𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, December 14, 2021 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Wed 15 Dec 02:40:19 GMT 2021 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/2021/12/14/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmSWwJ7eRdx1kz73nTFtXRp2vF9nhTnV7sYYZVwuM6t9c5 QmWM7VYrVdqPgZh8JgwKyiXxRcVGNjoM8cBVEUyQXKcR5T QmWSgWCNaXdj4bqpVXJtFwGUpuJtUjJhMJNpvzpyfvb343 QmcVbvyKViSMyKpSnvawYzxL7fTBuhBFrU1Qs3vw1Dka8p QmUKBswRXMsDq5RCK5eUe68NysKpHtQ9EhcoUWes6WJbtG QmUS4fYkvuMboBGcVkEMNHsnTxKWQm7WKvLr6wGqwSsgk1 QmWxGDdEJSbvkgneVRR2pbXgmVk3pi5U6cgy64gq54Dsi7 QmThpqmVrTBjQ3aKEp3yrZKJUdKapNAGts5Lu3eYkGeBwf QmQPL4aU5VkHzGprihFtysZx7tMGqLPQa11SU2s4ao6H6r QmWDLoPpML1exaPTP8wfzYiKd4whiRGaCCqWNHJQ8Tgfgg QmXP9uUCLGPXq5XphWSHwKkEcNvzBUFmcGuun1rgVhDoMf QmbcSKJZiufM2XfxxnB92wQE323m9MsiAMo5YFmwFPu8VN QmWmC3AgPDFykej4Jpay8nnpKKVGMMEfv8MjggJ9Qw5Lm9 QmNPpiGqWGFQNEECwNKt72LSricBeH2VuxSzamtqTrESHV QmUNbGTar72DvDUxqyAh6Jdzfvu4JHUqaTFKqWpu9P64bk QmXFHTXDoB1z4Af36pfwwfrJcsZWK4nkbqqF2EndNyJ9YA QmcFJuq5PVoQgjijbLaMibeRbgr4h5pFcpzBYWqLap1cNu QmSBPP9JjsnqHFcHfShHhNsQwTc4eHz66BF5ihuBjaxpKM QmPrW6GPykdMyQtg8txV2DXmRYjghF1TQPv6CJcwVUx6iy QmVNVya1kBzPYdBdJekAHEpk3m857qJsnQet4QNxycPonK QmUQmiHKq1wV1JkS2hwXEf1etD3jM43Afc68V6omxpqaCi ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ Up Next: Arrest and Police Report for Microsoft’s Chief Architect of GitHub Copilot | Techrights ⦿ Tomorrow is the First Anniversary of Strike Against President Campinos at the European Patent Office | Techrights ⦿ If EPOnia Was a Country, It Would Rank About 6th in the World for Union Density | Techrights ⦿ IRC Proceedings: Monday, December 13, 2021 | Techrights ⦿ The Precarious Situation of Slovakia as One of Battistelli’s EPO ’Pawns’ in the East | Techrights ⦿ The EPO’s Overseer/Overseen Collusion — Part XXXV: Slovakian Scruples | Techrights ⦿ [Meme] [Teaser] Buying Power or Securing Control (the Leadership Positions) of Europe’s Largest Patent Office | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2021/12/14/alex-graveley-mugshot-and-2-links/#comments http://techrights.org/2021/12/14/epo-rally-for-change/#comments http://techrights.org/2021/12/14/if-eponia-was-a-country-it-would-rank-about-6th-in-the-world-for-union-density/#comments http://techrights.org/2021/12/14/irc-log-131221/#comments http://techrights.org/2021/12/14/slovakia-as-epo-pawn/#comments http://techrights.org/2021/12/14/slovakia-epo-lobbying/#comments http://techrights.org/2021/12/14/tomas-malatinsky-and-epo/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2021/12/14/amd-aocc-3-2/#comments http://techrights.org/2021/12/14/linux-mint-20-3-una-beta/#comments ䷩ 𝚕𝚒𝚗𝚎 66 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/14/alex-graveley-mugshot-and-2-links/#comments Gemini version at gemini://gemini.techrights.org/2021/12/14/alex-graveley-mugshot-and-2-links/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Up_Next:_Arrest_and_Police_Report_for_Microsoft’s_Chief_Architect_of_GitHub Copilot⠀✐ Posted in Microsoft at 8:40 pm by Dr. Roy Schestowitz Last week: [Teaser]_Meet_Microsoft’s_Chief_Architect_of_GitHub_Copilot, Balabhadra_(Alex)_Graveley_(Updated) | Microsoft_Corporation_is_Still Protecting_a_Violent_Criminal_Who_Assaults_Women_(Employing_Him_as_Manager, Protecting_Him_From_Arrest,_Paying_Him_a_Salary) 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Alex_Graveley_mugshot⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Austin_police_photo__-_legal_notice⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Austin_police_photo⦈_ Summary: The mugshot_is_now_online, accessible through the_Web_site_of_the police_department; The Austin police report itself (there was an arrest) should come up next as we’re redacting the material to protect the victims ⣁⡽⣊⣁⠙⠶⢾⣨⡙⣭⢏⠯⢚⡽⢁⣤⣄⠤⠼⣷⣿⡿⢟⣫⣶⣩⣅⠏⠿⠖⡂⣠⠂⣼⣷⡃⠸⣿⣭⠿⣿⣿⣿⣻⡿⣿⡟⣻⣿⡿⣯⣽⣿⣷⢿⣿⣟⣳⣿⣽⣹⣿⣿⣯⣻⣫⣭⣿⣷⡟⣾⣿⣿⣫⡖⣻⣿⣽ ⣳⠲⠎⣉⠵⢒⣵⡭⡺⣖⢧⣈⣛⢳⢻⠤⡞⢚⡖⠗⠬⣯⣏⣛⣦⡮⢸⠛⡷⡚⠷⡶⠮⣁⢨⢅⢸⣿⣧⣴⣿⢻⣿⣿⣟⡿⣟⣻⣿⣝⣿⣷⡽⣿⣻⢣⡟⢿⣭⣽⢭⣽⣿⣿⣿⣿⣿⣟⣿⣯⣵⣯⣺⣭⡿⣿⣟⣽ ⢯⣟⣛⣯⢷⣵⡠⢫⣯⡛⠟⢕⡄⠭⠀⣝⣗⠦⣇⡿⣶⡲⢻⢥⣎⣟⢁⠈⣿⢚⢛⣏⣩⢝⣲⡄⢸⣿⣿⣿⣿⣿⣿⣟⣷⣿⡒⣿⣿⣻⣾⣿⣿⣿⢿⣿⣻⣿⣷⡿⣿⣽⢿⣿⣷⣯⣷⣿⣾⣧⡇⡿⣷⢝⡟⣽⣓⣷ ⣿⡽⣯⣮⣿⣿⣷⣿⣖⢮⡵⣿⠹⣷⣿⣫⡋⣿⢷⣆⣱⣋⣽⡲⣶⣚⣵⠾⠑⡵⣪⡞⢭⣗⣏⡃⠩⣿⣟⣿⡿⢾⣿⣿⢿⣿⣿⣽⡿⢧⣿⢽⣭⣽⣿⣿⠿⣪⣕⣻⣻⣿⣯⣵⢿⣽⣿⣷⣼⣯⡾⣗⣶⣬⣟⣫⣩⣿ ⣭⣗⣾⢾⣟⡿⠿⡛⡣⢵⡟⣸⣦⣹⢺⡵⢃⢥⣿⠛⢷⣿⣋⠾⣇⣤⣀⢫⠶⢚⡝⢎⡗⠮⡐⣃⡾⠓⢀⠉⠉⠈⠘⠛⠻⠷⠙⠛⣼⣿⣷⠿⣿⢟⣿⠿⣿⣿⣿⣿⣶⣿⣷⣺⣿⡤⣛⣶⣾⣿⣾⣯⡻⣟⣿⣿⣿⣿ ⡿⢮⣱⣼⣼⣿⣖⣷⡟⣻⣍⡿⡭⢛⣿⣳⣶⣭⢵⣳⣻⣿⡞⢫⣻⣿⢧⡿⠉⠉⢠⣟⠑⠚⠁⡀⠀⠀⠀⠀⠀⠠⣀⠒⢀⠀⠠⠀⠈⠙⠿⠿⠿⣿⡿⣾⣯⣿⣿⣯⡽⣽⣽⢿⣷⣮⣿⣾⣿⣽⣿⣭⣿⣿⣿⣿⣿⣿ ⢿⣷⢿⣛⣿⡽⣽⣮⣞⣭⣷⣿⠯⣿⣽⣟⣿⣶⣿⣿⣿⣻⢿⡏⣳⣒⣾⠗⠀⠈⠀⠀⠀⠀⡤⠄⠀⠀⠉⠁⠀⠀⠚⠄⠀⠈⠀⠀⣀⠀⠀⠀⠈⠉⠻⣿⡿⣷⣿⣿⣾⣿⠿⢟⣧⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣛⣟ ⣮⣭⣿⠿⡿⢿⣟⣿⣟⡷⣾⢿⡻⣿⡟⣵⣿⡟⣿⣶⠔⣌⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠻⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣟⣟⡻⣟⣻⣽⣟⣿⣷⣻⣿ ⣟⣷⣿⣽⠟⣧⣽⣿⣿⣿⣿⣾⣟⣽⣷⢟⣻⣽⣟⡗⢋⣿⣽⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣿⡭⢻⠾⢿⣯⣹⣷⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿ ⣯⣿⣿⣿⣿⣿⣿⣾⡿⣗⣾⣿⣿⣿⣿⣺⢫⣲⣿⣿⣶⣿⣋⢌⡆⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣽⣿⣿⣿⣿⣿⣿⣭⣟⣿⣿⣿⣿⣿⣽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⡶⢿⣿⣿⣿⣿⣿⣿⡽⡁⠆⠀⠀⠀⣠⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣷⣶⣄⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣹⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠁⠀⠀⢠⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢘⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿ ⣿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠹⡿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣯⣿⣿⣾⣿⣻ ⡿⣿⣿⣾⣿⣿⣿⣿⣯⣟⣿⣿⡿⡛⣀⡶⠿⠿⠛⠿⣔⢈⣵⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠛⠋⠀⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉ ⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣄⣀⣄⣤⣿⣾⢿⢶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣤⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⡻⣿⣿⡿⢿⢿⣿⣿⢿⣿⣧⣿⣾⠏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠇⢨⣿⠟⢟⣻⣛⣻⠿⣟⡿⢿⣻⡿⢿⣿⡟ ⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢈⠰⣺⠭⡱⣦⣪⣍⢽⣯⢍⢿⣫⡃⡷⣿⣽ ⣛⣿⣿⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿⣿⣽⣽⣿⣿⣽⣽⣇⠀⠀⢸⣿⣿⡿⠛⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠸⡟⢌⠽⠤⢰⠅⠪⡥⠆⢟⡿⢴⢔⢵⡷⢿ ⣿⣟⡿⣿⣻⣷⢞⣿⣿⡾⣿⡿⣯⣾⣟⣿⣿⣇⣄⣞⣁⠀⠀⢸⣿⠁⠀⣀⣠⣠⣤⣄⣀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⢿⠆⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠁⠀⠡⠕⡑⢙⠨⠟⠯ ⠿⣿⣽⣯⣿⢿⣿⣿⣿⣿⠝⣿⣿⢿⣿⣿⣽⣿⣿⣿⣿⡀⠀⣿⣿⣆⣠⡿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰⠦⠆⠀⠀⠀⢘⠀⠀⠀⠁⠀⠀⢀⠁⠐⠀⢀⠀⠀⠢⠀⠈⠀⠂⠀⡀ ⣿⣷⣿⣿⠿⣿⡿⣿⣿⣿⣾⡿⣿⣿⣼⢯⣏⣿⠉⣹⣿⡇⢀⣿⣿⣿⣿⣷⣤⣤⣦⡀⠀⢀⡀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣴⡄⢠⣾⣿⣧⠀⠀⠀⠀⠂⠂⠀⠀⡀⠀⠀⠁⠀⠀⠐ ⣿⣿⣿⣿⣯⣼⣿⣿⣹⣿⣿⣟⣿⣿⣿⢏⣴⣿⣠⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣾⣶⣶⣶⣿⣿⣿⡇⢸⢟⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⠀ ⣿⣿⣿⣷⣷⣿⣿⣿⣿⣟⣽⣽⣻⣷⣭⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢨⣾⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢀ ⣿⣷⣯⣽⣿⣿⣟⣾⢿⣻⣿⡹⢞⣻⡭⠙⠑⣿⣿⣿⡿⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⣍⣽⣽⢿⣿⣿⣿⣿⣛⣣⣹⣿⣿⠾⢜⡍⡚⣻⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠠⣿⣿⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⣿⣿⣿⣾⣿⣿⣟⡼⡿⣿⣟⡧⠛⢺⡚⣒⡿⢋⠻⣿⣿⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡷⣿⢿⢭⡳⢆⣹⣐⡪⠰⢍⣛⠍⠟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠈⠁⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈ ⣿⣿⣿⣻⣿⣿⣟⣻⣷⣯⡿⣜⢣⠞⡒⢒⡀⠂⠃⣬⢡⡀⠀⢈⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⣵⡟⣿⣿⣿⣿⣿⣿⣯⡿⣃⢰⡳⠚⠰⠶⠷⢊⠃⠂⠐⠀⠀⠈⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣀⣰⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⣿⠟⣿⣿⣿⣧⠭⢃⠬⠍⡃⠈⠀⠐⠐⠀⠐⠂⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣭⣭⣍⣉⣉⣉⣉⠛⠂⠀⠀⠀⠀⠘⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣿⣿⣿⣟⣿⣿⣒⡊⠟⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠚⡿⠀⠀⠀⠀⣠⢿⢿⠿⠿⠿⠛⠿⠿⠿⣿⣿⣦⣄⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⡟⡏⠏⡠⢺⣢⠷⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⢞⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢺⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣽⣿⣻⡍⡴⠏⠣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠿⠻⢋⢼⣌⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣘⣠⣯⣄⡀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠬⡋⡁⠅⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⠘⠒⢿⣿⠛⠃⠀⠀⠀⠈⡎⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢓⠒⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⢀⢺⠿⠃⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣧⡑⢤⣤⡤⢴⠦⠦⠤⠤⠤⠴⠶⠶⠦⠴⠶⠶⠦⠴ ⠿⠿⠛⠛⠗⠚⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⢹⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣦⣴⡤⠆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣶⠈⣈⣀⣀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶ 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at gemini://gemini.techrights.org/2021/12/14/epo-rally-for-change/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Tomorrow_is_the_First_Anniversary_of_Strike_Against_President_Campinos_at_the European_Patent_Office⠀✐ Posted in Europe, Patents at 11:38 am by Dr. Roy Schestowitz ‘Team UPC’ is now doing to European patent courts what it has already done to Europe’s largest patent office, the EPO (the comments below are only hours old) 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇UPC⦈_ Summary: The science-hostile Team Battistelli/Campinos is likely to see industrial action some time soon; as workers put it last year, “ENOUGH IS ENOUGH” As we noted_here_yesterday, we’re fast approaching the one-year anniversary of the EPO’s strike that saw nearly_half_of_the_workers_in_Austria_refusing_to work_for_the_whole_day. Now that Team UPC is scheming to undermine the law through Austria and Slovenia (see the 15_comments_here) we thought it would be worthwhile reproducing here reasons that are still valid to protest or strike. They’re not been tackled and we didn’t publish this two-page publication last year. The following text is as relevant as ever: 02.12.2020 su20015mp – 0.2.1/0.3.2 § SUEPO CALL FOR STRIKE⠀➾ Defending our working conditions from permanent erosion. Defend your future. ENOUGH IS ENOUGH Attacks on staff working conditions Dear colleagues, During this year of pandemic our management has not hesitated to carry out far-reaching reforms negatively impacting our work package, our lives and our futures while completely ignoring most of staff representations input: salary adjustment procedure (SAP), preposterous distribution of cash injections1 into the SSP disproportionately benefiting higher management, and no fix to the broken career, or the uncertain fate of our colleagues on fixed-term contracts. The cut in adjustment of our salaries and pensions through the application of an imposed salary adjustment procedure (SAP)1 is the latest and most brutal attack on all of us. Instead of an adjustment of about 3.8 % in July 2020, EPO staff and pensioners will get 0.5% in January 2021 (in The Netherlands and in Germany). This is equivalent to a pay cut of about one step and causes a loss of purchasing power (-0.3% below German inflation) in its first year of the application. For next year, a result of 0% adjustment is expected and already announced by the administration. If not fixed, the SAP will year by year decimate our salaries and pensions just for the sake of unnecessary savings. The EPO is a rich Organisation Even in this year of pandemic the EPO will make hundreds of millions of euros in profit: €380 M surpluses in 2020 The year-to-date performance of the EPO funds (EPOTIF and RFPSS) is €3 bn higher than forecasted in the Base 2 scenario of the Financial study chosen by Mr Campinos and thereby already proves today that even based on the flawed Financial Study, the cut in adjustment our salaries and pensions with the new SAP is unnecessary. ____________________________ 1 “16 for me and 1 for you” (sc20153cp) by the CSC (16-10-2020) 2 “Proposals for repairing the EPO new salary “adjustment” procedure” (sc20172cl) by the CSC (17-11-2020) ===================================================================== The_current_application_of_the_SAP_results_into_accumulated_savings amounting_to_€_1_bn_from_2021-2025. The money taken from our salaries will add a further huge pile of money to the one of the EPOTIF amounting to € 2.9 bn. The creation and governance of the EPOTIF constitutes an anomaly for a public institution such as the EPO and has even been brought to the attention of the European parliament3 4. Contempt for staff and their representation Management seems to believe that the staff of the EPO are in a state of paralysis and will not react, no matter how hard they will be hit, as if the pandemic would have anesthetised our senses. This seems to be the only explanation for the current attacks after years of loyal and competent work. Indeed, year after year, Council meeting after Council meeting, managers and Heads of Delegations keep praising the results of our work, the great working atmosphere, the huge production with ever reducing working staff. Only to come some days later with new and inventive attacks on our working conditions. Changes are always imposed, making a mockery of the consultation with Staff Representatives. SUEPO is determined to fight these attacks. The future of the Staff, the stability for our families, the respect of the engagements made (pensions, careers) are more important that the big pile of cash the president wishes to accumulate. Nobody should play with our salaries and our pensions. We propose for staff to stand up and face these attacks. For the kick-off we propose to send a strong signal: 1 day of strike of all EPO staff during the plenum of the Administrative Council 15 December 2020 In the same manner we have shown that we can work during the pandemic we will now show that we can defend our future during the pandemic. Speak with your colleagues and invite them to join us even if they are not members of the Union. We will need all your support! Let’s show together our strength! ENOUGH IS ENOUGH _____________ 3 Question for written answer E-003298/2020 to the Commission 4 Answer given by Mr Breton on behalf of the European Commission So tomorrow (or midnight when we publish The EPO’s Overseer/Overseen Collusion — Part XXXV) is the one-year anniversary of the strike. More strikes might get the message across to the “anesthetised” (to borrow the above word) Administrative Council. █ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Abraham_Lincoln_quote⦈_ ⣿⢿⡿⣿⣿⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣀⣄⣀⣊⣺⣐⣀⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⠻⢻⡛⡿⠛⠟⢻⡟⠿⡿⢟⠟⢻⠿⢻⢿⠻⠻⢻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣾⣾⣶⣾⣶⣷⣶⣷⣿⣷⣶⣶⣾⣶⣾⣾⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⠿⠿⠿⡿⠿⠿⣿⠿⢿⠿⢿⠿⠿⠿⠻⠿⠿⡿⢿⠿⡿⠻⠿⢿⠿⡿⡿⠿⠿⠿⢿⠻⠿⢿⠟⠿⠿⡿⠿⠟⡿⠿⠟⡟⠿⡿⠿⢿⢿⠿⠿⢻⠿⠿⠿⡿⠿⠿⡿⠿⠿⢿⡿⠿⠿⠿⡿⢿⢿⠿⠿⠿⢿⣿⣿⣿⡇ ⣿⣦⣾⣦⣧⡼⡴⣤⣤⣿⡤⣼⣤⢴⣿⣤⣴⡿⢤⣼⣤⣧⣼⣤⣼⣤⡦⣷⣶⣵⣷⣼⣤⣤⣼⣥⡤⣼⣤⣤⣤⣧⣤⡤⢿⣷⡦⢶⣴⡼⣤⣤⣿⠿⣤⢿⣧⢼⣦⣯⢤⣴⣼⣴⣾⣦⣤⣧⣧⣼⣤⣴⣤⣾⣿⣿⣿⡇ ⣿⣤⣤⣴⣤⣤⣧⣤⣧⣤⣧⣤⣤⣤⣤⣤⣬⣧⣥⣴⣦⣴⣦⣦⣹⣤⣤⣤⣦⣤⣧⣴⣼⣤⣧⣬⣧⣼⣤⣤⣦⣴⣤⣤⣤⣰⣿⣷⣤⣷⣄⣤⣤⣤⣠⣾⣤⣦⣤⣤⣴⣧⣴⣤⣧⣤⣼⣤⣤⣀⣤⣦⣤⣤⣤⣤⣦⡅ ⣿⣨⣉⣈⣉⣉⣻⣉⣨⣉⣸⣭⣉⣀⣉⣉⣿⣹⣍⣸⣉⣭⣉⣉⣹⣸⣈⣡⢉⣉⣏⣉⣩⣠⣉⣈⣹⣉⣸⣉⣁⣉⣉⣉⣇⣨⣉⣽⣉⣉⣀⣹⣩⣬⣉⣙⣩⣇⣉⣩⣉⣉⣀⣈⣉⣉⣏⣉⣉⣩⣉⣉⣻⣿⣿⣿⣿⡇ ⣿⠿⢿⡿⣿⣿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⢿⢿⡿⣿⣿⢿⣿⠿⢿⢿⣿⣿⣿⢿⣿⢿⣿⢿⣿⣿⣿⣿⢿⣿⢿⠿⢿⣿⣿⣿⣿⢿⣿⢿⣿⡿⢿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⡇ ⣿⣤⣤⣧⣤⣼⣤⡤⣼⡤⣤⣬⢤⣦⣶⣤⣤⣼⣥⣤⣤⣴⣾⣤⣴⣦⣤⣤⣤⣤⣤⣼⣶⣤⣤⣴⣤⣧⣤⣤⣤⣤⣼⣤⣧⣤⣦⣧⣦⣼⣤⣄⣴⣤⣤⣇⣤⣤⣴⣤⣰⣧⣤⣤⣧⣤⣤⣤⣤⣦⣤⣠⣧⣦⣤⣿⣿⡇ ⣿⣀⣀⣜⣔⣀⣸⣀⣀⣇⣀⣀⣀⣀⣸⣀⣀⣇⣰⣰⣀⣀⣰⣀⣀⣡⣀⣀⣆⣂⣇⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⢿⠿⠿⠿⠿⠿⢿⠿⡿⢿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⢿⠟⠿⠿⠿⡿⢿⠛⢿⠿⠿⢿⠿⠿⡿⡿⠿⠟⡿⢿⠿⡿⠿⠿⡿⡿⠿⠿⠿⠿⠟⡿⢿⠿⡿⠿⠿⡿⠿⠿⠿⠟⠿⠿⡿⠿⠻⠿⠿⠿⢿⣿⣿⣿⣿⡇ ⣿⢤⣮⣤⣤⣤⣴⣿⣤⣧⡼⣤⣼⡵⣦⣴⣵⣧⣿⣴⣾⣤⣼⣤⣤⣤⡤⣯⣦⡤⡴⣵⡶⢴⣤⣧⢿⣦⣦⣤⣧⣼⣵⡴⣥⣦⣦⡧⣮⣤⣤⣴⣤⣯⣧⢤⢧⣤⣤⣿⣤⣤⣤⣤⣴⣤⣧⣦⣤⣯⣦⣤⣼⣿⢿⣿⣿⡇ ⣿⣤⣴⣤⣤⣤⣴⣧⣄⣤⣦⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣤⣦⣼⣦⣤⣤⣬⣧⣥⣥⣤⣤⣤⣧⣤⣬⣤⣤⣤⣷⣤⣤⣤⣼⣤⣶⣦⣤⣼⣤⣼⣤⣤⣄⣦⣤⣼⣀⣤⣤⣼⣤⣤⣦⣤⣤⣤⣧⣤⣦⣾⣿⡇ ⣿⢉⣨⣉⣩⣉⣭⣉⣉⣙⣇⣉⣁⣇⣉⣉⣉⣌⣈⣉⣏⣼⣉⣍⣩⣍⣍⣁⣸⣀⣭⣙⣆⣦⣉⣇⣄⣡⣩⣏⣹⣠⣁⣸⣅⣍⣹⣁⣠⣐⣏⣈⣁⣭⣈⣌⣇⣁⣇⣈⣈⣯⣡⣉⣇⣉⢹⣉⣉⣄⣈⣁⣉⣿⣿⣿⣿⡇ ⣿⠈⢙⡉⡉⡉⣏⣉⠉⡉⡉⠁⣏⢉⡉⢩⢫⢨⠈⠉⣏⠉⢹⠁⠉⠉⡏⣩⡉⠉⢉⢩⠉⡏⡉⠙⡏⡙⣹⠈⠉⢹⢉⢉⠉⢹⠉⢉⢹⡉⢽⠉⠉⢹⢝⠅⠈⠈⠉⢩⠉⡏⢉⠁⡏⠈⢙⠉⠉⠈⣉⢹⠉⢙⢹⣿⣿⡇ ⣿⠙⠛⡛⠋⠋⡏⠛⡏⠙⡉⢉⢻⠙⢻⠙⠟⠛⠛⠛⡏⢉⢻⠛⡟⠙⠛⠋⠛⠛⠛⠛⡻⠋⡟⠛⠋⠙⠛⢛⢛⠛⡟⠛⠛⠋⡟⠛⠛⣻⢛⠛⡟⠻⠛⠛⠟⢹⠙⠛⠛⠛⡛⠛⠋⠛⠛⠛⢹⠛⠋⠉⠙⠛⠛⠛⣿⡇ ⣿⠿⠟⠟⠿⡟⠿⠟⡿⠟⠛⠿⠿⡿⠻⠟⠿⡟⠺⠿⠻⠻⠛⠻⠿⢿⠻⡻⠟⠿⠿⢻⠿⠿⠗⠿⢻⠻⠳⢾⠟⠻⠻⠟⠿⠻⡟⠿⡿⠿⢻⠿⠿⠷⠿⠿⠿⠟⡿⠟⠿⠿⠻⠻⢿⠛⠟⠿⡟⠻⠛⡿⠛⠻⡟⢿⣿⡇ ⣿⠶⠶⣶⠿⡗⠶⠶⢷⠲⣶⠲⠴⠷⠾⢷⡶⠷⠶⠾⠶⠶⢶⣶⣧⣾⣶⣿⣾⣶⣶⣾⣴⣾⣶⣷⣼⣶⣶⣾⣶⣶⣶⣼⣶⣶⣷⣶⣷⣷⣾⣶⣶⣿⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣾⣶⣶⣶⣷⣷⣶⣾⣾⣶⣷⣶⣿⡇ ⣿⣤⣤⣧⣤⣧⣦⣴⣼⣼⣼⣤⣤⣤⣴⣤⣧⣤⣴⣤⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣤⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⡐⠀⢸⠈⡉⡉⡍⣿⣈⢈⢉⠈⠉⠉⢩⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⠿⠿⠿⢿⠿⠿⢿⡿⣿⡿⠿⠿⢿⢿⢿⠿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣾⣶⣾⣾⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⢿⣿⣿⣿⢿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡇ ⣿⣤⣤⣦⣤⣦⣤⣾⣤⣤⣦⣤⣤⣤⣴⣼⣤⣤⣼⣦⣤⣧⣤⣤⣤⣧⣤⣤⣬⣤⣤⣤⣧⣌⣷⣤⣼⣤⣤⣤⣼⣤⣤⣼⣤⣦⣤⣤⣧⣴⣠⣤⣤⣤⣤⣴⣤⣧⣼⣤⣤⣼⣦⣦⣼⣠⣴⣤⣴⣦⣶⣤⣦⣼⣤⣤⣼⡇ ⣿⣈⣄⣸⣀⣀⣃⣀⣦⣇⣈⣴⣢⣁⣇⣈⣀⣀⣀⣱⣇⣐⣌⣀⣀⣠⣌⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⠿⡿⠿⡿⠿⠿⡿⢿⢿⠿⠿⣿⢿⠿⡿⠿⢿⠿⠿⠿⡿⡿⣿⠿⣿⢿⢿⠿⢿⡿⡿⠿⠿⢿⠿⠿⠿⡿⡿⠿⡿⠿⠿⡿⣿⠿⡿⠿⠿⡿⠿⡿⠿⡿⠿⡿⠿⡿⡿⠿⠿⠿⠿⡿⡿⢿⠿⢿⡿⠿⡿⡿⢿⠿⠿⡿⠇ ⣿⣤⣥⣮⣴⣤⣼⢤⣤⣽⡤⣤⣴⣥⣤⢼⣤⣤⣦⣴⣶⣴⣤⣶⣥⡬⣤⣼⣤⣼⢤⣤⣤⣤⣼⣥⣿⣽⣤⣧⡤⣬⣤⣤⣼⣿⢤⣧⣴⣤⣯⣤⣴⣴⣤⡤⣯⣥⣾⣤⣤⣤⣤⣤⣼⢤⣼⡬⡤⣥⡯⣧⣤⣤⢤⣤⣧⡅ ⣿⣤⣤⣼⣠⣤⣤⣤⣴⣤⣤⣧⣤⣤⣧⣤⣤⣇⣤⣤⣤⣤⣾⣤⣤⣮⣤⣴⣱⣤⣼⣥⣤⣤⣥⣤⣧⣴⣬⣼⣤⣤⣤⣿⣤⣤⣤⣤⣤⣠⣧⣤⣴⣴⣤⣤⣷⣤⣤⣼⣤⣝⣠⣤⣧⣤⣬⣤⣦⣤⣧⣦⣤⣥⣤⣤⣤⡄ ⣿⣉⣍⣸⢉⣋⣁⣉⣉⣇⣀⣩⣉⣉⣉⣹⣉⣍⣹⣈⣋⣁⣩⣉⣛⣀⣉⣉⡉⣉⡈⣭⣉⣉⣙⡉⣈⣻⣈⣍⣉⣉⣏⣙⣽⣉⣉⣏⣈⣹⣉⢉⣉⣉⣈⣏⣁⣇⣈⣩⣃⣙⣉⣉⣈⣉⣇⣌⣩⣈⣩⣍⣉⣅⣗⣸⣿⡇ ⣿⠉⢉⡋⡏⠉⢩⠙⡉⣏⢍⠋⡯⠉⠫⠉⠉⢫⡟⠉⡏⠉⠙⡩⢉⡉⠍⢽⠛⠉⢹⠉⠏⠝⠉⢩⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⠙⠉⡛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⣿⣿⣿⣿⣿⣟⣻⣯⣭⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⢳⢱⡆⣶⠀⣖⣶⢰⡆⢸⣖⣶⣲⡇⢰⣾⠀⢰⣺⢲⣶⠀⣖⢰⣶⣲⣖⣾⣶⠄⣶⣖⣶⢲⣶⡆⢰⣢⡗⢸⣺⢢⣶⠀⡗⣷⠒⣶⡦⡀⣲⣴⡦⣺⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣽⣿⡷⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⣀⠀⡃⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠯⠿⠸⠏⠾⠇⠨⠏⠇⠹⠸⠷⠟⢸⠽⠿⠪⢿⠽⠗⠿⠠⠿⠿⠀⠏⠏⠸⠇⠹⠸⠿⠹⠿⠠⠸⠽⠧⠸⠁⢱⠹⠿⠼⠀⠯⠿⠏⠿⠹⠯⠿⠁⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⡀⡄⣀⢠⡄⢠⢠⡀⣀⠀⣀⣀⣀⡀⣀⡄⣀⠀⣀⣤⠀⣄⣄⣀⡀⢠⢠⣀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣿⣿⣿⣿⣿⣿⣿⣏⣉⣡⣤⡞⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠙⠃⠃⠛⠘⠃⠘⠘⠋⠛⠀⠚⠛⠙⠃⠟⠃⠛⠀⠛⠛⠀⠓⠃⠛⠃⠘⠘⠃⠛⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣿⠃⣯⣿⣿⣷⣷⡖⠀⠀⠉⠛⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠋⠉⠄⢼⢻⢹⣿⣿⣿⣿⡟⡾⣾⣰⠀⢄⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⡄⡆⣀⢀⣰⢀⣀⣀⣀⠀⡆⠀⣀⢀⢀⡀⣄⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⢸⣴⣷⡟⣸⣿⣿⣿⣿⣿⠱⠀⠉⠀⣿⠁⢐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠙⠓⠙⠘⠛⠘⠛⠃⠋⠀⠓⠀⠛⠙⠚⠊⠛⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⡇⣿⣿⣿⡟⣿⡟⠅⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠃⠿⡿⣿⠋⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 480 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/14/if-eponia-was-a-country-it-would-rank-about-6th-in-the-world-for-union-density/#comments Gemini version at gemini://gemini.techrights.org/2021/12/14/if-eponia-was-a-country-it-would-rank-about-6th-in-the-world-for-union-density/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ If_EPOnia_Was_a_Country,_It_Would_Rank_About_6th_in_the_World_for_Union Density⠀✐ Posted in Europe, Patents at 11:00 am by Dr. Roy Schestowitz Merpel (in 2016): “SUEPO has about 3400 (about half of the EPO staff, and increasing over recent years).” 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Union density defined⦈ Union_density_defined 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Statistics on union membership⦈ Statistics_on_union_membership (ILO) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Slovakia's union membership⦈ Slovakia’s_union_membership (NKOS is the big one) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Banning industrial action? Stay Classy⦈ Benoît_Battistelli played with fire and António_Campinos enjoyed its warmth 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇EPO STAFF and EPO President⦈ If the EPO obeys ILO rulings, then 8 years of strike restrictions were invalid and profoundly unjust Summary: As per publicly-available statistics, EPO staff still enjoys the power of collective action as most staff is part of the union — a membership/ affiliation that ILO must respect ⣿⡟⠿⡿⠟⠿⢿⣿⠻⢿⠿⠿⠟⡿⠻⠿⠿⠿⠿⣿⠻⢿⠟⣟⡟⡟⢻⠿⠻⠿⠿⠿⡿⠿⠿⠿⢿⡟⡿⢻⡟⠿⠿⡿⣿⠿⠻⠿⢿⡿⠿⠿⠿⢿⠿⠿⠿⢿⣿⠿⠿⠿⣿⢻⠟⣿⢻⠿⢿⠿⡿⡿⡿⠟⠿⣿⣿⣿ ⣿⣧⣴⣿⣥⣴⣼⣯⣤⣿⣮⣤⣤⣯⣴⣥⣴⣥⣤⣾⣼⣼⣤⣯⣧⣭⣼⣮⣤⣤⣼⣤⣧⣶⣤⣼⣴⣧⣵⣼⣧⣶⣤⣷⣽⣧⣤⣤⣿⣿⣧⣤⣼⣿⣵⣤⣼⣬⣿⣤⣤⣤⣿⣼⣤⣵⣴⣷⣼⣤⣦⣮⣦⣦⣤⣿⣿⣿ ⣿⣏⣉⣉⣉⣉⣍⣉⣹⣏⡉⣽⣉⣉⣀⣉⣉⣈⣍⣍⣹⣈⣋⣫⠉⣉⣻⣍⣯⡉⢹⣉⣯⣏⣋⣽⣉⣉⣹⣩⣉⢉⣉⣉⣉⣉⣉⣈⣩⣁⣉⣩⣻⣟⣈⣍⣏⣩⣹⣩⣝⣉⣍⣁⣉⣉⣍⣁⣁⢉⣿⣉⣍⣉⣻⣿⣿⣿ ⣿⣟⢻⡟⡟⠻⡟⢛⣿⠻⠛⠿⡟⠟⠟⡿⠻⠻⡛⡛⠟⣿⡟⠟⠟⣿⠛⠛⠛⠻⡟⠛⡟⣛⠿⢿⢟⢿⠟⠟⠻⣻⠟⠟⢟⠻⡻⢻⡟⢟⣿⡛⠻⢻⣟⠻⠛⢿⠻⠻⡛⠻⠻⠛⣿⢻⡛⠟⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢷⣷⣷⢷⣷⣾⣿⣶⡶⣷⣶⣷⡶⡷⢶⡶⡶⣶⣶⣿⣷⣶⣾⣾⣶⣶⣷⣶⣷⣶⣷⣾⡶⣾⣴⣷⡶⢶⣶⣾⣶⣶⡶⣶⢶⢷⣷⣾⢿⣶⣷⢾⢿⣶⡷⣾⢶⣶⢧⣴⢶⣶⣾⣶⣶⢶⣶⢶⣶⢿⣿⡿⢿⡿⣿⣿ ⣿⣧⣻⣨⣥⣄⣀⣶⣸⣀⣇⣮⣨⣸⣇⣓⣘⣀⣆⣌⣇⣸⣮⣕⣥⣸⣰⣮⣀⣀⣼⣪⣀⣆⣀⣆⣐⣽⣷⣅⣤⣇⣀⣼⣄⣓⣸⣠⣙⣇⣦⣔⣵⣀⣀⣸⣕⣽⣀⣦⣸⣿⣌⣅⣍⣰⣇⣔⣵⣀⣟⣨⣬⣻⣴⣄⣿⣿ ⣿⡟⡛⠙⠛⡏⣻⠛⠋⡛⠛⠋⢻⡟⢻⠙⣻⠛⡟⠛⠛⢿⡛⠙⡛⡋⣿⠟⣟⠛⢹⣿⢹⢛⠟⠋⠻⣟⠛⠛⢻⡏⠏⠹⠍⡋⠛⢇⣂⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⠉⣿⠍⠋⡫⡋⢫⠉⠉⠋⣯⡯⢉⢍⠩⠽⢿⡏⢏⡻⠍⡍⠙⡏⠉⣿⠍⡙⢹⢏⠋⠉⠉⢯⠉⠉⠉⢩⣿⠋⡩⠋⠉⢭⠝⡙⠍⢹⡙⢛⠙⡍⢹⡿⢫⢻⠉⢉⡟⣍⠋⠉⢩⠫⠋⠉⠉⢿⡯⠉⡏⢹⣿⣿⣿⣿ ⣿⡿⠿⠿⠿⡿⢿⡿⠻⠿⠟⠻⠿⢿⡿⠟⡿⠿⡿⠿⠿⡿⠿⠿⠿⢿⡟⣿⠿⡿⡿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠻⠟⠿⣿⢿⠿⡿⠿⢿⡛⢟⡟⡟⢻⡿⠿⡿⢻⠿⡿⡿⡿⠻⢿⡟⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣶⣤⣤⣧⣼⣮⣦⣤⣥⣶⣴⣼⣯⣶⣧⣿⣮⣾⣦⣿⣽⣦⣴⣾⣯⣾⡤⠦⢾⣬⣤⣼⣮⣤⣤⣦⣿⣵⣴⣴⣶⣧⣿⣼⣾⣦⣧⣼⣤⣮⣧⣧⣾⣦⣾⣦⣼⣼⣦⣦⣷⣦⣼⣧⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⣉⣉⣍⣉⣉⣡⣉⡉⢉⣹⣏⣉⣁⣉⣘⣹⣏⣉⣍⣉⣉⣗⣀⣪⣂⣀⣣⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⡿⡿⣿⡿⣿⣿⢿⠿⠿⡿⣿⡻⡟⣟⠻⢻⢿⣿⣿⣿⢿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣤⣿⣪⣤⣦⣤⣤⣠⣾⣏⣤⣤⣄⣴⣿⣠⣄⣴⣄⣴⣆⣼⣤⣤⣤⣼⣄⣕⣶⣬⣧⣴⣿⣵⣤⣧⣎⣿⣶⣶⣧⣶⣼⣤⣾⣇⣼⣼⣴⣮⣠⣧⣬⣢⣦⣤⣔⣿⣢⣢⣡⣤⣴⣦⣄⣤⣧⣤⣤⣶⣼⣤⣿⣿⣿⣿ ⣿⡏⠙⠙⠛⢛⡟⡟⠛⡛⠋⠛⣟⡛⣛⣻⠙⠛⡛⠛⠙⠛⣻⢿⠩⠛⠛⠛⣛⠟⡟⠙⣿⠻⡛⠋⡏⡉⢛⠹⠛⡛⠋⣛⣻⠟⠛⠙⠛⣻⡟⠙⠛⡛⠋⡹⢛⡏⠛⡟⠋⢛⣻⠛⠻⢹⡍⠫⡉⠙⢿⡟⣻⡟⠋⢹⣿⣿ ⣿⡿⠿⡿⠿⠿⢿⠿⠷⢿⡿⡿⠿⡿⡿⣿⠿⠿⢿⢿⢿⡿⠿⠿⢿⢿⠿⡿⡿⢿⢿⢿⡿⠿⠿⠿⠿⢿⢿⠿⣟⠻⢻⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣽⣤⣤⣤⣼⣬⣤⣮⣿⣬⣼⣤⣤⣼⣤⣴⣴⣵⣧⣧⣤⣤⣧⣼⣮⣰⣧⣧⣬⣼⣯⣤⣤⣥⣤⣤⣴⣥⣵⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⡠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⡟⠛⡟⠛⡿⡟⠻⠛⠛⡿⡟⢛⠛⢛⣟⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠭⡏⣻⠛⢛⢙⢹⠛⣛⢙⢹⢟⢻⠛⣻⡿⡛⡟⡛⢿⡟⡟⡟⢛⢿⢹⢛⢿⢛⢻⣿⢛⢛⢻⠛⢻⢛⢛⢻⢙⢻⠛⢻⢛⡟⢻⠉⡻⡏⡟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣧⣽⣬⣼⣬⣼⣥⣼⣬⣼⣮⣼⣥⣼⣷⣥⣧⣿⣼⣷⣥⣧⣿⣼⣼⣬⣾⣼⣼⣿⣼⣼⣼⣤⣼⣼⣼⣼⣬⣼⣤⣼⣼⣯⣤⣤⣧⣧⣇⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⡛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠁ ⣏⣋⣋⣏⣩⣹⣍⣉⡉⣙⣉⣯⣏⣉⣉⣩⣋⣏⣋⣉⣉⣉⣍⣉⣹⣉⣹⣹⡉⣉⣉⣉⣏⣉⣉⣯⣹⣉⣉⣽⣯⣉⣝⢹⣹⣉⣍⣉⣉⣹⣭⣹⣏⣉⣁⣏⣝⣹⣉⣏⣉⣏⣙⣩⣧⣹⣉⣉⣋⣹⣹⣉⣭⣉⡅⠀⠰⠀ ⣟⣫⡝⣻⣹⣉⣟⣯⣟⣍⣹⣏⣛⣏⣫⣛⣿⣍⣟⣫⣏⡋⣛⣛⣍⣟⣙⣝⣝⣉⡫⢛⣍⣫⣫⣉⣉⣫⣋⣯⣙⣽⣹⣹⣏⣛⣉⣛⣟⣉⣙⣫⠋⣛⣹⣉⣟⣉⣉⣛⣍⣏⣙⣹⣯⣝⣛⣽⣋⣙⣋⣫⣛⣽⡅⠀⠀⠀ ⡟⢛⠛⣛⡻⡻⢻⢻⠛⠙⣻⠛⡿⢟⡟⡟⢛⠛⠙⣿⡻⡟⡿⣟⠋⠙⠻⣿⠻⡿⠛⡟⣛⠋⣿⠛⡟⠛⠛⡻⢛⡟⠛⠋⡟⠛⠋⠛⡏⠛⢛⠛⡟⢿⠝⣟⣟⢟⢟⠛⠛⡟⠛⡻⡻⡛⠛⢛⢟⡛⢿⠛⠛⢹⡇⠘⠈⠃ ⡟⠟⢛⠻⢿⠻⠛⠛⢟⡛⡟⠛⠛⢛⠛⡟⢛⠛⡟⣟⡛⠛⠛⠛⢻⠟⠛⠛⠿⣻⣛⠟⠛⠛⣻⠟⢛⡛⣟⠻⡟⠛⡟⠛⢻⡛⢻⠛⠛⡛⠛⠟⠛⡛⢻⠟⠛⢻⡟⠛⠟⠻⠛⢻⢻⡛⡛⢛⣛⡛⠛⢻⠛⡛⠃⢰⣒⡂ ⡿⠿⠻⠛⠿⡻⡻⣻⣟⢿⢿⡻⠟⡿⣳⣿⠿⡻⣻⠛⣟⡿⠛⡻⡻⡿⢿⡻⢻⢿⣟⠟⡟⢟⢿⠻⡛⠛⣿⠻⢻⠻⠟⠿⠻⠿⡿⣛⠟⠷⠞⠿⠻⣻⠺⣟⢟⢟⠟⠟⣻⠻⡻⣻⠻⡻⣿⠛⣿⠛⠿⠿⢻⠿⡃⠀⢀⠀ ⡿⠻⠿⢻⠿⠻⠻⡿⢿⡿⡿⠿⠿⢿⡿⢿⢿⠿⢿⡿⡿⢿⡿⠟⠺⢿⠿⠿⢿⠿⡿⠿⣗⡻⠿⡿⠿⠿⠿⠿⡿⢟⢿⠿⡟⠿⡿⠻⠞⠿⠿⡿⢿⠻⠿⢿⢿⠟⠻⠿⡿⡟⠿⢿⡿⢿⡿⠿⢿⠿⡿⠻⡟⠿⢇⣀⣁⣀ ⡷⢶⠷⠾⠶⡶⠶⢷⠶⠾⢿⢶⠶⠶⡷⢾⠶⠾⡾⡿⠷⡾⡿⠶⠶⡶⠶⢾⠾⠶⠶⣾⡿⢿⠷⠷⠾⠿⡶⢶⣷⣿⣶⣾⣶⣾⣷⣶⣶⣶⣶⣾⣾⣶⣾⣾⣾⣶⣾⣾⣶⣷⣿⣷⣷⣾⣾⣶⣾⣶⣶⣶⣷⣾⣿⣿⣿⡟ ⣷⣾⣶⣶⣶⣷⣶⣶⣷⣶⣾⣴⣾⣶⣿⣷⣶⣷⣷⣷⣾⣶⣷⣾⣶⣷⣾⣾⣷⣶⣶⣼⣶⣾⣶⣷⣾⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣋⢛⣛⢹⣛⣛⢻⣻⡫⡋⠫⡛⣛⡋⣛⣛⢽⣿⣿⣿ ⣿⣿⣿⢙⣿⢉⡉⢙⡫⣯⣻⢹⠉⠙⣯⡋⢩⣉⡏⣹⢹⢹⡯⠉⡋⣿⡝⠉⠉⣙⢹⢹⢽⢹⡍⢙⢽⢙⡟⠉⢙⡫⣋⢹⠉⡋⣯⡋⣏⢩⢻⣿⣿⣿⣿⣿⡿⠿⡛⡻⠟⢛⢛⣟⢟⠛⠻⡻⣟⠛⡻⣻⡻⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡻⢛⡛⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⡖⠿⢿⠟⠿⢿⠿⡿⠿⠿⠿⠿⣿ ⣿⣿⣿⣿⣿⣷⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⡾⣶⡶⢶⣶⡶⣶⣿⣶⣿⣶⣶⣿⡾⣶⣷⡶⢶⣶⣿ ⣿⣿⣿⣮⣮⣭⣼⣭⣼⣬⣭⣦⣭⣩⣥⣭⣭⣵⣭⣧⣭⣽⣯⣤⣬⣾⣭⣥⣭⣵⣭⣭⣇⣼⣍⣭⣵⣮⣵⣄⣻⣭⣤⣭⣾⣥⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣥⣦⣴⣤⣤⣤⣤⣧⣾⣮⣷⣵⣤⣤⣤⣤⣴⣌⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣬⣬⣿⣶⣇⣽⣸⣤⣸⣕⣼⣥⣕⣵⣼⣨⣆⣿⣬⣸⣿ ⣿⣿⣿⣿⣟⣿⣬⣭⣽⣬⣽⣯⣥⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣫⣉⣯⣭⣋⢍⣏⣛⡩⣹⣹⣉⣉⢻⣩⣝⣋⣏⣝⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢛⡟⡿⡟⠻⢻⠛⢻⢻⠋⠋⢛⠟⢻⠛⢛⠟⢛⣻⣿ ⣿⣿⣿⠛⠛⠛⠛⠛⠻⠻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⢿⠿⠿⢿⠿⡿⡿⣿⡿⠿⠟⡿⠿⡿⡿⠿⠿⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣶⣾⣿⣿⣿⣿⡿⡶⡷⡶⠾⠶⡿⡾⣾⢾⡿⣷⠶⢶⣷⣾⣶⣿⣶⣶⣾⣿ ⣿⣿⣿⣬⣥⣤⣤⣥⣵⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣶⣶⣶⣶⣿⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠙⢛⡛⠛⢛⡛⡿⠙⠋⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣶⣷⣧⣷⣤⣦⣠⣿⣿⣮⣤⣤⣧⣤⣶⣥⣤⣢⣿ ⣿⣿⣿⢿⣿⣿⢿⣿⡿⢿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣟⣿⣻⣅⣉⣉⣹⣿⣙⣉⡍⣋⣈⣁⣽⢹⣿⣿⣿⣿ ⣿⣿⣿⣴⣶⣤⣤⣶⣧⣴⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡻⡛⢛⠛⡏⠛⠛⡛⡟⢻⠟⡟⠛⡿⡟⣻⠻⠛⢻⢿⣿ ⣿⣿⣿⢉⠛⡙⠛⢋⠫⠫⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢟⢿⠻⠛⠛⠛⢟⠻⣿⡛⠟⢟⠻⣻⡻⣻⢻⣿⣿⣿⣿ ⣿⣿⣿⠿⡿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣴⣴⣤⣮⣶⣶⣧⣴⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣘⣉⣉⣉⣙⣗⣈⣩⣋⣿⣈⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⢰⢑⢪⢣⢹⢰⢹⢒⣺⡿⡇⣯⠃⣿⢱⢎⢈⢿⢕⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿ ⣿⣇⣡⣀⣨⣀⣀⣿⣀⣅⣁⣀⣀⣄⣎⣸⣇⣠⣺⣀⣁⣄⣁⣈⣄⣀⣿⣂⣂⣃⣌⣿⣀⣰⣇⣀⣄⡀⣨⣅⣠⣩⣈⣀⣀⣛⣇⣀⣿⣀⣀⡀⣀⣠⣂⣌⣾⣀⣨⢀⣠⣁⣀⣾⣸⣎⣇⣂⣨⣈⣇⣀⣀⣠⣠⣀⣀⣿ ⣿⣇⣘⣉⢉⣉⣁⣉⣀⣉⣯⣀⣍⣉⣩⣹⣈⣹⣏⣉⣉⣉⣭⢩⣏⣉⣀⣉⣉⣩⣏⣉⣉⣩⣈⣉⣙⣏⣉⣼⣉⣉⣉⣁⣉⣍⣁⣿⣉⣩⣉⣸⣇⣊⣉⣁⣉⣉⣉⣹⣇⣘⣉⣩⣉⢉⣉⣙⣿⣰⣨⣉⣉⣍⣹⣇⣉⣿ ⣿⡏⢹⡏⡃⠉⡋⠁⡉⣿⠁⡫⡉⢉⡏⠉⠉⡋⢉⢹⡙⠉⠉⡫⡉⢹⡏⠍⠉⡍⢈⠙⠁⡋⠋⡍⠉⠍⠉⣉⠙⣿⠉⡡⡉⠩⡏⢙⠉⢿⡏⠉⡉⢈⡋⢉⢋⠉⢉⢹⠉⣿⠉⡋⡋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⠛⠛⡛⢉⠛⠋⠛⠛⡛⠋⠋⠛⢛⢻⠙⠟⠛⢻⡟⠛⠛⠛⠛⡛⠉⡙⢻⡟⠛⠛⠛⠛⣟⡙⠛⠛⢛⠛⠙⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣆⣍⣩⣍⣹⣉⣫⣉⡏⣉⣍⣁⣉⣁⣉⡍⣽⣉⣩⣉⣋⣉⣉⣿⣪⣢⣀⣯⣊⣀⣀⣯⣉⣉⣉⣈⣹⣙⣯⣹⣉⣍⣈⣁⣉⣇⣩⣿⣁⣉⣹⣇⣀⣉⣉⣉⣈⣿⣄⣉⢉⣙⣉⣁⣈⣙⣧⣈⣮⣁⣹⣿⣿⣿⣿⣿ ⣿⡟⠹⠏⡽⡩⢻⢩⡝⣹⣙⢝⠉⣟⢉⣍⠉⠉⠉⡙⡋⡋⠋⡹⡏⠉⣝⢍⡏⠉⢛⡍⣝⠍⡏⢙⢝⢝⢝⢟⡍⢹⡫⣩⡏⢭⡋⢹⠉⢙⢭⢽⠉⣝⠙⢹⢩⡫⡫⡏⢙⣿⡿⢉⠉⠉⣯⣿⡍⠉⠉⣭⠋⠉⠉⡍⣿⣿ ⣿⡟⠛⡛⣻⠛⠛⡛⠛⠛⠛⡛⠛⠛⠻⣟⠏⠋⠛⡟⠛⠛⢛⠛⠛⠛⠙⢻⠹⡛⠛⢹⡟⢛⠛⠻⣟⠛⢹⡍⡏⡏⠛⡟⢛⣹⠛⠛⣻⠛⡟⠛⠛⠛⠛⢻⡟⢛⠛⡏⣟⣿⠛⠛⠙⠛⡛⠻⣿⣯⡍⡋⠛⣿⠛⣿⣿⣿ ⣿⡟⢻⠛⠋⠙⠛⣳⠻⣻⣗⠙⠟⣿⠓⠟⠛⡟⢛⡏⡝⠛⣚⠊⠛⢻⢟⠛⢹⠛⡛⢛⢛⠛⠛⢛⠛⡟⠛⣽⡟⠛⠙⡛⣻⣟⠙⠛⣻⠻⢛⢗⣿⠛⠋⡋⢛⢙⣿⠻⠛⠟⣿⣻⠻⡛⠛⣿⡛⡋⣿⢻⢝⡝⢟⣻⠙⢻ ⣿⣷⣿⣷⣶⣶⡞⣿⢾⣾⣷⣾⣷⣿⣷⣶⣷⣷⣷⣷⣶⣾⣷⣷⣷⣷⣿⣷⣾⣷⣷⣷⣿⣶⣶⣷⣶⣷⣾⣿⣶⣶⣾⣾⣿⣷⣶⣶⣿⣾⣷⣾⣾⣿⣷⣷⣷⣾⣿⣶⣷⣷⣿⣿⣾⣿⣾⣾⣿⣶⣿⣾⣾⣾⣾⣿⣶⣿ ⣿⣗⣌⣺⣸⣀⣷⣾⣾⣍⣇⣍⣟⣉⣍⣩⣿⣭⣫⣉⣉⣹⣈⣽⣯⣈⣉⣿⣉⣉⣁⣩⣝⣉⣉⣹⣥⣉⣙⣭⣹⣀⣝⣉⣇⣉⣉⣉⡯⣉⣉⣉⣝⣉⣍⣸⣿⣲⣶⣌⣡⣔⣄⣟⣅⣉⣈⣹⣍⣉⣉⣉⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⢿⡿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⣿⡿⠿⣿⣿⣿⡿⡿⣿⣿⣿⣿⢿⠿⣿⠿⢿⢿⣿⣿⡿⠿⢿⢿⢿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣴⣤⣤⣤⣼⣧⣬⣤⣿⣥⣦⣤⣤⣾⣧⣥⣤⣤⣤⣴⣹⣧⣦⣧⣤⣤⣤⣦⣤⣤⣤⣧⣤⣼⣭⣬⣿⣽⣦⣼⣧⣾⣯⣤⣼⣼⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣇⣮⣸⣗⣀⣀⣰⣭⣎⣀⣠⣔⣗⣰⣈⣂⣀⣧⣫⣄⣀⣀⣾⣕⣗⣵⣀⣀⣕⣄⣁⣀⣔⣀⣀⣾⣯⣎⣗⣰⣅⣿⣀⣀⣠⣁⣸⣔⣇⣀⣀⣪⣃⣀⣀⣐⣇⣀⣇⣄⣃⣁⣿⣈⣠⣻⣇⣷⣀⣸⣀⣠⣂⣀⣀⣿ ⣿⣇⡈⢉⣋⣍⣉⣹⢉⣙⣉⣁⣈⣁⣉⣉⣹⣏⡉⣹⣘⣍⣉⣏⣉⣉⣻⣍⣉⡍⣵⣉⣏⣉⣉⣘⣈⣋⣈⣉⣁⣏⣉⣤⣈⣉⣹⣉⣈⣉⣍⣹⣏⣨⣉⣙⣇⣸⣩⣉⣉⣸⣂⣇⣋⡘⣀⣃⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⣿⣿⢿⡿⡿⣿⡿⣿⡿⢿⠿⢿⠿⣏⠏⢹⢿⢿⣿⣿⣿⣿⡿⡿⣿⢿⢿⣿⡿⣿⢿⣿⣿⢿⠿⣿⣿⣿⠿⣿⣿⡿⣿⠿⣿⣿⣿⣿⡿⡿⣿⡿⠿⢿⢿⠿⣿⢿⣿⢿⣿⠿⠿⠿⠿⡿⠿⢿⡿⣿⣿⣿⣿⣿ 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⣿⣧⣤⣆⣤⣤⣤⣤⣤⣬⣧⣴⣬⣧⣭⣤⣤⣥⣥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠈⣿⣷⣄⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⠛⢛⣛⣛⢻⢛⣑⢟⣛⢛⣛⠝⣛⠛⣛⡱⣛⡻⢟⣛⠿⣛⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⢻⣿⣿⣷⣌⠛⢁⣴⣦⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣿⡏⣿⡇⢸⣿⣿⡆⢸⣿⣼⣿⢸⣿⣆⣿⠀⣿⡇⣿⣿⣸⣿⢸⣿⢹⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣫⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿ ⣿⣿⣿⣿⠘⣿⣿⣿⣿⣷⣿⡿⣻⣯⡻⣿⡿⣿⣿⡟⠉⠀⠀⠀⠀⣿⡟⣿⡆⣼⣟⣿⣇⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⡇⣿⣿⣿⣿⢸⣿⢶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⢋⣴⡾⣫⣶⡶⢰ ⣿⣿⣿⣿⡇⠈⢻⣿⣿⡿⣫⣾⣯⡧⣾⣿⡿⣿⠋⠀⠀⠀⠀⠀⠀⠿⠷⠿⠇⠿⠏⠻⠿⠸⠇⠻⢿⠸⠿⠸⠿⠀⣿⡇⣿⡇⢿⣿⡸⣿⡾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⡿⢱⣿⢟⣵⣿⡿⣵⣿ ⣿⣿⣿⣿⣯⣴⢿⣟⢋⣾⠿⣿⡿⣦⣚⡛⠃⣇⣀⢀⣀⠀⣀⣀⡀⢀⣀⣀⣀⢀⣀⣀⠀⢀⣀⠀⢀⣀⡃⠀⣀⡀⠀⣿⣿⣿⣿⢿⡿⣟⣛⠿⢟⣻⣿⣿⢛⣓⠯⢛⣛⡻⠿⣛⡿⣿⡿⡿⣟⣃⢿⢫⣾⣿⡟⣼⣿⡿ ⣿⢿⣿⣿⣿⡿⢸⣿⢸⣿⡆⣿⡇⣿⡟⣿⣇⣿⣿⢸⣿⢸⣿⡹⠿⣘⢻⣿⠛⢸⣿⢻⣷⢸⣿⡇⣿⣿⣿⠀⣿⡇⠀⢸⢹⣿⣿⡎⣼⣿⢻⣿⢘⢻⣿⢛⣿⣿⢰⣿⢻⣿⡄⣿⣧⣿⡇⣾⡟⣿⣷⢸⣿⣿⣿⣿⣿⣿ ⢓⣕⢝⠿⠋⠀⢸⣿⢸⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⢈⣻⢿⣶⢻⢸⣿⢸⢸⣿⢻⣯⢸⣿⡇⣿⣿⣿⡄⣿⡇⠀⢸⣼⣿⣿⡇⣿⣿⢈⣉⢾⢸⣿⢈⣿⣿⢸⣿⢸⣿⡇⣿⣿⣿⡇⣷⣦⣿⡿⡐⢶⣶⣶⣾⣿⡷ ⣷⣌⢷⠅⠐⣡⢸⣿⢸⣿⢸⣿⡇⣿⣧⣿⡏⠻⣿⣼⡿⠸⣿⣼⣿⣻⢸⣿⢸⣸⣿⢸⣿⢸⣿⣸⣿⡟⣿⡇⣿⣷⡆⠁⣿⡟⢿⣿⠹⣿⣼⡿⢘⢸⣿⢸⣿⣿⠸⣿⣼⡿⡃⣿⡟⣿⡇⣿⣧⣴⣾⣿⣶⣤⣉⠉⣉⣤ ⣍⣉⠛⠰⠿⠿⠷⠶⢂⣂⣤⣶⣾⣶⣶⣶⣿⠀⠀⠀⠀⠀⣶⣶⣾⣿⣷⣶⣿⣷⣶⣷⣶⣷⣶⡶⣶⣾⣶⠀⠀⠀⠀⣼⣦⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣿⣶⣶⣿⣷⣶⣾⣿⣶⣾⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣙⣒⡀⠀⠀⠀⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⠟⠋⠉⢀⣤⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣷⡀⠀⣿⣶⣦⣤⣤⣤⣤⣽⣿⣷⣶⣿⣿⣿⣿⣿⣿⡇⢀⣼⣿⣯⣟⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡻⣮ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⢿⣿⣿⣮⡻⣿⠿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣙⡺⢷⣿⣿⣿⡿⣪⣾⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡿⡿⣫⣥⣥⣾⣿⣿⠏⣸⣹⣿⣿⣟⣿⡿⣟⡻⠿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿ ⣿⣿⣿⣟⠁⢻⢿⣿⣿⣷⣿⣾⣩⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⢠⡢⠝⢿⣿⣟⡿⢻⣿⣿⣿⣿⣿⡿⠃⠀⢿⣿⣿⣾⣦⣶⣶⣤⣚⡛⣲⣾⣷⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣫⣾⣿⣿⣫⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⠟⠡⠀⣨⡐⠔⠙⣿⣴⣿⣿⣿⣏⡟⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣮⣻⣿⣿⣿⣻⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠁⠀⣠⣾⣿⣿⣦⣼⣿⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣍⣛⠛⠛⠉⡉⣼⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⣿⣿⣾⡻⣿⣿⣿⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣄⠀⢈⠻⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⡄⢀⢾⣿⣿⡇⣥⡀⠀⠀⣶⣶⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠙⢷⣤⣶⣿⣿⡿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠐⠀⠉⢻⣿⣷⣽⣿⣧⠀⢹⣿⠿⠻⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠀⠈⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠘⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⡠⠀⠀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣷⡻ ⡛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡻⣫⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠈⠀⡀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣝⢾⢿⣽⣻⠿⣿⣿⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠰⠁⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢿⣿⣝⣛⣿⣿⣾⣽⣛⣫ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠃⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⢻⣿⣿⣝⣯⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⢀⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣷⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢀⠂⠀⠀⠀⡀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠾⠃⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠄⠀⣰⠃⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⠈⠻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢠⡳⠠⠀⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢀⢀⠀⠀⠀⠈⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠁⠀⠀⢀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢸⣻⣿⣿⣿⣿⣠⡀⠀⠀⢀⣼⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣿⣹⣿⣿⣿⣿⡧⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⡸⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠫⡫⡻⣿⡿⡫⡪⠀⢸⣿⣷⣿⣿⣿⣷⣿⠏⠀⠀⠀⠀⢿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⣀⣀⠀⣀⣀⡀⣀⡀⢀⣀⠀⠀⣀⣀⣐⠀⣀⡀⠀⢀⣀⣀⠀⢀⣀⣀⠀⢀⣀⣘⠛⣂⡈⣊⡊⠂⢈⣴⣯⣿⣿⣿⣿⣿⣿⣟⠛⠀⢀⣄⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣦⠀⠀⠀⠀⠀⠀⢸⣿⣹⠿⠞⢻⣿⠛⢰⣿⣿⡇⢸⣿⣾⡏⠀⢸⣿⣟⣿⡇⣿⡇⠀⣾⣿⣿⠀⣿⣏⠿⠇⣿⣏⠿⠇⢻⣧⣿⠃⠴⠿⠿⣿⣿⠿⣫⣭⣷⣤⣤⡀⠀⠀⠻⠇⣼⣦⡀ ⠀⣠⣤⣤⡄⠀⠀⠀⠀⠠⣄⠛⠀⠀⠀⠀⠀⠀⢀⣙⢿⣷⡄⢸⣿⠀⢸⣿⣹⣷⠀⣿⣿⠀⠀⢸⣿⡇⣭⡅⣿⡇⠀⣿⣇⣿⡇⣙⡻⣿⡆⣙⡻⣿⡆⠘⣿⡟⣶⣶⣤⣤⡿⢡⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠉ ⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠘⢿⣶⡿⠃⢸⣿⠀⣾⡿⢹⣿⠀⢿⡿⠀⠀⠘⢿⣿⡿⠃⣿⣷⣶⣿⠏⣿⡇⠿⣷⣿⠇⠿⣷⣿⠇⠀⣿⡇⣿⣿⣿⣏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⠿⢿⣦⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡀⠀⠙⢿⣿⣿ ⠀⠀⠀⢠⣤⣼⡿⠂⡄⠀⠀⢸⣿⣿⣿⣿⣿⢄⣰⣿⠠⣿⣿⣯⣴⣿⣦⣽⣿⣷⣷⣿⣿⣿⣿⡇⢁⣴⣾⣿⡿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⣛⠉⢉⡍⢁⠻⣿⣿⣿⣿⣿⣿⣿⣟⣉⣭⣄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣷⣤⣀⣀⣠⣴⣾⣿⣿⢉⣴⣿⣿⠂⢀⣀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣓⣶⣀⠀⠀⠀⠀⠀⠀⣀⡐⠚⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⣇⠀⠀⠀⠀⠰ ⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⣆⣸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣗⣀⣷⠀⠀⣤⢀⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢛⣩⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠋⠁⠀⠙⠛⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣠⣄⣼⣧⠤⠴⠶⠗⠶⠖⠛⢿⣿⣿⣿⣿⣩⣠⣠⣠⣤⡤⣄ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⠿⠿⢤⡤⠴⠶⠛⠛⢿⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣼⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠨⢽⢰⣿⣿⣿⣿⣷⢸⣷⣾⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡏⡟⣿⢿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣼⠇⠹⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⣽⠀⠀⣶⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠰⣟⣸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⢀⡀⠀⢸⠀⠀⢹⠸⠀⠀⢹⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢇⣧⣤⣿⣇⡀⠉⠀⣠⣿⣧⣀⣬⣧⣤⣤⣷⣶⠖⠒⠒⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⣿⣿⣿⣷⣍⠻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⣿⣿⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣿⣿⡟⠒⠀⠹⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⢯⣶⣶⣴⣿⣿⣶⣀⣸⣿⣿⣍⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣽⠟⠀⡄⠀⠀⢸⣿⣿⣿⣿⣿⣄⣰⣿⡀⣿⣿⣯⣴⣿⣦⣽⣿⣷⣷⣿⣿⣿⣿⡇⣋⣤⣿⣿⡿⠟⠟⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⣛⠈⢉⡍⢁⠻⣿⣿⣿⣿⣿⣿⣿⣟⣋⣭⣅⣠⣤⠖⠉⠉⠉⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣶⣤⢀⣀⣠⣴⣾⣿⣿⢃⣴⣿⣿⠂⠀⣀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣶⡀⠀⠀⠀⠀⠀⠀⣀⡐⠚⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⣇⠀⠀⠀⠀⠀ ⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣇⣘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣇⣀⣷⠀⠀⣤⢀⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣛⣩⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠙⠻⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣠⣄⣼⣧⠤⠴⠶⠓⠲⠖⠛⢿⣿⣿⣿⣿⣉⣠⣠⣠⣤⡤⣄ ⠉⠉⠉⠉⠍⠉⠉⠉⠉⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠰⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣿⠿⠿⢥⡤⠶⠶⠛⠛⢿⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣼⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠬⢽⢰⣿⣿⣿⣿⣷⢸⣿⣾⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡏⡟⣿⢿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣸⠇⠻⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⣽⠀⠀⣶⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠰⣟⣸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⢀⡀⠀⢸⠀⠀⢻⠸⠀⠀⢹⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣯⣤⣾⣇⡀⠉⠀⣠⣿⣧⣀⣬⣧⣤⣤⣷⣶⠖⠒⠒⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⣿⣿⣿⣷⣍⠛⢿⣿⣿⣿⣿⢿⢿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⡀⢻⣿⣿⣿⣿⣿⣻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⣿⡟⠓⠀⠹⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⣿⣷⣶⣴⣾⣿⣶⣀⣸⣿⣯⣍⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢨⣤⣿⠟⠄⡄⠀⠀⢸⣿⣿⣿⣿⣿⣄⣰⣿⡀⣿⣿⣯⣴⣿⣤⣽⣿⣷⣷⣿⣿⣿⣿⡇⢙⣴⣿⣿⢿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⣛⠈⢉⡍⢁⠻⣿⣿⣿⣿⣿⣿⣿⣟⣋⣭⣅⣠⣤⡶⠻⠋⠉⠉⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣶⣤⢀⣀⣠⣴⣾⣿⣿⢉⣴⣿⣿⠂⠀⣀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣓⡦⠄⠀⠀⠀⠀⠀⠀⣀⡐⠚⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⣇⠀⠀⠀⠀⠀ ⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⣿⣿⣆⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣀⣷⠀⠀⣤⢀⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢛⣩⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠁⠀⠙⠛⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣠⣄⣼⣧⠤⠴⠶⠓⠶⠖⠛⣿⣿⣿⣿⣿⣁⣠⣠⣠⣤⡤⣀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣿⠿⠿⢥⡤⠶⠶⠛⠛⢿⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣼⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠬⢽⢰⣿⣿⣿⣿⣷⢸⣿⣿⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡏⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣸⠏⠹⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⣽⠀⠀⣶⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠰⣟⣸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⢀⡀⠀⢸⠀⠀⢹⠸⠀⠀⢹⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣼⣤⣾⣇⡀⠉⠀⣠⣿⣧⣀⣬⣧⣤⣤⣷⣶⠖⠒⠒⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⣿⣿⣿⣿⣍⠛⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⣿⡟⠒⠀⠹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⣯⣶⣶⣴⣿⣷⣶⣀⣸⣿⣿⣍⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣿⡟⠀⡄⠀⠀⢸⣿⣿⣿⣿⣿⣄⣰⣿⡠⣿⣿⣯⣴⣿⣤⣽⣿⣷⣷⣿⣿⣷⣿⡇⢉⣴⣿⣿⣿⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⣛⠈⢉⡍⢁⠻⣿⣿⣿⣿⣿⣿⣿⣟⣋⣭⣅⣠⣤⡾⠛⠋⠉⠉⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣶⣄⠀⣀⣠⣴⣾⣿⣿⢃⣴⣾⣿⠂⠀⣀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣓⡶⠄⠀⠀⠀⠀⠀⠀⣀⡐⠚⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⣇⠀⠀⠀⠀⠀ ⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⣿⣿⣦⣘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⣀⣶⠀⠀⣤⢀⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣛⣩⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠋⠁⠀⠙⠛⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣠⣄⣸⣧⠤⠴⠶⠓⠶⠒⠛⢿⣿⣿⣿⣿⣁⣠⣠⣠⣤⡤⣀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣿⠿⠿⢥⡤⠶⠶⠛⠛⢿⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣼⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠨⢽⢰⣿⣿⣿⣿⣷⢸⣿⣾⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡎⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⢿⣿⣿⣿⣸⠏⠻⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⣽⠀⠀⣶⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠰⣟⣸⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠋⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⢀⡀⠀⢸⠀⠀⢻⠸⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣼⣤⣾⣇⠀⠉⠀⣠⣿⣧⣀⣬⣧⣤⣤⣷⣶⠖⠒⠒⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⣿⣿⣿⣿⣍⠛⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⡀⢹⣿⣿⣿⣿⣿⣻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⣿⡟⠒⠀⠹⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⣿⣶⣶⣼⣿⣿⣖⣀⣸⣿⣯⣉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣿⠿⢠⠆⠀⠀⢸⣿⣿⣿⣿⣿⣀⣰⣿⡀⣿⣿⣯⣤⣿⣦⣽⣿⣷⣷⣿⣿⣿⣿⠇⢉⣴⣿⣿⣿⢟⠛⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⣛⠈⢉⡍⢁⠻⣿⣿⣿⣿⣿⣿⣿⣟⣋⣭⣍⢠⣤⣾⠿⠿⠛⠛⠋⠀⠀⠀⠈⠹⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣶⣄⠀⣀⣠⣴⣾⣿⣿⢉⣴⣿⣿⠀⠀⣀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣳⡦⠄⠀⠀⠀⠀⠀⠀⣀⡐⠒⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⣇⠀⠀⠀⠀⠀ ⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⣿⣿⡆⣘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢀⣶⠀⠀⣠⢀⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢛⣩⣴⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣿⠋⠁⠀⠙⠛⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣠⣄⣸⣧⠤⠴⠶⠗⠶⠖⠛⣿⣿⣿⣿⣿⣁⣠⣠⣠⣤⡤⣀ ⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣿⠿⠿⢥⡤⠴⠶⠛⠛⢿⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣼⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧⢽⢰⣿⣿⣿⣿⣷⢰⣿⣿⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡎⠟⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⢿⣿⣿⣿⣸⠏⠻⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⣽⠀⠀⣶⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠰⣟⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠏⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⠀⡀⠀⢸⠀⠀⢹⠸⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣼⣤⣼⣇⡀⠉⠀⣠⣿⣧⣀⣬⣧⣤⣤⣷⣶⡖⠒⠒⠀⠀⠈⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣯⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⣿⣿⣿⣿⣍⠙⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣄⢹⣿⣿⣿⣿⣿⣻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⡟⠒⠀⠸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⣯⣶⣶⣼⣿⣿⣶⣀⣸⣿⣯⣉⠁⠀⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣿⠷⠠⠆⠀⠀⢸⣿⣿⣿⣿⣿⣄⣐⣿⡀⣿⣿⣯⣤⣿⣦⣭⣿⣷⣷⣿⣿⣷⣿⡇⢉⣴⣿⣿⣿⣟⢛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⣛⠀⢉⡍⢁⠻⣿⣿⣿⣿⣿⣿⣿⣟⣉⣭⣅⣠⣤⣾⡿⠿⠟⠛⠋⠋⠀⠀⠈⠹⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣶⣄⢀⣀⣠⣴⣾⣿⣿⢉⣴⣾⣿⠀⠀⣀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣛⠤⠄⠀⠀⠀⠀⠀⠀⣀⡐⠚⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⣇⠀⠀⠀⠀⠀ ⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⣿⣿⡦⣘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢀⣰⠀⠀⣠⣄⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣉⣵⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣿⠋⠁⠀⠉⠛⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣿⣿⣿⣿⣿⣿⣶⣶⣠⣄⣸⣧⠤⠴⠶⠓⠶⠖⠛⢿⣿⣿⣿⣿⣉⣠⣠⣠⣤⡤⣀ ⠭⠉⠉⠉⠍⠉⠉⠉⠉⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣿⠿⠿⢥⡤⠴⠶⠛⠛⢿⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣼⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⢼⢰⣿⣿⣿⣿⣿⢸⣿⣿⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡎⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⣿⣿⣿⣸⠟⠻⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⣽⠀⠀⣶⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣟⣸⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠏⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⢀⡀⠀⢸⠀⠀⢹⠸⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⣸⣤⣼⣇⡀⠉⠀⣠⣿⣧⣀⣬⣧⣤⣤⣷⣶⡖⠒⠒⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣇⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⣿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⣿⠟⠒⠀⠸⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⣿⣷⣶⣴⣾⣷⣶⣀⣸⣿⣿⣍⠁⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣿⠗⠠⠆⠀⠀⢸⣿⣿⣿⣿⣿⣄⣀⣿⡀⣿⣿⣿⣤⣿⣦⣽⣿⣷⣷⣿⣿⣷⣿⡇⢁⣼⣿⣿⣿⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⣛⠈⢉⠍⠁⠻⣿⣿⣿⣿⣿⣿⣿⣟⣉⣭⣅⣠⣤⣶⣿⣿⡿⠿⠟⠛⠛⠉⠉⠹⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣶⣤⣀⣠⣤⣴⣾⣿⣿⢁⣴⣾⣿⠀⠀⣀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⡶⢂⡀⠀⠀⠀⠀⠀⢀⡔⠚⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⡇⠀⠀⠀⠀⠀ ⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣆⣿⣿⣿⣇⣘⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣀⣸⡆⠀⣠⡄⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣉⣵⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⠋⠁⠀⠈⠛⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣶⢠⣄⣸⣧⠤⠴⠶⠓⠶⠖⠛⣻⣿⣿⣿⣿⣁⣠⣠⣠⣤⡤⡀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⣾⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⠿⠿⢥⡤⠴⠶⠛⠛⢿⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣼⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⢴⢶⣿⣷⣷⣶⣶⢰⣿⣿⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡏⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠘⠿⣿⣿⣿⣿⣸⠟⠻⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⣽⠀⠀⣶⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣟⣸⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠏⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⠀⡀⠀⢸⠀⠀⢹⠸⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣸⣤⣼⣇⡀⠉⠀⣠⣿⣧⣀⣬⣧⣤⣤⣷⣶⡖⠒⠒⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠯⣧⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⢾⣿⣿⣿⣯⡙⠻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣿⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠒⠀⠸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⠰⣶⣿⣷⣶⣴⣾⣷⣶⣀⣸⣿⣯⡥⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣼⡿⠇⠠⠂⠀⠀⢸⣿⣿⣿⣿⣿⢄⣐⣿⡀⣿⣿⣿⣤⣾⣦⣬⣿⣧⣷⣿⣿⣷⣿⠇⣡⣾⣿⣿⣿⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⣛⠀⢉⠌⠁⠻⣿⣿⣿⣿⣿⣿⣿⣟⣩⣭⣄⣤⣤⣾⣿⣿⣿⡿⠿⠿⠛⠛⠛⠹⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣶⣤⣀⣀⣤⣶⣿⣿⣿⢡⣴⣿⣿⠂⠀⣀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣲⣒⡀⠀⠀⠀⠀⠀⢀⡔⠒⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⡇⠀⠀⠀⠀⠀ ⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣶⣿⣿⣿⣇⣈⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⢀⣸⡇⠀⢠⣆⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣉⣵⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣷⣿⠛⠁⠀⠈⠙⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣶⣶⢠⣤⣸⣧⠤⠴⠶⠓⠶⠖⠋⣻⣿⣿⣿⣿⣁⣠⣠⣤⣤⡤⣀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⠿⠿⢥⡤⠴⠶⠛⠛⢿⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣼⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⢷⢴⣷⣶⣷⣶⣶⢸⣿⣿⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡎⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠿⣿⣿⣿⣿⢸⡟⠻⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⢽⠀⠀⣶⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⣏⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⠀⡀⠀⢸⠀⠀⢻⠸⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣘⣥⣼⣇⡀⠉⠀⣠⣿⣧⣀⣬⣧⣤⣤⣷⣶⡖⠒⠒⠀⠀⠈⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣇⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢾⣿⣿⣿⣯⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠏⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣿⣿⣿⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⣿⣛⠃⠀⠸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⠰⣶⣿⣶⣶⣴⣾⣶⣶⣀⣸⣿⣯⡭⠀⠀⠀⣨⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣼⢿⠗⠠⠂⠀⠀⢸⣿⣿⣿⣿⣿⢄⣀⣿⡀⣿⣿⣿⣤⣾⣷⣬⣿⣧⣷⣿⣿⣷⣿⠇⣡⣾⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⣛⠀⢉⠌⠁⠹⣿⣿⣿⣿⣿⣿⣿⣏⣉⣥⣄⣠⣴⣾⣿⣿⣿⡿⠿⠟⠟⠛⠛⠙⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣶⣦⣀⣠⣤⣶⣿⣿⣿⢡⣴⣿⣿⠀⠀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣒⣒⡀⠀⠀⠀⠀⠀⢀⡔⠚⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⡇⠀⠀⠀⠀⠀ ⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣆⣈⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡗⢀⣠⣿⠀⢠⣾⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣉⣵⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⣿⠛⠁⠀⠀⠙⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠻⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣶⢢⣦⣸⣧⠤⠴⠶⠓⠒⠒⠋⢻⣿⣿⣿⣿⣁⣀⣠⣠⣤⡤⡀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⠿⠿⢥⡤⠴⠶⠛⠛⢻⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣼⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⠶⣶⣶⣶⣶⣶⢸⣿⣿⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡌⠏⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⢸⡟⠻⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⢽⠀⠀⣶⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠘⣏⣸⣷⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⠀⡀⠀⢸⠀⠀⢹⠸⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡇⠀⢠⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣘⣧⣼⣇⡀⠉⠀⣠⣿⣇⣀⣬⣧⣤⣤⣷⣶⡖⠒⠒⠀⠀⠈⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⡀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢺⣿⣿⣿⣿⡙⠻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠃⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣾⣿⣿⣿⣿⣿⣦⡈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡛⠁⠀⠸⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣶⣿⣶⣶⣴⣾⣷⣖⣀⣸⣿⣯⠄⠀⠀⠄⣠⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⡿⠃⠠⠂⠀⠀⠸⣿⣿⣿⣿⣿⠄⢐⣷⡀⣸⣿⣿⣥⣾⣷⣬⣿⣿⣷⣿⣿⣧⣿⠇⣡⣾⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠟⣛⠀⢉⠍⢀⠸⢿⣿⣿⣿⣿⣿⣿⣟⣩⣭⣄⣠⣴⣾⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⢿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣶⣤⣀⣠⣤⣶⣿⣿⣿⢡⣴⣿⣿⠀⠀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⣓⡀⠀⠀⢀⠀⠀⠀⡔⠒⠉⠉⢿⠉⠉⡉⠉⢻⠃⠀⣤⠀⠘⡇⠀⠀⠀⠀⠀ ⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⣿⣿⣿⣆⣈⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣀⣠⣼⡇⠀⣾⣿⠀⠀⣾⣿⠀⠀⠿⠀⢸⡀⠀⢻⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣉⣵⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠋⠀⠀⠉⣿⠀⠀⣀⣼⡇⠀⢠⣤⣾⡇⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡆⠀⠘⠛⡇⠀⢸⣿⣿⣧⡀⠈⠁⣀⡾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣶⢢⣦⣸⣧⠤⠴⠶⠓⠶⢖⠉⢻⣿⣿⣿⣿⣁⣠⣠⣠⣤⡤⡀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢷⣿⠿⠿⢥⡤⠴⠶⠛⠛⢿⠛⠛⠉⣿⡏⠉⠁⠀⡇⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⢶⣶⣶⣶⣶⣶⢸⣿⣿⠀⢠⡄⠀⢻⣤⠀⠀⣶⣾⠀⢀⠀⢸⣧⠀⠈⠿⣧⠀⠀⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡄⠏⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣟⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⢸⡟⠻⡀⠀⠙⠻⢿⣿⡆⠀⢸⣿⠀⢸⡀⠀⣿⠀⠀⣤⢽⠀⠀⣶⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠐⢏⣸⣷⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⢀⠛⠓⣦⠀⠈⣿⡇⠀⢸⡿⠀⠀⡀⠀⢸⠀⠀⠻⠸⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣐⣧⣼⣇⡀⠉⠀⣠⣿⣧⣀⣬⣧⣤⣤⣷⣶⡶⠒⠒⠀⠀⠈⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⡀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⢺⣿⣿⣿⣿⡉⠻⢿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠁⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⣿⣿⣿⣿⣦⡈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣋⠉⠀⠘⢿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠲⣶⣿⣶⣶⣶⣾⣷⣶⣀⣸⣿⣶⠤⠀⠀⠂⣨⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⠿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⣷⠀⢸⣿⣿⣧⣾⣷⣦⣾⣿⣷⣿⣿⢷⣿⠃⣠⣼⣿⣿⣟⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣻⣿⣿⢙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠛⣋⠀⠈⠌⠀⠘⢿⣿⣿⣯⣽⣿⣿⣟⣩⣥⣄⣠⣴⣾⣿⣿⣿⡟⠛⠋⠻⠛⠛⠙⢿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣶⣄⣀⣠⣤⣶⣿⣿⣿⢡⣴⣿⣿⠀⠀⣀⡀⠀⢸⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣻⣛⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣉⣁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢀⣣⣤⣾⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣻⣿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠍⠀⠀⠀⠈⢙⡿⠛⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⣿⣶⣶⣴⣶⣶⣖⣀⣸⣿⡖⠀⠀⠀⠀⢀⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⠿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠐⣷⠀⢀⣿⣿⣿⣶⣾⣷⣶⣿⣷⣿⣻⠳⡿⠁⣠⣾⣿⣿⣟⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣻⣿⣿⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⢛⣉⠀⠈⠄⠀⠀⢛⣿⣿⣿⣯⣽⣿⣿⣯⣥⣄⢠⣶⣾⣿⣿⣿⡿⠛⠋⠛⠛⠛⠙⢿⡿⠿⠟⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣶⣦⣀⣠⣤⣶⣿⣿⣯⢡⣶⣿⣿⠀⠀⣀⠀⠀⢸⢿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣻⣋⣛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣤⣤⡀⠀⠀⢠⣤⠀⢀⡀⢂⠀⢸⣿⣿⣿⣿⣿⡛⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣀⣾⣿⣿⣆⣠⣾⣿⣿⣤⣴⣿⡿⠛⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⢤⣶⣿⣿⡷⣾⣷⣶⡄⣠⣤⣼⣭⣿⣯⡅⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠉⣁⣠⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠉⠛⠋⠀⠈⠁⢹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⢢⣦⣠⣴⠾⠛⠁⠀⢀⣀⡈⠻⢷⡿⢸⡗⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⢷⡟⢻⠟⠁⠀⣠⣴⣿⣿⣿⣿⣿⣷⣅⠸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣼⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⡟⣾⣶⣷⣾⡷⢹⡿⠈⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠈⢸⡏⠙⠹⣿⣿⣿⣿⣿⣿⣿⡛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠻⢿⣷⢸⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡙⠀⠀⠻⣄⢲⣶⣿⣿⣿⣿⣿⣿⣏⣩⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡞⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⣻⣤⣾⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠄⠀⠀⠀⠈⠋⣿⠟⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⢶⣶⣾⣶⣶⣴⣶⣶⣖⣀⣸⣿⡇⠀⠀⠀⠂⢠⣡⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⠿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢀⠐⣷⠀⣀⣼⣿⣿⣶⣾⣷⣶⣾⣿⣿⣿⠳⡿⠂⣠⣾⣿⣿⣏⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⢛⣉⠀⠈⠄⠀⠀⢙⣻⣿⣿⣿⣽⣿⣿⣯⣥⣄⣠⣶⣾⢿⣿⣿⠿⠛⠋⠛⠛⠛⠛⢿⡿⠛⠛⠋⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣶⣦⣀⣠⣤⣶⣿⣿⣯⢡⣴⣿⣿⠀⠀⣀⡀⠀⢸⠟⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣍⡛⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⡄⠀⠀⠠⣶⣆⠀⣀⠀⠀⠘⣿⣿⣿⣿⣿⡟⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣠⣼⣿⣿⣆⣠⣾⣿⣿⣦⣤⣾⡿⠟⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢰⣶⣿⣿⣿⢾⣿⣶⣦⣠⣤⣼⣭⣿⣿⡇⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠉⢁⣠⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡄⠉⠛⠛⠁⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠿⣿⣿⣿⣇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⢢⣦⣠⣴⡾⠛⠁⠀⢀⣀⣈⠹⢷⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢷⡟⠻⡟⠁⠀⣠⣴⣿⣿⣿⣿⣿⣷⣅⠸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣼⣿⡆⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⡿⡿⠶⣿⣿⡷⢹⣿⠈⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠃⠈⢸⡏⠙⠋⢿⣿⣿⣿⣿⣿⣿⡛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⢸⡿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠌⠀⠀⠙⢤⢒⣶⣿⣿⣿⣿⣿⣿⣯⣩⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣤⣼⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⠤⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠂⠀⠀⠀⠀⠻⣿⠟⢉⣩⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣖⣶⣶⣿⣶⣶⣶⣶⣶⣖⣀⣸⣿⡇⠀⠀⠀⢂⢼⣀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣼⠿⠃⠐⠀⠀⠀⠸⣿⣿⣿⣿⣿⢀⠰⣷⠀⣀⣼⣿⣿⣷⣶⣿⣶⣶⣿⣿⣿⢷⡿⠂⣠⣾⣿⣿⣏⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⢛⣉⠀⠈⠄⠀⠀⢙⣻⣿⣿⣿⣯⣿⣿⣿⣥⣄⣠⣶⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⣿⣿⠛⠛⠋⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣶⣦⣀⣤⣴⣾⣿⣿⣯⢡⣶⣿⣿⠀⠀⣀⡀⠀⢻⠋⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣟⣛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣤⣄⠀⠀⠀⣶⣶⡀⣠⡔⡀⠈⣿⣿⣿⣿⣿⡛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣲⣿⣿⣿⣆⣠⣾⣿⣿⣷⣆⣾⣿⠟⣻⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠶⣶⣿⣿⣿⣿⣿⣷⣷⣀⣦⣼⣭⣿⣿⡇⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠁⣠⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡆⠉⠙⠛⠛⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⢿⣿⣿⡧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⢢⣦⣤⣴⡾⠛⠁⠀⢀⣀⣀⡙⢷⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⢷⡟⠻⡿⠋⠀⣠⣴⣿⣿⣿⣿⣿⣷⣅⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣼⣿⡇⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠿⠲⢿⣿⡿⢻⣿⠘⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠃⠈⢸⡟⠙⠉⢿⣿⣿⣿⣿⣿⣿⣟⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡿⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠘⢢⣚⣶⣿⣿⣿⣿⣿⣿⣯⣽⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠤⠄⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡂⠀⠀⠀⠀⢯⣿⠻⠋⣉⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣶⣶⣶⣿⣶⣶⣶⣶⣶⣖⣀⣸⣿⡇⠀⠀⠀⢢⣾⣡⣤⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣽⠿⠃⠴⠀⠀⠀⠸⣿⣿⣿⣿⣿⣤⣸⣷⠀⣀⣼⣿⣿⣿⣷⣾⣿⣶⣾⣿⣿⢷⡿⠇⣡⣿⣿⣿⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢛⣉⠁⠩⠄⡀⠀⣉⣛⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡟⠟⠿⣿⣿⣿⡟⠉⠉⠉⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣶⣆⣀⣤⣴⣾⣿⣿⣯⢡⣾⣿⣿⠀⣀⣄⣀⠀⢿⠋⣽⣿⣿⡿⠿⢿⣿⣿⣿⣿⣯⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣦⣴⣤⡀⠀⠀⣐⣿⣿⣄⣤⢵⠀⣿⣿⣿⣿⣿⡟⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣫⣿⣿⣿⣆⣤⣾⣿⣿⣿⣷⣶⣿⠿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣦⣦⣼⣽⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡋⠉⠉⣀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠉⠉⠛⠿⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⢀⣿⣿⡿⠿⢿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣣⣶⣤⣴⣾⠋⠁⠀⣀⣀⣀⣙⢷⡟⢺⡇⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣧⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣸⣿⡿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⡟⠑⠋⠻⣿⣿⣿⣿⣿⣿⣟⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡷⠀⠀⠈⣱⣈⣲⣾⣿⣿⣿⣿⣿⣿⣿⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠓⠒⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⠀⠀⠀⠈⣿⣿⣿⡏⢙⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣶⣶⣶⣿⣶⣶⣶⣾⣷⣶⣀⣸⣿⡇⠀⠀⢠⣶⣿⣴⠶⠂⣨⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⡿⠗⠔⠀⠀⠀⠸⣿⣿⣿⣿⣿⣤⣸⣿⠀⣄⣼⣾⣿⣿⣷⣶⣿⣷⣶⣿⣿⣿⡿⢇⣱⣿⣿⣿⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢋⡉⠀⠨⠄⡀⠈⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⠉⠁⠉⠉⠑⠃⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣶⣆⣀⣤⣴⣾⣿⣿⣯⢡⣾⣿⣿⠀⣀⣤⣂⠀⣿⢋⣴⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⡄⠀⢀⣀⣿⣿⣧⣴⣾⡄⣿⣿⣿⣿⣿⡟⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣤⣿⣿⣿⣿⣿⣶⣾⡿⠟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣦⣼⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⢀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣉⠉⠛⠿⠿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⣠⣴⣾⣿⣿⣿⠿⢿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣗⠀⣀⣀⣈⣙⣷⡿⢻⡯⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⢿⡿⡿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⣿⣿⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⢠⡿⢉⠛⠻⣿⣿⣿⣿⣿⣿⣿⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠈⢱⣎⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⣿⡇⠀⠀⠀⢸⣿⣿⣿⠻⠁⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣶⣶⣶⣿⣶⣶⣶⣾⣿⣶⣀⣼⣿⡿⠀⠀⣰⣾⣿⡷⠗⠂⠀⣼⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⠗⠞⠀⠀⠀⠹⣿⣿⣿⣿⣿⣤⣼⣿⠀⣤⣾⣾⣿⣿⣿⣶⣿⣿⣶⣿⣿⣿⡿⢇⣵⣿⣿⣿⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠁⠉⠀⠀⠀⠀⠀⢰⣿⣿⠿⣋⣉⠀⡩⠄⡀⠈⣉⣉⡿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠉⠉⠀⠀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣾⣶⣆⣀⣤⣴⣾⣿⣿⣿⢡⣾⣿⣿⣂⣀⣄⣂⠀⣿⢋⣴⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣶⣶⣄⣀⣀⣀⣼⣿⣿⣴⣾⡇⣿⣿⣿⣿⣿⡟⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣆⣤⣿⣿⣿⣿⣿⣿⣾⣿⠟⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣧⣧⣼⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⠉⠁⣀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣉⣻⡿⠿⢿⡟⣹⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡏⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣹⣷⡿⢺⡧⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣿⣿⠆⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⢿⣿⠀⠠⡿⠁⡋⠹⣿⣿⣟⣻⣿⣿⣿⡻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠃⠀⠀⢸⣎⣽⣿⣿⣿⣿⣿⣿⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡍⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣏⡵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣶⣶⣶⣿⣶⣶⣶⣾⣿⣶⣀⣿⣿⠏⠀⠀⣴⣾⣿⡾⠋⠁⠀⠀⣴⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⠧⠞⠀⠀⠀⠻⣿⣿⣿⣿⣷⣤⣼⣿⠀⣤⣿⣴⣿⣿⣿⣷⣾⣿⣶⣾⣿⣿⡿⢇⣵⣿⣿⣿⣏⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠁⠉⠀⠀⠀⠀⠀⣰⣿⡿⠿⣋⡉⠁⠩⢄⡀⠈⣉⣉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⡿⠿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠈⠉⠁⠀⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣾⣶⣆⣀⣤⣶⣿⣿⣿⣯⢡⣾⣿⣿⢠⣀⣤⣂⠀⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣶⣶⣆⣀⣀⣀⣼⣿⣿⣶⣾⣇⣿⣿⣿⣿⣿⡟⣿⣿⡟⠁⠀⠀⠀⠀⠀⠐ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣧⣾⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠉⠉⢀⣠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⣷⡟⢻⡏⠀⠀⠀⠀⠀⠀⠀ ⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠻⠿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣿⣿⡇⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣾⠉⡘⠹⣿⣿⣟⣫⣿⣿⣿⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠛⠀⠀⢸⣾⣽⣿⣿⣽⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⡏⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⡟⠱⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣿⣶⣶⣶⣾⣷⣶⣀⣿⣿⠏⠀⢀⣴⣾⣿⣿⠟⠀⠀⠀⠀⣤⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⠷⠞⠀⠀⠀⠻⣿⣿⣿⣿⣷⣤⣸⣷⠀⣤⣿⣤⣿⣿⣿⣿⣶⣾⣷⣾⣿⣿⡿⣇⣵⣿⣿⣿⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣛⡃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⣴⣿⡿⠿⣋⡍⠀⠤⠄⠀⠈⣉⣩⡜⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⠿⠿⠻⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠀⣀⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣾⣶⣆⣀⣤⣶⣿⣿⣿⣯⣴⣿⣿⣏⣠⣠⣤⣂⠀⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣶⣶⣀⣤⣀⣤⣿⣿⣷⣶⣧⣿⣿⣿⣿⣿⡏⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣆⣠⣿⣿⣿⣿⣿⣿⣿⣴⣿⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠁⣀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛⠙⠛⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠘⠋⠛⣿⣿⣿⣿⣿⣷⡟⣻⡏⠀⠀⠀⠀⠀⠀⠀ ⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣷⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣾⣿⡷⠸⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣼⠁⠀⢠⡏⠁⠈⢿⣿⣟⣩⣿⣿⣿⡙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠈⠋⠀⠀⢀⣶⣯⣿⣿⣥⣿⣿⣿⣿⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡃⠀⠀⠀⢸⣿⣿⣿⣿⡿⡿⣿⣿⡿⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⣄⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿⣿⡗⠀⠀⠀⢸⣿⣿⣿⡁⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣿⣶⣶⣶⣾⣷⣶⣠⣿⣿⡀⠀⢠⣴⣿⣿⡿⠑⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⡿⠣⠂⠀⠀⠀⢻⣿⣿⣿⣿⡗⣤⣸⣧⠀⣤⣿⣴⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⡿⢇⣵⣿⣿⣿⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢛⣋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣿⣿⣟⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⣋⡉⠀⠴⠄⡀⠈⣉⣡⡈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⠟⠟⠻⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢁⣴⣶⣤⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣾⣶⣆⣀⣤⣶⣿⣿⣿⣯⣴⣿⣿⡯⠀⣀⣤⡀⠀⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣶⣷⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆⣰⣿⣿⣿⣿⣿⣿⣷⣠⣾⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠁⢀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⢠⠾⠋⠉⢿⣿⣿⣿⣿⣷⡟⢻⡏⠀⠀⠀⠀⠀⠀⠀ ⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⡯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⢿⡏⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢾⠃⠀⠀⡟⠁⠁⠹⣽⣟⣉⣿⣿⣿⡙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠈⠀⠀⠀⠀⣴⣮⡷⢦⣥⣽⣿⣿⣿⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⠀⠀⠀⢸⣿⣿⣿⣿⠿⡿⣿⣿⡿⠄⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠃⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣠⣿⣿⡄⠀⣠⣤⣿⣿⣿⠹⠈⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢻⣿⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⠟⠣⠂⠀⠀⠀⢻⣿⣿⣿⣿⡇⣤⣻⣧⢀⣤⣷⣼⣿⣿⣿⣿⣧⣴⣿⣮⣿⣿⠿⣀⣴⣿⣿⣿⣏⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢟⣋⣀⣤⣶⣄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⣉⡉⠀⠴⠀⠀⠈⣉⣡⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⠛⠛⠛⠋⠻⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣄⣼⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣶⣆⣠⣤⣶⣿⣿⣿⣯⣴⣿⣿⡇⢀⣠⣄⣀⠘⡟⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣶⣷⣄⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⣿⣿⠂⣰⣿⣿⣿⣿⣿⣿⣯⡀⣼⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⢀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠉⠙⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠋⠉⣿⣿⣿⣿⣿⣿⡏⣻⡇⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣷⣝⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢤⣾⢿⣿⠀⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⢼⠇⠀⠀⡾⠉⠈⢩⣿⡟⢋⣿⣿⣿⡛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠉⠀⠀⠀⠀⣴⣬⣷⢦⣤⣽⣿⣿⣿⣥⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣥⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⠓⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣿⠅⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢠⣿⣿⣿⡇⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣰⣿⣿⡆⠀⣤⣤⣿⣿⣿⠟⠈⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⠟⠂⠂⠀⠀⠀⢻⣿⣿⣿⣿⡇⣤⣿⡇⢠⣤⣷⣼⣿⣿⣿⣿⣯⣬⣿⣬⣿⣿⠿⣠⣴⣿⣿⣿⣏⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣻⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⢟⣉⡁⠀⠴⠀⠀⢉⣉⣡⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠿⠟⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⠛⠻⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣶⣄⣠⣤⣶⣿⣿⣿⣇⣴⣿⣿⡇⢀⣠⣔⡀⠸⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣄⣤⣼⣿⣦⣄⠈⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣯⠁⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠀⣠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠻⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⢴⠞⢻⣿⣿⣿⣿⣿⣿⣾⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣕⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⢤⣾⢿⣿⠀⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⢰⠃⠀⠀⡼⠉⠉⢉⣈⡿⢛⣻⣿⣿⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠀⠈⠀⠀⠀⣴⣔⣲⣦⣉⣹⣿⣿⣿⣍⣵⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢀⣿⣿⣽⣿⣿⣟⣿⣯⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⠁⢀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣿⣶⣶⣶⣾⣶⣶⣸⣿⣿⡄⢀⣤⣤⣾⣿⣏⡀⠐⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⠟⠖⠀⠀⠀⠈⢿⣿⣿⣿⣿⢢⣤⣿⡄⢠⣼⣧⣾⣿⣿⣿⣿⣟⣉⣿⣝⣿⡿⢿⣠⣾⣿⣿⣿⣯⣏⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⢽⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⢋⣉⠁⠠⠦⠀⠀⢉⣉⡤⢈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠻⠋⠛⠉⠉⠁⠙⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⣶⣀⣠⣴⣾⣿⣿⣿⣥⣾⣿⣿⡀⣀⣤⣔⡀⢸⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡗⢀⣾⣿⣿⣿⣿⣿⣿⡟⠉⣹⣿⠋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⠿⠋⠈⠉⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢿⠿⠿⠛⠉⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣠⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠴⣿⣿⣿⣿⣿⣶⣮⣽⣿⠃⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣿⣏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣿⠿⣷⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢁⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠠⠋⠀⠀⣾⠋⠉⢉⣙⣿⠛⢻⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⠈⠁⠀⠀⠀⣥⣐⣦⣌⠉⢱⣾⣿⣿⣏⣡⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⣿⣿⣿⣛⣭⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡏⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣀⣤⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⡁⠈⠉⠉⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣸⣿⣷⠀⢠⣤⣴⣿⣿⣿⣃⠀⠈⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢻⣿⣿⣿⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⡷⠔⠀⠀⠀⠘⣿⣿⣿⣿⣿⢦⣸⣿⠀⣤⣼⣦⣿⣿⣿⣿⣿⣟⣹⣿⣙⣿⡿⢇⣵⣾⣿⣿⣿⣭⣏⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠭⣿⣷⡈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⣋⣍⠀⠠⠆⠀⠀⣉⣡⡄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠻⠛⠉⠁⠈⠀⠀⠉⢿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⣷⣦⣀⣤⣴⣾⣿⣿⣿⣤⣾⣿⣿⠁⣀⣤⣀⠀⠹⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⠛⣻⣿⠛⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠋⠟⠉⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⣤⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣾⣿⣿⢹⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣴⣿⡿⡇⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢁⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠰⠛⠀⢀⡿⠛⠉⢙⡩⣿⠟⢿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠅⠀⠀⠀⠀⠀⣥⡰⣤⣬⠉⢳⣾⣿⣿⡏⣡⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⣻⣾⣿⣿⣿⣟⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢀⣿⣿⣟⠁⠀⠉⠉⠉⠉⠀⠀⠀⢡⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣿⣶⣶⣶⣾⣶⣶⣿⣿⣿⠀⣤⣤⣴⣿⣿⣿⣧⠀⠊⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⡷⠃⠀⠀⠀⠻⣿⣿⣿⣿⣗⣄⣻⣿⢀⣤⣷⣼⣿⣿⣿⣿⣿⢟⣻⣟⣻⣿⡿⣏⣶⣿⣿⣿⣿⡽⢹⠿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠛⠷⣿⣿⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⣼⣿⡿⠟⣩⡍⠀⠴⠠⠀⢉⣉⣡⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣄⣀⣀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣾⣶⣄⣠⣤⣶⣿⣿⣿⣯⣴⣿⣿⡇⠀⣤⣤⣀⠈⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⠿⢿⠇⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠛⣻⡿⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠟⠃⠁⠉⢀⣾⣿⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⣢⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣾⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢭⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⣿⣿⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⠄⠈⢀⡿⠛⠋⠛⢉⡿⠿⢿⣿⣽⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠛⠁⠀⠀⢈⣄⡠⣤⡌⠛⢲⣾⣿⣿⣏⣡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⢸⣿⣟⣷⣿⣿⣿⣿⣛⣩⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⣟⠉⠉⣹⠛⠋⠉⠀⠀⠀⣽⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣶⣶⣶⣿⣶⣶⣼⣷⣶⣾⣿⣿⡇⢠⣤⣤⣶⣿⣿⠿⣃⠀⠊⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣽⣿⣿⡾⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣴⣿⡇⣠⣼⣶⣿⣿⣿⣿⣿⣿⢛⣿⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠿⢿⠿⢿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠑⠺⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠏⠋⠁⠡⠀⠀⠀⢠⣾⣿⠿⢛⣩⠁⠠⠆⠤⠈⣉⣉⡤⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⣷⣄⣀⣀⢀⣤⣶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣿⣦⣀⣠⣴⣾⣿⣿⣿⣥⣾⣿⣿⡇⣤⣤⣄⡀⠹⢛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠻⠃⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢿⠟⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⣰⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣖⣶⣾⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣼⣿⣿⡟⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢩⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣷⣧⡄⠉⢰⡿⠟⠛⣛⣿⡿⠿⣿⣿⣿⠿⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠛⠛⠉⠀⠀⢹⣄⠤⣄⡹⠛⣶⣾⣿⣿⢋⣵⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣽⣿⣿⣿⣟⣹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡏⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣿⣿⣟⠃⠀⠀⠀⠀⣿⣿⣿⣿⠏⠻⣻⠟⠋⠉⠀⠀⣩⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣷⣶⣶⣿⣷⣶⣽⣷⣶⣿⣿⣿⡅⣤⣤⣶⣾⣿⣿⣿⣿⠶⠛⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣾⣿⣿⡿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣶⣿⣿⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⣿⠻⠛⠛⠛⠟⢿⣿⣿⡟⠁⠀⠀⠈⠉⢻⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠿⠛⠋⣽⣆⠀⠀⢠⣾⣿⠿⣟⣫⡉⢠⠶⡬⠉⣉⣉⣥⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣤⣠⣶⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠄⠀⠀⠀ ⣷⣿⣦⣄⣠⣴⣿⣿⣿⣿⣷⣾⣿⣿⣿⣴⣦⣴⣄⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠉⠋⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠿⠁⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⢿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⠏⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠯⠿⠭⠭⠩⠍⠭⠭⠭⠭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣿⣿⣿⠟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦⠤⠛⢉⣾⡿⠿⢿⣿⣿⡿⣿⣿⣿⡿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣿⣿⠟⠛⠛⠉⠀⠀⢘⣏⡠⣄⣸⠟⢻⣾⣿⣿⣿⣳⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⡧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣦⣤⠤⠤⠀⠀⠴⠿⡿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡶⠶⢦⡄⠰⠴⡤⣼⣿⣿⣇⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣀⡀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣐⠈⢺⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⡿⠛⠉⠁⣸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⣷⣶⣶⣿⣿⣿⣿⣾⣿⣿⣿⣧⣤⣤⣶⣾⣿⣿⣿⣿⡿⠟⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣶⣿⣿⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠋⠉⠛⠻⠿⠁⠀⠀⠀⠈⠙⣿⣿⣿⣷⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⣿ ⠼⠟⠋⢹⣷⠀⠀⢀⣼⣿⠿⢟⣻⡍⠀⠶⢬⠌⢉⣉⣥⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⣴⣾⣿⡟⠿⢿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⣿⣶⣄⣠⣵⣾⣿⣿⣿⣷⣾⣿⣿⣿⣶⣦⣴⣄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⠉⠛⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢩⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⠟⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠽⠿⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠂⠀⠀⠀⠀⠀⢤⣤⣤⣼⣿⣿⡿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⡤⠜⠋⣱⣿⠿⢿⣿⣿⣿⠿⣿⣿⣿⢿⣷⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⠟⠿⠟⠋⠀⠀⠀⣻⡀⣤⣀⡻⠛⣷⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠛⠛⠛⠛⠋⠉⠁⠙⠉⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢶⡶⠖⠰⠰⠧⢠⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡡⠀⣀⢀⣀⣄⣉⠽⣿⣿⣿⡗⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⢡⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣵⣷⣶⣾⣿⣿⣿⣾⣿⣿⣿⣯⣤⣤⣶⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣰⣿⣿⣿⣿⣿⠟⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠉⠉⠉⠉⠻⠀⠀⠀⠀⠈⢙⣿⣿⣧⣄⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⡀⢀⠀⠀⣿⣿ ⡿⠛⠛⣿⡆⠀⠀⣴⣿⡿⢿⣻⣍⠁⡴⢦⡬⢉⣩⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣶⣾⣿⠿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⠂⠀⠐⢿⣿ ⣷⣤⣀⣭⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣦⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠻⠟⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠉⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠈⠉⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⡿⠟⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠽⠿⠯⠿⠽⠽⠭⠭⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠄⠀⠀⠀⠠⠤⣤⣤⣴⣿⣿⣿⠟⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣤⠤⠼⠋⣼⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⣀⣀⣾⣿⣿⠿⠿⠛⠉⠀⢀⢘⣯⣀⣄⣈⡿⠛⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢐ ⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⣿⣿⣿⣿⣿⠿⢿⣿⠿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣾⣶⣶⣶⢷⣾⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⢫⡋⣀⣨⣻⡿⣿⣿⣿⣿⡗⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢉⣵⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣶⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⣾⣿⣿⣿⣿⡿⠋⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣾⣿⣿⣤⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠛⠋⠉⠀⠈⠉⠉⠛⠀⠀⠀⠀⠈⢹⣿⣿⡇⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠀⠀⠀⠠⣿⣿ ⠟⠛⣻⣷⠀⠀⢠⣼⣿⠿⣿⣿⡍⠠⠶⣬⠌⣉⣭⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠚⠹⠀⠀⠐⣿⣿ ⣦⣄⣨⣵⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣶⣴⣤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠿⠟⠀⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢰⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣷⣐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⠛⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣦⣾⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀ ⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠋⠉⠉⠁⠉⠈⠙⠙⠃⣠⣀⣠⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠁⠀⠀⢸⣿⣿⣿ ⠛⢿⣷⡀⢀⣠⣾⣿⣿⣿⣭⡁⠴⠶⡤⢈⣭⣭⣥⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⡁⠹⢶⡇⠀⢹⣿⣿⣿ ⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠿⠛⠛⠛⠛⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣶⡤⠉⠙⠀⣼⡿⢿⠟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⢿⣿⣿⣴⡀⢠⣿⣿⢁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⣹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡈⠉⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⠟⠃⠀⠈⠉⠁⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⡿⠿⠭⡿⠿⠿⠯⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠄⠀⠀⠤⠤⢤⣤⣤⣼⣿⣿⣿⠟⠉⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣠⣤⣴⣶⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⣤⠄⠘⠋⣾⡿⢿⣿⣿⣿⣿⠿⢿⣿⣯⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀ ⠀⠀⠀⣀⣀⣀⣠⣿⣿⠟⠛⠛⠉⠀⢀⣀⣀⣵⣤⣶⣤⣼⣛⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⠂⠀ ⠀⠀⠀⠙⠛⠛⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀ ⠀⠀⠀⣄⣀⢀⣿⣿⣿⣯⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀ ⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡂⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢲⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢻⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣿⣿⣿⣿⣿⡿⠟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀ ⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠟⠋⠛⠛⠉⠈⠛⠛⠛⢠⣄⣠⣴⣤⣀⣀⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⢻⠁⠀⠀⣿⣿⣿⣿ ⠛⣿⣦⠀⣀⣴⣿⡿⣿⣯⣍⠀⠶⢦⠄⢩⣭⣭⣍⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⢛⣺⡛⠆⠴⢿⣿⣿⣿ ⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠛⠟⠉⠉⡉⠙⠻⢿⣿⣿⣿⣿⣾⣭⠖⠂⢰⣾⡿⠿⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⢿⣤⡠⢸⣿⡧⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⢉⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠙⠉⠉⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠈⠋⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠄⠀⠀⠠⠤⣤⣤⣤⣾⣿⣿⡿⠏⠉⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣦⡤⠀⠘⢉⣾⠿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⡿⠿⠟⠀ ⠀⠀⠀⡀⢄⢀⣼⣿⣿⠛⠛⠛⠁⠀⢀⣀⢈⣵⣤⣖⣦⣼⣟⣻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀ ⠀⠀⠈⠉⠄⢺⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠠⢀⣀⣼⣿⣿⣿⡭⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠐⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣏⣵⣿⣿⣿⣿⣿⣿⣿⠃⡀⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣿⣿⣿⣿⣿⡿⠟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⣸⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⣿⡏⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠟⢡⣄⣠⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠋⢙⣍⣽⣃⣀⣸⣿⣿⣿⣿ ⢻⣿⣆⣀⣠⣾⣿⣿⣿⣿⣅⢰⠶⣦⠌⣩⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣱⣐⣿⣿⣿⣿⣶⢿⣿⣿⣿⣿ ⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠟⠛⠉⣙⠙⠿⣿⣿⣿⡯⣿⣿⣿⣷⠏⣿⣿⣿⣿⢟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠯⢄⣿⣿⣿⣵⡾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⣉⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠘⠟⠉⠙⠋⠛⠛⠉⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⢿⡿⡿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⠐⠲⠀⠤⢤⣤⣤⣴⣿⣿⣿⡿⠋⠉⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣤⠤⠀⠘⢡⣿⠿⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟ ⠀⠀⣀⣀⣤⣬⣿⣿⣿⠛⠛⠉⠀⠀⣀⡀⢈⣷⣶⣶⣶⣼⡟⢛⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀ ⠀⠀⢩⠟⠙⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀ ⣀⠀⢀⣤⣄⣿⣿⣿⣿⠄⠀⢀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⠇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣰⣾⣧⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣼⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⡿⠟⢁⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣼⣿⣿⣿⣿⣿⡟⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀ ⣿⡃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⡿⡿⡿⠿⡷⣤⣤⣤⣤⡀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠛⢩⠯⣯⣃⢀⣿⣿⣿⣿⣿ ⣿⣷⣀⣀⣴⣿⣿⣿⣿⣥⣠⠾⣶⠦⣠⣼⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣧⣰⣽⣿⣿⣿⡻⡔⣿⣿⣿⣿⣿ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠟⠙⠹⣿⣿⣻⢿⣿⣿⡿⠛⠟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠉⠛⠋⢺⣿⣯⡓⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘⡿⠛⢿⡿⢿⣿⡿⠟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⣿⢻⡿⢻⣿⢛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠖⠒⠒⠠⠤⢶⣤⣶⣾⣿⣿⣿⠟⠉⠈⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠠⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣿⣿ ⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣥⠤⠄⠀⠉⣠⣿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿ ⠀⠀⣀⣠⣤⣼⣿⣿⡍⠉⠉⠀⠀⣀⣠⠀⢩⣶⣶⣷⣦⣾⡿⢻⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠿⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⢀⣤⣤ ⠀⠈⠹⠧⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠟ ⠀⡀⣄⣠⣾⣿⣿⣿⣷⠀⠀⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣀⣤⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀ ⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⣤⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⡟⠙⠋⠻⣽⣩⣡⢀⣿⣿⣿⣿⣿ ⣿⣆⣀⣠⣾⣿⢿⣿⣿⡄⣴⠶⣦⠄⣤⣽⣯⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠁⠁⠉⠀⠸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣤⢭⣺⣿⣿⣿⣽⣴⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡛⠛⣿⣿⣿⣿⣿⣿⡿⠿⢟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠟⠛⠋⠉⠀⠁⠀⠀⠀⠀⠉⠈⠁⠘⠛⠛⢿⣿⣿⡇⠈⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣄⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠘⣿⠿⢿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣩⣙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⡿⠿⡿⠻⡻⢛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠖⠒⠒⠢⢤⣴⣦⣶⣿⣿⣿⡿⠛⠁⠘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿ ⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣤⠤⠀⠀⠉⣰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⡄⠀⠀⠀⠀⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿ ⠀⢀⣀⣤⣬⣿⣿⣿⡉⠉⠉⠀⠀⣀⡤⠀⣹⣶⣴⣶⣦⣾⠿⠿⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠿⠿⠿⠛⠛⠛⠁⠀⠀⠀⢀⣠⣤ ⠀⠈⠭⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿ ⠀⢀⣈⣽⣿⣿⣿⣿⣆⠀⢀⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣄⡂⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡷⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀ ⡟⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⣄⠀⢸⣿⣿⣿⣿⣿⣿⠇⠙⠛⠫⣽⣭⡅⣼⣿⣿⣿⣿⣿ ⣿⣄⣀⣴⣿⣿⣿⣿⣯⢀⡶⢶⡤⢠⣤⣿⣧⣵⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠈⠉⠁⠉⠁⠀⠁⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⠿⡻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠟⠛⠋⠉⠁⠊⠈⠉⠉⠁⠉⠈⠈⠛⠿⢿⣿⣿⠅⠀⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢈⣄⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠉⣿⡿⢿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠁⠀⠀⠁⠀⠙⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻ ⡿⠟⡛⠿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠦⢴⣦⣶⣾⣿⣿⣿⡿⠛⠁⢹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣴⣶ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡤⠤⠀⠈⠋⣰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⣠⣤⣼⣿⣿⣯⠉⠉⠁⠀⢀⣀⡤⠀⢻⣦⣴⣾⣬⣿⡿⢿⣷⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠿⠿⠿⠟⠛⠉⠁⠀⠀⢀⣀⣤ ⠀⠙⠿⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿ ⢀⢄⡥⣼⣿⣿⣿⣿⣆⠀⢠⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀ ⡃⠀⠀⢹⣿⣿⣿⣿⣿⣾⡿⡯⢴⣾⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⢀⣠⣤⣄⠀⢸⣿⣿⣿⣿⣿⡇⠀⠉⠁⠈⠁⠈⠀⠨⣿⣿⡏⠀⠀ ⠧⢀⣠⣾⣿⠟⣫⣭⡄⠀⠒⠦⠀⢠⣤⣶⣀⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠉⠉⠉⠉⠁⠉⠈⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠀ ⣾⣿⣿⣿⣷⣿⣿⣿⣷⣤⣶⣦⣀⠸⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⢿⡿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠙⠋⠙⠙⠉⠛⠉⢉⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢤⣤⣤⣾⣿⣿⣿⠟⠋⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠂⠀⠀⠀⠀⢀⣤⣴⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⣤⠤⠀⠀⠋⢱⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣤⡀⠀⠀⠀⠀⣼⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⢾⠀⡆⡙⢡⠈⢳⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⣤⣴⣶ ⠀⠀⠀⠀⣸⣿⣿⡉⠉⠉⠁⠀⢀⣠⠤⠀⢿⣅⣠⣤⣌⣽⣿⣿⣧⣶⣿⣿⡟⣾⣿⡇⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⡏⢀⣶⡇⢸⠀⣿⣀⣤⣶⣿⣿⣿⡿⠿⠛⠻⠟⠿⠿⠿ ⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⡿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠲⢶⠶⠦⣤⠤⣤⣽⣿⣗⣚⣩⣷⣶⣶⠟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣤⣤⡀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠃⣸⠀⠇⣸⠀⠶⡇⢠⣸⠇⣹⠉⡍⢻⠙⣛⡟⢻⠒⠖⠶⢦⠀⠀⠀⣿⣿⣿⣷ ⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⣀⡿⡏⢀⠃⡼⠀⢾⠛⡆⢸⠀⡟⢠⠃⣸⠀⣹⠁⠈⢰⡟⢀⡟⠀⠀⠀⢿⣿⣿⣿ ⣀⣀⠀⢸⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠚⠓⠒⠚⠶⠧⠤⠤⢧⣤⣽⣀⣇⣸⣇⢸⠇⠀⠀⠀⠈⠙⢿⣿ ⣼⣿⣿⣶⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⣿⣧⡸⠿⢿⠿⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⢻⣿⣿⣿⣿⣷⡼⣿⡆⢴⣿⣷⣿⡿⠿⠿⣿⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⢀⣠⣤⡄⠀⢸⣿⣿⣿⣿⣿⠁⠀⠈⠁⠈⠁⠈⠀⢸⣿⣿⡇⠀⠀ ⡦⠀⣠⣾⡿⢟⣫⣥⠀⠐⠒⠄⠀⣠⣤⣦⣠⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠙⠉⠉⠉⠀⠻⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀ ⣾⣿⣿⣿⣷⣿⣿⣿⣧⣤⣶⣤⡀⠽⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠙⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⠛⠁⠀⠈⢿⡿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣟⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠍⠉⠉⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢤⣤⣤⣾⣿⣿⣿⠟⠋⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠆⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣥⣤⡄⠀⠀⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣤⡀⠀⠀⠀⠀⣼⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢾⠀⡆⡙⢡⠈⢳⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀ ⠀⠀⠀⠀⣸⣿⣟⡉⠛⠋⠉⠀⢀⡠⠤⠀⠾⣁⣠⣤⣉⣽⣿⣿⣷⣾⣿⣿⡿⣾⣿⡇⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⡏⢀⣶⡇⢸⠀⣿⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣷⣶⣾⣿ ⠀⠀⠀⠨⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⣿⣷⣶⣿⣿⡿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠲⢶⠶⠦⣤⠤⣤⣽⣿⣗⣚⣁⣳⣦⣶⣿⣟⠛⠿⠿⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛ ⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠃⣸⠀⠇⣸⠀⠶⡇⢠⣸⠇⢹⠉⡍⢻⠙⣛⡟⢻⠛⠟⠷⢶⡀⠀⠀⢠⣶⣤⣄ ⠀⠀⠀⢸⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡿⡟⠀⠃⡼⠀⢾⠛⡆⢸⠀⡟⢠⠃⣸⠀⣹⠁⠈⢰⡟⢀⡟⠀⠀⠀⣿⣿⣿⣿ ⣀⠀⠀⢸⣯⣿⣿⣿⡅⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠚⠓⠒⠚⠶⠧⠤⠤⢧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⢿⣿⣿⣿ ⣭⣿⣷⣶⣿⣿⣿⣿⣷⣶⡶⠀⠀⠀⣿⣇⡹⡿⡿⠟⠛⠁⠀⠀⢼⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠻⣿⣿ ⠃⠀⠘⣿⣿⣿⣿⣿⣶⣾⣿⡤⢴⣿⣿⣿⡿⠿⢿⣿⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⡀⣀⣤⡀⠀⣽⣿⣿⣿⣿⣿⠀⠀⠈⠁⠈⠁⠈⠀⢸⣿⣿⡇⠀⠀ ⡆⠀⣰⣿⡿⢛⣫⣭⠀⠐⠲⠄⠀⣤⣤⣄⣰⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⠛⠛⠛⠟⠃⠛⣿⣿⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀ ⣾⣿⣿⣿⣶⣿⣿⣿⣆⣰⣶⣄⡀⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠉⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠸⠃⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⢿⡿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠭⠍⠝⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣤⣤⣤⣾⣿⣿⣿⠟⠛⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⠀⠀⠀⠀⢀⣤⣤⣤⣶⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣏⣀⣀⠀⠀⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⣤⡀⠀⠀⠀⠀⣼⣿⡟⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢾⠀⡆⡙⢡⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣟⡙⠛⠛⠉⠁⢀⡠⠄⠠⡾⡁⢠⣍⣉⣻⣿⣿⣿⣾⣿⣿⡿⢮⣿⡇⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⣀⣤⣤⣦⣶⣶⣤⣀⣀⣠⣤ ⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠲⢶⠶⠦⣤⠤⣤⣽⣿⣗⣚⣁⣳⣦⣶⣧⣴⣾⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠃⣸⠀⠇⣸⠀⠶⡇⢠⣸⠇⢹⠉⡍⢻⠙⣛⡟⢻⠛⠟⠿⢷⡄⠀⠀⠀⠈⠈⠁ ⠀⠀⠀⢸⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡿⡟⢀⠃⡼⠀⢾⠛⡆⢸⠀⡟⢠⠃⣸⠀⣹⠁⠈⢰⡟⢀⡿⠁⠀⠀⣠⣶⣶⡄ ⠀⠀⠀⢸⣯⣿⣿⣿⡅⠀⠀⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠚⠓⠒⠚⠶⠧⠤⠤⢧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠠⣿⣿⣿⣿ ⣭⣿⣷⣶⣿⣿⣿⣿⣷⣶⡶⠀⠀⠀⣾⣆⡹⣿⣿⠿⠻⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢻⣿⣿⣿ ⠂⠀⢹⣿⣿⣿⣿⣿⣶⣿⣷⠠⣴⣿⣾⣿⡿⠿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣄⠀⢀⣀⡀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠈⠁⠈⠁⠈⠀⣰⣿⣿⠀⠀⠀ ⠀⢀⣼⣿⡿⢟⣭⡅⠀⠶⠦⠀⢈⣭⣥⢄⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠛⠛⠻⠛⠛⠈⠻⣿⣷⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀ ⣾⣿⣿⣿⣶⣿⣿⣷⣦⣤⣤⣀⠨⠟⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⣿⠄⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠉⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡯⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣗⣶⣿⣿⣿⣿⡿⠛⠉⠀⠈⣿⡿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠻⠋⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣄⣠⣾⣿⣿⣿⠿⠛⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⣤⣄⣴⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣉⣀⣀⠀⠐⠟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣦⣤⡀⠀⠀⠀⠀⣾⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢾⠀⡆⡙⢡⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣏⠛⠛⠛⠉⠉⢀⣀⠀⢠⡾⠋⢉⣌⣙⣻⣿⣿⣿⣾⣿⣿⡿⢾⣿⡇⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⣿⣿⣷⣶⣿⣿⡿⢿⣿⣿⣿⡅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠲⢶⠶⠦⣤⠤⣤⣽⣿⣗⣚⣁⣳⣦⡶⢃⣀⣠⣴⣶⣾⣿⣿⣿⣿⣷⣦⣤⣴⣦ ⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠃⣸⠀⠇⣸⠀⠶⡇⢠⣸⠇⢹⠉⡍⢻⠙⣛⡟⢻⠛⠟⠿⢿⡟⠙⠛⠛⠛⠿⠿ ⠀⠀⠀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡿⡟⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢠⠃⣸⠀⣹⠁⠈⢰⡟⢀⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣽⣿⣿⡅⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠚⠓⠖⠚⠶⠧⠤⠤⢧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⢀⣶⣶⣦⡀ ⣙⣷⣶⣾⢿⣿⣿⣿⣷⣶⡶⠀⠀⠀⣾⡌⠻⣿⡿⠿⠏⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⢿⣿⣿⣿⣿⣿⣀⢠⣿⡀⠈⣸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠁⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⠂⠀⠀⠈⠁⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⡿⠿⠛⢙⡿⠁⠸⡿⠛⡻⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⠀⠀⠀⣤⣦⡀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀ ⣤⣿⣿⣟⣩⣿⣿⠀⠀⢀⡀⠀⢾⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡆⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠼⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣠⡄⣠⣿⣿⣿⣿⣿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠛⠛⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠙⠉⠙⠟⠛⠻⠿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⣽⣿⣿⣿⣿⡟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢤⣶⣾⣿⣿⣿⠟⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣼⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢾⠀⡆⡙⢡⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡦⠀⠀⠀⠈⠛⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⠀⠉⠁⠀⠀⠀⠀⠀⠘⢟⣅⣀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⢶⠴⠦⣤⠤⣤⣙⣿⣓⣊⣀⣳⣦⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠂⣸⠀⠃⣸⠀⠶⡇⢠⣨⠃⢹⠉⡍⢻⠙⣛⡗⢻⠛⠟⠿⢿⣶⣶⣦⣄⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢠⠃⣸⠀⣹⠁⠈⢰⡇⢀⣿⠿⠿⠿⠿⢷⣤⣀ ⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠚⠓⠶⠺⣶⣧⣤⣤⣧⣤⣹⣀⣇⣸⣇⢸⡏⠀⠀⠀⠀⠀⠈⠀ ⣀⠶⠶⣾⠿⣿⣿⣿⣷⠶⠆⠀⠀⠀⠀⠈⢹⣿⣿⣿⡿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡗⠈⢹⣇⠀⠎⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⠋⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⡿⠆⠸⡿⠀⢰⣿⠿⣿⠿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠀⠀⠀⠀ ⢀⣿⣿⡟⢻⣿⡆⠀⠈⠁⠀⠀⣵⣶⢂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⢿⣦⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣄⣠⣶⣤⠀⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⣤⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠿⢿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠿⠿⠿⣿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⡿⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⡆⣴⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⡇⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⠛⠛⠛⠁⠀⠀⠀⠀⠰⣿⠋⠁⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣿⡇⠛⠁⠀⠀⠀⠀⠀⠀⢠⠒⠒⢶⠶⠦⣤⠤⣤⣙⣿⣓⣊⣀⣓⣦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠂⣸⠀⠃⣸⠀⠶⡇⢠⣈⠃⢹⠉⡉⢻⠉⣛⡖⢲⠒⠒⠶⢶⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡼⠀⢶⠛⡆⢸⠀⡏⢀⠃⣸⠀⣹⠁⠈⢰⡇⢀⣿⣿⣿⣿⣦⣀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠚⠓⠒⠺⣶⣧⣤⣤⣧⣤⣹⣀⣇⣸⣇⢸⡿⠉⠉⠉⠛⠛⠛⠂ ⠀⠶⠶⣾⣿⣿⣿⣿⣷⠶⠆⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⡇⠸⠿⠀⠀⡜⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠉⠉⠙⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡧⠀⣼⣇⠀⢠⣿⣿⣿⣿⣿⢿⣯⣼⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⢀⣿⣿⣿⢿⣛⡁⠀⠨⠃⠀⠘⣋⣉⠉⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣤⡀⣸⣿⣿⡟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⣾⣿⣿⣤⣾⣿⡇⠀⢀⣄⠀⠀⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢉⣽⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠘⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣾⣿⣿⡿⠟⠋⠀⠀⠈⢻⣿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋⠁⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡀⣠⣤⣶⣶⣶⣶⣶⡶⠶⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠲⣶⣿⣿⣿⣿⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣏⠀⠀⠀⠀⠀⣾⡇⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⡏⠀⣶⡇⢸⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠉⣿⡿⠋⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⡇⣿⠿⠋⠁⠀⠀⠀⠀⢠⠒⠒⢦⠴⠤⣤⠤⣄⣉⣻⣓⣊⣀⣱⣦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢸⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⣸⠀⠃⣸⠀⠶⡇⢀⣈⠃⢹⠉⡉⢻⠉⣛⡖⢲⠒⠒⠶⢤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡼⠀⢶⠛⡆⢸⠀⡏⢀⠃⡸⠀⣹⠀⠈⢠⡇⢀⣾⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠦⢧⣤⣤⣧⣤⣹⣀⣇⣸⣇⢸⣿⣿⣿⣿⣷⣦⡀⠀ ⠀⠖⠶⣾⣿⣿⣿⣿⣷⠶⠆⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠛⠻⣷ ⢰⣿⣿⣿⣿⣿⡄⢸⣿⠀⠘⡛⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⡇⠀⣩⡄⠀⢃⣾⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠙⠋⠀⠀⠀⠻⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⠇⠀⠻⠇⠀⢸⡿⠟⠿⠛⣋⣸⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⠋⣭⣿⡄⠀⠀⠀⠀⠀⣶⡞⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⡀⣴⣷⣄⠀⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢻⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⠿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⢀⣼⣿⣿⡿⠛⠋⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠛⠛⠻⢿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠐⠛⠉⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠛⢛⣿⣿⣿⣿⡏⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠛⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡿⠃⠀⠀⠀⠀⢰⡆⣾⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⡏⠀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣫⡀⠀⠀⠀⠀⠛⢿⣿⡿⠟⠃⣤⣼⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣼⡇⣿⣿⡿⠟⠉⠀⠀⠀⢠⠒⠒⢦⠤⠤⢤⠤⢤⣙⣿⣓⣊⣀⣱⣦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣟⠋⠛⠛⠁⠀⠀⠀⠀⠀⠾⠏⠀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⠿⠋⠀⠀⠀⠀⠀⠀⢸⠀⠂⣸⠀⠃⣸⠀⠶⡇⠀⣈⠃⢸⠉⡉⢻⠉⣛⡖⢲⠒⠒⠶⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡏⢀⠃⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠂⠧⠤⠤⣧⣤⣹⣀⣇⣸⣇⢸⣿⣴⣦⣄⠀⠀⠀⠀ ⠀⠖⠶⣶⣿⣿⣿⣿⣷⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠿⠿⠿⣿⣷⣤⠀⠀ ⢀⣠⣤⣴⣿⣿⠀⢠⡄⠀⢻⣿⢇⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⡆⠸⢿⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣿⣿⣿⣿⣿⡇⠀⣾⡆⠀⢰⣿⣽⣿⣿⡿⢿⡏⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠈⠀⠀⠀⠈⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⡿⢟⠁⠀⠈⠁⠀⠙⠋⣉⠉⣠⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣠⣾⣿⡆⠀⢀⡀⠀⠰⡿⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣷⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣩⡿⠻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠋⠁⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⢻⡿⢿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⢀⠈⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⣤⣤⣀⣨⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡿⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠰⢾⠀⠆⡙⢁⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣤⣤⣤⣶⣶⡶⠀⠀⠀⠀⠀⠀⢸⠇⠰⡇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣟⠛⠛⣿⣿⣿⣿⣿⣿⣦⣌⡁⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⠛⠛⠋⢡⠒⠒⢦⠤⠤⢤⠤⢤⣙⣿⣓⣊⣁⣑⣤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⢨⣿⠛⠉⠀⠐⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⠀⠀⠀⠀⢸⡇⣿⣿⡿⠋⠁⠀⠀⠀⣸⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡖⢲⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⠃⠛⠉⠀⠀⠀⠀⠀⠀⢻⡀⡿⡏⠀⠃⡸⠀⢶⠓⡆⢸⠀⡏⢀⠃⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠂⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⡀⠖⠶⣶⢿⣿⣿⣿⣷⡶⠆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢁⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣶⣧⠀⢀⡀⠀⢿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣶⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⡀⠸⣧⠀⠈⡏⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣧⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⡇⠀⣿⡀⠀⢠⣟⣻⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣭⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠀⠀⠀⠈⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⠃⠀⠙⠃⠀⠻⠟⠛⠛⢉⣁⣈⢃⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣟⣉⣴⣾⡄⠀⠀⠀⠀⢰⣷⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⡀⣾⣷⡆⠀⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⢉⣿⡿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠟⠋⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣁⣀⣀⣀⣤⣿⣿⡿⠛⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠉⠙⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣴⣦⣀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠰⢾⠀⠆⡙⢁⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⢸⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋⠉⠀⠀⢸⣿⣿⣿⣿⣿⠿⢟⢿⣿⣿⣿⣿⣿⣦⣈⠉⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⠛⠿⠿⢻⠛⠓⢶⠤⠤⢤⠤⢤⣙⣿⣓⣊⣀⣱⣦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡅⠀⠀⠀⠀⠀⠉⣿⡿⠛⠉⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⡇⣿⣿⣿⠿⠛⠀⠀⠀⢸⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡖⢲⠒⠒⠶⠦⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⣾⣿⣋⠉⠛⠁⠀⠀⠀⠀⠀⠀⠛⣀⡠⣶⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⡇⠿⠟⠁⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡏⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠂⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀ ⢿⠖⠶⣶⠿⣿⣿⣿⣿⡶⠆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣆⠀⠀⠀⠀⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⢯⣮⣷⣶⣤⣄⣈⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣾⣿⣿⣿⣿⠀⢸⣇⠀⠘⡏⢸⣿⣿⣿⣿⣿⣿⣿⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠀⣹⠀⠀⢁⡞⢿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣏⣻⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠃⠀⠀⠙⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠃⠀⠻⠃⠀⢾⠟⠛⠛⠛⣉⠈⠂⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⡿⠋⣥⣶⠀⠀⠀⠀⠀⢠⣶⠖⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⢀⣼⣶⡄⠈⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢻⡿⣷⣷⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠾⠟⠁⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠁⠀⠀⠀⣠⣽⣿⣿⣿⠛⠋⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠚⠋⠉⠛⠛⠛⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣤⣦⣄⣠⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣿⣿⣿⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢸⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣯⡩⠛⠃⠀⠀⠀⠀⠀⣶⣿⣷⣶⣾⠿⣿⣿⣿⠛⠓⢦⠴⠤⢤⠤⢤⣉⣿⣓⣊⣁⣑⣤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡆⠀⠀⠀⠀⠀⣠⣿⣿⣿⡛⠀⠀⠀⠀⠀⠛⢻⣿⠿⠋⠁⣠⣀⣿⡿⣿⣿⣿⣿⡻⣷⡆⠀⠀⠀⠀⡄⣿⣿⣿⣿⠿⠀⠁⠀⢸⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡗⢲⠒⠒⠲⠦⡀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⢠⣿⠿⠛⠿⠗⠀⠀⠀⠀⠀⠀⠿⠃⠀⣤⣤⣉⣿⣿⣿⣿⣿⣿⣯⣯⣾⡏⠀⠀⠀⠀⡇⣿⡿⠛⠁⠀⠀⠀⠀⢻⡀⡿⡏⠀⠃⡘⠀⠶⠓⡆⢸⠀⡏⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠂⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⠲⣶⠏⣿⣿⣿⣿⣶⠖⠀⠀⠀⠀⠸⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡄⠀⠀⠀⠐⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⢛⣬⣭⣤⣤⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⣾⣿⣿⣿⠀⢸⡆⠀⠹⡏⣰⣿⣿⣿⣿⣿⣿⣿⣩⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠈⣧⠀⠀⢁⡿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠏⠀⠀⠙⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠀⠿⠆⠀⣾⡿⠿⠿⠛⠋⠹⠄⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠛⣩⣤⠀⠀⠀⠀⠀⢠⣤⡆⢀⣾⣿⣷⣶⡿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣾⣿⣿⡆⠀⣴⣦⡀⠈⢋⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠘⣷⣶⣆⣜⣧⣀⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣧⣯⣿⣿⣿⣿⣿⣦⠀⠤⠀⠃⠉⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⡾⣏⣿⣟⠛⠛⠛⠋⠀⠀⠀⠀⠘⠛⠛⠛⠊⠛⣧⡟⣼⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠿⠿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⠶⠶⠶⠂⠀⠻⠷⠶⠶⠀⠀⣀⠃⡏⠍⠸⠛⠙⠻⠿⠿⠟⠛⠟⠈⠀⠀⠀⠀⠀⠀⡠⠤⢤⣤⣤⣄⣀⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⣵⢞⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠉⠙⠉⠉⠋⠙⠛⠛⢛⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣺⠷⣬⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠿⠃⠀⠀⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⠆⠁⠀⠀⣴⣶⣶⣤⣴⢶⣶⣶⣿⠛⠓⢶⠴⠤⢤⠤⣤⣙⣿⣓⣊⣁⣳⣦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠻⢿⣿⡿⠟⠃⢀⣈⣻⣿⣿⣿⣿⣿⡿⢷⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠋⠉⣹⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡟⢲⠒⠒⠶⢦⡀⠀⠀⠀⠀⠀⢀ ⢹⣇⠀⠀⠀⠀⣾⣿⠿⠿⠷⠂⠀⠀⠀⠀⠀⢼⠏⠀⣠⣀⣘⣿⣿⣿⣾⣿⣿⣿⣿⣽⣿⠀⠀⠀⠀⡀⣿⣿⠿⠋⠀⠀⠀⠀⢻⡀⡿⡏⠀⠃⡘⠀⠶⠓⡆⢸⠀⡏⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠘ ⠀⢿⡀⠀⠀⢸⣿⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣬⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠂⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠾⡷⣶⠏⢿⣿⣿⣿⣶⠶⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⠀⠀⣀⡀⠀⠀⠀⢰⣿⣿⡏⢩⣿⣿⣿⣿⣿⣿⣿⠛⣝⣛⣋⣉⡉⠉⠻⣶⣾⣿⣿⣿⣿⣿⣦⣤⣴⣾⣦⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣴⣾⣿⣧⠀⢰⡄⠀⢻⡟⣱⣿⣿⣿⣿⣿⣿⣿⡛⠈⣽⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠘⣇⠀⠠⠃⢿⣿⣿⣿⣿⣿⡿⣯⣿⣾⣿⣿⣿⣿⠟⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠋⠉⠒⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠀⣿⡄⠀⣼⣶⡾⡿⠿⠋⢫⡄⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⢛⣉⠀⠀⠀⠀⠀⢈⣀⡄⢀⣶⣶⣦⣴⡶⣾⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⣴⣿⣿⡀⠀⣠⣄⠀⠸⠋⣰⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠸⣿⣦⢆⣝⣏⠀⢷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣧⣯⣿⣿⣿⣿⣿⣇⠀⠀⠀⠟⠉⢿⣿⣿⣿⣶⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣛⣿⣿⡼⣏⣿⣟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠙⠛⠛⠊⠟⣯⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣛⣿⣿⣿⣿⡿⣿⣿⣿⣿⡶⠄⠒⠒⠀⠀⠐⠲⠶⠶⡖⠁⣀⠋⡏⠍⠈⠿⠿⠿⣿⣿⣿⡿⣿⡯⠃⠀⠀⠀⠀⠀⡠⠤⢤⣤⣤⣍⣁⣀⡉⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣮⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡰⣿⣞⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⠛⠁⣿⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣯⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⠆⠁⠀⠀⣠⣤⣤⣀⣀⣀⣤⣤⣴⠒⠒⢶⠶⠤⢤⠤⢤⣝⣿⣗⣚⣁⣳⣦⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⡯⠉⠀⠀⠀⠸⣿⣿⣿⡿⠟⠉⠉⠻⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠈⠿⠛⢿⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣛⡟⢲⠒⠒⠶⢦⠀⠀⠀⠀⠀⠀⢈ ⠀⠸⣷⠀⠀⠀⢀⣼⣿⣿⣿⣤⠀⠀⠀⠀⠀⢀⣼⠋⠀⡀⠀⠛⣿⣾⣽⣿⣿⣿⡿⣆⣿⡇⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⢻⣀⡿⡏⠀⠃⡘⠀⠶⠓⡆⢸⠀⡏⢀⠃⠸⠀⣹⠀⠈⢠⡇⠀⡾⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⢻⡄⠀⠀⢸⣿⣩⣀⠉⠁⠀⠀⠀⢸⡄⠈⢁⣤⣌⠙⣻⣿⣮⣼⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠂⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠺⣷⠏⢶⢿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣟⡛⠉⠛⠻⣶⣾⣿⣿⣿⣿⣷⣄⣀⣤⣾⣄⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣶⣿⣇⠀⢠⡀⠈⢿⡿⣡⣿⣿⣿⣿⣿⣿⣿⠟⠈⢹⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠘⡇⠀⢠⠃⣿⣿⢿⣿⣿⣿⡿⣏⣿⣶⣿⣿⣿⣿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠀⣿⡀⠀⣰⣤⣿⣿⠿⠟⢻⣁⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠟⣋⠀⠀⠈⠀⠀⢉⣁⡀⠀⣤⣶⣤⣤⡴⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣇⣴⣿⣿⠀⠀⢀⡀⠀⠸⠟⣡⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣷⢂⣟⡏⠈⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⡇⠀⣴⣿⣿⣿⣿⣿⣧⣯⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⠋⢾⣿⣿⣷⣤⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⢿⣿⣿⣿⡼⣏⣿⣟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⠛⠛⢊⡿⣯⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢟⣻⣿⣿⣿⡿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠒⠶⠶⣶⠏⣀⠻⡟⠍⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⡠⠤⢤⣤⣤⣽⣻⣉⡙⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣮⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡰⣿⣮⡞⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠏⢹⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⠇⠀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣶⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⠆⠁⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣠⠒⠒⢶⠶⠤⢤⠤⢤⣽⣿⣗⣚⣁⣳⣦⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠘⣿⡀⠀⠀⠀⠀⢀⣾⣿⣯⠉⠉⠀⠀⠀⣿⣿⣿⣿⡿⠏⠉⠹⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠙⣿⠿⣿⠀⠂⣸⠀⠂⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡟⢲⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⢹⣇⠀⠀⠀⢠⣿⣿⣿⣅⡀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠲⣶⣿⣯⣽⣿⣿⡿⢮⢹⣿⠀⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡎⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⣿⡀⠀⠀⣿⣟⡉⠉⠉⠁⠀⠀⢠⡇⠀⠉⣤⣄⠛⠶⣶⣷⣮⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠂⠧⠤⠤⠧⣄⣹⣀⣇⣸⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠲⣾⡿⢶⢴⣿⣿⣿⡷⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠟⠁⠀⠀⠀⠀⠈⠀⢸⣻⣿⡇⢟⣿⣿⣟⣿⡿⢿⣿⠿⣻⣿⡟⠛⠛⠛⠻⣤⣼⣷⣾⣿⣿⣧⣀⣀⣀⣼⡀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣴⣿⡇⠀⢠⡀⠈⣿⡿⣡⣾⣿⣿⣿⣿⣿⣿⠿⠀⢸⣿⣿⣿⣿⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠸⡇⠀⢈⠆⣿⣿⣿⣿⣿⣿⣿⡟⣷⣴⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠀⣷⡀⠀⣰⣤⣿⣿⣿⠿⢛⠁⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⣿⣿⣿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠈⠀⠀⠀⠸⣿⣿⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠟⠛⠀⠀⠉⠁⠀⠛⠉⡁⠁⣤⣤⣌⣡⡵⣿⣼⣼⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣷⢾⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣏⣠⣾⣿⠀⠀⢀⠀⠀⢸⠟⢡⣾⣿⣿⣿⡿⣿⣷⣿⣯⣿⣿⢿⣿⣷⢰⣿⡿⢊⣿⠟⠈⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣆⢰⣿⣿⡆⠀⣰⣿⣿⣿⣿⣿⣧⣯⣿⣿⣟⣾⣿⣧⠉⠀⠀⣽⠏⢾⣿⣾⣶⣼⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣰⣿⣿⡿⠿⣿⣿⡼⣏⣿⣟⡛⠛⠛⠛⠃⠀⠀⠁⠀⠀⠛⠛⢋⣿⣯⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠿⢟⣿⣿⣿⡿⣿⢿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠐⠐⠲⣶⠟⣉⢻⡟⠍⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡕⠀⠀⠀⠀⠀⡠⠤⢤⣤⣤⣼⣿⣟⡛⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣾⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡰⣿⣾⡞⠀⠀⠀⠀⠈⠙⠛⠛⠛⠙⠛⠓⠀⠀⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢻⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⠟⢻⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⠇⠀⣶⡇⢸⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⠆⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⠒⠒⢶⠶⠦⢤⠤⢤⣽⣿⣗⣚⣉⣳⣦⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⢹⣿⠂⠀⠀⠀⠀⣰⣿⣿⡛⠛⠁⠀⠀⢿⣿⣿⣿⣿⠟⠛⠋⣿⣿⣿⣿⣿⣿⣧⣄⡉⠀⠀⠀⠀⣾⣿⣿⣿⣿⠻⣿⣿⣿⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡟⢲⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⢘ ⠀⠀⠈⢿⡆⠀⠀⠀⣴⣿⣿⣟⠁⠀⠀⠀⠀⠈⢉⣿⠋⠀⠀⠰⢦⣬⣏⣿⣿⣿⣿⣯⣝⣿⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠁⠀⢻⡀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡎⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠘⣧⠀⠀⢸⡿⠛⠛⠛⠋⠀⠀⢀⣦⠀⠘⢡⣀⠚⠲⣦⣼⣍⣹⣿⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠢⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣶⠿⢷⠄⣾⣿⣿⡷⠀⠀⠀⠀⢸⣿⡄⠀⣿⣿⣷⣾⣿⣿⣿⣿⣟⣩⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠾⠉⠁⠀⠀⠀⠐⠀⢸⢿⣷⡗⠿⣷⣿⡿⣿⣿⣿⣿⡿⣿⣿⡿⠟⠛⠟⠿⣤⣼⣦⣴⣾⣿⣧⡀⠀⣀⣼⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣤⣾⡆⠀⢀⠀⠘⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⡿⠀⠈⣾⣿⣿⣶⣶⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠸⡇⠀⢈⠆⣿⣿⣿⣿⣿⣿⣿⠟⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠀⣷⠀⠈⢠⣍⣿⣾⣿⡿⠟⠃⣷⣿⣿⣿⣿⣿⣿⣧⣴⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠀⠀⠸⣿⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⡿⠟⠀⠀⠙⠁⠀⠛⠋⠉⠉⣠⣤⣈⣀⡹⣿⣼⢹⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣶⣼⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡏⣡⣶⣿⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⣿⡿⣿⣿⣿⣟⣟⣿⣿⣿⣶⢰⣾⣿⢚⣿⠟⠘⢷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣆⢠⣾⣷⡄⠀⣰⣿⣿⣿⣿⣿⣧⣯⣿⣿⣟⣾⣿⣯⠉⠉⠈⣹⠏⢾⣿⣦⣤⣩⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢰⣿⣿⣿⣿⣿⣿⡼⣏⣿⣟⠛⠛⠛⠛⠃⠀⠀⠃⠀⠀⠛⠛⢋⣿⣯⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⡿⢾⣿⣿⣿⡿⣿⢿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢿⣙⢹⡟⠍⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡝⠀⠀⠀⠀⠀⡠⠤⢤⣤⣄⣸⣿⣶⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣮⣾⡿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡳⣿⣾⡞⠀⠀⠀⠉⠉⠹⠿⠿⠿⠟⠿⢿⠄⠀⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢻⡀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠰⠇⠀⣶⡇⢸⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠇⠀⠀⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⢶⠶⠶⢤⠤⢤⣹⣿⣗⣚⣁⣳⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠈⢿⡦⠀⠀⠀⠀⢀⣿⣿⠿⠿⠃⠀⠀⢹⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣦⣈⠉⠀⠀⠀⠀⢸⣿⣷⣶⣶⢶⣶⣶⣿⠀⠂⣸⠀⠂⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⠟⢲⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠘⣷⠀⠀⠀⢠⣾⣿⣟⠋⠀⠀⠀⠀⠈⠉⣿⠟⠉⠀⠠⣤⣄⣽⡻⣿⣿⣿⣭⡛⣿⡆⠀⠀⠀⣸⣿⣿⣿⣿⠈⠋⠀⢻⡀⡿⡏⠀⠃⡘⠀⠶⠑⡆⢸⠀⡎⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢻⡆⠀⠀⣿⠿⠿⠿⠖⠂⠀⠀⣠⠀⠐⠋⣀⠐⠦⣤⣤⣍⣙⣿⣿⣿⣿⣮⣿⣿⠃⠀⠀⠀⢹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠂⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣶⠹⢷⠄⢸⣷⣾⣶⠆⠀⠀⠀⢸⣿⡆⠀⣾⣿⣳⣶⣿⣿⣿⣿⣟⣋⣿⣽⣿⣿⣿⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠿⠟⠋⠀⠀⢀⠀⢸⣿⣄⡏⣼⣿⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣀⢀⣠⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⢀⣠⡀⠀⠀⠀⢸⣿⣿⠇⣹⣿⣿⣯⣿⣿⣿⡟⠋⢛⣿⣿⣿⣤⣀⣀⠉⢻⣿⣿⣿⣿⣿⣦⣴⣶⣿⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣿⣿⣇⠀⢸⡄⠀⠻⡋⣾⣿⣿⣿⣿⣿⣿⣿⣃⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⠀⠈⡇⠀⠐⢁⠿⣟⣿⣿⣿⣿⡟⣇⣿⣿⡯⣽⣿⣿⣿⠋⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣉⡉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠙⠋⢻⣿⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⠀⠿⠀⠀⣾⡷⠿⠿⠛⠋⠱⠰⡿⣿⡼⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⢹⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⡿⠛⣉⣅⠀⠀⠀⠀⠀⢠⣤⠆⣠⣾⣿⣶⡾⣿⣷⣷⣶⠟⣿⣿⣿⣿⢀⣺⣿⣿⣿⣿⢻⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⣾⣿⣿⡀⠀⣴⣄⠀⠘⢁⣼⣿⣿⣿⣿⣧⣯⣿⣿⣟⣼⣿⣿⠻⠿⠘⠿⢿⣿⣿⣄⠀⠻⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⠇⢀⣾⣿⣿⣿⣿⣿⡜⣏⣿⣿⡚⠛⠛⠛⠃⡀⠀⡀⠚⠉⠛⠛⢓⣾⣯⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣻⣿⣿⣿⡿⣿⢿⣿⣿⡶⠲⠒⠛⠃⠀⠀⠀⠀⠐⡶⣿⣿⢻⡟⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠂⠀⠀⠀⠀⡠⠤⢤⣤⣀⣀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣉⣽⣿⣿⣿⣿⣮⣾⡿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣾⡿⣿⣾⡾⠀⠀⠀⢛⡿⠿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⠎⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠛⠛⠀⠀⠀⠸⠃⠰⠇⠀⣶⡇⢸⠀⣾⣄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡟⠛⠛⠛⠛⠛⢻⣿⣿⡟⠟⠃⢸⣿⣿⣿⣷⣶⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠒⢶⠶⠶⢦⠤⢄⣙⣷⣓⣊⣁⣱⣤⠴⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣴⣿⣿⣿⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⠷⠀⠀⠀⠀⣤⣀⣀⣀⡀⢀⣀⣼⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⠟⢲⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣿⣿⣯⠍⠉⠀⠀⠀⠻⠿⣿⡿⠟⠉⠉⠉⠻⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣿⣿⣿⣿⢹⡾⠛⢿⡀⡿⡏⠀⠃⡘⠀⠶⠓⡆⢸⠀⡎⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⣰⣿⣿⣇⣀⠀⠀⠀⠀⠀⢠⡟⠀⢀⠀⠈⠻⣿⣮⣿⣿⣿⣿⠷⣸⣿⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠚⠓⠒⠚⠢⠧⠤⠤⢧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠰⢶⠀⠰⠿⠴⢾⣿⣿⣉⠉⠉⠀⠀⢠⣦⠀⠈⣱⣦⣈⡙⣿⣾⣦⣼⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢰⣿⡿⠛⠀⠀⠀⠀⢰⣿⣭⡟⣸⣿⣳⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠁⠀⣀⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡿⠯⠿⣿⣿⣿⣉⣉⠉⠀⠺⣿⣿⣿⣿⣷⣄⣠⣤⣾⣄⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣤⣾⣿⡇⠀⣴⡀⠈⢿⠟⣴⣿⣿⣿⣿⣿⣿⣿⡃⠀⣈⣽⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⠀⠙⡇⠀⠠⠃⣿⡿⣻⣿⣿⣿⡿⣯⣿⣾⡿⣻⣿⣿⣿⠟⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠛⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠀⢰⣷⠀⠀⣼⣦⣿⡿⠿⠛⢫⠰⡿⣿⣼⠁⢿⣿⣿⣿⣶⣿⣿⣶⣿⣟⠛⢻⣼⡿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⠿⠛⡉⠀⠀⠀⠀⠀⢉⣀⡄⢀⣴⣶⣤⡼⣿⣷⣇⣤⡞⣿⣿⣿⣿⠀⢺⣿⣿⣿⣿⢿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣅⣴⣿⣿⠀⠀⣀⡀⠀⠸⠋⣰⣿⣿⣿⣿⣧⣯⣿⣿⡏⣬⣿⣿⢿⡿⠰⣿⢿⣿⣿⡋⠈⢿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⡆⠀⣼⣿⣿⣿⣿⣿⡜⣏⣿⣿⡛⠛⠛⠛⢃⡀⠀⣀⠚⠛⠛⠛⢂⣼⣧⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⡶⠶⠾⠿⠃⠀⠉⠁⠀⠀⣶⣿⣿⢹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠢⠀⠀⠀⠀⡠⠤⢤⣤⣄⣀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⣻⣿⣿⣿⣿⣮⣾⡿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣶⣶⣿⡿⣿⣮⡾⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⠎⠀⠀⠀⠀⠀⠉⠉⠻⠛⠛⠿⠿⠿⣿⡆⠀⠀⠸⠃⠰⠇⠀⣶⡇⢸⠀⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠿⠹⣿⣿⣿⣷⣶⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠛⢶⠾⠿⢦⠤⢄⣙⣿⣓⣊⣁⣳⣤⠔⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣠⣼⣿⣿⡁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣸⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⠟⢳⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠛⠀⠀⠀⢹⣿⣿⣿⣿⠟⠻⠛⠻⣿⣿⣿⣿⣿⣷⣤⡈⠀⠀⠀⠀⢸⣿⣿⣿⢲⣴⡿⢿⡀⡿⡏⠀⠃⡸⠀⠶⠑⡆⢸⠀⡎⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣽⠋⠀⠀⠐⢶⣶⣼⣿⣿⣿⣿⣿⣝⣿⡆⠀⠀⠀⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠈⠉⠉⠉⠓⠚⠓⠒⠚⠦⠧⠤⠤⢧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠰⢶⠀⠰⠄⠳⠶⣿⣿⠟⠛⠓⠀⠀⠀⣠⠀⠈⢣⣄⠘⠓⣶⣶⣤⣹⣿⣿⣿⣿⣾⣿⣿⠃⠀⠀⠀⢻⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢠⣾⣿⠷⠀⠀⠀⠀⢠⣼⣛⡿⣸⣿⢧⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠇⠀⠀⣾⡇⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠎⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⢿⣿⣿⣿⣿⡿⣿⣿⢇⢿⣿⣿⣿⡟⠛⠛⠀⠸⣶⣶⣿⣿⣧⣀⣀⣀⣾⡀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣴⣿⡆⠀⣀⠀⠘⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⡻⣿⣿⣿⣿⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⠀⠻⡆⠀⢸⠂⣿⣿⢿⣿⣿⣿⡿⣿⣷⣴⡾⠷⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⠀⢠⣧⠀⠀⣰⣉⣷⣿⣿⠿⢟⢱⡿⣿⣼⠁⢾⣿⣿⣿⣧⣼⣷⣦⣿⡿⠿⢿⣼⡿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠈⠛⠻⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⠋⠀⠀⠉⠀⠀⠛⠉⡉⠁⣤⣤⣈⡘⣿⣵⣅⣀⡜⣿⣿⣿⣿⠨⠽⣿⣿⣾⣷⣼⣷⣷⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣋⣠⣶⣷⠀⠀⢀⠀⠀⢸⠟⢡⣾⣿⣿⣿⣧⣯⣿⣿⡏⣈⣹⣿⢿⣿⠀⣾⣿⣿⣿⠏⠘⢿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡄⢰⣿⣷⡄⠀⣰⣿⣿⣿⣿⣿⡜⣏⣿⣿⠚⠛⠛⠛⢃⡁⠀⠁⠘⠛⠛⠓⢂⣸⣧⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢰⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⡶⠶⠾⠿⠃⠀⠘⠓⠀⠀⡲⣿⣿⢻⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⠀⠀⠀⠀⡠⠤⢤⣤⣄⣀⣸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣮⣿⡿⣿⣿⣧⣄⣀⣀⣀⣀⢀⣀⣶⣿⡽⣿⣾⡾⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣇⣴⣶⡟⣿⣿⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠎⠀⠀⠀⠀⠀⠙⠛⠻⡿⣿⣿⣿⣿⣿⣷⠀⠀⢸⠃⠰⠇⠀⣶⡇⢸⠀⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣷⣶⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠛⢿⠿⠿⢷⠤⢄⣉⣷⣗⣂⣀⣑⣤⠔⠋⢻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢀⣼⣿⣿⡟⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⠟⢳⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⣿⣿⡿⠷⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠟⠿⣿⣿⣿⣿⣿⣷⣄⡉⠃⠀⠀⠀⢸⣶⣶⣶⢢⣠⣶⣿⡀⡿⡏⠀⠃⡘⠀⠶⠑⡆⢸⠀⡎⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⣰⣿⣿⠛⠁⠀⠀⠀⠀⠉⢹⡟⠉⠀⠀⢤⣤⣼⣻⣿⣿⣿⣯⡟⣿⡆⠀⠀⠀⢸⣿⣿⣿⠘⠋⠀⠀⠀⠀⠈⠉⠉⠉⠓⠚⠓⠒⠚⠦⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠰⢶⠀⠠⠄⠸⠶⢶⣿⡿⠿⠶⠀⠀⠀⠀⠀⠀⠻⣀⠐⠶⣤⣄⣏⣙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⢀⣾⣿⣧⠀⠉⠀⠀⢀⣴⠶⡶⢠⣿⣆⣴⣿⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⣼⡇⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠜⠛⠋⠀⠀⠀⠠⠀⢹⣿⣾⡧⣿⣿⣾⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⠛⠀⢸⣧⣤⣶⣿⣇⠀⠀⣀⣼⠀⠀⢀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⡄⠀⢀⠀⢸⣿⣿⢡⣾⣿⣿⣿⣿⣷⣿⡏⠀⠺⡿⢿⣿⣿⣷⣶⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣧⠀⢿⡄⠀⢹⠄⣿⣿⣿⣿⣿⣿⣿⣧⣦⣠⣶⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⠀⢀⣆⠀⠈⢠⡛⣯⣿⣿⡿⡿⢣⡿⣿⣽⡑⣴⣿⣿⣿⣯⣤⣿⣤⣽⣿⣿⣿⣼⡿⣿⣶⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠈⠙⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠟⠀⠈⠛⠀⠀⠿⠛⠙⠋⣉⣀⠘⡘⣿⣵⡉⠀⣈⣿⣿⣿⣿⢘⣻⣿⣿⣿⣦⣴⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣿⠟⣉⣴⣦⠀⠀⠀⠀⠀⢰⡾⢃⣴⣿⣿⣿⣧⣯⣿⣿⡟⠘⣛⣿⣿⣿⠀⣴⣿⣿⣿⡟⠘⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡀⢠⣾⣦⡀⠈⣠⣿⣿⣿⣿⣿⡾⣏⣿⣿⠚⠛⠛⠛⢛⡋⠀⠋⠛⠛⠛⠓⢀⣹⣧⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣷⡶⠶⠾⠿⠃⠀⠐⠓⠂⠀⡶⣿⣿⢹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠀⠀⠀⠀⡠⠤⢤⣤⣄⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡾⠟⣿⣿⣿⣻⣿⣿⣮⣾⡿⣿⣿⣿⣍⡉⠉⠀⠀⠀⠤⣶⣿⡿⣿⣾⡾⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⡇⠰⢾⠀⠆⠙⢁⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⣠⣴⡞⣿⣿⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠎⠁⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⠇⠰⠇⠀⣶⡇⢸⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢿⣿⣿⣷⣶⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠛⠛⢿⠿⠿⢿⠤⢄⣉⣷⣗⣊⣀⣳⣤⠔⠋⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠏⠉⠉⢀⣸⣿⣿⣿⠫⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⠟⢳⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⣿⣿⣿⣷⡗⠀⠀⠘⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣯⣉⠙⠋⠀⠀⠀⠀⣤⣤⣤⢄⣀⣀⣿⡀⡿⡏⠀⠃⡸⠀⠶⠑⡆⢸⠀⡎⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣼⣿⡿⠗⠀⠀⠀⠀⠛⠉⣾⠟⠁⠀⣀⣀⣙⡿⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⣿⠘⠋⠁⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠦⠧⠤⠤⢧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠰⢶⠀⠰⠄⠠⠾⠶⣾⣿⣿⣧⡤⠀⠀⠀⠀⠀⢸⡇⠀⣤⣄⣈⠙⠻⣿⣿⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⣤⣿⣆⠠⠋⠀⠀⠀⣠⣤⣤⢡⣶⡍⣠⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡏⠈⠉⢸⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⠿⠛⠁⠀⠀⠀⠀⢾⣷⣼⣅⣿⣯⣽⣷⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⠿⠇⢠⡇⣀⣠⣿⣇⠀⠀⠀⣸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⢀⣤⠀⠀⠀⠀⢻⣿⣿⢁⣵⣿⣿⣾⣿⣭⣿⡟⠋⢽⣿⣿⣿⣿⣶⣦⣤⣄⣈⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⣶⣿⣿⡇⠀⣶⠀⠈⢻⠁⣾⣿⣿⣿⣿⣿⣿⣏⡅⣀⣴⡒⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⠼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⡇⠀⢈⡂⠀⠘⢐⠿⣏⣷⣿⣿⣿⢫⡾⣿⣼⡉⣣⣴⣿⣿⣿⣁⣼⣯⣙⣿⣿⣿⣼⡿⣿⣤⣤⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡏⠀⠸⠿⠀⠰⡿⠶⠻⠟⠛⠁⠰⡜⣿⣷⠉⠉⠉⣸⣿⣿⣿⢸⣛⣿⣿⣿⣭⣉⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⠟⢛⣡⡄⠀⠀⠀⠀⠀⢠⡴⠆⣰⣿⣿⣶⣧⣯⣾⣷⠞⠾⠟⢫⣿⣿⠈⣤⢬⣿⣿⣿⠛⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣿⣿⣷⠀⢀⣶⣄⠀⠘⢠⣾⣿⣿⣿⣿⡼⣏⣿⣿⠚⠛⠚⠚⢛⡏⠀⠋⠛⠛⠛⠃⢀⢻⣧⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣿⣿⣿⣿⣧⣾⣿⡿⠃⢠⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣷⡴⠶⠾⠿⠃⠀⠀⠐⠒⠂⠐⣿⣿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⡠⠤⢤⣤⣤⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠙⢿⣿⣿⣿⣿⣶⡾⠿⣿⣿⡽⠿⣟⣻⣮⣿⡿⣿⣿⣿⣟⠛⠛⠃⠀⠀⠠⣤⣿⡿⣿⣾⡾⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⡇⠰⢾⠀⠆⠙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⢀⣭⡶⣿⣿⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣯⡞⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢼⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⢿⠿⠿⣿⠯⢤⣉⣓⣓⣊⣁⣱⣤⠴⠛⠳⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠉⢹⣿⣿⣿⡿⠛⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡟⢳⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠻⠃⠀⠀⠀⢀⣀⣀⡀⠀⠀⢿⡀⡿⡏⠀⠃⡘⠀⠶⠑⡆⢸⠀⡏⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣿⣿⡿⠥⠀⠀⠀⠘⠛⢩⡿⠛⠁⢀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⠸⠗⠀⠀⠀⠀⠈⠉⠉⠉⠓⠚⠓⠒⠚⠦⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠰⢶⠀⠰⠄⠠⠠⠶⠆⣼⣿⣿⣦⡄⠀⠀⠀⠀⠀⡾⠁⢀⣀⣈⠉⠿⢿⣾⣿⣿⣿⣿⣷⣿⠇⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈ ⠛⠋⣠⣿⡆⠀⠟⠀⠀⠀⣠⣠⣬⢉⣤⡍⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡟⠉⠉⢹⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⠿⠛⠋⠀⠀⠀⠀⢾⣧⣼⣍⣽⣏⣽⣷⣾⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⠿⠇⠀⡇⣀⣠⣿⣇⠀⠀⠀⢸⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⢀⣠⠀⠀⠀⠀⢺⣿⣿⢉⣽⣿⣯⣭⣿⣭⣿⡟⠉⢻⣿⡿⣿⣿⣶⣶⣤⣤⣀⣻⣿⣿⣿⣷⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⣶⣿⣿⡇⠀⣶⠀⠈⢿⠁⣮⣿⣿⣿⣿⣿⣿⣏⡇⣀⣬⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠓⠝⠿⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⢘⡂⠀⠘⠐⠿⣟⣿⣿⣿⣿⢫⡾⣿⣼⠙⣁⢰⣿⣿⣿⣅⣸⣯⣉⣿⣿⣿⣼⡿⣿⣥⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠸⠿⠀⢠⣿⠶⠿⠟⠛⠉⠴⡜⣿⣿⠋⠉⠉⣀⣿⣿⣿⢸⣟⣻⣿⣿⣯⣉⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⢛⣩⡄⠀⠀⠀⠀⠀⣠⣴⠆⣰⣿⣿⣶⣧⣯⣿⣶⠞⣾⠟⢫⣿⣿⠨⣥⢬⣿⣿⣿⠿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣿⣿⣷⠀⢀⣦⣄⠀⠘⢡⣾⣿⣿⣿⣿⡾⣏⣿⣿⠚⠓⠒⠘⢛⡏⠀⠋⠛⠛⠛⠃⢀⢿⣧⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠻⣿⣿⣿⣿⣦⣾⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣧⣴⠶⠾⠿⠃⠀⠀⠐⠖⠂⢐⣿⣿⢹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡠⠤⢤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⠹⣿⣿⣿⣿⣦⣼⠿⣟⣯⡭⠿⣿⣻⣮⣿⡿⣿⣿⣿⣟⠛⠛⠓⠀⠀⢠⣤⣾⡿⣿⣾⡾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⡇⠰⢾⠀⠆⠙⢁⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⢀⣩⡶⣾⣿⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡞⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣿⣛⠿⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⠛⠛⢿⠿⠿⣿⠯⢤⣉⣿⣓⣊⣀⣳⣦⠴⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋⣹⣿⣿⣷⣿⠿⠛⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠂⣸⠀⠂⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⠗⢲⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⣾⣿⣿⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠿⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡎⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⣹⣿⣿⣭⠉⠀⠀⠀⠟⢫⣿⠟⠃⠀⣀⡈⣿⣿⣿⣿⣿⣿⠿⣶⡀⠀⠀⠀⠘⣿⣿⢸⠖⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠦⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠖⢰⣿⣿⣦⣀⠀⠀⠀⠀⠀⡼⠃⢀⣀⣈⡉⠻⢿⣶⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠜⣡⣿⡄⠠⠏⠀⠀⠀⣀⣠⣭⢉⣤⡍⣠⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡟⠉⠉⢹⡇⠀⠀⠈⢹⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⠿⠟⠃⠀⠀⠀⠀⣾⣧⣼⣉⣽⣏⣽⣷⣾⣿⣿⣾⣿⣿⣿⣿⣻⣿⣿⡿⠇⠀⠇⠀⣀⣾⣇⠀⠀⠀⢸⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⢀⣀⠀⠀⠀⠀⣾⣿⣿⠉⣽⣿⣯⣭⣿⣫⣿⡞⠹⣿⣿⡿⣿⣿⣶⣶⣤⣤⣀⣸⣿⣿⣿⣶⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣴⣶⣿⣿⡆⠀⣦⠀⠘⢟⢃⣼⣽⣿⣿⣿⣿⣿⣟⡃⣀⣴⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠃⠙⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⢹⡂⠀⠈⠰⠿⣟⣿⣿⣿⣿⢫⡼⣿⣽⣉⣿⠀⣿⣿⣿⣇⣠⣿⣉⣻⣿⣿⣼⡿⣿⣥⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠸⠷⠀⢠⣿⠶⠿⠿⠛⠉⠥⡜⣿⣿⠛⠋⠉⣀⣿⣿⣿⢸⣟⣻⢿⣿⣯⣉⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⠛⣩⡄⠀⠀⠀⠀⠀⣠⣤⠄⣰⣾⣷⣶⣧⣯⣿⣶⠞⣾⠿⣋⣿⣿⠸⣥⢤⣿⣿⣿⠿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣿⣿⣧⠀⢀⣤⣀⠀⠛⢁⣾⣿⣿⣿⣿⡾⣏⣿⣿⠚⠒⠒⠈⢛⡏⠀⠛⠛⠛⠛⠋⢀⢿⣧⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⢿⣿⠿⣿⣴⣾⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣇⣴⠶⠶⠿⠃⠀⠀⠀⠲⠒⠠⣿⣿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⡠⠤⢤⣤⣤⣄⣀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠈⢻⣿⣿⣷⣦⣾⡿⣟⣿⣭⢿⢿⣿⣮⣾⡿⣿⣿⣿⣿⡛⠛⠓⠀⠀⠀⣤⣾⡿⣿⣾⣾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡇⠰⢾⠀⠆⠙⢁⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⢈⣩⡷⣶⣾⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣯⣾⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⠛⠛⢿⠿⠿⣾⠯⢤⣙⣷⣓⣂⣀⣳⣤⠔⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⣿⣿⣇⣿⡿⠟⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⠗⢲⠒⠒⠲⠦⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣶⣿⣿⣀⠂⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⡀⡿⡏⠀⠃⡘⠀⠶⠓⡆⢸⠀⡏⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢻⣿⣿⡭⠍⠁⠀⠀⠟⢋⣿⠟⠋⠈⣁⡉⢻⣿⣿⣿⣿⣿⠿⣶⣄⠀⠀⠀⠀⣿⣿⢰⡖⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠺⠦⠧⠤⠤⢧⣄⣹⣀⣇⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠰⢶⠀⠰⠄⠠⠠⠖⠆⠀⣾⣿⣤⣤⠀⠀⠀⠀⠀⡼⠃⢀⣀⣀⡉⡻⣿⣾⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛ ⠀⠈⣫⣷⡄⢰⠟⠁⠀⠈⣀⣀⣍⢉⣤⡉⣠⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡟⠛⠉⢹⡇⠀⠀⠈⢹⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⠟⠃⠀⠀⠀⠀⣶⣧⣽⣉⣿⣏⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⠇⠀⠇⠀⣀⣾⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠁⠀⢀⣀⠀⠀⠀⠀⣾⣿⣾⠉⣽⣿⣿⣭⣿⣻⣿⡾⠹⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣸⣿⣿⣿⣦⣴⣶⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣴⣶⣿⣿⡄⠀⣦⠀⠘⠟⢃⣾⣿⣿⣿⣿⣿⣿⣟⡃⣀⣼⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠐⠙⠻⠿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⢹⠀⠀⠌⠸⢿⣟⣿⣿⣿⣿⢻⡼⣿⣽⠋⣕⠀⣿⣿⣿⣯⣠⣿⣍⣹⣿⣿⣼⡿⣿⣥⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠸⡧⠀⢠⣿⡾⠿⠿⠟⠉⠥⡜⣿⣿⠛⠋⠋⢀⢿⣿⣿⢸⣿⣻⢿⣿⣿⣉⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠟⣉⡀⠀⠀⠀⠀⠀⣀⣤⠄⣰⣶⣶⣴⣦⣯⣿⣶⢞⣾⣿⢊⢿⣿⠸⣧⢤⣽⣿⣿⠿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣴⣿⣿⣇⠀⢀⣤⡀⠀⠛⢁⣾⣿⣿⣿⣿⡾⣏⣿⣿⠘⠒⠒⠉⢛⡏⠀⠋⠛⠛⠛⠋⢀⣿⣯⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⡿⠿⣶⣾⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣇⣰⠶⠶⠿⠃⠀⠀⠀⠲⠖⠀⣿⣿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⡠⠤⢤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⠘⢿⣿⣷⣤⣾⣿⢟⣻⣿⡿⠿⣿⣮⣿⡿⣿⣿⣿⣿⡛⠛⠛⠀⠀⢀⣠⣾⡿⣿⣾⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⡇⠰⢾⠀⠆⠙⢁⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⢘⣫⣿⣶⣾⣿⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⠋⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⠛⠛⢿⠿⠿⣶⠿⢤⣹⣿⣓⣊⣀⣑⣤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣇⣿⣿⡟⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡖⢲⠒⠒⠶⠦⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣶⣿⣿⣇⡂⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡎⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣭⠁⠀⠀⠻⠋⣽⠟⠋⠉⣉⣙⢻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⡟⢰⡆⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠦⠧⠤⠤⢧⣄⣹⣀⣇⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠰⢶⠀⠰⠄⠠⠠⠖⠆⠀⠸⢿⣧⣤⡀⠀⠀⠀⠀⣰⠏⠀⣀⣀⣉⣿⢿⣿⣾⣿⣿⣿⣟⣾⡿⠀⠀⠀⠀⢸⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛ ⠀⠀⢺⣶⡀⢸⠟⠁⠀⠈⢀⣀⣙⢋⣀⡊⢁⣅⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡿⠛⠛⢻⡇⠀⠀⠙⢻⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠃⠀⠀⠀⠀⣶⣏⣽⢋⣻⢏⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⠸⠇⠀⢀⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠁⠀⣽⣿⣾⠙⣽⣻⣛⣛⣿⣻⣿⡿⣟⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣹⣿⣿⣤⣤⣶⣾⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣾⣿⡀⠀⣄⠀⠹⡿⢃⣞⣿⣿⣿⣿⣿⣿⡿⠃⣀⣽⡏⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⢻⠀⠀⡜⢸⣿⡿⣿⣿⣿⣿⢟⡹⣿⣼⠟⣆⠸⣿⣿⣿⣿⣁⣼⣏⣙⣿⣿⣿⡿⣿⣉⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⢸⣧⠀⣠⣷⣴⣿⡿⠿⠛⣅⡜⣿⣽⠿⠚⠗⢀⢿⣿⣿⢸⣿⣿⢿⣿⣿⣟⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠿⢋⡁⠀⠠⠀⠀⠈⣁⣠⠀⢠⣶⣦⣤⣧⣯⣷⣤⣶⣾⣿⣎⢻⣿⢸⣯⢉⣹⣿⣿⢻⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣤⣾⣿⡇⠀⢀⣄⠀⠀⠿⢁⣴⣿⣿⣿⣿⡾⣏⣿⣿⠘⠋⠙⠛⢛⡟⠀⠟⠛⠛⠛⠋⢀⣿⣯⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⡿⠶⣾⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠇⣲⠲⠶⠿⠇⠀⠀⠀⠐⠶⠆⣻⣿⢹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠄⠀⡠⠤⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠘⢿⣷⣄⣾⣿⡿⣟⣻⣿⣿⠿⣮⣿⡿⣿⣿⣿⣿⣟⠛⠛⠂⠀⠀⣠⣦⡿⣿⣾⣾⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⣿⡇⠰⢾⠀⠆⠙⢁⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣏⠑⣛⣯⣥⣶⣾⣿⣿⣮⣟⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣭⣾⡇⠋⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⠛⠻⢿⠿⠿⣤⠿⢤⣽⣿⣗⣊⣀⣑⣤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣿⣿⡿⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡖⢲⠒⠒⠶⠦⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣭⣿⣿⣆⡅⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡏⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣍⠁⠀⠸⠟⣹⡟⠛⠀⢉⣉⢻⣿⣿⣿⣿⣿⡿⢷⣤⠀⠀⠀⠀⢸⡇⢰⣤⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠦⠧⠤⠤⢧⣄⣹⣀⣇⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠰⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠈⢫⣭⣤⡄⠀⠀⠀⢠⡟⠀⣀⣀⣉⣿⣿⣷⣿⣿⣿⣿⣿⣦⣿⠇⠀⠀⠀⢰⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠿ ⠀⠀⠀⣷⠀⢸⡿⠃⠀⠂⠀⠐⠛⠛⡁⠞⢑⡀⠡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡟⠟⠟⣿⡇⠀⠀⠛⢻⠀⠀⠈⠁⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠿⠇⠁⠀⠀⠀⣤⣟⣻⠋⣾⠟⣴⣟⣿⣿⣏⣿⣿⣿⣿⣿⢿⣿⣿⣿⠁⠸⠇⠀⢀⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⣝⣿⣽⠘⣻⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣹⣿⣷⣄⣠⣤⣾⣦⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣾⣿⠀⠀⡄⠀⠻⡿⢋⣰⣿⣿⣿⣿⣿⣿⡿⠃⣙⣿⡟⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⢻⠀⠀⡑⢸⣿⡿⣿⣿⣿⣿⢿⡹⣿⣽⣿⠗⢸⣿⣿⣿⣿⣏⣨⣿⡙⢿⣿⣾⣿⣿⡋⠉⢉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⢸⡆⠀⢀⣶⣼⣿⣿⣿⠛⣋⡘⣿⣷⠿⠵⠞⢈⣿⣿⣿⢹⣿⡿⢿⣿⣿⣿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠿⢛⠃⠀⠈⠁⠀⠈⡉⣁⠀⢠⣤⣤⣡⣧⣯⣧⣤⣴⣶⣿⣯⢻⣿⢸⣿⣉⣙⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⢠⣶⣿⡇⠀⢀⡀⠀⠀⡿⢋⣴⣿⣿⣿⣿⡾⣏⣿⣿⠘⠛⠛⠛⠋⡏⠀⡟⠚⠛⠛⠛⢈⣿⣯⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⠶⣾⣿⣷⠀⢠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠲⠒⠶⠿⠇⠀⠀⠀⠀⠶⠞⢹⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⡷⠲⠀⡠⠤⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠈⠹⣿⣄⣾⣿⡿⡿⢿⣿⣻⣿⣮⣿⡿⣾⣿⣿⣿⣿⡿⠛⠓⠀⠀⣠⣤⡿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⡇⠰⢾⠀⠆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⠹⢞⣻⣭⣵⣶⣶⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⡿⠋⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢼⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⣿⣿⠁⠀⠀⠀⠀⠀⠐⠛⠛⣿⠛⠻⢿⠿⠿⣥⠾⣯⣽⣿⣗⣊⣀⣑⣤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⣿⣿⣿⡿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⠖⢲⠒⠒⠶⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⣿⣿⣯⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡏⢀⠁⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣍⠁⠀⠘⠟⢩⡿⠛⠉⢉⣛⢽⣿⣿⣿⣿⣿⣿⢷⣦⡀⠀⠀⠀⠀⡆⢠⣤⠀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠶⠧⢤⠤⢧⣄⣹⣀⣇⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠙⢭⣥⡄⠀⠀⠀⢀⡾⠁⣀⣀⡉⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⠇⠀⠀⠀⠀⡇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠿ ⠀⠀⠀⣺⠀⢸⡿⠂⠀⢟⠀⠐⠻⠟⠡⠗⠑⠀⢩⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠿⠿⣿⡇⠀⠀⠛⣿⠀⠀⠘⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⠖⠀⠀⠀⠀⣤⡞⣻⠗⣾⡟⣤⣟⣷⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠃⠀⢀⣿⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⣻⣿⣵⠸⣻⢾⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⢘⣿⣧⣀⣠⣤⣿⣦⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣶⣷⠀⢀⡀⠀⢻⣿⠏⡴⣿⣿⣿⣿⣿⣿⡿⠋⣈⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡆⠀⢿⠀⠀⡱⢸⣿⡿⣿⣿⣿⣿⣿⡻⣿⣽⢿⣧⢺⣿⣿⣿⣿⣟⣉⣿⡉⢻⣿⣿⡿⣿⠋⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⢴⡄⠀⢀⣮⣹⣶⣿⣿⠿⡋⡸⣿⣷⣿⠾⠟⢸⣿⣿⣿⢹⣿⣿⢿⣿⣿⣿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠟⠃⠀⢈⠁⠀⠙⠋⢉⠉⢁⣤⣄⣉⣧⣯⣧⣀⣄⣴⣿⣯⢿⣿⢸⣿⣋⣙⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠁⣴⣾⡆⠀⠀⠀⠀⠀⡿⠋⣴⣿⣿⣿⣿⡾⣯⣿⣟⠚⠛⠛⠛⠛⡟⠀⡟⠛⠛⠛⠛⢈⣿⣯⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣧⠠⢾⣿⣦⠀⢀⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠶⠒⠲⠿⠇⠀⠁⠀⠀⠶⠾⢻⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠿⢆⡠⠤⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠈⢿⣦⣾⣿⣿⡿⢿⣿⣿⣿⣮⣿⡿⣶⣿⣿⣿⣿⡿⠟⠓⠀⠀⢠⣴⡾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣿⡇⠰⢾⠀⡆⡙⢁⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡭⢷⣟⣋⣭⣿⣶⣿⣮⣟⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣯⣾⣿⠛⠋⠁⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠇⠰⠇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠋⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⣿⣿⠁⠀⠀⠀⠀⠀⠠⠿⠿⣿⠛⠻⢿⠿⠿⣥⠼⣿⣿⣿⣗⣊⣀⣱⣦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡖⢲⠒⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣻⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡏⢀⠃⠸⠀⣹⠀⠈⢠⡇⠀⡾⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⡉⠀⠈⠿⢫⡿⠛⠉⠛⣉⣻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⡆⢠⣤⡀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠶⠧⢤⠤⢧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⢁ ⠀⠀⠰⣶⠀⠰⠄⠠⠠⠶⠆⠀⠀⠀⠈⠉⣭⣤⠀⠀⠀⠀⡼⠃⢀⣀⣈⡹⢿⣷⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⡇⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⠘⠃⢸⡇⢸⡿⠆⠀⠝⠁⠰⠾⠿⠁⠵⠢⠐⢫⣵⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⣧⠿⠿⣿⠁⠀⠈⠿⣿⠀⠀⠙⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠇⠈⠀⠀⠀⣠⡖⠾⠇⣾⡿⣤⣞⣷⣾⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠁⠀⢀⣿⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⡻⣿⣽⠸⢻⣶⠿⠿⣿⢿⣟⣿⢿⣿⣿⣿⣾⣿⣿⣿⣦⣤⣄⣀⡈⢿⣦⣀⣀⣤⣿⣄⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣴⣶⠀⢀⡀⠀⢿⣿⠏⡰⣿⣿⣿⣿⣿⣿⣿⠃⣹⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⡆⠀⢷⠀⠀⡡⢸⣿⡿⡿⣿⣿⣿⡿⡳⣿⣼⣿⣧⢼⣿⢻⣿⣿⣟⣉⣿⡋⠻⣿⣾⡿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⢴⡄⠀⠁⣎⣹⣶⣿⡿⠿⡋⡘⣿⣷⣿⢮⡇⢸⣿⣿⣿⢸⣿⣿⠿⣿⣿⣿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⠃⠀⢈⠁⠀⠙⠛⠉⠉⢉⣠⣀⣁⣧⣯⣧⣀⣤⣴⣿⣯⢿⣿⢸⣿⣋⣙⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠉⠉⣴⣾⡆⠀⠀⠀⠀⠀⡿⠏⣠⣿⣿⣿⣿⡾⣏⣿⣟⠚⠛⠛⠛⠛⡿⠀⡟⠛⠛⠛⠛⢊⣿⣯⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⡇⠀⠰⢿⣤⠀⢁⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠶⠖⠐⠿⠇⠀⠂⠀⠀⠰⡾⠋⣿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⠻⣷⡤⠤⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣾⣿⣿⡿⢿⣿⣿⣿⣮⣿⡿⣶⣿⣿⣿⣿⡿⠟⠓⠀⠀⢀⣠⡴⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻⡇⠰⢾⠀⡆⡙⢁⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⠷⣟⣛⣩⣽⣷⣾⣮⣟⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣿⣿⣷⣯⣾⣿⠋⠉⠁⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⠰⡇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⣿⣿⡃⠀⠀⠀⠀⠀⠀⠻⠛⣿⠛⠻⢿⠿⠿⣥⠼⣿⣿⣿⣗⣚⣀⣑⣦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡖⢲⠒⠒⠶⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⠶⠓⡆⢸⠀⡏⢀⠃⠸⠀⣹⠀⠈⢠⡇⠀⡾⠀⠀⠀⠀⠀⠀⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣍⠁⠀⠿⢋⡿⠛⠋⠛⣙⣻⣿⣿⣿⣿⣿⣿⠿⣦⡀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠦⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢰⠇⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠲⣶⠀⠰⠄⠠⠠⠶⠆⠀⠀⠀⠀⠈⠩⣤⠀⠀⠀⠀⣸⠃⢀⣀⣈⣹⣿⣿⣾⣿⣿⣿⣿⣷⣾⡟⠀⠀⠀⠀⠀⣸⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⢟⢉⣿⢸⡿⠀⠐⣿⠃⠰⠿⠿⠁⠵⠲⠒⢫⣵⣽⣽⣿⣿⣿⣿⣿⣿⣿⠀⢸⠿⠿⠿⣿⠁⠀⠘⠿⡇⠀⠀⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⣒⠾⠆⣾⡿⣴⣞⣿⣾⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠐⠀⢰⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⡿⣟⣿⠸⢻⣶⡿⢿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⢉⣆⣀⣀⣤⣷⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠿⢿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣶⠀⢀⡀⠀⢿⣿⢇⡴⣿⣿⣿⣿⣿⣾⣿⠛⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⡄⠘⣷⠀⠀⡣⢸⣿⡿⢿⣿⣿⣿⡿⡴⣾⣽⣿⣷⢾⣿⠛⣿⣿⣿⣋⣽⣏⡙⣿⣿⣿⣟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡅⠀⣼⡄⠀⢀⣎⣹⣶⣿⣿⠿⡋⡼⣿⣷⣿⣿⡏⢸⣿⣶⣿⢸⣿⣿⠿⣿⣿⣿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⡿⠟⠃⠀⢈⠁⠀⠙⠛⠉⠉⢉⣤⣀⣉⣧⣯⣧⣀⣤⣴⣿⣯⣿⣿⢸⣿⣏⣉⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠁⠰⣾⡆⠀⠀⠀⠀⠀⡿⠋⣴⣿⣿⣿⣿⡾⣯⣿⣟⠚⠛⠛⠛⢋⡟⠀⣟⠛⠛⠛⠛⢛⣿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠛⢛⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠳⢶⣄⢠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠶⠖⠰⠿⠇⠀⠓⠀⠀⠠⡾⠟⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣿⡿⣿⡷⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⡿⣶⣿⣿⣿⣿⣿⠛⠛⠀⣀⣀⣠⡾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡇⠰⢾⠀⠆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣛⣛⣭⣿⣶⣾⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠟⠛⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⠰⡏⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣯⣛⠿⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠛⣿⠛⠻⢿⠿⠿⣦⠾⣿⣿⣿⣗⣚⣁⣱⣦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⣸⠀⠃⣸⠀⠶⡃⠀⣈⠃⢸⠉⡉⢻⠉⣙⡖⢲⠒⠒⠶⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡿⡏⠀⠃⡸⠀⢶⠓⡆⢸⠀⡏⢀⠃⠸⠀⣹⠀⠈⢠⡇⠀⡾⠀⠀⠀⠀⠀⠀⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⡍⠀⠘⠋⡼⠛⠋⢉⣉⣽⣿⣿⣿⣿⣿⣿⡟⢷⣤⠀⠀⠀⠀⠀⣶⣦⣤⠀⠀⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠲⠧⠤⠤⠧⣄⣹⣀⣇⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⣁ ⠀⠀⠲⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⢰⠃⢠⣤⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⣿⡏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠘⠟⣿⣻⡿⠀⠘⠽⠁⠐⠿⠟⠨⠖⠑⠚⢩⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⣼⢻⠿⠿⣿⠁⠀⠘⠟⡇⠀⠀⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⡙⠉⠀⠀⢀⣴⣛⣻⢣⣾⠿⣴⣻⣿⣻⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠿⠈⠀⠸⣿⠀⠀⠀⠀⡇⠀⢀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⢠⣿⣿⡷⠺⡳⣿⡟⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣤⣤⣀⣄⣀⣤⣴⣷⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⡿⠿⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣷⠀⢠⡀⠘⢿⡿⢇⣾⣿⣿⣿⣿⣿⣿⣿⠛⣻⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⡄⠘⢧⠀⠈⡃⣸⣿⣿⣿⣿⣿⣿⣟⡾⣿⣽⣿⣷⣾⣿⠋⣿⣿⣿⣭⣼⣯⣉⣻⣾⣿⣟⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⡄⠀⣾⡄⠀⣐⣦⣹⣾⣿⡿⠿⡋⡿⣿⣿⠿⠿⠇⢸⣿⣿⣿⢸⣿⣿⣟⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠻⢿⡿⠛⠁⠀⠉⠁⠀⠙⠉⣉⠁⣠⣤⣌⣩⣧⣯⣧⣠⣴⣾⣿⣿⣿⣿⢸⣿⣏⣀⣹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⠀⠀⢀⡀⠀⠐⡿⢋⣴⣿⣿⣿⣿⡾⣯⣿⣟⠈⠙⠛⠛⠛⡇⠀⡟⠛⠛⠛⠛⢛⣿⣯⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠛⣻⣶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠛⠻⣶⣤⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠶⠒⠶⠿⠇⠀⠛⠀⠀⠰⠾⠛⣸⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⡿⠦⢤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠿⣿⣿⣿⣿⣾⣿⡿⣶⣿⣿⣿⣿⣿⣛⣉⣀⣀⣀⣴⡾⣿⣾⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣭⣵⣶⣶⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠏⠉⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠇⠰⡇⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣿⣛⠿⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⣿⠛⠻⢿⠿⠿⣿⠿⣿⣿⣿⣗⣚⣁⣳⣦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⣸⠀⠃⣸⠀⠶⡇⠀⣈⠃⢸⠉⡉⢻⠉⣛⡖⢲⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣿⡏⠀⠃⡸⠀⢶⠓⡆⢸⠀⡏⢀⠃⠸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠆⠀⠈⠉⣼⠋⠉⠩⣧⣿⣿⣿⣿⣿⣿⣿⣟⢿⣶⠀⠀⠀⠀⠀⣿⣷⣶⠀⠉⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠲⠧⢤⠤⠧⣤⣹⣀⣇⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⢠ ⠀⠂⠲⣶⠀⠲⠄⠠⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣿⣏⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈ ⡀⠀⠀⡿⣿⣿⠟⠀⠘⢿⠁⠘⠛⢛⡰⠛⢐⡉⢱⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⣾⢻⠛⢻⣿⠀⠀⠘⠛⡇⠀⠀⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⢀⡉⠉⠀⠀⢠⣴⣟⡻⢳⣿⢛⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡟⠈⠀⠸⠿⠀⠀⠀⠀⡇⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⢛⣹⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣤⣤⣤⣤⣴⣾⣷⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠿⠿⠿⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣷⠀⢠⡀⠘⢿⡿⢣⣞⣿⣿⣿⣿⣿⣿⢿⠏⣛⣿⠟⢹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⣿⠄⠘⢷⠀⠀⠃⢼⣿⢿⣻⣿⣿⣿⣟⡾⣿⣿⢿⣿⣿⣿⡉⣹⣿⣿⣧⣶⣿⣄⣿⣿⣿⣏⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⠄⠀⣿⡆⢀⣰⣧⣼⣿⣿⠟⠛⣁⡿⣿⣿⠿⠿⠟⣸⣿⣿⣿⢸⣿⣿⣟⣛⣿⣿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠘⠻⠟⢛⠁⠀⠤⠀⠀⠉⣉⣀⠀⣠⣶⣤⣤⣧⣯⣷⣤⣶⣾⣿⣿⣿⣿⢸⣿⣧⣤⣬⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠀⠀⢀⡀⣀⠘⠟⢡⣾⣿⣿⣿⣿⡾⣯⣿⣟⠊⠉⠛⠛⠋⡇⠈⣟⠛⠛⠛⠛⢛⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠛⠛⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⢿⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠏⢖⠢⠶⠿⠇⠀⠛⠂⠀⠀⠚⢋⣽⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠧⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣻⣿⣿⠿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣯⣤⣀⣤⣤⣾⣿⣿⣾⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠋⠉⠁⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⡏⠀⣶⡇⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣛⣽⣿⣿⣿⣿⣛⠿⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⢿⠿⠿⣿⠿⣿⣿⣿⣷⣚⣉⣳⣦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⣸⠀⠃⣸⠀⠶⡇⠀⣈⠃⢸⠉⡉⢻⠉⣛⡖⢲⠒⠒⠶⢤⠀⠀⠀⠀⠀⠀⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠀⠀⠀⠀⠀⢀⡀⠀⢿⣀⣿⡏⠀⠃⡼⠀⢶⠓⡆⢸⠀⡏⢀⠃⡸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠓⠀⠀⠁⣸⠋⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡀⠉⠀⠈⠉⠉⠉⠛⠚⠓⠒⠚⠲⠧⠤⡤⠧⣄⣹⣀⣇⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠲⣶⠀⠴⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇⣀⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣯⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡀⢀⠻⣿⣿⠟⠀⠉⢿⣁⣙⡛⣛⣐⢋⣈⣉⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢿⠛⢻⣿⠀⠀⠈⠹⡇⠀⢀⡉⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠗⠀⢀⠾⠁⠀⠀⢰⣾⣭⡟⣱⡿⣻⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣛⣈⠀⠘⠻⠀⠀⠀⠀⡇⠀⢰⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠈⠀⢸⣿⣿⡏⢛⣿⣿⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠟⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣷⠀⢰⡄⠈⢻⠟⢣⣿⣿⣿⣿⣿⣿⣿⣿⠉⣻⣿⡟⢹⣿⣿⣿⣿⣿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⣿⠀⠈⣧⠀⠠⠁⢾⣿⢿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⢿⣿⣁⣽⣿⣿⣷⣶⣿⣦⣽⣿⣿⣯⣀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⡂⠀⣿⡆⠠⣼⣷⣼⣿⠿⠟⢻⣄⡿⣿⣿⠟⠻⢋⣼⣿⣿⣿⢹⣿⣿⠯⠽⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠙⠛⣉⠀⠀⠄⠀⠀⢉⣁⣤⠀⣴⣶⣶⣴⣧⣯⣷⣶⣿⣿⣿⣿⣿⣿⢸⣿⣷⠤⣴⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣈⠟⣠⣿⣿⣿⣿⣿⡾⣏⣿⣿⠒⠚⠛⠛⢛⡇⠈⣟⠛⠛⠛⠛⢛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣉⣉⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠏⣲⠴⠶⠿⠏⠀⠻⠃⠀⠀⠚⣩⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣛⣿⡿⢿⢿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣶⣾⣿⣿⣾⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠋⠉⠀⠀⠀⢈⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣿⡿⠿⣛⣽⣿⣿⣿⣿⣛⢿⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⢿⠿⠿⣿⠿⣿⣿⣿⣷⣚⣉⣳⣦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠂⣸⠀⠃⣸⠀⠶⡇⢀⣈⠃⢹⠉⡉⢻⠉⣛⡗⢲⠒⠒⠶⠦⠀⠀⠀⠀⠀⠀⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠇⠸⣿⢟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠀⠀⠀⠀⢠⣄⣀⣿⣀⣿⡏⠀⠃⡼⠀⢶⠛⡆⢸⠀⡏⢀⠃⡸⠀⣹⠀⠈⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡛⠀⠀⠁⣸⠁⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⣼⣿⣿⠍⡏⠁⠈⠉⠉⠙⠛⠚⠓⠒⠚⠦⠧⠤⠤⢧⣄⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠐ ⠀⠄⠲⣶⠀⠴⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⣤⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢿⣿⣟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⡀⣸⢿⣿⠋⠉⠙⢿⣀⣉⡛⣫⣘⢁⣭⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⠛⢻⣿⠀⠀⠈⠙⡇⠀⢀⡋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠃⠘⡿⠃⢀⠀⢰⣾⣭⡟⣹⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣄⣀⠈⠙⠀⠀⠀⢀⡇⠀⢸⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠈⠀⢸⣿⣿⡏⢩⣿⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⠿⠿⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣧⠀⢰⡀⠈⢻⠛⣱⣿⣿⣿⣿⣿⣿⣿⣟⢉⣭⣿⣏⢹⣿⣿⣿⣿⣿⣿⠟⣿⡿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⣿⣿⣿⠀⠘⣧⠀⠠⠁⠿⣿⣻⣿⣿⣿⡿⣯⡻⣿⣿⣿⣿⢸⣿⣅⣤⣿⣿⣿⣿⣿⣷⣾⣿⣿⣯⣤⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⡀⠀⣿⡄⢠⣼⣷⣾⡿⠿⠟⢫⣤⡿⣿⣿⠟⠛⣋⣼⣿⣿⣿⢹⣿⣿⠿⠼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⠀⠂⠀⠀⢀⣠⡤⢀⣶⣶⣶⣶⣷⣯⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣦⣴⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣂⡐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠇⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣄⣤⣼⠋⣰⣿⣿⣿⣿⣿⡿⣯⣿⣿⠒⠛⠛⠛⢛⡋⠈⣟⠛⠛⠛⠛⢛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣉⣉⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢟⣳⠤⠶⠿⠋⠀⠻⠗⠀⠀⠈⣩⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣾⣿⣿⣿⣾⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠋⠁⠀⠀⠀⠀⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣿⣿⠿⣛⣽⣿⣿⣿⣿⣛⣿⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⠛⠻⢿⠿⠿⣿⠿⣿⣿⣿⣷⣞⣉⣳⣦⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣸⠀⠂⣸⠀⠃⣸⠀⠶⡇⢠⣈⠃⢹⠉⡉⢻⠙⣛⡟⢲⠒⠒⠶⢦⠀⠀⠀⠀⠀⢀⣬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠀⠀⠀⠀⢰⣶⣶⣿⣀⣿⡏⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢀⠃⣸⠀⣹⠀⠈⢠⡇⠀⡟⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢸⠇⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠙⡏⠏⠋⠉⠉⠛⠛⠚⠓⠒⠚⠦⠧⢤⡤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣟⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣠⡼⣿⣿⠋⠉⠻⣿⣀⣉⡛⣭⣘⢁⣥⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⠛⢻⣿⠄⠀⠈⠙⡇⠀⢀⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠋⠘⣿⠇⢀⠀⢰⣿⣯⡟⣹⣿⣹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣤⣀⡀⠉⠀⠀⠀⢀⣇⠀⢸⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⢀⡁⠀⠈⠀⢸⣽⣿⡇⣩⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣇⠀⢴⡀⠈⢿⠛⣼⣿⣿⣿⣿⣿⣿⣿⣟⢋⣽⣿⣟⢹⣿⣿⣿⣿⣿⣿⠟⣿⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⠀⠚⣧⠀⠰⢁⠿⣿⣻⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⢻⣿⣅⣄⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⡀⠤⣿⠆⢠⣼⣷⡿⠿⠿⠟⣫⣴⡿⣿⣿⠛⠛⣋⣼⣿⣿⣿⢹⣿⣿⠿⠞⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⠀⠂⠀⠀⢀⣠⡤⢀⣶⣶⣶⣶⣷⣯⣷⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⣴⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣂⡀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠸⠇⠀⠀⠀⠁⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣼⣋⣴⣿⣿⣿⣿⣿⡿⣯⣿⣿⡚⠛⠛⠛⢛⡏⠈⣟⠛⠛⠛⠛⢛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣉⣉⣟⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⠤⠶⠿⠇⠀⠻⠗⠀⠀⠀⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠾⣷⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠋⠀⠀⠀⠀⠸⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣿⣿⢿⣛⣿⣿⣿⣿⣿⣛⣿⣶⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢹⠛⠻⢿⠿⠿⣿⠿⣿⣿⣿⣷⣚⣉⣳⣦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠃⣸⠀⠃⣸⠀⠶⡇⢠⣈⠃⢹⠉⡉⢻⠙⣛⡟⢲⠒⠖⠶⢦⠀⠀⠀⠀⠀⢠⣬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⣿⠟⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⠀⠀⠀⢠⣿⣿⣿⣀⣿⡏⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢀⠃⣸⠀⣹⠁⠈⢠⡇⠀⡟⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⠇⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⢹⡏⠏⡟⠉⠉⠛⠛⠚⠓⠒⠚⠶⠧⠤⡤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣟⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣤⣼⣿⣿⠋⠉⠻⣿⣀⣩⡛⣭⣿⢁⣥⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠟⢻⣿⡄⠀⠀⠙⡇⠀⢀⡏⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠃⠘⡟⠃⢀⠀⢰⣿⣯⡟⣽⣿⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣤⣤⣀⠉⠀⠀⠀⠀⣇⠀⢸⢁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⢈⡀⠀⠈⠀⢺⣽⣿⡇⣹⣿⣿⣭⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠿⠟⠿⠿⠟⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣇⠀⣴⡀⠈⢻⡛⣼⣿⣿⣿⣿⣿⣿⣿⣟⢉⣭⣿⣟⢸⣿⣿⣿⣿⣿⣿⠟⢻⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⠀⠛⡇⠀⠰⢁⠿⣿⣻⣿⣿⣿⣿⣗⡿⣿⣿⣿⣿⢹⣿⣥⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⠦⠬⣿⠀⠤⣾⣷⢿⠿⠿⠏⢭⣴⡿⣿⣿⠟⠛⣋⣼⣿⣿⣿⢸⣿⣿⠟⠚⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠐⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⢠⣤⠆⢠⣾⣷⣶⣶⣷⣯⣷⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣴⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣢⣀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠸⠇⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣼⣋⣴⣿⣿⣿⣿⣿⣿⣯⣿⣟⡒⠛⠛⠛⢛⡟⠈⣟⠛⠛⠛⠛⢛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣋⣩⣟⣻⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢟⣧⠤⠶⠿⠃⠀⠿⠷⠂⠀⢀⣡⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⣿⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⡏⠁⠀⠀⠀⠘⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢷⣿⣿⠿⣛⣽⣿⣿⣿⣿⣛⣿⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⠛⠻⢷⠶⠾⣿⠿⣿⣿⣿⣷⣚⣉⣳⣦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢀⣀⣼⠀⠂⣸⠀⠃⣸⠀⠶⡇⢠⣈⠃⢹⠉⡉⢻⠙⣛⡟⢳⠒⠒⠶⢦⠀⠀⠀⠀⠀⢠⣬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡛⠀⢿⠟⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⢀⣿⣿⣿⣀⣿⡏⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢀⠃⣸⠀⣹⠁⠈⢰⡇⠀⡟⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⠇⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⢹⡏⢏⡟⠉⠉⠛⠛⠚⠓⠒⠚⠶⠧⠤⠤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣽⣿⣤⡇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⣼⣿⣿⠉⠉⠻⣯⣀⣭⣋⣥⣯⣡⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⡏⠹⣿⡆⠀⠀⠉⡇⠀⠀⡟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠃⢙⡿⠁⢀⠀⢶⣷⣿⡏⣽⣟⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣥⣤⣄⠈⠀⠀⠀⠀⣇⠀⢨⣃⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⢰⡁⠀⠈⠀⢺⣽⣿⠇⣹⣿⣿⣭⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⢿⡿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣇⠀⣶⡀⠈⢻⡛⣾⣿⣿⣿⣿⣿⣿⣿⣟⢫⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⠀⠙⡧⠀⠰⢁⠿⣿⣻⣿⣿⣿⣿⣗⡿⣿⣿⣿⡟⢹⣿⣥⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⠤⠼⢿⠀⠤⣾⣷⡿⠿⠿⠏⢩⣼⣿⣿⣿⠛⢛⣏⣼⣿⣿⣿⢸⣿⣿⠟⠚⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠔⠂⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣤⠆⣠⣿⣿⣶⣶⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣷⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⣄⡀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠇⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣋⣼⣿⣿⣿⣿⣿⣿⣯⣿⣿⡚⠛⠛⠛⢛⡏⠠⣟⠛⠛⠛⠛⢛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣏⣹⣿⣿⣿⣿⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⠤⠶⠿⠇⠀⠻⠗⠂⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣿⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣿⠿⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢾⠀⡆⡙⢡⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⡏⠁⠀⠀⠀⠘⠉⣿⠿⢿⣿⠿⠿⢿⣿⣿⣾⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣿⣿⠿⣛⣽⣿⣿⣿⣿⣛⢿⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠟⠻⢶⠶⠶⣽⠿⣿⣿⣿⣷⣚⣉⣳⣦⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣠⣄⣾⠀⠂⣸⠀⠃⣸⠀⠶⡇⢠⣈⠃⢹⠉⡍⢻⠙⣛⡟⢻⠒⠖⠶⢦⠀⠀⠀⠀⠀⠠⣬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠻⠟⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡄⠀⠀⠀⠀⢀⣿⣿⣿⣀⣿⡏⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢀⠃⣸⠀⣹⠁⠈⢰⡇⠀⡟⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⠇⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⢸⣿⣿⢹⡍⣯⣿⠉⠙⠛⠛⠚⠓⠖⠚⠶⠧⠤⠤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣽⣯⣴⡆⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⡾⣿⡿⠁⠉⢻⣧⣠⣭⣉⣥⡍⣠⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠏⠉⣿⡇⠀⠀⠈⣿⠀⠀⣯⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀ ⣿⡟⠁⠀⡿⠁⣀⠀⣿⣷⣾⣉⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣶⣤⣄⣀⠀⠀⠀⠀⣿⡀⠀⣃⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠀⠀⠀⠀⣿⣿⣿⢋⣽⣿⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠟⠻⠛⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⡇⠀⣷⠀⠉⢿⠋⣾⣿⣿⣿⣿⣿⣿⣿⡟⣫⣽⣿⣿⣼⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⡗⠀⢹⡇⠀⠘⢐⠿⣟⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⡟⢻⣿⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⠄⠼⠿⠀⢴⣿⡷⠿⠿⠟⠋⢷⡼⡿⣿⣿⠛⣛⣥⣾⣿⣿⣿⢘⣿⣿⡟⠛⠻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣤⣴⠆⣰⣿⣿⣶⣶⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣲⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⡄⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠸⠀⠀⠀⠘⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣡⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⠚⠛⠛⠛⢋⣏⢠⣟⠛⠛⠛⠛⢛⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣏⣏⣹⣿⣿⣿⣿⠷⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⢹⣦⠶⠶⠿⠇⠀⠻⠓⠂⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣿⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⣿⣟⣻⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠛⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠃⠀⠀⠀⠀⠁⠸⠟⢿⠿⠉⠉⠉⠻⢿⣧⣼⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢷⣿⣿⢿⣛⣽⣿⣿⣿⣿⣛⢿⣶⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠛⠻⢶⠶⠶⣶⠿⣿⣿⣿⣷⣚⣉⣳⣦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣠⣦⣿⠀⠂⣸⠀⠃⣸⠀⠶⡇⢠⣨⠃⢹⠉⡍⢻⠙⣛⡟⢻⠒⠒⠶⢦⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠂⠹⠟⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣿⣿⣿⣀⣿⡏⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢀⠃⣸⠀⣹⠁⠈⢰⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠇⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠸⣿⡿⢻⠙⣯⣿⠉⠉⠛⠛⠚⠓⠒⠚⠶⠧⠤⠤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣥⣼⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣾⣿⠟⠀⠉⢻⣧⣤⣭⣩⣭⣍⣠⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⠏⠙⣿⡆⠀⠀⠈⣿⠀⠀⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠁⠈⠟⠀⡄⠀⣿⣷⣾⣩⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣶⣦⣤⣀⣀⠀⠀⢀⣿⡀⠀⣧⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⢉⣿⣿⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠛⠛⠛⠛⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⡆⠀⣷⠀⠘⢿⢩⣾⣿⣿⣿⣿⣿⣿⣿⡟⣩⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⡇⠀⢙⡂⠀⠊⣸⠿⣿⣿⣿⣿⣿⢿⣾⡿⣿⣿⣿⡟⢿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠏⠢⠼⠿⠀⢴⣿⠿⠿⠿⠛⠉⠷⠾⡿⣿⣿⠛⣻⣥⣾⣿⣿⣿⢘⣿⣿⡟⠛⠻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠉⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣤⡴⠆⣴⣿⣿⣶⣾⣷⣯⣿⣿⢿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣄⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡄⠘⠀⠀⠀⠈⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠛⠛⠛⢛⡯⢠⣟⠛⠋⠉⠙⠛⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣍⣹⣿⣿⣿⣿⠿⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⠶⠶⠿⠇⠀⠛⠓⠂⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣾⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣟⣻⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠋⠉⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠁⠀⠀⠀⠀⠀⠚⠛⠿⠏⠀⠀⠉⠛⢿⣡⣾⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢷⣿⣿⠿⣛⣿⣿⣿⣿⣿⣛⢿⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠓⢶⠶⠶⣾⠿⣿⣿⣿⣷⣚⣉⣳⣦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⣴⣦⣿⠀⠂⣸⠀⠃⣸⠀⠶⡇⢠⣨⠃⢹⠉⡍⢻⠙⣛⡟⢻⠒⠒⠶⢦⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⠀⠹⠋⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢰⣿⣿⣿⣀⣿⡏⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢀⠃⣸⠀⣹⠁⠈⢰⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⠇⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⡿⣿⠙⣿⣿⠉⠉⠙⠛⠚⠓⠲⠚⠶⠧⠤⠤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢈⣿⣵⣾⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠟⠀⠈⢻⣧⣤⣬⣩⣮⡍⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠿⠋⠙⣿⠇⠀⠀⠈⣿⠀⠀⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠁⠹⠟⠀⡄⠀⣿⣷⣾⣩⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣷⣶⣦⣀⣀⡀⠀⢀⣿⡀⠀⣇⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣮⠀⠀⠀⠀⣷⣿⣿⢈⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⡄⠀⣧⠀⠘⢟⢱⣿⣿⣿⣿⣿⣿⣿⣿⡏⣩⣿⣿⣷⣿⣿⡿⠿⢿⣿⣿⣟⣹⣿⣿⣿⣿⣿⠿⠷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⡇⠀⢹⡂⠀⠊⣸⢿⣿⣿⣿⣿⡿⢿⣾⡿⣿⣿⣿⡏⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠃⠲⠾⠷⠀⢶⣿⠿⠿⠿⠛⠩⢷⠾⡿⣿⣿⢛⣻⣵⣾⣿⣿⣿⢘⣿⣿⡟⠙⠻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⢂⣼⣿⣿⣷⣿⣿⣯⣿⣿⠿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡤⠛⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⣠⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡛⠛⠛⠛⢛⣿⢠⣟⠛⠋⠉⠙⠛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⡟⢶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡿⣿⣿⣿⣽⣴⠶⠾⠿⠇⠀⠛⠛⠂⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣛⣟⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠉⠀⢩⠿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⢿⡇⠰⢾⠀⡆⡙⢡⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠃⠀⠀⠀⠀⠀⠛⢻⡟⠇⠀⠀⠈⠙⢿⣡⣾⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣿⣿⠿⣛⣿⣿⣿⣿⣿⣛⡿⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠳⢶⠶⠶⣿⠿⣿⣿⣿⣗⣚⣉⣳⣦⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣴⣦⣿⠀⠂⣸⠀⠃⣸⠀⠶⡇⢠⣨⠃⢹⠉⡍⢻⠙⣛⡟⢻⠒⠒⠶⢦⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠙⢋⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢰⣿⣿⣿⣀⣿⡟⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢠⠃⣸⠀⣹⠁⠈⢰⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⡃⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⡏⣿⢹⣿⣿⠉⠉⠛⠛⠚⠓⠖⠚⠶⠧⠤⠤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣸⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣵⣾⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡟⢿⣿⠋⠀⠉⢻⣥⣴⣤⣨⣮⣅⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠿⠋⠘⠿⠇⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠿⠋⠀⡐⠋⠀⡄⠀⣿⣷⣾⢡⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⣶⣦⣄⣀⣀⠀⣀⣿⡀⠀⣆⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣶⣦⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣇⠀⠀⠀⠘⣷⣿⡿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠋⠁⠀⠁⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⡄⠸⣧⠀⠘⣯⢱⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⣾⣿⣷⣿⣿⠿⠿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⡇⠈⣹⡀⠀⠃⡜⢻⣿⣿⣿⣿⡿⣿⣯⡿⣿⣿⣿⡋⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠃⠂⠿⠇⠐⠶⠿⠿⠿⠛⠛⠱⠶⠿⡿⣿⣿⣋⣫⣷⣿⣿⣿⣿⢸⣿⣿⡋⠉⢻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡧⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⡶⢂⣾⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠃⠀⠀⠀⠁⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⣴⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡛⠛⠛⠛⢛⣿⢠⣟⠛⠋⠉⠙⠛⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⡟⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠾⠿⠇⠀⠛⠛⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣻⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⠁⠀⠸⢻⣿⣿⣿⡿⠟⠻⣿⣿⣿⣿⢿⡇⠰⢾⠀⡆⡙⢁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠁⠀⠀⠀⠀⠘⠙⠻⠛⠀⠀⠀⠈⠉⡟⣠⣾⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣿⢷⣿⣿⠿⣛⣿⣿⣿⣿⣿⣛⡿⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠓⢶⠶⠾⣿⠿⣿⣿⣿⣷⣚⣉⣳⣦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣾⣶⣿⠀⠂⣸⠀⠃⣸⠀⠶⡇⢠⣨⠃⢹⠉⡍⢻⠙⣛⡟⢻⠒⠒⠶⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠙⢣⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⣿⡏⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢠⠃⣸⠀⣹⠁⠈⢰⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣸⣿⡏⡏⢹⣿⣿⠉⠉⠙⠛⠚⠓⠶⠚⠶⠧⠤⢤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣸⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣯⣷⡗⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠻⢻⡟⠁⠀⠈⣿⢶⣶⣦⣴⣾⣤⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡟⠁⠘⠿⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠘⠁⠠⠄⢸⣿⣿⣯⢼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣶⣤⣤⣄⣀⣀⣿⣀⢀⣦⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠻⠿⠿⣷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⣆⠀⢀⠀⢸⣿⣿⡏⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⠀⣸⡇⠀⠙⣯⢼⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⣧⣼⣯⣽⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠟⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⡀⠀⣿⡀⠀⢡⣟⢻⣿⣿⣿⣿⠟⣿⣿⡿⣿⣿⣿⢸⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠘⠛⠃⠐⠿⠿⠛⠛⢛⣉⡘⠷⠛⡿⣿⣿⣩⣿⣿⣿⣿⣿⣿⢨⣿⣿⣉⢉⣹⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⣶⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⢾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡛⠛⠛⠛⢛⣿⢰⣟⠛⠃⠀⠘⠛⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣿⣿⣿⣿⣿⣟⣻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠾⠿⠇⠀⠉⠁⠀⠀⣤⣴⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠁⠀⠀⠟⣿⣿⣿⡟⠛⠉⠻⢿⣿⣿⡿⢻⡇⠰⢾⠀⡆⡙⢡⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⢽⠉⣠⣾⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢳⣿⣿⢿⣛⣿⣿⣿⣿⣿⣛⣿⣶⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⠀⣰⠛⠲⢶⠶⠿⣾⠿⣯⣿⣿⣗⣚⣁⣳⣦⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⣷⣿⠀⠃⣸⠀⠃⣸⠀⠶⡇⢠⣨⠃⢹⠉⡍⢻⠙⣛⡟⢻⠒⠒⠶⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠉⢹⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣾⣿⣿⣿⣀⣿⡏⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢠⠃⣸⠀⣹⠁⠈⢰⡏⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⢥⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣿⣿⡽⡇⣻⣿⡿⠉⠉⠛⠛⠚⠓⠒⠚⠶⠧⠤⠤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢐⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠋⣿⠏⠀⠀⢈⣿⢶⣶⣦⣾⣶⣰⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣛⠀⠈⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣆⣀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠐⠁⠀⠰⠀⢸⣿⣿⣷⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣷⣦⣤⣤⣀⣀⣿⣄⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠛⠛⠻⠛⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣶⡆⠀⢀⠀⠸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⠀⣸⡇⠀⠙⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⣿⣿⠟⠛⠛⣿⣿⣿⣥⣿⣯⣽⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⡁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⡀⠀⣿⡀⠈⢠⣟⣻⣿⣿⣿⣿⠟⣿⣿⡿⣿⣿⣿⢸⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠛⠃⠘⠿⠟⠛⠛⢋⣉⣘⢟⣛⡻⣿⣿⣭⣿⣿⣿⣿⣿⣿⢸⣿⣿⣉⣈⣹⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠟⣴⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⢛⣿⢸⣟⠛⠃⠀⠙⠛⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣟⣻⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⠶⠾⠿⠏⠀⠋⠁⠀⠠⣤⣶⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣽⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠏⠀⠀⠀⠉⣿⣿⣿⠏⠁⠈⠻⢿⣿⣿⡿⢻⡇⠰⢾⠀⡆⡙⢡⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⡏⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⡿⠁⣰⣿⡇⠰⡏⢀⣶⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⢱⣿⣿⠿⣛⣿⣿⣿⣿⣿⣛⣿⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⣰⠖⠲⢶⠶⠷⣾⠿⣭⣿⣿⣗⣚⣁⣳⣦⠶⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠃⣸⠀⠃⣸⠀⠶⡇⢠⣨⠃⢹⠉⡍⢻⠙⣛⡟⢻⠒⠒⠶⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠉⢸⡏⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣿⡟⠀⠃⡼⠀⢾⠛⡆⢸⠀⡏⢠⠃⣸⠀⣹⠁⠈⢰⡏⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⢴⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⠹⡏⣿⣿⡿⠉⠉⠙⠛⠚⠓⠒⠚⠶⠧⠤⢤⣧⣤⣹⣀⣇⣸⣇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣷⣿⡇⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 1955 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/14/irc-log-131221/#comments Gemini version at gemini://gemini.techrights.org/2021/12/14/irc-log-131221/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Monday,_December_13,_2021⠀✐ Posted in IRC_Logs at 2:58 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-131221.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-131221.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-131221.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-131221.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 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12.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_Precarious_Situation_of_Slovakia_as_One_of_Battistelli’s_EPO_‘Pawns’_in the_East⠀✐ Posted in Europe, Patents at 6:42 pm by Dr. Roy Schestowitz Video_download_link | md5sum 992c807e9f012d248cde331fb1ea9c27 http://techrights.org/videos/slovakia-epo.webm Summary: Slovakia ended up abstaining on the “Strike Regulations”, maybe (at least partly) because Slovakia’s representative was a former EPO labourer, who had worked in Austria for a number of years Slovakia is a relatively ‘new’ nation because, as Wikipedia_puts_it: “Slovakia became an independent state on 1 January 1993 after the peaceful dissolution of Czechoslovakia, sometimes known as the Velvet Divorce.” 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Slovakian flag⦈ Slovakia is also not a difficult nation for the EPO to control; with a population just over 5 million people and GDP about 37 times less than Germany’s the Slovakian people (Slovaks) don’t get much of a say in the EU’s policy and the EPO’s operations. There aren’t many European Patents that are Slovakian in origin, partly due to prohibitive costs (number of patents isn’t the same as innovation; rich nations like Switzerland can afford to amass patents). They cast a vote, sometimes under political pressure (clout), and hope it doesn’t rock the boat ‘too much’. As their neighbours found out — notably Poland and Hungary — the EU can be very harsh when it does not agree politically, resorting almost to sanctions (see what_presidential candidate_Štefan_Harabin said about the EU). 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Bratislava⦈ Around the time of Benoît_Battistelli‘s visits to the_capital, as we’ve just_noted (also in this_meme about the role of António_Campinos) the agenda of the EPO became increasingly apparent. Battistelli and/or his ‘convoy’ visited the nation every year until the vote on the unlawful “Strike Regulations”. The video above discuses the situation; as we recently saw, Slovenia was used by richer nations as a pawn of ‘Team UPC’ (facts_don't_matter;_they're_not_even_brought_up) and maybe Battistelli counted on Slovakia too becoming a pawn of his. █ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⢀⢀⠀⡀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢂⣀⣄⡀⠄⠄⢃⡁⡠⣄⣀⣤⣰⡕⣂⣬⣰⣠⢤⣠⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣌⠀⢠⡄⣁⠈⣀⠀⢣⣍⣦⡄⣼⣔⡒⣴⣬⣀⣤⣨⡱⣆⣤⢦⣦⡝⣤⣣⣷⠊⢞⣢⠈⠀⣩⣖⢾⢾⣥⣽⣳⣥⣷⣾⣿⣾⣿⣿⣿⣿⣿⣾⣻⣾⣿⣯⣿ ⠀⠀⠀⠠⡠⠀⢀⠀⠀⠃⠀⠀⠄⡄⢌⠄⣴⠈⡂⢖⣲⣥⣪⣮⣿⣾⣿⣽⣷⣾⣿⣿⣿⣿⣿⣷⣿⣿⣾⣽⣿⣷⣾⣷⣿⣿⣿⣿⣾⣿⣷⣾⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡂⢄⣦⣐⡣⠼⡣⡔⢋⣯⣶⣼⣶⣿⣷⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣾⢿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠙⠃⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣇⠀⠀⠀⠀⠀⠀⣾⣧⡀⠀⠀⠐⢦⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⠀⣄⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⠀⡠⠀⠀⣼⣿⣿⣿⣿⣷⣿⢿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⡐⠱⣀⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣦⢱⣿⣿⣿⠿⠿⣿⣿⡿⠿⠿⡧⡹⣮⣿⢿⣿⠿⠟⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣷⣿⣿⠁⠀⠀⠀⠋⠀⠀⠀⠀⢻⣽⣿⣾⣿⠀⢠⡇⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⣉⡁⠁⠈⠉⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠮⠦⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠔⢀⠀⠀ ⣿⣿⣿⣿⣓⣶⣾⣿⣿⣿⣿⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠀⠀⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣦⣠⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠿⠿⢿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣶ ⣿⣿⡿⠉⠉⠉⠉⠉⠉⠹⠉⠉⢩⠉⠉⠉⠁⠀⠀⡇⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣿⣷⠀⠀⠘⠀⠀⠀⡀⠀⠀⠇⠀⠀⢡⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⢰⠀⣠⠀⠀⠶⢂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⡆⠀⠀⠁⠀⠀⢠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠺⣿⣿ ⣿⣿⣉⣈⣀⣀⣀⣀⣤⣄⣤⣤⣦⣤⣤⣴⣤⣤⣼⣦⣤⣈⢹⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡄⢠⣶⣿⣶⣶⣿⣶⣶⣾⣷⣶⣾⣷⣶⣶⣶⣶⣶⣦⣽⣿ ⣿⣿⣿⣿⣿⣿⠿⠿⢿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠉⡇⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⣿⣿⣿⢸⣿⢸⣿⢸⡇⢿⡇⣿⡇⡇⣿⡟⣿⠀⠀⠀⠀⢿⣷⠄⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠉⠸⣿ ⣿⡥⢐⣒⢀⡆⣒⡂⡄⢐⣒⢰⠀⣒⡃⠁⣛⡃⡿⢸⡇⠁⡇⠀⠀⠀⠀⠀⠙⠛⠛⢸⠀⠉⠉⠉⠈⠉⠈⠉⠈⠁⠈⠁⠉⠁⡇⠉⠁⠉⠁⠀⠀⠀⢹⣿⢠⠀⠀⠀⠀⠀⠀⠆⠀⠀⠄⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⣿ ⣿⡄⣼⡟⢸⢀⣿⠀⠃⡏⡅⣸⢀⣿⢰⢠⣿⠇⡇⣸⣇⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸ ⢏⠁⠉⠁⠈⠈⠉⣸⣄⠈⠁⠁⠈⢉⣬⣈⡉⠀⣁⠉⠉⣲⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⡆⡀⠀⠀⠀⣠⣀⣖⣦⣠⣤⣤⣤⣄⣶⣤⣤⣠⠀⠀⠀⠄ ⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣦⣀⣀⠀⣀⣸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡼⣧⢄⣄⣠⣴⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⡋⠋⠀⠀⠀⠀⢲ ⠏⠉⣡⣿⣭⣭⣷⣾⣿⣿⣯⣍⡉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⢹⢽⡿⡿⠘⠐⣿⠿⢿⠞⣟⣿⠿⣏⠵⠿⠿⢿⠿⢿⡿⠟⠛⡁⠀⣹⠁⠈⢹⠿⠿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣤⣶⣿⣿⠿⡻⠡⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣔⣿⣿⣿⣿⣿⣿⣶⣶⣦⣷⣴⣶⣾⣿⣶⣶⣶⣿⣿⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀ ⡀⡀⡀⠀⠉⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠙⠋⠉⣿⢟⠋⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣦⢔⠿⣿⣿⣿⣿ ⠏⠱⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣏⠿⠿⢿⡿⠿⠺⠮⠾⠤⠿⠿⣿⠟⠿⡿⠿⣇⣀⡀⠴⢻⠆⠤⣼⣗⡈⢺⣿⠧⡟⠿⠿⠿⣿⠿⠻⡟⠛⠻⢿⣽⠙⠉⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠙⠶⣝⡻⣿ ⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣾⣷⣶⣶⣶⣷⣾⣾⣾⣷⣿⣿⣷⣾⣿⣿⣿⣶⣾⣷⣾⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠙⣶ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣀⣼⠿⠛⠛⠛⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡗⣦⣶⣿⣿⣷⣶⣶⣶⣶⣶⣦ ⠿⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣻⡃⢀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠻⢿⣿⣿⣿⣿⣿⣿⡿⡇⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⢸ ䷩ 𝚕𝚒𝚗𝚎 2227 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/14/slovakia-epo-lobbying/#comments Gemini version at gemini://gemini.techrights.org/2021/12/14/slovakia-epo-lobbying/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXV:_Slovakian_Scruples⠀✐ Posted in Europe, Patents at 5:58 pm by Dr. Roy Schestowitz Series parts: 1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In! 2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous” Endorsement? 3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes 4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States 5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja” 6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch Courage 7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity 8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and Pusillanimous_Hibernia 9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss Cheese 10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the Controversial_Christian_Bock 11. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_– Battistelli’s_Swiss_Apprentice? 12. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection 13. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIII:_Battistelli’s_Iberian Facilitators_–_Spain 14. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XIV:_Battistelli’s_Iberian Facilitators_–_Portugal 15. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XV:_Et_Tu_Felix_Austria… 16. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVI:_The_Demise_of_the Austrian_Double-Dipper 17. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVII:_The_Non-Monolithic Nordic_Bloc 18. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XVIII:_Helsinki’s_Accord 19. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXX:_The_Baltic_States 20. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XX:_The_Visegrád_Group 21. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXI:_The_Balkan_League_–_The Doyen_and_His_“Protégée” 22. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXII:_The_Balkan_League_– North_Macedonia_and_Albania 23. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIII:_The_Balkan_League_– Bulgaria 24. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXIV:_The_Balkan_League_– Romania 25. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXV:_The_Balkan_League_– Fresh_Blood_or_Same_Old,_Same_Old? 26. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVI:_A_Trojan_Horse_on_the Budget_and_Finance_Committee 27. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVII:_Cypriot_Complicity 28. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXVIII:_Benoît_and_António’s Loyal_“Habibi” 29. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IXXX:_The_EPOnian_Micro- States_–_Monaco_and_Malta 30. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXX:_San_Marino_and_the Perfidious_Betrayal_of_Liberty 31. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXI:_The_Abstentionists 32. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXII:_“Plucky_Little Belgium”? 33. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIII:_Swedish_Scepticism 34. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XXXIV:_An_“Extremely Dubious”_Proposal 35. YOU ARE HERE ☞ Slovakian Scruples 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Luboš Knoth⦈ Head of the Slovak delegation, Luboš_Knoth. [PDF] Summary: Today we examine the Slovakian vote on the unlawful “Strike Regulations”; Luboš Knoth used to work for the EPO, so he could relate somewhat to his former colleagues As already noted in an_earlier_part of this series, Slovakia was the only member of the Visegrád Group that actively withheld its support from Benoît Battistelli‘s “Strike Regulations” proposal. The delegations from Hungary and the Czech Republic did not bother to turn up for the vote and Poland voted in favour. In June 2013, the Slovak delegation was headed by Luboš_Knoth. “A former EPO employee like Susanne Sivborg from Sweden, Knoth seems to have had a certain degree of empathy with his erstwhile colleagues at the EPO…”Knoth was head of the Industrial_Property_Office_of_the_Slovakian_Republic between June 2012 and October 2016 and prior to that he had worked at the Vienna branch Office of the EPO as a “project manager for administration of cooperation activities” between September 2005 and 2008. A former EPO employee like Susanne Sivborg from Sweden, Knoth seems to have had a certain degree of empathy with his erstwhile colleagues at the EPO, unlike the majority of his peers on the Administrative Council who behaved in the manner of “absentee_landlords”. In this regard, Knoth and Sivborg acted in stark contrast to the_San_Marino delegate_Bruno_Cinquantini, a shameless opportunist who appears to have had no scruples about selling out his former colleagues at the EPO. “The Slovak refusal to support the “Strike Regulations” is noteworthy because Battistelli had done his level best to co-opt this junior member of the Visegrád Group.”However, like Sivborg, Knoth’s criticism of the manifestly unlawful “Strike Regulations” was rather muted and timid and gives the impression that there were only minor problems with Battistelli’s proposal. This can be seen from the statement of the Slovak position recorded under point no. 115 of the minutes_of_the_136th [PDF] Administrative Council meeting: “The Slovak delegation commented on some of the detailed drafting. On balance, it felt that the proposal was a good faith one, but not ideal. Having said that, it shared the understanding that a legal basis should be set and rules established. It would favour a review of the policy and its results, should the Office’s proposal be adopted. It would like to see a fair and constructive, functioning social dialogue in the Office in future.” The Slovak refusal to support the “Strike Regulations” is noteworthy because Battistelli had done his level best to co-opt this junior member of the Visegrád Group. “The backdrop to this conference was the European Union’s plan for “the introduction of a unitary patent and litigation system”.”Already in June_2011 (warning: epo.org link) – that is to say, approximately one year after he had assumed the position of EPO President – Battistelli convened a conference of “the EPO and its member states” in Bratislava for the purpose of discussing “how to bring co-operation forward in a number of areas in order to improve the quality and efficiency of the European patent system, and thus better serve industry”. The backdrop to this conference was the European Union’s plan for “the introduction of a unitary patent and litigation system”. The official records show that Battistelli was accompanied on that occasion by his cooperation_fund_"bagman" François-Régis Hannart and his virtuoso_of_legal sophistry, EPO Vice-President Raimund Lutz. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Battistelli, François-Régis Hannart, and Raimund Lutz⦈ Battistelli (r.) accompanied by EPO “bagman” François-Régis Hannart (l.) and EPO Vice-President Raimund Lutz (c.) at an EPO conference held in Bratislavia in June 2011. The following year, in_November_2012 [PDF], Battistelli sent a delegation headed by his “bagman” Hannart on a visit to the Slovak Industrial Property Office to discuss “bilateral cooperation” affairs. Hannart was accompanied by Georg Artelsmair from the EPO’s “European Cooperation Directorate” and Katarína Laššová, a cooperation projects co-ordinator. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇François-Régis Hannart, Georg Artelsmair, and Katarína Laššová⦈ EPO “bagman” François-Régis Hannart (c.) flanked by Georg Artelsmair (l.) and Katarína Laššová (r.) visiting the Slovak Industrial Property Office in November 2012. In May 2013 just before the 136th Meeting of the EPO Administrative Council, Battistelli turned up in Bratislava in person. The ostensible purpose of this visit was to attend an_event (warning: epo.org link) to mark the 20th anniversary of the Slovak Industrial Property Office. “With hindsight it seems clear that as far back as 2013, Campinos was being carefully groomed as the “designated successor” of Battistelli at the helm of the EPO, a role which he ultimately assumed in July 2018.”Battistelli was accompanied by an “EPO delegation” which met with the Slovak Minister of Economic Affairs Tomáš Malatinský. This “EPO delegation” included an “observer” in the person of António_Campinos, who was at that time the head_of_EU_trademark_agency_OHIM. With hindsight it seems clear that as far back as 2013, Campinos was being carefully groomed as the “designated successor” of Battistelli at the helm of the EPO, a role which he ultimately assumed in July 2018. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Battistelli and Tomáš Malatinský⦈ Battistelli meeting with Slovakian Minister of Economic Affairs Tomáš Malatinský in Bratislava in May 2013. His “designated successor”, António Campinos, can be seen in the background. Despite Battistelli’s attempts to turn Slovakia into one of his “captured states” on the EPO Administrative Council, the head of the Slovak delegation Luboš Knoth did not succumb to the blandishments of the Corsican despot and refused to endorse the liberticidal “Strike Regulations” at the 136th Meeting of the EPO Council in June 2013. Slovakia’s abstentionist position was followed by two EPO member states from the Balkan region, namely Serbia and Slovenia. In the next part we will take a look at the delegation representing the Republic of Serbia. █ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠛⠻⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣦⣤⣀⣀⠀⠀⣀⣀⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠸⠸⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⠿⠋⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⢄⢀⣀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠖⠂⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡫⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢳⡝⠌⠙⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢉⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡾⣃⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣟⣡⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠘⣤⣸⡏⣼⡏⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣈⠀⠞⢻⡇⣿⣧⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⢉⣠⣤⣴⣶⣶⣿⣿ ⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⢸⣷⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢍⡋⢉⣩⣤⣴⣶⣾⣿⡇⣼⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠸⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡀⢀⡀⣾⢿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠲⢝⠻⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⣿ ⡄⠀⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢸⠇⣸⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⠮⡉⢩⣥⠈⠀⠀⢸⣿⣿⣿⣿⣿ ⢿⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⡖⢸⡇⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡑⠌⠀⠀⠀⠈⠻⠻⣿⠁⣿ ⣿⠀⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡋⠸⠃⣛⣣⣽⣽⠿⠛⢿⣿⣿⣿⣿⣿⣿⡿⢋⣉⠀⠀⣀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⢸⣿⠀⣿ ⣿⡀⣿⣷⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠱⠀⢁⣴⣿⣿⣿⣿⣿⣷⡀⠀⠙⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠙⠻⢷⣭⣿⡇⠀⠀⠀⠀⠀⠀⠘⠿⣀⣿ ⣟⠀⣿⣿⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣡⠀⠀⠈⠻⠇⠀⠀⠀⠀⢠⣶⣦⡁⠈⣿ ⣿⢀⣸⡧⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣛⣛⠟⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⠨⣻⣿⣖⣾⣿⣿⣏⣃⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢨⣯⣾⣷⣶⣾ ⣿⣂⣾⡇⡆⠀⠀⠀⠀⢦⢈⣾⣿⣿⣿⣿⣷⣿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⢉⣭⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣤⡂⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿ ⠀⠈⠻⡇⡄⠀⠀⠀⠀⠈⠳⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡿⢾⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⠛⠿⣿⣿⣿⣷⣤⡠⢤⠀⠀⠀⠙⠻⣿ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠳⣾⣿⣿⡿⠿⣟⣽⣿⣧⢀⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠙⠻⢷⣿⣷⣶⣷⣶⣿⣷⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⢛⣫⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡀⠀⢀⠈⣥⣾⣿⣿⣿⡿⠁⠀⠙⠟⠋⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢞⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⡄⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠣⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡵⣛⣛⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣿⣾⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⡼⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⣿⣿⣿⢻⣷⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿ ⣧⣤⣤⣤⣤⣀⣀⣼⣿⠇⠠⣽⢀⣶⣤⡼⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⣾⣛⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣼⣿⣿⣿⣿⣖⢺⣤⡄⠀⣤⣤⣭⣥⣤⣤⣤⣴⣲⣶⣏⣹⣿⣿⣀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⠶⣶⢶⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠚⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⢀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠏⠉⠉⠀⠀⠀⠀⠀ ⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣀ ⠀⠀⡄⠀⢀⠞⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠹⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛ ⠀⠀⠁⢀⠎⠀⠠⠆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⢛⣿⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢐⠀⣀⣀⣀⠀⣤⣤⢤⣄⣤⠀⠀⣤ ⠀⠀⠀⡞⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠀⠀⠀⠀⠀⣎⣿⡇⠘⠷⢤⡇⠀⠀⣿⡤⢠⡇⠀⠀⠀⢰⠀⠀⠀⠀⣧⠀⠘⢆⣰⠘⣾⣿⣷⣶⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⣺⢷⣿⣿⡿⠀⠄⠀⢨⣷⣿⠀⠀⣹ ⠀⠀⠀⠀⠀⠙⠁⠘⠁⠀⠈⠀⠉⣹⠟⠛⠙⠛⠛⠛⠛⠟⠛⠻⠿⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣰⠄⠀⠀⠈⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⡆⠀⠀⠀⢀⣼⠀⠀⢰⣶⣿⣿⠣⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣄⢠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣧⠀⠀⠀⣼⣿⠀⠀⣾⣿⣿⣿⣧⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⡀⠀⢀⣠⣿⣤⣴⣄⣤⠀⣤⠀⢀⢀⣤⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⠀⣠⣾⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣾⣿⣿⣹⣟⣿⣿⣿⣿⡿⣷⢻⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡇⠐⣿⣿⣿⣿⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⠇⣸⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡧⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠏⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⣼⣾⣿⣿⣿⡇⣼⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣿⣿⣿⣿⣿⡇⣿⡿⠋⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢻⡿⠟⠃⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠋⠉⠙⢿⣿⣿⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣭⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⡍⠙⠀⠀⠀⠀⠙⢿⠀⢀⠿⣿⡿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⣿⣿⣿⣿⣟⢆⠛⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢹⡾⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠛⠻⢿⣗⠀⢰⣿⠂⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠅⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⡿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣹⣿⠛⢸⡏⠀⢿⣿⠘⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢹⡿⠀⠼⠄⡄⢾⣿⡆⠸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠟⠁⠠⡚⠘⠁⠘⣿⣷⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⠀⠀⢠⡗⠀⠀⠀⣿⣿⡅⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠁⠀⠀⢸⣇⠀⠀⠀⢹⡿⡇⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠃⠀⠀⠀⣿⡏⠀⠀⠀⠸⣿⡄⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡰⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⢿⣷⣽⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⠀⠀⠀⠀⠀⠐⢻⠁⠀⠀⠀⠀⠐⡟⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢴⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣀⣠⣤⣀⡀⠀⢀⠀⠀⢀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡀⠇⠀⣺⣿⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠁⠀⠻⠿⣿⣉⡄⠙⢷⣿⣄⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢠⡀⠀⠀⠀⠘⠛⠓⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 2552 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/14/tomas-malatinsky-and-epo/#comments Gemini version at gemini://gemini.techrights.org/2021/12/14/tomas-malatinsky-and-epo/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_[Teaser]_Buying_Power_or_Securing_Control_(the_Leadership_Positions) of_Europe’s_Largest_Patent_Office⠀✐ Posted in Europe, Patents at 3:50 am by Dr. Roy Schestowitz Who needs elections when you_can_buy_the_vote(r)s (by meeting the boss of the boss while offering cash, conditionally)? 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Buying_the_office:_Tomáš_Malatinský_and_EPO⦈_ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Slovakia abstains⦈ Summary: Slovakian Minister of Economic Affairs Tomáš Malatinský met Benoît_Battistelli and António_Campinos in May 2013, only weeks ahead of the vote on the EPO‘s unlawful “Strike Regulations” ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⢸⣿⣿⠀⣿⣿⡇⢻⣿⡏⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣹⢸⣿⡇⣟⣷⣿⡿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢸⢸⣿⣿⠀⣿⣿⡇⡟⣿⣿⣼⣿⢧⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡰⢾⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠱⣴⡄⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢾⢸⣿⣿⠀⣿⣿⡇⣿⢻⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢫⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⠀⠀⠎⢳⡴⠆⠀⠀⠀⣤⣄⠀⠀⢈⡇⣶⣿⠏⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⣿⣿⡇⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⡇⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠑⣄⠁⠀⠀⠀⠀⠰⠄⠁⠀⠀⠀⠐⠘⢻⣷⡶⠾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡼⣿⣿⣴⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⡇⣟⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⣌⣀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠈⢿⣿⣿ ⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣷⣿⣿⣾⣽⣿⣯⣷⣿⣿⣷⣭⣭⣽⣿⣿⣭⣭⣽⣯⣭⣽⣿⣭⣭⣵⣿⣾⣽⣯⣵⣭⣭⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣿⣿⣿⣿⣿⣿⣿⢿⣍⣉⡝⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣹⣿⣿⣿⡟⣬⣽⣿⣟⣿⣿⣘⣾⣮⣯⡾⣿⣿⣿⣯⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⡿⠿⢿⣿⣿⣿⢿⣿⠿⢿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⡷⠼⠿⡿⠧⣿⣿⢸⡿⠿⠿⢿⡼⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣩⣟⣿⣶⣶⣿⣿⢰⣶⣾⣿⣭⣧⣾⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⢀⢀⡀⢀⡀⣀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣷⣿⣿⢿⣿⣟⣿⣿⠸⣿⣿⣾⣯⣽⣿⣿⣿⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠻⠇⠏⠫⠟⡯⠇⠿⠱⠿⠸⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⡿⠿⠿⠿⣟⠏⠁⠉⠈⠈⠻⣿⡿⠿⠿⣿⣿⣣⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⢠⡤⡦⣠⡄⡤⡤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢘⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⠃⠙⠂⠁⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣜⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡻⣦⣀⠀⠀⠀⠀⢀⣤⡾⣫⣞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡾⠛⠟⠿⠻⣶⣴⢾⡻⠵⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠟⠻⠿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⡇⣾⣿⡇⢸⣿⡇⢰⣿⣿⣿⡇⢓⣴⢋⣶⣿⢿⣷⣌⠀⣿⣿⣿⣿⢸⣿⣿⣿⡇⣾⣿⡇⢋⣶⣿⢿⣷⣎⠃⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⠀⡄⣿⣿⣇⣸⣿⡇⢸⣿⣿⠀⠒⣿⣿⢸⣿⣿⢸⣿⣿⠀⣿⣿⠀⠠⢸⣿⣿⠐⠄⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⣿⣿⡇⠂⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⡇⣿⣿⡿⢿⣿⡇⢸⣿⣿⠿⠇⣿⣇⢸⣿⣿⢸⣿⣿⠀⣿⣿⡿⠇⢸⣿⣿⠿⠇⣿⣿⡇⢸⣿⣿⠀⠭⠭⠄⣿⣿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⡇⣿⣿⡇⢸⣿⡇⢸⣿⣿⠐⠋⢷⡽⢸⣿⣿⢸⣿⣿⠀⣿⣿⠀⢶⢸⣿⣿⢰⡆⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⣿⣿⡇⠒⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠿⢀⡇⠿⠿⠇⠸⠿⠇⠸⠿⠿⠿⠿⡘⣧⣈⠻⢿⣿⠿⢋⡄⠿⠿⢀⠗⠸⠿⠿⠘⡇⠿⠿⠇⡌⠻⢿⣿⠿⢋⠄⠿⠿⠿⠿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣾⣾⣾⣷⣷⣾⣿⣶⣶⣶⣶⣷⣿⣷⣿⣶⣶⣾⣷⣾⣾⣿⣿⣾⣷⣿⣶⣿⣿⣾⣾⣾⣿⣿⣶⣶⣾⣿⣾⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣏⣉⣻⣿⣿⣿⣷⣰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣦⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡀⣾⡟⠋⠛⣿⠟⣻⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⢀⣿⡏⣻⣿⣟⠀⠉⠙⢩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠸⠟⠃⠘⢻⣿⡆⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣄⣰⣂⢠⣠⣔⠁⠀⠙⠛⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠻⠿⠀⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣔⣦⣤⣾⣿⣿⠀⢽⣿⣿⣧⠄⠠⣿⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣛⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⠋⠀⠐⣾⣽⣿⣿⣿⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⡆⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡆⠀⠀⠀⠀⠀⢈⣏⣿⣿⣿⣿⣿⣷⡄⠀⣠⣿⣷⣄⡀⠀⠀⠀⠀⢻⣶⣦⣄⠀⠀ ⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⡀⠀⣤⣤⣴⣿⣿⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣆⣀⣠⣾⣿⣿⣿⡦⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣿⣿⣿⣿⣿⠘⣿⣶⠎⣿⣿⣿⣿⣿⣿⣿⢷⠙⢿⣿⣿⣿⣿⣿⣿⠋⠀⠳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣇⠁⠿⣿⣿⣿⣿⣿⣿⣷⡄⠉⢿⣿⣿⡿⣿⡦⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⢣⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⡆⠘⠻⠷⣶⣽⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣽⣭⣥⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠀⠀⠀⠀⢸⢹⠏⠁⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣧⡋⢹⣿⣿⣿⣿⠁⣙⠙⠛⣿⣿⣿⣿⠿⠼⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⠀⢸⣷⠀⠀⢹⣿⣿⣿⣿⣿⣟⣀⣀⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣶⡶⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣿⣿⠀⠀⠈⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠋⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣯⣉⣻⣿⣿⣿⣷⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣦⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡍⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⠿⠿⠿⠦⣿⣟⠉⠉⢻⠛⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣻⣿⣛⠀⠉⠙⣩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⣿⣿⣷⣾⢿⣷⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⠿⠁⠘⢻⣿⡆⣀⣴⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⡀⠀⠀⣸⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⣀⣰⣆⢠⣠⣔⠀⠁⠛⠋⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⠷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣤⣤⣾⣿⣿⠈⠽⣿⣿⣧⠄⢠⣿⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⣛⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠋⠀⠐⣾⣹⣿⣿⣿⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡆⠀⠀⠀⠀⠀⢈⣏⣿⣿⣿⣿⣿⣷⡄⠀⣠⣿⣷⣄⡀⠀⠀⠀⠀⢻⣶⣦⣄⠀⠀ ⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣛⡀⠀⣤⣤⣴⣿⣿⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣆⣀⣠⣾⣿⣿⣿⡦⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⠘⣿⣿⠎⣿⣿⣿⣿⣿⣿⣿⠶⠙⢿⣿⣿⣿⣿⣿⣿⠃⠀⠳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣇⠉⠻⣿⣿⣿⣿⣿⣷⣷⡄⠈⢿⣿⣿⡿⣿⡦⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣡⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡏⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⡄⠘⠿⢷⣾⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣽⣭⣭⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠉⠀⠀⠀⠀⢸⢟⡇⠀⣼⠺⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⡏⢹⣿⣿⣿⣿⢁⣛⢛⡛⣿⣿⣿⣿⠿⠼⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⣿⠀⠙⢻⣿⣿⣿⣿⣿⣏⣀⣀⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣶⡶⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢠⣿⡇⠀⠀⠀⠙⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⠷⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣭⣉⣽⣿⣿⣿⣧⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣦⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣷⡀⣿⣟⠉⠉⣻⠛⣿⣿⣿⣿⣿⣿⣇⠂⠀⠀⠀⠀⠀⠀⢀⣿⡏⣻⣿⣛⠀⠉⠙⣩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣾⣿⣿⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠸⠟⠃⠘⢻⣿⠆⣀⣴⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣄⣰⣇⢠⣠⣴⠀⠀⠛⠛⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⢿⡿⠛⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣔⣠⣤⣾⣿⣿⠈⢽⣿⣿⣧⠀⢤⣿⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠘⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠽⠋⠀⠐⣾⣽⣿⣿⣿⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡄⠀⠀⠀⠀⠀⢈⣏⣿⣿⣿⣿⣿⣷⡄⠀⣠⣿⣷⣄⡀⠀⠀⠀⠀⢻⣶⣦⣄⠀⠀ ⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡛⡀⠀⣤⣤⣴⣿⣿⢺⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣄⣀⣠⣾⣿⣿⣿⡦⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⠘⣿⣶⠎⣿⣿⣿⣿⣿⣿⣿⢷⠙⢿⣿⣿⣿⣿⣿⣿⠃⠀⠳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣇⠉⠿⣿⣿⣿⣿⣿⣿⣷⡄⠈⣿⣿⣿⡿⣿⡦⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣶⣄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡥⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⡄⠘⠻⠷⣶⣿⣿⣯⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣻⣿⣿⣿⣟⢿⣿⣿⣿⣿⡗⠀⠀⢰⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠈⡟⡟⢠⡟⠀⢹⣿⣿⣿⠘⠛⠿⡿⠏⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⡏⢸⣿⣿⣿⣿⢁⣉⢛⣛⣿⣿⣿⣿⠿⠼⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⠁⠀⠀⢻⣿⣿⣧⠀⠀⢀⣀⣀⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⡶⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠃⠀⠀⠀⠈⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠟⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⠋⣯⣿⣅⣈⣽⡻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣦⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠻⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡷⠀⣿⡋⠉⠉⢙⠋⣽⣾⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡍⠛⠿⠓⠀⠀⠉⢩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⣿⣿⣷⣾⣿⣿⡶⠶⠿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⠀⠀⠟⠀⢀⣴⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠘⠛⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀⠀⠀⠈⠉⣩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⢿⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣾⣿⠋⠀⠸⠟⠋⠀⠀⠀⢿⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣶⣶⣢⣴⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠐⣺⡀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠡⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⠛⠙⠛⣃⣀⣀⠀⣨⣥⣄⠀⣤⣤⣤⠀⣶⣶⣶⠀⠀⠀ ⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠿⠿⠛⢿⣿⢟⣛⣛⣛⣛⣛⠻⣿⡟⣁⣤⣤⣦⣤⡀⢰⣶⣶⣶⣶⣶⣿⡆⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⠀⣿⣿⣿⡆⢹⣿⣿⠀⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣶⣿⣿⣿⡇⠃⢸⣿⣿⣿⢿⣿⣷⡌⢸⣿⣿⡟⢿⣿⣿⡘⠛⢻⣿⣿⡟⠉⠁⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⡀⢿⣿⣿⣿⣼⣿⣿⡀⢸⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠋⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⢸⣿⣿⡇⠸⣿⣿⣷⣬⡉⠉⢥⡗⢸⣿⣿⣿⠀⠀⣿⣿⡇⣿⣿⣧⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡆⠀⠀⢸⣿⣿⢹⣿⣿⡇⠘⣿⣿⣿⣿⣿⣯⣄⠀⠙⠻⢿⣿⣿⣷⡌⢻⠀⣿⣿⣿⠀⢸⣿⣿⣇⣹⣿⣿⡄⢻⣿⣿⡇⢸⣿⣿⡹⣿⣿⣿⡇⠀⠿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡏⣶⠀⢸⣿⣿⣀⣿⣿⣷⠀⣿⣿⣿⠀⣿⣿⣿⠀⣶⣶⣶⠙⣿⣿⣿⠀⠀⣿⣿⣿⠀⢸⣿⣿⡿⢿⣿⣿⣧⢸⣿⣿⡇⠸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣧⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠈⠀⠏⠀⣾⣿⣿⡿⢿⣿⣿⡆⣿⣿⣿⣤⣿⣿⣿⠀⢻⣿⣿⣶⣿⣿⡟⣼⠃⣿⣿⣿⡇⢸⣿⠿⠇⠀⠿⠿⠿⠘⠛⠛⣃⣀⣛⠋⠥⠦⣭⠭⢵⣶⣯⣤⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⡇⠸⠿⠿⠷⠿⠿⠟⠛⠛⣛⣉⣠⣶⣭⣙⣻⣭⣥⣾⣷⣽⣆⣢⣤⣿⣷⣶⠶⠶⣖⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠲⠶⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠙⠛⠉⠉⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⢛⣿⣿⣅⣈⣽⣻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣦⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠘⢿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⡧⢠⣿⡋⠉⠉⣹⠋⣽⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⠛⠿⠓⠀⠀⠉⢩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢛⣿⣯⡉⢉⣛⢿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠁⢿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣎⢿⣿⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⡇⢰⡟⠛⠙⠛⠛⢛⣻⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡍⠛⠿⠋⠀⠁⠙⢩⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣷⣾⡿⠦⠤⣾⣷⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠁⠀⠀⠟⠀⠀⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⡀⠀⠀⠈⠉⣩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠟⠹⣷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣶⣿⠏⠀⠸⠿⠏⠀⠀⠀⣿⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠙⠋⠈⣿⣿⣿⣿⣿⣧⣬⣶⣠⣴⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠁⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⠛⠙⠛⣃⣀⣀⠀⣨⣥⣄⠀⣤⣤⣤⠀⣶⣶⣶⠀⠀⠀ ⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⡿⠿⠛⠻⢿⣿⢟⣛⣛⣛⣛⣛⠻⢿⡿⣁⣤⣤⣦⣤⡀⢰⣶⣶⣶⣶⣶⣾⡆⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⠀⣿⣿⣿⡆⢹⣿⣿⠀⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⣶⣿⣿⣿⡇⠃⢸⣿⣿⣿⢿⣿⣷⡌⢸⣿⣿⡟⢿⣿⣿⡘⠛⢻⣿⣿⡟⠉⠁⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⡀⢿⣿⣿⣿⣼⣿⣿⡀⢸⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⠛⠛⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⢸⣿⣿⡇⠸⣿⣿⣷⣬⡉⠉⢡⡷⢸⣿⣿⣿⠀⠀⣿⣿⡇⣿⣿⣧⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⡄⠀⠀⢸⣿⣿⢻⣿⣿⡇⠘⣿⣿⣿⣿⣿⣯⣄⠀⠙⠻⢿⣿⣿⣷⡌⢻⠀⣿⣿⣿⠀⢸⣿⣿⣇⣹⣿⣿⡄⢻⣿⣿⡇⢸⣿⣿⡹⣿⣿⣿⡇⠀⠿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣄⠀⢸⣿⣿⣀⣿⣿⣷⠀⣿⣿⣿⠀⣿⣿⣿⠀⣶⣶⣶⠙⣿⣿⣿⠀⠀⣿⣿⣿⠀⢸⣿⣿⡿⢿⣿⣿⣧⢸⣿⣿⡇⠸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣧⣼⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠁⠀⠀⠀⠀⢸⠁⣿⠀⣾⣿⣿⡿⢿⣿⣿⡆⣿⣿⣿⣤⣿⣿⣿⠀⢻⣿⣿⣶⣿⣿⡟⣼⠆⣿⣿⣿⡇⢸⣿⠿⠇⠀⠿⠿⠿⠘⠛⠛⣃⢀⣛⠋⠥⠦⣭⡭⠽⣶⣯⣤⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⡇⠸⠿⠿⠷⠿⠿⠛⠛⠛⣛⣉⣠⣶⣭⣙⣿⣭⣥⣾⣷⣺⡆⣦⣤⣾⣷⣶⡶⠶⠶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠗⠀⠀⠀⣿⡓⠲⠶⢶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢛⣻⣏⡉⣉⣛⢿⣷⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠁⢿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣞⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⡇⢰⡿⠛⠙⠛⠛⢛⣻⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡍⠛⠿⠛⠀⠁⠙⢩⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢛⣻⣏⠉⢙⡻⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠘⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡞⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⡇⢰⡟⠛⠛⠛⠛⢛⣧⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠻⡿⠃⠀⠉⠙⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⢀⣿⣿⣿⣷⣾⣿⢦⢤⣾⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠗⠀⠀⣴⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠆⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠘⠉⣹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡇⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣶⣿⠇⠀⠸⢻⠋⠀⠀⠀⣿⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠘⠛⠘⣿⣿⣿⣿⣿⣿⣶⣦⣄⣴⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠁⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣤⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⠋⠙⠄⠀⠀⠀⠀⠀⠀⠀⠋⠃⠙⠃⠙⠙⣁⣀⣀⠀⣩⣤⣄⠀⣤⣤⣤⠀⣶⣶⣶⠀⠀⠀ ⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⡿⠿⠛⠻⢿⣿⢟⣛⣛⣛⣛⣛⠻⢿⡟⣁⣤⣴⣦⣤⡀⢰⣶⣶⣶⣶⣶⣾⡆⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⠀⣿⣿⣿⡆⢹⣿⣿⠀⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢰⣶⣿⣿⣿⡇⠉⢸⣿⣿⣿⣿⣿⣷⡌⢸⣿⣿⡟⢿⣿⣿⡘⠛⢻⣿⣿⡟⠉⠁⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⡀⢿⣿⣿⣿⣼⣿⣿⡀⢸⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⣉⠛⠋⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⢸⣿⣿⡇⠸⣿⣿⣷⣬⣉⠉⢡⡷⢸⣿⣿⣿⠀⠀⣿⣿⡇⣿⣿⣧⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡄⠀⠀⢸⣿⣿⢻⣿⣿⡆⠘⣿⣿⣿⣿⣿⣯⣄⠀⠙⠻⢿⣿⣿⣷⡄⢻⠀⣿⣿⣿⠀⢸⣿⣿⣇⣹⣿⣿⡄⢻⣿⣿⡇⢸⣿⣿⡹⣿⣿⣿⡇⠀⠿⣿⡇⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣻⣏⠉⢙⡻⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠨⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⣿⡜⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⡇⢰⡟⠛⠛⠛⠛⢛⣧⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⠻⠿⠃⠀⠉⠛⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣧⣾⡷⢆⢤⣾⣦⣼⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠀⠀⠐⠆⠀⠀⣰⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⡇⠀⠐⠆⠿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡇⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣠⣴⡿⡇⠀⠺⡿⡇⠀⠀⠀⣿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠁⠀⠀⠙⠛⢹⣿⣿⣿⣿⣿⣷⣶⡔⢄⣴⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠁⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣦⣄⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠋⠛⠄⠀⠀⠀⠀⠀⠀⠀⠋⠃⠙⠋⠛⠛⣁⣀⣀⠀⣠⣤⣄⠀⣤⣤⣤⠀⣶⣶⣶⠀⠀⠀ ⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠿⠟⠻⠻⢿⣿⢟⣛⣛⣛⣛⣛⠻⢿⡟⣁⣤⣤⣦⣤⡀⢰⣶⣶⣶⣶⣶⣾⡆⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⠀⣿⣿⣿⡄⢹⣿⣿⠀⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣶⣿⣿⣿⡇⠉⢸⣿⣿⣿⢿⣿⣷⡌⢸⣿⣿⡟⢿⣿⣿⡘⠛⢻⣿⣿⡟⠉⠁⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⡀⢿⣿⣿⣿⣼⣿⣿⡀⢸⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠿⠿⠁⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⢸⣿⣿⡇⠸⣿⣿⣷⣬⡉⠉⢱⡷⢸⣿⣿⣿⠀⠀⣿⣿⡇⣿⣿⣧⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡄⠀⠀⢸⣿⣿⢻⣿⣿⡆⠘⣿⣿⣿⣿⣿⣯⣄⠀⠙⠻⢿⣿⣿⣷⡄⢻⠀⣿⣿⣿⠀⢸⣿⣿⣇⣹⣿⣿⡄⢻⣿⣿⡇⢸⣿⣿⡹⣿⣿⣿⡇⠀⠿⣿⡃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⡇⡀⠀⢸⣿⣿⣀⣿⣿⣷⠀⣿⣿⣿⠀⣿⣿⣿⠀⣶⣶⣶⠙⣿⣿⣿⠀⠀⣿⣿⣿⠀⢸⣿⣿⡿⢿⣿⣿⣧⢸⣿⣿⡇⠸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣧⣴⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠁⠀⠀⠀⠙⠠⣿⠀⣾⣿⣿⡿⢿⣿⣿⡆⣿⣿⣿⣤⣿⣿⣿⠀⢻⣿⣿⣶⣿⣿⡟⣴⠆⣿⣿⣿⡇⢸⣿⠿⠇⠀⠿⠿⠿⠘⠛⠛⠃⠀⡛⣋⣥⣦⣭⣭⢵⣶⣯⣤⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⠸⠿⠿⠷⠿⠿⠛⠛⠛⢛⣉⣰⣶⣭⣽⣿⣭⣥⣾⣧⣻⡦⣦⣴⣾⣷⣶⣶⠶⠶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠄⠀⢰⣿⠓⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠋⠉⠉⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣋⠉⢙⡻⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⢩⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⡇⢰⡿⠛⠛⠻⠿⢛⣧⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⠿⠿⠃⠀⠉⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣶⣿⣿⣿⡇⠋⢸⣿⣿⣿⢿⣿⣷⡌⢸⣿⣿⡟⢿⣿⣿⡘⠛⢻⣿⣿⡟⠉⠁⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⡀⢿⣿⣿⣿⣼⣿⣿⡀⢸⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⢸⣿⣿⡇⠸⣿⣿⣷⣬⡉⠉⢱⡷⢸⣿⣿⣿⠀⠀⣿⣿⡇⣿⣿⣧⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⡉⠉⠀⢸⣿⣿⢹⣿⣿⡆⠘⣿⣿⣿⣿⣿⣯⣄⠀⠙⠻⢿⣿⣿⣷⡄⢻⠀⣿⣿⣿⠀⢸⣿⣿⣇⣹⣿⣿⡄⢻⣿⣿⡇⢸⣿⣿⡹⣿⣿⣿⡇⠀⠿⣿⡃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⡀⠀⢸⣿⣿⣀⣿⣿⣷⠀⣿⣿⣿⠀⣿⣿⣿⠀⣶⣶⣶⠙⣿⣿⣿⠀⠀⣿⣿⣿⠀⢸⣿⣿⡿⢿⣿⣿⣧⢸⣿⣿⡇⠸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣧⣴⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⠁⠀⠈⠹⠁⣿⠀⣾⣿⣿⡿⢿⣿⣿⡆⣿⣿⣿⣤⣿⣿⣿⠀⢻⣿⣿⣶⣿⣿⡟⣴⡆⣿⣿⣿⡇⢸⣿⠿⠇⠀⠿⠿⠿⠘⠛⠛⡃⠀⣛⣋⣡⣦⣭⣭⣵⣶⣯⣤⣶⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⣿⣿⣿⡇⠸⠿⠿⠷⠿⠿⠟⠛⠛⢛⣉⣰⣶⣭⣽⣛⣭⣥⣾⣷⣿⡦⣆⣰⣾⣶⣤⣤⡤⠤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠄⠀⢰⣿⠳⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣶⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠉⠁⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠋⠉⠉⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠿⠿⠿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⠿⣿⣿⣉⣉⣛⢻⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣷⡹⣿⣿⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠛⠉⢛⡛⠛⣻⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠿⡿⠇⠈⠉⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⠉⠉⠉⠛⢷⡶⣾⣷⣶⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠰⡇⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠛⠃⢻⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠛⠛⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⡀⠀⠀⢠⡀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⢺⣿⡓⠀⠀⡀⣾⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⣦⡀⠀⠀⠀⠛⠛⢹⣿⣿⣿⣿⣿⣷⣴⣦⢄⣴⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠠⣾⠘⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠁⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠄⠀⠀⠀⠀⠀⠀⠀⠛⠃⠙⠋⠻⠛⣁⣀⣀⠀⣠⣤⣄⠀⣤⣤⣤⠀⣶⣶⣶⠀⠀⠀ ⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⢿⣿⢟⣛⣛⣛⣛⣛⠻⣿⡟⣁⣤⣴⣦⣤⡀⢰⣶⣶⣶⣶⣶⣾⡆⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⠀⣿⣿⣿⡆⢹⣿⣿⠀⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢰⣶⣿⣿⣿⡇⠋⢸⣿⣿⣿⣿⣿⣷⡌⢸⣿⣿⡟⢿⣿⣿⡘⠛⢻⣿⣿⡟⠉⠁⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⡀⢿⣿⣿⣿⣼⣿⣿⡀⢸⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⢸⣿⣿⡇⠸⣿⣿⣷⣬⣉⠉⢱⣷⢸⣿⣿⣿⠀⠀⣿⣿⡇⣿⣿⣧⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⢿⡇⢸⣿⣿⢻⣿⣿⡆⠘⣿⣿⣿⣿⣿⣯⣄⠀⠙⠻⢿⣿⣿⣷⡄⢻⠀⣿⣿⣿⠀⢸⣿⣿⣇⣹⣿⣿⡄⢻⣿⣿⡇⢸⣿⣿⡹⣿⣿⣿⡇⠀⠿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡄⣈⠁⢸⣿⣿⣀⣿⣿⣷⠀⣿⣿⣿⠀⣿⣿⣿⠀⣶⣶⣶⠙⣿⣿⣿⠀⠀⣿⣿⣿⠀⢸⣿⣿⡿⢿⣿⣿⣧⢸⣿⣿⡇⠸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣧⣴⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠁⠀⠈⢹⠁⣿⠀⣾⣿⣿⡿⢿⣿⣿⡆⣿⣿⣿⣤⣿⣿⣿⠀⢻⣿⣿⣶⣿⣿⡟⣴⡆⣿⣿⣿⡇⢸⣿⠿⠇⠀⠿⠿⠿⠘⠛⠛⡃⢀⣛⣋⣡⣦⣭⣭⣵⣶⣯⣤⣶⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡇⠸⠿⠿⠷⠿⠿⠛⠛⠛⢛⣉⣰⣶⣭⣽⣟⣭⣥⣾⣗⣿⡶⣆⣰⣾⣦⣤⣤⡤⠤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⢰⣿⠳⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣶⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠉⠋⠉⠉⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 3116 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_14/12/2021:_AMD_AOCC_3.2_Compilerand_DietPi_7.9_Released⠀✐ Posted in News_Roundup at 7:34 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Server⠀➾ # ⚓ webassembly:_the_new_kubernetes?⠀⇛ I had an “oh, duh, of course” moment a few weeks ago that I wanted to share: is WebAssembly the next Kubernetes? [...] K8s itself is an evolution on a previous architecture, OpenStack. OpenStack had each container be a full virtual machine, with a whole kernel and operating system and everything. K8s instead generally uses containers, which don’t generally require a kernel in the containers. The result is that they are lighter-weight — think Docker versus VirtualBox. # ⚓ What_is_K8?_Is_it_the_Same_as_Kubernetes?⠀⇛ You probably have heard of Kubernetes, the hottest, in-demand DevOps tech in the market these days. It is an open source container orchestration platform. You’ll also come across the term K8s. You’ll find it being used as a synonym to Kubernetes. And that could confuse you. Is K8s same as Kubernetes or are they different? The short answer is Kubernetes and K8s refer to the same thing. But why so? I throw some light on this matter. o § Applications⠀➾ # ⚓ Get_All_Kind_of_System_Information_in_Linux_Terminal_With inxi⠀⇛ For the individuals who have to diagnose issues with computers and it’s system information that they are not aware about, inxi can be incredibly helpful. It shows the processes that are consuming CPU, memory; you can check if the correct graphics drivers are being used, if the motherboard UEFI/ BIOS is up to date, and much more. In fact, on It’s FOSS Community forum, we ask members to share the output of inxi command while seeking help so that it is easier to see what kind of system is in use. I know there are other tools that provide hardware info on Linux but inxi combines both hardware and software details and that’s why I like it. Do you use inxi or some other tool? Share your experience in the comments please. o § Instructionals/Technical⠀➾ # ⚓ installpkg_with_version_check_|_Weldr⠀⇛ Lorax version 36.1 added a new feature to the template’s installpkg command. This was brought about by a change to grub2 where the latest version installs the unicode.pf2 file to a different path than what is expected by the Lorax templates. This ended up causing a bit of a mess because some of the tests depend on building a new boot.iso but the new boot.iso cannot be built until the templates have been fixed to use the new path. The error wasn’t completely obvious, and wouldn’t happen until after running through most of the boot.iso build. First a bit of background for those not familiar with how Lorax works. Lorax builds the boot.iso by parsing a set of templates that define what packages to install, what files (and packages) to remove, and what to customize to make the iso bootable. These templates use dnf to install the packages, but the only dependency they had was on package names. There was no way to express version requirements in the runtime-install.tmpl template. Usually you don’t want to include version requirements in Lorax templates, that would just make it more difficult to keep up to date with the package changes. But in the case where you have a template that depends on a specific package version’s behavior – or change in behavior – it would be useful for the boot.iso build to fail early and with a clear error message. # ⚓ Extract_SCHEDULE_from_an_openQA_job_–_openQA_bites⠀⇛ Then using openqa-clone-job (and derivates) one can use the SCHEDULE variable to clone a test run with a custom set of test modules. This is particular useful, when developing a new test case and you need a verification run with e.g. one additional test module or excluding some failing ones. However it is sometimes cumbersome to type out a neverending of tests into a custom SCHEDULE variable, if the amount of test modules exceeds 5 or more tests (e.g. extra_tests_textmode – good luck!). # ⚓ tail_-f_/var/log/messages_|_grep_vegard:_Using_C-Reduce_to debug_LaTeX_errors⠀⇛ My wife is currently writing her HDR thesis (in France, this is an “accreditation to supervise research”). As part of this, she asked me if it would be possible to split her bibliography into two parts: one containing her own publications and another for the rest of her references. After a tiny bit of searching, I found this stackoverflow answer: https:// tex.stackexchange.com/a/407363 However, the answer uses the biblatex package, and my wife was using plain BibTeX. (Dun dun duuun!) No matter, we can probably switch to biblatex, right? We only had about 6k lines of LaTeX source code and 3k lines worth of BibTeX data, how hard could it be? # ⚓ Dolphin_–_Wii_Emulator_(even_the_newest_versions_of_Ubuntu) |_Linux.org⠀⇛ With gaming consoles being sought after at an all- time high, most consoles are hard to find or too expensive. Older consoles, such as the Wii, are favorites for some people. For those running Linux, we can use a Wii emulator called Dolphin to play Wii games. The process is a fairly simple one that will get you up and running so you can play Wii games on your Linux system. # ⚓ How_to_install_TeamCity_(Continuous_Integration)_on_Ubuntu Server._–_Unixcop_the_Unix_/_Linux_the_admins_deams⠀⇛ In this post, you will learn how to install TeamCity on Ubuntu. TeamCity is a build management and modern Continuous Integration (CI) tool from JetBrains widely used by software development teams. It is a commercial tool and licensed under a proprietary license, Freemium software license up to 100 build configurations and 3 free build agents are available. # ⚓ ibus_not_changing_keyboard_layout_with_enlightenment_| LordVan’s_Page_/_Blog⠀⇛ So I had been wondering for a while why ibus was not doing anything for swapping keyboard layout on enlightenment anymore (after a re-install) # ⚓ How_To_Install_Caddy_on_AlmaLinux_8_–_idroot⠀⇛ In this tutorial, we will show you how to install Caddy on AlmaLinux 8. For those of you who didn’t know, Caddy is a powerful, enterprise-ready, open- source web server with automatic HTTPS written in Go. It is a lightweight, commercially supported web server that can acquire and renew SSL/TLS certificates automatically using Let’s Encrypt. 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 Caddy web server on an AlmaLinux 8. You can follow the same instructions for CentOS and Rocky Linux. # ⚓ How_to_install_Counter-Strike:Global_Offensive_Server_on Ubuntu/Deban_-⠀⇛ Counter-Strike:Global Offensive (CSGO) is a first person shooter game developed and released by Valve. Like previous Counter-Strike Games, It also allows us to host our own dedicated server which gives us full control to our server. We can install custom plugins which gives our server a new look or we can configure our server for different modes like Tournament Matches, Better Deathmatch etc. # ⚓ How_to_Install_Ubuntu_Desktop_Environment_–_TREND_OCEANS⠀⇛ Ubuntu Desktop Environment is one of the most popular and recommended desktop environments. While trying a new desktop environment, you may accidentally delete your current one, or another system upgrade corrupted some of the files of the desktop environment. It can be anything, but restoring the original is pretty straightforward and takes just a couple of minutes, depending on your internet speed. Note: While trying a new desktop environment, it’s better to have a complete backup for your system using tools like timeshift. # ⚓ How_to_Create_Hard_Link_in_Linux_or_UNIX_–_TREND_OCEANS⠀⇛ Noobies often come to the point when they hear symbolic or soft links and hard links that; how do we create a hard link in Linux, UNIX, or macOS. Hard Link is a way to create a link that points to file data in the filesystem by assigning a common inode value to source file data and the hard link. There is another type of reference linking known as a soft link. # ⚓ How_to_install_Discord_on_a_Chromebook⠀⇛ Today we are looking at how to install Discord on a Chromebook. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ Install_and_Enroll_Elastic_Agents_to_Fleet_Manager_in_Linux –_kifarunix.com⠀⇛ This tutorial will take you through how you can install and enroll Elastic agents to Fleet manager in Linux. # ⚓ Oracle_Linux_checklist:_What_to_do_after_installation⠀⇛ Oracle Linux is certainly a viable option for anyone looking to replace CentOS. It’s also one of the best distributions for using with the Oracle Database. This is especially true for those users who tend to go the TL:DR route. In fact, I walked away from my Oracle Linux testing seriously impressed. The OS was fast, stable, and just as easy to use as any RHEL-based distribution. o § Games⠀➾ # ⚓ Get_Shadow_Tactics:_Blades_of_the_Shogun_free_during_the GOG_Winter_Sale_|_GamingOnLinux⠀⇛ GOG have put up their Winter Sale and it’s a good chance to not only grab some cheap games but also get a free copy of the truly excellent Shadow Tactics: Blades of the Shogun. For the giveaway, scroll down a bit on the GOG.com homepage and find the giveaway banner. Click it when logged in and it will add it to your GOG library. I do love a free game, especially when it’s as good as Shadow Tactics. The free game will be up until December 15th, at 2 PM UTC. However, there will be another giveaway on December 16 but they haven’t said what game it will be. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Kdenlive_21.12_Adds_Slip_Editing_&_Multicam_Editing Support_[Ubuntu_PPA]⠀⇛ The Kdenlive video editor 21.12 was released this Monday with exciting new features! As the last release in 2021, it introduced Slip trimming mode support. By selecting a clip in the timeline, use may use menu “Tool -> Slip tool” to drag moving the clip. This will change the start and end points of the clip simultaneously while keeping the original duration. # ⚓ Simpler_applications_to_attract_more_users?⠀⇛ A few days ago, the KDE developer Nate Graham wrote an article that gave a lot to talk about and that is worth recovering, whose subject could be summarized in the idea that is reflected in the headline: Could making KDE software simpler attract more users? These types of reflections never hurt and the case at hand has its point, because as you know, KDE has always been accused of being bloated in terms of options and, therefore, of being more complicated for the newcomer. By KDE software we mean everything, including the KDE Plasma desktop, its accompanying applications, and all other components; and by Nate Graham we mean the person who keeps us promptly informed with his This week in KDE, in addition to contributing to many other technical issues with special attention generally to the user experience, one of the most delicate vectors when we talk about free software. However, on this occasion I think he has missed the mark, so I am going to give my opinion on it, although in no case is it a reply, but rather to complement the reflection and at most open debate. First, his, which he develops in this article Y this other, emerged the last of the comments raised by the first. Summing up the story, Graham says that the percentage of advanced users capable of using what he calls complicated applications is very tight and KDE as a project cannot turn its back on what is a majority user base. But let’s start at the beginning. o § Distributions⠀➾ # § SUSE/OpenSUSE⠀➾ # ⚓ Can_you_help_me_real_quick?_–_Home_Office!_|_SUSE Communities⠀⇛ I never thought I would move to home office exclusively, ever! I was all about being in the office, enjoying the coffee and kitchen chat as well as being very keen on working in the office. How would I be able to work from home without talking to my direct peers? # § IBM/Red Hat/Fedora⠀➾ # ⚓ Fedora_36_To_Support_OSTree_Native_Containers_/ CoreOS_Layering_–_Phoronix⠀⇛ Fedora 36 feature work continues building up for what will make another exciting update to this Linux distribution come April. The latest approval is more exciting work on the OSTree / CoreOS front. The Fedora Engineering and Steering Committee (FESCo) has approved a change to enhance the RPM OSTreee stack to natively support OCI/ Docker containers as a transport and delivery mechanism for operating system content. This feature is the basis for “CoreOS Layering” as a means of allowing operating system updates from container images and easily generating layered images from a CoreOS base image. # § Canonical/Ubuntu Family⠀➾ # ⚓ Data_Pipelines_Overview⠀⇛ A Data Pipeline is a series of processes that collect raw data from various sources, filter the disqualified data, transform them into the appropriate format, move them to the places you want to store them, analyze them and finally present them to your audience. As we can see from this chart, a data pipeline is analogous to a water flow: data flows from one stage to another while being processed and reshaped. And in some cases, data will be needed to loop back to previous stages or be processed multiple times in the same stage. # ⚓ Ubuntu_Fridge_|_Ubuntu_Weekly_Newsletter_Issue_713⠀⇛ Welcome to the Ubuntu Weekly Newsletter, Issue 713 for the week of December 5 – 11, 2021. o § Devices/Embedded⠀➾ # ⚓ Raspberry_Pi_4_gets_Armbian_test_images,_DietPi_7.9 released⠀⇛ Ubuntu and Debian images built by Armbian got popular because of the sad state of affairs of most single board computers. But since Raspberry Pi boards are rather well-supported by the Raspberry Pi Foundation and community, plus part of it is closed-source, there’s been little motivation by the Armbian community to work on it, and that means there’s no official support for Raspberry Pi. But some Armbian test images have just been released for Raspberry Pi 4, specifically Ubuntu 22.04 “Jammy Jellyfish” images with a CLI (headless) version, and two desktop variants with Cinnamon and XFCE desktop environments which you can download on their server(s). Separately, DietPi 7.9 lightweight Linux distribution based on Debian has also been released with various improvements. # ⚓ 5G_IoT/AIoT_industrial_gateway_ships_with_Raspberry_Pi Compute_Module_4⠀⇛ WPC-632-Pi CM4 is an industrial IoT gateway based on Raspberry Pi Compute Module 4 with optional 5G or 4G LTE cellular connectivity, that joins other Raspberry Pi CM4 industrial gateways such as CompuLab IOT-GATE-RPI4, CatsPi Industrial Lite, Modberry M500 CM4, among others. The Linux gateway features two Ethernet ports, RS232/RS485 and other I/Os via terminal blocks, mPCIe and M.2 sockets for expansion with 5G modem 4G LTE mode, AI accelerator, or an NVMe SSD, as well as support for 9V to 32V wide-range input power. # ⚓ AI_box_PC_combines_a_10th_Gen_CPU,_dual_2.5GbE_and_dual PCIe_for_medical_analytics⠀⇛ IEI’s Linux-ready “HTB-210-Q470 AI Box PC” runs on Comet Lake-S and supplies up to 128GB DDR4, 2x 2.5GbE, M.2 A- and M-key, and PCIe x4 and x16 for Nvidia Tesla T4. Intel plans to phase out Comet Lake-S in 2022. IEI announced an edge AI desktop computer based on Intel’s 10th Gen Comet Lake-S. The HTB-210-Q470 “AI Box PC” is especially suitable for medical analytics due to its support for Nvidia Tesla T4 graphics cards, as well as its ease of cleaning and white, streamlined, medical appliance design. # § Open Hardware/Modding⠀➾ # ⚓ PneuMod_is_a_wearable_haptic_device_that_produce pressure_and_thermal_feedback_|_Arduino_Blog⠀⇛ When trying to imagine a new way of interacting with either a video game or even another person remotely, being able to feel both temperature and touch sensations isn’t what most people would have in mind. However, thanks to some very interesting research being done by University of California, Santa Barbara student Bowen Zhang and professor Misha Sra, a novel method for interacting with the virtual world could come quite soon. The project, which Zhang calls the “PneuMod,” is a modular system of tiny air bladders that each have a Peltier element on their surface. Then using an Arduino Mega and a custom- designed control board, commands can be sent from a laptop that open or close solenoid valves to let air inflate/deflate the air bladders, thus creating pressure against the wearer’s skin. Different temperatures are safely produced by combining the Peltier elements with temperature sensors, and by adjusting the polarity of the current headed to these elements, both hot and cold can be achieved with the exact same hardware. # ⚓ An_Open_Source_Detector_For_Identifying_Plastics_| Hackaday⠀⇛ One of the challenges involved in recycling plastic is determining the specific type of plastic a given item is actually made of. To keep up with demand, large scale recycling centers rely on various automated systems to separate different types of plastic from a stream of incoming material. But in less technologically advanced parts of the world, workers can find themselves having to manually identify plastic objects; a time consuming and error-prone process. To try and improve on the situation, [Jerry de Vos], [Armin Straller], and [Jure Vidmar] have been working on a handheld open hardware device that they refer to simply enough as the Plastic Scanner. The hope is that their pocket-sized unit could be used in the field to positively identify various types of plastic by measuring its reflectivity to infrared light. The device promises to be very easy to operate, as users simply need to bring the device close to a piece of plastic, push the button, and wait for the information to pop up on the OLED display. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ This_Tool_Can_Check_Your_Phone_for_Apps_With Android’s_911_Bug⠀⇛ # ⚓ Holiday_Android_app_deals:_Townscaper,_Bad_North, Sendmate,_Data_Defense,_more_–_9to5Toys⠀⇛ # ⚓ Android_13_may_add_a_toggle_to_disable_Android’s_new background_app_limitations⠀⇛ # ⚓ It’s_no_Android_12,_but_the_Galaxy_A50_did_just_get the_latest_security_update_–_SamMobile⠀⇛ # ⚓ Samsung_attempts_to_fix_One_UI_4_(Android_12)_bugs with_new_beta_update_|_Android_Central⠀⇛ # ⚓ Samsung_One_UI_4.0_(Android_12)_update_tracker: Eligible_devices_&_more⠀⇛ # ⚓ You_can_change_the_Android_12_square_clock_on_Google Pixel_lock_screen⠀⇛ # ⚓ Google_Pixel_6_free_earbuds_offer_is_best_deal_yet_on Android_phone_|_Express.co.uk⠀⇛ # ⚓ LG_Wing_gets_Android_11_update_on_Verizon_– 9to5Google⠀⇛ # ⚓ The_LG_Wing_isn’t_dead_yet_as_Android_11_finally arrives_on_LG’s_last_phone_|_Android_Central⠀⇛ # ⚓ What_you_can_do_with_AirTags_on_Android_– 9to5Google⠀⇛ # ⚓ Best_gifts_for_Android_users_under_$100_– 9to5Google⠀⇛ # ⚓ Top_10_Best_Music_Android_Games_–_2021⠀⇛ # ⚓ The_Top_10_Android_Sports_Betting_Apps⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ 4_Best_Free_and_Open_Source_Proof_Assistants⠀⇛ In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. This type of software provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs. # ⚓ 6_ideas_for_building_an_equitable_partner_program_for_your open_source_project⠀⇛ The organizations that partner with you to contribute to your open source project deserve recognition. But there is more to showcasing these organizations than simply adding a logo to your website. I work at Acquia where I am the Project Lead for the open source marketing automation project, Mautic. In the Mautic project, we wanted to have a way to showcase these contributors in order to say, “These are the folks who are the makers. They support this project—work with them so they can do more!” As we started to plan, we immediately bumped into some pretty major challenges. We needed to develop an equitable program with entry requirements that reflect both the complexities of worldwide financial systems and the nuances of what we considered a contribution to our community. # ⚓ The_Apache_Weekly_News_Round-up:_week_ending_10_December 2021⠀⇛ ASF Board – management and oversight of the business affairs of the corporation in accordance with the Foundation’s bylaws. # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ LibreOffice_Community_Member_Monday:_Ravi_Dwivedi⠀⇛ I am from India, and I recently received my masters degree (M.Math) in mathematics from the Indian Statistical Institute in Kolkata. I am looking forward to doing a PhD in mathematics. My hobbies include listening to music, reading novels, playing chess, and meeting new people. I campaign that software must respect users’ freedom. We call such a software free software, where ‘free’ refers to freedom and not price. In Indian languages, we call it “swatantra/mukt software” to remove the confusion. Free Software gives users the freedom to run, study, modify, share and improve the software. If the software lacks any of these freedoms, it is called non-free/ proprietary software. In my computing, I use only free software, except for some blobs in my phone. I volunteer for the Free Software Community for India. (FSCI). FSCI is not a registered organization, but a community of free software activists. It is also a non- hierarichal group. I raise awareness on why free software is important and the dangers of non-free/proprietary software. [...] I meet people on streets, trains, buses and wherever I find the opportunity – and I talk about the issue of free software and privacy. Usually, I try to understand what issues other people care about, and then relate digital privacy and free software with their issue. For example, once a bookseller told me how people have stopped buying from physical bookstores, especially in COVID times, and instead buy books online from Amazon. I understood their issues and I told them that I never bought from Amazon even once (after June 2020) because ordering from Amazon puts me under surveillance. This way, I related the issues of privacy and free software with the ones they already care about. This is one good way to explain people. Even when people don’t care, I tell them about these issues because it might be their first trigger, and they might need several triggers to consider the idea. I hope to raise some questions in people’s minds rather than convincing them. Also, I need to remind myself time and again that we cannot convince everyone that they should care for privacy. Apparently, it is a hard change to bring in today’s world and therefore, even small changes (like convincing and installing a few free software apps in their device) requires a lot of hard work. # § Programming/Development⠀➾ # ⚓ AMD_AOCC_3.2_Compiler_Released_Along_With_AOCL_3.1 CPU_Libraries_–_Phoronix⠀⇛ AMD has issued a nice end-of-year update to the AMD Optimizing C/C++ Compiler (AOCC) that also includes Fortran support as well as a new release of their AMD Optimizing CPU Libraries (AOCL). AMD AOCC 3.2 is the new version of their LLVM Clang downstream focused on providing the latest optimized compiler support for Zen- based processors whether it be EPYC, Ryzen, or Ryzen Threadripper processors. With AOCC 3.2 they have re-based to LLVM/Clang 13.0 as their compiler release. LLVM 13.0 was released this autumn and is the latest stable LLVM version. AMD now has all of their yet- to-be-upstreamed or unsuitable for upstream patches re-based on this new version. # ⚓ What_the_New_PHP_Foundation_Means_for_PHP’s_Future_– CloudSavvy_IT⠀⇛ The PHP Foundation is a newly established organization that will provide funding to sustain the language’s development. It’s been founded by ten influential companies in response to the departure of long-standing contributor Nikita Popov. The Foundation was announced in November 2021 shortly before the release of the PHP 8.1 feature update. Popov’s decision to move on from PHP and focus on LLVM development will impact the language as he’s been responsible for many of the most noteworthy changes through the PHP 7 and 8 release series. Popov created or contributed to improvements including typed properties, readonly properties, constructor property promotion, arrow functions, union types, and named arguments, as well as much more besides. He holds significant knowledge and expertise which means his departure affects the language’s bus factor. In JetBrains’ words, the loss of Popov is “a blow to the community.” The contributor behind key components of the language’s revitalization and push towards more strongly typed code is stepping away without a direct replacement. The Foundation has been founded to fund new core developers and help increase the project’s bus factor, so the loss of another stakeholder would be less significant. # § Perl/Raku⠀➾ # ⚓ 2021.50___for_Micros_–_Rakudo_Weekly_News⠀⇛ Daniel Sockwell wrote two advent blog posts (1, 2) about the problem of dependencies. This resulted in the release of the _ module (aka “lowbar” module), a growing collection of micro packages of less than 70 lines of code. This caused quite some discussion on Hacker News and made it to the top posts list! Good to see the Raku Programming Language in the news! # ⚓ gfldex:_Recursive_caves⠀⇛ Day 12 asks to find paths in a directed cyclic graph, whereby the root and the outer most leaf are only visited once. This is basically a call-tree of a recursive function. # § Python⠀➾ # ⚓ [Old] How_to_Create_Full_Screen_Window_in Tkinter?⠀⇛ There are two ways to create a full screen window in tkinter using standard python library for creating GUI applications. * § Leftovers⠀➾ o ⚓ A_Year_on_a_Hinge_of_History⠀⇛ Explore all the content from our 2021 year in review here. o ⚓ Sangli_Farmers:_Milked_by_Private_Players⠀⇛ o ⚓ Cat’s_Cradle⠀⇛ Tom Stoppard has long been averse to weaving explicitly autobiographical material into his plays, so it’s only appropriate that one of his more revealing lines about himself would be voiced by a 19th-century liberal literary critic. The speech, which appears in Voyage, the first of Stoppard’s trilogy on the Russian intelligentsia, is delivered by Vissarion Belinsky to a small gathering of friends that includes a young “Michael” Bakunin and his aristocratic father. “I am not an artist,” Belinsky says.1My play was no good. I am not a poet. A poem can’t be written by an act of will. When the rest of us are trying to be present, a real poet goes absent. We can watch him in the moment of creation, there he sits with the pen in his hand, not moving. When it moves, we’ve missed it. Where did he go in that moment? The meaning of art lies in the answer to that question.2Books in ReviewTom Stoppard: A LifeBy Hermione LeeBuy this book o § Hardware⠀➾ # ⚓ Adding_Wire_Races_Improves_3D-Printed_Bearings_|_Hackaday⠀⇛ Like a lot of power transmission components, bearings have become far easier to source than they once were. It used to be hard to find exactly what you need, but now quality bearings are just a few clicks away. They’re not always cheap though, especially when you get to the larger sizes, so knowing how to print your own bearings can be a handy skill. Of course, 3D-printed bearings aren’t going to work in every application, but [Eros Nicolau] has a plan for that. Rather than risk damage from frictional heating by running plastic or metal balls in a plastic race, he uses wire rings as wear surfaces. The first video below shows an early version of the bearing, where a pair of steel wire rings lines the 3D-printed inner and outer races. These worked OK, but suffered from occasional sticky spots and were a bit on the noisy side. # ⚓ USB_LED_Christmas_Tree_Is_Making_Spirits_Bright_| Hackaday⠀⇛ [Piotr SB] knows there is no way out of the holidays; the only path is through. You’ve got to find cheer wherever and however you can, so why not cater to your own interests and build the cutest little LED Christmas tree you ever did see? And did we mention it’s USB and absolutely free (as in carols, not eggnog)? This O-Christmas tree is made up of concentric rings that are built into a tier as you solder the LEDs. And of course you’re supposed use the LED legs as supports! One leg from each LED — 18 green and a red one for the top. Because the PCB is not quite thick enough, you’ll need to add a plastic spacer to get it to stay in the USB port. Not only is this a nice design, the snowflakes and snowman on the silkscreen totally seal the cuteness deal. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Gender-Affirming_Health_Care_Saved_My_Life._Everyone_Should Have_Access_to_It.⠀⇛ # ⚓ Black_Oxygen_Organics_(a.k.a._BOO):_Magic_dirt_quackery_to treat_COVID-19⠀⇛ Last Thursday, NBC News published a story by Brandy Zadrozny titled “‘Magic dirt’: How the internet fueled, and defeated, the pandemic’s weirdest MLM“. The story was about something called “BOO”, which stands for Black Oxygen Organics, a company and product that over the last several months had become a hit among believers in alternative medicine as a miracle treatment for COVID-19. I debated about writing about BOO because the story seemed almost too unbelievable for even me, but then I considered the simple fact that antivaxxers had been using a form of bleach solution, known as Miracle Mineral Supplement (MMS, also sometimes called Miracle Mineral Solution) to treat autism and lots of other conditions for years and years (or, as I put it, bleaching away what ails you) and I had been writing about it. (Unsurprisingly, MMS is also now billed as a treatment for COVID-19, as I’ll touch on later.) # ⚓ US_Supreme_Court_Refuses_to_Intervene_Against_NY_Vaccine Mandate⠀⇛ The U.S. Supreme Court on Monday refused to intervene against a vaccine mandate in New York state, ruling against healthcare workers in a pair of challenges to the order based on religious objections. According to the Associated Press: # ⚓ Tory_Partying_as_the_Alpha_Covid_Variant_Took_Hold_is_a Grim_Symbol_of_Their_Pandemic_Response⠀⇛ I still think of it as the Kent variant because the Covid-19 Genomics UK Consortium said that the key sample came from “near Canterbury”, where I live. A local medical source, who wanted to remain anonymous, gave me more precise information, saying that the first patient suffered from a weak immune system and lived in Margate on the Isle of Thanet, which is 15 miles from Canterbury. As Britain faces the onset of the potentially more infectious and vaccine-resistant Omicron variant, it is worth comparing this current wave of the pandemic with the one that started in Kent a year ago. Much has changed since then because of mass vaccination, but many medical, social and political factors, both negative and positive, remain the same. # ⚓ Travel_Bans_and_Boosters_Alone_Won’t_Protect_Us_From Covid⠀⇛ If it weren’t so damn serious, it would be funny. In early December, Stephen Colbert riffed on the travel bans inflicted on South Africa and neighboring nations after the South Africans alerted the world to the emergence of a new variant of SARS-CoV-2: “We’re all lucky that South Africa alerted us to the dangers of Omicron. Thanks to them, the White House has issued a ban on travel from eight countries in southern Africa. Well, that’s good: You’ve got to contain the virus. So far, it’s only been found in the southern African countries of Austria, Belgium, Canada, Czech Republic, Denmark, France, Germany, Hong Kong, Israel, Italy, Japan, Netherlands, Portugal, Spain, Sweden, and the United Kingdom.” Once again, our comedians are our truth-tellers. # ⚓ Ministry_launches_national_action_plan_for_the_preservation of_pollinating_insects⠀⇛ The Ministry for the Environment, Climate and Sustainable Development has launched a new action plan in an effort to preserve pollinating insects, such as bees or wasps, here in the Grand Duchy. A total of 21 measures, spread out across different sectors, are to be implemented by 2026. # ⚓ Air_Force_discharges_27_for_refusal_to_get_COVID_vaccine⠀⇛ The Air Force gave its forces until Nov. 2 to get the vaccine, and thousands have either refused or sought an exemption. Air Force spokeswoman Ann Stefanek said Monday that these are the first airmen to be administratively discharged for reasons involving the vaccine. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Inside_Ireland’s_Public_Healthcare_Ransomware_Scare⠀⇛ The consulting firm PricewaterhouseCoopers recently published lessons learned from the disruptive and costly ransomware attack in May 2021 on Ireland’s public health system. The unusually candid post-mortem found that nearly two months elapsed between the initial intrusion and the launching of the ransomware. It also found affected hospitals had tens of thousands of outdated Windows 7 systems, and that the health system’s IT administrators failed to respond to multiple warning signs that a massive attack was imminent. # ⚓ The_battle_of_the_computing_clouds_is_intensifying⠀⇛ Mr Hodges’s widget is a window onto the future. As bills soar, every firm of any size will need to understand not just the benefits of the cloud, but also its costs. Gartner, a consultancy, reckons that spending on public- cloud services will reach nearly 10% of all corporate spending on information technology (IT) in 2021, up from around 4% in 2017. Plenty of technophile startups spend 80% of their revenues on cloud services, estimate Sarah Wang and Martin Casado of Andreessen Horowitz, a venture-capital firm. The situation is analogous to a century ago, when electricity became an essential input (and prompted some firms to hire another kind of CEO: the chief electricity officer). # § Security⠀➾ # ⚓ CISA_Creates_Wbpage_for_Apache_Log4j Vulnerability_CVE-2021-44228⠀⇛ CISA and its partners, through the Joint Cyber Defense Collaborative, are tracking and responding to active, widespread exploitation of a critical remote code execution vulnerability (CVE-2021-44228) affecting Apache Log4j software library versions 2.0-beta9 to 2.14.1. Log4j is very broadly used in a variety of consumer and enterprise services, websites, and applications—as well as in operational technology products—to log security and performance information. An unauthenticated remote actor could exploit this vulnerability to take control of an affected system. # ⚓ Worst_effects_of_logging_flaw_yet_to_be experienced:_security_pro⠀⇛ “Without any incentive or motivation, many developers are unable to continue maintaining, updating or reviewing software they’ve written, which leads to security issues that sometimes cannot be detected early on. “There’s a lot of taking and very little giving which tips the balance severely. It would behoove organisations that utilise open-source software to consider investing the time and resources needed to make them more secure.” # § Privacy/Surveillance⠀➾ # ⚓ Fraternal_Order_Of_Police_Opposes_Biden FCC_Nom_Because_She….Supports_Encryption⠀⇛ We’d already noted how telecom and media giants eager to keep their spoils from the Trump era have been waging a not so subtle smear campaign on Biden FCC Commissioner nomination Gigi Sohn, using loyal GOP lawmakers as marionettes. Sohn is broadly popular across both sides of the aisle, but she’s also a fairly fierce advocate of functional regulatory oversight, transparency, and market competition. So companies like AT&T and News Corporation have been seeding a lot of gibberish in DC and in select press outlets about how she’s a “radical” who wants to “censor conservatives” and hurt puppies. # ⚓ ICE_Loses_Access_To_Sensitive_Utility Customer_Records_Following_Pressure_By Senator_Ron_Wyden⠀⇛ Another one of ICE’s (Immigration and Customs Enforcement) data spigots has been shut off. Don’t cry too many tears for poor old ICE. It still has plenty of options. It’s still hoovering up location data from app developers who either don’t know or don’t care that this data is buyable through data brokers. It also still has plenty of privileges, thanks to laws and judicial decisions that say most constitutional rights are null and void within 100 miles of our nation’s ports of entry (borders, coasts, and — making this far more concerning — any domestic airport offering international flights). # ⚓ This_Is_Not_the_Privacy_Bill_You’re Looking_For⠀⇛ A strong privacy bill must place consumers first. EFF has laid out its top priorities for privacy laws, which include a full private right of action that allows people to act as their own privacy enforcers, and measures that prevent companies from discriminating—by charging more or offering less—against those who wish to protect their privacy by exercising their rights. EFF also advocates for an opt-in consent model that requires companies to obtain a person’s permission before they collect, share, or sell their data, rather than an opt-out model. The UPDPA falls short on many of these fronts. And why? Because, despite years of evidence that companies will not protect consumer privacy on their own, the UPDPA defers to company complaints that respecting people’s privacy is a burden. In fact, UPDPA Committee Chairman Harvey Perlman openly admitted that one of the drafting committee’s main goals was to lower business compliance costs. By lowering its standards to coax companies into compliance, the UPDPA leaves consumers twisting in the wind. # ⚓ Disagreeable,_Lazy,_and_an_Addict_–_What Genetic_Tests_Can_Tell_an_Employer_or_a Partner⠀⇛ # ⚓ Zoom_invests_in_13_more_apps_as_part_of $100_mn_Apps_Fund⠀⇛ Video meet app Zoom on Monday said it has funded 13 new apps as part of its $100 million Apps Funds, taking the total number of selected platforms to 25. The Zoom Apps Fund is a $100 million global venture to stimulate growth of Zoom apps, integrations and hardware. # ⚓ Instagram_Activism_Can_Be_an_Entry_Point to_Real-World_Engagement⠀⇛ Kyley Schultz spends her days fact-checking viral claims on Instagram. Natalie Held posts blush-colored carousels of tweets in support of vaccines, abortion, and refugees. Nicole Cardoza tries to push her 648,000 Instagram followers to actually take action, not just share her posts to their story and continue scrolling. Instagram was never meant to be a place for advocacy (just like Facebook was never meant to change the outcome of global politics). Instagram started as a photo-sharing app in 2010, with built-in filters to change the look of your pictures. The Instagram of yore was a radically different place than it is now, where we posted hazily filtered photos of our breakfast or a sunset or badly posed group photos with friends. The number of likes we got didn’t matter that much. # § Confidentiality⠀➾ # ⚓ The_Future_of_Sequoia_PGP⠀⇛ NLnet recently held a webinar on the future of OpenPGP. The Sequoia team made five short presentations. In addition to an introduction summarizing the past, present, and future of Sequoia, we presented four of our current projects, which provide a nice cross section of our current work. o § Defence/Aggression⠀➾ # ⚓ ‘Stomach-Wrenching’_Report_Reveals_Secret_US_Strike Command’s_High_Civilian_Death_Toll⠀⇛ Peace advocates on Monday responded to a report about a U.S. military unit that killed Syrian civilians at 10 times the rate of similar operations in other theaters of the so-called War on Terror by accusing the United States of hypocritically sanctioning countries while committing atrocities of its own, and by reminding people that there is no such thing as a “humane” war. “Years later, we hear about all the civilians obliterated but are left with a fait accompli and no accountability.” # ⚓ The_Real_Lesson_of_the_Afghanistan_Disaster⠀⇛ After the dinner was over, I was waiting for my car to be brought to me when I saw a friend of mine who was working at the conservative Heritage Foundation. I asked how things were going. He didn’t hesitate. He told me that they were jumping right into supporting Bush’s “war on terrorism” with “position papers” that they were already writing and publishing. Shortly after that dinner, I delivered a speech at a libertarian gathering in Arizona. I explained how U.S. foreign policy was the motivating factor behind the 9/11 attacks and why it was critically important to understand and examine that point. I also told the audience that an invasion of Afghanistan would prove to be a disaster, not only for the Afghan people but also with respect to the liberty and well-being of the American people. # ⚓ Israel_Pushes_Hardline_in_Iran_Nuclear_Talks⠀⇛ Less than a week into negotiations, Britain, France, and Germany accused Iran of “walking back almost all of the difficult compromises” achieved during the first round of negotiations before Iran’s new president, Ebrahim Raisi, was sworn into office. While such actions by Iran certainly aren’t helping the negotiations succeed, there is another country — one that is not even a party to the agreement that was ripped up in 2018 by then President Donald Trump —whose hardline position is creating obstacles to successful negotiations: Israel. On Sunday, amid reports that the talks might collapse, Israeli Prime Minister Naftali Bennett called on the countries in Vienna to “take a strong line” against Iran. According to Channel 12 news in Israel, Israeli officials are urging the US to take military action against Iran, either by striking Iran directly or by hitting an Iranian base in Yemen. Regardless of the outcome of the negotiations, Israel says that it reserves the right to take military action against Iran. # ⚓ Citizens_Hide_From_Active_Shooters_as_Alaska_Is_Slow_to Deliver_on_2019_Promise_of_Village_Troopers⠀⇛ As the summer months stretched into fall, Justin Edwards would sometimes bump into the man wanted for his attempted murder. In the street or by the schoolhouse or village store. “He’d say, ‘Hi,’ and act like nothing happened,” said Edwards, 46, who has about 30 shotgun pellets seeded from forearm to bicep in his right arm. Edwards usually said hi back. # ⚓ Opinion_|_America’s_Loser_Generals_Finally_Win_Big… Paychecks_With_the_Military-Industrial_Complex⠀⇛ Yes, four-star General Lloyd Austin commanded American forces in Iraq back in 2010 and 2011. In 2013, he took over from General James Mattis (remember him?) as the head of United States Central Command, or CENTCOM, overseeing America’s wars in the Greater Middle East and Afghanistan (where he had earlier commanded troops himself). Retiring from the Army in 2016, he promptly joined the board of directors of weapons giant Raytheon Technologies. When he became secretary of defense for President Biden and divested himself of his Raytheon shares, it was estimated that he had made $1.7 million from that company alone and he was then believed to be worth $7 million. As for James Mattis, who had left the U.S. military to become a board member for another major weapons maker, General Dynamics, he was believed to be worth $10 million when he came out of retirement as Donald Trump’s secretary of defense. # ⚓ No_Punishment_for_US_Troops_Who_Slaughtered_10_Afghan Civilians,_Says_Pentagon_Chief⠀⇛ In a continuation of a long history of impunity for U.S. troops who harm noncombatants during wartime, the Pentagon said Monday that none of the military personnel involved in an unmanned aerial drone strike that killed 10 civilians—seven of them children—during the final days of the war in Afghanistan would be punished. “How can our military wrongly take the lives of 10 precious Afghan people and hold no one accountable in any way?” # ⚓ Here’s_How_We_End_America’s_Forever_Wars⠀⇛ As August ended, American troops completed their withdrawal from Afghanistan, almost 20 years after they first arrived. On the formal date of withdrawal, however, President Biden insisted that “over-the-horizon capabilities” (airpower and Special Operations forces, for example) would remain available for use anytime. “[W]e can strike terrorists and targets without American boots on the ground, very few if needed,” he explained, dispensing immediately with any notion of a true peace. But beyond expectations of continued violence in Afghanistan, there was an even greater obstacle to officially ending the war there: the fact that it was part of a never-ending, far larger conflict originally called the Global War on Terror (in caps), then the plain-old lower-cased war on terror, and finally—as public opinion here soured on it—America’s “forever wars.” # ⚓ Unrestrained_killer_robots_in_Geneva⠀⇛ A UN convention on lethal autonomous weapons systems is not in sight # ⚓ Jan._6_rally_organizers_sue_Verizon_to_stop_release_of_cell phone_records⠀⇛ On Jan. 6, each of the plaintiffs played a role in organizing the rally held on the Ellipse where then-President Donald Trump spoke to a crowd of his supporters prior to the deadly attack on the Capitol. Some attendees marched to the Capitol following the rally, but organizers say their event was unrelated to the subsequent attack and had no connection to what transpired at the Capitol. All the plaintiffs are longtime Republican political operatives, and most worked for Trump since his first presidential campaign in 2015. Some have continued to work for the Save America PAC as the former president has continued campaign-like events around the country in his post-presidency life. # ⚓ Trump_election_lie_allies_Stone,_Eastman_and_Clark_plead the_Fifth._It_won’t_do_much.⠀⇛ While these witnesses may be able to avoid testifying before the select committee by standing on the Fifth, they are merely postponing — and perhaps increasing — their future legal woes. # ⚓ Jan._6_Committee_Issues_Contempt_Charges_for_Former_Trump Aide_Mark_Meadows⠀⇛ # ⚓ Meadows_texts_show_Hannity,_Don_Jr._wanted_Trump_to_stop Jan._6_[insurrection]⠀⇛ As rioters stormed the Capitol on Jan. 6, several leading Fox News pundits and Donald Trump’s eldest son all voiced desperate concerns that the former president was doing nothing to quell the violence and protect those in the building, according to damning text messages unveiled Monday night by the select committee investigating the attack. The stunning messages, submitted to the panel by Mark Meadows, Trump’s former chief of staff, revealed that Sean Hannity, Brian Kilmeade and Laura Ingraham — all superstar Fox personalities with enormous conservative followings — and Donald Trump, Jr. were all pressing Meadows to convince the president to intervene during the early hours of the siege. o § Environment⠀➾ # ⚓ There_Will_Never_Be_Climate_Justice_If_African_Activists Keep_Being_Ignored⠀⇛ # ⚓ Climate_Groups_Blast_ALEC’s_Model_Legislation_Targeting Fossil_Fuel_Divestment⠀⇛ Over three dozen advocacy groups on Monday responded to recent reporting about a U.S. right- wing group’s efforts to advance model legislation opposing fossil fuel divestment by calling on state officials to “disavow” the proposed bills and ditch climate-wrecking industries. “It was only a matter of time before ALEC and Big Oil would attempt to hold even Wall Street banks hostage to their climate-, economy-, and community- destroying agenda.” # ⚓ Environmental_groups_call_on_Biden_to_appoint_permanent head_of_mine_reclamation_agency⠀⇛ The Sierra Club and a coalition of Appalachian environmental groups called on President Biden to nominate a permanent director of the agency that regulates mine reclamation in a letter Monday. In the letter, the organizations called for a permanent head of the Office of Surface Mining Reclamation and Enforcement (OSMRE). They noted the numbers of unreclaimed mines that have been abandoned amid falling demand for coal, which creates increased risks of aquifer contamination, flooding and landslides. # ⚓ Amazon_Rainforest_on_the_Verge_of_Becoming_a_Dry_Savannah, Scientists_Say⠀⇛ One scientist told New Scientist that it would take just between 20 to 25 percent deforestation to reach an ecological tipping point due to the level of warming the forest is experiencing. This is a recipe for “savannisation” — a process that describes a forest drying up due to reduced rainfall, and transforming into a dry, arid savannah grassland, according to the magazine. # ⚓ Climate_Migration_Will_Worsen_the_Brutality_and_Confusion on_the_Mediterranean⠀⇛ In July of 2018, an Italian-flagged oil supply ship called the Asso 28 that was crossing the Mediterranean Sea encountered a stalled rubber raft carrying a hundred desperate migrants. Trying to make the dangerous journey from Libya to Europe, the migrants had reached international waters when the supply ship rescued them and its captain opted to take them not to a port of safety in Europe, as required by law, but back to a gulag of migrant detention facilities in Libya where the United Nations and others have documented systematic torture, rape, extortion, forced labor and death. In October of this year, the captain of that supply ship, Giuseppe Sotgiu, paid a heavy price for his decision: an Italian judge sentenced him to a year in prison for violating humanitarian law. The painful irony of this conviction is that Sotgiu is headed to jail for what EU officials have been doing on a far grander scale for several years — pushing migrants back to a place of extreme human rights abuses.  # ⚓ “A_Bigger_Picture”:_Ugandan_Activist_Vanessa_Nakate_on Bringing_New_Voices_to_the_Climate_Fight⠀⇛ We go to Kampala, Uganda, to speak to climate activist Vanessa Nakate on the occasion of her first book being published, “A Bigger Picture: My Fight to Bring a New African Voice to the Climate Crisis.” In an extended interview, she describes the challenges of being a young Ugandan woman from a continent that contributes less than 4% of the world’s carbon emissions yet suffers the worst consequences of the climate crisis and is often ignored by the Global North. “There won’t be climate justice if specific groups of people are being left behind,” says Nakate, founder of the Africa-based Rise Up Movement. “We are facing the same storm, but we are definitely in different boats.” # ⚓ “This_Isn’t_a_Natural_Disaster”:_Climate_Scientist_Michael Mann_on_Deadly_Tornadoes_in_8_States⠀⇛ At least 100 people are feared dead after 30 deadly tornadoes devastated towns in eight states, from Kentucky to Arkansas, in a supercell thunderstorm that raged more than 200 miles, leaving behind scenes some compared to a war zone. President Biden has declared a major federal disaster and called for an investigation into the role climate change played in the storms. We speak to climate scientist Michael Mann about the role of climate change in the storms and climate denialism among Republican leaders. “Make no mistake, we have been seeing an increase in these massive tornado outbreaks that can be attributed to the warming of the planet,” says Mann, director of the Earth System Science Center at Penn State University. # ⚓ Opinion_|_Why_Carbon_Capture_Really_and_Truly_Sucks⠀⇛ “Finally! Bill Gates and Elon Musk Agree on Something” the headline says. I wonder what they might agree on? Could it be that neoliberal capitalism is the greatest system ever devised by old white men in Europe? Could it be that they both think electric cars are the answer to our transportation problems? Could it be they both think technology can solve any problem that technology creates? No, apparently what the two plutocrats “finally” agree on is that technology that sucks carbon dioxide out of the atmosphere is the greatest solution to the climate crisis. # ⚓ Campaigners_Say_Biden_‘Deserves_Lump_of_Coal_This Christmas’_for_Broken_Climate_Promises⠀⇛ Friends of the Earth on Monday concluded its campaign calling out U.S. President Joe Biden for breaking his promise to end new leasing of public lands and waters to fossil fuel companies with the release of three parody movie trailers based on classic Christmas films. “It’s time for President Biden to live up to his promises to the American people.” # ⚓ Amid_Tornado_Devastation,_Sunrise_Says_‘Call_It_What_It_Is: A_Climate_Disaster’⠀⇛ As emergency workers and local residents sifted through the wreckage of towns left devastated by the tornado system that hammered six U.S. states over the weekend, the youth-led Sunrise Movement implored policymakers to “call it what it is: a climate disaster”—and act accordingly. “People’s homes have been demolished, 40,000 people are without power, and there are so many unanswered questions that the government should have solutions for,” said Rachael Fantasia, hub coordinator of Sunrise Bowling Green, a Kentucky city where more than 500 houses were reportedly destroyed by tornadoes that left dozens dead in the state. # ⚓ ‘Monster’_Antarctic_Glacier_at_Risk_as_Key_Ice_Shelf_Faces Collapse_Years_Earlier_Than_Expected⠀⇛ The ice shelf holding back one of Antarctica’s most perilous glaciers is eroding from below due to higher ocean temperatures, prompting scientists to warn Monday that this key reinforcement could shatter in the next three to five years—a development that would threaten millions of people with intensifying sea level rise. “Until recently, the ice shelf was seen as the most stable part of Thwaites Glacier, a Florida-sized frozen expanse that already contributes about 4% of annual global sea level rise,” the Washington Post reported. “Because of this brace, the eastern portion of Thwaites flowed more slowly than the rest of the notorious ‘doomsday glacier.’” # § Energy⠀➾ # ⚓ Groups_Move_to_Uncover_Why_Biden_Held_Huge_Drilling Sale_That_DOJ_Said_Was_Not_Required⠀⇛ When the Biden administration first announced in August that it would soon hold a massive auction of oil and gas drilling rights in the Gulf of Mexico, officials told angry critics that they had no choice but to proceed with the historic—and ecologically catastrophic—sale because of a ruling by a Trump-appointed federal judge. “We don’t know… why the administration went ahead with this sale.” # ⚓ Major_pulp_mill_halts_production_due_to_record electricity_price⠀⇛ One of Estonia’s most energy-intensive producers, Kunda-based aspen pulp mill AS Estonian Cell temporarily halted production last week due to soaring energy prices and is expecting the government to offer rapid solutions for restoring the competitive ability of Estonian companies. Estonian Cell had to shut down it s pulp mill on December 8 due to extreme electricity prices as unexpected power and gas price hikes have impacted competitive ability. Despite partially fixed-price contracts, the company spent €1.5 million more than usual on power and gas in November. The company has paid an extra €5 million for energy in recent months. # ⚓ Burning_money:_Three-story_cryptocurrency_farm destroyed_in_fire⠀⇛ There are a lot of factors at play in the current shortage of graphics cards: higher demand for PC upgrades, a manufacturing crunch, scalpers inflating secondary markets. But perhaps none are more reviled by gamers than cryptocurrency miners, who repurpose devices previously used for entertainment to try and spin electricity into speculative cryptographic gold. Last week gamers got to revel in a bit of schadenfreude, as a suspected crypto mining farm in Thailand burst into flames. # § Wildlife/Nature⠀➾ # ⚓ How_to_Save_Sharks_and_Rays_From_Extinction⠀⇛ # ⚓ ‘A_Gut_Punch’:_Biden_Interior_Dept_Quietly_Plans_to Strip_Protections_From_Key_Species⠀⇛ Conservation advocates accused the U.S. Fish and Wildlife Service of “deep rot within the agency” Monday as they condemned the Biden administration’s plan to weaken or eliminate protections for several endangered species—a step that officials appear to be taking without any consideration for the threats the climate crisis poses to the animals. Writing to Interior Secretary Deb Haaland, Interior Department Inspector General Mark Lee Greenblatt, and other officials, the Center for Biological Diversity (CBD) demanded to know why the USFWS would decide now to reduce protections for species including the Florida panther, the Key deer, the Canada lynx, and the whooping crane. o § Finance⠀➾ # ⚓ Investigation_Finds_at_Least_48_Members_of_Congress_Have Violated_STOCK_Act⠀⇛ # ⚓ White_House_Says_Restarting_Student_Loans_Is_“High Priority,”_Sparking_Outrage⠀⇛ # ⚓ Build_Back_Better_Could_Help_End_Subminimum_Wages_for People_With_Disabilities⠀⇛ # ⚓ Reopening_Issues_Remain_a_Big_Factor_Driving_Inflation_In November⠀⇛ Cars are still a huge factor driving inflation. Factories are getting back up to speed, but it may be a few more months before this pushes prices back down. Supply chain issues may persist, but demand is likely to wane for big ticket items which people don’t buy every month. TV prices have fallen sharply in the last three months, appliance prices (which do not include TVs) are down slightly in the last two months. It seems likely that monthly inflation (not year-over-year) will be sharply lower in December and future months. # ⚓ Progressive_Lawmakers_Signal_Support_for_Four-Day_Workweek Proposal⠀⇛ # ⚓ Opinion_|_Wage_Inequality_Continued_to_Increase_in_2020⠀⇛ Newly available wage data from the Social Security Administration allow us to analyze wage trends for the top 1.0% and other very high earners as well as for the bottom 90% during 2020. The upward distribution of wages from the bottom 90% to the top 1.0% that was evident over the period from 1979 to 2019 was especially strong in the 2020 pandemic year, yielding historically high wage levels and shares of all wages for the top 1.0% and 0.1%. Correspondingly, the share of wages earned by the bottom 95% fell in 2020. # ⚓ Yearly_Wages_of_Most_US_Workers_Grew_Just_28%_Since_1979 But_‘Skyrocketed’_for_Top_0.1%⠀⇛ Wage inequality in the United States has continued unabated for over four decades, according to an analysis published Monday by a Washington, D.C.- based economic think tank. “This disparity in wage growth reflects a sharp long-term rise in the share of total wages earned by those at the very top.” # ⚓ Time_Selects_Tax-Dodging,_Anti-Union,_Mega-Billionaire_Elon Musk_as_Person_of_the_Year⠀⇛ Elon Musk, the wealthiest human being in history, is Time’s Person of the Year, and on Monday progressives reacted by mocking the magazine’s selection and renewing calls for changing the U.S. tax code so that the Tesla co-founder and other plutocrats like him pay their fair share. “Let’s change the rigged tax code so the Person of the Year will actually pay taxes and stop freeloading off everyone else.” # ⚓ ‘Tax_Billionaires_Already’:_Viral_Video_Shows_Teachers Scramble_for_Cash_in_‘Dystopian’_Contest⠀⇛ Footage of public school teachers in Sioux Falls, South Dakota scrambling on an ice rink to gather one-dollar bills for school supplies went viral over the weekend, with labor leaders and economic justice advocates pointing at the video as the latest evidence that schools are drastically underfunded and corporations and the wealthy must pay their fair share in taxes. Onlookers cheered Saturday night as the teachers participated in the first-ever “Dash for Cash” at a hockey game. Five thousand dollars in one-dollar bills were laid out on a mat on the ice and the educators were given five minutes to stuff the cash into their shirts so they could use the money to buy school supplies and pay for classroom upgrades. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ The_Right_Is_Now_Weaponizing_Recall_Elections_at_Every Level_of_Government⠀⇛ # ⚓ Will_Chile_Return_to_a_Pinochet-like_Darkness?⠀⇛ In Chile, my country, the date took on a special meaning after the 1973 coup by General Augusto Pinochet that overthrew the democratically elected government of socialist president Salvador Allende. During the 17 years of dictatorship that followed, 10 December was an occasion to publicly rally for those rights that were being egregiously violated, as the regime arrested, tortured, executed or exiled opponents, and abrogated free speech and the right to assemble peacefully. In such an atmosphere of terror, the very congregating of citizens to protest was considered by our rulers to be an act of defiance. I can remember one such insubordinate meeting in the central plaza of Santiago – it must have been in the late 1980s – when I barely escaped being dragged into a van and beaten by riot police, even though we were merely singing Beethoven’s Ode to Joy. After democracy was restored in 1990, those gatherings became less dangerous to attend but more necessary than ever to hold, as a reminder that never again – nunca más – should such an oppressive regime be allowed to return. # ⚓ Opinion_|_Hey_Congress!_Pass_Voting_Rights…or_Violate_the Constitution⠀⇛ I feel like an exhausted well digger, shovel in hand, who was just handed a jack hammer. But in my case, it is a tool I didn’t even know existed—a tool for saving our beleaguered democracy. # ⚓ Wounds_the_Size_of_Oranges⠀⇛ # ⚓ Filings_Reveal_Manchin’s_Blind_Trust_Can’t_Explain_Away ‘Blatant_Conflict_of_Interest’⠀⇛ The blind trust that Sen. Joe Manchin frequently cites to deflect criticism of potential conflicts of interest stemming from his family’s lucrative West Virginia coal empire is—according to newly reported financial documents—”much too small” to cover his total earnings from the dirty energy business, raising further questions about the right-wing Democrat’s possible financial stake in preventing climate action. “Manchin is not only very wealthy, but most of his assets and wealth are invested in a single industry, coal.” # ⚓ Opinion_|_It’s_No_Mystery:_Joe_Manchin_Represents_the Monied_Interests_and_Nobody_Else⠀⇛ The next ten days may well offer the last opportunity to enact Biden’s agenda, because once Congress returns from Christmas break it’s the new year—which is a danger zone for new legislation. Even when Democrats control all three branches—as they do now and did during first two years of Obama and Clinton—the second year is perilous because of the overwhelming gravitational pull of the midterm elections (I have a searing memory of Bill Clinton unable to summon a Democratic majority in 1994 for his healthcare bill). # ⚓ ‘This_Is_Manchin_Against_Us’:_Poor_People’s_Campaign Targets_Corporate_Democrats_at_DC_Rally⠀⇛ With the rallying cry “Get It Done in ’21,” low- wage workers, caregivers, and activists from across the country converged on Washington, D.C. Monday to demand that Sen. Joe Manchin and other right-wing Democrats stop stonewalling progress on the Build Back Better Act, voting rights legislation, and other urgent priorities. “If you don’t get it done in ’21, we are coming double in ’22, and ’23, and ’24, and ’25.” # ⚓ Defining_Racism:_Individuals_and_Institutions,_Systems_and Structures⠀⇛ Clichés sum it up best: This is the best and the worst of times, a crisis fraught with danger and opportunity. So, let’s take a moment to define terms. # ⚓ Éric_Zemmour,_the_French_Establishment’s_Far_Right Candidate⠀⇛ Only this November, the 63-year-old went on trial again on similar charges, over a remark made on TV in September 2020 that unaccompanied foreign minors were “thieves and rapists” and that France “must send them back”. The court case is ongoing, with Zemmour’s lawyer claiming the charges are “unfounded”. His first electoral rally, held in the Parisian suburb of Villepinte earlier this week, was marred by scenes of violence: Zemmour supporters, some of whom belong to far-Right and Neo-Nazi groups, beat up antiracist activists who peacefully demonstrated. o § Misinformation/Disinformation⠀➾ # ⚓ How_Conspiracy_Theories_in_the_US_Became_More_Personal, More_Cruel_and_More_Mainstream_After_the_Sandy_Hook Shootings⠀⇛ These conspiracy theories are part of a dangerous misinformation crisis that has been building for years in the U.S. American politics has long had a paranoid streak, and belief in conspiracy theories is nothing new. But as the news cycle reminds us daily, outlandish conspiracy theories born on social media now regularly achieve mainstream acceptance and are echoed by people in power. # ⚓ Facebook_exec_says_‘people,’_not_platform,_to_blame_for vaccine_misinformation⠀⇛ Bosworth told Axios it was undemocratic for a social platform to attempt to control people’s speech, even in cases when it might be harmful. “I don’t believe that the answer is ‘I will deny these people the information they seek, and I will enforce my will upon them.’ That can’t be the right answer. That cannot be the democratic answer,” Bosworth said, noting “the onus is and should be, in any meaningful democracy, on the individual.” Last month, a poll indicated that roughly 3 in 4 Americans said Facebook was making society worse. However, those respondents were still divided on where they placed the blame. # ⚓ Facebook_exec_blames_society_for_COVID_misinformation⠀⇛ The big picture: Pressed on whether Facebook and others are amplifying those views, Bosworth characterized it as a demand problem rather than one caused by the amount of misinformation on social media. “People want that information,” Bosworth said. “I don’t believe that the answer is ‘I will deny these people the information they seek and I will enforce my will upon them.’ “ o § Censorship/Free Speech⠀➾ # ⚓ DOJ_Tells_Courts_They_Don’t_Need_To_Explore_The Constitutionality_Of_Section_230_To_Toss_Donald_Trump’s_Dumb Lawsuits_Out⠀⇛ Last month, we noted that the DOJ had announced it was going to intervene in Donald Trump’s bombastically silly lawsuits against Facebook, Twitter, and YouTube for suspending his account for violating the websites’ terms of service. Those lawsuits have not been going well. While Trump filed them in his home court in Florida, they’ve all been transferred to California. His decision to use the case to claim Section 230 is unconstitutional only served to wake up the Justice Department, and have them step in to respond to that particular point. # ⚓ The_Year_in_Sports:_Athletes_Face_Backlash_but_Refuse_to Back_Down⠀⇛ You can’t wrap your head around the year of 2021 in sports without understanding 2020. During that year of pandemic and protest, athletes found their voices like at no time since the 1970s, if not ever. After the police murder of George Floyd, athletes at every level of sport spoke out, led demonstrations, and took on the weight of being the spokespeople of the deliberately unheard. In addition to the emergence of outspoken players throughout leagues that depend upon Black talent, world-class athletes like tennis star Naomi Osaka, NASCAR driver Bubba Wallace, and Formula One’s budding legend Lewis Hamilton took the struggle into predominantly white spaces, sending an electric current through the complacency of their respective landscapes. But it wasn’t just the issue of racial justice that animated 2020. That the Tokyo Olympics were not staged in 2020 was not only due to the pandemic but also because of a large number of athletes declared that they wouldn’t go. The struggle of young transgender kids to have a place on high school sports teams continued in the face of a coordinated and well-funded attack to keep them off the field and out of the locker room. The coup de grâce, of course, was the WNBA’s effectively swinging the US Senate by opposing the GOP run by then–league franchise owner Kelly Loeffler and throwing their support behind the Rev. Raphael Warnock. # ⚓ The_bare_minimum⠀⇛ The nuance that can be added to this discussion is that the idea of law and order can be expanded beyond just exemplary punishment after violence has occurred. To this end, I want to draw on some case studies of how religious extremism and local administrative structures interact with one another and produce undesirable or desirable outcomes. # ⚓ Hong_Kong_Pro-Democracy_Activist_Jimmy_Lai_Given_13-Month Jail_Term⠀⇛ Lai and other pro-democracy activists have been targeted by Hong Kong authorities since China imposed a strict national security law last June in response to the massive and sometimes violent anti- government protests in 2019. The crackdown has transformed the financial hub from a semi- autonomous city to one increasingly under Beijing’s control. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ Coming_Feature:_Enemy_of_the_State⠀⇛ Look, it’s a new cinematic experience: “Julian” is up on the screen and they’re hating on him, two minutes strong, like there’s no tomorrow, Tasmanian devils in their seats, to borrow an expression never used before, berating his call for crypto- privacy. Delerience consumes the wretched theatre, 2 + 2 is 5, when a leaky condom is displayed to shock. And radical transparency of government confirms that Julian is that rare aberrant; the pretty blonde starts egging; someone pulls a Glock; nobody’s ever seen such anger in the hive. Then the feature begins with a rolling tomtom:The Sorrow and the Pity, a romcom. # ⚓ Your_Man_Back_in_the_Public_Gallery:_Assange_Extradition, US_Appeal_Result⠀⇛ On Thursday afternoon I was in Edinburgh High Court to get back my passport, which had been confiscated during my own court proceedings avowedly to stop me going to Spain to testify in the trial of David Morales of UC Global. He stands accused by whistleblowers in his own company of spying on Julian Assange, his lawyers and other associates (including myself), on behalf of the CIA, and in engaging with them on plans to kidnap or assassinate Assange. # ⚓ Opinion_|_The_US_Empire’s_Slow_But_Determined_Execution_of Julian_Assange⠀⇛ Let us name Julian Assange’s executioners. Joe Biden. Boris Johnson. Scott Morrison. Theresa May. Lenin Moreno. Donald Trump. Barack Obama. Mike Pompeo. Hillary Clinton. Lord Chief Justice Ian Burnett and Justice Timothy Victor Holroyde. Crown Prosecutors James Lewis, Clair Dobbin and Joel Smith. District Judge Vanessa Baraitser. Assistant US Attorney in the Eastern District of Virginia Gordon Kromberg. William Burns, the director of the CIA. Ken McCallum, the Director General of the UK Security Service or MI5. # ⚓ Barnaby_Joyce_makes_Assange_an_issue_in_Australian_federal poll⠀⇛ There are a few Australian politicians who understand the real implications of the Assange issue, among them people like Andrew Wilkie and Rex Patrick. It is time for them to step up as well, and increase the pressure on Morrison. Assange is said to have suffered a stroke after the Friday hearing. The time to act is now and if Morrison cannot see that, then one would have to seriously doubt his political acumen. # ⚓ Chris_Hedges:_The_Execution_of_Julian_Assange⠀⇛ Let us name Julian Assange’s executioners. Joe Biden. Boris Johnson. Scott Morrison. Teresa May. Lenin Moreno. Donald Trump. Barack Obama. Mike Pompeo. Hillary Clinton. Lord Chief Justice Ian Burnett and Justice Timothy Victor Holroyde. Crown Prosecutors James Lewis, Clair Dobbin and Joel Smith. District Judge Vanessa Baraitser. Assistant US Attorney in the Eastern District of Virginia Gordon Kromberg. William Burns, the director of the CIA. Ken McCallum, the Director General of the UK Security Service or MI5. # ⚓ John_Pilger:_The_Judicial_Kidnapping_of_Julian_Assange⠀⇛ Sartre’s words should echo in all our minds following the grotesque decision of Britain’s High Court to extradite Julian Assange to the United States where he faces “a living death”. This is his punishment for the crime of authentic, accurate, courageous, vital journalism. # ⚓ Journalism,_Assange_and_Reversal_in_the_High_Court⠀⇛ In recent memory, fewer blemishes can be more profound and disturbing to a legal system than the treatment of Australian citizen and WikiLeaks founder, Julian Assange.  The British legal system has been so conspicuously outsourced to the wishes of the US Department of Justice and the military- industrial complex Assange did so much to expose.  The decision of the UK High Court, handed down on December 10, will go down in the annals of law as a particularly disgraceful instance of this. From the outset, extradition proceedings utilising a First World War US statute – the Espionage Act of 1917 – should have sent legal eagles in the UK swooping with alarm.  17 of the 18 charges Assange is accused of have been drawn from it.  It criminalises the receipt, dissemination and publication of national security information.  It attacks the very foundations of the Fourth Estate’s pursuit of accountability and subverts the protections of the First Amendment in the US constitution.  It invalidates motive and purpose.  And, were this to be successful – and here, the British justices seem willing to ensure that it is – the United States will be able to globally target any publisher of its dirty trove of classified material using an archaic, barbaric law. # ⚓ UK_Court_Says_US_Can_Extradite_Julian_Assange_And_Prosecute Him_For_Doing_Things_Journalists_Do⠀⇛ Julian Assange and Wikileaks did a lot over the past few years to destroy the goodwill they’d managed to accumulate prior to that by being a fearless publisher of leaked documents. At times, Assange has acted hypocritically and there’s some evidence he worked with Russian operatives to gather information in an attempt to damage the Democratic Party’s 2016 election hopes. o § Civil Rights/Policing⠀➾ # ⚓ Warehouse_Workers’_Deaths_Prompt_Renewed_Scrutiny_of Amazon’s_No-Phone_Policy⠀⇛ # ⚓ Opinion_|_What’s_Next:_Fascist_Takeover_or_New_Era_of Progressive_Renewal?⠀⇛ Do we stand on the edge of a grand new progressive era, with good wages for all, racial and gender equality and justice, and a reduction of the political power of reactionary forces in America? Or will the next president gleefully overthrow American democracy, shutter the free press, and imprison those who object? # ⚓ After_a_Year-Long_Strike,_India’s_Farmers_Win_Big⠀⇛ # ⚓ Court_Tells_Cops_Who_Got_A_Man_Wrongly_Imprisoned_For_25 Years_That_Of_Course_Framing_People_For_Crimes_Is_A_Rights Violation⠀⇛ There’s a constitutional right not to be framed by cops for a crime you didn’t commit. This shouldn’t even need to be argued in court once, much less twice. But “framed by cops” is exactly what happened to James Dennis, who spent 25 years in prison after being falsely accused of murdering a high school student back in 1991. # ⚓ EFF_to_Federal_Appeals_Courts:_Hold_Police_Accountable_for Violating_Civilians’_Right_to_Record⠀⇛ After police officers beat Dijon Sharpe during a traffic stop, he decided that next time he was in a car that was pulled over, he would livestream and record the police. So in October 2018, Sharpe, sitting in the passenger seat of a stopped car, took out his phone and started livestreaming on Facebook. When an officer saw that he was livestreaming, he grabbed Sharpe and tried to take the phone. Sharpe filed a civil rights lawsuit for the interference, a federal district court dismissed his claims in two opinions, and he appealed. Abade Irizarry was recording a traffic stop as a bystander when another police officer interfered. The officer shined lights into Irizarry’s phone camera, stood between the camera and the traffic stop, and menaced Irizarry with his car and blasted him with an air horn. Irizarry appealed after a federal district court dismissed his lawsuit. EFF thinks these officers should be held accountable. The First Amendment protects people who gather and share information, especially when it is about official misconduct and advances government accountability. Police body cameras point towards the public, effectively surveilling those already being policed. The civilian’s camera, by contrast, is appropriately pointed towards the officer. Ordinary people’s livestreams and recordings of the police have always been necessary to inform the public—before the police murder of George Floyd went viral in June 2020, there was the beating of Rodney King in March 1991. # ⚓ Why_Xiomara_Castro’s_Win_in_Honduras_Could_Address_the Country’s_Endemic_Corruption_and_Violence⠀⇛ Castro was referring to the 12 years of repressive rule by the National Party, which took power after Zelaya was ousted in a 2009 military coupthat, as per Siu, “the United States orchestrated.” Years after the coup, Hillary Clinton, who was the U.S. state secretary at the time of the coup, justified Zelaya’s removal, saying in a 2016 interview, “I didn’t like the way it looked or the way they did it but they had a very strong argument that they had followed the constitution and the legal precedence.” The Intercept later exposed how U.S. military officers at the Center for Hemispheric Defense Studies assisted Honduran coup leaders in their efforts. National Party leader Juan Orlando Hernández claimed electoral victory in 2013 against Castro and then again in 2017 against Salvador Nasralla in the face of credible accusations of massive fraud. The man who has been deeply implicated in narco- trafficking in the U.S. (his brother was convicted in a New York court of smuggling in hundreds of tons of cocaine) used the Honduran security forces as his personal militia during his tenure. # ⚓ Abortion_Restrictions_Could_Prompt_an_Avalanche_of_Attacks on_Bodily_Autonomy⠀⇛ # ⚓ Chicago_expected_to_pay_woman_$2.9M_over_botched_police raid⠀⇛ Not only did the officers who raided Young’s apartment not let her get dressed, but she was right when she repeatedly told them they were at the wrong address. After the committee meeting, Cabanban said the investigation revealed that police forced Young to remain naked for 16 seconds and that what they put over her kept falling off before she was allowed to get dressed about 40 minutes after the officers arrived. Meanwhile, Lightfoot’s claims that she had no knowledge of the raid were proven false when emails revealed that her staff had told her. Lightfoot came under more criticism when city attorneys tried to get a court order to prevent a local television station from airing video of the raid at Young’s home. # ⚓ How_the_Taxi_Workers_Won⠀⇛ In late September of 2020, the New York Taxi Workers Alliance had drawn up a plan to cap drivers’ loans and limit their monthly payments. The city ignored it, just as, for years, it had brushed off NYTWA’s protests against medallion debt. This sit-in was an escalation—an attempt to force New York City Mayor Bill de Blasio’s hand. Inspired by the drivers’ struggle, I kept coming back, night after night, then week after week. I listened to their stories, drew their portraits, marched in their picket lines, and ultimately joined their hunger strike. Despite their defiant assurances of victory, I could not shake the sense that I was witnessing the doomed last stand of yet another group of working-class New Yorkers who would be crushed by the hedge-fund Bretts who run this city. Instead, on November 3, NYTWA announced that the city had adopted almost every detail of its plan. The drivers had won. # ⚓ Factory_workers_threatened_with_firing_if_they_left_before tornado,_employees_say⠀⇛ Employees congregated in bathrooms and inside hallways, but the real tornado wouldn’t arrive for several more hours. After employees decided that the immediate danger had passed, several began asking to go home, the workers said. “People had questioned if they could leave or go home,” said Emery, who preferred to stay at work and make extra money. Overtime pay was available, but it wasn’t clear whether those who stayed were offered additional pay. Supervisors and team leaders told employees that leaving would probably jeopardize their jobs, the employees said. o § Internet Policy/Net Neutrality⠀➾ # ⚓ The_Bipartisan_Attacks_On_The_Internet_Are_Easily Understood_If_You_Realize_They_Just_Want_To_Control_Speech Online⠀⇛ Understanding the “bipartisan” approach to internet regulations over the last couple of years really boils down to “both parties want to control the internet” and twist it to their own advantage. Almost everything you hear about “harms” from the internet are disingenuous nonsense from grandstanding politicians. That’s not to say there aren’t real problems with things on the internet or how it’s structured — but there is almost no realistic exploration of those issues by those in various legislatures. It’s all about grabbing control over the internet. Two recent articles highlight pretty clearly how both Republicans and Democrats are clearly salivating to control speech online for their own benefit — and not for the actual good of society or the internet. # ⚓ Dream_Job_Alert:_Senior_Fellow_for_Decentralization_at EFF⠀⇛ We are hiring a Senior Fellow of Decentralization, a position that is a public advocate helping to establish EFF as a leader in the civil liberties implications of decentralizing the Internet. You’ll help chart a course for EFF to have real impact in the public conversations about decentralization of the Internet as it fits into our mission of ensuring that technology supports freedom, justice, and innovation for all people of the world. Through fierce and informed public advocacy, blogging, and social media, this Fellow will help us create a future internet that is more decentralized, resilient, and protective of both civil liberties and innovation. Apply today. Note that this is a two year fellowship, with the possibility of extending up to one to two additional years depending on the outcomes of those two years and EFF’s needs. The landscape of Decentralization is broad. Technologies that can re-decentralize the internet and provide for increased competition and provide for resources to those who are not being served properly by the existing world point to the future we would like to help bring about. There are three major areas of activity where we expect you to work: We will prioritize the work in that order.  o § Digital Restrictions (DRM)⠀➾ # ⚓ The_Law_Bytes_Podcast,_Episode_112:_Aaron_Perzanowski_on the_Right_to_Repair⠀⇛ Tomorrow Unlocked, No Right to Repair: Farmers are Forced to Hack Their Own Tractors # ⚓ TikTok’s_2021_music_recap_says_it’s_getting_even_better_at creating_billion-listen_megahits⠀⇛ TikTok’s yearly recap also includes some numbers on how these songs performed when not attached to a TikTok video. Over 175 trending TikTok songs made it to the Billboard Hot 100 this year, up from 90 in 2020. TikTok also takes credit for helping a number of artists skyrocket themselves to stardom, like ex-Verizon employee Tai Verdes, who made it to the Billboard Hot 100 for the first time with his trending TikTok song “A-O-K.” Another emerging artist on TikTok, PinkPantheress, racked up “hundreds of millions of combined streams” on Spotify. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ ‘Succession,’_‘Sex_and_the_City’_and_the_Age_of Zombie_IP⠀⇛ It’s a trend that’s been dubbed the zombification of intellectual [sic] property [sic] : No show ever dies anymore. By no means is this a new trend, but what was once a treatment reserved for the biggest hits will be extended to any series that managed to eke out even a small devoted audience for just a few years. # ⚓ Dear_Users_of_CC_Search,_Welcome_to_Openverse⠀⇛ # ⚓ EUIPO_Study_Indicates_It’s_Likely_That_Piracy_Traffic Has_Decreased_Significantly,_Even_During_The_Pandemic⠀⇛ Back in April of 2020, which feels roughly like a damned lifetime ago, we discussed a much-publicized report that indicated explosive growth in traffic to pirate torrent and streaming sites for movies, music, television, and video games. Much hand- wringing ensued, which was largely silly. All kinds of media consumption traffic rose during the initial lockdown months of the COVID-19 pandemic and it only made sense that piracy traffic would follow suit, particularly when you consider the broader economic impact of the pandemic. This wasn’t some new paradigm shift in the piracy landscape; it was literally one of the most predictable things that could have happened. # ⚓ Faulty_DMCA_Takedown_Notice_Makes_American_TV_Network Unfindable_in_Google⠀⇛ American free-to-air TV network Mega.tv has had its homepage stripped from Google due to a dubious takedown request. The apparent mistake is tied to an overbroad DMCA notice sent on behalf of the European football organization UEFA. The issue has gone unnoticed for more than a year and persists today. # ⚓ Sites_With_>100_Links_to_Pirated_Content_Will_Be Banned_From_Search_Engines⠀⇛ After being signed by some of Russia’s most powerful tech and entertainment companies in 2018, the memorandum designed to remove infringing content from the internet is being revamped. The most aggressive change is that rather than taking a proactive stance on removals, domains carrying more than 100 links to movies and TV shows will be excluded from search results. ䷩ 𝚕𝚒𝚗𝚎 5951 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_14/12/2021:_Linux_Mint_20.3_“Una”_Beta_and_Kaisen_Linux_2.0⠀✐ Posted in News_Roundup at 7:14 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o ⚓ Linux_Distros:_Year_in_Review⠀⇛ 2021 was a pretty exciting year for Linux distributions within the cloud native and developer world. Not only did two CentOS replacements release new iterations, but they also reached a level of stability to surpass that of the platform they replaced (Red Hat changed the direction of CentOS late last year towards a more experimental approach). And although there were no new distributions released that were purpose-built for cloud, container, and edge use cases, there were plenty of updates for other operating systems that strengthened the offerings to make nearly every Linux server distribution widely appealing to most businesses and developers. o § Desktop/Laptop⠀➾ # ⚓ System76_Launches_Pop!_OS_21.10_with_Linux_5.15_LTS,_New Application_Library⠀⇛ Coming almost six months after Pop!_OS 21.04, the Pop!_OS 21.10 release introduces a new Application Library feature for its GNOME-based desktop environment that replaces the big Application Wall window that opened in full-screen when you wanted to search for and open an installed application. Now, in Pop!_OS 21.10, the Application Library feature, which you can access it from the dock, menu bar, using a 4-finger swipe, or the Super+A keyboard shortcut, will open in a smaller window over the current workspace. # ⚓ Linux_needs_to_be_pre-installed_on_more_hardware_to_hit mainstream⠀⇛ Honestly, it really is that simple. There’s a fair bit of that now already with the likes of System76, Slimbook, TUXEDO , Star Labs and others I’m forgetting. However, none of those are particularly known outside of Linux circles (TUXEDO claim otherwise). Even if they’re slowly pulling in newer non-Linuxy customers, they’re still tiny and often expensive. Other vendors like Dell and Lenovo may have a few but they’re often harder to find. It’s a bit like the old Linux gaming loop — people don’t want to switch due to “no games” and developers don’t want to support directly due to “no users”. Vendors don’t often do it because they don’t perceive there to be enough interest. # ⚓ System76_Releases_Pop!_OS_21.10⠀⇛ Linux PC vendor System76 has released Pop!_OS 21.10 as the newest version of their Ubuntu-based operating system. Pop!_OS 21.10 is the latest version of their popular open-source desktop OS that features desktop improvements and other mostly UI alterations compared to Ubuntu 21.10. One of the new features with Pop!_OS 21.10 is its “Application Library” window that they aim as an alternative to GNOME’s Application Wall. # ⚓ Pop!_OS_21.10_has_landed!⠀⇛ Pop!_Pi Tech-Preview for Raspberry 4 Tinkerers, this one’s for you! A tech preview of Pop!_OS 21.10 is now available on the Raspberry Pi, a mini computer for STEM learning and experimentation. We built Pop!_Pi for the Raspberry Pi 4 to gain experience building for ARM platforms. The Raspberry Pi 4 performed much better than we anticipated, so we decided to release it to the public. It’s a Tech-Preview because it doesn’t receive as much Quality Assurance focus as Pop!_OS for the desktop, but is nonetheless an excellent option for users. We plan to continue releasing Pop!_Pi with future Pop!_OS releases. Latest Hardware Support Pop!_OS 21.10 features the 5.15.5 kernel and latest NVIDIA driver. Pop!_OS has a new kernel policy whereby the latest kernels will be released once they’ve passed extensive quality assurance tests. This is the same release policy we’ve used for NVIDIA drivers. The System76 hardware lab contains a broad spectrum of chipsets, processors, and components to test for regressions prior to release so customers and users can be confident that new kernel releases will only improve their hardware performance and support. New, More Intuitive Refresh OS Feature Your system will now recognize when Pop!_OS is installed from the recovery partition and offer the Refresh OS option prior to unlocking an encrypted drive. This makes it easier to see when the Refresh OS option is available. # ⚓ First_Look_at_System76’s_Pop!_Pi_OS_for_Raspberry_Pi_4⠀⇛ That’s right, Pop!_OS Linux has been ported to Raspberry Pi devices, and 9to5Linux.com is the first website to take the new Pop!_Pi 21.10 operating system for a spin on a Raspberry Pi 4 board with 8GB RAM. System76 informed me that Raspberry Pi 400 models are also supported. According to System76, Pop!_Pi was built for the Raspberry Pi 4 to help them gain experience building for ARM platforms, but the system performed so well that they decided to release it to the public. # ⚓ Pop!_OS_21.10_is_Here,_Jumps_Ahead_to_GNOME_40⠀⇛ System76 has released Pop!_OS 21.10, its bespoke Linux distribution based on Ubuntu. So let’s take a quick look what’s new! For those of you unaware, Pop!_OS was born when Canonical, the company behind Ubuntu, abandoned the Unity desktop. The distro is developed by System76, a US computer manufacturer of Linux-based laptops, desktops and servers. Pop!_OS 21.10 is the latest version of the System76’s popular open-source desktop operating system that features some improvements and other mostly desktop alterations. # ⚓ Pop_OS_21.10_Introduces_Mini_Application_Menu_+_Bumper Updates⠀⇛ The Pop team officially released the POP OS 21.10. In this post, we wrap up the release highlights and give you download & upgrade details. # ⚓ Pop!_OS_21.10_rolls_out_with_new_Application_Library_| GamingOnLinux⠀⇛ System76 has rolled out Pop!_OS 21.10 today, the latest major upgrade to their Ubuntu-based operating system designed to be used by everyone – professionals and gamers alike. It comes with some absolutely massive improvements too and it really does look fantastic. The big user-facing feature is the new Application Library. Instead of getting a big full-screen wall of information and icons, you now get a smaller searchable window over your currently used workspace. It can be opened in a few ways too like the top bar, a 4-finger swipe right on the trackpad, or by using Super + A on the keyboard. With this change it gives a better workflow for multi-monitor users (hooray!) since it will go to the display that has your current mouse focus. The list is sorted alphabetically too making it more natural, you have the ability to drag and drop into folders for organisation and of course the search makes it quick and easy to find exactly what you want. # ⚓ Pop!_OS_21.10_Released_with_New_App_Library_Feature_+_More –_OMG!_Ubuntu!⠀⇛ System76 have slipped in to their Santa suits to deliver Linux users an early festive treat: Pop!_OS 21.10. Yes, the latest version of their Ubuntu-based Linux distro is available to download. It includes a new Linux kernel, the bulk of GNOME 40, a new App Library feature (more on that in a mo) and refinements to its (handy) OS restore options. Notwithstanding a recent red-faced encounter with a tech YouTuber, Pop!_OS has proven a popular choice with Linux gamers since launching in 2017. Part of the reason is that this distro offers a newer Linux kernel and more recent graphics drivers than vanilla Ubuntu. But soon there’ll be an even greater distinction: System76 plans to build its own desktop environment! Having found that the direction of upstream GNOME is out of kilter with their needs they’re going it (sort of) alone. # ⚓ Pop!_OS_is_Now_Available_for_the_Raspberry_Pi_4_–_OMG! Ubuntu!⠀⇛ Pop!_OS is now available for the Raspberry Pi. The sweetly-named Pop!_Pi is available to download as a ‘tech preview’ alongside the latest Pop!_OS 21.10 release from System76. While Pop!_Pi is the first version of Pop!_OS to be available for Raspberry Pi devices it doesn’t support all Raspberry Pi Models. Instead, the Pop!_Pi tech preview caters to the ‘desktop class’ Raspberry Pi 4 board (which regular Ubuntu also supports). It requires the model with 4GB RAM or more. If you use Linux (whatever flavour) you’ll have no doubt heard of the Raspberry Pi even if you haven’t ever used one. The line of cheap mini-computers has been nothing short of a revolution, lowering the barrier to entry for tech across the world and throughout industry. # ⚓ Pop!_OS_21.10_Introduces_a_New_Application_Library,_GNOME 40,_and_a_Refresh_Install_Option⠀⇛ Pop!_OS is undoubtedly one of the best Linux distributions, also happens to be a popular recommendation currently for Linux newbies (and gamers). If you do not prefer non-LTS releases, you should stick to Pop!_OS 20.04 LTS. But, if you are looking for the latest and greatest update, Pop!_OS 21.10 is finally here for you to download! Not to forget, the Pop!_OS 21.10 release sets things in motion for a potential list of features that you can expect with Pop!_OS 22.04 LTS, April next year. # ⚓ Five_Linux_distributions_to_resurrect_an_old_laptop_– TechStony⠀⇛ It seems that Microsoft is making it difficult to run Windows 11 on a large number and variety of hardware, especially if it is not recent and does not meet certain requirements. Seeing this situation, that Windows 7 is officially “defunct” and that Windows 10 may not shine on those computers, we are going to publish a list of Five Linux Distros That Could Bring An Old Laptop To Life. Of course, when we talk about an old laptop, we are not referring to what some may be thinking. In this post we will focus on old 64-bit x86 computers, because those computers exist, although in a large part of the collective imagination it is not like that. More concretely, we will put the ground on the Intel Core 2 Duo, the generation of processors that together with the Core 2 Quad ended up standardizing the 64-bit x86 processors 15 years ago in the consumer market. The extremely long life that Windows XP enjoyed, together with the fact that applications compiled for 64-bit x86 did not begin to be standardized in Windows until approximately 2011-2012, ended up generating in the collective imagination the idea that the processors of this architecture has been with us for a few years. In fact, few remember the hype that arose around Battlefield 3 when Electronic Arts announced in 2011 that it would require Windows 7 64-bit as a system. At that time Windows XP was still widely used, which aroused the complaints of many users, but DICE and Electronic Arts remained firm and did well, because that was the beginning of a technological leap necessary for video games to take better advantage of the processors that They have been with us for years. o § Server⠀➾ # ⚓ What’s_New_In_Kubernetes_v1.23?⠀⇛ Kubernetes v1.23 is the last major release of 2021. The latest update to the leading container orchestration platform promotes 11 features to the stable channel, marking them as suitable for general use. Here’s what you need to know before you upgrade. [...] While an “ephemeral” volume may initially sound strange, there are several use cases for this functionality. Volumes are often used to provide a Pod’s process with first-run config values that are only accessed once. In this scenario, an ephemeral Pod is ideal as it’ll be deleted when the Pod stops, instead of being reattached to future Pods that’ll never use the data. Another possible case is processes which cache large amounts of data but don’t need it to be persisted between individual Pod terminations. o § Audiocasts/Shows⠀➾ # ⚓ Destination_Linux_256:_Linux_Geek_Buying_Guide_for Christmas⠀⇛ This week’s episode of Destination Linux, we are going to list out the best gifts to give the Linux geek in your life or just the best gifts to get yourself. If you want to drop some hints to your significant other about what to get your for the holidays…make sure they listen to this episode. Then we’re going to discuss some troubling reports regarding Debian. Plus we’ve also got our famous tips, tricks and software picks. All of this and so much more this week on Destination Linux. So whether you’re brand new to Linux and open source or a guru of sudo. This is the podcast for you. # ⚓ Protonup_QT:_Essential_Tool_For_Lutris_and_Steam_– Invidious⠀⇛ A few weeks back a did a video covering Protonup for managing your versions of ProtonGE but protonup qt does so much more than that the name really holds it back # ⚓ 7_Privacy_Measures_that_won’t_make_your_life_difficult_– Invidious⠀⇛ # ⚓ Use_KDE_Plasma_Applets_on…_GNOME!_–_Kockatoo_Tube⠀⇛ o § Kernel Space⠀➾ # ⚓ Linux_5.15.8⠀⇛ I'm announcing the release of the 5.15.8 kernel. All users of the 5.15 kernel series must upgrade. The updated 5.15.y git tree can be found at: git://git.kernel.org/pub/scm/linux/kernel/git/ stable/linux-stable.git linux-5.15.y and can be browsed at the normal kernel.org git web browser: https://git.kernel.org/?p=linux/kernel/git/stable/ linux-s... thanks, greg k-h # ⚓ Linux_5.10.85⠀⇛ # ⚓ Linux_5.4.165⠀⇛ # ⚓ Linux_4.19.221⠀⇛ # ⚓ Linux_4.14.258⠀⇛ # ⚓ Linux_4.9.293⠀⇛ # ⚓ Linux_4.4.295⠀⇛ # ⚓ Don’t_expect_a_new_cut_of_Linux_to_ease_your_NYE hangovers⠀⇛ The Register can at last reveal the answer to the question on everyone’s lips: who would win a hypothetical fight between Santa Claus and Linus Torvalds? And the winner is … Santa! We have reached this decision based on Torvalds’s regular state of the kernel post for this week, in which he rated the development process for version 5.16 of the Linux kernel as “fairly normal”. “This rc5 is perhaps a bit bigger than usual, but it’s not like it’s breaking any records,” Torvalds wrote. “I blame people trying to get stuff done before the holidays, and/or just random timing effects.” Torvalds thinks the holidays will slow the release of this version of the kernel. “With the holidays coming up, things are probably going to slow down both on the development and testing front, and as a result I expect that I will also extend the rc series by another week,” he added. That addition won’t be because the extra rc is needed – although Torvalds left open the possibility of messes making it necessary – “but simply because nobody will want to open the next merge window immediately in the new year”. # § Graphics Stack⠀➾ # ⚓ LLVM_Working_On_“HIPSPV”_So_AMD_HIP_Code_Can_Turn Into_SPIR-V_And_Run_On_OpenCL_–_Phoronix⠀⇛ Upstreaming progress is being made on a new “HIPSPV” toolchain for AMD’s HIP path so that SPIR-V kernels can be executed and ultimately allowing for execution by OpenCL drivers. This HIPSPV effort driven outside of AMD aims to be able to allow HIP code to work on other GPU drivers such as those from Intel. AMD’s HIP is their C++ Runtime API and kernel language for portable applications on AMD and NVIDIA GPUs from a single source tree. HIP has been AMD’s answer to NVIDIA’s CUDA by aiming to make it easy to port CUDA code to run on AMD Radeon / Instinct hardware. With tools like their open-source HIPIFY they even aim to make it easy and automated as possible for converting CUDA sources to HIP. # ⚓ Radeon_RADV_Lands_Emulated_ETC2_Support_For_Improving Android_Support_–_Phoronix⠀⇛ While the ETC2 texture compression standard is royalty-free and popular for OpenGL / GLES / Vulkan use, recent AMD Radeon GPUs and APUs have removed their native support for this alternative to the likes of ASTC and S3TC. But now in Mesa 22.0 there is emulated ETC2 support for the Radeon “RADV” Vulkan driver to in turn improve this open-source driver’s Android support. As covered last week, RADV ETC2 emulation has been in the works with only the likes of AMD Stoney APUs and Vega/GFX9 featuring native ETC2 hardware support. # ⚓ X.Org_Server_Hit_By_Its_Latest_Batch_Of_Security Vulnerabilities_–_Phoronix⠀⇛ Given the age of the X.Org/X11 code-base security issues have become quite frequent. It was nearly a decade ago that the X.Org Server was considered a “security disaster” and a security researcher saying it’s even worse than it looks. Today another batch of X.Org Server security vulnerabilities have been made public. Four more CVEs were made public today around input validation failures in the X.Org Server that could lead to local privilege escalation. This is for cases where the X.Org Server is still running as a privileged process and supporting remote code execution for SSH X forwarding sessions. o § Benchmarks⠀➾ # ⚓ AMD_Ryzen_7_PRO_5850U_Linux_Performance⠀⇛ For those looking at upgrading your business notebook this holiday season, here are our first benchmarks of the AMD Ryzen 7 PRO 5850U mobile processor under Linux using a Lenovo ThinkPad T14s Gen2. For ~$1299 USD this holiday season on sale, this Linux-friendly ThinkPad offers a lot with the 8-core / 16-thread Zen 3 processor with Vega graphics, 32GB LPDDR4X 4266MHz system memory, 1TB NVMe SSD, 4K IPS display, and legendary ThinkPad build quality. While the AMD Ryzen 6000 “Rembrandt” processors are expected in the coming months with Zen 3+. Zen 3 mobile APUs are widespread these days. While I hadn’t planned on upgrading my main production system/laptop to Cezanne given what’s on the road- map for 2022 and after not finding any compelling laptop options readily available when Cezanne first appeared, Lenovo has been oferring some surprisingly aggressive holiday sales. o § Applications⠀➾ # ⚓ Best_Video_Editors_For_Ubuntu_[_Completely_Free_] [Ed: Newer one, might not be very original]⠀⇛ This is the list of free and best video editors for Ubuntu-based operating systems. Try these editors which are completely free to use and share your experience. # ⚓ PeerTube_4.0_Free_Video_Platform_Comes_More_Powerful_Than Ever⠀⇛ PeerTube 4.0 with channel customization, playlists search, custom instance homepage and more video filters is out! PeerTube is an open source piece of software that enables anyone to run their own tube site (like YouTube) very easily. All of the sites everyone runs can talk to each other, and people with accounts on one can interact with people on others. To put it short, PeerTube is a network of tube sites. PeerTube is decentralized by most useful definitions of the word. Anybody can run their own PeerTube instance, and the instances can follow (or “connect”) to each other to form a larger whole. This is not an option you have with YouTube. When you watch a video on PeerTube the data will come from the instance hosting the video, any other instance that follows that instance and has redundancy enabled and other people watching the video at the same time as you do. Now the PeerTube’s devs has finally released PeerTube 4.0. Let’s see what are the new features. # ⚓ Flamerobin_0.9.3.11_Snapshot_released_with_new_firebird_4 features_and_fixes⠀⇛ Flamerobin 0.9.3.11 Snapshot released with new firebird 4 features and fixes… o § Instructionals/Technical⠀➾ # ⚓ Install_Gnome_Tweak_Tool_on_Ubuntu_22.04_LTS_Jammy JellyFish⠀⇛ With the help of GNOME Tweaks on Ubuntu 22.04 LTS and other Linux running Gnome GUI can be used to customize this desktop environment. Using it, many settings can be edited on the GNOME Shell and on the rest of the system. More settings can be configured than in the system settings. Such as changing of Desktop theme, icons, colour, top, app dock. It is available via the default system repository and can also enable the missing minimize and maximize icons on default Gnome Interface. Here we will learn the command to install Gnome Tweaks on Ubuntu 22.04 LTS Jammy JellyFish. # ⚓ How_to_become_a_Linux_pro_|_ZDNet⠀⇛ As technical job site Dice wrote in its most recent job report, “Job postings in the third quarter demonstrated that employers are looking for technologists who understand the core concepts of software development and project management, in addition to possessing technical skills such as … .” # ⚓ MAAS_3.1_for_hot_metal⠀⇛ Back a few months ago, we did a feature poll on our MAAS forum, and the most-requested new feature turned out to be “Recommission/rescan a machine after it has been deployed“. With the release of MAAS 3.1, we’ve added that feature, making MAAS an even better choice for linux deployment tools. Here’s a sample of how it works. # ⚓ How_to_Install_Apache_to_Host_Website_with_SSL_in AlmaLinux⠀⇛ AlmaLinux is tagged as a forever-free Linux Operating System Distribution because of the numerous benefits it has to offer to its user community. If you were too attached to CentOS before it got discontinued, think of AlmaLinux as its renamed and continued OS version. AlmaLinux is a free and open-source server-oriented Linux operating system distribution is a carbon copy of the discontinued CentOS. It offers the same user footprints with features like Errata and Secure Boot Support. Also, it is easy to migrate from CentOS to AlmaLinux. # ⚓ How_to_Create_HTTPS_Server_in_Node_Js_–_TREND_OCEANS⠀⇛ How do I create an HTTPS server for Node Js? This is the most frequent question asked by node js developers. For various security reasons, many popular modules ask to enable HTTPS protocol. What is HTTPS protocol? If you remove S from HTTPS, we get HTTP, which is a standard protocol for accessing web applications. It’s not secure; anyone can intercept your data packets connected to the same network. While HTTPS is a secure protocol for web applications, here, all the communication between your browser and server is encrypted and decrypted by only using a private key. This makes communication more secure and private. # ⚓ How_To_Launch_RHEL_8_From_Amazon_EC2_In_AWS_–_OSTechNix⠀⇛ In this article, we are going to learn the step-by- step process to create and launch RHEL 8 from Amazon EC2 in AWS Cloud and how to access the RHEL 8 instance using Putty application. Before we create the RHEL 8 instance on AWS EC2, let me give you a brief introduction to Amazon EC2. # ⚓ How_To_Install_SuiteCRM_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install SuiteCRM on Debian 11. For those of you who didn’t know, SuiteCRM is an open-source alternative to the popular customer relationship management (CRM) software, SugarCRM. It is a fully-featured and highly-extensible CRM application that runs on any operating system. It became popular when SugarCRM decided to stop the development of its community edition. It is used for creating business strategies, actions, and decisions. 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 SuiteCRM on a Debian 11 (Bullseye). # ⚓ How_to_Install_Tor_Browser_on_Linux⠀⇛ Privacy and anonymity are hard to come by on the internet. Luckily, there are a few steps you can take to safeguard your personal data from the prying eyes of data collection algorithms, marketers, and advertisers. This guide will show you how to install Tor Browser on Linux. Tor Browser is an open-source, cross- platform, and modern web browser with privacy at heart. The main purpose of the browser is to give you the basic right to privacy on the internet. # ⚓ How_to_Install_R_Programming_Language_on_Fedora_35_– LinuxCapable⠀⇛ R is an open-source programming language and free software environment for statistical computing and graphical representation created and supported by the R Core Team and the R Foundation. R’s popularity is widely used amongst statisticians and data miners for statistical and data analysis software developers. In the following tutorial, you will learn how to install R on Fedora 35. # ⚓ How_to_Install_OpenProject_on_Debian_11⠀⇛ R is an open-source programming language and free software environment for statistical computing and graphical representation created and supported by the R # ⚓ How_to_build_an_initramfs_using_Dracut_on_Linux⠀⇛ In a previous article we talked about listening and extracting the content of an initramfs image using standard, simple tools like gzip, dd and cpio or with dedicated scripts like lsinitramfs, lsinitrd and unmkinitramfs. In this tutorial we learn how to (re)build an initramfs on Linux using dracut. # ⚓ How_to_Setup_Samba_Server_in_RHEL,_Rocky_Linux_and AlmaLinux⠀⇛ 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. One of the widely used file- sharing software is Samba. Samba, a re-implementation of the popular SMB (server message block) protocol, is a stable and free application that allows sharing of files and print services across a network. The software is installed on a central Linux server from which shared files can be accessed from both Linux and Windows systems. In this guide, we will walk you through the installation of the Samba Server on RHEL-based distributions such as CentOS Stream, Rocky Linux, and AlmaLinux. # ⚓ How_to_Setup_Opencart_with_LAMP_(PHP,_Apache,_Mariadb)_on Debian_11⠀⇛ In this guide, we will explore setting up Opencart in a Debian 11 Server with Apache serving it and Mariadb10 acting as the database. Opencart describes itself in its website as “The best FREE and open-source eCommerce platform. Everything you need to create, scale and run your business”. It is an Open Source online store management system. It is PHP-based, using a MySQL database and HTML components. Its github page can be found here. Apache is a popular web web server software that is often used to serve php content. Mysql is also a popular relational management system used by popular websites. # ⚓ How_to_Install_Wireshark_Network_Packet_Analyzer_on_Ubuntu 20.04⠀⇛ Wireshark (formerly Ethereal) is an Open-Source software that is used for capturing and investigating network traffic. It is a very popular packet analyzer among network professionals, security analysts, and research scholars around the world. The good thing is that it is open source and freely available under the GNU General Public License version 2. It can examine data from various network interfaces like: Ethernet (IEEE 802.3 ), FDDI, Token ring, IEEE 802.11 wireless LAN etc. It is available for major OSes like Windows, macOS, Linux, and UNIX. Wireshark has many features like profound inspection of network traffic, real-time capture, offline analysis, R/W support for different capture file types etc. It also organizes SharkFest, an annual educational conference, around the world for imparting knowledge of their product. These conferences are focused on best practice of using Wireshark. # ⚓ How_to_install_Java_17_in_OpenSUSE_Leap_15.3⠀⇛ In this guide we are going to explore how to install Java Runtime Environment (JRE) and the Java Developer Kit (JDK) in OpenSUSE Leap 15.3 system. Java and the JVM (Java’s virtual machine) are required for many kinds of software, including Tomcat, Jetty, Glassfish, Cassandra and Jenkins. Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. Java was developed by Sun Microsystems (which is now the subsidiary of Oracle) in the year 1995. James Gosling is known as the father of Java. # ⚓ How_to_install_Java_17_in_FreeBSD_13_–_Citizix⠀⇛ In this guide we are going to explore how to install Java Runtime Environment (JRE) and the Java Developer Kit (JDK) in FreeBSD 13 system. Java and the JVM (Java’s virtual machine) are required for many kinds of software, including Tomcat, Jetty, Glassfish, Cassandra and Jenkins. Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. Java was developed by Sun Microsystems (which is now the subsidiary of Oracle) in the year 1995. James Gosling is known as the father of Java. # ⚓ How_to_install_Envoy_Proxy_server_on_Ubuntu_20.04_– NextGenTips⠀⇛ In this tutorial, I will show you how to install the Envoy proxy server on Ubuntu 20.04. Envoy is an L7 proxy and communication bus designed for large modern service-oriented architecture. The project was born out of the belief that the network should be transparent to applications. When network and applications problems occur, it should be easy to determine the source of the problem. Envoy is an open-source edge and service proxy, designed for cloud-native applications. # ⚓ How_to_install_and_set_up_PHP_and_Apache(LAMP_stack)_on Debian_11⠀⇛ In this guide we are going to Install and set up Apache virtual host to serve PHP content on a Debian 11 system. The Apache HTTP Server(Apache), is one of the most popular free and open-source cross-platform web server software, released under the terms of Apache License 2.0. Apache is popular as part of the LAMP setup, being the A in the Acronym. The apache server functionality can be extended with the many available modules. PHP is a general-purpose scripting language geared towards web development. It is one of the popular programming languages for the web. Popular tools such as WordPress are coded using php. Big companies like Facebook also uses php heavily. # ⚓ How_to_install_Nextcloud_Hub_II_with_Nextcloud_Office_– TechRepublic⠀⇛ Nextcloud 23 brings a major overhaul to the platform and introduces Nextcloud Office and plenty of other features and fixes to make it an outstanding choice for anyone looking to host a full-fledged cloud service in-house (in your data center, your cloud-hosted provider or even on a server in your home). # ⚓ How_to_install_Kali_Linux_2021.4_–_Invidious⠀⇛ In this video, I am going to show how to install Kali Linux 2021.4. # ⚓ How_to_uncompress_and_list_an_initramfs_content_on_Linux⠀⇛ Suppose we have our Linux system setup with an almost-full disk encryption, with only the /boot partition unencrypted. Assuming we achieved encryption by using a LUKS container, we need the appropriate software to unlock it at boot. This software, however, is part of the encrypted system. Since the Linux 2.6 series, the solution to this, and other similar problems, is called initramfs (Initial ramfs). In this article we see how an initramfs is composed and how to extract or list its content. # ⚓ How_to_upgrade_Linux_Kernel_on_Ubuntu_20.04_to_5.16_Release –_NextGenTips⠀⇛ In this tutorial, we are going to learn how to upgrade Linux Kernel to 5.16 on Ubuntu 20.04. Linux Kernel is a free and open-source, monolithic, modular, multitasking Unix-like operating system. It is the main component of a Linux operating system and is the core interface between the computer’s hardware and its processes. It makes communication possible between computer hardware and processes running on it and it manages resources effectively. Linux 5.15 mainline was released recently by Linux Torvalds with better new features to try out. The mainline tree is maintained by Linus Torvalds and It is where all new features are added and releases always come from. # ⚓ How_to_install_the_SuiteCRM_Customer_Resource_Manager_on Ubuntu_Server_–_TechRepublic⠀⇛ As your business grows, you’ll probably find yourself needing to manage customer relations. With such a platform available to your business, your staff can better manage their clients, customers, opportunities, leads and much more. [...] I’ll walk you through the process of installing the open-source SuiteCRM platform, one that focuses on sales, marketing and services administration. The only things you need to make this work are a running instance of Ubuntu Server and a user with sudo privileges. With those things at the ready, let’s get to work. # ⚓ How_to_test_if_your_Linux_server_is_vulnerable_to_Log4j_– TechRepublic⠀⇛ This vulnerability has the highest CVSS score of 10.0, so you need to pay attention. One of the big problems is knowing if you’re vulnerable. This is complicated by the many ways Log4j can be deployed. Are you using it as part of a Java project, is it rolled into a container, did you install it with your distribution package manager, and (if so) which log4j packages did you install? Or did you install it from source? Because of this, you might not even know if your server is vulnerable. Fortunately, for Linux servers, GitHub user, Rubo77 created a script that will check for for packages that include vulnerable Log4j instances. It’s in beta, and it’s not one 100%, but it’s a great place to start. Understand, this script doesn’t test for jar files that were packaged with applications, so do not consider it anything more than a launching point to start your forensics. I tested this script against a server that I knew had a vulnerable Log4j package installed, and it correctly tagged it. Here’s how you can run that same script on your Linux servers to find out if you might be vulnerable. # ⚓ Control_Keyboard_Backlight_Brightness_via_System_Menu Slider_Bar_in_Ubuntu_|_UbuntuHandbook⠀⇛ Has a backlit keyboard in your PC? This extension makes possible to control the backlight brightness by adding a slider bar into upper right corner system tray menu in GNOME desktop. Under system volume and screen brightness sliders, it adds a third slider bar allows to easily control the keyboard backlight. # ⚓ Creating_your_first_deployment_on_a_Kubernetes_Cluster⠀⇛ In this article, we will see how to create your first deployment on a Kubernetes Cluster. As an example, we will create a deployment for NginX. Once we have a running Kubernetes cluster, we can deploy our containerized applications on top of it. We can create a Kubernetes Deployment configuration to achieve this. A Deployment provides declarative updates for Pods and ReplicaSets. We describe a desired state in the Deployment and the Deployment Controller changes the actual state to the desired state at a controlled rate. # ⚓ Install_OpenShift’s_Web_Terminal_Operator_in_any_namespace |_Red_Hat_Developer⠀⇛ The Web Terminal Operator in Red Hat OpenShift provides a web terminal with common cluster tooling pre-installed. The operator gives you the power and flexibility to work with your product directly through the OpenShift web console, eliminating the need to have all your tooling installed locally. This article is an overview of the new features introduced in Web Terminal Operator 1.4. One of the most important improvements is that you can now install the Web Terminal Operator in any namespace. In addition, our tooling has been updated to be compatible with OpenShift 4.9. # ⚓ how_to_configure_centos_8_to_boot_with_old_kernel_version_– Unixcop_the_Unix_/_Linux_the_admins_deams⠀⇛ We will edit CentOS 8 the GRUB2 configuration parameter and change it using grubby to boot with old kernel or to change the default boot entry for kernel in the system. Grubby is a command line tool for updating and displaying information about the configuration files for various architecture specific bootloaders. It primarily designed to be_used from scripts which install new kernels and need to find information about the current boot environment. Grubby will use these default settings to search for an existing configuration. If no bootloader configuration file found, grubby will use the default value for that architecture. o § Wine or Emulation⠀➾ # ⚓ Use_Wine_for_gaming_on_Linux?_Try_out_Bottles_| GamingOnLinux⠀⇛ Bottles isn’t exactly a new Linux application but it’s one I had only heard about recently. It’s been advancing a lot in the last year and it’s really looking great. Unlike other manager applications including Lutris, GameHub and so on it has a singular purpose — Bottles is designed to give you the best possible experience when managing the Windows compatibility layer Wine. It includes a lot of options to allow you to easily tweak your installs with a few clicks of a button, which is exactly what I love about it. There’s a few “runners” included which are various versions of Wine like their own Vaniglia, that has a few wine-staging patches and a newer updated theme and Lutris’ Wine. # ⚓ Bottles_Wine_Prefix_Manager_Released_With_Stable_Versioning Feature,_New_Console_For_Flatpak_Users_And_A_Bottles_Runtime –_Linux_Uprising_Blog⠀⇛ Bottles is a graphical tool that makes it easy to run Windows software and games on Linux, via Wine. For handling Wine prefixes, the tool uses environments, which is a combination of ready-to- use settings, libraries and dependencies. Wine / Proton, DXVK and the required dependencies are downloaded using a built-in download manager. Bottles also features the ability to easily add environment variables, override DLLs, various gaming optimization options (esync, fsync, DXVK, cache, shader compiler, etc.), built-in task manager for Wine processes, import / export bottles, as well as an experimental installers database, among many other features. o § Games⠀➾ # ⚓ Retro_game_maker_GB_Studio_gets_a_big_upgrade_| GamingOnLinux⠀⇛ Want to make retro games? How about making games on Linux that can be played on a Game Boy or the upcoming Analogue Pocket? GB Studio is your new best friend and a huge new release is out. A free and open source app (MIT license) developed by Chris Maltby, it’s pretty fancy and incredibly easy to use too. # ⚓ Perhaps_now_I’ve_seen_it_all_–_have_a_dance_and_a_fight_in Sewer_Rave_|_GamingOnLinux⠀⇛ What do you get when you put together a sewer and a bunch of rats? Obviously a rave, plus a little fighting and lots of really weird stuff happening around you. Sewer Rave is out now. I feel like now, perhaps, I might just have “seen it all” when it comes to gaming. “SEWER RAVE is a surreal randomized exploration game where you crawl around a rat infested sewer during a giant rave. Search the labyrinthine sewers to discover games, secrets, and wisdoms meant only for rodents. Grab a cup of sludge and meet some rats!” # ⚓ Wrought_Flesh_is_a_delightfully_grotesque_new_FPS_out_now_| GamingOnLinux⠀⇛ Wrought Flesh is a game where you not only eat your enemies corpses to regain health, you also harvest their organs to place inside yourself to gain improved character stats. Totally grotesque and awesome. “Rip out enemies organs and equip them in your own body. Fight biopunk monsters and drugged-up space bandits. You are a Gajeshian Cultist: A near- mythological being built from the bodies of long- dead saints. You have arrived on the partially terraformed planet of Chrisembourgh on a temple- ordained mission to find and kill someone. Explore the planet and trace your victims steps to the end.” # ⚓ PlanetSide_2_is_now_available_on_Linux⠀⇛ PlanetSide 2 (PS2) is a free-to-play/pay-to- customize massively multiplayer online first-person shooter game. It was released for Windows in 2012 and three years later for PlayStation 4 in 2015. Now, nine years later, it’s debuting on Linux through the Proton Compatibility layer in Steam. In PS2, three factions fight for dominance over the four continents on the planet Auraxis. It has been my go-to game during the pandemic. The game has set and currently holds the world record for most simultaneous players participating in the same battle in an online game. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Kdenlive_21.12_introduces_artificial_intelligence_and multi-camera_support_–_itsfoss.net⠀⇛ KDE Gear 21.12 has recently appeared as the latest release of the suite of applications that follow the parent project’s schedule (others like Krita and the Calligra suite do not). As usual in an environment as lively as KDE, applications tend to receive major improvements and changes at each iteration, so we take the opportunity to dig deeper into Kdenlive, the non-linear video editor. Kdenlive is a well-known editor that little by little has made a place for itself in non- professional and even professional video editing that does not require the advanced possibilities offered by solutions such as DaVinci Resolve and Adobe Premiere. Within its segment, it is probably the most popular application among Linux users, although it also has a Windows user base. Its codebase is currently released under the GPLv3 license. Kdenlive 21.12 comes with important new features that will surely make the application take an important qualitative leap, since it has incorporated a tracking algorithm based on deep learning. In other words, it has included support based on artificial intelligence, thus, at least roughly, in the wake of OpenShot. # § GNOME Desktop/GTK⠀➾ # ⚓ New_GNOME_Text_Editor_–_Everything_You_Need_to_Know⠀⇛ We give you details about the new default text editor of GNOME – the Gnome Text Editor. o § Distributions⠀➾ # § Reviews⠀➾ # ⚓ Impressions_of_Linux_Mint_&_elementary_OS⠀⇛ In a recent post, I spoke about some things that Linux distros need to do better to accommodate end-users. I was reminded that there are some Linux distros which are, at least to some extent, following my recommended playbook, and have been re- evaluating two of them over the past couple of weeks: Linux Mint and elementary OS. I installed these on one of my laptops and used it as my daily driver for a day or two each. Both of these distributions are similar in a few ways. For one, both distros required zero printer configuration: it just worked. I was very impressed with this. Both distros are also based on Ubuntu, though with different levels of divergence from their base. Ubuntu is a reasonably good choice: it is very stable and mature, and commercially supported by Canonical. I started with elementary OS, which does exactly what I proposed in my earlier article: charge users for the OS.1 The last time I tried elementary, I was less than impressed, but they’ve been selling the OS for a while now so I hoped that with a consistent source of funding and a few years to improve they would have an opportunity to impress me. However, my overall impressions were mixed, and maybe even negative. The biggest, showstopping issue is a problem with their full disk encryption setup. I was thrilled to see first-class FDE support in the installer, but upon first boot, I was presented with a blank screen. It took me a while to figure out that a different TTY had cryptsetup running, waiting for me to enter the password. This is totally unacceptable, and no average user would have any clue what to do when presented with this. This should be a little GUI baked into the initramfs which prompts for your password on boot, and should be a regularly tested part of the installer before each elementary release ships. The elementary store was also disappointing, though I think there’s improvements on the horizon. The catalogue is very sparse, and would benefit a lot by sourcing packages from the underlying Ubuntu repositories as well. I think they’re planning on a first-class Flatpak integration in a future release, which should improve this situation. I also found the apps a bit too elementary, haha, in that they were lacking in a lot of important but infrequently used features. In general elementary is quite basic, though it is also very polished. Also, the default wallpaper depicts a big rock covered in bird shit, which I thought was kind of funny. There is a lot to like about elementary, though. The installer is really pleasant to use, and I really appreciated that it includes important accessibility features during the install process. The WiFi configuration is nice and easy, though it prompted me to set up online accounts before prompting me to set up WiFi. All of the apps are intuitive, consistently designed, and beautiful. I also noticed that long-running terminal processes I had in the background would pop-up a notification upon completion, which is a nice touch. Overall, it’s promising, but I had hoped for more. My suggestions to elementary are to consider that completeness is a kind of polish, to work on software distribution, and to offer first-class options for troubleshooting, documentation, and support within the OS. # § New Releases⠀➾ # ⚓ CasaOS:_Open-source_home_cloud_based_on_the_Docker ecosystem⠀⇛ For parents and families, the thought of someone gaining access to sensitive information can be nothing short of a nightmare. However, one group of developers are on a mission to empower families to take their privacy into their own hands. IceWhale Technology uveiled CasaOS, an open-source home cloud OS based on the Docker ecosystem. # ⚓ Kaisen_Linux_|_Kaisen_Linux_2.0⠀⇛ After 4 months of intensive work, here is the 2.0 version of Kaisen Linux, two years to the day after the release of the first alpha version! This new release is a major revision of the previous rolling versions! Detailled and significant changes: Numerous improvements and bug fixes make this the most stable release ever. That’s partly why it is called 2.0, the numerous refactorings justified the version number change. Kaisen is now based on Debian Bookworm (Debian 12), also justifying the version number change. Among the most important things done on this new release, a complete overhaul of the menu with new, nicer and more modern icons, simplification of the menu and removal of about 15 launchers among the basic commands (such as mount and umount for example), new implementation of BTRFS snapshot tools, new tools dedicated to Cloud engineers! # § Screenshots/Screencasts⠀➾ # ⚓ Linux_Mint_20.3_Beta_MATE_Run_Through_–_Invidious⠀⇛ In this video, we are looking at Linux Mint 20.3 Beta, MATE edition. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Installing_syslog-ng_on_CentOS_Stream_9⠀⇛ CentOS Stream 9 has been around for a while, but it was officially announced just a few days ago. I already tested some earlier snapshots and they had some rough edges. The current version installed without random crashes, has networking and runs smoothly. EPEL – the semi-official repository by Fedora maintainers – is already there, but practically empty, syslog-ng or it’s dependencies are not yet there. As someone asked about syslog-ng support, I had a first try at building it. I built syslog-ng for CentOS Stream 9 in the Copr build service. Many of the syslog-ng dependencies are not yet available, so I had to compile them myself. EPEL 9 is expected to have the latest Fedora versions, so I used those. I could not get MongoDB client libraries compiled, but the rest of the dependencies are there. # ⚓ Fedora_36_Planning_To_Use_plocate_As_New_“locate” Replacement_–_Phoronix⠀⇛ Fedora 36 is planning to use plocate as its new provider of the locate command for finding files on file-systems. Plocate should make for even faster locating of files on disk as well as doing so using less CPU cycles. Currently Fedora uses mlocate as its locate command while for the next Fedora Linux release they intend to move to Plocate as a compatible re-implementation. # ⚓ Gathering_security_data_for_container_images_using the_Pyxis_API⠀⇛ In the previous post, we covered how to use the Red Hat Security Data API to collect useful security information about CVEs and Red Hat products programmatically. In this post, we’ll look at how to collect security data for container images by using the Pyxis API. As before, we will be addressing real world use cases and concerns programmatically. Each of the examples used below can be easily modified to address your own needs. # ⚓ How_open_source_is_making_diabetes_more_manageable⠀⇛ For the average person, you go about your day without too much thought to what is happening within your body. For diabetics however, their entire day is built around monitoring the minute changes that could have serious health implications for them. In order to manage these changes, they need special tools that are designed to track as blood sugar levels rise and fall, produce insulin and time its delivery to maintain health. But what happens when the tools and systems don’t serve the people who need them? Premiering today, “Opening the Loop: Autonomy, Access, and Insulin”—the latest documentary in the Open Source Stories series from Red Hat—follows the growing DIY community of makers, patients and caregivers that are reshaping those systems to better match their needs. Their work happens in bedrooms, at kitchen tables, in conference rooms and at the lab bench. And it’s making life better for untold numbers of others. In the film we learn about the challenges type 1 diabetics and caregivers face as they identify the need for insulin, access and acquire it and actually inject it. These challenges stem from the use of closed-source solutions like off-the-shelf blood glucose monitors that only share data with certain devices, insulin pumps that communicate with some monitors, but not others, and issues with the insulin itself. # ⚓ Use_Ansible_to_test_containers_in_OpenShift_4_| Enable_Sysadmin⠀⇛ Are you developing or maintaining containers to run in OpenShift 4 environments? If so, you will want to test the container to be sure that it is working correctly. # ⚓ 4_new_IT_leadership_habits_for_the_new_year⠀⇛ The new year offers a natural time to set new goals and build strong leadership habits that can help you achieve everything on your priority list for the year ahead. It’s also a good time to take a hard look at practices that are no longer serving you. We asked CIOs who recently won the 2021 SoCal CIO of the Year ORBIE Awards what habits IT leaders should try to cultivate in the year ahead, and which they should leave behind. The awards were presented by the SoCal CIO Leadership Association, a professional community that annually recognizes CIOs for their excellence in technology leadership. # § Canonical/Ubuntu Family⠀➾ # ⚓ Linux_Mint_20.3_“Una”_Cinnamon_–_BETA_Release⠀⇛ This is the BETA release for Linux Mint 20.3 “Una” Cinnamon Edition. Linux Mint 20.3 is a long term support release which will be supported until 2025. It comes with updated software and brings refinements and many new features to make your desktop even more comfortable to use. # ⚓ Linux_Mint_20.3_“Una”_MATE_–_BETA_Release⠀⇛ # ⚓ Linux_Mint_20.3_“Una”_Xfce_–_BETA_Release⠀⇛ # ⚓ Linux_Mint_20.3_‘Una’_gets_a_Beta_release⠀⇛ The look and feel of Linux Mint has been tweaked with this release to have larger titlebar buttons, rounded corners and an overall “cleaner” theme with better dark mode support. Accent colouring to grab your attention in places was also adjusted, and removed from some places. There’s also the ability for some applications to have a dark theme while the desktop keeps its lighter theme. Only a few applications currently support this mixed theming. o § Devices/Embedded⠀➾ # ⚓ Module_and_dev_kit_run_Linux_on_i.MX8M_Plus⠀⇛ MYIR’s “MYC-JX8MPQ” module runs Linux on an i.MX8M Plus with 3GB LPDDR4 and 8GB eMMC. A “MYD-JX8MPQ” dev kit adds 2x GbE, 2x CAN, 2x USB 3.0, 2x Type-C, HDMI, 40-pin GPIO, MIPI-DSI/CSI, and 2x M.2. MYIR announced a SODIMM-style module and feature- rich development board that showcase NXP’s NPU- equipped i.MX8M Plus. The $115 to $129 MYC-JX8MPQ module and $335 to $349 MYD-JX8MPQ dev kit follow other i.MX8 family boards from MYIR, including the i.MX8M based MYC-JX8MX module and MYD-JX8MX carrier, the i.MX8M Mini powered MYC-C8MMX and MYD- C8MMX, and the Mini-driven MYS-8MMX SBC. # ⚓ 5G_IoT/AIoT_industrial_gateway_ships_with_Raspberry_Pi Compute_Module_4_–_CNX_Software⠀⇛ WPC-632-Pi CM4 is an industrial IoT gateway based on Raspberry Pi Compute Module 4 with optional 5G or 4G LTE cellular connectivity, that joins other Raspberry Pi CM4 industrial gateways such as CompuLab IOT-GATE-RPI4, CatsPi Industrial Lite, Modberry M500 CM4, among others. The Linux gateway features two Ethernet ports, RS232/RS485 and other I/Os via terminal blocks, mPCIe and M.2 sockets for expansion with 5G modem 4G LTE mode, AI accelerator, or an NVMe SSD, as well as support for 9V to 32V wide-range input power. # ⚓ Ubuntu_Blog:_Canonical_teams_with_Xilinx_to_accelerate_the development_of_adaptive_SoCs⠀⇛ Canonical and Xilinx Inc. announced today the publication of Ubuntu images optimised for Xilinx Zynq UltraScale+ evaluation boards and the production-ready Kria System-on-Modules (SOM). The companies are collaborating to bring enterprise- grade Linux to the world of adaptive SoCs to accelerate the development of new software-defined devices across all IoT verticals. The goal is to ensure a smooth experience from prototyping on evaluation and starter kits to production-grade SOMs, reducing development costs and time. The past decade saw huge growth in the demand for fully configurable adaptive computing devices, integrating the traditional hardware programmability and flexibility of an FPGA with the software programmability of embedded processors. Xilinx addresses this market need with the Zynq UltraScale+ MPSoC family of products widely adopted across various industry verticals, including the industrial, vision, and healthcare markets. Now, Xilinx and Canonical are working together to enable Ubuntu on select Xilinx Zynq UltraScale+ MPSoC- based platforms to bring the reliable and proven Ubuntu OS experience. # § Open Hardware/Modding⠀➾ # ⚓ Unsurv_offline_–_An_ESP32_GNSS_receiver_board_with NFC,_accelerometer_(Crowdfunding)⠀⇛ # ⚓ DIY_4G_Air_Quality_and_Environment_Monitor_–_Record Data_Anywhere_–_The_DIY_Life⠀⇛ In this project, we’re going to use the Maduino Zero 4G by Makerfabs to make an air quality and environment monitor that transmits the recorded data wirelessly over a 4G mobile network to a Thingspeak dashboard. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Android_13_may_add_a_toggle_to_disable_Android’s_new background_app_limitations⠀⇛ # ⚓ Nokia_X20_Android_12_update_rolling_out_today_| Trusted_Reviews⠀⇛ # ⚓ What_Is_Macro_Mode_on_an_iPhone_or_Android_Phone?⠀⇛ # ⚓ Top_10_Best_Apps_for_Senior_Citizens_To_Make_Life Easier⠀⇛ # ⚓ 10_of_the_Best_Android_Apps_of_2021,_According_to Google⠀⇛ # ⚓ Kodak_7XPRO_Android_4K_Smart_TV_Series_With_HDR10 Support,_40W_Audio_Output_Launched_in_India_| Technology_News⠀⇛ # ⚓ Freebox_Remote_is_an_unofficial_remote_control_app for_your_Android_TV⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ SeaMonkey_2.53.10.1_looking_good⠀⇛ I have compiled SeaMonkey 2.53.10.1 in EasyOS. Went to some sites and it looked good, unfortunately youtube.com did not look good… # ⚓ Final_fixes_before_releasing_3.1.15⠀⇛ The post commented that Chromium startup time is 20 seconds and Firefox 24 seconds on my Compaq Presario. Well, I am happy to report 8 seconds for SeaMonkey. Which is blink-of-an-eye startup on a modern computer. EasyOS 3.1.15 will have SeaMonkey. No Chromium, Firefox, Balsa or Claws, or BlueGriffon, just SeaMonkey. I must comment on SM Mail module, it is good. I have played a little bit with Balsa, Claws Mail and SM News module — and my preliminary “goodness rating” is in that order, going up. The SM News module is pretty much the same as Thunderbird. # ⚓ Firefox_Add-on_Reviews:_Firefox’s_most_popular and_innovative_browser_extensions_of_2021⠀⇛ About one-third of Firefox users have installed an add-on—be it an extension to equip Firefox with a custom feature or a visual theme to personalize their browsing experience. What kind of extensions did we use most in 2021? And what are some of the new, innovative extensions to emerge this year? Let’s find out! # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ Record_number_of_LibreOffice_downloads⠀⇛ The chart says it all! Last week, we had a record number of downloads for LibreOffice in a single week. More and more people are discovering the free and open source office suite, the successor to OpenOffice, that respects users’ privacy and freedom. Downloads have been growing steadily over time, and one week ago we released an important security update, so we recommend downloading it, if you’re using an older version. # § FSF⠀➾ # ⚓ Be_part_of_LibrePlanet_2022:_submit_today!⠀⇛ The call for LibrePlanet sessions and Awards nominations will close this Wednesday. With holiday preparations taking up its share of energy, we thought a last reminder just might be the last push you needed to bring pen to paper (or finger to keyboard!) and submit your ideas for a presentation, workshop, panel, or instructional video at LibrePlanet 2022: Living Liberation. The event will be held on March 19 and 20, 2022. Registration for the conference will open in a few weeks. Keep an eye on our communications as well, because we’ll be announcing our first keynote soon! # § Public Services/Government⠀➾ # ⚓ European_Commission_to_Open_Source_its_Software Solutions⠀⇛ The European Commission has announced plans to make its software solutions open source. On the heels of a recent report detailing the impact of open source, the Commission has adopted new rules that will “enable its software solutions to be publicly accessible whenever there are potential benefits for citizens, companies or other public services.” “The new rules will increase transparency and help the Commission, as well as citizens, companies and public services across Europe, benefit from open source software development. Pooling of efforts to improve the software and the co-creation of new features lowers costs for the society, as we also benefit from the improvements made by other developers. This can also enhance security as external and independent specialists check software for bugs and security flaws, said Johannes Hahn, Commissioner for Budget and Administration, in the announcement. # § Programming/Development⠀➾ # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ How_to_disable_internal_keyboard/touchpad_when a_cat_arrives⠀⇛ I’m using an external keyboard (1) and mouse (2), but the laptop lid is usually still open for better cooling. That means the internal keyboard (3) and touchpad (4) – made of comfortable materials – are open to be used by a cat searching for warmth (7), in the obvious “every time” case that a normal non-heated nest (6) is not enough. The problem is, everything goes chaotic at that point in the default configuration. The solution is to have quick shortcuts in my Dash to Dock (8) to both disable (10) and enable (9) keyboard and touchpad at a very rapid pace. It is to be noted that I’m not disabling the touch screen (5) by default, because most of the time the cat is not leaning on it – there is also the added benefit that if one forgets about the internal keyboard and touchpad disabling and detaches the laptop from the USB-C monitor (11), there’s the possibility of using the touch screen and on-screen keyboard to type in the password and tap on the keyboard/touchpad enabling shortcut button again. If also touch screen was disabled, the only way would be to go back to an external keyboard or reboot. # § Java⠀➾ # ⚓ Explore_Java_17_language_features_with Quarkus⠀⇛ Quarkus is a Kubernetes-native Java framework made for Java virtual machines (JVMs) and native compilation, optimizing Java for containers. Java 17, the latest long-term support release of standard Java, became generally available on September 14, 2021. If you’d like to experiment to see how Quarkus works with the new language features that have rolled out since Java 11, this article offers a technical preview to help you get started. * § Leftovers⠀➾ o § Hardware⠀➾ # ⚓ Fixing_a_Tiny_Corner_of_the_Supply_Chain_«_bunnie’s_blog⠀⇛ No product gets built without at least one good supply chain war story – especially true in these strange times. Before we get into the details of the story, I feel it’s worth understanding a bit more about the part that caused me so much trouble: what it does, and why it’s so special. [...] It’s clearly a great part for a low-power mobile device like Precursor, which is why I designed it into the device. Unfortunately, there’s also no real substitute for it. Nobody else makes a MEMS oscillator of comparable quality, and as outlined above, this device is smaller and orders of magnitude lower power than an equivalent quartz crystal. It’s so power-efficient that in many chips it is less power to use this off-chip oscillator, than to use the built-in crystal oscillator to drive a passive crystal. For example, the STM32H7 HSE burns 450uA, whereas the SiT8021 runs at 160uA. To be fair, one also has to drive the pad input capacitance of the STM32, but even with that considered you’re probably around 250uA. To put it in customer-facing terms, if I were forced to substitute commonly available quartz oscillators for this part, the instant-on standby time of a Precursor device would be cut from a bit over 50 hours down to about 40 hours (standby current would go from 11mA up to 13mA). If this doesn’t make the part special enough, the fact that it’s an oscillator puts it in a special class with respect to electromagnetic compliance (EMC) regulations. These are the regulations that make sure that radios don’t interfere with each other, and like them or not, countries take them very seriously as trade barriers – by requiring expensive certifications, you’re able to eliminate the competition of small upstarts and cheap import equipment on “radio safety” grounds. Because the quality of radio signals depend directly upon the quality of the oscillator used to derive them, the regulations (quite reasonably) disallow substitutions of oscillators without re- certification. Thus, even if I wanted to take the hit on standby time and substitute the part, I’d have to go through the entire certification process again, at a cost of several thousand dollars and some weeks of additional delay. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Landmark_COVID-19_vaccine_trial_in_sub-Sahara_| EurekAlert!⠀⇛ A highly anticipated clinical trial in eight sub- Saharan countries is the first to specifically evaluate the efficacy of a COVID-19 vaccine in people living with HIV, including those with poorly controlled infections. It also is the first study to evaluate the efficacy of vaccines – in this case, Moderna mRNA-1273 – against the omicron variant of SARS-CoV-2, the virus that causes COVID- 19. In addition to examining the efficacy of COVID-19 mRNA vaccines in people living with HIV, the study investigators seek to identify the optimal regimen for this population and how it might vary based on whether an individual has previously had COVID-19 or not. The trial will be conducted in East and Southern Africa – regions of the world that have been highly impacted by HIV. It is expected to enroll about 14,000 volunteers at 54 clinical research sites in South Africa, Botswana, Zimbabwe, Eswatini, Malawi, Zambia, Uganda and Kenya, where adult HIV prevalence ranges from 4.5% to 27%. [...] The trial is sponsored by the SAMRC and funded by the U.S. government and supported by the National Institute of Allergy and Infectious Diseases (NIAID) within the National Institutes of Health. Funding originates from the Department of Health and Human Services (HHS) through the Countermeasures Acceleration Group (CAG). o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Vivaldi_CEO_criticizes_Microsoft_Edge_for_anti- competitive_practices⠀⇛ In 2013, the European Union slapped a massive $731 Million fine on Microsoft for failing to offer users a choice to set a default browser. 8 years have passed since then, has the Redmond company learned its lesson? Vivaldi’s CEO/Co-founder Jón von Tetzchner, says no. Tetzchner founded Opera browser along with Geir Ivarsøy in the mid-90s, before leaving the company in 2011. He founded Vivaldi Technologies in 2013, though the browser they created was released a couple of years later. # § Pseudo-Open Source⠀➾ # § Privatisation/Privateering⠀➾ # § Linux Foundation⠀➾ # ⚓ Linux_Foundation_Research_Reveals New_Open_Source_Diversity,_Equity_and Inclusion_Trends [Ed: LF is already buying press releases (e.g. in KPVI News 6) to distract from its abuses. IMHO, it’s trying to distract from a bunch_of_new_things.]⠀⇛ # ⚓ Addressing_Diversity,_Equity,_and Inclusion_in_2021_and_Beyond [Ed: LF talks about “inclusive language” while elevating_to_the_top_of_its Board_someone_who_protects_a_man_who physically_assaults_and_nearly_kills women; Also, the LF participates_in racism while the LF, by its own standards, is_practically_racist.]⠀⇛ Communities that adopt inclusive language and actions will be able to attract and retain individuals from diverse backgrounds. The Linux kernel community adopted inclusive language in the Linux 5.8 release, showing its commitment to Diversity and Inclusion. For other projects, the Inclusive Naming Initiative launched at KubeCon North America to standardize inclusive language across the industry. It released a training course, LFC103: Inclusive Strategies for Open Source Communities, to support this. # ⚓ Linux_Foundation_Research_Reveals New_Open_Source_Diversity,_Equity, and_Inclusion_Trends [Ed: Leveraging identity politics today]⠀⇛ The Linux Foundation, the nonprofit organization enabling mass innovation through open source, today announced the release of its latest LF Research study, “Diversity, Equity, and Inclusion in Open Source.” # ⚓ Thanking_our_Communities_and Members,_and_Building_Positive Momentum_in_2022_–_Linux_Foundation⠀⇛ We could not imagine what was on the horizon ahead of us as we saw COVID peek its head in late 2019. Locally and globally, we’ve weathered many challenges, adjusted our sails, and applied new tools and approaches to continue our momentum. As we now approach 2022, our hopes aim even higher as we pursue new horizons and strengthen our established communities. We’re emerging stronger and better equipped to tackle these great challenges and your help has made it all possible. # ⚓ Increasing_Open_Source_Diversity Reflects_Growing_Global_Adoption, Still_Much_Room_To_Improve:_Study⠀⇛ According to the Linux Foundation‘s latest LF Research study, Diversity, Equity, and Inclusion in Open Source, the global adoption of open source technologies grows rapidly, so, too, is diversity within open source communities. But there remains a lot of room for growth. # § Security⠀➾ # ⚓ Security_updates_for_Tuesday_[LWN.net]⠀⇛ Security updates have been issued by Debian (libsamplerate and raptor2), Fedora (pam-u2f and python-markdown2), openSUSE (chromium, fetchmail, ImageMagick, and postgresql10), Oracle (samba), SUSE (fetchmail, postgresql10, python-pip, python3, and sles12sp2- docker-image), and Ubuntu (apache- log4j2, flatpak, glib, and samba). # ⚓ Apple_Releases_Security_Updates_for_Multiple Products_|_CISA⠀⇛ Apple has released security updates to address vulnerabilities in multiple products. An attacker could exploit some of these vulnerabilities to take control of an affected system. # ⚓ Google_Releases_Security_Updates_for_Chrome_| CISA⠀⇛ Google has released Chrome version 96.0.4664.110 for Windows, Mac, and Linux. This version addresses vulnerabilities that an attacker could exploit to take control of an affected system. # ⚓ More_new_malicious_files_discovered_in_2021 than_ever_before [Ed: ITProPortal running de facto ads for a Russian malware company (proprietary) and then says "ITProPortal is supported by its audience"]⠀⇛ A larger number of new malicious files were discovered in 2021 than ever before, researchers at security firm Kaspersky researchers have suggested. According a new report, 5.7 percent more malicious files have been detected this year, compared to 2020. Kaspersky says its systems have detected 380,000 new malicious files every day on average. # § Log4j⠀➾ # ⚓ Log4Shell_vulnerability:_What_we_know_so far_|_WeLiveSecurity [Ed: Insecurity profiteers comment on it]⠀⇛ The zero-day flaw in the ubiquitous Log4j utility has sent shockwaves far beyond the security industry – here’s what you should know. # ⚓ Log4j_hole_revives_chatter_on_Big_Biz funding_open_source_•_The_Register⠀⇛ The disclosure of a critical security hole in Log4j last week has renewed calls to rethink how open-source software gets developed, paid for, and maintained, not that the long- simmering issue ever really went away. The Log4j bug, an unauthenticated remote code execution flaw (CVE- 2021-44228) in Apache’s open- source Log4j Java-based logging library, is particularly serious and far-reaching because exploitation is not difficult and the software is widely used and buried deep within many programs. Annoyance with the handful of project maintainers for failing to catch the bug prompted one, developer Volkan Yazici, to voice indignation about all the people bashing the maintainers for their unpaid, volunteer labor without offering any financial support or contributed code fixes. # ⚓ On_the_Log4j_Vulnerability_–_Schneier_on Security⠀⇛ Threat advisory from Cisco. Cloudflare found it in the wild before it was disclosed. CISA is very concerned, saying that hundreds of millions of devices are likely affected. # ⚓ Log4j_Vulnerability_Puts_the_Entire Internet_at_Risk:_What_You_Need_to_Know_– It’s_FOSS_News⠀⇛ Log4Shell is a Remote Code Execution Class vulnerability denoted as CVE-2021-44228 disclosed as an exploit that affects millions of servers that run Java applications, or particularly the open-source Apache Log4j library. If you are curious, a wide range of applications/servers and digital systems across the internet use Log4j for logging purposes. Even the back-end systems used by Steam, Minecraft, Cloudflare, and iCloud were found vulnerable. Why is it one of the most significant vulnerabilities in recent times? Let me tell you more about it. # ⚓ The_Log4j_bug_exposes_a_bigger_issue: Open-source_funding_(Updated)⠀⇛ While you were watching the F1 title decider between Max Verstappen and Lewis Hamilton or excited for the Succession finale, companies running the internet were scared shitless. You might not have noticed it because services like Twitter, Facebook, Gmail, and smaller ones all stayed up. But a bug in an open-source tech called Log4j was (and still is) causing panic amongst the infosec community across the world. While the bug has affected billions of devices, and companies are scrambling to apply fixes, the open-source community has a raging debate going on about funding volunteers that maintain projects like Log4j. # ⚓ Log4j_Bug_Highlights_Open_Source_Funding Issues⠀⇛ A critical bug in a bit of open source tech called Log4j has been causing panic in the infosec community, reports Ivan Mehta. And, while major companies are scrambling to apply fixes, “the open source community has a raging debate going on about funding volunteers that maintain projects like Log4j.” Many large corporations depend heavily on free and open source software projects such as Log4j, Mehta notes; however, project contributors and maintainers often receive only a small amount of financial support through GitHub or Patreon. o § Environment⠀➾ # ⚓ Measuring_Air_Quality_Using_Mobile_Sensors_For_The_Masses_| Hackaday⠀⇛ Poor air quality is a major problem for city dwellers the world over. Dust, smoke, particles and noxious gases from vehicles, industry and agriculture makes many megacities downright hazardous to live in. Pinpointing the source of pollution and developing strategies for mitigation requires accurate data on pollutant levels, but obtaining these numbers is not always easy. Enter CanAirIO, a citizen science project that aims to gather air quality data from around the world by putting sensors into the hands of as many people as possible. Its team has developed two different sensor nodes for this purpose: an indoor one that can measure CO2, and a mobile one that can measure particulate matter (PM) levels. Both versions are powered by an ESP32 microcontroller that reads out the air quality sensors and connects to the Internet using WiFi or BlueTooth. The data can then be shared online to create detailed maps showing local variations in air quality. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ Victories_in_the_DSA_vote:_IMCO_Committee_puts_people’s rights_before_corporate_interest_–_Access_Now⠀⇛ Access Now welcomes important victories green- lighted by the Committee for Internal Market and Consumer Protection (IMCO) in yesterday’s Digital Services Act (DSA) vote, indicating concrete steps towards the further protection of freedom of expression and opinion online across the European Union. Since the beginning of negotiations, Access Now has fought side-by-side with partner organisations to protect freedom of expression and opinion online, while countering short-sighted proposals that would only bolster the undesirable status quo in the content governance in defiance of fundamental rights standards. “We see victories in yesterday’s DSA vote. The fact that the IMCO Committee did not cave in to corporate interest, and centred people’s empowerment and their fundamental rights in the negotiations is an encouraging sign for the next stages,” said Eliska Pirkova, Europe Policy Analyst and the Global Freedom of Expression Lead at Access Now. “But there is still room for improvement, and the fight for a truly human rights centric model of platform governance will continue throughout the trilogue negotiations, where we must fix prevailing issues in the text. Yesterday’s vote is a reason to celebrate, but there is more hard work to ensure the protection of free expression and opinion online on the horizon.” ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 8560 ➮ Generation completed at 02:42, i.e. 150 seconds to (re)generate ⟲