𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, June 02, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Fri 3 Jun 02:39:51 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/2022/06/02/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmUxQwv1jUfzi531ZuZrgpoeTEygBXJMeJirAMe6hn9xvc QmYCG1uZdDgMXspdLbXDQngGQ4yhXE6HgWMFpDUPkCaRGd QmTdhVnRhcX2HJtHu7hvsFB2dPhh13SYWRaYKwBnekmLnn QmWGuKVt9tMTyye5MHtLdeBL5hHhvDZoSE9g4AF3tHEXLb QmV77UUsBEhooN1dsoMAMhGoY8sFLrHFAQyWzaCs8HqHct QmXwe8jeZh6Do5S8g1LTRjAN8HWyTrQYN5F55Z6MpCv1VJ Qmc8X4uW8RnLD5zrXfPvxwXw7Nq2ZFGY57D6sF8akoXBLz QmYmvpg18UDAFnTbdqNMiYxSDxC7nUtBFhuAe5VeRpxJza QmUDTqvqrXc6psJWBRDhpDQ7KmoWYpr5GJR3VrxvKhjqyc Qme5YRqRD2nNFguK86DA7U515gXMgkk7XTh9q848YXMD91 QmcydyTo5aL4HeiG6DafkjkaNTwgnDyQLR43x4KdNjfVKw QmQpJuAsuxM7rmt71cHrnPYHq3yDfDViu6N7MVLqXMKNFi QmQdANbcTEaZJ6my2fyMJy8z7hLkDG3PSmwrg5BgrSJUWE QmeiAoJp2bFLnfeXRMywwDqmFDpxrnccTw79hv3XpSU1WA QmesZFZtaQyPujdg2nTczATr3E45jULmh5GbNNGVzmgHLE QmbdHztStntudMnkVURYKTyZxgmnBTbeqCSGw55fNBDyoC QmaXs6nissBVhNYAYHVGqvFS4Kfy7Nq2ECoYf2jAVZYgbq QmSHHTdp6sLdmKQogL17XxUxtwd4yBjY2Lb634AgE8Uiij Qmcr7RG6Vn1Qk6so2Qqdx9upsB4AxyT1yb7f2Khqv4fKwT QmZ6LkeL4fZh9DTpRFrBNgmYKFoJn8TvGhP6J84MfkvYcP QmYUZtwpfW3SXobxRTXB4UAgicLysKVf5S6GPNsGsWJepo ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ Richard Stallman in France, Speech This Coming Saturday (With Live Stream) | Techrights ⦿ GNU/Linux at Over 10% in Norway (Over 11% in April), Not Even Counting Chromebooks | Techrights ⦿ Happy Birthday to Our Very Own IRC Network | Techrights ⦿ IRC Proceedings: Wednesday, June 01, 2022 | Techrights ⦿ In Picture: Updated and Finally Presented About 10 Minutes Ago, Windows Market Share in Turkey Down to 10% | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/06/02/francophone-rms/#comments http://techrights.org/2022/06/02/gnu-linux-norway/#comments http://techrights.org/2022/06/02/happy-birthday-techrights-irc/#comments http://techrights.org/2022/06/02/irc-log-010622/#comments http://techrights.org/2022/06/02/turkey-in-pictures/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/06/02/armbian-22-05/#comments http://techrights.org/2022/06/02/fedora-linux-36-elections/#comments http://techrights.org/2022/06/02/gnome-42-2/#comments http://techrights.org/2022/06/02/nitrux-2-2/#comments ䷩ 𝚕𝚒𝚗𝚎 62 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/02/francophone-rms/#comments Gemini version at gemini://gemini.techrights.org/2022/06/02/francophone-rms/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Richard_Stallman_in_France,_Speech_This_Coming_Saturday_(With_Live_Stream)⠀✐ Posted in Free/Libre_Software, GNU/Linux at 9:49 am by Dr. Roy Schestowitz A headups to Francophone readers 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇rms-france⦈_ Summary: The founder of the GNU/Linux operating system (many people call it just “Linux”) will speak in French in two days and the talk will be streamed in video.chalec.org June 4, 2022, 15h00–18h00, 25 Rue des Jeuneurs, 75002 Paris Title: Les libertés du logiciel et du matériel Richard Stallman will give a talk in French on June 4, 15h00 to 18h00, at Espace Vinci (25 Rue des Jeuneurs, 75002 Paris) near métro Grands Boulevards. Web page: https://www.a-lec.org/libre-en-conf-04062022-richard- stallman-libertes-du-logiciel-et-du-materiel.html Recording and streaming on PeerTube site video.chalec.org. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠐⠀⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⣿⣿⣿⣿⠟⠛⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣿⠀⢸⣧⢛⣛⠛⢿⡇⠀⣿⠀⢸⡟⢛⡿⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⢸⣿⠉⣤⠀⢸⡇⠀⣿⠀⢨⡀⠻⡧⣄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣶⣶⣿⣦⣴⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣻⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⡿⢿⢿⠿⠿⡿⡿⠿⣿⣿⠿⣿⣿⡿⠿⡿⠿⡿⠿⡿⠿⣿⣿⡿⠿⡿⠿⡿⣿⢿⠿⢿⠿⢿⣿⡿⢿⡿⠿⠿⡿⠿⠿⡿⠿⢿⣿⡿⠿⢿⠿⢿⡿⠿⢿⢿⠿⠿⠿⣿⠿⠿⡿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⡇⢸⠘⢠⢠⡀⡇⠀⣿⣇⠀⡟⣿⡟⠁⣇⠃⡟⠁⡟⠁⡟⣿⡟⠀⡇⠀⡇⣤⢠⠘⣠⠘⣨⣉⡟⠘⡁⢀⡀⡄⢀⠀⣀⠂⡘⢻⡟⠁⠚⠀⣹⡇⢀⢸⠘⢀⠀⠈⣿⠀⢃⡅⠀⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⡗⢻⠛⠛⢻⢻⠛⠟⡟⠛⡟⡟⠛⠛⢻⠛⣻⣿⣿⣛⢛⠛⢻⢛⠻⢛⢻⣛⢻⣿⢛⠛⠛⢻⠛⠻⠛⡟⢛⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⡇⣸⣀⣠⣈⣸⣠⣄⣇⣀⣇⣁⣄⣠⣸⣀⣸⣹⣿⣇⣾⣀⣰⣌⣰⣌⣸⣁⣸⣿⣰⣆⣠⣈⣰⣌⣀⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣟⡛⣛⠉⠛⠿⢹⠿⠿⡿⣿⣿⢻⣿⠿⠿⡿⠿⣿⡏⢹⢹⠙⠿⡿⠿⢿⠿⠟⠻⠿⠩⡿⠿⣿⡿⠿⢹⠿⡿⣿⣿⢹⠿⠿⡿⠿⠏⢹⠿⢿⢹⠿⠿⡏⣿⣿⠿⢿⠛⢿⣿⠿⠋⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣇⣿⣀⣄⣛⣸⣀⣀⣇⣿⣿⣈⣛⣀⣀⣇⣀⣿⣇⣸⣸⣀⣂⣄⣀⣸⣰⣇⣘⣀⣀⣆⣀⣿⣇⣘⣸⣀⣁⣿⣿⣠⣘⣀⡄⠃⢀⣠⣐⣻⣸⣀⣀⣇⣿⣧⣀⣀⣄⣻⣿⣐⣀⣇⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠟⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⡇⢠⠀⠀⠃⠀⡅⠠⠁⠀⡁⢠⠀⡃⠀⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⠿⢿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⢿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⢐⠠⡇⡏⣤⡇⣥⢹⢁⡈⡏⣥⢡⡅⣿⣧⣘⢺⢠⡍⣀⢹⢸⢸⢩⡌⣥⢹⢁⢹⢉⡌⣿⣯⠙⡹⢹⢸⢸⢸⣿⡏⡌⢹⢸⠹⢩⠉⣈⣻⡿⢁⢹⣿⡅⣽⢁⠙⡇⡇⠩⣿⡿⢸⢩⠌⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣾⣷⣷⣷⣤⣷⣿⣾⣦⣶⣷⣿⣦⣶⣿⣷⣤⣾⣶⣶⣴⣾⣾⣾⣾⣷⣿⣾⣦⣾⣾⣷⣿⣿⣶⣷⣾⣾⣾⣾⣿⣇⣂⣼⣾⣷⣾⣶⣴⣿⣷⣶⣾⣿⣷⣶⣦⣶⣷⣷⣷⣾⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⠠⢤⠛⡻⠛⢻⢛⡛⡟⣛⡋⣘⢻⣿⢛⡛⡟⣛⢻⣿⢹⡟⣿⠛⢛⢻⠟⠛⢿⣿⢋⢸⣿⣿⣿⡄⣿⠀⠠⡇⣛⢻⢡⡌⡏⣤⢹⣿⢙⡛⣛⢻⣿⣯⢸⣏⠠⢹⠈⡛⡏⣤⢹⢡⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣇⣾⣿⣸⣧⣀⣸⣸⣡⣄⣉⣇⣏⣼⣿⣌⣡⣇⣿⣸⡿⢸⣇⣁⣠⣸⣸⣄⣀⣿⣷⣶⣰⣏⣿⣿⣁⣹⣉⣡⣇⣿⣸⣌⣡⣧⣉⣼⣿⣌⣡⣉⣼⣿⣏⣈⣧⣈⣰⣠⣇⣧⣉⣼⣌⣡⡏⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⠿⢿⠛⢿⣿⢛⣛⡿⠿⡿⠿⣿⠿⢿⡿⠿⡿⠿⣿⡟⢻⡟⡏⡿⠿⣿⠿⢿⢹⣿⡟⣽⣛⢻⡟⢛⣿⣿⢛⡛⡿⣿⢿⠿⢿⣿⡿⠿⢹⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣏⠡⢸⡀⢿⣿⠰⠶⠢⠍⡇⠗⣈⠩⢸⡐⠿⡀⠥⣿⣿⡌⢰⡇⡇⣷⢸⠸⢿⢸⣿⡇⣿⠋⢾⠳⠆⣿⣿⢠⡄⠇⠟⢨⠨⠄⣿⡇⠗⢸⠨⢤⠠⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⣿⠿⢿⡿⠿⣿⠿⢷⣾⡿⠿⢿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⢸⢀⣈⠹⡇⣿⢠⢸⢁⣀⡇⣿⢸⢠⣄⡀⣿⣿⣿⡟⢰⣧⡍⢻⢸⠆⡇⡷⢸⠟⣸⣿⡇⣋⡀⣀⢹⢠⡄⣏⡀⢿⢸⣿⡇⣤⠉⢀⣈⢃⡈⡇⣤⣿⡇⡄⣥⢸⢁⣈⡆⣴⢠⡌⣤⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣋⣼⣶⣶⣷⣶⣿⣾⣾⣶⣶⣷⣶⣾⣾⣷⣶⣧⣿⣿⣷⣿⣷⣶⣿⣶⣾⣷⣶⣷⣶⣾⣿⣷⣿⣷⣶⣾⣾⣷⣷⣶⣮⣾⣿⣷⣿⣾⣶⣾⣶⣶⣷⣿⣿⣷⣷⣿⣾⣶⣶⣷⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⡟⣠⠦⠝⢋⡛⠙⡟⢋⢻⢋⡁⡟⢉⣿⣿⠀⠈⡟⣙⢻⢻⠛⡇⡟⠙⠟⢿⢻⠋⠻⡟⣙⢋⠀⠛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣷⣬⣩⣤⣿⣦⣡⣧⣼⣼⣬⣥⣯⣠⣿⣿⣬⣥⣧⣩⣼⣌⣤⣧⣧⣩⣿⣤⣾⣌⣤⣧⣿⣌⣤⣍⣠⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣏⢻⠉⡏⡿⠻⢿⠙⢿⣿⡿⠛⢿⠟⢿⠟⠻⡿⠟⢿⠿⣿⡏⠟⢿⠹⠏⢿⠿⠻⡿⠻⡿⣿⢫⡏⡿⡿⡿⡿⡿⣿⠿⡿⢿⢿⣿⠛⢿⣿⡏⡿⠛⢿⠟⢿⣿⠿⠻⡿⠟⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣀⣶⣡⣄⢒⣺⡘⣸⣿⡇⣛⣨⣐⣸⣌⡃⣇⡒⣺⣛⣿⡇⠿⠸⠘⠇⠻⠘⠃⠗⠈⠟⠟⠾⠸⠇⠸⠡⠧⠱⠀⠷⠡⠌⠞⠏⠒⠸⠤⠇⠇⠒⠺⠘⠻⠻⠜⠃⠇⠿⣘⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⡟⢻⣿⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⡿⠚⢿⡿⢻⡿⠛⢿⠟⠻⡟⠻⣿⠟⢻⡟⠻⡿⠛⢿⣿⣿⣿⢻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⡿⣸⢸⢸⠠⠦⡁⣴⠁⠀⣏⣹⠀⠈⡇⣶⢉⣹⠰⠶⡱⠆⡇⣶⢸⢰⣉⡇⠿⢸⣑⢘⡇⠿⢸⠠⠌⡿⠣⣯⠸⢇⡟⠡⡿⠋⢼⣉⡇⣶⢸⠱⠶⡇⣶⠙⠀⢸⢠⡆⠶⢸⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣷⣭⣬⣭⣭⣤⡭⣭⣥⣤⣭⣭⣥⣬⣭⣭⣭⣭⣥⢬⢥⢬⣥⣭⣬⣭⣭⣭⣤⣭⣭⣬⣭⣤⣭⣥⢬⣥⣤⣭⣥⢬⣥⣤⣭⣤⣬⣭⣥⣭⢭⣥⣤⡥⣭⣭⣤⣬⣭⣭⣤⣬⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣟⠩⢭⢨⡯⠉⡇⡇⣿⢩⢉⡍⡯⠍⢻⢩⡝⠿⢿⢸⢸⢨⡝⠏⠍⠋⣩⡅⡽⠩⢹⠩⢽⠿⡏⣭⢸⢹⡏⡿⢿⢸⢩⡙⢋⡍⡟⡟⣩⣽⢸⠩⠝⡇⡿⠟⠩⠹⢨⡽⢿⢩⡅⡏⣿⢹⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣇⣉⣚⣈⣂⣁⣃⣓⣛⣘⣘⣃⣃⣁⣘⣘⣃⣛⣛⣘⣘⣈⣐⣃⣉⣃⣛⣃⣙⣈⣙⣈⣑⣛⣓⣉⣘⣊⣁⣛⣛⣘⣈⣐⣆⣁⣗⣓⣈⣙⣘⣊⣁⣃⣛⣓⣈⣙⣊⣙⣛⣊⣁⣓⣁⣘⣛⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⠛⠻⠻⡟⠛⢟⠙⡿⠛⢿⠛⡏⡿⠛⢿⢹⣿⠙⠻⡏⢻⠛⠻⠛⢿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⡿⠸⠸⠇⠇⠒⠸⠘⠇⠒⠺⠸⠇⠇⠒⠺⠸⠻⠸⠇⠇⠻⠸⠇⠿⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⢛⠻⡿⠿⣿⠿⢿⠿⢿⠿⢿⠿⢹⢻⠿⠿⣿⠿⢿⣿⡿⠿⡿⠿⢿⡿⠏⣿⣿⠿⠿⠻⡿⢿⠿⢿⠿⢿⡿⠿⡿⢿⢻⡿⠿⣿⠿⢿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⢠⡔⡀⠥⣇⠺⢆⠺⢸⢰⣇⠺⢸⢸⢰⡇⡇⠒⢸⣿⡉⠅⡇⣾⢸⠸⠂⣿⡧⠌⢱⠸⡇⣇⠨⢤⠨⠅⡇⣶⢸⠀⢸⡇⣷⢀⠺⢸⣿⡇⠗⣸⢸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⡿⣿⣿⣿⣷⣤⣾⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⢘⣠⢁⣈⠋⣀⡉⢠⣿⢸⢸⡇⡇⣤⢹⢁⣈⣿⣇⠀⡇⡇⣤⢁⣈⣿⣧⠻⣹⢸⢡⡄⡏⣀⣹⢡⡌⣿⡏⣤⡇⣤⢹⢀⡘⡇⡋⣀⡙⣤⣼⣿⢡⡌⡇⣤⢡⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣾⣿⣶⣶⣷⣶⣶⣾⣿⣾⣶⣶⣷⣶⣾⣶⣶⣿⣷⣶⣷⣷⣶⣶⣶⣿⣯⣤⣭⣬⣤⣤⣥⣤⣬⣤⣬⣤⣥⣤⣥⣭⣬⣤⣤⣥⣥⣤⣬⣤⣬⣬⣤⣤⣥⣭⣐⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣽⣿ ䷩ 𝚕𝚒𝚗𝚎 169 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/02/gnu-linux-norway/#comments Gemini version at gemini://gemini.techrights.org/2022/06/02/gnu-linux-norway/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ GNU/Linux_at_Over_10%_in_Norway_(Over_11%_in_April),_Not_Even_Counting Chromebooks⠀✐ Posted in GNU/Linux, Microsoft, Windows at 5:56 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNU/Linux_at_Over_10%_in_Norway⦈_ Not_just_Turkey but also very_rich_countries Summary: Norway’s adoption of GNU/Linux was noted_here_last_year; it has since then_increased_a_lot; if one counts mobile devices as well, not to mention ChromeOS, it’s looking far worse for Microsoft and good for “Linux” as even in rich countries we see that it’s not about price but about control/freedom ⡀⠤⠐⠂⠉⣁⣰⣶⣶⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠐⠶⠶⢦⣄⣀⣀⠀⠀⠀⠉⠐⠂⠤ ⣀⠤⠒⣰⣿⣿⣿⣿⣿⣿⣷⡄⢠⡤⣶⠤⣤⢴⠤⡤⢤⣤⣽⡟⣤⡤⡤⡦⣠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣟⠁⠈⣿⣿⣿⠄⢘⣛⡙⠛⡛⠚⢓⣓⢿⡿⠟⠛⠛⠃⠃⠓⠙⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠞⠋⠁⠉⣀⠀⠀⠈⠉⣒⡒⠢⠤⣀⠀⢀⡀⠀⣀⠀⠶⣈⣝⠒⠉⠉⠉⠉⠛⠛⢘⣛⣛⣃⠀⠀ ⠄⠒⠢⢿⣿⣿⣷⣾⣿⡿⠉⠀⠸⠼⠿⢽⡯⠾⠿⠽⠫⠿⣿⣿⣒⡮⠵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠒⠉⠀⠀⣠⠒⢞⠒⠁⠀⠀⠀⠀⠙⠽⠯⠿⠓⠚⠙⠓⠋⠁⠒⠒⠒⠺⠷⠢⠤⣀⣔⠒⠓⣦⣠⣀⣀⣀ ⣀⣀⣀⣀⣉⣿⣿⣟⣛⣀⣀⣀⢠⢖⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⣤⣴⣬⢀⣀⣀⣙⢲⣾⣷⣄⣤⢾⢅⡼⠿⣛⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠩⢥⣤⣿⡿⣭⢋⣙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 217 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/02/happy-birthday-techrights-irc/#comments Gemini version at gemini://gemini.techrights.org/2022/06/02/happy-birthday-techrights-irc/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Happy_Birthday_to_Our_Very_Own_IRC_Network⠀✐ Posted in Site_News at 4:57 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇RC_at_techrights_birth_-_BN⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇_IRC_at_techrights_birth_-_TB⦈_ Summary: IRC network for #techrights (being controlled by us directly) was a great improvement; its birth was one year ago (after 13.5 years with Freenode) Libera.Chat recently turned_one, but we never turned to Libera.Chat. Amid chaos in Freenode we implemented what we had been wanting and planning to do for years, and nearly did two years ago. We wanted our own network, which isn’t occupied by ‘thought police’ with its own blacklist. Last night we reached the one-year anniversary of our migration to our_own_network, which runs in tandem with transient fallbacks or safety nets (very seldom used). “We wanted our own network, which isn’t occupied by ‘thought police’ with its own blacklist.”Our network has been listed_by_netsplit.de_since_December, alongside about_500_others. Unlike all those corporations with their fake hype (they come and go all the time), IRC has been around for a very long time. It predates_the_World_Wide_Web. We certainly hope that more sites and organisations will see the value of self- determination in the speech sense; there will hopefully be tens of thousands more IRC networks out there, not tens of thousands of channels centralised in few giant IRC networks with opaque governance structures and corporate patrons, typically euphemised “donors” (the money tends to come with strings or implicit demands). Our associate has reflected upon this anniversary as well, noting that “rather than celebrate libera.chat the focus ought to be on the unfortunate demise of freenode; freenode was great and very important for many years, but eventually its main disadvantage, that of centralization, brought down many projects. While some moved to libera.chat, many just gave up on IRC altogether. However, some, and these are the ones to praise, started their own IRC networks. (Re- )Decentralization is the solution to many of the problems people associate with the Internet nowadays.” █ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⢸⣰⠶⠶⡶⠶⡶⠶⢶⠶⠶⠶⢶⠶⠶⡶⠶⡶⣶⡶⡶⢶⢶⡶⣶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣸⠀⠀ ⠀⠀⢸⣿⣮⣾⣷⣼⣷⣵⣤⣧⣦⣬⣾⣥⣴⣧⣥⣧⣦⣧⣮⣶⣤⣤⣴⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⢤⠄⠀⠀⠠⢠⢠⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡤⠀⠤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⡀⠀⠠⠀⠀⠠⢤⠀⠀⢹⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⢸⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀ ⠀⠀⢰⢶⠶⠶⢶⠶⠶⠶⢶⠶⠶⢶⣶⣶⡶⠶⠶⠶⠶⡶⠶⠶⢶⠶⠶⠶⢶⠶⠶⠶⡖⢶⢶⠶⠶⢶⣶⠶⠶⢶⠶⠶⠶⠶⠶⡶⠶⠶⡶⡶⡶⢶⢶⢶⠶⠲⢶⠶⠶⠶⡶⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⢶⣶⠀⠀ ⠀⠀⢸⣿⣶⣿⣶⣦⣴⣶⠶⣶⣶⣼⣿⣷⣾⣶⣶⣶⣶⣷⡶⡶⢤⣶⣶⣶⣷⢶⣶⣶⣷⣶⣿⣷⣷⣴⡶⢷⣶⣾⣷⡶⣤⣷⣶⣶⣾⣤⣧⣷⢿⣾⣾⣶⣶⢿⣶⡶⣷⣾⣶⢾⣷⣧⣿⡾⣶⣶⣶⣾⣶⣦⣼⣿⠀⠀ ⠀⠀⢸⣤⣷⣽⢴⣤⣤⢴⣤⣤⣤⣷⢦⣤⣤⣮⣦⣤⣧⣧⣤⣯⡤⣴⣤⣼⣤⣤⣴⣯⣤⣤⣤⣴⣼⣴⣤⣴⣶⣼⣧⣧⣴⣤⣬⣮⣴⣾⣽⣧⣤⣤⣤⣴⣧⣤⣦⣧⣵⣴⣧⣾⣤⣤⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣤⣤⣤⣤⣤⣀⣤⣤⣧⣤⣤⣼⣤⣤⣄⣦⣤⣤⣤⣤⣥⣤⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠤⠄⠄⠄⠄⠤⠄⠀⠀⠠⠠⠠⠠⠤⠤⠄⠄⠄⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀ ⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠀⠀ ⠀⠀⢸⣿⢛⠿⡟⠛⡟⡻⠻⡛⠛⢻⢻⡛⡻⡛⢻⡿⠿⡿⠿⠿⠿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⠿⠶⠾⠷⠶⠾⠾⠶⠶⠶⠾⠾⠶⠶⠶⠿⠷⠽⠷⠶⠿⠶⠶⠾⠷⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀ ⠀⠀⢸⠟⠻⠻⢿⠿⠿⢿⣿⠿⡻⠿⡿⢟⡻⡟⠟⡿⢻⠿⠿⠿⠿⡿⢟⣿⠻⢿⣛⠿⡟⠟⠻⠻⠿⡿⠻⠿⠛⡿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣾⣷⣶⣶⣶⣷⣾⣶⣿⣾⣷⣷⣿⣿⣶⣾⣷⣾⣶⣶⣶⣶⣷⣾⣷⣶⣾⣿⣶⣾⣶⣷⣶⣶⣷⣷⣶⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 354 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/02/irc-log-010622/#comments Gemini version at gemini://gemini.techrights.org/2022/06/02/irc-log-010622/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Wednesday,_June_01,_2022⠀✐ Posted in IRC_Logs at 2:51 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-010622.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-010622.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-010622.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-010622.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  QmTjMJNsLd9wsbJxAewgWRKsvEpyYR7dXsRFbuiGrLxnBh #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmcpwhuAWg97mC9XbD1MHRYgvmXA8uSvZVFsSBqVoKLuRy (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell- 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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/02/turkey-in-pictures/#comments Gemini version at gemini://gemini.techrights.org/2022/06/02/turkey-in-pictures/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ In_Picture:_Updated_and_Finally_Presented_About_10_Minutes_Ago,_Windows Market_Share_in_Turkey_Down_to_10%⠀✐ Posted in Microsoft, Windows at 5:07 am by Dr. Roy Schestowitz Over a month ago: In_Picture:_Windows_Falls_Below_30%_Market_Share_as_April Ends 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Windows_drowning???_⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Get_a_grip,_Steve_Ballmer⦈_ Summary: Anyone can check StatCounter for the start of a month (June); for particular countries (e.g. for_Turkey and for Poland) and globally/in general (no ‘stable’ data yet) the_data_indicates another epic collapse for Windows 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Windows_in_Turkey⦈_ The numbers (Windows share in 2022): 2022-01: 25.63% 2022-02: 23.87% 2022-03: 18.68% 2022-04: 16.59% 2022-05: 10.93% 2022-06: 10.9% The_full_set_of_numbers_as_OpenDocument_Format_(ODF). ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⡄⣶⡆⣶⡆⣶⣆⣶⢶⣦⠀⠀⣶⣶⣶⣴⣶⣶⣶⢠⣾⣿⣦⣶⣶⣶⣶⢰⣶⢲⣶⣰⣶⣶⣶⣶⣶⣶⣶⣴⣿⣷⡄⣴⡶⣶⡄⣴⣶⣦⢀⣶⢶⣦⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣷⣿⡏⠿⣶⣄⠀⠀⣿⣿⣿⣿⣿⣿⣟⢹⣿⣹⣿⢹⣿⣿⣿⣿⣿⣹⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⣩⣅⣿⡇⣭⣴⣿⣮⣭⣸⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡇⢹⣿⡏⣿⣿⠙⣿⣼⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡇⣽⡏⠉⠀⣿⡏⡏⣿⣿⠉⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠈⠁⠉⠉⠀⠀⠉⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣲⣾⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠋⠀⠈⣽⡏⠁⡀⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠨⡼⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣶⣤⣶⣾⣿⣷⣶⣦⣤⣤⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⢤⣾⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣷⢉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⠆⠀⠀⣾⣿⣿⣿⡿⠉⠸⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⠓⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠀⢀⠀⠈⢻⡿⠃⠀⠀⡀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣀⠀⣀⠀⠀⠀⠀⠀⢀⣄⣀⣸⣟⢿⣿⡿⢿⢿⣿⣿⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠠⡴⠆⣾⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⡟⠙⢿⣿⣿⣿⣭⣃⡁⠀⠉⡉⠁⠀⠀⠀⠀⠀⢈⣥⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠂⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣅⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⡇⡆⠀⠻⠋⠻⠃⠀⠀⠀⠀⠀⠈⠉⣛⣿⡇⠀⣤⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣡⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣦⡀⠀⠉⠁⠀⢲⠂⣶⡆⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⣻⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣢⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⣻⠿⠋⠰⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠟⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⣿⠟⠡⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⣵⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠟⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢟⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠀⢀⡈⢀⡀⣀⣄⣐⣶⣿⣀⣴⣾⣿⣿⣷⣽⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢭⣉⠉⠉⠉ ⣿⣿⣿⡿⣿⡿⡫⢉⣀⣋⣹⡟⠛⠛⠛⠻⣿⣿⣿⠟⠝⠀⠀⠀⢘⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⢟⣽⣿⣿⣿⣇⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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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 5416 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_02/06/2022:_Armbian_22.05_and_pgAdmin_4_v6.10_Released⠀✐ Posted in News_Roundup at 4:41 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Desktop/Laptop o Audiocasts/Shows o Applications o Instructionals/Technical o Games * Distributions_and_Operating_Systems o New_Releases o Debian_Family o Canonical/Ubuntu_Family o Open_Hardware/Modding o Mobile_Systems/Mobile_Applications * Free,_Libre,_and_Open_Source_Software o Web_Browsers # Mozilla o SaaS/Back_End/Databases o Content_Management_Systems_(CMS) o Programming/Development # Perl_/_Raku # Rust * Leftovers o Health/Nutrition/Agriculture o Security # Privacy/Surveillance o Internet_Policy/Net_Neutrality * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Slashdot ☛ HP_Dev_One_Laptop_Running_System76′s_Ubuntu Linux-based_Pop!_OS_Now_Available⠀⇛ # ⚓ 9to5Linux ☛ You_Can_Now_Pre-Order_the_HP_Dev_One_Linux Laptop_Powered_by_Pop!_OS_Linux⠀⇛  Unveiled last month, the HP Dev One laptop is the culmination of several years of collaboration between HP and System76 in an attempt to provide developers of all sorts with a premium notebook that ships with the Ubuntu-based Pop!_OS Linux distribution pre-installed. HP Dev One is not a configurable laptop and it features an 8-core AMD Ryzen 7 PRO processor with AMD Radeon integrated graphics, 16GB DDR4 3200MHz RAM, 1TB PCIe NVMe M.2 storage, and a beautiful Full HD (1920×1080) 1,000 nit display. # ⚓ XDA ☛ Does_the_Dell_Latitude_5430_run_Linux?_Can_you install_it?⠀⇛ If you’re fully committed to Linux as your main operating system, your best option is to configure the Latitude 5430 to come with Ubuntu installed out of the box. Dell sells this laptop with Ubuntu 20.04 LTS pre-installed, with LTS standing for long-term support. Going with Ubuntu actually saves you some money, since it costs almost $80 less than getting the Windows license. You can buy the laptop below, and the option to choose Ubuntu is near the top, right below the processor. o § Audiocasts/Shows⠀➾ # ⚓ Jupiter Broadcasting ☛ Linux_Action_News_243⠀⇛ Our thoughts on NixOS’ new GUI installer, winning hearts and minds one firmware update at a time, the performance bug that hit Linux 5.18, and preparation begins for the open-source NVIDIA driver. # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_956⠀⇛ # ⚓ The BSD Now Podcast ☛ BSD_Now_457:_The_NetBSD_Wheelbarrow⠀⇛ Journey to ZFS RAIDZ1 on NetBSD, FreeBSD networking basics: WiFi and Bluetooth, smuggling code into the playstation via NetBSD driver hole, KDE FreeBSD CI, remembering buildtool, and more # ⚓ Video ☛ Mobile_GNOME,_Deepin_20.6,_elementary_OS_7,_Mint takes_over_Timeshift_–_Linux_and_open_source_news_– Invidious⠀⇛ # ⚓ Video ☛ Linux_Lite_6.0_overview_|_Simple_Fast_Free._– Invidious⠀⇛ In this video, I am going to show an overview of Linux Lite 6.0 and some of the applications pre- installed. # ⚓ Video ☛ Enterprise_Linux_Security_Episode_29_–_High_Level Threats_–_Invidious⠀⇛ In this episode, Jay and Joao unpack some recent news around the BVP47 vulnerability, and some very interesting details around it and how it came to be. This is one of those “spy thriller” type episodes, so don’t miss it! o § Applications⠀➾ # ⚓ Hackaday ☛ Linux_Fu:_Easy_Widgets_|_Hackaday⠀⇛ # Here’s a scenario. You have a microcontroller that reads a number of items — temperatures, pressures, whatever — and you want to have a display for your Linux desktop that sits on the panel and shows you the status. If you click on it, you get expanded status and can even issue some commands. Most desktops support the notion of widgets, but developing them is a real pain, right? And even if you develop one for KDE, what about the people using Gnome? Turns out there is an easy answer and it was apparently inspired by, of all things, a tool from the Mac world. That tool was called BitBar (now XBar). That program places a widget on your menu bar that can display anything you want. You can write any kind of program you like — shell script, C, whatever. The output printed from the program controls what appears on the widget using a simple markup-like language. That’s fine for the Mac, but what about Linux? If you use Gnome, there is a very similar project called Argos. It is largely compatible with XBar, although there are a few things that it adds that are specific to it. If you use KDE (like I do) then you’ll want Kargos, which is more or less a port of Argos and adds a few things of its own. # ⚓ Ubuntu Pit ☛ Top_20_Best_Project_Management_Software_for Linux_in_2022⠀⇛ In this world of business and commerce, project management tools are an inseparable part of human life. The reason lies in these tools’ excellent assistance capability of organizing work and managing tasks and projects efficiently for individuals or teams. If you are a Linux user, you can certainly find a lot of Project Management Software for Linux. But all of them may not fit well for your particular projects. Well, if you are looking for one that fits most project types, we can help. As it is a crucial issue, we took it seriously and researched the 20 best project management applications that you can use comfortably with Linux. Here, we divided the list into two groups; where the first one will introduce you to the best installable project management software, and the next one is for the web-based project manager. We hope you will go through the entire section to enrich your Linux experience. o § Instructionals/Technical⠀➾ # ⚓ GNU_Linux_–_neatest_function_ever_–_virt-manager_kvm_qemu pass_through_usb_device_to_vm_works_like_a_charm⠀⇛ # ⚓ OpenSource.com ☛ The_only_Linux_command_you_need_to_know_| Opensource.com⠀⇛ Information about Linux and open source abounds on the internet, but when you’re entrenched in your work there’s often a need for quick documentation. Since the early days of Unix, well before Linux even existed, there’s been the man (short for “manual”) and info commands, both of which display official project documentation about commands, configuration files, system calls, and more. There’s a debate over whether man and info pages are meant as helpful reminders for users who already know how to use a tool, or an intro for first time users. Either way, both man and info pages describe tools and how to use them, and rarely address specific tasks and how to accomplish them. It’s for that very reason that the cheat command was developed. # ⚓ Software-Only_Setup_to_Diagnose_QEMU_SCSI_Passthrough_and Multipath_Failover⠀⇛ # ⚓ GNU_Linux_how_to_–_quick_tmux_tutorial_–_alternative_to screen_–_multi_tab_multi_window_multi_session⠀⇛ # ⚓ Francesco Mazzoli ☛ How_fast_are_Linux_pipes_anyway?⠀⇛ In this post, we will explore how Unix pipes are implemented in Linux by iteratively optimizing a test program that writes and reads data through a pipe. # ⚓ LWN ☛ Mazzoli:_How_fast_are_Linux_pipes_anyway?⠀⇛ Francesco Mazzoli delves deeply into the kernel’s implementation of pipes (and more) in an attempt to maximize the throughput of data. # ⚓ How_to_make_a_local_NixOS_cache_server⠀⇛ # ⚓ DebugPoint ☛ How_to_Install_FFmpeg_in_Ubuntu_and_Other Linux⠀⇛ A tutorial on how you can install the FFmpeg package in Ubuntu and other Linux distributions, also some examples to get you started. # ⚓ How_To_Use_Tags_In_Ansible_Playbooks_–_OSTechNix⠀⇛ In this article, we are going to learn what are Ansible tags and the effective ways to use tags in Ansible playbooks to run only specific tasks. # ⚓ ID Root ☛ How_To_Install_TensorFlow_on_Ubuntu_22.04_LTS_– idroot⠀⇛ In this tutorial, we will show you how to install TensorFlow on Ubuntu 22.04 LTS. For those of you who didn’t know, TensorFlow is a wildly popular open-source framework used for numerical computation that makes building machine learning algorithms easy and convenient. It includes comprehensive tools, libraries, and a community, ensuring a robust environment for the researchers to develop machine learning and AI-related applications with ease. 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 TensorFlow open-source framework on Ubuntu 22.04 (Jammy Jellyfish). You can follow the same instructions for Ubuntu 22.04 and any other Debian-based distribution like Linux Mint, Elementary OS, Pop!_OS, and more as well. # ⚓ Auto-generating_build-requires_for_packages_built_with Maven⠀⇛ For a few months all Fedora packages built using Maven in rawhide have auto-generated build-requires included in their build.logs, which after some adjustments can be copied to .spec files. # ⚓ Running_rawhide_app_in_chroot_by_example_of_Eclipse⠀⇛ You don’t need rawhide machine to test Fedora rawhide packages. In fact you don’t even need Fedora machine, any Linux distro should do. # ⚓ How_To_Add_Swap_Space_On_Ubuntu_22.04_LTS_|_Itsubuntu.com⠀⇛ How To Add Swap Space On Ubuntu 22.04 Swap space is the part of the HDD or SDD that is designed to help the operating system temporarily store data. The data or information that the OS cannot hold in RAM is stored in Swap space. It is useful when there is more load on RAM. In this tutorial, we will see the steps to add swap space on Ubuntu 22.04 LTS. # ⚓ Techtown ☛ How_to_Install_Smartctl_on_Ubuntu_20.04_?_– Monitor_the_health_of_your_hard_disks_–_Atechtown⠀⇛ Knowing how your system’s hardware is doing can help solve many performance problems and can also prevent dangerous situations with your data. For example, one of the most sensitive components of the computer is the hard disk because that is where we store data. Therefore, today you will learn how to install Smartctl in Ubuntu 20.04. Thanks to this command, you will learn how to monitor the health of the hard disk. # ⚓ The Server Side ☛ How_do_I_install_Java_on_Ubuntu?⠀⇛ While Ubuntu does not come with a Java runtime preinstalled, it does come prepackaged with the ability to easily install Java with the apt command. There are many different ways to install Java on Ubuntu, but if all you need is the ability to run a Java program or even develop and compile some Java source code, the apt-based installation path is the easiest one to follow. # ⚓ How_To_Set_JAVA_HOME_Environment_Variable_On_Ubuntu_22.04_| Itsubuntu.com⠀⇛ How To Set JAVA_HOME Environment Variable On Ubuntu 22.04 Before setting Set JAVA_HOME Environment Variable On Ubuntu 22.04 LTS, make sure that you have Java installed in your Ubuntu 22.04 LTS. # ⚓ Red Hat Official ☛ How_to_configure_your_system_to_preserve system_logs_after_a_reboot⠀⇛ Log entries for the systemd-journald service, which is at the heart of the logging architecture in Red Hat Enterprise Linux (RHEL), do not persist across reboots. This means entries are wiped after a reboot, so you won’t have historical data for analysis. However, with a little configuration, you can keep log entries even after a reboot. # ⚓ UNIX Cop ☛ How_to_enable_REMI_repository_in_CentOS_9 Stream⠀⇛ Hello, friends. In this simple post, you will learn how to enable REMI repository in CentOS 9 Stream. This way, you will be able to have multiple PHP versions or upgrade the one you already have on the system. o § Games⠀➾ # ⚓ Make Use Of ☛ What_Is_Steam_Proton_and_How_Does_It_Run Windows_Games_on_Steam_Deck?⠀⇛ Valve has ventured into console gaming with Steam Deck, a handheld device with hardware comparable to the PS5 and Xbox Series S & X. It’s a solid device that should run most AAA titles reliably. The Deck stands out in its ability to run a wide range of games out of the box. It comes with the entire Steam catalog of games, so users don’t have to wait for popular titles to release for the console. Steam Deck runs on SteamOS, an Arch-based Linux distro with built-in Proton support. You can run almost any Windows game on the Deck using Proton. * § Distributions and Operating Systems⠀➾ o § New Releases⠀➾ # ⚓ Nitrux ☛ Release_Announcement:_Nitrux_2.2.0_—_Nitrux_— #YourNextOS⠀⇛ Today is the day! — Nitrux 2.2.0 is available to download We are pleased to announce the launch of Nitrux 2.2.0. This new version brings together the latest software updates, bug fixes, performance improvements, and ready-to-use hardware support. Nitrux 2.2.0 is available for immediate download. o § Debian Family⠀➾ # ⚓ 9to5Linux ☛ Armbian_22.05_Released_with_Support_for_Orange Pi_R1+_LTS,_Radxa_Rock_3A_and_Zero⠀⇛ Armbian 22.05 is here three months after Armbian 22.02 and introduces support for the Orange Pi R1+ LTS, Orange Pi 3 LTS, Radxa Rock 3A and Zero, and ClockworkPi’s DevTerm A06 boards, support for the Linux 5.17 kernel series on the mvebu64 and UEFI EDGE kernel flavors, support for running x86_64 (64-bit) apps, as well as support for the NVIDIA graphics driver on the x86 desktop images. o § Canonical/Ubuntu Family⠀➾ # ⚓ Linux Shell Tips ☛ Ubuntu_22.04_Released_–_Download_DVD_ISO Images⠀⇛ As of April 21st, 2022, Canonical Ubuntu 22.04 LTS (Long Term Support) was officially released and it has significantly raised the bar for open source technologies associated with workstations, IoT, edge, and cloud computing. Other significant leaps associated with Ubuntu 22.04 LTS include a real-time kernel (a prime feature for industrial applications), cloud confidential computing, Enterprise Active Directory, and cumulative FedRAMP, HIPAA, FIPS, and PCI-DSS compliance. Thanks to canonical partners, all major clouds, hardware, and architectures after Ubuntu 22.04 LTS will benefit from long-term maintenance and enterprise-grade security support. o § Open Hardware/Modding⠀➾ # ⚓ Arduino ☛ Get_fit_while_you_scroll_TikTok_with_the PELOTok!⠀⇛ The convenience of smartphones combined with our infinitely scrolling social media feeds has led to some less-than-ideal results, including the fact that a person can sit down and be entertained for hours without even realizing it. This inactivity and lack of exercise can lead to a whole host of health problems, which is why Eric Guidry built the PELOTok device after coming across one of Simone Giertz’s tweets. The PELOTok relies on a Hall effect sensor and a magnet positioned on the back wheel of a stationary bike to read its current speed by multiplying the number of rotations in a few seconds by the tire’s circumference. This value is then displayed on a small OLED screen and is used to determine if the rider is pedaling fast enough to scroll through their feed. Along with these components, an Arduino Micro also checks for any button presses from the user that signal a command to either scroll up/down or like the video. However, any speed below 16kph will result in a loud buzz letting the rider know they need to increase their pace. o § Mobile Systems/Mobile Applications⠀➾ # ⚓ XDA ☛ Developers_can_now_implement_Ultra-Wideband_(UWB) support_in_apps_with_Android_Jetpack⠀⇛ # ⚓ Why_Is_Call_Recorder_Not_Recording_Incoming_Voice_on Android_–_Guiding_Tech⠀⇛ # ⚓ 9to5Google ☛ Android_Automotive_OS_12L:_Quick_Controls, Bluetooth,_more_–_9to5Google⠀⇛ # ⚓ Digital Trends ☛ Hurray,_Android_phones_don’t_look_like_the iPhone_anymore_|_Digital_Trends⠀⇛ # ⚓ Android Central ☛ Best_Android_tablets_for_drawing_2022_| Android_Central⠀⇛ # ⚓ Phone Arena ☛ Vulnerability_in_Moto_G20_and_similar_Android phones_makes_them_easy_targets_for_hackers_–_PhoneArena⠀⇛ # ⚓ 9to5Google ☛ Android_Auto_for_Phone_Screens_shutting_down ‘soon’_–_9to5Google⠀⇛ * § Free, Libre, and Open Source Software⠀➾ o § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Mozilla ☛ The_Mozilla_Blog:_Mozilla_releases_local machine_translation_tools_as_part_of_Project_Bergamot⠀⇛ In January of 2019, Mozilla joined the University of Edinburgh, Charles University, University of Sheffield and University of Tartu as part of a project funded by the European Union called Project Bergamot. The ultimate goal of this consortium was to build a set of neural machine translation tools that would enable Mozilla to develop a website translation add-on that operates locally, i.e. the engines, language models and in-page translation algorithms would need to reside and be executed entirely in the user’s computer, so none of the data would be sent to the cloud, making it entirely private. In addition to that, two novel features needed to be introduced. The first was translation of forms, to allow users to input text in their own language that is dynamically translated on-the-fly to the page’s language. The second feature was quality estimation of the translations where low confidence translations should be automatically highlighted on the page, in order to notify the user of potential errors. # ⚓ Mozilla ☛ The_Mozilla_Blog:_Social_media’s ‘Doomscrolling_Reminder_Lady’_on_her_favorite_corners of_the_internet⠀⇛ o § SaaS/Back End/Databases⠀➾ # ⚓ PostgreSQL ☛ PostgreSQL:_Citus_Con:_An_Event_for Postgres—It’s_a_wrap!⠀⇛ Citus Con: An Event for Postgres is a free and virtual developer event that took place Apr 12-13, 2022—and we owe a huge THANK YOU to everyone who participated in the first ever Citus Con—from the attendees to the 42 amazing speakers. We trust you had fun and learned a lot. # ⚓ PostgreSQL ☛ pgAdmin_4_v6.10_Released⠀⇛ The pgAdmin Development Team is pleased to announce pgAdmin 4 version 6.10. This release of pgAdmin 4 includes 23 bug fixes and new features. For more details please see the release notes. o § Content Management Systems (CMS)⠀➾ # ⚓ Kiwi_TCMS:_Survey:_How_do_testers_and_QA_use_GitHub,_GitLab and_Bitbucket⠀⇛ Hello testers, we are conducting a little research/ survey into how other testers and QA professionals use modern platforms like GitHub, GitLab and Bitbucket. At this moment in time our goal is to collect as much information as possible in order to understand the existing ecosystem. # ⚓ The_Month_in_WordPress_–_May_2022⠀⇛ WordPress has a lot to celebrate this month. The newest release “Arturo” is here. WordPress turned 19 years old last week. And WordCamp Europe, the first in-person flagship WordCamp in two years, is starting today in Porto, Portugal. Read on to learn more about these and other exciting news around WordPress! o § Programming/Development⠀➾ # ⚓ Barry Kauler ☛ OpenEmbedded_Dunfell_revision-9_compile⠀⇛ Yocto/OpenEmbedded released a minor bump of their Dunfell release to 3.1.16, so I have sync’d with that and done another complete recompile. A total of 935 packages and it took 19½ hours. The compile was on a USB3.0 SSD (1TB Crucial MX500 SATA), Lenovo Ideacentre PC with i3 CPU and 32GB RAM. # ⚓ OpenSource.com ☛ Get_started_with_Cadence,_an_open_source workflow_engine_|_Opensource.com⠀⇛ Modern applications require complicated interactions between long-running business processes, internal services, and third-party APIs. To say it’s been a challenge for developers is putting it mildly. Managing these processes means tracking complex states, preparing responses to asynchronous events, and communicating with often unreliable external dependencies. Developers typically take on these complex challenges with solutions that are just as convoluted, assembling unwieldy systems that leverage stateless services, databases, retry algorithms, and job scheduling queues. Because these complex systems obscure their own business logic, availability issues are common, often stemming from the application’s dependence on scattered and unproven components. Developer productivity is regularly sacrificed to keep these sprawling, troubled systems from collapsing. # ⚓ Qt ☛ DEADLINE_EXTENDED_–_Call_for_Presentations:_Qt_World Summit_2022⠀⇛ We’ve extended the deadline for the Qt World Summit 2022 Call for Presentations until June 24, 2022. With this extension, you’ll have an additional two weeks to finalize your submission. As a reminder, we are looking for speakers, collaborators and industry thought leaders to share their expertise with the community during the upcoming virtualQt World Summit on November 9, 2022. We are looking for a wide range of topics that you think are important to the community. # § Perl / Raku⠀➾ # ⚓ Replay_Cron_Events_With_Cron::Sequencer⠀⇛ Trivially find out which cron events ran, or will run, for an arbitrary time range; allowing you to rerun, debug, fast forward (speed up test iterations), with cron- sequencer: cron-sequencer –show “last hour” /path/to/ crontab At Humanstate we still use cron to drive many of our backend processes. While we continue to move some to event and message driven logic, there will always be a number of jobs that have to run at very specific dates and/ or times: communications with banks, archiving, backups, and so on. That’s where cron comes in. # § Rust⠀➾ # ⚓ Rust Weekly Updates ☛ This_Week_In_Rust:_This_Week_in Rust_445⠀⇛ * § Leftovers⠀➾ o § Health/Nutrition/Agriculture⠀➾ # ⚓ WSWS ☛ [Older]_Biden_marks_1_million_US_COVID_deaths_by preparing_for_the_next_million⠀⇛ On Thursday, US President Joe Biden finally acknowledged that over 1 million Americans have now died from COVID-19. He did so by issuing a perfunctory written statement and a pre-recorded video, both of which were characterized above all by their cynicism and indifference to the lives of those lost and their loved ones still mourning. Various COVID-19 trackers rely on different data sets, and the Biden administration artificially delayed official recognition of this horrific milestone, choosing to use the Reuters tracker. The 1 million death milestone was first reached by Worldometer nearly two months ago on March 22, which only the World Socialist Web Site commented on at the time. This was followed by the NBC and News Nodes trackers last week, which led to a handful of additional comments in the corporate media but continued silence from the White House. # ⚓ New York Times ☛ [Older]_How_America_Lost_One_Million People⠀⇛ # ⚓ Los Angeles Times ☛ [Older]_After_less_than_2½_years,_U.S. COVID-19_death_toll_surpasses_1_million⠀⇛ The U.S. death toll from COVID-19 reached 1 million Monday, a once-unimaginable figure that only hints at the multitudes of loved ones and friends staggered by grief and frustration. The number of dead, as tallied by the Centers for Disease Control and Prevention’s National Center for Health Statistics, is equivalent to that of a 9/11 attack every day for 336 days. It is roughly equal to how many Americans died in the Civil War and World War II combined. It’s as if Boston and Pittsburgh were wiped out. o § Security⠀➾ # ⚓ USCERT ☛ CISA_Updates_Advisory_on_Threat_Actors_Chaining Unpatched_VMware_Vulnerabilities [Ed: While VMware, infiltrated_by_Microsoft, runs many anti-Linux FUD campaigns it turns out VMware itself is a back door of sorts]⠀⇛ CISA has updated Cybersecurity Advisory AA22-138B: Threat Actors Chaining Unpatched VMware Vulnerabilities for Full System Control, originally released May 18, 2022. The advisory has been updated to include additional indicators of compromise and detection signatures, as well as tactics, techniques, and procedures reported by trusted third parties. # ⚓ Hacker News ☛ EnemyBot_Linux_Botnet_Now_Exploits_Web Server,_Android_and_CMS_Vulnerabilities [Ed: This isn't about Linux but about flaws in some software or some plugins that aren't being patched]⠀⇛ Also incorporated is a new scanner function that’s engineered to search random IP addresses associated with public-facing assets for potential vulnerabilities, while also taking into account new bugs within days of them being publicly disclosed. [...] Besides the Log4Shell vulnerabilities that came to light in December 2021, this includes recently patched flaws in Razer Sila routers (no CVE), VMware Workspace ONE Access (CVE-2022-22954), and F5 BIG-IP (CVE-2022-1388) as well as weaknesses in WordPress plugins like Video Synchro PDF. # ⚓ LWN ☛ Security_updates_for_Thursday⠀⇛ Security updates have been issued by Debian (firefox-esr), Fedora (thunderbird and vim), Red Hat (firefox, postgresql:10, postgresql:12, and postgresql:13), Scientific Linux (firefox and rsyslog), SUSE (hdf5, hdf5, suse-hpc, postgresql14, rubygem-yajl-ruby, and udisks2), and Ubuntu (imagemagick and influxdb). # ⚓ The Register UK ☛ Zero-day_vuln_in_Microsoft_Office: ‘Follina’_will_work_even_when_macros_are_disabled⠀⇛ Infosec researchers have idenitied a zero-day code execution vulnerability in Microsoft’s ubiquitous Office software. Dubbed “Follina”, the vulnerability has been floating around for a while (cybersecurity researcher Kevin Beaumont traced it back to a report made to Microsoft on April 12) and uses Office functionality to retrieve a HTML file which in turn makes use of the Microsoft Support Diagnostic Tool (MSDT) to run some code. # ⚓ Optics⠀⇛ # § Privacy/Surveillance⠀➾ # ⚓ The Register UK ☛ ExpressVPN_moves_servers_out_of India_to_evade_data_law_•_The_Register⠀⇛ Virtual private network operator ExpressVPN will pull its servers from India, citing the impossibility of complying with the nation’s incoming requirement to record users’ identities and activities. ExpressVPN offers software that routes traffic through servers that load their operating systems entirely into RAM and therefore leave no trace of users’ activities on persistent media. The outfit suggests that’s a point of difference to other VPN providers. # ⚓ Reuters ☛ India’s_new_VPN_rules_spark_fresh_fears over_online_privacy⠀⇛ Virtual private networks (VPNs) that encrypt data and provide users with anonymity online have seen a surge in use in India in recent years as the government tightened its grip here on the internet to curb dissent, and as more people worked from home. Now, some VPN providers are leaving India while others are considering doing so ahead of new rules that the government says are aimed at improving cybersecurity, but that the firms argue are vulnerable to abuse and could put users’ data at risk. Under legislation scheduled to take effect this month, VPN providers are required to retain user data and IP addresses for at least five years – even after clients stop using the service. # ⚓ AccessNow ☛ Indian_IT_Ministry’s_amendments_to_the 2021_IT_Rules:_not_enough_to_protect_rights_and freedoms_–_Access_Now⠀⇛ Earlier today, the Indian Ministry of Electronics and IT (MeitY) published a notice on their website calling for inputs on amending the Information Technology (Intermediary Guidelines and Digital Media Ethics Code) Rules, 2021. Shortly afterwards, the document was inaccessible on the Ministry’s website. While the Government of India clarifies its process on this notice and the extent of this planned consultation, Access Now is urgently calling on MeitY to substantially amend the Rules, ensuring the rights of people across India are upheld. MeitY must meaningfully engage with all stakeholders and address the criticism from many quarters, including United Nations experts, that the Rules jeopardise the right to privacy and free speech. “The MeitY Rules endanger people’s rights and freedoms, and removal of such provisions should be the primary goal of any proposed amendments, and MeitY’s current draft fails to do so,” said Raman Jit Singh Chima, Asia Pacific Policy Director and Senior International Counsel at Access Now. “The version of proposed amendments that was made available today shows that the Indian Government intends to continue to impose frameworks, including on grievance redressal, that are beyond the executive branch’s legal competence, and are regrettably doing their utmost to avoid public and parliamentary scrutiny.” o § Internet Policy/Net Neutrality⠀➾ # ⚓ Re:_A_Reader_Friendly_Browser⠀⇛ But the dream died, either from an overdose of RDF, or it was murdered by Facebook and Google. # ⚓ Recommendations_for_changing_your_gemini_server’s_TOFU certificate⠀⇛ So you want to change your certificate, but don’t want users who’ve visited you before to get scary warnings? Here is what I advise. ䷩ 𝚕𝚒𝚗𝚎 6426 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_02/06/2022:_Fedora_Linux_36_Elections_and_GNU/Linux_on_iPad⠀✐ Posted in News_Roundup at 8:19 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Desktop/Laptop o Audiocasts/Shows o Kernel_Space o Instructionals/Technical o Games o Desktop_Environments/WMs # K_Desktop_Environment/KDE_SC/Qt * Distributions_and_Operating_Systems o New_Releases o SUSE/OpenSUSE o Fedora_Family_/_IBM o Debian_Family o Canonical/Ubuntu_Family o Open_Hardware/Modding o Mobile_Systems/Mobile_Applications * Free,_Libre,_and_Open_Source_Software o Web_Browsers # Mozilla o FSFE * Leftovers o Hardware o Linux_Foundation o Security o Finance o Internet_Policy/Net_Neutrality o Monopolies # Copyrights * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Have_an_old_iPad_lying_around?_You_might_be_able_to_make_it run_Linux_soon_|_Ars_Technica⠀⇛ If you have a 2013- or 2014-era iPad sitting around unused because it’s not getting updates from Apple anymore and has stopped running the apps you need, some developers are working on an alternative software solution for you. Developer Konrad Dybcio and a Linux enthusiast going by “quaack723″ have collaborated to get Linux kernel version 5.18 booting on an old iPad Air 2, a major feat for a device that was designed to never run any operating system other than Apple’s. The project appears to use an Alpine Linux-based distribution called “postmarketOS,” a relatively small but actively developed distribution made primarily for Android devices. Dybcio used a “checkm8″ hashtag in his initial tweet about the project, strongly implying that they used the “Checkm8″ bootrom exploit published back in 2019 to access the hardware. For now, the developers only have Linux running on some older iPad hardware using A7 and A8-based chips—this includes the iPad Air, iPad Air 2, and a few generations of iPad mini. But subsequent tweets imply that it will be possible to get Linux up and running on any device with an A7 or A8 in it, including the iPhone 5S and the original HomePod. This isn’t the only project devoted to running Linux on Apple’s hardware. One project, Asahi Linux, has been dedicated to reverse-engineering support for the M1 chips in Apple’s Macs and sending the patches upstream so that they can be integrated into the Linux kernel. Another, Project Sandcastle, has a build of Android up and running on an iPhone 7. Apps like iSH will give you a Linux shell running on top of iOS or iPadOS—not the same as running Linux on the hardware directly, but useful in some circumstances. # ⚓ Older_iPads_May_Soon_Be_Able_To_Run_Linux⠀⇛ Older iPads with the Apple A7- and A8-based chips may soon be able to run Linux. “Developer Konrad Dybcio and a Linux enthusiast going by “quaack723″ have collaborated to get Linux kernel version 5.18 booting on an old iPad Air 2, a major feat for a device that was designed to never run any operating system other than Apple’s,” reports Ars Technica. # ⚓ Make Use Of ☛ Hackable_$219_Pinebook_Pro_Linux_Laptop_Back on_Sale_After_Frustrating_Yearlong_Delay⠀⇛ Pine64, the developers of Linux-based single-board computers, has announced the upcoming availability of the Pinebook Pro, an inexpensive laptop with upgradable components meant as an alternative to Chromebooks. The laptop had been out of stock for a year due to supply chain problems that have gripped the technology industry. Pinebook Pro Back on Sale After Delays Pine64′s Lukasz Erecinski made the announcement of the Pinebook Pro’s going back on sale in an official blog post, while the company also issued a YouTube video summarizing the announcement: The announcement had itself been meant to go out earlier in May, but Erecinksi had become ill. After a year of unavailability, the laptop will be available in June 2022 for $219 from Pine64′s official store. The laptop had been previously enthusiastically reviewed by MUO as a “FOSS laptop that doesn’t suck.” “It has been a year since we were able to ship the Pinebook Pro, and ever since the last batch sold out we have been continually asked to bring it back,” Erecinski said. The main reason for the delay in the availability of the machine has been sourcing IPS panels for the Pinebook Pro’s 14-inch screen. # ⚓ Beta News ☛ HP_Dev_One_laptop_running_System76′s_Ubuntu Linux-based_Pop!_OS_now_available⠀⇛ Last month, the open source community was abuzz with excitement following a shocking announcement from System76 that HP was planning to release a laptop running the Pop!_OS operating system. This was significant for several reasons, but most importantly, it was a huge win for Linux users as yet another hardware option was becoming available. Best of all, HP employees have been trained by System76 to offer high-quality customer support. If you aren’t aware, System76 support is legendary. At the time of the announcement, details about the hardware were a bit scarce, but I am happy to report we now have full system specifications for the 14-inch HP Dev One laptop. Most interestingly, there is only one configuration to be had. The developer-focused computer is powered by an octa- core AMD Ryzen 7 PRO 5850U APU which features integrated Radeon graphics. The notebook comes with 16GB RAM and 1TB of NVMe storage, both of which can be user-upgraded later if you choose. # ⚓ HP_releases_its_$1,099_Linux_laptop_for_developers_|_Ars Technica⠀⇛ The previous workstations used Ubuntu 20.04 preloaded with software packages aimed at data scientists. However, the Dev One runs Pop!_OS, an Ubuntu-based Linux distribution from System76. System76 also makes its own laptops, desktops, servers, and the Launch mechanical keyboard. HP’s Dev One marks the first laptop to run Pop!_OS without “System76″ stamped on the lid—although, you can download Pop!_OS and install it on your own system. # ⚓ OMG Ubuntu ☛ HP’s_New_Linux_Laptop_is_Available_to_Pre- Order⠀⇛ HP is taking orders for the HP Dev One, its first developer-focused laptop preloaded with the Ubuntu- based Pop!_OS Linux distribution. Shocked? Don’t be. We learned of this device’s existence last month when System76 CEO Carl Richell dropped mention of it on his Twitter, proper casual like. Reaction from Pop fans was understandably effusive, with folks wanting to learn the salient what, why’s, how’s and where’s. # ⚓ LinuxInsider ☛ New_Linux_Laptop_Line_Advances_HP,_System76 Open-Source_Collaboration_|_LinuxInsider⠀⇛ Collaboration between Linux computer and software firm System76 and HP is pushing for greater commercial adoption of open-source software and hardware optimized for Linux. System76 and HP on Thursday announced a new premium computer line designed to attract a wider audience to the developer-focused HP Dev One laptop computer. HP’s new Dev One, powered by System76’s popular Pop!_OS Linux distribution, empowers developers to create their ideal work experience with multiple tools to help them perform tasks at peak efficiency not available on other computing platforms. The Pop!_OS platform features auto-tiling, workspaces, and easy keyboard navigation. This flexibility allows software developers to create unique optimized workflows to unleash their coding potential. Typically, Linux users install their preferred Linux platform as a replacement for the default Microsoft Windows on computers they purchase. Relatively few OEMs build their own hardware line and tune it for specific Linux offerings. Denver-based System76 developed its own customized version of the GNOME desktop environment to help advance Linux as the future of computing. The company developed Pop!_OS after Canonical decided to stop the development of the Unity 8 desktop shell in 2017 and replaced its default desktop with GNOME 3. “By bringing together our engineering, marketing, and customer support, System76 [and] HP are introducing HP Dev One to combine powerful hardware with optimized Pop!_OS for the app dev community,” announced Carl Richell, CEO, System76. o § Audiocasts/Shows⠀➾ # ⚓ Linux in the Ham Shack ☛ LHS_Episode_#469:_I_Can_Has Cheezburger⠀⇛ Hello and welcome to the 469th episode of Linux in the Ham Shack. In this short topics episode, the hosts discuss attendance and other topics about the recent Hamvention 2022, memes, the Platinum Jubilee special event station, pulseaudio, Distrobox, The LInux Foundation and security, wfview and much more. Thank you for listening. We hope you have a great week. # ⚓ Video ☛ Linux_Lite_6.0_Run_Through_–_Invidious⠀⇛ In this video, we are looking at Linux Lite 6.0. # ⚓ Linux Made Simple ☛ Linux_Lite_6.0⠀⇛ Today we are looking at Linux Lite 6.0. It comes with Linux Kernel 5.15, based on Ubuntu 22.04, XFCE 4.16, and uses about 1GB of ram when idling. Enjoy! # ⚓ Video ☛ XDG_Desktop_Portals_Fix_Waylands_Biggest_Problem_– Invidious⠀⇛ Wayland doesn’t have working global keybindings and this is a serious problem but it’s a problem with a solution in the works in the form of xdg desktop portals # ⚓ Video ☛ Use_GitLab_Groups_To_Organize_Your_Projects_– Invidious⠀⇛ In GitLab, you use “Groups” to help manage one or more related projects at the same time. This allows you to grant access to all projects that are a part of a Group. It also just helps keeping your projects better organized. So I’ve decided to use GitLab Groups and move all of my DTOS-related repos to a new DTOS Group. o § Kernel Space⠀➾ # ⚓ Collabora ☛ Kernel_5.18:_Milestones_for_the_road_ahead⠀⇛ Released by Linus Torvalds on May 22 after a busy two-month development cycle, Linux kernel 5.18 brings new features and lights up new hardware. As usual, for a general overview, please head to LWN.net to read more about the merge window for 5.18 (part 1 & part 2). And now, without further ado, let’s take a look at the contributions made by our engineering team! # ⚓ Linux Plumbers Conference (LPC) ☛ Microconferences_at_Linux Plumbers_Conference:_Zoned_Storage_Devices_(SMR_HDDs_&_ZNS SSDs)⠀⇛ Linux Plumbers Conference 2022 is pleased to host the Zoned Storage Devices (SMR HDDs & ZNS SSDs). The Zoned Storage interface has been introduced to make more efficient use of the storage medium, improving both device raw capacity and performance. Zoned storage devices expose their storage through zone semantics with a set of read/write rules associated with each zone. o § Instructionals/Technical⠀➾ # ⚓ ByteXD ☛ How_to_Install_and_Use_Telnet_on_Linux_–_ByteXD⠀⇛ Telnet is a protocol that is used to communicate two-way texts over a network. This protocol was developed intending to communicate texts that could work as interactive commands to control/operate a remote machine. # ⚓ Linux Made Simple ☛ How_to_install_FNF_Psych_Engine: Modchart_editor_on_a_Chromebook⠀⇛ Today we are looking at how to install FNF Psych Engine: Modchart editor on a Chromebook. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ Install_and_setup_GlusterFS_on_Ubuntu_22.04/Ubuntu_20.04_– kifarunix.com⠀⇛ Welcome to our guide on how to install and setup GlusterFS on Ubuntu 22.04/Ubuntu 20.04. Well, so what is GlusterFS? GlusterFS is an opensource distributed and scalable network file system that clusters various disk storage resources into a single global namespace. GlusterFS is suitable for data-intensive tasks such as cloud storage and media streaming. # ⚓ Einstein@Home_–_Faster_GPU_linux_app_available_for_Gamma- ray_pulsar_binary_search_project⠀⇛ There is a new linux only gpu app (anonymous type) for gamma-ray pulsar binary search (FGRPB1G) project. It runs anywhere from 50%-80% faster than the current app (version 1.28 in linux) and only for nvidia cards. # ⚓ ID Root ☛ How_To_Install_Microsoft_Teams_on_AlmaLinux_9 [Ed: This is malware. You don't want to ever install this on a system with this level of access to the system.]⠀⇛ o § Games⠀➾ # ⚓ Linuxiac ☛ Arch_Linux_Topped_the_List_as_the_Most_Used Linux_Platform_for_Steam⠀⇛ Arch Linux surpassed Ubuntu 20.04 as the leading Linux distribution on the Steam game market in May. If you’re into Linux gaming, you’ve heard of Steam, Valve’s platform for distributing, updating, and running games. Steam allows you to buy a game, install it over the internet, and launch it directly from the Steam interface. Thanks to Proton, the tradition of PC gaming, formerly reserved mainly for Windows users, is now gaining popularity among Linux users. So it’s no surprise that one of the market’s major players, Valve Software, is paying more attention to Linux. What better example than the Arch Linux- powered Steam Deck gaming console? o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ KDE_e.V._is_looking_for_a_developer_to_help_further KDE’s_presence_on_app_stores⠀⇛ KDE e.V., the non-profit organisation supporting the KDE community, is looking for a someone to help KDE be present in different application stores. We are looking for people who can start working on the projects soon, we expect this to be a part-time position. Please see the call for proposals for the App Stores project for more details about this contracting opportunity. Looking forward to hearing from you. # ⚓ A_GSoC_–_2022_Participant⠀⇛ I am Samarth Raj, a second-year undergrad at KIIT University, India, with a computer science major. My project for adding new activities to GCompris has been accepted for Google Summer of Code 2022. I’ll be working as a contributor this summer. Since the first year of college itself, I’ve always aspired to learn tech that would actually create an impact on people. And it was this time only when I got to know about “open source”. I feel because of open-source, college students who have no idea about what programming means (like me) can learn and contribute to industry-level projects with a little bit of hard work. In this way, we are learning about new technology by understanding its application at the same moment. Open source, in general, is a very practical way of learning. It can be slightly overwhelming at first, but with the help of people around us who are always ready to help, we start to get the hang of it. I participated in the Season of KDE earlier this year, in which I added a new activity, “Left Right Click”. This was my first experience as an open-source contributor, and I cannot list the number of things I got to learn with the help of my mentors during this short period because the list is enormous. * § Distributions and Operating Systems⠀➾ o § New Releases⠀➾ # ⚓ DEEPIN_20.6_RELEASE!⠀⇛ Deepin is the top Linux distribution from China, devoted to providing a beautiful, easy-to-use, safe, and reliable operating system for global users. (Global Ranking) In deepin 20.6, we have developed and integrated a great number of practical features from the functional level based on the community users’ feedback, synchronized with the upstream kernel version, fixed underlying vulnerabilities, upgraded the stable kernel to V5.15.34 and further improved system compatibility and security. Welcome to try it! o § SUSE/OpenSUSE⠀➾ # ⚓ SUSE’s Corporate Blog ☛ OpenCost_–_open_source_Kubernetes cost_monitoring_|_SUSE_Communities⠀⇛ We are excited to share the launch of OpenCost, an open source project that provides real-time cost monitoring for teams running Kubernetes workloads. As container and Kubernetes adoption continues to grow, navigating the complexities around measuring and allocating cost is becoming a business-critical challenge. A recent CNCF survey showed overspend is increasingly a problem for teams scaling their Kubernetes deployments, and more than 70% of organizations do not have accurate cost monitoring in place. # ⚓ SUSE’s Corporate Blog ☛ Impressions_from_the_openSUSE_Conf 2022_–_Day_One:_openQA_and_BCI_|_SUSE_Communities⠀⇛ First I have been busy saying hello and salute to all my dear SUSE colleagues coming from Czechia, Italy, Spain and of course Germany. I have not seen them all for a long time. Finally, Doug deMaio, the openSUSE Community Manager, welcomed all open source enthusiasts in the Z-Bau in Nuremberg and directed us through the options that are offered by the rich and diversified program. A lot of really good sessions were offered, many of them in parallel. I am a big fan of openQA and of course I listened to Oliver Kurz’ talk about the newest highlights of that open source testing framework, the heart and soul of the automated QA behind the openSUSE, SUSE Linux Enterprise and Fedora distributions. o § Fedora Family / IBM⠀➾ # ⚓ Fedora Project ☛ Fedora_Community_Blog:_F36_elections voting_now_open⠀⇛ Voting in the Fedora Linux 36 elections is now open. Go to the Elections app to cast your vote. Voting closes at 23:59 UTC on Thursday 16 June. Don’t forget to claim your “I Voted” badge when you cast your ballot. Links to candidate interviews are below. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_Mindshare_election: interview_with_Madeline_Peck⠀⇛ I’ve worked on Fedora wallpapers as a designer since Fedora 33 to varying degrees, with Fedora 36 and 37 wallpapers discussions led between me and Mo Duffy. I’ve been taking courses in html to try and increase my skills to contribute towards some of the Fedora websites. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_Mindshare_election: interview_with_David_Duncan⠀⇛ I work on the Fedora Cloud-Sig and have a strong interest and investment in the downstream viability of the work. I enjoy learning from the Fedora community and building support for the community. I am very focused on the messaging that relates to how we can drive additional adoption and support for the Fedora community overall. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_Mindshare_election: interview_with_Sumantro_Mukherjee⠀⇛ I am a part of Fedora QA team where I focus on onboarding new members and running test days (Kernel Test Week starts 5th June; participate and earn badges – Just saying). I have helped out by running events, writing docs, blogs/articles, mentorship programs and revamping the Ambassador Program. In the recent past, I am working towards building a strong digital ambassadorship program. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_Council_election: interview_with_Sumantro_Mukherjee⠀⇛ I hail from APAC (India) and would like to focus on bringing in more non-US perspectives, which includes bringing in more contributors from diverse backgrounds. Efficient utilization of our brand new design assets which are now in multiple languages (Hindi, for example) to onboard variety of users (general and power-users) to the Fedora community as contributor either to functional sides (QA, packaging..etc) and/or outreach. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_Council_election: interview_with_Eduard_Lucena⠀⇛ There are several things that we can measure, like number of users, number of contributors, number of reviews per release. But the most important thing is to check how people feel about the project, some stuff that can’t be measure with numbers, but are really important, like how ambassadors feel about the revamp, how members and former members of mindshare perceive the work that have been done. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_FESCo_election: interview_with_Neal_Gompa⠀⇛ As a long-time member of the Fedora community as a user and a contributor, I have benefited from the excellent work of many FESCo members before me to ensure Fedora continues to evolve as an amazing platform for innovation. For the past year, I have had the wonderful privilege of serving as a member of FESCo for the first time, and I enjoyed my time serving to steer Fedora into the future, and I wish to continue to contribute my expertise to help analyze and make good decisions on evolving the Fedora platform. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_FESCo_election: interview_with_Stephen_Gallagher⠀⇛ I’ve been a member of FESCo for many years now, and it’s been a great experience. It gives me the opportunity to see a much wider view of the project than just the pieces I would otherwise contribute to. As for steering the direction of Fedora, I think I would mostly just continue to do as I have been doing: pushing for Fedora to continue to be both the most advanced and one of the most stable open- source distributions in the world. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_FESCo_election: interview_with_Benjamin_Beasley⠀⇛ As a Fedora Linux, CentOS, and Red Hat Enterprise Linux user for well over a decade, and as a contributor to the community for the last couple of years, I find that wise and steady technical leadership has been one of the Fedora project’s great strengths. I would like to help continue that tradition. I was asked to run for FESCo by a community member I respect, and I’m happy to be of service. I would listen more than I speak; respect different people’s perspectives and styles of communication; and remember that idealism and pragmatism can exist in complementary rather than adversarial opposition. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_FESCo_election: interview_with_Tom_Stellard⠀⇛ I have a background in compilers and toolchains, and I would like to use some of the knowledge I’ve gained over the years of building and troubleshooting applications to help make Fedora better. Specifically, I’m interested in helping packagers avoid common mistakes through standardized macros and packaging practices and also by increasing the reliance on CI. # ⚓ Fedora Project ☛ Fedora_Community_Blog:_FESCo_election: interview_with_Major_Hayden⠀⇛ Fedora remains a core part of my Linux deployments on desktops, servers, and cloud instances since I first discovered it back in the Fedora Core 2 days. It strikes a balance between fast updates, simple management, and mature development processes. My service on the Fedora Board from 2012 to 2014 gave me valuable insight into how Fedora works at a community level and the best ways to make changes. Changes affect everyone differently, and thoughtful consideration and communication around those changes makes all the difference. # ⚓ Using_Composefs_in_OSTree⠀⇛ Early on in the boot some code runs that reads this and mount this directory (called the deployment) as the root filesystem. If you look at this you can see a long hex string. This is actually a sha256 digest from the signed ostree commit, which covers all the data in the directory. At any time you can use this to verify that the deployment is correct, and ostree does so when downloading and deploying. However, once the deployment has been written to disk, it is not verified again, as doing so is expensive. In contrast, image-based systems using dm-verity compute the entire filesystem image on the server, checksum it with a hash-tree (that allows incremental verification) and sign the result. This allows the kernel to validate every single read operation and detect changes. However, we would like to use the filesystem to store our content, as it is more efficient and flexible. # ⚓ Red Hat Official ☛ Delivering_event-driven_apps_with_Apache Kafka⠀⇛ Traditionally, enterprise organizations operate using data-centric integration approaches to connect multiple systems, services and applications. This approach is ideal for maintaining and improving data consistency and integrity across all systems and applications. It also allows moving large amounts of data, connecting to disparate systems, and creating master data fabrics that accommodate multiple data management scenarios. # ⚓ Red Hat Official ☛ Introducing_the_Red_Hat_Academy_Talent Network⠀⇛ At Red Hat, we believe that closing the technology skills gap is vitally important to the future of enterprise software and that the opportunity to do so should be available to all. Red Hat Academy bridges the gap between education and industry by collaborating with academic institutions around the world to provide the next generation of IT talent with free access to a range of Red Hat’s training courses and discounted certification exams. With more than 90% of the Fortune 500 using Red Hat products and solutions, individuals with Red Hat skills and knowledge are highly desirable in the job market. Additionally, 93% of hiring managers report difficulty finding sufficient talent with open source skills, up from 87% two years ago. We’re also seeing a greater need to match students who are trained in Red Hat technologies with employers who are seeking open source talent. That’s why we created the Red Hat Academy Talent Network. # ⚓ SDx Central ☛ 7_Layers_Finds_Out_How_Kubernetes_Complexity Can_be_Overcome⠀⇛ Dan Meyer: Hello, I’m Dan Meyer, executive editor at SDxCentral, and welcome to this episode of the 7 Layers podcast. I recently had the chance to speak with Stu Miniman, director of market insights for cloud platforms at Red Hat, to discuss why Kubernetes is so complex, how enterprise IT teams should approach that challenge, and what the vendor ecosystem can do to help deal with that complexity. # ⚓ Red Hat Official ☛ Red_Hat_Joins_Forces_with_U.S. Department_of_Energy_Laboratories_to_Bridge_the_Gap_Between High_Performance_Computing_and_Cloud_Environments⠀⇛ Red Hat, Inc., the world’s leading provider of open source solutions, today announced it is collaborating with multiple U.S. Department of Energy (DOE) laboratories to bolster cloud-native standards and practices in high-performance computing (HPC), including Lawrence Berkeley National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratories. # ⚓ Forbes ☛ Observing_Life_Inside_The_Open_Source_Cloud-Native Stack⠀⇛ As a key trend that has shaped the last decade of cloud in particular, cloud computing evolved to the point where organizations started to consider the possibility of skipping past that cumbersome cloud migration phase. They said, why don’t we just build cloud native then? So they did. o § Debian Family⠀➾ # ⚓ [armbian]_v22.05_(2022-05-28)⠀⇛ Note: If a new sub-version is released this does not necessarily mean all boards receive a new version number since most of the time these fixes are targeting a specific board or board family only. o § Canonical/Ubuntu Family⠀➾ # ⚓ Lubuntu ☛ Lubuntu_21.10_End_of_Life_and_Current_Support Statuses⠀⇛ Lubuntu 21.10 (Impish Indri) was released October 14, 2021 and will reach End of Life on Thursday, July 14, 2022. This means that after that date there will be no further security updates or bugfixes released. After July 14th, the only supported releases of Lubuntu will be 20.04 and 22.04. All other releases of Lubuntu will be considered unsupported, and will no longer receive any further updates from the Lubuntu team. # ⚓ Ubuntu ☛ Private_cloud:_Avoiding_the_high_cost_of operations⠀⇛ Technology plays a strategic role in the success of any organisation. Whether you’re part of an enterprise with thousands of employees across the globe or running a startup from the garage of your home, the success of the business comes down to how you consume technology. However, it’s not that straightforward, and IT decision makers usually have to make a lot of trade-offs when investing in technology. It’s very common to hear phrases like “We would like to implement this solution… but we don’t have the budgets” or “we don’t have the knowledge and skills” or maybe “it doesn’t work well with our environment”. o § Open Hardware/Modding⠀➾ # ⚓ Arduino ☛ Using_an_old_printer_to_create_organic_pottery_| Arduino_Blog⠀⇛ Traditional pottery has been around for many thousands of years and is known for the mixing, shaping, and baking of clay in order to create artful items. Tools such as the pottery wheel and kiln are iconic, and Guillermo Perez Guillen wanted to make a pottery wheel of his own that would not only be inexpensive, but also work with organic cornstarch-based mediums instead of clay. Guillen started his project by finding an old printer and removing the exterior and paper tray, leaving just the horizontal rail and base. From here, he added a potentiometer on the side that enables the user to control how fast the wheel below rotates. In terms of electronics, the platter was taken from a CD player and its motor is driven by a single TB6612FNG dual-motor driver. On the back is an Arduino Mega 2560, which is responsible for reading the analog output of the potentiometer and mapping it to an 8-bit speed that can be outputted via a PWM signal to the motor driver. o § Mobile Systems/Mobile Applications⠀➾ # ⚓ FOSSLife ☛ Murena_Offers_Privacy-Focused,_Open_Source Smartphone⠀⇛ The /e/OS-based phone, which sells for US $379, aims to improve privacy by removing dependency on Google services. “For instance, Google’s default search engine has been replaced with Murena’s own meta-search engine. Other internet-based services, such as Domain Name Server (DNS) and Network Time Protocol (NTP), use non-Google servers,” Vaughan- Nichols says. * § Free, Libre, and Open Source Software⠀➾ o ⚓ Medevel ☛ Doctor_DMS:_an_Open-source_Markdown_Document_Server⠀⇛ Doctor is an open-source, free documentation server for all your project docs. It is built to aid developers creating a complex documentation website just by using Markdown text. o ⚓ Medevel ☛ GeoServer_GeoServer_is_an_Open-source_Geospatial Server⠀⇛ GeoServer is an open source software server written in Java that allows users to share and edit geospatial data. Designed for interoperability, it publishes data from any major spatial data source using open standards. Being a community-driven project, GeoServer is developed, tested, and supported by a diverse group of individuals and organizations from around the world. GeoServer is the reference implementation of the Open Geospatial Consortium (OGC) Web Feature Service (WFS) and Web Coverage Service (WCS) standards, as well as a high performance certified compliant Web Map Service (WMS), compliant Catalog Service for the Web (CSW) and implementing Web Processing Service (WPS). GeoServer forms a core component of the Geospatial Web. o ⚓ 3_Advantages_of_Participating_in_Open_Source_Projects⠀⇛ Open-source software (OSS) is more of a household name in 2022 than ever before. Consumers – i.e., those not in tech – are exposed to OSS with more regularity via content management systems, like Drupal, and car, laptop and smartwatch uses supported by Linux. But once you dive into the technology community, specifically the community of the developer, the value of OSS is undeniable. Developers and engineers love the web, want it to succeed, and have a vested interest in building technologies that serve their community’s goals. OSS projects span a wide list of technology development today from analytics to development and DevOps, to machine learning, website development, and more. In understanding the breadth of development, what exactly is the draw to contribute to the broad community? In other words, what are the advantages of participating in open source projects? o ⚓ Down_in_the_Goldman_Sachs_IT_engine_room,_old_school_and_open source_rub_shoulders⠀⇛ In an overlooked yet insightful blog the bank recently detailed the critical OSS tool it has deployed to help tackle query latency. (Goldman Sachs has also spun up a range of its own open source tools like database deployment software Obevo, open sourced under an Apache 2.0 license in 2017 to help developers manage database schema definitions for new and existing sytems under a a standard software development lifecycle or SDLC approach.) o ⚓ TechCrunch ☛ Iterative_launches_MLEM,_an_open-source_tool_to simplify_ML_model_deployment⠀⇛ o § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Mozilla ☛ Mozilla_Performance_Blog:_Prioritized_Task Scheduling_API_is_Prototyped_in_Nightly⠀⇛ In bug 1734997, we prototyped the Prioritized Task Scheduling API. Having the API prototyped empowers us to experiment with the benefits of this API. It is enabled by default in Nightly at the moment. # ⚓ Firefox_Nightly:_These_Weeks_In_Firefox:_Issue_117⠀⇛ Firefox 101 releases today! Here are the release notes. # ⚓ Enable_VA-API_by_default_in_nightly⠀⇛ # ⚓ LWN ☛ Mozilla_releases_a_machine-translation_plugin_ [LWN.net]⠀⇛ Mozilla has announced the release of a translation plugin for Firefox as part of the Project Bergamot initiative. o § FSFE⠀➾ # ⚓ FSFE ☛ German_administration_is_re@di_for_the_use_of_Free Software⠀⇛ A network of nine cities in Germany shows the benefits of ‚Public Money? Public Code!‘ 2020, in the midst of the corona pandemic, the city of Bühl launched a video conferencing platform called “Palim! Palim!”, which is based on the Free Software “Jitsi Meet”. Based on the need of the municipal music school to be able to continue to offer group lessons in times of pandemic, the city offered the platform. * § Leftovers⠀➾ o § Hardware⠀➾ # ⚓ PC Mag ☛ The_20_Most_Influential_PCs_of_the_Past_40_Years_| PCMag⠀⇛ Yes, we know: The first entry in this list is a cheat, as the IBM PC (released in August 1981) predates our first issue (February/March 1982). We also know the IBM PC was no more the first personal computer than ours was the first computer magazine—the MITS Altair 8800 kit reached hobbyists in 1975, with the Apple II narrowly beating the Radio Shack TRS-80 to market in 1977. PC Magazine didn’t cover 8-bit platforms, which is why you also won’t find the Commodore 64 in this list. o § Linux Foundation⠀➾ # ⚓ Linux Foundation’s Site/Blog ☛ Why_Do_Enterprises_Use_and Contribute_to_Open_Source_Software⠀⇛ When people find out I work at the Linux Foundation they invariably ask what we do? Sometimes it is couched around the question, As in the Linux operating system? I explain open source software and try to capture the worldwide impact into 20 seconds before I lose their attention. If they happen to stick around for more, we often dig into the question, Why would enterprises want to participate in open source software projects or use open source software? The reality is – they do, whether they know it or not. And the reality is thousands of companies donate their code to open source projects and invest time and resources helping to further develop and improve open source software. o § Security⠀➾ # ⚓ USCERT ☛ CISA_Releases_Security_Advisory_on_Illumina_Local Run_Manager⠀⇛ CISA has released an Industrial Controls Systems Advisory (ICSA) detailing multiple vulnerabilities in Illumina Local Run Manager. Successful exploitation of these vulnerabilities may allow an unauthenticated malicious actor to take control of the affected product remotely and take any action at the operating system level. These vulnerabilities could impact settings, configurations, software, or data on the affected product and interact through the affected product with the connected network. # ⚓ Hacker News ☛ Attackers_Can_Use_Electromagnetic_Signals_to Control_Touchscreens_Remotely⠀⇛ Researchers have demonstrated what they call the “first active contactless attack against capacitive touchscreens.” GhostTouch, as it’s called, “uses electromagnetic interference (EMI) to inject fake touch points into a touchscreen without the need to physically touch it,” a group of academics from Zhejiang University and Technical University of Darmstadt said in a new research paper. # ⚓ USENIX ☛ GhostTouch:_Targeted_Attacks_on_Touchscreens without_Physical_Touch⠀⇛ Capacitive touchscreens have become the primary human-machine interface for personal devices such as smartphones and tablets. In this paper, we present GhostTouch, the first active contactless attack against capacitive touchscreens. GhostTouch uses electromagnetic interference (EMI) to inject fake touch points into a touchscreen without the need to physically touch it. By tuning the parameters of the electromagnetic signal and adjusting the antenna, we can inject two types of basic touch events, taps and swipes, into targeted locations of the touchscreen and control them to manipulate the underlying device. We successfully launch the GhostTouch attacks on nine smartphone models. We can inject targeted taps continuously with a standard deviation of as low as 14.6 x 19.2 pixels from the target area, a delay of less than 0.5s and a distance of up to 40mm. We show the real-world impact of the GhostTouch attacks in a few proof-of-concept scenarios, including answering an eavesdropping phone call, pressing the button, swiping up to unlock, and entering a password. Finally, we discuss potential hardware and software countermeasures to mitigate the attack. # ⚓ Red Hat Official ☛ Command_Line_Heroes:_Season_9:_All Together_Now⠀⇛ For InfoSec professionals, sharing information is vital for shedding light on security vulnerabilities and cyber attacks. But it wasn’t always the norm. It took SATAN, an infamous vulnerability scanning tool, to create that cultural shift. # ⚓ CISA ☛ Atlassian_Releases_Security_Updates_for_Confluence Server_and_Data_Center,_CVE-2022-26134_|_CISA⠀⇛ Atlassian has released a security advisory to address a remote code execution vulnerability (CVE- 2022-26134) affecting Confluence Server and Data Center products. An unauthenticated remote attacker could exploit this vulnerability to execute code remotely. Atlassian reports that there is known exploitation of this vulnerability. # ⚓ USCERT ☛ CISA_Adds_One_Known_Exploited_Vulnerability_(CVE- 2022-26134)_to_Catalog [Ed: About half of the latest actively-exploited critical issues are Microsoft; CISA doesn't call out Microsoft on it]⠀⇛ CISA has added one new vulnerability—CVE-2022- 26134—to its Known Exploited Vulnerabilities Catalog, based on evidence of active exploitation. These types of vulnerabilities are a frequent attack vector for malicious cyber actors and pose significant risk to the federal enterprise. Note: to view the newly added vulnerabilities in the catalog, click on the arrow on the of the “Date Added to Catalog” column, which will sort by descending dates.   There are currently no updates available. Atlassian is working to issue an update. Per BOD 22-01 Catalog of Known Exploited Vulnerabilities, federal agencies are required to immediately block all internet traffic to and from Atlassian’s Confluence Server and Data Center products until an update is available and successfully applied. # ⚓ Bleeping Computer ☛ Microsoft_shares_mitigation_for_Office zero-day_exploited_in_attacks [Ed: Even Microsoft boosters cannot deny that the worst threats come from using Microsoft]⠀⇛ Microsoft has shared mitigation measures to block attacks exploiting a newly discovered Microsoft Office zero-day flaw abused in the wild to execute malicious code remotely. The bug, described by Redmond as a Microsoft Windows Support Diagnostic Tool (MSDT) remote code execution vulnerability and tracked as CVE-2022- 30190, was reported by crazyman of the Shadow Chaser Group. # ⚓ Naked Security ☛ Firefox_101_is_out,_this_time_with_no_0- day_scares_(but_update_anyway!)_–_Naked_Security⠀⇛ The latest scheduled Firefox update is out, bringing the popular alternative browser to version 101.0. This follows an intriguing month of Firefox 100 releases, with Firefox 100.0 arriving, as did Chromium 100 a month or so before it, without any trouble caused by the shift from a two-digit to a three-digit version number. o § Finance⠀➾ # ⚓ ALM ☛ Another_State_Appellate_Court_Nixes_a_COVID-19 Business_Interruption_Claim_|_Law.com⠀⇛ The Court of Special Appeals of Maryland, the state’s intermediate appellate court, fell in line with several recent state and federal appellate court rulings, unanimously upholding a lower court’s decision that a restaurant’s losses resulting from COVID-19 shutdown orders aren’t recoverable under its business interruption insurance policy. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Refugee_incoming_from_corpweb.⠀⇛ Corporations sucked all the fun out of the net without me really noticing. I vaguely remember posts on Digg, then old Reddit warning the web would be taken over, filled with banner ads, controlled by massive corporations. Then it happened, we are living it. # ⚓ AccessNow ☛ Internet_shutdown_types_and_taxonomy:_tech behind_network_interference⠀⇛ Network interferences are impacting the lives of billions of people around the world. Different types of deliberate internet shutdowns can block the free press and access to life-saving information, undermine democratic elections and facilitate coups, and even hide war crimes and genocide, among other devastating impacts. What is less well understood is how perpetrators, typically governments, technically implement them. That matters because it affects our capacity to fight back. Our new paper, A taxonomy of internet shutdowns: the technologies behind network interference, scrutinizes eight internet shutdown types and helps technologists and digital help desk practitioners better understand, prepare for, circumvent, and document the shutdown of networks. o § Monopolies⠀➾ # ⚓ Canada’s_Online_News_Act_threatens_information-sharing,_the online_ecosystem,_and_international_trade_–_Disruptive Competition_Project⠀⇛ On April 5th, Canadian Heritage Minister Pablo Rodriguez introduced Bill C-18, “An Act respecting online communications platforms that make news content available to persons in Canada”. The bill, dubbed the Online News Act, “regulates digital news intermediaries to enhance fairness in the Canadian digital news marketplace and contribute to its sustainability” by establishing “a framework through which digital news intermediary operators and news businesses may enter into agreements respecting news content that is made available by digital news intermediaries.” In a nutshell, this law forces digital news intermediaries, defined as any online communications platform “that makes news content produced by news outlets available to persons in Canada”, into negotiation with Canadian news companies to make those intermediaries pay to carry news content or any portion thereof (including audio, video, and seemingly mere hyperlinks) onto the intermediary’s platform. In its definitions section, the bill states that news content is made available if “(a) the news content, or any portion of it, is reproduced; or (b) access to the news content, or any portion of it, is facilitated by any means, including an index, aggregation or ranking of news content”. This Canadian policy tracks closely with the recent Australian framework on news media. Like its Australian counterpart, which Project DisCo has extensively covered, the following will focus on four aspects of the Canadian legislation: procedural concerns, changes to the competitive landscape, trade harms, and copyright and related concerns. First regarding procedure, the Online News Act requires the Canadian Radio-television and Telecommunications Commission (CRTC) to maintain a list of digital news intermediaries to whom this new enactment applies, giving certain intermediaries exemptions if they already have agreements with news businesses that satisfy certain vague criteria, such as providing for fair compensation, ensuring an “appropriate” portion of the money is used to support local, regional, and national content, and not allowing “corporate influence to undermine the freedom of expression and journalistic independence” (as phrased by its section 11). As was the case with the Australian law, the Canadian bill “authorizes the Governor in Council to make regulations respecting how the Commission is to interpret those criteria and setting out additional conditions with respect to the eligibility of a digital news intermediary for an exemption” (Summary-F). In other words, the CRTC and the government are given unilateral power to determine which companies may be exempted from this bill, and those who must follow it. # § Copyrights⠀➾ # ⚓ DJ_Vole’s_Week-End_June_3,_2022⠀⇛ Playlists for this show are available on Gemini protocol at n n i x dot com, that’s november november india x-ray dot com. ䷩ 𝚕𝚒𝚗𝚎 7868 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_02/06/2022:_Godot_4.0_Alpha_9_and_GNOME_42.2_Release⠀✐ Posted in News_Roundup at 1:02 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Server o Instructionals/Technical o Games o Desktop_Environments/WMs # GNOME_Desktop/GTK * Distributions_and_Operating_Systems o Fedora_Family_/_IBM o Devices/Embedded o Mobile_Systems/Mobile_Applications * Free,_Libre,_and_Open_Source_Software o Web_Browsers # Mozilla o Programming/Development * Leftovers o Hardware o Health/Nutrition/Agriculture o Proprietary o Security # Privacy/Surveillance o Defence/Aggression o Transparency/Investigative_Reporting o Environment # Energy # Wildlife/Nature o Finance o AstroTurf/Lobbying/Politics o Civil_Rights/Policing o Internet_Policy/Net_Neutrality o Digital_Restrictions_(DRM) o Monopolies # Copyrights * § GNU/Linux⠀➾ o § Server⠀➾ # ⚓ Kubernetes Blog ☛ Kubernetes:_Annual_Report_Summary_2021⠀⇛ Last year, we published our first Annual Report Summary for 2020 and it’s already time for our second edition! 2021 Annual Report Summary This summary reflects the work that has been done in 2021 and the initiatives on deck for the rest of 2022. Please forward to organizations and indidviduals participating in upstream activities, planning cloud native strategies, and/or those looking to help out. To find a specific community group’s complete report, go to the kubernetes/ community repo under the groups folder. Example: sig-api-machinery/annual-report-2021.md o § Instructionals/Technical⠀➾ # ⚓ TecAdmin ☛ How_to_Delete_Let’s_Encrypt_Certificate_using Certbot_–_TecAdmin⠀⇛ Certbot is a free and open-source software tool used for managing the Let’s Encrypt certificates. This tool allows users to issue certificates in a single command and also configure the web servers. The default certbot stores all the client certificates under the below-mentioned directories. We are not recommending you delete files manually. In this tutorial, we will discuss deleting unused SSL certificates using the Certbot command line. # ⚓ ID Root ☛ How_To_Install_Gitea_on_Ubuntu_22.04_LTS_– idroot⠀⇛ In this tutorial, we will show you how to install Gitea on Ubuntu 22.04 LTS. For those of you who didn’t know, Gitea is a free and open-source version control system similar to GitHub. However, it is more straightforward, lightweight, and easy to configure as compared to GitLab. One can use it across any major OS like Linux, Windows, macOS, etc. 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 Gitea open-source version control system on Ubuntu 22.04 (Jammy Jellyfish). You can follow the same instructions for Ubuntu 22.04 and any other Debian-based distribution like Linux Mint, Elementary OS, Pop!_OS, and more as well. # ⚓ ID Root ☛ How_To_Install_Git_on_AlmaLinux_9_–_idroot⠀⇛ In this tutorial, we will show you how to install Git on AlmaLinux 9. For those of you who didn’t know, Git is an open-source and popular tool control system, mainly used by programmers to issue changes to applications and keep track of the revisions. Git enables both local and collaborative history tracking. The benefit of collaborative history tracking is that it documents not just the change itself but the who, what, when, and why behind the change. When collaborating, changes made by different contributors can later be merged back into a unified body of work. 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 Git on AlmaLinux 9. You can follow the same instructions for CentOS and Rocky Linux. # ⚓ Run_10_curl_commands_in_parallel_via_xargs⠀⇛ # ⚓ Run_10_curl_commands_in_parallel_via_xargs_(v2,_faster_then v1)⠀⇛ # ⚓ Cloudbooklet ☛ How_to_Install_Elasticsearch_on_Ubuntu_22.04 with_SSL⠀⇛ How to Install Elasticsearch on Ubuntu 22.04 with SSL. Elasticsearch 8 is a powerful scalable real time distributed search and data analysis. Here you will learn how to configure SSL to your Elasticsearch installation with Nginx reverse proxy on Ubuntu 22.04. You will create a subdomain for your Elasticsearch service and install free Let’s Encrypt SSL certificate using Certbot. This setup is tested on Google Cloud Platform running Ubuntu 22.04 LTS. So this guide will work perfect on other cloud service providers like AWS, Azure or any VPS or dedicated servers. # ⚓ TecMint ☛ Install_Nagios_Core_on_openSUSE_15.3_Linux⠀⇛ Nagios is an open-source, industry-leading, and enterprise-grade monitoring tool that you can use to keep an eye on most if not all aspects of your IT infrastructure including networks, hosts (and their resources), services, as well as applications. It is a powerful and feature-packed system that helps technical personnel in an organization to quickly identify and resolve IT infrastructure issues before they affect critical business processes. Some of its key features are an extendable architecture – extensible using community offered or custom-built add-ons (made possible by the availability of powerful APIs), an alert engine for issue reporting, and advanced reporting (that provides records of alerts, notifications, outages, and alert response). # ⚓ Firefox_CPU_management⠀⇛ As many of you, I’m struggling to keep my browsing experience as CPU efficient as possible. The modern web makes this near impossible. It’s silly, but with both chromium and FF I need to keep ‘task manager’ on a second monitor open at all times. Because there’s usually a site or two that are eating the CPU for breakfast. Modern computing is simply draining your attention reserves because you are dual tasking between doing the task you want to do and babysitting task manager. If you have a powerful laptop, the fans will let you know when a site is misbehaving. That’s the sign to go check task manager. So is life. (if anyone has any solutions for this, do let me know! –disabling JS??) o § Games⠀➾ # ⚓ GamingOnLinux ☛ Monster_Boy_and_the_Cursed_Kingdom_gets_a Steam_Deck_update⠀⇛ Monster Boy and the Cursed Kingdom from Game Atelier and DG Entertainment recently gained a small but sweet update to improve gameplay on the Steam Deck. # ⚓ GamingOnLinux ☛ Try_out_the_demo_for_Ragtag_Crew,_a_turn- based_tactical_rogue-lite⠀⇛ With a demo arriving as part of the DreamHack Beyond event, Ragtag Crew seems like a promising upcoming turn-based tactical rogue-lite to sink your teeth into. # ⚓ GamingOnLinux ☛ Valve_delay_the_Steam_Deck_Docking Station⠀⇛ In a move that’s not exactly unexpected, Valve has now delayed the launch of the official Steam Deck Docking Station. # ⚓ GamingOnLinux ☛ Steam_Client_Update_released_with_Remote Play_improvements⠀⇛ Valve has released a small update to the stable version of the Steam Client, with it mostly being about fixing up Remote Play. It’s not a big surprise to see the focus on Remote Play right now with the Steam Deck, especially with the SteamOS 3.2 update bringing full Remote Play Together compatibility for the Deck too. # ⚓ GamingOnLinux ☛ Prison_Architect_–_Gangs_DLC_and_free_Kite update_announced⠀⇛ Paradox and Double Eleven have announced the Prison Architect: Gangs expansion, along with the free Kite update. Here’s what to expect from it. # ⚓ GamingOnLinux ☛ Golfie_mixes_together_minigolf_with_a_deck- builder⠀⇛ We’ve seen a few attempts to spice-up Golf like Golf with Your Friends which is great but how about blending it together with a deck-building card game? Golfie is the answer to that. Note: key provided for me. It works out of the box on Linux desktop and the Steam Deck, thanks to Steam Play Proton. # ⚓ ‘V_Rising’_comes_to_Linux_and_Steam_Deck_as_it_sells_a million_copies⠀⇛ V Rising is now playable on Linux and Steam Deck consoles, while developer Stunlock Studios has announced the vampire survival game has sold 1million copies. # ⚓ Godot Engine ☛ Godot_Engine_–_Dev_snapshot:_Godot_4.0_alpha 9⠀⇛ Another fortnight, another alpha snapshot of the development branch, this time with 4.0 alpha 8! It includes notably Text-to-Speech support on all platforms (as a feature for games/applications, the Godot editor itself doesn’t make use of it for now), and a refactoring of the module/extension initialization levels to allow more flexibility for third-party code. See past alpha releases for details (alpha 1, 2, 3, 4, 5, 6, 7, 8). Be aware that during the alpha stage the engine is still not feature-complete or stable. There will likely be breaking changes between this release and the first beta release. Only the beta will mark the so-called “feature freeze”. As such, we do not recommend porting existing projects to this and other upcoming alpha releases unless you are prepared to do it again to fix future incompatibilities. However, if you can port some existing projects and demos to the new version, that may provide a lot of useful information about critical issues still left to fix. Most importantly: Make backups before opening any existing project in Godot 4.0 alpha builds. There is no easy way back once a project has been (partially) converted. o § Desktop Environments/WMs⠀➾ # § GNOME Desktop/GTK⠀➾ # ⚓ 9to5Linux ☛ GNOME_42.2_Release_Improves_Support_for Flatpak_and_Snap_Apps,_Fixes_Many_Bugs⠀⇛ Coming a little over a month after GNOME 42.1, the GNOME 42.2 point release is here with more bug fixes and other changes to make your GNOME desktop experience more stable, secure, reliable, and ultimately enjoyable. This second point release in the GNOME 42 desktop environment series fixes focus tracking in Magnifier on Wayland, fixes on- screen keyboard gestures, addresses an issue with the top bar menus on the lock screen, and aligns space-padded times in world clocks in GNOME Shell. * § Distributions and Operating Systems⠀➾ o § Fedora Family / IBM⠀➾ # ⚓ Fedora Project ☛ Fedora_Community_Blog:_We_want_to_hear from_you:_take_the_Fedora_Annual_Contributor_Survey_for 2022!⠀⇛ The Fedora Council wants to hear what you have to say! Like last year, the goal of this survey is to collect valuable feedback to provide the right support for our Fedora community. We will evaluate the gathered information and discuss them at Nest with Fedora 2022. We are excited to have another set of data so we can run a comparative analysis and understand changes in the Fedora community over the last year. The survey will be open for all of June, and you will have the opportunity to earn a fun Fedora Badge. Take this year’s Annual Contributor Survey today! # ⚓ Madeline_Peck:_Fedora_37_Wallpaper⠀⇛ We are officially in the process of working on Fedora 37 wallpaper! Our candidate with an L last name has been chosen and it’s Hedy Lamarr!!! # ⚓ Red Hat ☛ Use_compiler_flags_for_stack_protection_in_GCC and_Clang_|_Red_Hat_Developer⠀⇛ Smash-stacking attacks are common, but the GCC and Clang compilers have a number of flags that can help defend against them. Read on for more info. # ⚓ Red Hat ☛ How_to_create_Kafka_consumers_and_producers_in Java⠀⇛ Kafka has emerged as one of the more popular open source technologies for powering message-driven applications at web scale. It can handle hundreds of thousands, if not millions of messages a second. And, it will store any message it receives for a configurable amount of time, whether the message is consumed or not. That timespan can be weeks, or it can be years. These capabilities alone make Kafka a very powerful technology. Yet, while Kafka is powerful, it is also complex. There are many moving parts that need to be accounted for. Fortunately, there are client libraries written in a variety of languages that abstract away much of the complexity that comes with programming Kafka. One of the more popular libraries is the one written for Java, which is published as the Apache Kafka Clients. The Java client libraries for Kafka streamline a lot of the work that goes into producing messages to and consuming messages from Kafka brokers. But they are not magical. You need to know a thing or two in order to use them effectively. Java is an object-oriented programming (OOP) language, which means there’s a bit more to understand, particularly if you are new to OOP. # ⚓ Phoronix ☛ Red_Hat_Experimenting_With_“NVK”_Nouveau_Open- Source_Vulkan_Driver⠀⇛ # ⚓ Enterprisers Project ☛ Welcome_back_boomerangs:_6_tips_for a_smooth_transition⠀⇛ In the past, leaving one’s employer was considered the final goodbye. Not anymore. Given today’s tight labor market, companies are now welcoming back former employees – known as boomerangs – with open arms. It can be unclear how to integrate these employees into your organization. They usually know more about the inner workings than new hires, but they will still need direction to assimilate seamlessly back into the company. # ⚓ The Register UK ☛ IBM’s_self-sailing_Mayflower_suffers another_fault_in_Atlantic_crossing_bid⠀⇛ No, this isn’t deja vu. IBM’s self-sailing Mayflower ship, tasked with making it across the Atlantic without any humans onboard to help, has suffered another mechanical glitch preventing it from continuing its intended journey. Named after the vessel that brought passengers from England to America in the 17th century, the Mayflower Autonomous Ship (MAS) was expected to retrace that historical voyage. But its attempts to cross the ocean, led by ProMare – a non-profit organization focused on marine research, with support from IBM – haven’t exactly gone smoothly. o § Devices/Embedded⠀➾ # ⚓ CNX Software ☛ NanoPi_R5S_router_review_–_Part_1:_Unboxing, OpenWrt,_and_iperf3_benchmarking⠀⇛ FriendlyElec has just launched the NanoPi R5S mini router powered by a Rockchip RK3568 processor, and the company kindly sent me two samples for review. In the first part of the review, I’ll check out the device itself, the internal design, the preinstalled OpenWrt, and run some networking benchmarks with iperf3. The router comes fully assembled together with a 3M sheet with 6 rubber feet, which, as we’ll see below, are not really necessary. # ⚓ Linux Gizmos ☛ IBASE_CMI211-989_houses_Ryzen_V2000_based Mini-ITX_w/_quad_DP_displays⠀⇛ IBASE Technology has launched an expandable embedded system that integrates their own MI989 Mini-ITX motherboard. The processor featured on this device is the AMD Ryzen Embedded V2000 (up to 4.15GHz) which is designed using the Zen 2 x86 core architecture (7nm process). Last year, LinuxGizmos made an article about the MI989 Mini-ITX from IBASE which can be found here for additional details. Other notable features of the CMI211-989 include, up to 64GB DDR3, quad DisplayPort, dual Gigabit ethernet ports, triple USB 3.1 Gen2, one M.2, and PCIe x16 interface. # ⚓ Raspberry Pi ☛ Join_us_at_the_launch_event_of_the_Raspberry Pi_Computing_Education_Research_Centre⠀⇛ Last summer, the Raspberry Pi Foundation and the University of Cambridge Department of Computer Science and Technology created a new research centre focusing on computing education research for young people in both formal and non-formal education. The Raspberry Pi Computing Education Research Centre is an exciting venture through which we aim to deliver a step-change for the field. # ⚓ Techdirt ☛ John_Deere_Still_Sucks_On_‘Right_To_Repair,’ Despite_Years_Of_Promises⠀⇛ Not only have corporate efforts to monopolize repair resulted in a flood of proposed state and federal laws, the Biden Administration’s recent executive order on monopoly power and competition urged the FTC to tighten up its rules on repair monopolization efforts, whether it’s ham- fisted DRM, or making repair manuals, parts, and diagnostics hard to come by. o § Mobile Systems/Mobile Applications⠀➾ # ⚓ Hacker News ☛ Critical_UNISOC_Chip_Vulnerability_Affects Millions_of_Android_Smartphones⠀⇛ # ⚓ Notebook Check ☛ Early_Xiaomi_Android_13_update_list includes_the_Xiaomi_12,_Xiaomi_Pad_5,_Redmi_Note_11_series and_a_host_of_other_models_–_NotebookCheck.net_News⠀⇛ # ⚓ How_To_Bypass_Google_Account_Verification_After_Android Smartphone_Reset_–_Phandroid⠀⇛ # ⚓ How_to_fill_and_sign_PDF_documents_on_Android_–_Phandroid⠀⇛ * § Free, Libre, and Open Source Software⠀➾ o § Web Browsers⠀➾ # ⚓ A_Reader_Friendly_Browser⠀⇛ As a user of the web I spend a lot of my time either disappointed or frustrated with sites I visit. After watching a movie I might hop over to the relevant Fandom page to learn about a character but instead get an irrelevant video taking up the entire screen. # § Mozilla⠀➾ # ⚓ 9to5Linux ☛ Firefox_102_Enters_Beta_Testing_with Geoclue_Support_on_Linux,_Improved_PDF_Reading⠀⇛ For Linux users, Firefox 102 appears to add support for Geoclue, a D-Bus service that provides location information, which Mozilla will use in Firefox 102 to provide geolocation services when needed by certain websites. Other than that, Firefox 102 looks to improve PDF reading in High Contrast mode, adds support for filtering style sheets in the Style Editor tab of the developer tools, and implements a new enterprise policy. o § Programming/Development⠀➾ # ⚓ Hackaday ☛ Building_Faster_Rsync_From_Scratch_In_Go⠀⇛ For a quick file transfer between two computers, SCP is a fine program to use. For more complex, large, or regular backups, however, the go-to tool is rsync. It’s faster, more efficient, and usable in a wider range of circumstances. For all its perks, [Michael Stapelberg] felt that it had one major weakness: it is a tool written in C. [Michael] is philosophically opposed to programs written in C, so he set out to implement rsync from scratch in Go instead. * § Leftovers⠀➾ o ⚓ Counter Punch ☛ The_Story_Of_Sly_and_the_Family_Stone⠀⇛ o ⚓ The Nation ☛ Illusions⠀⇛ The third season of HBO’s My Brilliant Friend opens where the second left off, in a bookshop in Milan. It’s 1968, and Elena “Lenù” Greco (Margherita Mazzucco) has just finished an event for her debut novel. The first face we see, emerging from behind a gold metalwork spiral on the door, is that of Nino Sarratore (Francesco Serpico). Lenù has loved him since she was a girl, and now, after many twists and turns, including Nino’s tortured affair with her best friend, Lila (Gaia Gerace), he finally seems ready. He holds the gilded door open for Lenù, and he holds her gaze in the crowd. These two working-class kids from Naples have made it in the cultured North; with their matching glasses, they’re practically made for each other. Too bad she’s already engaged to Pietro Airota (Matteo Cecchi), a classics scholar from one of the preeminent left-wing families in Italy. o ⚓ The Nation ☛ The_Stalwart⠀⇛ Hubert Harrison represents one of the clearest examples of the difficulties of being a Black intellectual and activist in the 20th century. Upon his death in 1927, Harrison was recognized in many magazines and journals for the prominent role he’d played in this country’s socialist and Black radical politics. As someone who’d organized a number of advocacy groups, as well as edited Negro World for Marcus Garvey’s Universal Negro o ⚓ Meduza ☛ ‘Gnarled_and_stunted_and_wrong’:_How_a_renowned_film director_sunk_over_$100_million_in_government_loans_on_a_bizarre box_office_flop⠀⇛ In the late 2000s, Andrey Konchalovsky released his most ambitious project yet: a large-scale movie version of The Nutcracker, with Hollywood actors and cutting edge graphics. He got funding for the film from Vnesheconombank (VEB), Russia’s state development corporation — but the film was a box office bust, leaving him unable to pay back the money. A new investigation by Transparency International Russia found that Konchalovsky owes VEB almost $130 million — roughly equivalent to Russia’s entire state film production budget for 2021. Below, Meduza is publishing a translation of Transparency International Russia analyst Lizaveta Tsybulina’s report, which tells how the Nutcracker money ended up in Konchalovsky’s offshore account — and how VEB is trying to get it back. o ⚓ Re:_I’m_moving_to_the_country⠀⇛ youtube vids on that, seems to be reasonably logical! Next week our old house in Canberra goes to auction, it has been magnificently refurbished and looks amazing. Real estate agents are confident we’ll get the number we need for us and the refurb company to be happy, so that’s something! When that sells, I’ll be able to commit to getting our electrical system refreshed in the new house, want to get some cat6 run around, and a PV solar and Battery system, integrated with our electric car charger and with some sort of grid disconnect, but have to wait to see how much we can spend! o ⚓ The_Hitchhiker’s_Guide_to_the_Galaxy⠀⇛ I was still going to school when I came across Douglas Adams through radio plays. And apparently, this is how the increasingly inaccurately numbered trilogy came to be. But that is not so important. What is important in my humble opinion is the amalgam of absurd or apparently absurd ideas all mixed together. And even as a scientist by education I can enjoy reading the countless episodes of “impossible” things, which in the end are far to plausible to be truely impossible. I agree, that if you come home now from a few years of space-time travel, people will not believe you anyway. o ⚓ New_Ribbon:_Black_and_White⠀⇛ matto has a new and shiny capsule running on a beaglebone black, using vger and ed. Yay, that is indeed smol computing. o ⚓ Counter Punch ☛ The_Ukrainian_Childhood_of_Writer_Irène Némirovsky⠀⇛ That Ukrainian girl, named Irina Nemirovskaia, looks at the whiteness of the landscape and thinks of the elegant district of Kiev where she lives, a stone’s throw away from the imperial palaces. From her balcony, she would look out over the countless city parks that descended the hill in successive terraces until they reached the river. In summer she would accompany her beloved father on cruises on the Dnieper. At night they would let themselves be rocked by the waves, by day they would visit villages where her father had business dealings with Ukrainian landowners. To Irina, that rural world seemed neglected and reminded her of the descriptions of landscapes and villages she read in Gogol’s books Taras Bulba and Evenings on a Farm Near Dikanka. Gogol was her favorite Ukrainian writer. The rest of the summer she would walk through her sunny Kyiv swept by the Caucasus wind: with her French governess she would climb the steep streets, walk along the boulevards sheltered by rows of linden and chestnut trees that protected her eyes from the brightness of the golden domes of the churches. From the Orient Express the girl looks out over the winter plain and remembers the recent New Year’s celebration in Odessa. Her grandmother prepared delicious salmon, caviar, pasta and pickle zakuski, which everyone washed down with champagne, and even Irina tried a few sips. In Odessa, every morning she used to walk with her grandfather down to the bustling port through the huge, icy staircase that she would later recognize in Sergey Eisenstein’s film Battleship Potemkin. o ⚓ June_update_2022⠀⇛ Waiting for some paperwork and burocracy to get resolved, until then I can’t really travel anywhere so this is a bummer because I need to make plans to go to HOPE in NY end of July and visit friends and hackers in the US. o § Hardware⠀➾ # ⚓ Hackaday ☛ Alternative_Display_Technologies_And_Where_To Find_Them⠀⇛ [Blair Nearl] has been working on an information database for artists and hackers – a collection of non-conventional display technologies available to us. We’ve covered this repository before, six years ago – since then, it’s moved to a more suitable platform, almost doubled in size, and currently covers over 40+ display technology types and related tricks. This database is something you should check out even if you’re not looking for a new way to display things right now, however, for its sheer educational and entertainment value alone. # ⚓ Hackaday ☛ New_Resin_Printing_Method_Creates_Objects_In Seconds⠀⇛ For anyone looking to buy a 3D printer at home, the first major decision that needs to be made is whether to get a resin printer or a filament printer. Resin has the benefits of finer detail, but filament printers are typically able to produce stronger prints. Within those two main camps are various different types and sizes to choose from, but thanks to some researchers at Switzerland’s École polytechnique fédérale de Lausanne (EPFL) there’s a new type of resin printer on the horizon that can produce prints nearly instantaneously. # ⚓ Hackaday ☛ Bulk_Material_—_What_IS_This_Stuff,_Anyway?⠀⇛ I hope last week’s introduction to bulk material handling got you all thinking up amazing hacks, and we’ll soon be reporting on DIY Cap’n Crunch Robots galore. This week we’ll look at how to measure particle sizes, separate particles, and even grind them up when you need to. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Counter Punch ☛ Marijuana:_John_Carney_and_Delaware’s_Law Enforcement_Lobby_versus_“The_Children”⠀⇛ Carney’s justification: “I do not believe that promoting or expanding the use of recreational marijuana is in the best interests of the state of Delaware, especially our young people.” Yep. Even though the bill applies only to those over 21 years of age, Carney felt compelled to play “for the chilllllllllldren” card. # ⚓ Counter Punch ☛ After_the_Meltdown:_the_Health_Risks_of Nuclear_Reactors_in_War_Zones⠀⇛ Media articles often dwell on the conditions that could spark a meltdown, but attention should also be paid to the possible human health consequences. We answer some questions about the short-term and long-term consequences for human health of a radiological disaster at a nuclear power plant. What happens at a reactor during a major nuclear power disaster? # ⚓ Common Dreams ☛ ‘A_Gift_to_McConnell’:_Biden_HHS_Won’t Reverse_Medicare_Premium_Hike_This_Year⠀⇛ The Biden administration quietly announced last week that it will leave in place one of the largest-ever Medicare premium hikes for the remainder of 2022, despite federal health officials’ decision to restrict coverage of the expensive and potentially ineffective Alzheimer’s drug that drove the increase. Progressive healthcare advocates responded with outrage to the administration’s Friday announcement, warning that it will inflict entirely avoidable financial pain on vulnerable seniors and hand the GOP an effective talking point heading into the November midterms. # ⚓ Orac ☛ ABIM_vs._medical_disinformation:_A_day_late_and_a dollar_short_or_better_late_than_never?⠀⇛ Over its 14 years of existence, one of the core messages of Science-Based Medicine has been very consistent. We have bemoaned how easily doctors who are quacks, antivaxxers, and grifters not only manage to avoid professional penalties and keep their medical licenses and board certifications, but often to keep practicing more or less unimpeded by either state medical boards or the private boards that certify them in their chosen medical specialties. Flowing from this dismay, we have also advocated for change to empower state medical boards and specialty boards to hold doctors accountable for professional misdeeds, up to and including being able to revoke their medical licenses and board certifications. After all, without a medical license, a physician cannot practice, and without a board certification it is very difficult to practice, as Medicare and Medicaid, as well as most insurance companies, require it to reimburse a physician, and most hospitals require it to grant privileges. One has only to consider the example of Texas cancer quack Stanislaw Burzynski, who “discovered” antineoplastons in the early 1970s and has been charging large consultation fees to administer them since the late 1970s to treat cancer patients despite no good evidence that they are effective. Over the more than 40 years of having plied his quackery on cancer patients, Dr. Burzynski had managed to avoid significant sanctions from the Texas Medical Board (most recently in 2017) and the FDA for his “clinical trials” that were designed primarily as marketing tools to let him keep using antineoplastons rather than actual clinical trials to determine if antineoplastons work. So it was with great interest that I encountered an op-ed in The New England Journal of Medicine by the President and CEO of the American Board of Internal Medicine (ABIM) Richard J. Baron, MD, and the chair of its board of directors, Yul D. Ejnes, MD, titled “Physicians Spreading Misinformation on Social Media — Do Right and Wrong Answers Still Exist in Medicine?” Obviously, I think you know how I will answer, but first let me start with a little context. # ⚓ TruthOut ☛ Right-Wing_Dark_Money_Is_Coming_for_Reproductive Rights_in_Your_State⠀⇛ # ⚓ TruthOut ☛ GOP_Is_Already_Dropping_Abortion_Exceptions_for Rape,_Incest_and_Risk_to_Life⠀⇛ # ⚓ WSWS ☛ Officials,_media_spread_complacency_as_US_enters third_summer_of_COVID_infections_and_death_–_World_Socialist Web_Site⠀⇛ o § Proprietary⠀➾ # ⚓ ZDNet ☛ If_you’re_having_problems_with_Microsoft_Azure_AD today,_this_is_probably_what’s_causing_it [Ed: Microsoft PR operative Liam Tung making excuses for unacceptable disservice from his handlers, the threat_to_national security]⠀⇛ Microsoft just rolled out a hotfix for a glitch in Azure Active Directory (AD) that caused long delays in logging data for more than 12 hours. o § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ EFF ☛ Community_Activists_Reach_Settlement_With_Marin County_Sheriff_for_Unlawfully_Sharing_Drivers’ Locations_with_Out-Of-State_and_Federal_Agencies⠀⇛ # ⚓ Techdirt ☛ Clearview_Is_Now_Selling_Its_AI_To_App Developers,_School_Security_Contractors⠀⇛ Well, this doesn’t sound like a good idea. The company that recently swore in court filings it would cease and desist sales to all private companies in the United States is offering its product to a number of private companies elsewhere in the world. And it’s courting private contractors doing business with government entities in the United States with a product that would collect data on minors. # ⚓ The Register UK ☛ Indian_authorities_issue conflicting_advice_about_biometric_ID_card_security [Ed: Quoting Jeffrey Epstein's enabler and generally Famous Criminal Bill Gates like an Aadhaar "expert" is much like the media painting him COVID-19 expert when he's in fact COVID profiteer]⠀⇛ The Unique Identification Authority of India (UIDAI) has backtracked on advice about how best to secure the “Aadhaar” national identity cards that enable access to a range of government and financial serivces. UIDAI promotes the cards as “a single source offline/online identity verification” for tasks ranging from passport applications, accessing social welfare schemes, opening a bank account, dispersing pensions, filing taxes or buying insurance. Although Bill Gates has lauded Aadhaar cards for improving access to services, the scheme has been the subject of many security-related scares as inappropriate access to personal information has sometimes been possible, UIDAI’s infosec has sometimes been lax, and the biometrics captured to create citizens’ records have sometimes been used for multiple individuals. Privacy concerns have also been raised over whether biometric data is properly stored and secured, if surveillance of individuals is made possible through Aadhaar, and and possible data mining of the schemes’ massive data store. o § Defence/Aggression⠀➾ # ⚓ Common Dreams ☛ At_Least_5_Killed_in_Tulsa_Mass_Shooting⠀⇛ This is a breaking news story… Check back for possible updates. Tulsa police confirmed Wednesday that five people were killed, including the shooter, during a mass shooting at a medical facility in the northeastern Oklahoma city.  # ⚓ Techdirt ☛ Texas_Rep_Bemoans_Discussion_About_Guns_After School_Shooting_When_Rap_Music_And_Video_Games_Are_The_Real Culprit⠀⇛ It feels somewhat strange to write this post today, short though it may be. We now live in the wake of yet another mass shooting, this time at an elementary school in Texas. It was only weeks ago that we were dealing with the aftermath of the racist attack on a Buffalo grocery store. In that aftermath, everyone began the usual practice of retreating to their political silos in order to blame whatever they already didn’t like for the shooting. Social media led the way, stupid as that is, followed by the equally dumb idea that somehow video games made a racist assbag murder a bunch of African Americans in cold blood. And now, after the Texas shooting, here we are again. # ⚓ TruthOut ☛ The_AR-15_Has_No_Business_Being_in_the_Hands_of Civilians⠀⇛ # ⚓ Counter Punch ☛ Going_Backwards⠀⇛ I was shocked and angered by this presentation. During the Q & A, I told them they either knew no history or were consciously trying to mislead us, for what they were describing was a move backward in terms of regulating state behavior, to a time prior to World War II. They were trying to resurrect an ugly and very dangerous period in history. I think they would have ejected me from the room if they could have gotten away with it. As misleading as this presentation was, it framed a seminal issue: we are in fact regressing in terms of post World War II values and obedience to international laws. One can rightly ask, going backwards from where, to what, and why? # ⚓ TruthOut ☛ Uvalde_Students_Fought_for_Desegregation_in 1970s._Now_Let’s_Rise_Up_for_Them.⠀⇛ # ⚓ TruthOut ☛ Uvalde_School_District_Police_Chief_Is_Refusing to_Cooperate_With_Investigation⠀⇛ # ⚓ TruthOut ☛ Will_the_Gun_Lobby_Block_New_Safety_Laws Again?⠀⇛ # ⚓ Democracy Now ☛ Will_the_Gun_Lobby_Block_New_Safety_Laws Again?_The_NRA_Is_Imploding,_But_Its_Ideology_Still Dominates⠀⇛ In the aftermath of the mass shootings in Uvalde and Buffalo, demand for gun control at the state and federal level is mounting. We speak with Frank Smyth, longtime investigative journalist who has been covering the National Rifle Association, about the gun lobby’s grip on U.S. lawmakers. He says the Democratic strategy to “find common ground” with conservatives is failing, as the growing gun rights movement refuses to do the same, and discusses how the NRA’s history of hypocrisy and corruption has weakened the formal, centralized power of the group. “The NRA is imploding … but the ideology that they have cooked at the same time they are waning is stronger than ever,” says Smyth. # ⚓ Counter Punch ☛ The_Chimeras_of_French_Naval_Power⠀⇛ Taking two decades as its time framework, Canuel’s book grapples with the fortunes of France’s La Marine Nationale. The study traces this navy as it was divided between dispersed navy units under the control of the collaborationist regime of Vichy (after the defeat in July 1940) and those small units that escaped to England in the following months and were commanded by Brigadier General Charles de Gaulle, the leader of Free France in exile. As the U.S. diplomatically recognized Vichy, President Franklin D. Roosevelt adamantly refused to recognize de Gaulle’s structure, Free France with its Free French Fleet and preferred to deal with another dissident from Vichy, de Gaulle’s nemesis, Vice Admiral Émile Muselier. The rivalry and disunion within the French navy leadership were later exasperated when the Allies approached General François Darlan in Algiers, a Vichy loyalist, to facilitate landing in North Africa in November 1942. Darlan’s assassination a mere six weeks later did not ease matters for that navy. Indeed, Canuel wants us to trust that it is this same navy, marred in disunity and foreign influence (not only defeat), that in the space of two decades somehow magically manage to surmount major challenges, rebuild itself from scratch, and become somehow equal with, for example, the Royal Navy or the United States Navy. This wishful thinking cannot stand scrutiny. Meanwhile, such an assessment cannot deny that statistical improvements in the number of active units, their qualitative capabilities, and overall tonnage with 300 vessels displaying more than 745000.00 tons” (p. 241) have been achieved, quite a breath in such a short period. Still, the decision to allocate considerable sums from the defense budgets to initially, terrestrial, and subsequently nuclear chapters is indicative of French Admirals’ understanding not only of the changing role of the Navy in the Cold War context but the overall constraints imposed by the United States as the power that has been cashing in on its victory in WWII. The world still remembers how President Donald Trump in November 2018 reacted to French President Emmanuel Macron’s allusion to the need to create an independent/true European army. Trump angrily retorts: “Without the U.S. help in two world wars, today’s Parisians would be speaking German.”[1] More important than the rivalry and divisions than marked the top leadership of the French navy in the two decades making the study is the allied naval cooperation, military aid programs, and other structures, which impacted not only the rebuilding of the French Navy but its autonomy of movement. The abrupt, even humiliating end of the Suez campaign of 1956 speaks volumes concerning the limitations of the French naval planners. # ⚓ FAIR ☛ ‘More_Guns,_More_Gun_Deaths—That’s_Really_It’⠀⇛ # ⚓ Counter Punch ☛ Putin’s_Conquest_of_Southeast_Ukraine: Vexed_Questions_of_‘Negotiations’,_Gotcha_Moments_and_Real Imperial_Interests⠀⇛ # ⚓ Counter Punch ☛ Old_Men_Talking_Sense_on_Ukraine⠀⇛ I have never been tempted to write many good words about Kissinger, but his realism about the war is a welcome contrast to those who would like to see it go on ad infinitum in vain pursuit of some unattainable victory. Asked who will win the Ukraine war, Prof Dror, who has advised six Israeli prime ministers, replied: “This war, like most wars, will end with no absolute winner. Both sides will lose. The question is which side loses more. Ukraine is fighting bravely. President Volodymyr Zelensky has become a mass media hero. Western countries are condemning Russia and providing Kyiv with weapons and sanctions. But meanwhile, Ukraine is being partly devastated and depopulated. It is paying a very high price in blood and material, while Russia remains secure.” # ⚓ Meduza ☛ ‘This_is_not_just_a_piece_of_land’:_Viral_maps show_just_how_much_of_Ukraine’s_territory_Russia_has_seized⠀⇛ On May 29, Alex Bokoch shared a Facebook post that went viral. “For my European friends! Just keep in mind this area of Ukraine that has been occupied now by Russia, when you listen [to the] statements of your politicians,” he wrote.  # ⚓ The Nation ☛ The_Injustices_Endured_by_Native_American Youths_Continue_to_This_Day⠀⇛ When Joe Wheeler was sent to a boarding school for Native American youths in Oklahoma, he would later tell his grandson, his teachers taught him his first lesson by cutting his hair. Then, when he spoke Wichita instead of English, they made him eat soap. And when he kept speaking Wichita, they beat him—or as they’d say, “civilized” him. # ⚓ Scheerpost ☛ Patrick_Lawrence:_Biden’s_Taiwan_Talk⠀⇛ We are witnessing the gradual dismantling of strategic ambiguity in favor of the clarity urged by Trump’s belligerent secretary of state, Mike Pompeo. # ⚓ Meduza ☛ ‘People_are_surviving_however_they_can’:_Donbas residents_describe_life_in_three_cities_where_Russia_is slowly_wresting_control⠀⇛ As the battle for the Donbas rages on, Russian forces continue to make gains. They’ve seized Lyman, destroyed much of Sievierodonetsk, and are currently advancing on Sloviansk, Kramatorsk, and Lysychansk, which are currently still under Ukrainian control. Meduza spoke to residents of these cities about what life looks like right now — and how they’re preparing for the Russian army’s invasion. # ⚓ Scheerpost ☛ War_as_Terrorism:_Conflicts_We_Can’t_Win, Suffering_We_Don’t_See⠀⇛ Honoring troops on national holidays like the Memorial Day just past helps obscure a grim reality of our time — that wars are won (or in the case of this country, it seems, never won) only by making it impossible for the communities we oppose to carry on with their daily lives. # ⚓ Scheerpost ☛ Does_America_Stand_for_Guns_or_for_Sanity?⠀⇛ Ann Wright at rally in Houston. By Colonel (Ret) Ann Wright / Popular Resistance On Memorial Day where our country honors its wars and its war dead, it seems to me that too many in our country have… # ⚓ Common Dreams ☛ Opinion_|_America_Needs_a_Jubilee⠀⇛ The horrifying mass murder of 18 school children and two teachers in Uvalde, Texas last week occurred at the same time as the funeral of Celestine Chaney, grandmother of six and Buffalo, New York mass shooting victim, was taking place. Only two of the ten Black Americans killed in Buffalo by avowed white supremacists had been yet laid to rest when that tragedy had to be pushed out of top news to make room for yet another gruesome U.S. mass shooting. # ⚓ Common Dreams ☛ ‘Slippery_Slope…_Just_Got_a_Lot_Steeper’: US_to_Send_Ukraine_Advanced_Missiles_as_Russia_Holds_Nuke Drills⠀⇛ Peace advocates warned Tuesday that the Biden administration’s newly unveiled decision to arm Ukraine with advanced missile systems further heightens the risk of a direct military conflict between the U.S. and Russia, which accused the White House of “adding fuel to the fire deliberately” as Moscow’s deadly invasion of its neighbor rages on. “The slippery slope leading to a direct U.S. confrontation with Russia just got a lot steeper,” Medea Benjamin, co-founder of the progressive anti- war group CodePink, wrote in response to the Biden administration’s move, which was followed by news that Russian forces are holding nuclear drills northeast of Moscow on Wednesday. # ⚓ Common Dreams ☛ Call_Embraced_for_Prolonged_Student_Walkout Over_Nation’s_Refusal_to_Act_on_Guns⠀⇛ As 21 families in Uvalde, Texas hold funerals for the 19 children and two adults who were killed in the shooting at Robb Elementary School last week, gun control advocates are grappling with the question of what it will take to stop gun violence, with some proposing that students and teachers hold the largest school walkout yet—one in which they would refuse to return to school until lawmakers pass far-reaching reforms. With summer vacation approaching, Gal Beckerman wrote at The Atlantic Tuesday, “students should refuse to go back to school” in the fall without the passage of an assault weapons ban—a law which existed in the U.S. in the past and whose expiration correlated to a rise in mass shootings, according to researchers. # ⚓ Common Dreams ☛ 48_Lawmakers_Unveil_Measure_to_End ‘Unauthorized’_US_Involvement_in_War_on_Yemen⠀⇛ Four dozen U.S. House lawmakers on Wednesday introduced a War Powers Resolution to end “unauthorized” United States military involvement in a Saudi-led coalition’s war on Yemen. “We should not be involved in yet another conflict in the Middle East—especially a brutal war that has created the world’s largest humanitarian crisis.” # ⚓ Democracy Now ☛ Yemeni_Man_Maimed_in_U.S._Drone_Strike Raises_Funds_Online_for_His_Surgery_as_Pentagon_Refuses Help⠀⇛ Calls are growing for the Pentagon to acknowledge that a U.S. drone strike on March 29, 2018, in Yemen mistakenly struck civilians. Adel Al Manthari was the only survivor of the drone strike, which killed his four cousins as they were driving a car across the village of Al Uqla. The Pentagon refuses to admit the men were civilians and it made a mistake. Now supporters are demanding the U.S. pay for the devastating injuries Al Manthari sustained and fund the surgery he urgently needs. “He’s effectively fighting for his quality of life and his dignity and to survive,” says Aisha Dennis, project manager on extrajudicial executions for the rights group Reprieve. “It’s a scandal that the Pentagon can completely dodge responsibility,” says Kathy Kelly, peace activist and a coordinator of the Ban Killer Drones campaign, which is fundraising for Al Manthari’s medical care. # ⚓ Common Dreams ☛ ‘Shut_Down_This_War_Machine’:_Peace Activists_Block_Entrances_to_Major_Weapons_Fair_in_Canada⠀⇛ More than a hundred anti-war campaigners traveled to Ottawa on Wednesday to protest outside of the E.Y. Center, where they obstructed access to the opening of CANSEC, North America’s largest weapons and “defense industry” convention. “The weapons companies sponsoring and exhibiting in CANSEC are raking in record billions in profits. They are the only people who win these wars.” o § Transparency/Investigative Reporting⠀➾ # ⚓ EFF ☛ Hearing_Wednesday:_EFF_Testifies_Against_SFPD_for Violating_Transparency_Laws⠀⇛ In September 2020, SFPD arrested a man who was suspected of illegally discharging a gun, and a San Francisco Chronicle report raised concerns that the arrest came after a local fusion center ran the man’s photo through a face-recognition database. The report called into question SFPD’s role in the search, particularly because the city’s Surveillance Technology Ordinance, enacted in 2019, made San Francisco the first city in the country to ban government use of face-recognition technology. EFF filed a public records request with the SFPD in December 2020 about the investigation and the arrest, but the department released only previously available public statements. EFF filed a complaint with the Sunshine Ordinance Task Force for SFPD’s misleading records’ release, after which SFPD produced about 20 pages of relevant documents. At Wednesday’s hearing, EFF Director of Investigations Dave Maass will ask the task force to uphold EFF’s complaint about the SFPD, arguing that San Francisco’s transparency policies won’t work well unless public agencies are held to account when trying to skirt their responsibilities. # ⚓ Techdirt ☛ Ninth_Circuit_Takes_Another_Look_At_NSLs,_Says Indefinite_Gag_Orders_Still_Aren’t_A_Constitutional_Problem⠀⇛ Back in 2017, the Ninth Circuit Court of Appeals decided there was nothing wrong with the indefinite gag orders the government slapped on its (extremely plentiful) National Security Letters (NSL). It told Cloudflare, Credo Mobile, and other parties challenging these gag orders that the Constitution remains untroubled by the government’s demands for silence, which could easily be extended until forever. # ⚓ Digital_Transparency:_A_Right_to_Information_Report_for_May 2022⠀⇛ For the month of May 2022, IFF has filed 7 Right to Information (“RTI”) applications and 4 first appeals. In response to our RTI application to Varanasi Smart City on the use of facial recognition by them, the PIO requested a sum of one lakh rupees as fees for a hard copy of the documents, without specifying the number of pages the document contains. This is against the letter and spirit of the Right to Information Act, 2005 (“the Act” or “the RTI Act”) which provides that information be given to the applicants at the cost of Rs 2/- per page. o § Environment⠀➾ # § Energy⠀➾ # ⚓ Common Dreams ☛ Fossil_Fuel_‘Addiction’_Is_Sabotaging Every_Sustainable_Development_Goal:_Report⠀⇛ A first-of-its-kind report published Wednesday warns that the continued extraction and burning of fossil fuels worldwide—particularly in the rich countries most responsible for planet-warming carbon emissions—is imperiling every single sustainable development goal adopted by United Nations member states in 2015. The 17 SDGs are far-reaching, ranging from ending global poverty to eliminating hunger to combating the climate emergency, and achieving them by 2030 would require ambitious and coordinated action on a global scale. # ⚓ Hungary ☛ Croatian_Prime_Minister:_Hungary_will_lose the_case_if_the_dual_fuel_price_case_goes_to_court⠀⇛ # ⚓ Common Dreams ☛ Big_Oil_Accused_of_Trying_to_‘Hijack Democracy’_With_Spending_on_Local_Ordinance_Fight⠀⇛ Leading up to a vote on a pair of ordinances in California’s Ventura County, an environmental advocacy group on Wednesday accused the fossil fuel industry of trying to “hijack democracy.” “Ventura County must vote yes on measures A and B to ensure consistent permitting for the oil and gas industry and the basic environmental regulations to protect public health.” # § Wildlife/Nature⠀➾ # ⚓ Counter Punch ☛ Public_Lands:_More_Use_Doesn’t_Mean More_Conservation⠀⇛ For decades many conservation organizations have posited that if more people use our public lands and waters it will result in more people appreciating those resources and subsequently supporting their conservation. It’s a handy theory — and certainly has a couple of advantages. First, as more wealthy out-of-staters buy up huge chunks of Montana to close off for their private hunting and fishing reserves, they make an inviting target to oppose — although out-of-staters are certainly not the only ones trying to close off public land access. # ⚓ Counter Punch ☛ A_Letter_from_India⠀⇛ In point of fact, there’s just no getting around the evidence that the Anthropocene, which is the current geological age of human dominance, carelessly, relentlessly undermines foundations of life-supporting ecosystems. The normally robust Great Barrier Reef is halfway gone in only 25 years ever since a series of mass coral bleaching started in 1998 at the same time as the spectacular Amazon rainforest now emits more CO2 than it absorbs in some regions of the gigantic rainforest (confirmed in 2021) at the same time as only 10% of large predatory fish remain in the oceans since 1950. o § Finance⠀➾ # ⚓ The Nation ☛ We’re_So_Close_to_a_Win_Against_the_Student Debt_Crisis⠀⇛ College students have been key allies in bolstering the fight to end the student debt crisis, joining the existing coalitions of borrowers who have been paying off their loans for years. Now, it looks like their activism is working. President Biden announced earlier this month that he is considering canceling some federal student debt. Student debt continues to impact more than 45 million Americans with a combined $1.7 trillion in debt, robbing retirees of their Social Security payments, workers of their wages, and students of their future. # ⚓ Common Dreams ☛ Opinion_|_How_Corporations_Are_Using Inflation_to_Take_Your_Money⠀⇛ So what are corporations doing with their record profits? Using them to boost share prices by buying back a record amount of their own shares of stock. # ⚓ Counter Punch ☛ The_What,_Where,_How_and_Why_of_the_Indo- Pacific_Economic_Framework⠀⇛ In a joint statement, the participating countries said that the purpose of the IPEF is to “advance resilience, sustainability, inclusiveness, economic growth, fairness, and competitiveness for our economies. Through this initiative, we aim to contribute to cooperation, stability, prosperity, development, and peace within the region”. During the East Asia Summit in October 2021, President Biden announced plans to launch a U.S.- led IPEF. Subsequently, U.S. officials conducted exploratory discussions with their traditional allies in the region. In February 2022, an Indo- Pacific strategy was revealed, which mentioned the formal launch of the IPEF in early 2022. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Common Dreams ☛ Progressives_Call_for_Greater_Outreach_by DNC_as_GOP_Invests_in_Community_Centers⠀⇛ The Republican National Committee is investing considerable money and energy in expanding its voter base by building up its presence in largely Black, Latino, and Native American communities, according to new reporting by The American Prospect which led progressives on Wednesday to warn that Democrats have largely abandoned such boots-on-the- ground efforts. As Alexander Sammon wrote at the outlet, the Republican Party has opened at least 21 community centers in places including Robeson County, North Carolina—a former Democratic stronghold which former Republican President Donald Trump won in 2016—and the College Park section of Atlanta. # ⚓ Hungary ☛ We_went_to_the_mass_held_for_Viktor_Orbán⠀⇛ Viktor Orbán is a gift from God, who shines like a torch, revealing the light of the world – the priest said at the Mass held for the Prime Minister in the Budapest-Inner City Church of Our Lady of the Assumption. The lonely prime minister, surrounded by enemies, was greeted with mass and prayer for the tenth time this year on his birthday, where we also found out that liberalism is exactly the same as Nazism. (English subtitles available) # ⚓ Democracy Now ☛ Civil_Rights_Orgs_Challenge_Racist_“Insular Cases”_Used_to_Legally_Discriminate_Against_Puerto_Rico⠀⇛ Civil rights groups are challenging a series of racist U.S. Supreme Court rulings that have been used for over a century to legally justify discrimination against people in Puerto Rico and other U.S.-occupied territories. The rulings are known as the Insular Cases and have allowed the federal government to deny Puerto Ricans living on the island voting rights, access to public social programs like Medicaid and food stamps, and other equal protections guaranteed to those residing on the mainland. The renewed effort to overturn the Insular Cases comes after the Supreme Court sided with the Biden administration to continue denying Supplemental Security Income benefits to seniors and people with disabilities living in Puerto Rico. We speak with Lía Fiol-Matta, senior counsel for LatinoJustice PRLDEF, which is helping to lead the new campaign, and with Democracy Now! co-host Juan González, who has long reported on this issue. “The Insular Cases established a doctrine that has no constitutional basis,” says Fiol-Matta. # ⚓ Counter Punch ☛ Reactionary_Succession:_Peter_Dutton, Australia’s_New_Opposition_Leader⠀⇛ As he has done before, Peter Dutton, former Queensland policeman and failed university student, high priest of division and shorn of compassion, the face of Fortress Australia, survived the electoral challenge.  Earlier in the night, it did not seem that he would hold on to the Queensland seat of Dickson.  His opponent, Labor’s Ali France, looked ready to assume the reins.  But survive, he did, as he has done previously at several ballots.  His rival and obvious successor to take over the Liberal Party, Josh Frydenberg, did not. Dutton, Australia’s new opposition leader, is a reactionary, though he must couch his ascent to the leadership in more accommodating terms.  He is a reminder of a brand of politics that Australia’s conservative Prime Minister John Howard made the norm: callous, self-centred, free of vision and hostile to outsiders. Under Howard, illegal wars were launched, a national security state created, and torturous offshore detention centres established in Pacific outposts.  His time in office was characterised by an oleaginous, ignorant smugness. # ⚓ Counter Punch ☛ A_New_Colombia?_Petro_Wins_First-Round Victory_in_Presidential_Vote⠀⇛ If they prevail in second-round voting on June 19, they will head Colombia’s first ever people- centered government. Petro’s opponent will be the May 29 runner-up Rodolfo Hernández. The tallies were: Petro, 40.3 percent (8.333.338 votes); Hernández, 28.1 percent (5.815.377 votes); Federico Gutiérrez, 23.9 percent (4.939.579 votes). Other candidates shared the remaining votes. The voter participation rate was 54 percent, standard for Colombia. # ⚓ Counter Punch ☛ Turn_Out_for_the_Poor_People’s_Campaign, Regardless_of_Its_Shortcomings⠀⇛ In a normal country, the streets would long since have been packed, government offices surrounded, public squares occupied, and change demanded. The U.S. — and the world with it — is suffering severely from unrepresentative government, the hoarding of wealth by a tiny group of overlords, the devastation of the Earth’s climate and ecosystems, the normalization of violence and massive warmaking and the risk of nuclear apocalypse, and the spread of all kinds of racist hatred and bigotry. People have been conditioned to suppose that the proper response to this is to spend several months chattering about how they’re going to vote, and then take 5 minutes to vote for either an outright fascist or a completely unprincipled facilitator of maintaining a steady pace toward the approaching cliff — one or the other of whom has already been guaranteed victory by gerrymandering. # ⚓ TruthOut ☛ Progressives_Blast_Manchin’s_Hypocrisy_in Calling_for_Lower_Drug_Prices⠀⇛ # ⚓ Hackaday ☛ It’s_TikTok,_On_Your_Wrist!⠀⇛ One of the ultimate objects of desire in the early 1980s was the Seiko TV wristwatch. It didn’t matter that it required a bulky external box in your pocket for its electronics, it was a TV on your wrist, and the future was here! Of course, now we have the technology to make wrist-mounted video a practical reality, but it’s sad to see we’ve opted to use our phones for video and never really followed up on the promise of a wrist-mounted television. There’s always hope though, and here it is in the form of [Dave Bennett]’s ESP32-powered TikTok wristwatch. # ⚓ The Nation ☛ Fear_&_Loathing_in_San_Francisco:_How_Chesa Boudin_Got_Blamed⠀⇛ After just two years in office, Chesa Boudin, the district attorney of San Francisco, gets blamed for every crime in the book—even offenses committed before he took office and beyond the city limits. For his efforts to tackle wage theft, end cash bail, expand the program that diverts nonviolent offenders from prison, and prosecute abusive cops, Boudin has been rewarded with a recall campaign scapegoating him for all of this city’s woes. The vote takes place on June 7, and recent polls suggest it will be an uphill battle for Boudin and progressives. # ⚓ Common Dreams ☛ Opinion_|_Note_to_Judges:_If_You_Don’t_Want to_Be_Called_a_Partisan_Hack,_Stop_Being_One⠀⇛ Today’s six-member supermajority on the Supreme Court has surrendered all claim to being an impartial moral force for blind justice. Instead, the GOP’s small network of corporate and right-wing operatives has painstakingly fabricated and weaponized the court as its own political oligarchy. In only a couple of decades, backed by a few billionaires, these anti-democracy zealots have incrementally been imposing on America an extremist political agenda that they could not win at the ballot box. # ⚓ Common Dreams ☛ Tapes_Expose_GOP_Plot_to_Install_Poll Workers_in_‘Massive_Election_Subversion_Program’⠀⇛ New reporting on Wednesday exposes a strategy by Republican Party operatives to disrupt upcoming elections in strongly Democratic areas that includes mobilizing “an army” of GOP-friendly lawyers ready to aid newly recruited poll workers positioned on the frontlines of this year’s midterms. The “huge story” by Heidi Przybyla at Politico is based on multiple recordings from meetings lead by GOP operatives over the past year. # § Misinformation/Disinformation⠀➾ # ⚓ Counter Punch ☛ How_Muslim_are_Portrayed_Negatively in_the_Media⠀⇛ Political scientist David Laitin has highlighted the role that religious identities play in this dynamic. As he pointed out in a recent interview, Syrian refugees were “mostly Muslim and faced higher degrees of discrimination than will the Ukrainians, who are largely of Christian heritage.” The media provide information that shapes such attitudes toward Muslims. A 2007 Pew Research Center survey of Americans found that people’s negative opinions on Muslims were mostly influenced by what they heard and read in the media. Communications scholar Muniba Saleem and colleagues have demonstrated the link between media information and “stereotypic beliefs, negative emotions and support for harmful policies” toward Muslim Americans. o § Civil Rights/Policing⠀➾ # ⚓ The Nation ☛ “The_Streets_Belong_to_the_People”_of_Rio_de Janeiro⠀⇛ Every day during the weeklong holiday of Tiradentes in Brazil, Luísa Classen woke up at 8 in the morning, put on a comfortable swimsuit, applied glitter makeup to her face, and headed to a street party in the city center of Rio de Janeiro. Though Carnaval is usually in February, from Thursday, April 19, to Sunday, April 22, Classen and thousands of partygoers, musicians, dancers, and street sellers attended their second Carnaval of 2022. # ⚓ The Nation ☛ Joy_Is_Resistance⠀⇛ # ⚓ The Nation ☛ What_Is_Organizing,_Anyway?⠀⇛ To begin, an anecdote. This past summer, a pigeon walked through my open balcony door while my attention was elsewhere. I shooed it out, but when I turned around two more pigeons walked out of my bedroom. In the 20 years I’ve lived in my apartment, this had never happened to me, though my balcony door was often open. All I could imagine was that those poor birds had gotten as disoriented as the rest of us in these pandemic years when nothing feels faintly normal. # ⚓ Pro Publica ☛ Trial_Diary:_A_Journalist_Sits_on_a_Baltimore Jury⠀⇛ By the end of our first afternoon of deliberations in the jury room up the narrow stairs from the courtroom, the water cooler was running low, the lock on the bathroom door kept sticking and the wheezing HVAC system was making it even harder to make out the audio in a crucial jailhouse phone recording. We were also nowhere close to a consensus on whether or not Domonic White was guilty of attempted murder and lesser charges in the 2021 shooting of Chris Clanton in the presence of Clanton’s 5-year-old son. It was hardly unusual for a jury to struggle to come to an agreement. What made this case unusual was the context provided by the victim’s identity. Clanton was an actor on “The Wire” and is now appearing on “We Own This City,” the new HBO miniseries produced by the creators of “The Wire” and based on Baltimore journalist Justin Fenton’s nonfiction book about an eye-popping police corruption scandal exposed five years ago. # ⚓ AccessNow ☛ Alaa_Abd_El_Fattah_RightsCon_Keynote_Address_– 2011⠀⇛ Alaa has travelled to California to give a keynote address at the RightsCon conference in Silicon Valley, which he delivers in English. While there he learns he has been summoned to the military prosecutor. # ⚓ Common Dreams ☛ Facing_Activist_Pressure,_Pillsbury_Pulling Out_of_Israeli-Occupied_West_Bank⠀⇛ Following years of grassroots pressure, multinational food giant General Mills announced Tuesday that after a 20-year partnership, it will sell its majority share of an Israeli company operating a plant where Pillsbury products are made on stolen Palestinian land. “With this move, General Mills is joining many other American and European companies that have divested from Israel’s illegal occupation.” o § Internet Policy/Net Neutrality⠀➾ # ⚓ Winding_down_my_Gemini_engagement⠀⇛ It’s been fun interacting with a small enthusiastic community. Members like Sandra (Idiomdrottning)[3] and Björn (ew0k)[4] have their hearts in the right place and are all-around menschs. The IRC channel on tilde.chat is welcoming too. And Lagrange[5] is an amazing client. # ⚓ Hackaday ☛ Dissecting_A_T1_Line⠀⇛ When it comes to internet connections, here in 2022 so many of us have it easy. Our ISP provides us with a fibre, cable, or DSL line, and we just plug in and go. It’s become ubiquitous to the extent that many customers no longer use the analogue phone line that’s so often part of the package. But before there was easy access to DSL there were leased lines, and it’s one of these that [Old VCR] is dissecting. The line in question is a T1 connection good for 1.536 Mbit/s and installed at great cost in the days before his cable provider offered reliable service, but over a decade later is now surplus to requirements. The ISP didn’t ask for their router back, so what else to do but give it the hacking treatment? o § Digital Restrictions (DRM)⠀➾ # ⚓ EFF ☛ New_York:_Tell_Your_Assemblymembers_to_Pass_This Landmark_Repair_Bill⠀⇛ Asm. Fahy and the Repair Coalition have worked hard to stand up for users’ rights and stand strong for a bill that would be a landmark piece of legislation. # ⚓ Techdirt ☛ Netflix’s_Effort_To_Thwart_Password_Sharing_Is Already_A_Bit_Of_A_Mess⠀⇛ Back when Netflix was a pesky upstart trying to claw subscribers away from entrenched cable providers, the company had a pretty lax approach to users who shared streaming passwords. At one point CEO Reed Hastings went so far as to say he “loved” password sharing, seeing it as akin to free advertising. The idea was that as kids or friends got on more stable footing (left home to job hunt, whatever), they’d inevitably get hooked on the service and purchase their own subscription. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ Creative Commons ☛ Episode_34:_Open_Culture_VOICES_– Kristina_Petrasova⠀⇛ Welcome to episode 34 of Open Culture VOICES! VOICES is a vlog series of short interviews with open GLAM (galleries, libraries, archives, and museums) experts from around the world. The Open Culture Program at Creative Commons aims to promote better sharing of cultural heritage in GLAMs collections. With Open Culture VOICES, we’re thrilled to bring you various perspectives from dozens of experts speaking in many different languages on what it’s like to open up heritage content online. In this episode, we hear from Kristina Petrasova, Project Lead Digital Heritage & Public Media at the Netherlands Institute for Sound & Vision, a cultural archive and museum in Hilversum. Kristina has a deep passion for international art and culture, and has worked in the cultural heritage sectors for several years. After working as conservator of the National Numismatic Collection (NNC) in the Netherlands, she is now focusing on research and production of cultural and artistic projects, exhibitions and documentary films. # ⚓ Techdirt ☛ Are_‘Fast_Movies’_Really_A_Substitute_For The_Real_Thing?_Or_Just_Good_Marketing?⠀⇛ There’s an interesting post on the TorrentFreak blog about “fast movies“…. # ⚓ Techdirt ☛ Not_Fit_For_Purpose:_Libraries_Explain_How Copyright_Failed_Libraries_During_The_Pandemic⠀⇛ It’s no secret that copyright and libraries are often in conflict with one another. We’ve pointed out repeatedly how modern publishers would never allow libraries to come into existence if they weren’t here already. The publishers have made that clear by trying to sue out of existence all sorts of things that appear to be indistinguishable from libraries, including the Internet Archive. # ⚓ artificial_intelligence:_a_lament_for_the_future_of art⠀⇛ Algorithms have already been created that mimic those aspects of art that catch our eye and are interesting enough to us that people fascinated by what AI can spit out in a short period of time having gone through human works and blended them into their mush start sharing these images en masse. “Look, look what the artificial intelligence created for me today!”. The images show human figures, landscape elements, distinct interesting colors, textures, contrasts. Everything strangely shuffled, twisted. People without faces, with parts of their faces placed in random places. The images, if one assumes them to be a representation of some existing reality, are not only like those from a nightmare like many of the paintings by Zdzisław Beksiński, but in addition completely dehumanized, devoid of all sense and spitting this senselessness in the face. “Here, a flak for you human beings, enjoy again like a child”. And people enjoy and play with these images. ䷩ 𝚕𝚒𝚗𝚎 10007 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_02/06/2022:_Nitrux_2.2_Released⠀✐ Posted in News_Roundup at 3:48 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Desktop/Laptop o Kernel_Space o Benchmarks o Applications o Instructionals/Technical o Desktop_Environments/WMs # GNOME_Desktop/GTK * Distributions_and_Operating_Systems o Fedora_Family_/_IBM o Debian_Family o Canonical/Ubuntu_Family o Devices/Embedded o Open_Hardware/Modding o Mobile_Systems/Mobile_Applications * Free,_Libre,_and_Open_Source_Software o Web_Browsers o Education o Programming/Development # Python o Standards/Consortia * Leftovers o Science o Education o Hardware o Health/Nutrition/Agriculture o Proprietary o Security # Privacy/Surveillance o Defence/Aggression o Environment # Energy # Overpopulation o Finance o AstroTurf/Lobbying/Politics o Censorship/Free_Speech o Freedom_of_Information_/_Freedom_of_the_Press o Civil_Rights/Policing o Monopolies # Software_Patents # Copyrights * § GNU/Linux⠀➾ o ⚓ Liliputing ☛ Lilbits:_The_$219_Pinebook_Pro_Linux_laptop_returns, GNOME_is_becoming_more_mobile-friendly,_and_Google_Pixel_7 prototypes_in_the_wild_–_Liliputing⠀⇛ It’s been a few years since Pine64 began shipping the PineBook Pro laptop to customers looking for a cheap, Linux-friendly notebook with an ARM-based processor. But due to global supply chain issues, it’s been out of stock at the Pine64 Store for most of the past year. Now it’s coming back and should be available for purchase by July for $219. While the laptop’s specs are starting to look a little dated by 2022 standards, it’s hard to beat that price, and Pine64 isn’t ready to announce a new model just yet. The company’s been keeping plenty busy with other product launches though. Here’s a roundup of recent tech news from around the web. The PineBook Pro is a $219 Linux laptop with a 14 inch FHD IPS LCD display, a Rockchip RK3399 processor, 4GB of RAM and 64GB of eMMC storage. It’s been out of stock for a year due to supply chain issues, but it will be available again by July, 2022. o § Desktop/Laptop⠀➾ # ⚓ Why_Use_A_Computer_Meant_For_Bitcoin_–_Bitcoin_Magazine⠀⇛ I suggest people use an open-source operating system like Linux Mint, but use Windows or Mac if you must — that’s better than using a regular, well-used computer that invariably has malware hidden in it. o § Kernel Space⠀➾ # ⚓ LWN ☛ Statistics_from_the_5.18_development_cycle⠀⇛ The 5.18 kernel was released on May 22 after a nine-week development cycle. That can only mean that the time has come to look at some of the statistics behind this release, which was one of the busiest in a while. Read on for a look at the 5.18 kernel, where the code in this release came from, and how it found its way into the mainline. The 5.18 development cycle saw the addition of 14,954 non-merge changesets from 2,024 developers, 289 of whom made their first kernel contribution during this time. None of these numbers are records, though the number of developers came close to the maximum seen so far (2,062 for 5.13). This work resulted in the addition of 756,00 lines of code to the kernel. # ⚓ LWN ☛ Sharing_memory_for_shared_file_extents⠀⇛ # ⚓ LWN ☛ Change_notifications_for_network_filesystems⠀⇛ # ⚓ LWN ☛ Making_O_TMPFILE_atomic_(and_statx()_additions)⠀⇛ # ⚓ LWN ☛ CXL_2:_Pooling,_sharing,_and_I/O-memory_resources⠀⇛ # ⚓ LWN ☛ Cleaning_up_dying_control_groups,_2022_edition⠀⇛ # ⚓ LWN ☛ get_user_pages()_and_COW,_2022_edition⠀⇛ # ⚓ LWN ☛ Fixing_a_race_in_hugetlbfs⠀⇛ # ⚓ LWN ☛ Preserving_guest_memory_across_kexec⠀⇛ # ⚓ uni Toronto ☛ The_basics_of_Linux_fair_share_CPU_scheduling in_cgroup_v2_(‘unified_cgroups’)⠀⇛ Linux has long been able to do fair share CPU scheduling, where CPU time was evenly divided between, for example, the various different users. Originally this took some manual work, but systemd wound up making it fairly easy. This is done through the Linux kernel ‘cgroup’ feature. This comes in two versions, the now-old cgroup (v1), and the not so new any more unified cgroups (cgroup v2). When using systemd, these turn out to be different in some important ways. To understand implementing fair share CPU scheduling with systemd in a cgroup v2 world, I want to start by understanding how cgroup v2 works and does fair share scheduling. o § Benchmarks⠀➾ # ⚓ Free Desktop ☛ [ANNOUNCE]_mesa_22.1.1⠀⇛ Hi list, I'd like to announce mesa 22.1.1, the first maintanence release of the 22.1 series. Things are about where I'd expect for where we are in the cycle, and I'm happy. We've got a bit of everything here, zink, intel, and Panfrost being the biggest sets of changes, but some aco, zsn, llvm/lavapipe radv, nir, glsl, r300, aco, svga, and core mesa changes as well. I'll see you all again shortly for 22.0, and then again in two weeks for 22.1.2 Cheers, Dylan o § Applications⠀➾ # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Software_–_May_2022 Updates⠀⇛ Here are the latest updates to our compilation of recommended software. For our entire collection, check out the categories below. This is the largest compilation of recommended software. The collection includes hundreds of articles, with comprehensive sections on internet, graphics, games, programming, science, office, utilities, and more. Almost all of the software is free and open source. o § Instructionals/Technical⠀➾ # ⚓ [Old] Working_with_SSL_certificates⠀⇛ This post is about dealing with the various tasks involved in handling SSL certificates. For the moment, it only covers the tasks related to already existing certificates. # ⚓ Bozhidar Batsov ☛ Having_Fun_with_Custom_Domains_for Email⠀⇛ All those points were important to me to some extent. Here’s how I make use of custom domains in general: [...] o § Desktop Environments/WMs⠀➾ # ⚓ TuMFatig ☛ Give_WindowMaker_a_macos_Mojave_look⠀⇛ Once again, I was wandering on r/unixporn when a screenshot raised my attention. It was probably featuring a obscure window manager that I would never use but I felt like I could tune my beloved WindowMaker to not look so 1990. Before deciding to read further, you may want to look at what is achieved. # § GNOME Desktop/GTK⠀➾ # ⚓ Accessibility_repositories_are_now_merged_– Federico’s_Blog⠀⇛ at-spi2-core’s DBus interfaces, the way the registry daemon works, atk’s interfaces and their glue in at-spi2-atk via libatspi… all of these are tightly coupled. You can’t make a change in the libatspi API without changing at-spi2-atk, and a change in the DBus interfaces really has to ripple down to everything, but keeping things as separate repositories makes it hard to keep them in sync. I am still in the process of learning how the accessibility code works, and my strategy to learn a code base, besides reading code while taking notes, is to do a little exploratory refactoring. However, when I did a little refactoring of bit of at-spi2-core’s code, the tests that would let me see if that refactoring is correct were in another repository! This is old code, written before unit tests in C were doable in a convenient fashion, so it would take a lot more refactoring to get it to a unit-testable state. I need end-to-end tests instead… * § Distributions and Operating Systems⠀➾ o § Fedora Family / IBM⠀➾ # ⚓ The Register UK ☛ IBM_ends_funding_for_employee_retirement clubs⠀⇛ IBM has confirmed to former staff that it will no longer provide grants for the Retired Employee Club, meaning no more subsidized short trips to the Italian Riviera or golf days. The clubs are regionally split. In the UK, for example, there are 28 local organizations that have run short trips or national tournaments including corporate games or group runs. Joining a club was free for all Big Blue retirees with at least 10 years of service under their belt, regardless of pension age. For Local Clubs, members were asked to pay a small annual subscription. Elisa Pearson, HR director for the UK and Ireland, confirmed in an email to members – seen by The Register – that IBM has “decided to reconsider its relationship with its IBM Clubs globally.” “This re-appraisal is being made within the context of developing new contemporary approaches to employee engagement. With that, from the end of June 2022 IBM will cease its formal support to UK clubs.” o § Debian Family⠀➾ # ⚓ 9to5Linux ☛ Debian-Based_Nitrux_2.2_Switches_to_Linux Kernel_5.17,_Adds_Full-Disk_Encryption⠀⇛  Nitrux 2.2 is the first release of the distribution to ditch the long-term supported Linux 5.15 LTS kernel and switch to the more recent Linux kernel 5.17 series by default, of course in a XanMod flavor just like with the previous releases. One of the coolest changes in this release is the ability for users to perform full-disk encryption of their new Nitrux installations when using the automated partition options (Replace Partition and Erase Disk) in the Calamares graphical installer. o § Canonical/Ubuntu Family⠀➾ # ⚓ Its FOSS ☛ Linux_Mint_to_Maintain_Timeshift_Backup_Tool_as an_XApp⠀⇛ Timeshift is arguably the best tool to back up and restore the Linux system. Linux Mint also utilizes the tool to let users easily take snapshots before updates, and ensure hassle-free operation. Of course, that’s not the only thing that makes Linux Mint potentially better than Ubuntu. # ⚓ OMG Ubuntu ☛ Linux_Mint_Takes_Over_Development_of Timeshift,_the_Nifty_Backup_Tool⠀⇛ Linux Mint is taking over development of Timeshift, a popular open-source backup tool. Anyone familiar with Mint will be familiar with this utility. Timeshift is, as the distro’s own lead Clement Lefebvre says in the latest monthly update, a central plank in the system’s backup and update ‘strategy’. Sadly, as happens, the creator of Timeshift is unable to keep working on it owing to other responsibilities. Not keen to see it stagnate, Mint says it ‘got in touch’ to see how they could help. Long story short: Linux Mint is assuming maintenance of the app henceforth. o § Devices/Embedded⠀➾ # ⚓ CNX Software ☛ FastRhino_R68s_router_offers_4GB_RAM,_dual 2.5GbE,_dual_Gigabit_Ethernet_for_$80_(in_China)⠀⇛  Rockchip RK3568-powered NanoPi R5S router has gotten a direct competitor courtesy of FastRhino R68s with the same processor, but more memory up to 4GB RAM, two 2.5GbE ports, and two Gigabit Ethernet ports (or one extra compared to R5S), and two USB 3.0 ports. FastRhino R68s is purely a router in the traditional sense, and you don’t get an HDMI port acting as a display interface or an M.2 NVMe socket to add extra storage as found in NanoPi R5S. The plastic enclosure used with R68s will not be able to cool the Rockchip RK3568 as well as the metal enclosure of the FriendlyElec device, but there are plenty of ventilation holes so that may be sufficient. o § Open Hardware/Modding⠀➾ # ⚓ CoryDoctorow ☛ How_John_Deere_leverages_repair-blocking into_gag_orders⠀⇛ But the anti-repair axis – led by Apple, and incorporating Big Car, Big Ag, and Big Appliances – are determined to milk their monopoly over repair for as long as they possibly can, and this is one area where their innovative genius can’t be denied: Here’s one way that Deere can extend the life of its repair monopoly: they can refuse service to farmers who complain about Deere’s behavior. That’s what happened to Jared Wilson, a Missouri farmer and vocal repair advocate: [...] # ⚓ Vice ☛ Farmer_Says_Dealer_Wouldn’t_Repair_His_Tractor_Until He_Filed_FTC_Complaint⠀⇛ According to the affidavit, Wilson felt the manager’s words were “a veiled threat that if I continued to complain to ‘outside people’ about my dissatisfaction with Heritage Tractor that I could or would no longer authorize [sic] repair assistance from Heritage Tractor in the future.” Wilson is a fierce and vocal advocate for a farmer’s right to repair their tractors. He’s testified about it in the Missouri state house, been interviewed by NBC News, and is quoted by name in a complaint to the FTC. o § Mobile Systems/Mobile Applications⠀➾ # ⚓ Hacker News ☛ FluBot_Android_Spyware_Taken_Down_in_Global Law_Enforcement_Operation⠀⇛ # ⚓ Giz China ☛ AnTuTu_Released_Lists_Of_Best_Android_Phones_In May⠀⇛ # ⚓ Digital Trends ☛ Sorry_Murena,_a_successful_Android_phone needs_Google_|_Digital_Trends⠀⇛ # ⚓ SlashGear ☛ Why_Samsung_Is_Being_Sued_Over_A_Fundamental Android_Feature⠀⇛ # ⚓ TechRadar ☛ Is_Samsung’s_Galaxy_Tab_S8_Ultra_the_Android tablet_to_replace_your_laptop?_|_TechRadar⠀⇛ * § Free, Libre, and Open Source Software⠀➾ o ⚓ Open_Source_Encryption_Still_Rocks!⠀⇛ Generally, the security certificates are very expensive and complicate to install. However, Let’s Encrypt provides free, automated and Open Source certificates. They are offering free Secure Sockets Layer/Transport Layer Security (SSL/TSL) Certificates and the best thing about it is the automated installation process. o § Web Browsers⠀➾ # ⚓ I_closed_all_tabs⠀⇛ The last time I had less than 30 tabs opened in my browser was in January 2021 The last time I had less than 20 tabs opened in my browser was August 2020 The last time I had fewer than 10 tabs opened in my browser was March 2020 o § Education⠀➾ # ⚓ SICP ☛ Structure_and_Interpretation_of_Computer Programmers⠀⇛ When a programmer says that they are ‘self-taught’ or that they “taught themselves to code”, what do they mean by it? o § Programming/Development⠀➾ # ⚓ People_in_your_software_supply_chain⠀⇛ Production and consumption of open source software is maturing for the better and along the way we shouldn’t forget that the leaves in our dependency trees are living and feeling people. # ⚓ Bozhidar Batsov ☛ Who_Needs_Modern_Emacs?⠀⇛ A building material for you to create the best editor for yourselves. By definition the number of people who want/need to build their own editors is not that big, so I think we’d be on a wild goose chase trying to change this.2 Not to mention that Emacs being different from the pack is probably its biggest competitive advantage. Do we need one more editor that’s essentially the same as every other editor? # ⚓ Matt Rickard ☛ Programming_to_the_Interface⠀⇛ Interfaces are the building blocks of software. Interfaces explain what software can do but not how. They can be an API, a wire protocol (think HTTPS), or ABI (application binary interface). How you implement these interfaces is up to you. And if done in the right way, the software should be a drop-in compatible replacement for anything else that shares the same interface. # § Python⠀➾ # ⚓ LWN ☛ Improved_error_reporting_for_CPython_3.10—and beyond⠀⇛ In a fast-paced talk at PyCon 2022 in Salt Lake City, Utah, Pablo Galindo Salgado described some changes he and others have made to the error reporting for CPython 3.10. He painted a picture of a rather baffling set of syntax errors reported by earlier interpreter versions and how they have improved. This work is not done by any means, he said, and encouraged attendees to get involved in making error reporting even better in future Python versions. Galindo Salgado prefaced his talk with something of a warning that he has been told that he speaks rather quickly; with a chuckle, he suggested attendees prepare themselves for the ride. He introduced himself as a CPython core developer and a member of the steering council; beyond that, he is also the release manager for versions 3.10 and 3.11 of the language. He began with a story of his days as a PhD student in physics, where he was using Python as a tool for his research. One day a friend showed him a Python syntax-error message that they could not figure out. They showed it to another student and all three of them were stumped; three physics students who were studying to try to solve the mysteries of the universe were unable to find a simple syntax error. o § Standards/Consortia⠀➾ # ⚓ Tom MacWright ☛ Are_new_geospatial_formats_useful_(to me?)⠀⇛ So that’s a lot of words to say it’s a new, nice format that advertises a bunch of benefits. There are a whole bunch of these formats – Zarr, Parquet and GeoParquet, Arrow, Cloud Optimized GeoTIFFs, . All claim some combination of a compact, or zero- copy, encoding, as well as efficient random access. Some have built-in indexes. Buried the lede but here it is: do any of the benefits of these new formats translate into wins for any of my applications within my constraints? The answer may be yes, but I have a hunch that it’s closer to no. Now, these formats are definitely useful to a lot of people, especially those using Python or low- level languages like C++ or Rust. Some of the more established options like Cloud Optimized GeoTIFFs have been a game-changer for people working with satellite data, and those people sing the praises all the time. * § Leftovers⠀➾ o ⚓ Shadowproof ☛ Protest_Song_Of_The_Week:_‘Rise_Above’_By_Ibeyi_ (Featuring_Berwyn)⠀⇛ Originally published at Ongoing History of Protest Music. The second anniversary of the murder of George Floyd was May 25, and sadly nothing has really changed. Racially motivated killings and cops murdering black people still occur frequently.To comment on this issue, twin sisters Naomi and Lisa Diaz of the Cuban-Venezuelan duo Ibeyi reworked Black Flag’s 1981 classic hardcore punk anthem “Rise Above.” It appeared on their recent album, “Spell 31,” and Trinidad rapper Berwyn added a verse that pays tribute to Floyd.“Berwyn is on this track,” Naomi shared. “He listened to it, and he did his verse really fast. For him, listening to this song made him think of George Floyd, and it’s beautiful.”“I think the thing is, with this song, you can think about everything. It could be for women. It could be for minorities. It’s a song for the oppressed. It could be something small or something really big, but I think this song is just empowering,” Naomi added.The song is empowering. The lyrics, “We are tired of your abuse. Try to stop us; but it’s no use,” still hold as much impact as they did when Black Flag recorded them. And Ibeyi’s reworking delivers a galvanizing message to stand against oppression. o ⚓ BBC ☛ Amber_Heard_and_Johnny_Depp’s_‘Trial_by_TikTok’⠀⇛ The trial between two Hollywood actors turned warring ex- spouses is a reminder that when it comes to certain stories the idea of a mass media or a mainstream media dominated by a few major news organisations is beginning to look a bit creaky. It is also, for some, deeply troubling. There have been essentially two cases here – one decided by a jury and another by the public. o ⚓ Guide_for_analysing_forest_canopy_photos⠀⇛ o ⚓ racing_to_1,000⠀⇛ I used to be hung up on post counts, for some reason. On my ten year sludge through Twitter (2009-2019 (years lost forever)), I used to get worked up and enthusiastic about that I had 75K Tweets. It was a testament to how much time I *wasted* there, but it was 75K of SOMETHING I had “done”. Ridiculous thing to care about. o § Science⠀➾ # ⚓ Salon ☛ Humanity’s_most_distant_spacecraft_is_sending_back weird_signals_from_beyond_our_solar_system⠀⇛ The mystery likely has something to do with the fact that Voyager 1 is the farthest artificial object in space. At a distance of 14.5 billion miles away from Earth, Voyager 1 passed through the heliopause in 2012. The heliopause is the barrier separating the Sun’s solar winds from the interstellar medium, or all of the matter and radiation that exist in the space in-between various solar systems in the galaxy. This means that Voyager 1 is literally in the interstellar void of the Milky Way. Perhaps that has something to do with why the Jimmy Carter-era machine is sending back signals that can best be described as strange. o § Education⠀➾ # ⚓ Ish Sookun ☛ AFRINIC_restricts_attendance_to_the_Annual General_Members_Meeting_(AGMM)_even_ONLINE_😐⠀⇛ The Africa Internet Summit 2022 is being held on 30th May – 3rd June at Le Méridien Hotel, Pte aux Piments in Mauritius. The AFRINIC Annual General Members Meeting (AGMM) is scheduled on the last day of the Africa Internet Summit, i.e Friday 3rd June 2022. Many AFRINIC Resource Members look forward to this meeting and they travel every year to attend the meeting in person. Others who cannot make it can still participate and ask questions via the online conference system. # ⚓ Times Higher Education ☛ US_students_make_gains_in_lawsuits over_online_teaching⠀⇛ Two years into the pandemic, US students are having some initial success in suing their institutions for abruptly moving courses online, aided by the pre-Covid custom of colleges charging less for virtual formats. The shift from in-person teaching has produced more than 200 lawsuits across the US, most commonly involving students who contend that online alternatives are lower quality and therefore merit lower tuition rates. None of the cases has yet produced a courtroom verdict, although judges have agreed in several instances to allow complaints to move to trial, and a few institutions already have accepted settlements. # ⚓ Writing_Effectively⠀⇛ Larry McEnerney of the University of Chicago gives an excellent lecture on writing effectively. Though his audience is academic, his concept is portable to non-academic audiences. These are my notes on the lecture. o § Hardware⠀➾ # ⚓ memory_lane⠀⇛ mentioned the Z80 processor, which had me remembering having a “Timex Sinclair” computer (I *believe* with a 16K (whoa!) memory expansion unit), on which I first tinkered with assembly language (vaguely remembering the book describing the instruction set seeming to cost a fortune at the time). o § Health/Nutrition/Agriculture⠀➾ # ⚓ Bridge Michigan ☛ University_of_Michigan_gun_violence researchers_hope_to_curb_shooting_deaths⠀⇛ As of May 25, less than halfway through the year, the United States has had 213 mass shootings. And yet for every person who died in a U.S. mass shooting in 2020, about another 86 died from other forms of gun violence. # ⚓ Gannett ☛ Michigan-made_chemical_used_in_Vietnam_War_led_to Wyandotte_veteran’s_passing⠀⇛ She will be joining others who will read off the names of Michiganders being inducted into the national In Memory program — part of the Vietnam Veterans Memorial Fund. The inductees include soldiers like her husband, who is believed to have died of cancer caused by Agent Orange exposure during the conflict, and others who faced similar problems. # ⚓ Covid_again…⠀⇛ I just tested positive — something that surprised me even though I am on day 3 of a strange little cough. I had received my fourth dose just on May 19th and was feeling somewhat bulletproof. When I got the cough I started home-testing every day, and tested negative. I almost skipped today, because, you know, it’s kind of unlikely… But then I felt the familiar joint ache which alternates with an almost ecstatic feeling when I shift my legs to a more comfy position. That, to me, is the symptom unique to covid. I don’t know if I am physiologically weird as I haven’t heard anyone mention that. The muscle/joint aches that turn to an extremely pleasurable sensation after getting more comfortable… # ⚓ Lonely⠀⇛ About three weeks ago I was afflicted with awful allergies to the high spring pollen count. My nose ran like a creek, I sneezed in paroxysms lasting several minutes, my red eyes watered and itched. A cold sore began to present on my left eyelid. # ⚓ Orderlies⠀⇛ If you’re unit restricted in the psych hospital where I work, you can’t go to the cafeteria or Rec. Nursing staff can put you on UR or take you off it. It doesn’t need a doctor’s order. o § Proprietary⠀➾ # ⚓ Rapid_Response:_Microsoft_Office_RCE_–_“Follina”_MSDT Attack⠀⇛ Microsoft has now revealed the CVE identifier for this vulnerability is CVE-2022-30190, including a Security Update and article with guidance… but no patch looks to be available as of yet. Huntress is keeping a close eye on the developing threat of a zero-click remote code execution technique used through MSDT (Microsoft Diagnostics Tool) and Microsoft Office utilities, namely Microsoft Word. Throughout the next coming days, we expect exploitation attempts in the wild through email-based delivery. # ⚓ The Verge ☛ China-linked_[crackers]_are_exploiting_a_new vulnerability_in_Microsoft_Office⠀⇛ Details shared by Proofpoint on Twitter suggest that a hacking group labeled TA413 was using the vulnerability (named “Follina” by researchers) in malicious Word documents purported to be sent from the Central Tibetan Administration, the Tibetan government in exile based in Dharamsala, India. The TA413 group is an APT, or “advanced persistent threat,” actor believed to be linked to the Chinese government and has previously been observed targeting the Tibetan exile community. In general, Chinese hackers have a history of using software security flaws to target Tibetans. A report published by Citizen Lab in 2019 documented extensive targeting of Tibetan political figures with spyware, including through Android browser exploits and malicious links sent through WhatsApp. Browser extensions have also been weaponized for the purpose, with previous analysis from Proofpoint uncovering the use of a malicious Firefox add-on to spy on Tibetan activists. o § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ The Verge ☛ Google_is_combining_Meet_and_Duo_into_a single_app_for_voice_and_video_calls⠀⇛ Getting this right will be tricky for Google. If it wants to build a cross-platform, cross- purpose platform for audio and video calls, it has to get a lot of little things right. Should every single device and browser tab you’re signed into ring every time you get a call? (Google says no, and that it’s getting better at recognizing which device you’re actually using and sending calls and notifications to that one.) Should you be able to get calls on your personal and work device at the same time? (No good answer yet, but Soltero said he’s leading the charge to figure it out.) o § Defence/Aggression⠀➾ # ⚓ Common Dreams ☛ Biden_Plans_to_Sell_Armed_Attack_Drones_to Ukraine:_Report⠀⇛ The Biden administration is planning to sell Ukraine armed attack drones as the embattled country continues to defend itself from Russia’s nearly 100-day invasion, a move that experts say would risk increasing the chance of war between the United States and Russia. “Supplying large, long-range drones would be a significant escalation in the types of systems supplied to Ukraine.” # ⚓ The Hill ☛ Cyber_Command_chief_confirms_US_took_part_in offensive_cyber_operations⠀⇛ Nakasone previously said his agency deployed a “hunt forward” team in December to help Ukraine shore up its cyber defenses and networks against active threats. But his latest remarks appear to be the first time that a U.S. official said publicly that the U.S. has been involved in offensive cyber operations in response to Russia’s invasion of Ukraine. The general, who was speaking in Tallinn, Estonia, told Sky News that the “hunt forward” operations have enabled the U.S. to look for foreign hackers and identify their strategies before they target the United States. # ⚓ The Register UK ☛ US_conducted_offensive_cyber_ops_to support_Ukraine_against_Russia,_says_general [Ed: It'd easy when Windows has so many back doors]⠀⇛ America’s military conducted offensive cyber operations to support Ukraine in its response to Russia’s illegal invasion, US Cyber Command chief General Paul Nakasone has said. “We’ve conducted a series of operations across the full spectrum; offensive, defensive, [and] information operations,” General Nakasone told Sky News in an interview that aired Wednesday. Nakasone, who also serves as director of the NSA, didn’t provide specific details about the offensive operations, though he said they were lawful and complied with US policy. “My job is to provide a series of options to the secretary of defense and the President, and so that’s what I do,” he said. White House press spokesperson Karine Jean-Pierre doubled down on the message, saying: “We don’t negotiate our security assistance packages to Ukraine. We are doing exactly what the President said he would do … to provide security assistance that is above and beyond.” # ⚓ JURIST ☛ Ireland_court_finds_former_soldier_guilty_of_ISIS membership⠀⇛ In 2015, Smith traveled to Tunisia and was voluntarily taken to Syria by members of the Islamic State. There, Smith alleges she was pressed into marrying an unnamed British/Pakistani man in Raqqa, Syria. Smith alleges her husband became violent in 2016, and the violence continued through 2017 when Smith gave birth to their daughter. After the leadership of ISIS fell in 2018, Smith fled at the urging of her husband and was placed in the Al- Hawl refugee camp by Turkish armed forces. Smith was then deported to Ireland amid the Covid-19 pandemic. In Ireland, Smith was charged with being a member of ISIS and of financially supporting ISIS; she was later acquitted of the financial charges. # ⚓ Scheerpost ☛ Elon_Musk_Is_Not_A_Renegade_Outside—He’s_A Massive_Pentagon_Contractor⠀⇛ Musk’s company has been awarded billions of dollars in contracts to launch spy satellites for espionage, drone warfare and other military uses. For example, in 2018, SpaceX was chosen to blast a $500 million Lockheed Martin GPS system into orbit. While Air Force spokesmen played up the civilian benefits of the launch, such as increased accuracy for GPS devices, it is clear that these devices play a key role in global surveillance and ongoing drone wars. SpaceX has also won contracts with the Air Force to deliver its command satellite into orbit, with the Space Development Agency to send tracking devices into space, and with the National Reconnaissance Office (NRO) to launch its spy satellites. These satellites are used by all of the “big five” surveillance agencies, including the CIA and the NSA. Thus, in today’s world, where so much intelligence gathering and target acquisition is done via satellite technology, SpaceX has become every bit as important to the U.S. war machine as more well- known companies like Lockheed Martin and Boeing. Without Musk’s company, the U.S. would not be able to carry out such an invasive program of spying and drone warfare around the world. Indeed, China is growing increasingly wary of this power, and is being advised to develop anti-satellite technologies to counter SpaceX’s all-seeing eye. Yet Musk himself continues to benefit from a general perception that he is not part of the system. # ⚓ US News And World Report ☛ Hindu_Families_Flee_Kashmir After_Targeted_Killings⠀⇛ Some 250,000 Kashmiri Pandits left the Kashmir valley because of a sharp rise in killings of Hindus and attacks on their homes at the start of a rebellion by Muslim militants in 1989. # ⚓ Common Dreams ☛ Opinion_|_Does_America_Need_an_Emmett_Till Moment_for_Mass_School_Shootings?⠀⇛ In the days since the Uvalde shooting, media outlets have shared heartbreaking images of the small victims as they were cherished in life. As Americans, we’re forced to look into their young, innocent eyes and accept our shame that we failed to protect them. # ⚓ Common Dreams ☛ Opinion_|_With_Investors_Dismissing_Chances of_Gun_Control_Legislation,_Firearm_Stocks_Spike_After_Mass Shootings⠀⇛ The day after an armed 18-year-old entered the Robb Elementary School in Uvalde, Texas, and shot dead 19 children and two teachers, the share prices of gun and weapons manufacturers jumped. o § Environment⠀➾ # ⚓ Neil Selwyn ☛ Reframing_Ed-Tech_as_a_matter_of_eco- justice⠀⇛ Yet framing what needs to be done in terms of a ‘climate emergency’ is perhaps not as helpful as might seem. As Hema Vaishnavi Ale (2021) reasons, emergencies are finite and time-bound, after which our lives can hopefully revert back to ‘normal’. As such, the idea of ‘climate emergency’ implies a form of extraordinary mitigating responses that might stand a chance of addressing and eventually overcoming the problem. This neatly sidesteps more awkward expectations that we are not facing a finite ‘emergency’ that can be nipped in the bud. Instead, it seems more realistic to take the stance that this is a fast-changing condition that we need to permanently readjust our lives around. # ⚓ BBC ☛ Why_city_forests_are_getting_sick⠀⇛ Though it can be easy to think of them as little more than city furniture, urban trees are very much alive – and their struggle to survive is only becoming more extreme. Without a radical rethink of the living conditions of this long-overlooked community, some experts are concerned that our cities could soon lose much of their greenery altogether. How have some trees survived in these dystopian environments for so long? And what can be done to save the others? # ⚓ Common Dreams ☛ Hawaii_Youth_Launch_Landmark_Climate_Case Targeting_Transportation_Pollution⠀⇛ Fourteen young people on Wednesday filed a groundbreaking constitutional climate lawsuit against the Hawaii Department of Transportation and its director, Jade Butay; Hawaii Gov. David Ige; and the State of Hawaii. “Climate change is drastically changing lives around the world and we need our governments to take it and us seriously.” # § Energy⠀➾ # ⚓ YLE ☛ €140m_of_tax_revenue_collected_via cryptocurrencies⠀⇛ According to figures reported to tax authorities, residents of Finland sold more than 2.14 billion euros worth of cryptocurrencies. In 2020, the corresponding amount was just 190 million euros. # § Overpopulation⠀➾ # ⚓ VOA News ☛ US_Elevates_Water_Security_as_Foreign Policy_Priority⠀⇛ With the world’s population rising and climate change bringing more erratic rainfall and severe droughts, experts say the number of water-related violent incidents is growing. More than 200 such conflicts occurred in the past three years, according to data from the Pacific Institute, which tracks water-related violence around the world. # ⚓ NBC ☛ Sweeping_water_restrictions_begin_in_Southern California_in_ongoing_drought⠀⇛ Households are now forbidden from watering their lawns more than once a week in many jurisdictions. The goal is to slash water use by 35 percent as the state enters its third straight year of drought. The rules come after California officials in March announced they were cutting State Water Project allocations from 15 percent to 5 percent of normal amid declining reservoir levels and reduced snowpack. California’s two largest reservoirs have already dropped to critically low levels, and the state this year experienced its driest January, February and March on record. o § Finance⠀➾ # ⚓ David Rosenthal ☛ Generally_Accepted_Accounting Principles⠀⇛ In simple terms, this excess depreciation means that the company’s real cost for creating income is much higher than they report, and thus their real profit as a continuing business is much less than they report, because they are not putting aside the money they will need to replace obsolete hardware. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ NBC ☛ Sheryl_Sandberg_to_leave_Facebook_parent_company_this fall⠀⇛ Sandberg joined Facebook in 2008 from Google and helped build the company’s online advertising operation into one of the internet’s most profitable businesses and expand the company’s reach outside the U.S. But her high-profile role alongside co-founder Mark Zuckerberg also made her among the most recognizable figures tied to Facebook’s various scandals, including data privacy and misinformation issues that have continued to surround the company. # ⚓ India Times ☛ Key_Facebook_force_Sheryl_Sandberg_steps down⠀⇛ Key Facebook force Sheryl Sandberg steps downSan Francisco: Meta’s second most powerful executive Sheryl Sandberg made the shock announcement Wednesday she will leave after a 14-year tenure that included helping steer scandal-prone Facebook to advertising dominance. Sandberg, 52, has been one of the most influential women in Silicon Valley and her departure comes as the social media juggernaut faces an uncertain future and fierce competition. Her exit from Facebook parent Meta will be effective in the fall, she wrote on the platform, adding she planned to remain on the firm’s board. # ⚓ The Hill ☛ Hillicon_Valley_—_Sandberg_stepping_down⠀⇛ Next up: Sandberg will be replaced as COO by Javier Olivan, the company’s chief growth officer, but his role will differ from the work Sandberg did for the company, Meta CEO Mark Zuckerberg said in a post. # ⚓ The Verge ☛ Sheryl_Sandberg_on_leaving_Meta⠀⇛ In her own words, there are two big factors in Sandberg’s decision to leave now: the fact that Meta’s executive team has been built up to make way for her departure, and that, as the leader of the “Lean In” movement, she wants to focus more on philanthropy and women’s rights. “There’s no perfect time,” she told me during a brief phone interview Wednesday afternoon. “It is a job that’s been an honor and a privilege, but it’s not a job that leaves a lot of time to do much else.” Here’s my full conversation with Sandberg about her stepping down as COO of Meta, edited lightly for clarity: [...] # ⚓ Reason ☛ Texas_Can’t_Start_Enforcing_Social_Media_Law,_Says SCOTUS⠀⇛ In response, tech industry groups NetChoice and the Computer and Communications Industry Association (CCIA) asked the Supreme Court to intervene and vacate the 5th Circuit’s stay. And now it has, in a 5-4 decision issued Tuesday. The majority—a conservative-liberal mix that included Chief Justice John Roberts and Justices Stephen Breyer, Sonia Sotomayor, Brett Kavanaugh, and Amy Coney Barrett—did not offer reasoning for their ruling. A dissent penned by Justice Samuel Alito, joined by Clarence Thomas and Neil Gorsuch, can be found here. Justice Elena Kagan also dissented. # ⚓ JURIST ☛ US_Supreme_Court_temporarily_blocks_Texas_social media_law⠀⇛ The Applicants alleged that HB20 “interferes with their exercise of ‘editorial discretion,’ and they maintain that this interference violates their right ‘not to disseminate speech generated by others.’” Justice Alito wrote that HB20 is “ground-breaking” and “of great importance” due to the fact that it “addresses the power of dominant social media corporations to shape public discussion of the important issues of the day.” His dissent also stated that the court’s decision to block HB20 is “a significant intrusion on state sovereignty, and Texas should not be required to seek preclearance from the federal courts before its laws go into effect.” The law will remain blocked until the US Court of Appeals for the Fifth Circuit decides whether the law is constitutional or not. # ⚓ Common Dreams ☛ Opinion_|_Say_Yes_to_Being_‘Woke’⠀⇛ I am tired of rightwing politicians distorting our language to suit their bigoted ideology. # ⚓ The_Hermit’s_Cell⠀⇛ It’s so disappointing to see people who don’t realize they’re being used to deliberately divide people. Smart, caring, thoughtful people whose hearts are umdoubtedly in the right place so frequently get caught up in culture-war bullshit that is just so obviously designed to divide people or to create new subcultures and identities for capitalists to market to. The perfect wedge issues are those that deal not with morality, but with the nature of reality itself. People aren’t going to agree about those, not easily, especially when you keep moving the goalposts and pulling the rug out from people who were previously on board. And, of course, you have to realize what the end goal is of cannibalistic movements that seem all too keen on cutting people out at the slightest transgression. In a strange twist of fate, it’s religion. We all know the boiled frog never reacts if the temperature is raised slowly enough. You’re being used to facilitate the rise of fascism. It’s happened before and it’ll happen again. The last time culture-war bullshit like this was so prevalent, it was used to radicalize people into right-wing extremism and galvanize the fascists. Of course by the time you realize this it will be too late. o § Censorship/Free Speech⠀➾ # ⚓ JNS ☛ Can_free_speech_be_protected_without_helping_the haters?⠀⇛ To those who decry their censorship, the companies and their liberal defenders respond by citing their property rights as private companies and the constitutional principle that guarantees publishers the right to accept or decline material as they see fit. Were these sites normal publications, whether online or traditional print, they’d be within their rights to publish what they like as America’s founders intended when they wrote the First Amendment. But they are nothing of the sort. # ⚓ No_monetary_solution⠀⇛ I read something that struck me: “Throwing money at a problem is unlikely to resolve it, as actual sit- uations require genuine, not monetary, action.[^1] I don’t have to add context. You brought your own. An online acquaintence had money but couldn’t pay rent for his server because all means of payment are sanctioned. Finally he found Mir (Russian) can transfer money to UnionPay (Chinese), accepted in the Netherlands. o § Freedom of Information / Freedom of the Press⠀➾ # ⚓ VOA News ☛ Reporter:_World_‘Must_Not_Be_Silent’_on_Afghan Media_Restrictions⠀⇛ An award-winning journalist who fled from Afghanistan last August says the international community must not remain silent on Taliban restrictions for female journalists. Anisa Shaheed, a former TOLOnews broadcaster who on May 23 was honored with the International Center for Journalists’ Knight award, says she is troubled by orders that impact the ability of female journalists to work. In an interview with VOA’s Dari service, Shaheed said the Taliban mandate that women cover their faces when reporting is “not acceptable.” o § Civil Rights/Policing⠀➾ # ⚓ Medforth ☛ An_Afghan_who_vandalised_a_German_church_did_not act_with_intent_but_only_had_problems_with_a_Christ_figure because_of_his_faith⠀⇛ He allegedly removed church inventory at the end of October last year, tore the valuable Christ figure from the wall and damaged it, and broke an altar panel. He is charged with damage to property and trespassing. # ⚓ DNA India ☛ Hindu_idols_vandalized_in_Karnataka’s_Hassan, tension_grips_district⠀⇛ The police said the miscreants, who came to the premises of the temple on Monday, swam in the Kalyani (sacred water body of the temple). They also smoked despite objections and threatened and chased away the labourers working in the premises. Later, they went to the exhibition centre and vandalised the idols which were ready for installation and some were under construction to be set up in the temple premises. The miscreants used rods and other equipment to break idols. # ⚓ Quillette ☛ The_Wobblies’_Return⠀⇛ The IWW was founded in Chicago in 1905 by the legendary firebrand William D. “Big Bill” Haywood, the perennial socialist presidential candidate Eugene V. Debs, and the beloved matriarch of radicalism Mother Jones. “Every working man or woman who earns his livelihood by brain or muscle” must “organize as a class, take possession of the earth and the machinery of production, and abolish the wage system,” read the preamble to the organization’s founding document. “They were a little vague,” admits one interviewee, “on where they went from there.” From the start, the “Industrial” billing was something of a misnomer: the IWW welcomed migratory workers, lumberjacks, and any other weather-beaten laborer with calloused hands. Unlike the exclusionary crafts and guilds, every working “stiff” (a tag worn as a badge of honor) was entitled to membership. University students and intellectuals—those who came to radical politics by way of the head not the stomach, as Lenin put it—tended to join up elsewhere. o § Monopolies⠀➾ # ⚓ The Register UK ☛ Amazon_not_happy_with_antitrust_law targeting_Amazon⠀⇛ Amazon has blasted a proposed antitrust law that aims to clamp down on Big Tech’s anti-competitive practices. The American Innovation and Choice Online Act (AICOA) led by Senators Amy Klobuchar (D-MN) and House Representative David Cicilline (D-RI) is a bipartisan bill, with Democrat and Republican support in the Senate and House. It is still making its way through Congress. The bill [PDF] prohibits “online platforms” from unfairly promoting their own products and services in a way that prevents third-party businesses from competing. Companies with 50 million-plus active monthly users in the US or 100,000-plus US business users, and $550 billion-plus in annual sales or market cap, that act as a “critical trading partner” for suppliers would be affected. In practice, it would mean Amazon, at its current rate of revenue growth, would not be able to push its own products and those sold by vendors that have signed up to its Fulfillment by Amazon program to the detriment of other sellers. Businesses hawking fare via FBA pay the e-commerce giant to store and package their goods in Amazon’s warehouses. In return, Amazon ranks these items more highly on its website and sends them to consumers more quickly using its Prime delivery service. # § Software Patents⠀➾ # ⚓ The Verge ☛ Looking_Glass_might_have_just_invented the_GIF’s_3D_successor⠀⇛ On June 15th, 1987, CompuServe introduced the GIF, a way to share images — or animated sequences of images — anywhere. The incredible portability of the late Steve Wilhite’s “graphics interchange format” made it the perfect canvas for viral memes. Now, a company called Looking Glass is trying to make holograms effortlessly portable, too. # § Copyrights⠀➾ # ⚓ Torrent Freak ☛ Mega_Reports_Surge_in_Copyright Takedown_Requests⠀⇛ Mega is one of the leading file storage platforms on the Internet with more than 117 billion files stored on its servers. Given this scale, it is no surprise that these files include some infringing content. During the first quarter of 2022, Mega reported a significant increase in copyright takedown requests, targeting more than a million links. # ⚓ Torrent Freak ☛ Piracy,_It’s_a_Crime:_UK_Govt. Ignored_Warnings,_Now_Families_Pay_The_Price⠀⇛ Before the UK passed the Digital Economy Act in 2017, critics warned that categorizing file-sharers as criminals would encourage “copyright trolls” to demand cash settlements while implying a criminal conviction might be an alternative. The government didn’t listen and it is now happening. One of the parties involved is FACT, the company behind the infamous ‘Piracy, It’s a Crime’ campaign. # ⚓ Public Domain Review ☛ The_Discarnates:_*Thomas Carlyle_in_the_Spirit-World*_(1920)_–_The_Public_Domain Review⠀⇛ Over the course of a year, Thomas Carlyle supposedly transmitted this text to Dr. Wm. J. Bryan from beyond the grave. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 11655 ➮ Generation completed at 02:44, i.e. 253 seconds to (re)generate ⟲