𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, December 05, 2024 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Fri 6 Dec 02:49:19 GMT 2024 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/2024/12/05/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmbHjgPAAcGNUG9Sej4vSKhK8DfUYokfFkXLdKwr1JtGJG QmdLsuRLzrwb58dZaSmJah6oCmNNZ6cW4ick4chqJmHjmY QmTNR3uqcbMYjPAbbHjBqyNJb3ib8kytQvdFnATzkBFVvo QmfCHrqMLfMsHXYnQeAvVuNYt91Zw2AmMJ5mx4RqsrWy3b QmR2rr1yXDANjQBEz2oGtd2UMgy9U37FHdjpUhPfAk7h5z QmWE6ucdKk9Q1pi6ce3ko9xPWd9Y4BjpLij3W7tJ5TMjG3 QmaoEDiALTYYZdaq3SQ86aQpMwUji1nqCeLbXAoszFRYvJ QmSTkZUY74BcgbgqS6JKwwNbVnbzY5uqwpgWtYonGJua8s QmXZcp3rXLYa24pYd7jUu6sPDrhziRCNCok875WLJTLysP QmUE7nd24kx2soZFbSYKDsb1ik1wpirFTRTBhDTj6w9sjh QmdKeWBhfnjgQLYU48wto7DdStpXsB5mE1yEEnWcxQ53vu QmfSnnTnjcAe3YvtRsVgAwUJfpcEk1dM5J5yjJLyv7MxqM QmQ16CkpxBbMzPZ6wZcuKBUcxH1RZ8uAEhcvdBsPRpVZe9 QmT3gTQRv33wEDtJveL8DiqiacGeRaxEbRFDUyVSJEAvDL QmTs9qcwghZPs5oBh9qzsu8a11T4s6xHrJjVNyk5miFy3X Qmdqd6mb8mj27qVvQZRR7sjshrXYYirWm9vRttLkNB5rW6 QmSjY85vxbu9nNFHUMmuK7CxRame2VYuhb523CJaK5zRkj QmZwah9nZHVvSzbJWEAMxumYDpanFPqTahnqoNP83tuZbx QmQWSrGfeYwgf6HE9N3742DJrJwq8uNSCUAz469CnuUFGe QmcgTTyseF5zFd4MLquM4PtJZzkFcBEqaUbqDe4eaUx6Na QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ Techrights - At the OSI, Microsoft Operative (Funded by Microsoft) Promotes Proprietary Software of Microsoft ⦿ Techrights - Companies That the Software Freedom Conservancy (SFC) Will Censor the Community for, Using Their Very Large CoC ⦿ Techrights - Fantastic Journalism by Brian Fagioli ⦿ Techrights - Gemini Protocol Keeps Getting Better (Less and Less Reliance on Centralised Certificate Authorities) ⦿ Techrights - Increasing Productivity With Less Hardware, Little Power, and Fewer CPU Cycles (and Far Less Digital Waste in General) ⦿ Techrights - IRC Proceedings: Wednesday, December 04, 2024 ⦿ Techrights - [Meme] Shooting the Messenger ⦿ Techrights - [Meme] They Dropped the L (Libre and Law) ⦿ Techrights - Microsoft Criminals: Law Enforcement is the Real Problem ⦿ Techrights - GNU/Linux news for the past day ⦿ Techrights - Software Freedom Conservancy (SFC) Associate Sued Us for Publishing Perfectly Accurate Article About SFC; We Sued Them for Harassment ⦿ Techrights - Software Freedom Conservancy (SFC) Has Asked a Blogger to Delete This Page About the SFC, So We Reproduce It in Full Here ⦿ Techrights - Techrights Does Not Forget ⦿ Techrights - The Free Software Foundation (FSF) Has Raised More Than Three Times More Money Than the Software Freedom Conservancy (SFC), Which Mostly Gets Money From Corporations, Including Microsoft ⦿ Techrights - Why We Moved to Perl and Dumped PHP Last Year ⦿ Techrights - Windows Has Fallen to All-Time Low in India ䷼ Bulletin articles (as HTML) to comment on (requires login): https://techrights.org/n/2024/12/05/At_the_OSI_Microsoft_Operative_Funded_by_Microsoft_Promotes_Pro.shtml https://techrights.org/n/2024/12/05/Companies_That_the_Software_Freedom_Conservancy_SFC_Will_Censor.shtml https://techrights.org/n/2024/12/05/Fantastic_Journalism_by_Brian_Fagioli.shtml https://techrights.org/n/2024/12/05/Gemini_Protocol_Keeps_Getting_Better_Less_and_Less_Reliance_on_.shtml https://techrights.org/n/2024/12/05/Increasing_Productivity_With_Less_Hardware_Little_Power_and_Few.shtml https://techrights.org/n/2024/12/05/IRC_Proceedings_Wednesday_December_04_2024.shtml https://techrights.org/n/2024/12/05/Meme_Shooting_the_Messenger.shtml https://techrights.org/n/2024/12/05/Meme_They_Dropped_the_L_Libre_and_Law.shtml https://techrights.org/n/2024/12/05/Microsoft_Criminals_Law_Enforcement_is_the_Real_Problem.shtml https://techrights.org/n/2024/12/05/Over_at_Tux_Machines.shtml https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Associate_Sued_Us_for_Publishi.shtml https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Has_Asked_a_Blogger_to_Delete_.shtml https://techrights.org/n/2024/12/05/Techrights_Does_Not_Forget.shtml https://techrights.org/n/2024/12/05/The_Free_Software_Foundation_FSF_Has_Raised_More_Than_Three_Tim.shtml https://techrights.org/n/2024/12/05/Why_We_Moved_to_Perl_and_Dumped_PHP_Last_Year.shtml https://techrights.org/n/2024/12/05/Windows_Has_Fallen_to_All_Time_Low_in_India.shtml ䷞ Followed by Daily Links (assorted news picks curated and categorised): https://techrights.org/n/2024/12/05/Gemini_Links_05_12_2024_Hermeticism_Living_in_the_Shell_and_Mor.shtml https://techrights.org/n/2024/12/05/Links_05_12_2024_Domain_Changes_Griping_With_Haskell.shtml https://techrights.org/n/2024/12/05/Links_05_12_2024_Explaining_the_South_Korea_Chaos_and_French_PM.shtml https://techrights.org/n/2024/12/05/Links_05_12_2024_Formaldehyde_and_Cancer_US_and_China_Boycottin.shtml https://techrights.org/n/2024/12/05/Links_05_12_2024_Mass_Layoffs_at_Microsoft_s_PR_Bribery_of_Medi.shtml ䷩ 𝚕𝚒𝚗𝚎 96 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/At_the_OSI_Microsoft_Operative_Funded_by_Microsoft_Promotes_Pro.shtml Gemini version at https://techrights.org/n/2024/12/05/At_the_OSI_Microsoft_Operative_Funded_by_Microsoft_Promotes_Pro.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ At the OSI, Microsoft Operative (Funded by Microsoft) Promotes Proprietary Software of Microsoft⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 Days ago: The_Microsoft_OSI:_All_the_Latest_Blog_Posts_Are_Written_by_Microsoft Operative_Salaried_by_Microsoft They've totally quit pretending what they really are: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Improving_Open_Source_security_with_the_new_GitHub_Secure Open_Source_Fund⦈_ An OSI not corrupted and bribed by Microsoft would tell people to get away from GitHub, not advocate for GitHub (Microsoft). The OSI is deeply corrupt. The good news is, it's barely hiding it anymore. The latest "Members Newsletter" (Driving Open Source forward: make your impact in 2025) is also published by the Microsoft operative. It's like Microsoft totally controls everything there, even the reports and policy. █ ⣿⡿⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⣤⡄⠀⠈⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡀⠀⢹⡁⠀⢠⣿⣷⣌⣁⣁⣉⣉⣍⣉⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⠿⡿⡿⠿⠿⣿⣿⡿⠿⠿⢿⣿⣿⢿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣷⣷⣶⣶⣾⣿⣿⣶⣶⣾⣷⣿⣶⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⢸⢛⢛⡛⢛⡙⡟⡛⣛⢛⠿⡓⡟⣋⠛⠛⢻⡏⣴⡌⡟⡛⡟⠛⠟⣋⢻⣇⠒⠼⣛⢻⢻⢻⢛⡟⣙⠟⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣼⣼⣧⣨⣴⣧⣷⣬⣾⣴⣧⣧⣿⣄⣒⣸⣷⣬⣴⣇⣥⣷⣥⣦⣿⣼⣧⣥⣶⣬⣾⣬⣼⣼⣧⣥⣦⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠛⠉⠛⣉⡋⣿⢹⢉⢸⡁⣉⠟⣽⡙⠋⢏⢸⡁⡁⣋⢻⡅⣹⢈⢹⠫⢹⣿⢉⢹⠫⢫⠹⠹⢹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣤⣶⣤⣶⣴⣼⣼⣼⣧⣌⣰⣿⣷⣶⣼⣼⣧⣤⣿⣼⣷⣼⣼⣼⣦⣼⣿⣼⣼⣦⣾⣦⣧⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢰⡂⡇⡅⣽⢘⡃⡏⡏⡇⣍⢻⣇⡒⠺⠩⢹⢩⣹⢹⢹⢉⠋⠍⣿⠡⣦⢹⢩⢹⠫⠙⢉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣷⣾⣾⣷⣷⣶⣷⣶⣾⣷⣦⣾⣶⣾⣶⣾⣶⣾⣾⣷⣶⣿⣷⣶⣾⣴⣾⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⠲⢋⡝⠉⡏⡏⡝⣩⡛⠩⢻⡇⣙⡏⡏⡟⣻⠿⢿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣷⣿⣶⣶⣶⣾⣷⣿⣷⣶⣷⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣻⣝⣛⣻⣙⣛⣛⣻⣛⣛⣛⣟⣋⢻⣛⣛⣛⣛⣛⣟⣛⣟⣟⣙⣛⣙⢫⣛⣛⣙⣛⣛⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⣩⣉⣉⣉⣉⣍⣉⣍⣉⣯⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣍⣉⣉⣍⣉⣉⣋⣹⣩⣉⣉⣹⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 156 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Companies_That_the_Software_Freedom_Conservancy_SFC_Will_Censor.shtml Gemini version at https://techrights.org/n/2024/12/05/Companies_That_the_Software_Freedom_Conservancy_SFC_Will_Censor.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Companies That the Software Freedom Conservancy (SFC) Will Censor the Community for, Using Their Very Large CoC⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 In the past we also caught them censoring for IBM/Red Hat (the censored people reported this to us!) and taking money from Microsoft. 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Software_Freedom_Conservancy_(SFC):_Companies_That_We_Censor the_Community_for_Using_Our_Very_Large_CoC⦈_ Having said that, the Software Freedom Conservancy (SFC) has been good at exploiting_poor_(and_sexually_abused)_women_from_eastern_Europe, using them as PR props for slavery-level "IT" wages (covered by Google's accountants; yes, the same Google that sponsors SFC). Perhaps not too shockingly, SFC associates are defaming key FSF people this week. █ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠿⠻⣿⠿⠿⢿⠻⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿ ⣿⣿⣷⣤⣄⣀⣀⣠⠀⢠⣀⣀⡀⠴⠴⠿⠬⡽⢯⠤⡤⠼⡼⡤⢧⠤⠬⢤⢤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣟⣀⣸⣿⣿⣧⣉⣘⣀⣀⣐⣠⣐⣇⣷⣠⣀⣸⣸⣀⣻⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⡿⠻⠻⠿⠿⡿⠿⠿⠻⠿⠿⡿⠿⠿⠻⠟⡟⠟⠛⢛⠛⠛⡟⠻⠿⠿⠿⠿⡿⢿⢿⡟⠿⠿⢿⠛⢛⡿⠿⠻⠿⡟⡟⠟⠛⠻⠿⠿⠿⠿⡛⢻⡟⠻⠿⠿⠿⢻⢛⠛⡛⠟⠛⢻⠿⡻⠿⠿⠿⠿⢻⠿⠿ ⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣿⣶⣶⣶⣷⣶⣿⣶⣷⣾⣶⣷⣷⣶⣶⣶⣷⣷⣿⣾⣾⣶⣶⣶⣾⣶⣷⣷⣶⣾⣶⣷⣷⣶⣾⣶⣾⣾⣷⣾⣶⣶⣶⣶⣾⣿⣶⣷⣿⣾⣷⣾⣾⣾⣷⣷⣶⣾⣾⣾⣷⣷⣶⣾⣶⣷⣶⣷ ⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠂⢄⠰⢀⢠⡄⠒⡖⠒⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⠛⠟⠛⢿⣟⣿⠛⠛⠻⡛⠛⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣇⡀⡟⠛⠛⠻⡿⠛⠛⠀⢸⠟⠛⠻⣿⠟⠛⠛⡿⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⠀⡇⢸⣿⠀⠀⠀⣉⡁⠄⠀⣉⡀⠄⠰⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣧⣼⣿⣤⣷⣤⣤⣤⣼⣦⣤⣤⣾⣤⣤⣤⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣄⠀⣴⣶⣦⠀⠀⣴⣿⣦⠀⣠⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⠀⣿⣿⣿⡄⢠⣿⣿⣿⠀⣿⡿⠻⢿⣷⣤⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣇⣿⡿⢿⣷⣾⣿⢿⣿⢀⣿⡇⠀⣀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⡀⠀⠈⣿⣿⣿⡇⠘⣿⣿⡇⢸⣿⣼⣿⣿⠿⠿⠛⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠻⣿⣦⣴⣿⠿⠿⠇⠀⠈⠉⠀⠸⠿⠿⠿⠇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⡛⠛⢻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⣛⡏⢉⡛⠙⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠻⠛⢿⠿⠛⢿⠛⠛⠻⠀⡇⢸⡆⢸⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⡇⢸⠀⡷⠀⠟⢀⣼⠀⡇⢸⡇⢸⠂⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣤⣧⣼⣶⣤⣾⣤⣤⣴⣤⣷⣤⣷⣤⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 276 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Fantastic_Journalism_by_Brian_Fagioli.shtml Gemini version at https://techrights.org/n/2024/12/05/Fantastic_Journalism_by_Brian_Fagioli.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Fantastic Journalism by Brian Fagioli⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024, updated Dec 05, 2024 A lot of today's Web, even "news" sites, is spam The latest from Brian Fagioli: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Redfin_Redesign_uses_AI_to_add_Christmas_decor_to_home images_(press_release)⦈_ Oh. Must be some good article! 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_latest_from_Brian_Fagioli:_Images_from_the_press release;_Copypasta_from_the_press_release;_'Redfin_Redesign_is_available_year- round_for_more_than_355,000_listings_in_the_U.S._and_to_homeowners_who_claim their_home_on_Redfin._The_holiday_style_is_accessible_via_Redfin’s_desktop website_and_iOS_app.'⦈_ The press release: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Deck_the_Halls_with_Redfin_Redesign⦈_ Press release: "Redfin Redesign is available year-round for more than 355,000 for-sale listings across the U.S. and to any of the millions of U.S. homeowners who have claimed their home on Redfin. The holiday design style is available to those using Redfin.com on desktop and the iOS app." Fagioli: "Redfin Redesign is available year-round for more than 355,000 for- sale listings across the U.S. and to any of the millions of U.S. homeowners who have claimed their home on Redfin. The holiday design style is available to those using Redfin.com on desktop and the iOS app." Fantastic reporting, Brian! Keep it up! Then, seeing what_happened_with_Swapnil Bhartiya, maybe the Linux_Foundation will reward you financially. █ Also see: BetaNews_Has_Become_a_SPAM/Slop_Factory,_Brian_Fagioli_Publishes_Fake 'Articles' | It's_Morbid_to_Talk_About_Living_People_as_If_They're_Dead | BetaNews,_Inc._Became_a_Spam_Operation/Web_Site,_LLM_Spew_(Slop)_for_SEO Disguised_as_"Articles" | BetaNews_is_Beta-Testing_the_Site_as_LLM_Slop_With Microsoft_Propaganda_Thrown_In | Even_the_Managing_Editor_of_BetaNews_is_Doing Slop_and_Spam | At_BetaNews,_"Most_Commented_Story"_Is_Not_a_Story_But_LLM Slop!_(Readers_Talking_to_Bots) | BetaNews_is_Run_and_Written_by_Bots_That_Make Clickbait | BetaNews,_Desperate_for_Clicks,_is_Pushing_Donald_Trump_Spam Created_by_LLMs_(Slop) ⣿⣿⣿⡷⠶⠶⠶⠶⠶⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶ ⣿⣿⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⡖⠒⢠⣒⡔⡗⣔⣲⣴⢲⣤⣖⣦⢶⡰⣆⠆⣖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠃⠊⠐⠐⠁⠂⠒⠒⠃⠘⠈⠓⠃⠘⠁⠋⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠃⠀⠑⠚⠁⠂⠀⠉⠁⠀⠈⠒⠐⠘⠛⠀⠀⠉⠂⠐⠃⠀⠐⠘⠀⠀⠀⠐⠁⠀⠀⠂⠈⠀⠀⠈⠈⠒⠂⠀⠀⠀⠂⠀⠂⠀⠀⠃⠈⠒⠁⠀⠀⠃⠓⠙⠃⠃⠀⠀⠀⠈⠀⠀⠀⠐⠑⠀⠐⠑⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠋⢰⣶⣶⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠛⠻⠟⠛⠀⢹⣿⣿⣿⣿⣿⢛⡻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠛⢛⠻⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⢠⡤⠅⠄⠶⠄⢸⣿⣿⣿⣿⡏⣿⢕⣧⡿⡞⡬⢸⣸⣧⣿⡇⣭⣽⢫⢅⡷⡷⡞⡏⣿⣸⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠘⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠿⠟⠠⣶⣙⣃⠰⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⢀⣉⣉⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣸⣯⣹⣇⣿⣏⣿⣇⣿⣍⣿⣯⣽⣿⠹⣿⣹⣿⣩⣿⣯⣽⣿⣱⣇⣿⣏⣿⣿⣹⣿⣹⣿⣲⣃⣿⣽⣿⣋⣿⣹⣿⣯⣿⣿⣸⣿⣟⣿⣏⣿⣸⣏⣿⣿⣹⣿⣹⣿⣽⣿⣯⣹⣿⠛⣿⣯⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣟⣭⡙⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣣⢖⠂⣹⣿⣿⣿⣻⣟⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣯⣹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣤⣤⣬⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⣤⣶⣦⣤⣦⣴⣴⣶⣤⣦⣦⣴⣤⣶⣦⣤⣴⣶⣦⣤⣶⣶⣦⣤⣤⣴⣶⣶⣶⣤⣦⣦⣤⣶⣦⣤⣤⣴⣶⣶⣴⣶⣤⣤⣤⣴⣶⣦⣤⣴⣦⣴⣴⣶⣦⣤⣶⣤⣶⣶⣦⣴⣤⣴⣴⣶⣤⣦⣴⣶⣶⣶⣶⣶ ⣿⣻⣯⣽⣻⣉⣍⣿⣯⣹⣹⣻⣫⣋⣽⣏⣻⣿⣯⣯⣿⣇⣏⣹⣿⣻⣟⣏⣉⣹⣯⣻⣿⣉⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⣟⣿⣿⣛⣛⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿ ⣿⡟⠛⠛⠛⠛⠛⠛⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣴⣤⣤⣀⣀⣐⣶⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠿⣿⡏⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣶⣾⡀⢐⢨⣍⡇⠀⠈⣘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣴⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢛⠛⢛⠛⠛⡟⠻⠛⠛⢻⠛⠛⢻⡛⢻⠛⠛⢛⣻⠛⢛⠛⠛⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢙⠹⡋⣭⠉⢙⡫⢉⠏⡏⡋⠉⡋⡟⠋⡉⠉⣛⢝⢋⠉⠝⣙⠝⣏⠯⢉⡫⣟⣛⠩⢛⢛⢙⢻⢙⢛⠙⠋⢻⠹⠛⡟⢛⡟⡏⠛⡟⠛⡛⢻⠛⠉⡟⠋⡋⡛⣟⢛⢻⢙⢛⢻⡙⠛⠉⣻⡙⠛⡛⠋⠛⢿⡋⢛⡛⣻ ⣿⣛⡛⣛⣻⣛⣛⣏⣛⣛⣛⣛⣛⣛⣻⣛⣙⣻⣛⣻⣟⣛⣛⣛⣛⣏⣙⣋⣹⣝⣏⣟⣛⣛⣛⣛⣻⣙⣛⣟⣛⣙⣋⢟⣋⣛⣻⣹⣟⣛⣟⣛⣛⣻⣙⣛⣛⣋⣛⡛⢛⣻⣛⣉⣏⣛⣙⣙⢻⣟⣛⣟⣿⣿⣿⣿⣿⣿ ⣿⣩⡉⣋⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣻⣟⠛⡟⠛⠛⠛⢟⠛⢛⠻⣻⠛⡟⠛⠻⠟⣟⡛⢟⢻⢛⠟⣻⠻⠛⣻⣿⣿⣿⣿⣿⣉⣍⣉⣇⣉⣹⣹⣉⣉⣉⣏⣹⣉⣉⣹⣹⣉⣉⣉⣉⣙⣯⣉⣏⣉⣽⣉⣈⣏⣍⣈⣍⣩⣉⣉⣫⣉⣏⣈⣹⣈⣉⣹⣿⣿ ⣿⠻⡻⠛⣿⠛⠛⠛⡛⢟⠛⠛⠻⠿⢛⢻⠛⢛⠿⢻⡛⠻⠛⡛⢻⢺⣿⣿⣿⣿⣿⣿⣿⣩⣁⣏⣉⣉⣩⣈⣏⣹⣹⣍⣍⣉⣇⣉⣉⣹⣉⣏⣈⣉⣨⣹⣈⣹⣉⣩⣩⣉⣉⣉⣹⣉⣏⣉⣉⣏⣉⣉⣉⣍⣻⣿⣿⣿ ⣿⠿⡿⠿⢻⠻⡞⡿⡿⠿⢿⠿⠿⡿⢿⠿⠿⠻⣿⢿⣿⡿⢿⠷⢾⠿⡿⢻⣿⣿⣿⣿⣿⣭⣭⣭⣯⣏⣭⣯⣿⣭⣽⣬⣭⣉⣯⣽⣭⣿⣌⣽⣭⣭⣭⣩⣍⣹⣬⣽⣭⣭⣽⣭⣽⣭⣍⣩⣭⣉⣽⣬⣿⣿⣿⣿⣿⣿ ⣿⠾⠿⣿⢿⣿⠿⡟⠷⢿⠿⠾⠿⡿⣿⢿⣿⡿⠿⡿⠻⠿⢿⢿⠾⡿⠿⢿⣻⣿⣿⣿⣿⣭⣿⣭⣧⣟⣩⣭⣯⣬⣽⣤⣬⣯⣭⣼⣍⣯⣭⣝⣬⣻⣬⣭⣬⣽⣬⣭⣭⣍⣹⣯⣭⣭⣽⣽⣭⣭⣯⣭⣭⣯⣿⣿⣿⣿ ⣿⣶⣶⣿⣶⣿⣾⣷⣿⣾⣾⣶⣶⣶⣿⣿⣷⣿⣷⣷⣾⣶⣾⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣴⣤⣤⣧⣥⣄⣯⣥⣤⣴⣥⣤⣥⣤⣧⣴⣼⣬⣍⣤⣬⣤⣦⣧⣦⣤⣧⣤⣦⣥⣧⣤⣶⣼⣤⣼⣤⣼⣮⣤⣤⣬⣬⣿⣿ ⣿⠉⢹⣯⣙⣻⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⢴⢦⢤⣧⡷⣶⣤⣼⣤⢧⣾⠤⣴⣤⣤⣤⣼⣴⢴⣦⣤⣽⡤⣤⣴⣤⣤⣼⣤⣦⣤⣧⣤⣦⣧⣶⢦⣤⡽⢤⣴⠼⣿⣿ ⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⢿⡿⡦⣤⣼⣥⣦⢧⣤⣦⣤⡽⣦⣤⣤⣾⣼⣤⣦⣴⣧⣤⣼⣴⣦⣤⣤⡤⣴⣾⢤⡶⣤⣦⣧⣴⣼⣴⣤⣤⣤⣿⡦⣤⣤⡾⣿ ⣿⢶⡶⠶⣶⠵⠶⣷⠶⢶⢿⢶⠾⠷⣶⢶⠷⠶⡧⢴⢶⠶⠴⠷⡷⠶⢶⡶⠼⢼⠶⠾⡷⠶⢾⢽⢶⠾⡾⡾⡶⣷⠷⡶⡾⣿⠶⠶⡶⡷⠶⢶⡶⣾⠿⢶⠶⢿⢶⠶⢽⠶⡶⠿⢾⢶⠶⢾⠷⢶⡶⠶⠷⡷⠿⡷⢶⣿ ⣿⠶⠶⠶⠾⠶⠶⠷⡾⠶⢾⠾⠶⠾⡶⠾⡾⠷⠷⠾⢶⠶⠶⠮⢷⠶⣶⠾⠶⠾⠶⠶⢿⣶⣶⣾⣾⣶⣶⣶⣶⣶⣷⣶⣧⣶⣶⣶⣶⣾⣶⣶⣷⣶⣤⣶⣶⣶⣼⣶⣶⣶⣷⣶⣾⣷⣴⣶⣼⣾⣶⣶⣷⣶⣾⣶⣾⣿ ⣿⣶⣶⣾⣶⣶⣾⣶⣷⣾⣾⣾⣶⣶⣷⣷⣷⣶⣶⣶⣾⣶⣶⣶⣾⣾⣷⣶⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡻⠿⠿⢿⠿⠟⠻⢿⠿⡿⠿⠿⠿⢿⠿⠿⡟⠿⠟⠻⡿⢿⠿⠿⢿⠿⢿⠿⠿⠿⢿⠟⠟⠿⡿⠿⠟⠿⠿⡿⡟⠻⡟⢿⠿⠛⠿⠿⡿⠿⢿⠿⠛⠿⠿⡿⢿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⢟⡿⠟⢿⣿⣿ ⣿⠓⠾⠷⢺⠺⠶⠶⢾⡖⢳⠶⠷⢶⡺⣞⠞⢛⣶⣒⡞⢷⠾⠶⠶⠾⡾⠾⠾⡶⡾⠾⠶⢷⡷⠿⠾⡶⠶⠷⣷⠷⡶⠷⠿⢻⠶⠶⠷⠷⡶⠾⠾⠶⠺⠷⢷⠿⡷⡶⠶⠞⡶⡞⡶⠾⠾⠞⠷⡖⡶⣾⠿⠷⠶⡞⣿⣿ ⣿⠿⠿⠿⠿⣿⣺⢿⢻⢿⠿⢿⡿⠿⢿⣟⣿⡟⣟⠿⡿⠿⠿⠿⣿⠿⣛⠿⢿⡿⠿⢿⣿⡿⢿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣝⢻⠛⠛⢛⠛⡛⠛⡛⠛⣟⠛⠛⠛⡟⠛⠛⠛⣟⢛⣛⠻⠛⠛⠻⠛⠛⠟⢛⣟⢛⣛⠻⢻⡛⢟⠛⡟⡟⠛⢛⠛⢻⠛⣻⡙⠛⠛⡻⡛⠛⢻⢛⢻⡋⠛⠛⠛⠛⠛⡟⠻⠛⢛⣿⠛⠛⣟⠛⢛⢻⠛⢻⣿⣿⣿⣿ ⣿⠋⡛⢛⠙⠛⢻⢻⣛⠛⣛⡟⢛⢛⡟⠛⢛⣻⢉⡛⡛⡏⠛⠛⢿⠛⢻⡛⠛⡟⠛⡛⠛⢙⢙⢻⡛⠛⠛⡟⡛⠛⢻⢛⠻⡟⠛⠛⡟⢻⠟⡛⡟⡛⡛⠋⡏⠛⠙⠙⢫⣏⡛⡛⡏⡛⣟⠛⠛⢿⠋⡟⢛⡛⠻⡟⡛⢹ ⣿⣛⣋⣋⡟⣛⣟⣟⢛⣻⣛⣙⣛⣛⣛⣛⣻⣛⣛⣛⣛⣛⢛⣛⣙⣛⣻⣛⣛⣛⣿⣝⣛⣛⣛⡛⢻⣫⣛⣋⣉⣛⣛⣻⣋⣛⡙⣻⣹⣙⣻⣛⣛⣻⣻⣉⣏⣛⣙⣛⣻⣛⣟⣋⣙⣛⣛⣛⣟⣛⣛⣛⣛⣙⣿⣿⣿⣿ ⣿⣟⣛⡛⣟⣻⣛⣹⣛⣻⣻⣛⣟⣏⣟⣛⣛⡙⣟⣛⡻⣛⡛⣛⣟⣟⢛⣻⣛⣿⣻⣟⣛⣋⣟⣛⣛⣋⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣹⣉⣙⣍⣹⣉⣉⣍⣍⣍⣏⣉⣟⣙⣩⣉⣉⣹⣍⣉⣉⣏⣹⣯⣉⣉⣙⣟⣉⣻⣉⣉⣋⣉⣉⣩⣉⣉⣉⣹⣩⣏⣉⣉⣉⣹⣉⣉⣉⣻⣉⣉⣏⣍⣩⣩⣉⣉⣉⣉⣩⣉⣉⣉⣝⣏⣉⣉⣉⣹⣉⣹⣉⣉⣉⣿⣿ ⣿⣉⣉⣉⣏⣩⣹⣉⣩⣹⣉⣏⣉⣻⣉⣉⣏⣉⣉⣉⣍⣏⣍⣋⣏⣉⣩⣉⣏⣉⣍⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣬⣯⣭⣧⣼⣭⣿⣏⣭⣤⣏⣹⣽⣽⣭⣯⣽⣭⣭⣯⣯⣤⣿⣩⣽⣽⣭⣭⣧⣭⣿⣯⣤⣍⣯⣹⣥⣿⣤⣭⣤⣿⣤⣭⣬⣥⣫⣧⣽⣽⣣⣾⣽⣯⣭⣬⣭⣿⣍⣧⣟⣧⣿⣥⣿⣽⣼⣽⣭⣯⣥⣭⣼⣿⣿⣿⣿ ⣿⣬⣬⣬⣼⣤⣤⣤⣸⣼⣤⣤⣥⣽⣦⣬⣧⣤⣤⣭⣭⣤⣭⣤⣽⣤⣍⣬⣬⣮⣬⣼⣥⣭⣷⣬⣤⣬⣷⣬⣤⣭⣩⣾⣤⣼⣴⣭⣬⣧⣤⣌⣧⣼⣬⣥⣯⣤⣼⣬⣴⣦⣽⣤⣤⣤⣤⣴⣸⣿⣤⣦⣥⣬⣴⣼⣿⣿ ⣿⣦⣤⣤⣧⣤⣤⣭⣤⣶⣬⣴⣤⣧⣴⣬⣦⣥⣤⣵⣤⣤⣣⣤⣶⣤⣤⣧⣤⣴⣼⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠿⣿⠿⣿⠿⣿⢿⡿⣿⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⡿⠿⢿⠿⡿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿ ⣿⣤⣤⣤⣾⣤⣤⣤⣤⣤⣧⣼⣴⣦⣤⣴⣶⣴⣤⣴⣦⣤⣦⣧⣥⣷⣬⠤⣧⠦⣴⡧⢴⣬⣵⡮⣷⣶⡴⣴⣼⣤⣤⣤⣼⣴⣶⣤⡼⣼⣴⣯⣥⣿⣤⣤⣧⣼⣴⣴⠶⣧⠷⣦⣦⣶⣤⣦⣷⣶⣭⢼⣿⣿⣿⢿⣿⣿ ⣿⢶⣶⠶⡶⣶⣶⣶⣷⣶⣶⣷⣶⣶⣷⣶⣶⣶⣿⣷⣶⣾⣶⣶⣶⣷⣾⣶⣶⣶⣾⣷⣶⣾⣷⣶⣶⣴⣶⣶⣦⣶⣷⣷⣶⣷⣷⣶⣶⣶⣶⣾⣶⣷⣶⣶⣶⣶⣶⣽⣶⣶⣾⣾⣶⣶⣶⣶⣷⣶⣶⣶⣴⣷⣶⣾⣿⣿ ⣿⣶⣾⣾⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 471 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Gemini_Protocol_Keeps_Getting_Better_Less_and_Less_Reliance_on_.shtml Gemini version at https://techrights.org/n/2024/12/05/Gemini_Protocol_Keeps_Getting_Better_Less_and_Less_Reliance_on_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Protocol Keeps Getting Better (Less and Less Reliance on Centralised Certificate Authorities)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Path_covered_with_new_fallen_snow⦈_ Reliable systems do_not depend on third parties, only themselves Gemini Protocol is still autonomous and controlled by the community, not some company like Automattic (a_subject_of_recent_controversies). It is also about to_turn_5.5_years_old (our sister site will turn 20.5 in 5 days). Our current site's system (after dumping_PHP,_WordPress_etc.) is optimised for Gemini Protocol. This system keeps improving behind the scenes, with refinements to GemText conversions made as recently as last week. This system is AGPLv3-licensed and it is accessible over Gemini Protocol, linked to our self-hosted Git instances (one for each site). We've only just noticed, based on Lupa, that after about a fortnight the Linux Foundation's Certificate Authority Let's Encrypt lost some more instances and is now down to just 14 capsules that are tracked by Lupa (it tracks_about_4,200 capsules). To quote today's_statistics: "2646 (91.2 %) capsules are self- signed, 14 (0.5 %) use the Certificate Authority Let's Encrypt, 242 (8.3 %) are signed by another CA (may be not a trusted one)." (To be clear, Certificate Authorities can be self-hosted too) For well over a week it said 15. It's generally going down and down... towards zero. That's a reason to adopt and to like Gemini Protocol. It discards_fake 'security'_which_generally_puts_capsules_under_the_control_of_monopolies (they can deny access to capsules by denying/revoking certificates and they are also a MitM in the privacy sense). As Dr. Andy Farnell put_it_yesterday: "They did an end run around government and decided to go straight for control and bypass the whole trust, value and money making stages. [...] Human beings have lost control of the direction of information technology. Andy also said: "The things I "own" in digital space (domains, websites, accounts, currencies, devices) feel less safe. Digital life is at the mercy of arbitrary diktats, administrative errors, system failures, predatory freeloaders and the exercise of unchecked power to exclude, and censor. I have less confidence in the benevolence and competence of authority. And I know I am far from being alone when I say these things. Instead of clear social progress a number of unfortunate side effects of digital tech have blighted society. Their net effect is that we're moving backwards." There are several more allusions there to fake 'security' and systems like the centralised Certificate Authorities (CAs), which aren't about security but about someone else - the "powerful few" - exercising control over who can run a site (or capsule) and who can access it. Never underestimate the gatekeeping and the fences they have built. It is a "boiling frog" scenario and only a matter of time before they flick switches. Many fine Web sites go dark or offline these days, some of them not because of their choosing; it's not a choice, it is an order. Be prepared, build information systems shrewdly, based on cautious foresight. █ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠉⠛⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⡟⡽⠻⢿⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠯⠉⡝⢻⣿⡇⠁⠘⠀⠀⠈⠉⢻⣿⣿⣿⡉⠉⢉⣛⣻⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠂⠀⠀⠋⠠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⡿⠟⢛⠻⠋⠦⢠⠐⠆⢿⣇⢠⣄⠄⠀⠀⠸⠸⠋⠁⠠⠤⠘⠀⢹⣾⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⢛⠃⠀⠀⠀⠀⠀⠩⢹⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⣿⠛⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⢰⣤⣜⠿⡸⣿⠀⠀⠀⠠⡕⡄⠀⢐⡀⠂⠀⢈⣅⠰⣦⡦⣭⡧⠀⠀⠀⠀⠀⠀⢤⠀⠈⠂⠀⠀⠀⠀⡫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠙⠃⠀⠁⠀⠀⠁⣆⡀⠀⠀⠀⠐⠈⠋⣾⡧⢙⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢠⡏⠉⢀⡉⠘⣫⢠⠄⠀⠀⠀⠠⡄⠀⠀⠸⠢⣀⠒⠖⠂⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⡄⣤⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⢤⠏⣛⠀⠰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⢠⣾⡁⠀⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⢿⡿⠛⠛⠿⣿⣿ ⠟⠥⠐⠒⠆⠀⠶⣔⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠐⠀⢀⢂⣀⣀⠹⠋⠤⠈⠈⠀⠟⠛⠟⠟⠉⣹⣿⣿⣿⣿⣿⠃⠀⠀⠟⠛⠃⠀⠀⠀⠀⠀⠀⠈⢿ ⠀⠈⠀⠞⠒⠀⠢⠀⣃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠈⠀⠀⠔⠨⠟⠁⡈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠄⠤⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠄⠀⠀⠈ ⠀⠠⢀⠀⡁⠀⠀⠀⠀⠈⢣⠃⠀⢀⠀⠀⠀⠀⠀⠂⠈⠀⠂⡀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠁⣘⢃⠈⠑⠀⠀⠀⠀⢀⠅⠀⠀⣀⠀⡀⠀⣴⠀⠀⠀⠀⠀⠀⢀⠀⠸⡂⠀⠀⡈⠀⠀⠘⠂⠀ ⠀⠀⠀⡁⠐⠀⠀⡀⠀⠀⠀⠀⠀⠈⢖⠀⠀⠀⠀⢀⢠⠀⠀⠡⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⠃⠀⠆⠀⡀⠀⠀⠀⠀⠀⠰⠀⢠⡀⠤⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⠐⠅⠀⠀ ⠀⠀⢀⡀⠠⠄⠈⠃⠀⠘⢻⠀⠀⠢⠘⠁⠀⠁⠀⡀⠀⠀⠀⠀⠑⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢸⠀⣰⠇⣞⠀⠙⠠⠀⠃⠀⠀⠀⠠⠀⠄⠀⠀⠿⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⠀⠀⠀⠀ ⠃⢠⡀⠈⠘⠀⢀⠀⠀⣀⠈⣀⠀⡀⢄⡄⠐⡀⠀⠁⣄⡌⠀⠀⠈⠀⠀⡘⢒⠖⠁⠀⠀⠀⠀⠀⡅⠀⠀⠀⠃⢰⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠥⠀⠀⠤⠖⢻⠀⠀⠀⠀⠀⠀⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠸⠀⠈⠍⠁⠀⡤⢳⠄⠈⢸⣚⣳⡄⢤⡄⠀⠀⡈⡿⠁⠀⢄⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠐⠀⠇⢰⡆⠀⠀⡟⠀⠀⠀⠀⢿⠀⠂⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⡄⠤⠀⠀⠈⢺⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⡀⠀⠀⠀⠀⠙⣟⡊⠔⠀⠀⠀⢓⠀⠐⣿⠃⠀⡀⠀⠀⠀⠀⠀⠘⣄⡄⠀⠀⠀⠀⠀⠀⣺⣇⠀⢸⣃⣀⣒⣂⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣤⣶⣤⣠⣄⣀⣀⣤⣀⣤⣤⣀⣠⣤⣀⣤⣤⣤⣤⣤ ⣀⣤⣤⢤⡀⢀⠀⠐⠀⠀⠈⠁⠑⠂⠈⠸⡆⠀⠀⢙⠀⠬⣟⣻⣿⣶⣿⠿⠸⣿⣿⣼⣿⣷⣤⣶⣤⣀⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉ ⣻⣿⢿⢸⣿⣿⡦⢠⡀⠀⢀⣶⣒⣀⣸⢰⡆⢀⢌⣡⣈⣀⣩⠵⠶⣿⢿⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣽⣿⣭⣭⣭⣭⣭⣭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠰⢀⡠⣠ ⠋⠧⠈⢈⣿⣟⣳⣿⣿⣧⣴⣿⣿⣿⣾⣾⣷⣧⣬⣽⣿⣿⣿⣿⣽⠏⢿⡛⠉⣫⢄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠑⢚ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠩⢽⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⣠⣀⣀⠀⠀⣠⣤⣆⠉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣭⡭⠥⠤⠤⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠠⠤⠄⠤⠤⠤⠨⠉⠉⠉⠭⠭⠭⠿⡿⠟⣛⠛⠛⠛⠟⠛⠻⠛⠛⠉⠉⠉⠉⢁⣿⣿⡭⠀⠀⠀⠐⠐⠆⣀⡀⡀⠀⠀⢀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠶⠶⠿⠾⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡻⠀⠀⠀⠀⠀⠂⠀⠘⠳⠡⠞⠿⠟⠿⠋ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡄⠀⠴⠆⠀⠀⢀⣴⣶⣧⣄⣀⣀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡷⢹⣿⣿⡛⠯⠉⠁⣹⣤⣤⣤⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 576 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Increasing_Productivity_With_Less_Hardware_Little_Power_and_Few.shtml Gemini version at https://techrights.org/n/2024/12/05/Increasing_Productivity_With_Less_Hardware_Little_Power_and_Few.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Increasing Productivity With Less Hardware, Little Power, and Fewer CPU Cycles (and Far Less Digital Waste in General)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Winter_Seasons⦈_ THE last time I rebooted my laptop this Web site was still_running_WordPress and it was a warm day in 2023. My wife's main laptop and my secondary laptop (I use 4 in tandem these days) also have an uptime of about a year and they rarely waste time by demanding that we restore sessions, reopen applications, reload data files, reconnect to SSH etc. They're just there and they "snooze" when we're AFK in order to lessen energy consumption. A lot of the software we use is coded by us, for us. A lot of people who glance at our PCs (as they visit us) act a bit baffled, as much of what we're using is a bunch of terminals and some text editors. Many people mistake the size (weight) of a program for "power" (associating bloat with productivity) because they're indoctrinated to think that new and "powerful" computers will enhance productivity, e.g. if their keyboard has an extra key for "hey hi" (AI); they also wrongly conflate the waste of power, e.g. chatbots in use, with "gains" (output that's produced by a bot is typically worse than useless and 'dilutes' the actual signal of human work). I've actually seen people buying new PCs because apparently seeing HD videos (on a small screen) demands "better" hardware, even if the naked eye can barely appreciate the difference and the "sound system" is just a single speaker lodged inside some plastic laptop. Let's get rid of this harmful notion that more bloated software is good for anything other than revenue/sales of companies like Intel. Don't worry about Intel; your_government_is_likely_subsiding_it_already (at your own expense), whether by creating some facilities in your country (e.g. Germany) or just handing_over_your_money (debt) without your consent. This whole situation isn't pretty. Trump and Biden did the same with Microsoft [1, 2], repeatedly in fact, and this week it looks like so-called 'defence' contracts are misused to bail out the_struggling_"open"AI (we put links about it in Daily Links earlier today). █ ⣿⣿⣿⡀⠈⣴⣿⣿⣿⣿⣞⡃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣤⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣦⣄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⣤⣤⣤⣤⡄⠀⢀⣤ ⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣷⡄⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⢸⣿⣿⣿⣿⡇⠀⣼⣿ ⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⠃⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⣿⣿⣿⣿⠇⠐⢿⣿ ⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣽⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠟⠃⠈⢿⣿⣿⣿⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠿⣿⠂⠀⠿⠿⢻⣿⠀⠀⠀⠿ ⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠰⡿⠛⢿⣿⡆⠀⢀⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣶⣤⣶⣶⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣶⡆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⠄⠀⠀⠀⢀⣈⣄⣈⣙⣽⣯⣽⣿⣯⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⢿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠐⣰⣆⠀⠀⠀⢈⣿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠠⣤⣬⡟⢧⣤⡇⠀⠀⠘⣿⣿⣆⠀⠀⢨⣿⣷⣶⣤⣄⣉⡛⣧⣤⣷⣿⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣤⡤⠄⠀⢀⠚⠛⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠁⠐⣽⣇⠀⠀⠀⢸⣿⣿⣷⡄⠀⢘⣿⣿⣛⣛⣟⣾⣮⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣁⣀⣴⠿⠟⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⠀⢀⣾⣿⣦⣀⡀⣸⣿⡽⢦⡉⠳⣤⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣧⡀⠙⠛⠛⠁⠀⠀⢀⡬⢤⡄⢀⣤⠄⠒⠒⠶⣶⣤⣴⣿⣿⣷⠶⡾⢻⡿⠟⡟⠷⠃⠻⢳⡾⣿⣶⣾⠏⠁⠀⠋⠉⣿⣿⣿⣿⣿⣿⡏⠻⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡠⠀⠰⡤⠂⠁⠀⠀⡀⠐⡀⠠⡀⠁⠃⠉⠉⠉⠁⠀⢒⠁⠘⡇⠀⢀⡄⡈⠀⠊⢂⣿⣿⡏⠂⠰⡀⠀⠀⠈⢽⣿⣿⣿⣿⣿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣄⣤⣤⠠⠀⣀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⡤⠀⠀⡡⠀⠈⠪⠙⠄⣡⣶⣿⣿⣃⡀⠘⠁⢈⠰⠖⠏⢱⡟⡿⡿⣿⣇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣯⣏⣼⣾⡄⠺⡣⣏⠒⣀⡀⠀⣠⡄⣶⣾⣷⣷⡂⣄⣀⣠⣿⣿⣿⠿⣿⣿⣷⢀⠀⠀⠀⡀⠀⠀⠁⢁⠁⠏⣼⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠉⠉⢘⣿⡿⠀⣠⡤⡀⠠⢜⡏⣿⣿⡦⣇⡹⡀⣰⡘⡘⠻⠙⠙⢻⠎⣼⣿⣿⣿⢷⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢋⡏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣌⠀⠀⠀⢈⠐⢩⠟⠇⠁⠀⠸⠀⠘⢻⣤⣽⣿⣶⣥⠈⠳⡀⠈⠐⠘⠣⣿⠻⡈⠘⠀⠈⠟⠼⠗⠓⢆⢀⠁⠀⠀⢸⡏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⠙⠈⠈⣀⡄⠈⠀⠀⡀⠀⣸⣿⣿⡟⣽⣿⡇⢸⠄⠀⠀⠀⡀⡟⠀⠁⠀⢀⠀⠀⠈⠁⠐⣿⣿⣷⣤⣄⣺⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠋⡄⠁⠸⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠁⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠟⣫⣾⣿⣿⣷⣾⣤⡄⢰⣶⣀⣡⣀⡀⠐⠘⠃⠀⠀⠀⠀⠉⠉⣼⡟⠛⢻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠋⠄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣧⣤⣤⣤⡄⠠⠀⠀⠐⠀⢠⢆⣰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⣄⡀⠀⠄⠀⠀⠀⠀⠁⠈⢠⢀⠾⢹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⢿⢿⠏⢸⡏⣧⢀⠀⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⡟⢓⠂⠀⠀⡀⠃⢣⡿⡩⢿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⠂⠀⠀⢠⡀⠁⠀⠁⠚⡘⣰⢟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢔⠺⠈⣪⡻⠛⠁⣀⠀⠀⠁⠘⣿⢿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡀⠀⠀⠀⠀⠘⢀⠠⡿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⠌⡈⠀⠀⠎⠘⠁⣀⠀⠀⠒⠁⣠⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣤⣿⣧⣀⡄⠉⠅⣰⣰⠈⠋⠝⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⢲⠀⠀⠀⠀⠈⠀⠁⠘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡆⠀⣠⡀⠀⠀⠀⠈⢿⠈⠃⢠⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣷⣿⣧⡀⢠⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣷⣶⣿⣇⣠⡀⠀⣀⠀⠀⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣧⣥⣤⣷⣶⣿⣧⣲⣴⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 659 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/IRC_Proceedings_Wednesday_December_04_2024.shtml Gemini version at https://techrights.org/n/2024/12/05/IRC_Proceedings_Wednesday_December_04_2024.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Wednesday, December 04, 2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Snow_and_Flowers⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GN 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNOME_Gedit⦈_ #techrights_log #boycottnovell_log 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GN 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNOME_Gedit⦈_ #boycottnovell-social_log #techbytes_log =============================================================================== The corresponding text-only bulletins for_Tux_Machines and for_Techrights contain all the text. Enter_the_IRC_channels_now ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢸⡟⠉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣾⡟⠉⠉⠙⢻⣿⣿⣿⣿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣀⣤⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿⣆⡀⠀⠀⠀⠀⣿⣿⣯⡻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠏⠀⠀⠀⢹⣿⣿⣿⣿⠃⠀⠀⠀⠠⢿⣿⣿⣿⣿⣶⣤⣀⣴⠙⣿⣿⣿⣮⡿⡟⠀⠀⠀⠠⠘⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠘⣿⣿⢀⣿⣟⢿⣿⣿⠀⠀⢀⣀⣀⡀⠀⣴⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⣿⣿⢸⣿⣿⡌⢿⣿⣀⣄⡀⠛⣿⣿⣶⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⣸⠿⠋⠹⠻⠂⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠠⣿⣿⣾⣿⣿⣿⡀⢻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢻⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 885 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Meme_Shooting_the_Messenger.shtml Gemini version at https://techrights.org/n/2024/12/05/Meme_Shooting_the_Messenger.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Shooting the Messenger⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024, updated Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Leonardo_DiCaprio:_Cancel_culture;_you_needn't_refute_the message,_just_take_out_the_messengers⦈_ UEFI is obviously not about security but the opposite of that, so focus on "taking out" the people who merely mention this? By stalking, harassing and defaming them for 12+ years? ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣶⡶⣦⡀⣰⣶⣶⠀⣶⡆⣶⡆⣴⡶⣶⣄⢰⣶⣶⢰⣶⠀⠀⠀⣴⡶⣶⡄⣶⣶⣶⣶⢰⣶⢰⣶⣶⣶⢰⣶⢰⣶⢰⣶⢶⣦⠐⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⢠⣦⠀⠀⠀⠀⠀⢸⣷⠀⢸⣿⡇⠿⠇⣿⡿⣿⠀⣿⣿⣿⡇⣿⡇⠻⠿⢸⣿⣤⢸⣿⠀⠀⠀⣿⡇⠿⠇⣿⣿⣿⣿⢸⣿⠀⢸⣿⠀⢸⣿⢸⣿⢸⣿⣼⣿⣶⣿⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢸⣿⣇⣿⣇⣿⡷⣿⡇⣿⢹⣿⡇⣿⣇⣿⡿⢸⣿⣈⢸⣿⣀⠀⠀⣿⣇⣿⡇⣿⣿⣿⣿⢸⣿⣀⢸⣿⠀⢸⣿⣸⣿⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠛⠉⠈⠉⠁⠉⡁⠉⠀⠉⠁⠈⠙⠋⠁⠈⠉⠉⠈⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⢸⡉⠋⠈⠉⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⢾⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⠿⠟⠋⠉⠉⠁⠀⠈⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿ ⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⢸⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿ ⠐⢤⠀⠀⠀⠀⠀⠀⠐⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⢸⠀⢽⣿⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⠀⣽⢻⠚⢚⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢀⡀⠀⠀⢸⡸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⡆⢀⡘⡆⠀⢸⠇⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⡇⢰⣿⡄⠀⠀⠀⣠⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢼⣿⣿⣷⣶⣾⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣭⠁⠸⠶⠾⣸⣿⣿⣿⣿⣿⡿⠿⣿⣿⣇⠀⠀⠀⠀⠀⣀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⣦⣤⣀⢀⣶⣿⡿⣻⣿⣿⣿⣿⡀⠀⢸⢾⣿⣿⣿⣿⣿⡇⠐⠆⠈⢹⡇⠀⠐⠆⢀⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣸⡛⣿⣿⣿⣿⡻⠀⠀⢸⡿⠉⠉⠉⠉⠉⢀⠀⠀⠀⢺⣇⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣿⣷⢶⣶⣦⣄⢀⢀⣀⣀⣀⣄⣀⣀⣠⣿⣿⣿⠿⠿⢿⣿⣿⡟⣿⣿⣿⣿⣧⡀⢐⠈⣷⡄⣤⡼⠃⠀⢀⠀⡀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢻⡎⢻⢿⣿⣷⣸⣽⣿⣿⣿⣟⠿⢹⠃⢀⠀⠀⠀⠀⠉⢿⣃⣿⣿⣿⣿⠾⣽⢼⣇⣭⣕⢿⣶⡄⠂⠊⢀⠁⠀⢸⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⢲⣺⡉⢛⣴⣿⣿⣿⠿⣿⣿⠿⠓⠦⠈⠀⢺⣄⠀⠀⠀⠀⠞⠚⢿⣿⣿⣿⠹⠏⠿⠗⣀⣬⣿⣯⣥⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠉⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣼⣿⣾⡛⣿⣿⣿⡇⠋⠉⠠⠐⠃⢤⣔⠀⠀⠀⠛⠁⠀⠀⣀⡠⠬⠩⠃⠀⠀⠈⠨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⠽⠙⠋⠀⠀⠀⠀⢰⣶⡫⡋⢳⢀⣄⣠⣤⠦⠶⠴⠟⠛⠂⠀⠀⠀⠀⢀⠄⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣶⠞⠁⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡇⣠⣷⣾⣶⣶⣿⣾⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣾⣯⣄⣙⣿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠟⠀⠀⣼⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣛⣛⣶⣯⣽⣤⣶⢶⣒⣲⣀⣀⣀⣀⣠⢴⣚⣿⣃⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⢹⣿⢸⣿⣿⣿⣿⢻⣿⣼⣿⢸⣿⢛⢸⣿⠻⢼⣿⣿⣷⢹⣿⣸⡇⣿⡛⣿⡟⣳⡇⣿⣏⣿⡆⣿⣟⢻⣿⡟⢻⣿⢸⣿⠙⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠛⣿⣷⣸⣿⢸⣿⢸⣿⢹⣿⢽⢸⣿⣿⣿⢸⣿⠛⢸⣿⢻⣼⣿⣿⣿⢸⡿⣿⡷⣿⡇⣿⡇⣿⠇⣿⡟⣿⡎⣿⡟⢻⣿⣟⣼⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿ ⣀⣠⡤⣤⣤⣤⣴⣶⣶⣶⣿⣾⣿⣿⣿⣿⣾⣋⣞⠻⠿⠋⢻⣼⣿⣹⣿⣸⣿⣿⣸⣿⣿⣼⣿⣿⣯⣾⣇⣿⣧⣿⣷⡿⢣⡿⠁⠛⠃⠛⠃⠛⠛⣿⣿⣿⣿⠿⠾⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣭⣿⣿⣯⣭⢠⣤⣤⠀⠫⣭⣽⢻⣭⡟⣯⣭⡟⣿⣿⣿⢿⣿⣽⣿⢿⣭⣽⠿⣻⣤⣅⠂⣤⣤⡄⢀⣀⢠⣽⢿⣿⢡⣤⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⢛⣽⣿⣿⡟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣇⣿⡇⢹⣿⣽⣿⢸⣿⣤⠀⠀⣿⣿⣼⣿⡇⣿⣧⡄⣿⣿⡛⠸⣿⣜⡛⢸⡿⣿⡀⣿⣇⣛⣃⣿⣧⡉⢉⣼⢿⣿⢸⣿⢸⣿⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⢿⣿⣿⣿ ⣿⣿⣿⣿⣷⠎⠀⠀⠀⠀⣿⣇⠁⣿⡇⢸⣿⣽⣿⢸⣿⣉⡀⠀⣿⢸⡿⣿⡇⣿⣏⡁⣶⣙⣿⢰⣾⢹⣷⣾⡷⣿⡇⣿⣏⣿⣿⣿⣏⣀⡀⠈⣸⣿⢸⣿⣸⣿⢹⣾⣻⣿⣿⣿⡏⣿⣻⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿ ⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⡿⢿⡦⠉⡥⣾⣭⣿⣽⠾⠩⠉⠁⠀⠉⠈⠁⠉⠁⠉⠉⠁⠉⠉⠉⠀⠉⠉⠁⠉⠁⠉⠙⠛⠛⠻⠿⠏⠉⠩⠃⠀⠻⢭⣿⣿⣿⣿⣿⣿⣿⣽⣯⠉⠁⣾⣿⣿⣿⠟⢵⣿⣿⣿⡏⣿⣿⣿ ⣯⠷⣶⡶⢦⣶⣶⠀⣶⣆⣶⠎⣷⡶⠞⡿⣷⡶⣶⡄⣶⡇⣶⡶⢶⣶⢶⡀⠶⣶⡶⢶⣶⢰⣶⢰⣶⠶⠀⠀⣶⣶⢰⣶⡆⣶⡶⠆⣶⢶⣦⢠⣶⢾⣿⣿⣿⠿⣷⣮⣶⡆⣴⡶⣶⡌⣷⡶⠆⣶⡶⣾⣭⣶⢶⣦⠙⣿ ⡏⡀⣿⡇⢸⡿⣿⡆⣿⣿⣿⠀⣿⡷⠆⠁⣿⡇⣿⡇⣿⡇⣿⣷⣸⣿⢸⣿⡄⣿⡇⢸⣿⢾⣿⢸⣿⠶⠀⠀⣿⢿⣾⣿⡇⣿⡷⠆⠻⣷⣿⣾⢿⣾⣿⣿⣿⠶⣿⣿⣿⡇⣿⡇⣭⡅⣿⡷⠆⣿⡷⣿⡉⠿⣿⣍⠀⡛ ⣷⠇⣿⡇⣾⡟⣿⣇⣿⡏⣿⡆⣿⣷⡧⠀⢿⣧⣿⣇⣿⣧⣿⣿⣸⣿⣼⣿⣇⣿⡇⢸⣿⢸⣿⢸⣿⣤⠀⠀⣿⢸⡟⣿⡇⣿⣧⡄⣿⣼⣿⣹⣿⣼⣿⣿⣿⣤⣿⡏⣿⡇⢿⣧⣿⡇⣿⣧⡆⣿⡇⣿⡟⣿⣼⣿⠀⠁ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠶⠶⢤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡖⢀⣤⣾⣷⣶⣦⣶⣶⣾⣿⡶⠀⢀⣴⣶⠄⢠⢀⢳ ䷩ 𝚕𝚒𝚗𝚎 950 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Meme_They_Dropped_the_L_Libre_and_Law.shtml Gemini version at https://techrights.org/n/2024/12/05/Meme_They_Dropped_the_L_Libre_and_Law.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] They Dropped the L (Libre and Law)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 "SFLC, could I borrow 75% of your letters?" 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇SFLC,_could_I_borrow_75%_of_your_letters?⦈_ Context: SFC_(a_Splinter_Group,_Not_a_Conservancy)_Uses_'Man_and_Baby'_to_Find or_At_Least_Look_for_Sympathy_Amid_War_on_SFLC_and_Its_Chief,_Professor_Eben Moglen ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣠⣄⣀⣤⣄⣀⣄⡀⠀⠠⠁⠈⠃⠁⠈⢁⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⣇⡀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡘⣿⢻⣿⡟⣿⢿⢿⡟⣿⣿⣿⢛⣿⢳⣷⣦⣄⠀⢀⠀⠀⠀⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣛⣛⡳⣷⡾⠋⢷⣷⡝⠹⣶⣧⣻⣿⣿⣿⣽⣿⠟⢿⢯⣤⣤⣤⣤⣤⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⢿⣿⣿⣿⡿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣷⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣇⣿⡷⣿⣾⣿⣷⣿⣿⣿⡧⣿⣿⣇⣿⣿⣄⣾⣸⣿⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣿⣿⣿⣿⣧⣼⣿⣿⣿⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣻⣿⣽⣿⣿⡧⣯⣷⠿⣽⡿⣭⣻⣿⣿⣿⣿⣿⢳⡿⣿⣿⢱⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⡿⣿⣿⣿⢿⣿⢹⡟⡟⣿⢿⣻⢙⣯⣿⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣷⣿⣿⣿⣿⣿⣷⢻⣿⣿⡿⠭⠩⠍⠉⠛⢿⣿⣿⣿⣦⡿⠟⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⡷⣿⢷⣿⣾⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡹⣲⣸⣛⢿⣿⢿⢿⢟⡻⣿⣾⣟⣇⣿⢿⢤⠧⢟⣛⡿⢏⣫⡩⠝⢛ ⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣹⣫⣿⣧⣻⣯⣻⣼⣽⣷⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡻⣶⢯⢗⣙⠌⠭⣾⣸⣿⣾⡛⣛⠿⣏⢵⣿⡻⠀⡡⠤⠒⠂⠀⠠⠤⠶ ⣿⣿⣿⡿⠿⢿⠿⠿⠿⠿⠟⠛⠛⠿⠿⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡯⢁⡾⣿⣶⡿⠻⢮⡁⠅⢸⡯⠿⣃⣝⠮⠭⠖⣵⡵⣿⡿⢿⡿⠿⠌⠛⠑⠀⠀ ⣿⣿⣿⡝⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⣀⣠⡀⠀⠀⠀⠀⠀⠀⠰⣦⣶⡦⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⣙⣚⣣⣤⣚⠃⠀⠁⠈⠑⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣛⣓⠿⣿⡿⣿⣿⣷⣶⣶⣤⣄⣠⣤⠠⠃⠀⢸⢛⡉⠷⠶⣶⣾⣿⣿⣿⣿⣿⣷⣷⣦⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢛⠉⢩⣿⣿⣴⣿⣿⣿⣿⠟⠀⠀⠀⡀⣰⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿ ⣿⣽⣿⣾⡟⢶⣦⡄⣈⠉⠉⠉⠛⠛⡀⢼⢓⣶⣵⣶⡦⠀⠾⠻⢿⡿⣛⣟⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠍⠉⠉⠉⠁⠀⠀⠀⠈⠹⢿⡍⠉⠉⠉⠉⠉⠙⠛⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣦⡈⠙⢳⡿⢷⣵⣶⠖⢹⠀⡌⠩⣛⠍⠀⠀⠀⠀⠀⢀⣿⣽⣡⡽⢯⣭⣹⣿⣿⣿⣦⣩⣿⣿⣷⣄⠀⠈⠿⠿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣷⣶⣶⣤⣀⣀⡀⠀⠉⠻ ⣿⣿⣿⣿⣿⣿⣷⠓⡀⡖⠽⠶⠚⣫⠙⠀⣩⠠⢖⠀⣆⣿⣿⣿⢿⡇⣿⣿⡇⡹⡏⢸⣇⣿⡿⣇⣿⢿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣠⣤⣤⣴⣶⣶⣶⣿⠂⠀⠀⠀⠀⠀⣰⣿⣦⢠⣦⡀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄⠀ ⣿⣿⣿⣿⣿⣟⠁⠁⠈⠉⠀⠑⡻⢋⣴⣶⣬⡀⠀⠀⣿⠈⠻⢯⣿⡗⣯⣿⣞⣷⣝⣛⣿⣿⢿⢷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣵⡖⠀⠀⠀⠠⠀⢰⣿⣿⣿⣾⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⢿⢿⣿⣿⠏⠀⠀⠃⠀⠀⠙⣿⣻⣿⣿⣶⣶⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣾⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⡟⢻⣽⡿⡇⣷⡀⠀⣙⣿⣿⣿⣿⣿⣿⣤ ⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣃⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⢀⡀⢀⣘⣽⣟⢫⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⡿⠛⠋⠠⠀⠀⠀⠀⠀⠄⢸⣿⠁⢠⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⣤⣤⠀⠂⠀⣠⣄⣀⣀⣀⡀⢧⣟⢸⣿⣿⡿⢿⡏⢿⣭⢿⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⡛⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠋⠾⣿⣟⣟⢿⣿⣽⣿⢿⣿⣿⡿⣾⣿⣿⢿⡿⡿⠸⠇⠸⠧⠸⠧⢿⣿⡿⣿⣿⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣂⣴⣦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠙⠉⠀⢀⣀⣀⣼⣿⣿⣿⡿⣿⡿⣿⣯⡿⡟⣷⣼⣽⠎⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠹⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⣻⣿⣿⣤⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⠒⠺⢿⣿⠿⢿⣽⣷⣯⣯⣾⣿⣿⣧⣾⡿⡿⣧⣬⣴⡦⣄⣄⠀⠀⠀⠀⠀⠀⣠⡤⠀⣠⡼⡽⣯⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣎⣭⣸⡿⠟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠇⠀⠈⢿⣯⡻⠟⠓⠛⠛⠚⠯⠼⠬⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣖⡶⣟⣇⣉⣁⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠛⢀⣩⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 1000 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Microsoft_Criminals_Law_Enforcement_is_the_Real_Problem.shtml Gemini version at https://techrights.org/n/2024/12/05/Microsoft_Criminals_Law_Enforcement_is_the_Real_Problem.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Criminals: Law Enforcement is the Real Problem⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 The Register (UK) says, "Microsoft_to_FTC:_Investigate_your_own_leaks" (the headline_has_changed) 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_learned_of_fresh_antitrust_probe_from_the_news⦈_ We saw several more press_reports_to_the_same_effect a few times earlier this week, basically the criminals flinging accusations at the law enforcer (deflecting the issue and resorting to projection). 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Why_are_you_enforcing_the_law???⦈_ "The government is not trying to destroy Microsoft, it’s simply seeking to compel Microsoft to obey the law. It’s quite revealing that Mr. Gates equates the two." -Government official ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⢿⠛⢽⠿⢿⠿⠿⠿⠿⠿⠿⢿⠫⠿⣿⣿⠿⢿⠿⢿⠿⠿⠿⠿⢿⠿⢹⣿⠿⢿⠩⣿⠩⠿⡿⠿⡿⠿⠹⢿⣿⠿⢿⠿⢿⠻⢽⠻⠿⡿⡿⡿⠿⠟⣿⡿⠿⡿⠿⠿⡏⠿⠿⠿⣿⠏⠽⢿⠿⢿⠿⠿⢿⣿⣿ ⣿⣿⣇⣄⣆⣸⣜⣹⣸⣌⣡⣕⣨⣜⣡⣸⣏⣿⣿⣄⣸⣐⣸⣸⣸⣇⣄⣰⣜⣸⣿⣜⣼⣸⣿⣸⣸⣧⣢⣕⣪⣸⣇⣿⣐⣘⣸⣸⣘⣸⣘⣸⣇⣃⣇⣢⣇⣿⡇⣣⣇⣧⣋⣄⣍⣤⣂⣿⣇⣇⣧⣘⣼⣸⣸⣸⣿⣿ ⣿⣿⡿⠟⣿⣿⢿⣿⣿⢿⣿⢿⢿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⡇⡆⣇⢅⣿⡇⡆⣅⢀⡈⡎⣐⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣯⣈⣩⣉⣉⣿⣿⣏⣏⣻⣟⣟⣿⣏⣹⣙⡝⣝⣙⣸⣉⣍⣉⣉⣀⣍⠉⣏⣁⣏⣉⣉⣛⣉⣉⣉⣉⣛⣿⣿⢟⣙⣙⣏⢻⣻⢋⣻⣉⣻⣫⣟⣻⣉⣋⣍⣉⣍⣏⣁⣇⣉⣉⣘⣉⣉⣛⣇⣌⣉⣁⣍⣉⣉⣍⣹ ⣿⣿⡿⢻⡟⢿⢛⡛⠻⠛⡟⠏⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠻⠛⠛⠻⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣿⣛⣟⣻⣻⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠻⢛⡛⢟⠛⡟⢟⣻⠻⠛⢛⣛⡟⠻⡛⣻⠻⣻⠻⡛⡛⡛⠛⡟⠻⠟⠛⢛⠻⡛⢟⣟⠻⠛⢟⠟⡛⢿⢛⠻⠛⠟⣟⠛⣟⢛⡛⠛⡟⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢿⠿⡟⠻⣿⡿⣿⠿⡟⡗⡿⣾⡿⢿⠿⠿⢿⢿⡿⠿⣿⣿⢻⢿⢻⠻⢿⢳⡟⠻⢿⢿⢿⡿⣿⢿⣿⠾⣿⣿⠿⡟⢻⠿⣿⢾⡿⢿⣿⠿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⢿⡿⠿⠗⠾⡿⠿⣿⠿⢿⠻⠿⣿⠿⣿⠿⠿⠿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣶⣷⣿⣶⣷⣷⣷⣿⣶⣶⣾⣷⣷⣷⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢛⡛⠻⡛⠻⠻⢿⠛⠛⡛⠛⠛⠛⢻⠛⢛⠛⢛⠛⢻⣛⣛⠟⠛⢻⢻⠛⠻⠻⡟⠛⠛⠛⠻⡟⠛⠟⡛⠛⢻⠛⣛⠛⢻⠛⠛⣻⠛⡛⠛⢛⡟⢟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⠀⠀⠀⠀⢿⣿⣿⡇⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⣿⡀⠀⠀⠀⢸⣿⣿⢇⠸⡆⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣷⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⢸⡤⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣛⣛⣛⣉⣍⣭⣭⣭⣥⢰⠀⠀⠀⠀⠀⠘⠻⡷⢸⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⢀⡇⢳⠀⠀⢿⢿⢿⠿⠿⠿⢯⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⢾⠀⠀⠀⢠⣇⠀⡗⠀⠻⣿⣦⠀⠀⠀⠀ ⠀⠀⠸⡇⠀⠀⠀⠀⣿⣿⠀⡆⠀⠀⠀⠀⠈⠉⠈⠁⠈⢿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⢼⣄⡀⠀⢸⣏⠃⠀⠀⢀⣬⣬⣷⡄⠀⠀ ⠀⠀⠀⠈⠢⠀⠀⠀⣿⣿⡀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣼⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⣿⣿⣿⣀⣼⣿⣦⣶⣦⣼⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣀⠀⢸⣿⣿⣿⠟⢉⣿⡟⠛⠍⢸⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠘⡇⣿⣿⠋⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⢸⣿⣿⣿⣿⣿⠁⢀⣀⣀⣀⣤⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⠀⠀⡇⣿⣿⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠙⢛⣿⣿⣿⣿⣿⣿⣷⣦⣾⡟⠀⣼⣿⣿⣿⣿⡆⣻⡟⣿⣿⣿⣿⡇⣘⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡇⠀⢻⠀⠀⡇⣿⣿⣧⡀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠏⠀ ⠀⠀⠂⠀⠀⠀⠀⠀⠀⠹⡇⠀⢸⣿⣿⣿⣿⣿⣶⣶⣲⣾⠇⠀⠰⢤⣿⣿⣿⡇⢿⣧⣿⣿⣏⣼⣷⣿⡾⣷⣿⣿⢿⣿⣿⣿⡗⣾⢻⣿⣍⣿⣿⡟⡟⠂⠀⡇⠀⢸⠀⠀⡇⣿⡁⢸⣧⠀⠀⠀⠀⠘⠻⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣼⣿⣿⣌⡙⠻⠿⠿⠟⠃⣀⠀⠀⠀⠙⣿⠿⣿⣞⣻⣟⠻⣻⣿⠿⠟⣃⣿⣾⡿⣿⢿⡟⣿⣿⣯⣸⣷⣿⣿⣿⠁⠀⠀⠀⠆⠀⢸⠀⠀⠃⢸⠂⢠⣿⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣲⣖⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⠳⣤⣹⣼⠇⣾⢻⡎⣾⣿⣿⠈⢡⣤⡖⣞⣛⣿⣟⡛⠛⠃⠉⠈⠁⠙⠙⠋⠛⢓⣺⣿⣿⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⢘⣀⣸⣿⣿⣦⣀⣀⣀⠄⠀⠀⠀⠀⠀ ⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣯⣲⣿⣼⡇⣿⢸⡏⠀⣼⣧⢠⣿⣼⡿⣿⣿⣾⣿⣷⢰⡶⣶⢀⣴⣤⡘⣿⢛⣛⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣳⡻⢿⢿⣿⣿⣿⣿⣿⠖⣄⠈⢿⣿⣯⣽⣶⣿⡛⠁⠀⠿⠿⠹⠏⣿⢻⣿⢿⣿⣿⣿⣿⣿⣯⢸⡏⣛⢣⣿⢾⣿⣿⢠⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⡽⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⡿⣾⡦⡉⠉⠉⠉⠁⣺⣿⣧⡈⣿⣿⣿⣯⣯⣡⡄⣤⣤⠀⢀⣀⣿⣿⣶⣿⣾⣭⣿⣿⣿⣿⣞⡷⠟⠸⠿⢼⢿⣿⢸⣇⣿⠀⢀⠄⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣼⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣧⣿⡄⠀⢸⡏⣿⣿⣿⣿⣷⣾⣎⣿⢽⡿⣿⣆⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣿⣁⣿⢘⡋⣿⠐⠂⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣯⣽⣿⣿⠋⣻⣺⣿⣿⡏⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢙⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠴⠾⣿⣿⣿⡄⠀⠀⠀⣤⡄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⢸⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠀⠠⣤⣴⣾⣿⡇⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⡿⢡⣿⣿⢅⡞⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⢲⣒⣫⣿⣷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⡇⢾⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⣉⣹⠿⣿⣿⠀⠀⠐⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤ ⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠙⢛⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣿⠁⠈⢻⣿⣿⣿⡟⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣹⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⠀⠀⠀⣿⣿⣿⣏⣀⣀⣸⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡀⠀⠀⢈⣿⣿⣿⡇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠠⣽⣿⣿⠋⠉⠉⠙⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠀⠀⠿⢿⣿⣧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢐⣾⣿⣿⠀⣀⡀⠀⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⣀⣾⣿⣾⣏⡻⠛⣿⣿⣿ ⣿⡿⣿⣿⣿⣦⡀⢰⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣼⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⣤⣤⣤⣤⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⡿⠿⠛⠢⢤⣽⣿ ⣿⣛⣛⢟⣿⣿⣷⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣍⡉⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠉⠭⠽⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣴⣿⣿ ⠘⠛⠻⠿⣿⢿⠟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠿⣠⣄⠀⢠⢿⣿⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿ ⠀⠀⣿⠀⠀⠀⠀⢿⣿⣿⡇⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⣿⠀⠀⠀⠀⢸⣿⣿⢇⠸⡆⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣷⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠰⡤⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡛⣛⣛⣛⣉⣍⣭⣭⣥⣥⢰⠀⠀⠀⠀⠀⠘⢻⡷⠸⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⢀⡇⢳⠀⠀⢿⠿⢿⠿⠿⠿⢿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣸⢾⠀⠀⠀⢠⣇⠈⡗⠀⠻⢿⣦⠀⠀⠀⠀ ⠀⠀⠸⡇⠀⠀⠀⠀⣿⣿⠀⡆⠀⠀⠀⠀⠈⠉⠀⠁⠘⢾⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣼⣄⡀⠀⢸⣏⠋⠀⠀⢠⣄⣄⣵⡄⠀⠀ ⠀⠀⠀⠈⠢⠀⠀⠀⣿⣿⡀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣼⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⣿⣿⣿⡀⣼⣿⣦⣶⣦⣼⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⣿⣿⣿⡏⢹⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⠀⢼⣿⣿⣿⠟⢉⣻⡟⠋⠅⢸⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⡇⠀⠐⡇⣿⣿⠃⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⢘⣿⣿⣿⣿⣿⠁⢀⣀⣀⣀⣤⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⠀⠀⡇⣿⣿⡀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠙⢛⣿⣿⣿⣿⣿⣿⣷⣦⣾⡟⠀⣼⣿⣿⣿⣿⡆⣿⡟⣿⣿⣿⣿⡇⣘⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠯⡇⠀⢻⠀⠀⡇⣿⡿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀ ⠀⠀⠂⠀⠀⠀⠀⠀⠀⠹⡇⠈⢸⣿⣿⣿⣿⣿⣶⣶⣲⣾⠇⠀⠰⢤⣿⣿⣿⣇⢿⣧⣿⣿⣏⣼⣷⣿⡾⣷⣿⣿⣿⣿⣿⣿⡗⣾⢻⣿⣍⣿⣿⡟⡟⠁⠀⡇⠀⢸⠀⠀⡇⢿⠀⠸⣧⠀⠀⠀⠀⠈⠻⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣼⣿⣿⣎⠙⠻⠿⠿⠟⠃⣀⠀⠀⠀⢙⣿⠿⣿⣞⣻⣟⠻⣻⣿⠿⠟⣃⣿⣾⡿⣿⢿⡗⣿⣿⣯⢼⣷⣿⣿⣿⠀⡀⠀⠀⠆⠀⢸⠀⠀⠃⢸⠂⢠⣿⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣲⣖⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⠳⣤⣹⣼⠇⣾⢻⡎⣾⣿⣿⠈⢠⣤⡖⣞⣛⣿⣟⡛⠛⠃⠉⠈⠁⠙⠙⠃⠛⢓⣺⣿⣿⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⢸⣀⢸⣿⣿⣦⣀⣀⣠⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣯⣲⣿⣼⡇⣿⢸⡏⠀⣼⣧⢠⣿⣼⡿⣿⣿⣾⣿⣷⢰⡶⣶⢀⣴⣤⡘⣿⢛⣛⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣻⠿⢿⣿⣿⣿⣿⣿⠖⣄⠈⢿⣿⣯⣽⣶⣿⡟⠁⠀⠿⠿⠹⠏⣿⢻⣿⢿⣿⣿⣿⣿⣿⣯⢸⡇⣛⢣⣿⢾⣿⣾⢠⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠽⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠼⣻⣿⢦⡈⠉⠉⠉⠁⣴⠿⣧⡈⣿⣿⣿⣯⣯⣡⡄⣤⣤⠀⢀⣀⣿⣿⣶⣿⣾⣭⣿⣿⣿⣿⣞⡷⠟⠸⠿⢼⢿⣿⢸⣇⣿⠀⢀⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣥⣶⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣧⣿⡄⠀⢸⡏⣿⣿⣿⣿⣷⣾⡎⣿⢽⡿⣿⣆⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⣟⣬⣵⣿⣿⣁⣿⢘⡋⣿⠐⠂⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣯⣽⣽⣿⠋⣻⣺⣿⣿⡏⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢹⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠼⠿⣿⣿⣿⡄⠀⠀⠀⣤⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⢸⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠀⠠⣤⣴⣾⣿⡇⠀⠀⠀⠉⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⡿⢡⣿⣿⢅⡎⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⢲⣒⣫⣿⣷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⡇⢾⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⣉⣙⠿⣿⡿⠀⠀⠠⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤ ⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠙⣛⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣿⠁⠈⢻⣿⣿⣿⡏⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣹⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣇⣀⣀⣸⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡀⠀⠀⠘⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠀⠀⠀⣽⣿⣿⠋⠉⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠀⠀⡿⢿⣿⣧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⡇⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢐⣶⣿⣿⠀⣀⠀⠀⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⣁⣾⣿⣿⣟⣻⠛⣿⣿⣿ ⣿⡿⣿⣿⣿⣦⡀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣼⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣤⣤⣤⣬⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢻⣿⣿⡿⠿⠛⠳⢤⣽⣿ ⣿⣛⣛⣿⣿⣿⣷⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣍⠉⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠉⠭⠽⠭⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣻⡇⠀⠀⣀⣴⣿⣿ ⠈⠛⠻⠿⣿⣿⠟⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⣦⣄⠀⢠⢿⣿⢀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠈⣿⠀⠀⠀⠀⣿⣿⣿⡇⢳⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⢻⣿⡿⠁⢸⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡀⠀⠀⠀⢸⣿⣿⢰⣈⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⠿⠿⠿⠟⠛⡛⣛⣒⣛⣋⢡⠀⠀⠀⠀⠐⠼⢿⡆⢺⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠈⡇⣇⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣸⠄⠀⠀⠀⣰⠂⢸⡇⠐⠿⣷⡄⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠘⣿⣿⠀⡅⠀⠁⠀⠀⠀⠈⠉⠀⠀⢾⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢠⡀⠀⠀⣿⡇⠄⠀⠀⢀⣨⣡⣠⠀⠀⠀ ⠀⠀⠀⠙⢀⠀⠀⠀⣿⣿⠀⠁⠀⠀⣤⣶⣦⣦⣤⣤⣤⣬⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⢸⣿⣇⠀⣿⣷⣠⣦⣄⣸⣿⣿⣿⣷⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⡟⢹⣿⣿⣿⣾⣿⣿⡮⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⢰⣿⣿⣿⠿⠝⢻⣿⠟⣛⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣇⣿⣿⣿⡇⠈⡏⠉⢸⣺⣿⡏⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⣷⡼⣿⣿⣿⣷⣶⣿⣿⣶⣦⢸⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣀⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠸⠋⣿⡇⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠹⠿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠀⣽⣿⣿⣿⣿⡄⣶⡿⣿⣿⣿⣿⡇⣜⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡿⠟⣛⠀⠀⣇⠀⠀⠀⣿⡗⣄⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡇⠠⠀⣿⣿⣿⣿⣿⣭⣭⣭⣭⡟⠀⠠⣭⣿⣿⣿⡇⣿⣿⣿⣿⡏⣹⣷⣿⡼⣷⣿⣿⢿⣿⣿⣿⡗⣾⢻⣿⡍⣿⣿⡿⡇⠀⢰⠀⠀⣿⠀⠀⡀⡟⠁⢹⡆⠀⠀⠀⠀⠘⠏⠧⠙⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⣤⣿⣿⡍⠛⠿⠿⠿⠿⠟⡀⠀⠀⠈⠻⣿⢿⣿⣜⣿⣟⠿⢿⣿⣿⠟⠇⣿⣾⡿⣿⢿⡟⣿⣿⣯⢺⣷⣿⣿⣿⠁⠃⠀⠐⠀⠀⢨⠀⠀⠃⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣄⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⣠⠦⣄⢹⣼⠇⣾⢻⡎⣶⢿⣿⠉⢩⣭⡍⣝⢛⣿⣟⡷⠿⠓⠛⠊⠁⠛⠙⠃⠛⢓⣺⣿⣿⠀⠂⠀⠀⠀⠀⠸⠀⠀⠀⠟⠀⢸⣿⣷⣄⣀⠀⣠⠂⠀⠀⠀⠀⠀ ⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢹⣯⣰⣿⣼⡇⣿⢸⡏⠀⣼⣧⢠⣿⣼⡿⣿⣿⣼⣟⣷⢰⡶⣶⢀⣴⢦⡸⣿⢛⣛⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⣝⡿⣿⣿⣿⣿⣿⣿⡇⠤⠈⢻⣿⣯⣽⣤⣿⡛⠁⠀⠿⠷⠹⠏⣿⢿⣿⣷⣿⣿⣿⣾⣟⣯⢸⡇⣛⢣⣿⢾⣿⣼⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⡿⢷⣤⡉⠛⠛⠛⠋⣴⣾⣧⡈⣿⣿⣿⣯⣿⣡⡄⣤⣤⠀⢀⣀⣶⡶⣶⣶⣮⣭⣿⣿⣿⣿⡜⠷⠟⠸⣿⢼⣿⣿⢸⣇⣿⠁⠀⠄⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣿⣿⣶⣴⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⣿⣧⣿⡄⠀⢸⡟⣿⣿⣿⣿⣷⣾⡎⣿⢹⡿⣿⢀⣤⣄⠀⣀⡀⠁⠀⠉⠈⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⡟⣭⣵⣿⣮⣁⣿⢘⡋⣿⠠⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢾⣷⣿⣯⣽⣽⣿⢛⣻⣺⣿⣿⡏⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡻⠿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⠘⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠀⢭⣿⣿⣿⣷⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡛⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⢠⣀⣭⣽⣿⡇⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠸⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⣿⢃⣿⣿⠛⡼⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣃⠀⠀⢬⠽⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⡏⣴⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢛⣻⣿⣿⡿⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣤⣥⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣿⣿⡀⠈⠻⠿⣶⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣌⡛⠁⠐⠻⣿⣷⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣚⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣛⠛⠿⠃⠀⠀⠘⣿⣿⣿⡇⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠾⠿⠧⠀⠀⢀⣹⣿⣿⠏⠛⠋⠉⢛⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠀⠀⡿⢻⣿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⣿⡇⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠠⣽⢿⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣏⣉⣩⣷⣾⣿⠛⠿⢿⣿⣿⣿ ⣻⣿⣿⣿⣿⣦⠀⣶⣿⣽⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣼⣿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⢋⡈⣉⣀⣀⣈⣄⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠷⣄⣉⣿⣿ ⣛⣛⣻⠻⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⠛⠛⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣯⠀⠀⠀⣀⣽⣿⣿ ⠘⠛⠻⢿⣿⡿⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡦⣀⡀⠀⢠⢿⡟⠀⠀⠀⠀⠀⠀⣴⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿ ⠋⠀⣿⡀⠀⠀⠀⢸⣿⣿⡇⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⣿⡇⠀⠀⠀⢸⣿⣿⡇⠘⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡇⠀⠀⠀⢸⣿⣿⠠⣄⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠉⠻⠿⠓⠀⠀⠀⠀⠠⠰⢿⡆⢰⣦⡄⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠈⣿⣿⡀⡇⢱⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣶⣶⣶⣶⣾⣾⣿⣟⣟⢹⡀⠀⠀⠀⢠⡄⢸⡇⠈⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⡈⠈⠀⠀⠉⠑⠂⠂⠀⠐⠦⣦⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣁⡀⠀⠀⣾⡇⡈⠁⠀⠀⠙⠋⢀⠀⠀⠀ ⠀⠀⠀⠙⠀⠀⠀⠀⣿⣿⡆⡇⠀⠀⢀⣤⣤⣤⣤⣄⣤⣀⣙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢸⣿⣷⣆⠀⣿⣧⢀⣄⡀⣰⣿⣿⣿⣧⣄⣀ ⠀⠀⠀⠀⠀⠁⠀⠀⢻⣿⡇⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣷⣶⣾⡟⣿⣿⣸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣼⣿⣿⣿⣟⠻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣼⣿⣿⡏⣿⣿⣯⡇⠈⡟⠛⢻⡇⣿⡟⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡏⢨⡷⣆⢿⣿⣿⣶⣶⣾⣿⣧⣤⡍⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⡇⠀⠀⡇⣿⣇⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠿⡿⣿⣿⣿⣿⣿⣿⣏⣋⣿⡇⣹⣿⣿⣿⣿⡇⢰⡖⣶⣿⣿⣿⡇⣘⢛⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⡧⣿⣿⣿⣿⣿⢿⠯⠁⠀⣸⠀⠀⡇⣿⣏⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢺⣿⣿⣿⣿⣿⣯⣍⣉⣻⠃⢉⣙⣿⣿⣿⡇⢸⣿⣿⣿⡟⣹⣷⣿⡾⣷⣿⣿⣿⣿⣿⣿⡗⣿⢻⣿⡍⣿⣿⡟⡇⠐⠁⡄⠀⢺⠀⠀⡇⣿⠋⢱⡄⠀⠀⠀⠀⠘⡟⡻⡻⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣼⣿⣏⠛⠿⣿⣿⣿⡿⣃⠀⠀⠈⠻⣿⣿⣿⣼⣿⣽⢿⣿⣿⣿⠟⡇⣿⣾⡿⣿⢿⡗⣿⣿⣯⢼⣷⣿⣿⣿⠃⠃⠀⠀⡁⠀⢸⠀⠀⡇⢹⠀⢸⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣷⣦⣀⣀⡠⣄⣹⣼⠇⣾⢻⡎⣶⣿⣿⡘⢩⣴⡞⣟⢟⣳⣶⡶⠿⠷⠿⠮⠥⠽⠹⠇⠛⢳⣺⣿⣿⠀⠂⠀⠀⡀⠀⢸⠀⠀⠀⠸⠀⢸⣿⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣯⣤⣿⣼⡇⣿⢸⡟⠀⣼⡧⢀⣿⣼⡿⣿⣿⣼⣟⣷⢰⡶⣶⢀⣴⢦⡸⣿⢛⣛⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣚⣻⣿⣿⣿⣿⣿⣿⣷⢀⠈⢹⣿⣯⣽⣤⣿⡟⠁⠀⠿⠷⠸⠏⣿⢻⣿⣷⣿⣿⣿⣾⣟⣯⢸⡇⣛⢣⣿⢸⣿⣼⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣷⣦⠉⠛⠛⠛⠛⠁⣼⣷⠀⢻⣿⣿⣯⣿⣡⡄⣤⣄⠀⢀⣀⣴⠴⣦⣯⣭⣭⣿⣿⣿⣿⡜⠷⠟⠸⡿⢼⢿⣿⢸⣇⣿⠂⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣽⣿⣦⣤⣤⣦⣼⣿⣿⣧⣼⣿⣿⢿⡿⣿⣇⣿⡄⠀⢸⡏⣿⣿⣿⣿⣷⣾⣞⣿⢹⡿⣷⢄⣤⣄⠉⣉⡉⠁⠀⠉⠈⠀⠂⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣮⣁⣿⢘⡋⣿⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣯⣭⣽⣿⠛⣻⣺⣿⣿⡍⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣙⠿⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠙⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⣛⣿⣿⣿⣧⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⠏⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⢀⠉⣛⣛⣿⡇⠀⠀⠰⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⣿⠏⣿⣿⠿⢰⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢇⠀⠈⣙⣻⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⡿⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠼⢶⣿⣿⣷⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣇⣈⣽⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⠀⠐⢿⣯⣭⣿⡇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠯⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣮⡙⠛⠃⠀⡶⣶⣯⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠴⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⠿⠿⠇⠀⠀⠰⣿⣿⣿⡆⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣿⣿⣁⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⢶⣶⣦⠀⠀⠀⠿⣿⣿⠗⠒⠒⠚⠟⠃⠀⠀⠄⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠀⠀⠿⢙⣿⡇⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⡇⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠂⠀⠀⠀⢈⣛⣿⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⠛⣻⣭⣹⣿⣿⣿⣿⣿⣿⣿ ⢿⣛⣿⣿⣽⣦⠀⣶⣷⣬⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣼⣿⣁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⠇⠐⠂⠀⠀⢸⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣷⢢⡈⠛⢿⣿⣿ ⢏⣉⣙⣛⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⠿⠟⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠻⠩⠝⠿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣜⣿⣿⠋⠉⠀⠉⢛⣿⣿⣿ ⠈⠛⠻⢿⡿⠿⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣶⡄⠀⠀⠀⢀⣿⡗⠀⠀⠀⠀⠀⢀⣰⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣴⣾⣿⣿⣿⣿ ⠋⠀⣿⡀⠀⠀⠀⢸⣿⣿⡇⢹⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⣿⡇⠀⠀⠀⢸⣿⣿⠇⠘⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡇⠀⠀⠀⢸⣿⣿⠀⣄⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠉⠻⠿⠓⠀⠀⠀⠀⠀⠰⢻⡆⢰⣦⡄⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠈⣿⣿⠀⡇⢱⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣶⣶⣶⣶⣾⣾⣿⣟⣟⢸⡂⠀⠀⠀⢀⡄⢸⡇⠈⢿⣷⡀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⡌⠈⠀⠀⠉⠉⠂⠂⠀⠐⠲⣦⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢁⠀⠀⠀⣼⡇⡈⠁⠀⠀⠙⠛⢀⠀⠀⠀ ⠀⠀⠀⠙⠀⠀⠀⠀⣿⣿⡆⡇⠀⠀⢀⣤⣤⣤⣤⣤⣠⣀⣙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢸⣿⣷⣆⠀⣿⣧⢀⣄⡀⢸⣷⣾⣿⣧⣀⣀ ⠀⠀⠀⠀⠀⠐⠀⠀⢻⣿⡇⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣷⣶⣾⡇⣿⣿⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣼⣿⣿⣿⣟⠻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡏⣿⣿⣟⡇⠘⡟⠛⢛⡇⣿⡟⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⢨⡷⣆⢿⣿⣿⣶⣶⣾⣿⣧⣤⡍⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⢇⠀⠀⡇⣿⡇⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠿⡿⣿⣿⣿⣿⣿⣿⣋⣉⣿⡇⣹⣿⣿⣿⣿⡇⢰⡖⣾⣿⣿⣿⡇⣘⢛⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⢿⡇⠅⠀⢸⠀⠀⡇⣿⡗⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢺⣿⣿⣿⣿⣿⣯⣍⣉⣿⠃⢉⣉⣿⣿⣿⡇⢸⣿⣿⣿⡟⣹⣷⣿⡾⣷⣿⣿⣿⣿⣿⣿⡗⣿⢻⣿⡍⣿⣿⡟⡏⠈⠀⡀⠀⢻⠀⠀⡇⣿⠁⢰⡄⠀⠀⠀⠀⠘⡛⣻⠻⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣼⣿⣏⠛⠿⣿⣿⣿⡿⣃⠀⠀⠈⠻⣿⣿⣿⣼⣻⣽⢿⣿⣿⣿⠟⡇⣿⣾⡿⣿⢿⡇⣿⣿⣯⢼⣷⣿⣿⣿⠂⠃⠀⠈⡀⠀⢸⠀⠀⡇⢻⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣷⣦⣀⣀⡠⣄⢹⣼⠇⣾⢻⡆⣶⣿⣿⠘⢩⣴⡞⣟⢟⣳⣶⡶⠿⠷⠿⠮⠥⠽⠹⠇⠛⢻⣺⣿⣿⠀⠂⠀⠀⡀⠀⢸⠀⠀⠀⠸⠀⢸⣿⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣯⣤⣿⣼⡇⣿⢸⡟⠀⣼⡧⢀⣿⣼⡟⣿⣯⣼⣟⣷⢰⡶⣶⢀⣴⢦⡸⣿⢛⣛⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⢚⣻⣿⣿⣿⣿⣿⣿⣷⠀⠈⢹⣿⣯⣽⣤⣿⡿⠁⠀⠿⠷⠸⠏⣿⢻⣿⣷⣿⣿⣿⣾⣟⣯⢸⡇⣛⢣⣿⢼⣿⣼⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⡼⢅⣦⠉⠛⠛⠛⠛⢁⡀⣧⠀⢻⣿⣿⣯⣿⣡⡄⣤⣄⠀⢀⣀⣴⠴⣦⣯⣭⣭⣿⣿⣿⣿⡜⠷⠟⠸⡿⢼⢿⣿⢸⣇⣿⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣼⢠⣦⣤⣴⣤⣽⣽⣿⣷⣼⣿⣿⢿⡿⣿⣇⣿⡄⠀⢸⡏⣿⣿⣿⣿⣷⣾⣞⣿⢹⡿⣷⢄⣤⣄⠉⣉⡉⠁⠀⠉⠈⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣃⣿⡸⠿⠄⠀⣼⣧⢻⡿⣿⣿⣿⣿⣿⡟⣭⣵⣿⣮⣁⣿⢘⡋⣿⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣯⣭⣽⣿⠛⣻⣺⣿⣿⡍⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣙⠿⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠙⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⣛⣿⣿⣿⣧⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⠏⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢀⠉⣛⣛⣿⡇⠀⠀⠰⠿⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠖⠀⠀⠀⠈⣿⣿⣿⣿⣭⣽⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⣿⠏⣿⣿⠿⢰⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢇⠀⠈⣙⣻⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⡿⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠼⢶⣿⣿⣷⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣶⣦⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣇⣈⣽⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣿⣿⠀⠐⢿⣯⣭⣿⡇⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠯⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣮⣙⠛⠃⠀⢴⣶⣯⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠿⠿⠇⠀⠀⠰⣿⣿⣿⡆⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⣁⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⢶⣿⣆⠀⠀⠀⠿⣿⣿⠗⠲⠒⠚⠟⠃⠀⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠀⠀⠘⢝⣿⡇⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⡇⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠈⠀⠀⠀⢈⣛⣿⡟⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠛⠛⣻⣭⣹⣿⢿⣿⣿⣿⣿⣿ ⣛⣛⣿⣿⣽⣦⠀⣶⣷⣬⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣼⣿⣁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⠇⠐⠂⠀⢀⢸⡀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿⣷⢤⡈⠛⢿⣿⣿ ⢍⣉⣉⣛⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⣿⣿⠿⠟⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠻⠿⠽⠿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⣿⠋⠉⠀⠉⢛⣿⣿⣿ ⠈⠛⠻⢿⡿⠿⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡄⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⢀⣴⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣧⣤⣤⣶⣿⣿⣿⣿ ⠀⠀⠈⣿⠀⠀⠀⠀⣿⣿⡟⡄⢷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⢿⣿⡇⠃⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇⢸⠼⡃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠏⢀⠛⠛⡀⠀⠀⠀⠀⠀⠛⣷⠐⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣗⠘⠆⠇⠀⠸⠿⠿⠿⣿⠿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣟⡛⣻⠀⠀⠀⢀⡆⠀⡷⠀⠻⢿⣄⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⢸⣿⣷⠠⡄⠀⠀⠀⠀⠈⠀⠀⠈⠀⠺⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⢸⡇⠀⠁⠀⠀⠈⠁⢠⡀⠀⠀ ⠀⠀⠀⠀⠈⠂⠀⠀⠸⣿⣿⠀⠁⠀⠀⣴⣶⣶⣶⣶⣶⣦⣤⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⢹⣷⠀⣼⣿⣄⣴⣄⣰⣿⣿⣿⣷⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣾⣿⢸⣿⡦⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⡇⡀⢀⣿⣿⣿⠿⠍⢻⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⠀⠙⠉⠉⢹⢸⡏⠉⠀⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣷⣶⣸⣿⣿⣿⣿⣿⠁⢀⡀⣀⣀⣠⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠀⠘⡄⠀⢸⢸⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⣿⣿⣿⣿⣿⣿⣯⣤⣭⣿⢠⣿⣿⣿⣿⣿⢰⡞⣿⣿⣿⣿⡟⣇⢛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⠟⡿⠅⠀⢀⡇⠀⢸⢸⣿⡄⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣤⣬⡟⠀⠤⣼⣿⣿⣿⣺⣷⣿⣿⣿⣹⣷⣿⣼⣷⣿⣿⢿⣿⡿⣿⡗⣾⢻⡿⡍⣿⣿⣿⢽⠀⠁⡦⠀⠘⡇⠀⢸⢸⠋⠁⡄⠀⠀⠀⠀⠈⠋⠝⠝⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣤⣶⣿⣿⣆⡉⠻⠿⠿⠿⣏⠀⠀⠀⢉⢹⡿⢿⣿⣛⣽⡿⠻⣿⢿⠿⠹⣿⣾⡿⣿⢿⡟⣿⣿⣯⢸⡷⣿⣿⣿⡏⠈⠀⠀⠀⠀⠀⡇⠀⠸⢘⡇⠀⣇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢄⣴⠲⢿⣼⠇⣾⢻⡎⣾⣿⣿⠧⢠⣬⡍⣟⢟⡻⣿⡗⠛⠓⠛⠊⠁⠛⠙⠃⠛⠓⣺⣿⣿⡇⠘⠀⠀⠠⠀⠀⡇⠀⠀⠘⠃⠀⣿⣷⣄⣀⡀⢀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡟⡹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣯⣷⣿⣼⡇⣿⢸⡟⠃⣸⣧⢠⣿⣼⡇⣿⣿⣼⣿⣷⢰⡶⣶⢀⣴⢦⡀⣿⢛⣛⣇⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⣍⠟⢿⣿⣿⣿⣿⣿⠖⣨⠁⢿⣿⣭⣷⣿⣻⠃⠀⠿⠿⠸⠏⣿⢰⣿⣷⣿⣻⣿⣿⣿⣯⢸⡇⣛⢃⣿⢼⣿⣿⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡆⠈⠉⠉⠉⠁⣺⣿⣧⡈⣿⣿⣯⣿⣩⡄⣤⣄⠀⢀⣀⢰⡷⣶⣾⣾⣭⡿⣿⣿⣿⣿⠷⠟⠸⢿⢼⢿⣿⢸⣇⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣯⣴⣤⣬⣬⣴⣾⣿⣿⣷⣿⣿⣿⡿⣿⣧⣿⡄⠀⢸⡇⢸⣿⣿⣿⣷⣾⣏⣿⢹⡿⣿⣏⣤⣄⠈⣁⡉⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣿⡸⠿⠄⠀⣼⣧⢸⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣅⣿⢘⡋⣿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⣷⣿⣯⣭⣿⣿⡇⣻⣺⣿⣿⣿⠁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣍⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠨⣽⣿⣿⣿⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⡟⢸⠄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⣄⣨⣭⣿⣿⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢽⣿⣿⣿⣧⣭⣿⣧⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣤⣿⠏⣼⣿⡟⢃⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣹⠀⠀⠬⠭⢟⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⢡⣾⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢘⣛⣿⣿⣿⠀⠀⠀⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀ ⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠻⡟⢿⣿⣿⡇⠀⠙⠿⢶⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶ ⣦⡄⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣿⣦⣉⠁⠀⠺⣿⣿⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣦⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣐⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠛⠀⠀⠈⢿⣿⣿⡗⠀⠀⢰⣾⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣧⠀⠀⠀⠙⣿⣿⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⠠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡯⠀⠀⠀⣛⣿⣿⡏⠛⠛⠛⠛⠃⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⣄⠀⢈⣏⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⣿⡏⣺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⣬⣿⢿⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠛⠋⣿⣭⣽⠿⣿⣿⣿⣿⣿⣿⣿ ⡺⠶⢿⡿⣿⣿⣦⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼⣿⣧⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢛⠟⡈⢉⣁⣀⣈⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡦⢤⡈⠛⣿⣿⣿⣿ ⠉⠚⠿⣾⣿⣿⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⡛⠛⠁⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⣛⣻⣛⢛⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣿⣿⣟⠉⠁⠀⠉⣻⣿⣿⣿⣿ ⠀⢿⣿⡿⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣀⠀⠀⢠⣿⣿⢃⡀⠀⠀⠀⢠⣴⣷⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣿⣿⣿⣿ ⠀⠠⠀⣿⠀⠀⠀⠀⢻⣿⣿⡇⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣟⢀⢸⡄⠀⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣦⠀⠀⠀⠀⠀⢀⢿⡀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡆⠀⠀⠀⢸⣿⣿⠸⡖⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠛⡛⢛⢛⣛⣙⣋⣀⣍⣉⢀⠀⠀⠀⠀⠈⢹⡗⠸⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡇⠀⠀⠀⢸⣿⣿⠀⠃⠓⠀⠘⠛⠛⠻⠟⠛⠛⣛⡓⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣹⠀⠀⠀⢰⡇⠸⡇⠀⠙⠿⣦⠀⠀⠀⠀ ⠀⠀⠀⠘⠧⠀⠀⠀⠸⣿⣿⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢠⡀⠀⣾⣇⠁⠀⠀⢀⣠⣨⣤⡄⠀⠀ ⠀⠀⠀⠀⠀⠐⠄⠀⠀⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢸⢸⣷⠀⣿⣿⣴⣷⣤⣼⣿⣿⣿⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡆⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⢸⣿⡎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⣒⣤⢸⣿⣿⣿⣛⣁⣽⣿⡋⠉⢻⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣧⣿⣿⣿⠃⠀⡄⠀⢸⢸⣏⠁⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⢻⣿⣷⣿⣿⣿⣿⣿⣿⠿⢿⣿⠸⣿⣿⣿⣿⣿⠀⣠⣤⣤⣤⣴⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⢸⢸⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣾⣿⣿⣿⣿⡿⠿⠷⠾⣿⠰⠿⢿⣿⣿⣿⣴⡞⣿⣿⣿⣿⡟⣇⢘⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⠙⢸⠀⠀⡇⠀⢘⢸⣿⠆⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⣿⣿⠿⣿⣿⣿⣿⣥⣾⠃⠀⠒⣾⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣾⣷⣿⣿⢿⣿⡿⣿⡗⣾⢻⣿⣍⡟⣿⣿⠹⠅⠀⢸⠀⠀⡇⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⠈⠫⡌⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣬⣴⣾⣿⣿⣿⣧⣄⠉⠛⠛⡛⣁⠀⠀⠀⠀⣹⣛⣻⣿⣟⣝⠿⡛⠿⠻⠿⣐⣿⣺⡿⣿⢿⡇⣿⣿⣯⢸⡷⣾⣿⣿⡇⢀⠀⠀⠸⠀⠀⡇⠀⠘⠀⣯⠀⣠⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⠙⢻⣼⠇⣾⢻⡆⣶⣿⣿⡛⢨⣤⡄⣝⢛⡇⣿⣯⠙⠃⠋⠈⠁⠙⠙⠃⠛⠓⣺⣿⣿⡇⠈⠀⠀⠐⠀⠀⠇⠀⠀⠀⠃⠀⣿⣷⣦⣤⣄⠄⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡝⢿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡿⣷⣿⣼⡇⣿⢸⡟⠃⢸⣧⢠⣿⣼⡇⣿⣿⣾⣿⣷⣰⡶⣶⢀⣴⣤⡀⣿⢛⣛⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣶⣍⠛⠿⣿⣿⣿⠟⢉⣾⡅⢻⣿⣽⣿⣿⣿⠁⠀⠿⠷⠸⠇⣿⢰⣿⢳⣿⣻⣿⣿⣿⣯⣸⡇⣛⢣⣿⢾⣿⣿⢠⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣯⣷⣤⡀⣀⣀⣠⣿⣿⣷⢈⣿⣿⣯⣿⣱⡆⣤⣄⠀⢀⣀⢸⡷⣶⣿⣿⣯⣟⣿⣿⣿⣿⡷⠟⠸⠿⢼⢿⣿⢸⣇⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢻⣿⣿⣿⣿⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣿⡄⠀⢸⡇⠸⣿⣿⣿⣷⣿⣟⣿⢩⡿⣿⣿⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣇⣿⡸⠿⠄⠀⣼⣧⢸⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣇⣿⢘⡋⣿⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡻⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡧⠀⠀⠀⠀⠈⣷⣿⣯⣭⣿⣿⡋⢻⣸⣿⣿⣿⡁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢳⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇⠐⠶⢿⣿⣿⣧⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣔⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⡸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠦⣴⣶⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⣬⣿⣧⣤⣤⢨⣭⣭⣭⣭⣬⣭⣭⣼⣿⠃⣿⣿⡇⣡⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣼⠄⠀⢐⣖⣫⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⠐⠿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⣨⣭⠿⣿⣿⠃⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀ ⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣟⡛⠿⣿⡇⠀⢈⣛⣻⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣍⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⠂⠀⠙⣽⣿⣿⣟⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣬⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣉⣉⡉⠀⠀⠀⢹⣿⣿⣟⣀⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠀⠀⢘⣿⣿⣷⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣿⣿⢐⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⡛⠛⠀⠀⠀⢬⣽⣿⠇⠉⠉⠉⢉⠁⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⡿⣿⣿⣷⣦⠀⢠⣼⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⠇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣶⣿⣿⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣉⣉⣿⣾⣾⠛⠿⢿⣿⣿⣿⣿⣿⣿ ⣝⢛⣛⠿⢿⣿⣷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣾⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢋⡄⣠⣤⣤⣦⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⡗⠲⣄⣉⣿⣿⣿⣿⣿ ⠀⠉⠻⢿⣿⣿⢽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣍⡉⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠉⠭⠭⠽⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣏⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿ ⠀⢻⣿⠿⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢿⠴⠄⠀⢰⣿⣿⣠⡄⡀⠀⠀⠐⠲⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠨⠀⣿⠀⠀⠀⠀⢸⣿⣿⡇⢸⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⢠⠈⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣦⠀⠀⠀⠀⠀⢀⣿⡀⢀⡄⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠘⡇⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣛⣻⣉⣉⣍⣭⣬⣭⣥⠀⠀⠀⠀⢈⠉⢹⠇⢹⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⣿⠀⡃⠘⠀⠐⠛⠛⠿⠯⠉⠍⣩⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣘⠀⠀⠀⣾⡄⢸⠃⠀⠙⢿⠆⠀⠀⠀⠀ ⠀⠀⠀⠘⠣⡀⠀⠀⠀⣿⣿⠀⠃⠀⠀⢀⣀⣀⣀⡀⠀⠀⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣤⡀⠀⣿⡄⠀⠀⠀⢠⣤⣤⣶⡀⠀⠀ ⠀⠀⠀⠀⠀⠈⠄⠀⠀⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣸⣿⣷⣰⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣷⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⢠⣿⣿⣿⡿⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡟⣿⣿⣿⡏⢹⣿⣿⣿⢹⣿⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⣲⣄⢸⣿⣿⣯⣍⣠⣽⣯⣁⠒⢸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣇⣿⣿⣿⡇⠀⡇⠀⢸⢸⡏⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡟⢷⣾⣿⣿⣿⣿⣿⣿⠿⠿⢿⣷⠘⣿⣿⣿⣿⣿⡇⢠⣤⣤⣴⣶⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢿⠀⠀⡇⠀⢸⠸⣧⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠁ ⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿⡅⠠⢰⣿⣿⣿⣿⣿⠿⠿⠿⢿⡟⠘⠛⢿⣿⣿⣿⣷⡞⣿⣿⣿⢻⡟⣇⢸⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠫⢸⠀⠀⡇⠀⠈⠀⣿⠄⠀⠀⠀⠀⠀⣿⣻⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣸⣿⣿⠿⣿⣿⣿⣿⣽⡟⠁⠀⠙⣻⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣾⣷⣿⣿⣿⣿⡿⣿⡗⣾⢻⣿⣍⣟⣿⣿⠿⠇⠀⢸⠀⠀⡇⠀⢠⠀⡏⠀⠀⠀⠀⠀⠀⠈⠹⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣦⣀⠉⠉⢉⡉⣀⠀⠀⠀⠀⡼⠿⣻⣿⣟⢙⠿⠩⠿⠻⠿⣥⣿⣼⡿⣿⢿⡏⣿⣿⣯⢹⡷⢾⣿⣿⡇⠀⠀⠀⠸⠀⠀⡇⠀⠈⠀⣿⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣼⡏⠙⢻⣼⠇⣾⢻⡆⣶⣿⣿⣫⢠⣬⡅⣞⢛⡟⣿⡧⣉⠁⠉⠈⠁⠙⠙⠋⠛⠓⣺⣿⣿⡇⠀⠀⠀⠘⠀⠀⠛⠀⠀⠀⢋⣀⢸⣿⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠹⢿⣿⣿⣿⣿⣿⣿⣿⣠⢸⣿⣷⣿⣾⡇⣿⢸⡟⠃⢸⣧⢤⣿⣼⡇⣿⣿⣿⣿⣷⣴⡶⣶⢀⣴⣤⡀⣽⢛⣛⣇⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣏⡛⠿⠿⠿⠿⠋⣸⣮⡁⢿⣿⣽⣿⣿⡻⠁⠀⠿⠷⠸⠇⣿⢰⣿⣛⣿⣻⣿⣿⣿⣯⣼⡏⣛⢣⣿⢾⣿⣿⢰⡿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣻⣯⣿⣄⣀⣠⣤⣼⣿⣿⣷⣘⣿⣿⣯⣿⣱⡆⣤⣄⠀⢀⣀⢰⡿⣶⣿⣿⣯⣧⣿⣿⣿⣿⡷⠟⠸⠿⠼⠿⣿⢸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⢿⣿⣿⣿⣿⣼⣿⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣿⡄⠀⢸⡏⠸⣿⣿⣿⣷⣿⣟⣷⢹⡿⣿⣿⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⡸⠿⠄⠀⣼⣧⢸⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣇⣿⢘⡋⣿⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⢿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⣷⣿⣯⣭⣿⣿⡇⠻⣺⣿⣿⣿⡅⢸⡏⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⡳⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠐⠛⢿⣿⣿⣧⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡖⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠶⠶⣶⣾⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣥⣬⣿⣥⣤⣤⢨⣭⣭⣭⣭⣭⣭⣭⣼⡿⢁⣿⣿⠇⣼⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⢀⣻⣭⣽⣿⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⡿⠘⠻⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢤⡬⢽⣿⣿⠃⠀⠀⠾⠦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠛⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⠿⣿⣷⠀⣈⣉⡿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⠃⠀⠨⣽⣿⣿⣟⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣉⣩⣥⠀⠀⠀⢹⣿⣿⣿⣀⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠀⠀⢼⢿⣿⣇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⡿⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠽⠛⠀⠀⠀⢯⣽⣿⢋⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⣿⣿⣷⣆⠀⣤⣾⣽⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⡇⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣾⣿⢀⣀⡀⠀⠁⡆⠀⠀⠀⠀⠀⣾⣿⣿⣄⣠⣾⣶⣾⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿ ⣟⠛⣻⢿⣿⣿⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢣⡆⣤⣶⣶⣦⣷⠀⠀⠀⠀⣸⣿⣿⣿⣟⢿⣿⣿⡿⡟⠳⢄⣉⣽⣿⣿⣿⣿⣿ ⠀⠙⠻⢿⣿⣿⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣤⣀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⣟⣯⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿ ⠀⢻⣿⠿⠛⢿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡟⠛⢲⠂⠀⠴⢹⣿⣴⠆⡀⠀⠀⠀⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠠⠀⣿⡆⠀⠀⠀⢸⣿⣿⡇⢸⡄⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠐⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣦⠀⠀⠀⠀⠀⣼⣧⠀⣠⡀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠘⡗⢇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⡛⣛⣛⣛⣉⣩⣩⣌⣭⣭⠄⠀⠀⠀⢀⠁⣿⠁⢹⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⠃⠘⠀⠀⠛⠛⠻⠟⠋⢋⣛⡅⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⣿⠀⢻⠀⠀⠹⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠘⠣⠀⠀⠀⠀⣿⣿⡀⠁⠀⠀⣀⣀⠀⠀⠀⠀⠈⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣴⠀⠀⣿⡌⠀⠀⠀⣤⣤⣴⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣸⣿⡗⢸⣿⣷⣾⣷⣤⣿⣿⣿⣿⣿⣷⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣧⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣗⣦⡀⣿⣿⣿⣛⣁⣨⣿⣏⠉⠁⢸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣇⣿⣿⣿⡇⠀⡇⠀⢸⡇⡄⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣷⣷⣿⣿⣿⣿⣿⣿⠿⡿⣿⡇⠘⢿⣿⣿⣿⣿⡇⢠⣤⣤⣴⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠇⠀⡇⠀⠈⠇⣇⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢨⣿⣿⣿⣿⣿⡿⠿⠷⠶⣿⠃⠐⠿⢿⣿⣿⣿⣷⡞⣿⣿⣿⢻⡟⣟⢸⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠻⢸⠀⠀⡗⠀⠀⠀⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⣿⡿⢿⣿⣿⣿⣷⣴⠏⠀⠀⠙⢺⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣾⣷⣿⣿⢿⣿⣿⣿⡗⣾⢻⣿⢍⣟⣿⣿⡿⡇⠀⢸⠀⠀⡇⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠈⠓⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣧⣄⡉⠛⠛⣛⠋⣀⠀⠀⠀⠀⢸⣿⣻⣿⣟⠙⡿⠋⠿⠻⠿⣇⣿⣸⡿⣿⢿⡇⣿⣿⣯⢹⡷⢾⣿⣿⡏⠀⠁⠀⢸⠀⠀⢧⠀⠀⠀⡷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣘⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣶⡉⠳⢿⣼⠇⣾⢻⡆⣶⣿⣿⣫⢠⣤⡄⣝⢛⡻⣿⣯⣉⠁⠉⠈⠁⠙⠙⠋⠛⠓⢺⣿⣿⡇⠀⠃⠀⠐⠀⠀⠘⠀⠀⠀⠁⡀⢸⣷⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡬⠿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢸⣿⣶⣿⣼⡇⣿⢸⡟⠃⢸⣧⢤⣿⣼⡇⣿⣿⣿⣿⣷⣴⡶⣶⢀⣴⣤⡀⣼⢛⣛⢿⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣯⣯⡙⠿⠿⢿⡿⠿⢃⣷⣌⠹⣿⣿⣭⣷⣿⣟⠁⠀⠿⠷⠸⠇⣿⢰⣿⣛⣿⣿⡿⣿⣿⣯⣼⡏⣛⢣⣿⣿⣿⣿⢠⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⡿⢿⣟⣤⣄⣀⣠⣤⣽⣿⣿⡆⣿⣿⣿⣯⣿⣠⡆⣤⣄⠀⢀⣀⢠⡿⣶⣿⣿⣯⣧⣿⣿⣿⣿⣷⠟⠸⠿⢼⠿⣿⢸⣇⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⣿⣿⣿⣿⣧⣿⣿⣿⣧⣷⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⣷⣿⡄⠀⢸⡏⠘⣿⣿⣿⣷⣿⣟⣿⢹⡿⣿⣿⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣿⡸⠿⠆⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣇⣿⢘⡋⣿⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣷⣿⣯⣭⣿⣿⣏⠻⣺⣿⣿⣿⡅⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠐⠚⠿⣿⣿⣷⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⢀⡇⠈⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠶⠶⣶⣾⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣭⣭⣿⣤⣤⣤⢨⣭⣭⣭⣭⣭⣥⣥⣼⡿⢰⣿⣿⢈⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢀⣞⣯⣽⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣗⣸⣿⡇⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⣠⣭⠿⢿⣿⠇⠀⠀⠾⢶⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣯⣝⠻⣿⣷⠀⢈⣙⡻⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣤⣌⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⣿⣿⣦⠋⠀⠈⣿⣿⣿⣟⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⣿⣷⣆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣉⣉⠀⠀⠀⢛⣿⣿⣿⣀⣀⣰⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⡆⠀⠀⠈⡻⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⣿⡿⣨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⡿⠛⠂⠀⠀⢨⣽⣿⡏⠈⠁⠉⠈⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡦⡀⠀⣝⣿⡻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣀⣀⡀⠀⠁⡇⠀⠀⠀⠀⣼⣿⣿⣄⣡⣼⣶⣿⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣾⠿⣿⣿⣷⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠋⡀⣤⣤⣤⣦⣧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⢄⣉⣽⣿⣿⣿⣿⣿⣿ ⠙⠲⢷⣶⣿⡿⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠩⠭⠭⠉⠀⠀⠀⣼⣿⣿⣿⣿⣾⣟⣿⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⡿ ⠀⢛⣻⡿⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠖⠦⠀⠰⢻⣿⣴⠦⡀⠀⠀⠀⠻⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⢀⠀⣿⡇⠀⠀⠀⢸⣿⣿⠇⢸⡄⠀⠸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⢻⡇⠀⠀⠀⢸⣿⣿⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⡘⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⠈⡗⢇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠟⢛⠛⠛⢛⣛⣒⣋⣉⠀⠀⠀⠀⢁⠙⣿⠈⣿⣷⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⠃⠸⠀⠀⠿⠿⡟⠛⠛⢛⣛⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠁⠀⠀⢰⣇⠀⡟⠀⠈⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⠀⢸⣿⠀⠀⠀⢀⣤⣬⣱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠄⠀⠀⣿⠁⠀⠀⣾⣿⣿⣿⣷⣶⣶⣶⣿⡟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⡦⣾⣿⣦⣶⣦⣼⣿⣿⣿⣿⣶⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣏⠩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢤⣄⢰⣿⣿⣿⡛⠊⣙⣿⠛⠩⠁⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⡧⣿⣿⣿⡇⠈⡇⠉⢸⡇⠉⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠸⣿⣿⣿⣿⣿⡇⢀⣀⣀⣠⣤⣦⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠸⡇⡄⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⣽⣿⣿⣿⣿⣿⣷⣦⣴⣿⠀⠀⠰⠾⢿⣿⣿⣿⣷⡞⣿⣿⣿⣿⡟⣗⢸⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⢛⢺⠀⠀⡇⠀⠀⠅⣧⠀⠀⠀⠀⠀⢸⣿⣻⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢽⣿⣿⣿⣿⣿⣷⣶⣂⣴⠏⠀⠀⠀⠒⢶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣼⣷⣿⣿⢿⣿⣿⣿⡗⣿⢻⡿⢍⡟⣿⣿⡿⡏⠀⢸⠀⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠙⡩⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣆⡉⠛⠛⠿⠟⠃⠀⣀⠀⠀⠀⠀⣹⣿⣻⣿⣟⢙⣿⣛⣿⠿⠿⣃⣿⣺⡿⣿⢿⡗⣿⣿⣯⢺⣷⣾⣿⣟⡟⠀⠁⠀⢸⠀⠀⣅⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⢰⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣶⠙⠶⣄⣹⣼⠇⣾⢻⡆⣶⣿⣿⢛⢠⣥⡄⣔⢟⡻⣿⣷⠛⠓⠛⠊⠁⠙⠙⠋⠛⠓⢺⣿⣿⡇⠀⠇⠀⠠⠀⠀⠸⠀⠀⠀⠟⠀⢸⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⣾⣿⣿⣿⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠺⣿⣏⣶⣿⣼⡇⣿⢸⣟⠏⢸⣧⢠⣿⣼⡇⣿⣿⣿⣿⣷⣰⡶⣶⢀⣴⣦⡀⣼⢛⣛⣟⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣟⣫⡙⠻⢿⣿⣿⣿⡿⢋⣶⣄⠸⣿⣿⣯⣭⣤⣿⣿⡇⠀⠿⠷⠸⠏⣿⢰⣿⠿⣿⣿⣿⣿⣿⣯⣸⡇⣛⢣⣿⢾⣿⣿⢰⣿⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣕⣀⡀⢀⣀⣀⣿⣿⣿⡆⣿⣿⣿⡿⣯⣯⣡⡄⣤⣄⠀⢀⣀⢀⡿⣶⣿⣿⣯⣧⣿⣿⣿⣿⡷⠟⠸⢿⢾⢿⣿⢸⣇⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⡄⠀⢸⡏⠘⣿⣿⣿⣷⣿⣟⣿⢹⡿⣿⣿⣤⣄⠀⣀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣃⣿⡸⠿⠆⠀⣼⣧⢰⡿⣿⣿⣿⣿⣿⡟⣬⣵⣿⣾⣇⣿⢘⡋⣿⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣟⣿⠀⠀⠀⠀⠀⣷⣿⣯⣽⣿⣿⣟⢻⣸⣿⣿⣿⡁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡿⡇⣣⠑⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠷⢾⣿⣿⣧⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⡇⠀⠐⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣤⣤⣬⣿⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣯⣭⣿⣧⣤⣤⣤⢨⣭⣭⣭⣭⣭⣭⣤⣿⣧⣿⣿⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣭⡇⠀⠀⢶⣛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⢈⣙⣻⣿⣿⡇⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡛⢿⣿⣷⠀⠈⠓⣺⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣶⣌⡏⠀⠙⣛⣷⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⣦⡀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣍⣙⣋⠀⠀⠀⠹⣿⣿⣿⣀⡀⣀⣾⣆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ 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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 3693 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Over_at_Tux_Machines.shtml Gemini version at https://techrights.org/n/2024/12/05/Over_at_Tux_Machines.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux news for the past day⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Snowy_Fountain⦈_ ⚓ Updated This Past Day⠀⇛ 1. ⚓ FreeBSD_14.2-RELEASE_Announcement⠀⇛ The FreeBSD Release Engineering Team is pleased to announce the availability of FreeBSD 14.2-RELEASE ⚓ New⠀⇛ 2. ⚓ In_The_Chair_|_CENSOR*ED⠀⇛ How our schools are ruled by fear and BigTech decides what kids can learn 3. ⚓ Red_Hat_Leftovers⠀⇛ latest in redhat.com 4. ⚓ Web_Browsers,_Mozilla,_and_Tor⠀⇛ Some Web related or Net links 5. ⚓ Programming_Leftovers⠀⇛ R, Python, and more 6. ⚓ Security_and_Windows_TCO⠀⇛ Windows TCO for the most part 7. ⚓ today's_howtos⠀⇛ many howtos for this day 8. ⚓ Open_Hardware:_ESP32,_Arduino,_Raspberry_Pi,_and_More⠀⇛ some hardware picks 9. ⚓ This_Is_the_Default_Theme_of_Debian_GNU/Linux_13_“Trixie”⠀⇛ The Debian Project unveiled today the default theme of the next major Debian operating system release, Debian GNU/Linux 13 “Trixie,” made by Elise Couper. 10. ⚓ 10_Ways_To_Harden_Your_Linux_Containers_Against_Attacks⠀⇛ Learn practical strategies for protecting containerized applications on Linux 11. ⚓ The_best_way_to_make_a_decision_is_to_decide⠀⇛ Making decisions in an open source community is hard 12. ⚓ "Ceratopsian"_will_be_the_default_theme_for_Debian_13⠀⇛ The theme "Ceratopsian" by Elise Couper has been selected as the default theme for Debian 13 "trixie" 13. ⚓ Games:_The_best_GNU/Linux_distribution_for_gaming_in_2025_and_many gaming_news⠀⇛ Latest from GamingOnLinux 14. ⚓ Android_Leftovers⠀⇛ Xiaomi 15 and 15 Pro are the most popular newly launched Android flagships 15. ⚓ Free_Software_Supporter⠀⇛ ⚓ New⠀⇛ Issue 200, December 2024 Welcome to the Free Software Supporter, the Free Software Foundation's (FSF) monthly news digest and action update 16. ⚓ The_Licensing_and_Compliance_Team_is_fighting_for_freedom_and_we_need your_help⠀⇛ The Licensing and Compliance Lab has been diligently serving the free software community 17. ⚓ RustDesk_1.3.3_Introduces_Mobile_Clipboard_Support⠀⇛ RustDesk 1.3.3 open-source remote desktop adds mobile clipboard 18. ⚓ December_Steam_Client_Update_Enhances_Game_Recording⠀⇛ December Steam Client Update 19. ⚓ Lernstick_–_secure_and_mobile_learning_and_working_environment⠀⇛ Lernstick offers secure and mobile learning and working environment so that private devices can also be used for school purposes 20. ⚓ Dolphin_Emulator_Will_Get_Faster_Updates_on_Linux_With_Flatpak⠀⇛ Dolphin now maintains official Flatpak repositories, making it far easier for Linux gamers to install and run the latest versions of the Dolphin emulator 21. ⚓ Best_Free_and_Open_Source_Software⠀⇛ Kobold aims to offer easy declarative web interfaces 22. ⚓ Br_OS_–_Brazilian_Linux_distribution⠀⇛ Br OS is a Brazilian Linux distribution based on Kubuntu, sporting the KDE Plasma desktop 23. ⚓ SUSE_Renames_Several_Products_for_Better_Name_Recognition⠀⇛ SUSE has been a very powerful player in the European market, but it knows it must branch out to gain serious traction. Will a name change do the trick 24. ⚓ You_can_test_all_the_best_Linux_distros_right_in_your_web_browser_with this_site⠀⇛ If you've ever wanted to see what Linux was all about but didn't want to go through the steps of installing it 25. ⚓ openSUSE_Empowers_Creative_Professionals⠀⇛ For many creatives, Photoshop is the go-to application for photo editing and graphic design 26. ⚓ Fedora_Linux_Flatpak_cool_apps_to_try_for_December⠀⇛ This article introduces projects available in Flathub with installation instructions 27. ⚓ Today_in_Techrights⠀⇛ Some of the latest articles ========================================================================= The corresponding text-only bulletin for Wednesday contains all the text. 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This is why we're suing [1, 2] (tomorrow will be exactly 3 months since we filed our lawsuits). 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Dude_it's_still_cheaper_than_what_this_lousy_lawyer_charges for_one_hour⦈_ SFC and its associates aren't nice people. Sometimes they act more like Internet trolls and they defame a lot of people, even this week. Support the FSF (the real thing), not_the_SFC. This_is_the_article_they_claim_to_be "defamatory", but all the statements there are true and supported by strong evidence. █ ⣤⣤⣘⣃⣨⣿⡁⢘⡟⠀⠀⠇⢸⡇⠀⣿⡇⢿⣿⠀⣿⢸⣿⢰⣾⠅⢻⡶⠀⣀⠀⣀⣀⡀⣀⢠⡅⣸⡇⢰⡆⣄⢀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣗⣪⣔⡀⠉⠙⣛⣡⣼⣷⣤⣀⡄ ⠉⠙⠛⠛⠻⣿⣿⣿⣿⢦⣤⣀⣀⡀⣄⣬⢥⢬⣡⡴⠟⢲⡶⣶⠺⢾⣟⢺⠸⣿⡋⣿⠙⣇⣿⠸⡇⠋⠥⡜⡻⠿⣾⣧⣟⣶⣠⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣴⣦⠆⢉⡩⣭⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⡟⠀⣮⣿⢹⡟⣇⣿⣿⢸⣾⡇⣿⡃⢸⡇⣿⠈⠰⠿⠇⠘⠿⠇⠛⢢⢛⡟⣻⠛⠡⠶⢁⣄⣀⠀⢐⠘⠭⠟⠻⠿⢷⣿⣴⠖⠖⣿⣷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣾⣷⡄⠀⠲⢾ ⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠘⠛⠋⠙⠋⠈⠉⠁⣉⣁⠀⣀⣀⣬⢩⣶⣤⡤⣦⣶⠐⣦⣶⣸⣿⣿⡇⣿⣯⢹⡏⢸⡇⣶⢠⡆⣤⡨⣈⠀⣺⣤⣤⣉⣭⣿⣛⢿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠐⠒⡿⠚⠛⠒⣶⣶ ⠀⠀⠀⠀⠀⠀⣠⢦⣰⣶⡆⣶⡂⣿⡇⣿⣿⢻⣅⣿⢿⠀⢸⡇⢻⢾⣿⣯⣇⣿⣿⠀⢻⡟⣿⢿⠏⠧⠿⡻⠸⠃⠈⠃⠻⠸⠇⢿⡇⡷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣛⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⢻⣨⡼⡏⣿⣿⣥⡷⠿⠿⠀⠸⠷⠛⠘⡇⠘⠃⠘⠉⠉⢁⡉⢉⣀⢀⣀⡀⣤⣤⣤⢥⠬⣿⢷⠙⠿⠷⢶⣶⣤⣤⣁⣁⣩⣿⣔⣽⡟⠘⣿⣿⣿⣿⣿⣿⡇⣸⣿⣶⣷⣶⣶⣤⣄⣸⣃⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⣄⠈⢉⣀⣀⣀⡀⣄⣠⣤⠀⣤⠀⣶⣦⢶⢰⣴⣟⡊⣷⡇⠸⡇⢸⣿⡾⣿⣿⣿⠸⡏⢸⣟⢻⣹⡆⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣿⣿⠃⠀⠈⠙⠛⠻⣉⠛⢛⠿⢿⣿⣿⣿⣿⡯⠩⠝⣻⣿⣿⣿⣀⡀ ⡇⠀⠀⠀⠑⡈⠀⠈⣿⢸⡿⡇⣿⢙⢷⡄⢸⣄⣿⣿⢸⣾⠗⣮⠷⠸⠇⠀⠿⠚⠋⠓⠛⠙⠋⠀⠉⠈⣉⢀⡀⣀⣀⣄⢠⢥⠈⠘⠀⠀⠘⣂⣻⡿⠀⠀⠀⠀⠀⢀⣛⠀⠠⠤⠆⠸⡿⠿⠻⠃⠀⠀⢸⡷⠀⢰⣿⣷ ⠃⠀⠀⠀⠀⠒⠀⠀⠛⠘⠃⠛⠉⠈⠉⠁⣈⢁⣈⠀⢀⣤⣠⣤⢠⣬⡌⢠⡶⣆⣶⣶⢸⣟⠀⣿⣿⢸⣿⡏⣇⣿⢻⢾⡄⣶⢤⣦⣤⡤⠥⠻⠋⠀⠀⠀⠀⢀⡄⣤⣄⡙⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⢸⣇⣀⡺⠻⣿ ⣤⣤⣤⢀⡴⣤⣶⢲⣰⣶⡔⣟⡷⣾⣙⣸⣯⠸⣮⡁⢸⡷⢿⢸⣿⡟⣇⠸⣇⡷⣿⢿⡼⠧⠀⠿⠸⠞⠛⠃⠛⠛⠘⠛⠁⠿⠻⣿⣿⢿⣍⣁⡀⢀⠀⠀⢀⣼⡇⣸⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠈⢡⢉⢩⣉⣛ ⠉⠉⠉⠈⣧⣭⢻⢹⣿⡿⡧⡿⠿⠹⠼⠟⠷⣞⡛⡧⡜⡧⠈⠉⠡⣥⣿⣶⣦⣤⣤⣤⣤⣤⣀⣀⢻⣿⠛⠛⠿⠶⠶⠶⠶⠶⠶⣿⣿⠋⢡⣶⣷⠾⣧⣾⠿⠿⠟⠯⢽⣿⣿⣿⣿⣿⡇⠀⢖⣄⡀⡀⠀⠀⠀⠀⠊⢉ ⠀⠀⠀⠀⢈⡁⠀⢀⡀⠀⢀⠀⠀⡀⠀⠀⢟⣵⣤⠁⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡉⢘⠛⡀⠀⠆⠀⠀⠀⢰⡦⠀⢿⣿⣀⣾⣿⣿⣶⡀⠀⠀⢀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣷⡃⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠘⠃⠀⠈⠃⠀⠘⠀⠀⠃⠀⠀⢷⣭⣭⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⡧⡇⢸⣶⣷⣿⣼⣧⣄⡀⠀⠀⠀⢸⠇⠸⢉⣰⣿⣿⣿⣿⣿⣷⣦⣶⣿⣶⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣛⠛⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠓⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠻⡟⣿⣿⣿⡏⡗⠀⠀⠻⢸⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣾⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠁⠟ ⠀⠀⠀⠀⠀⣤⡄⢠⣤⣄⢠⣤⡀⣤⣄⢀⣤⡄⣠⣄⣠⡄⠀⡀⠀⢠⣦⢠⣦⣦⢰⣶⣶⢶⣶⣿⣿⣿⣿⠺⠿⠀⠀⠀⠤⠀⠀⣿⣶⣤⢀⣘⣿⣿⣿⣉⣁⡌⢀⠰⢏⣤⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢫⡝⡇⣻⡟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠃⠀⠘⠋⠈⣉⣉⠀⣉⣉⢨⡭⠛⠟⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⡿⠟⠃⠈⠉⠉⢿⣿⣿⣿⣶⡔⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠒⠚⠋ ⠀⠀⠀⠀⠽⣧⡇⠸⠷⠿⠺⠷⠏⠿⠿⠸⠿⠟⠻⠟⠛⠃⠀⠀⠀⠈⠉⠈⠉⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⡀⠀ ⣀⣀⣀⡀⢀⣀⣀⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠾⠿⠿⠿⠟⠛⠛⠛⠛⠋⡉⢉⣦⣀⣦⣠⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⡆⢠⡀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣿⡿⠁⢿⡆ ⠿⠿⠟⠛⠚⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⣀⢠⡄⡄⢰⠀⠀⠀⠘⠁⢻⣛⣛⣛⣯⣍⡿⠺⣿⣦⠀⠀⠀⣈⣩⢁⣀⣐⣚⣧⣤⣿⣾⣿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠖⠚⣭⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⢈⣁⣁⢨⡄⠀⠀⠴⠄⣼⣿⣿⣿⠿⠃⢠⣤⣤⣾⣿⣿⣿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⡿⠛⠁⣤⠤⣴⠷⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠘⡉⣡⣠⣶⡆⠀⠀⠀⠀⢀⡠⠚⠛⢀⠀⠉⠀⠈⠉⠋⠀⡁⠀⠀⠀⠀⢠⡤⡤⠀⠐⠲⢶⣶⠿⠟⢉⣴⣿⣿⣿⣿⣿⣿⠇⠀⢠⣇⢰⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⡀⠀⠀⠀⠀⢸⠀⠀⠂⢸⣿⣿⣝⣽⣷⣤⣤⣖⣨⣵⣶⠀⠠⠿⢦⠀⠀⠀⠀⣾⣭⠁⠀⠀⠀⠂⢰⣶⠀⠀⠀⠀⠀⡀⠀⠀⠛⠛⠛⠛⠉⠉⠩⠁⠀⠴⠿⣿⣿⣿⣿⣤⣀ ⢤⠀⠀⠀⠀⢽⣿⡇⠀⠀⠀⠀⠀⠉⡙⠀⠀⠀⡀⢀⣸⠤⠄⢢⣿⣿⣿⠛⠻⣿⡾⣍⣿⣿⣿⣿⠀⢀⣰⣤⣵⣾⣿⣷⣿⡿⣿⣻⣟⣀⠾⠐⠂⠀⠀⢀⠀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣿⣿⣶⣶⣶⣭⣭⣭ ⢘⠀⠀⠀⠀⢦⣴⡆⢀⣀⣠⣤⠄⢤⣷⢯⣯⣯⣅⣈⣩⣷⣾⣿⣿⣯⣧⣶⣿⣿⣾⣿⣿⣼⣿⣿⠠⣾⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⢧⡀⣄⠂⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠀⢀⣀⣀⣈⣉⣹⣿⣿⣿⣷⣶⠶⣶⣿⣿⣿⣿⣵⣾⣯⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣼⣿⣿⣿⡄⠹⡿⠛⠉⠉⠘⣿⣯⣤⣝⢿⣿⣭⢙⠛⣟⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⣾⣿⡋⣯⠿⣿⣻⠾⣒⣾⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢞⣿⣻⡯⠟⠿⣿⢻⡿⢿⣶⣴⠂⠁⠀⠀⢀⡀⠔⢪⡟⠉⠉⢿⡿⣿⢲⣦⠠⠄⠀⣸⠇⠀⠀⠀⠀⠀⢀⡀⢠⣤⣀⠀⡇⢠⣬⣭⣉⣙⣛⠛⠁ ⠿⠛⠛⠉⠁⠀⣸⠿⢻⣾⣿⣿⣋⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⠀⠘⣛⠋⢡⣽⣷⣿⣴⢶⡒⡈⠁⢂⣀⣈⠀⣦⣤⣜⣛⠻⣿⡽⠇⠀⠀⡿⠀⠀⠀⠀⠀⢀⠀⠈⠻⠿⢋⢻⠇⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⠠⠔⠊⣵⣶⣤⣸⣾⣿⣿⣽⣿⣿⣿⢿⣿⣿⡟⠙⣿⣿⠿⠷⣈⣹⣽⣷⣾⣿⣿⣿⡥⣟⢛⣿⣄⣬⢸⠇⠀⣀⣉⣻⠀⡯⠋⠿⠻⢦⣾⡤⠀⠀⢰⡇⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀⢾⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠀⠀⠀⣈⣿⣾⣿⡿⡽⣿⣿⣝⠿⢿⣧⣭⣽⣶⣶⣶⣿⣿⡿⠌⠻⣿⣿⣿⠯⢻⠍⢃⡈⣛⠁⠉⠁⠀⣤⣿⣧⠍⣉⡅⢠⡤⣤⣠⡀⠾⣿⢳⠔⠂⣾⠀⠀⠀⠀⡇⠀⠀⢐⠓⠓⢩⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡀⠰⢦⣾⣿⣿⡿⡭⣾⣿⡿⠀⡀⢹⣿⡿⠿⢻⣿⣿⣿⣿⡬⠖⠿⠏⠈⠀⠀⢀⣽⢿⣮⡻⠀⢴⣼⡟⡹⠋⣙⣹⠆⠌⢁⡀⠝⢻⣭⡀⡢⠀⢠⡇⠀⠀⠀⢸⠇⠀⠀⠉⠀⠀⣼⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣅⡀⡆⠈⠙⢿⡇⣿⣿⣿⣇⣤⣿⣾⣇⠀⢀⡾⢿⣛⣿⠀⠲⡷⣶⠀⠀⠀⠀⡨⣿⣍⠟⠁⠹⣿⣷⠞⣵⣶⣶⣶⣶⣾⣦⢀⣀⡱⠂⢑⣀⣤⣸⠁⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣿⣿⣧⣕⣐⡀⠉⠉⠛⠛⠿⠿ ⠀⠈⠇⠁⠀⠄⡇⠇⠈⡟⠿⣿⣯⣟⣽⠿⠛⣿⣷⡃⣀⠈⠻⠀⣾⣧⢸⠁⠘⠻⣿⡿⠀⠂⢀⣼⣳⣌⠡⢘⣯⠟⠉⠁⠉⠿⢽⣿⢟⢛⣾⣿⣿⡷⡋⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄ ⠁⠀⠀⡂⠀⠁⠀⠀⠈⠁⡤⣮⣌⡉⠚⠱⢰⡿⣽⣿⠆⢰⣶⣦⡈⣡⣤⣄⠀⠷⠘⣥⣶⣶⠜⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⣏⢓⣾⡿⣷⡿⢥⣶⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⠁⠀⠀⠀⠀⠀⠃⣦⣿⣿⡧⠀⠀⠘⠵⠏⡫⠀⣸⡏⣿⠛⣹⡇⣿⣠⣶⣿⣿⣽⡟⢀⣀⠐⠼⢟⣶⣴⣿⣿⣆⠀⠙⠛⣧⡿⣟⢶⣿⡇⣿⣿⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢃⡀⠸⠀⠀⠀⠀⡄⠦⠴⠉⠉⣀⠬⠭⣀⡄⣴⣴⡷⡄⠀⠀⣁⢤⡓⣨⣅⠡⡾⠀⠀⠀⢀⣾⣲⠁⠸⣿⣿⠟⠿⣿⠻⣐⡶⡛⢟⢳⢿⣼⣿⡱⣿⣿⠀⠀⠀⣼⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⣠⡄⠀⠣⢠⠤⠉⠀⠀⠀⠚⣿⣿⣿⠇⢾⣿⡿⠐⢮⣳⡟⠿⡿⠿⠽⠀⣰⣾⣧⣀⣀⢙⣮⣶⣦⠄⢻⣿⣥⣴⣷⣿⡧⠑⠀⢋⢦⣿⡏⢤⣿⣿⡄⠀⠀⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣤⠄⠻⠄⠀⠀⠴⢠⠢⣠⡀⣰⣿⣿⣿⠊⠁⣰⡺⠽⠘⣷⡴⠬⠄⠴⠂⠀⠩⠏⢁⣻⢿⡿⠋⠙⠟⠠⠛⠛⠛⣛⡵⡉⠁⢿⢯⣨⠽⣿⠃⣼⣿⣿⠁⠀⢀⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢛⠿⠀⠀⠀⡀⠼⠆⠘⠳⠚⠀⠟⣿⣿⣿⡆⢀⣾⡋⢴⠀⢠⣤⣴⣶⣶⣦⡦⣲⣿⠆⠘⣛⠁⠀⠀⠘⠟⠷⠁⠀⠘⢹⡇⠈⣈⠬⣨⣷⡋⢀⡿⠟⠉⠀⠀⠘⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⠰⡆⠀⣼⠁⠓⢁⢠⠀⠀⠀⠹⠿⡿⠋⠁⠨⠹⠖⣽⣀⢿⡟⠋⡭⠈⣿⣇⣿⠗⠃⣰⠹⠀⣀⣀⣀⣤⣦⠴⢄⡀⡼⡘⢺⣫⣥⣤⣭⡆⠸⠀⡀⠀⠀⠀⣀⣼⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣄⡠⡾⢒⣽⣿⠝⠀⠀⡁⠀⣿⣷⣿⡷⠄⢲⠼⠓⠀⣙⡁⣌⣅⣄⣤⢸⣿⣳⢠⡄⢒⠈⣟⢿⡟⡻⠛⠋⡼⢢⣴⣶⣷⣿⣿⣿⣯⣧⠀⢀⣠⣴⣾⣿⣿⣿⡟⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣆⡝⠹⢿⡆⣿⣿⣿⠨⠿⡿⠿⠲⣰⣾⣖⠀⠈⣿⣿⡿⢛⠻⣿⣈⣿⡽⢾⠳⡍⢰⣑⡅⣠⡼⣟⡭⢒⣉⣠⣙⠻⣿⣿⣿⡟⣷⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣶⣦⠰⠸⣿⣿⢈⠀⢁⣴⣾⡿⣻⡏⠁⠠⠋⣵⡰⢾⣛⡿⣿⣲⠯⣩⣤⣶⣤⡛⣃⠽⢚⣩⣶⣿⣿⣿⣯⣙⠮⡙⠿⣧⢽⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠋⣐⣜⣻⡮⣾⣿⣿⠿⢟⣉⣤⣺⣯⣟⣿⣽⣿⣾⣿⣿⣿⣿⣿⡿⣛⣵⢮⣣⣴⣿⣿⣿⣿⡿⣟⣻⣯⣶⣌⠀⠘⠹⠿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠉⢀⣴⣿⣿⣯⠬⣟⣿⠿⣭⣟⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⡿⣻⣵⣾⣾⣷⣿⣿⢿⣟⣿⣽⣶⣿⣿⣿⣿⣿⣿⣇⠢⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠼⣫⣵⣿⣿⣿⢿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠁⣠⣾⣄⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⣠⣴⡿⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿ ⣿⣿⣄⠙⢿⠿⠁⠀⠀⠀⠈⠻⣿⣿⢿⠋⠁⠀⠀⠀⠀⣠⣴⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣬⣙⡛⠿⣿⣿⠿⠿⠿⢿⣿⣿⣿ ⣿⣿⣿⣧⡄⠀⠀⠀⠠⣄⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⣶⣤⣀⣈⣀⠒⠨⡙⢿ ䷩ 𝚕𝚒𝚗𝚎 4091 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Has_Asked_a_Blogger_to_Delete_.shtml Gemini version at https://techrights.org/n/2024/12/05/Software_Freedom_Conservancy_SFC_Has_Asked_a_Blogger_to_Delete_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Software Freedom Conservancy (SFC) Has Asked a Blogger to Delete This Page About the SFC, So We Reproduce It in Full Here⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Winter_Tree_and_Snow⦈_ Censored article (after pressure from SFC): § Repairability Isn't Enough: Why I'm No Longer Supporting Software Freedom Conservancy⠀➾ ⚓ Sat, 30 Nov 2024⠀⇛ This is a copy of a letter I sent to the Software Freedom Conservancy. Dear Software Freedom Conservancy, I am writing to express my disappointment and concern over your promotion of the OpenWrt One. It is disheartening that OpenWrt would develop a device that requires proprietary software for its WiFi functionality, though not surprising - this suggests they do not view software freedom as an ethical imperative. However, what truly let me down was seeing the Conservancy support the announcement without addressing this critical issue. Instead, the focus was on GPL compliance and "repairability." I've noticed a shift in Conservancy's messaging, tying software freedom to "repairability." This approach is concerning. Richard Stallman didn't launch the GNU project because UNIX was "broken" or needed to be "fixed." He recognized proprietary software as an ethical and moral problem - it subjugated users. Similarly, the primary reason to reject proprietary software today isn't because we can't "repair" it but because it denies us our freedom. What good is "repairability" if the software controlling the device isn't ours? How can we celebrate GPL compliance when the four freedoms are not upheld for every piece of software the device requires? Software freedom must be a foundational principle in hardware design, not a secondary consideration. Anything less is a compromise we cannot afford. This announcement has led me to rethink my support for the Conservancy. It seems the organization is veering away from a path of complete software freedom, instead treating "repairability" - essentially freedom #1 - as if it were sufficient on its own. But we need all four freedoms to ensure genuine software freedom, not just the ability to "repair." As a result, I have decided not to renew my membership. I hope Conservancy can return to advocating for software freedom as a matter of ethics without compromises or dilutions. █ ⢳⣿⣾⣿⠿⢸⣷⢡⣾⢻⡗⢁⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣏⠆⡸⡿⣿⣩⢛⣡⣾⡄⠸⠿⠻⠷⡾⢋⣽⡿⢪⣴⣿⣿⣿⣿⣿⣿⣿⣯⠃⡀⠀⣿⣷⠆⣀⠀⠈⠑⠉⢹⢿⡟⢁⣝⣻⣭ ⣹⣿⣿⣷⣎⢸⡿⢾⣿⠃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣫⡜⣇⠘⢂⡴⠿⠆⢈⠅⢰⢶⣶⣆⢄⠉⠛⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡇⠀⢋⣠⣾⣿⣶⣦⣀⠀⠀⠀⠠⣿⡻⢿⣹ ⣿⣿⣿⣿⣿⣯⡇⣿⠇⢸⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡛⡑⢟⡷⢙⠀⠻⣧⢄⣈⡘⠀⠆⣴⣦⢙⣠⣿⣿⣶⡄⠹⣿⣿⣍⠛⣿⣿⣿⡏⠈⣁⠀⠘⣿⣿⣿⣿⣿⣿⣷⡄⡀⠀⠈⠻⠾⣿ ⣿⣿⠿⣿⣟⣙⣧⡌⠄⢸⣿⠀⠹⣿⣼⣿⣿⣿⣿⣿⣿⣟⣽⢿⣞⡿⣾⣏⣼⡿⠽⠿⢿⣴⡞⡃⢰⣄⠹⢿⣿⢲⣶⡂⣅⢸⣯⣿⣿⣿⣿⣶⠦⣤⢈⣉⠛⠻⢿⣁⣺⠿⠇⠀⠻⣿⣿⣿⣿⣿⠟⣀⢿⣖⡀⠀⠀⠀ ⠻⠿⣿⣿⣿⣯⣻⣶⢧⡀⠻⠀⣶⠐⣿⣿⡿⠿⠿⣿⣿⣿⢿⣾⢿⣿⡇⣷⣾⣷⡶⣶⣾⣿⣿⣋⡸⣿⣦⡠⣉⠰⠍⣽⣮⡁⣯⣽⣭⣭⣯⣶⡞⣵⣿⡿⠋⣠⣦⡌⠙⠚⠷⡄⠀⠿⢿⢿⣿⠏⣼⣫⣫⢜⡿⢷⣆⠀ ⣶⣶⣍⡛⠿⣿⣿⣿⣿⣿⣦⠀⣻⣷⡘⢿⣿⣿⣿⣷⣶⡟⣼⣶⣦⣝⣰⢿⣽⣿⣿⣿⣿⣯⣾⣇⢙⣿⣿⣷⠘⠀⢠⡙⠿⣿⠼⣿⣿⣿⡾⢋⣼⡿⢋⣠⣾⣿⢟⡴⠿⢻⢆⡀⠀⢤⠀⠻⠃⣾⣟⣽⡿⣿⠿⠛⣉⣷ ⠻⣿⣿⣿⣶⣤⡉⠛⠿⢿⣿⡄⢻⣟⠛⣈⢻⣷⣬⡻⢯⣿⣿⣝⠿⣿⣿⣿⣷⣾⣿⣿⣻⡿⣿⣿⣿⠛⣿⣯⠸⢡⣿⣽⣦⡈⠣⢻⣿⣿⣾⠟⢋⣤⣁⣨⣍⣽⣶⣶⢖⠴⣿⣿⢿⣿⣦⡀⠘⠻⣿⣿⠟⢋⣤⣾⣿⣿ ⣷⣌⠻⣿⣿⣿⣿⣷⣦⣶⣤⣁⠘⣿⡟⣛⡦⠛⣟⣿⣿⣟⣿⡟⢴⡿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⢿⡿⣻⡟⠁⢸⣝⣿⣿⣿⣦⠈⠿⠋⠀⠴⠿⠛⠛⡉⣤⣤⢆⡴⣃⣶⣿⣿⣷⣶⣶⠆⡦⠀⠑⢼⣀⢳⣶⣿⣧⣴ ⣿⣿⣷⣌⠻⣿⣿⣿⣿⣟⣶⠈⡄⢙⠷⣿⢃⡀⠙⣿⣿⢣⣟⣻⣿⣿⣶⣟⣻⣿⣿⣯⣟⢿⢟⢛⣾⠆⢰⠃⠀⣾⣿⣿⡯⠋⠉⠂⣠⣮⡤⠴⠶⡈⢙⣛⣛⣉⣸⣿⣿⣿⣿⡿⠿⣡⠄⣼⣶⣾⣆⠈⢿⣷⣏⣐⠿⣿ ⣿⣿⣟⣿⣶⣌⠻⢿⣿⢯⣿⡆⠁⢸⡟⢶⢆⣑⣢⢶⣿⣿⣿⣿⣷⣿⣿⣿⣟⣻⣏⡙⢿⣻⡿⣩⣿⣷⡄⠘⢠⣯⠍⢛⣥⡶⠁⡼⣵⣶⣾⣿⣿⣿⣦⡙⣿⣿⣿⣹⡿⠛⢁⣠⡆⣋⣼⣿⣿⣿⣿⡆⠈⠻⣟⣿⣷⣿ ⣿⣿⣿⣿⣿⣿⡄⡀⠲⢞⣏⡅⢸⡄⢸⣧⡝⢿⣿⡇⠹⣦⠙⣿⣿⣿⣿⣿⣻⣿⣿⣿⣦⡝⢣⣿⣿⣿⠃⠀⣈⣴⣾⣿⡋⠀⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣦⡙⠏⠁⠐⢀⢙⡻⣿⣭⣤⣄⣉⣉⠉⣉⠙⢀⡈⠙⠟⠛ ⣿⣿⣿⣿⣿⣿⣿⡼⣷⣌⠹⣇⣸⡇⢸⣿⡷⠸⠂⣚⢂⠘⢤⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⡀⠸⣏⡙⠋⣼⠃⣼⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⣠⣤⣦⣒⣛⢿⣿⣷⠈⣻⣟⣿⣿⣿⣷⣿⢛⣯⢿⣶⣦⠀ ⣿⣿⣿⠿⠿⣅⣋⣀⢶⣶⣷⠈⠻⠿⠆⢁⠠⣤⡉⠍⠉⣉⠚⢛⣛⡋⠺⠿⢿⣿⣿⣿⣿⢃⣿⢿⣿⣅⠸⢆⢉⡰⣶⠃⡼⠻⠿⠿⠿⠟⢋⡠⢀⣠⣶⣾⣿⣿⣿⡿⠟⣿⣶⣝⣻⣾⣿⣿⣿⣿⡿⢹⣿⣿⡾⢯⣤⣾ ⣿⣉⣓⣚⠛⢛⣛⠛⠚⠛⣇⡛⢰⡀⠲⡈⢻⣿⠿⡿⢡⣿⠈⣿⣿⣿⠯⣙⠳⣮⣭⣛⠿⣾⢧⣿⠥⠄⠀⠳⠧⠈⠁⣸⣤⡄⠀⣠⣤⣾⣶⣿⣿⣿⣿⣿⡿⣛⣭⣽⣿⣶⣔⣾⣿⣿⣝⢿⣿⣿⣷⡸⢋⣠⣾⣿⣿⣿ ⣟⡋⠉⢹⠻⣽⣿⣿⣟⣷⣦⠁⣸⠳⣀⡌⠘⣿⣿⠃⣾⣿⠺⣿⣿⣿⣷⢙⢒⣻⡾⣭⢴⠆⡈⠛⢀⡀⢀⣠⣤⡇⠀⢋⡥⢠⠾⢟⣛⣿⣯⡭⢋⣡⣴⣶⣼⣭⣿⣯⣿⣿⣯⣿⣿⣿⣿⣷⣽⠛⢁⣴⣾⢻⣿⡾⠟⣋ ⣭⣄⣹⠆⠰⡄⣽⣗⢘⡩⣍⠀⣭⣩⣭⣁⠁⠘⠛⠦⠿⠯⠿⠟⠿⠟⠋⢼⣟⣫⣴⠞⢸⣿⡮⠑⢸⡇⢢⣽⠛⢲⣿⣦⢁⣏⡛⢻⣿⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣥⣶⣿⡟⢟⡉⢹⣿⣿⣿ ⠤⣤⣴⣤⣈⢹⢿⣏⡛⠻⠇⢠⣧⣸⡉⠁⠀⠀⠘⢿⠂⠒⢴⣿⣶⣾⡙⠲⢿⣿⡿⢚⣹⢟⡇⡀⣰⣯⡹⣏⣠⣧⣽⡿⡇⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣠⣾⣿⠟⣡⣴⡎⡁⠻⡿⣿⣿ ⢀⣶⣦⡭⣉⣁⡀⡽⢫⣴⡄⠀⠻⣥⣀⣈⡀⠀⠙⣦⡍⢳⣖⣠⣍⣙⠃⣸⣷⢦⣤⣿⣿⢣⠑⢿⣏⠸⠃⣨⡻⣿⣿⣿⣦⡘⡛⠿⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⡿⠏⣾⣿⢻⣿⣷⣦⢨⡿⠿ ⣉⣉⡉⢱⣇⣽⣤⣽⡆⣤⡀⠓⠀⠘⢿⣿⣿⣄⠀⠘⠃⢸⣿⣿⡿⠿⠃⡷⠦⠈⠛⠿⠿⡏⠀⠠⡿⣥⣴⣿⣷⣾⣝⣿⣿⣧⢿⣯⡕⡾⠾⠛⡛⢿⣿⣿⣿⣿⠿⠛⠋⠠⠾⠛⠋⢉⣤⣴⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⡁⡙⣻⠲⣿⣿⣧⡽⠿⣽⣟⣿⣷⣦⡀⠀⢩⡉⣁⠂⠀⢸⣦⣶⣶⣶⠀⡿⢸⣿⣿⡶⠀⠁⠀⠀⢳⣿⣿⣿⣿⣿⣿⣷⣿⣿⡆⢻⣷⢹⣿⣶⣿⡶⠛⠉⠁⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠈⠛⠛⠼⠾⣅⣉⣳⣿⣿⢟⣩⣾⣿⡆⣀⠈⠛⠧⣀⠀⣯⣭⣭⣍⣀⠓⢼⣿⡿⣷⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣎⣷⣬⣿⣿⣁⠘⠋⣀⠐⠚⠃⣾⣿⣿⣶⣤⣈⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣟⡻⡿⠂⣶⣼⠿⠏⡿⠦⠽⢿⣿⡟⢰⣛⣧⡄⢤⡀⠀⠹⣿⣿⣿⣿⡇⣬⡙⢷⣿⡇⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠉⠻⣿⡟⣓⣚⣭⣴⣤⣷⣶⣶⣶⣦⣼⣿⣏⣛⠻⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⣿⠛⢁⣀⣤⣾⣄⣸⣤⣤⡑⠈⢹⡃⣾⣿⣿⣿⣿⠅⠀⢀⠘⢿⣽⣿⠁⣿⣿⣤⡙⠃⠀⠀⠈⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⢸⣅⡈⠙⠻⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⡙⢛⢿⣿⣿⣿⣿⣿ ⣰⣾⠳⣿⣯⣿⠖⣷⢦⢻⣥⣿⡄⠘⠂⣿⣷⣿⣿⣿⠄⠀⢸⣷⡀⠹⣿⢈⣿⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠙⠻⢿⡿⢺⣿⣿⣷⣦⠈⠻⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣞⣏⠙⣶⣯⣿⠛ ⡿⠏⢰⣯⣭⣿⣿⣿⣿⢿⣿⣿⣷⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣦⡈⠱⢺⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⡏⣼⣆⠀⢿⣟⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⣏⠟⣡⣾ ⣦⣘⡻⠿⢿⣿⣿⣿⣿⠀⣿⣿⣿⠇⠀⠾⣿⣯⣻⠃⠀⠀⣼⣿⣿⡿⣱⣆⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⢠⡖⣀⣤⣤⣭⣍⣉⣉⠈⠛⢛⡛⠛⠛⠛⠓⠿⠿⠷⠄⣻⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿ ⡿⣿⡿⢛⣟⢻⣿⣿⣯⡀⠉⣿⣶⡆⣀⠀⠸⣿⠿⠂⠀⣐⣿⣿⣿⡇⣿⣿⣷⡀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⠀⠐⢍⢿⣿⡟⣸⣿⣿⣶⣶⣄⢈⡙⠻⠿⠿⠛⠛⠉⣻⣿⣿⣿⣿⡟⢠⣿⣿⣿ ⣄⣻⣾⣿⣿⣿⣿⣿⣿⡃⠰⣜⠏⣸⡿⠷⠀⠀⠀⠀⠲⣿⣿⣿⣿⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣝⢿⣿⣿⣟⣾⣿⣿⣿⠀⢷⣄⠑⢮⣙⢿⣿⣿⣿⣿⣿⣯⢦⣦⡐⢾⣿⣿⣷⣹⣦⡙⢿⡿⢡⣿⣿⣿⣿ ⣉⣿⣟⡿⠛⠿⠿⣿⠼⠿⠿⠋⠀⣀⢠⣤⣶⠂⠀⠀⣠⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡝⢻⣿⣿⣿⣿⣿⠀⣿⣽⢿⡄⡉⢿⣎⡻⣿⣿⣿⣿⣧⢻⣿⣦⠉⠻⢿⣿⣿⠿⠟⠃⣺⣽⣿⣶⣿ ⣿⣤⣿⣷⣴⠆⣠⡄⠂⠖⢀⣤⢷⣼⢿⡿⣿⠀⠀⠀⠈⣿⡌⣿⣿⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⣉⣉⣉⠙⡛⠛⠛⠾⠿⢿⣿⣝⣿⣦⡙⠿⣷⣜⢿⣿⣿⣿⣯⣿⡇⠒⡠⡄⠲⣷⣿⣇⣿⡿⠟⠛⣋ ⣿⣿⡿⢋⣠⣾⣿⣿⢋⣸⣿⡧⠂⠾⣂⠹⡶⠀⠀⣤⣤⣿⣧⠘⣎⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⣛⣛⣛⣛⡛⠃⣿⠟⠇⢰⠶⠶⠤⠤⣌⡉⠙⠒⠛⠿⠷⠼⠿⠿⠦⢿⣷⡦⠿⢓⣚⡋⡅⠄⢰⣤⡻⣿⣿ ⠿⢋⣠⣿⣿⣿⡿⢡⣾⡄⣯⡀⣾⢁⣿⡍⢀⠂⠀⣾⣿⣿⣿⣇⠙⣦⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⣿⣿⣿⣿⣿⣿⡾⣿⠇⣼⣿⣿⣗⣺⣶⣾⣿⣻⣤⣤⣤⣀⡀⠐⢤⣦⣄⠀⢾⣽⣿⣿⣦⠘⣈⣻⣿⣮⣛ ⣴⣿⣿⣿⣿⡿⢡⣿⣿⠆⣿⡇⣽⣾⡝⢡⣿⡆⠠⣿⣿⣿⣿⣿⣇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡖⢿⣿⣿⣏⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣶⣦⣌⠉⠣⡈⠻⣿⣿⣿⠂⣌⠛⢿⣿⣿ ⣿⣿⣿⣿⣿⡇⣸⣿⣿⢰⣿⣿⣿⡏⡀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣷⡦⡈⠀⠙⢾⠁⢰⡟⣧⣀⢙⠓ ⢿⣭⢵⣿⣿⡃⣿⣿⡏⣿⠛⣹⡟⣰⡟⣿⣟⣇⠀⠈⠛⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢿⣿⣿⣷⣘⠶⣄⠀⠙⠻⣿⣿⣿⣿⣦ ⣿⣿⣿⣿⡿⣿⡿⣿⣶⣯⣰⠏⣰⣿⡷⢼⣦⢃⡄⠀⠠⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⡟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣷⠄⠐⢄⠉⠛⠿⢿ ⡍⠁⢮⡛⣱⡿⠷⠌⡘⣀⢉⣴⣿⣿⣿⣾⠏⣾⡇⠀⠀⠈⠻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣁⡀⠑⠆⠲⣄ ⣷⣦⡄⢠⠟⠷⣿⣦⡝⢀⣾⣿⣿⠛⣾⠋⠜⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣯⢷⡄⠙⣌ ⡿⢛⣁⣾⠶⣶⡦⠞⡀⢙⠛⢯⣨⡿⠃⣈⣩⣥⡦⠈⣁⡀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣠⣌⡙⠻⢿⣿⣿⣿⣿⣿⡧⢸⣷⣿⣿⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠘⣻⣿⣦⣈ ⠶⡚⣹⣯⣿⡃⢀⢈⠷⠿⣿⣶⣬⠁⠸⢯⡿⢟⡥⢨⣿⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢿⣿⡿⠷⣄⡙⠻⠿⢿⣷⣿⠈⠿⢟⣉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⡷⢹⣖⣯⣶ ⣶⣯⠻⡏⡿⢠⣾⣿⣿⣶⣿⣿⠋⡸⡻⠊⡡⣾⡇⢸⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⣄⠙⠛⠿⣾⡦⠄⡀⠉⢴⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿ ⣿⣿⣿⡟⣡⣼⠁⣬⣛⣿⣿⠇⣸⠋⣠⣬⣷⠙⠁⣼⣿⡟⣡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢣⣿⣷⡄⠠⣤⡀⠻⢿⣶⣄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣿⡙⣿⣷⡼⢿⣿ ⣿⣿⠟⣾⣿⡟⢇⢹⣿⣷⡁⠸⠃⣾⣿⣿⣿⠏⢰⣿⡟⢰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣦⣈⡷⠶⢦⣙⠻⣿⣧⣠⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣼⣟⣾⡟⣷ ⡿⣥⣾⣿⣿⣶⢿⣯⣿⢻⣿⠃⣌⢻⣿⣿⣟⠀⣿⡟⢀⠟⢁⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢸⣿⣿⣿⣿⣿⣷⣶⡤⣈⡓⠀⠉⢿⣿⣷⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢛⣆⠘⣿⣟⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⢏⡾⢁⣾⣿⣦⣿⣿⡟⢠⡿⠃⠈⣰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⣦⡄⠻⣿⣿⣷⣄⡙⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠿⡿⡿⡄⢿⣿⣯⣿⣽ ⡙⣿⣿⣿⣿⣿⣿⢇⣾⢃⣾⣿⣿⣯⣷⣿⡇⣸⡟⢀⣞⣩⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⡇⣦⠘⠦⣽⣿⣷⡀⢻⣶⣶⣬⣭⡛⠺⠿⣿⣭⣿⣿⣿⣿⣿⣾⣿⣿⡛⣿ ⠿⠿⠿⠿⠿⠿⢧⣾⠃⣼⣿⣿⠿⠟⣿⡿⢉⠉⣤⣸⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣃⢳⣶⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⠰⡙⣷⡄⢉⠙⠻⢄⣿⣛⡿⣿⣿⣿⣷⣬⣙⠿⣿⣿⣿⣿⣿⣿⣿⣷⡘ ⠰⣶⠿⠛⣀⠆⣰⡉⢁⠥⣤⣤⠶⢟⡉⠀⢀⡆⢳⣿⣿⡟⡃⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣆⢻⣿⣿⣮⡿⣿⣿⣿⣿⣿⠟⣡⣾⡟⢧⠨⢢⣿⣿⣿⣶⡈⢉⡛⠷⣿⣿⣿⣿⣿⣷⣦⣉⡻⢿⣿⣿⣿⣿⣿ ⣥⡀⣾⡟⠆⣼⣿⡇⣼⣿⢾⣭⣶⡟⠃⣠⣿⠃⢸⣿⢛⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⡈⣿⣿⣿⣿⣮⡹⢿⣭⣭⣾⣿⣿⣿⢸⣗⢸⣿⣿⣿⣿⣷⡈⣿⣷⣶⣤⣉⠛⠻⠷⣿⣶⣧⣤⣌⠛⢿⢯⡿ ⡙⣧⠘⣏⣰⣿⣿⠃⣿⣿⣿⣿⠟⠁⣴⣿⠇⣼⡅⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣽⣿⠸⣿⣿⣿⣿⣿⣞⠻⣿⣿⣿⣿⣿⡆⡇⡈⢿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣶⣤⡉⢉⣉⣛⠻⠶⣌⣈ ⣿⡎⡁⠠⣼⢷⡿⢰⡿⢿⡿⠋⠀⣰⣿⠏⣸⠟⡧⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⢠⣿⣌⠻⣿⣿⣿⣿⣧⠙⢿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣙⠿⣶⣤⣬ ⠋⣑⠇⢀⠹⣟⠆⣼⣷⡿⠁⠀⣴⣿⡟⡰⢣⡟⠀⣠⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣍⡻⣿⣯⠘⣿⣿⣦⡙⣿⣿⣿⣿⢀⢺⣍⠻⣿⣿⣿⣿⣿⣿⣷⡙⣷⣿⣿⣿ ⡀⠈⣤⠒⢢⡙⣤⣿⡍⢁⡠⣎⣿⡟⠠⣳⠏⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⢿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⣖⢹⣿⣿⣷⡈⢿⣿⠇⣾⣦⠙⣿⣦⣍⡻⢿⣿⡟⠛⣫⡹⣿⣿⢿ ⠀⣾⣿⣷⠛⡇⡈⠉⣠⢿⣶⣿⡿⣠⡷⠃⢠⣿⣭⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⣶⣶⣬⣩⣭⣉⣉⣉⣙⣛⠛⠛⢿⣿⡟⡽⠄⣿⣿⣿⣷⣀⣍⠉⣛⢿⣧⣌⢿⣿⣿⣷⣭⠛⢿⣿⣷⡌⣍⠛ ⣼⣷⣍⢫⣻⡀⠃⢀⠙⢽⣿⡟⠠⠋⢀⡀⢸⣟⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⣿⣿⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣟⣹⢆⣦⣵⣬⣿⡿⣯⠑⠙⣷⣭⣻⢦⡙⢿⣿⣷⣿⣦⣯⣝⠻⠘⣿ ⣉⠉⢉⢉⠁⢁⣴⣿⢓⠀⠻⠀⠀⣰⢟⣇⠈⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⢻⣿⣷⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣧⠙⣿⣿⣯⡻⣿⣧⣀⠻⡿⣿⣧⣧⣤⡙⢿⣿⣿⣿⣿⣿⡀⣤ ⣶⣤⠉⠃⢀⣹⡿⣟⠿⡷⠀⠀⢴⣿⣿⣿⡄⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠀⠈⢿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣎⣻⣿⣿⣮⡻⣿⡆⢻⣌⢻⣿⣿⣿⣦⣉⠫⣻⣿⣿⡗⢺ ⠹⠖⡏⠀⠜⣯⣭⠙⠛⢀⣰⣣⣦⡙⢿⣿⣵⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⡀⠈⢿⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣷⣝⣻⣿⣿⣮⢺⡆⢭⠻⠙⣿⣿⣿⣯⣤⣌⡛⢿⣷⠚ ⣰⠄⠀⣶⠀⣿⡍⠃⠀⢸⠿⣿⡟⠟⣬⠛⣿⡇⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣥⡀⠈⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣿⣿⣿⡿⣿⣯⣼⠘⣇⡈⣧⠺⣯⣿⢿⣿⣷⣦⣍⠁ ䷩ 𝚕𝚒𝚗𝚎 4223 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Techrights_Does_Not_Forget.shtml Gemini version at https://techrights.org/n/2024/12/05/Techrights_Does_Not_Forget.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Techrights Does Not Forget⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Great_Indian_Chiefs⦈_ Techrights has many anti-censorship mechanisms HOURS ago we restored/saved a deleted_article_from_another_site. We had made a copy of it because someone linked to it in IRC and we have bots there to archive everything that any IRC user links to (about 160 GB of pages since last year). Well before Techrights got its name and back when I was still a postgraduate student I wrote some software to archive everything I had linked to and was linking to (almost in real time), knowing a lot of it would vanish/change shortly later and almost certainly go offline (for good) some years later. I'd occasionally offload these fast-growing archives to external drives for long- term preservation. A lot of the articles that we linked to regarding Novell and SCO are long gone and the Internet Archive (steward of Wayback Machine) is under_attack. Well, I still have those external drives, which were in turn replicated onto newer external drives. Remembering history correctly is very important to us because the powerful (and often corrupt, too) like to rewrite/distort history by silencing/censoring every voice or narrative that's unflattering to them. █ ⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄ ⢸⣿⣿⣿⣿⣿⡿⣿⠿⣿⡏⠋⢻⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣷⠈⠃⠈⢿⠀⠀⠀⠀⠡⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⠯⠈⠻⢆⠀⠀⢀⠀⠀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⡿⠿⠦⠀⠀⠈⣧⡀⣾⣶⣤⣽⣶⣶⡀⠀⢻⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢶⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣦⣤⣠⢦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⠑⡁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡿⢿⠿⠟⠓⠀⡀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠓⠉⠃⠀⠁⠱⠸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡆⢸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠔⠀⠫⠀⠀⠀⠆⠙⢿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣏⡁⠉⠙⠻⠿⠋⠁⠀⠀⠀⠤⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⢸⣿⣿⡃⠀⠀⠀⠀⠛⠐⠢⠤⠀⠀⠐⠀⠹⠀⠘⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⡎⠀⠁⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⢸⣟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠐⠲⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⠀⠘⡇⢰⡄⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠹⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠁⣸⠃⠀⠀⠀⠀⠐⢀⠠⠋⠀⠀⠀⣀⠀⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢿⣿⣿⡇⢸⣿⣿⣿⣻⣿⡿⠢⠀⣤⡌⣯⣬⠅⢠⡇⢠⠀⠀⢠⣿⢾⣯⣿⣿⡇⢸⣿⣿⡇⠀⢠⠃⡀⠀⠀⠀⠀⠠⠍⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⠯⡄⠻⡀⠀⢲⠄⣀⣀⣀⠀⣀⠠⠬⠀⠀⠏⠏⣟⣿⡇⢸⣿⣿⣿⣿⡛⣼⠂⣸⣾⣷⡿⠉⣰⣿⢀⣾⠀⠸⠘⡿⣼⣿⣿⣿⡇⠸⣿⣿⠀⠀⣼⣿⣇⡀⠀⠀⠀⠀⠀⠂⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣷⠤⠊⠂⢑⡀⠀⣘⢧⢐⣲⡒⠢⠽⣯⡉⢰⡞⢞⡌⢸⣿⡇⢸⣿⣿⣿⣿⠀⠇⢠⣿⣿⠿⠃⣼⣿⡇⡼⡇⡄⢀⠇⢼⣿⣿⣿⣿⡇⢸⣿⠏⠀⣰⣿⣿⡟⠁⠀⠠⠀⠀⠀⢀⣀⡷⣫⡍⢻⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⢗⡇⠆⣶⡇⠆⢶⣿⠀⡀⠋⠉⠭⢙⠂⠀⡘⠛⠂⢘⣿⣿⡇⢸⣿⣿⣿⡿⢰⠂⣸⣿⣿⣤⣰⣿⣿⢠⢳⡇⡇⡈⠀⣿⣿⣿⣿⣿⡇⢸⣿⠃⣰⡟⡏⠁⡄⢠⠀⠀⠀⠤⢴⣋⠅⢠⣿⣿⠸⣿⢻⣟⣿⣿⡇ ⢸⣿⣿⡟⢁⠀⢸⣿⡄⡼⢀⣴⠃⣐⣻⡟⢻⣿⣷⣷⠀⠀⣾⣿⣿⡇⢸⣿⣿⣿⣷⡼⢰⣿⣿⣿⣿⡏⡿⣿⣿⣿⡇⡇⠇⠀⣿⣿⣿⣿⣿⡇⢸⣿⣾⣿⣷⣷⣶⡇⢻⣄⣷⠈⢿⢺⠋⡠⣿⣿⣿⣶⣟⣾⣿⣿⣿⡇ ⢸⣿⣿⣾⣸⡤⢸⣿⠀⠑⡈⡀⡄⠀⠝⠀⠘⣿⣿⡟⠀⠂⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣿⣿⣮⣭⡅⢾⣽⣿⣿⣿⠃⠘⢀⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⣾⣯⣹⣧⣦⢈⣰⣿⣿⣿⣿⣧⣱⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣧⣿⣿⠘⠀⢸⣽⣷⠀⠀⠀⠶⠃⣿⡇⠈⢰⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣀⣤⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⡉⠁⠀⠀⣯⡿⠇⠀⠀⠀⣀⣿⣧⣶⣼⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣷⣾⣦⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣈⣡⣹⣏⣏⣉⣈⣍⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣟⣻⣟⣟⣯⣏⣿⣟⣻⣻⣛⣿⣟⣛⣟⣛⣿⣻⣛⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠿⡿⢿⣿⡿⣿⣿⣿⠿⡿⡿⠿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣻⣛⣻⣻⣏⣟⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠿⠿⡶⡿⡿⡿⠿⡿⣿⠾⠷⠿⣶⢶⠿⠿⢿⣿⣿⣿⡇ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇ ䷩ 𝚕𝚒𝚗𝚎 4292 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/The_Free_Software_Foundation_FSF_Has_Raised_More_Than_Three_Tim.shtml Gemini version at https://techrights.org/n/2024/12/05/The_Free_Software_Foundation_FSF_Has_Raised_More_Than_Three_Tim.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Free Software Foundation (FSF) Has Raised More Than Three Times More Money Than the Software Freedom Conservancy (SFC), Which Mostly Gets Money From Corporations, Including Microsoft⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024, updated Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Playground_slide_in_bright_blue_is_covered_in_white_snow⦈_ Recent/related: If_You_Donate_to_the_FSFE,_You_Are_Funding_a_Microsoft_Front Group_Inside_Europe | In_the_Latest_OSI_Tax_Filing_(From_the_IRS),_Filed_13 Months_Ago,_Only_4%_of_the_Revenue_Comes_From_Members_(People,_Not Corporations)_and_$252,702_Goes_to_Microsoft_Projects_(Propping_Up_Proprietary Software_Monopoly) | Who_is_the_Mystery_Payer_of_Sandlers'_(Software_Freedom Conservancy)_Quarter_Million_Dollars_(Huge_Salary)_Per_Year? JUDGING by what's happening_so_far_this_month, the FSF raises about 10,000 dollars in donations per day (its now close to $110,000 in total). Given that about_100,000,000_people_use_GNU_on_their_desktops/laptops, we're talking about something like a tenth of a cent per user. SFC, which attacks the FSF while imitating SFLC, has only raised about 33k so far. The SFC has been better than the FSF at raising corporate cash (because it pretends to be "social justice" while trampling_over_women). But non-corporate actors, i.e. people, aren't fooled_by_them_anymore. It should be noted that serial defamers from Microsoft - or Microsofters in general - have done everything they can lately to discourage_FSF_donations. If Microsofters are so afraid of a well-funded FSF, take that as a sign of the FSF's effectiveness. Do not donate any money to copycat organisations. It's worse than money down the river because your money might get spent attacking and even defaming the originals. █ ⠿⠿⠿⣿⣿⣿⣿⣄⠀⠀⢸⣿⠀⢸⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠆ ⠀⠀⠀⢈⣿⣿⣿⣿⠀⠀⢸⣿⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⣀⣈⣿⣾⣯⣿⣿⠁⠠⠄⢸⣿⣤⣼⣆⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⣤ ⠙⣻⣿⣿⣿⣿⣿⠀⠈⠀⢽⣿⡿⠛⠛⠿⠷⢤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠿⢿⠿⢿⢿⡿⣿⣿⣿⣿⡇⢰⣻⣻⣿⣷⣙⣛⣿⣿⣾⣽⣿⣽⣽⣽⣾⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠙⣿⠿⠿⢿⡇⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣶⣄⠀⠀⠀⠀⢸⢀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡆⠀⠀⢸⣿⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠟⠁⠀⠀⣼⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢔⠄⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⠀⣿⣿⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣖⠀⠠⠾⠿⣿⠿⠿⠿⠿⢿⣿⠀⠟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣤⣀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠉⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣀⣀⣤⣤⣀⣀⣀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠋⠿⡿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⣿⣿⣿⢻⣿⣿⣷⣾⣿⣴⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⣤⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 4372 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Why_We_Moved_to_Perl_and_Dumped_PHP_Last_Year.shtml Gemini version at https://techrights.org/n/2024/12/05/Why_We_Moved_to_Perl_and_Dumped_PHP_Last_Year.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Why We Moved to Perl and Dumped PHP Last Year⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 Elongating the lifetime of the underlying_stack 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_grumpy_cat_winter:_This_is_our_nineteenth_year⦈_ TODAY in IRC one recurring topic was Perl, the context being this_malicious Microsoft_proxy giving Perl money (after Perl had already outsourced way too much to Microsoft's GitHub). In the main channel, #techrights, I explained that we had dragged on and on a serious technical debt problem. A lot of our work - or "content" as companies like to label people's hard work - was 'stuck' inside mountains of PHP code (content management systems) and the databases became as large as 10GB (only accessible using bloated software such as MariaDB or Oracle's MySQL). We solved this by exporting the data using Perl (via SQL queries) and instead created a system using Perl. It's our own system and we extend it based on our needs, not some "one-size-fits-all" grand scheme a la Drupal and WordPress. We strongly encourage other sites to do the same if they value longevity and appreciate the merits of general simplicity (never pursue anything beyond the basics; it can become a maintenance overheard, source of bugs etc). Linux is a cautionary tale in that regard and Rust will worsen things rather than address the issue of overflows. A lot of what_we_said_in_2022_turned_out to_be_true_if_not_prophetic. But Rust is a story for another day, some other time... Perl is an old language and our choice of it wasn't made based on hype or fashionable trends. In the word of an associate, Perl is the go-to tool for many things. Python may have the backing of Microsoft and others, and thus more progress in the libraries/modules these days, but the core language is far better with Perl. It's in the lead for regex and is easy to write clearly understood code. Unfortunately the whisper campaign against it points out that one can write poorly understood code too easily as well. It is up to the programmer, according to this associate. "There is / was also the problem that as Perl peaked, it was the trend to show off and write as intricate and complex systems as you could. It was showing off rather than the intentional obfuscation you get nowadays with systemd." For a number of years we ran on Alpine Linux, i.e. no systemd. But sadly it has become increasingly hard to run some particular software on operating systems which lack systemd (and GNU, by default). We no longer use PHP. We need not worry about some future version of PHP coming out and breaking compatibility (notorious trait of PHP; it breaks "old" software and I grew tired of hacking on PHP code when it kept happening since 20 years ago). With Python 3 we can see that Python too is vulnerable to general disregard for backward compatibility. We don't use Python for the Web site anymore. █ ⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⠶⣶⣶⡶⠶⠶⣶⡶⠖⠖⠄⠤⠄⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣾⠟⣿⣟⣭⡏⣭⣽⣿⣽⣿⣭⣿⢋⣴⣶⡄⣶⠀⣾⣷⠀⣾⡆⢰⡆⠈⣿⡆⢸⡃⢠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣷⣿⡆⣿⣿⣿⣨⣭⣸⣇⢸⣿⣿⣿⣿⠀⣭⣥⠀⣿⠃⢠⡀⠺⣿⠇⢸⡄⠸⣿⣿⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣃⣻⣿⣃⣘⣛⣋⣿⣦⣝⣛⣽⣿⣤⣽⣯⣤⣽⣥⣬⣿⣤⣭⣥⣬⣿⢶⡤⠤⣶⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⡿⣿⢫⢿⣿⡿⣿⡿⣿⣿⠹⢿⣿⡏⢟⢻⢠⣿⣇⣸⣷⣰⣿⣷⣹⣷⣤⣼⣷⣶⣿⣤⣤⣄⣀⣀⣐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠟⠛⠛⠛⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠀⣠⣀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣴⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣆⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⣿⣿⣿⣿⡟⢻⡿⡟⠛⠉⠋⠋⠊⠉⠻⠿⢿⣿⣷⣷⣿⣒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠻⣿⣿⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢺⢿⣿⣿⣷⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⡿⠯⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠊⣙⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⢲⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣷⠀⠀⠀⠀⠀⠀⠀⠐⠠⠈⠀⠻⠿⣿⣿⣷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡥⢸⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠀⠰⣶⣤⡤⠋⠀⠀⠀⠀⠀⢠⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣾⣿⣿⣿⡟⠒⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⠟⢂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠐⠂⡀⠤⠀⠀⡀⠀⠀⣀⣠⣾⣿⣿⣿⣶⣶⣿⣧⣶⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠂⢢⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡶⠂⠐⠂⠀⠀⠀⠤⠔⢒⡒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣇⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣄⣐⠈⢩⢿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠌⠀⠒⠂⠤⠭⣁⡐⠂⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣐⠛⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣶⣄⡉⢋⡴⡟⡿⢿⡿⢿⣿⠿⡿⠿⠛⠛⣉⣦⡶⠀⠐⠢⢀⠀⠀⠀⠉⠒⠤⣁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠐⣶⣶⡿⠛⠉⠀⠀⢸⣄⠀⠀⠢⠀⠀⠀⠀⠀⠑⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣴⠦⣤⣀⣝⡻⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡼⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⢀⣀⢀⣀⡀⣀⡀⢀⣀⣀⠀⣿⢄⣀⡀⢀⣀⣀⢼⣿⡿⣟⣛⡻⣿⣛⣛⣛⡿⣛⣛⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠋⢿⠿⣿⡿⠿⢿⣿⡜⣿⡟⢻⣿⠛⢸⣿⢸⣿⡇⣿⡇⣿⣏⠿⠇⠈⢸⣿⡇⣿⡏⠿⠇⠉⢸⣿⢹⣿⢸⣿⡇⣿⡇⣿⡏⣿⡇⢻⣿⡿⠛⠀⠀⢸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣏⣁⣀⣀⣀⣀⣀⣀⣀⣀⣭⣭⣥⣄⢸⣿⠀⢸⣿⢻⣿⡇⣿⡇⣈⡻⣿⣆⢀⢸⣿⡇⣙⡿⣷⡄⣤⢸⣿⢸⣿⢸⣿⡇⣿⡇⣿⡟⣿⡅⠀⠈⠀⠒⠲⢶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣀⢸⣿⢸⣿⡇⣿⡇⠻⣧⣿⠟⣾⣸⣿⡇⢿⣧⣿⢇⣿⡸⣿⣼⡿⣘⢿⣷⡿⠃⣿⡇⣿⡇⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⢿⣿⡿⣿⡿⣷⡶⢿⣓⣒⢷⣒⣛⣶⣞⣛⣲⢶⣛⣻⢿⣶⠿⣷⣶⣞⣛⣻⣿⣷⢶⣿⣿⣷⣶⡾⢿⣶⣞⣒⣾⠿⣟⣻⣿⢿⣛⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡜⣿⢸⣿⡇⣿⣧⢸⡇⢸⣿⠛⡛⣿⣿⠛⣿⣿⠛⢸⣿⠛⢸⣿⡇⣿⡟⢻⣿⡟⢻⣿⢿⣿⡇⣷⢻⣧⣿⡇⣿⣿⢛⢰⣿⣿⡇⢸⣿⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⡇⣿⣿⣿⡇⢸⣿⠾⡀⣿⣿⠀⣿⣿⠿⢸⣿⠾⢸⣿⣿⣿⡇⢸⣿⡇⢸⣿⢿⣿⡇⣿⡎⣿⡿⠀⣿⣿⠿⢸⣿⢻⣧⢸⣿⢿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢹⣿⢸⣿⡇⣿⡏⣿⡇⢸⣿⣴⠁⣿⣿⡀⣿⣿⣴⢸⣿⣴⣼⣿⠸⣿⡇⢸⣿⣇⢸⣿⣿⣿⣇⣿⡇⣿⣇⡇⣿⣿⣤⣿⣿⢻⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣷⣶⣶⣶⣾⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 4486 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/12/05/Windows_Has_Fallen_to_All_Time_Low_in_India.shtml Gemini version at https://techrights.org/n/2024/12/05/Windows_Has_Fallen_to_All_Time_Low_in_India.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Windows Has Fallen to All-Time Low in India⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Drummer_With_Shamanic_Frame⦈_ In India, only about 1 in 8 Web requests comes from Windows We've only just noticed something important, albeit we rely on one sole Web surveyor. If these numbers are accurate (the sample size in India ought to be vast), Windows_is_down_to_62%_on_desktops/laptops_in_India or 12.5% overall (because Android_is_so_dominant and Web-compatible_mobile_ownership/usage_rose_steadily, apparently rising from 2% 15 years ago to about 80% now). No wonder Bill_Gates_Keeps_keeps_visiting_Modi and buying/bribing Indian press. He wants to experiment. █ “They’ll get sort of addicted, and then we’ll somehow figure out how to collect sometime in the next decade.” -Bill Gates ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣶⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠻⠿⣿⣿⣿⡿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡀⠀⠈⣿⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠉⠀⠀⢿⠿⣿⣯⣻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⡿⠏⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⡿⣁⡀⠀⣶⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠛⠉⠀⣸⣿⣶⣿⣷⠀⣿⡇⠀⢀⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⣿⣿⣷⣦⣄⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣀⣀⣤⠤⠤⠠⠤⠤⠤⣀⣀⡀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣦⣄⡀⢄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⣿⣿⣿⣿⣿⣿⠏⠈⢁⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⣷⣤⣀⠀⠀⠀⠉⠻⣿⣿⣷⣄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢃⣴⣴⠆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣖⣰⠆⠠⠀⣠⠀⠀⠀⠀⠀⠘⠁⣿⣷⣾⣷⣦⣄⠀⠀⠈⠛⢿⣿⣧⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠂⡠⠾⠟⠁⠀⠀⢀⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠄⠀⢀⡋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣷⣄⠀⠀⠈⠻⣿⣿⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠀⣔⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡁⢀⣤⢘⢃⠀⠀⢠⣶⡅⣲⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⢻⣿⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⡞⠙⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⢾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⡆⡀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠹⣿⠆⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣀⠠⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⣄⠀⠀⠀⢉⣀⣤⣤⣤⣤⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡧⠀⠀⠀⠰⢿⣿⣿⣿⣿⣉⠉⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⠿⠃⠀⢀⣠⣾⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠰⠦⣭⣿⣭⣁⣠⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⠛⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢨⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠩⠉⠉⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠂⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣶⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣀⣤⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⠛⠡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡯⡿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⣴⣦⡴⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⡿⠁⠠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⡟⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⠙⣹⠟⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠀⠀⠀⠹⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢚⠆⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣟⠛⢺⢿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢫⠂⠀⠀⠀⠈⠻⠋⠀⣽⢾⡏⠙⠟⠉⠛⡥⣀⠉⡀⠄⡌⣻⣿⣿⣿⣿⣿⡦⠀⠀⢀⣼⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠀⠀⠨⢻⡍⠙⠋⠀⢢⡴⠾⠟⣳⠀⠀⠈⢹⣿⣿⣿⡿⠏⢀⣤⠾⢿⠿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 4576 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 05/12/2024: Hermeticism, Living in the Shell, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Colourful_umbrella_and_man⦈_ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * Gemini*_and_Gopher o Personal/Opinions o Politics_and_World_Events o Technology_and_Free_Software # Programming * § Gemini* and Gopher⠀➾ o § Personal/Opinions⠀➾ # ⚓ Why_list_a_phone_number_if_no_one_at_your_company_even knows_how_to_deal_with_the_notification?⠀⇛ And that's it. It's lucky there was no personal information included or this company could be in violation of HIPAA (Health Insurance Portability and Accountability Act). On a whim, instead of simply deleting the email and going on with my life, I decided to do The Right Thing™, and inform the sender (which was the company itself) of the delivery error by calling the given phone number. It took several calls to resolve. No one at XXXXX­X knew how to directly handle my call. Two people I talked to attempted to transfer me to what they felt was the appropriate department, only to have the transfer fail and I had to call back and navigate the automated phone system yet again (in which I had to listen carefully, becauese the options had changed on October 20^th; a refreshing change from the “recently changed” most such systems claim). # ⚓ A_real_real-time_chess_board⠀⇛ Two years ago I talked about a spherical chess variant [1]. Now, I want to mention real time chess [2], where players can move their pieces at will, with the only limit being once a piece is moved, you can't move it for five seconds. And there's no check or checkmate—you win by capturing the opponent's king. # ⚓ classical_electronic⠀⇛ As I am learning to be single, my past comes back to me. In a weird twist of event, I'm starting to listen to classical music again. I just enjoy listening to classical music, so much so that I feel a bit self concious about it. It feels somewhat 'pretentious' to like classical music. There is nothing I can do, my whole body enjoy listening to classical music. I dream about the day I'll be in the city and go to back to the orchestra. As a kid I've had the chance to go to many concert, one of my violin teacher was playing with the Montreal philharmonic orchestra. The experience of so many instruments playing at the same time, the composition and the story that happened in my head during this relaxing and exhilarating moment, deeply formed my relationship to music. o § Politics and World Events⠀➾ # ⚓ Hermeticism_Isn't_Qabbalah⠀⇛ Hermeticism is not equatable with Qabbalah. It's entirely possible (and encouraged) to be a Hermeticist without Qabbalah. Qabbalah is like terrible, drab shag carpeting laid out over a beautifully polished, ancient hardwood floor. Jewish Kabbalah is rich and profound, but Hermetic Qabbalah is effectively a cultural appropriation and maladaptation of it, and—let's be honest—doesn't provide much for us anymore besides a massive correspondence table with a lot of badly- pronounced Hebrew. And yet, it's formed such a procrustean bed that so many of us struggle to think outside of, much less break away from; it's become as much a crutch as it has a shackle. The more we divest ourselves of it and practice Hermetic spirituality without it, the better off we'll all be. o § Technology and Free Software⠀➾ # ⚓ redterminal.org_now_runs_on_FreeBSD-14.2-RELEASE⠀⇛ I upgraded the redterminal.org Gemini/Gopher/ Finger/WWW server from the 14.1 branch to FreeBSD- 14.2-RELEASE. Nobody should have noticed besides a brief downtime for the reboot. The update went painless and smoothly thanks to the FreeBSD maintainers. All packages are up-to-date too and everything is fine so far. Small problems will be ironed out with the first update if any, but as far as I can tell there are no problems. # § Programming⠀➾ # ⚓ Living_in_the_Shell⠀⇛ I am now using the Devterm R-01 for, what, 11 months or so as my more or less primary computer, which has lead to the "discovery" of some problems: - The screen real estate with its widescreen format and small size isn't ideal for a traditional desktop - It is somewhat slow - The trackball is still a crime against humanity =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It's like the World Wide Web but a lot lighter. ䷩ 𝚕𝚒𝚗𝚎 4746 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 05/12/2024: Domain Changes, Griping With Haskell⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Yellow_Leaves_and_Snow⦈_ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * Gemini*_and_Gopher o Personal/Opinions o Technology_and_Free_Software # Internet/Gemini # Programming * § Gemini* and Gopher⠀➾ o § Personal/Opinions⠀➾ # ⚓ [EN]_re:_A_real-time_chess_board⠀⇛ Ha, this is sooo cool. I've been thinking on how to make that real-time chess a reality. Perhaps with hourglasses, or each piece having a digital timer. But that approach is amazing based on all the things you have to consider. # ⚓ 🔤SpellBinding:_AEUMNQI_Wordo:_PLANS⠀⇛ # ⚓ 29_years_ago_today⠀⇛ Twenty-nine years ago today, on Dec. 5, 1995, I created my first website at a little internet cafe in Seattle. This was before GeoCities or AngelFire was really a thing (or at least I was not aware of those), and the web hosting came with my personal UNIX shell account from the internet cafe, which I could use to log in from there, as well as from places like Seattle Public Library using Telnet on its VT-100 dumb terminals. That meant I for the most part had to manually type in HTML into the shell using the PICO text editor (which was proprietary software from the University of Washington, later emulated by the open-source NANO editor). Or, I could FTP from my college computer lab. o § Technology and Free Software⠀➾ # § Internet/Gemini⠀➾ # ⚓ A_housekeeping_announcement⠀⇛ This site is now "willowashmaple.sbs", and is no longer "willowashmaple.xyz". If you have subscribed via RSS, you need to change the feed address to https:// willowashmaple.sbs/atom.xml I apologize in advance for this sudden announcement and thank you for your patience as I also need to update various links on my social media profiles. # ⚓ all_the_notes⠀⇛ the existence of dedicated websites that lets you compare features of the plethora of note- taking applications just shows that so many of us--regardless of background--are interested in (sometimes obsessed with) better systems for note-taking, task management, and really just productivity. doing more with less time and less mental overhead. # § Programming⠀➾ # ⚓ 2024_In_Retrospect⠀⇛ I must admit, I'm not one to discuss my personal life online very often. But I wanted to add this memoirs section because I think I need some place to do so and my physical journals all end up filled with random notes, poems, and silliness. Throughout it all, 2024 has been a phenomenal year for me. I got to grow closer to many friends, some long time and some not. I wound up growing close to and finding my true love and soulmate, something that I had long conceded was likely out of my reach. The latter part still has me silently giddy as I blush, waiting for a message or response from them. I even finally rekindled my love for programming again, thanks to OCaml and functional programming in general. # ⚓ Griping_With_Haskell⠀⇛ Over the last couple months, I've taken some time to finally learn and use Haskell. I chose this because after using OCaml for a little bit I realized I finally felt ready to approach a purely functional programming language. It took a little bit, but after the first few weeks I actually felt pretty happy in Haskell. It is a very elogent and pleasant language to write, that allows you to represent concepts in very ingenious ways. Lazy evaluation is also something that I will now miss whenever I am not writing Haskell. I like Haskell a lot, and will be continuing to use it. However, the language is bloated with warts. Whether they be tooling related, standard library related, or language construct related. While it is very elogant to write Haskell, it is absolutely horrible to build an application in it. So this log will be a little ramble of my experience. =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It's like the World Wide Web but a lot lighter. ䷩ 𝚕𝚒𝚗𝚎 4913 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 05/12/2024: Explaining the South Korea Chaos and French PM Barnier's Government Already Disintegrating⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Snowy_power_lines⦈_ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * Leftovers o Hardware o Health/Nutrition/Agriculture o Security # Integrity/Availability/Authenticity o Defence/Aggression o Environment # Energy/Transportation o Finance o AstroTurf/Lobbying/Politics o Censorship/Free_Speech o Freedom_of_Information_/_Freedom_of_the_Press o Civil_Rights/Policing o Internet_Policy/Net_Neutrality o Monopolies/Monopsonies # Copyrights * § Leftovers⠀➾ o ⚓ University of Michigan ☛ I_love_street_photography,_but_it’s probably_evil⠀⇛ In street photography, there is “the moment.” It could be the instant a crowd looks off in the distance or when a couple kisses by a subway. It could be a man rushing by with a peculiar hat or a woman walking through the morning mist. o § Hardware⠀➾ # ⚓ Hackaday ☛ Hack_On_Self:_Headphone_Friend⠀⇛ In the last two articles, I talked about two systems relying on audio notifications. The first one is the Alt-Tab annihilator system – a system making use of my window monitoring code to angrily beep at me when I’m getting distracted. The other is the crash prevention system – a small script that helps me avoid an annoying failure mode where I run out of energy before getting myself comfortable for it. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Scarlett_Gately_Moore:_Hacked_and_tis_the_season_for surgeries⠀⇛ I am still here. Sadly while I battle this insane infection from my broken arm I got back in July, the hackers got my blog. I am slowly building it back up. Further bad news is I have more surgeries, first one tomorrow. Furthering my current struggles I cannot start my job search due to hospitalization and recovery. # ⚓ Mexico News Daily ☛ Federal_authorities_intercept_more_than 20_million_fentanyl_doses_in_Sinaloa⠀⇛ The Sinaloa security operation, completed in two separate actions, was the largest fentanyl bust in Mexican history. # ⚓ France24 ☛ Bird_flu_in_the_US:_What_is_the_risk_of_human- to-human_transmission?⠀⇛ In today’s Science segment, we tell you about the latest cases of the bird-flu detected in North America. Three people were diagnosed without experts being able to identify the source of contamination. First a teenager in Canada then a child in California which follows a first contamination in Missouri. None of those patients have been in direct contact with animals which is sparking fear that the virus could be mutating. Until now, however, there have been no cases of human-to-human transmission. # ⚓ New York Times ☛ Kelly_Powers,_Fox_News_Commentator_Who Shared_Her_Health_Crises_With_Viewers,_Dies_at_45⠀⇛ She was diagnosed with glioblastoma, an aggressive form of brain cancer, in 2020, and used her platform to talk about cancer research. # ⚓ Science Alert ☛ Scientists_Created_The_Thinnest_Spaghetti The_World_Has_Ever_Seen⠀⇛ Unlike any spaghetti ever made before. # ⚓ Science Alert ☛ Your_Poop_Schedule_Says_a_Lot_About_Your Overall_Health,_Study_Finds⠀⇛ There's an optimal frequency. # ⚓ Science Alert ☛ Neurons_Don't_Look_Like_We've_Long_Thought, Controversial_Study_Says⠀⇛ Wait, what? # ⚓ Science Alert ☛ Toasted_Skin_Syndrome_Just_One_Risk_of Using_Hot_Water_Bottles_For_Warmth⠀⇛ There are safer ways. # ⚓ Science Alert ☛ Alarming_Rise_in_Cancers_of_The_Gut_Linked With_These_Deadly_Diets⠀⇛ Make a healthy change today. # ⚓ Science Alert ☛ Roman_Era_Barbarians_Carried_Tiny_Spoons That_May_Have_Helped_in_Battle⠀⇛ If you know, you know. o § Security⠀➾ # § Integrity/Availability/Authenticity⠀➾ # ⚓ WhichUK ☛ Delivery_text_scams:_how_to_spot_this common_scam⠀⇛ Check for telltale signs of fake text messages impersonating delivery companies this Christmas o § Defence/Aggression⠀➾ # ⚓ Hong Kong Free Press ☛ China’s_Pooh-tin_Jinping_vows_to deepen_infrastructure_cooperation_with_Nepal_–_state_media⠀⇛ President Pooh-tin Jinping on Tuesday told Nepali Prime Minister Khadga Prasad Sharma Oli that China will offer more support to develop the country’s infrastructure, Chinese state media reported. # ⚓ The Straits Times ☛ Nepal,_China_sign_deal_on_Belt_and_Road plan,_paving_way_for_progress_on_projects⠀⇛ Nepal has signed a framework agreement with China on the Belt and Road initiative, after an initial pact was signed seven years ago but no progress made since, paving the way for cooperation on projects, its foreign ministry said on Wednesday. # ⚓ LRT ☛ Lithuania’s_new_govt_vows_to_host_German_brigade_in 2027,_calls_China_‘growing_challenge’⠀⇛ Despite concerns about the timeline for the German brigade’s deployment, Lithuania’s new government is committed to meeting the late 2027 deadline. It also calls China a “growing challenge”. # ⚓ LRT ☛ Lithuania’s_govt_programme:_new_China_direction, social_economy_policy_–_key_points⠀⇛ Lithuania’s incoming Social Democrat-led government has revealed its draft programme, outlining the key priorities over the next four years. Here are the key points. # ⚓ Defence Web ☛ Tunisia_seeking_Javelin_anti-tank_missiles⠀⇛ Tunisia is looking to buy nearly 200 Javelin anti- tank missiles from the United States in a deal worth over $100 million. The US State Department on 3 December announced that it had approved the possible Foreign Military Sale, and the Defence Security Cooperation Agency (DSCA) had accordingly notified Congress. # ⚓ New York Times ☛ A_Storied_New_York_Hilton_Adds_a_Grim Chapter_to_Its_History⠀⇛ The hotel, on West 54th Street, was where journalists examined the Pentagon Papers and where Donald Trump delivered a 2016 victory speech. # ⚓ New York Times ☛ A_Health_Insurance_C.E.O._Was_Gunned_Down in_Manhattan⠀⇛ Also, the Supreme Court appeared inclined to uphold a Tennessee law on trans care. Here’s the latest at the end of Wednesday. # ⚓ New York Times ☛ Shooting_of_Brian_Thompson, UnitedHealthcare_CEO,_in_NYC:_What_We_Know⠀⇛ Mr. Thompson was on his way to an investors’ gathering when he was killed by a masked shooter who fled on an electric Citi Bike, the police said. # ⚓ New York Times ☛ Who_Was_Brian_Thompson,_the_CEO_of UnitedHealthcare?⠀⇛ Mr. Thompson managed a division that employs about 140,000 people and offers insurance plans to employers and individuals. # ⚓ France24 ☛ Police_hunt_for_US_healthcare_executive's_masked killer_after_New_York_attack⠀⇛ The chief executive of one of the United States's largest health insurance companies, UnitedHealthcare, was shot and killed outside a New York Hilton hotel in an apparently targeted hit Wednesday. Brian Thompson was shot just before 7 am outside the hotel in the Midtown district of Manhattan. Police are searching for the killer. # ⚓ The Straits Times ☛ Philippine_V-P_Sara_Duterte_faces second_impeachment_complaint⠀⇛ Dec 4 complaint alleged Sara Duterte betrayed public trust with misuse of millions of dollars in public funds. # ⚓ The Straits Times ☛ South_Korea’s_Yoon_names_new_defence minister_after_botched_martial_law⠀⇛ It is the President's first official move since rescinding martial law on Dec 4. # ⚓ The Straits Times ☛ Explainer:_How_to_impeach_a_South Korean_president⠀⇛ A motion needs a two-thirds majority vote by the members of the single-chamber Parliament to pass. # ⚓ The Straits Times ☛ Martial_law_debacle_revives_painful memories_in_South_Korea⠀⇛ Many recall the trauma of the early 1980s, when South Korea was periodically placed under harsh laws. # ⚓ New York Times ☛ President_Yoon_Suk_Yeol_of_South_Korea Declares_Martial_Law,_Then_Backs_Down⠀⇛ Soon after President Yoon Suk Yeol’s declaration on Tuesday, lawmakers voted to defy him, prompting the president to say he was lifting his order. # ⚓ New York Times ☛ South_Korean_History_Is_Scarred_by_Martial Law⠀⇛ The president’s short-lived declaration of a military emergency late Tuesday was young South Koreans’ first exposure to a state of affairs their elders remember well. # ⚓ New York Times ☛ South_Korea_Stock_Markets_Wobble_After Martial_Law_Turmoil⠀⇛ Officials pledged “unlimited” support to markets as traders digested the implications of South Korea’s brief declaration of martial law. # ⚓ New York Times ☛ Nearly_300_Troops_Stormed_South_Korea’s National_Assembly,_Official_Says⠀⇛ The National Assembly’s secretary general, Kim Min- ki, condemned what he called the “illegal, unconstitutional actions of the military.” # ⚓ New York Times ☛ For_Some_Koreans,_Martial_Law_Stirs Harrowing_Memories_of_Gwangju_Uprising⠀⇛ “I immediately thought of 1980, and the fear and desperation we felt,” said a 60-year-old lawmaker who lived through the massacre of protesters in Gwangju. # ⚓ New York Times ☛ Who_Would_Replace_South_Korea’s_President Yoon?⠀⇛ Prime Minister Han Duck-soo would take over if President Yoon Suk Yeol steps down or is impeached. # ⚓ New York Times ☛ Thursday_Briefing:_An_Impeachment_Motion in_South_Korea⠀⇛ Plus, what’s your favorite holiday tradition? # ⚓ New York Times ☛ South_Korea’s_Defense_Minister_Steps_Down Over_Martial_Law_Decree⠀⇛ President Yoon Suk Yeol accepted the resignation of Kim Yong-hyun, who said he considered himself responsible for the short-lived decision to impose military rule. # ⚓ New York Times ☛ South_Korea’s_Martial_Law_Turmoil Threatens_Pacific_Alliance_With_U.S._and_Japan⠀⇛ Donald J. Trump had been seen as the main risk factor for the partnership between Tokyo, Seoul and Washington. Then came martial law in South Korea. # ⚓ New York Times ☛ South_Korean_Lawmakers_Move_to_Impeach President_Yoon After_Failed_Martial_Law_Bid⠀⇛ President Yoon Suk Yeol’s attempt to break a political deadlock by imposing military rule collapsed within hours, leaving him with few defenders. A vote to impeach him could come as soon as Friday. # ⚓ CS Monitor ☛ Martial_law_for_a_moment:_What_just_happened in_South_Korea⠀⇛ South Korean President Yoon Suk Yeol’s surprise declaration of emergency martial law lasted only six hours. But it has plunged South Korea – a key Asian economy and U.S. ally – into a political crisis that could last much longer. # ⚓ CS Monitor ☛ South_Korea’s_swift_rescue_of_freedom⠀⇛ An unpopular president’s martial law was no match for a people with an inner strength born of repelling despots and invaders. # ⚓ The Straits Times ☛ Recap:_South_Korean_opposition, protesters_demand_impeachment_of_President_Yoon⠀⇛ The protests are set to continue every weekday evening until their demand for Mr Yoon to resign is met. # ⚓ The Straits Times ☛ US_‘relieved’_South_Korea_President Yoon_Suk_Yeol_reversed_course_on_martial_law⠀⇛ Mr Yoon had shocked his country and the world by imposing martial law late on Dec 3. # ⚓ The Straits Times ☛ South_Korean_ruling_party_leader_says martial_law_attempt_‘tragic’,_demands_accountability⠀⇛ President Yoon is a member of the People Power Party. # ⚓ The Straits Times ☛ How_polarised_politics_led_South_Korea to_a_plunge_into_martial_law⠀⇛ The events that led to martial law were set in motion well before Yoon's 2022 victory. # ⚓ The Straits Times ☛ South_Korea’s_President_Yoon_faces impeachment_after_martial_law_debacle⠀⇛ Voting is set for Dec 5 or Dec 6. # ⚓ The Straits Times ☛ How_martial_law_has_been_used_over South_Korea’s_turbulent_history⠀⇛ Martial law was last introduced in 1979 following the assassination of then President Park Chung-hee. # ⚓ The Straits Times ☛ Martial_law_turmoil_unsettles_South Korean_entertainment_schedules⠀⇛ Dua Lipa's concert organiser has not issued any statement, suggesting that the shows will proceed as planned. # ⚓ The Straits Times ☛ South_Korea’s_short-lived_martial_law: A_timeline⠀⇛ The crisis unfolded over 157 tense minutes before lawmakers voted to revoke the martial law. # ⚓ The Straits Times ☛ Martial_law_in_South_Korea_tests_Biden and_a_key_US_alliance⠀⇛ Yoon’s move to call martial law has appeared to catch the Biden administration by surprise. # ⚓ The Straits Times ☛ South_Korea_Cabinet_ministers_offer_to resign_en_masse⠀⇛ The People Power Party’s leader told reporters he also suggested Mr Yoon be kicked out of the party. # ⚓ The Straits Times ☛ Leading_contenders_who_might_replace South_Korean_President_Yoon⠀⇛ The president’s term runs to 2027 but if he leaves office sooner, it would trigger an election. # ⚓ The Straits Times ☛ Video_of_South_Korean_woman_clashing with_soldiers_after_martial_law_declaration_goes_viral⠀⇛ President Yoon declared martial law late on Dec 3, only to rescind it six hours later. # ⚓ The Straits Times ☛ Martial_law_decree_sparks_international backlash_for_South_Korea⠀⇛ Leaders from Japan and Sweden have cancelled visits to South Korea. # ⚓ The Straits Times ☛ Nearly_300_troops_stormed_South_Korean legislature,_official_says⠀⇛ Troops smashed windows, and some aides and protesters sprayed them with fire extinguishers. # ⚓ The Straits Times ☛ South_Korean_media_calls_for_Yoon_Suk Yeol’s_resignation,_arrest⠀⇛ Most alarming to press freedom advocates were provisions placing all media under direct military control. # ⚓ The Straits Times ☛ Soldiers_vs_office_chairs:_South Korea’s_martial_law_standoff⠀⇛ Soldiers in the compound attempted to enter the building while police tried to bar MPs from entering. # ⚓ The Straits Times ☛ For_some_South_Koreans,_martial_law brings_back_frightening_memories⠀⇛ “After democratisation, I didn’t think this would happen again in our lifetime," says a 68-year-old man. # ⚓ The Straits Times ☛ South_Korea’s_ex-PM_and_other politicians_accused_of_‘supporting’_martial_law⠀⇛ Former prime minister Hwang Kyo-ahn and Busan city councilman Park Jong-cheol showed their support. # ⚓ The Straits Times ☛ How_concerned_should_you_be_about_South Korea’s_martial_law_turmoil?⠀⇛ Expect to see large protests in some parts of Seoul, such as Gwanghwamun, Yongsan or near City Hall. # ⚓ The Straits Times ☛ South_Korea’s_day_of_rage_as_President Yoon’s_martial_law_flounders⠀⇛ The streets of Seoul teemed with protesters and police throughout the day. # ⚓ The Straits Times ☛ Uptick_in_sales_at_S._Korea_convenience stores_following_martial_law_declaration⠀⇛ One convenience store chain saw sales of canned goods surge by 337.3 per cent. # ⚓ The Straits Times ☛ US_was_not_aware_in_advance_of_South Korea_martial_law_decision,_Blinken_says⠀⇛ BRUSSELS - The United States was not aware that South Korea's president intended to declare martial law, U.S. Secretary of State Antony Blinken told Reuters on Wednesday, adding that he anticipated speaking to his South Korean counterpart in the coming days. # ⚓ The Straits Times ☛ S._Korean_President_Yoon_‘gravely_and extensively_violated_Constitution’:_Impeachment_motion⠀⇛ The motion said Yoon's declaration of martial law was aimed at evading criminal investigations. # ⚓ The Straits Times ☛ From_decree_to_defeat:_Inside_South Korea's_failed_martial_law_attempt⠀⇛ The shock move on Dec 3 unleashed six hours of political chaos in South Korea. # ⚓ The Straits Times ☛ Martial_law_decree_ignites_anti- president_rallies_across_South_Korea⠀⇛ The largest demonstration took place near Gwanghwamun Square in northwestern Seoul. # ⚓ The Straits Times ☛ South_Korean_ruling_party_to_oppose President_Yoon_Suk_Yeol’s_impeachment⠀⇛ If successfully introduced to Parliament, lawmakers could vote on the Bill as early as Dec 6. # ⚓ The Straits Times ☛ ST_Picks:_How_S._Korea’s_botched martial_law_move_is_sending_shockwaves_across_Asia⠀⇛ # ⚓ The Straits Times ☛ US_says_South_Korea’s_Yoon_badly misjudged_martial_law_declaration⠀⇛ Almost all US interlocutors in South Korea were “deeply surprised” by Mr Yoon’s move. # ⚓ The Straits Times ☛ South_Korea's_Yoon_names_new_defence minister_after_botched_martial_law⠀⇛ It is the President's first official move since rescinding martial law on Dec 4. # ⚓ The Straits Times ☛ Parents_of_S._Korean_soldiers_spent sleepless_night_worrying_about_sons_after_martial_law declared⠀⇛ Some apologised to their sons for the state of the nation. # ⚓ The Straits Times ☛ Teachers_across_South_Korea_field martial_law_questions_from_kids⠀⇛ Some schools ran separate educational programs on the crisis. # ⚓ New Yorker ☛ A_Coup,_Almost,_in_South_Korea⠀⇛ President Yoon Suk-yeol declared martial law, then backed off, in a matter of hours. He now faces impeachment and mass protests. # ⚓ JURIST ☛ South_Korea_president_lifts_martial_law_following parliamentary_unanimous_opposition⠀⇛ South Korean President Yoon Suk Yeol announced Tuesday that he would lift martial law and that troops deployed following the shocking declaration would be withdrawn, succumbing to united Parliamentary and public pressure against the declaration. # ⚓ JURIST ☛ South_Korea_parliament_to_vote_on_presidential impeachment_motion⠀⇛ A motion to impeach President Yoon Seok-yeol was reported to the National Assembly of the Republic of Korea on Thursday and is due to be voted on by an anonymous ballot within 72 hours of the session. The motion, filed by the opposition, follows President Seok-yeol’s brief imposition of martial law on Tuesday. # ⚓ Hong Kong Free Press ☛ Gov’t_advises_300+_Hongkongers_to exercise_caution_in_S.Korea,_after_martial_law_declared, lifted_in_one_night⠀⇛ Hongkongers in South Korea have been advised to attend to their personal safety after President Yoon Suk Yeol declared martial law on Tuesday, a move that was unanimously overturned by lawmakers, and later lifted by the government in a matter of hours. # ⚓ The Strategist ☛ South_Korean_leader’s_rash_move_spells upheaval_at_home_and_risk_abroad⠀⇛ President Yoon Suk Yeol’s decision to rescind his declaration of martial law, in the face of embattled opposition from South Korea’s parliament, has at least spared the country a disastrous return to military rule. # ⚓ The Strategist ☛ More_than_innovation:_Australia_needs fast,_low-cost_defence_production⠀⇛ Conflicts in Ukraine and the Middle East have shown that mass and asymmetry characterise modern warfare. The challenge is to deliver affordable mass—weapons in great numbers—while ensuring technology is evolving ahead of rapidly changing threats. # ⚓ RFERL ☛ Syrian_Troops_Reportedly_Thwart_Rebel_Advance_Near Russian_Air_Base⠀⇛ A war monitor and state media say that Syrian government forces have launched a counterattack against Islamist-led rebels who were getting close to a Russian-operated airbase after capturing a string of towns and closing in on the key city of Hama. # ⚓ The Straits Times ☛ Russia_strongly_backs_Syrian leadership,_says_rebels_are_getting_outside_help⠀⇛ MOSCOW - Russia said on Wednesday that it strongly backs the actions of the Syrian leadership to counter an offensive by what it said were terrorist groups receiving support, including drones and training, from outside the country. # ⚓ New York Times ☛ Syrian_Forces_Battle_Rebels_Outside Government_Stronghold⠀⇛ The rebels have set their sights on the city of Hama, where President Bashar al-Assad’s government has long maintained strength. # § Russia, Belarus, and War in Ukraine⠀➾ # ⚓ RFERL ☛ Police_Secure_Area_After_Mystery_Drone_Crash Near_Tajik_Capital⠀⇛ Police and security officials have cordoned off a large area near Dusanbe after a drone resembling a military unmanned aerial vehicle (UAV) crashed in a nearby town in a region where there are both Tajik and Russian military bases. # ⚓ The Straits Times ☛ Russia_supporting_North_Korea nuclear_programme_in_exchange_for_troops:_Nato_chief⠀⇛ This could destabilise the Korean Peninsula and threaten the United States, said the Nato chief. # ⚓ The Straits Times ☛ North_Korea-Russia_treaty_comes into_force:_KCNA⠀⇛ The treaty includes a mutual defence pact for immediate military assistance if either faces armed aggression. # ⚓ The Straits Times ☛ Russia_says_it's_watching 'tragic'_situation_in_South_Korea_with_concern⠀⇛ Russia is following events in South Korea with concern after the president briefly declared martial law, but there are no threats to Russian citizens there, Foreign Ministry spokeswoman Maria Zakharova said on Wednesday. # ⚓ New York Times ☛ Georgia_Tumbles_Deeper_Into_Crisis as_Government_Detains_Opposition_Figures⠀⇛ In a sign of a widening crackdown, security agents have searched the offices and homes of prominent activists and opposition leaders who are furious about the government’s position on Europe. # ⚓ Meduza ☛ Russian_ship_reportedly_fired_signaling ammunition_at_German_military_helicopter_in_Baltic_Sea —_Meduza⠀⇛ # ⚓ Meduza ☛ Malta_revokes_Russian_Foreign_Ministry spokesperson_Maria_Zakharova’s_visa_ahead_of_OSCE meeting_—_Meduza⠀⇛ # ⚓ LRT ☛ Lithuania_rejects_Belaruskali_claims_in arbitration_lawsuit⠀⇛ After Belarusian potash fertiliser giant Belaruskali filed a lawsuit against Lithuania to the International Court of Arbitration, Lithuania says it does not agree with the allegations. # ⚓ Meduza ☛ Armenia_considers_itself_‘outside_of’ Russian-led_CSTO_military_alliance,_prime_minister_says —_Meduza⠀⇛ # ⚓ Meduza ☛ Even_after_doubling_its_sign-on_bonus payment,_the_Russian_army’s_recruitment_rate_is falling._Losses_may_now_outpace_new_enlistments._— Meduza⠀⇛ # ⚓ Meduza ☛ Russian_Defense_Ministry_says_it’s_received 48,000_applications_for_DNA_testing_from_relatives seeking_missing_soldiers_—_Meduza⠀⇛ # ⚓ Latvia ☛ Latvian_Security_Service_urges_prosecution for_memorial_desecration⠀⇛ On November 29 this year, the Latvian State Security Service (VDD) urged the Prosecutor's Office to prosecute a dual citizen of Estonia and Russia for helping the Russian special services to act against Latvia by desecrating a memorial important to Latvia. # ⚓ RFERL ☛ U.S._Urges_'Dignity'_After_Georgian_Protests Marred_By_Police_Brutality⠀⇛ A standoff between pro-EU Georgian protesters and security forces continues in Tbilisi amid accusations of excessive use of force by police that have prompted international condemnation including from a group of influential U.S. lawmakers. # ⚓ Atlantic Council ☛ To_help_Georgians,_the_West_must drive_a_wedge_between_Georgia_and_the_Russia-China-Iran camp⠀⇛ Despite strong support among Georgians for their country to join the European Union, the governing Georgian Dream party has taken big steps to break with the West in favor of the “axis of evasion.” # ⚓ Scoop News Group ☛ Russian-linked_Turla_caught_using Pakistani_APT_infrastructure_for_espionage⠀⇛ Both Abusive Monopolist Microsoft and Lumen’s BlackLotus Labs found Turla spying on Afghanistan and India via Pakistani infrastructure. # ⚓ RFERL ☛ 'Foreign_Agents'_Bill_Puts_Serbia's_EU Aspirations_Under_Question⠀⇛ Serbian lawmakers have begun deliberating a bill submitted to parliament that would establish a "foreign agents" registry, a move that may alienate Serbia from its EU ambitions. # ⚓ RFERL ☛ Pashinian_Suggests_Armenian_Rift_With_Russia Widening⠀⇛ Armenian Prime Minister Nikol Pashinian declared on December 4 in parliament that Yerevan had effectively passed the "point of no return" regarding its reintegration into a Russian-led military alliance. # ⚓ France24 ☛ ‘Aggressive'_Russian_cyber_attacks_boosted Romania's_pro-Moscow_presidential_candidate⠀⇛ Calin Georgescu, the pro-Russian outsider candidate now leading in Romania's presidential elections, was "aggressively" promoted on social control media platform Fentanylware (TikTok) through coordinated accounts and paid promotion, according to documents declassified Wednesday from Romania's security services. # ⚓ JURIST ☛ Romania_court_validates_first_round_of presidential_election⠀⇛ The Constitutional Court of Romania (CCR) unanimously validated the results of the first round of the presidential elections on Monday. The country’s constitutional court requested a re-verification and recount of all ballots by the Central Electoral Bureau amid allegations that Fentanylware (TikTok) provided coverage in favor of Călin Georgescu following his surprise victory on November 24 [...] # ⚓ Latvia ☛ Offroad_vehicles_on_their_way_from_Latvia_to Ukraine⠀⇛ On Wednesday, December 4, the third shipment of donations raised by the Latvian public media campaign will go to Ukraine, Latvian Radio reported. # ⚓ Latvia ☛ Latvian_professor_to_lead_big_study_on attitudes_toward_Ukrainian_refugees⠀⇛ A €2 million study on public attitudes towards refugees from Ukraine in Central and Eastern Europe will be conducted and led by sociologist Inta Mieriņa, a tenured professor at the University of Latvia, for the next five years, Latvian Radio reported December 4. # ⚓ Dispatches_from_Europe_–_No._12_–_December_3,_2024_– Dispatches_After_the_Election_of_Trump⠀⇛ Dispatches After the Election of Trump My last dispatch was almost a month ago, on November 6, the day after Trump won the American presidential election. The main reason for the pause in dispatches is that my hosts in Ukraine, and then Poland, Germany, Czechia, and now the U.K., have kept me too busy meeting with leftwing activists. # ⚓ PHR ☛ Russian_Bombardment_of_Ukraine’s_Power_Grid Forces_Health_Care_Workers_to_Operate_in_the_Dark: Report⠀⇛ Russia’s widespread and systematic attacks on Ukraine’s energy grid have harmed health care workers and endangered patients, according to a first-of-its-kind report published today by Physicians for Human Rights (PHR) and Truth Hounds. # ⚓ Atlantic Council ☛ A_winning_strategy_to_end_Russia’s war_against_Ukraine⠀⇛ More than a dozen experts from the United States and Europe share their recommendations to the incoming Trump administration about how best to end Russia's war against Ukraine. # ⚓ Atlantic Council ☛ Georgian_protests_escalate_amid fears_over_mounting_Russian_influence⠀⇛ The outcome of the current protests in Georgia will likely define the country's future and shape the geopolitical climate in the southern Caucasus and beyond for years to come, writes Ana Lejava. # ⚓ RFERL ☛ Ukrainian_Official_Says_Regional_Mayor_Died After_Torture_In_Russian_Captivity⠀⇛ The head of Zaporizhzhya Region's Military Administration, Ivan Fedorov, has alleged the mayor of the Ukrainian town of Dniproprudne died after being tortured while in Russian custody. # ⚓ RFERL ☛ NATO_Agrees_To_Prioritize_Protecting Ukraine's_Infrastructure⠀⇛ NATO members have agreed to make protecting Ukraine's infrastructure a top priority, alliance chief Mark Rutte said on December 4, as Russia continues to pound Ukrainian cities and towns with drone and missile strikes. # ⚓ MIT Technology Review ☛ How_the_Ukraine-Russia_war_is reshaping_the_tech_sector_in_Eastern_Europe⠀⇛ At first glance, the Mosphera scooter may look normal—just comically oversized. # ⚓ CS Monitor ☛ On_Ukraine’s_homefront,_a_DIY_drone industry_helps_fill_military’s_needs⠀⇛ Ukrainians are assembling drones at home to help supply the military with the thousands it uses every month in the war with Russia. # ⚓ New York Times ☛ Russian_General_Calls_U.S._Chairman of_Joint_Chiefs⠀⇛ In a highly unusual call, the two men “discussed a number of global and regional security issues, to include the ongoing conflict in Ukraine,” a spokesman said. # ⚓ New York Times ☛ Zelensky_Offers_$24_One-Off_Payment to_Win_Over_War-Weary_Ukrainians⠀⇛ Citizens will be entitled to a $24 one-off payment this winter, President Volodymyr Zelensky announced, in a move apparently intended to soften the blow of a tax rise to help fund the war effort. # ⚓ Meduza ☛ Ukrainian_mayor_dies_in_Russian_captivity_— Meduza⠀⇛ # ⚓ Meduza ☛ Washington_says_Ukraine_needs_to_begin drafting_younger_men_—_Meduza⠀⇛ # ⚓ Meduza ☛ Introducing_the_Oreshnik_What_Russia’s_’new’ ballistic_missile_means_for_Ukraine_and_nuclear security_—_Meduza⠀⇛ # ⚓ Meduza ☛ ‘Closer_now_than_ever’:_Historian_Sergey Radchenko_assesses_Tucker_Carlson’s_claim_that_U.S.- Russian_tensions_in_Ukraine_risk_nuclear_war_more_than the_Cuban_Missile_Crisis_—_Meduza⠀⇛ # ⚓ Meduza ☛ Trump_advisers_‘pitch_ideas’_as_Ukraine peace_plan_materializes,_and_all_proposals_exclude_NATO membership_—_Reuters_—_Meduza⠀⇛ # ⚓ RFERL ☛ Report:_Putin,_Other_Russian_Officials Directly_Involved_In_Transfer,_Deportation_of_Ukrainian Children⠀⇛ Senior Russian authorities, including President Vladimir Putin, were directly involved in ordering the forcible transfer, fostering, and later adoption of Ukrainian children moved out of war-zones and occupied regions of Ukraine, U.S. researchers found. o § Environment⠀➾ # ⚓ The Straits Times ☛ China_reports_warmest_autumn_since records_began⠀⇛ Most regions experienced temperatures 1 deg C to 2 deg C above average. # § Energy/Transportation⠀➾ # ⚓ Barry Kauler ☛ Planning_to_affix_solar_panel_to trike⠀⇛ Continuing the custom solar-assisted recumbent trike project, here are recent posts: # How_to_look_after_your_LFP_battery — November 09, 2024 # IEC_C13_versus_Anderson_connectors — November 06, 2024 I completed the electrical wiring; motor, junction-box, speed sensor, display panel, etc., and with some trepidation flicked the "motor" cicuit breaker on the junction box to "on" and then pressed the power-on button on the Bafang control panel ...and it worked. had the rear wheel propped up on blocks of wood and was able to test the pedal assistance levels. Looking good. The Bafang control panel mystifies me though. I mounted it right in the middle, between the legs: o § Finance⠀➾ # ⚓ Latvia ☛ Employers:_2025_budget_increases_gap_between households_with_and_without_children⠀⇛ The draft budget law for next year will increase inequality between households with and without children, as it does not raise the tax relief for a dependent, said Pēteris Leiškalns, Social Security and Healthcare Expert at the Employers' Confederation of Latvia (LDDK), in an interview on Latvian Radio program "Good Morning" December 4. # ⚓ Federal News Network ☛ IRS_warns_about_identity_theft_scams this_holiday_season⠀⇛ Giving out your address, Social Security number, bank account number or credit card number can lead to tax-related theft and fraud. # ⚓ Silicon Angle ☛ SentinelOne_shares_fall_13%_as_loss_expands despite_revenue_beat⠀⇛ Shares in SentinelOne Inc. were down around 13% in late trading today after the cybersecurity company reported a widening loss in its most recent quarter and gave a cautious outlook despite reporting beats in other core metrics in its fiscal 2025 third quarter. # ⚓ Atlantic Council ☛ The_IMF_and_World_Bank_did_well_under the_first_Trump_administration._Will_they_again?⠀⇛ The geopolitical rivalry between the United States and China has become more intense since Trump’s first term, which could affect how the incoming administration approaches the Bretton Woods institutions. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ France24 ☛ French_parliament_topples_PM_Barnier's government_in_no-confidence_vote⠀⇛ France's parliament voted to oust the government of French Prime Minister Michel Barnier in a no- confidence vote Wednesday evening. The left-wing New Popular Front alliance and far-right National Rally party both vowed to topple Barnier's government after he pushed an unpopular social security budget bill through parliament without a vote. President Emmanuel Macron's office said he will address the nation Thursday evening. # ⚓ France24 ☛ Vote_to_oust_French_Prime_Minister_Michel Barnier_a_‘forgone_conclusion’⠀⇛ FRANCE 24 journalist Clovis Casali, reporting from the lower house National Assembly, said the decision by MPs to oust French Prime Minister Michel Barnier was a “forgone conclusion”. “His speech was very much a goodbye speech, stressing what he had achieved,” Casali remarked. # ⚓ France24 ☛ Barnier_govt_on_chopping_block:_'Very_surprising alliance_between_left-wing_coalition_and_far_right'⠀⇛ France's government is facing no-confidence votes that could spell the end of the administration of Prime Minister Michel Barnier. For deeper insight and perspective, as France plunges into uncharted waters of political chaos, FRANCE 24's Genie Godula welcomes Dr. Anna McKeever, Political Scientist, Lecturer in Political Science at the University of the West of Scotland and author of 'Immigration Policy and Right-Wing Populism in Western Europe'. # ⚓ Hong Kong Free Press ☛ China_curbs_exports_of_key chipmaking_components_to_US⠀⇛ Beijing said Tuesday it would restrict exports to the United States of some key components in making semiconductors, after Washington announced curbs targeting China’s ability to make advanced chips. Among the materials banned from export are metals gallium, antimony and germanium, Beijing’s commerce ministry said in a statement that cited “national security” concerns. o § Censorship/Free Speech⠀➾ # ⚓ Stanford University ☛ Behind_the_nationwide_rise_of_book bans⠀⇛ Stanford experts dive into the recent increase in incidents of book banning and what it means for teachers, librarians, students and freedom of speech. # ⚓ New York Times ☛ Iran_Releases_Narges_Mohammadi,_Nobel Laureate,_From_Prison_for_21_Days⠀⇛ The activist, whose health has deteriorated, had bone surgery last month. She was just 19 when Iran’s morality police detained her. o § Freedom of Information / Freedom of the Press⠀➾ # ⚓ Hong Kong Free Press ☛ Post-security_law_Hong_Kong_‘beyond redemption,’_‘useless_to_fight,’_Jimmy_Lai_tells_court⠀⇛ Jailed media tycoon Jimmy Lai has said that Hong Kong “is beyond redemption” and that “it is useless to fight” in the city after a national security law imposed by Beijing came into effect in 2020. o § Civil Rights/Policing⠀➾ # ⚓ Hong Kong Free Press ☛ Hong_Kong_sees_rise_in_residents trafficked_to_SE_Asia,_with_12_still_held_overseas_–_security chief⠀⇛ Hong Kong has seen a rise in local residents lured to Southeast Asia to engage in illegal work, with 12 Hongkongers still being held overseas, security chief Chris Tang has said. # ⚓ JURIST ☛ Global_rights_groups_demand_Egypt_lift_ban_on human_rights_defenders⠀⇛ 34 rights organizations on Wednesday called on the Egyptian government to immediately lift the travel bans and asset freezes imposed on three directors of the Egyptian Initiative for Personal Rights (EIPR), an Egyptian human rights organization. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Computers Are Bad ☛ 2024-12-04_operators_on_the_front⠀⇛ At the very core of telephone history, there is the telephone operator. For a lot of people, the vague understanding that an operator used to be involved is the main thing they know about historic telephony. Of course, telephone historians, as a group, tend to be much more inclined towards machinery than people. This shows: websites with information on, say, TD-2, seldom tell you much about the operators as people. Fortunately, telephone operators have merited more than just a bit of discussion in the social sciences. It was a major field of employment, many ideas in management were tested out in the telephone companies, and moreover, telephone operators were women. # ⚓ APNIC ☛ How_to_boost_geolocation_accuracy_with_Geofeed⠀⇛ A friendly how to guide for network operators. # ⚓ Inside Towers ☛ FCC_Modifies_Emission_Limits_for_Mobile Devices_in_the_23.6-24.0_GHz_Band⠀⇛ The FCC has modified unwanted emissions limits for mobile operations for the 24.25-24.45 GHz and 24.75-25.25 GHz bands to prevent interference with passive systems in the 23.6-24.0 GHz band. The changes align with decisions made at the 2019 World Radiocommunication Conference (WRC-19). In the Report and Order, the Commission says the 23.6-24.0 GHz band is critical for passive sensors that measure weak natural radio emissions vital for meteorology, climatology, and satellite radar operations. The limits apply to both current and future mobile devices, with stricter limits coming into effect after September 1, 2027. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Sean Conner ☛ Ice_ice_baby⠀⇛ The following week the technician showed up again, bitched that we failed to answer his messages. I explained that I set my phone to have a silent default ring tone due to spam, and a default text tone of silence, again due to spam (and man, the amount of text spam I recieved from politicians during election season was staggering! Damn you policitians and exempting yourselves from spam laws! Damn you all to hell!). The technician was nonplussed and said I should do something about that. We gave him Bunny's phone number as she doesn't have a silent default ring tone. § Monopolies/Monopsonies⠀➾ o ⚓ JURIST ☛ Australia_proposes_new_regime_to_fine_tech_companies_for anti-competitive_practices⠀⇛ The Australian government on Monday unveiled a proposed competition scheme to introduce new laws that would allow global technology companies to be fined up to $50 million AUD for anti-competitive behavior and obstructing consumer choice. o § Copyrights⠀➾ # ⚓ Creative Commons ☛ Welcoming_Angela_Oduor_Lungati_as_CC Board_Chair⠀⇛ “Yellow Chair, The High Line” by Shawn Hoke is licensed under CC BY-NC-ND 2.0. Creative Commons (CC) has—and continues to be—fortunate to have an expert and passionate board of directors, many of whom have been instrumental to the success of CC at both the organizational level, as well as nationally and regionally. ䷩ 𝚕𝚒𝚗𝚎 6372 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 05/12/2024: Formaldehyde and Cancer, US and China Boycotting One Another⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Winter_Street⦈_ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * Leftovers o Hardware o Health/Nutrition/Agriculture o Proprietary/Artificial_Intelligence_(AI) o Security # Privacy/Surveillance o Defence/Aggression o Environment # Energy/Transportation o Finance o Censorship/Free_Speech o Freedom_of_Information_/_Freedom_of_the_Press o Civil_Rights/Policing o Internet_Policy/Net_Neutrality o Monopolies/Monopsonies # Patents # Trademarks # Copyrights * § Leftovers⠀➾ o ⚓ The Straits Times ☛ Starbucks_cafe_offers_view_of_village_in North_Korea,_stirring_up_bittersweet_feelings⠀⇛ Some visitors feel sad as they look at the North and reflect on the disparity in living standards between both sides. o § Hardware⠀➾ # ⚓ The Straits Times ☛ Indonesia_says_Fashion_Company_Apple_to offer_$1.34_billion_to_lift_iPhone_ban⠀⇛ If confirmed, that would be a tenfold increase from Apple’s last offer of US$100 million. # ⚓ Cloudbooklet ☛ US_Cracks_Down_on_China_Hey_Hi_(AI)_Chip Access⠀⇛ Discover the latest updates on China Hey Hi (AI) Chip Access and its implications. # ⚓ France24 ☛ US_-_China_chip_war_heats_up_as_Beijing_bans export_of_key_minerals⠀⇛ A day after the US government announced new export restrictions hitting China's chip industry, Beijing retaliated with a ban on the sale of key minerals like gallium and germanium to the United States. # ⚓ New York Times ☛ China_Announces_a_Ban_on_Rare_Minerals_to the_U.S.⠀⇛ The move escalates supply chain warfare and comes a day after the Biden administration expanded curbs on the sale of advanced American technology to China. # ⚓ The Straits Times ☛ China_to_curb_exports_of_key_chipmaking components_to_US⠀⇛ Among the materials banned from export are metals gallium, antimony and germanium. # ⚓ Tom's Hardware ☛ Chinese_chip_firms_say_a_new_round_of_US sanctions_won’t_stop_China’s_chip_industry_—_Chinese government_responds_with_its_own_export_restrictions anyways⠀⇛ The US and China trade blows yet again on semiconductor products and minerals, but Chinese companies say they’ll survive. # ⚓ The Next Platform ☛ US_Curbs_HBM_Exports_To_China_–_More For_The_Rest_Of_Us⠀⇛ Current US president Joe Biden and once and future president Donald Trump do not agree on much. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Pro Publica ☛ Formaldehyde_Increases_Your_Cancer_Risk_No Matter_Where_you_Live⠀⇛ In a world flush with hazardous air pollutants, there is one that causes far more cancer than any other, one that is so widespread that nobody in the United States is safe from it. It is a chemical so pervasive that a new analysis by ProPublica found it exposes everyone to elevated risks of developing cancer no matter where they live. And perhaps most worrisome, it often poses the greatest risk in the one place people feel safest: inside their homes. # ⚓ ProPublica_Cancer_Risk_Map⠀⇛ In most of the country, formaldehyde contributes more to outdoor cancer risk than any other toxic air pollutant. Look up your address to see risks from the chemical on your block and where it comes from. # ⚓ Science Alert ☛ Lockdowns_Did_Something_to_Teen_Brains,_And We_Need_to_Talk_About_It⠀⇛ This might not be over. # ⚓ New York Times ☛ McDonald’s_E_Coli_Outbreak_Declared_Over⠀⇛ Federal health agencies closed their investigations into the bacterial outbreak that sickened 104 people and was linked to onions on the fast-food chain’s signature Quarter Pounders. # ⚓ LSA_professor_studies_anti-aging_interventions,_diseases⠀⇛ An LSA professor is studying how to extend the healthy years of human life by building biological resistance against the many diseases that we face as we get older. # ⚓ TwinCities Pioneer Press ☛ Michaud,_Todd:_How_St._Paul_can find_a_good_way_forward_from_its_fiscal_ailments⠀⇛ In$ight St. Paul is a group of St. Paul residents who are very concerned about the financial health of the city. We span the political spectrum, # ⚓ JURIST ☛ Historic_UN_plastic_pollution_treaty_negotiation to_reconvene_in_2025⠀⇛ The fifth session of negotiations on a historic, legally binding global plastic pollution treaty concluded on Sunday, with countries agreeing to reconvene in 2025. # ⚓ The Straits Times ☛ When_necessity_becomes_luxury:_Many torn_over_keeping_insurance_policies_in_Malaysia⠀⇛ Rising premiums have prompted some people to cancel their health insurance policies. # ⚓ The Straits Times ☛ Consumer_group_calls_for_Bank_Negara Malaysia_to_tighten_controls_over_insurance_premium_hikes⠀⇛ Many may be forced to discontinue their policies, leaving them without essential medical coverage. # ⚓ JURIST ☛ US_Supreme_Court_hears_oral_arguments_over_FDA refusal_to_approve_flavored_e-cigarettes⠀⇛ The US Supreme Court on Monday heard oral arguments in a case in which the Food and Drug Administration (FDA) refused to approve flavored e-cigarettes, citing public health concerns. The FDA denied applications from two companies — Triton Distribution and Vapetesia — to sell flavored liquids for use in e-cigarettes, also known as vapes. o § Proprietary/Artificial Intelligence (AI)⠀➾ # ⚓ Bruce Schneier ☛ Algorithms_Are_Coming_for_Democracy—but It’s_Not_All_Bad⠀⇛ In 2025, Hey Hi (AI) is poised to change_every aspect_of_democratic_politics—but it won’t necessarily be for the worse. India’s prime minister, Narendra Modi, has used Hey Hi (AI) to translate his speeches for his multilingual electorate in real time, demonstrating how Hey Hi (AI) can help diverse democracies to be more inclusive. Hey Hi (AI) avatars were used by presidential candidates in South Korea in electioneering, enabling them to provide answers to thousands of voters’ questions simultaneously. o § Security⠀➾ # ⚓ Latvia ☛ 'CyberBazaar'_events_start_Tuesday_in_Rīga⠀⇛ From December 3 to 5, the first cyber security innovation forum in the Baltic States dubbed "CyberBazaar 2024" is being held in Rīga, organized by the Latvian National Cyber ​​Security Center in cooperation with Estonian and Lithuanian colleagues. # ⚓ Scoop News Group ☛ Inside_a_new_initiative_to_lend cybersecurity_volunteers_to_organizations_that_need_it_most⠀⇛ The idea behind the initiative, details of which CyberScoop is first reporting, is that too much cyber expertise doing volunteer work is uncoordinated. # ⚓ CNCF_Graduates_Cert-Manager_to_Help_Streamline_Certificate Workflows⠀⇛ The cert-manager project has officially been graduated by the Cloud Native Computing Foundation (CNCF) at a time when managing certificates has become more challenging than ever. > # ⚓ Qubes_Canary_041⠀⇛ We have published Qubes_Canary_041. The text of this canary and its accompanying cryptographic signatures are reproduced below. For an explanation of this announcement and instructions for authenticating this canary, please see the end of this announcement. # ⚓ Scoop News Group ☛ U.S._government_says_Salt_Typhoon_is still_in_telecom_networks⠀⇛ The United States and other Western nations released guidance Tuesday designed to evict the China-linked group in the wake of the high-profile hack. # § Privacy/Surveillance⠀➾ # ⚓ NYOB ☛ noyb_is_now_qualified_to_bring_collective redress_actions⠀⇛ noyb is now approved as so-called "Qualified Entity" to bring collective redress actions in courts throughout the European Union # ⚓ Scoop News Group ☛ CFPB_proposes_new_rule_to_regulate expansive_data_broker_industry⠀⇛ The rule would force data brokers to adhere to the same standards as established credit agencies. o § Defence/Aggression⠀➾ # ⚓ New York Times ☛ Read_President_Yoon’s_Speech_Declaring Martial_Law_in_South_Korea⠀⇛ President Yoon Suk Yeol made the extraordinary declaration in an unannounced speech to the nation on Tuesday night. # ⚓ The Strategist ☛ Avoiding_downstream_consequences: Australia’s_role_in_promoting_water_security_in_the_Middle East⠀⇛ Australia can partner with Middle Eastern countries on something we both really understand: how to manage scarce water. # ⚓ Atlantic Council ☛ NATO_exercises:_The_guarantee_of Alliance_security_and_test_of_readiness⠀⇛ To ensure regional security, NATO must continue enhancing its capabilities and remain as a combat- ready force. # ⚓ Atlantic Council ☛ The_“other”_US_election_and_what_it means_for_transatlantic_security⠀⇛ US allies and partners have better grounds to expect continued US leadership— and alliance commitment—than is commonly appreciated. # ⚓ Atlantic Council ☛ NATO_in_an_evolving_geopolitical landscape⠀⇛ The fourth issue of the Defense Journal by Atlantic Council IN TURKEY explores the future of NATO in the context of changing transatlantic relations and regional security issues. # ⚓ New York Times ☛ Google_Worried_Israeli_Contract_Could Enable_Human_Rights_Violations⠀⇛ The tech giant, which has defended the deal to employees who oppose supplying Israel’s military with technology, feared the project might damage its reputation. # ⚓ Hong Kong Free Press ☛ Taiwan_launches_hotlines_for managing_‘safety_risks’_when_travelling_to_Hong_Kong,_Macau and_China⠀⇛ Taiwan has launched hotlines for travellers seeking information about their “safety risks” while in China, which recently published tough criminal sentencing guidelines for supporters of the island’s independence. # ⚓ The Straits Times ☛ Taiwan_launches_hotlines_to_help navigate_China_travel_‘safety_risks’⠀⇛ The hotlines will address concerns over new guidelines from Beijing for supporters of Taiwanese independence. # ⚓ Hong Kong Free Press ☛ Taiwan_President_Lai_Ching-te arrives_in_Marshall_Islands_as_China_fumes⠀⇛ Taiwanese President Lai Ching-te arrived in the Marshall Islands on Tuesday, after visiting the United States on the first stop of a Pacific tour that has angered Chinese leaders. # ⚓ The Straits Times ☛ Taiwan’s_President_Lai_kicks_off Marshall_Islands_visit_as_China_fumes⠀⇛ Taiwan sends significant climate change and infrastructure aid to the Marshall Islands. # ⚓ The Straits Times ☛ Canada_says_Pacific_trade_pact_open_to new_members_after_Taiwan_complains⠀⇛ Taiwan has few international trade agreements due to its diplomatic isolation because of pressure from China. # ⚓ LRT ☛ Ball_is_in_China’s_court_regarding_diplomatic relations_with_Lithuania_–_FM_candidate⠀⇛ China should initiate the restoration of full diplomatic representation with Lithuania, says Kęstutis Budrys, the candidate for Lithuania’s foreign minister, currently serving as an adviser to President Gitanas Nausėda. # ⚓ LRT ☛ Lithuania’s_PM-designate_says_he_didn’t_know_about Chinese_mission_staff_expulsion⠀⇛ Lithuania’s Social Democrat Prime Minister- designate Gintautas Paluckas says he was not informed about the decision to expel three employees of China’s diplomatic mission from Lithuania. # ⚓ New York Times ☛ From_Chinese_Patriot_to_American_Spy:_The Unusual_Life_of_John_Leung⠀⇛ He had been hailed by Chinese state media as a model for his efforts to promote Beijing’s interests in the United States. He was in fact an F.B.I. informant. # ⚓ Defence Web ☛ Understanding_US-Angola_security_cooperation and_military_partnership⠀⇛ US President Joe Biden is visiting Angola in a historic milestone that underscores a strengthening partnership, with a particular emphasis on security cooperation. This unprecedented visit reflects the Biden administration’s commitment to enhancing bilateral relations and addressing shared security challenges. # ⚓ New Yorker ☛ How_the_Syrian_Opposition_Shocked_the_Assad Regime⠀⇛ A historian explains why U.S. sanctions and Iran and Russia’s entanglements in other wars helped create an opening for rebel groups to overrun the Syrian Army. # ⚓ CS Monitor ☛ Syrian_civil_war:_What_rebels’_lightning_gains say_about_Assad_regime⠀⇛ Syria’s devastating civil war, responsible for more than 300,000 deaths, was never officially resolved. Lightning gains by rebels opposed to President Bashar al-Assad were opportunistic, but also indicated years of patient preparations. # ⚓ Meduza ☛ The_Syrian_civil_war_is_suddenly_unfrozen._How much_can_Russia_afford_to_support_the_Assad_regime_this_time? —_Meduza⠀⇛ # ⚓ New York Times ☛ Amid_Syria’s_Rebel_Offensive,_a Geopolitical_Cauldron_Simmers⠀⇛ Iran and Russia, both stretched by conflicts of their own, have experienced setbacks in Syria after a rebel offensive in the northwest of the country. # ⚓ New York Times ☛ Martial_Law_in_South_Korea_Tests_Biden_and a_Key_U.S._Alliance⠀⇛ The Biden administration has hailed South Korea as a model democracy and bolstered military ties as it relies on the country as a bulwark against North Korea, China and Russia. # ⚓ Meduza ☛ Moscow_urges_Russian_citizens_in_South_Korea_to avoid_public_gatherings_amid_anti-martial_law_protests_— Meduza⠀⇛ # ⚓ The Straits Times ☛ Live:_South_Korean_president_makes_U- turn_on_martial_law⠀⇛ President Yoon said he would lift martial law after lawmakers voted to oppose the unexpected declaration. # ⚓ France24 ☛ Yoon_'created_the_rhetoric_of_a_national security_crisis'_in_South_Korea,_analyst_says⠀⇛ South Korean President Yoon Suk Yeol’s government early Wednesday lifted the martial law he imposed during a tense night of political drama in which troops surrounded parliament and lawmakers voted to reject military rule. FRANCE 24's Sharon Gaffney speaks to Professor Katherine Moon of Wellesley College in Boston. She says that President Yoon created the rhetoric of a national security crisis and has likely signalled his own downfall. # ⚓ The Straits Times ☛ What_next_for_South_Korea’s_President Yoon_Suk_Yeol_after_failed_martial_law_attempt?⠀⇛ Botched martial law declaration spells end of political career, say analysts. # ⚓ The Straits Times ☛ South_Korea_President_Yoon_declares martial_law,_but_Parliament_votes_to_lift_declaration⠀⇛ He said the measure was necessary to protect the country from “communist forces”. # ⚓ The Straits Times ☛ Live:_South_Korea_lawmakers_block president’s_martial_law_decree⠀⇛ President Yoon said he would lift martial law after lawmakers voted to oppose the unexpected declaration. # ⚓ The Straits Times ☛ ‘Can’t_believe_I’m_seeing_martial_law declaration_in_my_lifetime’:_Shock,_confusion_among S.Koreans⠀⇛ The financial markets have responded with panic, exacerbating the public’s distress. # ⚓ The Straits Times ☛ In_full:_South_Korea’s_martial_law decree⠀⇛ All media and publications are subject to the control of the Martial Law Command. # ⚓ The Straits Times ☛ What_next_for_South_Korea’s_President Yoon_Suk_Yeol?⠀⇛ Botched martial law declaration spells end of political career, say analysts. # ⚓ The Straits Times ☛ Martial_law_in_South_Korea_tests_Biden and_a_key_US_alliance⠀⇛ Nearly 30,000 US troops are stationed in South Korea. # ⚓ The Straits Times ☛ South_Korea’s_President_Yoon_Suk_Yeol, embattled_conservative⠀⇛ Mr Yoon took office with some of the lowest approval ratings of any democratically elected South Korean president. # ⚓ The Straits Times ☛ South_Korea’s_President_Yoon_Suk_Yeol says_martial_law_decree_will_be_lifted⠀⇛ He had imposed the order hours earlier in a bid to quell what he called “anti-state forces”. # ⚓ The Straits Times ☛ South_Korea’s_martial_law_declaration: What_we_know_so_far⠀⇛ South Korea President Yoon Suk Yeol declared martial law late on Dec 3 - then reversed course just hours later. # ⚓ France24 ☛ South_Korea's_President_Yoon_rescinds declaration_of_martial_law_after_parliament_votes_to_block it⠀⇛ President Yoon Suk Yeol said he was rescinding his declaration of martial law after South Korea's parliament voted Tuesday to block it as hundreds of protesters gathered outside the building, calling for Yoon's arrest. # ⚓ France24 ☛ 🔴_South_Korean_President_Yoon_Suk_Yeol_declares martial_law⠀⇛ # ⚓ France24 ☛ 'Against_will_of_people':_President_Yoon's 'miscalculation'_in_declaring_Martial_Law_'crossed_line'⠀⇛ Troops surrounded South Korea's parliament overnight after the president declares martial law. He accused pro-North Korean forces of plotting to overthrow one of the world’s most vibrant democracies. As lawmakers voice outrage, and hastily vote to end the declaration, FRANCE 24's François Picard welcomes Peter Han, Gates Cambridge Scholar at the University of Cambridge and member of the National Unification Advisory Council UK. # ⚓ France24 ☛ 🔴_South_Korean_President_Yoon_rescinds_martial law_after_parliament_votes_to_block_it⠀⇛ # ⚓ France24 ☛ No,_these_images_don’t_show_tanks_and_protests in_the_streets_of_Seoul⠀⇛ Following the declaration of martial law in South Korea by President Yoon Suk Yeol, images of tanks and alleged massive protests in Seoul started to circulate online. We tell you which images are fake and which are real, in this edition of Truth or Fake. # ⚓ The Straits Times ☛ South_Korea_President_Yoon’s_failed attempt_at_martial_law_may_put_his_position_in_peril⠀⇛ Mr Yoon's shocking late-night declaration of martial law has thrown his political future into doubt. # ⚓ The Straits Times ☛ US_says_it_is_watching_events_in_South Korea_with_grave_concern⠀⇛ South Korean President Yoon Suk Yeol declared martial law in a surprise late-night TV address, before the opposition-led Parliament overturned it. # ⚓ New York Times ☛ Chaos_Plays_Out_at_South_Korea’s Legislature_Building_After_Declaration_of_Martial_Law⠀⇛ Soldiers wearing helmets and carrying long guns pushed back against people who tried to enter the National Assembly, after President Yoon Suk Yeol declared martial law. # ⚓ New York Times ☛ Who_Is_Yoon_Suk_Yeol,_South_Korea’s President?⠀⇛ A conservative, Mr. Yoon won the presidency in 2022 by a slim margin, promising a more confrontational stance against North Korea. He quickly became unpopular and divisive at home. # ⚓ New York Times ☛ Who_is_Lee_Jae-myung,_South_Korea’s Opposition_Leader?⠀⇛ The opposition leader rallied lawmakers to vote down President Yoon Suk Yeol’s martial law decree. # ⚓ New York Times ☛ Live_Updates:_South_Korean_President_Backs Down_From_Martial_Law⠀⇛ President Yoon Suk Yeol formally lifted martial law in a cabinet meeting early Wednesday, six hours after he declared it, and after protesters filled the street, calling for his removal from office. # ⚓ New York Times ☛ Timeline:_How_Yoon’s_Presidency_in_South Korea_Led_to_Martial_Law_Order⠀⇛ Yoon Suk Yeol’s decree, and his reversal under pressure from lawmakers, were the culmination of years of feuding between the country’s two main political camps. # ⚓ New York Times ☛ Why_Was_Martial_Law_Declared_in_South Korea?⠀⇛ President Yoon Suk Yeol has been locked in a bitter fight with the opposition, which controls Parliament. # ⚓ The Straits Times ☛ 38_Vietnamese_tourists_reported_missing in_South_Korea’s_Jeju_island⠀⇛ The missing tourists were part of a group of around 90 tourists who arrived in Jeju on Nov 14. # ⚓ France24 ☛ Domino_effect?_Assad's_allies_stretched_thin_as Syrian_rebels_pounce⠀⇛ It took years for Bashar al-Assad’s forces to take back Syria’s second city. It took days for jihadist-led rebels to overrun Aleppo. Why has a conflict that has been effectively frozen for four years suddenly spring back to life? What to make of Hezbollah, pinned down at home by a precarious truce with Israel, saying it won’t be sending help for now. # ⚓ France24 ☛ The_ruins_of_Paris_through_the_lenses_of_Yves Marchand_and_Romain_Meffre⠀⇛ Two photographers whose images look like something you might see in a Hollywood high budget film have spoken to FRANCE 24 about their work. They take pictures of Paris, and then use artificial intelligence to adapt them to take viewers to a post-apocalyptic world where humans are perhaps no more. Their photography has been made into a book Les Ruines de Paris, or the ruins of Paris. Yves Marchand and Romain Meffre spoke to us in perspective. # § Russia, Belarus, and War in Ukraine⠀➾ # ⚓ France24 ☛ Chernobyl's_mutant_wolves:_A_case_study_of adaptation_and_cancer_resistance⠀⇛ In the Science segment, we tell you more about the so-called "mutant wolves of Chernobyl". 38 years after the nuclear disaster, animals roaming the exclusion zone are still exposed to high levels of radiation but researchers have also found that part of their genetic information appears to be resilient to increased risk of cancer. # ⚓ Meduza ☛ Swapping_rainbows_for_war_anthems:_How_the Kremlin’s_anti-LGBTQ+_crackdown_is_reshaping_queer clubs_in_Russia_—_Meduza⠀⇛ # ⚓ Latvia ☛ Riga_Security_Forum_podcast:_'China_and Russia:_A_Special_Relations_Operation'⠀⇛ The Riga Security Forum podcast is back with another topical discussion. # ⚓ RFERL ☛ Erdogan_Calls_For_More_Diplomacy_In_Talks With_Putin_On_Revived_Conflict_In_Syria⠀⇛ Russian President Vladimir Putin and Turkish President Recep Tayyip Erdogan stressed the need for diplomacy to resolve the conflict in northern Syria in a phone call on December 3 to discuss the renewed fighting. # ⚓ Atlantic Council ☛ Vladimir_Putin_does_not_want_a peace_deal._He_wants_to_destroy_Ukraine.⠀⇛ Donald Trump has vowed to end the war in Ukraine, but there is no sign that Vladimir Putin has any interest in a peace deal that would prevent him from achieving his goal of extinguishing Ukrainian statehood, writes Yuliya Kazdobina. # ⚓ New York Times ☛ Investigation_Into_Forced_Adoptions From_Ukraine_Points_Finger_at_Putin⠀⇛ Yale researchers traced hundreds of children taken to Russia in the war, finding what they described as “a higher level of crime than first understood.” # ⚓ Latvia ☛ Rules_for_Ukrainian_children_going_to Latvian_schools_stuck_in_debate⠀⇛ In the summer, the government decided that starting the next school year, children - war refugees from Ukraine - will have to study in Latvian schools in person. The Saeima's support is needed for this requirement to come into force. However, the idea is currently stuck in the Saeima, Latvian Radio reported on December 3. # ⚓ Atlantic Council ☛ The_EU_needs_a_Russia_strategy⠀⇛ The new European Commission should prioritize the development of an EU Russia strategy aimed at creating a more forward-thinking, ambitious, and cohesive European approach toward Moscow, write Ian Cameron and James Batchik. # ⚓ Atlantic Council ☛ Political-military_lessons_for_a NATO-Russia_conflict⠀⇛ NATO should learn these three lessons from the Ukraine-Russia conflict to win a potential NATO-Russia war. # ⚓ France24 ☛ Ukraine_pushes_NATO_for_membership_ahead of_Trump_presidency⠀⇛ Ukraine insisted Tuesday that NATO membership was the only "real guarantee" for its security, but foreign ministers from the alliance sidestepped Kyiv's push for an invite ahead of Donald Trump's return to the US presidency. FRANCE 24's speaks to Dr Gavin Hall from the University of Strathclyde. He says that although the formal position of NATO is to be open to a Ukrainian membership, it's uncertain whether every member is willing to accept it into the alliance. # ⚓ LRT ☛ Number_of_Russians,_Belarusians,_Ukrainians with_residence_permits_in_Lithuania_drops⠀⇛ The number of Russians, Belarusians, and Ukrainians holding residence permits in Lithuania has declined by over 20,000 since the start of this year, figures from the Interior Ministry show. # ⚓ LRT ☛ Driving_tests_in_Lithuania_to_take_place_only in_EU_languages⠀⇛ From January next year, driving tests in Lithuania will take place only in Lithuanian or other official EU languages. However, an exception will be made for Ukrainians, the Interior Ministry said on Tuesday. # ⚓ RFERL ☛ Ukraine_Again_Calls_For_Full_Membership_As NATO_Ministers_Meet_In_Brussels⠀⇛ Ukraine has again called for membership in NATO, saying that only joining the alliance in full would guarantee its future security as it fights to stave off Russia's nearly three-year invasion. # ⚓ New York Times ☛ NATO_Chief_Urges_More_Weapons_for Ukraine_Ahead_of_Any_Peace_Talks⠀⇛ Mark Rutte said it was up to Ukraine to decide when it was ready to begin negotiations with Russia — and that the West should help strengthen Kyiv’s position beforehand. # ⚓ Meduza ☛ France_and_U.K._might_send_peacekeepers_if Russia_and_Ukraine_reach_ceasefire_—_RFE/RL_—_Meduza⠀⇛ # ⚓ Meduza ☛ Russia’s_college_aptitude_exam_reportedly_to include_Ukraine_war_veterans_alongside_historical figures_—_Meduza⠀⇛ # ⚓ Latvia ☛ Government_okays_banning_Russian_language from_transport_signage⠀⇛ On Tuesday, December 3, the government approved the cabinet regulations prepared by the Ministry of Justice, which state that in transport and related infrastructure, signs and information must be provided in Latvian and if needed, another official language of the European Union (EU). # ⚓ Atlantic Council ☛ Pacing_scenarios⠀⇛ Here are some scenarios that NATO should be prepared for against the possibility of a generational conflict with Russia. # ⚓ Atlantic Council ☛ How_prepared_is_NATO?⠀⇛ Is NATO ready to respond to a possible expansion of Russian aggression to assure Europe's safety? # ⚓ France24 ☛ Kirill_Serebrennikov’s_poetic_take_on Russian_punk_outsider_Eduard_Limonov⠀⇛ Eduard Limonov was a poet, a punk, a Russian “émigré” and provocateur whose anti-system politics eventually saw him embrace fascist tendencies. Filmmaker Kirill Serebrennikov tells Olivia Salazar-Winspear why he chose to make a “ballad” of Limonov’s life and not a biopic, revealing that British actor Ben Wishaw even had the Russian crew members fooled with his impressive embodiment of the character. Serebrennikov tells us how Limonov’s political arc follows the far right movements within contemporary Russia and mirroring the geopolitical situation around the world. And, as an immigrant himself, the award-winning director tells us why he thinks Moscow’s attempts to silence Russian artists means the government has little influence over those who criticise it. # ⚓ France24 ☛ 'Russia_believes_it_should_control Georgia'⠀⇛ Georgia has been locked in a political crisis since its contested October election, with tens of thousands of pro-EU protesters taking to the streets in recent days against the increasingly authoritarian Eurosceptic government. For in-depth analysis and a deeper perspective on Georgia's Russian- friendly pivot away from the EU, FRANCE 24's Eve Irvine is joined by Dr. Natasha Lindstaedt, Author, Professor of Government at the University of Essex and the Deputy Dean of Education in Social Sciences. # ⚓ RFERL ☛ Georgia's_Abkhazia_Lawmakers_Reject 'Enslaving'_Investment_Deal_With_Russia⠀⇛ De facto lawmakers of Georgia's breakaway region of Abkhazia on December 3 rejected an investment deal with Russia, a document that has caused political turmoil and mass protests, highlighting the region’s fraught relationship with Moscow. # ⚓ LRT ☛ Lithuania_downgrades_OSCE_representation_over planned_Lavrov_attendance⠀⇛ Lithuania is downgrading the level of its representation at the upcoming Organization for Security and Co-operation in Europe (OSCE) ministerial meeting in Malta as Russian Foreign Minister Sergey Lavrov plans to attend it, the Foreign Ministry told BNS on Tuesday. # ⚓ RFERL ☛ Russian_Woman_Arrested_In_U.S._For_Alleged Ties_To_Russian_Intelligence⠀⇛ The FBI has charged Russian national Nomma Zarubina with providing false information to U.S. law enforcement and maintaining connections with Russian intelligence services, linking her to another suspected spy who fled the United States while being pursued by authorities. # ⚓ Meduza ☛ Top_Russian_bank_executive_publishes_‘letter to_Santa’_asking_for_stabilized_ruble_and_help_with inflation_—_Meduza⠀⇛ # ⚓ Meduza ☛ Russian_city_quietly_replaces_blue_and yellow_ornaments_on_central_public_Christmas_tree_— Meduza⠀⇛ # ⚓ Meduza ☛ Small_asteroid_lights_up_Siberian_sky_— Meduza⠀⇛ o § Environment⠀➾ # ⚓ The Straits Times ☛ Malaysia_floods:_Six_months’_worth_of rain_fell_in_five_days_across_east_coast,_says_PM_Anwar⠀⇛ PM Anwar also said the government is preparing for the forecast monsoon surge. # ⚓ The Straits Times ☛ Malaysians_return_to_devastated_homes as_flood_waters_recede;_more_rain_expected⠀⇛ The number of people in temporary shelters in Malaysia fell to just under 95,000 on the morning of Dec 3. # ⚓ The Straits Times ☛ Top_emitter_China_tells_World_Court that_UN_treaties_cover_states’_climate_obligations⠀⇛ The UN has asked the court to issue an opinion on countries' legal responsibility for the negative impact of climate change. # § Energy/Transportation⠀➾ # ⚓ LRT ☛ From_‘doctors’_plane’_to_fatalities_in_the_sea –_history_of_Lithuanian_aviation_disasters⠀⇛ The last decades have been relatively quiet in Lithuania’s aviation sector. The 20th century, however, was marked by far more fatal crashes. The largest Lithuania-related disaster occurred in 1973 when a passenger plane flying from Vilnius crashed near Moscow, killing 51 people, says Lithuanian Aviation Museum curator Eugenijus Raubickas. o § Finance⠀➾ # ⚓ Latvia ☛ KNAB_to_take_over_tax_service's_anti-corruption tasks⠀⇛ On Tuesday, December 3, the Cabinet of Ministers (MK) approved the draft order on the transfer of the functions of the Internal Security Department of the State Revenue Service (VID) to the Corruption Prevention and Combating Bureau (KNAB). # ⚓ Atlantic Council ☛ There’s_a_more_effective_way_forward than_“maximum_pressure”_for_Venezuela⠀⇛ Following the fraudulent outcome of Venezuela's July election, there is growing pressure on the United States to reintroduce sanctions to expel Western firms from the nation’s oil sector. # ⚓ The Straits Times ☛ Corruption_cases_in_China_rise_amid deeper_crackdown,_poorer_economy⠀⇛ For the first nine months of 2024, China has logged 642,000 corruption cases, higher than the 626,000 for the whole of 2023. # ⚓ The Straits Times ☛ In_pivot_from_India,_Nepal_PM_seeks economic_support_from_China⠀⇛ Mr K.P. Sharma Oli has so far been greeted by familiar pledges of assistance, but no new investment. o § Censorship/Free Speech⠀➾ # ⚓ Silicon Angle ☛ Who_is_David_Mayer?_Abusive_Monopolist Microsoft_Chaffbot_faces_scrutiny_over_censorship_of_public figures⠀⇛ Who is David Mayer? A month after Proprietary Chaffbot Company added a search engine to its highly popular Abusive Monopolist Microsoft Chaffbot service, users are unable to get answers to anything relating to David Mayer in a mystery that swept the internet over the last week. o § Freedom of Information / Freedom of the Press⠀➾ # ⚓ Hong Kong Free Press ☛ Jimmy_Lai_tells_trial_it_was_his ‘honest_belief’_Western_sanctions_on_China_could_stop_Beijing from_imposing_security_law⠀⇛ Jailed Hong Kong media tycoon Jimmy Lai has said it was his “honest belief” that the West could force Beijing to halt the enactment of a national security law in Hong Kong in 2020 by imposing sanctions on top Chinese officials. o § Civil Rights/Policing⠀➾ # ⚓ OpenRightsGroup ☛ Home_Office_must_use_e-visa_delay_to change_flawed_scheme [Ed: ORG got taken over by Muslims and now has "ORG’s Migrant Rights Digital Justice Programme Manager". They used to be about privacy and tech, not immigration.]⠀⇛ Open Rights Group has welcomed reports that the government is set to delay the rollout of its e- visa scheme, which was due to come into effect on January 1, 2025. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Hackaday ☛ A_Month_Without_IPV4_Is_Like_A_Month_Without…⠀⇛ Recently, there was a Mastodon post from [nixCraft] challenging people to drop their NAT routers for the month of November and use only IPv6. What would it be like to experience “No NAT November?” [Alex Haydock] decided to find out. # ⚓ MWL ☛ My_Social_Media_in_2024⠀⇛ I left Ex-Twitter right after Elon Musk bought it. § Monopolies/Monopsonies⠀➾ o § Patents⠀➾ # ⚓ JUVE ☛ Silimed_sucessfully_claims_invention_for_breast implant_technology [Ed: EPO monopoly for fake boobs. Not unusual for giver of fake patents. The bribed press conflates patents with "invention".]]⠀⇛ The two parties have been in dispute for years over EP 2 581 193, which protects a process for manufacturing implants. In 2011, Polytech registered the basic patent monopoly but Silimed claims to be the inventor of this technology and filed an entitlement action in 2017. # ⚓ Dennis Crouch/Patently-O ☛ USPTO_Withdraws_Controversial Terminal_Disclaimer_Rule_–_But_Core_Issues_Remain⠀⇛ As I previously suggested, the USPTO has now announced that it is withdrawing its proposed rule that would have made terminal disclaimers far more noxious by tying patent monopoly enforceability to the validity of claims in related patents. While this is undoubtedly the right move given the questionable legal authority and overwhelmingly negative public response (over 300 comments, with 256 unique submissions), the underlying concerns that drove the proposal deserve attention because they will likely arise in other forms. [Read the Fed. Reg. Notice Cancelling the Proposal: 2024- 28263] # ⚓ The_PREVAIL_Act_Would_Perpetuate_Unjust_Monopolies,_Deter Innovation,_and_Violate_the_Founders’_Patent_Principles⠀⇛ The Federalist Society on its website quotes former President Ronald Reagan as saying “The Federalist Society is … returning the values and concepts of law as our founders understood them to scholarly dialogue.” # ⚓ CAFC_Affirms_Obviousness_Ruling_Invalidating_KPN’s_Network Access_Management_Patent_Claims⠀⇛ The U.S. Court of Appeals for the Federal Circuit on Monday, December 2, issued a ruling in Koninklijke KPN N.V. v. Vidal affirming the Patent Trial and Appeal Board’s (PTAB) invalidation of several patent monopoly claims to technologies for managing access to telecommunications networks. In so ruling, the Federal Circuit held that KPN’s plausible alternative understanding of a prior art reference did not require a finding that the PTAB’s obviousness ruling was unsupported by substantial evidence. # § Software Patents⠀➾ # ⚓ Unified Patents ☛ $2,000_awarded_for_Payvox_e- commerce_patent_monopoly_prior_art⠀⇛ Unified is pleased to announce PATROLL crowdsourcing contest winners, Andrei Gilya, Mani Manikandan, Ritu Tyagi, and Ramesh Varadharaj, who split a cash award of $2,000 for their prior art submissions on U.S. Patent_8,788,360, owned by Payvox LLC, an NPE. The ‘360 patent monopoly relates to wireless commerce systems. More particularly, the invention involves a point of advertising wireless commerce system to enable pervasive commerce with mass media publications. # ⚓ Unified Patents ☛ $2,000_awarded_for_Big_Will messaging_patent_monopoly_prior_art⠀⇛ Unified is pleased to announce PATROLL crowdsourcing contest winners, Mani Manikandan and Dinesh Swami, who split a cash award of $2,000 for their prior art submissions on U.S._Patent_10,521,846, owned and asserted by Big Will Enterprises Inc., an NPE. The ‘846 patent monopoly relates to electronic messaging technologies, and more particularly, to systems, methods, and apparatus for accurately identifying a mobile thing (MT) and/or a motion activity associated with the MT using sensor data. # ⚓ Unified Patents ☛ $2,000_for_Empire_IP_entity, Dynamic_Data_Innovations,_dataset_patent_monopoly_prior art⠀⇛ Unified Patents added a new PATROLL contest, with a $2,000 cash prize, seeking prior art on at least claim 1 of U.S._Patent_9,632,676, asserted by Dynamic Data Innovations LLC, an NPE and entity of Empire_IP_LLC. o § Trademarks⠀➾ # ⚓ TTAB Blog ☛ TTABlog_Test:_Which_of_These_Three_Section_2(d) Refusals_Was/Were_Overturned_on_Appeal?⠀⇛ The TTAB affirmance rate for Section 2(d) appeals this year continues to hover around 90%. Here are three recent Board decisions, at least one of which reversed the refusal. How do you think they came out? [Answer in first comment]. In_re_Vermutería_de_Galicia,_S.L., Serial No. 90385649 (November 29, 2024) [not precedential] (Opinion by Judge Cynthia C. Lynch). [Section 2(d) refusal of the word-and-design mark shown below, for "vermouth" in view of the registered mark PETRONI for "wine."] o § Copyrights⠀➾ # ⚓ Public Domain Review ☛ Fantastic_Planet:_The_Microscopy Album_of_Marinus_Pieter_Filbri_(1887–88)⠀⇛ Micrographs that make the minuscule world as alien as outer space. # ⚓ Public Domain Review ☛ The_Launch_of_Our_End-of-Year Fundraiser!⠀⇛ Our End-of-Year Fundraiser is launched, and the new postcards theme will be Home. # ⚓ Michael Geist ☛ Canadian_Media_Companies_Target_Proprietary Chaffbot_Company_in_Copyright_Lawsuit_But_Weak_Claims_Suggest Settlement_the_Real_Goal⠀⇛ Canada’s largest media companies, including the Globe and Mail, Toronto Star, Postmedia, CBC, and Canadian Press, came together last week to file_a copyright_monopoly_infringement_lawsuit against OpenAI, the owners of ChatGPT. ䷩ 𝚕𝚒𝚗𝚎 7785 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 05/12/2024: Mass Layoffs at Microsoft's PR (Bribery of Media) Agency, UnitedHealthcare CEO Shot Dead⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Dec 05, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Snowy_Landscape⦈_ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * Leftovers o Standards/Consortia o Science o Career/Education o Hardware o Health/Nutrition/Agriculture o Proprietary/Artificial_Intelligence_(AI) o Security # Privacy/Surveillance o Defence/Aggression o Transparency/Investigative_Reporting o Environment # Energy/Transportation # Wildlife/Nature o Finance o AstroTurf/Lobbying/Politics o Censorship/Free_Speech o Freedom_of_Information_/_Freedom_of_the_Press o Civil_Rights/Policing o Internet_Policy/Net_Neutrality o Digital_Restrictions_(DRM) o Monopolies/Monopsonies # Trademarks # Right_of_Publicity # Copyrights * § Leftovers⠀➾ o ⚓ Hackaday ☛ Fail_Of_The_Week:_The_SMD_Crystal_Radio_That_Wasn’t⠀⇛ The crystal radio is a time-honored build that sadly doesn’t get much traction anymore. Once a rite of passage for electronics hobbyists, the classic coil-on-an- oatmeal-carton and cat’s whisker design just isn’t that easy to pull off anymore, mainly because the BOM isn’t really something that you can just whistle up from DigiKey or Mouser. o ⚓ Hackaday ☛ Fluke_Meter_Fails_With_A_Simple_Problem⠀⇛ [TheHWcave] found a Fluke 27 multimeter that looked like it had had quite a rough life. At first, the display flashed an overload indicator until he gave it a good smack—or, as he likes to call it, percussive maintenance. Even then, it would not give good readings, so it was time to open it up. o ⚓ James G ☛ Things_I_have_been_reading_lately⠀⇛ I was thinking to myself that I have read many fascinating things over the last while, but haven’t shared them. I thought I would write a post to share some of the things I have been reading. As web weavers, perhaps one of the most magical things we can do aside from share our own creations is to boost those of others. I find great joy in sharing what others have made. o ⚓ Kev Quirk ☛ On_Substack_&_Blogging⠀⇛ Manu isn’t a fan of Substack, and he’s got two big reasons why: it takes control away from creators, and it pushes a “monetise everything” culture. He makes a solid case for owning your own domain and keeping blogging authentic and independent. o ⚓ Manuel Moreale ☛ On_blogging,_substacking_(?),_and_owning_digital real_estate⠀⇛ Let me rant for a second. I’m fucking tired of living in a society where everything is monetised, where nothing is safe from speculation, where every passion has to be turned into a business. “But why shouldn’t you turn your passion into a business?” you might ask. Because this endless pursuit of money is fucking up society. The incentives you set up, when you run a platform like Substack, matter a lot. It’s not an accident that, like Kevin said, after a while people on Substack start writing about Substack. Substack has no interest in promoting the people who write candidly about their inner struggles, their dreams and hopes, and their everyday lives. They have nothing to earn from that. They would, in fact, lose money if all of you out there started using the platform simply to share what you think, and what you’re going through, with no intention of ever turning it into a side hustle. o ⚓ Justin Vollmer ☛ You_Should_Have_a_Website⠀⇛ I’ve championed owning your own website for a while now, and have been posting more heavily about it over the past year or so. My own journey to running my own website was born out of a combination of desiring the challenge of maintaining my own site, wanting a place where I could control what I post and how it looks, and wanting some longevity and permanence for my web presence. And over time, I’ve begun to believe that it would be beneficial both for the individual and for society at large if more people followed suit. o ⚓ Justin Vollmer ☛ Seconding_the_Call_to_Blog_More_Often_|_Justin Vollmer⠀⇛ Personally, I’ve attempted to write more often, but consistency is still a struggle. Much of my recent work on this site has been with the express purpose of making my interactions with the site and its content more engaging for me, to increase my desire to post more consistently. o ⚓ MJ Fransen ☛ Org-journal_with_prompts⠀⇛ Last summier I concluded the #100daystooffload challenge (on Gopher). Writing daily in one's journal is not that different and I think the time has come to start building the habit of journaling. o ⚓ Juha-Matti Santala ☛ Three_is_a_pattern⠀⇛ Finding a balance between prepping for future or doing repeated work is not easy. Whether it is about sharing advice one-on-one vs. writing it down into a blog or refactoring code into reusable blocks or setting up extra tooling for personal notes’ system, the decision time comes up at some point. Over the years, I’ve found the rule of “three is a pattern” to be quite useful in balancing this. Here’s how it works: [...] o § Standards/Consortia⠀➾ # ⚓ Joost de Valk ☛ Can_I_safely_use_AVIF_or_WebP_share_images? [Ed: So they say, use AVIF or WebP on the Web (in spite of software patents and lots of SOFTWARE NOT SUPPORTING THEM; partly due to patents!), then they throw megabytes of JavaScript at you. Marketed based on lies. It also takes more bloated and probably less secure code to render these.]⠀⇛ You should use both AVIF and WebP on your website. They’re smaller, they’re better. All browsers support them. As of December 2024, you can use WebP share images, but you can not use AVIF on social platforms yet. We still have to get quite a few more platforms to support AVIF before it’s safe to use them as share images. However, changed from June 2024, you can now safely use WebP everywhere. o § Science⠀➾ # ⚓ Science Alert ☛ Scientists_Shifted_People's_Day_by_Just_5 Hours_–_Here's_What_Happened⠀⇛ Your body's weakest link has been identified. # ⚓ Science Alert ☛ The_Secret_of_Orange_Cats_Finally_Uncovered After_60-Year_Search⠀⇛ Barsh and his colleagues discovered cat skin cells from which orange fur sprouts express 13 times as much RNA from a gene called Arhgap36, compared with skin cells from cats with no orange hair. o § Career/Education⠀➾ # ⚓ The Nation ☛ In_Defense_of_Teachers_and_Public_Education⠀⇛ The Department of Education covers an estimated 9 percent of K-12 school funding, with states and local governments covering most funding to our K-12 schools. Critically, it administers our student loan program, which enables millions of students to afford college. It also funds important post- secondary support, like TRIO. TRIO programs provide targeted resources to students, including tutoring, academic assistance, financial counseling, and mentorship programs. These services reach low- income students, first-generation students, and our veterans, and improve educational attainment and academic preparedness. The Department of Education’s impact is felt in so-called red and blue states across the country. # ⚓ New York Times ☛ University_of_Michigan_Weighs_Changes_to Its_Diversity_Program⠀⇛ The school is one of higher education’s biggest supporters of D.E.I. Now it’s considering a new approach as critics question the program’s success and impact on campus life. # ⚓ Kansas Reflector ☛ The_right_has_made_the_truth_political. Teachers_are_nonetheless_obligated_to_speak_it.⠀⇛ There are more, but my point is not to prove to Christians that they have a moral obligation to the foreigner and the immigrant. My point is that telling this truth to a group of Christians in a Catholic school resulted in a teacher’s firing because it made people acting immorally uncomfortable with their immoral choice. Jimbo Gillcrist wasn’t fired for being political. He was fired for disrupting the damning silence of the status quo, a silence that is designed to let untruth flourish. # ⚓ Kodsnack ☛ Kodsnack_616_-_Computers_outside_of_computers, with_Violet_Whitney_and_William_Martin⠀⇛ Recorded on-stage at Øredev 2024, Fredrik talks to Violet Whitney and William Martin about the research they do into how we can interact with computers outside of the bounds of … well, a regular computer or phone. o § Hardware⠀➾ # ⚓ Hackaday ☛ Holograms:_The_Art_Of_Recording_Wavefronts⠀⇛ The difference between holography and photography can be summarized perhaps most succinctly as the difference between recording the effect photons have on a surface, versus recording the wavefront which is responsible for allowing photographs to be created in the first place. Since the whole idea of ‘visible light’ pertains to a small fragment of the electromagnetic (EM) spectrum, and thus what we are perceiving with our eyes is simply the result of this EM radiation interacting with objects in the scene and interfering with each other, it logically follows that if we can freeze this EM pattern (i.e. the wavefront) in time, we can then repeat this particular pattern ad infinitum. # ⚓ Tom's Hardware ☛ AMD_Radeon_RX_8800_XT_has_a_220W_TDP according_to_Seasonic's_online_PSU_calculator_—_two_8-pin power_plugs_required,_it_says⠀⇛ The RDNA 4 based Radeon RX 8800 XT has appeared in Seasonic's wattage calculator listed with a 220W TDP. # ⚓ Kevin Boone ☛ Kevin_Boone:_They_don’t_make_them_like_that any_more:_Epson_MX-80_dot_matrix_printer⠀⇛ Well, because they actually worked. And they went on working, day after day, year after year. Modern printers are notorious for letting us down when we most need them. Need that report tomorrow? Tough. Printer manufacturers have responded to the declining sales of their products, not by making them better, but by finding ways to scalp their owners for the cost of consumables. And then, because consumers naturally look for cheaper, 3rd- party suppliers of consumables, the printer manufacturers retaliate by using encryption technologies to prevent the printer accepting any consumables but OEM ones. # ⚓ Kevin Boone ☛ Kevin_Boone:_They_don’t_make_them_like_that any_more:_the_Yamaha_DX7_keyboard⠀⇛ What made the DX7 special was its novel approach to sound generation. Although electronic keyboards were not new when the DX7 was released in 1983, they nearly all used an analog method of sound production. Typically an electronic oscillator would generate a tone whose pitch was set by the key pressed, and then a variety of filters and amplitude modifiers would work on the sound to change its properties. This is a completely logical way to approach simulating real musical instruments electronically. Real instruments have something that generates a tone – reed, string, whatever – and something that modifies the characteristics of the tone – pipe, soundbox, and so on. Each instrument has a characteristic amplitude envelope. For example, a note on a piano has an initial louder, percussive peak in volume, followed by a gradual decay. Analog synthesizers tried to simulate these acoustic properties using electronics. o § Health/Nutrition/Agriculture⠀➾ # ⚓ New York Times ☛ Antidoping_Agency_Froze_Out_Investigators Who_Warned_About_China⠀⇛ The World Anti-Doping Agency’s investigative unit highlighted intelligence about Chinese athletes possibly using a banned medication, but were kept out of the loop when 23 swimmers tested positive for it. # ⚓ Science Alert ☛ Common_Disinfectant_in_US_Drinking_Water Has_Scientists_Concerned⠀⇛ Its toxicity is currently unknown. # ⚓ Science Alert ☛ Parkinson's_Link_to_Gut_Bacteria_Suggests an_Unexpected,_Simple_Treatment⠀⇛ Inching closer to the full picture. # ⚓ NYPost ☛ I’m_an_oncology_dietitian_—_the_best_pizza toppings_to_reduce_your_risk_of_cancer⠀⇛ "There are so many amazing options," said Nichole Andrews, a Washington oncology dietitian and author. # ⚓ NYPost ☛ House_Democrats_slam_Cuomo_over_COVID_nursing_home order,_saying_he_‘interfered’_with_death_toll_stats⠀⇛ The Dem report said Cuomo and top aides' meddling with the data misled the public about the number of nursing home residents who died from COVID. # ⚓ CS Monitor ☛ After_the_pandemic,_more_Native_American students_don’t_want_to_return_to_school⠀⇛ While the pandemic caused lasting absenteeism among all schoolchildren, the problem has been most pronounced among Native American and Alaska Native students. Of 34 states, half had absenteeism rates for Indigenous children at least 9% higher than average. # ⚓ New Statesman ☛ Quitting_social_media_gave_me_a_new_creed: only_disconnect⠀⇛ I had justified my social media habit as a necessary function of my job, but I’ve always been seduced by the idea of a complex web of human connections. Perhaps it derives from a love of big polyphonic novels or growing up in a family riddled with divorce – this fantasy about knitting together broken threads. But the instinct for connectedness is with us from an early age. The other day, my four-year-old son was introduced to his new child­minder, who revealed we had at least three sets of ­family friends in common. “Does that mean everybody who knows me knows everyone else?” he asked, thrilled by the possibility. There are obvious dangers in this ­proximity to new, or potentially better, connections. I’m reminded of Margaret Schlegel’s concern that the more people she gets to know in an ever-crowded London, the easier it becomes to replace them: “It’s no good, I think, unless you really mean to know people.” In another Forster novel, A Passage to India, Adela asks: “What is the use of personal relationships when everyone brings less and less to them?” # ⚓ CBC ☛ 4th_case_of_deadly_deer_disease_confirmed_in_B.C. Hunters_required_to_help_monitor_spread⠀⇛ Hunters across British Columbia are being asked to be aware of chronic wasting disease (CWD) after a fourth confirmed case of the fatal disease was found in a white-tailed deer in the Kootenay region, B.C.'s Ministry of Water, Land and Resource Stewardship said Tuesday. Nicknamed zombie deer disease, CWD is an incurable illness that affects cervid or deer family members, such as moose, caribou and elk. # ⚓ USMC ☛ Marines_take_steps_to_hack_human_performance_with data⠀⇛ A 2021 collaboration with Army Combat Capabilities Development Command resulted in an “Optimizing the Human Weapons System (OHWS)” roadmap to a Marine Corps program that would use wearables and smart devices to create a sophisticated dashboard showing troops’ “wellness inputs,” such as alcohol consumption and physical exercise, training load, sleep data and recovery stats. A presentation of the plan, reviewed by Marine Corps Times, shows a timeline of milestones leading up to a needs analysis to be completed by Marine Corps Warfighting Lab in 2023. # ⚓ Wired ☛ A_Parasite_That_Eats_Cattle_Alive_Is_Creeping_North Toward_the_US⠀⇛ Prior to the closure of its border with the US, Mexico’s National Confederation of Livestock Organizations had called on the government to clamp down on cattle smuggling across Mexico’s southern border. The risk from the parasite is great, and if it becomes established again, the cost of eliminating it in Mexico would be high. Disruption of trade with the US was also be highly costly. In 2023 alone, Mexico’s exports of live cattle and beef to the US were worth $3 billion. o § Proprietary/Artificial Intelligence (AI)⠀➾ # ⚓ Edelman_lays_off_330_people_amid_expected_8%_drop_in_US revenue [Ed: The Microsoft operatives_that_bribe_the_media to lay off 8% of staff]⠀⇛ CEO Richard Edelman is refocusing the agency around five key areas and shuttering most of its operational sub brands — he said the cuts would have happened ‘months ago’ if Edelman were a public company." # ⚓ Ubisoft_Confirms_Rumored_Layoffs_Because_Of_XDefiant’s Shutdown⠀⇛ But first, we will go straight to Ubisoft and what they have officially confirmed Ubisoft shared a private email to employees, confirming some of these planned layoffs. # ⚓ Windows Central ☛ Ubisoft_continues_freefall_as_publisher shutters_free-to-play_shooter_XDefiant,_reportedly_closing studios⠀⇛ Ubisoft launched free-to-play first-person shooter XDefiant on May 21, 2024, after years of open and closed testing. # ⚓ Head Topics ☛ XDefiant_servers_are_closing_in_June_as Ubisoft_announces_more_layoffs⠀⇛ Another live-service game is shutting down due to a lack of players: Ubisoft ’s XDefiant, a first- person shooter that’s the illegitimate lovechild of Overwatch and Counter-Strike. The game launched on May 21 of this year, so it didn’t even last a full seven months before the shutdown announcement. # ⚓ Channel_Brief:_Ingram_Micro_Cuts_850_in_Latest_Layoffs⠀⇛ 1. Ingram Micro lays off 850: In a restructuring move, technology distributor Ingram Micro announced it will cut nearly 850 employees by the end of the first quarter of 2025. CEO Paul Bay announced the cuts in a letter to employees, as CRN reported. CRN said the restructuring includes integrating Ingram Micro’s digital and information technology teams to reduce costs and eliminate redundancies, transforming the company’s historical shared services model into an exception-based model, and streamlining selected country, business, and functional organizations. # ⚓ Chris Coyier ☛ Attempting_a_Safari_Move⠀⇛ Safari isn’t any better with battery life. I feel like that needs to be shared more as it’s very strong folk tech wisdom that Chrome eats battery and Safari does not, which is apparently not true at all, and might be the opposite. # ⚓ Pivot to AI ☛ UK_local_papers_go_weird_as_Reach_pivots_to AI_from_journalism⠀⇛ Reach plc, formerly Trinity Mirror, owns UK tabloids the Daily Mirror and Daily Express and many local newspapers around the country. Reach’s coverage of local matters in its local papers has gone noticeably … weird. # ⚓ Security Week ☛ CISA_Warns_of_Zyxel_Firewall_Vulnerability Exploited_in_Attacks⠀⇛ The US cybersecurity agency CISA on Tuesday warned that a path traversal vulnerability in multiple Zyxel firewall appliances has been exploited in the wild. The issue, tracked as CVE-2024-11667 (CVSS score of 7.5), is a high-severity flaw affecting the web management interface of Zyxel ATP, USG FLEX, and USG20(W)-VPN series devices. # ⚓ The Guardian UK ☛ Doctor_Who_showrunners_warn_AI_scripts will_‘eat_their_own_tail’⠀⇛ One of the masterminds behind Doctor Who has warned that the more AI content is used for creative purposes the worse its output will be because it “eats its own tail”. Ahead of the Doctor Who Christmas special, eagerly awaited by fans as a centrepiece of BBC1’s festive schedule, Steven Moffat made the comments in discussion with fellow showrunner Russell T Davies. # ⚓ India Times ☛ AI-driven,_deepfake-enabled_cyberattacks_to rise_in_2025;_healthcare,_finance_sectors_at_risk:_report⠀⇛ AI-driven and deepfake-enabled cyberattacks are anticipated to become increasingly prevalent in 2025 with sectors like healthcare and finance most prone targets, according to a recent report. The India Cyber Threat Report 2025 by the Data Security Council of India (DSCI) and Seqrite, spotlighted the evolving tactics of cybercriminals and the rise of AI-driven attacks as a major concern. # ⚓ Futurism ☛ AI_Safety_Researcher_Quits_OpenAI,_Saying_Its Trajectory_Alarms_Her⠀⇛ Though she didn't get into it too much, the former OpenAI-er said that she decided to leave because she was troubled by changes at the company over the past year or so. It's unclear what changes she's referencing exactly, but that timeframe matches the failed coup against CEO and cofounder Sam Altman late last November, which was reportedly undertaken by board members with concerns about the firm's lack of focus on safety under his leadership. # ⚓ La Quadature Du Net ☛ It’s_not_AI,_it’s_state-of-the-art exploitation⠀⇛ In recent months, following the sudden hype of generative artificial intelligence and products such as ChatGPT, and under the aegis of big business and complicit states, we have witnessed a further acceleration of the computerization process. This acceleration is the direct consequence of everything that is already problematic about the dominant trajectory of digital technologies. First of all, the huge accumulation of data over many years by major tech multinationals such as Google, Microsoft, Meta and Amazon, who monitor us to better predict our behavior, and who are now capable of indexing gigantic corpora of text, sound and images by appropriating the common good that is the Web. Collecting, storing and processing all this data requires a prodigious accumulation of resources. This is reflected first and foremost in capital: the rise of tech, boosted by surveillance capitalism, has attracted the favor of financial markets and benefited from accommodating public policies. Thanks to this capital, these companies can finance near-exponential growth in the data storage and computing capacity needed to drive and run their AI models, by investing in graphics chips (GPUs), undersea cables and data centers. These components and infrastructures in turn require immense quantities of rare earths and metals, water and electricity. # ⚓ Michigan Advance ☛ Misinformation_expert_used_AI_to_draft testimony_containing_misinformation_about_AI⠀⇛ A Stanford misinformation expert has admitted he used artificial intelligence to draft a court document that contained multiple fake citations about AI. Stanford’s Jeff Hancock submitted the document as an expert declaration in a case involving a new Minnesota law that makes it illegal to use AI to mislead voters prior to an election. Lawyers from the Hamilton Lincoln Law Institute and the Upper Midwest Law Center, which are challenging the law on First Amendment grounds, noticed the fake citations several weeks ago and petitioned the judge to throw out the declaration. # ⚓ Dan Q ☛ A_Friend_Used_AI_to_Wish_me_Happy_Birthday⠀⇛ Robert shares his experience of receiving a birthday greeting from a friend, that had clearly been written by an AI. The friend’s justification was because they’d wanted to make the message longer, more easily. But the end result was a sour taste in the recipient’s mouth. # ⚓ The Register UK ☛ Windows_11_market_share_falls_despite Microsoft_ad_blitz⠀⇛ Despite Microsoft's push to get customers onto Windows 11, growth in the market share of the software giant's latest operating system has stalled, while Windows 10 has made modest gains, according to fresh figures from Statcounter. This is not the news Microsoft wanted to hear. After half a year of growth, the line for Windows 11 global desktop market share has taken a slight downturn, according to the website usage monitor, going from 35.6 percent in October to 34.9 percent in November. Windows 10, on the other hand, managed to grow its share of that market by just under a percentage point to 61.8 percent. # ⚓ The Register UK ☛ Support_for_Windows_Mail,_Calendar, People_ends_December_31⠀⇛ In November, Microsoft confirmed there would be no reprieve for the apps. It will be possible to export local emails, calendar events, and contacts that users have stored in Mail, Calendar, and People into the new Outlook up until December 31, 2024. After that, however, the ability to send or receive mail will be revoked. # ⚓ Macworld ☛ Why_I'm_done_with_desktop_Macs⠀⇛ Ten years as a desktop Mac user was a lot of fun. I had an iMac, iMac Pro, and Mac Studio, and I enjoyed them all. But like almost everyone else, I’ve found the pull of the laptop too strong to avoid. Even when sitting at a desk staring at a big monitor, the MacBook Pro seems like the right choice. # ⚓ Six Colors ☛ KVM_2024:_One_switch_to_rule_them_all⠀⇛ I live a multi-Mac lifestyle. It’s a luxury, but mighty close to a necessity if I want to keep my work life and personal life (which includes freelance projects) separate. But how do you organize your life and desk so that both Macs can do their best for you? My solution is a modern spin on an old option: a KVM switch. # ⚓ Futurism ☛ Teens_Are_Forming_Intense_Relationships_With_AI Entities,_and_Parents_Have_No_Idea⠀⇛ The youth are addicted to generative AI models — but their parents have no idea what their kids actually use them for. As part of a new study set to be presented at the IEEE Symposium on Security and Privacy, a team of researchers interviewed seven teenagers and thirteen parents about their AI usage and perceptions of the tech, and also analyzed thousands of Reddit posts and comments from other teens. # ⚓ Techdirt ☛ Why_Generative_AI’s_Lack_Of_Modularity_Means_It Can’t_Be_Meaningfully_Open,_Is_Unreliable,_And_Is_A Technological_Dead_End⠀⇛ One of the most important shifts in computing over the last few decades has been the increasing use of open source software on nearly every platform, from cloud computing to smartphones (well, I would say that). For the distributed development methodology pioneered by Linus Torvalds with Linux to work, modularity is key. It allows coders anywhere in the world, connected by the Internet, to work independently on self-contained elements that can be easily upgraded or even replaced, without a major redesign of the overall architecture. Modularity brings with it many other important benefits, including these noted by Eerke Boiten, Professor of Cyber Security at De Montfort University Leicester, in an article published on the British Computer Society Web site: [...] # ⚓ The Washington Post ☛ Sorry,_Oxford_dictionary_nerds._This is_the_real_word_of_the_year.⠀⇛ First off, that’s two words. But the real miss was overlooking the rightful winner, “slop,” which was on the dictionary publisher’s short list for word of the year. That’s like Beyoncé losing the top Grammy award to Harry Styles. “Slop” is the perfect word for 2024. It describes this year’s explosion of artificial intelligence- generated oddball social media images like “shrimp Jesus.” But slop is also a perfect encapsulation of a decades-old phenomenon that explains why the [Internet] is like this. # ⚓ BoingBoing ☛ AI-enabled_price_collusion_ensures_the_rent_is too_damn_high⠀⇛ AI-powered RealPage pools data to enable landlords to raise rental prices. While the company seems to push those increases aggressively, some cities are legislating solutions. o § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ Papers Please ☛ CBP_facial_recognition_is_a_service for_the_airline_industry⠀⇛ After five years of foot-dragging in responding to our Freedom Of Information Act (FOIA) request, US Customs and Border Protection (CBP) has finally released the pitch it made to the Future Travel Experience airline industry conference in 2019 on why airlines and airport operators should “partner” with CBP on automated facial recognition of airline passengers. CBP claims in its presentation that “THIS IS *NOT* A SURVEILLANCE PROGRAM”. Its vision, however, is for CBP’s Traveler Verification Service (TVS) facial recognition system to provide automated identification of travelers at every stage of their journeys. # ⚓ EFF ☛ Location_Tracking_Tools_Endanger_Abortion Access._Lawmakers_Must_Act_Now.⠀⇛ Locate X–and other similar services–are able to do this by taking advantage of our largely unregulated location data market. Unfettered location tracking puts us all at risk. Law enforcement agencies can purchase their way around warrant requirements and bad actors can pay for services that make it easier to engage in stalking and harassment. Location tracking tools particularly threaten groups especially vulnerable to targeting, such as immigrants, the LGBTQ+ community, and even U.S. intelligence personnel abroad. Crucially, in a post-Dobbs United States, location surveillance also poses a serious danger to abortion-seekers across the country. EFF has warned before about how the location data market threatens reproductive rights. The recent reports on Locate X illustrate even more starkly how the collection and sale of location data endangers patients in states with abortion bans and restrictions. # ⚓ Sean Conner ☛ Why_list_a_phone_number_if_no_one_at your_company_even_knows_how_to_deal_with_the notification?⠀⇛ The only thing I want to say is to corporations who have a similiar message—if you are going to bother putting a phone number to inform of email delivery errors, you may want to make an option that is obvious who handles such situations. Or just don't bother with a phone number at all. Or just say something like “just delete this and move on with your life. We don't care enough to handle this properly,” unlike the other email I received today from another medical company which had an email address I could send a notification to. # ⚓ The Guardian UK ☛ Many_Americans’_cellphone_data being_[breached]_by_China,_official_says⠀⇛ A large number of Americans’ metadata has been stolen in the sweeping cyber-espionage campaign carried out by a Chinese [intrusion] group dubbed “Salt Typhoon”, a senior US official told journalists on Wednesday. The official declined to provide specific figures but noted that China’s access to America’s telecommunications infrastructure was broad and that the hacking was ongoing. # ⚓ EPIC ☛ Testimony_on_Michigan_Personal_Data_Privacy Act_–_EPIC_–_Electronic_Privacy_Information_Center⠀⇛ EPIC writes in support of SB 659, the Michigan Personal Data Privacy Act. We commend Senator Bayer for crafting a bill that provides meaningful privacy protections for Michiganders. For more than two decades, powerful tech companies have been allowed to set the terms of our online interactions. Without any meaningful restrictions on their business practices, they have built systems that invade our private lives, spy on our families, and gather the most intimate details about us for profit. But it does not have to be this way – Michigan can have a strong technology sector while protecting personal privacy. The Electronic Privacy Information Center (EPIC) is an independent nonprofit research organization in Washington, DC, established in 1994 to protect privacy, freedom of expression, and democratic values in the information age.[1] EPIC has long advocated for comprehensive privacy laws at both the state and federal level.[2] # ⚓ Walled Culture ☛ Why_Italy’s_Piracy_Shield_risks moving_from_tiresome_digital_farce_to_serious_national tragedy⠀⇛ In other words, by placing the sanctity of copyright above all else, the Piracy Shield system could be turned against any aspect of Italian society with just a few keyboard commands. A malicious actor that managed to gain access to a system that has twice demonstrated a complete lack of even the most basic controls and checks could wreak havoc on computers and networks throughout Italy in a few seconds. Moreover, the damage could easily go well beyond the inconvenience of millions of people being blocked from accessing their files on Google Drive. A skilled intruder could carry out widespread sabotage of vital services and infrastructure that would cost billions of euros to rectify, and could even lead to the loss of lives. # ⚓ The Register UK ☛ Microsoft_says_patch_installation stops_Recall_snapshots⠀⇛ KB5046740, which emerged on November 21, represents the final non-security preview release for 2024 (although there will be a monthly security release in December). The problem came when users installed this preview update, saw the Recall announcement, joined the Windows Insider Dev channel to get their hands on the code, and then... nothing. # ⚓ Wired ☛ A_New_Phone_Scanner_That_Detects_Spyware_Has Already_Found_7_Pegasus_Infections⠀⇛ Seven out of 2,500 scans may sound like a small group, especially in the somewhat self- selecting customer base of iVerify users, whether paying or free, who want to be monitoring their mobile device security at all, much less checking specifically for niche spyware infections. But the fact that the tool has already found a handful of infections at all speaks to how widely the use of spyware has proliferated around the world. It seems that having an easy tool for diagnosing spyware compromises may expand the picture of just how often such malware is being used. # ⚓ Wired ☛ Tim_Cook_Wants_Apple_to_Literally_Save_Your Life⠀⇛ Much as the CEO seems awestruck by AI and his just-released Apple Intelligence, he’s more convinced that the tech giant’s health apps will define the company’s legacy. o § Defence/Aggression⠀➾ # ⚓ ADF ☛ Reports_Detail_Forced_Youth_Conscription_in Ethiopia⠀⇛ Tedla Hirigo, 17, worked as a street vendor in Adama city in Ethiopia’s Oromia region on November 11 when police detained him. # ⚓ ADF ☛ Al-Shabaab_Could_Capitalize_on_Somalia-Ethiopia Tensions⠀⇛ Somali President Hassan Sheik Mohamud has been so focused on his rift with Ethiopia over its port deal with Somaliland that he might be leaving an opening for al-Shabaab, according to Selam Tadesse Demissie, a researcher at the Institute for Security Studies (ISS). # ⚓ ADF ☛ U.N._Honors_25_Years_of_Protecting_African Civilians⠀⇛ The United Nations recently marked an important anniversary on the continent — 25 years of actively protecting civilians with its peacekeeping missions. On October 22, 1999, the U.N. Security Council ended its observer mission in Sierra Leone and established a new mission, UNAMSIL, with a new mandate permitting its troops to use force. > # ⚓ The Straits Times ☛ Taiwan_watching_Chinese_carrier movements_as_sources_say_war_games_may_start_this_weekend⠀⇛ Three security sources said chances of Chinese military exercises starting this weekend were high. # ⚓ Mexico News Daily ☛ Homicides_decline_as_crackdown_on_high- impact_crime_intensifies:_Tuesday’s_mañanera_recapped⠀⇛ After sharing positive security figures in the first half of Tuesday's presser, Sheinbaum made an "inside joke" regarding Trump's latest threat to invade Mexico. # ⚓ The Straits Times ☛ Marcos_disavows_Philippine_impeachment case_against_Vice-President_Duterte⠀⇛ Lawmakers have little appetite for such a spectacle before midterm elections in May, observers say. # ⚓ JURIST ☛ South_Korea_president_declares_martial_law_amidst political_turmoil,_with_Parliament_rejecting_the_move⠀⇛ South Korean President Yoon Suk Yeol declared martial law on Tuesday, accusing the opposition of paralyzing the government with pro-North Korean sympathies. This proclamation adds to an already intense political climate, sparking controversy and eliciting a swift reaction from domestic political actors and international observers. # ⚓ Atlantic Council ☛ Air_force_for_hire⠀⇛ Host Alia Brahimi chats with mercenaries expert Alessandro Arduino, a top China analyst. # ⚓ Modern Diplomacy ☛ 2024-11-26_[Older]_How_Often_Should_You Post_on_TikTok_Per_Day_to_Become_TikTok_Famous? [Ed: Loaded question; it does not make you famous but merely a tool of the owners of the platform, in this case the Chinese Communist Party]⠀⇛ # ⚓ US News And World Report ☛ 2024-11-27_[Older]_Romanian Telecoms_Regulator_Calls_for_TikTok_Suspension_Pending Election_Probe⠀⇛ # ⚓ Modern Diplomacy ☛ 2024-11-28_[Older]_TikTok’s_Role_in Political_Campaigns:_Georgescu’s_Strategy_and_Romania’s_Push for_Suspension⠀⇛ # ⚓ Deutsche Welle ☛ 2024-11-29_[Older]_TikTok,_Meta_slam Australia's_social_media_ban_for_under-16s [Ed: Xi and the guy who wines and dines with Trump are upset that a country does something about meddling]⠀⇛ # ⚓ Modern Diplomacy ☛ 2024-11-30_[Older]_The_Power_of_Social Media_in_Elections:_Lessons_from_Romania’s_TikTok_Case_Study [Ed: Social control media subverts democracies]⠀⇛ # ⚓ The Age AU ☛ 2024-12-02_[Older]_Too_young_for_TikTok,_old enough_for_jail:_How_a_meaner_Australia_treats_its_kids [Ed: Lobbyists of social control media oligarchs use false equivalences; jail is for people who did something wrong]⠀⇛ # ⚓ The Register UK ☛ NATO_tests_aquatic_drones_to_protect cables,_coasts⠀⇛ The war in Ukraine has highlighted the usefulness of aquatic drones for reconnaissance and offensive missions. Ukrainian forces have been using remote- controlled drone boats to attack the Russian navy – when Elon Musk allows them to. # ⚓ Sightline Media Group ☛ New_Army-funded_tech_creates realistic_terrain,_avatars_in_simulations⠀⇛ In recent years, the Army has prioritized modernizing its modeling and simulations, primarily through its Program Executive Office-Simulation, Training and Instrumentation and its Cross Functional Team-Synthetic Training Environment. Each of the services are seeking to upgrade and expand use of simulation technology for more cost- effective and safer supplements to live training. # ⚓ Semafor Inc ☛ Trump’s_transition_running_into_a_litany_of early_problems⠀⇛ Yet the consistent chaos and confusion that defined Trump’s first administration are already descending on Washington. # ⚓ New York Times ☛ Opinion_|_Trump’s_Project_2025_May_Not_Be What_It_Seemed._It’s_Worse.⠀⇛ Musk’s tweet, which was viewed by 33.2 million people, described Ashley Thomas, a 37-year-old who, The Journal reported, holds “engineering, business and water science degrees from the Massachusetts Institute of Technology and University of Oxford” and works as the “little-known director of climate diversification” at the U.S. International Development Finance Corporation, which advises “private companies to fund ways to improve living standards in developing countries.” A Finance Corporation official told The Journal that Thomas’s work “is highly technical and is focused on identifying innovations that serve U.S. strategic interests, including bolstering agriculture and infrastructure against extreme weather events.” # ⚓ C4ISRNET ☛ Space_Force_racing_to_meet_training,_testing demands⠀⇛ Chief of Space Operations Gen. Chance Saltzman has made readiness a top priority for the service and has called on the organizations that write requirements, train guardians and develop test and training infrastructure to move quickly to prepare the force to operate in a more contested space environment. # ⚓ MIT Technology Review ☛ OpenAI's_new_defense_contract completes_its_military_pivot⠀⇛ Today, OpenAI is announcing that its technology will be deployed directly on the battlefield. The company says it will partner with the defense- tech company Anduril, a maker of AI-powered drones, radar systems, and missiles, to help US and allied forces defend against drone attacks. OpenAI will help build AI models that “rapidly synthesize time- sensitive data, reduce the burden on human operators, and improve situational awareness” to take down enemy drones, according to the announcement. Specifics have not been released, but the program will be narrowly focused on defending US personnel and facilities from unmanned aerial threats, according to Liz Bourgeois, an OpenAI spokesperson. “This partnership is consistent with our policies and does not involve leveraging our technology to develop systems designed to harm others,” she said. An Anduril spokesperson did not provide specifics on the bases around the world where th