𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Sunday, January 16, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Mon 17 Jan 02:42:24 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/2022/01/16/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmUnmYrNuwB9WxrYeqcbFyf8Bew66hMkdU1YVc9WsKh4JC QmYjUQnBiQsqQMypkyvfTj7b9arksYuzUe1BzJ9a6JUTk4 QmarLrYBMcbMFgab1qAkPGRjRr57niwUpd5PEPbMp8225S QmYYUiUwcwdiuMNs9EXu5Ci3ELNhZcY4b7JsFUZqp7drnc QmTWhb5PucmgsMLVAJufczuFnxY37RcgjXGMTczMdhndPd QmVgY18p35Thp6aWh7cRUuoocqLYGYFW2QnLEJhuqn69Kw QmcN2LseMFZtt5HtSJMT5h9HDZa4ZNy6B7uWe7gK8fPeF9 QmfH2by4K6HCiZyvyGQ1L5syH6ZSfcHH12ph6TDo82aovk QmbfkzNgEcSLWg1uktyXVKRqXdn8cURLS2BGZZ8j7BRu53 QmYyjvuyCsmKepqGvikeVazrauZqV2sNgUg5p2UhdxvGXe QmeizGYhw45pUpaYcuwBfE8NWgRhpFbkNtg8fZ7tGbAMXw QmfKHqGowjRxdQqskGCLaTJvfCGFi19QHkyd8kwa9PMJ21 QmP9Us6BzAW1DtJJVXeJt8AyhFyfNcNAfWtLTvSMzp6Ltp QmRocUr84sVRrmmhApYkrairZ9gM3urZnz5pkw4h6pxA9b QmQ1r9n2zgVqwtQ4bsQLNP2kbfnhn22xRMWVDD5qUuwkKF QmU5vYfwSWKbwcf52ai4QQxmeVvq2qk4Rno1afMvVcdEUm QmSRxd1L1Tjg5YFR28UqaVozsZZh3xMVhvDKvnfHxuctNe QmUYb6AJaHEaYvQGdw1Z8bffPkohvdveAhmoUhNFHe4PB6 QmRXpMsysY15jnTdXabNj8RQWyYQoA287zCaWvJJjNWzB2 QmaSCmshgLNtetvtehrJTkVzA4UKVtdrEf2DcHz8b5gBoV QmZWJhSMSsSbuTS3JfxxEo3tfs2QfTCENeVipKSaQVU5b2 ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ [Meme] Gemini Space (or Geminispace): From 441 Working Capsules to 1,600 Working Capsules in Just 12 Months | Techrights ⦿ [Meme] European Patent Office Space | Techrights ⦿ IRC Proceedings: Saturday, January 15, 2022 | Techrights ⦿ EPO’s Web Site Constantly Spammed by Lies About Privacy While EPO Breaks the Law and Outsources Data to the United States | Techrights ⦿ Gemini Rings (Like Webrings) and Shared Spaces in Geminspace | Techrights ⦿ The Corporate Cabal (and Spy Agencies-Enabled Monopolies) Engages in Raiding of the Free Software Community and Hacker Culture | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/01/16/1600-working-gemini-capsules/#comments http://techrights.org/2022/01/16/epo-data-meme/#comments http://techrights.org/2022/01/16/irc-log-150122/#comments http://techrights.org/2022/01/16/just-enough-privacy-lies/#comments http://techrights.org/2022/01/16/shared-spaces-in-geminspace/#comments http://techrights.org/2022/01/16/stealing-hacker-culture/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/01/16/librest-0-9-0/#comments http://techrights.org/2022/01/16/mumble-1-4-released/#comments http://techrights.org/2022/01/16/tsunami-and-patents/#comments ䷩ 𝚕𝚒𝚗𝚎 64 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/16/1600-working-gemini-capsules/#comments Gemini version at gemini://gemini.techrights.org/2022/01/16/1600-working-gemini-capsules/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Gemini_Space_(or_Geminispace):_From_441_Working_Capsules_to_1,600 Working_Capsules_in_Just_12_Months⠀✐ Posted in Free/Libre_Software at 6:58 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gemini_capsules⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇1600_working_Gemini_capsules⦈_ Summary: Gemini space now boasts 1,600 working capsules, a massive_growth compared_to_last_January, as we noted_the_other_day (1,600 is now official) ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⠟⣿⡏⠋⠻⣿⢛⡿⠛⣻⣿⣿⠋⣿⢭⣟⠛⢿⣻⠟⠙⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠛⣎⣿⡇⣿⣛⣛⣛⣻⣿⣍⢿⠟⠋⡟⠽⢻⢿⢛⢿⡛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣯⣙⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⠛⠿⠿⡿⣿⡿⠿⡿⣻⠿⡿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠛⠋⠙⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⣿⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣷⢴⣷⣶⣶⣾⣶⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠃⠈⠀⠉⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣟⢭⣢⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣮⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠛⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣒⢐⣛⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⢏⢪⣽⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⣴⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⣿⣿⣷⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣑⣿⣿⣿⠿⢉⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣭⢨⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣵⣿⣿⣳⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠒⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⣿⣿⣿⠩⣡⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠙⣻⣷⣥⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣀⣤⣶⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣒⣿⣿⣿⣿⡻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡀⠴⠾⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣯⢘⣴⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣠⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠿⠛⠋⠁⣠⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠝⣿⡇⣿⣿⡏⠁⠀⣀⣠⣤⣬⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⣸⣾⣿⡇⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣛⢐⣿⡆⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ 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⣷⣶⣿⣦⣤⣤⣤⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠲⡆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣾⡇⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⢆⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠈⠃⠀⠀⠤⠀⠀⠀⠘⠀⠀⠀⠀⠰⣳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⢦⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣷⣶⣤⡈⡇⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⣿⡿⠋⠙⠻⠟⠛⢻⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣽⣿⣿⣧⣿⣿⣿⣼⣿⡟⣿⣿⣇⣿⣿⣼⣿⡿⠀⢠⣾⣿⣿⣿⣆⣿⣿⢿⣿⣆⣾⣿⣿⡇⣠⣾⣿⣿⣿⣆⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣾⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢰⣿⣿⣧⢤⣿⣿⣿⣿⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣯⣿⣿⠃⠀⢸⣿⣷⣯⡉⣹⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⡷⠿⠿⣻⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣷⡀⠘⠋⣹⣿⣿⡿⠀⠀⠀⠀⣾⣿⡟⠛⣼⣿⣿⣿⣿⣿⡿⣼⣿⡟⣾⣿⣿⣿⣿⣸⣿⡿⠠⢠⣤⣽⣿⣿⣇⣿⣿⣟⣿⣹⣿⣿⣿⣿⢹⣿⣿⣶⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣷⣾⣿⣿⠟⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣿⣿⢻⣿⡟⣿⣿⣇⣿⣿⠇⣖⠸⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⢻⣿⣿⢻⣿⣷⣿⠿⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠄⠀⠀⢻⣷⣤⣭⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⣀⣤⣤⣤⣤⣾⣿⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣶⣿⣷⣶⣶⡶⣟⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⢀⠒⢠⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⡿⠇⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡯⣀⣍⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡪⢼⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢛⡉⢻⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣤⠮⢊⢯⡾⡾⣯⠿⠟⠝⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡋⢙⣢⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣛⡙⠱⢟⠽⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⠀⠁⠀⣟⠑⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣥⣽⣦⣿⣿⡁⠚⠚⠁⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠫⠝⠉⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠁⠀⣀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⣶⡾⣧⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⡤⠤ ⣷⣷⣿⣶⣶⣩⣵⣴⣇⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢰⡀⢢⣤⢗⢆⣿⡇⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣒⡂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣘⣶⡇⠀⢨⢼⡾⡛⣥⢤⣉⡹⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠘⣶⣥⠴⠂⠀⢀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⢦⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣷⣶⣤⡈⡇⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣿⡿⠋⠙⠻⠟⠛⢻⠇⠀⠀⠀⠀⠀⣼⣿⣿⡿⣼⣿⣿⣧⣿⣿⡿⣼⣿⡟⣿⣿⣇⣿⣿⣸⣿⡟⠀⢠⣾⣿⣿⣿⣆⣿⣿⢿⣿⣆⣾⣿⣿⡇⢠⣾⡿⣿⣿⣆⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣾⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢠⣿⣿⣥⢄⣿⣿⣿⣿⣿⣿⢧⣿⣿⢳⣿⣿⣿⣿⣇⣿⣿⠃⠀⢸⣿⣷⣯⡉⢹⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⠧⠿⠿⣹⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠘⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡟⠛⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠀⢠⣤⣽⣿⣿⡇⣿⣿⣟⣿⣱⣿⣿⣿⣿⢸⣿⡿⣴⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⢧⣿⣿⢳⣿⡟⣿⣿⣇⣿⣿⠇⣤⠸⣿⣿⣿⣿⣹⣿⣿⣿⣷⣿⣿⢻⣿⣿⢻⣿⣷⣿⠟⣹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⢻⣷⣤⣭⡿⠛⠋⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣤⣤⣤⠄⢠⣤⣴⣾⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣴⣾⣶⣶⣦⣴⠆⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠒⢠⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡻⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣧⣐⠪⠇⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠘⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⠈⠉⣯⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⡿⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⡿⣿⡿⠋⠙⠻⠟⠛⢻⠇⠀⠀⠤⠀⠀⣼⣿⣿⣿⣼⣿⣿⣧⣿⣿⣿⣼⣿⡟⣿⣿⣇⣿⣿⣼⣿⡿⠀⢠⣾⣿⣿⣿⣆⣿⣿⢿⣿⣆⣾⣿⣿⡇⣠⣾⡿⣿⣿⣆⣿⣿⣿⡟⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣾⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢠⣿⣿⣧⢄⣿⣿⣿⣿⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣧⣿⣿⠃⡀⢸⣿⣷⣯⡉⣹⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⠧⠿⠿⣹⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠘⠋⣹⣿⣿⡟⠀⠀⠀⠀⣾⣿⡟⠛⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⢸⢣⣤⣽⣿⣿⡇⣿⣿⣿⣿⣱⣿⣿⣿⣿⢸⣿⣿⣶⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣷⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣧⣿⣿⢳⣿⡟⣿⣿⣇⣿⣿⢇⣾⡸⣿⣿⣿⣿⣹⣿⣿⣿⣷⣿⣿⣻⣿⣿⢻⣿⣷⣿⠟⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⢻⣷⣤⣭⡿⠛⠋⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⣤⣤⣠⣤⣀⣤⣴⣶⣶⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣶⣶⣼⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠒⢠⠄⠀⠀⣀⠀⠿⢮⡆⠀⠀⠀⠀⠀⠀⠀⠀⣨⣃⣚⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣝⡻⠇⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠆⠄⠛⠴⠀⠀⠀⠁⠀⠂⡀⠀⠀⠀⠀⠀⢒⢳⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣶⡖⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⣙⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠢⠄⠀⠀⡀⠰⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣛⡹⠿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣟⠉⢻⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣰⢾⣿⡯⣝⣫⡟⢻⣯⣿⣿⣿⣿⣿⠿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⡋⢡⣤⠀⢀⠀⠀⠀⠀⠀⠶⠄⠀⠁ ⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠇⠀⠠⠄⣾⣽⣿⣿⣿⣿⢿⣿⣙⣢⣬⣙⣋⣶⢆⡝⢻⠻⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣷⣾⠀⠁⠀⣿⠐⠛⠀⠀⠀⠀⠁⢀⠀⠀⠀ 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⠀⠀⠀⢠⡀⠀⠀⠁⠀⣤⠀⠀⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉ ⣴⣾⡆⢀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣶⣄⡠⣤⣢ ⣿⣿⣾⣷⣿⣶⣶⢔⠒⠉⣢⣤⣤⣄⣠⣄⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⣀⡲⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⢿⣿⣿⣿⣿⣿⣖⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣶⡇⠀⠠⢚⠂⠰⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠤⠀⠀⠀⠸⠀⠀⠀⠀⠰⣶⣌⠋⠁⠈⢈⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡇⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠃⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⣧⣿⣿⡟⣼⣿⡏⣾⣿⣇⣿⡿⣸⣿⡟⠀⢀⣾⣿⣿⣿⡆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⣆⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣾⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢠⣿⣿⣥⢄⣿⣿⣿⣿⣿⣿⢇⣿⣿⢳⣿⣿⣿⣿⣇⣿⣿⠃⡀⢸⣿⣷⣭⡉⢸⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡟⠛⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠠⢡⣤⣽⢿⣿⡇⣿⣿⣻⣿⢱⣿⣿⣿⣿⢸⣿⡿⣴⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⣿⣾⣿⣿⣿⢧⣿⣿⢱⣿⡟⣿⣿⣇⣿⣿⠃⣦⠸⣿⣿⣿⣿⣹⣿⣿⣿⣷⣿⣿⢻⣿⣿⢻⣿⣷⣿⠟⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⢹⣷⣤⣭⡽⠛⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣠⣤⣤⣴⣤⣶⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣿⣷⣶⣶⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠒⢠⠀⠀⠀⣀⠀⠛⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⣻⣓⣻⠇⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠚⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢄⣈⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠢⠄⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡏⣷⣿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣟⠛⠉⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣶⣰⣛⣛⣹⠭⢙⠿⡿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⠻⢷⣿⠋⠣⣤⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢛⡃⢐⠹⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠿⠿⣷⣾⠁⠀⠀⣿⠐⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⠓⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣿⣏⡆⠲⠞⠁⠀⠀⠀⠀⠀⠀⡃⠈⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣾⣿⣿⡯⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠁⠀⣀ ⠀⠀⠀⢀⠀⠀⠀⠁⠀⣄⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠉ ⣶⣼⡆⢀⣀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣴⣄⣶⣶⡄⡒ ⣿⣿⣿⣷⣶⣩⣫⣶⣦⣤⣆⣰⣦⣆⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠔⣦⣶⣾⣾⣿⣻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣶⡇⠀⠀⣾⣮⣭⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⠰⣷⣭⠚⠂⠉⢀⡚ ⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠁⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⢦⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡇⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠇⠀⠀⠀⠀⠀⣼⣿⣿⡿⣼⣿⣿⣧⣿⣿⡿⣼⣿⡟⣾⣿⣇⣿⣿⣸⣿⡟⠀⢠⣾⣿⣿⣿⣆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⣆⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢠⣿⣿⣥⢄⣿⣿⣿⣿⣿⣿⢧⣿⣿⢳⣿⣿⣿⣿⣇⣿⣿⠃⡀⢸⣿⣷⣭⡉⢹⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⠧⠿⠿⢹⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠘⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡟⠛⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⢸⢡⣤⣽⢿⣿⡇⣿⣿⣿⣿⣱⣿⣿⣿⣿⢸⣿⡿⣴⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣧⣿⣿⣾⣿⣿⣿⢧⣿⣿⢳⣿⡟⣿⣿⣇⣿⣿⢃⣮⡸⣿⣿⣿⣿⣹⣿⣿⣿⣷⣿⣿⣻⣿⣿⢻⣿⣷⣿⠟⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⢹⣷⣤⣭⡽⠛⠉⠁⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣤⣴⣶⣤⣴⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣿⣷⣶⣶⣾⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠒⣠⠤⠀⠀⣀⠀⠛⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⠀⠀⠀⠀⠀⠀⠀⡀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⡂⢌⠐⠄⠉⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠠⠀⠀⠉⠛⠏⠘⠃⠈⣵⣿⣿⣿⠟⠛⠻⢛ ⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⢦⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡇⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠃⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⣧⣿⣿⡟⣼⣿⡟⣾⣿⣇⣿⣿⣸⣿⡟⠀⢀⣾⣿⣿⣿⡆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⣆⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢠⣿⣿⣥⢄⣿⣿⣿⣿⣿⣿⢇⣿⣿⢳⣿⣿⣿⣿⣇⣿⣿⠃⡄⢸⣿⣷⣭⡉⢹⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠘⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡟⠛⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⢰⢡⣤⣽⢿⣿⡇⣿⣿⣿⣿⢱⣿⣿⣿⣿⢸⣿⡿⣴⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣧⣿⣿⣾⣿⣿⣿⢧⣿⣿⢱⣿⡟⣿⣿⣇⣿⣿⢃⣾⡸⣿⣿⣿⣿⣹⣿⣿⣿⣷⣿⣿⣻⣿⣿⢻⣿⣷⣿⠟⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⢹⣷⣤⣭⡿⠛⠋⠁⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⣤⣴⣴⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣿⣷⣶⣶⣾⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠈⠉⠁⠀⢀⠒⣠⠤⠀⠀⣀⠀⠟⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣇⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠛⠦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠈⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢧⣿⣿⡟⣼⣿⡏⣾⣿⡇⣿⡿⣸⣿⡟⠀⢀⣾⣿⣿⣿⡆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢠⣿⣿⣥⢄⣿⣿⣿⣿⣿⣿⢇⣿⣿⢳⣿⣿⣿⣿⣇⣿⣿⠃⡀⢸⣿⣷⣭⡉⢸⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡟⠋⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⢠⢫⣤⣽⢿⣿⡇⣿⣿⣻⣿⢱⣿⣯⣿⣿⢸⣿⡟⣴⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⣿⣾⣿⣽⣿⢧⣿⣿⢡⣿⡏⣿⣿⣇⣿⣿⢁⣿⡸⣿⣿⣿⣿⣹⣿⣿⣿⣷⣿⣿⣻⣿⣿⠻⣿⣷⣿⠟⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⢹⣷⣤⣭⡽⠛⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣤⣤⣠⣤⣤⣴⣤⣶⣾⣿⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣿⣷⣶⣶⣾⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠈⠉⠁⠀⣀⠒⣠⡤⠀⠀⣀⠀⠟⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠘⠶⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡖⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣅⣍⣴⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠢⠄⠀⠀⡀⠰⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣻⠉⢻⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣶⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣋⢹⣶⡄⠠⠀⠀⠀⠀⡀⠶⠄⠀⠁ ⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⢂⠴⡦⠜⣾⣿⣿⣿⣿⣿⣿⣿⣻⣏⠏⠿⠙⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⠈⡀⢠⣿⠔⠛⠀⠀⠀⠀⠁⢀⠀⠀⡀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠹⠻⠯⢚⢟⣿⣿⣿⣿⣿⣿⢼⡒⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢉⣽⣶⣿⣿⡇⠹⠞⠁⠀⠀⠀⠀⠀⠀⡃⠈⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⠀⠀⡀⠁⠈⠈⠃⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⠍⠋⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠁⠀⣀ ⣠⣀⡐⣠⡄⠀⠀⠡⢀⣤⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠐⠀⡤⠄⡀⠀⣀⣃⡀⣀⢷⣤⡬⡭ ⣿⣿⣷⣿⣶⡦⣀⣄⡠⠛⡄⣀⣀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠠⢔⡀⣮⡅⣦⡌⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠕⢩⢶⣿⣿⣯⣾⣿⣿⣾⣾⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣧⣧⣾⣪⣶⣡⢶⡾⣻⢦⡀⢝⣷⣿⣗⣄⢾⣶⢖⠀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⣀⣬⣢⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⣷⣳⣶⡚⣛⠫⠑⣩⡝⠃⠛⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣯⣍⡞⠦⣍⣉⠉⠁⠂⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠤⠀⠀⠌⠻⠿⠩⠵⣿⡷⣿⣾⣿⣿⣻⣿⡿ ⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠁⠀⢀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢧⣿⣿⡟⣼⣿⡏⣾⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢳⣿⣿⣿⣿⣇⣿⣿⠃⠀⢸⣿⣷⣭⡉⢸⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡟⠋⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⢰⢣⣤⣽⢿⣿⡇⣿⣿⣻⣿⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⣿⣾⣿⣼⣿⢧⣿⣿⢡⣿⡏⣿⣿⣇⣿⣿⢁⣿⡸⣿⣿⣿⣿⣹⣿⣟⣿⣿⣿⣿⣻⣿⣿⢻⣿⣷⣿⠟⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⢹⣷⣤⣭⡽⠛⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣄⣤⣄⣤⣤⣶⣴⣶⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣿⣷⣶⣶⣾⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠈⠉⠀⠀⢀⠒⣠⠄⠀⠀⣀⠠⠛⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣇⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠘⠦⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢁⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⢈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣌⣍⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠢⠄⠀⠀⡀⠰⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢥⢽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⠉⠻⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⢶⣕⠧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣋⣡⣤⡀⢠⠀⠀⠀⠀⡀⠶⠆⠀⠁ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠂⠐⡞⢿⣿⡯⣻⣿⣿⣿⣿⣿⡅⣿⠉⠉⠃⠑⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣶⣾⠈⠀⢠⣿⠔⠛⠀⠀⠀⠀⠁⢀⠀⠀⡀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠊⠹⠿⠧⡠⠟⣿⡿⡿⣿⣞⡏⡠⠀⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣬⣴⣿⣿⡆⠻⠚⠁⠀⠀⠀⠀⠀⠀⡃⠈⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣬⠭⠍⠉⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠁⠀⣀ ⣤⡤⠤⣠⡀⠀⠀⠡⠀⣤⠀⠀⠂⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘⠀⠄⠄⠀⠀⣀⠃⠀⠤⣰⣰⢄⣩ ⣿⣿⣟⣵⣖⡆⣠⡀⡀⠃⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⢠⣠⣤⣔⡴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡸⢶⣺⣢⣜⣿⣶⣵⣽⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣾⣿⣾⣶⣾⣥⣾⣶⡕⣤⠰⢦⣶⣽⡯⡟⣟⣶⡋⠄⣢⣲⡦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⣠⣴⢐⡶⣴⣹⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡽⣏⣽⢎⢭⡯⡀⠈⠂⣀⠉⠠⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣧⣫⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣧⣖⠿⡬⠆⠀⠏⠀⠐⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠤⠀⠀⠐⠻⡰⠁⠴⠉⣕⣶⣟⠻⢻⠛⢿⡿ ⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠁⠀⢀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢧⣿⣿⡟⣼⣿⡏⣾⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢳⣿⣿⣿⣿⣇⣿⣿⠃⡀⢸⣿⣷⣭⡉⢸⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡟⠋⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠰⢡⣤⣽⢿⣿⡇⣿⣿⣻⣿⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⣿⣾⣿⣼⣿⢧⣿⣿⢡⣿⡏⣿⣿⣇⣿⣿⢁⣶⡸⣿⣿⣿⣿⣹⣿⣟⣿⣷⣿⣿⣻⣿⣿⢻⣿⣷⣿⠟⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⠹⣷⣤⣭⡽⠛⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣤⣀⣤⣤⣤⣤⣴⣤⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣿⣷⣶⣶⣼⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠈⠉⠁⠀⢀⠒⣠⠄⠀⠀⣀⠠⠛⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⣇⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠘⠦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⢈⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⣍⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠢⠀⠀⠀⡀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⣯⡻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠉⠻⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⢶⢳⣩⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣋⢡⣤⠀⢠⠀⠀⠀⠀⡀⠶⠆⠀⠁ ⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠆⠁⣷⢷⣼⣿⣾⣿⣿⣿⣿⣿⡏⡟⠉⠈⠁⠉⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⠈⠀⢠⣿⠐⠛⠀⠀⠀⠀⠁⢀⠀⠀⡀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠙⠿⡇⢘⢞⢿⡿⢿⣿⣟⠏⢀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣬⣬⣿⣿⡆⠻⠚⠁⠀⠀⠀⠀⠀⠀⡃⠈⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠑⠙⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠭⠍⠉⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠁⠀⣀ ⣄⡄⠄⣠⡀⠀⠀⠱⠀⣤⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⠀⠀⠄⠀⠀⢀⢃⠀⢐⣶⣤⢩⣉ ⣿⣿⣿⣷⣶⣆⣀⣄⡀⢃⠀⠀⣀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⣔⣠⡅⣦⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⠵⣪⣬⣦⣽⣥⣯⣿⣭ ⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣿⣽⣿⣿⣿⣾⣷⣢⣢⣤⣀⣆⣐⣑⣻⡻⣿⣿⣖⢏⠊⡦⢖⡐⠀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⣀⡤⡀⡰⣪⢟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣝⣿⡝⣻⡭⠷⠛⠅⠜⣘⠙⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡻⣭⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣷⣯⡯⢍⠇⡈⠌⠑⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠤⠀⠀⠐⠻⠒⠈⠛⠍⠵⣿⣿⣿⡻⠉⢝⡿ ⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠁⠀⢀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢧⣿⣿⡟⣼⣿⡏⣾⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢳⣿⣿⣿⣿⣇⣿⣿⠃⡄⢸⣿⣷⣭⡉⢸⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡟⠋⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⢰⢡⣤⣽⢿⣿⡇⣿⣿⣻⣿⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⣿⣾⣿⣼⣿⢧⣿⣿⢡⣿⡏⣿⣿⣇⣿⣿⢁⣶⡸⣿⣿⣿⣿⣹⣿⣟⣿⣷⣿⣿⣻⣿⣿⢻⣿⣷⣿⠟⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⠹⣷⣤⣭⡽⠛⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣤⣤⣠⣄⣠⣤⣴⣤⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣿⣷⣶⣶⣼⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠈⠉⠀⠀⢀⠒⣠⠄⠀⠀⣀⠠⠻⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣇⠀⠀⠀⠀⠀⠀⠀⡀ 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⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢧⣿⣿⡟⣼⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢱⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣭⡉⢸⣿⣿⣾⣿⣽⣿⣿⣿⡇⣿⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡏⠋⣼⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠀⢠⣤⣽⢿⣿⡇⣿⣿⢻⣏⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⡿⣾⣿⣼⣿⢧⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⣀⠸⣿⣿⣿⡿⣹⣿⡟⣽⣧⣿⣿⢻⣿⣿⠻⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⠹⣷⣤⣭⡽⠛⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⣤⣤⣴⣾⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣴⣿⣷⣶⣦⣴⠖⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠒⢠⠀⠀⠀⣀⠀⠘⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣰⣽⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣗⣁⡲⠇⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣾⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢲⣿⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⠂⢀⣀⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⡛⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣟⡾⠟⢋⠛⠀⠻⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⠀⠀⠁⠀⠀⠀⠋⠙⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣏⠻⢷⠴⠃⠀⡤⠀⠠⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢉⡃⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣟⠛⠻⢶⡌⠀⠀⠀⣟⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⡟⢿⣿⣿⣿⣿⣿⣿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠀⠀⠈⠁⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⡤⠜⢏⡄⠐⠒⠁⠀⠀⠀⠀⠀⠀⡃⠈⠀⠀⠰ ⣿⣷⣶⣿⣿⣿⡿⠏⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣾⠿⣧⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠁⠀⣀ ⢿⣿⡿⢟⠁⠀⠀⠁⠀⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈ ⣄⡰⠆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣯⣧⣤⣠⣤⠀⠀⠀⠀⠀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠊⠲⠇⠀⠀⠀ ⣿⣿⣿⣷⣿⣯⡯⣤⠥⢗⠧⠳⠞⣽⣿⣿⣿⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠰⠆⠀⠀⠘⠀⠀⠀⠀⠱⠂⠠ ⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣏⣷⣾⣇⡦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠘⠀⠀⠀⠀⠐⢲⣄⠛⠁⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢧⣿⣿⡟⣼⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢱⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣽⣿⣿⣿⡇⣿⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣼⣿⡏⠉⣸⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠀⢠⣤⣽⢿⣿⡇⣿⣿⢛⣏⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⡿⣼⣿⣼⣿⢧⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⣀⠸⣿⣿⣿⡿⣹⣿⡟⣼⣧⣿⣿⢻⣿⣿⠺⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⡄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⡠⣤⣤⣴⣿⣷⣴⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣴⣾⣷⣶⣦⡰⠖⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠒⢠⠀⠀⠀⢀⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠹⣂⣀⡲⠇⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣼⠈⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠜⣺⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⢿⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢛⠂⠀⡀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣫⡶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⣛⣷⡶⠟⢉⠉⠀⠻⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣴⡏⠛⢳⠼⠃⠠⡤⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡛⢛⠛⠻⢶⣌⠀⠀⠀⡟⠀⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⢀⡠⠘⠏⡀⠐⠂⠁⠀⠀⠀⠀⠀⠀⡃⠈⠀⠀⠰ ⣿⣿⣿⣶⣦⣽⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣾⢿⣧⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠁⠀⣀ ⣿⠿⣿⣿⣿⡿⠛⠉⠁⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁ ⣭⣱⣄⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣦⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠂ ⣿⣿⣿⣿⣿⣿⣶⣆⡂⠀⠀⠀⠩⣽⣷⣟⣱⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢶⣬⣥⣡⠯⢿⣿⢿⣗⢖⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠐⢢⣄⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢧⣿⣿⡟⣼⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢱⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣽⣿⣿⣿⡇⣾⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠀⢠⣤⣽⢿⣿⡇⣿⣿⢛⡏⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⢀⠸⣿⣷⣿⡿⣹⣿⡟⣸⣧⣿⣿⢻⣿⣿⠺⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣦⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣿⣿⣷⣶⣶⣶⣤⣴⣶⣶⣦⡤⠰⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠐⢠⠀⠀⠀⢀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢏⠹⠁⣀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⢀⣀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⡄⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⢷⡖⠀⠻⠏⢚⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡍⢙⠂⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣠⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢩⠀⠀⠸⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⣉⣆⡴⠟⠉⠉⠀⠹⡦⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣰⡍⠛⠑⠰⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣯⣹⣿⡟⢛⡛⠛⠛⠛⢦⡄⠀⠀⠀⡟⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⣿⣦⣀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⡀⠈⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⣛⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣿⣽⣿⡞⠿⢤⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣭⡛⠂⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⣼⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠠⢠⠄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⢢⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢧⣿⣿⡟⣼⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣽⣿⣿⣿⡇⣾⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⣿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠀⢠⣤⣽⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⡿⣹⣿⡟⣸⣧⣿⣿⢻⣿⣿⠺⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢄⢤⣴⣩⣠⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣿⣿⣶⣶⣶⣶⣤⣤⣶⣶⣤⡤⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠐⢠⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠏⠙⠁⢀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⢀⠀⠀⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⡀⣳⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⣻⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣇⢴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢴⠆⠀⠻⠇⠈⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡅⠙⠂⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢩⠀⠀⢰⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⢿⠇⣀⣆⡴⠞⠉⠁⠀⠹⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣤⣠⡉⠙⠁⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⣿⣿⣦⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣻⣿⡛⢛⠛⠛⠙⠛⢦⡄⠀⠀⠀⡝⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⣿⣿⣿⣶⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠻⠿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣿⣽⣿⡞⠿⢤⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⢟⣛⠫⠍⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣅⣸⣿⣷⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⡿⣹⣿⡟⣸⣧⣿⣿⢻⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣿⣿⣷⣶⣶⣶⣤⣤⣶⣦⣤⠠⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠏⠙⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣦⡀⣱⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⣆⢠⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢱⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⡿⣹⣿⡟⣸⣧⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣶⣶⣤⣤⣶⡦⡤⠤⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠐⢀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠘⠁⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⢀⠀⠀⠈⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡄⣱⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⣇⠠⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢴⠆⠀⠻⠆⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⣥⠇⠘⠂⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢨⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⢿⡅⣀⣂⠰⠞⠁⠁⠀⠙⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⣤⢠⡉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⡟⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⢟⣿⣿⣯⣹⣿⡛⠛⠋⠛⠙⠛⢦⡄⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣦⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡟⠙⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣿⣽⣿⠞⠿⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠝⠛⠛⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣟⣁⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢧⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⡿⣹⣿⡟⣸⣡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣶⡖⡤⣠⣶⡦⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⠲⠌⠄⡉⠃⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡑⠫⠐⠠⣤⡀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡴⣁⢄⠠⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠻⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣉⡻⣥⠀⠘⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤⠋⢹⠿⠄⣀⣂⠠⠚⠁⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡴⣤⢠⡉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⡿⠟⣿⣿⣏⣹⣟⡛⠛⠋⠋⠈⠛⢦⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣷⣶⣿⣿⣿⣧⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐ ⠀⠘⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣿⣽⡿⠒⠷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀ ⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣉⣻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⣿⡿⠟⠛⠛⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣟⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⠿⣹⣿⡟⣸⣡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣶⡖⠤⣠⣶⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⢷⠑⠆⠄⡉⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡂⠃⠂⢠⣤⡀⣠⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣵⡴⢁⢄⠠⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠻⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⡉⠻⣥⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤⠋⢹⠿⠄⣀⣂⠠⠚⠁⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡢⣄⢠⡉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣶⣿⣿⠿⣿⣿⣆⠀⠀⠀⠀⠀⠂⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡿⠿⠟⣿⣿⣏⣹⣟⡛⠛⠉⠉⠈⠛⢦⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣿⣿⣿⣇⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐ ⠀⠀⠀⠀⠸⢿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⢿⣽⡿⠒⠷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠘⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣤⡁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠧⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⠿⣹⣿⡟⣸⣡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⣶⣶⣦⡖⠠⣠⣶⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠷⠀⠀⠄⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠠⣤⡀⣠⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡴⢂⢆⠠⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠻⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣻⣯⢁⠹⣥⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣤⠋⢸⠿⠄⣀⣂⠠⠚⠁⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⡠⣄⢠⡉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⡀⠀⠀⠂⠀⠀⠀⢠⣴⣶⣿⣿⣿⣶⣶⣶⣦⣤⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡿⠿⠟⣿⣿⣇⣹⣟⡛⠛⠉⠁⠈⠛⠦⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣥⣴⣿⣿⣿⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⢿⡿⣩⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⡶⢯⣽⡟⠒⠳⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠔⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⡑⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⠿⣹⣿⡟⣸⣡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⣶⣶⠶⣖⠠⣠⣶⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡓⣻⠹⠀⠄⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⢸⣡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣶⡖⢠⣠⣶⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡐⣺⠁⠤⠄⠉⠃⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⡈⡀⠀⠂⠠⣤⡀⣠⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⡴⣀⢄⠠⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⠿⣹⣿⡟⣸⣡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣦⣖⡠⣠⣶⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣷⠢⠀⠄⠉⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡌⡀⠀⠀⠠⣤⡀⣠⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⢂⢄⠠⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠴⠆⠀⠻⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣯⡉⠹⡥⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⠋⢸⠿⠆⣀⣂⠠⠘⠁⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣉⡦⣤⣠⡈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠿⢟⣿⣿⣏⣹⣭⡛⠛⠋⠉⠈⠛⢢⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠛⢶⣶⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣴⣿⣿⣇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠉⠛⠿⣿⡷⢿⣽⡟⠒⠳⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⣀⣀⣠⣄⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⢿⣿⠿⠿⠛⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣰⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⠿⣹⣿⡟⣸⣡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⡶⣦⡤⡖⠠⣠⣶⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣔⣷⠤⠀⠄⡉⠃⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⡌⠒⠀⠁⠠⣤⡄⣠⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⡴⢈⢄⠠⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠻⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣯⡁⠹⡥⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣤⠋⢸⠿⡆⣀⣂⠰⠘⠁⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣫⣉⡲⣤⣠⡈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠿⠟⣿⣿⣏⣹⣭⡛⠛⠋⠉⠀⠛⢦⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣿⣿⣿⣿⣿⣿⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣃⣽⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣶⣦⣄⣀⠀⠉⠛⠿⢿⡷⢯⣽⡿⠒⠳⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⣀⣀⣀⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣷⣶⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣤⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⣸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⠿⣹⣿⡟⣸⣡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⣶⢶⣦⡖⠠⣠⣶⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⢿⠾⠂⠄⠉⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⡏⡀⠐⠃⠠⣤⡀⣠⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⠴⢀⣄⠠⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠴⠆⠀⠻⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣭⡁⠙⡥⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠋⠹⠿⡆⣀⣂⡰⠚⠁⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣩⡧⣤⣠⡈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡿⠿⠛⣻⣿⣇⣹⣿⡛⠛⠉⠉⠀⠛⢦⡄⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠛⠿⣿⣷⢿⣽⣟⠒⠳⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣾⣿⣯⡀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣽⣯⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⡾⣵⡿⠋⠉⠻⠟⠛⢋⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣼⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢸⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣿⣿⡿⣸⣿⡏⣾⣿⣿⣿⣿⣸⣿⡟⠀⢀⣤⣽⢿⣿⡇⣿⣿⢛⣏⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣾⣿⡿⠟⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⣿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⢇⣿⣿⠁⠀⠸⣿⣷⣿⡿⣹⣿⡟⣸⣥⣿⣿⢻⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣦⣴⣶⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⣷⣶⣶⣖⣤⣤⣶⡦⠤⠠⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠐⢠⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣧⡉⠃⠈⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⢀⠀⠀⠀⢠⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⢿⢛⣠⣤⡄⣰⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣿⣖⡠⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢴⠆⠀⠻⠆⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⢿⣽⢵⠉⠂⠀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢨⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⢻⠿⡆⣀⣒⡰⠚⠁⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣷⣤⣠⡎⠈⠁⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠿⣿⣿⣿⣯⣹⣿⣛⠛⡋⠙⠙⠛⢷⡄⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⠀⠀⠉⠛⠿⣿⣷⣿⣽⣿⠖⠻⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣘⣿⡧⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣦⣤⣤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠐⢠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣶⣤⡈⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣵⡿⠋⠉⠻⠟⠛⢻⠁⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣼⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣴⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣿⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⡇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣹⣿⣿⣿⡇⣾⣿⠧⠿⠿⢸⣿⣿⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⡶⠆⠤⠀⠀⠠⣢⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣯⡀⠀⠵⢶⡀⠀⠀⠀⠀⠤⡀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣛⣰⣿⣿⣿⣶⣶⠳⣤⣤⠤⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡝⠻⠋⣡⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢅⣽⠕⢷⣷⣷⣄⠉⠹⠇⠆⢀⡀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⡿⠧⣿⣶⣷⣿⣽⣢⣀⡀⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠈⠙⣁⣴⣄⣀⣄⠉⠉⠉⠉⠀⠙⠂⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠴⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢟⠷⠦⠄⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⠀⡀⡀⠀⡀⠀⡀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣶⣶⣤⣀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⢀⣀⡀⣀⠀⠀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡾⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣾⣿⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⠛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣷⡄⠀⠀⠀ ⠀⠘⣷⡆⢸⣿⡇⢘⡛⢻⡇⢸⡅⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⠀⡇⢸⡇⢸⡇⠘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣷⠁⢸⣇⠘⠇⢸⡇⢸⡇⢸⠀⢰⠀⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠐⠿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⣿⣷⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⣿⣷⣶⣿⣶⣾⣿⣷⣶⣿⣷⣾⣷⣾⣶⣾⣶⣾⣶⣿⣶⣿⣶⣿⣷⣾⣾⣿⣿⣷⣶⣿⣷⣾⣷⣾⢶⣿⣿⣿⣶⣾⣿⣿⣶⣾⣿⣶⣶⣷⣶⠶⠿⢶⡾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢔⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⢘⢠⣿⣿⢩⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⡦⠦⠤⠀⠀⠠⣢⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣯⣁⠀⠵⢾⡀⠀⠀⠀⠀⠤⡀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣛⣱⣿⣿⣿⣶⣶⡿⣦⣤⠤⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡝⢻⠋⣩⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⢿⠿⢷⣿⣷⣄⠉⠹⠇⠆⢀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣿⡧⣿⣷⣷⣿⣽⣲⣀⡣⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡩⠋⠙⣁⣴⣄⣀⣄⠉⠉⠉⠉⠀⠛⠂⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠴⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠷⠦⠄⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⡀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⠀⣀⠀⠀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡾⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⡿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⠛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣷⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⠘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣷⠁⢸⣇⠘⠇⢸⡇⢸⡇⢸⠀⢰⠀⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⡇⠀⠀⠀ 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⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⣀⣀⠀⠁⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣷⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⢀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠰⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣧⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠐⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⢾⣿⣷⣿⣷⣿⣷⣶⠿⠿⡶⣾⣿⣿⣶⣾⣿⣿⣷⣶⣿⣶⣾⣿⣷⣶⣿⣷⣾⡷⣾⣶⣾⣷⣾⣶⣿⣶⣿⡶⠿⠷⠾⠾⠋⠻⠷⠶⠿⠷⡾⠷⠾⣶⣿⣋⣻⣷⣾⣿⣿⣶⣾⣿⡶⠶⠷⠶⠾⠿⢶⡾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⢸⢠⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⡶⠤⠤⠀⠀⢠⣲⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣉⠀⠵⢶⡆⠀⠀⠀⠀⠤⡀⣠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣛⣵⣿⣿⣿⣷⣶⣿⣦⣤⠤⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠻⠏⣹⣥⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠽⢷⣿⣷⣤⠈⠹⠗⠆⢀⡀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⣷⣷⣿⣽⣺⣀⡃⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡹⠋⠛⣡⣴⣆⣈⣤⠉⠉⠉⠉⠀⠙⠂⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⠷⠦⠥⠛⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⡀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⡿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⣿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠀⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠸⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⣿⣷⠶⣿⣿⣶⠾⣿⣿⣶⣾⣿⣿⣷⣶⣿⣶⣾⣿⣷⣶⣿⣷⣾⣷⣾⣶⢾⣶⣾⣶⣿⣶⣿⣶⣿⠷⠾⠾⠋⠛⠷⠶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⣿⣿⣶⣾⣿⡶⢶⠷⠶⠾⠿⢶⡾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⢸⢠⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⡶⠦⠤⠀⠀⢠⣲⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣁⠀⠵⢶⡆⠀⠀⠀⠀⠤⡄⣠⡾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣛⣳⣿⣿⣿⣿⣾⣿⣦⣤⠤⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠻⠏⣹⣥⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣿⠿⢷⣷⣷⣦⠈⠙⠗⠆⢀⣀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⣷⣿⣿⣽⣺⣠⡃⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡹⠋⠙⣣⣴⣆⣈⣤⡉⠉⠉⠉⠀⠘⠂⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠴⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⠷⠦⠭⠛⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⣀⣀⠀⠀⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣷⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⠸⡇⢸⡇⠘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠨⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠸⢿⡏⠹⠆⣹⡇⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣸⢠⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⡶⠴⠤⠀⠀⢠⣲⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡇⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣁⠠⠵⢶⡆⠀⠀⠀⠀⠤⡄⣠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣱⣿⣿⣿⣷⣶⡿⣦⣤⠤⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠻⠏⣻⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣿⠿⢷⣷⣿⣦⠈⠉⠗⡆⢀⡀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⣷⣷⣿⣽⣺⣅⣃⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡹⠋⠛⣣⣴⣆⣈⣤⡉⠉⠉⠉⠀⠘⠒⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠴⣿⣿⣿⣿⣿⣿⢷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⠷⠦⠭⠟⠒⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣷⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⠘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣧⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠸⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠀⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⣿⣶⣾⣿⣿⠷⠶⣿⣶⣾⣿⣷⣶⣿⣷⣾⣷⣾⣶⣾⣷⣾⣶⣿⣶⣿⣶⡿⣷⣾⣾⣿⣿⣷⡶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⠟⠿⠶⠾⠿⠶⠶⠷⠶⣾⣿⣶⣾⣿⣅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⠀⢀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⠀⡀⣀⣀⣀⡀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⣀⣀⠀⢀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣿⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣷⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⠘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⠶⠾⠿⠿⠶⢾⣿⣿⣷⣶⡿⠶⢾⣿⣷⣶⣿⣷⣾⣷⣾⣶⣾⣷⣾⣶⣿⣶⣿⣶⣿⣷⣾⢾⣿⣿⣷⣶⣿⠷⡾⠷⠾⠶⠟⠋⠻⠷⠾⠟⠿⠶⠾⠿⠶⠶⠷⠶⠾⠿⢶⣾⣿⣁⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠏⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⢸⢠⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⡶⠶⠤⠀⠀⢠⣲⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣇⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠨⠱⢶⡆⠀⠀⠀⠀⠤⡄⣠⡾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣷⣷⡿⣦⣤⡤⠀⠀⡀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⠏⣹⣽⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⢾⡽⢷⣷⣿⣤⠈⠉⠇⠆⢀⡀⡀⠐⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⣷⣷⣿⣽⣺⣤⣇⢦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡉⠋⠛⢣⣴⣦⣀⣦⡉⠉⠉⠉⠀⠙⠓⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠴⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⠷⠶⠭⠛⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⣀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠁⣀⣀⠀⢀⣀⣀⡀⣀⠀⠀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⣿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⠀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠳⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠨⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠀⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⣷⣶⣿⣶⣾⠿⢷⣶⣿⣷⣾⣷⣾⣶⣾⣷⣾⣶⣿⣶⣿⣶⣿⣷⣾⣾⣿⢿⣷⣶⣿⣷⡾⠷⠾⠶⠟⠋⠻⠷⠾⠟⠿⠶⠾⠿⠶⠶⠷⠶⠾⠿⢶⡾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠏⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣶⣶⣿⣿⣶⣾⣿⡶⠶⠤⠀⠀⠠⣲⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣇⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠹⢶⡆⠀⠀⠀⠀⠤⡄⣠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣷⣾⡿⣶⣴⠶⠀⠀⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⢻⠏⢹⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⢿⠽⢷⣷⣿⣦⠈⠁⠗⠆⢀⡀⡀⠐⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⣷⣿⣿⣽⣾⣥⣇⢦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡉⠋⠛⢩⣵⣧⣀⣦⡉⠉⠉⠉⠀⠘⠂⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠴⣿⣿⣿⣿⣿⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⡷⠶⠥⠛⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⢀⣀⠀⣀⣀⣀⣀⡀⢀⣀⡀⠀⢀⡀⣀⡀⣀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⣿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠳⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠸⢿⡏⢹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⢾⣿⣷⣶⣿⡷⠾⣷⣾⣶⣾⣷⣾⣶⣿⣶⣿⣶⣿⣷⣾⣾⣿⣿⣷⣶⣿⣷⣾⣷⣾⣶⠟⠋⠻⠷⠾⠟⠿⠶⠾⠿⠶⠶⠷⠶⠾⠿⢶⡾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠏⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢇⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢠⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⡶⠴⠤⠀⠀⢠⣰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣇⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠽⢶⡆⠀⠀⠀⠀⠤⡄⢠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣾⡿⣶⣤⠦⠀⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣸⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣿⣶⣾⣿⡶⠤⠤⠀⠀⢠⣰⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠪⠿⢷⡆⠀⠀⠀⠀⠤⡄⢠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣶⣴⠦⠀⠀⡀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⠟⢙⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣿⠿⢿⣷⣿⣤⡈⠁⠗⠆⢀⡐⠀⠐⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⣷⣿⣿⣽⣿⣅⣇⢦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡹⠋⠛⢩⣵⣧⣀⣦⡉⠉⠉⠉⠀⠙⠃⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⠷⠶⠬⠛⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⢀⣀⠀⣀⠀⣀⣀⠀⢀⣀⣀⣾⣿⣦⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠳⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣧⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⣶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⣷⣾⣷⣾⡷⠾⣶⣿⣶⣿⣶⣿⣷⣾⣾⣿⣿⣷⣶⣿⣷⣾⣷⣾⣶⣿⣿⣿⣷⣾⠿⠿⠶⠾⠿⠶⠶⠷⠶⠾⠿⢶⡾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡏⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣾⣿⣿⣶⣾⣿⡶⠠⠤⠀⠀⠠⣰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠠⠰⢶⡆⠀⠀⠀⠀⠤⡄⢠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣟⣓⣾⣿⣿⣷⢶⡿⣶⣤⠦⠀⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⢻⠏⢙⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⢿⡿⢿⣷⣿⣤⡈⠁⠗⠆⢀⡐⠀⠐⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣽⣷⣿⣿⣿⣾⣄⣃⢦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡉⠋⠛⢩⣵⣦⣀⣦⣉⠉⠉⠉⠀⠘⠓⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⠷⠶⠬⠛⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣾⣿⣿⣧⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠁⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣾⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⠛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡿⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠸⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⣶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⣷⣾⣶⣿⡶⢿⣶⣿⣷⣾⣾⣿⣿⣷⣶⣿⣷⣾⣷⣾⣶⣿⣿⣿⣷⣾⣿⣿⣶⡾⠿⠶⠶⠷⠶⠾⠿⢶⡾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣿⣶⣾⣿⡶⠰⠤⠀⠀⠠⣰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠰⢶⡆⠀⠀⠀⠀⠤⡄⢠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣳⣿⣿⣿⣷⣾⡿⣶⣴⡶⠀⠀⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠺⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⠟⢙⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣿⡿⢿⣷⣿⣦⡈⠁⠗⠆⢀⡐⠀⠐⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢾⣷⣿⣿⣽⣞⣄⣁⢦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⠋⠛⢡⣵⣦⣀⣦⣉⠉⠉⠉⠀⠘⠓⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠷⠶⠭⠛⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⣼⣿⣿⣿⡀⣀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⣀⣀⠀⠀⣀⣀⠀⢀⣀⣀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⡿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⣿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡿⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠸⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠷⠾⣶⣿⣶⣿⣶⢿⣷⣾⣾⣿⣿⣷⣶⣿⣷⣾⣷⣾⣶⣿⣿⣿⣷⣾⣿⣿⣶⣾⣿⠶⠶⠷⠶⠾⠿⢶⡾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢠⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣿⣶⣾⣿⣶⠴⠤⠀⠀⠠⣰⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠬⠹⢶⡆⠀⠀⠀⠀⠤⠄⢀⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣓⣿⣿⣿⣷⣿⡿⣶⣴⡶⠄⠀⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣯⢻⠟⢙⣭⡄⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⢻⡿⢿⣷⣿⡦⡈⠁⠗⠆⢀⡐⠀⠐⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢿⣷⣿⣾⣽⣟⣄⣅⢤⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⠋⠛⢩⣵⣦⣀⣦⡉⠉⠉⠉⠀⠘⠓⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣿⣿⣿⣿⣿⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⠷⠶⠭⠛⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⢀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⠀⡀⣀⣀⣀⠀⣀⣸⣿⣿⣿⣆⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⣿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⠘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠶⠾⠶⠿⣶⣿⣶⣿⣷⣾⣾⣿⣿⣷⣶⣿⣷⣾⣷⣾⣶⣿⣿⣿⣷⣾⣿⣿⣶⣾⣿⣶⡶⠷⠶⠾⠿⢶⡾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣿⣶⣾⣿⣶⠰⠤⠀⠀⠠⣰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠤⠱⢶⡇⠀⠀⠀⠀⠤⡄⢠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣟⣣⣿⣿⣿⣷⣿⡿⣶⣴⡶⠀⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣏⣀⣀⠀⠁⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡿⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣧⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠸⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠷⠾⠷⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠋⠻⠷⠶⠿⠷⡾⠷⣾⣶⣿⣟⣿⣷⣾⣿⣿⣶⣾⣿⣶⣶⣷⣶⣾⣿⣶⣾⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡿⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣿⣶⣾⣿⣶⠰⠤⠀⠀⠠⣰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣫⠠⠸⢶⡇⠀⠀⠀⠀⠤⠄⢀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⣿⣷⣾⡮⣶⣴⡶⠆⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⠟⢙⣭⡄⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣻⡿⢻⣶⣿⡦⡌⠁⠗⠒⢀⣀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢽⣷⣾⣾⣯⣗⣅⣅⠢⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡙⠋⠛⢃⣰⣶⣀⣦⣉⠉⠉⠉⠁⠈⠓⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⡟⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⢀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⣰⣿⣿⣿⣏⡀⠀⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⡿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣷⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣧⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⡇⠀⠀⠀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠶⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠋⠻⠷⠶⠿⠷⡾⠷⠾⠶⢿⣿⣿⣷⣾⢿⣿⣶⣾⣿⣶⣶⣷⣶⣾⣿⣶⣾⣿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢠⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣿⣶⣾⣿⣶⠰⠤⠀⠀⠠⣰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣩⠠⠹⢶⡇⠀⠀⠀⠀⠤⠄⢀⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⣿⣷⣿⡮⣶⣴⡶⠆⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣯⢿⠟⢉⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣻⡿⠿⣶⣿⡦⡌⠁⠗⠒⠀⡀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢽⣷⣿⣾⣯⣗⣅⣅⠠⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡙⠋⠛⢃⣵⣦⣀⣦⣈⠉⠉⠉⠁⠈⠓⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣾⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⣀⣸⣿⣿⣿⣏⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⣇⡀⠀⠀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠶⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠋⠻⠷⠶⠿⠷⡾⠷⠾⠶⠟⠛⠿⢷⣾⢿⣿⣶⣾⣿⣶⣶⣷⣶⣾⣿⣶⣾⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣿⣶⣾⣿⣶⠰⠤⠀⠀⠠⣰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠤⠼⢷⣇⠀⠀⠀⠀⠤⠄⢀⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⡾⣶⣤⡶⠆⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣶⣶⣿⣿⣶⣾⣿⣶⠰⠤⠀⠀⠠⢰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣇⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣭⠤⠰⢶⣇⠀⠀⠀⠀⠤⠄⢀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣳⣾⣿⣿⣷⣿⡺⣶⣶⡶⠄⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⢿⠟⢙⣭⣄⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣺⡿⢻⣶⣿⡦⡌⠁⠗⠒⢀⣀⠄⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢼⣿⣿⣾⣮⣗⣅⣅⠠⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⠛⠛⢣⣵⣦⣀⣦⣈⠉⠉⠉⠁⠈⢓⣤⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⠿⠂⠀⠀⢠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡷⠶⠤⠛⠒⠒⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣿⣿⣿⣿⣇⣀⣀⠀⠀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⣿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⣇⣀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣧⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⣿⣿⣿⣶ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠷⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠛⠻⠷⠶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⠟⠿⠶⠾⠿⢶⣶⢷⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢔⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣶⣶⣿⣿⣶⣶⣿⣶⠰⠤⠄⠀⠠⣰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⠄⠰⢶⣇⠀⠀⠀⠀⠤⠄⢀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⡪⢶⢴⡶⠆⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣯⢻⠟⢉⣭⡄⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣺⡟⢳⣶⣿⡦⡌⠁⠟⠒⠀⣀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢼⣷⣿⣾⣮⣗⣅⣁⠠⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡙⠋⠛⢓⣰⣦⣀⣦⣈⠉⠉⠉⠁⠈⠓⠀⠀⠀⣠⣴⣤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡗⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡷⠶⠤⠛⠒⠒⠀⠀⠀⠀⣰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣴⣿⣿⣿⣿⣇⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⠛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⣿⣿⣶⣤ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⣿⣿⣿⣿ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠶⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠋⠻⠷⠶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⠿⠿⠶⠾⠿⠶⠶⠷⠶⠾⢿⣶⣾⣿⢏⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣿⣶⠰⠤⠄⠀⠠⢰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡠⠸⢷⣧⠀⠀⠀⠀⠤⠄⢀⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣣⣾⣿⣿⣷⣿⡪⣷⢶⡶⠆⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣯⢿⠟⢉⣯⣄⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣻⡿⢻⣶⣿⡦⡌⠁⠟⠒⠀⣀⠄⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢽⣷⣾⣾⣮⣗⣅⣁⠢⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡹⠙⠛⢃⣱⣦⣀⣢⣉⠉⠉⠉⠁⠈⠓⠀⠀⠀⠀⠀⣠⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⡷⠶⠤⠛⠒⠒⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⣀⣀⠀⠀⣀⣀⠀⢀⣀⣀⣾⣿⣿⣿⣿⣇⣀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⣦⣄⣀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⣿⣿⣿⣿ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣧⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⣿⣿⣿⣿ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠷⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠋⠻⠷⠶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⠿⢿⣶⣾⠿⠶⠶⠷⠶⠾⠿⢶⣾⣿⢻⡿⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢔⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢠⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣿⣶⠰⠤⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠰⢶⣇⠀⠀⠀⠀⠤⠄⢀⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣓⣾⣿⣿⣷⣿⡪⣶⢶⡶⠄⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣯⢛⠟⢉⣭⣄⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⣺⡿⢳⣶⣿⡦⡌⠁⠟⠒⠀⣀⠄⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢼⣷⣾⣾⣮⣗⣅⣁⠠⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡉⠋⠛⢃⣱⣦⣀⣦⡈⠉⠉⠉⠁⠈⠓⠀⠀⠀⠀⠀⠀⠃⣴⣾⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡏⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡷⠶⠤⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣁⣀⣀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⣿⣷⣦⣤ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⣿⣿⣿⣿ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⣿⣿⣿⣿ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠶⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠋⠛⠷⠶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⠟⠿⣶⣾⣿⣶⣶⣷⠶⠾⠿⢶⡾⠿⣷⡟⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢔⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣿⣶⠰⠤⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠰⢶⣇⠀⠀⠀⠀⠤⠄⢀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣓⣾⣿⣿⣷⢿⡪⣶⢶⡶⠄⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡏⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣶⣶⣿⣷⣶⣶⣿⣶⠰⠤⠄⠀⠀⢰⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢭⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣧⡀⠸⢿⣇⠀⠀⠀⠀⠴⠄⢀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣣⣾⣿⣿⣿⣿⣯⢶⢶⡶⠆⠀⡀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢟⠟⢉⣮⣅⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣺⡿⠻⣶⣿⡦⡌⠁⠟⠲⠀⣀⠄⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⢽⣿⣾⣾⣯⣗⣏⣑⠠⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡉⠉⠙⢃⣵⣦⣀⣠⣈⠉⠉⠉⠁⠈⠓⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡷⠶⠤⠛⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⢀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⠀⡀⠀⡀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⡀⣀⠀⢀⣀⡀⢀⣠⣾⣿⣿⣿⣿⡿ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⣿⣿⢿⣤ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⠘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡟⠁⢲⣿ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠸⢿⡏⠹⠆⣹⣇⠀⠀⠈ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠶⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠋⠻⠷⠶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⠟⠿⠶⠾⠿⠶⠶⣷⣶⣾⣿⣶⣾⣿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢔⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡋⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣘⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣷⣶⣶⣿⣶⠰⠤⠄⠀⠀⢰⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⡁⠸⢿⣇⠀⠀⠀⠀⠰⠄⢀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣣⣾⣿⣿⣿⢿⣯⣶⢶⡶⠆⠀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣻⣿⢟⠟⢉⣮⣅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣺⡿⠳⣶⣿⡦⡌⠁⠟⠲⠀⣀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⢽⣷⣾⣾⣮⣗⣇⣵⠠⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡩⠉⠙⢋⣵⣦⣀⣠⣈⠉⠉⠉⠁⠈⠓⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣴⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠷⠶⠤⠙⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿ ⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⡀⣀⡀⣀⠀⠀⣀⡀⢀⣀⣀⣼⣿⣿⣿⣿ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⣿⣿⣿⡿ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⠘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠉⠈ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣇⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠐⢿⡏⠹⠆⣹⣧⣤⣄⡀ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠶⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠋⠛⠷⠶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⠟⠿⠶⠾⠿⠶⠶⠷⢶⣶⣿⣶⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢔⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠋⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡏⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡏⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣸⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣶⣶⣿⣷⣶⣶⣿⣶⠰⠤⠄⠀⠀⢰⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢯⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡅⠸⢷⣇⠀⠀⠀⠀⠰⠤⢀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣟⣧⣾⣿⣿⣿⣿⣯⢶⢶⡶⠆⠀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢟⠟⢉⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣺⡿⠳⣶⣿⣦⡌⠉⠟⠲⠀⣀⠄⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⢽⣿⣾⣾⣮⣗⣏⣼⠰⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡹⠋⠙⢃⣵⣷⣀⣢⣌⠉⠉⠉⠁⠈⠓⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡷⠶⠤⠛⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⣀⠀⢀⣀⣀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⢠⣿⣿⣿ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡌⠛⠻⣿ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠻⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠲⣿⡇⠀⠀⠀ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣇⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠘⢿⡏⠹⠆⣹⣿⣷⣶⣶ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⡶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠶⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠋⠛⠷⠶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⠟⠿⠶⠾⠿⠶⠶⠷⠶⠾⣿⣶⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣶⣶⣤⡀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⣵⡿⠉⠉⠻⠟⠛⢋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣸⣿⣿⢇⣿⣿⡟⣸⣿⡇⣼⣿⡇⣿⡿⢸⣿⡏⠀⢀⣾⣿⣿⣿⠆⣿⣿⢿⣿⡆⣾⣿⣿⡇⢠⣾⡿⣿⣿⡄⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣿⡇⠀⢠⣤⣶⣶⣿⣿⠀⠀⠀⠀⢀⣿⣿⣤⢄⣿⣿⣿⣾⣿⣿⢃⣿⣿⢡⣿⣿⣿⣿⠇⣿⣿⠃⠀⢸⣿⣷⣍⠉⢰⣿⣿⣾⣿⣸⣿⢿⣿⡇⣾⣿⠣⠿⠿⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠈⠋⣹⣿⣿⡟⠀⠀⠀⠀⣸⣿⡏⠉⣸⣿⢿⣿⣟⣿⡿⣸⣿⡏⣾⣿⣿⣿⡿⢸⣿⡟⠀⢀⣤⣭⢻⣿⡇⣿⣿⢛⡏⢱⣿⣯⣿⣿⢸⣿⡟⣰⣶⡆⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣶⣶⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⡿⣼⡿⣸⣿⢃⣿⣿⢡⣿⡏⣿⣿⠇⣿⣿⠁⠀⠸⣿⣷⣿⠿⢹⣿⡟⣸⢡⣿⣿⢹⣿⣿⠸⣿⣷⣿⠟⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠹⣷⣤⣭⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣶⣶⣿⣿⣶⣶⣿⣶⠰⠤⠄⠀⠀⢐⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢯⣀⡀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠸⢿⣧⠀⠀⠀⠀⠰⢤⣀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡶⠆⠀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠆⠀⠲⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣻⣿⢟⠟⢉⣯⣅⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣺⡿⠻⣶⣿⣦⡌⠉⠟⠲⠀⣀⠄⠐⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⣿⣾⣾⣮⣗⣏⣼⡰⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡹⠉⠙⢛⣵⣶⣀⣣⣌⠉⠉⠉⠁⠈⠓⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣾⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⡷⠶⠦⠛⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣀⠀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⣀⣀⣀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⣀⣀⠀⠉⣀⣀⠀⢀⣀⣀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀ ⠠⢰⣶⠿⢻⣷⡿⢛⡛⢿⡿⢛⠛⣿⠟⣛⠻⣷⣿⠛⡿⠛⣿⠛⣿⠛⡛⢿⡟⢛⠛⢿⠛⢻⠛⣿⠛⣿⠛⣿⠛⣿⠛⡛⢿⣦⣾⠛⡛⢻⣿⠛⠛⣿⠛⢛⠻⡿⢛⡛⢿⠛⢻⠛⣿⠛⣿⡟⠛⢻⡟⢛⠛⣿⡄⠀⠀⠀ ⠀⠘⣿⡆⢸⣿⡇⢘⡛⢻⡇⢸⡇⢸⠀⣿⠀⣿⣿⠀⡇⡀⣿⢀⡇⢸⡇⢸⡇⢘⠃⣼⠀⠈⢰⣿⠀⣿⠀⠸⠀⡇⠀⡧⢼⣿⡇⠀⣧⣼⡟⢰⡀⣿⠀⠿⢀⣧⡘⠳⣾⠀⢸⠀⣿⠀⣿⡇⠘⢻⣇⡘⠳⣿⡇⢀⣠⣤ ⠀⠀⣿⡇⢸⡿⣇⠸⡇⢸⡇⢸⠇⣸⡀⢿⠀⣿⣿⡄⠁⣿⠁⢸⣧⠸⠇⢸⡇⢸⡇⢸⠀⢰⠈⣿⠀⣿⠀⣇⠀⣇⠀⠇⢸⣿⣧⠀⠏⢹⡇⢨⡁⢹⠀⣿⣿⡏⠹⠆⢸⡀⠸⠀⣿⠀⠿⡇⠸⢿⡏⠹⠆⣹⣷⣿⣿⣿ ⠁⠶⠿⣷⣿⣷⡿⠷⠶⠿⠿⣶⠾⠿⠿⠶⠾⠟⠻⠷⠶⠿⠶⠾⠿⠷⠶⠿⠷⠾⠷⠾⠶⠾⠶⠾⠶⠿⠶⠿⠶⠿⠷⠾⠾⠛⠻⠷⠶⠿⠷⡾⠷⠾⠶⠟⠉⠻⠷⠾⠿⠿⠶⠾⠿⠶⠶⠷⠶⠾⠿⢶⣾⢿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 1752 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/16/epo-data-meme/#comments Gemini version at gemini://gemini.techrights.org/2022/01/16/epo-data-meme/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_European_Patent_Office_Space⠀✐ Posted in Deception, Europe, Microsoft, Patents at 6:37 pm by Dr. Roy Schestowitz Something about “Data” and “Protection”… 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_waffle⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇If_you_could_send_all_of_the_EPO's_data_to_Microsoft,_that would_be_great⦈_ Summary: The EPO maintains a culture of illegal surveillance, inherited from Benoît_Battistelli and taken to a_whole_new_level by António_Campinos Recent: The_European_Data_Protection_Supervisor_(EDPS)_Needs_to_Get_Its_Act Together_on_the_EPO’s_GDPR_Violations | EPO’s_Illegal_Surveillance_Covered_Up by_Buzzwords_Bingo_and_Acronyms:_Data_Protection_Board_(DPB),_Data_Protection Rules_(DPR),_and_Data_Protection_Officer_(DPO) | [Meme]_EPO_Data_Protection Older: The_so-called_data_protection_officer_of_the_EPO_signed_off_on keylogging,_hidden_cameras ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠉⢿⠹⢛⠻⡟⡛⢛⢻⢸⠛⠛⠟⡛⠏⢙⠸⢛⠻⠛⡛⢿⣿⢛⠻⠁⣸⡏⣩⡍⠻⢛⢻⠉⠟⡛⢿⣿⢩⡭⠙⠛⠟⡛⠏⠹⢛⠻⠟⡛⡋⡃⠛⢛⢻⠛⠛⣿⡏⠩⠉⠟⡛⢿⢛⠻⠛⠛⢛⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣄⣠⣘⣃⣇⣇⣸⣸⣸⣸⣀⣁⣂⣀⣘⣠⣘⣀⣀⣇⣸⣿⣘⣁⣀⣿⣇⣙⣃⣄⣐⣘⣀⣁⣂⣸⣿⣰⣶⣇⣸⣀⢃⣄⣀⡐⣒⣄⣋⣅⣃⣀⣛⣸⣸⣀⣿⣇⣐⣂⣄⣛⣈⣐⣀⣀⣇⣛⣸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢩⠉⡍⡏⠭⠉⢩⠉⡍⡇⣭⠙⠩⠙⠉⡍⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣼⣤⣧⣧⣭⣤⣼⣤⣧⣧⣥⣴⣬⣴⣤⣧⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⢿⠿⡿⠿⠿⠿⠿⡿⡿⢿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣯⣤⣤⣯⣤⣤⣤⣤⣤⣤⣀⣯⣤⣤⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⠿⡿⢿⢿⡿⢿⠿⠿⡿⠿⠿⡿⢿⢿⢿⡿⢿⢿⢿⠿⡿⠿⢿⢿⠿⠿⠿⡿⡿⢿⠿⠿⡿⠿⠿⡿⡿⢿⡿⠿⠿⠿⠿⣿⢿⢿⡿⢿⠿⠿⠿⡿⣿⠿⠿⢿⠿⢿⠿⢿⢿⢿⡿⠿⢿⠿⢿⠿⣿⢿⠿⢿⣿⣿⣿ ⣿⣧⣶⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣧⣤⣤⣤⣤⣧⣄⣄⣠⣤⣤⣤⣤⣦⣼⣤⣤⣧⣭⣤⣤⣤⣼⣤⣼⣧⣤⣤⣧⣦⣤⣤⣜⠈⠀⣀⠀⡙⡐⢀⢀⣀⠀⢀⢀⠀⢢⣧⣤⣤⣤⣤⣤⣽⣴⣤⣼⣿⣿⣿ ⣿⡟⠛⠉⢹⠙⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠋⡏⠛⢻⢉⡙⠛⠋⡏⠉⠛⠛⠉⠙⠛⠛⢙⢻⠛⠛⠛⢹⢉⠛⠛⠛⠛⢛⠛⠙⢻⠉⠉⠙⡛⠻⡟⠙⠉⡟⠋⡏⢙⠛⢻⠛⠛⠛⢛⠙⠛⠛⠛⡛⢹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣾⣶⣿⣿⢿⢿⡿⣿⢷⣿⢿⣿⣿⣿⡿⣿⣿⢾⣿⣿⡿⣿⢿⣿⣿⣿⣿⢿⣿⡿⡿⣿⢿⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⢷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿ ⣿⣇⣴⣀⣀⣀⣀⣄⣄⣀⣇⣀⣄⣸⣠⣀⣀⣆⣀⣼⣀⣀⣄⣄⣁⣄⣄⣀⣀⣀⣀⣢⣄⣼⣀⣠⣔⣰⣀⣄⣀⣀⣀⣼⣠⣠⣀⣀⣀⣠⣅⣠⣠⣀⡃⠀⠀⠂⠘⠀⠐⠀⠀⠀⠀⠀⠂⠂⢇⣀⣀⣠⣠⣄⣀⣿⣿⣿ ⣿⡟⠛⠉⠙⡟⠛⠛⠙⠛⠛⠋⠛⠛⢻⠛⠛⡛⠙⠛⠛⠋⠛⠛⠛⠋⡟⠛⠛⠛⠛⡋⠛⠛⠛⠛⠿⠛⢹⠛⢛⢻⠙⠋⠛⠛⠛⠛⠉⠛⢛⠛⠋⡏⠛⠛⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⣶⣶⣿⣶⣶⣶⣶⣷⣶⣷⣷⣿⣴⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣦⣶⣶⣷⣶⣶⣶⣶⣿⣶⣾⣶⣾⣾⣾⣶⣶⣶⣷⣶⣶⣶⣾⣶⣶⣷⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣏⢉⠙⠛⡟⡙⠛⢛⠛⡏⠙⠛⠛⠛⠟⠛⠙⠛⢻⠋⠛⠛⠛⡛⢹⠙⠛⠛⢻⠙⠛⠛⠟⢻⠛⠛⢛⢻⠛⢻⠛⢛⠟⠙⠛⣛⠋⠛⢻⢛⠛⠛⠛⡏⢙⠙⢋⢻⡏⠻⠛⠛⢻⠉⠛⠛⠛⠛⠛⠋⠛⠛⣿⣿⣿⣿⣿ ⣿⣿⣾⣶⣶⣷⣶⣶⣶⣶⣷⣿⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣷⣾⣶⣶⣶⣾⣶⣶⣶⣶⣾⣶⣶⣶⣶⣦⣾⣶⣾⣶⣶⣶⣿⣶⣶⣾⣾⣶⣶⣾⣷⣶⣾⣷⣾⣑⣀⣀⣂⣈⣈⣁⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿ ⣿⣇⣄⣀⣈⣈⣈⣻⣁⣀⣀⣀⣀⣇⣀⣀⣠⣀⣇⣈⣂⣀⢀⣀⣈⣂⣇⡀⣸⣀⣎⣀⣏⣌⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣭⣐⣐⣉⣀⣀⣀⣸⣀⣸⣃⣘⣀⣀⣸⣂⣐⣀⣐⣸⣁⣁⣀⣸⠠⠀⠀⠀⠀⠀⠈⢾⣿ ⣿⡿⠻⠻⠛⠛⠛⠟⢻⠛⠛⠛⢿⠛⠛⠛⠟⢿⡟⢻⠛⠟⠛⡟⠻⠛⣻⠻⠻⡟⠛⠻⠻⠻⠛⠛⠛⠟⠟⠛⠻⠻⠻⢻⠛⠟⠻⠻⠻⡻⠛⢻⠛⢟⠟⠻⢻⠟⠛⠛⢻⠟⠟⢿⠛⠻⠟⠟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿ ⣿⣧⣤⣥⣤⣤⣤⣤⣬⣤⣤⣤⣬⣤⣤⣤⣤⣴⣷⣾⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣦⣾⣶⣶⣶⣦⣾⣶⣶⣶⣾⣶⣶⣾⣶⣶⣶⣾⣶⣦⣴⣶⣿⣿⣿⣿⣿⣿ ⣿⣇⣘⣉⣉⣁⣈⣉⣹⣋⣉⣉⣸⢉⣁⣉⢉⣏⣹⣈⡉⠉⣽⣉⣁⣉⣅⣨⣹⣀⣉⣉⣀⣉⠉⣉⣸⣉⣉⣁⣉⣉⢉⣉⣏⣉⣉⣉⣨⣉⣉⣁⣉⣉⣍⣁⣉⡏⣁⣉⡉⣉⣹⢉⣸⣀⣍⣉⣇⣀⣠⣐⣸⣅⣉⣹⣿⣿ ⣿⡿⠟⠿⠻⢿⠿⠿⠿⠻⠿⠿⠟⠿⠿⡿⠿⠿⠟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣁⣁⣀⣧⣶⣦⣤⣤⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⡛⠿⠿⠿⢿⠿⠿⠿⢻⠿⠿⠿⠟⠟⡿⠿⡿⠿⠟⠻⠟⠿⠿⠿⠟⠻⠿⠿⡟⠿⠿⠿⠿⠿⠿⠿⡟⠻⠿⢿⠛⠛⠻⢛⢿⠿⠿⠟⠻⠛⠿⢿⢛⠻⠿⠿⢿⠛⠻⠿⠿⠿⠿⠛⠿⠿⡟⠛⠿⠿⠿⠟⣿⣿⣿⣿ ⣿⣷⣤⣤⣦⣤⣼⣤⣼⣤⣼⣤⣮⣦⣦⣴⣴⣤⣧⣤⣤⣤⣤⣴⣵⣤⣤⣴⣵⣦⣧⣴⣴⣤⣴⣤⣤⣤⣶⣼⣤⣼⣤⣤⣶⣤⣾⣤⣤⣤⣾⣤⣤⣼⣀⣀⣀⣁⣈⣐⣁⣀⣀⣀⣀⣀⣀⣀⣡⣤⣤⣤⣼⣤⣿⣿⣿⣿ ⣿⣏⠉⠀⢸⠈⠉⣋⢍⠉⠉⠁⠉⢸⠉⢍⡏⠉⠉⢉⠏⠁⠉⠉⣟⢍⠉⠉⠉⠁⠈⠉⡍⠉⠉⡏⡉⠀⠈⡏⢀⠉⢹⠰⠈⠁⠉⢹⢀⢩⠉⠈⢉⢍⠁⢍⠉⡇⡀⠉⠈⠉⢉⡋⠉⠉⢸⠩⠉⠉⠈⠉⠉⠀⠉⠉⣿⣿ ⣿⡿⠻⠿⢿⠟⠿⠿⠿⠿⣿⠻⠿⠿⠿⠻⠿⠿⠿⢿⠿⠿⠿⢳⠻⠿⠿⠿⠷⠿⠿⢿⠿⠟⡿⠟⢻⠟⠿⠿⠿⡿⠷⠖⠖⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿ ⣿⣧⣼⣤⣼⣤⣀⣴⣤⣤⣹⣤⣦⣤⣤⣤⣥⣧⣤⣼⣤⣼⣤⣼⣤⣤⣤⣼⣤⣤⣤⣼⣬⣤⣧⣄⡜⠀⠀⠈⠀⠁⠀⠀⠁⠀⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⢿⠿⠿⠿⡿⠿⢿⠿⠿⠿⢿⠿⠿⢿⠿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⣶⣘⣀⣆⣠⣄⣀⣾⣀⣆⣠⣂⣰⣀⣆⣀⣐⣀⣠⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠻⠆⣇⠂⡉⡉⠉⡍⡁⠉⣉⢹⡉⡁⣄⢁⢉⢉⣉⠉⠉⢀⡉⣏⢁⡉⡉⢉⡉⣉⠁⡉⣹⠉⣀⡅⢈⡉⣹⢉⢉⢈⢉⡉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⣹⡇⠀⠉⠉⠉⡏⠍⠉⠍⠈⢉⢍⠀⠉⠉⢹⠉⢩⠉⢸⠉⠉⠈⢉⠉⠉⠉⡍⠉⠉⡁⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠐⠲⠒⣴⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣐⣶⣶⣦⣤⣤⣤⣦⡄⠀⠀⢠⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠉⠀⠁⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠋⠙⠑⠀⠃⠉⣽⡇⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠯⣿⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄ ⠀⠀⠀⠀⠀⡀⡀⢀⡀⣀⡀⢀⢀⡉⣁⡀⣁⢀⡈⠛⣛⠛⢛⡛⢛⣛⡛⣛⢛⣛⡛⠉⢀⡀⢀⣀⢀⢀⣉⣉⡀⠀⢀⡀⢀⡀⣀⠑⠀⣀⡀⣀⣀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⢀⢌⠀⢸⡇⣿⡅⢸⣿⢻⡏⣿⣿⢹⡇⢸⡿⠇⣿⣿⢸⣿⡇⣿⢸⣿⣿⠀⢿⣟⢸⣯⣿⣿⣿⣿⣿⠀⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⣭⠠⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣨⣮⠀⠸⠇⠿⠀⠀⠿⠘⠷⠟⠻⠾⢃⠸⠿⠇⠿⠿⠸⠿⠇⠿⠾⠿⠿⠀⠿⠿⠸⠷⠿⠹⠿⠿⠿⠀⠿⠿⠼⠷⠿⠦⠘⠿⠟⠿⠀⠀⠘⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣤⣤⣤⣤⡄⣤⡄⢠⣤⣤⣤⡄⣤⣄⣤⣨⣥⡐⢠⣤⡄⣤⣤⣤⣤⣤⡄⠀⣤⣤⣠⣤⡀⢠⣄⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣄⣤⣤⣤⣤⠀⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⢸⣿⢸⣿⡇⣿⠆⢸⡷⢸⡿⢿⣿⣿⠈⣙⢾⡄⢸⣿⣇⣿⣷⢼⡇⣟⣿⠀⢸⡇⣿⢸⡇⢸⣿⣿⣿⡇⣿⣹⣹⣿⡇⣿⣿⢘⣿⣽⣿⣿⢿⡗⢸⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⢸⡇⢘⡋⠘⠛⠃⣛⣃⣘⡛⠛⠃⠀⣛⣋⣤⣙⣛⣁⡘⢛⠙⠋⠛⡙⣛⣃⢛⡀⠘⠃⢙⣛⣠⣘⣛⣙⣛⣃⣙⣛⣘⣛⠃⠙⠛⠈⠛⠁⠛⠋⠙⠃⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠁⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⡖⢢⠀⣿⣿⣿⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢱⢙⡎⣆⠛⣿⡟⣸⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣽⣿⣿⣿⣿⣿⣿⡇⢀⣐⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠂⠀⠀⠀⢠⣿⣿⣿⣿⣹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⢇⢧⡸⣀⠀⣿⡇⣿⣷⠀⠀⢸⢹⢻⣿⣿⣿⡟⢛⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⠿⣿⣿⡇⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠻⣿⠀⠀⣿⣿⣿⣿⣿⣿⣯⢿⡜⣤⢣⠓⠀⣿⣇⠹⡟⠀⠀⠈⣼⠈⣿⣿⣿⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢇⠘⠦⠤⢻⣿⣿⣿⣿⡟⣚⡖⢳⠛⡎⢲⠀⣿⣿⣀⣿⣤⣤⣤⣯⣠⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⡧⢂⠄⠀⠈⣿⣿⣿⣿⡷⢹⣉⣏⣹⣸⣙⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠲⢺⠿⠿⠿⠻⠿⠿⠗⠀⠀⠀⠀⠻⠿⠿⠛⠒⠻⠿⠿⠶⠇⠘⠚⠛⠛⠛⠛⠛⠛⠛⠛⠃⠑⠀⠀⠋⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠲⠒⣤⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣾⣾⣶⣤⣤⣤⣦⡄⠀⠀⢠⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠈⠀⠁⠀⠁⠈⠉⠛⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠉⠐⠐⠉⣽⡇⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠯⣿⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄ ⠀⠀⠀⠀⠀⣀⠀⢀⡀⣀⡀⢀⢀⡉⣁⡀⣀⢀⡈⠛⣛⠛⢛⡛⢛⣛⡛⣛⢛⣛⡛⠉⢀⡀⢀⣀⢀⢀⣉⣉⡀⠀⢀⡀⢀⡀⣀⠑⠀⣀⡀⣀⣀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⠰⠀⢸⡇⣿⡅⢸⣿⢻⡏⣿⣿⢹⡇⢸⡿⠇⣿⣿⢸⣿⡇⣿⢸⣿⣿⠀⢿⣟⢸⣯⣿⣿⣿⣿⣿⠀⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⣭⠠⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣬⣯⠀⠸⠇⠿⠀⠀⠿⠘⠷⠟⠻⠾⢃⡸⠿⠇⠿⠿⠸⠿⠇⠿⠾⠿⠿⠀⠿⠿⠸⠷⠿⠹⠿⠿⠿⠀⠿⠿⠼⠷⠿⠦⠘⠿⠟⠿⠀⠀⠘⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣥⣤⣤⣤⡄⣤⡄⢠⣤⣤⣤⡄⣤⣄⣤⣨⣥⡘⢠⣤⡄⣤⣤⣤⣤⣤⡄⠠⣤⣤⣠⣤⡀⢠⣄⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣄⣤⣤⣤⣤⠀⠉⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⢸⣿⢸⣿⡇⣿⠆⢸⡷⢸⡿⢿⣿⣿⠈⣙⢾⡄⢸⣿⣇⣿⣷⣺⡇⣿⣿⠀⢸⡇⣿⢸⡇⢸⣿⣿⣿⡇⣿⣹⣹⣿⡇⣿⣿⢘⣿⣽⣿⣿⢿⡷⢸⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⢸⡇⢘⡋⠘⠛⠃⣛⣃⣘⡛⠛⠃⠀⣛⣋⣤⣙⣛⣁⡘⢛⠙⠋⠛⡙⣛⣋⢛⡀⠘⠃⢙⣛⣠⣘⣛⣙⣛⣃⣙⣛⣘⡛⠃⠙⠛⠈⠛⠁⠛⠋⠙⠃⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠁⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⡖⢢⠀⣿⣿⣿⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢱⢙⡎⣆⠻⣿⡟⣸⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣽⣿⣿⣿⣿⣿⣿⡇⣀⣐⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠂⠀⠀⠀⢠⣿⣿⣿⣿⣹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⢇⢧⡸⣀⠀⣿⡇⣿⣿⠀⠀⢸⢹⢻⣿⣿⣿⣟⢛⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⠿⣿⣟⡇⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠳⣿⠀⠀⣿⣿⣿⣿⣿⣿⣯⢿⡜⣤⢣⠓⠀⣿⣇⠹⡟⠀⠀⠈⣼⠈⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢇⠘⠦⠤⢻⣿⣿⣿⣿⡟⣚⡖⢳⠛⡎⢲⠀⣿⣿⣀⣿⣤⣤⣤⣿⣠⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⡯⢂⠄⠀⠈⣿⣿⣿⣿⡷⢹⣉⣏⣹⣸⣙⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠲⢺⠿⠿⠿⠻⠿⠿⠗⠀⠀⠀⠀⠛⠿⠿⠛⠒⠻⠿⠿⠶⠇⠘⠚⠛⠛⠛⠛⠛⠛⠛⠛⠃⠑⠀⠀⠋⠉⠉⠁⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠐⠒⠀⢰⣖⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣐⣒⣶⣆⣤⣤⣤⣦⡄⠀⠀⢠⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠻⠯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⠀⢀⣾⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠋⠀⠈⠀⠁⣽⡇⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠯⣿⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⠇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀ ⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⡀⢀⢀⡈⣁⡀⣀⢀⡈⠛⣛⠛⢛⡛⢛⣛⡛⣛⢛⣛⡛⠉⢀⡀⢀⣀⢀⢀⣉⣉⡀⠀⢀⡀⢀⡀⣀⠑⠀⣀⡀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⢀⢴⠀⢸⡇⣿⡅⢸⣿⢻⡏⣿⣿⢹⡇⢸⡿⠇⣿⣿⢸⣿⡇⣿⢸⣿⣿⠀⢿⣟⢸⣯⣿⣿⣿⣿⣿⠀⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⣭⠠⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣠⣿⠀⠸⠇⠿⠀⠀⠿⠘⠷⠟⠻⠾⢃⠸⠿⠇⠿⠿⠸⠿⠇⠿⠾⠿⠿⠀⠿⠿⠸⠷⠿⠹⠿⠿⠿⠀⠿⠿⠼⠷⠿⠦⠘⠿⠟⠿⠀⠀⠘⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣤⣤⣤⣤⡄⣤⡄⢠⣤⣤⣤⡄⣤⣄⣤⣨⣤⡙⢠⣤⡄⣤⣤⣤⣤⣤⡄⠀⣤⣤⣠⣤⡀⢠⣄⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣄⢤⣤⣤⣤⠀⠁⠑⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⢸⣿⢸⣿⡇⣿⠆⢸⡷⢸⡿⢿⣿⣿⠈⣙⢾⡄⢸⣿⣇⣿⣷⢸⡇⣿⣿⠀⢸⡇⣿⢸⡇⢸⣿⣿⣿⡇⣿⣹⣹⣿⡇⣿⣿⢘⣿⣽⣿⣿⣿⡗⢸⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⢸⡇⢘⡋⠘⠛⠃⣛⢃⣘⡛⠛⠃⠀⣛⣋⣤⣙⣛⣁⡘⢛⠙⠋⠛⠘⣛⣃⢛⡀⠘⠃⢙⣛⣠⣘⣛⣙⣛⣃⣙⣛⣘⣛⡃⠙⠋⠈⠛⠁⠛⠋⠙⠃⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠁⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡞⡞⢢⠀⣿⣿⣿⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⡿⣻⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣹⢙⡌⡆⠛⣿⡏⣸⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⣿⣿⣿⣿⣿⢿⡇⣀⣐⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠂⠀⠀⠀⢠⣿⣿⣿⣿⣹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢇⢇⡸⡀⠘⣿⡇⣿⣿⠀⠀⢸⢹⠻⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⢞⣿⣿⣿⣿⡿⣿⣿⡇⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠳⣿⠀⠀⣿⣿⣿⣿⣿⣿⣯⢿⡟⡔⢣⠓⠀⣿⣇⠹⡟⠀⠀⠈⣼⠀⡿⣿⢿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢇⠘⠦⠤⢻⣿⣿⣿⣿⡟⡚⡞⢳⠑⡎⣲⠀⣿⣿⣀⣷⣀⣀⣀⡏⠀⠧⣼⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⡧⢂⠄⠀⠈⣿⣿⣿⣿⠟⢹⣉⣇⣯⡸⣉⢻⣟⣛⣻⣿⣿⣿⣿⣿⣿⣄⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢺⠿⠿⠿⠻⠿⠿⠗⠀⠀⠀⠀⠛⠿⠿⠋⠚⠻⠿⠿⠶⠇⠘⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠹⠿⠚⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠐⣰⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⠶⢶⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⡴⢖⣶⣆⣤⣤⣤⣤⡄⠀⠀⢠⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠛⠽⢭⡽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣻⣿⣿⡟⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠉⠁⠉⠉⣽⡇⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠯⣿⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⢀⢀⡉⣁⡀⣀⢀⡈⠛⣛⠛⢛⡛⢛⣛⡛⣛⢛⣛⡛⠉⢀⡀⢀⣀⢀⢀⣉⣉⡀⠀⢀⡀⢀⡀⣀⠑⠀⣀⡀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⢀⡐⠀⢸⡇⣿⡅⢸⣿⢻⡏⣿⣿⢹⡇⢸⡿⠇⣿⣿⢸⣿⡇⣿⢸⣿⣿⠀⢿⣟⢸⣯⣿⣿⣿⣿⣿⠀⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⣭⠠⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣤⣶⠀⠸⠇⠿⠀⠀⠿⠘⠷⠟⠻⠾⢃⠸⠿⠇⠿⠿⠸⠿⠇⠿⠾⠿⠿⠀⠿⠿⠸⠷⠿⠹⠿⠿⠿⠀⠿⠿⠼⠷⠿⠦⠘⠿⠟⠿⠀⠀⠘⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣤⣤⣤⣤⡄⣤⡄⢠⣤⣤⣤⡄⣤⣄⣤⣨⣥⡘⢡⣤⡄⣤⣤⣤⣤⣤⡄⠠⣤⣤⣠⣤⡀⢠⣄⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣄⣤⣤⣤⣤⠀⠉⠙⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⢸⣷⢸⣿⡇⣿⠆⢸⡷⢸⡿⢿⣿⣿⠈⣙⢾⡄⢸⣿⣇⣿⣷⢸⡇⣿⣿⠀⢸⡇⣿⢸⡇⢸⣿⣿⣿⡇⣿⣹⣹⣿⡇⣿⣿⢘⣿⣽⣿⣿⣿⡗⢸⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⢸⡇⢘⡋⠘⠛⠃⣛⣃⣘⣛⠛⠃⠀⢛⣋⣤⣙⣛⣁⡘⢛⠙⠋⠛⠘⣛⣋⢛⡀⠘⠃⢙⣛⣠⣘⣛⣙⣛⣃⣙⣛⣘⣛⣃⠙⠛⠈⠛⠁⠛⠋⠙⠃⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠁⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡞⡞⢲⠀⣿⣿⣿⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣹⢙⡉⡆⠛⣿⡏⣸⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣽⡿⣿⣿⣿⣷⡅⢀⣐⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠂⠀⠀⠀⢠⣿⣿⣿⣿⡹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⢇⡸⡀⠘⣿⡇⣿⣿⠀⠀⢸⢻⡏⣿⣿⣿⣿⠟⠝⣿⣿⣿⣿⢾⣿⣿⣿⣟⡿⢿⣿⡇⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠳⣿⠀⠀⣿⣿⣿⣿⣿⣿⣧⢿⡟⡴⢣⠓⠀⣿⣇⠻⡏⠀⠀⠈⣸⠀⡿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣣⠘⠦⠤⢻⣿⣿⣿⣿⡟⡚⡞⢳⠑⡎⣲⠀⣿⣿⠀⣇⣀⣀⠀⡿⠀⣇⣸⣀⣈⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠃⠄⠀⠈⣿⣿⣿⣿⠟⢹⣉⣇⣯⡸⣉⢸⣟⡛⠛⣻⣿⣿⣿⣷⣶⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢺⠿⠿⠿⠻⠿⠿⠗⠀⠀⠀⠀⠻⠿⠿⠛⠞⠻⠿⠿⠷⠧⠚⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠐⢠⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⡵⣶⣶⣖⣤⣤⣤⣦⡄⠀⠀⢠⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⠯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠉⣽⡇⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠿⣻⠸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄ ⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⡀⢀⢈⡉⣁⡀⣀⢀⡈⠛⣛⠛⢛⡛⢛⣛⡛⣛⢛⣛⡛⠉⢀⡀⢀⣀⢀⢀⣉⣉⡀⠀⢀⡀⢀⡀⣀⠑⠀⣀⡀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⢀⢻⠀⢸⡇⣿⡅⢸⣿⢻⡏⣿⣿⢹⡇⢸⡿⠇⣿⣿⢸⣿⡇⣿⢸⣿⣿⠀⢿⣟⢸⣯⣿⣿⣿⣿⣿⠀⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⣭⠠⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣠⣾⠀⠸⠇⠿⠀⠀⠿⠘⠷⠟⠻⠾⢃⠸⠿⠇⠿⠿⠸⠿⠇⠿⠾⠿⠿⠀⠿⠿⠸⠷⠿⠹⠿⠿⠿⠀⠿⠿⠼⠷⠿⠦⠘⠿⠟⠿⠀⠀⠘⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣥⣤⣤⣤⡄⣤⡄⢠⣤⣤⣤⡄⣤⣄⣤⣨⣥⡘⢡⣤⡄⣤⣤⣤⣤⣤⡄⠠⣤⣤⣠⣤⡀⢠⣄⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣄⣤⣤⣤⣤⠀⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⢸⣿⢸⣿⡇⣿⠆⢸⡷⢸⡿⢿⣿⣿⠈⣙⢾⡄⢸⣿⣇⣿⣷⢸⡇⣿⣿⠀⢸⡇⣿⢸⡇⢸⣿⣿⣿⡇⣿⣹⣹⣿⡇⣿⣿⢘⣿⣽⣿⣿⣿⡷⢸⡇⠀⠀⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⢸⡇⢘⡋⠘⠛⠃⣛⣃⣘⡛⠛⠃⠀⣛⣋⣤⣙⣛⣁⣘⢛⠙⠋⠛⠘⣛⣃⢛⡀⠘⠃⢙⣛⣠⣘⣛⣙⣛⣃⣙⣛⣘⣛⣃⠙⠛⠈⠛⠁⠛⠋⠙⠃⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣼⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⡖⢲⠀⣿⣿⣿⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣹⣉⡏⣇⠛⣿⡿⣸⣿⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣹⣿⠿⣿⣿⣷⡇⣀⡐⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠂⠀⠀⠀⢀⣿⣿⣿⣿⡻⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢇⠧⡸⣤⠀⣿⡇⣿⣿⠀⠀⠀⢷⡏⣿⣿⣿⣿⡛⠛⣿⣿⣿⣿⢷⣻⣿⣿⣟⡻⢿⣿⡇⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣯⢿⡟⣴⢳⠛⠀⣿⣧⠻⣏⠀⠀⠀⢸⠁⠈⢿⣿⣿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣣⠈⡧⠤⢻⣿⣿⣿⣿⡟⡊⡞⢳⠙⡎⣲⠀⣿⣿⠀⣿⣀⡀⠀⣾⠀⢀⣘⣁⣈⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣷⠁⠄⠀⠈⣿⣿⣿⣿⠟⣹⣉⣇⣹⣸⣉⠜⣟⡟⠛⣻⣿⣿⣿⣷⣶⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠿⠿⠿⠻⠿⠿⠞⠀⠀⠀⠀⠻⠿⠿⠛⠜⠻⠿⠿⠿⠷⠘⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒⠒⢰⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢭⣅⢒⣶⣖⣤⣤⣤⣴⡄⠀⠀⢠⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠈⠘⠉⡹⠿⠻⢯⢿⡿⣿⣿⣷⣿⣿⣷⣿⣿⢻⣿⣿⡟⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠀⣹⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣿⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⠇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄ ⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⡀⢀⢈⡈⣁⡀⣁⢀⡈⠛⣛⠛⢛⡛⢛⣛⡛⣛⢛⣛⡛⠉⢀⡀⢀⣀⢀⢀⣉⣉⡀⠀⢀⡀⢀⡀⣀⠑⠀⣀⡀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⢀⣀⠀⢸⡇⣿⡅⢸⣿⢻⡏⣿⣿⢹⡇⢸⡿⠇⣿⣿⢸⣿⡇⣿⢸⣿⣿⠀⢿⣟⢸⣯⣿⣿⣿⣿⣿⠀⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⣭⠠⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣤⣶⠀⠸⠇⠿⠀⠀⠿⠘⠷⠟⠻⠾⢃⠸⠿⠇⠿⠿⠸⠿⠇⠿⠾⠿⠿⠀⠿⠿⠸⠷⠿⠹⠿⠿⠿⠀⠿⠿⠼⠷⠿⠦⠘⠿⠟⠿⠀⠀⠘⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣥⣤⣤⣤⡄⣤⡄⢠⣤⣤⣤⡄⣤⣄⣤⣨⣥⡘⢡⣤⡄⣤⣤⣤⣤⣤⡄⠠⣤⣤⣠⣤⡀⢠⣄⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣄⣤⣤⣤⣤⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⢸⣧⢸⣿⡇⣿⠆⢸⡷⢸⡿⢿⣿⣿⠈⣙⢾⡄⢸⣿⣇⣿⣷⢼⡇⣿⣿⠀⢸⡇⣿⢸⡇⢸⣿⣿⣿⡇⣿⣹⣹⣿⡇⣿⣿⢘⣿⣽⣿⣿⣿⡗⢸⡇⠀⠀⢀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠸⡇⢘⡋⠘⠛⠃⣛⣃⣘⡛⡛⠃⠀⣛⣋⣤⣙⣛⣡⡘⢛⠙⠋⠛⠙⣛⣋⠛⣀⠘⠃⠙⣛⣠⣘⣛⣙⣛⣃⣙⣛⣘⣛⣃⡙⠛⠈⠛⠁⠛⠋⠙⠃⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⣶⢱⠃⣿⣿⣿⢸⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣷⣿⡿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣹⣉⡏⣡⠙⣿⣿⢸⣿⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣿⠿⢿⣧⣯⠇⣀⡐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠂⠀⠀⠀⢀⣿⣿⣿⣿⡼⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⢇⠼⡸⢤⠀⢻⡇⣿⣿⡄⠀⠀⡇⡏⢻⣿⣿⣿⠟⠋⣿⣿⣿⣿⢷⣿⣿⣿⣿⣻⢿⣿⡆⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡙⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⠾⡟⢦⢳⠞⠀⣼⣧⠹⣿⠃⠀⠀⢸⠃⠈⢹⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡷⡈⡧⠤⢹⣿⣿⣿⣿⡿⡉⣶⢱⠋⡎⢱⠀⣿⣿⢀⣻⣄⣀⡀⢸⠀⣀⣘⣡⣤⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢷⠁⠄⠀⠈⣿⣿⣿⣿⡷⢹⣉⢏⡹⣸⣍⠏⣿⣛⢛⣻⣿⣿⣿⣿⣶⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠲⢲⠿⠿⠿⠻⠿⠿⠟⠀⠀⠀⠀⠛⠿⠿⠛⠐⠻⠿⠿⠿⠷⠜⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠎⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠂⠐⣰⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣧⣕⣀⢂⣶⣆⣤⣤⣤⣶⡄⠀⠀⢠⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠈⠀⠀⠁⠉⠹⠯⠵⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⡟⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠀⠉⠘⠀⣹⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣿⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄ ⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⡀⢀⢀⡈⣁⡀⣁⢀⡈⠛⣛⠛⢛⡛⢛⣛⡛⣛⢛⣛⡛⠉⢀⡀⢀⣀⢀⢀⣉⣉⡀⠀⢀⡀⢀⡀⣀⠑⠀⣀⡀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⢬⠀⢸⡇⣿⡅⢸⣿⢻⡏⣿⣿⢹⡇⢸⡿⠇⣿⣿⢸⣿⡇⣿⢸⣿⣿⠀⢿⣟⢸⣯⣿⣿⣿⣿⣿⠀⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⣭⠠⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣨⣿⠀⠸⠇⠿⠀⠀⠿⠘⠷⠟⠻⠾⢃⠸⠿⠇⠿⠿⠸⠿⠇⠿⠾⠿⠿⠀⠿⠿⠸⠷⠿⠹⠿⠿⠿⠀⠿⠿⠼⠷⠿⠦⠘⠿⠟⠿⠀⠀⠘⠀⠀⠘⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣤⣤⣤⣤⡄⣤⡄⢠⣤⣤⣤⡄⣤⣄⣤⣨⣥⡐⢡⣤⡄⣤⣤⣤⣤⣤⡄⠠⣤⣤⣠⣤⡀⢠⣄⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣄⣤⣤⣤⣤⠀⠉⠉⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⢸⣷⢸⣿⡇⣿⠆⢸⡷⢸⡿⢿⣿⣿⠈⣙⢾⡄⢸⣿⣇⣿⣷⢸⡇⣿⣿⠀⢸⡇⣿⢸⡇⢸⣿⣿⣿⡇⣿⣹⣹⣿⡇⣿⣿⢘⣿⣽⣿⣿⣿⡗⢸⡇⠀⠀⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠸⡇⢘⡋⠘⠛⠃⣛⣃⣘⡛⡛⠃⠀⡛⣋⣤⣙⣛⣡⣘⢛⠙⠋⠛⠘⣛⣋⠛⣀⠘⠃⠙⣛⣠⣘⣛⣙⣛⣃⣙⣛⣘⣛⣃⡙⠛⠈⠛⠁⠛⠋⠙⠃⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⣶⢱⠁⣿⣿⣿⢸⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠸⣿⣿⣿⡿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣹⣉⡏⣡⠙⣿⣿⢸⣿⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⠷⢿⣯⣷⡇⢀⡐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠂⠀⠀⠀⢀⣿⣿⣿⣿⡼⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⢇⠽⡸⢤⠀⢿⡇⣿⣿⡄⠀⠀⡇⡇⢻⣿⣿⣿⠛⠛⣿⣿⣿⣿⢷⣿⣿⣿⣿⣻⢿⣿⡇⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡙⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⡾⡟⢦⢳⠞⠀⣼⣧⠹⣿⠃⠀⠀⢸⠃⠈⢹⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡷⡈⡧⠤⢹⣿⣿⣿⣿⡿⡉⣷⢱⠋⡎⢱⠀⣿⣿⢀⣻⣄⣀⡀⢸⠀⣀⣘⣡⣤⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢷⠁⠆⠀⠈⣿⣿⣿⣿⡷⢹⣉⢏⡹⣸⣍⠟⣿⣛⢛⣻⣿⣿⣿⣿⣶⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠲⢲⠿⠿⠿⠻⠿⠿⠟⠀⠀⠀⠀⠛⠿⠿⠛⠔⠛⠿⠿⠿⠷⠜⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠎⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠻⠟⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠒⠀⠀⣰⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀⣲⣶⣆⣤⣤⣤⣶⡄⠀⠀⢠⣨⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠿⠽⣿⣿⡿⢿⣿⣿⣾⣿⣿⣿⠿⣿⣿⣿⡟⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠊⠁⠁⠈⠁⣼⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣿⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀ ⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⡀⢀⢀⡈⣁⡀⣈⢀⡈⠛⣛⠛⢛⡛⢛⣛⡛⣛⢛⣛⡛⠉⢀⡀⢀⣀⢀⢀⣉⣉⡀⠀⢀⡀⢀⡀⣀⠑⠀⣀⡀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⢀⠀⠀⢸⡇⣿⡅⢸⣿⢻⡏⣿⣿⢹⡇⢸⡿⠇⣿⣿⢸⣿⡇⣿⢸⣿⣿⠀⢿⣟⢸⣯⣿⣿⣿⣿⣿⠀⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⣭⠠⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣤⣯⠀⠸⠇⠿⠀⠀⠿⠘⠷⠟⠻⠾⠃⠸⠿⠇⠿⠿⠸⠿⠇⠿⠾⠿⠿⠀⠿⠿⠸⠷⠿⠹⠿⠿⠿⠀⠿⠿⠼⠷⠿⠦⠘⠿⠟⠿⠀⠀⠘⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣥⣤⣤⣤⡄⣤⡄⢠⣤⣤⣤⡄⣤⣄⣤⣠⣥⡘⢡⣤⡄⣤⣤⣤⣤⣤⡄⠠⣤⣤⣠⣤⡀⢠⣄⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣄⣤⣤⣤⣤⠀⠉⠋⠙⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⢸⣧⢸⣿⡇⣿⠆⢸⡷⢸⡿⢿⣿⣿⠈⣙⢾⡄⢸⣿⣇⣿⣷⢸⡇⣿⣿⠀⢸⡇⣿⢸⡇⢸⣿⣿⣿⡇⣿⣹⣹⣿⡇⣿⣿⢘⣿⣽⣿⣿⣿⡷⢸⡇⠀⠀⢀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠸⡇⢘⡋⠘⠛⠃⢛⣃⣘⡛⡛⠃⠀⡛⣋⣤⣙⣛⣡⣘⠛⠙⠋⠛⠘⢛⣋⠛⣀⠘⠃⠙⣛⣠⣘⣛⣙⣛⣃⣙⣛⣘⣛⣃⡙⠛⠈⠛⠁⠛⠋⠙⠃⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⣻⣿⣿⣿⣿⣿⣿⡟⢳⠑⠂⢺⣿⣿⢃⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⡯⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣹⣇⣏⣹⠘⣿⣿⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣿⠿⢿⣯⣿⡇⣀⡐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠂⠀⠀⠀⠀⣾⣿⣿⣿⡟⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⢧⢧⡼⡠⢇⠀⢻⡿⢸⣿⡇⠀⠀⡇⡇⢹⣿⣿⣿⠏⠙⣿⣿⣿⣿⢆⣿⣿⣿⣿⣛⢿⣿⡇⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡝⢿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡞⡟⢣⠓⡞⠀⣸⣧⠸⢿⡁⠀⠀⢡⠃⠀⢹⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡷⡈⡧⠤⠼⣿⣿⣿⣿⡿⡉⢳⢱⡎⡎⢱⠁⣿⣿⣀⣸⣅⣀⣀⣸⠀⢀⣬⣥⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⠕⡄⠀⠀⣿⣿⣿⣿⡷⢋⣇⢏⡹⣈⢏⠏⣿⣛⣻⣿⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠲⢲⠿⠿⠿⠻⠿⠿⠟⠀⠀⠀⠀⠛⠿⠿⠟⠔⠛⠻⠿⠿⠷⠞⠐⠛⠛⠛⠛⠛⠛⠛⠛⠃⠰⠚⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⣲⣖⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣝⣐⡲⢶⣆⣤⣤⣤⣤⡄⠀⠀⢠⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠯⢖⡿⣷⣾⣿⣿⣿⣿⣿⣿⢻⠿⣿⣿⡟⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠘⠀⣼⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣿⠸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄ ⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⡀⢀⢀⡈⣁⡀⣉⢀⡈⠛⣛⠛⢛⡛⢛⣛⡛⣛⢛⣛⡛⠉⢀⡀⢀⣀⢀⢀⣉⣉⡀⠀⢀⡀⢀⡀⣀⠑⠀⣀⡀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⢻⠀⢸⡇⣿⡅⠸⣿⢻⡏⣿⣿⢹⡇⢸⡿⠇⣿⣿⢸⣿⡇⣿⢸⣿⣿⠀⢿⣟⢸⣯⣿⣿⣿⣿⣿⠀⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⣭⠠⠆⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣠⣦⠀⠸⠇⠿⠀⠀⠿⠘⠷⠟⠻⠾⠃⠸⠿⠇⠿⠿⠸⠿⠇⠿⠾⠿⠿⠀⠿⠿⠸⠷⠿⠹⠿⠿⠿⠀⠿⠿⠼⠷⠿⠦⠘⠿⠟⠿⠀⠀⠘⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣥⣤⣤⣤⡄⣤⡄⢠⣤⣤⣤⡄⣤⣄⣤⣠⣤⡐⢡⣤⡄⣤⣤⣤⣤⣤⡄⠠⣤⣤⣠⣤⡀⢠⣄⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣄⣤⣤⣤⣤⠀⠉⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⢸⣿⢸⣿⡇⣿⠆⢸⡷⢸⡿⢿⣿⣿⠈⣙⢾⡄⢸⣿⣇⣿⣷⢸⡇⣿⣿⠀⢸⡇⣿⢸⡇⢸⣿⣿⣿⡇⣿⣹⣹⣿⡇⣿⣿⢘⣿⣽⣿⣿⣿⡷⢸⡇⠀⠀⢀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠸⡇⢘⡋⠘⠛⠃⢛⣃⣘⡛⡛⠃⠀⠛⣋⣤⣙⣛⣡⣘⡛⡙⠋⠛⠘⢛⣋⡛⣀⠘⠃⠙⣛⣀⣘⣛⣙⣛⣃⣙⣛⣘⣛⣃⡙⠛⠈⠛⠁⠛⠋⠙⠃⠘⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⣻⣿⣿⣿⣿⣿⣿⣷⢱⠉⡆⢸⣿⣿⡇⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣏⣇⣹⣸⠈⢹⣿⢸⣿⡇⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⡿⠿⢿⣿⣫⠅⢀⡐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠂⠀⠀⠀⠀⣾⣿⣿⣿⣟⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⢿⠿⡼⣤⢧⠄⢻⡿⢸⣿⣧⠀⠀⠘⡇⠘⣿⣿⣿⠛⠙⣿⣿⣿⡯⣾⣿⣿⣿⣽⣛⢿⣷⡇⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡜⢿⡇⠀⢸⣿⣿⣿⣿⣿⡿⡞⣿⢳⠚⡞⠂⢸⣧⡼⢿⡟⠀⠀⠀⡇⠀⢸⡿⢿⡄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣟⡄⠳⠤⠜⣿⣿⣿⣿⡿⢉⢱⠉⡎⣷⢱⡁⣾⣿⣁⣸⣧⣀⣀⣰⠀⣠⣬⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢻⠔⡄⠀⠀⣻⣿⣿⣿⡷⢋⢇⡿⡸⣀⢇⡙⣟⣛⣻⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠿⠿⠿⠿⠿⠿⠟⠂⠀⠀⠀⠛⠿⠿⠟⠐⠛⠛⠿⠿⠿⠾⠓⠛⠛⠛⠛⠛⠛⠛⠛⠋⠰⠘⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠒⣶⣦⣤⣆⠀⠰⠦⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢉⠻⠟⠿⡿⠿⠿⠟⠿⢿⣿⡿⠿⣴⢤⠤⢄⢀⠀⡀⠠⣀⣀⣤⣤⣤⡄⠀⠀⢠⣩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠸⠃⢶⣽⣝⡔⣋⣟⣬⠉⠝⢛⣿⡏⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣷⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣆⡙⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣏⣋⣠⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠠⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢠⡀⢠⢀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡀⢀⣠⣤⠐⠀⠀⠀⢐⡩⢄⡄⠀⠀⠉⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣶⠀⠀⠀⣶⣶⣤⣶⣿⣿⡅⠀⠀⠐⠒⠂⠀⠀⠀⠀⠘⠛⠇⠀⠘⠀⠀⠈⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠃⠀⠀⠀⠀⠙⠛⠁⢀⡀⠃⢡⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⣧⢻⡄⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⠀⠁⠁⠉⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⡏⠀⠀⣾⣿⣿⣿⣿⣿⠏⢹⡂⠀⠙⣿⣿⣸⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⠿⠿⢟⠀⢸⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠸⡇⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣤⢲⠃⠀⠀⣯⣿⣿⢸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⠀⢸⠓⠒⠆⣈⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⡎⢱⠀⣿⣿⡇⣾⣿⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⢁⠂⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⡽⡸⢅⠇⢹⣿⢣⣿⣿⠀⠀⠸⣿⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣿⠿⠶⣾⣅⠀⠀⢀⡀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠚⠂⠀⠀⠀⠀⣾⣿⣿⣿⣯⢿⡇⠀⢠⣿⣿⣿⣿⣿⣿⡿⡼⣥⢣⠜⡄⠘⣿⢸⣿⣿⠀⠀⠀⢸⠀⢻⣿⣿⠙⠹⣿⣿⣿⡵⣹⣿⣿⣯⣟⣻⢿⣧⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡎⢺⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷⢻⠛⡞⢲⠁⢰⣿⡼⢿⣿⠀⠀⠀⡈⠀⠸⡿⠿⡄⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣟⡄⠹⠤⠜⣿⣿⣿⣿⣿⢏⢉⡏⣿⢹⡉⡏⢸⣿⠇⢸⣇⣀⠀⠀⣇⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣹⠎⠀⠀⠀⢹⣿⣿⣿⡿⢊⠥⡸⣄⢇⠼⣸⣼⠿⢿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠿⠿⠿⠿⠿⠿⠗⠂⠀⠀⠀⠙⠿⠿⠟⠑⠛⠛⠻⠿⠿⠷⠇⠒⠛⠛⠛⠛⠛⠛⠋⠃⠰⠙⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶⠴⠶⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠍⣩⠿⠿⢿⡿⡿⠿⢿⣻⠿⣿⣿⣿⣴⡾⠤⣤⣤⠀⣀⠂⣀⣠⣤⣤⣤⡄⠀⠀⢠⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⠉⢀⠾⠿⢷⡾⣾⣮⣷⢽⣻⠭⠽⠿⣿⡟⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠁⠈⠀⠀⠀⣸⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣷⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⠇⠀⠀⠀⠀⠀⣠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣆⡙⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣏⣋⣠⡀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠠⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠈⠀⡉⠠⠀⢀⣥⡀⠀⢠⡀⢠⢀⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡀⢀⣠⣦⠙⠂⠂⢁⢰⠷⣿⡅⠀⠀⠉⢈⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⠀⠀⠀⣶⣿⣦⣶⣿⣿⡍⠀⠀⠐⠒⠂⠀⠀⠀⠀⠘⠛⠇⠀⠘⠀⠀⠈⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠃⠀⠀⠀⠀⠙⠛⠑⢙⡙⠋⢡⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⣧⢻⡄⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡄⠀⠀⠀⠉⠁⠈⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⡏⠀⠀⣾⣿⣿⣿⣿⣿⠏⠹⡒⠀⠙⣿⣿⣸⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⡿⣾⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠸⡇⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣤⢢⠃⠀⠀⣿⣿⣿⢸⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠀⢸⣻⡟⣔⣾⡃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⡎⢱⠀⣿⣿⡏⣾⣿⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣠⡱⣒⠶⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣻⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⡽⡸⢅⠇⢙⣿⢣⣿⣿⠀⠀⠸⣿⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣿⠿⠶⣿⣷⡢⠄⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠂⠀⠀⠀⠀⠾⠛⠻⠻⠋⠻⠃⠀⠀⠛⠛⠿⠿⠟⠟⠛⠜⠅⠣⠘⠀⠘⠿⠘⠛⠛⠀⠀⠀⠘⠀⠛⠿⣿⠙⠛⠛⠿⠟⠑⠙⢿⡿⠍⠙⠛⠿⠃⠀⠀⠀⠀⠐⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⣿⠿⣿⣿⣿⡇⢸⣿⣿⠻⣿⡿⠇⠘⣿⣷⣿⡇⣿⡇⣾⣿⣷⣼⣿⣿⣿⢸⣿⡇⢸⣿⢿⣷⠀⢸⣿⢻⣷⢸⣿⠿⠀⢀⣾⣿⣷⡈⣿⡿⣷⢸⣿⠿⠀⣿⣿⡿⢿⣿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣾⡏⣿⡄⣿⡇⢸⠀⣿⣿⣿⣧⣿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⢸⣿⠀⢸⣿⢾⣯⢸⣿⠶⠀⢸⣿⣧⣭⡄⣿⣿⣿⢸⣿⠷⢸⣿⢻⣇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣿⡟⣿⡇⣿⡇⢸⡇⢻⣿⡏⣿⣿⠀⢿⣿⡿⠋⢿⣿⡿⢸⣿⣷⢸⣿⣾⡿⠀⢸⣿⣼⡿⢸⣿⣶⡄⠈⢿⣷⣿⡇⣿⣧⣿⢸⣿⣶⣾⣿⢻⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠷⠶⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠴⠿⠟⠀⠀⠒⠒⠶⠶⠶⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠛⠂⠀⠀⠀⠀⠀⠐⠾⠷⠂⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ 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⠀⠀⠙⠛⠛⠃⠀⠀⠀⠉⠙⠛⠈⢉⡉⠋⢡⣿⣿⣿⣿⣿⣿⣿⡻⠻⣿⣿⣿⡏⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡄⠀⠀⠀⠋⠀⠁⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⡟⠀⠀⣸⣿⣿⣿⣿⣿⡟⠈⢇⠀⠘⢿⣿⣷⢸⣇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠘⡇⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣧⣼⡞⡄⠀⣼⣿⣿⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣏⣱⢑⠁⣿⣿⡿⢸⣿⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⡿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⡸⢄⢇⡸⠈⣿⡇⣿⣿⡇⠀⠀⡿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⠿⠾⣿⣿⣼⡅⢀⡐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠂⠀⠀⠀⠀⠾⠛⠻⠛⠇⠻⠃⠀⠀⠛⠻⠿⠿⠿⠟⠛⠣⠣⠘⠜⠂⠀⠻⠛⠛⠛⠃⠀⠀⠁⠀⠙⠿⣿⠙⠛⠻⠿⠟⠑⠙⢿⡽⠍⠛⠛⠿⠃⠀⠀⠀⠀⠐⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⣿⠿⣿⣿⣿⡇⢸⣿⣿⠻⣿⡿⠇⠘⣿⣶⣿⡇⣿⡇⣾⣿⣷⣼⣿⣿⣿⢸⣿⡇⢸⣿⢿⣷⠀⢸⣿⢻⣷⢸⣿⠿⠀⢀⣾⣿⣷⡈⣿⣿⣷⢸⣿⠿⠀⣿⣿⡿⢿⣿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣾⡏⣿⡄⣿⡇⢸⠀⣿⣿⣿⣧⣿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⢸⣿⠀⢸⣿⢾⣯⢸⣿⠶⠀⢸⣿⣧⣭⡄⣿⣿⣿⢸⣿⠷⢸⣿⢻⣇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣿⡟⣿⡇⣿⡇⢸⡆⢻⣿⡏⣿⣿⠀⢿⣿⡿⠋⢿⣿⡿⢸⣿⣷⢸⣿⣾⡿⠀⢸⣿⣼⡿⢸⣿⣶⡄⠈⢿⣷⣿⣇⣿⣿⣿⢸⣿⣶⣾⣿⢻⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠷⠶⠶⠲⠶⠶⠆⠀⠀⠀⠀⠀⠰⠿⠿⠀⠀⠒⠂⠰⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠐⠾⠷⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⢴⠴⠶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠩⡉⠭⡻⠛⡛⢟⢿⣿⣿⣿⣿⣿⡿⡷⣬⢬⡤⠁⣀⡀⠂⣄⣀⣤⣤⣤⡄⠀⠀⢠⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠭⠩⢤⠤⡞⣾⣷⣾⡗⣿⢿⡿⠋⠻⢛⣿⡏⠀⢀⣾⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣿⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣆⡙⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣏⣋⣠⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠠⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠐⠃⡒⠂⢀⠄⣐⣤⠀⢠⡀⢀⢀⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣠⣼⣋⠑⠀⣀⣻⣿⣥⡄⠀⠀⠈⢈⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣶⣦⣤⣶⣿⣿⡅⠀⠀⠐⠒⠂⠀⠀⠀⠀⠐⠓⠆⠀⠘⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠋⠀⠀⠀⠉⠙⠙⠉⢉⡉⠋⢁⣿⣿⣿⣿⣿⣿⡿⡻⠻⣿⣿⣿⡟⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⠀⠁⠀⠉⠊⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⡟⠀⠀⣸⣿⣿⣿⣿⣿⡿⠉⢗⠀⠈⢿⣿⣇⢿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⡿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠘⡇⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣧⡜⡞⠄⠀⢸⣿⣿⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣟⣱⠉⡀⢼⣿⣿⢸⣿⡆⠀⠀⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠸⢯⡝⢽⡻⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⡨⢇⢧⡸⠈⣿⡏⣿⣿⡇⠀⠀⡿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⠿⠾⣿⣏⠔⠀⢀⠐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠚⠂⠀⠀⠀⠀⠾⠛⠻⠛⠗⠛⠃⠀⠀⠛⠛⠿⠿⠿⠿⠛⠣⠓⠘⠄⠃⠀⠻⠃⠛⠛⠃⠀⠀⠃⠀⠙⠿⣿⠙⠛⠻⠿⠟⠑⠙⢿⡽⠍⠛⠛⠿⠃⠀⠀⠀⠀⠘⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⣿⠿⣿⣷⣿⡇⢸⣿⣿⠿⣿⡿⠇⠘⣿⣷⣿⡇⣿⡇⣾⣿⣷⣼⣿⣿⣿⢸⣿⡇⢸⣿⢿⣷⠀⢸⣿⢻⣷⢸⣿⠿⠀⢀⣾⣿⣷⡈⣿⣿⣷⢸⣿⠿⠀⣿⣿⡿⢿⣿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣾⡏⣿⡄⣿⡇⢸⠀⣿⣿⣿⣧⣿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⢸⣿⠀⢸⣿⢾⣯⢸⣿⠶⠀⢸⣿⣧⣭⡄⣿⣿⣿⢸⣿⠷⢸⣿⢻⣇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣿⡟⣿⡇⣿⡇⢸⡆⢻⣿⡏⣿⣿⠀⢿⣿⡿⠋⢿⣿⡿⢸⣿⣷⢸⣿⣾⡿⠀⢸⣿⣼⡿⢸⣿⣶⡄⠈⢿⣷⣿⣇⣿⣿⣿⢸⣿⣶⣼⣿⢻⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠷⠶⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠰⠿⠿⠂⠀⠒⠂⠰⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠀⠀⠀⠀⠐⠺⠷⠆⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣛⠋⠛⢿⢿⢿⣿⣿⡿⣿⣿⣿⡻⢾⣴⣤⠄⡀⠀⢠⣲⣄⣀⣤⣤⣤⡄⠀⠀⢠⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠠⢀⠶⠾⢿⣿⣽⣟⣾⠿⡟⡋⠛⢿⣿⡏⠀⢀⣾⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⣸⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣿⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢡⣆⡙⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣏⣋⣠⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠠⡵⠐⠠⠠⡅⣁⣀⡃⢠⡀⢀⢄⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡀⢀⣠⣼⠋⠔⠀⠈⢘⣻⣽⡇⠀⠀⠈⢈⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣴⣤⣤⣶⣿⣿⡅⠀⠀⠐⠒⠃⠀⠀⠀⠀⠘⠒⠆⠀⠘⠀⠀⠘⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠙⠛⠉⢉⡙⠋⢡⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿⣿⣿⡟⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⡿⠉⣷⠀⠈⢿⣿⣇⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠘⡇⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣧⡜⡞⠂⠀⢸⣿⣿⢸⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢹⡉⡆⢸⣿⣿⢸⣿⡆⠀⠀⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠸⣿⣿⣿⣯⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣧⢇⠽⡸⠈⣿⡏⣾⣿⡇⠀⠀⡿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⠷⢿⣿⣏⠮⠁⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠚⠂⠀⠀⠀⠀⠾⠛⠻⠏⠟⠛⠃⠀⠀⠚⠛⠿⠿⠿⠿⠛⠣⠛⠜⠀⠃⠀⠻⠃⠛⠛⠃⠀⠀⠁⠁⠘⠿⣿⠙⠛⠻⠿⠟⠑⠙⢿⡭⠍⠛⠛⠿⠋⠀⠀⠀⠀⠘⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⣿⠿⣿⣿⣿⡇⢸⣿⣿⠻⣿⡿⠇⠘⣿⣶⣿⡇⣿⡇⣾⣿⣷⣼⣿⣿⣿⢸⣿⡇⢸⣿⢿⣷⠀⢸⣿⢻⣷⢸⣿⠿⠀⢀⣾⣿⣷⡀⣿⣿⣷⢸⣿⠿⠀⣿⣿⡿⢿⣿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣾⡏⣿⡄⣿⡇⢸⠀⣿⣿⣿⣧⣿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⢸⣿⠀⢸⣿⢾⣯⢸⣿⠶⠀⢸⣿⣧⣭⡄⣿⣿⣿⢸⣿⠷⢸⣿⢻⣇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣿⡟⣿⡇⣿⡇⢸⡆⢻⣿⡏⣿⣿⠀⢿⣿⡿⠋⢿⣿⡿⢸⣿⣷⢸⣿⣾⡿⠀⢸⣿⣼⡿⢸⣿⣶⡄⠈⢿⣷⣿⣇⣿⣿⣿⢸⣿⣶⣾⣿⢻⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠷⠶⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠰⠿⠿⠂⠀⠒⠀⠰⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠰⠾⠷⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣖⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⠶⠶⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣩⠿⠿⠿⠿⠻⠿⡿⣿⢿⣿⣿⣿⣿⣶⣬⢌⣁⠀⠀⢂⣄⣀⣤⣤⣤⡄⠀⠀⢠⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠩⢤⠸⡾⢯⣿⣽⣛⣽⢿⣯⠋⠻⢿⣿⡟⠀⢀⣾⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢸⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣷⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢉⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣆⡙⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣏⣋⣠⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠘⡪⡀⠔⠀⣘⣀⣡⠀⢠⡀⢀⢀⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣠⣬⢙⠈⠀⠁⣺⣹⣿⡇⠀⠀⠈⢈⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⣤⣦⣤⣶⣿⣿⡍⠀⠀⠐⠒⠂⠀⠀⠀⠀⠘⠓⠆⠀⠘⠀⠀⠘⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠋⠀⠀⠀⠈⠙⠛⠉⢉⡙⠋⢡⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⡿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠵⠀⠈⢻⣿⡇⡿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠘⡇⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣿⣿⣿⣷⣔⡖⢢⠀⢸⣽⣿⡇⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣯⣓⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⢹⡋⡆⢸⣿⣿⢹⣿⡇⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣯⣸⠭⠉⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⢇⡼⡸⠌⣹⡿⣿⣿⡇⠀⠀⡿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⡿⠿⢿⣯⣟⠎⡁⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠂⠀⠀⠀⠀⠾⠛⠻⠇⠗⠛⠓⠀⠀⠘⠛⠿⠿⠿⠿⠛⠻⠛⠜⠂⠃⠀⠹⠇⠛⠛⠃⠀⠀⠁⠃⠘⠿⣿⠙⠛⠛⠿⠟⠑⠙⢿⡭⠍⠛⠛⠿⠋⠀⠀⠀⠀⠐⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⣿⠿⣿⣿⣿⡇⢸⣿⣿⠿⣿⡿⠇⠘⣿⣶⣿⡇⣿⡇⣾⣿⣷⣼⣿⣿⣿⢸⣿⡇⢸⣿⢿⣷⠀⢸⣿⢻⣷⢸⣿⠿⠀⢀⣾⣿⣷⡈⣿⡿⣷⢸⣿⠿⠀⣿⣿⡿⢿⣿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣾⡏⣿⡄⣿⡇⢸⠀⣿⣿⣿⣧⣿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⢸⣿⠀⢸⣿⢾⣯⢸⣿⠶⠀⢸⣿⣧⣭⡄⣿⣿⣿⢸⣿⠷⢸⣿⣻⣇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣿⡟⣿⡇⣿⡇⢸⡆⢻⣿⡏⣿⣿⠀⢿⣿⡿⠋⢿⣿⡿⢸⣿⣷⢸⣿⣾⡿⠀⢸⣿⣼⡿⢸⣿⣶⡀⠈⢿⣷⣿⣇⣿⣧⣿⢸⣿⣶⣾⣿⢻⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠷⠶⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠰⠿⠿⠂⠀⠒⠀⠲⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠀⠾⠷⠂⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⢠⣖⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠖⠶⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⠿⠻⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠯⠽⢄⣐⠀⡆⣆⣀⣤⣤⣦⡄⠀⠀⢠⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠭⠥⢿⠾⣿⣿⣿⣿⣿⣹⣟⠛⠻⣻⣿⡟⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⣸⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣷⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢡⣆⡙⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣏⣋⣠⠀⠀⠀⠀⠀⠠⡷⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⢨⡥⢥⠠⢤⣀⣊⢠⡇⢠⡀⢀⢤⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣠⣶⠙⠑⠊⠊⣻⣿⣮⡇⠀⠀⠉⢈⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⣤⣤⣤⣶⣿⣿⡉⠀⠀⠐⠒⠂⠀⠀⠀⠀⠘⠓⠆⠀⠘⠀⠀⢹⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠙⠛⠉⢉⡙⠋⢡⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⡿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⠀⠈⠈⠉⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠑⡀⠈⢻⣿⡇⡟⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠘⡇⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⡖⢣⠀⢸⣽⣿⡇⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣉⡎⡎⢸⣿⣿⢡⣿⡇⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢗⠧⡸⡀⠟⢹⣿⣼⣿⡇⠀⠀⣿⡇⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⡿⠷⢿⣿⣏⡊⠇⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠂⠀⠀⠀⠀⠾⠛⠻⠇⠿⠛⠛⠀⠀⠘⠛⠿⠿⠿⠿⠛⠛⠜⠄⠃⠃⠀⠙⠏⠛⠛⠛⠀⠀⠀⠃⠘⠿⣿⠛⠛⠻⠿⠟⠑⠙⢿⡭⠍⠛⠛⠿⠋⠁⠀⠀⠀⠘⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⣿⠿⣿⣿⣿⡇⢸⣿⣿⠿⣿⡿⠇⠘⣿⣷⣿⡇⣿⡇⣾⣿⣷⣼⣿⣿⣿⢸⣿⡇⢸⣿⢿⣷⠀⢸⣿⢻⣷⢸⣿⠿⠀⢀⣾⣿⣷⡈⣿⣿⣷⢸⣿⠿⠀⣿⣿⡿⢿⣿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣾⡏⣿⡄⣿⡇⢸⠀⣿⣿⣿⣧⣿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⢸⣿⠀⢸⣿⢾⣯⢸⣿⠶⠀⢸⣿⣧⣭⡄⣿⣿⣿⢸⣿⠷⢸⣿⣻⣇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣿⡟⣿⡇⣿⡇⢸⡆⢻⣿⡏⣿⣿⠀⢿⣿⡿⠋⢿⣿⡿⢸⣿⣷⢸⣿⣾⡿⠀⢸⣿⣼⡿⢸⣿⣶⡄⠈⢿⣷⣿⣇⣿⣿⣿⢸⣿⣶⣾⣿⢻⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠷⠶⠶⠴⠶⠶⠖⠀⠀⠀⠀⠀⠰⠿⠿⠆⠀⠒⠀⠲⠶⠶⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠂⠀⠀⠀⠀⠀⠰⠾⠷⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢰⣖⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠒⠲⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡯⠛⢿⡿⣿⢿⠿⢿⣿⣿⡿⣿⣿⣿⣶⣤⣇⡁⠀⠀⡶⣆⣀⣤⣤⣤⡄⠀⠀⢠⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠝⠢⢈⠽⣿⣿⣿⣿⣿⡟⣳⣿⠏⢻⣿⣿⡇⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠀⣸⡇⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣷⠸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠈⢡⣆⡙⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣏⣋⣠⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠰⡿⠽⡆⠤⣦⣆⣶⡇⢠⡀⢀⣤⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣠⣴⢚⢛⠍⣚⣷⣿⣶⡇⠀⠀⠈⢈⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⣤⣦⣤⣶⣿⣿⡉⠀⠀⠐⠒⠂⠀⠀⠀⠀⠐⠒⠆⠀⠘⠀⠀⢹⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠛⠛⠉⢙⡙⠋⢡⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⡿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠂⠀⢀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠱⡀⠈⢻⣿⡇⡏⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠘⡇⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣶⢣⠀⢸⣽⣿⡇⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣷⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣉⡎⡎⢸⣿⣿⢳⣿⡇⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣯⣿⡿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⢗⠯⡸⣀⠟⢹⣿⣺⣿⣇⠀⠀⡿⡏⢷⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡿⠿⢿⣿⣟⡦⡃⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠂⠀⠀⠀⠀⠾⠛⠻⠇⠿⠛⠛⠀⠀⠘⠛⠿⠿⠿⠿⠛⠛⠜⠄⠃⠃⠀⠙⠏⠛⠛⠛⠀⠀⠀⠃⠘⠿⡯⠙⠛⠻⠿⠟⠐⠻⢿⡭⠝⠛⠛⠿⠋⠁⠀⠀⠀⠘⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⣿⠿⣿⣿⣿⡇⢸⣿⣿⠿⣿⡿⠇⠘⣿⣶⣿⡇⣿⡇⣾⣿⣷⣼⣿⣿⣿⢸⣿⡇⢸⣿⢿⣷⠀⢸⣿⢻⣷⢸⣿⠿⠀⢀⣾⣿⣷⡈⣿⣿⣷⢸⣿⠿⠀⣿⣿⡿⢿⣿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣾⡏⣿⡄⣿⡇⢸⠀⣿⣿⣿⣧⣿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⢸⣿⠀⢸⣿⢾⣯⢸⣿⠶⠀⢸⣿⣧⣭⡄⣿⣿⣿⢸⣿⠷⢸⣿⣻⣇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣿⡟⣿⡇⣿⡇⢸⡆⢻⣿⡏⣿⣿⠀⢿⣿⡿⠋⢿⣿⡿⢸⣿⣷⢸⣿⣾⡿⠀⢸⣿⣼⡿⢸⣿⣶⡄⠈⢿⣷⣿⣇⣿⣿⣿⢸⣿⣶⣾⣿⢻⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠰⢲⠷⠶⠶⠲⠶⠶⠖⠀⠀⠀⠀⠀⠐⠿⠿⠆⠀⠒⠐⠲⠶⠶⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠂⠀⠀⠀⠀⠀⠠⠾⠿⠆⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣖⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠖⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣫⣿⠿⡻⢿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⡷⡴⣦⣄⡀⣀⡠⣆⣀⣤⣤⣤⡀⠀⠀⢠⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠧⠥⠽⠿⣿⣿⣿⣿⣟⡻⡟⡛⠿⣿⣿⡇⠀⢀⣾⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⣼⡇⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠁⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⣷⠘⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣦⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⢉⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡈⢡⣆⡙⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣏⣋⣠⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠠⠈⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠈⡳⡿⣄⠠⡄⢠⣶⡆⢠⡀⢀⢄⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢀⣠⣶⠋⠓⠟⠐⢾⣷⣷⡅⠀⠀⠈⢈⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⣤⣤⣤⣶⣿⣿⡉⠀⠀⠐⠒⠀⠀⠀⠀⠀⠐⠒⠆⠀⠘⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠙⠛⠛⠋⠀⠀⠀⠈⠙⠛⠙⢋⡙⠋⢡⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⡿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⠀⠀⠂⠂⠀⢀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠈⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠑⡀⠈⢻⣿⡇⡏⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠸⡇⢸⡇⠀⠀⠀⣠⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣶⢣⠀⢸⣽⣿⡇⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⢸⣿⡿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣉⡎⡎⢸⣿⣿⣧⣿⡇⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⢿⣟⣿⣛⡁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⢇⠯⡸⣀⠏⢹⣿⢺⣿⣇⠀⠀⡿⡏⣷⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⡿⠷⢾⣿⣴⠗⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠂⠀⠀⠀⠀⠾⠛⠻⠇⠿⠙⠛⠀⠀⠘⠛⠿⠿⠿⠿⠛⠛⠜⠄⠃⠂⠀⠙⠏⠛⠛⠛⠀⠀⠀⠃⠘⠿⡏⠛⠛⠻⠿⠟⠊⠻⢿⡽⠍⠛⠻⠿⠁⠁⠀⠀⠀⠘⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⣿⠿⣿⣿⣿⡇⢸⣿⣿⠿⣿⡿⠇⠘⣿⣷⣿⡇⣿⡇⣾⣿⣷⣼⣿⣿⣿⢸⣿⡇⢸⣿⢿⣷⠀⢸⣿⢻⣷⢸⣿⠿⠀⢀⣾⣿⣷⡈⣿⣿⣷⢸⣿⠿⠀⣿⣿⡿⢿⣿⠿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣾⡏⣿⡄⣿⡇⢸⠀⣿⣿⣿⣧⣿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⢸⣿⠀⢸⣿⢾⣯⢸⣿⠶⠀⢸⣿⣧⣭⡄⣿⣿⣿⢸⣿⠷⢸⣿⣻⣇⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⣿⡟⣿⡇⣿⡇⢸⡆⢻⣿⡏⣿⣿⠀⢿⣿⡿⠋⢿⣿⡿⢸⣿⣷⢸⣿⣾⡿⠀⢸⣿⣼⡿⢸⣿⣶⡄⠈⢿⣷⣿⣇⣿⣿⣿⢸⣿⣶⣾⣿⢻⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠲⢲⠷⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠐⠿⠿⠆⠀⠒⠂⠰⠾⠶⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠐⠾⠷⠂⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ䷩ 𝚕𝚒𝚗𝚎 2235 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/16/irc-log-150122/#comments Gemini version at gemini://gemini.techrights.org/2022/01/16/irc-log-150122/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Saturday,_January_15,_2022⠀✐ Posted in IRC_Logs at 2:01 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-150122.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-150122.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-150122.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-150122.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmavHA8TwYT2BKeuRFbDuaJm5eULehqDyFmraiuwY61o6x #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmWiBAC2s6eHaqF7WMtw3fQf8ZsQ4VYG4Pzoz8A9LBdccE (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  QmUPXMp5b3pCCpBDYVrvXrszExDMYmaAZu6GyJrQDMR3Cb social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmRPV73iUc1kZtRjsUUEh7VHWNzMTduxQtL3SzzuQ1qy2r social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmZLXoCuL26LNNjGrnSdpC4JUrPNgjD8JYV8Zqwh6XMjNN #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmdUJ7T1NLKqVpXButmvciwV2rwfNynrdV9iRjBbsGVcwm (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  Qmdmj1CfCAtRyVUU2h1A365MYmHE7SQzydbrjDJJxLs4Au #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmQCNEf3p9knTPWQzEmKLs4ig68qt1edFUWGy2Sb7Rf5AP (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmZWJhSMSsSbuTS3JfxxEo3tfs2QfTCENeVipKSaQVU5b2 ䷩ 𝚕𝚒𝚗𝚎 2362 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/16/just-enough-privacy-lies/#comments Gemini version at gemini://gemini.techrights.org/2022/01/16/just-enough-privacy-lies/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ EPO’s_Web_Site_Constantly_Spammed_by_Lies_About_Privacy_While_EPO_Breaks_the Law_and_Outsources_Data_to_the_United_States⠀✐ Posted in Deception, Europe, Microsoft, Patents at 6:23 am by Dr. Roy Schestowitz Video_download_link | md5sum ca82f07ff4a0e3089b08a7be917d8f65 EPO Lies About Privacy Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/epo-data-protection-waffle.webm Summary: The António_Campinos-led EPO works for imperialism, it not only protects the rich; sadly, António’s father isn’t alive anymore and surely he would blast his son for doing_what_he_does_to_progress_his_career while lying to staff and European citizens THE “late_Friday”_post (warning: epo.org link) from the EPO was that typical "privacy"_hogwash; we’ve seen a lot of that lately, probably because the EPO is quietly coming under a lot of pressure for its privacy_infringement_crimes. A day earlier the EPO pretended (warning: epo.org link) it was interested in oversight — the very thing that Benoît_Battistelli had scuttled. In the video above I show that the very survey about this seems to be (very likely) a privacy violation with false claims of “confidentiality” and anonymity. “Imagine a small African nation doing the same while claiming to be immune/ protected from prosecution.”Let’s face it; the EPO of 2022 is a total_disaster already — a rogue institution which still bribes the media and bribes academia to keep_perceptions_under_control. At the same time it spies on the whole world, illegally, on behalf of the United States while claiming diplomatic immunity. Imagine a small African nation doing the same while claiming to be immune/protected from prosecution. █ ䷩ 𝚕𝚒𝚗𝚎 2416 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/16/shared-spaces-in-geminspace/#comments Gemini version at gemini://gemini.techrights.org/2022/01/16/shared-spaces-in-geminspace/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Gemini_Rings_(Like_Webrings)_and_Shared_Spaces_in_Geminspace⠀✐ Posted in Free/Libre_Software at 5:51 pm by Dr. Roy Schestowitz Video_download_link | md5sum 00694971abd0b010920fe27e4fa4f1d5 Connected Communities in Geminispace Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/shared-capstules-and-rings.webm Summary: Much like the Web of 20+ years ago, Gemini lets online communities — real communities (not abused tenants, groomed to be ‘monetised’ like in Facebook or Flickr) — form networks, guilds, and rings THE ‘old’ Web was, in a lot of ways, far more charming than today’s bloated and hostile ‘Web’, which became increasingly proprietary (Web browsers are rapidly becoming little but a canvas for proprietary software that runs remotely). The original Web emancipated people, whereas today’s Web mostly oppresses them. “Each service we use that’s operated by someone other than ourselves is another point of failure in our lives,” one_Gemini_blogger_recently_noted. “Each of these corporations is handling staggeringly large amounts of personal data.” “The original Web emancipated people, whereas today’s Web mostly oppresses them.”In the old Web we had things like Geocities (where I had a site when I was 15 or 16) and shared spaces like chiark, which still remains unchanged (not trying to become more “modern”). There’s something very similar to it in tilde.team, which even includes LEO, “a webring but for Gemini instead of the web” (yes, remember webrings?) and it certainly seems to have grown quite a bit. Gemini space is a lot bigger than people care to realise and it_grows_rapidly. Towards the end the video above shows that there are now close to 2,000 known capsules and we’re very, very close to 1,600 active capsules which are known_to Lupa (maybe it will exceed that number by the end of the day). There are a lot more users than capsules, probably tens of thousands regular users. Suffice to say, those are people who install a 'proper'_client instead of using some Web gateway. █ ䷩ 𝚕𝚒𝚗𝚎 2478 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/16/stealing-hacker-culture/#comments Gemini version at gemini://gemini.techrights.org/2022/01/16/stealing-hacker-culture/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_Corporate_Cabal_(and_Spy_Agencies-Enabled_Monopolies)_Engages_in_Raiding of_the_Free_Software_Community_and_Hacker_Culture⠀✐ Posted in Deception, Free/Libre_Software, GNU/Linux, Microsoft at 8:46 am by Dr. Roy Schestowitz Video_download_link | md5sum 6fda57fbbfbb0443719a2afd74df26d5 Raiding the Community Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/raiding-of-the-freesw-century.webm Summary: In an overt attack on the people who actually did all the work — the geeks who built excellent software to be gradually privatised through the Linux Foundation (a sort of price-fixing and openwashing cartel for shared interests of proprietary software firms) — is receiving more widespread condemnation; even the_OSI_has_been_bribed_to_become_a_part-time_Microsoft_outsourcer as organisations are easier to corrupt than communities FOUR days ago we_mentioned what Microsoft had done to Marak, in effect confiscating his work on Free software though he wasn’t working for Microsoft or even being paid for his work. This caused an uproar; does Microsoft covertly own and control everything in GitHub? If so, it’s not free hosting, it’s the passage of one’s work to Microsoft. What about projects that used GitHub for 14 years? Did they ever consent to such a transaction? And also, what did Microsoft actually pay for when it took_over_GitHub? Was this a non-consensual sale of code other than the proprietary software of GitHub itself? “Recently, as we noted here several times, Microsoft tried to claim credit for the mission to Mars by merely asserting that everything in GitHub (as in every project with presence there) is property of Microsoft.”The video above talks about an upcoming series regarding the raiding of the Commons or the privatisation of volunteers’ hard work; not only Microsoft is doing it and I mention AWS_as_another_example — raking in all the profits (financial gains) while denying a living wage to those who actually did all the work. This crisis isn’t new and discussion about it is well overdue. Yes, Free software powers this planet (also our presence in space and Mars to some degree), but who controls this software? Recently, as we noted here several times, Microsoft tried to claim credit for the mission to Mars by merely asserting that everything in GitHub (as in every project with presence there) is property of Microsoft. █ “Nobody accidentally makes a billion dollars while working on protecting human rights and democracy. The only way you make a billion dollars is by working on making a billion dollars.” — Aral_Balkan ䷩ 𝚕𝚒𝚗𝚎 2548 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_16/1/2022:_Latte_Dock_0.11_and_librest_0.9.0⠀✐ Posted in News_Roundup at 12:15 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⠀➾ # ⚓ Top_4_Linux_Distros_for_Beginners_(2022)⠀⇛ As we come into the new year, it might be part of your New Year’s Resolution to make the big move to the amazing world that is the Linux OS. If so, then the first hurdle you will have to overcome is choosing what distribution (distro) you want to use. o § Kernel Space⠀➾ # ⚓ New_Xilinx_Drivers,_GNSS_Reciver_USB_Driver_&_Habana_Labs Updates_Land_In_Linux_5.17_–_Phoronix⠀⇛ Sent in to the Linux kernel on Friday were the “char/misc” updates as the smorgasbord of kernel changes not fitting formally within other areas of the kernel. The char/misc changes range from AI accelerator driver updates to new Xilinx code to other random changes littered throughout. Char/misc for Linux 5.17 is as diverse as ever. Among the many changes bringing in roughly 26.9k lines of new code (and 4.5k lines removed) include items such as: - The Xilinx event management driver is new and is used for notifications from firmware. This can be used for error events, device events, and more. # ⚓ Page_Table_Check_Feature_Merged_For_Linux_5.17_To_Help Fight_Memory_Corruption_–_Phoronix⠀⇛ Merged into Linux 5.17 this weekend is the Google- developed Page Table Check feature that can help combat some forms of memory corruption. Google engineers last year uncovered a reference count underflow issue in the kernel that affected all kernel releases going back to Linux 4.14 four years prior. Stemming from uncovering that issue, Google engineers came up with Page Table Check to help uncover issues like that moving forward. The Page Table Check feature is principally about ensuring there is no illegal sharing of pages such as one process accidentally (or otherwise) leaking to another process. # § Graphics Stack⠀➾ # ⚓ GravityMark_1.44_Released_With_Ray-Tracing_Support_– Phoronix⠀⇛ Those wanting to enjoy some impressive Vulkan ray-traced visuals on Linux (and macOS or Windows) now have GravityMark to add to the list of Linux-native ray-traced software for testing. GravityMark is the new graphics benchmark from Tellusim, the company led by Alexander Zapryagaev who was one of the original Unigine co-founders. GravityMark has been quite impressive for a free and cross- platform, cross-API benchmark while with this weekend’s v1.44 release is even more impressive now that there is DirectX 12 / Vulkan / Metal ray-tracing support. o § Applications⠀➾ # ⚓ ‘Secrets’_–_Modern_Simple_GTK4_App_to_Store_Your_Passwords in_Ubuntu_/_Fedora_|_UbuntuHandbook⠀⇛ Looking for an app to store your passwords? Secrets is a good choice for those using GNOME desktop. “Secrets” is a free open-source password manager that integrates perfectly with GNOME desktop and provides a modern and easy to use user interface. It’s formerly Password Safe (nothing to do with pwsafe). Since v6.0, it’s called Secrets. # ⚓ JACK2_1.9.20_Released_With_Official_FreeBSD_Support⠀⇛ A new version of JACK2 is available this weekend, the latest version of this cross-platform, professional sound server. While PipeWire continues taking off on the Linux desktop for roles filled by PulseAudio and JACK, that hasn’t let up development of JACK2. With JACK2 1.9.20 for that modern version of JACK there is fixes around the 32-bit support in the ALSA driver, multiple fixes affecting Windows and macOS, new build options around the example tools, and official FreeBSD support. o § Instructionals/Technical⠀➾ # ⚓ How_to_Install_Linux_Kernel_5.17_on_Fedora_35_– LinuxCapable⠀⇛ For users of Fedora, most packages are almost up to date with what is present and classed as stable. However, when it comes to Kernels, users often may want to try the latest release candidate without switching to Fedora Rawhide and having an unstable system. With Fedora becoming more popular and mainstream, newer users do not realize you can enable the Fedora repository and install upcoming release candidates constantly being updated by the Fedora team. In the following small tutorial, you will learn how to install the Latest Linux Kernel from the Fedora Rawhide repository on your Fedora 35 Workstation or Server. # ⚓ Wouter_Verhelst:_Backing_up_my_home_server_with_Bacula_and Amazon_Storage_Gateway⠀⇛ Initially conceived and sized so I could digitize my (rather sizeable) DVD collection, I started using it for other things; I added a few play VMs on it, started using it as a destination for the deja-dup-based backups of my laptop and the time machine-based ones of the various macs in the house, and used it as the primary location of all the photos I’ve taken with my cameras over the years (currently taking up somewhere around 500G) as well as those that were taking at our wedding (another 100G). To add to that, I’ve copied the data that my wife had on various older laptops and external hard drives onto this home server as well, so that we don’t lose the data should something happen to one or more of these bits of older hardware. # ⚓ How_To_Install_Let’s_Encrypt_SSL_with_LEMP_on_AlmaLinux_8_– idroot⠀⇛ In this tutorial, we will show you how to install Let’s Encrypt SSL with LEMP on AlmaLinux 8. For those of you who didn’t know, Let’s Encrypt is the free SSL option for you. Let’s Encrypt can be signed through Certbot, a free, open-source software tool for automatically issuing the SSL Certificate. 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 a free SSL certificate with LEMP on an AlmaLinux 8. You can follow the same instructions for CentOS and Rocky Linux. # ⚓ Install_Arch_Linux_as_fast_as_possible_–_Invidious⠀⇛ This includes downloading, bootloader, and all the fixing for a functional arch system. Using this new branch you can do it as well! # ⚓ How_to_Install_Java_on_AlmaLinux_–_Linux_Stans⠀⇛ AlmaLinux is a FOSS alternative to the old CentOS. It’s a great server distro and a lot of people switched to Alma after the whole CentOS Stream announcement. In this tutorial, we’ll show you how to install and configure Java on AlmaLinux via the CLI. Java has different editions to choose from, so we’ll include instructions for the most popular and widely used one – the Standard Edition. Java also has different packages to choose from, Java Runtime Environment (JRE) and the Java Development Kit (JDK). The JDK also includes JRE, so this tutorial will show you how to install JDK on Alma Linux. There are also two different implementations – OpenJDK (FOSS), and Oracle Java. Most people prefer OpenJDK, so that’s what we’ll use. If you don’t know the differences between any of these, you can either google them or don’t worry about it – this tutorial will set up the environment that will most likely work for you. o § Games⠀➾ # ⚓ Solve_Wordle_using_the_Linux_command_line_| Opensource.com⠀⇛ I’ve recently become a little obsessed with an online word puzzle game in which you have six attempts to guess a random five-letter word. The word changes every day, and you can only play once per day. After each guess, each of the letters in your guess is highlighted: gray means that letter does not appear in the mystery word, yellow means that letter appears in the word but not at that position, and green means the letter appears in the word at that correct position. # ⚓ Mac_and_Linux_games_leave_Humble_Bundle’s_Trove_after January_31st_–_Yahoo_Tech⠀⇛ o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ psifidotos:_Latte_Dock_v0.11~_|_Multi-Screens_Dream, an_AllScreens_option…⠀⇛ This is a long awaited feature for multi- screens users. In Latte upcoming v0.11 users can now choose their docks and panels to be on all screens or on all secondary screens. Docks and panels will be up to date in such case and it is also easier for users to make changes to them and use them in general. # § GNOME Desktop/GTK⠀➾ # ⚓ Günther_Wagner_–_Announce_new_release_0.9.0_of librest⠀⇛ I’m pleased to announce the release of 0.9.0 of librest, a library meant to interact with “Restful” web services. This library is very old and not really big but it handles the aspect of interaction with REST-APIs in a convenient fashion. After a long period of maintenance state i picked it up and brought it into 2022. Most of the deprecated API calls are gone now and it should be now possible to parallel-install librest with the previous release. # ⚓ ‘Nordic’_GTK_Theme_Brings_Nord_Color_Scheme_to_Linux Desktops_–_OMG!_Ubuntu!⠀⇛ If you want to bring the chilled out tones of the popular Nord theme to your Ubuntu desktop you simply must check out the ‘Nordic’ GTK theme. The Nordic GTK theme is a faithful implementation of the popular colour-scheme of the Nord theme For GTK-based desktop environment. Like the similarly-ubiquitous Dracula theme, Nord is a hugely popular colour scheme with developers, and there are a ton of ports for all kinds of applications. Originally created to provide “optimal focus and readability for code”, Nord has bloomed in popularity with developers and non- developers alike. o § Devices/Embedded⠀➾ # ⚓ Raspberry_PI_Kiosk:_creating_a_touchscreen,_informative stand_–_peppe8o⠀⇛ Welcoming guests in stores or exibitions can require a lot of effort when peak hours are in progress. Usually, informative stands help managing guests with self-service devices, giving the first info and reducing guests bounce rate. You can build them on low costs solution by creating kiosks with Raspberry PI computer boars and touchscreen display In this tutorial, I’m going to show you how to create a kiosk with Raspberry PI, mounted with a touchscreen display. A lot of tutorials on this topic focus on installing specialized kiosk software. I will make things simpler: our kiosk will just show a web page for the user. I’ll build my kiosk configuration on Chromium running in a special configuration named “kiosk”. All the logic and customer services will be built on web pages to be shown. A good practice will be creating these web pages with a clear navigation menu so that guests can easily understand where they are and how to go back to the home page. # ⚓ Pine64′s_Newest_Linux_Smartphone_‘PinePhone_Pro_Explorer Edition’_Now_Available_for_Pre-Order_–_Slashdot⠀⇛ “Linux fans rejoice!” writes Hot Hardware. ” Pine64′s newest smartphone is officially available for pre-order.” # ⚓ PinePhone_Pro_Explorer_Edition_Linux_Handset_Opens Preorders_At_An_Attractive_Price⠀⇛ Linux fans rejoice! Pine64’s newest smartphone is officially available for pre-order. Here is everything you need to know to get your hands on the PinePhone Pro Explorer Edition. PinePhone Pro Explorer Edition pre-orders opened up yesterday. Devices that are pre-ordered before January 18th will be shipped from Pine64’s Hong Kong warehouse by January 24th and should arrive by early February. Devices ordered after that date will not be shipped until late February. The team will be on vacation for Chinese New Year, which begins on February 1st. There are a few other things to note about pre- orders. First, consumers can only purchase a single device. Second, the PinePhone Pro Explorer Edition must be purchased separately from other items on the Pine64 website. Consumers will otherwise receive an error at check-out and be unable to complete their transaction. This includes adding items like the charging case. Last, Pine64 notes, “The PinePhone Pro Explorer Edition is aimed at Linux developers with an extensive knowledge of embedded systems and/or experience with mobile Linux.” The device is intended for “developers and early adopters” and not for those who rely upon mainstream apps. # ⚓ Intel_launches_NUC_11_Essential_mini_PC,_Kits,_and_SBC_with Jasper_Lake_SoC_–_CNX_Software⠀⇛ Details about the Intel NUC 11 Essential “Atlas Canyon” mini PCs with Jasper Lake processor were leaked in May 2021, but Intel has now made it official with the “launch” of five NUC 11 Essential SKUs with one Windows 11 mini PC with 4GB RAM and 64GB storage, three kits (bare mini PC), and one bare board all listed on Ark Intel. # § Open Hardware/Modding⠀➾ # ⚓ Glitch_Your_Way_To_Reverse-Engineering_Glory_With_The PicoEMP_|_Hackaday⠀⇛ Most of our projects are, to some extent, an exercise in glitch-reduction. Whether they’re self-inflicted software or hardware mistakes, or even if the glitches in question come from sources beyond our control, the whole point of the thing is to get it running smoothly and predictably. That’s not always the case, though. Sometimes inducing a glitch on purpose can be a useful tool, especially when reverse engineering something. That’s where this low-cost electromagnetic fault injection tool could come in handy. EMFI is a way to disrupt the normal flow of a program running on an embedded system; properly applied and with a fair amount of luck, it can be used to put the system into an exploitable state. The PicoEMP, as [Colin O’Flynn] dubs his EMFI tool, is a somewhat tamer version of his previous ChipSHOUTER tool. PicoEMP focuses on user safety, an important consideration given that its business end can put about 250 volts across its output. Safety features include isolation for the Raspberry Pi Pico that generates the PWM signals for the HV section, a safety enclosure over the HV components, and a switch to discharge the capacitors and prevent unpleasant surprises. o § Free, Libre, and Open Source Software⠀➾ # ⚓ Serial_Studio_One_Year_On⠀⇛ The program is open-source and multi-platform. You can build it yourself or download pre-compiled binaries for Windows, Linux, and Mac. # § Programming/Development⠀➾ # ⚓ Osmo_PIM_0.2.14_compiled_in_OpenEmbedded⠀⇛ Very good news about Osmo. “PIM” means Personal Information Manager, and Osmo has been in the pups for a very long time. However, it is somewhat neglected and not as well integrated as could be. The way this latest work with Osmo came about, is I have an elderly relative who has a mobile phone with prepaid account with a telco. I pay it, every 4 weeks. Don’t want to do a direct-debit with a bank, so renewal requires me to remember when to pay… and I forget. Besides, renewal is peculiar. I have to pay $15 for the renewal, then separately have to pay $5 international-calls addon. That second payment requires a manual online choice. I cannot see how to automate this with direct- debit or bpay. The telco is Optus. # ⚓ Josef_Strzibny:_Configuring_Rails_system_tests_for headless_and_headfull_browsers⠀⇛ Want to run your system tests headless? And why not both ways? Here’s how to extend Rails tasks to run your system tests with the driver of your choice. # ⚓ 3_Best_Free_and_Open_Source_JavaScript_Engines_– LinuxLinks⠀⇛ JavaScript is an interpreted programming language. It means that source code isn’t compiled into binary code prior to execution. The role of the JavaScript engine is to turn plain text script into executable code. In other words, the engine is a container in which you run your program. JavaScript engines are often developed by web browser vendors, and every major browser has one. In a browser, the JavaScript engine runs in concert with the rendering engine via the Document Object Model. JavaScript engines implement specification of the language provide by ECMAScript. Standardization enables the development of independent engines and ensures scripts give the same results no matter wherever they run. The first JavaScript engines were mere interpreters, but all relevant modern engines use just-in-time compilation for improved performance. The use of JavaScript engines is not limited to browsers. For example, the V8 engine is a core component of the Node.js and Deno runtime systems. Engines which use runtime interpreters and do not compile into native machine code are excluded from this roundup. Here’s our verdict captured in a legendary ratings chart. We feature free and open source software only here. # ⚓ Kasm_Workspaces_–_Stream_Docker_Containers_Easily_& Quickly⠀⇛ Kasm Workspaces is an intriguing platform for security and development aficionados. It is accessible by web browser and allows users to deploy container apps, including full-fledged Ubuntu desktops. In our daily lives, we must deal with a wide range of challenges that arise in our workplace. As an independent developer, I am concerned with designing secure code, optimizing application speed, and hunting and fixing bugs. But what if, when searching for something on the Internet, I accidentally click on a site that steals my session or downloads ransomware or malware? That is beyond frustrating. Isn’t that right? Every day, I’m sure firms of various sizes have the same difficulty. What if one of their employees accidentally downloads malware in the workplace? Kasm Workspaces, on the other hand, attempts to solve the same problem to a large extent. # § Perl/Raku⠀➾ # ⚓ Fooled_by_complexity_|_Playing_Perl_6␛b6xA Raku⠀⇛ And that fool would be me. After realising that HyperSeq is lazy, I managed to simplify the code in my last post. [...] The sub needle transforms it’s argument or returns Nil. By turning Nil into Empty, any call to .head will skip all values that where not a hit. At least for strongly CPU-bound tasks, which allow for small batch sizes, .hyper doesn’t overshoot much. # § Rust⠀➾ # ⚓ GStreamer_Rust_bindings_0.18.0_release⠀⇛ A new version of the GStreamer Rust bindings, 0.18.0, was released. Together with the bindings, also a new version of the GStreamer Rust plugins was released. As usual this release follows the latest gtk-rs release and the corresponding API changes. This release includes optional support for the latest new GStreamer 1.20 APIs. As GStreamer 1.20 was not released yet, these new APIs might still change. The minimum supported version of the bindings is still GStreamer 1.8 and the targetted GStreamer API version can be selected by applications via feature flags. * § Leftovers⠀➾ o ⚓ Giant_Wheels_Make_For_Exciting_Powered_Rollerskates⠀⇛ Roller skates are fun and all, but they’re pretty well limited to rolling on relatively smooth surfaces. [Fireball Tool] wanted something a little more rugged, so set about a build of his own. The challenge of the design was to build these skates using as many wheelchair parts as possible, including the wheels. Roughly 22″ tall, the wheels have great bearings inside and are designed to run on a single-sided axle support, perfect for the skates. A metal bracket is then used to attach a snowboard boot binding so the wheels can be fitted to the wearer’s feet. Training wheels were fitted to the rear to make it easier for the rider, while a chainsaw engine was pressed into service to provide some welcome propulsive force. o § Hardware⠀➾ # ⚓ Giant_3D_Prints_Piece-by-Piece_|_Hackaday⠀⇛ While FDM printers have gotten bigger lately, there’s almost always going to be a part that is bigger than your bed. The answer? Break your design into parts and assemble them after printing. However, the exact method to do this is a bit of a personal choice. # ⚓ Coin_Sorter_Is_Elegant_And_Beautiful_|_Hackaday⠀⇛ Counting change is a great way to teach children about mathematics and money, but it grows tiresome for those of us that have passed the first grade. Thus, a machine should the job, as [Daniele Tartaglia] demonstrates. A vibrating motor is used to shake a hopper full of coins, letting them fall through a feeder slot into the machine at a steady rate. They then go through a size-based sorter, which flicks the coins into a different channel depending on their physical dimensions. The coins are counted via infrared sensors wired up to an Arduino, and then pass through a rather lovely maze on their way down to sorting bins at the bottom of the machine. o § Health/Nutrition/Agriculture⠀➾ # ⚓ COVID-19_in_2021_—_a_timeline_of_the_coronavirus_outbreak⠀⇛ # ⚓ The_Omicron_Shift_in_Europe:_Pandemic_or_Endemic?_–_The_New York_Times⠀⇛ In Britain, France, Spain and other countries across Europe, politicians and some public health experts are pushing a new approach to the coronavirus pandemic borne of both boldness and resignation: that the illness is becoming a fixture of daily life. Governments are seizing a moment in which their populations have experienced less severe illness, and, in some instances, a drop in new daily cases after weeks of record growth. And they are moving their mitigation policies off emergency footing. In Spain, for instance, Prime Minister Pedro Sánchez declared last week that citizens would “have to learn to live with it, as we do with many other viruses,” and said that the country should adjust the national approach to more closely align with how it handles influenza outbreaks. Olivier Véran, the French health minister, said recently that France’s high level of infection and strong vaccination rate could “maybe” mean this would be the final wave. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ GCC_12_Ready_To_Help_Fend_Off_Trojan_Source Attacks_–_Phoronix⠀⇛ Disclosed a few months back were “Trojan Source” attacks against compilers where specially crafted code could be rogue but not appear so due to exploiting Unicode issues. Unicode control characters could be used to reorder tokens in source code that could alter the behavior when compiled. With the upcoming GCC 12 compiler release there is a new warning to help point out possible Trojan Source attacks. # ⚓ Vulnerability_in_cryptsetup_Allows_Decrypting Part_of_LUKS2-Encrypted_Device⠀⇛ An attacker with physical access to the medium could use this flaw to force a user into permanently disabling the encryption layer of that medium. Many enterprises, small businesses, and government users need to encrypt their laptops to protect confidential information such as customer details, files, contact information, and much more. LUKS (Linux Unified Key Setup) is the standard for Linux hard disk encryption and it is transparent to the user as it operates below the filesystem layer. Basically, it is a block device encryption, which means that when a block from disk is read or written the encryption module at kernel level works for us, like a translator. [...] This attack requires repeated physical access to the LUKS device but no knowledge of user passphrases. The decryption step is performed after a valid user activates the device with a correct passphrase and modified metadata. There are no visible warnings for the user that such recovery happened. The attack can also be reversed afterward with possible modification of revealed plaintext. # ⚓ Microsoft_Warns_of_Destructive_Malware Targeting_Ukrainian_Organizations [Ed: Highly misleading headline and misdirection, suggestive of Microsoft controlling CISA and using it to deflect blame]⠀⇛ Microsoft has released a blog post on possible Master Boot Record (MBR) Wiper activity targeting Ukrainian organizations, including Ukrainian government agencies. According to Microsoft, powering down the victim device executes the malware, which overwrites the MBR with a ransom note; however, the ransom note is a ruse because the malware actually destroys the MBR and the targeted files. # § Privacy/Surveillance⠀➾ # ⚓ Brussels_Playbook:_David_Sassoli_dies_— Russia_talks_—_Surveillance_scandal_– POLITICO⠀⇛ o § Transparency/Investigative Reporting⠀➾ # ⚓ Why_Hawaii_Needs_A_Chief_Data_Officer_—_Now⠀⇛ It’s a familiar story at the Hawaii State Capitol: A bill is authored by top legislative leaders, strongly supported by experts in the field and publicly opposed by no lawmakers, and yet it mysteriously dies in the waning days of session. Such was the case of House Bill 532 in 2019, which called for establishing a chief data officer within the state Office of Enterprise Technology Services. Along with creating a data task force, the legislation authorized the new employee to develop, implement and manage statewide dataset policies, procedures and standards. A chief data officer, a favorable committee report explained, “will help to standardize the sharing of data among agencies, increase government transparency, and promote data-driven government policies.” o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Novak_Djokovic,_Sport,_Politics,_Harassment,_Defamation_and Misdirection⠀⇛ British newspapers have given heavy coverage to the association between Prince Andrew and the Epstein saga. Yet the Australian press, faced with strict laws about defamation, can not give the same level of attention to the relationship between the Prime Minister and Hillsong allegations. What we have just seen this week can be summarized as the defamation and harassment of a foreigner, the distraction from more serious issues and most critical of all, the trivialization of consent. o § Civil Rights/Policing⠀➾ # ⚓ Survivor993_Is_Not_Alone:_Lawsuits_Show_Abuse_at_School_for At-Risk_Teens⠀⇛ Decades later, lawsuits submitted under the Child Victims’ Act have exposed rampant claims of physical, emotional and sexual abuse. o § Monopolies⠀➾ # ⚓ FOSS_Patents:_Google’s_call_on_Apple_to_support_the_RCS messaging_standard_is_consistent_with_what_an_EU_commissioner already_wanted_11_years_ago:_the_EU’s_unfinished interoperability_business⠀⇛ I may not always agree with The Verge on Apple- related issues, but I have no problem acknowledging that they’ve been right all along to ask Apple when iMessage would finally support the RCS messaging standard in order to achieve interoperability with other messengers. Now that Google’s Android chief Hiroshi Lockheimer publicly called on Apple to do so, there is at least some hope for change. While the iMessage lock-in problem and the social pressures it exerts on low-income families has been discussed on the Internet for some time (see this Septemer 2020 thread on Hacker News, which contains pretty good explanations of how it works), it took a recent Wall Street Journal article to draw the attention of influential people to that problem. It also came up during the Epic Games v. Apple trial, with Apple-internal communications revealing a lock-in strategy. When I ditched my iPhone last summer, I knew (not least thanks to the public debate surrounding Epic v. Apple) that one can switch off iMessage, which I did about a week before making my Google Pixel my primary phone. It was a non-issue since I primarily use WhatsApp and Signal. Then I’m not a teenager in the United States. The problem is real, and I do feel sorry for low-income families impacted by it. However, let’s be clear that Apple’s “culpability” in this context is merely a refusal to be interoperable. No one can reasonably expect them to provide an iMessage app on Android, but I agree with Google that supporting RCS would be the morally right thing to do. # ⚓ European_Union:_Don’t_Wait_Too_Long_To_Enforce_Your_IP Rights,_Especially_Community_Plant_Variety_Rights [Ed: No, there is no such thing as “IP” and what Márk Kovács is neither legally nor technically a right; moreover, life monopolies_or_patents on plants are insane!]⠀⇛ Mark Twain famously said “Never put off till tomorrow what may be done day after tomorrow just as well.” Although procrastination usually does not have serious consequences, careful consideration is needed when enforcing IP rights. In its recent decision in case C-186/18, the Court of Justice of the European Union (“CJEU”) concluded that an unjustified delay in enforcing IP rights may result in the loss of a large part of the claim due to time-limitation. # ⚓ Guest_Book_Review:_Research_Handbook_on_Design_Law [Ed: There is no such thing as “IP” and what’s alluded to here is not “rights”, either. Hayleigh Bosher/Rosie Burbidge drank too much Kool-Aid. Bardehle_Pagenberg_is_itself_notorious.]⠀⇛ Designs overlap with all the other IP rights and are vital for a wide range of industries from fashion to automotive. I was delighted to have the opportunity to read and review the Research Handbook on Design Law edited by Henning Hartwig, Bardehle Pagenberg, Munich, Germany. # § Patents⠀➾ # ⚓ CVC_Substantive_Preliminary_Motion_No._1_for_Priority Benefit [Ed: These affairs show that the patent system became all about profiteering and privatisation, nothing_at_all_to_do_with_discovery_and_invention]⠀⇛ On November 19th, Junior Party the University of California, Berkeley; the University of Vienna; and Emmanuelle Charpentier (collectively, “CVC”) filed its Substantive Preliminary Motion No. 1 in Interference No. 106,132 (which names Sigma-Aldrich as Senior Party), asking the Patent Trial and Appeal Board for benefit of priority to U.S. Provisional Application No. 61/652,086, filed May 25, 2012 (“P1″), U.S. Provisional Application No. 61/716,256, filed October 19, 2012, (“P2″), and U.S. Provisional Application No. 61/757,640, filed January 28, 2013 (“Provisional 3″), pursuant to 37 C.F.R. §§ 41.121(a)(1)(ii) and 41.208(a)(3) and Standing Order ¶ 208.4.1. # ⚓ CVC_Files_Substantive_Preliminary_Motion_No._3_to Substiture_the_Count [Ed: This is wasting courts’ time; they should just reject all of these ludicrous patents]⠀⇛ On November 19th, Junior Party the University of California, Berkeley; the University of Vienna; and Emmanuelle Charpentier (collectively, “CVC”) filed its Substantive Preliminary Motion No. 3 in Interference No. 106,132 (which names Sigma-Aldrich as Senior Party), asking the Patent Trial and Appeal Board to substitute the Count of the interference pursuant to 37 C.F.R. §§ 41.121 (a)(1)(iii) and 41.208(a)(1). # ⚓ CVC_Files_Substantive_Miscellaneous_Motion_No._4_to Add_Senior_Party_Patents_and_Designate_Claims Corresponding_to_the_Count [Ed: Total lunatics still trying to patent_life_itself, not because of inventiveness but pure greed, deceit, Hubris]⠀⇛ On November 19th, Junior Party the University of California, Berkeley; the University of Vienna; and Emmanuelle Charpentier (collectively, “CVC”) filed its Substantive Miscellaneous Motion No. 4 in Interference No. 106,132 (which names Sigma-Aldrich as Senior Party), asking the Patent Trial and Appeal Board to add Sigma-Aldrich’s U.S. Patent Nos. 10,731,181 and 10,745,716 to the interference and designate claims 1-17 of the ’181 patent and claims 2-4, 11, 14, and 21-22 of the ’716 patent as corresponding to the Count, pursuant to 37 C.F.R. §§ 41.121(a)(1) (i) and 41.208(a)(2) and Standing Order (“SO”) 203.2. CVC’s substantive argument is that these claims would have been obvious over Count 1 and the Jinek 2012 reference (Jinek et al., 2012, “A Programmable Dual- RNA–Guided DNA Endonuclease in Adaptive Bacterial Immunity,” Science 337(6096): 816- 21) in light of the Krebber 2000 reference (Krebber and Silver, 2000, “Directing Proteins to Nucleus by Fusion to Nuclear Localization Signal Tags,” Methods in Enzymology 327: 283-96) or the Lange 2007 reference (Lange, 2007, “Classical Nuclear Localization Signals: Definition, Function, and Interaction with Importin α,” J. Biol. Chem. 282(8): 5101–05). [...] The brief then explicates with particularity the disclosures in the cited references which in combination with the limitations in the Count satisfy the requirements for obviousness. These include 1) disclosure of dual-guide (dgRNA) and single-guide (sgRNA) RNA embodiments of CRISPR in the Jinek 2012 reference; and 2) the use of the nuclear localization signal from SV40 T antigen as the “canonical NLS for targeting proteins to the nucleus” in the prior art, citing references in exhibits. The brief then subjects each of the claims CVC asks the Board to designate as corresponding to the count to the test established by the Supreme Court in Graham v. John Deere and KSR v. Teleflex Int’l to support its obviousness argument with regard to those claims. # ⚓ Bioionix,_Inc._Announces_Issuance_of_European_Patent for_Electrochemical_Water_Treatment [Ed: Is Bioionix aware that EPO grants loads of invalid patents, based on_insiders?]⠀⇛ Bioionix, Inc, (www.bioionix.com) a technology platform company that develops, manufactures and distributes proprietary electrolytic systems to eliminate biological and chemical contaminants from water, announced today that the European. Patent Office issued the Letter of Acceptance for EP. Pat. No. 3507002 covering the configuration for electrochemical water treatment. # ⚓ Admissibility_of_post-published_evidence [Ed: Well, the_Enlarged_Board_of_Appeal_is_rigged, but they do not mention it]⠀⇛ Inventive step and thus patentability of the claimed invention may be based on experimental data demonstrating a technical effect. In interim decision EPO T 116/18 – “Insecticide compositions” of October 11, 2021, questions on the admissibility of taking into account experimental data filed after the filing date of the patent application were referred to the Enlarged Board of Appeal (reference G 2/21). # ⚓ Austrian_government_completes_ratification_of Protocol_on_Provisional_Application_of_the_UPC Agreement_–_once_this_is_deposited_the_UPC_may_start within_8_months [Ed: Team UPC still pushing hard with fake news [1, 2], trying to advance totally illegal agenda]⠀⇛ The EPO has announced that the Austrian government has successfully completed its ratification of the Protocol to the Agreement on a Unified Patent Court on provisional application (PPA). Once this ratification is deposited with the EU Council, then the provisional application period can commence and final preparations can be made for the arrival of the UPC, with the knowledge that its commencement is assured. The UPC Preparatory Committee has estimated that this preparation period would need to last around 8 months, so the UPC could start around 8 months from Austria’s deposit (depending of course on when Germany deposits its ratification of the UPC Agreement (UPCA) itself – see below). # ⚓ Korean_tech_giants_fall_prey_to_patent_trolling⠀⇛ Though the pandemic has driven record- breaking profits for tech firms as demand for at-home leisure and communication hardware rises, it has also stoked a growing threat coming from patent trolls. Companies specializing in exploiting patent rights have been buying up intellectual property from firms struggling amid the pandemic and using it as ammunition against Korean firms. The approach is often seen as a “file-and- settle” strategy, as their targets would often prefer to avoid fighting a time- consuming court battle and the associated costs, even if they are likely to win the case. As a result, they are settling an increasing number of patent suits at an early stage of court proceedings, particularly in the United States, where the tech market is largest. # ⚓ Doctor_at_Maynooth_University_awarded_€1.5_million grant_for_‘PatentsInHumans’_biology_project ⠀⇛ …European Research Council (ERC) starting grant worth €1.5 million to undertake a five- year research project examining the bioethical implications posed by patents over technologies related to the human body. # ⚓ Texas_Two-Step_Cannot_Avoid_Licensee_Liability⠀⇛ There is a lot going in this decision, but the crux of the appeal is a license interpretation question. [...] Statute of Limitations: Plastronics also had a counterclaim. In particular, Hwang had a right to further license the patent, but only with approval from Plastronics. Hwang admitted that he had licensed the patent, but that the license occurred 9 years before the lawsuit began and thus was outside of the 4- year statute of limitations under Texas law. The Texas allowed the claim — since it was an ongoing license. On appeal, however, the Federal Circuit reversed — holding that the “breach of contract … arose from a single, unauthorized license grant … almost ten years before Plaintiffs filed suit.” As such, the case was beyond the statute of limitations. The court distinguished other situations regarding periodic payments of royalties, where each missed payment is seen as another breach and thus can restart the statute of limitations. See Hooks v. Samson Lone Star, LP, 457 S.W.3d 52, 68 (Tex. 2015). # ⚓ Admitted_Prior_art_in_1886⠀⇛ Field’s patent uses a spring to make it easier to slip on tight-fitting gloves. The case reached the Supreme Court in 1886, but the court sided with the accused infringer. The case involved admitted-prior-art. In particular, the patent specification admitted “that springs had been combined before with the wrists of gloves” in the past. That admission assured the court that the patent cannot cover “the combination of springs in every form with the wrists of gloves to close them.” The accused infringer was also using a spring-glove combination, but a different form than that claimed. As such, no infringement. # ⚓ Supreme_Court_Patent_Decisions⠀⇛ We are 2 years into the 2020s and have 5 decisions thus far (counting Google v. Oracle, which discusses substantive patent issues). If that trend continues, then the final figures for the 2020s would be similar to that of the 2010s. Of course, thus far in the 2021-22 term, the Supreme Court has not yet granted certiorari in any patent cases. # ⚓ Overruling_the_First_Patent_Case⠀⇛ The Patent Act permits a patent to be divided up regionally within the United States. [...] 35 U.S.C. 261. The provision was (I believe) added as part of the Patent Act of 1870 and overruled the very first Supreme Court patent law decision, Tyler v. Tuel, 10 U.S. 324 (1810). In Tyler, the Supreme Court found that a patent assignment excepting a few specific counties was not a “true assignment” and therefore the purported assignees had no right to sue on the case. The court suggested that exceptions might be found in equity. # ⚓ Opinion:_SCOTUS_study_is_good_idea,_but_little_will come_of_it [Ed: Managing IP downplaying severe corruption of US patent courts, having courted the culprit (Albright) for puff pieces "interviews"]⠀⇛ Albright’s actions are unusual enough to warrant the Supreme Court’s patent venue study, but they aren’t nefarious # ⚓ Ones_to_Watch_in_UK_patent_litigation_2022 [Ed: Nowadays JUVE posts mostly marketing spam instead of articles; to make matters worse, Amy Sandys keeps posting fake news (lies) for people who break the law]⠀⇛ # ⚓ Vaccines_and_Vidal:_what_pharma_in-house_are_watching in_2022 [Ed: Speaking only to patent boosters (and sponsors) to install a Microsofter as USPTO Director]⠀⇛ Innovator and generics counsel weigh in on key court cases and why they have high hopes for Kathi Vidal # ⚓ One_Step_Closer_To_The_Unified_Patent_Court [Ed: No, UPC_is_illegal, but litigation profit drool over the money, so they promote fake news and lie to politicians]⠀⇛ Germany and Slovenia have both deposited the Protocol on Provisional Application (PPA) with the Council of the European Union. Now only one more country will need to ratify the PPA before the Council can initiate the final step for implementation of the UPC, which is expected to enter into force in late 2022. # ⚓ Federal_Circuit_Dataset_&_Stats:_2021_Update [Ed: Patent maximalist Jason Rantanen taking on CAFC, which has been pushing back against such maximalists]⠀⇛ Figure 1 shows the number of Federal Circuit opinions and Rule 36 summary affirmances by origin since 2010. Once again, the highest number of merits terminations arose from the PTO. The most notable change for 2021 was a drop in the number of decisions arising from the district courts: from 197 in 2020 to 142 in 2021. These represent individual documents (i.e.: a single opinion or Rule 36), not docket numbers, but there’s also a 25% drop when looking at the data on a per-docket number basis. Overall, the Federal Circuit issued 653 merits decisions in regular appeals in 2021 as compared with 690 in 2020. # ⚓ AutoBrilliance_patent_challenged_as_first_US_reexam in_new_Unified_V2X_Zone⠀⇛ On January 10, 2022, Unified Patents filed an ex parte reexamination against U.S. Patent 6,615,137, owned and asserted by AutoBrilliance, LLC, an NPE. The ‘137 patent is generally directed to inter-vehicle communication systems and methods for detecting objects and notifying drivers of possible collision conditions and has been asserted against General Motors and Volvo. This filing marks the first U.S. reexamination within Unified’s new V2X Zone. # ⚓ $2,000_for_AutoBrilliance_prior_art⠀⇛ On January 13, 2022, Unified Patents added a new PATROLL contest, with a $2,000 cash prize, seeking prior art on at least claim 1 of U.S. Patent 7,337,650. The patent is owned by AutoBrilliance, LLC, an NPE. The ’650 patent generally relates to a vehicle sensor system consisting of video, radar, ultrasonic or laser sensors, oriented to obtain a 360 degree view around the vehicle for the purpose of developing a situation or scene awareness. The patent is currently being asserted against General Motors. # ⚓ UK:_The_Patent_Prosecution_Highway [Ed: The patent system warped to favour aggressors at the expense of due process and presumption of innocence]⠀⇛ The Patent Prosecution Highway (PPH) provides a mechanism for accelerating examination of a patent application at a second patent office, if examination work has already been conducted at a first patent office with whom a PPH agreement is in place. If claims of an application have been found acceptable by a first office (often the office of first filing), accelerated examination of a corresponding application at a second office may be requested. The PPH allows a second patent office to make use of relevant work already conducted by a first office when examining an application. # ⚓ 2022_forecast:_what_lies_in_store_for_the_UPC? [Ed: World Intellectual Property Review or WIPR is peddling fake_news_for_Team_UPC, as it has been doing for years (and proven wrong, repeatedly)⠀⇛ # ⚓ Crunchfish_announces_12th_Gesture_Interaction patent⠀⇛ Crunchfish Gesture Interaction AB (“Crunchfish”) has received an Intention to Grant from the European Patent Office (EPO) regarding gesture interaction with a physical or virtual display to type PIN codes or passwords in a unique way every time. The patent protects scrambling the keypad or display to ensure different touchless interaction patterns every time PIN codes or passwords are entered to lock or unlock the wearable. The patent number is EP18197711.7 and is valid until September 2032. # ⚓ Mazda_3_May_Receive_A_Two-Door_Coupe_Version⠀⇛ # ⚓ Mazda_Is_Back_With_Another_Rotary_Patent!_This_Time For_A_3-Rotor_Hybrid_Design_–_The_Fast_Lane_Car [Ed: Well, but EPO_grants_a_lot_of_fake_patents]⠀⇛ Mazda recently filed a patent application for a rear-wheel drive rotary design with the European Patent Office. (Images: European Patent Office) [...] If you’re interested in learning more about Mazda’s patent, you can search the EPO listings through a service called Espacenet, using the top search bar. The case numbers are EP3932712A1, EP3932714A1 and EP3932730A1 respectively. # ⚓ FOSS_Patents:_2022′s_most_interesting_patent enforcement_question:_how_to_raise_a_successful_FRAND defense_in_Munich_and_Mannheim_under_Sisvel_v._Haier_ (short_of_§_315)⠀⇛ Standard-essential patent (SEP) litigation will be an even bigger topic in 2022 than in recent years, and a major reason is a wide discrepancy between the “ask” and the “bid” prices for 5G licenses. Of course, agreements do silently fall into place here and there (be they license or arbitration agreements), but some 5G litigation is already underway and storms are brewing elsewhere. Let’s not forget about WiFi 6 either–or the problem that one video codec pool (Access Advance) makes exorbitant demands. Bluetooth may be the only Sea of Tranquility in the digital standards space. Munich and Mannheim will remain the world’s primary SEP injuntion hotspots. London is also key, but let’s talk about that one on a different occasion. Vintage year 2021 and 2022 SEP cases in Munich and Mannheim will raise important new questions and have the potential to lead to more nuanced outcomes. That is so because cases that have been decided so far in the Sisvel v. Haier era–starting with the two Sisvel v. Haier cases themselves–presented fact patterns characterized either by implementers’ reliance on a strictly sequential application of the ECJ’s Huawei v. ZTE guidance or by defiance, ignorance, sometimes maybe terrible advice. Now we’re going to see what happens when reasonably sophisticated defendants who benefit from realistic advice go out of their way to comply with German SEP case law during the entire course of negotiations. That wasn’t the case before as far as I can tell. Global players typically have significant exposure to patent assertions in Germany. That was already the case when the Munich I Regional Court issued its SEP guidelines about two years ago. Those guidelines did not even come as a surprise. For example, Presiding Judge Dr. Matthias Zigann of the court’s Seventh Civil Chamber even went to an ETSI meeting to explain his plans beforehand. He listened to a lot of input, but then he and his colleagues decided. At that point, the prudent thing for implementers of FRAND- pledged SEPs to do would have been to heed that guidance in everyday licensing negotiations. It appears, however, that many parties were hoping that they wouldn’t be slapped with a Munich SEP injunction before the appeals court would overturn those SEP Local Rules. Wishful thinking. # ⚓ Is_Work_From_Home_a_U.S._Venue_Work-Around? [Ed: Symptom of a corrupt patent system in the US, wherein the courts can act like for-profit corporations to treat lawsuits like business and then facilitate "form shopping"]⠀⇛ As we begin year three of the COVID-19 pandemic, the rise of the Omicron variant has caused many workers, who had returned to the office during summer and fall 2021, to revert to working from home. This trend has further increased speculation that remote working arrangements will become more widespread, even after the pandemic ends, and may be here to stay. In the United States, “[a]ny civil action for patent infringement may be brought in the judicial district where the defendant resides, or where the defendant has committed acts of infringement and has a regular and established place of business.” The shift to working from home has raised new questions regarding a defendant’s “regular and established place of business” and thus, the proper venue for a patent infringement suit when a company’s remote employees work within many judicial districts in the United States. Recently, however, Hatch-Waxman plaintiffs in Celgene Corporation v. Mylan Pharmaceuticals Inc., 17 F.4th 1111 (Fed. Cir. 2021), received the clearest guidance to date from the Federal Circuit regarding venue. # ⚓ Vidal_and_Stark_nominations_go_to_full_Senate [Ed: Biden still trying to shoehorn a_Microsoft_aggressor and proponent of software patents into the USPTO’s leadership]⠀⇛ The Senate Judiciary Committee confirmed the nominations of Kathi Vidal for USPTO director and Len Stark for the Court of Appeals for the Federal Circuit, sending them off for a full Senate hearing. The committee confirmed Vidal by a vote of 17 to five and Stark by 16 to six. The hearing had originally been scheduled to take place last week but was postponed to allow committee members to attend the funeral of former senator Johnny Isakson on January 6. Senator John Kennedy led the votes against Vidal’s nomination, saying: “If you took big tech and turned it upside down and shook it, our patent office directors would fall out of big tech’s pocket.” Michael Hawes, partner at Baker Botts in Houston, said he was pleased by Stark’s confirmation. “With Judge Stark’s experience as chief judge in Delaware, he can hit the ground running and add hands-on experience with Section 101 patentable subject matter procedures and pharmaceutical trials to the Federal Circuit,” he said. “He will also bring understanding of how Federal Circuit decisions on petitions for mandamus and interlocutory appeals, considering, for example, temporary injunction decisions, can affect a district court with a heavy docket of patent cases.” Vidal, the managing partner of Winston & Strawn’s Silicon Valley office, was nominated by President Joe Biden last October. Stark, a judge at the District Court for the District of Delaware, was nominated in November to replace Kathleen O’Malley, who will leave the Federal Circuit in March. A full Senate hearing is the last hurdle Vidal and Stark will face before they take their new position. A date for the hearing has yet to be announced. # ⚓ Christmas_Patents [Ed: Are even holidays and traditions being patented?]⠀⇛ The festive season is, for many, a magical time of the year. And when magic is in the air, our imaginations are often encouraged to work a little harder – whether it’s children listening for sleigh bells in the snow, or grown-ups trying to find a perfect gift for that difficult-to-buy-for person in their life. For some inventors, however, imaginations are focussed on how to solve problems that come but once a year, such as how to stop the angel at the top of the tree from sitting lop-sided, or how Father Christmas can get into a house with no chimneys. There’s a certain kind of innovation which is special to the holiday season, and in this edition of Insight we explore some of the patents filed (and in some cases even granted) for Christmassy inventions. # ⚓ Snow_Brakes⠀⇛ We have snow on the ground here in Missouri. That makes me think of Gary Reinert’s new patent entitled “method and apparatus for rapid stopping of a motor vehicle particularly on snow or ice.” U.S. Pat. No. 11,091,154. The image below from the patent tells the story. Conventional brakes are awful. Antilock Brakes are much better, but the Reinert Snow Brakes take the cake. Rather than just stopping the wheels, the Reinert Snow Brakes actually shift the car into reverse and spin the tires backward to slow- down the car. I feel like I saw this in Cannonball Run II, but I’m probably misremembering. # ⚓ EU_lays_down_law_on_UK_rights_of_representation [Ed: Is_this_an_attempt_to_distract_from_illegality_of UPC?]⠀⇛ The General Court has clarified the law on rights of representation before EU courts, but some lawyers think further challenges are possible # ⚓ Motorola_Wrap-around_Display_Tech_Surfaces_In_A Patent,_Covers_Four_Sides_Of_Device [Ed: Focusing too much on patents instead of actual products (not the same)]⠀⇛ Motorola has been reportedly working on an all-screen smartphone. A patent submitted by the company has been published recently, suggesting that it has plans for making a smartphone with a screen that wraps all around it, such that only the top and the bottom edge of the smartphone is left with the frame. Read along to find out more details about the all-screen Motorola smartphone. # ⚓ What_It_Means_to_Support_a_Waiver_of_COVID-19_Vaccine Patents [Ed: With COVID-19, the patents have killed millions of people needlessly. A lot of the media is in the pocket of the patent holders, so it's not informing readers.]⠀⇛ “We can no longer rely on these big superpowers to come in and save us.” These words of biotechnologist Emile Hendricks capture the sentiment of countries unable to pay for the same quantities of COVID-19 vaccines as wealthier countries. In Africa, Hendricks and others are currently working, with backing from the World Health Organization (WHO), to reverse-engineer the Moderna COVID-19 vaccine because the pharmaceutical company has not released the intellectual property rights for its vaccines. Moderna, Pfizer, BioNTech, and other vaccine manufacturers have profited billions of dollars by selling their patented vaccines to wealthy countries, while nations such as Nigeria and Ethiopia endure the world’s lowest vaccination rates. But the Biden Administration—despite publicly supporting a waiver of COVID-19 vaccine patents—has done little to help under- vaccinated countries lift the patents. # § Trademarks⠀➾ # ⚓ Precedential_No._1:_TTAB_Sustains_Spotify’s_Dilution- By-Blurring_Claim_Against_POTIFY_for_Clothing_and Marijuana-Related_Software_and_Services⠀⇛ In a rare dilution ruling, the Board sustained this opposition to registration of the mark POTIFY, in standard character and word-plus-design form, for clothing and for software and services related to medical marijuana dispensaries, on the ground of likelihood of dilution by blurring of the famous, registered mark SPOTIFY for downloadable software and online services. The Board found the mark SPOTIFY to be “as famous as marks comes” and dilution not just likely but “inevitable.” Spotify AB v. U.S. Software, Inc., Oppositions No. 91243297 and 91248487 (TTAB 2022) [precedential] (Opinion by Judge Michael B. Adlin). [...] To prevail on its dilution claims, Spotify was required to show that: “(1) it owns a famous mark that is distinctive; (2) Applicant is using a mark in commerce that allegedly dilutes Opposer’s famous mark; (3) Applicant’s use of its mark began after Opposer’s became famous; and (4) Applicant’s use of its mark is likely to cause dilution by blurring or tarnishment. N.Y. Yankees P’ship v. IET Prods. & Servs., Inc., 114 USPQ2d 1497, 1502 (TTAB 2015) (quoting Coach Servs., 101 USPQ2d at 1723-24).” # ⚓ $4,000_for_Big_Will_Enterprises_prior_art⠀⇛ On January 4, 2022, Unified Patents added two separate PATROLL contests with an opportunity to collect up to $4,000 in cash for prior art on at least claim 1 of two patents – U.S. Patent 8,452,273 and U.S. Patent 9,049,558. The patents are owned by Big Will Enterprises, Inc., an NPE. The patents generally relate to electronic messaging technologies for accurately identifying motion activity (MA) associated with mobile things (MT) using sensor data from a wireless communication device (WCD) transported by the MT so as to enable or initiate an activity based actions. The patents have been asserted against Montblanc, Unaliwear, and Kronoz. # ⚓ European_Union:_Bubble_Trouble_For_Names_Similar_To Champagne,_EU_Court_Rules⠀⇛ In the recent EU case C-783/19, a Spanish tapas bar chain had used CHAMPANILLO in its name, why Champagne producers had brought action. The EU Court clarified the scope of protection and found that there was significant similarity between the name CHAMPANILLO and the world-famous Champagne protected by EU law due to its origin. New and interestingly, a service provider’s use of a name similar to names protected due to their special origin was deemed an infringement. # ⚓ Russian_Federation:_The_Eurasian_Trademark_And Appellations_Of_Origin_Registration_System_May_Start Operating_In_2022⠀⇛ The EAEU trademark Treaty that introduces a new regional trademark and appellations of origin protection system was signed in Moscow on February 3, 2020 by five member-states of the EAEU: Armenia, Belarus, Kazakhstan, Kyrgyzstan and Russia. The Treaty governs legal relations concerning filing application for registration and protection of trademarks and appellations of origin within the member- states of the EAEU. The said Treaty was ratified by all member-states and came into force on April 26, 2021. However, after the ratification procedure was completed it was not clear when the new regional trademark and appellations of origin protection system will become available for applicants. On December 16, 2021 a new development has been made – the Russian government adopted a schedule of official fees for certain legal operations related to registration of Eurasian trademarks and appellations of origin which enter into force on July 1, 2022 (The Government Resolution No.2318 dated December 16, 2021). It may be expected that the governments of the rest of the member- states are to adopt the local fees this year as well in order for the Eurasian trademark and appellations of origin system to start operating. # ⚓ USPTO_must_back_up_new_TM_sanctions_with_action:_in- house [Ed: By "sources" they mean sponsors; this is lobbying disguised as "journalism"]⠀⇛ The USPTO should make sure it deters attorneys and filers from bad practices if it wants its new process to be effective, say sources # ⚓ Sunday_Surprises [Ed: Giorgio Luceri is posting misleading PR spam for EUIPO, looking to distract from the EUIPO’s destruction_and_corruption]⠀⇛ # ⚓ In_2021,_How_Often_Did_the_TTAB_Affirm_Section_2(e) (1)_Mere_Descriptiveness_Refusals?⠀⇛ I have again reviewed the TTAB’s FOIA page (now called the “TTAB Reading Room”) in order to estimate the percentage of Section 2(e)(1) mere descriptiveness refusals that were affirmed by the Board during the last calendar year (2021). I counted 92 refusals, of which 84 were affirmed and 8 reversed. That’s an affirmance rate of about 91.3%, a five-point rise from last year’s 88%. # ⚓ US_judge_says_gruyere_is_a_common_food_name⠀⇛ A ruling in the US courts says gruyere is a generic style of cheese that can come from anywhere. The decision means US cheesemakers, not just those in France or Switzerland, can continue to create and market cheese under the common name. # ⚓ E.D._Va._District_Court_Upholds_TTAB_Decision_Finding “GRUYERE”_Generic_for_Cheese⠀⇛ In a convincing opinion, the United States District Court for the Eastern District of Virginia has upheld the Board’s decision [TTABlogged here] finding the term GRUYERE to be generic for cheese, and thus unregistrable as a certification mark. On the Dairy Export Council’s motion for summary judgment, the court found that “the undisputed evidence produced by the parties in this case makes clear that the primary significance of the term GRUYERE, as understood by the relevant purchasing public in the United States, is a generic term for a type of cheese and does not refer solely to cheese from a specific geographic region.” Interprofession du Gruyère et al. v. U.S. Dairy Export Council et al., Civil Action No. 1:20-cv-1174 (E.D. Va. December 15, 2021). [...] “The central issue in this matter is whether the term GRUYERE has become generic for a certain type of cheese and is no longer understood to refer only to cheese which comes from the Gruyère region of Switzerland and France.” # ⚓ Is_Gruyère_Still_Gruyère_if_It_Doesn’t_Come_From Gruyères?⠀⇛ In Europe, the mild, smooth and nutty cheese called gruyère must have a slightly damp texture, with average spring and low crumble. It must be in the shape of a wheel, weighing between 55 and 88 pounds. Fruity notes must dominate. Perhaps most importantly, according to Swiss guidelines, gruyère must be made in the region around Gruyères, Switzerland, which has produced the cheese since the 12th century. In the United States, however, gruyère can be made anywhere, according to a federal court ruling that was made public last week. It was the latest development in a long-running legal tangle between American cheese producers and producers in Switzerland and France over what makes gruyère gruyère. In the ruling last month in U.S. District Court for the Eastern District of Virginia, Judge T.S. Ellis III wrote, “Although the term gruyère may once have been understood to indicate an area of cheese production, the factual record makes it abundantly clear that the term gruyère has now, over time, become generic to cheese purchasers in the United States.” Under U.S. law, trademarks cannot be given to generic terms. # ⚓ UK:_By_Design:_Update_On_Registered_Design_Filing_At The_UK_IPO⠀⇛ Following a referendum in the UK in 2016, the UK’s official membership of the European Union ended in January 2020, triggering the start of an 11-month transition period which was relevant for various IP rights, including UK registered designs. Prior to the UK’s departure from the EU, a Registered Community Design (RCD) (also known as an EU design) would cover the UK. To ensure that rights from existing RCDs continue to be protected in the UK, the UK Government agreed to create an equivalent “cloned” registered UK design for all existing RCDs. # ⚓ In_2021,_What_Was_The_Rate_of_TTAB_Affirmance_of Section_2(d)_Refusals_to_Register? [Ed: UJSPTO very often wrong in granting trademarks]⠀⇛ Yours truly, the TTABlogger, has once again reviewed the TTAB’s FOIA page (now called the “TTAB Reading Room”) in order to estimate the percentage of Section 2(d) likelihood-of- confusion refusals that were affirmed by the Board in the past calendar year. I counted 273 decisions, of which 240 were affirmances and 33 were reversals. That’s an affirmance rate of approximately 87.9%, or a bit less than 9 out of 10. A follow-up question is: how many were WYHAs? [...] How does this compare with past years? Here’s a bar chart (prepared by the incomparable Francesca (“Frankie”) Householder of Wolf Greenfield), covering the last ten years… ䷩ 𝚕𝚒𝚗𝚎 4596 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_17/1/2022:_postmarketOS_21.12_Service_Pack_1_and_Mumble_1.4_Released⠀✐ Posted in News_Roundup at 7:48 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o ⚓ 9to5Linux_Weekly_Roundup:_January_16th,_2022⠀⇛ This week has been really great for Linux news and releases. We kicked off with a new major Firefox release, pre-orders of the PinePhone Pro Linux smartphone for everyone, and a new GNU Linux-libre kernel for those who want to build a 100% free computer without any proprietary code or drivers. We also got a new major FFmpeg release with lots of goodies for all your multimedia creation, a new major NetworkManager release with great stuff for all your networking needs, and a new major release of the SystemRescue live Linux system for all your system rescue and recovery needs. o ⚓ Linux_Weekly_Roundup_#165⠀⇛ I hope that you are doing well. We had a peaceful week in the world of Linux releases with the releases of Sparky Linux 5.16, Bluestar Linux 5.16.0, and Slackware 15.0-rc3. o § Audiocasts/Shows⠀➾ # ⚓ FOSS_dev_SABOTAGED_their_libraries,_EAC_isn’t_so_easy, Humble_Bundle_disappoints_–_Linux_News_Jan._–_Invidious⠀⇛ # ⚓ Terminal_Based_Gaming_Is_Just_Better_#shorts_–_Invidious⠀⇛ Have you ever thought modern graphics are just too much and want to go back to a simpler time a time where we just played games using ascii symbols in our terminal, well now you can. # ⚓ How_to_install_FreeOffice_on_Elementary_OS_6.0_– Invidious⠀⇛ In this video, we are looking at how to install FreeOffice on Elementary OS 6.0. # ⚓ It’s_easy_to_replace_Windows_with_Linux:_Here’s_how⠀⇛ o § Kernel Space⠀➾ # ⚓ Kernel_Updates_Available_»_PCLinuxOS⠀⇛ The following Kernels are available for PCLinuxOS. Kernel 5.15.15, Kernel LTS 5.10.92 and Kernel LTS 5.4.172. # ⚓ Linux_To_Adopt_New_Multi-generation_LRU_Page_Reclaim Policy⠀⇛ Based on observed behaviour on Android and Chrome OS, Google began working on a new page reclamation strategy for its Linux-based OSes aimed to improve how the virtual memory subsystem reclaims unused memory pages. More recent work shows the new MGLRU policy can benefit server environments, too. o § Applications⠀➾ # ⚓ ‘Rnote’_is_an_Impressive_Freehand_Note_Taking_App_Built_in Rust_&_GTK4_–_OMG!_Ubuntu!⠀⇛ Rnote is a seriously impressive freehand note taking app written in Rust and GTK4. I came across it on Flathub this week and, within seconds of installing it, I knew I had to give it a bit of a spotlight. If you’ve got a laptop with a stylus or touch-enabled screen and you use GNOME Shell you have to try it out. Rnote is billed by its developer as a “simple note taking application written in Rust and GTK4”. I spent about 20 minutes playing around with it (albeit with a mouse as primary input) and it’s really quite polished considering that it’s likely far from feature complete. # ⚓ Mumble_1.4.230_|_Mumble⠀⇛ We are proud to present you with the first stable release of the Mumble 1.4.x release series, which brings many new features, bug fixes and general improvements. You can download the new version from our Downloads page or the GitHub release page or from within your Windows client or software package management system. # ⚓ Mumble_1.4_Released_For_Open-Source_Voice_Chat⠀⇛ It’s been over two years since Mumble 1.3 was released for this open-source VoIP / voice chat program that is popular with gamers and open-source enthusiasts while today it’s been succeeded by Mumble 1.4. Mumble 1.4 has reached stable and comes with a new plug-in framework for extending this high quality voice chat software. This new framework can be used for extending the functionality offered by Mumble and can be used for a variety of general purpose use-cases. Mumble 1.4 also adds a full-featured search dialog, channel listeners, TalkingUI as a convenient non-gamer overlay for showing who is talking, various other UI improvements, stereo audio streams support, and support for Markdown in text messages. # ⚓ Spectator_is_an_open-source_REST-API_testing_app_for Linux⠀⇛ Spectator is a free, open-source (Libre) REST-API testing program for Linux. It is written in Vala programming language and GTK. The app allows developers to make requests to test their web endpoints, create custom environments, and save everything within a collection. o § Instructionals/Technical⠀➾ # ⚓ How_to_Install_and_Configure_Samba_File_Sharing_on_Rocky Linux/Alma_Linux_8⠀⇛ Samba is a suite of open source applications that implements the Server Message Block (SMB) protocol. Many operating systems, including Microsoft Windows, use the SMB protocol for client-server networking. Samba enables Linux / Unix machines to communicate with Windows machines in a network. Samba provides file and print services for various Microsoft Windows clients and can integrate with a Microsoft Windows Server domain, either as a Domain Controller (DC) or as a domain member. Sharing files is an essential part of server administration. It allows sharing of resources across the network which are needed by users to carry out their tasks. Samba server is usually installed on central Linux server where information is stored in variety of media and accessed using windows client or Linux using Samba client. # ⚓ How_To_Install_FTP_Server_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install FTP Server on Debian 11. For those of you who didn’t know, The vsftpd FTP Server is one of the most trusted applications among the Linux professionals. The official website of vsftpd FTP Server claims that the security, stability and performance is the key points due to which it has gained much popularity among the Linux users. 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 FTP Server on a Debian 11 (Bullseye). # ⚓ How_to_fix_the_issue_“No_authenticators_available”_with Mutt_in_Fedora⠀⇛ # ⚓ Install_Pydio_With_Ubuntu_21.04s⠀⇛ What can come among the top 5 open source firewalls? Yes, this I was thinking of! Of course, there are lots of services and ready use os available. Deciding # ⚓ How_to_install_Cpanel_and_WHM_on_Ubuntu_20.04_– NextGenTips⠀⇛ In this tutorial, we are going to learn how to install Cpanel on Ubuntu 20.04. Also, I will show you the free alternatives to Cpanel. This will make a big impact while trying to choose which free web hosting to use without worrying about the licenses. Cpanel provides a way where you can send emails by providing email hosting services which makes it easy to communicate with your customers. Cpanel is a web hosting control panel. It provides a GUI interface where administrators key in the information they want to configure, this simplifies the process of hosting a web site to the website end-user. # ⚓ How_to_install_Steam_on_a_Chromebook_in_2022⠀⇛ Today we are looking at how to install Steam 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. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ SFXR-Qt_1.4.0_is_out!_|_agateau.com⠀⇛ Last release of SFXR-Qt was in September 2019. I kept using it for Pixel Wheels, it had its quirks and bugs but I did not have the time and motivation to work on it, so the poor app was left on its own for more than two years. Fast forward to November 2021: SFXR-Qt was added to Debian! It always feels good to see an app getting more widespread, with the minor issue that I learned about it because tests did not pass on big-endian machines… Working on that bug was a bit frustrating because I do not own a big-endian machine and failed to setup a working big-endian VM to test my changes on, but after a few blind fixes I eventually got it fixed. Kudos to Alex Myczko, the bug reporter, for the responsiveness in testing my changes. Entering Debian probably gave a bit more exposure to the app, because I then received a bug report for that crash I had known for a long time but never got to fix… Now that someone else reported it, I finally fixed it. o § Distributions⠀➾ # ⚓ EasyOS:_Rollback_exceptions_extended⠀⇛ Currently only bringing up this erase-exceptions window when do a rollback to pristine first bootup, but perhaps should consider it for other rollback choices — such as rollback to an earlier version of EasyOS or a snapshot. Note, the “Web browser profile” checkbox will save all firefox, seamonkey, chrome and chromium profiles under /home, as well as all mozilla profiles running as root (/root/.mozilla). o § Devices/Embedded⠀➾ # ⚓ How_to_Build_a_Morse_Code_Transmitter_Light_with_Raspberry Pi_|_Tom’s_Hardware⠀⇛ I recently moved into a new place, and discovered that my friend and I live in buildings that face each other. We’re about a kilometer apart, but both our balconies have line of sight to each other. I’ve always wanted to build a communications network with my friends since I was a kid, so I dusted off an old book about Morse, one of my Raspberry P’s and got to work. I’m a big fan of mixing old and new technologies, so instead of using something modern, I decided to use Morse code. This tutorial is the first in a two part series for building a building-to-building morse code communications system. In it, we’ll explore how to create a morse code transmitter using a Raspberry Pi and a DJ light. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ The_Best_FPS_Games_for_Android_2022_–_Call_of_Duty Mobile,_Infinity_Ops_and_More_–_Droid_Gamers⠀⇛ # ⚓ 13_new_Android_games_from_the_last_week:_The_best, worst,_and_everything_in_between_(1/9/22-1/16/22)⠀⇛ # ⚓ Android_users_warned_some_Google_features_will_stop working_next_month_–_change_these_settings_now⠀⇛ # ⚓ Motorola’s_next_flagship_Android_phone_could_have insane_specs_|_Android_Central⠀⇛ # ⚓ postmarketOS_//_v21.12_Service_Pack_1⠀⇛ Welcome to 2022! This is the first service pack of the year bringing some of the improvements from edge to stable. This also brings a few nice new features to the v21.12 release that were not ready for inclusion yet when the last stable release was made. * § Leftovers⠀➾ o ⚓ Aeroponic_Cell_Grows_Garlic,_Forwards_CellSol_Packets_| Hackaday⠀⇛ Certain pictures draw attention like no other, and that’s what happened when we stumbled upon a Twitter post about “resuscitating supermarket garlic” by [Robots Everywhere]. The more we looked at this photo, the more questions popped up, and we couldn’t resist contacting the author on Twitter – here’s what we’ve learned! This is an aeroponics cell – a contraption that creates suitable conditions for a plant to grow. The difference of aeroponics, when compared to soil or hydroponics methods, is that the plant isn’t being submerged in soil or water. Instead, its roots are held in the air and sprayed with water mist, providing both plenty of water but also an excess of oxygen, as well as a low-resistance space for accelerated root growth – all of these factors that dramatically accelerate nutrient absorption and development of the plant. This cell design only takes up a tiny bit of space on the kitchen countertop, and, in a week’s time, at least half of the cloves have sprouted! o ⚓ Thirty_Seconds_At_100_Megakelvins_|_Hackaday⠀⇛ Back in Dec 2020 we wrote about the Korea Superconducting Tokamak Advanced Research (KSTAR) magnetic fusion reactor’s record-breaking feat of heating hydrogen plasma up to 100 megakelvins for 20 seconds. Last month it broke its own record, extending that to 30 seconds. The target of the program is 300 seconds by 2026. There is a bit of competition going, as KSTAR’s Chinese partner in the International Thermonuclear Experimental Reactor (ITER), the Experimental Advanced Superconducting Tokamak (EAST) did a run a week later reaching 70 million degrees for 1056 seconds. It should be noted that KSTAR is reaching these temperatures by heating ions in the plasma, while EAST takes a different approach acting on the electrons. o § Hardware⠀➾ # ⚓ Printable_Portable_Mask_Gives_You_The_Numbers_On_Your Workout_|_Hackaday⠀⇛ We’re currently in the midst of New Year’s Resolutions season, which means an abundance of spanking new treadmills and exercise bikes. And one thing becomes quickly obvious while using those machines: the instruments on them are, at best, only approximately useful for measuring things like your pulse rate, and in the case of estimating the calories burned by your workout, are sometimes wildly optimistic. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ Josh_Bressers:_Episode_306_–_Open_source_isn’t broken,_it’s_an_experience⠀⇛ Josh and Kurt talk about the faker and colors NPM events. There is a lot of discussion around open source being broken or somehow failing because of these events. The real answer is open source is an experience. How we interact with our dependencies determines what the experience looks like. # ⚓ Top_5_opensource_firewalls_that_secure_your network⠀⇛ What can come among the top 5 open source firewalls? Yes, this I was thinking of! Of course, there are lots of services and ready use os available. Deciding to deploy any firewall can be difficult. Why difficult? Well, the reason is simple, we never know what consequences will be there while not taking care of security. From the very beginning of the Linux era, things started with Squid, where Administrators were supposed to manage everything manually. I remember still, how we were supposed to get install service with RPM manually. How all ACLs, IP address ranges were supposed to take care of very precisely. Getting access to logs, reports was altogether a tedious job. Applying IPTable to provide extra layer security made Linux admins feel like some sort of saviors. # § Fear, Uncertainty, Doubt/Fear-mongering/ Dramatisation⠀➾ # ⚓ The_Log4j_lesson_for_open-source_users [Ed: Trying very hard to distract from the real threat, which is back doors in proprietary software and no transparency at all]⠀⇛ # ⚓ CrowdStrike_expands_Zero_Trust_support_to macOS_and_Linux [Ed: CrowdStrike spam (press release) edited into a fake ‘article’ by Mitchell Hagema, who crossposts_this_in_shadow_domains; these Microsofters_spam_the_media_with_FUD_in order_to_promote_their_pure_garbage]⠀⇛ o § Monopolies⠀➾ # ⚓ 6_Tips_For_Ensuring_Your_Intellectual_Property_Works_For You [Ed: False terminology; "Intellectual Property" is a misleading misnomer, it should say trademarks instead]⠀⇛ IP rights are valuable assets to any business. Patents and utility models protect new technologies and give you a monopoly over them. Trademarks protect your brand and ensure that only you can use it. Industrial design rights protect the appearance of a given product and gives you exclusive rights over it. These rights provide significant commercial advantages which can lead to higher revenues and profits. # § Patents⠀➾ # ⚓ Official_expresses_concern_that_pandemic_will_drag_on until_the_world_is_vaccinated⠀⇛ How patent law and corporate profits keep variants crawling the globe # ⚓ A_review_of_railway_innovation_through_patenting trends⠀⇛ Turning first to Figure 1 below, which shows EU patenting trends across the aforementioned subsystems, the data indicates that the ENE and INF areas have remained relatively stable in terms of patent filings, but that CCS and RST have seen significant increases in patent filings since around 2010. Of note, the “High value inventions” referred to on the Y-axis of Figure 1 represents patent families “that include patent applications filed in more than one patent office”. # ⚓ Deferred_Subject_Matter_Eligibility_Response_(DSMER) Pilot_Program⠀⇛ Back in 2010, I wrote an article with Prof Rob Merges titled Operating Efficiently Post- Bilski by Ordering Patent Doctrine Decision- Making. We suggested that patent examiners often lack capacity to judge metaphysical questions centered around abstractness and laws of nature. In addition, we noted that many eligibility questions substantially overlap with bread-and-butter patent doctrines such as obviousness, enablement, and indefiniteness. What that means is that delaying eligibility decisions can often result in entirely avoiding eligibility decisions. In a 2019 article, Professor Chien provided more detailed guidance on how this could be accomplished. # ⚓ Serstech_files_nine_patent_applications [Ed: Serstech acting as if patents, even software patents which are mostly bunk, are a substitute for actual products]⠀⇛ Serstech has filed nine patent applications to the European patent office over the last two weeks. The patent applications are filed to protect the newly launched Serstech Arx products and the next generation product platform that is currently under development. Due to ongoing and expected sales opportunities in particularly the US market, Serstech recently decided to ramp up its IPR efforts to better protect its innovations. # ⚓ UK:_With_News_That_The_Austrian_Parliament_Has Ratified_The_Protocol_On_The_Provisional_Application_Of The_Agreement_On_A_Unified [Ed: And yet more_shameless fake_news_from_Team_UPC]⠀⇛ With news that the Austrian parliament has ratified the Protocol on the provisional application of the Agreement on a Unified Patent Court on 2 December 2020, the #UPC opening in 2022 is becoming more likely. # ⚓ IP_in_2022_–_What_next_and_where? [Ed: Truly ridiculous propaganda item with the misnomer “IP”; it also promotes fake_news_about_UPC_along_the_way]⠀⇛ # ⚓ Mazda_May_Be_Cooking_Up_a_Rotary-Powered_Sports_Car After_All [Ed: EPO patent valid_though?]⠀⇛ Rumors about Mazda building a new rotary- engined sports car have proliferated ever since Mazda pulled the RX-8 after 2012. Mazda stoked those rumors with their spectacular RX-Vision rotary sports car concept they unveiled in Tokyo in 2015, and the company has affirmed the desire to build such a rotary sports cars — if it becomes feasible. Now, however, we have some new evidence the brand has been working on one behind the scenes. # ⚓ Mazda_Patent_App_Shows_Hybrid_Rotary_Engine_That Powers_the_Rear_Wheels⠀⇛ Everyone’s been waiting for a new rotary- powered Mazda since the RX-8 bowed out in 2012. Mazda itself even built an RX-Vision Concept that many believed would preview an eventual RX-9; that was way back in 2015, though, and we still haven’t seen anything like it enter production. The car world had more or less accepted that rotaries would only have a future as EV range extenders—that is, until Friday when a patent application was unveiled showing what looks like a hybrid rotary engine that drives the rear wheels. Detailed patent drawings from Europe were published on a Japanese Hatena blog, which pointed out key details that hint this may be a three-rotor engine. Indeed, there are what look like three spark plug holes and three rotor housings, so it would likely be pretty potent. Factor in the electrification aspect and it’s doubtful anyone would call it underwhelming like they did with the naturally aspirated RX-8. # ⚓ Is_Amending_the_Description_of_a_European_Patent Application_to_be_Consigned_to_History? [Ed: These_EPO boards_are_stacked_and_besieged; this merits a mention all the time, but they_leave_that_out]⠀⇛ In a notable decision on an apparently mundane legal topic, a Technical Board of Appeal of the EPO recently decided (in T 1989/18) that requiring applicants to amend their description so that it is consistent with the claims has no basis in the EPC. This decision may help to consign this practice to history, streamlining the prosecution process at the EPO in a way that will be welcomed by applicants and attorneys alike. It is a historic feature of European practice that the description of a patent application must be amended so that it is consistent with the claims. The Guidelines for Examination at the EPO refer to a number of examples of inconsistencies that must be corrected. One example includes inconsistencies where a statement in the description suggests that the invention is limited to a particular feature, but the claims are not so limited. Another example is where it is stated or implied in the description that certain features are essential to the invention when those features are not present in the claims. A further example is where parts of the description give the impression that they disclose ways of carrying out the invention, when those examples are no longer within the scope of the claims. Examiners can be particularly enthusiastic in pursuing these objections. In order to overcome these objections it is often necessary to make amendments wherever the word “embodiment” or “invention” appears. It can also be necessary to delete passages or to indicate in the description that certain examples are not within the scope of the claims. # § Trademarks⠀➾ # ⚓ IP_Court_Clarifies_What_Constitutes_Token_Use_For Trademarks_Vulnerable_To_Non-Use⠀⇛ Russian law stipulates that if an owner does not use a trademark within three years, it can be cancelled. To avoid this happening, some owners try to keep their marks alive by producing evidence of use, though in very small volumes. However, token use is generally insufficient to establish that a trademark is, in fact, being used. The IP Court of the Russian Federation often issues rulings to this effect, and has published some criteria for what it defines as ‘token use’. # ⚓ Quality_no_longer_affects_assessment_of_trademark recognition_in_Polish_courts [Ed: When trademark law becomes just a pipeline for rubber-stamping]⠀⇛ Proving the reputation of a trademark is not an easy task. The owner must prove that the mark is recognised by a significant share of the population in a substantial part of the territory in which it is registered. In the European Union this is mainly assessed using quantitative criteria. However in Poland, one must also provide qualitative criteria to prove recognition. The reputation of a mark is not defined by the EU Trademark Regulation, nor by Polish industrial law. Pursuant to case law, a well- known mark must have sufficient recognition that the relevant public, when confronted by a similar mark, may possibly make an association between the two, even when they are used for non-similar products or services, consequently damaging the reputation of the established mark (14/09/ 1999, C-375/97, Chevy, EU:C:1999:408, § 22- 23). There is no EU case law specifying that a qualitative threshold must be met in order to enjoy protection deriving from reputation. # § Copyrights⠀➾ # ⚓ Turkey:_What_Amendments_Does_Law_No._7346_On Amendment_Of_Certain_Laws_Envisage_In_Law_No._5846_On Intellectual_And_Artistic_Works? [Ed: Treating people who share like criminals]⠀⇛ Law No. 7346 aims to redraw the boundaries of criminal liability by expanding the scope of the acts stipulated in Article 72 of the Copyright Law. # ⚓ Federal_Supreme_Court_seeks_clarification_on visibility_criterion_in_German_design_law⠀⇛ ‘What you see is what you get’ is one of the vital principles of EU (and German) design law. Particularly in relation to designs for component parts of a complex product (ie, parts used in or incorporated into a complex product, eg, a car hood), EU design law ties availability of design protection to visibility of such parts during normal use. This ‘visibility criterion’ has massive practical relevance in design law. Still, the Court of Justice of the European Union (CJEU) – despite a few incidental remarks in the more recent Ferrari ruling (C-123/20) on unregistered EU designs – has not yet had the chance to give specific guidance on how ‘visibility’ is to be assessed. Upon a referral (I ZB 31/20) from the German Federal Supreme Court (BGH), an inconspicuous bicycle saddle might now write history in that it could trigger the CJEU to define the contours of the visibility criterion in more detail. ䷩ 𝚕𝚒𝚗𝚎 5423 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_16/1/2022:_Tsunami_and_Patents⠀✐ Posted in News_Roundup at 4:33 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Kernel Space⠀➾ # § Graphics Stack⠀➾ # ⚓ DRM_updated⠀⇛ Johathan Gray (jsg@) has updated DRM to Linux 5.15.14 (with support for several additional chips): [...] o § Instructionals/Technical⠀➾ # ⚓ There_is_no_such_thing_as_a_static_website⠀⇛ A common distinction in technology for building websites is a separation between “static” and “dynamic” websites. The idea is that a “static” website always returns the same HTML/CSS/etc, whereas a “dynamic” website changes the content that the server returns depending on the request. This seems, at first glance, to be a pretty sharp and useful distinction, letting us easily distinguish between static and dynamic. However, I don’t think it holds up to real scrutiny, and I believe that this distinction is holding us back from building better types of software that exist in the blurry space between static and dynamic. First off, we should look at why people care about this distinction in the first place. When looking at any sort of taxonomy, a good first question to ask is “who is this useful to, and why?” # ⚓ Pi-hole_Installation_Guide⠀⇛ You probably know already the concept of the Pi- hole. If not, it’s a (forwarding) DNS server that you can install on your private network at home. All your clients, including every single smartphone, tablet, laptop, and IoT devices such as smart TVs or light bulb bridges, can use this Pi- hole service as their DNS server. Now here’s the point: it not only caches DNS entries, but blocks certain queries for hostnames that are used for ads, tracking, or even malware. That is: you don’t have to use an ad- or track-blocker on your devices (which is not feasible on smart TVs or smartphone apps, etc.), but you’re blocking this kind of sites entirely. Nice approach! Yes, there are already some setup tutorials for the Pi-hole out there. However, it’s not only about installing the mere Pi-hole, but setting it up with your own recursive DNS server (since the default installation forwards to public DNS servers), using DNSSEC, and adding some more adlists. That’s why I am listing my installation procedure here as well. However, it’s not a complete beginners guide. You’ll need some basic Linux know-how. I am using a Raspberry Pi 3 B+ Rev 1.3 with Raspberry Pi OS for this setup. (While in the meantime I’m running Pi-hole on my Intel NUC with Ubuntu server.) # ⚓ How_To_Add,_Remove_and_Update_Software_in_Linux_Using_Apt⠀⇛ Linux has many ways to install software. We can build our own executables or use AppImage to run containerized applications. But at the heart of many Linux distros is a package management system, which for Debian based systems, such as the Raspberry Pi and Ubuntu, is Apt. Apt, the Advanced Packaging Tool is a command line application which handles the installation, categorization and removal of applications and their dependencies from the software repositories. Apt is the heart of Debian systems and the lessons learnt are applicable from the $35 Raspberry Pi to million dollar super computers. Apt is available via the Terminal and we can even administrate systems remotely using a remote connection such as SSH. A command line tool may seem daunting but here we detail the most common commands that you will use to keep your system updated with the latest software. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Lots_of_Video_News!⠀⇛ I’ve been incredibly happy with the very early success and interest with the videos produced the past couple weeks… Both of them. While I think the attention received may have been oddly disproportionate to the quality of the content, I feel I can do far better and will be stepping up my video game! First, I’m going to be breaking up my current YouTube account into 3 distinct channels outside of my personal videos; “Kver Create!”, “Kver Play!” and “Kver Workshop!”. I’m furiously trying to get everything ready, but here’s what everyone can expect: Kver Create! Will focus on work, and will be mostly livestreams. This is where I’ll be doing things like wallpapers, icons, other art, development, and even personal projects. It’s also where I’ll publish excerpts of the previously recorded livestreams when there’s interesting segments. In the future it might be neat to feature other artists and developers as well. Expect regular KDE content here. Kver Play! May or may not have a future, but if my first livestreams taught me anything it’s that I’m not yet comfortable with the mic, so what’s a better teacher than a more casual and fun environment while I rehabilitate my voicebox? This will probably have the most livestreams out-of-gate, but I imagine it will slow down in favour of other channels as time goes on. o § Distributions⠀➾ # § BSD⠀➾ # ⚓ freebsd-update_fetch_install_->_Cowardly_refusing_to proceed_any_further.⠀⇛ o § Devices/Embedded⠀➾ # § Mobile Systems/Mobile Applications⠀➾ # ⚓ How_To_Block_Phone_Number_on_Your_Android:_No_3rd Party_App_Needed⠀⇛ # ⚓ How_to_cancel_your_Netflix_membership_on_Android_and web_–_9to5Google⠀⇛ # ⚓ How_to_stop_apps_from_running_in_the_background_on Android⠀⇛ # ⚓ Even_BlackBerry’s_best_Android_apps_are_reaching_end- of-life_this_year⠀⇛ # ⚓ 4_best_library_apps_for_Android_to_read_for_free_– Android_Authority⠀⇛ # ⚓ The_5_Best_Firewall_Apps_to_Secure_Your_Android Phone⠀⇛ # ⚓ android_smartphone:_6_Android_smartphone_settings_you should_change_right_now_–_Times_of_India⠀⇛ # ⚓ Androids_have_six_‘secret_codes’_that_unlock_hidden features⠀⇛ # ⚓ 5_Android_apps_you_shouldn’t_miss_this_week_–_Android Apps_Weekly⠀⇛ # ⚓ Report:_Android_updates_make_users_happier_than_iOS_– Android_Authority⠀⇛ # ⚓ Android_13_release_date_rumors,_supported_phones_and what_we_want_to_see_|_TechRadar⠀⇛ # ⚓ Samsung_Galaxy_A13_5G_review:_Cheap_in_a_good_way⠀⇛ # ⚓ Pixel_5a_review:_The_best-kept_secret_in_Android⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ Best_Free_and_Open_Source_Alternative_to_IBM_Rational DOORS⠀⇛ International Business Machines Corporation (IBM) is an American multinational technology corporation headquartered in Armonk, New York. They sell computer hardware, middleware and software employing over 370,000 people. IBM acquired Red Hat in 2019. But you can trace IBM’s history of open source far further back. They were one of the earliest champions of open source, backing influential communities like Linux, Apache, and Eclipse, advocating open licenses, open governance, and open standards. # ⚓ Best_Free_and_Open_Source_JavaScript_Engines⠀⇛ JavaScript is an interpreted programming language. It means that source code isn’t compiled into binary code prior to execution. The role of the JavaScript engine is to turn plain text script into executable code. In other words, the engine is a container in which you run your program. JavaScript engines are often developed by web browser vendors, and every major browser has one. In a browser, the JavaScript engine runs in concert with the rendering engine via the Document Object Model. JavaScript engines implement specification of the language provide by ECMAScript. Standardization enables the development of independent engines and ensures scripts give the same results no matter wherever they run. # § Programming/Development⠀➾ # ⚓ Comparing_Static_Site_Hosts;_Which_Is_The_Best_Host For_A_Static_Site?⠀⇛ I have compared a number of static site hosts to see which is the best for me in terms of performance, build times and pricing. This post contains the results of that research. # ⚓ Opencv_compiled_in_OpenEmbedded⠀⇛ Opencv is an optional dependency for mlt, lives, flowblade and other video editor packages. I have compiled it in OE, and it brings in these new dependencies: ade 0.1.1f gflags 2.2.2 glog 0.3.5 libeigen 3.3.7 libunwind 1.3.1 opencv 4.5.2 tbb 1_2020.2 § Perl/Raku⠀➾ * ⚓ Eagle’s_Path:_DocKnot_6.01_(2022-01-15)⠀⇛ This release of my static site generator and software release manager finishes incorporating the last piece of my old release script that I was still using: copying a new software release into a software distribution archive tree, updating symlinks, updating the version database used to generate my web pages, and archiving the old version. * § Leftovers⠀➾ o ⚓ Tsunami_Triggered_by_Huge_Volcanic_Eruption_Hits_Tonga⠀⇛ This is a developing news story… Check back for possible updates… A major volcanic eruption near Tonga triggered tsunami waves that hit the shores of the Pacific island nation on Saturday, forcing people to flee the streets and their homes in search of higher ground. o § Education⠀➾ # ⚓ Schneier:_Upcoming_Speaking_Engagements⠀⇛ This is a current list of where and when I am scheduled to speak: [...] # ⚓ The_Developers_Conference_2022_has_been_postponed⠀⇛ The Developers Conference (DevCon) was due to happen on the 17ᵗʰ, 18ᵗʰ and 19ᵗʰ of February 2022 at the Caudan Arts Centre. We were hoping that restrictions would be eased before the DevCon day. Unfortunately, that did not happen. No new dates have not been announced as that would be pending negotiation with the conference venue owner and several other stakeholders. o § Hardware⠀➾ # ⚓ New_leak_claims_the_Galaxy_S22_series_will_use_the_Exynos 2200_in_Europe_after_all_–_NotebookCheck.net_News⠀⇛ Recent reports excited Samsung fans in Europe with the idea of the Galaxy S22 Ultra being shipped with the Snapdragon Gen 1 across all regions. New information might just have put paid to those thoughts, however, as it now appears that the Galaxy S22 series will ship with the Exynos 2200 in Europe. # ⚓ SSD_Endurance_«_etbe_–_Russell_Coker⠀⇛ I previously wrote about the issue of swap potentially breaking SSD [1]. My conclusion was that swap wouldn’t be a problem as no normally operating systems that I run had swap using any significant fraction of total disk writes. In that post the most writes I could see was 128GB written per day on a 120G Intel SSD (writing the entire device once a day). My post about swap and SSD was based on the assumption that you could get many thousands of writes to the entire device which was incorrect. Here’s a background on the terminology from WD [2]. So in the case of the 120G Intel SSD I was doing over 1 DWPD (Drive Writes Per Day) which is in the middle of the range of SSD capability, Intel doesn’t specify the DWPD or TBW (Tera Bytes Written) for that device. The most expensive and high end NVMe device sold by my local computer store is the Samsung 980 Pro which has a warranty of 150TBW for the 250G device and 600TBW for the 1TB device [3]. That means that the system which used to have an Intel SSD would have exceeded the warranty in 3 years if it had a 250G device. My current workstation has been up for just over 7 days and has averaged 110GB written per day. It has some light VM use and the occasional kernel compile, a fairly typical developer workstation. It’s storage is 2*Crucial 1TB NVMe devices in a BTRFS RAID-1, the NVMe devices are the old series of Crucial ones and are rated for 200TBW which means that they can be expected to last for 5 years under the current load. This isn’t a real problem for me as the performance of those devices is lower than I hoped for so I will buy faster ones before they are 5yo anyway. o § Health/Nutrition/Agriculture⠀➾ # ⚓ It’s_Not_‘Encouraging’_That_Mostly_People_With_Disabilities Die_Despite_Covid_Shots⠀⇛ Asked on ABC‘s Good Morning America (1/7/22) about “encouraging headlines that we’re talking about this morning, this new study showing just how well vaccines are working to prevent severe illness,” CDC director Rochelle Wallensky responded: # ⚓ Djokovic_Is_Obnoxious,_But_His_Story_Highlights_Cruelty_of Australian_Detention⠀⇛ # ⚓ April_3_is_D_day,_COVID-related_deaths_exceed_40,000_and Hungarian_govt_backs_Kazakh_regime⠀⇛ Hungarian President Janos Ader called the general elections and also set the date for the homophobic “Child protection” referendum for April 3 in an official statement published on Tuesday. “The general parliamentary elections will be held on April 3″, Ader declared in the statement, recalling that the first free general parliamentary elections in Hungary were held 32 years ago. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ [Crackers]_disrupt_payroll_for_thousands_of_employers —_including_hospitals [iophk: Windows TCO]⠀⇛ A month-old ransomware attack is still causing administrative chaos for millions of people, including 20,000 public transit workers in the New York City metro area, public service workers in Cleveland, employees of FedEx and Whole Foods, and medical workers across the country who were already dealing with an omicron surge that has filled hospitals and exacerbated worker shortages. # ⚓ Ransomware_attack_on_New_Mexico_prison_knocks_systems offline,_forces_lockdown⠀⇛ A prison in New Mexico was forced to go into lockdown last week after a ransomware attack knocked its systems offline. The ransomware attack hit the Metropolitan Detention Center in Bernalillo County on Jan. 5. Systems affected by the attack included the jail’s internet, most of its data systems and its security cameras. # § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ Good_News_for_GDPR_Enforcement_against Cookie_Walls,_but_Also_a_Dangerous_Legal Challenge_from_WhatsApp⠀⇛ In 2019, the EU’s top court, the Court of Justice of the European Union (CJEU), ruled that pre- ticked checkboxes, used to encourage people to consent to the storage of and access to cookies, weren’t valid under the GDPR. Despite that, research the following year showed that many websites were still using “dark patterns” — online tricks to nudge visitors to accept privacy- hostile cookies. # ⚓ Meta_faces_billion-pound_class-action case⠀⇛ Facebook “abused its market dominance to impose unfair terms and conditions on ordinary Britons, giving it the power to exploit their personal data”, Dr Lovdahl Gormsen says. And this data, harvested between 2015 and 2019, provided a highly detailed picture of their internet use, helping the company make “excessive profits”. # ⚓ TikTok_isn’t_silly._It’s_serious⠀⇛ TikTok derives its magic from its algorithm and the data on which it is trained. Unlike Facebook’s rolling feed, TikTok’s simple, one-video interface means that the app always knows exactly what a user is watching. Clips are short, so viewers see a lot of them, generating plenty of information. This, combined with few friends and family clogging up the feed, allows the algorithm to match users with content creators that actually entertain them. And because videos are mostly shot on a smartphone, anyone can make them. Barriers to entry are low. Virality is high. o § Defence/Aggression⠀➾ # ⚓ Opinion_|_10_Reasons_the_OAS_Secretary-General_Must_Go⠀⇛ The Organization of American States (OAS) has never been a friend to the peoples of the Americas. This institution, ostensibly a space for multilateralism, has instead always been a tool for the U.S. Department of State. As Fidel Castro said in 1962, it is nothing but the U.S. Ministry of Colonies. That is truer now more than ever under the leadership of Secretary General Luis Almagro, who has been at the helm since March 2015. He is quite possibly the worst leader since the OAS was founded in 1948. # ⚓ Hawkish_Pundits_Downplay_Threat_of_War,_Ukraine’s_Nazi Ties⠀⇛ With the United States and Russia in a standoff over NATO expansion and Russian troop deployments along the Ukrainian border, US corporate media outlets are demanding that Washington escalate the risk of a broader war while misleading their audiences about important aspects of the conflict. # ⚓ Opinion_|_Untangling_Ourselves_From_the_Dark_Side_of_War⠀⇛ Guess what? I direct the following insight to, among others, the U.S. Congress, which annually and without comment, with only a few objectors, passes a trillion-dollar (and growing) military budget, by far the largest such budget on Planet Earth. # ⚓ How_the_states_have_become_“Laboratories_of_Autocracy”_— and_why_it’s_worse_than_you_think⠀⇛ Pepper’s book provides a detailed, nitty-gritty explanation of how the general conditions Mika describes have been created in Ohio and many other states across America. And when Pepper writes about how to fight back, it’s about fighting back against the conditions that made Trump possible, if not inevitable. Of course Trump himself remains a danger, but Pepper’s book provides a roadmap for action that addresses the roots of the problem. This conversation with David Pepper has been edited for clarity and length. # ⚓ Small_bands_of_mercenaries_extend_Russia’s_reach_in Africa⠀⇛ Yet Russia’s mercenaries will probably find it no easier to battle jihadists than do the Western forces they hope to supplant. Their record is certainly uninspiring. In 2019 Wagner sent men to fight jihadists in northern Mozambique. It pulled out after about ten of them were killed, including some who were beheaded. In Libya roughly 1,200 Wagner men fought on the side of a rebel general, Khalifa Haftar, against the UN-recognised government. Yet the rebel push to topple the government failed and Wagner’s troops were accused of war crimes, including murdering prisoners and civilians. # ⚓ Drones_Over_Ethiopia⠀⇛ Less than two months ago, the Ethiopian government was on the brink of defeat as Tigrayan forces closed in on the capital. Now the Tigrayan troops have turned about and withdrawn north back into Tigray. The government’s use of foreign-supplied unarmed aerial vehicles (UAVs) and armed drones appears to have played a significant role in reversing those spectacular gains made by the Tigrayan forces that had Prime Minister Abiy Ahmed calling on citizens to arms themselves and be ready to defend the capital, Addis Ababa. o § Environment⠀➾ # ⚓ Opinion_|_Families_in_Brazil_Face_Devastating_Floods; Social_Movements_Respond⠀⇛ Since the beginning of this year, hundreds of thousands of families have faced devastating flooding in the state of Bahia, Brazil. The floods have displaced more than 93,000 people and have taken 26 lives. People are scrounging for their few remaining belongings, and frantically searching for loved ones. # § Energy⠀➾ # ⚓ Opinion_|_Rest_Is_Important,_but_Corporate_Polluters Want_Us_to_Stay_Distracted⠀⇛ When people do things they shouldn’t, they often try to distract attention from their actions. Guardian writer George Monbiot notes that many corporations fueling the planet’s destruction spend significant resources to shift attention away from themselves and onto us. # ⚓ “Appalling”:_Climate_Groups_Slam_Biden_for_Prolonging Trump_Coal_Policy⠀⇛ # ⚓ Cities_facing_issues_with_street_lighting_during soaring_energy_prices⠀⇛ In 2020, Tartu city government’s electricity bill for December was €96,000. This past December, that number grew to €241,000. Although much of the electricity bill stems from street lighting, Tartu has not cast darkness on any streets yet, Tartu road service authority’s street lighting chief specialist Andrus Reinmann told ERR. o § Finance⠀➾ # ⚓ Opinion_|_Time_for_AG_Garland_to_Create_Corporate_Crime Database⠀⇛ # ⚓ Opinion_|_The_Ethics,_Economics,_and_Imperative_of Cancelling_Student_Debt⠀⇛ Economist Marshall Steinbaum recently appeared on my radio show The Zero Hour to discuss the economic and ethical issues surrounding student debt cancellation. Steinbaum, a Senior Fellow in Higher Education Finance at the Jain Family Institute and a professor at the University of Utah, is one of the authors of a seminal 2018 study from the Levy Economics Institute on the macroeconomic impact of student debt.  As pressure grows for a solution, Steinbaum discussed with me both the economics and the ethics of student debt. The following selections from the interview have been lightly edited for clarity. # ⚓ How_Did_We_Go_From_Stimulus_Checks_to_“Go_to_Work_With COVID”?⠀⇛ # ⚓ Monthly_Child_Tax_Credit_Payments_Have_Ended_as_Congress Debates_Its_Future⠀⇛ # ⚓ Poor_People’s_Campaign_Readies_‘Massive,_Nonviolent’_Effort to_Save_Democracy⠀⇛ Don’t call it a day of action. On June 18, the Poor People’s Campaign and its partners in organized labor, the civil rights movement, and religious communities are planning to mobilize their members and allies from across the U.S. to Washington, D.C. for what they hope will be the “largest mass assembly of poor people and low- wage workers in this nation’s history.” # ⚓ If_you_see_your_employer_offer_you_any_benefits_managed_by Auxiant,_run_like_hell.⠀⇛ Lately, it appears that they’re basically stealing from the employees by freezing them out of their accounts and threatening them with having the IRS called on them if they don’t pay back FSA money that the employees spent on eligible medical care. It’s happening to many people my mom works with, including her. They froze her out of nearly $2,000 that was left in her account and then tried to blackmail her into paying back money that she used on HSA/FSA eligible dental care. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ State_Legislatures_Are_Silencing_Native_Voices_Through Redistricting⠀⇛ # ⚓ Opinion_|_Eight_New_Year’s_Resolutions_for_NPR_to_Consider Now⠀⇛ The reasons Congress created NPR (National Public Radio) under the Nixon Administration was to fill the yawning gaps of commercial radio in local, national, and international news coverage and to give voice to the people, without ads. It was to be publicly funded by taxpayers. Almost 51 years later, NPR is now funded heavily by national corporations, with its local affiliates soliciting local business advertisements. # ⚓ Sanders_Says_Manchin_and_Sinema_Are_Undermining_US Democracy⠀⇛ # ⚓ Sanders_Says_Manchin_and_Sinema_Are_Imperiling_US Democracy⠀⇛ Sen. Bernie Sanders said Friday that by vowing to uphold the archaic Senate rule standing in the way of voting rights legislation, his colleagues Joe Manchin and Kyrsten Sinema are putting “the future of American democracy” at risk. “It is a sad day when two members of the Democratic caucus are prepared to allow the Freedom to Vote Act to fail,” the Vermont senator tweeted. “I hope very much they will reconsider their positions.” # ⚓ China_Seen_Backing_‘Digital_Authoritarianism’_in_Latin America⠀⇛ Chinese technology and expertise is making it possible for Venezuela and Cuba to exercise suffocating control over digital communications in the two countries, according to insider accounts and several international investigations. Venezuela and Cuba do more to block internet access than any other governments in Latin America, according to the U.S.-based advocacy group Freedom House, which has documented what it describes as “digital authoritarianism” in the region since 2018. # ⚓ China,_Iran_Begin_Implementation_of_Sweeping_Strategic Agreement⠀⇛ Chinese foreign minister Wang Yi and Iranian counterpart Hossein Amir-Abdollahian announced the start of the partnership’s implementation at a meeting in east China’s Wuxi on Friday, Beijing’s foreign ministry said in a statement. Few details of the secretive deal have been published, but the New York Times reported in 2020 that it would secure a regular supply of oil for China, citing a draft of the agreement leaked to the paper. o § Censorship/Free Speech⠀➾ # ⚓ Disney_Censors_‘The_Simpsons’_Episode_From_Hong_Kong_Site⠀⇛ If an episode of “South Park” that satirizes the Chinese Communist Party (CCP) was conspicuously excluded from an American streamer’s Hong Kong site, Trey Parker and Matt Stone would skewer them for it. However, Disney+ did exactly that when it censored for its HK customers the episode of “The Simpsons” wherein Homer Simpson visits Beijing. If you live in Hong Kong, you can’t watch “Goo Goo Gai Pan” (S16 E12), but the rest of us still can—for now. According to Google, there has been no response from Matt Groening yet. # ⚓ This_is_messed_up:_a_Swedish_village_decides_to_rename itself.⠀⇛ The earliest records of Fucke date back to 1547, when it was described as being “by a lake, situated very high up on a hillside with very steep fields,” according to the Institute for Language and Folklore. Despite its historic roots, residents of Fucke are fed up, particularly with Facebook’s censorship of their posts when they try to write about their village on social media or sell items online. o § Civil Rights/Policing⠀➾ # ⚓ REVEALED:_Portland_Police_Riot_Training_Presentation Included_Graphic_Slide_on_Brutalizing_‘Dirty_Hippies’⠀⇛ The image — cataloged at Know Your Meme as the “Prayer of the Alt-Knight” — is again stirring controversy about the practices of the notorious Portland Police Bureau, which recorded more than 6,000 uses of force while policing racial justice protests in the summer of 2020. The Bureau is currently under supervision by the Department of Justice, which blasted the Portland police last May for its unconstitutional reliance on violence and a leadership that “portrays all force as justified.” # ⚓ UK:_Scotland_young_persons’_free_bus_travel_scheme_—_is_it “Your_papers,_please!”_time?⠀⇛ # ⚓ This_Private_Equity_Firm_Is_Amassing_Companies_That_Collect Data_on_America’s_Children⠀⇛ # ⚓ A_bill_to_ban_geofence_and_keyword_search_warrants_in_New York_gains_traction⠀⇛ o § Internet Policy/Net Neutrality⠀➾ # ⚓ DirecTV_to_Drop_Rabidly_Pro-Trump_One_America_News⠀⇛ Facing a wave of grassroots pressure, one of the largest television providers in the U.S. reportedly plans to drop the far-right, rabidly pro-Trump One America News Network, an outlet that has come under fire for disseminating falsehoods about the 2020 election results, the coronavirus pandemic, and other major issues. Bloomberg reported late Friday that DirecTV has informed OANN’s owner, Herring Networks Inc., that it intends to “stop carrying the company’s two channels when their contract expires” in early April. o § Digital Restrictions (DRM)⠀➾ # ⚓ 2022_Ford_F-150_Lightning_Will_Come_With_One_Year_No-Sale Provision⠀⇛ When the second-generation Ford GT was released a few years ago, it came with a big asterisk for buyers – they weren’t allowed to sell the car for two years. This was the very first time Ford had imposed such a restriction, and it was serious about it. In fact, more than one person tried to circumvent the requirement and sell their cars early, including professional wrestler/actor John Cena, who wound up getting sued by The Blue Oval and eventually settled the case out of court. Now, it appears that the 2022 Ford F-150 Lightning will also come with the same sort of no-sale provision, albeit for one year, according to a dealer memo seen by Ford Authority. o § Monopolies⠀➾ # ⚓ Zuckerberg,_Pichai_signed_‘big_deal’_to_carve_up_ad_market: Report⠀⇛ San Francisco, A serious anti-trust complaint in the US has reportedly revealed that Meta CEO Mark Zuckerberg and Alphabet and Google CEO Sundar Pichai were allegedly involved in an ad collusion plot, a charge that both tech giants denied. Attorneys for Texas and other states alleged in newly unsealed court filings that Zuckerberg and Pichai “personally approved a secret deal that gave the social network a leg up in the search giant’s online advertising auctions”, reports Politico. # ⚓ Tokenization_of_intellectual_property_for_IP_rights management [Ed: There is no such thing as "intellectual property" (a misnomer and lie) and they're not rights, either; this is just a bunch of charlatans stroking their egos as they help plutocrats ban their competition]⠀⇛ Interest in blockchain technology, tokens, and IP, continues apace. Consider the recent WIPO webinar, “Blockchain Whitepaper for IP Ecosystems”, at which the view was expressed that the future of IP management rights could include a solution that utilizes tokens, and, in particular, non-fungible tokens. While the tokenization of IP, namely for anti-counterfeiting purposes, was already outlined by the European Intellectual Property Office several years ago, WIPO sees potential applications of blockchain technology in IP ecosystems for “ [a]ll types of IP assets: Registered and Unregistered Rights”. # ⚓ Counterfeits_study_raises_questions_over_social_media influencers [Ed: Max Walters uncritically passes on self- serving_UKIPO propaganda in “study” clothing]⠀⇛ A new UKIPO study prompts counsel to ponder the power of influencers in promoting counterfeits and what should be done about it # § Patents⠀➾ # ⚓ Philip_Morris_and_Hoyng_ROKH_Monegier_strike_back against_BAT’s_Glo_products [Ed: EPO has granted patent monopolies to company that killed millions of humans, including some family members of mine, using cancer (smoking)]⠀⇛ The Düsseldorf Regional Court has found that BAT infringes Philip Morris’ European patent EP 32 66 323. As a result, according to a court spokesperson, the court has prohibited the cigarette manufacturer from marketing its Glo products in Germany (case ID: 4b 105/20). However, JUVE Patent is not yet aware if Philip Morris will enforce the injunction against BAT. [...] Furthermore, Dreiss partner Andreas Pfund is handling the patent-in-suit from the Düsseldorf proceedings at the EPO. Powell Gilbert is conducting the UK proceedings for Philip Morris. # ⚓ France_to_push_design,_GI,_UPC,_and_safe_harbours reform_as_president_of_the_Council_of_the_EU [Ed: IP Kat is again repeating lies_from_the_UPC’s_Preparatory Committee]⠀⇛ In the area of patents, France plans to support the establishment of the Unified Patent Court (UPC), which has been delayed, first by the Brexit, and then by the German Constitutional challenge. As GuestKat Frantzeska Papadopoulou reported last November, the UPC’s Preparatory Committee has set out a timeline for the UPC to commence its activities. According to this timeline, the UPC will become operational by mid-2022. # ⚓ User_survey_on_future_Ombuds_services [Ed: The criminals who have taken over the EPO want_you_to_think they_will_regulate_themselves; they’re above the law and they made corruption the norm; perhaps more amusingly, if one attempts to answer the EPO’s survey there’s a notice at the bottom (“Data protection and privacy”) suggesting that they’re_lying_about_anonymity and_will_likely_outsource_all_this_data_to_Microsoft/ NSA/USA]⠀⇛ The EPO plans to launch a new informal, confidential and neutral Ombuds service in mid-2022 as part of its commitment to continuously improve its products and services. The Ombuds Office will assist stakeholders who have exhausted the existing mechanisms for resolving problems that may have been encountered when using EPO services. # ⚓ Gowling_and_Kirkland_go_head-to-head_in_UK’s_next major_FRAND_trial [Ed: EPO-granted patents weaponised by patent_trolls euphemised as “NPEs” here]⠀⇛ InterDigital initially alleged that Lenovo infringed five SEPs in the UK. The NPE claimed that all patent were essential to the 3G and 4G UMTS and LTE standards. The patents, EP 2 485 558, EP 23 63 008, EP 2 557 714, EP 24 21 318 and EP 33 55 537 are part of InterDigital’s portfolio and are regulated by the European Telecommunications Standard Institute (ETSI). The portfolio also contains patents granted in the US and China. [...] Since 2009, the parties have discussed licensing EP 558, with InterDigital claiming it made global licensing offers to Lenovo on FRAND terms under the ETSI declaration. InterDigital also offered a licence on alternative terms. InterDigital claimed that Lenovo was an unwilling FRAND licensee and would not accept the offered FRAND licence, while Lenovo rejected claims that InterDigital’s offer was FRAND. # ⚓ Egetis_Therapeutics_gets_Notice_of_Intent_to_Grant for_a_new_European_patent_for_a_combination_therapy with_Aladote [Ed: Egetis Therapeutics seems unaware that European Patents are nowadays_suspect, with many not in compliance with the law]⠀⇛ Egetis Therapeutics AB (publ) (ticker: EGTX) today announced that the European Patent Office (EPO) has issued a Notice of Intent to Grant for a new patent covering a combination treatment with the company’s clinical candidate drug Aladote® (calmangafodipir) and N-acetylcysteine ​​(NAC). The new patent further improves the unique value proposition of the Aladote franchise and provides patent protection until year 2037 in Europe, before a potential extension. # ⚓ Patent:_Suspension_of_Infringement_Proceedings_in_the Case_of_(Future)_Nullity_Suit [Ed: When fake_patents get_granted_by_the_deeply_corrupt_EPO and these patents do a lot of damage regardless]⠀⇛ Higher Regional Court of Düsseldorf, order of 22 September 2021, Case No. I-2 W 17/21 – Suspension standard After the Technical Board of Appeal of the European Patent Office (EPO) upheld the patent in suit and a subsequent nullity suit based on prior art not yet taken into account in the opposition proceedings, the parallel infringement dispute was initially suspended by the Regional Court of Düsseldorf by order of 3 September 2020. Inresponse to the admissible and valid immediate appeal of the infringement plaintiff, the Higher Regional Court of Düsseldorf repealed the order of the Regional Court to stay the proceedings and referred the case back to the Regional Court for a new decision. For the reasons set out below, the Higher Regional Court concludes that the Regional Court had applied an incorrect standard for a stay of proceedings. # ⚓ Mazda_3_2-door_hatchback_patent_hints_at_sporty coupe⠀⇛ First spotted by CarBuzz, patent documents filed with the United States Patent and Trademark Office (USPTO) and European Patent Office show a car with the same basic silhouette as the current Mazda 3 hatchback, but with two doors. # ⚓ Mazda_three-rotor_hybrid_engine_plans_appear_in patent_filings [Ed: Judging companies by patents instead of actual products]⠀⇛ # ⚓ Motorola_patents_a_crazy_phone_that’s_all_screen [Ed: As if getting a patent is indicative of real success]⠀⇛ While some companies are moving away from curved screen smartphone design, others seem to be taking things to new extremes. Our good friends at LetsGoDigital have unearthed yet another patent application, this time depicting something truly peculiar. # ⚓ Motorola_may_be_serious_about_making_a_phone_with_a wrap-around_display⠀⇛ Motorola appears to be actively working on a smartphone with a wrap-around display, with the company publishing repeated patents for such a device. # ⚓ [Older]_UK:_Essential_Information_On_Confidentiality [Ed: EPO is now flagrantly_in_breach_of_confidentiality principles]⠀⇛ Anybody to whom you disclose your invention must agree in advance that it is confidential and that the information will not be used by them or passed on. Outside an immediate circle of family and possibly friends, you should have a written confidentiality agreement signed. The safest thing is to limit disclosures strictly until a patent application has been filed. If there have already been disclosures of your invention, you should give us details of those. In many cases they may be treated as confidential in any event but we need to assess the situation. Even if patent protection cannot be obtained in the UK or elsewhere in Europe, there will be other countries where it may be possible. One of those is the United States, where a patent application can be filed up to a year after your own disclosures. # ⚓ [Older]_UK:_COP26_&_New_Materials_For_The_Green Industrial_Revolution [Ed: More greenwashing_of patents, monopolies, and basically oligarchy]⠀⇛ # ⚓ [Older]_UK:_IP_At_Sea [Ed: Marks & Clerk, convicted corrupt_firm, repeatedly calling patents “rights”; this is a lie, they’re repeating a falsehood. It’s a falsehood they look to profit from.]⠀⇛ A patent is an Intellectual Property (IP) right. As a legal right, patents have geographical limitations that set the area in which the patent owner can exercise their rights. Understanding the geographical extent of a patent right is especially important for inventions used at sea where potentially infringing products may transit between may different territories. # ⚓ Taliens_hires_senior_partner_from_Gide_in_Paris [Ed: This is an excellent new example of JUVE posting marketing spam and pretending that the mere hiring of one person is some kind of important news; once upon a time JUVE was a new source, not spamfarm]⠀⇛ IP disputes partner Grégoire Triet (67), who has joined Taliens as a partner, previously worked for Gide Loyrette Nouel for 32 years. Over the past 20 years, he was instrumental in building the current patent litigation team. Following his departure, three partners and eleven associates remain at Gide. # ⚓ The_successful_development_of_the_Eurasian_community [Ed: Conveniently mistaking patent cartels for a "community"]⠀⇛ Since the Eurasian Patent Convention was signed in 1994 it has been shaping the global IP landscape. In the 25 years 22.700 Eurasian patents were granted at the Eurasian Patent Organization (EAPO). Recently Eurasia expanded the activities to include the applications of industrial designs and although it is not yet possible to file Eurasian trademarks, there is a relevant agreement. IP experts Vladimir Biriulin and Nikolay Bogdanov, both partners in the Russian Law Firm Gorodissky & Partners, expect some interesting development in the future. [...] The Eurasian Patent Office has been accepting patent application since then. A Eurasian patent, unlike European patent is a unitary patent and does not require translation into national languages. A Eurasian patent application is filed and examined in the in the Russian language, the patent is issued in Russian and is valid in all those countries. # ⚓ $22,000_for_III_Holdings_prior_art [Ed: You can make a living by helping to squash fake patents]⠀⇛ On January 13, 2022, Unified added 11 new PATROLL contests, with a $2,000 cash prize for each, seeking prior art on at least claim 1 of the list below. The patents are owned by III Holdings, LLC. The contests will all end on April 15, 2022. Please visit PATROLL for more information or click on each link below. # § Software Patents⠀➾ # ⚓ Sound_View_’860_patent_successfully challenged⠀⇛ On January 11, 2022, less than 10 months after Unified filed the request for ex parte reexamination, the USPTO issued a final office action rejecting claims 1-3, 5, 7, 8, 10, and 18 of U.S. Patent 8,135,860, owned by Sound View Innovations, LLC. The ‘860 patent relates to data processing that transforms web content into a format suitable for display by a client device and was previously asserted against Facebook. # ⚓ $2,000_for_Setala_Juha_prior_art [Ed: This looks like abstract stuff again, leveraged by patent trolls]⠀⇛ On January 4, 2022, Unified Patents added a new PATROLL contest, with a $2,000 cash prize, seeking prior art on at least claim 1 of U.S. Patent 8,495,167. The patent is owned by Setala Juha, an NPE. The ’167 patent generally relates to data communication networks and has been asserted against Apple, Google, Sony, Microsoft, Netflix, Cisco, Amazon, and Akamai Technologies. # § Trademarks⠀➾ # ⚓ Perfume_N°5_v_N°9:_Chanel_won_an_unfair_competition case_in_China⠀⇛ In 2019, after spotting a perfume product in China’s market highly similar to its classic N°5 perfume, Chanel took a ‘notarization- throughout purchase’ online and located the alleged infringing product shown below on the right. The side-by-side comparison captures several common features. The obvious difference lies in the text: whilst Chanel has ‘N°5, CHANEL’, the alleged infringing product uses ‘N°9, FLOWER OF STORY’ (hereinafter ‘the N°9 perfume’). # ⚓ Written_Description:_Jessica_Litman:_Who_Cares_What Edward_Rogers_Thought_About_Trademark_Law?⠀⇛ Professor Jessica Litman has a fascinating forthcoming book chapter on the history of the Lanham Act and the influence of Edward S. Rogers, “Edward S. Rogers, the Lanham Act, and the Common Law. ” Litman tells the history of the drafting of the Lanham Act of 1946 through the lens of Edward S. Rogers, detailing how his advocacy and drafting work influenced the final statutory text. Readers may be surprised to learn that Litman started research on the topic as a law student in the 1980s, while writing a student note on trade dress infringement. She went into the stacks of the Columbia Law Library and started reading bound copies of legislative history. She noticed it seemed like Rogers was everywhere, from 1932 all that way up to 1946, and that the chairs of the committees were deferring to him. That was really interesting, she thought. But after the note was done, she kind of forgot about it. Now, forty years later, Litman is a professor at the very institution Rogers attended, the University of Michigan. She was surprised to find no one seemed to remember Rogers had been at Michigan, even though he “earned three law degrees and was a member of the adjunct faculty for 18 years” (3). In this book chapter, Litman is making up for that, returning to the topic of Rogers and his legacy. She’s found her notes from 1981. She’s read everything he wrote, and all his cases, starting in 1895 all the way until his death in 1949. # ⚓ Precedential_No._2:_TTAB_Rejects_Summary_Judgment Motion_Filed_Three_Days_Too_Late⠀⇛ The Board denied Opposer Lumber Liquidator’s request for reconsideration of the denial of its summary judgment motion because the motion was untimely. A summary judgment motion must be filed before the deadline date for pre-trial disclosures, but Lumber Liquidator filed its motion three days after the deadline date. Lumber incorrectly applied Rule 2.196 in adding three days to the deadline. Lumber Liquidators Services, LLC v. Columbia Insurance Co., 2022 USPQ2d 31 (TTAB 2022) [precedential] (Order by Interlocutory Attorney Jennifer Krisp). [...] The Board faced a similar issue in Asustek Comput. Inc. v. Chengdu Westhouse Interactive Entm’t. Co., 128 USPQ2d 1470 (TTAB 2018), involving a motion to compel discovery. Pursuant to Rule 2.120(f)(1), such a motion must be filed “before the day of the deadline for pretrial disclosures for the first testimony period as set or re-set.” The Board rejected Austek’s position that, because the day before the deadline day was a Sunday, it could timely file its motion on the following day. Not so said the Board. The motion to compel had to be filed before the deadline day. In Asustek, the Board pointed out that Rule 2.196 “does not apply to the relevant provision of Trademark Rule 2.120(f)(1), which does not fix a particular day by which a motion to compel must be filed, but instead ensures that the motion be filed before the day of another event (pretrial disclosures) occurs.” The Board, anticipating that similar timeliness issues might arise with respect to a motion for summary judgment, stated that “ [m]otions for summary judgment, just as motions relating to discovery, must be filed before the proceeding enters the trial phase.” In the case at hand, the Board observed that “[t]he overriding interest in assuring that all matters relating to the discovery phase are closed and resolved prior to trial is evident in and achieved from a proper application of Trademark Rule 2.196 to motions for summary judgment as well as motions to compel discovery. # § Copyrights⠀➾ # ⚓ Copyright_of_Software_API⠀⇛ This week, the Federal Circuit is hearing oral arguments in an important software copyright case, SAS Institute, Inc. v. World Programming Ltd., Docket No. 21-1542. The SAS is an important follow-on to the Supreme Court’s 2021 decision in Google v. Oracle, 141 S. Ct. 1183 (2021). In Google, the Supreme Court sided with the accused infringer on fair use grounds, but did not decide the broader issue of whether Oracle’s API naming convention was copyrightable. WPL created a clone version of SAS that allows users to use SAS-style inputs and receive SAS-style outputs. SAS argues that those input and output formats are protected by copyright. However, the district court (E.D.Tex. Judge Gilstrap) sided with the accused infringer — holding that WPL presented unrebutted evidence that these elements were not protectable by copyright. # ⚓ Manga_Artist_Maki_Murakami_Targets_Large_Pirate_Site NyaHentai.com⠀⇛ Japanese manga artist Maki Murakami has gone to court in the United States after several pirate sites published her work without permission. Among the platforms is NyaHentai, a large pirate service with an estimated 24 million visits per month, making it Japan’s 75th most visited site overall. Murakami’s legal team is attempting to find out who runs this platform and several more. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 6997 ➮ Generation completed at 02:43, i.e. 66 seconds to (re)generate ⟲