𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, April 11, 2024 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Fri 12 Apr 02:49:20 BST 2024 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/2024/04/11/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmbHjgPAAcGNUG9Sej4vSKhK8DfUYokfFkXLdKwr1JtGJG QmdLsuRLzrwb58dZaSmJah6oCmNNZ6cW4ick4chqJmHjmY QmTNR3uqcbMYjPAbbHjBqyNJb3ib8kytQvdFnATzkBFVvo QmfCHrqMLfMsHXYnQeAvVuNYt91Zw2AmMJ5mx4RqsrWy3b QmR2rr1yXDANjQBEz2oGtd2UMgy9U37FHdjpUhPfAk7h5z QmWE6ucdKk9Q1pi6ce3ko9xPWd9Y4BjpLij3W7tJ5TMjG3 QmaoEDiALTYYZdaq3SQ86aQpMwUji1nqCeLbXAoszFRYvJ QmSTkZUY74BcgbgqS6JKwwNbVnbzY5uqwpgWtYonGJua8s QmXZcp3rXLYa24pYd7jUu6sPDrhziRCNCok875WLJTLysP QmUE7nd24kx2soZFbSYKDsb1ik1wpirFTRTBhDTj6w9sjh QmdKeWBhfnjgQLYU48wto7DdStpXsB5mE1yEEnWcxQ53vu QmfSnnTnjcAe3YvtRsVgAwUJfpcEk1dM5J5yjJLyv7MxqM QmQ16CkpxBbMzPZ6wZcuKBUcxH1RZ8uAEhcvdBsPRpVZe9 QmT3gTQRv33wEDtJveL8DiqiacGeRaxEbRFDUyVSJEAvDL QmTs9qcwghZPs5oBh9qzsu8a11T4s6xHrJjVNyk5miFy3X Qmdqd6mb8mj27qVvQZRR7sjshrXYYirWm9vRttLkNB5rW6 QmSjY85vxbu9nNFHUMmuK7CxRame2VYuhb523CJaK5zRkj QmZwah9nZHVvSzbJWEAMxumYDpanFPqTahnqoNP83tuZbx QmQWSrGfeYwgf6HE9N3742DJrJwq8uNSCUAz469CnuUFGe QmcgTTyseF5zFd4MLquM4PtJZzkFcBEqaUbqDe4eaUx6Na QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ Techrights - Aggressive Efforts (and Threats) for Those Who Speak About What Happened in the Balkans ⦿ Techrights - Anzacathon: a hackathon for Anzac day at home ⦿ Techrights - DebConf22 Kosovo segregation of women exposed ⦿ Techrights - First They Came for Iranian Developers... ⦿ Techrights - How Kosovo won DebConf21 ⦿ Techrights - IRC Proceedings: Wednesday, April 10, 2024 ⦿ Techrights - Over at Tux Machines... ⦿ Techrights - [Video] A Debian Project Leader Needs to Also be a Technical Project Leader ⦿ Techrights - [Video] How the Media Blamed SSH and Linux (for Nearly a Whole Fortnight!) Instead of Microsoft's GitHub and Systemd ⦿ Techrights - [Video] Trainline Finally Issues a Refund, But It Took 9 Days and Showed How 'Modern' Systems Fail Travelers ䷼ Bulletin articles (as HTML) to comment on (requires login): https://news.techrights.org/n/2024/04/11/Aggressive_Efforts_and_Threats_for_Those_Who_Speak_About_What_H.shtml https://news.techrights.org/n/2024/04/11/Anzacathon_a_hackathon_for_Anzac_day_at_home.shtml https://news.techrights.org/n/2024/04/11/DebConf22_Kosovo_segregation_of_women_exposed.shtml https://news.techrights.org/n/2024/04/11/First_They_Came_for_Iranian_Developers.shtml https://news.techrights.org/n/2024/04/11/How_Kosovo_won_DebConf21.shtml https://news.techrights.org/n/2024/04/11/IRC_Proceedings_Wednesday_April_10_2024.shtml https://news.techrights.org/n/2024/04/11/Over_at_Tux_Machines.shtml https://news.techrights.org/n/2024/04/11/Video_A_Debian_Project_Leader_Needs_to_Also_be_a_Technical_Proj.shtml https://news.techrights.org/n/2024/04/11/Video_How_the_Media_Blamed_SSH_and_Linux_for_Nearly_a_Whole_For.shtml https://news.techrights.org/n/2024/04/11/Video_Trainline_Finally_Issues_a_Refund_But_It_Took_9_Days_and_.shtml ䷞ Followed by Daily Links (assorted news picks curated and categorised): https://news.techrights.org/n/2024/04/11/Gemini_Links_11_04_2024_Activity_and_Motivation_in_Geminispace_.shtml https://news.techrights.org/n/2024/04/11/Links_11_04_2024_Web_Diversity_and_More_Crackdowns_in_Russia.shtml ䷩ 𝚕𝚒𝚗𝚎 75 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/04/11/Aggressive_Efforts_and_Threats_for_Those_Who_Speak_About_What_H.shtml Gemini version at gemini://gemini.techrights.org/n/2024/04/11/Aggressive_Efforts_and_Threats_for_Those_Who_Speak_About_What_H.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Aggressive Efforts (and Threats) for Those Who Speak About What Happened in the Balkans⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024, updated Apr 11, 2024 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Easter background decorative with balkan anemone wallpaper⦈ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Toastmasters_Prishtina⦈_ THE video_on_the_left-hand_side covers "Toastmasters_Prishtina" and shows Daniel Pocock speaking about the event to TV in Kosovo. In case of censorship we've made a local copy with audio and everything (skip_the_first_minute_or_so for_English). Censorship around Free software events in that region is a good reason to copy/ reproduce Pocock's articles about Kosovo [1, 2]. Tonight we'll republish "DebConf22 Kosovo segregation of women exposed" because it seems to have struck a nerve and it ruined the event (people did not want to go). The organisers sent_me_threats_2_years_ago and another person has just sent me an E-mail with a threatening language. We may reproduce this for the public to judge later. Acting in this way in an effort to censor people typically results in a second scandal on top of the original scandal and may also fall under the umbrella of "Streisand Effect". █ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢈⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠈⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠿⢿⠿⠟⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠉⠉⠉⠉⠛⠻⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣤⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣀⣻⣿⣿⣿⣷⡄⣀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠂⠀⢀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⣿⣿⣿⠃⠀⠀⣴⣶⣶⣤⣄ ⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠾⠋⠀⣤⠀⢹⣿⣿⣿⣿⣿⡿⣫⣵⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠗⠀⣠⣾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⣿⣿⠟⠁⢀⢀⠀⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⡟⠀⢸⣿⣿⣿⣿⣿⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠟⠀⠀⠀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣥⣴⣶⣯⠗⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠙⠻⠿⣿⣿⣀⡀⠀⠀⠀⠀⣼⣷⠀⠘⠿⢿⣿⣿⣿⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣥⣤⡀⠈⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠹⠿⠻⢿⣷⡆⠀⢰⣿⣧⣴⣦⠀⠀⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣤⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠿⣿⣛⠦⠽⠭⠟⠃⠛⠛⠁⠀⠰⠾⠿⠿⢿⣿⣿⣿⠏⠀⣿⣿⣿⣿ ⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⡀⠈⠙⠀⢰⣿⣿⣿⣿ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠁⠀⣠⣾⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣶⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠇⠀⠀⠀⠉⠉⠉⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⣿⡿⠿⠟⢋⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣙⣻⣿⣿⣿⣿⣄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣤⣾⣀⣠⣀⣀⣉⣥⣤⣾⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢳⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣬⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⠟⠉⠀⠀⢿⠷⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠟⠁⠀⠀⠐⠛⠛⠿⠿⠶⠶⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠈⠛⠟⠃⠘⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⣨⣏⠀⠀⠀⠈⠉⠙⠛⠛⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠟⠛⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⣀⣀⣠⣤⣤⣼⣿⣿⣷⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 169 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/04/11/Anzacathon_a_hackathon_for_Anzac_day_at_home.shtml Gemini version at gemini://gemini.techrights.org/n/2024/04/11/Anzacathon_a_hackathon_for_Anzac_day_at_home.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Anzacathon: a hackathon for Anzac day at home⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024 [Article 3 years old] Reprinted with permission from Daniel_Pocock. With Coronavirus cancelling_many_of_the_major_events_for_Anzac_Day_this_year and the RSL asking people to go_online, I found myself in a position to help, having just organized an online event for groups in Kosovo on Remembrance Day. The Anzacathon was born. § How did we get here?⠀➾ Students from Kosovo first approached me in Kotor, Montenegro, at the Digital- Born_Media_Carnival. They asked if I could support their Hackathon_for_Girls_in Prizren a few weeks later. Twenty-five young women participated. I helped the organizers, Albiona and Qendresa Hoti, to devise tasks for them, including some scraping and data pipelines: 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Dhurata Kamberi⦈ In 2018, three of these students were selected for Google Summer of Code. I went to visit them for a few days at the beginning of the program, we had a daily scrum meeting in a coffee shop which is, coincidentally, located beside the British memorial in Prishtina. Being based in Europe, around Anzac_Day each year I typically look for any events or Anzac sites nearby. Many Australians descend on Gallipoli and the Australian_National_Memorial_in_France, the latter being very accessible for ex-pats in the UK. Last year I had asked myself: are there any sites where there is only one Australian casualty, where nobody has visited them for Anzac day? Searching the alpine region around me on the Commonwealth_War_Graves Commission, I was curious to find a number of local sites. The lone Australian war grave did exist, in fact, he died alongside the_most_senior_RAF_officer killed_in_the_war and I decided to go there later in the year, when the snow had gone. In the Jura, I found another site where a RAAF crew died on_a_top- secret_mission_to_the_French_resistance. A local photographer had published_a gallery_of_photos: the French had just replaced the crash monument ahead of the 75th anniversary of the crash. At SFK_in_2019 (this year's event postponed/cancelled due to Coronavirus), I met Douglas Arellanes from the Mural_project. Arellanes gave a very thorough workshop about the Mural_software and the concepts of digital storytelling in general. It occurred to me that this would be a great tool to document the stories of these Australians. In November, I was encouraged to make another visit to Kosovo for a number of activities, including the latest Prishtina_Toastmasters_meeting. As the meeting was on 11 November, Remembrance_Day and as some of the students had attended Arellanes's workshop on Mural, I suggested we could bring these themes together for another hackathon. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Remembrance Day Hackathon, Prishtina, Kosovo⦈ We could see various synergies between the legacy of the Commonwealth countries and the needs of the Kosovan participants. As Kosovo has only recently had a war, it would be useful for them to see how Commonwealth countries have continued to commemorate war casualties over many generations. This could provide insights for Kosovans as they record and preserve their own history and experiences. Furthermore, as Albanian Kosovans have very distinctive names, it would be a very easy data matching activity to try and identify all the people with Albanian names who had served in the armed forces of any Commonwealth country, including the UK and Australia. The Prizren hackathon had been entirely for programmers. For the Remembrance Day hackathon, we decided to include research activities for people who don't do programming as well as some data science activities. As I had recently looked at some of the data sources for my own research, it provided a solid base for me to prepare some coding tasks. Once again, scraping was one of the major themes and that is how we have so many_data_sets_for_the_Anzacathon. The winners of the Remembrance Day hackathon, Leotrime_Maxharraj and Xhejdi Coku, had created another Mural site for John_Goddard,_VK6JG,_who_perished_in Operation_Thesis,_Crete. The honour roll of the Wireless_Institute_of_Australia was one of the lists we used as a basis for the research. Please remember to stay home and join the Anzacathon for Anzac day this year. █ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⢒⣂⣡⣤⣴⣶⣶⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⢂⣈⣡⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠐⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠐⢂⣈⣩⣬⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠸⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠀⢐⣂⣈⣯⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀ ⠤⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠳⠾⠾⠷⢶⣶⣦⣴⣴⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣠⡄⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⡿⠿⠿⠿⠛⠛⠛⠛⢛⣛⣛⣉⣉⡉⠉⠠⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠇⠸⠘⠛⠉⠉⠉⠉⠉⠉⠩⢭⠭⠭⠭⠭⠭⠭⠍⠉⠉⠁⠀⠀⢐⠒⠒⠒⠒⠒⠒⠀⠀⠀⠉⠋⠉⠉⠉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⢀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠿⢷⡦⠽⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⢸⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠘⢛⠃⢡⠖⠀⠀⠀⠀⠀⠀⠁⠀⢀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠈⢉⠀⠀⢨⠀⠠⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⢠⢀⣶⡷⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢸⠿⠟⠛⠿⠿⠛⠫⠽⢛⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠈⠉⠅⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢸⡀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⣰⣤⣀⠘⠃⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠺⠀⠀⠀⠀⠀⠀⠦⣯⣫⣿⠢⢀⣤⣤⣤⡄⠀⠀⡀⠀⠀⠀⠀⠒⣶⡀⠀⠀⠀⠀⠀⢈⠁⠀⠾⠄⠀⡄⠀⠀⠀⢀⡁⠀⢸⣿⢿⡿⡖⠘⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠄⣸⡆⠀⠀⠀⠘⣶⠀⢉⠉⣙⠕⢸⡿⠿⢿⡁⠂⣤⡇⠀⠐⠀⣀⣀⡨⠁⠀⠀⢠⣿⣷⡎⠀⠀⠀⠀⡀⠃⠀⠀⡀⣼⣮⣿⣞⠀⠀⠀⠀⠀⠋⢡⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⡀ ⠀⢀⣤⣼⣿⣿⠟⠀⢀⡄⠀⠀⠀⢠⡹⡇⠀⠀⠀⠹⠿⣇⠀⢁⠀⠀⠈⠉⠽⠞⠀⠈⠉⠁⢀⡟⣛⣟⣉⠀⠀⠀⠀⠈⢿⠏⡀⢀⣀⣀⡀⣽⣄⠠⣈⣛⣛⣛⣋⣉⠂⠀⠀⠀⠀⠀⠐⠏⢠⣆⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⠿⣿⡟⠀⢐⣾⣷⣾⣿⣿⣿⣹⣆⡀⠀⠀⠀⠀⡘⠆⠀⠀⠀⢄⡠⠄⠀⠀⠀⠀⠀⠀⠁⣿⡏⠉⡇⠀⠀⠀⠀⠈⣆⠁⠆⢞⢿⢻⣿⢿⣧⠀⠀⠀⠀⠈⠀⣉⠀⠀⠀⠀⠀⠀⣀⡟⠙⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠺⠿⢿⣿⡟⣿⣿⠟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠄⠀⠀⣿⠃⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠁⠈⠻⣧⠀⢤⣠⣀⣾⣿⣷⠇⠀⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠓⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣴⠿⣿⣿⣿⣿⣿⢿⣾⣇⠀⠸⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣭⣀⣸⣿⣿⣿⣗⢕⡯⡏⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⢸⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⢀⣀⣀⡀⣀⣀⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢠⢔⡁⢀⠴⠽⠀⠈⢭⣭⡌⡌⢭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠛⠀⠀⠀⠀⠠⠿⠀⠀⠀⢀⠀⠊⢀⣸⣷⡙⠫⠀⠀⠤⠢⠢⠶⠔⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣭⣿⣟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⢀⣃⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠙⠿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⡯⠻⠀⢀⡘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⢚⣿⣦⠀⠀⠀⠀⠀⠀⣼⣦⠀⠀⢀⣭⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣠⡀⡀⣻⢿⣿⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⣾⠋⣦⠀⠀⠀⠀⠀⠀⡟⠷⣿⣦⣼⠟⠀⡇⠀⠀⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⠟⠉⡏⢀⣛⣿⣦⠈⠁⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠘⠏⠓⠀⠀⠀⠀⠈⠛⠀⠉⠀⠀⠀⠀⠀⢰⣧⣥⣆⠀⣀⣀⣀⣀⣀⣤⣿⣿⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡻⠏⠋⣀⣴⠋⠉⠀⠀⠈⠀⠀⠀⠀⢀⡀⣠⠤⠿⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⠀⢀⣀⣀⣤⣾⣿⡿⠿⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⡶⠄⠀⠀⠀⠀⢀⣎⣻⢳⡇⢀⣦⣤⣤⣈⡉⣤⣠⠴⠒⠦⠿⠿⡛⠛⠻⠿⠿⠛⠛⠛⠉⠉⠁⣠⣤⣤⣶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠞⠀⣾⣿⢿⣿⡿⠘⣟⠅⠀⠀⠠⠀⠀⠀⣰⣶⣦⣤⣄⣀⠀⠀⢀⡴⠋⠉⠀⠀⠁⢃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡀⠀⠀⠀⠉⠉⢣⣼⠃⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠛⠶⠯⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⢡⣄⣀⣒⠲⠒⠂⠋⠀⠛⠛⠸⣧⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⢀⣠⣦⡤⠐⠄⠀⠀⠀⠀⠓⠤⠄⢀⣏⡗⠀⠀⠀⠀⠘⣤⣾⣿⣿⡟⠀⠀⡐⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣀⣀⣴⣶⢰⣶⠖⠒⠤⠤⠤⣭⣭⣍⣉⠛⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣯⣉⣈⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⡋⠀⠀⠀⠀⠀⠀⠘⢿⣯⣿⣋⡁⢢⣶⣶⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⡈⠛⠛⠋⣿⣿⣬⣤⣅⣀⣀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⠷⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⡿⢏⣠⠄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⢿⣿⣿⣥⣤⣶⡤⠀⠀⠀⣀⣠⣤⣤⣿⣿⢸⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢣⡶⡋⠁⠀⠀⣼⢷⠋⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⠁⣷⠄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠈⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⠃⣿⡿⣿⣿⣿⠿⡿⣟ ⠀⠀⠀⠀⢰⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡾⠁⠀⠀⠀⢠⢟⠇⠀⠀⠀⠈⠛⣉⣠⣿⣿⣿⣿⣿⣿⣽⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣶⣾⣿ ⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢁⡶⠋⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠂⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢆ ⣷⣾⣶⡀⢂⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣿⣾⣦⣴⠚⠋⢉⣻⣿⣿⡿⠟⠛⣻⣿⣿ ⣿⣿⣿⣷⡀⠺⠉⠊⠛⠷⣾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣋⣧⣷⣿⠿⠛⠉⢁⣤⣶⣿⣿⣿⣿ ⠻⠿⣿⣿⠇⠈⠀⠀⠀⠀⢻⢿⣟⣿⣶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠟⢫⣵⣾⡿⠟⠛⠉⠀⣤⠂⠀⣿⣿⠿⣿⣿⣿⣿ ⠨⠅⠒⠨⠀⠀⠀⠀⠀⡐⠈⠛⠹⠋⢐⠏⠉⠑⣦⣝⢀⠀⠀⠀⣤⣦⣤⣤⣀⣐⠻⣿⠿⣟⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⣠⣴⣾⣷⠀⠸⠀⢸⣿⣿⣿⣿⣿⣶⣶ ⣴⣶⣿⠅⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡥⠑⡄⢸⡿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⠇⠀⠀⣠⣶⣿⣿⣿⣿⣇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣟ ䷩ 𝚕𝚒𝚗𝚎 333 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/04/11/DebConf22_Kosovo_segregation_of_women_exposed.shtml Gemini version at gemini://gemini.techrights.org/n/2024/04/11/DebConf22_Kosovo_segregation_of_women_exposed.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ DebConf22 Kosovo segregation of women exposed⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024 [Article 2 years old] Reprinted with permission from disguised.work. DebConf22 call_for_papers is now open. Accommodation_plans_have_been_published. We are alarmed to see that segregation will be in force. It makes poor_doors look respectable. Ninety-eight percent (98%) of Debian Developers are male. These are employees of Google, Red Hat and Ubuntu disguised in Debian t-shirts. Accommodation advice_gives_them_a_list_of_hotels, their rooms paid by their employers. Each man will have an air-conditioned private room in the historic village center. Balkan women from Albania, Macedonia, Serbia and other low-income countries will be bussed in to the conference to correct the male imbalance. Fifty tickets_have_been_reserved_for_this_purpose, the equivalent of one bus, as we previously_anticipated_here. The accommodation_advice tells us that Balkan women will be stored in the Innovation and Training Park (ITP). In fact, the ITP is the former KFOR_base_for_military_peacekeepers. Women will be there in the bunk beds in the dormitories. In every other part of the world, when organizing a conference, organizers try to ensure that all attendees are treated equally. When your Silicon Valley company goes for a weekend in Las Vegas, everybody from the interns to the CEO each have a private room in the same hotel. Debian has decided to experiment with segregation. █ It is a scary thought: if you stay in the dormitories on a bursary, will your path cross with the underage_girlfriends staying in the same corridor? 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇DebConf22, Kosovo, Prizren, ITP⦈ § Debian men in uniforms (tartan kilts)⠀➾ More_details_about_Debian_uniform_tartan_here 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇DebConf22, Kosovo, Prizren, ITP, Kurt Roeckx, Mark Brown, Steve McIntyre, Neil McGovern, Keith Packard, Anthony Towns⦈ § Albanian / Balkan women in red t-shirt uniforms⠀➾ Debian_money_was_already_used_to_traffic_Albanian_women_to_Brazil. Photo courtesy Andis_Rado,_Albanian_photographer. Women in the Handmaid's Tale also wear_red_uniforms. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇OSCAL 2019⦈ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇DebConf22, Kosovo, Prizren, ITP⦈ § More Debian men in uniforms (tartan kilts)⠀➾ More_details_about_Debian_uniform_tartan_here 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇DebConf22, Kosovo, Prizren, ITP, Luca Capello, Martin Ferrari, Bdale Garbee, Phil Hands, Jonathan Riddell, Alejandro Barcena⦈ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇DebConf22, Kosovo, Prizren, ITP⦈ § Historic city center, where the men from Google, Red Hat & Ubuntu will sleep in hotels⠀➾ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇DebConf22, Kosovo, Prizren, city center⦈ § Who funds the diversity bus?⠀➾ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇DebConf22, Kosovo, Prizren, Google⦈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣛⢋⢙⢻⣿⠟⢉⠙⠋⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠉⠘⠿⠁⠈⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⠿⢿⡿⢿⢿⣿⠛⠛⠻⠟⠟⠝⠛⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⣀⡀⢸⣿⠤⠤⠬⠤⠀⠀⠀⣾⣶⢠⡄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⡇⠀⣽⣿⣿⣿⢸⡅⠀⣽⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠉⠉⢹⣿⣿⢸⠯⠀⠙⠉⠁⠀⠀⠀⣭⢿⢺⣇⣿⣿⡏⠉⠉⣿⣿⣿⣿⣿⣿⠀⠀⠀⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⡇⠀⠈⣿⣿⡇⠀⣿⣿⣿⣟⠘⠇⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣀⣀⣸⣿⣿⢸⢺⠀⠀⠀⠀⠀⠀⠀⡟⣿⣻⢹⣿⣿⣇⣀⣀⣿⣿⣿⣿⣿⣿⣀⣀⣀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡇⠀⢿⣿⣿⣿⢸⠇⠀⢿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⢸⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿ ⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⢸⡇⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⢠⣷⣿⠀⠀⠀⣭⣭⣭⣭⣭⣭⠀⠀⠀⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⠭⣭⣿⣿⣿⣿⡧⠤⠤⣿⣿⣷⠀⢸⣿⠛⠛⠀⠀⠀⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⠒⠒⢺⣿⣿⠀⡄⠀⠄⠤⠤⠠⠤⠤⠀⠀⢘⢨⣽⠿⠀⠀⠀⠷⣶⣷⣶⣶⡖⠤⠤⠤⢾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣯⠀⢸⣿⠀⠀⠀⠀⠀⢹⡿⣿⠛⠛⢻⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡏⠀⠀⠀⠀⠀⠈⠉⠙⠛⠃⠛⠿⠇⠘ ⢀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠁⠉⠁⠉⠁⠀⠐⠛⠛⠛⠂⠈⠉⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠋⠉⠛⠋⠈⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠄⠀⠀⠀⠠⠠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣀⣀⢀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠭⠍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠊⣈⣀⣽⣤⣮⣥⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⡾⠶⢶⠖⠂⠀⠠⠀⠈⠉⠀⠤⠄⣠⣩⣄⣤⣀⠈⣿⣿⣿⣿⡊⢳⣦⣤⡄⠀⠐⢋⡁⠒⠒⠀⢠⣤⣤⣠⠀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣚⢦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⡽⠍⠶⠢⠀⢤⣤⣤⠀⣄⠄⠠⢽⣿⣿⡿⡿⠿⠀⠈⠀⠀⠀⠄⢹⡿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠈⠻⣿⢿⡶⡦⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⢀⠀⢘⢿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡗⠉⠉⠠⠄⠦⠠⠀⢀⣀⠠⠈⠀⠂⠦⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠰⠿⢏⢛⣶⣿⣿⣿⣿⣿⠿⢿⡿⢿⣿⡿⣿⡿⠖⠌⠀⠈⠀⣰⠦⠠⠤⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠉⠁⠀⠀⠀⠀⠠⠀⠀⠐⠂⠒⠀⠀⠀⠀⠀⠀⠘⠉⠀⢀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣟⡿⣆⣦⣶⠊⠀⠀ ⠀⠀⣿⣿⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣻⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠻⠿⡿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣧⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢹⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣻⣻⣻⣿⣿⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢺⢿⣿⣿⣿⣿⣿⣿⣿⢸⠘⣟⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⡿⣿⡇⠀⣈⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⠀⠀⠀⠀⠸⣿⡄⠀⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⢘⣻⣿⣿⣿⣿⣿⣿⢸⠈⠿⣿⣿⣿⣿⣿ ⢀⠀⣾⣿⣿⡿⣿⣿⣿⣷⣥⡀⠀⠀⠀⢸⣟⣿⠸⣿⠀⠀⠀⣠⣤⣄⣠⡀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣛⣫⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡃⠀⣊⣿⣿⣿⣿⣿⣿⡟⢸⣼⣿⣿⣿⣿⣯⣿ ⣬⣦⣿⣿⣿⡀⣿⣻⣟⣻⣧⠀⣶⣭⣧⣿⠃⡛⠀⣿⣶⣶⡄⣿⠿⡿⢿⣇⣶⣿⢸⣿⣿⣿⣿⣿⡏⢩⣶⣿⣿⣿⡙⣾⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣭⡥⢴⡯⣙⣾⢸⣾⣻⣿⡌⣽⣿⣿⡗⣸⣿⣷⣿⣿⣿⣿⣿ ⣿⢿⣧⣭⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣥⣄⢿⣿⣿⢷⣿⡿⣻⣿⣿⢿⣧⣨⡿⣿⣿⣿⢿⢧⣸⣶⣼⣯⣾⣧⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣷⣜⣿⢞⣿⣿⣿⣷⣟⠀⢿⣿⡿⡟⢸⠻⢋⠉⢻⣛⣿⣿ ⠉⠈⠉⠀⠈⣀⠸⣟⣛⣻⣿⢀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠈⢹⣿⣿⣿⡏⠈⠉⢉⠡⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢹⣿⣿⠹⣿⣏⣼⣟⣻⣿⣿⢷⣿⣿⣿⣿⣿⣗⠀⣿⣿⡇⡧⢸⡀⣿⢿⣿⣿⢺⣿ ⡀⠠⡔⠘⢘⢩⠃⠹⣿⣿⡿⠲⠥⡇⡆⢄⠀⠀⠀⠀⠀⠀⠀⢰⠉⢛⣁⡀⠀⠀⠀⠐⠐⢂⠒⠂⠃⣿⣿⣿⣿⣿⡇⠐⠲⠙⠐⢲⠜⡧⢖⢾⢛⣿⣟⣻⣿⡟⠒⣽⣿⣿⣿⣿⣷⠀⣖⠢⠢⠄⢔⠻⣿⣶⣷⣾⡶⣢ ⣔⠉⠃⠄⢀⢰⢠⠀⠈⠃⠁⢀⡀⡇⡇⠐⠒⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⣟⡿⠀⠀⠀⠀⠀⠈⢠⣝⣛⣫⣮⣿⣿⣿⣿⡜⠋⢸⣿⣿⣿⡟⢿⣀⣯⠴⠁⠁⠚⠀⢿⡿⢿⠋⠡⠙ ⡇⣀⠀⠅⠽⢸⢸⠀⠥⠥⠀⠀⠂⡇⢃⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠱⠁⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣽⣿⠿⡅⠀⠈⠁⠀⠀⠀⠀⠀⣨⣥⡉⠀⠀⠀ ⡯⠀⠀⠀⠚⢸⢸⠀⠀⡉⠈⠠⡂⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀ ⣿⡁⠀⠐⠂⡚⢸⢐⡀⣖⡷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀ ⣿⡂⠀⣀⠄⠇⢸⢸⠀⡇⢠⡏⣁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀ ⣿⡓⠰⠌⢉⠃⠸⠸⠈⠏⢙⠙⠣⠶⠂⠀⠀⣄⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⠀⠀⠄⠀⠀⠀⠏⠀⠀⠀⠀ ⠉⠁⡁⠀⠲⠴⠇⠀⠠⠀⠸⡟⣿⣧⠀⠀⠀⠉⠁⠀⠀⢀⡀⣀⣛⠂⢀⣀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀ ⠄⠄⠀⢲⢲⠀⠀⣀⣀⣀⣀⣀⠒⣁⡀⠀⠀⡆⠀⠀⢨⣸⡇⠀⠀⠀⢨⠀⠀⠀⠀⠀⠄⠘⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⠿⠋⠛⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀ ⠀⠀⣶⣺⣷⣦⠇⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⡇⢸⢠⣄⣀⡁⠀⠀⠀⠈⠀⣀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣤⡄⠀⣀⢀⣴⣿⣿⣿⢋⣀⣀⣠⡀⠃⢱⣦⣄⠠⠬⠥⠤⢄⣴⣿ ⠀⠀⣿⢻⣿⣿⡅⠀⠀⠀⠀⠀⡸⣿⣧⠀⠀⡷⢸⢸⣿⢻⠟⠿⠻⣆⢰⣾⣶⡗⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⠋⠘⠛⠿⠛⠁⠀⢸⠈⡟⠀⠀⠀⠀⠀⠉⡏ ⠀⠀⠀⢸⠉⠉⠉⠀⠀⠀⠀⠀⡏⢻⠁⠀⠀⠇⠈⠘⠛⠉⠀⠀⠀⠉⠀⠸⠽⠁⠀⢀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⢿⣿⣿⣿⢿⠟⢛⣿⠁⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⢸⢹⠀⣷⠀⠀⠀⠀⡏⣿⣍⠀⠀⡀⠀⠀⢰⠀⠀⠀⡄⠀⠃⠀⠀⠄⠀⠀⠀⢸⡻⠼⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⠀⠙⠉⠀⠀⠀⢸⣿⠉⠀⠀⠀⢠⠁⠀⢸⣿⡯⠀⠀⠀⣤⣿⣿⣿ ⠀⢸⣯⢸⣷⣶⣿⡤⢀⣆⠀⣿⣿⣿⣿⠆⠀⠀⠀⢰⣤⣀⣤⠀⠀⠀⢠⡤⠤⠄⠀⠀⢸⠁⠀⠀⠸⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢸⣾⣶⣷⠀⠀⠀⢀⢠⣾⣿⣿⡀⠀⠾⠿⠂⠄⠸⠿⠷⠤⠶⠶⡿⣿⣿⡿ ⠀⠸⢞⣼⣿⣿⣿⣧⣤⣧⣤⣿⣿⣿⣿⠶⠆⠀⡀⢸⣿⣋⣿⣀⣀⣈⢹⣿⣯⢉⡁⠀⢨⠀⠀⣒⡒⣶⣷⣒⡀⡀⡀⠀⣿⣿⣥⠀⡛⠰⢸⣿⣿⣿⠤⢴⠤⢼⣾⣿⣿⣿⡇⠠⠀⠀⠀⠐⠠⢼⡇⠀⠄⠀⡇⡗⣻⡇ ⣿⣧⢀⢸⢸⡀⠠⡇⠀⠀⠀⢀⢿⣔⣿⠀⠀⢨⡇⢸⠉⠉⣿⠉⠉⠉⢹⠉⠉⠈⠁⠀⠀⠀⢠⠅⠂⣿⣿⣿⡇⣤⣤⣤⣿⣿⣿⠀⢈⠀⠀⠀⠩⢹⠉⠈⠀⢸⢹⣿⣿⠀⠀⠀⠀⠠⠒⠲⠂⠈⠁⠀⢀⠀⠁⠃⡋⠁ ⣿⣿⣄⣸⣀⠉⠸⠇⣀⣀⡀⠀⠺⠙⣟⣤⣤⣼⢧⡈⠀⠀⠹⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡏⣿⣽⡇⠀⠀⠀⢣⣀⣀⠀⢸⣤⠀⡈⠿⠍⠉⠉⠁⢸⠹⠿⠿⢀⣀⣤⣶⡄⠀⠀⠸⣿⣿⣿⠀⠈⣿⣾⣿⠇ ⠀⠀⠀⠀⣼⣿⣶⣤⠀⠀⣴⣶⣶⣶⡀⠁⠁⠀⠈⠁⢸⣿⣿⣿⣧⠀⢰⣿⣿⣷⣼⠉⠉⠀⠠⠀⠀⡏⡿⣿⡇⠀⠀⠀⠈⠊⠀⠀⠈⠛⠛⣷⣦⣤⡄⠀⢸⣶⣶⣾⠀⠸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀ ⠂⠀⠀⠀⣿⣿⣿⣿⣃⡀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠰⣦⣤⣤⣤⢠⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⠀⠀⢻⣿⣿⠇⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⠿⠀ ⣀⣀⣀⣀⣸⣿⣿⣿⣀⣀⣸⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣟⣠⣭⣿⣿⣿⣁⣀⣀⣀⣀⣀⣿⣿⣿⣇⣀⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣻⣿⣿⣇⣀⣿⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⡋⣾⠀⠀⢹⣷⠇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⡏⠝⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢟⣿⡿⠿⠿⠿⢻⡛⢿⣼⡟⠛⠿⡿⠟⢛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⡣⣀⣹⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⢧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⠁⠀⠀⠠⠭⠭⣭⠍⠁⠺⠆⠬⠀⠀⠃⠱ ⣿⣿⣿⡿⠛⠻⣿⢿⣿⣿⡿⠛⠁⠈⠻⣿⣿⣿⣿⣿⣿⣷⠀⢭⠁⢿⡟⠀⠘⠅⠙⢿⣿⣿⣿⣿⣿⠟⣱⠉⠟⠋⠁⢣⡻⣿⣿⣿⣿⣿⣿⣿⡁⠀⢩⣦⠈⠁⢀⠁⣿⣿⣷⣶⣦⣤⣤⣤⣶⣦⣀⣀⣀⣶⣶⣤⣀⣠ ⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⣇⣀⡀⠀⠀⠈⢹⣿⣿⣿⣿⠏⠠⠄⠀⣬⣷⣶⣄⣀⣀⣀⣿⣿⣿⣿⠋⠈⠁⢀⣀⣀⡀⠀⠀⠈⢿⣿⣿⣿⣿⡏⣰⠲⢦⣥⣤⣄⡀⠘⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣤⣾⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣾⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⡀⠀⢀⠀⠹⣿⣿⣿⡿⢿⣿⣿⠟⢿⣿⣿⢿⡿⣻⡿⠿⠗⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⢩⣼⣿⣧⡹⡿⡿⣹⣯⣭⣭⡄⠀⠀⠉⠉⠉⠁⠁⠓⠻⠙⠤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣠⣄⣤⣠⣶⣦⣤⣤⣠⣤⣦⣤⣤⣤⣴⣴⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⣦⢰⣶⢰⡆⣿⣷⣶⣾⢰⡆⣧⣶⣼⢰⡇⣦⣷⣶⣶⣧⣤⢰⡆⣦⣄⣶⢰⢸⣭⡨⣽⠀⢰⠀⢴⡀⢀⠀⠀⣿⣿⣿⡇⠀⠄⠀⡄⠀⠀⠀⢸⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⡇⢨⡅⢸⡇⣿⣿⣿⣿⢸⡇⡇⡇⢸⠈⡇⠃⣿⣿⣿⣿⣧⠠⠅⡿⠅⡿⠸⢸⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠷⠾⠿⠿⠷⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛ ⡄⠤⠤⣀⠆⠀⠠⠀⢀⠠⠀⠠⠄⠤⠀⠂⠠⠀⠠⠀⠄⠤⠀⠰⢂⠰⢶⣿⣿⡿⢿⠿⡾⡿⣿⡿⣿⠿⠿⢟⠿⡛⠿⠒⠠⠂⠐⠒⢒⡂⡂⠒⢲⣸⠇⠒⠒⠒⠐⠀⠂⢀⠀⢀⣂⣀⣀⡀⢀⡀⡈⣉⢁⣒⠐⣒⣂⣒ ⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡿⢼⡿⣿⣿⣿⣿⣶⡫⡿⢿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠿⠾⠟⣷⣿⣿⡶⠐⠐⠠⢿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠈⠈⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠈⢻⣿⡆⠀⠈⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⢨⣿⣿⠀⠀⠈⠉⠀⠈⣻⣿⣿⣿⣿ ⣿⢿⣿⡇⢰⡆⠀⢀⡆⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⡿⢐⠀⠀⠀⠀⠀⢸⡿⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠐⣿⣿⣧⠄⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠒⠒⠒⢾⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⢸⡀⠀⢘⣷⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣻⣿⡆⠀⠀⠀⠀⠠⣿⣿⡅⠀⠠⣿⡿⠃⠀⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⢴⣿⣿⠃⠀⢀⣀⣀⣸⣿⣿⠀⠀⡄⠀⠀⠀⢽⣿⣿⣿⣿ ⣿⣿⣿⠃⢸⡃⢀⣾⣿⠀⠀⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣯⣿⣾⣿⣿⡅⠀⠀⣁⠀⠀⢰⣿⡄⠀⠀⣿⡄⠀⠀⠈⠈⠀⣹⣿⠀⠀⣿⢠⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡄⠀⣤⡀⠀⢠⣿⣿⣿⣿⣿ ⣿⣿⣯⠀⢸⠀⡀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣦⣤⣿⣿⣿⣿⣿⣿⣤⣼⣾⣲⣤⣼⣿⣿⣤⣼⣿⣿⣤⣤⣄⣤⣤⣿⣿⣷⢀⣿⢻⣧⣤⣽⣿⣿⣤⣶⣶⣶⣾⣿⣿⣧⣤⣿⣿⣤⣼⣿⣿⣿⣿⣷ ⣿⣾⣿⠀⢸⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⣿⣿⡇⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡄⠸⠀⠀⢸⣿⠀⠀⠇⠀⠀⠀⣿⣿⡟⠁⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣄⣀⡀⠀⠛⠀⠀⠀⣀⣀⣤⡿⠃⠀⠀⢹⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣼⣿⣿⣿⣷⣤⣀⣴⣿⣿⣿⣿⠀⠐⠄⠀⠘⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣿⣿⣿⡿⣿⣿⡿⣿⡿⣿⣿⣿⣦⣆⠃⠀⠈⣿⣿⡇⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣿⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠻⠿⠛⠝⠿⠿⠋⠋⠛⠿⠿⠿⢿⡿⠃⠀⣴⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠻⠪⠍⠩⠍⠿⠒⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠛⠛⠛⠻⠿⢿⣿ ⣿⣶⣖⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⠰⠄⠀⠒⠤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣷⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⠀⠀⠈⠉⠃⠀⠀⠀⠒⢺⢸⡇⣿⣿⣿⣿⣾⣿⣦⡼⠇⠀⠀⣿⢸⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢾⣧⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⣿⣺⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⣿⢸⡥⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⣿⣾⣿⣿⣶⣄⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣧⣿⣼⣿⣿⣿⡇⣠⣿⢹⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡏⣈⣭⣭⣭⣿⣿⠀⠀⠀⠀⣿⢾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⢾⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣽⣿⣷⢿⣿⡏⠀⠀⠀⠀⣿⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⢸⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠟⠟⠻⣿⣿⣿⣿⣿⣤⣤⣀⣀⡄⠀⣠⣀⣀⣼⣿⢸⡿⢿⣿⣭⣿⣿⣇⣄⣀⣀⣄⣿⢸⢸⡟⣿⣿⣿⣿⣿⣯⣿⣿⣗⣸⣿⢸⡇⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⣼⣿⣿⣿⡎⢿⡇⣿⣿⣿⣿⠟⢁⣴⣿⣶⡝⡿⠟⠛⠈⠀⢻⣯⣛⢛⣿⠀⠀⠈⠉⠻⣿⣸⢸⡇⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⡏⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣤⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿ ⣿⡏⠰⣻⣧⡾⢾⡷⠈⢥⣿⣿⣿⠋⠀⢈⣿⣯⣿⣇⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣧⠀⠀⠀⠀⣿⡆⣤⣾⡈⢣⣶⡖⣽⣿⣿⡏⣿⣿⣿⢠⣀⢿⣿⣿⣿⣿⣿⣿⣿⢸⣯⣿⢿⣿⣿⣸⣟⣻⣻⣯⣼⣿⡏⣿⣿⡇⣿ ⡈⠀⠀⢀⠑⠾⠗⠃⠀⡈⣈⣭⣉⠀⠀⠸⣿⣷⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣼⣿⣿⡆⠀⠀⠀⠈⠀⠉⠉⢷⣤⣤⣼⡀⠠⠀⣁⡁⡉⢋⣘⢿⣿⣿⣿⣿⣃⡻⣿⢟⣘⢿⢟⣀⡻⡿⣻⡿⣛⡿⣿⢿⢟⣀⠻⡿⣃⡻ ⠿⠀⠀⢾⠒⠀⠚⠂⠀⠈⠙⠣⠆⠀⠀⠀⣷⣭⠕⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⠘⡏⠁⠀⠀⠀⠐⣠⣥⣶⣿⣿⣿⣿⣿⣿⣷⣦⣭⣂⢂⢮⢨⣽⣐⢰⣎⠛⢃⣾⣆⣦⣬⣱⠀⣔⣽ ⠀⠀⠀⠈⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣵⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣷⡄⣥ ⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣞⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠟ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⡀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⡌⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣴⣾⣿ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⣒⠈⠀⠀⠀⠈⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⣭⡡⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢜⠃⠀⠀⠀⠀⠠⢀⣠⣤⣄⢀⠀⠀⠀⢀⠁⠿⠿⠿⡿⠛⠙⢍⣿⣿⣿⡇⢸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠠⢸⠀⠀⠀⠀⠀⠐⠺⠁⠉⠘⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠉⠁⠸⣿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢭⠅⠒⠂⠐⠀⠉⢽⡇⠀⠀⠀⠄⠐⠒⠒⠂⠈⠀⠀⡦⠀⠀⠀⣀⣀⡆⠠⠀⠠⢼⡄⢹⡿⡄⠀⠀⠠⠀⠀⠀⠀⠁⡿⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⡆⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⢿⣿⣿⣿⡟ ⢄⠀⠉⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⡇⢠⠀⣸⣿⡇⡀⠃⠃⣦⣤⠀⠀⠁⠀⢠⣠⣧⠀⠛⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡿⡹⠄⠠⢀⠀⢀⠀⠀⠀⠀⠀⠸⠿⡿⣿⣦ ⣤⠨⢿⡄⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⡇⠉⠀⠀⠀⡀⣀⠀⢡⠀⢸⣿⣿⣀⣈⡀⢰⣾⣾⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢸ ⣿⠠⠾⡇⠀⠀⠀⡷⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⠀⠀⠁⠀⠀⠀⢸⠉⠟⠉⠉⠉⢨⠹⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢸ ⠚⠀⢤⡅⠀⠀⠀⡇⡧⢼⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣄⠀⠀⣴⣿⡆⠀⠀⠀⢠⠀⠘⠉⠍⠀⠀⠀⠄⠈⣿⡇⠀⢸⡇⠈⣀⡤⢀⣤⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠘⠏⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠚⡒⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣚⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠭⠭⠽⠃⠉⠹⠿⢿⣿⣿⠟⠉⠙⣛⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡂⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠈⡠⠿⠍⠛⡟⠛⠒⠒⣲⢾⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⣤⣤⣀⣀⣀⢀⠄⠀⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿ ⠀⠀⠀⠀⠀⠀⣀⢄⣠⣴⢄⠀⠀⠂⠈⠀⠀⢉⡙⣡⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⢰⣿⡀⠀⢀⠀⠀⡄⠀⢤⡄⠀⠀⠉⠉⠉⠉⠋⠾⠇⠀⠀⠀⠀⠀⠘⠒⠒⢲⣶⢿⠽⣟⣶⡴⠒⠒⠀⠀⠀⠠⠤⠤⠤ ⠀⠀⠀⠀⠐⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀⡤⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⠀⠀⣿⡇⠀⣾⠀⠀⡀⢀⣿⡆⠀⠨⢙⠐⠒⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢁⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⠆⠀⠹⡅⠀⢿⠀⠠⠇⠘⣿⡇⠀⠟⢻⡠⡐⠀⠈⠀⠙⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢠⣿⣿⣿⣿⡟⣹⢿⣿⡿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠍⠀⣰⣿⣿⣿⣿⣿⠁⡀⠉⡨⡹⡗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠠⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⡟⠁⠀⣴⣿⣿⣿⣿⣿⡏⠊⠂⠀⠢⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠠⣦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⠙⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣐⡒⠂⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠃⠀⠀⢀⡘⠼⣿⣿⣿⣯⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠄⢹⣷⢰⡿⠻⣷⣄⣶⣟⣷⡆⢿⡿⠿⠿⣿⡟⠁⠀⣀⣀⣷⢀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⡄⣰⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣠⣾⠏⢸⡗⠀⣿⡟⣿⣍⣭⡉⢻⣧⡄⣼⣿⣬⢀⡀⣿⣀⣿⢿⣒⡛⠀⠀ ⠀⠄⠀⠀⠀⠀⣠⣼⣿⡿⡿⠿⢿⣿⣿⣻⠋⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠈⠉⢉⠀⠀⠉⠁⠀⠉⠀⠀⠉⠉⠀⠀⠉⠈⠉⠉⠉⠀⠁⠈⠁⠉⠀⠉⠁⠀⠀ ⠄⠀⠀⠈⠫⠝⠛⠛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⡿⣿⣟⡿⠿⠿⠏⠿⠿⢿⡻⠻⡉⢉⠛⢟⡻⠛⠋⠛⠉⠯⠿⠛⠻⠻⠻⣿⣿⡏⠊ ⠄⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠿⣿⣿⡿⠿⠿⠟⠛⠋⠉⠉⠉⠀⠀⠀⠁⠀⠂⠀⠈⠁⠁⠙⠍⠙⠂⠋⠉⠉⠀⠀⠀⠈⠌⠀⠀⠀⠐⠂⠀⠀⠐⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠠⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠦⠐⠀⣿⣿⣧⡦ ⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⢼⣇⠀⠀⠀⠀⠀⠀⢠⢿⣿⣻⣿⣿⣿⣯⣿⣿⣯⣭⣿⣆⡀⠀⣿⣿⡏⠀ ⡀⠀⠀⠀⠀⠐⠀⠀⠀⣴⣶⡤⡤⡙⣽⣾⣀⣀⠀⠀⠀⢀⣤⣴⣤⡠⣿⣦⡄⠺⡟⣿⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡿⠳⠿⠿⠄⠀⠀⢀⣤⡴⡿⢿⣻⣿⣿⣿⣯⣽⣿⣿⣿⣿⣭⣽⣧⠰⣿⡿⠧⢐ ⠀⠀⠀⠀⠀⠀⠀⡤⢤⠿⡿⠯⣷⣿⣻⡿⣧⣤⡤⠠⣄⣣⣿⣿⡶⢃⡀⠀⠁⠂⠴⡬⣀⣪⡶⠆⠀⠀⠀⠀⠀⠀⠀⠠⡕⠠⢄⡀⠂⠀⠀⣀⣠⣤⣤⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⠻⠁⠳⠬⠓⢤ ⠀⠀⠀⠀⠀⠀⠀⠿⠹⠀⠏⠿⠛⠿⠿⣶⣶⡀⠀⢐⡒⣲⣖⣯⠀⠀⠀⠀⠷⡀⢦⣱⣾⣾⣦⣴⣽⡄⠀⢠⣴⣢⢄⣛⣡⣤⣄⡀⣠⣿⣾⣷⣿⣶⢿⣶⣾⣿⣿⠿⣿⣿⣿⣿⠿⠿⣿⣿⣭⣤⣤⣬⣤⣶⣶⣾⢿⢒ ⠀⠀⠀⠀⢀⢀⣨⣼⣶⣶⣶⣶⠶⠶⠶⠶⣶⣦⣤⣭⣯⣭⡥⠨⣶⣼⣿⣿⣿⣾⣿⣿⣧⣤⣬⣵⣿⣉⠤⠄⠐⠝⠛⠿⡧⡭⠳⡖⠙⣿⠿⠛⣿⣿⣿⣯⣿⡋⠀⠀⠀⢹⡟⠀⣀⣠⣬⣿⡿⣿⠿⣿⠿⠿⠿⠟⠛⠚ ⠀⠀⠀⠀⠐⣳⣿⣷⠧⣾⣾⣾⣾⡷⡷⢾⣿⣿⠶⣶⣾⢽⠀⡟⡟⣿⣿⣿⣿⣿⣿⢿⣿⡟⣘⣊⣹⣯⣭⣿⣆⠀⠃⣀⠴⣐⣶⣹⣯⣷⣰⣆⣝⣛⣿⣟⣿⣻⣿⢿⢓⣚⣛⣛⣩⣤⣴⣶⢶⣶⣤⣤⣤⣴⠒⠠⠀⠰ ⢀⣠⣄⣄⣘⣻⣟⣿⣿⣿⣿⢛⡿⣟⣟⣋⡭⠏⠋⢛⣍⡾⠵⠿⠿⠿⠿⠯⢓⣈⠛⠫⠥⠦⠒⣵⣶⣿⢟⣿⣷⠂⣊⡑⢑⣿⣾⣛⠉⠉⠂⢸⢹⡏⠙⠏⣿⣿⣿⠓⢹⣿⣿⣿⣿⡿⠿⠿⠾⣿⣿⣿⣿⣿⠀⢸⣀⣼ ⣭⡇⣿⢷⢾⡿⠿⠋⠻⠿⠿⠿⣿⣾⣿⣷⣡⣤⡧⠄⣿⣽⣭⣯⣿⢧⣿⡼⢹⠿⢾⣣⣘⣀⡈⣷⢷⣿⣤⣤⣟⣶⡿⣼⣼⠟⠉⠁⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠠⠁⡀⠂⢀⠀⠀⠀⠀⠀⠀⠨⠬⠽⢛⠟⠞⠖⠲⣺⡇⣀⣚⠿⡇⣗⣔⣻⡶⢹⠛⣋⣉⣀⠇⠐⠀⠀⣓⣃⠀⡔⢤⠀⣀⠀⠀⠚⠛⠻⠛⠉⠉⠉⠩⠍⠉⠉⠉⢹⡖⢑⡄⠈⢸⡟⠍⢸⠉⠉⠛⠛⠃⣈⠉⠉⠀ ⠀⠀⢁⠘⠀⠈⢤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⣻⣋⠛⢢⢲⢯⣿⣿⣻⣷⣿⣿⣍⢻⣏⣀⣅⣀⣉⣽⢜⣾⣻⢁⡐⣶⣲⢶⣦⠄⣢⢤⣤⣤⢠⣀⠠⠥⢀⣀⣀⡁⠀⣧⡀⢉⡁⡀⠈⠠⠌⠃⠅⠂⠀⠀⠀⠉ ⡇⠀⣼⢠⣀⣤⠘⡋⣀⠀⠀⠀⠀⢀⡀⣀⣀⡶⢋⣿⡱⡑⠵⡿⢿⢡⣀⡼⣨⠛⠛⢋⠙⣻⡿⣿⣏⣿⠛⢫⣾⣿⡿⡶⠷⠍⣿⣌⡹⢲⡛⠠⣽⡾⠯⣿⡿⣸⢯⠳⣷⢯⣉⣿⠽⢛⣭⣿⣽⡿⢇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣾⣨⣺⣤⣧⠬⠤⠂⠚⣳⣿⣶⣦⣷⣿⣿⣿⣿⣷⣷⣶⣆⣵⣵⢟⣠⢳⡐⡀⠎⣹⡾⣻⡽⣦⢄⡆⣹⣿⣷⣻⡿⢿⣺⠿⣺⠓⡤⢴⠿⢶⣶⣿⠟⠛⠿⠙⠺⠤⡀⡛⣿⢿⠟⡛⢃⡅⠂⠢⠠⠀⠀⢀⠀⠀ ⣿⣿⣿⠕⠩⠿⠿⠽⠭⢽⣯⣭⢒⣿⣿⣿⣿⣛⣿⣿⢿⡿⣻⣿⣿⣿⣿⢿⡮⣝⣿⣟⢷⣦⣶⣧⣄⢡⣐⠄⣘⠙⠳⣗⣠⢛⢟⠁⠦⠐⠄⠙⠫⡠⡚⡍⢠⠀⠀⡀⢀⣠⢨⡑⠁⡂⡨⣑⡈⠀⣀⠤⢀⠀⣙⢠⠀⠀ ⣿⣿⢻⡃⠁⠬⠭⠭⠭⠭⠽⢿⠐⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣉⡽⢿⢽⣿⢁⣿⣿⢿⣫⢿⡶⣶⣶⣾⣭⡩⠐⣀⠀⠠⠁⠀⢀⠇⠈⠀⡸⡏⠸⢒⣼⣧⠀⠀⢑⣿⣯⡒⡓⣆⠈⢀⡋⢾⠀⠀ ⣿⡿⣾⡒⣀⣐⡯⠩⣭⠭⠭⠭⠅⣶⢤⣤⡄⣻⣟⣿⣿⣽⣾⠟⣻⣿⣿⣿⡿⣿⣶⣿⢿⡿⢷⢣⣿⣁⣻⣿⣶⣼⢿⣿⢷⡯⣏⠉⡯⠥⠈⡐⣢⣄⣄⣀⢀⢀⠠⠀⢀⠻⢿⣿⣮⡨⢻⠿⠮⠈⠖⠓⠀⠐⢘⡄⠒⠠ ⣿⡿⣿⡆⠐⠒⢚⣛⣊⣍⣭⠭⡭⠓⣓⠒⠒⠀⢾⡏⣛⣛⣻⣽⣿⠟⢻⣛⣻⠿⣿⣿⣷⣿⣳⣿⣿⣾⣿⣯⣛⣻⡿⠿⣿⣿⣿⣶⣾⣷⣬⣵⣈⣙⡊⠍⠙⡻⠧⠶⠰⢤⠄⡠⢄⠲⠐⠀⠈⣉⠀⠀⠐⠀⠀⠁⠀⠀ ⡷⣷⢟⡏⢡⠭⠤⠵⠔⢒⡒⣒⣓⡪⠵⣶⣾⣿⣿⣷⡾⡴⢷⣮⣿⣿⡿⣒⠫⣋⡭⠭⠽⠳⢿⣿⣿⣿⣿⣟⣿⣯⣿⣿⣶⢶⡾⣷⣿⣿⣿⣶⣿⣽⣿⣷⣿⡥⣮⣅⢂⣌⣉⡳⡏⡙⠟⢦⡈⡁⠀⠀⠀⠀⠀⠀⠁⠀ ⣷⣷⣷⣗⢓⣒⣂⣉⣉⡭⣭⠽⠤⠤⣛⣿⣿⣿⣿⣿⣿⣷⣝⣻⣭⣿⣯⣶⣮⣭⣳⡶⠃⢟⣿⣯⣿⢽⢿⣏⣿⣿⣿⣿⣿⠭⣭⣿⣿⣿⣿⣿⣿⣿⢿⣯⣽⣟⣽⠿⠾⡻⢶⣬⣄⣀⣀⠐⠒⣴⠀⠒⠚⠦⡄⡀⣠⡠ ⣼⠟⣿⣿⢭⡤⠤⠴⠖⠛⠒⣒⣊⣉⡠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣯⣽⣿⡶⣿⢫⣟⡱⢒⣛⢙⣃⣚⣋⣯⡽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣯⣭⣽⣯⣿⣶⣮⣽⣣⡺⣻⠀⠙⠀⠀⠀⠀⠀⠈⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⢶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠈⣿⣿⣿⣿⣿⣿⣷⣖⣶⣤⣴⣴⣷⠆⠀⠀⠀⣿⡿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠘⢻⣿⣿⣿⣿⡿⠁⠀⠸⣿⣿⣿⡅⢀⠀⠀⠀⣿⣇⡆⠀⢹⣿⢷⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠏⢿⠑⠗⠐⡀⠛⠿⠟⣳⣆⠀⠠⠘⠛⠛⠓⡀⡀⢀⣤⣿⣿⣿⣤⣾⣿⣏⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠰⠶⠀⠀⠀⣄⣀⠶⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠆⠐⠓⠁⠀⠀⣼⠏⠀⠒⢨⡇⠀⡀⡺⣽⣿⣧⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡤⠦⠀⣾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⢀⠀⠀⠀⠀⠁⡀⢰⢆⡀⠀⠀⠀⢠⣬⣝⣻⣯⡀⠉⣿⡍⣻⣿⣿⣿⣿⣿⣼⠏⠀⠀⠀⠀⠀⠘⠯⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⠀⠀⢀⡿⡟⠹⢿⠿⢿⣿⡗⣉⢽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠚⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣧⢍⠉⠉⠉⠀⠀⠀⠉⠀⠀⣮⣿⣤⣧⠓⠛⠅⠈⣿⡛⠁⠋⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⢶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣯⣭⣭⣭⣭⣭⣭⠁⠀⠀⠁⢦⠘⠀⠀⠀⢀⠀⢰⠉⠉⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣺⣟⠆⣿⡿⠛⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⢠⡜⣠⠄⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣽⣿⣿⣾⣻⣣⣼⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿⣿⣯⣩⣿⣿⠀⠀⠀⠀⣵⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣵⣿⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⠀⠀⠀⠀⢍⣜⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⣾⣅⡀⠀⠀⠀⣀⢠⣤⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠶⠶⠶⠶⠶⢷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣦⣤⣄⡀⠀⠀⠀⠀⡶⠬⠄⠀⠈⠉⠉⠨⢤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 668 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/04/11/First_They_Came_for_Iranian_Developers.shtml Gemini version at gemini://gemini.techrights.org/n/2024/04/11/First_They_Came_for_Iranian_Developers.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ First They Came for Iranian Developers...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024 Context: Should_Fedora_banish_Russians_as_they_banished_Iranians? | Imperialistic_Blacklist_Machines:_Racist_IBM_and_Red_Hat_--_Just_Like_Donald Trump_--_Have_Turned_Fedora_Into_an_Utterly_Racist_Project_That_Blacklists, Shuns_and_Permanently_Bans_People_Based_on_Their_Nationality_Alone | There's Apparently_a_New_Boss_(or_Policy)_at_Red_Hat/IBM 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇lyude tooting⦈ THIS article seems like the sort of stuff we typically limit ourselves to covering on Mondays_only. It's just so astonishingly familiar, but at the same time it is exceptionally worrying. Community elements are being 'culled' from... well, the community. Companies_that_profited_from_ethnic_cleansing insist this is done to "protect minorities". Every so often we see the term "CoC" being used by one side. Sometimes the other side calls out "SJW" or something to that effect. The terms or acronyms being thrown around (like insults) don't matter as much as the overall objective/s and the outcomes. We want to understand the outcomes and ask ourselves, cui bono? From what we can gather, based on publicly-available material (accessible legally, no doubt about it!), and a whole bunch of us have studied the situation today and yesterday, we must set aside ad hominem call-outs and focus on substance. Evidence is not "doxing", evidence is evidence. Without evidence, we'd get nowhere. It's like saying Julian Assange deserves death for the way he acquired footage of war crimes; why not demand that the war criminals are held accountable with this footage as evidence? So, what's this all about anyway? FDO (Free Desktop) and Red Hat. I first became aware of this because of a post from Drew DeVault, whom I lost respect for last year or the year before that (after he had gained trust and respect of many people in prior years; mine included). Months ago DeVault was recklessly_generalising_to_reach_the_ludicrous_(and_collectively_offensive) conclusion_that_Free_software_tolerates_pedophilia_or_something_along_those lines. Deducing that because of a chat with one person is laughable. I wanted to understand what was behind the namecalling and "isms". Hurling insults at people isn't storytelling. I spoke to several people (internally) and wanted to hear their interpretation. We all more or less agreed on this, without even having to convince one another. We independently reached the conclusion that DeVault plays ball for the 'cancel brigade' and even though he no longer does social control media he seems to believe whatever the brigadiers allege. "Weird post on DeVault's blog" one person told me about it (I hadn't even asked; it was spotted independently by someone who used to respect DeVault). To quote this person: "I decided to check out DeVault's blog this morning and found a shitshow. It looks like a textbook example of all the stuff you wrote on Techrights about Red Hat behavior towards independent Freedom Software projects, about CoCs, and related stuff." "The curious thing for me was that the guy whom DeVault attacked just dumped everything on his blog. I read it all, and it's just insane!" "A per from FDO/RH contacted him to wave FDO's CoC in front of his face, and he in a (in my opinion excessively) polite way told the per to fuck off." "Roy, I just can't believe these people are so stupid. The FDO/RH member may be, but DeVault... He seems to be spinning propaganda targeted at those who are already on the SJW hook or on his side, because, in my opinion, any sensible person will discover by just reading the stuff exposed by Vaxry that DeVault and the FDO/RH member are the worst of hypocrites. DeVault even framed it as if Vaxry doxxed the FDO/RH member! :O" I checked for myself. There's no doxing there, period. The same false accusations were once thrown at me. The doxing was actually directed at myself. What an incredible reversal of victim/accuser narrative. The links are important as we want readers to judge for themselves. We encourage critical thinking. This_is_what_DeVault_wrote and a two-part write-up from Vaxry [1, 2] contains some screenshots. "It may be good material for a piece on Techrights in the "CoC series"," I was told. For the third time and for the second day I sought input from other people, who are technical and very reasonable in my experience (quite left- leaning and definitely not racist!). I had already criticised DeVault in the past (similar stuff). I saw DeVault's blog post over a day ago and discussed it with an associate. We could not determine all the facts at first, but upon reading the other side the lead-up was illuminated. There was prior provocation of sorts, at least some agitation leading to strife if not online feud/conflict. The large companies (with their precious "brands") are very afraid of not siding with a super-loud minority, so this can be easily exploited for grotesque censorship and overreach. So far I've not seen any other article about this (DeVault left out the balancing acts; he wants to be believed without full or fools' context). If I do find something new and substantial, and if that introduces truly new evidence, then I'll read up on that and write something sooner or later. I see some of the same tactics there that I saw in the years-old campaign against me. It's horrible to see what some human beings do to other human beings in an effort to "get ahead". Thanks for the links, as above, I am able to make up my own mind. To quote things that DeVault does not want seen (from Vaxry): "As we can see, X.org/Freedesktop/RedHat utilizes people who are power-hungry, hypocritical and self-obsessed as moderators to say the least. Moderators that do not wish to look at themselves in a mirror, and treat any and all disagreement as a personal attack." "Harassment under guise of code of censorship concern trolling and other tactics" is what an associate has labeled this, "also similar tactics used against Techrights and many others, it's part of a large pattern." There seem to be a gross overreach beyond one's professional/personal life or between projects. We already saw how FSFE, which does many bad things, sought revenge against Daniel Pocock (who merely talked about these bad things as part of his responsibilities as a representative of FSFE Fellows). FSFE tried to crush him in Debian, Fedora, Mozilla, and so on. FSFE should never be forgiven for this. We saw this kind of abuse by the person who coined "Ethical Source" and sought to extinguish Software Freedom (even the first freedom) under the guise of "ethics" (however that's judged... by whoever's standards). People were being chased out of projects (or abused, demonised etc.) for completely unrelated activities, even things that are decades old. Drupal and Mozilla had similar scandals (maybe we can elaborate on those some other day). To quote Vaxry: "Now, you might agree with Lyude here, or you may not agree. That does not matter. What matters is that you can see someone in a position of power (spanning across the X.org board, the Freedesktop CoC board, and a RedHat employee) abusing their power to enforce their own CoC outside of where they are allowed to - the size of their project does not equip them with the power to enforce their set of rules over unrelated projects." As a reminder, the person who keeps harassing my wife and committing hate crimes against her had_the_audacity_to_phone_her_employer. This kind of thuggery is why even Mastodon/Fediverse, not just Twitter, gives_them_the_boot. As our associate explains: "It's all about censorship, but ultimately about control over the projects and wresting it away from the skilled people and into the hands of those controlled by hostile interests." Quoting Vaxry: "Regardless of what some people might say about me, I focus on writing good code, and don't go around and discriminate people based on who they are and what they believe." It is this thing "which puts him squarely in their crosshair," the associate adds. "However, I have not read the social control media / discord posts in question. I won't get around to that because it would be too much politics for me to try to track." It's actually another reason not to even bother with social control media and why I_quit_participating_4_years_ago. It's mostly a liability as context is lacking and "brigading" is encouraged (rewarded). "However," the associate concludes, "where do the CoC wavers have the right to block people arbitrarily for stuff that happens off-list or outside the project anyway. I suspect that the CoC wavers are in the wrong but even if not wrong, stuff outside the project is outside the project." We object to the CoC culture because we've seen it abused countless time, also by the Linux_Foundation. There are many utterly disturbing examples of tactless enforcement. Some became "viral", but many go under the radar undetected, just like patent trolling. Vaxry says: "It's a shame to see such an important pillar of the modern Linux desktop, Freedesktop, in such a state. "I truly hope it can improve with time, regardless of whether I am a part of it or not. I really do hope so. Not because of me, but because of all the past and possibly future instances of similar behavior. "If anyone here is marring the reputation of Freedesktop, unfortunately, in my opinion, it's you, Lyude." Based on what I've read there, it boils down not to code. Not by a long shot. Maybe they should worry about real issues like gaping holes (or even deliberate back doors) in the code rather than people's whims and moods. "DeVault seems to use the exact same tactics as the others attacking FOSS," the associate said in hindsight. "Is he that confused or just malicious?" "Either way, he does seem to have lost it completely and may end up "offline" completely for a few weeks or months. He had been a reasonable developer and AFAIK a decent person before flipping out and losing contact with reality." In the meantime corporations like Google and IBM solidify their power over the Free software stacks, often removing their originators and leaders in the process. Is that the endgame? And wait, it gets worse. Microsoft is joining from behind. They are all "partners" now. Notice how the FSF has not bothered to even mention (or promote) Richard Stallman's 5 talks across Europe in recent weeks. Does the FSF try to distance itself from its own founder due to the relentless_campaign_of_defamation? █ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣤⢤⣠⣤⣤⡄⣤⣤⣤⢤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⣤⣤⢠⣤⣤⣠⡄⡤⣤⣠⣤⣤⢠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠓⠛⠞⠓⠉⠛⠄⠙⠛⠸⠚⠛⠐⠚⠚⠚⠛⠚⠓⠛⠛⠊⠹⠛⠛⠛⠛⠓⠫⠛⠚⠛⠃⠙⠛⠛⠛⠛⠚⠛⠓⠙⠛⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠘⠛⠋⠛⠛⠛⠛⠘⠛⠘⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠚⠃⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠘⠃⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 951 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/04/11/How_Kosovo_won_DebConf21.shtml Gemini version at gemini://gemini.techrights.org/n/2024/04/11/How_Kosovo_won_DebConf21.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ How Kosovo won DebConf21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024 [Article 3 years old] Reprinted with permission from Daniel_Pocock. On 20 February, the DebConf team announced that Kosovo_will_host_DebConf21_in the_summer_of_2021. DebConf is an annual, week-long conference of Debian Developers, typically attracting between 300 and 600 people to a different host city each year. The DebConf21 win is a strong endorsement of the work done by local groups including FLOSSK, CoderGals_Kosovo and Toastmasters. FLOSSK operate the amazing_Prishtina_Hackerspace and they have been running an annual event, Software_Freedom_Kosovo_(SFK) for ten years now. The CFP deadline for SFK 2020 is imminent, please_submit_your_proposal_before_1_March. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇sfk2019 bird⦈ CoderGals Kosovo ran their first Hackathon_for_Girls_in_Prizren,_2017. As a Debian Developer, I've visited and helped organize a number of events in the region covering Albania, Montenegro and Kosovo. At the Digital-born Media Carnival in Kotor, 2017, I was fortunate to meet four students from Kosovo, including Albiona and Qendresa Hoti, who told me about their plans to run a hackathon in Prizren. They invited me to attend as an advisor to their event and this was a great opportunity to see the possibilities in Kosovo. During the hackathon, I could see that the two main strengths of their group were their commitment to team work and the quality of the presentations on the final day. We collaborated on a number of events together: * CoderGals_Hackathon_in_Prizren,_2017 * Prishtina's_first_Mini_DebConf_and_Fedora_Women's_Day_in_2017 * MiniDebConf_Tirana * Debian_booth_at_OSCAL * joint_meeting_of_the_Prishtina_Hackerspace_and_SHRAK,_Kosovo's_amateur radio_society * SFK_2019 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Enkelena and Amire⦈ Three of the young women from Kosovo were successful in being selected_for Google_Summer_of_Code_in_2018 and a number of women from the region also received diversity bursaries to attend DebConf18 (Taiwan) and DebConf19 (Brazil). After their success in GSoC, I went down there personally to welcome them to the program. Based on my observations from that first event in Kosovo, the hackathon, I felt that many of the students would immediately be able to apply their teamwork and presentation skills with regular Toastmasters meetings. We couldn't find any official group in Kosovo or Albania through the Toastmasters_club_search so I suggested starting a new one in the Innovation_Centre_Kosovo_(ICK). The ICK has been an indispensable partner in this activity. Among other things, their publicity unit helped us bring Toastmasters to Kosovan_TV. 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Toastmasters_Prishtina⦈_ After a number of Toastmasters meetings in ICK, it was Albiona Hoti and Enkelena Haxhiu who jumped up at DebConf19 in Brazil to launch a surprise bid for DebConf21 at the last minute. Here_is_their_presentation_(fast_forward_19: 30). Enkelena has been particularly attentive in following through on the relations with the DebConf team over the last six months, engaging FLOSSK in the bid, documenting_the_bid_on_Debian's_wiki and establishing Kosovo's strengths to host the event. Albiona has been a key part of the team that is bootstrapping the new Toastmasters group. It has been a privilege for me to mentor and collaborate with a number of these young leaders on this journey. █ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡅⠀⠘⠇⠐⢾⣿⣿⣿⣿⢰⣸⢿⣾⣷⢤⡀⠻⣿⣗⡁⠀⠀⢑⣄⠿⠁⣰⠉⢀⣖⣯⡯⡻⢿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⠃⠈⡯⡂ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠃⠀⠀⠀⠐⠊⢿⣿⣿⣾⡚⣾⡽⣻⣿⢻⡧⣄⠀⠁⠀⠀⠀⢀⡠⠐⠔⠊⠀⡼⣷⡟⢺⢞⣷⣿⣿⣿⡿⣯⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣟⠻⠟⠛⠁⠀⠈⠙⢱ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢀⠀⠀⠀⠀⠀⡀⠈⡛⣿⣏⠃⠵⣻⡿⣛⠭⣛⠗⣄⠡⠀⠀⠁⠀⣀⣄⠁⠀⣛⣪⡙⣹⣻⣫⡿⣫⣿⣾⣮⣯⣯⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⣶⣶⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠆⢀⠀⠀⠀⠀⡜⠮⠉⡀⠮⠁⠢⡣⣨⠷⠀⣽⡇⠄⠀⢖⠐⠾⠋⠀⢨⢸⣿⣺⣾⢱⣽⢿⣯⣿⣿⣿⣽⣾⣿⣿⠟⣿⡾⣿⢿⣿⣿⣿⣿⣿⣿⣼⣿⣻⢻⣿⣿⣿⡤⡂⡹⣣⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢥⠀⠀⠀⠀⡨⠁⢩⢀⡇⢱⡿⢐⣡⠨⣠⢝⣿⠇⠑⠀⡞⣺⠕⠀⢠⢲⣿⣫⡫⠾⣟⡽⣿⣿⣷⣿⣿⡾⣳⣛⢿⡝⣙⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣧⣭⣾⣾⣯⣿ ⣧⠿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠐⢿⠬⢂⣤⣤⣄⠈⢈⢿⡀⡻⢤⡟⣡⣜⠎⢌⠃⠀⠀⢘⣥⠇⠀⡺⣿⡴⣯⡤⣰⡗⢻⡿⠿⣿⣮⣿⣿⣻⣿⣿⣿⣷⢯⣿⣿⣿⡇⣇⣏⡾⡿⣿⣿⣿⣟⣿⣷⡽⣿⣿⣿⣿⣿ ⠟⠛⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠉⢻⣿⣿⣷⣷⣅⣩⣿⣶⣷⣦⣤⡀⠀⠀⠠⢥⣶⠀⢀⢿⢫⡷⣷⢫⢹⣽⡿⣵⣿⡳⢾⡏⣟⣟⡯⣻⢻⣵⡷⣿⣿⣻⣧⣿⣇⣷⣾⣿⣯⣽⣿⣿⣿⣿⣊⡻⣿⣿⣿ ⠓⠲⠶⠶⢶⣴⣬⣭⣭⣉⣜⣛⡛⠛⢩⣿⣿⡀⠈⣿⣿⣿⣿⣿⣿⡿⣿⢻⣻⣿⢵⠀⠀⠀⣫⡡⠀⣼⣖⣯⣟⠟⢸⡯⣯⡽⣿⢾⢟⣮⣳⡣⠓⣃⣿⢿⠿⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣥⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠻⣿⣧⣦⣼⣿⣭⣄⣐⣻⣷⣼⣼⣕⣿⡻⢠⡀⠀⣹⠀⣸⢧⣿⣟⡵⣿⣳⣾⣿⣟⣶⣞⢷⣿⣯⡇⡡⣿⡾⣧⣻⣴⣷⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠈⠛⠛⠋⠀⠀⠠⠤⠀⠻⣿⣿⡿⠋⠸⠰⠀⠈⢁⡈⣩⢟⣿⣟⣿⡿⣵⣶⡯⣾⢟⣯⢷⣿⣿⣿⣿⣼⣏⣭⡽⢾⢿⣷⣿⣿⣿⣿⣿⣿⡟⢛⣛⣛⣛⣿⣿⣿⣿⣿⣯⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡳⣞⣙⣋⢪⣛⠟⡿⠷⢿⠇⣿⡺⢷⣿⣽⣿⣵⣷⣽⣋⣿⣣⣿⣿⡽⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⡋⠠⠗⢟⠟⡃⡝⠴⣽⣮⠾⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣛⣿⣿⣻⣷⣿⣛⣘⣿⣿⣬⣥⣜⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣓⢘⡔⢢⣀⡩⣠⡵⣞⣟⣝⢾⣻⣾⡟⣾⣹⣿⣻⣿⣿⣵⣿⣿⡿⣫⣿⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣟⣛⠛ ⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠋⣬⡿⢿⣿⣵⣽⡯⣞⣶⣾⣿⣗⣜⣠⢷⣿⣿⣽⣿⣿⣿⣏⣿⣿⣿⣿⣹⢭⣯⢹⡯⢻⣿⣿⣿⣿⣿⠚⠛⣽⣿⣷⡇⣹ ⠀⠠⠤⠄⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡆⠷⠿⠾⢾⣿⣿⣿⣿⣾⢿⣯⣿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠆⢘⣻⣿⣿⣇⣿ ⠉⠉⠉⠛⠛⠒⠒⠒⠶⠤⢤⣀⣀⣠⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠱⠇⠶⠦⠄⢘⣿⡽⢿⡕⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⢶⡆⣲⢲⡆⣀⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠻⣟⢨⣼⠀⠀⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡤⠆⠀⠀⢀⣨⣇⠇⢸⣿⢸⣿⡿⢿⠿⠿⠿⠿⠿⠿⣿⣿⣿⢿⣿⣿⠿⠿⠿⣿⠿⠿⣿⣿⣿⣿⣁⣀⣂⡀⣐⣉⡏⠅⠩⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠀⠀⠙⢏⠀⠀⣻⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣄⣀⢀⣸⣿⣿⡂⢸⣿⣿⣿⡇⣿⣷⠀⢀⢀⡀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢫⠍⡍⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣿⢿⣿⡇⠀⠀⠀⠀⠁⠀⠠⠴⣶⡧⠿⠿⠿⠟⣛⡁⣤⣤⠹⡿⡃⣿⣿⠀⠀⠀⢰⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⢿⣇⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣽⡾⠿⠀⢰⠀⢀⡀⢀⠀⠈⠈⣛⡆⠀⠀⠀⠙⠿⠇⠛⠉⠀⠚⢃⣸⣿⣰⣶⣌⣺⣸⡿⣿⡏⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⠀⣀⡤⣄⣠⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠨⠯⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⢰⡻⠃⠀⠀⠀⠀⢀⠂⠀⠀⢰⡖⢳⢣⣆⣀⣀⣀⣸⣶⣿⣇⠀⣀⣠⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣰⢟⡇⣿⣿⠠⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠀⢀⡇⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣟⣿⣷⣷⣶⣶⡶⣶⡌⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠒⠣⠘⣁⢿⡇⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣯⣭⣭⣿⣧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡟⠛⡿⠉⢷⠤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠨⠀⠀⠀⠰⠂⠀⠀⢜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⣿⣿⣿⣿⣿⣟⣛⣓⣸⣿⣿⠀⢱⠀⠀⠀⠀⠀⠀⡸⠿⠍⠁⠀⠀⠀⢐⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⡷⠢⠀⠀⠀⠀⠀⠀⢶⣶⣾⣶⣶⣶⣶⣶⠀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⢠⡀⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⠀⠀⠀⢀⠀⣠⣿⣿⣆⣀⡀⠀⠀⣾⣦⣦ ⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠾⣧⣺⣁⣴⡇⠀⠀⠀⣠⣿⣿⣷⣾⣿⣿⣿⣿⣿⡔⠀⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣾⢿⢿⡿⣷⠿⠿⠿⢿⣽⣫⣍⣽⣿⣇⣘⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿ ⡶⢿⡾⢿⡿⢿⡿⠿⠿⢻⣿⣻⣟⣻⣟⣿⣟⣟⣛⣛⠛⣛⣙⣋⡛⣯⣿⣽⣯⣭⠁⠀⡶⣥⠽⠛⠓⢛⣚⣓⣓⣶⣶⣧⣭⣭⣭⣭⣭⣭⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠍⠿⠏⠉⠀⠀⠙⢃⣀⣭⠍⢠⠶⡶⠿⠿⠿⠿⠿⢇⣿⠿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠩⠍⠋⠉⠉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠛⡛⣹⢛⡡⠷⢠⠤⢵⢬⠩⠩⡥⡿⣛⣻⣟ ⣤⣤⡤⣤⣤⣤⣤⣄⣀⣂⣀⣀⣀⣠⣤⣀⣤⣠⣤⣀⣀⡄⠀⢤⠦⠀⡠⡀⣀⣀⣄⢀⡀⠀⠠⠄⠀⠀⠁⢃⡠⣴⣀⣠⣶⣤⣦⣠⣖⣒⣢⣐⣞⣆⣰⣴⣄⣔⣲⣞⣥⣥⣦⣦⣿⡿⣦⣜⣛⣻⣍⣛⣭⣯⣶⣾⣮⣯ ⣿⣭⣦⣭⣮⣛⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣷⣿⣶⠿⣟⣻⣻⣇⣂⣾⣷⠢⡬⠵⢾⣜⣯⣶⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣯⣭⣿⣿⣭⣟⣻⠟⠻⠿⡺⢿⠿⠿⣻⠻⠿⠽⢷⣿⣿⣟⣛⣟⣿⣿⣿⣙⣿⡿⠿⢿⣽⣿⣿⡿⠿⠽⠿⢿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣦⣤⣄⣀⣈⣉⠁⠀⠉⠙⠓⠺⠻⢺⣿⣿⣿⣔⣛⣲⢿⠍⢻⢯⠬⡯⠱⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢉⣿⣯⣽⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣹⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⣿⣿⣿⣿⠓⢻⣿⣿⣿⣿⣿⣿⡿⡿⣿⡿⢿⣿⡛⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⢰⠀⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣾⣷⡀⠀⠀⠈⢠⡟⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠀⢻⣿⡍⢉⣭⣥⣿⣿⣿⣿⣷⣲⣒⣒⣚⣒⣒⠾⠗⠞⠳⠆⠠⠩⠭⠭⣿⣻⣭⣯⣽⣽⣭⣭⣥⡠⠻⡇⠀⢿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠁⠀⣀⣤⣤⡄⠘⣿⣿⢸⣿⣿⣿⡇⠃⠀⣿⣿⣿⣿⣿⢢⣀⡀⠀⠀⠀⠀⢈⣿⣿⡿⠇⠀⠐⢚⣽⣿⣿⣿⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⡇⠀⠀⠀⠀⠀⠀⣠⣄⠀⢸⣿⣿ ⣶⣲⣾⣿⣿⣿⣿⣿⣿⠀⠿⢿⠁⠀⠈⠁⢀⣿⣏⣿⣿⣿⢿⠁⠀⢀⣿⣿⣿⣿⣿⣮⣿⣇⡀⠀⠀⠈⢸⣿⣿⣷⣶⡀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣛⣧⢰⣦⣀⣼⣤⣾⣿⣿⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡀⠀⠀⠀⠀⠀⠙⠋⠚⠿⠿⠏⠀⠀⠀⣾⣿⣿⣿⣿⡿⠘⣿⣿⣧⣬⣶⣾⣾⣿⣿⣿⣿⣟⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⠈⣿⣿ ⣿⣿⣿⣯⣻⣿⣻⣿⣻⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿ ⠀⠈⠙⠸⠾⠃⢹⣿⣿⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿ ⢀⣀⣤⣴⣶⣾⣿⣿⣏⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢍⠙⠻⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢥⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠃⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿ ⣿⡿⠿⠿⠟⠛⠛⠑⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⣶⣤⣤⡄⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿ ⠀⠀⠀⠀⠈⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣽⠿⠛⢿⣿⣆⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿ ⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠈⢁⣥⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠐⠀⠉⢟⢻⣿⣿⣿⣿⣿⡿⣋⣩⣙⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹ ⠈⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡉⠉⠻⣿⣿⣿⣿⣿⣯⢻⣦⡀⠀⠰⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸ ⠀⢀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡿⠿⠶⠽⠛⠛⠻⠿⠛⠛⠋⠛⠻⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠐⠉⠉⠉⠻⣿⣿⣿⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠭⠀⠙⡄⠀⠀⡀⠄⠀⠀⠠⠄⡤⣤⣤⣶⣶⣶⠤⡀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡤⣖⣯⣤⣤⣤⣤⣤⡀⠀⠀⠌⢺⣿⣿⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠁⠀⠀⢠⡁⠀⠁⠀⠀⠀⠤⠝⠻⣮⣌⢻⣿⣿⣿⣿⣷⠀⢀⢀⠈⢉⡀⢐⢊⡢⠖⠋⠉⠪⣙⢛⣛⣻⣿⣿⣥⣄⣀⣤⣶⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠏⣭⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠁⠀⠀⡰⠋⠀⠀⡠⠀⠀⠀⠀⠀⠀⠯⢿⣷⣝⢯⡉⠀⠠⠀⠰⠝⠻⠥⠶⠺⠉⠀⠀⠀⠀⣦⣬⣆⠟⠛⠻⠯⣍⣭⣶⣿⣿⣿⣿⣿⡆⠀ ⣷⢄⠀⠀⠀⠀⣴⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⣰⣪⠄⠶⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣿⣷⣶⣬⣉⡯⠉⢣⣵⣆⠄⠀⠀⠀⠀⣴⣿⣿⠏⠀⣼⠂⠲⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⠿⢁⣄⡀⠀⠚⣿⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢲⣤⣤⣯⣶⣶⣶⡿⣀⠉⠀⠀⠀⠀⠀⢰⣿⣿⣯⠇⣀⠏⠀⣤⡙⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣴⢋⣾⣿⣿⣦⡀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠐⠘⠛⡋⣿⣉⣽⣿⣛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣾⣿⡜⣿⣿⣿⣿⣿⣿⡇⠀ ⣡⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠰⢄⠑⠵⣄⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣴⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠟⠛⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⣀⣀⣠⣤⣤⣼⣿⣿⣷⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 1147 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/04/11/IRC_Proceedings_Wednesday_April_10_2024.shtml Gemini version at gemini://gemini.techrights.org/n/2024/04/11/IRC_Proceedings_Wednesday_April_10_2024.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Wednesday, April 10, 2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Karkloof_waterfall_against_a_sheer_rock_face⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GN 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNOME_Gedit⦈_ #techrights_log #boycottnovell_log 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GN 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNOME_Gedit⦈_ #boycottnovell-social_log #techbytes_log =============================================================================== The corresponding text-only bulletins for_Tux_Machines and for_Techrights contain all the text. Enter_the_IRC_channels_now ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⡿⠿⡿⡛⣃⢻⣿⣿⣿⣿⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡿⡿⠏⡏⠙⣿⣿⢟⣤⣷⡿⣯⣼⣿⢿⣿⢿⠿ ⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣛⣳⣿⣷⣿⣿⣿⣿⣷⣤⣼⣷⣿⣆⣿⣿⣯⣟⠟⠉⠛⣾⣿⣷⡁⠔⠓⡗⠂ ⡎⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠛⣦⡈⠈⣿⠿⡻⣽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⡿⣏⣈⣿⣿⣗⣰⣿⠟⠙⣋⠃⠶⣾⡷⠛⣋⣀⠨⡉⠀⣴ ⡀⡨⣿⣯⣿⣶⣿⣿⣿⣿⣿⣿⢨⡛⢂⠀⠻⢶⠨⠬⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣏⠛⠻⣮⣅⠠⠥⠐⢷⢿⣿⡿⠿⠂⠷⠋⠄⠂⠤⣚⠿⠟⢧⡚⡭⠉⢀⢤⡘⠉⠀⠡⠂⢘⣡⠀⡜⠑⣀⠹ ⣴⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠑⠃⣶⣂⠠⠠⠕⢾⣿⣿⣿⣿⣿⡿⠌⠲⢿⣿⣭⢰⣶⣶⣶⢯⣿⣣⣂⠤⣘⡿⢶⠄⠟⣇⡜⠀⠀⠠⣺⡿⠀⡠⠔⠀⠁⠛⣁⡀⠄⠁⠂⠟⠸⠣⢠⣄⠉⡰⠛⠉⠀⢀⣠⠵⢫ ⣯⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡀⠀⠀⠀⠁⠀⠐⠐⢻⡿⣿⣿⣿⣿⣗⠙⢧⣵⢆⡚⡹⢿⣿⣿⠾⠿⡟⣿⣷⣨⠟⠀⠀⣄⠘⢀⠂⠀⠂⠀⠰⠞⠀⠤⠖⠐⠏⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⣠⣭⠀⠀⠠⠊⠀⠨⠉ ⣿⣯⣿⣿⣿⣿⢿⣿⡋⢹⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢸⡧⠶⣿⣿⣿⡷⠀⠀⠀⠀⠟⠿⠟⣧⠿⢻⣷⣤⣬⣏⢠⣤⣾⠟⠛⠧⢒⠾⠄⠀⠠⠛⠒⠰⠀⠀⠀⠀⠀⠀⠤⣞⡋⠀⠀⠀⡀⠠⠁⠀⠀⠀⣐⠂⠀⠀⠀ ⠈⠘⢤⣩⡿⠛⠁⠄⢙⣿⡉⠹⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⢀⣿⣿⣿⡏⠀⠀⣤⡬⠒⣾⣾⠇⠀⠀⠉⠁⠈⠀⠐⢀⠁⠈⠉⠉⠉⠀⠀⠀⠀⠤⠀⡀⠑⠀⢿⠳⢀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠶⠎⠠⠐⣀⠀ ⠠⢍⠀⠄⠡⠀⠀⠀⠈⢫⣙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠒⣉⣁⠄⢠⡛⠋⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠈⠁⠤⠆⢠⣤⣶ ⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠰⠚⠉⠀⠠⠤⢀⠈⠀⠀⡢⠀⠁⠀⠀⠉⠀⠀⠀⣤⣀⣠⡿⢿⣿ ⡈⢢⢀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠡⠐⡐⠀⢤⡄⠀⠀⠀⠀⣤⡬⣾⣟⠵⣯⣷⠾⠉ ⠀⠂⢢⣎⣷⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠂⣦⠍⠟⡁⠃⠀⡄⢧⠴⢻⣋⡐⠀⠄⠈⠁ ⢓⠀⠀⠨⢏⡄⢈⣵⣀⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠔⠐⠀⠈⢁⠀⠁⣈⠀⠤⠀⠀⠠⠂⠀⠀⢀⡀⠤⠔⠒⣂⡀⠀ ⢢⡙⡃⠀⠄⠂⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣯⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⡤⠚⠁⡀⣠⢤⣶⣦⢤⠐⡄⠈⠀⠀⠀⠀⠀⠈⠉ ⢨⠀⠀⠸⠂⠃⠒⢀⠀⠀⠀⠢⠀⠀⠀⢀⠦⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣠⢶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠚⠉⠑⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠈⠁⠀ ⠀⠐⣴⠂⡀⠀⡈⠺⢒⢤⡄⠀⠀⠀⠀⠠⠀⢀⢀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠤⠀⠄⢀⡀⠀⠀⣀⠐⢈⣹⡤⠀⡤⠀⠲⡈⠀⠀⠀⠀⠀⠐⠤⠀⡄⠒⠀⠀⠂⠀⠀⠀⢀⡤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡊⠀⠀⣉⠁⠑⠠⢄⡏⠉⣐⣄⣀⠐⠀⠀⠈⠀⠀⠀⠈⠈⠀⠉⢉⠉⠉⠀⠀⠀⡀⠄⠒⡀⡤⣤⠤⣄⣶⣶⡮⠁⠨⣠⡂⠢⠂⠈⠀⠂⡀⠁⠀⠂⠀⠀⠀⢀⢀⣠⠤⠀⢀⣀⠄⠋⠉⠈⠀⠀⠂⠀⠀⠀⠀⠀⠰ ⠸⢿⡆⠀⠀⠀⠀⠀⢈⠟⣹⠶⢷⣧⣤⠠⠀⠀⠀⠀⠀⠒⠄⠀⠐⢹⡮⠛⠒⠦⠀⣐⡃⠝⠉⠋⠙⠁⠝⣟⠻⡰⣿⣾⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠐⠁⠀⠠⠦⠀⡡⠴⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 1373 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/04/11/Over_at_Tux_Machines.shtml Gemini version at gemini://gemini.techrights.org/n/2024/04/11/Over_at_Tux_Machines.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Over at Tux Machines...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Bunch_of_orange_Lilies_in_a_cascading_bouquet⦈_ ⚓ Updated This Past Day⠀⇛ 1. ⚓ SiFive_Unveils_HiFive_Premier_P550:_A_RISC-V_Development_PC_with_Linux 6.60_Support⠀⇛ SiFive and Canonical are teaming up to optimize Ubuntu Linux for the HiFive Premier P550, ensuring a smooth experience for developers ⚓ New⠀⇛ 2. ⚓ Linux_continues_to_be_above_4%_on_the_desktop⠀⇛ According to the StatCounter, Linux on the desktop has continued to rise and remains above 4%, with this being the healthiest it's ever looked on the desktop 3. ⚓ Gentoo_Linux_becomes_an_SPI_associated_project⠀⇛ Gentoo Linux, as a collective of software developers, is pretty good at being a Linux distribution ⚓ New⠀⇛ 4. ⚓ Windows_in_Pakistan:_Down_From_98%_to_69%_in_10_Years_(on_Desktops/ Laptops) [original]⠀⇛ based on data from statCounter ⚓ New⠀⇛ 5. ⚓ today's_leftovers⠀⇛ a small mix of remaining links 6. ⚓ Windows_TCO_Stories⠀⇛ Windows TCO: the real cost of Microsoft 7. ⚓ Open_Hardware:_Arduino_and_Raspberry_Pi⠀⇛ hardware related items 8. ⚓ Security_Leftovers⠀⇛ Some incidents and bugs 9. ⚓ today's_leftovers⠀⇛ a collection of relevant stories 10. ⚓ Mozilla,_Rust,_and_More⠀⇛ Some Mozilla news 11. ⚓ Security_and_Windows_TCO_Leftovers⠀⇛ Windows TCO: holes 12. ⚓ today's_howtos⠀⇛ some howtos for today, more in a number of hours 13. ⚓ Android_Leftovers⠀⇛ ‘Pixel Experience’ Android ROM shuts down new builds after nearly six years 14. ⚓ Stable_kernels:_Linux_6.8.5,_Linux_6.6.26,_Linux_6.1.85,_and_Linux 5.15.154⠀⇛ I'm announcing the release of the 6.8.5 kernel 15. ⚓ Default_wallpaper_has_common_path_across_openSUSE,_SUSE⠀⇛ We will be newly using png for the default wallpaper set on openSUSE Tumbleweed and upcoming versions of openSUSE Leap and Leap Micro 16. ⚓ Best_Free_and_Open_Source_News⠀⇛ Only free and open source software is eligible for inclusion 17. ⚓ Dynebolic_is_a_portable_Linux_distribution_that_can_be_used_without installation⠀⇛ Dynebolic is back after a 10-year hiatus 18. ⚓ BSD:_OpenBSD_on_DigitalOcean_and_undeadly.org_turns_20⠀⇛ Some OpenBSD news 19. ⚓ today's_leftovers⠀⇛ FOSS centric articles 20. ⚓ Programming_Leftovers⠀⇛ development and coding 21. ⚓ Hardware:_BBC_Micro,_Swiss_Light_Source_SLS,_and_Raspberry_Pi⠀⇛ mostly open hardware 22. ⚓ today's_howtos⠀⇛ 4 howtos 23. ⚓ Games:_Video_Games,_DOS_Games,_and_GNU/Linux_Games⠀⇛ Some handful of stories 24. ⚓ Windows_TCO_Leftovers⠀⇛ Windows causing major blunders 25. ⚓ Android_Leftovers⠀⇛ How to save deleted files on Android using Stellar Data Recovery 26. ⚓ Open_Source_Self-Hosting_And_Mail_Server⠀⇛ Excitingly, just a month after the server code was open-sourced 27. ⚓ LXQt_2.0_Gears_Up_for_Wayland:_What’s_Ready_and_Next?⠀⇛ LXQt 2.0: A Wayland journey begins. Not fully ready, but a significant step toward a comprehensive Wayland experience in LXQt 2.1 28. ⚓ Celebrating_Creativity:_Announcing_the_Winners_of_the_Kubuntu Contests!⠀⇛ We are thrilled to announce the winners of the Kubuntu Brand Graphic Design contest and the Wallpaper Contest 29. ⚓ GNOME_46:_Does_It_Make_the_Switch_to_Linux_Worth_It?⠀⇛ Could GNOME 46 seal the deal on switching to Linux 30. ⚓ Netplan_1.0:_Canonical_Makes_Network_Management_Simpler_and_Secure_for Ubuntu⠀⇛ Netplan utility is the next generation of network management for Ubuntu and Debian 31. ⚓ Linux_vs_Windows_AES_performance_to_be_intriguing_as_Google_boosts_AMD and_Intel⠀⇛ The latter has not had the cleanest track record though as CPUs with VAES from both AMD and Intel were found susceptible to potential data damage 32. ⚓ 7_Reasons_Why_I_Prefer_Linux_Over_Windows_for_My_Desktop⠀⇛ Windows is good, but Linux is better when it comes to desktops 33. ⚓ Variscite_DART-MX95_SoM_–_Edge_Computing_with_dual_GbE,_10GbE,_Wi-Fi_6, and_AI/ML_capabilities⠀⇛ Variscite has confirmed support for a wide range of operating systems such as Yocto, Android, Debian, Boot2Qt, and FreeRTOS, for different development needs 34. ⚓ Best_Free_and_Open_Source_Scala_Static_Site_Generators_And_Useful_Free Linux_Network_Tunnels⠀⇛ All of these tools are released under a freely distributable license 35. ⚓ Today_in_Techrights⠀⇛ Some of the latest articles ========================================================================= The corresponding text-only bulletin for Wednesday contains all the text. 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Some_superb_people_had_been_fired_(IBM_priorities)_and_some_of those_promoted_lacked_technical_background. You can't expect geeks to take instructions from people_like_these. Now there's a change of leadership in Debian because DPL Carter decided to pass the baton [1, 2] and one_candidate stands out as conspicuously nontechnical (yes, that's a word). I've decided to cover the issue in video/audio as this way it's harder to take people's words out of context or 'mis-comprehend' (misinterpret maliciously or not) people's tone/intention/motivation. I'm typically sincere in my writings; I don't self-censor or mince words, but in videos it's generally harder to distort what people say (or said). The licence can hopefully prevent people 'clipping' things out of context (not that's I'd bother with legal enforcement, it's more like a "gentleman's_agreement"). There's still a voting process taking place (the only "media" coverage we've found about it says "Two_developers_in_running_for_post_of_Debian_project leader"). We do not vouch for one (or none) horse in this race; the video does not even name the candidates, but we insist that there's a needs for diversity, specifically init diversity, just like some distros let people choose between Wayland and XOrg or between various renders. Monoculture is a bad thing in nature; the same is true in computing. Software diversity is important because it makes us robust to situations like dead developers or fatigue/neglect in some projects. We_saw_that_in_xz_recently. █ ⠀⠀⠀⡏⢰⠀⠢⠀⢢⠀⡐⡄⡆⡄⠀⡇⢀⠀⢀⢢⠀⠈⡏⠀⠢⡀⠂⡇⡄⡆⡄⡇⠔⢀⢢⢸⠀⢸⠱⠠⢢⠢⢸⠀⠢⡀⠂⡖⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠂⠀⡂⠀⢺⣿⣿⣷⣿⣟⡟⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠁⠈⠉⠈⠁⠀⠉⠁⠁⠁⠀⠁⠉⠀⠈⠉⠀⠀⠁⠈⠉⠈⠁⠁⠁⠁⠁⠁⠉⠈⠉⠈⠀⠈⠀⠀⠈⠉⠘⠈⠉⠈⠁⠩⣠⡄⠀⠈⠉⣍⣭⢹⣿⣿⡇⠋⠀⠀⠀⠛⠻⣿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣻⢿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⣴⣶⣶⣶⣶⣶⡄⠐⢶⣶⣾⣿⣿⡿⣿⡢⡠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣀⡀⣀⢀⣀⡀⢡⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⠉⠉⠉⣿⣏⣿⣿⣿⣷⣿⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠚⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣄⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣤⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠈⠸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡆⢰⢠⣠⠠⢠⠀⣀⡄⡄⡄⠀⡅⣀⠀⢠⣠⠀⠀⡆⢠⣠⡠⠀⡇⡄⡄⡄⡅⠄⢀⣠⢸⠀⢰⠰⠠⢠⠠⢨⢠⣠⡠⠀⡆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⠂⠒⠂⠀⢚⣟⣿⣿⣛⣟⡛⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠁⠁⠈⠈⠈⠀⠀⠁⠁⠁⠁⠀⠁⠈⠀⠈⠈⠀⠀⠁⠈⠈⠈⠀⠁⠁⠁⠁⠁⠁⠈⠈⠈⠀⠈⠀⠀⠈⠈⠘⠈⠈⠈⠀⠡⣠⡄⠀⠈⠉⣍⣭⢹⣿⣿⡷⠛⠖⠀⠈⠻⠿⣿⠿⠟⠁⠀⠀⠀⠀⠉⠙⣻⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⣴⣶⣶⣶⣶⣦⡀⠐⢶⣶⣾⣿⣿⡇⣟⣗⡑⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⣀⠀⣤⡀⢩⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⡄⠁⠉⠉⠉⢿⣗⣿⣿⣿⣿⣿⣄⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣾⣶⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣤⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡔⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡆⢢⢠⣤⠠⢄⠀⣤⡄⡤⡄⠀⡄⣤⠀⢠⣤⠀⠀⡆⢠⣤⡠⠄⡦⡄⡤⡄⡄⠤⠠⣤⢰⠀⢰⡰⠠⢤⠤⢠⢠⣤⡠⠄⡦⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣃⠒⠒⠀⢘⣿⣿⣶⣳⣿⡟⠀⠀⠋⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠁⠈⠈⠀⠈⠈⠀⠁⠁⠁⠁⠀⠁⠀⠀⠈⠈⠀⠀⠁⠈⠀⠀⠀⠁⠁⠁⠁⠁⠁⠈⠈⠈⠀⠈⠀⠀⠈⠈⠜⠈⠀⠀⠀⠡⣠⡄⠀⠈⢩⢩⣭⢹⣿⣿⡷⢒⠅⠀⠀⠟⠿⡿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⣴⣶⣶⣶⣶⣦⡀⠐⢶⣶⣾⣿⣿⡇⢾⡪⡱⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⣀⠀⣠⡀⣡⣬⣷⣾⣿⣿⣿⣿⣿⣿⣿⡄⠁⠉⠉⠉⢻⣷⣿⣿⣿⣷⣿⣤⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣤⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡒⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡖⢢⢠⣄⠠⢄⠀⢤⡄⡤⡄⠀⡆⡤⠀⠠⣤⠀⠐⡖⢠⣄⡠⠄⡦⡄⡤⡄⡆⠤⠠⣤⢰⠀⢰⡲⠠⢄⠤⢰⢠⣄⡠⠄⡦⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣄⠖⠒⠀⢒⣿⣿⣿⣶⣿⡷⠀⠀⠉⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠓⠈⠀⠂⠀⠊⠀⠑⠁⠃⠁⠀⠃⠂⠀⠈⠚⠀⠀⠃⠀⠂⠀⠂⠃⠁⠃⠁⠃⠑⠈⠊⠘⠀⠈⠀⠀⠈⠊⠼⠀⠂⠁⠀⠡⣠⡄⠀⠈⢉⢭⣭⢹⣿⣿⡷⠚⠖⢠⠀⠛⠻⠟⠿⠟⠁⠀⠀⠀⠈⠋⠙⣛⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣴⣶⣶⣶⣶⣶⣄⠀⠲⣶⣾⣿⣿⡆⣾⡛⡡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⠀⣀⠀⣠⡀⣠⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆⠁⠉⠉⠉⣾⣷⣿⣿⣾⣷⣾⣤⣦⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠏⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣴⣤⣀⣀⣴⣶⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣤⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⡒⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣛⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡖⢢⠀⢄⠀⢄⠀⠠⡀⡤⡀⠀⡆⠤⠀⠀⢄⠀⠒⡖⠀⢄⠀⠄⡦⡀⡤⡀⡆⡠⠀⢄⢰⠀⢰⣢⠀⢄⢄⢰⠀⢄⠠⠄⡦⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⡚⡒⠐⢘⣿⣿⣷⣟⣿⡟⠀⠈⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠓⠊⠐⠒⠐⠊⠀⠓⠃⠃⠃⠀⠃⠚⠀⠘⠚⠀⠀⠃⠐⠒⠑⠂⠃⠃⠃⠃⠃⠒⠘⠚⠘⠀⠘⠀⠀⠈⠒⠸⠐⠂⠁⠀⠡⢠⡄⠀⠈⠩⢍⡉⢹⣿⣿⡗⢿⠎⠀⠀⠙⠻⢿⠿⡟⠁⠀⠀⠀⠈⠋⠙⢻⣿⢯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣶⣶⣶⣶⣦⡀⠐⢲⣶⣾⣿⢿⡇⣼⠃⡲⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⡀⡀⣀⡀⣩⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⠉⠉⠉⢻⣿⣿⣿⣿⣷⣿⣼⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣤⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡐⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡖⢠⠀⢀⢀⢀⠀⠀⡀⡀⡀⠀⡂⠀⠀⠀⢀⠀⠐⡖⢀⢀⠀⠀⡆⡀⡀⡀⡂⡀⠀⢀⢰⠀⢰⢢⢀⢀⢀⢐⠀⢀⠀⠀⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢂⠒⡂⠑⢒⣿⣿⣿⣿⣿⡛⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠃⠊⠘⠛⠐⠊⠀⠛⠃⠃⠃⠀⠃⠚⠀⠘⠛⠀⠀⠃⠘⠛⠑⠂⠃⠃⠃⠃⠃⠂⠘⠛⠘⠀⠘⠀⠀⠘⠒⠸⠘⠋⠁⠀⠡⣠⡄⠀⠈⠩⠉⣭⢹⣿⣿⡦⠹⠊⠀⠈⠙⠿⠽⡿⠟⠁⠀⠀⠀⠈⠋⠙⣻⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢠⣶⣶⣶⣶⣶⣶⣄⠀⠲⣶⣾⣿⣿⡏⣾⡾⡣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⣀⠀⢀⡀⣠⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⠈⠉⠉⢺⣷⣿⣿⣾⣿⣿⣴⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⡂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣤⣦⣤⣀⣀⣴⣶⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣤⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣶⣿ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡦⡐⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡄⢄⢀⢀⢀⠀⠀⡀⡀⡀⡀⠀⡂⠀⠀⢀⢀⠀⠀⡄⢀⢀⢀⠀⡆⡀⡀⡀⡂⡀⢀⢀⢰⠀⢠⢠⢀⢀⢀⢐⢀⢀⢀⠀⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢆⠖⠂⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠋⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠃⠊⠘⠉⠐⠘⠀⠋⠃⠃⠃⠀⠃⠙⠀⠘⠙⠀⠀⠃⠘⠙⠑⠀⠃⠃⠃⠃⠃⠂⠘⠙⠘⠀⠘⠁⠀⠘⠐⠸⠘⠉⠁⠀⠡⣠⡄⠀⠈⠩⣭⣭⢹⣿⣿⡷⠃⠖⠀⠀⠙⠿⠿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⡀⠀⢲⣶⣾⣿⣿⣇⢉⡆⡲⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⣀⢀⢀⡀⣨⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠉⠉⠉⢽⣿⣻⣿⣿⣷⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠛⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⠂⣠⣦⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡐⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡤⢄⢀⡀⢀⡀⠀⣀⡀⣀⡀⠀⡀⣀⠀⢀⣀⠀⠠⡤⢀⣀⢀⡀⣄⡀⣀⡀⡀⣀⢀⣀⢠⠀⢠⢤⢀⣀⣀⢠⢀⡀⢀⡀⣄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠂⠲⠒⠀⢘⣿⣿⣿⣻⣿⡓⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠧⠘⠈⠍⠀⠜⠀⠪⠃⠇⠃⠀⠇⠅⠀⠘⠹⠀⠀⠇⠘⠍⠁⠄⠇⠃⠇⠃⠇⠢⠐⠝⠸⠀⠘⠁⠀⠘⠔⡸⠈⠍⠁⠀⠡⣠⡄⠀⠈⢉⢩⣭⢹⣿⣿⡗⠚⠁⠀⠀⠛⠿⣿⠿⠟⠁⠀⠀⠀⠈⠋⠙⢻⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣶⣶⣶⣶⣦⣄⠀⢲⣶⣾⣿⢿⡇⢗⠫⢰⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠅⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⣀⣀⣀⠀⣠⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⠉⠉⠉⢹⣷⣿⣿⣿⣷⣾⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣦⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡄⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡐⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡤⢄⢀⡀⠀⡀⠀⢀⠀⣀⡀⠀⡄⣀⠀⠀⡀⠀⠤⡤⠀⡀⢀⡀⣄⡀⣀⡀⡄⢀⠀⡀⢠⠀⢠⢄⠀⡀⡀⢠⢀⡀⢀⡀⣄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠆⠒⠆⠀⢚⣿⣿⣿⣰⣾⡗⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠧⠜⠠⠬⠠⠜⠀⠦⠇⠇⠇⠀⠇⠴⠀⠰⠼⠀⠀⠇⠠⠬⠢⠄⠇⠇⠇⠇⠇⠤⠰⠼⠸⠀⠸⠉⠀⠘⠼⢸⠠⠌⠁⠄⠡⢠⡄⠀⠈⢩⣍⣭⢹⣿⣿⠇⠹⡀⠀⠈⠙⠻⠟⡿⠟⠁⠀⠀⠀⠘⠋⠙⣻⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢠⣴⣶⣶⣶⣶⣶⡄⠀⢲⣶⣾⣿⢿⡇⣼⡓⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡀⠀⡀⣀⡄⣡⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠉⠉⠉⣾⡷⣿⣿⣿⣷⣾⣼⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡂⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡶⡐⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡄⠀⠀⠀⡀⠀⠠⡤⠀⡀⠀⠀⡄⠀⡀⠀⠄⢀⠀⡀⢠⠀⢠⢄⠀⡀⡀⢠⠀⡀⠀⡀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢂⠒⠁⠀⢐⣿⣿⣿⣿⣟⡓⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠧⠜⠠⠬⠠⠜⠀⠦⠇⠇⠇⠀⠇⠴⠀⠰⠼⠀⠀⠇⠠⠬⠢⠄⠇⠇⠇⠇⠇⠥⠰⠼⠸⠀⠸⠈⠈⠸⠬⢸⠠⠌⠀⠀⠥⢠⡄⠀⠈⠉⣍⣭⢹⣿⣿⡏⠻⠄⠀⠀⠙⠿⠿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣛⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⡀⠀⢲⣶⣾⣿⣿⡟⢸⡇⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⢀⣀⠀⣀⠀⣡⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⠉⠉⠉⢻⣿⣿⣿⣿⣷⣾⣼⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠙ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠋⢛⡅⠁⠀⠀⠀⢀⣴⣿ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡶⡔⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀⢠⠀⢀⢀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠃⠲⠀⠀⢈⣻⣿⣷⣲⣿⡗⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠇⠜⠸⠺⠨⠘⠀⠗⠇⠇⠇⠀⠇⠲⠀⠸⠺⠀⠀⠇⠸⠺⠪⠀⠇⠇⠇⠇⠇⠅⠰⠺⠸⠀⠸⠈⠈⠸⠨⢸⠸⠊⠈⠀⠡⢠⡄⠀⠈⠩⢩⣭⢹⣿⣿⡇⡃⠆⠀⠀⠻⠿⢿⠿⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⣤⣴⣶⣶⣶⣦⡄⠐⢶⣶⣾⣿⢿⡷⢾⡒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⡀⠀⣀⡀⣠⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠉⠉⠉⢹⡷⣿⣾⣿⣷⣿⣤⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⠂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣤⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠙ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡶⡐⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡂⠐⠃⠐⢺⣿⣿⣿⣝⣿⡟⠀⠀⠛⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠇⠸⠸⠓⠈⠱⠀⠟⠇⠏⠇⠀⠇⠛⠀⠸⠻⠀⠀⠇⠸⠛⠊⠁⠏⠇⠏⠇⠇⠍⠨⠻⠸⠀⠸⠊⠈⠹⠩⢸⠸⠋⠈⠁⠩⣠⡄⠀⠈⠩⢍⣭⢹⣿⣿⡗⠟⠀⠀⠀⠹⠿⢿⠿⠟⠁⠀⠀⠀⠀⠉⠙⢿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⣤⣤⣤⣴⣶⣶⣄⠀⠲⣶⣾⣿⢿⡇⢾⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⣀⠀⣡⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⠉⠉⠉⣿⣿⣿⣿⣿⣷⣦⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣤⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⡐⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣙⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢰⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⢀⠀⠈⠀⠀⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠂⠒⡒⠐⢈⣿⣿⣿⣝⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣇⡸⢘⡑⢀⡱⠀⣌⡆⡏⡇⠀⡇⣉⠀⢨⣳⠀⠀⡇⢘⣓⢎⡁⡏⡇⡏⡇⡇⣉⠠⣻⢸⠀⢸⠚⠀⠱⣹⢸⢘⡃⠈⠁⢭⣠⡄⠀⠈⠩⢍⡉⢹⣿⣿⡷⠒⠂⢈⠀⠻⠻⣿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣻⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⢀⣤⣤⣤⣴⣶⣶⡀⠀⢲⣶⣾⣿⣿⣇⣿⠳⣢⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣥⢁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣀⡀⣀⠀⣀⡀⣡⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⠉⠉⠉⢿⣧⣿⣿⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡒⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣻⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠈⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇⡂⠀⠐⢸⣿⣿⣿⣉⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣇⡸⢀⣑⢀⡱⠀⣌⡆⡏⡆⠀⡇⣩⠀⢠⣱⠀⠀⡇⢀⣑⢄⡁⡇⡆⡇⡆⡇⣊⢠⣱⢸⠀⢸⠚⠀⢱⣑⢸⢀⡁⠀⠁⢭⣠⡄⠀⠈⠩⠉⣭⢹⣿⣿⡟⠻⢆⠀⠈⠛⢻⢿⡿⢟⠁⠀⠀⠀⠈⠉⠙⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢠⣤⣤⣤⣴⣶⣦⡀⠐⢶⣶⣾⣿⣿⡗⣿⡣⡳⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⠀⣀⣀⣀⡀⣠⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠉⠉⠉⢿⣿⣿⣿⣿⣷⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⣂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠏⠃⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣄⣠⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⢒⠁⠂⢘⣿⣿⣿⣷⣿⡛⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡇⡸⢠⢴⢐⡰⠀⡤⡆⡆⡆⠀⡆⣠⠀⢠⣴⠀⠀⡇⢰⢴⢄⠀⡇⡆⡆⡆⡆⡂⢠⣴⢸⠀⢸⠘⠐⢰⣐⢰⢰⡄⠀⠀⢥⣠⡄⠀⠈⠉⣭⣭⢹⣿⣿⡗⠓⢍⢀⠀⠙⠻⢿⡿⠟⢁⠀⠀⠀⠈⠉⠙⣻⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢠⣤⣤⣤⣴⣶⣦⡀⢐⢶⣶⣾⣿⣿⣷⣿⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⠀⢀⣀⡀⣩⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠉⠉⢸⣿⣿⣿⣾⣷⣷⣴⣔⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠻⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠒⠀⠀⢚⣿⣿⣿⣓⣟⡟⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡇⢹⢰⠴⢐⢠⠀⡦⡆⡆⡆⠀⡆⠦⠀⢰⢴⠀⠀⡇⢰⢴⢔⠀⡇⡆⡆⡆⡆⡂⢰⢴⢸⠀⢸⠜⠐⢰⢐⢰⢰⠄⠀⠀⠥⣠⡄⠀⠈⢉⢩⣭⢹⣿⣿⡗⠻⠄⠀⠀⠛⢿⢿⠿⡟⠁⠀⠀⠀⠈⠋⠙⡻⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡀⣀⣠⣠⣤⣰⣶⣦⡀⢀⢶⣶⣾⣿⣿⡆⣼⣲⣰⠂⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣀⣀⣀⡀⣡⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠉⠉⠉⣻⣿⣿⣿⣿⣷⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣷⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠆⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⡂⣰⣤⣤⣀⣠⣴⣶⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠙ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡒⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢃⣚⠀⠀⢚⣿⣿⣿⣻⣿⡟⠀⠈⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡏⢱⠰⠦⠐⢢⠀⡰⡆⡖⡆⠀⡇⠖⠀⢐⢦⠀⠉⡏⠰⠦⡔⠂⡗⡆⡖⡆⡇⠒⢀⢶⢸⠀⢸⠽⠐⢢⢲⢸⠰⠆⠀⠀⠡⣠⡄⠀⡌⠉⣍⣭⢹⣿⣿⡿⠚⠁⠀⠀⠛⢻⢿⡿⠏⠁⠀⠀⠀⠈⠉⠙⣻⣿⣿ ⠀⠀⠀⠉⠁⠈⠁⠀⠁⠀⠈⠁⠁⠁⠀⠁⠉⠀⠈⠉⠀⠀⠁⠀⠁⠈⠁⠁⠁⠁⠀⠁⠈⠀⠉⠈⠀⠈⠀⠀⠀⢉⡘⡈⢁⣀⣀⣀⣰⣶⣶⡀⠀⢲⣶⣾⣿⣿⡟⣿⣢⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⡀⢀⠀⢠⡄⣡⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠉⠉⠉⢹⣿⣿⣿⣿⣷⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣤⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠊⠒⢀⢘⣿⣿⣷⣽⣿⡛⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡏⢱⠐⠢⠀⢢⠀⡐⡄⡖⡄⠀⡇⢒⠀⢀⢢⠀⠉⡏⠀⠢⡐⠂⡗⡄⡖⡆⡇⠔⢀⢢⢸⠀⢸⠵⠠⢢⢢⢸⠐⠂⠀⠀⠡⢠⡄⠀⡌⠉⣍⣭⢹⣿⣿⡷⠿⠀⠀⠈⠻⠻⢿⡿⠟⠁⠀⠀⠀⠀⠉⠙⣻⣿⢟ ⠀⠀⠀⠉⠁⠈⠉⠈⠁⠀⠉⠁⠁⠁⠀⠁⠉⠀⠈⠉⠀⠀⠁⠈⠉⠈⠁⠁⠁⠁⠁⠁⠉⠈⠉⠈⠀⠈⠀⠀⠀⢉⠘⠈⢁⣀⣀⣀⣰⣶⣶⡀⠀⢲⣶⣾⣿⣿⡷⣾⡇⣲⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⢀⣀⣠⡀⣩⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠉⠉⠉⢿⣿⣿⣿⣿⣷⣿⣮⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⣂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⠂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣤⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠊⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⢖⠂⠐⢘⣿⣿⣷⣷⣿⡗⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡏⢰⠀⠠⠀⢠⠀⡀⡄⡆⡄⠀⡅⢀⠀⢀⢠⠀⠈⡏⠀⠠⡀⠀⡇⡄⡄⡄⡅⠄⢀⢢⢸⠀⢸⠱⠠⢢⠢⢸⠀⠂⠀⠀⠤⣠⡄⠀⡌⢩⢩⣭⢹⣿⣿⡷⠻⠉⠀⠈⠙⠿⠿⠿⠟⠁⠀⠀⠀⠀⠉⠙⣻⣿⢿ ⠀⠀⠀⠉⠁⠈⠉⠈⠁⠀⠉⠁⠁⠁⠀⠁⠉⠀⠈⠉⠀⠀⠁⠈⠉⠈⠁⠁⠁⠁⠁⠁⠉⠈⠉⠈⠀⠈⠀⠀⠈⢉⡘⠈⢁⣀⣀⣀⣰⣶⣦⡀⠐⢶⣶⣾⣿⣿⣿⣶⣤⡳⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣠⡀⢀⣀⣠⡀⣡⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠉⠉⠉⢺⣿⣿⣿⣿⣷⣷⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡄⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠏⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠹⢿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⡂⣠⣦⣤⣀⣠⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣤⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠻⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣓⠚⠓⠐⢸⣿⣿⣿⣿⣿⡿⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡆⢰⢠⣠⠠⢠⠀⣄⡄⡄⡄⠀⡅⣀⠀⢠⣠⠀⠀⡆⢠⣠⡠⠀⡇⡄⡄⡄⡅⠄⢠⣠⢸⠀⢰⠰⠠⢠⠠⢨⢠⡀⠀⠀⠠⣠⡄⠀⡌⢩⢍⣭⢹⣿⣿⡿⠛⠄⠀⠀⠙⠿⢿⠻⠟⠃⠀⠀⠀⠈⠉⠙⣻⣿⡯ ⠀⠀⠀⠁⠁⠈⠈⠈⠈⠀⠁⠁⠁⠁⠀⠁⠈⠀⠈⠈⠀⠀⠁⠈⠈⠈⠀⠁⠁⠁⠁⠁⠁⠈⠈⠈⠀⠈⠀⠀⠈⠈⠘⠈⠀⣀⣀⣀⣰⣶⣶⡄⠀⠲⣶⣾⣿⣿⡯⣿⢗⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢀⠀⣀⣀⣀⡀⣠⣵⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆⠁⠉⠉⠉⢿⣿⣿⣿⣿⣷⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠏⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠇⠚⠁⠐⢚⣿⣿⣿⣟⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡖⢢⢠⣄⠠⢄⠀⢤⡄⡤⡄⠀⡆⡤⠀⠠⣤⠀⠐⡖⢠⣄⡠⠄⡦⡄⡤⡄⡆⠤⠠⣤⢰⠀⢰⡲⠠⢄⠤⢰⢠⡄⠀⠀⠤⣠⡄⠀⡌⠩⢍⡉⢹⣿⣿⡷⢒⠉⠀⠀⠻⢿⢿⣿⠟⠐⠀⠀⠀⠈⠉⠙⣻⣿⣿ ⠀⠀⠀⠓⠈⠀⠂⠀⠊⠀⠑⠁⠃⠁⠀⠃⠒⠀⠘⠚⠀⠀⠃⠀⠂⠐⠂⠃⠁⠃⠁⠃⠑⠈⠊⠘⠀⠘⠀⠀⠈⠊⠼⠀⠂⠐⠂⠒⢰⣶⣶⡄⠀⢲⣶⣾⣿⣿⡷⠿⣣⠰⢄⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⣀⣀⣀⡄⣩⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⡆⠁⠉⠉⠉⢽⣷⣿⣿⣿⣷⣷⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⣂⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⡂⣠⣦⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣤⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡦⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠻⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣀⢚⠂⠀⢘⣿⣿⣿⣛⣿⡳⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡖⢢⢠⢄⠀⢄⠀⠠⡀⡤⡄⠀⡆⠤⠀⠠⢄⠀⠒⡖⢠⢄⡠⠄⡦⡄⡤⡄⡆⠤⠀⢤⢰⠀⢰⣢⠀⢄⢤⢰⢠⡄⠀⠀⠤⣠⡄⠀⡌⠩⠉⣭⢹⣿⣿⡷⡻⠐⢀⠀⠛⢿⢿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⣿ ⠀⠀⠀⠓⠊⠐⠂⠐⠊⠀⠓⠃⠃⠃⠀⠃⠒⠀⠘⠚⠀⠀⠃⠐⠒⠑⠂⠃⠃⠃⠃⠃⠒⠘⠚⠘⠀⠘⠀⠀⠈⠚⠸⠐⠂⠐⠂⠒⢰⣶⣦⡀⠀⠲⣶⣾⣿⣿⡿⢥⡢⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⣠⣀⣀⡀⣡⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠉⠉⠉⣿⣿⣿⣿⣿⣷⣿⣮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠋⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⢿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⢀⡂⣠⣦⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣤⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣶⣿ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣂⡜⠂⠀⢛⣿⣿⣿⣾⣿⡟⠀⠈⠛⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡖⢢⠀⢄⠀⢄⠀⠠⡀⡄⡀⠀⡆⠤⠀⠀⢄⠀⠒⡖⠀⢄⠀⠄⡆⡀⡄⡀⡆⠠⠀⢄⢰⠀⢰⣢⢀⢄⢄⢰⠀⠄⠀⠀⠠⣠⡄⠀⡌⠩⣭⣭⢹⣿⣿⡗⡛⠂⠀⠈⠻⠿⢿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⣿ ⠀⠀⠀⠓⠊⠐⠒⠐⠊⠀⠓⠃⠃⠃⠀⠃⠚⠀⠘⠚⠀⠀⠃⠐⠒⠑⠂⠃⠃⠃⠃⠃⠒⠘⠚⠘⠀⠘⠀⠀⠘⠒⠸⠐⠒⠐⠂⠒⢰⣶⣦⡀⢐⢶⣶⣾⣿⣿⡷⣽⡣⣒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⡀⡀⣠⡀⣡⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠉⠉⠉⢽⣿⣿⣷⣿⣷⣷⣮⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠒⡁⠀⢘⣿⣿⣿⣋⣿⡓⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡄⢠⢀⢀⢀⢀⠀⠀⡀⡀⡀⠀⡂⠀⠀⠀⢀⠀⠐⡖⢀⢀⢀⠀⡆⡀⡀⡀⡂⡀⠀⢀⢰⠀⢰⢢⢀⢀⢀⢐⢀⠀⠀⠀⠠⣠⡄⠀⡌⢉⢩⣭⢹⣿⣿⡿⡳⠟⢈⠈⠛⢿⣝⡿⠟⠁⠀⠀⠀⠈⠋⠙⣿⣿⣫ ⠀⠀⠀⠃⠊⠘⠙⠐⠊⠀⠋⠃⠃⠃⠀⠃⠙⠀⠘⠙⠀⠀⠃⠘⠙⠑⠀⠃⠃⠃⠃⠃⠂⠘⠙⠘⠀⠘⠀⠀⠘⠒⠸⠘⠑⠐⠂⠒⢰⣶⣶⡀⠐⢶⣶⣾⣿⣿⡧⣞⠫⢠⣂⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠡⣱⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⢀⣀⣀⡀⣠⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠉⠉⠉⣽⣯⣿⣿⣿⣿⣿⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣵⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠃⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡅⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡒⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠇⠖⡓⠐⢘⣿⣿⣿⣽⣿⡷⠀⠈⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡤⢄⢀⡀⢀⡀⠀⣀⡀⣀⡀⠀⡄⣀⠀⢀⣀⠀⠠⡤⢀⡀⢀⡀⣄⡀⣀⡀⡄⣀⢀⣀⢠⠀⢠⢤⢀⣀⣀⢠⢀⡀⠀⠀⣤⣠⡄⠀⡌⢩⣍⣭⢹⣿⣿⡇⠻⠀⠀⠀⠻⠻⢿⠿⠟⠁⠀⠀⠀⠈⠉⠙⣿⣿⣿ ⠀⠀⠀⠧⠘⠈⠍⠀⠜⠀⠪⠃⠇⠃⠀⠇⠅⠀⠘⠽⠀⠀⠇⠈⠍⠁⠄⠇⠃⠇⠃⠇⠢⠐⠝⠸⠀⠘⠁⠀⠘⠔⣸⠈⠅⠢⠄⠢⢰⣶⣦⡀⠀⢶⣶⣾⣿⣿⣿⢿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡀⣀⣀⣀⡀⣠⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⠀⠁⠉⠉⠉⢿⣟⣿⣿⣿⣿⣿⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡋⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣴⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣖⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠋⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⡒⠒⠐⢛⣿⣿⣿⣚⣿⡋⠀⠀⠛⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡤⢄⢀⡀⢀⡀⠀⢀⡀⣀⡀⠀⡄⣀⠀⢀⡀⠀⠤⡤⢀⡀⢀⡀⣄⡀⣀⡀⡄⣀⠀⣀⢠⠀⢠⢤⢀⡀⣀⢠⢀⡀⠀⠀⣠⣠⡄⠀⡌⢩⣍⣭⢹⣿⣿⡧⡛⢀⠈⠈⠛⠿⣿⠿⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⣿ ⠀⠀⠀⠧⠜⠨⠍⠀⠜⠀⠪⠇⠇⠇⠀⠇⠥⠀⠰⠽⠀⠀⠇⠨⠍⠣⠄⠇⠇⠇⠃⠇⠤⠐⠽⠸⠀⠸⠉⠀⠘⠼⢸⠨⠅⠢⠄⠦⢰⣶⣦⡀⠀⢶⣶⣾⣿⣿⣷⣜⡫⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⢄⠀⣀⡄⣠⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⠀⠁⠉⠉⠉⢻⡿⣿⣿⣿⣿⣿⣶⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠉⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣴⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢔⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⡿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠂⠒⠀⠀⢘⣿⣿⣷⣞⣿⡾⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡤⢄⠀⡀⠀⡀⠀⢀⠀⣀⠀⠀⡄⣀⠀⠀⡀⠀⠤⡤⠀⡀⢀⡀⣄⠀⣀⠀⡄⢀⠀⡀⢠⠀⢠⢄⠀⡀⡀⢠⢀⡀⠀⠀⢠⣠⡄⠀⡌⠩⢩⣭⢹⣿⣿⡷⠛⠂⠠⠁⠙⠻⢿⠯⠟⠁⠀⠀⠀⠈⠉⠙⣿⣿⣿ ⠀⠀⠀⠧⠜⠠⠬⠠⠜⠀⠦⠇⠇⠇⠀⠇⠴⠀⠰⠼⠀⠀⠇⠠⠬⠢⠄⠇⠇⠇⠇⠇⠥⠰⠼⠸⠀⠸⠉⠀⠘⠬⢸⠠⠤⠢⠄⠦⢰⣶⣦⡀⢐⢶⣶⣾⣿⣿⡧⢾⡇⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀⣀⣀⣀⡀⣠⣴⣶⣶⣶⣶⣶⣾⣿⣿⣷⠀⠁⠉⠉⠉⢾⣟⣿⣿⣿⣷⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⣀⣤⣤⣴⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣿ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡔⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⡿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠇⠒⡃⠀⢐⣿⣿⣿⣿⣷⡻⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀⢠⠀⢠⢄⠀⠀⡀⠠⠀⠀⠀⠀⢠⢠⡄⠀⡌⠩⢍⣭⢹⣿⣿⡯⠛⠅⠀⠀⠻⠿⢿⠿⠟⠉⠀⠀⠀⠈⠉⠹⣿⣿⢿ ⠀⠀⠀⠧⠜⠠⠬⠠⠜⠀⠦⠇⠇⠇⠀⠇⠴⠀⠰⠼⠀⠀⠇⠰⠬⠢⠄⠇⠇⠇⠇⠇⠥⠰⠾⠸⠀⠸⠈⠈⠸⠬⢸⠰⠴⠢⠄⠦⢰⣶⣦⡀⠐⢶⣶⣾⣿⣿⡏⢼⡅⡲⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠀⣀⣀⣠⡀⣠⣴⣶⣶⣶⣶⣶⣾⣿⣿⣷⠀⠁⠉⠉⠉⣿⣯⣿⣿⣿⣷⣿⣦⣂⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠃⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣴⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢔⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⡿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣂⢒⠀⠐⢺⣿⣿⣿⣛⣿⡟⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡄⠀⡌⠩⢍⡉⢹⣿⣿⡯⠃⠁⠀⠀⠛⠿⢿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣛⣿⢿ ⠀⠀⠀⠇⠸⠘⠓⠈⠱⠀⠝⠇⠏⠇⠀⠇⠛⠀⠸⠻⠀⠀⠇⠸⠛⠊⠁⠏⠇⠏⠇⠇⠍⠨⡻⢸⠀⠸⠊⠈⠹⡩⢸⠸⡓⠆⡀⢆⢰⣶⣶⡀⠐⢶⣶⣾⣿⣻⣯⣽⡳⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⡀⣀⣀⣀⡀⣠⣥⣤⣤⣤⣤⣤⣼⣿⣿⣿⡀⠁⠉⠉⠉⣽⡷⣿⣷⣿⣷⣿⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠏⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢔⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⡿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⡎⡁⠐⢚⣿⣿⣿⣽⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠠⣠⡄⠀⡌⠉⠉⣭⢹⣿⣿⡷⡳⠇⠀⠀⠙⠿⢿⡿⠿⠁⠀⠀⠀⠈⠉⠹⣛⣿⣿ ⠀⠀⠀⣇⡸⠘⡓⠈⡱⠀⢝⠇⡏⠇⠀⡇⣋⠀⢨⣳⠀⠀⡇⠘⡓⢊⡁⡏⠇⡏⠇⡇⢉⠨⡻⢸⠀⢸⠊⠈⠱⡩⢸⢘⡓⢆⡀⣆⢰⣶⣦⡄⠐⢶⣶⣾⣿⣿⡗⣿⣓⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⣀⣀⣀⡀⣠⣭⣤⣤⣤⣤⣤⣼⣿⣿⣿⡄⠁⠉⠉⠉⣿⣷⣿⣿⣿⣷⣿⣾⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠂⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢔⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠻⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢠⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⡿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡊⠞⠂⠀⢸⣿⣿⣿⣝⣿⡟⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠠⣠⡄⠀⡌⠉⣭⣭⢹⣿⣿⡿⠻⠃⠀⠈⠹⠿⢿⠿⠟⠁⠀⠀⠀⠀⠉⠙⣿⢿⢿ ⠀⠀⠀⣇⡸⢈⡑⢀⡱⠀⣌⡆⡏⡇⠀⡇⣉⠀⢨⣱⠀⠀⡇⢘⣑⢌⡁⡏⡇⡏⡇⡇⣈⢠⣱⢸⠀⢸⠚⠀⠱⣹⢸⢈⣑⢆⡀⣆⢰⣶⣶⡀⠀⢲⣶⣾⣿⣿⡗⣿⡣⡺⢄⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣭⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⡀⣀⠀⣀⡀⣠⣬⣤⣤⣤⣤⣤⣼⣿⣿⣿⡄⠁⠉⠉⠉⣽⣷⣿⣿⣿⣷⣾⣤⣮⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⣂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠉⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⡂⣠⣦⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣴⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣿ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡒⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢔⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⡿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣛⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⢂⠒⠐⢚⣿⣿⣿⣕⣷⡟⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠠⣠⡄⠀⡌⠉⢩⣭⢹⣿⣿⠗⠻⠆⠀⠀⠙⠻⢿⡽⠟⠁⠀⠀⠀⠀⠉⠩⣻⣿⣿ ⠀⠀⠀⣇⡸⢀⣑⢀⡱⠀⣌⡆⡏⡆⠀⡇⣩⠀⢠⣱⠀⠀⡇⢀⣑⢄⡁⡇⡆⡇⡆⡇⣊⢠⣱⢸⠀⢸⠘⠐⢱⣑⢸⢀⣑⢄⡀⣆⢰⣶⣶⡀⠀⠲⣶⣾⣿⣿⡇⣿⡣⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⢀⣀⢀⣀⡀⣠⣬⣤⣤⣤⣤⣤⣼⣿⣿⣿⠀⠁⠉⠉⠉⢻⣷⣿⣿⣾⣷⣿⣼⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠻⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠸⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⣀⣤⣤⣴⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠙ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡐⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⡿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠃⠺⠃⠀⢘⣿⣿⣷⣟⣿⡿⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢠⡄⠀⠈⠉⣍⣭⢹⣿⣿⡷⠓⠁⢀⠀⠻⠻⢿⠿⠟⠁⠀⠀⠀⠈⠋⠙⣻⣿⢿ ⠀⠀⠀⡇⢱⢰⠴⢐⠢⠀⡦⡆⡆⡆⠀⡆⠶⠀⢰⢴⠀⠀⡇⢰⠴⠔⠀⡇⡆⡆⡆⡆⡂⢰⢶⢸⠀⢸⠜⠐⢲⢒⢰⢰⢶⢔⠂⡖⢰⣶⣦⡀⠀⢶⣶⣾⣿⣿⡯⣿⡧⡢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⣀⣀⣀⡀⣀⣊⣀⣤⣤⣤⣤⣼⣿⣿⣿⡀⠁⠉⠉⠉⢹⣿⣿⣿⣿⣷⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠁⠀⢀⡂⣠⣦⣤⣀⣠⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣴⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣿ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡒⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢔⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⡿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⠐⠂⠐⢚⣿⣿⣿⣿⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡄⠀⠈⠉⣍⣭⢹⣿⣿⡷⡻⠕⢊⠈⠙⠿⢿⠿⠟⠁⠀⠀⠀⠈⠋⠙⣻⢿⡿ ⠀⠀⠀⡏⢱⠰⠦⠐⢢⠀⡲⡆⡖⡆⠀⡇⠖⠀⢰⢶⠀⠈⡏⢰⠦⠔⠂⡗⡆⡖⡆⡇⡒⢐⢶⢸⠀⢸⠝⠐⢲⢒⢸⠰⠦⡔⠂⡖⢰⣶⣦⡀⠐⢶⣶⣾⣿⣿⡷⣿⣗⣡⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠀ ⠀⠀⠀⠉⠀⠀⠁⠀⠁⠀⠈⠀⠁⠀⠀⠁⠁⠀⠀⠉⠀⠀⠁⠀⠁⠀⠁⠁⠀⠁⠀⠁⠈⣀⡁⢈⡀⣀⡀⣀⡀⣁⣚⣀⣁⣈⣁⣈⣸⣿⣿⣿⡀⠁⠉⠉⠉⣿⣿⣿⣿⣿⣷⣿⣶⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠻⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⢀⠂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣒⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣾⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠂⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡶⡖⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢔⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠔⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⡿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠑⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⣩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠫⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠄ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢲⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⣒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ䷩ 𝚕𝚒𝚗𝚎 2529 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/04/11/Video_How_the_Media_Blamed_SSH_and_Linux_for_Nearly_a_Whole_For.shtml Gemini version at gemini://gemini.techrights.org/n/2024/04/11/Video_How_the_Media_Blamed_SSH_and_Linux_for_Nearly_a_Whole_For.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] How the Media Blamed SSH and Linux (for Nearly a Whole Fortnight!) Instead of Microsoft's GitHub and Systemd⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024, updated Apr 11, 2024 k Video_download_link | md5sum 0343d2a5fb805701dab56eb12ef302ac How_Media_Failed_at_XZ_Coverage Creative Commons Attribution-No Derivative Works 4.0 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Preview_for_How_Media_Failed_at_XZ_Coverage⦈_ § Introduction⠀➾ THIS MORNING we made some new videos. We recorded 3 videos in total, but this one is the worst of them all for purely technical reasons. It ends after about 33 minutes even though the original plan was to go through almost 150 titles/ articles, illuminating the way the media likes to smear "Linux" and illustrating the dishonesty of so-called 'journalists' (parrots and stenographers). After the technical issues I thought of recording a "part 2", but eventually it seemed like enough material had been covered and, at the very least in order to avoid repetition, it was probably OK to just leave things (fine as is). It deals with a small sub-sample of coverage we've gradually collected in a roughly chronological order, showing how FUD gets recycled and sometimes upcycled. As noted here last week, some ludicrous articles went as far as praising Microsoft, reiterating the lie that it "loves Linux" (it loves using "Linux" for distraction) and framing Microsoft as some sort of authority/expert at security. § The Present⠀➾ The "xz" (or "Xz" or "XZ" or the name of the encapsulating package; most of the media went for more familiar "brands") story and/or the hype isn't over per se, but I saw that "XZ BS" only once yesterday and my wife also saw it once (another example, some blog in Planet Fedora). So now it's probably safe to take stock of the whole thing. Tomorrow this thing turns 14 days ("officially"). And prior Techrights articles set aside - as most of them over a week old with a high view count already - we take a fresher look at these things. This long_page (no JavaScript or bloat) was updated about 50 times and some people asked why we keep updating it so often (several times per day). "What we are describing here will be covered in my upcoming video about xz," I said, "I just wait for "the news" to calm down a bit..." So let's look back and consider what had been published until yesterday's "trickle" ('only' 2 instances in one day). The longer version of it is in the video at the top. § Microsoft Not to the Rescue⠀➾ Microsoft-connected sites have said a whole bunch of lies. Some of them were covered here a week ago, so we would rather not air those lies again. To give one example, Risky Business (RB, or Australia's RiskyBiz where Microsoft's mouthpieces like Brett Winterford [1, 2] work) had three_recordings on xz [1, 2, 3], "casting aspersions at SSH in general (they hate SSH and campaign against it) and blame Linux specifically and the OSS development model in general," an associate has noted. "Again, if distros had the minimum of three developers per subproject, the Xz breach would have been harder to pull off. However, when the same technique is tried against proprietary softer, there is basically no chance at detection." This associate keeps saying that we "need to pound the drum on the benefits of OSS (and especially FOSS) and the same attack against proprietary would slide by undetected." Richard Stallman covered this already, even close to 2 decades ago [1, 2]. Stallman said it many times; he spoke of how someone had been arrested for trying to put backdoors from within Microsoft on behalf of Al-Qaeda. No kidding! I spoke to another person last week. "Something that's changed culturally, at least in the US, which Microsoft seems way ahead in exploiting, is vanity and need for popularity among the new gen tech devs," he said. We have said this for years! "Instead of coders just scratching an itch and putting up a project in case a few dozen people find it useful, Github has set up a pageant, a frenzy of egotistical self-promotion, with badges and "likes" and ways to track activity and whatnot. The recent tech layoffs and it's proximity to Linked-In is amplifying that desperation." And the media tells them that's the right thing to do. We covered many examples in the past. Sometimes you cannot even apply for things unless you provide a GitHub (i.e. Microsoft) handle. "Microsoft wanna set themselves up as a Dickensian workhouse with Nancy and Bill Sikes (Gates) ruling a gang of kids who will pick pockets and write code for gruel," the person told me. "When I interview young devs now, instead of giving me a a URL to their domain, or even a written CV, they just give me their GitHub ID. I say, "So you already work for Microsoft?". That's a good line! On the upside, those are easy to reject promptly and upfront. If this is how they develop and write code, maybe they lack a lot of basic skills. "Anyway," the person told me, "what concerns me is the terrifying cybersecurity implications of this." So today I will explain what this media frenzy served to distract from. I want to focus on why GitHub is actually part of the problem here. We also need to remind readers what Microsoft is ALWAYS hoping to distract from. Aside from tributes_to_Ross_Anderson, who valued real security, Microsoft distracted from at least 3 major security blunders. We'll revisit this towards the end of this article. "Regarding the Xz-based FUD," an associate stresses, "the fact that many projects (curl, linux, etc) actually issue their own CVEs is a major improvement. There is an_article_about_that and this fact should be folded somehow into the eventual Xz round-up." Also see "Verified_curl" from yesterday. "Conceivably," Daniel wrote, "the xz attackers have infiltrated more than one other Open Source project to cover their bases. Which ones?" Daniel is the founder of curl going back 2.5 decades and he already wrote about what would happen if he "fell under a bus". § A Theory⠀➾ Is there a "bigger story" here? Check where the CSO of GitHub came from! Spoiler: 20 years inside NSA. Is there a US state role in the revelation? Hard to tell. Here is a hypothetical possibility. It is not at all unthinkable that the massively-staffed NSA (or sibling agency/ partner in the US; they're malicious and they are as big as megacorporations), with staff dedicated to audits and back doors, informed GitHub (i.e. Microsoft) of what had happened some time earlier. The CSO of GitHub is a 20-year NSA veteran and Microsoft knew that right after Easter it would get blasted by official authorities for getting clients cracked by China, not to mention getting cracked itself (also by China). So they could pass on some details to a Microsoft employee (not high-level and not particularly well known) on Friday before the holiday and days before the release of the 'dreadful' report (to Microsoft; it knew it was coming as there was a degree of cooperation with the investigation, ultimately castigating the company), promptly weaponising sensationalist language to occupy news searches for "China" and "security" while at the same time smearing "Linux" (not GitHub or systemd), even if it's over some beta releases that few people use, casually and swiftly while having the audacity to paint Microsoft not just as security expert but also "saviour" of "Linux". Yes! All this while in fact the real China breach was the fault of Microsoft and the impending report spoke of a tall chain/cascade of failures, showing sheer incompetence and neglect at Microsoft, leading up to the actual breach that cost a lot to the US government (espionage). Microsoft tried to cover up this breach until the government demanded and pressured it to admit what had happened. It turned out to be worse than initially assumed/believed/ seen on the surface. So if Microsoft used its staff as "mules" for inversion/ invention of narratives, aided by lazy "media", that would need substantial proof. We might never have that. Anyway, that's just a theory. Plausible? Needs proof. § What It Still Distracts From⠀➾ Even days later the Microsoft-connected (or sponsored) publishers are spamming the media with "China" stuff that isn't the above-mentioned breach. Days ago Microsoft was accusing China of fakes (calling everything "AI"). One example is "Chinese_hackers_turn_to_AI_to_meddle_in_elections" and it misrepresents Microsoft as an authority in this domain. In reality, Microsoft is the very source (or generator) of these fakes. So Microsoft has quite some audacity weighing in on this. This is only one way in which Microsoft is distracting from the report about how China cracked Microsoft's entire infrastructure. That's a fact and the US Government blasted it for it only days earlier until ~2 days ago (the video above covers this). Here is an example_from_5_days_ago: China is ramping up use of AI-generated content and fake social control media accounts to inflame division in the United States and elsewhere, according to the latest report from Microsoft’s threat center. In relation to Asia (it's not known if the crack in the case of xz can be attributed to China, but it's likely someone in Asia), there's also pure_noise like_this. The "India" stuff and lots more like this "Hey Hi" (AI) nonsense stole the thunder - to the point nobody spoke or said anything about how Microsoft failed the whole nation. Articles about India, Microsoft, Modi, and Bill Gates help distract from high_usage_of_GNU/Linux_in_India. Earlier this week we saw that Microsoft had managed to (once again!) engineer a security blunder for itself. To quote a new piece or an_article_by_Sam Varghese: A suspected Russian intrusion into Microsoft's corporate systems, which was disclosed in January, also affected US federal government systems, according to the US Cybersecurity and Infrastructure Security Agency. Also see "US_Cyber_Safety_Review_Board_on_the_2023_Abusive_Monopolist_Microsoft Exchange_Hack" and this_morning's pick from Federal_News_Network, stating: "Oregon Senator fed up with data breaches, blasts Big Tech, demands mandatory standards Sen. Ron Wyden (D-Ore) cites a Cyber Safety Review Board report that blames Microsoft's inadequate cybersecurity culture." This is what Microsoft wants nobody to pay any attention to. Please keep the eyes on the ball. █ ⣿⣿⡟⡧⢼⡴⢣⢇⢆⡆⠀⢣⣼⢠⠢⠠⢺⢸⣐⡀⠀⡯⠅⣐⡄⣟⢠⣢⢠⢺⠀⢀⢢⢰⠂⠈⣲⠉⡩⠃⠀⡎⡁⡔⠄⡄⢄⠐⠄⠀⣐⡄⡔⡆⣔⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣷⣶ ⣿⣿⣇⣃⣈⣈⣉⣈⣈⡀⠀⠀⠈⠈⠉⠈⠉⠈⡉⣁⣀⣁⣀⣉⣁⣉⣈⣉⣈⠉⠀⠈⠉⠈⠁⠈⠀⢉⣉⣁⣀⣉⣁⡉⠁⠈⠀⢩⣡⡄⠉⠁⠉⣅⣭⢁⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠋⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢤⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣄⡀⣤⢄⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠶⡍⠈⣇⢄⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⠏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡄⠀⢠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⡬⣳⣅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣏⣧⡝⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠽⣿⣿⣿⡭⠭⣙⠀⠀⠠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣷⠟⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣟⡵⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣻⣿⣿⡏⢂⣀⡀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡾⠠⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⣻⣿⡯⠍⢉⡍⢀⠘⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⣠⣤⡄⠀⡐⠠⠐⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡦⠀⢠⢹⡟⠁⡼⣏⣵⣿⣷⡄⣿⣧⠀⢸⣿⢿⣿⠀⢸⣷⣵⠛⡆⠀⠐⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠁⠀⠘⠃⠅⠀⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⢰⡿⠤⠋⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣥⡤⣰⣶⣿⣯⣤⣼⣿⢿⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣻⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠛⢽⣿⣿⡟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣸⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣻⣇⣂⣿⣿⣽⣶⣿⣿⣟⣠⣿⣿⣿⣧⣿⣷⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣖⠲⣤⣄⠋⡉⠟⠛⠟⠙⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⡧⢼⡠⢦⢄⣄⡄⠀⢢⣴⢠⣠⠠⢸⢨⣀⡄⠀⡮⠅⣄⡄⣕⢠⣠⢠⢸⠀⢠⣠⢰⠀⠀⣶⠀⡩⠃⠀⡎⡁⡄⠄⡄⢄⣄⡄⠄⣄⡄⡄⡄⣄⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⣇⣃⣈⣈⣉⣈⣈⠀⠀⠁⠈⠈⠈⠈⠈⠈⠉⡁⠀⢁⣀⣉⣁⡉⣈⡉⠈⠈⠀⠈⠈⠈⠀⠈⠀⢉⣉⣁⣀⣉⣁⡁⠁⠈⠀⢡⣡⡄⠁⠁⠍⣇⣭⢁⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠋⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣄⡀⣀⢤⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠗⡇⠠⡁⠄⠄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡀⠀⢠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣯⢉⣭⢣⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⢯⠭⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠽⣿⣿⣿⡭⠮⣝⡀⠀⠠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡗⡳⣎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⢏⣱⢆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣟⣻⣿⣿⡏⢂⣀⡀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡛⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⡯⠍⢉⡍⢁⠘⠩⣟⡍⠉⢩⣿⣿⣯⠉⢹⡏⣠⣤⡄⠀⡄⠠⠐⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡧⠀⢠⢻⡟⠁⡼⢋⣵⣿⣿⡄⣿⣧⠀⢸⣿⢿⣿⠀⢸⣷⣾⢛⡃⠀⠘⠂⠈⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡠⠚⠏⠁⠀⠘⠃⠁⠀⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⢰⡛⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣟⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣡⡤⣴⣶⣿⣯⣤⣼⣿⢿⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣟⣻⣿⣿⣽⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠙⢼⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣻⣇⣂⣿⣿⣽⣷⣿⣿⣿⣠⣿⣿⣿⣧⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⢿⣜⣟⣽⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣻⣿⣿⡖⠲⣤⣤⠋⡉⠟⠛⠿⠍⠑⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡏⡦⢴⡠⢦⢄⣄⡄⠀⢂⣴⢠⣤⠠⢴⢠⢠⡄⠀⡦⠆⣤⡄⡕⢠⣤⢠⢴⠀⢠⣤⢰⠄⠀⣤⠀⡲⠂⠀⡖⡂⡤⠄⡄⣄⣤⡀⠄⣤⡄⡤⡄⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣷⣶ ⣿⣿⣇⣃⣘⣘⣋⣘⡘⠀⠀⠀⠈⠈⠀⠈⠈⠈⠑⠁⠀⠁⠀⠑⠃⠉⠈⠂⠈⠊⠀⠈⠈⠈⠀⠀⠀⢀⢓⣂⣀⣑⣃⡁⠁⠈⠀⢡⣠⡄⠁⠁⠡⢣⣥⢁⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠋⠛⠛⠛⠋⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣄⠤⡄⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⡽⢃⡀⢈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡄⠀⢠⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⢩⡴⣹⣄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣣⡬⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣫⡭⣙⡀⠀⠠⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣝⣻⣎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣷⣶⣿⠇⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣟⡙⠏⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⡟⠀⣄⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⡇⡚⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⡛⠏⢉⡭⠁⠘⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⣨⣤⡄⠀⡀⠤⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡧⠀⢠⢻⡟⠁⣼⢟⣵⣾⣷⡜⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣽⠻⡄⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠁⠀⠘⠃⠁⠀⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⠰⡛⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣟⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⡤⣠⣶⣿⣯⣤⣼⣿⢷⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣟⣻⣿⣿⣽⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠇⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⡛⢽⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣿⣇⣂⣿⣿⣝⣷⣿⣿⣟⣠⣿⣿⣿⣧⣿⣿⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⢿⣜⣟⣽⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣻⣿⣿⡖⠲⣤⣤⠋⡉⠟⠛⠿⠍⠑⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡯⣆⣰⡠⢦⣄⡄⡄⠀⢂⣴⢠⣤⠠⢴⢰⢠⡄⠀⣖⡂⣤⡄⣖⢠⣤⢠⢴⠀⢠⣤⢰⠄⠐⣤⠒⣲⠂⢀⡖⡒⡤⡄⡄⣄⣤⡀⠤⣤⡄⡤⡄⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣷⣶ ⣿⣿⡇⠃⠘⡙⠊⠘⠘⠀⠀⠁⠘⠈⠂⠈⠚⠘⠑⠁⠀⠃⠀⠓⠃⠋⠈⠒⠈⠚⠀⠈⠚⠘⠂⠐⠉⠒⠓⠂⠀⠑⠂⠑⠁⠈⠀⢠⣠⡄⠁⠁⠥⢇⣥⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠋⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣀⠠⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣏⣊⣅⢂⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡄⠀⢈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢀⡖⢲⡔⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡏⢛⢌⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠽⣿⣿⣿⡭⠮⣝⡀⠀⠠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣸⣗⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣏⡱⣆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⡏⢀⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡆⠲⠎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣻⣭⡭⠍⢉⡍⢀⠘⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⣡⣤⡄⠀⠐⠄⠘⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡦⠀⢠⢹⡟⠁⠼⢛⣵⣿⣶⡄⣿⣧⠀⢸⣿⢿⣿⠀⢸⣷⣿⠿⡆⠀⠐⠁⠀⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠁⠀⠘⠃⠅⠀⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⠰⡟⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣥⡤⣰⣶⣿⣯⣤⣼⣿⢿⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣟⣻⣿⣿⣽⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣍⡛⢙⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣻⣇⣂⣿⣿⣿⣷⣿⣿⣟⣠⣿⣿⣿⣧⣿⣿⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣻⣿⣿⡶⢲⣤⢄⠋⡉⠛⠛⠛⠉⠑⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡯⣆⣰⣠⢆⡅⡄⡄⠀⣆⣰⢀⢄⢀⢴⢰⠠⠄⠀⣖⡂⠤⡀⣖⢀⠤⢀⢴⠀⠀⢄⢠⠄⠐⢤⠒⢒⠆⠀⡔⡂⡠⡀⡀⡄⠠⡀⠠⠠⡀⡤⡄⡠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⠃⠘⡕⠊⠘⠘⠀⠀⠈⠘⠘⠒⠐⠚⠘⠑⠂⠀⠃⠀⠓⠃⠃⠘⠒⠘⠚⠀⠘⠚⠘⠂⠐⠉⠒⠓⠂⠈⠓⠂⠓⠃⠑⠈⢢⣠⡄⠃⠃⠣⢇⡁⠂⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠋⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⢤⣤⢄⡀⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢘⡱⢊⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡆⠀⢠⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⡯⡧⣟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⡗⣬⣟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣽⣿⣿⡭⠶⢭⡅⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣯⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢏⣷⠏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⡟⠀⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠽⠋⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⣻⣿⡿⠟⢉⡍⢁⠘⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⣩⣤⡄⠀⡴⠄⠘⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡧⠀⢠⢹⡟⠁⡼⢋⣡⣾⣷⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣿⠿⡇⠀⠐⠁⠘⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡠⠚⠋⠁⠀⠈⠃⠁⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣴⣶⠀⢸⠛⠄⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠺⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣍⣤⣠⣶⣿⣯⣤⣼⣿⢿⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡽⡛⢹⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡁⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣚⣻⣇⣂⣿⣿⣿⣷⣿⣿⣟⣠⣿⣿⣿⣧⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢈⡉⠈⠋⠿⢿⣜⣟⣾⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣻⣿⣿⣶⢲⣤⣄⠋⡩⠟⠛⠿⠟⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡯⣏⣹⣩⣍⡍⡍⡀⠀⢆⣰⢀⢀⢀⢰⢐⠠⡀⠀⣞⡋⡨⡉⡛⢉⢍⢀⢴⠀⠀⢀⢠⠀⠐⣤⠒⢛⠏⢉⡝⡋⡁⡀⡀⡀⠀⡀⡀⠀⡀⡀⡀⡠⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣷⣶ ⣿⣿⡇⠃⠘⡑⠚⠘⠙⠁⠀⠈⠙⠘⠛⠐⠚⠘⠛⠃⠀⠃⠀⠛⠃⠋⠘⠛⠘⠚⠀⠘⠛⠘⠂⠐⠉⠒⠓⠂⠈⠓⠂⠓⠂⠑⠈⢩⣡⡄⠋⠃⠣⠇⣯⠁⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠛⠛⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣄⡤⡀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣍⢺⣥⢊⠅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⠏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣆⠀⠠⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⢃⣴⠣⣂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡢⡞⢿⣎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⢿⣿⣿⢏⣭⢍⡇⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣾⠣⣆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢆⠴⢎⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣾⣿⣿⠁⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣇⡑⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⡽⠏⢉⣭⠁⠐⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⣡⣤⡄⠀⠤⢄⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡧⠀⢠⢻⡟⠁⣾⢟⣩⣾⣷⣼⣿⣧⠀⢸⣿⢿⣿⠀⢸⣷⣿⠿⡆⠀⠀⠁⠈⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠁⠀⠘⠃⠁⠠⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢰⠟⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⢟⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣤⣠⣶⣿⣯⣤⣼⣿⢻⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⡛⢓⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣿⣇⣀⣿⣿⣋⣶⣿⣿⣿⣡⣿⣿⣿⣧⣽⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣻⣿⣿⡗⢲⣤⣄⢋⡉⠟⠛⠻⠝⠙⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⣭⣩⢉⣋⡉⡉⡀⠀⢄⣠⢀⢀⢀⣰⢐⢉⡉⠉⣍⡉⣉⡉⡫⢉⣉⢉⢸⠀⢀⢀⢠⠀⠀⣀⠀⢉⠍⠉⡭⡍⡁⡀⡀⡀⡀⡀⡀⣀⡀⣀⡉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⠃⠘⡕⠚⠘⠙⠁⠀⠉⠙⠘⠙⠐⠘⠘⠊⠃⠀⠃⠀⠋⠃⠋⠘⠙⠘⠘⠀⠘⠙⠘⠀⠐⠉⠐⠃⠀⠈⠃⠂⠃⠂⠁⠉⢩⣡⡄⠉⠃⢣⣧⣯⠁⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡄⢄⡀⢄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡷⠣⡰⢀⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⠏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣆⠀⠀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣅⢘⣅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡿⣧⡾⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⢿⣿⣿⢏⣭⢍⡇⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡫⢞⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⢧⡵⡆⠠⠀⠀⠀⠀⠀ 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⣿⣿⣷⣷⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣶⣾⣿⡆⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣄⢤⡀⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠖⡁⢠⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⠏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡄⠀⢠⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⡅⣢⢅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⡿⢩⣞⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⣿⣿⣿⣫⣭⣍⡇⠀⠀⢤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡗⡢⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣎⡘⠎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣛⣿⣿⡿⠂⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡇⡣⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⡿⠟⢉⡭⠁⡘⢩⣝⡍⠉⣩⣿⣿⣯⠉⢹⡏⣠⣤⡄⠀⢔⠄⠐⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣶⡧⠀⢠⡻⡟⠁⡼⠟⣡⣾⣧⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣿⡿⡆⠀⠘⠁⠀⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠁⠀⠈⠓⠁⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣴⣶⠀⠰⠟⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡺⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣥⣠⣶⣿⣯⣤⣼⣿⣧⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡛⢣⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣿⣇⣃⣿⣿⣏⣶⣿⣿⣿⣠⣿⣿⣿⣧⣿⣿⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣻⣿⣿⡗⢲⣤⣄⠋⠉⠟⠛⠛⠝⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡯⡍⢩⢉⡋⡉⡉⡁⠀⡄⢠⠀⡀⢀⣨⢡⢉⡉⠉⡭⠍⣉⠉⡍⠉⣉⢉⣩⠉⢀⡀⢀⡀⠠⣀⠬⢭⡍⠉⡭⡍⢁⠀⠀⡀⣀⠀⣀⣀⠈⣉⡉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⠏⠹⠫⠜⠱⠱⠁⠀⠘⠹⠸⠬⠨⠼⠸⠢⠅⠀⠏⠁⠮⠇⠇⠘⠬⠸⠼⠀⠰⠼⠸⠄⠠⠚⠤⠮⠄⠈⠧⠄⠧⠇⠡⠁⢤⣥⡄⠤⠇⢥⣇⣭⠁⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣷⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣶⣶⣷⡆⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢴⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣀⠄⣀⢀⡠⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠖⣶⠀⣁⠀⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡆⠀⢠⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⡷⢹⣼⣢⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⡍⢻⡜⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⣿⣿⣿⣭⠶⢌⡆⠀⠠⢤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣷⣳⡆⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⡙⢌⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣛⣿⣿⡿⠀⣄⢀⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⡏⠱⠖⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⣻⣿⡻⠉⢉⡭⠁⠈⢹⣭⡍⠉⣩⣿⣿⣯⠉⢹⡏⣠⣤⡄⠀⡀⢀⠘⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣯⣿⣯⣿⣿⣿⣏⣿⣿⣯⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⢾⡧⠀⢠⢻⡟⠀⣼⠟⣡⣾⣧⣼⣿⣷⠀⢸⣿⣿⣿⠀⢸⣷⣵⡻⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢋⡠⠚⠋⠁⠀⠈⠃⠅⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢘⠛⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣟⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠼⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣩⣥⣠⣶⣿⣯⣤⣼⣿⢧⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡛⢓⣿⣿⣟⢻⣿⣿⣿⠘⣽⣿⣿⡏⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣿⣆⣂⣿⣿⣅⣶⣿⣿⣿⣠⣿⣿⣿⣧⣿⣿⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣻⣿⣿⡶⠲⣤⣄⠋⠉⠛⠛⠿⠍⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⡿⢩⣛⡛⡋⡉⡁⠀⡄⢠⠀⡀⠀⣨⢩⢉⠉⠉⡭⠍⢉⠉⡍⠉⡉⠉⣩⠉⠀⡀⢀⡀⠠⣀⠬⠭⡍⠉⡩⠍⢃⠀⠀⠀⢀⠀⢀⢀⠈⢉⡉⢉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣷⣶ ⣿⣿⡇⠏⠹⡪⠼⠱⠱⠃⠀⠘⠻⠸⠬⠨⠼⠸⠶⠆⠀⠏⠁⠶⠇⠏⠸⠾⠸⠼⠀⠰⠼⠸⠄⠠⠛⠤⠮⠄⠘⠧⠤⠧⠅⠡⠁⢤⣥⡄⠦⠇⠥⣇⣥⠅⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣷⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣶⣶⣷⡆⠀⠀⠀⠀⠰⣶⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣀⠠⡄⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣴⡏⢀⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⠏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣆⠀⢠⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣷⢭⣅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡁⣿⡇⡈⢰⣶⣶⣅⢢⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣬⣣⣅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⢿⣿⣿⣯⣵⢍⡇⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣻⠧⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢹⣿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣽⢏⠐⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣗⣿⣿⡿⠂⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣯⡡⠋⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⡛⠙⢉⡭⠁⠘⢩⣝⡍⠉⣩⣿⣿⣯⠉⢹⡏⢩⣤⡄⠀⣰⠀⠐⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡧⠀⢨⢻⡟⠁⣼⢟⣡⣾⣷⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣿⣿⠀⠀⠙⠁⠐⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡠⠚⠋⠁⠀⠘⠃⠅⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣴⣶⠀⠸⢏⠬⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣟⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡲⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣥⣤⣠⣶⣿⣯⣤⣼⣿⢷⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⡛⢓⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣻⣇⣁⣿⣿⣵⣧⣿⣿⣿⣡⣿⣿⣿⣧⣿⣿⣂⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢈⡉⠈⠋⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣻⣿⡿⣗⢲⣤⣄⢋⡩⠟⠛⢻⠝⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⡿⢻⠛⠛⠛⠛⠁⠀⡀⢀⠀⠀⠀⢨⠡⠉⠙⠉⡫⠟⠛⠛⢟⠋⠋⠋⢩⠉⠀⠀⢀⠀⠀⣀⠈⠿⡟⠛⡻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⠏⠹⠮⠽⠱⠱⠃⠀⠘⠻⠸⠺⠨⠸⠸⠴⠇⠀⠏⠁⠷⠇⠇⠸⠾⠸⠸⠀⠸⠺⠸⠀⠠⠛⠤⠮⠄⠘⠧⠤⠇⠅⠁⠁⢡⣥⡅⠧⠇⠥⣧⣥⠁⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣷⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣶⣶⣷⡆⠀⠀⠀⠀⠠⣤⠖⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣠⠄⡀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣕⠮⣄⢈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣧⠀⠀⢈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣥⣼⢦⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣕⣳⠔⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣿⣯⣭⢭⣻⠀⠀⠠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢏⠠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⠹⢎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣟⣻⣿⣿⡏⢀⣀⣀⣀⣀⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢆⡡⠒⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⣻⣿⡫⠍⢉⡍⢀⠘⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⣠⣤⡄⠀⢀⡄⠀⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡦⠀⢠⢻⡟⠀⡼⢛⣵⣾⣷⡄⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣽⢿⠆⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡠⠚⠋⠀⠀⠘⠃⠁⠠⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣴⣶⠀⠰⡟⠈⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣍⡤⣰⣶⣿⣯⣤⣼⣿⢧⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⡙⢹⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣻⣇⣃⣿⣿⣝⣧⣿⣿⣟⣠⣿⣿⣿⣧⣽⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠋⠿⢿⣜⣟⣾⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⡿⡗⠲⣤⣤⢋⡉⠟⠛⠛⠝⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⡛⢛⡛⠛⠛⠛⠁⠀⡀⢀⠀⠀⠀⢘⠓⠛⠛⠛⣛⡛⠛⠛⣛⠛⠛⠛⢛⠋⠈⠀⢀⠀⠀⠀⠘⣛⡛⠛⣛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣷⣶ ⣿⣿⡇⡏⢹⢮⡹⢱⢳⠃⠀⠐⠻⠸⠛⠨⠹⠸⢜⠇⠀⠇⠁⢟⡇⠏⠸⡛⠸⡹⠀⠸⠻⠸⠁⢀⠛⣀⣎⡀⠘⢇⡠⠏⠅⠃⠁⢻⣦⡍⠝⠇⠭⣇⣿⠃⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣷⣶⣶⣶⣶⣦⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣶⣶⣷⡆⠀⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⠋⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⢤⣄⠄⡠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡭⣿⢻⣡⢈⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡄⠀⢠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣺⣞⣢⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣝⣷⣽⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠽⣿⣿⣿⡭⠶⣝⡄⠀⠠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡻⢏⠠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡴⠖⠐⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⡏⠂⣄⠀⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⢵⡇⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⡯⠍⢉⡭⢁⠘⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⢨⣤⡄⠀⡔⠠⠐⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡦⠀⢠⢻⡟⠁⡾⢛⣵⣾⣷⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣿⢻⡆⠀⠘⠃⠈⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡠⠚⠋⠁⠀⠘⠃⠅⠠⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢸⠟⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣍⣥⣠⣶⣿⣯⣤⣼⣿⢧⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠇⠽⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⡛⢓⣿⣿⣟⢿⣿⣿⣿⠘⣿⣿⣿⡏⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣚⣿⣇⣂⣿⣿⣟⣧⣿⣿⣿⣠⣿⣿⣿⣧⣽⣿⣆⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢈⡉⠈⠋⠿⣿⣜⣟⣿⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⡷⢲⣤⣔⢋⡉⠟⠛⢿⠝⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⡻⢛⠛⠛⠛⠛⠁⠀⡀⢀⠀⠀⠀⢐⢛⠛⠛⠛⣛⡛⠛⠛⣛⠛⠛⠛⢛⠋⠀⠀⢀⠀⢀⠀⣘⣛⡛⠛⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⡗⢺⢞⡱⢣⢣⠃⠀⠵⢺⠰⣓⢈⣹⢸⢜⡃⠀⡗⠂⣝⡆⡏⠰⣛⢸⣹⠀⢨⣳⢸⡁⢀⠿⣀⣜⡁⠐⣇⡀⣏⡇⢂⠁⢩⣢⡍⣉⡆⢩⣇⣉⡃⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣧⣤⣦⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣬⣤⣤⣧⡄⠀⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⢤⣀⠠⡀⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣩⣿⠁⣕⢀⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣆⠀⠠⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣇⣠⣗⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡼⢳⡏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣿⣿⢯⣭⢍⡃⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣑⢏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣟⣿⣿⣿⠂⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣮⡰⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⣻⣿⡻⠏⢉⣭⠁⠐⢩⣝⡍⠉⣩⣿⣿⣯⠉⢹⡏⢡⣤⡄⠀⣠⠠⠰⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡦⠀⢠⠻⡟⠁⣴⠾⣻⣾⣧⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⡷⣿⠿⡆⠀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠁⠀⠘⠃⠁⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢸⠿⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣍⣥⣠⣶⣿⣯⣤⣼⣿⢷⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠇⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡛⢣⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣿⣇⣁⣿⣿⣷⣶⣿⣿⣟⣠⣿⣿⣿⣧⣿⣿⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢀⡉⠈⠋⠿⣿⣜⣟⣾⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⡿⡗⠲⣤⣄⠋⡉⠟⠛⢻⠝⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⡛⢛⠛⠛⠛⠛⠁⠀⡀⢀⠀⠀⠀⢐⢛⠛⠛⠛⣛⡛⠛⠛⣛⠛⠛⠛⢛⠃⠀⠀⠀⠀⢀⠀⣘⣛⡛⠛⢛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⡗⢺⢞⣱⢣⢣⠇⠀⡳⢺⢰⣑⢐⣹⢸⢌⡁⠀⡗⠂⣍⡆⡏⢰⣙⢰⣹⠀⢠⣱⢸⡁⢀⠿⣀⣔⡁⠐⣇⡀⣎⡆⢀⠁⣨⣠⡌⣌⡆⣉⡇⣬⡀⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣧⣤⣦⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣬⣤⣤⣧⡄⠀⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⡀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢟⡭⢠⡀⢀⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢦⡽⣲⣞⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣣⡆⢉⡌⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⢟⣭⢍⡃⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣗⣳⣞⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡟⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡝⠎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⣺⣿⣿⠃⣀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡏⠹⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⣻⣿⡟⠛⢉⣭⠁⠀⢩⣙⡍⠉⣩⣿⣿⣯⠉⢹⡏⣡⣤⡄⠀⠶⠀⠘⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡧⠀⢠⠻⡟⠁⣼⠿⣫⣾⣧⣼⣿⣧⠀⢸⣿⢿⣿⠀⢸⣷⣽⠿⡆⠀⠐⠁⠈⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠁⠀⠘⠓⠁⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣴⣶⠀⢸⠟⠌⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣤⣠⣶⣿⣯⣤⣼⣿⢷⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣻⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⠛⢃⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡁⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣸⣻⣇⣁⣿⣿⣿⣷⣿⣿⣟⣠⣿⣿⣿⣧⣿⣿⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⢿⣜⣟⣽⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⡗⠲⣤⣔⠋⡉⠟⠛⢿⠝⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⡿⢿⠿⠿⠿⠿⠁⠀⡀⢀⠀⠀⠀⢐⢛⠛⠛⠛⢟⡿⠟⠿⡟⠿⠟⠛⢛⠋⠀⠀⠀⠀⢀⠀⣘⣛⡿⠛⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⡗⢺⢔⣳⢣⢣⠆⠀⠱⢾⢰⣴⢐⣸⢰⣤⡆⠀⡗⠂⣮⡆⡎⢰⣴⢰⣸⠀⢠⣴⢸⠀⢀⠿⣀⣔⡁⠐⣇⣀⣆⡂⢀⠂⣠⣤⡄⣤⡆⡀⣦⣬⠂⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣧⣤⣦⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣬⣤⣤⣧⡄⠀⠀⠀⠀⠀⣠⠄⠀⠐⠁⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣀⠄⡠⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⡭⠫⡃⢈⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣆⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⢣⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣙⢿⡥⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠿⣿⣿⢟⣭⢍⡃⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⡟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢟⠱⡎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣟⣺⣿⣿⠃⣄⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣜⣷⠲⠊⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⣻⣿⡭⠏⢉⡭⠁⠀⢩⣙⡍⠉⣩⣿⣿⣯⠉⢹⡏⢡⣤⡄⠀⡐⠀⠘⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠧⠀⢰⡻⡟⠁⣼⢟⣡⣾⣧⣼⣿⣧⠀⢸⣿⣿⣿⠀⢨⣷⣿⣿⠆⠀⠐⠀⠘⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡠⠚⠋⠁⠀⠈⠓⠁⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣴⣶⠀⠐⡻⠎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣍⣤⣠⣶⣿⣯⣤⣼⣿⣧⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠵⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⠍⡳⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣚⣿⣇⣃⣿⣿⣧⣶⣿⣿⣟⣠⣿⣿⣿⣧⣽⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢀⡉⠈⠋⠿⣿⣜⣟⣾⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⡿⡗⠲⣤⢄⠋⡉⠟⠛⢻⠟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⢐⢛⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⢟⠃⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠸⠾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⡗⢺⣔⣲⢢⢦⠆⠀⡱⢾⢰⠴⢐⢺⢰⡰⡆⠀⡗⠂⡶⡆⡆⢰⠶⢰⢺⠀⢰⢴⢸⠀⢀⠷⢀⠔⠁⠰⣏⣁⡆⡂⠀⠂⢤⣤⡄⡤⡄⡆⣦⣦⠆⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣧⣥⣦⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣬⣤⣬⣧⡄⠀⠀⠀⠀⠀⣀⠀⠀⠒⠁⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣄⠄⡀⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣯⠘⡁⢈⠄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡄⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡶⢢⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣯⢌⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡭⣿⣿⣿⣭⡭⣍⡇⠀⠀⢄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣺⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢏⡹⣆⠐⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⡟⠂⣄⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣇⠻⠄⠐⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⣻⣭⡫⠍⢉⡍⠁⠘⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⢡⣤⡄⠀⠤⠄⠘⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡦⠀⢠⠻⡟⠁⣼⢟⣡⣾⣷⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣿⣿⡆⠀⠈⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡠⠚⠋⠁⠀⠈⠓⠁⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⠸⠟⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠾⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣍⡤⣠⣶⣿⣯⣤⣼⣿⣷⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣻⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠅⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠙⢝⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡂⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣚⣿⣇⣀⣿⣿⣙⣧⣿⣿⣟⣠⣿⣿⣿⣧⣽⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⣿⣜⣟⣿⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⡗⠲⣤⣄⠉⡉⠟⠛⢿⠝⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠿⠿⡿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⡿⠇⠀⠀⠀⠀⠀⠀⠠⠼⠾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⡧⢼⣔⢢⢂⢦⠆⠀⣧⢾⢰⠶⠐⢺⢸⡰⠆⠀⡯⠅⡲⡆⡇⢠⠶⢰⢺⠀⢐⢦⢸⠂⠈⣶⠉⡽⠃⠠⡏⠁⡖⡆⠄⠄⢰⣤⡄⡰⡄⠔⣆⣴⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣇⣁⣊⣈⣁⣈⣈⣀⠀⠀⠈⠀⠉⠈⠉⠈⠈⠁⠀⠁⠀⠉⠁⠁⠀⠉⠈⠉⠀⠈⠉⠈⠁⠈⠀⣉⣉⣉⣀⣉⣁⡉⠀⠈⠀⠈⠀⣀⠀⠀⠒⠃⠈⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣄⠤⣀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣟⠦⡀⢈⡁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣶⣿⣿⣿⣿⣿⡄⠀⢠⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣦⣣⣄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢪⣽⣻⡅⠂⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣋⣭⣙⡇⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡳⣟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣥⣾⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⠱⠎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⠂⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢿⠰⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⣻⣿⡿⠟⢉⡭⠁⠘⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⣩⣤⡄⠀⢔⠀⠐⠋⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡦⠀⢠⠻⡟⠁⣼⠟⣹⣾⣧⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣿⢿⠆⠀⠀⠃⠈⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠁⠀⠈⠃⠁⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢰⡟⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣍⣤⣠⣶⣿⣯⣤⣼⣿⢷⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣻⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠅⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡽⡛⢱⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⡼⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣚⣿⣆⣂⣿⣿⣝⣷⣿⣿⣿⣠⣿⣿⣿⣧⣽⣽⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠋⠿⣿⣜⣟⣾⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⡿⡗⠲⣤⢄⠋⡉⠟⠛⠻⠝⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠿⠿⠿⠿⠿⠿⠅⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⡧⢼⡴⢢⢆⢆⠆⠀⢧⢼⢠⠢⠐⢺⢸⡐⠆⠀⡯⠅⡒⡄⡇⢠⠲⢠⢺⠀⢐⢢⢰⠂⠈⣲⠉⡹⠃⠠⡏⠁⡖⡄⠄⠄⢠⣤⡄⡠⡄⠄⣄⣤⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣇⣁⣚⣈⣁⣈⣈⣀⠀⠁⠈⠈⠉⠈⠉⠈⠈⠁⠀⠁⠀⠉⠁⠁⠀⠉⠈⠉⠀⠈⠉⠈⠁⠈⠀⣉⣉⣉⣀⣉⣋⡉⠁⠈⠀⠈⠀⣀⠉⠁⠚⠃⠈⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⠄⣀⢤⡀⢀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣭⢰⡀⣤⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣆⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢻⣥⣯⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⢟⣭⢍⡃⠀⠀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡯⣟⠠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⡗⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢟⡵⢇⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⠃⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⢏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⡛⠛⢉⣭⠁⠐⢩⣝⡍⠉⣩⣿⣿⣯⠉⢹⡏⣩⣤⡄⠀⡤⠀⠐⠇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡧⠀⢠⢻⡟⠁⣼⡿⣻⣾⣷⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣿⣿⡆⠀⠀⠃⠈⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢋⡠⠚⠋⠁⠀⠘⠃⠅⠀⣿⣾⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢸⡟⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⣤⣠⣶⣿⣯⣤⣼⣿⣧⣷⣶⣶⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣻⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡝⡛⢙⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡃⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣿⣆⣀⣿⣿⣏⣶⣿⣿⣿⣠⣿⣿⣿⣧⣽⣽⣧⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢈⡉⠈⠋⠿⣿⣜⣟⣽⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⡗⢲⣤⣔⠋⡉⠟⠛⢿⠝⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠀⠀⠀⠀⠀⠀⠸⡿⢿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠼⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⡧⢼⡴⢢⢆⢆⡆⠀⢣⣼⢠⠢⠠⢺⢸⣐⡀⠀⡯⠅⣐⡄⡏⢠⣢⢠⢺⠀⢀⢢⢰⠂⠈⣲⠉⡩⠃⢠⡏⠁⡔⠄⠀⠄⢠⣤⡄⡀⡄⠠⣤⣤⠄⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣇⣁⣊⣈⣉⣈⣈⣀⠀⠁⠈⠈⠉⠈⠉⠈⠉⠁⠀⠁⠀⠉⠁⠁⠈⠉⠈⠉⠀⠈⠉⠈⠁⠈⠀⣉⣉⣉⣀⣉⣋⡉⠁⠈⠀⠁⠀⣀⠁⠁⠁⠃⠁⠁⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠤⡤⢄⠄⢠⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣯⠌⡐⢢⡁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠋⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢞⣴⢢⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣯⣍⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡯⢽⣿⣿⢏⢭⢍⡃⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢫⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠏⠐⠆⠂⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣾⣿⣿⠁⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⡃⠐⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣻⣿⡿⠍⢉⡭⠁⠘⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⣩⣤⡄⠀⠴⠠⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡧⠀⢈⢹⡟⠁⣼⠟⣡⣾⣧⡌⣿⣧⠀⢸⣿⢿⣿⠀⢸⣷⣿⠿⡆⠀⠀⠁⠘⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢋⡠⠚⠋⠀⠀⠘⠃⠅⠀⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣴⣶⠀⢰⡟⠖⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡺⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣍⡤⣠⣶⣿⣯⣤⣼⣿⢻⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠇⠹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡝⡛⢹⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣬⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡂⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣻⣆⣀⣿⣿⣝⣷⣿⣿⣟⣡⣿⣿⣿⣧⣿⣷⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠋⠿⣿⣜⣟⣾⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⡿⡗⠲⣤⢄⠋⡉⠟⠛⢻⠟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⠿⠿⠿⠯⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠼⠾⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⡧⢼⡤⢤⢄⣄⡄⠀⢢⣴⢠⣠⠠⢸⢨⢀⡄⠀⡦⠅⣄⡄⡅⢠⣠⢠⢸⠀⢠⣠⢰⠀⠀⣦⠀⡩⠃⢠⡎⠃⡄⠄⠀⠄⢠⣤⡄⣀⡄⠤⣄⣤⠄⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⣇⣁⣊⣈⣉⣈⣈⡀⠀⠁⠈⠈⠈⠈⠈⠈⠁⠁⠀⠁⠀⠁⠁⠁⠈⠈⠈⠈⠀⠈⠈⠈⠀⠈⠀⣉⣉⣈⣀⣉⣋⡁⠁⠀⠀⠀⠀⠀⠁⠁⠡⠃⠁⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢴⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⡀⣀⢤⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⠬⡀⢈⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⡽⢁⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣗⣝⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢽⣿⣿⢏⢵⢭⡇⠀⠀⢄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⢟⡵⠌⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⠃⣀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣇⡱⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⣻⣯⡽⠏⢉⡭⠁⠀⢩⣘⣍⠉⣩⣿⣿⣯⠉⢹⡏⣨⣤⡄⠀⡴⠠⠐⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡧⠀⢠⠻⡟⠁⡾⢟⣭⣾⣧⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣿⠿⠆⠀⠘⠃⠀⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡠⠚⠋⠁⠀⠈⠃⠁⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢰⡛⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡤⣠⣶⣿⣯⣤⣼⣿⣧⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣻⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠇⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⡛⢓⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣚⣾⣇⣀⣿⣿⣏⣦⣿⣿⣟⣠⣿⣿⣿⣧⣽⣿⣢⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢈⡉⠈⠋⠿⣿⣜⣟⣿⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⡗⠲⣤⣄⠉⡉⠟⠛⢿⠝⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⣆⣰⡠⢄⣄⡄⡄⠀⣂⣴⢠⣤⠠⢴⢰⢠⡄⠀⣖⡂⣤⡄⡆⢠⣤⢠⢴⠀⠠⣤⢰⠄⠐⣤⠒⣲⠂⢀⡖⠂⡤⡄⡀⠄⢤⣠⡤⢤⡄⡤⣄⣤⡄⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⠃⠚⠙⠊⠘⠘⠀⠀⠉⠘⠈⠒⠘⠚⠘⠑⠀⠀⠁⠀⠓⠃⠃⠈⠒⠈⠚⠀⠘⠚⠘⠂⠐⠉⠒⠓⠊⠀⠑⠃⠑⠁⠐⠀⠒⠀⠀⠒⠃⠴⠃⠐⠀⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠼⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⠤⣤⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⢆⣮⠦⡑⢺⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣆⠀⢠⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣨⡿⣫⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣞⢯⡤⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣿⣿⣿⣯⣭⢍⡆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡹⣦⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣾⣷⣾⡇⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⢐⡊⡁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣛⣿⣿⡟⠀⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡿⠳⠊⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⣻⣭⡙⠉⢉⡭⠀⠘⢩⣟⡍⠉⣩⣿⣿⣭⠉⢹⡏⣠⣤⡄⠀⠤⠠⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡧⠀⢈⢻⡟⠀⡼⠟⣱⣾⣿⡄⣿⣧⠀⢸⣿⢿⣿⠀⢸⣷⣿⠿⡆⠀⠐⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢋⡠⠞⠋⠁⠀⠘⠃⠁⠀⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⠰⠟⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠺⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣩⡤⣴⣶⣿⣯⣤⣼⣿⢻⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣻⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠓⠟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⡛⢹⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣻⣇⣂⣿⣿⣿⣷⣿⣿⣟⣡⣿⣿⣿⣧⣽⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠋⠿⣿⣜⣟⣾⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⡿⡗⠲⣤⢄⠋⡉⠟⠛⠻⠝⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⣆⣰⡠⢄⡄⡄⡄⠀⢆⣰⢀⣄⠠⢴⢰⢠⡄⠀⣖⡂⢤⡀⡆⢀⣤⢠⢴⠀⠠⣄⢰⠄⠐⢤⠒⢲⠆⢀⡖⠂⡤⡀⡀⠀⢠⣠⡤⠠⡄⠠⡄⣤⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⠃⠘⠙⠊⠘⠘⠀⠀⠋⠘⠈⠒⠐⠚⠘⠑⠂⠀⠃⠀⠓⠃⠃⠈⠒⠘⠚⠀⠘⠚⠘⠂⠐⠉⠒⠓⠊⠀⠓⠃⠓⠃⠐⠀⠒⠒⠀⠒⠃⠶⠇⠒⠂⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⢤⢠⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⢤⣥⢂⠄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⡄⠀⢀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡯⢺⣽⣲⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣫⠄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⢏⣭⢍⡂⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣧⣆⡁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣻⣟⢱⠎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣺⣿⣿⠃⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢵⣮⠡⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⣻⣿⡿⠏⢉⣭⠁⠈⢩⣍⡍⠉⣩⣿⣿⣭⠉⢹⡏⣨⣤⡄⠀⠐⠠⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢶⡧⠀⢘⠹⡟⠁⣾⡿⣫⣾⣷⣼⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣵⠿⡆⠀⠐⠃⠘⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠀⠀⠘⠓⠅⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⠰⡛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡺⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣄⣤⢤⣶⣿⣯⣤⣼⣿⣯⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣻⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⠛⠋⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣻⣇⣐⣹⣿⣽⣶⣿⣿⣿⣠⣿⣿⣿⣧⣽⣿⣂⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢈⡉⠈⠋⠿⢿⣜⣟⣽⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⡗⠲⣤⣔⠋⡉⠟⠛⢿⠝⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡇⣆⣰⣠⢄⡄⡄⡄⠀⣆⣰⢀⢄⢀⢴⢰⠠⠄⠀⣖⡂⠠⡀⡆⢀⢄⢀⢴⠀⠀⢄⢠⠄⠐⢤⠒⢒⠆⢀⡖⠂⡠⡀⡀⡀⢠⣠⡄⠠⡄⠠⣤⣤⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⠃⠚⠑⠚⠘⠘⠁⠀⠋⠘⠘⠒⠐⠚⠘⠑⠂⠀⠃⠀⠓⠃⠃⠘⠒⠘⠚⠀⠘⠚⠘⠂⠐⠉⠒⠓⠊⠀⠓⠃⠓⠃⠐⠀⠒⠒⠀⠓⠃⠒⠇⠒⠂⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⠃⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⢠⡀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⡧⣂⡄⢀⡁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣆⠀⢠⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢝⣧⣡⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢀⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣎⣯⣏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⠟⠭⠬⣁⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣫⡞⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⠂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⡟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⢟⡙⢦⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣮⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣺⣿⣿⠇⣄⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡖⡨⣆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣻⣿⡯⠏⢉⣭⠉⠀⢩⢨⡍⠉⣩⣿⣿⣯⠉⢹⡏⣠⣤⡄⠀⢰⠀⠀⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡧⠀⢨⠹⡟⠁⣼⠿⣫⣾⣧⣼⣼⣷⠀⢸⣿⣿⣿⠀⢸⣷⣽⡿⡆⠀⠈⠁⠘⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⡠⠚⠋⠁⠀⠘⠓⠄⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⠰⠻⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠺⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣄⣤⢤⣶⣿⣯⣤⣼⣿⣧⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢈⡭⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡝⠛⣼⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⣀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣚⣿⣇⣐⣸⣿⣻⣷⣿⣿⣿⣠⣿⣿⣿⣧⣽⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠋⠿⣿⣜⣟⣾⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⡿⡗⠲⣤⢄⠋⡉⠟⠛⢻⠟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡏⣏⣹⣉⢍⡉⡍⡀⠀⢆⣰⢀⢀⢀⢰⢐⠀⡀⠀⣔⡋⡉⡉⡋⢀⢀⢀⢰⠀⠀⢀⢠⠀⠐⣤⠒⢛⠏⢉⡝⠫⡁⡀⠀⡀⢠⣠⡄⠀⡄⣀⣠⣤⡈⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⠃⠘⠑⠚⠘⠙⠁⠀⠋⠙⠘⠙⠐⠚⠘⠚⠃⠀⠃⠀⠛⠃⠃⠘⠛⠘⠚⠀⠘⠛⠘⠀⠐⠉⠒⠓⠊⠈⠓⠓⠃⠂⠐⠀⠒⠒⠀⠓⠃⢒⠇⠒⠂⠉⠙⠛⠿⠿⣿⣿⣿⣧⣾⣗⣽⢺⢏⣿⢟⣿⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠴⠂⠀⠀⠀⠈⠁⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⠤⣠⠤⣀⢀⡀⠄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡣⡅⠂⡁⢨⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣷⡀⠀⢢⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⠜⣠⣄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣋⢣⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡆⢀⠀⢠⣾⢩⣿⣿⣿⣿⢭⣤⣍⠀⠀⠠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠺⢆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠿⠛⠀⠈⣼⣾⠇⣼⣶⣿⣿⣷⣷⣶⣾⠇⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⢟⠵⡆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣴⣾⣿⠋⠀⣿⣿⣿⣿⡿⣿⣿⡟⠀⣄⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡮⡱⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠤⠺⠿⠿⠏⠛⠛⠁⢀⠂⠘⢻⣟⡻⠛⢋⣭⠁⠀⢹⣯⣍⠉⢩⣿⣿⣯⠉⢹⡏⢠⣤⡄⠀⠔⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⣸⣟⠀⣜⡋⠀⠀⠀⠸⠀⠀⠀⠈⠟⠁⣴⠾⣣⣾⣷⡼⣿⣷⠀⢸⣿⣿⣿⠀⢸⣷⣧⢿⡄⠀⠀⠂⠈⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⠇⢸⣿⣿⠀⠹⠍⠀⠀⠀⠃⠁⠀⠈⠛⠂⠀⡿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣴⣶⣶⠀⢸⡟⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣴⣾⣿⡇⠸⣷⡉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿⠃⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⡿⠇⠀⠯⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣌⡬⣵⣶⣿⣯⣤⣼⣿⣧⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣻⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⡓⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⢴⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣟⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣃⣛⣚⣀⡀⡀⢀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣸⣟⣇⣳⣻⣿⣿⣷⣿⣿⣟⣠⣿⣿⣿⣧⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠋⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⡟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⡗⢲⡤⣤⠉⡉⠟⠛⠛⠉⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡏⡏⢩⣉⣉⡉⡉⡀⠀⡄⣠⢀⣀⢀⣠⢩⢉⡉⠉⡭⠍⣉⡉⡍⢉⣉⢉⣩⠁⢀⣀⢠⡀⠀⣀⠭⢭⠍⢉⡭⠭⣁⡀⠀⡀⣠⣠⣄⣈⡍⣉⣍⣭⠉⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⠏⠻⠳⠜⠸⠹⠁⠀⠋⠙⠘⠍⠐⠼⠘⠪⠃⠀⠃⠀⠫⠇⠇⠘⠍⠘⠼⠀⠘⠽⠘⠄⠠⠉⠤⠯⠌⠈⠣⠗⠣⠃⠱⠀⠩⠑⠀⠪⠇⣢⠇⠫⠁⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⣿⣿⣿⣿ ⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⡀⠴⠂⠀⠀⠀⠀⠀⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⠄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⠽⣍⢂⡁⢀⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⡄⠀⢠⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣼⢢⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⡦⢫⣶⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⢭⣴⣌⡇⠀⠀⠄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣺⣆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣿⣿⣿⣿⣶⣾⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣟⡿⣲⣏⡱⠯⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣜⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡀⢀⣀⣿⣿⣿⣿⣟⣿⣿⡿⠀⣤⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡯⠱⢎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⢿⡿⠎⡗⣸⠛⠁⠫⣍⡛⠋⢉⡭⠁⠀⢹⣭⣭⠉⢩⣿⣿⣯⠉⢹⡏⢠⣤⡄⠀⠤⠠⠐⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⣿⡗⠀⠀⠀⠀⠀⠀⠀⠛⠀⣼⠿⣡⣾⣧⣼⣿⣷⠀⢸⣿⣿⣿⠀⢸⣷⣿⣻⡅⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠸⠀⠼⠁⠁⠀⠀⠃⠁⠀⠈⠓⠂⠀⣶⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⠰⡟⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⡠⠄⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡤⣵⣶⣿⣯⣤⣼⣿⣧⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣄⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⠍⠙⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣟⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣴⣿⣇⣟⣿⣄⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣹⣇⣁⣿⣿⣶⣧⣿⣿⣿⣠⣿⣿⣿⣧⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠋⠿⢿⣜⣟⣽⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣗⠲⣤⣄⠋⡉⠟⠻⠻⠝⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡏⡏⢩⢍⡉⡉⡉⡁⠀⡄⣠⢀⣀⢀⣠⢩⢉⡉⠉⡭⠍⣉⡉⡍⠉⣉⢉⣩⠁⢀⡀⢠⡀⠠⣀⠭⢭⡍⠉⡭⠭⣁⡀⠀⡀⢠⣠⣄⣉⡍⢉⣍⣭⠉⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⠏⠻⠻⠜⠱⠱⠁⠀⠟⠹⠘⠭⠠⠼⠸⠪⠅⠀⠏⠁⠮⠇⠇⠘⠭⠘⠼⠀⠰⠽⠸⠄⠠⠛⠤⠮⠌⠈⠧⠇⠧⠃⠡⠀⠤⠱⠀⠦⠇⣦⡇⠢⠄⠉⠙⠛⠿⠿⣿⣿⣿⣧⣾⣗⣽⢺⢏⣿⢟⣟⣻⢿⣿⣿⣿ ⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⡀⠴⠂⠀⠀⠀⠀⠀⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣀⠤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⠦⡧⠼⡁⢉⡁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣆⠀⢀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⢎⣶⣶⣤⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣤⣝⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢽⣿⣿⢏⣭⢌⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⡞⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠏⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣜⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣺⣿⡿⢀⣄⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⢲⠆⠐⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⣻⣿⡿⠟⢉⡭⢁⠘⢩⣽⡍⠉⣩⣿⣿⣭⠉⢹⡏⢨⣤⡄⠀⡰⡀⠈⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⢾⡧⠀⢨⢹⡟⠁⠼⢟⣵⣾⣼⡄⣿⣶⠀⢸⣿⣿⣿⠀⢸⣷⣿⠻⠇⠀⠘⠃⠀⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢋⡠⠚⠏⠁⠀⠘⠓⠁⠠⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⠸⡛⠃⠚⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⣵⣶⣿⣯⣤⣼⣿⢹⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⡩⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡍⡑⣿⣿⣟⢿⣿⣿⣿⠜⣿⣿⣿⡏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⣀⡀⢀⢀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣸⣿⣇⣢⣻⣿⣽⣧⣿⣿⣏⣧⣿⣿⣿⣧⣯⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢀⡉⠈⠋⠿⣿⣜⣟⣿⣿⣟⣷⣽⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣗⢲⣤⣄⠋⡉⠟⠻⢿⠝⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣷⣶ ⣿⣿⡏⡏⢩⢉⡉⡉⡉⡁⠀⡄⢠⠀⡀⢀⣠⢩⢉⡉⠉⡭⠍⣉⠉⡍⠉⣉⠉⣩⠁⠀⡀⢀⡀⠠⣀⠭⢭⡍⠉⡭⠍⣁⠀⠀⠀⢠⣠⡄⢉⡍⢩⢩⣭⠉⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⠏⠹⠫⠜⠱⠱⠁⠀⠟⠹⠸⠬⠠⠼⠸⠢⠄⠀⠏⠁⠦⠇⠇⠘⠬⠸⠼⠀⠰⠼⠸⠄⠠⠚⠤⠮⠌⠈⠧⠇⠧⠇⠣⠐⠤⠵⠀⠦⠇⣤⡇⠦⠄⠉⠙⠛⠿⠿⣿⣿⣿⣧⣾⣗⣽⢻⢏⣿⢟⣿⣻⢿⣿⣿⣿ ⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡤⡤⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⠸⡁⣈⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⡛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣶⡀⠀⢈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣻⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣟⣿⣿⣿⢛⣭⣛⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣷⣦⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⢧⡻⡎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣜⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⡟⢀⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡱⠆⠐⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢛⣻⣿⡟⠛⢋⡭⠁⠘⠁⣽⡭⠉⣩⣿⣿⣯⠉⢹⡏⣩⣤⡄⠀⠲⠀⠘⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⢾⡧⠀⢘⢿⡟⠁⣴⠟⣩⣾⣼⡄⣿⣤⠀⢸⣿⣿⣿⠀⢸⣷⣿⡻⡆⠀⠐⠃⠈⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⡠⠚⠋⠁⠀⠘⠊⠁⠠⣶⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢰⡛⠎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⡤⣰⣶⣿⣯⣤⣼⣿⢻⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡆⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠛⣙⣿⣿⣟⢿⣿⣿⣿⠜⣽⣿⣿⡏⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣟⢿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣿⣆⣐⣿⣿⣹⣷⣿⣿⣏⣣⣿⣿⣿⣧⣽⣿⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢀⡉⠈⠋⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣷⢲⣤⣄⠋⡉⠟⠛⠟⠝⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡟⡟⢻⣟⡛⡛⡉⡀⠀⡄⢠⠀⡀⠀⢠⠩⢉⠉⠉⡭⠍⢉⠉⡍⠉⡉⠉⣩⠁⠀⡀⢀⠀⠠⣀⠭⠽⡟⠙⡫⢟⢃⠀⠀⠀⢠⣠⡄⠈⡍⠩⢍⣭⠉⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⠏⠻⠪⠼⠱⠱⠃⠀⠟⠻⠸⠾⠨⠼⠸⠲⠆⠀⠏⠁⠶⠇⠇⠸⠾⠸⠼⠀⠰⠾⠸⠄⠠⠚⠤⠮⠌⠈⠧⠇⠧⠇⠢⠑⠶⠶⠀⠶⠇⠤⡇⠶⠆⠉⠙⠛⠿⠿⣿⣿⣿⣧⣾⣗⣽⢺⢏⣿⢟⣟⣻⣿⣿⣿⣿ ⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠒⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣠⠄⣀⢀⡄⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣽⢿⣅⢀⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡄⠀⢠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣸⡞⣪⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⢸⣾⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⢟⣫⣉⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣫⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⠃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣶⣼⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢯⣹⣇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣜⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⣿⣿⡿⢀⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⡩⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢛⣻⣿⡿⠟⢉⣭⠁⠘⢩⣝⡭⠉⣩⣿⣿⣯⠉⢹⡏⢡⣤⡄⠀⠀⠄⠐⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢲⢾⡧⠀⠘⢿⡟⠁⣼⠟⣣⣾⣼⡄⣿⣧⠀⢸⣿⣿⣻⠀⢸⣷⣽⡿⠆⠀⠑⠃⠈⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⡠⠚⠋⠁⠀⠘⠊⠃⠀⣶⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⢸⠻⠪⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣡⣠⣶⣿⣯⣤⣼⣿⢹⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠞⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠟⢓⣿⣿⡟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣷⣇⣀⣿⣟⣃⣷⣿⣿⣟⣡⣿⣿⣿⣧⣽⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠋⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣗⢲⣤⣄⠋⡉⠟⠛⢛⠟⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡟⡛⢛⠟⠛⠛⠛⠀⠀⡀⢀⠀⠀⠀⢀⠛⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⢛⠃⠀⠀⢀⠀⠀⠀⢙⣛⡛⠛⣛⣛⠃⠀⠀⠀⢠⣠⡄⠈⡍⠩⢍⡉⠙⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⡏⢺⢮⡹⢱⢳⠃⠀⠖⠻⠸⡛⠨⢹⠸⢜⠇⠀⠇⠀⢟⡇⠇⠸⡛⠸⡹⠀⠸⠻⠸⡁⢀⠛⣠⣎⡈⠘⢇⡃⢏⠅⢢⠓⢖⠲⠀⠖⡆⠅⡇⢗⠃⠉⠙⠛⠿⢿⣿⣿⣿⣧⣾⣗⣽⢺⢏⣿⢟⣟⣻⣿⣿⣿⣿ ⣿⣿⣷⣴⣶⣶⣶⣴⣶⣦⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣶⣶⣶⡆⠀⠀⠀⠀⠤⠀⠀⠀⠉⠀⠀⠐⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣠⠄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣦⣤⣄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢇⣿⢠⡉⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⢰⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢭⡯⣠⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣎⢻⣔⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣐⣛⣢⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣳⡮⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣟⡿⢷⣾⡵⡎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣜⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣽⣿⣿⡏⢠⣄⣄⣄⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣯⢿⣽⠎⠸⠂⠐⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⢘⣻⣶⡶⠖⢊⡍⣀⠘⠀⣯⡍⠉⢩⣿⣿⣯⠉⢹⡏⢠⣤⠄⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢺⢿⡧⠀⢈⢻⡟⠁⣜⣫⣼⣿⣿⣄⣿⣷⠀⢸⣿⣿⣿⠀⢸⣷⡽⣟⠇⠀⠀⢁⠐⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢋⡠⠚⠋⠁⠀⠘⠃⠄⠀⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢸⠟⠄⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠇⠀⣿⣿⠀⢸⣿⡿⣿⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠰⠿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢄⣴⣶⣿⣯⣤⣼⣿⢳⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠂⠄⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠝⢞⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣟⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣸⣿⣇⣒⣿⣿⣰⣧⣿⣿⣟⣠⣿⣿⣿⣧⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠊⠿⢿⣜⣟⣽⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣗⠲⣤⣄⠋⡉⠟⠛⠛⠝⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡟⡛⢛⠟⠛⠛⠛⠀⠀⡀⢀⠀⠀⠀⢀⢛⠛⠛⠛⣛⡛⠛⠛⡛⠛⠛⠛⢛⠃⠀⠀⢀⠀⢀⠀⣙⣛⡛⠛⣛⣛⠃⠀⠀⠀⢠⣠⡄⠈⡍⠉⠉⣭⠙⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⡗⢺⢮⡱⢣⢳⠃⠀⠗⢻⠸⣛⢨⣹⢸⢜⠃⠀⠗⠂⣟⡇⡇⠰⣛⠸⣹⠀⢨⣻⢸⡁⢀⠿⣀⣞⡈⠐⣇⡃⣏⠇⢢⠓⣛⠲⠀⣞⡆⢍⡇⢞⡂⠉⠙⠛⠿⠿⣿⣿⣿⣧⣾⣗⣽⢺⢏⣿⢟⣟⣻⣿⣿⣿⣿ ⣿⣿⣧⣤⣦⣤⣤⣤⣤⣤⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⡀⠤⠀⠀⠀⠉⠀⠀⠀⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⠀⡀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣭⢆⡀⢠⠅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣆⠀⢠⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⢻⣇⣳⡔⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣣⣗⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⢛⣭⢙⡇⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡳⣞⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⠏⡱⢌⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⡿⠀⣄⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡏⠱⠇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⣻⣿⡻⠏⢉⡭⠁⠘⢩⣝⡍⠉⣩⣿⣿⣯⠉⢹⡏⢡⣤⡄⠀⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⢾⡧⠀⢘⢻⡟⠁⡴⢟⣯⣾⣽⡄⣿⣧⠀⢸⣿⢿⣿⠀⢸⣷⣽⠟⠇⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢋⡠⠚⠋⠁⠀⠘⠂⠁⠠⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⢠⡛⠀⠛⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⡥⣰⣶⣿⣯⣤⣼⣿⢻⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣛⠟⣙⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣾⣷⣆⣐⣿⣿⣿⣶⣿⣿⣿⣠⣿⣿⣿⣧⣽⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠊⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣗⢲⣤⣄⠋⡉⠛⠛⢛⠟⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡟⡛⢛⡛⠛⠛⠛⠀⠀⡀⢀⠀⠀⠀⢀⢛⠛⠛⠛⣛⡛⠛⠛⡛⠛⠛⠛⢛⠃⠀⠀⢀⠀⢀⠀⣙⣛⡛⠛⣛⣛⠃⠀⠀⠀⢠⣠⡄⠈⡍⠉⣭⣭⠙⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⡗⢺⢾⡱⢣⢣⠃⠀⡷⢺⢰⣑⢈⣹⢸⢌⡃⠀⡗⠂⣝⡆⡇⠰⣛⢸⣹⠀⢨⣱⢸⡁⢀⠽⣀⣜⡉⠐⣇⡃⣏⡆⢆⠢⣘⣲⠀⣜⡆⣂⡇⣎⡂⠉⠙⠛⠿⠿⣿⣿⣿⣧⣾⣗⣽⢺⢏⣿⢟⣟⣻⣿⣿⣿⣿ ⣿⣿⣧⣤⣦⣤⣤⣤⣤⣤⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡆⠀⠀⠀⠀⠤⠀⠀⠀⠉⠁⠀⠀⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⠀⡀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡵⢠⣅⢀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡄⠀⢀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⢲⡔⢂⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣲⣾⢢⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣿⣿⣿⣭⡭⣙⠀⠀⠠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡃⣆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣟⡕⢆⠠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣘⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣻⣿⣿⠇⢀⣀⡀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢏⠡⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣻⣿⡿⠏⢋⡍⢀⠘⠉⣟⡍⠉⢩⣿⣿⣯⠉⢹⡏⣡⣤⡄⠀⢤⠄⠀⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⢾⡧⠀⠸⢿⡟⠀⡼⢋⣴⣾⣼⡄⣿⣧⠀⢸⣿⢿⣿⠀⢸⣷⣷⣿⠆⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡠⠚⠋⠁⠀⠘⠊⠃⠀⣾⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣴⣶⠀⠸⡟⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡥⣠⣶⣿⣯⣤⣼⣿⢻⣷⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠑⠹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⠟⣙⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣟⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣿⣆⣑⣿⣿⣹⣧⣿⣿⣟⣠⣿⣿⣿⣧⣿⣿⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠊⠿⢿⣜⣟⣽⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣗⠲⣤⣄⠋⡉⠟⠛⠛⠍⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡟⡛⢛⡛⠛⠛⠛⠀⠀⡀⢀⠀⠀⠀⢀⢛⠛⠛⠛⣛⡛⠛⠛⡛⠛⠛⠛⢛⠃⠀⠀⠀⠀⢀⠀⣙⣛⡛⠛⣛⡛⠃⠀⠀⠀⢠⣠⡄⠈⡍⠉⢩⣭⠙⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⡗⢺⢞⣱⢣⢣⠇⠀⡷⢺⢰⣑⢐⣹⢸⢌⡀⠀⡗⠂⣌⡆⡇⢰⣑⢰⣹⠀⢠⣱⢸⡁⢀⠽⣀⣔⡉⠐⣇⣃⣎⡆⢆⠢⣀⣲⠀⣄⡆⣂⡆⣆⡂⠉⠙⠛⠿⠿⣿⣿⣿⣧⣾⣗⣽⢺⢏⣿⢟⣟⣻⣿⣿⣿⣿ ⣿⣿⣧⣤⣦⣤⣤⣤⣤⣤⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⡀⠤⠀⠀⠀⠀⠁⠀⠀⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣠⠀⣄⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡖⠲⡝⠦⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣆⠀⢠⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⢗⡄⢋⡕⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣞⣵⣏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⡯⢿⣿⣿⢟⣭⢍⡃⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣎⡹⡆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣟⡿⣻⣏⡽⢏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣜⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣾⣿⣿⠀⣄⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⠷⢸⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣻⣿⡿⠛⢋⣭⠁⠘⢹⣍⡍⠉⣩⣿⣿⣯⠉⢹⡏⢠⣤⡄⠀⠠⠠⠐⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⢾⡧⠀⢘⢻⡟⠀⣼⠛⣩⣾⣷⣼⣿⣷⠀⢸⣿⣿⣿⠀⢸⣷⣵⢿⡆⠀⠐⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢋⡠⠚⠋⠁⠀⠘⠂⠅⠠⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣴⣶⠀⢸⣟⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣍⣤⣠⣶⣿⣯⣤⣼⣿⢹⣷⣶⣶⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢈⠯⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣝⡛⢓⣿⣿⣟⢿⣿⣿⣿⠜⣿⣿⣿⡏⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣻⣆⣂⣿⣿⣽⣷⣿⣿⣿⣠⣿⣿⣿⣧⣽⣿⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠊⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣗⢲⣤⣄⠋⡉⠟⠛⢛⠟⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡿⠿⠿⡿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠛⠻⠿⠿⠿⠿⠿⠿⡿⠿⠿⠟⢛⠃⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠇⠀⠀⠀⢠⣠⡄⠨⠉⠍⣭⣭⠹⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⡗⢺⢔⣲⢢⢦⠆⠀⠧⢾⢰⠶⢐⢺⢰⡰⡆⠀⡗⠂⡶⡆⡆⢰⠶⢰⢺⠀⢰⢶⢸⠀⠀⠶⣀⡜⠉⠠⣏⣋⡖⡂⢆⠦⡶⣶⠒⡶⡆⡒⡆⡶⠆⠉⠙⠛⠿⠿⣿⣿⣿⣧⣾⣗⣽⢺⢏⣿⢟⣟⣻⣿⣿⣿⣿ ⣿⣿⣧⣥⣮⣤⣥⣬⣤⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣭⣭⣥⣤⣬⣥⡄⠀⠀⠀⡀⠀⠀⠀⠀⠒⠁⠀⠀⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⠤⣠⢄⡠⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡶⢨⣡⢈⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡄⠀⢈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢹⡍⢢⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢽⣟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢛⣭⣉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡗⢢⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⣽⠎⠠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣜⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⡟⢀⣀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣇⡰⢆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣻⣿⡛⠛⢉⡭⠁⠘⠉⣿⡭⠉⣩⣿⣿⣯⠉⢹⡏⢨⣤⡄⠀⠠⠀⠘⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⢶⡧⠀⠸⢿⡟⠁⡶⠟⣡⣾⣼⡄⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣽⣻⠆⠀⠐⠃⠀⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢋⡠⠚⠋⠁⠀⠘⠈⠃⠠⣿⣿⣿⣿⡍⠉⣿⣿⠀⢨⣤⣶⣶⠀⢐⡛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠾⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡤⣰⣶⣿⣯⣤⣼⣿⢹⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠎⠇⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⠟⣙⣿⣿⡟⢿⣿⣿⡏⡜⣽⣿⣿⡏⡬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣟⢿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣗⣇⣐⣿⣿⣽⣷⣿⣿⣇⣧⣿⣿⣿⣧⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠋⠿⢿⣜⣟⣽⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣗⠲⣤⣄⠋⡉⠟⠛⠛⠝⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢿⣿⣿⡿⣿⣿⣿⣶⣶ ⣿⣿⡿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠇⠀⠀⠀⢠⣠⡄⠨⠉⠍⣭⣭⠹⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣿⣿⣿⣯⣿⣿⣯⣿⢽⣿⣿⣿ ⣿⣿⡇⡧⢼⣴⢲⢦⢦⠆⠀⡧⢾⢰⠶⢐⢺⢸⡰⠆⠀⡏⠁⡶⡆⡇⢰⠶⢰⢺⠀⢰⢶⢸⠂⠀⢶⣉⡽⠉⠠⡏⢋⡖⡆⢆⠦⠶⢴⠒⡶⡆⡒⡆⡶⠆⠉⠙⠛⠿⠿⣿⣿⣿⣧⣾⣗⣽⢺⢏⣿⢟⣟⣻⣿⣿⣿⣿ ⣿⣿⣇⣡⣪⣨⣁⣈⣈⣀⡀⠀⡀⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠉⠀⠀⠉⠀⠁⢈⣀⣉⣉⣁⣀⣈⣁⡈⠀⠈⠀⠈⠀⠀⠈⠁⠚⠁⠈⠀⠢⠤⣀⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣾⣿⣮⣛⣊⡟⣼⣺⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠚⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⠄⡠⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣭⢤⡕⢚⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⡟⢋⢻⡟⠛⣿⡟⠛⠉⣉⡛⠛⢿⣿⣿⡏⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⠀⠀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢲⣾⣢⡅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⢂⠘⣿⣿⡟⢀⢀⣾⠇⡀⣿⡇⡈⢰⣶⣶⣅⢂⠙⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣾⣠⣎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠂⠸⠟⢀⢀⣾⣿⠀⠃⣿⡇⡆⣸⣿⣿⣿⠀⠇⣿⠃⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢽⣿⣿⠟⣭⠍⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⠻⣏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡌⣦⣤⢂⣾⣿⣿⠀⠆⣿⡃⡁⢽⡿⠿⢋⣰⢠⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣶⡟⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⠏⡹⢯⠡⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣜⣃⣾⣿⣿⣿⣄⣀⣿⣇⣂⣀⣀⣐⣾⣶⣿⣿⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣺⣿⣿⠃⣀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡹⢎⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠙⣻⣿⡟⠛⢉⣭⠁⠐⢩⣟⡍⠉⣩⣿⣿⣯⠉⢹⡏⢡⣤⡄⠀⠤⡠⠘⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⢶⡧⠀⠸⢿⡟⠁⣾⠟⣣⣾⣼⣜⣿⣧⠀⢸⣿⣿⣿⠀⢸⣷⣿⢿⠆⠀⠐⠃⠘⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⡠⠚⠋⠁⠀⠘⠊⠃⠠⣿⣿⣿⣿⡍⠁⣿⣿⠀⢨⣤⣶⣶⠀⠐⣟⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣥⣠⣶⣿⣯⣤⣼⣿⢻⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠤⠫⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠟⢓⣿⣿⣟⢿⣿⣿⣿⠘⣽⣿⣿⡏⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣀⣀⡀⢀⣀⣀⡀⡀⣀⣀⣀⠀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣺⣿⣇⣀⣿⣿⣩⣷⣿⣿⣟⣠⣿⣿⣿⣧⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⡉⠈⠊⠿⢿⣜⣟⣿⣿⣟⣷⣽⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⣹⣿⣿⣗⢲⣤⣄⠋⡉⠟⠛⢛⠟⠓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 3530 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2024/04/11/Video_Trainline_Finally_Issues_a_Refund_But_It_Took_9_Days_and_.shtml Gemini version at gemini://gemini.techrights.org/n/2024/04/11/Video_Trainline_Finally_Issues_a_Refund_But_It_Took_9_Days_and_.gmi ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] Trainline Finally Issues a Refund, But It Took 9 Days and Showed How 'Modern' Systems Fail Travelers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024 Video_download_link | md5sum 9ed9efd3df9169ef39dcdc2a441f8df3 Smart_is_Dumb Creative Commons Attribution-No Derivative Works 4.0 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Preview_for_Smart_is_Dumb⦈_ LAST WEEK I published "When_Electronic_(or_Digital)_is_Objectively_Worse" based on a personal experience, which wasn't the first (the video on the left covers more examples). I wrote about it over one week ago (as of today) and first, the good news: § Refund successful⠀➾ Your refund is being credited back to the account used to make the purchase. This transfer is normally completed within 5 working days but is dependent on your card issuer. OK, but how many hours did that take, including a trip to the Post Office? How many communications needed to be made prior to this? How many webforms needed to be filled? A week ago I wrote: "Now we have two irritated customers, 4 members of staff spending time on it, and maybe another 4 at the customer disservice centre. Total 10 people? How do these companies define "productivity"? Time getting nothing done?" Total 10 people? Now it's more like 12! That's really awful and "and that is happening at scale across all industries and yet people (politicians) wonder why productivity is declining," a friend has told me. So we had to interact with about 10 different people. It's like a big project. Had the the traditional (offline) process been followed, a refund would be issued on the spot (interaction with one person necessary, not 10). Put another way, years ago the issue would get settled at the station or stop, which was always manned (attended by persons with powers to correct things). Just say the train got canceled, get the money back. Simple, right? Or maybe, in some cases, pick up the phone, some local person would answer straight away (no voice menus), explain the train got canceled and the transaction can then be undone (rolled back). But now the goal they have in mind isn't helping customers but retaining the money of customers by making them tired, distracted, miserable. "Of course," a friend told me. "There was no excuse for the initial failure and even less for their footdragging." So I wanted to document what happened and do a video about it. I don't discuss my general, personal story as much as the general issue and how "modern" technology fails people, contributing to anxiety and a waste of valuable (increasingly scarce) time. Here is a message sent to my wife from Trainline a few days ago: Dear Rianne, Thank you so much for your email. I hope you are doing great. I have gone through your query and I sincerely apologize for the inconvenience may have caused to you due to train cancellation. I understand that this may disrupt your travel plans. Please rest assured, I will certainly check the details of the journey and assist you further in best possible manner. I have confirmed the cancellation in the journey and therefore I immediately requested full refund of 19.20 GBP successfully. As you have collected the tickets in this case I would kindly request you to please send your unused physical tickets back to the Trainline. Once our team will receive the tickets the refund will be processed within 7 to 10 working days or likely to be sooner. And please make sure that you send the tickets back to us within 28 days after that the refund validity will be expired and we won't be able to request refund from our end due to the UK rail industry policy on refund. Trainline PO Box 23972 Edinburgh EH3 5DA I would like to inform you that as an online retailer, we Trainline only sell tickets on behalf of the Train Operating Companies. Since we do not manage or operate the services hence on-board issues, last moment cancellations, disruptions or delays of any Train Operating Company are something out of Trainline's control. However I completely understand the disappointment of unexpected disruptions to travel plans and are committed to assisting you promptly. I really appreciate your patience and understanding with us throughout the process. I also wanted to provide you with a reminder of the terms and conditions associated with your tickets for future reference. Under the booking reference xxxxxxxxxxxxxx, I can see that you have purchased Advance single tickets for the journey. These tickets give the best value for your money and valid to travel on the specific date and time mentioned on the ticket. These are non-flexible and non-refundable tickets (only refundable in case of train cancellation). These tickets are subject to availability. I hope the information is useful. Please feel free to contact us back if you have any further query regarding this concern. I'd be more than happy to assist you. Once again, thank you so much for giving me an opportunity to assist you Rianne, Warm regards, Abhay Customer service representative. Rianne was unhappy about this for the following reasons: Hello, I'm not really happy with my recent experience and with Trainline. Please see the points below: 1. Trainline is asking me to send back the tickets that I have printed. Why did you insist on taking the booking reference numbers and shouldn't taking screenshots or taking photos of the ticket be sufficient in this protocol? 2. What is the address to send to, where should I post these tickets? 3. This will cost me money to pay for the post, set aside the time of preparation. Thus Trainline expects me to shoulder the hassle that they have cause me? You are giving me a lot more work, 4 days after the journey, as you are like the 9th person I speak to already, and you also want me to pay for the trouble Are you aware that after destroying the holiday for 2 people you also ruins a whole week for two people? Do you view us as valuable customers or a mere nuisance to tire down? Also, by insisting I post you the physical ticket you are insinuating that we are presumed guilty? Do you think I am defrauding you? Is that the policy of Trainline? The client is presumed a liar? 4. Trainline didn't even offer to refund the money they charged to print the tickets. 5. Are you aware that you flagrantly try to deflect blame to another company, thus further humiliating the client? The station manager already explained to me where the fault lies and here you are trying to play 'tennis' by pointing at one another and that further exacerbates how the client feels I could go on and on, but I will write about my bad experience with you and report accordingly. Unhappy Customer, Rianne Trainline responded: Dear Rianne Thank you for your response, First of all I am extremely sorry for all inconvenience may have caused to you through out the process. However, it is our responsibility to protect the valuable data of our valuable customers and that is why we are only authorized to assist only if our customer contact us using their registered email address. As per the identification and Verification policy, the registered email is required to access the account/booking and so that our team could assist you as per law. Secondly, I have already mentioned the address in the email that I sent to you. I apologize if I was unable to highlight the address properly in my previous response. Here is the complete address : Trainline PO Box 23972 Edinburgh EH3 5DA Lastly, I completely understand your concern that this may cost you money for sending tickets via recorded post. If you wish you can send your tickets via normal post. We only recommend recorded delivery to locate the tickets so that and to ensure that they are being sent to us successfully. However if you wish you can send your tickets via normal post as well. I completely understand that this may have increased your efforts, however even if you have purchased these tickets from other train operating company even in that case you would have to send unused tickets back to them. I hope you understand. I also understand that you have a concern regarding why booking fee was not refunded back to you. these fees really do go towards improving our products and services. We want to give you great value and hassle-free travel by rail and coach. It’s pretty much our thing. We keep a close eye on our fees to make sure we're always putting your money to the best use. For more information I have shared this link with you regarding booking fee : https://support.thetrainline.com/en/support/solutions/ articles/78000000706-fees We are not blaming anyone. It's a disruption and it can happen with anyone. We completely understand that there is no fault of yours at all and sincerely apologize for the unpleasant experience you had due to this unfortunate cancellation. Therefore I have requested refund on the tickets for you successfully and assure you that our team will process the refund once they receive the unused physical tickets. It will be credited back to the same payment address within 7 to 10 working days or likely to be sooner. Once again, thank you so much for your patience and understanding with us Rianne. Please feel free to contact us back if you have any further query. I'd be more than happy to assist you. Thanks and kind regards, Abhay Customer service representative And Trainline to me: (after I had stepped in; it was me who initiated the process, but my wife's account was used) Good Morning, Thank you for your email and I hope you are doing well. I completely understand your concern regarding the tickets that you had purchased with us. However, the tickets are under a different email account and to keep your details safe, we request you to kindly contact us using the same email address that was used for the booking in order to assist the query. As per the identification and Verification policy, the registered email is required to access the account/booking and so that I can help you better. I hope you understand we have to abide by the policies. Kind Regards, Deepali - Customer Service Representative So we had to speak to about 10 different people, making a total of about 12 (including us) to process what ought to have been a very trivial case. We spent so many hours on this. In the video above I include some examples of airlines with their notorious practice of "overbooking". They treat people like a bunch of animals or cattle, not like valuable customers. █ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Mother duck with ducklings, novodevichy, moscow⦈ ⠀⠀⠀⠮⡀⡔⡄⡄⡐⡄⡔⡖⠀⠨⠔⡀⠀⡏⢰⠀⢠⠀⠢⢢⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠂⡚⠑⠀⢘⣿⣿⣾⣟⣟⡛⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠁⠁⠁⠁⠉⠁⠁⠈⠀⠈⠉⠁⠀⠉⠁⠈⠁⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠉⣍⣭⢹⣿⣿⡧⠷⠇⢀⠐⠙⠿⢿⡿⠟⠁⠀⠀⠀⠈⠋⠙⢻⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣶⣶⣶⣶⣶⣶⣶⡄⢠⡲⣾⣿⣿⡆⣼⡣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⣀⣀⠀⣀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣟⣿⡇⠈⠁⠉⠉⢹⣿⣿⣿⣾⣿⣿⣔⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⢠⠀⠈⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡆⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⣨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣛⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢢⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣾⡿⠛⢙⢻⡟⠻⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠦⡀⡄⡄⡄⣄⡄⡄⡆⠀⢠⢄⡀⠀⡆⢠⠀⢠⠠⠠⢠⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣃⠒⠁⠐⠰⣿⣿⣿⣿⣿⡻⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠁⠁⠁⠁⠁⠁⠁⠁⠀⠀⠈⠁⠁⠀⠁⠁⠈⠉⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⣍⣭⢹⣿⣿⡷⢛⠅⢀⠀⠹⠿⢿⡿⠟⠁⠀⠀⠀⠈⠋⠹⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢠⣶⣶⣶⣶⣶⣶⣶⡄⢢⡲⣾⣿⣿⡗⢷⡢⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣀⠀⣠⡀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣟⣿⣇⠈⠁⠉⠉⢹⡟⣿⣿⣿⣷⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣦⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡆⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢢⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠆⡀⡤⡤⡄⣤⡄⡤⡦⠀⢠⢤⠄⠀⡆⢢⠀⢠⠠⢤⢤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢒⣻⣿⣿⣘⣟⡛⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⠁⠁⠁⠁⠁⠁⠁⠀⠈⠀⠁⠀⠁⠁⠀⠀⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠩⢩⣭⢹⣿⣿⡷⠁⠀⠀⠀⠙⠻⢿⠿⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣶⣶⣶⣶⣶⣶⣶⡀⢤⢲⣾⣿⢿⡧⢥⡦⡱⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⢀⢀⣀⡀⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠉⠉⢿⡿⣿⣿⣿⣿⣷⣾⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣿ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣛⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢢⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠖⡂⡤⡤⡄⢤⡀⡤⡦⠀⢀⢠⠄⠀⡖⢢⠀⢠⠠⢤⢄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣂⡐⠂⠐⢸⣟⣿⣾⣑⣿⡟⠀⠀⠉⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠒⠁⠃⠃⠁⠑⠃⠁⠑⠀⠈⠐⠁⠀⠓⠈⠐⠈⠀⠀⠘⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠈⠉⢍⣭⢹⣿⣿⡿⠱⠄⠀⠀⠻⠿⠿⠿⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣄⠐⣄⢶⣾⣿⢿⡇⢜⡃⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⠀⠀⣀⡀⣡⣴⣾⣿⣿⣿⣿⣿⣯⣿⣿⠀⠉⠈⠉⠉⢻⣿⣷⣿⣿⣧⣿⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⠂⣠⣤⣤⣀⣠⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣴⣤⣶⣄⣠⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⣀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⢃⣚⣛⣛⣛⣛⣛⣛⣛⣛⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠉⠉⠠⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⣔⡂⡠⡀⡀⠠⡀⡠⡤⠀⢐⡠⠀⠀⡖⢂⠀⢀⠀⢄⢄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠂⠒⠂⠀⢘⣿⣿⣳⣟⣿⡛⠀⠀⠉⢻⣿⣿⣿⣿⣿ ⠀⠀⠀⠒⠃⠃⠃⠃⠓⠃⠃⠑⠀⠈⠒⠃⠀⠓⠊⠐⠚⠀⠀⠘⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠈⠩⢍⡉⢹⣿⣿⠗⠂⠀⠀⠀⠛⠿⢛⠯⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣄⠀⣆⢲⣾⣿⢿⡇⣹⡒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⢀⣀⣀⠀⣠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠀⠉⠉⢻⡟⣿⣿⣿⣷⣷⣖⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⣾⡧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣴⣷⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⠂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣴⣤⣶⣄⣠⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⢃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠉⠉⠠⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⣔⠀⡀⡀⡀⠀⡀⡀⡄⠀⢐⡀⠀⠀⡖⢀⠀⢀⢀⢀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡂⠒⠀⠀⢘⣿⣿⣳⣛⣷⡟⠀⠀⠋⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠂⠃⠃⠃⠃⠛⠃⠃⠑⠀⠈⠚⠃⠀⠓⠊⠐⠚⠀⠀⠘⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⠉⣭⢹⣿⣿⡷⠂⠅⠀⠀⠛⠿⠿⡯⠟⠁⠀⠀⠀⠀⠉⠙⣻⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣴⣶⣶⣶⣶⣶⣶⣦⠀⣦⢲⣾⣿⣿⡇⣸⡆⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⣀⣀⣀⡀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡂⠉⠁⠉⠉⢹⣿⣿⣿⣿⣷⣿⣮⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣥⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠉⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠙ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡆⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⢃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠈⠉⠠⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡄⠀⡀⡀⡀⡀⡀⡀⡄⠀⢀⡀⠀⠀⡄⢄⠀⢀⢀⢀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠂⠐⠂⠐⢐⣿⣿⣿⣉⣾⡟⠀⠀⠛⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠃⠃⠃⠃⠋⠃⠃⠃⠀⠈⠊⠃⠀⠃⠊⠀⠘⠀⠀⠘⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⣭⣭⢹⣿⣿⡇⠊⠁⠀⠈⠙⠻⢿⡿⠗⠁⠀⠀⠀⠀⠋⠙⣻⡿⠯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣶⣶⣶⣶⣶⣶⣦⠀⣦⠲⣾⣿⢿⡇⢛⡃⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⣀⣀⠀⡠⡀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣻⣿⡇⠈⠁⠉⠉⢹⣷⣻⣿⣾⣷⣶⣤⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡋⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣴⣤⣶⣄⣠⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡆⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⢃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠉⠉⠠⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡤⠄⣀⣀⡀⣀⡀⣀⣄⠀⢀⣀⡀⠀⡤⢄⠀⢀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡆⠒⠀⠀⢐⣿⣿⣿⣙⣿⡗⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠃⠃⠇⠃⠋⠇⠃⠣⠀⠘⠨⠂⠀⠧⠈⠀⠘⠀⠈⠘⠐⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⢉⢩⣭⢹⣿⣿⡇⠻⠆⠀⠀⡛⠻⢟⡿⠟⠁⠀⠀⠀⠈⠉⠉⣻⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣶⣶⣶⣶⣶⣶⣦⠀⣦⡲⣾⣿⣿⡗⢾⡖⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⡀⢀⢀⣀⡀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠁⠉⠉⣻⣷⣿⣿⣿⣷⣷⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢢⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡤⠄⣀⢀⡀⢀⠀⣀⣀⠀⢠⢀⡀⠀⡤⢄⠀⠀⠀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠔⠒⠀⢘⣿⣿⣿⣙⣿⡗⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠭⠇⠇⠇⠇⠦⠇⠇⠣⠀⠸⠥⠆⠀⠧⠜⠠⠼⠀⠸⠸⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⣍⣭⢹⣿⣿⠇⠲⠄⠀⠀⠻⠻⠯⡯⠟⠁⠀⠀⠀⠀⠉⠙⣻⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣶⣶⣶⣶⣶⣶⣦⡀⢢⡰⣾⣿⢻⡇⠘⡏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⡀⠀⣀⡀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠉⠉⢹⡗⣿⣿⣿⣷⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣠⣴⣤⣶⣄⣠⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠙ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣔⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⢃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠉⠉⠠⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣤⣶⣾⣿⣷ ⠀⠀⠀⡠⠀⠀⠀⠀⢀⠀⢀⣀⠀⠠⢀⠀⠀⡤⢀⠀⠀⠀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣂⢈⠂⠀⢸⣿⣿⣿⣚⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠭⠆⠇⠇⠇⠦⠇⠇⠣⠀⠸⠥⠆⠀⠧⠜⠠⠼⠀⠈⠸⠨⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⣍⣭⢹⣿⣿⠿⠳⠈⠀⠀⠻⠿⢿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣿⣿⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣴⣶⣶⣶⣶⣶⣶⣦⠀⢦⡰⣾⣿⢻⣗⣶⡢⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡀⢀⢀⣀⠀⣡⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠉⠉⢹⣿⣿⣿⣿⣷⣿⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣾⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⣤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡅⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢢⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠊⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠚⠂⠀⢘⣿⣿⣿⣩⣿⡛⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠆⠇⠇⠇⠗⠇⠇⠃⠀⠸⠕⠆⠀⠇⠜⠠⠼⠈⠨⠸⠨⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⢩⣭⢹⣿⣿⠷⠛⠀⠀⠀⠻⠿⢿⡿⠟⠁⠀⠀⠀⠀⠉⠙⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣰⣶⣶⣶⣶⣶⣶⣶⡄⢰⡐⣾⣿⢿⡗⣴⡃⡢⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⢀⠀⣀⡀⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠈⠉⢿⣗⣿⣿⣿⣷⣿⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣷⣾⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠆⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⢛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣛⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢢⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢂⠖⡂⠀⢸⣟⣿⣳⣓⣿⡛⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠁⠆⠏⠏⠇⠟⠇⠏⠏⠀⠸⠙⠅⠀⠇⠘⠀⠸⠈⠩⠹⠨⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⢍⣭⢹⣿⣿⡇⠑⠀⠀⠈⠹⠿⢿⡿⠟⠁⠀⠀⠀⠀⠉⠙⢻⢿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢰⣶⣶⣶⣶⣶⣶⣶⡆⢰⡐⣾⣿⣿⠇⣪⠲⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⡀⢀⠀⣀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠁⠈⠉⢻⣿⣿⣿⣿⣷⣶⣖⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡶⠆⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠛⢿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣶⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⢃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠉⠉⠠⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢃⡒⠀⠀⢘⣿⣿⣷⣻⣿⡛⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣑⡆⡏⡎⡇⣍⡆⡏⢏⠀⢸⢊⡅⠀⣇⡸⢀⣸⠀⢱⢱⢀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠩⢍⡉⢹⣿⣿⡟⠛⠀⠈⠀⠛⢿⠿⠿⠟⠁⠀⠀⠀⠈⠉⠙⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢰⣶⣶⣶⣶⣶⣶⣶⡆⢰⡔⣾⣿⢿⡏⢙⡃⣩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⢀⢀⡀⣀⡀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣏⠈⠁⠈⠉⢿⣟⣿⣿⣿⣷⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣦⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠏⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠿⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣶⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⢃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢢⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢆⡒⠂⠀⢚⣿⣿⣿⣞⣿⡓⠀⠀⠉⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣓⡄⡎⡆⡆⣌⡆⡎⢏⠀⢰⣊⡄⠀⣇⡸⢀⣰⠀⢱⢱⢐⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⠉⣭⢹⣿⣿⡿⠻⠖⢀⠀⠛⠿⢿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣻⢿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣶⣶⣶⣶⣶⣶⣶⡆⢠⡐⣾⣿⢿⡗⣿⡡⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⢀⢀⣀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠈⠉⢻⣿⣿⣿⣿⣷⣾⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣾⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠙⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣤⣶⣄⣰⣶⣶⣶⣶⣆⡀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡇⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠗⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢢⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠡⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠖⠈⠀⠀⢚⣿⣿⣿⣛⣿⡟⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡓⡄⡆⡆⡆⣤⡆⡆⠇⠀⢐⡢⡄⠀⡇⡰⢀⣰⠐⢰⢰⢐⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⣭⣭⢹⣿⣿⡇⠰⠂⠀⠀⠻⠿⢿⠿⠟⠁⠀⠀⠀⠈⠉⠉⣻⣟⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢠⣶⣶⣶⣶⣶⣶⣶⡆⢰⡐⣾⣿⠿⡆⢚⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢀⢀⣀⡀⣩⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⠈⠁⠈⠉⢹⣟⣻⣿⣾⣷⣿⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⡂⣤⣴⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣴⣤⣶⣄⣠⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠙ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡧⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⡇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⢃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠈⠉⠠⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣂⣚⠃⠀⢲⣿⣿⣿⣷⣿⡟⠀⠀⠉⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠃⡄⡆⡆⡆⡦⡆⡆⠇⠀⢰⠢⡂⠀⡇⡱⠀⢰⠐⠲⢰⢐⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠉⢩⣭⢹⣿⣿⡷⣲⠆⢀⠀⠛⠿⢿⠿⠟⠁⠀⠀⠀⠀⠉⠉⣛⡿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢰⣶⣶⣶⣶⣶⣶⣶⡆⢰⡐⣾⣿⢿⡗⣞⡃⣰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⣠⣀⣄⡀⣩⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠁⠈⠉⢹⣟⣿⣿⣿⣶⣿⣮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣶⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣦⣤⣀⣠⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣤⣤⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠐⡂⠀⢠⣿⣿⣿⣫⣿⡛⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠫⡅⡖⡖⡆⠲⡄⡖⡗⠀⠸⠔⡂⠀⡏⢱⠀⢰⠐⠢⢢⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⣍⣭⢹⣿⣿⡇⠻⠆⠀⠀⢛⠻⠿⡯⠟⠁⠀⠀⠀⠈⠉⠉⣻⣿⡿ ⠀⠀⠀⠉⠀⠁⠁⠁⠉⠁⠁⠈⠀⠈⠈⠀⠀⠉⠁⠈⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣶⣶⣶⣶⣶⣶⣶⡆⢠⡐⣾⣿⣿⡇⢽⡓⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⣀⢀⣀⠀⣡⣤⣶⣾⣿⣿⣿⣿⣿⣟⣿⣇⠈⠁⠈⠉⢹⣟⣿⣿⣿⣷⣿⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⣂⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠏⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣤⣤⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠻⢻⠃⠀⠀⠊⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡃⢚⡂⠐⢺⣿⣿⣿⣿⣿⡝⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠮⡅⡖⡔⡆⡐⡄⡔⡖⠀⢨⠔⡂⠀⡏⢱⠀⢠⠀⠢⢢⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⣍⣭⢹⣿⣿⠧⠚⠀⠀⠀⠛⠿⢿⡿⠟⠁⠀⠀⠀⠈⠉⠙⣟⣿⣿ ⠀⠀⠀⠉⠁⠁⠁⠁⠉⠁⠁⠈⠀⠈⠉⠁⠀⠉⠁⠈⠉⠀⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣶⣶⣶⣶⣶⣶⣶⡆⢰⡔⣾⣿⢿⡇⢾⡃⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⠀⣀⠀⣄⡀⣨⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠈⠉⢻⣷⣿⣿⣾⣷⣯⣾⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣾⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡠⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣤⣤⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢧⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠂⠲⡂⠀⢐⣻⣿⣷⣶⣾⡛⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠮⡀⡄⡄⡄⡀⡄⡄⡆⠀⢨⠄⡀⠀⡏⢰⠀⢠⠀⢠⢠⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⢩⣭⢹⣿⣿⡧⠙⠆⠐⠀⡻⠻⢽⡿⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⠟ ⠀⠀⠀⠉⠁⠁⠁⠁⠉⠁⠁⠈⠀⠈⠉⠁⠀⠉⠁⠈⠉⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣶⣶⣶⣶⣶⣶⣶⡆⢰⡔⣾⣿⣿⡇⢝⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⠀⢀⠀⣀⡀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉⠈⠉⢹⡟⣿⣿⣾⣷⣷⣔⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠀⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣤⣤⣶⣆⣠⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠧⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣷⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣔⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⠇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣾⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠉⠉⠀⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡂⠒⠒⠀⢊⣻⣿⣷⣒⣿⡟⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠦⡀⡄⡄⡄⣄⡄⡄⡆⠀⢠⢄⡀⠀⡆⢢⠀⢠⠠⠠⢠⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠈⢍⣭⢹⣿⣿⡟⠰⠄⠀⠀⠙⠿⢯⡿⠟⠀⠀⠀⠀⠈⠉⠙⣻⣿⠿ ⠀⠀⠀⠀⠁⠁⠁⠁⠁⠁⠁⠀⠀⠀⠁⠁⠀⠁⠁⠀⠉⠀⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣶⣶⣶⣶⣶⣶⣶⡆⢰⣄⢾⣿⢿⡇⢙⠑⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡀⠀⣀⡀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠉⢹⣿⣿⣿⣾⣷⣿⣴⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣠⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣠⣤⣤⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣿ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣷⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣔⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣠⠟⢨⠵⣾⠿⢿⣯⡵⠻⠇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣾⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⡃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠉⠉⠀⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠐⠀⠐⢈⣿⣻⣿⣃⣿⡓⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⢖⡂⡤⡤⡄⢤⡀⡤⡦⠀⢠⣠⠄⠀⡖⢢⠀⢠⠠⢄⢄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠩⢍⡉⢹⣿⣿⡃⠰⠄⠀⠀⠛⠟⢟⠿⠗⠁⠀⠀⠀⠀⠉⠙⢛⣿⠿ ⠀⠀⠀⠒⠁⠃⠃⠁⠓⠃⠁⠑⠀⠈⠐⠁⠀⠓⠈⠐⠈⠀⠀⠘⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣶⣶⣶⣶⣶⣶⣶⡆⢰⡔⢾⣿⢻⡇⣛⡂⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⠀⡀⢀⣀⡀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠈⠉⢹⣿⣻⣿⣿⣧⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣾⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠆⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⢀⠂⣠⣤⣤⣀⣠⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣤⣤⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢇⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣷⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣔⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⠇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⡃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠈⠉⠀⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡅⠒⠀⠀⢺⣿⣟⣻⣡⣿⡟⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⢖⡂⡤⡠⡄⠤⡀⡤⡤⠀⠰⡠⠄⠀⡖⢢⠀⢠⠀⢄⢄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⠉⣭⢹⣿⣿⡷⠳⠃⠀⠀⠙⠿⢿⠿⠗⠀⠀⠀⠀⠀⠉⠙⣿⢿⠯ ⠀⠀⠀⠒⠃⠃⠃⠃⠓⠃⠃⠑⠀⠘⠐⠃⠀⠓⠊⠐⠚⠀⠘⠘⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢠⣶⣶⣶⣶⣶⣶⣶⣆⢰⡔⣾⣿⣿⡇⣼⡢⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢀⠀⣀⡀⣩⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠉⢼⣿⣿⣿⣾⣯⣿⣬⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠛⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢀⡂⣠⣦⣤⣀⣀⣴⣾⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣤⣤⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠧⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡇⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠄⠂⠀⠀⢀⣿⣿⣿⣸⣾⡓⠀⠀⠉⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⣔⠂⡠⡀⡀⠠⡀⡠⡤⠀⢐⡠⠀⠀⡖⢠⠀⢀⠀⢄⢄⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⣭⣭⢹⣿⣿⠧⠝⠄⠀⠀⠙⠿⠿⠿⠟⠁⠀⠀⠀⠀⠉⠙⣻⢿⢯ ⠀⠀⠀⠒⠃⠃⠃⠃⠓⠃⠃⠑⠀⠘⠒⠃⠀⠓⠊⠐⠚⠀⠘⠘⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢰⣶⣶⣶⣶⣶⣶⣶⡆⢰⡐⣾⣿⢿⡇⢒⡢⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⣀⡀⣀⡀⣡⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠈⠁⠈⠉⢽⣟⣿⣿⣾⣷⣿⣖⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣶⣾⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠏⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡋⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣶⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣤⣤⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣷⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣔⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⠇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⡃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠉⠉⠀⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡃⠒⠆⠀⢐⣿⣿⣿⣷⣿⡷⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⣄⠀⡀⡀⡀⠀⡀⡀⡄⠀⢀⡀⠀⠀⡆⢀⠀⢀⢀⢀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⢉⢩⣭⢹⣿⣿⡧⠚⠁⠂⠈⠙⠻⠟⠩⠟⠁⠀⠀⠀⠀⠉⠙⣻⢿⣿ ⠀⠀⠀⠂⠃⠃⠃⠃⠋⠃⠃⠁⠀⠘⠊⠃⠀⠃⠊⠐⠚⠀⠐⠘⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢰⣶⣶⣶⣶⣶⣶⣶⡆⢠⡰⣾⣿⢿⡆⣚⡡⣁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣀⠀⣀⡀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠁⠉⠉⢻⣟⣿⣿⣿⣷⣿⣌⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣴⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣤⣤⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠂⠲⠀⠀⢘⣻⣿⣿⣋⣷⡛⠀⠀⠛⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡤⠄⣀⣀⡀⣀⡀⣀⣄⠀⢀⣀⡀⠀⡤⢄⠀⢀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⣍⣭⢹⣿⣿⡗⠐⠀⠀⠀⠛⠻⢽⡯⠟⠁⠀⠀⠀⠈⠉⠙⣻⢿⠿ ⠀⠀⠀⠠⠃⠃⠇⠃⠋⠇⠃⠣⠀⠘⠨⠂⠀⠧⠘⠠⠘⠀⠘⠘⠐⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣶⣶⣶⣶⣶⣶⣶⡄⢢⡲⣾⣿⢿⡆⢰⡂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⡀⠀⣀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠉⠉⢹⣗⣻⣿⣿⣷⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣠⣤⣤⣶⣆⣠⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣷⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣔⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⠇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⡃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠈⠉⠀⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡆⢔⠂⠀⠈⣿⣿⣿⣙⣿⡉⠀⠀⠛⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡤⠄⣀⣀⡀⣀⠀⣀⣄⠀⢠⢀⡀⠀⡤⢄⠀⢀⢀⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⢍⣭⢹⣿⣿⡦⠐⠀⠀⠀⠙⠛⢿⠿⠟⠀⠀⠀⠀⠈⠉⠙⣻⣿⢿ ⠀⠀⠀⠬⠃⠇⠇⠇⠮⠇⠇⠣⠀⠘⠡⠂⠀⠧⠜⠠⠜⠀⠘⠸⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣶⣶⣶⣶⣶⣶⣶⡄⢠⡰⣾⣿⢻⣇⢜⡆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⡀⣀⣀⡀⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠉⠉⢹⣟⣻⣿⣿⣧⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠆⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⠂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣠⣤⣤⣶⣆⣠⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠙ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣷⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣔⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣠⠟⢨⠵⣾⠿⢿⣯⡵⠻⠇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣾⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⡃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠉⠉⠀⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣁⡖⠂⠐⠘⣿⣿⣶⣒⣿⠓⠀⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡠⠄⣀⢀⠀⢀⠀⢀⣀⠀⠠⢀⡀⠀⡤⢄⠀⠀⠀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⢩⣭⢹⣿⣿⠗⠩⠀⠀⠀⠙⠻⠿⠯⠟⠁⠀⠀⠀⠀⠉⠙⣻⢿⡿ ⠀⠀⠀⠭⠇⠇⠇⠇⠦⠇⠇⠣⠀⠘⠥⠆⠀⠧⠜⠠⠼⠀⠸⠸⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣶⣶⣶⣶⣶⣶⣶⡆⢠⡐⣾⣿⢿⠆⢍⠃⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⠀⣀⠀⣠⡀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠈⠉⢹⡟⣿⣿⣾⣿⣿⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠆⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣂⢀⣤⣤⣤⣴⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠸⣾⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡛⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣷⠄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣬⣤⡀⠀⠐⣔⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⠇⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⠉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡂⢰⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⡃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠈⠉⠀⢾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠘⠒⠚⠚⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⢲⣿⣿⣷⣚⣿⡛⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⢍⣭⢹⣿⣿⡗⡛⠄⠀⠀⠟⠿⣿⠿⠟⠁⠀⠀⠀⠈⠉⠙⢻⣿⢿ ⠀⠀⠀⠭⠆⠇⠇⠇⠦⠇⠇⠣⠀⠸⠵⠆⠀⠧⠜⠠⠼⠀⠘⠸⠨⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣶⣶⣶⣶⣶⣶⣶⣆⢠⡔⣾⣿⢿⡗⣾⠗⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⣀⢀⣀⡀⣡⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⠀⠉⠈⠉⢻⣿⣿⣿⣿⣷⣿⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⠄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣄⣀⣴⣶⣿⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣤⣤⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣖⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠸⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⠏⠋⢛⡅⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣯⡵⠻⡗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣏⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⣻⠿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠂⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢻⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣃⠒⠂⠀⢐⣿⣿⣿⣻⣿⡟⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠩⢍⡉⢹⣿⣿⡷⠻⡄⠀⠀⠛⠿⠿⠯⠟⢁⠀⠀⠀⠈⠉⠙⣻⣿⠻ ⠀⠀⠀⠁⠆⠏⠏⠇⠟⠇⠏⠏⠀⠸⠙⠅⠀⡇⠘⠀⠸⠈⠹⠹⠨⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣶⣶⣶⣶⣶⣶⣶⡆⠐⡔⣾⣿⣿⡇⢾⡂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⢀⠀⣀⡀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠉⢻⣗⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠛⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠒⠂⠐⢚⣿⣿⣿⣻⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⠉⣭⢹⣿⣿⡷⠱⠂⠀⠈⠛⠿⠿⠻⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⢿ ⠀⠀⠀⣑⠆⡏⡏⠇⣝⡆⠏⢏⠀⠸⢚⠅⠀⣇⠸⢀⠸⠈⠱⢱⠈⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣶⣶⣶⣶⣶⣶⣶⡆⠐⡔⣾⣿⣿⡇⣽⡃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⣀⠀⣀⡀⣨⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣏⠀⠉⠈⠉⢻⣏⣿⣿⣿⣷⣿⣤⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣤⣤⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠛⠛⠋⠉⠙ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣶⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠈⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠐⢛⣟⣿⣷⣾⣿⡟⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⡄⠈⣭⣭⢹⣿⣿⡧⠳⠒⠀⠀⠛⠟⣿⠿⠟⠁⠀⠀⠀⠈⠉⠙⣻⢿⠯ ⠀⠀⠀⣑⡆⡏⡎⡇⣍⡆⡏⢏⠀⠸⣊⡅⠀⣇⡸⢀⣸⠀⠑⢱⢀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣆⠀⣔⢾⣿⣿⡆⢼⡦⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⠀⢀⢀⠀⣩⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠉⢹⣏⣿⣿⣿⣷⣿⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣤⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢃⢀⠂⠀⢐⣿⣿⣿⣛⣿⡛⠀⠀⠛⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⡄⠉⢩⣭⢹⣿⣿⡗⠛⠚⢀⠀⠛⢿⣿⠿⠟⠁⠀⠀⠀⠈⠋⠙⣻⡿⡿ ⠀⠀⠀⣓⡄⡎⡆⡆⣌⡆⡎⢏⠀⠰⣊⡄⠀⣇⡸⢀⣰⠀⠑⢱⢐⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⣶⣶⣶⣶⣶⣶⣶⣆⠐⡔⣾⣿⣿⣖⢿⣓⡲⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣀⢀⣀⡀⣡⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠉⢹⣟⣿⣿⣿⣷⣾⣴⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡴⠄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣆⣅⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⠀⠻⠏⠋⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡗⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠊⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡂⠒⡃⠀⢠⣿⣿⣿⣛⣿⡓⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠈⣍⣭⢹⣿⣿⡗⡱⠄⠀⠀⠙⠿⢿⠿⠏⠁⠀⠀⠀⠈⠉⠙⣿⡿⢟ ⠀⠀⠀⠃⡄⡆⡖⡆⡦⡆⡆⡇⠀⠰⠢⡂⠀⡇⡱⠀⢰⠐⠒⢰⢐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⣶⣶⣶⣶⣶⣶⣶⣆⠐⡔⣾⣿⣿⣧⢙⡳⣲⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⡀⣀⢀⡀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠉⢹⣟⣻⣿⣿⣿⣿⣴⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣾⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠉⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⡂⣠⣤⣤⣀⣀⣴⣾⣿⣦⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣤⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡂⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⠃⢈⠃⠀⢀⣿⣿⣿⣾⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠈⣍⣭⢹⣿⣿⡇⠛⠂⠀⠀⠹⠿⠿⠯⠟⠁⠀⠀⠀⠈⠉⠙⣻⣿⢿ ⠀⠀⠀⠋⡅⡖⡖⡆⡶⡄⡖⡗⠀⠰⠰⡂⠀⡏⢱⠀⢰⠐⠲⢢⢐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⢀⣶⣶⣶⣶⣶⣶⣶⣆⠀⣔⢾⣿⣿⣇⣜⡖⣹⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠈⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⢀⣀⣀⡀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠉⢿⡟⣿⣿⣿⣷⣿⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣾⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡴⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣖⣂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠙⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⢰⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡂⣠⣦⣤⣀⣀⣴⣾⣿⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣆⣀⣤⣴⣴⣶⣆⣰⣶⣶⣶⣶⣆⠀⠀⠐⠒⣶⣒⣀⡀⢰⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠸⣾⣿⣿⣿⣿⣿⡿⠻⠛⠋⠉⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠻⠏⠛⢛⡕⠁⠀⠀⠀⢀⣴⣾ ⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⢾⣿⣀⣄⣀⣠⣴⣿⠉⠀ ⣤⣾⣿⣯⣿⣿⣿⢿⡟⠉⠀⠀⠀⢐⡟⢫⠁⣴⢴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⠙⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⠄⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠻⠟⠿⠛⠛⣫⡀⠀⢁⣤⣀⣄⣼⣯⣿⡄⡀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣀⢀⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡯⠡⠚⠁⠀⠰⣽⣿⣿⣿⣿⣿⠟⠋⠙⠓ ⠀⠀⠀⠀⠀⠈⢹⣿⡋⠉⣩⣭⣭⣤⡀⠀⠐⣖⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠛⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⣰⠟⢨⠵⣾⠿⢿⣿⡵⠻⠗⠀⠀⠀⡴ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠿⢃⠀⡏⠉⡉⣿⣿⣿⣿⣾⣝⠿⣿⣿⣿⣟⣿⣿⡟⠀⠀⡒⢴⣿⣾⣧⡀⢩⣉⠊⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠃⠀⠩⠓⢣⣶⣧⢐⠴⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⡟⣵⣠⣿⣿⣿⣿⠛⠻⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀ ⣄⠰⠗⠰⣃⣚⣛⣛⣛⣛⣛⣛⣛⣚⣙⡻⡿⢠⣮⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠀⠀⠀⢠⢰⣿⣿⡄⠀⢁⣻⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⣼⡿⠛⢉⢻⡟⠿⢿⠃⠀⠀⠋⠉⠁⢾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠈⠰⠿⠟⠛⠻⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣦⠄⠉⣿⢻⢻⢿⠛⣿⠛⡛⢓⢒⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢙⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢒⡾⠒⠓⠓⠚⠒⠚⠚⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣶⣾⣿⣷ ⢤⡴⠶⠖⠒⠒⠈⠀⠈⠤⠀⡀⣀⠒⠒⠛⠉⢘⣛⣟⣿⣟⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣅⣀⣀⣀⣀⡀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛ ⣤⣤⣤⣾⣷⣾⣷⣖⣐⣶⣶⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣅⠀⢿⣿⠟⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣙⢿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠗⠀⢿⡋⠛⠁⠀⢛⡁⠀⠀⢸⡆⠄⠠⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠛⠘⠉⢈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠵⠀⠀⠀⡅⠀⠀⢀⠸⣗⣀⣀⣸⢶⠾⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡘⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⢭⣄⣤⠤⣠⡭⣭⣭⣷⣲⣵⣾⣯⡾⣶⣼⣭⣫⣭⣛⡛⠟⠛⢺⡽⣭⣿⣛⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣦⠄⣾⣿⣿⣿⣿⣟⢯⣽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡤⢛⣹⣾⢟⣩⡿⢛⣿⠟⢛⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣛⡷⠿⢎⣾⡞⣻⣟⢢ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠁⣿⣿⣿⣿⣿⣖⠿⣷⣿⠋⠀⠀⠀⠀⠀⠀⠐⣀⣴⡖⣂⣤⡾⠟⠁⠾⢿⣿⣿⢟⠭⢾⢖⣶⣾⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⠗⣄⣉⠡⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⠻⠻⢟⣫⠑⠞⢫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠛⠛⠛⠿⠿⢯⣶⠿⠯⢵⣟⠏⠙⠻⢟⣽⣿⡿⣩⣿⡿⠛⠟⠿⠏⠹⠉⠁⣾⠿⢧⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠴⠀⠀⠀⢀⠀⡀⢀⡈⡻⠾⠿⢿⣵⣿⡟⣓⣦⣟⠃⣠⡤⠀⠀⢢⠬⡁⠈⠛⢻⣿⣿⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢽⡿⠯⢒⣉⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⢋⣁⣈⡉⣒⣒⡶⠿⣥⡶⣿⢷⡴⠾⠷⠬⠘⠒⠟⢝⠿⠿⢽⣰⣭⠟⢠⣖⣯⢁⡩⠽⣺⣿ ⣿⣿⣿⣿⠿⠟⠋⣭⠀⠀⠒⣛⠩⠗⠚⢋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⣤⣤⣔⢒⣶⣾⣿⢟⢯⣿⣿⣛⣡⣶⡶⢆⣡⣤⣬⢉⣤⣿⡇⠀⠀⠀⠐⢓⡚⠻⠏⠙⠿⠿⠿⢿⣒⢰⣿⣿ ⠟⠋⠉⠀⠀⠀⣀⣠⣤⠂⠀⣀⠀⠀⠀⢀⣤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣴⣿⡿⢛⣽⣾⡿⢿⣿⣿⣿⠒⢀⠀⡜⠉⠩⢿⡿⠿⢤⡾⣾⢯⣤⢤⣭⣉⣲⢈⢕⣶⣶⠶⢢⣿⣿⣿ ⠀⠠⠘⣯⣵⡶⢒⣀⣰⠛⣉⣡⣶⡤⠔⠂⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣭⡭⠛⣁⣒⣻⡿⠿⠿⢿⣯⢙⠤⠞⢋⠛⣳⣿⣿⣞⣁⣲⡷⢷⠰⣷⣜⣿⣧⣶⣯⣭⠉⠛⠓⢂⣿⣿⣿⣿ ⠐⠛⠛⢉⢁⡤⣄⡴⠖⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡿⢻⠤⠄⠈⠉⢡⣴⣶⣾⣿⣯⣿⣓⢲⠶⣾⣿⠿⣇⣈⣩⣿⣏⣿⣿⣿⠿⠟⠛⢿⣋⣁⣶⣶⢶⣾⣿⣿⣿⣿ ⠀⠀⠁⣉⣁⡤⠤⠀⠀⠀⠀⠀⠀⠠⢴⣿⢛⣡⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣉⣡⣤⣶⣶⢛⢭⣿⣵⣖⣫⣘⣉⣘⡻⢻⡻⠿⠦⠄⠀⣟⣛⡛⠛⣩⣤⢭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠤⣶⡶⠈⠉⠁⠀⠀⠀⠀⠀⠀⠁⢘⣠⣼⣟⡛⠛⠻⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣾⣿⡿⢿⡿⠿⠟⠛⠛⠉⠩⣭⣷⣾⣤⣴⣿⡾⢿⣵⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣈⣠⣄⣀⣀⣀⡀⠲⠶⢺⣶⣾⣷⣾⣩⣤⣴⣖⣦⣤⣤⣿⣿⣿⣍⣘⣻⣭⡉⢈⣝⣛⡛⣺⣿⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠉⠉⠽⠿⠿⣿⣿⣃⣀⣚⠻⢿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣄⣤⣠⠀⢀⣤⢤⡉⠙⠋⠠⣤⡄⠀⠀⠀⢈⣿⣿⡟⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠁⣀⣝⣿⠿⢻⣽⣿⣿⣿⡿⣠⣴⣿⣶⣶⠄⠀⠀⣀⣘⡛⠿⠂⠀⣴⣥⡀⠀⠉⣨⣩⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠀⡤⠂⠀⠀⠀⠀⢉⢉⢙⡋⠽⠛⡂⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠴⠮⠍⠉⠀⠀⠶⢯⠩⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⣛⠿⠎⢰⡖⠚⠶⠒⢀⡄⠀⠀⠀⡶⢾⠶⠈⠀⠀⠀⠀⠒⣀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 4640 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 11/04/2024: Activity and Motivation in Geminispace, gwit Implementations⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Browsers_On_Their_Sailboat⦈_ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * Gemini*_and_Gopher o Personal/Opinions o Technology_and_Free_Software # Internet/Gemini # Programming * § Gemini* and Gopher⠀➾ o § Personal/Opinions⠀➾ # ⚓ I'm_also_not_paid_enough_for_the_rest_of_this⠀⇛ More work, more work hell, more things added to my ~duties~ and more shite making me the villain dealing with homeless folks hiding in here, stashing stuff in here, being aggressive and I am / still/ not paid enough for this shit. Or enough to cover the eye exams + new glasses the household is getting, but at least I can drop those on credit and we have a (household) payment plan sorted. # ⚓ 🔤SpellBinding:_ADFLMNR_Wordo:_SPROG⠀⇛ # ⚓ April_11,_2024_-_Saint_Leo_I_(W)⠀⇛ Simon Peter, if thou lovest Me, feed My lambs, feed My sheep. Psalm: I will extol Thee, O Lord, for Thou hast upheld me: and hast not made mine enemies to rejoice over me. Glory by to the Father. Simon Peter, if thou lovest Me, feed My lambs, feed My sheep. # ⚓ The_Girl_Tech_IM-Me_and_My_Desire_for_a_Modern_Version⠀⇛ Recently I’ve become aware of a device from the early 2000s called the IM-ME. It’s a handheld instant messaging tool created by Girl Tech, a company that was known for producing tech toys aimed at young girls during the late 90s and early 2000s. They are perhaps most well known for their voice activated diary (or their annoyingly catchy slogan.) # ⚓ Ancient_language_scholarship⠀⇛ As I keep mentioning in all my posts, I like to learn languages, and I have been studying Chinese, modern and classical, for the better part of 5 years. I have also dabbled in a number of other languages, such as German, Russian, and Latin. Recently I've been getting more and more into the ancient world, the history of it's sciences and religions, among other things. By the ancient world I mean mostly the Hellenic period down to the flourishing of Islam. Actually that's closer to the medieval period than the ancient one proper, but of course, nothing is as fragmentary as our conceptual delimitations suggest, and to have a more or less complete picture implies going back all the way to archaic Greek, Perisa, and even India (I have long been interested in the Sanskrit language as well). Just outlining this scope of study comfronts me with a very wide variety of languages to consider. I've already mentioned Sanskrit, and that one is at the fringes of the region that I've set myself to learn about. Latin, though at the western extreme of the (geographical) continuum, is a lot more present since we have inherited much through them and I have the advantage of speaking a romance language as well as my previous, albeit far from complete, study of it. # ⚓ The_Case_of_Mistaken_Identity_Part_7⠀⇛ “Well, Watson, Ms. Stoliz appeared in the doorway like a lovely version of a wraith shortly after you left. Indeed, as I was involved in my studies, I actually mistook her for your premature return. Since you were out on the errand on which I sent you, I had no door greeter and lacked the proper kind of screening necessary to filter those who come in the office on desultory, impulsive urges. Ms. Stoliz, has, so far, provided the outlines of a case she feels that I am a good fit for, and it involves, somewhat ironically, the labyrinth machinations of the church both as a political and spiritual entity.” # ⚓ Adler_Tippa_1_(EN)⠀⇛ So I've cleaned and serviced my nice litte typewriter, the Adler Tippa 1 (from 1965, according to the serial number database - typewriterdatabase.com). I'm writing this page on my Olivetti Dora, because I like the design better. But in direct comparison, I must admit that the Adler does a very good job in actual typing. It is fast and easy going, much better handling than this Olivetti. Now what to do with it? I certainly can't start my own collection of typewriters. I need the space in the drawers for some work and study-related things. Sell it on eBay? o § Technology and Free Software⠀➾ # ⚓ Why_would_you_write_a_search_engine?⠀⇛ I dunno man, I saw a post on fedi where somebody was talking about doing it and it seemed cool! The first iteration was all backed by a gigantic JSON file which quickly grew too large to handle. The current version has been ported to PostgreSQL which is obviously a little more suitable! After the SQL refactor, I started tinkering with boolean search terms. My implementation is inelegant but works okay! It simply iterates over each word in the query and checks the next word. On an and or an or, it puts the next and previous word in an array and does some SQL sorcery to pull the data. On top of that, it pre-calculates n-grams[1] during the indexing process to enable "phrase search" with quote marks. # ⚓ Profectus_Browser_Alpha_0.2_Update⠀⇛ I have released a minor update to Profectus that fixes DPI scaling on Linux environments that use Wayland... # ⚓ Fidget_spinners⠀⇛ Sometimes the fidget spinner will hit into your fingers, causing insignificant pain. Then, as time goes on, it will rotate with more and more friction. Eventually, it will spin so badly that you won't bother picking it up again. It will stay somewhere on your desktop, occupying minimal headspace until you loose it overnight without even noticing it. # § Internet/Gemini⠀➾ # ⚓ Seeking_Autumn:_Activity_and_Motivation_in Geminispace⠀⇛ I started my gemlog in December of 2022. To be honest, it felt a little like coming home, since I kept a journal in the very early days of the internet, inspired by mc and others. I kept my HTML journal for a little over two years - first on a community network, then at a revolving series of sites based on where I could get space and who was offering. And then, in late 2001, our scene, of teenagers keeping journals and oversharing their lives to online friends and whoever stumbled in, vanished. Well, not really. It's hard to pick an end date. We woke up one day, looked around, and it was gone. At that point I'd been posting on Facebook for a half a decade, less and less as every person I'd ever met requested we be friends. With that said, I can point to an event that preceeded it, and which was predictive of the current and unending social media age: the move to LiveJournal. # § Programming⠀➾ # ⚓ gwit_implementations⠀⇛ A few days ago I was contacted by +mala. After learning about gwit from a toot by Ploum, he launched himself into testing whether a MicroPython-based implementation of a gwit client would be possible, taking the example commands in the gwit spec as a reference. For such a limited platform (esp. regarding cryptography), he was able to figure out a good chunk of initial site retrieval, and he has documented his progress in a public Python notebook. Good luck and keep the good work! # ⚓ Vim_visual_block_mode_for_column_editing⠀⇛ The visual block mode in Vim lets you edit text simultaneously across adjacent lines, similar to the "Alt-drag" feature in modern editors, but there's more you can do with it. =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It's like the World Wide Web but a lot lighter. ䷩ 𝚕𝚒𝚗𝚎 4906 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 11/04/2024: Web Diversity and More Crackdowns in Russia⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ posted by Roy Schestowitz on Apr 11, 2024 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇World_Flag⦈_ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * Leftovers o Science o Education o Hardware o Health/Nutrition/Agriculture o Proprietary/Artificial_Intelligence_(AI) o Security # Privacy/Surveillance # Confidentiality o Defence/Aggression o Transparency/Investigative_Reporting o Environment # Energy/Transportation # Overpopulation o Finance o AstroTurf/Lobbying/Politics o Censorship/Free_Speech o Freedom_of_Information_/_Freedom_of_the_Press o Civil_Rights/Policing o Internet_Policy/Net_Neutrality o Digital_Restrictions_(DRM) o Monopolies/Monopsonies # Trademarks # Copyrights * § Leftovers⠀➾ o ⚓ Scott Willsey ☛ Cool_Site_Spotlight⠀⇛ If the web is ever going to be cool again, this is how it starts: finding and linking to things that make it a better place. o ⚓ EAPL.mx ☛ [EN]_Notifications⠀⇛ I think we have 2 opposite extremes: - Being obsessed checking something due to FOMO, every time your mind asks for it - Being interrupted in any random moment, so you 'have' to stop what you are doing to check the notification o ⚓ Jack Baty ☛ The_current_blog_situation_-_Jack_Baty⠀⇛ Hooboy, it’s happened again. I made the mistake of falling in love with too many tools. Combine that with my short attention span, and I’ve spread myself too thin, blog-wise. The problem is that one day I want to burn it all down and find One True Blog. Other days, most days, I want to use them all. Why force a decision when I can waffle between a half-dozen playgrounds? o § Standards/Consortia⠀➾ # ⚓ India Times ☛ EU's_new_tech_laws_are_working_-_small browsers_gain_market_share⠀⇛ Independent browser companies in the European Union are seeing a spike in users in the first month after EU legislation forced Alphabet's Google, Microsoft and Apple to make it easier for users to switch to rivals, according to data provided to Reuters by six companies. The early results come after the EU's sweeping Digital Markets Act, which aims to remove unfair competition, took effect on March 7, forcing big tech companies to offer mobile users the ability to select from a list of available web browsers from a "choice screen." # ⚓ Bryan Lunduke ☛ Myth:_"HTML_was_invented_by_Tim_Berners- Lee"⠀⇛ o § Science⠀➾ # ⚓ Niall Murphy ☛ Rice's_Theorem_and_Software_Failures⠀⇛ Enter computational theory. Rice’s Theorem is related to the Halting Problem, which we won’t itself specifically discuss here, except to say that it is hugely important and generally well covered in undergraduate Computer Science. Rice’s Theorem, a generalization of the Halting Problem, states that all non-trivial semantic properties of programs are undecidable. o § Education⠀➾ # ⚓ BIA Net ☛ Educators'_union_urges_scrapping_of_intelligence agency's_Children's_Day_event⠀⇛ The activities of institutions like MİT and Diyanet targeting children “exceed their constitutional boundaries and responsibilities,” according to the Eğitim-Sen union. # ⚓ Barry Hess ☛ My_First_Program⠀⇛ In the early 80’s my aunt and uncle sent our family a TI-99/4A for Christmas. It came with a couple code listing books and some games: [...] # ⚓ Jim Nielsen ☛ You_Are_What_You_Read,_Even_If_You_Don’t Always_Remember_It⠀⇛ Then a couple days later my wife sent me this quote from Ralph Waldo Emerson: "I cannot remember the books I've read any more than the meals I have eaten; even so, they have made me." YES! # ⚓ Juha-Matti Santala ☛ Prepare,_Perform,_Ponder⠀⇛ Over the years, I’ve adopted a three-step feedback cycle to my life. To make it sound cool in a title of a blog post, I wanted to make it into an alliteration Prepare, Perform and Ponder. I like the sound of it. I use it for most of the things I do in my life: from work projects to meetings to doing talks to my goals in life. o § Hardware⠀➾ # ⚓ CNX Software ☛ Maiyunda_M1_Alder_Lake-N_mini_PC_comes_with four_quick-release_M.2_NVMe_SSD_slots,_four_2.5GbE_ports⠀⇛ Maiyunda M1 is an unusual defective chip maker Intel N100 or Core i3-N305 Alder Lake-N mini PC and soft router equipped with four M.2 NVMe SSD slots so users can replace storage devices without having to open the enclosure, as well as four 2.5GbE ports for networking applications. # ⚓ CNX Software ☛ Arm_Ethos-U85_NPU_delivers_up_to_4_TOPS_for Edge_Hey_Hi_(AI)_applications_in_Cortex-M7_to_Cortex-A520 SoCs⠀⇛ Arm has just Introduced its third-generation NPU for edge Hey Hi (AI) with the Arm Ethos-U85 that scales from 256 GOPS to 4 TOPS or up to four times the maximum performance of the previous generation Ethos-U65 microNPU, while also delivering 20% higher power efficiency. While previous Arm microNPUs were paired with Cortex- M microcontroller-class cores potentially embedded into a Cortex-A application processor, the new Ethos-U85 can be married with Cortex- M microcontrollers and Cortex-A application processors up to the Cortex-A510/A520 Armv9 cores. # ⚓ CNX Software ☛ Axelera_Metis_PCIe_Arm_Hey_Hi_(AI) evaluation_kit_combines_Firefly_ITX-3588J_mini-ITX_motherboard with_214_TOPS_Metis_AIPU_PCIe_card⠀⇛ Axelera has announced the general availability of several Metis PCIe Hey Hi (AI) Evaluation Kits that combine the company’s 214 TOPS Metis AIPU PCIe card with x86 platforms such as Dell 3460XE workstation and Lenovo ThinkStation P360 Ultra computers, Advantech MIC-770v3 or ARC-3534 industrial PCs, or the Firefly ITX-3588J mini-ITX motherboard powered by a Rockchip RK3588 octa-core Cortex-A76/A55 SoC. # ⚓ India Times ☛ Google_unveils_Arm-based_data_center processor,_new_AI_chip⠀⇛ Google's tensor processing units (TPUs) are one of the few viable alternatives to the advanced AI chips made by Nvidia, though developers can only access them through Google's Cloud Platform and not buy them directly. o § Health/Nutrition/Agriculture⠀➾ # ⚓ JURIST ☛ Norfolk_Southern_reaches_tentative_$600M settlement_in_train_derailment_class_action_suit⠀⇛ Norfolk Southern Corporation (NSC) announced on Tuesday that it had reached a tentative settlement of $600 million in a class action lawsuit regarding the February 2023 freight train derailment in East Palestine, Ohio. # ⚓ The Conversation ☛ Young_people_are_getting_unhappier_–_a lack_of_childhood_freedom_and_independence_may_be_partly_to blame⠀⇛ Younger generations have less freedom and independence than previous generations did. The area where children are allowed to range unsupervised outside has shrunk by 90% since the 1970s. # ⚓ The Revelator ☛ Bioplastics_Are_Not_the_Solution⠀⇛ o § Proprietary/Artificial Intelligence (AI)⠀➾ # ⚓ Bitdefender ☛ Targus_business_operations_disrupted following_cyber_attack⠀⇛ But if it is ransomware, chances are that the attackers have not just encrypted systems, but have also exfiltrated large amounts of data from Targus's network and are threatening to release it to the wider world if the company doesn't give in to the extortionists' demands. Without SEC regulations that came into effect late last year, we might not have known so quickly about the problems Targus was experiencing. # ⚓ Arduino ☛ Arduino_featured_in_the_2024_State_of_the_Edge_AI Report⠀⇛ “Simplicity is the key to success. In the tech world, a solution is only as successful as it is widely accepted, adopted and applied — and not everyone can be an expert. You don’t have to know how electricity works to turn on the lights, how an engine is built to drive a car, or how large language models were developed to write a ChatGPT prompt: that plays a huge part in the popularity of these tools,” Violante adds. “That’s why, at Arduino, we make it our mission to democratize technologies like edge AI — providing simple interfaces, off-the-shelf hardware, readily available software libraries, free tools, shared knowledge, and everything else we can think of. We believe edge AI today can become an accessible, even easy-to-use option, and that more and more people across all industries, in companies of all sizes, will be able to leverage this innovation to solve problems, create value, and grow.” # ⚓ Wevolver ☛ 2024_State_of_Edge_AI_Report⠀⇛ This is the second in-depth report on Edge AI by Wevolver after its inaugural report in 2023, which focused primarily on the technological side of Edge AI. This report explores Edge AI’s application side and its impact on the various industries mentioned above. Will Edge AI be one of the world’s fundamental technologies going forward? Will it continue to reshape our industries and become ubiquitous? If so, how? Let’s find the answers in the chapters below. # ⚓ The Conversation ☛ To_understand_the_risks_posed_by_AI, follow_the_money⠀⇛ We ought to heed Collingridge’s warning that technology evolves in uncertain ways. However, there is one class of AI risk that is generally knowable in advance. These are risks stemming from misalignment between a company’s economic incentives to profit from its proprietary AI model in a particular way and society’s interests in how the AI model should be monetised and deployed. # ⚓ NYPost ☛ Waymo_offering_paid_robotaxi_rides_in_LA⠀⇛ Despite pushback from local officials who cited safety concerns following the self-driving vehicles’ rocky test period, more than 50,000 people are sitting on the waitlist to try out the futuristic venture. # ⚓ Axios ☛ Robotic_dogs_could_take_charge_of_work_tasks instead_of_humanoid_robots⠀⇛ • Spot is a four-legged dog-shaped robot that's being used by first responders as well as for industrial inspections. About 1,500 are at work for Boston Dynamics customers, handling around 200,000 industrial inspections per quarter. • Stretch is a rolling warehouse worker that can lift up to 50 pounds and move boxes for up to 16 hours on a single charge — more than four times longer than today's humanoid robots. • Orbit is fleet management software for robots that was introduced in January. # ⚓ CBC ☛ Tesla_settles_lawsuit_on_eve_of_trial_in_deadly automated-driving_crash⠀⇛ The settlement, the terms of which were not disclosed, came as Chief Executive Elon Musk is making major promotions of self-driving technology, which he has touted as key to the financial future of the world's most valuable automaker. The 2018 accident killed 38-year-old Walter Huang. His family had alleged that Autopilot steered his 2017 Model X into a highway barrier. Plaintiffs' lawyers asked a Tesla witness whether the company knew drivers would not watch the road when using its driver-assistance system, Reuters reported last month citing deposition transcripts. # ⚓ The Register UK ☛ Arm_looks_to_generative_AI_models_at_the edge_with_Ethos-U85⠀⇛ Arm is aiming to boost AI performance at the edge with its latest embedded neural processing unit (NPU) and a Reference Design Platform for it to slot into, and said it expects to see devices based on it running generative AI models next year. # ⚓ Futurism ☛ AI_Can_Pretend_To_Be_Stupider_Than_It_Really_Is, Scientists_Find⠀⇛ Published in the journal PLOS One, researchers from Berlin's Humboldt University found that when testing out a large language model (LLM) on so- called "theory of mind" criteria, they found that not only can AI mimic the language learning stages exhibited in children, but seem to express something akin to the mental capabilities related to those stages as well. In an interview with PsyPost, Humboldt University research assistant and main study author Anna Maklová, who also happens to be a psycholinguistics expert, explained how her field of study relates to the fascinating finding. o § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ NPR ☛ The_government_announced_winners_of_a_contest to_tell_real_voices_from_deepfake_audio⠀⇛ OriginStory's technology leverages sensors in existing hardware, though it's not available in all recording equipment - newer Android phones and iPhones don't have them. Berisha says they are focusing on hardware that already can use it. # ⚓ [Repeat] NYOB ☛ 'Pay_or_Okay'_explained:_Why_more_and more_websites_make_you_pay_for_your_privacy⠀⇛ So-called pay or consent systems are on the rise in Europe. First introduced by journalistic websites that were suffering from the loss of advertising revenue to big tech platforms, Meta adopted the approach for Instagram and Facebook in November 2023. In this video, we explain what this is all about and why this approach is dangerous for free consent online. # ⚓ Scoop News Group ☛ FCC_looks_to_limit_how_domestic violence_abusers_use_connected_cars⠀⇛ Vehicle manufacturers have in recent years increased the number of communication services included in cars. These include GPS and remote start-up features that are offered as conveniences but can be used by abusers to track or harass their victims. “No survivor of domestic violence and abuse should have to choose between giving up their car and allowing themselves to be stalked and harmed by those who can access its connectivity and data,” FCC Chairwoman Jessica Rosenworcel said in a statement. “We can — and should — do more to make sure these new forms of communications help keep survivors safe.” # § Confidentiality⠀➾ # ⚓ [Old] Bruce Schneier ☛ Academic:_The_Risks_of_Key Recovery,_Key_Escrow,_and_Trusted_Third-Party Encryption⠀⇛ A variety of “key recovery,” “key escrow,” and “trusted third-party” encryption requirements have been suggested in recent years by government agencies seeking to conduct covert surveillance within the changing environments brought about by new technologies. This report examines the fundamental properties of these requirements and attempts to outline the technical risks, costs, and implications of deploying systems that provide government access to encryption keys. o § Defence/Aggression⠀➾ # ⚓ YLE ☛ Court_documents_show_possible_domestic_violence behind_fatal_McDonald's_stabbing⠀⇛ The man suspected in woman's deadly stabbing was previously under a restraining order. # ⚓ Defence Web ☛ Op_Aspides_repels_11_Red_Sea_attacks_in_two months⠀⇛ In less than two months the newest European Union (EU) naval force – Operation Aspides concentrated on the Red Sea – repelled 11 attacks and escorted close to 70 ships in the Indian Ocean inlet between Africa and Asia. # ⚓ ADF ☛ Trilateral_Exercise_Strengthens_Maritime_Security_in Indian_Ocean⠀⇛ Piracy is making a resurgence in the western Indian Ocean, and the region is rife with other sea crimes such as illegal fishing, drug smuggling, and human and weapons trafficking. # ⚓ ADF ☛ Allied_Democratic_Forces_Attack_Threat_has_Uganda_on High_Alert⠀⇛ ADF STAFF Ugandan security forces are on high alert after members of the Allied Democratic Forces terrorist organization entered the country from the Democratic Republic of the Congo in mid-March. # ⚓ France24 ☛ Security_stepped_up_for_PSG-Barcelona_Champions League_match_over_terrorist_'threat'⠀⇛ Security will be "considerably reinforced" at Wednesday's Champions League match in the French capital between Paris Saint-Germain and Barcelona after a "threat" from the Islamic State group, the interior minister said. # ⚓ New York Times ☛ Champions_League:_Security_Increased_After ISIS_Threats⠀⇛ Online messages urged violent attacks on four matches, prompting the police in England, France and Spain to step up precautions. # ⚓ ADF ☛ Intercommunal_Violence_Continues_to_Plague_South Sudan⠀⇛ Violence between rival communities has a long history in South Sudan, but the past year has seen a worrying rise in attacks that observers fear could become a wider crisis. # ⚓ France24 ☛ Germany_denies_aiding_'genocide'_in_Gaza,_says Israeli_security_at_'core'_of_foreign_policy⠀⇛ Israel's security is at the "core" of German foreign policy, the UN's highest court heard on Tuesday, where Berlin has denied a claim that it is aiding in a "genocide" in Gaza. # ⚓ Los Angeles Times ☛ The_U.S._might_ban_TikTok._Record labels_are_cutting_ties._What's_music's_Plan_B?⠀⇛ In February, Universal Music Group, the largest record label conglomerate in the world, pulled its catalog from TikTok. Videos using music from Taylor Swift or Bad Bunny suddenly fell silent. After a contentious U.S. House Committee on Energy and Commerce hearing about ByteDance, the app’s Chinese parent firm, and its potential risks for data security and political influence, the House overwhelmingly passed a bill in March that could force a sale or ban TikTok (President Biden has said he’s open to signing that bill). The Senate has held closed-door meeting on the topic, and TikTok urged its users to contact Congress to protest. # ⚓ Tech Central (South Africa) ☛ TikTok_owner_ByteDance_is_now bigger_than_Tencent⠀⇛ The results mark the first time that ByteDance has overtaken arch-rival Tencent both in revenue and profit, as it leveraged its popular short-video platforms to expand into international e-commerce and sustain its global popularity. While ByteDance’s internal figures haven’t been independently audited, they suggest the ad-churning social media juggernaut became one of the world’s fastest-growing tech giants in 2023. # ⚓ Hong Kong Free Press ☛ US_will_hold_China_responsible_if Russia_makes_gains_in_Ukraine⠀⇛ With Moscow renewing its Ukraine offensive amid a deadlock in the US Congress on approving more weapons to Ukraine, Campbell warned that Russian territorial gains could “alter the balance of power in Europe in ways that are, frankly, unacceptable.” “We have told China directly, if this continues, it will have an impact on the US-China relationship. We will not sit by and say everything is fine,” Campbell said. # ⚓ NPR ☛ Prosecutors_say_an_Idaho_man_planned_a_church_attack to_support_the_Islamic_State⠀⇛ The recording was to accompany a photo the informant took of Mercurio in front of the IS flag holding up a knife and his index finger in a gesture commonly used by the group, the statement alleged. After attacking the church, Mercurio told the informant he planned to attack others in town — as many as 21 — before being killed in an act of martyrdom, according to the statement. # ⚓ Truthdig ☛ Everything_You_Need_to_Know_About_the_TikTok Debate⠀⇛ Earlier this month, the U.S. House of Representatives made international headlines when it gave the green light on a bipartisan bill to force ByteDance, the majority owner of TikTok, to divest or face a nationwide ban in the United States. Invoking “national security,” officials expressed two fears: that TikTok will hand data on Americans to the Chinese government, and that the Chinese government will use its algorithm to influence American politics. To the chagrin of teenagers and influencers hooked on the app, the ban has support from nearly half of America. # ⚓ [Repeat] Digital Music News ☛ Senator_Mitch_McConnell Comments_on_Potential_TikTok_Ban⠀⇛ “This is a matter that deserves Congress’ urgent attention. And I’ll support, common sense, bipartisan steps to take one of Beijing’s favorite tools of coercion and espionage off the table,” he adds. “With TikTok, we’re not talking about meddling or hijacking an American platform. In this case, PRC influence and control have been baked in from the beginning. With Beijing’s blessing, TikTok’s algorithm pours gasoline on alarming trends.” # ⚓ RFA ☛ Analysts:_White_House_summit_to_bolster_South_China Sea_security_ties⠀⇛ The leaders of the Philippines, Japan and the US will meet amid friction with Beijing over its maritime claims. # ⚓ The Straits Times ☛ Expect_more_joint_South_China_Sea patrols,_US_says_ahead_of_summits_with_allies⠀⇛ WASHINGTON - More joint patrols can be expected in the South China Sea after drills by the United States, Australia, the Philippines and Japan last weekend, U.S. national security adviser Jake Sullivan said on Tuesday, ahead of U.S. summits this week with the Japanese and Philippine leaders. # ⚓ teleSUR ☛ Egypt,_Jordan,_France_Urge_Immediate_Ceasefire_in Gaza⠀⇛ Al-Sisi, Abdullah II, and Macron called for the implementation of United Nations Security Council Resolution 2728. # § Russia, Belarus, and War in Ukraine⠀➾ # ⚓ Latvia ☛ Aven_wins_court_case_in_Europe,_but sanctions_remain_in_place_for_now⠀⇛ According to a release from the Latvian Ministry of Foreign Affairs April 10, Latvian citizen and Russian businessman Petr Aven has won a European-level court case seeking to annul sanctions imposed upon him in the wake of Russia's invasion of Ukraine. However, the ruling does not mean sanctions will be immediately lifted against him, the MFA stressed. # ⚓ Latvia ☛ Two_detained_for_damaging_Ukrainian_flag_in Rīga⠀⇛ State Police said April 10 it had detained two people who had torn a Ukrainian flag off a building in Rīga and filmed it. # ⚓ Latvia ☛ Latvia_and_Ukraine_to_sign_long-term_support agreement⠀⇛ On April 9, 2024, the Latvian Cabinet decided at its weekly meeting to support the signing of an Agreement between Latvia and Ukraine on Long-Term Support and Security Commitments. # ⚓ AntiWar ☛ US_Should_Adopt_the_Mearsheimer_Plan⠀⇛ During a recent panel discussion sponsored by the Neutrality Studies YouTube channel and The American Committee for US-Russia Accord, the distinguished political scientist John J. # ⚓ France24 ☛ Switzerland_to_host_'high-level'_Ukraine peace_summit_in_mid-June,_says_Russia_will_not_attend⠀⇛ The Swiss government on Wednesday announced that it would host a high-level peace conference for Ukraine in mid-June, but said Russia would not attend. # ⚓ Hong Kong Free Press ☛ Beijing_‘does_not_accept criticism_or_pressure’_over_ties_with_Russia,_Chinese foreign_ministry_says⠀⇛ China vowed Wednesday it would not accept “criticism or pressure” over its ties with Russia, after Washington warned that it will hold Beijing responsible if Moscow makes gains in Ukraine. # ⚓ Hong Kong Free Press ☛ US_warns_it_will_hold_China responsible_if_Russia_makes_gains_in_Ukraine,_after Beijing_renews_Moscow_support⠀⇛ The United States warned Tuesday that it will hold China responsible if Moscow makes gains in Ukraine, after Beijing renewed pledges of cooperation during a visit by Russia’s top diplomat. # ⚓ RFA ☛ With_eyes_on_Beijing,_US_and_Japan_pledge stronger_ties⠀⇛ ‘Ukraine today may be East Asia tomorrow,’ Japan's prime minister said at the White House. # ⚓ RFERL ☛ Russia_Ranked_Top_Of_Global_Cybercrime_Index, With_Ukraine_Second⠀⇛ Russia, Ukraine, and China have been named as the world’s cybercrime hotspots in a new study ranking the most significant sources of cybercrime threats. # ⚓ RFERL ☛ Top_U.S._General_Tells_Congress_Ukraine 'Cannot_Sustain_Fight_Against_Russia_Alone'⠀⇛ The top U.S. general in Europe has warned that Ukraine cannot sustain its fight against Russia alone as a major spending bill languishes in the House of Representatives, blocked by a small number of Republicans who believe domestic matters should take priority. # ⚓ RFERL ☛ Siberian_Court_Sends_Man_To_Prison_For Attempt_To_Join_Pro-Ukrainian_Militia⠀⇛ A court in the Siberian city of Nizhnevartovsk on April 10 sentenced a 20- year-old man to nine years in prison for attempting to join the so-called Russian Volunteers' Corps (RDK) that has fought alongside Ukraine's armed forces against occupying Russian troops. # ⚓ RFERL ☛ Former_Pro-Russia_Lawmaker_Detained_During Attempt_To_Leave_Ukraine⠀⇛ The Security Service of Ukraine (SBU) said on April 10 that its officers had detained a former regional lawmaker of the banned pro- Russia Party of Regions as he tried to leave the country. # ⚓ RFERL ☛ Igor_Girkin,_Imprisoned_Russian_Nationalist, Plans_To_Join_Troops_Invading_Ukraine⠀⇛ Russian nationalist Igor Girkin (aka Strelkov), who was sentenced to four years in prison in January on a charge of making public calls for extremist activities, will apply to join Russian troops invading Ukraine, his lawyer told the RBK news agency on April 10. # ⚓ RFERL ☛ Russia_Seeks_To_Recruit_400,000_Contract Soldiers_This_Year,_U.K._Says⠀⇛ Russia is aiming to sign up 400,000 contract soldiers this year to beef up its forces that have suffered huge losses in the Ukraine war, Britain's Ministry of Defense said in an intelligence update. # ⚓ RFERL ☛ Russia_Accuses_Ukrainian_Gas_Company_Linked To_Biden’s_Son_Of_Financing_Terror⠀⇛ Russia's top investigative body said it had opened a probe into a Ukrainian company that formerly had ties to the son of U.S. President Joe Biden, in what likely is an effort to spread disinformation in the midst of the heated U.S. presidential election campaign. # ⚓ RFERL ☛ 2_Russians_Jailed_For_Attempting_To_Join Legion_Fighting_For_Ukraine⠀⇛ A military court in Russia on April 10 sentenced two men to nine years in prison each in separate cases for their plans to join the Freedom of Russia legion fighting with Ukraine against Russian forces. # ⚓ RFERL ☛ Russian_Helicopter_Downed_In_Crimea, Ukrainian_Navy_Says⠀⇛ A Russian Ka-27 helicopter was destroyed in Ukraine's Moscow-occupied Crimea region, Ukrainian Navy spokesman Dmytro Pletenchuk wrote on Facebook (Farcebook) on April 10. # ⚓ New York Times ☛ Ukraine’s_New_Draft_Unsettles_the Young⠀⇛ Reporters from The New York Times spoke to men who could be affected by the change. # ⚓ Latvia ☛ MEP_Ždanoka_gets_penalty_from_European Parliament⠀⇛ On Wednesday, April 10, the European Parliament (EP) sanctioned MP Tatjana Ždanoka of the Russian Union of Latvia for violating the European Parliament's code of conduct, Latvian Radio and Latvian Television reported. # ⚓ Latvia ☛ More_Russians_could_be_required_to_pass Latvian_language_test⠀⇛ Several thousand more Russian citizens in Latvia could be required to pass a Latvian language exam. These are the persons who received a permanent residence permit in Latvia in 1992. The Saeima will begin to view the relevant amendments this week, Latvian Television reported. # ⚓ Latvia ☛ Survey_suggests_most_schools_plan_to_replace Russian_with_German⠀⇛ Instead of Russian, schools could offer to teach German, French and Spanish as a second foreign language, according to a survey conducted by the Ministry of Education and Science (IZM), LETA reported on April 9. # ⚓ France24 ☛ Tens_of_thousands_evacuated_in_Russia, Kazakhstan_amid_worst_floods_in_decades⠀⇛ Russia and Kazakhstan ordered more than 100,000 people to evacuate after swiftly melting snow swelled mighty rivers beyond bursting point in the worst flooding in the area for at least 70 years. # ⚓ LRT ☛ Tajik_opposition_activist_arrested_in_Lithuania over_alleged_terrorist_links⠀⇛ Tajik opposition activist Sulaimon Davlatov has been detained in Lithuania for two months, his representatives say. According to the State Security Department (VSD), Davlatov has links to terrorist organisations. # ⚓ JURIST ☛ ECHR_rules_Russia_violated_Georgia_citizens’ humans_rights_following_2008_conflict⠀⇛ The European Court of Human Rights (ECHR) ruled Tuesday that Russia’s occupation and border enforcement of two regions in Georgia systematically violated Georgians’ human rights. # ⚓ LRT ☛ Kaunas_mayor’s_company_exported_dual-use_goods to_Russia_–_LRT_Investigation⠀⇛ A Lithuanian company co-owned by the mayor of Kaunas has been exporting sanctioned items, classified as “battlefield goods”, to Russia, the LRT Investigation Team has found. Vičiūnai Group admits it was shipping goods needed to maintain its factory in Kaliningrad, but claims it was not aware the items were sanctioned. # ⚓ RFERL ☛ Kara-Murza's_Wife_Accuses_Russia_Of_Using Punitive_Cell_To_Hasten_Prisoners'_Illnesses⠀⇛ The wife of Russian opposition politician Vladimir Kara-Murza said her husband has been held in solitary confinement for the last six months in a jail cell that is just a few square meters with a single stool, a tiny window covered with bars, and a bed that folds into the wall. # ⚓ RFERL ☛ Russia_Issues_Arrest_Warrant_For_Ex-Chief_Of Memorial's_Branch_In_Perm⠀⇛ A court in the Russian city of Perm on April 10 issued an arrest warrant for Robert Latypov, the self-exiled former chief of the Nobel Prize-winning Memorial human right group's branch in the city. # ⚓ RFERL ☛ 'Very_Tense':_Anger_Rises_To_Surface_Over Government_Response_To_Kazakh,_Russian_Floods⠀⇛ Floodwaters continue to submerge large areas of southern Russia and northern Kazakhstan with officials predicting the worse is yet to come as a massive snowmelt amid unseasonably warm temperatures forced tens of thousands from their homes. # ⚓ RFERL ☛ Russia_Investigates_Online_Post_By_Journalist In_Exile⠀⇛ Russia's government-linked Baza Telegram channel said on April 10 that the Investigative Committee had launched a probe against Zalina Marshenkulova, a self-exiled activist journalist, on a charge of justifying terrorism. # ⚓ RFERL ☛ Romania_Cancels_Showing_Of_2_Russian_Movies⠀⇛ Romania's Culture Ministry has canceled the showing of two Russian movies after RFE/RL publicized an initiative by the Russian Center, which ostensibly promotes Russian culture, to show films dedicated to a celebration of Soviet cosmonaut Yuri Gagarin's first flight into space in 1961. # ⚓ RFERL ☛ Russian_Space_Agency_Scrubs_Launch_Of_Rocket For_Second_Day_In_A_Row⠀⇛ Russia's space agency scrapped the launch of a heavy-lift rocket from a new facility for the second day in a row. # ⚓ RFERL ☛ Former_Russian_Anti-War_Lawmaker_Reportedly Wanted_In_Murder_Case⠀⇛ Magomed Gadzhiyev, a self-exiled former member of Russia's State Duma, is reportedly wanted for ordering the assassination of Maksud Sadikov, the rector of the Institute of Theology and International Relations, and his driver in Daghestan in 2011. # ⚓ teleSUR ☛ 7,700_Evacuated_in_Russia's_Orenburg_Region Due_to_Floods⠀⇛ Russia and Kazakhstan will intensify cooperation to address floods affecting border regions. # ⚓ The Straits Times ☛ Water_levels_rise_in_Russian rivers_in_flooding_zone⠀⇛ Water levels in the Ural and Tobol rivers kept rising on Thursday near Russia's cities of Orenburg and Kurgan, respectively, authorities said in the regions hit by unusually strong spring floods. # ⚓ New York Times ☛ Floods_in_Russia_and_Kazakhstan Force_Thousands_to_Evacuate⠀⇛ More than 100,000 people had to leave their homes after spring floods engulfed cities and villages in vast sections of neighboring countries. # ⚓ Meduza ☛ ‘If_we_didn’t_take_them,_they’d_die’:_A_dam breach_in_Russia’s_south_forced_thousands_to_flee_their flooded_homes._Volunteers_describe_trying_to_save_the animals_left_behind._—_Meduza⠀⇛ # ⚓ Meduza ☛ ‘He_had_no_chance’:_Ilya_Bakharev_thought joining_the_Russian_army_would_be_a_ticket_to exoneration._His_unit_mates_tortured_him_to_death._— Meduza⠀⇛ # ⚓ Meduza ☛ War_criminal_Igor_Strelkov,_jailed_in_Russia for_hardline_Kremlin_criticism,_seeks_to_enlist_in_the military_—_Meduza⠀⇛ # ⚓ LRT ☛ Belarusian_businesses_in_Lithuania_feel_the squeeze_under_prospect_of_more_restrictions⠀⇛ As politicians in Lithuania call for more restrictions on Belarusians, the latter say this makes it difficult for them to run businesses that relocated after the 2020 repressions. They are asking for clearer rules and for Vilnius to continue its previously declared open-door policy. # ⚓ LRT ☛ Lithuanian_MPs_debate_restricting_Belarusian travel_home⠀⇛ Lithuanian MPs are considering new restrictions on Belarusian nationals residing in Lithuania. One proposal would not let them return home more than once a year. # ⚓ New York Times ☛ Nijole_Sadunaite,_Lithuanian_Nun_Who Opposed_Soviet_Rule,_Dies_at_85⠀⇛ A dissident who promoted democracy and religious freedom, she was arrested by the K.G.B. After independence from Moscow, she was honored by Lithuania’s Parliament. # ⚓ Techdirt ☛ Putin_Orders_Russian_Tech_Companies_To Somehow_Make_Competitive_Game_Console_In_3_Months⠀⇛ Back when Vladimir Putin launched his aggressive war on Ukraine, even before western government sanctions began rolling out, the video game industry started its own mini warfront on Russia. Companies began suspending sales in Russia entirely and otherwise disallowing Russian citizens to participate in global gaming culture. Groups like Itch.io began selling game bundles with proceeds going to groups that provide medical services to the people in Ukraine. And because of this and other sanctions, Russia voiced plans to essentially legalize copyright infringement on products from “unfriendly” countries. o § Transparency/Investigative Reporting⠀➾ # ⚓ NPR ☛ A_Boeing_whistleblower_raises_fresh_concerns_about the_787,_and_the_FAA_investigates⠀⇛ Longtime Boeing engineer Sam Salehpour went public Tuesday with claims that he observed problems with how parts of the plane's fuselage were fastened together. Salehpour warns that production "shortcuts" could significantly shorten the lifespan of the plane, eventually causing the fuselage to fall apart in mid-flight. o § Environment⠀➾ # ⚓ Wired ☛ The_Honeybees_Versus_the_Murder_Hornets⠀⇛ Teams of volunteers now hunt Asian hornets landing on British soil, but detection is only the tip of the iceberg, says Elmes. The true challenge is tracing the hornet back to its nest, to destroy the colony. “If something can automate and help us, it will shave off time,” he says. This is the rationale behind Pollenize’s latest project—a network of AI-camera bait stations that can detect and track Asian hornets. # § Energy/Transportation⠀➾ # ⚓ DeSmog ☛ EPA’s_New_Rule_Aims_to_Cut_Toxic_Emissions, But_Cancer_Alley_Air_Pollution_Could_Worsen⠀⇛ Leaders in the fight for clean air from Louisiana’s Cancer Alley joined the Environmental Protection Agency’s Administrator Michael Regan on April 9 in Washington, D.C., for the announcement of a new rule governing air toxics-spewing chemical plants. The rule is intended to prevent cancer in surrounding low-income and minority communities. The announcement represents a milestone for environmental justice in communities historically overburdened by air-toxics pollution. But a growing number of proposed industrial projects threaten to further pollute the mostly low-income black neighborhoods along the Mississippi River between Baton Rouge and New Orleans — already home to a large number of petrochemical plants and refineries.  # ⚓ The Register UK ☛ AI_datacenters_might_consume_25%_of US_electricity_by_2030⠀⇛ Haas estimates that while US power consumption by AI datacenters sits at a modest four percent, he expects the industry to trend towards 20 to 25 percent usage of the US power grid by 2030, per a report from the Wall Street Journal. He specifically lays blame at popular large language models (LLMs) such as ChatGPT, which Haas described as "insatiable in terms of their thirst." The Arm CEO isn't alone in making this prediction. The International Energy Agency's (IEA) Electricity 2024 report [PDF] expects power consumption for AI datacenters around the world to be ten times the amount it was in 2022. Part of the problem is that LLMs like ChatGPT require far more power than traditional search engines like Google. The IEA estimates that one ChatGPT request consumes almost ten times as much power as a Google search. # § Overpopulation⠀➾ # ⚓ Overpopulation ☛ Overpopulation_Is_Still_a_Huge Problem:_An_Interview_with_Jane_O’Sullivan⠀⇛ Jane: “Declining sharply” and “dropping rapidly” are emotive terms that exaggerate the trends and distract from the far more rapid growth elsewhere. Globally we increase by somewhere between 70 million and 90 million annually, and that pace has been unrelenting for more than 40 years. We don’t have hard evidence that the curve has started to bend, let alone that it is on track to peak any time soon. So, the problem hasn’t gone away, and the impacts of the human population get more serious and intractable every year. # ⚓ CBC ☛ Water_is_in_short_supply_in_southern_Alberta. Is_a_massive_expansion_of_irrigation_possible?⠀⇛ The brown area in the photo is very concerning because it means virtually zero to no snowpack in an expanse that extends across the Prairies, said Tricia Stadnyk, a professor and Canada Research Chair in hydrologic modelling with the University of Calgary's Schulich School of Engineering. "It's highly unlikely that we can avoid drought at this point. Because without the snowpack, we don't have the soil moisture, which means that the ground is dry," she said. "That's going to have a significant impact on agriculture." # ⚓ US News And World Report ☛ The_Losing_Battle_Against Greece's_Tumbling_Birthrate⠀⇛ "To have a family these days, you need to become a hero," Giannakidis said on the sideline of a recent soccer practice. "To have a second child, more money must come into the house." As much of Europe struggles with tumbling birthrates that experts say threaten long- term economic wellbeing, Greece is a stark example of how hard it will be to reverse the trend. o § Finance⠀➾ # ⚓ India Times ☛ American_IT_company_cuts_800_jobs_across India_and_US_to_hire_talent_with_these_skills⠀⇛ o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Breach Media ☛ The_Big_China_Con⠀⇛ How Canada’s establishment media manufactured the foreign interference scandal # ⚓ TwinCities Pioneer Press ☛ House_to_delay_sending_Mayorkas impeachment_articles_to_Senate⠀⇛ Speaker Mike Johnson will not send the House’s articles of impeachment against Homeland Security Secretary Alejandro Mayorkas to the Senate this week as previously planned. Republican senators have requested more time Tuesday to build support for holding a full trial. The sudden change casts fresh doubts on the proceedings, the historic first impeachment of a Cabinet secretary in roughly 150 years. House Republicans impeached Mayorkas over the Biden administration’s handling of security and immigration at the U.S.-Mexico border. Democrats, with control of the Senate, are expected to swiftly dismiss the charges against Mayorkas, arguing they do not rise to impeachable offenses. # ⚓ Latvia ☛ The_little_bit_of_Beethoven_in_the_heart_of_Rīga⠀⇛ Only about a hundred meters from the building of the Latvian National Art Museum, on Skolas Street 3, there is a four-story brick building with elements of romanticized historical styles. # ⚓ Tech Central (South Africa) ☛ Starlink_profits_are_more elusive_than_investors_think⠀⇛ People familiar with the finances of one of the world’s most valuable private companies say Starlink has — at times — lost hundreds of dollars on each of the millions of ground terminals it ships, casting doubt on claims by CEO Elon Musk and the company’s top brass that the business is in “profitable territory”. # ⚓ India Times ☛ Italy_considers_tougher_penalties_for_AI- related_crimes⠀⇛ Italy's government is mulling tougher penalties for crimes using Artificial Intelligence (AI) tools including market rigging and money laundering, according to a draft law bill seen by Reuters on Tuesday. The 25-article draft bill lays down general principles "on research, experimentation, development, adoption and application" of AI in Italy, to cope with "the impact on fundamental rights" and related economic and social risks. # ⚓ Scoop News Group ☛ House_hurtles_toward_showdown_over expiring_surveillance_tools⠀⇛ Foremost among those prospective amendments is a requirement for U.S. government officials to get a warrant to query the communications of Americans collected under the authority of Section 702. Privacy hawks say such a requirement is necessary to overhaul a law that has been implicated in past abuses, such as improper searches of government officials and protesters. Biden administration and law enforcement officials argue such a requirement would badly inhibit their ability to conduct timely queries, including in cybersecurity cases. # § Misinformation/Disinformation/Propaganda⠀➾ # ⚓ RFA ☛ Media_Watch:_Baltimore_bridge_collapse_floods internet_with_rumors⠀⇛ The incident fuels rumors and inaccurate information both in English and Chinese media outlets. # ⚓ Digital Music News ☛ Meta_Pledges_to_Label_More_AI- Generated_Content_Across_Photo,_Video,_&_Audio⠀⇛ As AI-generated content runs rampant on Facebook (Farcebook) and Instagram, Meta says it is making some changes to how it labels manipulated media. Meta says it agrees with the Oversight Board’s argument that the company’s existing approach to AiIcontent is not enough since it only covers images in which a person is being manipulated. # ⚓ Defence Web ☛ Mapping_a_surge_of_disinformation_in Africa⠀⇛ Disinformation campaigns seeking to manipulate African information systems have surged nearly fourfold since 2022, triggering destabilizing and antidemocratic consequences. The proliferation of disinformation is a fundamental challenge to stable and prosperous African societies. The scope of these intentional efforts to distort the information environment for a political end is accelerating. The 189 documented disinformation campaigns in Africa are nearly quadruple the number reported in 2022. Given the opaque nature of disinformation, this figure is surely an undercount. # ⚓ VOA News ☛ Nigerian_presidential_adviser_falsely claims_Nigeria_is_safer_than_US⠀⇛ Nigeria is plagued by kidnappings, terrorist attacks, banditry and multiple other crimes. The Global Terrorism Index, a report published annually by the Institute for Economics and Peace (IEP), a global think tank headquartered in Sydney, Australia, ranks Nigeria eighth among the ten countries most impacted by terrorism. In its most recent annual ranking, the Global Organized Crime Index, produced by the Global Initiative Against Transnational Organized Crime (GI-TOC), a Geneva-based international non-governmental organization, assessed Nigeria as having the world’s sixth “highest criminality rate,” far worse than the U.S., which it ranked 67th. # ⚓ Scoop News Group ☛ Civil_society_groups_press platforms_to_step_up_election_integrity_work⠀⇛ Over 200 nonprofits, online research organizations and civil society groups are calling on social media platforms to step up their content moderation efforts ahead of elections in the United States and dozens of other countries this year. In an open letter sent to executives at 12 major tech and social media companies, the groups chided the platforms over their lack of investment in personnel and resources to combat election-related disinformation and influence operations. o § Censorship/Free Speech⠀➾ # ⚓ Reason ☛ Louis_Farrakhan_Loses_Lawsuit_Against_Anti- Defamation_League⠀⇛ From Friday's decision by Judge Denise Cote (S.D.N.Y.) in Farrakhan v. Anti-Defamation League: The challenged statements referring to Farrakhan as antisemitic are non-actionable statements of opinion. The communications in which they were published contain "a recitation of the facts on which [they are] based"—namely, direct quotes from Farrakhan. # ⚓ Hong Kong Free Press ☛ Hong_Kong_student_charged_with loitering_in_store_linked_to_47_democrats_case_said_he_was ‘just_playing_around’⠀⇛ A Hong Kong student charged with loitering at a chain store linked to the city’s largest national security case has said he was “just playing around.” The student, who was 14 when he was arrested last year, is among five people standing trial after pleading not guilty to a charge of “loitering causing concern.” # ⚓ Hong Kong Free Press ☛ Tiananmen_vigil_trio_turn_to_Hong Kong’s_top_court_to_try_and_challenge_convictions_over_nat. security_request⠀⇛ Three former organisers of the annual Tiananmen vigils in Hong Kong are seeking to take a challenge against their convictions over refusing to comply with a data request from national security police to the city’s top court. # ⚓ RFERL ☛ 'I'm_Not_Going_To_Quit':_Facing_Prison,_Soviet-Era Dissident_Skobov_Speaks_Out_Against_War,_Repression⠀⇛ Aleksandr Skobov has been a thorn in the side of authoritarian governments for more than four decades, from the Soviet era to President Vladimir Putin's long rule. And now, in pretrial detention in St. Petersburg and facing prison, he is in no mood for compromise. "On principle I refuse to comply with fascist laws," he told RFE/RL late last month, shortly after the Russian government designated him a "foreign agent" on March 22. "I don't intend to get into debates with the government. I will not try to prove my innocence. I will not label my writings, and I will not write any financial reports for them." o § Freedom of Information / Freedom of the Press⠀➾ # ⚓ Hong Kong Free Press ☛ Beijing’s_security_law_prompted_Hong Kong_activists_to_consider_setting_up_‘gov’t-in-exile,’_Jimmy Lai_trial_hears⠀⇛ The enactment of a national security law in Hong Kong prompted activists to discuss the prospect of setting up a “government-in-exile” to continue lobbying international allies against the city, the trial of media mogul Jimmy Lai has heard. # ⚓ The Guardian UK ☛ Biden_says_he_is_‘considering’_Australian call_to_drop_Julian_Assange_charges⠀⇛ Biden’s comment is the latest indication that his administration may have cooled on the idea of putting Assange on trial, which could prove politically toxic in an election year. Last month, the Wall Street Journal reported that the Biden administration was exploring the possibility of allowing the WikiLeaks founder to cut a plea deal that would see him admit to a misdemeanor offense of mishandling classified documents in return for an early release. # ⚓ CNN ☛ Biden_says_US_is_considering_Australia’s_request_to drop_prosecution_of_Julian_Assange⠀⇛ Asked Wednesday about Australia’s call to end Assange’s prosecution, Biden told reporters at the White House, “We’re considering it.” CNN has reached out to the National Security Council for additional comment on the president’s remark. # ⚓ NBC ☛ Biden_says_he_is_'considering'_Australia's_request_to end_Julian_Assange's_prosecution⠀⇛ Assange, an Australian citizen, has been engaged in a battle against U.S. extradition efforts from prison in the United Kingdom for more than a decade. He spent seven years in self-exile in the Ecuadorian Embassy in London and the last five years in the high-security Belmarsh Prison on the outskirts of the British capital. # ⚓ New York Times ☛ Biden_Says_U.S._Is_Considering_Dropping Assange_Case⠀⇛ President Biden said on Wednesday that the United States was considering dropping its prosecution of Julian Assange, the WikiLeaks founder who has been jailed in London for years while fighting extradition to face U.S. charges related to his publication of classified documents. # ⚓ CPJ ☛ Turkish_authorities_attack,_threaten,_arrest_several journalists_during_post-election_unrest⠀⇛ Police intervened in the protests with arrests, tear gas, rubber bullets and water cannons, targeting several field reporters, some of whom were taken into custody. Multiple journalists also reported receiving threats and insults online and offline. o § Civil Rights/Policing⠀➾ # ⚓ VOA News ☛ European_court_tells_nations_to_shield_people from_climate_change_in_case_with_wide_implications ⠀⇛ "The most important thing is that the court has said in the Swiss women's case that governments must cut their emissions more to protect human rights," said 19-year-od Sofia Oliveira, one of the Portuguese plaintiffs. "Their win is a win for us, too, and a win for everyone!" The court — which is unrelated to the European Union — ruled that Switzerland "had failed to comply with its duties" to combat climate change and meet emissions targets. # ⚓ Site36 ☛ New_Schengen_Border_Code_leads_to_70_%_more warrants_and_alerts_stored_by_German_police_in_SIS⠀⇛ # ⚓ Democracy Now ☛ Arizona_Supreme_Court_Revives_1864_Abortion Ban_Passed_Before_Women_Could_Even_Vote⠀⇛ In a historic ruling, Arizona’s conservative Supreme Court has upheld an 1864 law banning almost all abortions in the state. The court sent out this warning: “Physicians are now on notice that all abortions, except those necessary to save a woman’s life, are illegal.” The 160-year-old law predates Arizona becoming a state and was passed decades before women could even vote. Although Arizona’s Attorney General Kris Mayes said she will not enforce the “draconian law,” the ruling sent shockwaves across the nation. “The central strategy of the anti-abortion movement is to roll back the clock to the Victorian era, because they know that they cannot win through the democratic process,” says Amy Littlefield, abortion access correspondent at The Nation, who says conservatives supporting these unpopular restrictions face an uphill battle this fall. “Democrats are banking on this being a huge way to lift their boats in the next election.” Activists are preparing a November ballot measure to enshrine abortion rights in the Arizona Constitution, and reproductive rights will be a key issue in the state’s closely watched Senate race. o § Internet Policy/Net Neutrality⠀➾ # ⚓ NBC ☛ FCC_chair_holds_roundtable_on_net_neutrality_in Campbell_ahead_of_agency_vote⠀⇛ “We, as carriers, should not be — in my opinion — picking and choosing not only what people can get to, but how it performs when they interconnect,” Jasper said. Stanford law professor Barbara van Schewick at the meeting pointed out, in the case of firefighters losing [Internet] access, it doesn’t matter who was right or wrong. “What matters is, as they were fighting a fire — in the middle of one of the worst fires in California history — there was nobody firefighters could turn to to ensure that they get connection first and resolve the issue later,” said van Schewick, # ⚓ David Rosenthal ☛ The_Little_Garden⠀⇛ Below the fold is the story of how I got a full- time Internet connection at my apartment 32 years ago next month, and the incredible success of my first ISP. The reason I'm now able to tell this story is that Tom Jennings, the moving spirit behind the ISP has two posts describing the history of The Little Garden, which was the name the ISP had adopted (from a Chinese restaurant in Palo Alto) when I joined it in May 1993. Tom's perspective from the ISP's point of view contrasts with my perspective — that of a fairly early customer enhanced by information via e-mail from John Gilmore and Tim Pozar, who were both involved far earlier than I. o § Digital Restrictions (DRM)⠀➾ # ⚓ Stian Kristoffersen ☛ The_Open_Secret_about_Confidential Computing⠀⇛ The three main technologies used by Azure and GCP are AMD SEV-SNP (VM), Intel SGX (enclave) and Intel TDX (VM). Intel TDX uses Intel SGX for attestation. Both Intel SGX and AMD SEV have had their attestation keys extracted. In the case of Intel SGX this was used to break UHD Blu-Ray DRM. There are so many side channels in Intel SGX that they used a table to keep track of which CPUs are vulnerable to which attacks. When Google looked at both AMD SEV-SNP and Intel TDX they found a bunch of issues in both. This week further issues in both solutions were published by researchers at ETH Zurich. # ⚓ Ruben Schade ☛ Rubenerd⠀⇛ I’ve decided my time is worth more than this. I agree with Marcel; if your page implements these, I make like a cliché Gainax character and bounce. § Monopolies/Monopsonies⠀➾ o ⚓ APNIC ☛ Email_is_getting_harder_to_self-host._Or_is_it?⠀⇛ A post recently featured on Hacker News (HN) discusses the modern dilemma of implementing anti-spam control features in self-hosted email. It refers to XOMedia’s article titled ‘A Deep Dive into Email Deliverability in 2024‘, which explores the application of three email- securing features: SPF, DKIM and DMARC. This post is particularly relevant now as Google, Yahoo, and Outlook (Microsoft) have recently disclosed their plans to enforce stricter compliance standards on self- hosted email implementers starting in the second quarter of this year. Implementing these measures likely has already begun, indicating a tightening of regulations in this domain. o § Trademarks⠀➾ # ⚓ TTAB Blog ☛ TTABlog_Test:_How_Did_These_Three_Recent_2(d) Appeals_Turn_Out?⠀⇛ A TTAB judge once said to me that one can predict the outcome of a Section 2(d) appeal 95% of the time just by looking at the marks and the involved goods/services. Here are the three such appeals recently decided by the TTAB. How do you think these three came out? No hints this time. [Answers in first comment.] # ⚓ TTAB Blog ☛ Divided_9th_Circuit_Says_District_Court_Has Power_to_Adjudicate_TM_Applications⠀⇛ Section 1119 of the Trademark Act gives a federal district court the power to "determine the right to registration, order cancelation of registrations, in whole or in part, restore canceled registrations, and otherwise rectify the register with respect to the registrations of any party to the action." Does it give a court power to invalidate pending trademark applications? A divided panel of the U.S. Court of Appeals said yes in BBK Tobacco & Foods LLC d/b/a HGI v. Central Coast Agriculture, Inc., Appeals Nos. 22-16190 and 16281 (9th Cir. April 2, 2024). o § Copyrights⠀➾ # ⚓ New York Times ☛ Da_Vinci’s_Been_Dead_for_500_Years._Who Gets_to_Profit_from_His_Work?⠀⇛ In the late 15th century, when the Italian Renaissance artist Leonardo da Vinci completed “Vitruvian Man” — one of his most famous drawings, which depicts the proportions of the human body — he could not have predicted it would be reproduced onto cheap notebooks, coffee mugs, T-shirts, aprons, and even puzzles. Centuries later, the Italian government and the German puzzle maker Ravensburger are battling over who has the right to reproduce “Vitruvian Man” and profit from it. # ⚓ Digital Music News ☛ New_Bill_Would_Force_AI_Companies_to Disclose_Copyright_Use⠀⇛ Called the Generative AI Copyright Disclosure Act, the legislation would require anyone creating training datasets or making significant changes to an existing dataset to submit a notice to the Register of Copyrights. That notice must contain a “detailed summary of any copyrighted works used” and the URL for any publicly available material. The Register of Copyrights would then publish a publicly available online database containing all the notices. # ⚓ Digital Music News ☛ Twitter/X_Refutes_Remaining_Claims_in NMPA_Copyright_Suit:_‘Any_Infringement_Was_Innocent_and_Was Not_Willful’⠀⇛ Twitter/X has officially pushed back against the remaining copyright monopoly infringement claims it’s facing in a complaint levied by the National Music Publishers’ Association (NMPA). The social control media platform just recently submitted its answer to the NMPA’s suit, which was filed in June of 2023. # ⚓ Silicon Angle ☛ New_bill_aims_to_force_Hey_Hi_(AI)_firms_to disclose_use_of_copyrighted_material⠀⇛ Lawmakers in the U.S. Congress introduced a new bill on Tuesday that would force artificial intelligence companies such as Proprietary Chaffbot Company and Surveillance Giant Google LLC to reveal exactly what copyrighted material they use to train their large language models, which power generative Hey Hi (AI) chatbots such as Abusive Monopolist Microsoft Chaffbot and Bard. # ⚓ Torrent Freak ☛ 'X'_Denies_Music_Companies'_Remaining Piracy_Liability_Claims_in_Court⠀⇛ Elon Musk's social media platform X has denied all copyright infringement claims in response to a 'piracy' complaint filed last year by a group of record labels. The Nashville federal court already dismissed several key allegations and X hopes to defeat the remaining contributory infringement claims as well. Among its defenses, X notes that the music companies demand "unconstitutionally excessive and disproportionate" damages. # ⚓ Torrent Freak ☛ MPA:_Site-Blocking_Will_Stop_Pirate_Site Owners_Who_Abuse_Kids_&_Traffick_Drugs⠀⇛ After a wait of more than 12 years, rightsholders in the United States will again seek legislation that will provide the framework for a site-blocking regime to combat online piracy. After promoting and guiding similar regimes in dozens of countries overseas, the push will see the Hollywood studios of the Motion Picture Association urge Congress to bring the United States up to date. # ⚓ EFF ☛ The_Motion_Picture_Association_Doesn’t_Get_to_Decide Who_the_First_Amendment_Protects⠀⇛ What the MPA wants is the power to block entire websites, everywhere in the U.S., using the same tools as repressive regimes like China and Russia. To it, instances of possible copyright infringement should be played like a trump card to shut off our access to entire websites, regardless of the other legal speech hosted there. It is not simply calling for the ability to take down instances of infringement—a power they already have, without even having to ask a judge—but for the keys to the internet. Building new architectures of censorship would hurt everyone, and doesn’t help artists. The bills known as SOPA/PIPA would have created a new, rapid path for copyright holders like the major studios to use court orders against sites they accuse of infringing copyright. Internet service providers (ISPs) receiving one of those orders would have to block all of their customers from accessing the identified websites. The orders would also apply to domain name registries and registrars, and potentially other companies and organizations that make up the internet’s basic infrastructure. To comply, all of those would have to build new infrastructure dedicated to site- blocking, inviting over-blocking and all kinds of abuse that would censor lawful and important speech. In other words, the right to choose what websites you visit would be taken away from you and given to giant media companies and ISPs. And the very shape of the internet would have to be changed to allow it. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 6912 ➮ Generation completed at 02:49, i.e. 26 seconds to (re)generate ⟲