as well

                   opposition from regulators in Britain.

                   Nvidia and SoftBank said early Tuesday they agreed

                   to terminate the planned deal because of

                   “significant regulatory challenges.”

            # ⚓ SoftBank_dumps_sale_of_Arm_over_regulatory_hurdles,_to_IPO

              instead⠀⇛

                   On a company earnings call on Tuesday, SoftBank CEO

                   Son, who had said the company initially considered

                   listing Arm but opted to sell it instead due to the

                   pandemic, sought to put a positive spin on the

                   scrapped sale.

      o § Health/Nutrition/Agriculture⠀➾

            # ⚓ Worse_than_ineffective:_Two_independent_studies_have

              confirmed_that_EpiVacCorona_is_a_worthless_vaccine_—_and_it

              should_be_taken_off_the_market⠀⇛

                   Despite a recent report that Russia’s Health

                   Ministry has stopped placing orders of the

                   EpiVacCorona vaccine, its manufacturer is

                   optimistic and claims to expect the next production

                   order to come in February. Meanwhile, scientists,

                   as well as journalists at Meduza, have obtained

                   convincing evidence that EpiVacCorona is

                   ineffective and gives recipients a completely false

                   sense of security (unlike Sputnik V, which has been

                   proven to protect recipients from COVID-19’s most

                   severe effects). Meduza explains the two studies

                   that led to that conclusion.

            # ⚓ Opinion_|_On_What_Just_Happened_to_Medicare_for_All_in

              California—and_the_Organizing_We_Need_to_Win⠀⇛

                   Why is a healthcare system—Medicare for All—that

                   costs less described as “too expensive?”

            # ⚓ Covid_Survivors_at_Higher_Long-Term_Risk_of_Cardiovascular

              Damage:_Study⠀⇛

                   Covid-19 survivors are at an elevated long-term

                   risk of developing heart disease, strokes, blood

                   clots, and other cardiovascular disorders,

                   according to new peer-reviewed research out Monday.

                   Published in Nature Medicine, the study finds that

                   individuals who survive Covid-19 are more likely to

                   suffer from cardiovascular disease one year later.

                   That’s true even if they “were not hospitalized

                   during the acute phase of the infection,” although

                   disease risks and burdens are higher for patients

                   who were hospitalized and especially for those who

                   were admitted to intensive care units (ICUs).

      o § Integrity/Availability⠀➾

            # § Proprietary⠀➾

                  # ⚓ Windows_11_–_six_months_later,_still_totally_meh⠀⇛

                         Early in July 2021, I reviewed the Dev Build

                         of Windows 11. I was underwhelmed on so many

                         levels. The new operating system, if it can

                         be called that, was raw, unfinished, and came

                         with a slew of bugs and ergonomic annoyances.

                         But that was then. Since, this thing has been

                         officially released, and it even received a

                         handful of big, critical patches, designed to

                         help resolve some of the early problems.

                  # ⚓ Vivaldi_5.1_Introduces_Horizontal_Scrollable_Tabs_and

                    a_New_Reading_List

                    ⠀⇛

                         Vivaldi is a pretty good option for Linux

                         users. They focus on Linux as one of the

                         first-party platforms, which is impressive.

                         With Vivaldi 5.0 release, it proved to be a

                         versatile Chromium-based option for many

                         Linux users. Now, Vivaldi 5.1 is finally

                         here!

                  # ⚓ Microsoft_Patch_Tuesday,_February_2022_Edition⠀⇛

                  # ⚓ How_a_Texas_[crack]_changed_the_ransomware_business

                    forever [iophk: Windows TCO]⠀⇛

                         Last year, a security analyst named Dmitry

                         Smilyanets had a long online chat with

                         someone who claimed to be a member of REvil’s

                         management team. He went by the online handle

                         ‘Unknown.’

                         “Unknown was not a hacker. He was the

                         operator. He was the manager,” Smilyanets

                         said. “His job was to control the

                         infrastructure, make sure it all works. Make

                         sure that communication lines with victims

                         were up and that payments go through.”

                  # ⚓ Protecting_your_business_in_the_age_of_ransomware

                    [iophk: Windows TCO]⠀⇛

                         The GDPI survey uncovered that 64% of leaders

                         are concerned they’ll experience a disruptive

                         event, such as data loss or downtime, in the

                         next year. With the frequency of ransomware

                         attacks on the rise, all businesses should

                         expect an attack. Whether or not you should

                         be fearful depends on how prepared you are.

                  # § Security⠀➾

                        # ⚓ Security_updates_for_Wednesday_[LWN.net]⠀⇛

                               Security updates have been issued by

                               CentOS (aide), Debian (connman), Fedora

                               (perl-App-cpanminus and rust-

                               afterburn), Mageia (glibc), Red Hat

                               (.NET 5.0, .NET 6.0, aide, log4j,

                               ovirt-engine, and samba), SUSE

                               (elasticsearch, elasticsearch-kit,

                               kafka, kafka-kit, logstash, openstack-

                               monasca-agent, openstack-monasca-log-

                               metrics, openstack-monasca-log-

                               persister, openstack-monasca-log-

                               transformer, openstack-monasca-

                               persister-java, openstack-monasca-

                               persister-java-kit, openstack-monasca-

                               thresh, openstack-monasca-thresh-kit,

                               spark, spark-kit, venv-openstack-

                               monasca, zookeeper, zookeeper-kit and

                               elasticsearch, elasticsearch-kit,

                               kafka, kafka-kit, logstash, openstack-

                               monasca-agent, openstack-monasca-

                               persister-java, openstack-monasca-

                               persister-java-kit, openstack-monasca-

                               thresh, openstack-monasca-thresh-kit,

                               spark, spark-kit, storm, storm-kit,

                               venv-openstack-monasca, zookeeper,

                               zookeeper-kit), and Ubuntu (bluez,

                               linux, linux-aws, linux-aws-5.4, linux-

                               gcp, linux-gcp-5.4, linux-hwe-5.4,

                               linux-ibm, linux-kvm, linux-oracle,

                               linux-oracle-5.4, nvidia-graphics-

                               drivers-450-server, nvidia-graphics-

                               drivers-470, nvidia-graphics-drivers-

                               470-server, nvidia-graphics-drivers-

                               510, python2.7, and util-linux).

                        # § Privacy/Surveillance⠀➾

                              # ⚓ ‘Party_of_Union_Busters’:_McCarthy

                                Opposes_Congressional_Staff_Union⠀⇛

                                     The sincerity of the GOP’s

                                     attempt to rebrand as a party of

                                     workers was called into further

                                     question Monday when Rep. Kevin

                                     McCarthy—the Republican leader in

                                     the U.S. House—spoke out against

                                     congressional staffers’ nascent

                                     unionization push, which has won

                                     the enthusiastic support of

                                     progressive lawmakers and

                                     Democratic leaders.

                                     “I don’t think it would be

                                     productive for the government,”

                                     McCarthy (R-Calif.), a top ally

                                     of former President Donald Trump,

                                     told Punchbowl News of the

                                     unionization effort by Capitol

                                     Hill aides, many of whom are paid

                                     annual salaries in the low

                                     $20,000 range and struggle to

                                     afford basic necessities in one

                                     of the nation’s most expensive

                                     cities.

                              # ⚓ Interview_With_Eugene_Shablygin_–

                                WWPass⠀⇛

                                     Eugene Shablygin: My background

                                     is in fundamental physics, but at

                                     some point, I realized I wasn’t

                                     really a good physicist. In my

                                     opinion, I was not on par with

                                     good physicists like Einstein,

                                     and I didn’t feel the essence of

                                     physics. However, I felt that I

                                     understood how data flows through

                                     different computers.

                              # ⚓ Faith_Leaders_Denounce_Zuckerberg’s

                                Instagram-for-Children_Scheme⠀⇛

                                     Saying that “children’s wellbeing

                                     must come first” above profit,

                                     dozens of faith leaders on

                                     Tuesday told Facebook chief Mark

                                     Zuckeberg to permanently end any

                                     plans for a version of the photo-

                                     and video-sharing app Instagram

                                     for kids under 13.

                                     “Childhood should be all

                                     movement, play, messiness, and

                                     wriggle—life-affirming against

                                     the sleek, flat, rapacious world

                                     of screens.”

                              # ⚓ Private_Internet_Access_Releases_Updated

                                Transparency_Report_in_Q1_2022⠀⇛

                                     The requests were as follows:

                              # ⚓ UK_Government_Refreshes_Its_Terrible

                                ‘Online_Safety_Bill,’_Adds_Even_More

                                Content_For_Platforms_To_Police⠀⇛

                                     The UK’s internet censorship bill

                                     rebranded from “Online Harms” to

                                     “Online Safety” last spring. The

                                     name change did nothing to limit

                                     the breadth of the bill, despite

                                     supposedly shifting the focus

                                     from “harm” to “safety.” Whatever

                                     the name, it’s still being touted

                                     by supporters as a fix for

                                     anything anyone doesn’t like

                                     about the internet.

                              # ⚓ If_EARN_IT_Passes,_What_Happens_On_Your

                                iPhone_Won’t_Stay_On_Your_iPhone⠀⇛

                                     Now, Congress wants to force

                                     Apple’s hand—along with

                                     essentially every company that

                                     allows users to store or share

                                     messages or content—and

                                     essentially mandate such

                                     scanning. 

                                     While Apple’s plan would have put

                                     the privacy and security of its

                                     users at risk, the EARN IT Act

                                     compromises security and free

                                     speech for everyone. The bill

                                     would create serious legal risk

                                     for business that hosts

                                     content—messages, photos stored

                                     in the cloud, online backups—and,

                                     potentially, even cloud-hosting

                                     sites like those using Amazon Web

                                     Services, unless they use

                                     government-approved scanning

                                     tools. 

                              # ⚓ Ohio:_Don’t_Give_Big_Tech_a_Pass_On

                                Privacy⠀⇛

                                     The OPPA would enshrine privacy

                                     violating practices from Big Tech

                                     and other companies, and place

                                     the responsibility for managing

                                     privacy entirely on

                                     individuals—without actually

                                     improving protections for the

                                     people of Ohio or offering them a

                                     way to stand up for their own

                                     privacy. If it is not

                                     substantially improved before it

                                     is enacted, it risks locking in

                                     industry-friendly provisions that

                                     would directly benefit tech

                                     giants such as Facebook, Google,

                                     and Amazon. In many ways, passing

                                     this bill would be worse for the

                                     everyday consumer than passing

                                     nothing at all.

                              # ⚓ Send_Surveillance_Robot_Dogs_to_the

                                Pound,_Not_the_Border⠀⇛

                                     The dogs are not yet in the

                                     field, but having been pushed

                                     through early stages of testing,

                                     they are undergoing evaluation in

                                     El Paso, Texas. The robot dogs

                                     would eventually be expected to

                                     walk miles through the remote

                                     terrain at the border, all the

                                     while filming and scanning.

                                     People who live along the border

                                     are some of the most heavily

                                     surveilled people in the United

                                     States. A massive amalgamation of

                                     federal, state, and local law

                                     enforcement and national security

                                     agencies are flying drones,

                                     putting up cameras, and just

                                     generally attempting to negate

                                     civil liberties—capturing the

                                     general goings-on of people who

                                     live and work in proximity to the

                                     border. But the civil liberties

                                     of these communities are of no

                                     concern to a government with

                                     nearly limitless resources to

                                     throw at putting entire regions

                                     of the United States under

                                     surveillance.

                                     Even if you live hundreds of

                                     miles from the border, don’t

                                     think these “innovations” can’t

                                     or won’t affect you. As we saw

                                     when Customs and Border

                                     Protection drones flew over a

                                     protest in Minneapolis, the $68

                                     billion border surveillance

                                     industry won’t stop expanding if

                                     there’s money to be made further

                                     inland.

                              # ⚓ More_Fallout_For_NSO_And_Israel:_Gov’t

                                Police_Illegally_Deployed_Malware_Against

                                Person_Involved_In_Netanyahu_Bribery

                                Trial⠀⇛

                                     More troubling developments for

                                     both NSO Group and the country it

                                     calls home.

                              # ⚓ Apple_says_a_‘small_portion’_of_iPhones

                                recorded_interactions_with_Siri_even_if_you

                                opted_out⠀⇛

                                     Apple’s release of iOS 15.4 beta

                                     2 fixes a bug that may have

                                     recorded interactions with Siri

                                     on some devices, regardless of

                                     whether you opted out, according

                                     to a report from ZDNet. The bug,

                                     which was first introduced in iOS

                                     15, automatically enabled the

                                     Improve Siri & Dictation setting

                                     that gives Apple permission to

                                     record, store, and review your

                                     conversations with Siri.

                              # ⚓ How_to_delete_your_Instagram_account⠀⇛

                                     If you’ve made the decision to

                                     delete Instagram, whether because

                                     you’ve outgrown the need for a

                                     certain finsta or because its

                                     parent company Meta is courting

                                     controversy again, doing so isn’t

                                     as quick or easy as it should be.

                                     Up until recently, it couldn’t

                                     even be done from within the

                                     Instagram app.

                                     Go ahead and take a moment to

                                     make an obligatory “I’m deleting

                                     Instagram” post if you’d like.

                                     After that, you have two ways you

                                     can go about it.

                              # ⚓ Companies_Should_Mandate_Two-Factor

                                Authentication,_Says_Head_of_National

                                Cybersecurity_Alliance⠀⇛

                                     The interim executive director of

                                     a non-profit that has on its

                                     board members from Lenovo,

                                     Facebook, Microsoft and a number

                                     of other prominent tech firms

                                     said that companies should

                                     mandate two-factor

                                     authentication.

                                     Lisa Plaggemier of the National

                                     Cybersecurity Alliance, which

                                     advocates for cybersecurity

                                     across the country, made the

                                     comment at an event hosted by

                                     Axios Media on Tuesday.

                              # ⚓ A_safer_Internet_starts_with_more

                                encryption⠀⇛

                                     The Internet has been vital to

                                     help parents balance work and

                                     parenting through a lingering

                                     pandemic, yet it’s hard to ignore

                                     the societal issues increasingly

                                     amplified online. And with

                                     children increasingly learning

                                     and socializing online, the

                                     reality is we can’t always be

                                     there to hold their hand.

                                     What’s even more frightening is

                                     when government proposals

                                     undermine people’s best efforts

                                     to keep kids safe online by

                                     ignoring a simple truth: security

                                     is crucial to a safer Internet.

                                     It might seem like an obvious

                                     statement, but it’s not.

      o § Defence/Aggression⠀➾

            # ⚓ Internal_Investigation_Confirms_Border_Patrol_Failures

              Leading_Up_to_a_16-Year-Old’s_Death_on_the_Floor_of_His

              Cell⠀⇛

                   A government investigation into the 2019 death of a

                   Guatemalan teenager in Border Patrol custody has

                   found serious problems with the agency’s handling

                   of sick detainees.

                   The report, obtained by ProPublica through a public

                   records request, concludes that Border Patrol

                   agents did not check on 16-year-old Carlos

                   Hernandez Vasquez, who died of the flu after

                   writhing on the floor of his cell in Weslaco,

                   Texas. The report also found that the case

                   reflected broader problems with care in a detainee

                   system that at the time was overwhelmed with

                   migrants, many of whom were ill.

            # ⚓ Wave_of_Coups_Disrupts_Africa_as_U.S.-Trained_Soldiers_Play

              Key_Role_in_Overthrowing_Governments⠀⇛

                   The African Union is condemning a wave of coups in

                   Africa, where military forces have seized power

                   over the past 18 months in Mali, Chad, Guinea,

                   Sudan and, most recently, in January, Burkina Faso.

                   Several were led by U.S.-trained officers as part

                   of a growing U.S. military presence in the region

                   under the guise of counterterrorism, which is a new

                   imperial influence that supplements the history of

                   French colonialism, says Brittany Meché, assistant

                   professor at Williams College. Some coups have been

                   met with celebration in the streets, signaling

                   armed revolt has become the last resort for people

                   dissatisfied with unresponsive governments.

                   “Between the U.S.-led war on terror and the wider

                   international community’s fixation on ‘security,’

                   this is a context that centers, if not privileges,

                   military solutions to political problems,” adds

                   Samar Al-Bulushi, contributing editor for Africa Is

                   a Country.

            # ⚓ The_Nightmare_Continues⠀⇛

                   We Own the World

                   The United States Department State Department

                   continued in its QAnon-like claim that Russia is

                   planning to fabricate a mass casualty event as a

                   pretext to invade Ukraine – an allegation for which

                   “State” provided no, um, evidence. It was vaguely

                   reminiscent of the George W. Bush administration’s

                   unsubstantiated Weapons of Mass Destruction (WMD)

                   and al-Qaeda alliance claims against Iraq before

                   the criminal, mass-murderous US petro-imperialist

                   invasion of that country.

            # ⚓ US_Sanctions_Caused_Mass_Civilian_Deaths_in_Iraq._Afghan

              Civilians_Are_Up_Next.⠀⇛

            # ⚓ Israeli_Policies_Satisfy_the_Definition_of_Apartheid_Under

              International_Law⠀⇛

            # ⚓ Policing_on_Trial:_Attorney_Ben_Crump_on_Fed_Case_Against

              Three_Cops_Involved_in_George_Floyd_Murder⠀⇛

                   The Minneapolis judge who signed the no-knock

                   warrant that led to the fatal police shooting of

                   22-year-old Black man Amir Locke also presided over

                   the trial of Derek Chauvin, the ex-police officer

                   convicted for the murder of George Floyd. The trial

                   of three officers facing lesser charges — Tou Thao,

                   Thomas Lane and J. Alexander Kueng — is currently

                   underway after being delayed when one of the

                   defendants tested positive for COVID. The trial

                   will show the importance of accountability even

                   from police who are bystanders to murder, says

                   Benjamin Crump, part of the legal team for George

                   Floyd’s family.

            # ⚓ Cover-Up_in_Minneapolis?_Police_“Executed”_Amir_Locke_in

              “No-Knock”_Raid,_Say_His_Parents,_Activists⠀⇛

                   Protests are continuing in Minneapolis after police

                   fatally shot 22-year-old Amir Locke during an

                   early-morning “no-knock” raid on February 2.

                   Bodycam video shows that Locke appeared to be

                   asleep on the couch and wrapped in a blanket when a

                   SWAT team entered the apartment. Locke held a gun

                   he was legally licensed to carry, and was not named

                   in the warrant. Minneapolis interim city Police

                   Chief Amelia Huffman claimed Locke pointed his

                   weapon in the direction of the officers, and

                   suggested he could have been connected to crime,

                   despite not being a suspect in their investigation.

                   “It was very jarring for many people in our

                   community to see Amir painted almost like a

                   criminal,” says attorney and police accountability

                   activist Nekima Levy Armstrong. No-knock warrants,

                   which Mayor Jacob Frey promised to eliminate but

                   never did, “have deadly consequences for innocent

                   Black people like Amir Locke and Breonna Taylor and

                   so many others,” says civil rights attorney

                   Benjamin Crump, part of the legal team for Amir

                   Locke’s family. This week the Biden administration

                   responded to the raid saying it may consider a

                   federal policy that limits the use of no-knock

                   warrants.

            # ⚓ Mass_Student_Walkouts_Over_Police_Killing_of_Amir_Locke⠀⇛

                   Demanding accountability from local leaders,

                   hundreds of high school students in Minneapolis and

                   St. Paul walked out of their classes on Tuesday at

                   noon in protest of the fatal police shooting of

                   Amir Locke during a no-knock raid.

                   The youth-led group MN Teen Activists organized the

                   walkout, which included students at St. Paul

                   Central High School and Capitol Hill Magnet School

                   in St. Paul and Southwest, Roosevelt, and Washburn

                   high schools in Minneapolis, as well as other

                   schools in the surrounding suburbs.

            # ⚓ Opinion_|_America’s_Strategic_Blunders_of_the_Past_That

              Created_This_Crisis_Over_Ukraine⠀⇛

                   Understandably enough, commentaries on the crisis

                   between Russia and the West tend to dwell on

                   Ukraine. After all, more than 100,000 Russian

                   soldiers and a fearsome array of weaponry have now

                   been emplaced around the Ukrainian border. Still,

                   such a narrow perspective deflects attention from

                   an American strategic blunder that dates to the

                   1990s and is still reverberating.

            # ⚓ Opinion_|_Memo_to_Congress:_Diplomacy_for_Ukraine_Is

              Spelled_M-I-N-S-K⠀⇛

                   While the Biden administration is sending more

                   troops and weapons to inflame the Ukraine conflict

                   and Congress is pouring more fuel on the fire, the

                   American people are on a totally different track. 

            # ⚓ ‘Beyond_the_War_Paradigm’:_Report_Offers_Alternative_to_20

              Years_of_Post-9/11_Failures⠀⇛

                   After more than two decades of the widely condemned

                   “global war on terror” launched by the United

                   States government in the wake of the 9/11 attacks,

                   a report released Tuesday offers 10 alternatives to

                   the nation’s militarized approach to national

                   security.

                   “A reevaluation of the U.S. approach to

                   counterterrorism is a moral and strategic

                   imperative.”

            # ⚓ ‘My_task_is_to_kill_you’_Domestic_violence_victim_who_fled

              Dagestan_describes_family_members’_thwarted_attempt_to_kidnap

              her_in_Moscow⠀⇛

                   Aishat Khiramagomedova fled her family home in

                   Dagestan in October 2021, after reaching out to

                   Krepost (Fortress), a charity organization that

                   assists victims of domestic abuse. She made it to

                   Moscow, where Krepost provided her with shelter and

                   access to a psychologist. Within a few months she

                   was starting to find her feet — she had a job and

                   was looking for an apartment with her boyfriend.

                   But on February 4, Aishat’s family tried to kidnap

                   her and bring her back to Dagestan. 

            # ⚓ Ukraine_and_the_Threat_of_Nuclear_War⠀⇛

                   As the crisis in Ukraine deepens, it is appropriate

                   to consider what the actual consequences of war

                   there might be. An armed conventional conflict in

                   Ukraine would be a terrible humanitarian disaster.

            # ⚓ Behind_the_Olympic_Curtain⠀⇛

            # ⚓ China’s_Olympic_Battle_for_Legitimacy:_the_Prehistory_of

              the_2022_Beijing_Games⠀⇛

                   In 1949, the Communist Party of China decisively

                   prevailed over Chiang Kai-shek’s Kuomintang (KMT)

                   after 22 years of civil war, forcing the latter to

                   flee to Taiwan. The founding of the People’s

                   Republic of China (PRC) brought a definitive end to

                   a “century of humiliation” inaugurated by the First

                   Opium War, which had seen colonial powers reduce

                   China to the “sick man of Asia.” This sickness had

                   been a byword for the weakness, internal rupture,

                   and forced narcotic dependency of the Chinese body

                   politic—transposed inevitably onto the racialized

                   Chinese body.

                   Overcoming these scars, in all their physical and

                   psychological manifestations, was the guiding

                   principle for sports policy in the PRC. Only

                   through this lens can we understand why it fought

                   in such an obstinate, pugnacious, and unabashedly

                   political way for a place in the Olympic movement

                   on its own sovereign terms. China turned the

                   Olympics into a battleground in its contest for

                   legitimacy with the KMT regime on Taiwan and its

                   imperialist backers, elevating the dispute to “the

                   main burden of Olympism,” in the words of Otto

                   Mayer, chancellor of the International Olympic

                   Committee (IOC) from 1946 to 1964. And as with the

                   parallel struggle for recognition by the United

                   Nations, this one ended after three eventful

                   decades in unqualified triumph. University of Hong

                   Kong historian Xu Guoqi relates this fascinating

                   saga in his 2008 book Olympic Dreams: China and

                   Sports, 1895-2008.

            # ⚓ Helsinki_2.0⠀⇛

                   You might think that’s an overstatement. NATO is

                   alive and well. The Organization for Security and

                   Cooperation (OSCE) in Europe is still functioning

                   at a high level.

                   Of course, there’s the possibility of a major war

                   breaking out between Russia and Ukraine. But would

                   Russian President Vladimir Putin really take such

                   an enormous risk? Moreover, periodic conflicts in

                   that part of the world—in Ukraine since 2014, in

                   Georgia in 2008, in Transnistria between 1990 and

                   1992—have not escalated into Europe-wide wars. Even

                   the horrific bloodletting of Yugoslavia in the

                   1990s was largely contained within the borders of

                   that benighted former country, and many of the

                   Yugoslav successor states have joined both the

                   European Union and NATO.

            # ⚓ Bernie_Sanders_Says_US_War_With_Russia_Over_Ukraine_Must_Be

              Avoided_at_All_Costs⠀⇛

                   Warning of the potentially catastrophic

                   consequences of what could be the deadliest

                   European conflict since World War II, U.S. Sen.

                   Bernie Sanders on Tuesday stressed the imperative

                   for a diplomatic solution to the Russia-Ukraine

                   crisis that’s brought the world’s two nuclear

                   superpowers perilously close to war. 

                   “Wars rarely turn out the way the experts tell us

                   they will. Just ask the officials who provided rosy

                   scenarios for the wars in Vietnam, Afghanistan, and

                   Iraq.”

            # ⚓ Aid_Groups_Warn_Biden_Not_to_Revive_Trump’s_Terror

              Designation_for_Houthis_in_Yemen⠀⇛

                   Twenty international aid groups on Tuesday urged

                   U.S. President Joe Biden to refrain from restoring

                   the Trump administration’s terrorist designation

                   for the Houthis—warning that reinstating the label

                   would have devastating impacts on civilians already

                   struggling to survive amid a worsening humanitarian

                   catastrophe in Yemen.

                   Biden was praised last year by peace and anti-

                   hunger advocates for rejecting former Secretary of

                   State Mike Pompeo’s eleventh-hour designation of

                   Ansar Allah—as the Houthi movement is officially

                   called—as a “Foreign Terrorist Organization” (FTO)

                   and a “Specially Designated Global Terrorist”

                   (SDGT).

            # ⚓ Opinion_|_North_Carolina’s_New_Education_Bill_Promotes

              Historical_Erasure_and_White_Supremacy⠀⇛

                   In the state of North Carolina, the legislature saw

                   fit to pass House Bill 324 in response to the

                   Critical Race Theory madness set off by a FOX News

                   interview. The bill outlaws teaching that includes

                   the following:

            # ⚓ Up_to_90_more_new_tanks_for_police_in_Germany⠀⇛

                   The Federal Police and the riot police of the

                   federal states are paying € 81 million for armoured

                   vehicles from Rheinmetall. Some procured them

                   already for their special forces

            # ⚓ Not_another_no-fly_list⠀⇛

                   In a letter first reported by Reuters and first

                   published in full by The Points Guy, CEO Edward

                   Bastian of Delta Air Lines has called on Attorney

                   General Merrick Garland to “support our efforts

                   with respect to… putting any person convicted of an

                   on-board disruption on a national, comprehensive,…

                   ‘no-fly’ list that  would bar that person from

                   traveling on any commercial air carrier.”

                   The latest letter from Delta steps up a lobbying

                   campaign the airline began last fall, and which

                   remains as misguided as ever. The letter highlights

                   the urgent need for Congress to enact the Freedom

                   to Travel Act (H.R. 6030) to make clear the rights

                   of travelers, the duties of airlines and other

                   common carriers, and the limitations on when, by

                   what authority, on what grounds, and according to

                   what procedures the right to travel can be

                   restricted.

            # ⚓ Baloch_insurgency_and_continued_tale_of_apathy_and

              violence⠀⇛

                   The province of Balochistan is once again in the

                   vortex of turmoil and violence. On February 5,

                   2022, Pakistani military said it has killed at

                   least 20 rebels in Balochistan after two army posts

                   were attacked within hours of each other on

                   February 2.[1] The attacks targeted paramilitary

                   post in the town of Panjgur, about 450km (280

                   miles) south of the provincial capital, Quetta, and

                   another one in Noshki, about 330km (205 miles)

                   north of the first attack spot. Following the twin

                   attacks, in a statement emailed to the media, the

                   ethnic Baloch separatist group Baloch Liberation

                   Army (BLA) claimed responsibility for the attacks.

                   Jeayand Baloch, the BLA’s spokesman, said the raids

                   were carried out by attackers who were prepared to

                   “self-sacrifice”.[2]

      o § Environment⠀➾

            # ⚓ Montana_Plaintiffs_Announce_First_Children’s_Climate_Trial

              in_History_of_US⠀⇛

            # ⚓ Climate_Expert_Debunks_Big_Oil’s_Lies_About_Carbon_Capture,

              Nature-Based_Solutions⠀⇛

                   A world-renowned climatologist made clear to

                   Congress on Tuesday that some of fossil fuel

                   companies’ key proposals to reduce planet-heating

                   emissions are talking points rather than

                   “meaningful” solutions to the climate emergency the

                   industry created.

                   “The climate crisis… is real and it is here. In

                   order to confront it, we need real solutions that

                   are proven to work and to keep our planet safe.”

            # ⚓ Climate_Coalition_Calls_on_Biden_to_Cease_All_Gulf_of

              Mexico_Drilling_Operations⠀⇛

                   A new legal petition filed Tuesday calls on the

                   Biden administration to stop all fossil fuel

                   exploration and extraction plans throughout the

                   Gulf of Mexico, saying its ongoing approval of such

                   activities violate federal requirements to properly

                   assess climate impacts.

                   The filing with the Interior Department, signed by

                   a diverse collection of 310 groups, begins with a

                   blunt assertion that “fossil fuels are killing us

                   and killing our planet” and points to a federal

                   judge’s ruling last month blocking the

                   administration’s planned oil and gas lease sale of

                   over 80 million acres in the Gulf of Mexico.

            # § Energy⠀➾

                  # ⚓ Footage_of_Offshore_Oil_Accident_Highlights_Risks_of

                    Deepwater_Drilling⠀⇛

                         Video footage obtained by DeSmog shows an

                         offshore oil drilling incident in which heavy

                         equipment fell from a drillship onto an oil

                         and gas wellhead deep below the ocean’s

                         surface. 

                         The three short clips offer those on land an

                         unusual window into the world of offshore

                         drilling accidents. Two experts who reviewed

                         the footage for DeSmog said that the videos

                         appear to show a blowout preventer (BOP) —  a

                         kind of heavy oilfield equipment that is used

                         to control or seal the flow of oil and gas

                         from wells — falling suddenly during a

                         relatively routine procedure. An additional

                         video appears to show the resulting

                         underwater damage filmed from a remotely

                         operated vehicle. Text displayed in one clip

                         reads, in part, “Monitoring BOP Unlatch” and

                         “Pontus,” and a second video of the incident

                         bears the date November 20, 2021.

                  # ⚓ ‘Obscene’:_BP_Profits_Hit_8-Year_High_Amid_Climate

                    Emergency⠀⇛

                         Fueled by rising oil and gas prices that have

                         left millions struggling to afford energy

                         bills, British fossil fuel giant BP reported

                         its highest yearly profits in nearly a decade

                         on Tuesday while rejecting calls for a tax on

                         its financial windfall.

                         The company raked in $12.8 billion in profits

                         in 2021—more than its annual income for the

                         past eight years. The announcement comes a

                         week after BP’s rival Shell reported $19.3

                         billion in profits last year.

                  # ⚓ PG&E_is_on_the_Loose_Again⠀⇛

                         What were the terms of probation he had been

                         asked to oversee? In Judge Alsup’s statement,

                         “Rehabilitation of a criminal offender

                         remains the paramount goal of probation.

                         During these five years of criminal

                         probation, we have tried hard to rehabilitate

                         PG&E. As the supervising district judge,

                         however, I must acknowledge failure.”

                         An ordinary citizen on probation is

                         admonished not to break any laws, deal in

                         guns, drugs, and so on. Probation officers

                         supervise the probationers with weekly

                         visits. At the discovery of a single

                         violation, the probationer is remanded to

                         prison, with an additional burden of time on

                         their sentence.

                  # ⚓ Nornickel’s_Potanin_sees_bright_future_for_NFTs,_not

                    cryptocurrencies⠀⇛

                         Risky cryptocurrencies, such as much-hyped

                         Bitcoin, will give place to asset-backed

                         digital financial assets like non-fungible

                         tokens (NFTs) in the long-term due to the

                         latter’s reliability, Vladimir Potanin, one

                         of Russia’s richest men with assets in

                         different industries and countries, including

                         Finland, told Bloomberg in an interview.

                         Last week, Atomyze Russia, a fintech startup

                         backed by Potanin’s conglomerate Interros,

                         became the first in Russia to obtain the

                         central bank’s license to issue digital

                         financial assets.

                  # ⚓ How_Much_Electricity_Does_Bitcoin_Mining_Use?⠀⇛

                         Researchers from Cambridge University

                         estimates that the mining process devours 143

                         terawatt-hours (TWh) of electricity annually,

                         which is more than the yearly electricity

                         consumption of some countries. For instance,

                         Norway consumes only 124 TWh, and Bangladesh

                         consumes 71. Also, Bitcoin mining requires

                         more energy than the largest technology

                         companies like Google and Facebook.

                  # ⚓ ‘The_Entire_Cryptocurrency_Market_Is_Basically_a

                    Ponzi_Scheme’⠀⇛

                         Janine Jackson interviewed Sohale Mortazavi

                         about cryptocurrency for the February 4,

                         2022, episode of CounterSpin. This is a

                         lightly edited transcript.

                  # ⚓ Crossing_the_Wires_of_Energy_and_Cryptocurrency

                    Policy:_U.S._Congress_Investigates_the_Environmental

                    Impact_of_Crypto_Mining⠀⇛

                         There are currently two primary ways that

                         network participants lend their processing

                         power, which are framing part of the modern

                         energy policy debates around cryptocurrency.

                         The first form is “proof of work,” which is

                         the original method that Bitcoin and Ethereum

                         1.0 employ. When a group of transactions (a

                         block) needs to be verified, all of the

                         “mining” computers race to solve a complex

                         math puzzle, and whoever wins gets to add the

                         block to the chain and is rewarded in coins.

                         The competitive nature of proof of work

                         consensus systems has led to substantial

                         increases in computing power provided by

                         institutional cryptocurrency mining

                         operations and, with that, higher energy

                         demands.

                  # ⚓ 7_countries_where_cryptocurrencies_are_banned⠀⇛

                         Besides, the report found that the number of

                         countries subjecting crypto to anti-money

                         laundering and tax laws has surged 3 times

                         since 2018. For example, all the members of

                         the European Union, except Bulgaria, have

                         currently put these regulations in place.

                         Here are some countries that decided to say

                         no to crypto and why.

                  # ⚓ A_cringe_rapper_slash_Forbes_contributor_allegedly

                    found_with_billions_in_stolen_Bitcoin⠀⇛

                         The Department of Justice has finally found

                         almost all of the billions worth of Bitcoin

                         stolen during the 2016 hack of cryptocurrency

                         exchange Bitfinex — in the hands of a

                         published Forbes and Inc. writer and rapper,

                         who calls herself the “Crocodile of Wall

                         Street,” and her startup founder husband.

                         The DOJ says it seized about $3.6 billion

                         worth of the cryptocurrency, allegedly held

                         by Heather Morgan and her husband, Ilya

                         Lichtenstein. The couple is accused of trying

                         to cover their tracks by laundering the

                         stolen funds through “a labyrinth of

                         cryptocurrency transactions.” It’s the

                         department’s “largest financial seizure

                         ever,” according to a Tuesday press release.

      o § Finance⠀➾

            # ⚓ Amazon_Dodged_$5.2_Billion_in_Taxes_Last_Year,_Report

              Finds⠀⇛

            # ⚓ ‘Class_Warfare’_in_Action:_Amazon_Dodged_$5.2_Billion_in

              Taxes_in_2021⠀⇛

                   An analysis released Monday shows that Amazon

                   utilized several perfectly legal mechanisms to

                   avoid paying $5.2 billion in federal corporate

                   income taxes in 2021, a year in which the online

                   retail behemoth saw its profits and sales

                   skyrocket.

                   Matthew Gardner, a senior fellow at the Institute

                   on Taxation and Economic Policy (ITEP), estimated

                   that given Amazon’s record-breaking $35 billion in

                   U.S. pretax income for fiscal year 2021, the

                   Seattle-based corporate giant paid an “effective

                   federal income tax rate of 6%”—far lower than the

                   statutory corporate tax rate of 21%.

            # ⚓ Opinion_|_Paying_Rate_of_Just_6%,_Amazon_Avoided_More_Than

              $5_Billion_in_Taxes_Last_Year⠀⇛

                   Amazon’s latest annual financial report released

                   last Friday paints a vivid picture of a company

                   that is edging toward monopoly status—and doing so

                   at the expense of U.S. taxpayers.

      o § AstroTurf/Lobbying/Politics⠀➾

            # ⚓ Opinion_|_Will_US_Turn_Away_From_Fascism_and_Abandon_This

              GOP_Death_Cult_Before_It’s_Too_Late?⠀⇛

                   While Republican successes in blocking legislation,

                   judges and even presidential nominations may seem

                   like the Party is on a roll, the reality is that

                   the GOP is in the midst of an existential crisis as

                   severe as any party has seen since the Whigs died

                   out in the early 19th century.

            # ⚓ Manchin_Says_He’s_Skeptical_of_Congressional_Workers’_Union

              Drive⠀⇛

            # ⚓ Palin_Redux⠀⇛

                   Refusing the vaccine means freedom, she says, And

                   no one can ever negate hers. The shots would be

                   o’er her dead body, she says. But what if the

                   body’s the waiter’s?

            # ⚓ ALEC_Is_Driving_Laws_to_Blacklist_Companies_That_Boycott

              the_Oil_Industry⠀⇛

            # ⚓ Is_Korea_Heading_Toward_a_Political_Crossroads?⠀⇛

                   The two candidates, who are currently running neck-

                   and-neck in opinion polls, present a stark

                   contrast. Lee Jae-myung of the ruling Democratic

                   Party advocates South Korea taking the lead on

                   inter-Korean relations, in contrast to President

                   Moon Jae-in’s unwillingness to adopt any measure

                   that would elicit Washington’s disapproval. “In

                   succeeding the Moon Jae-in administration, the Lee

                   Jae-myung government should act as a more

                   independent and active mediator and problem

                   solver,” Lee announced late last year. [1] That

                   will come as a welcome change in direction if it

                   comes to fruition.

                   Lee is also disinclined to accede to U.S. demands

                   to join the anti-China campaign, questioning why

                   South Korea should be forced to choose between

                   China, its leading trading partner, and the U.S.,

                   with whom it has a military alliance. “I think the

                   situation is coming where we can make decisions

                   independently, putting our national interests

                   first. Any thinking that we have to choose between

                   the two is a very disgraceful approach,” Lee

                   argues. [2]

            # ⚓ Biden_Claims_Credit_for_ISIS_Leader’s_Death,_But_It_Will_Do

              Little_Damage_to_Terror_Group⠀⇛

                   Islamic State (IS) is much reduced from the all-

                   conquering force it was for several years after

                   2014 when it had surprised the world by capturing

                   the city of Mosul in northern Iraq. It went on to

                   seize an area the size of Great Britain in western

                   Iraq and eastern Syria, but lost all this territory

                   between 2016 and 2019. The fact that al-Qurayshi

                   was killed so far from previous IS strongholds may

                   indicate that the movement no longer has any bases

                   that it considers secure.

                   But as a guerrilla group that no longer tries to

                   hold territory, it has recently shown renewed

                   strength with an attack on a prison in Hasakah, a

                   Kurdish controlled city in north east Syria. IS

                   leaders who had escaped the prison were at first

                   believed by locals in Idlib to be the target of the

                   US raid.

            # ⚓ No_Attack_on_Voting_Rights_Is_Too_Racist_for_This_Supreme

              Court⠀⇛

                   I honestly do not know what kind of attack a state

                   would have to launch against the voting rights of

                   its Black citizens to make the current Supreme

                   Court step in and stop it. I do not know what form

                   of voter-suppression law, intimidation tactic, or

                   redistricting map would be so racist that this

                   court would strike it down. We are back to the Jim

                   Crow era, not just in terms of the laws that states

                   are passing against the franchise but also in how

                   the Supreme Court refuses to enforce the

                   constitutional amendments prohibiting apartheid. We

                   have literally been here before, when the Supreme

                   Court remained inert as the 14th and 15th

                   Amendments were violated with impunity by any state

                   with enough aggrieved whites to do so. All that’s

                   missing is the violent enforcement of these racist

                   voting rules… but we’ll see what happens when Black

                   people still try to vote this fall.

            # ⚓ What_America’s_Voting_Rights_Activists_Can_Learn_From

              Previous_Civil Rights_Movements⠀⇛

                   Senate Democrats Joe Manchin of West Virginia and

                   Kyrsten Sinema of Arizona joined Senate Republicans

                   in blocking both the Freedom to Vote Act and the

                   John Lewis Voting Rights Advancement Act. These

                   bills would have combated voter suppression by

                   creating a national automatic voter registration

                   system, and they also would have banned partisan

                   gerrymandering.

                   In the wake of the vote, President Joe Biden said

                   he was “profoundly disappointed that the United

                   States Senate has failed to stand up for

                   democracy.”

            # ⚓ The_Five_(Rosa)_Luxembergs⠀⇛

                   Today, many know Rosa Luxemburg as Rosa Luxemburg

                   but when she was born – 5th March 1871 – her real

                   name was actually Róża Luksemburg. Rosa was also

                   known as Rozalia Luksenburg. On 13th June, 1919, an

                   unimaginably large funeral procession walked

                   through Germany’s capital, Berlin almost five

                   months after Rosa Luxemburg was murdered. Germany’s

                   digital library shows thousands and thousands of

                   workers have lined Berlin’s streets to pay tribute

                   to Rosa Luxemburg.

                   Yet, among one of the largest number of people ever

                   seen at a Berlin rally were also four people with

                   whom Rosa Luxemburg knew extremely well during the

                   forty-eight years before her murder by right-wing

                   death squads known as free corps. During the 1918/

                   19 revolution, Germany’s majority social-democratic

                   party, the SPD, had, what Rosa Luxemburg would call

                   a choice between Socialism or Barbarity. It used

                   Gustav Noske – known as the bloodhound – and the

                   free corps to shoot a massive amount of workers

                   and, thereby ending the revolution.

            # ⚓ Peter_Thiel_to_Exit_Meta’s_Board_to_Support_Trump-Aligned

              Candidates⠀⇛

                   Mr. Thiel has been on Meta’s board since 2005, when

                   Facebook was a tiny start-up and he was one of its

                   first institutional investors. But scrutiny of Mr.

                   Thiel’s position on the board has steadily

                   increased as the company was embroiled in political

                   controversies, including barring Mr. Trump from the

                   platform, and as the venture capitalist has become

                   more politically active.

            # ⚓ White_House_science_adviser_Lander_quits_over_bullying

              claims⠀⇛

                   Ms Wallace told Politico that Professor Lander

                   “retaliated against staff for speaking out and

                   asking questions by calling them names, disparaging

                   them, embarrassing them in front of their peers,

                   laughing at them, shunning them, taking away their

                   duties, and replacing them or driving them out of

                   the agency. Numerous women have been left in tears,

                   traumatised, and feeling vulnerable and isolated.”

      o § Misinformation/Disinformation⠀➾

            # ⚓ Homeland_Security’s_Attempts_to_“Combat_Misinformation”_Are

              Suspect⠀⇛

            # ⚓ Neil_Young_urges_Spotify_employees_to_quit⠀⇛

                   Spotify has also said it will add advisories to any

                   podcast episodes that discuss Covid-19.

            # ⚓ Joe_Rogan_Offered_$100M_to_Quit_Spotify_for_Right-Wing

              Platform⠀⇛

                   The controversial podcaster was offered $100

                   million on Monday to quit Spotify and join a right-

                   wing platform.

                   Chris Pavlovski, the CEO of the Canadian video-

                   sharing platform Rumble, tried to entice Rogan to

                   jump ship in a letter posted to the company’s

                   Twitter account Monday.

      o § Censorship/Free Speech⠀➾

            # ⚓ Techdirt_Podcast_Episode_310:_A_Global_History_Of_Free

              Speech⠀⇛

                   We talk a lot about free speech in different

                   countries, and about the history of free speech in

                   the US — but what about the global history of this

                   fundamental concept? A new book released today,

                   Free Speech: A History from Socrates to Social

                   Media by Jacob Mchangama, tackles exactly this

                   subject in great and insightful detail. This week,

                   Jacob joins us on the podcast to discuss the

                   sweeping story of free speech throughout the ages

                   and around the world.

            # ⚓ Book_Bans_Are_on_the_Rise._But_Librarians_and_Authors_Are

              Fighting_Back.⠀⇛

                   The idea of banning books conjures images of piles

                   of hardcovers in the street going up in flames. But

                   over the past few decades in the United States,

                   book banning has taken on a decidedly more genteel

                   character. It has taken place in deliberative

                   school board meetings and in quick after-school

                   chats between librarians and concerned parents.

            # ⚓ Israel_Gets_Georgia_to_Strip_Free_Speech_Rights_(Again)⠀⇛

            # ⚓ Opinion_|_Divestment_Is_Wisdom,_Not_Censorship⠀⇛

                   We live in a time when bribery, in the form of

                   campaign donations, is construed by our nation’s

                   Supreme Court as free speech, and divestment of the

                   kind that helped pressure South Africa to dismantle

                   its apartheid system is equated in the corporate

                   media as censorship. These are signs that the

                   culture in our democracy is unhealthy, diseased. 

            # ⚓ Platform_vs._Publishers⠀⇛

                   How do you distinguish between a platform and a

                   publisher? The debate has been reignited with the

                   backlash against Joe Rogan’s Spotify podcast. Some

                   have accused Rogan of spreading misinformation

                   about COVID on Spotify. Spotify isn’t taking Rogan

                   down and its important to note that Spotify has a

                   $100mm+ exclusive deal with Rogan for his content.

                   Is Spotify a neutral audio platform? Or is Spotify

                   a publisher?

            # ⚓ TikTok_bans_misgendering,_deadnaming_trans_people⠀⇛

                   In updated community guidelines, the company noted

                   that it is “adding clarity on the types of hateful

                   ideologies prohibited on our platform,” stating

                   that it will ban deadnaming, or using a transgender

                   person’s pre-transition name, and misgendering,

                   using incorrect pronouns.

            # ⚓ TikTok_is_banning_misgendering,_deadnaming,_and_content

              promoting_disordered_eating⠀⇛

                   The company announced today it would begin removing

                   videos that promote disordered eating symptoms like

                   short-term fasting and overexercising. Content

                   promoting eating disorders is already banned on the

                   platform, but news reports have repeatedly shown

                   users are exposed to videos featuring unhealthy

                   eating habits. During an October congressional

                   hearing, senators pressed TikTok representatives on

                   further protecting young users.

            # ⚓ [Updated:]_EARN_IT_Act_—_an_attack_on_free_expression_and

              privacy_—_is_back⠀⇛

                   A civil society coalition letter voicing opposition

                   to the EARN It Act was delivered to the U.S. Senate

                   Judiciary Committee leadership in advance of the

                   Committee markup. Access Now is a signatory to the

                   letter, signed by over 60 organizations and led by

                   the Center for Democracy and Technology.

      o § Freedom of Information/Freedom of the Press⠀➾

            # ⚓ BBC_News_Russian:_Nearly_half_of_people_labeled_‘media

              foreign_agents’_have_left_or_are_preparing_to_leave_Russia⠀⇛

                   Russia has designated 75 individuals as “media

                   foreign agents.” And according to BBC News Russian,

                   at least 32 of these people have left or are

                   preparing to leave the country. Another 14

                   individuals had already left Russia due to pressure

                   from the authorities before they were added to the

                   “foreign agent” blacklist.

            # ⚓ Journalist_Mary_Heaton_Vorse_Spent_Decades_on_the_Front

              Lines_of_Labor⠀⇛

                   Coverage of labor, unions, and workers’ rights

                   issues has exploded across a variety of media,

                   particularly as the Covid-19 pandemic exposes the

                   plight of vulnerable workers and changes the nature

                   of work itself. Mainstream publishing behemoths are

                   now trying to catch up to the left-leaning

                   publications that have always cared about such

                   stories. The organizing streaks of media unions

                   like the Writers Guild of America, East (for which

                   I’m a council member), and the NewsGuild have

                   resulted in a generation of labor-savvy media

                   workers with a fierce commitment to improving their

                   workplaces. (This is how I unexpectedly morphed

                   from a heavy metal journalist into a labor

                   reporter!)

            # ⚓ Update_on_Julian_Assange_Case,_Future_of_Gulf_of_Mexico

              Drilling,_and_is_Graphika_Really_a_Fake_News_Watchdog?_–_The

              Project_Censored_Show⠀⇛

                   Notes: Kevin Gosztola is the managing editor of

                   ShadowProof as well as other press-freedom and

                   whistleblower cases. Jayeesha Dutta is co-founder

                   of AnotherGulf.com; she also works with the Climate

                   Justice Alliance. Kevin Gosztola is the managing

                   editor of ShadowProof. He has covered the Julian

                   Assange legal proceedings in the UK from the

                   beginning. Alan MacLeod is a media scholar and a

                   senior staff writer at Mint Press News.

            # ⚓ Didn’t_Those_Now_Enraged_at_Boris_Johnson’s_‘Smears’_of

              Keir_Starmer_Defame_Corbyn_at_Every_Turn?⠀⇛

                   The reason? Last week the British prime minister,

                   Boris Johnson, blamed Starmer, now the Labour party

                   leader, for failing to prosecute Jimmy Savile, a TV

                   presenter and serial child abuser, when his case

                   came under police review in 2009. Between 2008 and

                   2013, Starmer was head of the Crown Prosecution

                   Service (CPS). Savile died in 2011 before he could

                   face justice.

                   Johnson accused Starmer, who at the time was

                   Director of Public Prosecutions, of wasting “his

                   time prosecuting journalists and failing to

                   prosecute Jimmy Savile”.

            # ⚓ ‘They_were_mostly_shouting_about_Assange!’_Tory_MP_hits

              back_at_Boris-Starmer_row⠀⇛

                   “I’ve also watched the clip in full, it’s about

                   three minutes long and these people were mostly

                   talking about Julian Assange for some reason that I

                   don’t understand.

            # ⚓ Keir_Starmer:_No_10_has_no_intention_of_apologising_after

              protesters_surround_Labour_leader⠀⇛

                   “Why did you go after Julian Assange, why did you

                   go after journalists?” one man shouted.

            # ⚓ Police_rescue_Sir_Keir_Starmer_from_mob_who_surround_him

              and_accuse_him_of_‘protecting_paedophiles’⠀⇛

      o § Civil Rights/Policing⠀➾

            # ⚓ Russia’s_Justice_Ministry_seeks_dissolution_of_charitable

              foundation_behind_Russian_LGBT_Network⠀⇛

                   The St. Petersburg branch of the Russian Justice

                   Ministry has asked the courts to liquidate the

                   charitable foundation Sfera, the operator of the

                   Russian LGBT Network.

            # ⚓ Sanders_Unveils_Bill_to_Boost_Understaffed_US_Fire

              Departments⠀⇛

                   Citing the “unprecedented challenges” in

                   “recruiting and retaining” career and volunteer

                   firefighters across the United States, Sen. Bernie

                   Sanders on Monday introduced legislation aimed at

                   tackling the staffing crisis in the essential

                   profession. 

                   “The difficulty in recruiting and retaining

                   personnel is an absolute crisis.”

            # ⚓ Religious_Support_for_Democratic_World_Federation⠀⇛

                   But some religious groups and leaders have rejected

                   the idea that warfare is a necessary part of human

                   nature and human history.

                   In order to eliminate the war system and solve

                   humanity’s many global problems–such as genocide,

                   terrorism, violations of human rights, and

                   environmental degradation due to global

                   warming–they have advocated for the creation of a

                   democratic world federal government that would

                   create just world laws and prosecute individuals

                   who violate them. Violent conflicts would be

                   settled and global problems would be solved through

                   a nonviolent democratic process.

            # ⚓ The_Black_Migrant_Trail_of_Tragedies⠀⇛

                   Julliana Essengue arrived in Tapachula, Mexico,

                   from São Paulo, Brazil, in March 2020. She was

                   broke but determined to reach the United States.

                   After nearly two months traversing rain forests,

                   borders, and rivers by bus, car, boat, and foot,

                   she needed money. At first, Essengue and her travel

                   companions squatted. “We slept on the floor for two

                   weeks in a hallway,” she told me. “There were

                   Africans, Haitians—everybody was sleeping on the

                   floor.”1This story was published with the support

                   of a fellowship from Columbia University’s Ira A.

                   Lipman Center for Journalism and Civil and Human

                   Rights.

            # ⚓ Ohio_Supreme_Court_Rejects_Republican-Drawn_Congressional

              Maps_–_Again⠀⇛

            # ⚓ Affirmative_Action_on_the_Block⠀⇛

            # ⚓ Connecting_the_Dots_and_Rejecting_the_“Rule_of_Law”

              Hypocrisy⠀⇛

                   Lindiwe Sisulu’s parents, Walter and Albertina

                   Sisulu, were leading figures with Nelson Mandela in

                   the African National Congress (ANC) movement that

                   resisted the racist apartheid regime of South

                   Africa. Their daughter’s opinion column shows that

                   she inherited her parents’ zeal for justice.

                   “Whose law is it anyway” bristles with truth about

                   economic reparation, a subject that the

                   beneficiaries of colonization always try to avoid.

                   Consider the following excerpt:

            # ⚓ ‘They_Are_Firing_the_Entire_Committee!’_Memphis_Workers_Say

              Starbucks_Targeting_Union_Organizers⠀⇛

                   Workers at a Memphis Starbucks who were fired

                   Tuesday after launching a unionization effort vowed

                   to carry on their fight, with one employee invoking

                   the legacy of the Rev. Martin Luther King Jr.—who

                   was assassinated in the Tennessee city while

                   campaigning for workers’ rights. 

                   “Starbucks has been fighting desperately to silence

                   us because we did not back down or let them shake

                   us.”

            # ⚓ Hunger-Striking_Teachers_Say_Oakland_Plan_to_Close_Schools

              Will_Hurt_Black_&_Brown_Communities⠀⇛

                   We go to Oakland, where a group of teachers are on

                   a hunger strike to protest a plan to close and

                   merge over a dozen schools due to under-enrollment.

                   This comes ahead of a critical school board vote

                   Tuesday that will decide whether to proceed with

                   the plan. Activists argue the move threatens to

                   divert resources to charter schools and displace

                   hundreds of Black and Brown children from their

                   neighborhood schools. The hunger strike across

                   multiple different schools has empowered many to

                   speak up against longtime systemic racism, says

                   Moses Omolade, one of the striking workers and a

                   community schools manager at Westlake Middle

                   School. “The school board is attempting to close

                   predominantly Black and Brown schools without

                   engaging with us at all.”

            # ⚓ How_a_Cooperative_Run_by_the_Formerly_Incarcerated_is

              Reshaping_Chicago’s_Food_Industry⠀⇛

                   These school meals were supplied by

                   megacorporations like PepsiCo Inc., Tyson Foods

                   Inc., Pilgrim’s Pride Corporation, Cherry Meat

                   Packers Inc., Central Valley Meat Co. Inc.,

                   American Beef Packers Inc. and Jennie-O Turkey

                   Store LLC. As detailed in a 2020 article by

                   Jennifer E. Gaddis in the professional journal for

                   educators Phi Delta Kappan, 95 percent of U.S.

                   public schools participate in the government-

                   subsidized National School Lunch Program, and this

                   program is made up almost entirely of contracts by

                   giant corporate food brands. Gaddis writes:

                   It happened again in 2020 when the Trump

                   administration proposed making the rules more

                   flexible, Gaddis adds.

            # ⚓ The_student_forced_out_after_standing_up_for_women⠀⇛

                   Yet from the minute it was announced, it became a

                   target for militant trans activists among the

                   university students – who objected to Woman’s Place

                   UK’s stance on gender recognition issues, and

                   demanded the event be cancelled.

                   Why? “The issue they had was with the meeting

                   taking place at all,” Rosario Sanchez replies.

                   “They didn’t want women to have these

                   conversations.”

            # ⚓ Why_This_Feminist_Is_Taking_the_University_of_Bristol_to

              Court⠀⇛

                   Next week, I am taking my university to court. To

                   my knowledge, it is the first time an academic

                   institution has been forced, at trial, to justify

                   why it prioritises trans rights over women’s

                   rights. The other party in the case is the

                   University of Bristol, which one might suppose to

                   be an unlikely defendant given its distinction as

                   the first higher-education establishment in England

                   to have admitted women on an equal basis to men.

                   Unfortunately, the university has more recently

                   become known as a hotbed for anti-feminist

                   militancy.

            # ⚓ LABOR_After_Amazon_Tragedy,_Workers_Come_Together_to_Demand

              Safe_Working_Conditions⠀⇛

      o § Digital Restrictions (DRM)⠀➾

            # ⚓ Automakers_Can’t_Give_Up_The_Idea_Of_Turning_Everyday

              Features_Into_Subscription_Services_With_Fees⠀⇛

                   At the same time car companies are fighting the

                   right to repair movement (and the state and federal

                   legislation popping up everywhere), they’re

                   continuing the quest to turn everyday features —

                   like heated seats — into something users have to

                   pay a recurring fee for.

            # ⚓ What_on_Earth_is_going_on_with_Peloton?⠀⇛

                   In 2020, Peloton’s supply chain was struggling to

                   keep up with the unexpected surge in demand created

                   by people suddenly eager to work out at home.

                   Facing months-long fulfillment delays, Peloton

                   decided to heavily invest in building out its

                   manufacturing capabilities. It dropped millions to

                   expedite shipping and another $420 million buying

                   Precor, one of the world’s largest commercial

                   fitness equipment makers. It spent another $400

                   million on a factory in Ohio. The company was

                   positioning itself to rapidly build bikes and

                   treadmills for a market that couldn’t get enough.

      o § Monopolies⠀➾

            # § Patents⠀➾

                  # ⚓ Pfizer_Forecasts_Record-Breaking_2022_Profits_—_as

                    Billions_Remain_Unprotected⠀⇛

                  # ⚓ Pfizer_Forecasts_Record_Vaccine_Revenue_for_2022_as

                    Billions_Remain_Unprotected⠀⇛

                         Pfizer projected Tuesday that it will

                         generate a record-shattering $32 billion in

                         revenue from its publicly funded coronavirus

                         vaccine in 2022 as the U.S. pharmaceutical

                         giant refuses to share its technology with

                         other nations, leaving billions of people

                         around the world without access to lifesaving

                         shots as the pandemic continues to rage.

                         “We’ve let Pfizer withhold this essential

                         medical innovation from much of the world.”

            # § Trademarks⠀➾

                  # ⚓ Apple_Opposes_Trademark_For_Indie_Film_‘Apple-Man’

                    Claiming_Potential_Confusion⠀⇛

                         When it comes to silly trademark disputes,

                         Apple has come up for discussion many, many

                         times. The mega-corporation is a jealous

                         defender of all of its IP, but most of our

                         stories have focused on its disputes with

                         companies that created logos that involve any

                         sort of apple or other fruit. Sometimes it’s

                         not even companies that Apple is fighting

                         with, but entire foreign political parties.

                         The idea here is that when it comes to logos

                         or trade dress, Apple appears to think that

                         it owns all the apples.

            # § Copyrights⠀➾

                  # ⚓ Appeals_Court_Can_Rule_That_DMCA’s_Anti-Circumvention

                    Rules_Are_Unconstitutional⠀⇛

                         As you hopefully know, there are two main

                         parts to the DMCA law that was passed in

                         1998. There’s DMCA 512, which is what you

                         hear about most of the time. That’s the part

                         that includes the rules for notice and

                         takedown regimes for user uploaded content

                         (among other things). It’s got problems, but

                         in its current form has also enabled many

                         important services to exist. The other part,

                         which is much more problematic, is DMCA 1201,

                         which is the anti-circumvention rules — or

                         you could call it the “DRM” part of the law.

                         This has no redeeming value whatsoever. Under

                         1201 basically any attempt to circumvent a

                         “technological” protection measure, can be

                         deemed infringing even if the underlying

                         content is never infringed upon. This part of

                         the law is not only not necessary, but it’s

                         drafted in a manner that has been regularly

                         abused — enabling everyone from printer

                         manufacturers to garage door opener companies

                         to argue that simple reverse engineering to

                         create competition is “infringement.”

                  # ⚓ Do_not_feed_the_trolls⠀⇛

                         Recently, there has been an increase in

                         threatened and actual lawsuits involving CC

                         licensed works, and in some cases, license

                         enforcement has even become a business model.

                         We have now learned that even long-time

                         friend and contributor to Creative Commons,

                         Cory Doctorow, has been targeted.

                         Put simply, “license-enforcement-as-business

                         model” is a perversion of the founding ideals

                         of Creative Commons. We condemn this

                         behavior. These aggressive enforcement

                         actions lessen trust in open licensing, and

                         they erode the good faith ecosystem that is

                         the basis of the commons.

                  # ⚓ MPA_&_ACE_Embed_Staff_at_US_Govt._IPR_Center_To_Fight

                    Movie_&_TV_Show_Piracy⠀⇛

                         The Motion Picture Association and anti-

                         piracy coalition Alliance for Creativity and

                         Entertainment will embed their own personnel

                         at the US Government’s National Intellectual

                         Property Rights Coordination Center. Under

                         the umbrella of the Department of Homeland

                         Security and Immigration and Customs

                         Enforcement, they hope to tackle movie and TV

                         show piracy more effectively.

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