𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, February 07, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Tue 8 Feb 02:41:16 GMT 2022 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2022/02/07/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): Qmf3TSbMJS9koYs7ieZ1w3WBpaDp6x7rx5xnhC6B134fFL QmbAVHY5Ges1nF9HNsiNn6FsQW8UdTFHURKDG1QgSKpKw7 QmZnZkCBXLzZg5rkewh3peFLzQ5xAZRm6HpjAvmtf39ELR QmZeHUaFKnCwMohgf9hT7KAvQEFvHbBZ8MUZTtceSkoLZc QmQLbqvdSXzQ59gWzwwt9RARegF8vZB68qihXTbNcDNoxy QmXRhRDa28yw47e5ym8hgWTNSCTtmH5t22GCpvFvaGYDwN QmNrH8cLM4mYaiBXzhdkhAQm8XM54JzRQa3Z1Ng4a41kcV QmZjLA2jtgeEhSJihNxjJW3q7KaEU6iyCKve9pmkci3m61 QmTWgjCkngZ2r4jN8fZGmd7bpEdJL3pBfU6vKWFNxPmkYf QmUa6NW563bcVpbJi9K42Aap4iTTXYmJcu5bTsjAcRc9yG QmPENr81muU2jHsHXxDP2oXCR4itHu2Pb54BpV4z2a6v8g QmT1WmWT8oyJF7h6FDnkDWXE6tEV7sUdo6MyboEn1kLiFx Qmd7o1W8PgtXmeAFmAGFoVreMpLA1AVtvVjUMvVr7zc1YQ Qma88nEdV64rLJsqR8uVd62B8zwrDvuX6Etg42wsovLPUQ QmWMn5rx4mwf86jmAsH6KUasKtr2WVybRVa9b2sJECtwpz QmS1wrYoYvTPNPTvZYppVeYPXTR8rHjtMkwCEYGCEaEWUU QmTLUpA1Pbmatf5PSQgBbMk1Hj8eJFQAcNy7ahAe769Anx QmbQWJTJVwCBMn6Bc7J9W2fhZtZYwQh4SrKoy4dF1Rj3Pm QmZ3Z9HPLFuFUYdDqN8YY1cZW5M8k9MCEyfwYQiJSBdgg9 Qme1XwuhK1F1t6m8AJGPXQ8U9wCeB9UCDmmkPBEmWLharx QmQdk83ourWknf8WYXr4Z6LnuaLWYmqhpidR9Crga89wZn ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ [Meme] Drunk on Power and Diplomatic Immunity | Techrights ⦿ EPO Pays Out Millions of Euros in Compensation - to Thousands of Workers Who Deserve a Lot More for Moral Damage - for Battistelli’s Illegal Acts (But Battistelli Himself Has Not Been Punished at All, Nor Have His Enablers) | Techrights ⦿ Self-Hosted Gemini Proxy (HTTP and HTTPS) | Techrights ⦿ The EPO’s Overseer/Overseen Collusion — Part XXXXIV: Immunity = Impunity? | Techrights ⦿ IRC Proceedings: Sunday, February 06, 2022 | Techrights ⦿ Microsoft GitHub Exposé — Part XVII — Backsliding Into 1990s-Style Digital Slavery by Microsoft | Techrights ⦿ Nobody Should be Above the Law | Techrights ⦿ The EPO is Bleeding in Courts | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/02/07/epo-diplomatic-immunity-meme/#comments http://techrights.org/2022/02/07/epo-moral-damage/#comments http://techrights.org/2022/02/07/http-and-https-gemini-proxy/#comments http://techrights.org/2022/02/07/immunity-and-impunity/#comments http://techrights.org/2022/02/07/irc-log-060222/#comments http://techrights.org/2022/02/07/monday-github-outline/#comments http://techrights.org/2022/02/07/the-above-the-law-complex/#comments http://techrights.org/2022/02/07/the-epo-is-bleeding-in-courts/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/02/07/fragments-2-0/#comments http://techrights.org/2022/02/07/openmandriva-lx-4-3/#comments ䷩ 𝚕𝚒𝚗𝚎 69 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/epo-diplomatic-immunity-meme/#comments Gemini version at gemini://gemini.techrights.org/2022/02/07/epo-diplomatic-immunity-meme/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Drunk_on_Power_and_Diplomatic_Immunity⠀✐ Posted in Europe, Humour, Patents at 9:08 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Slippy guy: Internal appeals, ILOAT, Dutch Supreme Court⦈ Summary: When you let unqualified (in the area of patents) psychopaths run the EPO you can expect the worst; Benoît_Battistelli and António_Campinos have repeatedly misused diplomatic immunity to avoid investigation and possible prosecution ⣧⣶⣤⣦⣴⣴⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣘⠛⠛⣛⣛⠛⣛⡛⢛⣛⣙⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⡘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣤⣤⣠⣤⣠⣄⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⠿⠾⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠈⠻⠛⠛⠛⣛⣛⢛⣛⣛⣛⣛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣶⣶⣤⣶⣶⣤⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⡀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣠⣤⠀⠀⠀⠸⢿⡿⠀⠀⠀⠀⠂⠀⠀⢹⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⣁⡀⠀⠀⠀⠀⢀⣀⣼⣛⣛⣿⡇ ⣿⣿⣿⣿⣿⢿⣿⣟⠏⠋⠉⠋⠉⠹⠿⠟⠉⠁⠀⠀⠀⠀⢠⣿⣷⡆⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣀⣼⣿⣿⣿⣿⣿⡇ ⠛⠛⠙⣟⠽⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⡄⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼⡟⠁⠀⠀⠉⠀⠈⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⡛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠈⠀⠈⠙⠋⠉⠛⠻⠿⠋⠀⠙⠉⠙⠉⠉⠁ ⠋⠛⢶⢀⡀⠀⠂⣀⡀⡀⠀⠀⠚⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣤⣄⣨⣿⣧⣼⣿⣿⣯⣿⡬⣿⣿⡶⠂⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣴⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⣛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠈⠛⠛⠛⠛⡛⢛⠛⣛⠛⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⣶⣦⣤⣶⣶⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣠⣄⠀⠀⠀⠸⢿⡧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠈⣁⠀⠀⠀⠀⠀⠀⣀⣸⣛⣻⣿⡇ ⣿⣿⣿⣿⡿⣿⣿⣿⡟⠋⠙⠛⠛⠿⠿⠿⣿⢿⣿⠿⠉⠁⠀⠀⠀⢠⣦⡀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇ ⠿⠛⠛⣿⠿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠈⠛⠛⠛⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⡍⠛⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠙⠋⠙⠋⠙⠛⠻⠿⠿⠋⠁⠙⠉⠉⠉⠉⠁ ⠉⠓⣦⣀⡀⠀⠂⣀⢀⣀⢀⠀⠶⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣄⣸⣿⣤⣽⣿⣿⣿⣥⣼⣿⡷⡔⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣯⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠎⠂⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣴⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⡛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣀⣈⣀⣀⣀⣀⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠀⠻⡟⣟⣛⣟⣛⡛⣛⣛⣛⡛⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣦⣶⣦⣤⣶⣶⣤⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣠⣄⠀⠀⠀⠼⢿⡧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠘⣁⠀⠀⠀⠀⠀⢀⣀⣘⣛⣻⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠛⠛⠿⠿⢿⣿⢿⣿⣿⣿⠏⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇ ⠿⠟⠟⢿⡽⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠼⠊⠉⠉⠁⠀⠀⠀⠀⠀⢠⣿⣦⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠍⠁⠁⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠈⠛⠛⠛⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⢟⠛⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠉⠉⠉⠋⠙⠋⠻⠿⠿⠋⠀⠙⠉⠉⠉⠉⠁ ⠉⠳⣤⣀⡀⠐⠒⡀⢀⣀⢀⠀⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣀⣸⣿⣧⣼⣿⣿⣿⣥⣼⣿⣷⡔⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⣶⣶⡶⠄⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣦⣤⣤⣤⣴⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⡛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣀⣀⣀⣀⣀⣀⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠛⢛⢻⣟⣛⣛⣛⣛⣛⢛⠛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣦⣶⣦⣤⣶⣶⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⣄⠀⠀⠀⠸⢿⡧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠘⣁⠀⠀⠀⠀⠀⠀⣀⣘⣛⣻⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠛⠛⠿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇ ⠻⠛⠛⡿⠷⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠔⣞⠟⢻⡿⠛⠋⠉⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡄⠈⠛⠛⠛⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⢠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠏⠛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠘⠉⠙⠋⠛⠛⠛⠿⠿⠋⠀⠙⠉⠉⠉⠉⠃ ⠉⠳⣤⣀⠀⠐⠒⡂⠀⠀⢀⠀⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣄⣸⣿⣤⣸⣿⣿⣿⣥⣼⣿⡷⠦⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⣶⣶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣼⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⣛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣀⣈⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠳⠒⠖⢒⣒⣒⡒⡒⢒⡖⣗⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠀⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣦⣴⣤⣤⣶⣶⣤⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣻⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣃⣄⠀⠀⠀⡠⢿⡇⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠁⠀⠀⠀⠀⠀⢀⣀⣘⣛⡻⣿⡇ ⣿⣿⣻⣿⣿⣿⣿⣿⠿⠋⠛⠛⠛⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇ ⠿⠟⠛⠫⠿⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡔⣺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠙⠛⠛⠛⠿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠋⠉⠋⠙⠛⠛⠿⠿⠋⠀⠛⠉⠙⠉⠉⠃ ⠉⠳⡤⣀⠀⠐⠂⣒⡂⠀⢀⡀⡴⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣄⣸⣿⣤⣺⣿⣿⣿⣥⣽⣿⣶⡤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⣶⣶⡶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣼⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣙⠛⠛⣛⡛⠛⣛⡛⢛⣛⣛⡛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡅⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⢿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣀⣈⣈⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠳⠒⠖⠒⠲⣒⡒⣒⡒⡒⡗⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠀⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠀⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣦⣴⣤⣤⣶⣶⣤⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⣛⣻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣃⣀⠀⠀⠀⡠⢿⡇⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠁⠀⠀⠀⠀⠀⢀⣀⣘⣛⡻⣿⡇ ⣿⣿⣿⢿⡿⣿⣿⣿⠟⠋⠛⠛⠛⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇ ⠟⠟⠛⢻⡯⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡕⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠟⠁⠀⠀⠀⠀⠉⠿⠏⠉⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠋⠉⠋⠙⠛⠻⠿⠿⠏⠀⠛⠉⠙⠉⠉⠃ ⠋⠳⣤⣀⠀⠐⠂⠒⠀⠀⢀⠀⠴⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣄⣸⣿⣥⣼⣿⣿⣿⣤⣿⣿⡧⡤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⣶⣶⡶⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡷⠶⠶⠷⠾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣛⠛⠛⣛⣛⠛⣛⡛⢛⣉⣉⡉⠙⣛⣛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⢿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⣘⡛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠶⠾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠈⡛⠛⠛⠻⡿⣛⣛⡛⣛⣛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣴⣦⣤⣴⣶⣤⣴⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⣛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⣤⣤⣤⣄⣘⣁⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣄⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣋⣃⣄⡀⠀⠀⡠⢿⡷⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣀⣘⣛⠻⣿⡇ ⣿⡿⣿⣿⣿⣿⣿⣿⠻⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇ ⠿⠟⢛⣿⡟⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠸⢓⣿⣿⣿⣿⡟⢿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠹⠫⠁⠥⠂⠀⠨⢿⣦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠛⠻⢿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠏⠙⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃⠀⠂⠈⠙⠛⠛⠛⠻⡿⡿⠟⠉⠙⠛⠛⠛⠛⠃ ⠳⣄⡀⠀⠠⠤⠔⠒⡒⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣀⣘⣷⣞⣷⣿⣿⣿⣯⣛⣾⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣷⣶⣶⠦⠴⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡷⠶⠶⠷⠾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣛⠛⠛⣛⣛⠛⣛⡛⢛⣉⣉⡉⠙⣛⣛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⢿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⣘⡛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⣛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⠿⠿⠷⠾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠈⠛⠛⠛⠿⠛⣛⢛⡛⣛⣛⠛⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣴⣦⣤⣴⣶⣤⣴⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢀⣀⣀⣤⣄⣤⣄⣘⣁⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣄⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣋⣃⣄⡀⠀⠀⡠⢿⡷⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣀⣘⣛⠻⣿⡇ ⣿⣿⢿⣿⣿⣿⣿⣿⠻⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇ ⠿⠿⠻⣿⡟⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⢸⢻⣿⣿⣿⣿⡿⢿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠹⠋⠣⠬⠀⠀⠘⢿⣦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠙⠛⠻⢿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠏⠛⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠊⠀⠒⠉⠙⠛⠛⠛⠻⢿⡿⠟⠉⠙⠛⠛⠛⠛⠃ ⠳⡄⡀⠀⠠⡤⠖⠒⡒⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣀⣘⣷⣝⣟⣿⣿⣿⣯⣛⣷⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⡯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣷⣶⣶⡦⠴⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣈⣛⠛⠛⣉⣉⠉⣉⡉⢉⣉⣉⡉⠙⣛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⣘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⢓⣛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠗⠲⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⡙⠛⠛⠿⢿⣛⣛⢛⢛⣛⡛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣦⣶⣤⣤⣶⣶⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣆⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣧⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣃⡀⠀⠀⠀⡠⢿⡷⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣀⣘⡛⠻⣿⡇ ⣿⣿⢿⣿⣿⣿⣿⡿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣀⣸⣿⣿⣿⣿⣿⡇ ⡿⠿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⡹⣻⣿⣿⣿⣿⡟⠛⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠽⠛⠃⠍⠀⠀⠺⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠛⠛⢿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠲⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠙⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠑⠛⠻⠟⠛⠻⠿⢿⣿⠟⠉⠙⠛⠛⠛⠛⠃ ⣦⣀⠀⠀⣠⣤⡤⠀⠂⠒⠂⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣈⣻⣤⣒⣷⣿⣿⣿⣚⣢⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⣤⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⣷⣶⠦⠤⠦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣈⣛⠛⠛⣋⣉⠉⣉⡉⢉⣉⣉⡉⠛⣛⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣆⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⣘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⣓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠟⠺⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⢙⡛⠛⢿⣛⣛⣛⣛⣛⣛⡛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣶⣶⣀⣹⣿⣿⣿⣿⣿⡇ ⠿⢻⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⡏⠛⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠻⠯⠁⠬⠉⠀⠾⢿⡇⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⠛⠻⢿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠒⠲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠫⠙⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠁⠘⠓⠛⠛⠛⠛⠛⠿⣿⠿⠋⠈⠙⠛⠛⠛⠛⠃ ⢧⣄⠀⠀⣰⣤⠦⢒⠐⠒⠀⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣈⣻⣶⣛⣿⣿⣿⣿⣝⣷⣾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣶⠦⠤⠦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣘⣛⠛⠛⣛⣛⠛⣛⡛⢛⣛⣛⡛⠟⣛⣛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣷⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣇⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠛⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⢛⡘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⣓⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡎⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠰⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣶⣶⣦⣤⣶⣶⣤⣾⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⣦⣤⣤⣤⣤⣀⣀⡀⠀⠘⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣁⣡⣤⠀⠀⠀⢼⣿⡿⠀⠀⠀⠀⠇⠀⠀⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣄⠀⠀⠀⢤⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣀⡀⣈⣁⠀⠀⠀⠀⠀⢠⣀⣽⣛⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠛⠛⠿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣠⣿⣿⣿⣿⣿⣿⣿⡇ ⡿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣯⠛⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠿⠿⠿⠿⠏⠑⠿⢿⣿⠀⠈⠁⠑⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠛⠛⠛⠛⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⡀⡀⠒⣙⣿⢷⠦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡄⠀⠴⠂⢤⡕⡁⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠙⠉⠙⠛⠛⠛⢿⣿⠿⠏⠀⠙⠉⠉⠙⠋⠹⠇ ⢳⣦⣄⣔⣺⣺⣿⣿⣇⣭⣸⣿⣿⠖⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢄⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⡟⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣷⣶⣶⣷⡿⠆⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣾⣶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣙⣛⠛⠛⣛⣛⠛⣛⡛⢛⣛⣛⡛⠟⣛⣛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣇⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⢛⡘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⢛⣓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠟⠻⠷⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣾⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⢻⡿⠿⢿⣿⣿⣿⢿⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣶⣶⣦⣴⣶⣶⣴⣾⣶⣤⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣤⣤⣄⣀⣀⡀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣀⣥⣄⠀⠀⠀⡼⢿⡧⠀⠀⠀⠐⠀⠀⠘⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣦⣤⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⣈⣀⠀⠀⠀⠀⠀⣠⣀⣽⣛⣻⣿⣿⡇ ⣽⣿⣿⣿⣿⣿⡿⠟⠉⠙⠋⠛⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣠⣿⣿⣿⣿⣿⣿⣿⡇ ⠛⢻⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣟⠛⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠮⠿⠻⠿⠟⠟⠃⠀⠘⢻⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠘⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⣀⠚⠙⠻⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠙⠋⠀⠁⠀⠈⠋⠙⠙⠛⠿⠟⠁⠀⠉⠉⠉⠉⠉⠹⠇ ⢳⣄⣀⠀⡒⢒⣛⣫⣀⣀⡐⣿⡵⠂⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣿⣿⣭⣿⣿⣿⣿⣽⣿⣿⣿⣶⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⡇⠀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣘⣛⣉⠉⠛⣉⣉⠉⣉⡉⢉⣉⣉⡛⠟⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣷⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣇⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⢛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⢘⣛⡓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠃⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡎⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⢉⣉⣋⣽⣟⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠰⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣶⣿⣿⣶⣿⣿⣷⣾⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣀⡀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣤⣤⣤⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⠀⠀⠸⢿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣶⣤⣀⣤⣤⣄⡀⠀⠀⠀⣠⣤⣤⣭⣽⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠙⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇ ⣻⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⡯⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⠃⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⠛⠉⠉⢱⣤⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠿⠛⠛⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⡠⠄⠉⠻⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⣿⣿⣿⠿⢿⣿⢿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⠐⠈⡐⠐⠀⠀⠀⠀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⡅⠀⠈⠀⠀⠀⠀⠈⠁⠁ ⢲⣖⡊⣛⣯⣭⣽⣦⣭⣝⣻⣗⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣥⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡛⡃⢀⣠⣤⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣙⣛⣉⠉⠉⣉⣉⠉⣉⡉⢉⣉⣀⡛⠟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣷⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣇⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠛⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⡛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⢘⣛⠓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠃⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡎⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠈⠉⢹⣭⣿⣏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠰⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣾⣿⣻⣶⣿⣿⣷⣿⣷⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠆⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣀⣀⢀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣤⣤⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣀⣤⣤⣄⡀⠀⠀⠀⣤⣤⣦⣭⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⠿⠉⠉⠉⠉⠉⠙⠛⠛⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠙⠛⠋⠂⠸⣇⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠛⠿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⢀⠤⢀⢍⠿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⠘⠛⣒⣲⣀⣀⣀⣀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢺⣎⣚⣹⣿⣿⣿⣾⣿⣿⣿⣟⣃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣥⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣠⣄⠀⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⣍⡤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣘⡛⣀⣀⣀⠀⠀⣀⣀⠀⣀⡀⢀⣛⣛⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⢿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣄⡀⣿⣿⢸⣿⡇⣿⣏⣿⣿⡇⣿⣿⣾⣿⡆⣿⣿⣀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠠⣤⣤⣤⣤⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠒⠒⠒⠒⠒⠚⠓⠒⠀⠀⠀⠐⠂⠀⠐⠒⠒⠚⠚⠛⠛⠛⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢼⣿⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀⣀⣍⠉⣻⣿⣿⣿⣭⣽⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣤⣀⠀⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢻⣻⡿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⣰⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠁⠀⠁⠉⠉⠉⠉⠀⠈⠉⠘⠉⠉⠈⠈⠉⠉⠉⠁⠀⠀⠈⠛⠉⠉⠛⠛⠛⠁⠀⣰⣿⣯⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⣀⡶⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠃ ⣿⠛⠋⣀⣀⣠⣤⣤⠦⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⢹⣻⣿⣴⣾⣿⣿⣿⣿⣿⣿⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢳⣄⣀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣦⣤⣶⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠛⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣼⣿⣅⣧⣤⠴⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣥⣤⣄⡀⠀⠀⠀⠀⢀⣤⡠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣘⡛⣀⣀⣀⠀⠀⣀⡀⠀⣀⡀⢀⣛⣋⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠠⡤⣤⢤⣤⣤⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠐⠂⠀⠀⠒⠒⠚⠒⠚⠉⠛⠃⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣤⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢼⣿⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀⣀⣍⠉⣻⣿⣿⣿⣭⣽⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣤⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣤⣀⠀⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠽⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⢛⣻⡿⣿⣿⣿⣿⣿⡿⢿⣿⣟⣟⣻⣿⣿⣿⣿⣿⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⣰⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠛⠛⠛⠁⠀⢰⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⣀⠴⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁ ⣗⠁⠈⢀⣀⣤⡤⣤⠄⣀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⢙⣛⣷⣠⣶⣿⣿⣿⣿⣷⣿⣷⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢳⣄⣀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣤⣤⣰⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠛⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣤⣏⣠⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⣤⡠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠯⠿⠾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣘⡛⣀⣀⣀⠀⠀⣀⡀⠀⣀⡀⢀⣛⣋⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠠⡤⣤⢤⣤⣤⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠐⠂⠀⠀⠒⠒⠚⠒⠛⠉⠛⠃⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣤⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢼⣿⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀⣀⣍⠉⣻⣿⣿⣿⣭⣽⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣦⣄⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⡟⠀⠀⣴⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡹⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣻⣿⣛⢻⡿⣿⣿⣿⣿⣿⡿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠿⠀⠀⣶⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠁⠁⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠾⣿⣿⣿⣯⣽⣿⣿⣧⠀⠀⠠⣤⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠄⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⣠⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠃ ⣟⠋⠁⢀⣀⣤⡤⣤⠄⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀ ⢙⣻⣷⣴⣶⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣤⣤⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣬⣏⣀⣀⡀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠯⠿⠿⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣘⡛⣀⣀⣀⠀⠀⣀⡀⠀⣀⡀⢀⣛⣛⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⠿⠇⣿⣿⢻⣿⡆⣿⣿⡄⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣀⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡤⣤⣤⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠠⠤⣤⣴⣶⡶⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠓⠒⠒⠒⠒⠓⠚⠒⠒⠀⠀⠀⠐⠂⠀⠐⠒⠒⠒⠚⠒⠒⠚⠓⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢀⣾⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣶⣶⣿⣷⣶⣿⣿⣶⣾⣶⣶⣶⣦⣤⣄⣀⣀⣀⣄⣀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣿⠀⠁⠀⠀⠂⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠉⡀⠀⠀⠀⠀⢠⣄⣌⣉⣹⣿⣿⣿⣯⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⡿⠛⠋⠀⠀⠀⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠶⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣏⣋⠉⡙⠿⠿⢿⡿⣿⣿⠿⠿⢟⣿⣿⡟⠿⠿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⢿⣿⣿⢯⣽⣿⣶⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⡄⣼⡿⠿⠿⠿⢿⣿⣿⣿⡇ ⣠⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠀⠁ ⣥⡁⣀⣀⡤⠤⠤⢴⣄⣠⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⢟⣷⣦⣾⣿⡿⣿⣿⣿⣿⣿⠤⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣤⣤⣬⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣨⣏⣀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠽⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣙⡛⣀⣀⣀⠀⠀⣀⡀⠀⣀⡀⢀⣛⣋⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⣶⡆⣿⣿⢾⣟⡃⣿⣿⣷⣿⡇⣿⣿⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡏⣿⣿⡇⢸⣿⡇⠀⣿⣿⣆⡀⣿⣿⢸⣿⡇⣿⡏⣿⣿⡇⣿⣿⣾⣿⡄⣿⣿⣀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠙⠛⠃⠘⠛⠃⠀⠛⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠘⠛⠛⠛⠛⠘⠛⠓⠛⠛⠛⠰⣾⡿⠶⣶⢶⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠒⠛⠛⠛⠓⠚⠛⠂⠀⠀⠀⠐⠂⠀⠀⠐⠒⠒⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⡿⣿⡆⣿⣿⣿⣿⡆⣿⣿⠿⠀⣿⣿⣿⡆⢸⣿⡇⢠⣾⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⢸⣿⣧⣿⡇⣿⣿⣿⣿⡇⣿⣿⣤⢠⣿⡟⣿⡇⢸⣿⡇⠈⢿⣿⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢸⣿⡏⠉⠀⣿⣿⡏⠉⠀⣿⣿⠉⢸⣿⣷⣿⣿⢸⣿⡇⠠⣶⣮⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠿⠿⠇⠀⠠⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠿⠇⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠎⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⠋⠽⠿⠿⠿⢿⠿⢿⡿⠿⠻⠛⣻⣿⡿⠿⠿⠿⡿⣿⠿⠿⢿⣿⣿⠇⠀⢸⣦⠀⠀⠈⢿⣷⣶⣆⡀⠀⠀⠀⠀⠀⠈⠉⠁⠶⠆⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠊⠉⠀⠀⠀⠈⠉⠹⠿⣿⣶⣶⣶⣶⣶⣶⣄⠀⠀⢀⣶⣄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠴⢴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠃⠉⠀⠀⠀⠀⠿⠿⠿⠿⠿⡿⢿⡇ ⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⣍⡀⠀⠤⠤⠤⠤⣤⣠⣴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣯⣿⣶⣿⣿⡿⣿⣿⣿⣿⣿⠦⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣶⣿⣯⣄⣠⣤⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣇⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⣶⣤⣤⣄⣀⣀⣄⡀⣠⣤⣤⣤⣄⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣛⡃⣀⣀⣀⠀⠀⣀⣀⠀⣀⡀⢈⣛⣁⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣷⣸⣿⡿⠿⣿⡿⠿⣿⣿⡿⠇⣿⣿⢻⣿⡆⣿⣿⡆⣿⡇⢸⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣾⣏⣶⣾⣿⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣦⣤⣿⣿⣣⣿⣿⣿⡇⣈⣿⣿⡇ ⣿⣿⣿⠟⠛⠁⠀⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇ ⠏⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣻⣛⡻⣿⡽⠿⢿⣿⢿⣿⡿⠿⣿⣟⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠈⠉⠉⠀⠀⠀⠈⠈⠈⠀⠀⠉⠙⠀⠀⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠿⠿⠻⠿⢿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⣿⣿⡇ ⣠⣤⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃ ⡋⠁⣀⣠⣤⠤⠤⣦⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣧⣴⣦⣻⣃⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣽⣏⣠⣄⣤⣀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣧⣄⣀⠀⠀⠀⠠⢠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠼⠿⣧⡤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠀⠒⠒⠒⠒⠚⠓⠓⠓⠚⠚⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⣄⣀⣉⣉⣻⣿⣿⣿⣭⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⠟⠛⠉⠀⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠏⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⡿⣻⡿⠿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣟⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠁⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠻⠄⠀⢠⣤⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠠⣦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠉⠻⠿⠿⠿⠿⢿⠿⠿⢿⠿⠿⡿⠿⠿⠿⢿⣿⣿⣿⣿⡇ ⣤⣼⣷⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃ ⡟⢁⣤⣤⣤⠤⠴⣶⣠⣶⣶⣄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣯⣶⣶⣿⣏⠁⣠⣠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣽⣷⣬⣤⣄⢠⠶⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣯⣤⣤⡀⠀⢀⢀⣀⣤⣤⣤⣤⣀⣀⡀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠼⠿⣧⣤⣤⣥⣤⣤⣼⣷⣦⣤⣶⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠒⠒⠒⠒⠚⠚⠒⠓⠚⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⡿⢽⡿⠿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣶⡆⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠘⠻⣿⣷⣶⢤⡄⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⢠⣦⣤⣄⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠻⠻⠿⠿⠿⢿⠿⣿⢿⠿⠿⣿⠿⠿⡿⢿⣿⣿⣿⣿⡇ ⣤⣾⣷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃ ⣯⢀⣤⣤⣤⠤⠶⣦⣴⣶⣶⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣯⣶⣾⣿⣯⡁⣠⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣽⣷⣬⣤⣄⢔⢞⠂⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣯⣤⣤⡀⠀⢠⣀⣀⣤⣤⣤⣤⣤⡀⣀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣾⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠼⠿⣧⣤⣤⣿⣬⣦⣾⣷⣾⣿⣶⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠀⠒⠒⠒⠒⠛⠛⠒⠓⠚⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⠀⣤⣤⣤⡄⠀⠀⢀⣤⣤⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣿⣿⣵⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣄⣀⣠⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣿⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⣎⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢠⡤⠈⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⣾⣿⣿⣶⣄⡀⠀⠈⢁⠀⠀⠀⠀⠀⣤⣀⣉⣉⣻⣿⣿⣿⣭⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⢴⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⠟⠛⠉⠀⠈⠉⠉⠙⠛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⢀⠀⠤⠈⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠠⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠆⠠⠼⠿⠿⠿⢿⣿⣿⠿⠿⠿⣿⠿⠿⡿⢿⣿⣿⣿⣿⡇ ⣤⣾⣿⢶⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃ ⣟⢁⣥⣤⡴⣶⣶⣶⣴⣶⣶⡆⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⣶⣾⣿⣟⣁⣠⣄⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣴⣦⣴⣔⣿⠂⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣤⣤⡄⠐⣤⣤⣤⣦⣶⣤⣤⣤⣀⡀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⢤⡤⣤⣤⣤⢤⡤⣼⣿⣧⣤⡤⣤⣤⣤⢤⢤⣤⣤⣤⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠀⠘⠒⠒⠓⠚⠛⠛⠛⠒⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⢀⡀⠀⠀⠀⠀⠴⣾⠑⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⣍⠋⣻⣿⣿⣿⣭⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠸⣷⣤⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⡿⠟⠛⠁⠉⠉⠉⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠎⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉⠈⠉⠁⠀⠈⠁⠉⠁⠀⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠙⠙⠃⠀⠀⠀⠀⠹⠿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠛⠛⠛⠛⠋⠉⠛⠻⢿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣤⣤⡷⠰⢤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠈⠃ ⣟⡋⣀⣀⣤⣤⠴⢶⣦⣴⣦⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢜⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣤⣶⣾⣟⡇⢀⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣾⣿⣀⣤⣄⡰⢠⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣬⣤⣇⣀⠀⠀⠀⠀⠀⣠⣄⣤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣤⢤⡤⢤⣤⡤⠤⣤⢤⡿⢧⣤⡤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠚⠛⠛⠒⠛⠂⠀⠀⠘⠓⠂⠁⠐⠛⠛⠛⠛⠒⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⡿⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠉⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣤⣤⣦⣥⠀⠄⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠈⠃ ⣿⢏⢁⣀⣠⣤⡴⢶⣆⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣯⣬⣿⣿⣿⣿⣧⣴⣶⣿⠒⠀⡀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣼⣟⣀⣤⡀⠀⠀⠄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣤⢤⣤⣤⣤⣤⢤⣤⣤⣿⣿⣤⣤⣤⣤⣤⠤⡤⣤⣤⣤⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠓⠒⠛⠛⠓⠛⠂⠀⠀⠘⠚⠂⠃⠐⠛⠛⠛⠓⠚⠛⠛⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⣤⣤⣤⡄⠀⠀⢀⣤⣤⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣷⣶⣾⣿⣶⣶⣶⣶⣦⣤⣤⣀⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣉⣉⣹⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⣌⠙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⠀⢸⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡟⢓⣠⡀⠀⠀⢠⣼⣶⡆⠂⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣾⣿⣯⣅⡀⠈⠀⠉⠁⠀⠀⠀⠀⢀⡀⢈⡙⢻⣿⣿⣿⣿⣹⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢀⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣄⠀⠀⠀⢻⣷⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⠀⠀⠀⠸⣿⣦⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠁⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠏⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣤⣤⣾⠤⠄⠄⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠃ ⣿⡏⢁⣀⣠⣤⡴⢶⣆⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣧⣴⣾⣿⡓⠀⣠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣀⣠⣄⢀⠀⠤⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⡀⠀⠀⠀⠀⠠⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⠤⢤⣤⣤⣤⣤⣤⣤⣿⣿⣤⡤⠤⢤⡤⣤⠤⢤⣤⣤⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠓⠒⠛⠛⠓⠚⠂⠀⠀⠐⠒⠀⠀⠀⠒⠒⠒⠒⠀⠐⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢓⣠⡀⠀⠀⢠⣤⣶⡆⠂⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣷⣾⣿⣿⣄⡀⠈⠀⠉⠁⠀⠀⠀⠀⢀⡀⢈⡙⢻⣿⣿⣿⣯⣹⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣤⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠿⠛⠋⠈⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⠁⠉⠉⠉⠈⠉⠉⠀⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠈⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠫⠿⠻⠿⠿⠿⢿⡿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣠⣤⣴⠱⠀⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠃ ⣿⠟⢁⣀⣠⣤⠴⢶⣆⣰⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣴⣾⡿⡓⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣜⣟⣂⣠⡀⠀⠠⠤⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣴⣤⡀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣤⡤⠤⣤⡤⠤⠤⡤⠤⠿⠿⠤⠤⠤⠤⣤⠤⠤⠤⢤⠤⢤⢼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠓⠒⠛⠛⠛⠒⠂⠀⠀⠐⠒⠀⠀⠀⠚⠒⠒⠒⠒⠐⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠜⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⢛⣋⣙⠿⢿⣿⣿⣿⠿⠿⣛⣋⣻⣿⣿⢿⣿⡷⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠁⠉⠁⠀⠀⠉⠀⠉⠁⠀⠀⠁⠁⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠛⠿⠻⠿⠿⠿⠿⢿⢿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⣤⡴⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠃ ⣟⠏⢀⣀⣤⡤⠤⠤⣄⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⣅⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣥⣴⣶⡟⠃⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣛⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣬⣅⡀⠀⠀⠀⠀⠀⢀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⡤⡤⣤⣤⣤⣤⣤⢤⡿⣿⡤⠤⠤⢤⣤⠤⣤⣤⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠚⠛⠛⠓⠛⠂⠀⠀⠐⠚⠒⠓⠚⠚⠓⠓⠛⠚⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⣤⣤⣤⡄⠀⠀⢀⣤⣤⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣶⣶⣾⣟⣶⣾⣿⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⣩⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⣛⣣⣌⡙⠿⠿⠟⠋⠀⠘⠛⠛⠛⠀⠛⠛⠛⠃⢀⠛⠛⠛⠀⠀⠈⠑⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⣤⣤⣤⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡽⣶⡇⠀⠀⠀⠠⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⡀⢀⡛⠹⣿⣿⣿⣿⣹⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠿⠛⠉⠈⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣿⣿⣟⣿⠿⣿⣿⣿⣿⠿⢿⣿⣋⣿⣿⣿⣿⡇⠀⠉⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠉⠁⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢠⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠻⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣄⣤⣦⠥⢤⠤⢤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⡁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠘⠃ ⣟⣏⣀⣀⣤⣤⣶⢶⣆⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢮⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣵⣴⣶⡿⠓⠀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣟⣃⣀⡀⠀⠠⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣬⣄⡀⠀⠀⠀⠀⠀⣤⣤⣀⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣤⡤⣤⣤⢤⣤⡤⢤⡿⣿⡤⠤⡤⢤⡤⡤⡤⣤⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠒⠛⠛⠛⠓⠂⠀⠀⠐⠛⠒⠓⠒⠛⠓⠒⠒⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠿⠛⣀⡀⠀⠀⢀⡽⣶⡇⠀⠀⠀⠠⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢹⣿⣿⣦⠀⠀⠀⣾⣿⣿⣅⡀⠈⠀⠉⠁⠀⠀⠀⠀⠀⡀⢈⡙⠹⣿⣿⣿⣿⣹⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣿⣿⣿⣽⠿⣿⣿⣿⣿⠿⢿⣿⣋⣿⣿⡿⠇⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠉⠁⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣽⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠿⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣤⣤⣖⠠⢤⡀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⠋⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠃ ⣿⣯⣀⣀⣠⣤⠴⢶⣆⣰⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢮⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣧⣴⣶⣿⠗⠀⡀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣸⣟⣀⣀⡠⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣬⣅⡀⠀⠀⠀⠀⠀⢠⣤⣠⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠌⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⡤⠤⣤⡤⠤⠤⠤⠤⠿⠿⠤⠤⠤⠤⡤⠤⠤⢤⡤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠋⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠒⠛⠛⠛⠓⠂⠀⠀⠐⠒⠂⠀⠐⠓⠒⠒⠒⠚⠚⠚⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣏⣫⣻⣏⣹⠿⢿⣿⣿⣿⠿⠿⢛⠋⣿⡛⠋⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠀⠀⠁⠀⠀⠁⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⢹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⡛⣿⠿⠟⠿⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠉⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠃ ⣿⡇⢀⣀⣤⠤⠤⠤⣆⣰⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣿⣶⣶⣶⣾⣿⡿⣿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣥⣴⣶⡾⠓⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣷⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣽⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣅⣀⠀⠀⠀⠀⠀⠀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⠿⠿⠿⠿⠶⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⠤⠤⣤⡤⠤⠤⠤⢤⠿⠿⠤⠤⠤⠤⡤⢤⠤⢤⣤⡤⢤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠋⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠒⠒⠛⠛⠚⠒⠂⠀⠀⠐⠒⠂⠀⠀⠒⠒⠒⠒⠀⠐⠐⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⣤⣤⣤⡄⠀⠀⢀⣤⣤⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠻⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢻⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣶⣶⣾⣟⣶⣾⣿⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⠀⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣷⣶⡆⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣉⣩⣿⣿⣿⣿⣖⣛⣛⣛⣀⣛⣛⣛⣛⡛⠃⠈⠙⠿⠿⠟⣋⣀⡘⠛⠛⠛⠀⠛⠛⠛⣣⣀⠛⠛⠛⠀⠸⣿⣿⠆⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣤⡀⠀⠘⠛⣠⣄⠀⠀⢀⡽⣶⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠈⢻⣿⣥⡀⠈⠀⠉⠁⠀⠀⠀⠀⠀⡀⢀⡙⠹⣿⣿⣿⣿⣩⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠟⠛⠉⠈⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣏⠉⣛⣋⣹⠿⢿⣿⣿⣿⠿⠟⢙⠉⠀⠀⠀⣌⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠀⠈⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠋⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⢿⣿⡿⠿⠿⠿⣿⠿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠙⠈⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠃ ⣿⡇⢀⣀⣤⡤⠤⠤⣄⣰⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣭⣶⣶⣶⣿⣿⠿⣿⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣾⣤⣿⣿⣿⣿⣥⣤⣦⡎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠿⠿⠿⠷⠶⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⢤⠤⣤⣤⠤⠤⠤⠤⠿⠿⢤⠤⠤⢤⡤⠤⠤⠤⣤⠤⢤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠒⠒⠛⠛⠛⠒⠂⠀⠀⠐⠒⠀⠀⠀⠒⠒⠒⠒⠒⠀⠐⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣿⣿⣿⣿⠀⠀⢀⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢠⡽⣶⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣶⣶⡾⠁⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⢡⣀⠈⠀⠉⠁⠀⠀⠀⠀⠀⡀⢈⡙⠹⣿⣿⣿⣯⣩⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠓⠂⠀⣸⣿⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠟⠛⠋⠀⠉⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣍⡉⣿⣋⣙⠿⢿⣿⣿⣿⠁⠀⠀⠀⠌⢟⠿⣿⣿⠏⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⣾⣿⣿⠿⠿⠿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠈⠉⠋⠛⣛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠈⠁ ⣯⠏⢀⣀⣠⡤⠤⠤⢄⣰⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣭⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣥⣤⣠⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣐⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣅⡀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⡿⠿⠿⠿⠷⠿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣤⡤⣤⣤⣤⢤⠤⢤⠿⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠓⠛⠛⠛⠓⠂⠀⠀⠐⠚⠂⠀⠐⠚⠛⠒⠚⠛⠛⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣟⣿⣏⣿⢿⣿⣿⣿⣿⠿⠿⣿⠻⠛⠉⠉⠁⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠈⠉⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢠⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠴⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⣤⣴⣶⣴⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠐⠉⠋⠘⠛⠋⠛⢛⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠃ ⣿⡏⢁⣥⣤⣤⡶⠶⣆⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠘⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣿⣶⣶⣾⣿⣿⡿⣻⣿⣿⣿⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣥⣤⣤⣿⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣨⣽⣄⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣬⣥⣄⠀⠀⠀⠀⠀⢀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠬⠭⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠠⢁⡀⠀⡀⣄⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠂⠐⠀⠀⠫⠑⣀⣀⣀⣀⣀⡐⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣤⣷⣦⣤⡿⠀⠉⠐⣨⣹⣀⠀⡇⠀⠀⠀⠀⡇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣤⣤⣥⣬⣭⣭⣬⣤⣿⢿⣤⣬⣭⣿⣾⣿⣯⣭⣿⣿⣿⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣿⣷⡆⠅⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⡂⢐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⢿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣴⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⠇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⠈⣿⣿⣿⠀⣿⣿⣿⡇⠘⢀⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⠐⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢜⣛⠛⢛⣀⣛⣛⠛⠛⠛⠃⠈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⢛⣲⣿⣿⣿⠆⠀⠀⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⣀⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⠀⠀⠀⠛⣿⣿⣿⢛⣢⣄⡀⠀⢠⡼⣿⡏⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣦⡀⠀⢸⣿⣿⣿⣿⣿⣷⣄⠈⠁⠉⠁⠀⠀⠀⠀⠀⣄⣨⣉⢙⣿⣿⣿⣿⣭⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣆⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠉⠉⠈⠙⠛⠛⠛⠻⣿⡿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠛⠃⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠛⠛⠛⣻⣿⣿⣿⣿⠀⠀⠀⠀⢀⠁⠘⠛⠛⠛⠁ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠝⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⣟⡟⠂⠁⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣧⣤⣴⣶⣾⣄⣀⣀⡀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣷⢦⡇⠀⠀⣠⣄⣅⣀⠀⠀⠀⠀⠀ ⠀⠸⠿⠻⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠼⠝⠿⠿⠇⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠼⠯⣷⠗⠀⠁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣼⣯⣭⡧⣠⡀⣔⠌⠀⠀⠀⠠⠜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⠞⣾⡶⠗⡡⠯⠑⣀⣀⣀⣀⣀⡀⡀⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣤⣿⣶⣥⣾⠯⡿⢝⣭⣻⣅⠀⡇⠀⠀⠀⠀⡇⠁⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣥⣬⣭⣭⣭⣭⣥⣥⣿⣿⣧⣭⣯⣯⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⠇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⡀⠀⢃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⡛⠛⠛⠃⠈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⢆⣛⣛⣛⣺⣿⣿⣿⠇⠀⠀⠉⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⣣⣄⡀⠀⠀⡼⣿⡏⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠁⠉⠁⠀⠀⠀⠀⠀⣀⣀⣙⢙⣿⣿⣿⣿⣭⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠇⢀⣤⣤⣤⣤⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⡟⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢠⠈⠛⠛⠻⠛⢿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠀⠀⠀⠀⠠⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⠋⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⡁⠙⠁⠃⢠⡁⠘⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⢦⣟⡿⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡩⡐⠛⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠻⠋⢱⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠾⠗⠆⢿⣿⣿⣿⠗⠅⠀⠀⠀⢀⣠⣀⣀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣬⣿⣶⣿⣧⣤⣤⣄⣠⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣷⣾⣀⢤⣤⣤⣭⣄⠀⠁⠀⠀⠀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⣿⡿⠿⠿⠿⠷⠶⠶⠦⠦⠤⠴⠶⠅⠴⠴⠤⠦⠴⠦⠿⠿⠿⠿⠿⠷⠇⠈⠈⠋⠉⠉⠉⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠭⡿⣳⡆⠈⡁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣽⣯⢉⣥⢼⣈⣕⢌⠀⠀⠀⠠⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠿⡾⠶⢏⡡⠯⠑⣀⣀⣀⣀⣀⡒⡒⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣵⣿⣷⣷⣿⠾⠿⢕⣭⣻⣁⠀⡇⠀⠀⠀⠀⡇⠁⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣤⣤⣥⣤⣤⣥⣭⣬⣧⣿⣿⣧⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣽⣿⣿⣿⣿⣶⣿⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡅⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⡀⠀⠃⢀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡟⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⡛⠛⠛⠃⠈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⢛⣛⣛⣺⣿⣿⣿⡇⠀⠀⠈⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠻⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣣⣤⡀⠀⠀⡼⣿⡏⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣰⡄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠉⠁⠀⠀⠀⠀⠀⣀⣀⣉⢙⣿⣿⣿⣿⣭⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⢜⣤⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣷⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣧⣄⠀⠀⣤⣦⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⢻⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⢝⡻⠻⠛⠟⠛⢻⣿⣿⣿⣿⠃⠙⠫⠛⢩⠁⠘⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⢿⠿⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⣀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⡑⠋⢲⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠲⠻⠠⣳⣿⣿⣿⡟⠅⠀⠀⠀⢀⣀⡄⣠⡀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣶⣾⣷⣶⣿⣥⣤⣤⣤⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⣿⣿⣿⣷⣾⡀⣠⣤⣤⣬⣄⠀⠁⠀⠀⠀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⠿⢿⠿⠿⠿⠷⠶⠶⠦⠶⠤⠴⠾⠤⠁⠤⠤⠦⠤⠶⠼⠿⠿⠿⠿⠿⠏⠀⠈⠹⠋⠋⠉⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠭⠝⣳⠆⠀⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢽⣽⣯⢉⣡⣮⣈⣔⠌⠀⠀⠀⠀⠜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⡾⠶⢏⡹⠯⠑⣀⣀⣀⣀⣀⡐⡂⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣷⣾⠯⡿⢝⣭⣻⣉⠀⡇⠀⠀⠀⠀⡇⠁⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣬⣥⣥⣭⣬⣿⣧⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣽⣿⣿⣿⣿⣶⣿⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠁⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⢃⣀⣘⣿⣿⢘⣿⣿⣿⠀⣿⣿⣿⡇⡿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠚⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⠛⠛⠛⠣⣌⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⢛⣛⣛⣺⣿⣿⣿⡧⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⢹⠋⠀⠝⠛⠃⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣣⣤⡀⠀⠀⡼⣿⡏⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⢇⡿⣿⣿⣿⣿⣿⣿⣿⣹⣁⠁⣠⣬⡶⠆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠉⠁⠀⠀⠀⠀⠀⣀⣀⣉⢙⣿⣿⣿⣿⣭⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡯⣜⣤⡿⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣿⡄⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣷⣷⣽⣿⣿⣿⣿⣿⣿⣇⣀⠀⠙⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠇⠛⠉⠉⠉⠋⠉⠉⠙⠛⠻⠟⢿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⡋⣿⠛⢟⠟⠛⣻⣿⣿⣿⣿⠁⠙⠫⠛⢩⠁⠘⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢾⣿⢿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣠⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡐⠓⠓⣺⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⣀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⠿⠠⢾⣿⣿⣿⡟⠅⠀⠀⡀⠀⣀⡀⣠⡀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣷⣶⣿⣥⣤⣤⣤⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣗⣾⠠⢤⣤⣤⣭⣄⠀⠀⠀⠀⠀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⣿⠿⢿⢿⠿⠿⠷⠶⠶⠦⠶⠴⠶⠾⠥⠽⠤⠤⠦⠴⠶⠾⠿⠿⠿⠿⠿⠏⠉⠉⠹⠩⠋⠉⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠽⡏⢳⠆⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⣿⣿⣋⣡⣴⣂⣄⢈⠀⠀⠀⠠⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⡾⠷⢏⡡⠯⠑⣀⣀⣀⣀⣐⡒⡂⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣾⠯⣿⢽⣩⣻⣁⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣬⣭⣤⣦⣭⣭⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣿⣿⣿⣿⣶⣿⣾⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠃⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⡇⠁⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⠛⠛⠛⠛⠣⡌⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⣛⣺⣿⣿⣿⡷⠀⠀⠈⠉⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡛⢹⠃⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣳⣤⡀⠀⠀⡤⢿⡏⠘⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡷⣱⢇⡾⣼⢳⠿⣹⠹⡏⢟⢱⣁⠁⣀⡀⠀⠀⠉⠉⠁⠀⠠⠖⠂⠉⠀⠀⢦⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠈⠁⠀⠀⠀⠀⠀⣀⣀⣍⣛⣿⣿⣿⣿⣭⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡫⣜⢤⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆⠠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⠟⠛⠉⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⡩⣿⠿⠿⠛⠛⣿⣿⣿⣿⣿⡇⠈⠒⠛⢣⡍⠈⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢾⢿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡊⡀⠘⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠛⠋⢱⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠠⠿⠎⠳⣿⣿⣯⡟⠃⠀⠀⠀⠀⣠⣄⣀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣦⣼⣷⣶⣾⣥⣤⣤⣤⣤⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣾⣿⣿⣷⣶⠀⢠⣤⣤⣬⣥⠀⠀⠀⠀⠀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⠿⠿⠷⠶⠴⠤⠶⠤⠶⠾⠤⠁⠤⠤⠴⠤⠶⠾⠿⠿⠿⠿⠷⠍⠉⠉⠹⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⡭⠯⢗⠆⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣯⣛⣅⣼⣂⣄⢈⠀⠀⠀⠠⣜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⢸⡿⠾⠶⢏⠠⠯⠑⣀⣀⣀⣀⣀⡒⡂⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣾⠿⣽⢝⣩⣻⣉⠀⡇⠀⠀⠀⠀⡇⡆⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣬⣥⣥⣤⣬⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣿⣿⣿⣿⣶⣿⣾⣾⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠃⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡻⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⡇⠂⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣿⠀⣿⣿⣿⡇⡁⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⡛⡛⢛⣣⣌⡙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⢛⣺⣿⣿⣿⡷⠀⠀⠈⠉⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠟⠛⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⣳⣤⡀⠀⠀⡤⢿⡯⠘⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣹⢇⡿⣾⣿⡿⣹⢻⣟⣿⣻⣛⠿⣸⣉⠀⠀⣀⣆⠤⠀⠀⠀⣀⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠈⠁⠀⠀⠀⠀⠀⣀⣀⣉⣛⣿⣿⣿⣿⣭⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⡯⣞⣤⡓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⡿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⣟⣯⡀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡉⢉⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣧⢱⣿⣿⣿⣿⣿⣿⣷⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⠀⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠒⠒⠲⠾⠿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣋⣟⠛⠛⠿⠛⣿⣿⣿⣿⣿⡇⠀⠋⠛⢫⡌⠀⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢾⣿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣀⠙⣿⣿⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⢛⠋⢰⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠰⠻⠂⢫⢿⣿⣯⡟⠁⠀⠀⠠⠀⣠⡄⣀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣼⣶⣶⣾⣥⣄⣤⣤⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣻⣿⣿⣿⣶⢀⢠⣤⣤⣬⣤⠀⠀⠀⠀⠀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠧⠤⠤⠖⠦⠤⠔⠾⠤⠁⠤⠤⠶⠤⠶⠼⠿⠿⠿⠿⠷⠍⠉⠉⠹⠯⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⢟⣗⠆⠀⡀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⣫⣋⣣⣮⣂⣄⠀⠀⠀⠀⠀⠜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⢸⣿⣾⢷⢇⣡⠫⠁⣀⣀⣀⣀⣀⡀⡒⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠿⠑⣩⣻⣁⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣯⣿⣿⣿⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠃⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⣏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⣿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⣿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡏⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⣿⣿⠀⣿⣿⣿⡇⠁⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠁⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⣛⡛⣛⣣⡈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⢺⣿⣿⣿⡷⠀⠀⠈⠉⢁⡀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠛⠋⠁⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣬⠄⠀⠀⠀⠀⠀⠈⣿⣿⣟⣻⣤⡀⠀⠀⡴⢿⡯⠘⠀⠀⠐⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣿⣿⣿⣿⢿⣿⣿⣹⣁⠁⡠⡠⠀⣠⣿⡇⠀⠀⠀⠐⠀⠀⣠⠔⠂⠂⠀⠉⠀⠀⠀⠀⣤⠀⢰⣿⣿⣿⣿⣿⣷⣶⡀⠁⠈⣁⠀⠀⠀⠀⠀⣠⣀⣭⣉⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣹⡫⢞⣤⡋⠂⠈⠛⠛⠋⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⣀⡀⢰⣿⠿⠟⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⠈⠁⣄⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⡹⣹⢫⣧⣧⢠⣾⣿⣿⣿⣿⣿⣽⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠒⠀⠀⠀⠀⠐⠀⠀⠐⠒⠻⠻⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⣻⠿⢿⢿⣿⣿⣿⣿⣿⣿⡇⠘⠉⠛⠉⡄⠀⠛⠉⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠾⢿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠸⣋⣅⡘⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣦⡻⢁⣽⣿⣿⣿⡟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠯⣿⣽⣿⣿⡟⠂⠀⠀⠤⠀⣤⡄⡀⣀⡀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⣾⣷⣷⣮⣥⣤⣤⣤⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣶⢀⣠⣤⣴⣽⣤⠀⠀⠀⠀⠀ ⠀⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⠿⠧⠤⠤⠶⠶⠦⠶⠶⠠⠅⠰⠴⠦⠤⠶⠶⠿⠿⠿⠿⠗⠏⠁⠈⠹⠭⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣠⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠿⢟⢷⢖⠂⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⣫⣉⡣⢼⣈⣔⠈⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠁⢀⢸⣿⣿⣷⠇⣡⠯⠁⣀⣀⣀⣀⣀⡐⡐⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠯⠟⢐⢨⣻⣊⠀⡇⠀⠀⠀⠀⡇⡀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣽⣿⣿⣿⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠛⠛⠋⠀⠀⠀⠉⠋⠛⠉⠛⠛⠛⠛⠛⠉⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⢀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡏⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⠀⣿⣿⣿⡇⠧⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⣛⡛⠛⠛⠃⡈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⠛⢺⣿⣿⣿⡟⠀⠀⠈⠉⠁⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⡿⡛⠹⢋⢰⡿⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠲⠆⠀⠀⠀⠀⠀⢹⣿⣿⣏⣧⣤⡀⠀⠀⡴⢿⡇⠈⠀⠀⠐⠂⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣿⣿⡿⣻⠻⡏⢾⢱⡁⠁⢠⣬⣾⣿⡨⠇⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠚⠅⠀⠀⢠⣶⠀⢸⣿⣿⣿⣿⣿⣷⣶⡀⠁⠈⣁⠀⠀⠀⠀⠀⣠⣤⣭⣭⣻⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣹⣫⣞⣤⣿⣿⣿⣿⢯⠄⠀⠀⠀⢀⠀⠔⠃⠀⠀⠀⠀⠀⠠⣴⣿⡿⠃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠊⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⢠⣤⣤⠀⠉⠋⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⡼⠱⢱⢂⣧⣷⣵⣿⣿⣿⣿⣿⣿⣝⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠚⠛⠛⠻⢿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⢽⢟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠉⠃⡄⠀⠛⠉⠙⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣕⣌⢈⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⠻⢁⣵⣿⣿⣿⡟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠟⠁⢷⣿⣿⣿⡿⠅⠀⠠⡤⠄⣤⡄⡠⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣶⣮⣷⣶⣤⣥⣤⣤⣤⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣧⣾⣠⣠⣤⣶⣼⣤⠀⠀⠀⠀⠀ ⠄⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⡿⠿⠧⠤⠤⠶⠶⠦⠤⠴⠆⠫⠰⠶⠶⠴⠶⠶⠷⠿⠿⠿⠗⠏⠈⠈⠹⠭⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣠⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢽⠴⣇⢲⢆⠂⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⣫⣙⡉⣮⣊⣔⠈⠀⠀⠀⠀⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⢷⢟⡡⠿⠁⣀⣀⣀⣀⣀⡐⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠿⡟⢘⠨⣻⣋⠀⡇⠀⠀⠀⠀⡇⠂⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣽⣿⣿⣿⣶⣷⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⣿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⢀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⣿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⡛⠛⠛⠛⠃⠈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⠃⠀⠛⠛⢛⣺⣿⣿⣿⡟⠀⠀⠈⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣻⢿⢋⢔⡇⠀⠅⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⣽⠁⠀⠀⠀⠀⢻⣿⣿⣿⣟⣧⣤⡀⠀⠀⡴⢿⡇⠈⠀⠀⠐⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⢾⣱⣁⠁⣸⣬⡾⠁⠀⡇⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢿⡆⠀⠀⣠⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⡀⠁⠈⣁⠀⠀⠀⠀⠀⣠⣀⣭⣉⣻⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠿⣻⣯⣞⣴⣿⣿⣷⣶⠤⡁⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢠⣤⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠊⠁⠀⠀⠀⠀⠀⣀⣀⠈⠛⠋⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⡾⡱⢱⢀⣧⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣰⣶⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⠁⠀⠀⠀⠀⠈⠁⡠⠀⠀⠚⠛⠻⢻⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠈⠋⠉⡄⠀⠛⠉⠙⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⢏⣷⡍⣿⣿⣿⣟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣵⡛⣃⣹⣿⣿⣿⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠟⠓⣿⣿⣿⣿⡾⠆⠀⠀⠤⠠⢤⡄⢠⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣤⣶⣷⣬⣥⣤⣤⣤⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣗⣾⢠⣠⣴⣶⣼⣤⠀⠀⠀⠀⠀ ⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⠿⠿⠧⠤⠤⠤⠴⠦⠤⠄⠤⠡⠴⠶⠦⠶⠶⠶⠿⠿⠿⠿⠶⠏⠉⠈⠩⠭⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣠⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠿⢿⢿⠆⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⣝⣿⣉⡣⣪⣈⣄⢀⠀⠀⠀⠀⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⣾⣷⢏⡠⠯⠑⣀⣀⣀⣀⣐⡒⡂⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠿⠿⠑⣨⣻⣉⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣭⣿⣿⣿⣶⣷⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⣿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⢀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⢃⣀⣘⣿⣿⠨⣿⣿⣿⠀⣿⣿⣿⡇⡽⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⢰⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠂⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⡄⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⡛⠛⠛⠛⠃⡈⠛⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⠛⣣⣇⣛⣛⣛⣺⣿⣿⣿⡷⠀⠀⠈⠉⢁⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢹⠃⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⣣⣤⡀⠀⠀⡤⢿⡏⠘⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠁⣠⠀⠀⠀⣶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠁⠈⢁⠀⠀⠀⠀⠀⣠⣀⣍⣙⣿⣿⣿⣿⣭⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⢟⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠡⢹⣿⣿⠃⠀⢀⣴⣶⣤⣀⡀⠀⠀⠀⣀⡀⢀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣗⠑⣀⣾⡿⠊⠀⣰⣿⣿⣿⣿⣿⣿⣶⣀⣀⣠⡆⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡏⠆⠐⠉⠉⠉⠉⠉⠙⠛⠛⠿⠿⠿⣷⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣯⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠋⠋⡅⠈⠛⠉⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠳⠿⠿⣿⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠩⣂⠉⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣾⠚⠓⢫⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⠛⠛⣯⣿⣿⣿⡿⠆⠀⠀⠤⠀⢠⣤⣠⣀⡀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣗⣾⢠⣄⣤⣤⣶⣧⠀⠁⠀⠀⠀ ⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠿⠿⠆⠀⠤⠠⠤⠤⠰⠤⠀⠀⠰⠤⠶⠴⠶⠶⠿⠿⠿⠿⠷⠍⠀⠈⠹⠯⠏⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠴⢭⠓⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢽⣿⢻⣋⡣⣠⣀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⡚⡷⠏⡡⠯⠑⣀⣀⣀⣀⣐⡒⡂⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣾⠯⠿⢒⣨⣻⣈⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣽⣿⣿⣿⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠂⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⢘⣿⣿⣿⠀⣿⣿⣿⡇⡻⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⠸⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⣿⣿⣿⠀⣿⣿⣿⡇⠰⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠀⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⡛⢛⣀⣛⠛⠛⠛⠛⠃⡈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⢀⣛⣛⣛⣳⣇⣛⣛⣛⣺⣿⣿⣿⡷⠀⠀⠈⠉⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢻⠃⠀⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣣⣤⡀⠀⠐⡼⣿⡏⠈⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣻⣷⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡗⣠⡄⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠁⠈⠁⠀⠀⠀⠀⠀⣄⣀⣉⣙⣿⣿⣿⣿⣭⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡗⠀⢰⠟⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠂⠀⣯⠃⠀⠀⢀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧ ⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣟⣿⡷⠀⠐⣊⠀⠀⠀⣿⣿⣿⣿⣶⣶⣤⣶⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠑⠀⢈⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠻⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣯⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠛⠛⢫⡁⠈⠛⠋⠛⠃ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠷⠿⡿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣶⠉⣀⠉⢿⣿⣿⡿⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠬⡏⡻⠃⣡⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠛⠒⡾⣿⢿⣿⡟⢄⠀⠀⠤⠀⣤⣤⣤⣀⡀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣄⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣽⣾⣿⣗⣾⢠⣤⣤⣴⣾⣷⠀⠀⠀⠀⠀ ⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠠⠤⠤⠠⠄⠀⠀⠤⠤⠶⠤⠴⠶⠷⠿⠿⠿⠶⠏⠁⠈⠻⠹⠏⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣄⣠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡯⢿⣟⣶⡆⠂⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣙⣫⣹⡧⣮⡀⣄⢈⠀⠀⠀⠀⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⣿⢿⣿⣷⠟⡢⠫⠙⣀⣀⣀⣀⣀⡒⡒⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣿⣿⠀⡀⣀⣀⣀⣀⣀⡀⠀⠀⣀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠾⡟⢕⠠⣻⡓⠀⡇⠀⠀⠀⠀⡇⠃⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣽⣿⣿⣿⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢫⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣼⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⡀⠀⠃⢀⣘⣿⣿⠸⣿⣿⣿⠀⣿⣿⣿⡇⣾⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⠰⣿⣿⣿⠀⣿⣿⣿⡇⣿⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⣷⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠇⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠐⡀⣿⣿⣿⢀⣄⣀⣀⠀⠀⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⠛⠛⣀⠛⠛⠛⠛⠛⢃⣈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⢛⣳⣇⣛⣛⣛⣺⣿⣿⣿⠁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣶⣦⣄⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⡛⡿⡛⢹⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⠄⠀⠰⠛⣿⠇⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢾⣱⣁⢱⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣀⣈⣄⠀⠀⠀⠀⢠⣶⣶⣿⣽⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⣞⣽⣿⣿⣿⣿⡇⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⡟⠀⠀⠀⢠⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗ ⢻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣧⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢿⠿⠁⠀⠀⠀⠸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠘⠽⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⡿⢿⠿⢿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢮⣽⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⠟⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢤⢤⠠⢶⣡⣤⢘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣶⢾⡯⡉⣼⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠉⠀⠿⣽⣿⣿⣖⡇⠀⠐⠒⠖⢾⠧⠴⠄⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⡇⠲⢲⣶⣾⣦⣤⠀⠀⠀⠀⠀ ⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠦⠤⠤⠴⠶⠤⠶⠆⠀⠠⠶⠶⠶⠾⠶⠾⠷⠿⠿⠿⠿⠀⠀⠀⠈⠈⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡧⠶⢖⡖⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣈⣩⣃⡡⢀⡀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢀⠀⠀⢀⣿⠟⣺⣶⢄⠀⠫⠑⣀⣀⣀⣀⣀⡀⡐⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣿⣿⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠮⠛⠑⠨⣻⡊⠀⡇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣽⣿⣿⣷⣾⣾⣷⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣙⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⢣⣤⣤⣤⠀⣤⣤⣤⡄⡇⠘⢁⣤⣴⣶⣤⣄⡀⠀⠀⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⣿⢠⣿⣿⣿⠛⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⠸⣿⣿⣿⠀⣿⣿⣿⡇⡟⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⡿⢸⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣾⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⣷⣶⡎⣿⣿⣿⣤⣿⣿⡿⢸⣿⣿⣿⠛⣿⣿⣿⠐⡀⣿⣿⣿⢀⣄⣀⣀⠀⠀⠉⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣛⠛⠛⠀⠛⠛⠛⠛⠛⢃⡈⠙⠿⠿⠟⠋⠁⠘⠛⠛⠛⠀⠛⠛⢛⣳⣇⣛⣛⣛⣺⣿⣿⣿⠁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣶⣶⣄⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⠿⡛⡿⡛⢸⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣴⣤⠄⠀⠰⠛⣿⠇⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢧⡿⣾⣿⣿⣿⢿⣏⢞⣱⣁⢱⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣀⣈⣄⠀⠀⠀⠀⢠⣶⣶⣿⣽⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⣞⣽⣿⣿⣿⣿⡇⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⣼⣿⡟⠀⠀⠀⢠⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⢇⡿⣾⡹⣹⢫⣧⣧⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢿⠿⠁⠀⠀⠀⠸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠙⠝⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⣿⠿⠿⡿⢿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣬⣯⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⢤⣠⢤⣧⣁⣤⢘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢶⡾⣏⠩⣼⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⡿⣾⣿⣿⣂⡇⠀⠐⠂⠐⠿⠦⠰⠄⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣿⣿⣿⡇⠰⢦⣶⣶⣤⣤⠀⠀⠀⠀⠀ ⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠦⠄⠤⠴⠴⠤⠴⠶⠠⠠⠶⠶⠶⠾⠶⠾⠷⠿⠿⠿⠿⠄⠀⠀⠀⠈⠀⠈⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⢠⣄⣤⣤⣤⣴⣦⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣿⢗⡁⠄⡰⠤⠀⠀⠂⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣝⡚⠅⠀⠀⠩⣟⠀⡁⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⠙⣂⣀⣀⣀⣒⡒⣲⢖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠀⡇⠀⠀⠀⠀⡇⡃⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡟⢿⣿⣏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⣇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⡀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣾⣿⣶⣴⣾⡦⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣤⣶⣀⣀⣤⣄⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠁⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢘⠿⡛⡿⡛⢽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣤⣤⠄⠀⢠⠾⣿⡇⠀⠀⠀⠒⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡏⢞⣱⣁⣿⣾⣿⣿⣿⡿⢡⣶⣄⠀⠀⠀⠀⠈⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⣉⡀⠀⠀⠀⠀⢀⣦⣼⣭⣹⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣧⠀⠀⠀⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢋⢧⣧⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠚⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠿⠿⠿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠋⠁⠀⠈⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢤⡤⣴⢦⣉⣷⣻⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣛⣍⢽⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠙⣿⣿⣿⣿⣽⡇⠀⠀⠤⠤⢶⠤⠤⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣿⣿⣿⣿⡇⣤⣠⣤⣦⣽⣷⡄⡀⠀⠀⠀ ⠄⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⠦⠤⠤⠤⠤⠤⠴⠤⠴⠴⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠇⠀⠈⠿⠟⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣤⣤⢤⣤⣶⢶⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢸⣿⣿⣿⣿⢷⣯⣻⠖⡁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠀⠠⣿⣿⣿⣿⣿⣿⣺⣕⣏⠁⠀⠀⠲⣗⠤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠠⣿⣿⣿⣿⣿⣿⡿⠙⣂⣀⣀⣀⣒⡒⡖⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⠀⡇⠀⠀⠀⠀⡇⡇⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣯⣭⣭⣵⣿⣿⣽⡽⠧⣿⣿⣦⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡆⡇⠀⠀⠀⠀⡇⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣌⠂⢀⡀⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡟⣿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⣇⠸⠿⠀⣀⡀⠀⠀⠀⠀⠠⠜⠂⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣬⣿⣼⣿⣧⣾⣿⡀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣶⣴⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣤⣤⣀⡀⣀⡀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠉⠁⣀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⡛⡿⡛⢿⢋⢾⣿⡏⠀⠀⠀⠀⠀⠀⠳⣾⣿⣿⣧⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣛⣤⣄⡀⠀⢠⠾⣿⡇⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡏⢞⣱⣁⠁⣸⣬⣾⣿⣷⣆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠈⠀⠉⠁⠀⠀⠀⠀⢀⣄⣸⣍⣹⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣞⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣧⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⠿⡿⠁⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠚⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⠛⢣⠀⠙⠛⠋⠋⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⡿⠿⢿⣿⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⢀⣤⣀⣤⣿⣸⣿⣻⣿⣿⣿⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠫⣿⣿⡿⠟⢻⣿⣿⣿⡇⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠾⠻⠟⢿⣿⣿⣿⣿⡇⠀⠠⢄⣄⣤⡄⣠⣀⠀⠀⠀ ⠀⠤⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣤⣤⣤⣤⣤⣠⣀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣿⣿⣿⣿⡇⣀⢤⣤⣷⣭⣥⡀⠀⠀⠀⠀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⣿⢿⠿⠿⠿⠆⠀⠀⠀⠄⠀⠀⠄⠀⠀⠴⠤⠶⠶⠶⠾⠿⠿⠿⠿⠿⠇⠁⠈⠹⠿⠉⠙⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⢠⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⡧⠽⢕⡒⠖⠀⡢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣹⡪⣇⡡⣢⡀⣄⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢟⣾⡶⣟⠱⠫⠑⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣦⣴⡿⢺⠿⢟⣪⣻⡂⠀⡇⠀⠀⠀⠀⡇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣴⣦⣦⣦⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣾⣿⣶⣾⣿⣷⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡝⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠂⠀⠀⠘⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⣄⠀⣇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣾⣿⣦⣴⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠌⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠉⠉⠁⠨⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣹⡷⠀⠀⠀⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⡿⡋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢓⣠⣀⡀⠀⢠⣽⣶⡇⠂⠀⠀⠠⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣏⢞⣱⣁⠁⣠⠀⣶⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣀⠈⠀⠉⠁⠀⠀⠀⠀⢀⣀⢨⡛⢻⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⣞⣤⣏⣼⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⡍⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧ ⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣿⢂⣽⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠈⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠼⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣻⣿⡿⠀⠛⠓⠘⢂⠁⠙⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⢼⣯⡟⠂⡅⠀⠀⠀⣀⣠⣀⣀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣷⣶⡇⠀⢀⣀⣄⣉⢁⠈⠈⠀⠀⠀ ⠀⠸⠿⠻⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠾⠿⠿⠟⠿⠃⠀⠈⠉⠫⠉⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢸⡯⠽⢏⡲⠖⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣸⣤⣃⡡⢄⣀⣄⢀⠀⠀⠀⠠⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢞⣒⠶⠏⠠⠫⠑⣀⣀⣀⣀⣀⡒⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣦⣤⡿⢪⠟⠟⣸⣻⣈⠀⡇⠀⠀⠀⠀⡇⠂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣦⣤⣴⣦⣶⣦⣶⣦⣧⣿⣿⣤⣤⣤⣥⣤⣥⣭⣭⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣾⣾⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡅⣴⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠒⠀⠀⠘⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠁⠀⡀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⣄⠀⣇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠖⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡻⢻⣿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢔⠇⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡷⠋⠉⠀⠁⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣙⡷⠀⠀⠀⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⡿⡋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢓⣠⣀⠀⠀⢠⣽⣶⡇⠂⠀⠀⠠⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣾⣿⣿⣿⣿⡏⢾⣱⣁⠁⡀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣄⠈⠀⠉⠁⠀⠀⠀⠀⢀⣀⢨⡛⢻⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⡯⣞⣠⣇⣼⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣟⣽⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠼⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⢀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣻⣿⣿⠀⠙⠓⠘⢂⠁⠛⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠒⣿⣿⡿⠃⡅⠀⠀⠀⠀⣠⡀⣀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡇⠀⠀⣀⣀⣍⣠⠀⠀⠀⠀⠀ ⠀⠼⠿⠻⢻⡿⠿⠿⡷⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠰⠷⠽⠿⠿⠿⠃⠀⠈⠉⠛⠉⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢘⡧⠽⢌⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠠⠁⡁⠀⡀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠀⠂⠐⠀⠠⠫⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣤⣶⣤⣤⡟⠠⠛⠐⣨⣻⡁⠀⡆⠀⠀⠀⠀⡇⠀⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣴⣤⣴⣦⣶⣦⣤⣿⣿⣤⣤⣤⣤⣮⣥⣬⣥⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣶⣾⣾⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠡⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣧⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠉⠀⠀⠀⠀⢠⡏⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠄⠀⠀⠀⠄⠈⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣦⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠿⠏⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⡿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣠⡀⠀⠀⢠⣽⣶⡇⠂⠀⠀⠠⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣿⢿⣿⣞⣑⣁⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣥⣀⠈⠁⠉⠁⠀⠀⠀⠀⢀⡀⢨⡛⢻⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣖⣤⡛⠀⠠⠷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⡹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣿⣗⣷⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠽⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠰⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠙⡋⠚⢂⠃⠙⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⠠⢾⣿⣿⠋⡅⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⡇⠀⠀⣀⣄⣌⣁⠀⠉⠀⠀⠀ ⠀⠼⠿⠿⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠿⠿⠿⠃⠀⠈⠋⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣄⡀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢈⡯⢴⡟⢒⠖⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣼⡤⣏⡱⢀⣀⣄⢀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⢺⣺⡷⢟⠱⢯⠑⣀⣀⣀⣀⣀⡒⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣦⣤⡿⡻⠟⢟⣪⣻⣃⠀⡇⠀⠀⠀⠀⡇⠇⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣤⣦⣦⣦⣤⣿⣿⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣾⣾⣿⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣌⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡄⠀⢲⡖⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⣹⡛⠛⣿⡍⢩⣿⡝⢿⣿⡯⠉⡿⢃⣤⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⣄⠀⡇⠸⠟⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣬⣿⣼⣿⣧⣾⣿⡀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡁⠀⠀⠀⠀⢠⡏⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠀⠀⠀⡆⠀⠀⠀⢰⣾⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠯⡦⠀⠀⠀⠁⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⡛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣠⡀⠀⠀⢠⣽⣶⡇⠂⠀⠀⠠⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣷⡿⣿⣿⣿⣿⣿⣿⣿⣹⣁⠁⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣥⣀⠈⠁⠉⠁⠀⠀⠀⠀⢀⡀⢨⡛⢻⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣞⣤⣏⠏⠀⠀⠾⢷⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣔⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠛⡻⠟⣇⠃⠹⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠈⠒⠀⠀⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠅⠡⣾⣿⡿⠋⡇⠀⠀⢀⣀⣀⣀⣂⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡇⠀⢤⣠⣦⣝⣥⠉⠉⠁⠀⠀ ⠀⠼⠿⠿⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠄⠀⠶⠾⠿⠿⠿⠇⠀⠈⠋⠿⠉⠙⠁⠄⠀⠀⠀ ⠀⠀⠀⠀⢀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢘⡧⠵⢍⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠨⢁⠁⠀⡀⣄⢀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠀⠂⠐⠀⠠⠫⠑⣂⣀⣀⣀⣀⡒⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣤⣶⣤⣤⡟⠀⠉⢐⡩⢻⡁⠀⡅⠀⠀⠀⠀⡇⠂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣿⣿⣤⣤⣬⣥⣬⣤⣤⣤⣤⣤⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣉⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢁⡤⠀⠀⠀⠀⠿⠏⡄⡆⠄⠀⡜⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠷⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣬⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⢧⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣠⣄⡀⠀⢠⡽⣿⡇⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣿⣿⣿⣻⢿⣿⣿⣿⣿⡿⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠈⠀⠉⠁⠀⠀⠀⠀⢀⣀⣨⣙⢻⣿⣿⣿⣿⣽⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠇⠃⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣆⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣵⣿⣿⣿⣿⣿⢸⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠇⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠸⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠈⠑⠈⢁⠁⠘⠛⠙⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠚⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠠⠶⠄⠠⣾⣟⣟⠃⡄⠀⠀⠀⠀⣠⡀⣀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣿⣿⣶⡇⠀⢀⣠⣤⣭⣀⠀⠉⠀⠀⠀ ⠀⠼⠿⠹⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠴⠠⠀⠖⠽⠿⠿⠾⠇⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⡇⠵⢥⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠨⠁⠀⠀⡀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⠀⠀⠐⠀⠠⠫⠁⣀⣀⣀⣀⣀⡀⠂⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣤⣶⣤⣤⡿⠀⠉⠀⣨⣻⡁⠀⡅⠀⠀⠀⠀⡇⠁⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣤⣬⣬⣥⣤⣿⣿⣤⣤⣭⣭⣯⣥⣴⣭⣭⣬⣥⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣿⣿⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢁⣤⠀⠀⠀⠀⠿⠇⡄⡆⠄⠀⡜⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⢧⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⠿⠅⠀⠀⠀⠀⠸⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣠⣄⡀⠀⢠⡽⣿⡇⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⡠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠈⠀⠉⠁⠀⠀⠀⠀⢀⣀⣨⣙⢻⣿⣿⣿⣿⣽⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⠛⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣆⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⡃⠃⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠈⠋⠀⢂⠁⠘⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣸⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠠⠖⠄⠰⣿⣿⣿⠇⡅⠀⠀⠀⠀⣠⡀⣀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣶⡇⠀⠠⣠⣄⣍⣁⠀⠉⠀⠀⠀ ⠀⠼⠿⠿⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠴⠴⠤⠰⠾⠿⠿⠿⠿⠇⠀⠈⠉⠙⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡧⠵⢭⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡯⠐⠨⠁⠁⠀⡀⣄⠀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠄⠒⠰⠀⠠⠫⠑⣀⣀⣀⣀⣀⡀⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣤⣷⣶⣴⡟⠀⠉⠀⣨⣻⣀⠀⡇⠀⠀⠀⠀⡇⠁⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣥⣤⣤⣤⣬⣭⣭⣿⢥⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣽⣿⣿⣿⣷⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣵⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡦⠂⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠂⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠺⠺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⡆⠄⡄⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢙⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠣⠞⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⣄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠾⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠂⠀⠀⠀⠀⠀⢠⡇⠀⠀⠸⢳⣶⣤⣤⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠉⠁⣀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣟⣛⣤⣄⡀⠀⢠⠼⣿⡇⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣻⢿⣿⣿⣿⣿⠋⡠⡌⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⠀⠉⠁⠀⠀⠀⠀⢠⣄⣸⣉⣹⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⡗⠃⠀⠀⠀⢤⡿⠿⡿⠿⠿⠿⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⢿⣽⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠠⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⣿⠀⠈⠁⠀⢂⠀⠙⠛⠉⠙⠃ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠒⠀⠨⣿⣿⡏⠋⡇⠀⠀⠀⠀⢠⡄⡀⣀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣤⣤⣤⣤⣄⣤⣄⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⢶⡇⠀⠠⣠⣤⣥⣀⠀⠀⠀⠀⠀ ⠀⠾⠿⠽⢻⡿⠿⠿⡷⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠤⠰⠦⠤⠠⠿⠿⠿⠿⠿⠇⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠤⠿⢇⣓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣙⣻⣅⡅⣆⣀⣄⢀⠀⠀⠀⠠⡔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣧⠿⡚⠶⠇⡂⠯⠑⣀⣀⣀⣀⣀⡒⡐⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠾⠛⢒⣨⣻⣊⠀⡇⠀⠀⠀⠀⡇⠃⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠟⠃⠉⠁⠉⠉⠀⠘⠛⠿⠿⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣿⣿⣿⣷⣾⣾⣿⣶⣿⣿⡆⡇⠀⠀⠀⠀⡅⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠶⠆⠀⠀⠘⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠘⠆⢀⣀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠁⠰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢻⣧⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡌⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢠⠤⠼⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⢁⣀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣟⣫⣤⣄⠀⠀⢤⠾⣿⠇⠁⠀⠀⠂⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠁⣠⡈⠄⠀⠀⠀⢀⣰⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠀⠉⡀⠀⠀⠀⠀⢠⣄⣸⣍⣹⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣞⣤⣷⣋⠀⠤⠼⢿⡿⠿⡿⠿⠿⠿⠿⣧⡄⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⣿⣾⣹⣹⢫⣷⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠤⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⡇⠀⠉⠃⠈⠀⠀⠛⠋⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢞⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣾⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⢿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⢼⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⢸⠇⠀⠀⠀⠠⢤⡄⡀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣶⣤⣤⣤⣤⣤⣄⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⢺⡇⢀⢤⣥⣆⣯⣠⠀⠀⠀⠀⠀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⠿⠷⠀⠀⠀⠠⠄⠄⠠⠀⠀⠠⠠⠤⠴⠶⠴⠴⠿⠿⠿⠿⠼⠀⠀⠈⠉⠉⠉⠉⠀⠆⠀⠀⠀ ⠀⠀⠀⠀⢠⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠿⢟⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠭⣙⣻⣃⡅⢠⡀⣄⠀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡧⠿⠺⡷⠟⡀⠯⠑⣀⣀⣀⣀⣀⡀⡐⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠇⠎⠝⢔⣨⣻⣈⠀⡇⠀⠀⠀⠀⡇⡂⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠂⠀⠀⠀⠀⣀⠸⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣽⣿⣿⣶⣾⣾⣾⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠐⠚⠋⠀⠘⠓⠟⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠢⠐⠀⠾⠧⠀⢺⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠋⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠟⠇⠀⠀⠀⠀⠀⠄⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠒⠀⠼⠴⠂⠀⡄⢠⣤⣶⣀⣀⣄⣀⠀⠀⠀⠀⠀⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠉⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣫⣤⡤⠀⠀⢴⠾⣿⠇⠁⠀⠀⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡌⠂⠀⠀⠀⠀⠀⣀⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⣉⡀⠀⠀⠀⠀⣰⣤⣼⣍⣽⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣗⠇⠀⠀⠀⢤⡾⠿⡿⠿⠿⠿⠿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⣶⣶⣶⡦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣷⣷⣵⣿⣿⣿⣿⣿⣝⣗⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠡⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⢀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⣿⣿⡇⠀⠀⠈⠀⠀⠀⠉⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢞⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣾⣿⣸⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢪⣿⢿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢹⣿⣿⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⣘⠛⠃⢸⣿⣿⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠐⡀⢹⡆⠀⠀⠠⢤⠤⠄⠠⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣷⣶⣤⣤⣤⣤⣤⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣿⢾⡇⣠⣤⣤⣴⣶⣤⠀⠀⠀⠀⡀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⢿⠿⡿⠿⠿⠀⠠⠤⠠⠄⠠⠤⠀⠀⠀⠴⠦⠦⠦⠰⠴⠿⠿⠿⠿⠠⠀⠀⠈⠅⠉⠉⠉⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⢠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠈⠾⢟⡗⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠭⢙⢻⣋⡁⢀⡀⣄⠀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡧⠿⠚⠶⢿⠁⠫⠑⣀⣀⣀⣀⣀⡀⠐⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣿⠇⠮⠙⢔⢨⣻⣀⠀⡇⠀⠀⠀⠀⡇⡂⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠂⠀⠀⠀⠀⣀⠸⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣽⣿⣿⣶⣾⣾⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠐⠚⠋⠀⠘⠓⠟⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠢⠐⠀⠾⢦⠀⢺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠋⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⢘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠄⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠒⠤⠸⠴⠆⠀⡄⢠⣤⣶⣀⣀⣄⣀⠀⠀⠀⠀⠀⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠉⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣫⣤⡤⠀⠀⢴⠾⣿⠇⠁⠀⠀⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡌⠂⠀⠀⠀⠀⠀⣀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⣉⡀⠀⠀⠀⠀⣰⣤⣼⣭⣽⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡗⠗⠁⠀⠀⢤⡾⠿⡿⠿⠿⠿⠿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣯⢋⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠡⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⢿⡿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⣿⣿⡇⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢞⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣾⣿⣸⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢪⣿⢿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢹⣿⣿⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⣘⠛⠃⢸⣿⣿⡇⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠐⡂⢸⡇⠀⠀⠀⢤⠤⠄⠠⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣷⣦⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣾⢾⡇⡤⣤⣤⣤⣶⣤⠀⠀⠀⠀⡀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⠀⠀⠤⠠⠄⠀⠤⠀⠀⠀⠴⠦⠦⠦⠤⠤⠾⠿⠿⠿⠤⠀⠀⠈⠃⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠠⠶⠏⡖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠼⣛⣻⣃⡥⢠⣀⣄⢀⠀⠀⠀⠠⡔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠢⠟⠾⡷⠗⠠⠫⠑⣀⣀⣀⣀⣀⡒⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡂⠎⠹⢄⢠⣻⣈⠀⡇⠀⠀⠀⠀⡇⡂⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠿⠓⠒⣶⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣭⣿⣿⣶⣾⣾⣾⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠁⠀⠀⠘⠛⠛⠛⣻⣯⣤⣤⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⡤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣞⡿⣏⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢹⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣮⡿⠔⠃⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠴⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡟⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⢃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣮⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⣼⠀⠀⠀⠀⡀⣀⣤⣄⡀⣀⢀⠀⠀⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⡇⢿⣿⣿⣿⣿⡏⠀⠀⠈⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣡⣤⡤⠀⠀⠴⠿⣿⠀⠀⠀⠐⠃⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣷⣶⣤⡀⢀⣉⡀⠀⠀⠀⠀⣰⣦⣾⣭⣽⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⢷⣤⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣷⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢰⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠼⠿⠦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢞⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣾⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢪⣿⢿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠸⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⢃⣾⣿⢿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢄⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⡭⠆⢸⡇⠀⠀⠀⠴⠷⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⣿⣿⣾⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⢇⡤⣤⣦⣴⣶⡖⠀⠀⠀⠀⡄ ⠀⠼⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠦⠴⠦⠶⠶⠤⠄⠀⠤⠤⠴⠶⠶⠶⠶⠴⠶⠾⠿⠿⠆⠀⠀⠀⠃⠈⠀⠁⠠⠂⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠤⢉⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠼⠀⠊⢁⡀⠀⡀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠈⠂⠐⠀⠠⠫⠑⣀⣀⣀⣀⣀⡀⠐⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣿⠀⠀⠉⠐⣠⣹⣀⠀⡇⠀⠀⠀⠀⡇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣯⣿⣿⣶⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⢛⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⢧⣿⣿⡟⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⣏⠉⡟⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣩⡇⣶⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⣿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⡷⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⢰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠐⣶⣶⣾⠄⠀⠀⢰⠀⠀⢸⣿⣿⣿⡏⠀⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⣿⣟⣡⣤⡄⠀⠀⠴⠻⣿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣶⣤⠀⢀⣉⡀⠀⠀⠀⠀⣰⣦⣾⣭⣽⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢰⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠸⠿⠦⠤⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢾⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⣼⣿⣿⠆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠂⢸⠂⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣶⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣾⡿⠸⠀⢤⣠⣦⣴⣦⡖⠀⠀⠀⠀⡄ ⠀⠼⠿⠽⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠦⠤⠦⠶⠴⠤⠀⠠⠠⠠⠴⠶⠶⠶⠦⠶⠿⠿⠿⠿⠆⠀⠀⠀⠂⠈⠀⠁⠠⠀⠀⠀⠁ ⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠠⠬⠍⡒⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠼⣙⢫⣃⡁⣀⣀⣄⢀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠂⠟⠚⠶⠟⠠⠫⠑⣀⣀⣀⣀⣀⡒⡀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠊⠹⠖⣨⣻⣈⠀⡇⠀⠀⠀⠀⡇⡀⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣭⣿⣿⣶⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣷⣶⡢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠛⠛⣥⡱⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢹⣇⠈⠃⣄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡟⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣠⣾⣄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠉⠙⠛⠛⠀⠀⠀⠀⠀⠠⡀⠘⣏⣡⣤⡄⠀⠀⠴⠻⣿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢸⣿⣿⣷⣶⣤⠀⢀⣉⡀⠀⠀⠀⠀⣰⣦⣾⣭⣽⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠛⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢠⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠸⠄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⡿⣿⠿⣿⣿⡿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⢃⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⢸⠂⠀⠀⠀⠐⠳⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⣿⣶⣦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⠼⠀⠀⢠⣤⣤⣤⡆⠀⠀⠀⠀⡀ ⠀⠼⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠖⠶⠦⠶⠶⠦⠤⠠⠄⠠⠦⠶⠶⠶⠶⠼⠷⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠠⠥⢌⡓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠜⠀⠊⢁⡁⠀⡀⣄⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠌⠒⠐⠀⠠⠫⠑⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣿⠀⠀⠉⠐⣈⣻⡀⠀⡇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣯⣿⣿⣶⣶⣾⣶⣶⣾⣷⡆⠇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⢠⠇⠈⠀⠆⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣮⣿⣦⣤⠆⠀⠀⠀⠀⠀⡆⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣦⠀⠀⠀⠀⡄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣶⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠈⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣡⣤⡄⠀⠀⠴⠻⣿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣶⣤⠀⢈⣁⡀⠀⠀⠀⠀⣰⣦⣾⣭⣽⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⣿⣿⡿⠙⣿⣿⡿⡿⠿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡌⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⠉⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢾⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⠐⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⣈⡛⠛⢋⣬⡙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⢀⣀⠀⠀⠀⠸⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠈⠛⠛⠻⠧⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣮⣿⣿⣶⣦⣤⣤⣤⣤⣤⣍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣾⣾⣿⠼⠀⡤⣠⣤⣤⣴⡖⠀⠀⠀⠀⡀ ⠀⠼⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠤⠾⠦⠶⠶⠦⠦⠤⠀⠀⠴⠶⠶⠶⠶⠾⠿⠿⠿⠿⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⡄⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢡⠀⠤⠉⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠸⠈⠉⢁⡁⠀⡀⣄⢀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠂⠀⠂⠐⠀⠀⠫⠑⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣿⠀⠂⠉⠐⣠⣹⣈⠀⡇⠀⠀⠀⠀⡇⡀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣭⣿⣿⣶⣶⣶⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⣏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣾⣿⣦⣤⡆⠀⠀⠀⠀⢀⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⡆⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣀⠀⠀⠈⠃⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠈⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⢀⣶⣄⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⢿⣿⣏⣡⣤⡄⠀⠀⠼⢻⡿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣶⣤⠀⣈⣡⡀⠀⠀⠀⠀⣲⣦⣾⣭⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⡿⠿⠿⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠰⠿⠿⠟⠦⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡿⠹⣿⣿⡿⡿⠿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣼⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⣠⣙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠀⠀⠀⢿⣾⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣤⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠀⠀⠠⡄ ⠀⠼⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠷⠶⠼⠴⠳⠶⠾⠶⠝⠤⠤⠶⠶⠶⠶⠶⠴⠿⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁ ⠀⠀⠀⠀⡄⠀⠀⢄⡠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣗⠀⠶⠍⡒⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢽⠑⢫⣁⡥⠠⡀⣄⢀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠢⠞⠚⠷⠏⠀⠫⠑⣀⣀⣀⣀⣀⡀⡐⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣿⠀⠊⠙⠐⣨⣹⣀⠀⡇⠀⠀⠀⠀⡇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣽⣿⣿⣶⣶⣶⣶⣾⣿⣷⡆⠇⠀⠀⠀⠀⡇⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠙⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣝⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⣏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣮⣿⣦⣤⡂⠀⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⡆⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀⣀⠀⠀⠈⠃⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠐⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⢿⣿⣏⣥⣤⡄⠀⠀⠝⢻⡿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣾⣿⡿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢱⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣿⣿⣿⣶⣶⣄⠀⣈⣠⡀⠀⠀⠀⠀⣶⣶⣾⣭⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⡿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠐⠶⠤⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⢹⣿⣿⢿⡿⠿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢡⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠉⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⣸⣿⣏⣹⣿⢹⣿⣿⡇⣿⣿⣉⠀⢸⣿⣳⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠛⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⢀⣶⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢷⣀⣓⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣤⠀⠀⠀⢀⡄ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⠶⠬⠤⠷⠶⠦⠆⠦⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⡀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠽⠈⡗⠖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠝⠉⣺⣁⡅⠀⡀⣔⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠢⠞⠺⡷⢏⠀⠫⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠎⠙⠔⣨⢹⣀⠀⡇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣭⣿⣿⣶⣶⣾⣶⣶⣿⣷⡆⠆⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡅⢸⣷⣄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠫⠅⠀⠀⠇⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⡶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠃⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠉⢃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣏⣥⣤⡄⠀⠀⠛⢻⡿⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣧⡿⣾⣿⣿⣽⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣶⣶⣄⢀⣈⣠⡀⠀⠀⠀⠀⣶⣶⣾⣽⣿⣿⣿⣿⣿⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⢀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢻⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⣾⣹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⣿⣿⣿⣦⣉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠘⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⡿⣿⠿⠿⠿⣿⣿⡿⠿⡇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣡⣤⣤⣤⡄⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢰⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠚⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣢⡛⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠀⠀⠀⠒⠦⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣧⣴⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⢠⡄⣠⡄⠀⠀⠀⠀⡄ ⠀⠾⠿⠻⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠤⠥⠟⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣀⡀⣀⣀⣀⣀⡀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣲⣖⣻⣶⡟⠀⠀⠀⠀⠀⢹⡀⠀⡃⠀⠀⠀⠀⠇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣥⣭⣭⣿⣿⣶⣶⣶⣶⣶⣾⣷⡆⠆⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣉⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠉⡿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⠄⢸⣧⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣤⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣻⣹⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⠙⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡦⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠈⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣷⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄⣀⣀⣀⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠁⠀⠈⠛⢿⣿⠁⠙⠛⣿⣿⣿⣿⣿⣿⣏⣤⣦⠄⠀⠀⠛⢻⠿⠀⠀⠀⠈⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣀⣤⡀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣶⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⣾⡹⣹⢫⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠠⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿⡟⠹⠿⠿⠿⠿⠿⣿⠿⠿⠿⡇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣾⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠘⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠚⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⣀⡚⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣸⣧⠀⠠⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡄ ⠀⠸⠿⠻⢺⡿⠿⠿⡿⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠄⠀⠀⠠⠶⠆⠀⠀⠀⠤⠶⠶⠴⠴⠦⠂⠀⠠⠄⠀⠀⠀⢽⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠕⢄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠈⠂⠐⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⡀⠀⣀⣀⣀⡀⢸⣿⡇⢀⢀⡀⣀⣀⣀⣀⠀⠀⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⣿⠀⠀⠈⠀⠀⢻⠈⠀⡇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣭⣿⣿⣶⣶⣶⣶⣶⣾⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠸⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⢸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣼⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣻⣿⣻⣻⢿⣿⣿⡟⠀⠀⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⠋⠀⠀⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡦⠀⠀⠀⠀⠖⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣄⡀⠀⠈⢁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣄⣀⣀⣤⣠⣤⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣧⣤⣶⠄⠀⠀⠛⠻⠿⠀⠀⠀⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣷⣶⣦⣀⣠⣴⣀⡀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣿⣶⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⣹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠿⠿⢿⣿⣿⣿⡟⠙⠿⠿⠿⠿⠿⡿⠿⠿⠿⡇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠘⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠈⠉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⣀⡐⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠸⡓⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣼⣿⣿⣷⣦⣤⡀⢠⡆⠀⠀⠀⠀⡄ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠤⠤⠄⠤⠶⠆⠤⠄⠠⠰⠶⠶⠦⠦⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠀⠋⠑⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣀⣀⡀⣀⣀⣀⣀⢸⣿⡇⢀⢀⡀⣀⣀⣀⣀⡀⢀⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣛⣟⣿⣿⡟⠀⠀⠀⠀⠀⢻⠈⠀⠇⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣭⣽⣿⣿⣶⣶⣶⣶⣶⣾⣷⡆⠆⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡝⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠸⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡄⢸⣷⡄⠀⡅⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣤⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣻⡿⣛⣹⢿⣿⣿⣟⣡⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⡋⢸⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡦⠀⠀⠀⠀⠖⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣄⡀⠀⠈⢁⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣆⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣄⣀⣠⣤⣠⣤⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣧⣤⣶⠄⠀⠀⠛⠻⠿⠀⠀⠀⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣷⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣿⣿⣷⣶⣦⣀⣠⣴⣀⡀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣿⣶⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠿⠿⢿⣿⣿⣿⡟⠙⠿⠿⠿⠿⠿⡿⠿⠿⠿⡇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠋⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⣀⡐⣒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⡆⠠⡄⠀⠀⠀⠀⡄ ⠀⠼⠿⠽⢻⡿⠿⠿⡿⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠤⠄⠄⠶⠶⠆⠤⠦⠀⠴⠶⠶⠶⠖⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠤⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠂⠐⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣀⣀⢀⡀⠀⣀⣀⢸⣿⡇⠀⠀⡀⢀⢀⣀⡀⣀⣀⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣛⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⠀⠀⠇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣭⣿⣿⣶⣶⣶⣶⣶⣾⣷⡆⠄⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢋⣉⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡅⢸⣷⡄⠀⡆⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣤⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠀⠀⠀⠀⠆⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣴⣶⣶⣤⣤⣤⡄⠀⠀⢡⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⣤⣤⣦⣤⣶⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣧⣴⣶⡄⠀⠀⠛⠻⠟⠀⠀⠀⠈⠁⠀⠀⠿⣿⣿⣿⣿⣿⡿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢷⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⣷⣶⣠⣤⣶⣄⡀⠀⠀⠀⣶⣶⣷⣾⣿⣿⣿⣿⣶⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⡹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⠿⠿⢿⣿⣿⣿⡟⠙⠿⠿⠿⠿⠿⠿⠿⠟⠿⡇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢻⣿⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠋⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢗⣀⣄⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢿⣤⣤⣤⣤⡙⠓⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⣿⣿⣿⣿⣷⠄⡄⠀⠀⠀⠀⠄ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠤⠠⠄⠴⠶⠆⠴⠠⠤⠶⠶⠶⠾⠶⠦⠲⠴⠦⠀⠀⢾⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠤⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠄⠀⠠⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠂⠘⠐⠒⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⠀⡀⠀⠀⢀⣀⢸⣿⡇⠀⠀⠀⢀⣀⡀⠀⣀⠀⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⢹⡀⠀⡅⠀⠀⠀⠀⠇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣽⣶⣷⣶⣶⣶⣶⣶⣾⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡟⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡅⢸⣷⡄⠀⡆⠸⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣫⢿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣿⣋⠀⠀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠀⠀⠀⠀⠂⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣶⣦⣤⣤⡄⠀⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣀⠀⠀⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣄⣀⠀⠀⠀⠀⡀⠀⢰⣶⣶⣶⣤⣶⣶⣴⣶⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣧⣴⣶⣄⠀⠀⠛⠻⠿⠀⠀⠀⠀⠁⠀⠀⠿⣿⣿⣿⣿⣿⡿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⢧⡿⣾⣷⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣷⣶⣤⣤⣶⣆⣀⠀⠀⠀⣶⣶⣷⣶⣾⣿⣿⣿⣷⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⣹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠡⣶⣬⣉⣉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠠⠽⠿⠿⠿⠿⠿⢿⣿⣿⣿⡏⠘⠿⠟⠛⠿⠻⠿⠿⠿⠿⡇ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠙⠋⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢻⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⣣⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⣤⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠛⢿⠓⠀⠀⠐⠘⠀⠀⠄⠀⠀⠀⠀⠀ ⠀⠾⠿⠻⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠦⠀⠄⠴⠶⠦⠷⠤⠴⠶⠶⠶⠶⠶⠷⠶⠿⠷⠶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠠⠤⠄⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢈⠀⠠⠁⡀⠀⡀⣄⢀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⢀⠀⠀⣸⠠⠜⠒⠔⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢸⣿⡇⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠉⠀⣠⣻⡁⠀⠅⠀⠀⠀⠀⠇⠀⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠛⠛⠛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣷⡆⠄⠀⠀⠀⠀⡇⣴⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡂⢐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡇⣘⡀⢹⣿⢹⣧⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡆⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣼⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣤⣼⣿⣿⣦⣿⣦⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣯⣉⡀⠀⣀⣀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠀⠀⠀⠀⠂⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡟⠋⠉⠙⣿⡿⠿⠿⣿⣧⣴⣶⣶⣦⣤⣤⡄⠀⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡶⡶⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣄⣀⠀⠀⠀⠀⡀⠀⢰⣶⣶⣶⣦⣶⣶⣴⣶⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢧⣴⣶⣄⠀⠀⠛⠻⠿⠀⠀⠀⠀⠁⠀⠀⠿⣿⣿⣿⣿⣿⡿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣧⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣷⣶⣤⣤⣶⣆⣀⠀⠀⠀⣶⣶⣷⣶⣾⣿⣿⣿⣷⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⣹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠤⢾⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡏⠸⠿⠿⢻⠿⠻⠿⠿⠿⠿⡇ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢻⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⢘⢿⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣨⣔⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠘⠛⠀⠐⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠲⠘⠄⠠⠄⠀⠀⠀⠠⠀ ⠀⠾⠿⠽⢻⡿⠿⠿⡿⠣⠻⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠄⠀⠠⠤⠤⠦⠤⠀⠀⠠⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠠⢼⣬⡖⠖⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢌⣈⣨⣧⡡⠠⡀⣔⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⢀⠀⢀⣸⠠⠝⠚⡶⠔⠠⠋⠁⣀⣀⣀⣀⣀⡀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⡀⡀⠀⡀⣀⠀⠀⢀⢸⣿⣇⣀⣀⣀⣀⣀⣠⣀⣀⣄⣀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠿⠿⠿⢿⠀⠈⠉⠕⣨⣻⢀⠀⡇⠀⠀⠀⠀⠇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣶⣶⣶⣶⣾⣷⣶⣿⣷⡆⠇⠀⠀⠀⠀⡅⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⡃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡆⠸⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣍⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⡶⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢤⡄⠀⠀⠀⠀⠀⠀⠘⠉⠲⠶⣶⣶⣦⣤⡄⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠇⠀⠀⠀⠀⢰⣆⣠⠀⠀⠀⢀⡀⠀⠰⣿⣿⣶⣶⣶⣶⣶⣶⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣴⣿⣄⡀⠀⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⡸⠿⢿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣻⢷⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣦⣶⣶⣦⣄⡀⡀⠀⢶⣶⣷⣶⣾⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⡹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠛⠛⠛⠙⠿⠿⠿⠿⠇ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠘⣿⣿⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⢀⣘⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠈⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠃⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣴⣽⣛⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠊⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠐⢘⠂⠐⠄⠀⠀⠀⠀⠀ ⠀⠾⠿⠻⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠕⠄⠢⠶⠶⠶⠦⠤⠠⠾⠿⠿⠶⠿⠿⠿⠶⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠠⠼⣬⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠈⠀⢨⢁⡁⠀⡀⣄⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⢸⠀⠈⠂⠐⠀⠀⠋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⡀⠀⠀⡀⡀⡀⠀⢀⢸⣿⣇⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠀⠀⠉⠐⣠⢹⣈⠀⡇⠀⠀⠀⠀⠇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡛⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣷⣦⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣅⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⡶⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢡⡄⠀⠀⠀⠀⠀⠀⠘⠉⠲⠶⣶⣶⣦⣤⡄⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠇⠀⠀⠀⠀⢰⣆⣠⠀⠀⠀⠀⡀⠀⠰⣿⣿⣶⣶⣶⣶⣶⣶⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣴⣿⣄⡀⠀⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⡸⠿⢿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣻⢧⡿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣦⣶⣶⣦⣄⡀⡀⠀⢶⣶⣷⣶⣾⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⡹⣹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠻⠛⠛⠛⠙⠿⠿⠿⠿⠇ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠘⢿⣿⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⣘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠈⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠐⠀⠀⠀⠸⠂⠀⠂⠀⠀⠀⠀⠀ ⠀⠾⠿⠽⢻⡿⠿⠿⡿⠣⠺⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠄⠠⠷⠶⠶⠦⠤⠴⠶⠿⠾⠶⠿⠾⠷⠷⠿⠿⠧⠇⠀⠀⠀⠁⠀⠀⠀⠀⠴⠖⠀⠀ ⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠠⢶⠴⠖⢖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢌⣈⢨⣃⡥⠀⡀⣔⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣠⣀⣀⣸⠢⠟⠚⠷⠗⠠⢋⠁⣀⣀⣀⣀⣀⡀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣄⣤⣠⣤⣤⣤⣤⣤⣤⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠯⠿⠿⠿⠀⠈⠉⢄⣨⣻⣁⠀⡇⠀⠀⠀⠀⡇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣶⣶⣶⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣙⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⣯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣭⣁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⣶⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣶⣶⣶⡆⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠇⠀⠀⠀⠀⢲⣦⣠⠄⠀⠀⢀⡀⠀⠸⣿⣿⣷⣶⣶⣶⣶⣶⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⡺⠿⢿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⣶⣶⣶⣦⣤⡀⡀⠀⢾⣶⣷⣶⣾⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠿⣿⡾⠟⠛⠿⠛⠙⠿⠿⠿⠿⠇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⣤⣯⣯⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠰⠛⠉⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠰⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠚⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣳⣿⣿⣧⣀⢱⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⢀⠈⠁⠀⠊⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⣀⣌⣷⣿⣦⡋⠀⠀⠀⢘⠀⠐⠇⠀⠀⠀⠀⠀ ⠄⠾⠿⠹⢻⡿⠿⠿⡿⠣⠻⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠮⠶⠾⠿⠾⠿⠿⠿⠷⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠠⠰⠴⠀⠀ ⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠠⠴⢜⡖⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢌⣈⣨⣏⡧⠀⡀⣔⢀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣠⣀⣠⣼⠢⠟⠚⠷⠄⠠⠋⠁⣀⣀⣀⣀⣀⡀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣄⣀⣄⣤⣄⣸⣿⣇⣠⣦⣤⣤⣤⣴⣦⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠀⠀⠈⢄⣨⣻⡊⠀⡃⠀⠀⠀⠀⡇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣶⣶⣶⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⡂⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣉⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡆⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣩⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣀⣀⣤⣤⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢲⣶⣶⡆⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⡀⠀⠀⠀⣲⣦⣤⠦⠀⠀⢀⡀⠀⠸⣿⣿⣷⣶⣶⣶⣶⣶⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⡀⠀⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⡻⠿⢿⣿⣿⣿⣟⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣾⣿⣿⣻⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣶⣶⣶⣦⣤⣀⡀⠀⢾⣶⣷⣶⣾⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠇⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣇⡿⡾⡹⢹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⢀⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⡏⠀⠛⠻⠯⠛⠉⠿⠿⠿⠿⠇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠈⢣⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⠈⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠘⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠚⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⣼⣭⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡷⡄⣀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣶⣾⣷⣯⡛⠀⠀⠉⠛⠒⠒⠃⠀⠀⠀⠀⠀ ⠀⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠧⠇⠷⠾⠷⠶⠦⠦⠤⠶⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠶⠰⠀⠀ ⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⠠⠴⢌⡖⠖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢌⣨⣨⣃⡡⠀⡀⣔⢀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣀⣀⣼⠢⠟⠚⠷⠞⠠⠋⠁⣀⣀⣀⣀⣀⡀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣄⣤⣤⣤⣤⣤⣤⣸⣿⣇⣠⣴⣦⣶⣶⣶⣦⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠽⠿⠿⠿⠀⠂⠉⠐⣨⢻⡁⠀⡇⠀⠀⠀⠀⡇⠀⢐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡂⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⡙⣿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡏⠁⡿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣇⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣦⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣫⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣤⣄⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢲⣶⣶⡆⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⣀⠀⠀⠀⣸⣦⣴⠦⠀⠀⠀⡀⠀⠸⣿⣿⣿⣶⣶⣶⣶⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣆⡀⠀⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⡟⠿⢿⣿⣿⣿⣟⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣦⣀⣀⠀⢺⣷⣿⣶⣾⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠀⠀⠘⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠩⠶⠿⠿⠿⠿⠿⠿⠿⠿⢯⣀⠻⠿⠏⠛⠉⠿⠿⠿⠿⠇ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠀⠈⢻⣥⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⠀⠈⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡿⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⠘⢳⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣯⣭⣾⣿⣧⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⡧⡄⣀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢠⡀⣖⣿⣿⣾⡛⠀⠀⠘⠒⠂⠐⠃⠀⠀⠀⠀⠀ ⠀⠾⠿⠽⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⠎⠷⠾⠿⠶⠧⠤⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠶⠴⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢡⠠⠤⢠⡔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢄⠀⠀⢁⡁⠀⡀⣄⢀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣠⣠⣾⠀⠘⠚⠐⠀⠠⠫⠁⣀⣀⣀⣀⣀⡀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣠⣀⣤⣤⣦⣤⣤⣤⣴⣸⣿⣧⣠⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠯⠿⠿⠿⠀⠀⠀⠀⣀⢻⡀⠀⡇⠀⠀⠀⠀⡇⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣶⣶⣶⣶⣾⣶⣶⣿⣷⡆⠇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡂⢐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣉⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡙⠛⣿⡍⢩⣿⡟⢿⣿⣯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣾⣿⢁⠘⣿⣿⣇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡇⣘⡀⢹⣿⢻⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣾⣥⣿⣷⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⣀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣫⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡆⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠇⣀⠀⠀⠀⣸⣦⣴⠶⠀⠀⠀⡀⠀⠸⣿⣿⣿⣶⣶⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣆⡀⠀⠛⠙⠛⠀⠀⠀⠀⠀⢀⠀⡛⠿⢿⣿⣿⣿⣟⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢧⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣦⣀⣀⠀⣺⣿⣿⣶⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⢹⢫⣧⣷⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⠿⠻⠿⠟⠛⠉⠉⣿⣿⣿⠯⠉⠉⠿⠿⠿⠿⠇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠀⢠⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠘⠛⠋⠀⠸⢿⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⣷⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠠⠠⠠⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣯⣴⣯⣽⣧⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣼⣾⡤⣀⠀⠀⠀⠀⠈⠉⡀⠁⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡂⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⣐⣲⣿⣷⣧⡛⠀⠀⠙⠐⠛⠐⠃⠀⠀⠀⠀⠀ ⠀⠾⠿⠿⢻⡿⠿⠿⡿⠣⠺⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠮⠽⠾⠷⠾⠶⠮⠴⠽⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠠⠴⠶⠄⠀ ⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠠⠼⢤⠖⠖⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢬⣈⣬⣃⡥⠂⡀⣄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣶⣾⠢⠟⠚⠳⠗⠀⠮⠑⣀⣀⣀⣀⣀⡐⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣦⣴⣶⣶⣶⣶⣦⣶⣦⣼⣿⣧⣠⣶⣶⣦⣶⣶⣤⣤⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠀⠂⠉⠀⣨⣻⣂⠀⡃⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠍⠈⠉⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣶⣶⣶⣶⣾⣶⣶⣾⣷⡆⠆⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠷⣈⠀⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⡉⢿⣿⡟⣿⣿⣦⠘⢿⣿⣿⡿⠉⣿⡍⠉⢉⡙⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⢿⡇⠀⢸⡇⠀⣿⡇⢸⣿⠇⢀⠻⡇⠀⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠀⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣦⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⡿⣿⣿⣿⣿⣩⣿⣿⣿⡷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⣀⠀⠀⠀⣘⣶⣶⠖⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠋⠉⠛⠀⠀⠀⠀⠀⢀⡀⣚⠻⣿⣿⣿⣿⣟⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⢷⡿⣾⣿⣿⣹⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣶⣶⣀⣄⠀⣺⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⢹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⢤⣉⣉⣥⣦⠉⠁⠀⠈⠉⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠉⠉⠉⠉⠀⠹⣿⣾⡟⠉⠉⠉⠈⠿⠿⠿⠟⠇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠀⠀⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⠀⠈⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣰⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⠀⠀⢺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣦⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣧⡤⣀⠀⠀⢀⡄⠀⢉⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣄⣀⡄⠀⢠⣤⣟⣿⣷⣶⡛⠀⠀⠙⠛⡃⠐⠃⠀⠀⠀⠀⠀ ⠀⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠻⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠷⠿⠿⠶⠧⠶⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠇⠀⠀⠀⠁⠀⠀⠀⠰⠤⠴⠆⠀ ⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠠⠴⠧⡒⠖⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢬⣀⣠⣃⡥⠀⡀⣄⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣶⣾⠢⠟⡚⠷⠖⠀⠮⠑⣀⣀⣀⣀⣀⡀⠂⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣶⣶⣶⣶⣶⣶⣶⣶⣴⣼⣿⣧⣠⣶⣴⣶⣶⣶⣦⣤⣤⣤⣤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠀⠈⠉⠐⣸⣻⡂⠀⡃⠀⠀⠀⠀⡇⠀⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠍⠉⠉⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣤⣶⣶⣶⣶⣶⣾⣶⣶⣿⣷⡆⡇⠀⠀⠀⠀⡇⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡷⣈⠂⢀⡀⠔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣉⣿⣿⡟⣿⣿⣦⠙⢿⣿⣿⡿⠉⣿⡍⠉⢩⡛⠛⣿⡍⢩⣿⡟⢿⣿⡯⠉⡿⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⢁⠘⣿⣿⡇⠈⢿⡿⠁⠀⣿⡇⠀⢸⡇⠀⣿⡇⢸⣿⡇⢀⠻⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⣘⡀⢹⣿⢹⣧⠈⠃⡄⠀⠸⡇⠀⢰⣶⣾⣿⡇⢸⣿⡇⢸⣷⡄⠀⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣭⣼⣥⣿⣧⣤⣿⣼⣿⣧⣾⣿⠀⠀⠃⢀⣘⣿⣿⣿⣧⣼⣿⣥⣼⣿⣿⣶⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣥⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣦⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⣀⠀⠀⠀⣘⣰⣶⡖⠆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠙⠉⠛⠁⠀⠀⠀⠀⢀⡀⣚⠻⣿⣿⣿⣿⣟⣻⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣽⣷⡿⣾⣿⣿⣽⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣶⣶⣄⣄⠀⣺⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⠏⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣦⢰⣶⣶⣶⠶⣶⡶⠆⣶⡖⣶⡄⣶⡆⣶⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢇⡿⡾⡹⣹⢫⣧⣧⣱⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⡇⠛⠃⣿⣷⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⠀⣿⣇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠉⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁⠀⠈⢉⣉⡀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⢿⣿⣿⡏⠀⠋⠛⠉⠉⠉⠿⠿⠿⠟⠇ ⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠉⠉⢉⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⢠⣤⣤⣤⢠⣤⣤⣤⣤⣤⢠⣤⡄⣤⣤⣤⠘⠋⣤⣤⣤⠀⣤⣤⣤⢠⣤⣤⣤⡄⣤⣤⣤⣠⣤⣤⣤⡄⢙⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣙⢹⣿⣿⣿⡇⣿⣇⣿⢿⣿⣿⡿⢸⣿⣇⣸⣿⣿⣼⣿⡇⣿⣿⣀⠀⢸⣿⡸⠿⢾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣿⠇⢸⣿⡇⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⣿⣿⣿⣿⣿⡇⣿⡏⠉⢸⣿⣿⣿⢸⣿⣏⣹⣿⢸⣿⣿⡇⣿⣿⣉⠀⢸⣿⣱⣶⢺⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⡇⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠋⠁⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠘⠋⠛⠓⠛⠛⠛⠀⠈⠛⠛⠋⠈⠙⠛⠛⠀⠙⠛⠛⠁⠛⠃⠛⠃⠘⠛⠃⢀⠀⠈⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣧⣾⣿⣷⣄⣀⣀⣂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣄⣯⣿⣤⣸⡀⠀⢀⣄⠀⠉⠓⠁⠂⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠠⡁⣤⣈⠂⣤⢀⠁⢤⣤⣠⣤⣤⣤⣴⣾⣿⣿⣿⡙⠀⠀⠘⠛⡓⠘⠒⠀⠀⠀⠀⠀ ⠀⠿⠿⠿⢻⡿⠿⠿⡿⠣⠻⠟⠿⠿⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠯⠿⠿⠿⠿⠾⠦⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠁⠀⠀⠀⠰⠤⠴⠆⠀ ䷩ 𝚕𝚒𝚗𝚎 2658 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/epo-moral-damage/#comments Gemini version at gemini://gemini.techrights.org/2022/02/07/epo-moral-damage/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ EPO_Pays_Out_Millions_of_Euros_in_Compensation_—_to_Thousands_of_Workers_Who Deserve_a_Lot_More_for_Moral_Damage_—_for_Battistelli’s_Illegal_Acts_(But Battistelli_Himself_Has_Not_Been_Punished_at_All,_Nor_Have_His_Enablers)⠀✐ Posted in Courtroom, Europe, Law, Patents at 11:36 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇The people who committed these crimes Are still in power!⦈ Summary: The staff union of the EPO (SUEPO) is pushing ahead for justice after more than a decade of chronic, ongoing, systematic injustice, which saw the rule of law abolished, patent quality as “collateral damage”, and Europe’s reputation/leadership in tatters SUEPO Central is circulating_this_letter_today [PDF]. Of course we’ve managed to get a copy (the EPO is getting more leaky as corruption grows there and people feel desperate to speak out). “SUEPO expresses again its solidarity to all staff in the HR Department,” it says, “who strived to conclude all payments by the end of the year 2021 to repair the damages caused by their upper management.” “Over the years we heard from aggrieved and unhappy workers from the HR Department.”The short story is, payments were made to 4,523 workers, in effect undoing penalties but not paying anything in compensation for moral harm, amongst other aspects. How many more industrial actions would have been possible if it weren’t for the illegal “strike regulations” persisting illegally for 8 years? Over the years we heard from aggrieved and unhappy workers from the HR Department. Some left, some stayed while hating the grossly under-qualified boss, and we still have some stories we can share one day. People hate her guts more than she can possibly imagine, but in order to pay the mortgage people need to maintain a shallow, superficial, appearance of an amicable relationship. “Some of the people responsible are still clinging onto top positions at the Office!”Of importance and of note in this case: nobody was punished for these illegal acts! Not the people who voted for something illegal. Not the management that proposed these illegal regulations. Some of the people responsible are still clinging onto top positions at the Office! Welcome to the EPO, where immunity means that crimes pay off and doing illegal things is the “smart” thing to do. Like trying to kick off the UPC, even though it is patently and manifestly illegal, as_per_the_simple_treaties. This will be a permanent injury not just to the image of the EPO but also the EU’s (UPC is an EU system). What have we sunken to and how can these crises be rectified? Just like cops who never pay for their crimes (the police departments pay compensation to victims — however rarely — at taxpayers’ expense), Battistelli paid nothing and instead got rewarded with huge compensations upon his departure in 2018. To make matters worse, he also wasted an unbelievable sum of money trying to “get even” (ego-tripping) with judges by illegally sending them to Haar. Those spendings did not come out of his own pocket. █ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⣾⣿⣿⡏⠁⠹⠁⡇⢿⣿⢹⠃⣷⡟⢿⣿⣿⡿⠃⠤⡄⠙⠠⢼⡿⠿⠿⠀⡀⢀⣤⣷⣽⣿⣿⣿⣿⣿⣿⣿⡇⠚⠛⠒⠓⠓⠛⠘⠚⠒⠚⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠝⠃⠀⠀⠀⠀⠀⠉⠈⠙⠘⢈⡏⠁⠉⠀⠋⠀⠀⠈⠀⢀⠀⡀⠈⠂⡀⣠⣷⣾⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣚⣽⣿⣯⠉⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⢒⠂⠺⣿⣿⣿⡏⢻⠿⢷⢲⠇⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⡻⠄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠃⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⠌⡄⠀⣐⢐⣒⣶⢙⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣟⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣠⣘⡃⢄⣶⢿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠄⠀⠀⠉⠹⣿⣿⣿⣿⠟⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣟⣿⡆⠾⡭⠕⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠋⠀⠈⠀⠀⣸⣿⣿⣿⣟⣀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠿⠿⡿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⢀⣼⣷⣿⣯⠼⢉⣠⠤⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⠘⠿⠿⠇⠰⠤⣈⣽⣿⣿⣿⣷⣾⣿⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⣿⣿⣿⣷⣧⣗⠂⠀⢈⣧⣴⣶⣄⣿⣿⣿⣿⣿⡄⣠⡀⣄⡤⠤⢌⡉⢻⣿⣿⣿⠆⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢻⣿⣷⡄⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⣆⠀⠀⠀⠀⠉⠋⠹⣟⡛⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣠⣶⣶⣶⣿⡏⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⣀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⡉⣽⣿⣩⣠⣤⣶⣶⣦⡀⣴⣶⣷⣶⡰⣶⣶⢾⣷⡾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣟⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣩⣭⣯⢹⣿⡧⠠⢿⣾⣿⣿⣾⢿⣿⡿⣯⣅⣿⣿⡘⠛⠻⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿ ⡀⠀⠀⡀⢠⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣽⣿⣟⠃⢳⣦⣠⣤⣤⢤⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣿⣖⢸⣿⣿⣟⣿⢙⢿⣼⣇⣻⣋⣿⣿⣷⣿⡇⣿⣿⣼⣿⡇⣿⣿⢸⣿⡇⢿ ⣔⣶⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⠿⣿⣽⡊⡈⡿⣿⣿⢟⡟⠜⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠁⠀⢻⢏⢻⣯⡼⠾⠻⠛⠟⠋⠈⠙⠋⠉⠀⠀⠉⠉⠉⠀⠉⠉⠀⠉⠁⠀ ⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠰⢞⠯⢹⠇⠐⣀⠚⠏⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⠀⠠⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣻⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠀⠛⠣⠃⠁⠈⠑⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⢿⠇⠿⠿⣿⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠾⣟⣟⣟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⣿⡾⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⣿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⡶⠘⣷⡄⠀⠀⠀ ⣈⢯⡿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠴⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⠂⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⠿⠿⠿⢇⣻⠷⠿⠃⣀⣀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣧⠀⣿⣿⡄⠀⠀ ⠂⢘⣉⣁⠋⢼⣛⣻⠿⣛⣻⢟⣛⡿⣛⣋⢀⣀⡙⣛⣟⣛⣛⣛⣂⣀⣙⣛⣛⡛⣂⣀⣀⠐⠐⣛⣛⣛⢋⣀⣀⡻⣛⣛⡻⢟⣛⣻⢿⣛⣛⢻⣿⢛⣛⡻⢟⣛⣓⡦⣘⣻⢀⣀⡻⣛⣛⢛⣉⣁⢀⣀⣀⢿⣿⣿⡄⠀ ⡇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣠⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢼⢰⣿⣿⣿⢸⣿⣹⣿⢹⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⢺⣿⣿⣿⣦ ⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⣾⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣾⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠛⣬⡟⣿⡞⣿⣿⣿⣿ ⣿⣜⣻⣿⣷⣽⠿⢻⣡⣟⣚⣃⡛⠃⡛⢘⣃⣛⣃⡛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣳⣿⣞⣛⣃⡘⣛⣛⣃⣛⣛⣛⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⡛⠛⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⣾⣿⣿⡏⠁⠙⠀⡆⢻⣿⢹⠃⢷⡛⢿⣿⣿⡿⢃⠤⠄⠙⠀⢴⣤⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠛⠒⠓⠓⠛⠘⠚⠒⠒⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡴⠁⢳⡁⠆⣴⣾⣿⣿⠝⠃⠀⠀⠀⠀⠀⠈⠀⠙⠈⠀⡎⠁⠈⠀⠋⠀⠀⠈⠀⠀⠀⡀⠈⠻⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢠⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡜⠑⣈⣽⣿⣿⣿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡘⣿⠺⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣚⣽⣿⣯⠁⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠸⣿⣿⣿⣧⣾⣿⣶⣿⣶⣲⡶⠀⠀⠁⠓⣿⣾⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⡻⠄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣕⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢠⠘⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣟⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣠⣌⣂⢌⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⡇⠀⠀⠀⠀ ⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠈⠘⣿⣿⣿⣿⠛⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣟⣻⡆⠺⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠋⠀⠀⠀⠀⡰⣿⣿⣿⣟⣀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡷⠐⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠻⠟⠿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⢀⣼⣿⣿⣯⠼⢉⡠⠤⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠘⠿⠻⠃⠰⠤⣈⣽⣿⣿⣿⣷⣼⣿⢰⠈⠀⠈⠉⠉⢤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⣿⣿⣿⣶⣦⣗⠂⠀⢈⣷⣤⣶⣄⣿⣿⣿⣿⣿⡄⣠⡀⣄⡤⠤⢄⡉⢻⣿⣿⣿⡆⣿⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⢀⣿⣤⠻⣿⣿⠀⠘⣇⠀⢄⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠸⣞⠀⠀⠀⠀⠀⠹⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡀⡝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⣟⣀⣀⠀⠀⠀⠀⡀⣠⣦⣤⣦⣄⠀⢀⠀⢠⣠⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡯⠇⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⣀⠠⣿⣿⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣂⡀⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢣⡇⣇⢸⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣷⣾⣿⣶⣘⣿⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⣞⡇⢿⣾⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠗⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣛⣁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣈⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣻⡿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠈⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡬⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⠆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣟⣉⣍⣍⣟⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠹⠃⠀⠀⠀⠉⠁⠀⠈⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢹⣿⣷⡀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⣆⠀⠀⠀⠀⠉⠋⠹⣍⡛⢿⣿⣷⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⢀⣴⣶⣶⣾⣏⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⣀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⣆⢠⣿⡄⢸⣿⢋⣁⣤⣴⣶⣦⡀⣴⣿⣿⣶⡄⣿⣶⢶⣷⡶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣛⣯⣿⠻⣿⣯⠀⢿⣿⣿⣿⣯⣿⣿⣿⣿⣍⣾⣿⡟⠛⠓⣿⣿⣸⣿⣇⣿⣿⢸⣿⡇⢻ ⡀⠀⠀⡀⢠⣄⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣽⣿⣿⠃⢳⣤⣤⣤⣤⢀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣷⣿⣦⠰⣿⣻⣿⣹⠋⢿⣽⡇⣻⣟⣿⣿⣇⣿⡷⢿⣿⣿⣿⡿⣿⣿⡟⣿⣿⢸ ⣄⣶⣴⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⢿⣿⣽⡈⠈⡿⣿⣿⠟⡗⠄⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠛⠋⠀⢻⣏⠹⣿⣤⠶⠿⠛⠿⠛⠁⠙⠛⠋⠁⠀⠉⠉⠉⠀⠈⠉⠁⠁⠁⠀ ⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠠⠞⠿⢹⡇⠐⣀⠚⠏⠀⠀⠈⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⠀⠀⠜⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣻⣻⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠀⠛⠂⠁⠀⠈⠐⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⢿⠇⠺⠿⣿⡿⢿⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠾⣋⣟⣝⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⣿⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢹⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡾⢿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⣿⠟⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡾⣿⣿⣿⣿⡟⣾⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠊⠓⢀⣠⡴⠀⢰⣿⡆⠀⠀ ⢀⢾⡾⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⠂⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⠿⠿⠿⢇⣻⠷⠿⠃⢰⣢⠀⠀⢀⣼⣷⣿⣿⣿⣿⣧⠞⢻⣿⠁⠀⠀ ⠂⢘⣉⣁⠋⢼⣛⣻⠿⣛⣻⢟⣛⡿⣛⣋⢀⣀⡙⣛⣛⣛⣛⣛⣂⣀⣘⣛⣛⡛⣀⣀⣀⠀⠐⣛⣛⣛⢋⣀⣀⡻⣛⣛⡻⢟⣛⣻⢿⣛⣛⠿⣿⢛⣛⡛⢟⣛⣓⡦⣈⣻⢀⣀⡘⣛⣻⢛⣛⣉⢀⣀⣀⢸⣿⣧⠀⠀ ⡇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣠⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢴⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⢂⣿⣿⣷⣤ ⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢾⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣼⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡆⣿⣿⣿⣿ ⣿⣜⡻⣿⣷⣽⠿⢻⣁⣛⣚⣃⠛⠃⡛⢘⣃⣛⣃⡛⣳⣜⣛⣾⣟⣛⣴⣛⣛⣛⣛⣛⣛⣣⣿⣞⣛⣃⠘⣛⣛⣃⣛⣛⣛⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣘⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⡛⠛⠁⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⣾⣿⣿⡎⠁⠙⠂⡆⢻⣿⢹⠋⢿⡿⢿⣿⣿⡿⢃⠄⠄⠙⠄⢴⣤⣴⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡘⠛⠒⠓⠓⠓⠘⠚⠚⠚⠒⠚⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣴⣾⣿⣿⠝⠋⠀⠀⠀⠀⠀⠈⠀⠉⠈⠄⡞⠁⠘⠀⠋⠀⠀⠈⠁⢠⠀⠀⠀⠀⠁⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣚⣽⣿⣯⠁⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠸⣿⣿⣿⡟⢿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⡻⠄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠁⠀⢠⠜⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣟⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣠⣌⣃⢌⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠏⠀⠀⠀⠀⠀ ⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠐⠉⠑⣿⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⣻⣦⠹⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀ ⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠋⠀⠀⠀⠀⡰⣿⣿⣿⣟⣠⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠻⠿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠈⠀⢀⣼⣿⣿⣯⠼⢉⡠⠤⣄⡀⠀⠀⠀⣴⣿⣿⣿⣿⠘⠿⠿⠗⠴⠦⢈⣽⣿⣿⣿⣿⣮⣿⠳⡁⠀⠈⠻⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⣿⣿⣿⣷⣦⣛⠂⠀⢈⣿⣤⣶⣄⣿⣿⣿⣿⣿⡄⢀⣤⣤⣤⠤⢤⡉⠻⣿⣿⣿⡇⢻⠃⠀⠀⠀⠀⠈⣿⣿⣷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢈⣹⣦⡹⣿⣿⡆⠘⣶⠀⢀⠀⠀⠀⢻⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠘⡎⠀⠀⠀⠈⠋⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡁⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⢰⡗⣀⢀⠀⠀⠀⠀⣿⣿⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡯⡇⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⣀⡠⣿⣿⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⡀⣼⣿⣷⣶⣦⣠⣤⣾⣿⣿⣿⣿⣿⣶⣦⣤⣀⣠⣠⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣣⡇⣗⢸⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣷⣾⣿⣷⣘⣿⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣴⣢⣆⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡪ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⡙⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡧⣯⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡄⣿⡄⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⡕⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣷⠎⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⣟⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠟⣿⡏⠙⠛⠛⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡎⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢫⣿⣷⣄⠀⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣾⣿⣿⣿⣆⠀⠀⠀⠀⠙⠋⢿⣿⡻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⣴⣦⣶⣾⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢳⣶⣦⢀⣿⣇⢨⣿⡟⣉⣠⣤⣤⣤⡄⣠⣿⣿⣶⡄⣷⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⠛⣿⣿⠀⢸⣿⣿⣿⣯⡿⣿⣿⢿⣏⣹⣿⡇⠛⠛⣿⣿⡏⣿⣿⢹⣿⡇⣿⣿⢸ ⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣷⣷⣾⣦⠀⣷⡻⣿⣻⡏⢻⣯⡿⢙⣿⣻⣿⣧⣾⣿⢸⣿⣧⣿⣿⢸⣿⡇⣿⣿⢸ ⢀⣲⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⢿⣿⣿⡿⡞⣿⣿⣿⣿⣿⡾⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠁⢻⣿⠙⣿⣥⡶⠿⠟⠻⠟⠁⠙⠛⠛⠁⠀⠉⠉⠉⠁⠈⠉⠁⠉⠉⠀ ⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⡟⡿⣿⣷⠘⣁⠟⠏⠉⠈⠘⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡄⠀⠀⠀⠀⠼⠋⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠈⠓⠢⡧⠂⠈⠛⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⢿⠏⠸⠿⣿⡿⢿⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠾⢏⣿⣝⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⣟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⢓⡾⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠅⣿⣿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠜⠻⠋⡈⠉⠀⢠⣾⣧⠀⠀ ⡊⢾⣼⣿⣟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢦⡿⠿⠿⢇⡿⠷⠆⠀⠿⠧⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⠆⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⣇⠿⠿⠿⢇⣻⠷⠿⠃⢠⣚⡄⠀⠀⣰⣷⣶⣶⣼⣿⣷⠞⠋⠉⠁⠀⠀ ⡄⢚⣁⣃⠋⢸⣛⣻⠿⣛⣻⢟⣛⡿⣛⣋⢀⣀⡹⣛⣟⣛⣛⣛⣂⣀⣙⣛⣛⡛⣂⣀⣀⠀⠀⣛⣛⣛⢋⣀⣀⡺⣛⣛⡻⢟⣛⣻⢿⣛⣛⠿⣿⣛⣛⡻⢟⣛⣓⡦⣈⣻⢇⣀⡘⣛⣻⢟⣛⣋⢁⣀⣀⠀⠀⠀⠀⠀ ⡆⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣠⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢴⢰⣿⣿⣿⢸⣿⣹⣿⢹⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀ ⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⣿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⣸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡟⣿⡆⠀⠀⠀⠀ ⣿⣞⡻⣿⣷⣿⠿⢻⢁⣛⣚⣃⠛⣃⡛⢘⣃⣛⣃⡛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣳⣿⣞⣛⣃⡘⢛⣛⣃⣛⣛⣛⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⡛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⣾⣿⣿⡎⠁⠙⠂⡆⢻⣿⢹⠋⢿⡿⢿⣿⣿⡿⢃⠤⠄⠙⠄⢴⣤⣴⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡘⠛⠒⠓⠓⠛⠘⠚⠚⠚⠒⠚⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣾⣿⣿⠝⠋⠀⠀⠀⠀⠀⠈⠀⠉⠈⠄⡞⠁⠘⠀⠋⠀⠀⠈⠁⢠⠀⠀⠀⠀⠁⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣚⣽⣿⣯⠁⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠸⣿⣿⣿⡟⢿⠿⠻⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⡻⠄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠁⠀⢠⠜⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣟⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣰⣄⣃⢌⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠺⠏⠀⠀⠀⠀⠀ ⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠉⠙⣿⣿⣿⣿⠻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣟⣻⣦⠹⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀ ⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠋⠀⠈⠀⠀⣰⣿⣿⣿⣟⣂⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠻⠿⡿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠈⠀⢀⣼⣿⣿⣯⠼⢉⡠⠤⣄⡀⠀⠀⠀⣰⣿⣿⣿⣿⠘⠿⠿⠓⠴⠦⣈⣽⣿⣿⣿⣷⣮⣿⠳⡁⠀⠈⠻⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⣿⣿⣿⣷⣦⣛⠂⠀⢈⣿⣤⣶⣄⣿⣿⣿⣿⣿⡄⢀⣤⣤⣤⠤⢤⡉⠻⣿⣿⣿⡇⢻⠃⠀⠀⠀⠀⠀⣿⣿⣷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢈⣹⣦⡹⣿⣿⡆⠘⣶⠀⢀⠀⠀⠀⢻⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠘⡏⠀⠀⠀⠈⠉⢻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⢰⡗⣀⢀⠀⠀⠀⠀⣿⣿⣏⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡯⡇⡇⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⣀⡠⣿⣿⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⡀⣼⣿⣷⣾⣧⣤⣤⣾⣿⣿⣿⣿⣿⣶⣦⣤⣀⣠⣤⡀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣣⡇⣗⢸⣿⣿⣿⣿⣿⣿⡿⣳⣿⣿⣷⣾⣿⣷⣘⣿⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣗⣂⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⡇⢿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡥ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢟⢛⡁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⡹⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣣⣯⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡆⣿⡆⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⡅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣷⠆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣍⣭⣟⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠟⣿⡏⠉⠛⠛⠛⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡎⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢫⣿⣷⣄⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣿⣆⠀⠀⠀⠀⠙⠟⢿⣟⡻⢿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⣴⣦⣶⣾⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢳⣶⣦⢀⣿⣇⢨⣿⡟⣉⣠⣤⣤⣤⡄⣡⣿⣿⣶⡄⣿⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⠛⣿⣿⠀⢸⣿⣿⣿⣯⡿⣿⣿⢿⣏⣹⣿⡇⠛⠛⣿⣿⡏⣿⣿⢹⣿⡇⣿⣿⢸ ⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣷⣷⣾⣦⠀⣷⡻⣿⣻⡏⢻⣯⡿⢙⣿⣻⣿⣧⣾⣿⢸⣿⣧⣿⣿⢸⣿⡇⣿⣿⢸ ⢀⣲⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⢿⣿⣿⡿⡞⣿⣿⣿⣿⡿⡜⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠁⢻⣿⠙⣿⣥⡶⠿⠟⠻⠟⠁⠙⠛⠛⠁⠀⠉⠉⠉⠁⠈⠉⠁⠉⠉⠀ ⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠠⡛⡿⣿⣇⠘⣉⠿⠟⠉⠈⠈⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡄⠀⠀⠀⠀⠼⠋⠃⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠈⠓⠢⡆⠀⠈⠻⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⢿⠏⠸⠿⣿⡿⢿⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠾⢏⣿⣝⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⢳⡾⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠅⣿⡿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠜⠻⠃⡈⠉⠀⢠⣿⣦⠀⠀ ⡊⢾⣼⣿⣟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢴⡿⠿⠿⢇⡿⠷⠆⠀⠿⠧⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⠀⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⣇⠿⠿⠿⢇⣻⠷⠿⠃⢠⣚⡄⠀⠀⣰⣷⣶⣶⣼⣿⣷⠖⠋⠉⠁⠀⠀ ⡄⢘⣁⣋⠋⢸⣛⣻⠿⣛⣻⢟⣛⡿⣛⣋⢀⣀⡹⣛⣟⣛⣛⣛⣂⣀⣙⣛⣛⡛⣂⣀⣀⠀⠀⣛⣛⣛⢋⣀⣀⡺⣛⣛⡻⢟⣛⣻⢿⣛⣛⠿⣿⢛⣛⡻⢟⣛⣓⡦⣈⣻⢇⣀⡘⣛⣻⢟⣛⣋⢁⣀⣀⠀⠀⠀⠀⠀ ⡆⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣠⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢴⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀ ⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⣿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⣻⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡟⣿⡆⠀⠀⠀⠀ ⣿⣞⡻⣿⣷⣽⠿⢻⢁⣛⣚⣃⠛⠃⡛⢘⣃⣛⣃⡛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣳⣿⣞⣛⣃⡘⢛⣛⣃⣛⣛⣛⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⡛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⡾⠁⠈⡃⢾⠙⣿⢾⠋⠸⡿⢻⣿⣿⡿⢇⡠⡤⠈⠃⠤⣤⣄⣀⣀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠛⠒⠒⠒⠑⠘⠚⠒⠒⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣾⣿⣿⡿⠙⠀⠀⠀⠀⠀⠈⠀⠇⠉⠀⡼⠁⠀⠉⠘⠁⡀⠀⠁⠀⡀⠀⠀⠀⠈⠉⠛⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⡿⢿⠿⠓⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⢤⣀⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⣿⣿⣿⠁⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣾⣶⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⢾⣝⣷⣶⠗⠿⠿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣛⡦⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢼⣾⣿⣿⣷⣿⣼⣬⣠⣄⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢿⣿⣿⣿⢽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣀⣅⣑⠠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡦⢀⡘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣻⣧⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠨⠁⢰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣙⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⣿⠂⢼⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠟⠿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠐⠻⠀⠘⠀⢠⣿⣿⣿⣿⣿⣿⡿⠶⢤⣬⣿⠿⠀⢠⣿⣿⣿⣿⠈⠿⠿⠟⠳⠶⢀⣼⣿⣿⣿⣿⣦⣿⡗⠀⠀⣼⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣃⡈⢀⣿⡿⣴⣆⣼⣿⣿⣿⣿⣆⢀⣄⢀⣤⠤⠄⣉⠛⣿⣿⣿⡇⢸⡗⠀⠀⠛⠋⠉⠉⠑⠀⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠈⠙⢻⣿⣿⠋⠉⠻⠟⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⣴⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⣋⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡷⠘⣶⣶⡄⢰⣿⡀⣽⣿⢋⣉⣠⣤⣤⣭⠉⣽⣿⣿⣦⢹⣷⣶⣶⣶⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⠿⣿⢸⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⡟⢻⣿⡇⠀⢿⣿⣿⣿⣽⢿⣿⡿⣿⣉⣿⣿⠹⠿⢻⣿⣿⢹⣿⡏⣿⣿⢸⣿⡇ ⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣾⣾⣿⡄⢰⣌⢿⣟⣿⠙⣯⣽⠏⠿⢟⣿⣿⣱⣶⡦⣿⣿⣼⣿⡇⣿⣿⢸⣿⡇ ⠀⣀⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠛⠛⠛⠛⠋⠘⣿⡎⢻⣏⣤⡼⠿⠛⡿⠋⠉⠛⠛⠋⠁⠈⠛⠛⠉⠀⠉⠉⠈⠉⠁ ⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣄⠀⠀⠀⠀⢀⠟⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠻⠿⠿⠿⣿⠿⠿⠿⠟⠀⠙⠻⠟⠛⠿⠿⠟⠿⠿⠿⢿⡿⠸⠿⣿⡿⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡇⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⡇⣿⣿⢟⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣽⡼⣿⣿⣿⣿⡟⢸⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⣁⠿⠿⣼⡼⠿⠷⠞⠿⠾⠟⠸⠿⣸⡆⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⠿⠿⠿⢇⡻⠷⠿⠃⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢟⣛⣛⠛⢹⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢁⣀⡻⣛⣛⣛⣛⣛⣂⣙⣛⣛⣛⡛⣛⣛⣛⢿⡟⣛⣛⣛⢛⣁⣈⡸⣛⣛⡻⢟⣛⣻⢿⣛⣛⢿⣿⢛⣛⡻⢟⣛⣓⡦⣀⣘⢟⣀⡀⣚⣛⢋⣁⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⣇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⣧⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢴⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀ ⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡆⠀⠀⠀⢀ ⣿⣞⡻⢿⣷⣽⣿⢻⠅⣛⣚⣃⣛⣃⡛⢘⣃⣛⣃⣛⣳⣜⣛⣾⣞⣛⣴⣛⣛⣛⣛⣛⣛⣡⣿⣜⣛⣃⣘⢛⣛⣃⣛⣛⣛⣙⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⣛⠛⠁⠀⠀⠀⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⠁⠈⠁⢺⠃⣿⡏⡋⡸⣿⢻⣿⣿⡿⢟⡠⢤⢈⠣⠲⣾⣿⠿⣥⣤⣤⣼⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣞⡛⠒⠓⢓⠓⠚⠚⠚⠚⠒⠚⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣾⣿⣿⡿⠙⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⣹⠁⠀⠁⠘⠁⠀⠀⠁⠠⡀⢠⠀⠀⠀⠀⠈⠉⠉⠋⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣈⣽⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⣿⣿⣶⣶⡄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠉⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠒⡒⠀⢶⣼⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡻⠋⠛⠍⠒⢐⡑⡀⡀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣛⡧⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⢉⠘⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⢵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠀⢀⡤⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣛⠛⢋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣀⣧⣙⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿ ⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠦⠀⠀⠀⠉⣿⣿⣿⣿⠟⠻⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋ ⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠈⠀⠀⣰⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠆⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⠿⠿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠘⢻⠄⠈⠀⠀⣼⣿⣿⠯⠜⢁⡠⠤⢤⡀⠀⠀⠀⢠⣾⣿⣿⣿⡀⠻⠿⠟⠓⠶⠀⣼⣿⣿⣿⣿⣧⣿⡗⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⣸⣿⣿⣿⣧⣿⣼⡃⠈⠀⣿⡤⣴⣦⣼⣿⣿⣿⣿⣇⢀⣤⠄⣤⠤⠀⣈⠙⣿⣿⣿⣷⢸⡟⠀⠀⡿⡟⠋⠉⠀⠐⠀⠄⠾⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠂⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣀⡁⣸⣷⡌⣿⣿⣧⠐⢳⡀⠀⡄⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠃⢷⠇⠀⠀⠀⠀⠀⠀⠀⢘⢟⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡼⢀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡯⢇⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⣀⡀⣽⣿⠏⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⡀⢰⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡿⣶⣸⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣷⣶⣿⣿⣍⣿⣾⣷⣬⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣽⣇⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢂⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣿⣛⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣄⠀⠈⠙⠿⣿⡿⠃⠉⠛⠋⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢯⣿⣷⣀⠀⠀⠉⠻⢿⣽⣿⣿⣿⣿⣿⣿⣧⡈⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠸⠿⠻⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣾⣿⣿⢹⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢀⠀⠀⣴⣤⣶⣶⣟⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⢀⢰⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢠⣿⡄⢸⣿⢟⣉⣁⣤⣤⣤⡀⣩⣿⣿⣯⡍⣿⣿⣿⣷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⡿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⠛⣿⣿⡉⣻⣿⣿⣾⣯⣿⣿⣿⢿⣋⣽⣿⡟⠿⠗⣿⣿⣼⣿⣷⣿⣿⡼⣿⣧ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣧⣎⣏⣿⣦⣀⣀⣀⣄⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣧⣦⣿⣦⠀⣶⢿⣿⣻⠟⢷⣽⡏⠻⠿⣻⣿⣇⣶⣶⢿⣿⣯⣿⣿⢹⣿⡇⣿⣿ ⠀⣀⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣽⡏⠅⢻⣿⣟⢿⢷⣤⢢⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⠛⠛⠁⢛⣏⠻⣿⣠⣤⠿⠟⢻⠟⠉⠛⠛⠛⠁⠈⠙⠛⠋⠁⠈⠉⠁⠉⠉ ⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡹⢿⣻⡧⠐⣉⡽⠿⡀⠙⠙⠩⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣆⠀⠀⠀⠀⠀⡼⠛⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠈⠺⠐⠁⠈⠈⠳⠂⠀⠀⠀⠀⠀⠼⠿⠟⠿⠿⠿⢿⡿⠸⠿⣿⡿⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣽⡟⣿⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣼⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⡿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀ ⢌⡷⣺⣿⡟⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡄⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⡿⠿⠿⢇⡻⠷⠿⠃⠀⠀⢀⠀⠀⠀⣰⣷⣶⣶⣿⣿⣇⡀⠀⠀⠀⠀ ⠌⢘⣁⣉⠛⢸⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢁⣀⡻⣛⣟⣛⣛⣛⣂⣀⣘⣛⣛⡛⣃⣀⣀⠐⠀⣘⣛⣛⢛⣁⣀⡸⣛⣛⡻⢟⣛⣻⢿⣛⣛⢿⣿⣛⣛⡻⢟⣛⣛⡦⣀⣘⢟⣂⡀⣘⣻⣟⣛⣛⢉⣁⣀⠀⠀⠀⠀⠀ ⡅⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢰⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⣉⣿⣏⡿⠀⠀⠀⠀⠀ ⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⣺⣿⠀⣿⣿⠃⣿⡇⣿⡇⣾⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⣾⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡿⣿⢿⣿⢸⣿⠋⣬⡟⣿⡆⡆⠀⠀⠀ ⣿⣞⣻⢿⣷⣽⣿⠿⠵⢛⣚⣃⡛⠃⡛⢘⣃⣛⣃⣛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣣⣿⣞⣛⣃⡘⢛⣛⣃⣛⣛⣛⣙⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣚⣛⣛⣝⣻⠛⣱⣷⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⠁⠈⠁⢺⠋⣿⡏⡋⡸⣿⢻⣿⣿⡿⢟⡠⢤⢈⠳⠲⣿⣿⡿⣧⣤⣤⣼⣷⣽⢿⣿⣿⣿⣿⣿⣿⣿⣞⠛⠒⠓⢓⠓⠘⠚⠚⠚⠒⠚⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣾⣿⣿⡿⠑⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⣹⠁⠀⠁⠘⠁⠀⠀⠁⠠⡀⢠⠀⠀⠀⠀⠈⠉⠉⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣈⣽⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⣿⣿⣶⣶⡄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠉⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣶⣶⣶⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠒⡒⠀⢲⣼⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠿⠏⠻⠍⠐⢀⠂⡂⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣻⡧⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⢙⠐⣿⡿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠀⢀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢨⣷⣷⣲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣛⠛⢋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣀⣧⣙⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿ ⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠦⠀⠀⠀⠉⣿⣿⣿⣿⠟⠻⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋ ⣴⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠈⠀⠀⣰⣿⣿⡿⣿⡀⠄⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠆⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠻⠿⡿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠘⢻⠄⠘⠀⠀⣼⣿⣿⠯⠜⢁⡠⠤⢤⡀⠀⠀⠀⢠⣾⣿⣿⣿⡀⠻⠿⠟⠓⠶⢀⣼⣿⣿⣿⣿⣷⣿⡗⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⣸⣿⣿⣿⣧⣿⣼⡃⠈⠀⣿⡤⣴⣦⣼⣿⣿⣿⣿⣇⢀⣤⢄⣤⠤⠀⣈⠙⣿⣿⣿⣧⢸⡟⠀⠀⡿⡟⠋⠉⠀⠀⠀⡠⡿⣿⣿⣶⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠂⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣀⡁⣸⣷⡌⣿⣿⣇⠰⢻⡀⠀⡄⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠃⢷⡃⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡼⢀⣄⡆⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡯⢇⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⣀⡀⣽⣿⠏⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⣀⢰⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⡀⣠⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡿⣶⣸⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣷⣶⣿⣿⣍⣿⣾⣷⣬⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣮⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣿⣛⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠈⠙⠿⢿⡿⠃⠉⠛⠏⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢯⣿⣷⣄⠀⠀⠉⠻⢿⣽⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠸⠿⠻⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣴⣾⣿⣿⢹⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⢀⠀⠀⣴⣤⣶⣶⣟⠁⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣺⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢠⣿⡄⢸⣿⢟⣉⣁⣤⣤⣤⡀⣩⣿⣿⣯⡍⣿⣿⣿⣷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⡿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⠛⣿⣿⡉⣻⣿⣿⣾⣯⣿⣿⣿⢿⣋⣽⣿⡟⠿⠗⣿⣿⣼⣿⣷⣿⣿⡼⣿⣧ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣧⣎⣟⣿⣦⣀⣀⣀⣄⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣷⣦⣿⣦⠀⣶⢿⣿⣻⠟⢷⣽⡏⠻⠿⣻⣿⣇⣶⣶⢿⣿⣯⣿⣿⢹⣿⡇⣿⣿ ⠀⣀⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣽⡏⠅⣻⣿⣟⢿⡷⣤⢢⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⠛⠛⠁⢻⣏⠻⣿⣠⣤⠿⠟⢻⠟⠉⠛⠛⠛⠁⠈⠙⠛⠋⠁⠈⠉⠁⠉⠉ ⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠹⢿⣿⡧⠐⣉⡻⠿⢀⠉⠉⠩⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣆⠀⠀⠀⠀⠀⡼⠛⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠈⠛⠃⠁⠈⠈⠳⠂⠀⠀⠀⠀⠀⠼⠿⠟⠿⠿⠿⢿⠿⠸⠿⣿⡿⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣽⡟⣿⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣽⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⡿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡼⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀ ⢌⡷⣺⣿⡟⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠷⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⡄⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⢇⡿⠿⠿⢇⡻⠷⠿⠃⠀⠀⢀⠀⠀⠀⣰⣷⣶⣶⣿⣿⣇⡀⠀⠀⠀⠀ ⡌⢘⣁⣉⠛⢸⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢁⣀⡻⣛⣛⣛⣛⣛⣂⣀⣘⣛⣛⡛⣃⣀⣀⠐⠀⣘⣛⣛⢛⣁⣀⡸⣛⣛⡻⢟⣛⣻⢿⣛⣛⢿⣿⣛⣛⡻⢟⣛⣛⡦⣀⣘⢟⣂⡀⣘⣻⣟⣛⣛⢉⣁⣀⠀⠀⠀⠀⠀ ⡇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢰⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠀⠀⠀⠀⠀ ⣧⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣾⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⣾⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡿⣿⢿⣿⢸⣿⠋⣬⡝⣿⡆⡆⠀⠀⠀ ⣿⣞⣻⢿⣷⣽⣿⠿⠵⢛⣚⣃⡛⠃⡛⢘⣃⣛⣃⣛⣳⣜⣛⣾⣟⣛⣶⣛⣛⣛⣛⣛⣛⣣⣿⣞⣛⣃⡘⢛⣛⣃⣛⣛⣛⣙⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⣻⠛⣱⣷⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⢿⢿⠉⠈⠋⢻⠇⣿⡯⡏⡙⣿⢻⣿⣿⣿⢟⡠⢠⢈⠻⠲⣷⠁⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⢸⣿⣿⣧⠚⠛⠒⠛⠓⡓⠚⠛⠚⠚⠒⠚⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⣳⠁⠈⠁⠈⠁⠀⠀⠁⠤⣄⢀⠀⠀⠀⠀⠀⠀⣷⣤⣠⡀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⣶⣶⣤⡄⠀⠙⠁⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⣿⣿⣿⠏⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠐⠒⣒⠀⢳⣶⣽⢿⣖⣲⣶⣶⣿⣦⣿⣟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣻⣧⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⢿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠀⠀⣤⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣛⠛⢋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣾⣙⡤⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡖⠀⠀⠉⠛⣿⣿⣿⣿⡿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠐⠨⠀⠀⣴⣿⣿⣿⣿⡷⠄⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡗⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠄⠈⠀⢀⣼⣿⣿⡿⠽⢋⡠⠤⢤⣀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠻⠿⠿⠿⠶⢤⣽⣿⣿⣿⣿⣷⣿⡟⡆⠁⣸⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃⠀⠀⣸⣿⣿⣿⣿⣿⣾⡃⠈⠀⣿⡤⣶⣦⣼⣿⣿⣿⣿⣧⢀⣤⠄⣤⡤⠄⣈⠙⣿⣿⣿⣿⠸⣟⠂⠀⡾⢿⠿⠏⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣁⣩⣷⣌⢿⣿⣷⠀⢻⡆⠀⣦⣞⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠈⠳⢻⣿⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠀⣾⣿⣿⣧⣄⣄⢠⣭⠈⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡮⢗⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠫⣀⡀⣽⣿⡏⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣀⢠⣿⣿⣿⣿⣿⣿⣾⣾⣿⣄⣤⣦⣷⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡿⣾⣸⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣾⣿⣿⣍⣿⣿⣷⣦⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣿⣛⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠻⠿⠛⠛⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⣿⣿⣄⠀⠉⠉⠻⢿⣽⣿⣿⣿⣿⣿⣿⣧⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠄⣠⣦⣴⣶⣾⡋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠉⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣾⣇⢀⣿⡟⣋⣉⣠⣤⣤⣄⢀⣴⣿⣯⣍⢹⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⡛⣿⣿⡍⣹⣿⣿⣿⣿⣻⣿⣿⣿⣛⣻⣿⣿⠿⠿⢸⣿⡇⣿⣿⣸⣿⣇⣿⣿ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣶⣄⣤⣤⣤⣀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣵⣼⣧⡄⣷⡿⣿⣿⡿⢻⣯⣿⠹⠿⢻⣿⣿⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⣰⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⡟⣯⣿⣿⣿⣿⣿⣷⢷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠛⠛⠛⠁⢘⣿⡙⣿⣇⣧⡽⡿⢻⡿⠋⠙⠛⠛⠋⠀⠙⠛⠛⠋⠈⠛⠋⠈⠉ ⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠨⡽⣿⣿⣿⡵⣉⣿⠿⢏⡛⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣦⠀⠀⠀⠀⠀⣠⠟⠓⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠧⠀⠘⠻⠟⡻⠘⠈⠳⠆⠈⠀⠀⠀⠀⠽⠿⠟⠿⠿⠿⢿⡿⠁⠿⣿⡿⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡀⣿⣿⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣽⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡇⣿⡿⠇⠀⣿⣿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⢿⣽⡾⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀ ⣽⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣼⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⡇⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⣇⡿⠿⠿⢇⡻⠷⠿⠃⠀⠀⠀⡀⠀⠀⢠⣿⣶⣶⣾⣿⣿⡀⠀⠀⠀⠀ ⡜⢘⣋⣛⠛⢹⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢉⣀⡻⣛⣿⣛⣛⣛⣂⣀⣘⣛⣛⡛⣃⣁⣈⠐⠀⣘⣛⣛⢛⣁⣀⣰⣛⣛⡻⢟⣛⣻⢿⣛⣛⢿⣿⣟⣛⡻⢟⣛⣛⡶⣄⣈⢛⣃⡀⣀⣻⣟⣛⣛⢋⣉⣁⠀⠀⠀⠀⠀ ⡇⣼⣿⣿⣇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣿⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡃⣿⣏⡿⢸⣿⣋⢼⣲⣿⣿⣿⢸⣿⣹⣿⢹⣿⢸⣿⣷⣿⣿⢸⣿⣉⣿⣏⡿⢂⠀⠀⠀⠀ ⣯⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⣿⣿⡇⣿⢻⣿⣿⡇⣿⡇⢸⣿⢸⣿⣿⠀⣿⣿⠃⣿⡇⣿⡇⣾⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⣾⣿⣿⣧⣤⢸⣿⢹⣷⢹⣿⢸⡿⣿⢿⣿⢸⣿⠛⣬⡟⣿⡎⣧⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⣀⣠⣿⣦⢻⣿⣿⠀⠟⡇⠀⣼⡼⠆⠒⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠑⠸⣿⣿⣶⣶⣽⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣮⢇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⣀⣀⢼⣿⡏⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣖⣤⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣾⢰⡘⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿⣶⣿⣿⣌⣻⣿⣷⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣵⡿⣸⣾⣿⣿⣿⡿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣧⢸⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠄⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢻⣧⣿⣻⣿⣿⣿⣿⣿⣿⣝⡻⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⢋⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⢱⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⠟⠛⠿⠿⠿⣿⣿⣿⢟⠐⠚⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠆⠀⢻⣻⣿⣿⣿⣿⣿⣿⣟⣋⣉⣉⣛⣛⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⣽⣿⣄⠀⠀⠉⠛⢿⣽⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣿⣿⣿⣧⡀⠀⠀⠀⠈⠿⠛⡿⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡟⣛⣋⣡⣤⣤⡀⢀⣤⣤⣤⡄⣤⣤⣤⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⡟⣿⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠿⢟⣛⣛⣛⠛⣛⣻⡉⣻⣿⣿⣾⣯⣿⣾⣿⢿⣛⢹⣿⡏⠿⠿⣿⣿⡏⣿⣿⢹⣿⡇⣿ ⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣟⣿⣯⣛⣸⣢⣄⣀⣀⡀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣤⣽⣯⠀⣶⣿⣿⢻⡟⣷⣿⣿⣾⡿⢻⣿⣇⣶⣶⢻⣿⣇⣿⣿⢸⣿⡇⣿ ⠀⠀⣀⣤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣷⣵⠇⢁⢹⢿⣟⠿⢷⢧⠲⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠿⠟⠁⢻⢟⠻⣿⣙⣯⡿⡿⢿⠿⠋⠛⠿⠛⠋⠀⠙⠛⠛⠉⠘⠛⠃⠙ ⣾⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⡙⠿⡻⠶⠀⠈⠙⠏⠈⠈⠈⠱⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣷⡀⠀⠀⠀⠀⠀⡨⠖⠂⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠨⠿⠟⠻⠿⠿⠿⠿⠃⠿⣿⡿⢿⡷⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣷⣾⣤⣤⣤⣤⣤⣤⣤⡀⠀ ⣿⣿⡗⢫⣻⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢹⣿⣿⡇⣾⡟⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤ ⡾⣭⣿⣷⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⡿⠟⢻⣿⡟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣽⡼⣿⣿⣿⣿⡟⣾⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠍⣳⣻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠾⠿⠶⣸⣇⠿⢿⡸⠿⢇⡿⠿⠿⢇⡻⠷⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⡄⢀⣉⣙⠛⢐⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢋⣀⡙⣛⣛⣛⣛⣛⣂⣀⣈⣛⣛⡛⣀⣀⣈⠀⠀⣈⣓⣛⢛⣃⣀⡀⣛⣛⡻⢟⣛⣻⢿⣛⣛⠻⡿⢟⣛⡛⢟⣛⣛⡿⣟⣻⢟⣛⡿⣛⣻⢟⣛⣻⢟⣛⣻⢿⣿⣿⠏⠁ ⡅⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢰⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⣿⣿⡏⠀⠀ ⣇⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣼⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡞⣿⡇⠀⠀ ⣿⣞⣻⢿⣷⣽⣿⣻⠥⠛⡚⣃⣛⠃⠛⠘⣃⣛⣃⣛⣳⣜⣛⣼⣞⣛⣴⣛⣛⣛⣛⣛⣛⣣⣿⣜⣛⣣⠘⠛⣛⣃⣛⣛⣛⣙⣻⣛⣝⣛⣛⣻⣧⣛⣟⣛⣘⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣽⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⠿⠿⠁⠀⠁⠰⡋⢻⡇⡏⠘⣻⠉⢿⣿⡿⠛⠠⢐⠂⡉⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠘⠛⠒⠒⠓⠓⠐⠒⠒⠘⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠶⠶⢦⣶⠀⠀⠁⠀⠀⠀⠀⠀⠐⠛⠿⠿⠞⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣦⣄⠀⡀⠀⠀⠀⠀⢀⣀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣷⣿⣿⠇⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠙⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⣒⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣤⠈⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡋⠉⠉⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣴⣌⣄⢌⠀⠈⠀⠉⠙⠛⠛⠻⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠆⠀⠀⠀⠉⣿⣿⣿⣿⠯⠻⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣿⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣝⡿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢾⠃⠞⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⢱⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡿⠿⠟⠛⠻⠿⠿⢿⣿⣿⢿⠐⠻⠼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠆⠀⢻⣻⣿⣿⣿⣿⣿⣿⣟⣋⣉⣉⣛⣛⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠟⠀⠀⠀⠀⠈⠀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⣿⣿⣄⠀⠀⠉⠛⢿⣽⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣿⣿⣿⣧⠀⠀⠀⠀⠘⠿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡿⢿⣿⡟⣛⣋⣡⣤⣤⡀⢀⣤⣤⣤⡄⣤⣤⣤⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣟⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⢟⣛⣛⣛⠛⣛⣻⡉⣻⣿⣿⣾⣯⣿⣾⣿⢿⣛⢹⣿⡏⠿⠿⣿⣿⡏⣿⣿⢸⣿⡇⣿ ⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣏⣿⣯⢟⡸⣦⣄⣀⣀⡀⡀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣤⣽⣯⠀⣶⣿⣿⢻⡟⣷⣿⣿⣾⡿⢻⣿⣇⣶⣶⢻⣿⣇⣿⣿⢸⣿⡇⣿ ⠀⠀⣀⣤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣷⣥⡆⢁⢹⢿⣟⢿⢷⢧⠢⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠿⠛⠁⢻⢿⠻⣿⣘⣯⡿⡿⢿⠿⠋⠛⠿⠛⠋⠀⠛⠛⠛⠉⠘⠛⠃⠙ ⣾⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡙⠿⡿⠖⠀⠈⠘⠛⠈⠁⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣷⡀⠀⠀⠀⠀⠀⡸⠒⠂⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠨⠿⠿⠻⠿⠿⢿⠿⠃⠿⣿⡿⠿⡷⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣷⣾⣤⣤⣤⣤⣤⣤⣤⡀⠀ ⣿⣿⡷⢻⣿⢷⣧⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢹⣿⣿⡇⣾⡟⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤ ⠾⣭⣿⣧⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠀⣿⣿⣿⡇⣿⡿⠇⠀⣿⡿⠟⢻⣿⡟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣽⡼⣿⣿⣿⣿⡟⣾⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠍⣱⣻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠯⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠾⠿⠶⣸⣇⠿⢿⡸⠿⢇⡿⠿⠿⢇⡻⠷⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⡔⢁⣉⣉⠛⢑⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢋⣀⡙⣛⣛⣛⣛⣛⣂⣀⣈⣛⣛⡛⣀⣀⣈⠀⠀⣈⣓⣛⢛⣃⣀⡀⣛⣛⡻⢟⣛⣻⢿⣛⣛⠻⡿⢟⣛⡛⢟⣛⣛⡿⣟⣻⢟⣛⡿⣛⣻⣟⣛⣻⢟⣛⣻⢿⣿⣿⠏⠁ ⡅⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣋⢰⢰⣿⣿⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⣿⣿⡏⠀⠀ ⣇⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣼⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠛⣬⡝⣿⡞⣿⡇⠀⠀ ⣿⣞⣻⢿⣷⣽⣿⣻⠥⠛⡚⣃⣛⠃⠛⠘⣃⣛⣃⣛⣳⣜⣛⣼⣞⣛⣴⣛⣛⣛⣛⣛⣛⣣⣿⣜⣛⣣⠘⠛⣛⣃⣛⣛⣛⣙⣻⣛⣝⣛⣛⣻⣧⣛⣟⣛⣘⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣽⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⣿⠻⠟⠁⠀⠁⠐⡁⢻⠇⡇⠀⣱⠉⠿⠟⡿⠋⠀⠠⠀⠀⠀⠲⢌⣤⣀⣀⣀⠀⠘⠃⠛⠻⠿⠿⣿⣷⡄⠀⠐⠂⢒⠒⠒⠐⠀⠒⠒⠐⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⣀⣤⣦⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣫⣵⣿⡿⠃⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣶⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣋⣂⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⣿⠺⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢠⠈⠎⠉⠙⠙⠛⠋⠛⠿⢿⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠿⠍⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⢀⣤⣤⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⢿⠃⠀⠀⠀⠀⣿⣿⣿⣿⡏⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡸⣮⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⣰⣿⣿⡿⣿⡉⠒⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⡿⣿⣿⣿⡿⠿⠛⠛⣿⣿⣿⣿⡿⢿⣏⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣼⣿⣿⢿⡛⢃⡤⠖⠢⣄⠀⠀⠀⢠⣿⣿⣿⣿⡇⠙⠛⠋⠉⠐⠀⢤⣾⣿⣿⣿⣟⠼⣿⠀⠀⢀⣸⣤⣦⣀⣸⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⣸⣿⣿⣿⣿⣿⣾⣍⣀⣀⣸⡔⣾⣷⣼⣿⣿⣿⣿⣷⣀⣤⠀⣠⠖⠂⠀⡈⠹⣿⣿⣿⠀⢿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣀⣠⣿⣦⣹⣿⣿⠀⠈⡇⠀⢸⣿⣿⢿⡿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠘⣿⣿⣿⡰⠄⢿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣧⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣅⡄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣬⢿⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢠⣤⢼⣿⡏⠀⠀⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⣿⣿⣿⣿⣷⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⡃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣼⢸⡜⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣇⣻⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢠⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣯⣤⣿⢸⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⡆⡿⠉⢉⣤⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣧⣤⡈⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠉⠁⠀⠀⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣵⡌⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠛⠿⣿⣿⡝⠛⠛⠟⠛⠙⠛⠛⠿⣿⣿⣿⣿⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣷ ⠀⠀⣰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣉⣡⣄⣉⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠺⠿⡿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣽⣿⣆⡀⢥⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣇⣿⣿⣿⣷⡀⠀⠀⠀⠘⣭⡍⣿⠿⠿⠿⣿⣿⣿⣿⠿⠿⣛⢿⣦⣶⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣋⣯⣿⣄⠀⣠⣤⣤⣄⢠⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⡗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣿⣿⣿⣿⣿⠾⠟⣛⣛⣛⡛⢛⣛⣋⢙⣿⣿⣷⣿⣹⣷⣿⡿⣟⡋⣿⣿⠹⠿⢾⣿⣿⢹⣿⡇⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⣿⡿⣿⣷⣤⣤⣤⣄⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣥⣬⣯⡅⢰⣿⣿⣟⣿⢻⣾⣿⣷⣿⢟⣿⣿⣰⣶⡾⣿⣿⣸⣿⡇⣿⣿⢸ ⠀⠀⣀⣤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣿⣾⡇⢡⣿⣿⣿⣻⣿⢷⠦⠄⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠟⠛⠃⠘⠿⠛⢿⣇⣻⡽⠿⠿⡿⠛⠙⠻⠟⠛⠁⠙⠛⠛⠋⠁⠛⠛⠈ ⣶⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⡽⡶⠈⢉⣼⠿⢚⠊⠀⠠⠎⠻⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠔⠒⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠁⠀⠁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠽⠛⠻⠿⠿⠿⠿⠃⠸⣿⡿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣸⣇⣀⣀⣠⣄⣀⠀⠀⠀ ⣿⡻⠃⢀⠉⠎⣇⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣻⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡎⣿⣿⣿⣿⣷⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠆⣤⣒⣀⣙⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⣿⣿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⡟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣼⡼⣿⣿⣿⣿⡟⢸⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾ ⠀⣠⠘⡭⣟⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⣤⡿⠿⠿⢇⠿⠷⠆⠀⠿⠧⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠾⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠀⣁⣉⠉⢀⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢋⣀⡙⣛⣛⣛⣛⣛⣃⣀⣀⣛⣛⡋⣁⣀⣀⠀⠀⣈⣀⣘⢋⣃⣀⡀⣛⣛⡻⢟⣛⣻⢿⣛⣛⠻⠿⢟⣛⡛⢟⣛⣛⡻⣟⣛⢟⣛⡻⣛⣻⢟⣛⣻⢟⣛⣛⢿⣿⡏⠀⠀ ⡄⣸⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣟⡁⣿⡏⣿⡇⠀⢙⣿⡋⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢰⢰⣿⢻⣿⢸⣿⣹⣷⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⣺⣿⠀⠀⠀ ⡇⢻⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣟⠃⣿⡇⣿⡇⣰⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣽⣿⢡⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡞⣿⣇⠀⠀ ⣿⣜⣻⢟⣧⣽⣿⣻⠥⠛⡚⣃⡛⠃⠛⠘⣃⣛⣃⣛⣳⣜⣛⣼⣞⣛⣴⣛⣛⣛⣛⣛⣛⣡⣿⣜⣛⣣⠘⠛⣛⣃⣛⣛⣓⣙⣻⣛⣝⣛⣛⣻⣧⣛⢛⣛⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣽⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡿⣯⠛⠋⠀⠀⠀⠘⠀⠸⠇⡇⠀⣸⠀⠻⠟⡿⢉⠀⠨⠁⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠐⠀⠒⠒⠒⠐⠀⠒⠒⠀⠒⠐⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣄⠹⡧⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⢿⣿⣿⣿⣋⣩⣭⣯⡁⢠⣤⣤⣤⡀⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣄⣄⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢛⣛⣛⠛⣛⣋⠉⣻⣿⣿⣾⣏⢿⣾⣿⢿⣛⣻⣿⡏⠿⠷⣿⣿⣿⣿⣷⢻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣭⣭⣭⣥⣤⣽⣅⠀⣮⢿⣿⣻⡟⣷⣿⣿⣿⡿⣻⣿⣇⣶⣶⢿⣿⣇⣿⣿⢸⣿⡇ ⠀⠀⣀⣠⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠻⠿⠿⠛⠋⠀⠛⠟⠻⣿⣘⣭⠿⠿⣿⠟⠋⠛⠿⠛⠋⠈⠛⠛⠛⠁⠘⠛⠃ ⣶⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠠⠐⠂⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⣿⠿⠿⠿⠿⠿⠟⠿⠟⠻⠿⠿⠿⠿⠿⠿⢿⡿⠟⠸⣿⡿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠅⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⠛⣹⣏⣿⡇⣿⡟⠃⡇⣿⡟⣿⡞⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣹⡿⣿⡇⣿⡿⠃⡇⣿⡿⢟⢣⣿⠟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣼⡼⣿⣿⢿⣾⡏⢸⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⣠⡾⠧⠿⠇⠿⠷⠆⡀⠿⠇⣼⡸⠿⠷⠎⠿⠾⠟⠸⠿⣸⡇⠿⠷⠸⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⣛⣛⠻⢃⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢋⣁⡙⣛⣛⣛⣛⣛⣓⣙⣛⣛⣛⡛⣛⣛⣛⢿⡟⣛⣛⣛⢛⣛⣚⡀⣚⣛⡻⢟⣛⣻⢿⣛⣛⢻⡿⢟⣛⡛⢟⣛⣛⡻⢗⣂⢀⣀⡀⣀⣀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⡇⢸⡟⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣼⣿⡇⣿⡏⢹⣿⢩⢹⣿⠉⣿⣟⡁⣿⡏⣿⡇⣤⠙⣿⠋⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢼⣧⣿⢹⣿⢸⣿⣹⣷⢸⣿⢸⣿⣧⣿⣿⢸⣿⡉⣿⣏⡿⠀⠀⠀⠀⠀ ⣇⢸⡏⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⡟⠃⣿⡇⣿⡇⣿⠈⣿⠀⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⡿⣿⢠⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢻⣿⢸⣿⠃⣬⡝⣿⡄⠀⠀⠀⠀ ⣿⣜⣻⢛⣧⣝⣛⣛⡥⠛⣚⣃⣛⣃⣛⠘⣃⣛⣃⣛⣣⣜⣛⣼⣞⣛⣤⣛⣛⣛⣛⣛⣛⣡⣿⣞⣛⣢⣘⠛⢛⣃⣛⣛⣃⣙⣛⣛⣝⣛⣛⣻⣧⣛⣛⣋⣜⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⡛⣛⣥⣶⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢿⣏⠛⠋⠀⠀⠀⠸⠀⠟⠇⠇⠄⡿⠀⠻⠋⠟⠱⠀⠘⠀⠀⠈⠱⠃⣺⣿⣶⣶⣦⣤⣤⣄⡀⠀⠉⠉⠋⠉⠋⠐⠂⠒⠒⠒⠐⠈⠒⠒⠐⠒⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⢀⣠⣴⣵⣿⣿⠇⢐⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠛⠁⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣯⣷⣿⡿⠃⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣫⣇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠑⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⣻⣿⣿⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢲⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠻⠿⢛⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠿⠍⠉⠁⠈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠠⢴⣦⣆⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠂⠀⠀⠀⠀⣹⣿⣿⣿⠋⠙⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣴⣻⣿⠿⡻⠅⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⡟⣿⣿⣿⣟⣛⠉⠉⣿⣿⣿⣿⣟⢻⡟⠙⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠂⠀⠀⠀⣼⣿⠟⢓⠊⢀⣔⠂⠐⣤⠀⢀⡀⠀⣿⣿⣿⣿⡇⠈⠉⠉⠁⠉⠑⠾⢿⣿⣿⣿⣿⠻⣿⠐⠀⢠⣀⣤⣤⣴⣾⡇⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⣸⣷⣿⣿⣿⣾⣮⣅⣀⣠⣾⣞⣾⣷⣾⣿⣿⣿⣿⣿⣀⣴⣂⢴⠛⠁⠀⣄⠹⣿⣿⣿⠀⢿⡀⠀⠘⣲⣿⣿⣿⣿⢿⠀⠠⠦⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⣧⣇⠀⠀⠐⠼⢯⣿⠿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣹⣿⣆⠀⠀⠀⠈⠳⠈⣾⣽⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⡿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⡿⣿⣟⣋⣿⣿⣿⢿⣤⣤⣤⣄⢠⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⡌⢱⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢛⣛⣻⡛⣛⣛⡉⢹⣿⣿⣷⣯⣻⣾⣿⣿⣟⣻⣿⣿⠿⠿⢾⣿⣏⣿⣿⣸⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⢿⣍⡁⡄⡐⢀⠳⣄⣀⣀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠉⣩⣭⣭⣥⣽⣯⡄⢰⣿⣿⣟⡿⢻⣿⣿⣿⣿⢿⣿⣿⢰⣶⣾⣿⣿⣿⣿⡏⣿⣿ ⠀⠀⣀⣠⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⠿⣷⣦⡇⠀⠈⠛⢯⠙⠂⠀⠀⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣆⠈⠙⠿⠿⠟⠛⠃⠘⠿⠛⣿⣇⣯⡽⡿⢿⡿⠋⠙⠻⠟⠛⠀⠙⠛⠛⠋⠀⠛⠛ ⣶⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢉⠷⡍⠒⠄⠀⠀⠁⠀⠀⠀⠀⠘⢻⢿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⠔⠒⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⡯⢿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠁⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠨⠴⠛⠻⠿⠟⠿⠿⠏⠸⣿⡿⠿⠿⠷⠄⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣫⡇⢂⠏⠞⣄⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⣤⣖⣥⣛⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⠟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣼⡸⣿⣿⣿⣿⡟⢸⣿⣿⡇⣿⡇⣿⡇⣸⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢱⣐⣻⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⣤⡿⠿⠿⢇⠿⠷⠆⠀⠿⠧⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠸⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⡄⠀⣁⣉⠙⢀⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢉⣀⡙⣛⣛⣛⣛⣛⣓⣀⣀⣛⣛⡋⣁⣈⣀⠀⠀⣀⣐⣚⢛⣁⣀⡀⣚⣛⡻⢟⣛⣻⢿⣛⣛⠙⡿⢟⣛⡛⢟⣛⣛⡻⣟⣛⢟⣛⡿⣛⣻⢟⣛⣛⢛⣉⣀⠀⠀⠀⠀⠀ ⡄⣸⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣼⣿⡇⣿⡏⢹⣿⢩⢹⣿⠉⣿⣟⡁⣿⡏⣿⡇⠀⠹⣿⡋⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢤⢰⣿⢻⣿⢸⣿⣹⣷⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀ ⡇⢺⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⡟⠃⣿⡇⣿⡇⣴⠐⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⡾⣿⢣⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠃⣬⡝⣿⡆⡄⠀⠀⠀ ⣿⣜⡻⢟⣧⣽⣿⣻⠥⠛⡚⣃⣛⠃⠛⠘⣃⣛⣃⡛⣣⣜⣛⣼⣞⣛⣴⣛⣛⣛⣛⣛⣛⣡⣿⣜⣛⣣⡘⠛⢛⣃⣛⣛⣓⣝⣛⣛⣝⣛⣛⣿⣧⣛⡛⣛⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣥⡋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⢿⣯⠟⠛⠀⠀⠁⠸⠀⡟⡏⠁⢌⠿⠘⠟⢛⠟⠑⠈⠞⠀⠈⠈⠓⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠒⠒⠓⠓⠈⠒⠒⠀⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣦⣄⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡟⠛⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣶⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣭⣿⣿⡿⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⣿⣿⡇⠂⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠑⢫⠛⠋⠉⠁⠈⠈⠀⠈⠁⠉⠛⠛⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⢲⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠅⠍⠀⣨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢴⣶⣶⣦⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⠀⠀⠀⠀⠁⣻⣿⣿⣿⡋⠙⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠁⢿⢿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠙⠹⡇⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⣫⣻⢻⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠹⣟⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣇⠀⠀⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣽⣿⣦⠀⠀⠀⠈⠻⢾⣿⣿⣿⣿⣿⣿⣿⡆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣿⣿⣿⣧⡀⠀⠀⠀⠘⠙⠛⠿⠿⢿⠿⢿⡿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⣿⣿⢿⣿⣋⣿⣿⣿⡛⣿⣤⣤⣤⡀⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠘⣿⡿⣿⣟⣿⡗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⢛⣛⡟⢛⣛⣋⢉⣿⣽⣿⣿⣽⣷⣿⣿⣾⣛⣿⣿⡿⠿⠷⣿⣿⣹⣿⣇⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣿⣯⡽⣾⡝⢻⢳⣤⣤⣤⡄⢠⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠉⢉⣩⣽⣥⣬⣿⡅⢰⣼⣿⣿⣿⠻⣿⣿⣿⣿⡿⣿⣿⡇⣶⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⣠⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⠿⣿⣮⡇⠀⣼⡟⣿⡛⢟⣏⡴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣦⠀⠙⠙⠿⠿⠿⠋⠈⠻⠟⢻⣟⣸⣭⢿⠿⣿⠟⠉⠛⠿⠛⠃⠈⠛⠛⠛⠁⠘⠛ ⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢙⢿⡭⠲⠆⠀⡀⠻⠯⠁⠀⠽⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡤⠚⠊⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠀⠀⠁⠂⡨⠀⠀⠁⠀⠀⠀⠀⠀⠀⠨⠵⠻⠻⠿⠿⠿⠿⠟⠸⣿⡿⠿⠿⠷⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠰⠲⠃⠀⠀⠀⠀⣀⣤⡤ ⣿⣯⣇⣮⣏⠞⣇⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡞⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠺⠛⠁⠀ ⣿⣮⣿⣷⣟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⠀⣿⣿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⡟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠻⣼⡼⣿⣿⣿⣿⡟⢸⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣟⣷⣾⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣱⣹⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⣤⡿⠿⠿⢇⠿⠷⠆⠀⠿⠯⣸⡸⠿⠷⠞⠿⠾⠟⠸⠿⢸⡀⠿⠷⠾⠿⠶⣸⣇⠿⠿⡸⠿⢇⡿⠿⠿⠇⡹⠷⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⡕⠁⣁⣙⠙⢀⣛⣛⠿⣛⣻⢟⣛⡻⣛⣛⢋⣀⡙⣛⣛⣛⣛⣛⣓⣀⣀⣛⣛⡛⣋⣀⣀⠀⠂⣀⣒⣚⢛⣃⣀⡀⣚⣛⡻⢟⣛⣻⢿⣛⣛⠙⡟⢛⣛⡛⢟⣛⣛⡻⣟⣛⢟⣛⡿⣛⣻⢛⣛⣛⢛⣀⣀⠀⠀⠀⠀⠀ ⡄⣸⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠋⣿⣿⡁⣿⡏⣿⡇⠀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢤⣰⣿⣻⣿⢸⣿⣹⣿⢸⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⠂⠀⠀⠀⠀ ⡇⢻⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⣿⠃⣿⡇⣿⡇⣴⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠋⣬⡝⣿⡆⠀⠀⠀⠀ ⣿⣜⣻⢿⣧⣽⣿⣻⠥⠛⡚⣃⣛⡃⠛⠘⣃⣛⣃⡛⣳⣜⣛⣼⣞⣛⣴⣛⣛⣛⣛⣛⣛⣡⣿⣜⣛⣣⡘⠛⢛⣃⣛⣛⣓⣝⣻⣛⣝⣛⣛⣿⣧⣛⣟⣛⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣝⣛⣛⣥⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⢿⣿⠛⠋⠀⠀⠀⠙⠀⠛⠈⠀⢠⠃⠈⠛⠹⠋⠀⠀⠂⠀⠀⠈⠓⠀⠰⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠒⠐⠈⠒⠒⠀⠒⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣾⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣷⣷⣆⣤⣄⣢⣤⣐⣷⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠋⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣿⣿⠿⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⢿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⣿⣭⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣿⣿⡟⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠲⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡟⠏⠁⠉⠀⠈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢴⢶⣆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⡿⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠁⠀⠀⠀⢀⣾⣿⡿⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⣿⣿⣿⠋⡉⠉⠉⣿⣿⣿⣿⡟⢻⡇⠉⠃⠀⠀⠀⠀⠀⣠⣠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⢠⣾⡻⢛⡐⠈⣀⡒⢁⠐⣄⠀⢀⠀⢰⣿⣿⣿⣿⡄⠈⠀⠀⠀⠀⠁⠛⢿⣿⣿⣿⣍⠚⣧⠀⠀⠠⠀⡄⣀⢴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠀⠀⠀⣼⣼⣿⣿⣷⣿⣷⣄⣠⣤⣧⣊⣪⣷⡞⣿⣿⣿⣿⣷⣤⣶⣠⣾⠋⠀⠤⣄⠹⣿⣿⣿⠀⠿⡀⠀⠘⠀⣠⡟⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣖⣆⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣿⣷⣼⣿⣿⠀⠀⡇⢀⣸⣻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡆⠎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠋⠘⢿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⣸⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡎⢁⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣀⣀⣤⢄⠸⣿⣁⣀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣀⣿⣿⣿⣿⣿⣿⡏⠈⢹⣿⣷⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⡏⡀⢸⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣷⣿⣦⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⠀⠀⠀⠉⠉⠉⢀⡄⠀⣿⡿⠇⠀⠀⢻⣿⣿⣿⣿⣿⡶⣼⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣧⣴⡇⠻⣼⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣾⣼⡀⠀⢠⣄⡀⠈⠁⠀⢸⣷⣶⣷⡄⠈⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡇⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⡿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⡀⡀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠈⢿⠿⠟⠻⠿⠟⠻⠿⠻⠻⠿⢿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣌⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⡟⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣯⣠⣤⣤⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠹⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⣹⣿⣆⠀⠀⠀⠈⠀⠐⢻⣿⣟⢋⣿⣿⣷⠄⢸⣿⣿⣿⣿⢿⠻⠟⠏⣵⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣇⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⠘⠿⠿⠿⠿⠿⠟⠛⠛⣋⣠⣦⣾⣾⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⡏⠉⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣯⢸⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⢿⣿⣷⣤⣀⢠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⠸⣯⠇⡼⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣿⣿⣿⣿⣿⣇⠀⠈⠻⠿⠟⣛⠛⣟⣛⡉⣹⣯⣿⣾⣏⣿⣾⣿⣷⣟⢻⣿⣏⠿⠿⢼⣿⡏⣿⣿⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⢿⣄⠀⠄⠀⢀⠑⡄⣤⡄⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠙⠩⣤⣽⣭⠀⣦⣿⣿⢻⡟⣷⣿⣿⣾⣿⢿⣿⣿⢰⣶⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣠⣤⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠊⠓⢄⠃⠀⠀⠙⢮⠙⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣦⠀⠀⠀⠀⠉⠛⠟⠀⠙⠟⠻⣿⣙⣯⣿⡿⢿⠿⠋⠙⠿⠟⠋⠀⠙⠛⠛⠋⠀⠛ ⣶⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠃⠉⠒⠀⠀⠀⠁⠀⠀⠀⠀⠈⠻⢻⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⡏⢟⢫⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠻⠿⠟⠿⠿⠟⠸⣿⡿⠿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣀⢀⣶⣾⣀⣤⣀⣠⣤⣤⣤ ⣿⣋⠇⠀⠏⠖⣄⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⠛⢹⣏⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛ ⠡⣤⣒⣅⢙⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⡿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⠟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠛⣼⡸⣿⣿⢿⣿⡏⢸⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣿ ⠀⢱⠱⡋⣟⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⣠⡿⠧⠿⢇⠿⠷⠆⠀⠿⠇⣸⡸⠿⠷⠎⠿⠾⠟⠸⠿⢈⡀⠿⠷⠾⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣣⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⣁⣈⠉⢀⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢉⣀⡙⣛⣛⣛⣛⣛⣓⣀⣀⣙⣛⡋⣀⣀⣀⠀⠀⣀⣐⣐⢋⣁⣀⡀⣘⣛⡻⢟⣛⣻⢿⣛⣛⠉⠛⢛⣛⡛⢟⣛⣛⡻⢛⣛⢛⣛⡛⣛⣛⢟⣛⣻⢟⣛⣻⢿⣿⣿⣿⣿ ⡀⢸⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠉⣿⣟⡁⣿⡏⣿⡇⠀⢹⣿⠋⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢤⢠⣿⢹⣿⢸⣿⣹⣷⢸⣿⢸⣿⣧⣿⣿⢸⣿⡉⣿⣏⡿⣸⣿⣿⣿⣿ ⡇⢸⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⡟⠃⣿⡇⣿⡇⢴⢸⣿⠀⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⡼⣿⢠⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠃⣬⡝⣿⡞⣿⣿⣿⣿ ⣿⣜⡻⢟⣧⣝⣟⣛⠥⠛⠚⢃⣛⠃⠛⠘⣃⣛⣃⡛⣣⣜⣛⣼⣞⣛⣤⣛⢛⣛⣛⣛⣛⣡⣿⣜⣛⣢⡘⠛⢛⣃⣛⣛⣃⣙⣛⣛⣝⣛⣛⣻⣧⣛⡛⣋⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣽⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⢿⣿⠛⠋⠀⠀⠀⠙⠀⠛⠈⠀⢠⠃⠈⠛⠹⠋⠀⠀⠂⠀⠀⠈⠓⠀⠠⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠒⠐⠈⠒⠒⠀⠒⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣾⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣦⣦⣤⣒⣷⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡌⢁⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣀⣀⣤⢆⠸⣿⣁⣀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣀⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣷⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⡏⡀⢸⣿⣾⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⠀⠀⠀⠉⠉⠉⢀⡄⠀⣿⡿⠇⠀⠀⢻⣿⣿⣿⣿⣿⡶⢺⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣧⣴⡇⠻⣼⣿⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣾⣼⡀⠀⢠⣄⡀⠈⠁⠀⢸⣷⣶⣷⡄⠈⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠁⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⡀⡀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠘⢿⠿⠟⠻⠿⠟⠿⠿⠿⠻⠿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣌⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⡟⢿⡿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣯⣠⣤⣤⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠹⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢡⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⣹⣿⣄⠀⠀⠀⠈⠀⠀⢻⣽⣟⢙⣿⣿⣷⠄⢹⣿⣿⣿⣿⢿⠻⠟⠍⣴⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣇⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠋⠨⠿⠿⠿⠿⠿⠟⠛⠛⣃⣴⣦⣾⣾⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⡟⠙⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣯⢹⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⢿⣿⣷⣤⡀⢠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⠸⣯⡅⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣿⣿⣿⣿⣿⣇⠀⠈⠻⠿⠟⣛⠛⣟⣛⡉⣹⣯⣿⣾⣏⣿⣾⣿⣷⣟⢻⣿⣏⠿⠿⢼⣿⡏⣿⣿⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣷⣄⡀⠄⠀⢀⠑⡄⣤⣄⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠙⢩⣤⣽⣭⠀⣦⣿⣿⢻⡟⢷⣿⣿⣾⣿⢿⣿⣿⢰⣶⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣠⣤⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠘⠓⢄⠃⠀⠀⠉⢮⠙⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣦⠀⠀⠀⠀⠉⠛⠟⠀⠙⠟⠻⣿⣙⣯⣽⡿⢿⠿⠋⠙⠿⠟⠋⠈⠙⠛⠛⠋⠀⠛ ⣶⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠂⠉⠒⠀⠀⠀⠁⠀⠀⠀⠀⠈⠫⢻⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⡏⢟⢫⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠻⠿⠟⠿⠿⠟⠸⣿⡿⠿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣀⢀⣶⣾⣀⣤⣀⣠⣤⣤⣤ ⣿⣋⡇⠀⠎⠆⣄⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⠛⣻⣏⣿⡇⣿⡟⠃⠀⣿⡟⣿⣾⣿⠛⢳⣿⢻⣷⢸⣿⢻⡆⣿⡇⢸⣿⠛⣼⢸⣿⣸⣿⢸⣿⢸⣿⣿⡇⣾⡟⣿⡎⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛ ⠡⣤⣒⣥⠙⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⡿⣿⡇⣿⡿⠃⠀⣿⡿⠟⢻⣿⠟⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠛⣼⡸⣿⣿⢿⣿⡏⢸⣿⣿⡇⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣿ ⠀⢱⠰⡋⣟⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⣠⡿⠧⠿⢇⠿⠷⠆⠀⠿⠇⣸⠸⠿⠷⠎⠿⠾⠟⠸⠿⢈⡀⠿⠷⠾⠿⠶⣸⣇⠿⠿⡸⠿⢇⡼⠿⠿⠇⡹⠷⠿⣣⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⣁⣈⠉⢀⣛⣛⠿⣛⣛⢟⣛⡻⣛⣛⢉⣀⡙⣛⣛⣛⣛⣛⣃⣀⣀⣙⣛⡋⣁⣀⣀⠀⠀⣀⣐⣐⢋⣁⣀⡀⣘⣛⡻⢟⣛⣻⢿⣛⣛⠉⠛⢛⣛⡛⢟⣛⣛⡻⢛⣛⢛⣛⡛⣛⣛⢟⣛⣻⢟⣛⣻⢿⣿⣿⣿⣿ ⡀⢸⣿⣿⡇⣿⡏⣿⡇⣿⣿⣼⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⢹⣿⠉⣿⣟⡁⣿⡏⣿⡇⠀⢹⣿⠋⢸⣿⣿⡇⣿⣟⡁⣿⣏⠿⢸⣿⣋⢤⢠⣿⢹⣿⢸⣿⣹⣷⢸⣿⢸⣿⣧⣿⣿⢸⣿⡉⣿⣏⡿⣸⣿⣿⣿⣿ ⡇⢸⣿⣤⡄⣿⡇⣿⡇⣿⢻⡿⣿⡇⣿⢻⡿⣿⡇⣿⡇⢸⣿⢸⢸⣿⠀⣿⡟⠃⣿⡇⣿⡇⣤⢸⣿⠀⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⢼⡼⣿⢠⣤⢸⣿⢹⣷⢸⣿⢸⡟⣿⢿⣿⢸⣿⠃⣬⡝⣿⡞⣿⣿⣿⣿ ⣿⣜⡻⢟⣧⣝⣟⣛⠥⠛⠚⢃⣛⠃⠛⠘⣃⣛⣃⡛⣣⣜⣛⣼⣞⣛⣤⣛⢛⣛⣛⣛⣛⣡⣿⣜⣛⣢⡘⠛⢛⣃⣛⣛⣃⣝⣛⣛⣝⣛⣛⣻⣧⣛⡛⣋⣘⣛⣘⣛⣘⣛⣘⣃⣛⣘⣛⣘⣛⣛⣙⣛⣛⣵⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⠛⠋⠀⠈⠀⠧⢸⠻⠹⢰⡽⠃⠻⠛⡿⠃⢋⠑⠋⢙⠁⠈⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠒⠒⠓⠑⠀⠚⠒⠒⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠛⠛⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣽⣿⣿⠿⠈⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠒⢰⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡗⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠠⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣔⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠯⠩⢉⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣯⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠊⣠⠬⠚⢻⣿⣿⣿⣿⣿⠛⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠁⣉⠂⠀⢠⣿⣿⡿⣿⠿⠛⠓⠀⠀⠀⠀⠉⢙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣧⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⢐⠀⣰⣿⣿⣿⣟⡉⣴⡛⠉⠳⣄⠀⣀⠀⣾⣿⣿⣿⣿⡄⠉⠁⠀⡀⣈⠙⠻⢿⣿⣿⣿⣿⠻⣿⡁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⠉⠌⢳⣄⠻⣿⣿⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠂⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⣿⣿⣦⡀⢝⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣿⣿⣿⣿⡌⢠⠀⠠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠀⠀⢹⠋⠀⠀⠁⠀⢠⡄⣴⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⠿⣿⣿⣿⣿⣋⣯⣿⣟⠛⣿⣧⣤⣤⣠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⢀⠀⢀⢠⠂⠑⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⠙⠿⠟⢟⡿⢿⣿⡇⢘⣿⣿⣷⣿⣹⣷⣿⣿⣿⡛⣿⣿⠹⠿⢷⣿⣿⢹⣿⡇⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣶⣶⡀⢞⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢈⠟⣥⣼⣯⡁⢸⡽⣿⡿⣿⠻⣾⣿⡷⣿⡿⣿⣿⣧⣶⣾⣿⣿⣾⣿⣿⣿ ⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠐⠁⠀⠈⠙⠻⠃⠘⣿⡛⢿⣏⣲⣽⣿⠿⣿⠟⠙⠻⠿⠟⠁⠉⠛⠛⠛⠁⠙ ⣶⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⡿⠓⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠷⠀⠈⠛⠿⡿⠌⠂⠹⠶⠉⠁⠀⠀⠈⠹⠿⠿⠿⠿⠿⢿⡿⠟⠸⣿⡿⢿⡿⠿⡶⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠀⣀⣰⣶⣆⣀⣄⣀⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⡇⣿⡟⠃⡄⣿⣿⣿⣾⣿⡟⢳⣿⢻⣷⢸⣿⢻⡇⣿⡇⢸⣿⠛⣼⢸⣿⣼⣿⢸⣿⣿⣿⣿⡇⣾⡟⣿⡆⢿⣿⣿⣿⡇⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿ ⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣿⣿⣿⡇⣿⡿⠇⠄⣿⣿⠿⢻⣿⡿⢸⣿⢸⣿⢸⣿⠿⠃⣿⡇⢸⣿⠿⣽⡾⣿⣿⣿⣿⡟⣿⣿⣿⡇⣿⡇⣿⡇⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡿⠿⠿⢇⡿⠷⠆⠀⠿⠿⣼⡸⠿⠷⠞⠿⠾⠟⠸⠿⣸⡅⠿⠷⠾⠿⠶⣹⣇⠿⢿⡸⠿⣇⡿⠿⠿⢇⡻⠷⠿⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⢋⣋⣙⠛⢓⣛⣻⠿⣛⣻⢟⣛⡿⣛⣛⢋⣁⡻⣛⣟⣛⣛⣛⣓⣀⣀⣛⣛⡛⣛⣘⣓⠃⠒⣀⣛⣛⢛⣛⣀⡀⣘⣛⡻⢟⣛⣻⢿⣛⣛⠍⡿⢛⣛⡻⢟⣛⣛⡻⣟⣻⢟⣛⡿⣛⣻⣟⣛⣻⢿⣛⣻⢿⣿⣿⣿⣿ ⡇⣼⣿⣿⡇⣿⡏⣿⡇⣿⣿⣾⣿⡇⣿⣿⣾⣿⡇⣿⡏⢹⣿⢩⣹⣿⠋⣿⣿⡁⣿⡏⣿⡇⢀⢹⣿⡏⢸⣿⣿⡇⣿⣟⡁⣿⣏⡿⢸⣿⣛⣶⣵⣿⣿⣿⢸⣿⣹⣿⢹⣿⢸⣿⣷⣿⣿⢸⣿⡉⣿⣏⡿⣿⣿⣿⣿⣿ ⣇⢿⣿⣤⡄⣿⡇⣿⡇⣿⢻⣿⣿⡇⣿⢻⣿⣿⡇⣿⡇⢸⣿⢸⣿⣿⠀⣿⣿⠃⣿⡇⣿⡇⣿⢸⣿⡇⢸⣿⣿⡇⣿⡟⠃⣬⡟⣿⣼⣿⠛⣾⣿⣿⣧⣤⢸⣿⢹⣷⢸⣿⢸⡿⣿⢿⣿⢸⣿⠛⣬⡟⣿⣾⣿⣿⣿⣿ ⣿⣞⣻⣿⣷⣿⣿⣿⡵⠛⡚⣃⣛⣃⣛⠘⣃⣛⣃⣛⣳⣜⣛⣾⣟⣛⣶⣟⣛⣛⣛⣛⣛⣷⣿⣞⣛⣣⡘⣛⢛⣃⣛⣛⣻⣝⣻⣛⣝⣛⣛⣿⣧⣛⣿⣛⣜⣛⣘⣛⣚⣛⣘⣃⣛⣘⣛⣚⣛⣛⣝⣻⣛⣽⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⠛⠋⠀⠈⠀⠇⠸⠻⠱⢰⡽⠇⠻⠛⡿⠃⢋⠑⠋⠙⠀⠈⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠒⠒⠓⠑⠀⠚⠒⠒⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠛⠋⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣽⣿⣿⠿⠈⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠒⢰⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠠⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣄⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠯⠡⢉⢄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠂⢠⠤⠚⢻⣿⣿⣿⣿⣿⠛⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠊⠀⠀⠀⠀⠀⠀⢹⣯⠻⣿⣃⣮⣿⡷⢿⡿⠛⠛⠿⠿⠛⠈⠛⠛⠛⠋⠘ ⣴⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠿⠇⠛⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠋⣹⣽⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⡀⠀⢀⡈⣀⣀⣀⣶⣶⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢤⢤⢤⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡿⡶⣿⣿⣿⣿⣿⣿⡟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⢻⣿⣿⣿⣿⣰⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣯⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⢻⣿⣿⣿⣿⣿⣷⡀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀⣠⠈⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣴⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠟⣡⣰⢸⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⣏⣥⣶⣿⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡟⠛⠃⠀⠈⠘⠇⠹⠏⡏⢻⡿⢁⠟⠟⠟⠙⡩⠺⡑⣩⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠚⠓⠓⠐⠛⠚⠚⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣴⣿⣿⣿⣿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠂⠁⠀⠖⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣱⣶⣾⣿⣿⣤⣄⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡪ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣤⣠⣤⣤⣄⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣸⠎⢐⢶⣀⣰⣯⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⣀⣀⠄⣉⠳⣿⣦⣧⣯⡺⣝⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣒⠻⣛⢿⠋⠓⠓⠼⣷⣌⠛⠩⠍⠚⠑⢕ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠽⢯⡻⣿⣷⠁⡤⠈⣉⣾⣝⢳⠔⡙⠒⠋⣐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣦⣉⢿⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠑⡛⠍⡠⡬⣥⡤⠼⠨⠟⢒⣮⣽⣧⣎⠁⠀⠀⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣷⣿⣿⣿⣿⡌⢲⣄⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠊⠋⡁⠊⢀⣤⣤⣤⣶⡖⠊⠛⠑⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠐⠈⢿⠻⠏⠙⠫⠅⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⡀⢰⣿⠀⣺⣿⠟⠋⣉⣉⣄⣀⠀⣠⣤⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⡚⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡀⣠⠤⠄⠀⣿⣿⣷⣿⣻⣷⣿⣿⣾⡛⣿⣿⣻⣿⢷⣿⣿⢹⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣶⣦⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⠜⠡⠘⢢⡀⢰⡽⣿⡿⣿⠻⣿⣻⡟⣿⡿⣿⣿⡧⣶⣶⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠔⠁⠀⠀⠀⠀⠀⠘⣿⡝⢿⡟⣀⣹⣿⠶⣾⠿⠛⠿⠿⠿⠃⠙⠻⠿⠛⠋ ⣥⣶⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠜⠟⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠛⣿⣿⣿⣿⣿⣿⣿⡿⣁⠀⠈⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣀⣀⣰⣦⣆⣀⣀⣀⣤⣤ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣯⣭⣿⣿⣎⢀⠀⣁⣸⢿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯ ⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣷⡶⠖⢒⢾⣿⣿⣿⣿⣿⡿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠻⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠹⣿⣿⣿⣿⣷⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣯⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢻⣿⣿⣿⣿⣿⣷⡄⠊⣿⣿⣿⣿⣿⣿⣯⣽⣾⣿⣿⣿⡿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣠⠈⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⠟⢡⠰⢰⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣷⣿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠟⣛⣛⠻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣮⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⡿⢿⡿⠿⢿⣿⠿⠟⠀⠀⠀⠀⣀⣤⣀⠠⣤⡄⢠⣤⡄⣴⣶⢰⣶⡶⠆⢻⣿⠿⣿⡄⢿⣿⠀⣿⣿⡿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡷⠿⠿⡿⠿⠈⢓⣀⢀⣛⠛⣉⣉⠛⢩⣭⡝⣿⡟⢱⣶⡆⣶⣦⠸⣿⡆⣿⢸⣿⡟⣿⡇⢼⣿⢹⣿⡇⣿⣧⢸⣿⣇⣿⣿⢸⣿⣧⣄⢸⣿⣶⣿⡃⢸⣿⠀⠉⠉⠀⠀ ⠀⠀⣀⣀⣀⠀⣤⣤⣤⣤⠀⣤⣶⣿⣻⣿⢳⣾⠿⣷⡆⠿⣿⣿⠛⢸⣿⡄⣿⣿⠀⢸⣿⡇⢿⣧⢸⣿⡇⢹⣿⣧⣿⡇⣿⡀⣿⣧⣿⡟⢸⣿⠈⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠽⢸⣿⡇⣿⣷⢘⣛⣀⣤⣤⣤⡀ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣐⣻⣿⡼⣿⣶⣍⡐⡇⣿⣿⠀⢸⣿⡇⢿⣿⠀⢸⣿⡇⢨⣷⠘⣿⡇⢸⣿⢻⣿⡇⢿⡇⣿⣿⠀⠀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⣿⡀⠿⠿⠿⠌⠿⣇⣛⠛⣬⢟⣿⣿⢹⣿⣧ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡟⣿⣿⡯⣤⡍⣿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⢸⡄⣿⠧⠸⠿⢈⠿⢧⣼⣧⣛⡛⠀⠀⠀⢉⠍⠉⠐⢢⡀⢠⡼⣷⡿⣿⠻⣾⣻⡗⣿⡿⣿⣿⡧⣶⣶⣿⣿⣿⣿⣿ ⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣿⢸⣿⣷⣾⣿⣧⣻⠷⠿⠋⣴⣘⣛⣃⣄⣛⣡⣬⣩⣭⣥⣥⣤⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄⠀⠔⠁⠀⠀⠀⠈⠀⠘⣿⡝⣿⣟⣀⣹⣿⠶⣾⠿⠛⠿⠿⠿⠋⠙⠻⠿⠛⠋ ⣥⣦⣿⣧⣮⣭⣥⣹⣷⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⡜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠞⠟⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠈⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣀⣀⣰⣶⣆⣀⣀⣀⣤⣤ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣹⣿⣿⣿⣿⣿⣿⣿⣾⣤⡀⣉⣽⢿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⠶⢲⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠻⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠹⣿⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣯⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢻⣿⣿⣿⣿⣿⣷⡄⠋⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣠⠈⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⠟⢡⣰⢰⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣡⣶⣾⣷⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡟⠛⠃⠀⠈⠘⠇⠻⠯⡇⢺⠟⢡⠟⠏⠟⠙⠉⠺⡁⣉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠚⠓⠓⠚⠛⠚⠛⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣿⣿⣿⣿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠂⠁⠀⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⢻⠋⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣽⣿⣿⠷⡘⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣓⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠠⠀⢀⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣦⢿⡅⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢯⠯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣿⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⣿⣿⠃⣤⡽⠻⣿⣿⣿⣿⣿⣿⠋⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣿⢸⣿⣷⣾⣿⣧⣻⠿⠿⠋⣼⣘⣛⣣⣄⣛⣡⣬⣩⣭⣥⣥⣤⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠞⠁⠀⠀⠀⠀⠀⢻⣷⠻⣿⡇⣊⣿⣿⢶⣷⠟⠻⠿⠿⠟⠉⠛⠿⠿⠟ ⣠⣤⣿⣷⣮⣭⣥⢭⣷⣶⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⡌⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⠻⠛⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠸⣿⣿⣿⣿⣿⣿⣿⣿⣍⡁⠈⣋⣫⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣴⣆⣀⣀⣠⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣤⡦⢍⣽⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡁⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡁⢹⣿⣿⣿⣿⣽⣿⣿⣿⠶⢾⣿⣿⣿⣿⣿⣿⣿⠏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛ ⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡌⢿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⣿⡄⠉⣿⣿⣿⣿⣿⣿⢯⣿⣾⣿⣿⣿⣿⠃⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣀⣀ ⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⡈⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠎⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⡿⢃⡤⡴⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠟⢩⣴⣼⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⣿⡟⠛⠀⠀⠀⠈⠀⠘⠃⠇⢠⠞⠁⠋⠋⠟⠀⠁⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⡄⠀⠐⠀⠒⠒⠒⠐⠀⠒⠒⠀⠒⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢟⠛⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣾⣿⠿⠈⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣶⣤⣶⣴⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣗⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⠻⠌⠙⣿⣿⣿⣿⣿⡈⣁⠀⠀⣀⣠⣿⣿⣿⣦⣌⠻⣿⣿⣿⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⡿⠏⠉⠉⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⣺⡛⣷⡉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⣴⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣇⠀⠀⠀⠀⠘⣿⣿⣿⣟⠈⠋⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⢀⣾⣿⡿⢛⠍⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠹⣿⣿⠿⠿⠥⠈⣹⣿⣿⣿⣿⣏⢹⣇⠈⠓⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠀⠀⠀⢠⣾⣿⣛⡂⠁⣄⠂⠈⢲⣄⠀⢀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⣀⡈⠛⠿⣿⣿⣿⣯⠘⣿⠄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠰⠀⠀⠀⣾⣿⣿⣿⣿⣷⣧⣤⣤⣼⣇⣹⣾⣷⣿⣿⣿⣿⣿⣷⣴⣻⡴⣿⠁⠀⠒⣆⡘⣿⣿⣿⠀⠻⡄⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣾⣿⣿⡄⠀⠷⠠⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁⠀⠀⠀⠀⢠⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠉⠙⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣘⠃⠀⢨⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣀⣀⣶⣆⠹⣿⣤⣄⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⢤⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣼⢠⠸⣿⣿⣿⣿⣿⣿⡏⣴⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡿⢸⣼⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣤⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣧⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣀⣄⣄⣀⣀⣀⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣽⣿⢿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠟⢃⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠉⢽⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⣟⣛⢿⣿⠿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢹⣿⣧⡀⠀⠈⠉⠻⣿⣿⡿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⠿⠿⠿⠿⢿⣿⠟⠛⠋⠁⠀⠀⣀⣤⣀⠠⣤⡝⢩⣭⡍⣵⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⣨⣴⣾⡿⠘⠿⠿⠓⠀⠀⣀⢀⣈⠉⣁⣉⠉⢩⣭⡙⠿⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⠀⢠⣤⣤⣄⠀⣤⣴⣶⢹⣿⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠇⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠉⢸⣿⡇⣿⣇⢈⣛⡀⠀⢀⣠⣤ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢹⣿⣀⡺⣿⡸⣿⣶⣅⡀⠀⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡄⣿⣷⠀⠀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⣀⠿⠿⠿⣀⣿⠃⠛⣛⣤⢛⣷⣦⣿⣿⣻ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡏⣤⡍⢿⣷⠀⢸⣿⠀⠈⣿⡇⢸⣿⣤⡄⣿⣷⣶⠠⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⠀⠀⠀⠉⠉⠉⠐⠃⠀⢤⠀⠀⡰⣾⡿⣿⢷⣝⢻⡏⣿⣷⣿⣿⡇⣤⣤⣿⣿⣿ ⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣻⣧⡻⠷⠿⠋⢠⠘⠛⠂⠀⠛⠁⢌⡉⠉⡅⠁⢀⣤⣾⣷⣶⣶⣿⣶⣿⣿⣿⣿⡿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠹⣷⡟⢀⣹⣿⣵⣶⡶⠛⠿⣷⡿⠋⠙⠿⠿ ⠀⣀⣻⣥⣮⣭⣥⡍⣵⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣆⠀⠈⢻⣝⡳⡄⠀⠀⠙⠲⠁⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⠟⠛⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠒⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⣩⣵⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⠀⣀⣀ ⣿⣿⠿⠋⢻⢟⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣸⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⣽⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⢰⣶⣤⣶⣶⣆⡀⠀⣾⢿⣿⣷⣌⣿⣿⣿⣿⣿ ⣿⡋⠚⣢⠀⢠⡼⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⣿⣶⣆⣀⣐⡤⠄⠀⠀⠀⠶⢿⣿⣿⣿⣿⠟⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡘⣿⣿⣿⣿⣿⣷⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠩⢛⢳⡿⠶⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢿⣿⣿⣿⡿⣷⡄⠂⠀⠈⣾⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠁⠋⠆⠏⠓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠹⣿⣿⣿⣿⣿⣿⣆⠀⠸⣿⣿⣿⣧⣡⡠⠁⠀⠀⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⡙⠀⢋⠈⡄⢃⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣆⢠⣿⣿⣿⣿⣾⣶⠀⠀⢀⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⣾⡆⣸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢰⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⡿⠋⠁⣀⣲⡤⢸⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣗⠀⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⣿⣿⠛⠋⠀⠈⠀⠃⠸⠻⠙⢰⡞⠃⠛⠋⠝⠁⠉⠐⠁⠈⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠁⠒⠒⠒⠐⠀⠒⠒⠐⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⠟⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣄⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⠄⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡷⣀⣀⠀⠀⠀⠀⠀⠀⢀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⡆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠹⢻⣷⣿⣦⣶⣶⣴⣿⠿⣿⠟⢿⣿⣿⣿⠌⠽⢞⣧⡀⣀⣰⣮⣉⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡘⠄⢙⣿⣿⣿⣾⣿⣿⣿⠃⡿⣄⣀⠿⣿⣿⣷⣼⠄⠻⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡿⠿⠉⠉⢁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣟⢻⣌⢫⣿⣿⣿⣿⣿⣿⣀⠷⠋⠁⠄⡀⣹⣿⣟⣧⡀⠐⠉⠏⠁⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣟⠀⠀⠈⠀⠘⣿⣿⣿⣿⡉⠛⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⠀⣙⠛⢩⣿⣿⣿⣷⣶⣧⣾⣿⣾⣿⣿⣿⣿⣷⣶⣾⣤⣀⣰⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⢟⡿⠛⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⡏⣿⣿⣿⠿⢧⣌⣹⣿⣿⣿⣿⣷⣙⣿⠄⠉⠀⣸⣷⣿⣿⣿⣿⣟⣫⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠀⢀⣾⣿⣟⡓⡉⣠⡒⢁⠳⣦⢀⢀⡀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⡀⠙⠻⢿⣿⣿⣿⡌⢻⠢⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠂⠀⠀⣸⣿⣿⣿⣷⣿⣿⣤⣤⣤⣷⣹⣷⣿⣾⣿⣿⣿⣿⣿⣶⣿⣴⣻⠁⠀⠀⣧⣘⢿⣿⣿⡇⠸⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⡇⠀⠸⠆⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣿⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢿⣿⡟⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠉⠀⠀⠀⠀⠀⠀⣠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡻⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣶⣦⠸⣿⣧⣤⣀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡴⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣴⢷⡌⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⣤⠀⠀⡂⠀⠀⢠⣤⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣼⢸⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣤⣤⣠⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠟⠋⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡔⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⣟⣛⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣿⣷⣀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⠿⢿⡿⠿⢿⣿⠟⠛⠛⠀⠀⠀⣀⣤⣀⠠⣤⡄⢡⣬⡍⣰⣶⢰⣶⡶⠇⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠇⠿⠿⠛⠂⠀⣀⢀⣈⠉⣉⣉⠉⢩⣭⡙⠿⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣧⢸⣿⡇⣿⣿⠸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⠈⠟⠋⠉⠀ ⠀⠀⣀⣀⣀⠀⣠⣤⣤⣄⠀⣤⣶⣶⢸⣿⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣿⠗⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠉⢸⣿⡇⣿⣧⢈⣛⡀⡀⠀⢀⣠ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⡺⣿⡸⣿⣶⣅⡐⠆⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢻⡆⣿⣷⠀⠀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⢀⠿⠿⠿⣀⣿⣃⠛⠛⣤⣛⢳⣿⣦⣿⣿ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⣿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠠⡀⣿⠧⠸⠿⠈⠿⠇⣸⣧⣛⣛⣄⠀⠀⠉⠉⠉⢀⠔⡀⠠⣄⠀⢀⢻⣿⡿⣿⢿⣝⣿⠿⣿⡷⣿⣿⣠⣤⣼⣿⣿ ⡀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⠋⠠⡘⠛⣃⠄⠛⢁⣌⣉⠉⣡⢡⣤⣤⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣆⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠸⣧⠻⣷⡏⢈⣻⣿⣴⣾⡶⠻⢿⣿⡿⠃⠙⠿ ⠀⢀⣛⣥⣬⣭⣥⣭⢱⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⡀⠌⢻⣿⣻⣦⠈⡍⢹⢷⣟⠿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠦⠹⠟⠋⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠯⣟⣻⣴⡌⣳⣄⠄⠁⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀ ⣿⣿⡿⣿⣿⡿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢨⣿⣿⣥⠈⠣⡆⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣘⠀⠀⣠⣴⣶⣶⡶⣶⣶⣶⣶⣿⣺⣶⣶⣭⣿⣷⣿⣿ ⣿⣿⡟⣿⣿⣵⣭⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⣿⣿⣿⣄⣐⣶⣤⡤⠤⠀⢶⣿⣿⣿⣿⣿⡿⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡯⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢻⣿⣿⣿⣿⣿⣧⠒⠀⠈⣾⣿⣿⣿⡿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣝⡿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⣿⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⣿⣿⣯⣭⢍⠑⠀⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣯⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣧⠤⢀⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣾⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⠟⢁⠀⢰⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⡿⠟⢁⣀⣼⣦⠌⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⣿⣿⠛⠋⠀⠀⠀⠃⠸⠳⠙⢰⡞⠃⠛⠉⠝⠁⠉⠐⠁⠈⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠒⠒⠒⠐⠀⠒⠒⠒⠒⠚⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⠛⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣄⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⡀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡷⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⡆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠹⢻⣷⣿⣦⣶⣶⣴⣿⢿⣿⠟⢻⣿⣿⣿⠍⠽⢮⣧⠀⣀⣰⣦⣈⣲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡘⠄⢙⣿⣿⣿⣿⣿⣿⣿⠃⡟⢄⢀⠿⣿⣿⣶⣬⠄⠻⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡿⠿⠉⠉⠁⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣟⢿⣈⢫⣿⣿⣿⣿⣿⣿⠀⠷⠋⠃⠀⡀⣽⣿⣟⢤⡀⠐⠡⠎⠁⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣟⠐⠀⠈⠀⠘⣿⣿⣿⣿⡈⠛⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⠀⡙⠛⢩⣿⣿⣿⣷⣦⣶⣿⣿⣼⣿⣿⣿⣷⣷⣾⣾⣤⣀⢸⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⢟⡽⠙⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⡏⣿⣿⣿⠿⢯⣌⣹⣿⣿⣿⣿⣿⣙⣿⠄⠉⠀⣸⣿⣿⣿⣿⣿⣯⣏⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠀⢀⣾⣿⣟⡓⡉⣠⡒⢁⠲⣦⠀⢀⡀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⡀⠙⠻⢿⣿⣿⣿⡍⢻⠢⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠂⠀⠀⣸⣿⣿⣿⣷⣿⣿⣤⣤⣤⣷⣹⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⣵⣻⠁⠀⠀⣧⣘⢻⣿⣿⡇⠹⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⡇⠀⠸⠆⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣿⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢿⣿⡟⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠁⠀⢀⣠⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡻⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣶⣦⠸⣿⣧⣤⣀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡴⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠙⠃⢀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣴⢷⡜⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⡤⠀⠂⡀⠀⢀⢀⣤⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣼⢸⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⣠⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣤⣤⣠⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠟⠋⣐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣴⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡖⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠿⠿⡿⣛⣛⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣿⣷⣀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⠿⢿⡿⠿⢿⣿⠟⠛⠛⠀⠀⠀⣀⣤⣀⠠⣤⡄⢡⣬⡍⣰⣶⢰⣶⡶⠇⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠇⠿⠿⠛⠂⠀⣀⢀⣈⠉⣉⣉⠉⢩⣭⡝⠿⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⠈⠟⠋⠉⠀ ⠀⠀⣀⣀⣀⠀⣠⣤⣤⣄⠀⣤⣶⣶⢸⣿⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣿⠗⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠉⢸⣿⡇⣿⣧⢈⣛⡀⡀⠀⢀⣀ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⡺⣿⡸⣿⣶⣅⡀⠆⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠘⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⠀⠀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⢀⠿⠿⠿⣀⣿⣃⠛⠛⣤⣛⢳⣿⣶⣿⣿ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⣿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⡀⣿⠧⠸⠿⠈⠿⠇⣸⣇⣛⣛⡄⠀⠀⠉⠉⠉⢀⠔⡀⠠⣄⠀⢀⢻⣿⡿⣿⢿⣝⣿⠿⣿⡷⣿⣿⣠⣤⣼⣿⣿ ⡀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⠋⠠⡘⠛⣃⠄⠛⢁⣌⣉⠉⣡⢡⣤⣤⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣆⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠸⣧⠻⣷⡏⢈⣻⣿⣴⣾⡶⠻⢿⣿⡿⠃⠙⠿ ⠀⢀⣛⣥⣬⣭⣥⣭⢱⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⡐⠌⣻⣿⣻⣦⠌⡌⠹⢷⣟⠿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠦⠹⠟⠋⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠯⣟⣻⣴⡈⡳⣄⠄⠀⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀ ⣿⣿⡿⣿⣿⡿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣨⣿⣿⣥⠈⠧⠆⠀⠀⠀⠀⢸⠿⣻⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣘⠀⠀⣠⣴⣶⣶⡶⣶⣶⣶⣶⣿⣺⣶⣶⣯⣿⣷⣿⣿ ⣿⣿⡟⣿⣿⣷⣭⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⣿⣿⣿⣄⣰⣶⣤⡤⠤⠀⢾⣿⣿⣿⣿⣿⡿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡯⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢻⣿⣿⣿⣿⣿⣧⠐⠀⠈⣾⣿⣿⣿⡿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣟⣟⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⣿⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⣿⣿⣿⣭⢍⠑⠀⣽⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣯⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣷⠄⢀⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣾⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⠟⢁⠀⢰⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⡿⠟⢁⣀⣼⣦⠌⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢾⢿⣿⠛⠉⠀⠀⠀⠘⠀⠻⠘⠀⡸⠃⠘⠙⠙⠁⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⠿⠿⣯⡚⠛⠒⠚⠓⠒⠘⠒⠒⠘⠒⠒⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣋⡁⠀⠀⠀⠀⠀⠀⢈⠻⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠛⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣠⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣾⡯⠇⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣢⢼⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡁⠛⣿⣷⣶⣤⣤⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣠⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⠳⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠿⠉⠉⠁⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣻⣇⠙⣿⣿⣿⣿⣿⣿⣿⡟⠛⡿⠿⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⡐⠀⠀⠀⠀⢻⣿⣿⣿⡃⠙⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⣠⣿⣿⢟⡿⠇⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⡏⢿⣿⡿⠿⠿⢬⣙⣿⣿⣿⣿⣿⣎⣿⡆⠈⠁⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⣴⣿⣟⣓⠋⢠⣖⠉⠙⢦⡀⢀⡀⠀⣿⣿⣿⣿⣧⠀⠀⢀⠀⣀⡀⠈⠙⢿⣿⣿⣿⣇⢹⡇⠀⠀⢸⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣺⡇⠐⠐⣲⣄⠹⣿⣿⣇⠈⢳⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠈⠃⠰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠉⠉⢹⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡜⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⢻⣿⣧⣀⣴⣶⠀⢿⣧⣤⣄⡸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡴⢆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢧⡇⡀⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⢀⣀⣀⣰⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣸⡇⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣼⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⢀⣤⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠤⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠃⠨⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡿⣿⣿⣿⣿⣿⣦⣄⣤⣄⣤⣤⣤⣄⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣻⡃⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠛⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⣶⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠠⣷⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⡻⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡇⠀⠀⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⡿⣟⣛⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢹⣿⣄⠀⠐⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠿⠿⠿⠟⢻⣿⠟⠛⠛⠛⠸⠃⣀⣤⣀⠠⣤⡄⢠⣤⡍⣰⣶⢰⣶⡶⠆⢸⣿⠻⣿⡄⢻⣿⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⠀⠀⣠⣴⡿⠟⠸⠿⠛⠃⠀⣀⢀⣀⠈⣉⣉⠉⢩⣭⡉⠿⠟⢰⣶⡆⣶⣦⠘⣿⡀⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿ ⠀⠀⣀⣀⣀⠀⢠⣤⣤⣄⠀⣤⣴⣶⢸⣿⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⡄⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠇⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡘⣿⡛⠛⣉ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢹⣿⣀⡺⣿⡸⣿⣦⣅⡀⠀⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⠀⠀⠸⣿⣇⣿⡇⠀⣿⣿⡇⢻⣿⡿⡀⠿⠿⠿⢀⣿⣃⣛⠛⢀⣛⣧⢿⣿⣼⣿ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡏⣤⡍⢿⣷⠀⢸⣿⠀⠈⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣤⡀⠀⠉⠉⠉⠀⢀⠀⠀⠠⡀⠀⢈⢿⣿⢿⣿⢯⡛⣿⢹⣿⣾⣿⣿⢠⣤⣼⣿ ⣀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣻⣧⡻⠷⠿⡋⠀⠘⠛⣂⣀⠋⣁⣈⣉⣉⣥⣥⡤⣤⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠸⡎⢻⣾⡇⢈⣻⣿⣴⣾⠾⠻⢿⣾⠿⠃⠛ ⠥⠄⣛⣥⣬⣭⣥⣭⢅⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⣿⣷⣿⣿⣯⣿⢾⣱⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠤⠿⠟⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⢿⣿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣿⣯⣉⣽⣷⢶⣍⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀ ⣿⣿⣿⢿⣩⣽⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢼⣿⣿⣿⡉⡹⢿⡦⢠⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠠⡀⢠⣤⣴⣦⡆⣰⣤⡶⢉⣾⣶⣿ ⣿⣿⣻⢻⣿⣿⣯⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⢻⣿⣿⣷⣥⣶⣮⣧⠷⠆⠰⣿⣿⣿⣿⣿⣿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣼⣶⣦⣷⣌⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⢽⣿⣿⣷⣾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⣿⣿⣿⣿⠏⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡜⠒⡳⢿⣿⣿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣄⠀⢹⣿⣿⣿⣿⣿⡯⡭⡆⣹⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⣻⣶⣿⢿⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⠀⢿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣷⡧⠽⣻⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣾⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣂⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠋⣀⣠⣶⠄⢿⣿⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢡⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⡿⠛⠁⠀⠀⠈⠇⠘⠃⠇⢘⠏⠁⠉⠋⠋⢈⠀⠈⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠞⠛⠒⠛⠓⠛⠚⠛⠚⠛⠒⠚⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣯⡤⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡛⠟⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠄⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣽⡀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⡆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠐⢀⠀⠀⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢰⡈⣓⢀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠿⠉⠍⢉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣻⣦⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣻⣿⠏⠉⠉⣛⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣟⠆⠀⠈⠀⠘⣿⣿⣿⣿⡈⠋⠁⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⣼⣿⣿⢻⠟⠊⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⠿⠿⠿⠟⠳⢧⣽⣿⣿⣿⣿⣿⣌⣿⠠⠈⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠀⠀⣾⣿⣿⣟⡁⣴⡎⠉⠙⡦⣀⣠⡀⢸⣿⣿⣿⣿⣇⠀⣀⡀⣀⡤⠄⢉⠙⢿⣿⣿⣿⡆⢹⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠆⠀⠀⣸⣿⣿⣿⣷⣿⣿⣤⣤⣴⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⡀⠀⢉⣷⣤⢻⣿⣿⡇⠘⢷⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠂⢲⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠁⠈⣿⣿⡏⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⡈⠰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣤⣿⣧⡘⢿⣶⣦⣄⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡖⣆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡿⣄⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢹⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡙⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⠷⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣷⡾⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠣⡈⠀⠀⢐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠚⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣔⣼⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡀⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⡀⠿⠂⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠁⠀⠀⠀⠒⠀⠀⠀⢻⣿⣿⣿⣿⠿⠿⠿⠿⡿⣟⣛⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⣿⣄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠿⠿⠿⠿⢿⣿⠿⠛⠛⠛⠿⠟⣁⣤⣀⠠⣤⡄⢠⣤⡄⣰⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡶⠿⠇⠿⠛⠛⠓⣀⢀⣀⠀⣉⣉⠉⢩⣭⡉⠛⠛⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿ ⠀⠀⣀⣀⣀⠀⢠⣤⣤⣄⠀⣤⣴⣶⢠⣾⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠗⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡘⠻⣿⣿⡿ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢹⣿⣀⣺⣿⡸⣿⣶⣅⡐⡆⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⢠⡀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⠀⠿⠿⠿⣀⡿⣃⣛⣛⣤⠛⢳⣿⡟⣿⣿ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⢿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣼⣷⡀⠉⠉⠉⠀⠀⠀⡠⠂⠐⢤⠀⠀⡘⣿⣿⢿⡿⣯⡿⣿⢽⣿⣾⣿⣿⢠⣤ ⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⣋⡄⠘⠛⢂⣄⣛⢁⣈⣉⣭⣡⢥⣤⣤⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣄⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⢿⡜⢿⣾⠃⢙⣿⣧⣶⣿⠞⠿⣿⣾⠿ ⣷⡀⠛⣁⣬⣭⣵⣿⣷⣦⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⡿⠏⣹⡿⠿⠉⠋⠁⠚⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡱⡌⠿⠞⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⣿⣧⡆⠈⠦⠆⠀⠀⠀⠀⠨⣽⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⡆⡀⡈⠀⠀⠀⠀⠀⠀⡸⢿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⣿⣿⣿⣿⢻⣳⣿⣯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢹⣿⣷⣦⣤⣶⣦⣖⠲⠒⠰⡿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣤ ⣿⣿⠿⢽⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⣿⣿⣿⣿⣿⣿⠖⣲⠀⠴⣿⣿⣿⣿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣼⣦⡀⠀⢸⣿⣶⣄⢀⣾⣿⣿ ⢻⠸⠀⠱⢻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⣿⣄⠀⢹⣿⣿⣿⣿⣽⡧⡅⠂⢰⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡗⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣿⣿⣿⣿⣿⣿⣿ ⣾⣇⣿⣲⣾⢽⣽⢡⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣾⠍⣺⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣶⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⣾⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣌⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠟⢋⣀⣠⣷⠄⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⢡⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⡿⠛⠁⠀⠈⠈⠇⠘⠃⠇⢘⠏⠁⠉⠋⠋⢈⠀⠈⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠟⠛⠓⠛⠛⠛⠚⠛⠚⠛⠒⠚⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣯⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡛⠟⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠀⠀⠀⠀⣀⡿⠋⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣿⡄⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢢⡧⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⡆⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠐⢀⠀⠀⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢰⡘⣓⢀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠿⠉⠍⢉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣟⣻⣧⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣻⡿⠏⠉⢉⣛⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣟⠒⠀⠈⠀⠘⣿⣿⣿⣿⡉⠋⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⣾⣿⣿⢻⠿⠋⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⠿⠿⠿⠟⠷⢧⣽⣿⣿⣿⣿⣿⣬⣿⠠⠈⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠀⠀⣾⣿⣿⣟⡁⣴⡎⠉⠙⡦⣀⣠⡀⢸⣿⣿⣿⣿⣇⠀⣀⡀⣀⡤⠤⢉⠙⢿⣿⣿⣿⡆⢹⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⡀⠀⢉⣷⣤⢻⣿⣿⡇⠘⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠃⢲⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠁⠈⣿⣿⡏⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣿⠈⠰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣤⣿⣷⡘⢿⣶⣦⣄⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡖⣦⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡿⣄⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢹⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡩⡋⠃⠀⠐⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣷⡾⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠡⣀⠀⠀⡔⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠚⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣼⣿⣿⣷⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠠⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠸⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⢿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠉⠀⠀⠀⠲⠀⠀⠀⢻⣿⣿⣿⣿⠿⠿⠿⠿⡿⣟⣛⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⣿⣤⠀⠈⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠿⠿⡿⠿⢿⣿⠿⠛⠛⠛⠿⠛⣁⣤⣀⠠⣤⡄⢠⣤⡄⣴⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⡶⠿⠇⠿⠛⠛⢓⣀⢀⣀⠀⣉⣉⠋⢩⣭⡉⠻⠛⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣇⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿ ⠀⠀⣀⣀⣀⠀⢠⣤⣤⣄⠀⣤⣶⣶⢠⣾⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠗⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡘⠻⣿⣿⡿ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢹⣿⣀⣺⣿⡸⣿⣶⣅⡐⡆⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⢠⡀⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⠀⠿⠿⠿⣀⡿⣃⣛⣛⣤⠛⢳⣿⡟⣿⣿ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⢿⣷⠀⢸⣿⠀⠈⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣼⣷⡀⠉⠉⠉⠀⠀⠀⡠⠂⠐⢦⠀⠀⡘⣿⣿⢿⡿⣯⡿⣿⢽⣿⣾⣿⣿⢠⣤ ⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⣋⡄⠘⠛⢂⣄⣛⢁⣈⣉⣭⣡⢥⣤⣤⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⡄⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢿⡜⢿⣾⠃⣙⣿⣧⣶⣿⠞⠿⣿⣾⠿ ⣷⡀⠛⣁⣬⣭⣵⣿⣷⣦⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⡿⠏⣙⡿⢿⠉⠋⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡱⡌⠿⠞⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⢿⣿⣷⡅⠉⠦⠆⠀⠀⠀⠀⠨⣽⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤ ⣿⣿⣿⣿⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣺⣿⣿⡇⡀⡈⠀⠀⠀⠀⠀⠀⡸⢿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⣿⣿⣿⣿⢿⣻⣿⣯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠁⢻⣿⣷⣦⣤⣶⣦⣖⠲⠒⠰⡿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣤ ⣿⣿⡟⢽⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⣿⣿⣿⣿⣿⣿⠖⣲⠀⢸⣿⣿⣿⣿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣼⣦⡀⠀⢸⣿⣶⣄⢀⣾⣿⣿ ⠻⠐⠄⠱⢻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⣿⣿⣿⣿⣿⣄⠀⢹⣿⣿⣿⣿⣿⡧⡅⠆⢸⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣿⣿⣿⣿⣿⣿⣿ ⣾⣎⣿⣶⣿⢽⣽⢡⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣾⠝⣻⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⣾⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣄⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠟⢋⣠⣠⣷⠄⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⢡⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⢿⣿⠟⠉⠀⠀⠁⠹⠀⠛⠘⠀⡽⠁⠘⠉⠘⠀⠁⠈⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⠚⠛⠓⠛⠓⠛⠘⠛⠚⠛⠒⠚⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⢛⠃⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣽⣿⣯⣇⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⢂⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡀⠃⡀⠀⠀⠀⢠⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣆⣙⡂⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠟⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠿⠏⠩⢉⡉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣝⣷⡌⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣝⣩⣵⡄⠉⠀⠈⣀⣠⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡓⠀⠀⠀⠀⢿⣿⣿⣿⣇⠙⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡗⠀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣰⣿⣿⣟⡿⠛⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠻⠿⠿⠿⠻⠶⣼⣿⣿⣿⣿⣿⣷⣽⡇⠄⠁⠀⠄⣾⣿⣿⣿⣿⣿⣿⡿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠀⠀⠀⣰⣿⣿⣻⢋⢠⣾⠉⠉⢷⢔⣀⣄⢀⣿⣿⣿⣿⣷⡀⢀⣀⢄⣠⠤⠈⡉⠻⣿⣿⣿⣷⠨⣿⠀⠀⢸⣀⣿⣿⣿⣿⣿⣟⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣇⣐⠈⣹⣦⡝⣿⣿⣿⠀⢻⡆⠀⢈⣿⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠳⠘⢶⢻⡗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡈⠀⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠉⠀⢹⣿⡟⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⢏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣆⢿⣷⣶⣦⣜⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢲⡄⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣾⢧⣸⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢘⡇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⠐⠢⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠮⢀⡀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠒⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣔⠁⢄⣴⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠘⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡔⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⡿⣛⣛⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣷⡄⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⡿⠿⢿⣿⠟⠛⠛⠛⠿⠛⣉⣤⣀⠠⣤⡄⢠⣤⡄⣰⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡴⠾⢿⠼⠟⠛⢛⣂⢀⣀⠀⣈⣉⠋⢩⣥⡉⠛⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣧⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿ ⠀⠀⣀⣀⣀⠀⣠⣤⣤⣄⠀⣤⣶⣶⢀⣴⢱⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠇⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡸⡿⠻⣿⣿ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⡺⣿⡸⣿⣶⣍⡀⠇⣿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠘⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⢰⣆⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⠀⠿⠿⠿⣀⣿⡃⣛⣛⣤⣛⠷⢿⣿⡿⣿ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡏⣤⡍⢿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⣿⠧⠸⠿⠀⠿⠇⣼⣇⣛⣛⣸⣿⣦⠉⠉⠉⠀⠀⠀⠀⡠⠂⠐⢤⠀⠀⡸⣿⣿⢿⡿⣿⢿⣿⣿⣷⣾⣿⣧⣠ ⠀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⣋⣦⠘⠛⣂⣄⣛⡁⣈⣉⣩⣅⡥⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣧⡀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢷⡙⣿⣿⠁⣙⣿⣧⣶⣿⠞⠿⣿⣿ ⣻⣦⡛⢁⣨⣭⣵⣿⣷⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣿⣿⣿⣿⡛⣹⡿⡿⡋⠛⠙⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⡜⠿⠞⠋⠉⠁⠈⠁⠀⠀⠀⠀ ⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⢻⣿⣿⣾⡨⠱⠶⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⣿⣿⣿⣿⡿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢐⣿⣿⣿⢄⣀⠱⠂⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣘⠂⠀⣀⣠⣄⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⣿⣿⣿⣿⣿⣻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢿⣿⣿⣤⣼⣶⣶⠒⠖⠒⢿⢿⣿⣿⣿⣿⡿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀ ⣿⣿⣿⡯⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢻⣿⣿⣿⣿⣿⣿⣟⣦⠀⣿⣿⣿⣿⡿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⠀⢀⣾⣿ ⡟⣧⣷⣘⣟⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⣿⣿⣿⣿⣿⣿⣷⡀⠈⣿⣿⣿⣿⣿⣿⢠⠰⠀⣿⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿ ⣿⣿⣿⠗⣾⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⡀⢹⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣗⢩⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠏⣀⠀⢸⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⡿⠋⣁⣤⣾⡧⠸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⣿⡟⠛⠁⠀⠀⠘⠃⠙⠏⠃⢆⠟⠈⠋⠉⠃⠈⠀⠁⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣚⠛⠓⠚⠓⠐⠀⠚⠒⠚⠒⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡛⠟⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣽⠨⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠠⡗⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡗⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣀⣈⣒⢠⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣽⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠿⠉⠍⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣻⣦⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠂⢀⠈⠀⢸⣿⣿⣿⣿⣜⠋⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠻⣿⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⠀⠀⢀⣾⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠙⠿⠿⠟⠛⠲⢦⣿⣿⣿⣿⣿⣿⣬⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠈⠀⢀⣾⣿⣿⣟⣅⣤⡏⠉⠹⡦⣂⣠⡀⣿⣿⣿⣿⣿⣆⠀⣀⡠⣀⡤⠄⣉⠙⢿⣿⣿⣿⡆⣿⡆⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠃⠀⠀⣼⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣀⡀⢁⣷⣌⢻⣿⣿⡄⠈⣷⠀⠀⡀⣤⣶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠓⠸⠟⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡏⠀⠈⣿⣿⠋⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠀⠈⢀⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣽⢼⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣴⣿⣷⡹⣿⣶⣶⣤⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⡖⣦⠀⠈⠓⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢹⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠚⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣦⣶⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢤⠄⣀⣴⢼⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢂⣀⡌⠄⠈⡠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠡⠀⠆⠀⠀⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠿⠿⠿⡿⣛⣛⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢻⣿⣯⡨⢍⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠿⠿⠿⢿⣿⠟⠛⠛⠛⠿⠛⣉⣭⣉⠫⣤⡄⢠⣤⡄⣰⣶⢰⣶⡶⠇⢹⣿⠿⣿⡄⢿⣿⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠶⢿⡇⠛⠛⢛⣓⢈⣁⠀⣈⣉⠛⢩⣭⡉⠿⠟⢰⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣧⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿ ⠀⠀⣀⣀⣀⠀⣠⣤⣤⣄⠀⣤⣴⣶⠀⣠⢰⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠇⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡸⣿⡿⠿⣿ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⣺⣿⡸⣿⣶⣅⡰⠀⢿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⢰⣶⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⠀⠿⠿⠿⢀⣿⣃⠛⣛⣤⣻⣧⡷⣿⣿⣿ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡯⣤⡍⢿⣷⠀⢸⣿⠀⠘⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣼⣿⣷⡍⠉⠉⠀⠀⠀⠀⠀⡰⠂⠰⢄⠀⠀⡻⣿⣿⣿⣿⣝⢿⡿⣿⣷⣿⣿⡇ ⣀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣿⣧⡻⠷⠿⣋⣾⡘⠛⢂⣄⣛⣁⣈⣉⣭⣥⣥⣤⣤⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠐⣷⠹⣷⣿⠀⢙⣿⣧⣬⣵⠞⢿⣿ ⢛⣢⣟⠁⣈⣩⣥⣿⣷⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⡸⡿⠞⠋⠉⠁⠈⠁⠀⠀⠀ ⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠠⠭⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣻⣿⣿⡿⡭⡟⠯⠄⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣸⠀⠀⣀⣠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⣿⣿⣧⣴⣿⣶⣶⠒⠒⠺⣿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⣿⣿⣿⣿⣿⣿⣾⣱⠄⢘⣿⣿⣿⣿⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⢀⣶ ⣿⢻⣽⣦⣷⣻⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⡟⣄⠂⢰⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿ ⣿⣿⣯⣿⢶⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣷⡊⣽⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠃⡀⠀⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⢿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⠟⢉⣰⣴⣷⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⣿⡿⠛⠁⠀⠀⠘⠃⠙⠏⠃⢆⠟⠈⠋⠉⠃⠈⠀⠁⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣚⠛⠓⠚⠓⠐⠀⠚⠚⠚⠒⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡻⠟⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣽⠈⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠢⡗⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡗⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣀⣈⣓⢠⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣽⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠿⠉⠍⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣯⣻⣦⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠂⢀⠈⠀⢸⣿⣿⣿⣿⣌⠋⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⠻⣿⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢁⠀⠀⢀⣾⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠘⠿⠿⠟⠛⠲⢦⣿⣿⣿⣿⣿⣿⣬⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠈⠀⢀⣾⣿⣿⣟⣁⣤⡏⠉⠹⡦⣂⣠⡀⣿⣿⣿⣿⣿⣆⠀⣀⡠⣀⡤⠄⣉⠙⢿⣿⣿⣿⡆⣿⡆⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠂⠀⠀⣼⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣀⡀⢁⣷⣌⢻⣿⣿⡆⠘⣷⠀⠀⡀⣤⣶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠂⠃⠸⠟⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠈⣿⣿⠋⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠈⢀⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⡽⢼⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣦⣴⣿⣷⡸⣿⣶⣶⣄⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡖⣦⠀⠈⠃⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠚⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣦⣶⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡠⢤⠄⠀⣴⢜⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣂⣂⡉⡄⠈⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠡⠈⠆⠀⠀⠀⠩⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠿⠿⠿⡿⣛⣛⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢻⣿⣯⡀⢉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢿⡿⠿⢿⣿⠟⠛⠛⠛⠿⠛⣋⣭⣉⠩⣤⡄⢠⣤⡄⣰⣶⢰⣶⡶⠆⢹⣿⠿⣿⡄⢻⣿⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠶⢿⡇⠛⠛⠛⣓⢈⣁⠀⣈⣉⠛⢩⣭⡉⠿⠟⢱⣶⡆⣶⣦⠘⣿⡄⣿⠸⣿⡟⣿⡇⢸⣿⢹⣿⡇⣿⣧⢸⣿⡇⣿⣿⢸⣿⣧⡄⢸⣿⣴⣿⡃⢸⣿⢸⣿⣿⣿⣿ ⠀⠀⣀⣀⣀⠀⣠⣤⣤⣄⠀⣤⣴⣶⠀⣠⢰⣾⠿⣷⡄⠿⣿⣿⠛⢸⣿⡀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣧⣿⡇⣿⠀⣿⣧⣾⠇⢸⣿⠀⣿⡇⢸⣿⣾⡟⣿⣿⣿⠀⣿⡏⠩⢸⣿⡇⣿⣧⢈⣛⡸⣿⡿⠿⣿ ⠀⠀⣿⣿⣿⡀⢸⣿⢉⣿⡇⢻⣿⣀⡺⣿⡸⣿⣶⣅⡰⠀⢿⣿⠀⢸⣿⡇⢻⣿⠀⠸⣿⡇⠀⠀⠈⣿⡇⢸⣿⢻⣿⡇⢹⡆⣿⣷⢰⣶⠸⣿⣇⣿⡇⠈⣿⣿⡇⢻⣿⡿⠀⠿⠿⠿⢀⣿⣃⠛⣛⣤⣻⣧⡷⣿⣿⣿ ⠀⠀⣿⡇⣿⣇⢸⣿⡟⣿⡆⢸⣿⡛⣷⣿⡏⣤⡍⢿⣷⠀⢸⣿⠀⠈⣿⡇⢸⣿⣤⡄⣿⣷⣶⠀⠀⡿⠧⠸⠿⠀⠿⠇⣸⣇⣛⣛⣼⣿⣷⡍⠉⠉⠀⠀⠀⠀⠀⡰⠂⠰⢄⠀⠀⡻⣿⣿⣿⣿⣟⢿⡿⣿⣷⣿⣿⣇ ⣀⠀⣿⡿⢿⣿⠸⣿⡇⣿⣷⢸⣿⣷⡦⣻⣧⡻⠷⠿⣋⣾⡘⠛⢂⣄⣛⣁⣈⣉⣭⣥⣥⣤⣤⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣆⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠐⣷⠹⣷⣿⠀⢙⣿⣧⣬⣵⠾⢿⣿ ⢛⣦⣟⠁⣈⣩⣥⣽⣷⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡸⡿⠟⠋⠉⠁⠈⠁⠀⠀⠀ ⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠙⣿⣿⣿⣿⣿⣿⠿⢄⠀⠀⠠⢭⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣺⣿⣿⡿⡽⡟⠻⢎⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣸⠀⠀⣀⣠⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠁⢻⣿⣿⣷⣴⣿⣷⣶⠖⠒⠺⣿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⣿⣿⣿⣿⣿⣿⣾⣳⠀⠘⣿⣿⣿⣿⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⢀⣶ ⣿⣻⣽⣦⣵⣻⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⡟⣄⠆⢸⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿ ⣿⣿⣯⣿⣶⣿⣽⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⠈⣽⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠃⡀⠀⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⠟⢉⣰⣴⣷⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 3981 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/http-and-https-gemini-proxy/#comments Gemini version at gemini://gemini.techrights.org/2022/02/07/http-and-https-gemini-proxy/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Self-Hosted_Gemini_Proxy_(HTTP_and_HTTPS)⠀✐ Posted in Site_News at 10:12 am by Dr. Roy Schestowitz Video_download_link | md5sum 86afc898cafbc432ca6331cdfc14f165 A Gemini Proxy Unveiled Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/gemini-proxy-site.webm Summary: Easing people’s transition to Geminispace using a Web proxy is a_long- term_objective, seeing that some people are intimidated by the idea of using something other than a Web browser for hypertext (interconnected pages with textual formatting) THE Gemini_proxy_of_Techrights has been working for about 2 days, but we needed to deal with bugs and edge cases, some of which remain. It’s not perfect, but it mostly works. So the address gemini.techrights.org no longer responds only to requests over gemini:// protocol (port 1965) but also HTTP/S (ports 80 and 443, which apparently replaces 80 almost_entirely, caveats_notwithstanding). I’ve decided to do a detailed video about the proxy even though it is still “work in progress” so to speak. The proxy, which I think is ready for wider use by now, isn’t meant to actually be used, we just try to lower the entry barrier for people who haven’t yet installed Gemini_client_software. We’ve already reviewed many clients and other tools. They’re maturing and they continue to broaden in reach and usage, which in turn motivates further development and maturity/stability. In the video above I show 3 graphical Gemini clients: Kristall, Lagrange, and Moonlander. Here is the_latest_(generated_today_at_1AM) graph_of_Gemini’s_growth. The orange curve shows the number of active capsules as a function of time. January was a surge. Lupa, which keeps track of Geminispace in Stéphane Bortzmeyer’s Gemini server, knows_of_nearly_1,690 working_capsules_right_now. █ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Geminispace_Statistics_Visualized⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Statistics_on_the_Gemini_space⦈_ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⠟⣿⡏⠋⠻⣿⢛⡿⠛⣻⣿⣿⠋⣿⢭⣟⠛⢿⣻⠟⠙⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣛⣛⣛⣻⣿⣍⢿⠟⠋⡟⠽⢻⢿⢛⢿⡛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣟⢩⣡⣿⡇⣿⣿⣿⣿⣿⣿⠛⠿⠿⡿⣿⡿⠿⡿⣻⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠁⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣠⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣷⣴⣷⣶⣶⣾⣶⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⠋⠁⠈⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠛⣿⡃⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠿⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⢯⣲⣽⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⢛⢊⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⣿⣯⣕⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣑⣿⣿⣿⣿⠿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠠⠰⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣵⣿⡿⣟⢌⣴⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠒⣿⣿⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⣿⣿⣿⠿⠝⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠙⣻⣟⡓⣸⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣒⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣟⡹⣡⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡀⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⠿⠛⠁⣠⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡻⣿⡇⣿⣿⡟⠉⠁⠀⣀⣀⣚⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣏⢰⣴⣿⡇⣿⣿⣧⡄⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢻⢋⣿⡇⣿⣿⣯⡅⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⡿⣷⣿⣿⣿⣿⣿⡿⡟⣷⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠿⢻⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⡽⣭⣼⣾⣿⣿⢿⣻⡹⣭⣼⣾⣿⣿⠿⡻⡽⣭⣼⣾⣿⣿⡿⡛⡝⣥⣼⣾⣿⣿⡿⣟⣏⢯⣥⣿⣿⣿⡿⢟⢫⢫⣮⣷⣿⣿⣿⢿⢫⢹⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣇⣮⣷⣿⣿⣿⣿⣿⣎⣤⣷⣿⣿⣿⣿⣿⣆⣦⣷⣿⣿⣿⣿⣿⣗⣪⣶⣿⣿⣿⣿⣿⣷⣡⣼⣾⣿⣿⣿⣿⣿⣐⣽⣾⣿⣿⣿⣿⣿⣞⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ 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⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 4104 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/immunity-and-impunity/#comments Gemini version at gemini://gemini.techrights.org/2022/02/07/immunity-and-impunity/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXIV:_Immunity_=_Impunity?⠀✐ Posted in Europe, Fraud, Law, Patents at 2:52 pm by Dr. Roy Schestowitz Series parts: 1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In! 2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous” Endorsement? 3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes 4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States 5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja” 6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch Courage 7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity 8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and Pusillanimous_Hibernia 9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss Cheese 10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the Controversial_Christian_Bock 11. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_– Battistelli’s_Swiss_Apprentice? 12. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection 13. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian Facilitators_–_Spain 14. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian Facilitators_–_Portugal 15. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XV:_Et_Tu_Felix_Austria… 16. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVI:_The_Demise_of_the Austrian_Double-Dipper 17. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVII:_The_Non-Monolithic Nordic_Bloc 18. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVIII:_Helsinki’s_Accord 19. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXX:_The_Baltic_States 20. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XX:_The_Visegrád_Group 21. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXI:_The_Balkan_League_–_The Doyen_and_His_“Protégée” 22. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXII:_The_Balkan_League_– North_Macedonia_and_Albania 23. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIII:_The_Balkan_League_– Bulgaria 24. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIV:_The_Balkan_League_– Romania 25. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXV:_The_Balkan_League_– Fresh_Blood_or_Same_Old,_Same_Old? 26. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVI:_A_Trojan_Horse_on_the Budget_and_Finance_Committee 27. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVII:_Cypriot_Complicity 28. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVIII:_Benoît_and_António’s Loyal_“Habibi” 29. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXXX:_The_EPOnian_Micro- States_–_Monaco_and_Malta 30. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXX:_San_Marino_and_the Perfidious_Betrayal_of_Liberty 31. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXI:_The_Abstentionists 32. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXII:_“Plucky_Little Belgium”? 33. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIII:_Swedish_Scepticism 34. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIV:_An_“Extremely Dubious”_Proposal 35. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXV:_Slovakian_Scruples 36. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVI:_Serbian_Sour_Grapes 37. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVII:_Stubbornly Independent_Slovenia 38. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXVIII:_Ensnared_in_the Tentacles_of_the_SAZAS_Octopus 39. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIX:_On_the_Slippery_Slope to_Capture 40. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXX:_The_Idiosyncratic Italians 41. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXI:_Public_Service_or Self-Service? 42. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXII:_A_Parcel_of_Rogues? 43. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXXIII:_A_Legal_No-Man’s Land 44. YOU ARE HERE ☞ Immunity = Impunity? 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Diplomatic immunity⦈ According to reputable legal experts, the immunity granted to international organisations “encourages or at least allows IO managers and executives to engage in illegal or unlawful practices which would otherwise expose them and their organizations to civil or criminal liability in national courts there.” Summary: The EPO‘s administration has come to the point where it shamelessly and systematically misuses “immunity” to break the law without any consequences either to ringleaders such as Benoît_Battistelli and António_Campinos or their facilitators, whom they typically appoint based on loyalty rather than skills; this erodes confidence in the institutions they run, whose impact can be highly corrosive or detrimental to their original/stated goals In the last part we saw how international organisations suffer from a lack of transparency and accountability and how those who become implicated in serious maladministration or other wrong-doings seldom – if ever – get called to account or suffer any prejudice to their “career”. A key issue here is the bubble of “immunity” in which international organisations operate and which effectively shields them from any external oversight or control. “A key issue here is the bubble of “immunity” in which international organisations operate and which effectively shields them from any external oversight or control.”Immunity is granted to these organisations for the ostensible purpose of ensuring their political and financial independence and, thus, their impartiality. However, like any other kind of legal privilege, it is open to abuse. The immunity accorded to international organisations has long been recognised as a contentious issue by legal scholars and lawyers who represent the staff of these organisations in disputes before international tribunals such as the ILOAT. In an article published in 2010 under the title “International_Organisation Reform_or_Impunity?_Immunity_is_the_problem”, legal practitioners Greta Rios and Ed Flaherty explored the topic in detail. “The immunity accorded to international organisations has long been recognised as a contentious issue by legal scholars and lawyers who represent the staff of these organisations in disputes before international tribunals such as the ILOAT.”According to the authors, the immunity granted to international organisations “encourages or at least allows IO managers and executives to engage in illegal or unlawful practices which would otherwise expose them and their organizations to civil or criminal liability in national courts there.” Due to the absence of a threat of criminal sanction or substantial civil damages awards, “the normal incentive of civil society for managers and executives to run their organizations lawfully and/or in accord with best practices is non-existent, encouraging rather than preventing unacceptable behavior within IOs which clearly also has a negative effect on their performance and effectiveness.” “And so the rank-and-file staff of international organisations like the EPO continue to be exposed to the abuses of managers and senior executives for whom “immunity” all too often translates into “impunity”.”But despite extensive academic literature on the subject, there has been little follow-up on a political level. It almost seems like those who call the shots in the corridors of power have a vested interest in the status quo and are not particularly keen about pushing for the badly-needed reforms of this sector. Of course there are occasional attempts to pay lip-service to calls for reform such as the resolution “Accountability_of_international_organisations_for_human rights_violations” (No. 1979) which was adopted by the Parliamentary Assembly of the Council of Europe in 2014. But to date there are no visible signs of concrete political action as a follow-up to such parliamentary grandstanding. And so the rank-and-file staff of international organisations like the EPO continue to be exposed to the abuses of managers and senior executives for whom “immunity” all too often translates into “impunity”. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Immunity and impunity⦈ For senior executives of international organisation, “immunity” effectively translates into “impunity”. In the upcoming parts we will take a closer look at the internal justice systems of international organisations on which staff are obliged to rely in order to safeguard and assert their rights. And we shall also see how these systems often turn out to be hopelessly dysfunctional. █ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠋⡴⣨⠡⢿⡿⠿⢿⡿⠿⡿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣶⣶⣯⣟⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⣼⢿⠃⣔⠘⡀⣁⣚⣰⣀⣃⣛⣃⣑⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣷⡟⢛⡏⢹⣶⠀⣿⣿⠀⣿⠀⣾⠙⣛⠿⠿⣟⣫⣽⣿⡏⠡⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣟⣿⣟⣻⣿⡿⠁⣼⠃⣸⣿⢠⣿⡿⠀⣿⠀⡿⢀⡿⢢⣿⣿⣿⡿⠟⠁⠀⠀⢙⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⠿⠿⠛⠋⣠⡾⠃⣠⡿⢃⣾⡿⣃⣘⣋⡸⠃⠼⠃⠼⣟⣻⣿⣆⠀⠀⢀⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠁⡄⢸⠀⡇⠰⠈⡇⣿⣿⠀⡆⢸⠀⠘⠀⢸⡇⡀⢻⡄⢠⣿⠀⡏⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠒⠒⠒⠚⠋⣁⣤⠾⢋⣤⣾⡿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠇⣸⠀⡇⢰⣿⡁⠛⢻⠀⠃⣼⠀⣦⡇⠸⢀⡄⢸⡇⢸⡟⢸⣇⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣘⡛⠛⠛⠛⣉⣩⣤⣶⣿⠟⠋⣠⣾⠎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣛ ⣿⣿⣿⣿⣿⡷⢾⠿⢿⡿⢿⡟⠿⣿⠿⢿⠿⣿⢿⢿⢿⢿⡿⠿⠿⠿⠟⢻⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣈⣉⡉⠙⠛⠛⠛⠛⠋⣉⣠⣴⡾⠛⢁⣴⠟⠘⣿⣿⣿⣿⣿⢿⣻⣽⣶⡿⠿⣿⣿⡿⣛⣵⣿⣿ ⣿⣿⣿⣿⣿⡇⢸⠀⡈⡀⢸⡇⢀⠀⡀⢸⠀⡟⢸⠀⠈⢸⡇⣶⡆⣴⣿⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣬⣍⣉⠙⠳⣦⢀⣟⡿⠛⠛⢋⣡⣴⡾⠟⢁⣴⡿⢹⣿⠀⠀⠻⣿⣷⣶⣿⣿⡿⣛⣽⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣅⣾⣀⣿⣇⣸⣇⣸⣿⣇⣸⣄⣁⣼⣀⣇⣸⣇⣿⣇⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⢶⣤⣌⡙⠻⡦⣰⣿⣿⣷⡝⣛⣛⣉⣡⣴⡾⠛⠉⣠⠞⣿⡄⠀⠀⠈⠻⣿⣟⣵⣿⣿⣿⣿⡿⣟⣭⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⣿⣾⣿⣷⣦⣌⢙⣻⣴⣾⣿⣿⣿⣿⢇⣉⣉⣉⡌⣡⣤⠶⠛⣁⠄⣿⣿⣖⠀⠀⠀⠀⠀⠈⢿⣿⣿⣛⣻⣭⣿⠷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣛⣛⡻⠯⣻⡿⣾⣿⣿⣿⣿⣿⣿⡟⣈⣉⣉⣉⡄⣩⣤⡴⠞⢁⡴⢿⣏⣿⢱⡦⠀⠀⠀⠀⠈⢿⠿⣟⣻⣽⣾⣿ ⣿⣿⣿⡟⢛⢻⠛⣛⣟⠛⣻⣿⣿⢋⠹⡟⠛⢻⡛⢛⣿⣿⡟⡙⣿⢛⣻⣿⣿⣿⢻⡟⠛⣿⢻⡟⣿⡿⣡⢡⣘⣁⣿⣿⣿⣿⣿⣿⣿⡇⣄⣉⣠⣤⡤⢠⠤⠴⠚⣁⡴⠸⣿⣿⣏⣿⣆⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠮⢹⠀⠶⣿⠀⣿⣿⣿⠸⢠⣇⠀⣸⡇⢸⣿⣿⡇⠇⣿⢰⣾⣿⣿⠻⢸⠇⡀⢿⢸⡇⠿⣶⣮⣥⡵⠛⣿⣿⣿⣿⣿⣿⣿⣷⢬⣭⣭⣤⡶⠆⠶⠖⠛⢁⡴⢃⣬⡻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡩⡢⣡⡭⣻⣿⣿⡉⢲⡌⣿⣎⢉⣡⣤⣴⠞⢃⣐⣚⣉⡴⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠩⣽⠉⠙⡏⢭⣽⠉⠭⣿⣿⣿⣿⣿⣿⣿⠇⡔⠐⢩⣿⣿⣿⣷⣬⣉⣴⣿⣿⣿⣥⣴⣶⣿⣿⣷⣭⣠⢤⣶⣿⡟⣿⣿⣿⣞⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣾⠀⠀⡇⠐⢻⡀⠒⣿⣿⣿⣿⣿⣿⣿⣬⣉⣁⣸⣿⣿⣿⣿⣿⣿⠛⠩⣌⠋⢐⠨⠍⣼⣿⣿⣿⣿⣷⣽⣿⣿⢹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠷⢞⣃⣐⣚⣰⣿⣿⣿⣿⣿⣿⣷⣻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣼⣾⣾⣿⣾⣿⣿⣾⣿⣾⣿⣾⣾⣷⣷⣿⣾⣷⣷⣷⣷⣿⣾⣷⣿⣾⣿⣾⣾⣾⣷⣳⣷⣷⣷⣿⣿⣾⣾⣾⣣⣿⣿⣾⣿⣿⣷⣷⣿⣿⣷⣷⣷⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⡟⣻⡿⡽⣛⢟⢻⢛⠻⡻⣿⡿⡿⣛⢿⣝⣛⣿⢻⣟⣱⢟⢟⡻⡟⣛⢟⢿⣿⢛⣻⢿⡟⡿⣛⡿⣟⣻⢿⡻⡿⡻⣛⡿⣛⡟⣛⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣣⢷⣿⣧⣷⣏⣿⣞⣾⣸⣻⣝⣣⣷⣟⣏⣇⣻⣱⣿⣇⣏⣿⣜⣣⣷⣇⣟⣾⡏⣛⣽⣘⣹⣹⣧⣧⣓⣸⣼⣻⣸⣷⣇⣇⣒⣷⣏⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 4349 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/irc-log-060222/#comments Gemini version at gemini://gemini.techrights.org/2022/02/07/irc-log-060222/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Sunday,_February_06,_2022⠀✐ Posted in IRC_Logs at 2:36 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-060222.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-060222.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-060222.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-060222.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmeLVi6dD7nB8edEkgxmQ1sCn5KARFU3ffe2SBU8kkBpKQ #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmcJcUAm5cqifPhNEsZ8DaVqgKuC4yksh1y5VVrZL14cHj (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC 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═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/monday-github-outline/#comments Gemini version at gemini://gemini.techrights.org/2022/02/07/monday-github-outline/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Microsoft_GitHub_Exposé_—_Part_XVII_—_Backsliding_Into_1990s-Style_Digital Slavery_by_Microsoft⠀✐ Posted in Microsoft at 7:43 pm by Dr. Roy Schestowitz Series parts: 1. Microsoft_GitHub_Exposé_—_Part_I_—_Inside_a_Den_of_Corruption_and Misogynists 2. Microsoft_GitHub_Exposé_—_Part_II_—_The_Campaign_Against_GPL_Compliance and_War_on_Copyleft_Enforcement 3. Microsoft_GitHub_Exposé_—_Part_III_—_A_Story_of_Plagiarism_and_Likely Securities_Fraud 4. Microsoft_GitHub_Exposé_—_Part_IV_—_Mr._MobileCoin:_From_Mono_to Plagiarism…_and_to_Unprecedented_GPL_Violations_at_GitHub_(Microsoft) 5. Microsoft_GitHub_Exposé_—_Part_V_—_Why_Nat_Friedman_is_Leaving_GitHub 6. Microsoft_GitHub_Exposé_—_Part_VI_—_The_Media_Has_Mischaracterised_Nat Friedman’s_Departure_(Effective_Now) 7. Microsoft_GitHub_Exposé_—_Part_VII_—_Nat_Friedman,_as_GitHub_CEO,_Had_a Plan_of_Defrauding_Microsoft_Shareholders 8. Microsoft_GitHub_Exposé_—_Part_VIII_—_Mr._Graveley’s_Long_Career_Serving Microsoft’s_Agenda_(Before_Hiring_by_Microsoft_to_Work_on_GitHub’s_GPL Violations_Machine) 9. Microsoft_GitHub_Exposé_—_Part_IX_—_Microsoft’s_Chief_Architect_of_GitHub Copilot_Sought_to_be_Arrested_One_Day_After_Techrights_Article_About_Him 10. Microsoft_GitHub_Exposé_—_Part_X_—_Connections_to_the_Mass_Surveillance Industry_(and_the_Surveillance_State) 11. Microsoft_GitHub_Exposé_—_Part_XI_—_Violence_Against_Women 12. Microsoft_GitHub_Exposé_—_Part_XII_—_Life_of_Disorderly_Conduct_and_Lust 13. Microsoft_GitHub_Exposé_—_Part_XIII_—_Nihilistic_Death_Cults_With Substance_Abuse_and_Sick_Kinks 14. Microsoft_GitHub_Exposé_—_Part_XIV_—_Gaslighting_Victims_of_Sexual_Abuse and_Violence 15. Microsoft_GitHub_Exposé_—_Part_XV_—_Cover-Up_and_Defamation 16. Microsoft_GitHub_Exposé_—_Part_XVI_—_The_Attack_on_the_Autonomy_of_Free Software_Carries_on 17. YOU ARE HERE ☞ Backsliding Into 1990s-Style Digital Slavery by Microsoft Video_download_link | md5sum f567010fa87bcd06249a2194c4f4450d GitHub is a Threat Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/microsoft-untrustworthy-for-code.webm Summary: The fake “social justice” claims or posturing by Microsoft ought to have been exposed by recent affairs, involving the very CEO or public face of GitHub, who moreover thinks_rape_jokes_are_appropriate A few weeks ago we published the arrest_record_of_Balabhadra_(Alex)_Graveley, but as court days are being scheduled we await the latest developments, which implicate not only Graveley but also GitHub’s CEO Nat Friedman and his_wife, whom we’ll pay more attention to later in this series. Microsoft has a terrible track record with women, and moreover this goes all the way up to the top (CEO who says things_like_this and co-founder who treats women like sexual objects while he flies_the_Lolita_Express_with_Jeffrey Epstein). 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GitHub: Because you want Microsoft as your boss.⦈ That Microsoft treated the Graveley situation so poorly is well documented [1, 2]. It would rather protect men who assault women than admit (possibly to the public) that it was hiring and employing criminals, elevating them to management positions based on nepotism (GitHub CEO) and in spite of a bad track record with women. Microsoft is — as I’ve long put it (for well over a decade for sure) — run by crooks, criminals, and liars. They’re shamelessly committing the crimes and then selling us a Microsoft that is “woke” because it changed the default name of Git branches while keeping the highly controversial (racist) contract with ICE (because that's_just_what_Microsoft_truly_believes_in as long as the Pentagon_can_bail_it_out). The video above discusses the GitHub situation. In relative terms they lose market share and people should definitely object to Microsoft ‘bossing’ them (and their projects) through GitHub. Over time more and more realise this, so we expect that one day GitHub will fold just_like_CodePlex_did. █ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⡖⢀⣶⡄⢶⣴⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢀⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣈⠻⡻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠐⠳⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠠⣶⣿⣿⣿⣶⣷⣿⢿⣿⣿⣷⣶⣶⣆⣦⣧⠀⠀⠀⢠⠟⠿⠟⠛⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠈⠲⣎⡷⡌⢺⣿⣿⣿⡿⠛⠛⠛⠋⠀⠀⠀⡾⠂⢠⣤⣰⣿⣿⡳⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠸⣦⠹⢿⣿⣷⡀⠀⠀⠀⠀⠀⣤⢁⣤⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡈⢯⣿⣿⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣻⣿⣷⡄⢀⠾⠋⠋⠉⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡷⠀⠐⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠏⠁⡘⠁⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠰⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠉⡂⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣅⣀⣼⣿⠿⣧⡄⢠⣼⠀⠀⢸⣷⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⠀⠒⠘⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣷⣶⣶⣿⣿⣾⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⢩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠰⠷⢆⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⡟⠀⠀⠀⣰⣿⣿⣿⣇⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡷⠆⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⣹⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢳⡏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢯⡿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⡾⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⢀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣾⠿⣿⣿⣿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣁⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⣿⡟⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⢰⡄⣶⣾⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣸⣽⣿⣿⣿⣶⣆⡀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣼⣿⣷⣦⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠙⢿⣿⡋⠉⢹⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠶⠶⣶⠿⢷⠶⠸⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠚⢢⣶⣆⢰⣦⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡤⠄⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⡹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡙⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠤⠤⠄⠀⠀⠤⣶⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣶⣶⣴⣰⣴⡄⠀⣴⠿⠿⠿⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣨⠷⢭⣽⣦⡙⢿⣿⣿⣿⠟⠛⠛⠋⠀⢠⠷⠀⣤⣀⣴⣿⣿⠧⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠙⠙⢷⡌⢿⣿⣿⣆⠀⠀⠀⠠⡬⢠⣤⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣴⣶⣾⣿⣿⣿⢸⠇⠀⠀⣠⣿⣆⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣏⣿⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢡⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢫⡿⠁⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⣱⠟⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡾⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡾⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣿⠿⣿⣿⣿⠿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⣿⡟⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢰⡄⣶⣼⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣼⣿⣷⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠙⢿⣿⡋⠉⢹⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠶⠶⣶⠿⢷⠶⠸⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠿⣴⣶⡄⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⡻⡿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠿⠀⠀⠀⠂⠀⠀⠤⠤⠀⠀⠀⠠⠄⠀⠄⠀⠀⠠⣤⣽⣿⣿⣷⣾⣾⣿⣿⣿⣷⣦⣤⣤⣤⡴⠻⠿⠟⡛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣩⡯⢿⣿⣯⠿⣿⣿⣿⣿⠟⠿⢿⠟⠀⣤⣄⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠁⠀⠈⠻⢛⣷⡹⣿⣿⣿⣇⢰⣎⣠⣶⣿⣿⣿⣿⡿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⢱⣄⢻⣿⣿⣾⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢧⣹⡿⡛⠉⠁⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⢹⡿⠀⠀⠀⠀⠀⠂⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⠄⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠙⢂⢄⡀ 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⠀⢰⣿⡟⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢰⡄⣶⡄⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣾⣿⣿⣶⣤⣤⣤⣤⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠹⢿⣿⡏⠉⢹⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠶⠶⣶⠿⢷⠶⠸⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠀⠘⡶⠶⣿⣦⣤⡄⢴⣶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡆⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄⢹⣿⣿⠘⣻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⠇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣧⡘⢿⣿⣿⣿⣿⡄⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠠⠀⠴⠶⠀⠀⠀⠠⠄⠠⠤⠀⠀⠤⢤⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣴⡾⠙⠛⠛⠙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⡻⣿⣿⣿⡻⢿⣿⣿⣿⣿⠛⠁⣶⣦⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠛⣿⣿⣌⢿⣿⣿⣟⣴⣶⣿⣿⣿⣿⡿⠜⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣿⣦⣽⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⢟⠋⠙⠚⠈⢧⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡾⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣁⡰⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⣿⡟⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢰⡄⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣾⣿⣿⣶⣶⣶⣴⣤⣿⣿⣿⣶⣶⣶⣶⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠹⣿⣿⡏⠉⢹⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛ ⠀⠶⠶⣶⠿⢷⠶⠼⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠶⠾⣿⣿⣆⣀⠠⢦⣶⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⠇⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠁⠀⠙⠋⣼⣿⡟⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣄⢻⣿⣿⣿⣿⣷⣴⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⡿⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⣷⠀⠀⣴⣶⣤⠀⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⣧⣀⡹⠿⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣶⣿⡆⠀⠀⠀⢸⣷⣦⠈⢷⡀⠛⣿⣿⣿⣿⣿⣿⣿⠖⠂⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⣿⠏⠀⣼⠇⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡟⠀⣸⡟⢀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡏⠀⣰⡟⢠⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⡍⠀⣰⠟⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢲⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⣿⡟⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⢀⣰⡄⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠹⣿⣿⡏⠉⢹⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠷⠶⣶⠿⢷⠶⠼⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠦⠀⡷⢒⣿⣿⣂⣶⣆⣶⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⠇⠀⢰⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⣾⣿⡗⢿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣤⣿⣿⣿⣿⣷⣷⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⠃⠀⠹⠿⠇⠀⠀⠀⠀⠀⠰⠶⠄⠀⠀⠀⠠⠄⠤⠄⠀⠤⢤⣬⣿⣿⣿⣿⣿⣿⣟⡙⠛⠉⢉⣿⣿⣷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣙⠿⣿⣿⣿⠋⠀⣿⣷⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠛⣿⣯⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠁⢐⡄⠻⢿⣿⣿⣷⡄⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢰⡏⠄⠸⣿⣿⣿⣿⣄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠈⠘⠀⢀⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢸⣿⣿⠃⠀⣼⠃⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⣿⡟⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⢀⢲⣌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠹⣿⣿⡏⠉⢹⣿⡿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠷⠶⣶⠿⢷⠶⠼⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠀⠲⡦⣸⠟⣶⣶⣆⣶⣴⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠅⠀⠀⠁⠀⠀⠀⣾⣿⣿⠫⣿⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣺⣿⣷⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠻⠟⠀⠀⠐⠲⠆⠰⠶⠦⠀⠀⠀⠠⠤⠤⠤⠄⠤⠤⣭⣿⣿⣿⣿⠋⠛⠋⠉⣹⣿⣿⣶⣦⣤⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣝⣻⡟⠁⢰⣶⣼⣿⣿⣿⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⣰⣿⠿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣻⣯⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⣿⡟⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⢴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠈⠹⣿⣿⡏⠉⢹⣿⡿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠶⠶⣶⠿⢷⠶⠼⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⢀⣸⣶⣿⣶⣤⣤⡀⣠⣰⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢹⣿⣿⢏⣹⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⣯⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠻⠇⠀⠀⠴⠶⠀⠲⣶⠦⠀⠀⠀⠠⠄⢤⣄⣀⡤⣤⡟⠙⠛⠋⢙⣻⣿⣿⣿⣿⣷⣤⣤⣠⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠉⢀⣶⣶⣿⣿⣿⣿⢿⣿⣿⣿⠿⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠛⢻⣻⣿⣿⠋⠙⠙⠛⢽⢿⣻⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⣗⣿⣿⣦⠀⠀⠀⢠⠀⠙⣽⣿⣿⣿⣿⣄⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⡟⣛⠃⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡤⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⢀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⢀⠟⠀⠀⠀⠀⠀⠈⠻⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣂⠀⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠁⠙⠛⠃⠀⠀⠀⠀⠀⣴⣿⣿⠧⠀⠀⠀⠀⠀⠀⡀⠘⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠢⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⡻⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⢸⡇⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠟⠂⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠘⣷⠠⠆⠀⠀⠄⢠⠖⠐⠒⠃⠀⠀⠀⠀⠀⠠⠶⠶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣇⠄⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣾⣿⡿⠷⠀⠀⠀⠀⢰⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿ 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⠀⠀⠘⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⡀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡆⠀⠀⠀⠀⠉⠛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⣇⣦⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡸⠻⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠠⡻⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠰⠀⠀⡴⠂⠐⠀⠀⠀⠀⠀⠀⠠⢾⠿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠇⠀⢠⣄⠀⠀⠀⠘⣿⣿⣿⣾⣶⣶⣾⣷⣶⠶⠆⠀⠀⠀⠐⠂⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣀⣠⣿⣃⢀⣀⠀⣀⡿⣿⣿⣿⣟⣿⣿⣿⢟⣀⢀⣀⢠⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡆⣿⡟⢳⣿⢻⣿⢸⣿⣿⣸⣿⣿⣿⢸⣿⡿⠇⣿⡟⢻⠏⣿⣼⡟⣾⡟⣿⣾⣿⣿⣿⢸⢸⣿⣾⣿⣼⣿⣾⣿⣷⢸⣿⣼⣿⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡆⣿⡟⢻⣿⢨⣭⣸⣿⣿⡿⣿⣿⣿⢨⣿⣿⡆⣿⡟⠃⠀⢹⣿⠁⣿⡇⣿⡿⣿⣿⣿⠈⠸⣿⣿⣿⣿⡇⣿⣿⣿⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠛⠛⠋⠻⣿⣛⣟⣋⣛⣃⣻⣿⣻⣼⣻⢿⡃⠛⠛⠃⠀⠘⣛⣼⣟⣿⣟⣥⣿⣿⠛⠀⠀⠛⠛⠙⠛⠃⠛⠛⣛⣛⣻⣛⣻⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⢀⣤⣤⣄⣠⣤⣤⡀⣠⣤⣝⢛⣯⣽⡿⣻⣿⣿⢿⣿⣿⣿⣯⣥⡄⠀⣤⣤⡰⣿⣿⣿⢿⣿⣿⣿⡯⣠⣤⣄⢠⣤⢠⣤⣤⣤⣤⣻⡿⣿⣿⣿⡿⣿⣿⣟⢿⣿⣿⡻⣿⣿⣟⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⠹⠿⣿⣿⣿⢷⣿⣿⣿⣼⣿⣿⡃⣿⡏⣿⣿⣿⣯⣍⣿⣏⣁⣰⣿⣿⡇⣿⣿⣛⣾⣟⣿⣿⠃⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⢯⡇⣿⣯⣿⢻⣿⣿⣿⢻⣿⣟⠛⣿⣿⣛⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⢸⣿⣰⣶⣿⣿⣿⡟⣿⣿⣿⢳⣾⣿⡷⣿⣇⣿⢿⣿⣿⡿⣿⡿⠿⢻⣿⣿⣷⣶⣿⣿⣾⣿⢹⣿⠀⣿⣿⣿⢿⣿⣸⣿⣿⣿⣿⡏⡇⣿⣏⣿⡿⣿⣿⣿⢰⣾⣿⡗⣶⣿⣿⣘⣻⣿⣿⣿ ⣀⣀⣤⣬⣭⣬⣥⣭⣭⣭⣤⣽⣯⣥⣭⣭⣭⣥⣭⣿⣽⣾⣽⣯⣷⣮⣿⣿⣾⣭⣿⣧⣍⣡⣤⣌⣉⣈⣩⣯⣿⣽⣿⣿⣮⣭⣶⣭⣿⣭⣶⣽⣿⣷⣯⣭⣭⣽⣿⣯⣭⣽⣷⣯⣿⣵⣿⣽⣯⣷⣯⣿⣽⣯⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠖⠲⣶⠆⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠐⢲⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣰⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣿⡄⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⠃⠀⠀⠠⠤⠀⠠⢤⡆⠀⠀⠀⠀⠀⡰⠛⠙⠛⠋⢛⣿⣿⣷⣶⣶⣾⡀⣻⣶⣦⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⣤⡀⣴⣿⣿⣯⠁⠈⠃⠀⠀⠻⠿⠿⠖⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⣶⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣧⣬⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⢿⢻⣿⣿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⢠⠀⢈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⣿⣷⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢤⡀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⠀⠀⠀⠂⠈⠁⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠰⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢹⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠂⠀⠆⠀⠄⠀⢤⠀⢠⠶⠀⠂⠀⠀⠀⠀⠀⣀⠾⡿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⢰⠃⠀⠀⣰⣿⣿⣷⣄⠀⠀⠀⠙⣿⣿⣿⣷⣶⣶⣶⣶⣾⠄⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⢀⣘⡿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣋⠀⣀⣰⣿⣿⣿⣿⣃⠀⣀⡀⢠⣿⣿⣿⣿⣿⣿⢟⣿⢂⣀⢀⣀⣴⣶⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡆⣿⡟⢳⣿⢻⣿⢸⣿⣿⣸⣿⣿⣿⢸⣿⡿⠇⣿⡟⢿⣏⣿⣼⡟⣾⡟⣿⣾⣿⣿⣿⢸⢸⣿⣾⣿⣼⣿⣾⣿⣷⢸⣿⣼⣿⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡆⣿⡟⢻⣿⢨⣭⣸⣿⣿⡯⣿⣿⣿⢨⣿⣿⡆⣿⡟⣿⣿⢹⣿⠁⣿⡇⣿⡿⣿⣿⣿⢸⡿⣿⣿⣿⣿⡇⣿⣿⣿⣸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠛⠛⠋⡻⣿⣛⣛⣋⣛⣃⣻⣿⣛⠘⠻⠟⣣⣛⣛⣿⡿⠘⠛⠀⠙⣿⣟⣥⣿⣿⣻⣿⡇⠛⠛⠙⠛⠃⠛⠛⣛⣛⣻⣛⣻⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⢀⣤⣤⣄⣠⣤⣤⡀⣠⣤⣝⢛⣯⣽⡿⣻⣭⣿⢿⣯⣤⣤⣤⣿⣿⡿⣿⣿⣶⣤⣤⣼⢿⣿⣿⣿⡿⣻⣭⣅⢠⣤⢠⣤⣤⣤⣤⣻⡿⣿⣭⣿⠿⣿⣿⣟⢿⣿⣿⡻⣿⣽⣟⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⠸⠿⣿⣿⣿⢷⣿⣿⣿⣸⣿⣟⡃⣿⡏⣿⣿⣿⣯⣉⣿⡏⣿⢰⣿⣿⡇⣿⣿⣛⣾⣟⣿⣿⠃⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⢯⡇⣿⣯⣿⢻⣿⣿⣿⢻⣿⣟⠛⣿⣿⣛⣾⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⢿⡿⣿⣿⣿⢸⣿⣰⣶⣿⣿⣿⡟⣿⣿⣿⢱⣾⣿⡷⣿⣇⣿⢿⣿⡿⠏⣿⡇⣿⢸⣿⣿⣷⣶⣿⣿⣾⣿⢹⣿⡶⣿⣿⣿⢿⣿⣸⣿⣿⣿⣿⡏⡇⣿⣏⣿⡿⣿⣿⣿⢰⣾⣿⡗⣶⣿⣿⣘⣻⣿⣿⣿ ⣤⣤⣤⣬⣭⣬⣥⣭⣭⣭⣤⣽⣯⣥⣭⣭⣭⣥⣭⣿⣽⣾⣽⣯⣷⣮⣿⣽⣬⣭⣥⣤⣍⣉⣉⣭⣽⣮⣭⣍⣿⣽⣿⣿⣮⣽⣿⣯⣿⣭⣶⣭⣿⣥⣭⣭⣭⣿⣿⣭⣭⣭⣶⣯⣿⣵⣾⣽⣯⣷⣯⣿⣽⣯⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠆⠲⣶⠆⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠐⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⣀⣀⠀⠀⠀⢽⣿⣧⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠛⠀⠀⠀⠤⠤⠀⠶⣶⠄⠀⠀⣠⠞⠻⠿⠛⠻⣷⣦⣭⣽⣿⣶⣤⣦⡆⢸⣿⣦⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⡀⣠⣾⣿⣏⣀⣀⡀⠀⠈⠀⠀⠘⠟⠿⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤ ⠆⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⣤⣤⣿⣿⣿⣿⣿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠩⣤⡜⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠟⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠩⠹⠟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠠⠄⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠉⣼⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠃⠀⠾⠷⣶⣤⠀⠙⠻⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠚⠛⠂⠘⠛⠀⡠⠀⠀⠀⣠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠁⠀⠐⠂⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠨⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡱⢿⠿⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⡟⣾⠀⠀⠀⣼⣿⣿⣿⣷⣤⠀⠀⠀⠙⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⢀⣘⢿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣃⠀⣀⣸⣿⣿⣿⢿⣿⠇⣀⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⢏⣈⢀⣀⣠⣤⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡆⣿⡟⢳⣿⢻⣿⢸⣿⣿⣸⣿⣿⣿⢸⣿⡿⠇⣿⡟⢿⣏⣿⣼⡟⣾⡟⣿⣾⣿⣿⣿⢸⢸⣿⣾⣿⣼⣿⣾⣿⣷⢸⣿⣼⣿⢻⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡆⣿⡟⢻⣿⢨⣭⣸⣿⣿⡿⣿⣿⣿⢨⣿⣿⡆⣿⡟⣿⣿⢹⣿⠁⣿⡇⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣸⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠛⠛⠋⡻⣿⣛⣟⣋⣟⣃⣻⣿⡛⠘⠻⢿⣣⣛⣛⣿⣿⣿⡛⠀⠙⠿⢟⣥⣿⣿⣻⣿⣷⡛⠛⠙⠛⠃⠛⠛⢛⣛⣻⣛⣻⣞⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⢀⣤⣤⣄⣠⣤⣤⡀⣠⣬⣝⢛⣯⣽⡿⣻⣯⣿⢻⣥⣤⣤⣽⣿⣿⡿⣿⣿⣿⣷⣤⣄⢀⣾⣿⣿⡿⣻⣿⣟⢣⣤⢠⣤⣤⣤⣤⣸⣿⣿⣿⣿⠟⣻⣿⣟⢿⣿⣿⡻⣿⣿⣟⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⠸⠿⣿⣿⣿⢷⣿⣿⣿⣸⣿⣿⡃⣿⡏⣿⣿⣿⣯⠉⣿⡏⣿⣷⣿⣿⡇⣿⣿⣛⣾⣟⣿⣿⢃⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⢧⡇⣿⣯⣿⢳⣿⣿⣿⢻⣿⣟⠛⣿⣿⣛⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⢸⣿⣰⣶⣿⣿⣿⡟⣿⣿⣿⢱⣾⣿⡷⣿⣇⣿⢿⣿⣿⣇⣿⡇⣿⢹⣿⣿⣷⣶⣿⣿⣾⣿⢹⣿⡶⣿⣿⣿⢿⣿⣸⣿⣿⣿⣿⡇⡇⣿⣏⣿⡿⣿⣿⣿⢰⣾⣿⡇⣶⣿⣿⣘⣻⣿⣿⣿ ⣤⣤⣤⣬⣭⣬⣥⣭⣭⣭⣤⣽⣯⣥⣭⣭⣭⣥⣭⣿⣽⣾⣽⣯⣷⣮⣿⣭⣬⣭⣥⣍⣉⣽⣿⣯⣽⣮⣽⣯⣿⣭⣻⣿⣮⣽⣿⣯⣿⣽⣦⣭⣿⣥⣭⣭⣭⣵⣿⣯⣭⣽⣷⣯⣿⣵⣾⣽⣯⣷⣯⣿⣽⣯⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠈⠀⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠆⠲⣶⠆⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠯⠹⠛⠿⠟⠆⠀⠀⠀⠀⠁⠀⠀⠀⠄⢀⠀⠀⠐⣴⠤⣤⣔⢴⢶⢿⣞⣻⣟⣿⣿⣻⣿⣼⣿⣟⠾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠋⠂⠀⠀⠀⠀⠀⠘⠂⠠⣴⠵⠀⠀⢻⡿⠗⠈⠀⠀⠀⢈⠋⠀⠀⢸⣷⣭⠏⣩⣽⡿⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢒⡀⢀⠀⠀⠁⠂⠀⢘⢳⢴⣾⣏⣃⡠⣠⠒⠛⠨⣿⣻⣿⣿⣿⢻⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠀⠀⠖⣢⠈⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠛⠁⠀⠻⠿⠋⢰⣶⣶⣿⣶⣾⡿⢻⡟⠿⠿⣿⣿⣤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣶⣦⣴⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠨⠠⠠⣧⢠⡄⢸⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠚⠛⠓⠼⣿⠇⢀⣤⣀⣾⣿⣿⠟⣙⣉⣀⣉⣙⣿⡿⢿⣟⣯⡻⣿⣿⣿⡟⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣶⡼⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣤⣼⣿⣿⣿⣿⣿⡄⠈⠛⠛⠟⠋⠉⠀⠀⠊⢿⣿⡉⢻⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀ ⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⢠⡀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⡠⢄⣼⣿⣿⣿⣿⣿⡿⠿⡁⠂⠀⠀⠁⠀⡖⠶⠀⠐⢰⣿⣿⣿⣈⠻⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⣭⣏⣬⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣾⣿⡟⠻⣻⣿⣿⡗⣂⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⠗⠉⠞⢄⢀⣸⣶⣆⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⢐⣠⣤⡄⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣽⠂⠙⠇⠀⢿⡏⣿⠿⠿⠿⠿⡯⠄⠿⢿⠿⠿⠿⠟⠛⣺⠀⠀⠀⣽⣿⣿⣿⣿⣦⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠹⣿⣏⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⠟⠃⢤⢠⣄⣿⡇⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⠀⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈⠼⠀⢀⠀⡼⠛⠻⣤⣼⣠⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠶⣦⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠙⠊⠀⠀⠀⠉⠉⠛⠳⠶⠶⣤⣧⣄⡀⠀⠀⠀⠀⠀⠹⠰⠄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠈⠡⠁⢀⡦⣤⡀⠀⠀⠻⣿⣿⣿⠿⠂⠀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⣿⣇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⢿⣿⢃⠀⠀⠀⠎⡅⢠⣈⠙⠋⡁⠀⠀⠀⠤⡏⠁⢀⢤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠒⢠⣆⠀⠀⠀⡿⣿⡆⢾⣧⠄⠆⢀⣈⡇⠒⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡗⠀⠀⠀⢠⡾⢿⡀⢼⡗⣶⠴⠛⠁⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢁⣼⡇⠀⡀⠀⠍⣿⣿⣿⣿⣟⠟⠀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⠒⣴⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⣿⡦⡀⠀⠁⠐⠀⢺⣿⣛⣩⣼⡿⣻⡖⠃⣿⢆⣐⡾⠦⠷⠀⠸⠀⠀⠒⠂⠗⠲⠀⠀⠀⠀⣈⡿⣿⡿⣖⡋⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠆⡠⠿⠂⠀⠸⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⠃⠀⠀⠬⠽⢨⠉⣿⣿⣿⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣺⣏⣀⡠⠈⠀⠀⠀⠀⠀⠀⢮⣿⣿⣿⡜⠵⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠛⠃⠠⣶⣶⣾⠟⠿⠛⠛⢿⣿⣶⣤⠤⢤⡤⢤⠤⣶⣿⣿⣿⣿⣾⣾⣿⣿⣿⣷⣶⣶⣴⣦⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣄⠀⣼⣷⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⠀⢴⣤⣰⣿⣿⡿⠀⠀⠀⢀⣀⣀⣀⣀⣨⣏⠅⣽⣯⡉⠘⣿⣿⡿⠛⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢤⣶⠿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣶⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠀⠛⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⢶⡀⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠐⢭⣭⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⠉⠩⣽⡿⠀⠐⣓⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⡀⣀⣿⣶⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡀⣠⣤⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣬⠀⠈⠀⠦⠀⣹⢷⠀⠽⠿⠿⠿⠿⠧⠄⠀⠐⠾⠟⠛⠛⢋⣉⡇⠀⠀⢠⣿⣿⣿⣿⣧⡀⠀⢙⠀⠀⠀⠀⠀⠀ ⠀⠠⠿⠉⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡹⡅⠀⠀⠀⡼⢿⣿⡆⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣼⠷⠀⢀⠄⢙⠀⠂⠉⠳⣮⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⢠⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢐⠛⠂⡭⠀⢀⠀⠀⠀⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠸⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠈⠀⠀⠐⠀⠛⠀⠀⠀⢀⠀⠀⠈⣩⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠟⢃⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣶⣼⡀⠀⠀⡗⢲⡄⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣠⣾⣿⣷⣏⣀⣸⣟⡛⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡀⢠⡾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣿⣯⢿⣿⣷⣂⡙⣋⣀⡿⠿⡇⣀⣐⡃⠀⠺⠀⠀⠀⠠⠆⠠⣴⠂⠘⠚⠀⠀⠀⠀⢀⡰⠿⠿⢶⡂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⢾⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣛⣸⢇⣘⢛⣹⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⣿⣯⣹⢿⣿⣿⡿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠏⠉⠇⠉⡙⢣⣿⠭⢵⢰⣿⣻⣹⣿⣿⣛⣰⣿⠿⠇⠉⡍⠃⠈⣿⡮⡟⣿⡟⠻⡿⣿⣻⣿⣿⣿⣿⣎⣙⠜⢻⠈⢩⡨⢸⣿⢼⣿⣻⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠂⠠⠤⢠⣤⠨⠍⠀⡇⣭⣽⢀⣨⣭⣭⡆⣾⡏⣣⣆⢸⣿⢀⣿⡇⠒⣿⣿⣽⣿⣽⣷⠾⠛⣭⠿⠇⠂⠀⠰⢨⣩⠉⠁⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠒⠂⠀⠈⣉⣻⣶⣲⣥⣔⣀⣠⣆⣅⣜⣼⠩⠥⢂⣓⣛⣿⣿⡜⠛⠘⣯⣿⣿⣿⣯⣵⣪⣿⣿⡛⠋⠈⠉⠐⠀⠈⠀⠂⣘⣒⣶⣵⣒⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⠀⠄⠤⠀⠀⠀⣀⠤⠤⢄⢠⣤⣤⡀⣨⣭⣽⢝⣿⣿⡻⣿⣿⣿⣿⣿⣭⣤⣬⣿⣿⡿⣿⣿⡷⣠⣤⣹⢿⣿⣟⢿⡿⣿⣿⣟⢡⣤⠠⢄⡤⢄⣤⡀⠀⣿⣿⣟⣿⣿⣿⣿⣿⡏⣿⡻⢿⣻⣟⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠌⠢⠀⡄⠀⠀⠀⠀⠰⠀⠘⠄⢦⣶⡎⠩⠎⠑⢹⡓⣿⡇⠈⢿⣿⣻⡟⣶⡆⣼⣷⣿⣛⣇⣿⣯⡿⣾⣯⣭⣷⢳⣿⠁⠀⠈⠉⡀⠺⠀⠀⢀⠇⠀⣛⣋⣀⢾⣿⠿⣹⢻⣿⣝⢓⡻⢝⣻⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⠀⠃⠀⠀⠃⠀⡀⠀⠈⠱⠀⠰⠀⠄⠸⢇⣐⢴⣶⣄⣣⢭⡇⠀⢶⣿⣾⣆⣉⣏⣿⠹⠭⢶⣷⡷⡖⠨⢿⣿⢨⣭⣝⠛⠀⠀⠄⣀⣶⣶⣤⣤⡆⠇⡀⣿⣇⣬⣏⣉⡨⠀⢴⣖⠖⠑⡶⢆⢙⠙⣿⣿⣿⣿ ⣷⣶⣶⣦⣭⣬⣥⣭⣥⣤⣶⣽⣯⣶⣯⣥⣭⣵⣶⣶⣶⣾⣯⣿⣿⣾⣽⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣶⣾⣯⣯⣭⣤⣭⣬⣭⣿⣿⣿⣿⣶⣷⣭⣷⣮⣭⣥⣴⣷⣭⣭⣽⣷⣾⣯⣷⣾⣾⣿⣷⣯⣿⣷⣷⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠆⠐⠀⠀⠶⠀⠰⠆⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠋⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣷⠟⠲⡶⣿⣿⣿⡆⣧⣠⣶⡶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠈⠙⠟⠉⢹⣿⣿⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢀⣠⣤⣤⣄⣀⠐⠆⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡏⠇⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠛⢳⠋⠉⠉⠉⠛⣻⣷⣦⠀⠠⠤⠤⠤⠤⣤⠤⡤⢴⣾⣿⣿⣿⣶⣷⣿⣿⣿⣿⣶⣦⣤⣤⡤⣼⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⣠⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⢰⣦⣴⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣀⣼⡥⠹⠿⡉⠈⠻⣿⡿⠛⠛⠛⠃⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣴⡿⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠈⠀⠀⠹⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡇⣀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣮⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⢰⣆⠸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠂⣭⣡⠼⠁⠀⠀⠀⢀⢿⣿⠒⠉⠁⠸⣿⡆⠀⠀⡆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈⡀⠀⣸⣶⡀⠀⠀⠀⡄⠀⠀ ⡀⠀⠀⠀⠀⣶⣖⣦⣤⣥⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣦⡆⠀⠀⢠⡀⠈⣻⣧⡶⣶⡤⠀⠠⠾⠿⠟⠻⠓⠀⠀⠀⠈⠛⠚⠿⠋⡉⣩⠀⠀⠀⣼⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠙⠊⠻⣇⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢠⠀⠐⠀⠂⠀⠼⢧⡀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠌⠀⠀⠀⠈⠻⣧⣄⠠⣤⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣧⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡉⠈⠀⠐⣲⣀⠀⠀⠀⢀⣄⠀⠀⣿⠿⠟⠃⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⣰⣿⣿⡷⣀⠀⢸⠗⠀⠀⣾⢐⡣⠄⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢻⡿⣿⠇⠀⠸⡈⢃⣘⣿⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠾⠷⣖⡒⠀⠀⠀⣀⠀⠀⠀⠘⣷⠀⠈⣿⡮⠼⠿⣿⣿⣆⣈⣋⣁⣙⡛⠓⠀⠀⠀⠀⠀⠀⠀⠖⢠⢶⠤⢠⡖⠀⠓⠃⠀⠀⠀⠀⣀⠾⠿⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢷⡰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣄⠐⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣃⡀⢀⣀⢸⣇⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣃⢚⣻⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠇⠉⡝⢣⣿⠯⢵⢹⣿⣻⣸⣿⣿⣿⢸⣿⠿⠇⡍⡍⠃⠈⣿⣮⡟⣾⡟⠻⡿⣿⣻⣿⣿⣿⣿⣎⣙⠜⢻⠈⢩⡸⢹⣿⢼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠊⠣⠤⢠⣥⠸⠏⠀⣇⣭⣼⢭⣨⣭⣭⡆⣾⡏⠃⣴⢻⣿⣰⣿⡇⠒⣿⣿⣽⣿⣿⣷⣾⣛⣯⠿⠇⠂⠀⢰⢸⣻⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠒⠂⠀⠈⣉⣻⣶⣲⣵⣶⣀⣠⣆⣅⣸⣾⣩⣥⡆⠓⢛⡿⠃⢘⣛⣿⣯⣿⣿⣿⣯⣵⣺⣿⣷⠛⠛⠈⠉⠐⠀⠈⠀⢂⣸⣶⣾⣿⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⠄⠄⠤⠠⠀⣤⣀⠤⠤⣄⢠⣤⣤⡀⣨⣭⣟⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⣥⣤⡈⣿⣿⣻⣿⣿⣟⢿⡿⣻⣿⣏⢠⣤⢠⣄⡤⢄⣤⡀⠘⣿⣿⣟⣿⣿⣿⣿⣿⣯⣿⡿⢿⣿⣟⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠢⠀⡄⠹⠀⠀⠁⠱⠀⠸⠄⢤⣶⡎⠩⠎⠙⢻⡓⣿⡇⠈⣿⣿⣫⣍⣾⡷⣿⣿⣿⣛⣇⣿⣯⣟⣾⣏⣽⣷⢳⣿⠇⠀⠈⠉⠆⠺⠀⠘⢀⠇⠀⣿⣏⣊⢾⣿⠽⣽⢻⣿⣟⢟⡻⢝⣛⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⠀⠃⠐⠀⠃⠀⡀⠀⠈⠱⠀⠸⠀⠄⠸⣇⣘⢵⣶⣄⣳⢭⡇⠀⢾⣿⣿⣗⣿⡇⣿⣻⣿⣶⣷⡷⡖⠨⢿⣿⢩⣭⣝⠛⠀⠀⠄⣀⣷⣾⣤⣤⡆⠇⡀⣿⣇⣭⡏⣉⡨⠀⢴⣖⣖⡑⡶⢖⢛⠙⣿⣿⣿⣿ ⣾⣿⣶⣶⣭⣬⣥⣭⣬⣭⣶⣽⣯⣶⣯⣽⣯⣵⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣭⣯⣭⣭⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣽⣿⣶⣷⣭⣷⣯⣭⣥⣴⣷⣯⣭⣽⣷⣾⣯⣷⣾⣾⣿⣷⣿⣿⣷⣷⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠀⠁⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠆⠒⠀⠀⠶⠀⠰⠦⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠋⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡷⠟⠒⡶⣶⣿⣿⡆⣦⣠⣦⡶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠍⠀⠀⠀⠭⠟⠉⢽⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢀⣠⣤⣤⣄⣀⠘⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠇⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠛⢳⠋⠉⠉⠉⠛⣻⣷⣦⠀⠠⠤⠤⠤⠤⢤⠤⡤⢴⣾⣿⣿⣿⣶⣷⣿⣿⣿⣿⣶⣤⣤⣤⠤⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣀⣠⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⢰⣦⣴⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣬⡭⠸⠿⡉⠀⠻⣿⡿⠛⠛⠛⠃⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣴⡶⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠘⠀⠀⠹⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡇⣀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣮⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⢰⡀⠸⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣭⣁⠼⠁⠀⠀⠀⢀⠯⣿⠒⠉⠁⠸⣿⡆⠀⠀⡆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈⡀⠀⣸⣶⠀⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⣲⣆⣦⣤⣤⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣦⡆⠀⠀⢠⡀⠈⣻⣧⡶⣦⠤⠀⠠⠾⠿⠝⠻⠓⠀⠀⠀⠈⠛⠚⠿⠋⡈⣨⠀⠀⠀⣼⣷⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢙⠈⠻⣇⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣿⠁⠀⢠⠀⠐⠀⠂⠀⠼⢧⡀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠻⣧⣄⠠⣤⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣧⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⠈⠀⠐⣲⣀⠀⠀⠀⢐⣄⠀⠀⣿⠿⠟⠃⢀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠆⠒⠀⠀⠶⠀⠰⠦⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠟⠋⠁⠥⠃⠈⠣⠠⣀⢀⠐⣠⣀⡤⡠⡲⠲⠴⡂⠀⠀⠀⠀⠀⢀⣼⣿⡿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣾⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠀⠀⡀⠀⠜⠐⠀⠺⠺⠘⡷⠺⠂⠘⠿⢯⡀⠍⠀⠀⠀⠀⠀⠀⠀⣸⡝⠁⣀⣿⠉⠬⣿⣻⣿⣿⣷⣿⢍⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠉⠀⠀⢀⠀⠀⠀⠀⠠⢡⢀⠀⠀⢁⠀⠀⣠⣶⣶⣦⣤⣄⠈⡤⠀⠛⢂⠔⠿⠨⠆⠀⠀⠀⠀⢡⣿⣿⣿⣿⡸⣝⢿⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠒⡆⣄⣰⣄⣠⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⢁⣿⠋⠈⠉⠉⣋⣽⣿⣿⣶⣶⡆⢠⡤⣄⢤⡤⢠⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⣶⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⢚⣦⣻⣿⣿⣿⠿⠋⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣻⠁⠀⣾⣷⣾⣿⣿⡟⠀⠐⠖⠂⠀⠘⠓⠀⠀⠀⣀⣀⣀⣀⣉⣨⣿⢷⠿⢧⡁⠹⢿⡿⠟⠛⠛⠛⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣾⢿⣿⣿⣿⢿⣿⣷⡀⠀⠀⠀⢀⣀⠠⣀⠀⡐⢶⣶⡄⠀⠀⠀⠀⠀⢏⣴⡿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠈⠀⠈⠀⠀⠀⠀⠈⢱⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⣿⣿⣿⣆⠀⢰⡾⠀⠀⠁⠀⠘⢛⣻⣿⢨⡀⠀⠀⣰⣿⣿⣿⣿⢿⣯⠋⠬⡁⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠒⠀⢠⡼⢿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣽⣿⣿⣿⣧⡈⠀⠀⠀⠀⠀⠀⠸⣭⣍⡬⠟⠀⢸⣿⣿⠛⣊⠉⣻⣿⢀⣀⣀⣂⣀⣺⠂⠀⢸⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡂⠀⠚⡻⢇⢘⣿⣆⠀⠀⠀⢠ ⢀⣀⣀⡀⠀⠀⠀⣾⣶⢿⣴⣿⡇⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠐⣯⡟⠀⡀⢡⡀⢨⣿⢺⣿⣿⣿⣾⣷⡆⠠⣽⠟⠹⠛⠿⠆⠀⠿⠶⠿⠟⢺⠏⣋⣩⡇⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠰⡄⠀⢰⠗⠀⠀⠀⠈⢂⠙⢿⡎⠉⠋⠋⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠹⢿⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀⠀⠀⠀⠀⠀⠙⢧⣿⡇⠐⠹⠄⠀⠀⠂⠐⣿⡀⠀⠀⠀⢤⠀⢀⡄⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠲⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣄⡀⠀⠀⠀⠀⡯⠎⠁⠀⠀⠂⠀⠀⠀⠀⠈⣷⣀⠀⠀⣾⣰⠀⣤⡄⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠁⠀⠀⠀⠀⠀⠻⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⣸⣭⠁⠀⠀⠀⠀⡆⠀⠀⣀⡀⠘⠻⣧⡄⠿⠞⢌⣿⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠂⠠⠀⣀⣌⡄⠠⠀⠘⠿⠿⣦⠀⣘⣻⣯⡀⠀⢩⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢸⡉⠀⢄⢀⣖⠀⢀⣤⡄⢿⣿⣿⣿⠀⢾⡇⡀⠀⠀⡀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢘⢷⣆⠴⣿⣿⣖⡾⣿⣷⠌⢻⡿⠛⠀⢸⡗⣶⠴⠊⠁⠇⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣤⡤⠀⠀⢄⠀⠀⠊⢩⢻⣆⠀⢻⣿⣃⣻⣏⡙⡚⣧⣸⡄⣿⣟⡟⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣀⠀⠀⡀⠀⠀⠀⠐⡀⠒⠀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⣀⣠⠾⠿⣾⣶⣂⢀⠀⠀⠀⠨⡀⠹⣧⠈⣹⣷⣯⡯⢿⣿⣿⣷⣀⠙⡋⠘⠋⠁⠀⠀⠀⠈⣀⣿⣂⠿⢂⣴⠧⢄⣶⠆⠒⠚⠀⠀⠀⠀⣀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣷⠘⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⡙⠙⠚⠻⠛⣻⢿⣿⡿⣿⣿⣿⣿⡿⡿⡿⣿⣃⣀⠀⠘⣿⢟⡀⡿⠋⣹⡿⣿⣿⡿⣿⣿⣿⢿⡿⠿⣿⢛⣻⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠏⠓⡇⢛⡗⢣⣿⠯⢴⠘⠛⢚⣹⣿⣿⣽⠀⠙⠿⠆⡯⠝⠃⡅⣿⡬⡍⡽⡟⠉⡬⣥⠨⣍⢸⡦⠭⣎⣱⠈⠩⠈⢉⣑⢱⣾⣐⣿⡻⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠂⠀⣁⣥⡤⢄⣐⡷⠶⢖⣛⠈⡩⠙⡃⣵⡆⠂⠀⢩⣭⠁⠉⠁⠀⣏⣭⡩⢭⢼⢖⠚⠒⠦⠤⠄⠂⠀⠸⢠⢠⠈⢘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠓⠂⠀⠈⠀⣠⠼⣛⣐⣢⣄⣠⣀⢌⣍⣌⣩⣤⣤⢭⣽⡃⢠⣜⠛⣸⣟⣷⣲⣰⢢⣄⣠⣾⣧⠭⠍⠀⠀⠁⠀⠘⠀⣈⣩⣤⣴⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠄⠀⠀⠠⠀⠤⣀⠠⠄⢀⢠⣤⣄⡀⡠⣄⡉⠙⢉⣽⡿⣿⡿⣿⢫⣿⢭⢿⣿⢿⣟⣿⣿⣿⣷⣾⣿⣿⣿⣹⡿⢿⡿⣻⠟⢏⠠⢤⠀⢠⠄⢤⣄⠀⠿⣿⣿⢿⣻⣿⣿⣿⣟⣭⣽⡿⠻⢹⡻⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⠰⠀⠸⠀⢢⣤⠂⠉⠌⠙⠒⠂⠭⡗⠛⣶⣶⣻⡿⠿⢯⣿⢇⣉⠿⠇⢾⣯⣲⣼⣏⠿⠭⢣⠿⡁⠀⠄⠀⠍⠉⠀⠘⢈⠃⠀⠤⠄⢀⢬⣭⡯⠭⢀⣙⣛⠓⡙⠑⣺⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠄⠐⠀⠈⠀⡄⠰⣀⣀⢄⣤⠄⢀⠀⠇⠀⠧⠤⣘⠧⣭⠿⣿⣰⣶⣤⡶⠳⠆⠈⣾⣿⢉⡁⢚⣉⣇⣀⠄⣀⢴⣾⠀⠀⡆⠁⡄⣉⡆⠈⡈⡉⠇⠰⢶⣔⣄⡷⣶⣲⣿⢙⣿⣿⢿⣿ ⣿⣿⣾⣦⣭⣤⣤⣤⣤⣀⡰⣠⣆⣴⣮⡵⣷⣶⣿⣴⣼⣿⣴⣶⣷⣦⣴⣞⣄⣤⣷⣿⣽⣷⣾⣭⣥⣽⣿⣤⣽⣴⣿⣿⣾⣵⣧⣶⣶⣾⣶⣷⣯⣷⣦⣬⣧⣴⣷⣿⣿⣶⣶⣦⣶⣷⣾⣾⣿⣿⣮⣿⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛ ⠀⠀⠒⠄⠀⢀⠂⠰⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⡻⠃⠠⡤⢶⠄⠀⠤⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠶⠿⣿⣿⣶⣾⣷⣽⣧⣼⣤⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⡀⠆⠀⢑⠁⠆⠳⠓⠆⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣏⡽⠀⠠⠟⠹⠿⠋⢿⣿⣿⡹⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⣶⣷⣶⣦⣌⠁⠀⠀⠂⠀⠀⠐⠓⠀⠹⠏⠁⠀⠀⠀⠀⠀⠐⣿⣿⣿⣇⠉⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣆⣐⣄⣴⠄⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠉⢉⣭⣿⡷⢸⣶⣶⡶⢶⣶⣶⠀⠤⠤⠤⢤⣤⣤⣤⡤⢴⣾⣿⣿⣿⣷⣿⣿⡷⣿⣿⣶⠄⣴⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢘⣾⣽⣏⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠀⢰⣿⣶⣿⣿⣿⠁⠀⠚⠛⠂⠀⠒⠃⠀⠀⠒⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⡶⠏⠻⣌⠁⠛⣿⠛⠛⠛⠛⠛ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣀⡀⢀⡄⠀⠒⣶⣦⡀⠘⢡⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠒⣆⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⡄⠀⢀⡾⠀⠀⠁⠀⠀⢛⣿⢗⣤⣿⣿⣷⢿⣿⣯⠁⠫⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠆⠀⠀⠘⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⢯⣭⣿⡿⠿⠃⠉⢙⣿⡏⠀⠀⠀⢀⣀⢀⡀⣀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠈⠸⣀⣈⣿⣿⣆ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⣾⣿⣿⣿⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢿⡿⡉⠀⠀⠀⠀⣯⢰⡀⠀⠀⠀⢼⣶⣤⣶⣿⠄⠀⠼⠽⠙⠿⠿⠷⠡⠠⠄⠏⠍⠛⠿⠟⠋⣹⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠐⠀⢠⡍⠐⠰⣿⢴⡆⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠙⠿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⣸⡆⠀⢾⠀⠀⣴⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⡀⣿⠗⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠂⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⣾⣿⠆⠀⠀⠀⠀⢈⣿⣅⣀⢀⣀⣀⣀⣀⡀⠀⢠⠇⠁⠀⢈⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⣀⢠⠀⠸⢿⡿⠿⢿⡿⣿⣿⣿⠀⠘⠃⠀⠀⢸⠀⠀⠀⠀⠰⠂⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⢼⡡⠹⡄⣤⣽⣿⡤⠄⣀⣼⣿⡄⠀⢨⣥⠀⠀⣿⠆⠀⠀⢀⣰⡆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣿⣿⣿⣿⠈⠛⢿⣿⡅⠀⢸⡿⠀⠀⣾⠖⠦⠔⠊⠙⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⣦⣤⣤⣀⠀⠀⠀⠡⡹⣧⠀⠉⢿⡍⠀⠀⢀⣽⢷⣆⢺⡃⢀⠘⣋⣘⠏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⢀⣀⣰⠿⠇⠈⠀⠠⢄⡀⢈⠈⢷⡄⢘⣿⣤⣤⡼⠿⢿⣯⠿⠿⠀⠀⠉⠁⠀⠈⠘⣀⡃⡺⢤⣴⣦⠠⠿⢀⣼⠦⢠⡶⠀⠒⠛⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣺⣿⣿⣿⡆⢻⣞⢻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⣀⡒⢛⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣟⠃⣀⠀⡀⣿⣿⣿⣿⠃⠸⡿⢘⣿⣿⢿⣿⣿⣿⣿⡿⢿⣿⢿⣛⢿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠄⣁⡇⠛⡛⠣⠭⠉⢹⠘⠛⠚⢠⣭⡅⢹⣘⣛⠭⠇⡟⡟⢳⣿⣙⠬⠍⣮⡛⠛⠾⠯⢽⣿⢽⣟⡛⡂⢉⠌⠙⠘⠻⠲⢹⣾⣸⣻⢙⣙⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠀⠀⢃⣀⡁⢥⠐⢂⣐⣷⣿⡆⠛⠀⣄⠙⠂⣇⡈⣿⣿⣿⣿⠀⣿⡗⠛⣇⣀⣸⣿⣽⣶⢾⣛⡭⣿⡇⠁⠀⢰⢸⣳⠛⢳⣱⣶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠓⠂⠀⠈⢁⣺⣶⣚⣁⣐⣀⣠⣄⣄⣤⣾⠩⠤⠂⢧⣽⣿⣿⡏⠉⣰⡟⠷⣶⣦⣄⣤⣤⣿⣿⡿⠖⠀⠀⠑⠀⠘⠀⣢⣜⣂⣰⣾⣛⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⢠⣄⢀⣀⠀⡀⣠⣬⣿⢿⣯⣽⡻⣿⣿⠛⣷⣿⣯⣤⣤⡬⢾⣿⠻⢿⣿⣿⣯⣤⣽⣿⣿⣿⠿⣣⢽⣿⠡⠠⠠⠄⠠⠤⠠⠀⣿⣿⣿⣍⣿⡿⠿⣿⣟⡫⠿⡿⣻⣿⣿⣿⣿⣿⢿⡿ ⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠠⠀⠰⠄⣣⢿⠃⠀⠄⠘⠐⠂⣛⡇⠀⣶⣶⣙⣾⠿⣯⣿⣯⣿⠽⡏⢽⣯⣿⣾⡇⣾⣿⢒⣭⠁⠀⠅⠀⡂⠀⠀⠀⢀⠅⣿⣛⣃⣿⢯⣉⡿⠉⢀⣘⣐⠓⠾⢗⣲⣾⣿⣿⣟⣿ ⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⡄⠸⣀⣀⠰⣶⠄⠠⢴⣇⣀⢖⣒⡿⠯⣉⡻⣿⡟⠉⢀⡁⠒⠖⠈⢹⣷⢸⣯⢋⠛⢀⣀⠆⣀⠗⠒⠀⠀⡆⠁⣿⣛⣃⣉⡐⠀⠯⢨⢔⣓⣖⡧⣶⣶⣿⢙⣿⣿⣿⣿ ⣶⣶⣴⣶⣭⣦⣼⣭⣿⣭⣶⣦⣶⣖⣧⣴⣧⣶⣶⣯⣷⣿⣦⣦⣾⣯⣿⣿⣿⣿⣷⣷⣭⣭⣿⣯⣿⣶⣾⣦⣤⣼⣿⣿⣾⣿⣿⣶⣦⣶⣶⣷⣭⣷⣯⣽⣷⣶⣿⣿⣽⣿⣿⣶⣶⣿⣟⣮⣮⣶⣯⣿⣷⣿⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉ ⠀⠆⠂⠄⠀⢆⠀⠰⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠟⠠⠀⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠷⢷⢶⣿⠷⢾⣷⣴⣦⣰⣶⠻⣶⡄⠀⠀⠀⠀⠀ ⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠙⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢩⠑⠀⠀⠈⠛⠢⢸⣿⣿⡇⠿⣧⣽⣧⡀⠀⠀⠀⠀ ⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠⣀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠆⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠉⠻⡉⢿⣆⠀⠀⠀ ⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢠⡀⢀⢀⣖⢀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡏⠀⠀⠈⢉⣭⣿⡇⠀⠀⠰⣶⡾⣶⠶⣶⣶⡆⠀⠤⠤⣤⢤⣤⠤⠤⠤⣶⣿⣿⣿⣿⣶⣾⣷⢼⣿⣷⣶⣤ ⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⢻⡀⣼⣮⡹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⣿⣶⣿⣿⣿⠁⠀⠀⠀⠚⠛⠋⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⣀⣀⣀⣀⣠⣽⠷⠙⢧⡉⠘⢿⡿⠛⠛ ⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣀⠀⡀⠀⠀⢰⣶⣦⡾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣦⠀⠀⡼⠃⠀⠁⠀⠙⠛⣿⡿⠿⢾⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⢀⡀⠰⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⡈⠀⠀⠀⠀⠀⠀⠹⠿⢁⠀⠃⠽⣿⡿⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⣀⡉ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢰⣿⣿⣯⣽⣧⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢈⡀⠀⠀⠅⠀⢹⣿⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⠶⡶⠄⠀⠺⠿⠿⠿⠿⠧⠄⠀⠜⠺⠛⠙⠟⠉⠀⡀⠀⠀⠸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⢠⣏⠀⠀⠀⢠⡆⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣠⠏⠀⠀⠀⠂⠙⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⢤⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠇⠀⠛⠆⠀⠀⠀⠀⠈⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⠀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⠛⡀⠀⠀⠀⠀⠿⠿⡿⣿⣿⣿⣿⣿⡧⠀⠛⢀⠀⠀⡇⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢂⣠⣥⡄⠀⠀⠀⠀⠀⠀⢠⣄⣰⣿⣧⠀⠀⣬⡌⠀⢸⡧⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣘⡂⠀⠀⠀⠀⠀⠙⠿⢿⣿⠆⠀⡿⠃⠀⢸⡗⢲⠤⠂⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠂⠹⣿⡙⢩⡅⠀⠀⠀⠀⠀⠀⠀⢀⣿⡓⡒⠃⠀⡀⢛⣁⠻⠁⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠀⠀⠀⠀⠸⣇⢈⣇⠀⢀⠀⠀⠀⣤⣤⡯⠯⠿⠽⠟⠀⠀⠈⠉⠀⡘⣛⠃⢁⣰⢦⣤⣶⡆⠴⠄⣠⡏⠄⣴⠆⠐⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻⣧⢷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⢰⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⡀⣀⡀⢈⡙⡿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⠿⣛⣃⡀⢀⣀⢆⣈⠿⡞⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢙⣂⢙⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠏⣁⡇⠛⡟⠣⠭⠛⢹⢘⣻⣺⣨⣭⣹⣿⣘⣛⠿⠇⡿⡟⢃⣬⣿⡬⡍⣮⡟⠛⡿⠿⣽⣿⣽⣿⣿⡟⢛⠌⠹⠘⢻⣿⢹⣾⣼⣿⢹⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠚⢃⣀⠡⢥⠸⢗⣐⣿⣿⣿⣿⢤⣾⠿⠆⣇⡘⣿⣿⣿⣿⠀⣿⡇⠛⣟⣛⣻⣿⣿⣾⢾⣛⡯⣿⡇⠀⠀⢰⢸⣻⠛⢳⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠓⠂⠀⠈⠉⠺⣾⣛⣑⣲⣆⣠⣄⣥⡐⠘⠫⠥⣢⣧⣽⣿⣿⣯⠭⢰⡟⠷⣶⣦⣄⣥⣠⣿⣿⡿⠟⠀⠀⠓⠀⠈⢀⣪⣼⣂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠄⠄⠤⠠⠀⠤⠀⠠⢠⣄⢠⣄⣀⡀⣠⣤⣌⢻⣯⣽⡿⣿⣿⣿⣿⣿⣤⣤⣼⡿⢿⣿⣿⣿⡋⣠⣽⣥⢢⣿⣿⣿⡿⣯⣽⣿⠧⢤⠠⠄⠠⠄⣤⡀⢿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠌⠢⠀⠀⠀⠀⠀⠁⠸⡇⠸⠄⣣⢿⡇⠈⠔⠙⢛⠃⣛⡇⠀⣾⣿⣽⣾⣿⣿⣿⣯⣿⣿⣇⣿⣯⣟⣼⡏⣿⣿⢓⣿⡇⠈⠷⠿⢊⣉⠀⠀⢀⠇⠀⣿⣯⣿⢯⣉⡿⠉⢂⣘⣒⣗⡾⢗⣺⣿⣿⣿⣟⣿ ⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠈⠱⠇⠸⠀⡄⠸⣇⣀⢴⣶⣄⣡⢴⣇⣀⢞⣛⣿⣿⣭⣿⣿⠿⠿⢥⣷⢷⣖⣈⣽⣿⢸⣿⢏⠛⢇⣀⠆⣀⠗⠒⠀⠀⡆⠁⡀⣿⣇⣭⡍⠉⡯⢨⢔⣒⣖⡷⣶⣶⣿⣙⣿⣿⣿⣿ ⣶⣿⣴⣶⣭⣤⣽⣭⣯⣭⣶⣧⣶⣶⣧⣴⣥⣶⣮⣯⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⣬⣬⣴⣬⣼⣿⣭⣽⣿⣿⣯⣿⣶⣷⣯⣷⣯⣽⣧⣶⣿⣿⣿⣿⣿⣶⣶⣿⣿⣮⣾⣷⣯⣿⣵⣿⣷⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉ ⠀⠆⠂⠀⠀⢆⠀⠰⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡠⣶⢶⣲⣦⣾⣿⣿⣿⣿⣿⣿⢏⢐⣊⣔⡼⣦⢴⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡌⢿⣷⡽⣟⣻⣿⣿⣿⣴⣦⣴⣰⣺⣷⣄⡀ ⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠛⡗⠒⠚⢋⢻⠘⠝⠉⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⡯⠧⠺⠛⠽⠿⠻⠿⠋⣻⣿⡟⠋⣿⣽⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢿⣿⣿⣿⣾⣿⣿⣿⡿⠋⠁⠀⡀⠀⢠⣠⠶⣿⣶⣿⣦⣤⠀⠀⠐⠀⠂⠀⠰⠀⠀⠑⠀⠀⠛⠀⠀⠇⠐⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⢜⢩⠹⣿⣿ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢠⣀⣀⣡⣦⡤⣐⡰⣼⣿⣿⣿⣴⣿⣿⡿⠋⠐⠀⠁⠀⠀⢁⣧⠯⠀⢀⠧⢉⣿⣿⡇⠀⠀⠂⠶⠀⠰⣾⣶⣶⣶⣶⣶⡆⠠⠤⢤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣽⣷⣿⣋ ⠀⠀⠠⣤⡬⢄⡀⠀⠁⠀⠀⠀⢠⠀⠨⠄⢩⠆⣾⡽⢿⣿⣯⣏⣿⣿⣿⣿⡿⠋⠀⠀⠠⠀⠀⠀⠀⢸⠇⣀⣸⣿⣶⣿⣿⣯⠁⠀⠀⠀⠐⠒⠒⠘⠛⠁⠀⠽⠛⠀⠀⠒⠂⠀⠀⠀⣀⣀⣀⣀⣈⣠⣬⠝⣽⠷⡌⠉ ⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣅⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠰⡀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠈⠀⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣖⠀⢨⣿⣿⣿⠟⠻⣿⣿⣿⣯⣿⡋⠍⠄⠀⠀⠀⠐⠈⢄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠁⠀⢈⢻⣿⣿⣿⣿⣿⣏⠋⢿⠘⢩⡶⠀⢿⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣽⣿⣿⣿⣿⣧⠄⢸⡿⡿⠹⢿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠘⠏⠘⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢜⣯⣴⣦⣴⡾⠆⠰⣿⡿⠿⠿⠁⠧⠀⠀⠈⠙⠛⠖⠛⢛⣀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⠀⠉⠐⠈⠠⢯⠉⢿⣿⣿⢩⣭⡿⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠟⠛⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⢸⠋⣤⠈⠁⠀⠀⠀⠠⣂⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣲⣄⠀⢿⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⣀⠀⠀⡟⠀⠀⠀⡄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢼⡇⠀⠀⠰⣎⣅⣉⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⡟⠂⠀⢱⡇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⣯⠃⠐⢴⢶⣿⣽⡉⠀⠀⠈⠀⠀⢻⣶⣴⣭⣿⣞⠀⢰⣭⠆⠀⢾⡧⠀⠀⠁⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⡂⣿⠀⠀⠙⡻⠿⡿⠟⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣯⡄⢸⡿⠃⠀⢼⡗⣶⠴⠊⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠉⣿⡠⠀⢀⣿⡟⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣟⣗⡛⡃⢰⡀⣻⣕⠟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣰⣀⣐⢿⡇⢀⡆⢹⣇⣁⣀⢀⠀⢀⣀⡤⠈⢠⣤⣴⠿⡿⠛⠽⠿⠀⠀⠙⣉⢸⣿⣿⣃⣣⣰⠦⣴⣷⡆⢺⠄⣰⡯⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⡙⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣧⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣄⣶⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⢂⣁⠙⠛⠛⡿⣿⢿⡿⠿⣿⢿⠿⣿⠿⣿⣿⣏⣿⢄⠀⢀⣿⣿⣿⣿⡿⢿⣿⡿⢿⡿⠛⢙⠋⢘⣿⢿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠌⠅⢀⡝⠣⠿⢠⠝⠸⣿⠿⢌⣓⡈⠉⠾⢷⠿⡇⡶⠏⠋⠈⣽⡬⠍⠈⠉⠓⠮⠿⣟⣒⢹⣾⡷⠚⢓⠊⠹⠌⣩⢵⠠⠭⠄⠑⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠂⠀⠈⠂⠀⠡⢍⠘⠋⠈⣎⣉⣁⣀⢀⣺⠿⡆⣷⡎⠃⠀⢹⣿⠀⣶⡇⠀⣐⣒⣛⣛⣿⠗⠚⠻⠉⠛⠃⠁⠠⠠⠐⢲⠚⢒⢿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠁⠁⠠⠬⠁⠶⣂⣁⣀⣆⣼⣺⣿⣫⣤⣄⠧⠽⠇⣠⢬⣭⢸⣤⣄⣤⣈⣉⣹⣺⣿⠘⠿⠟⠀⠀⠀⠀⠐⢀⣃⣀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⢤⣀⠀⠠⠠⡀⣨⣠⣁⠀⣤⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣆⣼⣿⡸⣻⣬⣿⣿⣟⣿⢿⡻⣻⡡⢤⠠⣄⢀⣀⠀⠠⢤⡸⡿⢿⣿⣻⢿⣿⣽⣿⣿⣿⣽⡿⣻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢑⠀⢟⠀⠃⠀⠀⠠⠀⠠⠀⡣⢠⡆⠈⢥⣉⣝⠃⠭⡇⠈⣺⣿⣿⡅⠶⢾⣿⣿⣶⠀⢇⢋⣀⣽⣿⡟⣽⣛⠑⣿⡇⠈⠷⠿⢏⣉⠀⠀⠂⠇⠀⣶⣦⣉⠳⠿⠊⠁⢻⠯⣝⢏⠻⢭⠩⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⠀⠂⠀⠀⠀⠀⠂⠰⢇⣈⠑⠶⡄⠀⠀⠇⠀⢾⣿⣷⡶⠒⠆⡿⠳⣶⢶⣦⣷⣶⣘⣼⣶⣹⣿⡆⣉⣃⣀⠆⠀⢶⣶⠀⠀⠁⠃⠀⣒⣂⣹⡗⠀⠀⠀⢔⣀⡄⠟⠦⠋⠹⢙⢿⣿⣿⣿ ⣿⣻⣿⣶⣭⣦⣬⣭⣿⣭⣷⣴⣶⣴⣶⣤⣦⣶⣶⣦⣶⣿⣧⣤⣾⣮⣦⣶⣾⣭⣿⣿⣿⣿⣿⣮⣷⣦⣤⣤⣴⣬⣿⣿⣥⣿⣿⣿⣶⣶⣶⣶⣦⣷⣦⣤⣵⣴⣷⣿⣯⣿⣶⣶⣴⣧⣷⣥⣴⣾⣶⣦⣶⣶⣷⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠈⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠋ ⠀⠆⠀⠄⠀⢆⠆⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 5186 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/the-above-the-law-complex/#comments Gemini version at gemini://gemini.techrights.org/2022/02/07/the-above-the-law-complex/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Nobody_Should_be_Above_the_Law⠀✐ Posted in Europe, Law, Patents, Site_News at 8:48 am by Dr. Roy Schestowitz Video_download_link | md5sum 8fac8245e0f6ad5c568ad4b61870d0c8 EPO and Immunity Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/epo-immunity-issues.webm Summary: The EPO regime of Benoît_Battistelli and António_Campinos has demonstrated that immunity begets impunity, which in turn gives an incentive to commit crimes, making corruption the “norm”; if European_officials_fail_to tackle_this_problem, the EU too will be at risk due to legitimacy_problems THE “immunity complex” (or syndrome, unrelated to immune_complex) in Europe’s second-largest institution was_covered_here_last_night… with more to come regarding impunity tonight. Why is it that some people are effectively above the law? Is it a coincidence that officials who are above the law are placed there mostly to serve the financial interests of multinational corporations and oligarchs? What does that tell us about the state of the law in Europe? Seeing that Team UPC is pushing and compelling officials to do something illegal, shouldn’t they too be held accountable for incitement_to_break_the_law? “Why is it that some people are effectively above the law?”In any event, I’ve put my thoughts in the video above. Towards the end I show these_3_comments (3 at the time of recording) on a post mentioned_by_SUEPO_last_week, along with translations (“Translation is available in German, the French translation will follow soon”). █ ䷩ 𝚕𝚒𝚗𝚎 5240 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/07/the-epo-is-bleeding-in-courts/#comments Gemini version at gemini://gemini.techrights.org/2022/02/07/the-epo-is-bleeding-in-courts/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_EPO_is_Bleeding_in_Courts⠀✐ Posted in Europe, Patents at 7:59 pm by Dr. Roy Schestowitz Video_download_link | md5sum 11baf7038f147c5e9f122d2285ad9748 EPO Immunity Backfiring and Media is Silent Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/epo-immunity-and-media-deficit.webm Summary: The abuses of the EPO are causing an embarrassment; media in the pockets of the EPO’s management isn’t covering that, but sooner or later the truth will come out regardless Mondays are typically the time when we cover bigger stories because during the weekends there’s a sort of ‘backlog’ of developments. So far today we’ve published quite a lot about EPO President António_Campinos and his appointer, Benoît_Battistelli, whose legal of crime was covered up and moreover extended by Campinos. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Dr Evil Jesper Kongstad Laughing; Worst-case scenario: I move to another job⦈ There’s a bit of a positive development; aside from ILOAT confirming further violations, as we noted here the other day, the Office now admits culpability by paying over 4,500 EPO workers after wrong punishment, based upon unlawful regulations which should never have materialised in the first place. There’s a lot to be learned from all this; even Team UPC should take a moment to consider or reconsider what it’s trying to do by force-feeding an unlawful system, bound_to_explode for obvious_reasons. █ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢌⠱⡯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣅⠀⠀⠠⡀⠐⢢⣈⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣕⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢷⣿⣯⣭⣿⡅⠀⠞⠲⢕⠁⢀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣏⣩⣿⠛⡃⣀⣀⣀⣁⠎⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣞⣘⢧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣲⡾⠟⠛⣿⣿⣿⢿⣟⣗⣀⣟⣸⢿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣾⣿⣷⣿⡁⠀⠀⣤⣴⡾⠄⠙⣿⣿⣿⠟⢣⣼⣿⣿⣿⣿⣏⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⣸⣿⣿⣿⣟⠙⠁⠀⠀⠈⢩⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⣾⣿⣿⣇⣬⡀⠀⠀⠈⠄⠀⠀⠀⠈⢻⣿⡝⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣷⡄⢀⣿⣿⣷⣿⣟⣫⡞⠀⠀⠀⢠⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⠋⠈⠿⣿⣿⣿⠇⢾⠁⠀⠀⢀⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⠗⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠘⢿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠋⠸⠻⢥⣴⠤⢢⠀⠈⠋⠀⠈⠀⠀⠀⠌⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢾⣷⠙⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⠌⠀⠐⢷⣘⠅⢻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⠆⢽⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠀⠚⣰⠿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢢⣤⡈⣿⣼⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣿⣿⣿⠀⠀⠀⠀⠀⣀⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⣌⣿⠛⢸⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠁⠀⠀⠼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠔⡶⡅⠀⠀⠀⠃⠀⠀⠀⠤⠴⠄⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⢴⣿⡿⠿⠃⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⣤⡅⠁⠀⣡⣥⣨⣤⢁⢨⣧⠁⠈⡈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠌⠡⡯⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⣄⠀⢀⢤⣄⠀⣂⣩⡑⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⢿⣿⣯⣭⣿⡌⠐⡘⣹⣷⣏⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣁⣼⣟⠛⣇⣀⣀⣔⢫⡧⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢤⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⢻⣿⣿⣿⣮⢪⣧⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⢺⡾⠛⠛⣿⣿⣿⠿⡿⣗⣀⣜⠹⢿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣿⡄⠀⢀⣤⣶⣿⠀⠙⣿⣿⡿⡟⠃⣤⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠀⠀⠀⢸⣿⣿⣿⣟⢉⠁⠀⠁⠀⠁⣿⣯⡿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣴⡄⠀⠀⠉⠁⠀⠀⠀⠈⢿⣿⡌⠀⢹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡄⢀⣿⣿⣿⢻⣟⣫⡞⠀⠀⠀⢠⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⢸⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠿⣿⣿⣿⠇⢼⠁⠀⠀⢀⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⠟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠈⢿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠋⠸⠻⣥⣴⢤⢢⠁⠉⠋⠀⠈⠀⠀⠀⡈⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣼⣷⠙⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⠄⠀⠐⢷⣘⠁⢻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⠆⢹⣿⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⠀⠚⣰⠿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢠⣤⡈⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣀⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⣼⡿⠟⢹⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠛⠁⠀⠼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠴⡶⡅⠀⠀⠀⠃⠀⠀⠀⠤⠴⠄⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⡿⠃⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣮⣤⡅⠁⠀⣡⣥⣨⣤⢁⢨⣧⠁⠈⡌⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠰⡯⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⣄⠀⠀⡄⠄⠀⢢⢨⠙⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣎⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⣿⣿⣥⣭⣶⡀⠀⢠⠨⠠⠨⠅⢢⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣮⣠⣿⡟⢻⡇⣀⣀⣠⢫⡄⣳⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠹⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⢄⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃⣿⣿⣿⣯⠻⡵⡑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣭⢲⡾⠛⠛⣿⣿⢿⠿⡿⡛⣀⡈⢹⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡅⠀⢀⣤⣶⡿⠀⠙⣿⣿⡿⡿⠓⣤⣿⣿⣿⣿⣿⣰⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⣸⣿⣿⣿⣟⣙⡍⠀⠀⠈⠉⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣡⡄⠀⠀⠈⠀⠀⠀⠀⠈⢿⣿⡌⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠀⣿⣿⣿⣿⣟⣛⡴⠀⠀⠀⢐⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⢸⣿⣿⡯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠋⠈⠻⠿⣿⢿⡗⢸⠃⠀⠀⠀⣘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⢻⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁⠊⠸⠻⣥⣶⠤⢢⠁⠀⠘⠀⠈⠀⠀⠀⠀⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⢸⣷⠙⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⠄⠀⠀⢷⣘⠁⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⠆⠘⣿⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⠀⠚⣴⠿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡟⢰⣤⡈⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⣌⣿⠿⢹⣿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠁⠀⠼⣿⡿⣿⣿⣿⠿⣿⣿⡿⠿⠛⠛⠃⠀⠀⠀⠴⡶⡅⠀⠀⠀⠃⠀⠀⠀⠤⠴⠄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⡿⠃⠀⠈⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⢨⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⡅⠁⠀⣡⣥⣨⡤⢁⢨⣧⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠰⠯⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⡄⠀⢀⠠⡄⠒⠠⡨⠙⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣤⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣧⣷⣷⣶⡀⠀⠀⠋⣵⠰⡃⠢⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣼⣿⠛⢻⢃⣀⣀⣁⢠⣂⣰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣦⡅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠃⣿⣿⣿⣮⡛⠻⣑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡭⣶⡟⠛⠛⣿⣿⢿⡿⣿⣛⢂⣬⠙⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣾⡄⠀⢀⣤⣶⡿⠀⠙⣿⣿⠿⡟⠑⣤⣿⣿⣿⣿⣿⣾⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠀⠀⠀⢸⣿⣿⣿⣿⡛⡏⡀⠀⠉⠈⣿⣿⣵⠾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣷⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡜⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡄⢠⣿⣿⣿⡿⣿⣛⣵⠀⠀⠀⠀⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡔⢸⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⢿⣿⡿⠃⠈⠟⢿⡿⢿⡟⢸⠇⠀⠀⠀⣜⡅⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⢻⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠉⠸⡻⣤⣶⢄⢆⠁⠀⠘⠀⠈⠀⠀⠀⠀⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢸⣷⠙⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡧⠀⠀⠰⢗⣚⠁⢺⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠻⣿⣧⣿⣷⣾⠀⠀⠠⠔⡂⠱⠅⡨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣼⣿⠛⣻⢂⣀⣈⣁⡈⢨⢡⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⡀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⠁⣿⣿⣷⣷⡜⢵⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡴⣶⠛⠛⠻⣿⣿⢿⡿⢿⣿⣣⡤⠛⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣾⣇⠀⢀⣴⣶⡿⠀⠙⣿⣿⡿⡟⠑⣤⣿⣿⣿⣿⣿⣿⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠏⡀⠀⠀⣿⣿⣿⣿⣿⡛⡋⠉⠁⠈⠀⣽⡿⣣⡾⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⡌⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⠀⢠⣿⣿⣿⣯⣿⣟⣥⠃⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢸⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⢿⣿⡿⠁⠘⠛⣟⣿⣿⡿⢠⡏⠀⠀⠀⣼⣫⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⢻⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠁⠘⡯⣤⡶⢔⡄⠀⠘⠁⠁⠀⠀⠀⠀⠀⠉⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢸⣿⠙⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡧⠀⠀⠸⠇⡫⠘⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠠⣴⣦⣤⣿⠂⠘⢻⣆⣄⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠃⡼⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡟⢠⣤⠈⣿⣿⢿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣠⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠰⡀⢠⣿⡟⠃⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠇⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣯⠈⠋⠁⠀⠀⠀⠠⢴⡶⡅⠀⠀⠀⠀⠀⠀⡀⠤⠔⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣾⣾⣿⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⡿⠃⠀⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣥⠁⠀⣥⡥⣨⡄⢁⢸⡧⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⠀⠀⢀⠀⠂⡈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⣶⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠻⣿⢗⣷⣶⣾⠀⠀⠀⠐⡃⣀⡐⠏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⣿⡋⢹⡂⢄⣀⣁⡪⣯⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⡄⡀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⠁⢹⣿⣿⣶⡜⢫⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡴⡶⠻⠛⠻⣿⣿⣿⣿⣿⠿⣿⣛⣤⣌⣻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣶⡆⠀⢀⣤⣶⡞⠀⠹⣿⡿⠿⡟⠁⢴⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⢛⠉⠁⠀⠈⢿⣿⣟⣰⡶⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣏⡤⠀⠀⠁⠀⠀⠀⠀⠘⣿⣿⡌⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⡀⣠⣿⣿⣿⣿⣿⣿⣟⣋⡼⠀⠀⡀⣴⣯⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠁⠘⠿⠿⣿⣿⣿⣿⠇⣼⠁⠀⠸⢡⣋⣭⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡟⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⢻⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠛⠻⠮⠖⣖⠄⠀⠚⠙⠁⠃⠁⠁⠀⠀⠂⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢸⣿⠙⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠿⠀⠀⠀⣘⡀⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣿⠂⠈⣹⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠟⢛⡏⠐⠀⠂⣴⠟⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡟⠀⠀⡈⠛⣹⣿⢻⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠑⢐⠛⢽⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢈⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⣿⣿⢿⣿⣿⠷⠠⠀⠐⠈⠂⠀⢠⠶⢈⠅⠀⠀⠀⠀⠀⠀⠠⠤⠶⠂⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣾⣾⣿⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⢴⡾⣿⡿⠃⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠌⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣦⡅⠁⠀⣡⡥⣬⡀⠀⡾⠅⠀⠀⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢌⠱⡭⡻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⠀⠀⠀⡠⠂⢈⠑⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⣿⣿⣷⣿⣶⠀⠀⠀⠰⠓⣎⠌⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣯⣠⣿⡋⢹⡊⢀⣈⣥⣪⢲⣭⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⡦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⡑⢸⣿⣿⣿⣦⠣⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣲⠾⠿⠛⢿⣿⣿⣿⣿⣿⡿⣿⣿⣏⣀⣽⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣷⡆⠀⢀⣤⣶⡿⠀⠙⣿⣿⡿⡿⠣⢰⣾⣿⣿⣿⣿⣿⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣟⡙⡋⠉⠀⠁⠟⣿⡿⡉⠠⡶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣏⡤⠀⠀⠈⠀⠀⠀⠀⠘⣿⣿⡌⠀⢀⣹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⢼⣿⣿⣿⣷⣾⣧⡄⠀⣼⣿⣿⣿⣿⣿⡟⣿⣛⣵⠃⣠⣿⢰⣟⡱⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠁⠀⠿⠿⡿⢿⣿⣿⣷⡟⢰⠋⢀⡿⢋⢿⣟⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡿⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢻⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⠛⠂⠛⡆⠆⠀⠃⠘⠺⠟⠘⠌⠈⠀⢸⡇⡘⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⣿⢈⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⡃⠀⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⣿⡂⠀⢹⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢿⠃⡆⠀⠀⡾⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠃⢀⣿⠀⣴⣏⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡺⢿⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⢬⠿⢿⠟⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣇⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠒⠒⠊⠁⠀⣤⠄⠨⠃⠀⠀⠀⠀⠀⠀⠠⠴⠶⠂⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⢴⣾⣿⡿⠁⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣦⠁⠁⠀⣡⡥⠈⠀⢠⠌⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢠⢀⠁⢀⢌⠱⡯⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢎⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⠄⠀⠄⣑⠠⠈⠙⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⣿⣿⣷⣾⣮⠐⠐⠒⠈⠠⢀⡈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣤⣿⡋⢹⡚⠁⣨⣵⣎⣾⣾⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⡁⠈⣿⣿⣿⣧⢛⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣶⠾⠟⠻⢿⣿⣿⣿⣿⣿⡿⢿⢿⢛⣤⣽⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⡆⠀⣠⣤⣶⡿⠀⠙⣿⣿⡿⡿⠇⢮⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⢀⣿⣟⡿⣿⣿⣿⣿⡛⡛⠁⠁⠀⡟⣿⡿⡋⢀⡦⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⡤⠀⠈⠉⠀⠀⠀⠀⠘⢿⣿⡜⠄⢀⣸⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣷⣾⣧⡀⢠⣾⣷⣿⣿⣿⣿⣿⣿⣛⣥⠃⣴⣿⢰⣟⠹⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⢿⣿⣄⠸⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡟⠁⠘⣿⢟⡛⠻⠿⢿⣿⡿⢰⠇⢰⡿⢋⣿⣟⣥⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡿⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠋⠪⠓⢴⠌⠁⠀⠀⠚⠘⠉⠑⠈⠀⢸⠇⡸⠋⠀⠀⠀⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣐⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⣿⡂⠀⢘⡿⣿⢿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡋⣿⣿⠁⠆⠀⢠⡟⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠃⢄⣼⡇⣠⣆⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⡞⢻⡄⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⠀⢀⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⢷⠶⠿⠟⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣯⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠒⠓⠋⠁⠀⡄⠀⠨⠂⠀⠀⠀⠠⠄⠀⠠⠶⠞⠃⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣿⣾⣿⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⢴⣿⡿⡿⠁⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡄⠁⠁⠀⣡⠅⠈⠀⠉⠨⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢈⠹⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⢀⠀⠄⠑⣠⠻⡽⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠿⣿⣯⣴⣾⣯⠀⠀⠄⠉⡸⠠⠊⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣠⣿⡋⢹⡲⠀⣄⣴⣎⡗⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⢄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠑⠁⣿⣿⣿⣷⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢲⠾⠟⠛⢿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣥⢸⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣾⡆⠀⣠⣤⣶⡿⠀⠙⣿⣿⡿⡿⠇⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⢈⣿⣟⣿⣿⣿⣿⣿⣛⣻⠉⠁⢀⡟⣿⣿⡋⠀⡤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣯⡄⠀⠀⠈⠀⠀⠀⠀⠘⢿⣿⡌⠄⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣾⣧⡀⢀⣼⣷⣿⣿⣿⣿⣿⢻⣛⣵⠇⣼⣿⢰⣿⡓⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⢺⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡁⠘⣿⣿⠻⠿⣿⣿⣿⡿⢠⠏⢼⡿⢏⣟⣟⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⡟⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⢹⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠛⠃⠛⢳⠰⠈⠁⠄⠀⠛⠛⠁⠁⠈⠀⣽⠇⣘⠋⠀⠀⠀⡰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠸⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⣀⠀⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣶⣿⡆⠀⢩⣿⢿⡿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢹⢿⣿⢁⠀⠀⢠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠃⢄⣿⣿⣌⣼⢇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⢿⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⠀⠀⢀⣀⠘⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⢳⡶⠾⠟⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⢸⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠇⠐⠒⠃⠋⠀⢠⠠⠄⠝⠀⠀⠀⠀⠸⠆⠀⠀⠶⠛⠃⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠆⢶⠄⢴⣿⣿⠿⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⡄⠁⠁⢀⢡⠅⠈⠀⡁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢌⠰⠬⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢈⠅⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⡄⠀⠀⠈⢄⣀⠠⢸⠽⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡚⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠿⢿⣧⣴⣾⣯⢐⠂⠀⡂⡱⣠⡪⠜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⣿⣏⢹⡢⡂⢔⣉⣥⣢⣙⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⢄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠁⠈⢸⣿⣿⣿⣦⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠔⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣾⣷⣾⡆⠀⢀⣴⣶⣷⠀⠙⣿⣿⡿⡿⠫⠄⢲⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣛⣻⠉⠑⣀⡟⣿⣿⡋⢀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢧⡄⠀⠀⠈⠁⠀⠀⠀⠈⢿⣿⡌⠀⢀⣠⣿⣿⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣿⣿⣾⣧⠀⢀⣾⣿⣭⣶⣿⣿⣿⢻⡟⣯⢏⣼⣿⢰⣿⡇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⡿⣿⣿⣏⠀⠘⣽⢟⣿⠻⢿⣿⠿⡾⡃⠏⣼⡿⢏⣟⣟⣦⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⠟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠛⠃⠙⢳⠰⠈⢋⠅⠀⠸⠋⠁⢩⠁⠀⣿⠃⡸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡀⠀⠸⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣶⣶⣿⡇⠀⢸⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠏⢿⣿⣿⢰⠀⠀⢨⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠃⢤⣿⣿⣿⣀⡶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣻⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣅⡄⠀⠀⠀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠹⡶⠶⠾⠈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠿⢿⢻⡇⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⣄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠐⠚⠋⠉⠀⢠⠀⠀⠝⠀⡂⠀⠀⠠⠀⠀⠐⠾⠛⠃⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⣴⢿⣿⠿⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⡌⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⠀⠁⠁⢀⠥⠁⠈⠀⡅⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢌⠸⢯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠹⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣶⣶⠄⠀⠀⢈⠀⢐⠠⠸⡳⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⢿⢧⣾⣿⣧⠀⠀⠐⡊⣐⠘⠲⢞⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣤⣿⣏⣹⡕⢄⣆⣁⣤⣜⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣶⡶⢄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠌⠀⠀⣿⣿⣿⣧⢱⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠔⠿⠿⢿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣧⣸⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⣾⣷⣾⡄⠀⢀⣤⣶⣷⠀⠙⢿⣿⣟⣟⠁⡄⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣛⣻⠉⠁⢠⡟⣿⣿⡋⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣣⡄⠀⠀⠈⠀⠀⠀⠀⠈⢻⣿⡌⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣧⠀⢀⣼⣿⣾⣿⣿⣿⣿⢹⡟⣯⣿⣼⣿⢰⣿⠧⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⠀⠙⣿⣿⣿⠿⣿⣿⡿⡾⡃⠏⢾⡿⢧⢟⣟⣤⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⠿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠛⠑⠙⢱⡲⠈⢙⠇⠀⠙⠙⠁⢨⠁⠀⣿⢁⡜⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠀⠀⢀⡀⠀⢸⡅⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣿⡇⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠧⠿⣿⣿⠀⠀⠀⢨⠂⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠃⢤⣿⣿⣿⡅⣰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣯⡀⠀⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⡶⠾⠿⠈⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡛⡿⠿⣿⢻⠃⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠅⠀⠚⠋⠈⠀⠤⠄⠀⠕⠀⣃⠀⠀⠠⠀⠀⠐⠾⠛⠂⢺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠤⣴⢿⣿⠷⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣷⣬⣮⠄⠁⠁⡀⣥⠁⠈⠀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰⠬⡻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⣶⠀⠀⠀⠀⡀⢀⠀⠈⠵⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡕⣴⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢛⡿⠃⣿⣿⣇⠀⠀⠐⠂⡠⢄⡌⢚⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡊⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣦⣾⢆⢠⠈⣀⣼⣽⡞⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⢄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡏⠀⠀⠁⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠔⠿⠻⢿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣧⣨⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⣾⣷⣾⡄⠀⢀⣤⣶⡧⠀⠙⢿⣿⣟⣍⠅⡦⠐⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡁⠀⠀⠀⣻⣿⣻⣿⣷⣿⣿⣛⣻⠉⠑⣀⡟⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⢧⡄⠀⠀⠈⠀⠀⠀⠀⠈⢻⣿⡌⠀⠀⣀⣸⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣧⠀⢀⣼⣾⣻⣿⣿⣿⣿⢻⡟⣯⣾⣼⣿⣸⣿⠣⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⠀⠘⣿⣛⡿⠟⣿⣿⣿⡾⠃⠯⣾⡿⢳⢿⣟⣤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⠿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠛⠁⠙⢱⡒⠀⠉⠉⠀⠊⠛⠁⠠⠁⠀⣿⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠛⠀⠀⢀⡀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣼⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠧⠿⣿⣿⠐⠀⠀⢨⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠤⣾⣿⣿⡇⢠⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠲⠾⠿⠈⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⠛⡿⠿⣿⢻⠁⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠄⠁⠒⠋⠉⠀⠄⠄⠀⠇⠀⣀⠀⠀⠢⠄⠀⠐⠿⠋⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠤⣴⢿⡿⠗⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠌⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣮⣬⠀⠁⠁⡠⣥⠁⠈⢀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠡⠀⢌⠰⠬⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠈⣇⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⢛⣿⣅⠀⠀⠀⠀⠀⡀⠠⣨⠹⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⣐⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠙⣻⡿⢹⣿⠿⡄⡀⡀⢀⠀⣂⣤⡁⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡎⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣿⠫⠆⣠⢄⣭⣌⡝⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣤⣶⠶⢄⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⡇⠄⡨⠁⢸⣿⣿⣿⡤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⡔⠿⠿⠿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣧⣨⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⣾⣿⣾⡄⠀⢀⣤⣶⣧⠀⠙⢿⣿⣟⡌⠂⡧⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠋⡁⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣝⣻⠉⠑⣀⡟⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⡄⠀⠀⠈⠁⠀⠀⠀⠀⢻⣿⣌⠀⠉⣀⣨⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣼⣿⣚⣿⣽⣿⣿⢻⡟⣷⣯⣼⣿⣼⣟⠏⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣺⣿⣿⡿⣿⣿⣏⠀⠙⣿⣿⣿⠛⢿⣿⣿⡾⡂⢯⣾⡿⣱⣯⣿⣤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠛⠁⠙⢱⡒⠈⠋⠇⠀⠂⠙⠁⢠⠀⠘⡟⢀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⠟⠀⠀⢀⡀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠈⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⠿⣿⡽⠀⠀⠀⢨⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡟⠰⣸⣿⣿⡇⢨⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡥⠀⠀⡀⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠶⠿⠿⢀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⠛⡿⠿⣿⢺⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣤⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠄⠂⠒⠋⠁⠀⠤⠄⠨⠃⠀⡀⠀⠀⠶⠀⠀⠒⠛⠋⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠤⣴⢿⡿⠗⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⢨⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣮⣬⠀⠁⠁⡠⡅⠁⠈⢠⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢀⠍⠠⠑⡴⠮⠟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣭⣭⡀⠀⠠⢥⣄⡙⠠⠅⠂⠗⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠳⠭⣲⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣽⣿⣏⣿⣿⢳⣀⠎⠥⠢⢰⣖⠏⢣⣋⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠕⠧⢱⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠧⠄⠲⠐⣈⣞⣏⣅⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠺⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⢄⡀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⢿⡏⡀⢁⠤⠁⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡦⠸⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣁⠀⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣶⡇⠀⠀⢠⣶⡷⠀⠈⠻⣿⡟⡕⠁⠁⠠⢲⣶⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠏⠁⠀⠀⠀⣹⣯⣻⣿⣷⣿⣿⣝⣻⠉⠁⠈⡿⣿⣿⠟⠁⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣧⡅⠀⠀⠐⠈⠀⠀⠀⠀⠙⢿⣄⠀⠨⢀⣀⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣰⣿⣽⣿⣿⣿⣿⢿⣻⣿⣧⣴⡿⣼⡿⠃⡀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠈⢿⣿⢻⠝⣿⣿⣿⡾⢡⢯⣿⠿⣽⣫⣿⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡟⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠛⠃⠙⢑⡒⠀⠹⠗⠀⠟⠙⠃⢨⠈⣿⡏⢰⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡀⠂⠸⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠑⠚⣿⡿⠰⠀⠀⢸⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⡧⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠆⣙⣿⣏⢻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣣⠀⠀⠀⠐⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠿⠾⠁⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⠿⣿⠺⠀⠀⠀⠀⡀⠀⡦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⡿⣿⠿⠄⠃⠒⠛⠀⠀⠤⠄⠨⠃⠀⡇⠀⠀⠶⠄⠀⠚⠛⠑⠿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠤⣴⢿⣿⠟⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⢈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣬⣬⠀⠁⠁⡤⡅⠁⠈⢠⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠍⠠⠕⣾⡮⣽⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣭⣭⡀⡀⠰⢭⡐⡁⠡⠥⠦⣝⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠪⠮⣲⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣏⣿⣿⢳⣀⠦⠩⠠⢠⣐⣕⢣⡃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⢱⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠧⢄⢢⠀⠝⣯⣎⣼⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠺⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⢄⡀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⠿⡻⡀⢀⠬⠀⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡦⠸⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣅⠀⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣶⣇⠀⠀⢠⣶⣷⠀⠈⠻⣿⡏⡝⠁⠅⠬⢲⣶⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠁⠀⠀⠀⣸⣿⣿⣿⣷⣿⣿⣟⣻⠉⠑⠈⡿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣧⡅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠩⢄⣈⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣰⣿⣿⣿⣿⣿⣿⢿⣻⣿⣧⣴⡿⣼⡿⡓⡀⠈⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡁⠘⢿⣿⣿⠻⣿⣿⡿⡾⢡⢯⣿⡿⣹⣫⣿⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠛⠃⠙⢑⡒⠈⢹⠝⠀⠉⠋⠁⢠⠈⢿⡏⣴⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣿⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⠚⣿⡟⠰⠀⠀⢨⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠆⣹⣿⣏⢻⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣣⠀⠀⠀⠐⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⢠⡤⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠿⠾⠁⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⠿⣿⢻⠀⠀⠀⠀⡀⠀⡦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⡿⡿⠿⠄⠃⠒⠛⠀⠀⠤⠄⠨⠃⠀⡇⠀⠀⠶⠄⠀⠚⠛⠑⠿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠤⣴⢿⣿⠟⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⢈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣬⣬⠀⠁⠁⡤⡅⠁⠈⢠⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠠⠀⠈⢑⢀⠼⠿⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⡀⠈⠀⡂⢔⢂⣼⡐⡕⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣺⡲⣼⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣯⣿⣿⣱⡀⠒⠀⠀⡢⡚⢏⠵⢞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡟⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡷⠐⠀⡁⣀⣄⣷⣅⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣄⡀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠿⠓⠐⢘⡉⠀⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡔⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣠⡰⢿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣾⡆⠀⠀⠠⡶⠷⠆⠀⠙⢿⣟⡀⢤⢑⠑⣲⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡁⠀⠀⢘⣿⣿⣿⣾⣿⣿⣻⠋⠉⠑⣲⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣥⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠂⣀⣠⣼⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⡟⣤⣾⣧⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡹⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⢻⣿⣿⠻⣿⣿⣿⠃⡾⣼⡿⢏⣾⣽⡯⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡟⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠛⠚⠟⡲⡂⠙⠝⠀⠇⠛⢠⠇⠹⣿⢃⡾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣀⠹⣿⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠁⠀⠀⢀⠐⠀⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⡏⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠆⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠯⠀⣿⠃⠆⠀⠰⠕⠁⠀⢺⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢣⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣖⢻⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠻⠟⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⡯⠡⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣿⡿⡿⣿⣿⠿⣿⠿⠇⠀⠍⠅⠁⠀⠠⢠⠂⠝⠀⠿⠀⠀⠤⠀⠐⠚⠛⠸⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⣴⣿⣿⡿⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣧⣬⣬⡀⠁⠁⣠⡥⣥⠈⠀⡗⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⠢⠉⠈⠥⢸⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠩⡁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣯⡄⠀⠀⠀⡆⠐⠅⠸⠸⣳⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣢⢇⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣹⣿⡙⡀⠀⠀⠀⣐⠥⠂⠐⠞⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⡃⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⣿⣿⢟⠀⠠⡨⣦⣥⣷⣂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⠝⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣄⡀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠿⠗⡀⢚⠁⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣶⠽⠿⠻⣿⣿⡿⣿⣿⣿⣿⣅⣄⠼⢿⣿⣿⣿⣴⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣾⣇⠀⠀⠠⠶⠷⠆⠀⠙⢿⣏⡄⠐⢀⡀⣶⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠂⠀⠀⣿⣿⣷⣿⣿⣟⣟⠙⠉⠃⢰⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠒⣀⣃⣿⣿⣷⣦⣾⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣼⣿⣿⣿⣿⣿⣿⣵⢋⣴⣾⣧⣿⣯⡅⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡹⣿⣿⣿⡗⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡁⠘⣿⡟⢏⣿⣿⢟⣰⢇⣾⣿⣟⣾⣽⣯⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⡿⡳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⡿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠙⠓⢻⠓⣖⠈⠙⠐⠉⠀⢸⠀⠪⣿⠇⣼⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣸⣀⢻⣷⠘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⠇⢱⡿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠄⢻⣼⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠋⢘⡇⠀⠀⢁⣾⠎⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⠸⢻⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣶⠚⡆⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠞⢻⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣠⠉⠀⠀⠀⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣧⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡧⠈⠿⠿⠿⣿⣿⠿⣿⡿⠇⠈⠻⠿⠃⠀⠀⡔⠒⠉⠁⠨⠀⠀⠀⠀⠰⠟⠛⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠎⢶⠄⢰⣶⣿⡿⠃⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢀⣶⣿⣾⣾⣾⣾⣾⣶⣥⣬⣬⡄⠁⠁⢠⣥⢥⡌⠁⢱⠊⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢄⠠⠉⠈⠥⠼⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠼⡁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣯⡄⠀⠀⠀⠀⠐⠷⠪⠸⡳⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⡀⢇⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣹⣿⡙⡀⡀⠀⠐⣐⡭⢂⡑⠚⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢓⠇⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⣿⣿⡟⠀⠠⡨⣆⣥⣥⣂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢿⣿⣿⣿⣿⠝⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣄⡀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠿⠗⡀⢚⠁⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⡶⠽⠿⠿⣿⣿⡿⣿⣿⣿⣿⣅⣄⠼⢿⣿⣿⣿⣴⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣾⣇⠀⠀⠰⡶⠷⠆⠀⠙⢿⣟⡄⠐⢀⣀⣶⣿⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠂⠀⠀⣿⣿⣿⣿⣿⣿⣟⠙⠉⠇⢰⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠂⣁⣀⣽⣿⣷⣦⣾⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣼⣿⣿⣿⣿⣿⣿⣵⢋⣴⣾⣧⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡹⣿⣿⣿⡗⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡁⠘⣿⡿⢟⣿⣿⢟⣰⠇⣾⣿⣏⣾⣽⣯⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⡿⡳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⡿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠙⠓⢻⠓⣖⠈⠑⠀⠋⠁⢸⠀⠪⣿⠇⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣸⣀⠹⣷⠘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⠇⢱⡿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠅⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⣿⣿⠄⢻⣼⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡋⢘⡇⠀⠀⢁⣾⠎⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⠲⢻⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣶⠒⡆⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⢰⣯⡄⠀⢀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠞⢻⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣠⠉⠀⠀⠀⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣧⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠿⠿⠿⣿⣿⠿⣿⡿⠏⠈⠻⠿⠃⠀⠀⡔⠒⠉⠁⠨⠁⠀⠀⠀⠰⠟⠛⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠎⢶⠄⢰⣶⣿⡿⠃⠀⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢀⣶⣿⣾⣾⣾⣾⣾⣶⣥⣬⣬⡄⠁⠁⢠⣥⢥⡌⠀⢱⠊⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰⠾⡾⡛⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣭⣅⠀⠁⠠⠗⢔⣀⠆⠂⡙⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠰⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣟⣸⣿⡛⡆⠀⠀⠀⢀⡣⡖⠡⡝⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⠟⠀⢠⢐⣤⣷⡠⢆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠺⣿⣿⣿⣿⡋⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢄⡀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⡿⡗⢘⠋⢸⣿⣿⣿⡄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⢵⠶⠟⠛⢿⣿⣿⢾⣿⣿⣿⣯⣠⣄⠾⢿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣶⣇⠀⠀⡠⠶⠷⡆⠈⠙⣿⣏⠄⠄⠠⢱⣾⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⢸⣿⣿⣽⣿⣿⣻⠋⠉⠉⠢⢸⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣬⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⢂⣈⣸⣿⣿⣦⣴⣿⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⢀⣼⣿⣿⣿⣿⣿⢻⡾⠁⣴⣾⡇⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠻⣿⣿⣿⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢋⠈⢿⡯⢹⣿⡇⢇⠰⠁⣼⣿⡟⣸⣿⣛⣅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢹⣿⢿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠙⠛⠺⡟⢒⡂⠉⠀⠈⠀⠃⠀⠀⢈⡟⢠⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢿⡆⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢀⡸⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⠃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⠘⣷⣢⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣟⡀⠉⠸⠀⠘⣴⡟⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣄⢿⡹⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⣿⠖⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠖⠯⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⡃⠀⡄⠀⠀⢀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢘⣿⣄⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠻⠿⠿⣿⡿⠿⣿⡿⠏⠈⠿⠿⠃⠀⠀⢦⠶⠪⠁⠀⠸⠀⠀⠀⠴⠶⠂⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⠰⣶⣿⣿⠛⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣬⣬⣄⠁⠁⢠⣥⣕⣮⠄⠀⣾⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠁⠄⢄⢤⢌⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣿⣿⣭⣅⠀⠀⠀⠀⠐⠤⠼⡰⢐⢬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡥⢴⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⣻⣿⠛⡆⠀⠀⡀⠠⠄⢲⡠⢝⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⣿⣿⣿⣿⡟⠱⡄⢂⣷⣠⡑⡱⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⡿⣿⣿⣿⣟⡗⠅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠿⠗⡸⠃⣿⣿⣿⣷⣔⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡽⢶⠛⠛⠛⣿⣿⣿⡿⣿⣛⣿⣭⣤⠀⣿⣿⣿⣿⣯⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣶⣮⠀⠀⠴⠾⠿⠆⠈⠙⣿⣯⠄⠅⠀⣶⣿⣿⣿⣯⣥⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠍⠀⠀⠀⣸⣿⣟⣿⣯⣟⡿⠉⠉⠈⢂⢸⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣬⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⢂⣃⣸⣿⣿⣦⣴⠿⢿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣀⠀⣿⣿⣿⣿⡟⣟⣿⡞⠀⣴⣿⡇⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢻⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠀⢻⡏⢹⣿⠧⠇⡾⠀⢼⣿⡿⣰⣯⣟⣁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⠙⠛⠺⠿⢰⢂⠀⠀⠍⠀⠃⠀⠀⠸⡿⢀⠯⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣿⡈⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀⢀⣀⠁⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣿⣿⡷⠙⣃⢠⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣏⡀⠉⠸⠀⠐⢠⡿⠃⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠯⡀⣿⣸⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⡖⠃⠀⠀⠀⠀⠀⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⣲⡀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⢟⠿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠹⠿⠿⣿⡿⠿⣿⠿⠏⠘⠿⠿⠋⠀⠀⠠⢰⢊⠅⠀⠀⠅⠀⠀⠴⠶⠂⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⢿⢛⣿⠿⡀⢀⠀⢙⠆⣤⣸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⠷⠀⡀⣊⠈⢟⣿⣽⡫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠚⡙⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⡤⡀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⠆⠜⠼⡟⠁⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⠟⠙⣿⣿⣟⣻⣿⣭⣤⠰⡃⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⣠⣴⣶⡇⠈⢿⣿⣿⡫⣭⣧⣼⣼⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡀⠀⣼⣾⣽⣛⡿⠋⢉⠈⠁⢠⡼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣾⣿⣿⡧⡴⠀⠈⡏⠉⠀⠀⠀⠙⣿⣷⡄⢠⣤⣤⣴⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⢛⣩⡾⠃⠀⣶⣿⢷⡿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⢿⣿⣿⣿⣿⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠣⠀⣙⡿⠟⠞⠰⠁⠀⢸⡿⢏⣞⣵⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⢟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⢹⣿⣿⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠋⠃⣻⣇⠒⡻⠛⡅⠀⠀⠀⠀⠀⠘⠇⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⣿⣿⠈⠻⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⡀⠂⣾⢗⠚⣥⠆⠀⡧⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣦⠘⠻⣿⣷⠄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠈⠀⠹⣋⡾⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡅⠀⠀⠈⠃⠀⠘⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⢠⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⠀⠀⠀⠘⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢙⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣸⣄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠉⠀⠀⠀⠀⠀⡄⠞⠒⠖⠀⢠⡇⠀⠀⠀⠀⠀⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⣴⣾⡿⠗⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⠘⡆⠁⡍⠀⠁⢡⡌⠀⠀⠈⠡⣱⠊⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢁⡁⠸⣧⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢄⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡀⠀⠀⠀⠀⠓⠀⡌⠉⠅⠺⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡛⢂⣼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡿⣿⣟⣿⣟⡀⠀⠀⠀⠚⡾⡼⢨⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣿⣿⣿⣏⠁⠀⠀⠀⣈⣙⢷⣫⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣟⡇⣿⣿⣿⣿⣿⡝⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢴⣦⣄⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣧⠀⠠⢃⠁⠠⠃⣾⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠛⢻⡿⣿⣿⣿⣿⣧⡀⡟⠾⢿⣿⣿⣿⣯⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣾⣿⣿⣿⡄⠀⠀⣀⣴⣤⠈⠙⢿⣿⣇⡠⠀⠒⠐⠀⢀⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡁⠀⢸⣾⣿⣟⣿⣿⠛⠀⠴⣤⡸⢻⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⣿⣿⣯⣤⡄⠀⠀⠉⠉⠁⠀⠀⠀⢻⣿⣖⢀⣤⣤⣶⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣿⠟⣿⣿⠞⢀⣴⣿⣷⣿⣿⠾⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣧⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡻⣿⣿⣿⣿⣿⠁⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠏⠀⣙⡿⣿⡼⢩⠋⠀⣾⡿⣳⣻⣯⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡿⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⣿⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣏⠇⣸⡟⡀⡛⠿⢫⠀⠫⠐⠀⠀⡿⢰⠷⠙⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⢸⣿⣿⣄⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡣⣀⠃⣾⢟⠚⣩⠆⠘⣿⠀⠀⠀⠀⠀⠃⠎⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣻⣿⣿⡆⢺⡿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠁⠨⡀⠸⣾⡶⠋⠀⢸⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣷⣎⠀⠸⠇⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢾⠆⠀⠀⢠⠀⢀⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠸⠿⠧⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⢀⣽⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢠⠀⠀⠀⢀⠤⠋⠚⠗⠀⠀⠎⠀⠀⠀⠘⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠎⢶⢴⡿⡿⠷⠆⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠃⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⡄⢁⡅⠀⠁⣱⡈⢰⠀⠈⣁⣡⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢁⠁⠸⣧⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢄⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡀⠀⠀⠀⠀⠓⠀⡌⠉⠅⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡓⢂⣼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡿⣿⣟⣿⣟⣀⠄⠀⠀⠊⡾⡨⢨⣾⢟⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣹⣿⣿⣿⣟⠁⠀⠀⠅⠈⣙⢷⣫⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣗⡇⣿⣿⣿⣿⣿⡝⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢴⣦⣄⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣧⠀⠢⠀⠀⠐⠃⣾⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠛⢻⡿⣿⣿⣿⣿⣣⡀⡾⠿⢿⣿⣿⣿⣯⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣾⣿⣿⣿⡄⠀⠀⣀⣴⣤⠈⠙⢿⣿⣍⡠⠂⢒⠠⠀⢀⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡁⠀⢸⣿⣿⣟⣿⣿⠛⠀⠦⣤⡸⢻⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢶⣿⣿⣯⣤⡄⠀⠀⠈⠉⠉⠀⠀⠀⢻⣿⣖⢀⣤⣤⣶⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣿⡟⣿⣿⠞⢀⣴⣿⣷⣿⣿⠾⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣯⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡻⣿⣿⣿⣿⣿⠁⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠏⠀⣙⡿⣿⡼⣩⠋⠀⣾⡿⣳⣻⣯⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡿⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⣿⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣏⠇⣸⡛⡀⡛⠿⢫⠀⠋⠐⠀⠀⡿⢰⠷⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⢸⣿⣿⣄⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡣⣀⠃⣾⢟⠚⢩⠆⠘⣿⠀⠀⠀⠀⠀⠃⠏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⡻⣿⣿⠆⢸⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠁⠨⡀⠸⣾⡶⠋⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣶⣎⠀⠸⠇⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢾⠆⠀⠀⢀⠀⢀⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠸⡿⠧⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⢀⣼⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢠⠀⠀⠀⢀⠤⠋⠚⠗⠀⠀⠎⠀⠀⠀⠘⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠎⢶⢴⡿⡿⠷⠆⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠃⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⡄⢁⡅⠀⠁⣱⡈⢰⠀⠈⣁⣡⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠘⢣⢩⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣆⠀⠀⠀⠀⠀⠀⢈⠠⡀⠐⠝⠊⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⡀⢀⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣻⣿⡃⡀⠀⠀⠀⠐⠉⠈⢚⠍⠶⠮⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠞⢱⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢃⢿⣙⣥⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⠙⢸⣿⣿⣿⣿⣛⠙⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇⢀⠀⠁⠀⠀⠤⢠⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣴⠿⠻⢿⣿⢿⣿⣿⣿⣧⡀⠨⡆⠝⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⡅⠀⠀⠀⣀⣤⣄⠉⠹⣿⣿⡁⠀⠈⠀⠀⠀⠀⢰⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣹⣿⣻⣿⣿⣿⠟⠁⠰⣄⡸⣻⣿⡟⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣶⣿⣿⣯⣤⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⠻⣿⡤⣁⣴⣤⣤⣤⣼⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣾⡿⣻⣷⡞⠁⣴⣿⣷⣿⣿⢿⠖⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣯⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⠿⣿⣿⣿⣿⣿⠅⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⠃⠈⡹⡿⣿⡴⣣⠏⠀⣾⡿⣿⣿⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⠟⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⣿⣿⣿⡻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⠇⠘⠙⢒⠚⢯⠋⠀⠏⠘⠀⠐⡏⠺⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣤⣿⣿⣿⣷⡉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢻⣅⠇⣤⠄⠂⠈⠄⢸⣻⡀⠀⠀⠀⠐⠠⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠫⠅⣼⣤⡿⠜⠀⠀⡏⡇⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣯⠉⠀⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⠃⠙⠃⠀⠀⠁⠀⠸⡷⠀⠀⡄⠀⣤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣾⣿⣿⣽⣿⣿⣿⣿⡿⠟⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡀⠀⣴⣶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡄⠀⠀⠁⠀⠤⠆⠨⠓⠀⠀⠙⠁⠀⠀⠹⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⣶⡶⢿⠷⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣴⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⠀⢡⡁⠀⠁⢁⡈⠀⡄⠈⠁⣤⣬⡈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠄⡰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⢶⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢩⢷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄⠀⠄⣀⣴⣾⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⣻⣿⡃⠀⠀⠀⠀⡀⠀⠁⠰⠍⠶⣲⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠈⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠨⣷⣝⣲⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⡻⢌⣿⣿⣿⣿⣟⣟⠿⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣦⣤⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠂⣾⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡤⣾⠿⣿⣿⣿⢿⣿⣿⣿⣗⡄⢘⠙⠪⣻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣾⣿⣿⣿⣧⠀⠀⠀⢀⣤⣄⡈⠙⢿⣿⡁⢀⠐⠆⠀⠀⠀⢴⣾⣿⡿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠨⣿⣾⣿⣿⣿⣿⡟⠃⠸⢠⡞⣹⣿⣟⡁⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣧⣥⣧⠄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠻⣿⡍⣄⣤⣴⣶⣦⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⢸⣿⣿⣿⡿⡻⣳⡶⢡⣴⡿⣿⢿⣿⢿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⠿⣿⣿⣿⣿⣿⡏⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⠀⢙⣻⢿⣿⡡⢧⠝⢠⣿⡿⣿⣽⠗⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣿⣿⣿⡟⣇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠇⠙⠙⢞⠛⢯⡇⠀⡾⠻⢋⢿⠏⡟⠋⠏⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣤⣷⣿⣿⡇⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢻⣏⠇⠀⠀⠀⣨⠀⢸⢻⡀⠀⠀⠀⠸⡰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⢤⣽⣧⣵⡧⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⣿⡅⡀⣤⣤⣴⣤⣘⣿⣿⣷⣾⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⢺⣿⣿⣿⡿⡻⣳⡶⢃⣴⣿⣿⣿⣿⢿⠷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢹⣿⣭⣥⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⠿⣿⣿⣿⣿⣿⡏⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⠀⣙⣻⢿⣿⡠⢇⡝⢠⣾⡿⣽⣿⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡋⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣿⣿⣿⡿⣇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃⠟⠑⠞⠛⢫⡇⠀⡼⠪⠋⢼⡏⡿⠙⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣤⣿⣿⣿⡧⡋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢻⣇⠇⡀⠀⠀⣨⠀⢸⢿⡀⠀⠀⠀⠸⢠⠁⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡏⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⡷⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢛⡯⢧⣾⣦⡼⠅⠀⠀⣿⣇⠀⠀⠀⡐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢿⠿⣿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠑⠳⠛⠋⠀⠀⠂⠀⠁⠳⠀⠀⡀⠀⣠⠶⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⢰⣭⣭⣭⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠈⠁⢠⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⡿⣿⣿⣿⢶⣿⣿⣿⠟⠀⠈⠀⠀⠁⠀⠤⠄⠐⠏⠀⠀⠁⠀⠀⠀⠸⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣾⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⢦⢶⡶⣿⠷⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣴⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡆⢰⠁⠀⠀⠁⡎⠄⢠⠈⠁⠀⢀⣬⣄⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠅⡑⢭⣯⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠅⠓⠾⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⡶⡀⣀⠀⣀⣤⣶⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⣿⣋⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡢⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡢⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⣐⣴⣀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢾⡆⢁⣾⣿⣿⣿⠿⠿⢻⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠴⣤⣀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇⠀⠀⠀⠄⢀⡠⠆⣾⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⡤⣼⠿⣿⣿⣿⡿⣿⣿⣿⣿⣀⠀⠗⠀⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇⠀⠀⢀⣤⣤⡌⠙⢿⣿⡍⠀⠀⠀⠀⠄⠀⠲⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⣽⣝⣷⣿⣿⣟⣿⡿⠛⠀⢠⡜⣻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣽⣧⣴⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣍⡀⣠⣤⣶⣦⣐⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡇⠀⢿⣿⣿⣿⣿⠛⣿⣷⢋⣴⣾⣿⣿⣿⢿⠗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢩⣿⣽⣥⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠿⣿⣿⣿⣿⣿⡯⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⡿⠀⣙⣻⣿⣿⣣⠇⡽⢡⣾⡿⣽⣿⠿⠶⠀⡈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡏⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⣿⣿⣿⡟⡧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠃⠟⠑⢞⠛⢫⣇⠈⢰⢽⠏⢭⡏⡽⠛⠃⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣤⣯⣿⣿⡧⡝⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠘⢿⣇⠇⡀⠀⠀⣨⠀⢸⢿⡀⠀⠀⠈⢸⢠⠁⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢿⣿⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢛⡯⢧⣾⣦⣼⠅⠀⠀⣿⣇⠀⠀⠀⡐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡘⢿⢿⢿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠑⠳⠛⠋⠀⠀⠂⠀⠁⠿⠀⠀⠀⠀⣠⠶⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⢸⣯⣭⣭⣽⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⠁⢠⣶⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⣾⣿⡿⣿⣿⣷⣶⣿⣿⣿⠏⠀⠈⠀⠀⠁⠀⠤⠄⠐⠏⠀⠀⠉⠀⠑⠀⠸⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣾⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠦⢶⣶⣿⠷⠶⠆⠀⠀⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡄⢱⠁⠀⠁⠁⡎⠄⢠⠈⠁⠀⠀⢈⣄⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠷⡁⠽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢂⠾⠢⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡐⠄⠀⠀⣠⣴⣿⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣿⣋⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⡐⠉⡃⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠈⡀⢣⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠄⠀⢒⣁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡗⠫⠌⣸⣿⣿⣿⣿⣿⡫⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣷⠀⢂⠀⠀⠀⡀⡆⣴⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣥⢄⣾⠿⣿⣿⣿⣿⢿⣿⣿⣿⡃⡀⠁⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣠⣦⡌⠉⢻⣿⡏⠀⠀⡀⠀⠈⠀⠀⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⣝⡟⣍⣿⣿⣿⣻⣿⠿⠃⢠⢜⣿⣿⣯⠁⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣥⣿⣥⡝⡉⠀⠀⠀⠁⠁⠀⠀⢹⢿⣇⠄⣀⣲⣴⣀⣂⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡇⠀⣿⣿⣿⣿⣿⣟⢻⣿⣖⣤⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣯⣿⣠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡻⣿⣿⣿⣿⣿⣿⢹⣯⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⢿⣿⡟⠀⣙⣿⣿⣿⡟⣼⢨⠏⣾⠿⣹⣿⣯⠯⠌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠙⣿⣿⣿⡟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠋⠳⡛⠻⣿⡅⠘⠀⡧⣿⣟⡿⢸⡿⠝⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣤⣭⣿⣿⣿⡸⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠻⢿⡀⢀⠀⠀⢀⠅⠀⣽⠣⠀⠀⠍⠀⠁⠇⠄⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠠⠐⣻⠽⣄⣶⣤⠧⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠻⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠈⠻⠆⠛⠁⠀⠀⠀⠀⢀⠀⠀⠀⣦⠀⠀⡠⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠘⣿⣿⢀⣶⣶⣿⣭⣿⣿⣿⣿⡿⠟⠛⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⣹⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣴⣿⣿⡿⣿⣿⣶⢾⣿⣿⡶⠂⠀⠐⠀⠀⠁⢀⠤⠄⠸⠁⠀⠀⠁⠸⠀⠀⠀⠿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠆⢶⣴⣶⣾⡶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⣼⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⠀⢠⠁⠀⠁⠁⠨⢀⡄⠈⠁⠀⠀⢨⣾⡆⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢤⠀⣠⣶⣿⣿⣷⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢿⣛⣻⣿⠂⠀⠀⠀⠀⠀⠀⠀⣡⡟⢇⡛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠇⣺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⡐⠘⢢⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠂⣻⣿⣿⣿⣛⡫⠵⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠠⠀⡄⣶⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⡤⣾⡿⣿⣿⣿⣿⢿⣿⣿⣿⣇⡀⠀⢻⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣶⣿⣿⣗⠀⠀⣠⣦⣄⠉⢻⣿⡏⠁⠀⠀⠀⠀⡀⠀⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢘⣏⣞⣿⣿⣿⣿⣿⡿⠋⢠⢞⣿⣿⣫⠂⣠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⣉⣽⣉⡙⠋⠀⠀⠀⠀⠀⠀⠀⠜⢿⣆⠀⣐⣠⣄⣐⣀⣿⣿⣷⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⣼⣿⣿⣿⣾⣟⡻⣻⣶⣤⣿⣿⣿⣿⢿⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣊⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡹⣿⣿⣿⣿⣿⣿⢋⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⢿⣿⡿⠀⣙⣻⣿⣿⣿⡸⣩⡝⣾⠟⣹⣿⣯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡿⢻⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⣿⣿⣿⣿⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⡿⣿⠀⠋⠳⡛⠻⢿⡇⠘⠀⠨⢼⣿⣿⠸⡷⢽⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⣬⡻⣿⣿⡮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠹⣾⡀⢀⠀⠀⠀⠅⠀⣿⠃⠀⠀⠃⠀⠄⡇⡰⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢻⣿⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⠻⠽⢀⣦⣼⠇⠀⠀⠹⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡁⠙⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠿⠂⠛⠁⠀⠀⠀⠀⡀⠀⠀⠀⣠⠄⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⢹⣿⣟⢰⣶⣾⣯⣽⣿⣿⣿⣿⡿⠛⠋⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⣇⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣼⣿⣿⡿⣿⣿⣷⣾⣾⣶⡖⠀⠀⠛⠀⠈⠀⠠⠤⠀⠪⠃⠀⠀⠁⡇⠀⠀⠀⠹⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡾⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⣤⣴⣶⣶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⣾⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⡎⠀⢡⠁⠀⠁⡁⠨⢠⠀⠈⠁⠀⠀⢸⣾⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠧⡭⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⢁⢿⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠂⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢿⣟⣹⣿⡃⠀⠀⠀⠀⠀⠀⠀⢠⠓⠇⠱⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠋⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠊⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠨⠀⢣⣁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢽⣿⣿⣿⣏⡉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠐⢀⠈⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣠⣭⣿⣿⣿⡿⣿⣿⣿⣿⣀⡈⢿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⣿⠀⠀⣠⣤⣤⠉⠻⣿⣏⠁⠀⠀⠀⠀⠁⢪⣶⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣻⣛⢽⣛⣿⣿⣿⣿⠟⢁⢏⣿⣿⠏⡀⣀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⣻⣉⣛⠟⠁⠀⠀⠁⠁⠀⠄⢌⢿⣧⠀⢀⣀⣀⣀⣄⣿⣿⣷⣬⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠀⢰⣿⣿⣿⣷⣟⣻⣻⣶⣷⣟⣿⣿⣿⠷⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣎⡿⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡹⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢽⡟⣿⣿⠀⢘⢻⣿⣿⣿⡧⣏⣼⢷⡿⢁⣯⣟⣯⡍⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⢛⣵⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⢿⡿⢿⠃⠟⠁⠞⠺⠯⡅⠘⠁⠀⡇⠽⢽⠃⠺⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣳⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⣤⣭⣿⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡀⠈⢺⣀⢀⢀⠀⠀⡈⠀⢸⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⡇⠀⢛⠿⡄⣤⣼⡯⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠹⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠧⠀⠀⠘⠆⠛⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⣤⠀⠀⣀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⢩⢬⣿⣟⣛⡿⣿⣿⣿⣿⡿⠛⠛⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣀⠀⠀⢹⣂⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣼⣿⣿⡿⣿⣿⣿⢯⣿⣤⠆⠁⠁⡏⠀⠀⠁⠀⠤⠄⠨⠛⠀⠀⢸⠀⠀⠁⠀⠀⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡾⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠂⢶⣤⣴⣶⣶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⣾⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⡌⠀⣤⠁⠀⠀⠁⠈⢠⠀⠈⠁⢠⢨⣾⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢐⠁⣉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠀⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⢿⣟⣘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⣲⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⠈⣾⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠋⣿⣿⣿⣷⣄⣿⣿⢻⡿⣇⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣿⡗⠀⢀⣤⣤⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣿⣿⣿⣿⢸⣿⣶⣯⡏⣿⣿⣿⣟⢋⢉⡟⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣩⣋⣛⣟⠋⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢀⣂⣀⣁⣄⣿⣿⣯⣽⣿⣷⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⡣⣿⣿⣿⣀⢹⣿⣿⣭⡟⣴⣿⣿⣿⣿⣿⢹⡤⣶⣿⣿⣰⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢿⣿⣿⣿⣿⣿⡛⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣻⣹⣿⣿⡿⣿⠀⣝⠒⠈⠉⠙⠋⠘⠐⣿⣿⡟⢸⢻⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡟⣫⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢻⣿⣿⣿⡿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡿⠿⠛⠋⠈⢿⠀⡃⣤⡙⡁⠰⠀⠀⠀⠀⠀⠁⣿⠁⡇⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣭⠻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠝⠀⠀⣄⠀⣠⢸⡿⢿⢋⡏⢸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠁⠀⠀⢿⡀⠐⠀⣠⣃⠊⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠘⠀⠀⠀⠐⠔⠉⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡱⠂⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⡟⠻⠿⠿⠏⠉⠁⠏⠀⠀⠀⣨⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣗⣞⣶⣷⣿⣾⣷⢻⣷⣷⢆⡏⣾⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠊⢶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⣾⣶⣷⣾⣾⣾⣾⣾⣶⣷⣬⠈⠀⢰⡟⠀⠀⢱⡎⠀⢰⠈⠁⡄⠀⠈⠀⢀⣁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠩⢘⠉⡫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠄⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣟⣋⣿⡗⠀⠀⠀⠀⠀⠠⡀⠐⠲⠀⢈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⣻⣿⣿⣿⡟⠀⠀⠀⢀⠀⠀⢅⡊⢞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠐⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⣾⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣷⣌⣻⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣿⣶⣿⣿⣷⠀⣠⣤⣤⠈⠙⣿⣿⠁⠀⠐⠀⠀⠪⣠⣴⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡯⢰⣶⣿⣿⣿⣿⢸⣿⣿⣿⣮⣻⣿⣽⣟⢉⢉⡟⣿⣿⠏⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣉⣏⣙⣻⠛⠀⠀⠈⠉⠀⠀⠘⡻⣧⡀⠀⠀⢀⡣⢨⣿⣿⣯⣽⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢻⣿⣿⣭⠿⢼⣿⣿⣿⣿⣿⢯⡤⣴⣿⣿⣡⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡝⢿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⣝⠛⠁⠀⠈⠁⠸⠁⣾⣿⣿⢹⢏⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡿⣻⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠯⣗⠛⠊⢻⠃⠊⠀⢌⡃⠰⠀⠀⠀⠀⠀⠑⢿⠃⡌⠌⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣯⠻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡏⠀⣤⢠⡀⢲⡄⣵⠿⠃⠹⠀⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠺⣁⠠⠀⢀⣜⡜⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢸⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠂⠀⠀⠀⠢⠋⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠆⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠃⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⣿⣿⣿⡿⠻⠿⠟⠓⠀⢸⠀⠀⠀⣬⡲⠀⠐⠀⠂⠀⠀⠀⠀⠀⠡⠐⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢆⡏⣶⣷⣶⣷⡶⣾⢆⣿⣾⢀⣿⣶⣷⣷⣿⣿⣶⣷⡗⣸⣾⣾⣿⠀⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⣦⣴⣶⣶⠖⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣦⡌⠀⠀⣯⠆⠀⠁⣬⡄⠀⠈⠁⢠⠀⠈⠀⠀⠁⣭⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣒⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣋⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⣻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡼⡊⢚⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣷⣎⢻⣿⣿⣿⣛⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣿⣶⣿⣿⣷⠀⣀⣤⣤⠈⠙⢿⣿⠉⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣟⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡗⠰⣶⣿⣿⣿⣿⣙⠿⢿⣿⡛⢻⣾⣽⡏⢉⡉⡟⣿⣿⠏⠀⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣉⣟⣉⣻⡛⠀⠀⠈⠀⠀⠀⠀⡻⣷⡀⠀⠀⠠⠈⠠⣿⣿⣯⣽⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣀⢻⣿⣿⣯⡿⣴⣼⣿⠿⣿⣿⠯⡤⣴⣿⣿⡃⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡜⢿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⢿⠀⣝⠚⠁⠀⠀⠀⠰⠃⣾⣿⣿⢱⣏⡖⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⣻⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⢻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠿⣷⠛⠆⠹⠇⠘⠀⢄⣃⠐⠀⠀⠀⠀⠀⠉⢻⠊⡘⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣸⣭⢻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡏⠁⣤⠡⠀⢠⣄⣠⠶⡀⡸⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡡⠀⠀⠳⣇⣀⠄⠀⣰⡔⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠺⣿⠿⠟⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠙⠀⠀⠀⠘⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢸⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⡆⡀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⣿⣿⣿⢿⠿⠿⠿⠋⠂⠸⠇⠀⠀⣤⣗⠊⠀⠀⠐⠀⠀⠀⠀⠀⠈⠆⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢆⡏⣶⣷⣶⣷⡶⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠈⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠎⢶⣦⣴⣶⣶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⡌⠀⠀⢹⡤⠁⠁⡌⣤⠀⠈⠁⠀⠀⠈⠀⠀⠁⠉⢨⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⢈⢟⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣖⡂⠀⠀⠀⠀⠀⠀⠀⠘⠠⠒⠌⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣛⣻⣿⠆⠀⠀⠀⢀⠀⠀⠀⠀⠠⢄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠅⣹⣿⣿⣿⣿⠂⠀⠀⠀⠀⠐⢫⢏⢌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠂⠀⠀⠀⠀⣾⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡏⢻⠿⣺⣿⣷⣝⣿⢿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢐⣷⣿⣿⣿⣇⠀⠀⣠⣴⣦⠀⠙⢿⣿⡋⠀⠀⠀⢀⡀⣄⣤⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⢺⣷⣿⣿⣿⣿⣿⣷⣿⡟⢽⣿⣯⣏⠛⡛⡻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⣩⣽⣉⣍⠋⠀⠀⠀⠉⠀⠀⠀⠐⠛⣷⡄⠀⠄⠠⠈⠠⣿⣿⣯⣭⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣆⢀⣿⣿⣿⣿⢷⣿⣾⢻⣿⣿⡏⣥⢤⣿⣿⡃⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣋⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⢿⣿⣿⣿⣿⣿⡟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⠿⡇⠘⠚⠃⠀⠀⠈⠀⠇⢰⢿⡿⢣⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢹⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣯⡭⢔⠃⠛⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠇⠸⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣸⣍⢻⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟⠀⠨⣿⡳⠆⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⢤⣿⣥⣭⡥⠌⠀⠀⠀⠀⠈⠀⠀⠀⠀⢙⢿⡄⡀⠀⠠⠀⠸⣽⣿⣯⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣻⢿⣿⣿⡿⡿⣾⢩⢤⣾⣿⢁⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢹⣯⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣻⢿⣿⣿⢿⠙⠛⠟⠁⠀⠀⠀⠞⢰⣿⡿⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⢹⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣟⡁⢤⠘⢻⡟⠰⠀⠁⠆⠀⠀⠀⠀⠀⠘⠺⠇⠘⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣈⡫⢿⣿⣇⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡇⠀⠀⣤⢰⣣⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⢶⣿⣿⣿⣿⣾⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠀⠀⠰⢿⠀⠈⡫⢀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁⠹⣿⢿⡿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠁⠀⢈⠀⠀⠐⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠊⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⢠⠻⠱⢠⠀⠀⠄⠀⠀⠀⢶⠀⠒⠂⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢆⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠎⣶⣶⣶⣾⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⣶⣷⣾⣾⣾⣾⣾⣶⣷⣼⡌⠀⠁⠁⠀⠁⠁⠈⠀⠀⠈⠁⠁⠈⠈⠀⠀⠁⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⠌⠟⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣒⡀⠀⠀⠀⠀⠀⠀⣄⠰⠁⠸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⢸⣿⠷⠀⠀⠀⡀⠐⢘⠒⢘⡂⠥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣶⠷⡀⠀⠀⠀⠙⢄⣚⣹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠄⠀⠀⠘⠀⣿⣿⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢿⠟⢺⣷⣦⡿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⣠⣴⣦⡀⠉⢿⣿⡏⠁⠀⠀⠀⡈⠬⣶⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢺⣦⣾⣿⣿⣏⣾⣿⣿⣟⢿⣿⣟⢻⣻⣻⣿⣿⠃⠀⠀⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢴⣿⣥⣭⡤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⡄⡀⠄⠀⠈⢸⣽⣿⣯⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣻⢿⣿⣿⣿⡿⣾⢩⢤⣾⣿⢁⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢹⣯⣿⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠻⣿⣿⣿⣿⣿⡟⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣻⢿⣿⣿⢿⠉⠛⠟⠁⠀⠀⠀⠞⢰⣿⡿⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⢹⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣟⡁⢤⠚⢻⡟⠰⠀⠁⠆⠀⠀⠀⠀⠀⠘⠺⠇⠘⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣈⡙⢿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡆⠀⠀⣤⢰⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⢶⣿⣿⣿⣿⣾⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠀⠀⠰⢿⠀⠈⡫⢀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁⠹⣿⢿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠊⠁⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠊⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⢠⠻⠱⢠⠀⠀⠀⠀⠀⠀⢶⠀⠒⠂⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢦⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⣶⣶⣶⣾⠶⠆⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⣶⣿⣾⣾⣾⣾⣾⣶⣷⣶⡌⠀⠁⠁⠀⠁⠁⠈⠀⠀⠈⠁⠁⠈⠈⠀⠀⠁⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠘⢝⢾⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡿⠷⠶⠀⠀⠐⠀⢀⣀⠁⢸⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⣿⣿⣿⣿⣿⡄⠀⠀⡄⠐⣔⣋⠗⢌⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣾⣿⣄⣷⠀⠀⠠⢁⢚⣂⣃⡬⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠁⠤⠄⠠⣌⠀⣿⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡿⢻⣷⣶⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⡀⠀⠀⠀⣤⣶⣦⠄⠙⢿⣿⡟⠉⠀⠠⠀⢪⢰⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣟⣿⣿⠏⠀⢐⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣏⣨⡍⠀⠀⠀⠀⢀⠈⠀⠀⠐⠀⡙⢿⣖⠄⣈⣂⣀⣑⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢰⣿⣿⣿⣿⢟⣻⣿⣿⣿⢿⢯⡧⣶⣿⡇⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢽⣿⣯⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠻⣿⣿⣿⣿⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⢿⠛⡛⠻⠇⠀⠀⠀⠸⠁⡾⣿⢧⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠘⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣟⣋⡡⡖⢻⣿⠠⠀⠘⠆⠀⠀⠀⠀⠀⠀⠛⡇⠸⠐⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠻⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡆⠀⢀⣦⢠⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣻⣿⣿⡆⠀⠁⠈⠀⣥⠀⡀⢀⣒⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⣿⣤⣧⠄⠀⠈⢀⣁⣠⣤⡃⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⡐⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⢿⣿⣿⣷⣿⣿⣿⣿⣿⢯⣿⣽⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣷⣶⣿⡅⠀⠀⠀⠀⣤⣶⣦⠀⠉⢿⣿⣋⠉⠀⠀⠀⡄⣲⣿⣿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢶⣾⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣟⣉⣹⢿⣿⡟⠀⠀⣶⠀⠀⠀⠀⠀ ⠀⠀⠠⣬⣿⣿⡏⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⠐⣀⣈⣪⣾⣿⣷⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣛⣻⣿⣿⣿⣿⡿⡿⡯⢴⣿⡇⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡙⣿⣿⣿⣿⣟⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⡿⢿⠉⠙⠛⠛⠀⠀⠀⠱⠣⡺⣿⢇⡿⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠈⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⡭⠥⠶⠛⢻⡇⢸⠆⠀⠠⠄⠀⠀⠀⠀⠀⠃⡇⠸⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠛⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠃⠃⣼⡗⠂⢻⡀⠀⡐⠎⠉⢰⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⠃⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⠆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠀⠀⠙⠆⢀⢈⠅⢤⢀⡗⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢳⣬⣇⣹⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠾⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣠⣄⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠋⠸⠀⠀⣄⡚⠘⠄⠀⠠⠀⠀⠀⠀⠀⠀⠛⠁⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣿⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠈⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⣪⢶⣶⡾⡶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠃⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⠀⠁⠁⣤⠁⠁⠈⣄⠀⠈⠁⠀⠈⠈⠀⠀⡅⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠂⢀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡶⠦⠀⠀⠀⠀⠀⠀⠄⠈⠈⠁⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⡉⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣿⣵⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣾⣿⣅⣽⡈⠀⠀⠀⠀⣀⡠⠤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡅⠈⠀⠰⠄⣿⣿⣿⣤⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⢿⣿⣿⣶⡽⣿⣿⣿⣟⡏⣽⣯⣿⣿⡿⢿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣶⣶⣾⠀⠀⠀⠀⠀⣠⣴⣶⠀⠉⢻⣿⣟⢉⠁⠀⠀⠁⣶⣿⣿⣛⣿⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣿⣿⣿⣞⣿⣿⣿⣷⣧⣹⣿⣽⠏⠘⣉⢻⣿⡟⠁⠀⢀⠀⠀⠀⠀ ⠀⠀⠠⣾⣿⣿⡏⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠠⣈⣺⣯⣁⣘⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣧⣼⣹⣿⣿⣿⣿⣿⣿⢩⣥⣶⣿⡇⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡈⢿⣿⣿⣿⠍⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠻⣿⠀⢐⡺⠿⠁⠁⠀⠁⠞⢰⣿⠏⡼⢁⣠⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡟⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠹⠿⠛⢋⠘⡟⢀⣷⣦⣀⠁⠐⠀⠀⠀⠀⠀⠀⠻⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠀⢀⠘⣀⡀⠈⠁⡁⠁⠀⡞⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠋⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⣶⣾⣿⣿⡆⠀⣸⣻⣿⡟⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠸⣎⡤⠅⣶⣾⡀⠀⠀⠣⢰⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠀⠀⠙⠃⠻⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⣿⣿⡐⠀⠂⠀⠀⠀⠐⠃⠀⠀⠀⠁⠊⠀⠀⠀⠃⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠠⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠟⠀⠀⠀⠀⠂⠀⠂⠠⠀⠲⠀⠀⠀⠀⠘⠋⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⢆⣶⣶⠷⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠀⠁⠀⠀⠁⠈⠀⢠⠈⠁⠀⠀⣨⣄⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢁⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣶⡦⠀⠀⠀⠀⠀⠀⠄⠈⠌⢁⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡲⡍⡚⣽⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠂⠐⡼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣧⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣧⣼⣿⣍⣽⡄⠀⠀⠀⠀⢀⡀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⡇⠀⠀⠠⡠⣾⣿⣧⡄⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⢿⣿⣿⣶⣽⣿⣿⣿⣿⠓⣹⣿⣿⣿⣏⣽⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣷⣶⣿⠀⠀⠀⠀⠀⣀⣴⣖⡀⠉⢻⣿⣟⢋⠁⠀⠀⠀⣼⣟⣟⠟⣏⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣾⣿⣿⣿⣟⣿⣿⣾⣦⣆⣹⣿⣽⠏⠑⠉⠞⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⡏⣩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠂⠀⠀⣀⣿⡛⠉⢻⠿⣿⣣⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣷⡽⣱⣿⣿⣿⣿⣿⣿⢩⣅⣴⣿⡿⣼⣟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡌⢿⣿⣿⣦⢿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⡿⠀⢘⠺⠿⠁⠀⠀⠉⠞⢰⣿⠏⡼⣳⣥⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡟⢽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠈⠻⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠻⢉⢹⡏⢘⠅⠢⠘⠛⠀⠀⠀⠀⠀⠀⠈⠝⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣻⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠀⢀⠸⢀⡀⠀⢀⠀⠂⠰⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠁⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⣾⣿⣿⡆⠀⣏⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢨⣇⡜⠸⣷⣇⡀⠀⢰⡏⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠉⠈⠻⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⡐⠀⠀⠀⠀⠂⠘⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣵⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠀⠀⠀⠀⣾⣿⣿⡿⣿⣿⣿⢿⣿⣿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠐⠂⠠⠐⠖⠀⠀⠀⠀⠛⠋⠙⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠂⣶⣴⠷⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠀⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠀⠁⠀⠀⠁⠈⠀⡅⠈⢡⠀⠀⣬⡄⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣶⡦⠀⠀⠀⠀⠀⠀⠄⠈⠌⢁⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢡⡢⡄⣨⣾⣿⣿⣿⣦⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠴⣾⣿⣷⠀⠀⠀⠂⢂⠀⠁⢠⡼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣂⡁⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣴⣿⣍⣹⡄⠀⠀⠐⠪⠅⡠⠆⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣇⠀⠀⠌⠄⣴⣶⡦⠉⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣦⣽⣿⣿⣿⣿⠟⣹⣿⣿⣿⡍⣠⢿⣿⣿⣿⣿⣥⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⣷⣶⣮⠀⠀⠀⠀⠀⢀⣤⣖⠀⠈⢻⣿⣟⠛⠁⠀⠀⢔⣀⣿⣿⣿⡆⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣽⣿⣿⣿⣿⣿⣿⣿⣦⣾⢿⣾⣽⠏⠑⠉⠠⢻⣿⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠠⣬⣿⣿⣟⢩⡅⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠘⡿⡧⣽⣽⣥⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣯⣽⢏⣿⣿⣿⣿⣿⣞⢻⣁⣴⣾⣶⣣⣿⡻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢽⣿⣿⣇⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⢻⣿⣷⡠⣄⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⠿⣿⠏⠙⠿⢿⠋⠉⠁⠉⢞⣰⣿⠏⣹⣫⣯⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡟⢽⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢹⣿⣷⣿⣗⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠾⡟⠛⣿⡟⠐⠇⠠⠀⠛⠂⠀⠀⠀⠀⠁⠋⡟⢰⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⣿⣿⡟⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠀⢨⣼⣀⠀⠀⣀⢀⡅⠀⡴⠀⠀⠀⠀⠈⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⣶⣾⣿⣿⡆⠀⣛⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣃⠔⢸⣾⣧⡁⠁⢸⠃⠀⠀⠀⢠⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠙⢿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡀⠀⠀⠀⠼⠟⠙⠀⠀⠀⠈⠀⠀⠀⠀⡸⡄⢀⡤⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣀⣀⣶⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⡿⣿⡿⠂⠀⠀⠈⠀⠈⠀⠂⠚⠔⢸⠃⠀⠘⠛⠁⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⣶⣶⡿⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢠⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⡀⠀⠁⠀⠀⠁⠈⠀⠀⢈⠁⠀⢸⣮⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠹⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠿⠷⣖⠀⠀⠀⠀⠀⠁⠄⠉⠈⢡⢠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⢥⣠⠤⢠⣶⣾⣿⣶⣤⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⠸⣿⣿⣧⠀⠀⠐⠀⡀⡔⠀⠁⡬⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣀⡐⢀⢁⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣧⣼⠖⠀⠀⠃⠂⣉⢀⡂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡗⠘⣿⣿⣿⣿⣯⠾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣇⠀⠀⠅⠢⢭⣦⣄⠁⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣯⣙⣿⣿⣿⣻⡟⣻⣿⣿⣿⡅⣀⢿⣿⣿⣿⣿⣅⠀⠀⠀⠀ ⠀⠀⠀⠀⢩⣿⣶⣷⠀⠀⠀⠀⠀⣀⣤⣖⠀⠉⢿⣿⣛⡛⠁⠀⠀⠄⡁⣿⣿⣮⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣮⣿⣿⣿⣿⣿⣿⣾⣿⣽⢿⣿⣽⠟⠓⠉⠀⢿⣿⣿⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⢤⣽⣿⣿⣋⣅⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠙⣿⣷⡁⠀⠐⢄⣿⣽⣹⣛⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⡄⢻⣿⣿⣽⡟⣽⡿⣿⣾⣿⣾⣻⣁⣴⣾⣴⢣⣿⡯⠀⠀⠐⠀⠀⠀⠀ ⠀⠀⠀⢬⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⢿⣿⣯⢠⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣳⣿⡿⣿⡏⠂⠤⢻⠏⠉⠉⢣⢟⣰⣿⠟⣻⣻⣯⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⠁⠀⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢹⣿⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣛⣿⡿⠀⠋⠠⡀⠺⠆⠀⠀⠀⠀⠁⠓⡟⢰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡎⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⠀⠉⣿⣿⡟⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠀⠀⢹⣿⣙⠁⠀⡀⢂⡭⠠⣤⠀⠀⠀⠀⠀⢠⠡⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⣤⣿⣿⣿⢋⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠙⢿⣷⡁⠀⠀⠀⢻⣽⣻⣛⢃⣤⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣛⣿⡇⠀⣯⣿⣿⣿⡼⣛⣉⣤⣮⣴⢢⣿⣻⢁⡴⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣼⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⢻⣿⣇⢀⢉⠁⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣽⣿⣿⡿⠀⢶⢿⠿⠯⠹⠧⡟⣼⣿⠟⣽⣿⠽⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⡏⠁⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢹⣿⣾⣿⠄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⡿⠀⠿⣁⠠⠶⠬⠀⠀⠐⢐⠁⢳⠏⣼⠏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠞⠀⠀⠶⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⠙⣿⣿⡟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠃⠫⣿⣿⣹⡁⠀⠛⢛⠯⠀⣠⠀⠀⠀⠈⠁⡘⠐⢡⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⣿⣿⣿⣿⡀⠺⣿⣿⡋⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠻⣿⣿⢀⣿⣟⠏⠀⢠⢿⠀⠀⠀⡠⠀⠁⠀⠀⣠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡀⡀⠀⠻⣷⠃⠃⠀⠀⠀⢈⡀⠀⠀⠀⠗⢀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⣀⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⡿⢹⣿⣿⡿⠀⠀⠀⠀⠤⠂⠘⠏⠠⠀⠃⠀⠛⠁⠹⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣶⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠂⢶⡤⣶⠶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠀⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⠀⠀⠁⡄⠀⠁⢨⢐⣠⢈⣴⣧⠀⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠄⠀⠀⠀⠀⠀⢕⠁⠄⠠⠍⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣵⣿⣿⣦⠀⢀⠀⠀⡐⠀⢤⢠⣊⡰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠠⠀⠂⠀⣴⣾⣿⣿⣶⡀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣯⣀⣿⣯⣨⣦⡀⠀⠀⠀⠄⣀⢐⠤⠢⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠐⢆⠂⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃⣂⠀⠀⠀⣀⡇⣒⠤⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⡟⠉⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⠿⠀⠅⠀⠀⣰⣿⣛⡛⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣻⣿⣿⡿⣿⡟⣿⣿⣿⣿⣇⡀⠼⣿⣿⣿⣿⣧⠄⠀⠀⠀ ⠀⠀⠀⠀⠐⠉⣶⣶⣦⠀⠀⠀⠀⢠⠾⡅⠀⠀⠙⢿⣷⣔⡢⠄⠈⢰⢟⠿⣿⡃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠎⠉⠉⣿⣟⣧⢷⣿⣿⣿⢛⠽⠁⠀⢺⣿⡿⠋⠁⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⣼⣿⣿⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠈⠙⠳⣾⣷⣏⣴⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣾⠀⠀⢿⣗⣿⣿⡹⡛⣿⣴⢖⣴⣶⣿⡿⠶⠿⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⢤⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣿⡜⢻⣷⠀⢀⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠀⠬⠿⠟⣯⡿⢧⡏⡽⣿⢟⣿⣿⠛⠚⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡿⠍⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠨⣿⣾⣿⠯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡍⣸⣟⡓⠲⠶⠆⠀⠈⠛⢸⡙⢹⢃⠟⡫⠁⠀⣠⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⠀⠐⠲⣿⣦⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣾⣿⣿⡝⣿⣿⡟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⠏⣿⣟⠏⣾⠿⢛⣭⠅⣷⠂⠀⠀⠀⠈⠁⡌⠈⠌⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠉⠉⠰⠺⣿⣿⡍⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠹⣯⢃⣈⣿⣯⠆⠀⡎⠀⠀⠀⠀⡴⠀⠀⢀⣠⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡁⠀⠂⠙⠀⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⣃⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠠⠠⠀⠠⠀⠀⠀⡌⠀⠀⣀⡠⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣷⠇⠀⠀⠴⠆⠁⠸⠉⢸⠇⠀⠀⠋⠀⠹⠋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠊⢶⢤⣴⡶⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⢈⠾⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠁⠉⠀⠁⠁⣌⢠⠀⠈⠁⣡⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⡀⠀⠀⠀⠀⠀⠐⠁⠠⠀⠉⠍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣑⠰⡂⠀⠀⣴⣿⣿⣷⣶⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣥⣾⣿⣦⣼⠆⠀⠠⡀⠀⡀⡠⢈⡢⣔⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣀⠸⠐⢡⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣽⠀⠁⠁⠀⣠⣁⣤⣄⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⡀⠐⠻⣿⣿⡿⠿⠀⠀⠄⣧⣿⣭⡍⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣿⣿⣿⣿⡯⣿⣿⣿⣿⣀⠀⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⢭⣶⣶⡀⠀⠀⠀⠰⠾⠟⠀⠀⠈⠻⣿⣾⠇⣅⠀⣻⣿⣿⣇⣠⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠎⠀⠈⣽⣿⣿⢹⣿⣿⣿⣿⠿⠁⠠⣻⣿⢟⠉⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠠⣬⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⢀⢻⡙⠛⠽⢿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣷⣿⠀⠀⣽⣾⢧⣿⡹⡟⣏⣴⢆⣴⣴⣿⡿⠾⠓⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡎⢻⣿⠁⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠀⠠⣿⠻⣯⡽⢣⠏⡽⣳⢛⣿⣿⠿⠆⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⢋⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣇⢸⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠍⣸⣿⣓⠲⣶⠆⠀⠉⠇⢸⢙⢽⠃⠟⡫⠃⠀⣠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⠂⠀⠲⢿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡿⠿⠉⣿⣿⡟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠋⣿⡟⣏⡾⠿⢋⣥⠀⡿⠀⠀⠀⠀⠅⠁⡈⠈⠌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⢴⣻⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣧⡄⠘⣿⣿⣿⣟⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⠀⢸⣿⣿⣇⠿⡟⣇⣤⢆⣤⣼⣿⡿⠄⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣬⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠇⠠⡿⢿⣿⡯⣣⠇⣽⣱⢻⣿⡿⠧⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡟⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣧⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡟⣸⣿⡓⠲⣶⠆⠀⠛⠁⣘⠚⢷⠇⡾⡣⠁⠀⡤⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠖⠀⠩⢭⣷⠀⠀⠀⠀⠀⡀⡀⢀⣠⣾⣿⡿⣿⠀⠘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡟⢏⡾⢟⢛⡩⢠⠗⠀⠀⠀⠀⠃⠀⠘⡘⡰⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⠀⠀⠀⠀⠀⠁⠀⠉⠿⠟⠉⠁⠀⠀⢠⡍⣿⣿⣟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⡻⠀⢘⣿⡹⠁⢀⠂⠀⠀⠀⠀⠀⡀⠈⠈⢀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠛⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇⠀⠂⠀⠰⠃⠀⠀⠁⢀⠀⠀⠀⠀⠀⢸⠀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣷⠀⠠⠆⢤⠄⠀⠀⠀⡘⠀⠀⣠⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠸⣿⣿⡎⠀⢠⠄⠃⢼⠆⠀⢰⠇⠀⠀⠁⠀⠘⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠂⢶⣤⣴⣾⠶⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠬⣤⣰⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡄⠀⠙⣀⠃⠁⡌⡄⠀⠈⠡⢃⠊⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠑⢡⠀⠠⠭⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣻⣽⣶⣿⡄⠀⠀⠠⠀⠀⠀⠀⠀⢎⡤⡻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡧⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⣿⠛⢻⣿⠀⠀⠀⠀⠀⢠⠈⡤⠈⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡐⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⢿⡇⠀⠐⢀⣀⣰⡎⣔⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⢰⣶⣶⣮⠙⠙⠳⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢽⣿⣿⣿⣧⡸⢿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠚⢉⣽⣶⣦⠀⠀⠀⣠⣶⡿⠂⠀⠙⣿⣿⣧⠳⡀⢼⣿⣿⣧⣤⡄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡷⠋⠉⠉⣿⣇⣿⣿⣿⣿⡷⠃⠰⢻⣿⠏⣠⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢼⣽⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⢸⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣶⡇⠀⠀⣿⣷⣺⣛⠻⣥⡶⣣⢦⣿⣿⡷⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣼⣿⣿⡿⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡎⠻⡟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⡷⠀⣾⢿⣿⣟⣼⣨⠏⣸⢫⣿⣯⡥⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡟⡛⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⠀⢡⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣩⣿⡛⠶⣶⠆⠙⢛⢡⡯⠃⠂⡇⡾⠫⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢦⠁⠨⢭⡇⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠙⡇⠀⠘⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡟⠟⡾⠿⡛⡭⢡⠷⠀⠀⠀⠘⠀⠀⢠⠠⠁⠂⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⢠⣾⣿⡿⠷⠀⠀⠀⠀⠀⢤⢿⣿⣿⣾⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠸⠹⠁⢘⣿⢹⠁⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⡘⣿⣿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⠀⠰⠃⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡆⠤⠄⢤⠆⠀⡀⢀⡎⠀⠀⣀⠀⠀⠀⣍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠇⣿⣿⡧⠀⠠⠜⠃⣽⠆⠀⠼⠀⠀⠀⠁⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣶⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢇⡏⣾⣷⣶⣷⡷⣾⢆⣿⣾⢀⣿⣾⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠈⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠊⢶⢤⣴⡾⡿⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢨⠄⢡⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⡁⠙⡲⠗⠁⠎⡀⠀⠈⠑⣡⠀⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠬⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢛⣿⣭⣵⣆⠀⠀⠀⠀⠀⠀⠀⠀⠪⢄⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣴⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⣿⠿⢻⣿⠄⠀⠀⠂⠀⢀⢀⣰⡸⡕⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠃⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣷⣾⣿⡇⠀⠀⠀⢀⣂⣺⣕⣰⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣶⣿⠃⠀⠀⢰⣿⣿⣶⠉⠉⠣⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⠟⣿⣿⣿⣿⣅⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠊⠋⣽⣷⣄⠀⠀⠀⣠⣴⣾⠃⠈⠻⣿⣿⣏⠶⠀⠀⣿⣿⣿⣷⣴⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⠏⠉⠙⣜⡐⣿⣟⣿⡻⠟⠁⠹⣿⣿⠋⢀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢤⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⢻⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⡿⠀⠀⣷⣿⣘⢛⢻⣴⢞⣴⢠⣿⡷⡥⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣿⣿⡿⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡌⠸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠀⢸⢿⣿⢯⡞⣬⠋⣸⢣⣾⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡟⡛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡧⠀⠋⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣣⣿⡛⠲⣶⠖⠈⢻⢸⡿⠁⠈⡎⢸⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢶⠁⠈⢭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠐⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⠝⡹⠿⠛⣩⠁⡗⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ 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⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣽⣭⣭⣿⠀⡁⠄⡆⣿⣦⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⡿⠿⢿⣿⠄⠄⣥⣨⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣾⣿⠀⠀⣰⣯⣿⡿⠟⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣻⠿⣿⣿⣟⣿⣿⣯⣽⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⣽⣿⣶⣆⠀⠀⢀⣠⣴⡶⠃⠘⣿⣿⣷⣾⠯⠄⠰⣿⣯⣯⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡁⠀⠀⣽⣿⣻⡛⠟⡉⠈⠉⣫⣿⣿⢏⢀⣠⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣩⡄⠀⠙⠛⠁⠀⠀⠀⠸⣿⣶⣷⡀⠀⠀⢸⣿⣯⣄⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣿⣟⣏⣵⡿⠃⠀⣴⡇⣾⡏⠄⠊⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣼⣿⣿⡏⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣿⣿⣧⠀⠀⢈⣿⡟⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⠟⠀⠿⣿⢷⡇⡾⠁⠀⠠⡿⢡⣏⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠰⢾⡏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡟⢡⣿⡛⡻⠿⠟⠈⠸⡄⠁⠀⠀⠀⡇⠘⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠰⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⠘⢰⢿⠛⣭⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⢀⣠⣙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠟⠁⠘⣻⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢿⣿⣿⣿⠟⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣇⠢⠀⠀⠊⠀⠀⠊⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡼⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⠤⠀⡴⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣿⡧⠀⠀⠄⠚⢹⡷⠰⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡧⣤⠀⠙⠛⠁⠀⠀⠀⢹⣿⣯⣽⡉⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠀⢸⣿⣿⣿⣥⣿⠋⠀⠀⣴⡿⣸⡟⠅⠘⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⠟⠀⡘⠿⡯⣟⢸⠃⠀⠀⢀⣾⠇⣞⡽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢠⡄⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⠃⠸⢛⢚⠿⢿⠁⠀⠃⠁⠀⠀⠀⠈⠿⢰⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⡾⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⡅⠠⠨⢛⡥⠀⠘⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠁⠀⠀⣡⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⢹⠀⠘⣻⠟⢃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⣼⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠠⠆⠀⠀⠊⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠛⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⣠⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⠋⠁⠀⠀⠘⢹⢷⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⠰⣶⣶⣶⣶⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⠀⠉⣾⣾⣾⣾⣾⣶⣷⣾⣾⣦⣷⣿⡖⠁⢁⣬⣦⡅⠈⠁⠡⢨⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⠯⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣂⢁⢑⡂⣛⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⢿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⢻⣿⣦⠀⢀⣘⣐⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⣰⣿⣿⣿⣿⣛⣳⣾⠃⠀⠀⠀⠉⣴⣧⣿⣿⣿⠏⠁⠀⠀⠀⠀ ⠀⠀⠀⠰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠈⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠰⠝⠉⠛⣿⣿⡿⢼⠃⠀⠀⠀⢀⣾⣿⣿⠿⠆⠐⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⢟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⢻⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⡿⠷⡲⢠⠦⠀⠠⠘⠙⠀⠃⠀⠀⠀⠀⡌⣼⢫⠊⠀⣰⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⣿⣽⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠁⠰⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡑⠁⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠹⣿⡯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠀⢀⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⡟⠀⠂⠀⠀⠛⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⢂⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⡀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢰⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡿⠿⠃⠀⠀⠀⠀⡀⠰⡀⠀⠀⠀⠶⠂⠀⠀⠸⠿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣷⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠎⢶⣤⢶⣿⡷⠆⠀⠀⠀⠀⢀⣥⣤⣬⠀⠀⠈⠈⠁⠈⠈⠁⠈⠀⠁⠈⠈⣴⣿⣾⣾⣾⣾⣾⣶⣷⣾⣬⣶⣧⠁⠀⠁⡥⣼⣦⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡷⠦⢆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠔⠆⢒⣸⠵⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣶⣥⡄⢀⣶⣶⣷⣶⡦⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣽⠟⢻⣷⡓⢃⠀⢰⣷⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢁⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣈⠟⢙⣿⡿⣇⠐⡺⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⠯⣛⢓⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣷⣿⣷⣴⡯⣒⡙⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠃⣹⠫⠀⢿⣿⣿⣿⣿⣤⠀⠀⠀⠀ ⠀⠀⠀⣶⣿⣿⡿⠳⠀⠀⠀⠀⠀⠀⢀⣤⣶⠏⠈⢿⣿⣿⣿⣷⠇⠴⠿⢝⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⢋⠀⠅⡑⠅⡀⠠⢿⣿⢿⣉⡀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠹⠋⠁⠀⠀⠀⢻⣷⣦⠀⢀⣙⣮⣛⣳⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⠀⠀⣴⣿⣿⣿⣿⢻⣻⣷⠟⠀⠀⠀⠈⣵⣢⣿⣿⡿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⡿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠸⡟⠛⢛⢻⡟⡾⢠⡏⠀⠀⠀⢀⡾⣿⣿⠿⠌⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⢟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⠿⠕⠲⢲⡒⠀⠠⠝⠋⠑⠘⠀⠀⠀⠀⠞⡼⢋⠋⠀⣼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠰⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⡑⠁⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠈⠘⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⢤⣄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡦⠊⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⡿⠀⠃⠀⠈⠋⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣼⢂⣴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⠿⠻⠃⠀⠀⠀⢀⠀⠢⣀⠀⠀⠰⠿⠃⠀⠀⠸⠿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⡤⢲⣿⠷⠆⠀⠀⠀⠀⢁⣡⣤⣌⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⡅⠁⠀⠁⠅⢈⠀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠨⠱⢌⢞⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣤⣄⣀⠀⡀⠀⣀⣺⠟⢯⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣺⡇⢠⣾⣿⣿⣿⣶⠄⠀⠀⠀⠀ ⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣿⣿⣏⣫⣿⣇⣈⠀⠠⡀⣠⢗⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣁⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⢉⣿⠿⢻⠀⢐⣏⠗⡗⠅⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠿⡚⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣷⡾⡥⣼⢢⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⢤⠀⢓⢅⠸⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣿⣿⣿⢷⠀⠀⠀⠀⠀⢀⣤⣶⠇⠈⢿⣿⡿⠿⠾⠁⣂⢬⠷⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⢹⣿⣿⣿⣿⣟⣿⠟⢋⠀⠁⢂⠁⠽⣿⡿⢋⣤⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣷⣾⠆⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⢻⣷⡆⠀⢰⢰⣳⣞⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⣿⢻⣿⣷⠟⠀⠀⢀⣴⣷⣿⣿⠿⡋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣷⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢏⣀⠹⡟⠫⢹⣿⡏⡞⢰⠏⠀⠀⠀⡞⣿⣯⠭⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡓⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠃⠛⠛⠻⡿⢻⠃⠀⠘⠛⠉⠀⠊⠀⠀⠀⠸⡸⢋⠃⢀⡼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠡⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠐⣾⣿⣿⣷⣾⠆⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⢻⣿⡆⠀⢰⢸⣧⣟⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⣿⢻⣿⣷⠟⠀⠀⢀⣴⣷⣿⣿⠿⡋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣷⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢏⣀⠙⡻⠫⠹⣿⡋⡞⢰⠏⠀⠀⠀⡾⣿⣯⠭⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡓⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠃⠛⠛⠻⡿⢻⠃⠀⠨⠙⠁⠀⠊⠀⠀⠀⠸⠸⢛⠃⢀⡼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠡⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢩⠋⠀⡀⠀⠘⣶⡖⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⢨⣵⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣯⢀⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣏⣿⣿⠁⢀⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⣀⠀⠀⠀⢨⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠇⠀⠂⠀⠀⢺⡮⡆⠀⠇⠀⠀⠛⠋⠀⠀⠀⠺⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣶⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣶⣾⣿⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⢄⣴⢶⣾⠗⠀⠀⠀⠀⠀⣁⣤⣬⡀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣮⡄⠁⠁⠀⠁⣡⠈⠀⠁⠈⠁⠁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡊⠭⠿⠻⢽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡩⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⠦⠀⠠⠈⠮⢆⠎⣠⠭⣧⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡇⢰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠈⠋⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⣰⣶⣶⣶⠂⠀⠀⠀⠁⠁⢠⣾⣾⡆⠈⠈⠁⠈⠈⡅⠈⠀⠁⠈⢸⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⠀⠁⠁⠀⢁⣡⠌⢤⡇⠈⠁⡁⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⡲⢬⢼⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡷⠦⠀⠀⠈⠎⠻⠁⢒⣵⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⣿⣿⣿⣷⠀⠐⠀⠀⠠⣬⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣿⣏⣈⣿⠀⠴⢍⢀⢰⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢄⡰⠈⢀⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣇⠀⢀⣠⣶⡮⠈⠻⣿⣿⡻⠓⣒⣖⡘⣗⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⠀⠀⢹⣿⣿⣿⣿⣿⣿⠿⠛⠁⢱⠹⢿⣿⣏⣤⣦⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣴⡇⠀⠈⠙⠋⠀⠀⠀⠘⢿⣿⡁⠈⣿⣿⣿⣽⣿⣿⢷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣾⣿⣿⣿⣿⢛⣛⣯⡞⠁⢰⣦⣿⣧⣿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠨⣿⣿⣷⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⡘⢿⣿⣿⣿⣏⡾⢠⠟⠀⠀⡞⡼⣟⣋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠟⠁⠋⠸⠋⠻⢿⠿⡓⠀⠹⠟⠉⠆⠛⠀⠀⢸⢡⡟⡃⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠹⣻⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢋⣄⠐⠀⠀⠈⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣓⠀⠟⠀⠀⢈⡼⠊⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⢀⡙⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⣋⣻⣿⣿⣿⣿⣿⣿⣿⢿⠿⡿⣷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⣀⠀⠀⠀⠀⣿⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠰⣿⣿⣿⡿⣿⣿⣿⢿⣿⡿⠤⠃⠉⠁⠀⠀⠀⡠⠞⣲⠆⠀⠀⠄⠀⠐⠛⠁⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣶⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣿⣾⣿⠀⠙⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠎⢶⠄⠰⣶⣶⣶⡦⠀⠀⠀⠀⠁⠀⠸⣾⣿⣾⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⣶⣿⣾⣾⣾⣾⣾⣶⣷⣾⣾⡄⠁⠁⠀⣁⣥⣌⠀⠧⠈⠁⢡⠈⠈⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡈⢭⢼⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⠶⠄⠀⠀⠀⠀⠀⡀⠄⠐⡋⣃⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢾⣿⣿⣿⡆⠀⠀⠀⠐⣐⠦⣰⠄⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣅⣸⡇⠀⠀⠀⢀⡪⢿⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠠⢥⣸⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⣿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣾⡀⢀⣠⣶⠆⠙⢿⣿⣟⢏⠓⠀⢸⠹⡻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠟⠹⠽⣿⣿⣃⣠⣤⠀⠀⠀⠀⠀ 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⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢠⣾⣿⣿⡄⠀⠄⢦⠰⠀⣊⠠⢄⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣰⣿⣏⢩⣧⠐⡉⠂⣠⠞⡩⣶⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢀⣽⣿⣿⣿⣿⡇⠀⠀⠀⢔⠇⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣏⣀⣤⡶⠀⠙⣿⣿⣟⢟⡁⢠⢘⠙⠅⣷⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⠉⠀⡯⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⡿⠁⢀⣤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡉⠁⠉⡍⠁⠀⠀⠀⠻⣿⣷⡋⠀⣮⣦⣌⣿⣿⣷⣭⣿⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⣿⣿⣿⣿⡟⣛⣻⡶⣾⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣎⢻⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢠⣿⣿⣿⡿⣰⡋⡽⠁⡟⢸⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠸⣿⣿⢿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢸⠿⠯⣤⣦⣭⠋⢟⡇⠘⠘⠐⠈⡇⡾⠢⠖⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣿⡟⠏⣴⣷⠶⠷⠚⢭⡷⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢠⣄⣛⣯⣼⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⡟⠀⠻⢿⠉⠵⣶⡊⠊⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⢻⠻⠿⠟⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠜⠉⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣄⠀⠀⠝⠀⠁⠀⠀⠁⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⡿⣿⣿⣿⣿⣿⡿⠹⠏⠙⠀⠀⠀⢠⡖⠈⠰⠄⠀⠀⠀⡼⠀⠘⠋⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣶⣷⣷⣿⣿⣶⣷⡗⣸⣷⣾⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠎⢶⠄⠰⢶⣶⣶⣴⣤⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠁⠈⠈⠑⠈⠀⠁⠈⠈⠀⣽⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⡅⢡⠂⠡⣁⢨⣄⡄⠈⠁⠁⢨⣬⡆⠀⠁⠉⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠅⠶⢠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣷⣶⠤⠀⠀⠀⠀⠀⠀⠁⠰⠋⠭⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣥⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢆⣷⣿⣿⡆⠀⠐⡀⢀⢀⣁⡰⠒⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣿⣏⢉⣧⠀⢰⡀⠠⠐⣚⣫⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⢀⣽⣿⣿⣿⣿⠃⠀⠀⠄⡄⠖⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣀⣤⡶⠀⠙⢿⣿⣟⢟⣁⢠⢜⠙⢴⣷⣿⣿⣿⣯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⠋⠁⢻⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠁⠀⣰⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡉⠉⠉⠟⠁⠀⠀⠀⠻⣿⣷⡉⢠⣮⣭⣧⣿⣿⣷⣬⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⣸⣿⣿⣿⡟⣛⣳⣷⣿⢸⣿⠃⠀⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣎⢹⣿⣿⣿⣿⠁⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠠⡿⣿⣿⣿⢡⠏⡼⢡⡏⢸⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠘⣿⣿⢿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢹⢿⠯⣤⣤⣬⠙⢻⡇⠐⠁⠹⠈⡇⣼⢸⡴⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠿⣿⡆⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣻⡟⡝⣰⣯⠶⠷⠶⢩⣽⠀⠈⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢠⣄⣛⢿⣴⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⡟⠀⠹⣻⠉⢭⣶⡞⠐⠃⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢠⣤⣤⣄⠈⠻⠙⠛⡟⢿⣿⡏⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠀⠀⠁⠀⠔⠉⠀⠀⠀⠘⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠙⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⣤⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⢀⠶⠀⠐⠆⠀⠀⠀⢰⠀⠀⠉⠀⠀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡗⣸⣿⣾⣿⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠎⢶⠄⠰⢶⣶⣦⣴⣤⠀⠀⠀⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣧⢁⠂⢡⢁⠈⡄⠀⠨⠁⠁⠈⢨⣪⡄⠁⠉⠈⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⡅⠬⣬⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⡤⠀⠀⠀⠀⠁⠀⠀⢘⢒⠽⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣥⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠯⣽⣷⣿⡆⠀⠀⠀⠀⠂⠀⣀⢐⣖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣤⣼⣟⠉⣯⠀⢐⠀⢀⢈⣱⣱⣶⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢀⣽⣿⣿⣿⣻⠏⠁⢀⣁⡁⠴⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣀⣤⣶⠀⠙⢿⣿⣟⢟⣇⢄⠕⠁⠤⣾⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡱⠋⠉⢛⢻⣿⡿⣿⣿⣿⣿⢿⢿⣿⡿⠁⠀⣠⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡅⠉⠉⠋⠁⠀⠀⠀⠻⣿⣷⡻⣀⣬⣦⣧⣽⣿⣷⣮⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⣰⣿⣿⣿⡾⣻⢹⡼⣾⢸⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣎⢻⣿⣿⣿⣿⠃⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⠀⣿⣿⣿⣿⢧⢟⣼⠃⡏⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠘⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⠿⣤⣤⢥⠙⢻⠟⠀⠇⠣⠊⡇⢸⢐⡤⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⣿⡌⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣻⣿⠟⢠⣫⠶⠳⠆⢩⣿⠀⠀⠁⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢠⣈⠛⢏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⡟⠀⠹⣿⠏⢫⣶⣞⠑⠃⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣰⣿⣿⣷⡄⠻⣿⣾⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡾⠀⠀⠁⠀⠕⡋⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⣀⡈⠉⠉⠁⠉⠛⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠘⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⠁⠀⠀⢀⠶⠒⠀⠆⠀⠀⠠⠂⡇⠀⠘⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣾⣲⣷⡧⣴⣓⣾⣲⣷⣷⢰⣷⣞⣶⣷⣿⣾⣷⢻⣷⣷⢧⡏⣾⣷⣶⣷⣿⣾⢆⣿⣾⢀⣾⣾⣷⣷⣿⣿⣶⣷⡟⣸⣶⣾⣿⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠊⢶⠄⠰⢶⣶⣶⣴⣦⠀⠀⠁⠁⠀⠈⠀⠀⠈⠈⠀⠈⠈⠁⠈⠀⠁⠈⠈⠀⢹⣾⣾⣾⣾⣾⣶⣷⣾⣾⣶⣥⢁⠂⢡⢁⠈⡄⢠⣬⠁⠁⠈⠈⢠⣢⠁⠉⠈⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 6570 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_8/2/2022:_Fragments_2.0_and_Comparing_Various_GNU/Linux_Distros Online⠀✐ Posted in News_Roundup at 7:30 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ 5_Reasons_to_Install_Linux_on_an_Old_Computer⠀⇛ Short on cash to upgrade your PC? Installing Linux is a great way to breathe new life into your aging computer and save money. A lot of people like to use Linux on older machines. The reasons for doing so obviously vary from person to person. Some may want to save money by not upgrading to a new computer, whereas others may wish to avoid e-waste. And yes, you’ll also find many people who think running Linux is fun. If you’re struggling to find a solid excuse, we’ll list out various reasons why you should consider installing Linux on your old computer. o § Audiocasts/Shows⠀➾ # ⚓ WP_Briefing:_Episode_24:_Three_Goals_in_2022⠀⇛ In episode 24 of the WordPress Briefing, the Project’s Executive Director reviews three big- picture goals for the year: Increased Gutenberg adoption, support of all open source alternatives, and stewarding the open source ethos. # ⚓ Late_Night_Linux_–_Episode_163_–_Late_Night_Linux⠀⇛ Why FOSS is unlikely to gain traction in education, what’s great about Discourse, Linux gaming, the uncertain future of Termux, our thoughts on Snap and Flatpak, and more. # ⚓ Middle_Mouse_On_Linux_Is_Incredibly_Powerful_–_Invidious⠀⇛ I rarely touch my middle mouse button but it turns out it has a lot more power than I ever knew, there’s the obvious autoscroll feature in browsers which I didn’t know worked on Linux but there’s so much more # ⚓ If_you’re_not_using_Flatpaks,_you’re_doing_Linux_wrong._– Invidious⠀⇛ They’re the future of Linux app distribution. Distros like Elementary, Pop, and even Steam OS support them by default. So here’s what they are, how they work, and a bit of their history! o § Applications⠀➾ # ⚓ Flatpak_App_of_the_Week:_Fragments_–_Modern_BitTorrent Client_for_the_GNOME_Desktop⠀⇛ Fragments is an easy-to-use BitTorrent client based on the well-known Transmission BitTorrent client (uses transmission-daemon), which is used as a backend for transferring data. The app is written in GTK and it’s designed specifically for use with the GNOME desktop environment. You’re probably already using Fragments since it is being developed for a few years now. But the latest release, Fragments 2.0, caught my attention as it brings lots of new features and improvements, and it’s completely rebuilt using Rust, GTK4, and the libadwaita library. # ⚓ GNOME_BitTorrent_Client_Fragments_2.0_Released!_GTK4, Libadwaita_&_Remote_Control⠀⇛ The Fragments BitTorrent client finally released version 2.0. It’s now uses Rust, GTK4 and the new Libadwaita library to provide a stylish user interface for those running Linux with GNOME desktop. For those never heard of Fragments, it’s a free open-source torrent app that uses Transmission as backend for transferring data. With it, user may starting downloading via… # ⚓ BitTorrent_Client_‘Fragments_2.0′_for_Linux_is_Here, Rebuilt_Using_Rust_with_a_New_UI⠀⇛ Fragments is one of the best torrent clients for Linux. The latest Fragments 2.0 is a significant upgrade, completely rewritten from scratch using Rust, GTK 4, and Libadwaita. In addition to the technical improvements, you will also find some new features and an improved user interface. # ⚓ The_road_to_Fragments_2.0⠀⇛ It was a bit quiet around Fragments, many had the fear that Fragments will no longer be maintained. These rumors I can proudly counter, and can now announce that Fragments 2.0 is now available after about a year of development! # ⚓ Twine:_Open_Source_Tool_for_Making_Games_with_Words,_aka Interactive_Fiction⠀⇛ Everyone has a game inside them waiting to come out, just like a chestburster. Unfortunately, not everyone has the skills to create a game, especially one complete with graphics. Thankfully, there is a way to create a fun game using only words. Let me share an application that could help you with it. As I alluded to above, Twine allows anyone to create a game without needing to know how to write code. Remember those Choose-Your-Own-Adventure books? That’s essentially how Twine works. You create a series of passages, which can be one sentence or a wall of text. You named each of these passages, so you can keep track of them. After that, you connect these passages and create several paths for the player to follow based on their decisions. o § Instructionals/Technical⠀➾ # ⚓ Metasploit_Tutorial_for_Beginners_–_Basics_to_Advanced⠀⇛ Metasploit, one of the most widely used penetration testing tools, is a very powerful all-in-one tool for performing different steps of a penetration test. If you ever tried to exploit some vulnerable systems, chances are you have used Metasploit, or at least, are familiar with the name. It allows you to find information about system vulnerabilities, use existing exploits to penetrate the system, helps create your own exploits, and much more. In this tutorial, we’ll be covering the basics of Metasploit Framework in detail and show you real examples of how to use this powerful tool to the fullest. # ⚓ Running_unit_tests_in_Jenkins_–_Octopus_Deploy⠀⇛ Verifying code changes with unit tests is a critical process in typical development workflows. Jenkins provides a number of plugins to collect and process the results of tests allowing developers to browse the results, debug failed tests, ignore some test failures, and generate reports on the history of tests over time. In this post, you learn how to add unit tests to a Jenkins project and configure plugins to process the results. # ⚓ Running_end-to-end_tests_in_Jenkins_–_Octopus_Deploy⠀⇛ End-to-end (E2E) tests represent the final stages of automated testing. E2E tests are long-running, especially compared to unit tests which can complete thousands of checks in seconds. They are typically executed by external tools which interact with the application under test, through public interfaces like web pages or HTTP APIs. In this post, you learn how to run E2E tests with Cypress to validate interactions with web pages and with Newman, the command-line test runner for Postman, to validate HTTP APIs. # ⚓ Install_Facebook_Messenger_On_Ubuntu_22.04_LTS_[Update]⠀⇛ No doubt Facebook is one of the most popular social media networks these days. Now under Meta, Facebook has a massive userbase with a high volume of usage. 1.93 billion people use Facebook on daily basis. You can access Facebook from the web browser or from its official mobile application. Meanwhile, there are plenty of third-party apps available these days from where you can access and manage your Facebook account. In this tutorial post, we are going to show you the process to Install Facebook Messenger on Ubuntu 22.04 LTS. # ⚓ How_to_Setup_Django_with_Postgres,_Nginx_and_Gunicorn_on Ubuntu_20.04_–_RoseHosting⠀⇛ Django is an open-source web framework written in Python. It is a popular all-in-one web framework and one of the top choices for many developers. Django offers many advantages, such as MVT (Model View Template) architecture, automatic admin panel, and powerful ORM (Object Relational Mapping) database support. It also offers awesome debugging tools for developers. In this tutorial, we will show you how to install Django with PostgreSQL as the database storage instead of the default SQLite, Nginx as the reverse proxy, and Gunicorn as the application server on Ubuntu 20.04. # ⚓ How_to_Install_Angular_on_Ubuntu_–_VITUX⠀⇛ Angular is a free and open-source JavaScript-based framework for developing single-page applications, it is the successor of the AngularJS framework. It is maintained by Google, the same company that created JavaScript and made Angular a household name. According to Google Developers, it can be used on top of “MongoDB, Node.js by IBM, Express by Nodejitsu”, etc., which makes it possible for you to develop an app without having to worry about what technologies will power your application. If you’re looking to get started with Angular, one of the best ways to do that is to install it on your own Ubuntu server. This will allow you to test your app on different browsers like Google Chrome and Mozilla Firefox. In this guide, we’ll show you how to install Angular on Ubuntu 20.04. The same procedure works on Ubuntu 22.04 as well. We’ll also cover some basic steps for getting started with Angular development. So, whether you’re a beginner or an experienced developer, this guide is for you! # ⚓ How_to_Set_Up_Nginx_with_Google_Pagespeed_Module_on_Debian 11⠀⇛ Google Pagespeed Module is an open-source module for optimizing your websites under the Nginx and Apache web-server. The Pagespeed module is a server-level module installed alongside the Nginx and Apache webserver. The Pagespeed module improves the performance and speed of your website by optimizing static files on your websites. The Pagespeed module optimizes images on your websites, minify static files such as HTML, CSS, and JavaScript, and optimize file caching. In this tutorial, we will show you how to build the Nginx Pagespeed module on the latest Debian 11 Bullseye. This guide can be applied to the current of your Nginx installation because you just build the Nginx module. # ⚓ Linux_for_freshers:_How_to_Install_ranger_in_Ubuntu 18.04?⠀⇛ Ranger is a free and open-source command-line file manager for Linux. It comes with a minimalistic text-based user interface and VI key bindings support. The main design goal of this file manager is switch directories and browse files in a quick and easy way. Some of the main features are preview the selected file or directory and automatically determining file types and running them with correct programs. It supports VIM like hotkeys, UTF-8, multi-column display, mouse support, builds in Tabs, and bookmarks support. # ⚓ How_to_Install_Lighttpd_with_PHP_in_Ubuntu_20.04⠀⇛ The concept of web servers has crossed the minds of most, if not all, Linux enthusiasts; especially the ones interested in pursuing web-based projects and careers. Due to the numerous web servers offered to the Linux community, you might feel like tossing a coin or rolling a dice to find the one that ‘might’ suit your web-based needs. Lighttpd is best attributed as a compatible, very flexible, fast, and secure web server. It is therefore optimized for high performance on whichever operating system environment hosts it. Also, this web server is indeed light such that it needs very few resources to run or execute its functional objectives like handling AJAX applications. This web server is BSD licensed, open-source, with flawless compatibility on UNIX- like systems. This article seeks to walk you through the installation and configuration of Lighttpd as an ideal web server for your Ubuntu 20.04 operating system. # ⚓ How_To_Install_MySQL_Workbench_on_AlmaLinux_8_–_idroot⠀⇛ In this tutorial, we will show you how to install MySQL Workbench on AlmaLinux 8. For those of you who didn’t know, MySQL Workbench is a graphical user interface tool for general administration and maintenance of MySQL/MariaDB database systems available in a free and a commercial edition. For detailed features differences among MySQL Workbench Edition have been described on MySQL Workbench features. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the MySQL Workbench on an AlmaLinux 8. You can follow the same instructions for CentOS and Rocky Linux. # ⚓ How_To_Install_Anaconda_on_Fedora_35_–_idroot⠀⇛ In this tutorial, we will show you how to install Anaconda on Fedora 35. For those of you who didn’t know, Anaconda is an open-source package and environment manager that houses thousands of predictive analysis, machine learning, and data science packages. It is written in Python and R programming language by data scientists, for data scientists. It includes the packages related to data science for various platforms like Linux, Windows, and macOS. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you the step-by-step installation of the Anaconda on a Fedora 35. # ⚓ How_to_Use_Hadolint_to_Lint_Your_Dockerfiles_–_CloudSavvy IT⠀⇛ Dockerfiles define the content of Docker images as a set of instructions in a text file. The Dockerfile syntax is generally straightforward but there are some gotchas to avoid. Adhering to best practices while writing complex Dockerfiles in a team setting can be tricky unless you’re automatically validating your file’s content. Hadolint is a Dockerfile linter that can spot common issues for you. It uses an abstract syntax tree (AST) to parse your Dockerfile against predefined rulesets. Hadolint also incorporates ShellCheck so it can lint the shell scripts in your Dockerfile’s RUN instructions too. # ⚓ How_to_get_the_directory_size_using_the_Linux_command_line –_PragmaticLinux⠀⇛ With the help of your desktop environment’s file manager, you can easily obtain the size of a directory’s contents. Right-click the directory and select Properties from the pop-up menu. When working on the command line in the terminal, it’s a different story. For example, when interacting with a server over SSH. This article explains who to get the size of a directory using the Linux command line, while working in the terminal. # ⚓ How_to_create_a_custom_image_from_a_Docker_container_| TechRepublic⠀⇛ Your containers are all based on images, most of which you probably pull from DockerHub or some other public repository. But why not create your own custom images? After all, it’s easier for you to not only get the exact image you need to work with, it’s also a better route to security. It’s also a great way to create a base image you can use for a repeatable development environment (so, it has exactly the tools you need). # ⚓ How_to_install_Friday_Night_Funkin_on_a_Chromebook_– Windows_64_Bit_version⠀⇛ Today we are looking at how to install Friday Night Funkin, the 64 bit Windows version, on a Chromebook. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ How_to_install_Friday_Night_Funkin_on_a_Chromebook_– Windows_64_Bit_version⠀⇛ # ⚓ How_to_install_YubiKey_Manager_GUI_on_Linux⠀⇛ One can use a hardware security key such as YubiKey for OTP or FIDO2 for additional security on Linux to protect disks, ssh keys, password manager, web applications and more. Since I am a full-time Linux desktop user, I thought today I would document how to install the YubiKey GUI Manager to configure functionality on your YubiKey on a Linux desktop. # ⚓ How_to_install_whois_on_Ubuntu_/_Debian_Linux⠀⇛ While working on the client’s system, I found that the whois client was missing. So I used that in one of my deployment scripts. I should add that to cloud-init or Ansible, but the Ubuntu server was already running. The whois command searches an object in an RFC 3912 database without using online websites. For example, you can find out who is the owner of an IP address or domain name from your Debian Linux command-line. You can automate stuff in your shell script. Here is how to install whois client on your Debian or Ubuntu Linux. # ⚓ Install_Kate_Text_Editor_on_Ubuntu_22.04_LTS_– LinuxCapable⠀⇛ Kate is a powerful and intuitive editor that may be the perfect fit for you. With its robust yet straightforward interface, Kate offers everything from word processing to development tools in one place – which saves time! And with 200+ languages available on-board alongside plugins galore (think code hooks), this tool will help maximize productivity, whether it’s coding or content creation. In the following tutorial, you will learn how to install Kate Text Editor on Ubuntu 22.04 LTS Jammy Jellyfish. # ⚓ Install_Fragments_2.0_On_Ubuntu_/_Rocky_Linux_&_Fedora_| Tips_On_UNIX⠀⇛ Fragments is an open-source BitTorrent client for Linux systems and developed by the GNOME desktop environment. This tutorial will be helpful for beginners to install fragments 2.0 on Ubuntu 20.04 LTS, Rocky Linux 8, AlmaLinux 8, and Fedora 35. It is used to transfer huge files like videos, Installation media images and it uses BitTorrent protocol. Fragments 2.0 is the major update with many new features and improvements. Fragments now use the GTK4 and the new GNOME Libadwaitaa Library under the hood. # ⚓ Install_7-Zip_on_Debian_11_Bullseye_–_LinuxCapable⠀⇛ 7-Zip is a free, open-source file archiver software used to compress files into archive containers or, in more popular terms, zip files into archive containers that can beat most other forms of compression by 2 to 10% and strong AES-256 encryption in 7z and ZIP formats. 7-Zip isn’t as famous as some of the other archives, but it is capable of having multi archive format support across most known software. Another benefit is that it supports all cross-platforms, making it efficient to use amongst different operating systems. # ⚓ Install/Upgrade_GNOME_Subtitles_on_Ubuntu_20.04_LTS_– LinuxCapable⠀⇛ GNOME Subtitles is an easy-to-use subtitle editor for Linux. It allows you to add subtitles and captions with preview, timing synchronization capabilities (including language translation), spell-checking support, and more options that are only possible in this simple tool! The interface of GNOME Subtitles includes emphasis styles such as bold/italic or underline applied automatically when needed alongside multi-level undo & redoes, making it the perfect choice if minimalism isn’t really what matters most here… In the following tutorial, you will learn how to install or upgrade your existing GNOME Subtitles using PPA for Pedro Castro, endorsed by the GNOME Subtitles team. # ⚓ Install_WhatsApp_Client_On_Ubuntu_22.04_LTS/_Ubuntu_20.04 LTS_|_Itsubuntu.com⠀⇛ WhatsApp is one of the most popular messaging apps right now in the World. Facebook bought WhatsApp in February 2014, for $16 billion. WhatsApp is currently available for Android, iOS, and Windows operating systems. Sadly it is not available for Linux-based operating systems. WhatsApp’s official client app is not available to install on Linux but doesn’t worry we are here to help you in this process. In this post, we are going to show you the way to use the WhatsApp clients on Ubuntu. Thanks to the third-party tool WhatsDesk that lets us use WhatsApp client on Ubuntu. Whatsdesk is an unofficial WhatsApp client for Linux and is available as a Debian package. You can also get it on the snapcraft repository. # ⚓ Install_RPM_Packages_on_Ubuntu_22.04_LTS_–_LinuxCapable⠀⇛ The Ubuntu repositories contain thousands of deb packages that can be installed from the Software Center or by using the apt command line. Deb is an installation package format used in all Debian- based distributions, including Ubuntu, but some aren’t available through these methods; alternative sources such as existing RPM repositories may contain these. RPM package format is used by Red Hat and its forks such as Almalinux, CentOS Stream, and Rocky Linux, to name a few. For Ubuntu users, an application called alien allows you to install RPM packages on Ubuntu or convert an RPM package into a Debian (.deb) file for Ubuntu. In the following tutorial, you will learn how to install RPM packages and convert a Debian package into an RPM package on Ubuntu 22.04 LTS Jammy Jellyfish. # ⚓ Install_Neofetch_on_Debian_11_Bullseye_–_LinuxCapable⠀⇛ Neofetch is a free, open-source command-line system information tool written in bash 3.2+. Neofetch displays system information in a beautiful aesthetic way, such as system, software, memory resources, kernel version, and much more. In the following tutorial, you will learn how to install Neofetch and some basic commands on Debian 11 Bullseye desktop or server. o § Games⠀➾ # ⚓ FEX-Emu_is_a_promising_project_for_gaming_on_64bit_Arm_| GamingOnLinux⠀⇛ Want to play more games on Arm devices? Projects like Box86 and Box64 do already exist but is there a better option? FEX-Emu sounds like it’s going to be another great open source way to do what you want. The problem is that most games and software aren’t really built for Arm, games especially of course since we’re not exactly swimming in powerful Arm hardware market for gaming on Linux (or Windows). Emulation and translation layers once again to the rescue then. FEX-Emu is getting quite advanced now, and it’s even able to run Wine / Proton too. # ⚓ Top_10_New_Games_You_Can_Play_on_Linux_with_Proton_–_Feb 2022_Edition_–_Boiling_Steam⠀⇛ We are back with our usual monthly update! Boiling Steam looks at the latest data dumps from ProtonDB to give you a quick list of new games that work (pretty much?) perfectly with Proton since January 2022 – all of them work out of the box or well enough with tweaks… # ⚓ Steam_Deck_Previews_are_up,_plus_dbrand_announce_Project Killswitch_|_GamingOnLinux⠀⇛ The flood gates are beginning to open around the Steam Deck with a few big YouTube channels doing a hands-on preview now live. Plus, dbrand poke fun at Nintendo with their upcoming Steam Deck accessory kit. # ⚓ Building_a_Retro_Linux_Gaming_Computer_–_Part_11:_Forgotten Heresies_|_GamingOnLinux⠀⇛ Almost from the very start Raven Software and id Software had a symbiotic relationship. Raven would use id tech to power their games for years, but one of their deepest collaborations was on Heretic, with then id Software designer John Romero even acting as producer. Given the Linux friendly atmosphere at id, it is no surprise that some of that would start to rub off on Raven, culminating in Loki Software negotiating to make a port of Heretic II. # ⚓ RPG_game_engine_Flare_gets_improved_gamepad_support,_fonts and_more_in_v1.13_|_GamingOnLinux⠀⇛ Flare is a free and open source game engine for creating RPGs, plus it also has its own Empyrean Campaign to play through and it continued to get enhanced to be a bit more modern. Version 1.13 was just recently release, bringing with it some pretty major enhancements. A big one is improved gamepad support that was overhauled. They’ve moved from using the SDL_Joystick API to using the SDL_GameController API, along with improved gamepad mapping and fixes to some deadzone issues. Navigating the UI is also quite a bit easier now too, as various actions give you a pop-up now to easily pick what to do. # ⚓ Heroic_Games_Launcher_for_Epic_Games_on_Linux_gets_some more_fixes_|_GamingOnLinux⠀⇛ Readying up for the onslaught of users on the Steam Deck who will probably want to play some of their Epic Store loot, the free and open source Heroic Games Launcher has a new bug fix release up. An application that has only become more important with the Steam Deck, since it ships with Linux and Epic Games don’t support Linux with their store. This at least gives Linux desktop gamers and Steam Deck users a really easy way to get all their games in one place. # ⚓ Linux_Kernel_getting_prepped_for_the_Steam_Deck_| GamingOnLinux⠀⇛ While it’s already known that the Steam Deck will ship with Valve’s own SteamOS 3 based on Arch Linux, what about running more standard Linux distributions? It will get easier in a future version of the Linux Kernel. Since it’s open source, Linux gives Valve a lot of true control on what they can do and tweak for the Steam Deck and that’s a big part of the reason they went with Linux instead of Windows. At release it will likely be using a good number of Valve special patches, many of which will be upstreamed to various projects and we’re starting to see part of that now. # ⚓ Indie_store_itch.io_comes_out_swinging_against_NFTs_| GamingOnLinux⠀⇛ Not only has Valve banned NFT games from Steam but another store has come out clearly against them, with the official itch.io Twitter account releasing a very clear statement. # ⚓ Open_source_evolution_sim_Thrive_adds_a_new_cell_to_grow with_|_GamingOnLinux⠀⇛ Currently in Early Access, Thrive is an impressive scientific evolution sim developed in Godot Engine that continues to mature with a new version up. Sounds like a pretty fun release too, adding in a “chemoreceptor organelle” cell you can evolve your creature with. This will allow you to sniff-out needed resources from quite a distance so you won’t get as lost once you manage to acquire it through a little basic exploration and growth. There’s also now a timeline tab in the reports screen, which allows you to view the current history of the microscopic world you’ve been exploring and surviving in. Plus, lots of bug fixes and optimizations and a Godot Engine upgrade too. # ⚓ Online_multiplayer_for_OpenMW_(Morrowind)_TES3MP_is_alive again_|_GamingOnLinux⠀⇛ OpenMW is a fantastic open source game engine reimplementation for Morrowind, plus there’s the online fork of TES3MP which has sprung back to life with a new release. A project that should eventually merge with OpenMW officially, for now it’s a separate fork until OpenMW hits the big 1.0. TES3MP 0.8.0 is now out and based on the latest OpenMW 0.47.0 release, and the developer said it “fixes a large part of the remaining gameplay problems and also adds some major features”. It took a little while, as the developer explained how they “lost my motivation for TES3MP during the pandemic, but I’ve been regaining it recently because I want to look back on this project as one that I ended up finishing instead of one that I just got very far on”. # ⚓ Yacht_Club_Games’_newest_title_is_the_upcoming_Mina_the Hollower_|_GamingOnLinux⠀⇛ Yacht Club Games, know for the popular Shovel Knight series has a new game in development called Mina the Hollower, and it’s currently crowdfunding on Kickstarter with it being a clear early success. “Descend into a frightful world of action-adventure in Mina the Hollower. Take control of Mina, a renowned Hollower hurtled into a desperate mission to rescue a cursed island. Burrow beneath hazards and monsters, whip foes into oblivion, and gear up with an arsenal of sidearms and trinkets. Explore a vast world filled with pixel-perfect graphics, masterful gameplay, beastly bosses, and infectious music. Encounter a cast of bizarre characters, search out secrets in an array of exotic locales, and illuminate the omnipresent darkness in Mina the Hollower, a brand new game from the developers who brought you Shovel Knight!” o § Distributions⠀➾ # ⚓ Zorin_OS_16_Educational_Spin_Now_Available⠀⇛ Zorin OS 16 Education is a Linux distribution aimed at pre-schools as well as primary and secondary schools. Building on their already-fantastic desktop experience, the developers have added a few tools to help educational institutions prepare students with the skills they need to navigate the waters of an ever-growing complicated world. One of the key pieces of software added is Kolibri, which aims to bridge the educational divide by giving access to an enormous library of educational content. Even better, an internet connection isn’t required to use the tool. With Kolibri, school administrators can either create their own curriculum or download materials from educational leaders such as Khan Academy, Open Stax, MIT, TED- Ed, and Sikana. Once downloaded, the content can be shared, peer to peer, over a local network. # ⚓ Qubes_OS_4.1.0_released⠀⇛ Version 4.1.0 of the secure-desktop-oriented Qubes OS distribution has been released. “The culmination of years of development, this release brings a host of new features, major improvements, and numerous bug fixes”. New features an experimental GUI domain separate from dom0, the “Qrexec” policy system, progress toward a reproducible build, and more. See below and this article for more information. # ⚓ How_to_Test_Various_Linux_Distros_Online⠀⇛ Most Linux aficionados switch and test distros as often as they change their socks. However, searching and downloading your distro, creating a bootable USB drive, and installing and configuring the distro is time-consuming and oft-times an exercise in futility. DistroTest.net allows you to test drive 373 operating systems with 782 different versions, so you can “test it before you hate it.” # § Slackware Family⠀➾ # ⚓ Hello_Slackware,_our_old_friend:_Veteran_Linux distribution_releases_version_15.0_at_last⠀⇛ It’s been a long time coming but version 15 of Slackware finally showed up at the weekend. Fans of the distro, which debuted in 1993, have waited since 2016′s 14.2 for the full fat update. Now, nearly a year after the beta turned up, “the Slackhog emerged from its development den, did *not* see its shadow, and Slackware 15.0 has been officially released,” according to Benevolent Dictator For Life Patrick Volkerding. The release is a big one; after all – it’s been nearly six years since the previous, which came after 2013′s 14.1. Version 14 goes all the way back to 2012. Hopefully the next iteration will not take quite so long, although Volkerding warned that he would be taking “a bit of a breather” after the lengthy gestation period of version 15. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Best_Free_and_Open_Source_Alternatives_to_IBM_Maximo Application_Suite⠀⇛ International Business Machines Corporation (IBM) is an American multinational technology corporation headquartered in Armonk, New York. They sell computer hardware, middleware and software employing over 370,000 people. IBM acquired Red Hat in 2019. But you can trace IBM’s history of open source far further back. They were one of the earliest champions of open source, backing influential communities like Linux, Apache, and Eclipse, advocating open licenses, open governance, and open standards. # ⚓ This_New_Linux_Distro_Combines_Fedora_With_Great Gaming_Software⠀⇛ What happens when a senior engineer at Red Hat, a member of the Lutris development team, and the creator of Proton-GE decides to create a Linux distribution? Well, the aforementioned titles belong to the same person, Thomas Crider (aka “Glorious Eggroll). And what you get is the promising Nobara Project, a distro powered by Fedora and targeted squarely at gamers and content creators. “Fedora is a very good workstation OS, however, anything involving any kind of 3rd party or proprietary packages is usually absent from a fresh install,” Crider says. o § Devices/Embedded⠀➾ # ⚓ Qualcomm_IPQ8076A_WiFi_6E_access_point_offers_dual_10GbE, supports_PoE++⠀⇛ Lanner LWR-X8460 is an enterprise-grade 12-stream, tri-band Wi-Fi 6E access point powered by Qualcomm IPQ8076A quad-core Cortex-A53 processor also equipped with two 10GbE multi-speed ports, and four additional Gigabit Ethernet ports. The access point also supports IEEE 802.3bt standard for the PoE++ power delivery, Bluetooth 5.1 for IoT management, and its features set makes it suitable for remote video conferencing, telehealth, distance learning, public safety monitoring, IoT applications, as well as general connectivity in any crowded and dense Wi-Fi environments. # ⚓ Add_four_PCIe_x1_slots_to_Raspberry_Pi_CM4_IO_with Waveshare_PCIe-Packet-Switch-4P_board⠀⇛ The 1-lane PCIe Gen 2 interface in Broadcom BCM2711 processor is exposed in Raspberry Pi CM4, and most carrier boards are exploiting the interface including the official Raspberry Pi Compute Module IO carrier board. But if you ever wanted to connect multiple PCIe cards to the CM4 IO board, Waveshare has got you covered with the PCIe-Packet-Switch-4P that provides four PCIe x1 slots through an ASMedia ASM1184e PCIe switch. # ⚓ RPi_HAT_features_high-frequency_RFID_reading_at_up_to_200 tags/sec.⠀⇛ SB Components is Kickstartering a “UHF HAT for Raspberry Pi” with high-frequency UFC RAIN RFID technology for reading up to 200 tags per second. If you read this before noon PST, you have a few minutes left to get the Kickstarter early bird special for the UHF HAT for Raspberry Pi at 199 UK Pounds ($269). Otherwise, it goes to 225 Pounds ($304), with shipments due in April. The Kickstarter packages ship with 5x UHF RFID tags. The UHF HAT is an RFID add-on for the Raspberry Pi that uses Ultra High Frequency (UHF) RFID technology operating over the 865MHz to 870MHz and 915MHz to 928MHz ranges. The UFC HAT offers adjustable RF output range of 0 dBm to +27 dBm with 0.01 dB increments and supports the reading of up to 200 tags per second. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Is_Google_Play_Store_Not_Working?_Here_Are_Some Possible_Fixes⠀⇛ # ⚓ Video:_Top_5_Must-Have_Android_Apps_For_February_2022 |_NDTV_Gadgets_360⠀⇛ # ⚓ Nokia_G21_Android_smartphone_leaked_–_Geeky_Gadgets⠀⇛ # ⚓ New_CapraRAT_Android_Malware_Targets_Indian Government_and_Military_Personnel⠀⇛ # ⚓ Android_12_February_security_patch_OTA_for_Pixel rolling_out_–_9to5Google⠀⇛ # ⚓ Tecno_Pop_5S_goes_official_with_5.7″_LCD_and_Android 10_Go_–_comments⠀⇛ # ⚓ What_is_Android_Auto_and_what_can_it_do?_– SlashGear⠀⇛ # ⚓ Tecno_Pop_5S_goes_official_with_5.7″_LCD_and_Android 10_Go_–_GSMArena.com_news⠀⇛ # ⚓ How_to_free_up_space_on_Android_–_Geeky_Gadgets⠀⇛ # ⚓ How_to_see_deleted_notifications_on_Android smartphones⠀⇛ # ⚓ Here’s_An_Easy_Way_To_Block_Websites_On_Android⠀⇛ # ⚓ YouTube_For_Android_Is_Reportedly_Testing_“Listen With_YouTube_Music”_Button⠀⇛ # ⚓ Truecaller_teams_up_with_global_Android_smartphone manufacturers_to_preload_app_in_key_mkts_|_Business⠀⇛ # ⚓ PinePhone_call_quality⠀⇛ I bought a PinePhone a couple of months ago, mainly for the opportunity to play with it and see what it could do. Since I work for a company that does voice call quality testing, the first thing I wanted to do was figure out how to play back our audio quality test files and then do some call audio quality tests. When doing call audio quality testing, it’s very important that the audio you’re playing back not be transcoded or even resampled, so using PulseAudio or PipeWire was completely out of the question. Figuring this process out turned out to be far harder than I expected, so I thought I should document how I made it work. My background is in IT infrastructure, and I am not an audio engineer or a telephony expert, so I wouldn’t be surprised if there are better ways of doing things. Suggestions are very welcome on Twitter or via email. o § Free, Libre, and Open Source Software⠀➾ # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ LibreOffice_ecosystem_interview:_Caolán_McNamara_at Red_Hat⠀⇛ We try and do a lot of different things, from integration with the GNOME desktop, Calc and UNO work, and porting to architectures such as aarch64 and ppc64le, but I can highlight some of the efforts we make in detecting flaws close to when they get introduced into LibreOffice. We maintain the regular crashtesting infrastructure, where we import and export 120,000+ documents and typically fix, or identify the triggering commit, any new import/export failures as they are discovered. # ⚓ Improving_LibreOffice’s_network_file_access⠀⇛  Thanks to a tender by The Document Foundation, we have been able to implement a new and much improved curl-based HTTP/WebDAV UCP for LibreOffice 7.3. This is the technology that sits under almost every public network file access LibreOffice can do, like loading and saving from a NextCloud instance, or working on a file sitting on a SharePoint server. Please read on for how we implemented that. * § Leftovers⠀➾ o ⚓ What_are_sparse_files_and_how_to_tell_if_a_file_is_stored sparsely⠀⇛ Sparse files are files stored in a file system where consecutive data blocks consisting of all zero-bytes (null-bytes) are compressed to nothing. There is often no reason to store lots of empty data, so the file system just records how long the sequence of empty data is instead of writing it out on the storage media. This optimization can save significant amounts of storage space for other purposes. On most file systems, programs don’t need to do anything special to take advantage of sparse files when it’s supported by the file system. It all depends on how individual programs use the lower-level operating system application programming interfaces (API) to save the data to a storage medium. Some programs might write out consecutive blocks of null-bytes to the disk. These programs are non-sparse-aware. o § Internet Policy/Net Neutrality⠀➾ # ⚓ School_exams_and_morning_TV_shows_behind_the_latest_raft_of internet_shutdowns_–_Coda_Story⠀⇛ Cutting off the internet has become a go-to strategy for governments eager to disrupt expressions of dissent. Entire regions and even countries have gone offline, ripped clean from the internet from one day to another. This happened during a coup a year ago in Myanmar, large-scale opposition protests in India, or elections in Uganda, Democratic Republic of the Congo and Chad. [...] 1) In January, Kazakhstan made headlines because of its mass anti-government protests and the total internet blackout that followed. The Kazakh government has been in the habit of throttling the internet for a while though. For example, on May 9, 2019, the presidential election day, authorities cut off internet access coinciding with detentions of activists and journalists participating in the demonstrations at the time. In 2012, Kazakhstan’s parliament amended a national security law allowing the government to shut down internet and mobile connections during riots or anti-terrorist operations. o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ The_boundaries_of_causing_loss_by_unlawful_means: Secretary_of_State_for_Health_v_Servier [Ed: EPO patents versus human lives or public health]⠀⇛ Servier obtained a UK patent for a drug “perindopril”, upheld by the European Patent Office (“EPO”). It defended the validity of the UK patent in English court proceedings, obtaining an interim injunction preventing the sale of generic perindopril. Subsequently, the patent was held invalid on the basis it lacked novelty (with the decision upheld on appeal). In 2009, the EPO revoked the patent. The NHS claimed that in obtaining, defending and enforcing its patent, Servier had deliberately deceived (the unlawful means) the EPO and/or the English courts (the third parties) with the intention of profiting at the expense of the NHS. Further, but for this deceit, the NHS claimed other manufacturers of generic perindopril would have entered the market sooner and driven down the price the NHS had to pay. Servier applied to strike out the NHS’s claim. For the purposes of the application, the allegations were assumed to be true (notwithstanding that Servier disputed the basis of the claim). The claim was struck out at first instance on the basis that following OBG Ltd v Allan, the unlawful means must have interfered with a third party’s ability to deal with the claimant. It was common ground that here, it had not (the NHS had not dealt with the EPO or the courts). The decision was upheld by the Court of Appeal and was referred to the Supreme Court to determine whether… # ⚓ Montenegro_Ratifies_EPC,_Amends_Patent_and_Copyright Laws [Ed: Montenegro ratifies something which does not even exist because_it_is_being_violated_routinely without_any_consequences_to_the_violators]⠀⇛ On December 29, 2021, Montenegro adopted the Law on Ratification of the Convention on the Grant of European Patents, commonly known as the European Patent Convention (EPC), as well as amendments to the Patent Law and the Law on Copyright and Related Rights. ䷩ 𝚕𝚒𝚗𝚎 7921 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_7/2/2022:_OpenMandriva_Lx_4.3_Released_and_Lots_About_Patents⠀✐ Posted in News_Roundup at 6:03 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o ⚓ 9to5Linux_Weekly_Roundup:_February_6th,_2022⠀⇛ This week has been generous in Linux week as we got lots of cool stuff, starting with the launch of the LibreOffice 7.3 office suite, the end of life of the Linux 4.4 LTS kernel series, Education editions of Zorin OS 16, 64-bit edition of the official Raspberry Pi OS, major Slackware and Peppermint OS releases, and a new Linux laptop from System76. We also got new releases of the Linux Lite, Trisquel GNU/ Linux, and Escuelas Linux distributions, as well as new updates to the KDE Falkon, NVIDIA graphics driver, KDE Gear, Raspberry Pi Imager, Inkscape, and GStreamer software. o § Audiocasts/Shows⠀➾ # ⚓ Much_Ado_About_Ubuntu_|_LINUX_Unplugged_444⠀⇛ There’s just something off about Ubuntu these days, this week we put it all together. # ⚓ Josh_Bressers:_Episode_309_–_The_bright_future_of_open source_secuirty⠀⇛ Josh and Kurt talk about NPM requiring 2FA for the top 100 packages. We discuss the new Alpha and Omega projects from the OpenSSF and what it could mean for the future of open source security. Then we end on a note about the new Samba critical vulnerability. o § Kernel Space⠀➾ # ⚓ Kernel_prepatch_5.17-rc3⠀⇛ The 5.17-rc3 kernel prepatch is out for testing. Linus says: “Things look fairly normal so far, with a pretty average number of commits for an rc3 release”. # § Graphics Stack⠀➾ # ⚓ NVIDIA_Adds_GeForce_RTX_2050,_MX570_&_MX550_Laptop GPU_Support_To_Linux_Through_Latest_Drivers⠀⇛ Last December, NVIDIA launched three new mobility GPUs, the RTX 2050, MX550, and MX570. While the MX550 is a Turing variant for NVIDIA, the RTX 2050 and MX570 utilize identical GA107 cores, similar to the RTX 3050. Laptop manufacturers will use these new chips in their notebooks during this first quarter of 2022. [...] A new Linux driver (470.103.01) for the RTX 2050, MX570, and MX550 is available, offering more compatibility and capability in the open-source operating system. o § Instructionals/Technical⠀➾ # ⚓ How_To_Install_Gnome_Tweak_on_Ubuntu_20.04_LTS_–_idroot⠀⇛ In this tutorial, we will show you how to install Gnome Tweak on Ubuntu 20.04 LTS. For those of you who didn’t know, The Gnome Tweak Tool is a utility used to customize the overall look and behavior of elements on the Gnome Desktop Environment. Some of the things you can do with GNOME Tweaks are edit font colors and scaling, disable animations for desktop speed improvement, change themes, manage GNOME extensions, bar changes, and much more. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the Gnome Tweak on Ubuntu 20.04 (Focal Fossa). You can follow the same instructions for Ubuntu 18.04, 16.04, and any other Debian-based distribution like Linux Mint. # ⚓ Centralized_log_management_by_installing_rsyslog_on_Debian 11!⠀⇛ Hello, friends. In this post, we will talk a little about rsyslog on Debian 11. Besides that, we will show you how to install it and set it up, so you can work from the clients. Let’s get started. # ⚓ Introduction_to_Powerline_the_statusline_plugin_for_VIM⠀⇛ Vim is one of most used and famous text editors on Linux and other Unix-based operating systems. It is free and open source software, based on the original Vi editor (Vim stands for Vi IMproved) and mainly developed by Bram Moolenaar. The editor can be setup by editing the ~/.vimrc configuration file, and by using a vast range of plugins. In this article we see how to improve and customize the Vim status bar by installing Powerline, a nice plugin written in Python which can be also used to customize the Bash and Zsh shell prompts. # ⚓ Ubuntu_mirrors⠀⇛ People all over the world use Ubuntu Linux. In order to accommodate users from different regions of the world that wish to install updates or new software from Ubuntu’s official repositories, Canonical has “mirrors” all over the world. For example, if all the software is hosted on servers in North America, that will provide a fast connection for some users, but users in Asia will have much higher latency to the servers and their downloads will take longer. Therefore it is necessary to have the content hosted on multiple servers in multiple regions. On your Ubuntu system, your Ubuntu mirror should be selected automatically, but it is possible to change it manually. This can be useful if you notice that your system is connecting to a location that is far away, or your downloads are taking a long time. Let’s dive into the tutorial and see how this is configured via command line and GUI. # ⚓ How_To_Move_and_Rename_Files_in_Linux⠀⇛ Moving and renaming files in the Linux terminal is quick and painless, but first you need to understand how to do it. Whether you are sat at the machine, or remotely connected via SSH, these are the commands that will move files around your machine. In this how-to we’ll learn the basics of mv, an command that moves, and renames files. We will also learn a few advanced arguments for this command, arguments which will enhance its use and make our lives easier. # ⚓ How_To_Create_A_Bash_Script,_With_Example_Code_•_Python Land_Tutorial⠀⇛ With bash scripts, you can run sequences of commands. They prevent you from repeating yourself and allow you to store long and tedious to type commands for later usage. In this article, you’ll learn how to create a Bash script. You’ll also learn how to read arguments, use variables, and create for-loops to repeat actions. Before you start creating scripts, make sure you are familiar with the basic Linux commands. o § Desktop Environments/WMs⠀➾ # ⚓ JWM_documentation_now_builtin⠀⇛ I have started work on a radical change to the desktop user interface. ROX-Filer is more than just a file manager, in Easy it is also used to manage the icons on the desktop and the wallpaper. I am interested in taking that responsibility away from ROX, and reduce it to just being a file manager. The experiment is that the desktop icons will now be in the JWM (Joe’s Window Manager) systray. Hopefully, without the systray becoming too crowded. o § Distributions⠀➾ # § Reviews⠀➾ # ⚓ Review:_PlagueOS_R3_and_Ultramarine_Linux_35⠀⇛ This week I decided to dive into the DistroWatch waiting list and try out two projects selected at random. The first project my mouse pointer jumped to was something called PlagueOS. According to the project’s website, PlagueOS “Is designed to run as a hypervisor and launch guest virtual machines (VMs). The OS is designed to be a minimal build and have a restricted userspace. The guests are launched from virt- manager.” The PlagueOS documentation lists a number of security features the project provides. These include kernel hardening, driver blacklisting, hiding process IDs, locking the root account, using doas in place of sudo, randomized MAC addresses, more restrictive file permissions, and encrypted DNS. While other open source projects may provide many of these security options, most do not enable them out of the box. The ISO download for PlagueOS R3 is 959MB. This download can be verified using both a SHA512 checksum and a signature. The steps for fetching the verification key and checking the ISO file are laid out in detail and it’s nice to see this attention paid to security. I tested PlagueOS in a VirtualBox instance and on my laptop. In Legacy BIOS mode the operating system failed to boot with an error which read: “Failed to load ldlinux.c32″. When trying to start in UEFI mode the system began by displaying a GRUB prompt and was unable to continue. It’s difficult to argue against the security of an operating system which fails to boot on my test systems. However, it’s also difficult to accomplish anything with it, so I moved on to another project. # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾ # ⚓ OpenMandriva_Lx_4.3_released_–_OpenMandriva⠀⇛ OpenMandriva Lx is a unique and independent linux distribution, a direct descendant of Mandriva Linux and the first Linux distribution utilise the LLVM compiler. This release keeps using the entire LLVM toolchain which completes the work that began in 2015. We hope that you find that this link time optimised desktop and its supporting applications to be bright and responsive in use. You can find out more about link time optimisation here: https://llvm.org/docs/ LinkTimeOptimization.html The OpenMandriva Lx 4.3 operating system distribution is FREE and provides the user with all the software funtionality that is available on a proprietary system and then some. All this is supported by the world class KDE Plasma Desktop, a desktop user interface that provides comprehensive access to all the installed software toools. The Plasma desktop offers advanced feature such as multiple task based desktops, and a collection of desktop widgets that support a wide range of information gathering and display. We provide an OpenMandriva utility Desktop Presets (om-feeling-like) which offers a quick way to customize the appearance of your OpenMandriva Plasma desktop to look and feel similar to other systems you may be used to. We hope that this will help those who are new to OpenMandriva to feel at home with our desktop. We also provide an improved ‘OM-Welcome’ utility which guides you through initial setup and suggests some useful additional applications that you may wish to install other than those distributed of the iso. A third utility Software Repository Selector (om-repo-picker), to enable additional repositories with thousands of additional Free Software packages, updated and greatly improved. # ⚓ OpenMandriva_Lx_4.3_Released_with_Linux_Kernel_5.16, PipeWire_by_Default,_and_More⠀⇛ Almost a year in the works, OpenMandriva Lx 4.3 is powered by a Clang-compiled Linux 5.16 kernel to provide users with top-notch hardware support, and ships with the PipeWire low-level multimedia framework as default sound server and a replacement for PulseAudio. OpenMandriva Lx 4.3 features the latest (at the moment of writing) KDE Plasma 5.23 desktop environment, namely Plasma 5.23.5, which is accompanied by the KDE Frameworks 5.90 and KDE Gear 21.12.2 software suites, all compiled against Qt 5.15.3 with all patches proposed by the KDE Project. * § Leftovers⠀➾ o ⚓ Making_Something_Gorgeous_From_Framing_Lumber_|_Hackaday⠀⇛ Here at Hackaday, we typically cover things that blink, bleep, and occasionally they might even bloop. However, the name of the site is Hackaday. We’re about being clever, reusing things in new ways, and most importantly celebrating interesting projects. While not a traditional project that would grace the front page, we would argue that this nightstand made from framing lumber clearly belongs. o § Hardware⠀➾ # ⚓ The_next_microchip_crisis_will_be_bigger⠀⇛ What’s happening: Right now, no U.S. company can manufacture the most advanced leading edge chips used in smartphones, laptops, servers, supercomputers, gaming consoles and other products. Instead, most of the supply for those chips are made by Taiwan Semiconductor Manufacturing Company (TSMC), and is concentrated in Asian countries. o § Health/Nutrition/Agriculture⠀➾ # ⚓ U.S._considers_lengthening_gap_between_first_2_COVID_shots to_8_weeks⠀⇛ # ⚓ European_Commission_calls_for_evidence_on_anti-counterfeit toolbox_initiative [Ed: Disguising protection of monopolies as a matter of "public health" or "safety" is not a new trick/lie]⠀⇛ In the 2020 Commission IP Action Plan, the European Commission (‘EC’) announced that it would establish an EU Toolbox against counterfeiting. The EU Toolbox is part of the EU Strategy to tackle Organised Crime 2021-2025. The EC reports that despite efforts to battle counterfeit goods, the market is still thriving, with an increase of detained articles at EU borders. In 2019, the imports of counterfeit goods equaled 5.8 % of total EU imports, with a value of EUR 119 billion. The EC furthermore notes a surge in counterfeit COVID-19 related goods such as face masks, protective equipment and even vaccines. [...] Furthermore, the EC hopes that the toolbox will stimulate the use of new technologies to battle counterfeiting, such as data mining, AI powered image recognition and blockchain based solutions. # ⚓ [Older]_US_legislators_call_for_screws_to_be_tightened_on pharma_patent_strategies [Ed: When patents needlessly kill people for profit]⠀⇛ New report issued by Democrats in the House of Representatives indicates a change of tack in approaching potential reforms may be on the cards o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ [Crackers]_hit_Fortune_500_service_provider,_data_of over_500k_people_leaked⠀⇛ The incident began on August 1, 2021, when Morley’s data became unavailable. Michigan-based Morley thereafter began collecting contact information needed to provide notice to potentially affected 521,046 individuals, which was completed in early 2022, the company said last week. # ⚓ European_Oil_And_Port_Facilities_Suffer_Cyberattacks [iophk: Windows TCO]⠀⇛ Oiltanking GmbH and Mabanaft GmbH, an oil supplier, were impacted, both of whom are subsidiaries of the Marquard & Bahls group. Oiltanking GmbH supplies the 1,995 Shell gas stations in Germany, but local officials have stressed there are no fuel shortages. # ⚓ Oil_terminals_disrupted_after_European_ports_hit_by cyberattack_Access_to_the_comments [iophk: Windows TCO]⠀⇛ Port facilities in Belgium, Germany, and the Netherlands have been targeted by a large- scale cyberattack, authorities say. Officials say the hack began several days ago and has primarily disrupted operations at oil terminals, preventing tankers from delivering energy supplies. # § Security⠀➾ # ⚓ More_than_1,000_malware_packages_found_in_NPM repository [Ed: Microsoft (NPM) serves malware, and not just to Windows]⠀⇛ # § Privacy/Surveillance⠀➾ # ⚓ ‘No_ordinary_IT_department’_–_spy agencies_seek_tech_strategy_chief⠀⇛ The post as director of strategy, portfolio and partnerships sits within a shared IT organisation that was established within GCHQ in 2019 to serve not only the cyber and signals intelligence outfit, but also the UK’s two other intelligence and security agencies: MI5 and MI6. The tech unit also offers support to “many other government departments where there is a requirement for operating at Top Secret”. # ⚓ Meta_threatens_to_pull_Facebook_and Instagram_from_Europe_if_it_can’t_target ads⠀⇛ Meta states in an SEC filing it is considering leaving Europe if it can no longer exchange data from European users with the United States, following the Schrems II decision. # ⚓ Google_is_turning_search_history_tracking on_for_all_Google_Workspace_customers⠀⇛ # ⚓ Facebook_stock_plummets:_What_it_means for_antitrust⠀⇛ # ⚓ Microsoft_Edge_may_be_running_on_your Windows_PCs,_even_if_you_don’t_use_the browser⠀⇛ # ⚓ NSO_Group_Reportedly_Offered_‘Bags_of Cash’_for_Access_to_U.S._Networks⠀⇛ o § Defence/Aggression⠀➾ # ⚓ Wisconsin_Is_Ground_Zero_for_the_MAGA_Effort_to_Steal_the Next_Election⠀⇛ Nowhere is this crusade to subvert the 2020 election result more on display than in Wisconsin. Even though Republicans there do not control all the levers of power — the governor, Tony Evers, is a Democrat — they have launched a multifront effort to cast doubt on the 2020 election, intimidate local officials, and, in Ramthun’s case, throw out the state’s presidential-election result. Lawyers aligned with the Republican Party have filed suit after suit seeking to roll back reforms that made it easier to vote in the pandemic. A secretive investigation run by a conservative former judge with a controversial past has issued dozens of expansive subpoenas, demanded closed-door testimony of mayors and clerks, and sought jail time for those who didn’t cooperate. GOP candidates and elected officials have gone so far as to demand the elimination of the state’s bipartisan election commission — a body that Republicans created seven years ago — and potentially give the GOP-led Legislature the power to control elections. “Wisconsin is the ground zero for the fights over elections right now,” says Paul Nolette, a political-science professor at Marquette University. # ⚓ Man_Who_Attempted_to_Provide_Material_Support_to_ISIS Sentenced_to_16_Years_in_Federal_Prison⠀⇛ In 2019, law enforcement officers learned that Guerra Blanco was following widely distributed instructions from ISIS directing adherents to — on their own — publish ISIS propaganda, fundraising requests, recruitment material, justification for attacks on the United States, and all manner of material helpful to ISIS. Guerra Blanco attempted to provide material support to ISIS by translating the group’s materials into Spanish for his target audience. In addition, Guerra Blanco produced videos that he intended to use to recruit Spanish speakers to ISIS’s cause, as well as to terrorize regular citizens of Spain. Many of the videos that Guerra Blanco produced and distributed from his two ISIS media networks glorified the terrorist group’s violence and called for attacks on Spanish authorities. # ⚓ Christian_apologist_beaten_unconscious_in_Kampala,_Uganda⠀⇛ A resident of a town east of Kampala undisclosed for security reasons, Kamya on January 24 had debated Muslims in Jinja after going to the mosque there to buy a Quran on January 21, accompanied by a Muslim convert to Christianity, he said. He used the Koran in the January 24 debate, he said. # ⚓ Who_Is_the_ISIS_Leader_Killed_in_the_U.S._Raid?_Here’s_What to_Know⠀⇛ Al-Qurayshi’s death may disrupt the group’s momentum in the short term, but is unlikely to hurt its operations in the long term. “It’s an organization not focused on charismatic leadership, but ideas, which is why its leaders have been pretty low-profile,” Aaron Y. Zelin, a senior fellow at the Washington Institute for Near East Policy, said. “I think the IS machine will continue with whoever the new leader is.” Al-Qurayshi’s real name was Amir Mohammed Saeed Abdul-Rahman al-Mawla. He was an Iraqi in his mid- 40s, born in 1976 and believed to be an ethnic Turkman from the northern Iraqi town of Tel Afar. He held a degree in Islamic law from the University of Mosul. # ⚓ How_US-born_Allison_Fluke-Ekren_went_from_science_teacher to_ISIS_radical⠀⇛ As a high-ranking member of ISIS, who trained in Egypt, Libya and Iraq before heading to Syria in 2012, Allison Fluke-Ekren planned to detonate explosives at an unidentified US college campus and “fantasized” about bombing a shopping mall, according to court records. # ⚓ The_Washington_Post’s_Public_Relations_For_CAIR⠀⇛ The Council on American-Islamic Relations (CAIR), which calls itself a “civil rights organization,” though it is much more, in a sinister vein, than that, has been the beneficiary of journalistic malpractice. A recent example of this, at the Washington Post, is reported on here: “The Washington Post Gives CAIR a Boost,” by Sean Durns, Algemeiner, January 24, 2022: [...] o § Environment⠀➾ # ⚓ Opinion_|_It’s_Time_to_Overhaul_the_Chemical_Industry⠀⇛ Climate change is quickly evolving into climate catastrophe, and there’s a narrow window of time to do something about it. While the world works on solutions, there’s surprisingly little focus on the chemical industry, which accounts for roughly 7% of global greenhouse gas emissions — as well as other environmental harms. # § Energy⠀➾ # ⚓ Finland_unveils_plan_for_electric_aircraft_routes across_Lapland_region⠀⇛ An experimental project operating out of Enontekiö Airport in the northwest corner of Finland is set to test the viability of using electric airplanes to fly routes across the wider Lapland region. # ⚓ New_Study:_Gas_and_Oil_Drilling_Doesn’t_Create_Very Many_Jobs⠀⇛ According to a new analysis by the corporate watchdog Food and Water Watch, the actual number of people directly employed by the fossil fuel industry is only about half a million. Moreover, the Food and Water Watch report shows that the fossil fuel industry has been shedding jobs for years, even with oil and gas output at record levels. # ⚓ Botswana_passes_[cryptocurrency]_bill,_unlike_Zim they_want_to_stop_the_scams⠀⇛ Botswana’s push for a [cryptocurrency] bill comes after it was removed from the Financial Action Task Force’s (FAFT) list for countries that need more monitoring in relation to money laundering and terrorist financing. A little sidenote, Zimbabwe is, as I am sure you have already guessed, on the list with the organisation stating that: [...] # ⚓ El_Salvador_Has_Ambitious_Plans_for_Cryptocurrency⠀⇛ “It’s not like an entire nation has been Bitcoin-ized and in two years everyone will be using Bitcoin,” says cryptocurrency expert Jeff Gallas, the founder of fulmo, a Berlin, Germany-based Bitcoin Lightning network startup. Still, he considers it to be a successful start, “considering how little time there was.” He says the government now needs to show that it can deliver on all its promises and fix the bugs in Chivo. Security flaws in the software allowed scam artists to collect the credit balances of hundreds of citizens. Sometimes, money transfers haven’t worked, either. # ⚓ [Cryptocurrency]_Has_a_Climate_Problem⠀⇛ Bitcoin—the world’s oldest and most popular form of cryptocurrency, with a total market value that topped $1.3 trillion—now eats up half a percentage point of all the electricity consumed in the world. That puts it on par with the usage of the entire country of Sweden. In fact, Google could power all of its global operations on that amount of energy, seven times over. In comparison with more traditional online banking, a single bitcoin has the same carbon footprint as 330,000 credit card transactions. # § Wildlife/Nature⠀➾ # ⚓ Shipping_industry_needs_to_do_more_to_lessen underwater_noise_in_Arctic,_say_NGOs⠀⇛ “The workplan put in place at SDC 8 must be ambitious in scope and reflect the urgency needed to address underwater noise from ships as it continues to increase at alarming rates”, Bobbe said. “Advancements in new technologies such as quieter propellers have already been developed and can be installed on new ships and retrofitted on existing ships when in drydock for repairs. There are also very simple ways to reduce noise, like slowing ships down. This will bring co-benefits of reduced fuel use and emissions.” o § Finance⠀➾ # ⚓ Opinion_|_Labor_Win_in_Mexico_Augurs_Greater_Equality_for Workers_on_Both_Sides_of_the_Border⠀⇛ The U.S. labor movement, after a depressing January, needed some encouraging news. That encouraging news has just come — from Mexico. # ⚓ Flood_Insurance_Premiums_in_Louisiana_Are_Rising._Help_Us Investigate.⠀⇛ Sweeping changes are coming to the National Flood Insurance Program, which will result in premium increases for many Louisiana policyholders starting April 1, 2022. ProPublica and The Times-Picayune | The Advocate could use your help in understanding how these changes affect homeowners, other property owners and the real estate market in Louisiana. If you’ve explored purchasing flood insurance in Louisiana in recent months, if you plan to, or if you are in the real estate, mortgage or insurance fields, we may have some questions as our reporting continues. If you’re willing to help, please sign up here by answering a few questions below. # ⚓ Credit_Monitoring_services_are_mostly_a_scam.⠀⇛ Have you seen an offer from your bank, credit card company, or Lifelock about credit monitoring? Are you thinking about buying it? Well, the good news is you can ignore their pushy sales tactics, and decline it when dark pattern dialog boxes pop up, and prevent fraud yourself. A while back, I was talking about using strong randomly generated passwords and an authenticator program, such as Google Authenticator and GNOME Authenticator to manage one time codes. It’s unlikely that anyone will sign into your accounts and rip you off if you do that, but there are still other ways to bilk you, like credit fraud. The truth is, the credit reporting bureaus are required by federal and state laws to allow you to manage fraud alerts and credit file freezes on your own, but they don’t want you to know that because they were hoping you’d buy it from them. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Trump’s_Political_Depravity_Sank_to_a_New_Level_This_Past Week⠀⇛ # ⚓ Joe_Manchin_Gives_New_Reason_for_Why_He_Torpedoed_BBB⠀⇛ As progressive activists continue to push for the stalled social and climate spending package, Sen. Joe Manchin claimed Sunday that his biggest opposition to his party’s Build Back Better legislation was that it didn’t go through committee. Manchin’s (D-W.Va.) remark came in an interview with CNN’s “State of the Union” in which he endorsed Republican Sen. Lisa Murkowski and brushed off the idea that he wouldn’t get the backing of Senate Majority Leader Chuck Schumer (D-N.Y.) if he faced a primary challenge.  # ⚓ Manchin’s_Likely_Backing_of_Biden_SCOTUS_Pick_Reflects Court’s_Conservative_Role⠀⇛ # ⚓ Claims_Over_Broken_Promises_About_NATO_Simmer_at_the_Heart of_the_Ukraine_Crisis⠀⇛ # ⚓ Opinion_|_19_Facts_About_the_Poverty-Busting_Expanded_Child Tax_Credit⠀⇛ Date when the expanded child tax credit, which Congress approved last year as part of the American Rescue Plan pandemic stimulus, expired because the closely divided U.S. Senate failed to renew it as part of the Build Back Better Act: 12/31/2021 # ⚓ The_Movement_Grows:_Jayapal_Heralds_Record_120_Medicare_for All_Co-Sponsors⠀⇛ Rep. Pramila Jayapal on Sunday welcomed a new record number of co-sponsors—120—for her Medicare for All legislation. The latest support came from Rep. Sheila Cherfilus- McCormick (D-Fla.), who was sworn in just two weeks ago. # ⚓ Metamorphosis:_Facebook_and_big-tech_competition⠀⇛ Since listing in 2012 Meta has exemplified big tech’s prowess and pitfalls. For a glimpse of the caricature, consider the American government’s antitrust case against it first launched in 2020. It describes an invincible company in a world where technology is perpetually frozen in the 2010s: “this unmatched position has provided Facebook with staggering profits,” America’s Federal Trade Commission wrote in its lawsuit. # ⚓ Navalny_ally_in_Murmansk_flees_Russia_as_aides_face ‘terrorist’_labels⠀⇛ Another activist linked to jailed Kremlin critic Alexei Navalny has fled Russia, Reuters reported Thursday as the authorities’ year-long campaign to dismantle his network and label its leading figures “terrorists” showed little sign of slowing. Violetta Grudina, 32, was blocked from running for local office in the Arctic port city of Murmansk last year after being forcibly hospitalized despite testing negative for coronavirus. Grudina has said she faced an intimidation campaign that included several years of hefty fines and unknown people shooting at her office. # ⚓ 20_Million_Dollar_Saudi_Festival_Organized_by_Vice_Media⠀⇛ Vice’s name was not used in any public marketing materials as the company’s name was kept out as much as possible. Both sides seem to be a good match, as Saudi Arabia is desperately attempting to whitewash its human rights abuses with entertainment and Vice is dealing with allegations of sexual harassment. # ⚓ In_the_Netherlands,_it’s_‘Civilized’_to_Empower Terrorists⠀⇛ Not until January 18 of this year did Sahla’s past become a problem. On that day, during a discussion in the Tweede Kamer, the lower house of the Dutch parliament, Wilders, who since 2006 has been head of the PVV (Freedom Party) and who since 2004 has had to live with round-the-clock security owing to jihadist death threats, raised the subject of Sahla, saying that someone who’d been issued a gun with which to kill him and Ayaan Hirsi Ali had no business in a leading position in the country’s ruling party. Wilders also mentioned Sahla’s sister Fonda, who, as it happens, is a politician for the centrist D66 and a colleague of Wilders’s in the Tweede Kamer, where she routinely wears a hijab. # ⚓ Ankara_demanded_the_impossible_from_the_US_for_my_release, pastor_Brunson_says⠀⇛ Andrew Brunson, an American pastor who was jailed for two years in Turkey before his release in 2018, has said in a recent interview that Turkey’s demands from the US in exchange for his release were beyond what Washington could do, with the Turkish government using him as a bargaining chip to get its way on a number of issues. # ⚓ Islam:_Wave_of_the_Future?⠀⇛ “Islamism is the sole growing, developing, and truly popular populist ideology in the Middle East,” wrote House Taskforce on Terrorism and Unconventional Warfare Director Yossef Bodansky in 1999. His book, Bin Laden: The Man Who Declared War on America, documented the enduring appeal in Muslim-majority societies of Islam as a political system as opposed to other ideological alternatives. o § Misinformation/Disinformation⠀➾ # ⚓ Austria:_Left-wing_Turks_attack_a_mosque_and_Muslims_and Leftists_blame_it_on_Islamophobes⠀⇛ In a statement, the chairman of the Austrian Freedom Party (FPÖ) in the Vienna district of Favoriten, Stefan Berger, considers the radical left-wing and foreign PKK attack on the ATIB mosque to be proven on the basis of the video of the confession. Berger said: [...] # ⚓ How_a_Butterfly_Refuge_at_the_Texas_Border_Became_the Target_of_Far-Right_Lies⠀⇛ When people began showing up at the butterfly center, the nonprofit decided it needed to do more to provide security for staff members and visitors. It would remain closed, he said, until a plan could be developed for how to do so. # ⚓ Ilhan_Omar’s_Husband_Accuses_Iranian_Dissident_of ‘Islamophobia’⠀⇛ It all started last Tuesday, when human rights activist Masih Alinejad took to the Washington Post, of all places, to point out some of the risks involved in Omar’s “Islamophobia” bill. Alinejad, who was recently the target of a kidnapping plot launched by the Islamic Republic of Iran, wrote: “I should make clear: I have nothing against Omar personally. Like her, I have many relatives who are pious Muslims I love and respect.” Alinejad added: “My mother is a devout Muslim who wears hijab all the time. I, on the other hand, challenged clerical rule with my journalism until I was thrown out of Iran. I launched a campaign against compulsory hijab, demanding that Iranian women be given the freedom of choice to decide their own destiny. Will such criticism of compulsory hijab be labeled as Islamophobia?” o § Censorship/Free Speech⠀➾ # ⚓ ‘Message_is_clear,_Turkey_must_release_Osman_Kavala’⠀⇛ Amnesty International has released a statement about the infringement proceedings brought against Turkey by the Committee of Ministers of the Council of Europe over rights advocate and businessperson Osman Kavala’s continued detention despite the European Court of Human Rights (ECtHR) judgment of rights violation and immediate release. # ⚓ Three_Philippine_media_outlets_face_latest_in_a_string_of cyberattacks⠀⇛ All three sites have been openly critical of the Duterte regime. The National Union of Journalists of the Philippines released a statement condemning the attacks and called for an investigation. # ⚓ UK:_British_citizen_found_guilty_of_conspiring_to_kill exiled_Pakistani_blogger⠀⇛ RSF representatives monitored the two-week trial both in-person and remotely. The defendant, who had been hired as a “hitman” by a middleman referred to as “MudZ,” who appeared to be based in Pakistan, refuted claims that he had intended to kill Goraya. The defence argued that Khan had only planned to extract money from MudZ while maintaining the appearance that he would carry out the killing. Khan created multiple false identities to give the appearance of a larger team, allowing him to bill £5,000 for operational expenses, which he received in advance. A total fee of £100,000 was agreed for the job, with Khan to receive £80,000 and £20,000 to go to MudZ after Goraya was killed. They also discussed the possibility of future jobs contingent on the successful completion of this one. # ⚓ Tibetan_monks_sent_to_labor_camps_for_spreading_news_of Buddhist_statue’s_destruction⠀⇛ Eleven Tibetans beaten and arrested by Chinese authorities in January for spreading news of the destruction of a 99-foot-tall Buddha statue and dozens of prayer wheels in southwestern China’s Sichuan province have been sent to labor camps in the region, Tibetans with knowledge of the situation said Friday. Monks Tashi Dorjee, Tsering Samdup, Nyima Lhamo, and Abbot Pelga, along with Pelga’s assistant Nyima, and six other unidentified Tibetans were arrested following the destruction of the statue and 45 traditional prayer wheels in Drago (Luhuo) county of Kardze (in Chinese, Ganzi) Tibetan Autonomous Prefecture in December 2021, said a Tibetan in exile who declined to be named for safety reasons. # ⚓ Original_‘Fight_Club’_Ending_Restored_in_China_After Censorship_Backlash⠀⇛ But it would appear that the backlash has been deemed more troublesome than the fictional film’s ending, as Tencent has now restored 11 of the 12 minutes it originally cut from the 137-minute movie. The minute still missing is mostly comprised of brief nude sex scenes between Pitt’s and Bonham Carter’s characters. A spokesperson at Tencent didn’t respond to a request for comment. Reversals of censorship actions are extremely rare within China’s entertainment industry — but cuts to Hollywood movies are not. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ Iowa,_Kansas_lawmakers_bar_media_from_Senate_floors, stymieing_newsgathering⠀⇛ CPJ interviewed Erin Murphy, the Des Moines bureau chief for the Cedar Rapids Gazette and president of the Iowa Capitol Press Association, and Sherman Smith, the editor in chief of the Kansas Reflector, a non-profit news website focused on Kansas politics, about the changes. The interviews have been edited for length and clarity. # ⚓ Taliban_forces_detain_2_journalists_in_undisclosed location⠀⇛ On Monday, men who identified themselves as members of the Taliban arrested Hijab, a reporter, and Hasrat, manager of political programs and a political presenter, both with the independent broadcaster Ariana News TV, at the entrance of outlet’s headquarters in District 3 of Kabul, the capital, according to former Ariana News Director Sharif Hasanyar, who spoke to CPJ in a phone interview, and a statement by the independent press freedom group Free Speech Hub. The Taliban has not disclosed where the journalists are being held or any allegations against them, Hasanyar said. Ahmadullah Wasiq, a Taliban deputy spokesperson in Afghanistan, did not respond to CPJ’s request for comment sent via messaging app. # ⚓ Afghan_journalists_increasingly_harassed_by_Taliban intelligence_and_new_ministry⠀⇛ The Istikhbarat is not just directly involved in arresting journalists. RSF has learned that several media outlets have received threatening phone calls and summonses for questioning from Istikhbarat officials. Javad Sargar, the senior Istikhbarat official in charge of Department 53, which handles the media, recently horrified journalists by “inviting” them to stop covering certain subjects and stop asking certain journalists to participate in TV discussions, “if you don’t want me to rip your tongue out.” # ⚓ Convoy_protesters_threatened,_harassed_journalists_at Friday’s_demo⠀⇛ Yle’s reporter and cameraperson on the scene say they were continually threatened verbally and physically. Some protesters attempted to prevent reporters from moving around freely. Journalists were abused and threatened, and one protester attempted to steal a bag containing the camera operator’s equipment. # ⚓ Malian_journalist_who_disappeared_six_years_ago_is_very likely_dead,_RSF_says⠀⇛ After registering his upcoming marriage at Bamako’s city hall and spending the afternoon with his family, Touré, set off for home on his motorcycle on the night of 29 January 2016. None of his friends and relatives has seen him since then. Six years later, RSF is in a position to affirm not only that he was secretly detained at a clandestine prison run by Mali’s General Directorate for State Security (DGSE) but also that he most likely died as a result of being mistreated and tortured there, according to damning new testimony obtained in recent months. # ⚓ French_parliament_votes_against_handing_asylum_to_Wikileaks founder_Assange⠀⇛ After a long and intense debate, MPs in France’s national assembly (lower house) voted 31 against and 17 in support of a proposed text brought forward by MP Jennifer de Temmerman, from the opposition group known as Libertés et Territoires. According to the document, which is not legally binding, “Assange’s crime is that he told the truth and was engaged in journalism.” o § Civil Rights/Policing⠀➾ # ⚓ Opinion_|_Not_Retreat_But_Resistance_and_Resilience:_When Faced_With_Doomsday,_Look_to_Community⠀⇛ Sometimes at second hand books stores I find myself with an armful of books, thinking “These will come in handy if … If the internet goes away, if there is no more electricity, if there aren’t grocery stories anymore.” I cling to the books, push the nightmare scenarios out of my head and make for the cashier. # ⚓ Uber_Got_a_Sweetheart_Deal_With_One_of_Canada’s_Biggest Unions⠀⇛ Close inspection of the agreement reveals that the deal is not the victory for workers that it initially appeared to be. It is a victory for Uber and other platform apps. Under the agreement, Uber drivers will not actually become UFCW members; they will simply be able to access some representation in the case of disputes about pay and deactivation. Uber drivers will have no say in electing their representation. This violates the commitment to democracy fundamental to all trade unionism. # ⚓ We_must_listen_to_Iranian_feminists_who_protest_forced hijab_–_opinion⠀⇛ In response, Alinejad launched the #LetUsTalk campaign, which pushes back against the censorship of Middle Eastern women fighting for women’s equality. However, despite the fact that Alinejad showed up to the Women’s March five years ago in solidarity, none of the women there would join her in her fight for freedom of choice. “I found that hardly anyone was willing to support my campaign against compulsory hijab, lest they be accused of promoting Islamophobia,” she wrote in The Washington Post. o § Digital Restrictions (DRM)⠀➾ # ⚓ Spotify_CEO_Daniel_Ek_confirms_removal_of_Joe_Rogan episodes_after_n-word_video_resurfaces⠀⇛ Spotify CEO Daniel Ek addressed staff in a late night memo addressing Joe Rogan’s use of the n-word and the mysterious removal of 70 podcast episodes earlier this week. The total number of deleted Joe Rogan Experience episodes is now 113, according to the website jremissing.com. # ⚓ Spotify_CEO_Apologizes_to_Staff_Over_Joe_Rogan_N-Word Controversy⠀⇛ According to Ek, Spotify has had conversations “with Joe and his team about some of the content in his show, including his history of using some racially insensitive language. Following these discussions and his own reflections, he chose to remove a number of episodes from Spotify. He also issued his own apology over the weekend.” # ⚓ Spotify_CEO_Addresses_Joe_Rogan’s_N-Word_Use,_Doubles_Down on_Keeping_Podcaster_on_Platform⠀⇛ In a letter sent to staff, obtained by The Hollywood Reporter, Ek acknowledged that Rogan’s comments were “incredibly hurtful” and confirmed that Rogan decided to remove multiple past episodes from Spotify but said he did not believe in removing the podcast from Spotify. # ⚓ Disney,_Netflix,_Apple:_is_anyone_winning_the_streaming wars?⠀⇛ As revenue growth slows, costs swell. Media firms will spend more than $230bn on video content this year, nearly double the figure a decade ago, forecasts Ampere Analysis, a research firm. Netflix’s weak results came despite what it billed as its “strongest content slate ever”, including “Squid Game”, its most popular series, and “Red Notice”, its most successful film. Disney+ is doing far better than the company ever dreamed—but it is costing more, too. Three years ago Disney said it would spend about $2bn on streaming content in 2024. Mr Chapek recently said the figure would be more than $9bn. o § Monopolies⠀➾ # ⚓ Microsoft’s_Activision_Blizzard_Acquisition_Won’t_Save_the Games_Industry⠀⇛ Over the decades, Microsoft’s bid to consolidate more of the games industry for itself has only intensified. On January 18, 2022, Microsoft announced it will be acquiring Activision Blizzard. This deal — struck for a record-setting $68.7 billion — will give Microsoft control of some of the most popular gaming franchises in the world: StarCraft, Warcraft, Diablo, Call of Duty, and Candy Crush. This acquisition is good for Microsoft, which will now be the third-largest firm in games behind Sony and Tencent. But it’s bad for game workers at Activision Blizzard, who are fighting for their rights at a company that is synonymous with workplace abuse in the games industry. # ⚓ UK:_Tarilian_Laser_Technologies_–_A_Case_Study_In_Due Diligence [Ed: HGF Ltd promoting the fiction of “Intellectual Property” [sic]; companies that lack actual products cannot compensate with supposed exclusivity, but lawyers stand to benefit from the myths (selling false dreams)]⠀⇛ When deciding whether to invest in a company, an investor will inevitably have to decide the value of the company. Taking a simplified view, a company’s valuation can be considered to be made up of tangible assets (e.g. cash, inventory and fixed assets such as plant/machinery) and intangible assets (e.g. Intellectual Property (IP) and the skills and knowledge of the founders and key staff (Human Capital)). While it can be easier to place a monetary value on tangible assets, there is much more uncertainty regarding the monetary value of intangible assets. However, to decide on the value of a company, a monetary value must nonetheless be placed on these assets, in particular the IP portfolio of the company. # ⚓ Swedish_court_applies_C-762/19_CV-Online_Latvia_in_parking app_battle⠀⇛ Content and service aggregation is big business in 2022. Why having seven different newspapers clogging up your mailbox, when you can have that content carefully selected and curated for you according to your interests and taste? Why having seven different apps for ordering takeout if you can aggregate all that sushi into one app? This dynamic is not lost on entrepreneurs and innovators around the world, sensing and opportunity to create value for users and perhaps birthing a unicorn in the process. But digital aggregation often involves the use of different data sets, including the use of data protected as databases, and the makers of databases often want to protect their own investment against aggregators that are perceived as free riders. Since one person’s entrepreneurial aggregator is often another person’s parasitical competitor, balancing these interests is no easy task for national courts. [...] The argument that the aggregator app created an additional layer between the claimant and its customers seems in principle to be applicable to most situations when a database maker battles a content or service aggregator, whether it is a parking app, an online CV database (CV-Online Latvia) or a meta search engine (C-202/12 Innoweb). To this author, it is not clear how a litigant could quantify the adverse effect of this “additional layer” on the database maker’s ability to recoup its investment, and it is therefore not obvious that this circumstance by itself motivates a finding of infringement under the principles set out in CV-Online Latvia. The court’s conclusion that the aggregator app resulted in the claimant selling less additional services to its customers through its parking app on the other hand seems to be a stronger argument in this regard, and one that can in practice more easily be substantiated by evidence. It will be interesting to see whether this balancing of interests between makers of databases and content and service aggregators is confirmed on appeal or by other national courts in future litigation. # ⚓ Sunday_Surprises [Ed: These events promote the_lie_of “IP”]⠀⇛ On February 3, 2022, the European Commission formally closed its investigation under the EU Trade Barriers Regulation (TBR) into Mexican measures against the export of “Tequila” after successfully resolving the matter. The complaint had been filed by Brewers of Europe, which argued that Mexico’s refusal to issue export certificates for “Tequila” was incompatible with WTO rules and caused significant economic harm to an EU company that relies on “Tequila” as an input. In the course of its investigation, the Commission expressed concerns to the Mexican authorities about the WTO compatibility of the measure. The measure was also challenged by the exporter concerned in domestic courts in Mexico. In October 2021, the complainant informed the Commission that the EU company concerned had reached a solution with the Mexican authorities that would allow the removal of the alleged trade barrier. As a result of this development, Brewers of Europe has withdrawn its TBR complaint. Read more about the background and the TBR complaint by the TechieKat here. # § Patents⠀➾ # ⚓ Guest_Post:_Assessing_Responses_to_the_PTO’s_2021 Patent_Eligibility_Study [Ed: "It should be no surprise to readers of Patently-O that many are unhappy with the Supreme Court’s jurisprudence regarding patent eligibility under Section 101 of the Patent Act," it says. Because they're patent litigation profiteers, not scientists. This is lobbying, funded by the litigation fanatics.]⠀⇛ It should be no surprise to readers of Patently-O that many are unhappy with the Supreme Court’s jurisprudence regarding patent eligibility under Section 101 of the Patent Act. In response to various calls for “reform” of patent eligibility jurisprudence, on March 5, 2021, Senators Thom Tillis (R- NC), Mazie Hirono (D-HI), Tom Cotton (R-AR), and Christopher Coons (D-DE) requested that the US Patent and Trademark Office (PTO) conduct a study regarding public views on “how the current jurisprudence has adversely impacted investment and innovation in critical technologies like quantum computing, artificial intelligence, precision medicine, diagnostic methods, and pharmaceutical treatments.” The Senators also asked the PTO to evaluate the responses and provide a detailed summary of its findings by March 5, 2022. The PTO released its public request for information (RFI) on July 9, 2021. The original deadline for response was September 7, 2021, which the PTO extended until October 15, 2021. A total of 145 comments were submitted before the deadline. In advance of the official assessment, we have reviewed and tallied these public comments for those who are eager for the results in advance of the official release. # ⚓ Multinationals_and_renewable_energy:_boosting innovation_through_foreign_direct_investments [Ed: In spite of EPO corruption and crimes, LSE uses “European Patent Office” as a source, citing greenwashing_fluff designed_to_distract_from_the_crimes]⠀⇛ # ⚓ Sisvel_suing_Ford_Motor_Company_over_two_4G_standard- essential_patents_in_Munich;_Ford’s_answer_to_Delaware complaint_due_tomorrow [Ed: The so-called ‘media’ ain’t talking about it, but Europe already has its share of malicious, aggressive patent trolls like Sisvel [1, 2]]⠀⇛ The case numbers indicate that both Sisvel v. Ford cases in Munich have been assigned to the new 44th Civil Chamber under Presiding Judge Dr. Anne-Kristin Fricke, who replaced Presiding Judge Dr. Georg Werner yesterday as he moved on to head the court’s equally patent-specialized 21st Civil Chamber. In mid-December, Sisvel’s patent enforcement action against Ford Motor Company in the District of Delaware became known. The parties stipulated to an extension of time until tomorrow (February 3, 2022) for Ford to answer, or otherwise respond to, the complaint. It would have been out of character for Sisvel to enforce SEPs only in the U.S. and not also in Europe, and there, above all, in Germany, where it has already made history with two Sisvel v. Haier cases–case law that will come into play here as well unless they settle. In another case brought by an Avanci licensor–in that case, Japan’s IP Bridge–the Munich court will hold a hearing in three weeks unless the Federal Patent Court of Germany annulled the patent two weeks ago (haven’t been able to find out yet, but will know soon). # ⚓ Neurim_v._Mylan–_the_Illiad_was_shorter [Ed: Peddling this bogus, phony, misleading narrative that "parent patent was attacked on various grounds" is inversion of roles; the patents themselves are the attacks; those who challenge them act in self defence; Frantzeska Papadopoulou is either deeply brainwashed/indoctrinated or dishonest]⠀⇛ The Neurim v. Mylan saga, which started two years ago, is still going strong. The latest was a ruling by the High Court on 24 January 2022 (2022) EWHC 109 (Pat) (read here). The ups and downs, and the turns this dispute have taken, remind one of a rollercoaster. A year ago, Neurim was successful in the UK trial ([2020] EWHC 3270 (Pat)) when its claims of infringement were accepted by the court and counterclaims on the invalidation of its patent were rejected, only to shortly thereafter see its patent invalidated in the EPO (patent EP 1 441 702). For the sake of precision, the invalidity of the patent was the result of Neurim withdrawing its appeal to the Technical Board of Appeal (TBA), this in order to avoid an unfavorable decision. Some months ago, the court gave Neurim a new chance at obtaining injunctive relief against Mylan by agreeing that Neurim could have a expediated preliminary issue trial ([2021] EWHC 2198 (Pat)). On 24 January 2022, the court then ruled on preliminary issues of the case ((2022) EWHC 109 Pat). # ⚓ Hungary_Amends_Patent_Act [Ed: But the_corruption_at HIPO_will_prevail]⠀⇛ Amendments to the Hungarian Patent Act entered into force on January 1, 2022, introducing changes regarding the Bolar exemption and affecting the bifurcation system and the grant of preliminary injunctions. # ⚓ Patenting_AI:_the_nature_of_inventorship_and_the mechanics_of_ownership [Ed: Corrupt and (recently very) disgraced patent litigation firm uses buzzwords like “Hey Hi” to mislead people and push patent law into sheer_fantasy_world]⠀⇛ On 21 December 2021, the Boards of Appeal of the European Patent Office (EPO) released its latest decision on the “Dabus” cases relating to identification of artificial intelligence as an inventor of a patentable invention. Adopting a similar approach to that taken by the UK Court of Appeal in September 2021, the EPO decided that “AI cannot be named as inventor on patent applications… under the European Patent Convention (EPC) an inventor designated in a patent application must be a human being”[i]. # ⚓ Description_amendments:_Will_the_EPO_change_its examination_practice? [Ed: These_tribunals_are rigged.]⠀⇛ In the recent decision T 1989/18 one of the Boards of Appeal of the European Patent Office (EPO) ruled that there is no legal basis for requiring amendment of the description to be in line with the allowed claims. This is in contrast to what is stated in the 2021 Guidelines for Examination in the EPO, which are non-legally binding instructions for Examiners working at the EPO as well as parties interacting with the EPO. BACKGROUND For many years it has been common practice for Examiners at the EPO to require applicants to adapt the description to be in line with the amended claims. In particular, the applicant is required to prepare and file an adapted description which is in line with the allowed claims. # ⚓ Progress_and_promise_for_green_plastics [Ed: The greenwashing oxymoron of “green plastics” [oil], citing the corrupt EPO with its_PR_strategy, looking to distract from the EPO’s crimes]⠀⇛ In 2021, the European Patent Office (EPO) released a study investigating trends in plastic recycling and alternative plastics technologies. The report draws on the latest patent information available (particularly using patent filing data from 2010 to 2019) as well as the expertise of EPO Examiners to provide an analysis of the ways in which innovators are driving the transition towards a circular economy for plastics. In view of the global importance of the development of green technologies, Appleyard Lees (AL) has also recently produced its inaugural Inside Green Innovation: Progress Report 2021, which investigates patent trends in bioplastics and plastic recycling, as well as other green technologies including renewable energy storage and food production. The AL report reviews the impact of industrial activities on the environment and highlights how development of, and investment in, innovation can be used to tackle these serious problems. Here, we discuss the findings of these two reports. # ⚓ [Older]_PTO_Will_Transition_to_Electronic_Issuance_of Patents_and_Trademarks [Ed: It is going to get a lot easier to lose your patents; digital systems rot a lot faster than paper]⠀⇛ The US Patent & Trademark Office (PTO) announced on December 10, 2021, that it intends to transition to electronic issuance of patents and trademarks in 2022. Under the current rule (37 C.F.R § 1.315), the PTO must deliver or mail a patent “upon issuance to the correspondence address of record.” The PTO will soon issue a notice of proposed rulemaking to seek public feedback on revising the rules of practice to issue patents electronically. Under the proposed changes, the PTO would no longer mail patents to the applicant. Instead, the PTO would issue patents electronically via the Patent Center and Patent Application Image Retrieval, from which the patents could be downloaded and printed. While no changes to the trademark rules are necessary, the PTO will also issue a public request for comments on replacing paper registration certificates with digital versions. The PTO believes that electronic issuance will reduce the time it takes for a patent or trademark to issue by about two weeks. Once the transition is complete, applicants can still receive a paper copy of the issued patents and trademark registration certificates with an embossed gold seal and the director’s signature (i.e., a ribbon certificate) for a fee of $25 per copy. # ⚓ [Older]_A_Whole_Lot_of_“Cobbl[e]”-ty_Gook_After Wertheim⠀⇛ Holding: In Indivior UK Ltd. v. Dr. Reddy’s Laboratories S.A., No. 20-2073 (Fed. Cir. 2021), the Federal Circuit issued an opinion (“Majority Opinion”) affirming a decision of the Patent Trial and Appeal Board (“PTAB”) holding all but one of the challenged claims unpatentable in IPR2019-00329. Judge Linn concurred-in-part and dissented-in-part (“Linn Opinion”). # ⚓ Huawei_inks_its_first_Wi-Fi_6_patent_licence_with_an overseas_implementer [Ed: Wi-Fi is another sort of patent cartel and writers_sponsored_by_this_cartel say “patent [sic] owners spy monetisation [sic] opportunities”]⠀⇛ Latest patent deals related to the next-gen wireless internet standard suggest patent owners spy monetisation opportunities # ⚓ UK:_Why_Does_My_Start-Up_Need_Patents? [Ed: It does not need that. The_litigation_firms (like this liar) want any startup to be misled about a system designed to enrich those who are already rich and rip off the rest]⠀⇛ A patent is a legal monopoly granted by a government in return for public disclosure of an invention. A granted patent gives the proprietor the right to prevent others using the invention in the territory to which the patent applies. # ⚓ Battery_Innovation_Enhances_EV_Technology,_Generates Worldwide_Patent_Boom [Ed: The EPO’s_greenwashing, designed to glorify monopolies and distract from the EPO’s crimes, keeps getting cited by patent profiteers and fanatics]⠀⇛ Consider information from the joint study, “Innovation in batteries and electricity storage – a global analysis based on patent data,” published in 2020 by the European Patent Office (EPO) and the International Energy Agency. From 2005 through 2018, patents for electric storage technologies – primarily for lithium-ion batteries – increased annually by 14% worldwide. That’s four times as much as the average patent hike in all other technology industries. # ⚓ Serbia_Amends_Patent_Law [Ed: Bending over to monopolies that rip off ill people.]⠀⇛ Amendments to the Serbian Law on Patents entered into force on December 23, 2021 introducing important changes relating to Supplementary Protection Certificates (SPCs) and utility models. # ⚓ Supplementary_Protection_Certificates_For_Medicinal Products [Ed: A timely reminder that big pharmaceutical monopolies not only write the law but also pass the law to protect themselves using "the law"; they even make up new concepts and terms like "SPCs", quickly exacerbating inequality by their own design]⠀⇛ A Supplementary Protection Certificate (SPC) is an intellectual property right available for active ingredients of human and veterinary medicinal products requiring marketing authorisation. # ⚓ Introduction_To_Supplementary_Protection_Certificates For_Plant_Protection_Products [Ed: They’re going for monopolies on plants; these villanelles lawyers want you_to_think_humans_“invented”_and_“own”_nature]⠀⇛ Plant protection products protect crops or desirable or useful plants. They are primarily used in the agricultural sector, but also in forestry, horticulture, amenity areas and in home gardens. Plant protection products are defined as active substances, or preparations containing one or more such active substances, put up in the form in which they are supplied to the user, which are intended to: # ⚓ MediciNova_nabs_new_patent_in_Korea_for_MN-001_for treatment_of_blood_cholesterol⠀⇛ Recently, MNOV secured Canadian and European patent for MN-001 for hepatic ballooning. # ⚓ New_Referral_To_The_EPO_Enlarged_Board_Of_Appeal_On The_Entitlement_To_Priority [Ed: EPO management sends a case to a kangaroo court, which it_clearly_controls_in direct_and_obvious_violation_of_the_EPC]⠀⇛ The Board of Appeal in consolidated cases T 1513/17 and T 2719/19 has referred two new questions to the Enlarged Board of Appeal on the issue of priority entitlement, in particular relating to the “joint applicants” approach to claiming priority. # ⚓ USPTO_Tells_Fed._Circ._Only_Humans_Can_Be_Inventors [Ed: Provocateur Stephen Thaler should be spurned based on obviousness -- the obviousness that patents are not for bots]⠀⇛ The U.S. Patent and Trademark Office has urged the Federal Circuit to uphold a Virginia federal judge’s ruling that artificial intelligence cannot be listed as an inventor on a patent application. The USPTO’s Thursday brief formally opposed AI researcher Stephen Thaler’s challenge to U.S. District Judge Leonie Brinkema’s September decision that shut down his suit against the U.S. Patent and Trademark Office. The USPTO said that Thaler was trying “to rewrite the Patent Act” and added that “the plain language Congress chose to incorporate in the Patent Act unequivocally resolves this question — only a human being can be an ‘inventor.’” # ⚓ Federal_Circuit:_Did_you_get_their_digits? [Ed: Patent litigation-funded Dennis_Crouch still looking to defend defunct patents]⠀⇛ In December 2021, the Federal Circuit sided with the accused-infringer Mylan on claim construction of the term “0.001%” — vacating the judgment of infringement. See Crouch, Rounding Errors in Patent Law, Patently-O (Dec 8, 2021). Now Astrazeneca has petitioned for en banc reconsideration–seeking “consistent precedent regarding significant digits.” # ⚓ EU_set_to_put_spotlight_on_essentiality_in_new_SEP policy [Ed: Patent extortion agenda in EU and based on their support of EPO corruption it's clear whose side they will take]⠀⇛ In-house sources from both sides of the SEP licensing fence expect a new policy initiative to introduce further transparency in portfolios # ⚓ PTAB_Procedural_Decisions_Report:_Non-Merits_Based Decisions_Rise,_Denials_Fall_—_Unified_Patents⠀⇛ It was another year of hundreds of procedural denials at the PTAB, as many as any other previous year, save 2020’s record high. At the same time, the Board ruled on Fintiv and discretionary issues in almost half of all decisions. The dip in the number of discretionary denials in 2021 from 2020’s record high likely reflects parties adjusting to the recent requirements by filing so- called Sotera stipulations, devoting petition space to briefing the Fintiv factors, and shifting to file ex parte reexaminations over IPRs (which increased by half, as shown below). And while grants were down and it is difficult to measure how much time, money, and effort have been expended responding to Fintiv, data shows the Board considered discretionary issues in approximately 500 of the institution decisions issued in 2021, or roughly more than a third of all the 1,249 decisions it made. In short, Fintiv affected at least half the cases on the Board’s docket in 2021. 2021 saw 179 institution decisions denied on procedural grounds, compared to 228 in 2020 and 162 in 2019. [...] Over the same period, companies began to revive ex parte reexaminations–an old, but nonetheless effective, tool. From 2020 to 2021, the number of reexaminations increased by 47%. Over 300 reexaminations were filed in 2021, as parties occasionally forwent IPRs that raised discretionary or stay-related issues. # ⚓ Patent_Litigation_2022_in_Turkey [Ed: Just looking to profit by attracting patent trolls and such to Turkey]⠀⇛ Under Article 90 of the Constitution, in the event of a conflict between international agreements and national legislation relating to fundamental rights and freedoms, the provisions of international agreements prevail. # ⚓ Broad_Files_Substantive_Preliminary_Motion_No._1_to Substitute_the_Count [Ed: Hard to believe this is still going; the patent fanatics (profiteers) want to own or monopolise life itself through patents and "gene editing"]⠀⇛ On December 3rd, Junior Party the Broad Institute, Harvard University, and MIT (collectively, Broad) filed its Substantive Preliminary Motion No. 1 in Interference No. 106,133 (which names Sigma-Aldrich as Senior Party), asking the Patent Trial and Appeal Board to substitute the interference Count, pursuant to the provisions of 37 C.F.R. §§ 41.121(a)(1)(i) and 41.208(a)(2). Broad’s Proposed Substitute Count takes the “McKelvey” format (comprising in the alternative a claim from one of each Party’s applications in interference); the proposed change is in the portion of the Count reciting Broad’s claims… # ⚓ FOSS_Patents:_Apple_opposes_Ericsson_motion_to_amend FRAND_complaint_in_Eastern_District_of_Texas,_says_its own_FRAND_case_was_first_properly_filed_one⠀⇛ The procedural tussle between Ericsson and Apple in the Eastern District of Texas over whether and how to go forward with their mutual complaints continues. There’s even a meta-procedural question–relating to procedures related to defining the actual procedures–they disagree on: whether Judge Rodney S. Gilstrap should hold an early case management conference, which Apple insists on. It’s interesting and a first achievement for Ericsson (owing to its strategy of forging ahead in the fall with a first FRAND action) that the discussion is all about the structure of their litigation in the Eastern District of Texas–as opposed to the usual venue fight over whether that district court has jurisdiction over any case targeting Apple, which even closed its local Apple Stores to have a stronger case for a transfer. If not for Ericsson’s early filing, Apple would already have requested a transfer to the Northern District of California. # ⚓ Third_Party_Submissions [Ed: For the sake of money the USPTO runs in auto-pilot, not even checking with the public is something is novel; just grant, grant, grant...]⠀⇛ In a prior post, I wrote about third party prior art submissions, but that post was only looking at issued patents. I have gone back and pulled-in data from all publicly- available applications, including those that have been abandoned or are still pending. The results: third parties have submitted prior art in about 7,000 applications over the past decade. This is about 0.2% of all the applications in my dataset. # ⚓ FOSS_Patents:_EPICSSON:_Apple_makes_public_interest statement_in_Ericsson_patent_case_that_supports_Epic’s antitrust_market_definition⠀⇛ What Apple is telling the ITC there is this: even if patent infringements are identified, the iPhone can’t be banned because it’s a product category of its own. There’s nothing else quite like it. Android smartphones may also be smartphones, but they are not iPhones, so they are not “like” articles (which would count as a potential replacement under the ITC’s rules). In the Epic Games v. Apple App Store antitrust case, however, Apple argued that there was a broad market for game distribution. So, according to Apple, if Fortnite wasn’t available on the iPhone, who cares? It could still be played on an Xbox, a Windows PC, or a Samsung phone. The district court didn’t adopt that same market definition, but it did reject–as did Apple–Epic’s single-brand market definition, according to which there is a foremarket (mobile operating systems) and an aftermarket (app distribution for the iPhone). Single- brand markets are a rare exception, but this is such a case. Interestingly, when the question is whether iPhone imports could be excluded from the U.S. market (limited exclusion order, or colloquially “import ban”), Apple itself advances a single-brand market definition, claiming that the iPhone is a product category and Android phones are not capable of replacing any supply shortages or disruptions affecting the iPhone. # ⚓ Status_of_US_Utility_Patent_Applications.⠀⇛ David Kappos quickly reset expectations. And, since then we have seen a steady rise in allowance rate. # ⚓ FOSS_Patents:_Ericsson_seeking_preliminary_injunction against_Apple_distributor_in_Brazil,_filed_second_case in_Belgium;_Apple_wants_December_trial_in_Texas,_now challenging_10_Ericsson_patents⠀⇛ Ericsson keeps up the pressure on Apple. A filing made by Apple in the Eastern District of Texas on Monday (January 31) mentions that “[i]n Brazil [...], in addition to targeting Apple in a previous injunction request, Ericsson [...] filed for a second preliminary injunction on January 17 against Allied Tecnologia S.A., based on Ericsson’s claimed 4G cellular SEPs and merely because Allied resells Apple cellular products.” Apple is now intervening to protect its wholesaler. When I previously wrote about the preliminary injunction Ericsson is seeking against Apple itself in Brazil, I used the plural form “injunctions” though it appears to be a single motion for preliminary injunction involving three SEPs. And now there’s another such motion, also over three SEPs, targeting Allied Tecnologia because of its distribution of accused Apple products. # ⚓ CVC_Files_Responsive_Preliminary_Motion_No._1_for Priority_Benefit [Ed: The utter lunacy of patents on life and nature does not end; these patent extremists won't rest until everything -- including breathing air -- gets monopolised, with lawsuits they stand to profit from]⠀⇛ Pursuant to the Patent Trial and Appeal Board Order issued November 29, 2021, Junior Party the University of California, Berkeley; the University of Vienna; and Emmanuelle Charpentier (collectively, “CVC”) on December 17, 2021 filed its Responsive Preliminary Motion No. 1 in Interference No. 106,132 (which names Sigma-Aldrich as Senior Party), asking the Board for benefit of priority to U.S. Provisional Application No. 61/652,086, filed May 25, 2012 (“P1″), or in the alternative either U.S. Provisional Application No. 61/716,256, filed October 19, 2012 (“P2″); U.S. Provisional Application No. 61/757,640, filed January 28, 2013 (“P3″); U.S. Application No. 13/842,859, filed March 15, 2013; U.S. Application No. 14/685,504, filed April 13, 2015; or U.S. Application No. 15/138,604, filed April 26, 2016, pursuant to 37 C.F.R. §§ 41.121(a)(1)(ii) and 41.208(a) (3) and Standing Order ¶ 208.4.1, contingent on the Board granting Sigma-Aldrich’s Substantive Preliminary Motion No. 1 to Substitute the Count. # ⚓ Patent_Docs:_Sen._Tillis_Asks_ACUS_to_Conduct_Study on_Creation_of_U.S._IP_Office⠀⇛ Last month, Sen. Thom Tillis (R-NC), the Ranking Member of the Subcommittee on Intellectual Property of the Senate Committee of the Judiciary, wrote to the Administrative Conference of the United States (ACUS) to request that the agency “conduct a study on whether Congress should create a unified, stand-alone, and independent Intellectual Property Office.” ACUS is an independent agency of the U.S. government, which was established in 1964 by the Administrative Conference Act, and which conducts research and issues reports concerning various aspects of the administrative process and, when warranted, makes recommendations to the President, Congress, particular departments and agencies, and the judiciary concerning the need for procedural reforms. Stating that “[t]he current fractured approach to intellectual property (IP) in the federal government, with multiple IP functions housed in different agencies, leads to conflicting policy agendas and unnecessary bureaucracy,” Sen. Tillis (above right) noted that he was exploring the possibility of creating an independent agency that would unite the U.S. Patent and Trademark Office (USPTO) and the U.S. Copyright Office (USCO), and perhaps also the Intellectual Property Enforcement Coordinator and other relevant IP functions located in other agencies. The Senator indicated that he believed that “a single, Senate-confirmed, presidentially appointed Director should lead such an office and that it should have, at a minimum, separate Commissioners for Patent, Trademark, Copyright, and Policy Coordination that would report to the Director.” Before pursuing legislation to create a single agency, however, Sen. Tillis suggested that ACUS should contract with the USPTO and USCO to study the issue. # ⚓ Tillis_Floats_Idea_To_Consolidate_USPTO,_Copyright Office [Ed: Tillis has long been the mole or the "Manchin" of patent and copyright fanatics, in effect helping them ram policies that harm the public; but media in the pockets of those same fanatics won't describe him as such]⠀⇛ The top Republican on the U.S. Senate Subcommittee on Intellectual Property says there’s too much “unnecessary bureaucracy” in the federal government’s approach to patents, trademarks and copyright law and wants a study done on how to combine the agencies to create a “one stop shop.” In a letter dated Jan. 26, Sen. Thom Tillis, R-N.C., asked the Administrative Conference of the United States to launch an investigation into “whether Congress should create a unified, stand-alone and independent Intellectual Property Office.” The ACUS is an independent federal agency that makes process recommendations to the government. # ⚓ PCT_Direct_Procedure_–_Opportunity_To_Comment_On International_Application [Ed: EPO_is_not_for_Europe but for multinationals and oligarchs; PCT a reminder of this]⠀⇛ If a new PCT application fulfils both of these criteria, the Applicant may file a “PCT Direct letter” providing informal comments with the application. The Search Examiner is obliged to consider those comments when preparing the International Search Report and the Written Opinion on patentability. # ⚓ UPC:_Is_it_finally_here? [Ed: No, UPC is not legal and these loaded headlines are their fake_news_lobbying strategy]⠀⇛ The European Patent Office (EPO) issued 3 new notices on 19 January 2022 about the Unitary Patent. # ⚓ [Older]_Shots_Fired:_Challenger_Must_Have_Requisite Standing_Before_Appealing_Unfavorable_IPR_Decisions [Ed: More obstacles against removal of fake patents in the US]⠀⇛ The US Court of Appeals for the Federal Circuit found, in the context of an appeal from an inter partes review (IPR) decision, that the appellant had Article III standing and affirmed a Patent Trial & Appeal Board (Board) decision, holding the challenged claims unpatentable as obvious. ModernaTX, Inc. v. Arbutus Biopharma Corporation, Case No. 20-2329 (Fed. Cir. Dec 2, 2021) (Lourie, J.) Arbutus owns a patent pertaining to “stable nucleic acid-lipid particles (SNALP) comprising a nucleic acid (such as one or more interfering RNA), methods of making the SNALP, and methods of delivering and/or administering the SNALP.” Moderna petitioned for IPR of the patent, asserting three grounds… # ⚓ European_Union:_UPC:_Costs_And_Fees [Ed: Herbert Smith Freehills wants you to think UPC exists even though it does not, it’s moreover_illegal and will be challenged (lawyers lying to people does harm to the profession)]⠀⇛ Following a lengthy consultation, the Preparatory Committee for the Unified Patent Court (UPC) published its Rules on Court fees and recoverable costs (the Rules) along with Guidelines for the determination of value- based Court fees and the ceiling of recoverable costs of the successful party (the Guidance). # ⚓ Parties’_Duty_To_Keep_The_Patents_Court_Informed About_EPO_Proceedings [Ed: The convicted corrupt firm Marks & Clerk, lecturing us about law, even in relation to EPO (whose_corruption_it_actively_supports), is quite a howler]⠀⇛ Mr Justice Meade recently handed down judgment in the ongoing Neurim v Mylan (now named Viatris) saga. This judgment followed an expedited three-day trial of preliminary issues (see “Neurim v Mylan: Take Two”). Dealing predominately with the principles of issue estoppel, abuse of process and competition law issues, this judgment is also notable for imposing a new duty on parties to litigation before the Patents Court to keep it informed about scheduling issues and changes to hearing dates in parallel EPO proceedings, regardless of whether they intend to make case management applications themselves. # ⚓ Should_AI_Systems_Be_Eligible_For_Patents? [Ed: Misframing the debate or situation by interjecting meaningless and misleading_terms_such_as_“Hey_Hi”]⠀⇛ The line between artificial intelligence (“AI”) and pure human innovation has blurred as technology continues to evolve at a rapid pace. Technological advances and the parallel progress of AI has resulted in several key innovations: robots can double as radiologists and have the ability to interpret CT scans and other imaging, vehicles can drive themselves with automated technology, and algorithms have the ability to create written and artistic bodies of work. AI advances have been front and center during the COVID-19 pandemic. Algorithms were established to determine which patients could be discharged from the hospital, unique symptoms like loss of smell were identified as a distinguishing factor from the flu, and future outbreaks could be predicted using AI. A human vaccine was exclusively generated by an AI program called SAM, and clinical trials recently began in the United States. # ⚓ Competition_Law_Aspects_of_Patent_Licensing_& Enforcement_in_Israel⠀⇛ The Supreme Court of Israel recently held that Sanofi intentionally deceived and failed to provide material information to the Israeli Patent Office during the prosecution of a patent application in respect of Sanofi’s drug Plavix (Clopidogrel Bisulfate)1. Though Sanofi eventually withdrew the patent application, the Supreme Court held that such deception and failure to provide material information were not consistent with fair competition in the marketplace, since Sanofi’s actions significantly impacted how Sanofi’s competitors brought generic alternatives to market. As such, the Supreme Court held Sanofi liable under claims of unjust enrichment. # ⚓ Printed_Publication_Proof_–_Cross_T’s_And_Dot_I’s⠀⇛ On November 30, the PTAB entered its final written decision in Unified Patents, LLC v. 2BCom, LLC on the patentability of the claims of U.S. Patent No. 7,127,210 (the ‘210 patent). The claims in question were directed to a wireless communication apparatus, reciting a method by which a wireless communication apparatus, after establishing a connection with at least a first wireless communication device, is inhibited from establishing a connection with a second wireless communication device. The petitioner, Unified Patents, LLC, challenged the claims as obvious in view of a number of articles, one of which was a Fall 2000 IEEE article, Bluetooth-based wireless connectivity in an automotive environment (the Nüsser reference). # ⚓ [Older]_Design_Patent_Prior_Art_Must_Be_From_Same_or Analogous_Field_as_Claimed_Article_of_Manufacture [Ed: Well, design_patents_ought_not_even_exist_at_all; it’s misuse of patent law]⠀⇛ Finding that the Patent Trial & Appeal Board (Board) applied an erroneous interpretation of claim scope, the US Court of Appeals for the Federal Circuit reversed a Board decision, upholding an examiner’s rejection of a lip implant design patent as anticipated by a non-analogous art tool. In re: SurgiSil, Case No. 20-1940 (Fed. Cir. Oct. 4, 2021) (Moore, C.J.) # ⚓ [Older]_Ex_Parte_Reexamination_Not_Allowed_After Failed_IPR_Challenge⠀⇛ The US Court of Appeals for the Federal Circuit found that ex parte reexamination was unavailable to a challenger who repeatedly tried and failed to raise the same arguments for the same patent in a prior inter partes review (IPR) proceeding. In re: Vivint, Inc., Case No. 20-1992 (Fed. Cir. Sept. 29, 2021) (Moore, C.J.) Vivint sued Alarm.com in 2015 for infringement of several patents. In response, Alarm requested that the Patent Trial & Appeal Board (PTAB) institute “a litany of post-issuance review proceedings,” including three separate IPR petitions directed to one of the patents. The PTAB refused to institute two of the petitions because Alarm failed show to a reasonable likelihood that it would prevail on at least one challenged claim and also refused to institute the third petition because it represented an example of “undesirable, incremental petitioning.” According to the PTAB, Alarm had “used prior Board decisions as a roadmap to correct past deficiencies” and allowing such “similar, serial challenges to the same patent” by the same challenger risked, not only harassment of patent owners, but also frustration of congressional intent behind the America Invents Act (AIA). # ⚓ UK_IPO_announce_new_IP_Counter-Infringement_strategy [Ed: Latest brainwash campaign from the oligarchs’ protectors_at_UK-IPO]⠀⇛ The new strategy represents a step change in the IPO’s drive to protect IP rights. By partnering with others to set a global gold standard, it aims to make UK IP rights – and rights owned by UK businesses internationally – the best protected in the world. The strategy seeks to establish how enforcement agencies, government and industry can work together to build upon and improve current structures, ensuring that IP infringement is tackled coherently as a strategic economic and social threat – at home and internationally. It will be underpinned by a strong research plan, and the findings will be shared widely with partner organisations to build a robust evidence base to support and inform work. # § Software Patents⠀➾ # ⚓ [Older]_Analysis_indicates_that_Access_Advance is_currently_the_top_HEVC_patent_pool [Ed: |Software_patents_cartel boosted by IAM]⠀⇛ Licensees get access to higher-quality rights via the platform than those available through Velos Media and MPEG- LA # § Trademarks⠀➾ # ⚓ NFTs_and_new_tech_to_shake_up_domain_disputes_in_2022 [Ed: And once again legitimising scams like "NFT"]⠀⇛ Sources explain how disruptive tech such as NFTs, blockchain and the metaverse will affect domain name protection and enforcement this year # ⚓ TTABlog_Test:_Is_“CRC_BAKERY”_Confusable_with_the “CRC”_Kosher_Certification_Mark,_Both_for_Food Products?⠀⇛ The USPTO refused to register the proposed mark CRC BAKERY for various bakery products (Class 30), for wholesale food distributorship services (Class 35), and for bakery services (Class 40) [BAKERY disclaimed], finding confusion likely with the registered certification mark CRC & Design (shown below) for “fresh and processed foods for human consumption.” Applicant argued, inter alia, that the cited mark – used to certify rabbinical approval of food products as being kosher – limits the classes of consumers for those foods to sophisticated and discerning consumers. How do you think this came out? In re CRC Packaging, LLC, Serial No. 88696519 (January 28, 2022) [not precedential] (Opinion by Judge Elizabeth A. Dunn). The cited certification mark is owned by the Chicago Rabbinical Council, and states that the mark is “used by persons authorized by the certifier to certify a reliable rabbinical approval of food products as being kosher.” The Section 2(d) likelihood-of-confusion analysis does not change when the cited registration is for a certification mark; however, because the owner of a certification mark does not itself use the mark, the determination of likelihood of confusion is based on use of the cited mark by the certification mark users. # ⚓ Additional_“GARANIMALS”_Evidence_Yields_District Court_Reversal_Of_TTAB’s_“MANIMAL”_Opposition Dismissal⠀⇛ The United States District Court for the District of Oregon reversed the Board’s decision dismissing an opposition to registration of the mark MANIMAL for a wide variety of clothing, including “children’s clothing.” [TTABlogged here]. The Board found that opposers failed to establish a likelihood of confusion with its registered mark GARANIMALS for children’s shirts and pants. Reviewing de novo the TTAB record as well as substantial additional evidence, the court granted the plaintiffs’ motion for summary judgment on its cause of action for review under Section 1071 of the Trademark Act. Garan, Incorporated and Garan Services Corporation v. Manimal, LLC, Case No. 3:20- cv-00623-IM (D. Oregon January 25, 2022). Plaintiffs’ new evidence focused on establishing the fame of the GARANIMALS mark, including evidence of substantial media recognition. Plaintiffs also placed their sales and advertising figures in marketing context, “showing that it is the second largest children’s clothing brand by market share, second only to Carter’s and ahead of brands including Children’s Place, Old Navy, Gerber, OshKosh, Circo, Hanes, Wrangler, and Healthtex.” # ⚓ New_UAE_Patent_Law:_What_do_you_need_to_know?⠀⇛ The UAE has issued Federal Law no. 11 of 2021 (“the Law”) concerning the regulation and protection of Industrial Property Rights. The Law will repeal the former Patent Law, Law No. 17 of 2002 and covers patents, industrial designs, integrated designs, undisclosed information and utility certificates. It was published in Official Gazette no. 703 on 31 May 2021 and is expected to come into force when the Executive Regulations publish. # ⚓ UAE_Joins_Madrid_Protocol_International_Trade_Mark System [Ed: UAE in the monopolists' hegemony, now celebrated by convicted corrupt firm Marks & Clerk, which is inciting public officials to break the law by lying to them]⠀⇛ The Madrid Protocol allows businesses located in one member country of the Madrid Protocol system to obtain trade mark protection in any of the other 108 member countries through the filing of a single trade mark application. The Madrid Protocol currently extends to many countries of general commercial importance, including the UK, EU, US, Japan and China. It is also possible for owners of Madrid Protocol trade mark registrations to extend their trade mark protection to other member countries within the system as their business needs change. Due to the flexibilities of the system, using the Madrid Protocol to obtain trade mark protection overseas can be a very cost-effective mechanism, and can also simplify management of the trade mark portfolio moving forward. # ⚓ The_Dark_Pictures_developer_trademarks_five_future titles [Ed: This writer has no clue what he's writing about; he thinks trademarks are obtained via "European patent office"]⠀⇛ Supermassive Games, developer of Until Dawn and the ongoing The Dark Pictures anthology series, has trademarked logos and titles for five future projects. All five appear to be upcoming releases in The Dark Pictures series, are styled with the franchise’s logo, and were registered via the European patent office yesterday, 31st January (thanks, Gematsu). # ⚓ The_Dark_Pictures_Series_Developer_Trademarks_Five More_Games [Ed: Another clueless writer who thinks EPO does trademarks]⠀⇛ It seems more titles are coming to The Dark Pictures franchise as it got trademarked just recently. There were registered via the European Patent office. # § Copyrights⠀➾ # ⚓ Breaking:_UKIPO_outlines_five-year_IP_enforcement plan [Ed: UKIPO ramps up its attack_on_the_interests_of the_British_public]⠀⇛ The office will rely on intelligence sharing and educational campaigns as it looks to highlight the human impact of IP crime # ⚓ Metaverse_could_spark_C-suite_IP_investment,_say brands [Ed: Max Walters again pushing buzzwords and nonsense; the quality of so-called 'journalism' has fallen so sharply over the past 2 decade]⠀⇛ In-house counsel in the fashion, science and drinks industries say that, despite uncertainties, the metaverse may encourage top-level investment in IP # ⚓ Piracy_Icon_ETTV_Officially_Shuts_Down_Due_to_a_Lack of_Funds⠀⇛ ETTV has shut down and will not be coming back. The operator of the site informs TorrentFreak that he doesn’t have the funds to keep the site and upload bots going. The domain names are still registered for now but these won’t be renewed either. 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