𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, November 23, 2021 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Wed 24 Nov 02:40:25 GMT 2021 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2021/11/23/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmewryoNvgmB7zLqV7RQ2PTLYkagYXvBASicFQi1ESPiHm QmViJLHdiRf7wrstUaHcTaXuiWpGyTkptFkDjYAFoJBJoj QmVzPu6Qip7yK3FGSsrMzEt3zNmqWufLFF5CZNmsVbHZLd QmYTFyk7SSEVeJPYyyFr91pb7fbKnpS4kiFjty9U136upV QmYKBd728JBm11x2JbtET9sF2KJXtKjGPDD1jVnpt7fLqz QmQba8m7JeAYTn4JDwkhe5nDZfnw9TnSASsQqLF7LBYEg2 QmT9Hh5LgzS2eg26pkvFLpdGLNAEURRLod8DffDCczhxy1 QmdEutfCAc7HzKtnLt7k7b2dajGSqfBSGnEPAuD2bontJM QmSuWrcnwPk5e1gVWiJbTq7uxUkNn8DzRVm659JmGTFR5W QmRDvU3Bb1mJHK7qGvaLg5kKvJ9tXx4qDntaaZU2EPXgnr QmXnPPSuiAbypBs2W4Hu14xEgjjptzNmzCptadFdRv7xt5 Qmed7VnZALGrUYrCRnPW72Zg4XmWFjZQUFe7BHLQ4EWp12 Qmak6N1wRPKAPf9DxMtCC9P4rZVS2rKi58Zcinr7iLRtd5 QmYZPeUTA2uaPPdjbKd4Mhnwn8aLtQKzy7Ft175ssdW8PT QmcNLdXKwxdD6cLvdgRCUDzCTD4PfjtBzdq6btKA1VdHeD QmXkgs6nUp2YxKaphy2EXnEaHqcAAagQyA5Z44RUfN2uvD QmdGDdRX8ZuGj76UZ5fvhjBZ81N9v4RyisduQDvtX5i4bQ QmXUd8Sk2pSNG2yA8y1Ddfd7zDgDgQCfztF4s5mGnkZKin QmeDHFuwxMuWGXnXY8ELJ4X5fk6wWvRiyFNXRQ9noLwTQw Qma6fG1kUmKGPn5zAHpVWkUoTsUNdRgGNmFYPmFKcxGEHK QmcehsKRe5D9pD1MUq2cbSWmBriwyeQoqZP3fXiJWEjy4z ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ IRC Proceedings: Monday, November 22, 2021 | Techrights ⦿ Microsoft-Led Misinformation Campaign About Germany and Munich Reminds Us That Microsoft Hates and Actively Undermines GNU/Linux Adoption | Techrights ⦿ In Light of Fast-Accelerating Deterioration - Sometimes Weaponisation - Getting Off the World Wide Web (to the Extent Feasible) Makes You Saner and Less Susceptible to Manipulation, Lies | Techrights ⦿ Black Friday SPAM on the World Wide Web: A Reminder That the Web is a Dying Platform, Languishing Due to Marketing and Misinformation | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2021/11/23/irc-log-221121/#comments http://techrights.org/2021/11/23/misinformation-about-munich/#comments http://techrights.org/2021/11/23/weaponisation-of-www/#comments http://techrights.org/2021/11/23/web-as-a-spamfarm/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2021/11/23/mabox-linux-21-11-released/#comments http://techrights.org/2021/11/23/memories-of-david-h-adler/#comments http://techrights.org/2021/11/23/team-upc-still-faking-progress/#comments ䷩ 𝚕𝚒𝚗𝚎 58 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/23/irc-log-221121/#comments Gemini version at gemini://gemini.techrights.org/2021/11/23/irc-log-221121/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.23.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Monday,_November_22,_2021⠀✐ Posted in IRC_Logs at 2:02 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights- 221121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-221121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-social-221121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes- 221121.txt Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmNVjv6z9tNszUBK9mTDY1A9mqtnhQKnBDbo63BAxUgDnY #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmRctCGavQTb8dQuMWC41ajjsN17DwJ7wFmVoUTGTjJXvS (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  QmYticgXEvtanbDdYwpnKBrULFLnXxiwzRMYPMcU4yJtXp social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmShmPRAWJCJGYWf5xn27MG2bCefg3Av2LmxARVAWCLRyv social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmNpBCnUM2iahM6hNsyXbKu7gnFVjLDFTcMaD3kCAJi5Wt #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmT4UoVBxEeKTi8VKN1F88MkegK5BFopMh5AMoqcEQfDAu (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmdzpSQX4m4WoPUEwTpb81Q8DLVuPBy85NekREum6ot3Mt #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmcihMk5zG6e88iR1oE9nrsKU5dS2FRGhewL2AuxatbyyH (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmcehsKRe5D9pD1MUq2cbSWmBriwyeQoqZP3fXiJWEjy4z ䷩ 𝚕𝚒𝚗𝚎 187 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/23/misinformation-about-munich/#comments Gemini version at gemini://gemini.techrights.org/2021/11/23/misinformation-about-munich/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.23.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Microsoft-Led_Misinformation_Campaign_About_Germany_and_Munich_Reminds_Us That_Microsoft_Hates_and_Actively_Undermines_GNU/Linux_Adoption⠀✐ Posted in Deception, GNU/Linux, Microsoft at 7:15 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_loves_Linux⦈_ Microsoft loves Linux… as a “niche” 2019: Former_Mayor_(Christian_Ude)_of_Munich_Explains_How_Microsoft_Hates_Linux List of current media coverage in English, actively updated: German_state planning_to_switch_25,000_PCs_to_LibreOffice_and_GNU/Linux (there’s a lot more in German, but we’re an English-speaking site; links to coverage in German can be found in our IRC logs) Regarding the latest moves (or plans to move) to GNU/Linux in Germany we have 3 points to make: 1) It’s good news, there’s no caveat. 2) Microsoft ‘news’ sites already hijack the news to mob the initiators or play the move down with “Munich” misinformation and revisionism (see the list above, or recent Daily Links which contain the same) 3) Munich did NOT fail with GNU/Linux but was bribed and mobbed by the thugs from Microsoft Deutschland, HP, Accenture, and Gartner (we’ve meticulously covered their role at the time). To give just a tiny gist of a years-old saga (endless mobbing was required to accomplish this), Accenture was just one of those fake “consultants”/ ”contractors” assigned to act like marketing/lobbying agencies with the veneer of professionalism [1, 2]. In the case of HP [1, 2, 3], it’s another example of a company pretending to work for your interests while covertly working for Microsoft’s interests. In Gartner’s case, we’ve had leaks and whistleblowers [1, 2]. It’s not even a technical battle. Microsoft has turned it into politics and bribery, as_usual. This is the only way Microsoft can “win”. The purpose of the attack was, create a stigma about GNU/Linux and constantly say that Munich ‘failed’ with GNU/Linux. They keep beating a dead horse — a horse killed by Microsoft (by means of intensive and pervasive corruption). Here’s an infographic — a concise and factual visual presentation — shared among many including the President of the Open Source Initiative (OSI) at the time. That’s Simon Phipps before he sold out to Microsoft (he accepted a payment, leading up to a_change_of_mission_at_the_OSI; then the_change_of leadership following resignation by all staff): 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Simon_Phipps_on_Munich⦈_ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣶⣶⣶⣾⣿⣿⣿⣿⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠻⢿⣟⣿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣤⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠠⣿⡿⢀⢿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⣴⣾⣿⣷⣦⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⡛⠛⠛ ⠙⢶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠻⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠄⠦⠀⠀⠀⣤⣤⡀⣾⠀⠻⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⡤⣧⣿⠓⠚⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣀⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢿⠀⠀⠀⠀⠀⠀⠀⣠⣒⡂⠀⢉⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣟⠿⢿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠁⠀⠀⠀⠀⠀⠠⠔⠛⠟⠆⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠀⠀⠀⠟⠁⠀⠀⠉⠉⠉⠉⠉⠁⠘⠿⠿⠿⠛⢹⣿ ⠀⠀⣿⣿⣶⣿⣿⣾⣿⣇⣾⡿⣿⣦⣿⣿⣿⣦⣰⣿⣿⣶⢰⣿⣿⣷⣠⣾⣿⣷⡄⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢀⣾⡿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣴⣿⣿⣾⠀⢸⣿⡗⢸⣿⡇⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣾⣿⢸⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣍⢹⣿⣿⣿⡇⣿⣿⡆⢸⣿⡇⠀⠀⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⣿⣿⣍⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠴ ⠀⠀⣿⡿⣿⣿⣿⣿⣿⡿⣿⣇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⣿⣿⣼⣿⣇⣿⡿⢿⣿⣿⡇⣿⣿⣬⢾⣿⣹⣿⠆⢸⣿⣧⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠛⠃⠛⠙⠛⠙⠛⠃⠙⠛⠛⠁⠛⠛⠙⠛⠈⠛⠛⠋⠈⠙⠛⠋⠀⠙⠛⠋⠀⠛⠋⠀⠘⠛⠃⠀⠀⠛⠛⠋⠙⠛⠛⠁⠘⠛⠛⠁⠙⠛⠛⠈⠛⠛⠋⠀⠈⠛⠛⠋⠛⠃⠛⠃⠙⠛⠈⠛⠛⠋⠛⠛⠘⠛⠀⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣶⣶⣾⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠒⢿⣟⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⠈⠵⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣴⣤⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⠛⠛ ⠙⢶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⠴⡤⠇⠀⠀⠀⣠⣀⡀⣾⠀⠈⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⢠⣿⣾⠒⠐⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⣠⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⠀⠀⠀⠀⠀⠀⠀⣠⣒⡚⠉⢉⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⣿⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠠⠴⠛⠟⢇⠀⠀⠀⠀⠀⢻⡟⢿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠀⠀⠠⠿⠉⠀⠀⠉⠉⠉⠉⠉⠁⠺⠿⠿⠿⠛⢿⣿ ⠀⠀⣿⣿⣶⣿⣿⣾⣿⣇⣾⡿⣿⣦⣿⣿⣿⣦⣰⣿⣿⣶⢰⣿⣿⣷⣠⣾⣿⣷⡄⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢀⣾⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣾⠀⢸⣿⡗⢸⣿⡇⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣾⣿⢸⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣍⢹⣿⣿⣿⡇⣿⣿⡆⢸⣿⡇⠀⠀⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⣿⣿⣍⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿ ⠀⠀⣿⡿⣿⣿⣿⣿⣿⡿⣿⣇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⣿⣿⣼⣿⣇⣿⡿⢿⣿⣿⡇⣿⣿⣬⢾⣿⣹⣿⠆⢸⣿⣧⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠛⠃⠛⠙⠛⠙⠛⠃⠙⠛⠛⠁⠛⠛⠙⠛⠈⠛⠛⠋⠈⠙⠛⠋⠀⠙⠛⠋⠀⠛⠋⠀⠘⠛⠃⠀⠀⠛⠛⠋⠙⠛⠛⠁⠘⠛⠛⠁⠙⠛⠛⠈⠛⠛⠋⠀⠈⠛⠛⠋⠛⠃⠛⠃⠛⠛⠈⠛⠛⠋⠛⠛⠘⠛⠀⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣶⣶⣿⣿⣿⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠺⢿⣟⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠠⣿⣿⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡀⠀⠀⠒⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠉⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣴⣴⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⢁⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⠛⠛ ⠙⢶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠌⣆⠀⠀⠀⣠⣤⡀⣾⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣷⣼⠒⠒⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⠀⠀⠀⠀⠀⠀⠀⣠⣖⡂⠉⢉⠏⠁⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⣿⠻⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠠⠴⠛⠟⠇⠀⠀⠀⠀⠀⢻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠿⠉⠀⠀⠉⠉⠉⠉⠉⠑⠺⢿⠿⠿⠛⢿⣿ ⠀⠀⣿⣿⣶⣿⣿⣾⣿⣇⣾⡿⣿⣦⣿⣿⣿⣦⣰⣿⣿⣶⢰⣿⣿⣷⣠⣾⣿⣷⡄⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢀⣾⡿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣴⣿⣿⣶⠀⢸⣿⡗⢸⣿⡇⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣾⣿⢸⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣍⢹⣿⣿⣿⡇⣿⣿⡆⢸⣿⡇⠀⠀⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⣿⣿⣍⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠏ ⠀⠀⣿⡿⣿⣿⣿⣿⣿⡿⣿⣇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⣿⣿⣼⣿⣇⣿⡿⢿⣿⣿⡇⣿⣿⣬⢾⣿⣹⣿⠆⢸⣿⣧⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠛⠃⠛⠙⠛⠙⠛⠃⠙⠛⠛⠁⠛⠛⠙⠛⠈⠛⠛⠋⠈⠙⠛⠋⠀⠙⠛⠋⠀⠛⠋⠀⠘⠛⠃⠀⠀⠛⠛⠋⠙⠛⠛⠁⠘⠛⠛⠁⠙⠛⠛⠈⠛⠛⠋⠀⠈⠛⠛⠋⠛⠃⠛⠃⠛⠛⠈⠛⠛⠋⠛⠛⠘⠛⠀⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣒⣶⣾⣾⣿⣶⣶⣶⣖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠺⠿⣟⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣴⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥⣤⣤⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢛⠛⠛⠛ ⠙⢶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿ ⠀⠀⠛⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣧⣾⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⡾⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢻⠀⠀⠀⠀⠀⠀⠀⣠⣐⡊⠀⢈⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⢿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠟⠇⠀⠀⠀⠀⠀⢸⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠝⠁⠀⠈⠛⠛⠋⠉⠉⠳⠸⠿⠿⠟⠛⢛⣿ ⠀⠀⣿⣿⣶⣿⣿⣾⣿⣇⣾⡿⣿⣆⣿⣿⣿⣦⣰⣿⣿⣶⢰⣿⣿⣷⣠⣾⣿⣷⡄⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢀⣾⡿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣴⣿⣿⣶⠀⢸⣿⡗⢸⣿⡇⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣾⣿⠸⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣍⢹⣿⣿⣿⡇⣿⣿⡆⢸⣿⡇⠀⠀⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⣿⣿⣍⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘ ⠀⠀⣿⡿⣿⣿⣿⣿⣿⡿⣿⣇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⣿⣿⣼⣿⣇⣿⡿⢿⣿⣿⡇⣿⣿⣬⢾⣿⣹⣿⠆⢸⣿⣧⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠛⠃⠛⠙⠛⠙⠛⠃⠙⠛⠛⠁⠛⠛⠙⠛⠈⠛⠛⠋⠈⠙⠛⠋⠀⠙⠛⠋⠀⠛⠋⠀⠘⠛⠃⠀⠀⠛⠛⠋⠙⠛⠛⠁⠘⠛⠛⠁⠙⠛⠛⠈⠛⠛⠋⠀⠈⠛⠛⠋⠛⠃⠛⠃⠙⠛⠈⠛⠛⠋⠛⠛⠘⠛⠀⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣖⣒⣖⣶⣿⣿⣶⣾⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠻⢿⣟⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠠⣿⣿⢈⠽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣦⣤⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⢛⠛⠛ ⠙⢶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠄⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠻⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣧⣼⠒⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣀⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢿⠀⠀⠀⠀⠀⠀⠀⣠⣐⡂⠉⢉⠏⠁⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠠⠴⠛⠟⠆⠀⠀⠀⠀⠀⢺⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠟⠉⠀⠀⠉⠉⠉⠁⠉⠀⠾⠿⠿⠿⠟⢻⣿ ⠀⠀⣿⣿⣶⣿⣿⣾⣿⣇⣾⡿⣿⣆⣿⣿⣿⣦⣰⣿⣿⣶⢰⣿⣿⣷⣠⣾⣿⣷⡄⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢀⣾⡿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣴⣿⣿⣶⠀⢸⣿⡗⢸⣿⡇⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣾⣿⢸⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣍⢹⣿⣿⣿⡇⣿⣿⡆⢸⣿⡇⠀⠀⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⣿⣿⣍⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉ ⠀⠀⣿⡿⣿⣿⣿⣿⣿⡿⣿⣇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⣿⣿⣼⣿⣇⣿⡿⢿⣿⣿⡇⣿⣿⣤⢾⣿⣹⣿⠆⢸⣿⣧⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠛⠃⠛⠙⠛⠙⠛⠃⠙⠛⠛⠁⠛⠛⠙⠛⠈⠛⠛⠋⠈⠙⠛⠋⠀⠙⠛⠋⠀⠛⠋⠀⠘⠛⠃⠀⠀⠛⠛⠋⠙⠛⠛⠁⠘⠛⠛⠁⠙⠛⠛⠈⠛⠛⠋⠀⠈⠛⠛⠋⠛⠃⠛⠃⠙⠛⠈⠛⠛⠋⠛⠛⠘⠛⠀⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣒⣲⣶⣶⣶⣶⣖⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠒⠾⣟⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣴⣦⣤⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢀⢽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⣤⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛⠛ ⠙⢶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⠀⠀⠛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⢀⠀⢺⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣧⣼⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⣠⣔⡂⠀⢉⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠴⠛⠟⠆⠀⠀⠀⠀⠀⢸⡟⠿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠀⠀⠀⠟⠉⠀⠀⠉⠉⠉⠉⠉⠑⠾⠿⠿⠟⠛⢻⣿ ⠀⠀⣿⣿⣶⣿⣿⣾⣿⣇⣾⡿⣿⣦⣿⣿⣿⣦⣰⣿⣿⣶⢰⣿⣿⣷⣠⣾⣿⣷⡄⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢀⣾⡿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣴⣿⣿⣶⠀⢸⣿⡗⢸⣿⡇⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣾⣿⢸⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣍⢹⣿⣿⣿⡇⣿⣿⡆⢸⣿⡇⠀⠀⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⣿⣿⣍⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐ ⠀⠀⣿⡿⣿⣿⣿⣿⣿⡿⣿⣇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⡇⠀⠀⣿⣿⣼⣿⣇⣿⡿⢿⣿⣿⡇⣿⣿⣤⢾⣿⣹⣿⠆⢸⣿⣧⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠛⠃⠛⠙⠛⠙⠛⠃⠙⠛⠛⠁⠛⠛⠙⠛⠈⠛⠛⠋⠈⠙⠛⠋⠀⠙⠛⠋⠀⠛⠋⠀⠘⠛⠃⠀⠀⠛⠛⠋⠙⠛⠛⠁⠘⠛⠛⠁⠙⠛⠛⠈⠛⠛⠋⠀⠈⠛⠛⠋⠛⠃⠛⠃⠙⠛⠈⠛⠛⠋⠛⠛⠘⠛⠀⠀ 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⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠟⠀⢰⠷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⠀⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣷ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣿⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢴⡴ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡐⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⠿⠛⣷⡀⣼⣾⢓⢛ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠔⠙⠟⣆⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠟⠛⠐⣻ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡇⠀⠀⣠⣶⡏⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠸⣿⣷⣽⣿⣟⠋⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠾⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⠇⡔⠙⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣄⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠏⠏⢩⠋⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢠⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠟⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣦⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⣿⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠤⢴ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠐⠹⠿⢿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣗ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠄⠛⠟⣆⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠛⠀⣺ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡇⠀⠀⣠⣴⡏⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⠛⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠾⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⠇⡔⠙⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⣺⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣄⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠏⠏⢉⠋⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢠⢀⣰⣐⣸⣴⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠟⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣦⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠃⢠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠾⠛⠛⠟⠻⢷⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣠⡷⢠⡉⣹⣿⣿⣧⣼⡿⠀⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡿⠟⠆⠙⠆⠐⠚⠛⠻⠿⠿⠿⠿⢿⣷⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣄⠀⠀⢀⡾⠷⠒⠒⠻⠿⠟⢛⠋⠉⠀⢀⡈⠿⠟⠟⠋⣉⣬⣽⣦⣐⣾⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣿⣿⡧⣤⣤⡀⠀⠈⠑⠐⠒⠶⢀⣐⣐⣶⣶⠀⢠⠀⠀⠀⠀⠀⣠⣥⡔⣡⣷⣦⣤⣭⣿⡆⢠⣶⣦⣀⠀⣤⡆⢶⢀⣿⠀⢰⠀⠀⢀⡄⠀⢀⣾⣿⣿⣿⣿⣿⣸⣥⣠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀ ⢀⠈⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠟⠀⠚⠀⠀⠀⠈⢸⣿⣯⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣬⣿⣾⣿⣶⣿⠀⢠⣿⢇⠀⢾⣿⣿⣿⣿⣿⣿⣹⡏⢹⢸⣇⣀⣀⣤⣤⣴⣶⣶⣿⡿⠿⠿⠿⠋⠁ ⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢘⣿⣿⣿⣿⣿⣿⣿⠁⠰⠴⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢤⣄⠀⢄⠀⢲⣿⠀ ⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⢛⠻⣿⠟⠟⢹⠙⣿⠉⠀⣴⡿⣿⠛⣦⣤⣬⣿⣿⣿⣏⠾⢜⠀⠀⠀⠀⠀⠀⠐⢻⡇⠈⣽⣿⡎⠈⠀⠨⡏⠂ ⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⡷⠖⠋⠀⠀⠀⢸⣿⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠇⠈⡻⠺⠶⠚⠂⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⣟⢁⣀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢨⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢰⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠟⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠇⢠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠾⠛⠛⡟⠻⢷⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣠⡇⢠⣉⣹⣿⣿⣥⣼⣿⡄⠀⢸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡿⠟⠦⠙⠆⠐⠚⠛⠻⠿⠿⠿⠿⢿⣷⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣄⠀⠀⠀⡿⠷⠒⠒⠛⠿⠟⢛⠉⠉⠀⢀⡈⠿⠟⠻⢛⣩⣭⣽⣮⡲⣿⡏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠈⠙⠁⠀⠶⢀⣀⣐⣶⣶⠀⢠⠀⠀⠀⠀⠀⢰⣥⣤⣠⣷⣶⣤⣭⣿⡆⢠⣿⣦⣀⠀⣤⣆⢶⢀⣿⠀⣰⠀⠀⢀⡄⠀⢰⣿⣿⣿⣿⣿⣷⣹⣧⣠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄ ⢀⠈⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠟⠀⠒⠀⠀⠀⠀⢸⣿⣯⣼⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣮⣬⣿⣾⣿⣶⣿⠀⢠⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⡏⢹⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠁ ⣼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⠂⢸⣿⣿⣿⣿⣿⣿⣿⠁⠰⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢤⣀⠄⠄⢀⢸⣿⡀ ⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⢛⠻⣿⡿⠟⢻⠙⣿⠋⠀⣴⡿⣿⠛⣧⣶⣶⣿⣿⣿⡇⠻⢹⠀⠀⠀⠀⠀⠀⠐⢻⡇⠈⣽⣾⣖⢈⠀⠸⡏⠓ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⠷⠖⠋⠀⠀⠀⢸⣿⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠇⠈⡻⠲⠶⠛⠀⠀⠀⠀ ⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⡟⢁⣀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠟⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠇⢠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠞⠛⢛⡟⠿⢷⣄⡀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣖⢠⣉⣹⣿⣿⣤⣼⣿⡄⠀⢨⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡿⠟⠤⠙⠆⠒⠚⠛⠻⠿⠿⠿⠿⢿⣿⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣤⠀⠀⢀⡿⠗⠒⠚⠻⠿⠟⢛⠋⠉⠀⢀⡈⠿⠿⠿⣋⣭⣭⣿⣿⣶⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠈⠙⠁⠐⠶⢀⣐⣐⣲⣶⠀⢠⠀⠀⠀⠀⠀⢠⣥⣤⣱⣶⣦⣤⣬⣿⡆⢰⣶⣦⣤⠀⣴⣆⢶⢀⣿⠀⣰⠀⠈⢀⠀⠀⣸⣿⣿⣿⣿⣿⣇⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠲⠀⠀⠀⠈⢹⣿⣿⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣮⣮⣿⣾⣿⣶⣿⠀⢠⣿⡀⢰⣿⣿⣿⣿⣿⣿⣏⣿⡋⢹⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⢿⠿⠿⠟⠋⠁ ⢼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠄⢽⣿⣿⣿⣿⣿⣿⣿⠀⠸⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⣿⣿⣿⠀⠘⢿⣿⣿⣿⡿⣿⢿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢤⣄⠀⠄⢀⢸⣿⠀ ⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢙⠻⣿⡿⠛⢻⠙⣿⣍⠀⣴⡿⡿⠻⣷⣶⣴⣿⣿⣿⡇⠻⢝⠀⠀⠀⠀⠀⠀⠐⢻⡇⠈⣽⣿⡆⢈⡀⠨⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⠷⠖⠋⠀⠀⠀⢸⡿⠻⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠇⠈⡻⠲⠲⠙⠀⠀⠀⠀ ⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢰⣶⠠⡆⡟⢁⣀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠁⠀⠈⢉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠇⢰⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠞⠛⠛⡟⠿⢷⣄⡀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣶⢠⡉⣻⣿⣿⣤⣼⣿⡄⠀⢸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⢿⠟⠤⠙⠆⠐⠚⠛⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣤⠀⠀⢀⡿⠷⠒⠚⠻⠿⠟⣛⠋⠉⠀⢀⡈⠿⢿⠟⣫⣭⣽⣿⣿⢶⣿⡉⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠀⠙⠓⠒⠶⢂⣐⣐⣶⣶⠀⢠⠀⠀⠀⠀⠀⢠⣥⣄⣱⣷⣦⣠⣼⣿⡆⢰⣶⣶⣤⠀⣴⣆⢶⢠⣿⠀⣰⠀⠀⢀⠀⠀⣾⣿⣿⣿⣿⣿⡆⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠺⠀⠀⠀⠈⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣬⣿⣾⣿⣶⣿⠀⢠⣿⡀⢰⣿⣿⣿⣿⣿⣿⣇⣿⡋⢹⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⠿⠿⠿⠿⠋⠁ ⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡹⠎⣿⣿⣿⣿⣿⣿⣿⣿⠂⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣗⠀⠙⢿⣷⣿⣿⡿⣽⢿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢤⣄⠀⢄⣀⢸⣿⠀ ⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢛⠻⣿⡿⠟⢹⠘⣿⡍⠀⣴⡿⡿⠻⣶⣶⣼⣿⣿⣿⡆⠙⠜⠀⠀⠀⠀⠀⠀⠐⢻⣇⢘⣽⣾⣎⢈⡀⠜⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⠷⠒⠋⠀⠀⠀⢻⡿⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠇⠈⡻⠺⠲⠛⠀⠀⠀⠀ ⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢰⣶⠠⡆⡟⢁⣀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣄⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠘⠇⢰⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠞⠛⠛⠟⠿⣷⣄⡀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⢠⣉⣹⣿⡿⣠⣼⣿⡄⠀⢸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⣿⠟⠄⡙⠆⠐⠚⠛⠻⠿⠿⠿⠿⢿⣷⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣦⠀⠀⢂⠿⠷⠒⠚⠻⠿⠟⢛⠋⠉⠀⢀⡈⠿⣿⠟⣫⣭⣿⣿⣿⢶⣿⡉⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠈⠑⠑⠂⠶⢀⣐⣐⣶⣶⠀⢠⠀⠀⠀⠀⠀⢠⣥⣄⣡⣷⣦⣤⣼⣿⡆⢰⣶⣦⣄⠀⣴⣆⢶⢠⣿⠀⢰⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠑⣻⣇⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠟⠀⠺⠀⠀⠀⠈⢻⣿⣯⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣾⣬⣿⣾⣿⣶⣿⠀⢠⡇⠀⣼⣿⣿⣿⣿⣿⣿⣁⣿⡋⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠉ ⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢹⣿⣿⣿⣿⣿⣿⣿⣿⠅⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⡇⡀⠻⣿⣾⣿⣿⠿⣽⢿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢤⣄⠀⢄⢀⢰⣿⠀ ⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢛⠻⣿⡿⠛⢻⠙⣿⡍⠀⣴⡿⠿⢻⣶⣦⣾⣿⣿⣿⠀⠻⠸⠀⠀⠀⠀⠀⠀⠐⢻⣇⠘⣿⣿⡆⢈⡀⠼⡏⠃ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⠷⠒⠉⠀⠀⠀⢿⠟⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠈⡻⠲⠶⠛⠀⠀⠀⠀ ⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡦⣟⢁⣀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠏⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠇⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠞⠛⠛⠟⠻⢷⣄⡀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⢀⣀⣀⣀⣨⣴⢠⣉⣻⣿⡿⣤⣼⣿⡄⠀⢸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⠄⠙⠦⠒⠚⠛⠻⠿⠿⠿⠿⢿⣿⣶⣶⣶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣤⠀⠀⢂⠿⠷⠒⠚⠻⠿⠟⢛⠋⠉⠀⢀⡈⢿⣿⢟⣋⣿⣿⣟⢿⢶⣿⡉⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠀⠐⠒⠂⠶⢀⣐⣐⣶⣶⠀⢠⠀⠀⠀⠀⠀⣠⣥⢤⣣⣷⣦⣤⣼⣿⡆⢰⣶⣦⣤⠀⣤⣆⢶⢀⣿⠀⣰⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⡏⡓⣻⣇⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠀⠺⠀⠀⠀⠈⢹⣿⣯⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣯⣬⣿⣾⣿⣶⣿⠀⣠⡆⠀⣾⣿⣿⣿⣿⣿⡏⣀⣿⡋⢹⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠋⠉ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⣿⣿⡆⠘⢿⣿⣿⣿⣿⠋⣼⢿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢤⣄⠀⢤⣀⢰⣿⡀ ⠐⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢛⠻⣿⡿⠿⢻⠙⣿⣍⠀⣴⡿⡿⢻⣷⣦⣿⣿⣿⣿⠀⠟⢺⠀⠀⠀⠀⠀⠀⠐⢻⣇⢘⣿⣿⣆⢈⡀⠼⡏⠃ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⠷⠒⠉⠀⠀⠈⣿⠟⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠇⠈⣻⠲⠾⠛⠀⠀⠀⠀ ⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡦⣟⢁⣀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠸⡇⠰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠁⠀⠈⢉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠘⡁⡬⡆⡀⡇⡆⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠏⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠇⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⠞⠛⠛⠟⠿⣷⣄⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⢠⣉⣹⣿⣿⣣⣼⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡿⠟⠄⠙⠆⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⠀⠀⠀⠿⠷⠒⠚⠻⠿⠟⢛⠋⠉⠀⢀⡈⢿⡿⢟⣛⣿⣿⣿⢿⢶⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠈⠙⠓⠒⠶⢀⣀⣐⣶⣶⠀⢠⠀⠀⠀⠀⢀⣠⣥⣤⣳⣷⣶⣤⣭⣿⡇⢰⣶⣦⣤⠀⣴⡆⢶⢀⣿⠀⢰⠀⠈⠁⠀⣰⣿⣿⣿⣿⣿⣜⡗⣻⣇⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠀⠺⠀⠀⠀⠈⢸⣿⣯⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣾⣮⣿⣾⣿⣶⣿⠀⢠⡀⢠⣿⣿⣿⣿⣿⣿⣇⣥⣿⡋⢸⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠋⠁ ⣺⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡾⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⢫⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⠄⠙⣿⣿⣿⣿⡿⠃⣼⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢤⣄⠄⢤⣀⢺⣿⡀ ⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢛⠻⣿⡿⠛⢻⠙⣿⣍⠀⣤⡿⡟⢷⣷⣬⣿⣿⣿⡗⠀⠻⢘⠀⠀⠀⠀⠀⠀⠐⢳⡇⢀⣿⣿⣎⢈⡈⠸⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⠷⠒⠉⠀⠀⠸⣿⠟⠿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠈⡻⠲⠒⠛⠀⠀⠀⠀ ⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡦⣟⢁⣀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠹⡆⠰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡆⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢰⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠇⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠞⠛⠛⡟⠿⣷⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣠⣀⣠⣶⢠⣉⣻⣿⣿⣧⣼⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⣿⠟⠆⠙⠦⠒⠚⠛⠻⠿⠿⠿⠿⢿⣿⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣤⠀⠀⠀⠿⠷⠒⠚⠻⠿⠟⢛⠋⠉⠀⢀⡈⢿⡿⢟⣛⣿⣿⡏⣿⣶⣾⡃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠈⠑⠓⠒⠶⢀⣐⣐⣶⣶⠀⢠⠀⠀⠀⠀⢀⢠⣧⣤⣣⣷⣤⣀⣼⣿⡆⢸⣾⣦⣤⠀⣴⡆⢶⣠⣿⠀⣰⠀⠀⠀⢈⣾⣿⣿⣿⣿⣇⣚⡗⣻⣇⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠺⠀⠀⠀⠈⢻⣿⣏⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣾⣮⣿⣿⣿⣶⣿⠀⢠⠀⣼⣿⣿⣿⣿⣿⣿⠁⣥⣿⡛⢹⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠋⠉ ⣺⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⠀⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣿⣿⠈⢿⣯⣿⣿⣿⡟⠁⣾⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⢤⣄⠄⢄⢀⢲⣿⡀ ⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢛⠻⣿⡿⠛⢻⠙⣿⣍⠀⣴⡿⠟⣾⣷⣽⣿⣿⣿⡖⠀⠿⢽⠀⠀⠀⠀⠀⠀⠐⢻⡅⢘⣷⣿⡎⢈⠀⠼⡟⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠁⠈⣿⣿⡆⠀⢀⣼⠋⠷⠒⠉⠀⠀⢹⡿⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠇⠈⣻⠲⠺⠛⠁⠀⠀⠀ ⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡎⣟⢁⣀⡺⠃⠀⠀⠀⠀⠀⠀⠀⢻⠀⢾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡄⡀⡇⡆⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣄⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠇⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⠞⠛⠛⡟⠿⣷⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣠⣀⣠⣶⢠⣉⣻⣿⡿⣦⣼⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠟⠆⡛⠦⠒⠚⠛⠻⠿⠿⠿⠿⢿⣿⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⠀⠀⢀⡿⠷⠒⠚⠻⠿⠟⣛⠋⠉⠀⢀⡨⢿⡿⢟⣻⣿⣿⡟⣿⢶⣿⡉⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣿⣿⡧⣤⣤⡀⠀⠈⠙⠓⠒⠶⢀⣐⣐⣶⣶⠀⢠⠀⠀⠀⠀⢀⢠⣦⣄⣧⣷⣤⣀⣬⣿⡇⢰⣶⣦⣤⠀⣴⡆⢶⢠⣿⠀⣰⠀⠀⠀⢸⣾⣿⣿⣿⣿⡄⣞⡓⢻⣇⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠀⠺⠀⠀⠀⠀⢻⣿⣯⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣾⣮⣿⣾⣿⣶⣿⠀⢀⠀⣾⣿⣿⣿⣿⣿⡏⠃⣥⣿⡏⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠋⠁ ⣺⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣿⣿⣿⣿⣿⣿⣷⡾⣿⣿⠂⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⣿⣯⡿⣿⣭⣭⣿⣿⠟⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢤⣄⠀⢄⢀⢰⣿⡀ ⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢛⠻⣿⡿⠛⢻⠙⣿⣍⠀⣴⡿⢿⣶⣮⣿⣿⣿⣿⠒⠀⠿⣼⠀⠀⠀⠀⠀⠀⠐⢻⣇⢘⣿⣿⣆⢈⡀⠼⡟⠃ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⠷⠒⠋⠀⠀⢿⡟⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠇⠈⣻⠲⠾⠛⠁⠀⠀⠀ ⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⡺⠃⠀⠀⠀⠀⠀⠀⠈⢷⠂⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠁⠀⠈⢉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡆⡗⠌⣆⣇⣇⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠇⢸⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠾⠛⠻⡟⠻⣷⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣠⣷⢠⣉⣻⣿⡿⣧⣼⣿⡄⠀⢸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠟⠄⡙⢦⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⠀⠀⢀⠿⠷⠒⠚⠻⠿⠟⣛⠋⠉⠀⠀⣨⢿⡿⠟⣻⣿⣿⡏⣿⢶⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠀⠙⠒⠒⠶⢀⣐⣐⣶⣶⠀⢠⠀⠀⠀⠀⢀⢠⣧⣄⣧⣷⣤⣄⣬⣿⡆⢰⣶⣦⣤⠀⣴⡆⢶⢠⣿⠈⢰⠀⠀⠀⣸⣾⣿⣿⣿⣿⠠⣞⡓⣻⣇⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠀⠺⠀⠀⠀⠀⢻⣿⣯⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣬⣿⣾⣿⣶⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠃⣅⣿⡟⢹⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠟⠉⠁ ⣼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣼⣿⣿⣿⣿⣿⣿⣷⠼⢿⣿⠀⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠼⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⣿⡯⣿⣿⣯⣿⣿⣿⠋⠀⡸⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢤⣄⢄⢄⢀⢰⣿⠀ ⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢙⠻⣿⡿⠛⢻⠙⣿⣏⠀⣴⡿⢿⣷⣽⣿⣿⣿⣷⠒⠀⠻⢼⠀⠀⠀⠀⠀⠀⠐⢻⡇⢘⣿⣿⣎⢈⡀⠼⡏⠆ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢈⣼⠋⠷⠒⠋⠀⠈⢿⢟⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠇⠈⡻⠲⠲⠛⠀⠀⠀⠀ ⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⣟⢁⣀⡺⠃⠀⠀⠀⠀⠀⠀⠘⢧⠂⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡆⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢰⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠇⢸⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠾⠛⠛⡟⠿⣷⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣠⡵⢠⣉⣹⣿⣿⣣⣼⣿⡄⠀⣸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⠆⡙⢆⠒⠚⠛⠻⠿⠿⠿⠿⢿⣿⣶⣶⣶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⢀⡿⠷⠒⠚⠻⠿⠟⢛⠛⠉⠀⢀⣨⣿⠿⠟⣟⣿⣿⡇⣿⢶⣿⡉⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠀⠙⠓⠒⠶⢂⣐⣐⣶⣶⠀⢠⠀⠀⠀⢀⠀⢠⣇⢀⣧⣷⣤⣠⣼⣿⡆⢰⣶⣶⣤⠀⣴⣆⢶⢀⣿⠀⢰⠀⠈⠀⣽⣾⣿⣿⣿⣯⢠⣞⡓⢻⣇⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠀⠺⠀⠀⠀⠈⢻⣿⣏⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣾⣮⣿⣾⣿⣶⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⠘⠃⣕⣿⡏⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠋⠁ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣸⣿⣿⣿⣿⣿⣿⣶⠸⢿⣿⠃⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢤⣀⠀⢄⢀⢰⣿⡀ ⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢙⠻⣿⡿⠛⢻⠙⣿⣋⠀⣴⡿⢿⣿⣿⣿⣿⣿⣧⠒⠀⠻⣿⠀⠀⠀⠀⠀⠀⠐⢻⡇⢘⣿⣿⣎⢈⠀⢼⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠁⠈⣿⣿⡆⠀⢈⣼⠋⠷⠖⠋⠀⠘⣿⠟⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠈⣻⠳⠖⠛⠀⠀⠀⠀ ⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⣟⢁⣀⡚⠃⠀⠀⠀⠀⠀⠀⠘⡇⠰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠙⠇⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠾⠛⠿⠟⠻⣷⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣠⣷⢨⣉⣹⣿⣿⣧⣾⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠟⠆⡙⠇⠓⠚⠛⠻⠿⠿⠿⠿⢿⣿⣷⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣆⠀⠀⢀⡿⠷⠒⠚⠻⠿⠟⣛⠋⠉⠁⢀⣨⣿⣿⣿⣿⣿⣿⡏⢿⢶⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠙⠓⠒⠶⢆⣀⣰⣶⣶⠀⢠⠀⠀⠀⠀⢀⢠⣥⡔⣧⣶⣤⣤⣌⣿⡆⢰⣶⣦⣤⠀⣴⣆⣶⢠⣿⠂⣰⠂⠀⠙⣵⣶⣾⣿⣾⡙⢠⣜⡗⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠻⠀⠀⠀⠀⢹⣿⣏⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣾⣭⣿⣾⣿⣶⣿⠀⠀⣸⣿⣿⣿⣿⣿⡇⢘⠃⣵⣿⡏⢹⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣄⣿⣿⣿⣿⣿⣿⣷⣆⠸⢿⣿⠇⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⣟⣛⣿⣿⡿⠯⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠⣤⣄⠄⢠⢀⢲⣿⠀ ⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢙⠻⣿⡿⠛⢻⠘⣿⣫⠀⣴⡿⣿⣟⣿⣿⣿⣿⡅⠒⠀⣿⣿⠀⠀⠀⠀⠀⠀⠐⢻⡇⢘⣽⣿⣎⢈⡀⠬⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⢀⣼⠋⠷⠶⠛⠀⢹⣿⠿⣿⣿⣿⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡞⠇⠈⣻⠾⠺⠚⠐⠀⠀⠀ ⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡦⡟⢁⣀⡘⠁⠀⠀⠀⠀⠀⠀⠻⡔⢨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠉⠇⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠾⠛⠟⡟⢻⣷⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣁⣀⣠⣷⢨⣉⣹⣿⣿⣧⣾⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠟⢆⡛⠆⠓⠚⠛⠿⠿⠿⠿⠿⢿⣿⣷⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣦⠀⠀⢀⡿⠷⠒⠚⠻⠿⠟⣛⠋⠉⠁⢀⣨⣽⡿⢿⣿⣿⣿⡟⣿⢷⣿⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠑⠒⠶⢀⣀⣰⣶⣶⠀⢠⠀⠀⠀⠀⢀⢠⣥⡀⣗⣷⣤⣠⣨⣿⡆⢰⣶⣦⣤⠀⣴⡆⣶⢠⣿⠂⣰⠀⠀⢚⣥⣶⣾⣿⣯⠛⢥⣞⡗⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠻⠀⠀⠀⠀⢹⣿⣟⣽⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣾⣭⣿⣾⣿⣶⣾⠀⠀⣾⣿⣿⣿⣿⣿⡇⣘⠃⣩⣿⡏⢸⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣀⣿⣿⣿⣿⣿⣿⣧⡆⠸⢿⣿⠇⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⢿⣿⣿⣿⡿⠯⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠⣤⣀⠀⢤⠀⢲⣿⠀ ⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢙⠻⣿⡿⠛⢻⠙⣿⣋⠀⣴⡿⣿⣿⣿⣿⣿⣿⡄⠒⠀⢿⣻⠀⠀⠀⠀⠀⠀⠐⢻⡇⢸⣽⣿⢎⢈⠈⠼⡏⠅ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⠀⣼⠋⠿⠶⠛⠀⢻⣿⠿⣿⣿⣿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡞⠇⠘⣻⠶⠿⠚⠀⠀⠀⠀ ⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⣮⡟⢁⣀⡘⠁⠀⠀⠀⠀⠀⠀⢳⡄⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠙⠇⢸⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠾⠛⠟⡟⠻⣷⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣠⣳⢠⣉⣻⣿⣿⣧⣾⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⡟⢆⡙⢇⠒⠚⠛⠻⠿⠿⠿⠿⢿⣿⣷⣶⣶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⠀⠀⢀⡿⠷⠒⠚⠛⠿⠟⣛⠋⠉⠁⢀⣨⣿⡿⠿⢿⣿⣿⡟⢿⢶⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠓⠒⠶⢀⣀⣐⣶⣶⠀⢠⠀⠀⠀⠀⢀⢀⣤⡔⣷⣷⣤⣤⣼⣿⡆⢰⣶⣦⣤⠀⣴⣎⢶⢠⣿⠀⣰⠀⠀⢚⣭⣴⣾⣶⣞⠛⢡⣞⡓⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠺⠀⠀⠀⠀⢹⣿⣟⣽⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣾⣬⣿⣾⣿⣶⣿⠀⠀⣾⢿⣿⣿⣿⣿⡆⣘⠃⣥⣿⡏⢸⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣧⡆⠸⢿⣿⠇⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠹⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⠿⠩⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠠⣶⣀⡀⢄⢐⢲⣿⡀ ⠐⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢛⡻⣿⡿⠛⢻⠙⣿⣋⠀⣴⡿⣿⣿⣿⣿⣿⣿⡀⠒⠀⡿⢿⠀⠀⠀⠀⠀⠀⠐⢻⡇⢘⣿⣿⣌⢈⠈⠼⡟⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⢀⣼⠋⠷⠶⠛⠀⢻⣿⢿⣿⣿⣿⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡚⠧⠈⣻⠶⠷⠚⠐⠀⠀⠀ ⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣶⠠⡮⡟⢁⣀⡚⠁⠀⠀⠀⠀⠀⠈⢷⠄⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡆⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠙⠇⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠾⠻⠟⡟⠻⣷⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣷⢨⣉⣹⣿⣿⣷⣾⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⠆⡙⠧⠓⠚⠛⠿⠿⠿⠿⠿⢿⣿⣷⣶⣶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⠀⠀⢀⡿⠷⠒⠚⠛⠿⠟⣛⠋⠉⠁⢀⣨⣿⡿⠿⢿⣿⣿⡟⣿⢶⣿⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠙⠓⠒⠶⢄⣀⣰⣶⣶⠀⢠⠀⠀⠀⠀⢀⣀⣤⣀⢇⣷⣤⣤⣬⣿⡆⢰⣶⣦⣤⠀⣴⣆⢶⢠⣿⠀⣰⠂⠀⠚⣋⣤⣶⣶⡎⠻⢱⣞⡗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠻⠀⠀⠀⠀⢻⣿⣏⣱⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣾⣮⣿⣾⣿⣶⣿⠀⠀⣾⣿⣿⣿⣿⣿⠀⣈⠃⣥⣿⡏⢸⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣰⣿⣿⣿⣿⣿⣿⣧⡆⠸⢿⣿⠅⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⠿⠭⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠⣴⣀⢀⢤⢀⢲⣿⡀ ⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⢛⠻⣿⡿⠛⢻⠙⣿⡯⠀⣴⡿⣿⣿⣾⣿⣿⣿⠀⠒⠀⣻⣫⠀⠀⠈⠀⠀⠀⠐⢻⡇⢸⣿⣿⣎⢈⠀⠸⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⠀⣼⠋⡷⠶⠛⠀⢿⣿⢿⣿⣿⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡘⠇⠈⣻⠶⠶⠚⠐⠀⠀⠀ ⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢰⣶⠠⣮⡟⢁⣀⡚⠁⠀⠀⠀⠀⠀⠈⢧⠆⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⠈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢰⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠛⠇⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠿⠾⠿⠿⡟⠻⢷⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣠⣷⢨⣉⣹⣿⣿⣷⣾⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⠆⡙⢆⠓⠚⠛⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠀⠀⢀⡿⠷⠒⠚⠻⠿⠟⣛⠋⠉⠀⢀⡨⣿⡿⠿⢿⣿⣿⡟⣿⢷⣿⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠙⠑⠖⠶⢄⣀⣰⣶⣶⠀⢠⠀⠀⠀⠀⠀⢀⣰⣄⡼⣳⣦⣤⣤⣽⡇⢰⣶⣦⣤⠀⣴⣆⢶⢠⣿⠀⣰⠀⠀⠘⠟⢀⣠⣤⡌⠛⠡⣞⡓⣻⣧⢰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠲⠀⠀⠀⠀⠐⣿⣿⣟⣼⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣾⣮⣿⣾⣿⣶⣿⠀⠀⣴⣿⣿⣿⣿⣿⠀⣘⠋⣵⣿⡏⢸⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠓ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣰⣿⣿⣿⣿⣿⣿⣦⡆⠸⢿⣿⠇⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠹⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣿⣿⣿⣿⣿⣿⣿⠿⠭⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠⣤⣀⠀⢤⢀⢶⣿⡀ ⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⢛⠻⣿⡿⠻⢻⠙⣿⣋⠀⣴⡿⣿⣿⣿⣿⣿⣿⠄⠒⠀⢿⣻⠀⠀⠈⠀⠀⠀⠐⢿⡇⢸⣽⣿⣎⢈⡀⠸⡟⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⠀⣼⠋⠷⠶⠛⠀⣿⡿⢿⣿⣿⡿⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⡘⠇⠈⣻⠶⠲⠚⠐⠀⠀⠀ ⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⢰⣶⠠⣮⡟⢁⣀⡚⠁⠀⠀⠀⠀⠀⠘⣧⠄⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠙⠇⢸⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣴⣿⠿⠞⠻⠿⠟⠛⢷⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣠⣷⢨⣉⣻⣿⡿⣧⣾⣿⡄⠀⢼⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⢆⡙⠇⠓⠚⠛⠿⠿⠿⠿⠿⢿⣿⣶⣶⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠀⠀⠀⡿⠷⠒⠚⠻⠿⠟⣻⠋⠉⠁⢀⡨⣿⡿⠿⣿⣿⣿⡟⢿⢷⣿⡏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠹⠓⠒⠶⢂⣐⣰⣶⣶⠀⢠⠀⠀⠀⠀⠀⣀⢤⣴⣄⣶⣶⣄⣬⣽⡇⢰⣿⣦⣤⠀⣴⣎⢶⢠⣿⠀⢰⠀⠀⠐⠛⠀⢀⣀⡈⠻⢥⣞⡓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣾⣭⣿⣿⣿⣶⣿⠀⠀⣠⣶⣿⣿⣿⣷⠀⣈⠃⡥⣿⡏⢸⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣟⣻⣿⣿⣿⣿⣤⡆⠸⢿⣿⠇⠸⠴⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠽⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣾⣿⣿⣿⣿⣿⣿⡿⠭⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣴⣄⡄⢤⢐⢴⣟⡀ ⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣿⢙⠻⣿⡿⠛⢻⠙⣿⣋⠀⣴⡿⣿⣟⣿⣿⣿⣿⠄⠒⠀⢿⣿⠀⠀⠀⠀⠀⠀⠐⢿⣇⢸⣿⣿⡎⢈⡨⡼⡟⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⠀⣼⠋⠷⠶⠛⠀⣿⡿⢿⣿⣿⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡚⠇⠈⡻⠷⠷⠚⠓⠀⠀⠀ ⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⢰⣶⠠⡦⡟⢁⣀⡚⠁⠀⠀⠀⠀⠀⠘⣧⠄⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠙⠇⢸⣇⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣤⣿⠿⠚⠻⠿⠟⠛⢷⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣷⢠⣉⣹⣿⡿⣧⣾⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠟⢆⡛⠇⠓⠚⠛⠿⠿⠿⠿⠿⢿⣿⣶⣶⠶⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠂⡯⠷⠒⠚⠻⠿⠟⣻⠋⠉⠁⢀⣨⣿⣿⣿⣿⣿⣿⣟⣿⢶⣿⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠛⠓⠒⠶⢄⣀⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣰⣶⣶⣀⣽⣧⢰⣶⣦⣤⠀⣴⡆⣶⢠⣿⠀⣰⠀⠀⠰⠍⠀⠀⢀⠈⠻⠥⣞⡓⣻⣧⣠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠈⠉⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠃⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣾⣭⣿⣿⣿⣶⣿⠀⠀⢠⣤⣶⣿⣿⣷⠀⣘⠃⣵⣿⡏⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡿⣿⣿⣿⣿⣿⣤⡅⠸⢿⣿⠇⠰⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣾⣿⣿⣿⣿⣿⣿⡿⠍⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠠⣦⣄⡄⢤⢐⢲⣿⡀ ⠀⠀⠀⠀⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⢸⣿⢛⠻⣿⡿⠛⢻⠙⣿⢏⠀⣴⡿⣿⣿⣿⣿⣿⣿⠄⠒⠀⠿⣿⠀⠀⠈⠄⠀⠀⠐⢿⣇⢘⣿⣿⣎⢈⡉⡼⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⠀⣼⠋⠷⠶⠚⠁⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡚⠇⠈⣻⠶⠾⠛⠒⠀⠀⠀ ⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠀⠀⢰⣶⠠⡦⣟⢁⣀⡚⠁⠀⠀⠀⠀⠀⠘⣇⡄⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⠊⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠙⠇⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡿⠬⠭⠽⢭⠻⠧⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣁⣀⣀⣷⢨⣉⣻⣿⣿⣇⣾⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠟⢆⡙⠆⠓⠚⠛⠿⠿⠿⠿⠿⢿⣿⣷⣶⠶⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⠀⠀⢀⡿⠷⠒⠚⠛⠿⠟⣛⠋⠉⠁⢀⣨⣿⣿⣿⣿⣿⣿⣟⣿⢶⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠙⠓⠒⠶⢄⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⣀⣴⣶⣦⣨⡇⢰⣶⣦⣤⠀⣴⣎⢶⢠⣿⠀⣰⠀⠀⠰⠋⠁⠀⠁⠉⠻⢡⣜⡓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄ ⢀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠐⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣾⣯⣿⣾⣿⣶⣿⠀⠀⠀⣀⣀⣤⣤⣷⠀⣘⠋⣥⣿⡏⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠋⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣼⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣆⡇⠘⢿⣿⡃⠰⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣶⣿⣿⣻⣿⣿⣿⣿⠯⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣦⣤⠀⢤⠀⢴⣿⡀ ⠈⠀⠀⠀⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣵⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢸⣿⢛⠻⣿⡿⠛⢻⠙⣿⣏⠀⣴⡿⣿⡿⣿⣿⣿⣿⠅⠒⠀⢻⣸⠀⠀⠈⠁⠀⠀⠐⢻⡇⢘⣿⣿⣎⢉⡈⠼⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠉⠈⣿⣿⡆⠀⠀⣼⠋⣷⠶⠞⠁⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡚⠧⠈⡻⠷⠶⠛⠀⠀⠀⠀ ⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠃⠀⠀⠀⢰⣶⠠⡦⡟⢁⣀⡚⠁⠀⠀⠀⠀⠀⠸⡇⡉⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⠈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠛⠇⢸⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣿⣿⠮⠭⣽⢽⡿⠧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣁⣀⣠⣷⢨⣉⣻⣿⣿⣧⣾⣿⡆⠀⢼⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⢇⠛⠧⠓⠚⠛⠿⠿⠿⠿⠿⠿⣿⣶⣶⡾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢀⡿⠷⠒⠚⠛⠿⠟⣻⠋⠉⠁⢀⣨⣿⣿⣿⣿⣿⣿⣟⢿⢶⣿⡋⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠙⠓⠲⠶⢆⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⠠⠀⢀⠄⠀⢀⣀⣴⣦⡄⡆⢰⣶⣦⣤⠀⣴⡆⢶⢠⣿⠂⣰⠀⠀⠰⠋⠁⠈⠉⠉⠻⢥⣜⡗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⢞⡿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣮⣯⣿⣿⣿⣶⣿⠀⠀⠀⠀⢀⣠⣤⣷⡀⣘⠋⣭⣿⡏⢹⢸⣇⣀⣠⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠋⠃ ⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣤⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⡆⡗⠸⢿⣿⡇⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣦⣍⣽⣿⣿⣿⣿⣿⠯⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠⣶⣀⢤⢤⢀⢰⣿⡀ ⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⣄⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣿⢛⡻⣿⡿⠟⢻⠙⣿⣯⠀⣴⡿⣿⡿⣿⣿⣿⣿⠅⠒⠀⢻⣻⠀⠀⠀⠀⠀⠀⠐⢿⡇⢘⣽⣿⣏⢈⠈⠸⡏⠷ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠈⣿⣿⡖⠀⢀⣼⠋⣷⠶⠞⠁⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠠⡚⠇⠈⣻⠶⠲⠛⠀⠀⠀⠀ ⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠋⠀⠀⠀⢰⣶⠠⡦⣟⢁⣀⡚⠁⠀⠀⠀⠀⠀⠸⡇⡉⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠛⠇⢸⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡌⢭⣿⢿⡿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣁⣀⣀⣷⢨⣉⣻⣿⣿⣷⣾⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⠆⡛⢦⠓⠛⠛⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠛⢦⠀⠀⢀⡿⠷⠒⠚⠛⠿⠟⣛⠋⠉⠁⢀⣨⢿⣿⣿⣿⣿⣿⡟⣿⢶⣿⡋⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠛⠷⠲⠶⢄⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⢀⣴⣶⡄⣇⢰⣶⣦⣤⠀⣴⣆⢶⢠⣿⠀⣰⠈⠀⠚⠋⠁⠈⠉⠉⠻⢡⣜⡓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⠸⣻⣿⣾⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣮⣭⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⢀⣀⣦⡀⣘⠋⣽⣿⡏⢸⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠋⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣣⣽⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣿⣿⡇⣀⠨⣿⣿⡅⠰⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠾⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⣦⣿⣿⣿⣿⣿⣿⣿⠯⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠⣶⣄⢤⢦⠀⢴⣿⡀ ⠀⠀⠀⠀⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣄⣤⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢸⣿⢛⠻⣿⡿⠛⢻⠙⣿⡋⠀⣴⡿⣿⣿⣻⣿⣿⣿⠇⠒⠀⢿⣿⠀⠀⠈⠀⠀⠀⠐⢻⣧⢸⣿⣿⡎⢈⡉⠸⡏⠇ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠈⣿⣿⡆⠀⠀⣼⠋⡷⠶⠚⠁⣿⣷⣿⣿⣿⣿⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡞⠇⠈⣻⠶⠺⠚⠀⠀⠀⠀ ⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠋⠀⠀⠀⢰⣶⠠⡦⣟⢁⣀⡚⠁⠀⠀⠀⠀⠀⠸⡇⡙⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⠈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣿⠙⠇⢸⣇⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡞⠭⣿⣿⡿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⢀⣀⣄⣀⣠⣷⢨⣉⣻⣿⣿⣧⣾⣿⡆⠀⢸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡿⠟⢦⡹⣦⠒⠛⠛⠿⠿⠿⠿⠿⢿⣿⣷⣶⣶⠟⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢠⡿⠗⠒⠚⠻⠿⠟⣛⠋⠉⠀⢀⣨⠿⣿⣿⣿⣿⣿⡯⢾⢷⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠚⠳⠺⠶⢄⣀⣰⣶⣶⠀⠀⠁⡠⠀⠀⠀⡄⠀⣀⠀⠀⣀⣰⣶⣄⡆⢸⣶⣶⣤⡀⣤⣎⣶⢀⣿⠀⢰⠀⠠⠚⠉⠁⠈⠉⠉⠻⢥⡜⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠈⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⢸⢿⣿⣾⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣭⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⣀⣶⡀⢐⠋⡅⣿⡟⢸⢸⡇⣀⣀⣤⣴⣶⣶⣶⣿⡿⠿⠿⠟⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣶⣿⣿⣿⡇⣨⠸⢿⣿⠁⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣧⣒⣻⣿⣿⣿⣿⣿⠯⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⣦⣄⣄⢤⢐⢾⣿⡀ ⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣧⣄⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣿⢛⡻⣿⡿⠟⢻⠙⣿⣯⠀⣴⡿⣾⡿⢻⣿⣿⣿⡇⠒⠀⣿⢽⠀⠀⠀⠀⠀⠀⠐⢻⡧⢸⣿⣿⣿⢩⡈⠸⡏⠗ ⠔⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⠷⠶⠛⠁⢿⣷⣿⣿⣿⣿⠃⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠠⡟⠇⠈⡻⠿⠒⠛⠃⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠛⠉⠀⠀⠀⢰⣶⠠⡦⣟⢁⣀⠘⠀⠀⠀⠀⠀⠀⠘⣇⠙⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣿⠙⠇⢸⣇⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡾⠽⣿⡿⣿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣁⣀⣠⣷⢨⣉⣹⣿⡿⣧⣾⣿⡆⠀⣸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢦⡻⣧⠒⠛⠛⠿⠿⠿⠿⠿⢿⣿⣶⢶⣶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢀⡿⠗⠒⠚⠻⠿⠛⣻⠋⠙⠀⢀⣨⣿⣿⣿⣿⣿⣿⡟⢾⢷⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠻⠓⠲⠶⢄⣐⣰⣶⣶⠀⠠⠁⡠⠀⠀⠀⠄⠀⣀⠀⠀⣀⣴⣶⣄⡆⢸⣷⣦⣤⡀⣴⣞⣶⢐⣿⠂⣰⠀⢠⠞⠉⠀⠀⠉⠉⠻⣧⣞⣗⣻⣧⢰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄ ⢀⠈⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⠸⢿⣿⣾⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣾⣭⣿⣾⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⢦⡀⢙⠃⣵⣿⡟⢹⢸⣇⣀⣀⣤⣴⣶⣶⣾⣿⡿⠿⠿⠟⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣥⣾⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣤⣤⣿⣿⣏⢸⠸⢿⣿⠁⠸⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣧⠀⢼⣿⣿⣿⣿⣿⡏⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⣤⣄⡠⢦⢐⣺⣿⡀ ⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⣄⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣿⢛⡻⣿⡿⠟⢻⠙⣿⣏⠀⣴⡿⣴⣾⢯⣿⣿⣿⡏⠒⠀⢻⢼⠀⠀⠀⠀⠀⠀⠐⢿⣧⢸⣿⣿⣎⢉⡈⠼⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠈⣿⣿⡶⠀⢀⣼⠋⠷⠖⠚⠀⢿⣷⣼⣿⣿⣿⡇⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠠⡞⠧⠈⡻⠷⠓⠛⠂⠀⠀⠀ ⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠉⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠈⠀⠀⠀⠀⠀⠀⠘⣇⠙⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠩⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣿⠛⠇⢸⣇⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡾⠽⣿⡿⣿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣁⣀⣠⣷⢨⣉⣻⣿⣿⣧⣾⣿⡆⠀⣸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢧⡹⢦⠓⠛⠛⠿⠿⠿⠿⠿⢿⣿⣷⣶⣶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢀⡿⠗⠒⠚⠻⠿⠟⣻⠋⠙⠀⢀⣨⢿⣿⣿⣿⣿⣿⡗⢾⢷⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠓⠲⠶⣄⣀⣰⣶⣶⠀⢀⠁⡀⠀⠀⠀⡄⠀⣀⠀⠀⣀⣴⣶⡆⡇⢸⣶⣦⣤⠀⣴⣞⣶⢂⣿⠀⢴⠀⢀⠞⠉⠀⠀⠉⠉⠻⣧⡜⣓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠈⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⢸⢯⣾⣾⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣭⣿⣾⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⢤⡀⠘⠋⣵⣿⡏⢸⢸⣇⣀⣀⣤⣴⣶⣶⣶⣿⡿⠿⠿⠟⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣠⣶⣾⣿⢠⠸⢿⣿⠁⠸⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⣇⠀⢸⣿⣿⣿⣿⣿⡏⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⢠⣴⣤⢠⢆⢐⢾⣿⠀ ⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⣄⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣿⢛⡻⣿⡿⠿⢻⠙⣿⡯⠀⣴⡿⡄⣾⣯⣿⣿⣿⡿⠒⠀⢻⣹⠀⠀⠀⠀⠀⠀⠐⢻⣧⢸⣿⣿⣗⢩⡉⠼⡏⠧ ⡈⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠈⣿⣿⡖⠀⢀⣼⠋⠷⠒⠛⠀⢷⣿⣴⣿⣿⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠠⡜⠏⠈⡻⠷⠓⠛⠁⠀⠀⠀ ⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠉⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠘⠁⠀⠀⠀⠀⠀⠘⣇⠙⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⡈⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣿⠛⠇⢸⣇⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡞⠭⣿⡿⣿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣠⣀⣠⣷⢨⣉⣹⣿⣿⣧⣾⣿⡆⠀⣸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢦⡻⣧⠓⠛⠛⠿⠿⠿⠿⠿⢿⣿⣷⣶⣶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢀⡿⠗⠒⠚⠛⠿⠟⣻⠋⠉⠀⢀⣨⢿⣿⣿⣿⣿⣿⡗⢾⢷⣿⡋⠠⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠄⠉⠙⠗⠒⠶⢄⣀⣰⣶⣶⠀⠠⠁⠠⠀⠀⠠⠄⠀⣀⠀⠀⣀⣴⣶⡆⣇⢸⣶⣦⣤⡀⣴⣎⣷⢂⣿⠂⣴⠀⢀⡞⠉⠀⠀⠉⠉⠻⣧⣜⣓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠈⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⡸⢿⣿⣾⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣯⣿⣾⣿⣶⣿⠀⠄⠀⠀⠀⠀⠀⢠⡀⠘⠃⣵⣿⡟⢹⢸⣇⣀⣀⣤⣴⣶⣶⣶⣿⡿⠿⠿⠟⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣥⣼⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣴⣶⣿⠀⠸⢿⣿⠇⠸⠴⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣇⠀⢀⣿⣿⣿⣿⣿⡾⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⣤⣀⣤⢆⢐⢾⣿⠀ ⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣿⢛⡻⣿⡿⠟⢻⠙⣿⣯⠀⣴⡿⡆⣶⣿⣿⣿⣿⣿⠒⠀⢻⢻⠀⠀⠀⠀⠀⠀⠐⢻⣇⢸⣿⣿⣯⢩⡉⠸⡏⠗ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠈⣿⣿⡖⠀⢀⣼⠋⠷⠖⠚⠀⢷⡿⣤⣿⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⡞⠯⠈⡻⠿⠳⠛⠃⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠉⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠈⠀⠀⠀⠀⠀⠀⠘⣇⠛⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡊⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⠛⠇⢸⣇⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡞⠭⣿⡿⣿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣠⣤⣠⣷⢨⣉⣹⣿⣿⣧⣾⣿⡆⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢦⡻⣧⠓⠛⠛⠻⠿⠿⠿⠿⢿⣿⣷⣶⣶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢐⡿⠗⠒⠚⠻⠿⠟⣻⠋⠉⠀⢀⣈⢿⣿⣿⣿⣿⣿⣇⢿⢷⣿⡃⠠⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠓⠲⠶⢄⣐⣰⣶⣶⠀⢀⠁⡀⠀⠀⠠⠄⠀⡀⠀⠀⣀⣴⣶⡄⣗⢸⣷⣦⣤⡀⣤⣞⣶⢂⣿⠂⣰⠈⢀⡞⠉⠁⠀⠀⠈⠹⣧⡞⣓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠈⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⡸⣯⢿⣾⣿⣿⣿⣿⣿⣟⢸⣿⣿⣿⣿⣾⣯⣿⣾⣿⣶⣿⠀⠆⠀⠀⠀⠀⠀⢀⡀⠈⠋⣭⣿⡏⢸⢸⣇⣀⣀⣤⣴⣶⣶⣶⣿⡿⠿⠿⠟⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣾⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣤⣬⣿⡆⡼⣿⣿⠁⠸⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣇⠀⠀⣿⣿⣿⣿⣿⡷⠅⣾⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⣦⣀⣤⢆⢐⢾⣿⠀ ⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣿⢛⡻⣿⡿⠟⢻⠙⣿⣯⠀⣴⡿⡆⣤⣿⣿⣿⣿⣿⠓⠀⢻⢸⠀⠀⠀⠀⠀⠀⠐⢿⣇⢸⣿⣿⣟⢩⡈⠼⡏⠗ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠈⣿⣿⡶⠀⠀⣼⠋⠟⠂⠊⠀⢳⣿⣉⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠟⠈⡻⠿⠗⠛⠂⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠉⠀⠀⠀⢰⣶⠠⡆⣟⢁⣀⠊⠀⠀⠀⠀⠀⠀⠘⡇⠙⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠁⡈⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⠛⠇⢸⣇⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡾⠭⣿⠿⡿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣤⣀⣠⣷⢨⣉⣻⣿⣿⣧⣾⣿⡆⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡿⠟⢧⠻⣦⠓⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣶⣶⠿⠛⠋⠈⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢠⡿⠗⠒⠚⠻⠿⠟⣛⠋⠉⠀⢀⣨⢿⣿⣿⣿⣿⣿⡟⢾⢶⣿⡁⢁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠒⠲⠶⢄⣐⣰⣶⣶⠀⠠⠁⡀⠀⠀⠠⠆⠀⣀⠀⠀⣀⣴⣶⡄⡇⢸⣶⣦⣤⡀⣴⣞⣶⢠⣿⠂⣰⠀⢈⡞⠉⠀⠀⠀⠀⠙⢧⣞⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄ ⢀⠈⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⡸⣻⢿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⠀⠄⠀⠀⠀⠀⠀⢀⡀⠈⠁⣕⣿⡟⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⣠⣌⣿⡄⡸⢿⣿⠃⠸⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⣇⠀⠀⣶⣾⣿⣿⣿⡷⠁⣾⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⣦⣀⣤⣆⢐⣸⣿⡀ ⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⣄⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣿⢛⡻⣿⡿⠿⢻⠙⣿⣫⠀⣴⡿⡆⣠⣿⢿⣿⣿⣿⠓⠀⢻⣺⠀⠀⠀⠀⠀⠀⠐⢿⣧⢸⣿⣿⣯⢩⣈⠼⡏⠷ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠈⣿⣿⡶⠀⠀⡼⠋⠓⠂⠉⠀⢣⣿⢉⣿⣿⣿⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⡞⠧⠈⡻⠿⠓⠛⠂⠀⠀⠀ ⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠉⠀⠀⠀⢰⣶⠠⡦⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠻⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢁⡈⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠛⠇⢸⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡾⠭⣿⠿⡿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣤⣀⣠⣷⢨⣉⣻⣿⣿⣧⣾⣿⡆⠀⢸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢧⡻⣧⠓⠛⠛⠻⠿⠿⠿⠿⢿⣿⣷⣶⣶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢠⡿⠗⠒⠚⠻⠿⠟⣛⠋⠉⠀⢀⣨⢿⣿⣿⣿⣿⣿⡗⢾⢲⣾⡏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠚⠓⠲⠶⢄⣐⣰⣶⣶⠀⠠⠁⡔⠀⠀⠠⣆⢀⡄⠀⢀⣀⣴⣶⡄⣇⢸⣶⣧⣤⠀⣤⣞⣷⢀⣿⠂⣴⠂⢀⡞⠉⠁⠀⠀⠀⠉⢣⣜⣓⣻⣧⢰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⠽⡷⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⠀⠆⠀⠀⠀⠀⠀⢀⠀⠈⠁⣵⣿⡟⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠁ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⣾⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡁⠀⠀⠀⠀⢀⣈⣿⡄⡸⢿⣿⠇⠸⠴⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠚⣇⠀⠀⣶⣶⣿⣿⣿⣧⠅⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣶⣀⣠⣦⢐⣺⣿⡀ ⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣿⢛⡻⣿⡿⠿⢻⠙⣿⢯⠀⣴⡿⡆⣀⣿⣿⣿⣿⣿⠗⠀⣿⢹⠀⠀⠀⠀⠀⠀⠐⢻⣧⢸⣿⣿⣯⢩⡈⠼⡏⠗ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠈⣿⣿⡶⠀⠀⡼⠋⠓⠀⠉⠀⢡⣿⢉⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠷⠈⡻⠿⠗⠛⠁⠀⠀⠀ ⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⠉⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡈⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣧⠛⡇⢸⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠾⠭⣿⠿⡿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣠⣠⣠⣷⢨⣉⣻⣿⣿⣧⣾⣿⡆⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢦⡹⣦⠓⠛⠛⠻⠿⠿⠿⠿⢿⣿⣷⣶⣶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⣀⡿⠗⠒⠚⠻⠿⠟⣻⠋⠉⠀⢀⣨⣿⣿⣿⣿⣿⣿⡗⢾⢷⣿⡃⠡⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠄⠉⠘⠓⠲⠶⢆⣐⣰⣶⣶⠀⠠⠁⠀⠀⠀⠠⡀⢀⡄⠀⢀⣀⣴⣶⡄⡇⢸⣷⣦⣤⡀⣤⣞⣷⢀⣿⠂⣴⠂⢀⡞⠋⠀⠀⠀⠀⠈⢳⡞⡗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠀⠿⣷⣷⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⣥⣿⡛⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣿⣿⣿⣿⣿⣿⣿⡇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢀⣘⣷⡄⢸⢿⣿⠇⠸⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣇⠀⠀⣴⣴⣿⣿⣿⣧⠅⢼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣶⣀⢠⢆⢐⢾⣿⡀ ⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣄⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣿⢛⡻⣿⡿⠟⢻⠙⣿⣛⠀⣴⡿⡂⣀⣻⣿⣿⣿⣿⡗⠀⢿⣺⠀⠀⠀⠀⠀⠀⠐⢻⡧⢸⣿⣿⣏⢩⣉⠼⡟⠗ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠈⣿⣿⡦⠀⢀⡼⠋⠛⠀⠈⠀⠡⣿⠋⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠯⠈⡻⠿⠓⠚⠁⠀⠀⠀ ⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⠉⠀⠀⠀⢰⣶⠠⡎⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡘⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣧⠛⠇⢰⣇⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⣿⣿⠮⠭⢽⠿⡿⠧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣤⣄⣠⣷⢨⣉⣽⣿⣿⣧⣼⣿⡆⠀⢸⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡿⠟⢦⡻⣦⠓⠛⠛⠻⠿⠿⠿⠿⢿⣿⣷⣶⡾⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⢀⢢⡿⠗⠒⠚⠻⠿⠟⣛⠋⠉⠀⢀⣨⣿⣿⣿⣿⣿⣿⡟⢿⢶⣿⡋⠠⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠓⠲⠶⢄⣐⣰⣶⣶⠀⠀⢀⠄⠀⠀⠠⠀⢀⡄⠀⢀⣀⣶⣦⣄⡆⢸⣶⣧⣤⡀⣤⣞⣷⢀⣿⠂⣴⠈⠈⡾⠋⠈⠀⠀⠀⠈⠑⣞⣗⣻⣧⢰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⢀⡟⡷⣷⣿⣿⣿⣿⣿⣿⣏⣸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣿⡛⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠋ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡃⠀⠀⠀⠀⠀⡀⢷⣄⢀⣿⣿⠁⠸⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣧⠀⠀⣤⣤⣴⣿⣿⣿⠈⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⣶⣀⢠⣆⢐⣺⣿⡀ ⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣄⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢸⣿⢛⡻⣿⡿⠟⢻⠙⣿⣫⠀⣴⡿⡂⠀⢼⣿⣿⣿⣿⡟⠀⠿⢿⠀⠀⠀⠀⠀⠀⠐⢻⡧⢸⣿⣿⣏⢨⣉⠸⡏⠗ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠈⣿⣿⡶⠁⢀⡼⠋⠑⠀⠀⠀⠁⢸⠛⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠯⠈⣻⠿⠳⠛⠁⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠁⠀⠀⠀⢰⣶⠠⡎⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠰⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠁⡈⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣿⠛⠇⢸⣧⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⠬⠽⢿⢿⡿⠧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣡⣀⣀⡷⢨⣉⣽⣿⣿⣧⣾⣿⡬⠁⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⢧⡻⠦⠓⠛⠛⠿⠿⠿⠿⠿⢿⣿⣷⢶⡾⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠀⠀⢀⡿⠷⠒⠚⠛⠿⠟⣛⠋⠉⠀⢀⡨⣿⣿⣿⣿⢿⣿⡗⢿⢶⣿⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠳⠲⠶⢄⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⠰⡀⣠⡄⠀⢀⣀⣶⣶⢄⡆⢸⣶⣦⣤⡀⣴⣎⣷⢠⣿⠠⢰⠀⠈⡴⠋⠉⠀⠀⠀⠀⠑⢜⡓⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⢀⢿⡽⣷⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣾⣯⣿⣾⣿⣶⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⣿⡏⢹⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠟⠛⠓ ⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣶⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡃⠀⠀⠀⠀⠀⠈⣷⣤⠀⣿⣿⡇⠸⠼⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⣧⠀⠀⣀⣀⣰⣾⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣦⣠⣤⣦⢐⣲⣿⡀ ⢈⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⣄⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢸⣿⢛⡻⣿⡿⠿⢻⠙⣿⢏⠀⣴⡿⡂⠀⢽⣿⣿⣿⣿⡿⠀⠻⠿⠀⠀⠀⠀⠀⠀⠐⢻⣧⢸⣿⣿⣯⢩⡉⠸⡏⠗ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠈⣿⣿⡶⠁⠀⠼⠋⠁⠀⠀⠀⠀⢸⠟⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠯⠈⣻⠿⠚⠚⠐⠀⠀⠀ ⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⠁⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠂⠀⠀⠀⠀⠀⠀⠀⣠⠰⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠁⡈⣋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⠙⠇⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⠬⠭⢿⢿⡿⠧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⣀⣁⣄⣠⣷⢨⣉⣹⣿⣿⣯⣼⣿⡄⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⢦⡛⠧⠒⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⢶⡾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⢄⡿⠷⠒⠛⠛⠿⠟⣻⠉⠁⠀⢀⣨⣿⣿⣿⣿⣿⣿⡗⢿⢶⣿⡅⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠓⠲⠶⢆⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⠐⠀⣠⠄⠀⣀⣠⣶⣦⢄⡖⢰⣷⣦⣤⡀⣴⡆⣷⢠⣿⠀⣰⠊⠈⡴⠋⠉⠀⠀⠀⠀⠑⢞⣓⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⢠⢋⠾⣴⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣾⣯⣿⣾⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣿⡏⢸⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠋⠃ ⢺⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣶⣿⣿⣿⣿⣿⣿⣿⠇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⣶⣄⠀⣾⣿⠁⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠺⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣧⠀⠀⣀⠀⣠⣶⣾⣿⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠠⣶⣄⠄⢦⢐⣰⣿⡀ ⠠⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⣄⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢹⣿⢛⡻⣿⡿⠟⢻⠛⣿⢋⠀⣴⡿⡂⠀⢹⣿⣿⣿⣿⡿⠀⠻⠿⠀⠀⠀⠀⠀⠀⠐⢻⣧⢸⣿⣿⣏⢩⠈⠼⡏⠇ ⠈⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠈⣿⣿⡶⠀⠀⠼⠋⠁⠀⠀⠀⠀⢸⠟⣹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠗⠈⡻⠿⠒⠛⠀⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠁⠀⠀⠀⢰⣶⠠⣮⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡈⣋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⢰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⠛⠇⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⠬⠭⢿⢿⠿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⣀⣠⣀⣠⣷⢨⣉⣻⣿⣿⣧⣼⣿⡇⠁⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡿⠟⢦⡻⠧⠒⠛⠛⠿⠿⠿⠿⠿⢿⣿⣶⢶⡾⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠀⢀⢄⡿⠷⠒⠚⠻⠿⠟⣛⠉⠉⠀⢀⣨⢿⣿⣿⣿⣿⣿⡗⢿⢶⣿⡅⢀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠒⠒⠶⢆⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⠄⠀⡠⡀⠀⣀⣠⣶⣶⢠⡖⢸⣷⣦⣤⡀⣴⣆⣷⢢⣿⠀⢴⠈⠀⡰⠋⠉⠀⠀⠀⠀⠑⢞⡗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠂⠀⠀⠀⠀⠰⢫⢾⣾⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣮⣭⣿⣾⣿⣶⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⡏⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡃⠀⠀⠀⠀⠀⠀⢶⣠⠀⣼⣿⡇⠸⠴⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣧⠀⠀⠀⠀⢠⣼⣿⣿⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠰⣦⣤⣠⣦⢐⣰⣿⡀ ⢀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣴⣄⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⢸⣿⢛⡻⣿⡿⠟⢻⠘⣿⢋⠀⣴⠿⠂⠀⣻⣿⣿⣿⣿⣿⠁⠻⠿⠀⠀⠀⠀⠀⠀⠐⢻⣧⢸⣿⣿⣏⢨⡉⠸⡏⠇ ⠔⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠈⣿⣿⡖⠀⠀⠼⠋⠁⠀⠀⠀⠀⢰⠾⢽⣿⣿⣿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡘⠷⠈⡻⠿⠒⠚⠀⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠁⠀⠀⠀⢰⣶⠠⡮⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⡈⣋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⢰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⢹⣿⢙⡻⣿⡿⠛⢹⠙⣿⢉⠀⣴⠿⠀⠀⢶⣶⣾⣿⣿⣿⠏⠻⠿⠀⠀⠀⠀⠀⠀⠰⢻⣧⢸⣿⣿⣏⢩⠉⠸⡏⠇ ⠈⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⠀⠼⠋⠁⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠯⠈⡻⠿⠒⠘⠀⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠁⠀⠀⠀⢰⣶⠠⡮⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠁⡈⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣦⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣷⠛⠇⢸⣇⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣤⣿⡿⠭⠭⠿⢭⠿⠧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣁⣄⣤⣿⢨⣉⣿⣿⣿⣯⣾⣿⡯⠁⣸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠟⢦⣻⠧⠒⠛⠻⠿⠿⠿⠿⠿⢿⣿⣷⢶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⣆⠀⠀⣀⡿⠗⠒⠛⠛⠿⠛⢛⠉⠁⠀⢀⣨⢿⣿⣿⣿⣿⣿⣟⣿⢶⣿⡏⠡⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠳⠲⠶⢆⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⢆⢀⣤⠀⢀⣀⣰⣶⣴⢰⡗⢸⣷⣦⣤⠀⣴⣆⢷⢀⣿⠀⣰⠂⠀⢠⠟⠋⠉⠉⠉⠉⠑⠞⡓⣻⣧⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⠜⠱⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣬⣬⣿⣾⣿⣶⣿⡀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣟⢹⢸⣇⣀⣀⣤⣤⣶⣶⣿⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣾⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⣿⡇⠸⠼⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣷⠀⠀⠀⠀⠀⢀⣽⣿⡇⣸⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣤⣤⠤⣦⢐⣶⣿⡀ ⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢸⣿⢛⡻⣿⡿⠛⢹⠙⣿⢋⠀⣴⠿⠂⠀⣦⣤⣴⣿⣿⣿⡇⠻⠿⠄⠀⠀⠄⠀⠀⠐⢻⣧⢸⣿⣿⣏⢉⠈⠼⡏⠟ ⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⠀⠼⠋⠁⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⠈⡻⠿⠲⠛⠀⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠁⠀⠀⠀⢰⣶⠠⡮⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢡⣽⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⡈⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣴⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣷⠛⠇⢸⣇⣀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣿⡿⠭⠭⡿⠭⠿⠧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣡⣀⣀⣷⢨⣉⣹⣿⣿⣧⣼⣿⡏⠁⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠟⢦⡹⠧⠒⠛⠻⠿⠿⠿⠿⠿⢿⣿⣷⢶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⠀⢀⡿⠗⠒⠚⠛⠿⠛⣛⠉⠉⠀⢀⣨⠿⣿⣿⣿⣿⣿⡗⢿⢶⣿⡇⢡⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠲⠶⠶⢂⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⢂⢀⣤⠀⢀⣀⣰⣶⣤⣸⡖⢨⣷⣦⣤⠀⣴⣆⢷⢀⣿⠀⢰⠀⠀⢁⠞⠛⠛⠉⠉⠉⠙⠞⡓⢻⣧⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠟⠀⠀⠀⠀⠀⠀⠞⡵⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣬⣬⣿⣾⣿⣶⣿⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟⢸⢸⣇⣀⣀⣤⣤⣶⣶⣿⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡇⠸⠼⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⢻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣷⠀⠀⠀⠀⠀⠀⣹⣷⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⢠⣶⣄⣤⣦⢐⣲⣿⡀ ⢐⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢸⣿⢛⡻⣿⡿⠋⢹⠘⣿⢋⠀⣴⠿⠀⢀⣤⣀⣠⣾⣿⣿⡇⠻⠿⠀⠀⠠⠄⠀⠀⠐⢻⣧⢸⣿⣿⣏⢩⡈⠸⡏⠗ ⡌⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠈⣿⣿⡖⠀⠀⠼⠋⠁⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⠈⡻⠿⠒⠛⠐⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠁⠀⠀⠀⢰⣶⠠⣮⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡈⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠩⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣦⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣷⠛⠇⢸⣇⣀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⠭⠭⡿⠍⠿⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣡⣄⣀⣷⢨⣉⣹⣿⣿⣣⣽⣿⡯⠁⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⢦⡻⠧⠓⠛⠻⠿⠿⠿⠿⠿⢿⣿⣷⢶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⡿⠷⠒⠛⠛⠟⠟⣛⠋⠁⠀⢀⣨⠿⣿⣿⣿⣿⣿⡗⣿⢶⣿⡇⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠒⠰⠶⢆⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⡀⣠⡄⢀⣀⣠⣶⣶⣤⣸⡖⢨⣧⣦⣄⠀⣴⣆⢷⢀⣿⠀⢰⠈⠀⢀⡾⠛⠿⠛⠛⠋⠓⢞⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀ ⣀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⢻⢾⣷⣿⣿⣿⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⣮⣤⣿⣾⣿⣶⣿⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢹⢸⣇⣀⣠⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⣿⣿⣯⣿⣾⣿⣾⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠸⠼⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⢹⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣷⠀⠀⠀⠀⠀⠀⢲⣦⣦⠀⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⢰⣶⣄⣤⣦⢰⣲⣿⡀ ⠐⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢸⣿⢚⡻⣿⡿⠛⢹⠘⣿⢏⠀⣴⠿⠀⠀⠀⠀⠀⣠⣾⣿⣿⠔⠿⠀⠀⠠⠀⠀⠀⠐⢻⣧⢸⣿⣿⣏⢩⡉⠸⡏⠇ ⡜⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⠀⠼⠋⠁⠀⠀⠀⠀⠺⢿⣷⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⠈⡻⠿⠖⠛⠁⠀⠀⠀ ⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠁⠀⠀⠀⢰⣶⠠⣮⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡈⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⠛⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠩⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣷⠛⠇⢸⣇⣀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣄⣿⡿⠭⠭⡯⠍⠻⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣡⣀⣀⣷⢨⣉⣻⣿⣿⣣⣾⣿⡯⠁⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠟⢦⡹⠧⠒⠛⠛⠿⠿⠿⠿⠿⢿⣿⣷⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢀⠿⠷⠒⠛⠛⠿⠟⣛⠋⠁⠁⢀⣨⠿⣿⣿⣿⣿⣿⡟⢿⢶⣿⡁⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠶⠲⠶⢆⣐⣐⣶⣶⠀⠀⠄⠀⠀⠐⣀⣠⡄⢀⣀⣠⣶⣶⡄⣸⣆⢨⣶⣦⣤⠀⣤⣆⢷⢀⣿⠀⢰⠂⠀⢁⡼⠿⠿⠿⠽⠛⠓⠞⣗⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀ ⣀⠉⠉⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⢫⠾⣽⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣮⣬⣿⣾⣿⣶⣿⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢹⢸⣇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠁ ⣻⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠸⠼⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣧⠀⠀⠀⠀⠀⠀⢤⣤⢤⠀⣿⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣶⣄⣤⣦⢰⢶⣿⡀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢸⣿⢛⡻⣿⡿⠛⢹⠘⣿⢏⠀⣴⠿⠀⠀⠀⠀⠀⢀⣼⣿⣿⠠⠿⠀⠀⠈⠀⠀⠀⠐⢻⣧⢸⣿⣿⣯⢨⠈⠼⡏⠇ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⠀⠼⠋⠁⠀⠀⠀⠀⠿⣶⣤⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⠈⣻⠿⠲⠛⠑⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠀⠀⠀⠀⢰⣶⠠⣮⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡘⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⠛⢿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠩⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣿⠙⠇⢸⣇⣀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣤⣄⣿⡿⠭⠽⠯⠝⠻⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣡⣄⣤⣷⢨⣉⣹⣿⣿⣳⣾⣿⡌⠀⢹⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⢦⣛⡧⠒⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢠⡿⠷⠒⠛⠛⠿⠛⣛⠉⠁⠀⢀⣨⠿⣿⣿⣿⣿⣿⡟⢿⢶⣿⡃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠚⠳⠰⠶⢆⣐⣰⣶⣶⠀⠀⠀⠀⠀⠐⣀⣠⡆⢀⣀⣠⣶⣶⣄⣸⡆⢨⣶⣦⣄⠀⣴⣎⢷⢀⣿⠀⢰⠈⠀⢁⣼⡿⠿⠿⠿⠟⠳⠜⣗⣻⣧⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠉⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠸⢻⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣾⣮⣩⣿⣾⣿⣶⣿⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⢹⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣶⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⣿⣿⣯⣿⣾⣿⣾⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣧⠀⠀⠀⠀⠀⠀⣠⣠⢤⠀⣼⡀⠀⠀⠀⠀⠀⠀⣤⡄⢠⣶⣤⡤⣦⢐⣶⣿⡀ ⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣿⢙⡻⣿⡿⠛⢹⠘⣿⢋⠀⣴⠿⠀⠀⠀⠀⠀⠀⣼⣿⣾⢄⠿⠆⠀⠀⠀⠀⠀⠰⢻⣧⢸⣿⣿⣯⢩⡉⠼⡏⠇ ⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠉⠈⣿⣿⡗⠀⠀⠼⠋⠁⠀⠀⠀⠀⣶⣤⣤⣤⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠐⡜⠿⠈⡻⠿⠻⠚⠒⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡈⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠩⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣷⠙⠇⢸⣇⣀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣤⣤⣿⠟⠭⠽⠯⠍⠻⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣡⣄⣤⣷⢨⣉⣹⣿⣿⣷⣾⣿⡄⠁⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠟⢦⡙⠧⠒⠛⠻⠿⠿⠿⠿⠿⢿⣿⣷⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢀⡿⠷⠒⠛⠛⠿⠛⣛⠋⠁⠀⢀⣨⠿⣿⣿⣿⣿⣿⡗⢿⢷⣿⡇⠡⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠒⠒⠶⢆⣐⣰⣶⣶⠀⠀⠀⠀⠀⠐⣀⣴⡄⣀⣀⣠⣶⣶⣄⣼⡖⢠⣶⣦⣄⠀⣴⡎⢶⢀⣿⠀⢰⠈⠀⢁⣼⡿⢿⣿⣻⠟⠳⢜⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠐⢻⠾⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⣿⣿⣿⣿⣮⣬⣿⣾⣿⣶⣿⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣾⡟⢸⢸⣇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠁ ⣺⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣧⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣤⡀⢰⣦⣄⡤⣦⢐⢶⣿⡀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣿⢙⡻⣿⠿⠛⢹⠘⣿⣋⠀⣴⠿⠄⠀⠀⠀⠀⠀⣸⣿⣾⡇⠾⠀⠀⠀⠀⠀⠀⠰⢻⣧⢸⣿⣿⣟⢩⠈⠼⡏⠗ ⡈⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠉⠈⣿⣿⡖⠀⠀⠼⠋⠁⠀⠀⠀⠀⣦⣤⣀⣀⣴⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡜⠿⠈⡻⠿⠳⠚⠀⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡚⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡾⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣷⠙⡇⢸⣇⣀⡀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣄⣿⠟⠩⠽⡿⠍⠻⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣁⣀⣠⣷⢨⣉⣹⣿⡿⣣⣼⣿⡖⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠗⢦⡙⠧⠓⠛⠛⠻⠿⠿⠿⠿⢿⣿⣾⡶⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⡿⠷⠒⠛⠛⠿⠛⢛⠉⠁⠀⢀⣨⠿⣿⣿⣿⣿⣿⡇⢿⢷⣿⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠓⠲⠶⢂⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⣀⣴⠄⣀⣠⣤⣶⣶⣆⣼⡆⢠⣴⣦⣤⠀⣴⣆⢶⢀⣿⠀⢰⠈⠀⢁⣼⣿⣿⣿⣿⠿⠧⣞⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠘⡳⣿⣾⣿⣿⣿⣿⣿⣿⣿⡁⢸⣿⣿⣿⣿⣮⣬⣿⡾⣿⣴⣿⠀⢠⡿⠋⠁⠀⠉⠀⠀⠀⠀⠈⢻⡟⢹⢸⡇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠁ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣱⣾⣿⣿⣿⣿⣿⣿⣿⡿⠅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠼⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⣦⣄⢤⢤⢐⢶⣿⡀ ⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣻⢛⠻⣿⠟⠟⢹⠘⣿⢋⠀⣴⡿⠄⠀⠀⠀⠀⠀⢰⣷⣯⡷⢸⠂⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⣿⣯⢩⠈⠼⡏⠗ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⠀⡼⠋⠓⠀⠀⠀⠀⣄⡀⠀⠀⣀⣼⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⡜⠏⠘⣻⠿⠻⠛⠁⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣿⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡒⢋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣽⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣯⠙⠇⢸⣇⣀⡀⠀⢀⠀⠀⠀⠀⠀⢀⣤⣤⣿⠟⠩⠽⠿⠍⠻⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣡⣀⣀⣷⢨⣉⣹⣿⡿⣧⣼⣿⡯⠁⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⢦⡙⠧⠓⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⡶⠛⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⡿⠗⠒⠛⠛⠿⠛⣛⠉⠁⠀⢀⣨⠿⣿⣿⣿⣿⣿⡗⣿⢷⣿⡃⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⣄⠀⠈⠛⠓⠲⠶⢂⣐⣐⣶⣶⠀⠐⠂⠀⠀⠂⣀⣴⠀⣀⣠⣤⣶⣶⣆⣸⡆⢰⣾⣦⣤⠀⣤⡆⢶⢀⣿⠀⢰⠈⠀⢁⣼⣿⣿⣿⡿⣿⢧⣜⡓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠈⡱⢛⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣮⣬⣿⣾⣿⣴⣿⠀⢠⣿⠟⠉⠁⠉⠉⠁⠀⠀⠀⢺⡟⢹⢸⡇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠉ ⣻⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣤⡄⢠⣶⣤⣤⢦⢐⢶⣿⡀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣿⢛⠻⣿⠟⠟⢹⠙⣿⢏⠀⣴⡿⠄⠀⠀⠀⠀⠀⢀⣶⣖⣶⠀⠀⠀⠀⠀⠀⠀⠐⢻⣧⢸⣿⣿⣟⢈⠈⠸⡏⠗ ⡔⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⠀⡼⠋⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⣨⣿⣿⡿⠌⠀⠀⠀⠀⠀⠀⠀⡜⠿⠘⡻⠿⠾⠛⠀⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠂⠀⠀⠀⠀⠀⠀⠀⣿⢿⣶⣤⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⡐⢋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣦⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣷⠙⡇⢸⣇⣀⡀⠀⢀⡀⠀⠀⠀⠀⢀⣤⣤⣿⠟⠩⠽⠿⠍⠻⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣁⣀⣠⣷⢨⣉⣹⣿⡿⣣⣼⣿⡆⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢦⡙⠦⠒⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⡶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⡿⠷⠒⠛⠛⠿⠛⣛⠉⠁⠀⢀⡨⠿⣿⣿⣿⣿⣿⡇⣿⢷⣿⡇⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⣄⠀⠉⠛⠓⠲⠶⣂⣐⣐⣶⣶⠀⠐⠀⠀⠀⢀⣀⢴⠀⣀⣠⣤⣶⣶⣄⣼⡆⢰⣶⣦⣤⠀⣤⣆⢶⢀⣿⠀⢰⠈⠀⢁⣴⣿⣿⣿⣿⣿⣧⡜⡓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠈⡱⢻⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⣿⣿⣿⣾⣾⣬⣿⣾⣿⣴⣿⠀⢠⣿⠟⠋⠉⠙⠓⠂⠀⠁⠀⢻⡏⢹⢸⡇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠋⠉ ⣺⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠅⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠴⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⣤⣀⢠⣶⣄⣤⢤⢐⢰⣿⡀ ⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣿⢛⠻⣿⡟⠛⢹⠙⣿⢏⠀⣴⡿⠄⠀⠀⠀⠀⠀⠀⣤⡤⢤⠀⡁⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⣿⣟⢩⡈⠼⡏⠗ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠈⣿⣿⡗⠀⠀⡼⠋⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⢐⣽⣿⣿⠔⠀⠀⠀⠀⠀⠀⠀⡜⠏⠘⡻⠿⠻⠛⠀⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣀⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⡐⢉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⢽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠩⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣿⠙⠇⢰⣇⣀⡀⠀⢀⡀⠀⠀⠀⠀⢀⣤⣤⣿⠟⠉⠽⠻⠍⠻⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣁⣀⣠⣷⢨⣉⣹⣿⡿⣣⣼⣿⡖⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠗⢦⡙⠦⠓⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⡿⠷⠒⠛⠛⠿⠛⣛⠉⠁⠀⢀⡨⠿⣿⣿⣿⣿⣿⡗⢿⢷⣿⡃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠄⠉⠙⠳⠾⠶⣂⣐⣐⣶⣶⠀⠐⠀⠀⠀⢈⣀⣴⢀⣀⣤⣴⣶⣶⣄⣼⡆⢠⣷⣦⣤⠀⣤⣆⣷⢀⣿⠀⢰⠀⠀⢁⣼⣿⣿⣿⣿⣿⣧⡞⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠘⡷⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣾⣬⣿⣾⣿⣶⣿⠀⢠⣿⡿⠛⠋⠛⠛⠋⠈⠀⠁⢺⣏⢹⢸⡇⣀⣠⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠛ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠸⠼⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⣀⠠⣤⣤⣄⢤⢀⢶⣿⡀ ⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣿⢛⠻⣿⡟⠟⢹⠙⣿⢋⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠃⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⣿⣏⢩⠈⠼⡏⠗ ⡐⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⡼⠋⠗⠂⠉⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣾⡁⠀⠀⠀⠀⠀⠀⠀⡜⠟⠈⡻⠿⠳⠛⠁⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠂⠀⠀⠀⠀⠀⠀⠀⢶⣤⣀⡀⣠⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⡐⢋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣷⠙⠅⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⠟⠉⠿⠻⠝⠻⠧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣁⣀⣠⣷⢨⣉⣹⣿⡿⣧⣼⣿⡆⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢦⡙⠧⠓⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⡿⠷⠒⠛⠛⠿⠟⣛⠉⠁⠀⢀⣨⠿⣿⣿⣿⣿⣿⡟⢿⢷⣾⡃⢀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⣄⠀⠈⠙⠓⠲⠶⢂⣐⣐⣶⣶⠀⠐⠀⠀⠀⢂⡀⣶⢀⣀⣤⣴⣶⣶⣆⣼⡆⢠⣶⣦⣤⠀⣴⣆⣶⢀⣿⠀⢰⠂⠀⢁⣼⣿⣿⣿⣿⣿⢥⡜⡓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠈⠾⢳⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣾⣭⣿⣾⣿⣶⣿⠀⢠⣿⣿⡿⠟⠻⣿⡟⠟⠓⠂⢾⡏⢹⢸⡇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠋⠉ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣶⣤⢤⢦⢐⢶⣿⡀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣿⢛⡻⣿⡟⠛⢹⠙⣿⣏⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⢹⣧⢸⣿⣿⣟⢩⠈⠼⡏⠗ ⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠉⠈⣿⣿⡗⠀⠀⣼⠋⠷⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⡜⠟⠘⡻⠿⠛⠛⠀⠀⠀⠀ ⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠂⠁⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⡂⢉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣿⣶⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣻⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣦⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠙⠅⢰⣇⣀⡀⠀⢀⠀⠀⠀⠀⠀⢀⣤⣤⣿⠟⠉⠿⠻⠍⠛⠧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣁⣀⣠⣷⢨⣉⣹⣿⡿⣧⣼⣿⡆⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠏⢦⡙⠦⠒⠛⠛⠻⠿⠿⠿⠿⢿⣿⣷⡶⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⡿⠷⠒⠛⠛⠿⠟⣛⠉⠁⠀⢀⡨⠿⣿⣿⣿⣿⣿⡇⢿⢷⣿⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⣄⠀⠈⠻⠓⠺⠶⢂⣐⣰⣶⣶⠀⠐⠀⠀⠀⢀⡠⣶⢀⣀⣤⣴⣶⣶⣄⣼⡆⢐⣶⣦⣤⠀⣴⣆⣶⢀⣿⠀⢰⠈⠀⢁⣼⣿⣿⣿⣿⣿⢥⡞⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⠈⠞⢳⣿⣿⣿⣿⣿⣿⣿⣟⠁⢸⣿⣿⣿⣿⣾⣬⣿⣾⣿⣴⣿⠀⢠⣿⣿⣿⠿⠿⣟⡻⠟⠿⠥⢿⡟⢹⢸⡇⣀⣀⣤⣴⣶⣶⣶⣿⡿⠿⠿⠟⠋⠋ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣼⣿⣿⣿⣿⣿⣿⣿⡿⠅⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠼⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣤⣀⢠⣶⣄⠠⢦⢐⢶⣿⡀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣿⢛⠻⢿⡿⠛⢹⠙⣿⣏⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⢹⣧⢸⣿⣿⣟⢩⠈⠼⡏⠗ ⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠈⣿⣿⡗⠀⠀⣼⠏⠷⠾⠛⠀⠁⠀⠀⠀⠀⠀⠀⣰⣶⣖⡗⠐⠀⠀⠀⠀⠀⠀⡜⠏⠘⣻⠿⠲⠛⠀⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡎⣟⢁⣀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡂⢉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣶⣦⣤⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣦⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣿⠙⠅⢰⣇⣀⡀⠀⢀⠀⠀⠀⠀⠀⢠⣤⣤⣿⠟⠩⠿⠿⠍⠛⠧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣁⣀⣠⣷⢨⣉⣹⣿⡿⣣⣼⣿⡖⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⡿⠏⢦⡙⠆⠓⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⡿⠷⠒⠛⠛⠿⠟⣛⠉⠁⠀⢀⡨⠿⣿⣿⣿⣿⣿⡗⣿⢷⣿⡇⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠹⠗⠲⠶⢂⣐⣐⣶⣶⠀⠐⠀⠀⠀⢠⡠⣶⢀⣀⣤⣤⣶⣶⣀⣾⣆⢰⣷⣦⣤⠀⣴⣆⣶⢀⣿⠀⢠⠈⠈⢀⣼⣿⣿⣿⡿⣿⢥⣞⡗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⠈⠞⣳⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⣿⣿⣿⣮⣭⣿⣾⣿⣶⣿⠀⢠⣿⣿⣿⢿⢿⣶⠿⠾⢧⣥⢻⡟⢹⢸⡇⣀⣀⣤⣴⣶⣶⣶⣿⡿⠿⠿⠿⠛⠋ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣼⣿⣿⣿⣿⣿⣿⣿⡟⠇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⠉⠀⠀⠀⠈⠅⠸⠾⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣤⣄⢠⢤⢐⢶⣿⡀ ⠐⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣿⢛⡻⣿⡿⠛⢹⠙⣿⣯⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠐⢻⣧⢸⣿⣿⣯⢩⡈⠼⡏⠗ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠈⣿⣿⡗⠀⠀⣼⠋⣷⠶⠛⠀⠁⠀⠀⠀⠀⠀⠀⢠⣤⡤⣦⠈⠀⠀⠀⠀⠀⠀⡜⠏⠘⣻⠿⠲⠛⠑⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡎⣟⢁⣀⠘⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡚⢉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⣤⣄⣀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣦⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠙⠅⢰⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡿⠟⠛⠻⠻⠝⠛⢧⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣠⣀⣬⣷⢨⣉⣹⣿⡿⣧⣼⣿⡖⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢦⡙⠆⠒⠛⠛⠻⠿⠿⠿⠿⢿⣿⣾⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⡿⠷⠒⠛⠛⠿⠛⣛⠉⠁⠀⢀⡨⠿⣿⣿⣿⣿⣿⡟⣿⢿⣿⡃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⢤⣤⡀⠀⠈⠛⠲⠰⠶⢂⣀⣰⣶⣶⠀⠐⠀⠀⠀⢀⡠⡖⣀⣠⣤⣴⣶⣶⣀⣾⡆⢠⣷⣦⣤⠀⣤⣆⣶⢀⣿⠀⢰⠈⠀⢁⣼⣿⣿⣿⣿⣿⢡⡜⣓⣻⣇⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠈⠚⣽⣿⣿⣿⣿⣿⣿⣿⣏⠁⢸⣿⣿⣿⣿⣮⣬⣿⣾⣿⣶⣿⠀⢠⣿⣿⣿⣿⣿⣶⢶⣾⣧⣭⣾⡛⢹⢸⡇⣀⣀⣤⣴⣶⣶⣾⣿⡿⠿⠿⠿⠋⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⠃⠁⠀⠀⠘⡅⠸⠼⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠹⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣤⡀⠠⣶⣄⢠⢦⢀⢶⣿⡀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣶⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⢸⣿⢛⡻⣿⡟⠟⢹⠛⣿⣯⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⣿⣏⢩⠈⠼⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⠈⣿⣿⡆⠀⢀⣼⠋⣷⠶⠛⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⡤⣦⠘⠀⠀⠀⠀⠀⠠⡜⠏⠘⡻⠿⠲⠛⠀⠀⠀⠀ ⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡎⣟⢁⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡘⢉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⢀⡀⠀⣤⣽⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣮⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣿⠙⠅⢰⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡿⠟⠚⠟⠻⠝⠛⢧⣄⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⣀⣀⣠⣀⣬⣷⢨⣉⣹⣿⣿⣣⣾⣿⡄⠀⣸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠗⢦⡙⠦⠒⠛⠛⠻⠿⠿⠿⠿⢿⣿⣷⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⢀⡿⠷⠒⠛⠻⠿⠟⣛⠉⠁⠀⢀⡨⠿⣿⣿⣿⣿⣿⡧⣾⢿⣿⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠛⠓⠒⠶⢂⣀⣰⣶⣶⠀⠐⠀⠀⠀⢁⡰⡖⣀⣠⣤⣴⣶⣦⣀⣼⡆⢨⣶⣦⣤⠀⣤⣆⣶⢠⣿⠀⢰⠊⠀⢀⣼⣿⣿⣿⡿⣿⢡⡜⣓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠀⠀⠀⠀⠀⠨⠚⣼⣿⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣮⣬⣿⣾⣿⣶⣿⠀⢠⣿⣿⣿⣿⣿⣾⢷⣾⣯⣭⣿⡟⢹⢸⡇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠋⠁ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⠁⠀⠀⠀⠘⠇⠰⠼⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠟⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣶⣄⡠⢦⢐⢶⣿⡀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⢸⣿⢛⡻⣿⡿⠿⢻⠛⣿⣯⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⣿⣯⢩⠈⠼⡏⠗ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠈⣿⣿⡆⠀⠀⣼⠋⡷⠶⠛⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⠈⠀⠀⠀⠀⠀⠠⡜⠏⠘⡻⠿⠲⠛⠀⠀⠀⠀ ⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡘⢉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢺⠦⣄⣀⣀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡾⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠘⠇⢸⣧⣀⡀⠀⢀⠀⠀⠀⠀⠀⢠⣤⣤⣿⠟⠛⠛⠻⠙⠛⢧⣄⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⢀⣀⣁⣀⣀⣷⢨⣉⣹⣿⡿⣧⣼⣿⡦⠁⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠇⢦⣙⣧⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣾⠖⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⣀⡿⠷⠒⠛⠛⠿⠟⣛⠉⠉⠀⢀⣨⡿⣿⣿⣿⣿⣿⡟⣿⢷⣿⡅⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠛⠳⠒⠶⢆⣐⣰⣶⣶⠀⠀⠀⠀⠀⠀⢔⠇⣀⣤⣴⣶⣶⣶⣀⣾⡖⢰⣷⣦⣤⠀⣴⣆⢷⢀⣿⠀⢠⠀⠁⢁⣼⣿⣿⣿⡿⣿⢣⣞⣓⢻⣧⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⠐⠋⣾⣿⣿⣿⣿⣿⣿⣿⡇⡁⢸⣿⣿⣿⣿⣾⣬⣿⣾⣿⣶⣿⠀⢠⣿⣿⣿⠿⠿⣾⡿⡾⠷⠭⣾⡛⢹⢸⡇⣀⣠⣤⣴⣶⣶⣾⣿⡿⠿⠿⠿⠛⠛ ⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠈⠁⠀⠀⠀⠘⠃⠰⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠂⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣤⡄⠠⣦⣤⣤⢤⢐⢸⣿⡀ ⢘⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⢸⣿⢛⡻⣿⡿⠛⢹⠘⣿⣏⠀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠐⢻⣧⢸⣿⣿⣿⢨⡈⠬⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠈⣿⣿⡷⠀⠀⣼⠋⠷⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⣶⠁⠀⠀⠀⠀⠀⠀⡜⠯⠈⡻⠿⠶⠛⠃⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡚⢉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⢤⣤⣰⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣦⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠙⠇⢸⣧⣀⡀⠀⠀⡀⠀⠀⠀⠀⢠⣴⣤⠿⠛⠓⠚⠛⠙⠛⢧⣄⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⣀⣀⣁⣀⣀⡷⢨⣉⣹⣿⡿⣧⣾⣿⡇⠁⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢦⣙⣧⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣷⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⣀⡿⠷⠒⠛⠛⠿⠟⣛⠋⠉⠀⢀⣨⠿⣿⣿⣿⣿⣿⡟⣿⢷⣿⡅⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠓⠲⠶⢆⣐⣀⣶⣶⠀⠀⠀⠀⠀⠀⣺⢣⣤⣦⣶⣾⣷⣦⣠⣾⡆⢰⣷⣦⣤⠀⣴⣆⢶⢀⣿⠀⢰⠀⠈⢁⣴⣿⣿⣿⢿⣿⢧⣞⣓⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⢸⣿⣿⣿⣿⣾⣭⣿⣾⣿⣶⣿⠀⢠⣿⣿⡿⠟⠻⣿⡿⠟⠻⠿⣾⡛⢹⢸⡇⣀⣠⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠛ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⡟⠅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠰⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠂⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣤⡀⠠⣶⣤⡤⢦⢐⢰⣿⡀ ⠘⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢸⣿⢛⡻⣿⡿⠛⢻⠙⣿⣏⠀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠼⠀⠈⠀⠀⠀⠐⢹⣧⢸⣿⣿⣏⢩⡈⠼⡏⠗ ⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠉⠈⣿⣿⡗⠀⠀⣼⠋⠷⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣲⣿⣝⡟⠀⠀⠀⠀⠀⠀⠀⡜⠏⠈⣻⠿⠲⠛⠁⠀⠀⠀ ⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠂⠁⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡚⢋⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣛⣳⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠘⠇⢰⣧⣀⡀⠀⢀⡀⠀⠀⠀⠀⢀⣴⠶⠿⠛⠛⠛⠋⠉⠛⢷⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣁⣀⣠⣿⢨⣉⣻⣿⣿⣯⣾⣿⡄⠀⢸⣿⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠗⠢⡙⠦⠐⠚⠻⠿⠿⠿⠿⠿⢿⣿⣷⢶⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⡀⡿⠗⠒⠚⠛⠿⠟⣛⠉⠁⠀⢀⡨⠿⣿⣿⣿⣿⣿⡟⣾⢿⣿⡇⢠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⢤⣤⡄⠄⠉⠛⠓⠲⠶⢆⣐⣐⣶⣶⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣷⣤⣾⣿⡆⢈⣶⣶⣤⠀⣤⣆⢶⢀⣿⠀⢰⠀⠀⢀⣼⣿⣿⣿⢿⣿⣷⣞⣗⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠉⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣃⠁⢸⣿⣿⣿⣿⣶⣬⣿⣾⣿⣶⣿⠀⢠⣾⠟⠉⠉⠉⠉⠈⠀⠀⠉⢿⡏⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⣿⠿⠿⠿⠛⠛ ⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠰⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠝⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⡄⠠⣶⣤⣤⣦⢐⢰⣿⡀ ⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⢛⡻⣿⠿⠛⢹⠘⣿⣯⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⣴⣖⣶⠀⡇⠀⠀⠀⠀⠀⠀⢻⣷⢸⣿⣿⣯⢩⡉⡼⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠈⣿⣿⡖⠀⠀⣼⠋⠷⠒⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡶⠁⠀⠀⠀⠀⠀⠠⡜⠇⠈⣻⠿⠗⠛⠓⠀⠀⠀ ⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣤⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡊⣋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠙⠇⢸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⠿⠛⠛⠛⠋⠉⠻⣷⣄⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⢀⣀⣁⣀⣀⣷⢨⣉⣹⣿⣿⣧⣾⣿⡧⠁⢸⣿⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⠦⡙⣧⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⢀⠿⠷⠒⠛⠛⠿⠟⢛⠋⠁⠀⢀⣨⠿⣿⣿⣿⣿⣿⡿⣿⢷⣿⡍⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠓⠲⠶⢆⣐⣀⣶⣶⠀⠀⠀⠀⠀⠀⣶⣮⣾⣯⣿⣿⣶⣶⣿⣿⡒⢐⣷⣦⣤⠀⣤⣆⢶⢂⣿⠀⢠⠀⠈⢁⣼⣿⣿⣿⣻⣿⠷⣞⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠈⢸⣿⣿⣿⣿⣮⣬⣿⣾⣿⣶⣿⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠉⢿⡛⢹⢸⡇⣀⣠⣤⣤⣴⣶⣾⣿⣿⠿⠿⠿⠛⠛ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠅⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠄⠀⠀⠀⠀⠀⠀⣤⡀⠠⣦⣤⣤⢤⢀⢰⣿⡀ ⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⢛⡻⢿⡿⠟⢹⠙⣿⣯⠀⣠⡿⠀⠀⠀⠀⠀⠀⢸⣿⣯⣟⢠⠀⠀⠈⠀⠀⠀⠐⢻⣧⢘⣿⣿⣯⢩⠉⠬⡏⠗ ⡌⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠈⣿⣿⡖⠀⠀⣼⠋⠷⠂⠉⠀⠀⡀⠀⠀⠀⣀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠠⡜⠏⠈⣻⠿⠞⠚⠂⠁⠀⠀ ⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠁⠀⡚⢋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠒⠐⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣦⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠘⠇⢰⣧⣀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠴⠶⠟⠛⠛⠛⠋⠉⠻⣷⣄⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣷⢨⣉⣻⣿⡿⣧⣾⣿⡤⠀⢸⣿⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠗⠦⡙⢧⠒⠚⠛⠻⠿⠿⠿⠿⢿⣿⣶⠶⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢹⣿⡄⠀⠀⠠⡿⠷⠒⠚⠛⠿⠟⢛⠉⠉⠀⢀⣨⠿⣿⣿⣿⣿⣿⡟⣿⢷⣿⡅⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠈⠙⠓⠲⠶⢄⣐⣀⣶⣶⠀⠀⠀⠀⠀⢠⣦⣴⣷⣴⣿⣿⣶⣾⣿⣿⡒⢀⣦⣦⣤⠀⣤⡆⢶⢀⣿⠀⢠⠀⠀⢁⡼⠿⠿⠯⠝⠋⠓⠚⡓⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠁⢸⣿⣿⣿⣿⣮⣨⣿⣾⣿⣶⣾⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢹⢸⡇⣀⣠⣤⣤⣴⣶⣾⣿⡿⠿⠿⠿⠛⠛ ⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠸⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⡇⠀⠀⠀⠀⠀⠀⢠⣤⢤⡄⢸⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⣶⣤⢄⢤⢀⢰⣿⡀ ⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⢛⠻⢿⠿⠛⢹⠘⣿⣏⠀⣤⡿⠀⠀⠀⠀⠀⠀⣪⣿⣿⣧⣼⠀⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⣿⣟⢨⡈⠼⡏⠗ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠈⣿⣿⡆⠀⠀⡼⠋⠛⠂⠈⠀⠐⣤⣤⣤⣤⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠠⡜⠧⠈⣻⠿⠖⠚⠃⠀⠀⠀ ⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⢰⣶⠠⡮⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⡚⢋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠓⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠘⠇⢰⣧⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠴⠶⠟⠛⠛⠛⠉⠙⠿⣷⣄⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⣀⣀⣅⣀⣠⣿⢨⣉⣻⣿⣿⣧⣾⣿⡄⠀⢸⣿⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢂⡙⠧⠒⠚⠛⠻⠿⠿⠿⠿⢿⣿⣷⠶⠂⠀⠀⠀⠀⢀⠀⣀⣀⠀⠈⢹⣷⠀⠀⠀⢀⠿⠷⠒⠚⠛⠿⠟⣛⠋⠁⠀⢀⣨⣿⣿⣿⣿⠿⠿⣿⣿⢷⣿⡏⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⢤⣤⡄⠀⠈⠙⠓⠲⠶⢆⣐⣐⣶⣶⠀⠀⠀⠀⠀⣆⣴⣿⣦⣿⣿⣿⣿⣿⣿⡇⡂⠀⣶⣶⣀⠀⣤⡆⢶⢀⣿⠀⢰⠀⠀⠛⠉⠉⠀⠀⠀⠀⠈⠘⣷⣻⣧⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣦⣨⣻⣾⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠛ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣣⠀⠀⠀⠀⠀⠀⠀⣤⡠⡄⢀⣿⡇⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⡆⠀⠀⠀⠀⠀⢠⣿⣿⣇⣸⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣴⣄⢀⢤⢀⢰⣿⡀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⢚⠻⠿⡟⠛⢹⠘⣿⡏⠀⣴⡷⢤⣤⣤⣤⣶⣿⣿⣿⣿⠛⠿⠀⠀⠈⠀⠀⠀⠀⢻⣇⢸⣿⣿⣯⢨⡉⠬⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠉⠈⣿⣿⡖⠀⠀⠼⠋⠁⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠧⠈⡻⠷⠒⠚⠃⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢀⡚⣋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡛⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣇⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠘⠇⢰⣧⣀⡀⠀⢀⡀⠀⠀⠀⠀⠠⠴⠶⠟⠛⠛⠛⠉⠉⠿⣷⣄⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⢀⣀⣁⣀⣄⣷⢨⣉⣻⣿⣿⢧⣾⣿⡍⠀⢸⣿⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠟⢢⠙⢧⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣿⠶⠂⠀⠀⠀⠀⡀⠀⣀⣀⠀⠈⢿⣷⠀⠀⠀⢀⠿⠷⠒⠚⠛⠿⠟⢛⠉⠁⠀⢀⣨⢿⠿⠛⠛⠛⠻⢿⣿⢳⣿⡅⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⢤⣤⡀⠀⠉⠙⠓⠒⠶⢂⣐⣐⣶⣶⠀⠀⠀⠀⠠⣂⣴⣷⣆⣷⣿⣿⣿⣿⣿⡟⣆⠀⣶⣦⣀⠀⣤⡆⢶⢀⣿⠂⢰⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠈⢸⣿⣿⣿⣿⣬⣨⣻⣾⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡟⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⣿⠿⠿⠿⠛⠛ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠂⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⢘⣷⣾⡀⣸⣿⠇⠸⠴⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⡆⠀⣀⡀⢀⣠⣿⣿⣿⣥⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣄⠠⣶⣤⣤⢦⢀⢲⣿⡀ ⠐⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢸⣿⢚⠻⡿⡟⠛⢹⠘⣿⡏⠀⣴⠿⢾⣿⣿⣿⣿⣿⣿⣿⡏⠛⠹⠀⠀⠀⠀⠀⠀⠀⢻⣇⢘⣿⣿⣿⢩⣉⢼⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠉⠈⣿⣿⡖⠀⠀⠜⠋⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠏⠈⡻⠿⠖⠘⠃⠀⠀⠀ ⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢰⣶⠠⡮⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡈⣋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢉⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠂⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⣷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⢐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣸⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠘⠇⢰⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠾⠟⠛⠛⠙⠉⠉⠻⣷⣄⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⣀⣀⣠⣄⣀⡗⢨⣉⣻⣿⣿⣧⣾⣿⡤⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠗⢂⠙⠦⠐⠚⠛⠿⠿⠿⠿⠿⢿⣿⣷⠶⠂⠀⠀⠀⠀⡀⠀⣀⣀⠀⠈⢽⣷⠀⠀⠀⢀⡽⠗⠒⠚⠛⠿⠛⣛⠉⠁⠈⢀⡼⠛⠋⠉⠁⠉⠹⢷⣾⢳⣿⡅⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡧⢤⣤⡄⠀⠉⠙⠓⠲⠶⢆⣐⣐⣶⣶⠀⠀⠀⠀⠠⣠⣼⣶⣤⣷⣿⣿⣿⣷⣿⡖⣖⠀⣶⣦⣀⠀⣤⡆⢶⢀⣾⠀⢠⠢⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣗⣻⣇⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠉⢸⣿⣿⣿⣿⣤⢠⣿⣾⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⢤⡀⡀⠀⣿⣾⡏⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠋ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⢀⣼⣿⡷⢀⣿⣿⠇⠰⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠝⡆⣠⣴⣶⣶⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⣴⣄⢠⢤⢀⢠⣷⡀ ⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠸⣻⢚⠻⢿⠿⠛⢹⠘⣻⣏⠀⠴⠟⢛⣻⣿⣿⣿⣿⣿⣿⠀⠙⠹⠀⠀⠀⠀⠀⠀⠀⢻⣧⢘⣿⣿⣏⢈⡉⠬⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠉⠈⣿⣿⡗⠀⠀⠘⠋⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠏⠈⡻⠷⠒⠚⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⡈⢋⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡧⢠⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣿⠘⠇⢰⣇⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠴⠶⠟⠛⠛⠙⠉⠙⠿⣷⣄⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⣀⣀⣁⣀⣀⣷⢨⣉⣹⣿⣿⣧⣾⣿⡤⠀⢸⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠿⠗⠂⠙⠦⠐⠛⠛⠻⠿⠿⠿⠿⢿⣿⣷⢶⠃⠀⠀⠀⠀⡀⢀⣀⣀⠀⠈⢻⣷⠀⠀⠀⢀⡽⠷⠒⠚⠛⠿⠛⣛⠉⠁⠀⡠⠞⠉⠁⠀⠀⠀⠙⢷⣿⢳⣿⡁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡧⢤⣤⡀⠀⠈⠙⠓⠲⠶⢆⣐⣐⣶⣶⠀⠀⠀⠀⢀⣠⣾⣶⣴⣾⣿⣿⣿⣿⣿⡆⡆⠀⣦⣦⣀⠀⣤⡆⢶⢀⣿⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠀⢹⣿⣷⣾⣿⣿⣿⣿⣿⣿⡅⠁⢸⣿⣿⣿⣾⣤⣬⣻⣾⣿⣶⣿⠂⠀⠀⠀⠀⠀⠀⣷⣴⡀⢸⡏⣿⡋⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠛ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠂⢸⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣇⠀⠀⣀⢀⣀⣾⣿⣿⣇⣼⣿⣿⡇⠰⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠽⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠘⡆⢾⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣶⣄⡤⢄⢀⢰⣷⠀ ⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣻⢚⠻⠿⠿⠛⢹⠘⣿⡏⠀⠴⠟⢨⣽⣿⣿⣿⣿⣿⣿⠂⠉⠙⠂⠀⠀⠄⠀⠀⠀⢹⣇⢘⣿⣿⣯⢨⡈⠬⡏⠇ ⠄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠉⠈⣿⣿⡖⠀⠀⠘⠉⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠧⠈⡻⠿⠚⠚⠀⠀⠀⠀ ⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢰⣶⠠⡎⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡘⣋⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⢠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢩⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠏⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠟⠋⠉⠙⠉⠙⠿⣷⣄⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣀⣁⣀⣀⣷⢠⣭⠿⠿⠿⣧⣾⣿⡄⠀⢸⣿⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⠦⢙⠦⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣷⢶⠂⠀⠀⠀⠀⡀⢀⣀⡀⠀⠈⢹⣷⠀⠀⠀⠀⡿⠗⠒⠚⠛⠿⠛⢛⠉⠁⢀⠞⠉⠀⠀⠀⠀⠀⢹⣧⣾⢳⣿⡁⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠓⠲⠶⢆⣐⣐⣶⣶⠀⠀⠀⠀⢰⡠⣾⣶⣤⣾⣿⣿⣿⣶⣿⠐⡖⠠⣷⣦⣤⠀⣤⣆⢶⢀⣿⠀⢠⠊⠀⠀⠀⠀⠀⢠⡀⠀⠈⡟⣓⣻⣧⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠈⢺⣿⣷⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⣿⣿⣿⣶⣾⣀⢻⣾⣿⣶⢾⠀⠀⠀⠀⠀⣠⣶⣿⣇⠀⣏⣭⣾⡏⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠛ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠁⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⣿⣾⠿⢿⣿⠇⠰⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⡆⢘⣻⣿⣿⣿⣿⣿⠿⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⣤⣄⢄⠆⢐⢸⣿⡀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣿⢛⡻⢿⡟⠛⢹⠘⣿⡏⠀⠠⠋⢸⡟⣿⣿⣿⣿⣿⡇⠀⠙⠘⠀⠀⠀⠀⠀⠀⠐⢻⣧⢘⣿⣿⣏⢩⡈⠬⡟⠇ ⠄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠉⠈⣿⣿⡆⠀⠀⠈⠉⠀⠀⠀⠀⠈⣃⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠇⠀⣿⠶⠚⠘⠃⠀⠀⠀ ⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠫⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠁⢈⡒⢋⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡍⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⢿⣧⠙⠏⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠟⠋⠉⠙⠉⠙⠿⣷⣄⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣀⣄⣠⣀⣷⣠⡭⠿⠿⡿⣧⣾⣟⡄⠀⢸⣿⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⠆⢙⠦⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣶⣶⠂⠀⠀⠀⠀⡀⢀⣀⠀⠀⠈⠹⣧⠀⠀⠀⢄⡿⠷⠒⠚⠛⠿⠛⣛⠉⠉⢠⠞⠁⠀⠀⠀⠀⠈⢻⣷⣿⢲⣿⡅⢁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠓⠒⠶⢆⣐⣐⣶⣶⠀⠀⠀⠀⢠⡠⣾⣶⣼⣾⣿⣿⣾⣾⣿⠀⠆⢠⣶⣦⣤⠀⣤⣆⢲⢀⣿⠀⢰⠀⠀⠀⠀⠀⠀⢢⣄⠀⢸⣜⣗⣻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠈⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⣿⣿⣿⣾⣼⣀⣻⣾⣿⣲⡽⠀⠀⢀⣀⣠⣾⣿⣿⡇⢸⣇⣥⣼⡏⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠁ ⢾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⡁⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠙⡆⣨⡟⣿⣿⣿⣿⣿⠯⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣠⣄⣤⢆⢐⢰⣿⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣻⢛⡻⢿⡿⠛⢹⠘⣿⡏⠀⠠⠃⢸⡏⣿⣿⣿⣿⣿⡆⠈⠉⠚⠀⠀⠀⠀⠀⠀⠐⢹⣧⢘⣿⣿⣏⢨⡀⢬⡏⠇ ⠠⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠉⠈⣿⣿⡆⠀⠀⠈⠉⠀⠀⠀⠀⠈⣵⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠈⣻⠷⠚⠛⠁⠀⠀⠀ ⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢩⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⢀⡒⢋⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣺⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠟⡛⡍⢭⠉⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢰⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣧⠙⠏⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠟⠋⠉⠙⠉⠛⢿⣧⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣀⣠⣠⣀⣷⣠⠭⢿⡿⠿⣧⣼⣿⡄⠀⢸⣿⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⠢⢙⢦⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣷⢶⠂⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⢹⣧⠀⠀⠀⣄⡿⠗⠒⠚⠛⠟⠛⢛⠉⠉⢠⠋⠁⠀⠀⠀⠀⠈⢿⡟⢿⢳⣿⡅⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡧⣤⣤⡀⠀⠉⠙⠓⠒⠶⢄⣐⣐⣶⣶⠀⠀⠀⠀⢠⣠⣶⣶⣼⣾⣿⣷⣾⣾⣿⠀⡶⢈⣶⣦⣄⠀⣤⡆⢶⢀⣿⠀⢠⠀⠀⠀⠀⠀⠀⣶⣤⠀⢱⣞⣓⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠉⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠈⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣾⣾⣌⣻⣾⣿⣶⢿⠀⠀⢀⣤⣴⣿⣿⣿⡄⣸⠃⣥⣾⡋⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⣿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⢹⣿⣿⣿⣿⣿⣿⡟⠸⢿⣿⠅⠰⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠛⡆⣤⡝⣿⣿⣿⣿⡿⠭⠀⣾⢿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣤⣄⢄⠆⢐⢸⣿⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⢛⡻⢿⡿⠛⢹⠙⣿⡋⠀⠠⠃⢿⡁⣿⣿⣿⣿⣿⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠐⢻⣧⠸⣿⣿⣧⢩⡁⢬⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠉⠈⣿⣿⡆⠀⠀⠐⠉⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠧⠈⣻⠶⠚⠙⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢰⣶⠠⡎⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢁⡂⢋⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠑⠪⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣧⠙⠏⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠟⠋⠉⠙⠉⠛⢿⣧⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣀⣠⣤⣀⣷⣠⠭⢿⡿⣿⣧⣼⣿⡄⠀⢸⣿⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⠢⢙⢦⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣷⢶⠆⠀⠀⠀⠀⠀⢀⢀⠀⠀⠈⢹⣦⠀⠀⠀⢀⡿⠗⠒⠚⠛⠿⠛⢛⠉⠁⡠⠋⠁⠀⠀⠀⠀⠉⢿⡗⢿⢲⣿⡁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡀⠀⠉⠙⠓⠒⠶⢄⣐⣐⣶⣶⠀⠀⠀⠀⢀⣠⣾⣦⣼⣾⣿⣿⣾⣾⣿⠐⡆⢨⣷⣦⣤⠀⣴⣆⢶⢀⣿⠀⢰⠀⠀⠀⠀⠀⣀⣶⣤⠀⣷⣞⣓⢻⣧⢰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠉⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠈⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⠁⢸⣿⣿⣿⣶⣼⢨⣻⣾⣿⣲⢽⠀⠀⣤⣴⣾⣿⣿⣿⣀⣿⠋⣥⣾⡋⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠋ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⡂⠀⢻⣿⣿⣿⣿⣿⣿⡗⠸⢿⣿⠇⠰⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀ ⠻⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠚⡆⣶⡏⣿⣿⣿⣿⡏⠏⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣴⣄⢄⡄⢐⢺⣿⡀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⢛⡻⣿⡟⠛⢹⠘⣿⡏⠀⠠⠃⢿⡄⣿⣿⣿⣿⣿⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠐⢻⣧⢸⣿⣿⣏⢈⡀⠬⡏⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠉⠈⣿⣿⡆⠀⠀⠐⠉⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠀⣻⠶⠚⠘⠁⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠈⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢁⡒⢋⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⡟⠻⠟⡛⡍⢭⠉⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣧⠙⠇⢈⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠶⠟⠋⠋⠝⠉⠛⢿⣧⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣀⣠⣀⣀⣷⣠⠭⢿⣿⢿⣣⣾⣿⡄⠀⢸⣿⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠟⠆⣙⠦⠐⠚⠛⠿⠿⠿⠿⠿⢿⣿⣷⢶⠆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢹⣦⠀⠀⠀⢄⡿⠗⠒⠚⠛⠟⠛⢛⠉⠉⠀⠉⠁⠀⠀⠀⠀⠉⢿⡗⢿⢲⣿⡅⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠓⠲⠶⢆⣐⣐⣶⣶⠀⠀⠀⠀⢀⣄⣾⡦⣴⣿⣿⣿⣾⣾⣿⢰⠀⢀⣷⣦⣤⠀⣤⡆⣶⢀⣿⠀⠀⠀⠀⠀⠀⢀⣬⣷⡄⢸⣥⣞⣗⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀ ⢀⠈⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠈⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣶⣬⣠⣿⣾⣿⣴⢷⠀⠀⣶⣾⣿⣿⣿⣧⣰⣞⠃⣅⣾⡋⢹⢸⡇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠃ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⡑⠸⣷⣿⡇⠸⠼⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠑⡄⣿⢸⣿⣿⣿⣿⡇⠯⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣤⣄⢀⠄⢀⢰⣿⡀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⢛⡻⣿⡟⠛⢹⠘⣿⡏⠀⠤⠃⠿⢘⣿⣿⣿⣿⡏⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠐⢻⣇⢘⣿⣿⣏⢉⡁⢬⡏⠇ ⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠉⠈⣿⣿⡆⠀⠀⠘⠉⠀⠀⠀⠀⠠⡿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠇⠀⣻⠷⠚⠘⠀⠀⠀⠀ ⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠁⢁⡒⢋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡄⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣧⠙⠏⢸⣇⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡤⠶⠟⠋⠋⠙⠉⠛⠿⣧⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣀⣠⣀⣀⣷⣠⣭⣽⣿⢿⣧⣼⣿⡤⠀⢸⣿⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠏⠂⣙⢦⠒⠚⠛⠿⠿⠿⠿⠿⢿⣿⣶⢶⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢹⣦⠀⠀⠀⠀⠿⠗⠒⠚⠛⠟⠛⢛⠉⠉⠐⠋⠉⠀⠀⠀⠀⠈⢿⡟⢿⢲⣿⡅⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠓⠒⠶⢆⣐⣐⣶⣶⠀⠀⠀⠀⢀⣤⣶⡦⣴⣿⣿⣿⣾⣾⣿⠰⠂⢠⣷⣦⣤⠀⣤⡆⢶⢂⣿⠀⠀⠀⠀⠀⢀⣠⣼⣷⡄⢸⢥⣞⣓⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠈⠁⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠈⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣬⣬⣿⣾⣿⣶⣷⠀⠐⣿⣿⣿⣿⣿⣧⣰⣞⠋⣥⣾⡋⢹⢸⡇⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠿⠿⠛⠁ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠀⣻⢿⣿⣿⣿⣿⣿⣖⠸⢿⣿⠁⠸⠼⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠕⡌⣿⢸⣿⣿⣿⣿⡄⠭⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣤⣄⣀⠆⢐⢸⣿⡀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣻⢚⡻⢿⡟⠙⢹⠘⣿⣏⠀⠠⠃⠿⣸⣿⣿⣿⣿⡇⠒⠀⠛⠛⠀⠀⠀⠀⠀⠀⠐⢻⣧⢘⣿⣿⣇⢨⡀⢬⡏⠇ ⠄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠉⠈⣿⣿⡆⠀⠀⠘⠋⠀⠀⠀⠀⢻⡿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠈⣻⠶⠒⠚⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⣶⠠⡆⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠁⢀⡒⢉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡇⡗⠌⣆⣇⣇⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⡑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠿⣧⠙⠏⢸⣧⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡤⠶⠟⠋⠋⠙⠍⠛⢿⣧⡀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⣀⣁⣀⣀⣷⣠⣭⣿⡿⢿⣣⣼⣿⡤⠀⢸⣿⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠿⠏⢆⣙⢦⠐⠚⠛⠿⠿⠿⠿⠿⢿⣿⣾⢶⠆⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⢹⣦⠀⠀⠀⣀⠿⠗⠒⠚⠛⠟⠛⢛⠋⠉⠀⠋⠉⠀⠀⠀⠀⠙⣿⡗⣾⢲⣿⡁⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡧⣤⣤⡄⠀⠉⠙⠓⠲⠶⢄⣐⣐⣶⣶⠀⠀⠀⠀⢀⣄⣶⡦⣷⣿⣿⣿⣾⣾⣿⠰⡢⢀⣶⣦⣤⠀⣤⡆⢲⢀⣿⠀⠀⠀⠀⢀⣀⣴⣾⣷⠀⢸⢥⣞⡓⢻⣧⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄ ⢀⠉⠉⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠀⠀⠀⠀⠈⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⣿⣿⣿⣾⣾⣬⣿⣾⣿⣶⣷⠀⠘⣿⣿⣿⣿⣿⣇⣰⣌⠃⣤⣿⡋⢹⢸⡇⣀⣀⣤⣤⣶⣶⣶⣿⡿⠿⠿⠿⠛⠁ ⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⡄⢀⣽⢿⣿⣿⣿⣿⣿⡆⠘⢿⣿⡁⠰⠴⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠐⣌⣿⢸⣿⣿⣿⣿⡄⠭⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣤⣀⣄⢄⢐⢰⣿⡀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣻⢛⡻⢿⡟⠛⢹⠘⣿⠏⠀⡠⠫⡛⣸⣿⣿⣿⣿⡇⠒⠐⠟⠹⠀⠀⠰⠀⠀⠀⠐⢻⣧⢸⣿⣿⣿⢉⡈⢬⡟⠇ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠋⠀⠀⠀⠀⠀⠉⠈⣿⣿⡖⠀⠀⠘⠋⠁⠀⠀⠀⢿⡿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠀⣻⠶⠚⠚⠀⠀⠀⠀ ⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⣶⠠⡎⣟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⡒⢋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⢻⠛⡛⡍⢭⠉⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⡁⡬⡄⡀⡇⡇⡗⠌⣆⣇⣇⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣆⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠟⠏⢉⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠙⢸⠐⡧⠑⢿⡄⢧⢱⢀⣰⣐⣸⣴⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣧⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⣿⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⣷⠰⡐ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠊⠻⠿⣿⣿⣿⣿⡿⠟⠻⣷⣯⣬⣶⡬⠷ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠙⠟⡆⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠟⠟⠛⠈⡾ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡉⢭⠉⣿⣿⡇⠀⠀⣠⣶⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣿⣷⣽⣿⣿⠏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠼⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⠇⡔⠙⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠁⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣄⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠏⠏⢉⠋⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢠⢀⣰⣐⣸⣴⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠟⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣦⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠟⠻⣷⣿⣾⣿⣷⠦ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠄⠛⠟⡆⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠟⠋⠘⡿ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡇⠀⠀⣠⣶⡏⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠸⣿⣷⣽⣿⣟⠏⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠾⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⡃⡔⠙⠋⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠑⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣄⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠏⠏⢉⠋⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢡⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠟⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣦⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣵⡔⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣶⣾⣿⣿⣿⣿⣤⣩⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠾⠋⣣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣾⣶⣟⣯⣤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣤⣦⣤⠄⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣀⣠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⢟⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣦ ⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⡄⠀⠀⠀⠀⢿⢿⣿⡿⢿⣶⣶⡶⠂⠩⠽⠿⢿⡛⠛⠙⠙⠉⠉ ⠀⢲⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⣿⡿⠀⠀⢠⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣥⣖⣤⡄ ⠀⢀⣛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠴⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣿⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢍ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⡿⠛⣿⣻⣾⢷⣾⠧ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠄⠙⠟⣆⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠟⠟⠋⠈⡿ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡇⠀⠀⣠⣶⡏⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⠋⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠼⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡆⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⡇⡔⠙⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠉⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣄⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠏⠏⢩⠋⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢠⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠟⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣦⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣴⣿⣿⣿⣶⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠶⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣿⡅⣤⣆⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣀⣤⣄⡀⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣀⣤⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⡭⣽⡟⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣞⣾ ⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣄⠀⠀⠀⠀⠿⢿⠶⠶⠶⣦⣤⠿⠂⠻⠿⠿⠿⣛⡛⠋⠉⠉⠉ ⠀⢲⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⣿⡿⠀⠀⢠⣦⣶⣾⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣗⢑⣀⣄ ⠀⢀⣛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢀⠿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⢰⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢽ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⡅⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣪⣆ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡐⠂⠀⠈⠍⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⡿⠛⣷⣿⣿⣾⠿⣄ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠄⠛⠟⣄⠀⠀⠀⠀⠀⢸⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢘⣿⡟⠟⠛⠀⡽ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡉⢭⠉⣿⣿⡇⠀⠀⣠⣴⡏⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⠋⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠾⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⡇⡔⠘⠋⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠋⣻⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣄⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠏⠏⢉⠋⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢠⢀⣰⣐⣸⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠟⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣦⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣦⣤⣿⡿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠖⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣄⣀⣁⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⣀⣠⣴⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠭⢭⡛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣒⣶⣿ ⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣄⠀⠀⠀⠀⠿⠷⠶⠦⠶⣤⣴⠶⠗⠹⠿⠿⠿⠛⠛⠛⠉⠉⠉ ⠀⢲⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⣿⡿⠀⠀⢠⣶⣶⣶⣶⣿⣿⣷⣶⣿⣿⣿⣷⣿⣛⣿⣿⡗⠀⢀⣀ ⠀⢀⣛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠂⢀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢰⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠧⠤ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣿⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⡀⠐ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⡿⠛⣟⣗⣷⣼⠥⢂ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠛⠟⣄⠀⠀⠀⠀⠀⢸⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠐⢘⣿⡿⠟⠛⠀⡰ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡟⠻⠛⡛⡍⢭⠉⣿⣿⡇⠀⠀⣠⣴⡏⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⡋⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠾⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⠙⠁⡬⡄⡀⡇⡆⡗⠌⣆⣃⣇⣿⣦⣿⣿⠇⡔⠘⠋⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠑⣻⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣃⣄⣧⣧⣥⣷⡷⠿⣾⢿⡟⡟⠟⠏⠏⢉⠋⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⢩⢹⠘⢸⠐⡧⠑⢿⡄⢧⢠⢀⣰⣐⣸⣴⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠟⠿⣿⠿⢿⠿⠿⢿⣿⣿⣧⣘⣌⣨⣦⣼⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⢶⣷⡆⢸⣿⣷⣩⣭⣁⣕⣿⣽⣠⣰⣿⣩⣀⣇⣯⣚⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿ ⣿⣿⣿⣷⠀⠘⡚⣿⣸⣿⣿⣿⡿⢿⣿⣿⣟⠛⣛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⡇⢻⢩⠙⡍⡿⡹⣹⡽⡹⡍⡙⣿⣍⡇⣿⡇⡯⡝⡹⡍⣙⣿⡜⠃⣷⢫⠝⡝⡭⣏⣽⢭⠋⣭⣽⡇⢫⢽⠛⣿⢩⠛⣍⣿⢸⡇⣯⣽⢹⢩⣫⣿⡍⡏⡝⢫⢸⡿⡉⣿⢸⡇⡇⡝⢏⢩⢹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⡷⣵⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⠰⣉⠏⡇⣿⢹⠟⣿⣿⣶⢾⣇⠇⡏⡹⢽⡏⣿⡯⢏⡱⡅⡏⡟⢿⡙⣿⡱⢹⠿⡏⣿⣿⢱⢹⡇⣉⣾⠹⠉⡏⣿⡱⡅⡏⣿⠱⢹⡇⢎⢹⠸⣏⠯⡿⢟⢹⢉⠯⡿⢿⢹⢱⠉⣯⣾⠑⢴⢳⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⡟⠛⣿⢽⡍⡏⡟⢹⣿⠭⡛⠛⣻⠛⢻⣟⠹⢻⠛⢛⢻⣟⠛⢻⠓⡏⣻⣟⠛⡛⡟⠋⢹⡟⠟⢻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⢀⣠⠂⠀⠀⠀⣿⣿⣿⣲⢳⠳⡷⠾⠶⢷⠿⠾⡟⠿⡗⡾⠿⢾⡞⢓⣾⣾⣾⣶⣾⣷⣾⣾⣾⣷⣿⣿⣷⣷⣷⣷⣾⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⢰⠇⠀⠀⠀⠀⣿⣿⣿⣿⣤⣴⣧⣥⣧⣽⣤⣮⣦⣮⣧⣧⣤⣾⣷⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣷⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠶⠶⣶⣶⡆⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⢻⠉⢙⠍⢙⠙⡏⡋⡋⡋⠉⢹⣽⠨⡋⠉⠽⠙⠉⣝⠉⡏⣙⠉⢩⢯⠍⢩⣿⠉⡋⣻⢉⠛⠹⠉⡏⠹⡍⣿⠛⡫⡯⠉⣝⠍⢩⡝⠫⢽⣿⣿⣿⣿⣿⣿⣿⣿⡝⠛⠁⠐⠛⣭⡇⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣟⣝⢛⢟⠟⠛⣿⣛⠛⢛⠟⡟⢛⠟⣿⡻⠛⡟⠛⠻⣻⡛⡿⢻⠛⢓⣿⠙⠟⢿⢙⠟⢻⡟⠻⠻⠛⣿⠻⢻⠟⡛⡛⡻⠛⢟⠏⢛⡟⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⠀⣿⡇⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡷⡶⠖⡿⡶⢶⢾⢷⢶⡞⠶⠷⣷⠶⠟⠓⡾⠶⢶⠾⡾⡷⣷⠶⢷⠶⣿⢾⠷⢾⠚⢲⣾⣧⣾⣶⣶⣿⣶⣾⣷⣶⣷⣾⣶⣶⣷⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⡏⣿⡇⣀⠀⢸⡀⣿⣇⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⣦⣤⣬⣤⣭⣤⣤⣴⣧⣮⣤⣷⣥⣼⣤⣮⣥⣼⣤⣧⣮⣾⣤⣧⣤⣷⣽⣯⣲⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣯⣾⣮⡿⢟⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣻⢿⠿⠿⢿⡻⣿⠿⠿⣿⣻⡿⠿⣿⣿⢿⣿⠿⢿⠿⠿⣿⡿⡟⣿⠿⢻⣿⡿⢿⣿⠿⡿⢿⡻⠿⡟⠿⡿⢿⡿⢿⢿⠿⠿⢿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠿⢋⡀⢀⣀⡀⠀⢙⣿⠿⣿⣿⣿⢾⡶⣶⣶⣶⣶⠾⣶⣾⠾⡶⣾⡿⣷⢾⡿⣶⣶⣿⡶⣼⡿⣶⣿⣼⣷⣿⢶⣾⣿⣷⣶⢿⣷⣷⣿⣶⣶⣷⡼⣷⢿⡷⡤⣯⢴⣶⣿⣷⣶⣮⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⢀⣿⣑⢔⣭⡺⢽⣸⣧⠀⣿⣿⣿⣤⣦⣤⣼⣤⣭⣼⣿⣮⣼⣾⣤⣥⣼⣼⣼⣧⣥⣮⣷⣼⣥⣯⣴⣤⣯⣿⣤⣯⣤⣿⣼⣤⣧⣤⣾⣧⣤⣧⣤⣷⣧⣨⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⡎⠉⡉⠽⣛⠔⠕⠊⢫⣴⣿⣿⣿⣙⣵⣉⣉⣏⣋⣽⣯⣋⣳⣗⣩⣉⣹⣏⣽⣿⣰⣣⣉⣻⣿⣉⣩⣌⣉⣿⣈⣈⣗⣉⣏⣹⣘⣑⣅⣸⣎⣹⣣⣹⣇⣈⣘⣉⣑⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠉⠀⠉⢀⣠⣿⣿⣿⣿⣿⢉⡙⠹⠋⠟⢙⠙⢻⡟⢽⢹⡩⢩⡏⢻⡝⡝⠻⠙⢻⡏⢻⣿⡟⡟⢻⠛⣹⡟⡛⣹⡛⢻⡻⡟⢫⣿⠛⣿⡟⢟⠛⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣏⠏⣟⠽⡙⢝⡹⠉⣭⢽⠋⣯⠛⢽⢏⡙⠽⠽⠉⢫⠋⠹⣯⠋⣿⠉⣝⡝⠛⢋⡫⢹⠛⡝⠙⢽⡏⢩⡋⢻⠋⠏⠋⢩⡋⢻⢩⠛⠋⠙⠍⣏⠙⢽⣿⣿⣿⡻⠉⠉⢿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⠿⣻⡛⣿⠻⢛⡛⠻⡻⢟⠛⠻⡛⡿⠻⠻⢟⡟⢻⡟⠛⡛⠻⠻⢛⡛⢻⢟⠛⡻⠛⢟⠟⢟⠟⣻⡟⡻⠻⢛⠻⡟⠿⢻⣿⠛⢿⠟⠿⢻⡻⡓⢞⣿⣿⣿⡅⠀⠀⠈⠿⡟⠿⠂⠀⣸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡷⡶⢿⢶⣷⡶⡾⢶⡶⣷⢶⣶⣶⢶⠷⠾⣶⣶⣷⣾⣷⣶⣶⣾⣶⣾⣷⣾⣷⣦⣶⣶⣾⣶⣾⣦⣼⣧⣶⣶⣾⣶⣷⣶⣾⣿⣾⣶⣷⣶⣾⣾⣷⣤⣿⣿⣿⣷⣤⡀⢸⡟⡇⢀⣀⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⣤⣵⣥⣬⣧⣧⣼⣧⣤⣼⣧⣴⣤⣤⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠇⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣆⠀⣿⣿⣃⣉⣿⣯⣩⣹⣿⣙⣿⣩⣮⣻⣿⣃⣹⣿⣨⣹⣿⣁⣉⣿⣉⣹⣽⣻⢹⣯⣹⣯⣁⣹⣿⣉⣝⣿⣋⣉⣀⣿⣇⣣⣿⣉⣿⣻⣯⣱⣝⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⢯⡆⠀⠀⢰⣳⢯⣿⠏⠀⣿⣿⣿⣭⡿⡟⢛⣿⠙⠛⠟⢹⡟⢻⡛⡛⠛⢛⠋⡟⠛⠛⡋⢛⠟⢻⣿⢻⡛⠋⣻⣛⢻⡟⢙⣟⠛⣻⡏⠻⣟⢛⣿⡛⢛⣿⢹⢻⠛⠛⣻⡛⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⢸⡴⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⢿⣿⠿⣾⠿⠿⣶⡷⠶⣾⠓⠾⣿⡶⠾⡿⡲⣷⣷⣿⣷⣷⣿⣿⣿⣿⣶⣾⣿⣾⣿⣷⣿⣷⣾⣿⣿⣿⣾⣷⣿⣶⣿⣷⣾⣷⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣦⣤⣤⣤⣦⣶⣶⣖⣦⣤⣿⣿⣿⣿⣶⣿⣷⣷⣿⣿⣶⣿⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⣀⢀⠀⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⠀⠀⠀⠈⡁⣉⡉⡉⠡⡜⣀⡄⣉⣃⣉⣈⣁⢉⡉⠥⢨⡀⣈⢀⣀⣈⣁⠉⡀⠉⢉⣁⡁⣍⣀⡁⣉⢁⠁⢠⣉⡁⡈⠭⠍⠩⠉⢩⡉⣀⣁⡁⡈⣉⣉⡙⣍⢉⡈⠉⠉⠉⠉⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⠀⠀⠀⠠⡤⠠⠤⠄⢠⠤⠤⠄⠠⠀⠀⠀⠰⠈⠄⠀⠀⠤⠥⠤⠠⠠⠠⠀⠀⠀⠠⠌⠠⠰⠤⠀⠄⠤⠤⠠⠤⠠⠄⠀⠄⠠⠀⠄⠠⠤⠄⠤⠠⠠⠄⠴⠄⠤⠴⠠⠤⠤⠀⠴⠀⠤⠄⠄⠤⠤⠀⠀⠀⢸⣿ 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In_Light_of_Fast-Accelerating_Deterioration_—_Sometimes_Weaponisation_— Getting_Off_the_World_Wide_Web_(to_the_Extent_Feasible)_Makes_You_Saner_and Less_Susceptible_to_Manipulation,_Lies⠀✐ Posted in Deception, Free/Libre_Software, GNU/Linux, Microsoft, Windows at 11: 56 am by Dr. Roy Schestowitz Video_download_link | md5sum 2f8bde45095120607075cdc4e3549b56 http://techrights.org/videos/www-as-toxic-platform.webm Summary: Almost no sites are speaking about it (probably because they have no presence on the Internet except on the Web), but it’s time to motivate more people to get off the Web, for their own good and for society’s sake… THE WEB as a source of accuracy-assured or validated information — or any meaningful information at all (like investigative journalism) — died a few years ago. Many ‘articles’ are just referrer spam (or Amazon affiliate marketing). A lot of so-called ‘news’ sites are in the business of selling out. Some PR agents contact them to publish “plugs” on clients’ behalf. That’s not news! “Weaponising the Web (for spreading malicious but self-serving lies) isn’t just the ‘trade’ of nation states. Corporations and oligarchs do the same.”As we noted this morning, even Google News (“Gulag Noise”) became a hub of Microsoft misinformation_and_revisionism (basically corporate propaganda sold as “news”; ZDNet hasn’t even mentioned the big news from Germany!). We’re meant to think it’s “normal” to search for Linux news and instead get shilling of a password stealer_from_Microsoft as the top result! As an associate told us an hour ago, Microsoft “will be working overtime to promote revisionist histories concerning Munich: saturate, diffuse, confuse…” Newer articles are prioritised over older ones that are more accurate, so one can game the system and distort memories. “They will try to muddy the water and delay at the very least,” the associate continued, “and articles older than a few years are omitted from search results completely.” Weaponising the Web (for spreading malicious but self-serving lies) isn’t just the ‘trade’ of nation states. Corporations and oligarchs do the same. Nothing is beyond their reach; not_even_social_control_media,_which_is_all_about manipulation_(it's_the_business_model). In many ways, the Web has outlived its usefulness and it actively does harm too, e.g. by inciting people, based on falsehoods, or leading people into deep debt in pursuit of social acceptance (social control media like Facebook leads to insecurities). Earlier this year we ended up moving to our_own_IRC_network and to_Gemini (self-hosted from home) — things we had planned last year but never found the time to properly implement. The Web should never have had a near monopoly on hypertext; there’s more to the Internet than HTTP and HTML/ JavaScript (some sites are nowadays more JavaScript than HTML; they’re like Flash with ActionScript). We need to keep reminding people that having an Internet connection means more than just access to “Web” or “Web apps” or “Web browser”. IRC, for instance, needs neither Web nor “app”. It’s also widely supported by many devices, includes decades-old devices. The same is true for Gemini (many_client_implementations_exist_already;_all_of them_are_Free_software) and based on the “Daily_Stats” in Techrights we’ll have exceeded 400,000 pages requests over gemini:// in just 23.5 days of November. Misinformation and advertisers have thus far been off_limits in gemini://. Even if they attempted to infiltrate “Geminispace”, they would easily be shunned and marginalised because cross-capsule scripting (akin to XSS or sharing between domains) isn’t possible and the layout, which is strictly enforced, is chronically unsuitable_for_ads. █ ䷩ 𝚕𝚒𝚗𝚎 2154 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/23/web-as-a-spamfarm/#comments Gemini version at gemini://gemini.techrights.org/2021/11/23/web-as-a-spamfarm/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.23.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Black_Friday_SPAM_on_the_World_Wide_Web:_A_Reminder_That_the_Web_is_a_Dying Platform,_Languishing_Due_to_Marketing_and_Misinformation⠀✐ Posted in Site_News at 7:37 am by Dr. Roy Schestowitz Gemini does not have this problem, at least not yet 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Gemini_capsules_2021-11-23⦈_ Credit: Visualised_statistics by Botond Summary: The junk that overruns the Web this ‘Black Friday’ week (consumerism ‘on steroids’) is a good reminder that the Web isn’t healthy for the mind anymore; it’s mostly spying on people, trying to compel them to buy particular things or vote a certain way The “burning platform” which has long been on the demise as a source of information (many_'news'_articles_or_'reviews'_are_just_paid-for_plugs) cannot be repaired both for technical reasons (it’s controlled_by_monopolistic saboteurs) and for reasons connected to infiltration, both by commercial actors and political actors. It’s being weaponised and a growing number of people have become aware of it. That’s why more people appear to have returned to blogging this past year (no more social control media; even the popularity of YouTube wanes). There’s impact on privacy, performance, and accessibility (DRM for instance). Today’s “open” Web is just yesterday’s Adobe Flash, albeit openwashed a bit. Incidentally, yesterday the Google-sponsored EFF published “Manifest V3: Open Web Politics in Sheep’s Clothing” and to quote key parts (it even bit the hand that had fed it): “The security and privacy claims that Google has made about web extensions may or may not be addressed with Manifest V3. But the fact remains that the extensions that users have relied on for privacy will be heavily stunted if the current proposal moves forward. A move that was presented as user-focused, actually takes away the user’s power to block unwanted tracking for their security and privacy needs…“ “Let’s try to get more people to move elsewhere, e.g. Gemini for hypertext.”As we’ve stated before, eventually we need to accept that the Web is no longer open and Web browsers are mostly just clones of some proprietary (with DRM) monoculture that harms disabled people and mostly serves the copyright cartel. Let’s try to get more people to move elsewhere, e.g. Gemini for hypertext. Decentralised IRC is good for communication and it’s widely supported, it has minimal system requirements etc. IRC networks grew_in_number_significantly after_the_collapse_of_Freenode. 89_new_networks_were_recently_registered. According to Stéphane Bortzmeyer’s Gemini pages: “There are [as of moments ago] 1820 capsules. We successfully connected recently to 1474 of them.” And only two days ago we_noted_that_the_1,800_milestone_had_been_crossed. So it grew by another ~7 per day since then. The momentum is still there! █ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⠟⣿⡏⠋⠻⣿⢛⡿⠛⣻⣿⣿⠋⣿⢭⣟⠛⢿⣻⠟⠙⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣛⣛⣛⣻⣿⣍⢿⠟⠋⡟⠽⢻⢟⢛⢿⡛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠝⣿⡇⣿⣿⣿⣿⣿⣿⠛⠿⠿⡿⣿⡿⠿⡟⣻⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠏⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⡳⣻⣾⣿⡇⣿⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣷⣴⣷⣶⣶⣾⣶⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⢉⣿⡅⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣣⣵⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⣿⣿⣿⠻⢋⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣑⣿⣯⣛⣵⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣀⡄⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣵⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠒⣿⣿⡿⢛⢊⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⣿⣯⣍⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣠⣤⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠙⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣀⣴⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣒⣿⣿⡿⣛⣬⣿⡆⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠋⠀⡀⣴⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⣠⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠿⠛⠋⠉⠀⠀⣠⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⠩⣡⣿⡇⣿⣿⡇⢀⢀⣤⣶⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣟⣭⣠⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⡟⢷⣿⣿⣿⣿⣿⣿⣿⡿⠟⢷⣿⣿⣿⣿⣿⣿⣿⡿⡟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⡝⣧⣼⣾⣿⣿⣿⣿⠿⡻⡽⣭⣼⣾⣿⣿⣿⣿⠿⡻⡽⣭⣼⣾⣿⣿⣿⣿⠿⡻⡽⣭⣼⣿⣿⣿⣿⣿⡿⡛⡝⣥⣼⣾⣿⣿⣿⣿⡿⡛⡝⣵⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣗⣫⣴⣾⣿⣿⣿⣿⣿⣿⣇⣮⣷⣿⣿⣿⣿⣿⣿⣿⣇⣦⣷⣿⣿⣿⣿⣿⣿⣿⣇⣦⣷⣿⣿⣿⣿⣿⣿⣿⣇⣪⣷⣿⣿⣿⣿⣿⣿⣿⣇⣪⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2256 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.23.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_23/11/2021:_Libreboot_20211122,_Deepin_Linux_20.3,_Amazon_Linux_2022, and_Mabox_Linux_21.11_Released⠀✐ Posted in News_Roundup at 6:51 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Audiocasts/Shows⠀➾ # ⚓ How_to_install_Wire_Desktop_on_Elementary_OS_6.0_– Invidious⠀⇛ In this video, we are looking at how to install Wire Desktop on Elementary OS 6.0. # ⚓ Ask_Stupid_Linux_Questions_And_Get_Useful_Answers_– Invidious⠀⇛ You were lied to in school some questions are stupid but that doesn’t mean it’s a bad question before you ask anybody for help you first need to learn how to actually ask a question in a way that will get people to want to help you. # ⚓ Slow_Down_In_Your_Work_To_See_Real_Gains_–_Invidious⠀⇛ I woke up this morning intending to go through my usual routine: go to the gym and workout and then head to the office to make a video. But shortly after waking up I realized that I didn’t feel like doing anything today. So I’m taking the day off…and making this video. o § Applications⠀➾ # ⚓ Manage_Flatpak_Permissions_Graphically_With_Flatseal⠀⇛ The newer versions of Android give you a more granular control over the access and permission an individual app can have. This is vital because many applications were (are) abusing the system permissions. Download a weather app and it will ask to access your call logs as if that has anything to do with the weather. Why am I talking about Android app permissions? Because that is something you could relate with this application’s functioning. You probably already know what Flatpak is. These are sandboxed applications with selected access to system resources like file storage, network interface etc. # ⚓ Top_5_Video_Players_for_Ubuntu⠀⇛ With advancements in GUI OS design, most operating systems now have a default multimedia player. These multimedia players can provide good quality audio and video playback and offer support for a wide variety of video file formats. Despite their reliability, you may want to switch to a third-party media player because of the wide variety of features they have to offer. These multimedia players are designed to provide the most control to their users. If you’re someone looking for a different multimedia player for Ubuntu, then you’ve come to the right place! We’ve compiled a list of the best video players that provide extensive support for different file types and a plethora of features that will make the default video player seem lackluster. Without further ado, here’s the list of the top 5 video players for Ubuntu… # ⚓ Top_Tools_for_Taking_and_Editing_Screenshots_on_Linux⠀⇛ In the modern era of Digital communication, we have access to modern devices that simplify our lives through their ease of use. These devices include our handheld units, digital wristbands, modern computing systems, and many more. However, several other tools and utilities can make our daily tasks comparatively easier and less daunting should we have the right ones on our systems. A screenshot application can be a nifty tool for our operating systems to save time and provide additional features that enable us to cut corners and be more productive. While we can take screenshots with the stroke of a few keys or through buttons on our handhelds, the ones discussed here have fortes that make them outshine others in various areas. So without further ado, let us delve into the top tools for snapping and editing screenshots on Linux and analyze their strong points… o § Instructionals/Technical⠀➾ # ⚓ How_to_Install_Animated_Plymouth_During_Boot_Process_in Arch_Linux⠀⇛ A tutorial on how you can install animated Plymouth during boot process in Arch Linux. # ⚓ Tips_and_tricks_of_using_wget_Linux_command_|_FOSS_Linux⠀⇛ Wget is a command-line, open-source utility to download files and web pages from the internet. It gets data from the internet and displays it in your terminal or saves it to a file. The wget utility is non-interactive. You can get the most out of it through scripts or even schedule file downloads. Typically, web browsers such as Firefox or Chromium also download files except, by default, they render the information in a graphical window and require a user to interact with them. Alternatively, other Linux system users use the curl command to transfer data from a network server. The article illustrates how to use the wget command to download web pages and files from the internet. # ⚓ How_to_install_Pycharm_with_Python_3.9.2_on_a_Chromebook⠀⇛ Today we are looking at how to install Pycharm with Python 3.9.2 on a Chromebook. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ How_To_Install_OpenVPN_Server_on_AlmaLinux_8_–_idroot⠀⇛ In this tutorial, we will show you how to install the OpenVPN server on AlmaLinux 8. For those of you who didn’t know, OpenVPN is a robust and highly flexible open-source VPN software that uses all of the encryption, authentication, and certification features of the OpenSSL library to securely tunnel IP networks over a single UDP or TCP port. A VPN enables us to connect securely to an insecure public network such as a wifi network at the airport or hotel. Typically business and enterprise users need some sort of VPN before they can access services hosted at your office. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the OpenVPN on an AlmaLinux 8. You can follow the same instructions for CentOS and Rocky Linux. # ⚓ How_to_use_Search_Monkey_to_find_files_and_folders_on_Linux fast⠀⇛ Need to find files and folders on your Linux PC fast? Check out Search Monkey! It’s an excellent application that can find files and folders with lightning speed. This guide will show you how you can use Search Monkey to find files on your Linux system. # ⚓ Upgrading_Homelab_Kubernetes_Cluster_from_1.21_to_1.22_| Lisenet.com_::_Linux_|_Security_|_Networking⠀⇛ Calico 3.21 has been released with support for Kubernetes 1.22. Kubernetes 1.22 release brings alpha support for swap: we can now run nodes with swap memory. # ⚓ How_to_Install_Dota_2_on_Ubuntu⠀⇛ Dota 2 is one of the most popular free-to-play games that are available on Steam. The wide selection of characters referred to as “Heroes” combined with various spells and abilities ensures that every game in this MOBA is different from the rest. The beta version of Dota 2 was released on the 9th of July, 2013. Since then, its player base has only seen an increase every year. This is because Dota 2 offers a competitive esports environment like no other game. Dota 2 was the first game to have a tournament where the prize pool was more than 1 million USD. This was an astronomical amount for the players at that time. The tournaments only got bigger and more luxurious every year, with the prize pools reaching as high as 25 million USD. Despite having existed for more than eight years, Dota 2 continues to thrive and refuses to show signs of slowing down anytime soon. # ⚓ VRChat_Starter_Guide_for_Linux⠀⇛ VRChat is a virtual reality MMO platform that was released in 2017 by VRChat Inc. The game was initially released for Microsoft Windows and was accessible by Windows Mixed Reality headsets, Oculus Rift, HTC Vive, etc. It was later launched for Oculus Quest platforms in May of 2019. VRChat can also be played without a virtual reality headset on a PC. However, we recommend using a VR headset to get the finest VRChat experience. # ⚓ How_To_Save_Output_Of_A_Linux/Unix_Command_To_A_File_– nixCraft⠀⇛ I am new Linux and Unix-like system user who recently switched from MS-Windows XP. How do I save the output of a Linux / Unix ls command to a file named “lists.txt” using command prompt or POSIX shell such as SH/KSH/BASH? # ⚓ nixCraft_–_Linux_/_Unix_tutorials_for_new_and_seasoned sysadmin_||_developers⠀⇛ We all know we can use the xclip Linux command-line interface to X selections, aka clipboard. The xclip command to copy any Linux command output to the Linux clipboard directly. o § Distributions⠀➾ # ⚓ Top_8_Reasons_to_Use_Garuda_Linux⠀⇛ Have you been going back and forth between multiple Linux flavors in search of an exciting experience? Or perhaps you are coming from a Windows or MAC environment and want to try out a Linux distribution that offers a superb user experience with a colorful and zestful UI? If you are any of those, then Garuda Linux is one of the popular Linux distros to check out. Garuda Linux is a relatively new Arch-based Linux distribution that offers an unparalleled user experience. It comes in a stunning array of colorful and vibrant desktop environments including KDE, Xfce, Wayfire, GNOME, Qtile, Sway, i3wm, and LXQt-win. Since its release, Garuda Linux has won accolades for being one of the most user-friendly and exciting Linux flavors to use given its otherworldly appeal. Garuda Linux is a rolling release distribution. It comes with a huge collection of software and uses Pacman as its package manager. # § New Releases⠀➾ # ⚓ Deepin_Linux_20.3_Is_Out_as_One_of_the_First_Distros Powered_by_Linux_Kernel_5.15_LTS⠀⇛ Deepin Linux 20.3 is here almost two months after Deepin Linux 20.2.4 and it upgrades the stable kernel to Linux 5.15, bringing users features like a brand-new and fully functional NTFS file system implementation, support for 12th Gen Intel processors, in- kernel SMB server, realtime preemption locking, and many other goodies. # ⚓ Mabox_Linux_21.11_Herbolth_released⠀⇛ After almost half year of development, the next major Mabox Linux 21.11 release codename Herbolth is ready for download. # § BSD⠀➾ # ⚓ [Old] BSD,_Linux,_and_Snarfs⠀⇛ Why isn’t snarf going into M$ corporations, Windows user groups, Windows mailing lists, or even general computer groups talking about BSD’s superiority to Windows? Because he lacks the necessary guts and social skills. Snarf is too wimpy to endure the taunts and rejections of the Windows crowd. So he comes as a friend and fellow Unix guy to the Linux group, then slowly starts his put-downs and recruiting. # § IBM/Red Hat/Fedora⠀➾ # ⚓ AWS_commits_to_update_its_own_Linux_every_other_year •_The_Register⠀⇛ Amazon Web Services has announced that it will release an updated version of its own Linux every two years, starting with Amazon Linux 2022, which it is previewing now. The cloud colossus launched its first Linux distro in 2010, and seven … years … later … delivered a successor. In the name of speeding things up a bit, Jeff Bezos’s computer rental service has promised a new release every other year, each of which will be supported for five years and receive quarterly tweaks. AL2022 uses the Fedora project as its upstream, but AWS may add or replace specific packages from other non-Fedora upstreams. The preview of AL2022 is based on Fedora34, while the full release will move up to Fedora 35 (which was released on 2 November). The SELinux security module is enabled and enforced by default in AL2022, but EC2 instances running the OS won’t automatically implement patches or security updates. Users can instead choose to automate installation of packages, or patches, or both. # ⚓ Announcing_preview_of_Amazon_Linux_2022⠀⇛ Today, we are announcing the public preview of Amazon Linux 2022 (AL2022), Amazon’s new general purpose Linux for AWS that is designed to provide a secure, stable, and high-performance execution environment to develop and run your cloud applications. Starting with AL2022, a new Amazon Linux major version will be available every two years and each version will be supported for five years. Customers will also be able to take advantage of quarterly updates via minor releases and use the latest software for their applications. Finally, AL2022 provides the ability to lock to a specific version of the Amazon Linux package repository giving customers control over how and when they absorb updates. Customers use a variety of Linux based distributions on AWS, including Amazon Linux 1 (AL1) and Amazon Linux 2 (AL2). These have become the preferred Linux choice for AWS customers because of no license costs, tight integration with AWS-specific tools and capabilities, immediate access to new AWS innovations, and a single-vendor support experience. AL2022 combines the benefits of our current Amazon Linux products with a predictable, two year release cycle, so customers can plan for operating system upgrades as part of their product lifecycles. The two year major release cycle provides customers the opportunity to keep their software current while the five year support commitment for each major release gives customers the stability they need to manage long project lifecycles. # ⚓ Amazon_Linux_2022_Released_–_Based_On_Fedora_With Changes_–_Phoronix⠀⇛ Amazon Web Services has made Amazon Linux 2022 now publicly available in preview form as the newest version of their Linux distribution. Amazon Linux / Amazon Linux 2 had been based on a combination of RHEL and Fedora packages while in today’s Amazon Linux 2022 release they note it’s explicitly based on Fedora. Besides apparently being more Fedora oriented now than RHEL, with Amazon Linux 2022 they are transitioning to a formal two year release cadence between their releases while having quarterly point releases. AWS intends to provide major Amazon Linux updates every two years while each major release will see five years of support and quarterly minor release updates. o § Devices/Embedded⠀➾ # ⚓ This_mini_PC_has_an_ARMv8_processor_and_AMD_Radeon_RX_550 graphics⠀⇛ At the heart of the system is Phytium’s D2000 processor, which is a 14nm, 64-bit processor with 8MP L2 cache, 4MB L3 cache, and support for DDR4- 3200 memory and 34 PCIe 3.0 lanes. According to the DragonBox Shop, Phytium recommends running Ubuntu Kylin on the computer, but it should also support other GNU/Linux distributions including Debian or OpenSUSE and it supports booting from a USB flash drive. You can find more pictures of the Phytium D2000 ARMv8 mini PC as well as some additional details about the computer in the pyra-handheld forum. # ⚓ Phytium_D2000_ARMv8_Mini_PC_runs_Linux,_supports_gaming with_Box64_emulator⠀⇛ # § Mobile Systems/Mobile Applications⠀➾ # ⚓ ‘PhoneSpy’_Malware_Spotted_In_23_Android_Apps⠀⇛ # ⚓ Samsung_Game_Launcher_now_supports_Android_12,_non- game_apps_–_Android_Community⠀⇛ # ⚓ Google_is_prepping_a_big_update_to_At_a_Glance_that should_have_launched_with_Android_12⠀⇛ # ⚓ Android_Auto_bug_on_Android_12_has_sent_notifications haywire_|_T3⠀⇛ # ⚓ Oppo_Android_12_(ColorOS_12)_update_tracker:_Eligible devices,_release…⠀⇛ # ⚓ Why_Android_12_is_extra_special_for_Samsung_Galaxy smartphones_–_SamMobile⠀⇛ # ⚓ Google’s_latest_Android_version_distribution_numbers show_11_in_dead_heat_with_10⠀⇛ # ⚓ Motorola_Android_11_update:_List_of_eligible_devices &_release_date⠀⇛ # ⚓ The_Razer_Kishi,_our_favorite_Android_controller,_is at_its_lowest_price_ever_right_now⠀⇛ # ⚓ YouTube_TV_has_been_freezing_up_on_smart_TVs everywhere⠀⇛ # ⚓ Top_10_Best_Educational_Apps_For_Android⠀⇛ # ⚓ Huawei_tries_not-quite-Android_on_not-quite-iPad_– Pickr⠀⇛ # ⚓ How_to_Get_Chrome_Extensions_on_Android_–_gHacks_Tech News⠀⇛ # ⚓ Google_wants_to_build_an_‘Android’_for_India:_Can_it finally_win?_|_Technology_News,The_Indian_Express⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § FSF⠀➾ # § GNU Projects⠀➾ # ⚓ Libreboot_20211122_released!⠀⇛ The last Libreboot release, version 20210522, was released on May 22nd in 2021. This new release, Libreboot 20211122, is released today on November 22nd, 2021. This is yet another testing release, so expect there to be some bugs. Every effort has been made to ensure reliability on all boards, however. You can find this release in the testing directory on Libreboot release mirrors. If you check in the stable directory, you’ll still only find the 20160907 release in there, so please ensure that you check the testing directory! This is a bug fix release, relative to 20210522. No new boards or major features have been added, but several problems that existed in the previous release have now been fixed. # ⚓ Libreboot_20211122_Rebases_Against_Newer Coreboot,_Drops_“Very_Bloated”_TianoCore_– Phoronix⠀⇛ Libreboot 20211122 has been released as the downstream fork of Coreboot on providing fully free software boot firmware support. Libreboot continues taking the more fully free software approach to system firmware than upstream Coreboot that will accept ports requiring binary blobs and other non-free software components. Libreboot also aims to be easier to setup/deploy than Coreboot. # § Public Services/Government⠀➾ # ⚓ Munich_mk2?_Germany’s_Schleswig-Holstein_plans_to switch_25,000_PCs_to_LibreOffice⠀⇛ From the department of If At First You Don’t Succeed Try Try Again comes news that a German state is to have a crack at shifting thousands of PCs from proprietary software to an open-source alternative. In this instance, it is the north-German state of Schleswig-Holstein that is aiming to ditch proprietary code, including Microsoft Office, in favour of open-source software. According to open-source productivity platform LibreOffice, 25,000 PCs will be running its wares by the end of 2026. In an interview, digital minister for the region, Jan Philipp Albrecht, explained while LibreOffice would be the locally installed option, in the longer term the expectation was that most work would be done within the browser. # § Programming/Development⠀➾ # ⚓ Raspberry_Pi_IoT_In_C_Using_Linux_Drivers_–_1-Wire And_The_DS18B20⠀⇛ Linux drivers make working with devices so easy – assuming you know how. Here’s how to get a Raspberry Pi to get data from the 1- Wire Bus. * § Leftovers⠀➾ o ⚓ On_the_Overnight_from_Agadir⠀⇛ o ⚓ Life_in_West_Virginia’s_“Quiet_Zone”⠀⇛ I was on my way to a scheduled tour of the Green Bank Observatory when I noticed an artifact: a rural payphone, still standing in 2021. I was on a reporting trip, but it was purely for novelty that I pulled a U-turn to snap a photo with my disposable camera—which I had packed because cell phones and digital cameras are banned on observatory grounds. As lights flashed in my rearview mirror, it occurred to me that the U-turn probably wasn’t legal. o § Science⠀➾ # ⚓ Retrotechtacular:_Junior_Missile_Men_Of_The_1960s_| Hackaday⠀⇛ Just like the imaginative kids depicted in “Junior Missile Men in Action,” you’ll have to employ a fair bit of your own imagination to figure out what was going on in the original film, which seems to have suffered a bit — OK, a lot — from multiple rounds of digitization and format conversion. [GarageManCave] tells us he found the film on a newsgroup back in the 1990s, but only recently uploaded it to YouTube. It’s hard to watch, but worth it for anyone who spent hours building an Estes model rocket and had that gut-check moment when sliding it onto the guide rail and getting it ready for launch. Would it go? Would it survive the trip? Or would it end up hanging from a tree branch, or lost in the high grass that always seemed to be ready to eat model rockets, planes, Frisbees, or pretty much anything that was fun? # ⚓ Six_ways_shoebox-sized_satellites_are_trying_to_change_the world⠀⇛ The CubeSat is a small but mighty bit of tech. About the size of a shoebox, the tiny satellites were invented by Professor Bob Twiggs in 1999 as an educational tool for students. o § Hardware⠀➾ # ⚓ Simple_But_Stylish_Numitron_Clock_Can_Display_Time,_Date And_Temperature_|_Hackaday⠀⇛ While it seems like Nixie tubes get all the attention when it comes to making retro-style displays, there are plenty of other display technologies that can make a good-looking retro design. Take the Numitron tube: introduced by RCA in the early 1970s, these display tubes might look superficially similar to Nixies but work in a completely different way. The Numitron uses incandescent elements that make up seven-segment displays. The main advantage Numitrons have over Nixes is that they don’t require a high-voltage supply, which makes them much easier to hook up to modern low-voltage electronics. [mircemk] used this to his advantage when he built a simple clock using four numitrons that can display the time, the date, and the ambient temperature. o § Health/Nutrition/Agriculture⠀➾ # ⚓ White_House:_95_Percent_of_Federal_Workers_Compliant_With Biden_Vaccine_Rules⠀⇛ # ⚓ COVID_Antiviral_Pill_Success_Hinges_on_Access_to_Speedy_and Accurate_Tests⠀⇛ # ⚓ Pandemic_Response_Report_Denounces_Leaving_Global_Health ‘Hostage’_to_Big_Pharma⠀⇛ Ahead of a key World Trade Organization meeting at which ministers are being urged to finally back a temporary intellectual protection waiver proposal on coronavirus-related technologies, a new report highlights ongoing vaccine inequity and a situation in which global health has been “left hostage” to Big Pharma. Released Monday and entitled Losing Time: End this pandemic and secure the future, the publication comes from the Independent Panel for Pandemic Preparedness and Response, a body established by the World Health Organization (WHO). o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Google_Play_Store_starts_rolling_out_‘Offers’_tab_for few_users⠀⇛ Google Play Store recently received the Material You redesign and now the company is reportedly adding a new “Offers” tab on the app. Although the company has not revealed anything about the new tab, it has been spotted by several users. # § Security⠀➾ # ⚓ Arrest_in_‘Ransom_Your_Employer’_Email_Scheme⠀⇛ In August, KrebsOnSecurity warned that scammers were contacting people and asking them to unleash ransomware inside their employer’s network, in exchange for a percentage of any ransom amount paid by the victim company. This week, authorities in Nigeria arrested a suspect in connection with the scheme — a young man who said he was trying to save up money to help fund a new social network. # ⚓ Code_execution_bug_patched_in_Imunify360_Linux server_security_suite⠀⇛ A severe PHP deserialization vulnerability leading to code execution has been patched in Imunify360. # ⚓ New_Windows_zero-day_with_public_exploit_lets you_become_an_admin [Ed: Microsoft booster Lawrence Abrams knows that Windows_is_not secure]⠀⇛ A security researcher has publicly disclosed an exploit for a new Windows zero-day local privilege elevation vulnerability that gives admin privileges in Windows 10, Windows 11, and Windows Server. # § Privacy/Surveillance⠀➾ # ⚓ ‘Anonymized_Data’_Is_A_Gibberish_Term, And_Rampant_Location_Data_Sales_Is_Still_A Problem⠀⇛ As companies and governments increasingly hoover up our personal data, a common refrain is that nothing can go wrong because the data itself is “anonymized” — or stripped of personal identifiers like social security numbers. But time and time again, studies have shown how this really is cold comfort, given it takes only a little effort to pretty quickly identify a person based on access to other data sets. Yet most companies, many privacy policy folk, and even government officials still like to act as if “anonymizing” your data actually something. # ⚓ Hikvision’s_Director_Of_Cybersecurity_And Privacy_Says_IoT_Devices_With_Backdoors ‘Can’t_Be_Used_To_Spy_On_Companies, Individuals_Or_Nations’⠀⇛ Hikvision describes itself as “an IoT solution provider with video as its core competency”. It hasn’t cropped up much here on Techdirt: it was mentioned earlier this year as one of two surveillance camera manufacturers that had been blacklisted by the US government because they were accused of being “implicated in human rights violations and abuses” in Xinjiang. Although little-known in the West, Hikvision is big: it has “more than 42,000 employees, over 20,000 of which are R&D engineers.” Given the many engineers Hikvision employs, the following comment by Fred Streefland, Director of Cybersecurity and Privacy at Hikvision EMEA (Europe, the Middle East and Africa), reported by IPVM, is rather remarkable: # ⚓ NSO_Pegasus_Malware_Deployed_To_Spy_On Palestinian_Human_Rights_Activists⠀⇛ Another day, another revelation about the abuse of NSO malware by its customers. The latest report shows NSO Group’s powerful Pegasus malware was used to target Palestinian human rights activists. Citizen Lab is again on the case, providing the forensic examination of the detected malware and coming to this conclusion: # ⚓ Amazon’s_Dark_Secret:_It_Has_Failed_to Protect_Your_Data⠀⇛ ON SEPTEMBER 26, 2018, a row of tech executives filed into a marble- and wood-paneled hearing room and sat down behind a row of tabletop microphones and tiny water bottles. They had all been called to testify before the US Senate Commerce Committee on a dry subject—the safekeeping and privacy of customer data—that had recently been making large numbers of people mad as hell. o § Defence/Aggression⠀➾ # ⚓ Opinion_|_The_Costs_of_War_to_the_American_Taxpayer⠀⇛ As a Navy spouse of 10 years and counting, my life offers an up-close view of our country’s priorities when it comes to infrastructure and government spending. # ⚓ National_Defense_and_Dead_Children⠀⇛ How fascinating — and how irrelevant — that the vote is scheduled just a few days after the New York Times published its investigation of a U.S. airstrike in Baghuz, Syria two and a half years ago, which the Defense Department had been desperately trying to cover up. America, America . . . shall we celebrate our country, boys and girls? Here’s a passage from the story: “Civilian observers who came to the area of the strike the next day found piles of dead women and children.” # ⚓ Opinion_|_The_High_Stakes_of_the_U.S.-Russia_Confrontation Over_Ukraine⠀⇛ A report in Covert Action Magazine from the self- declared Donetsk People’s Republic in Eastern Ukraine describes grave fears of a new offensive by Ukrainian government forces, after increased shelling, a drone strike by a Turkish-built drone and an attack on Staromaryevka, a village inside the buffer zone established by the 2014-15 Minsk Accords. # ⚓ Opinion_|_Raids,_Arrests,_and_Death_Threats:_Israel’s Strategy_of_Silencing_Human_Rights_Defenders⠀⇛ On October 21, Israeli Defense Minister Benny Gantz announced the issuance of a military order designating six prominent Palestinian human rights groups as ‘terrorist organizations’. Gantz claimed that they are secretly linked to the Popular Front for the Liberation of Palestine (PFLP), a socialist political group that Israel considers, along with most Palestinian political parties, ‘a terrorist organization.’ # ⚓ Francia_Márquez_Mina_Confronts_Colombia’s_“Politics_of Death”⠀⇛ Francia Márquez Mina, 39, has defended Black and Indigenous land rights in Colombia since she was a teenager. She’s taken on multinational corporations, the government, and paramilitary groups. It’s a hazardous calling. A recent Global Witness report found that in 2020, for the second year in a row, Colombia had the highest number of deaths of environmental activists: 65. # ⚓ America’s_Decline_Started_at_Home⠀⇛ When the leaders of more than 100 nations gathered in Glasgow for the UN climate conference last week, there was much discussion about the disastrous effect of climate change on the global environment. There was, however, little awareness of its likely political impact on the current world order that made such an international gathering possible. # ⚓ On_the_Hook:_War,_Factory_Farming,_&_the_Lies_We_Tell_to Make_Them_Possible⠀⇛ On December 15th many Americans (and many more Iraqis) will celebrate the anniversary of the end of the Iraq war.  Because of the courage and dedication of war photographers and journalists, and their commitment to the truth, we have thousands of images to remind us of the terrible violence, brutality, and costs of war.  And yet when I recall that conflict, only (and perhaps thankfully) a few images come to mind, including the charred bodies of four American security contractors hanging from a bridge above the Euphrates; an Iraqi child wailing and squatting at the feet of soldiers, covered in her slain parents’ blood; and the rows of coffins containing American troops, dozens of them, war’s dark cargo tightly wrapped in American flags. By now far too many Americans—beset by a continuous stream of content from every corner of the world, and still somehow largely ignorant of recent wars and the toll of waging them—have likely become inured to images such as these.  But this steady stream of information, particularly information that might actually be useful when deciding the best course of action, has not always flowed so freely into the minds and hearts of the American populace.  Take, for instance, the images of the flagged-draped coffins of American troops killed in the Iraq war. # ⚓ Who_Can_Purchase_a_Gun?⠀⇛ # ⚓ January_6_Organizers_Were_“Following_POTUS’_Lead,” According_to_Leaked_Texts⠀⇛ # ⚓ Potential_Legislation_on_China_Amounts_to_a_New_Cold_War⠀⇛ Congress is itching to pass a sweeping bipartisan package that threatens to enshrine a new Cold War, this time against China, and they’re counting on the American public’s inattention to get it through by the end of the year. After months of stalling in the House, and a failed attempt to attach the legislation to the annual defense bill, majority leader Chuck Schumer and Speaker Nancy Pelosi struck a deal this week for a bicameral conference on the anti-China legislation. # ⚓ Nearly_3/4_of_the_World’s_Dictators_Receive_US_Weapons_and Military_Assistance⠀⇛ Comparing Freedom House’s list of Not Free nations* to FY 2020 US overseas weapons sales, military training and financial assistance**, we find that of the 57 nations considered undemocratic, 42 receive weapons, training and/or money for their military and security services. This means 74% of the non-democratic nations of the world are supported militarily by the US. Interestingly, the remaining 15 nations are nearly all sanctioned. The world’s countries can be divided into two parts: those who buy/receive weapons from the US and those sanctioned. It seems like it’s a pretty simple arrangement. 74% is a slight increase from four years ago when Rich Whitney at Truthout utilized the Freedom House list and compared it to FY 2015 military assistance data. It is likely no surprise to anyone that US support for non-democratic governments increased under President Trump, but, to be fair, it was a minor increase. The hypocrisy and dissonance between stated US support for democracy, liberty and freedom, and how the US government conducts itself exists whether a Democrat or Republican is in the White House. # ⚓ Former_US_Ambassador_to_Viet_Nam_Chooses_Expediency_Over Integrity_Time_and_Again⠀⇛ Madison Avenue Ted Shortly before President Donald Trump’s visit to Vietnam in November 2017, the White House requested that Osius leave his post and the country within six days. This was likely the result of his opposition to the Trump Administration’s cruel and vindictive policy of deporting Vietnamese American permanent residents who arrived in the US before the normalization of diplomatic relations in 1995 and had been convicted of a crime – in violation of a 2008 bilateral agreement. It was also a sure sign that the ambassador was on Trump’s hateful, revenge-seeking radar for that and perhaps other dubious reasons. # ⚓ At_Least_5_Dead,_40_Injured_After_SUV_Slams_Through ‘Comfort_and_Joy’_Christmas_Parade_in_Wisconsin⠀⇛ A Christmas holiday parade themed ‘comfort and joy’ in the town of Waukesha, Wisconsin turned deadly Sunday evening after a driver plowed into participants and observers, killing at least five people and injuring more than 40. According to the Greater Milwaukee Today, a local paper… # ⚓ Trapped_Between_Taliban_And_US_Empire:_Afghan_Women_Keep Hope_Alive_After_Occupation⠀⇛ This is Part 2 of a two-part feature on women in Afghanistan and the diaspora after the withdrawal of U.S. military forces in August. Part 1 can be read here.In Albany, New York, three young Afghan women organized a protest at the state capitol that brought out over 100 people. One of the organizers, Audrea Din, said that the “protest had a very general message, which was about addressing the humanitarian crisis and having resources to help out refugees in the area.”  She added that the organizers demanded a ceasefire, the end of proxy wars, and for the United States to accept more Afghan refugees. “We also want all actors engaged in the war of Afghanistan to be held accountable and pressure them to comply with international law,” said Din.   # ⚓ Corrupting_Science:_in_Syria_probe,_OPCW_erased_experts’ inconvenient_findings⠀⇛ # ⚓ EU_and_NATO:_Military,_police,_secret_services_against migration_as_„hybrid_threat“⠀⇛ Since the Lisbon Treaty, the EU Commission and the Council intertwined internal and external security and thus closer cooperate with NATO. In 2015, a fighting word was created for this, which is being positioned against disinformation, cyber attacks and migration. # ⚓ No_Surprise_With_the_Rittenhouse_Acquittal⠀⇛ Rittenhouse shot two people to death and wounded a third person on August 23, 2020, who were protesting the August 20, 2020 shooting of Jacob Blake, a Black man, by a white Kenosha, Wisconsin police officer. Video of the police officer shooting Blake in the back seven times – as Blake’s small children were present – sparked public demonstrations in Kenosha and elsewhere. Rittenhouse, who was seventeen years old at the time, drove from his hometown in Antioch, Illinois to Kenosha, Wisconsin, claiming that he did so to help protect property from looting and destruction. According to his trial testimony, Rittenhouse shot the three people in self-defense. A jury found Rittenhouse not guilty of all charges. Why are you surprised that a jury acquitted a white man who killed two people and wounded a third person when the victims of his conduct were protesting the police shooting of a Black man seven times in the back? # ⚓ Rittenhouse_Reflections:_Eight_“Upsides”_and_Eleven Forgotten_Martyrs⠀⇛ But terrible and ominous as the Rittenhouse trial is, I find it useful and even to some degree welcome in nine ways: +1. It is yet another nail in the coffin of the frankly ridiculous and often cowardly fascism- denialism that has crippled so many left and liberal hearts and minds in the USA. The Rittenhouse murders were classic fascism: a wicked white Trumpist teen came to Kenosha, Wisconsin to wield a fully loaded military-grade rifle as part of a neo-Nazi paramilitary presence meant to terrorize civil rights and social justice protesters under the cover of protecting small business private property. The fascist thugs operated in coordination and cooperation with the local racist police state. As one of the paramilitaries’ and police state’s pawns, baby- faced Killer Kyle epitomized a classic fascist calling card: violent lawlessness in the name of law and order. A clownish old white male Republikaner judge helped rig the trial for the cop-worshipping Hitler Youth and the Amerikaner jury complied. People on “the left” who can’t see the fascism in this (and in so much more that has taken place in Amerika in recent years and months) are outing themselves as morons and bootlickers. # ⚓ A_Land_Where_Justice_is_a_Game⠀⇛ Nothing could be more typically American than Kyle Rittenhouse’s murder spree and its aftermath. From the shooting itself to his courtroom defense that he “was only defending himself,” the entire scenario reeks of arrogance and sociopathy. Indeed, it’s a perfect metaphor for the US empire and its “foreign policy,” where the concept of self-defense often involves traveling away from one’s home with a loaded weapon, walking down unfamiliar streets away from home, and then murdering people who tell you to go away? This series of events is the template for what US politicians (and many citizens) call US foreign policy. The mindset it inculcates is one that creates the Kyle Rittenhouses among its residents. Make no mistake, the Rittenhouse trial was a political trial. The far-right knew it could manipulate the evidence in its favor, especially given the nature of stand your ground laws. The jury selection was also manipulated and the judge was not sympathetic to the murdered men. As for the prosecution, I was reminded of those grand juries that fail to indict murderous police officers because the state presents its case in such a way that makes indictment unlikely if not impossible. The assumptions of a jury’s members are played upon with the intention of bringing forth their fears and prejudices. A sophisticated legal team can convince a jury that what they see is not fact and that the legal team’s fiction is. Often, this manipulation involves removing the context of the acts being considered, shortening the timeline, and ultimately transferring the blame to the victims. This is a standard approach for the defense when police officers are charged with murder. It was used quite deftly by the Rittenhouse defense team. # ⚓ Rittenhouse_Verdict_Flies_in_the_Face_of_Legal_Standards for_Self-Defense⠀⇛ The Wisconsin jury believed Rittenhouse’s claims that he feared for his life and acted in self- defense after he drove about 20 miles from his home in Antioch, Illinois – picking up an AR-15-style semi-automatic rifle in Kenosha – in what he claimed was an effort to protect property during violent protests. The lakeside city of 100,000 was the scene of chaotic demonstrations after a white police officer shot Jacob Blake, an unarmed, 29- year-old black man, leaving him paralyzed from the waist down. In delivering its verdict, a Wisconsin jury decided that Rittenhouse’s conduct was justified, even though the prosecution argued that he provoked the violent encounter and, therefore, should not be able to find refuge in the self-defense doctrine. # ⚓ Anthony_Huber_Was_a_Hero:_Victim_of_Kyle_Rittenhouse Remembered_for_Trying_to_Save_Lives_At_Protest⠀⇛ The parents of Anthony Huber, one of two men killed by Kyle Rittenhouse, say they are heartbroken and angry over the jury’s Friday verdict, and argue it failed to deliver justice for any of Rittenhouse’s victims. In a statement Friday, they said: “Make no mistake: our fight to hold those responsible for Anthony’s death accountable continues in full force.” Rittenhouse shot and killed 26-year-old Huber within seconds after Huber attempted to disarm the gunman by hitting him with a skateboard. “Huber stepped in to try to stop this person. And in almost any scenario we call that person a hero,” says Anand Swaminathan, the attorney representing Huber’s parents, who have filed a federal lawsuit against the Kenosha Police Department, the Kenosha County Sheriff’s Department as well as the sheriff and police chief. # ⚓ “In_Our_DNA”:_Jacob_Blake’s_Father_&_Uncle_on_the_Family’s Long_History_of_Racial_Justice_Activism⠀⇛ Jacob Blake Sr., whose son was shot by Kenosha police in 2020 and left partially paralyzed, says the family is part of a larger movement fighting for victims of police violence and racial injustice. “We were always pro-Black activists and then after this happened to my son, we’ve become activists for everyone who’s been affected,” he says. The Blake family has a long history of activism going back to the civil rights movement and beyond. Justin Blake, Jacob Blake’s uncle, says it’s in the family’s DNA. “We cannot sit down, we must make change.” # ⚓ NYPD_Continues_To_Screw_Over_Its_Oversight_By_Denying Access_To_Bodycam_Footage⠀⇛ The NYPD’s war on its oversight continues. The secretive law enforcement agency has spent years fighting accountability and transparency, making up its own rules and engaging in openly hostile actions against public records requesters, city officials, internal oversight, and the somewhat- independent CCRB (Civilian Complaint Review Board). Journalists say the NYPD is worse than the CIA and FBI when it comes to records requests. The FBI and CIA say it’s worse than a rogue state when it comes to respecting rights. # ⚓ Jacob_Blake’s_Family_Hails_Rare_Conviction_of_KC_Police Officer_Who_Shot_Dead_Cameron_Lamb_in_2019⠀⇛ In Missouri, white Kansas City police detective Eric DeValkenaere was found guilty Friday of fatally shooting Cameron Lamb, a Black man, who was backing his truck into his garage in December of 2019. DeValkenaere, who had no arrest warrant nor evidence of a crime at the time of shooting, was convicted of second-degree involuntary manslaughter and armed criminal action. The jury decision was unexpected and may set a precedent for future cases in Missouri. The jury system “worked in Kansas City for the first time in 147 years,” says Jacob Blake Sr., who has been supporting Lamb’s family. “We should have that national coverage because that’s a victory.” # ⚓ The_System_is_Broken:_Jacob_Blake’s_Dad_&_Uncle_on_Kyle Rittenhouse_Acquittal_for_Vigilante_Killings⠀⇛ Protests erupted nationwide after a jury in Kenosha, Wisconsin, acquitted Kyle Rittenhouse on all five counts for fatally shooting two people and wounding a third last year during protests sparked by the police shooting that left Jacob Blake paralyzed. Kyle Rittenhouse claimed he acted in self-defense when he killed Anthony Huber and Joseph Rosenbaum with an AR-15-style rifle. The jury’s decision was announced Friday afternoon after about 26 hours of deliberations. To discuss the significance of their verdict, we speak with Jacob Blake Sr. and Justin Blake, the father and uncle of Jacob Blake, who protested outside the trial of Rittenhouse everyday. “This is a tragedy and a slap in the face to all the families that are involved. It made a mockery of the judicial system,” says Justin Blake. “The system of justice works if I look like Kyle Rittenhouse. It does not work if I look like Jacob Blake,” says Jacob Blake Sr. The Blakes say their family had predicted a not guilty outcome. Jacob Blake Sr. also responds to the Biden’s administration’s decision to not seek federal charges against the police officer who shot his son. # ⚓ Opinion_|_Five_Reasons_the_Left_Won_in_Venezuela⠀⇛ For the first time in four years, every major opposition party in Venezuela participated in elections. For the fifth time in four years, the left won in a landslide. Voters elected 23 governors, 335 mayors, 253 state legislators and 2,471 municipal councilors. The governing United Socialist Party of Venezuela (PSUV) won at least 19 of 23 governorships (one race remains too close to call) and the Caracas mayoralty in the November 21 “mega-elections.” Of the 335 mayoral races, the vote count has been completed in 322 of them, with PSUV and its coalition taking 205, opposition coalitions 96 and other parties 21. Over 70,000 candidates ran for these 3,082 offices, and 90% of the vote was counted and verified within hours of polls closing. Turnout was 42.2%, eleven points higher than last year’s parliamentary elections. # ⚓ “No_Mas!”_Nicaragua_Quits_OAS_as_EU_Tries_to_Undermine Venezuela_Elections⠀⇛ “We do not recognize ourselves as a colony of any power and we claim national dignity and decorum, in legitimate defense of our independence, sovereignty, and self-determination.”  With these words, Nicaraguan Foreign Minister Denis Moncada announced that Nicaragua would be joining Venezuela in quitting the Organization of American States (OAS). # ⚓ Ethiopia’s_Tigray_conflict:_What_are_Facebook_and_Twitter doing_about_hate_speech?⠀⇛ Only about 10% of the population in Ethiopia uses Facebook, according to the company. There are relatively low rates of internet adoption in the country and a lack of broadband infrastructure in some areas. However, social media is widely used by Ethiopians abroad, and Facebook posts by Prime Minister Abiy Ahmed regularly receive tens of thousands of likes and thousands of shares. The Ethiopian government – and those who oppose it – track what appears on social media closely. # ⚓ [Old] Wilson_the_Warrior⠀⇛ But in its time there was little dispute that the covert war was one of the most successful C.I.A. operations ever undertaken, a deadly confrontation conducted through a surrogate with the Soviet empire in its death throes. Only a handful of people in the government knew that behind the Afghan resistance was a pirate’s crew of misfits, most notably Charlie Wilson himself, whom Crile affectionately profiles as the lawmaker who widened the war through a series of backroom deals on Capitol Hill that were never publicly disclosed or debated. # ⚓ The_Whiniest_Nazis_Could_Still_Destroy_Our_Country⠀⇛ The plaintiffs still don’t know what to expect, since we never know what juries will do—well, that’s not true; we knew Rittenhouse’s jury would acquit him, but that was largely because of awful judge Bruce Shroeder—but this jury has been given clear directions on how to find these whiny Nazis culpable. Their defense has mainly consisted of insisting that they are all too incompetent to commit conspiracy, but Moon has defined conspiracy clearly. “You don’t have to do very much,” he told the defendants. “You just get in there, be there, go along with it, support it: You’re part of the conspiracy.” He also made clear that in a civil trial, the burden is not “beyond a reasonable doubt” but a “preponderance of evidence”—and he defined that as “50.1 percent.” Again, we never know what juries will do, but this jury has a path to justice. # ⚓ Youths_filmed_brutal_attack_against_senior_for_social_media post⠀⇛ A group of youths assaulted a senior in Guadalajara for no apparent reason last Thursday and shared a video of the attack on social media. o § Transparency/Investigative Reporting⠀➾ # ⚓ Local_Journalism_Matters:_Democracy_Needs_‘More_Muckrakers and_Fewer_Buckrakers’_(as_Project_Censored_founder_Carl Jensen_used_to_say)_–_The_Project_Censored_Show⠀⇛ Today’s guests are longtime independent, investigative reporters Will Carruthers and Peter Byrne. They return to the program to discuss their recent reporting which further examines some of Anderson’s ethically-questionable activities, and why the people of the area are likely to be kept uninformed about them. Then Peter Byrne stays for the second half of the program, and explains the now-widespread and dubious practice of “native advertising:” advertisements in the format of news stories, sometimes written by the newspaper’s own reporters, thereby pulling down the traditional ‘firewall’ between the editorial and business sides of journalism. o § Environment⠀➾ # ⚓ [Old] From_Buy_Nothing_to_Freecycle,_gifting_groups_help bolster_budgets_and_build_community⠀⇛ During the pandemic, “communities came to realize that one of the biggest ingredients of resiliency is sharing, is relying on your neighbor,” said Rockefeller, adding that during lockdowns, many people comfortable or able to go to stores but felt safe doing a contactless pick-up of a sanitized item from a neighbor’s porch. Freecycle experienced an uptick in activity during the pandemic, something Beal also noticed during the Great Recession more than a decade ago. The organization now has about 9 million members and is in more than 5,000 local communities across the globe. # ⚓ Opinion_|_Can_a_Doughnut_Heal_Our_World?⠀⇛ The human community faces two momentous challenges today that will loom ever larger in the years ahead. One is to establish the social and economic conditions necessary for everyone on this planet to flourish: to live with dignity and purpose and fulfill their life’s potentials. The other is to safeguard the natural environment on which we depend from the callous harm caused by an economy dependent on unrestrained extraction and consumption. These challenges to our collective well-being are bound to grow in severity and urgency over the coming decades. To meet them successfully calls for a transformation in the vectors that drive the economy both nationally and globally. Our current dominant economic system is pushing us toward a precipice, and we’re careening forward with hardly a thought for the plunge that lies ahead. It’s as if we’re in a car drawing ever closer to the edge of a cliff, and we continue to press down on the gas pedal while we argue over which station to listen to on the radio.  # ⚓ Chomsky_and_Pollin:_Protests_Outside_of_COP26_Offered_More Hope_Than_the_Summit⠀⇛ # ⚓ Ruralist_Lament:_COP_Out_26⠀⇛ “Nothing beside remains. Round the decay Of that  colossal Wreck, boundless and bare The lone and level sands stretch far away.” # § Energy⠀➾ # ⚓ To_Keep_Fossil_Carbon_Out_of_the_Air,_Just_Stop Pulling_It_Out_of_the_Earth⠀⇛ Nakate chided her audience for sleepwalking toward catastrophe: “We see business leaders and investors flying into COP on private jets. We see them making fancy speeches. We hear about new pledges and promises. … I have come here to tell you that we don’t believe you.” She added, “I am here to say, prove us wrong.” Throughout the summit, people of all ages and backgrounds had rallied in the streets outside to demand effective climate action, climate justice, an end to exploitation, and other policies through which the world’s governments might prove Nakate wrong. # ⚓ ‘Momentous_Day’:_Portugal_Becomes_Europe’s_4th Country_to_Quit_Coal⠀⇛ Environmentalists on Monday hailed the shutdown of Portugal’s last coal-fired power plant—a move that came nearly nine years ahead of the government’s 2030 target—while warning against converting the facility to run on unsustainable biofuel. “Ditching coal only to switch to the next worst fuel is clearly not an answer.” # ⚓ Canadian_Police_Arrest_Indigenous_Opponents_of_Gas Pipeline_and_2_Journalists_Covering_It⠀⇛ Starting on November 18, Canada’s RCMP violently cracked down on a group of Indigenous land defenders who had sought to block the construction of a major natural gas pipeline in northern British Columbia, arresting roughly 15 people over a two-day period. The RCMP also detained two journalists covering the events. The Coastal GasLink pipeline, under construction by TC Energy, will bring fracked natural gas from British Columbia to the Pacific Coast for export at a facility partly owned by oil giant Shell. The pipeline crosses unceded territory of the Wet’suwet’en, whose hereditary leaders never consented to the project. # ⚓ Opinion_|_Shareholder_Engagement_With_Fossil_Fuel Companies_Is_a_Failure_for_Climate_Change⠀⇛ What should pension funds, university endowments and other institutional investors do to help address climate change? The fossil fuel divestment movement calls on funds to divest from fossil fuel companies. Fund owners and managers often oppose divestment, preferring “shareholder engagement”—that is, owning fossil fuel company stocks and voting at shareholder meeting and urging companies to change. While shareholder engagement with fossil fuel corporations on climate change is well intentioned, I will argue that it harms rather than helps efforts to address climate change. # § Wildlife/Nature⠀➾ # ⚓ The_Win-Wins_of_Climate_and_Biodiversity_Solutions⠀⇛ # ⚓ Audubon_Society_Promotes_Livestock_Industry Propaganda⠀⇛ The video is a slick production of happy talk featuring some urban cowboys. And it plays on the old, tired Condos vs. Cows argument. The idea being if you don’t want to see land subdivided, you must support cattle ranchers. The numerous ways that livestock production negatively impacts the environment, from water pollution to Greenhouse Gas Emissions to soil erosion and displacement of wildlife, are never mentioned in the video. Promoting ranching as a way to protect birds is like encouraging alcoholism as a solution for heroin addiction. o § Finance⠀➾ # ⚓ Cuba’s_Post-Revolution_Architecture_Offers_a_Blueprint_for How_to_Build_More_With_Less⠀⇛ Construction and buildings account for more than one-quarter of global greenhouse gas emissions. Meanwhile, according to a September report by Realtor.com, the U.S. alone is short 5.24 million homes. Addressing both crises will require building structures more sustainably and more efficiently. # ⚓ ‘Big_Glaring_Problem’:_Democratic_Promise_for_Universal Pre-K,_Child_Care_About_to_Hit_GOP_Brick_Wall⠀⇛ Advocates have heralded the so-called “universal” pre-kindergarten and child care programs included in the Build Back Better Act as a “game-changer” for families across the United States, but progressive policy analyst Matt Bruenig warned Monday of a “glaring problem” in the legislation that’s likely to leave millions of children missing out on the benefits. As Democrats did when they passed an expansion of Medicaid benefits as part of the Affordable Care Act under the Obama administration, Bruenig wrote, the party has left an opening for states with Republican governors or legislatures to reject the federal funds needed for the programs, as well as the state-level cost-sharing required by the Build Back Better Act. # ⚓ ‘Extremely_Disappointed’:_Biden_Blasted_for_Renominating Powell_as_Federal_Reserve_Chair⠀⇛ U.S. climate campaigners and other critics of Jerome Powell’s record as Federal Reserve chair responded with frustration Monday to President Joe Biden’s renomination of him to the post despite opposition from progressive activists, economists, and lawmakers. “Powell as chair of the Federal Reserve will make it more difficult for Biden to ultimately be a successful president.” # ⚓ Asset_Master_Class:_Art_‘Appreciation,’_Billionaire-Style⠀⇛ # ⚓ Biden_Picks_Jerome_Powell_to_Lead_Federal_Reserve_Despite Progressive_Warnings⠀⇛ # ⚓ Labor_Department_Finalizes_Rule_Giving_Federal_Workers_$15 an_Hour_Minimum_Wage⠀⇛ o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Opinion_|_Americans_Now_Have_an_Opportunity_to_Determine Their_Response_to_Rising_Fascism⠀⇛ Every week we witness a new, sometimes hidden or subtle, sometimes very blatant step toward normalizing violence as the solution to political problems. The Republican party is taking the late 1920′s-1930′s strategy of the Nazi party in Germany and using this model of bringing fascism to our door and manipulating voting so it will appear to be an elected choice. # ⚓ Rights_Defenders_Decry_‘Unlawful_and_Cruel’_Texas_Anti- Migrant_Effort_as_Abbott_Surges_Troops⠀⇛ As Texas Gov. Greg Abbott on Monday announced the mobilization of 10,000 troops and police officers to the Mexican border as part of Operation Lone Star, human rights defenders condemned the effort as illegal, inhumane, and xenophobic and called on the Biden administration to stop the campaign. “The Justice Department should urgently investigate and take all available measures to stop these abuses and ensure accountability for violations of migrants’ rights.” # ⚓ ‘Total_Asymmetric_Warfare’:_Georgia_GOP_Redraws_Political Map_as_US_Senate_Dems_Do_Nothing⠀⇛ Voting rights advocates within and beyond Georgia ramped up calls for congressional action after the Peach State’s Republican lawmakers became the latest to approve a gerrymandered political map intended to give the GOP a political advantage for the next decade. “Congress must pass federal voting rights legislation. We can’t wait any longer.” # ⚓ GOP_May_Be_Feeling_Smug_About_2022,_But_Trump_Remains_an Unpredictable_Wild_Card⠀⇛ # ⚓ AOC_Warns_of_Political_Disaster_for_Democrats_If_They Under-Deliver_on_Promises⠀⇛ # ⚓ Donald_Duck_Quacks_Again_as_Chile_Elects_a_New_President⠀⇛ It is hard to believe that half a century has passed since Para Leer al Pato Donald (How to Read Donald Duck), a book I wrote with the Belgian sociologist, Armand Mattelart, was published in Chile in November 1971. # ⚓ Far-Right_Candidate_Surges_to_Win_Runoff_Spot_in_Chilean Presidential_Election⠀⇛ Far-right presidential candidate José Antonio Kast surged to victory in the first round of Chile’s election on Sunday, securing 28% of the vote and setting up a December runoff versus leftist runner-up Gabriel Boric, who garnered 26% of the ballots cast. The two candidates could hardly be more different. Kast, a 55-year-old former congressman and supporter of deceased military dictator Augusto Pinochet—who forcibly imposed neoliberal reforms after deposing democratically elected socialist President Salvador Allende in a bloody U.S.-backed coup on September 11, 1973—has drawn comparisons to other right-wing authoritarians, including Brazilian President Jair Bolsonaro and former U.S. President Donald Trump. # ⚓ Britain’s_Two_Job_Politicians⠀⇛ This condition has become rather acute in the British political scene.  While a backbencher earns £81,932 annually plus expenses, they may pursue consultancies in the private sector as long as they do not engage in lobbying – a ridiculous fine line.  Astonishingly, there is no limit on the number of hours they may spend on these additional jobs.  Accordingly, members of parliament have shown marked confusion on how to separate their various jobs.  Every so often, business has tended to find its way into the member’s office. A stunning feature of the British system is that there is no revolving door to speak of.  Politicians can seamlessly undertake contracts and perform services, irrespective of their parliamentary position.  The conditions and rules have a Gilbert and Sullivan absurdity to them. # ⚓ Bernie_Sanders_Endorses_Peter_Welch_of_Vermont_for_US Senate⠀⇛ # ⚓ Bernie_Sanders_Endorses_Fellow_Vermonter_Peter_Welch_for_US Senate⠀⇛ Sen. Bernie Sanders on Monday endorsed Rep. Peter Welch for the U.S. Senate seat being vacated by retiring Sen. Patrick Leahy of Vermont, calling the Democratic congressman a progressive champion of working people. “Peter Welch understands that if we are going to combat the existential threat of climate change, establish universal healthcare, lower the cost of prescription drugs, create good paying jobs in Vermont, and protect American democracy, now is the time to think big, not small,” Sanders (I-Vt.) said in a statement. # ⚓ Researchers_have_found_a_simple_way_to_reduce_online_hate speech⠀⇛ Yet a new study by New York University researchers found that a relatively simple move on behalf of social media site could have a huge impact on the effect and spread of hate speech. Their study involved sending alert messages online to Twitter users who had been posting tweets that constituted hate speech. Published in the scholarly journal Perspectives on Politics, the study explored if alerting users that they were at risk of being held accountable could reduce the spread of hate speech. Researchers based their definition of “hateful language” on a dictionary of racial and sexual slurs. Then, after identifying 4,300 Twitter users who followed accounts that had been suspended for posting language defined as hateful, the researchers sent warning tweets from their own accounts which (though phrased in slightly varying ways) let them know that “the user [@account] you follow was suspended, and I suspect that this was because of hateful language.” A separate control group received no messages at all. # ⚓ In_First,_US_Labeled_‘Backsliding’_Democracy_as_Global Authoritarianism_Grows⠀⇛ For the first time in its four years of compiling annual data on the state of democracy around the world, an international think tank added the United States to its list of “backsliding” democracies in the report it released Monday, pointing to factors including politicians’ continued false claims that the 2020 presidential election results were illegitimate as one of the key elements weakening the country’s democratic system. The Global State of Democracy report, released by the International Institute for Democracy and Electoral Assistance (IDEA), called former President Donald Trump’s public questioning of the election results in November 2020 “a historic turning point” both for U.S. democracy and the world, pointing to a knock-on effect in several countries. # ⚓ European_thinktank_adds_U.S._to_list_of_“backsliding” democracies_for_1st_time⠀⇛ The United States has joined an annual list of “backsliding” democracies for the first time, the International IDEA think-tank said on Monday, pointing to a “visible deterioration” that it said began in 2019. Globally, more than one in four people live in a backsliding democracy, a proportion that rises to more than two in three with the addition of authoritarian or “hybrid” regimes, according to the Stockholm-based International Institute for Democracy and Electoral Assistance. o § Misinformation/Disinformation⠀➾ # ⚓ The_Law_Bytes_Podcast,_Episode_109:_Striking_the_Balance_on Misinformation_and_Freedom_of_Expression_–_My_Examination_of Canadian_Policy_Solutions⠀⇛ CityNews Edmonton, Nearly All Canadians Saw COVID- 19 Misinformation Online, Study Says # ⚓ Paxlovid_is_NOT_“#Pfizermectin”⠀⇛ Recently, there were announcements of drugs that, unlike the “miracle cures” (primarily hydroxychloroquine in 2020 and ivermectin this year) that have been promoted so heavily on social media, actually have evidence for their efficacy against COVID-19. One announcement was about Pfizer’s new drug Paxlovid, which in its clinical trials was 89% effective in preventing hospitalization due to COVID-19 if taken soon after symptoms develop. The other drug announced was Merck’s molnupiravir (trade name to be Lagevrio), which is now available through a clinical trial in the UK. Both drugs are very promising, and the Pfizer drug (a combination of PF-07321332 and ritonavir—more on why it’s a combination later—before it received a trade name), for example, decreased the hospitalization rate from 7% to 0.8% over 28 days in a Phase 2/3 study, a good absolute and relative risk reduction, with no deaths in the drug treatment arm. (It was so good that Pfizer stopped the study, because it would be unethical to continue with such a result in an interim analysis.) As a result, Pfizer has applied for an emergency use authorization for its drug. In an interim analysis of a phase 3 study, the Merck drug demonstrated a 50% reduction in hospitalization, again with no deaths in the treatment arm. # ⚓ Hoax_report_that_US_Navy_‘raided_cargo_ship_full_of smuggled_children’_passed_off_as_real_news⠀⇛ Multiple Facebook posts have shared a purported news report claiming the US Navy “raided a cargo ship off the coast of California and rescued 200 foreign children”. Social media users thought the incident was genuine. But the claim originated on a satirical website. “There is no truth to these claims”, a Navy spokesperson told AFP. o § Censorship/Free Speech⠀➾ # ⚓ CNN_airs_live_footage_of_its_reporting_on_tennis_star_being censored_in_China⠀⇛ “I’ve lost count the number of times over the last eight years in Asia covering China, of how many times CNN’s coverage of controversial issues has been censored,” Ripley responded. “It used to go to straight black, now they’ve upgraded and went to color bars, but nonetheless it is a live real-time example of of the censorship that’s happening in the mainland.” Peng apparently went missing earlier this month after accusing a high-ranking Chinese official of sexual assault. Conversations about her allegations were reportedly blocked from China’s [Internet] and much of her online presence appeared to have been scrubbed. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ Donald_Trump_Says_He’s_Going_To_Sue_The_Pulitzer_Committee If_They_Don’t_Take_Away_The_NY_Times_And_WaPo_Pulitzers⠀⇛ Former President Donald Trump really has perfected every little thing he doesn’t like being a grievance that he thinks he can sue over. It’s funny because the Republican Party used to insist that “the left” was the party of victimhood, and yet in Trumpist world, they’re always victims all the time, and always have to whine about how victimized they are. The latest is that Trump is literally threatening to sue the Pulitzer Prize Committee if they refuse to retract the 2018 prize that was given to the NY Times and the Washington Post for reporting on Russia’s attempted interference with the 2016 Presidential campaign. o § Civil Rights/Policing⠀➾ # ⚓ ‘We_Must_Get_This_Done’:_House_Dems_Urge_Restoration_of Citizenship_Pathway_in_Reconciliation_Bill⠀⇛ Following a series of immigrant rights protests in cities across the U.S. in recent weeks over the exclusion of a pathway to citizenship in the Build Back Better Act, a group of 90 Democratic U.S. House lawmakers on Monday sent a letter to leading Senate Democrats urging them to restore the key provision in their version of the flagship budget reconciliation bill. “We cannot forget our ongoing fight for the millions of immigrants who are waiting for a pathway to citizenship.” # ⚓ Purge_at_DSA:_Why_Are_Activists_Trying_to_Expel Representative_Bowman?⠀⇛ The rise of the Squad in Congress has mirrored the explosive growth of Democratic Socialists of America. The leftist lawmakers, all of them national celebrities, have promoted DSA and partnered with the organization on crucial legislation. In turn, young socialists have flocked to the insurgent representatives, lending necessary volunteers for contentious campaigns. # ⚓ Petitioners_Seek_to_End_Nebraska_Education_Board_Over LGBTQ-Inclusive_Curricula⠀⇛ # ⚓ The_Corporate_Demolition_of_Our_Pillars_of_Freedom⠀⇛ Federal District Court Judge in Chicago, Jorge L. Alonso, couldn’t even wait for the scheduled hearing by Boeing’s law firms and the cooperating plaintiffs’ lawyers. He approved the stipulation a day earlier, without comment, that, among other surrenders, took away the right to argue punitive damages for Boeing’s admitted criminal conduct, stopped the discovery and depositions of the most culpable top executives, and set the stage for mediation to reduce the number of trials for compensatory damage to a very few of the 156 wronged families. These mothers and fathers, sisters and brothers lost their loved ones when a stealth software, unknown to the pilots, seized control of the 737 MAX planes and drove them down at 550 mph into smithereens. “Consolidated cases” like those of the 737 MAX disasters are not class actions. They are individual lawsuits from around the country brought together in one court for convenience and alleged efficiencies. Before plaintiffs are informed fully, they find themselves swept into one global deal after closed-door negotiations that unite both the corporate defendants and lawyers for the plaintiffs into one settlement framework. # ⚓ Protest_in_Cuba:_Why_it_Failed⠀⇛ On November 15, the US media primed us for a repeat of the events of July 11 in Cuba — only more massive and more dramatic. In July, tens of thousands of Cubans took to the streets to express their frustrations with their government and, more generally, the state of their country and its economy. # ⚓ “Freedom_to_Travel_Act_of_2021”_introduced_in_Congress⠀⇛ On the 20th anniversary of the creation of the Transportation Security Administration, the Freedom to Travel Act of 2021 (H.R. 6030, “To protect the right to travel by common carrier”), has been introduced in the U.S. House of Representatives by Rep. Paul Gosar (R-AZ) and referred to the Committee on Transportation and Infrastructure and the Committee on Homeland Security. If enacted into law, the Freedom to Travel Act would be the most significant step toward bringing the TSA within the rule of law since the creation of the TSA 20 years ago with the enactment of the Aviation and Transportation Security Act (ATSA) in 2001. It would rein in the TSA’s ability to substitute secret, extrajudicial edicts for court orders restricting American’s rights, and would remove key barriers that have stood in the way of judicial review of TSA actions and legal redress for those whose rights have been violated. The 20th anniversary of the creation of the TSA is an apt moment for Congress to step back from the post-9/11 panic that drove the enactment of the ATSA, take a deep breath, consider what it has actually wrought, and begin to restore the historic right to travel that the TSA has been steadily chipping away at for the entire 20 years of its existence. # ⚓ “If_Everybody’s_White,_There_Can’t_Be_Any_Racial_Bias”:_The Disappearance_of_Hispanic_Drivers_From_Traffic_Records⠀⇛ When sheriff’s deputies in Jefferson Parish, Louisiana, pulled over Octavio Lopez for an expired inspection tag in 2018, they wrote on his traffic ticket that he is white. Lopez, who is from Nicaragua, is Hispanic and speaks only Spanish, said his wife. In fact, of the 167 tickets issued by deputies to drivers with the last name Lopez over a nearly six- year span, not one of the motorists was labeled as Hispanic, according to records provided by the Jefferson Parish clerk of court. The same was true of the 252 tickets issued to people with the last name of Rodriguez, 234 named Martinez, 223 with the last name Hernandez and 189 with the surname Garcia. # ⚓ Police_Aerial_Surveillance_Endangers_Our_Ability_to Protest⠀⇛ You can sign the ACLU’s petition opposing this surveillance here.  Dragnet aerial surveillance is often unconstitutional. In summer 2021, the Fourth Circuit ruled that Baltimore’s aerial surveillance program, which surveilled large swaths of the city without a warrant, violated the Fourth Amendment right to privacy for city residents. Police planes or helicopters flying overhead can easily track and trace an individual as they go about their day—before, during, and after a protest. If a government helicopter follows a group of people leaving a protest and returning home or going to a house of worship, there are many facts about these people that can be inferred.  Not to mention, high-tech political spying makes people vulnerable to retribution and reprisals by the government. Despite their constitutional rights, many people would be chilled and deterred from attending a demonstration protesting against police violence if they knew the police were going to film their face, and potentially identify them and keep a record of their First Amendment activity. # ⚓ More_Than_100_Hertz_Customers_Are_Suing_The_Company_For Falsely_Reporting_Rented_Vehicles_As_Stolen⠀⇛ Earlier this year, a man, wrongfully arrested and imprisoned for murder, was finally able to prove his innocence by producing rental car receipts showing he could not have possibly committed the crime. When the murder occurred, Herbert Alford was twenty minutes away from the scene of the crime, renting a car from Hertz. # ⚓ Buy_Nothing_Day_Messages_2021⠀⇛ The special occasion of Buy Nothing Day is all about waking up against consumerism and living a much-sorted life. Warm greetings on Buy Nothing Day. # ⚓ Buy_Nothing_Day⠀⇛ Going an entire day without buying anything might seem alien to us within an age of instant gratification, though when did you last reflect on the damaging impact that excess consumerism has on our planet and society? You may never have, but the annual recurrence of ‘Buying Nothing Day’ – which takes place this year on Friday 26th November – can give us all food for thought and help improve our lifestyle habits for good. # ⚓ The_joy_of_buying_nothing_new_for_the_holidays⠀⇛ Every new purchase puts into motion a global chain of events, usually beginning with extracting oil to make the plastic that is in everything from stretchy jeans to the packaging they come in. Those materials travel from processing plant to factory to container ship, to eventually land on my front porch, and then become mine for a time. Sooner or later, they will most likely end up in a landfill. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Help_us_rekindle_the_night,_support_La_Quadrature_du_Net⠀⇛ # ⚓ Indonesian_Court_Allows_Internet_Blocking_During_Unrest, Tightening_Law_Enforcement_Control_Over_Users’_Communications and_Data⠀⇛ Indonesia’s Constitutional Court dealt another blow to the free expression and online privacy rights of the country’s 191 million internet users, ruling that the government can lawfully block internet access during periods of social unrest. The October decision is the latest chapter in Indonesia’s  crackdown on tech platforms, and its continuing efforts to force compliance with draconian rules controlling content and access to users’ data. The court’s long-awaited ruling came in a 2019 lawsuit brought by Indonesia NGO SAFEnet and others challenging Article 40.2b of the Electronic Information and Transactions (EIT) Law, after the government restricted Internet access during independence protests and demonstrations in Papua. The group had hoped for a ruling reining in government blocking, which interferes with Indonesians’ rights to voice their opinions and speak out against oppression. Damar Juniarto, SAFEnet Executive Director told EFF:   SAFENET and Human Rights Watch in Indonesia have been sounding the alarm about threats to digital rights in Indonesia ever since the government last year passed, without public consultation, Ministerial Regulation #5 (“MR 5/2020”), a human rights-invasive law governing online content and user data and imposing drastic penalties on companies that fail to comply.  In 2012, Indonesia adopted a data localization mandate requiring all websites and applications that provide online services to store data within Indonesia’s territorial jurisdiction. The mandate’s goal was to help Indonesian law enforcement officials force private electronic systems operators (ESOs)—anyone that operates “electronic systems” for users within Indonesia, including operators incorporated abroad—to provide data during an investigation. The 2012 regulation was largely not enforced, while a 2019 follow-up initiative (M71 regulation) limited the data localization mandate to those processing government data from public bodies.  o § Monopolies⠀➾ # ⚓ Manifest_V3:_Open_Web_Politics_in_Sheep’s_Clothing⠀⇛ The security and privacy claims that Google has made about web extensions may or may not be addressed with Manifest V3. But the fact remains that the extensions that users have relied on for privacy will be heavily stunted if the current proposal moves forward. A move that was presented as user-focused, actually takes away the user’s power to block unwanted tracking for their security and privacy needs. Large Influence, Little Challenge # § Patents⠀➾ # ⚓ EPO_considers_what_data_can_support_patent applications [Ed: This EBA that they speak of is_rigged and_corrupted]⠀⇛ The nature of evidence that businesses filing patent applications in Europe can rely on to demonstrate the patentability of their inventions is likely to be clarified in the months ahead, according to experts in patent litigation. Nicole Jadeja, Jules Fabre and Sarah Taylor of Pinsent Masons, the law firm behind Out- Law, were commenting after the European Patent Office’s (EPO’s) Enlarged Board of Appeal (EBA) was asked to determine what evidence must be included in the patent as filed and to what extent evidence published after a patent application has been filed can support claims made about the inventiveness of the process or product covered by the application. The EBA is the final arbiter on interpreting the European Patent Convention. “The answer to this question is key for applicants to decide when to file their application: whilst they may be tempted to file early to secure protection and avoid prior art, they must also ensure that there is sufficient data available at the time of filing to be included in the specification” said Fabre. To demonstrate that their inventions are patentable, applicants must, among other things, show that an inventive step has been taken that advances the known art and is not obvious to a person skilled in that art. At the EPO this is assessed by reference to the so-called problem-solution test. # ⚓ Technology_puts_China_at_the_top_of_the_global innovation_pyramid [Ed: Very poor article which conflates patents with innovation and says "technology" where it means something else]⠀⇛ 2019 was a remarkable year for global technological development and economic competitiveness. China filed 1.4 patent applications, accounting for 43.4% of all applications filed in the world, according to the World Intellectual Property Organization (WIPO). As for the United States, once the world’s leader in patent applications, the loss of the position has profound implications on two levels: first, the international economic competition is getting more intense; second, China is strengthening its position in the field of innovation. # ⚓ Ahead_of_WTO_Meeting,_Biden_Urged_to_Stop_Letting Europe_‘Block_Progress’_on_Patent_Waiver⠀⇛ With just over a week to go before a key World Trade Organization meeting starts, a coalition of civil society organizations is urging U.S. President Joe Biden to play a more active role in securing unanimous support for a temporary waiver of the intellectual property barriers that are limiting the global supply of Covid-19 vaccines, treatments, and tests required to bring the ongoing pandemic to a swift end. “U.S. passivity has empowered close U.S. allies… to block progress even as millions die or become seriously ill waiting for effective vaccines and treatments.” # § Trademarks⠀➾ # ⚓ Rock_Band_Doomscroll_Has_Trademark_App_Opposed_By_id Software⠀⇛ id Software is not a complete stranger to silly IP enforcement actions. Between trying to own concepts that are un-ownable and occasionally trying to throw its legal muscle around to bully others into not using common words in their own video game titles, the company has proven that it is perfectly capable of playing the IP bully. But at least in those specific instances, if you squint at them, they kinda sorta seem like industry- related, almost understandable IP disputes. # § Copyrights⠀➾ # ⚓ Introducing_the_Better_Internet_Series⠀⇛ This year at CC Global Summit, we hosted two workshops focused on the notion of a better version of the internet. For the workshops, we prepared in smaller groups, identified common areas of interest and concern, and gathered a global group of voices to dig into the issues. In this blog post, we introduce the Better Internet series, which we will use to share the findings of the workshops we hosted at the CC Global Summit, explore the perspectives communicated by those who participated, and share what we are working on with partners to drive these conversations forward and take action.  # ⚓ Disney_Seeks_Analyst_to_Spot_the_Latest_Online_Piracy Trends⠀⇛ Disney plans to add fresh blood to its anti- piracy team. The movie giant wants to hire an analyst who will be tasked with investigating the latest piracy trends, helping out with enforcement efforts, and evaluating new anti- piracy tools and services. A dream position for those who aspire to a career in the anti- piracy workforce. # ⚓ RIAA_Takes_Down_Popular_Music_Piracy_Discord_Over Adele_’30′_Leak⠀⇛ A popular Discord server specializing in music piracy has been taken down by the RIAA. Sources inside the RipRequests community suggest the problem stemmed from a pre- release leak of Adele’s new ’30′ album. This appears to be backed up by a cease-and-desist notice obtained by TF which cites criminal copyright law. ䷩ 𝚕𝚒𝚗𝚎 4863 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.23.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_23/11/2021:_New_GNU_Parallel_and_Memories_of_David_H._Adler_(Perl, Raku)⠀✐ Posted in News_Roundup at 4:27 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Sick_of_Windows?_How_to_log_into_and_start_using_Linux⠀⇛ I started using Linux in ’97, and in the past couple of weeks, I’ve actually watched Linux trend on Twitter at least three times. That’s something I never thought I’d see, but am thrilled it’s happened. To me, that’s a sign the open-source operating system is starting to gain more and more market share on the desktop. As the Linux desktop market share continues to climb, it means more and more new users will be hopping on board. That’s why I started this new “Sick of Windows?” series that walks new users through each step of using the open-source operating system. First I demonstrated how to test- drive Linux and followed it up with how to install Linux. During this series, I’ve used elementary OS as an example. The reason is that elementary OS offers one of the cleanest and simplest experiences (with one exception—more on that in a bit) in all of Linux land. Does that mean it’s the best distribution to use? Not necessarily. And given there’s a vast array of distributions to choose from, there is something for everyone. The good news is that the installation of elementary OS is a great representation of how easy Linux is to install. If you can install this operating system, you can install Ubuntu, Linux Mint, ZorinOS, Deepin and just about any of the modern versions of Linux. # ⚓ Phytium_D2000_Eight-Core_Arm_CPU_Appears_in_Mini_PC⠀⇛ The recommended OS is Ubuntu Kylin, the official Chinese version of Ubuntu, but with the ability to boot from USB other Linux distros should be viable. OpenSUSE and Debian can be installed without issue, according to Dragonbox. A USB to Ethernet adapter is included as the built-in Qualcomm AR 8035 network card doesn’t work well with all Linux distributions. Interestingly, two percent of the price of each unit sold goes to the developer of Box86/Box64. # ⚓ Star_Labs_StarBook_Mk_V_Support_Upstreamed_In_Coreboot_– Phoronix⠀⇛ British Linux PC vendor Star Labs now has support for their StarBook Mk V laptop upstreamed into Coreboot, which marks their second product having this achievement. Earlier this year the Star Labs LabTop Mk III/IV support was upstreamed into Coreboot. Now as of today the StarBook Mk V support has been upstreamed in Coreboot. While running on Coreboot, with the StarBook Mk V being Intel Tiger Lake based, it still is reliant on the closed-source Intel firmware support package (FSP) and Management Engine (ME). There are also blobs required for the ITE EC firmware and Intel Flash Descriptor. o § Server⠀➾ # ⚓ A_preview_of_Amazon’s_AL2022_distribution⠀⇛ Amazon has announced a preview release of its upcoming AL2022 distribution. The company plans to support AL2022 for five years after its release. # ⚓ AWS_is_making_a_major_commitment_to_Linux_|_TechRadar⠀⇛ Amazon’s cloud computing division, Amazon Web Services (AWS) has put out a preview of its custom Amazon Linux distro (AL2022), while committing to refreshing the distro every two years. Amazon Linux is popular with AWS users for its tight integration with AWS tools, and no license costs. The service also ensures that its new features work as advertised with the distro. # ⚓ November_2021_Web_Server_Survey_|_Netcraft_News⠀⇛ In the November 2021 survey we received responses from 1,175,392,792 sites across 267,027,794 unique domains and 11,525,855 web-facing computers. This reflects a loss of 4.06 million sites, but a gain of 1.60 million domains and 137,000 computers. nginx gained the largest number of domains (+741,000) and web-facing computers (+81,300) this month and continues to lead in both metrics with market shares of 30.1% and 37.3%. Further down in the market, there was also a noticeable increase in the total number of web- facing computers running LiteSpeed, which went up by 11,200 to 101,000 (+12.5%), although this resulted in only a 1.44% increase in domains. These counts include sites that run on LiteSpeed Web Server and its open source variant, OpenLiteSpeed, both of which exhibit the same “LiteSpeed” server banner. Both nginx and Apache lost nearly 4 million hostnames each, reducing their sites market shares to 34.7% and 24.4%. Meanwhile, Cloudflare gained 1.15 million sites, which has taken its total up to 58.6 million (+2.00%) and increased its sites share to 4.99%. nginx and Apache also suffered losses amongst the top million websites, paving the way for Microsoft to increase its presence by 2,369 sites (+3.75%). Microsoft web server software is now used by 65,600 of the top million sites, but Apache is still the most commonly used web server in this sector, with 240,000 of the top million sites using it, and nginx is not far behind with 224,000. o § Audiocasts/Shows⠀➾ # ⚓ KDE_News:_Overview_Effect,_Better_Notifications…_New Recording_Setup!_–_Kockatoo_Tube⠀⇛ # ⚓ Join_us_for_State_of_the_Word_2021,_in_person_or_online!_– WordPress.org⠀⇛ As previously announced, State of the Word will be livestreamed from New York City. That means that you can join the fun either online or in person, on December 14, 2021, between 5 and 7 pm EST! To join State of the Word 2021 online, check your Meetup chapter for a local watch party, or simply visit wordpress.org/news, where the livestream will be embedded. If you would like to participate in person in New York City, please request a seat by filling out the registration form by Sunday, November 28. Not all requests will receive a seat due to venue capacity, but everyone who requests one will receive further notification on Tuesday, November 30. # ⚓ If_you_HAVE_to_use_the_G_Suite_on_Linux…_–_Invidious⠀⇛ # ⚓ Late_Night_Linux_–_Episode_152⠀⇛ Mixed news for the Steam Deck, deja vu in Germany, Canonical looks to solve an industry-wide issue, Stadia’s death rattle, Apple’s nod towards right to repair, and KDE Korner. o § Kernel Space⠀➾ # ⚓ Google’s_Generic_Kernel_Image_is_the_next_step_towards solving_Android’s_fragmentation_problem⠀⇛ Google has been working on reducing fragmentation on Android for years, though part of the cause of that is the inherent nature of Android and the dual-edged sword of choice and freedom. There are countless OEMs active in the space, and all of them want to make their own modifications for their own devices. The problem then is that it looks like Android OS updates are slow to roll out across the board, but there’s not a lot that Google can actually do to force OEMs to update their devices. As such, the next best thing that Google can do is make the update process as easy and frictionless as possible. # ⚓ Another_Sizable_Performance_Optimization_To_Benefit_Network Code_With_Linux_5.17_–_Phoronix⠀⇛ Last week I wrote about a big TCP performance optimization having been queued up into net-next for Linux 5.17. That optimization can yield significant TCP throughput improvements especially with today’s high-end 100Gb+ network hardware. There is now another separate juicy optimization to benefit the Linux network performance in the next kernel cycle. This completely separate optimization but that will also benefit the Linux 5.17 network code path is optimizing the x86_64 csum_partial() function. This latest optimization also comes from Google’s Eric Dumazet. # ⚓ Get_Better_Desktop_Responsiveness_Under_Heavy_CPU_Load Using_CFS_Zen_Tweaks_–_Linux_Uprising_Blog⠀⇛ CFS Zen Tweaks is a bash script and systemd service that tweak the Linux CPU scheduler for better desktop responsiveness when under heavy CPU utilization. The default kernel settings are not tweaked for desktop usage, with high throughput being prioritized over latency, notes the CFS Zen Tweaks author. This results in a less responsive desktop under heavy CPU load. Using CFS Zen Tweaks, you should notice an improved desktop responsiveness – for example, its author mentions that before using this, YouTube would lag while compiling code, and that’s no longer the case using the CFS Zen tweaks. The CFS Zen Tweaks project adjusts the default kernel CPU scheduler (CFS or Completely Fair Scheduler) for better desktop responsiveness. The CFS CPU scheduler settings come from Linux ZEN kernel, which was created to provide a better Linux kernel for everyday systems. Note that only the CFS CPU scheduler tweaks are used from the ZEN kernel, while this custom kernel also has other tweaks. o § Benchmarks⠀➾ # ⚓ DDR4_vs._DDR5_Memory_Performance_For_Intel_Core_i5-12600K Alder_Lake_On_Linux⠀⇛ Given current memory pricing and extremely limited availability of DDR5 memory modules, many Phoronix readers have been requesting DDR4 vs. DDR5 memory benchmarks for Alder Lake on Linux. After picking up a DDR4 Z690 motherboard, here are some reference benchmarks between DDR4 and DDR5 when testing with the Core i5 12600K on Ubuntu Linux in a variety of real-world workloads. The Alder Lake benchmarking at Phoronix to this point has been with the ASUS ROG STRIX Z690- E GAMING WiFi and Corsair Vengeance 2 x 32GB DDR5- 4400 C36 memory, both kindly provided by Intel as part of our review kit. DDR5 commands a significant premium at the moment with that 64GB DDR5-4400 kit currently retailing for $555 USD or even the 32GB version for $295, but good luck finding it in stock or even close to that MSRP if finding it resold online. o § Applications⠀➾ # ⚓ GNOME_Painting_App_Pinta_1.7.1_Released_with_Some_New Features⠀⇛ Free and open-source clone of Paint.Net 3.0, Pinta, released version 1.7.1 a few days ago with improvements and bug-fixes. The release is the final version based on GTK2, as the GTK3 / .NET 6 version is nearly ready! Pinta 1.7.1 is a small release with minor new features to improve user experience. For image with large resolution (or zoomed in), you may use mouse wheel to scroll up / down. Now by holding Shift + mouse wheel, the canvas can be scrolled horizontally. Same to GIMP, user may now press X to exchange background and foreground palette colors quickly in Pinta since v1.7.1. And, zooming in and out can now be done without pressing the Ctrl key The release also improved the pop-up dialog when you trying to open an unsupported file format. The file open dialog by default shows only supported images, including ani, png, bmp, jpg, gif, icns, ico, jpeg, ora, pnm, qtif, svg, tga, tif, tiff, xbm, xpm. If you chose show “All files” and selected an unsupported file, it will prompt that file not support and show you all supported file formats. # ⚓ PAPPL_1.1_Nears_Release_As_Modern_Open-Source_Printer Application_Framework_–_Phoronix⠀⇛ While OpenPrinting is now leading development of the CUPS print server, PAPPL continues to be developed by CUPS founder Michael Sweet as a modern open-source printer application framework. PAPPL 1.1 as a big feature release is on the way. PAPPL 1.0 released last December for this open- source framework/library for developing CUPS Printer Applications as the replacement to conventional printer drivers. PAPPL was designed as part of Michael Sweet’s work on LPrint and Gutenprint software but can be used for other purposes too. o § Instructionals/Technical⠀➾ # ⚓ Using_the_script_command_on_Linux_to_record_command_line activity_|_Network_World⠀⇛ The Linux script command has been around for ages and provides a simple but useful service. It lets you record command line activity – both input and output. This can be very helpful in troubleshooting problems or verifying what was done later by reviewing the commands that were run along with their output. Even if you’ve used the script command time to time, it offers more options than many of us realize. In this post, we will look at the simplest use of script and some of the options that can make it even more useful. The easiest way to use the script command is simply to type “script” in the terminal window and press ^d when you want to stop the recording. The output, by default, will be saved in a file called “typescript”. You will see the file name that is used in the first line of output. # ⚓ Package_software_and_data_with_self-compressed_scripts_| Enable_Sysadmin⠀⇛ Self-compressed scrips are a quick, reliable way to distribute software or data to users without a package manager, elevated privileges, or other limitations. # ⚓ LFCS_–_Pluggable_Authentication_Module_(PAM)_|_Linux.org⠀⇛ With every type of Operating System (OS), there needs to be security in place. With CentOS or Ubuntu, there is the Pluggable Authentication Modules (PAM). # ⚓ (Resolved)_-bash:_/bin/mv:_Argument_list_too_long_– TecAdmin⠀⇛ One of my development server contains millions of files under a single directory. To free the disk space, we decided to move to them a new folder created on another disk attached to same system. When tried to move file with mv command, received the following error. # ⚓ Two_new_user_guides:_Impress_and_Calc⠀⇛ The latest user guides from the LibreOffice documentation team are LibreOffice 7.2 Impress and LibreOffice 7.2 Calc, available in free PDF, ODT, or to read in a browser. Low-cost printed copies are available from Lulu.com. # ⚓ HELK_–_An_Open_Source_Threat_Hunting_Platform_–_blackMORE Ops⠀⇛ The Hunting ELK or simply the HELK is an Open Source Threat Hunting Platform with advanced analytics capabilities such as SQL declarative language, graphing, structured streaming, and even machine learning via Jupyter notebooks and Apache Spark over an ELK stack. # ⚓ How_To_Install_FreeOffice_on_Ubuntu_20.04_LTS_–_idroot⠀⇛ In this tutorial, we will show you how to install FreeOffice on Ubuntu 20.04 LTS. For those of you who didn’t know, FreeOffice is a free, full- featured office suite developed by a German-based software company named SoftMaker. It is cross- platform and used in Windows, Mac, and Linux. It has a word processor, spreadsheet application, and presentation program that are seamlessly compatible with Microsoft Office. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you the step-by-step installation of the FreeOffice on Ubuntu 20.04 (Focal Fossa). You can follow the same instructions for Ubuntu 18.04, 16.04, and any other Debian-based distribution like Linux Mint. # ⚓ How_to_Install_UVdesk_Helpdesk_System_on_Debian_11⠀⇛ UVdesk is a free, open-source, and SaaS-based helpdesk solution for any business process to deliver the best customer service. It is a simple, flexible, user-friendly, and alternative to other popular support platforms. It is written in PHP and based on the Symfony framework. You can integrate UVdesk with multiple marketplaces including, Amazon, eBay, Etsy, and Flipkart to support your valuable customer. In this tutorial, I will show you how to install UVdesk helpdesk solution with Apache on Debian 11. # ⚓ How_to_Use_Android’s_Text_Schedule_Send_Feature⠀⇛ As we all know, this is the age of social media; and we all tend to text each other via Messenger, WhatsApp, Instagram, Imo, and other social media platforms. However, imagine the scenario that you are in a remote area and can’t get a strong internet signal or your Android device has run out of data. Furthermore, you’re also not able to communicate verbally because of having a poor network signal. Now, you only have one communication option: texting via phone to your recipient’s numbers as you’ve at least a signal for sending the text. Speaking of texting, Android introduces the text schedule send feature, and users can take advantage of this feature to many different degrees. For instance, there is something important you would like to SMS, and you need to type the message right now quickly; otherwise, you might forget what exactly you want to say. What should you do now? An alternative method could be taking a note, creating an event on your calendar, or setting up an alarm with the message to remind yourself later. However, does this sound convenient and easy if you already have a text schedule send feature on your Android device? I would say NO! # ⚓ How_to_encrypt_block_devices_using_LUKS_on_Linux_–_VITUX⠀⇛ Sometimes you may want to encrypt your hard disk so that when someone connects your hard drive to their computer they need to provide user credentials to mount the drive. In Linux, it is possible to encrypt individual block devices. In this article, we will learn how to encrypt block devices in Linux using LUKS. LUKS is the Linux encryption layer that can be used to encrypt the entire root partition, a logical volume, or a specific partition. # ⚓ Work-around_if_movie_subtitles_restart_after_the_final subtitle_is_displayed_|_Fitzcarraldo’s_Blog⠀⇛ If I’m watching movies in a language I don’t understand, I want subtitles. On my computers this is possible as long as there is a subtitles file with the name suffix .srt and the same prefix name as the .mp4 video file in the same directory. I usually prefer to view movies on my TV with a bigger screen, so I copy the movie to a HDD that is normally connected to my TV (a FINLUX model 43-FUD- 8020). However, the built-in media player in the TV does not show the subtitles in the .srt file, even when it is in the same directory as the .mp4 file. Therefore I use the MKVToolNix utility mkvmerge to put the movie and subtitles into a Matroska multimedia container (.mkv file), and the TV’s media player can play these .mkv files and does display the subtitles. In fact, so can my laptops and desktop running Linux (I have not tried on a machine running Windows 10, but I assume Windows 10 would have no trouble either). # ⚓ How_to_check_.deb_Package_Dependencies_in_Ubuntu⠀⇛ Most software or application in Ubuntu, does not come as one package and it depends on other packages to work as intended. These supporting packages are called dependency packages as they are required for the proper working of the software. Usually, the package manager in your system automatically resolves these dependencies, but sometimes an issue or error occurs and you have to resolve the issue manually. In that case, it is better to have a detailed picture of the dependencies of the package so that you can locate the issue easily. Therefore, You will learn how to check the dependencies of any package in this article. # ⚓ Install_Oracle_Virtualbox_6.1.30_In_Ubuntu_20.04_/_CentOS_8 &_Fedora_|_Tips_On_UNIX⠀⇛ Virtualbox is an open-source application for running operating systems virtually in our base system and this application is available for multiple operating systems (ie) Windows, Linux, and macOS. It has a large number of features, high performing software used in enterprise-level and licensed under General Public License (GPL). It is developed by a community based on a dedicated company. This tutorial will be helpful for beginners to install Oracle VirtualBox 6.1.30 in Ubuntu 20.04, Ubuntu 19.10, CentOS 8 / Redhat 8, and Fedora. # ⚓ How_to_Upgrade_to_Debian_11_Bullseye_–_Linux_Nightly⠀⇛ This guide will show how to upgrade to Debian 11 Bullseye, which is the latest version of the operating system, released on August 14, 2021. # ⚓ How_To_Set_Up_FTP_Server_In_Rocky_Linux_8.4_|_LinuxTeck⠀⇛ FTP stands for File Transfer Protocol, which relies on client/server technology. It is a software application that transfers files between systems. The FTP protocol was developed in the 1970s and is one of the most commonly used protocols to transfer data between computers over the Internet. However, despite being an old methodology, users still find it to be one of the best and most commonly used protocols, and users enjoy using it for uploading and downloading files in their day- to-day work. Setting up an FTP server on Linux is generally quite simple. Essentially, this FTP software package performs two (2) basic tasks: ‘Put’ and ‘Get. When “Put” is used, files will be copied from a local computer to a remote computer, while “Get” handles the opposite. FTP daemon ‘vsftpd’ is a server component that constantly listens for FTP requests from remote clients. It manages the log-in process and establishes the connection when a request is received. By default, it works with port 21 and executes any commands sent by the FTP client during the session. This step-by-step guide will teach you how to install and configure FTP servers (vsftpd) for users with local accounts to upload/download files in Rocky Linux 8.4. Similarly, this guide can be used with RHEL, CentOS, Fedora, Ubuntu, Debian, and Ubuntu with a few minor modifications. # ⚓ How_to_design_state_machines_for_microservices_|_Red_Hat Developer⠀⇛ Backend services and microservices typically use state machines to maintain the state of their resources, whether the state machine is defined explicitly or not. To create a well-written service, you must expressly and clearly define its state machine, so that users know what to expect and can ensure that tests cover all possible (and impossible) transitions. In this article, you’ll learn important guidelines for building state machines. You’ll also get an introduction to stateswitch, a Go library that you can use to organize a state machine’s transition logic. # ⚓ Running_Windows_Programs_on_Trisquel_with_WINE⠀⇛ This tutorial explains how to install Microsoft Windows applications on Trisquel operating sistem. This workaround uses a popular program called Wine, that is, a technology that allows GNU/Linux system to run a lot of W32 executable programs. With Wine, we technically can run both categories, libre software and proprietary software, however in this tutorial we only give examples using libre software. We will install and run W32 version of Gimp, Inkscape, and Super Tux Kart. Enjoy! # ⚓ How_to_deploy_your_first_pod_on_a_Kubernetes_Cluster⠀⇛ In this article we will see how to create our first Pod on Kubernetes Cluster. We shall see the steps to create a pod for Nginx. # ⚓ How_to_configure_Google_Cloud_CDN_for_External_Websites⠀⇛ In this guide you are going to learn how to configure Google Cloud CDN for external websites which is not hosted on Google cloud and have a custom origin server. Here we will configure a HTTPS load balancer and setup an external backend service with Network Endpoint Group (NEG) which connects to your server. # ⚓ How_to_compress_whole_directory_using_xz_and_tar_– nixCraft⠀⇛ The xz command on Linux, macOS, *BSD, and Unix-like systems offer excellent compression. It will outperform zip and other formats when we use xz with tar for maximum reduction in size. For instance, I compressed a directory having 37M size using both xz and zip. The zip file size was 31M, while the xz file was 16M after compression. Pretty impressive, isn’t it? Let us see how to compress the whole directory using xz and tar. # ⚓ How_to_Update_Google_Chrome_on_Ubuntu⠀⇛ Despite the strong competition over the years, Google Chrome has effortlessly surpassed the list of internet browsers to become one of the most popular and widely used search engines online. Its ease of use, availability and compatibility with several operating systems alongside various notable features has made it adept in the field of browsing. Whether you are using it on Windows, Linux, or Mac OS, Google Chrome is free, easily available, and comes along with many development tools for software developers. It is not just a web browser but also a complete package for both your desktop and phone. The simple yet fascinating interface is fast, secure and includes Google’s smart built-in extensions and themes, making your working experience a cut above the other browsers. # ⚓ Reset_Forgotten_Root_Password_in_Rocky_Linux_/_AlmaLinux⠀⇛ It happens. Yes, sometimes you can lose track of your passwords, including the root password which is critical in performing root privileged tasks. This can happen for a myriad of reasons including staying for a protracted period without logging in as a root user or having a complex root password – in which case you should consider using a password manager to safely store your password. In case you have forgotten your root password and have nowhere to retrieve it, worry not. If you have physical access to your server, you can reset your forgotten root password with a few simple steps. # ⚓ How_to_Migrate_CentOS_7_To_AlmaLinux_8:_A_Step-by-Step Guide⠀⇛ Have you ever asked yourself: How do I migrate from CentOS 7 to AlmaLinux? Well, you don’t need to worry about this anymore, because it’s now possible in just a few easy steps that I will show you in this guide. This will be especially helpful for users of CentOS 7 who will be left without a clear upgrade path after the end of the year when Red Hat withdraws support for CentOS 8. This is especially important because CentOS 7, which will will lose support in 2024, is assumed to have a much larger user base than CentOS 8, which had only been available for a little over a year when Red Hat announced it was being sunsetted. # ⚓ How_to_Force_“FSCK”_File_System_Check_on_Ubuntu⠀⇛ As Linux users, we can never undervalue the importance of the FSCK (File System Consistency Check) command, as it scans and troubleshoots your Linux filesystem for performance issues or errors and then tries to fix them if it can. FSCK is a default pre-installation on all Linux operating system distributions. Therefore, if you had yourself worried about mastering the steps for installing, configuring, and using this Linux filesystem tool. # ⚓ How_To_Install_ISPConfig_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install ISPConfig on Debian 11. For those of you who didn’t know, ISPConfig 3 is an open-source panel for Linux which is capable of managing multiple servers from one control panel. With ISPConfig we can easily add Apache virtual host or Nginx server blocks, create/ edit/delete databases, configure cron jobs, create email accounts, and many more. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the ISPConfig 3 on a Debian 11 (Bullseye). # ⚓ Installing_Alpine_or_other_Linux_on_VPS_or_Bare_Metal Server⠀⇛ When you get a VPS or a dedicated (bare metal) server, the hosting provider lets you choose the operating system you want to install. Typically, you can choose from a list of about ten systems. What if your favorite Linux system is not included in that list? Installing Alpine (or other Linux) on VPS or Bare Metal Server There are perhaps several methods to install a particular Linux distribution of your choice on a remote server. I wanted to use the ultra lightweight Alpine Linux. It is available as an option on Linode but not on OVH. I primarily use OVH so I used this method to get Alpine on my server. # ⚓ Introduction_to_Kubernetes_|_What_is_Kubernetes_– OSTechNix⠀⇛ Welcome to the introduction to Kubernetes course. Kubernetes, also known as k8s or kube, is the most popular container Orchestration tool in the industry which is a Google made product. This Kubernetes tutorial consists of series articles on Kubernetes. In the first part, we will be discussing what is Kubernetes and the basic concepts of Kubernetes. This course is for absolute beginners, you don’t need to have any pre-requisite knowledge to learn this technology. We will walk you through all the Kubernetes basics to make you understand the concepts. Before getting started with Kubernetes, let’s have a basic understanding of Docker and Containers. o § Games⠀➾ # ⚓ Stellaris:_Aquatics_Species_Pack_and_the_free_3.2_‘Herbert’ patch_out_now_|_GamingOnLinux⠀⇛ Something smells a bit fishy here! Paradox Interactive has released the Stellaris: Aquatics Species Pack DLC along with another big free update for all players. This actually sounds like one of the most interesting race packs released yet, especially with the new ship designs and the origins. # ⚓ Warhammer_40,000:_Gladius_–_Adeptus_Mechanicus_is_out_now_| GamingOnLinux⠀⇛ While Proxy Studios are currently working on their next strategy game with ZEPHON, they still had time to bring out a fresh DLC for their previous game with Warhammer 40,000: Gladius – Adeptus Mechanicus. In the only 4x strategy game set in Games Workshop’s Warhammer 40,000 universe, Gladius has been out for a while now since July 2018 and it remains quite popular. They’ve already expanded the game a number of times before with the likes of the Tyranids, Chaos Space Marines, T’au and Craftworld Aeldari but now it’s time for the Adeptus Mechanicus to rise and try to take Gladius Prime. # ⚓ After_growing_into_a_full_oceanic_adventure_Sail_Forth moves_to_2022_|_GamingOnLinux⠀⇛ Sail Forth showed off its interesting colourful open-world sailing in previous demos but it seems the whole game has grown and needs just a bit more time. Originally due this year, the developer and publisher has announced a move to Summer 2022 to give it more time. From the press release they said it’s now “a full- blown oceanic adventure with tons of new content, quests, characters, and narrative”. So we have to wait a bit longer but it sounds like it’s going to be far more impressive. # ⚓ Dead_Cells_gets_a_crossover_with_multiple_indie_games_| GamingOnLinux⠀⇛ Motion Twin / Evil Empire have released a big free upgrade for Dead Cells, bringing with it a number of items taken from other popular indie gems. This crossover takes the form of new weapons and outfits for your character, although you do need to hunt for clues and go find them to actually use them. “As we wanted to make this year’s Christmas special, our gift itself needed to be special. Something great, something more, something you’ve never seen before… something literally out of this world. # ⚓ Hearts_of_Iron_IV:_No_Step_back_is_now_out_alongside massive_patch,_some_thoughts_|_GamingOnLinux⠀⇛ While there’s plenty to chew on in terms of new free features and enhancements in the large patch that has come out alongside No Step Back, the most noticeable and important of these is the overhaul of the logistics system. Trains and rail lines make an appearance and, in order for armies to fight effectively, supply lines have to be protected and supply hubs captured. This new system is fairly elegant and adds an element of complexity that is easily understood and interacted with. I’ve played several games and observed the new supply system and how it fits in with the overhauled combat and weather systems. There’s plenty to love and I instinctively found myself planning offensives with supply hubs as primary objectives; disrupting enemy supply likewise was something that I found myself doing more and more. It’s safe to say that it’s a marked improvement to the old system and that in areas with low infrastructure it can be a right pain to keep momentum. o § Desktop Environments/WMs⠀➾ # ⚓ Arcan_0.6.1_Released_With_More_Features_Added_To_This_Open- Source_Display_Stack⠀⇛ Arcan as an open-source display server stack originally built atop a game engine and embracing VR/XR, and pushing forward on other new technologies is out with a new version. Arcan has become quite a large project for those not familiar with it from past articles over the years. Arcan describes itself on GitHub as “a powerful development framework for creating virtually anything from user interfaces for specialized embedded applications all the way to full-blown standalone desktop environments. At its heart lies a robust and portable multimedia engine, with a well-tested and well-documented Lua scripting interface. The development emphasizes security, debuggability and performance — guided by a principle of least surprise in terms of API design.” # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ KDE_Plasma_5.24_To_Add_a_GNOME-Style_Overview_and Will_Prevent_You_From_Uninstalling_Plasma⠀⇛ Ever since Gnome 3 in 2011, the activities overview has played a key role in interacting with it. Despite its heavy criticism at launch, many users have now come to love it, leading to some other desktop environments looking at implementing similar features. And, it looks like KDE Plasma is adding something like it, more like a brand new Gnome-like overview feature. Let us take a closer look. # ⚓ Catch_up:_Calamares⠀⇛ It’s been over a month since I last wrote anything; I acted as a caregiver for my mom for a while, then she moved house which led to frantic painting, unboxing, furniture assembling and all the other time-and-energy sinks associated with moving. Since the end of october I’ve been mostly back at work doing Calamares and KDE and FreeBSD- related things. Let’s catch up on Calamares, first. [...] The ZFS bits are something I’m quite excited about, but they do ask that the distro do some work – the ZFS kernel modules and tools need to be on the ISO, for instance. That doesn’t happen magically, and distro-makers still need to do their thing – and make their own choices; there’s nothing forcing ZFS onto distributions, but Calamares (through Evan) now makes it possible. # § GNOME Desktop/GTK⠀➾ # ⚓ Gnome_Next_Meeting_Applet_Shows_Your_Next_Google Calendar_Events_On_The_Panel⠀⇛ Gnome Next Meeting Applet is an AppIndicator that shows your next Google Calendar meetings / events in a menu on the panel. It also shows your next Google Calendar event title and remaining time directly on the panel, so you can quickly find out when your next event / meeting is due. The applet makes use of Gnome Online Accounts to grab your Google Calendar info, and has useful features like the ability to automatically detect video conference URLs (it supports Google Meet, Zoom and Bluejeans), allowing you to click on a meeting to join it. The application also shows the document links attached to the current meeting. o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ Deepin_Linux_20.3_Is_Out_With_Linux_Kernel_5.15_LTS⠀⇛ Deepin Linux 20.3 is now official as you can now download the latest version of Deepin Linux. One of the exciting features that you will see in Deepin Linux 20.3 is its kernel as it is powered by Linux Kernel 5.15 LTS. Meanwhile, Linux kernel 5.10 LTS is kept as the default kernel in this release. # ⚓ deepin_20.3⠀⇛ Deepin is the top Linux distribution from China, devoted to providing a beautiful, easy-to-use, safe, and reliable operating system for global users. (Global Ranking) In deepin 20.3, the Stable kernel is upgraded to version 5.15 with better compatibility, system security vulnerabilities are fixed, some deepin applications come with new features and optimizations to meet the needs under different scenarios, and DDE issues are fixed and optimized to improve the overall user experience. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Breaking_away:_Making_time_for_UX_innovation_with breakaway_sprints⠀⇛ As a user experience (UX) professional, do you ever get a little too comfortable in your product group bubble? Do you yearn to pursue an idea for a project or process improvement, but lack the time to do so? Are you missing an opportunity to engage with folks on projects outside your day-to-day tasks? From time to time, we’ve felt this way here on Red Hat’s User Experience Design (UXD) team for Red Hat Cloud Services. As a team of 22 people spread across various UX disciplines—research, design, content design, and front-end development—we often find ourselves engaging with many of the same people in the same product area every day as we focus on tasks and milestones. Recently, our team lead suggested we step away from our usual work and try out some new projects with different people by engaging in a three-week innovation or “breakaway” sprint. This wasn’t easy, but it was well worth it—so much so that we want to spread the word to other UX folks like you who might be looking for a way to expose your team members to new experiences, help them build skills, and infuse a bit of variety (and fun!) into their workday. # ⚓ Build_UBI_containers_in_GitHub_Actions_with_Buildah and_Podman [Ed: IBM/Red Hat shilling Microsoft's proprietary software and surveillance]⠀⇛ # ⚓ A_faster_way_to_access_JDK_Flight_Recorder_data⠀⇛ This article introduces a special rule definition in Cryostat 2.0 that lets you access JDK Flight Recorder (JFR) data on the fly, without waiting for your application’s normally scheduled archive process. We’ll introduce Cryostat’s new POST rule definition and show you how to use it to quickly diagnose performance problems in containerized applications running on Kubernetes and Red Hat OpenShift. # ⚓ 8_tech_and_leadership_podcasts_to_add_to_your playlist_|_The_Enterprisers_Project⠀⇛ Thank goodness we live in the golden age of podcasts. With fewer of us traveling to in-person events and conferences and less time available to connect with our IT peers, these audio gems can give us a bit of what we’re missing. Whether it’s hearing from fellow CIOs about their victories and losses, keeping tabs on the last trends in technology-enabled innovation, or learning from some of the leadership greats, these eight podcasts offer aural opportunities for IT leaders seeking education, entertainment, and connection. # ⚓ Digital_transformation:_4_IT_leaders_share_how_they fight_change_fatigue⠀⇛ One of the hardest aspects of digital transformation is that it’s never truly “done.” Being in a state of constant change and disruption can take a serious toll on employee motivation, causing fatigue, distrust, and burnout. We asked CIOs who recently took home a 2021 CIO of the Year ORBIE Award how they are avoiding transformation fatigue on their teams. The awards were presented by the Charlotte CIO Leadership Association and the Michigan CIO Leadership Association, professional communities that annually recognize CIOs for their excellence in technology leadership. Read on for advice that can help you keep up the pace of transformation, while keeping people motivated and connected to meaningful work. # § Canonical/Ubuntu Family⠀➾ # ⚓ Cloud-optimized_Linux_kernels_–_what_makes_Ubuntu_the top_OS_across_the_clouds_|_Ubuntu⠀⇛ Ubuntu is the platform of choice for deploying and running workloads on public clouds. No other operating system gives you better performance and consistency of experience across public clouds, including Amazon, Azure, Google, IBM and Oracle. There is a reason behind this exceptional experience. By design, Ubuntu images in public clouds include an optimized Linux kernel for each cloud, giving you the best performance and functionality across all instance types and services. At the same time, Ubuntu integrates with cloud-native tooling, enabling you to manage your fleet from the cloud’s dashboards. How do these cloud-specific kernel optimizations actually look in practice? Let’s do a deep dive on the optimizations Ubuntu enables on public clouds. # ⚓ Meet_Canonical_at_Cloud_Expo_Europe_Frankfurt_2021_| Ubuntu⠀⇛ The leading fair in London, Paris, Frankfurt and Singapore will open the doors to C-level experts and executives in Frankfurt. Canonical will be attending as a Gold Sponsor, presenting strategies and trends for industry leading companies. # ⚓ The_Fridge:_Ubuntu_Weekly_Newsletter_Issue_710⠀⇛ Welcome to the Ubuntu Weekly Newsletter, Issue 710 for the week of November 14 – 20, 2021. # ⚓ Canonical_at_RISC-V_Summit_2021_|_Ubuntu⠀⇛ RISC-V Summit is an annual conference that showcases the power that open collaboration can have on the processor industry. This year, the event is taking place in San Francisco and virtually on December 6-8th and is co-located with the Design Automation Conference and SEMICON West. Canonical is a proud bronze sponsor of the RISC-V Summit. Make sure to visit our physical or virtual booth for engaging conversations on the power of open source technology! # ⚓ Observability_vs._monitoring_debate:_An_irreverent view_|_Ubuntu⠀⇛ In the past few years, the word “observability” has steadily gained traction in the discussions around monitoring, DevOps, and, especially, cloud-native computing. However, there is significant confusion about the overlap or difference between observability and monitoring. Instead of providing yet another definition of “What is observability” and “Is observability different from monitoring and why” (you can read what I think about it on the What is observability page), I thought I would have a look at what the rest of the Internet seems to think about it. In this post, I’ll provide a few data points around observability and monitoring based on search term trends, social media, and various blog posts, and argue that the debate around observability vs. monitoring is, at best, poorly understood. o § Devices/Embedded⠀➾ # ⚓ Compact,_$529_desktop_runs_Linux_on_octa-core_Arm_SoC⠀⇛ DragonBox has launched a $529 “Phytium D2000 ARMv8 Mini PC” that runs Linux on an octa-core Phytium D2000 and offers a Radeon RX550 GPU, 16GB DDR4, a 512GB NVMe SSD, 6x USB, and HDMI 2.0b and GbE ports. Germany based DragonBox, which last December launched an open-spec DragonBox Pyra portable game console that runs Linux on a TI OMAP3530, has returned with a compact desktop system with a more powerful and exotic Arm processor. The Phytium D2000 ARMv8 Mini PC runs Linux on an octa-core Phytium D2000, a Linux-driven, desktop-oriented SoC based on 64-bit ARMv8. # ⚓ Meet_RobBob,_a_3D-printed_robot_head_that_works_with_an_N64 controller_|_Arduino_Blog⠀⇛ Inspired by a special two-axis mechanism that uses a pair of beveled gears to create panning and tilting motions, maker and YouTuber JBV Creative wanted to integrate it into a larger kinetic sculpture that could move electromechanically while also looking great at the same time. This led to the creation of RobBob, which is essentially a robot-shaped head that has been placed onto a pan/ tilt system. Initially, RobBob could only move with the help of a person turning a pair of opposing knobs — one for each axis. But after some minor additions, including mounts on each side for a single servo motor and adapters that allow servo horns to attach to the knobs, RobBob could now move on its own power. At first, JBV considered using a serial monitor to send rotation commands, although he eventually settled on an N64 joystick since it was a more natural choice for fluid motion. # ⚓ ESP32_Pac-Man_Clock_Keeps_Track_Of_How_Long_You_Watch_It_| Hackaday⠀⇛ [TechKiwiGadgets] built a Pac-Man clock a few years ago that was well-received, but not cheap or easy to mimic. Since then, they have ported the code to the ESP32 and made a new version that has fewer and friendlier components. Not only that, they have great instructions for building the ESP32 shield on protoboard and also offer the shield as an open- source fab-able PCB. Still too much work? The complete kit version is available over on Tindie. Be sure to check it out in crazy speed mode action after the break. # ⚓ Renesas_introduces_sub_50_cents_FPGA_family_with_free Yosys-based_development_tools_–_CNX_Software⠀⇛ You can even try the beta now, after registration, with the software running on Windows 7/8.1/10 32-/ 64-bit, macOS v10.13 or higher, Ubuntu 18.04/20.04 64-bit, and Debian 10/11/Testing 32-/64-bit. You don’t need a powerhouse to develop software for such low-end FPGA either as the minimum hardware requirements include a 2,500 MHz processor, at least 512MB RAM, 128MB graphics RAM, and 750MB of free hard disk space. Note the download link will be provided immediately, so you don’t need to share a working email. # ⚓ GBA_Remote_Play_Upgrade_Lets_You_Play_PlayStation_On_The Bus⠀⇛ However, [Rodrigo Alfonso] has recently upgraded his GBA Remote Play system that lets him play PlayStation games and others on his classic Game Boy Advance. We first featured this project back in July, which uses a Raspberry Pi 3 to emulate games and pipe video data to the handheld for display, receiving button presses in return. # ⚓ The_BBC_Micro_and_Raspberry_Pi⠀⇛ We love this video featuring BBC Micro co-designer Dr Sophie Wilson CBE and our own Eben Upton, both alumni of the University of Cambridge. Eben owned a BBC Micro as a kid, and as an adult he set about designing Raspberry Pi to do what the BBC Micro had done for him: inspire widespread interest in computer programming. # ⚓ Tough_little_Coffee_Lake_SBC_offers_choice_of_Ubuntu_or CentOS⠀⇛ VersaLogic has launched a rugged, Linux-ready “Eagle” SBC with a 9th Gen Xeon E-2276ML, up to 32GB DDR4 with ECC, 128GB of soldered NVMe, 2x GbE, 2x mini-DP++, 4x USB, 2x COM, and a SATA port. Versalogic has released a compact industrial SBC that runs Ubuntu, CentOS, or Windows on a hexa- core, up to 2.4GHz Xeon E-2276ML from Intel’s 9th Gen Coffee Lake Refresh generation. The “Eagle” follows other avian-themed SBCs from VersaLogic including its Apollo Lake based Owl. Other compact Coffee Lake Refresh SBCs include Advantech’s 3.5- inch MIO-5393 and Premio’s CT-MCL01, among others. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Is_the_PinePhone_Pro_the_Linux_Phone_Daily_Driver We’ve_Been_Waiting_For?⠀⇛ PINE64 has announced the upcoming release of the PinePhone Pro. Let’s take a look at its capabilities and see if it’s a good daily driver candidate. In late November of 2019, PINE64 released its first smartphone running on mainline Linux – the PinePhone. Since the phone’s hardware was simply too weak to handle the unrefined software, most of its users already knew that the phone was meant to be used for development and experimentations rather than a regular daily driver. About two years later, PINE64 has finally announced the upcoming release of the new PinePhone Pro. This updated version features more capable hardware and better software. With these improvements, is the PinePhone Pro Linux phone a reasonable candidate to be your next daily driver? Let’s take a look. # ⚓ How_to_Use_Android’s_Text_Schedule_Send_Feature⠀⇛ # ⚓ PUBG:_New_State_Makes_It_Difficult_To_Cheat_For Android_Smartphone_Users⠀⇛ # ⚓ You_can_change_the_Android_12_square_clock_on_Google Pixel_lock_screen⠀⇛ # ⚓ ColorOS_12_review:_Android_12_with_extra_spit_and polish_–_Technology_News⠀⇛ # ⚓ Galaxy_Z_Fold_3_&_Z_Flip_3_get_third_One_UI_4_ (Android_12)_beta_with_December_patch_|_Android Central⠀⇛ # ⚓ OnePlus_OxygenOS_11_(Android_11)_update_known_bugs_& issues⠀⇛ # ⚓ Android_11_still_isn’t_on_as_many_phones_as_Android 10_|_TechRadar⠀⇛ # ⚓ Android_10_continues_to_be_the_most_popular_version of_Android,_two_years_later_–_Phandroid⠀⇛ # ⚓ Improve_Your_WhatsApp_Experience_With_These_10_Top Android_Apps⠀⇛ # ⚓ Samsung_is_betting_big_on_cheaper_Android_tablets_in 2022_–_Phandroid⠀⇛ # ⚓ Google’s_Generic_Kernel_Image_is_the_next_step towards_solving_Android’s_fragmentation_problem⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ Register_for_Ohio_LinuxFest_2021_–_Linux.com⠀⇛ The Ohio LinuxFest is re-emerging as we reboot Open Libre Free Conference as a hybrid event. Re- emergence can mean simply reopening our non-profit for in-person operation. But to us, it is an invitation to reconsider how you use, experience, modify, and distribute technology in the new economy. # ⚓ Two_days_at_the_Open_Source_Experience_–_Le_blog d’Emmanuel⠀⇛ I was at the Open Source Experience event in Paris, France last week. While it was nice to see friends from the FLOSS community, it did feel that the general public decided to stay away, probably because Covid cases are on the rise in France again. I was manning a Perl booth but used the fact that we were 4 people to wander again and ask vendors if they would be willing to support their applications in Fedora. As you can probably guess, results were mixed… # § PostgreSQL⠀➾ # ⚓ PostgreSQL:_PGConf_NYC_2021_is_in_just_two_weeks!⠀⇛ The first community PostgreSQL conference in North America in many months is coming to New York City in just two weeks! PGConf NYC is a non-profit, community-run and PostgreSQL community recognized conference being run by the United States PostgreSQL Association (PgUS). Our schedule is up, the deadline for booking your hotel room is this FRIDAY, November 19th, and it’s time to get registered and confirm you have your ticket for this great event! PGConf NYC delivers two days packed with presentations about PostgreSQL and related technologies, as well as the usual hallway and social track. PGConf NYC is being held December 2nd and 3rd, 2021 in New York City. # ⚓ PostgreSQL:_PostgreSQL_Weekly_News_–_November_21, 2021⠀⇛ PGroonga 2.3.4 a full text search platform for all languages, released. Pgpool-II 4.2.6, 4.1.9, 4.0.16, 3.7.21 and 3.6.28, a connection pooler and statement replication system for PostgreSQL, re l ea s ed. Ora2Pg 23.0, a tool for migrating Oracle databases to PostgreSQL, released. https:// github.com/darold/ora2pg/blob/master/ changelog BigAnimal, a managed PostgreSQL database on Azure, released. pgAdmin4 6.2, a web- and native GUI control center for PostgreSQL, released. # § Education⠀➾ # ⚓ Top_5_Best_Open-Source_eLearning_Platforms_for_Linux System⠀⇛ Learning is all about how much you can get to learn from any source, how better the medium/ platform is for you, and how much you’re compatible with the medium. In this era, eLearning is not a myth or a dream anymore. Thousands of courses are available on the web that you can grab from different eLearning platforms. In the entire post, we have gone through a few most used and intuitive online eLearning platforms that you can run on your Linux machine. # § FSFE⠀➾ # ⚓ 20_Years_FSFE:_Interview_with_Nico_Rikken_on_country teams’_activities⠀⇛ I do remember most of my ‘firsts’ I had with the FSFE. Strictly my first contact was reading the FSFE website and becoming a Fellow (the construct at that time). But after this quite formal arrangement I was looking for more informal contact and a feeling of community. So I still have good memories how Felix Stegerman, then Deputy Coordinator Netherlands, invited me to the Linux Nijmegen User Group to get to know each other and learn more about the FSFE. Up until that evening my efforts in Free Software were a solo effort and that changed in that evening. I became part of a larger community of like-minded people, thanks to Felix. # § FSF⠀➾ # § GNU Projects⠀➾ # ⚓ GNU_Parallel_–_News:_GNU_Parallel_20211122_ (‘Peng_Shuai’)_released⠀⇛ GNU Parallel 20211122 (‘Peng Shuai’) [stable] has been released. It is available for download at: lbry:// @GnuParallel:4 No new functionality was introduced so this is a good candidate for a stable release. # § Licensing/Legal⠀➾ # ⚓ Open_Source_Compliance_for_SaaS_Vendors [Ed: She means Free software, not Open Source]⠀⇛ A pure end user of code cannot incur liability for violating an open source license. Open source licenses can be violated only by re-distributing software — or in the case of network licenses like AGPL, by modifying it and making it available to others as a service. In fact, GPL2 specifically says “Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted.” In contrast, if the vendor is distributing software to a customer for the customer to provide its own SaaS to others, customary open source diligence is appropriate. But this isn’t a SaaS deal, of course. It’s a distribution deal. So, end user customers of SaaS need not conduct diligence into open source licensing issues. If, for example, the SaaS vendor is using modified AGPL code to provide its service to the customer, then the customer may have a right to receive source code from the vendor. But that is a benefit, not a problem. In other words, the purpose of due diligence is to reduce the user’s risk, so even AGPL is not the user’s issue. # § Programming/Development⠀➾ # ⚓ Intel_Graphics_Compiler_1.0.9289_Released_As_A_Huge Update_–_Phoronix⠀⇛ Intel just released IGC 1.0.9289 as a huge update to their open-source Graphics Compiler used on Linux currently by their OpenCL/ oneAPI Level Zero compute stack and also by Windows with their official driver. The LLVM-based Intel Graphics Compiler has been maturing well over the past few years since its original introduction as part of their OpenCL “NEO” driver on Linux. Intel has even begun using IGC on Windows within their widely-used driver stack there while Intel’s Mesa OpenGL/Vulkan drivers may eventually transition to using IGC too for having a unified graphics compiler across targets. # § Perl/Raku⠀➾ # ⚓ Rakudo_Weekly_News:_2021.47_David_H._Adler RIP⠀⇛ This week brought the sad news that David H. Adler has passed away. David had many hobbies, in which he all excelled (like knowledge about Monty Python, Doctor Who, really, really bad movies, to name but a few of them). The Perl / Raku community was only one of the communities he was part of. David was involved in the very early Raku development process. More recently, he was involved in documenting various features of the Raku Programming Language. Attending many Perl and related Open Source Conferences, he was a familiar sight and a good person to spend time with (many pictures). He is sorely missed (FaceBook, /r/perl, blogs.perl.org, presentation from 2016). # § Python⠀➾ # ⚓ Python_3.11_new_and_deprecated_Features_– NextGenTips⠀⇛ Python 3.11 has just been released, we can explore the new features which had been added and removed from the previous release. Python programming language is an interpreted high-level general-purpose programming language. Its design philosophy emphasizes code readability with its use of significant code indentation. # ⚓ How_to_work_with_Jupyter_Notebooks_in_PyCharm⠀⇛ If you are someone in the field of Computer Science, chances are you’re a little familiar with Python. As this high-level, general-purpose programming language is rising in popularity, its strengths and impact are becoming more and more prominent. New developers want to delve into data analytics possible with Python’s elite data visualization and analysis tools. Python is Significant in the World of Programming According to a survey done by JetBrains, “Python is the primary language used by 84% of programmers. Furthermore, almost 58% of developers use Python for data analysis, while 52% use it for web development. The use of Python for DevOps, machine learning, and web crawling or web scraping follow close behind along with a multitude of other uses.” o § Standards/Consortia⠀➾ # ⚓ [ANNOUNCE]_wayland-protocols_1.24⠀⇛ wayland-protocols 1.24 is now available. This release adds feedback to the DMA buffer protocol, allowing smarter and more dynamic DMA buffer allocation semantics. Other changes include documentation improvements and improved testing infrastructure. This is also the first release of wayland-protocols that do not include a autotools build description. # ⚓ Wayland_Protocols_1.24_Released_With_Improvement_To_DMA-BUF Protocol_For_Multi-GPUs_–_Phoronix⠀⇛ Wayland Protocols 1.24 is out today as the latest revision to this official collection of the Wayland protocols/specifications. Notable with the 1.24 revision is the introduction of wp_linux_dmabuf_feedback. Added initially as an “unstable” addition for Wayland-Protocols 1.24 is wp_linux_dmabuf_feedback as the “feedback” addition to the Linux DMA-BUF protocol. This is particularly useful for modern multi-GPU setups where needing to know about the GPU device in use by the compositor and the semantics around it such as if using the secondary GPU that DMA-BUF can still exchange buffers with the main GPU and in a compatible format. # ⚓ Excellent_Free_Tutorials_to_Learn_CSS_–_LinuxLinks⠀⇛ Web pages are built with HTML, which specifies the content of a page. CSS (Cascading Style Sheets) is a separate language which specifies a page’s appearance. CSS code is made of static rules. Each rule takes one or more selectors and gives specific values to a number of visual properties. Those properties are then applied to the page elements indicated by the selectors. Here’s our recommended tutorials to learn CSS. * § Leftovers⠀➾ o § Science⠀➾ # ⚓ Blue_Origin_Rolls_Out_Test_Article_For_Next-Gen_Rocket_| Hackaday⠀⇛ By any metric you care to use, this is a very exciting time for America’s space program. NASA is refocusing their efforts towards the Moon and beyond, SpaceX is launching routine crew and cargo flights to the International Space Station with reusable rockets, and if you’ve got deep enough pockets, there are now multiple companies offering suborbital pleasure trips requiring little more than a few hours worth of training. It’s taken longer than many people had hoped, but it seems we’re finally making the confident strides necessary to truly utilize space’s vast resources. But things are just getting started. A new generation of massive reusable rockets are currently being developed, which promise to make access to space cheaper and faster than ever before. We’ve seen quite a bit of SpaceX’s Starship, thanks in no small part to the dramatic test flights that the media-savvy company has been regularly live streaming to YouTube. But Blue Origin, founded by Amazon’s Jeff Bezos, has been far more secretive about their New Glenn. That is, until now. # ⚓ PFAS:_The_Organofluorines_Your_Biochemist_Warned_You_About |_Hackaday⠀⇛ Sometimes it begins to feel like a tradition that a certain substance or group of substances become highly popular due to certain highly desirable chemical or physical properties, only for these chemicals then to go on to turn out to form a hazard to the biosphere, human life, or both. In the case of per- and polyfluoroalkyl substances (PFAS) it’s no different. Upon the discovery that a subgroup of these -the fluorosurfactants – have the ability to reduce water surface tension significantly more than other surfactants, they began to be used everywhere. Today, fluorosurfactants are being used in everything from stain repellents to paint, make-up, and foam used by firefighters. In a recent study of 231 cosmetic products bought in the US and Canada (Whitehead et al., 2021), it was found that all of them contained PFAS, even when not listed on the packaging. The problematic part here is that PFASs are very stable, do not decay after disposal, and bioaccumulate in the body where they may have endocrine-disrupting effects. o § Hardware⠀➾ # ⚓ Visualizing_WiFi_With_A_Converted_3D_Printer_|_Hackaday⠀⇛ We all know we live in a soup of electromagnetic radiation, everything from AM radio broadcasts to cosmic rays. Some of it is useful, some is a nuisance, but all of it is invisible. We know it’s there, but we have no idea what the fields look like. Unless you put something like this 3D WiFi field strength visualizer to work, of course. # ⚓ A_PDP_11_By_Any_Other_Name:_Heathkit_H11_Teardown_And Repair_|_Hackaday⠀⇛ [Lee Adamson] is no stranger to classic computers. He recently picked up a Heathkit H11A which, as you might remember, is actually a PDP-11 from DEC. Well, technically, it is an LSI-11 but still. Like a proper LSI-11, the computer uses the DEC QBus. Unlike a lot of computers of its day, the H11 didn’t have a lot of switches and lights, but it did have an amazing software library for its day. [Lee] takes us through a tour of all the different cards inside the thing. It is amazing when you think of today’s laptop motherboards that pack way more into a much smaller space. He also had to fix the power supply. # ⚓ Ender_3_Meets_MIG_Welder_To_Make_A_Metal_Benchy_—_Kind_Of_| Hackaday⠀⇛ When you can buy a 3D printer at Aldi, you pretty much know that 3D printing has been reduced to practice. At least for the plastic version of 3D printing; metal printing is another thing entirely. It’s easy to squeeze out a little molten plastic in a controlled fashion, but things get a little more — energetic — when you try to do the same with metal. At least that’s what [Lucas] has been experiencing with his attempts to build a metal 3D printer over on his Cranktown City YouTube channel. Granted, he set himself up for a challenge from the get-go by seeking to stick a MIG welder onto an Ender 3, a platform that in no way was ready for the abuse it was about to endure. Part 1 of the video series below shows the first attempt, which ended badly for both the printer and for the prints. # ⚓ Retrotechtacular:_Office_Equipment_From_The_1940s_| Hackaday⠀⇛ If you can’t imagine writing a letter on a typewriter and putting it in a mailbox, then you take computers for granted. But that’s just the tip of the iceberg. More niche applications begat niche machines, and a number of them are on display in this film that the Computer History Archives Project released last month. Aside from the File-o- matic Desk, the Addressograph, or the Sound Scriber, there a number of other devices that give us a peek into a bygone era. [...] I recognized, and actually used a few of the items featured in this film. My father’s workplace, where I would sometimes hang out after school, had a few of these machines back in the 1970s. The most spectacular was the Addressograph system, used to prepare mailings for newsletters, post cards, etc. It was basically a mechanical database. Each person was represented by a special card, prepared by a Graphotype machine, a specialized typewriter that embosses text on small metal plates, not unlike a dog-tag. The card was actually a frame, which held the embossed plate, a piece of card stock with the information typed by conventional means, and a series of slots along the top of the card which could hold metal tabs. These tabs denoted different user-defined categories. In an engineering company, for example, you could designate tab positions for each department, for each building, for each project team, etc. The entire company roster is now contained in one or more filing drawers, each about the size of an old-fashioned library card catalog drawer. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ Security_updates_for_Tuesday_[LWN.net]⠀⇛ Security updates have been issued by Debian (mbedtls), Red Hat (kernel and rpm), and Ubuntu (freerdp2). # ⚓ Over_a_million_WordPress_sites_breached_| ZDNet⠀⇛ WordPress is far more than just blogs. It powers over 42% of all websites. So whenever there’s a WordPress security failure, it’s a big deal. And now GoDaddy, which is the top global web hosting firm with tens of millions more sites than its competition, reports that data on 1.2 million of its WordPress customers has been exposed. o § Misinformation/Disinformation⠀➾ # ⚓ It’s_time_for_the_European_Commission_to_dismantle disinformation⠀⇛ As the EU is launching a legislative proposal on the transparency of sponsored political content, Access Now, the Civil Liberties Union for Europe, and EDRi are laying out a set of recommendations to help the European Commission effectively minimize the negative impact of disinformation sweeping Europe. “Europe already has many of the rules needed to quash the spread of dangerous disinformation,” said Eliška Pírková, Europe Policy Analyst at Access Now. “They simply need proper enforcement. We also have the resources and experience to draft new legislation that will fill the gaps — starting with targeted advertising.” # ⚓ Policy_recommendations_on_tackling_disinformation [PDF]⠀⇛ In this paper, Access Now, the Civil Liberties Union for Europe, and EDRi lay out out a set of recommendations to help the European Commission effectively minimize the negative impact of disinformation sweeping Europe. o § Civil Rights/Policing⠀➾ # ⚓ Microsoft_Shareholder_Resolutions_–_Facial_Recognition,_Pay Equity,_Sexual_Harassment,_and_more⠀⇛ Microsoft’s annual shareholder meeting is coming up, and the proxy statements include five excellent shareholder resolutions. One of them is on a topic I’ve written a lot about here: prohibiting sales of facial recognition technology to governments. Unsurprisingly, I support it! As Councilmember Jeanne Kohl-Welles and Jennifer Lee of ACLU of Washington said earlier this year in King County government must turn its back on facial recognition technology o § Internet Policy/Net Neutrality⠀➾ # ⚓ Burkina_Faso_Internet_Shutdown_Curtails_Information,_Draws Criticism⠀⇛ Following days of protests opposing French military involvement in counter-terrorism efforts and a spike in militant attacks, internet shutdown continues for third day # ⚓ Whither_net_neutrality?_On_the_urgent_need_to_implement_the TRAI’s_recommendations_on_net_neutrality⠀⇛ The fight for net neutrality is not over, yet. In September 2020, TRAI forwarded a set of recommendations to the Department of Telecommunications(DoT) regarding the enforcement of net neutrality principles by Internet Service Providers (ISPs) and telecom networks, which included the establishment of an independent Multi Stakeholder Body (MSB) to play an advisory and a regulatory role over the ISPs, by overseeing the Traffic Management Practices (TMP) by the ISPs. More than a year and several representations later, these recommendations have still not been implemented. We wrote to the Minister for Telecommunications, Ashwini Vaishnaw to highlight the lack of implementation of TRAI’s recommendations by the DoT despite our repeated efforts. [...] As per TRAI’s recommendations, the creation of a MSB is essential to safeguard citizens’ rights to access to the internet and it requires further support from DoT for its meaningful implementation. Managing the TMPs and updating them continually requires a framework, regulated by a functionally independent MSB, which would have agility and would be able to react fast and evolve with the changes in time, technology, services and other factors, without falling prey to industry capture. The MSB will also be responsible for enforcing standards for technical and operational procedures for monitoring and enforcement of Net Neutrality. Further, an inclusive MSB will effectively raise institutional capacity within the state to catch and punish net neutrality violations. The need for a strong and independent MSB is further illustrated by the repeated instances of licensees discriminating against certain types of internet content and blocking it with impunity. These instances conform with observations from a larger study published by the Centre for Internet and Society on January 17th, 2020, wherein they found that the website blocklists of licensed internet service providers (ISPs) across India are widely inconsistent with one another, suggesting that a larger pattern wherein internet providers are either a) not complying with blocking orders or b) arbitrarily blocking websites without legal orders. Any blocks which occur without legal orders are a clear violation of Net Neutrality principles now codified within the User Agreement License terms. In order to strictly enforce net neutrality, a strong and independent MSB is of crucial importance. [...] Earlier this year, DoT had exhibited hesitancy towards instituting a MSB . We had learnt, in response to an Right to Information request filed with them, that DoT has requested TRAI to reconsider their recommendations, and had cited COVID-19 related budgetary concerns and other feasibility concerns related to the implementation of MSB, among reasons for lack of establishment of an MSB. However, these constraints no longer apply as the Ministry of Finance on September 24th, 2021 has removed the expenditure curbs that were imposed on various Ministries/Departments, including the DoT, for the July-September quarter. Thus, we have requested Minister of Communications Ashwini Vaishnaw to operationalize the TRAI’s recommendations at the earliest, especially by establishing the multistakeholder body as recommended by TRAI. The recommendations from TRAI come at an opportune time to avert the massive damages caused by internet shutdowns upon the fundamental rights as well as the economic opportunities of the citizens. It now remains up to DoT to take this fight to its logical conclusion and act on the recommendations decisively in order to assist in public advocacy for vital information. # ⚓ When_the_internet_goes_dark_–_New_Statesman⠀⇛ The shutdown began for journalist Shams Irfan on 16 October 2019. Irfan lives in Pampore, a town known for growing saffron and being near to Srinagar, the traditional summer capital of the Indian- administered territory of Jammu and Kashmir, which is part of the wider Kashmir region. A few days before, there had been a gun battle between Kashmiri rebels and Indian security forces in which two rebels died, he says. “As it is a norm now, if there is a gunfight in any area, the first thing that is shut is the internet.” Usually, service is fully restored in around three days, but this time that did not happen. “I started noticing a pattern; it was not shut randomly,” Irfan continues. The internet was down from 7.30am to 11am and then from 2.30pm to 10.30pm. He believes it is a “proper curtailment plan”. During earlier internet shutdowns there was usually a reason given by the authorities, he says, but this current pattern has left even journalists like him “clueless”. “What I came to know is that the same pattern is followed in many other areas across Kashmir,” he says. As of October this year, there have been 317 internet shutdowns in Kashmir since 2012, part of 548 across India in the same period, contributing to a collapse in media freedoms. Governments are increasingly turning to internet shutdowns to control the spread of information often connected to political instability. The estimated cost to the global economy was $8bn in 2019. Shutdowns are also becoming more sophisticated and targeted. “No longer does a regime have to plunge a whole nation into darkness – it can lock onto a certain group of people it determines as a threat and disconnect them from each other and the rest of the world,” says Felicia Anthonio, a campaigner at Access Now, a digital rights NGO. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ Joseph_Perry’s_Medical_Illustrations_of_Miscarriage_ (1834)_–_The_Public_Domain_Review⠀⇛ On an unrecorded day in 1827, a woman in the first trimester of pregnancy suffered her sixth, perhaps seventh miscarriage. In the remarks written on her case, it is said that she endured three premature losses for every two successful pregnancies, and “her general health was greatly impaired” in the process. Most likely, she labored between her sweat- soaked and blood-soiled bed sheets, with a midwife watching nearby. Maybe it was a warm morning, in a small home where the walls grew slick with condensation. Heavy breathing and humidity. Maybe the breath was hers, hurried, alongside that of several children huddled outside in the hallway. Maybe her husband kept as close as he could, grave with concern. Or maybe, after so many consecutive losses, he was left feeling almost unfazed. One thing is certain, the woman and the midwife went about their painful work. And when, with a final push, the gestational sac, embryo, and placenta were passed, the midwife promptly collected them and took leave. She hurried through the streets of London until she reached the workplace of the Italian doctor and author, Augustus Bozzi Granville (1783–1872). In the midst of perfecting his book, Graphic Illustrations of Abortion and Diseases of Menstruation, Granville summoned his engraver, Joseph Perry, to perpetuate these particular tissues of miscarriage in detailed, undiminished lithographic color. It now bears the title: Plate 2, Figure 12. ䷩ 𝚕𝚒𝚗𝚎 7264 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.23.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_24/11/2021:_Rust_Crisis_and_Team_UPC_Still_Faking_‘Progress’⠀✐ Posted in News_Roundup at 8:14 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Audiocasts/Shows⠀➾ # ⚓ A_Look_at_WordPress_5.9⠀⇛ WordPress 5.9 is expected to be a ground-breaking release. It will introduce the next generation of themes with Twenty Twenty-Two joining the fun and over 30 theme blocks to build all parts of your site. In anticipation of the January 25th release, we hope you enjoy this sneak peek of 5.9. New design tools will allow you to create exactly what you want, from adding filters to all your images to fine-tuning the border radius on all your buttons. With WordPress 5.9 providing more design control along with streamlined access to patterns, you can easily change the entire look and feel of your site without switching themes. # ⚓ Zenith:_Like_Htop_But_With_Zoomable_Graphs?_–_Invidious⠀⇛ It’s been a while since we last looked at an htop clone but there’s shortage of them, this is zenith is like htop but also with zoomable graphs. At the time of recording the Github made no indication of the GPU graph only being available on Nvidia cards, I recorded this about 2 months ago and in that time nothing major has changed. # ⚓ Linux_Command-Line_Tips_&_Tricks:_Over_15_Examples!_– Invidious⠀⇛ The number of command combinations you can come up with on the Linux command-line is seemingly endless, and there are some real gems out there that you might not know about. In this video, Jay goes over some of his favorite command combos, time-saving tricks, and other various tips he wish he learned sooner. o § Kernel Space⠀➾ # ⚓ Linux_Prepares_For_Next-Gen_AMD_CPUs_With_Up_To_12_CCDs_– Phoronix⠀⇛ The latest Linux kernel patches confirm that next- gen AMD Zen processors are capable of featuring up to twelve CCDs. Currently the k10temp Linux driver for temperature monitoring of AMD processors can handle up to eight core-complex dies (CCDs) while next-gen AMD Zen processors will have configurations up to 12 CCDs to accommodate higher core counts. The latest Linux patches explicitly say, “The newer AMD Family 19h Models 10h-1Fh and A0h-AFh can support up to 12 CCDs. Update the driver to read up to 12 CCDs.” # § Graphics Stack⠀➾ # ⚓ Vulkan_1.2.200_Released_With_Two_New_Extensions_– Phoronix⠀⇛ Out today is Vulkan 1.2.200 as the newest spec revision to the Vulkan graphics/compute API. With Vulkan 1.2.200 is the usual assortment of clarifications and corrections to this leading cross-platform graphics API. But besides that usual documentation churn, there are also two new extensions: VK_ARM_rasterization_order_attachment_access and VK_EXT_depth_clip_control. o § Instructionals/Technical⠀➾ # ⚓ How_to_install_Python_3.11_on_Fedora_35_–_NextGenTips⠀⇛ In this tutorial, we are going to learn how to install Python 3.11 on Fedora 35. Python programming language is an interpreted high- level general-purpose programming language. Its design philosophy emphasizes code readability with its use of significant code indentation. We can begin by installing a python 3 interpreter on our system. This is a program that reads Python programs and carries out their instructions, you need it before you can begin python programming. # ⚓ How_to_install_and_configure_MongoDB_5_on_Ubuntu_20.04⠀⇛ In this guide we are going to learn how to install MongoDB 5.0 Community Edition on an Ubuntu 20.04 server. MongoDB is a cross-platform document-oriented NoSQL database program that uses JSON-like documents with optional schemas. MongoDB is developed by MongoDB Inc. and licensed under the Server Side Public License. MongoDB was built for people building internet and business applications who need to evolve quickly and scale elegantly. Companies and development teams of all sizes use MongoDB for a wide variety of reasons. Instead of storing data in tables of rows or columns like SQL databases, each record in a MongoDB database is a document described in BSON, a binary representation of the data. Applications can then retrieve this information in a JSON format. # ⚓ How_to_install_and_set_up_Jenkins_in_FreeBSD_13⠀⇛ In this Guide we are going to learn how to install and configure Jenkins in a FreeBSD 13 Server. Jenkins is a popular opensource automation tool to perform continuous integration and build automation. Jenkins allows to execute a predefined list of steps, e.g. to compile golang source code to build build binary file. The trigger for this execution can be time or event based. # ⚓ How_to_watermark_a_UTF-8_plain_text_file⠀⇛ Watermarking plain text isn’t easy. Plain text files don’t have headers (or magic numbers), and although you can insert invisible control characters, those characters may get revealed by text editors and word processors. # ⚓ How_To_Install_Wireguard_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install Wireguard on Debian 11. For those of you who didn’t know, Wireguard is one of the well-known and a great open-source VPN solutions. Wireguard aims for better performance and more power than IPsec and OpenVPN. Wireguard protocol passes traffic over UDP. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the Wireguard VPN server on a Debian 11 (Bullseye). # ⚓ How_to_play_Fable_Anniversary_on_Linux⠀⇛ Fable Anniversary is a remaster for Fable: The Lost Chapters by Lion Head Studios and Microsoft Game Studios. The remake was released on Steam in 2014, and there is no plan for a Linux release. However, with a few tweaks, you can get the game working on Linux. # ⚓ How_to_install_the_Elementary_OS_desktop_on_Arch_Linux⠀⇛ Elementary OS is a great operating system with a beautiful desktop environment. Unfortunately, Elementary OS’s desktop is attached to Ubuntu. While Ubuntu is a decent operating system, it’s not as versatile as Arch Linux. If you love Arch Linux and want to use the Elementary OS desktop environment, you can. The Pantheon desktop is now in the official Arch Linux repos and can be installed. Here’s how to get it working on your system. # ⚓ Really_lossy_compression_of_JPEG⠀⇛ Suppose you have a tool that archives images, or scientific data, and it has a test suite. It would be good to collect sample files for the test suite, but they are often so big one can’t really bloat the repository with them. But does the test suite need everything that is in those files? Not necesarily. For example, if one’s testing code that reads EXIF metadata, one doesn’t care about what is in the image. That technique works extemely well. I can take GRIB files that are several megabytes in size, zero out their data payload, and get nice 1Kb samples for the test suite. # ⚓ LibreOffice_Releases_User_Guides_for_Impress_and_Calc_7.2_– FOSS_Force⠀⇛ LibreOffice, the open source office productivity suite, announced on Tuesday the release of new user guides for two components of LibreOffice 7.2. Available now for free download are Impress Guide 7.2, for the suite’s slide presentation component (similar to PowerPoint), and Calc Guide 7.2, for LibreOffice’s spreadsheet component. A guide is already available for LibreOffice Writer 7.2, as well as a 7.2 Getting Started guide. These are remarkably complete guides, with the smallest (Impress) weighing in at 372 pages and the largest (Calc) containing 547 pages. # ⚓ Jolla/Sailfish_OS:_Developing_our_Developer_Docs⠀⇛ From a technical perspective Jolla has for a long time operated a three-pillar strategy; those pillars being Sailfish OS, Android App Support and our Developer Offering. If you watched Sami’s recent presentation at the ten year celebrations in Berlin, you’ll have seen the last of these highlighted as one of our unique assets: a “World- Class Developer Experience”. # ⚓ How_to_install_Balena_Etcher_on_Debian_11_Bullseye_–_Linux Shout⠀⇛ Tutorial to install and run Balena Etcher on Debian 11 Bullseye Linux using command line terminal (repository) or portable AppImage. Etcher, an open-source tool to write ISO/Image files on a USB stick or SD card. It is available to run for all mainstream OS such as Linux, Windows, and macOS. Furthermore, in addition to the installer version, Windows also has a portable Etcher version that can be used without installation Using this program to write image files to removable media. It supports various image formats are * .iso , * .img , * .bin and also packed variants. The program also recognizes whether the image is bootable. Optionally, the successful write process can also be compared with the image file in order to identify damaged data carriers. # ⚓ The_Calc_Guide_7.2_is_at_the_Station!⠀⇛ This 548 pages guide is for beginner to advanced users of Calc, the spreadsheet component of LibreOffice. You may be new to spreadsheet software, or you may be familiar with another program, this book covers the main features of Calc. The new Calc guide has been updated from Calc Guide 7.1. It covers changes that are visible in the user interface, including the new Search Commands tool, the global toolbar lock, details of the properties dialog, improvements in the Status and Sidebar, new menu entries, standard filter dialog and new cross-shaped cursor. The book also introduced contents on user interface variants, AutoInput tool, the Find toolbar, the Paste Special dialog, the AutoFilter tool, template dialogs, QR code generation, multi-column feature for text boxes, updates on the Solver, Print, PDF and Certificate dialogs, as well as External data tool for HTML tables, updates on the Scriptforge library and the new built-in UNO object inspector. # ⚓ How_and_When_to_Update_openSUSE_Tumbleweed_|_Blathering_– CubicleNate’s_Techpad⠀⇛ I am often asked how often and when I update my openSUSE Tumbleweed machines. There are lots of opinions out there and many of them might be more right than my own, but my method has been reliable for my uses for about four years and counting. I run openSUSE Tumbleweed and openSUSE Leap on various machines using multiple architectures and I am quite confident that my methods are sound. Ultimately, the frequency you update has to work with you, your use cases and your network limitations. It should also be noted, when doing an “update” in Tumbleweed, it is a full on Distribution Upgrade, not just the updating of packages as you would perform on an openSUSE Leap machine. I am using “Update” in the most general term possible. I had must consternation over this title, as a consequence of knowing the difference between update and distribution-upgrade. It is generally considered best to keep your system as up to date as possible, at all times to prevent nefarious actors from gaining access to your system and your data. I also realize that this is not always practical and as such have been noodling around what kind of frequency once should do their updates. This is a question I receive rather frequently and decided that I am going to blather a bit about how and when to update while including some of the difficulties I have experienced over the year. # ⚓ Using_SlickStack_to_Install_WordPress_Automatically_on Ubuntu_20.04_–_ByteXD⠀⇛ SlickStack is essentially a collection of scripts for quickly and easily installing WordPress, with Nginx1 as a web server, on Ubuntu LTS. It aims at making it easier for users to deploy lightweight, fast and secure WordPress websites, and guides users and helps them secure their server during the installation process. This is especially useful for new users who just need to painlessly setup a fast and secure WordPress website on a cheap Ubuntu server, which can be cheaper and faster than paying for shared hosting. These servers usually cost $5-$10. The philosophy of SlickStack can be found towards the end of their main page at slickstack.io. That, along with the fact that the developer is very experienced in web hosting and passionate about the project, are the factors that I think make SlickStack worth considering for your projects. The developer is very helpful and frequently asks for feedback regarding the direction of SlickStack, so they can improve. This is very important, because if you adopt a software for your long term project, you want to know that software will stay up-to-date, will get new features, and will patch any potential vulnerabilities. In this article we’ll go over how to use SlickStack to install WordPress on a server running Ubuntu 20.04 LTS, as well as give you a basic overview of some of its options. We won’t be able to cover all of its options, however, so be sure to check their Github and slickstack.io for more in-depth info. o § Games⠀➾ # ⚓ Crusader_Kings_III:_Royal_Court_releases_February_8,_2022_| GamingOnLinux⠀⇛ With the Crusader Kings III: Royal Court expansion, would-be monarchs will have new ways to manage courts, build nations, and display the prestige of their dynasty for everyone in the realm to see. It’s now set to release on February 8, 2022. This is the first major expansion for the game, that has gone on to receive a very warm reception from players both new and old with it seeing now over 42,000 user reviews on Steam with a Very Positive rating. We enjoyed it a lot here too, so we’re also very much looking forward to this! o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Linux_history:_KDE_and_Gnome_vie_for_the_Linux desktop [Ed: Automated translation from German]⠀⇛ As with so many open source projects, it all starts with a Usenet posting. In it, the Tübingen computer science student Matthias Ettrich announced a new project on October 14, 1996: the “Kool Desktop Environment (KDE)”. He is looking for comrades-in-arms in the Usenet group de.comp.os.linux.misc: Ettrich describes in detail the inadequacies of previous Unix user interfaces and has specific ideas about what needs to change. The name KDE is based on the Common Desktop Environment (CDE), which was common in the commercial Unix environment at the time. CDE is on the one hand too expensive for Ettrich, on the other hand he finds the Motif program library used for the surfaces terrible. One of the first to get involved in the new project is the Hamburg-based software developer Kalle Dalheimer, who is employed by Star Division: “Part of my work was also following the development of graphical interfaces under Linux. That was when Matthias Ettrich’s posting appeared.” In retrospect, Dalheimer describes his motivation to be there as a mix of ideology and selfishness. He didn’t want to use Windows on principle, but Dalheimer saw no future for Unix and Linux systems with the existing brittle graphical interfaces. o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ Grandma_will_be_thankful_when_you_install_deepin Linux_20.3_on_her_PC_this_Thanksgiving⠀⇛ This Thursday is one of my favorite holidays — Thanksgiving! While I will absolutely fill my (large) belly with turkey, stuffing, sweet potatoes, and other traditional foods, I will be sure to celebrate the true nature of the day as well — being thankful. This year, I am thankful for my health, my family, and of course… Linux! Yup, folks, we should all be thankful that many wonderful Linux distributions exist, making it possible for people to enjoy truly free and open source software. One of the prettiest Linux-based operating systems is deepin. Today, version 20.3 of the Debian- based operating system becomes available for download, meaning you can install it on your Grandma’s computer after eating her yummy cooking. What better way to thank your Thanksgiving host than replacing Windows with Linux for them? Forget dual-booting. She will be so pleasantly surprised when she turns on the computer! “In deepin 20.3, the Stable kernel is upgraded to version 5.15 with better compatibility, system security vulnerabilities are fixed, some deepin applications come with new features and optimizations to meet the needs under different scenarios, and DDE issues are fixed and optimized to improve the overall user experience. The Stable kernel is upgraded to version 5.15 with better support for Intel 12th Gen processors and NTFS file systems, and better system compatibility. Both LTS and Stable kernels can be installed and manually upgraded in deepin,” explains the developers. # § Screenshots/Screencasts⠀➾ # ⚓ Deepin_20.3_Run_Through_–_Invidious⠀⇛ In this video, we are looking at Deepin 20.3. Enjoy! # ⚓ Deepin_20.3⠀⇛ Today we are looking at Deepin 20.3. It comes with Linux Kernel 5.10 and uses about 1.5 – 1.9GB of ram when idling. # § IBM/Red Hat/Fedora⠀➾ # ⚓ 253:_Keepin_IT_RHEL_with_Red_Hat’s_Scott_McCarty_– Destination_Linux⠀⇛ This week’s episode of Destination Linux, we are speaking with Scott McCarty of Red Hat about their latest RHEL innovations. Then we talk a little Dungeons & Dragons with a callout to the community to get a D&DLN live session going. Plus we’ve also got our famous tips, tricks and software picks. All of this and so much more this week on Destination Linux. So whether you’re brand new to Linux and open source or a guru of sudo. This is the podcast for you. # ⚓ Scott_McCarty:_What_is_open_core? [Ed: Proprietary software disguised as “open”, i.e. #openwashing]⠀⇛ What is open core? Is a project open core, or is a business open core? That’s debatable. Like open source, some view it as a development model, others view it as a business model. As a product manager, I view it more in the context of value creation and value capture. # ⚓ Deep_dive_into_application_integration_with_our_TCS partner_–_IBM_Developer⠀⇛ Integrating and connecting your various applications with the right data across multiple clouds can be a daunting task. IBM Cloud Pak for Integration is an enterprise- ready, containerized software solution containing all the tools you need to integrate and connect application components and data within and between clouds. These tools include application integration, API integration, enterprise messaging and event streaming. Earlier this year, I collaborated with Santhosh Ramanathan, a Cloud Pak for Integration (CP4I) Consultant from TCS, to develop an entire series on all the significant features of CP4I for the Partner Developer Success Program. TCS, a leading global IT services, consulting, and business solution organization, has been an incredible partner with IBM. This program was built with a focus on educating the developer community through partner collaboration. We decided to work together to break our series into three significant parts. Here is how it went: o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Firefox_Brings_The_Fire:_Shifting_From_GLX_To EGL_|_Hackaday⠀⇛ You may (or may not) have heard that Firefox is moving from GLX to EGL for the Linux graphics stack. It’s an indicator of which way the tides are moving in the software world. Let’s look at what it means, why it matters, and why it’s cool. A graphics stack is a complex system with many layers. But on Linux, there needs to be an interface between something like OpenGL and a windowing system like X11. X11 provides a fundamental framework for drawing and moving windows around a display, capturing user input, and determining focus, but little else. An X11 server is just a program that manages all the windows (clients). Each window in X11 is considered a client. A client connects to the server over a Unix process socket or the internet. OpenGL focuses on what to draw within the confines of the screen space given by the window system. GLX (which stands for OpenGL Extension to the X window system) was originally developed by Silicon Graphics. It has changed over the years, gaining hardware acceleration support and DRI (Direct Rendering Interface). DRI is a way for OpenGL to talk directly to the graphical hardware if the server and the client are on the same computer. At its core, GLX provides OpenGL functions to X11, adds to the X protocol by allowing 3d rendering commands to be sent, and an extension that reads rendering commands and passes them to OpenGL. # ⚓ Do_you_run_Void_on_your_Power_Mac?⠀⇛ If so, heads up, because builds for your configuration may be ending soon (along with Void PPC on big-endian platforms generally). If you want this to continue, and you’ve got the interest, chops or gumption, you can help by becoming a maintainer — take a look at the Void PPC Github. Most of you are probably running the glibc variant, which will end by January 2023, but if you are running musl-based packages those repos will be taken down by the end of 2021. Don’t whine to the maintainer, please: the current matrix is four different repos which all require their own maintenance and builds. Even just 32-bit glibc would probably benefit a whole lot of people and yourself. If this is important to you, there’s no time like the present to step up. # § Funding⠀➾ # ⚓ Software_Freedom_Conservancy_donors_challenged_with largest_match_yet_–_Software_Freedom_Conservancy⠀⇛ Donations will be matched (up to $159,191) thanks almost entirely to contributions by a few very generous anonymous donors. Contributions by individuals keep Software Freedom Conservancy afloat, and it’s with your help that we are empowered to do the vital and sometimes overlooked work in software freedom. We also have some gracious donors who brought the amount up a little more to the prime number you see above: Chris Neugebauer and Josh Simmons, Mark Galassi, Stephen Paul Weber, Tony Sebro, and VM Brasseur are contributing to our match fund and encourage others to give as well. # § FSFE⠀➾ # ⚓ FSFE_Calls_for_‘Device_Neutrality’_in_EU’s_Proposed ‘Digital_Markets_Act’_–_FOSS_Force⠀⇛ In a press release issued Monday ahead of a planned preliminary vote on the EU’s proposed Digital Markets act by the Internal Market and Consumer Protection Committee, the Free Software Foundation Europe called for device neutrality to be included in the proposed law. The German-based FSFE is a sister organization to the Free Software Foundation, although the two are legally and financially separate entities “On the imminent voting of the Digital Markets Act – the latest EU proposal on internet platform regulation – the FSFE demands device neutrality as a fundamental element for safeguarding consumer protection in open, fair, and contestable digital markets,” the FSFE said in its statement. # § Programming/Development⠀➾ # ⚓ Use_symbolic_constants_instead_of_magic_numerical constants_–_EasyHack⠀⇛ There are many situations that you need to use numerical constants in your code. If you use numerical literal values directly instead of symbolic constants, it can cause problems. For example, consider this piece of code that calculate area of a circle: double area = 3.14 * r * r; This is not OK, because: 1. The value of π is not 3.14 nor 3.141592. π is an irrational number, and the suitable value depends on the number of decimal places that you can/want to use among unlimited decimals of π. 2. Suppose that you want to change the numerical literal to increase the number of decimals that you use. You should search for 3.14, and check one by one to see if it is actually π, or it is another 3.14 unrelated to the well-known mathematical constant. # § Rust⠀➾ # ⚓ Entire_Rust_moderation_team_resigns_•_The Register⠀⇛ The Rust language community is in disarray following the resignation of the entire moderation team, citing the “structural unaccountability” of the core development team. The moderation team, represented by Andrew Gallant, posted its resignation to GitHub yesterday, stating that it was “done in protest of the Core Team placing themselves unaccountable to anyone but themselves.” Therefore, the post goes on to explain, “we have been unable to enforce the Rust Code of Conduct [CoC] to the standards the community expects of us.” * § Leftovers⠀➾ o § Hardware⠀➾ # ⚓ Significantly_Improved_Egg_Timer_Makes_Pictionary_Better_| Hackaday⠀⇛ The traditional sand timer, known colloquially as an egg timer, served its purpose well over the centuries since its development. However, [MakerPaul] realised it had some significant flaws that were ruining Pictionary, and set out to fix the problem. If you’re not looking directly at an egg timer, it’s easy to miss the moment when the timer runs out. Resetting the timer before it runs out also requires waiting for the sand to filter to one side. Clearly the world needs a better mousetrap. The tipping timer from [MakerPaul] solves both those issues. In this design, sand flows down into an offset area, which tips the device over when reaching a certain time limit. Additionally, turning the device upside down and then rotating it instantly reloads the sand, meaning the timer can be reused immediately. # ⚓ Charging_Phones_With_The_Power_Of_Paper_Pulp_|_Hackaday⠀⇛ Here it is, the most exciting reveal since the Hackaday Prize ceremony — [Eric Strebel] uses the pulp mold he designed and built over the three previous videos. In case you missed our coverage so far, [Eric] set out to design an eco-friendly wireless charger that’s meant to be disposable after six months to a year of use, and looks good doing it. [Eric] started by cutting up a lot of cardboard and pulping it in a brand-new Oster blender that honestly looks to be pretty heavy duty. Pulping consists of blending the cardboard bits with water until a soupy chili-like consistency is reached. That blender lasted all of 20 minutes before breaking, so [Eric] promptly replaced it with a Ninja, which was way more up to the challenge of cardboard. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ Imunify360_Flaw_Can_Lead_to_Code_Execution [Ed: Security should never be an "addon"; it should be a design trait]⠀⇛ There is a vulnerability in some versions of the Imunify360 web server security platform that can allow an attacker to execute arbitrary code in some specific circumstances. The vulnerability is a PHP deserialization issue and it exists in versions 5.8 and 5.9 of Imunify360, a product designed to detect malware and other security issues on web-hosting servers. Researchers at Cisco Talos discovered the vulnerability, which is in the Ai-Bolit functionality of the product. The researchers found that an attacker can exploit it in a couple of different ways. # ⚓ Guarding_against_DCSync_attacks⠀⇛ Gaining access to domain admin credentials is part of the endgame in many sophisticated attacks where threat actors are trying to maintain persistence. One of the ways that adversaries accomplish this is through DCSync attacks. # ⚓ Attackers_Will_Flock_to_Crypto_Wallets,_Linux in_2022:_Podcast [Ed: They now post "SPONSORED CONTENT" attacking the security credibility of Linux]⠀⇛ # ⚓ Addressing_CPAN_vulnerabilities_related_to checksums⠀⇛ This blog post addresses checksum and signature verification vulnerabilities affecting CPAN, the cpan client, and the cpanm client, which were published in a security advisory on 23rd November 2021. If you’re not aware of this topic, you might like to start by reading the advisory. This post gives a high-level description of the issues, what has been done to address them, what is still left to do, and what you should do. If you have any questions on this, you can add comments here, or email the PAUSE admins (modules at perl dot org). Before we dig into the details, we’ll first give an overview of how the relevant parts of the CPAN ecosystem work. # § Fear, Uncertainty, Doubt/Fear-mongering/ Dramatisation⠀➾ # ⚓ WhiteSource_Adds_SBOM_Tool_That_Lists Vulnerabilities [Ed: WhiteSource is almost a de facto Microsoft proxy [1, 2, 3]]⠀⇛ WhiteSource has added a software bill of materials (SBOM) tool to its portfolio that, in addition to capturing the components of an application, also surfaces vulnerabilities that should be addressed. # § Privacy/Surveillance⠀➾ # ⚓ Apple_to_NSO:_sue_you⠀⇛ Today, Apple filed a lawsuit in California against Israeli spyware company NSO Group for allegedly facilitating surveillance of Apple users. Access Now applauds Apple in taking a bold stand against surveillance tech used to facilitate human rights abuses. o § Transparency/Investigative Reporting⠀➾ # ⚓ Facts_on_the_Ground_Panel_Discussion⠀⇛ Featuring guests: Dr. Piers Robinson, Max Blumenthal, Cory Morningstar, Nick Hudson, Whitney Webb, Ryan Christian, and Rick Munn. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Another_voter_fraud_accusation_blows_up_in_Republicans’ faces⠀⇛ The mysterious case of Rosemarie Hartle’s vote in the last presidential election, three years after her death, was trumpeted in November 2020 by the Nevada Republican Party and various prominent conservatives. From then-President Donald Trump on down, Republicans used stories about phony votes cast under the names of dead people as key evidence for their claim that Joe Biden’s victory was marred by major fraud. The Hartle mystery is now solved. And it turns out that the fraud was committed by a Republican. Hartle was married to Las Vegas businessman Donald Kirk Hartle, a registered Republican. In November 2020, Hartle told Las Vegas television station 8 News Now (KLAS-TV) that he felt “disbelief” when he found out that a mail-in ballot was submitted in his late wife’s name. It was “pretty sickening,” he said at the time, adding that he didn’t know how it could’ve happened. o § Civil Rights/Policing⠀➾ # ⚓ Interpol_Election_Raises_Fears_About_Authoritarian Influence⠀⇛ TIINA JAUHIAINEN KNOWS the reach of the United Arab Emirates firsthand. In 2018, Jauhiainen helped her friend and skydiving partner Sheikha Latifa bint Mohammed al-Maktoum escape the country after accusing her father, the ruler of Dubai, of restricting her basic freedoms and locking up her sister. Jauhiainen and Sheikha Latifa fled the UAE on Jet Skis and boarded a yacht, but they were captured by Indian commandos in international waters and sent back to the UAE, where Sheikha Latifa was returned to her family and Jauhiainen was detained for a few weeks. Months later, back in her native Finland, Jauhiainen applied for a visa to Australia, where she wanted to visit a friend. Australia rejected her application, stating that she was the target of a criminal investigation. She later learned that she was named in a “red notice” requested by the UAE and issued by international policing agency Interpol — and only after a lawyer intervened did she get the notice rescinded. “It just shows how easily they can abuse the system,” Jauhiainen told The Intercept. Now Jauhiainen and others who have been detained in the UAE are watching Interpol’s upcoming election with concern. Ahmed Naser al-Raisi, a senior official with the UAE’s Interior Ministry who oversees security forces and detentions, is running for president of the organization. Al-Raisi’s fate will be decided at a meeting of Interpol’s General Assembly in Istanbul next week, and human rights advocates have been waging a campaign to stop him and a Chinese official who is also running for office. # ⚓ It’s_the_University_of_Austin_Against_Everyone_—_Including Itself_–_POLITICO⠀⇛ # ⚓ Justin_Bieber_called_on_to_cancel_Saudi_Arabia_concert_by slain_journalist’s_fiancée⠀⇛ The fiancée of murdered journalist Jamal Khashoggi wrote an open letter published by the Washington Post calling for Justin Bieber to cancel his upcoming concert in Saudi Arabia. “That’s why I am writing to you with a plea: Cancel your Dec. 5 performance in Saudi Arabia,” Hatice Cengiz wrote Saturday. “This is a unique opportunity to send a powerful message to the world that your name and talent will not be used to restore the reputation of a regime that kills its critics.” Bieber is set to headline at Saudi Arabia’s Formula One Race in December, joined by artists such as ASAP Rocky, David Guetta and Jason Derulo in Jeddah’s inaugural Grand Prix. Cengiz urged Bieber to remember he is performing on an invitation from Saudi Crown Prince Mohammed bin Salman himself. “Nothing of significance happens in Saudi Arabia without his consent, and certainly not an event as important and flashy as this,” Cengiz wrote. “Your face is even featured on the event’s website with his — the executioner of my fiance, Jamal.” o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ Bill_for_Austria_to_ratify_UPC_Agreement’s_PPA continues_to_progress_in_parliament [Ed: Team UPC wants us to think that Austria_miraculously_replaces_the_UK, in complete violation of the Vienna_Convention. They’ve lied_all_along so why_stop_now?]⠀⇛ In its plenary session on Friday 19 November, Austria’s National Council unanimously approved the draft legislation enabling Austria to ratify the Protocol on the Provisional Application (PPA) of the Unified Patent Court Agreement (UPCA) (report, recording). The National Council’s approval followed the unanimous approval and report of its Committee on Research, Innovation and Digitisation. The bill has now passed to the Federal Council and was assigned yesterday to its Committee on Innovation, Technology and the Future. If the Federal Council raises no objections, the final steps to promulgation of the law are authentication by the Federal President, countersignature by the Federal Chancellor, and publication in the Federal Law Gazette. # § Copyrights⠀➾ # ⚓ The_EU_Copyright_Directive’s_Neighboring_Rights_for Press_Publishers:_A_work_in_progress⠀⇛ Italy and Spain are latest in the line of European countries to adopt the European Union’s Directive on Copyright. The EU finalized the Directive on Copyright in the Digital Single Market in 2019 with the objective of ensuring “fairer remuneration for creators and rightsholders, press publishers and journalists, in particular when their works are (re)used online.” The Copyright Directive has been the subject of much debate, with Article 17’s requirement of prior authorization for uploading copyright protected content responsible for the bulk of the controversy. However, another section of the Copyright Directive that has garnered substantial attention is Article 15, which creates “neighboring rights” for press publishers for the online use of their publications. According to the World Intellectual property Organization (WIPO), ‘neighboring rights’ or ‘related rights’ are ancillary to copyright, and essentially enable press publishers to exclusively authorize or prohibit the use, reproduction, indexing or aggregation of their content, while ensuring that the legal and financial interests of persons and entities that have contributed to making the work available to the public (such as the original author) remain protected. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 8488 ➮ Generation completed at 02:41, i.e. 48 seconds to (re)generate ⟲