𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, March 26, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Sun 27 Mar 02:40:19 BST 2022 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2022/03/26/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmdiYGBfC8M4iMZ6yr1JdiNS1NyQVUiifwJG7UhVRPbe67 QmNscHDxFvmbxvDEqfr6zcuFXdDCNeUGnUgEsinsAW5Bi5 QmWj5A9BPN6L7nMrjgkoYNjnbZGohimM91FNkxYhAviCty QmWmgXjX6qkCRFkbpUB7wqzzH3832E7d68SdFuRd8Ljihu QmenaQjMKay4WtcW1q8F5f8dn422GaePUyNj9EwpC1Qt8K Qmeib5xsJPjazHycfVRna3aDnNkGHeuML9KhMk6hoSRgPN QmbARvWXXpsrpvN2KJfYbfLLChGs47XEyhnbqtmdUVunxv QmS1PgXeAzFFBvUoMCQuiwWPZKaGqTxLQq1cv9CcFGgaRd QmVwa8MkmFjRWxxPuQ3riiwsjWwCaqnmn9QXr3tY1SM5we QmUBBiKfB4pj8VFJTBXigvomzXjJA1o2AAkwhjAQe4d5Xu QmeRSCJyWXDqQ2MMcGza1eugPxCGbNZcUDe857baH1LHKx QmUPqrHFRdqGwBx8p2FCLNocU3kbtbteb4MYP57ypavVZB QmYvgv9zmTR2cBLvzpLNvAdsLo7iFFrWKJtu79JkWKTaRZ QmQNiNjPkABhPdvb5wDciDcpwJ6XNWjUQ6er2que9tMRLG QmYTPvdifyTSUV9CuZ5gpuZVC7pHshJvZhZ5niheQb2vzE QmZkDEgYNnUUQtaGwFdmteyZ5W9URPTE1mBXTnYquZ1fsa QmYDUiQWeiJU7WCsdP3xeCnELkr2V2Y9aQVLP4Z8n6efVs QmVmhebNywnTu6B8SmaNwvmpQrK5uGfyPHsAeM383HwKRx QmbtCnKikT7Qr6XTD9CLjRmtU6T3bRTyVqgASiAa1S3VBY QmZAPYrP7hETWM5jGJE8DCf5TgW4hE1qdRnTa5DiwUyy2i QmbZUGxupu36yFf72bxj4yCNrYAfeMKD4kf3TzSvrLqGkT ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ [Meme] Words That ’Offend’ Corporations | Techrights ⦿ Canonical is Becoming Softer (Pro-Microsoft and Against Free Speech) | Techrights ⦿ Links 26/03/2022: Capyloon and Status of Chrome OS, Fuchsia | Techrights ⦿ IRC Proceedings: Friday, March 25, 2022 | Techrights ⦿ Mike Gerwitz on the Ethics Void | Techrights ⦿ Moving On | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/03/26/bribing-projects/#comments http://techrights.org/2022/03/26/canonical-self-censorship/#comments http://techrights.org/2022/03/26/fuchsia-woes/#comments http://techrights.org/2022/03/26/irc-log-250322/#comments http://techrights.org/2022/03/26/mike-gerwitz-ethics/#comments http://techrights.org/2022/03/26/moving-office/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/03/26/new-debian-releases/#comments ䷩ 𝚕𝚒𝚗𝚎 62 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/bribing-projects/#comments Gemini version at gemini://gemini.techrights.org/2022/03/26/bribing-projects/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Words_That_‘Offend’_Corporations⠀✐ Posted in Deception, Microsoft at 2:09 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Microsoft is tied to hundreds of millions of dollars in foreign bribes, whistleblower alleges - The Verge⦈ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Kylo Ren teaches Baby Yoda to speak: Say 'corruption', say 'crime', Say 'Microsoft' [awkward silence] Windows 7 was my idea!⦈ Summary: What happens when criminals_from_Microsoft get to impose speech restrictions on projects, by essentially bribing those projects to censor the community (volunteers)? ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⣶⣶⣶⣶⡆⣶⢶⣶⣶⣶⣶⣤⣶⣆⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠿⠏⠿⠿⠇⠘⠿⠸⠿⠻⠻⠞⠿⠟⠿⠆⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣿⣹⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣝⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⡾⣿⣿⣿⣷⣱⢿⣿⣿⣿⣞⣎⡇⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣶⣾⣿⣿⣿⢷⣶⣿⣿⣿⡿⣶⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⣠⣤⣶⣦⣄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡟⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠈⢻⣿⣿⣿⣿⡎⠛⠙⠛⠋⠻⠿⢻⣿⣿⣿⣿⣦⠀⠀⣿⣿⣿⣿⢛⣿⣿⡿⣿⡟⣺⣿⣿⣿⣿⣓⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃ ⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⢀⠀⠀⠉⠛⢻⣿⣿⡆⠀⠿⠿⠶⠿⠶⠾⠿⠷⠿⠷⠶⠿⠿⠾⠷⠶⠇⠀⠿⠿⠿⠷⠷⠿⠿⠿⠿⠾⠾⠿⠿⠿⠷⠷⠆⠀⠀⠀⢠⣿⣿⣿⡟⣿⣿⣿⡏⢩⣿⣿⣿⠉⣿⣷⢧⢰ ⠀⠀⠀⠀⢽⣿⣿⣿⡆⠤⠤⣴⣿⣧⣀⣀⣀⣀⣽⣻⡇⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣷⣿⣿⣾⣾ ⠀⠀⠀⠀⢸⣿⣿⣟⣛⣻⣧⡘⡎⣿⡽⣿⣿⣿⣿⣿⣧⠄⣿⣿⣿⣋⣓⣽⣿⣿⣟⣛⣺⣿⣿⣿⣛⣓⡇⣿⣿⣿⣿⣛⣛⣿⣿⣿⣟⣛⣻⣿⣿⣿⣾⣛⡀⣤⣤⣤⣾⣿⣿⣿⣿⣿⠿⡿⡿⠿⠿⢿⣿⠛⢻⣻⠉⡇ ⣤⣤⣤⣄⣿⣿⣿⡿⣿⣿⣿⣷⡀⢿⣷⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⢿⣿⣽⣿⠘⣿⣇⠀⣇⣧⠀⠀⢸⢸⠀⢸⣿⡄⢁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠿⠿⠀⠛⠛⠁⢛⣛⣀⠀⠛⠚⠀⠈⢿⣇⣘ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢇⣼⣿⣿⣿⠉⣁⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⠉⢁⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤ ⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⡏⢡⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣶⣿⣿⣿⣿⣇⣿⣿⣷⣿⣾⣷⣿⣿⣿⣻⣯⡿⣿⣿ ⣠⣤⣄⣀⢀⣿⣸⣿⣿⣿⡿⠁⠊⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠟⠻⠃⢸⣿⣿⣿⣿⠿⠃⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣠⠀⠀⠘⠋⣉⣁⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⣿⣿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠛⠛⠿⠿⠟⠛⠃⣿⣿⠿⠿⠿⠟⠛⣿⡟⠛⠛⠛⣿⣿⠿⢿⣿⣿⣿⣿⣿ ⢉⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣧⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⣼⣿⣧⠀⢀⠀⣿⣿⠀⡀⡄⢠⢠⣽⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠏⢠⣿⣿⡟⣿⣿⣻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣞⠷⡷⣾⣾⣿⣿ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠉⠉⠉⠀⠉⠉⠉⠁⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠉⠈⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣼⣿⣿⡟⢸⡇⡏⡟⣟⢸⡇⣏⢸⠁⢸⠸⡝⠀⣿⢸⢸⡁⣿⠀⢹⢹⢹⠀⣿⡇⣿⢸⣿⢸⣿⣿⡇⣏⢸⡇⢯⠃⢸⣿⣿⠁⢸⣼⣿⣿⡇⡇⣿⣾⡇⣧⡿⣟⠀⡏⡇⣏⠀⡏⡇⣿⢸⢸⡇⣿⢸⣹⢺⡃⠀⠀ ⠀⠸⠏⠛⠛⠟⠸⠃⠳⠛⠞⠸⠇⠇⠘⠀⠸⠘⠟⠀⠛⠸⠸⠆⠟⠀⠸⠘⠞⠀⠛⠇⠿⠘⠹⠸⠟⠛⠇⠷⠸⠇⠻⠃⠘⠟⠛⠀⠸⠋⠛⠛⠇⠷⠛⠻⠃⠟⠛⠞⠀⠳⠃⠇⠀⠷⠃⠿⠸⠞⠇⠟⠺⠹⠺⠇⠀⠀ ⠀⢸⢸⣿⠀⣏⢸⡇⣏⣿⣏⡇⣏⡃⣿⡇⢸⡷⣟⡇⡇⣿⢸⡁⢟⠂⠀⢧⣇⡇⣿⢸⠸⡓⢹⢹⠀⣏⣿⡇⡇⡏⡏⣿⣾⢸⡁⣿⠀⢸⡇⡇⡇⢸⡁⣟⢸⡁⢟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠸⠿⠀⠇⠸⠇⠏⠾⠧⠇⠣⠇⠿⠇⠸⠟⠟⠇⠇⠿⠸⠄⠿⢳⠀⠸⠹⠁⠿⠸⠰⠟⠸⠸⠄⠧⠻⠇⠧⠣⠇⠟⠿⠸⠄⠿⠀⠾⠇⠧⠷⠸⠄⠿⠸⠄⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠑⠆⢶⠆⠒⠦⡄⠆⠦⠄⠆⠦⠈⠰⠀⠙⠘⠶⠶⠆⠀⠀⠀⠀⠐⢖⠶⠄⡀⠲⠄⠶⠀⠲⠆⠀⠲⠆⠐⠶⠆⢲⠲⠶⠀⠈⠚⠈⠃⠇⠰⠶⠰⠀⠆⠐⠶⠆⠘⠄⠄⠐⠲⠰⠄⠲⠀⠆⠢⠲⠆⠐⠆⠀⠀ ⠀⠀⣠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣤⢀⢠⡀⣠⢄⡠⠀⣀⢠⢄⣤⠤⢠⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⡿⠋⠁⠀⠈⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣦⣤⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢶⣶⣶⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⣌⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡉⠻⣿⡿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⢠⣤⡆⠀⢹⣌⣹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⣤⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⣸⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠐⡏⠀⣰⡏⢻⡇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⢤⣤⣴⡿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⠿⠿⠿⣿⣿⣿⡿⣿⠟⠉⠟⠛⠉⠉⠉⠉⠛⠻⠆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠂⣀⡀⠀⣠⠀⣀⢀⣀⣩⣏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣣⠶⠛⠀⠀⠈⡻⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⡛⢁⡀⡀⣀⢀⣈⢓⡐⢁⣚⢟⣛⢙⣿⢉⣛⣿⣿⣿⣿⣿⡿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠈⠉⢹⣿⠁⠀⠀⠀⠀⠀⠈⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡟⠁⣻⣍⣿⣧⢻⡇⠈⠉⣿⣛⣿⣿⢸⣿⣸⣿⣻⣿⣿⡿⠏⣿⢹⣿⣿⣿⣷⡇⣿⣾⣿⣿⣿⣿⠀⠸⣿⣟⣛⣋⡉⠁⠀⠀⠀⠀⢀⠀⠀⢸⣿⣄⡀⠀⠀⠀⣠⣿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠀⠙⠋⠛⠛⠘⠁⠀⠀⠙⠋⠙⠛⠘⠙⠙⠛⠋⠛⠙⠃⠀⢿⣼⣯⣿⣽⣯⣷⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣅⡀⠀⢠⣾⣿⣿⣦⣌⡙⠅⠀⠤⠒⠛⠫⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠻⢿⣶⣶⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⡒⠛⠃ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠉⠉⠙⠛⠛⠉⠉⠿⠻⠟⠁⠀⠁⠀⠀⠀⠂⠙⠻⠿⠛⠋⠋⠁⠀⠀⠒⠚⠛⠉⠉⠉⠀⠁⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠄⠙⣿⢟⣃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣠⣄⣀⡀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⢰⣶⣇⠀⢸⣦⣼⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣼⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⡇⠀⠴⠆⣹⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠲⣶⣾⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⣀⣴⣶⣶⣾⣿⣿⡿⠟⡛⠛⠿⢿⣿⡟⣿⠋⠀⠋⠉⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⢤⡄⠀⡴⣀⣤⣠⣤⣴⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣇⣀⣤⣾⣿⣿⣿⡿⢿⣿⣿⣿⡵⠛⠋⠀⠀⠀⢝⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠉⠸⣦⣿⣿⣿⣾⡿⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠀⠀⠀⠀⢠⡶⣦⣰⣦⢰⣰⠆⢶⣾⣵⢾⣱⡶⡄⣶⢰⣏⣿⣿⡿⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣯⣭⣥⣄⡀⠀⠀⠀⢀⣠⣀⠀⢸⡿⡦⠄⠀⠀⣀⣴⢿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡏⠀⠀⠀⠀⠀⢠⣝⣷⣿⣿⠘⣿⠀⠀⠀⣿⣨⢼⡟⡇⣿⢸⢿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣦⣄⣀⣰⣿⣿⣿⣷⣦⣌⣀⠀⠒⠉⠉⠑⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠁⠁⠀⠀⠀⠈⠉⢈⠁⠁⠉⠈⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⠻⡿⠛⠙⠻⠿⣷⣾⣿⣷⣶⣤⡤⠀⠀⠀⢀⣠⣤⣤⣶⠶⡿⠿⠍⠉⠁ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⢠⣀⠀⠉⠉⠉⠀⠀⠿⠿⠿⠦⠄⠀⠀⠀⠀⠁⠸⠿⠛⠋⠃⠁⠀⠀⠈⠉⠉⠉⠀⠒⠂⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠋⠉⠓⠦⠀⠀⠀⠀⢻⣿⢿⣿⠇⠛⢸⣿⣿⣿⣿⣿⠀⠸⡿⢹⣿⠁⣿⣿⡇⢻⣧⣾⣿⢸⣿⢹⣿⣸⡿⢹⣿⢸⣿⣦⣿⡇⣿⣿⡇⢸⣿⢻⣷⢸⣿⢻⣿⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣀⣴⠀⠀⠀⠀⠀⠀⠈⠟⠂⠈⠐⠀⢾⢯⣿⣿⣿⣿⠀⠀⠀⢸⣿⢸⣿⣹⣷⢸⣿⣿⣿⣿⣿⢸⣿⣿⣇⢸⣿⣿⣿⣿⣿⢠⣿⣹⣿⢸⣿⢿⣯⢸⣿⢸⣿⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣼⣿⢻⣿⠸⣿⣿⢸⣿⡟⢸⣿⢸⣿⡀⣿⣿⠸⣿⣿⢸⣿⢻⣿⣸⣿⢸⣿⢸⣿⣾⡿⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠃⠀⣼⣿⣿⣿⣿⣿⣿⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⡀⠀⣀⡲⣚⡃⠀⣀⣀⡀⣀⠀⣀⡀⠀⣀⣀⠀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣷⣿⡿⠿⢸⣿⡇⣿⡇⡆⣿⡟⡇⣿⣧⣿⡇⣿⡏⣿⡇⣿⣿⢛⢹⣿⣤⣤⣤⣤⣤⣤⣤ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⣿⣿⣿⣇⣙⣿⣷⣸⣿⡇⣿⡇⠃⣿⡟⠃⣿⣿⣿⡇⣿⡇⣭⡅⣿⣿⠋⢸⣿⢹⣿⣿⣿⣿⣿⡏ ⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡟⣻⣿⣿⢻⡏⠿⣷⡿⠻⠿⠇⠿⠷⠆⠿⠷⠆⠿⠟⠿⠇⠻⣷⡿⠇⠿⠿⠶⠾⠿⢸⣿⣿⣿⣿⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠁⠉⠉⠉⠈⠉⠉⠀⠀⠁⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀ ⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣀⣀⣀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⣤⣶⣾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠽⢿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⠊⠉⢠⠂⠀⣤⣴⣶⣿⣟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢈⡁⠀⢻⠃⢤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠉⠓⠀⠂⠀⠁⠈⠉⠛⠿⠿⠟⠻⠿⠿⠿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡷⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⡿⠃⢐⡚⣿⡏⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠇⠀⣘⣃⣼⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠃⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠐⢦⢀⢸⣿⡿⠇⣿⣿⡇⢿⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨⣽⢿⡆⣿⣽⣧⠘⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠘⠛⠀⠛⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠃⣴⣴⣦⣶⡆⣶⣶⢰⣦⣠⡶⣦⣠⣶⣦⡄⣠⡶⣦⣀⣴⢶⡄⣭⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠈⠈⢹⣿⣿⣿⣿⢸⣿⣿⡇⠛⢻⣿⢾⡏⣿⡇⣿⡟⢿⣮⡅⣿⣿⣿⢸⣿⣾⣿⣿⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⢸⣿⢻⣿⣿⢸⣿⢻⣧⣿⢻⣿⢸⣿⢻⣧⣿⠛⣿⣼⠇⢿⣿⡿⣸⣿⠈⢹⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠑⠀⠀⠀⠀⠰⣿⡱⠾⢃⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣾⠁⠀⠀⠀⠀⠀⠀⢉⣀⠀⠈⠀⠻⣳⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡄⣤⡄⣤⣤⣤⢠⣄⢤⡄⣤⣤⣄⢠⣤⣤⢠⣤⢠⣤⢠⡄⣤⣤⡄⠀⣤⣤⡄⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⢠⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣿⢿⣿⢸⣿⣿⡇⣿⢸⣿⢸⡇⣿⡿⣿⣾⣿⣿⡏⢿⣮⡁⠀⠀⣿⠃⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⡟⣿⣿⢸⣿⢸⡏⣿⡇⣿⣼⡿⢸⣧⣿⠃⣿⣿⢻⣿⠃⣿⣼⡗⠀⢸⡿⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⢀⣀⢀⣀⢀⣀⡀⢀⣀⣀⠀⠀⣀⡀⣀⣀⣀⡀⣀⠀⢀⡀⣀⣀⡀⢀⣀⣀⢀⣀⡀⢀⣀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣾⣿⢸⣿⣧⢸⣯⡛⠀⠀⣿⣧⣿⣿⢹⣿⡟⠀⢸⡇⣿⡏⣿⢸⣿⣉⢸⣿⣧⢸⡏⠀⠀ ⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⡏⣾⣿⣿⢰⣟⣿⡆⠀⣿⣿⣿⣿⠈⣿⠁⠀⢸⡇⣿⣇⣿⢸⣿⣉⣿⣿⣿⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠁⠉⠉⠉⠉⠀⠀⠉⠈⠉⠉⠀⠉⠀⠀⠈⠁⠉⠉⠉⠈⠉⠉⠉⠁⠉⠉⠁⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 201 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/canonical-self-censorship/#comments Gemini version at gemini://gemini.techrights.org/2022/03/26/canonical-self-censorship/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Canonical_is_Becoming_Softer_(Pro-Microsoft_and_Against_Free_Speech)⠀✐ Posted in Free/Libre_Software, GNU/Linux, Microsoft, Ubuntu at 3:56 am by Dr. Roy Schestowitz Video_download_link | md5sum 803ce78aa023ddd2685a019f3aa941e6 Lessening Free Speech Is Not Ethics Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/canonical-ethics.webm 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I'm trying to blacklist; I mean, killfile; I mean, denylist⦈ Summary: In the name of “protecting us” the folks_at_Microsoft_Canonical herald a new era of censorship and self-censorship THE INTERNET is becoming more oppressive a space over time. I’m not so old — nor a “traditionalist” — but I think the way things are going is truly Orwellian. It’s further magnified by centralised platforms such as social control media and corporations that control Free software communities — to the point of policing speech. Of course they call that “Open Source” and speak of “conduct” (code word for control by those corporations). Enter_Canonical. Yesterday it published “Inclusive Language and its Future at Canonical” — a post that I wanted to respond to in video form. It’s harder to take videos out of context. “Are we mandating tolerance of corruption?”This issue isn’t a cross- generational thing. It’s not even about age. It’s about corporate interests and a divide-and-rule strategy, akin_to_trolling by the most_hypocritical_companies out_there. A few months ago I turned 40 and my site has just turned_20 (I’m hardly new to the Web; I’ve made sites since I was 15 and I’ve used IRC since I was about 13; it was prior to that when I had practised some simple programming). The actual technical progress made since then is nearly zero. We’ve had technology turned against its users, using misleading doublespeak like “smart” and “clown computing”. At the same time there was a watering down of language — to the point where condemning a_criminal_company_like_Microsoft is_considered_"hateful". You know we’ve gone too far when criminals are protected from “offence”. Are we mandating tolerance of corruption? █ Note/clarification regarding meme: When you ban someone or ban whole groups (e.g. IP addresses from China) there’s no “polite” term/way to put it. It’s a never-ending or circular game of word-shuffle. It’ll appease nobody but xenophobic corporations which abhor speech (except their own), and that appeasement will only be temporary anyway. It’s a pretext or excuse for ‘agenda creep’, governed_by_corporations,_not_communities. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠯⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣘⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣦⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠾⠋ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣍⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡋⠁⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣴⣦⣦⣶⣶⢶⠶⠶⠶⠶⢶⡦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠆⠀⠀⢀⠀⠀⠀⠀⣶⣶⡄⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣄⠀⠀⠀⠀⢲⣾⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⡾⠃⠀⠾⣿⣿⡇⠀⢰ ⠀⠀⢀⣠⣤⣿⡀⠀⢀⣤⣦⣤⣤⠀⠀⠀⢠⡆⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡏⠀⠀⠀⠀⣨⡟⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⢧⠸⠓⣾⣷⣿⣷⣄⠸ ⣤⣴⣾⣿⣿⣿⢟⣴⣾⣿⣿⢙⣋⣀⣀⣀⣸⣧⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠙⠇⠀⣀⣤⣾⣿⣿⣿⣭⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠰⠆⢘⣿⡄⠐⣸⣿⡏⠁⣾ ⠈⢻⣿⣿⠿⣿⠿⠟⠛⠛⠳⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣿⣿⣿⣿⣿⡄⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⠀⠈⡟⣇⠀⠘⢿⠃⠀⣽ ⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠈⠉⢿⣿⣿⣿⠏⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠸ ⠀⠂⠲⣶⠀⢶⣶⣶⣶⣶⣶⠀⣿⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⣿⣿⡀⠀⣸⠄⢠⡄⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠯⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣘⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⢿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠟⠋ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣍⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡋⢁⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣦⣦⣴⣶⣶⠶⠶⠶⠶⠶⢶⡦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠆⠀⠀⢀⠀⠀⠀⠀⣶⣶⡄⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣄⠀⠀⠀⠀⢲⣾⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠸⡿⠓⠀⠾⣿⣿⡇⠀⢰ ⠀⠀⢀⣠⣤⣿⡀⠀⢀⣤⣦⣤⣤⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡏⠀⠀⠀⠀⣨⡟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⢥⣸⠓⣼⣷⣿⣷⣄⠸ ⣤⣴⣾⣿⣿⣿⢟⣴⣾⣿⣿⢙⣋⣀⣀⣀⣸⣧⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠙⠇⠀⣀⣄⣞⣿⣿⣷⣭⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠐⠆⢸⣿⡀⠐⣰⣿⡟⠁⢺ ⠈⢻⣿⣿⠿⣿⠿⠟⠛⠛⠳⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢂⣾⣿⣿⣿⣟⡀⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢨⠀⠈⣿⣇⠀⠘⠻⠅⠀⢺ ⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠌⡙⣿⣿⣿⣿⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⡀⢻⡄⠀⠀⠀⠀⠸ ⠀⠂⠲⣶⠀⢶⣶⣶⣶⣶⣶⠀⣿⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⣻⣿⣿⡆⠀⢸⠀⢠⡄⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠯⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠞⠋ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣍⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡋⢁⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣴⣦⣴⣶⡶⠶⡶⠶⠶⠶⢶⡦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠒⠀⠀⢀⠀⠀⠀⠀⣶⣶⡀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣄⠀⠀⠀⠀⢲⣾⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⡿⠑⠀⠾⣿⣿⡇⠀⢰ ⠀⠀⢀⣠⣤⣿⡀⠀⠀⣤⣦⣤⣤⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢻⣿⡏⠀⠀⠀⠀⣨⡟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⢤⣸⠓⣾⣷⣿⣷⣦⠸ ⣤⣴⣾⣿⣿⣿⢟⣴⣾⣿⣿⢙⣋⣀⣀⣀⣸⣧⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠙⠇⠀⣀⣤⣾⣿⣿⣧⣭⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠰⠆⢸⣿⡀⠐⣨⣽⡟⠁⣿ ⠈⢻⣿⣿⠿⣿⠿⠟⠛⠛⠓⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢂⣼⣿⣿⣿⣿⡀⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⠀⠀⣿⣇⠀⠘⠻⠇⠀⢽ ⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠌⡈⢿⣿⣿⣿⠏⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣆⠀⠀⠀⠀⠸ ⠀⠂⠲⣶⠀⢶⣶⣶⣶⣶⣶⠀⣿⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢻⣿⣿⡇⠀⢐⠀⢠⡀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠿⠿⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⡁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡀⠀⠘⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠰⠿⠉ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣏⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠁⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠆⠀⠀⢀⠀⠀⠀⢠⣶⣦⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡄⠀⠀⠀⠐⢶⣾⣿⣷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⡾⠂⠀⠾⣿⣿⡇⠀⢸ ⠀⠀⢀⣠⣼⣇⠀⠀⢀⣤⣤⣠⣄⠀⠀⠀⢠⡂⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⢿⣿⡇⠀⠀⠀⠀⣸⡟⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣅⢰⠳⣶⣿⣿⣷⡤⠺ ⣤⣶⣿⣿⣿⣿⢧⣴⣿⣿⣯⢛⣋⣀⣀⣀⣻⡇⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠻⠇⠀⣠⣴⣾⣻⣷⣷⣭⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⠀⢻⣧⠀⢻⢽⣿⡟⠀⣿ ⠙⣿⣿⡿⢿⣿⠿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢀⣀⣼⣿⣿⣿⣿⡀⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢈⠀⢹⣿⠀⠈⠿⣿⠀⠀⢹ ⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢈⡁⣿⣿⣿⣿⠏⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠀⠀⠸ ⠀⠀⠲⣶⠂⢶⣶⣶⣶⣶⡶⠸⣿⣿⠁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⣿⣿⡇⠀⢸⠀⢀⡤⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠿⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⡁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢶⣴⣦⣶⡆⠰⣶⢶⣶⣦⢶⣴⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠀⣿⢸⣿⣿⢸⣿⢸⡇⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠉⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣷⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠟⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡀⠀⠘⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠰⠿⠉ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣿⢿⡿⣿⡿⢸⡿⣧⣿⣼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣏⣙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠁⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⣶⡶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠆⠀⠀⢀⠀⠀⠀⢠⣶⣦⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡄⠀⠀⠀⠐⢶⣾⣿⣷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⡿⠂⠀⠾⢿⣿⡇⠀⢸ ⠀⠀⢀⣠⣼⣇⠀⠀⢀⣤⣤⣠⣄⠀⠀⠀⢰⡀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⢿⣿⡇⠀⠀⠀⢀⣸⡟⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣅⢸⢷⣶⣿⣿⣷⡄⠺ ⣤⣶⣿⣿⣿⣿⢧⣴⣿⣿⣿⢛⣋⣀⣀⣀⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠻⠇⠀⡠⣴⣾⣿⣿⣶⣭⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⠀⢻⣶⠀⢻⣻⣿⠟⠁⣿ ⠙⣿⣿⣿⢿⣿⠿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⣂⣸⣿⣿⣿⣿⡄⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢈⠀⢸⣿⠀⠈⠿⣿⠀⠀⢸ ⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⢈⡉⣿⣿⣿⣿⠏⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠀⠀⠸ ⠀⠂⠲⣶⠀⢶⣶⣶⣶⣶⡶⠸⣿⣿⠁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⢻⣿⣿⡇⠀⢸⠀⢠⡤⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠛⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡄⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⡗⠀⣿⣿⣋⣹⣛⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠞⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠰⢰⠀⢶⣶⣴⣶⣶⡆⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠛⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡄⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⡗⠀⣿⣟⣋⣹⡛⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠⠞⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠛⢿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣧⢸⣿⣛⣩⣍⢹⣿⣿⣿⣿⣟⣏⣩⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣰⠖⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⢛⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣼⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠋⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⣴ ⠀⠀⢀⣀⣸⠀⠀⠀⢀⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⣿ ⣠⣴⣿⣿⣿⡿⣀⣤⣿⣿⡛⠛⠃⠀⠀⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀ ⠿⣿⣿⡿⣿⡾⠿⠟⠙⠋⣴⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠿⠛⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠛⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢰⠀⢶⣦⣴⣶⣶⠆⢸⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠒ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣧⢸⣿⣟⣭⣍⢹⣿⣿⣿⣿⣟⣏⣩⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣰⠖⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠰⢰⠀⢴⣦⣴⣶⣶⠆⢸⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠿⠭⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⠿⢰⢿⣋⣩⣍⣹⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⠿⠿⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⠖⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡉⣻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠋⠉⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⢠⣤⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣿⣿⣇⠀⠀⣴ ⠀⠀⠀⣀⡇⠀⠀⠀⢀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠙⠛⠟⠀⢀⣿ ⣠⣼⣿⣿⣿⡗⣀⣰⣿⣿⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⢿⣿⣿⢿⣿⣾⡿⠟⠛⠋⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠋⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢰⠀⢴⣤⣴⣴⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠭⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⠿⢰⠿⣋⣥⣍⣹⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⠿⠿⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⠆⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡉⣻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠋⠉⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⢠⣤⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣿⣿⡇⠀⠀⣴ ⠀⠀⠀⣀⡇⠀⠀⠀⢀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠀⢀⣿ ⣠⣼⣿⣿⣿⡷⣀⣰⣿⣿⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⣿⣿⣿⢿⣿⣾⠿⠟⠛⠋⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠏⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢰⠀⣴⣤⣴⣴⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠅⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⣿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠈⠛⠇⢼⣟⣩⣭⣉⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡀⠀⢀⠹⠿⠿⠿⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⠆⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⡄⠀⠐⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⠀⢼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⢿⣿⠟⠀⢸⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⣄⢸⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⣠⣿⣿⣧⠀⠀⣴ ⠀⠀⠀⣀⡃⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠀⢀⣿ ⣠⣼⣿⣿⣿⡗⣀⣰⣿⣿⠙⠟⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⣿⣿⣿⢿⣿⣾⠿⠟⠻⠋⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠋⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢰⠀⢴⣤⣴⣴⣶⠖⢿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠅⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠒ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠈⠙⠃⠾⣋⣥⣤⣌⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⡹⠿⠿⠿⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣠⠆⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⣿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣧⣤⣄⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⢿⣿⣟⣩⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⡄⠀⠐⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⠁⢼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⢿⣿⠟⠀⢸⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢸⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠠⠀⠀⠀⣠⣿⣿⣧⠀⠀⣴ ⠀⠀⠀⣀⡃⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠀⠀⣿ ⣠⣼⣿⣿⣿⡗⣀⣰⣿⣿⠛⠟⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⣿⣿⣿⢿⣿⣾⠿⠟⠻⠋⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠋⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢰⠀⢴⣤⣴⣴⣶⠖⢿⣿⡏⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠓⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠙⠛⠰⣛⣥⣤⣤⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧⢀⢀⣀⠻⠿⠿⠿⢿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⠖⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣷⣿⣾⣿⣾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⣨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠰⢰⠀⢴⣤⣴⣴⣶⠖⢺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠓⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠸⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠙⠛⢰⣛⣥⣤⣤⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧⢀⢀⣀⠻⠿⠿⠿⢿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⠖⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡟⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣷⣿⣾⣿⣾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⣨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣩⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠈⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠉⠛⠰⣋⣥⣶⣤⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⡀⣀⣀⡻⠿⠿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⠖⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⢿⡿⢸⡿⣧⣿⣼⣿⣾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣤⣶⣶⣄⠀⠀⠀⠀⠀⣀⡀⠀⠸⣿⣿⣭⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⣿⣿⣿⡆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣼⣿⣿⠀⠀⢠ ⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠀⠀⣸ ⣠⣤⣿⣿⣿⡷⢀⣠⣿⣿⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢿⣿⣿⡿⣿⡶⠿⠟⠛⠋⣶⣿⣿⣿⣿⣷⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠿⠟⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠛⠉⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢠⠀⢴⣤⣴⣶⣶⠖⢸⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣦⣤⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠓⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢶⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⢘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠉⠛⠰⣏⣥⣶⣤⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⡻⠿⠿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⠖⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣾⢿⡟⣿⡿⢸⡿⣧⣿⣼⣿⣾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠉⢠⠟⣋⣥⣄⣹⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣄⠀⣀⣈⠿⠿⠿⠿⢿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⠴⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡉⢙⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⡀⢀⣀⣀⣀⣀⣠⣶⣶⡄⢸⣿⣿⡿⣛⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣼⣿⣿⠀⠀⢠ ⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠀⠀⣸ ⣠⣤⣿⣿⣿⣷⢀⣠⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢿⣿⣿⣿⣿⣷⡿⠟⠛⠋⣴⣿⣿⣿⣿⣶⣷⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠻⣿⣿⡌⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠿⠟⠀⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠛⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣦⣤⡈⢙⣵⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢠⠀⢴⣤⣴⣴⣶⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢦⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠉⠠⠟⣋⣥⣄⣹⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⣀⣈⠿⠿⠿⠿⢿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⠤⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡟⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠰⢠⠀⢤⣤⣴⣤⣶⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣤⣤⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢦⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠁⠸⢟⣉⣀⣈⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⡘⠿⠿⠿⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⡤⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡟⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠙⢻⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⣀⣀⣀⣀⣄⣀⣴⣾⣶⡀⣿⣿⣿⠿⡋⠉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣶⣿⠿⢸⣷⡏⣿⢸⣿⢿⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠁⠼⠟⣉⣀⡉⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣧⡀⢀⣀⡘⠿⠿⠿⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⡴⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡟⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢫⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠙⢻⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⣀⣀⣀⣀⣄⣀⣴⣾⣶⡀⣿⣿⣿⠿⡋⠉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢿⣿⡇⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⡇⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠉⠉⢉⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢀⣼⣿⣿⠀⠀⢠ ⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠂⠀⣸ ⣠⣤⣿⣿⣿⣷⢀⣠⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢿⣿⣿⣿⣿⣷⡿⠟⠉⠋⣴⣾⣿⣿⣿⣶⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠈⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠿⠟⠀⠉⠀⠀⠀⠀⠀⠹⢿⣿⣿⠿⠛⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢠⠀⢤⣤⣤⣤⣤⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⣴⣆⣶⡆⠰⣶⢦⣶⣦⢶⣰⢶⡆⣶⣴⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⣿⡇⠀⣿⢸⣿⣿⠘⡟⢸⡇⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠁⠀⠉⠈⠉⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢻⣿⣷⠀⣿⣿⢸⡇⢸⣿⣦⣿⠿⢸⣷⡏⣿⢸⣿⢾⣿⠚⣿⠃⠀⠀⠀⠀⠀⠀⠀⠟⣋⣁⣀⣹⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⣀⣀⡻⠿⠿⠿⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⡤⠀ ⠀⠀⠀⠀⢸⡿⠸⣿⡿⠀⣿⣿⢿⣧⣼⢿⡟⢿⡿⢸⡿⣧⣿⡼⣿⢾⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢋⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠰⢠⠀⢤⣤⣤⣤⣴⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢴⢰⣆⣶⡆⠰⣶⢦⡶⣦⢶⣰⢶⡆⣶⣰⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⢿⣿⡇⠀⣿⢸⡟⣿⠘⡟⢸⡇⣿⣿⣼⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⠉⠁⠀⠉⠈⠁⠉⠀⠁⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣷⢰⣿⣿⣾⣿⣿⣿⣿⣿⠿⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠟⢋⣀⡀⢈⣿⣿⣿⣿⣿⣵⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⡻⠿⠿⠿⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⢃⡟⠛⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⠙⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣼⡇⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣼⣿⣟⣯⣴⣶⣶⣶⣶⣶⣿⣷⣿⣿⡿⠋⠀⢁⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⡇⠀⠙⠻⢿⣿⣿⣿⠿⠿⠛⢿⣟⣯⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣼⣿⣷⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠀⠀⢸ ⣀⣤⣿⣿⣿⡶⢀⣀⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⠛⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢿⣿⣿⢿⣿⣶⡿⠟⠈⠁⣰⣶⣿⣿⣿⣶⣦⠀⠀⠸⣿⣿⣿⣿⣿⣧⡄⠈⠻⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠿⠟⠀⠈⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠛⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⢤⣤⣤⣤⣤⠂⢸⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖ 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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠀⠀⢸ ⣀⣤⣿⣿⣿⣶⢀⣠⣾⣿⠛⠿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢿⣿⣿⣿⣿⣷⡿⠟⠉⠉⣰⣶⣿⣿⣿⣶⣶⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠿⠟⠀⠉⠀⠀⠀⠀⠀⠸⢿⣿⣿⠿⠛⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢠⠀⢠⣤⣤⣤⣤⠆⢸⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣋⣀⡀⢹⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⢀⣴⣶⡆⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⡟⠛⢸⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣯⠉⢙⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣼⣷⢀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⣿⡏⢸⣿⠆⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣷⣦⣄⠀⢀⣴⣿⣿⣿⡿⠋⠉⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣾⣿⣿⣿⣿⣷⣴⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣷⣶⣿⣿⣶⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢉⣽⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣰⣿⣿⣿⣿⡇⠀⠀⠉⠛⠛⠛⠉⠁⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠃⠀⢸ ⣀⣤⣿⣿⣿⣶⢀⣀⣾⣿⠛⠿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢿⣿⣿⣿⣿⣷⡿⠟⠉⠁⢰⣶⣿⣿⣿⣶⣶⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠠⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠿⠟⠀⠉⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠛⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⠀⢀⣴⣶⡆⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⣿⠛⢸⢇⣴⣿⣿⣿⠃⠀⠀⢸⣿⣿⣯⠉⢙⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣤⣄⢠⣤⣿⢀⣠⣼⣿⣿⣿⣧⣄⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣨⣿⣿⡟⠋⠀⠀⣀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣆⣿⣷⣶⣿⣿⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣿⣿⣇⣀⣬⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⡇⠀⠀⠉⠉⠉⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⣠⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠇⠀⢠ ⣀⣤⣿⣿⣿⣶⠀⣀⣾⣿⠋⠿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⡿⣿⣷⣾⠟⠉⠉⢰⣶⣿⣿⣿⣶⣶⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠾⠟⠁⠉⠁⠀⠀⠀⠀⠘⢿⣿⣿⡿⠛⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠇⠀⠀ ⣀⣤⣾⣿⣿⣷⠆⣀⣼⣿⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣧⣾⠿⠋⠉⢠⣶⣶⣿⣶⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠾⠿⠃⠈⠁⠀⠀⠀⠀⠘⠿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢠⠀⢠⣄⣠⣤⣤⡆⠠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠅⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢰⣿⣿⡆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠛⠛⠛⣿⣿⣿⣿⣿⠛⡛⣻⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⣘⠿⠿⠿⠿⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⡶⢦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⣿⠛⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣠⣄⢠⣤⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⠋⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣁⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⣄⣽⣿⣿⣿⣿⣿⣿⠄⣾⣿⣿⣿⡏⠛⠛⠛⠋⠉⢁⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠙⠻⣿⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠀⠀ ⣀⣠⣼⣿⣿⣷⡆⢀⣴⣿⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣾⡿⠋⠉⢠⣶⣶⣿⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠾⠿⠃⠈⠁⠀⠀⠀⠀⠈⠿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⢠⣄⣠⣤⣤⡆⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠿⣿⣿⣿⣿⣿⣿⡛⠿⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣌⠿⠿⠿⠿⠿⢿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⣠⡀⠀⣿⣿⣿⣿⣿⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿⣿⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⢹⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣠⣄⢠⣤⣼⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠿⣭⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⣀⣠⣾⣿⣿⣿⠟⠛⣻⣿⣿⣉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠟⠛⣿⣿⣵⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣼⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⣿⣯⣿⣿⡏⣿⣿⡟⠙⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠀⠀ ⢀⣠⣴⣿⣿⣷⡆⠀⣠⣿⡿⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⣍⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣴⡿⠏⠉⠁⣴⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠿⠏⠈⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢀⠀⠀⢄⣠⣤⣤⡆⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⣿⣯⣿⣿⡏⣿⣿⡟⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠀⠀ ⢀⣠⣴⣿⣿⣷⡆⠀⣠⣿⡟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⣍⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣴⡿⠟⠉⠁⣴⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠿⠏⠈⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢀⠀⠀⢄⣠⣤⣤⡆⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠿⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣈⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢉⣀⠀⠈⣿⣿⣿⣿⣿⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣆⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣰⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⢹⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣠⣄⢠⣤⣸⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⣿⣋⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⡇⠀⣀⣤⣤⣶⣶⣿⣿⣿⣟⠛⣻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⣠⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠸⣿⣿⣿⣿⣿⣿⡎⠛⠋⠹⣿⣿⣴⣾⣿⣿⡿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠃⠀ ⢀⣀⣤⣿⣿⣷⣶⠀⣠⣾⣿⠳⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⣿⣵⣿⠟⠉⠁⣴⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢠⠀⠀⢄⣠⣤⣤⣆⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠿⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣈⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢉⣀⠀⠈⣿⣿⣿⣿⣿⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣰⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⢹⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣠⣄⢠⣤⣸⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣋⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣄⣀⣴⣾⣿⣿⡏⠉⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠇⠀ ⠀⣀⣤⣾⣿⣿⣶⠀⣀⣾⣿⠓⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣿⣧⣾⠟⠉⠉⢰⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⠿⠁⠉⠁⠀⠀⠀⠀⠸⢿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⠀⠀⣠⣤⣤⣆⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣀⠿⠿⠿⠿⠿⠿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⠉⠙⣿⣿⣿⣿⣿⣨⣤⣴⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⣸⣷⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⠟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡗⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣟⡋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⣠⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣄⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣿⣿⣿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠁⣰⣿⣿⣿⣿⣇⡉⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣄⣠⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣄⣀⣴⣾⣿⣿⡏⠉⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠇⠀ ⠀⣀⣤⣾⣿⣿⣶⠀⣀⣾⣿⠳⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣿⣧⣾⠟⠉⠉⢰⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⠿⠁⠉⠁⠀⠀⠀⠀⠸⢿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⠀⠀⣠⣤⣤⣆⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⡻⠿⠿⠿⠿⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⠉⠉⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢓⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠙⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⣰⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⠟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠂⣿⡇⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣿⣿⣿⣿⡋⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀ ⠀⣀⣤⣾⣿⣿⣷⠆⣀⣼⣿⠏⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠈⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⣿⣷⣾⠿⠉⠉⢠⣶⣶⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠾⠿⠃⠈⠁⠀⠀⠀⠀⠘⠿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢀⠀⠀⠀⣠⣤⣴⣦⡀⠰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⢛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣠⣘⠿⠿⠿⠿⠿⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣤⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⡀⠀⣹⣿⣿⣿⣿⣧⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀ ⠀⣀⣠⣼⣿⣿⣷⡆⣀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠀⠀⠈⠻⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣾⡿⠋⠉⢠⣶⣶⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠺⠿⠋⠈⠁⠀⠀⠀⠀⠀⠿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢀⠀⠀⠀⣠⣤⣤⣤⡀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣦⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⢇⣿⣿⣿⣿⣿⣷⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣾⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⡀⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣩⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⠆⣿⡗⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⣧⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡀⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢼⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣇⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣷⣿⣿⣿⣿⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠀⣴⣿⣿⣿⣿⣿⣏⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣄⣀⣿⣿⣿⣿⣿⣿⡿⠃⠀⠘⢿⣿⣿⡿⠉⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣼⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣴⣿⣿⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀ ⠀⣀⣠⣼⣿⣿⣿⡆⣀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠀⠀⠈⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣶⡿⠋⠉⠁⣶⣶⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠺⠿⠏⠈⠁⠀⠀⠀⠀⠀⠻⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⡇⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡇⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⡏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣆⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠏⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣼⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢻⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣆⠘⢿⠟⣿⣿⣿⣿⣿⠉⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀ ⠀⣀⣠⣼⣿⣿⣿⡆⣀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠹⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣿⣿⣿⡏⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣶⡿⠏⠉⠁⣶⣶⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠿⠏⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢠⠀⠀⠀⢠⣤⣤⣦⡀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠛⠻⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⢰⣿⣿⣿⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠉⠉⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢀⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣄⢠⣤⡀⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⡆⣿⡷⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⠙⢛⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⠇⣿⡇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢼⣿⡏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⣿⣷⣸⣿⣇⣿⣷⣶⣿⣿⣶⢸⣿⡇⠀⣿⣿⢸⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠏⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣼⣿⣷⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢻⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣆⠘⢿⠟⣿⣿⣿⣿⣿⠋⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀ ⠀⣀⣠⣼⣿⣿⣿⡦⣀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠹⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣮⣿⣿⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣶⡿⠏⠉⠁⣶⣶⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣾⣷⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢠⠀⠀⠀⣠⣤⣴⣦⡀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠈⠀⠀⠀⠈⠉⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⠟⠛⠛⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⢰⣿⣿⣿⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⠙⠛⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣼⣿⣿⣿⣿⣦⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣀⢠⣤⡀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠀⠀⠀⢸⣿⣧⣿⡏⢸⣿⡆⣿⡷⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡇⣿⣇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⣸⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⠿⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣿⣶⣿⣿⣶⣸⣿⡇⠀⣿⣿⣼⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠟⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⢀⣴⣿⣿⡀ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃ ⠀⢀⣠⣴⣿⣿⣿⣶⢀⣠⣿⣟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠻⠃⠀⠀⠙⠷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣭⣬⣿⣿⣶⣿⣿⡏⠉⠉⣰⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠉⠉⣴⣶⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⠿⠿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⢰⣿⣿⣿⡀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣌⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣀⢠⣤⡀⣸⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⡆⣿⣷⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡇⣿⣯⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣿⣶⣿⣿⣶⣸⣿⡇⠀⣿⣿⣾⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣿⣿⣷⣾⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠟⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⢀⣴⣿⣿⡄ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃ ⠀⢀⣠⣴⣿⣿⣿⣶⢀⣠⣾⣿⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠃⠀⠀⠙⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⣁⣿⣿⣧⣼⣿⣿⠛⠛⢋⣵⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠛⠁⣶⣾⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢠⠀⠀⠀⢠⣤⣴⣦⣄⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡂⠀⠀⠀⠀⠊⠉⠀⠀⠀⠈⠉⠉⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣆⣿⣿⡇⣿⣿⠿⠀⣿⣿⣿⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⠿⠿⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⢰⣿⣿⣿⡀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡿⣿⣿⣿⡇⣿⣿⣀⣸⣿⣿⣿⡇⣿⡟⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠃⠛⠛⠛⠃⠛⠛⠛⠛⠛⠀⠛⠓⠛⠃⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣌⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢀⣀⡀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⣀⢠⣤⡀⣸⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠀⠀⠀⢸⣿⣧⣿⡇⢸⣿⡆⣿⡷⠀⣿⣿⠀⢸⣿⡟⠃⣿⣿⢸⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⢸⣿⣿⣿⡄⢸⣿⡇⣿⣇⠀⣿⣿⠀⢸⣿⡿⠇⣿⣿⢸⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⢸⣿⡏⣿⣷⣼⣿⣇⣿⣷⣶⣿⣿⣶⣸⣿⡇⠀⣿⣿⣸⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣿⣿⣷⣾⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⣿⣿⡄ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⣿⣿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃ ⠀⢀⣠⣴⣿⣿⣿⣶⢀⣠⣾⣟⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠃⠀⠀⠙⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⣁⣻⣿⣧⣼⣿⣿⠛⠛⠋⣵⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠋⠁⣶⣾⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡈⣿⡇⢸⣿⢀⣿⣏⣻⣿⡆⣼⣿⣤⡄⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠙⠛⠃ ⠀⢀⣠⣴⣿⣿⣿⣿⣛⣻⣿⣿⠛⠿⠛⠃⠘⠛⡛⠛⠛⠻⠟⠃⠿⠿⠿⠃⠀⠀⠙⠿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠉⠉⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣷⣿⠟⠛⠋⣶⣿⣿⣿⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠀⠄⣰⣴⣶⣦⣄⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠛⠛⠻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢠⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⠉⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢻⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠈⢹⣤⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢀⣼⣿⣿⡄ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡈⣿⡇⢸⣿⢠⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣽⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠙⠛⠃ ⠀⢀⣠⣴⣿⣿⣿⣿⣛⣻⣿⣿⠛⠿⠛⠃⠘⠛⠛⠛⠋⠻⠟⠃⠿⠿⠛⠃⠀⠀⠙⠿⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣷⡿⠟⠛⠉⣶⣿⣿⣿⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠲⢢⠀⠠⠄⢰⣤⣶⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡈⣿⡇⢸⣿⢠⣿⣎⣻⣿⡆⣼⣿⣶⡄⠀⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠙⠛⠃ ⠀⢀⣠⣴⣿⣿⣿⣿⣛⣻⣿⣿⠛⠿⠛⠃⠘⠛⠛⠛⠛⠻⠟⠃⠿⠿⠛⠃⠀⠀⠙⠿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣷⡿⠟⠛⠋⣶⣿⣿⣿⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠲⢢⠀⠠⠄⣰⣤⣶⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠉⠛⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⢐⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠡⠄⠀⠀⢀⣴⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣈⣿⡇⢸⣿⢸⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠛⠻⠇ ⠀⣀⣠⣴⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠛⠻⠟⠃⠿⠻⠻⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠛⠛⣶⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠲⢲⠀⠰⠄⢰⣶⣶⣶⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣴⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠛⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣴⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢰⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠛⠛⠿⠇ ⠀⣀⣠⣴⣿⣿⣿⣿⣛⣿⣿⣿⠛⠿⠛⠃⠘⠛⠛⠛⠛⠻⠟⠃⠿⠻⠿⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠛⠋⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣦⣽⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢲⠀⠠⠄⣴⣶⣶⣶⣤⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠫⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣠⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⡿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡛⢛⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠰⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠹⠅⠀⠀⠀⢀⣴⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢰⣿⣏⣻⣿⣆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠇ ⠀⣀⣠⣼⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠛⠻⠟⠃⠛⠛⠻⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⣾⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣤⡹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠠⠄⣴⣶⣶⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠓⠲⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢀⣀⣀⢀⣠⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣤⣴⣿⣿⣿⣿⣷⣤⣌⣉⣿⣿⣿⣿⣿⣿⣿⣿⡄⣰⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣦⣤⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠅⠀⠀⠀⢀⣴⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢠⣿⣏⣻⣿⡆⣾⣿⣶⡄⠀⢸⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠇ ⠀⣀⣠⣼⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⠛⠛⠛⠻⠟⠃⠛⠛⠛⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠛⠃⣾⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣌⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢲⠀⠠⠄⣴⣶⣶⣦⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠓⠲⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢀⣀⣀⢀⣠⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⢰⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠥⠀⠀⠀⢀⣴⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢠⣿⣏⣻⣿⣆⣾⣿⣶⡄⠀⢸⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠇ ⠀⣀⣠⣾⣿⣿⣿⣿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠋⠻⠟⠃⠛⠛⠛⠁⠀⠀⠙⠿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⡾⠿⠟⠛⠋⣾⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠠⠄⣴⣶⣶⣶⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠒⠒⠂⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣤⣤⣿⣿⣿⣿⣷⣦⣄⣈⣻⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣧⣦⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣏⣸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠐⣿⣴⣿⢿⡾⢿⣿⠇⠀⠈⢹⣦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⢀⣼⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢠⣿⣏⣻⣿⣆⣾⣿⣶⡀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠇ ⠀⣀⣤⣾⣿⣿⣿⡿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⠛⠛⠛⠻⠟⠋⠛⠛⠛⠃⠀⠀⠙⠿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⠿⠟⠛⠋⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠟⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠠⠄⣴⣶⣶⣶⣄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠙⠛⠋⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢀⣤⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⣵⣦⣄⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠡⠀⠀⠀⢀⣼⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⢀⣿⣏⣻⣿⣆⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠇ ⠀⣀⣤⣾⣿⣿⣿⡿⣛⣿⣿⣿⠛⠛⠛⠃⠘⠛⡛⠛⠛⠻⠟⠋⠛⠛⠛⠁⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⡿⠿⠟⠉⠉⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢲⠀⠰⠄⣴⣶⣶⣶⣄⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠋⠉⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⣄⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠚⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⡟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣼⣿⣿⣿⣿⣷⣤⣆⣈⣽⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⣵⣤⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⢀⣼⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣆⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠇ ⠀⣀⣤⣾⣿⣿⣿⡿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⠛⠛⠛⠻⠟⠋⠛⠛⠛⠁⠀⠀⠙⠗⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⡿⠿⠟⠙⠉⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢲⠀⠰⠄⣴⣶⣶⣶⣄⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠋⠺⠉⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣠⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣠⣄⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⣵⣦⣄⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⠉⠥⠀⠀⠀⢀⣼⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠇ ⠀⣀⣤⣾⣿⣿⣿⡿⣻⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠋⠻⠟⠋⠛⠛⠛⠁⠀⠀⠙⠗⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⡿⠿⠟⠛⢣⣾⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠰⠄⣴⣶⣶⣶⣄⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠋⠻⠉⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣠⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⠻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠋⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⠀⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⡆⣿⢸⣧⣿⢸⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠈⣼⣦⣄⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠙⠥⠀⠀⠀⢀⣼⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠛⠿⠇ ⠀⣠⣤⣾⣿⣿⣿⡿⣛⣿⣿⣿⠛⠟⠛⠃⠘⠛⡛⠛⠛⠻⠟⠋⠛⠛⠛⠁⠀⠀⠙⠗⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⣿⣿⡿⠿⠟⠻⢣⣾⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢲⠀⠰⠄⣴⣶⣶⣶⣄⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠋⠚⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣠⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠛⠻⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢠⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣤⣄⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⢰⣿⢿⡾⢿⣿⠇⠀⠈⣽⣦⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠙⠥⠀⠀⠀⢠⣼⣿⣿⡄ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠇ ⠀⣠⣤⣾⣿⣿⣿⣟⣛⣿⣿⣟⠛⠛⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠁⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣿⣿⣿⡿⠿⠛⠛⢃⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢲⠀⠰⠄⣴⣶⣶⣶⣄⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠋⠚⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣠⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠛⠻⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢠⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣤⣄⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠈⣼⣦⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠡⠀⠀⠀⢠⣼⣿⣿⡆ ⠀⠀⠀⠀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⡄⠀⢻⣿⡿⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠇ ⠀⣠⣤⣾⣿⣿⣿⣟⣛⣿⣿⡟⠛⠛⠛⠃⠘⠛⡛⠛⠛⠻⠟⠛⠛⠛⠛⠁⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⠿⠿⠛⠛⢣⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠨⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠋⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠰⠄⣴⣶⣶⣶⣄⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⣤⣤⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡟⠉⠉⠙⢻⢿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢸⣿⠀⣿⣰⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢈⠙⠤⠀⠀⠀⢠⣼⣿⣿⡄ ⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⣀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡟⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠃ ⠀⣠⣴⣾⣿⣿⣿⣟⣻⣿⣿⡟⠛⠛⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠛⢳⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠺⠿⠋⠀⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢠⠀⠰⠄⣴⣶⣶⣶⡄⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣄⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣶⣶⣾⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠀⣷⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⣠⣾⣿⣿⡀ ⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠃ ⢀⣤⣴⣿⣿⣿⣿⣟⣻⣿⣿⡟⠛⠛⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠋⢱⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠿⠋⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠰⠄⣴⣶⣶⣶⡄⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣤⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⣠⣾⣿⣿⡀ ⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠁ ⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠋⠛⠃⠘⠛⠛⠛⠋⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⠿⠿⠛⠋⢱⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠿⠋⠀⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢠⠀⠰⠤⣴⣶⣶⣶⡄⠐⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣄⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ 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⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠁ ⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠋⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠙⢱⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠿⠃⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠈⣻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠰⠤⣴⣶⣶⣶⡄⠐⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣤⣤⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣠⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣶⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⣠⣾⣿⣿⡀ ⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠁ ⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠋⠛⠃⠘⠛⠛⠛⠋⠻⠟⠛⠛⠛⠛⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⠿⠿⠛⠛⢱⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠿⠃⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠴⠤⣴⣶⣶⣶⡄⠰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣤⣤⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠛⠛⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⠏⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣾⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⡀⣀⣀⡀⣀⣀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⡇⣿⣏⢱⣿⣿⣸⣿⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⢀⣸⣿⣿⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠛⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣤⣀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣿⠗⣿⣆⣿⢸⣧⣿⢹⣿⠀⣿⣴⣿⢿⡾⢿⣿⠇⠀⠀⣶⣤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⣠⣾⣿⣿⠀ ⠀⠀⠀⢀⣿⣿⣿⢸⣿⠃⣿⣿⣿⡀⣿⡇⢸⣿⠀⣿⣏⣻⣿⣦⣾⣿⣶⠀⠀⢿⣿⡏⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠛⠻⠿⠁ ⢀⣤⣴⣿⣿⣿⣿⢟⣻⣿⣿⡟⠛⠛⠛⠃⠘⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⠿⠿⠛⠛⢱⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠿⠃⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠴⠤⣴⣶⣶⣶⡄⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 1870 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/fuchsia-woes/#comments Gemini version at gemini://gemini.techrights.org/2022/03/26/fuchsia-woes/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_26/03/2022:_Capyloon_and_Status_of_Chrome_OS,_Fuchsia⠀✐ Posted in Site_News at 4:33 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Kernel Space⠀➾ # ⚓ OS News ☛ The_first_Asahi_Linux_Alpha_Release_is_here⠀⇛ This is an absolutely stunning effort and achievement by the Asahi team, but as a mere user, this whole thing does not exactly instill me with the confidence needed to buy Apple hardware to run Linux on it. There’s no denying M1 hardware is amazing, but the idea of being entirely at the mercy of whatever Apple decides to do with the firmware and boot process seems like a terrible place to be in. That being said, few people will care about that possible issue, and for them, this is great news. # ⚓ uni Toronto ☛ Some_notes_on_Linux’s_/proc/locks_listing_of file_locks⠀⇛ As covered in the proc(5) manual page, /proc/locks lists current flock(2) and fcntl(2) file locks (and also lockf(3) locks, because those are actually fcntl() locks). Unsurprisingly, this /proc file is the fundamental source of information used by lslocks(8), and so understanding what appears in / proc/locks and what doesn’t can tell you something about what lslocks can show you. o § Instructionals/Technical⠀➾ # ⚓ Full_Circle_Magazine:_Full_Circle_Magazine_#179⠀⇛ # ⚓ ID Root ☛ How_To_Install_Mirage_on_Ubuntu_20.04_LTS_– idroot⠀⇛ In this tutorial, we will show you how to install Mirage on Ubuntu 20.04 LTS. For those of you who didn’t know, Mirage is an open-source application that is used to view photos on Linux systems. The graphical user interface enables the users to view the images easily. The Mirage, you have many options. Includes the ability to crop the image, resize it or change the color saturation. Furthermore, it automatically detects all the images found in the directory and displays them in the side panel. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you the step-by-step installation of the Mirage image viewer on Ubuntu 20.04 (Focal Fossa). You can follow the same instructions for Ubuntu 18.04, 16.04, and any other Debian-based distribution like Linux Mint. # ⚓ HowTo Forge ☛ How_to_Install_Chatwoot_Messaging_Platform_on Debian_11⠀⇛ Chatwoot is a free, open-source, and real-time messaging platform. It provides a simple and live chat for your website and integrates it with other apps. It helps your businesses to provide good customer support to their clients via social media channels. It can be easily integrated with social media apps including, Facebook, WhatsApp, and Twitter. It is a very good alternate solution to other commercial software like Intercom, Zendesk, etc. # ⚓ Finally⠀⇛ I gave up on WordPress for my personal blog, because after all of that effort and time spent yesterday, I have nothing to show for it. The site still was not rendering correctly. On the upshot, I discovered something called Hugo which generates a static site and I found the perfect theme for me called beautiful hugo. It is exactly the minimalist approach I am looking for an does not require a whole lot of resources to run. This is just a first post to put something up. There will be more to come soon. # ⚓ Vermaden ☛ ZFS_Compatibility⠀⇛ The best free filesystem on Earth – ZFS – also often named OpenZFS recently – has also become very portable in recent years of its development. The OpenZFS Distributions page lists 6 (six) operating systems already. [...] … but if you would like to create a ZFS pool compatible with all of them … which options and ZFS features should you choose? There is OpenZFS Feature Flags page dedicated exactly to that topic. # ⚓ Heap_Overflow_in_OpenBSD’s_slaacd_via_Router Advertisement⠀⇛ In this blog post we analyze a heap overflow vulnerability we discovered in the IPv6 stack of OpenBSD, more specifically in its slaacd daemon. This issue, whose root cause can be found in the mishandling of Router Advertisement messages containing a DNSSL option with a malformed domain label, was patched by OpenBSD on March 21, 2022. A proof-of-concept to reproduce the vulnerability is provided. o § Games⠀➾ # ⚓ Techdirt ☛ More_Gaming_For_Good:_Charity_Bundles,_Fortnite Team_Up_To_Raise_Millions_For_Ukraine⠀⇛ Once again, here comes the video game industry to do good in the world. Despite being the easy villain for many, including grandstanding politicians, video games and their communities can often be seen doing good for the world. A couple of weeks back, we discussed how one itch.io game bundle was offering thousands of dollars worth of games in a bundle that had over 1,000 titles to raise money for charities supporting Ukrainians. Despite a minimum price of $10 in a “pay what you want” format, that bundle had already raised $2 million from a $100k goal and was then aiming at $4 million instead. o § Distributions⠀➾ # § Gentoo Family⠀➾ # ⚓ Make Use Of ☛ Is_Chrome_OS_Desktop_Linux?_8_Points_to Consider⠀⇛ Do Chromebooks run Linux? This isn’t the way they’re advertised, for sure. Google doesn’t tell you Chromebooks come with Linux. They run Chrome OS, Google’s take on what a desktop operating system can be. But despite how different Chrome OS looks and feels, Chrome OS is based on Linux. So when we talk about Linux, are we also talking about Chrome OS? Here are eight points to consider. # ⚓ Extreme Tech ☛ Steam_Alpha_Has_Finally_Arrived_on Chromebooks⠀⇛ o § Devices/Embedded⠀➾ # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Forbes ☛ Android_Circuit:_Samsung_Galaxy’s_Surprising Victory,_OnePlus_10_Pro_Goes_Global,_First_Look_At Pixel_7_Pro⠀⇛ # ⚓ Android Police ☛ YouTube_Music_casting_to_Android_TV, Chromecast,_and_Google_TV_is_broken⠀⇛ # ⚓ 9to5Google ☛ Wireless_Android_Auto;_How_to_use_it,_or add_it_to_your_car_–_9to5Google⠀⇛ # ⚓ FOSSBytes ☛ Here’s_How_To_Mirror_Android_Phone_To TV⠀⇛ # ⚓ Vivo_Just_Showed_Its_First-Ever_Android_Tablet⠀⇛ # ⚓ Android Police ☛ Google’s_tightening_key_security_on Android_with_a_longer_(but_better)_chain_of_trust⠀⇛ # ⚓ Discord_app_crashing_on_Android_devices_after_every few_minutes⠀⇛ # ⚓ Express ☛ Popular_Android_app_just_got_banned_by Google_now_you_must_delete_it_|_Express.co.uk⠀⇛ # ⚓ CNX Software ☛ Capyloon_mobile_Web-based_OS_works_on Pinephone_Pro,_Librem_5,_Pixel_3a⠀⇛ Capyloon is an experimental Web-based OS leveraging b2gOS that served as the base for the now-defunct Firefox OS. The developers’ goal is to provide an open-source OS improving privacy and user control through web technologies. It’s still early stage, and some of the technologies used include the IPFS protocol, WebAssembly plugins, and the Tor network. Capyloon is more like a new phone shell as it replaces Phosh when installing it in a Linux smartphone. o § Free, Libre, and Open Source Software⠀➾ # ⚓ Business Insider ☛ Open-source_developers_are_burning_out, quitting,_and_even_sabotaging_their_own_projects_—_and_it’s putting_the_entire_internet_at_risk [Ed: Rosalie Chan still an_agent_of_FUD]⠀⇛ # § FSF⠀➾ # ⚓ SDTimes ☛ Free_Software_Foundation_award_winners⠀⇛ The winners of Free Software Foundation’s 2021 Software Awards for achievements in the field of free software, are SecuRepairs, Paul Eggert, and Protesilaos Stavrou. SecuRepairs was the winner of the Award for Projects of Social Benefit, which is presented to a project or team responsible for applying free software, or the ideas of the free software movement to benefit society. SecuRepairs helps to provide factual advice on information security issues like data privacy as they pertain to repairing devices and software, and works to help combat the anti-right-to-repair narrative spread by certain large hardware manufacturers. # § Programming/Development⠀➾ # ⚓ Swapping_two_Numbers_without_Temporary_Variables⠀⇛ Please never use this in any production code. The less we have to think about a piece of code, the better it is. It’s a fun thought experiment nevertheless! o § Standards/Consortia⠀➾ # ⚓ Hackaday ☛ High_Noon_For_Daylight_Savings_Time⠀⇛ The US Senate has approved the “Sunshine Protection Act”, a bill to make Daylight Saving time the default time and do away with the annual time changes. While I can get behind the latter half of this motion, redefining Daylight Saving time as Standard time is, in my opinion, nonsense. # ⚓ Patrick Breyer ☛ DMA:_European_Pirates_celebrate_success with_interoperability_requirements_in_final_trilogue results⠀⇛ The Pirates in the European Parliament welcome the final trilogue outcome of the Digital Markets Act (DMA) that was negotiated yesterday. Representatives of the EU Parliament, the Council and the Commission have agreed on including interoperability requirements for messaging services. According to Pirates, this will allow more choice for users, who will no longer be forced to use multiple platforms for private messenger communication. * § Leftovers⠀➾ o ⚓ Vice ☛ How_Is_There_Already_So_Much_‘Elden_Ring’_Porn?_We_Asked the_People_Who_Made_It⠀⇛ Elden Ring, one of the biggest games to launch this year, about being a miserable wandering maidenless wretch of a Tarnished on a Lord of the Rings type mission, is no exception. The [Internet] is already filled with high quality 3D Elden Ring porn. Who’s making it, and how are they doing it so fast? o ⚓ The Register UK ☛ China’s_annual_parliament_gives_tech_industry much_to_ponder⠀⇛ China is this week staging its annual “Two Sessions” meetings, which see its pair of top decision-making bodies meet to set the agenda for the coming year. As usual there is plenty of material that touches on tech. The two bodies are the National People’s Congress – a body of people installed by the Chinese Communist Party that is technically a parliamentary body but never votes against the Party’s wishes – and the National Committee of the Chinese People’s Political Consultative Conference. The latter is akin to the UK House of Lords or US Senate in that it has an oversight role. Premier Li Keqiang delivered the Two Sessions’ first big set piece on Saturday, in the form of the “Report on the work of the government”. Li emphasised increased adoption of digital government services, more 5G, and many more efforts to digitise many aspects of China’s society and economy. The importance of improving China’s ability to develop semiconductors, software, and AI was also highlighted. Those plans have been aired before, but Li this year said China’s government will “strengthen overall planning” of digitization initiatives, suggesting an acceleration. o § Education⠀➾ # ⚓ The Nation ☛ What_I_Learned_About_Standardized_Testing⠀⇛ In June 2018, I heard that then-Mayor Bill de Blasio wanted to do away with the Standardized High School Admissions Test (SHSAT)—the exam New York City students take to get into one of eight specialized high schools. These specialized schools are seen as huge stepping stones into elite colleges. # ⚓ Daniel Miessler ☛ How_to_Disagree⠀⇛ Paul Graham has a great piece on how to disagree with people in the best possible way. He provides a hierarchy, with 7 being best: [...] # ⚓ Reuters ☛ Taliban_orders_girls’_high_schools_to_remain closed,_leaving_students_in_tears⠀⇛ The last time the Taliban ruled Afghanistan, from 1996 to 2001, they banned female education and most employment. # ⚓ India ☛ Hijab_Row:_TNTJ_Issues_Death_Threats_To_Karnataka HC_Judges_Over_Case_Verdict⠀⇛ He also informed that Campus Front of India (CFI), the student wing of Popular Front of India, said that HC’s decision stands against the Constitution and they will continue to fight against it. Additionally, Amir-e-Shariat an Islamic organisation gave a bandh call against the Court’s verdict, Bhardwaj said. # ⚓ The Economist ☛ “A_library_is_more_powerful_than_Putin’s aeroplanes”⠀⇛ The museum’s collection spans the 12th to the 20th centuries, a period during which Lviv was part of the Mongol empire, Poland, the Austro-Hungarian empire, Imperial Russia, Poland again then, after the second world war, the Soviet Union. The city’s rich history is reflected in its architecture: Renaissance palaces mingle with baroque churches and neoclassical façades in ice-cream colours. The city has a strong intellectual tradition. Over the centuries it has been a hub for mathematicians, scientists and philosophers. o § Hardware⠀➾ # ⚓ Hackaday ☛ Polar_Planimeter_Quantifies_Area_By_Plotting Perimeter⠀⇛ These days it’s hard to be carry the label “maker” or “hacker” without also being proficient in some kind of CAD- even if the C is for Cardboard. But before there was CAD there was Drafting and its associated arts, and one couldn’t just select a shape and see its area in the square unit of your choice. So how could an old school draftsman figure out the area of complex shapes? [Chris Staecker] introduces us to the polar planimeter, a measuring tool created specifically for the purpose and explained in full in the video below the break. # ⚓ Hackaday ☛ Get_GitHub_Tickets_IRL_With_A_Raspberry_Pi_And_A Receipt_Printer⠀⇛ Thermal receipt printers are finding their way into all sorts of projects that are well beyond the point-of-sale environment that they normally inhabit. And while we applaud all the creative and artistic uses hackers have found for these little gems, this GitHub physical ticket printer has to be the best use for one yet. # ⚓ Hackaday ☛ DIY_Prony_Dyno_Properly_Displays_Power Production⠀⇛ When hackers in the US think of a retailer called Harbor Freight, we usually think of cheap tools, workable but terrible DVM’s, zip ties, and tarps. [Jimbo] over at [Robot Cantina] looked at the 212cc “Predator” engine that they sell and thought “I bet I could power my Honda Insight with that.” And he did, successfully! How much power did the heavily modified engine make? In the video below the break, [Jimbo] takes us through the process of measuring its output using a home built dyno. # ⚓ Hackaday ☛ DIY_SLS_3D_Printer_Getting_Ready_To_Print⠀⇛ Ten years ago the concept of having on our desks an affordable 3D printer knocking out high quality reproducible prints, with sub-mm accuracy, in a wide range of colours and material properties would be the would be just a dream. But now, it is reality. The machines that are now so ubiquitous for us hackers, are largely operating with the FDM principle of shooting molten plastic out of a moving nozzle, but they’re not the only game in town. A technique that has also being around for donkeys’ years is SLS or Selective Laser Sintering, but machines of this type are big, heavy and expensive. However, getting one of those in your own ‘shop now is looking a little less like a dream and more of a reality, with the SLS4All project by [Tomas Starek] over on hackaday.io. # ⚓ Hackaday ☛ A_Robot_Game_To_Open_Your_Hackerspace⠀⇛ It’s always good to welcome a new hackerspace to the fold, and thus we’re pleased to hear about the upcoming opening of Hackerspace Drenthe, on the north-eastern edge of the Netherlands. Starting a new space during a global pandemic is something of a feat. As part of their opening something is required to demonstrate a robot for the curious public, and what could be more accessible than a robot arm playing tic-tac-toe! # ⚓ Hackaday ☛ Hackaday_Podcast_161:_Laser_Lithography, Centurion_Hard_Drive,_And_Mad_BGA_Soldering⠀⇛ Join Hackaday Editor-in-Chief Elliot Williams and Staff Writer Dan Maloney for an audio tour of the week’s top stories and best hacks. We’ll look at squeezing the most out of a coin cell, taking the first steps towards DIY MEMS fabrication, and seeing if there’s any chance that an 80’s-vintage minicomputer might ride again. How small is too small when it comes to chip packages? We’ll find out, and discover the new spectator sport of microsoldering while we’re at it. Find out what’s involved in getting a real dead-tree book published, and watch a hacker take revenge on a proprietary memory format — and a continuous glucose monitor, too. # ⚓ SparkFun Electronics ☛ Arm_Opens_Innovation_Lab_in_South Africa⠀⇛ Arm is opening a new pilot innovation and demonstration (E3)NGAGE lab in partnership with the Cortex Hub, a regional technology incubator located in East London, Eastern Cape, South Africa. The lab will focus on engaging, educating and catalyzing local technology ecosystems while making Arm the computing foundation across the region. # ⚓ The Register UK ☛ Intel_axes_older_FPGA_cards,_moves development_to_customers_•_The_Register⠀⇛ Intel is discontinuing its original lineup of Programmable Acceleration Cards as it turns to an “ecosystem first” strategy that helps customers create their own FPGA-based products, including SmartNICs. The chipmaker issued an end-of-life notice Wednesday for three products in its FPGA-powered Programmable Acceleration Card lineup that debuted in 2017: the Intel PAC with Intel Arria 10 GX FPGA, the Intel FPGA PAC N3000, and the Intel FPGA PAC D5005. Intel is ending production of the cards “due to product transition and declining demand,” and customers have until July 11 to order them, the notice said. The final shipments will go out March 10, 2023, though Intel warned it can’t guarantee delivery for last-time orders “due to the unprecedented global demand for and limited supply of semiconductor components and substrates.” o § Health/Nutrition/Agriculture⠀➾ # ⚓ Common Dreams ☛ Opinion_|_Will_Privatization_Force Traditional_Medicare_Out_of_Business?⠀⇛ Five or ten years from now, seniors may wake up one morning and discover that their beloved Medicare program has been completely privatized. And it will not be because that’s what seniors want; it will be due to corporate influence and profiteering. Medicare was not created as a private program. In fact, it was enacted in 1965 as federal health insurance for seniors because many private insurers refused to cover them.  But over the past three decades, insurance companies and private investors have found a way to capture a growing share of federal Medicare dollars—money that should go toward patient care, not corporate profit. # ⚓ TruthOut ☛ Senators_Call_for_Inquiry_Into_Low_Medicaid COVID_Vaccination_Rates⠀⇛ # ⚓ TruthOut ☛ Our_Governments_Have_Chosen_Capitalism_Over Preparing_for_Next_COVID_Surge⠀⇛ # ⚓ Orac ☛ Autopsies_for_everyone_will_end_vaccine misinformation_immediately?⠀⇛ Although I had mentioned him before, first time I dedicated a post to discussing Steve Kirsch, the tech bro who started out the pandemic two years ago as somewhat reasonable in his desire to fund research into repurposed drugs to treat the COVID- 19 who later turned ivermectin zealot, misinformation firehose, and outright antivaxxer, it was about his “secret plan to end the vaccine madness.” More recently, he’s been whining that no one will “debate” him while harboring the apparent delusion that a free-for-all five hour video debate between him and his pseudoexperts versus real experts will end vaccine hesitancy, while complaining about “censorship.” (Of course, what he views as censorship I view as quality control.) Given Kirsch’s history of hare-brained schemes to “end vaccine hesitancy” or “end COVID-19 misinformation,” I was somewhat amused at his latest proposal; that is, until I realized that some people might wonder why it’s not a good idea. His proposal was published on his Substack earlier this week under the title—yawn, again?—A simple way to end vaccine misinformation immediately. The way? Kirsch thinks that an autopsies will do the trick, but not just any autopsies, rather: # ⚓ Counter Punch ☛ Two_Years_in_and_We_Still_Need_to_Learn_the Lessons_of_This_Pandemic⠀⇛ A global pandemic had reached the United States and changed each of our lives in ways we never imagined. Millions of Americans would lose jobs, friends, family, and even their lives to COVID-19, while billionaires would see record increases in their wealth. While the country ground to a halt, and I googled whether an imam would perform our marriage over Zoom, there was a glimmer of hope at the back of my mind. Surely, I thought, an event so monumental — one that laid bare every inequity of our economic system — would call for a change of equal measure. # ⚓ Pro Publica ☛ State_Launches_Cancer_Study_After_ProPublica Identifies_Toxic_Air_Pollution_Hot_Spot⠀⇛ After learning from a ProPublica analysis that his Missouri city is a hot spot of toxic air pollution, Verona Mayor Joseph Heck demanded that government officials look into the local cancer rate. Three months later, the state health department confirmed his fears: The rate of Non-Hodgkin lymphoma in the Verona zip code is more than twice as high as that of the surrounding county and state, officials told him. Non-Hodgkin lymphoma, a cancer that begins in the lymphatic system, can be caused by exposure to ethylene oxide, a potent carcinogen released by the BCP Ingredients plant in Verona. ProPublica’s unique analysis of air pollution data from the Environmental Protection Agency found the facility’s ethylene oxide emissions substantially increased local cancer risk; in some areas, the estimated industrial cancer risk was 27 times what the EPA considers acceptable. # ⚓ Gannett ☛ How_Russia’s_war_against_Ukraine_could_make_our food_prices_–_from_bread_to_beer_–_more_expensive⠀⇛ “The food supply chain is so integrated globally, that it’s hard to imagine that something happening half a world away is going to affect the price of food here in the United States,” says Robb MacKie, president and CEO of the American Bakers Association, an advocate for the commercial baking industry. “But it’s all intertwined.” # ⚓ RTL ☛ Scientists_find_microplastics_in_blood_for_first time⠀⇛ A Dutch study published in the Environment International journal on Thursday examined blood samples from 22 anonymous, healthy volunteers and found microplastics in nearly 80 percent of them. Half of the blood samples showed traces of PET plastic, widely used to make drink bottles, while more than a third had polystyrene, used for disposable food containers and many other products. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ The Verge ☛ Microsoft_is_tied_to_hundreds_of_millions of_dollars_in_foreign_bribes,_whistleblower_alleges⠀⇛ In the two years that followed, Elabd says he did everything in his power to stamp out these quiet bribes — a fight that made him a pariah among his colleagues and eventually cost him his job. But looking back, he believes Microsoft wasn’t interested in stopping the payouts, preferring to let phony contracts slip through and accept the associated cash. Elabd went public with his experiences in an essay published Friday by the whistleblower platform Lioness, alleging widespread bribery through Microsoft’s foreign contract business. Elabd estimates that more than $200 million each year is spent on bribes and kickbacks linked to the company, often in countries like Ghana, Nigeria, Zimbabwe, Qatar and Saudi Arabia. For the regions he worked in, he believes more than half of the salespeople and managers took part. If true, it’s a stunning look at the ongoing corruption associated with international tech contracting — and Microsoft’s ongoing struggles to contain it. # ⚓ Krebs On Security ☛ Estonian_Tied_to_13_Ransomware Attacks_Gets_66_Months_in_Prison [iophk: Windows TCO]⠀⇛ Maksim Berezan, 37, is an Estonian national who was arrested nearly two years ago in Latvia. U.S. authorities alleged Berezan was a longtime member of DirectConnection, a closely-guarded Russian cybercriminal forum that existed until 2015. Berezan’s indictment (PDF) says he used his status at DirectConnection to secure cashout jobs from other vetted crooks on the exclusive crime forum. Berezan specialized in cashouts and “drops.” Cashouts refer to using stolen payment card data to make fraudulent purchases or to withdraw money from bank accounts without authorization. A drop is a location or individual able to securely receive and forward funds or goods obtained through cashouts or other types of fraud. Drops typically are used to make it harder for law enforcement to trace fraudulent transactions and to circumvent fraud detection measures used by banks and credit card companies. # ⚓ Macworld ☛ Apple_plots_hardware_subscription_service for_iPhone_and_other_devices⠀⇛ According to Mark Gurman at Bloomberg, Apple has been working on a new subscription service for the iPhone and other hardware products that will let customers subscribe to Apple hardware with a monthly recurring payment. According to Gurman’s sources, Apple has been working on the subscription program for several months and is expected to launch it at the end of 2022. Unfortunately, that’s all the detail we have right now. We don’t know anything about pricing, bundles, which Apple hardware would be offered (other than the iPhone), or terms for trade-ins and upgrades. Apple already offers the iPhone Upgrade Program in the U.S., U.K., and China, which lets users pay for a new iPhone with AppleCare+ over 24 monthly payments with the option to upgrade after 12 months. # ⚓ The Verge ☛ Apple_will_reportedly_sell_the_iPhone_as a_subscription_service⠀⇛ According to Bloomberg’s report, the monthly charge wouldn’t simply be the price of the device divided by 12 or 24 months, but rather be a still-undecided monthly cost, potentially with the option to upgrade to new hardware as its released. And like Apple’s other subscriptions, it would be tied to a user’s existing Apple ID account, with the possibility of bundling in AppleCare or Apple One services as well. # ⚓ MacRumors ☛ Apple_Developing_Hardware_Subscription Service_for_iPhones_and_Other_Devices⠀⇛ Compared to the iPhone Upgrade Program, it would differ because Apple would charge a yet-to-be-determined monthly fee rather than splitting the cost of a device across a 12 or 24 month period. It would also cover other products while the iPhone Upgrade Program is limited to the iPhone. # ⚓ Mercury News ☛ Apple_is_working_on_a_subscription service_for_iPhones_and_other_products⠀⇛ Adopting hardware subscriptions, akin to an auto-leasing program, would be a major strategy shift for a company that has generally sold devices at full cost outright, sometimes through installments or with carrier subsidies. It could help Apple generate more revenue and make it easier for consumers to stomach spending thousands of dollars on new devices. # ⚓ Digital First Media ☛ Apple_is_working_on_a_hardware subscription_service_for_iPhones⠀⇛ Apple Inc. is working on a subscription service for the iPhone and other hardware products, a move that could make device ownership similar to paying a monthly app fee, according to people with knowledge of the matter. # ⚓ IT Wire ☛ Australia_ranks_number_one_in_Asia_Pacific for_most_ransomware_attacks [iophk: Windows TCO]⠀⇛ The research released from Unit 42 by global cybersecurity leader. Palo Alto Networks also found that ransomware payments hit new records in 2021 as cybercriminals increasingly turned to Dark Web “leak sites” where they pressured victims to pay up by threatening to release sensitive data. In Australia the research also found that 2021 saw a 642% increase in dark web leaks on the prior year and 38% of all attacks targeted organisations in NSW; ACT the least targeted geography. # ⚓ Trail Of Bits ☛ Towards_Practical_Security Optimizations_for_Binaries⠀⇛ This example is one of several well- documented instances of a compiler optimization inadvertently introducing a security weakness into a program. Recently, my colleagues at Georgia Tech and I published an extensive study of how compiler design choices impact another security property of binaries: malicious code reusability. We discovered that compiler code generation and optimization behaviors generally do not consider malicious reusability. As a result, they produce binaries that are generally more reusable by an attacker than is necessary. # ⚓ BBC ☛ US_charges_four_Russians_over_[cracking] campaign_on_energy_sector [iophk: Windows TCO]⠀⇛ They are accused of targeting hundreds of companies and organisations in around 135 countries between 2012-2018. Their activities are said to have caused two separate emergency shutdowns at one facility in Saudi Arabia. The conspiracy then allegedly attempted to [break into] the computers of a company that managed similar critical infrastructure entities in the US. # § Security⠀➾ # ⚓ Bleeping Computer ☛ Western_Digital_My_Cloud_OS update_fixes_critical_vulnerability⠀⇛ The vulnerability, which has a CVSS v3 severity score of 9.8, allows remote attackers to execute arbitrary code on the target device, in this case, WD PR4100 NAS, without requiring authentication. # ⚓ TechRadar ☛ Western_Digital_customers_urged_to update_to_latest_version_of_My_Cloud_OS⠀⇛ Western Digital has pushed a new firmware update for its My Cloud OS, fixing a high- severity vulnerability that was discovered during a recent hacking contest. As reported by BleepingComputer, cybersecurity experts from the NCC Group exploited a flaw in Netatalk Service, an open-source implementation of the Apple Filing Protocol (AFP) that allows for Unix-like operating systems to serve as file servers for macOS clients. The flaw, now tracked as CVE-2022- 23121, carries a severity score of 9.8/ 10, as it allows threat actors to run any code on the target endpoint, without authentication. # ⚓ WD_My_Cloud_Users_Should_Update_to_Avoid_a Dangerous_Vulnerability_–_Review_Geek [Ed: My Cloud? My clown? Whose clown? Everyone gets access...]⠀⇛ Western Digital just rolled out a My Cloud OS update that resolves a dangerous remote access vulnerability. All My Cloud users should install the firmware update (version 5.19.117) to defend themselves from remote hacking attempts. # § Privacy/Surveillance⠀➾ # ⚓ EFF ☛ Another_Tracker_Scanning_App Highlights_the_Need_for_a_Better_Way_to Protect_Victims_From_Digital_Stalking⠀⇛ # ⚓ EFF ☛ EFF_Client_Erik_Johnson_and Proctorio_Settle_Lawsuit_Over_Bogus_DMCA Claims⠀⇛ Johnson, who is also a security researcher, sued Proctorio a year ago after it misused the copyright takedown provisions of the DMCA to remove his posts. Proctorio had gone after a series of tweets Johnson published critiquing Proctorio that linked to short excerpts of its software code and a screenshot of a video illustrating how the software captures images of students’ rooms that are accessible to teachers and potentially Proctorio’s agents. Johnson’s lawsuit asked the court to rule that his posts were protected by the fair use doctrine and hold Proctorio responsible for submitting takedown notices in bad faith. Under the settlement, Proctorio dropped its copyright claim and other claims it had filed blaming Johnson’s advocacy for damaging its reputation and interfering with its business. In return, Johnson dropped his claims against Proctorio. Johnson’s tweets, which were restored by Twitter through the DMCA’s counter-notice process, will remain up. Proctoring apps like Proctorio’s are privacy-invasive software that “watches” students using tools like face detection for supposed signs of cheating as they take tests or complete schoolwork. Their use skyrocketed during the pandemic, leading privacy advocates and students to protest this new kind of surveillance. Johnson, whose instructors use Proctorio, was concerned about how much private information the software could collect from students’ computers and used his skills as a security researcher to examine its functions. # ⚓ CSO ☛ US,_EU_reach_preliminary_data privacy_agreement⠀⇛ The US and the European Union (EU) have a preliminary agreement over the storing of European data on US soil. It was announced by President Biden and EU President Ursula von der Leyen, speaking on Friday March 25. If successful, the data agreement would resolve a significant point of contention in US-EU relations since a previous deal regulating trans- Atlantic data flows—Privacy Shield—was deemed illegal by the EU’s top court in 2020. It ruled that the US did not provide EU citizens effective means to challenge US government surveillance of their data. # ⚓ India Times ☛ Twitter_expands_India_base for_global_boost⠀⇛ Twitter has formed an in-region team in India with cross- functional expertise as part of a move to accelerate globally its growth momentum by 2023 end. The social networking site expects its revenue to more than double to $7.5 billion in 2023, from $3.7 billion in 2020. It also plans to reach 315 million monetisable daily active users by the end of 2023. # ⚓ NYOB ☛ “Privacy_Shield_2.0″?_–_First Reaction_by_Max_Schrems⠀⇛ Today Commission President Ursula von der Leyen and President Biden have announced an “agreement in principle” on a new EU-US data sharing system. Some facts upfront: [...] # ⚓ EDRI ☛ Leaked_opinion_of_the_Commission sets_off_alarm_bells_for_mass_surveillance of_private_communications⠀⇛ A newly-revealed Opinion of a European Commission review board about their own colleagues’ upcoming proposal for a ‘Legislation to effectively tackle child sexual abuse’ shows strong concerns with the legislative proposal. Leaked by French media outlet Contexte yesterday (22 March), and dated 15 February 2022, the Opinion confirms the fears EDRi and 39 other civil society groups recently raised about the proposal which could destroy the integrity of private online communications across the EU, and set a dangerous precedent for the world. # ⚓ Pirate Party ☛ Chat_control:_Leaked Commission_paper_EU_mass_surveillance plans⠀⇛ Moreover, the opinion indicates that the draft law would also require this generalised monitoring to be done not just for material that has been assessed by authorities to ensure that it is unlawful, but also to search for “unknown” images as well as so-called evidence of “grooming” using notoriously unreliable AI-based tools. We’ve all seen pictures being automatically flagged on social media because an AI tool wrongly thought that the picture contained nudity, and have all suffered the frustration of an important email automatically going into your spam folder. # ⚓ Google_said_to_be_working_on_a_new_Nest Hub_with_a_detachable_tablet⠀⇛ This new Nest Hub will be a tablet that can be docked to a smart home device. There is not much about this, so we can speculate that the base might be used as a speaker that charges the device. This could be attribted to the work Google has done on Android 12L which has been made with tablets and foldables kept in mind. But we can’t be certain about the device running Android 12L. # ⚓ 9to5Google ☛ Chris_McKillop,_engineering director_of_Google’s_Fuchsia_project, leaves_the_company⠀⇛ Google has been known to be developing Fuchsia as a from- scratch operating system since at least 2016. Fuchsia ultimately saw its first launch last year on the first-gen Nest Hub smart display. For much of that time, the Fuchsia project has been headed up by Director of Engineering Chris McKillop. With a successful launch now in the rearview and Fuchsia firmly on the path to greater things, McKillop has announced on Twitter that he has left Google after ten years with the company. During that time, in addition to starting the Fuchsia project, McKillop helped shape the Flutter team — which has long had close ties to Fuchsia — and was also briefly involved with the Android TV team. o § Defence/Aggression⠀➾ # ⚓ Counter Punch ☛ Hulu’s_Catherine_the_Great:_Huzzah!⠀⇛ Among the reasons in play (at least, in my mind) are Putin is a Napoleonic asshole; Biden’s covering up his own corrupt doings in Ukraine by coaxing the kitty to the catnip; Zelensky is a Jew and history tells us that a kristallnacht can never be far behind these unfortunate diasporic people; the MIC needs something to do, now that the colossal waste of US taxpayer money and time (20 years) in Afghanistan is over; the American dollar, as global reserve, is about to be usurped by Russian and Chinese subversion, leading to the loss of pre-fab ‘middle class American lifestyle’ exports by way neo-liberal policies, and it’s now or never on the global hegemony front for the US, meaning all-out ‘limited’ war to save the PNACkers asses. And from whom do we garner our information about world events? The MSM that seems intent on endlessly milking their cashbull Trump? Lefty outrage rags? Personal history readings — from the POV of the winners or the losers (i.e. the People)? From facile, cynical, jaded wags like me, at the event horizon’s edge looking to take minds with me, oversupplied with the grist for lampoon? Who or what informs us? It’s a Socratic question. How do you know what you know? You’ll have to get off the social media juice — get sober to answer that. You need to get the fuck out of Plato’s Cave and away from the shadow play of implied dark doings. Fawk! This is supposed to be the Age of Aquarius, let’s act like it. # ⚓ Common Dreams ☛ Russian_Activists_Pen_Open_Letter_Demanding End_to_War_on_Ukraine⠀⇛ Several long-time Russian human rights advocates plan to publish an open letter urging Moscow to end its deadly assault on Ukraine, calling it “our common duty” to “stop the war [and] protect the lives, rights, and freedoms of all people, both Ukrainians and Russians.” As The Guardian, which obtained a draft statement, reported Friday: # ⚓ Counter Punch ☛ Putin_Abandons_Mankind⠀⇛ A simple German monk, Martin Luther (1483-1546), challenged the dominant Catholic Church of the Middle Ages. When he nailed his 95 theses on the door of the Castle church in Wittenberg in 1517, he set off the beginning of the Protestant Reformation and horrendous religious wars throughout Europe. When he refused to compromise, declaring before the authorities during his 1521 trial at Worms, “Here I stand I can do no other,” he went against all prevailing norms. The English philosopher and political theorist Michael Oakeshott describes Luther’s singularity as an individual and his irresponsibility for consequences as follows: # ⚓ Counter Punch ☛ The_United_States_is_Exceptional,_Just_Not in_the_Ways_Any_of_Us_Should_Want⠀⇛ That, in a nutshell, was the postwar version of U.S. exceptionalism and Washington was then planning to manage the world in such a way as to maintain that remarkably grotesque disparity. The only obstacle Kennan saw was poor people demanding a share of the wealth. Today, as humanity confronts a looming climate catastrophe, what’s needed is a new political- economic project. Its aim would be to replace such exceptionalism and the hoarding of the earth’s resources with what’s been called “a good life for all within planetary boundaries.” # ⚓ Counter Punch ☛ How_a_No-Fly_Zone_Could_Lead_to_Nuclear War⠀⇛ What they’re actually proposing is that we launch a war against nuclear-armed Russia. Proponents say that while Ukrainians fight Russians on the ground, the U.S. should tell Russia they’re barred from Ukrainian skies. But what happens when Russian planes fly over Ukraine anyway? Then our planes must try to shoot them down. # ⚓ Common Dreams ☛ ‘Dangerous’:_Experts_Slam_Biden_for_Keeping First-Use_Nuclear_Strike_on_the_Table⠀⇛ On the campaign trail, U.S. President Joe Biden said the “sole purpose of the U.S. nuclear arsenal should be deterring—and if necessary, retaliating against—a nuclear attack” and vowed to “put that belief into practice.” But amid growing tensions with Russia as it wages a deadly war on Ukraine, the president has reportedly abandoned that campaign promise, opting instead to leave in place a policy embraced by his predecessors that allows for the use of nuclear weapons in response to non-nuclear warfare—including conventional, chemical, biological, and cyber-related attacks. # ⚓ Meduza ☛ The_war_at_home:_Russia_is_de_facto_under_martial law,_human_rights_experts_warn⠀⇛ Rights and freedoms in Russia have been restricted to the point that the country is de facto under martial law. This is the conclusion of a new report authored by prominent human rights experts Pavel Chikov, head of the rights group Agora, and Damir Gainutdinov, head of the Net Freedoms Project. Indeed, against the backdrop of Moscow’s month-long invasion of Ukraine, the Russian authorities have moved to impose serious restrictions on basic constitutional rights and freedoms at home. As Chikov and Gainutdinov write, these restrictions have primarily affected freedoms of assembly, speech, and movement, as well as private property rights. Meduza summarizes the report’s main findings here. # ⚓ Meduza ☛ ‘Nobody_understood_what_was_happening’:_Meduza tells_the_story_of_Albert_Sakhibgareyev_—_a_Russian_contract soldier_who_deserted_from_the_war_in_Ukraine⠀⇛ Five weeks ago, 25-year-old contract soldier Albert Sakhibgareyev was in Russia’s Belgorod region, several miles from the Ukrainian border, where his brigade was “conducting training exercises.” Sakhibgareyev says he and his fellow soldiers would fire “wherever they were ordered to,” though what exactly they were firing at was unclear. According to him, he didn’t understand he was in a real war until the Ukrainian side started firing back; soon after that, he deserted. Meduza reports on how a soldier from Bashkortostan decided enough was enough. # ⚓ Meduza ☛ ‘We’ll_all_go_back_when_the_regime_falls’:_How Tbilisi_become_a_hub_for_Russian_political_emigrants⠀⇛ In the first weeks after Vladimir Putin announced his “special military operation” and invaded Ukraine, tens of thousands of Russians flew to Georgia, despite the fact that there are no direct flights there from Russia. Many continued on to other countries, but about 12,000 have stayed. For Meduza, journalist Gleb Golod — who is among those who moved to Georgia in recent weeks — reports on the problems these new arrivals have faced and how Georgians have responded to the Russian influx. # ⚓ The Nation ☛ Exclusive:_Ukraine’s_Defense_Intelligence Chief_Warns_of_“Real_Hell”_for_Russians⠀⇛ In November last year, Brig. Gen. Kyrylo Budanov sounded the alarm. Vladimir Putin, Budanov told the Military Times, was using the massive Zapad 21 exercises in western Russia and Belarus as a screen for a planned invasion of Ukraine. A day later, Bloomberg reported that US intelligence sources were saying that Russia was preparing for a multipronged push into Ukraine. # ⚓ The Nation ☛ A_Last_Gift_of_Love:_One_Way_to_Switzerland, Business_Class⠀⇛ On the night of February 6, my husband and I boarded a plane from New York to Zurich, Switzerland. It would be our last trip together and the first trip we’d taken in many years. In many ways, it felt like so many vacations we’d taken over our 52 years together: making the plans, booking the flight, finding a hotel—and a good restaurant to eat our last meal. I even joked that he had to be dying for us to fly business class. But this last trip was no joking matter. # ⚓ The Nation ☛ We_Don’t_Need_to_Go_Back_to_Cold_War Spending—We’re_Already_There⠀⇛ A growing chorus of pundits and policy-makers has suggested that Russia’s invasion of Ukraine marks the beginning of a new Cold War. If so, that means trillions of additional dollars for the Pentagon in the years to come coupled with a more aggressive military posture in every corner of the world. # ⚓ Counter Punch ☛ Ending_the_War_in_Ukraine⠀⇛ Initially, he’d hoped to do so by seizing Kyiv, replacing the government, and absorbing as much of Ukrainian territory into Russia as he thought feasible. Now, after the resistance of the Ukrainians, he is looking to eliminate their country by a different method. He will bomb it into submission from the air and depopulate the country by turning millions of its citizens into refugees. # ⚓ Counter Punch ☛ Ukraine,_Russia_and_the_Sporting McCarthyites⠀⇛ The main interest is never in the second answer, but the first.  Putin must be condemned and banished from your conscience, your mind and history.  Ignore the fact that he is the elected leader of a country – he remains a tyrant to be condemned to liberal democratic execration.  Best go about punishing people innocent of this fact. Such a cringeworthy approach has seduced and trapped some able minds over the years.  During the Cold War, the division of camps and ideologies demanded unthinking loyalty, not so much to truth but a version of it long lost in political drag and the hypocrisy of appearances.  On September 22, 1947, delegates from Communist parties across the European spectrum heard the infantile ravings of the main Soviet delegate Andrei Zhdanov, who suggested with nether clenching tediousness that the world was divided between the “imperialist and democratic camp”.  The US, allied with Great Britain and France, made up the former.  “The anti- fascist forces comprise the second camp”, rooted in the USSR and its various, anomalously named “new democracies.” # ⚓ Counter Punch ☛ End_Times_Can_No_Longer_Be_Postponed⠀⇛ The forecast is for an accelerating whirlpool of international violence that could possibly be remembered, historically, as the Third World War. The current situation involving Russia and Ukraine is what congeals the storm clouds of this forecast. In terms of geopolitical history, Russia has a longstanding worry—three major invasions (one by France, two by Germany) since the early nineteenth century—and therefore wanting Ukraine as a Slavic buffer against those encroaching, marauding Europeans. Perfectly rational in the world of geopolitics. # ⚓ Common Dreams ☛ Progressives_Demand_End_to_US_Involvement on_7th_Anniversary_of_Saudi-Led_War_on_Yemen⠀⇛ On Friday, the seventh anniversary of the beginning of the Saudi-led war on Yemen, four members of the Congressional Progressive Caucus implored President Joe Biden to immediately end U.S. military support for the deadly assault—and vowed to pass a War Powers Resolution to make it happen if the White House refuses. “With each passing day, the crisis in Yemen intensifies.” # ⚓ FAIR ☛ ‘Just_Pay_Attention_to_What_Our_Own_Government_Is Doing_in_Yemen’⠀⇛ # ⚓ Counter Punch ☛ Imperialism_and_the_Struggle_Against_It Begins_at_Home⠀⇛ Imperialism is born not in some abstract off-shore political vacuum. At first blush, it speaks to domestic expansion and repression… to the theft of lands in a veracious rush to swell and secure one’s base and the target of those who present a different look, a different history, a different aspiration. After-all, no imperial trek can hope to accomplish anything but failure while domestic dissent screams NOT. It was a costly lesson, one belatedly understood by the Romanovs as they took their well-deserved final royal stroll to the walls of rebellion where they were met with a fuselage of bullets and the bite of bayonets as their three- hundred-year imperial dynasty faded into the pathway of revolutionary history. For historical purposes, it matters less who the Romanovs were than what it is they represented… for those who fail to recall the lessons of history are doomed indeed to repeat its mistakes although, to some today, these same “missteps” are easily white- washed away as so much the unavoidable linchpin of political necessity and group chant. # ⚓ Counter Punch ☛ Roaming_Charges:_Both_Ends_Burning⠀⇛ + In our identity-obsessed political culture, Madeleine Albright finally proved that American woman (the Israelis and Brits had demonstrated this quality decades earlier) are fully capable of supervising mass death without flinching or showing the tiniest twinge of regret or remorse. + It is the ultimate moral crime to target for misery, pain and death those least responsible for the offenses of their tyrannical rulers. Yet this is the very policy Madeleine Albright made Standard Operating Procedure for US diplomacy. # ⚓ Counter Punch ☛ Ukraine_Could_Turn_Into_Another_Endless War,_Especially_if_NATO_Decides_More_Than_Just_Peace_is Needed⠀⇛ But if we look at a larger map that includes not only Europe but the Middle East and North Africa, we get an entirely different impression because Ukraine is no longer a blood-soaked exception in a zone of peace. It is, on contrary, the new northern extension of a giant zone of war that has extended over the last twenty years east-west from Afghanistan to north-east Nigeria and north-south from Turkey to Somalia and Yemen. Parallels are occasionally drawn between the Ukrainian war and a dozen or so conventional and guerrilla wars being fought out in this vast area of conflict to the south of Ukraine. When similarities between these conflicts are noted, it is usually on the grounds that Russian shelling and bombing of cities like Mariupol and Kharkiv is similar to that of Damascus and Aleppo by Russian- backed Syrian forces. This is true enough, but keep in mind that the bombardment of Gaza by Israel and Raqqa and Mosul by the Americans likewise led to massive physical destruction and heavy civilian loss of life. # ⚓ Counter Punch ☛ Putin_is_Not_Dealin’⠀⇛ Why Putin is running his dictatorship as a boy-in- the-bubble is anyone’s guess. In recent weeks, from varied sources, I have heard numerous diagnoses of the president’s condition: he has pancreatic cancer, is pumped up on steroids, lives in dread of Coronavirus, fears assassination (especially by poison—one of his own equalizers of choice), and imagines plotters behind every curtain (which is where the assassins of Tsar Paul I found him hiding in his St. Petersburg bedchamber in 1801). Putin’s self-imposed isolation can only mean that he’s cut off from his commanders in the field, as well as others in the Russian government, which probably explains why no one other than the president can make decisions about anything—be it a matter of strategy, tactics, economics, war or peace. # ⚓ Counter Punch ☛ A_Coward’s_War⠀⇛ In Book III of The Iliad, Paris shows up for battle clad in a lion skin and brandishing a bow, a sword and two bronze spears. His armor and weaponry are replete – too replete. So, when he challenges the bravest of the Achaeans to a duel, we know what to expect. Menelaus, aggrieved husband of the abducted Helen, springs from his chariot, Homer tells us, “like a hungry lion that lights on the carcass of some goat or horned stag and devours it then and there.” But Menelaus doesn’t get to enjoy his meal. Paris is a lover not a fighter, as J.L. David’s painting shows, and he flees the battlefield for the boudoir. Reproached by Hector for his cowardice, Paris finally agrees to the duel. Whoever wins, can claim victory in the war, preventing further bloodshed. Menelaus easily defeats Paris, but before he can administer the coup de grace, Aphrodite spirits away the vainglorious Trojan. The war resumes and many more die in place of craven Paris – who himself is finally killed. # ⚓ Counter Punch ☛ Immune_to_War_Fever,_Some_Countries_Stay Neutral_to_Russia⠀⇛ For many of these countries, Moscow’s attack on Ukraine does not look any different from Washington’s 2003 attack on Iraq. They stayed out of that and are staying out of this, despite the wall-to-wall coverage, the comparisons to Pearl Harbor and the media frenzy over this assault on a country whose citizens are white (and therefore apparently deserve more compassion than the millions of non-European Afghans starved by U.S. sanctions or the over 377,000 brown Yemenis slaughtered with U.S. weapons), with breathless claims that nothing like this has happened in Europe since World War II. Our propaganda outlets that call themselves media have apparently forgotten NATO’s 1999 bombing of Yugoslavia. For some unexplained reason, that didn’t count. Except of course to the Serbs – another demonized ethnic group, though I doubt their magnificent composers were banned from the repertoires of western orchestras, that their conductors and sopranos were ordered to revile their country or be fired or that their immortal novelists, like Dostoevsky, were deleted, if temporarily, from curricula at the University of Milan. There’s nothing easier than denouncing a national enemy. More arduous is attempting to regard something objectively awful – the Russia/Ukraine war – with clear eyes and without succumbing to the required Two Minutes Hate. Few do that in the west. Any western news report, any politician’s speech, even casual conversation about this conflict zooms quickly to Two Minutes Hate. Furious tirades against Moscow and Putin explode everywhere, are the norm, expected and those who don’t indulge thus are suspect at the least and very likely considered treasonous. Nothing nowadays comes more naturally or facilely than this western and European hatred of all things Russian. But that is not the case in the Global South. # ⚓ Counter Punch ☛ The_Blowback_from_Sanctions_on_Russia⠀⇛ Michael Hudson Thank you for inviting me. Ross Michael, sanctions, sanctions, sanctions is all we hear now. We’re sanctioning people. The West sanction people back to the Stone Age. What are the unintended consequences of sanctions? # ⚓ Counter Punch ☛ Russian_Military_Adapting_in_Ukraine⠀⇛ The latest developments, including: – How Russian tactics and strategy have changed since the war began – What the shift means for the future of the war – Impact to Russia from ban on semiconductor sales from Taiwan – Can China fill the gap for Russia? – What does the resignation and defection of Chubais mean for the future of Putin’s government? – Which of Putin’s top officials will be next to flee? # ⚓ Counter Punch ☛ Thinking_About_the_Unthinkable⠀⇛ “One Minute to Midnight” I doubt the people saying “stop worrying about WWIII” have any idea how close the world came to nuclear winter in October of 1962, when John Fitzgerald Kennedy decided to turn Soviet missiles sent to protect socialist Cuba from further U.S. invasions into a game of nuclear chicken. On October 27, 1962, Soviet submarine Second Captain Vasily Arkhipov’s refusal to agree with his Captain’s decision to assemble and launch a nuclear torpedo at US destroyers in the Saragossa Sea may well have saved humanity from annihilation. At the time, one-third of the United States’ nuclear bomb- carrying Air Force fleet was in the air at “Defcon 2,” the highest U.S. nuclear alert short of launch. Each of the B-52s in the sky could have set off terminal human catastrophe with or without direction from US Strategic Air Command (SAC). # ⚓ Common Dreams ☛ ‘Ukrainian_Blood_on_Their_Hands’:_Analysis Details_How_Big_Oil_Funded_Putin’s_War_Chest⠀⇛ Bolstering climate campaigners’ charges that fossil fuels have funded Russia’s ongoing assault of Ukraine, an analysis published Friday by three green groups reveals top energy companies helped build Russian President Vladimir Putin’s war chest to the tune of nearly $100 billion since 2014. “If we want to build a world based on equity, peace, and stability then we must urgently accelerate the move towards renewable energy.” # ⚓ Common Dreams ☛ Opinion_|_How_to_End_the_War_in_Ukraine⠀⇛ Vladimir Putin has a very clear strategy for ending his war in Ukraine. He intends to wipe the country off the map. # ⚓ Common Dreams ☛ Opinion_|_Before_Ukraine,_A_Massive_Refugee Crisis_Ignored_and_Largely_Created_by_the_West⠀⇛ Since Russia’s invasion last month, nearly 6.5 million people have been forcibly displaced within Ukraine and almost 3.4 million have fled across international borders. # ⚓ Common Dreams ☛ Ukraine_Officials_Say_300_Civilians_Were Killed_by_Russian_Bombing_of_Mariupol_Theater⠀⇛ Officials in the besieged Ukrainian city of Mariupol said Friday that they believe around 300 people were killed in a March 16 Russian airstrike on a theater in which at least hundreds of civilians were sheltering. “We still do not want to believe in this horror. We still want to believe that everyone managed to escape.” # ⚓ The Gray Zone ☛ BBC_correspondent-fixer_shaping_Ukraine_war coverage_is_PR_operative_involved_in_“war-messaging_tool”⠀⇛ # ⚓ TruthOut ☛ US_Hawks_Are_Trying_to_Increase_Military_Budget —_and_Use_Ukraine_as_Excuse⠀⇛ # ⚓ TruthOut ☛ Progressives_Demand_Congress_Cut_Military Support_for_War_on_Yemen⠀⇛ # ⚓ Pro Publica ☛ These_Children_Fled_Afghanistan_Without_Their Families._They’re_Stuck_in_U.S._Custody.⠀⇛ Seven months after the fall of Kabul, shelters in the U.S. caring for children evacuated without their parents are experiencing unprecedented violence while workers at the facilities have struggled to respond to the young Afghans’ trauma. Some children have run away, punched employees and stopped eating. Others have tried to kill themselves. At one shelter, ProPublica has learned, some children reported being hurt by employees and sexually abused by other minors. # ⚓ Democracy Now ☛ Start_of_a_New_Cold_War?_U.S._Hawks_“Want to_Jack_up_the_Military_Budget_and_Use_Ukraine_as_an Excuse”⠀⇛ With NATO countries recommitting themselves to the alliance and passing sweeping sanctions against Russia as punishment for Vladimir Putin’s invasion of Ukraine, is this the dawn of a new Cold War? We speak with foreign policy expert William Hartung, a senior research fellow at the Quincy Institute, who warns that hawks in Washington are pushing for a massive increase in the U.S. military budget, which is already a record-high $800 billion a year. “There’s a danger that not only will this be a war in Ukraine, but the U.S. will use it as an excuse for a more aggressive policy around the world, arguing that it’s to counter Russia or China or Iran, or whoever the enemy of the moment is.” Hartung also speaks about the Saudi-led war in Yemen, where U.S. support has allowed the conflict to rage for years, killing about 400,000 people. Unlike in Ukraine, where the U.S. has more limited leverage, the Biden administration could “end that killing tomorrow,” Hartung says. # ⚓ Democracy Now ☛ Yanis_Varoufakis:_The_West_Is_“Playing_with Fire”_If_It_Pushes_Regime_Change_in_Nuclear-Armed_Russia⠀⇛ A month after the Russian invasion of Ukraine, more than 3.6 million Ukrainians have left the country as refugees, and the war risks becoming “an Afghanistan-like quagmire,” warns Greek lawmaker Yanis Varoufakis, founder of the Progressive International with U.S. Senator Bernie Sanders. He says the West’s sweeping sanctions on Russia and bottomless military aid to Ukraine risk escalating the conflict and foreclosing chances of a peaceful resolution. “What is exactly the aim? Is it regime change in Russia?” asks Varoufakis. “Well, whenever the United States tried regime change, it didn’t turn out very well and has never been tried with a nuclear power. This is like playing with fire.” # ⚓ The Verge ☛ Russian_military_reportedly_[broke]_into European_satellites_at_start_of_Ukraine_war⠀⇛ American government officials told The Washington Post that the Russian military was responsible for a cyberattack on a European satellite [Internet] service that affected Ukrainian military communications in late February. The [break in] affected the KA-SAT satellite broadband network, owned by Viasat, an American satellite communications company. On February 24th, the day the Russian invasion of Ukraine began, the KA-SAT network was hit by outages that affected Ukraine and surrounding regions in Europe. A few days afterward, Viasat blamed outages on a “cyber event,” but did not release further details. # ⚓ New Yorker ☛ Can_Anyone_Unseat_Marjorie_Taylor_Greene?⠀⇛ Greene is now facing another challenge, this one legal rather than electoral. On Thursday morning, a group of lawyers led by Ron Fein, the legal director of a nonprofit called Free Speech For People, is filing a lawsuit that, were it to be successful, would prevent Greene from running for office again. The suit argues that Greene’s statements and activities related to the attack on the Capitol on January 6th make the congresswoman an insurrectionist. A clause of the Fourteenth Amendment specifically prohibits those who have “engaged in insurrection or rebellion” against the United States from holding public office. The suit, citing this clause, contends that Greene “is constitutionally disqualified from congressional office and, as such, ineligible to run as a candidate under state and federal law.” # ⚓ ME Forum ☛ Todd_Bensman:_Jihadis_Infiltrate_Texas⠀⇛ Todd Bensman, Writing Fellow at the Middle East Forum, Senior National Security Fellow at the Center for Immigration Studies, and author of America’s Covert Border War, spoke to participants in a February 14 Middle East Forum Webinar (video) to discuss the cases of unvetted migrants from countries “associated with terrorist organization activity” who are accompanying the mass migration at the Southern border. # ⚓ Daily Post ☛ Go_after_bandits,_terrorists,_not_those keeping_afro_–_Shehu_Sani_tells_Sharia_Police⠀⇛ “The need for them to reach out to rural communities and educate our citizens on the need for them not to join bandits and terrorists is also very important. So apart from them to be enforcing religious laws, there is need for them at this hour to be very more present, active and agile in finding a lasting solution to the problem of bandits and terrorists that have been kidnapping and killing our people,” Shehu Sani said. # ⚓ Medforth ☛ Employees_of_the_Koekelberg_Basilica_in_the Muslim_stronghold_of_Brussels_fear_for_their_lives_–_pelted daily_with_paving_stones⠀⇛ According to Martine Motteux-Abeloos, the church’s deputy rector, the acts were committed by young teenagers who had come on scooters or by adults travelling by car. On Tuesday, a brick flew past just 50 cm from her head while she was in her office. “The situation is becoming untenable and colleagues are starting to get seriously scared. It’s crazy that there is so much senseless vandalism that can injure or even kill. I never thought that you have to fear for your life in the Basilica,” she lamented on Facebook, adding photos of the damage. # ⚓ VOA News ☛ Did_Taliban_Infiltrate_Afghan_Evacuees_to_the US?⠀⇛ A report last month by the Department of Defense’s inspector general concluded that “U.S. agencies did not use all available data when vetting Afghan evacuees” and that “the United States faces potential security risks” if certain Afghans “are allowed to stay in the country.” o § Environment⠀➾ # ⚓ The Verge ☛ The_UN_plans_to_extend_weather_warning_systems to_everyone_on_the_planet⠀⇛ The United Nations wants to make sure every person on Earth can receive early warnings ahead of disastrous weather events. It set a goal of hitting that target within five years in an announcement this week. Early warning systems are needed urgently to save lives as climate change makes extreme weather even worse, UN officials said. Such systems include technology to forecast dangerous weather systems and the ability to share those forecasts with the public so that they can take precautions ahead of storms, floods, heatwaves, and droughts. One in three people in the world still aren’t protected by early warning systems, according to the World Meteorological Organization (WMO). # ⚓ Futurism ☛ Scientist_Warns_That_a_Huge_Tanker_Is_Probably Going_to_Spill_a_Million_Barrels_of_Oil_Into_the_Ocean⠀⇛ The tanker is filled with more than a million barrels of crude oil, which makes it a major cause of concern for scientists worried that any accident involving the Safer could result in it spilling into the ocean. # ⚓ CNN ☛ An_aging_oil_tanker_has_become_a_floating_time_bomb. It’s_an_environmental_disaster_waiting_to_happen⠀⇛ An aging, decaying oil tanker, the FSO Safer, has been anchored five miles off the coast of Yemen since March 2015, when Houthi rebels took control of the Red Sea coastline near the port city of Al- Hudaydah. International officials are working to stave off a potential environmental and human catastrophe: The 362-meter (1,118-foot) Safer is filled with more than a million barrels (40 million gallons) of light, sweet crude oil — liquid cargo which could lead to ecological disaster were the vessel to leak oil or explode. # ⚓ Common Dreams ☛ ‘Wake-Up_Call’:_Antarctic_Ice_Shelf_the Size_of_Los_Angeles_Has_Collapsed⠀⇛ Satellite imagery showing the recent “complete collapse” of the Conger Ice Shelf in East Antarctica sparked fresh alarm over the climate emergency on Friday. “While humans are killing humans, and governments are spending on weaponry as if there is no tomorrow, the environment is collapsing—so that there will be no tomorrow,” said former Greek finance minister and Progressive International co- founder Yanis Varoufakis. # ⚓ Common Dreams ☛ Green_Groups_Decry_US_Energy_Panel’s Reversal_on_Gas_Pipeline_Climate_Reviews⠀⇛ U.S. climate activists were outraged after a federal regulatory agency on Thursday walked back plans to consider the planet-heating emissions and environmental justice impacts when weighing whether to approve new fossil fuel infrastructure. “Even the suggestion that the agency be more than just a rubber-stamp for gas pipelines was a bridge too far for industry and their politicians.” # ⚓ Counter Punch ☛ The_Truth_About_IPCC_Reports⠀⇛ That provocative depiction is examined in a recent Nick Breeze ClimateGenn podcast interview: Existential Risk Management with David Spratt, research director of the Breakthrough National Centre for Climate Restoration in Melbourne. Dr. Spratt is highly regarded for solid research, which is evidenced throughout his refreshingly straightforward interview. Spratt’s interview tackles: (1) failings of the IPCC, (2) tipping points, and (3) a nearly out of control global warming challenge that’s not realistically understood, even as wobbly ecosystems start to falter. # ⚓ Common Dreams ☛ Groups_Rip_‘Climate-Wrecking’_Biden_Plan_to Boost_US_Gas_Exports_to_Europe⠀⇛ Global climate advocates on Friday panned as “misguided and dangerous” the Biden administration’s newly announced effort to ramp up U.S. gas shipments to European Union countries as they look to reduce their dependence on Russian fossil fuels. “If Europe truly wants to get off Russian gas, the only real option it has is phasing out gas altogether.” # ⚓ Common Dreams ☛ Locals_Warn_Biden’s_EU_Export_Plan_Would Make_Gulf_Coast_‘Sacrifice_Zone’_for_Fracked_Gas⠀⇛ Frontline community activists on Friday joined climate and environmental campaigners in denouncing the Biden administration’s plan to ramp up U.S. gas shipments to the European Union in response to Russia’s invasion of Ukraine. Elida Castillo, program director at Chispa Texas, said in a statement that “our thoughts are with those in Ukraine and Europe who are facing humanitarian and energy crises, but we cannot disregard the crises our communities are facing every day.” # ⚓ Common Dreams ☛ Youth_Strikes_Worldwide_Demand_Climate Action_That_Centers_‘People_Not_Profit’⠀⇛ From Dhaka, Bangladesh to Turin, Italy and beyond, youth climate strikers took to the streets across the globe Friday to demand that political leaders stop ignoring the scientific community’s deafening alarm bells and take action to slash carbon emissions before it’s too late. “The current system is widening the inequality gap—it has no place in our society.” # ⚓ TruthOut ☛ Activists_Decry_“Climate-Wrecking”_Biden_Plan_to Boost_US_Gas_Exports_to_Europe⠀⇛ # ⚓ The Revelator ☛ The_Legacy_of_Lake_Pedder:_How_the_World’s First_Green_Political_Party_Was_Born_in_Tasmania_50_Years Ago⠀⇛ # ⚓ Common Dreams ☛ Opinion_|_Navy_Decisions_on_Red_Hill_Jet Fuel_Tanks_Very_Costly_to_Military_Families,_Taxpayers,_and Hawaii’s_Environment⠀⇛ Total Congressional funding for all aspects of the Navy’s Red Hill water contamination debacle is now over $1.1 billion according to Hawai’i Congressional representative Ed Case and billions more are needed to complete clean-up, defueling and closing of the massive leaking Red Hill jet fuel storage facility. # § Energy⠀➾ # ⚓ Common Dreams ☛ Opinion_|_Largest_‘Built_All-At-Once’ Wind_Farm_Opens_in_Oklahoma,_Saves_Customers_$1 Billion⠀⇛ This week, American Electric Power (AEP), which operates in several states, inaugurated what it called the largest wind farm in the US ever built all at once. That is, there are larger wind facilities, but they were actually a congeries of several projects built over many years. # ⚓ DeSmog ☛ Media_Repeats_Kremlin_Anti-Fracking_Claims_– While_Ignoring_Russia’s_Promotion_of_Climate_Denial⠀⇛ In their latest attempt to use the Russian invasion of Ukraine to argue for more fossil fuel extraction, climate sceptics have revived an old claim that anti-fracking campaigns around the world have been bankrolled by the Kremlin. This claim is being amplified by mainstream conservative newspapers. “Did Putin plot with eco-warriors to halt Britain’s fracking and keep us all hooked on his gas?” asked Guy Walters in the Daily Mail. Days later, coal baron and climate sceptic Matt Ridley wrote in The Sun: “FRACK NEWS: How lying Putin spent millions spreading fake news about fracking”. Similar allegations have appeared in both The Telegraph and the Daily Express. # ⚓ The Nation ☛ Averting_Climate_Catastrophe⠀⇛ # ⚓ What_is_Earth_Hour_2022_and_how_does_the_event_help the_planet?⠀⇛ Earth Hour 2022 is an event run by the World Wildlife Fund (WWF) to raise awareness of the climate crisis. The premise is pretty simple: since 2007, people across the world have turned out their lights for one hour on the last Saturday in March. It’s a symbolic gesture that aims to ‘increase awareness and spark global conversations on protecting nature’. # ⚓ Lights_out_at_Helsinki_Expo_and_Convention_Centre_for Earth_Hour_2022⠀⇛ Messukeskus Helsinki, Expo and Convention Centre, takes part in the WWF’s Earth Hour by switching off all its lights on Saturday 26 of March from 8.30 pm to 9.30 pm. All the lights outdoors, in the exhibition halls, meeting rooms, corridors, hallways and billboards are switched off. # ⚓ CNN ☛ These_fossil_fuel_companies_sent_more_than_$15B in_taxes_to_Russia_since_it_annexed_Crimea,_NGOs_say⠀⇛ Nine European and US fossil fuel companies have paid a collective $15.8 billion to Russia in various forms of taxes and fees since the country annexed Crimea from Ukraine in 2014, a group of NGOs said Thursday. The groups, Global Witness, Greenpeace USA and Oil Change International, used data from the Oslo-based Rystad Energy, an independent energy research firm, to calculate how much money oil and gas companies based in North America and Europe had sent to the Russian state. They looked only at companies with exploration and production operations in Russia. # § Wildlife/Nature⠀➾ # ⚓ CNN ☛ ‘I’ve_never_seen_a_snow_leopard_in_the_wild’_— the_anthropologist_who_has_spent_two_decades_protecting Pakistan’s_elusive_big_cats⠀⇛ Through his non-profit — the Baltistan Wildlife Conservation & Development Organization — Hussain tracks snow leopards using camera traps and genetic testing, and works with local communities in 26 villages to resolve this conflict. With an estimated 30 to 50 snow leopards living in the region around those villages, his mission is to find ways for both humans and snow leopards to survive and thrive. CNN spoke to Hussain about his experiences protecting these beautiful big cats and how he’s found ways for them to live alongside local communities. o § Finance⠀➾ # ⚓ TruthOut ☛ Research_Finds_Investment_in_Permanent_Child_Tax Credit_Would_Pay_Off_10-Fold⠀⇛ # ⚓ Common Dreams ☛ Consumer_Rights_Groups_Applaud_EU_Passage of_Law_to_Rein_in_Tech_Titans⠀⇛ Digital and consumer rights advocates on Friday hailed a landmark European Union law aimed at curbing Big Tech’s monopolistic behavior. “This is a big moment for consumers and businesses who have suffered from Big Tech’s harmful practices.” # ⚓ Common Dreams ☛ Sanders_Intros_Revival_of_95%_Windfall Profits_Tax_From_WWII_to_Curb_Corporate_Greed⠀⇛ U.S. Sen. Bernie Sanders on Friday unveiled the Ending Corporate Greed Act, which aims to end corporate price gouging in the midst of multiple global crises by imposing a 95% tax on the windfall profits of major companies. “The working class cannot bear the brunt of this economic crisis, while corporate CEOs, wealthy shareholders, and the billionaire class make out like bandits.” # ⚓ Eesti Rahvusringhääling ☛ Former_board_of_Swedbank_handed suspicions_of_money_laundering⠀⇛ The Office of the Prosecutor General has brought suspicions of facilitating money laundering against Priit Perens (CEO of Swedbank Estonia in 2008- 2015), Robert Kitt (member of the board 2011-2019, successor of Perens as CEO), Ulla Illison (member of the board 2011-2017, head of customer service), Heiki Raadik (member of the board 2011-2017), Vaiko Tammeväli (member of the board 2011-2019, director of corporate banking), Rait Pallo (member of the board 2011-2017, head of credit and operational risk), Kaie Metsla (member of the board 2015-2019, director of private banking), Toomas Tuulin (former head of the anti-money laundering department) and Aleksei Averson (former account manager). o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ TruthOut ☛ Louisiana_Town_Passes_Texas-Style_Ordinance Barring_Abortion_Outright⠀⇛ # ⚓ TruthOut ☛ Fear-Based_“Parental_Bills_of_Rights”_Are_a Right-Wing_Siege_on_Public_Education⠀⇛ # ⚓ TruthOut ☛ Ilhan_Omar_Introduces_Bill_to_Guarantee_Housing as_a_Human_Right⠀⇛ # ⚓ TruthOut ☛ Wife_of_Supreme_Court_Justice_Texted_Trump’s Chief_of_Staff_to_Overturn_Election⠀⇛ # ⚓ Common Dreams ☛ Parkland_Survivors_Spell_‘Thoughts_and Prayers’_With_Body_Bags_on_Capitol_Hill⠀⇛ Marking four years since the March for Our Lives demonstration—and memorializing more than 170,000 people who have been killed in the United States by gun violence since then—survivors of the 2018 Parkland, Florida school shooting used more than a thousand body bags Thursday to spell out the words “Thoughts and Prayers” on the ground outside the U.S. Capitol building. Each of the 1,100 body bags represented more than 150 deaths, according to organizers, who based the numbers on data from the Gun Violence Archive. The phrase “thoughts and prayers” has infuriated gun control advocates in recent years, as the pro-gun lobby and lawmakers across the political spectrum have repeated the words after mass shootings, while doing little to stop gun violence. # ⚓ Common Dreams ☛ Opinion_|_QAnon_Arrives_in_the_US_Senate⠀⇛ Specious claims of soft sentences in child pornography cases were an unlikely theme for Republicans to pursue in a confirmation hearing on a U.S. Supreme Court nominee. Fact checkers had thoroughly debunked the claims. Thoughtful conservatives tried and failed to head them off. # ⚓ Common Dreams ☛ Jayapal_Rebukes_GOP_Over_‘Baseless_and Frankly_Racist’_Attacks_on_Judge_Jackson⠀⇛ In the wake of this week’s Supreme Court hearings—during which Judge Ketanji Brown Jackson was forced to endure what critics called “absolutely ridiculous” questions from Senate Republicans—Rep. Pramila Jayapal on Friday commended President Joe Biden’s nominee for maintaining her composure and denounced GOP lawmakers for engaging in “racist attacks.” “The baseless and frankly racist attacks we have seen in recent days demean the Senate Judiciary Committee.” # ⚓ Counter Punch ☛ Brazil,_Amazon,_World:_Govern_By_Hate⠀⇛ The horrible paradox is that, though Bolsonaro’s “Protector of Indigenous Communities” is a grotesque taunt, his Merit Medal still performs (the operative word) a very effective kind of political communication or, better said, propaganda. This kind of fake news provides a cover of white noise that’s so stupefying it’s impossible to see behind it. Nevertheless, if it’s difficult to produce direct evidence that the Bolsonaro government is committing a whole range of heinous crimes, we can state that the militia gangs that have been associated with the Bolsonaro family for years are engaged in drug trafficking, arms deals, and assassinations, creating a climate of fear which, duly disseminated, is the perfect medium in which such a regime can operate, especially with help from the new “digital militia”. Bolsonaro’s murderous antics are more than diversionary tactics from the real business of his shambles of a regime dominated by the interests of the bullet-beef-and-bible lobby, which is all about agribusiness (read: razing the Amazon), “family values” (read: extreme homophobia and hatred of all sexual and reproductive rights), and trigger-happy paramilitaries (read: narco-militia), a foul mix of drug traffickers, paramilitary forces, and neo- Pentecostal churches waging a holy war, some under an Israeli flag and with a copy of the Torah, against rival criminal groups and Afro-Brazilian religions. It’s not just about a bunch of Brazilian fanatics. No corner of the Earth is free of the politics of hate and fear which pervades almost all aspects of social life. Everyone’s affected, one way or another. In the case of Brazil, Bolsonaro and his henchmen present themselves as patriotic heroes when they’re blatantly committing lese- patria at the service of local racketeers and international corporations. This atrocious mix of ecocide, genocide, religion justifying deadly intolerance, and drug trafficking, all dressed up as “government”, does one’s head in when trying to understand the connections, the twists in the lies, or how a man like Bolsonaro can get away with political spectacles that as well as being morally repugnant are insulting to the intelligence. At this point we’d like to cite the whole of Guy Debord’s prescient The Society of the Spectacle (1967) but a few lines will have to suffice: # ⚓ Counter Punch ☛ To_the_Last_Ukrainian_or_All_of_Us?⠀⇛ Can anyone really believe that if Russia were again to place nuclear capable missiles anywhere in the Western hemisphere that Washington would not envision a threat identical to that felt by Russia today and act as aggressively and dangerously as it did in 1962? Or imagine a scenario wherein Canada aligned itself with China and invited Chinese military advisers and their advanced weapons into its territory. Those of us of an age remember all too well the first time our species faced self-extinction. Understand too that the missiles of that time were mere toys compared to the weapons that exist today. # ⚓ Counter Punch ☛ This_is_the_Time_to_Kick_Our_Oil Addiction⠀⇛ News headlines link this sharp increase to Russia’s war on Ukraine. But that assumes oil companies have no control over the price of oil — that high prices stem “naturally” from things like the war in Ukraine, or the U.S. decision to halt oil and gas imports from Russia. Collin Rees, senior campaigner with Oil Change International, told me in a recent interview that there is “a complex interplay” of forces that determine prices. Supply is only part of it. # ⚓ Counter Punch ☛ Stockholm_Syndrome_2022:_The_Faustian Bargain_of_Left_Militarism_in_Ukraine⠀⇛ The Stockholm Syndrome has had a dramatic revival. Where?  No place other than in Stockholm, Sweden, itself where the Left Party now embraces arms shipments to Ukraine.  Who are the hostage takers? Not your average criminal, but rather the Swedish military industrial complex comprised of defense contractors, leaders of the armed forces, the parliament, various parts of the media, and a small army of “security experts.”  Who are the police who have perceived not to have not cared for the hostages’ safety?   The analogy here only partially breaks down but relates to the supposedly indifferent view of the peace movement, anti- militarist intellectuals, and others opposed to the militarist hostage takers.  So, you say, “it is obvious that police oppose criminals!” So I say, “it is obvious that anti-militarists oppose militarism.”  We could end the story here, but the devil is in the details. # ⚓ Hungary ☛ Telex’s_animated_informational_video_wins prestigious_international_design_award⠀⇛ # ⚓ Hungary ☛ Orbán_is_requesting_the_EU_loan:_after_four_big blows,_Hungary_has_decided_that_cheap_money_is_better_than expensive_money⠀⇛ The combination of Covid, the costs of the green transition, inflation (especially of energy prices), and the damage caused by the Russian invasion of Ukraine have already brought Hungarian economic policy to its knees. The disasters of biblical proportions have finally made the Hungarian political leadership realise that, even at the cost of some political loss of face, it needs the money from Brussels available in the form of a loan. Translation by Andrea Horváth Kávai # ⚓ Hungary ☛ Zelensky_to_Orbán:_There_is_no_time_to_hesitate, once_and_for_all,_you_must_decide_whose_side_you_are_on⠀⇛ # ⚓ Counter Punch ☛ Cruelty_as_Border_Policy:_the_Biden Version⠀⇛ This formula to measure the efficiency of the CDS has been in use for more than a decade, but it is being reupped by the Biden administration. Indeed, the CBP guide was issued just as Biden was declaring that he would create a fair, orderly, and humane border and immigration system. While the administration talked about rescinding Trump initiatives such as the Migrant Protection Protocol (now reinstated) and was hinting that Title 42 would be stopped (it’s still in effect), the CDS and the more long-term deterrence strategies have continued on without much comment. And its policies and infrastructure of incarceration, which for decades has led families to be arrested, detained, and separated, lurks below the dominant rhetoric, particularly that of the White House. Behind closed doors, agents, like technocrats in a Fortune 500 company, create color-coded graphics to demonstrate the most “efficient” and “effective” enforcement techniques. Even though the effectiveness of deterrence has been questioned and refuted, and even though the question of human rights has not entered the equation at all, the U.S. federal government seems to be plowing ahead with this without any questions. # ⚓ Counter Punch ☛ Marxism_against_Marxism⠀⇛ It does so not least in light of the inevitable construction of a strawmen to tear down for the benefit of the party rank and file. It’s totally fine to pick on Proudhon as if any anarchist is wont (a) to quote him chapter and verse or (b) identify as a Proudhonist. Taking Stalin as representative of the entire Marxist tradition, to cherrypick his authoritarian excesses and ignore the Marxist critique of the commodity form is, on the contrary, absolutely opportunistic and disingenuous. No one with a shred of honesty would go there. # ⚓ Counter Punch ☛ The_Billion_Dollar_Deal_that_Made_Google and_Amazon_Partners_in_the_Israeli_Occupation_of_Palestine⠀⇛ In their letter, the signatories protested a $1.2 billion contract between Google, Amazon Web Services (AWS) and the Israeli government which provides cloud services for the Israeli military and government that “allows for further surveillance of and unlawful data collection on Palestinians, and facilitates expansion of Israel’s illegal settlements on Palestinian land”. This is called Project Nimbus. The project was announced in 2018 and went into effect in May 2021, in the first week of the Israeli war on besieged Gaza, which killed over 250 Palestinians and wounded many more. # ⚓ Common Dreams ☛ Watchdogs_Say_If_Clarence_Thomas_Won’t Resign,_‘Congress_Must_Move_to_Impeach’⠀⇛ Calls for Supreme Court Justice Clarence Thomas to resign—or face impeachment proceedings—mounted late Thursday after text messages revealed that his wife urged former White House Chief of Staff Mark Meadows to aggressively pursue efforts to overturn the 2020 election results. The Washington Post and CBS News obtained dozens of texts that Ginni Thomas, a long-time far-right activist who attended the January 6 rally that preceded the Capitol assault, sent to Meadows in the wake of Trump’s election loss, which she characterized as fraudulent while her husband was hearing election-related cases. # ⚓ Common Dreams ☛ Citing_New_Whiff_of_Corruption,_Wyden_Calls on_Thomas_to_Recuse_From_All_Jan._6_Cases⠀⇛ Sen. Ron Wyden on Friday called on U.S. Supreme Court Justice Clarence Thomas to recuse himself from all cases related to the January 6, 2021 attack on the U.S. Capitol, after the justice’s wife was found to have pushed for the overturning of the presidential election. “Justice Thomas’ conduct on the Supreme Court looks increasingly corrupt.” # ⚓ The Nation ☛ The_Corruption_of_Clarence_and_Ginni_Thomas⠀⇛ It’s long been clear there is one set of rules for liberal Democrats and another for conservative Republicans. While Judge Ketanji Brown Jackson promised this week to recuse herself from a case involving Harvard University if she’s confirmed to the Supreme Court (she’s on one of several Harvard governing boards), Justice Clarence Thomas has for months been ruling on issues relating to Donald Trump’s efforts to overturn the 2020 election and the January 6 coup attempt—even though it’s been known that his wing nut wife was involved in planning both. # ⚓ The Nation ☛ It’s_All_Connected⠀⇛ # ⚓ Democracy Now ☛ Meet_Francia_Márquez,_the_Afro-Colombian Land_Defender_Running_to_Be_Colombia’s_First_Black_VP⠀⇛ # ⚓ Xe ☛ Book_Release:_Closed_Projects⠀⇛ Closed Projects is a retelling of a four-part series on my blog where I process the events that lead to the death of freenode, the largest IRC network for peer-directed projects. freenode was the reason that I managed to get into tech. Without freenode I would be a vastly different person today. The death of freenode last year brought up many lingering memories and emotions. I talk about my history with freenode, the events that happened in the wake of its death and how a new community took its place. # ⚓ NewYorkTimes ☛ Israel,_Fearing_Russian_Reaction,_Blocked Spyware_for_Ukraine_and_Estonia⠀⇛ Israel feared that selling the cyberweapon to adversaries of Russia would damage Israel’s relationship with the Kremlin, they said. o § Misinformation/Disinformation⠀➾ # ⚓ CNN ☛ Deepfakes_are_making_information_warfare_more_high tech_and_worrisome_than_ever⠀⇛ Five years ago, nobody had even heard of deepfakes, the persuasive-looking but false video and audio files made with the help of artificial intelligence. Now, they’re being used to impact the course of a war. In addition to the fake Zelesnky video, which went viral last week, there was another widely circulated deepfake video depicting Russian President Vladimir Putin supposedly declaring peace in the Ukraine war. Experts in disinformation and content authentication have worried for years about the potential to spread lies and chaos via deepfakes, particularly as they become more and more realistic looking. In general, deepfakes have improved immensely in a relatively short period of time. Viral videos of a faux Tom Cruise doing coin flips and covering Dave Matthews Band songs last year, for instance, showed how deepfakes can appear convincingly real. o § Censorship/Free Speech⠀➾ # ⚓ Techdirt ☛ Project_Veritas_Loses_Its_Defamation_Lawsuit Against_CNN_Because_The_Truth_Is_Just_As_Damning_As_What_CNN Said⠀⇛ Very serious laughably ridiculous buffoon stunt journalists, Project Veritas, had its account banned from Twitter a year ago, a couple months before its founder James O’Keefe also had his own account banned as well. O’Keefe vowed to sue CNN and Twitter over the bans, and these plans seem to be going about as well as a standard Project Veritas special report: people too clueless to understand reality think it means something, but it falls apart under scrutiny. Just days after the threat to sue, Project Veritas did, in fact, sue CNN for defamation. # ⚓ FAIR ☛ New_York_Times’_Fear_of_Ordinary_People_Talking Back⠀⇛ Samuel Freedman, author and long-time New York Times writer, often told his journalism students that they needed to keep in mind while writing copy that they wouldn’t be able to literally stand behind their reader at the newsstand. A writer must make their copy as clean as possible, the lesson was, because once it’s printed, they won’t be able to clarify what they meant, or even have any kind of dialogue with the reader. # ⚓ Techdirt ☛ Ted_Cruz,_Mike_Lee_Join_Dumb,_Baseless_GOP_Quest To_Pretend_OAN_Was_Unfairly_Censored⠀⇛ So we’ve already noted how OAN was booted off of the DirecTV lineup, severing a massive mainstream distribution avenue for the conspiracy and fantasy channel. DirecTV, recently spun off by AT&T, made the decision because the channel, despite all the attention, really wasn’t being watched very much. # ⚓ Techdirt ☛ On_Elon_Musk_And_Free_Speech⠀⇛ Let’s start this off by noting that I actually think that Elon Musk sometimes receives both too much criticism from some circles and too much praise from others. I think he deserves tremendous praise for taking visions that, at the time, seemed nearly impossible, and then making them real. From electric vehicles with Tesla, to space flight with SpaceX, it’s unquestionable that he’s driven tremendous innovation. And even in areas like Starlink, which has been unfortunately overhyped, he deserves kudos for actually building a working (if somewhat limited) satellite internet service. And that’s not even getting into his various efforts with trying to create a hyperloop, or trying to deal with transportation issues via The Boring Company. Again, some of these have been massively overhyped, but Musk, unlike many others, gets a vision and then acts on it, and I find that commendable — and helpful in driving innovation forward. # ⚓ Project Censored ☛ THE_PROJECT_CENSORED_NEWSLETTER_–_March 2022_–_Censored_Notebook,_Newsletters⠀⇛ Independent News Stories We’re Tracking # ⚓ NPR ☛ Meet_the_Russians_who_are_fleeing_—_not_the_war,_but their_own_government⠀⇛ Voloshinov flew first to Armenia, where he planned to stay for a week or two. But after just a few days, his father called him — the police were looking for him in Moscow. Voloshinov is a political journalist and has worked for opposition publications. A new law introduced by Russian President Vladimir Putin after the Russian invasion of Ukraine means that Alexey could face up to 15 years in prison for even calling the war a war. After he hung up the phone with his father, he packed his bags again. “That day, I decided to leave Armenia and move to Georgia because there is no extradition from here,” he remembers. # ⚓ Book Riot ☛ The_Censorship_Story_I_Can’t_Tell_You:_This Week’s_Book_Censorship_News,_March_25,_2022⠀⇛ Despite the fact the job required library experience and a library degree, Eledge was approved by the Assembly without being qualified for the role. [...] On Tuesday, February 8, I submitted a FOIA request to the city of Anchorage. To do so requires sending the request to department heads, meaning that to FOIA information about the library, that request goes to the library director. As Demboski has ceded Eledge, this meant the FOIA request went to her. # ⚓ Patrick Breyer ☛ Chat_Control:_The_End_of_the_Privacy_of Digital_Correspondence⠀⇛ A majority of the Members of the European Parliament adopted the chatcontrol regulation on 6 July 2021 allowing providers to scan communications voluntarily. So far only some unencrypted US services such as GMail, Meta/Facebook Messenger and X-Box apply chat control voluntarily. But this is not the end of the story: The European Commission announced that it will propose follow-up legislation that will make the use of chatcontrol mandatory for all e-mail and messenger providers. This legislation will be presented on 30 March 2022 and would also apply to so far securely end-to-end encrypted communications services. However, a public consultation by the Commission demonstrated that the majority of respondents, both citizens and stakeholders, were opposed to an obligation to use chat control. Over 80% of respondents opposed its application to end- to-end encrypted communications. # ⚓ The Epoch Times ☛ China_Cancels_Keanu_Reeves_Over_Support for_Tibet⠀⇛ Reeves’s apparent offense had been appearing at a March 3 virtual concert organized by Tibet House, a New York-based nonprofit founded at the request of Dalai Lama. The spiritual leader is exiled in India where he established a shadow Tibetan government that Beijing has labeled as being separatist. # ⚓ [Old] Linehan_shock_as_family_targeted_for_his_role_in_RTÉ gender_debate⠀⇛ TV writer Graham Linehan has claimed that opposition to his inclusion on an RTÉ programme about transgender issues has resulted in him being abused and his family targeted. # ⚓ It’s_not_Cancel_Culture,_it’s_Cancel_Technology⠀⇛ The really interesting question is whether ostracism has changed in important and substantial ways in the age of social media and the internet. Even if human nature doesn’t change over time (and I think the jury is still out on that one), the tools we have access to do change, and that allows society to reshape itself in new ways. (That’s what I mean when I semi-ironically call myself a “technological determinist”, by the way.) What does the [Internet] do? Lots of stuff, but the two things I want to focus on here are distribution and memory. The [Internet]: 1. allows a very very large number of strangers to see what you say and do, and 2. keeps a record of most of the things you say and do online. # ⚓ Teacher_still_in_hiding_a_year_on_after_Prophet_Muhammed Batley_Grammar_School_controversy⠀⇛ A teacher is still in hiding one year on from the Prophet Muhammed Batley school row. The teacher had shown a caricature of the founder of Islam, during a religious studies lesson at Batley Grammar School in March 2021. The problem arose as the teacher claims he was unaware of the sensitivities surrounding showing a caricature. According to the BBC, there is no mention in the Koran of a ban against using images either drawn, carved or painted, of the Prophet Muhammed or Allah. # ⚓ Yorkshire Live ☛ A_year_on_from_Prophet_Muhammad_Batley school_row_and_teacher_still_in_hiding_as_family_‘at_risk’⠀⇛ Kim Leadbeater MP has said a teacher who showed an image of the Prophet Muhammad during a lesson at a Batley school faced “completely unacceptable” backlash as she offered him her “full support” a year on from the row. The teacher was “forced into hiding” after showing the caricature during a religious studies lesson at Batley Grammar School in March, 2021. He was suspended following heated protests outside the school’s gates and was reportedly moved into police protection after receiving death threats. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ VOA News ☛ ‘Press_Freedom_is_Dead_Already_in_Burma,’ Journalist_Says⠀⇛ All reporters in Myanmar are at risk of being jailed just for doing their job, says a veteran journalist now in exile. The comments from Ye Wint Thu come after a military-run court in Myanmar’s capital Naypyidaw sentenced two more journalists to prison this week. # ⚓ RFERL ☛ ‘No_Room_For_Journalism’:_Russia’s_Independent Regional_Press_Fights_To_Survive_Under_Wartime_Conditions⠀⇛ Kamalyagin and most of the newspaper’s long- embattled staff have since left Russia. He hopes to reassemble Pskovskaya Guberniya and renew publication from outside the country in the near future. “It is hard getting information when you are abroad, but we still have not only our own sources but also our local stringers,” Kamalyagin told RFE/ RL’s North.Realities. # ⚓ Mexico News Daily ☛ Inter-American_rights_commission_urges action_to_stop_violence_against_journalists⠀⇛ The Inter-American Commission on Human Rights (IACHR) has urged Mexican authorities to implement additional measures to prevent violence against journalists and protect them from the threat of physical attacks. In a press release issued Thursday, the Office of the Special Rapporteur for Freedom of Expression of the IACHR said that in the first 10 weeks of 2022, it received at least eight reports of murders of journalists for reasons that could be related to their work. It warned of the “normalization and deepening of violence” against journalists in Mexico. # ⚓ Craig Murray ☛ Free,_Enduring_Love⠀⇛ It was a cheap, white, trestle table, its thin top slightly bowed down in the middle, of the type made of a weetabix of sawdust and glue with a sheet of plastic glued on top and plastic strips glued to the sides, held up on four narrow, tubular, black metal legs. On it was a register. In front of it stood Stella Moris, looking beautiful and serene with delight. She wore a stunning gown in a light lilac, designed for her by Vivienne Westwood. It had a mild satin shimmer, and appeared both sumptuous and tightly tailored, with an expansively lapeled jacket section diving in to a wasp waist, that the apparently soft billows never intruded upon, no matter how she moved. o § Civil Rights/Policing⠀➾ # ⚓ Common Dreams ☛ Opinion_|_When_Jim_Crow_Greeted_Black Veterans⠀⇛ I figured I’d better write this column while doing so is still legal (at least I think it is), but I don’t recommend reading it aloud in a third-grade classroom. # ⚓ Counter Punch ☛ American_Democracy:_Alive_or_Dead?⠀⇛ To this point on November 22, 2021, the International Institute for Democracy and Electoral Assistance (IIDEA), based in Stockholm, Sweden, released its 2021 Report on “The Global State of Democracy.[1] The report’s introduction begins with these chilling statements. “Democracy is at risk,” “Its survival is endangered by a perfect storm of threats, both from within and from a rising tide of authoritarianism.” “The world is becoming more authoritarian as nondemocratic regimes become even more brazen in their repression, and many democratic governments suffer from backsliding by adopting their tactics of restricting free speech and weakening the rule of law.” Indeed, the annual report from Freedom House reports that freedom around the world declined in 2021 for the 16th consecutive year, that China and Russia are exporting authoritarianism, that undemocratic regimes are growing more so, and that even in established democracies, like the U.S., “internal forces have exploited the shortcomings of their systems, distorting national politics to promote hatred, violence and unbridled power.” Over the past year, 60 countries became less free, while only 25 improved.[2] 38% of the global population live in countries that are not free (the highest since 1997); 20% live in free countries; and 42% live in “partly free” countries. Sadly, the United States falls within this last category.[3] # ⚓ Counter Punch ☛ The_Shame_of_Santa_Rosa,_California: Whiteness,_and_the_Culture_of_Lynching⠀⇛ From 1959 to this year, Lebaron penned thousands of gossipy columns splashed with a bit of history, attesting to the old-fashioned goodness of local businesses, salt-of-the-earth ranchers, and police and sheriff’s deputies who can do no wrong. A ProQuest search of LeBaron’s columns in the Press Democrat from 1994 to the present reveals hundreds of stories glorifying white men wielding badges, batons, guns, and in some instances, hanging nooses. There is not a mention of the killing of 13-year-old Andy Lopez on Oct. 22, 2013 by Deputy Sheriff Erick Gelhaus. LeBaron, 86, has also not reported on killings by Sonoma County law enforcers, a fact that she acknowledged in an interview with the Bohemian last week. # ⚓ Counter Punch ☛ Want_to_Ensure_Marijuana_is_Safe?_Legalize and_Regulate_It⠀⇛ A case in point: Police in Brattleboro, Vermont recently generated headlines when they, along with agents from the federal Drug Enforcement Administration and Department of Homeland Security, arrested multiple people on charges of distributing fentanyl-tainted cannabis. Days later, however, lab tests confirmed that no fentanyl was present in any of the marijuana samples that had been seized in the raid. # ⚓ Techdirt ☛ ICE’s_‘Fierce_Commitment’_To_Ensuring_Detainees Are_Cared_For_Properly_Includes_Inadequate_Staffing, Unsanitary_Facilities⠀⇛ ICE has never really cared about the people it detains and processes for removal. It cared even less when President Trump made it clear he believed anyone less white and privileged than he is deserved to be excluded from the “American dream.” # ⚓ Techdirt ☛ Arizona_Legislators_Want_To_Make_It_Illegal_For People_To_Record_Cops_From_Whatever_Cops_Decide_Is_‘8_Feet Away’⠀⇛ It’s pretty much understood that filming police is protected by the First Amendment. Even in jurisdictions where the highest courts have yet to hand down a definitive decision, police departments have made it clear to officers that filming cops isn’t a crime. This has followed years of jurisprudence and laws being repealed/rewritten to reflect this position — something that has, years after it became necessary, prevented police from abusing wiretapping laws to arrest people for “nonconsensual” recordings of officers performing their public duties in public. # ⚓ Techdirt ☛ Ninth_Circuit_Says_Arresting_People_For_‘Fuck The_Cops’_Chalk_Writing_Is_Unconstitutional_Retaliation⠀⇛ Cops and obscenities don’t mix. # ⚓ Counter Punch ☛ We_Must_End_Family_Separations_and_Here’s How⠀⇛ I met him just five months after the Trump administration took office and began an onslaught of harsh immigration actions, including prioritizing the deportation of all undocumented immigrants. That included this 8-year-old citizen’s parents, and he was terrified of losing them. Despite the change in administration, our country still has too many children living with the same fear. With Congress failing again to create a pathway to citizenship, over 5 million U.S. children continue to face instability due to their parents’ precarious immigration status. # ⚓ FAIR ☛ Carol_Anderson_on_History,_Race_and_Democracy⠀⇛ # ⚓ The Nation ☛ California_Scrambles_to_Manage_Its_Housing Crisis_and_Rising_Gas_Prices⠀⇛ # ⚓ The Nation ☛ Kathy_Hochul_Is_About_to_Break_Ranks_With Progressives⠀⇛ The Kathy Hochul honeymoon is coming to an end. It’s New York, after all, and few politicians glide above scrutiny or avoid agita. For many months, it was good enough for Hochul to be not-Cuomo; smiling and shaking hands, taking everyone’s phone calls, and offering encouraging words. # ⚓ The Nation ☛ Why_Some_Ardent_Libertarians_Support_Judge Ketanji_Brown_Jackson’s_Confirmation⠀⇛ Republicans on the Senate Judiciary Committee are absolutely apoplectic about the fact that President Biden’s Supreme Court nominee, Judge Ketanji Brown Jackson, has been endorsed by progressive groups that defend civil rights and civil liberties. Senator Lindsey Graham got downright emotional on the subject, declaring Jackson to be the choice of “these left-wing radical groups that would destroy the laws we know.” Graham told the nominee during her confirmation hearing, “Every group that wants to pack the court, that believes this court is a bunch of right-wing nuts who are going to destroy America, that consider the Constitution trash, all wanted you picked.” # ⚓ Common Dreams ☛ Former_Amazon_Worker_Leads_Thousands_of Warehouse_Employees_in_Historic_Union_Vote⠀⇛ Thousands of Amazon warehouse workers in Staten Island, New York began voting Friday to whether or not to join the Amazon Labor Union, an independent group started by an employee who drew national attention to working conditions at the company in 2020. The union election could make the JFK8 warehouse the first unionized Amazon facility in the country. According to the Washington Post, the results of the Staten Island vote and a union election being held at an Amazon warehouse in Bessemer, Alabama will both be announced in early April. # ⚓ NewYorkTimes ☛ Mandatory_Meetings_Reveal_Amazon’s_Approach to_Resisting_Unions⠀⇛ On Staten Island, Amazon supervisors often refer to them as “training.” At an Amazon warehouse in Alabama, supervisors refer to them ambiguously as “meetings.” Amazon says they’re officially “small group meetings.” Whatever Amazon calls them, the anti-union sessions that the company has held for employees this year have been part of an effort to fend off unions in two contentious elections. # ⚓ RFA ☛ Officials_tell_Lao_Christians_to_remove_videos_of attack_by_authorities,_villagers⠀⇛ When the family from Savannakhet province’s Dong Savanh village took the body of their family patriarch to the cemetery for burial on Dec. 6, local authorities and residents angered by the group’s practice of a “foreign religion” beat the coffin with sticks and struck mourners and pallbearers with clubs. The family buried the man in their own rice field, but authorities and residents continued to harass them. Authorities expropriated their land in February, and other villagers torched their home, family members and other sources told RFA in an earlier report. # ⚓ BBC ☛ Selling_sex_to_survive_in_Iran⠀⇛ Iran’s conservative religious establishment has officially long denied the existence of sex workers in the country. Instead, authorities allude to prostitution there as a Western plot designed to corrupt youth, or blame women for falling foul of unscrupulous men. Unofficial data also suggests Iran’s sex workers are getting younger. Statistics from various NGOs suggest that in 2016 girls as young as 12 were involved in prostitution. Aftab Society, an NGO dedicated to treatment of drug-addicted women in Iran, said in 2019 that there could be almost 10,000 female sex workers in the capital, roughly 35% of whom were married. According to Amir Mahmoud Harrichi, a professor of social welfare at Tehran University, the figure for the number of female sex workers in Tehran could be twice as high. # ⚓ Morning Star News ☛ Family_Sprayed_with_Acid_for_Leaving Islam⠀⇛ Upset over conversions to Christianity, hardline Muslims in an area of eastern Uganda this month sprayed a newly Christian family with acid and beat a former mosque leader, sources said. [...] On March 9, while the three were receiving hospital treatment in, their house was set ablaze, he said. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Running_the_ua.-top_level_domain_in_times_of_war⠀⇛ Dmitry Kohmanyuk has been working for the Ukrainian ccTLD .ua since its foundation. In recent years he worked as the national ccLTD’s strategist, working on the monitoring and introduction of new technology, like for example DNSSEC. Caught outside of his country on February 24, Kohmanyuk cooperates with his colleagues at home to keep the registry for half a million .ua sites running. The company is also operating the gov.ua TLD, a much sought for and much attacked zone. Kohmanyuk connects with international partners and he tries to assure the .ua team dispersed over the Ukraine and beyond. Being “like a mum” to those trapped in Kiev felt strange and difficult, as he wanted to cry himself, he said in a chat with heise online. For now, the registry still has about 50 percent of their infrastructure in the Ukraine. But the .ua itself could become a refugee, operated from the outside. # ⚓ Vice ☛ DIY_Volunteers_Are_Repairing_Ukraine’s_Destroyed Internet_Infrastructure⠀⇛ Approximately 2,000 professional Ukrainian operators are working to aid the effort to fix broken [Internet] infrastructure and provide communication services, and hundreds of civilians have additionally volunteered to help repair and rebuild the country’s [Internet] infrastructure, according to Yurii Shchyhol, head of the State Service of Special Communications and Information Protection of Ukraine. This means reconnecting or laying new fiber cables, restoring power, and getting creative to keep people online. The agency has referred to those doing this work as the “invisible heroes” of the war effort—people risking their lives to put back together fiber-optic cables and mobile stations so that the nation can stay in contact with the outside world. # ⚓ The Economist ☛ The_degrading_treatment_of_Ukraine’s internet⠀⇛ DEGRADING AND ideally destroying your opponents’ ability to communicate are elementary military tactics. And, in its war on Ukraine, Russia has certainly attempted to do this. These days, closing down communications focuses on the enemy’s internet capabilities. So it is not surprising that analyses by NetBlocks, a firm in London that monitors [Internet] activity, suggest that the number of devices connected to Ukraine’s internet has fallen by nearly a quarter since Russia’s onslaught began. Alp Toker, NetBlocks’ founder, describes that loss as striking. But it could be a lot worse, for it means that most Ukrainians are still online. What is going on? o § Monopolies⠀➾ # ⚓ Hollywood Reporter ☛ MGM’s_Amazon_Era_Begins_With_Big, Unanswered_Questions⠀⇛ So MGM acquired UA, and its films, for some $380 million ($1.2 billion adjusted for inflation), with Frank Rosenfelt, MGM’s chairman, telling The Washington Post at the time that UA’s library would be critical as Hollywood transitioned “from the movie business to the entertainment software business.” # § Patents⠀➾ # ⚓ [Old] Cutting_Back_Patent_Over-Enforcement_–_How_to Address_Abusive_Practices_Within_the_EU_Enforcement Framework⠀⇛ The debate over the degree of flexibility at the disposal of national courts in Europe to grant, deny, or tailor, injunctive relief in patent litigation seems to be a never-ending story. In most jurisdictions, absent exceptional circumstances, findings of infringement lead national courts to grant, quasi-automatically, an injunction. However, some scholars as well as industry players, have argued that in light of recent changes in litigation behaviour as well as technology developments, a general principle of proportionality should play a more prominent role vis-à-vis injunctive relief. It is in particular with reference to Art. 3(2) of the Enforcement Directive that such claims have been made. If UK courts have been inclined to consider that, under certain circumstances, a balance of interests may take place before granting a permanent injunction, German courts on the other hand have firmly stood on the ground that the principle of proportionality should not interfere with the right of patent holders to obtain such remedy. However, most recently, the German Ministry of Justice published a draft amendment to the German Patent Act providing some guidance on the role of proportionality vis-à-vis the rules of injunctive relief. The issue of flexibility and injunctive relief is symptomatic of a broader debate regarding potential over-enforcement practices by right holders and the means to overcome or reduce the negative effects of these practices. Overall, this article examines how the origins and justifications of the Enforcement Directive, which focus on fighting piracy and counterfeiting, may affect the applicability of the principle of proportionality in the ever-changing context of patent law. How national courts have (or have not) relied on different mechanisms to infuse more flexibility in case of over-enforcement practices by right holders. And finally, how the principle of proportionality as well as the principle of the prohibition of abuse of rights may serve national courts in this endeavour of limiting excesses in patent litigation. # ⚓ EFF ☛ Defend_Innovation⠀⇛ The result is Defend Innovation: How to Fix Our Broken Patent System, a whitepaper providing a comprehensive view of the issues plaguing the patent system today, as well as a series of solutions that Congress, the Patent Office, the courts, and companies can implement. # § Copyrights⠀➾ # ⚓ Torrent Freak ☛ Court:_Null-Routing_is_Not_a Practical_Anti-Piracy_Measure⠀⇛ A federal court in Florida maintains that there is no reason to believe that hosting company Quadranet is liable for the pirating activities of its VPN customers. A group of filmmakers suggests that the provider could have null-routed IP-addresses, but the court doesn’t see this as a practical or effective measure. # ⚓ Torrent Freak ☛ Pirate_IPTV_Services_Disrupted_By Dozens_of_Rightsholders_On_Multiple_Fronts⠀⇛ Rightsholder measures against pirate IPTV providers, sellers and resellers are nothing new but in the last week alone, numerous actions have come to fruition in a number of regions. Whether in Canada, the Netherlands, France or the UK, life is getting just that little bit harder for those in the pirate TV business. ䷩ 𝚕𝚒𝚗𝚎 5462 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/irc-log-250322/#comments Gemini version at gemini://gemini.techrights.org/2022/03/26/irc-log-250322/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Friday,_March_25,_2022⠀✐ Posted in IRC_Logs at 2:13 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-250322.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-250322.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-250322.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-250322.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmPHKVsv9hbgpz7BfnfC351SPtY6Tf27hBf5ZdoMEreFUk #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmPbyqnJvrPDRUB9t7rCP3h1o3SRxG4XPbxWgNp8kTvPnU (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  Qmc3BrXv8Tp3HLJHjG2eXuydqu9iQF7PXCmvGGPU9Drdqf social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmatjUCz5TvUdioJvZyMo2QicdLYHuybchMHJGKTm1524o social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmbZPTVzGD5z8cnEAFcorV4TkpptAfPNeDykypVZqCMgyU #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmT5Mn6o7cP9XDdi3C9u7sLgpUurJMfGgtgK2LWx4qBpH7 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmUbknkZ9K3NQGcoZqiv8tGKUxEYnhZEwXyLxeoRwKexRE #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmXwvnw9MDf1YtTkT11VQRA45EAtCy3xSyCF8BwSYEa5Wd (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmbZUGxupu36yFf72bxj4yCNrYAfeMKD4kf3TzSvrLqGkT ䷩ 𝚕𝚒𝚗𝚎 5589 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/mike-gerwitz-ethics/#comments Gemini version at gemini://gemini.techrights.org/2022/03/26/mike-gerwitz-ethics/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Mike_Gerwitz_on_the_Ethics_Void⠀✐ Posted in Free/Libre_Software, FSF at 12:09 am by Dr. Roy Schestowitz Video_download_link https://media.libreplanet.org/mgoblin_media/media_entries/2039/stream- 101_20180325__11-34-46.webm Summary: From the_official_talk‘s description: “Many communities have widely adopted codes of ethics governing the moral conduct of their members and professionals. Some of these codes may even be enshrined in law, and for good reason—certain conduct can have enormous consequences on the lives of others.” Licence: CC_BY_SA_4.0 ䷩ 𝚕𝚒𝚗𝚎 5625 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/03/26/moving-office/#comments Gemini version at gemini://gemini.techrights.org/2022/03/26/moving-office/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Moving_On⠀✐ Posted in Free/Libre_Software, GNU/Linux at 4:42 pm by Dr. Roy Schestowitz Video_download_link | md5sum c583b13f70142fbc89e83abe030e0dd6 Adding Space Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/office-move.webm Summary: Today I moved to a more spacious desk and added a bunch of equipment to compensate for a failing SSD TODAY was a very unusual day. None of this was planned, but a solution for the failing SSD was long overdue. I took precautionary measures to avoid catastrophic data loss, but short of literally replacing the storage nothing would work properly. Postponing and procrastinating was a disaster waiting to happen. I also needed quite a lot of storage, so I ended up buying a low-budget machine, cobbling together all the machines from noon till evening time, taking the opportunity to also turn the dining room into an office, which is generally a lot safer as there’s no carpeting. There will be several practical benefits in the long run and at the moment I control 9 screens and 6 computers with one mouse and one illuminated (external) keyboard that I’m accustomed to. It is mechanical. Tomorrow will be a very busy day because of data migration, so I don’t anticipate much output. Today was a long-term investment that can pay off for months to come. Incidentally, today I finally became a KDE Neon user. I was always intrigued by and curious about this distro, now I can warmly recommend it to KDE lovers. I also really liked Linux Mint Debian Edition, which is only days old. Shame on Mozilla for turning Firefox into adware; I hadn’t imagined it would get this bad. I think several distros should consider making Falkon or LibreWolf the default Web browser. █ ䷩ 𝚕𝚒𝚗𝚎 5680 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 03.26.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_26/03/2022:_New_Debian_Releases⠀✐ Posted in News_Roundup at 4:27 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Unix Men ☛ How_Businesses_Can_Benefit_from_Using_Linux⠀⇛ Many businesses spend a lot of time weighing up the benefits of cloud automation and orchestration, without spending too much time considering operating systems. Historically, Microsoft Windows has been the OS of choice. However, when it comes to hosting services, Linux is definitely the better option. o § Audiocasts/Shows⠀➾ # ⚓ Video ☛ ProtonDB_Has_A_New_Linux_Game_Ranking_System_– Invidious⠀⇛ ProtonDB is an incredible website to check the state of Linux gaming but recently it received a massive change and ruined the site but now it has been redesigned and in many ways is better than ever # ⚓ Video ☛ I_Need_More_Audio_Jacks_On_My_Computer_– Invidious⠀⇛ I’ve got a problem. I’ve got multiple sets of speakers and headphones that I switch between, and I’m tired of having to constantly plug/unplug stuff into the one 3.5mm jack on the back of my computer. # ⚓ Video ☛ My_New_Linux_Desktop_–_Material_Shell_–_Invidious⠀⇛ This is an absolutely amazing desktop experience. By far one of my favorites, because we revisit one of my favorite layouts and developers of modern UI interfaces. o § Kernel Space⠀➾ # ⚓ Asahi_Linux_Is_Reverse-Engineering_Support_For_Apple Silicon,_Including_M1_Ultra⠀⇛ For months, a small group of volunteers has worked to get this Arch Linux-based distribution up and running on Apple Silicon Macs, adapting existing drivers and (in the case of the GPU) painstakingly writing their own. And that work is paying off — last week, the team released its first alpha installer to the general public, and as of yesterday, the software supports the new M1 Ultra in the Mac Studio. In the current alpha, an impressive list of hardware already works, including Wi-Fi, USB 2.0 over the Thunderbolt ports (USB 3.0 only works on Macs with USB-A ports, but USB 3.0 over Thunderbolt is “coming soon”), and the built-in display. But there are still big features missing, including DisplayPort and Thunderbolt, the webcam, Bluetooth, sleep mode, and GPU acceleration. That said, regarding GPU acceleration, the developers say that the M1 is fast enough that a software-rendered Linux desktop feels faster on the M1 than a GPU-accelerated desktop feels on many other ARM chips. o § Applications⠀➾ # ⚓ Make Use Of ☛ Why_Run_Windows_Apps_on_Linux?_Here_Are_15 Linux_Alternatives⠀⇛ As you might have noticed, more and more people are switching to Linux these days. However, it is still pretty common for Linux users to look for apps they are used to using on Windows. If you want to enjoy the Linux experience to the fullest, we recommend switching to Linux apps to perform your day-to-day tasks. That’s how your journey will come full circle. So, to aid you in this process, here is a list of Linux alternatives to popular Windows apps that you can download and use for free. o § Instructionals/Technical⠀➾ # ⚓ DT ☛ Upgrade_PostgreSQL_Database_(Cluster)_from_one_Major Version_to_Another⠀⇛ I’m in the process of finally upgrading my Debian install from oldstable (buster) to stable (bullseye). My DAViCal installation uses PostgreSQL for its database backend. Strangely, I have two versions of PostgreSQL (9.6 and 11) and I purged the older one (without deleting the databases, thankfully). # ⚓ ID Root ☛ How_To_Install_ExifTool_on_Ubuntu_20.04_LTS_– idroot⠀⇛ In this tutorial, we will show you how to install ExifTool on Ubuntu 20.04 LTS, as well as some extra required packages by ExifTool # ⚓ Streaming_the_Steam_Deck_to_OBS⠀⇛ Valve was kind enough to send Steam Deck devkits to Arch Linux maintainers and developers which gave us an opportunity to mess around with the device. Personally I find it a bit fun to mess around with video streaming, thus one of the first things I wanted to try figure out was how I could stream the gamemode on the Steam Deck. Installing the OBS flatpak and adding it to the menu doesn’t actually work so we sadly have to be a bit more clever. # ⚓ Ubuntu_22.04_Chromium_Browser_installation⠀⇛ The purpose of this tutorial is to show how to install the Chromium web browser on Ubuntu 22.04 Jammy Jellyfish. Chromium is an open source browser maintained by Google. Along with the Chromium browser itself, Google Chrome, Microsoft Edge, Opera, Vivaldi, and a slew of other notable web browsers are all based on the Chromium source code. It’s safe to say that Chromium plays a huge role in the way that many users view the web today. # ⚓ How_to_set_browser_environment_variable_on_Linux⠀⇛ The purpose of this tutorial is to show how to set the web browser environment variable on Linux. Setting environment variables is usually how users can set the default applications and programs used on their Linux system. Therefore, the browser environment variable should point to the user’s desired default web browser. In the case of a default web browser, this setting is best configured by the GUI itself. Simply setting the $BROWSER variable is not going to give you the the result you are expecting. Manually setting the web browser environment variable through other means is possible, but the process for doing so will vary across distributions and desktop environments. # ⚓ How_to_set_or_change_boot_partition_flag_on_Linux⠀⇛ The boot partition flag is used to indicate that an MBR partition is bootable. Although MBR has been superseded by GUID Partition Table in recent years, MBR is still very prevalent across many systems. The boot loader resides on a bootable partition and is what tells your system where to look for the operating system. In this tutorial, you will find the step by step instructions to set or change the boot partition flag on a Linux system via command line and GUI. # ⚓ Install_Couchbase_Server_on_Debian_11/Debian_10_– kifarunix.com⠀⇛ In this tutorial, you will learn how to install Couchbase Server on Debian 11/Debian 10. According to the documentation, Couchbase Server is an open source, distributed, JSON document database. It exposes a scale-out, key-value store with managed cache for sub-millisecond data operations, purpose- built indexers for efficient queries, and a powerful query engine for executing SQL-like queries. # ⚓ ByteXD ☛ How_to_Install_KDE_Plasma_or_Kubuntu_in_Ubuntu 22.04_or_20.04_–_ByteXD⠀⇛ The KDE desktop environment is called KDE Plasma, and also referred to as Plasma Desktop. It’s one of the most popular desktop environments, is very intuitive and easy to use, is available in many languages, and provides a consistent user experience across a wide range of devices. The KDE Plasma is also one of the most feature rich and customizable desktop environments, and it has a very modern look and feel. # ⚓ MakeTech Easier ☛ How_to_Use_WhatsApp_Web_on_Desktop_and Chrome_–_Make_Tech_Easier⠀⇛ If you have particularly chatty people on your WhatsApp list, you’ll know how annoying it can be to converse with them using a mobile keyboard. You can’t really get the gossip grapevine (or more important messages) going at a measly 20 words-per- minute. Thankfully, there is a way to use WhatsApp on your PC, so you can type with your hardware keyboard and really express yourself. # ⚓ How_to_customize_i3status_on_Linux⠀⇛ I3 is one of the most used tiling window managers on Linux. A tiling window manager arranges windows in a non-overlapping way: this allows us to use screen space efficiently, but can require a little bit of time to get used to. The i3 window manager on Linux is usually installed together with the i3status utility, which can be used to populate supported status bars with information such as memory or CPU usage. In this tutorial we see how to customize i3status and use some of its modules. # ⚓ How_to_set_alarm_on_Linux⠀⇛ Setting an alarm on Linux can be helpful to remind you of something or act as a timer. It might also come in handy if you take a little snooze at your desk. In this tutorial, we will show you how to set an alarm on Linux via command line and GUI. # ⚓ How_To_Install_and_Run_Linux_on_Android_(With/Without_Root) –_DekiSoft⠀⇛ Technology is moving at such a pace that users prefer smaller handhelds as their preferred choice of hardware. Phones have become smaller in size and more powerful in terms of computing power. They are more than enough capable of running a full-sized operating system. # ⚓ The New Stack ☛ How_to_Deploy_Kubernetes_with_Kubeadm_and containerd_–_The_New_Stack⠀⇛ There’s no easy way to say this, but Kubernetes is challenging. And although at one time it was actually fairly simple to deploy a Kubernetes cluster to bare metal (thanks, in part, to Docker), it’s not quite as simple as it once was. To complicate matters even further, there’s an almost endless amount of paths to getting the platform up and running. # ⚓ H2S Media ☛ How_to_Install_PowerShell_on_Ubuntu_22.04_LTS [Ed: Microsoft junk, but some people use this to migrate away from Windows]⠀⇛ # ⚓ H2S Media ☛ Install_PowerShell_on_Debian_11_Bullseye Linux⠀⇛ # ⚓ How_To_Install_OpenRGB_On_Ubuntu_22.04_|_20.04_LTS_| Itsubuntu.com⠀⇛ How to install OpenRGB tools on Ubuntu 22.04 LTS Jammy JellyFish or Ubuntu 20.04 LTS Focal Fossa. # ⚓ Install_Couchbase_Server_on_Ubuntu_22.04/Ubuntu_20.04_– kifarunix.com⠀⇛ In this tutorial, you will learn how to install Couchbase Server on Ubuntu 22.04/Ubuntu 20.04. According to the documentation, Couchbase Server is an open source, distributed, JSON document database. It exposes a scale-out, key-value store with managed cache for sub-millisecond data operations, purpose-built indexers for efficient queries, and a powerful query engine for executing SQL-like queries. # ⚓ AddictiveTips ☛ How_to_back_up_and_restore_your_website_on Linux⠀⇛ If you run a website on a Linux server, you should be keeping regular backups. We’ve got you covered if you’re new to Linux server administration. Here’s how to back up and restore websites on Linux. # ⚓ ID Root ☛ How_To_Install_Passbolt_on_AlmaLinux_8_–_idroot⠀⇛ In this tutorial, we will show you how to install Passbolt on AlmaLinux 8. For those of you who didn’t know, Passbolt is a free and open-source password manager based on PHP, MySQL, and OpenPGP which allows you to securely store and share login credentials of website, router password, Wi-Fi password, etc. It is self-hosted and available in both community and subscription-based editions. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the Passbolt password manager on an AlmaLinux 8. You can follow the same instructions for Fedora, RHEL, CentOS, and Rocky Linux distributions. # ⚓ AddictiveTips ☛ How_to_set_up_a_LAMP_server_on_Debian_11⠀⇛ While many people think of Debian as a rock-solid workstation operating system, that’s not all it can be used for. Debian is also one of the most used Linux-based server operating systems. There are a lot of server applications for Debian. However, one of the most popular things users set up is LAMP. LAMP is Linux, Apache, MySQL, and PHP, and it is essential for hosting web apps. Here’s how you can set up a LAMP server on Debian 11. o § Wine or Emulation⠀➾ # ⚓ 9to5Linux ☛ DXVK_1.10.1_Adds_Initial_Support_for_Shared Resources,_Fixes_God_of_War_and_GTA:_San_Andreas⠀⇛ DXVK 1.10.1 is the first point release in the DXVK 1.10 stable series and it’s here to implement initial support for shared resources in an attempt to fix video playback for several Koei Tecmo games, including the Atelier series and Nioh 2, as well as the D3D11-based UI in the Windows version of Black Mesa. However, “initial” means that this feature is considered experimental as it hasn’t been thoroughly tested against all graphics drivers. According to the release notes, only basic 2D texture sharing between the D3D9 and D3D11 implementations is supported when using DXVK for both APIs. # ⚓ GamingOnLinux ☛ DXVK_1.10.1_is_out_with_initial_support_for shared_resources_|_GamingOnLinux⠀⇛ DXVK is the free and open source project that translates Direct3D 9 / 10 / 11 to Vulkan for use with the Wine and Proton Windows translation layers. One of the major parts of Steam Play Proton that helps games run well on Linux desktops and Steam Deck. Version 1.10.1 brings on initial support for shared resources, fixing video playback in a number of Koei Tecmo games (Atelier series, Nioh 2), as well as the D3D11-based UI in the Windows version of Black Mesa. It’s still quite experimental now and needs more testing across various drivers. o § Games⠀➾ # ⚓ Boiling Steam ☛ Steam_Starts_Collecting_Feedback_From_Users on_Steam_Deck_Verified_titles_–_Boiling_Steam⠀⇛ Valve has just announced through the Steam community news that they are adding a new feature to collect feedback from end users about the Steam Deck Verified games they try out. In practice it will first ask you to opt-in to be part of the feedback service, and afterwards it will ask you questions about the titles you have just played on the Steam Deck to confirm if it matches your experience: # ⚓ GamingOnLinux ☛ Syncthing_is_a_great_way_to_transfer_files from_PC_to_Steam_Deck_|_GamingOnLinux⠀⇛ Recently I did a guide using the Warpinator tool to transfer files from PC to Steam Deck, here’s another way using the wonderful tool Syncthing that you might prefer. that you might prefer. A lot of people seemed to like the previous guide and video, however a few people couldn’t get Warpinator to work although most did. So as a bonus, I checked out Syncthing to see how that works. It’s just as easy to get going too. # ⚓ GamingOnLinux ☛ Valve_actually_announced_Steam_for_Chrome OS_now_too_|_GamingOnLinux⠀⇛ After a bit of a false start with an announcement made too early, Google has now announced Steam for Chrome OS and Chromebooks and now Valve has done their own brief announcement. So it’s all officially official now. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Wikidata_Data_Reuse_Days_2022_Recap⠀⇛ Over the past two weeks I attended a number of sessions of the Wikidata Data Reuse Days 2022 and presented KDE’s use of Wikidata in our travel apps there. Here are some of the things I found particularly interesting from a KDE perspective. o § Distributions⠀➾ # § IBM/Red Hat/Fedora⠀➾ # ⚓ Fedora ☛ Nest_with_Fedora_&_Fedora_Hatch:_Announcing dates_&_call_for_volunteers⠀⇛ Hi Fedora Friends! We made it through another year of living with COVID-19, with plenty of other challenges added on top. To everyone who make up Fedora – thank you for your presence, contributions, and efforts during this trying time. Because we have yet to see an end to living with COVID-19, I opened a discussion with the community about what we should do for this year’s contributor conference. Based on that feedback, I am pleased to announce that we will be holding the third edition of Nest with Fedora on August 4th, 5th, & 6th. I will be publishing info on the CfP in the upcoming months. We will also be funding local in person meetups that we have titled Fedora Hatch. If you want to participate in an in person meetup, make sure to read on and suggest your ideas on the Flock pagure! # § Debian Family⠀➾ # ⚓ Linuxiac ☛ Parrot_5.0_Released_with_Cloud_and Customizability_in_Mind⠀⇛ From release 5.0, Parrot is also available for Raspberry Pi 4. Without a desktop environment, you can install whatever you like. Penetration testing and ethical hacking have risen in popularity and industry needs over a previous couple of decades. From learning about the dangers of the internet to protecting data from hackers, the software industry has become increasingly aware of the millions of dollars that could be lost in a breach. Similar to Kali Linux, Parrot Security OS was created as an operating system for ethical hackers to raise awareness even further. It is a free and open-source Linux distribution based on Debian. # ⚓ Debian_—_News_—_Updated_Debian_11:_11.3_released⠀⇛ The Debian project is pleased to announce the third update of its stable distribution Debian 11 (codename bullseye). This point release mainly adds corrections for security issues, along with a few adjustments for serious problems. Security advisories have already been published separately and are referenced where available. Please note that the point release does not constitute a new version of Debian 11 but only updates some of the packages included. There is no need to throw away old bullseye media. After installation, packages can be upgraded to the current versions using an up- to-date Debian mirror. # ⚓ Debian_—_News_—_Updated_Debian_10:_10.12_released⠀⇛ The Debian project is pleased to announce the twelfth update of its oldstable distribution Debian 10 (codename buster). This point release mainly adds corrections for security issues, along with a few adjustments for serious problems. Security advisories have already been published separately and are referenced where available. Please note that the point release does not constitute a new version of Debian 10 but only updates some of the packages included. There is no need to throw away old buster media. After installation, packages can be upgraded to the current versions using an up- to-date Debian mirror. # ⚓ FLOSSLinux:_Debian_media_team_–_testing_and_releasing Debian_11.3_–_20220326_1243UTC⠀⇛ And back to relative normality : the usual suspects are in Cambridge. It’s a glorious day across the UK and we’re spending it indoors with laptops 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈ We’ll also be releasing a point release of Buster as a wrap up of recent changes. Debian 10 should move from full support to LTS on July 14th – one year after the release of Debian 11. All seems to be behaving itself well. # ⚓ Still_testing_Debian_media_images_20220326_2026UTC- almost_finished_11.3_–_Buster_starting_soon⠀⇛ # ⚓ FLOSSLinux:_Part_way_through_testing_Debian_media images_20220326_1555UTC_–_Found_a_new_useful_utility⠀⇛ For various obscure reasons, I have a mirror of Debian in one room and the main laptop and so on I use in another. The mirror is connected to a fast Internet line – and has a 1Gb Ethernet cable into the back directly from the router, the laptop and everything else – not so much, everything is wired, but depends on a WiFi link across the property. One end is fast – one end runs like a snail. o § Devices/Embedded⠀➾ # ⚓ Piwigo_and_Raspberry_PI:_a_Private_Open_Source_Photo Management_Platform⠀⇛ Keeping your pictures and videos in smartphones can suddenly drain your storage space. Piwigo with Raspberry PI can save your space and give you more features to manage them privately In this tutorial, I’m going to show you how to install Piwigo on your Raspberry PI computer board. It can also be considered a great Google Photo alternative, as the Google service requires a paid subscription once you require more space. An important thing is, after the Piwigo installation, to use the official users manual to keep our files secure from any outage with periodic backups. # ⚓ Wind_River_Studio_Addresses_Challenges_of_Managing_Secure Linux-Based_Intelligent_Systems⠀⇛ # ⚓ Linux On Mobile ☛ Weekly_Update_(12/2022):_GNOME_42,_Phosh 0.17.0,_Phoc_0.13.0,_Mepo_0.4_and_Capyloon_on_Linux_Phones!⠀⇛ A new PinePhone Modem Firmware release, updates on Nemo Mobile and GNUnet Messenger progress, Calls on the Poco F1, and a bunch of gaming centric PinePhone videos! And do try Capyloon on your Mobian-running Librem 5 or PinePhone Pro! # § Open Hardware/Modding⠀➾ # ⚓ New_Toy:_Hello_Precursor!⠀⇛ Those of you with a Spock-like mind will not be surprised to hear that a new toy has made it to my desk: the Precursor by the most respected Andrew “bunnie” Huang and his gang. # ⚓ Bye_bye,_openmoko!⠀⇛ Someone has responded to my message, that I would give away my trusty openmoko neo — I have changed technology for the last duty it had until recently. And I am happy that someone else is interested to keep it for a little longer. # ⚓ Arduino ☛ Top_Three_Arduino_Cloud_Games_Projects Revealed_|_Arduino_Blog⠀⇛ The Arduino Cloud Games was first hinted at just after Christmas, 2021. That’s how long these amazing members of the Arduino community have been toiling on some genuinely incredible projects. The top three were just announced live on the community day at Arduino Week 2022, so we thought we’d give you a closer look at what they built. Firstly though, even if it’s something of a cliche, we’ve got to say that picking them was insanely difficult. The quality, imagination and skills we’ve seen throughout the Arduino Cloud Games has been staggering. Seriously, there are very few people who work at Arduino that could build such amazing things. So if you didn’t make it into the top three, despair not! You were up against some of the toughest creative competition in the maker world. You all blew our minds with every new project that arrived on Project Hub, so you should be incredibly proud that you made it into the finals. Keep on building! # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Phone Arena ☛ Google_releases_Android_12_QPR3_beta 1.1_for_Pixel_6_and_Pixel_6_Pro_only_–_PhoneArena⠀⇛ # ⚓ Samsung_One_UI_4.0_(Android_12)_update_roll_out tracker_[Cont._updated]⠀⇛ # ⚓ Google_Maps_search_throwing_“No_results_found”_error on_Android_for_some⠀⇛ # ⚓ The_Best_New_Games_for_Android_This_Week_–_Cat Museum,_Critical_Slash_and_More_–_Droid_Gamers⠀⇛ # ⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss this_week_–_Android_Apps_Weekly⠀⇛ # ⚓ Android Central ☛ How_to_control_Chromecast_volume with_your_Android_phone_|_Android_Central⠀⇛ # ⚓ HowTo Geek ☛ Why_Doesn’t_My_Android_Phone_Have_a_WPS Button?⠀⇛ # ⚓ The Verge ☛ Global_science_project_links_Android phones_with_satellites_to_improve_weather_forecasts_– The_Verge⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ Projects_for_the_benefit_of_others⠀⇛ I recently saw @vidak@zoinks.one thinking about setting up a server where people could host Gemini or Gopher content, and how nobody really joined their previous effort of building something for the benefit of others, a tilde server. It felt like a very familiar problem. # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to Apple_Boot_Camp⠀⇛ Apple, Microsoft, Alphabet (Google’s parent), Amazon and Facebook dominate the tech landscape. Their dominance is so broad they account for more than 20% of the S&P 500. There are many things to admire about Apple’s hardware and software. Apple make great looking (albeit expensive) hardware. Over the years key successes include the iPhone, iPad, iPod, and the MacBook Air. The company designs its own hardware and software. This gives them the power to make an operating system and suite of apps that are tailor- made and optimized for their hardware. Apple also operates the Apple Music and Apple TV media distribution platforms. Mac OS X is Apple’s proprietary operating system for its line of Macintosh computers. Its interface, known as Aqua, is highly polished and built on top of a BSD derivative (Darwin). There’s a whole raft of proprietary applications that are developed by Apple for their operating software. This software is not available for Linux and there’s no prospect of that position changing. In 2020, Apple began the Apple silicon transition, using self-designed, 64-bit ARM-based Apple M1 processors on new Mac computers. Maybe it’s the perfect time to move away from the proprietary world of Apple, and embrace the open source Linux scene. # § Programming/Development⠀➾ # ⚓ Linux Links ☛ 3_Top_Free_and_Open_Source_Ruby_Web Frameworks_–_LinuxLinks⠀⇛ One of the types of software that’s important for a web developer is the web framework. A framework “is a code library that makes a developer’s life easier when building reliable, scalable, and maintainable web applications” by providing reusable code or extensions for common operations. By saving development time, developers can concentrate on application logic rather than mundane elements. A web framework offers the developer a choice about how to solve a specific problem. By using a framework, a developer lets the framework control portions of their application. While it’s perfectly possible to code a web application without using a framework, it’s more practical to use one. Ruby is a general purpose, scripting, structured, flexible, fully object-oriented programming language with a focus on simplicity and productivity. Ruby is a very conservative language. It’s equipped with very carefully chosen features that have been fully tested. When it comes to web development, there are a fairly small range of Ruby frameworks to choose. The choice depends on finding the right tool for the job at hand. Here’s our pick of the finest Ruby web frameworks. # ⚓ GCC ☛ LoongArch_port_accepted_and_maintainers appointed⠀⇛ I am pleased to announce that the GCC Steering Committee has accepted the LoongArch port for inclusion in GCC and appointed Chenghua Xu and Lulu Cheng as maintainers. Please work with Richard Sandiford on the final technical review and approval of the patches. Please coordinate with the GCC Release Managers for merging the port into the development tree, hopefully for inclusion in GCC 12 release. Please join me in congratulating Chenghua and Lulu on their new roles. Please update your listing in the MAINTAINERS file. Happy hacking! David * § Leftovers⠀➾ o § Education⠀➾ # ⚓ The_Rhodes_Scholars_Guiding_Biden’s_Presidency⠀⇛ The recent, pandemic-ridden years have involved a steep and often traumatic learning curve for many citizens across the Trans Atlantic. One particularly shocking revelation that has ripped virally across the internet in recent days revolves around the revelations that the World Economic Forum’s ‘Young Global Leaders’ have been positioned across western governments and powerful private institutions over the past three decades. Videos of Klaus Schwab bragging that Young Leaders have been positioned across the governments of Canada, Argentina, Europe and beyond are now being posted across social media platforms on a daily basis, confirming the suspicions of many that the World Economic Forum is not a benign business networking operation, as it has tried to project for the credulous. Rather, it is something much darker and insidious. Set up in 1993 as the Global Leaders of Tomorrow and renamed WEF Young Leaders Forum in 2004 (fueled with funds from such benevolent institutions as JP Morgan Chase and the Bill and Melinda Gates Foundation), over 1400 young leaders (under the age of 38) from both public and private sectors have been processed through the program. For those tapped to become members of this elitist clique, they agree to attend six years of regular WEF conferences featuring seminars, focus groups and other special experiences both at Davos and at regional WEF events, at which point they graduate and become “alumni” who, in turn, become capable of nominating future young leaders. Just a tiny sampling of the prominent figures who have been processed and installed into positions of influence to advance the WEF globalist agenda over the past 30 years include Angela Merkel, Nicholas Sarkozy, Emmanuel Macron, Tony Blair, Mark Zuckerberg, José Manuel Barroso, Bill Gates, Chrystia Freeland, Pete Buttigieg, Jacinda Arden (PM New Zealand), Jack Ma (Ali Baba founder), Larry Fink (Blackrock CEO), Larry Page (Google founder), Lynn Forrester de Rothschild (Council for Inclusive Capitalism founder), Jimmy Wales (Wikipedia founder), Peter Thiel (Paypal founder), Leonardo Di Caprio (tool), Richard Branson (Virgin Records CEO), Jeff Bezos (Amazon founder), Stephan Bancel (Moderna CEO), Pierre Omidyar (Ebay co-founder), Alizia Garza (co-founder BLM), Jonathan Soros (son of sociopath) and, according the Schwab, himself “half the Canadian Cabinet” under Prime Minister Justin Trudeau. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Business Standard ☛ Microsoft_paying_hundreds_of millions_in_bribes,_claims_whistleblower⠀⇛ # ⚓ International Business Times ☛ Whistleblower_Says_He Lost_Job_At_Microsoft_For_Exposing_$200_Million_Foreign Bribe_Scandal⠀⇛ # ⚓ Paul Thurrott ☛ Microsoft_Accused_of_Violating_the Foreign_Corrupt_Practices_Act_Again [Ed: More on this, even from Microsoft boosters]⠀⇛ # § Pseudo-Open Source⠀➾ # § Entrapment (Microsoft GitHub)⠀➾ # ⚓ The Register UK ☛ GitHub_explains_outage string_in_incidents_update [Ed: The liars from Microsoft blame Free software for their proprietary software failing]⠀⇛ Still, it’s not as if GitHub also chose this time to alienate large chunks of its customer base with an unpopular social-media-like algorithmic feed. # § Security⠀➾ # ⚓ The Register UK ☛ How_AI_can_help_reverse- engineer_malware:_Predicting_function_names_of code⠀⇛ Disassembling and analyzing malware to see how it works, what it’s designed to do and how to protect against it, is mostly a long, manual task that requires a strong understanding of assembly code and programming, techniques and exploits used by miscreants, and other skills that are hard to come by. What with the rise of deep learning and other AI research, infosec folks are investigating ways machine learning can be used to bring greater speed, efficiency, and automation to this process. These automated systems must cope with devilishly obfuscated malicious code that’s designed to evade detection. One key aim is to have AI systems take on more routine work, freeing up reverse engineers to focus on more important tasks. o § Internet Policy/Net Neutrality⠀➾ # ⚓ The_Change_Game:_MeitY_Resorts_To_Quick_Fixes_To_Silence Experts⠀⇛ On February 21, 2022, the Ministry for Electronics & Information Technology (MeitY) published the Draft India Data Accessibility & Use Policy, 2022. Immediately, civil society experts pointed out several flaws concerning data privacy and security rights of citizens. To our shock, on March 6, 2022, we noticed MeitY had made substantial changes to the Draft India Data Accessibility & Use Policy, 2022, during the consultation period, without any public acknowledgement. Effectively this resulted in multiple versions of it, contracted the consultation timeline, and confused stakeholders. Responding to this, IFF wrote to MeitY indicating the need for a fresh consultation process as these actions have completely vitiated the ongoing consultation process and led to an erosion of public trust. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 6770 ➮ Generation completed at 02:41, i.e. 63 seconds to (re)generate ⟲ gemini://gemini.techrights.org/tr_text_version/techrights-2022-03-26.txt

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