𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, February 23, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Thu 24 Feb 02:40:27 GMT 2022 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2022/02/23/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmTLUpA1Pbmatf5PSQgBbMk1Hj8eJFQAcNy7ahAe769Anx QmbQWJTJVwCBMn6Bc7J9W2fhZtZYwQh4SrKoy4dF1Rj3Pm QmZ3Z9HPLFuFUYdDqN8YY1cZW5M8k9MCEyfwYQiJSBdgg9 Qme1XwuhK1F1t6m8AJGPXQ8U9wCeB9UCDmmkPBEmWLharx QmQdk83ourWknf8WYXr4Z6LnuaLWYmqhpidR9Crga89wZn Qmae8sev1AAiuQdXEbMcdP8Nmxxz3DL81fAkGoiVLghjbB QmYBkNNgDtvjiZGy3f7RwY487FEsQEUQkXJN3yYkKnMGUa QmdmWehA6h2EsxLvmLQHxv9wFn9VZJZHVbgXQXVigmyUCo QmbqzbFLBLnEsD6wqjgRecqxx1eMiGqj8KkJ8LBeVS7kMR QmRogUf31QThSc3fc9qKNWAZGJTDSwdv1pupuEmsuUuu26 QmZRqBo3ysfz1YXExEqVuEuy5xb4ME8cK3jBDpd8wGSwwX QmT6UzkVGBqiGJqW9tNXHnJ2F7GjgkFTQ1tvxxFeYF4VH3 QmfSu9XMsGzj9YkPDP79UmwB6R9G9p3HQjsSCvUovR8y4o QmeC7QgpY53w9VR36JGVyYSzhMZkHLkGiYWgd57Dskr9pH QmZHDDpdkiKdpvVjLb94b8X2LhPVMcNQweiDqukj1DyKVT QmPgCJca3XFthf3S9xSXFzx2JdpEDjUZ3HPfAnGbLWi5kr QmXBF3kDxFdmKcnVa7vYpbU6MyXrd1r3Y1NNrKZ3hrTTFa QmbGvonNbAJzqBpoefSxdJSBAiUubKnrKDWzMQhqE8sKy9 QmNyjuGQ9G6aZFzvjbDENKmySNxf1JG2psBTi252HdEGHE QmdSS5zduBpaVEqHBiz53YJo7JbLv9XgUWbU3sJWZqfSG8 QmcEFBoREHvxtA22UaNuV5Mx1EPRF8ANqTeNuB9Sx6DA3x ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ [Meme] We’ve Been Here Before... | Techrights ⦿ IRC Proceedings: Tuesday, February 22, 2022 | Techrights ⦿ [Meme] Artificial ’Productivity’ | Techrights ⦿ What EPO Staff Really Thinks | Techrights ⦿ SPAM is Ruining the World Wide Web and We Need to Talk About That | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/02/23/deja-vu-2022/#comments http://techrights.org/2022/02/23/irc-log-220222/#comments http://techrights.org/2022/02/23/meme-artificial-ai-bs/#comments http://techrights.org/2022/02/23/what-epo-staff-says/#comments http://techrights.org/2022/02/23/www-of-spam/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/02/23/intel-acquires-linutronix/#comments http://techrights.org/2022/02/23/sqlite-release-3-38-0/#comments http://techrights.org/2022/02/23/truenas-scale-22-02/#comments ䷩ 𝚕𝚒𝚗𝚎 61 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/23/deja-vu-2022/#comments Gemini version at gemini://gemini.techrights.org/2022/02/23/deja-vu-2022/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_We’ve_Been_Here_Before…⠀✐ Posted in Europe, Patents at 8:43 am by Dr. Roy Schestowitz “I don’t trust anyone who’s nice to me but rude to the waiter. Because they would treat me the same way if I were in that position.” –Muhammad Ali 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Battistelli 2016, Campinos 2020, and Campinos 2022⦈ Campinos (in_2021) “shows no real understanding of the patent system, he cannot grasp the concept of social dialogue, and it won’t be long before just 0% of his staff trusts him (last year’s survey, conducted confidentially, showed that only 3% of staff still trusted him).” Anonymous eyewitness on Battistelli (in_2016): “People were chatting all around but all backs turned to him. He looked extremely alone, almost like a leper and maybe he also felt so. His body language showed enough: hunchbacked and looking down, avoiding eye contact with his staff.” ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠟⠀⠀⠀⠘⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠟⠛⢢⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠈⢉⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠀⠤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠈⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠁⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⢿⡿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣶⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⣀⣀⣼⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⠻⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⢣⣄⢠⣿⣿⠟⠋⠛⣿⣿⣿⠟⠋⠑⣲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠘⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣄⡘⠿⣦⡀⠀⣼⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⣿⡧⠉⠛⠀⠀⠰⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⢃⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠛⠻⣿⣿⣿⣿⣿⡇ ⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠹⣿⠇ ⠀⣨⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣇⣈⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣆⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡛⣛⣻⡯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣀⠀⠀⣀⣀⣀⠀⠀⠀ ⠀⢽⢸⣿⣿⣿⣿⡞⣷⣿⣿⣿⣯⠸⢿⣿⣿⡿⠻⢿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡏⠉⢻⣿⡿⠿⢿⣿⣿⣿⣿⣷⣤⣾⣿⢻⣿⣧⣤⣶⣿⣿⢠⣾⣿⢻⣿⣷⠀⠀ ⠀⠈⢸⣿⣿⣿⣿⢧⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠛⠛⣳⣿⣿⣿⣿⣿⢸⣿⣿⠈⢹⣿⣿⢸⣿⣿⣶⣿⣍⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠛⠃⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⣰⣿⡿⠁⢻⣿⣿⢸⣿⣿⣀⣸⣿⣿⢸⣿⣿⢸⣿⣿⢠⣅ ⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣸⣿⣿⣶⡆⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⡇⠀⠀⣼⣿⣿⣤⣤⠘⣿⣿⣼⣿⡿⠙⢻⣿⣿⠘⣿⣿⣼⣿⡿⢸⣷ ⠀⠀⠈⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣄⣈⣍⣭⣿⣿⣿⣿⣿⣧⡉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⢩⠉⠀⠈⠉⠉⠉⠀⢹⣿ ⠀⠄⠲⣶⠀⠴⠍⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⠇⠀⠀⠘⠟⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠖⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣶⣌⣉⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠠⠬⣉⡉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣠⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣿⡃⠀⠀⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠛⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⠇⢰⡿⠋⠉⢙⢿⣿⣿⠗⠂⠠⣄⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣇⠀⠀⠀⢸⣿⡇⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣤⣘⠲⠄⠀⢋⣿⣷⣤⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣾⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿⡏ ⠀⠀⢈⣩⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣄⠘⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉⣛⣛⡓⢾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢹⣋⠙⠹⣟⣛⣿⠟⠁⠁ ⠀⠀⢸⣿⣿⣿⣿⡞⣷⣿⣿⣿⣯⠸⢿⣿⣿⣿⠾⢿⣿⣿⣿⠷⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡏⠉⢻⣿⡿⠿⠿⣿⣿⣿⣿⣷⣄⣾⣿⢻⣿⣧⣤⣶⣿⣿⢠⣿⣿⢻⣿⣷⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⢧⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠛⠛⣳⣿⣿⣿⣿⣿⢸⣿⣿⠈⢹⣿⣿⢸⣿⣿⣶⣷⣅⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⣿⣻⡃⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⣰⣿⡿⠁⢹⣿⣿⢸⣿⣿⡀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢀⡇ ⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣼⣿⡿⠻⢿⣿⣿⣼⣼⣿⣿⣾⣧⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⡇⠀⠀⣼⣿⣿⣤⣤⠘⣿⣿⣼⣿⡿⠉⢹⣿⣿⠘⣿⣿⣼⣿⡿⢸⣿ ⠀⠀⠈⠉⠉⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⣭⣽⣿⣾⣿⣿⣿⣧⣭⡍⠉⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⣭⠀⠈⠉⠉⠉⠀⢸⣿ ⠀⠀⠲⣶⠀⢶⠄⠠⠰⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣿⡇⠀⠀⠀⠿⠼⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣤⣴⣌⣉⣸⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍⢉⣉⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠐⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣤⣴⣶⣿⣿⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⡟⠁⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⡾⠿⢿⣾⣿⣿⣤⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿ ⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣌⠻⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⠇⡟⠀⠀⠐⢻⣿⠟⠉⠉⣻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⡀⠀⠀⣾⣿⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣤⣴⣿⣿⣕⠤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⡿⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣿⡾⣻⣿⣿⣿⡿⠻⡿ ⠀⠀⢀⣑⣸⣿⡿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣷⠀⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⣉⣉⡓⠾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠛⢛⣋⠺⠿⣟⣛⣉⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡟⣧⣿⣿⣿⣯⠸⢿⣿⣿⣿⠿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠉⢹⣿⡟⠛⠛⣿⣿⣿⣿⣷⣄⣾⣿⢻⣿⣧⣤⣶⣿⣿⢠⣿⣿⢻⣿⣷⠀⠁ ⠀⠀⢸⣿⣿⣿⣿⢧⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠛⠛⣳⣿⣿⣿⣿⣿⢸⣿⣿⠈⢹⣿⣿⢸⣿⣿⣴⣷⣍⠀⠄ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛⣿⣿⢿⣿⣿⣿⣿⣿⣿⢻⢹⣿⣿⣿⣧⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⢀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢰⣧ ⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠙⢻⣿⣿⣾⣾⣿⣿⣿⡿⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⡧⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡟⠀⢸⣿⣿⠘⣿⣿⣼⣿⡿⣼⣿ ⠀⠀⠈⠉⠉⠉⠉⠉⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⡉⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⢩⠉⠀⠈⠉⠉⠉⠀⣿⣿ ⠀⠀⠰⣶⠀⠶⠄⠠⠤⠖⠆⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣿⣿⠀⠀⠀⢺⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢉⣭⣴⣌⣉⣰⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣙⠛⠛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠢⠈⣿⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣴⣾⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⣿⣷⣜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣟⠀⠀⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡾⠛⠿⣿⣿⣿⣦⣤⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣽⣿ ⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡍⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⡟⢸⠀⠀⠐⢹⣿⠋⠉⢉⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣄⠀⠀⣾⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣤⣶⣿⣿⣑⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠃⣤⣴⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣶⡿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⢃⣤⣤⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠃⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣿⣿⣿⣿⣿⣿⠟⣿⣿ ⠛⠁⠀⠀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⣿⣟⣾⣿⣿⠿⠋⠀⠻⡿ ⠀⠀⢀⣀⣁⣹⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢆⣘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣤⣸⣿⣿⣿⣿⣿⣿⣿⣷⣤⡌⣉⣉⡙⠾⣿⣿⡿⠿⢿⣿⣿⣿⣷⣦⣄⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢘⣋⠙⠿⣋⣀⣀⠀⢨⣿ ⠀⠀⢸⣿⣿⣿⣿⡞⣧⣿⣿⣿⣯⠸⢿⣿⣿⣿⠿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢿⣿⣿⢿⢿⣿⣿⣿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡏⠉⠙⣿⣿⡿⣿⣷⣀⣾⣿⢻⣿⣧⣤⣶⣿⣿⢠⣿⣿⢻⣿⣷⢸⣿ ⠀⠀⢸⣿⣷⣾⣿⢧⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣙⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠛⠛⣳⣿⣿⢿⣿⣿⢸⣿⣿⠉⢹⣿⣿⢸⣿⣿⣶⣿⣝⣾⣿ ⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⢿⣿⣿⣿⣿⣿⣿⣻⢸⣿⣿⣿⣧⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿ ⠀⠀⢸⣿⣿⣾⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣈⣹⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⣷⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡿⠀⢸⣿⣿⠘⣿⣿⣼⣿⡿⣾⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠙⠽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣷⣿⣭⡍⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⢉⡄⠈⠉⠉⠉⠸⣿⣿ ⠀⠀⠰⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣹⣿⡆⠀⠀⢸⣧⣾⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣋⣩⣽⣌⣉⣠⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⠻⠿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⣜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣗⠰⠄⢹⡇⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣴⣶⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠻⣿⣾⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⣾⠁⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⡾⠟⠻⣿⣿⣿⣦⣤⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣾⣿⣿ ⣤⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣬⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⡿⢸⠁⠀⠐⢹⣿⠏⠁⢉⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣛⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢆⠀⠀⣸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣋⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢿⣶⣦⣤⣶⣾⣿⣑⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠙⠢⠤⠾⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⠏⣤⣤⣤⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠃⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⣽⣿⣿⣿⣿⣿⣿⠟⠈⣿⣿ ⠛⠋⠀⢀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⠟⠁⠀⠀⣸⣿ ⠀⠀⢀⣀⣀⣀⠼⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢷⣀⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⣈⣉⡉⠛⣛⣛⡛⠿⢿⣿⣿⣿⣶⣦⣄⣀⣀⠀⠀⠀⣀⣀⡀⠀⠈⠀⢓⣻⠿⠉⣀⣀⣀⠀⣼⣿ ⠀⠀⢸⣿⣿⢿⣿⡞⣧⣿⣿⣿⣯⠸⢿⣿⣿⣿⠿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡏⠈⠉⣹⣿⡿⣿⣷⣀⣾⣿⢻⣿⣧⣤⣶⣿⣿⢠⣾⣿⢻⣿⣷⢿⣿ ⠀⠀⢸⣿⣯⣾⣿⢧⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠛⠛⣳⣿⣿⢿⣿⣿⢸⣿⣿⠉⢹⣿⣿⢸⣿⣿⣶⣿⣝⣾⣿ ⠀⠀⢸⣿⣿⢻⣿⣯⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣽⢻⣿⣿⢿⣿⣿⣿⣻⣸⣿⣿⣿⣧⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⠘⣾⣿⣿⢸⣿⣿⢸⣿⣿⣹⣿ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣽⣿⣿⣿⣿⡏⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⣿⠀⠀⣼⣿⣿⣤⣤⠘⣿⣿⣼⣿⡿⠀⢹⣿⣿⠘⣿⣿⣼⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠉⠉⠹⠿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣷⡿⠭⠉⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠀⠈⠉⠉⠉⢺⣿⣿ ⠀⠀⠰⢦⠀⠰⠄⠠⠴⠶⠆⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣼⣇⠀⠀⠘⣿⣸⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣈⠀⣹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠟⠛⢛⣫⣽⣌⣉⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⡿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡄⢻⡟⠀⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣄⣤⣴⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠾⠇⠀⠷⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣄⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣼⠁⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣰⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⠿⠿⣿⣿⣿⣦⣄⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣻⣿ ⢀⣠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⡝⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⠁⡇⠀⠐⢚⣿⠟⠉⢉⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢣⡀⠀⢸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⠟⣃ ⣮⣭⣛⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣴⣶⣷⣿⣝⡲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢫⣬⣽⣾⣿ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣀⣶⣿⣿⣿⣿⣿⣿⡿⣡⣶⣦⣄⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⣿⡿⠯⠀⠀⠀⠀⣶⣿⣿⣿⣿ ⠈⣻⣿⡿⠃⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⢀⠾⣿⣿⣿⣿⣿ ⠛⠛⠉⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣬⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡛⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⣀⠀⢾⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣧⣈⣻⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⣀⣀⡈⠛⣛⣛⡛⠛⢷⣄⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣀⠀⠀⣀⣀⣻⢿⣿⣿ ⠀⠀⢸⣿⣿⢿⣿⡆⣷⣿⣿⣿⣯⠸⢿⣿⣿⡿⠿⢿⣿⣿⡿⠟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⣰⣿⡟⣿⣷⣀⣾⣿⢻⣿⣧⣤⣶⣿⣿⢠⣾⣿⢻⣿⣿⣿⣿ ⠀⠀⢸⣿⣯⣼⣿⢇⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠛⠛⣳⣿⣿⢺⣿⣿⢸⣿⣿⠉⢹⣿⣿⢸⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⣧⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⠻⢿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣧⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣻⣿⣿⣾⣇⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⣿⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡿⠞⢸⣿⣿⠘⣿⣿⣼⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠉⠋⠿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣍⡉⠉⠉⠉⠉⠉⠈⠉⠁⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠀⠈⠉⢭⣽⣿⣿⣿ ⠀⠀⠰⣶⠀⠰⠄⠠⠴⠶⠆⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⠀⠀⠀⣿⣀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⢻⠇⢸⡇⠀⣿⣶⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡤⢤⠀⠀⠀⠀⠀⠀⠉⠛⠇⠸⠿⠛⣛⣀⣈⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⢠⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢠⠐⣿⠀⢸⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠴⢿⠀⡾⠞⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣸⠋⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣉⣛⣿⣷⣤⣀⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⡶⠿⣶⣿⣿⣆⣀⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡠⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣌⠛⠛⠛⠛⠛⠛⠛⠿⠿⢿⠇⡏⠀⠀⠚⣿⡟⠉⢉⣻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⡀⠀⢸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣷⣮⣍⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣶⣶⣶⣷⣿⣌⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⠛⠃⠀⠈⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⢏⣶⣶⣤⣀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢈⣿⣿⡟⠁⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿ ⠙⠛⠋⠉⠀⠀⠂⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣙⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠁⠀⠀⣸⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⡀⠀⠐⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣄⣙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡆⣀⣀⡈⠉⣉⣉⡛⠛⢛⣿⡿⣿⣷⣦⣤⣀⣀⠀⠀⠀⣀⣀⡀⠀⠁⠻⢋⣀⠀⠀⣈⣉⣻⣿⣿⣿ ⠀⠀⢸⣿⣿⢿⣿⡆⣠⣿⣿⣿⣯⠸⢿⣿⣿⣿⠿⢿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠈⣸⣿⣿⣿⣷⣀⣾⣿⢻⣿⣧⣤⣶⣿⣿⢠⣾⣿⢻⣿⣿⣿⣿ ⠀⠀⢸⣿⣧⣼⣿⠇⢹⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⢻⣿⣿⣤⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠛⠛⣳⣿⣿⢹⣿⣿⢸⣿⣿⠉⢽⣿⣿⢸⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⣧⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢻⣿⣿⣾⣾⣿⣿⢿⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣷⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⢹⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⡟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⣿⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡿⠀⢸⣿⣿⠘⣿⣿⣼⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣍⣉⠉⠉⠉⠉⠈⠉⠁⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠀⠈⢩⣯⣽⣿⣿⣿ ⠀⠀⠰⣢⠀⠠⠄⠠⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢹⡇⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡗⠀⠉⠁⠀⠀⠁⣿⡇⢸⡿⠀⣿⣯⣽⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠃⠀⠀⠘⠛⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⠀⠀⠀⠀⠉⠀⠉⠛⠿⠇⢠⣿⡿⢿⣀⢈⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠋⢩⡄⠉⣴⣾⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⢾⡇⢀⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣤⣾⠇⢸⠯⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣸⠉⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣭⣿⣷⣄⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢡⠞⠛⢿⣿⣿⣧⣤⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡝⠛⠛⠛⠛⠛⠛⠿⠿⢿⠇⡏⠀⠀⢹⣿⠋⠀⢨⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣪⣟⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠄⠀⠸⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⣿⣿⣦⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣬⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠑⠀⠚⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⡟⣵⣶⣦⣄⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣸⣿⣿⠟⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿ ⠈⠉⠉⠀⠀⠀⠀⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢴⣿⣿⣿⣿⣿⣿⣟⠛⠿⠿⠯⣹⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣽⠟⠁⠀⢠⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⡀⠀⠀⠹⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣷⣄⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⣀⣀⡈⠉⣉⣉⡉⠛⢛⣻⡿⢿⣿⣶⣤⣀⣀⠀⠀⠀⣀⣀⡀⠀⠘⠋⢀⣀⠀⠸⣟⣛⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢿⣿⡆⢠⣿⣿⣿⣯⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⣸⣿⣿⣿⣷⣀⣾⣿⢻⣿⣧⣤⣶⣿⣿⢠⣿⣿⢻⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⠇⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⢹⣿⣿⣤⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠛⠛⣳⣿⣿⢻⣿⣿⢸⣿⣿⠉⢹⣿⣿⢸⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⣧⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣹⣿⣿⣻⣿⣿⣿⣻⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⢹⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⡟⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⣿⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡿⠀⢸⣿⣿⠘⣿⣿⣼⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠙⠻⠫⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⠉⠉⠉⠈⠉⠁⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠀⠺⣭⣯⣽⣿⣿⣿ ⠀⠀⠰⢢⠀⠀⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⡇⣀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⠂⠈⠉⠀⠀⠀⠀⣿⠀⣿⡇⢸⣿⣩⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠿⠇⠀⠀⠘⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠦⠀⠀⠀⠀⠒⠈⠛⠷⢿⠃⢸⣿⣿⠿⢈⣉⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⠋⢋⠉⢩⣴⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠰⣿⠀⢸⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠬⣴⣿⠀⣿⠽⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣸⠉⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣙⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⢣⠞⠛⢿⣿⣿⣧⣤⣀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣾⣿⣿⣿⣿⣿⣶⣶⣶ ⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡼⠛⠛⠛⠛⠛⠛⠿⠿⢿⡟⢈⠀⠀⢹⣿⠋⠀⢨⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣶⡝⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣋⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠦⠀⠸⣿⡄⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⡀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣮⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠁⢼⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⡿⢱⣶⣶⣦⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⣾⡿⠟⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠒⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢰⣿⣿⣿⣿⣿⣿⣟⡛⠛⠿⠧⣽⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠏⠁⢸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⡀⠀⠀⠘⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣦⣈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣀⣀⡀⠈⣉⣉⡉⠙⢛⣛⡿⠿⣿⣶⣦⣀⣀⠀⠀⠀⣀⣀⡀⠈⠛⠁⢀⣀⢿⡿⣿⣻⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⡆⢠⣿⣿⣿⣯⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⠧⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⣸⣿⣿⣿⣷⣀⣿⣿⢻⣿⣧⣤⣶⣿⣿⢬⣿⣿⢻⣿⣷⢻⣿ ⠀⠀⢸⣿⣯⣾⣿⠇⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣝⠿⣿⣿⣿⣿⣿⣸⣿⣿⣼⣄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣇⠀⠀⠛⠛⣳⣿⣿⢻⣿⣿⢸⣿⣿⠉⢹⣿⣿⣾⣿⣿⣾⣿⣿⣾⣿ ⠀⠀⢸⣿⣿⢻⣿⣧⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⡟⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⣿⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡿⠀⢸⣿⣿⢿⣿⣿⣼⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠁⠉⠋⠹⠿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡉⠉⠉⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠸⣾⣭⣯⣽⣿⣿⣿ ⠀⠀⠰⢠⠀⠐⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠸⡿⢈⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⢸⣷⢸⣿⠀⣼⣟⣻⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠿⠞⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠿⢾⣿⠀⣿⣿⡿⠇⠈⡉⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⣶⣦⠤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⣿⠛⠛⠉⣭⣶⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡉⢾⡇⢀⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⡀⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⣥⣼⡇⢸⡯⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⢿⠿⠿⠿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣤⣾⣿⣿⣿⣿⣿⠃⠀⠀⢀⣠⠋⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢈⡻⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⢯⠞⠛⢿⣿⣿⣧⣤⣀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄ ⠀⠀⠀⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣮⠛⠛⠛⠛⠛⠻⠿⠿⠿⡿⢸⠀⠀⢉⣿⠋⠀⠨⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣴⣷⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢⠄⣸⣿⣄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣅⠀⠂⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠉⠠⢾⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⢫⣾⣷⣦⣄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠻⠿⠟⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣶⣤⣄⡀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣸⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠳⢽⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⡿⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⡀⠀⠀⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣷⣄⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣶⣶⡶⠦⣉⣉⡛⠛⢿⣿⣿⣿⣿⣶⣦⣀⣀⠀⠀⠀⣀⣀⡋⢻⠋⠀⢀⣀⠀⠀⣈⣛⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⡆⢀⣿⣿⣿⣯⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⡗⣿⣿⣻⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡏⠀⠉⣿⣿⣿⣿⣷⣀⣿⣿⢻⣿⣧⣤⣶⣿⣿⢠⣿⣿⢻⣿⣿⣿⣿ ⠀⠀⢸⣿⣯⣾⣿⠇⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠻⢿⢿⣿⣿⣽⣽⣿⣿⣤⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣧⠀⠀⠛⠛⣳⣿⣿⢻⣿⣿⢸⣿⣿⠉⢹⣿⣿⢸⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⣧⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣾⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⣴⣿⡿⠁⢸⣿⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠈⠉ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⡟⣿⣿⡇⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⣿⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡿⠀⢸⣿⣿⠘⣿⣿⣼⣿⣿⣴⣶ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠁⠀⠉⠉⠉⠻⢿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⠉⠉⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠘⢾⣭⣯⣽⣿⣿⣿ ⠀⠀⠰⢦⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠈⢀⣿⠃⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⠇⣿⡇⢸⣿⢷⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠿⣴⣿⠃⢸⠿⣿⠿⢀⠀⡈⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣸⣿⣿⣦⣠⣤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⢼⢯⣿⠋⣩⣭⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡈⢸⣿⠀⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⣍⣼⣿⣶⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⢿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⠋⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⣿⣿⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⡴⠛⢿⣿⣿⣧⣤⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡝⠛⠛⠛⠛⠻⠿⠿⠿⡿⢹⠀⠀⠉⣿⠏⠁⠨⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣴⣷⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠣⠄⣸⣿⢄⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⡀⠐⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣙⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠉⠀⠈⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⡟⣼⣿⣶⣤⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣤⣘⣿⣿⣿⣿⣿⣿⣯⣍⣙⠛⠓⠿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⡀⠀⠀⠀⣈⣻⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣦⡈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⣉⣉⡀⠀⣀⣈⡉⠉⢉⣉⡛⠛⠻⢿⣶⣀⣀⠀⠀⠀⣀⣀⡚⠋⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⡆⢀⣿⣿⣿⣯⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⣼⣿⡿⣿⣷⣀⣾⣿⢻⣿⣧⣤⣶⣿⣿⢩⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣯⣼⣿⠇⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣍⣉⡛⢻⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠛⠛⣳⣿⣿⢹⣿⣿⢸⣿⣿⣍⣽⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⣧⣼⣿⣧⣿⣿⡘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⡟⣿⣿⡇⢸⣿⣿⡏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⡿⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠁⠀⠈⠉⠉⠉⠉⠹⠿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⢽⣿⣿⣿⣿⣿⡟⠺⢭⣿⣽⣿⣿⣿ ⠀⠀⠰⢦⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⣿⣀⠀⠀⠹⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡏⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⡿⢰⣿⠀⣿⡿⣽⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠸⢯⣿⡿⠀⣿⣿⣿⠃⢀⠈⢌⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣘⣿⣿⣿⣀⣠⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡬⡍⣽⡏⢉⣯⣵⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠃⣿⡇⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣌⣁⣿⠁⣸⣿⠇⠀⠀⢴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⢀⣄⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⡏⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡟⡴⠛⢻⣿⣿⣧⣤⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣤⣴⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡬⠛⠛⠛⠛⠛⠻⠿⠿⢿⠃⠁⠀⠁⣿⠏⠁⠨⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣶⣷⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠓⠀⣨⣿⢄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡘⣿⣿⡿⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⡿⣱⣿⣷⣶⣄⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣷⣦⡤⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣭⡉⠉⠑⠻⠿⠿⠿⢿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⣀⠀⠀⠀⣀⣈⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡦⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⣀⣀⡀⠀⣀⣀⡀⠀⢈⣉⡙⠛⠻⣿⣇⣀⣀⠀⠀⠀⣀⣁⡀⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⡆⢠⣿⣿⣿⣯⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⢿⣿⣿⣿⠿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⣽⣿⡿⣿⣷⣤⣾⣿⢻⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣯⣼⣿⠇⢸⣿⡏⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣭⣉⣻⣿⣿⣻⣿⣿⣿⣿⡆⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠛⠛⣳⣿⣿⢹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⣧⣸⣿⣧⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⡟⣿⣿⡇⢸⣿⣿⡇⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⣟⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡿⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠁⠀⠈⠉⠉⠁⠈⠉⠉⠙⠻⢯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡈⠉⠉⠀⠀⠉⣉⣭⣭⣍⣀⠈⠉⠉⠉⠀⠀⠈⢩⣭⣿⣿⣯⣿⣿⣿⣿⣿ ⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⠷⢶⣤⣤⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣼⣿⠿⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠐⣿⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠠⠲⣖⣧⣤⣴⣾⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡆⠀⠀⠀⠀⠀⠀⣿⡆⣽⡇⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⠀⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⡀⣿⣇⣿⡇⢸⣷⣾⡿⠀⣀⢀⡌⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⢛⣻⣿⡃⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢤⣤⠄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣉⣛⣟⠉⣽⣯⡥⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⢸⣿⠀⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣛⣸⡏⢠⣟⡿⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⣠⡀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⠟⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⡱⠟⠻⣾⣿⣷⣤⣀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠛⠛⠛⠛⠛⠻⠿⠿⢿⠇⡇⠀⠈⣿⡏⠁⠨⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⣿⣏⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⠀⣀⣿⣆⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠘⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣘⣿⣿⠇⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⢣⣿⣿⣷⣤⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣷⣤⣍⣉⣙⡛⠿⠿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣀⣘⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡷⣄⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡛⣛⣛⡛⠛⣓⣒⡈⠉⢉⣛⡛⢿⣿⣿⣂⣀⣀⠀⠀⠀⣀⣀⡀⠀⠩⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⡆⢀⣿⣿⣿⣧⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣿⣿⣧⣿⣿⢿⣿⣿⢿⣿⣿⣿⠿⢿⣿⣿⠿⠇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣯⠀⠙⣿⣿⡿⣿⣷⣀⣾⣿⢻⣿⣧⣤⣶⣿⣿⣯⣿⣿⢿⣿⣿⣿⣿ ⠀⠀⢸⣿⣯⣾⣿⠇⢸⣿⡏⣿⣿⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣽⣿⣿⣿⣿⣿⣿⣤⡄⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠛⠛⣳⣿⣿⢸⣿⣿⢸⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⡇⣸⣿⣧⣿⣿⡀⢸⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡏⣿⣿⡟⣿⣿⡇⢸⣿⣿⡇⠀⢸⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⢸⣿⣯⠀⠀⣼⣿⣿⣤⣤⠘⣿⣿⣼⣿⡿⠻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠁⠀⠈⠉⠉⠁⠀⠉⠉⠉⠉⠉⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡉⠉⠈⠉⠁⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠈⢭⣽⣿⣿⣯⣿⣿⣿⣿⣿ ⠀⠆⠲⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠦⠀⠀⠀⣰⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠘⡟⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠆⠈⠛⠀⠀⠀⢈⣷⢨⣿⠀⢰⣾⣻⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀⠀⠀⣿⣰⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⣀⢸⣿⢸⣿⠀⣿⣷⣿⡇⠀⢀⢀⣈⣀⡀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⢿⣻⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣬⣉⣛⢻⡛⢉⣿⣭⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠂⣹⡇⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣃⣽⠃⢸⣻⡇⠀⠀⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣶⣿⣿⣿⣿⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⢀⣴⣦⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⡿⠁⠀⠀⢀⡟⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣣⠞⠻⣾⣿⣷⣤⣀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿ ⢠⠀⠀⠀⠀⠀⢠⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠝⠛⠛⠛⠛⠛⠿⠿⠿⠇⡇⠀⠈⣿⡟⠁⠨⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡆⠀⠀⠀⣴⣿⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡐⠀⢀⣿⣇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠃⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣭⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⠀⠙⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿ ⠀⠀⠀⠀⢠⣻⣿⠟⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⠏⣾⣿⣷⣦⣄⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⣿⣿⣷⣦⣤⣉⣉⣛⠻⠿⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⣀⠀⠀⠀⣀⣀⣀⡹⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣦⣈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣶⡶⠌⢉⣙⡛⢿⣿⣿⣄⣀⣀⠀⠀⠀⣀⣀⡀⠉⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⡆⢀⣿⣿⣿⣇⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣧⠀⠙⣽⣿⡿⣿⣷⣀⣾⣿⢻⣿⣧⣤⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿ ⠀⠀⢸⣿⣯⣾⣿⠇⢸⣿⡇⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠛⠛⣳⣿⣿⢹⣿⣿⢸⣿⣿⢹⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⣇⣸⣿⣧⣿⣿⡀⢸⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣯⠀⠀⠀⣰⣿⡿⠃⢸⣿⣿⢸⣿⣿⣸⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡏⣿⣿⡟⣿⣿⡇⢸⣿⣿⡇⠀⢸⣿⣿⡏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⢸⣿⣷⠀⠀⣼⣿⣿⣤⣤⠘⣿⣿⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠁⠀⠈⠉⠉⠁⠀⠉⠉⠁⠈⠉⠙⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡈⠉⠁⠀⠀⣉⣉⣉⣉⡉⠀⠈⠉⠉⠉⠈⠻⣯⣭⣿⣿⣿⣯⣿⣽⣿⣿⣿ ⠀⠆⠲⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠓⠒⠠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣥⣤⣤⡄⠀⠀⣶⠚⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡭⠄⢠⠀⢿⡏⠀⠀⠀⢸⡏⢓⡦⠈⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀ ⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⣿⡇⠀⠀⢿⣀⣜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠸⠀⠀⠀⠀⣀⡀⣸⡇⣿⡇⢸⣿⣽⣿⠀⠀⢀⠀⢄⣀⡀ ⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠻⠇⠸⠿⢿⠟⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣐⡛⠻⠟⠋⢸⣿⡅⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⢍⣿⠀⣿⣿⡇⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡐⢘⡟⢀⣿⣿⠀⠀⢠⣤⡄ ⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣷⣶⣶⣾⣿⣿⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠈⠉⢠⣴⣦⣾⣿⣃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⠋⠉⠉⠉⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⢏⣤⠶⣶⣾⣷⣀⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣄⣠⣴⣶⣿⣿⣿⣿⣿⣿⣧ ⢸⡆⠀⠀⠀⠀⠀⡠⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⡜⠛⠛⠛⠛⠛⠻⠿⠿⡿⢸⠁⠀⢺⣿⠋⠉⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⠀⠀⠀⢀⣾⣿⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠂⠀⡸⣿⡀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠘⠃⠀⠀⠀⠀⣿⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄⣀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣦⣭⣽⣿⣿⣿⣿⣿⣿⣇⡀⠉⠁⠀⠀⠈⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⢤⣿⣿⠏⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⡟⣼⣿⣿⣷⣤⣀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣶⡀⠀⣨⣿⣿⣿⣿⣿⡿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣶⣤⣤⣭⡛⠛⠻⠿⠿⠿⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠐⠙⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⣀⠀⠀⠀⣀⣀⣀⡀⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣷⣄⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣏⣁⡀⠀⣀⣀⡀⠀⢀⣀⡀⠉⠻⣧⣄⣀⣀⠀⠀⠀⣀⣀⡠⢾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⡆⢀⣿⣿⣿⣇⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣇⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣷⠀⠀⣼⣿⡟⣿⣷⣀⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿ ⠀⠀⢸⣿⣯⣾⣿⠇⢸⣿⡇⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣽⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡿⠀⠀⠛⠛⣳⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⡇⣸⣿⣧⣿⣿⡀⢸⣿⣿⡇⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡇⣿⣿⡟⣿⣿⡇⢸⣿⣿⡇⠀⢸⣿⣿⠇⠉⣿⣿⡏⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⢸⣿⡿⠀⠀⣼⣿⣿⣤⣤⠘⣿⣿⣼⣿⡿⠈⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠁⠀⠈⠉⠉⠀⠀⠉⠉⠁⠈⠉⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣍⣉⠀⣠⣭⣭⣭⣭⡉⠀⠈⠉⠉⠉⠀⠀⠈⠉⠩⣿⣿⣯⣿⣽⣿⣿⡿ ⠀⠆⠲⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣩⣭⣭⡄⠀⠀⣴⠶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⡒⢰⠀⠈⠛⠁⠀⠀⣿⡓⢦⡍⢩⣭⣷⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢸⡇⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢻⠀⠀⠀⠀⠀⠀⣿⢱⣿⠃⣾⣟⣿⡇⠀⠀⣀⠀⢍⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠛⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡉⠉⠙⠻⠿⠀⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⢐⡒⠺⠿⠿⠃⢿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢽⣷⣦⢰⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣶⣶⣿⣿⣧⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣇⡀⠀⠀⠀⠀⠀ ⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀ ⡸⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⢻⣿⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣿⣿⣿⣿⠿⡟⠉⢻⣿⣿⣿⣄⠀ ⣿⡆⣧⠀⠀⠀⠀⠀⢴⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡘⠿⠟⠛⠛⠛⠿⠿⠿⠿⠈⠉⠀⢀⣀⣤⣴⣷⣄⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣆⣴⣿⣿⣿⣿⣿⣷ ⣽⡇⣿⡆⠀⠀⢠⣿⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠙⠛⠛⣻⣿⣟⣛⣛⣿⣿⣿⣍⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠀⠉⠁⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣮⣿⡿⠃⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣶⣤⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⣿⡿⠿⣿⣿⣻⣿⣿⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠻⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣀⠀⠀⠀⠀⢀⡀⠀⠛⣁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⣀⣀⠀⠀⠀⣀⣀⣀⡀⢘⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣌⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⣀⣀⡀⠀⣀⣀⡀⠀⢀⣀⡀⠀⠘⠤⣄⣀⣀⢺⣿⣷⣌⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⡆⢀⣿⣿⣿⣇⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣧⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⣼⣿⡟⣿⣿⣉⣿⣿⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⠇⢸⣿⡏⣿⣿⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣼⡟⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡿⠀⠀⠛⠛⣳⣿⣿⢸⣿⣿⢸⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⣧⣸⣿⣧⣿⣿⡀⢸⣿⣿⡇⠀⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⣀⣿⣿⡇⠀⣸⣿⣗⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⡟⣿⣿⡇⢸⣿⣿⡇⠀⢸⣿⣿⡇⠀⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣸⣿⣿⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠁⠀⠈⠉⠉⠁⠀⠉⠉⠁⠈⠉⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣯⣍⠀⠈⠉⠉⠉⠀⠀⠈⠉⠭⡿⠿⠋⠉⠉⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣫⣭⠀⠀⢩⡤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢰⣆⠈⡙⠀⠀⠈⠀⢸⡗⠮⣍⠛⣛⣭⣭⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⠀⠀⢸⡇⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣃⡈⠇⠀⠀⠀⠀⢸⡟⣸⡿⢀⣿⣻⣿⠀⠀⠀⣀⠀⣈⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠘⠻⠿⡇⢸⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡒⠲⠶⣿⣿⠆⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠩⢕⣶⠀⣾⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡰⢞⣿⠸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣤⣤⣾⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣾⣟⣿⣿⡆⠀⠀⠀⠀ ⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣿⣿⣿⣦⣄⡀⠀⠀ ⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⣀⣿⣤⠤⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⣾⣯⡈⠄⠀⠀⠀⠀⢠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠿⠟⠛⠛⠛⠿⠿⠿⠿⠇⣹⣿⣄⣴⣶⡏⠉⠻⣯⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄ ⠛⢻⡷⢸⠀⠀⠀⣰⣿⡻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠻⣿⣧⣀⣠⣿⣶⣶⣿⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢴⠾⠁⠘⠀⠀⠀⢹⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⢆⣁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠈⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠰⣤⣿⠟⠁⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣷⣦⣀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⣿⡿⠿⠿⠿⣻⣿⣮⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠢⠄⠀⠀⠀⠀⣴⣦⡉⣡⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣃⣀⣀⠀⠀⠀⣀⣀⣀⡀⢀⣉⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣤⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣀⣀⡀⠀⣀⣀⡀⠀⢀⣀⡀⠀⠐⠢⢄⣀⣀⣽⣿⣿⣽⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⢸⣿⣿⣿⣿⡆⢀⣿⣿⣿⡇⠸⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⠿⢿⣿⣿⠿⠷⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⣼⣿⡟⣿⣿⣀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⠇⢸⣿⡏⣿⣿⠀⢸⣿⣿⡏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡍⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡟⠀⠀⠛⠛⣳⣿⣿⢸⣿⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢻⣿⣧⣸⣿⣧⣿⣿⡀⢸⣿⣿⡇⠀⢸⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⡇⠀⣸⣿⣧⠀⠀⠀⣰⣿⡿⠁⢸⣿⣿⢸⣿⣿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣾⣿⡟⣿⣿⡟⣿⣿⡇⢸⣿⣿⡇⠀⢸⣿⣿⡇⠀⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣶⣸⣿⣿⠀⠀⣼⣿⣿⣥⣤⠘⣿⣿⣼⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁ ⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠈⠉⠉⠁⠀⠈⠉⠉⠁⠀⠉⠉⠁⠈⠉⠉⠉⠁⠙⠋⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣍⠀⠈⠉⠉⠉⠀⡀⠈⠉⠉⠛⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣛⣿⣭⠀⠀⢩⡥⠤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢰⣦⠉⡽⠀⠀⠘⠃⢸⣷⠮⣭⠛⣻⣭⣭⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⢸⣏⣥⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣋⣚⡇⠀⠀⠀⠀⢸⣿⣾⣿⢠⣿⣻⣿⠁⠀⠀⣀⢈⣍⣁⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠀⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠘⠻⠿⡏⢸⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡳⠀⠀⡒⠶⠾⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣔⡀⠀⠀⣿⠯⣿⣶⠀⣾⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⢾⣿⢹⣿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣾⣷⣷⣿⣿⣿⣧⣶⣖⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣾⣟⣿⣿⡆⠀⠀⠀⠀ ⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⣿⣿⣿⣷⣶⣾⣿⣶⣦⣄⣀⣀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣿⣿⣿⣦⣄⡀⠀⠀ ⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⣀⣿⣦⠤⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⣿⣯⡘⢆⠀⠀⠀⠀⢠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡺⠿⠿⠻⠿⠿⡿⠿⠿⠿⢏⣿⣿⣦⣴⣶⡏⠉⠻⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅ ⠛⢻⣷⣿⡀⠀⠀⣰⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⣿⣧⣀⣠⣿⣶⣶⣿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⠿⢃⠟⠃⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢏⣁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠀⠀⠀⠰⣤⣿⠿⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣷⣦⣀⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣧⡀⢰⣿⣿⣿⣿⣿⡿⠿⠿⠿⣻⣿⣯⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠢⡄⠀⠀⠀⢀⣴⣦⡋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣙⡻⠿⠿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⢿⠏⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⡿⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠆⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠙⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣛⣛⣻⠀⠀⢩⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢰⣦⠉⡝⠀⠸⠟⣴⡮⣍⡛⢛⣛⣻⣭⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠸⣿⢩⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢸⡁⠨⠃⠀⠀⠀⣿⡷⣿⡇⢸⣿⣿⣿⠀⠀⠀⣀⢈⣍⣁⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿⠇⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠃⠛⠿⣿⠇⣾⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡆⠀⠀⠶⠷⣾⣿⣿⣶⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⡆⡇⠀⢸⣿⣿⢶⡆⢩⣾⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣷⠶⢻⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣬⣼⣿⣿⣿⣦⣔⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢷⣾⣿⣿⣿⠀⠀⠀⠀⠀ ⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡟⠛⠛⠻⣿⣿⣿⣶⣶⣾⣷⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣿⣿⣦⣄⡀⠀⠀ ⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⣀⣴⣿⣶⠶⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⣿⣿⡛⢳⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⠿⠿⠻⠿⡿⢿⠿⠿⠿⠏⣿⣿⣧⣴⣿⡟⠉⠻⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠛⠻⣿⢞⡇⠀⠀⢀⣬⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣧⣀⣠⣿⣷⣾⣿⣿⡿⠛⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣦⡾⠏⡸⠇⠀⠀⠘⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣾⣉⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠈⠁⠀⠀⠀⢠⣸⣿⡿⠃⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣦⣄⣀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣯⡀⢰⣿⣿⣿⣿⣿⣿⠿⠿⠿⣻⣿⣯⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠢⡄⠀⠀⠀⢠⣦⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢤⡀⢸⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠹⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⡛⢿⢿⣿⣿⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠻⠟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣁⣠⣤⣶⣶⣆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠄⠀⢀⠀⠄⠀⠹⢿⣿⣿⣿⣾⡿⠏⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣤⣤⣀⣀⣈⣉⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠿⠿⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢠⡀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠲⣶⠇⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⣛⡂⠀⠉⣉⣉⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢉⡍⠁⠀⠀⠀⣦⣍⣛⠿⠿⣟⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⢸⠃⠀⠀⠀⠀⣿⢶⣾⠀⣿⠿⣽⡇⠀⠀⠀⢀⢀⣈⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠷⠿⠇⠀⠀⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠆⠿⢾⣿⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠬⣽⣶⣾⣷⣴⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣺⣗⡖⣦⠉⣵⣾⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠜⣿⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣀⣤⣾⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠠⣿⣿⣼⣿⡇⠀⠀⠀⠀ ⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡟⠛⠛⠻⣿⣶⣶⣦⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣶⣦⡀⠀ ⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⣀⣴⣿⣶⠶⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠘⢻⣿⣷⠀⠀⠀⠀⠀⣠⢀⣤⣴⣤⠀⠀⠀⠀⠀⠀⠀⣀⠐⠿⠿⠛⠛⠛⠛⠿⠿⠿⠏⢹⣿⣦⣴⣿⡟⠉⠛⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⢰⣾⣿⣿⡇⠀⠀⠀⣰⢳⣭⣽⡿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣷⣄⣠⣿⣷⣾⣿⣿⡿⢿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦ ⢸⣿⣿⠟⠃⠀⠀⠀⠩⠾⢿⣿⣿⣿⠇⠀⠀⠀⢀⣴⣿⣿⣿⣿⡷⣈⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⠟⠋⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⠟⢀⣠⣴⣾⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣷⣄⣀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣷⣀⢰⣿⣿⣿⣿⣿⣟⠻⠿⠯⢻⣿⣽⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠢⠀⠀⠀⠀⣴⣤⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⠄⣼⢿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⣾⣿⣿⣯⣤⣤⡀⠀⢠⣤⣤⣤⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣭⣛⣿⣿⣻⣿⣿⣿⣿⡇⠀⣠⣤⣤⣄⠀⠀⠀⢀⣤⣤⣄⡀⠀⣀⣤⣼⣟⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵ ⠀⠀⠻⠏⣿⣿⡟⣿⣿⡆⢸⣿⣿⣿⡆⢸⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⢸⣿⣿⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⢰⣿⣿⢹⣿⡇⣾⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⣿⣿⡇⠛⠛⠃⣿⣿⢻⣿⡇⢸⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠰⣟⣉⣾⣿⡟⢸⣿⣿⢸⣿⣧⠉⠉⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀ ⠀⠀⠀⠀⣿⣿⡇⣶⣶⡆⣿⣿⣾⣿⣿⢸⣿⡇⣿⣿⢹⣿⡇⣿⣿⣿⠉⠁⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⢻⣿⣿⣶⣾⣿⣿⣿⣿⣤⣼⣿⣿⢸⣿⡏⠀⣼⣿⡟⠁⣿⣿⣿⢿⣿⣿⠙⠋⠁⠀⠀ ⠀⠀⠀⠀⠻⣿⣷⣿⡿⢹⣿⣿⠙⣿⣿⣸⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⠀⠀⢸⣿⣿⠀⣿⣿⢸⣿⣿⠻⢿⣿⣾⣿⣿⣿⣿⣿⣾⣿⠟⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠇⣾⣿⣿⣶⣶⠈⢿⣿⣾⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠲⢶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠻⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠼⠷⠄⠀⠘⣛⣛⣛⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢠⡀⠀⠀⠘⢡⣍⡛⠿⠿⠿⠟⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠟⡇⠀⠀⣿⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡃⠀⢸⡷⢨⡗⢠⡿⢏⡿⠀⠀⠀⠀⢀⢀⡀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠼⠧⠀⠀⠘⠒⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠸⢧⣾⡇⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠁⠈⠥⣬⣭⣶⣶⣦⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢒⢢⡍⠉⣵⣾⢃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠤⠸⡇⢸⣿⡿⣿⣦⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣤⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠚⠃⠘⠿⣿⣿⣿⡀⠀⠀⠀⠀ ⠈⣺⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣶⣶⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣶⣤⡀⠀ ⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⠯⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡤⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⢀⡀⠺⠿⢟⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⠉⠻⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀ ⠀⠀⠀⠀⢈⠀⠀⠀⠀⣾⢱⣽⣿⣭⢿⣧⠀⠀⠀⠀⠀⣽⣿⣶⣾⣿⣿⡿⠿⠋⠀⠀⣿⣿⣿⣿⡿⢿⣷⣄⣤⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀ ⠀⠀⠀⠈⠉⠀⠀⠀⠀⡋⠸⢿⣿⣿⣷⡟⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⣰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣡⣴⣾⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⠀⠀⠀⠀⠀⠘⠛⠀⠈⠉⠉⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣄⣐⣿⣿⣿⣿⣿⣟⡛⠻⠯⢿⣿⣾⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⠀⣤⣿⡿⠀⠀⠋⠉⠉⠛⢢⠀⠄⠀⢰⣿⣆⠺⣶⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡙⠻⠿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣶⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠠⠿⣿⣷⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⢀⣴⣦⣦⣤⡀⠀⢠⣤⣤⣤⠀⢠⣤⣤⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⡍⣽⣿⢿⣿⣿⣿⣿⣟⡀⣠⣤⣤⣄⠀⠀⠤⢄⣤⣤⣄⡀⠀⣀⣤⣽⣇⠀⠀⣨⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠈⣿⣿⡟⣿⣿⡄⢸⣿⣿⣿⡆⢸⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⢹⣿⣿⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⢰⣿⣿⢹⣿⡇⣾⣿⡏⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⣿⣿⡇⠛⠛⠃⣿⣿⢻⣿⡇⢸⣿⡟⣿⣾⣿⣿⡇⣿⣿⣯⣿⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣤⣀⠀⢛⣭⣭⣾⣿⡟⢸⣿⣿⢸⣿⡇⠉⠉⣽⣿⡿⣽⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀ ⠀⠀⠀⠀⣿⣿⡇⣶⣶⡆⣿⣿⣾⣿⣿⢸⣿⡇⣿⣿⢹⣿⡇⣿⣿⣿⠉⠁⢸⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⢻⣿⣿⣿⡿⢿⣿⣿⣿⣶⣾⣿⣿⢸⣿⡇⠀⣼⣿⡟⠱⢿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣷⣿⡿⢹⣿⣿⠙⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⠀⠀⢸⣿⣿⠀⣿⣿⢸⣿⣿⠙⢿⣿⣾⣿⣿⣿⣿⣿⣾⣿⠏⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠇⣾⣿⣿⣶⣶⠀⢿⣿⣾⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠰⢢⠀⠰⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠙⠛⠺⣿⣿⣿⣶⣤⣀⡀⠑⠿⢿⣿⣿⠟⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣾⣿⡏⠀⠀⠀⠀⢀⡉⠛⠇⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⠇⠠⠦⣿⣿⣿⡏⣬⡆⢰⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣧⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠻⣻⣿⣿⣿⠁⠀⠀⠘⠀⠉⠻⡏⠻⣿⠁⠨⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣍⠈⠀⠀⠘⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⣾⡄⠀⠀⠀⠀⠀⠀ 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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 1027 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/23/irc-log-220222/#comments Gemini version at gemini://gemini.techrights.org/2022/02/23/irc-log-220222/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Tuesday,_February_22,_2022⠀✐ Posted in IRC_Logs at 2:00 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-220222.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-220222.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-220222.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-220222.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 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02.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Artificial_‘Productivity’⠀✐ Posted in Deception, Europe, Patents at 8:01 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Grant, baby, grant⦈ Summary: Grant like_a_Philpott, say managers who think that the EPO is like a private, for-profit corporation and patents (monopolies) are just “products” to be sold to “customers” (applicants) ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢿⣾⣷⣶⣦⡌⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠏⠋⠀⠀⠉⠀⠀⠉⠁⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⣣⣨⣿⣿⣿⡅⢰⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠿⠛⠃⠀⠠⠄⠁⠒⠶⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣾⣿⣸⣿⣻⠷⠵⠗⠛⢙⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣯⣿⣿⣿⣿⣷⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣟⠛⢛⣛⡛⠋⣡⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣯⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡤⠀⠀⡀⠀⢹⣿⣾⣿⣿⣿⣿⡽⡄⠀⠀⠐⣂⣿⣿⢡⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡗⡿⠃⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠛⠛⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⣠⢇⠀⣸⣿⣿⣿⠛⣿⣿⣶⠿⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣿⣿⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣿⣿⣷⣴⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡾⠀⢀⣿⣷⠖⠀⠒⢞⡿⠃⢀⣀⠀⠀⣹⣶⡿⠆⠄⣠⣴⠖⠺⣿⣿⣿⣿⣿⣿⣿⣿⡷⢢⣤⣤⡀⠀⠀⢠⣿⣿⣿⠁⠀⣀⣤⣤⣄⢀⣻⣿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠛⡏⣿⡇⢠⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⣯⠀⣸⣿⣿⣗⣠⡿⢿⣇⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣆⠀⣾⣿⣿⣿⠴⣾⣿⡛⠁⠀⣿⣇⠙⠷⠭⠁⣘⣛⣿⡏⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⣿⣿⣿⣿⣿⣿⣿⣇⠰⣿⢿⡟⢰⢼⡿⠟⠋⠛⣿⠎⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣿⣿⣿⣿⡀⢿⡿⠿⠛⣿⡷⢹⠇⠀⣸⣿⣿⣿⣷⣶⣤⣤⣤⡞⠁⠀⠙⢿⣷⣦⡀ ⠀⢠⣾⠃⢸⣶⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠿⠃⠈⣿⣇⣀⣠⣤⣤⣤⣤⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣋⣽⣿⣿⣇⠀⠀⠀⠀⠘⠃⠈⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣷ ⠰⣿⣟⠀⢠⣿⣷⠀⠀⠀⠀⢸⣿⣿⠛⣩⣽⣽⣿⢿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠀⠈⠈⠀⠈⠉⠀⣼⢿⣛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠉⠛⠸⠟ ⠀⠀⠀⠐⠾⣿⣿⣧⠀⠀⠀⢸⣿⡇⢀⣿⣿⣿⣿⣵⣾⣯⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣮⣽⣛⣛⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀⢸⣿⠁⢸⣿⣿⣿⣿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⡟⠉⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⢸⣿⠖⠛⢿⡟⠻⠷⢶⡖⠒⢲⡖⠻⡟⢻⠻⠿⠛⣦⢠⡖⠺⠶⣶⡖⠓⢲⡖⠺⠿⢷⠒⢶⠒⣦⢀⡴⠛⠻⢶⠖⠿⠶⣶⠒⠒⣶⠞⢲⠛⠿⠳⠖⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⣾⣿⠀⠦⠤⡇⠀⠂⣸⠇⠀⠈⡇⠀⠃⢸⣶⠀⣶⡏⢸⡇⠀⠀⣸⠃⠀⠘⡇⠀⠂⢸⡆⠀⢠⡟⢸⡇⠀⠤⢼⠀⠐⠀⣿⠀⠀⢸⠀⠈⠀⢰⡆⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⣿⠀⠆⠀⡇⠀⡆⢸⠀⢀⠀⡇⢰⠀⢸⣿⠀⡿⢷⣾⡇⠀⠀⢸⠀⠀⠀⡇⠀⠆⢸⣿⠀⡾⠷⣾⡇⠀⠀⢸⠀⢰⠀⡇⠀⡁⠸⠀⢀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢠⠀⠀⠄⠠⠰⠿⠊⠫⣿⠶⣶⣶⣷⣶⠷⠾⠶⠾⠶⠶⠶⠷⠾⠿⠶⣷⣼⠟⠷⠶⠶⠾⠶⠶⠶⠷⠶⠶⠞⠛⠶⢷⡼⠏⠳⠶⠶⠾⠶⠾⠶⠷⠶⠷⠶⠶⠾⠶⢾⡷⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢿⣾⣷⣶⣦⡌⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠏⠋⠀⠀⠉⠀⠀⠩⠁⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⣣⣨⣿⣿⣿⡅⢰⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣷⣦⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠾⠻⠛⠃⠀⠢⠄⠁⠒⠶⠡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣾⣿⣸⣿⣻⠷⠵⠗⠛⢙⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠛⢛⣛⡛⠋⣁⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡤⠀⠀⡀⠈⢳⣿⣾⣿⣿⣿⣿⣽⡄⠀⠀⠸⣆⣿⣿⢣⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠛⠛⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⣠⢧⠀⣹⣿⣿⣿⠛⣿⣿⣶⠿⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣿⣿⣿⢻⠏⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣿⣿⣷⣴⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡾⠀⢀⣿⣷⠖⠀⠒⢞⡿⠃⢀⣀⠀⠀⣹⣷⡿⠆⠄⣠⣴⠖⠺⣿⣿⣿⣿⣿⣿⣿⣿⡷⢢⣤⣤⡀⠀⠀⢠⣿⣿⣿⠁⠀⣀⣤⣤⣄⢀⣻⣿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⡏⣿⡇⢠⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⣯⠀⣸⣿⣿⣗⣠⡿⢿⣇⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣆⠀⣾⣿⣿⣿⠴⣾⣿⡛⠁⠀⣿⣇⠙⠷⠭⠁⣘⣛⣿⡏⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⣿⣿⣿⣿⣿⣿⣿⣇⠰⣿⢿⡟⣰⣽⡿⠟⠋⠛⢿⠎⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣿⣿⣿⣿⡀⢿⡿⠿⠛⣿⡷⢹⠇⠀⣸⣿⣿⣿⣷⣶⣤⣤⣤⡞⠁⠀⠙⢿⣷⣦⡀ ⠀⢠⣾⠃⢸⣶⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠿⠃⠀⣿⣇⣀⣠⣤⣬⣤⣤⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣋⣽⣿⣿⣇⠀⠀⠀⠀⠘⠃⠈⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣷ ⠰⣿⣟⠀⢠⣿⣧⠀⠀⠀⠀⢸⣿⣿⠛⣩⣽⣽⣿⢿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠁⠉⠈⠀⠈⠉⠀⣼⢿⣛⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠉⠛⠸⠟ ⠀⠀⠀⠐⠾⣿⣿⣧⠀⠀⠀⢸⣿⡇⢀⣿⣿⣿⣿⣽⣾⣯⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣮⣽⣛⣛⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⡿⣿⣿⡿⣿⣿⣿⣿⠔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⢸⣿⠁⢸⣿⣿⣿⣿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⡟⠉⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⢸⣿⠖⠛⢿⡟⠻⠷⢶⡖⠲⢲⡖⠻⡟⢻⠛⠻⠛⣦⢠⡖⠺⠶⣶⡖⠒⢲⡖⠺⠿⢷⠚⢶⠒⣦⢀⡴⠟⠻⢶⠖⠷⠶⣶⠚⠒⣶⠞⢲⠛⠿⠳⠶⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⣾⣿⠀⠦⠤⡇⠀⠂⣸⠇⠀⠈⡇⠀⠃⢸⣶⠀⣶⡏⢸⡇⠀⠀⣸⠃⠀⠘⡇⠀⠂⢸⡆⠀⢠⡟⢸⡇⠀⠤⢼⠀⠐⠀⣿⠀⠀⢸⠀⠈⠀⢰⡆⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⣿⠀⠆⠀⡇⠀⡆⢸⠀⢀⠀⡇⢰⠀⢸⣿⠀⡿⢷⣾⡇⠀⠀⢸⠀⠀⠀⡇⠀⠆⢸⣿⠀⡾⠷⣾⡇⠀⠀⢸⠀⢰⠀⡇⠀⡁⠸⠀⢀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢠⠀⠀⠀⠠⠰⠿⠊⠣⣿⠶⣶⣶⣷⣶⠷⠾⠶⠾⠶⠶⠶⠷⠾⠿⠶⣷⣼⠟⠷⠶⠶⠾⠶⠾⠶⠷⠶⠶⠞⠛⠶⢷⡼⠏⠳⠶⠶⠾⠶⠾⠶⠷⠶⠷⠶⠶⠾⠶⢾⡷⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⢿⣾⣷⣶⣦⡌⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠋⠍⠋⠀⠀⠉⠀⠀⠩⠁⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⣣⣨⣿⣿⣿⡅⢰⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣷⣦⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠺⠿⠟⠃⠀⠠⠄⠀⠒⠶⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣾⣿⣸⣿⣻⠷⠵⠗⠛⢙⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣯⣿⣿⣿⣿⣷⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣟⠛⢛⣛⡛⠋⣡⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡤⠀⠀⡀⠘⢺⣿⣾⣿⣿⣿⣿⡽⡄⠀⠀⠘⣆⣿⣿⣡⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣗⡿⠃⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠛⠛⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⣠⣇⠀⣹⣿⣿⣿⠛⣿⣿⣶⠿⠀⠀⠀⠙⣷⣿⣿⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣿⣿⣿⢺⠇⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣿⣿⣷⣴⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡾⠀⢁⣿⣷⠖⠀⠒⢞⡿⠃⢀⣀⠀⠀⣹⣷⡿⠆⠄⣠⣴⠖⠺⣿⣿⣿⣿⣿⣿⣿⣿⡷⢢⣤⣤⡀⠀⠀⢠⣿⣿⣿⠁⠀⣀⣤⣤⣄⢀⣻⣿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠛⡏⣾⡇⢠⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⣯⠀⣸⣿⣿⣗⣠⡿⢿⣇⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣆⠀⣾⣿⣿⣿⠴⣾⣿⡛⠁⠀⣿⣇⠙⠷⠭⠁⣘⣛⣿⡏⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⣿⣿⣿⣿⣿⣿⣿⣇⠰⣿⢿⡟⢒⣽⡿⠟⠋⠛⣿⠎⠿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣿⣿⣿⣿⡀⢿⡿⠿⠛⣿⡷⢹⠇⠀⣸⣿⣿⣿⣷⣶⣤⣤⣤⡞⠁⠀⠙⢿⣷⣦⡀ ⠀⢠⣾⠃⢸⣶⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠿⠃⠀⣿⣇⣀⣠⣤⣬⣤⣤⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣋⣽⣿⣿⣇⠀⠀⠀⠀⠘⠃⠈⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣷ ⠰⣿⣟⠀⢠⣿⣷⠀⠀⠀⠀⢸⣿⣿⠛⣩⣽⣽⣿⢿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠀⠈⠈⠀⠈⠉⠀⣼⢿⣛⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠉⠛⠸⠟ ⠀⠀⠀⠐⠾⣿⣿⣧⠀⠀⠀⢸⣿⡇⢀⣿⣿⣿⣿⣽⣾⣯⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣮⣽⣛⣛⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⡿⣿⣿⣿⣿⠔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀⢸⣿⠁⢸⣿⣿⣿⣿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⡟⠉⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⢸⣿⠖⠛⢿⡟⠻⠷⢶⡖⠲⢲⡖⠻⡟⢻⠛⠻⠟⣦⢠⡖⠺⠶⣶⡖⠗⢲⡖⠾⠿⢷⠚⢶⠒⣦⢀⡴⠟⠻⢶⠖⠷⠶⣶⠒⠖⣶⠞⢲⠛⠿⠳⠶⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⣾⣿⠀⠦⠤⡇⠀⠂⣸⠇⠀⠈⡇⠀⠃⢸⣶⠀⣶⡏⢸⡇⠀⠀⣸⠃⠀⠘⡇⠀⠂⢸⡆⠀⢠⡟⢸⡇⠀⠤⢼⠀⠐⠀⣿⠀⠀⢸⠀⠈⠀⢰⡆⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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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 2132 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/23/what-epo-staff-says/#comments Gemini version at gemini://gemini.techrights.org/2022/02/23/what-epo-staff-says/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ What_EPO_Staff_Really_Thinks⠀✐ Posted in Europe, Patents at 9:37 am by Dr. Roy Schestowitz Video_download_link | md5sum 19a2d85576d04109fd3bcb0514397aa3 SUEPO/Staff Survey 2022 Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/survey-letter-2022.webm Summary: “Preparation for the 2022 fifth edition” of the EPO staff survey has begun; it remains to be seen if the messages get ‘lost in the mail’ of the ever-so-busy_President (Campinos), who is often responsive only when it suits him THE Central Staff Committee of the EPO wrote to António_Campinos last week, asking for permission to conduct a survey and also contact staff (to participate in this survey). This survey was last run 2 years ago and it showed that Campinos had become unpopular and untrustworthy even faster than Benoît Battistelli. So what will Campinos say to the Central Staff Committee? Time will tell… In the words of the Central Staff Committee: “On an average three-year rhythm, the Staff Representation runs an EPO-wide Staff Survey with the support of SUEPO and the company Technologia, which is well-known for its expertise in the field of psychosocial risk analysis and prevention. In this open letter, we request that the President facilitates the fifth edition of the survey.” Here’s the letter as HTML (later available as plain text and GemText): Reference: sc22015cl Date: 18/02/2022 European Patent Office | 80298 MUNICH | GERMANY Mr António Campinos President of the EPO By email Open letter Fifth edition of the Technologia EPO staff survey Dear Mr President, In 2010, 2013, 2016, and 2020 Staff Representation ran an EPO-wide Staff Survey with the support of SUEPO and the company Technologia, which is well known for its expertise in the field of psychosocial risk analysis and prevention. To maintain an average 3-year rhythm, and in view of the situation during the pandemic in the last two years, it is now time to organise the fifth edition of the staff survey. The timing appears particularly appropriate because this survey would complement the surveys ran by the Office at the beginning of the pandemic in May and October 2020, by providing data on any psychosocial risk in our organisation. Running the Technologia EPO staff survey again in 2022 will also allow internal benchmarking, i.e., assessing the trend within the EPO by comparing new results with the results of the past surveys (most of the questions are identical from one edition to the next). It is in the interest of all stakeholders, management, and staff, to know exactly how psychosocial risks evolved within the Office, and to provide these very valuable data particularly at the outcome of two years pandemic. The union SUEPO has again kindly accepted to be our partner in this project. Nevertheless, to facilitate the logistics we request that you authorise the dispatch of individual survey access codes to all staff members at their @epo.org email address. We trust that you will grant this request to use EPO channels to facilitate this survey as was done in the past. We ask for the courtesy of an answer by the end of February 2022. ===================================================================== We look forward to hearing from you soon and remain at your disposal for any further information you may require. Yours sincerely, Alain Dumont Chairman of the Central Staff Committee The letter and the context are discussed in the video above. Amidst industrial_action it is expected that things will worsen for Campinos. As recently noted in relation to The Hague (TH) and Munich (MU), “in two independent polls the staff in MU and in TH overwhelmingly indicated (93% MU and 93% TH) that they are not satisfied and don’t agree with the path the present administration is on. Also an overwhelming number of staff present in those GA’s indicated (83% TH and 89% MU) that they would be inclined to participate in actions lead by the union.” Who runs the Office? Not_scientists_but_litigation_fanatics and their_henchmen. Soft-spoken scientists will need to become just as loud as monopolists, their lobbyists, liars, and lawyers. █ “When asked by Ars, the EPO’s spokesperson mentioned the imminent arrival of the unitary patent system as an important reason for revising the EPO’s internal rules…” –Dr._Glyn_Moody ䷩ 𝚕𝚒𝚗𝚎 2280 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/23/www-of-spam/#comments Gemini version at gemini://gemini.techrights.org/2022/02/23/www-of-spam/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ SPAM_is_Ruining_the_World_Wide_Web_and_We_Need_to_Talk_About_That⠀✐ Posted in Deception, Marketing at 2:09 pm by Dr. Roy Schestowitz Video_download_link | md5sum be3f545cd31e04f98657cde097386943 Spamfarm or Webspam: Is This the Future of the WWW? Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/spamfarm-pandemic.webm Summary: The World_Wide_Web (WWW) has a pandemic of misinformation, but to make matters worse a lot of sites have turned into spamfarms, sometimes shrewdly disguised as “news”, “reviews” etc. LAST week’s long_rant about what CNX_Software had become certainly did not help. In fact, CNX Software got even worse in recent days (this ongoing worsening motivated the previous video) and it’s safe to say that about half the “content” there is nowadays borderline junk or outright spam. This is part of a worrying trend, so singling out Phoronix or CNX Software would be missing the point. To make matters worse, they imperil themselves and pave the way towards their very own demise. It’s the trust which took them years to build up — if not decades to build up (Phoronix turns 18 later this year) — which kept or keeps their momentum going. Lose the trust, and the audience will vanish, in turn removing any incentive for investment (either as author or advertiser). This is how sites die. What we said about the Linux_Foundation in that same (aforementioned) rant is still applicable, as demonstrated in the video above. This is part of a broader trend which we first_cautioned_about_around_2020. Once-legitimate sites are selling out and trying to ‘cash in’. It never ends well because existing audiences are alienated, nobody new comes knocking, and sooner or later one becomes a “SPAMnil” [1, 2] with more videos than actual daily views. “We hope to extend the dialogue about these issues; it’s the same problem in Gulag’s YouTube.”This problem is further exacerbated by spammy search and “social control media” oligopolies; they’re simply not in the business of prioritising accurate, objective information such as news sites; instead they promote_clickbait_(or_optimise_for_that)_because_they_aim_to_enhance "engagement",_which_is_related_to_mental/psychological_distress. It’s widely known people are more likely to do things they’re strongly passionate about; disagreement increases “screen time” (with space for ads). But it can be counterproductive, even corrosive. In the video above I show examples of the problem (using new material) and then randomly pick some Gemini_capsules, where the signal-to-noise ratio is a lot better (than today’s WWW). We hope to extend the dialogue about these issues; it's_the_same_problem_in Gulag's_YouTube. █ ䷩ 𝚕𝚒𝚗𝚎 2354 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_23/2/2022:_OpenSSH_8.9,_Levente_Polyak_Cemented_as_Arch_Project_Leader, Intel_Acquires_Linutronix⠀✐ Posted in News_Roundup at 3:14 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ The_Best_Linux_Distros_For_Old_Laptops⠀⇛ A wise man once said that when a relationship gets old, you don’t throw it away. Instead, you fix it and learn to navigate that relationship in a new way. The same can be said about the relationships we have with our technology. If you have an old laptop lying around, don’t throw it away just yet; it can be revitalized and put to good use. All you need to do is find a lightweight Linux distribution that’s compatible with your device’s hardware and you’ll be all set. All these lightweight distros are a far better choice than Windows or macOS for old hardware. They’re even better than the most popular options like Ubuntu. With that in mind, here are a few lightweight Linux distros that can bring your old laptop back to life. o § Kernel Space⠀➾ # ⚓ Linux_5.16.11⠀⇛ I'm announcing the release of the 5.16.11 kernel. All users of the 5.16 kernel series must upgrade. The updated 5.16.y git tree can be found at: git://git.kernel.org/pub/scm/linux/kernel/git/ stable/linux-stable.git linux-5.16.y and can be browsed at the normal kernel.org git web browser: https://git.kernel.org/?p=linux/kernel/git/stable/ linux-s... thanks, greg k-h # ⚓ Linux_5.15.25⠀⇛ # ⚓ Linux_5.10.102⠀⇛ # ⚓ Linux_5.4.181⠀⇛ # ⚓ Linux_4.19.231⠀⇛ # ⚓ Linux_4.14.268⠀⇛ # ⚓ Linux_4.9.303⠀⇛ # ⚓ Is_it_time_to_remove_reiserfs?⠀⇛ # ⚓ ReiserFS_Proposed_To_Be_Removed_From_Linux_In_2022⠀⇛ o § Applications⠀➾ # ⚓ Best_Free_and_Open_Source_Alternatives_to_Atlassian_Jira Service_Management⠀⇛ Atlassian Corporation Plc is a software company founded in 2002 that develops products for software developers, project managers and other software development teams. It employs over 7,000 people and is headquartered in Sydney, Australia. Atlassian produces a range of proprietary software including software for collaboration, development, and issue tracking software for teams. Atlassian dominates several markets where it still has intense competition. # ⚓ How_to_Use_Emacs_As_a_USENET_Reader_With_Gnus⠀⇛ USENET is a decentralized global messaging system. It is considered to be the first global social network with more than 100,000 groups that are talking about various topics and specializations. This makes USENET a particularly good repository of knowledge and discussion for the interested reader. o § Instructionals/Technical⠀➾ # ⚓ How_To_Install_DBeaver_CE_On_Ubuntu_/_AlmaLinux_&_Fedora_| Tips_On_UNIX⠀⇛ This tutorial will be helpful for beginners to download and install DBeaver CE on Ubuntu 22.04 LTS, Ubuntu 20.04 LTS, Linux Mint 20.3, and Debian 8 via the official repository and via Flatpak also. # ⚓ How_to_Install_and_Configure_Zabbix_Server_6_on_Ubuntu 20.04⠀⇛ Zabbix is an open-source monitoring software tool for diverse IT components, including networks, servers, virtual machines and cloud services. Zabbix provides monitoring metrics, among others network utilization, CPU load and disk space consumption. Zabbix has a rich set of features to enable users to monitor more than just hosts, offering great flexibility to administrators when it comes to choosing the most suitable option for each situation. Zabbix uses XML based template which contains elements to monitor. The backend of Zabbix is written in C programming and PHP is used for the web frontend. Zabbix can send you alerts to notify the different events and issues based on metrics and thresholds defined for your IT environment. It supports agent-based and agentless monitoring. But Zabbix agents installation can help you to get detailed monitoring e.g. CPU load, network, disk space utilization. # ⚓ How_to_Install_Zabbix_Agent_6_on_Rocky_Linux/Alma_Linux/ Oracle_Linux_8⠀⇛ A Zabbix agent is a program that runs on a remote machine that needs to be monitored through the Zabbix server. The agent collects the data on the remote server and send back to Zabbix server when requested. Zabbix agent must be installed on all the remote systems that need to be monitor through the Zabbix server. # ⚓ Listen_to_your_favorite_music_on_Linux_with_Juk_| Opensource.com⠀⇛ The KDE project doesn’t just provide a famous desktop, it generates a lot of software, from tools for video editng, photography, and illustration, to graphing calculators, email, and office work. Those are all productivity tools, but KDE is also good for relaxing. It has games and media players, and the music player I use is known simply as Juk. # ⚓ Two_DHCP_servers_in_a_libvirt_network_–_Lukáš_Zapletal⠀⇛ I write provisioning software that needs to integrate with DHCP servers. Libvirt is a great Linux virtual environment for development, but by default it runs its own DHCP server (dnsmasq). That is a very good feature for spawning ad-hoc VMs which get their IPs easily. But I want also to manage some VMs with my own DHCP server. How to do this? # ⚓ Easy_VM_access_with_routed_libvirt_mode_–_Lukáš_Zapletal⠀⇛ By default, libvirt comes with a virtual network called “default” that is configured with NAT. That is a very sane default configuration, VMs are accessible from the host machine directly and they can also access internet via NAT. Many people, however, want to access VMs from outside – typically when libvirt is used as a server hypervisor. You will find many blog posts explaining how to setup a bridge. Configuration of bridge is complex, you need to shut down the main connection and it is a challenge for users who only have SSH access to the machine. Only if there was a better way… Big news if you did not know: you don’t need a bridge to access your VMs. You can use a regular (routed) network! In this article, I will describe how it works. Spoiler alert: it is easier than bridge! # ⚓ How_I_Use_NFS_for_Sharing_Folders_in_My_Homelab_Setup⠀⇛ When you have several systems in your network, especially if you virtualize them like in a homelab or through your organization, having shared folders is extremely convenient and useful to make your work easier and faster. I, for example, have a folder that I share among different virtual machines. This way, whatever gets downloaded in one system, is immediately available on the other system. I have the folder located at a centralized file sharing NFS virtualized server. This folder is shared to a container that runs a torrenting app where I download files which get available at the same time to another container that can also use these same files for processing. Basically, I centralize my files in a location that I later share among different devices and instances for convenience and functionalities. # ⚓ Create_GUI_Dialog_Boxes_In_Bash_Scripts_With_Whiptail_– OSTechNix⠀⇛ A while ago, we briefly discussed about Zenity, a simple program that allows you to create graphical (GTK+) dialog boxes in command-line and shell scripts. In this article, we are going to discuss yet another GUI utility called Whiptail that can be used to create GUI dialog boxes in Bash scripts in Linux. Not every script that you write needs a frontend graphical interface. But sometimes it would be better if you create a graphical interface instead of relying on interacting with the command line. In my case, if there is a long list of responses needed in the script I would choose to go with a graphical interface. Whiptail is a friendly GUI utility that uses a newt programming library. Whiptail offers different dialog boxes for different purposes. Depending upon your use case you can use these dialog boxes to make your script more interactive. # ⚓ How_to_Install_and_Configure_Fail2ban_on_Alma_Linux_8⠀⇛ Fail2ban is a free and open-source Intrusion Prevention System written in Python. It is used to protect your system against brute-force attacks. It continuously monitors the SSH (and other) log files for authentication attempts, after a specified number of incorrect password attempts, the client’s IP address is banned by Fail2Ban. It can be used to secure several services including, SSH, vsftpd, Apache, and Webmin. In this tutorial, I will show you how to install Fail2Ban firewall on Alma Linux 8. # ⚓ How_to_Install_Zulip_Chat_Server_on_Debian_11⠀⇛ Zulip is an open-source chat server, similar to Microsoft Teams, Rocket Chat or Slack. It is written in Python and uses Django, PostgreSQL, and JavaScript. It integrates with over 90 third-party plugins, including Github, Jira, Stripe, Zendesk, Sentry, etc. You can expand the integrations by connecting them with Zapier and IFTTT. It comes with features like private messaging, group chats, threaded conversations, custom channels, video calls, drag-and-drop file uploads, custom emojis, Giphy integration, Image and Tweets preview and many more. Zulip comes with desktop and mobile apps for every platform, making it platform agnostic. In this tutorial, you will learn how to install and configure Zulip Chat on a Debian 11 based server. # ⚓ How_to_Install_and_Play_With_RetroArch_on_Linux⠀⇛ Video games have taken the world by storm. From the simple game of Pong created in the 1970s to the latest AAA titles available today, the industry has continued to be a source of entertainment for decades. This steady growth has allowed the video game industry to become one of the largest in the world, with the market reaching a net worth of $90 Billion in the year 2020. Different games are available on different platforms. These platforms compete with each other by offering video game titles that are exclusive to their console only. While this allows for market growth and competition, not everyone has the chance to purchase every console. Furthermore, some consoles and video game titles are no longer in production and it would mean that one would lose the chance to play these titles. This is where emulators come in. # ⚓ How_To_Install_Avidemux_on_Ubuntu_20.04_LTS_–_idroot⠀⇛ In this tutorial, we will show you how to install Avidemux on Ubuntu 20.04 LTS. For those of you who didn’t know, Avidemux is a free and open-source software application for non-linear video editing and transcoding multimedia files. It supports many file types, including AVI, DVD compatible MPEG files, MP4, and ASF, using a variety of codecs. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the Avidemux open-source video editing application on Ubuntu 20.04 (Focal Fossa). You can follow the same instructions for Ubuntu 18.04, 16.04, and any other Debian-based distribution like Linux Mint. # ⚓ Make_any_device_your_second_display_on_Linux⠀⇛ Do you use Linux? Need an extra monitor but only have one that you can use? Good news! With Deskreen, you can turn any smartphone, tablet, or Laptop into a second screen. Here’s how it works. # ⚓ How_to_use_Rescuezilla_to_clone_a_Linux_hard_drive⠀⇛ Do you need to clone a Linux hard drive? Unsure how to go about doing it? Check out the Rescuzilla live USB tool. What is Rescuezilla? Rescuezilla is a bootable live operating system that Linux users can use to “rescue” their system without dealing with complex, confusing options. In this guide, we’ll show you have to use Rescuezilla to clone a Linux hard drive. Note: you will need a USB flash drive of at least 1 GB in size to create a Rescuezilla live USB key. Additionally, you must have a source hard drive and a destination hard drive for the cloning process to work. # ⚓ How_to_install_the_Brave_nightly_browser_on_Linux⠀⇛ The people behind the Brave browser have a nightly release. The Nightly release allows users to get the latest features as soon as possible. Here’s how you can set up Brave nightly browser on Linux. # ⚓ How_To_Monitor_Your_Linux_Servers_with_Checkmk⠀⇛ The Checkmk is one of the most used and user- friendly applications for monitoring Linux servers. It can check the server status, load, network status, applications, database, cloud server load, storage, and other IoT devices connected with your Linux server. The Checkmk tool works in a hybrid way in Linux. Once you have the tool installed on your Linux machine, you can easily access all the configuration and dashboard tabs through the web browser. Unlike other server monitoring tools, the Checkmk tool does not hog a huge amount of system resources on Linux. Installing and using the Checkmk tool on Linux is easy and straightforward Linux. If you’re a system administrator, you must try out this tool and enjoy all the features and plug-ins that can reduce your workload a bit. # ⚓ How_to_install_DaVinci_Resolve_17_on_Linux⠀⇛ Davinci Resolve is a professional, high-end non- linear video editing tool. Best of all, it is available on Linux. So, if you require a good video editor, follow these installation instructions below to get Davinci Resolve to work on your system. # ⚓ Network_traffic_analysis_with_tcpdump⠀⇛ tcpdump is a data-network packet analyzer computer program. It allows the user to display network packets (including TCP/IP) being transmitted or received over a network. In this short article I will show how to do some packet capture for network traffic analysis with tcpdump. # ⚓ How_to_Install_Sublime_Text_4_on_AlmaLinux_8_– LinuxCapable⠀⇛ Sublime Text 4 is an excellent choice as your go-to program to edit code. Sublime is known for its speed, ease of use, cross-platform, and community contribution. It natively supports many programming languages and markup tongues, but users can also expand its functionality with plugins! The Python API makes it easy; make sure you download from within Sublime, or they won’t show up in settings. Also, you can further customize and enhance it by installing additional features using package control and custom settings. In the following tutorial, you will learn how to install Sublime Text 4 on AlmaLinux 8. # ⚓ Install_ProcessWire_on_Ubuntu_22.04_–_kifarunix.com⠀⇛ Follow through this guide to install ProcessWire on Ubuntu 22.04. ProcessWire is an opensource PHP based content management system and framework. o § Games⠀➾ # ⚓ View_Your_Steam_Deck_Compatible_Games_through_Steam_– Boiling_Steam⠀⇛ We’re less than three days from the official launch of the Steam Deck (less than 51 hours left in EST) and Valve, in addition to partnering with iFixit to offer replacement parts, has now made an official tool to view the games in your Steam library as being Steam Deck Verified, Playable, unsupported, and untested. Simply go to this page, log into your Steam account, and you’ll instantly be able to see what your games are categorized under. # ⚓ Valve_adds_official_Steam_Deck_compatibility_checker,_762 games_Playable_or_Verified_|_GamingOnLinux⠀⇛ While there’s been a few unofficial ways to check your own Steam Library for the Steam Deck, Valve has now put up the official way. Plus, we’re getting closer to a thousand Playable titles now. Things are really heating up, with only two days left until the official release on February 25! All you need to do is login with your Steam account and head to this page, which will give you an overview of what you can expect to work. # ⚓ UnderRail_is_preparing_for_the_Steam_Deck,_won’t_be_perfect just_yet_|_GamingOnLinux⠀⇛ Released back in 2015, UnderRail from Stygian Software is an old school turn-based isometric indie role playing game that focuses on exploration and combat. Now, they’re trying to get it looking good on a Steam Deck. # ⚓ How_to_play_Assassin’s_Creed_Unity_on_Linux⠀⇛ Assassin’s Creed Unity is an action-adventure game developed by Ubisoft Montreal and published by Ubisoft. It was released in 2014 on Windows, PS4, and Xbox One. Here’s how you can play Assassin’s Creed Unity on Linux. # ⚓ How_to_play_Days_Gone_on_Linux⠀⇛ Days Gone is a post-apocalyptic video game developed by Bend Studio and published by Sony Interactive Entertainment. It was released for PC and PS4. Here’s how to play it on your Linux gaming PC. # ⚓ Boosting_a_HP_Z400_Workstation_with_a_Modern_GPU_(GTX_1660 Ti)_–_Boiling_Steam⠀⇛ Let’s talk about hardware today! One of my machines at home happens to be an old HP Z400 workstation. A fairly old piece of hardware (manufactured sometimes in 2009-2010) that I use mainly for productivity because it’s built like a tank and is fairly silent – and really cheap second hand. I mentioned it before on Boiling Steam, back in 2017. While pre-built, you can replace and upgrade pretty much everything in it, be it the CPU, the RAM, and the GPU. It usually comes with a Quadro Nvidia GPU, but you can certainly switch it for a more modern card. Years ago I went for a Nvidia GTX 1060 (3GB, the weakest one) GPU to enjoy some decent gaming on that machine as well – unfortunately this card, along with Pascal generations cards in general, has issues with VKD3D and I wanted to do an affordable upgrade. # ⚓ Wordle’s_Digital_Predecessors:_The_Evolution_of_Online_Word Games⠀⇛ I’m sort of at that age in my adulthood where I’m not really a heavy gamer, but my love of word games knows no bounds. So when Wordle became a thing, I became a fast fan as well as that annoying guy on Twitter who shares his playthroughs each morning. (Never really a heavy a Words With Friends player, though I enjoyed Scrabble as much as the next guy.) But in a lot of ways, Wordle one of many obsessions of this type, and I think the real secret is that it’s a fairly simple game, with reasonable restrictions on how it’s played, that has a surprising number of layers that emerge over time. In honor of Wordle’s success, Today’s Tedium looks back at the imprint word games have left on the world of technology in the decades prior. May your brain be teased. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ KDE_vs_GNOME:_What’s_the_Ultimate_Linux_Desktop Choice?⠀⇛ When it comes to Linux, the desktop environment is a big deal. A desktop environment makes up the graphical user interface (GUI) along with a set of applications that you get on your Linux distribution. You can go through our article explaining what a desktop environment is. Choosing a good desktop environment can help you improve productivity, workflow, ease of use, and the overall experience. o § Distributions⠀➾ # § BSD⠀➾ # ⚓ OpenSSH_8.9_released_[LWN.net]⠀⇛ OpenSSH 8.9 has just been released. It will be available from the mirrors listed at https://www.openssh.com/ shortly. OpenSSH is a 100% complete SSH protocol 2.0 implementation and includes sftp client and server support. Once again, we would like to thank the OpenSSH community for their continued support of the project, especially those who contributed code or patches, reported bugs, tested snapshots or donated to the project. More information on donations may be found at: https://www.openssh.com/donations.html Future deprecation notice ========================= A near-future release of OpenSSH will switch scp(1) from using the legacy scp/rcp protocol to using SFTP by default. Legacy scp/rcp performs wildcard expansion of remote filenames (e.g. "scp host:* .") through the remote shell. This has the side effect of requiring double quoting of shell meta- characters in file names included on scp(1) command-lines, otherwise they could be interpreted as shell commands on the remote side. This creates one area of potential incompatibility: scp(1) when using the SFTP protocol no longer requires this finicky and brittle quoting, and attempts to use it may cause transfers to fail. We consider the removal of the need for double-quoting shell characters in file names to be a benefit and do not intend to introduce bug-compatibility for legacy scp/rcp in scp(1) when using the SFTP protocol. Another area of potential incompatibility relates to the use of remote paths relative to other user's home directories, for example - "scp host:~user/file /tmp". The SFTP protocol has no native way to expand a ~user path. However, sftp-server(8) in OpenSSH 8.7 and later support a protocol extension "expand- path@openssh.com" to support this. Security Near Miss ================== * sshd(8): fix an integer overflow in the user authentication path that, in conjunction with other logic errors, could have yielded unauthenticated access under difficult to exploit conditions. This situation is not exploitable because of independent checks in the privilege separation monitor. Privilege separation has been enabled by default in since openssh-3.2.2 (released in 2002) and has been mandatory since openssh-7.5 (released in 2017). Moreover, portable OpenSSH has used toolchain features available in most modern compilers to abort on signed integer overflow since openssh-6.5 (released in 2014). Thanks to Malcolm Stagg for finding and reporting this bug. Potentially-incompatible changes ================================ * sshd(8), portable OpenSSH only: this release removes in-built support for MD5-hashed passwords. If you require these on your system then we recommend linking against libxcrypt or similar. * This release modifies the FIDO security key middleware interface and increments SSH_SK_VERSION_MAJOR. Changes since OpenSSH 8.8 ========================= This release includes a number of new features. New features ------------ * ssh(1), sshd(8), ssh-add(1), ssh-agent(1): add a system for restricting forwarding and use of keys added to ssh-agent(1) A detailed description of the feature is available at https://www.openssh.com/agent- restrict.html and the protocol extensions are documented in the PROTOCOL and PROTOCOL.agent files in the source release. * ssh(1), sshd(8): add the sntrup761x25519- sha512@openssh.com hybrid ECDH/x25519 + Streamlined NTRU Prime post- quantum KEX to the default KEXAlgorithms list (after the ECDH methods but before the prime-group DH ones). The next release of OpenSSH is likely to make this key exchange the default method. * ssh-keygen(1): when downloading resident keys from a FIDO token, pass back the user ID that was used when the key was created and append it to the filename the key is written to (if it is not the default). Avoids keys being clobbered if the user created multiple resident keys with the same application string but different user IDs. * ssh-keygen(1), ssh(1), ssh-agent(1): better handling for FIDO keys on tokens that provide user verification (UV) on the device itself, including biometric keys, avoiding unnecessary PIN prompts. * ssh-keygen(1): add "ssh-keygen -Y match- principals" operation to perform matching of principals names against an allowed signers file. To be used towards a TOFU model for SSH signatures in git. * ssh-add(1), ssh-agent(1): allow pin- required FIDO keys to be added to ssh-agent(1). $SSH_ASKPASS will be used to request the PIN at authentication time. * ssh-keygen(1): allow selection of hash at sshsig signing time (either sha512 (default) or sha256). * ssh(1), sshd(8): read network data directly to the packet input buffer instead indirectly via a small stack buffer. Provides a modest performance improvement. * ssh(1), sshd(8): read data directly to the channel input buffer, providing a similar modest performance improvement. * ssh(1): extend the PubkeyAuthentication configuration directive to accept yes|no|unbound|host-bound to allow control over one of the protocol extensions used to implement agent-restricted keys. Bugfixes -------- * sshd(8): document that CASignatureAlgorithms, ExposeAuthInfo and PubkeyAuthOptions can be used in a Match block. PR#277. * sshd(8): fix possible string truncation when constructing paths to .rhosts/.shosts files with very long user home directory names. * ssh-keysign(1): unbreak for KEX algorithms that use SHA384/512 exchange hashes * ssh(1): don't put the TTY into raw mode when SessionType=none, avoids ^C being unable to kill such a session. bz3360 * scp(1): fix some corner-case bugs in SFTP- mode handling of ~-prefixed paths. * ssh(1): unbreak hostbased auth using RSA keys. Allow ssh(1) to select RSA keys when only RSA/SHA2 signature algorithms are configured (this is the default case). Previously RSA keys were not being considered in the default case. * ssh-keysign(1): make ssh-keysign use the requested signature algorithm and not the default for the key type. Part of unbreaking hostbased auth for RSA/SHA2 keys. * ssh(1): stricter UpdateHostkey signature verification logic on the client- side. Require RSA/SHA2 signatures for RSA hostkeys except when RSA/SHA1 was explicitly negotiated during initial KEX; bz3375 * ssh(1), sshd(8): fix signature algorithm selection logic for UpdateHostkeys on the server side. The previous code tried to prefer RSA/SHA2 for hostkey proofs of RSA keys, but missed some cases. This will use RSA/SHA2 signatures for RSA keys if the client proposed these algorithms in initial KEX. bz3375 * All: convert all uses of select(2)/pselect (2) to poll(2)/ppoll(2). This includes the mainloops in ssh(1), ssh-agent(1), ssh-agent(1) and sftp-server(8), as well as the sshd(8) listen loop and all other FD read/writability checks. On platforms with missing or broken poll(2)/ppoll(2) syscalls a select (2)-based compat shim is available. * ssh-keygen(1): the "-Y find-principals" command was verifying key validity when using ca certs but not with simple key lifetimes within the allowed signers file. * ssh-keygen(1): make sshsig verify-time argument parsing optional * sshd(8): fix truncation in rhosts/shosts path construction. * ssh(1), ssh-agent(1): avoid xmalloc(0) for PKCS#11 keyid for ECDSA keys (we already did this for RSA keys). Avoids fatal errors for PKCS#11 libraries that return empty keyid, e.g. Microchip ATECC608B "cryptoauthlib"; bz#3364 * ssh(1), ssh-agent(1): improve the testing of credentials against inserted FIDO: ask the token whether a particular key belongs to it in cases where the token supports on- token user-verification (e.g. biometrics) rather than just assuming that it will accept it. Will reduce spurious "Confirm user presence" notifications for key handles that relate to FIDO keys that are not currently inserted in at least some cases. bz3366 * ssh(1), sshd(8): correct value for IPTOS_DSCP_LE. It needs to allow for the preceding two ECN bits. bz#3373 * ssh-keygen(1): add missing -O option to usage() for the "-Y sign" option. * ssh-keygen(1): fix a NULL deref when using the find-principals function, when matching an allowed_signers line that contains a namespace restriction, but no restriction specified on the command-line * ssh-agent(1): fix memleak in process_extension(); oss-fuzz issue #42719 * ssh(1): suppress "Connection to xxx closed" messages when LogLevel is set to "error" or above. bz3378 * ssh(1), sshd(8): use correct zlib flags when inflate(3)-ing compressed packet data. bz3372 * scp(1): when recursively transferring files in SFTP mode, create the destination directory if it doesn't already exist to match scp(1) in legacy RCP mode behaviour. * scp(1): many improvements in error message consistency between scp(1) in SFTP mode vs legacy RCP mode. * sshd(8): fix potential race in SIGTERM handling PR#289 * ssh(1), ssh(8): since DSA keys are deprecated, move them to the end of the default list of public keys so that they will be tried last. PR#295 * ssh-keygen(1): allow 'ssh-keygen -Y find- principals' to match wildcard principals in allowed_signers files Portability ----------- * ssh(1), sshd(8): don't trust closefrom(2) on Linux. glibc's implementation does not work in a chroot when the kernel does not have close_range(2). It tries to read from /proc/self/fd and when that fails dies with an assertion of sorts. Instead, call close_range(2) directly from our compat code and fall back if that fails. bz#3349, * OS X poll(2) is broken; use compat replacement. For character- special devices like /dev/null, Darwin's poll(2) returns POLLNVAL when polled with POLLIN. Apparently this is Apple bug 3710161 - not public but a websearch will find other OSS projects rediscovering it periodically since it was first identified in 2005. * Correct handling of exceptfds/POLLPRI in our select(2)-based poll(2)/ppoll(2) compat implementation. * Cygwin: correct checking of mbstowcs() return value. * Add a basic SECURITY.md that refers people to the openssh.com website. * Enable additional compiler warnings and toolchain hardening flags, including -Wbitwise-instead-of-logical, - Wmisleading-indentation, -fzero-call-used-regs and -ftrivial-auto- var-init. * HP/UX. Use compat getline(3) on HP-UX 10.x, where the libc version is not reliable. Checksums: ========== - SHA1 (openssh-8.9.tar.gz) = 653310ba1a63959fe2df503fe7ad556445180127 - SHA256 (openssh-8.9.tar.gz) = mJigktP+Bk0sB7uRPuWgjcCOYZ+mIMdvRlZe66irtQA= - SHA1 (openssh-8.9p1.tar.gz) = 205cdf0040a238047e2c49f43460e03d76e5d650 - SHA256 (openssh-8.9p1.tar.gz) = / Ul2VLerFobaxnL7g9+0ukCW6LX/zazNJiOArli+xec= Please note that the SHA256 signatures are base64 encoded and not hexadecimal (which is the default for most checksum tools). The PGP key used to sign the releases is available from the mirror sites: https://cdn.openbsd.org/pub/OpenBSD/OpenSSH/ RELEASE_KEY.asc Please note that the OpenPGP key used to sign releases has been rotated for this release. The new key has been signed by the previous key to provide continuity. Reporting Bugs: =============== - Please read https://www.openssh.com/ report.html Security bugs should be reported directly to openssh@openssh.com # § Arch Family⠀➾ # ⚓ Arch_Linux_–_News:_Arch_Linux_Leader_Election Results⠀⇛ This month we held our leader election, and our current leader Levente Polyák ran unopposed. As per our election rules he is re-elected for a new term. Congratulations to Levente Polyak on a new term! # ⚓ Arch_Linux_Leader_Election_Results⠀⇛ # § Canonical/Ubuntu Family⠀➾ # ⚓ Ubuntu_addresses_Linux_kernel_vulnerabilities_•_The Register⠀⇛ Ubuntu has issued a batch of updates that cover the default as well as the AWS and KVM flavours for the current short-term release 21.10, both the original 5.04 and OEM 5.14 builds for the current 20.04 LTS release, as well as 18.04, and, surprisingly, even 16.04 and 14.04. While kernel releases trickle out all the time, the last two members of that list – 2016′s Xenial Xerus and 2014′s Trusty Tahr – emphasise that even very old releases in Extended Security Maintenance or ESM sometimes need a bit of TLC. It also might surprise some that multiple different Linux kernels are available for a single product release. Although Ubuntu pushes out a new Long-Term Support (LTS) release every even-numbered year, those get five years of bugfixes. o § Devices/Embedded⠀➾ # ⚓ OpenScan_DIY_3D_scanner_works_with_Raspberry_Pi,_DSLR,_or smartphone_cameras⠀⇛ OpenScan is an open-source DIY 3D scanner that relies on Photogrammetry and works with Raspberry Pi camera modules, compatible ArduCam modules, as well as DSLR cameras, or the camera from your smartphone. The open-source project was brought to my attention after I wrote about the Creality CR-Scan Lizard 3D scanner. The OpenScan kits include 3D printed parts such as gears, two stepper motors, a Raspberry Pi shield, and a Ringlight module to take photos of a particular object from different angles in an efficient manner. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Oppo’s_first_Android_tablet_looks_like_a_tempting iPad_Air_rival_|_TechRadar⠀⇛ # ⚓ Infinix_Zero_5G_to_get_Android_12_in_August_– GSMArena.com_news⠀⇛ # ⚓ Install_Android_12_on_Galaxy_S9_[How_To]⠀⇛ # ⚓ How_to_Prepare_Your_Android_Phone_to_Be_Stolen⠀⇛ # ⚓ How_to_record_a_call_on_your_Android_Phone_–_Geeky Gadgets⠀⇛ # ⚓ How_to_install_and_use_Magisk_modules_on_a_rooted Android_phone⠀⇛ # ⚓ Google_Assistant_Not_Working_on_Android?_Try_these Fixes_–_Gotechtor⠀⇛ # ⚓ The_Fastest_Android_Gaming_Phone_Features_Snapdragon 8_Gen_1_And_It’s_Affordable_Too⠀⇛ # ⚓ This_Google_update_can_help_you_free_up_space_on_your Android_smartphone_–_Times_of_India⠀⇛ # ⚓ A_hidden_gem_in_Gboard_on_Android_|_Computerworld⠀⇛ # ⚓ Android_game_modding_is_here_thanks_to_BlueStacks_– Android_Authority⠀⇛ # ⚓ The_6_best_podcast_apps_for_Android_in_2022⠀⇛ # ⚓ Wallpaper_Wednesday:_Android_wallpapers_2022-02-23_– Android_Authority⠀⇛ # ⚓ Jireno_Cube_4_Projector_review:_Carry_Android_TV_with you_|_Digital_Trends⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ OSI:_Open_source_legal_awareness_needs_to_grow [Ed: Propping up BFT (scam) using a Microsoft-linked firm, OpenLogic [sic]]⠀⇛ Second: respondents seem to be exploring blockchain and NFT at a surprisingly high rate. While NFTs got the lowest score of all as “not important”, more than 20% marked both blockchain and NFT as “very important”. I’d be interested to understand why. # § Events⠀➾ # ⚓ Call_for_Papers_opens_for_Summit_in_Albania_– openSUSE_News⠀⇛ The openSUSE community has opened the call for papers for a summit that will be held in conjunction with Open Source Conference Albania (OSCAL) 2022. People can submit a talk for the openSUSE Summit at OSCAL 2022 from now until April 26 on events.opensuse.org. OSCAL will take place from June 18 and 19 in Tirana, Albania, and will gather free (libre) open source technology users, developers, academics, governmental agencies and people who share the idea that software should be free and open for people to study, develop and customize. The conference is organized by Open Labs, which is a non-profit community that promotes the importance of an open source culture in Albania since 2012. # § Programming/Development⠀➾ # ⚓ JavaScript_devs_feel_language_moving_in_right direction_•_The_Register⠀⇛ The State of JavaScript 2021 survey has arrived, a little later than planned (no jokes about language performance, please) and in the wake of a somewhat embarrassing data leak. 2020′s State of JavaScript report came from a survey of 23,000 developers. 2021′s was the result of just over 16,000. And although the US leads the way, its share of survey respondents dropped to 14 per cent and Russia climbed to third place behind Germany with 4 per cent. Sadly, the vast majority (93.2 per cent) of those who answered the gender question listed themselves as male, up on last year’s 91.1 per cent. 82.4 per cent chose to fill out the survey in English. JavaScript might be impressively diverse from a technological perspective, but the same cannot be said for the respondents to this survey. # ⚓ Color_Sensor_with_Arduino_Uno:_TCS34725_explaination, wiring_and_code⠀⇛ To sort out the things with respect to the colors like different color balls, Arduino can interface the TCS34725 that is the cheap and best color sensor which can handle such application In this tutorial, I’ll show you how to interface the color sensor TCS34725 with Arduino, explaining with a wiring diagram, code, and components list. # ⚓ Bend_Your_Vase_Mode_Prints_By_Hacking_The_GCode⠀⇛ [Stefan] from CNCKitchen wanted to make some bendy tubes for a window-mountable ball run, and rather than coming up with some bent tube models, it seemed there might be a different way to achieve the desired outcome. Starting with a simple tube model designed to be quickly printed in vase mode, he wrote a Python script which read in the G-Code, and modified it allow it to be bent along a spline path. Vase mode works by slowly ramping up the Z- axis as the extruder follows the object outline, but the slicing process is still essentially the same, with the object sliced in a plane parallel to the bed. Whilst this non-planar method moves the Z-axis in sync with the horizontal motion (although currently limited to only one plane of distortion, which simplifies the maths a bit) it is we guess still technically a planar solution, but just an inclined plane. But we digress, non-planar in this context merely means not parallel to the bed, and we’ll roll with that. # ⚓ Unreal_Engine_5_is_now_available_in_Preview!_–_Unreal Engine⠀⇛ This release builds upon the features exposed in last year’s Early Access offering, with improvements to performance, quality, and feature-completeness across the board. # ⚓ Dev_snapshot:_Godot_4.0_alpha_3⠀⇛ We’re continuing on our fortnightly release schedule for alpha snapshots of Godot 4.0 – this time with 4.0 alpha 3. See past alpha releases for details (alpha 1, alpha 2). 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. # ⚓ 10_of_our_favorite_Jenkins_plugins_–_Octopus_Deploy⠀⇛ As an open-source Continuous Integration (CI) platform, one of our favorite things about Jenkins is its strong community. Nowhere is this more evident than in the Jenkins Plugins Index. There are over 1800 user-created plugins in the Index, allowing you to extend Jenkins’ features and change your instance to meet your team’s needs. # § Perl/Raku⠀➾ # ⚓ Perl_Weekly_Challenge_153:_Left_Factorials_and Factorions⠀⇛ # ⚓ The_progress_of_the_SPVM_language_2022_|_Yuki Kimoto_Perl_Blog_–_Perl_Club_[blogs.perl.org]⠀⇛ Hi, I write the progress of the SPVM module 2022. SPVM is a programming language that is build on top of the Perl ecosystem and provides fast calculation and array operation to Perl. SPVM can be transpiled to C language, and it can be compiled to shared libraries and executable files. SPVM can call C/C++/Cuda libraries by writing pure C/C++/Cuda language without XS. I wrote SPVM from 2016. I finally implement the all features that I think they are needed for modern applications. # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ Recursive_dwdiff_using_find_-exec_Using_find, sh⠀⇛ # § Java⠀➾ # ⚓ How_to_create_and_call_a_method_in_Java⠀⇛ A Java method contains a block of statements/instructions that perform some functionalities only when someone calls the method. When someone calls a java method, multiple statements executes at the backend to provide a certain output. The Java methods provide the reusability of the code, as we have to write/create a method once, and we can use it as many times as we want. * § Leftovers⠀➾ o § Hardware⠀➾ # ⚓ Intel_acquires_Linutronix_[LWN.net]⠀⇛ The plan is evidently to continue to run Linutronix as an independent company rather than absorbing it into Intel. # ⚓ Intel_Acquires_Linutronix⠀⇛ Linutronix is comprised of a team of highly qualified and motivated employees with a wealth of experience and involvement in the ongoing development of Linux. Led by CEO Heinz Egger and CTO Thomas Gleixner, Linutronix is the architect of PREEMPT_RT (Real Time) and the leading technology provider for industrial Linux. Gleixner has been the principal maintainer of x86 architecture in the Linux kernel since 2008. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ Top_U.S._Websites_Run_Afoul_of_European Data_Privacy_Law [Ed: And it’s_not_properly enforced_either]⠀⇛ Leading U.S. websites have failed to abide by European data privacy law, according to research by regulatory compliance software vendor Zendata. # ⚓ Counter_Comments_to_the_TRAI_for_the, “Consultation_Paper_on_Regulatory_Framework for_Promoting_Data_Economy_Through Establishment_of_Data_Centres,_Content Delivery_Networks,_and_Interconnect Exchanges”⠀⇛ IFF remains deeply committed to net neutrality and data privacy. On February 10th, 2022, IFF filed its main comments to TRAI’s ongoing consultation on “Regulatory Framework for Promoting Data Economy Through Establishment of Data Centres, Content Delivery Networks, and Interconnect Exchanges”. However, we were troubled by some requests made by telecom service providers and industry bodies. They called for a ‘light-touch’ regulatory framework for Content Delivery Networks as well as increased data monetization, with scant attention paid to regulatory oversight over data privacy and security. IFF has filed counter comments to rebut these suggestions and urged TRAI to develop robust mechanisms to enforce net neutrality and protect data privacy. [...] First, we called for urgency in creating a multi-stakeholder body (MSB) for the enforcement of net neutrality principles. While India has globally leading regulations on net neutrality on paper, it still lacks an institutional enforcement mechanism. In this regard, TRAI’s recommendation in 2020 to set up an MSB was not positively received by the Department of Telecommunications (DoT) due to COVID-19 budget constraints. However, the expenditure curbs have since been relaxed and so budgetary cuts no longer stand in the way. The MSB will prevent Telecom Service Providers (TSPs) from abusing interconnection agreements, and keep technical forms of discrimination, like website blocking, slowing down of web services, etc. in check. Second, we cautioned against regulating Content Delivery Networks (CDNs) given existing market efficiency. TRAI and other global regulators have determined that the CDN market is working adequately; it is competitive and provides user benefit. There is also a lack of existing evidence (real data) on any prospective harms, specifically in the Indian market. Hence, to facilitate the growth of the local CDN industry, TRAI should commence a deeper study prior to devising regulation. # ⚓ Bypassing_Apple’s_AirTag_Security_– Schneier_on_Security⠀⇛ A Berlin-based company has developed an AirTag clone that bypasses Apple’s anti-stalker security systems. Source code for these AirTag clones is available online. So now we have several problems with the system. Apple’s anti- stalker security only works with iPhones. (Apple wrote an Android app that can detect AirTags, but how many people are going to download it?) And now non-AirTags can piggyback on Apple’s system without triggering the alarms. # ⚓ Apple_Airtags’_anti-stalker_features_can be_bypassed_–_claim_•_The_Register⠀⇛ An infosec startup says it has built an Apple Airtag clone that bypasses anti-stalking protection features while running on Apple’s Find My protocol. Source code for the clones were published online by Berlin-based infosec startup Positive Security (not to be confused with US- sanctioned cybersecurity outfit Positive Technologies), which said its tags “successfully tracked an iPhone user… for over five days without triggering a tracking notification.” The user consented, added Positive’s Fabian Bräunlein in a blog post explaining his findings. o § Civil Rights/Policing⠀➾ # ⚓ Go_back_to_the_drawing_board:_Kenya_must_scrap unconstitutional_Huduma_Bill_2021_–_Access_Now⠀⇛ Civil society organizations are making their voices heard in Kenyan parliament, and the message is clear: the unconstitutional Huduma Bill 2021 must be scrapped. Currently sitting before parliament, the noxius draft bill that will transition the nation over to a new catch-all digital identity system stands to facilitate the violation of constitutionally guaranteed human rights including the rights to privacy, freedom from discrimination, freedom and security of the person, as well as socio-economic and citizenship rights. Huduma, which requires primary identification documents for registration, stands to potentially exclude people already affected by the shortfalls of the existing identification program — including border communities who are subjected to tough vetting processes to attain identification, and people at risk of statelessness. “The Kenyan parliament continuing to push the harmful Huduma bill through the legislative process is not only a waste of public resources, it’s telling the people of Kenya that their constitutional rights are nothing but words on paper,” said Elias Okwara, Africa Policy Manager at Access Now. “The government must withdraw this bill, and go back to the drawing board.” # ⚓ Public_petition:_withdraw_the_Huduma_Bill_2021_–_Access Now⠀⇛ o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ “Pajamas_from_Spirit_Land”:_Searching_for_William James_–_The_Public_Domain_Review⠀⇛ After the passing of William James — philosopher, early psychologist, and investigator of psychic phenomena — mediums across the US began receiving messages from the late Harvard professor. Channelling these fragmentary voices, Alicia Puglionesi considers the relationship between communication, reputation, and survival after death. ䷩ 𝚕𝚒𝚗𝚎 4078 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_23/2/2022:_Samsung_Failing_People,_SQLite_3.38_Released⠀✐ Posted in News_Roundup at 6:50 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Novena_Open_Source_Laptop_Reborn_As_Desktop_Machine_| Hackaday⠀⇛ When your 5-year-old laptop dies it’s usually time for a replacement. But [Andrew Menadue]’s Novena laptop is fully open-source. He has full access to all the documentation, so he decided to try his hand at repairing it instead. The power supply circuit board went up in smoke one day — he attributes this to poor battery health due to him not using it frequently enough. Given his usage pattern, he decided to switch the Novena into a desktop machine. He made the conversion with a new pass-through power supply board, and the computer booted up but with no display. It seems that the power supply failure took out additional circuits as well. [Andrew] goes down a deep rabbit hole of board and chip swapping, all to no avail. Eventually the display suddenly springs to life, and he concludes the problem was with the EEPROM configuration settings and not LCD display hardware. [....] We wrote about the Novena way back in 2014, and more recently the MNT Reform project. What are your thoughts on these open source laptop projects? Do you have any laptops that you’ve rehabilitated after five or more years? Let us know in the comments below. # ⚓ [Old]_MINISFORUM_DeskMini_UM700,_a_mini-PC_with_Ryzen_that now_launches_Manjaro_Linux⠀⇛ «Man does not live on Windows alone…» and the DeskMini UM700 is a compact computer with internal hardware based on AMD’s Ryzen, which now launches Manjaro Linux as its operating system. And we’re highlighting it because there aren’t too many new teams pre-installing the free system. o § Instructionals/Technical⠀➾ # ⚓ How_To_Install_Htop_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install Htop on Debian 11. For those of you who didn’t know, Htop is a free, open-source, cross-platform interactive process viewer. Htop was created as a replacement for the Linux program top, and it has a lot of the same features as the top, but with a lot more flexibility in terms of how system processes can be interpreted. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the Htop system monitoring tool on a Debian 11 (Bullseye). # ⚓ How_to_run_and_manage_containers_as_systemd_services_with Podman_|_FOSS_Linux⠀⇛ Linux containers are executable application components that combine app source code with operating system libraries and dependencies needed to run the code in different environments. Containers combine lightweight application isolation with the flexibility of image-based deployment methods. Developers use containers as an application packaging and delivery technology. RHEL based systems (CentOS and Fedora Linux) implements containers using technologies such as namespaces for system process isolation, control groups for resource management, and SELinux for security management. Red Hat also provides command- line tools like podman, skopeo, and buildah to manage container images and pods. This article illustrates how to run and manage containers as systemd services with podman. To get started, review our articles on introduction to Linux containers, managing containers with Podman, and managing systems units. # ⚓ 10_Useful_Tools_to_Create_Bootable_USB_from_an_ISO_Image⠀⇛ CD and DVD writers are a thing of the past. You are not likely to find them in modern-day laptops. If your goal is to create a bootable medium, then creating a bootable USB drive from an ISO file remains your best option. There are quite a number of tools that can help you create a bootable USB drive. Some will even go further and let you create a multi-boot USB drive where you get to choose the OS that you want to install. Here are some of the widely-used utilities for creating a bootable USB drive from an ISO file in Linux desktop systems. # ⚓ Fedora_Packaging:_resolving_/usr/bin/../bin/../lib/bfd- plugins/LLVMgold.so:_wrong_ELF_class:_ELFCLASS32_|_Definite’s Extractor⠀⇛ Resolving /usr/bin/../bin/../lib/bfd-plugins/ LLVMgold.so: wrong ELF class: ELFCLASS32 for fedora packaging. # ⚓ Install_Xubuntu_20.04,_21.10,_or_22.04_on_Raspberry_Pi_4_— Sean_Davis⠀⇛ The Raspberry Pi 4 and 400 are capable ARM devices able to run a desktop-class operating system, albeit slowly. Ubuntu has a tutorial for installing a desktop on the Raspberry Pi, but I recommend using Martin Wimpress’ desktopify script to install with improved hardware support. In this guide, I’ll be using a patched version that enables installation on Ubuntu 21.10 and 22.04. Please note that the Raspberry Pi is not supported by the Xubuntu Team. This installation method is made available for those looking for something different to use their Raspberry Pi for, or those needing to test against ARM hardware. # ⚓ 5_new_sudo_features_sysadmins_need_to_know_in_2022_| Opensource.com⠀⇛ When you want to grant administrative access to some of your users while controlling and checking what they do on your systems, you use sudo. However, even with sudo, there are quite a few unseen issues—just think about giving out shell access. Recent sudo releases added features that let you see these issues and even control them. For example, you can turn on more detailed and easier- to-process log messages and log each command executed in a shell session. Some of these features are brand new. Some of them build on features introduced in version 1.9.0 or even earlier. For example, sudo could record everything that happened on a terminal, even in version 1.8. However, the system stored these recordings locally, and they were easy to delete, especially those where the recordings were the most useful: Shell sessions. Version 1.9.0 added central session recording collection, so recordings cannot be deleted by the local user, and recent versions added relays, making the collection even more robust. # ⚓ Install_Zig_Programming_Language_on_Linux_–_TREND_OCEANS⠀⇛ Zig is an open-source, imperative, statically typed, compiled programming language designed by Andrew Kelley in 2016. Zig’s programming language has made some big claims by its designer that Zig utilizes C libraries better than C itself. You heard it correctly! First, its own programming language, and it can also compile the C/C++ program from its compiler, which we are going to learn today. # ⚓ Monitoring_your_sever_by_installing_Matomo_on_Debian_11⠀⇛ Matomo is an application that is installed on the server that allows us to analyze and track our website to obtain various statistics. Thanks to Matomo, anyy people who own websites in the world, can know the number of visitors, site performance, Google Ads behavior and so on. So if you own a blog or a website, you should learn how to install and use Matomo. # ⚓ How_to_Install_Wireshark_on_Debian_11_Bullseye_– LinuxCapable⠀⇛ Wireshark is a powerful and popular network communication tool that allows viewing individual recorded data packets or sorting them according to specific content. This networking software enables you to see what’s going on in your computer and helps take apart any encrypted messages being sent around it through analysis of their contents with ease! Some of the most common tasks Wireshark is used for amongst users of the software include troubleshooting networks with performance issues and cybersecurity tracing connecting, viewing contents of suspect network transactions, and identifying bursts of network traffic for further analysis. In the following tutorial, you will learn how to install WireShark on Debian 11 Bullseye. # ⚓ How_to_Install_Htop_on_Rocky_Linux_8_–_LinuxCapable⠀⇛ Htop is a free, open-source, cross-platform interactive process viewer. It is a text-mode application (for console or X terminals) and requires ncurses. The terminal UI is a great way to see what your system looks like inside, both in terms of processes and other info. It’s also completely customizable, so you can change colors or add different widgets for more visual representation! In the following tutorial, you will learn how to install Htop Interactive Process Viewer on Rocky Linux 8 Workstation or Server. # ⚓ Download_Ubuntu_22.04_LTS_Jammy_Jellyfish_–_LinuxCapable⠀⇛ Ubuntu 22.04 LTS (Jammy Jellyfish) is now available on the daily builds download page. In addition, there are other flavors, such as Kubuntu XFCE Netbook Edition, which features a KDE 4 desktop environment instead of GNOME pre-installed on this version; however, if that’s not what suits your taste, then go ahead with the standard edition. The download links below allow you to try out different flavors of Ubuntu. The desktop environment installed in each flavor varies, but all are up-to-date with the latest software from this distribution’s stable release schedule and daily sync process! # ⚓ How_to_Install_Apache_Tomcat_10_on_Ubuntu_20.04⠀⇛ The Apache Tomcat Server is an open-source and reliable web and Java Server Page container that is a popular option for developers building and maintaining dynamic applications based on Java. It is used to implement Java servlet and Java Server Pages (JSP) technologies and WebSocket APIs. The Apache Tomcat server is not as feature-rich compared to the traditional web servers such as Apache or Nginx. However, when it comes to applications built entirely on JSP, then Apache Tomcat is King. The latest stable version is Tomcat 10 and it was released on January 10, 2022. It provides support for JSP 3.0, Servlet 5.0, WebSocket 2.0, EL 4.0, and Authentication 2.0 to mention a few. In this tutorial, we walk you through the installation of Apache Tomcat 10 on Ubuntu 20.04. # ⚓ How_To_Install_Wine_to_Run_Windows_Applications_On_Debian⠀⇛ When it comes to installing Windows applications on Linux, there’s no application that does it better than Wine. Wine is a compatibility layer that enables users to run Windows applications on POSIX compliant operating systems such as Linux and UNIX derivatives such as BSD, FreeBSD, and macOS. Not all Windows applications are supported, and to get a comprehensive list of all supported applications, head over to the Wine application database – AppDB. # ⚓ How_to_Install_LibreOffice_on_Debian_11_Bullseye_– LinuxCapable⠀⇛ LibreOffice is a free, open-source office productivity suite used by millions worldwide. The office suite software uses a native file format ODF or Open Document Format, an accepted and almost required structure in multiple organizations across the globe. LibreOffice includes Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector graphics and flowcharts), Base (databases), and Math (formula editing). In the following tutorial, you will learn how to install LibreOffice’s latest release on Debian 11 Bullseye desktop. # ⚓ How_to_Install_Apache_Maven_on_Ubuntu_22.04_LTS_– LinuxCapable⠀⇛ Apache Maven is an open-source tool that allows the building automation of your java projects. It can also be used for projects in C#, Ruby, etc. Its most popular usage would likely involve Java development! The maven project comes from the Apache Software Foundation, where they were previously part of the Jakarta Project before moving on their own. In the following tutorial, you will learn how to install Apache Maven on Ubuntu 22.04 LTS Jammy Jellyfish. # ⚓ How_to_Install_Arduino_on_Debian_11_Bullseye_– LinuxCapable⠀⇛ The Arduino IDE is free and open-source software to write and upload your programming code. It consists of an editor with features like assisted editing enabled by the compiler so you can do everything from within one program without switching between files or windows as often – it does help streamline things! The tool also enables better compiling because errors will be noticed before they’re uploaded. In the following tutorial, you will learn how to install Arduino IDE on Debian 11 Bullseye desktop. # ⚓ How_to_Install_Eclipse_IDE_on_Fedora_36/35_–_LinuxCapable⠀⇛ Eclipse IDE is a robust, integrated development environment used in computer programming. It contains the base workspace and an extensible plug- in system that allows you to easily customize its features, making it one of the two most popular IDEs for Java developers (until 2016). Imagine working on any project, no matter what language or framework it uses. The Eclipse platform gives developers this flexibility by using different plug-ins for their individual needs, whether that’s developing rich client applications with Java-inspired features like mobile compatibility and multi-window support in mind OR creating an IDE tailored specifically toward programming languages such as JavaScript, which often requires more tools than others might offer out of the box. # ⚓ How_To_Install_Sublime_Text_on_AlmaLinux_8_–_idroot⠀⇛ In this tutorial, we will show you how to install Sublime Text on AlmaLinux 8. For those of you who didn’t know, Sublime Text software is a well-known lightweight source code editor. It offers features like command palette, goto anything, auto- completion, snippets, and plugins, among others, and works on all major platforms, including Linux, macOS, and Windows. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the sublime Text source code editor on an AlmaLinux 8. You can follow the same instructions for CentOS and Rocky Linux. o § Distributions⠀➾ # § IBM/Red Hat/Fedora⠀➾ # ⚓ Top_IT_skills_to_build_in_2022,_according_to_CIOs⠀⇛ Staying up to speed on relevant skills is critical for all IT professionals who want to grow in their careers, and when it comes to what skills are in high demand, these CIOs know what they need. We asked CIOs who recently won the 2021 New York CIO of the Year ORBIE Awards what skills they believe will be important for IT professionals in the coming year. The awards were presented by the New York CIO Leadership Association, a professional community that annually recognizes CIOs for their excellence in technology leadership. # ⚓ Getting_to_know_Albert_Chai,_general_manager_for_Red Hat_RoSEA⠀⇛ We’re delighted to welcome Albert Chai to Red Hat as a general manager for Red Hat’s Rest of Southeast Asia (RoSEA) region. In his new role, Albert will be responsible for Red Hat’s business operations in a dynamic region with accelerated growth. o § Devices/Embedded⠀➾ # ⚓ Bluefin_International_Debuts_R_Series_All-in-One_Digital Signage_System_–_rAVe_[PUBS]⠀⇛ Bluefin International has debuted the R Series all- in-one (player and display) digital signage system capable of running Android 10, Debian 10 and Linux. # ⚓ Apollo_Lake_telematics_system_features_Hailo-8_NPU⠀⇛ Nexcom’s rugged, Linux-ready “VTC 1021” in-vehicle telematics system combines Apollo Lake with an up to 13-TOPS Hailo-8 NPU with GPS, 2x GbE, 2x optional PoE, 2x mini-PCIe, SATA, HDMI, USB, CAN, COM, and DIO. Nexcom continues to sample different types of edge AI NPUs for its embedded systems. In 2020, the company announced three Apollo Lake systems equipped with Google’s Coral Edge TPU mini-PCIe cards for AI acceleration, including the VTC 6222- GCIoT. Last month, Nexcom introduced a smaller AIEdge-X 100-VPU edge AI system for smart retail that combines Apollo Lake with up to 2x Intel Movidius Myriad X VPUs. The company has now announced a partnership with Hailo to launch an Apollo Lake based VTC 1021 in-vehicle system aimed at telematics and ADAS that is loaded with Hailo’s 3-TOPS per Watt Hailo-8 NPU. # § Open Hardware/Modding⠀➾ # ⚓ Bringing_digital_skills_to_disadvantaged_children across_India⠀⇛ # ⚓ Making_a_Board_for_the_PIC32_VGA_Signal_Generation Project⠀⇛ Although I have tried to maintain an interest in computing hardware over the last two years or so, both contemporary and somewhat older technologies, I haven’t really had much time or energy to devote to electronics projects. However, I was becoming increasingly bothered by my existing VGA signal generation project taking up space on a couple of solderless breadboards, demanding lots of jumper wires, and generally not helping me organise and consolidate my collection of electronics- related acquisitions, components, and so on. I was also feeling a bit bad for not moving the VGA project to the next step, which is what I had virtually promised to do. Having acquired a new computer in 2020 but not having really looked at KiCad since migrating to the new machine, I finally picked up the courage to set out translating my existing notes into a proper circuit diagram, reacquainting myself with KiCad’s peculiarities, and then translating this into an actual board layout. [...] Several weeks later, I received the boards in the post, thankfully without any customs fees or other charges. In the meantime, I had also ordered components that I needed from a supplier in the UK, Technobots, who happen to sell logic chips and other things that suppliers targeting the “maker” community tend not to bother selling. Thankfully also in this case, the components arrived without incurring fees and charges, although I had kept the value of my order fairly low. In Norway, the industrial lobby hate to see people importing things, often taking the tone that people should buy locally produced goods, but since nobody makes these things here, anyone “local” that sells them has to import them, and the result is often just the cheapest stuff at ridiculously high prices and some middlemen making all the money, rather than anyone earning a decent living out of actually producing anything. But anyway. The boards themselves were well made, as I have seen before, although I was disappointed with the “tabs” around the edge. When boards get made, people will tell you that they are all put on a big panel together and that they therefore need to be attached to each other somehow. The manufacturer will then typically spell out that apart from separating the boards by snapping them apart, they don’t do any further finishing work on the edges because we, the customers, aren’t paying for that level of service. However, I don’t remember the remnants of these inter-board connections – the tabs – being so awkward on previous boards from OSHPark. If I had to do anything before, I’m sure it just involved some gentle trimming, but these needed the application of glasspaper to grind down the tabs to be level with the actual board edge. Given the sub-millimetre tolerances involved in board fabrication, I find it perverse that such finishing would fall to someone – me or someone in the factory – to do this by hand. [...] The three-board arrangement of VGA terminal block, VGA signal board, and Arduino Duemilanove. # ⚓ This_insane_kinetic_clock_robot_flips_itself_into position⠀⇛ Displaying the time these days is trivial — you could do it with any Arduino board and a simple four-digit seven-segment display. But as humans, we crave novelty and it isn’t uncommon to see a clock that is more art than a practical timekeeping device. That is true of AKUROBATTO, which is an insane kinetic clock robot that flips itself into position. AKUROBATTO consists of a skateboard deck- shaped platform and a motorized robot. The robot acts like the hands of an analog clock, with two arms joined by a pivot joint. One can tell the time by judging the relative angular positions of the two arms. That sounds straightforward, but it gets more interesting when you realize that the pivot point between the two arms is not hard- mounted. So to change the angle between the arms, the robot must lock itself into place on the platform and then flip around. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Why_I_will_never_buy_another_Samsung_device⠀⇛ One day, I took the phone out of my pocket and the screen had a black part in the middle and the top half no longer responded to touch. When I got home the black part has expanded and kept growing. The screen clearly had failed from the fold. But hey, no worries, I had not dropped the phone, it was in case and I’ve only used the phone the way I’ve always used my other phones. So I’ll just send it to Samsung for repairs and all is good. Folding is still new tech so shit happens, I didn’t really mind.. until I received a response from Samsung repair: [...] # ⚓ I’ve_switched_from_Samsung_phones_and_will_never_come back.⠀⇛ Samsung has the steepest subsidies, because you get the phone, and then you realize that one of the things they do, it’s like buying a new PC with Windows and then having to root through 40 pieces of bloatware, spyware, and trial software, only with the Samsung phone, you can’t even disable a lot of it. o § Free, Libre, and Open Source Software⠀➾ # ⚓ Ditching_Evernote?_Here_Are_Your_Top_Alternatives⠀⇛ Joplin is a free, open-source note-taking app that uses a lot of the same structure as Evernote, in terms of how you can group and organize notes and notebooks. It’s reasonably user-friendly, and you have the option of bringing your own storage and syncing or paying for Joplin Cloud, starting at 1.99 euros per month for 1GB of storage. # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Is_Firefox_OK?⠀⇛ The decline and potential demise of Firefox is a massive problem that everybody seems to be kind of tiptoeing around, too afraid to acknowledge that if Firefox were indeed to disappear, we’d be royally screwed. [...] The desktop Linux world is playing with fire by being so reliant on Firefox, and now that Firefox and Mozilla seem to be in some serious dire straits, I’m dumbfounded by the fact nobody seems to be at all preparing for what happens if Mozilla ever truly goes down. # § SaaS/Back End/Databases⠀➾ # ⚓ CouchDB_vs._MongoDB:_10_things_you_should_know_|_FOSS Linux⠀⇛ CouchDB is an Apache Software Foundation Product inspired by Lotus Notes. It is one of the NoSQL DB providers. It is a non- relational database meaning it does not use rows and columns to store data, as is the case with relational databases. Erlang is the most widely-used programming language by CouchDB. It is also an open-source document-oriented database, and in the document field, it is stored as key-value maps. The fields can be a simple key, value pair, list, or map. Documents stored in the database are given document-level unique identifiers (_id) and revision (_rev). # ⚓ SQLite_Release_3.38.0⠀⇛ # § Programming/Development⠀➾ # § Go⠀➾ # ⚓ Golang_GRPC⠀⇛ # ⚓ The_Golang_Mutex⠀⇛ # ⚓ Golang_YAML⠀⇛ # ⚓ Golang_WebSocket⠀⇛ # ⚓ Golang_Waitgroup⠀⇛ # ⚓ Golang_REST_API⠀⇛ # ⚓ Golang_Type_Alias⠀⇛ # ⚓ Golang_Select_Call⠀⇛ # ⚓ How_to_Read_and_Write_Excel_Files_in_Go⠀⇛ In this post, you will learn how to read and write Excel files using the Go programming language. For our examples, we will use the xlsx file format. # § Python⠀➾ # ⚓ Python_support_for_regular_expressions⠀⇛ Regular expressions are a common feature of computer languages, especially higher-level languages like Ruby, Perl, Python, and others, for doing fairly sophisticated text-pattern matching. Some languages, including Perl, incorporate regular expressions into the language itself, while others have classes or libraries that come with the language installation. Python’s standard library has the re module, which provides facilities for working with regular expressions; as a recent discussion on the python-ideas mailing shows, though, that module has somewhat fallen by the wayside in recent times. # ⚓ Asin()_Python⠀⇛ We have standard built-in math module functions in the Python programming language for higher-level mathematical calculations. We also use the math module for inverse trigonometric functions that perform operations opposite to trigonometric functions. This article focused on one of the inverse trigonometric functions, i.e., asin(). Asin() function is also referred to as the inverse of sine or arcsine of the number lies between the range of -1 and +1. To access this function, we have to import the math module then call this function by using math static objects. Let’s use this Asin() function to perform arcsine operations. # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ How_to_Echo_Newline_in_Bash⠀⇛ In Bash, there are multiple ways we can display a text in the console or terminal. We can use either the echo or printf command to print a text. Each of these commands has their unique behaviors. In this guide, we’ll learn how to print a newline in Bash. # § C++⠀➾ # ⚓ How_to_Insert_Data_into_a_C++_Set⠀⇛ # ⚓ How_to_Change_a_Set_to_a_Vector_in_C++⠀⇛ # ⚓ Create_a_STD_Set_in_C++⠀⇛ # ⚓ C++_String_Length⠀⇛ # ⚓ C++_Check_If_File_Exists⠀⇛ # ⚓ C++_Delete_Array⠀⇛ # ⚓ C++_Factorial⠀⇛ * § Leftovers⠀➾ o ⚓ Paul_Farmer,_1959–2022⠀⇛ I don’t even remember when I first met Paul Farmer, he was so much a part of my world, especially my world in Haiti. Maybe I met him down there, where he’d lived on and off for five years at a time, after college. Or maybe in Boston, where—when I met him—he was on the way to becoming a world-famous infectious diseases doctor with an endowed chair at Harvard Medical School. Once I knew him, he became a touchstone for me. We had the same attitudes about power and powerlessness, but that wasn’t what made him precious. o ⚓ Remembering_Dr._Paul_Farmer:_A_Public_Health_Pioneer_Who_Helped Millions_from_Haiti_to_Rwanda⠀⇛ We remember the life and legacy of Dr. Paul Farmer, a public health icon who spent decades building community health networks helping millions of poor people in Haiti, Rwanda, Sierra Leone and beyond. He died unexpectedly Monday at the age of 62. We feature Farmer’s past interviews with Democracy Now! and speak with his longtime colleague, Dr. Joia Mukherjee. Farmer leaves behind a remarkable legacy and an “enormous community of people that he brought to this large table that is now global health,” says Mukherjee, chief medical officer for Partners In Health, where she worked with Farmer for 23 years. o ⚓ Paul_Farmer_Leaves_Behind_the_Legacy_of_a_Global_Public_Health Movement⠀⇛ o § Education⠀➾ # ⚓ Florida_Pulls_Amendment_That_Would_Force_Teachers_to_Out Students_After_Uproar⠀⇛ # ⚓ When_the_MAGA_Movement_Comes_for_Your_School⠀⇛ Phillips’ fight with Collin College is part of a broader struggle over education here in the swath of suburbs and exurbs of the Dallas-Ft. Worth area, once conservative strongholds that in recent years have become more diverse — racially, culturally, and politically — as business-friendly tax policy draws emigration from across the nation and abroad. But the influx of new people and ideas has produced a backlash: The area was home to an unsettling number of Jan. 6 defendants, and in recent years, Philips says, there has been a resurgence in far- right extremism. Much of the struggle is playing out in schools. Despite right-wing pundits’ continued braying about “censorship” and “cancel culture,” the local brand of revanchism has pushed to penalize educators who speak their minds and ban books that challenge conventional wisdom or present uncomfortable truths. # ⚓ No_student_loan_for_pupils_who_fail_GCSE_maths_or_English⠀⇛ The Department for Education will announce plans to set minimum entry requirements to ensure students “aren’t being pushed into higher education before they are ready”. The proposals, which will be put to consultation, will suggest that students who fail to gain a Grade 4 – equivalent to a C in the previous grading system – in GCSE maths and English should be barred from accessing student loans. o § Hardware⠀➾ # ⚓ Bluetooth_LE_Audio_is_going_to_change_the_entire_wireless audio_game⠀⇛ Bluetooth is one of the most important open technologies in the world, right up there with Wi- Fi. While the Bluetooth spec is frequently updated, the underlying technology for Bluetooth audio, the most ubiquitous usage for Bluetooth most people depend on, hasn’t been meaningfully revamped for nearly its entire existence. This is where Bluetooth LE Audio comes in. The spec has been available for about two years for device makers to work on, but the first products to feature it should be released this year. It promises not only to improve the experience we have with current audio use cases, but build a foundation for new applications that weren’t possible before. It truly is a new generation of technology. Even better, it will be compatible with any Bluetooth 5.2 or newer-equipped device, which means most phones and audio devices from the last two years should be upgradeable to Bluetooth LE Audio via firmware update. # ⚓ Classic_Multimeter_Tells_You_If_Your_WiFi’s_Working_| Hackaday⠀⇛ Debugging network issues isn’t easy; many a sysadmin has spent hours trying to figure out which of the many links between client and server is misbehaving. Having a few clear pointers helps: if you can show that the internet connection is up, that already narrows down the problem to either the server or, most likely, the client computer. After hearing “is the internet up” one too many times, [whiskeytangohotel] decided to make a clearly visible indicator to show the status of the local uplink. He used his father’s old Simpson 260 VOM as a display, with its large analog indicator pointing at a steady value if the internet’s up, and wagging back and forth if there’s an outage. The exact value indicated is determined by the average ping time for a couple of different servers, so that you can also tell if the connection is slower than normal. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Billie_Eilish_Advocates_for_Plant-Based_School_Meals_on Capitol_Hill⠀⇛ Grammy Award-winning artist Billie Eilish and her mother Maggie Baird attended a Capitol Hill briefing Tuesday in support of legislation that would implement plant-based meals in the U.S. school system. “I’m proud to advocate for this legislation that will help to fight climate change, combat food insecurity, and promote health equity,” said Eilish, singer, songwriter, and activist.   # ⚓ GOP_Candidates_in_MI_AG_Race_Say_They_Oppose_Precedent_on Right_to_Birth_Control⠀⇛ # ⚓ Mask_Mandates_Lift_While_Uncertainty_About_New_Subvariant BA.2_Hangs_in_the_Air⠀⇛ # ⚓ “We_Could_Have_Really_Used_the_Compensation:”_COVID’s Second_Wave_in_Rural_India⠀⇛ # ⚓ Opinion_|_The_World’s_Failed_Response_to_Covid-19_in_Africa Must_End⠀⇛ When the Ebola virus was ravaging West African countries in 2014, health care providers, public health researchers and activists worked feverishly to stamp it out before it spread and turned into the type of life-shattering pandemic we’re all too familiar with today. # ⚓ All_they_wanted_for_Christmas_was_for_Mum_to_be_alive⠀⇛ There are no official figures for how many pregnant women received oxygen, how many are on ventilators or how many Caesarean sections have been carried out to save the lives of foetuses and mothers with Covid. Neither the relevant ministry nor the National Health Care Service Centre collects statistics on this. Or so they say. Nor can you find out how many pregnant women have died during the pandemic but from time to time in the register of coronavirus victims, pregnancy is given as the pre-existing health condition. Gábor Biszak’s wife Erika, who was 31 weeks pregnant, was one of the victims. The doctors saved their third child by performing a Caesarean section last spring. Nimród, Johanna and Boróka are now growing up without a mother. The older two try to process what happened in their different ways. We spent eight months following the life of Gábor and his children. Translation by Charles Hebbert. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Microsoft_is_testing_an_annoying_desktop_watermark_if you_install_Windows_11_on_unsupported_hardware [Ed: By Microsoft booster, Sofia Wyciślik-Wilson. Only_a masochist installs Microsoft Windows at this point…]⠀⇛ One of the obstacles standing in the way of some people upgrading from Windows 10 to Window 11 is system requirements. Even some relatively new systems are unsupported due to lacking features such as TPM 2.0, but where there’s a will there’s a way, and there are various workarounds that make it possible to install Windows 11 on pretty much any system. # ⚓ Slack_Down!_Issues_in_Sending_Messages,_Accessing Platform,_Experienced⠀⇛ Slack, the business communication platform of Slack Technologies, is currently down. Some of its users claimed that they are experiencing issues when sending messages and accessing the platform. # § Security⠀➾ # ⚓ CISA_Adds_Two_Known_Exploited_Vulnerabilities to_Catalog⠀⇛ CISA has added two new vulnerabilities to its Known Exploited Vulnerabilities Catalog, based on evidence that threat actors are actively exploiting the vulnerabilities listed in the table below. These types of vulnerabilities are a frequent attack vector for malicious cyber actors of all types and pose significant risk to the federal enterprise. # ⚓ Anti_Interdiction_on_the_Librem_14⠀⇛ Whether you face extreme threats or want some extra peace of mind, you might want to be able to detect if someone tampers with your laptop when it’s out of your possession. Anti- interdiction can be particularly handy when traveling and for the initial delivery. # ⚓ Report:_Missouri_Governor’s_Office_Responsible for_Teacher_Data_Leak⠀⇛ Missouri Governor Mike Parson made headlines last year when he vowed to criminally prosecute a journalist for reporting a security flaw in a state website that exposed personal information of more than 100,000 teachers. But Missouri prosecutors now say they will not pursue charges following revelations that the data had been exposed since 2011 — two years after responsibility for securing the state’s IT systems was centralized within Parson’s own Office of Administration. # § Privacy/Surveillance⠀➾ # ⚓ IRS:_Selfies_Now_Optional,_Biometric_Data to_Be_Deleted⠀⇛ # ⚓ Massachusetts_Court_Says_No_Expectation Of_Privacy_In_Social_Media_Posts Unwittingly_Shared_With_An_Undercover_Cop⠀⇛ Can cops pretend to be real people on social media to catfish people into criminal charges? Social media services say no. Facebook in particular has stressed — on more than one occasion — that it’s “real name” policy applies just as much to cops as it does to regular people. # ⚓ DC_AG_argues_Facebook’s_Zuckerberg_should be_required_to_answer_data_privacy questions⠀⇛ The allegations began in 2018 when a political consulting firm did not tell customers what information was collected on Facebook and how it was shared. In the Feb. 15 court filing, the lawyers said they should be allowed to “probe [Zuckerberg's] and the company’s knowledge about Cambridge Analytica’s actions and his decision to act or, as the case was, fail to act upon learning about it,” according to Reuters. The court filing comes as D.C. alleges Facebook ignored a court order on Jan. 10 from the District of Columbia Superior Court that allowed lawyers to question Zuckerberg. # ⚓ Find_You:_Building_a_stealth_AirTag clone⠀⇛ After AirTags are reportedly used more and more frequently for malicious purposes, Apple has published a statement that lists its current and future efforts to prevent misuse We built an AirTag clone that bypasses all those tracking protection features and confirmed it working in a real-world experiment (source code available here) # ⚓ AirTag_clone_bypassed_Apple’s_tracking- protection_features,_claims_researcher⠀⇛ A security researcher claims he bypassed the tracking protection features built into Apple’s Find My app and AirTag tracking devices with a custom-made AirTag clone. Amid mounting concerns that AirTags are ripe for abuse by stalkers and other wrongdoers, the researcher said he successfully tracked an iPhone user for five days (with their consent) without triggering a single tracking notification. Launched in April 2021, AirTags communicate with Apple’s Find My service to help users keep track of personal items such as keys, wallets, and luggage. However, several reports of malicious misuse have surfaced, from devices planted to facilitate grand theft auto to those surreptitiously slipped into victims’ coat pockets. # ⚓ AirTag_clone_developed_by_researchers works_around_Apple’s_anti-stalking measures⠀⇛ In a blog post published by security researcher Fabian Braunlein of Positive Security on Monday, several “quite obvious bypass ideas” for current and upcoming protection measures were published. Braunlein believes that all can be put into practice. To test the assumption, a cloned AirTag was produced. The report claims that the stealth AirTag was able to track an iPhone user for over five days, without triggering any tracking notifications. o § Defence/Aggression⠀➾ # ⚓ Arbery’s_Murderers_Found_Guilty_of_Federal_Hate_Crimes⠀⇛ This is a developing story… Please check back for possible updates… A jury on Tuesday found three white men who murdered unarmed Black jogger Ahmaud Arbery guilty of federal hate crimes. # ⚓ California_Advocates_Counterattack_Corporate_Crime_and Control⠀⇛ If you call the vendors for an explanation, be prepared to wait and wait and wait for any human being to answer or call back, even after you’ve pushed all the required buttons to leave a voice mail message. The vendors are counting on you to surrender, mumbling that you’ve got better things to do with your time. If you’re lucky enough to get a human and you disagree about the bill, you know that if you persist against their assurances of accuracy, your credit score can go down. Algorithms can be made to work so impersonally. # ⚓ Opinion_|_The_Sacralization_of_War,_American-Style⠀⇛ Lately, random verses from the Bible have been popping into my mind unbidden, like St. Paul’s famous line from Galatians, “A person reaps what they sow.” The words sprang into my consciousness when I learned of the death of the 95-year-old Vietnamese Buddhist monk and peace activist Thich Nhat Hanh, who helped encourage Martin Luther King to declare his opposition to the Vietnam War so long ago. # ⚓ The_Conflict_is_Now⠀⇛ Of course, such rhetoric is nothing new, as we can recall Reagan’s descriptor of the “evil empire” or Bush’s “axis of evil”, or hundreds of other such declarations about the “evils” of drugs, poverty, crime, etc. But ‘evil’ has become the assumed position of any ideological opponent in recent years, as the culture developed by both political parties, their demagogues, and their aligned corporate and media entities has been to present either ‘red’ or ‘blue’ (people, speech, books, etc.) as evil to be disallowed and overcome. Even non-partisans in the U.S. can now feel themselves drawn into these party debates as instances like vaccine mandates require them to take a partisan position in spite of themselves. There are some issues, in other words, that are so overwhelming politicized that they are difficult for anyone to ignore or remain ‘neutral’ on. One of the most shocking aspects of the January 6th, 2021 event is that, in contradistinction to nearly all dealings with mass protest, the state had so profoundly failed to protect itself, demonstrating law enforcement’s sympathies with hardcore right extremism in real time. Indeed, the state has consistently shown itself to brutalize protesters, most recently those from Black Lives Matter and labor movements, and so such a failure is especially striking given the optics and reality of preferential treatment for largely white, largely male, largely middle-aged crowds. It is unlikely that the state will lapse in this way again (recall the military occupation of Washington D.C. that followed January 6th) and is likely to take extreme measures to secure itself against anything resembling that attack. Especially since the 1960s, and intensified exponentially after 9/ 11/2001, the government has long used the paradigm of counter-revolution (or domestic warfare) against its own citizens in the name of national security. The violence that is consistently cause for alarm in the halls of government and media, however, is not that perpetrated by the state on its own citizenry, but extra-legal, inter-personal acts. These acts do not constitute a ‘civil war’ in the sense often imagined by the public, but rather as simmering conflict in which both the state and the public are often targeted in coordinated but ‘random’ attacks. Extra-state violence is most likely to proceed in more disjointed, seemingly random acts, not because mass mobilization has been defeated or delegitimized, but out of a tactical consideration. # ⚓ Critics_Want_to_Know_Why_‘Bloodthirsty_Warmonger’_John Bolton_Still_Invited_on_TV⠀⇛ Anti-war advocates on Tuesday denounced the corporate media for giving former National Security Adviser John Bolton—a longtime proponent of regime change and U.S. military action around the world—a platform to discuss his views on the current tension in Ukraine. MSNBC host Andrea Mitchell invited the former official for the Trump and George W. Bush administrations to discuss how President Joe Biden should confront Russian President Vladimir Putin’s recent escalation of tensions. # ⚓ Biden_Urged_to_Ignore_War_Hawks_and_Pursue_‘Real_Path_to Peace’_in_Ukraine⠀⇛ With Republicans, hawkish Democrats, and notorious warmongers pushing President Joe Biden to take more punitive action against Russia following its latest aggressive moves in Ukraine, peace advocates in the U.S. and abroad on Tuesday urged the administration to instead intensify cooperative diplomatic efforts and do everything in its power to prevent a military conflict. “We call for a re-examination of NATO, which has long outlived any good purpose, and holding serious disarmament talks with Russia.” # ⚓ Trump_Claims_Putin_Wouldn’t_Have_Invaded_Ukraine_on_His Watch:_‘No_Way!’⠀⇛ As demands for urgent diplomacy stacked up Tuesday due to the escalating crisis in Ukraine, former U.S. President Donald Trump issued a statement that ignored his administration’s contributions to regional tensions while reminding the world of his cozy relationship with Russian President Vladimir Putin. Trump’s move came after Putin recognized the Donetsk People’s Republic (DPR) and Luhansk People’s Republic (LPR) in eastern Ukraine as independent and authorized Russian “peacekeeping” forces. # ⚓ Bernie_Sanders_Denounces_Russia_for_‘Indefensible’_Invasion of_Ukraine⠀⇛ Sen. Bernie Sanders on Tuesday called for the U.S. and its allies to impose heavy sanctions on Russian President Vladimir Putin and other oligarchs in the country as he condemned Moscow’s escalating military aggression toward Ukraine. “Vladimir Putin’s latest invasion of Ukraine is an indefensible violation of international law, regardless of whatever false pretext he offers,” Sanders (I-Vt.) said in a statement. “There has always been a diplomatic solution to this situation. Tragically, Putin appears intent on rejecting it.” # ⚓ Putin_Recognizes_Ukraine_Separatists;_Khrushchev’s_Great- Granddaughter_Says_War_Can_Still_Be_Avoided⠀⇛ Russian President Vladimir Putin has ordered troops into two separatist regions in eastern Ukraine, drawing sharp rebukes from the U.S. and other Western countries that have warned for weeks of a Russian invasion of Ukraine. The Biden administration issued new sanctions, and Germany has stopped the certification of Russia’s Nord Stream 2 gas pipeline in an attempt to quash the country’s dependence on Russian natural gas. We speak with Nina Khrushcheva, professor of international affairs at The New School, who says she remains skeptical that Russia will launch an all-out war against Ukraine. She also says Russia’s recent attempts at allying with China should not be perceived as a threat, as “China is not going to make up for all the losses that the upcoming sanctions will bring onto Russia.” # ⚓ Traumatized_by_the_news_Levada_Center_director_Denis_Volkov on_why_we_shouldn’t_expect_a_‘Donbas_consensus’_following Putin’s_recognition_of_the_‘republics’_in_eastern_Ukraine⠀⇛ Russia recognized the self-proclaimed “people’s republics” in eastern Ukraine on February 21. President Vladimir Putin formally announced the decision following a National Security Council meeting that looked more like staged production than an actual debate. Senior Russian officials expressed unanimous support for recognition, even though it appeared to be a sure path towards an all-out war with Ukraine. At the same time, Putin claimed there was broad public support for the move. Will we see a repeat of the “Crimean consensus” that emerged after Moscow annexed the peninsula in 2014? And how do ordinary Russians really feel about the Kremlin’s further intervention into Ukraine? Meduza turns to sociologist and Levada Center director Denis Volkov for insight. # ⚓ ‘Many_moments_were_not_included’_Russia’s_Security_Council session_on_recognition_for_eastern_Ukraine’s_separatists_was billed_as_a_live_broadcast._Not_only_was_it_taped_—_it_was edited.⠀⇛ The Kremlin’s handling of recognition for the self- proclaimed separatist “republics” in eastern Ukraine has raised many questions, including purely logistical uncertainties surrounding the National Security Council session, where President Putin ordered senior officials to state their support or opposition to the recognition of the so-called DNR and LNR. The gathering was made available to the public in an unusual national broadcast on Monday evening. At first glance, the event seemed to be aired live, but some noticed signs (such as the time displayed on different wristwatches) that the footage was prerecorded and even edited. These viewers were right. # ⚓ MSNBC_Host:_Disastrous_Foreign_Policy_Leaves_US_With_Less ‘Credibility’_to_Condemn_Russia⠀⇛ MSNBC host Mehdi Hasan argued in a monologue Monday night that the United States would have “more credibility” to condemn the recent actions of Russia in Ukraine if it wasn’t currently supporting illegal occupations by its allies around the world—and if it didn’t have its own long record of carrying out brazenly unlawful invasions of sovereign countries. “I’d just like us to be consistent in our approach to illegal invasions and occupations.” # ⚓ Opinion_|_Bob_Dylan,_Masters_of_War,_and_the_Ukraine Crisis⠀⇛ Fifty-nine years ago, Bob Dylan recorded “With God on Our Side.” You probably haven’t heard it on the radio for a very long time, if ever, but right now you could listen to it as his most evergreen of topical songs: # ⚓ Opinion_|_The_Stakes_Are_Very_High_in_Ukraine⠀⇛ If the Ukraine crisis erupts into war—even intensified limited war in Eastern Ukraine with overt Russian intervention—the consequences will be severe and far-reaching. # ⚓ Opinion_|_What_Putin_Has_Done_in_Eastern_Ukraine_Is Illegal,_But_Is_It_a_Full_Invasion?⠀⇛ Russia’s official recognition of the separatist Donetsk and Lugansk republics is both illegal under international law and acutely unhelpful politically, and makes a diplomatic resolution of the existing crisis even less likely.  # ⚓ Afghanistan:_A_journey_from_war_to_terror⠀⇛ # ⚓ State_Department_Gratuitously_Invokes_Monroe_Doctrine Against_Russia⠀⇛ First, some particulars.  The mainstream media, particularly the New York Times and the Washington Post, are exaggerating Russian diplomatic efforts in South America, describing normal diplomatic activity as a frenzied campaign to increase influence in Washington’s backyard.  In the only evidence theTimes could produce, the article said that Putin “spoke” to Nicaraguan President Daniel Ortega for the first time since 2014; “called” the leaders of Cuba and Venezuela; “hosted” the president of Argentina; and “scheduled” a meeting with Brazil’s President Jair Bolsonaro.  The Times concluded that these contacts were proof of Putin’s efforts to “build on ties that go back to the Cold War and shed light on the global nature of his ambitions.”  Total boilerplate!! A day later, the Post—playing catch-up—castigated Bolsonaro for bringing “Latin America’s largest and most powerful country into an embrace with one of the United States’ greatest foreign adversaries.”  Like the Times, the Post maligned Putin’s “gambit to forge stronger relationships in Latin America, far from Russia’s traditional sphere of influence.”  The Post concluded that Putin was successfully “outflanking the West’s attempts to isolate his country.”  U.S. officials have contributed to this propaganda campaign with charges of Russian online influence operations to sow unrest in South America.  Again, no evidence was produced. # ⚓ As_Honduras’s_New_President_Seeks_End_to_Narco-State,_Will US_Stand_in_Her_Way?⠀⇛ # ⚓ Russia-Ukraine_is_an_Information_War,_So_Government Intelligence_Needs_More_Scrutiny_Than_Ever⠀⇛ The American and British intelligence services seldom got things right during the Iraq, Libyan and Syrian conflicts, but they are now being cited as reliable guarantors of the credibility of stories about an impending Russian invasion of Ukraine. This narrative is sold to the public as the fruit of “open intelligence”, supposedly more democratic than the more secretive approach of the past. The US Secretary of State Antony Blinken this week told the UN, apparently relying on information provided by US intelligence, that Russia could stage a provocation to provide a casus belli by fabricating “so-called terrorist bombing inside Russia, the invented discovery of a mass grave, a staged drone strike against civilians, or a fake – even a real attack – using chemical weapons.” # ⚓ Whistleblower_Exposes_Credit_Suisse’s_Bankrolling_of_Spy Chiefs_Involved_In_CIA_Torture⠀⇛ Over a year ago, a whistleblower provided Credit Suisse bank account data to the German newspaper Süddeutsche Zeitung from over 18,000 accounts, which belong to foreign customers. The German newspaper shared the data with the Organized Crime and Corruption Reporting Project (OCCRP), which brought in media partners from all over the world to investigate and verify the data. Now, in a major global journalism project called “Suisse Secrets,” OCCRP and several media organizations have revealed the names of criminals and corrupt government officials who had Credit Suisse accounts, including spy agency chiefs implicated in torture and rendition during the “war on terrorism.” Switzerland has a strict bank secrecy law, which allows the Swiss government to harshly punish whistleblowers who leak banking data containing alleged evidence of corruption. Swiss banks also enjoy a law that enables authorities to prosecute journalists for publishing, or even possessing, banking data. # ⚓ ‘War_Between_Nuclear-Armed_Powers_Is_Not_an_Option’:_Calls for_Diplomacy_Surge⠀⇛ The urgency of diplomatic steps to avert a war in Eastern Europe reached new heights Tuesday following Russian President Vladimir Putin’s move to recognize two breakaway regions in Ukraine as independent and deploy troops—described as “peacekeeping” forces—to the Donbas, heightening fears of an all-out military conflict. “As long as there is any hope of preventing a wider war, it is our duty to pursue it.” # ⚓ ‘Decisions_of_Koran_are_supreme’:_Safdar_Nagori,_key conspirator_of_Ahmedabad_blasts,_remorseless_after_death penalty⠀⇛ Safdar Nagori, one of the 38 convicts sentenced to death in the 2008 Ahmedabad serial bomb blasts case by a Gujarat court on Friday, appeared remorseless after the sentencing for a terror act that killed 56 people, and was heard saying the Constitution does not mean anything to him. Nagori (54), a native of Madhya Pradesh who was associated with the banned Students’ Islamic Movement of India (SIMI), was a key conspirator of the blasts, according to the prosecution. # ⚓ France:_Critic_of_Islam_Mila_attacked_again_by_migrants_in broad_daylight⠀⇛ She recounted these scenes later that evening, still in her posts. “I get so annoyed all the time, but 99% of the time you don’t feel like filming it,” she laments. “I’m not attacked as Mila, but as a woman,” she adds, describing an everyday life that has become unbearable for women. Finally, in the evening, she decided to press charges. On Twitter, she revealed that the police “probably can’t do much” because the main attacker was “probably an illegal”. o § Transparency/Investigative Reporting⠀➾ # ⚓ Identity_of_man_killed_by_police_after_starting_fire_at Dearborn_mosque_released⠀⇛ Dearborn police have identified the man as Ahmed Taqi, who started a fire at the Al-Huda Islamic Association in the early morning hours of Feb. 12. Police said after squad cars arrived at the scene of the fire, which caused damage to the women’s entrance of the mosque, Taqi fired at officers. o § Environment⠀➾ # ⚓ Climate_change:_Sea_ice_levels_reach_lowest_level_on_record in_the_Antarctic_Ocean⠀⇛ There is currently less ice in the Antarctic Ocean than at any time on record as climate change pushes up temperatures – and it is continuing to melt, according to new figures. Preliminary measurements show the sea ice around the continent fell to 1.98 million square kilometres on Sunday 20 February – below the previous record minimum, set in March 2017, of 2.1 million square kilometres. This is the lowest level since the National Snow and Ice Data Center began taking satellite measurements in 1979. # ⚓ The_Supreme_Court_Could_Hamstring_Federal_Agencies’ Regulatory_Power_in_a_High-Profile_Air_Pollution_Case⠀⇛ This case stems from actions over the past decade to reduce greenhouse gas emissions from power plants, a centerpiece of U.S. climate change policy. In 2016, the Supreme Court blocked the Obama administration’s Clean Power Plan, which was designed to reduce these emissions. The Trump administration repealed the Clean Power Plan and replaced it with the far less stringent Affordable Clean Energy Rule. Various parties challenged that measure, and a federal court invalidated it a day before Trump left office. The EPA now says that it has no intention to proceed with either of these rules, and plans to issue an entirely new set of regulations. Under such circumstances, courts usually wait for agencies to finalize their position before stepping in. This allows agencies to evaluate the evidence, apply their expertise and exercise their policymaking discretion. It also allows courts to consider a concrete rule with practical consequences. # § Energy⠀➾ # ⚓ Global_Gas_Pipeline_Boom_Poses_Climate,_Financial Disaster⠀⇛ As campaigners and scientists continue to demand keeping fossil fuels in the ground, an analysis on Tuesday revealed the incredible amount of gas development humanity has planned, despite the climate and financial risks. “The world is at an inflection point, where it can hasten the transition to renewables or further entrench itself in fossil fuels.” # ⚓ US_Gas_Exporters_Set_to_Benefit_After_Germany_Halts Russian_Pipeline⠀⇛ The U.S. fossil fuel industry is poised to benefit from an expected expansion of gas exports to Europe after German Chancellor Olaf Scholz on Tuesday suspended approval of the Nord Stream 2 pipeline in response to Russian military aggression toward Ukraine. “The crisis plays right into the hands of American shale gas companies, which are reaping a windfall.” # ⚓ Carbon_Footprint_of_The_Most_Popular_Social_Media Platforms⠀⇛ The advent of easily accessible technology, e-commerce, online streaming, and social networking platforms has led to massive amounts of data being stored and processed every second. The IT infrastructures needed to support this digital age consume a large amount of energy and have a negative impact on the environment. There have been several different efforts to estimate the carbon footprint of the [Internet], but there is no proven exact method for it. Therefore, the goals of this paper are, first—to critically review the carbon emission calculation methods and compare the results, and second—to publicize the environmental impact of our daily simple habit of [Internet] usage. We calculated the carbon footprint of the most popular four online services (TikTok, Facebook, Netflix, and YouTube) by using top-cited methods such those from Obringer, the Shift Project, Andrae, and Hintemann and Hinterholze. When comparing the emitted carbon dioxide, the weighted average of online video streaming usage per day is 51 times more than 14 h of an airplane ride. Netflix generates the highest CO2 emissions among the four applications due to its high- resolution video delivery and its number of users. # § Wildlife/Nature⠀➾ # ⚓ The_Surprising_Biodiversity_Hidden_in_the_World’s Fragile_Mangrove_Forests⠀⇛ o § Finance⠀➾ # ⚓ Rick_Scott_Panned_for_New_Plan_Pushing_Tax_Hikes_on_the Poor⠀⇛ GOP Sen. Rick Scott of Florida came under fire Tuesday in response to his new 11-point “Rescue America” plan for if Republicans reclaim a majority of Senate seats—particularly its call to raise taxes on low-income Americans. “Scott… wants working families and seniors to pay more.” # ⚓ Flags_on_the_March!⠀⇛ In January, the U.S. Consumer Price Index, generally known as the inflation rate, grew 0.6% for an annualized increase of 7.5%. That’s the highest rise in over 40 years. Though salaries have climbed almost as fast, especially among low-wage workers, the inflation increase has caused a political crisis for Democrats and the Biden administration. If, as seems correct, there’s an inverse ratio between gas prices and electoral success, Congressional Democrats face a drubbing in the 2022 midterms. And if they go down, the burden of preserving the republic will rest upon the hunched back and wobbly convictions of Joe Biden. There are of course things Biden can do about inflation: For example, he can crack down on price gouging by issuing executive orders to stop it.[1] He can encourage the Department of Justice to initiate anti-trust proceedings against fuel companies, drug companies, internet providers, agricultural commodity suppliers, and large landlords. And he can ask patriotic Americans to do their civic duty by not buying so many things – that will reduce prices too. # ⚓ Over_100_Starbucks_Locations_Have_Filed_for_Unionization⠀⇛ # ⚓ From_the_Kingpins_of_Private_Equity,_A_New_Dagger_to Democracy⠀⇛ # ⚓ It’s_Time_for_Young_People_to_Demand_a_Solution_to_the Student_Debt_Crisis⠀⇛ A common phrase said to the millions of young people that seek higher education is that “college is a ladder of upward mobility.” Unfortunately, from trade school to college, this ladder is sinking in a swamp of $1.7 trillion of student loan debt. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Indigenous_Nations_Allege_New_Maps_in_North_Dakota_Violate Voting_Rights_Act⠀⇛ # ⚓ Ocasio-Cortez_Calls_Out_Tucker_Carlson_for_His_Dangerous “Libelous_Harassment”⠀⇛ # ⚓ Redefining_Chile_Amid_Intersecting_Crises⠀⇛ Many of the issues being debated by the members of the convention are specific to Chile yet would seem far too familiar to readers in the United States and elsewhere: How to reduce wealth inequality, respond to an enormous influx of undocumented migrants, reform a violent police force, protect freedom of expression in an increasingly surveilled society, and contend with climate change without disrupting vital economic growth. And how to build a new national identity based on confronting the amnesia that has allowed the atrocities of the past, particularly against people of color and indigenous nations, to be buried and forgotten. If this experiment in national redefinition is successful, it could serve as an inspiring model for countries around the world. But if voters were to reject these reforms, in a referendum due before the end of September, it would further erode Chileans’ confidence in democracy as a solution to the ills of a country that, like so many nations today, could succumb to the temptations of authoritarianism. # ⚓ On_“Legitimate_Political_Discourse”⠀⇛ + Said “we’re going to take out country back” as they headed to physically assault the legislative branch of the US government. + Screamed “Hang Mike Pence” while invading the US Capitol to prevent the peaceful transfer of presidential power after the 2020 election. # ⚓ Flushing_Democracy⠀⇛ # ⚓ Supreme_Court_Rejects_Trump_Effort_to_Hide_Jan._6_Records⠀⇛ The U.S. Supreme Court on Tuesday stopped former President Donald Trump’s attempt to block the release of White House records to a congressional panel investigating last year’s deadly right-wing insurrection at the Capitol. The high court’s decision to formally reject Trump’s appeal comes just over a month after its near-unanimous order—with Justice Clarence Thomas dissenting—paved the way for the National Archives to share more than 700 documents with the House Select Committee to Investigate the January 6th Attack on the United States Capitol. # ⚓ When_Socialists_Govern⠀⇛ Just over five years ago, when Leah McVeigh moved to Astoria, a neighborhood in the New York City borough of Queens, one of the first things she noticed about her apartment building was the dangerous intersection next to it. There were so many car crashes, she told me, that she learned to identify the sound of one: “There’s this specific crunch. And then quiet.”1 # ⚓ Trump_Took_15_Boxes_of_Official_Documents_When_He_Left Office⠀⇛ So why’d he take those boxes home? Well, here’s a strong suspicion: He meant to put stuff on display And charge a steep admission. # ⚓ Who_is_Jamshid_Sharmahd_and_what_is_the_alleged_US_terror group_‘Thunder’?⠀⇛ Tehran has carried out operations in Europe in recent years, including attempted assassinations, but illegally kidnapping someone in Europe seems to be a bridge too far for Iran. There was an attempted assassination of an Iranian-Kurdish dissident in June in the Netherlands. # ⚓ EU_to_activate_cyber_response_team_to_help_Ukraine [iophk: Windows TCO]⠀⇛ The EU’s cyber security team, established in 2019, has experts from Croatia, Estonia, Lithuania, the Netherlands, Poland and Romania. o § Misinformation/Disinformation⠀➾ # ⚓ Why_the_Freedom_Convoy_is_More_American_Than_Canadian⠀⇛ By many accounts, it seems as though the United States has exported its brand of toxic right-wing extremism across the northern border. Indeed, there are credible reports of Confederate American flags and swastikas being displayed by the Canadian protesters. Unsurprisingly, the so-called Freedom Convoy has also garnered outsized media attention in the United States, becoming a cause célèbre among domestic conservatives who see it as yet another front in the culture war around which to whip up frenzied hysteria and score political points. # ⚓ No_scientific_basis_for_claims_of_ivermectin’s_success_in Uttar_Pradesh,_India⠀⇛ Claims regarding the supposed success of ivermectin in preventing COVID-19 in India have been around for months, and have recently popped up again as India’s case numbers subside. India stopped recommending the use of ivermectin for management of the virus in September, citing a lack of scientific evidence of its benefits. o § Censorship/Free Speech⠀➾ # ⚓ Trump’s_Truth_Social_Bakes_Section_230_Directly_Into_Its Terms,_So_Apparently_Trump_Now_Likes_Section_230⠀⇛ When Donald Trump first announced his plans to launch his own Twitter competitor, Truth Social, we noted that the terms of service on the site indicated that the company — contrary to all the nonsense claims of being more “free speech” supportive than existing social media sites — was likely going to be quite aggressive in banning users who said anything that Trump disliked. Last month, Devin Nunes, who quit Congress to become CEO of the fledgling site, made it clear that the site would be heavily, heavily moderated, including using Hive, a popular tool for social media companies that want to moderate. # ⚓ Killing_free_speech⠀⇛ At that time too, media and civil society organisations had protested the contents of the law and warned that it would be used to curtail the space for free speech. The PTI government has now gone many steps ahead in making this draconian law even more restrictive; its scope has been broadened to include state institutions, like the military and judiciary, as aggrieved parties. The latest amendments give the authorities the powers to arrest anyone accused of promoting or broadcasting fake news. The courts will have six months to decide whether or not the complaint is genuine but during this period the accused is liable to remain in incarceration unless given bail. This means that anyone can be arrested by the authorities on vague charges. This can lead to wild accusations resulting in random detentions. # ⚓ Muslim_scholar_against_‘wayang’,_Indonesia’s_traditional theatre⠀⇛ According to a Muslim cleric, Indonesia’s traditional puppet theatre should be outlawed. “Wayang should be destroyed,” said Khalid Basalamah, when someone asked him what Islamic teaching said about this local tradition. Wayang is not just a form of entertainment. Young and old alike love to watch performances, which usually take place from midnight to dawn, also because of the folk wisdom and philosophical teachings they impart. # ⚓ Mickelson_apologizes_for_PGA,_Saudi_remarks,_loses sponsor⠀⇛ Author Alan Shipnuck released excerpts last week from his upcoming book about Mickelson, the US star calling the Saudis “scary” with a “horrible record on human rights.” “Knowing all of this, why would I even consider it?” Mickelson said about the potential for joining the Saudi tour. “Because this is a once-in-a-lifetime opportunity to reshape how the PGA Tour operates,” he said. “They’ve been able to get by with manipulative, coercive, strong-arm tactics because we, the players, had no recourse.” # ⚓ Over_two-thirds_of_UK_social_scientists_warn_their_academic freedom_is_under_threat,_new_study_shows⠀⇛ Academics have said their freedom is under threat with evidence suggesting one of the reasons for this concern is the effect of internationalisation including risks associated with the rising influence of authoritarian states such as China. Half of those who took part in a major new study said they felt their freedom to select teaching content was under threat. Half of politics and international scholars questioned said their freedom to conduct research was under threat, and 39 per cent said they thought institutional censorship was a problem. When asked if academic freedom was discussed in universities, 74 per cent of teaching and research said it was. # ⚓ Lecturers_admit_self-censoring_classes_with_Chinese students⠀⇛ Academics are self-censoring to avoid causing offence to students from authoritarian states such as China, a new report has said. Two thirds said they believed that academic freedom was under threat in higher education and more than two fifths felt the same about their freedom to select teaching content. # ⚓ UK_scholars_‘more_likely_to_self-censor’_when_teaching Chinese_students⠀⇛ Forty per cent of academics specialising in China report self-censoring when teaching students from the nation, according to a survey looking at attitudes within universities on whether academic freedom is at risk from internationalisation. A new paper, published by academics from the universities of Exeter, Oxford and Portsmouth, presents the results of a survey distributed to 25,000 academics working in social sciences and humanities departments in UK universities and completed by 1,500 of them. # ⚓ Is_academic_freedom_at_risk_from_internationalisation? Results_from_a_2020_survey_of_UK_social_scientists⠀⇛ The question of the form that academic freedom takes and how it can be maintained in the context of the internationalisation of universities has become prominent in the UK in recent years. Both governmental and societal voices have raised concerns about perceived threats; however, much of the existing evidence is scattered and anecdotal. In October 2020, we distributed a survey in order to assess these issues. In this paper we report three main findings. First, UK social scientists express high levels of concern across a number of dimensions, from the effects of funding on research, to teaching content, to freedom of expression, and risks created by the online environment. Second, these concerns are somewhat greater in Politics, IR and Area Studies, suggesting that those disciplines which are most international in their content report greater risk. Finally, there appears to be demand for greater support. A majority of respondents did not know if guidelines existed in their department, and state that academic freedom was discussed infrequently or not at all. This suggests that institutional guidance and professional discourse have not kept pace with heightened concern. We find majority support for new legislation and even stronger support for a code of conduct. # ⚓ How_can_US_universities_combat_threat_of_teaching restrictions?⠀⇛ National higher education leaders have voiced some protest against the developments but have largely left individual institutions to fight back as best they can, creating what Dr Friedman and other experts see as a rapidly normalising atmosphere of ideological attacks on basic academic freedoms. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ The_Cypherpunks_Mobilize_to_Save_Julian_Assange⠀⇛ The prized object, which is part of an NFT collection called “Censored”, is not something one can take home, like, say, one of Louis XIV’s famous clocks; rather it’s a dynamic generative artwork that exists only in a digital format, changes daily, and was created with a very specific goal: to free Julian Assange through raising funds for his legal defense and raising awareness of the free-speech implications of his case. “Clock”, as its name suggests, does actually mark time—the number of days Julian has been incarcerated in high-security Belmarsh prison, that number being ONE THOUSAND THIRTY SEVEN days as of this writing, or so indicated the muted timer in uppercase white letters on a black background, blinking rhythmically, some have said, in sync with Julian’s heartbeat. # ⚓ Journalists’_union_challenges_Peca_ordinance_in_IHC⠀⇛ The Pakistan Federal Union of Journalists (PFUJ) on Tuesday filed a petition in the Islamabad High Court (IHC) challenging the Prevention of Electronic Crimes (Amendment) Act Ordinance 2022. o § Civil Rights/Policing⠀➾ # ⚓ In_Riverside_County_Jails,_Organizing_Against_Repressive Conditions_Takes_Many_Forms⠀⇛ Denied meals, forced to endure painful restraints, and subject to retaliation for participating in hunger strikes when he was incarcerated inside Riverside County jails, Salvador Venegas took the law into his own hands when he filed a lawsuit pro se against Riverside County Sheriff Chad Bianco in August 2019.  Venegas, who is currently imprisoned in the SATF- CSP in California’s Central Valley, organized and participated in more than one hunger strike while detained in Riverside County (RivCo) between February 2014 and September 2020. In his capacity as a pro se litigant, he also crafted and filed multiple lawsuits against the Riverside County Sheriff’s Department (RCSD) and the county – four in federal and three in state courts.    # ⚓ “Year_of_the_Worker”:_2021_Saw_Over_3_Million_Strike_Days With_140K_Participants⠀⇛ # ⚓ LA_Sheriff_Threatens_To_‘Subject’_City_Council_To ‘Defamation_Law’_If_They_Won’t_Stop_Calling_His_Deputies ‘Gang_Members’⠀⇛ The man presiding over a law enforcement agency filled with gangs and cliques would prefer city officials stop referring to his employees as gang members. # ⚓ Tapping_Fortress_Australia:_Priti_Patel’s_Border_Force Review⠀⇛ During the Howard years, Downer served in the role of a position that has become all but irrelevant, outsourced as it is to the US State Department and the fossil fuel lobby.  It was during that time that Australia supercharged its draconian approach to refugees and border security, repelling naval arrivals and creating a network of concentration camps that has since been marketed to the world.  The UK Home Affairs Minister Priti Patel is positively potty for it but has only managed to adopt aspects of the “Australian model”, including the relocation of arrivals to offshore facilities and co-opting the Royal Navy in an intercepting role. Efforts to use third countries to process asylum claims have been frustrated, though Patel has opted for a legislative route in stymieing the process and limiting the settlement rights of unwanted migrants.  While she has authorised the use of push backs on paper, these have yet to take place and are the subject of a legal challenge by the Public and Commercial Services Union (PCS) and charity, Care4Calais. # ⚓ She_Said_Her_Husband_Was_Abusive._A_Judge_Took_Away_Her Kids_and_Ordered_Her_Arrest.⠀⇛ After the judge in her Wisconsin divorce case ruled that her ex-husband — a man who had sought treatment for anger and alcohol issues — would get legal custody of and equal time with their four children, Julie Valadez vowed to fight back. But in every key ruling that followed, the Waukesha County Circuit Court judge overseeing her case, Michael J. Aprahamian, found Valadez’s concerns about her ex-husband not credible and her actions unacceptable. Aprahamian took away her ability to co-parent her children. He held her in contempt four times. And after Aprahamian ordered her arrest, she braced herself for jail. # ⚓ ‘Huge_Victory’:_Colombian_High_Court_Decriminalizes Abortion⠀⇛ Women in Colombia are now free to seek abortion care without fear of criminal prosecution following a ruling by the country’s Constitutional Court on Monday—the result of years of campaigning by reproductive rights groups. “Today, women in this country have won.” # ⚓ Redistricting_Tactics_Threaten_to_Suppress_Black Representation_in_Louisiana⠀⇛ # ⚓ Sexual_assault_victim_sentenced_to_100_lashes,_7_years jail⠀⇛ A Mexican woman who accused a Colombian man of sexually assaulting her while she was living and working in Qatar instead faces charges of engaging in an extramarital relationship, a crime that can be punished in the Middle Eastern country by up to seven years imprisonment and 100 lashes. # ⚓ Women_Workers_Must_Cover_Up_‘Even_With_A_Blanket’,_Say Taliban⠀⇛ Most women have been barred from their government jobs, since the Taliban retook power in August, though Afghanistan’s new rulers claim they will be allowed to return once some conditions are in place — such as segregated offices. On Tuesday, the Ministry for the Promotion of Virtue and Prevention of Vice issued a statement saying women should not go to work unless they were properly covered, and they could be fired if they did not follow guidelines # ⚓ JUI-F_opposes_Aurat_March,_threatens_to_stop_it_with ‘baton’⠀⇛ Aurat March, which was first held in Karachi in 2018, is now organised in numerous other cities across the country on March 8 every year to celebrate International Women’s Day and highlight the issues women face in Pakistan. # ⚓ Bajrang_Dal_activist_Harsha_killed_for_supporting_campaign against_hijab,_says_Goa_CM⠀⇛ Sawant alleged that Harsha was killed by anti- nationals,anti hindu fundamentalists, for favouring the campaign against wearing hijab in educational institutes in the state. # ⚓ Opinion_|_Divisions_Among_U.S._Evangelicals_–_The_New_York Times⠀⇛ Readers discuss how racial and sexual issues and Donald Trump have led to strife and whether and how evangelicalism should be saved. o § Internet Policy/Net Neutrality⠀➾ # ⚓ 15_Years_Late,_The_FCC_Cracks_Down_On_Broadband_Apartment Monopolies⠀⇛ A major trick dominant broadband providers use to limit competition is exclusive broadband arrangements with landlords. Often an ISP will strike an exclusive deal with the owner of a building, apartment complex, or development that effectively locks in a block by block monopoly. And while the FCC passed rules in 2007 to purportedly stop this from happening, they contained too many loopholes to be of use. # ⚓ Submarine_cable_fault_disrupts_[Internet]_services_in Pakistan⠀⇛ The Pakistan Telecommunication Authority (PTA) on Tuesday said users of Trans World Associates (TWA), one of the two license holders for international landing stations of submarine cables, could face bandwidth disruptions due to a reported breakage in the company’s submarine cable system. # ⚓ Local_TV_Giant_Tegna_Sold_to_Private_Equity_Firms_in Megadeal⠀⇛ Tegna owns 64 local TV stations in 51 markets and is the largest independent owner of NBC affiliates. The company was formed in 2015 when Gannett split itself in two, spinning out its TV station business as Tegna while retaining its legacy newspaper business. Following the close of the deal, Tegna stations in Austin (KVUE), Dallas (WFAA and KMPX) and Houston (KHOU and KTBU) are expected to be acquired by Cox Media Group, and Tegna’s over-the-top advertising platform Premion “is expected to operate as a stand-alone business majority owned by Cox Media Group and Standard General,” the companies said. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ Elon_Musk_Suggests_That_Piracy_is_Appealing_Once Again⠀⇛ The richest man on the planet tweeted a Pirate Bay-themed meme a few hours ago. Tesla CEO Elon Musk used the distracted boyfriend meme to suggest that paid streaming services have become a nightmare and that people are eying pirate alternatives instead. # ⚓ Hollywood_Wins_Pirate_Site_Blocking_Expansion_in Australia⠀⇛ Various Hollywood studios and Netflix are continuing their crusade against pirate sites Down Under. The companies have obtained a fresh blocking order at Australia’s Federal Court that requires local Internet providers to block dozens of websites. The targets mostly include streaming portals such as Soap2day, Yomovies, and 123movies. # ⚓ Hollywood:_PrimeWire_Pirate_Streaming_Site_is_Defying Court_Injunction⠀⇛ A coalition of major Hollywood studios and Netflix is demanding urgent action from the court after streaming site PrimeWire defied a court order to stop distributing their movies and TV shows. The studios previously won a preliminary injunction which included an order preventing the transfer of PrimeWire domains. Just days later two domains were transferred and the infringement continues. # ⚓ US_Copyright_Office_Gets_It_Right_(Again):_AI- Generated_Works_Do_Not_Get_A_Copyright_Monopoly⠀⇛ For years, throughout the entire monkey selfie lawsuit saga, we kept noting that the real reason a prestigious law firm like Irell & Manella filed such a patently bogus lawsuit was to position itself to be the go-to law firm to argue for AI-generated works deserving copyright. However, we’ve always argued that AI-generated works are (somewhat obviously) in the public domain, and get no copyright. Again, this goes back to the entire nature of copyright law — which is to create a (limited time) incentive for creators, in order to get them to create a work that they might not have otherwise created. When you’re talking about an AI, it doesn’t need a monetary incentive (or a restrictive one). The AI just generates when it’s told to generate. # ⚓ Video_Game_History_Foundation:_Nintendo_Actions ‘Actively_Destructive_To_Video_Game_History’⠀⇛ I’ve been banging on a bit lately about the importance of video game preservation as a matter of art preservation. It’s not entirely clear to me how much buy in there is out there in general on this concept, but it’s a challenge in this specific industry because much of the control over what can be preserved or not sits in the hands of game publishers and platforms compared with other forms of art. Books have libraries, films have the academies and museums, and music is decently preserved all over the place. But for gaming, even organizations like the Video Game History Foundation have to rely on publishers and platforms to let them do their work, or risk art being lost entirely to the digital ether or lawsuits over copyright. We’ve talked in the past about how copyright law is far too often used in a way that results in a loss of our own cultural history, and digital-only video games are particularly vulnerable to that. ䷩ 𝚕𝚒𝚗𝚎 6800 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_24/2/2022:_TrueNAS_SCALE_22.02_and_‘Linux’_FUD_in_Ukraine_Clothing⠀✐ Posted in News_Roundup at 8:19 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Audiocasts/Shows⠀➾ # ⚓ Tools_For_Renaming_Files_In_Linux_–_Invidious⠀⇛ In this video tutorial, I show several different methods for renaming files on Linux, including how to do more advanced things like bulk renaming, pattern substitutions, and changing lowercase to uppercase and vice versa. # ⚓ FLOSS_Weekly_669:_Free_+_/_vs._Open_–_Jon_“maddog”_Hall, Free_Software_vs_Open_Software⠀⇛ What does Jon “maddog” Hall—a man with 15,000 FLOSS-related t-shirts have to say? Lots about everything free, open and otherwise, in a conversation that occasionally turns to an argument between maddog, Simon Phipps, and host Doc Searls. # ⚓ How_to_install_KaOS_2022.02._–_Invidious⠀⇛ In this video, I am going to show how to install KaOS 2022.02. # ⚓ How_to_install_Notepadqq_on_Zorin_OS_16_–_Invidious⠀⇛ In this video, we are looking at how to install Notepadqq on Zorin OS 16. # ⚓ Discord_Is_A_Black_Hole_For_Information!_–_Invidious⠀⇛ Discord is a chat room plain and simple and that’s all it needs to be but a lot of new projects are trying to make it something that it isn’t, trying to make a forum, a wiki, an issue tracker and more it’s not good at this job and turns into a black hole for information o § Applications⠀➾ # ⚓ The_Tiling_Terminal_Emulator_Tilix_1.9.5_Released_| UbuntuHandbook⠀⇛ Tilix, the popular tiling terminal emulator, released v1.9.5 with a few new features and some bug-fixes. Tilix is a GTK+3 terminal emulator supports for splitting app window horizontally or vertically. It supports drag and drop re-arranging terminals, quake mode, custom hyperlinks, as well as many other features. After a year of development, it finally announced the new 1.9.5 with only a few new features due to lack of maintainers. o § Instructionals/Technical⠀➾ # ⚓ CKA_Practice_Questions⠀⇛ The goal of this post is to help you find the answer to the following question: am I ready for the CKA exam? The purpose of the Certified Kubernetes Administrator (CKA) program is to provide assurance that CKAs have the skills, knowledge, and competency to perform the responsibilities of Kubernetes administrators. # ⚓ Developer:_Add_an_IDT_map_design_reference_to_your_source tree_Using_cp⠀⇛ # ⚓ How_To_Install_Angular_CLI_on_Fedora_35_–_idroot⠀⇛ In this tutorial, we will show you how to install Angular CLI on Fedora 35. For those of you who didn’t know, AngularJS is a JavaScript framework that is used to develop web apps. It has MVC (Model-View-Controller) architecture. Angular CLI is used in Angular projects to automate tasks rather than perform them manually. Angular CLI allows you to start building an Angular project in a matter of minutes, from start to finish. 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 Angular CLI on a Fedora 35. # ⚓ »_GNU_Linux_Debian_11_(bullseye)_–_how_to_install virtualbox_6.1_|_dwaves.de⠀⇛ # ⚓ How_to_Install_Zabbix_Agent_6_on_OpenSUSE_Leap_15.3⠀⇛ A Zabbix agent is a program that runs on a remote machine that needs to be monitored through the Zabbix server. The agent collects the data on the remote server and send back to Zabbix server when requested. Zabbix agent must be installed on all the remote systems that need to be monitor through the Zabbix server. # ⚓ 2_ways_to_install_XFCE_Desktop_on_Debian_11_Bullseye_– Linux_Shout⠀⇛ Xfce is an alternative to GNOME or KDE and a pretty colorful and well-configurable desktop environment. Learn the commands to install XFCE desktop on Debian 11 Bullseye Linux. Xfce is designed to run easily on slightly less powerful computers, mainly because of the somewhat lower system requirements. This lightweight desktop environment is very easy to use with the mouse and can be used to run all GNOME and KDE programs. Friends of Compiz can use Xfce too. Ubuntu has been available with Xfce as the desktop environment in its official version – Xubuntu. However, since it is no longer a “pure” Xfce (various GNOME components have been integrated to increase comfort). Nevertheless – if you are a Debian Linux user with a command-line interface or graphical user interface with Gnome or any other, still we can install XFCE directly using the official Debian package source repository. # ⚓ How_to_Use_Spotify_in_the_Terminal_on_Linux,_Mac,_or Windows⠀⇛ Have you ever wanted to stream Spotify’s music and podcasts without distracting banners and pushy recommendations? With a tool called Spotify TUI, you can control your Spotify stream in your computer’s terminal. We’ll show you how to set it up. # ⚓ Easy_Jami_Install_on_Ubuntu_21.10_[In_2022]-_LateWeb.Info⠀⇛ Jami (formerly GNU Ring, SFLphone) is a SIP- compatible distributed peer-to-peer softphone and SIP-based instant messenger for Linux, Microsoft Windows, OS X, iOS, and Android. Jami was developed and maintained by the Canadian company Savoir-faire Linux, and with the help of a global community of users and contributors, Jami positions itself as a potential free Skype replacement. Jami is free and open-source software released under the GNU GPL-3.0-or-later. In November 2016, it became part of the GNU Project. # ⚓ How_to_Deploy_Flask_Application_with_Nginx_and_Gunicorn_on Ubuntu_20.04_–_RoseHosting⠀⇛ Flask is a small, lightweight, and micro web framework written in Python. It allows you to develop web applications easily without any tools or libraries. This web application may be a blog, wiki page, web pages, web-based calendar application, or a commercial website. It is simple, easy to use, easy to learn, and beginner-friendly because it does not require any dependencies. In this tutorial, we will show you how to deploy the Flask application with Gunicorn and Nginx on Ubuntu 20.04. # ⚓ Best_Free_Video_Converters_For_Linux_[GUI,CLI_and_Online]⠀⇛ Video downloads are fun until they become unplayable. So, here’s the list of the best video converters to help your downloads stay relevant everywhere. Video conversion is not the best thing you want to do with a video, but it becomes unavoidable sometimes. For instance, you can only upload videos in selected formats on YouTube, Facebook, etc. Similarly, media players don’t play every other format in which you download or create videos. # ⚓ Avoid_command_injection_with_Apache_Common_CLI_|_SUSE Communities⠀⇛ This article is about using secure coding patterns and correcting vulnerable code. Applications need third-party libraries to provide common facilities for repetitive tasks like logging, parsing, … When a developer uses an opensource library, he must understand that his code inherits also possible security issues. For this reason, opensource libraries must be audited for risks to avoid problems like log4shell vulnerability. o § Games⠀➾ # ⚓ The_next_release_of_free_RTS_0_A.D._will_have_some_new graphics_options_|_GamingOnLinux⠀⇛ 0 A.D. is a free and open source historical RTS that’s been in development for a long time. Each release is impressive and it sounds like the next release is going to look pretty shiny. [...] This next update won’t only be good for those with powerful computers though, there’s also new options for weaker systems too. You will be able to actually decrease the texture quality, something most other modern 3D games also allow. # ⚓ First-person_retro-fueled_RPG_Beyond_Sunset_gets_a_demo_| GamingOnLinux⠀⇛ Are you ready to dive into a new world? Beyond Sunset looks absolutely awesome and now you’ve got a chance to check it out, as a demo has been put up recently. Now, there’s even a Linux build of the demo too! I am truly loving this huge resurgence of modern-made low-fi experiences like this. More please. “SUNSET CITY, CALIFORNIA – 20XX: You’ve been awakened from cryostasis. Your name, your identity, your memories… All lost in the confusing fog of hypersleep. Not only a stranger in a strange place, you begin to manifest powerful abilities. Lightning-fast reactions. Innate combat skills. Near-supernatural agility. You’re not like everyone else. # ⚓ Build_your_ultimate_collection_of_the_Civilization_series in_this_new_bundle_|_GamingOnLinux⠀⇛ Love your strategy games and a bit of Sid Meier? You’re in luck as Humble Bundle have something new up giving you plenty of the Civilization series. Some of the titles come with native Linux support but it’s probable most will just work with Proton now too. # ⚓ How_to_install_texture_packs_in_Minetest_on_a_Chromebook⠀⇛ Today we are looking at how to install texture packs in Minetest 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. If you have any questions, please contact us via a YouTube comment and we would be happy to assist you! Please take note that Minetest must be already installed on your Chromebook, and needed to be launched at least once. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Plasma_5.24.2_available_on_Kubuntu_21.10⠀⇛ We are pleased to announce that Plasma 5.24.2 is now available in our backports PPA for Kubuntu 21.10 (Impish Indri). The release announcement detailing the new features and improvements in Plasma 5.24.2 can be found here. o § Distributions⠀➾ # ⚓ AV_Linux_MX-21_has_arrived,_and_it’s_almost_a_multi-media creator_dream_come_true_|_TechRepublic⠀⇛ I must confess, I do love creating video and audio content. I’ve recorded thousands of videos over the years, hundreds of podcast episodes, ebooks and much more. I’ve experimented with different applications for different purposes. Eventually, I arrived at a collection of tools that best fit my needs. Some of those tools are open-source, while others are not. For example, I use Audacity for audio and Final Cut Pro X for video. Why do I not opt to go with an open-source video editor? Mostly because none of them have either reached a level of reliability or they don’t offer the features I need to create pro-level content. # ⚓ blog.ipfire.org_–_Introducing_elementary_network protection:_Dropping_all_traffic_from_and_to_hostile_networks by_default⠀⇛ Starting with upcoming Core Update 164, the firewall options page will feature a new checkbox: Drop packets from and to hostile networks. For basic protection of our users and their networks, it will be enabled by default on new installations, staying disabled on existing IPFire systems (but we recommend to turn it on there as well). Improving network protection for the masses Although we always preach IPFire is not meant to be installed and then forgotten, we believe this is what happens to a decent amount of installations out there: They are set up once, perhaps being configured in a basic manner, and do not receive any attention afterwards. Resources are scarce, so why bother touching a running system? Of course, we neither endorse such a modus operandi, nor can we shed the load from our users to define and enforce a proper security policy (including firewall rules and IPS settings, just to name a few ingredients) on their networks. On the other hand, there are some shady areas of the internet, and virtually everyone in the security community knows about them. A subset of them is so dangerous that you don’t even want to process any IP connection from or to them, no matter what. # § BSD⠀➾ # ⚓ TrueNAS_SCALE_22.02_Is_a_Game_Changer_in_the_Linux NAS_Field⠀⇛ After 18 months of development and testing effort, TrueNAS SCALE is now released as a newest addition to the TruNASs family of storage software. First off, let me start with what is TrueNAS SCALE. TrueNAS SCALE is built on the same foundational software and middleware as TrueNAS CORE, which is probably the best known, the world’s most widely deployed, and powerful free and open-source storage software out there. TrueNAS SCALE is the first release of TrueNAS on Linux. It is Debian-based as opposed to the original which ran on FreeBSD, and that greatly increases the available tools to a user that wants better control and additional features over their networked storage devices. # § SUSE/OpenSUSE⠀➾ # ⚓ How_YaST_Development_is_Going_at_2022_|_YaST⠀⇛ We realized that, apart from the blog post presenting our D-Installer project, we have not reported any YaST activity during 2022 here in our blog. Since we are in the Beta phase of the development of SUSE Linux Enterprise 15-SP4 (which will also be the base for openSUSE Leap 15.4) we are quite focused on helping to diagnose and fix the problems found by the intensive and extensive tests done by SUSE QA department, partners and customers. We know that’s not the part of our job our audience wants to read about… and to be honest is not the part we enjoy writing about either. Fortunately, two months after our latest regular report, we have some interesting more bits to share. # § IBM/Red Hat/Fedora⠀➾ # ⚓ How_to_configure_firewalld_quickly⠀⇛ This article covers the fundamental tasks necessary to configure the firewalld service quickly. I’ll assume you already appreciate the importance of a firewall and have a general understanding of how firewalls protect servers and workstations. # ⚓ What_you_need_to_know_about_WebSphere_Hybrid Edition⠀⇛ IBM WebSphere Hybrid Edition is a bundle of IBM runtimes for enterprise and cloud-native Java workloads. WebSphere Hybrid Edition enables developers to flexibly deploy both WebSphere traditional runtimes and Liberty runtimes (including the open-source Open Liberty framework), depending on their needs while optimizing the use of WebSphere Network Deployment, WebSphere Application Server, and Liberty Core license entitlements. WebSphere Application Server traditional is a trusted application server for Java EE applications. Liberty is a fast, lightweight, and modular framework for cloud-native Java applications and microservices that are optimized for cloud and Kubernetes and supporting a wide spectrum of Java APIs, including the latest Eclipse MicroProfile and Jakarta EE API. # ⚓ Neither_old_nor_new:_The_CIO’s_paradox⠀⇛ Each year around this time people ask, “what’s the big trend?” or “what’s the new technology we should be watching?” But the truth is, immediately adopting the “next big thing” isn’t the best strategy for CIOs, trivializing the longevity and impact of IT in an organization. Some technology persists for decades if not longer, and the decisions IT leaders make today can affect their organizations’ nimbleness and market response down the road, whether it’s in two years or 20. As new infrastructure is being built out, you can’t just leave behind existing systems and tools. That’s not practical or sustainable. So how do you maintain existing systems that are critical to your operations while still keeping pace with a rapidly evolving IT world? # ⚓ Industry_4.0_and_OT_transformation:_technologies, benefits_and_challenges⠀⇛ While digital transformation is widely known to be impacting organizations that deal primarily with information and data—financial services, telecommunications, retail, etc.—it is also driving significant change in the world of manufacturing. This evolution towards computerizing and transforming manufacturing systems has been dubbed “Industry 4.0.” But, what is Industry 4.0? What technologies are making it possible? And what are the benefits and challenges it brings as operational technology (OT) environments transform? # ⚓ Awards_roll_call:_November_2021_to_February_2022⠀⇛ 2022 is in full swing and we wanted to take a moment to pause and celebrate some of our recent accolades. Our latest batch of awards includes recognition in categories ranging from Red Hat’s diverse and inclusive workplace culture, our talented individuals who make Red Hat so special, and the depth and experience of our business portfolio. o § Devices/Embedded⠀➾ # ⚓ Raspberry_Pi_CM4_automation_controller_has_optional_UPS_and M.2⠀⇛ Kristech announced a “Pigeon RB700” DIN-rail automation controller that runs Linux on the Raspberry Pi CM4 with GbE and 10/100 LAN, 3x or more serial, 8x DI, CAN, 1-wire, and optional HDMI, ADC, UPS, and dual M.2. Back in 2016, we covered the launch of the original Pigeon RB100 automation controller, which was built around the flagship, ARM11 based Raspberry Pi Compute Module. Since then, Kristech has upgraded the RB100 with a Raspberry Pi Compute Module 3 in its Pigeon RB100-CM3 and released more advanced CM3 based systems with the Pigeon RB300-CM3 and RB350- CM3. The company has now launched a Pigeon RB700 system built around the Raspberry Pi CM4. # ⚓ diziet_|_Rooting_an_Eos_Fairphone_4⠀⇛ Last week I received (finally) my Fairphone 4, supplied with a de-googled operating system, which I had ordered from the E Foundation’s shop in December. (I’m am very hard on hardware and my venerable Fairphone 2 is really on its last legs.) I expect to have full control over the software on any computing device I own which is as complicated, capable, and therefore, hazardous, as a mobile phone. Unfortunately the Eos image (they prefer to spell it “/e/ os”, srsly!) doesn’t come with a way to get root without taking fairly serious measures including unlocking the bootloader. Unlocking the bootloader wouldn’t be desirable for me but I can’t live without root. So. I started with these helpful instructions: https:// forum.xda-developers.com/t/fairphone-4- root.4376421/ I found the whole process a bit of a trial, and I thought I would write down what I did. But, it’s not straightforward, at least for someone like me who only has a dim understanding of all this Android stuff. Unfortunately, due to the number of missteps and restarts, what I actually did is not really a sensible procedure. # ⚓ 3.5-inch_Tiger_Lake-U_SBC_offers_triple_M.2_slots⠀⇛ Axiomtek’s 3.5-inch “CAPA55R” SBC runs Linux or Win 10 on an 11th Gen U-series CPU and provides triple display support, GbE, 2.5GbE, SATA, USB 3.2 Gen2, and 3x M.2 slots. Axiomtek, which is one of the more prolific manufacturers of Intel based embedded systems, has not done much with Intel’s 11th Gen Tiger Lake processors aside from its DSP511 signage player. The company has now launched a 3.5-inch form factor CAPA55R SBC that runs Linux or Win 10 on Tiger Lake-UP3 (Tiger Lake-U) processors. The SBC is aimed at IoT applications such as industrial control, machine vision, self-service terminal, digital signage, and medical imaging. # § Open Hardware/Modding⠀➾ # ⚓ Pressure_Gauge_Built_In_A_Vacuum⠀⇛ Necessity might be the mother of all invention, but we often find that inventions around here are just as often driven by expensive off-the-shelf parts and a lack of willingness to spend top dollar for them. More often than not, we find people building their own tools or parts as if these high prices are a challenge instead of simply shrugging and ordering them from a supplier. The latest in those accepting the challenge of building their own parts is [Advanced Tinkering] who needed a specialty pressure gauge for a vacuum chamber. In this specific case, the sensor itself is not too highly priced but the controller for it was the deal-breaker, so with a trusty Arduino in hand a custom gauge was fashioned once the sensor was acquired. # ⚓ 1960s_stereo_console_modernized_with_an_Arduino_| Arduino_Blog⠀⇛ The aphorism that “they don’t build them like they used to” is especially true of the consumer electronics industry. Most manufacturers today design their product to last only a few years — or with outright planned obsolescence. But mid-century stereo consoles were a different story and resembled high-end furniture that would last. Sherman Banks has a Penncrest stereo console from that era, but its electronics were failing. So he used an Arduino to modernize the unit while retaining the vintage appearance. This particular console had an AM/stereo FM radio receiver and a built-in phonograph turntable. Unfortunately, the aging electronic components were unreliable and lacked good sound quality. The console itself, however, was in fantastic shape. So Banks wanted to keep it looking as original as possible, but with modern electronics and all of the features they offer. He replaced the radio with a Denon DRA-800H stereo receiver that offered inputs for a turntable and SiriusXM receiver, as well as Bluetooth streaming and Ethernet connections. He also replaced the turntable with a new Denon DP- 29F. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Samsung_Galaxy_S22_Review⠀⇛ # ⚓ Android_game_modding_is_here_thanks_to_BlueStacks_– Android_Authority⠀⇛ # ⚓ Android_13_Developer_Preview_1_hands-on:_A_first taste_of_Tiramisu_|_Android_Central⠀⇛ # ⚓ Android_13_won’t_support_DNS_over_HTTPS_as_previously planned⠀⇛ # ⚓ Google_is_ditching_Chrome’s_data_saver_mode_on Android_–_The_Verge⠀⇛ # ⚓ Vivo_Y76_5G_arrives_in_Europe_for_over_€300_with Android_11_and_a_Dimensity_700_SoC_–_NotebookCheck.net News⠀⇛ # ⚓ Samsung_Galaxy_S22_vs._Google_Pixel_6:_Which_small Android_phone_should_you_buy?_|_Android_Central⠀⇛ # ⚓ What_Is_Android_TV?_How_Is_It_Different_From_Smart TVs?_–_Fossbytes⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Firefox_97_&_small_anti-Proton_CSS_fixes⠀⇛ I do realize that there’s a consistency problem and maintenance cost to my tweaks. After all, I cannot possibly account for every little change in the Firefox UI ever, and there might be tiny glitches occurring now and then. But then, these will be minor, and I will have quick fixes for them, whereas using a browser with sub-optimal looks all the time is a no-go. It’s not a fun situation, but even so, Firefox is still the best browser around, and you should be using it, for practical and philosophical reasons, hipsterology notwithstanding. Anyway, if you are a nerd, because let’s face it, otherwise you wouldn’t be here, and you like your things to be neat, clean, legible, ergonomic, and efficient, then you will have changed the Firefox UI looks in versions 91 and beyond. You might even be possibly using some of my tweaks. If so, you have a fresh round of polish, in case you encounter some small niggles with Firefox 97. There you go. Take care, and see you soon. # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ Getting_Started_Guide_7.3_companion_to_LibreOffice Community_7.3_–_The_Document_Foundation_Blog⠀⇛ The Documentation Team is happy to announce the immediate availability of the Getting Started Guide 7.3, only days after the release of the LibreOffice Community 7.3. # ⚓ Adding_a_new_UNO_command_–_LibreOffice_Development Blog⠀⇛ What are UNO commands, and why would you need them? If you want to add some feature to the LibreOffice UI, you may need to add or modify a UNO command, so it would be help much to learn more about these commands, and in general, the dispatch framework. So, stay tuned! # § FSF⠀➾ # § Licensing/Legal⠀➾ # ⚓ New_Committee_Will_Investigate_Copyleft Implications_of_AI-Assisted_Programming [Ed: Microsoft-funded SFC today: we are creating a "think tank" to check what Microsoft GitHub means to GPL violations disguised as "Hey Hi". We've created for this a group of RMS attackers (RMS is the pioneer of copyleft), who even publicly defended this practice...]⠀⇛ Software Freedom Conservancy announces a Committee On AI-Assisted Programming and Copyleft to develop recommendations and plans for a Free and Open Source Software (FOSS) community response to the use of machine learning tools for code generation and authorship. The ethics and morality of machine learning models, which are regularly being applied to many problems, are a serious concern to policy makers. This Committee will focus on the specific issue of AI-assisted programming using models trained with FOSS, such as we’ve seen with GitHub’s Copilot product. Microsoft, through their GitHub subsidiary, argues, without evidence, that use of Copilot (which has been trained with a large body of FOSS) is “fair use” of that FOSS, and that all output of Copilot is solely copyrighted by its users. This conclusion focuses on the legal details of issues rather than ethics and morality, and Microsoft and GitHub have refused to provide backing evidence. This Committee will focus on the ethics and morality of their position, and consider the proper policy positions for the FOSS community and copyleft activists in the advent of AI-assisted programming. # § Programming/Development⠀➾ # ⚓ Create_a_shared_library_in_C_with_CMake_– PragmaticLinux⠀⇛ This tutorial explains how to develop a shared library in the C programming language and how to generate its build environment with CMake. # ⚓ Some_things_about_getaddrinfo_that_surprised_me⠀⇛ To understand all of these, we need to learn about a function called getaddrinfo which is responsible for doing DNS lookups. There are a bunch of surprising-to-me things about getaddrinfo, and once I learned about them, it explained a bunch of the confusing DNS behaviour I’d seen in the past. # ⚓ announcing_zephyr-copilot⠀⇛ I recently learned about the Zephyr Project which is a rather neat embedded OS for devices too small to run Linux. This led me to wondering if I could adapt arduino-copilot to target Zephyr, and so be able to program any of the 350+ boards it supports using Haskell. At the same time I had an opportunity to give a talk at the Houston Functional Programmers group. On February 1st I decided to give that talk, about arduino-copilot. # ⚓ How_long_does_it_take_to_create_a_website?_(and_why your_FLOSS_project_doesn’t_need_one)_–_The_Open Sourcerer⠀⇛ One might wonder why then, with those upgraded skills, I didn’t seize the opportunity to make a new website for GTG or other open-source projects that could benefit from fancier marketing. The short answer is, even if my tooling and technique have improved, it’s still a metric crapton of work. It might seem easy (“Use Hugo!”, “Just slap a couple of pages together!”, etc.) but there’s much more to building a website than just the technical design and coding (or integration) aspects. This article provides you with an idea of the amount of time it takes to plan, write, design and build a “reasonably simple” website with a dozen pages or so. # § Perl/Raku⠀➾ # ⚓ Finding_Unused_Perl_Variables_– olafalders.com⠀⇛ I’ve been working on some linting projects at $work and one thing I’m working on is finding unused variables in our codebase. This can be pretty important in a larger codebase. When you find variables which have not been used, you may find yourself asking, “why is this here?” and you may not easily get an answer. Eliminating unused variables can be good for the performance of the code, but also good for everyone else on your team. So, we want to make sure we can remove old bits of unused code and also prevent new cases. One tool we have used for this is Test::Vars. It has some limitations (like it needs to be in a file with a package declaration) and it has some bugs, but it does find some unused variables as well. * § Leftovers⠀➾ o § Science⠀➾ # ⚓ AI_Maybe_Revives_Dead_Languages⠀⇛ While Star Trek’s transporter is hard to imagine — perfect matter movement across vast distances with no equipment on one end — it may not be the most far-fetched piece of tech on the Enterprise. While there are several contenders, I strongly suspect the universal translator is the most unlikely MacGuffin. After all, how would you decipher a totally unknown language in real-time? Of course, no one wants to watch 30 episodes of TV about how we finally figured out what Klingons call clouds, so pretty much every science fiction movie has some hand-waving explanation for speaking the viewer’s language. Farscape had microbes, some aliens have telepathy that works with alien brains of any kind, and still others study English from afar for decades off camera. Babelfish anyone? # ⚓ Big_Chemistry:_From_Gasoline_To_Wintergreen_|_Hackaday⠀⇛ Most of us probably have some vivid memories of high school or college chemistry lab, where the principles of the science were demonstrated, and where we all got at least a little practice in experimental methods. Measuring, diluting, precipitating, titrating, all generally conducted under safe conditions using stuff that wasn’t likely to blow up or burn. But dropwise additions and reaction volumes measured in milliliters are not the stuff upon which to build a global economy that feeds, clothes, and provides for eight billion people. For chemistry to go beyond the lab, it needs to be scaled up, often to a point that’s hard to conceptualize. Big chemistry and big engineering go hand in hand, delivering processes that transform the simplest, most abundant substances into the things that, for better or worse, make life possible. To get a better idea of how big chemistry does that, we’re going to take a look at one simple molecule that we’ve probably all used at one time or another: the common artificial flavoring wintergreen. It’s an innocuous ingredient in a wide range of foods and medicines, but the infrastructure required to make it and all its precursors is a snapshot of just how important big chemistry really is. # ⚓ How_Big_Is_The_Moon?_Figure_It_Out_Yourself_|_Hackaday⠀⇛ We have to confess that we occasionally send friends a link to “let me Google that for you” when they ask us something that they could have easily found online. Naturally, if someone asked us how big the moon is, we’d ask Google or another search engine. But not [Prof Matt Strassler]. He’d tell you to figure it out yourself and he would then show you how to do it. This isn’t a new question. People have been wondering about the moon since the dawn of human civilization. The ancient Greeks not only asked the question, but they worked out a pretty good answer. They knew approximately how big the Earth was and they knew the moon was far away because it is seen over a very wide area. They also knew the sun was even further away because the moon sometimes blocks the sun’s light in an eclipse. Using complex geometry and proto-trigonometry they were able to work out an approximate size of the moon. [Matt’s] method is similar but easier and relies on the moon occluding distant stars and planets. [Matt] explains that a distant sphere illuminated by a distant light source will cast a shadow on a plane about the size of the sphere. What’s more, is that anyone on the plane in the shadow who can’t see the light source must be in the shadow, which allows you to measure the shadow, and that gives an approximation of the sphere’s size. For this to work, the light source needs to be at least ten times further away from the plane than the sphere is. The further away the light source is, the lower the error in the final number. # ⚓ Levitating_With_Light_|_Hackaday⠀⇛ Of course, it is no secret that light can exert pressure. That’s how solar sails work and some scientists have used it to work with aerosols and the like. But this appears to be the first time light lifted a large item against gravity. The team claims that their tests showed that a sunlight- powered flying vehicle might carry up to ten milligrams of payload. That doesn’t sound like much, but it’s impressive and the paper mentions that since the lift is not from aerodynamic forces, there might be applications in flying at very high altitudes. o § Hardware⠀➾ # ⚓ Inputs_Of_Interest:_Canadian_MCM/70_Was_Kinda_Like_The First_Cyberdeck_|_Hackaday⠀⇛ We’re all used to personal computers as the norm, be they mobile, laptop, or desktop. But of course, in the early days, computers were large single- purpose machines used to crunch even bigger numbers. Go back even further in time, and the computers are humans operating fancy electromechanical calculators at high speeds, or, simply using pencils or chalk. Before the personal computer arrived, people had to share time on mainframe machines to do their computing. Imagine having to go down to the library every time you wanted to look something up on the Internet. Wouldn’t you much rather do it at home on your own machine? Of course you would. # ⚓ Coin_Cell_Eliminator_Does_More_Than_Save_Batteries_| Hackaday⠀⇛ Coin cells are useful things that allow us to run small electronic devices off a tiny power source. However, they don’t have a lot of capacity, and they can run out pretty quickly if you’re hitting them hard when developing a project. Thankfully, [bobricius] has just the tool to help. The device is simple – it’s a PCB sized just so to fit into a slot for a CR2016 or CR2032 coin cell. The standard board fits a CR2016 slot thanks to the thickness of the PCB, and a shim PCB can be used to allow the device to be used in a CR2032-sized slot instead. # ⚓ Pulling_Off_A_CRT_Transplant_Doesn’t_Have_To_Be_Tricky!_| Hackaday⠀⇛ Whether it’s an engine swap in an old car or pulling a hard drive out of an old computer, we often find ourselves transplanting bits from one piece of hardware to another. [Emily Velasco] recently attempted this with a pair of CRTs, and came away with great success. The donor was an old 1980s fishing sounder, which came complete with a rather fetching monochrome amber CRT display. [Emily]’s goal was to transplant this into the body of a early 2000s portable television. The displays were of a similar size and shape, though the Toshiba CRT from the 80s used a lot more glass in its construction. The tube socket in the TV used to hook up the display matched the old CRT perfectly, so there were no hassles there. A bit of soldering was all that was needed to hook up the yoke, and [Emily] was ready to test. Amazingly, it powered up cleanly, displaying rolling amber static as you’d expect, given that analog television stations have been off the air for some time now. # ⚓ What_To_Do_With_A_Broken_Television_When_You_Can’t_Fix_It_| Hackaday⠀⇛ Who can say ‘no’ to a free TV, even if it’s broken? This was the situation [Andrew Menadue] ended up in last year when he was offered an LG 39LE4900 LCD TV. As [Andrew] describes in the blog post along with videos (see first part embedded after the break), this particular television had been taken to a television repair shop previously after the HDMI inputs stopped working, but due to a lack of replacement parts the owner had to make due with the analog inputs still working. That is, until those stopped working as well. The nice thing about these TVs is that they are very modular inside, as [Andrew] also discovered to his delight. In addition to the LG controller board, an inverter board and the power supply board, this TV also contained a TCON PCB. After some initial unsuccessful swapping of the parts with EBay replacements, nothing was (surprisingly) working, but it did turn out that the TCON and inverter boards are made and sold by AUO (major Taiwanese display manufacturer), along with the display itself. # ⚓ Winding_Your_Own_Small_Coils_|_Hackaday⠀⇛ Depending on what you build, you may or may not run into a lot of inductors. If you need small value coils, it is easy to make good-looking coils, and [JohnAudioTech] shows you how. Of course, doing the winding itself isn’t that hard, but you do need to know how to estimate the number of turns you need and how to validate the coil by measurement. [John] uses a variety of techniques to estimate and measure his coils ranging from math to using an oscilloscope. He even uses an old-fashioned nomogram from a Radio Shack databook circa 1972. In fact, we get the idea that [John] really misses Radio Shack. In addition to the book, we noted guest appearances from a Radio Shack calculator and a caliper. We were a bit surprised that he didn’t use a Radio Shack pen as a coil form. # ⚓ Minimalistic_Doorbell_Doesn’t_Need_An_Internet_Connection_– Or_Even_a_Power_Supply⠀⇛ Doorbells are among those everyday objects that started out simple but picked up an immense amount of complexity over the years. What began as a mechanism to bang two pieces of metal together evolved into all kinds of wired and wireless electric bells, finally culminating in today’s smart doorbells that beam a live video feed to their owners even if they’re half a world away. But sometimes, less is more. [Low tech obsession] built a doorbell out of spare components that doesn’t require Internet connectivity or even a power supply. But it’s not a purely mechanical device either: the visitor turns a knob mounted on a stepper motor, generating pulses of alternating current. These pulses are then fed into the voice coil of an old hard drive, causing its arm to vibrate and strike a bell, mounted where the platters used to be. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ ‘Hundreds_of_computers’_in_Ukraine_hit_with wiper_malware [Ed: Microsoft Windows TCO; The cyberattack in Ukraine is a Microsoft Windows thing, but Microsoft-sponsored media keeps throwing in the word "Linux" to confuse and distract.]⠀⇛ It’s not entirely clear right now how the malware is dropped onto victims’ machines and run, though in one case, said ESET, an organization’s Active Directory server was probably compromised to distribute the wiper through the network via a group policy object. # ⚓ Anatomy_of_top-tier_suspected_NSA_backdoor_code [Ed: It seems like topic shifting now that Russia batters Windows, mostly in Ukraine]⠀⇛ Pangu Lab has identified what it claims is a sophisticated backdoor that was used by the NSA to subvert highly targeted Linux systems around the world for more than a decade. The China-based computer-security outfit says it first spotted the backdoor code, or advanced persistent threat (APT), in 2013 when conducting a forensic investigation on a host in “a key domestic department” – presumably a Chinese company or government agency. # ⚓ Chinese_Researchers_Detail_Linux_Backdoor_of NSA-Linked_Equation_Group [Ed: Media desperate to associate Linux with security problem because Ukraine is besieged by attacks on Microsoft Windows at the moment?]⠀⇛ A team of researchers from China’s Pangu Lab on Wednesday published a 50- page report detailing a piece of Linux malware allegedly used against many targets by the threat actor known as the Equation Group, which has been linked to the U.S. National Security Agency (NSA). It’s not uncommon for cybersecurity companies in the United States to publish reports detailing the tools and activities of threat actors linked to the Chinese government, and now a group of Chinese researchers have released a report detailing a piece of malware tied to the U.S. government. Pangu Lab is a research project of Pangu Team, which is best known for its iPhone jailbreaks. An iOS exploit earned them $300,000 last year at a major Chinese hacking contest. # ⚓ US,_UK_detail_malware_tied_to_Russian_hacking group_Sandworm_that_targets_Linux [Ed: They mostly target Microsoft Windows, but pundits try to distort what's actually going on]⠀⇛ As Russia begins its invasion of Ukrainian territories and Western governments continue to warn about the potential or Russian cyberattacks in response to sanctions, U.S. and UK agencies have detailed what they claim is another malware tool used by Russian APT hacking group Sandworm. # ⚓ New_Sandworm_Malware_Cyclops_Blink_Replaces VPNFilter⠀⇛ The United Kingdom’s National Cyber Security Centre, CISA, the National Security Agency, and the Federal Bureau of Investigation have released a joint Cybersecurity Advisory (CSA) reporting that the malicious cyber actor known as Sandworm or Voodoo Bear is using new malware, referred to as Cyclops Blink. Cyclops Blink appears to be a replacement framework for the VPNFilter malware exposed in 2018, which exploited network devices, primarily small office/home office routers and network-attached storage devices. # ⚓ Security_updates_for_Wednesday_[LWN.net]⠀⇛ Security updates have been issued by Debian (expat), Fedora (php and vim), Mageia (cpanminus, expat, htmldoc, nodejs, polkit, util-linux, and varnish), Red Hat (389-ds-base, curl, kernel, kernel-rt, openldap, python- pillow, rpm, sysstat, and unbound), Scientific Linux (389-ds-base, kernel, openldap, and python-pillow), and Ubuntu (cyrus-sasl2, linux-oem-5.14, and php7.0). # ⚓ Google_Online_Security_Blog:_Mitigating_kernel risks_on_32-bit_ARM⠀⇛ Linux kernel support for the 32-bit ARM architecture was contributed in the late 90s, when there was little corporate involvement in Linux development, and most contributors were students or hobbyists, tinkering with development boards, often without much in the way of documentation. # ⚓ Biesheuvel:_Mitigating_kernel_risks_on_32-bit ARM_[LWN.net]⠀⇛ Ard Biesheuvel writes about 32-bit Arm systems on the Google Security Blog, with a focus on why these processors are still in use and what is being done to increase their security at the kernel level. # § Fear, Uncertainty, Doubt/Fear-mongering/ Dramatisation⠀➾ # ⚓ New_Cloud_Cybersafety,_Malware_Miseries, Snap_Snafus_Lavish_Linux [Ed: “LinuxInsider” participates in FUD against “Linux”_(Snap_etc.)]⠀⇛ Qualys Research Team discovered multiple vulnerabilities in the snap-confine function on Linux operating systems. The most important of which can be exploited to escalate privilege to gain root privileges. Successful exploitation of this vulnerability allows any unprivileged user to gain root privileges on the vulnerable host. Qualys security researchers have been able to independently verify the vulnerability, develop an exploit, and obtain full root privileges on default installations of Ubuntu. The Qualys Research Team confirmed the vulnerability. Then it engaged in responsible vulnerability disclosure and coordinated with both vendor and open-source distributions in announcing this newly discovered flaw. Snap is a software packaging and deployment system used in Linux distributions. Its packages make it easy to install applications with all their dependencies included to run on all major Linux distributions. Snap has become reasonably widespread in the Linux world with a number of major vendors distributing packages using it. While any exploit that can give root access is problematic, being a local exploit reduces the risk somewhat, noted Mike Parkin, engineer at Vulcan Cyber. o § Civil Rights/Policing⠀➾ # ⚓ Privileged_Conversations:_March_2022_–_Public_Knowledge⠀⇛ Public Knowledge has the pleasure of hosting a multifaceted program focused on training and developing the next generation of tech policy experts and public interest advocates that reflects the diversity of voices and experiences in our society. Our monthly Career Breakfast Series is designed for students & recent graduates to learn about tech policy and public interest work, careers, and its community. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Upgrading_my_home_internet;_a_story_of_yak_shaving⠀⇛ When I migrated my home connection to FTTP I kept the same 80M/20M profile I’d had on FTTC. I didn’t have a pressing need for faster, and I saved money because I was no longer paying for the phone line portion. I wanted more, but at the time I think the only option was for a 160M/30M profile instead and I didn’t need it and it wasn’t enough better to convince me. Time passed and BT rolled out their GigE (really 900M) download option. And again, I didn’t need it, but I wanted it. My provider, Aquiss, initially didn’t offer this (I think they had up to 330M download options available by this point). So I stayed on 80M/20M. And the only time I really wanted it to be faster was when pushing off-site backups to rsync.net. Of course, we’ve had the pandemic, and that’s involved 2 adults working from home with plenty of video calls throughout the day. The 80M/20M connection has proved rock solid for this, so again, I didn’t feel an upgrade was justified. We got a 4K capable TV last year and while the bandwidth usage for 4K streaming is noticeably higher, again the connection can handle it no problem. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ Ancillary_Copyright_Graphic_–_Public_Knowledge⠀⇛ Ancillary copyright is a huge threat to people’s ability to freely share information on the internet, and it’s currently a concern in the Journalism Competition & Preservation Act. Check out this infographic slideshow to see why it’s a problem and what we can do to stop it. Then, read PublicKnowledge.org/ JCPACopyright for a deeper look. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 8373 ➮ Generation completed at 02:41, i.e. 61 seconds to (re)generate ⟲