𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, November 05, 2021 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Sat 6 Nov 02:40:31 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/2021/11/05/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmZ9XrCCvCG4m4kD1sxmesDGxEpk9EjEVk5vNUFHZ87Ryw QmZQbFL87wWvs9kFDSndgbof4kDmQTqYdyokNAjNg8H7Ca QmSfTwYRE2mM7875hHQK9fmXEAAZS4i3r9frAmfJcCFGks QmWq5A18omXMGWTTDzH6NZwrkQWd1pUiLRptBpgDHHhvXq QmVR1Se3jKzW513QvSLv9utzGvBbi5C3cdSBwWspCid4vi Qme5Me7St6kgikNpzT1KeDRhhmCJJtsLSFQyP8TDyvd8MW QmagsjCozdhV3doZKjmRs6GYXQb7U425VW5GsX4YUfg2Fu QmXdXQ45MDdfyLhvFXMoFQarrFy2cSYrkTKdKtneXpHrYF QmNooKJgn2ZLXZJyZNJCACY5R84RsQy1y85ycxgS8JMkdA QmcbJ2ejJ9JqECW5WmJC4LeEqkjC7w6kcJ6wjwLthVmoEU QmR26bCkmAgeJHsLEpDDduxsZtvTiPxLdppYuH4w8mzfdo Qmex86DPLV4yK5WC34kReVXbdEtRT7fvt7mBVzMTGbSCct QmUF9ey4dzyvtaKZQVc5QTVyN1uh5C8nqhzm5bDtAjMpUH QmQQsCU87GH58r3ULuJPn4a3DUUCqjRgtvTnrTgEzE32uB QmXo7j8hPUpwapnbFNNyHpSzJw8jxwrfGCZfVzhG6m46Fc QmWRUGR4iW5rnmLQnw9FgqKFSzKTya3pneRJvmK2VknwKJ QmRj8aGQBLtRqtiYJQreD9xtEMzqDcpaLPjFYLoe48xgQ5 QmceuRQeatSitbW6vADhod8yMXLWphJhT1uYZmcy4rjm6f QmewryoNvgmB7zLqV7RQ2PTLYkagYXvBASicFQi1ESPiHm QmViJLHdiRf7wrstUaHcTaXuiWpGyTkptFkDjYAFoJBJoj QmVzPu6Qip7yK3FGSsrMzEt3zNmqWufLFF5CZNmsVbHZLd ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ More Videos on Our 16th Year | Techrights ⦿ Gemini Protocol is Very Useful for Escaping Misinformation, Targeted (Spying) Ads, and Spam | Techrights ⦿ Gemini Protocol Does Not Need to Be Extended to Support Multimedia (It Already Supports Audio/Video as External/System-Level Objects) | Techrights ⦿ Linux Isn’t Loved by Microsoft, It is Being Googlebombed by Microsoft | Techrights ⦿ IRC Proceedings: Thursday, November 04, 2021 | Techrights ⦿ EFF Has Been Hijacked, and Just Like Mozilla and the Linux Foundation It Doesn’t Fight for What It Was Originally Made to Achieve | Techrights ⦿ The Web is Still Getting Obese and and Very Hostile, But NetSurf Makes Things a Little More Acceptable | Techrights ⦿ Celebrating 15 Years of a Perfect Record Protecting Our Sources | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2021/11/05/16th-year-videos/#comments http://techrights.org/2021/11/05/gemini-protocol-good-for-information/#comments http://techrights.org/2021/11/05/gemini-protocol-video/#comments http://techrights.org/2021/11/05/googlebombed-by-microsoft/#comments http://techrights.org/2021/11/05/irc-log-041121/#comments http://techrights.org/2021/11/05/not-the-frontier-anymore/#comments http://techrights.org/2021/11/05/revisiting-netsurf/#comments http://techrights.org/2021/11/05/techrights-source-protection/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2021/11/05/beta-3-of-freebsd-12-3/#comments http://techrights.org/2021/11/05/libreoffice-7-3-alpha-1/#comments http://techrights.org/2021/11/05/lxqt-1-0-0/#comments ䷩ 𝚕𝚒𝚗𝚎 70 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/05/16th-year-videos/#comments Gemini version at gemini://gemini.techrights.org/2021/11/05/16th-year-videos/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ More_Videos_on_Our_16th_Year⠀✐ Posted in Site_News at 5:16 am by Dr. Roy Schestowitz Video_download_link | md5sum c1416d0a9378cad60ea78cd9cd6074a6 http://techrights.org/videos/changes-with-video.webm Summary: Lately there has been a ton of misinformation and ‘spam’ in the media (Edge, UPC and so on) and we need to respond to it or at least explain what’s happening; in order to do this efficiently we’ll use video, together with short texts that accompany and explain the gist of it THE current publication format and style in this site will change in favour of more rapid and more frequent releases of short posts in the form of videos, Gemini pages, and Web pages. Over the past couple of days we adjusted the workspace accordingly. The video above explains more. Our 15-year anniversary is celebrated this coming Sunday, which means that Monday onwards it is our 16th year. The goal will be to respond to misinformation quickly and very often, focusing on software freedom, patents, and various “tech rights” issues. Today we expect to make about half a dozen videos (think of it as a “pilot”) and we’ll see how long we can sustain such a rapid pace for. The videos will of course be shorter than the more recent videos which were about an hour long (almost exclusively about EPO_scandals). █ ䷩ 𝚕𝚒𝚗𝚎 117 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/05/gemini-protocol-good-for-information/#comments Gemini version at gemini://gemini.techrights.org/2021/11/05/gemini-protocol-good-for-information/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Gemini_Protocol_is_Very_Useful_for_Escaping_Misinformation,_Targeted_(Spying) Ads,_and_Spam⠀✐ Posted in Deception, Site_News at 9:22 am by Dr. Roy Schestowitz Video_download_link | md5sum 7bceb8180d13f685ee9b9471224f7fb2 http://techrights.org/videos/gemini-evolving.webm Summary: Unlike the World Wide Web (WWW or Web for short), Geminispace has (thus far) kept corporate influence and corrupting advertisers completely shut out; for a better experience of the Internet (and of Techrights) we continue to recommend our_capsule THIS site has a lot of exclusive material left to publish. It’s going to take months and we have a schedule for it. Misinformation/disinformation has mostly ruined the Web and we’re trying not to depend on it too much (we still use RSS feeds extensively); our main presence online is IRC and this Web site. Techrights does not do any Social_Control_Media (disinformation as a “business model” for “engagement”) or “apps” or “clown computing” or all that pseudo- ”smart” stuff. We’re traditionalists and it’s widely being recognised that technology — including the Web — is moving in the wrong direction. This sentiment has gone universal. We don’t wish to play along or participate in bad things. “Expect a lot more output in weeks to come.”Following the good news about Mr. Friedman_falling_on_his_sword (we speculated_it_would_take_several_more_months, not a couple of weeks) and bearing in mind that EPO runs from one blunder to another — a subject we shall cover in the weekend — we’ve decided to take a 2- day ‘break’ (recess from publication) and regroup for a better publication strategy, which revolves_around_video,_Gemini_and_the_Web_(last_priority). We made many code changes to that effect (the_changes_are_visible_to_all_in_Git). Expect a lot more output in weeks to come. Efficiency is considerably improved when focusing on substance, texts, and hard documents as opposed to misleading “tweets” and needless provocation. Grown-ups need to reject such traps, where censors and spies reward their victims (like an addiction) with “likes” and fake popularity, if not just the false impression thereof. █ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Trump_Greta_Thunburg_Emmy_GTFO:_Social_Control_Media⦈_ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠈⠛⠛⠉⠛⠙⠛⠛⠋⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠉⠉⠉⠁⠈⠙⢿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡯⠛⠛⠛⠛⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢐⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⣉⣉⣉⣉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⢺⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⢉⣉⣉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠖⠶⣶⠿⢷⠄⠸⣿⣿⠷⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠛⠿⠟⠛⠛⠛⠛⢿⠟⠿⠛⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠛⠛⠛⠉⠙⠻⣿⣿⣿⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠠⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⢙⣋⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠖⠶⣶⠿⢷⠄⠸⣿⣿⠷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠹⠛⠿⠛⠛⠛⠻⠟⣻⠛⠙⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋⠉⠛⢿⣿⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣦⣤⣄⣈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢠⣾⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⢉⣛⣛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣻⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠖⠶⣶⠿⢶⠄⠸⣿⣿⠖⠀⠀⠀⠀⠀⠀⢘⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣺⣿⣿⣿⣿⣿⣿⡧⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠙⠛⠉⠛⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠙⠻⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣯⣏⠁⠁⠀⠈⠿⡿⣿ ⣤⣬⣿⣿⣿⣿⠿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣰⣿⠟⠋⣀⣰⣾⣿⣿⣿⣿⣿⣿⡁⠅⠀⠀⠀⠀⠀⠉⠀ ⣿⣿⣿⣿⣿⣿⣾⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢠⣿⢃⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠘⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⢤⡀ ⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⢀⣀⣲ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⢨⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢘⣿⣟⠙⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠈⣻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢐⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠽⡽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠈⠆⠼⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿ 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⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣼⣿⣿⣿ ⠈⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢼⣿⣿⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⣿⣿⣿ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠸⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢻⣿⣿ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⠿ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⡀⠀⣿⣿ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀⠻⣗⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢂⠀⠀⠀⠈⠙⢿⣿⣿ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠈⡲⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠸⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠈⢻⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢰⣿⣿ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂⣡⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⠛ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠈⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠖⠶⣶⠏⢶⠄⢸⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⢀⣸⣿⣿⣿⣿⣿⣿⡆⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠙⠛⠋⠙⠛⠛⠛⠛⠉⠉⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠛⠛⠉⠈⠙⠻⣿⣿⡇⠀⠀⢀⣤⣾⣿⣿⣿⣧⡁⠈⠁⠀⠈⠹⣿⣿⣿ ⣤⣭⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⣠⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣞⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣼⣿⠟⣁⣲⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⢻⠏⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣿ ⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⢰⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡀⠀⠀⠀⢹ ⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠈ ⠈⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⠐⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⢷⣦⣤ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠈⣧⢿⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠸⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠘⠛⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿ 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⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠘⣯⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⣗⢕⣬⣮⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠳⣦⣤ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠘⣔⢚⢪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠸⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿ ⠀⠖⠶⣶⠏⢶⠄⢸⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹ ⢀⣸⣿⣿⡟⣿⣿⣿⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉⠉⠛⠉⠉⠋⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⠉⠉⠉⠁⠈⠙⢿⣿⣿⠀⠀⠀⣠⣤⣼⣿⣭⣅⡁⠀⠀⠀⠀⠀⢻⣿⣿ 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⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣟⡿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⢛⡊⡽⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠲⣦⣄ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⠑⠞⡻⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⡀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠸⡿⠿⠿⢿⠿⢿⠿⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⣿ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠛⠛⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠠⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠸⣿ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢿ ⠀⠖⠶⣶⠏⢶⠄⢻⣿⡷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘ ⢀⣣⣿⣿⣿⣿⣿⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠈⠙⠛⠉⠉⠙⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠋⠛⠉⠉⠀⠙⠻⣿⣿⡄⠀⢀⣀⣤⣤⣿⣵⣔⡀⠀⠈⠀⠀⠀⠸⣿⣿ ⣈⣹⣿⣿⣾⣿⣿⡏⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣿⣿⡿⠇⠀⢸⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⢻⣿ ⣿⣿⣿⣿⣿⣧⣶⡆⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⡿⠋⣀⠀⣼⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠈⢿ ⣿⣿⣿⣿⣿⣿⣟⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠻⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘ ⣿⣿⣿⣿⣿⣿⣿⡆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡗⠀⠀⠈⣿⣿⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠐⠶⣤⣀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⠿⠿⢿⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠂⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠒⢲⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢹ ⠀⠖⠶⣶⠏⢶⠄⣿⣿⡷⠖⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸ ⢀⣌⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠛⠛⠟⠋⠋⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠛⠛⠛⠉⠙⠻⣿⣿⣧⠀⠀⢀⣀⣀⣅⣺⣎⠀⠀⠉⠉⠀⠀⠈⣿⣿ ⠿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠀⢸⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠸⣿ ⣿⣿⣿⣿⣿⣭⣿⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⣿⠟⠁⠀⢠⣾⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⢻ ⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⠁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⢐⣀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣧⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣇⠀⠀⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⡹⣿⣿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠲⢮⣽⣬⡆⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠈⠙⣿⣶ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠩⠯⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠸⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢈⣿ 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⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⡄⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣷⣤⣀⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⠻⣿⣿⣶ ⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⣿⡟⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿ ⠀⠖⠶⣾⣿⣿⣿⠰⠶⠶⠖⠀⠀⠘⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⡟⡿⣿⡿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇⠀⣀⣻⣿⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡋⠉⠉⠁⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠀⠀⠈⠹⣿ ⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢻ ⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠁⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ 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⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠶⠰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣆⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣹⣿⣿⣟⣿⣿⠗⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣴⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣬⣆⡀⠉⠐⠀⠀⠀⠀⢀⣽⣼⣿⣿⣿⣿⣿⠉⠁⣤⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠻⢿⣿⣿⣿⡿⠛⠙⠙ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⠀⠀⠀⠀⠚⠉⠘⣿⣿⣿⡿⠋⢠⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⣟⠛⠉⠁⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠀⠠⠀⠀⠀⠀⢠⣿⣿⠏⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⢰⣿⣿⡷⠀⠀⠀⠀⠀ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⡿⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡆⠀⠀⠀⠀⠀⠈⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠿⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣴⣿⣿⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠟⠛⠟⠛⠛⠛⠿⠿⠛⡿⠛⠀⠀⠀⢸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣀⠀⠀⠀⠀⢀⣻⣻⢼⡿⠋⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⢟⠇⠉⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣽⣯⡁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠃⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠈⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡷⠶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿ ⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿ ⠛⢛⠟⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿ ⣿⣿⣧⠄⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡈⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠙⢿⣿⣿⣿⣿⣤⣿⣿ ⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠉⠉⠉⠉⢉⡉⠈⠀⠀⠀⠁⠀⠀⠀⢀⠈⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠻⣿⣿⡇⠀⠀⠀⠀⠹⠿⠛⠋⠛⠛⢿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠊⠹⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣦⡀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀ ⡙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⡇⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀ ⠈⣺⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠄⠡⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠲⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣧⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⡮⣫⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⣶⠿⢿⠷⠾⠾⢿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣂⣃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢼⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣯⣽⠀⣿⣿⣿⣿⣿ ⠀⠀⠠⠪⡚⡛⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡍⣽⣿⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⠀⣿⣿⣿⣿⣿ ⠄⠀⠈⠀⠙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⠀⠙⠻⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣷⣶⣤⣄⣴⣽⣶⣽⣿⣅⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⡀⢘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⢳⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠿⣿⠀⣿⣿⣿⣿⣿ ⠀⠀⠈⠄⢚⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢿⡿⠿⠿⢿⣿ ⠀⠀⢀⢀⠘⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠉⠉⠙⠋⠉⠋⠉⠉⠉⠁⠈⠉⠀⠀⢐⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⠿⠟⠛⢿⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠄⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠏⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣄⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣻⡟⠁ ⠀⠀⠀⠀⠀⠁⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠐⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⢿⣿⣿⣷⠀⠀⠀⠀⠈⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠬⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⠷⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢩⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⢯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠰⠋⠻⠿⠿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⣿⣤⣸⣿⣶⣿⣿⣿⣁⣉⣠⡀⠸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣯⣸⣿⣿⣿⣿⣿⣗⠄⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣆⠈⠿⣿⣿⣿⡿⠏⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡀⡀⡀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡅⠀⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡀⣢⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢹⣿⣿⣿⣍⣹⣭⣿⣹⣳⣷⠀⣸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠚⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠄⠀⢟⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣄⡀⠀⠀⠀⠙⠉⠙⠛⠛⠻⠋⢰⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠠⢨⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⣿⣿⣿⣷⣶⣦⣤⣤⣠⡄⠀⡂⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠁⠸⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡄⠹⣿⣿⣿⣿⣿⣿⣽ ⠀⠀⠀⠀⠀⠄⠈⠁⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠫⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠻⡯⠽⣻⠿ ⠀⠀⠀⠀⠀⠀⠐⠲⢿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣻⣿⣶⣥⣴⣦⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⡛⠀⠀⠙⣿⣿⣿⣿⡿⠟⠛⠛⠋⠉⠻⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⡤⣨⠲⢽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀⠀⠀⢠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⢈⡮⣾⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⢗⢽⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣿⣿⡏⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠫⣼⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇⢠⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠱⣖⠻⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣟⣽⣻⣿⣿⣿⣿⡻⣟⣿⣾⡽⢽⡿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠼⠟⡃⠱⠏⢑⠆⢚⡮⡒⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠑⠁⡐⡸⢘⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⣽⣤⣀⣼⣿⡘⣿⣿⣏⣀⢁⡄⠀⠻⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⠑⢿⣿⣿⣿⣿⣿⢇⠆⣿⣿⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣇⠀⠀⠀⢻⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⡯⠈⢠⣿⣟⢿ ⠀⠀⠀⠀⠀⠀⠀⢬⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡁⠀⠀⠊⣻⣿⣿⣿⣿⣿⣼⣿⣿⡋⠀⠀⣾⣿⣿⣯ ⠀⠀⠀⠀⠀⠀⠀⡤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣇⣉⣩⣭⣭⣙⣷⣆⠀⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠠⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣅⣀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠉⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢈⡀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣧⣿⣿⣦⣦⣄⣀⣀⠀⠀⡀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣟ ⠀⠀⠀⠀⠀⢀⠠⠨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡤⢈⣀⡆⠙⠿⢿⣿⣿⡟⢅ ⠀⠀⠀⠀⠀⠀⠁⠨⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⡇⠀⠀⠀⠙⡏⠉⠀ ⠀⠀⠀⠀⠀⠀⠠⢄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⡿⠿⠿⢻⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠁⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠛⠛⠛⠉⠉⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠅⣹⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢰⣷⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢧⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⡳⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡑⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠔⢽⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠇⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⣟⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢤⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠨⢿⠿⣿⢿⣿⣿⣿⡿⣻⢯⣻⠏⣽⢻⢻⣟⡭⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠩⣭⣧⣯⡟⢽⠿⢍⢹⠿⢇⣂⣻⣙⠈⡔⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠘⠓⠊⠀⠰⠥⠃⠬⠂⠂⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢀⠈⠂⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣰⣦⣴⣴⣶⣟⠙⢿⣿⣤⣤⣴⡄⠀⢸⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡏⠀⠀⠀⢹⣿⣿⣿⡿⠗⣶⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⡁ ⠀⠀⠀⠀⠀⠨⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢿⣿⣿⣇⣀⣿⣿⣿⣿⣿⠏⠀⢸⣿⣿⣿⣇ ⠀⠀⠀⠀⠀⠨⠝⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠈⢻⣿⡿⠿⠿⣿⣿⣿⢯⠀⢠⣿⣿⣿⣿⡛ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢼⣿⣶⣶⣴⣶⣶⣿⡟⢀⣿⣿⣿⣿⣿⣟ ⠀⠀⠀⠀⠀⠁⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡜⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣤⣄⡀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⡿⡃ ⠀⠀⠀⠀⠀⠈⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⠀⠀⠈⠹⠿⡿⠿⠠⠏ ⠀⠀⠀⠀⠀⠀⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠈⢛⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠞⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠱⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸ 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⠀⠀⠀⠀⠀⠆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣇⡀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⢸⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⢀⣴⠀⠀⠙⠻⣿⣿⣿⣿⡿⢿⣿⡋⠀⠀ ⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⠀⠀⠀⣠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢁⣤⡭⢿⣏⠉⠉⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠦⠤⠚⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠈⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣴⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠻⣿⣿⡅⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⣆⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⡍⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡷⡿⢿⠠⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣷⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⣿⠿⣽⠉⠀⣀⠧⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡿⣿⣷⢿⣿⣏⠉⠫⠉⠀⠀⠈⠀⠀⠁⢡⠅⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠠⠄⠶⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣬⣽⣿⣿⡿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢬⠟⠛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⡤⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⠿⠃ ⠀⠀⠀⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⢭⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠃⠀⠀⠙⠿⡧⣬⣿⣿⠿⠏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⢁⡉⢅⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⢙⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠿⠇⠽⠚⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⡀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠸⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣂⡀⠀⠀⠀⠀⠀⢀⣄⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⢉⠴⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠃⠁⠁⠸⣿⣿⣿⣷⣄⠀⠀⠀⣠⣾⣿⠀⠀⠀⠙⠛⠛⠛⠛⠿⠻⠟⠇⠀⠀⠀⠀⠀⠀ ⠀⠈⢹⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢉⣩⣭⣭⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠦⠄⠚⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⡟⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⡄⠀⠀⠀⠀ ⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣴⣿⣿⣿⣿⣇⡀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣛⣿⣽⣷⣦⡀⠀⠀ ⠀⠀⠐⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠈⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⢹⣿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠩⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣟⣿⣿⣿⣿⣟⣻⣿⣿⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⡗⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡑⠍⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⢀⢫⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣢⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⣅⠀⠾⡞⠿⠅⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣽⣿⣿⣿⣿⠋⠀⠀⠀⠀⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⡿⢿⠙⠻⣝⣿⣿⣿⣟⠯⢽⡇⠀⠈⠁⠐⠠⠄⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⠈⠐⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢿⣯⣭⣍⠁⠀⠀⠀⠀⢠⣟⠛⠛ ⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣇⠀ ⠀⠀⠀⠀⠀⢰⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡋⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣈⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡋⠉⢻⣿⡟⢿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⢰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⠓⠺⠿⠿⠋⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣤⣄⣄⠊⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠉⠈⠙⠀⠀⠀⠀ ⠀⠌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⣪⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣺⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⢹⣿⣿⣶⣀⠀⠀⠀⣀⣾⣇⠀⠀⠈⠛⠛⠻⠻⠛⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠔⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣉⣉⣏⡛⠋⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⡿⠦⠄⠚⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠬⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢸⣿⣾⡿⠁⠀⢠⣄⠀⠀⠀⠀⠐⣿⣿⣿⣦⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢍⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣴⣿⣿⣿⣧⣄⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⡷⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣻⣿⣽⣾⣷⡄⠀⠀⠀⠀⠀⢠⣴⠀ ⠀⠁⠠⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠸⣿⣿⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢻⣿⣿⣿⡇ ⠀⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣀⣸⣿⣿⣿⣶ ⠀⠀⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣯⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠩⢠⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠃⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣰⣿⣿⣿⣟⡻⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠟⢺⡿⣿⡝⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠘⠛⠛⠥⢿⣟⠿⢻⣿⣻⠛⠒⠀⠐⡚⡁⠂⣠⣤⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣟⣽⣿⠋⠀⠀⠀⢀⣿⡿⠿⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⢐⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠰⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣷⣄⣤⣭⣍⣭⡛⠛ ⠀⠶⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠤⠤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛ ⠀⠀⠀⠀⠀⠠⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡛⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡾⠿⣿⣿⡿⢿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠈⠿⠧⣤⣿⢿⡿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣄⢀⠠⠁⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠐⠒⠺⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠈⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⣿⣿⣧⣀⠀⠀⠀⣀⣾⡇⠀⠀⠈⠛⠛⠻⠟⠻⠻⠇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⣙⣋⠋⠋⠉⠉⠉⠀⠀⠀⣿⣿⣿⣿⠧⠤⠚⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⢀⢀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢸⣿⣿⡟⠀⠀⢤⣀⠀⠀⠀⠀⢿⣿⣿⣦⡀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠛⠛ ⠀⠘⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⣴⣿⣿⣿⣧⣄⠀⠈⠉⠀⠀⠀⠀⣾⣿⣿⣿⡷⠀⠀⢺⣿⣿⠀⠀⠀⠀⠀⢀⣐⣻⣿⣽⣿⣿⣦⠀⠀⠀⠀⢀⣠⣦⡀⠀⠀⠀ ⠈⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠘⣿⣿⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠰⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⠊⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣠⣤⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⢙⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⣾⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠸⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠠ ⠀⠀⠀⠀⠈⠬⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠈ ⠀⠀⠀⠀⠀⠀⠂⠈⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⢿⡗⢽⣿⢟⠡⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢰⣿⣿⣿⣭⣭⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢙⡟⠯⡻⣿⣿⣿⢿⠿⡿⡏⠙⠈⠁⠼⠉⠂⠁⢀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠩⠎⠇⠈⠑⠀⠀⠀⠀⠀⡀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣷⣾⡟⠀⠀⠀⠀⣾⣿⡉⠙⠿⠿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠙⢻⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣾⣭⡅⠀⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠉⠉⠑⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣬⣉⣬⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠉⠻⣿⠛⠿⣿⣿⡿⠛⣹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠉⠀⠊⠉⠛⠁⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠐⠈⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣄⠀⠀⠀⠀⣠⣶⠀⠀⠙⠿⠿⡿⢿⠿⣿⡄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣿⠟⠛⠛⠋⠁⠀⠀⣿⣿⣿⣷⠄⠠⠾⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣦⣄⡀⠀⠀ ⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⣿⣿⣿⠁⠀⢀⡀⠀⠀⠀⢼⣿⣿⣄⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⢿⣿⣶⣄ ⠀⢐⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣤⣾⣿⣿⣿⣦⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣰⣿⣭⣿⣾⣿⡄⠀⠀⠀⢀⣠⣮⡀⠀⠀⠀⠀⣸⣿⣿⣿ ⠀⠀⠩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⢻⣿⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⢀⣼⣿⣿⣿ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣻⣿⣿⣿⣻⣿⣷⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⣿⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣶⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠾⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠘⢹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢰⡄⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⡿⠿⣿⣿⣿⡇⠸⠿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⢻⡿⢿⢿⣿⣿⣿⣿⢛⡿⠟⠛⡛⠨⢥⠺⠃⢈⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⡪⠹⠯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠹⠶⢹⢯⢷⠁⠁⠀⠀⠀⢀⣀⣧⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⣻⣭⣿⠋⠀⠀⠀⣸⡟⠻⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠲⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⠀⠀⠀⢠⣿⣿⣶⣶⣶⣿⣽⣟⡛⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠉⠒⠒⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀ ⠸⠷⠶⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡟⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡟⠉⢹⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣦⡀⢀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⠿⣾⣿⣿⣿⣿⡿⠗⣿⣿⣿⣿⣿⣿⣿⣿⠊⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠙⠀⠔⠙⠋⠃⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠄⢶⠈⣰⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣧⡀⠀⠀⠀⣠⣾⠀⠈⠙⠛⠻⠿⠿⠿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠺⡯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣟⡿⠟⠛⠛⠃⠀⠀⣿⣿⣷⡦⠠⠾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⣿⣿⡏⠀⠀⡀⠀⠀⠀⣿⣿⣷⡄⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣤⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⣴⣯⣿⣷⣿⡷⠀⠀⠀⢀⣠⣴⡄⠀⠀⠀⠀⣼⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⢈⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠘⣿⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢱⣾⣿⣷⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄ ⠀⠀⠀⠀⠀⡷⢮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣭⣿⣿⣿⣽⣿⡇⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣾⣾⣿⣿⣿⣷⠀⢰⣿⣿⣿⡿⠛⠉⠉⠙⣿ ⠀⠀⠀⠀⠀⠈⠱⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣵⣿⡿⢊⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣯⣀⣀⢰⣿⣞⣿ ⣇⠀⠀⠀⠀⠀⠀⠀⠰⢞⣾⣿⣿⣿⣿⣿⣿⣿⣿⠽⡿⢧⠐⠗⡷⠇⢉⠈⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣫⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⣭⣿⣿⣿⡇⠀⠙⠻⣿⡿⢿⣗⡮⠝⣻ 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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣏⠊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠉⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⡯⢻⣿⣿⣿⣿⣿⣷⣗⡀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⣾ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠘⠒⡛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣨⠻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣷⠄⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣦⠀⢰⣇⠀⠀⠀⠀⢀⠤⢖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿ ⠘⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣄⣀⣀⣰⣿⣿⣿⣷⡄⠀⠀⠸⣿⡇⠀⠀⢻⠀⠀⢀⣴⣿⣿⣿⡏⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿ ⠀⠻⠿⠛⠛⠉⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⡇⠀⠀⠈⠀⠀⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⢸⠛⣻⡿⠏⠀⠀⠀⠀⠚⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⠀⠀⠀⠀ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠁⠀⠀⠀⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡉⢉⣭⣿⣻⣿⣿⡋⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠸⠀⡠⠄⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣄⡀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣤⣤⡀⠉⠁⠀⠀⠀⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠦⠀ ⠀⠈⠛⠿⠛⠛⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢽⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⢿⣿⣿⡿⠿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⡇⠀⠀⠀⣠⣡⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⣀⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢠⣴⣤⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣥⣽⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢙⣿⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠇⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣉⣉ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠅⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⣿⣿ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣿⣿ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⡳⠾⡫⢻⡿⠿⠿⠻⠿⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⣿⡦⠀⠚⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠇⠀⠀⠀⣀⣀⡀⠐⠆⠀⠀⣿⣷⠄⠀⣿⠀⠀⠀⠀⢤⣖⣂⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢿⣿⣿⣿⡿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣄⣀⣀⣾⣿⣿⣿⡆⠐⠀⠀⣿⡟⠀⠀⢹⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡿⠋ ⠀⡀⠀⠠⠬⠿⠛⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢹⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⠆⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠉⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠐⣯⣽⡿⠋⠀⠀⠄⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠉⠁⠀⠀⢀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⢉⣭⣿⣛⣿⣿⢟⢻⣦⡀⠀⠀⠀⠀⠀⠀⠡⡴⠑⠀⠠⣧⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⡄⠀⠀⠠⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀ ⠀⠈⠻⠿⠟⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠛⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢨⢼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣀⢠⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠ ⣿⣿⣿⣿⣷⣆⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣤⣾⣿ ⠉⠉⠉⠉⠉⠀⠀⠉⠀⠀⠀⠀⠉⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣐⣤⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠿⠻⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠛⠛⠛⠛⠛⣛⣛⣛ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠚⠿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣻⣿⣯⢿⣿⠿⣿⡻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⠌⠉⠈⠁⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⡇⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⡶⠄⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡇⠀⠀⣀⣤⣀⠀⠲⠀⠀⢸⣿⡆⠀⢾⡄⠀⠀⢀⣴⣖⣄⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠼⢿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣄⣀⣸⣿⣿⣿⣷⠀⠀⠀⢸⣿⠀⠀⠈⠇⢀⣴⣿⣿⣿⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡿⠋⠁⠀ ⠀⢀⣀⠠⠤⠤⠛⠛⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⢿⠀⠀⠀⠁⠈⣿⣿⣿⣿⠂⠀⠀⠀⣰⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣯⣼⡟⠁⠀⢀⣀⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⡁⠀⡀⠀⠀⣤⡉⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡉⢉⣽⣿⣻⣿⣿⢛⠁⠀⠀⠀⠀⠀⠀⠀⠰⠞⠈⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣦⣴⣶⣤⡀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠻⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⣿⣿⣿⣿⣆⠠⣤⠡⠄⠂⠀⠀⣾⣿⣿⣿⣷⣀⢀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣀⠀⠄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣢⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣔⣤⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⢐⣢⣀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠁⢹⣿⣿⣿⣿⣿⣿ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠈⠁⠉⠁⠁⠀⠀⠀⠀⠀⠄⠀⢀⣠⣀⠄⣭⣴⣽⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⣱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠟⡿⢷⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⡋⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠔⠀⠰⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣟⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢈⣶ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠭⣏⠿⢿⡛⠙⠑⢠⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠸⣽ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠈⠁⠂⠀⠀⠀⣿⡖⠀⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⣶⣤⡀⠈⢃⠀⠀⣿⡿⠀⢸⡇⠀⣠⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠉⠛⢿⣿⣿⣿⡿⠟⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣟⣿⣟⣻⠀⠀⠀⠀⣿⡇⠀⠀⠇⣾⣿⣿⣿⠃⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠈⠙⠻⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠠⠤⠤⠒⠊⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡆⠀⠘⠇⠀⠀⠀⣿⢿⣿⡿⠁⠀⠀⠰⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⠛⠋⠀⠀⠰⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠖⣠⠦⠀⢀⣶⣆⠐⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡍⢛⣿⣿⣻⣿⣿⣟⡀⠀⠀⠀⠀⠀⡀⠉⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣶⣤⣤⣬⣏⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⡧⠀⠀⠀⠀⡀⠀⠀⢸⣟⣾⣿⠀⠀⠀⢀⢀⢀⢰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣖⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀ ⣴⣿⣿⣿⣿⡃⠂⠓⣅⢁⠀⠀⢸⣿⣿⣿⣆⠀⢐⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣾⣲⣵⡓⠀⠀⢺⣿⣿⣿⣿⣰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣖⣠⣤⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡖⣺⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠟⠻⠟⠛⠓⠀⠀⠀⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠓⠙⠁⠁⠉⠀⠀⠀⠀⠦⠄⠂⠐⣨⣀⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣴⣭⣷⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⢿⡵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠒⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢻⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠙⢿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠙⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢍⠓⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣰⣾⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⡟⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣶⡄⠀⣀ ⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡋⠛⠛⠉⡃⠐⠀⢸⡄⠀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠻⠿⡛⠆⣿ ⠀⠀⠀⠀⠀⠀⠈⢧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⠀⠀⠀⢡⡀⠀⢸⣿⡁⠈⣅⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⣤⣠⢿ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣆⠀⠀⠀⠀⠸⣿⠁⠀⢻⣤⣾⣿⡿⠂⠀⢠⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⢿⣿⡿⠛⠉⠀⠀⠀⠀⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿ ⠀⠀⠀⠀⠠⠀⠒⠂⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠈⠀⠀⢸⣯⣽⠟⠀⠀⣄⣈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿ ⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢈⠄⢤⠀⠀⣠⡉⠉⠀⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿ ⠀⢠⣶⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠚⠃⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢛⣿⣿⣿⣿⣿⢛⠀⠀⠀⠀⠐⠂⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠻⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠀⠀ ⡇⠀⣿⣿⣿⣷⡃⢸⠭⡀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣴⣄⠀ ⣿⣴⣿⣿⣿⣿⣾⣿⣷⣃⠀⠀⢸⣿⣿⣿⠃⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⡀⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⣴⣾⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⣿⣿⣿⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣧⡠⠠⠠⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠿⠿⠿⠿⠟⠻⠛⠛⠛⠃⠀⠸⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠚⠓⠂⠂⠁⠀⠀⢀⣈⣤⣄⡸⠥⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⠿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⣛⣻⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠙⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⠿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⡖⠉⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣤⣶⣿⣿⣿⣿⣿⣟⠀⢤⣄⡀⠀⠀⠀⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢰⣿⣿⣧⡀⣀⣾⣿⣿ ⣇⠀⠀⠀⠀⠀⠀⢦⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢥⡯⡉⠀⠅⠀⠀⢸⣦⠀⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⡿⣿⣿⣿⣿⣿ ⣯⠀⠀⠀⠀⠀⠀⠈⢿⣴⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡀⠀⠀⠐⠂⠀⢸⣿⠆⠰⣇⣴⣶⡄⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢨⠉⠀⠀⠩⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⢿⣾⣿⣿⡟⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠈⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣻⠀⠀⠀⠀⠀⠈⣿⠀⢰⣿⣿⣿⠁⠀⠀⢃⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠈⠀⠉⠛⠟⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡦⠞⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠉⠀⢸⢿⣿⡟⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀ 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⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣬⣭⣉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠫⢁⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⣷⡆⠀⡀⠀⢰⡿⠶⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⡀⠈⢠⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⠉⢹⣿⣿⣿⣿⣿⣷⡀⢐⣾⠟⢋⠀⢿⠃⣀⣤⣀⠙⢿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣶⣧⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⠂⢀⣼⣿⡥⠀⠀⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢰⡀⠀⠐⠙⠿⣿⣿⡿⠋⠁⠉⠀⠀⠸⣧⡇⢀⣿⣿⣿⡇⠘⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣠⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢻⠇⠸⣿⣿⣿⡟⠀⢹⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⠾⠟⠀⢠⣄⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠘⢿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣙⣟⣒⠠⠤⠀⠀⠀⠐⡴⠀⢀⣷⡀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀ ⣿⣿⣿⣿⣿⣷⣴⣶⣶⣤⣤⣤⣤⣄⣙⣿⣿⠛⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠒⠒⠒⠂⠀⠀⠀⠀⠀⣀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠀⡀⢤⠤⠤⠤⠤⣾⣿⣿⡀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠈⠉⠈⠀⠀⠀⠀⠻⣿⣿⣇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠻⠿⠿⠻⠿⡿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠛⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣴⣿⣿⣿⣷⣶⣶⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⠆⠀⠀⠀⠀⠀⣴⣸⡇⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣶⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡰⠀⠀⠀⠀⣿⣿⣇⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡔⡠⠠⢠⡐⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠙⠁⠁⠀⠀⠈⠛⠛⠓⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⡐⠀⠐⠀⠠⡐⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠕⠀⢠⣾⡷⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⢶⣶⣶⣶⡏⠁⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⡅⠀⠨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⡃⠀⢀⡀⠀⠘⠟⠀⢸⣿⡿⣿⣿⣿⣿⣧⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠰⠶⢶⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠘⠂⠍⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⢿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣄⣰⡧⠀⡰⠛⠛⠻⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠱⣄⣀⠂⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣇⠁⠀⠀⠀⠀⢂⠀⢈⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢶⠂⠘⢿⣿⣿⣿⣿⣿⠆⣼⠟⠉⠰⣄⠈⢠⣶⣶⣄⠹⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣷⡀⠀⠉⠙⠻⣿⠟⠀⠀⠀⠀⠀⠀⢻⠂⣼⣿⣿⣿⡀⢹⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠐⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠁⠀⣿⣯⠀⢠ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠄⠒⠀⠀⠀⢻⣿⣿⣿⣿⡉⢉⣿⡏⠶⠶⠂⠀⠀⠀⠘⢉⡁⠀⡠⠛⠦⠄⠀⠀⠀⢀⠀⠀⠀⠀⢘⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠈⠓⠀⣼ ⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠉⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠼ ⠁⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠈ ⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣧⣶⣶⣤⣤⣤⣤⣄⣙⣿⣟⡛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠤⠦⠄⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠤⠤⢤⣤⣤⢤⢤⣽⣿⣿⠀⠀⠀⢀⣄⠀⡏⠀⠀⠀⠀⠀⠙⠋ ⠀⠈⠻⣿⣿⡿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠛⠈⠃⠀⠀⠀⢿⣿⣿⡆⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠤⠶⠶⠒⠒⠒⠒⠒⠛⠓⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢺⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣿⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠾⣿⡿⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠲⠦ ⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣿⣿⣷⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣄⢀⠀⠀⠀⠀⣿⣽⣇⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣠⠀⢐⣿⣿⣗⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡕⠴⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠋⠉⠉⠀⠀⠈⠙⠙⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡀⠄⢠⢤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣾⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡐⢶⣿⣿⣿⡏⠁⠀⠁⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠴⢶⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢟⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣷⣿⣿⣿⣿⡁⠀⣄⣀⠀⢸⡏⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠗⠳⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡏⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⣿⣿⣇⠀⢿⣻⣤⢾⠷⡤⠚⠋⠙⢿⣿⣿⣿⡅⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣦⣠⡃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠡⢀⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡿⠁⠘⣻⣿⣿⣿⣿⠿⠢⠾⠋⠀⠰⣦⠀⣴⣿⣶⡄⢻⣿⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⡃⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣧⣿⡏⠀⠀⠀⠀⠀⣴⣿⣿⠁⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⣿⣄⠀⠈⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⠛⢀⣿⣿⣿⣧⠀⢻⣿⡁⠀⢰⣾ ⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⢀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⣿⣿⠟⠀⣀⣐⠿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡇⠀⠈⣿⠁⠐⢸⡿ ⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠄⠛⠀⠉⠀⠀⠀⠘⣿⣿⣿⣿⣦⣴⣿⣇⠙⠏⠈⠁⠐⠀⠣⠴⠀⢠⣍⠉⠀⠀⠀⠀⢀⡄⠀⠀⠀⠸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠉⠀⠀⣿⣷ ⠁⢀⠙⣿⣿⣿⡇⠀⠀⠀⠂⠀⠀⠀⣰⣿⣿⣿⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⣀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡈⠀⠀⠀⠀⣛⡋ ⠁⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⠳ ⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⣿⣿⣿⣧⣶⣶⣤⣤⣤⣤⣄⣙⣿⣿⡛⠻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣤⡤ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⢁⣀⢱⡖⠒⠒⢲⣿⣿⣷⠀⠀⠀⣶⡦⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⣿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⣀⣀⣀⣛⣿⣿⡆⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⢻⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠖⠲⣶⠿⣷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⠀⠀⢰⣿⣟⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓ ⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡀⠀⠀⠀⠀⠀⣂⣾⠀⠀⠀⠀⠀⠀⣠⣠⣤⣴⣿⣷⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⡧⣐⠂⠄⠀⢀⣿⣿⡦⠀⢀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣠⠀⢰⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣄⣵⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠋⠉⠉⠀⠀⠈⠛⠛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⡀⣠⣒⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠽⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢻⣿⣿⣿⡅⠀⠀⠀⠹⣿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣷ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⡿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⣤⡠⠀⣿⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠈⠛⠙⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿⣿⣿⣿⣆⠘⢿⣷⠔⠿⠗⠀⠀⠉⠹⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢷⣴⡅⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⣿⠁⠈⠟⣿⣿⣿⡿⠋⠐⠋⠀⠀⠈⠇⢰⣿⣿⡆⠸⣿⣿⡇⠀⠀⠀⣀⣀⣈ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⡅⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⣾⣿⣿⠀⢀⣣⡀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠈⢻⠀⢀⠀⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣀⣠⠄⠂⠀⠹⣿⣿⣿⣿⡿⠛⣿⡿⣿⣤⢄⡀⠀⡿⠿⠃⢀⢦⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠸⠀⠀⢠⣿⣛⣿⣿ ⢿⣿⡿⠛⠿⣿⣧⠀⠀⠀⠀⡀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣾⣿⣷⡈⠁⠀⠀⠀⠉⠛⠀⣾⣆⣀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠄⠐⠂⠈⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣦⣿⣿⣿⣶⣿⣿⣿⣧⣀⡐⢦⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠐⢧⡀⠓⠿ ⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢳⣄⣤ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠻⣿ ⠀⢀⣾⣿⣿⣶⣴⣶⣶⣤⣤⣤⣄⣀⣙⣿⣿⡛⢻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢀⣀⡀⢹ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣯⣦⣿⣿⣿⣿⣿⣿⣿⣿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⢤⠤⠤⠤⣬⣿⣿⡅⠀⠀⢠⣤⢠⣿⠁⠀⠀⠀⠀⠚⠛⠉⠉⠉⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠸⡟⠈⠉⠈⠀⠀⠀⠘⣿⣿⣧⠀⠀⣾⣿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠻⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠀⠀⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢻⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⠤⣤⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢀⠀⠀⠀⢩⣺⡇⠀⠀⠀⠀⠀⢀⣄⣤⣿⣷⣿⣿⣿⣧⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣯⡡⣎⡂⠀⣿⣿⣷⣀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣤⡄⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣴⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣖⣖⣦⣇⡀⡂⢀⡄⣐⢄⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢥⣍⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢘⢓⣛⣛⣻⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡂⠀⠀⠄⠘⠛⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣍⣿⣿⣿⡗⠀⠀⠀⠀⢻⣿⣿⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣾⣿⣵ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣦⠂⢸⣿⡇⠀⠸⣿⣽⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⡀⠩⡌⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⢿⣿⣿⣿⣿⣿⣄⣀⡿⠛⠙⢿⠁⣀⣄⡀⢻⣿⣿⡇⠀⠀⠀⠀⠸⠿⣿⠈ ⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⡏⠀⣠⣾⡷⠀⠀⡄⠀⠈⠰⡄⠀⠀⠀⠀⢸⣯⡀⠐⠟⠿⣿⡿⠋⠀⠉⠀⠀⠀⠀⢠⣿⣿⣿⠀⠛⠿⡇⠀⠀⠀⢀⣤⣤⣶⣿ ⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣿⣿⡗⠀⣦⣶⡀⠐⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠁⠀⠀⠃⠠⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⡄⠤⠐⠊⠁⠀⠘⣿⣿⣿⣿⡟⢹⣿⠻⣿⡷⢤⢄⣏⡉⠀⣸⠛⠿⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡄⠀⠀⠀⠀⢀⣲⣿⣭⣿⣿⣿ ⠉⠛⠛⠃⢀⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢻⣿⣿⣧⠈⠀⠀⠀⠀⠈⠀⣿⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠂⠀⠀⠀⠀⣿⡿⠿⣿⣿⣿ ⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣧⣀⡘⠆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠈⠳⡄⠉⠛⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣦⣶⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣿⣿⠛⢻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢤⣿⡧⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⣀⣤⡤⠤⠄⠘⣷ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⡿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠩⠍⠟⠉⠉⠉⣿⣿⣿⠀⠀⠀⣾⡆⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣄⡀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣘⣛⣛⡇⠀⠀⣿⡇⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢸⣿⡏⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⢻⠛⠛⠻⠿⠿⠻⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⢠⣀⠀⠀⢀⣿⡄⠀⠀⢀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣷⣷⣦⣦⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⡄⢠⣿⣿⡇⣄⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⣦⣶⣾⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠃⠸⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠷⠚⠚⠸⠚⢶⣤⡥⣰⢤⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤ ⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⢀⣤⣅⠀⠀⠀⠀⠀⠀⠀⠠⠩⠍⠩⣭⣽⣽⣿⡟⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⣼⣿⠟⠛ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠂⠀⠙⠰⠄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣾⣿⣿⣿⡃⠀⠀⢀⠀⢻⣿⡿⠛⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠰⠶⢷⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⣻⣀⣾⣿⡷⠀⠈⠻⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⡿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣄⣈⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⡀⠀⠀⠀⠰⢇⠀⠀⠀⠀⠀⠀⢸⡟⠀⢻⣿⣿⣿⣿⡿⠆⡴⠋⠁⠈⠋⢠⣶⣶⡄⠹⣿⣿⡇⠀⠀⠀⠀⠘⠛⠓⣠⣨ ⣿⣻⣿⣿⣿⣿⣿⠄⠀⠀⠸⣿⡃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⡏⠀⠰⡀⠀⠀⠙⠄⠀⠀⠀⠀⢸⣷⡀⠁⠉⠙⢿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⠀⠈⠙⠃⠀⠀⠘⢠⣶⣾⣿⣿⣿ ⣿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⠁⢀⣛⠿⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⣻⣿⡏⠀⠀⠀⠀⠀⠀⣁⢸⣿⢿⣿⣿⣿ ⢿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠘⣿⠄⠐⠀⠁⠀⠀⠀⠘⣿⣿⣿⣿⣧⣴⣯⠹⡯⠻⠲⠶⣅⢀⣧⡍⠑⠀⠀⠀⢠⡄⠀⠀⠀⢸⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⢘⡱⣿⣿⣿⣿⣿⣿ ⠀⠈⠉⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣻⣿⣿⣧⠀⠀⡀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠈⢦⢊⡉⠙⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣧⡀⡙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣿⣿⠛⢻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣀⣀⣀⣺⣿⡇⠀⠀⠀⣀⠀⣿⣿⠋⠀⠀⠀⠀⠠⠶⠒⠛⠛⠀⠹⣧ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣯⣴⣿⣿⣿⣿⣿⣿⣿⡿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠒⠂⠃⠀⠀⠈⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⡀⠀⠀⠡⠤⠤⠀⠀⠀⠒⠒⠚⠛⠛⠂⠀⢸⣿⡇⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠈⠛⠻⠟⠛⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠒⠒⠒⠒⠐⠂⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⣿⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠦⢤⣀⡀⠀⠀⠀⣰ ⣿⣿⣿⣇⡀⣾⣿⡿⠀⠀⠀⠀⢀⣦⣿⡄⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣴⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀⢰⣿⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣄⠀⠀⠀⡀⢀⠀⠀⢄⢄⣄⣄⢠⡠⣔⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠀⠘⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠉⠀⠉⠉⠈⢹⣾⣬⣬⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿ ⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⣶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠐⠂⢐⢶⣾⣿⣿⡏⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢰⣿⣿⢋⣉⡛ ⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠴⡶⠆⠀⠀⠀⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠁⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⡅⠀⢀⡀⠀⢹⣿⣿⠋⠈⢿⡿⢿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⣀⠘⠛⠻⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⣿⣿⣿⣿⣦⠀⠈⣹⠤⢿⣿⠟⠀⠀⠘⠿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡏⠿⠿⠏ ⣿⣿⣿⣿⣿⣿⣿⡖⠈⣶⣭⡁⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⢸⡟⠀⣹⣿⣿⣿⣿⠟⠃⠞⠁⠀⠀⠁⢰⢿⣿⣆⠘⠿⢿⠀⠀⠀⢀⣀⠘⣉⣠⣶⣷⣤ ⣿⣿⣿⠿⣿⡿⢿⠗⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣈⣤⠀⠀⠈⠂⠀⠀⠀⠀⣾⣿⡄⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⡀⠀⠀⠀⠀⢭⠃⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⢀⠠⠄⠀⠘⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠟⠀⡰⣌⡉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⢀⠤⠀⣼⣛⣽⣿⣿⣿ ⠙⠿⠿⠿⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣯⣾⣧⠹⢿⠛⠛⠂⠀⠓⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠸⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⢸⡖⠀⣿⡿⢿⣿⣿⣿ ⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣹⣿⣿⣧⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠳⠤⠷⡀⠙⠛⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣧⡀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣤⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠘⣿⡀ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣀⣙⣿⣟⠛⢻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠠⡤⠤⠤⢤⣽⣿⡇⠀⠀⢠⣤⠀⣿⣿⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢹⣷ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣯⣴⣽⣿⣿⣿⣿⣿⣿⡟⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠉⠁⠁⠀⠀⠀⠿⣿⣿⠀⠀⢸⣿⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣦⣤⣤⣄⡀⠀⠙⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠀⢸⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠈⠛⠿⠟⠛⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡄⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⠤⠤⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⡟⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣠⡟ ⣿⣿⣇⣀⣿⣿⣇⣀⠀⠀⠀⢐⣷⣿⡄⠀⡀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣤⣴⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⣞⣽⣰⠀⢺⣿⣿⣴⣈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣒⣴⠧⠀⡄⡀⠀⢀⠤⡀⢄⡄⢄⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡏⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⣐⣤⣭⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀ ⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⡀⠀⠀⠀⠅⢀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⢿⡋⡂⠀⠀⠀⠀⠀⠀⠁⠀⠀⣈⣻⣿⣿⣿⠆⠀⠀⠀⠘⣿⣿⣿⣿⢿⣿⣿⣿⡤⠀⠀⠀⠀⠀⣼⣿⣏⣤⣤⡜⠛ ⣿⣿⣿⣿⣿⣿⣿⠀⢀⣻⣛⠀⠀⠀⠀⠃⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⠄⠀⠢⡄⠀⣿⣿⣿⡏⠀⢹⣿⣹⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣆⠈⢥⠉⠀⠀⠀⠀⠀⠁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⡀⠄⠀⠀⠀⠀⠀⠀⣼⣿⠙⣿⣿⣿⣿⣿⣧⡀⣠⡴⠂⢻⡿⠋⣀⣀⠈⢝⣿⣿⠀⠀⠀⠀⠀⣿⣿⠏⠛⢛⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⠀⠀⠑⠄⠀⠀⠀⠀⠀⣿⡇⠀⠜⠿⢿⣿⡟⠉⠈⠁⠀⠀⠀⠀⣸⣻⣿⡇⠈⠙⠻⠀⠀⠀⣤⣴⠏⣤⣶⣶⣿⣿⣦ ⣿⣿⣿⣛⡟⠛⠛⠏⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⠀⠠⠀⠀⠀⠀⠟⣿⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⠠⠐⠂⠀⠘⢿⣿⣿⣿⣿⣟⢛⡿⣿⣿⣿⣿⠀⠚⠖⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣇⠀⠀⠀⠀⠀⢠⡄⠘⢲⣿⣿⣿⣿⣿⣿ ⠈⠙⠛⠛⠀⠀⠀⠀⠀⠘⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣿⣷⡘⠝⠉⠛⠒⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠰⡄⠀⢸⠿⠫⣿⣿⣿⣿ ⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣼⣿⣿⣧⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠙⠒⠀⠳⡄⠀⠈⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣧⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠁⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⣤⠴⠶⠶⠄⠸⣧⠀ ⠀⢀⣴⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣀⣙⣻⣟⠛⠻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠋⣠⠰⡖⠒⠒⢲⣿⣿⡆⠀⠀⢰⣶⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣦⣼⣿⣿⣿⣿⣿⣿⡿⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣛⣟⣿⠀⠀⢺⣿⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⣸⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠈⠛⠿⠛⠛⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠂⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠛⡟⠛⠛⠟⠿⠿⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⠖⠲⣶⠆⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣤⡞⢿ ⣿⣴⣼⣿⣿⣂⢀⣠⡀⠀⣸⣿⡟⠀⢀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣔⣶⣶⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⠷⠷⠁⠀⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠾⠼⠦⠄⠀⠂⡀⡄⢀⢀⢽⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣤⣀ ⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠩⣭⣭⣿⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣄⣶⡿⠿⠿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡆⢀⣤⣄⠀⠀⠀⠀⠰⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠿⠤⠁⠀⠀⠀⠀⠀⠀⣀⣀⣴⣤⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣿⣿⣷⣷⣶⡌⠉⣿ ⣿⣼⣿⣿⣿⣿⣷⣾⢿⡅⠀⠀⠀⠀⢁⡯⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠲⠀⢰⣿⣿⡿⠇⠀⢸⣿⣾⡇⠀⠀⠀⠀⠠⣿⣿⢿⣿⣿⠇⠀⠁ ⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠁⠄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⢘⡇⠀⠀⠀⠀⠀⠀⣿⠃⠸⣿⣿⣿⣿⣿⡧⢠⠖⠋⠈⠻⠋⣠⣶⣄⠀⠆⣿⡇⠀⠀⠀⠀⢸⣿⠿⠀⣉⣁⣄⡀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⡿⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⣿⡄⠀⠉⠛⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⢐⣾⣿⡏⢴⣿⣿⣿⣿⣿⡆ ⣿⣿⣿⣭⠉⠉⠉⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⡿⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠐⠀⠀⠀⠈⠉⢿⡇⣸⡿⣿⣿⣿⣿⣷ ⢿⣿⣿⣿⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠤⠂⠈⠀⠀⠈⢿⣿⣿⣿⣿⡟⢛⡿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⣄⠀⠀⠀⢸⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⢿⠁⠈⢡⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠉⡁⠀⡀⠀⠀⠸⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⣿⣿⣷⡈⠊⠈⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠐⡀⠀⠀⣋⠁⠺⠿⣿⣿⠤ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣾⣿⣿⣷⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢳⡀⢀⣸⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣶⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣧⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠛⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⣀⣀⣰⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠖⠛⠛⠛⠃⠈⣿⡄⢸ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣀⣀⣙⣿⣟⠛⠻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠐⠒⠹⠉⠀⠀⢻⣿⣿⡄⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣤⣿⣿⣿⣿⣿⣿⣿⠿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠭⠭⠅⠀⠀⣿⡇⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣦⣤⣤⣤⡐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟ ⠀⠈⠛⠻⠛⠛⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⡀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⠀⠀⠀⢸⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢻⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣄⣀⠀⠀⠀⠀⣰⣿⣿ ⡀⠆⠲⣶⠆⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠟⠛⠛ ⣿⣾⣿⣿⣶⠀⡠⡀⢠⣿⣿⡟⡂⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⡤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡀⣦⣼⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠛⠛⠛⠛⠛⠓⠂⠐⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠓⠛⠁⠀⠀⠐⠒⣅⡾⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣶⣶⣿⣄⡀ ⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢰⡞⠦⠀⠀⠀⠀⠀⠀⠐⠀⠒⠐⠶⣶⣶⣿⣿⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣶⣿⢟⣛⠛⠿⣿⣿⡇ ⡿⣿⣿⣿⣿⣿⡶⣶⡆⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠀⠀⠀⠀⠀⠀⢠⣤⣴⣾⣷⣿⣿⣿⡇⠀⢀⠀⠀⢸⣿⣿⣿⣿⠋⢻⣿⢿⡆⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⠀⢨⡿⠃ ⣷⣿⣿⣿⣿⣿⣿⠻⠇⠀⠀⠀⠀⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⠀⠀⠀⠀⠀⠀⢘⣿⡿⣿⣿⣿⣿⣿⣧⠀⠀⢹⣠⢼⣿⡿⠛⠉⠀⠸⠿⢟⡇⠀⠀⠀⠀⢸⣿⡟⠻⣿⡿⠁⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠈⠉⠙⣅⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠇⠸⡄⠀⠀⠀⠀⠀⢸⡿⠁⣘⣿⣿⣿⣿⡿⠓⠴⠋⠀⠀⠙⠁⣾⣿⣦⠈⠙⠿⠇⠀⠀⠀⣀⣸⣿⡿⣀⣤⣤⣷⣦⡄⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣩⣿⣿⣿⣟⠀⠀⠈⠂⠀⠀⠀⠀⢸⣿⣆⠈⠁⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠄⠀⢀⠀⠀⠀⠘⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⡀ ⣿⣿⣷⡾⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣯⠀⠀⠈⠀⠀⠀⣈⡈⢿⣿⢤⣿⣷⣿⣿⣿⣿⡇ ⠻⣿⣿⡷⠀⠀⠀⣿⠀⠀⠀⠀⡀⠤⠔⠂⠉⠀⠀⠀⢻⣿⣿⣿⣿⣏⢉⣿⢻⣿⣿⣿⠀⠀⠀⠀⠰⠆⠀⠀⠀⢸⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⡀⠀⠀⠀⠀⠛⠁⠀⣿⣿⡿⢿⣿⣿⣿⣿⠃ ⠀⠀⠀⡄⠀⠄⠀⠙⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⣿⣿⡆⠑⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⢆⠈⠉⠛⣿⣇⢲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣿⣿⣿⡄⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢳⣠⣤⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣷⡀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠈⣿⡍⠁⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠄⠠⣤⠤⠤⠤⣽⣿⣯⠀⠀⠀⣤⡀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢸⣷⠀⣿ ⠀⢀⣶⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣙⣿⣟⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠁⠁⠀⠀⠀⢻⣿⣿⡄⠀⠀⣿⡇⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡟ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢁ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣦⣤⣬⣭⡉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⢨⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡼ ⠀⠈⠛⠿⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠦⢤⡄⠀⠀⣸⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢻⠙⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⡿⡀⡀⠀⠿⠿⠿⠿⠇⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣀⠀⣸⣿⣿⣿ ⣄⠆⠲⣶⠆⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉ ⣿⣿⣧⣶⣄⢂⠀⢸⣿⣿⡦⣀⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⣆⣀⡂⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠉⠉⠉⠀⠀⠈⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠄⠠⠴⡂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣾⣿⣿⣿⣶⠀⠀ ⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣻⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢰⣿⣿⣩⣍⡙⠿⣿⣿⠰⣶ ⠟⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠨⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⡅⠀⢀⠀⠀⢸⣿⣿⣿⣿⠉⢹⣿⡻⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢾⠛⢸⣿ ⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡘⠎⠪⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⢸⣽⠟⣿⣿⣿⣿⣿⣧⠀⠀⣡⠄⢻⣿⠟⢉⡁⠀⢖⣻⢋⠀⠀⠀⠀⠀⢸⣿⡇⠻⠿⠋⠀⠀⠀⠀⠛ ⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠻⢀⠀⠀⠀⠀⠀⢸⡏⠀⣹⣿⣿⣿⣿⠟⠁⠋⠁⠀⠀⠉⢰⣿⣿⣇⠀⠈⠛⠀⠀⠀⢀⣤⣾⣿⡿⣢⣤⣶⣶⣿⣦⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠇⢀⠀⠀⠀⢞⣿⣿⣿⡇⢽⣿⢿⣿⣿⣿⣇⠀ ⣿⣿⣷⡆⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣯⣿⣇⠀⠀⠀⠀⠀⠀⢤⠈⢿⣿⡧⣿⣭⣿⣿⣿⣿⣿⠀ ⠿⣿⣿⠇⠀⠘⠇⠀⠀⠀⠀⠀⠀⠠⠐⠊⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⡉⣉⡟⣿⣿⣿⠀⠀⠀⠘⠂⠀⠀⠀⠸⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠘⠀⠀⢨⡟⡿⠟⣯⣿⣿⣿⠟⠀ ⠀⠀⠠⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⣾⣿⣧⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⣦⡀⠐⠙⠳⡄⠈⠉⢹⣿⣉⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣿⣿⣿⣇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣦⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠀⢿⡎⠀⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡖⣒⡲⡶⠖⠒⢲⣿⣿⡇⠀⠀⢠⣤⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⡀⣿⣿ ⠀⢀⣴⣿⣿⣶⣴⣶⣶⣤⣤⣤⣀⣀⣉⣻⣟⠛⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠿⠿⠿⠀⠀⢸⣿⠀⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡟⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣤⣿⣿⣿⣿⣿⣿⣿⡿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣉⣉⣉⣉⣉⣉⣉⠀⠀⢸⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⡟ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⡞⠀ ⠀⠈⠛⠿⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣶⣶⣶⣿⡆⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⠄⠀⢀⣸⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢻⠙⠛⠛⠛⠿⠿⠻⠿⢿⣿⣿⣿⡿⠀⠘⠛⠛⠛⠛⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣾⣿⣿⣿⣆ ⣦⡆⠲⣶⠆⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉ ⣿⣷⣄⣠⣀⡀⠀⣿⣿⣯⣤⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣀⣄⠂⠀⠀⡀⢀⠀⢄⣀⣤⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠁⠀⠉⠉⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⢐⢁⣾⢟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀ ⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠟⠿⠿⠿⠿⠿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣾⣿⣿⣷⣧⡆⠀⢠ ⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠉⢀⣙⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣾⣿⣫⣥⣍⠻⢿⣿⡇⣦⣿ ⢻⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣿⣧⠀⠀⢄⠀⢈⣿⣿⣿⣿⡏⠈⣻⣟⢿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡁⠸⠟⠁⣿⡟ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠚⠙⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⡟⢻⣿⣿⣿⣿⣿⡄⠀⣨⠴⠺⣿⡟⢉⣁⡀⢰⣛⡛⡁⠀⠀⠀⠀⢸⣿⣿⠙⠿⠟⢀⠀⠀⠀⠛⢹ ⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠃⣠⣾⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⠧⠀⠀⠀⠀⠀⠸⣿⠀⠈⢿⢿⣿⣿⠟⠉⠘⠁⠀⠀⠈⠀⣟⣿⣿⠀⢈⠘⠃⠀⠀⢀⣤⣼⣿⣿⡗⣤⣶⣶⣿⣷⣤⠀⠘ ⣿⡿⢿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⢸⠀⡄⠀⠀⠠⢿⣿⣿⣿⠠⣿⣿⣿⣿⢿⣿⡄⠀ ⣿⣿⣷⠇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢨⣽⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⡀⠀⠀⠀⠀⠀⢰⡄⠻⣿⣿⢢⣿⣶⣿⣿⣿⣿⡗⠀ ⠿⣿⣿⠇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠉⠀⠀⠈⢿⣿⣿⣿⣿⡏⠉⣩⢿⣿⣿⠀⠀⠀⠃⠀⠀⠀⠘⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢘⡿⢻⣽⣿⣿⣿⠁⠀ ⠀⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣷⣾⣿⡘⠢⠉⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⢰⣄⠀⠈⠋⢣⡀⠀⠉⣿⣿⡍⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣸⣿⣿⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⣶⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣦⣬⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⣀⣴⣦⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡄⠘⣷⠀⢸⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⢂⣐⢶⠒⠒⠒⣾⣿⣷⠀⠀⠀⣴⡆⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⣿⡇ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣀⣀⣉⣻⡟⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠿⣿⡇⠀⠀⣿⡇⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣼⢻⡇ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣤⣿⣿⣿⣿⣿⣿⣿⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣾⠁ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣸⠃⠀ ⠀⠈⠛⠿⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠀⠀⣠⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢻⠛⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⡿⠀⠛⠛⠛⠛⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⣴⣿⣿⣿⣷⣀ ⣦⡆⠲⣶⠀⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉ ⣿⣷⣥⠦⠀⢸⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⢀⡀⠀⠀⠀⡀⡠⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠁⠀⠈⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣤⣀⠀⠀⠀⠀⠀⠀⠀⠔⣢⣪⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⠀⠀⠀⠀⠀ ⣤⣤⣤⡀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⢿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣷⠐⠀⣴⡿ ⣿⣿⣿⣿⣦⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠁⣬⣙⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢸⣿⣏⣤⣤⡍⠛⣿⣿⢐⣾⡏⠀ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⢐⠧⢌⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢶⣷⣿⣿⣿⣿⣿⣿⡆⠀⢠⡄⠀⣸⣿⣿⣿⣿⠁⠘⣿⣟⠇⠀⠀⠀⠀⣼⣿⣿⡿⣿⡏⠀⠿⠋⢸⣿⢃⡤ ⣿⣿⣿⣿⣾⣇⠀⠀⠀⠀⠐⠨⠭⣫⡿⠿⢿⣯⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⣿⣿⣷⡀⢀⡴⠒⠻⣿⠋⣀⣀⠀⢦⣽⣣⠀⠀⠀⠀⠀⣿⣿⡇⠛⠛⠁⠀⣀⠀⠈⠉⣿⡅ ⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠉⠁⠀⣴⣶⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣇⠀⠸⠿⢿⣿⡿⠋⠀⠉⠀⠀⠀⠀⢸⣿⣿⣇⠀⡀⠙⠀⠀⠀⣠⣴⣿⣿⣿⠃⣴⣶⣿⣿⣿⣦⠀⠋⠸ ⣿⠿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⠃⠁⠀⠀⠀⠀⣾⣿⡦⠀⠀⠀⠙⠀⣀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡟⠀⡇⠠⠀⠀⠀⠻⣿⣿⣿⡿⠠⣿⣿⣿⣿⢿⣿⣆⠀⠀ ⣿⣿⡇⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣇⠀⠁⠀⠀⠀⠀⠶⠐⢿⣿⡇⢸⣷⣾⣛⣿⣿⣿⡟⠀⠀ ⠿⣿⠇⠈⠃⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠛⠛⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡏⠉⣩⣿⣇⠀⠈⠀⠀⠀⠀⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣇⣸⠛⠫⣽⣿⣿⣿⡉⠀⠀ ⠀⠰⠀⠐⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣾⣿⠨⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⣖⡀⠈⠈⠃⠳⡄⠀⠀⣹⣿⣌⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣦⣤⣽⣿⣿⣿⣿⣿⣿⣿⡀⠪⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠶⠤⠄⢸⣧⠀⢸⣿⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡰⡖⠒⠒⢲⣿⣿⡇⠀⠀⢰⣶⠰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⣼⣿⡄⠀ ⠀⢀⣶⣿⣿⣶⣶⣶⣶⣤⣤⣤⣀⣀⣉⣻⣟⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣛⣿⣿⠀⠀⢸⣿⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡿⣾⠁⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⡟⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡏⡞⠀⠀⠀ ⠀⠈⠛⠿⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂⠀⠀⣸⣧⣧⡄⠰⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢻⠟⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⡿⠉⠉⠉⠉⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣤⡞⢿⣿⣿⣷⣀⣤ ⣤⡖⠲⣶⠆⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀ ⣽⡷⡀⠀⣿⣿⣷⣄⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣔⣶⣶⡀⡀⣀⢠⠀⢀⢀⠠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠶⠜⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⡀⡀⠀⠀⠀⠀⠀ ⣶⣦⣤⡀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠛⠛⠛⠛⢻⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣤⣲⣿⣿⣿⣿⣿⡇⠒⣠⣾⠟⠛ ⣿⣿⣿⣷⡄⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠁⠀⢠⣽⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣥⣤⣤⠙⢻⣿⡇⡗⣿⠁⢠⣶ ⣿⣿⣿⣿⣯⠀⠀⠀⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⠤⠀⢀⣿⣿⣿⣿⡏⠈⡛⣿⡻⠇⠀⠀⠀⠀⣿⣿⢿⣿⣿⡅⠸⠿⠃⣿⣟⣠⢸⣿ ⣿⣿⣿⣷⣿⡀⠀⠀⠀⠀⠟⢹⣿⡿⣿⣿⣿⡿⠙⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡟⢻⣿⣿⣿⣿⣿⣆⠀⣠⠖⠚⢿⡟⢁⣀⡀⠰⣭⣟⡇⠀⠀⠀⠀⢨⣿⣿⡈⠛⠋⠀⠀⣀⣀⠋⢸⣧⡀⠛ ⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠈⠉⢠⣾⣦⠈⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⣿⡀⠠⣿⠿⣿⣿⠟⠁⠈⠁⠀⠀⠀⠀⣿⣿⣿⡄⢠⠀⠁⠀⠀⢀⣤⣾⣿⣿⡏⠈⣴⣶⣿⣿⣿⣦⠈⠁⢿⣶ ⡿⠿⣿⠿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢺⣿⣿⠇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⠃⠀⠀⢀⣿⣷⠄⠀⠀⠈⠋⢀⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⢸⡀⠄⠀⠀⠈⠽⣿⣿⣿⡇⠰⣿⡿⣿⡿⣿⣿⡆⠀⠈⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⡇⡀⠀⠠⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡄⠀⠁⠀⠀⠀⠐⠇⠙⣿⣿⠀⢸⣷⣾⣻⣿⣿⣿⡟⠀⠀⠘ ⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠍⢀⣤⢿⣄⣀⠀⠀⠀⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣂⢸⠟⠹⣿⣿⣿⣿⡉⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⡀⠞⠁⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠐⣦⠀⠋⠙⠀⢳⡀⠀⠀⣽⣿⣌⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿⣇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣾⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⣶⣶⣦⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⡀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⢿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⠶⠀⢸⣧⠀⣸⣿⠀⢤⣤ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⢲⠒⠒⠒⢾⣿⣿⡄⠀⠀⣶⡆⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⣿⣿⠀⠀⠀ ⠀⢀⣶⣿⣿⣶⣷⣶⣶⣤⣤⣤⣤⣀⣉⣻⡟⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣘⣛⣛⡇⠀⠀⣿⡇⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡟⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣬⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢰⡏⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⡇⠏⠀⠀⠀⠀ ⠀⠈⠛⠻⠟⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂⠀⠀⣾⣡⣦⡄⠰⠶⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⡟⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⠉⠉⠉⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣴⠏⢸⣿⣿⣿⣀⣤⠖ ⣄⡖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣈⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀ ⠄⠀⠈⣿⣿⣷⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣦⣄⠧⠂⠀⠀⠀⠀⡀⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡩⢾⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⣶⣦⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⣾⣿⣿⣿⣷⠀⣂⣠⡾⠟⠛⠂ ⣿⣿⣿⣦⠀⠀⠰⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣨⣝⣿⣿⣿⡗⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢰⣾⣿⣡⣤⣌⠛⢻⣿⡆⣵⣟⠁⣰⣶⣶ ⣿⣿⣿⣿⡇⠀⠰⠤⡱⠿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⡉⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣶⣿⣿⣿⣿⣿⣿⡇⠀⠦⠤⠀⢸⣿⣿⣿⣿⠏⠈⢻⣿⠿⠄⠀⠀⠀⢸⣿⣟⣯⢿⣿⠀⠺⣿⡇⣿⡟⡤⣿⣿⣿ ⣾⣿⣿⣿⣇⠀⠀⠚⠬⣯⠴⢿⡿⣿⣿⣿⡗⠋⡈⠉⠂⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⡟⢿⣿⣿⣿⣿⣿⡄⢀⣬⠖⠸⣿⠏⣁⣀⡀⢠⣬⣛⡂⠀⠀⠀⠀⢸⣿⣇⠙⠛⠃⠀⠀⢀⡀⠋⢹⣅⠈⠛⠽ ⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠁⣴⣶⣄⠘⠉⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣟⠀⢌⡿⢿⣿⣿⠋⠁⠉⠀⠀⠀⠀⢰⣿⣿⣷⠀⢀⠈⠁⠀⠀⢠⣤⣾⣿⣿⡇⠘⣵⣶⣾⣿⣷⣷⠘⠙⣷⡦⠤ ⡿⠿⠿⠿⠿⠟⠂⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠈⡿⠏⣿⣿⣿⣿⣿⣿⣿⣯⣥⣼⡿⠀⢸⣿⣷⠀⠀⠀⠙⠁⢀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⢸⠀⠄⠀⠀⠸⢾⣿⣿⣿⠃⠀⣿⣿⣿⣿⢿⣿⣆⠀⠸⣿⡜ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⡅⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⣿⢿⣿⠃⠀⢸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⡀⠈⠀⠀⠀⠀⠐⠀⠙⣿⣿⠀⢰⣷⣶⣿⣿⣿⣿⡿⠀⠀⢹⡇ ⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣀⣠⣴⢷⡦⢄⡘⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⢿⡀⢸⠟⠫⣽⣿⣿⣿⠉⠀⠀⠀⠇ ⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢻⣿⣿⣿⠀⠁⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⡄⠀⠈⠙⠈⠳⡄⠀⠀⣹⣿⡌⡧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠀⢸⣇⠀⢸⣿⠀⣠⣄⣀ ⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢐⠒⠒⠒⣾⣿⣷⠀⠀⠀⣶⡆⢾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣿⣿⠀⠀⠀⠉ ⠀⢀⣴⣿⣿⣾⣶⣶⣶⣤⣤⣤⣀⣀⣉⣛⣟⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⣛⣛⡃⠀⢰⣿⡇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡟⣿⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢰⡏⠀⠀⠀⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣶⣤⣤⣤⡀⠀⠀⠀⠀⢸⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡇⠟⠀⠀⠀⠀⠀ ⠀⠈⠛⠻⠛⠛⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂⠀⠀⣾⣃⣄⡄⠠⠤⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠛⠛⠻⠿⠿⠻⠿⢿⣿⣿⣿⡿⠉⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣤⣴⠏⢸⣿⣿⣿⣄⣠⠔⠁ ⣄⡖⠲⣶⠊⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠀⠀⠀ ⠀⢸⣿⣿⡆⠠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣧⣦⣤⣤⣆⣁⢐⡀⡀⠀⠀⡀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣤⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣾⣿⣿⣷⣮⠀⠀⣴⡿⠟⠓⠀⠀ ⣿⣿⣷⡄⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣈⣙⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢐⣾⣏⣤⣤⡉⠛⣿⣿⠐⣼⡏⠀⣴⣶⣶⡆ ⣿⣿⣿⣇⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⠄⠀⣸⣿⣿⣿⣿⠁⠙⢿⣟⠷⠀⠀⠀⠀⢸⣿⣷⡿⢿⣧⠀⠿⣿⢰⣿⠃⡄⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠀⠀⠚⠛⢿⣿⣿⣿⣿⣿⡟⠈⠙⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠟⣿⣿⣿⣿⣿⣷⡀⢀⡤⠖⠻⣿⠋⣀⣀⠀⢦⣽⣻⠀⠀⠀⠀⠀⢸⣿⡇⠛⠛⠁⠀⠀⠈⠀⠁⣿⡄⠙⠛⢽⠟ ⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠁⣴⣶⡄⠛⠁⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣇⠀⢼⡿⣿⣿⡿⠋⠁⠋⠀⠀⠀⠁⢸⣿⣿⣧⠀⡀⠘⠀⠀⠀⢠⣤⣾⣿⣿⡃⡛⣥⣶⣶⣿⣷⣦⠋⠸⣷⡤⠴⣆ ⠿⠿⠿⠿⠿⠓⠀⠀⠀⠀⠐⣿⣿⡷⠀⠀⠀⠀⠀⠘⣿⣿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣿⣿⡦⠀⠀⠀⠙⠁⢀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⢱⠠⠄⠀⠀⠈⢹⣿⣿⡿⠀⠁⣿⣿⣿⡿⢿⣿⣆⠀⢹⣿⠸⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣿⡀⠀⠤⠀⠀⠐⠊⠉⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣇⠀⠈⠀⠀⠀⠀⠒⠈⠹⢿⡇⠀⣰⣷⣾⣿⣻⣿⣿⣿⠀⠀⢻⡄⢿ ⠿⠀⠀⠀⠀⠀⠀⠀⢰⠟⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠁⣀⣤⡟⣦⣼⣟⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣇⠀⣿⠛⢫⣽⣿⣿⣿⠉⠀⠀⠈⡇⣸ ⠰⠀⠐⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠋⣿⣿⣿⡇⠙⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣄⠀⠈⠃⠁⢳⡀⠀⠈⣹⣿⡌⡦⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⣶⣿⣿⣿⡇⠀⠀⠀⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠀⢸⣇⠀⣸⣿⠀⣠⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠒⣾⣿⣧⠀⠀⢰⣶⠄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⠀⠀⠉⠙⠓ ⠀⢀⣴⣿⣿⣷⣶⣶⣶⣤⣤⣤⣠⣀⣉⣻⡟⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣛⣻⡀⠀⢸⣿⡇⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⡏⣿⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢰⡇⠀⠀⠀⠀⢀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⢸⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⡃⠟⠀⠀⠀⠀⠀⠈ ⠀⠈⠛⠻⠟⠛⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠀⠀⢀⣿⣇⣀⡀⢤⠤⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢿⡟⠛⠻⠿⠿⠟⠿⢿⣿⣿⣿⡿⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣀⣴⠏⢸⣿⣿⣿⣀⣠⠔⠀⠀ ⣄⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠋⠉⠉⠉⠀⠀⠀⠀ ⢼⣿⣷⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣾⣬⣦⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⣀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣦⡆⠀⢠⣾⠿⠛⠒⠀⠀⠀ ⣿⣿⣄⠀⠸⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣐⣾⣏⣤⣌⠙⠛⣿⡇⢢⢾⡁⢠⣶⣶⣶⡄⠀ ⣿⣿⣿⠀⠀⠈⣽⢿⣿⣿⣿⣿⣿⣿⠿⠿⡿⣏⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠙⣿⣻⠇⠀⠀⠀⠀⣿⣿⢽⠿⣿⡅⠀⠿⣿⢨⡟⢡⢼⣿⣿⣿⡇⠀ ⣿⣿⣿⣆⠀⠀⠙⠈⢮⣿⣿⣿⢿⠟⠁⠀⠔⠂⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣆⠀⣠⡴⠊⢿⡿⢉⣀⡀⠀⣄⣝⡃⠀⠀⠀⠀⠀⣿⣿⡈⠚⠛⠀⠀⠀⠈⠈⢹⣯⡀⠛⠫⠿⠃⠀ ⣿⣿⣿⣿⣷⠂⠀⠀⠀⢠⣴⣧⡀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠀⣽⣿⣿⣿⡟⠉⠘⠁⠀⠀⠀⠀⣞⣿⣿⡆⢀⡀⠁⠀⠀⠀⣤⣴⣿⣿⣿⢀⣏⣤⣶⣶⣾⣶⣞⠋⢻⣦⡤⢴⡄⠀ ⢿⣿⠿⠿⠟⠃⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⠻⠟⣽⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⠄⠀⠀⠈⠋⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⠀⡇⠠⠀⠀⠀⠀⢿⣿⣿⡏⠘⢨⣿⣿⣿⡿⢿⣿⡄⠀⢿⡇⢻⣿⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣼⡏⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡀⠀⠃⠀⠀⠀⠀⠂⠈⠻⣿⡇⠀⣾⣷⣿⣿⣻⣿⣿⡟⠀⠘⣷⠀⣿⣧ ⠏⠁⠀⠀⠀⠀⠀⣾⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⣀⣤⡿⠿⡿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡁⠐⣿⠛⢯⣭⣿⣿⣟⠁⠀⠀⠸⠀⣿⣿ ⠆⠐⠂⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢻⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠙⠃⠀⢣⠀⠀⠉⣿⣧⣉⡆⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⣾⣿⣿⣿⠇⠀⠀⠰⠆⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣦⣶⣶⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⠀⢿⡎⠀⣾⣇⠀⣀⣀⡀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢰⣶⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⡿⣿⠀⠈⠉⠙⠂⠈ ⠀⢀⣴⣿⣿⣶⣶⣶⣶⣤⣤⣤⣀⣀⣉⣻⡛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣃⠀⠀⢸⣿⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢇⡟⠀⠀⠀⠀⢀⡶ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣸⠇⠀⠀⠀⠀⠈⠠ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⡀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣹⠀⠋⠀⠀⠀⠀⠀⠈⠀ ⠀⠈⠛⠻⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠀⠀⢠⣟⣧⣀⡀⣤⡤⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢻⠟⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⡿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣄⣀⣼⠃⣿⣿⣿⣷⣀⣠⠔⠀⠀⠀ ⡀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⠛⠋⠉⠉⠁⠀⠀⠀⠀ ⣿⣇⢀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣬⣶⣤⣴⣾⣶⣦⣤⣄⡀⠀⠀⢀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣿⣿⣷⣷⡅⠀⣠⣾⠿⠛⠂⠀⠀⠀⠀ ⣿⣦⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⣷⣿⣡⣤⣌⠙⠛⣿⡇⢧⣿⠁⢠⣶⣶⣶⠀⠀⠀ ⢿⣿⡆⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣻⠻⠿⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢄⠀⢀⣿⣿⣿⣿⡏⠈⢻⣟⡻⠆⠀⠀⠀⠀⣿⣿⢿⠿⣿⠀⠰⢿⡇⣿⡟⢠⢼⣿⣿⣿⡆⠀⠀ ⣿⣿⣷⣖⠈⠐⠀⣾⢿⢿⣿⣿⡟⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⠴⠚⢿⡟⢁⣀⡀⠰⣬⣟⡀⠀⠀⠀⠀⠀⣿⣯⠘⠓⠋⠀⠀⠀⠁⠉⢸⣏⠈⠻⠯⠿⠁⠀⠀ ⣿⡿⣿⣿⣯⠀⠀⠀⢠⣶⣤⠀⠁⠀⠀⠁⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠏⡿⢿⣿⣿⠟⠉⠘⠁⠀⠀⠈⠀⣟⣿⣿⡀⢀⠀⠁⠀⠀⠀⣤⣴⣿⣿⣟⢐⢏⣤⣶⣶⣾⣧⡜⠁⢷⣦⡤⢶⡀⠀⠀ ⣿⣵⣿⣿⡏⠁⠀⠀⢺⣿⣿⠆⠀⠀⠀⠀⠀⢿⣿⡿⠙⠿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⢸⡆⠤⠀⠀⠀⠐⣿⣿⣿⠇⢸⢸⣿⣿⣿⠿⣿⣿⡀⠈⣿⡆⢿⣷⠀⠄ ⣿⣿⡿⠿⠃⠀⠀⣀⣠⣽⡇⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⢿⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡀⠀⠃⠀⠀⠀⠀⠀⠘⡿⣿⠀⢸⣺⣥⣿⢿⣿⣿⣿⡇⠀⠘⣧⠸⣿⣦⠀ ⠏⠙⠋⠀⠀⠀⣾⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⣀⣠⣶⠹⠟⠿⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⡀⢸⢟⠟⢛⣭⣿⣿⡟⠁⠀⠀⢹⢀⣿⣿⡄ ⠀⠐⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡋⣻⣿⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠙⠘⠀⢦⠀⠉⠉⣿⣧⣁⡆⠀⠀⠀⢹⣿⡇ ⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣴⣶⣿⣿⣿⠇⠀⠀⠰⡼⣿⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣦⣶⣶⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣻ ⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠀⢿⡌⠀⣾⡇⠀⣀⣀⠀⠀⢈⡩ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⣶⡦⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⣿⠀⠉⠉⠛⠆⠀⠭ ⠀⢀⣴⣿⣿⣶⣶⣶⣶⣤⣤⣄⣀⣀⣉⣻⡟⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣇⡟⠀⠀⠀⠀⠀⣄⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢸⠇⠀⠀⠀⠀⠘⠉⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⡀⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠻⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠀⠀⢀⡿⣲⣀⠀⣀⡠⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⠟⣿⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⡿⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⣰⠋⣿⣿⣿⡇⢀⣀⠔⠀⠀⠀⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀ ⡀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣤⣤⣥⣴⣼⣶⣾⣷⣶⣤⣀⠀⠀⠀⢢⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣶⣷⠀⠀⣠⣾⠿⠓⠀⠀⠀⠀⠀⠀ ⣷⡀⠊⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣶⣿⢡⣄⣉⠛⠻⣿⡁⢰⣿⠁⣰⣤⣤⣄⠀⠀⠀⠀ ⣿⣧⠀⠀⢙⠭⣿⣿⣿⣿⣿⣿⢛⠿⢿⠿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣟⣻⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⢸⣿⣿⣿⣿⠏⠘⢻⣛⡿⠀⠀⠀⠀⢸⣿⡟⡼⢿⣿⠀⠰⣿⡇⣯⡛⡀⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣷⣾⣿⣷⡔⠿⣿⡛⡿⠃⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣠⠔⠺⣿⠟⢉⣀⠀⢠⣛⡛⡀⠀⠀⠀⠀⢸⣿⡇⠙⠞⠋⠀⠀⠀⠁⠉⢿⡄⠘⠟⣻⡟⠀⠀⠀⠀ ⣿⢾⣿⣿⣿⣿⡏⣠⣶⣄⠘⠀⠀⠀⠀⠀⣀⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡯⣻⣿⣿⣿⠟⠉⠚⠁⠀⠀⠈⢀⣿⣿⣷⠀⢀⠐⠁⠀⠀⢀⣤⣼⣿⣿⡓⣺⢇⣠⣤⣴⣶⣄⡘⠉⣶⣤⣤⣶⠀⠀⠀⠀ ⢃⣸⣿⣿⣿⣿⡏⢿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡷⠘⣿⠟⣿⣿⣿⣿⣿⣿⣿⣥⣤⣼⣿⠁⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠂⢸⠀⡀⠀⠀⠀⠸⣿⣿⣿⠃⢛⢸⣿⣿⣿⣿⣿⣷⡀⠸⣿⡐⣿⡧⠠⠀⠀ ⠟⠿⣿⣿⣿⠛⠁⣨⣿⡁⠀⠀⠀⠀⠀⠀⠗⠛⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣇⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣬⣽⣇⠀⠘⠀⠀⠀⠀⠐⠀⠉⠛⣿⠀⢸⢼⣭⣿⣿⣶⣿⣿⡇⠀⢹⡇⢸⣿⡄⠀⠀ ⠀⠐⠈⠻⣿⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⣀⣴⡏⠋⠛⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢸⠻⠿⢟⣻⣿⣿⡟⠃⠀⠀⢇⣈⣿⣿⠀⠀ ⠀⠂⠀⠀⢙⣞⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠹⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⠹⠈⠰⡄⠉⠉⠛⣿⣏⢲⡀⠀⠀⠀⣿⣿⡀⢠ ⠀⠀⠀⠀⣤⢻⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣻⣿⣿⣿⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣆⣤⣴⣿⣿⣾⠀⠀⠀⢤⢼⣿⡇⡁ ⠀⠀⠀⠀⣹⣾⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣿⠴⢶ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠈⣿⡉⠉⣿⡇⠀⡀⠀⠀⠀⠁⠚⡛ ⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠀⢿⣇⢀⣿⡇⠈⠉⠛⠳⠄⠴⠂⠀ ⠀⢀⣴⣿⣿⣷⣴⣶⣶⣤⣤⣄⣀⣀⣉⣛⡟⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⢸⠇⠀⠀⠀⠀⠈⠉⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣀⣿⡟⠛⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⢿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠤⣤⠀⠀⢀⡿⢠⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣿⣿⣿⡟⡟⠛⠛⠛⠿⠿⠻⠿⠿⣿⣿⣿⡿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠀⣠⢿⣿⣿⣿⠀⠀⢀⡴⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠸⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⢀ ⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⡢⢠⣤⣤⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣾⣶⣆⡀⠀⢠⣶⡿⠶⠄⠀⠀⠀⠀⠀⠀ ⣦⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⣤⣼⢋⣍⣉⠛⠟⣿⡇⢄⣿⠉⢠⣤⣤⣤⠀⠀⠀⠀⠀ ⣿⡆⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢀⠀⠀⣿⣿⣿⣿⡟⠈⠻⡟⢻⠄⠀⠀⠀⠀⣿⣿⢸⣿⣿⡀⠀⣿⡇⣾⡟⠁⢸⣿⣿⣿⡆⠀⠀⠀⠀ ⣿⣿⣀⣾⣿⣿⣿⣿⣿⣿⡿⠁⠈⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⡤⠘⣿⡿⠋⠉⠁⠠⣘⡛⠁⠀⠀⠀⠀⠀⣿⣿⠐⠶⠛⠀⠀⠀⠁⠉⢸⣇⠈⠻⣛⣿⠃⠀⠀⠀⠀ ⡿⣿⣿⣿⣿⣿⣿⣿⣌⠀⠁⠀⠀⠀⠀⢀⣠⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⠋⠐⠉⠀⠀⠈⠁⡾⣿⣷⡀⢀⠀⠂⠀⠀⠀⣠⣤⣿⣿⣗⢐⡖⣀⣤⣤⣤⣄⡸⠋⢷⣤⣠⣴⡀⠀⠀⠀⠀ ⢁⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣿⡟⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠸⡇⢀⠀⠀⠀⠀⣿⣿⣿⡇⠸⠩⣿⣿⣿⣿⣿⣿⡀⠈⣿⡆⢿⣷⠀⡀⠀⠀ ⣿⠛⠻⣿⣿⣯⠉⣽⡏⠀⠀⠀⠀⠀⠀⠸⠿⠏⠀⠈⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢨⣭⣿⡀⠀⠃⠀⠀⠀⠀⠀⠈⠻⣿⠂⢸⣴⣋⣿⣿⣶⣿⣿⡷⠀⠘⣧⠈⣿⣦⠀⠀⠀ ⠀⠀⠐⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⠀⠀⢀⣽⠏⠛⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠿⠿⠿⣚⣿⣿⡿⠃⠀⠀⢹⢀⣿⣿⡄⠀⠀ ⠐⠀⠀⠀⠀⢘⣇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢵⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⠘⠈⣆⠈⠛⠛⣿⡇⢒⡄⠀⠀⠀⢹⣿⡇⢀⣤ ⠀⠀⠀⠀⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣾⣿⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣤⣿⣿⣿⡇⠀⠀⢤⡼⣿⡧⠈⠁ ⠀⠀⠀⠀⠀⣻⡏⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣡⣤⣴ ⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢻⡝⠉⢹⣿⠀⠀⠀⠀⠀⠉⠤⠟⠋ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢸⣷⠀⣿⣿⠀⠙⠛⠳⡄⠀⠀⠀⠀ ⠀⢀⣴⣿⣷⣷⣴⣶⣶⣤⣤⣄⣀⣀⣈⣛⡟⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣦⣤⣤⣤⣼⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⡿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣀⡀⠀⠀⣸⢧⡀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣷⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⢻⡟⠛⠛⠛⠿⠿⠻⠿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣄⣀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⣠⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠙⠿⠿⠿⠷⠚⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣮⣤⣤⠀⠀⢀⣴⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⣠⣲⢛⣉⠛⠿⡿⣿⡇⢀⣿⠋⢀⣄⣀⣀⠀⠀⠀⠀⠀⠀ ⣷⠀⢉⢿⣿⡿⠿⣿⣿⣿⣿⣿⡿⣟⠄⠀⠀⠈⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢘⣿⣿⣿⣿⡟⠙⠿⠿⣷⠀⠀⠀⠀⠀⣿⡟⣸⣿⣿⠀⠀⣿⡇⣶⠿⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⣿⣆⢐⡞⠃⣰⣶⣾⣿⣿⠃⠙⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣀⢼⣿⡿⠛⠉⠁⢀⠰⠿⠂⠀⠀⠀⠀⠀⣿⡇⠡⣮⠟⠀⠀⠈⠁⠙⢲⡀⠸⢿⢿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⡿⠓⠰⠋⠀⠀⠙⠁⡾⣿⣦⠀⠉⠑⠇⠀⠀⠀⢀⣠⣿⣿⡦⠠⡆⢀⣀⣀⣤⣀⠸⠟⣦⣀⣉⣡⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⢛⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡋⣻⣿⠋⠉⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⢸⡀⠀⠀⠀⠀⠉⣿⣿⣿⡇⢸⢰⣿⣿⣿⣿⣿⣧⠀⠘⣿⡍⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⣿⠛⠻⣿⣿⣿⠟⠃⠀⠀⠀⠀⣾⣿⠏⠀⠤⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢹⣛⣿⠀⠘⠇⠁⠀⠀⠀⠀⠙⠟⣿⠀⢸⣸⣛⣽⣿⣭⣿⣿⡇⠀⢹⡇⢸⣿⡄⠁⠀⠀⠉ ⠀⠘⠋⠀⠀⠊⠻⣿⠀⠤⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⡉⠉⠉⢛⣿⢳⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⢿⣿⡿⠿⣿⣿⡿⠇⠀⠀⢷⠈⣿⣿⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣰⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢸⢠⡄⠘⠻⠿⣿⡗⢤⡀⠀⠈⠈⢻⣿⡄⠀⢀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣄⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⣄⣀⣠⣿⣷⣾⡇⠀⠀⣀⣸⣿⡇⠘⠟⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⣿⠃⠀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡻⠛⢻⣏⠀⠀⠀⠀⠀⠛⢘⡿⠿⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠀⢸⣧⠀⣿⣿⠀⠛⠶⢦⡄⠀⠈⠀⠀⠀ ⠀⢀⣴⣿⣿⣶⣴⣶⣶⣤⣤⣄⣀⣀⣉⣻⡟⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣬⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⡿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀⡀⠀⠀⠀⢸⣇⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⣿⣼⣷⡄⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⡿⢻⡟⠛⠛⠛⠿⠿⠻⠿⠿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠶⠻⣿⣿⣿⡧⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⣻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣤⣤⣄⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⡿⣿⣿⡇⠀⣾⠟⠁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠛⢿⣿⣷⡄⠀⠀⠀⠀⣿⣿⢺⣿⣿⠀⠀⣹⡇⢰⠿⠆⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⣿⡀⢭⡽⣿⣿⡿⠋⣭⣭⣿⣿⢿⡯⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⢀⡠⣿⣿⠟⠛⠃⠀⠰⢷⡎⠁⠀⠀⠀⠀⣿⣿⠩⣭⡿⠁⠀⠈⠁⠺⢲⡀⠘⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀ ⣿⣷⣿⡍⠋⣻⠀⣸⣿⣿⣿⣿⡇⠀⢀⡠⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠗⢠⠞⠁⠀⠙⠃⣰⣶⣦⡀⠋⠑⠶⠀⠀⠀⠀⢀⣿⣿⡦⠠⡤⠀⢀⣀⣀⡀⠸⠟⢤⡀⠉⣩⡀⠀⠀⠀⠀⠀⠐ ⣿⣿⣿⠁⢸⣿⡾⣿⣿⣿⣿⣿⡇⢰⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⠉⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⡇⢰⡇⠀⠀⠀⠀⠋⣿⣿⣿⡟⢸⢱⣿⣿⣿⣿⣿⣧⠀⠘⣿⡍⣽⣧⠀⠀⠀⠀⠀⠀ ⠉⠉⠀⠀⢸⣿⣿⣾⣿⣿⣿⠿⠃⢸⣿⡟⠀⣰⡟⠟⢹⣿⣿⣿⣿⣿⣿⣟⣻⣾⣿⠇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⣛⣿⠀⠀⠇⠈⠀⠀⠀⠀⠙⢿⣿⡇⠀⢸⠛⣽⣿⣭⣿⣿⡆⠀⠸⣇⠘⣿⣄⠁⠀⠀⠘⠀ ⠀⠀⠠⣴⣾⠇⠀⢈⠻⣿⣿⠀⠀⠸⠺⠄⠀⠉⠀⠀⠈⣿⣿⣿⣿⡉⠛⠛⠛⢿⡿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⣾⣿⣯⡽⣿⣿⣿⠇⠀⠀⢹⠀⢿⣿⡄⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣀⣠⣴⣿⡇⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠶⡆⠑⡀⠐⠿⠿⣿⡧⠤⡀⠀⠈⠀⢹⣿⡇⠀⠀⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣋⢳⣿⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠱⡄⠀⣀⣼⣿⣦⡇⠀⠀⢀⡈⣿⣧⣰⠾⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠃⢿⠏⠀⠀⣀⡉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⢻⣿⠀⠀⠀⠀⠀⠸⠴⢺⣿⠿⠃ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠒⠒⠂⠸⣧⠀⢸⣿⠀⠰⠶⢦⣄⠀⠚⠋⠉⠀⠀ ⠀⢀⣴⣿⣿⣶⣴⣶⣶⣤⣤⣤⣀⣀⣙⣻⡿⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣸⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣦⣤⣤⣼⡿⠟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⠿⠟⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⢀⣇⡌⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⣼⣧⣧⡄⠐⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣿⣿⣿⣿⣿⢿⡟⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠦⣤⡞⣿⣿⣿⣧⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢈⣴⣾⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠻⠻⢃⣧⣶⣶⣾⣿⣿⣿⣿⣶⣬⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⣤⣤⡀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢠⣤⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡟⠛⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠛⢿⣿⣿⣿⠀⢠⡿⠋⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢹⣿⣿⣿⣿⠟⢻⣿⣿⡆⠀⠀⠀⠀⢸⣿⡇⣿⣿⣆⠀⠀⣿⠠⣾⡧⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⣿⡈⡽⣿⣿⣿⣿⣿⡏⠿⠏⠋⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣩⣿⣟⣻⣿⣿⣿⣿⣇⠀⠈⠳⣀⣼⣿⡿⠟⠛⠀⠀⢼⡦⠉⠀⠀⠀⠀⢸⣿⡇⢍⣽⡟⠀⠀⠉⠀⠽⣄⠀⢿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⣹⣷⣮⠜⠋⡟⠙⡗⢣⠞⢀⣿⣿⣿⣷⡄⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⡴⠚⠁⠈⠿⢁⣴⣶⡄⠘⠚⠲⡇⠀⠀⠀⠀⢸⣿⣧⡄⣠⠄⠀⠀⣀⡀⠀⣿⢦⣀⠀⠉⡁⠀⠀⠀⠀⠀⠀⢶ ⣹⣿⣿⡀⣿⣿⣷⠘⣿⣤⣼⣿⣿⣿⣿⣟⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⠛⢿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣖⠀⠀⠀⠀⠘⢻⣿⣿⣽⠂⠎⣶⣿⣿⣿⣿⣾⡀⠀⢻⣿⢉⣿⡄⠀⠀⠀⠀⠀⠀ ⠉⠋⠁⠀⠻⣿⠟⢰⣿⣏⣻⣿⣿⣿⣿⡏⢀⣨⣻⠿⢻⣿⣿⣿⣿⣿⣿⡯⣧⣴⣿⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣛⣿⡏⠀⢸⠀⠁⠀⠀⠀⠈⢻⣿⣿⠀⠀⡿⢟⣿⣛⣿⣿⣷⠀⠀⢿⡀⢻⣧⠈⠀⠀⠀⠂⠀ ⠀⠀⠠⣶⣾⣿⡀⣸⣟⠙⠛⣿⣿⣭⡟⠀⠸⠝⠋⠀⢸⣿⣿⣿⣿⠻⢿⣷⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⡇⠸⣿⣧⠀⠀⠀⠀⠀ ⣀⠀⠀⠘⣿⠏⠉⠛⠁⠀⠐⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡀⠀⠀⣀⣽⡏⠉⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠡⢠⠘⢉⠁⢶⣿⣿⣿⠄⡀⠀⠀⠁⠒⣿⣿⠀⠀⠀⣀⣠ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢷⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠘⣆⠀⠀⢸⣿⣤⣾⠀⠀⠀⠀⢹⣿⡄⣴⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣶⣶⣾⣿⣿⣿⣶⣼⣿⣾⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⡟⠀⠀⠀⠙⠸⡿⠁⠀⠀⠙⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠃⠤⣴⣴⡆⠀ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠴⠶⠆⠀⣿⡄⠀⣿⡇⠀⢦⣤⣄⠀⠠⠖⠛⠁⠀⠀ ⠀⢀⣴⣿⣿⣶⣴⣶⣶⣤⣤⣄⣀⣀⣙⣻⣟⠛⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⡏⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣼⡿⠇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⠿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠀⠀⠀⣿⣹⣄⠀⠰⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢻⡟⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣄⣠⠏⣿⣿⣿⣇⣠⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠾⠿⠶⠢⠎⣄⣦⣶⣤⣦⣤⣤⣔⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⣄⣀⡀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠄⠀⣤⣄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⡾⠛⠻⣿⣿⣿⡇⠀⣰⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⢠⣿⣶⡄⠈⢸⣧⢰⣿⡇⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⣿⣿⣿⣿⣿⣿⡏⣿⠻⠿⠫⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣿⣿⡿⠿⠋⠀⢀⣷⡎⠁⠀⠀⠀⠀⢿⣿⠸⣩⣿⠏⠀⠈⠋⠸⢧⡄⠘⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⠟⢻⠛⠻⡟⠇⠋⠀⠀⠀⠀⣴⣤⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡷⢀⡴⠋⠀⠙⠏⢠⣶⣦⡀⠓⠒⡬⠀⠀⠀⠀⠀⣿⣿⣄⢈⣤⠀⠀⠀⠀⠀⠀⡿⢀⡀⠘⢋⡀⠀⠀⠀⠀⠀⠐⣾ ⢸⣿⣿⣴⣿⣿⡆⠀⠀⠀⠀⢠⠂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⡿⠻⣿⠋⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣇⠀⡆⠀⠀⠀⠀⠺⣿⣿⣧⣷⠰⢡⣶⣿⣿⣿⣶⣄⠀⠈⣿⡟⢻⣷⠀⠀⠀⠀⠀⠀⠈ ⠈⠛⠉⠈⢿⣿⠃⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⣿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⡇⠐⠀⠀⠀⠀⠹⣿⡿⡇⠀⢸⢿⢻⡟⣿⣿⣿⡄⠀⠘⣧⠘⣿⡅⠂⠀⠀⠐⠀⠀ ⠀⠀⠀⢶⣿⣿⠀⢠⠀⠀⠀⣿⡧⢼⣿⣿⣻⣿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠁⠀⠨⠹⡇⠀⣴⣾⣟⣿⣿⣿⣿⡇⠀⠀⢹⠀⢻⣿⡄⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⢻⣿⡇⢸⡇⠀⢸⡿⠀⠀⠘⠛⠋⠁⠀⠀⢹⣿⣿⣿⣯⡀⠉⠙⠛⣻⠻⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠡⡄⡯⠉⢭⣾⣿⣿⡇⣀⠀⠀⠀⠒⢺⣿⡇⠀⠀⠀⣀⣠ ⠀⠀⠀⠀⠘⣿⠇⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣀⣤⣾⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠁⠈⢣⠀⠀⠀⣿⣧⣴⡇⠀⠀⠀⠀⣿⣿⢀⣴⣾⣿⣿ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣿⣿⣿⣿⣏⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣾⣿⣿⣿⠁⠀⠀⠈⠣⢻⡟⠀⠀⠈⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⢿⣿⠀⠀⠀⠀⠀⠘⣀⣀⣴⡖⠄⠀ ⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣤⠀⢸⣇⠀⢸⣿⠀⢠⣤⣄⡀⠀⡠⠼⠋⠁⠀⠀ ⠀⢀⣴⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣻⣟⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢸⢻⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣾⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣦⣤⣼⣿⡷⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠄⠀⠀⢰⣟⢠⣀⠀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢻⡟⠛⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠂⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣀⣰⠛⣿⣿⣿⣆⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣢⣒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⣤⣵⣾⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠶⠲⠧⠤⣄⣄⣴⣄⢟⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⣠⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⣠⡢⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠿⢿⣿⣿⣿⡆⠀⣼⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡆⡯⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⢿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣯⢰⣶⣦⠉⠉⢻⡇⣴⣷⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠈⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠐⡦⠀⢸⣿⣿⡿⠿⠃⠀⣹⣭⠛⠀⠀⠀⠀⢰⣿⡇⣟⣻⣿⠃⠀⠛⠃⣿⢍⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⠟⠿⠿⣿⣟⠸⢛⡪⠁⠀⠀⣆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡄⣀⠴⠋⠘⢿⠋⣠⣤⣄⠸⠼⢭⡇⠀⠀⠀⠀⢸⣿⣧⡈⢉⡁⠀⠀⠀⠀⠀⢸⡦⡀⠉⠚⢋⠀⠀⠀⠀⠀⠀⢴⣯ ⢸⣿⣿⣶⣿⣦⢐⠈⠀⠀⠀⠀⣩⣾⣷⠎⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠁⠀⠁⠀⠀⠀⠀⠠⣯⣿⣿⠀⢠⠀⠀⠀⠀⠠⢶⣾⣿⣽⡇⢈⣤⣶⣶⣿⣷⣆⠈⠀⢻⣷⠒⣿⡄⠀⠀⠀⠀⠀⠈⠋ ⠀⠿⠿⠻⣿⡿⠀⠀⠀⠀⠀⠀⣽⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠁⢸⠀⠂⠀⠀⠀⠘⣿⣿⣿⠃⠸⣿⢿⣿⢿⣿⣿⣄⠀⠀⢿⡇⢻⣿⠐⠂⠀⠀⠄⠀⠀ ⠀⠀⠀⠰⣿⡇⠀⣀⠀⠀⠀⠀⢻⣽⢀⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣦⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡄⠀⠀⠀⠀⠀⠀⠁⠈⠛⢻⠀⢰⣤⡿⢿⣾⣿⣿⡿⠀⠀⠈⡇⠘⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠀⣿⡀⠀⠀⠀⣉⠃⣼⡇⠀⠈⠁⢹⣿⣿⣿⣿⡟⠻⢿⣷⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢸⠟⢛⣭⣿⣿⣿⠁⠀⠀⠀⠙⠀⣿⣿⠀⠀⠀⠀⢀⣠ ⠈⠁⠀⠀⠀⢻⡇⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢿⣿⣿⣮⡁⡀⠀⠀⣠⡏⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠧⡀⠀⠘⠀⢢⡈⠉⠉⢿⣿⣈⡧⠀⠀⠀⠀⢸⣿⡇⣀⣤⣾⣿⣿ ⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣾⣿⣿⣿⣿⣷⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⣴⣿⣿⣿⡇⠀⠀⠈⠻⡟⣿⠗⠉⠻⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠏⢀⣠⣤⣀⡈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠈⣷⠁⠀⣿⡇⢀⣀⣀⠀⠀⠀⣹⡿⠟⠃⠀⠀ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣀⣙⣿⣟⡛⠻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⣇⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠀⢻⣇⠀⣿⡇⠀⠉⠉⠛⠀⠈⠁⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡇⡇⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣦⣼⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢰⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⡞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣄⠀⠀⠀⣼⠇⡀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣻⡟⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠶⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢦⣄⣀⠀⠀⠀⣼⢹⣿⣿⣿⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⢖⢺⠵⣆⣤⣠⣀⣀⣠⣤⣤⣢⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣿⣿⣿⣿⣆⠀⢠⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⠎⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⣿⣦⠀⠀⠀⠀⠀⣼⣿⢡⣶⣤⡙⠙⢹⣷⢡⣿⡆⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢦⡀⠀⣿⣿⣿⣿⡏⠀⢉⣯⡽⠇⠀⠀⠀⠀⣿⣿⢑⢛⣿⡶⠀⠘⠿⢸⣋⡁⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣌ ⣿⣿⡿⢿⠿⢿⠿⡏⠙⠛⠯⠃⢹⡧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣇⠀⣡⠖⠉⢻⡿⢁⣤⣄⠀⢮⡭⣵⠀⠀⠀⠀⠀⣿⣿⡈⠙⢋⠀⠀⠀⠀⠀⠘⣷⡀⠙⠹⠿⠁⠀⠀⠀⠀⠀⢠⣴⢿ ⣿⣿⣷⣾⣶⡄⠨⠀⠀⠀⠈⢁⣼⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠁⠀⠀⠀⠀⣸⣿⣿⡇⠀⡄⠈⠀⠀⠀⠴⣶⣿⣟⣯⠈⣡⣤⣶⣶⣶⣠⠐⠁⠸⣷⠶⢾⣇⠀⠀⠀⠀⠀⠀⠛⠉ ⠹⢿⡿⣿⣿⠇⠀⠀⠀⠀⠀⢸⢿⣿⠇⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡿⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⡇⠠⠀⠀⠀⠀⢿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⢹⣇⠸⣿⡀⠄⠀⠀⠠⠀⠀⠀ ⠀⠀⠀⢾⣿⠀⢀⠀⠀⠀⠀⢸⢙⡅⠀⣞⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⣄⠀⠁⠀⠀⠀⠀⠃⠀⠚⢻⡇⢸⣙⣾⣿⣾⣿⣿⣿⠀⠀⠀⢻⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠀⢈⡋⠀⢸⣿⠞⠁⢹⣿⣿⣿⣟⢿⠛⠿⣿⣶⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠎⢁⡈⡿⢗⣛⣿⣿⣿⠃⠀⠀⠀⠘⠠⢼⣿⡇⠀⠀⠀⠀⢀⣠ ⠈⠁⠀⠀⠀⠀⢸⣷⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⢻⣿⣿⣷⡙⠀⠀⠀⣀⡌⠛⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠵⡀⠁⠀⠃⢦⠈⠉⠛⢻⣿⢉⣦⠀⠀⠀⠀⠘⣿⣧⠀⣀⣴⣾⣿⣿ ⠀⠀⠀⠀⠀⣀⠺⠋⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣦⣾⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢳⣀⣤⣿⣿⣿⣿⠀⠀⠀⠲⣆⢿⡿⠚⠛⢿⣿⣿⢟ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠸⠀⠠⣀⠀⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡉⠉⣿⡇⠀⣀⡀⠀⠀⠀⠒⣿⠗⠂⠀⠀⠀ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣿⣟⡛⠻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣾⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠀⢹⣧⠀⣿⣷⠀⠉⠉⠓⠆⠐⠛⠁⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⢸⣿⡄⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⡿⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣾⣿⣷⣦⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣀⣀⡀⠀⠀⢰⣧⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣼⣷⣶⣷⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⣀⠀⠀⠀⠀⢠⠿⣿⣿⣿⡆⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⡀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣬⣮⣼⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣉⣙⣣⣶⣶⣶⣾⣾⣤⣆⣁⣑⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⠀⢀⣼⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡗⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠠⣷⡏⣤⣤⡜⠋⠛⣿⠐⣸⣇⠀⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢾ ⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⡿⡉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡦⠀⢰⣦⠀⣸⣿⣿⣿⣿⠁⠘⣻⣹⠷⠀⠀⠀⠀⢸⣿⡇⡾⢿⡷⠆⠀⠻⠀⣟⡉⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⣿⣿⡿⣿⡿⣿⣯⠘⠐⠏⠉⣿⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⡀⢀⡴⠂⠻⣿⠋⣀⣀⡀⢪⢽⣉⡆⠀⠀⠀⠀⢸⣿⣇⠙⠛⠁⠀⠀⠀⠀⠀⣿⡄⠈⠫⠿⠏⠀⠀⠀⠀⠀⠀⣠⡲⣷ ⣿⣿⣷⣶⣄⠡⠀⠀⠀⠉⠀⣿⣷⣧⠀⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠉⠀⠋⠀⠀⠀⠀⢠⣻⣿⣿⠀⣠⠈⠁⠀⠀⢠⣴⣾⣿⣻⡅⣩⣤⣤⣴⣤⣀⠀⠋⠈⢷⡦⠶⣷⡀⠀⠀⠀⠀⠀⠙⠋⠉ ⠟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⢸⠀⠄⠀⠀⠀⠹⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠘⣿⠈⣿⡇⠠⠀⠀⠀⠄⠀⠀⠀ ⠀⠀⠰⣿⠀⢀⠀⠀⠀⠀⠀⣟⣟⠀⢸⢻⠾⢹⣿⣿⣿⡿⣿⣿⣿⣿⣞⣻⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣧⠀⠈⠀⠀⠀⠀⠐⠀⠉⠿⣿⢠⣱⣼⣷⣼⣿⣿⣿⠀⠀⠀⠹⡆⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣛⠋⢀⠿⠛⠀⠈⢿⣿⣿⡯⠸⠃⠈⠛⠿⠿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠂⠀⠀⠀⠀⠀⠀⠀⠂⢋⣈⡿⠷⣛⣿⣿⣿⠛⠀⠀⠀⠀⠇⠬⣿⣿⠀⠀⠀⠀⠀⢀⣤ ⠐⠃⠀⠀⠀⠀⢿⣆⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣀⡀⢀⣠⣾⡈⠡⠁⠉⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠙⢄⠘⠚⠛⢿⣿⣁⢢⠀⠀⠀⠀⠀⢿⣿⡀⠀⣠⣴⣾⣿⡿ ⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢣⣀⣠⣿⣿⣿⣾⠀⠀⠀⠲⣶⢸⣿⠷⠻⢟⣛⠙⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⠘⠇⠀⠀⠈⠘⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡙⠉⢹⣇⠀⠀⠀⠀⠀⠀⠠⢶⡷⠁⠀⠀⠀⠀ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣿⣿⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣶⡆⢿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠛⠛⠛⠀⢸⣧⠀⣿⣿⠀⠙⠛⠓⠆⠀⠴⠋⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠀⠀⠀⠀⠀⠀⣿⡇⠪⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⣼⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢠⡏⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⣿⠈⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟⣿⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⣧⣼⣶⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣗⣿⣿⣿⣿⡇⢹⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⡾⣿⣿⣿⡇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⡀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣨⣾⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣼⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⣠⣼⣾⣿⣿⣿⣿⣧⠐⢠⣿⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣼⣿⢡⣤⣤⠛⠙⢻⣿⢰⣿⡄⢰⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿ ⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣷⠄⠀⠦⡄⢠⣿⣿⣿⣿⡏⠀⢙⣯⡹⠇⠀⠀⠀⠀⣿⣿⢱⠿⣿⡷⠀⠘⠿⢸⡯⠁⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠐ ⣿⣿⡿⠿⢿⣿⠇⠫⠋⠃⣧⠤⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⠔⠘⢿⡿⢁⣀⣀⠀⢮⣍⣹⠀⠀⠀⠀⠀⣿⣿⡈⠛⠋⠀⠀⠀⠀⠈⠹⣧⡀⠙⠩⠿⠁⠀⠀⠀⠀⠀⢠⣔⠾⣆ ⣿⣿⣷⣶⡈⠫⠀⠈⠁⠀⣿⣠⣿⡄⠀⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣝⣩⣿⣿⣿⣿⠏⠁⠘⠁⠀⠀⠀⠁⣘⣿⣿⡇⠀⡄⠉⠀⠀⠀⣤⣶⣿⣟⣿⣀⣤⣤⣤⣦⣤⠀⠐⠋⠸⣶⠤⢾⣇⠀⠀⠀⠀⠀⠈⠟⠋⠈ ⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⢉⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⡇⠠⠀⠀⠀⠈⢻⣿⣿⡗⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢻⡇⠸⣿⠀⠤⠀⠀⢠⠀⠀⠀⠀ ⠇⠀⢾⣿⠀⡀⠀⠀⠀⠀⢸⣻⡏⠀⣞⣿⠟⢿⣿⣿⡿⠟⢿⡿⢿⣿⣯⣽⣿⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⣷⣿⣆⠀⠁⠀⠀⠀⠀⠀⠈⠻⠿⡇⣑⣾⣷⣼⣿⣿⣿⠂⠀⠀⠀⢿⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢘⡛⠁⡸⠛⠃⠀⠈⢿⣿⣿⣆⠉⠁⠀⠉⠛⠛⣻⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡿⠷⣛⣿⣿⣿⡟⠀⠀⠀⠀⠘⠠⢼⣿⡇⠀⠀⠀⠀⠀⢀⣠ ⠀⠓⠀⠀⠀⠀⢻⣀⠠⠐⠈⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⣀⣀⣤⣶⠀⠂⠀⠁⠉⠐⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠰⡀⠀⠨⢣⠘⠒⠛⢻⣿⡅⢲⡀⠀⠀⠀⠀⠘⣿⣇⠀⠀⣀⣤⣾⣿⡿ ⠀⠀⠀⢀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠳⡀⣀⣼⣿⣿⣿⠃⠀⠀⠐⢶⡖⣿⣿⡴⢿⡿⠟⠟⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠃⢸⠃⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⣤⣶⠇⠀⠀⠀⠀⠀ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣿⡟⠛⢻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⣶⠰⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠚⠛⠀⠘⣿⡀⢸⣿⡆⠈⠙⠛⠶⠀⢠⠶⠋⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⠀⠀⠀⠀⠀⠰⣿⡆⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢸⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣽⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⢹⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⣼⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⠀⠀⢸⣤⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣿⣤⣷⡆⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢺⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣀⠀⠀⠀⠀⠀⣰⢿⣿⣿⣧⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣷⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣷⣷⣦⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣿⣟⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣶⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠒⠒⠒⠀⢹⣧⠀⣿⣿⠀⠙⠛⠓⠆⠀⢠⠤⠉⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡀⠀⠀⠀⠀⠈⣿⠰⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⣿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠟⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢄⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⣿⢘⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣯⣼⣶⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠇⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣾⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣠⣠⣴⣷⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⣶⠀⢀⣾⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⣿⣿⣛⡍⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢠⣾⡏⣤⣤⡝⠙⠻⣿⢐⣼⡇⠀⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿ ⣿⣿⣿⣿⣿⡇⡿⡿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⠟⣛⣐⣀⡰⣆⠀⣿⣿⣿⣿⣿⠁⠘⢻⣙⠷⠀⠀⠀⠀⢸⣿⡗⡿⢿⡷⠀⠘⠿⢸⡿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⡀⠣ ⣿⣿⡿⢻⡿⠠⠎⠀⣧⠀⢴⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⠔⠂⢿⣿⠋⣀⣀⡀⢢⣽⣁⡆⠀⠀⠀⠀⢸⣿⡇⠙⠛⠁⠀⠀⠀⠀⠀⣧⡀⠙⠫⠿⠃⠀⠀⠀⠀⠀⠀⣔⣶⣇⡀ ⣿⣿⣷⡄⠀⠀⠁⠀⣿⠂⣺⣴⡤⠀⢀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣟⣛⣹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠁⢸⣻⣿⣳⠀⡀⠈⠁⠀⠀⢠⢤⣞⣿⠟⣁⣤⣤⣤⣄⠀⠀⠀⠋⠘⣷⡤⢴⣇⠀⠀⠀⠀⠀⠀⠹⠋⠉⠉ ⢿⣿⣿⡿⠀⠀⠀⠀⠛⠀⣿⣿⡗⠀⡜⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡛⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⡟⠀⢳⠀⠄⠀⠀⠀⠸⣿⣟⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⠘⣿⡇⠠⠀⠀⢠⠀⠀⠀⠀⠀ ⠇⠈⠿⠀⠀⠀⠀⠀⠀⠀⣟⡛⠀⡸⠳⣾⠃⣿⣿⣿⡟⠉⠛⠿⠿⣿⣿⣝⣻⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⣷⣿⣇⠀⠘⠀⠀⠀⠀⠐⠀⠈⠉⣘⣪⣿⣯⣿⣿⣿⣿⠀⠀⠀⠀⢹⡄⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢠⡿⠟⠁⠀⠘⢿⣿⣿⡀⠀⠀⠀⠈⠙⠛⢻⣟⡁⠈⢣⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠾⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠇⠼⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⣀⠀⠀⣀⣄⠙⠫⠉⠋⠘⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⣄⠀⠘⡀⠛⠚⠻⢿⣿⠐⢢⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣀⣤⣶⡿⠏ ⠀⠀⠀⠀⢀⡠⠔⠈⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣆⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⣀⣿⣿⣿⣾⠀⠀⠀⠀⢶⣶⢹⣿⣀⠶⠾⠛⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠛⢹⣧⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣿⡟⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⡆⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠖⠒⠒⠀⢸⣧⠀⢸⣿⠀⠈⠛⠛⠶⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡞⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠻⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡙⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⢠⣿⣼⣦⡀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣽⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣰⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠁⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢹⣿⣿⠟⠡⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡄⠂⣰⣿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢼⣿⣻⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⣢⣿⢡⣤⣬⠋⠛⢿⡇⢂⣿⠀⢰⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿ ⣿⣿⣿⣿⣿⠸⠻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⡆⠆⠀⠤⠀⢸⣿⣿⣿⣿⡏⠀⠙⣏⠹⠄⠀⠀⠀⠀⣿⣿⢸⠿⣿⠄⠀⠻⠇⣿⡍⠀⢸⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶ ⣿⣿⣟⡿⠫⠌⠀⣧⠀⢶⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡟⠁⢠⣿⣷⣿⣿⡟⢁⣀⣀⠐⣬⣍⣡⠀⠀⠀⠀⠀⣿⣿⠈⠛⠋⠀⠀⠀⠀⠀⢸⣄⠈⠛⠽⠟⠀⠀⠀⠀⠀⠀⢠⡶⢿⣀⣀ ⣿⣿⣷⡀⠈⠁⠀⣿⠀⢺⣤⣦⠄⠀⣴⠟⢻⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣻⣿⡧⢰⣿⣿⣿⣿⣿⠀⣚⣿⣟⡆⢀⡀⠉⠀⠀⠀⠤⣴⣿⠟⣃⣤⣤⣤⣄⠀⠀⠀⠘⠁⢻⣦⠴⢾⡄⠀⠀⠀⠀⠀⠈⠋⠁⠉⠉ ⢿⣿⣿⠇⠀⠀⠀⠟⠀⢸⣿⣿⠀⢀⣷⣦⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣧⣸⣿⣿⣿⣿⣿⠃⢻⣿⣿⠇⠘⡇⠠⠀⠀⠀⠀⢿⣿⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⡇⢻⣿⠀⠄⠀⠀⠤⠀⠀⠀⠀⠀ ⡿⠈⠃⠀⠀⠀⠀⠀⠀⢸⢛⠃⠀⡗⡷⢇⠀⢺⣿⣿⣿⠋⠉⠙⠛⠻⣿⣦⣛⣿⣿⠻⠿⣿⣿⣿⠛⠛⠀⢸⣶⣿⡀⠀⠃⠀⠀⠀⠀⠂⠀⠙⢈⣓⣹⣯⣽⣿⣿⣿⠀⠀⠀⠀⠈⣧⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⠀⣸⡿⠟⠁⠀⠀⠻⣿⣿⣄⠀⠀⠀⠀⠙⠛⠻⢿⣟⠀⠠⠏⠻⡏⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⣷⣿⣿⣿⠋⠀⠀⠀⠀⠀⠸⠠⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠨⠄⠐⠉⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⢀⣠⠀⢎⠉⠉⠂⠠⠀⠙⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⣀⠛⠚⠛⢿⣿⣐⢢⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣀⣠⣴⣾⠋ ⠀⠀⠀⠀⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⣰⣾⣿⣷⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢦⠀⣀⣾⣿⣿⣾⠀⠀⠀⠀⢴⣶⡆⣿⡇⢰⡶⠚⠛⠛⠋⠁⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠃⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡻⠛⢹⣿⠀⠀⠀⠀⠀⠀⠀⠉⢁⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⣿⣿⣶⣴⣶⣶⣤⣤⣤⣠⣄⣙⣻⣟⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣷⡇⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠒⠒⠀⠸⣷⡀⢸⣿⡆⠈⠉⠙⠲⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣿⣿⣟⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡾⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⢸⣦⡃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠛⠿⠿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⠀⠀⣼⣯⣧⡄⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⡀⢀⡀⠀⠀⠀⡀⢀⢀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣠⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡎⠬⣄⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠻⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣷⣿⣿⣷⣶⠀⢠⣾⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢠⣶⡏⣤⣤⡜⠙⢹⣿⢐⣾⡇⠀⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷ ⣿⣿⣿⣿⡿⢯⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⠰⠐⠆⣾⣿⣿⣿⣿⣿⠁⠈⢻⣙⠿⠀⠀⠀⠀⢸⣿⡇⡿⢿⡧⠀⠘⠿⢘⣩⠁⠀⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⣾ ⣿⣿⣿⠻⠅⠉⣧⠀⢾⠀⠀⠀⠀⠀⠀⢸⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⣴⡶⠛⢩⣯⣯⣤⣀⡀⢢⢭⣉⡆⠀⠀⠀⠀⢸⣿⣇⠙⠛⠁⠀⠀⠀⠈⠀⣧⣀⠙⠫⠿⠃⠀⠀⠀⠀⠀⢠⣴⣶⣂⡀⣡ ⢻⣿⣿⠈⠁⠀⣿⠀⢻⣀⣴⡤⠀⢠⡎⠈⠛⣻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣻⣿⡿⣿⡇⢠⣾⣿⣿⣿⣿⣷⠀⢠⠈⠁⠀⠀⢠⢴⣞⡟⣉⣤⣤⣤⣤⡀⠀⠀⠀⠋⠘⣷⡦⢶⣧⠀⠀⠀⠀⠀⠀⠙⠁⠈⠉⠁ ⣿⣿⣿⠆⠀⠀⠻⠀⠈⣿⣿⡗⠀⢤⣴⡄⢤⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠃⣿⣇⢸⣿⣿⣿⣿⣿⡿⠀⢹⠀⠄⠀⠀⠀⠸⣿⡹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠸⣿⠘⣿⡇⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⡿⠉⠁⠀⠀⠀⠀⠀⠀⡟⡛⠀⡸⠳⢿⠃⠀⠀⣿⣿⣿⣿⠉⠁⠙⠛⠻⣿⣿⣿⣿⡟⢻⣿⣿⣾⣿⣿⣿⣿⣿⣇⠀⠘⠀⠀⠀⠀⠐⠀⠙⢠⣛⣸⣿⣭⣿⣿⣿⠆⠀⠀⠀⠀⢹⡄⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⢛⠁⢀⣿⣿⡬⠂⠀⠀⠈⢿⣿⣿⣄⠀⠀⠀⠀⠉⠛⠻⢿⣧⠾⠷⠀⢉⡿⣿⡟⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⢶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠇⢼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⢀⡀⠐⡟⠉⠛⠂⠀⠀⠀⠈⠧⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢄⠈⢁⠘⠒⠛⢻⣿⡇⢲⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣀⣤⣴⣾⠏ ⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⣰⣿⣿⣷⣦⣶⣶⣿⣿⣿⣿⣿⣯⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⣀⣼⣿⣷⣿⡇⠀⠀⠀⠠⣶⣶⢹⣿⠀⣶⣶⠟⠻⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠏⢸⣿⡆⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠛⢹⣿⠀⢀⣀⡀⠀⠀⠀⠈⠉⠁⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣻⣟⠛⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠖⠒⠒⠂⠘⣿⡀⢸⣿⡇⠈⠉⠉⠓⠂⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢸⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠗⢀⣀⣀⠀⠀⠀⠀⢠⣧⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⢠⣼⣯⣿⡄⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⠀⡀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⡀⠀⠀⢀⣠⣤⣦⣶⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣮⣂⣔⠄⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠻⢿⡿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣤⠀⢠⣿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣿⣿⣿⣿⡋⡍⠑⠀⠈⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢠⣾⣏⣤⣤⡝⠙⢻⣿⠀⣿⡇⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⠀ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⠁⠈⣻⣙⠇⠀⠀⠀⠀⢸⣿⡕⡿⢿⡧⠀⠸⠿⢨⣏⠁⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣾⠆ ⣿⣿⠯⠛⢲⡄⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠛⠛⣿⣿⡏⠠⣤⣤⣮⣽⢹⠄⠀⠀⠀⠀⢸⣿⡆⠙⠛⠁⠀⠀⠀⠈⠘⣧⡀⠙⠡⠿⠁⠀⠀⠀⠀⠀⢠⣾⣶⣂⣀⣱⠀ ⣿⣿⡟⠀⢸⡇⠘⡇⣠⣶⡤⠀⢠⡎⠉⠹⠿⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⣿⣿⠀⠀⢸⡇⢀⣼⣿⣿⣿⣿⠈⠁⠀⠀⢠⣴⣾⠟⣩⣤⣤⣤⣄⠀⠀⠀⠐⠋⠘⣶⠤⢶⣧⠀⠀⠀⠀⠀⠀⠋⠁⠈⠁⠀⠀ ⣿⣿⡷⠀⠘⠇⠀⠀⣿⣿⡇⢀⣼⣦⠀⠎⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇⠀⠀⢸⣷⡀⣿⣿⣿⣿⣿⡧⠄⠀⠀⠀⢸⣟⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠹⣷⠸⣿⡆⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠧⠁⠀⠀⠀⠀⠀⠀⡟⡛⠀⡘⢶⣿⠀⠀⠀⠁⢸⣿⣿⣿⡟⠉⠉⠻⠟⢿⣶⣶⣾⣿⠁⠀⠀⢻⣿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠐⠀⠃⢸⣓⣼⣿⣭⣿⣿⣿⠀⠀⠀⠀⠀⢻⠀⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣳⠁⢠⣿⡿⢁⣀⠐⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⠈⠻⠿⠿⣿⠀⠀⠀⣿⡍⠉⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠷⣷⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⠇⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢺⠟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⠃⢹⣿⠘⠿⠁⠀⠀⠛⠙⠉⠀⠈⠁ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠛⣿⡇⠀⠀⢀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣶⣴⣶⣶⣤⣤⣤⣤⣄⣙⣿⣿⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠆⠀⣿⡄⠀⣿⣧⠀⠉⠉⠙⠆⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣤⣬⠹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡅⣼⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠉⠛⠒⠀⢀⣤⣧⣹⣆⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣆⢄⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣤⣷⣿⣾⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣬⣤⣜⢼⢮⣄⡀⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣯⣍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⢿⣿⡗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠐⣢⣿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⣿⡏⢑⠉⠀⢿⣿⢇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⡄⠀⠀⠀⠀⢠⣿⡏⣤⣤⡝⠉⠛⣿⠰⣿⡇⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⠠⣶ ⣿⣇⠀⠀⠀⡲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠈⣷⣿⣃⡀⠀⡀⠀⢸⣿⡷⡿⣿⡷⠀⠐⠿⢰⣯⠁⠸⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⠆⢸⣶ ⣿⠛⣤⠠⢶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣀⣀⡀⢿⣿⣿⠁⣸⣿⣿⣿⣾⣿⡆⠛⠛⠁⠀⠀⠀⠈⠙⣧⡀⠙⠭⠿⠃⠀⠀⠀⠀⠀⣠⣦⣒⢄⣀⣽⠀⣈⣛ ⣿⡆⣿⠀⢻⠀⣠⣴⡤⠀⢠⡎⠉⢹⣶⡄⠀⠀⠸⡿⣿⣶⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣧⠀⣿⣿⠐⣿⣿⣿⣿⣿⢟⣁⣤⣤⣤⣤⡀⠀⠀⠀⠋⠘⣶⡤⢶⣧⠀⠀⠀⠀⠀⠘⠋⠀⠈⠁⠀⠀⢻⣿ ⣿⣧⠿⠀⠀⠀⣿⣿⡇⠀⣼⣷⡀⠾⠊⠉⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡟⠀⢿⣿⣧⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⣿⠘⣿⡆⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⡅⠀⠀⠀⠀⠀⢟⡛⠀⠸⢿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡟⠛⠻⠿⢿⣿⣥⣶⣾⡿⠀⣿⣿⣧⠀⢸⡿⠿⢿⣿⣿⡟⠛⣸⣛⣸⣿⣭⣿⣿⡧⠀⠀⠀⠀⠀⢻⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠘⠁⢠⣿⣿⠐⠀⠀⠀⠘⣃⡀⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⢻⣿⠿⠀⠟⠁⠀⠛⠙⢿⡀⠈⢿⡿⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠇⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠂⠀⠀⠀⠀⠀⠀⠀⠸⢛⢃⡠⣤⣠⡤⠞⠉⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠼⣅⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⣁⢃⢉⡄⠘⠛⠿⢿⣿⡒⣄⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡩⠟⠉⠀⣴⣿⣿⣿⣦⣶⣶⣦⣤⣬⣿⣿⣿⣿⣦⣴⣾⣇⠙⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠀⠹⡄⢀⣀⣾⣿⣷⡏⠀⠀⠀⠀⢠⣶⣶⢿⣿⠀⣶⡄⠀⠀⢠⣶⣿⣿⣿⡿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⠋⢸⣿⡈⠿⠃⠀⠀⠈⠙⠿⣿⠿⠃⠀ ⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠟⠛⣿⡇⠀⣀⣀⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣄⣙⣿⣿⡛⢻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⠶⠶⠆⠀⣿⡄⠀⣿⣷⠀⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣤⣤⡉⢙⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⡟⠛⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⡇⣞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⠀⠀⠈⠉⠛⠓⠀⢀⣤⣧⣹⡆⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠖⢾⣿⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣶⣭⣀⢬⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣖⣎⢂⣈⢴⡇⢹⣝⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣾⣿⣿⣿⣿⡇⢀⣾⣿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠉⢉⣹⠛⣿⠿⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⠀⠀⠀⠀⠀⣶⣿⣡⣤⣬⠛⠙⢻⡗⣺⣿⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣴⣶⣶ ⠀⠀⠀⠸⢯⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⠀⢻⡿⢿⠀⢠⣤⠴⢶⣿⣽⣾⣿⣿⠆⠀⠺⠇⣺⡉⠀⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⣾⡿⠠⣿⣿⣿ ⢢⠀⠼⠀⠈⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠸⠿⣷⣾⠀⣿⡇⢰⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠉⣿⣄⠈⠋⠽⠟⠀⠀⠀⠀⠀⢀⣔⢦⡀⣄⣸⣷⢠⣙⣻⣿ ⣿⡇⠘⡆⢀⣴⣦⠄⠀⣴⠉⠉⢷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣻⣿⡄⢱⡆⠋⠀⣿⣿⣘⣿⣿⣋⣥⣤⣤⣮⣄⠀⠀⠀⠚⠁⢻⡶⠴⣾⡄⠀⠀⠀⠀⠀⠛⠋⠀⠉⠀⠀⠸⣿⣿⣿ ⣿⠇⠀⠀⢸⣿⣿⠀⣠⣿⡆⢸⡈⠉⢁⠀⠀⠀⠀⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠃⠸⡇⠠⠀⣺⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣿⡇⢿⣿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿ ⠀⠀⠀⠀⠘⢛⠁⢠⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠸⣿⣿⣿⣿⡿⠛⠛⠿⢿⣿⣶⣶⣾⣿⣿⡄⠀⠛⠀⢠⡿⠋⢹⡿⣯⣟⣋⣽⣿⣽⣿⣿⡇⠀⠀⠀⠀⠸⡇⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿ ⠀⠐⠀⠀⠀⠀⠀⣾⣿⡗⠀⠀⠀⠀⠛⠀⠀⢀⠀⠋⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⢶⣿⣿⣿⢿⣿⣿⣇⠀⠀⠀⠈⠀⠀⠈⠀⠸⣿⡿⠿⢷⣿⣿⡿⠀⠀⠀⠀⠀⠀⠻⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣿ ⠀⠀⠀⠀⠀⠀⠀⢛⢛⣀⡤⠄⢀⣠⣶⢾⡟⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⠉⡡⣎⣁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠀⠛⠿⠿⣿⡗⢢⡀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡠⠖⠋⠉⣴⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣿⣿⣿⣿⣷⣖⣾⣇⠙⡆⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣀⣴⣿⣿⣿⠀⠀⠀⠀⢀⣶⣶⢺⣿⡇⣰⣦⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠟⠘⣿⡇⠻⠏⠀⠀⠀⠀⢈⢉⢿⣿⣿⡟⠓ ⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠛⣻⣿⠀⢀⣀⣀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣾⡃⠈⠈⠉⠀⠀ ⠀⢸⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣄⣙⣿⣿⡛⣻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠒⠶⠀⢻⣧⠀⣿⣿⡀⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⠉⢉⣹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⡟⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠈⠉⠛⠒⠂⢀⣀⣟⣹⣧⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀ ⢠⣿⣿⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⣦⢅⣀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣔⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣽⣯⣴⣬⡀⣤⡴⢆⣼⣅⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢟⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡇⢐⣾⣿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⡙⡐⠹⣻⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣿⣿⣥⣤⣬⠛⠙⢻⡇⣺⣿⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣴⣶⣶⠄ ⠀⠀⠶⡻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⢿⡿⠿⠀⠀⠀⣴⡶⢛⣿⣿⣿⣿⠇⠀⠺⠇⢿⡉⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⡠⢿⣿⣿⡇ ⠀⢼⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⠀⠀⢰⣿⡄⣽⣿⣿⣿⣿⠀⠀⠀⠀⠉⣿⣄⠈⠋⠿⠏⠀⠀⠀⠀⠀⠀⢀⠠⠀⣄⣩⣷⢄⣙⣻⣿⡃ ⠂⠸⠀⢀⣴⣶⠄⠀⣴⠉⠉⣷⣄⠀⠀⠀⠀⠀⣿⣿⡿⢛⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣿⢹⡆⠉⠀⠀⢨⣿⣧⣹⢋⣠⣤⣤⣴⣄⠀⠀⠀⠛⠁⢷⡶⠶⣿⡄⠀⠀⠀⠀⠈⠳⠋⠀⠉⠀⠀⠸⣿⣿⣿⣷ ⠀⠀⠀⢸⣿⣿⠀⣰⣿⡆⢴⠊⠉⠁⠀⠀⠀⠀⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡟⢸⣇⠠⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⣿⡇⣿⣗⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿ ⠀⠀⠀⠙⠛⠁⢠⠿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⠀⢿⣿⣿⣿⣿⠏⠋⠻⠿⢿⣷⣾⣿⣿⡇⠈⠛⠀⠀⠀⡾⠇⠈⣅⣟⣛⣽⣿⣽⣿⣿⡇⠀⠀⠀⠀⠸⡇⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⠀⠆⠀⠀⠀⠀⣾⣿⡿⠇⠀⠀⠀⠛⠀⠀⢀⣠⠿⠉⠀⠀⠈⢻⣿⣿⣯⠀⠀⠐⠶⣿⣿⣿⢿⣿⣇⠀⠀⠀⠀⠈⠀⠀⠀⠸⣿⡿⠿⢷⣿⣿⡿⠀⠀⠀⠀⠀⠀⠧⠨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣿⣿ ⠀⠀⠀⠀⠀⠀⠘⣛⣀⠄⠄⠀⣀⣴⡾⠾⡛⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⣠⣤⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠛⠿⢿⣿⡗⢢⡀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠁⠁⣠⠴⠞⠉⠁⣴⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣹⣿⣿⣿⣿⣗⣿⣧⠈⠣⡈⠉⠐⠄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣀⣼⣿⣿⣿⠀⠀⠀⠀⢀⣶⣶⢸⣿⡇⣶⣆⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠟⠘⣿⡇⠻⠇⠀⠀⠀⠀⠀⢠⡉⢿⣿⣿⣿⡿ ⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠛⣿⣷⠀⢀⣀⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠉⠁⠀ ⢸⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣠⣄⣙⣿⣿⣛⢻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠒⠒⠀⢿⣇⠀⣿⣿⠀⠉⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⡉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⢿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠟⠛⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠉⠓⠒⠀⢀⣀⣏⣹⣇⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀ ⣿⣿⠷⣾⠿⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡦⢐⣤⣖⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣄⣤⣿⣾⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣤⣵⣶⢒⣶⣟⣲⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⡇⣲⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠂⠀⠀ ⠹⣿⣽⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣥⣤⣬⡟⠙⢻⡗⣿⣿⠀⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⣴⣶⣶⠀⡠⡢ ⢰⣏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡃⠀⠀⠀⠀⠀⣿⣿⡟⢹⣾⣷⣶⡾⠇⣿⠉⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡸⣿⣿⣿⡇⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⠀⠉⣷⣄⠘⠫⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣿⣆⣛⣻⣿⠁⠀⠀ ⠀⢀⣴⣦⠄⢠⣜⠁⠈⣷⣄⠀⠀⠀⠀⠀⣿⣿⣿⠏⠻⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣿⠁⠀⠀⠠⢴⣾⡿⢋⣠⣤⣴⣾⣿⣿⠆⠀⠛⠁⢷⡶⢶⣿⡀⠀⠀⠀⠀⠀⠆⠑⠀⠈⠀⠀⠸⣿⣿⣿⣇⠀⠀ ⠀⣿⣿⡿⠀⣼⣿⡆⢼⠋⠉⠃⠀⠀⠀⠀⣿⣿⡟⠀⠐⠟⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢛⣛⣿⡿⠤⠀⠀⠀⠸⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⠘⣿⡇⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠒⠀ ⠀⠛⠛⠁⢰⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⢀⡀⠀⢻⣿⣿⣿⣿⠏⠁⠻⡟⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⣧⣿⣛⣽⣿⣭⣿⣿⡇⠀⠀⠀⠀⢹⡇⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀ ⣤⠀⠀⠀⠹⣿⡿⠀⠀⠀⠘⠛⠀⠀⠀⢀⣿⣴⠶⠉⠀⠀⠀⠙⣿⣿⣿⣄⠀⢚⠙⠽⢿⢿⠟⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠇⠼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⢉⣤⠤⠄⠀⢀⣠⣴⡶⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣀⡀⢀⡀⢰⣶⣤⣄⠀⠀⠀⠀⠀⠀⠈⣁⠀⠛⠿⢿⣿⡗⢦⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣷⣶⣶ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠛⠉⠁⠀⣴⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣈⣿⣿⣿⣿⣟⣿⣷⡀⢻⠈⠉⠓⠂⠀⠀⠀⠀⠀⠙⣧⠀⢀⣴⣿⣿⣿⠀⠀⠀⠀⢠⣶⣶⢻⣿⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠣⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠏⢸⣿⡆⠿⠃⠀⠀⠀⠀⠀⠀⠀⣠⡬⠻⢿⣿⣿⣿ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠟⣿⣧⠀⠀⣀⣀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠉⠁⠀ ⣿⣄⣶⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣄⣙⣿⣿⣛⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠴⠖⠶⠶⠀⢿⣇⠀⣿⣿⠀⠛⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣦⣤⣬⡉⢉⣩⣽⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⡀⠀⠀⠀⢿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⠛⠿⠟⠛⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣉⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⡏⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠶⠀⠀⣀⣏⣻⣆⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀ ⠁⠖⠿⣿⡏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀ ⣿⣿⣷⣦⣴⣂⣲⢠⣀⢤⡄⠀⠀⠀⠀⡀⠀⠀⠀⡤⣠⣤⣧⣿⣿⣿⣿⣿⣿⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣼⣾⣯⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢸⡯ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢠⡶⡻⡒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡂⣲⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠠⢱⣦⠭⠟ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣏⠢⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣯⣴⣤⣌⡟⠙⢻⡟⣿⣏⠀⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⡄⠀⣶⣶⣦⢿⣠⠿⣛⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡏⠀⠀⠀⠀⣿⡟⣿⣿⣿⡷⢒⣾⣿⣿⣟⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣇⡸⣿⣿⣿⡇⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡧⢼⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠐⣿⣇⠙⣿⣿⡇⣾⣿⣿⣿⣿⣆⠙⠫⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠿⣄⣛⣻⣿⠁⠀⠀⠀⠀ ⣴⣦⠀⢠⡎⠉⠙⢲⡀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⣼⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠀⢠⣴⣾⡿⢛⣁⣤⣤⣾⣿⣿⣿⣿⣿⡌⣷⡦⢶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⣿⡆⠀⠀⠀⠀ ⣿⡏⠀⣼⣷⡄⠘⣋⠉⡀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠱⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⡟⠀⠀⠻⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⣿⠘⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠂⠀⠀⠀ ⠛⠀⠸⢿⣿⠇⠀⠀⠀⡑⠀⠀⠀⢸⣿⠇⠀⡀⠀⢀⠏⠀⠻⣿⣿⣿⣿⠿⠺⡟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢄⣽⣛⣹⣿⣯⣽⣿⡿⠁⠀⠀⠀⢹⡄⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠘⠗⠀⠀⠀⠘⠛⠀⠀⠀⠘⠃⣀⣤⣴⡟⠁⠀⠀⠀⠙⣿⣿⣿⣆⠀⢘⠙⠛⠛⠻⠛⠟⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⣿⣿⣿⠟⠆⠀⠀⠀⠈⠧⢼⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣀⣠⣴⣾⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⡆⣀⡄⢶⣦⣄⡀⠀⠀⠀⠀⠀⢈⠀⠺⠿⠿⣿⡗⢤⡺⣄⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠁⣴⣿⣿⣿⣶⣶⣶⣤⣠⣤⣤⣈⣿⣿⣿⣿⣟⣿⣷⡀⢿⡉⠉⠓⠄⠀⠀⠀⠙⣧⠀⠀⢠⣿⣿⣾⠁⠉⠀⠀⢠⣶⣶⢿⣿⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠛⢤⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠃⢸⣿⡆⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡻⠛⢿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⠙⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⢿⣿⠀⠀⠀⣀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠀⠀⠀⠈⠁⠉ ⠀⢀⣶⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣀⣙⣿⣿⡛⣻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠶⠶⠦⠀⢹⣧⠀⢸⣿⡄⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣧⣤⣬⡉⢉⣩⣽⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠿⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⡀⠀⢻⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣬⣴⣦⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠟⠛⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢘⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⡰⠘⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀ ⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠀⠀⣼⢹⣆⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀ ⠀⡿⢿⣿⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 1941 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/05/gemini-protocol-video/#comments Gemini version at gemini://gemini.techrights.org/2021/11/05/gemini-protocol-video/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Gemini_Protocol_Does_Not_Need_to_Be_Extended_to_Support_Multimedia_(It Already_Supports_Audio/Video_as_External/System-Level_Objects)⠀✐ Posted in Free/Libre_Software at 6:41 am by Dr. Roy Schestowitz Video_download_link | md5sum e2b4f1f7cba7d3a4392961426b356067 http://techrights.org/videos/videos-in-gemini.webm Summary: There seems to be a misunderstanding or a misconception about what Gemini is and how skeletal it should be; unlike Web browsers, Gemini clients do not attempt to be an “all-in-one” giant blobfest; they do text (like articles) and focus on being very good at that (bookmarks, navigation, search and so on) THE founder of Gemini came_back_at_the_end_of_last_month, reaffirming his commitment or his longstanding work to debloat the Internet, not just imitate the Web with another complex ‘standard’. “Gemini is fine as it is; people should understand that any efforts to further expand it basically break compatibility with existing clients and likely miss the point of Gemini Protocol.”Well, the founder’s return was soon followed by multiple requests to “extend” the specification and include more things (e.g. [1, 2]) — things which as many the mailing lists have already explained should not be necessary at all. Throwing everything at Gemini would lead to the same mess the World Wide Web became — likely as old a problem as two decades ago with Internet Explorer, albeit it continues to get yet worse. Video, or multimedia in general, already has software for it. Throwing everything at the browser (or Gemini client) not only leads to security issues but also bloat and complexity, which in turn increases the entry barrier to implementers of more Gemini clients. In the above video I explain how people can access videos from a Gemini client like Lagrange, which by default opened with the (almost) real- time IRC log of #techrights. Gemini is fine as it is; people should understand that any efforts to further expand it basically break compatibility with existing clients and likely miss the point of Gemini Protocol. It’s a substitute, not a clone, of the Web. We don’t want Gemini clients to come preloaded with hundreds of megabytes of stuff and then take up hundreds of megabytes of RAM. Let the Web choke on its own making, including DRM (EME). █ “Fat operating systems spend most of their energy supporting their own fat.” –Nicholas Negroponte, MIT Media Lab, rediff.com, Apr 2006 ䷩ 𝚕𝚒𝚗𝚎 2009 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/05/googlebombed-by-microsoft/#comments Gemini version at gemini://gemini.techrights.org/2021/11/05/googlebombed-by-microsoft/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Linux_Isn’t_Loved_by_Microsoft,_It_is_Being_Googlebombed_by_Microsoft⠀✐ Posted in Apple, Deception, GNU/Linux, Marketing, Microsoft at 7:50 am by Dr. Roy Schestowitz Video_download_link | md5sum a2f1255b07abc18ef12c95556ba9e58a http://techrights.org/videos/linux-googlebombed-again.webm Summary: Journalism on the Web is dying and is being replaced by SEO/affiliate links/spam farms; the vacuum is moreover being exploited by PR operatives who boost brands of Microsoft by piggybacking opposing brands, such as “Linux” THE ATTACK on the brand or the name (or brand name) “Linux” carries on. It’s moreover being ‘hijacked’ by the very same people and companies that are looking to undermine GNU/Linux. They know exactly what they’re doing and the media helps them. It’s intentional. “It has been getting harder to find actual GNU/Linux news, partly because the media isn’t functioning anymore and a lot of self-described journalists are just PR spammers.”Earlier this year we stated that Phoronix_should_be_careful of_Microsoft after Phoronix had received ‘freebies’ from Microsoft. This is how sites self-nuke and drive away their audience. Looking at the front_page_of Phoronix, as I did in the above video, you find Phoronix doing Microsoft articles more than once per day. Some people point this out in the comments; they’re not happy. As a side note, we still see Visual Studio Code being wrongly described as “open source” and WSL being painted (sometimes even in Microsoft/Windows sites) as “Linux” even though it’s just Windows. ChromeOS with Crostini is “Linux” because ChromeOS is at least GNU/Linux-based (Gentoo to be more specific). It has been getting harder to find actual GNU/Linux news, partly because the media isn’t functioning anymore and a lot of self-described journalists are just_PR_spammers. We wrote some_things about this last year. Over the past few weeks we saw UbuntuPIT, a site that used to cover GNU/Linux/Ubuntu, becoming an Amazon spam farm (affiliate links, garbage disguised as recommendations) and over the past year that site promoted lots of Windows things, sometimes iOS and Android. They ought to drop “Ubuntu” from that site’s name. █ ䷩ 𝚕𝚒𝚗𝚎 2072 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/05/irc-log-041121/#comments Gemini version at gemini://gemini.techrights.org/2021/11/05/irc-log-041121/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Thursday,_November_04,_2021⠀✐ Posted in IRC_Logs at 2:23 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights- 041121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-041121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-social-041121.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes- 041121.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  QmZt4hoZJrF9YW2Q6UFSiJDyJYdKnUH27agrBuXzDEprSA #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmaFCPx5iQDgnoNW1DRCxiDozrndw7EgzD7pvVSkh42TZh (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  Qmc5vJwVBJf5gzzihPNi87UEiVvDAgPh8nosVgtTdV3v4n social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmfEEaSexjR3oWg6hW5uSAiVietatv6WdyrXsqBfbRNCZz social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmVdYawb9zgsLkwTD4XgTCpKuycUMjT92CveRJAJf9ztQq #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  Qmb5Y6NBiNyciW3HK2Xtxdii3vhfBCFgKH3j4u7sQ1ocp9 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmaGocU1g6p9SYkQ5XiJqYnzvqA2Ahf3RFVuxtZW8GfqGi #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmPE3L1qmPbZBFVUsLxCySc4NANPNWvpxGViXHXy6y34yh (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmVzPu6Qip7yK3FGSsrMzEt3zNmqWufLFF5CZNmsVbHZLd ䷩ 𝚕𝚒𝚗𝚎 2201 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/05/not-the-frontier-anymore/#comments Gemini version at gemini://gemini.techrights.org/2021/11/05/not-the-frontier-anymore/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ EFF_Has_Been_Hijacked,_and_Just_Like_Mozilla_and_the_Linux_Foundation_It Doesn’t_Fight_for_What_It_Was_Originally_Made_to_Achieve⠀✐ Posted in Deception, EFF, Free/Libre_Software, FSF, GNU/Linux, Microsoft at 1: 15 pm by Dr. Roy Schestowitz Video_download_link | md5sum 3dcd8fde06e9f18238d3e50f3a9252c5 http://techrights.org/videos/eff-changed.webm Summary: Institutions too frightened or hesitant (or simply compromised) to pursue their original goals are doomed to perish; EFF seems to have “joined the club” IT really pains me to say this, but the EFF isn’t an organisation I feel safe to support anymore as it is culling the people who I’ve long argued keep the EFF honest, sometimes. It looks like “reformist” (mainstream/conformist) elements are taking over, turning revolutionary collectives into corporate shills. Take for example the Microsoft-serving Linux_Foundation; it’s all about money and it's_good_at_losing_money. It pays massive salaries to people who undermine Linux itself. They just use the “Linux” brand to enrich themselves. These are the same people who had Linus Torvalds sent to therapists and forced to write an apology (on the face of it this was imposed, not really willful, as a condition to him getting back to his very own project!) and we’re meant to think this is perfectly normal because of corporate_trolls. “They just use the “Linux” brand to enrich themselves.”At the same time, as we noted here back_in_April, today’s EFF is shilling Microsoft proxies, giving EFF awards to Microsoft employees, and viciously attacking Richard Stallman for political reasons. Several hours ago Dr. Stallman wrote: “Cancellationists seek universal support for their political stances, not by convincing everyone that they are right, but by bullying everyone who states any doubts.” They don’t even attack their target based on technical grounds; they look for some phony pretexts and sometimes distort the facts to get people online riled up, demanding removal based on misunderstandings, misinterpretation, or selective (narrow) focus. To me, personally, the last straw was the EFF removing_its_co-founder_John Gilmore with face-saving_spin like “Board Member Emeritus”. They’re fine with truly troubling people inside the Board, but not the person who founded the whole thing! In the Linux Foundation pretty much every single Board member is an employee of a proprietary software company! “In the Linux Foundation pretty much every single Board member is an employee of a proprietary software company!”In the video above I use Mozilla/Firefox as an example or as an analogy that’s timely. They’ve used similar tactics. Cancellationists (to borrow Stallman’s term) removed a technical leader for political reasons, putting in his place the people who abandoned Mozilla’s “open Web” vision, choosing instead to put DRM in the browser (Brendan Eich openly_opposed_this) and putting people_from_Microsoft_inside_their_board. If Google wanted to slowly diminish Mozilla to nothing (that’s cheaper for Google, which pays based on the number of Firefox users), that would be beneficial to Google. People like Jim "Open_Source_loves_Microsoft" Zemlin and Mrs. Baker aren’t geeks, but they’re being put in positions of power, just like the EFF’s Cohn. The EFF’s IRS filings in the coming years (after the death of Barlow) will be interesting to read. Their donors gave them a_lot_of_money, but whose agenda will be served? To quote our Ryan, who is gay, “homophobe turned also proprietary browser vendor with DRM based on Chromium pushing crypto to crackpots.” “Google sees this thing of making Mozilla rely on them as attrition. Every year they pay them a ridiculous amount of money to keep them hooked on the money while they lose more users. Eventually they just stop paying them any money and let what’s left of Mozilla die off. If they defy Google, they get cut off now. So they keep doing what Google wants and feeding on the trough, knowing Firefox is a dead end. It’s possible someone can come and fork the state of Firefox when Mozilla goes under and turn it back into a community project. It used to operate more like one. What scares the hell out of companies like Microsoft and Google, although they would never admit it openly, are communities. Because it’s easier to corrupt a corporation. You just go to the corporation and talk their language, money.” █ ䷩ 𝚕𝚒𝚗𝚎 2309 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/05/revisiting-netsurf/#comments Gemini version at gemini://gemini.techrights.org/2021/11/05/revisiting-netsurf/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_Web_is_Still_Getting_Obese_and_and_Very_Hostile,_But_NetSurf_Makes_Things a_Little_More_Acceptable⠀✐ Posted in Free/Libre_Software, GNU/Linux at 12:35 pm by Dr. Roy Schestowitz Video_download_link | md5sum 1c6d2a3e8148a9bf243da9749d9926b1 http://techrights.org/videos/netsurf-resources.webm Summary: Limiting ourselves to only a few sites and a handful of domains (Wikipedia, Tux Machines, Techrights, FSF and GNU), we’re taking a look at what it means to use NetSurf in an era of World Wide Web on ‘DRM steroids’ (Bloated/ Wide_Web_which_treats_users/visitors_like_vicious_enemies); a lot more could be shown and demonstrated but it’s limited to 15 minutes just to make a point, narrowing the focus to usage of RAM and number of open files A FEW months back we showed how_to_get_and_then_use_NetSurf. For most Web pages it works just fine (maybe not self-styled “web apps” or so-called “online banks”) and it ought to be used by default by those who aren’t doing anything too fancy online. NetSurf is not so well known, so many consider it ‘esoteric’ or even daring to merely mention it. Let’s change that perception. Many Web browsers that are well known are mostly copies of one another; NetSurf is not. The video above focuses on the vast difference in the management of resources; unlike Firefox and Chromium ‘clones’ (similar/overlapping codebase), NetSurf is reasonably compact (also roughly the same as some advanced Gemini clients) and it does not support all sorts of hostile things that you probably don’t want running on your machine anyway. █ ䷩ 𝚕𝚒𝚗𝚎 2359 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/05/techrights-source-protection/#comments Gemini version at gemini://gemini.techrights.org/2021/11/05/techrights-source-protection/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Celebrating_15_Years_of_a_Perfect_Record_Protecting_Our_Sources⠀✐ Posted in Site_News at 4:06 pm by Dr. Roy Schestowitz Video_download_link | md5sum 962601433234aefbb0c1753227c020b4 http://techrights.org/videos/turning-15.webm Summary: 15 years of Techrights driving change by advocacy and whistleblowing have certainly served the Free software community (those whom we exposed for wrongdoing understandably hate us, but that’s a badge of honour); we intend to be around for another 15 years, even if the Web goes down the toilet (we have several_viable_contingencies_already; the eggs are in many baskets) and we’ll be making a lot more videos for the rest of this year and until further notice THIS is the last (and seventh) video for this special Friday (Guy_Fawkes Night; in this video the explosions outdoors are audible) and as our anniversary falls on a Sunday I’d like to extend my gratitude today, a weekday (I’ll be working this coming weekend), to all our sources and whistleblowers. We’ve successfully protected all of them (100%). That’s better than what’s typically conceivable (even one burned source is extremely damaging to one’s reputation). “Next week we can hopefully resume the current EPO series until its completion.”I’ve faced aggressive threats and took agonising, considerable personal risks to put out there the suppressed information we’ve received and our impact as a site (and online community, not just a Web site) only grows as time goes by. It makes some rich and powerful people very antsy. They’ll keep trying to silence us or identify our sources. We can outwit them. On Monday we’ll publish Microsoft GitHub Exposé — Part V and our_next_major goal (“high-priority project”) is putting_GitHub_in_the_coffin,_just_like CodePlex. CodePlex and GitHub can be buried alongside one another. Next week we can hopefully resume the current EPO series until its completion. █ ䷩ 𝚕𝚒𝚗𝚎 2419 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_5/11/2021:_Alpha_of_Wayland_1.20_and_Beta_3_of_FreeBSD_12.3⠀✐ Posted in News_Roundup at 12:47 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ TUXEDO_Nano_Pro_is_a_tiny_Linux_PC_that’s_upgradeable_and powered_by_AMD_Ryzen⠀⇛ AMD has been killing it these past few years. The company’s Ryzen processors have been universally praised by both reviewers and consumers alike. In both desktops and laptops, these Ryzen chips have largely put Intel to shame. AMD is undeniably the king of multi-core performance. Today, Linux-computer-maker TUXEDO announces an all-new AMD Ryzen-powered computer, but no, it is not a huge tower. Actually, it is a NUC-like mini PC powered by 4000 series Ryzen processors, with the top model being equipped with the Ryzen 7 4800U. Called “Nano Pro – Gen11,” it isn’t just small and powerful, but quite upgradeable too — you can change out the RAM, storage, and Wi-Fi card. And while the mini PC ships with Ubuntu by default, you can choose to also have Windows pre-installed for dual-boot. # ⚓ System76_Blog_—_Robert_Bunn_is_developing_an_AI_to_prevent preterm_births⠀⇛ The AI platform we’re using is PyTorch for fundamental deep learning. I use something on top of PyTorch called fast.ai, which is a good platform that’s great for prototyping and testing ideas without writing a ton of boilerplate code. AWS also has a ton of resources for deep learning. I use Ubuntu because I wanted to start with something I’m familiar with, but honestly, I’m thinking about switching to Pop!_OS. I’m always worried about using a new Linux operating system because if you ever want to do anything, you want to be able to search for problems. Pop!_OS obviously isn’t going to be as good a search word as Ubuntu, right? So, my problem might not appear, and I didn’t know how different it was going to be. But apparently, Pop! _OS is built on Ubuntu and is designed for the laptops you guys have. I like that it turns off the GPU when it’s not in use to save power, so I think it will be a lot more convenient to use on Pop!_OS. # ⚓ Managing_Linux_containers_is_about_to_get_a_lot_easier_on Chrome_OS⠀⇛ Earlier this year, after roughly three years, Google finally lifted the “Beta” label from the Crostini project that brought a Linux development environment to Chromebooks. While many may feel that the Linux side of Chrome OS is only for technical users, developers, and tinkerers such as myself, the ability to install in run Linux packages can bring a lot of value to Chrome OS for even the average consumer. Applications such as GIMP can give users access to more powerful image editing tools that are relatively scant in the web- based ecosystem of Chromebooks. Still, others may be interested in Linux on Chromebooks for the possibility of native gaming via the upcoming Borealis project that will use the same container tech to bring Steam to Chrome OS. # ⚓ How_to_install_FNF_Roblox_Youtubers_Mod_on_a_Chromebook⠀⇛ Today we are looking at how to install FNF Roblox Youtubers Mod on a Chromebook. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. If you have any questions, please contact us via a YouTube comment and we would be happy to assist you! o § Audiocasts/Shows⠀➾ # ⚓ Creating_A_“Help”_Program_For_DTOS_Using_Dmenu_– Invidious⠀⇛ I decided to create a simple bash script to create a “help” program for DTOS. This script will list (in dmenu) some of my tutorial videos on topics such as XMonad, Doom Emacs, etc. Creating such a script should take just a few minutes, so I thought I’d do it on camera. # ⚓ Technically_Speaking_(S1E09):_Get_into_GitOps_–_Invidious⠀⇛ What happens when your DevOps continuous delivery pipeline meets Git version control and cluster automation? In this episode, Red Hat CTO Chris Wright is joined by Stefan Prodan from Weaveworks to discuss the exciting topic of GitOps, the expanding landscape of everything-as-code- or better yet, data- and some of the tools that can help us with the automation of continuous deployment. # ⚓ This_AWESOME_Linux_App_Should_Be_On_Windows_+_macOS_– Invidious⠀⇛ …But it’s nice to have an exclusive! We’re back with another app spotlight, and nothing on Windows or macOS can compete with this robust tool! # ⚓ MX_Linux_21_Quick_overview_#Shorts_–_Invidious⠀⇛ o § Kernel Space⠀➾ # ⚓ ksmbd:_a_new_in-kernel_SMB_server_(SAMBA+_blog)⠀⇛ # ⚓ ksmbd:_a_new_in-kernel_SMB_server⠀⇛ “ksmbd” is a new Linux kernel module which implements an SMB server. It’s aimed at being low overhead, low footprint, performant fileserver covering many basic usecases, running on smaller devices with limited resources being the most apparent one: OpenWRT, the Linux distribution for embedded devices, adopted ksmbd already 18 months ago while ksmbd was still being developed. ksmbd hit the public in November 2021 as part of the next Linux kernel version 5.15. It is not meant to replace the existing Samba fileserver “smbd”, but rather be an extension and will integrate with Samba in the future. # ⚓ Linux_kernel_5.15_is_available,_and_it_has_something special_for_NTFS_users⠀⇛ The latest Linux kernel has been released and it has plenty to offer users and admins alike. But this particular release will be particularly pleasing to those who use Linux as either a file- sharing server or a device that must connect to and use NTFS-partitioned drives. On top of these headline changes, there are other new additions and improvements to be found. [...] In a word, no. Your best bet is to wait until the kernel is made available via your Linux distribution of choice. Although you can download and compile the latest kernel, it won’t be upgradable through your distribution’s package manager. If you use a rolling release, such as Arch or openSUSE Tumbleweed, you will receive the 5.15 kernel much sooner than if your distribution of choice is a static release. We might find kernel 5.15 land in Ubuntu 22.04, which will be released in late April 2022. So, unless you have an absolutely pressing need for these newest additions, your best bet is to hold off until your distribution maintainers include 5.15 in the official release. o § Benchmarks⠀➾ # ⚓ More_Linux_Performance_Benchmark_Data_For_Alder_Lake, Comparison_Data_Points_–_Phoronix⠀⇛ With the embargo lifted following this morning’s Intel Core i5 12600K + Core i9 12900K Linux review, I’ve begun uploading more public test data to OpenBenchmarking.org and making my earlier test results public. With that and initial data flowing in from others in the community, here is some more data to poke through if interested in Alder Lake on Linux. This page shows all of the amassed data on OpenBenchmarking.org for both the Core i5 12600K and Core i9 12900K. From there you can add in more processors for comparison from the available public data as well as input your own local pricing for seeing custom performance-per-dollar metrics. (As mentioned in today’s Alder Lake Linux review, currently CPUFreq reports bogus clock frequencies of 6.3GHz for the i5-12600K and 6.5GHz for i9- 12900K… That’s carried over into this auto- collected information on OpenBenchmarking.org as well, which is why you see those numbers albeit are at stock frequencies.) There’s much more data than could be potentially conveyed in one article. o § Applications⠀➾ # ⚓ HP_Linux_Imaging_and_Printing_(HPLIP)_Drivers_Now_Support Ubuntu_21.10_and_Debian_11⠀⇛ HPLIP 3.21.10 is here almost two months after HPLIP 3.21.8 and adds support for the Ubuntu 21.10 (Impish Indri), Debian GNU/Linux 11 “Bullseye”, Zorin OS 15, and Zorin OS 16 distributions. This means that you can now use your HP printer/scanner with any of these GNU/Linux distributions if you install the new HPLIP version. o § Instructionals/Technical⠀➾ # ⚓ How_To_Install_Deno_JavaScript_Runtime_on_Ubuntu_20.04_LTS –_idroot⠀⇛ In this tutorial, we will show you how to install Deno JavaScript Runtime on Ubuntu 20.04 LTS. For those of you who didn’t know, Deno is a simple, modern, and secure runtime for JavaScript and TypeScript that uses V8 and is built in Rust. it has high compatibility with existing JavaScript code written with full support for ECMAScript standards. 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 Deno JavaScript Runtime 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. # ⚓ Use_QEMU_to_create_a_hardware_dual-boot_without_rebooting⠀⇛ After downloading an ISO image, assuming you have QEMU installed, it’s possible to boot an ISO image in a virtual machine and then install that ISO from within the virtual machine directly to a physical drive, bypassing the need to reboot. Simply pass the ISO image as the -cdrom parameter, followed by “format=raw,file=/dev/sdb” (replace /dev/sdb with the drive you want to install to) as the hard drive parameter (making absolutely certain to specify the raw format, of course). Once you boot into the ISO image with QEMU, just run the installer as if it were a virtual machine — it’ll just use the physical device as an install target. After that, you’ll be able to seamlessly boot multiple distros (or even other operating systems) at once. # ⚓ Install_LimeSurvey_on_Ubuntu_20.04_–_Unixcop_the_Unix_/ Linux_the_admins_deams⠀⇛ LimeSurvey is an open-source online survey application, written in PHP and using MySQL, MariaDB, or PostgreSQL databases. This utility allows users without programming skills to develop, publish and collect responses to their surveys. The application has a friendly web interface that allows us to perform survey operations without any problems. As it is a web application, it can be installed on servers with different operating systems. The developers of the application believe in the open-source philosophy, so the application also follows it. This allows us to examine the source code and thus verify the security of the application. # ⚓ Using_chpasswd_to_change_account_passwords_on_Linux_| Network_World⠀⇛ The chpasswd command allows admins to change account passwords by piping username and password combinations to it. This can be done one-account-at-a-time or by putting all of the accounts to be modified in a file and piping the file to the command. # ⚓ Getting_Started_with_Docker:_Install_Docker_Engine_– LinuxLinks⠀⇛ Docker is a set of platform as a service (PaaS) products that use OS-level virtualization to deliver software in packages called containers. A container is software that packages up code and all its dependencies so the application runs quickly and reliably from one computing environment to another. A Docker container image is a lightweight, standalone, secure, executable package of software that includes everything needed to run an application: code, runtime, system tools, system libraries, and settings. The software that hosts the containers is called Docker Engine. Let’s go through you the steps to install Docker Engine. We’re using the 64-bit version of Ubuntu Impish 21.10. If you encounter problems with older releases, please share in the Comments box below. # ⚓ How_to_Change_or_Reset_Forgotten_Root_Password_in_RHEL_8⠀⇛ You can never really relate to the priceless beauty and performance of RHEL 8 Linux operating system distribution until you have given it a try. Its user interface is always scaling to better visual appeal, its multi-monitor handling technique is one of a kind, and its security model speaks for itself. The only thing that can come between an RHEL user’s full exploration of this Linux distribution is human nature. Human nature will convince us to create/set a one-of-a-kind root password on our Linux systems and be responsible for displacing the same unique password. # ⚓ How_To_Install_Mattermost_on_AlmaLinux_8_–_idroot⠀⇛ In this tutorial, we will show you how to install Mattermost on AlmaLinux 8. For those of you who didn’t know, Mattermost is a secure, open-source platform for communication, collaboration, and workflow orchestration across tools and teams. Mattermost is a free Slack alternative. Mattermost is available in open source and enterprise editions. Open Source edition is free, whereas Enterprise editions require a per-user license. You can find Mattermost Pricing plans on their official website. 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 Mattermost on AlmaLinux 8. You can follow the same instructions for CentOS and Rocky Linux. # ⚓ How_to_Install_and_Configure_Memcached_on_Debian_11⠀⇛ Memcached is an open-source and distributed memory object caching system that holds the most frequently queried data in memory. This will reduce data load time as well as provide ease of access to the database. You can use Memcached to speed up dynamic web applications by alleviating database load. It is simple, easy to deploy and can be integrated with several programming languages including PHP, Python and more. In this tutorial, I will show you how to install Memcached on Debian 11. # ⚓ Setup_simple_CI/CD_pipeline_using_Github_and_Jenkins_on_an AWS_EC2_Linux_instance⠀⇛ In this article we will see the steps to implement a simple CI/CD pipeline using Jenkins. We will be using a sample Java code and we will be deploying that code onto Apache Tomcat Web-Server as a .war file. We will be using Maven as a build tool. You can find the sample Java code on my Github Repository(repo). Before we proceed, let’s understand the basics of the tools and technologies that we will be using in setting up the CI/CD pipeline. # ⚓ How_to_install_RVM-_Ruby_Version_Manager_on_Ubuntu_20.04 LTS⠀⇛ RVM- Ruby Version Manager is a tool meant to use the command line for installing and managing the various ruby versions easily. Here we see the commands for installation of RVM on Ubuntu 20.04 LTS Focal fossa. # ⚓ How_do_you_tell_if_a_problem_is_caused_by_DNS?⠀⇛ I was looking into problems people were having with DNS a few months ago and I noticed one common theme – a lot of people have server issues (“my server is down! or it’s slow!“), but they can’t tell if the problem is caused by DNS or not. So here are a few tools I use to tell if a problem I’m having is caused by DNS, as well as a few DNS debuggging stories from my life. # ⚓ How_to_install_the_Wekan_kanban_server_–_TechRepublic⠀⇛ If you (or your teammates) aren’t using a kanban board to keep yourself and your projects on task, you’re missing out. Kanban boards make managing projects incredibly easier. And the more complex a task, the better. # ⚓ How_To_Download_Debian_CDs,_DVDs_and_Old_Versions_with Jigdo_Made_Easy⠀⇛ We know that Debian in every release is distributed in multiple volumes of CDs and DVDs which are numbered 1, 2, 3 and so on. One Debian release may amount to 20 GigaBytes total or equal to dozens of CDs or DVDs. Officially, Debian provides only CD1 and DVD1, while the rest of CD2 to CD50, DVD2 to DVD10, not provided in the Debian server and neither Debian mirrors. Although CD1 or DVD1 is sufficient to install Debian to computer, some people, like teachers and students, might want the additional CDs or DVDs for no internet access purposes. The official way to download the additional CDs or DVDs is by using a program called Jigdo. This tutorial explains how to do that simply and easily picture by picture. # ⚓ Things_To_Do_After_Installing_Fedora_35⠀⇛ Fedora releases a new version in approximately every 6 months. Each now version is supported with updates for 13 months in total. The distribution is a good place to get the latest stable software and technologies consistently. # ⚓ hings_To_Do_After_Installing_Ubuntu_21.10_&_20.04⠀⇛ Ubuntu releases a new version every six months. However, most of the stuff you may need to do after installing the new version are generally the same. This article will guide you through enhancing your new system. No matter what supported version of Ubuntu you use, you can follow those steps. # ⚓ How_to_install_Synfig_Studio_on_Elementary_OS_6.0⠀⇛ Firstly we run an optional command, this command is only needed if you cant launch Flatpak applications like your default browser on your system. For some reason, we couldn’t, so if you can, you can skip the first command. o § Distributions⠀➾ # § BSD⠀➾ # ⚓ FreeBSD_12.3-BETA3_Now_Available⠀⇛ The third BETA build of the 12.3-RELEASE release cycle is now available. Installation images are available for: o 12.3-BETA3 amd64 GENERIC o 12.3-BETA3 i386 GENERIC o 12.3-BETA3 powerpc GENERIC o 12.3-BETA3 powerpc64 GENERIC64 o 12.3-BETA3 powerpcspe MPC85XXSPE o 12.3-BETA3 sparc64 GENERIC o 12.3-BETA3 armv6 RPI-B o 12.3-BETA3 armv7 BANANAPI o 12.3-BETA3 armv7 BEAGLEBONE o 12.3-BETA3 armv7 CUBIEBOARD o 12.3-BETA3 armv7 CUBIEBOARD2 o 12.3-BETA3 armv7 CUBOX-HUMMINGBOARD o 12.3-BETA3 armv7 RPI2 o 12.3-BETA3 armv7 WANDBOARD o 12.3-BETA3 armv7 GENERICSD o 12.3-BETA3 aarch64 GENERIC o 12.3-BETA3 aarch64 RPI3 o 12.3-BETA3 aarch64 PINE64 o 12.3-BETA3 aarch64 PINE64-LTS Note regarding arm SD card images: For convenience for those without console access to the system, a freebsd user with a password of freebsd is available by default for ssh(1) access. Additionally, the root user password is set to root. It is strongly recommended to change the password for both users after gaining access to the system. Installer images and memory stick images are available here: https://download.freebsd.org/ftp/releases/ ISO-IMAGES/12.3/ The image checksums follow at the end of this e-mail. If you notice problems you can report them through the Bugzilla PR system or on the -stable mailing list. If you would like to use SVN to do a source based update of an existing system, use the "releng/12.3" branch. A summary of changes since 12.3-BETA2 includes: o A fix for use after free in combination with EVDEV_SUPPORT has been added to the usb(4) stack. Please note, the release notes page is not yet complete, and will be updated on an ongoing basis as the 12.3- RELEASE cycle progresses. === Virtual Machine Disk Images === VM disk images are available for the amd64, i386, and aarch64 architectures. Disk images may be downloaded from the following URL (or any of the FreeBSD download mirrors): https://download.freebsd.org/ftp/releases/VM- IMAGES/12.3-BETA3/ The partition layout is: ~ 16 kB - freebsd-boot GPT partition type (bootfs GPT label) ~ 1 GB - freebsd-swap GPT partition type (swapfs GPT label) ~ 20 GB - freebsd-ufs GPT partition type (rootfs GPT label) The disk images are available in QCOW2, VHD, VMDK, and raw disk image formats. The image download size is approximately 135 MB and 165 MB respectively (amd64/i386), decompressing to a 21 GB sparse image. Note regarding arm64/aarch64 virtual machine images: a modified QEMU EFI loader file is needed for qemu-system-aarch64 to be able to boot the virtual machine images. See this page for more information: https://wiki.freebsd.org/arm64/QEMU To boot the VM image, run: % qemu-system-aarch64 -m 4096M -cpu cortex-a57 -M virt \ -bios QEMU_EFI.fd -serial telnet:: 4444,server -nographic \ -drive if=none,file=VMDISK,id=hd0 \ -device virtio-blk-device,drive=hd0 \ -device virtio-net-device,netdev=net0 \ -netdev user,id=net0 Be sure to replace "VMDISK" with the path to the virtual machine image. === Amazon EC2 AMI Images === FreeBSD/amd64 EC2 AMIs are available in the following regions: af-south-1 region: ami-0474575e4743c09ef eu-north-1 region: ami-086d14e67901fbe18 ap-south-1 region: ami-0070d860537d0ded8 eu-west-3 region: ami-0b3dc01c43c0912fe eu-west-2 region: ami-0980e2d73f5d45dde eu-south-1 region: ami-0e7f23b4407ea2984 eu-west-1 region: ami-07e6a1fef7da32d00 ap-northeast-3 region: ami- 05abadc5c531ee229 ap-northeast-2 region: ami- 0d19b72fb447f1351 me-south-1 region: ami-04594b13da5f816c8 ap-northeast-1 region: ami- 0a22abde412c924dd sa-east-1 region: ami-0b1c3ebd4e3c3d110 ca-central-1 region: ami-00a7cbd0c72d71f34 ap-east-1 region: ami-04764a6d430eee081 ap-southeast-1 region: ami- 0eeeacb4006f6c3dc ap-southeast-2 region: ami- 090d2e10d03f4e7e2 eu-central-1 region: ami-08b58933a7123b517 us-east-1 region: ami-01c2add58c60cdaa0 us-east-2 region: ami-089ef8724c5788778 us-west-1 region: ami-09675dff8007c2120 us-west-2 region: ami-04dcf23effaa07fa2 These AMI IDs can be retrieved from the Systems Manager Parameter Store in each region using the keys: /aws/service/freebsd/amd64/base/ufs/12.3/ BETA3 FreeBSD/aarch64 EC2 AMIs are available in the following regions: af-south-1 region: ami-0ddb2ab71276a1cd2 eu-north-1 region: ami-067904d4b39b13b52 ap-south-1 region: ami-0914a27f72a3defcb eu-west-3 region: ami-0a067d26bbb475270 eu-west-2 region: ami-0445d628b7727bbc0 eu-south-1 region: ami-0f0c5ab6ae5a0222e eu-west-1 region: ami-0fe3c1f09940fc2a5 ap-northeast-3 region: ami- 041c97971472b0b2a ap-northeast-2 region: ami- 0dc899119ea13ebbe me-south-1 region: ami-01aba86d507b0caad ap-northeast-1 region: ami- 0177cd37b15b7cf32 sa-east-1 region: ami-00d3752ace91695cc ca-central-1 region: ami-0092b0802c7929b82 ap-east-1 region: ami-0c14a86ca5234df3f ap-southeast-1 region: ami- 09b5c8e04397b1a0c ap-southeast-2 region: ami- 0bd853e50e9cbd099 eu-central-1 region: ami-079e8694c2b8b9b71 us-east-1 region: ami-0006ee96beca8fec2 us-east-2 region: ami-0de58b11cdcc18d5b us-west-1 region: ami-0c96f66557b5771af us-west-2 region: ami-025360ab398d1f77a These AMI IDs can be retrieved from the Systems Manager Parameter Store in each region using the keys: /aws/service/freebsd/arm64/base/ufs/12.3/ BETA3 === Vagrant Images === FreeBSD/amd64 images are available on the Hashicorp Atlas site, and can be installed by running: % vagrant init freebsd/FreeBSD-12.3-BETA3 % vagrant up === Upgrading === The freebsd-update(8) utility supports binary upgrades of amd64 and i386 systems running earlier FreeBSD releases. Systems running earlier FreeBSD releases can upgrade as follows: # freebsd-update upgrade -r 12.3-BETA3 During this process, freebsd-update(8) may ask the user to help by merging some configuration files or by confirming that the automatically performed merging was done correctly. # freebsd-update install The system must be rebooted with the newly installed kernel before continuing. # shutdown -r now After rebooting, freebsd-update needs to be run again to install the new userland components: # freebsd-update install It is recommended to rebuild and install all applications if possible, especially if upgrading from an earlier FreeBSD release, for example, FreeBSD 11.x. Alternatively, the user can install misc/compat11x and other compatibility libraries, afterwards the system must be rebooted into the new userland: # shutdown -r now Finally, after rebooting, freebsd-update needs to be run again to remove stale files: # freebsd-update install # ⚓ Wayland_1.20_Alpha_Released_With_Upstreamed_FreeBSD Support,_Autotools_Nuked⠀⇛ With the plans to release Wayland 1.20 before Christmas, Wayland 1.20 Alpha was released on Thursday to kick off the start of the release process. Wayland 1.20 will arrive about ten months after Wayland 1.19 and comes at a time when most of the interesting Wayland work is happening in the compositor space or the various support libraries like wlroots and libweston or other components. Wayland 1.20 Alpha does feature upstreamed FreeBSD support that is also now receiving CI coverage for ensuring the Wayland support on this BSD remains in better shape moving forward. # ⚓ wayland_1.19.91⠀⇛ This is the alpha release for wayland 1.20. This release contains the following major changes: - FreeBSD support has been entirely upstreamed and has been added to our continuous integration system. - The autotools build system has been dropped. Meson has replaced it. - A few protocol additions: wl_surface.offset allows clients to update a surface's buffer offset independently from the buffer, wl_output.name and description allow clients to identify outputs without depending on xdg-output-unstable- v1. - In protocol definitions, events have a new "type" attribute and can now be marked as destructors. - A number of bug fixes, including a race condition when destroying proxies in multi-threaded clients. Full commit history below. Alex Richardson (17): Use MAP_FAILED instead of (void *) -1 os-wrappers-test.c: Correctly forward arguments to fcntl Change wl_os_dupfd_cloexec minfd to be int os-wrappers-test: Handle fcntl() being declared as a macro Use epoll-shim to emulate epoll(7) on FreeBSD gitlab-ci: update ci-templates to the latest commit gitlab-ci: remove duplicated lines in ci-templates include gitlab-ci: Fix copy-paste error in a comment gitlab-ci: add junit reports to the debian builder Support reading ucred from the socket on FreeBSD shm: Add mmap+memmove fallback if mremap() does not exist Use /dev/fd instead of /proc/self/fd test-runner: Implement is_debugger_attached() for FreeBSD test-helpers: use sysctl() to count open fds on FreeBSD Detect FreeBSD versions with broken MSG_CMSG_CLOEXEC Allow event-loop signal tests to pass on FreeBSD gitlab-ci: add a FreeBSD test job Alexander Dunaev (1): cursor: add one more directory to XCURSORPATH Damian Hobson-Garcia (1): server: stop wl_display event loop from any context Daniel Stone (10): ci: Add comments, rename build stages ci: Parameterise and template build ci: Add AArch64 build ci: Add ARMv7 build ci: Only run ci-fairy on MRs ci: Use consistent YAML indendation ci: Add release builds ci: Use appropriate concurrency level ci: Use Werror ci: Sanitise build and install paths Derek Foreman (6): client: Refactor wl_proxy_destroy critical section client: Add new proxy marshalling functions with flags scanner: Use the new atomic marshal/ destroy function connection: Rename wl_buffer tests: Destroy custom global object debug: Fix printing of new ids Duncan McIntosh (1): wayland-shm: Check the size of sealed memory if ignoring SIGBUS handlers Fergus Dall (6): connection-test: Encode size in message headers correctly connection: Handle non-nullable strings in wl_connection_demarshal util: Avoid undefined behaviour in for_each_helper server: Fix undefined behavior in wl_socket_init_for_display_name connection-test: Pad out strings with null bytes os-wrappers-test: Make syscall intercepts work with sanitizers James Hilliard (2): meson: only require cpp for tests build: add option to disable tests James Legg (2): scanner: Use descriptions in entries tests: Test wayland-scanner with a description in an entry Jonas Ådahl (2): ci: Use ci-fairy to check for Signed- off-by protocol: Add wl_surface.offset Manuel Stoeckl (3): client: print discarded events in debug log connection, client: Avoid locale- dependent float printing client: handle fcntl error on bad fd in wl_display_connect Marius Vlad (1): src: Add missing new lines to log messages Matt Hoosier (1): protocol: mention that buffers with alpha are assumed premultiplied Michael Weiss (1): meson: Only require expat when building wayland-scanner Nick Diego Yamane (1): Document serial param usage in wl_pointer.set_cursor Olivier Fourdan (1): shm: Relax shm_pool_create_buffer() validity check Olivier Tilloy (1): cursor: Try to fall back to a default xcursor theme first Pekka Paalanen (2): CI: turn on ASan and UBSan wayland-util: avoid memcpy(NULL) in wl_array_copy() Simon McVittie (1): build: Include the Wayland minor version in libraries' ABI versions Simon Ser (18): build: re-open master for regular development client: assert queue display matches proxy build: drop autotools build: replace assembly embedding with Python script protocol: drop reference to wl_drm shm: remove wl_shm_buffer.pool NULL checks protocol: allow immediate wl_buffer.destroy if not re-used shm: add safety assertions protocol: clarify wl_seat.name description shm: document wl_shm_buffer connection: print array size cursor: rename load_default_theme to load_fallback_theme cursor: remove unused wl_cursor_theme.name protocol: mention that keymap mapping must be read-only protocol: add note about wl_output.done in events protocol: add wl_output. {name,description} protocol: wl_shm uses pre-multiplied alpha build: bump to version 1.19.91 for the alpha release Tadeo Kondrak (2): protocol: Add type attribute to events protocol: Specify wl_callback::done to be a destructor event Tobias Stoeckmann (2): cursor: fix CVE-2013-2003 cursor: fix crash with weird input files Vlad Zahorodnii (1): server: add wl_display getter for wl_global sheepwall (1): server: remove duplicate include git tag: 1.19.91 # § SUSE/OpenSUSE⠀➾ # ⚓ The_Power_of_Caring:_Helping_the_flood_victims_in Germany_|_SUSE_Communities⠀⇛ This blog is a part of ‘The Power of Caring’, a series dedicated to sharing some of the inspiring stories from our team and how they leveraged SUSE’s Employee giving program ‘SUSEcares’, to make a positive impact around the world, through the act of giving. Our first blog features Monika Bach, Executive Assistant in the Engineering Operations team and a Women in Tech Ambassador, based in Nuremberg, who shares her experience in leading a company wide event to support Aktion Deutschland Hilft (ADH). # § IBM/Red Hat/Fedora⠀➾ # ⚓ Red_Hat_Enterprise_Linux_9_emerges_in_beta_form_•_The Register⠀⇛ # § Canonical/Ubuntu Family⠀➾ # ⚓ Data_centre_networking:_SDDC⠀⇛ In the previous blogs, we covered the architecture and main drivers behind software-defined networking. In this one, we discuss the impact of softwarisation on the other important data centre building blocks, culminating in software-defined data centres (SDDC). SDDC occupies a progressively larger segment of the cloud computing space, originally adopted by public cloud service providers and hyperscalers, and now finding a home with private cloud service providers, too. First, let’s consider which drivers influenced the evolution of data centres. o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Firefox_94_on_POWER⠀⇛ Firefox 94 is released. I have little interest in the colourizer, but I do like about:unloads and EGL support on Linux for great WebGL justice even on X11 (I don’t use the Wayland Wasteland), at least if you have an AMD/ATI card like the WX7100 Raptor sells as a BTO option. There are also various performance improvements and a fun feature where you can use a different Mozilla VPN server for each separate multi-account container, the latter probably being Firefox’s most useful capability right now. The LTO- PGO patch is unchanged from Firefox 93 and the .mozconfigs are unchanged from Firefox 90. # ⚓ Waterfox:_A_Firefox_fork_that_could_teach Mozilla_a_lesson [Ed: This has totally failed to mention that Waterfox is owned/controlled by the same_spying_company_that_owns_Startpage]⠀⇛ As Firefox’s share of the browser market continues to slide, the Waterfox Project shows some of the ways that Mozilla is failing to listen to its users – and it’s far from the only example. Waterfox, which has just released its fourth version, came to your correspondent’s attention after the arrival of Firefox 57, codenamed Quantum, which represented a major change in the program, complete with parts of the browser engine written in Rust. (The Rust language itself started out as a Mozilla project. Despite Rust’s popularity, within three years, Mozilla would also lay off members of the Rust language team.) The problem with Firefox Quantum is that it also dropped a very significant feature: Netscape’s XUL-based extension engine, added way back in 1997. To quote the Classic Addons Archive, dropping XUL meant losing “19,450 Firefox add-ons created by 14,274 developers over the past 15 years.” At a stroke this crippled one of Firefox’s killer features: how users could extensively customise it – unlike, say, Google Chrome. # § CMS⠀➾ # ⚓ The_Month_in_WordPress:_October_2021⠀⇛ October 2021 brought a lot of new things to WordPress, from release updates to new versions of Gutenberg. More notably, in the latest episode of WP Briefing, Executive Director Josepha Haden reminded us about the importance of freedom in open source platforms like WordPress. # § FSF⠀➾ # ⚓ Activists_(including_the_FSF)_helped_secure_a_new round_of_DMCA_anticircumvention_exemptions⠀⇛ We have some good news to share. The FSF was one of several activist organizations pushing for exemptions to the anticircumvention rules under the Digital Millennium Copyright Act (DMCA) that make breaking Digital Restrictions Management (DRM) illegal, even for ethical and legitimate purposes. We helped bring public awareness to a process that is too often only a conversation between lawyers and bureaucrats. As of late last week, there are now multiple new exemptions that will help ease some of the acute abuse DRM inflicts on users. However, the main lesson to be learned here is that we should and must keep pushing. Individual, specific exemptions are not enough. The entire anticircumvention law needs to be repealed. We want to thank the 230 individuals who co- signed their names to our comments supporting exemptions across the board. We should take this as a sign that even though it can be difficult, anti-DRM activism yields practical results. Section 1201 is one of the most nefarious sections of the DMCA. The provisions contained in 1201 impose legal penalties against anyone trying to circumvent the DRM on their software and devices or, in other words, anyone who tries to control that software or device themselves instead of leaving it up to its corporate overlords. Section 1201 opens up those who try to study, repair, or research restricted devices to potentially serious legal penalties. Something that doesn’t help matters is the intentionally complex series of hoops concerned citizens, researchers, and activists around the world are forced to jump through to voice objection to current anticircumvention rules, or to propose new exemptions. This bureaucratic nightmare is the only way to lobby for changes in Section 1201, and the fact that it has to be done every three years makes it a recurring one. Nothing abates the added terror of our being granted use anticircumvention exemptions, but being forbidden to share the tools that make this possible. It takes the hard work of hundreds to secure the anticircumvention use exemptions we already have, and even more work to eke out a few more. Yet thanks to the support of citizens, activists, and researchers around the world, the US Copyright Office has approved a few more, while at the same time demonstrating the DMCA’s serious flaws. # § Programming/Development⠀➾ # ⚓ an_inside_look_into_the_illicit_ad_industry⠀⇛ One day, I was chilling in IRC, when I got a PM from my friend: he had gotten an inquiry from a possible client that needed help reverse engineering a piece of obfuscated JavaScript. I said something like “sounds like fun, send it over, and I’ll see what I come up with.” The script in question was called popunder.js and did exactly what you think it does. The customer in question had started a popunder ad network, and needed help adapting this obfuscated popunder script to work with his system, which he built using a software called Revive Adserver, a fork of the last GPL version of OpenX. I rolled my eyes and reverse engineered the script for him, allowing him to adapt it for his ad network. The adaptation was a success, and he wired me a sum that was triple my quoted hourly rate. This, admittedly, resulted in me being very curious about his business, as at the time, I was not used to making that kind of money. Actually, I’m still not. A few weeks passed, and he approached me with a proposition: he needed somebody who could reverse engineer the JavaScript programs delivered by ad networks and figure out how the scripts worked. As he was paying considerably more than my advertised hourly rate, I agreed, and got to work reverse engineering the JavaScript programs he required. It was nearly a full time job, as these programs kept evolving. In retrospect, he probably wasn’t doing anything with the reports I wrote on each piece of JavaScript I reverse engineered, as that wasn’t the actual point of the exercise: in reality, he wanted me to become familiar with the techniques ad networks used to detect fraud, so that we could develop countermeasures. In other words, the engagement evolved into a red-team type engagement, except that we weren’t testing the ad networks for their sake, but instead ours. # ⚓ Automated_cross-platform_tools_for_ARM_developers⠀⇛ IAR’s Build Tools for ARM streamline automated build and test processes in software frameworks built on Ubuntu, Red Hat or Windows # § Python⠀➾ # ⚓ Python’s_Semi_Colon_Makes_Absolutely_No_Sense_– Invidious⠀⇛ I like Python it’s a fun and simple language to work with but every so often I remember it supports semi colon for what seems like absolutely no reason when nobody using the language actually uses it. # ⚓ Antoine_Beaupré:_A_Python_contextmanager gotcha⠀⇛ * § Leftovers⠀➾ o § Hardware⠀➾ # ⚓ Big_RGB_LED_Cube_You_Can_Build_Too_|_Hackaday⠀⇛ LED cubes are really nothing new, many of us consider the building of a good sized one almost an electronics right of passage that not so many manage to find the time or have the skill to pull off. It’s our pleasure to draw your attention to a lovely build, showing all the processes involved, the problems and the solutions found along the way. Building a small cube is somewhat of a trivial affair, especially without considering PWM colour mixing, however as simple maths will illustrate, as you increase the number of LEDs on each side, the total number will quickly get quite large. More LEDs need more power and increase control complexity considerably. A larger matrix like this 16 x 16 x 16 LED build, has a total of 4096. This would be a nightmare to drive with plain RGB LEDs, even with cunning multiplexing, but luckily you can buy indexable LEDs in a through-hole package similar to the ubiquitous WS2812-based SMT LEDs you see around. These are based on the PD9823 controller, which can be programmed as if they were a WS2812, at least according to this analysis. Now you can simply chain a column of LEDs, with the control signal passed from LED to nearest neighbour. o § Health/Nutrition⠀➾ # ⚓ Antibiotic_resistance_is_at_a_crisis_point_–_government support_for_academia_and_Big_Pharma_to_find_new_drugs_could help_defeat_superbugs⠀⇛ Antibiotic resistance poses one of the most important health challenges of the 21st century. And time has already run out to stop its dire consequences. The rise of multidrug-resistant bacteria has already led to a significant increase in human disease and death. The U.S. Centers for Disease Control and Prevention estimates that approximately 2.8 million people worldwide are infected with antibiotic-resistant bacteria, accounting for 35,000 deaths each year in the U.S. and 700,000 deaths around the globe. A 2019 joint report by the United Nations, World Health Organization and World Organization for Animal Health states that drug-resistant diseases could cause 10 million deaths each year by 2050 and force up to 24 million people into extreme poverty by 2030 if no action is taken. Superbugs are already able to evade all existing treatments – a 70-year-old woman from Nevada died in 2016 from a bacterial infection resistant to every available antibiotic in the U.S. I am a biochemist and microbiologist who has been researching and teaching about antibiotic development and resistance over the past 20 years. I believe that solving this crisis requires more than just proper antibiotic use by doctors and patients. It also requires mutual investment and collaboration across industries and the government. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Craig_Federighi_vehemently_speaks_out_against_iPhone sideloading_in_Web_Summit_keynote:_‘Sideloading_is_a cybercriminal’s_best_friend’ [Ed: Apple conflates owning and controlling your own device with a crime; just to make matters worse than presuming everyone is a pedophile]⠀⇛ # ⚓ Windows_11_hit_by_another_bug_as_Microsoft’s_File Explorer_nightmare_gets_worse⠀⇛ Windows 11 has been hit with a new bug, and this one is yet another glitch that’s proving problematic with a core part of the operating system’s interface – namely File Explorer. File Explorer simply refers to the files and folders on your drive, that you regularly interact with in windows on the desktop – that’s how central it is to the Windows 11 experience, and now a new gremlin in the works is slowing down performance when the context menu is invoked. The context menu appears when you right click on a file or folder (or the desktop itself), giving you a bunch of further possible context-sensitive actions to take. # § Security⠀➾ # ⚓ Critical_Linux_Kernel_Bug_Allows_Remote Takeover_|_Threatpost⠀⇛ The bug (CVE-2021-43267) exists in a TIPC message type that allows Linux nodes to send cryptographic keys to each other. A critical heap-overflow security vulnerability in the Transparent Inter Process Communication (TIPC) module of the Linux kernel could allow local exploitation and remote code execution, leading to full system compromise. # ⚓ GitLab_servers_are_being_exploited_in_DDoS attacks_in_excess_of_1_Tbps⠀⇛ Threat actors are exploiting a security flaw in GitLab self-hosted servers to assemble botnets and launch gigantic distributed denial of service (DDoS) attacks, with some in excess of 1 terabit per second (Tbps). The DDoS attacks, disclosed today by Damian Menscher, a Security Reliability Engineer at Google Cloud responsible for Google’s DDoS defenses, are exploiting CVE-2021-22205, a vulnerability that GitLab patched back in April 2021. # ⚓ GitLab_servers_are_being_exploited_in_DDoS attacks_(The_Record)⠀⇛ The vulnerability was fixed in April, but evidently a lot of sites have not updated. o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ Quantum_Technologies_and_Space_–_ESPI_Online_Event [Ed: Very worrying that the European Space Agency (ESA) would wish to associate in any way with the corrupt EPO and more troubling that the media ignores this corruption]⠀⇛ This webinar will be a launch event of an upcoming study “Quantum technologies and space”, produced by European Patent Office (EPO) and European Space Policy Institute (ESPI) in collaboration with the European Space Agency (ESA). This study explores the major contemporary trends in the domain of space applications of Quantum Technologies through patent data analysis. EPO, ESPI and ESA currently collaborate on a series of space-themed “Patent insight reports”, a publicly available series of studies available on EPO website, which focus on exploitation of global patent filing data in order to identify major trends and technology developments in specific sub- domains of the space sector. The first study of this series, exploiting patent statistics in the domain of Cosmonautics, has been published in July 2021. # ⚓ Immutep_Granted_Chinese_Patent_for_Eftilagimod_Alpha, a_Soluble_Lag-3_Protein,_in_Combination_with_a Chemotherapy_Agent [Ed: Chinese Patents of very low quality get granted by the millions (over a million a year); it's hard to know what they're worth, if anything...]⠀⇛ # ⚓ CVR_Medical_Corp._Announces_the_Intention_to_Grant_a Patent [Ed: Leaving out a mention of the considerable demise_of_patent_quality_at_the_EPO]⠀⇛ CVR Medical is pleased to announce that it has received a Communication under Rule 71(3) from the European Patent Office (the “EPO”) for its Sensor, Sensor Pad and Sensor Array for Detecting Infrasonic Acoustic Signals informing CVR of the intention to grant a patent based on the prosecuted application. This is the first allowed patent application for CVR Medical at the EPO and an integral part of the CVR IP portfolio with an early priority date of June 24, 2010. The application, which was prosecuted under application no. 11754558.2 is directed to a sensor, sensor pad and sensor array for detecting infrasonic signals in a living organism and can be used for detecting levels of stenosis, occlusion, or aneurysm in arteries. CVR Medical will issue an update on Patents and clinical developments as we move forward. # ⚓ EU_heads_plastic_recycling_innovation [Ed: It's evident that the criminals who took over the EPO still misuse the EPO's budget to spam the media with all those puff pieces, looking to convince us that Mafioso António Campinos is some sort of science expert; all those publishers that played along have helped corruption]⠀⇛ Europe leads the world in innovation in plastic recycling and bioplastic technologies, according to a report from the European Patent Office (EPO). The 38 member states covered by the EPO accounted for 30% of patenting activity worldwide in these sectors between 2010 and 2019. This effort, seen as crucial in tackling plastic waste, was matched only by the US – also on 30%. ‘While plastics are essential to the economy, plastic pollution is threatening ecosystems all over the planet,’ says EPO President António Campinos. ‘The good news is that innovation can help us to address this challenge by enabling the transition to a fully circular model.’ # ⚓ EBA_decision_in_G1/21_(ViCo):_“In-person_proceedings should_be_the_default” [Ed: Epic_EPO_corruption_was witnessed_in_this_case, but the so-called ‘media’ did not cover that corruption (which is a form of endorsement for it)]⠀⇛ The written decision of the Enlarged Board of Appeal (EBA) in G1/21 on the legality of video conferencing oral proceedings has been released. As previously reported, the EBA chose not to explicitly answer the referred question of the broader legality of mandatory ViCo oral proceedings. The EBA instead limited their order to addressing the situation arising from the COVID-19 pandemic. However, unlike the initial EPO press release (IPKat), the detailed reasoning of the EBA does provide a view on the appropriateness of continuing with mandatory ViCo oral proceedings post-pandemic, and goes so far as to state that in-person proceedings should be the default in the absence of a state of general emergency. The full decision can be read here. G1/21 Case catch-up In order to avoid a large back-log of cases during the COVID-19 pandemic, the EPO began holding Board of Appeal oral proceedings by video conference (ViCo). The EPO went further by also laying the groundwork for the continued use of ViCo in Boards of Appeal oral proceedings post-pandemic, with the introduction of a new Rule of Procedure of the Boards of Appeal (RPBA), Article 15a (IPKat). Article 15a RPBA permits a Board of Appeal to hold oral proceedings by ViCo whenever “the Board considers it appropriate to do so”. The EPO’s swift move to mandatory ViCo oral proceedings was controversial to say the least. It was therefore unsurprising when news broke of a new referral to the EBA on the legality of the new provision. The referral stems from appeal T1807/15 of the opposition decision to maintain EP1609239 in amended form (IPKat). # ⚓ In_the_aftermath_of_G_1/21:_The_Future_of_Video Proceedings_in_the_EPO [Ed: This case wasn't about ViCo but about just how corrupted the tribunals became; they're just kangaroo courts and everyone can see it]⠀⇛ The Enlarged Board of Appeal has now issued its long-awaited full decision in case G 1/ 21. Readers can access it here. The decision deserves a few comments. # ⚓ FOSS_Patents:_Qualcomm_executive:_‘everyone_involved_ [in_automotive_patent_licensing_negotiation_groups] should_go_to_jail’_for_cartel_law_violation⠀⇛ Just to avoid any misunderstanding, I must clarify that Qualcomm Senior VP Fabian Gonnell didn’t demand the immediate incarceration of automotive industry executives seeking an exemption from cartel law for the purpose of operating standard- essential patent (SEP) licensing negotiation groups (LNGs). Speaking at yesterday’s IAM Auto IP Conference in Munich, Mr. Gonnell was saying that “there is nothing innovative” about LNGs, as the proposal comes down to what’s been known–and deemed illegal–for over a century as a buyers’ cartel if the net effect was collective hold out. If–in the alternative–LNGs didn’t impede bilateral license agreements, they wouldn’t make any impact. Therefore, LNGs should remain illegal, and should some fail to abide by the law as it stands, “everyone involved should go to jail.” This blog doesn’t always agree with Qualcomm. Prior to that conference, the last time I saw Mr. Gonnell was when he testified at the FTC v. Qualcomm trial in San Jose, and I disagreed with much of it. But on the subject of LNGs I believe one cannot reasonably disagree that they are, and should remain, illegal. I’m not talking about a couple of small IoT startups joining forces to negotiate a SEP license, but about large corporations (with all the resources to engage in good-faith licensing negotiations) orchestrating collective holdout. In a recent speech, EU competition chief Margrethe Vestager outlined her plans and priorities for a new era of cartel enforcement. While automotive LNGs weren’t explicitly mentioned, they share some of the key characteristics of cartel problems Mrs. Vestager touched on. In my post on the commissioner’s speech you can also find links to my three July 2021 posts on LNGs. If I had to sum up those three posts in one sentence, I would not just point to Mr. Gonnell’s “everyone involved should go to jail” remark. # ⚓ Progress_on_Austria’s_bill_to_ratify_UPC_Agreement’s Protocol_on_Provisional_Application [Ed: Someone should remind Bristows that Austria is not London and UPCA is doomed without London; they try to violate the Vienna Convention, wrongly assuming there would be no legal challenge]⠀⇛ Draft legislation enabling Austria to ratify the Protocol on the Provisional Application (PPA) of the Unified Patent Court Agreement (UPCA) is currently passing through the parliamentary process. The National Council assigned the bill to its Research, Innovation and Digitisation Committee in July and, as reported here, yesterday the Committee unanimously approved the bill. The bill now returns to the National Council for its second and third readings, and if passed will be considered adopted and Austria would be able to ratify the PPA. If Austria does ratify and deposit the instrument of ratification with the Council of the EU, sufficient countries will have ratified (or otherwise consented to be bound by the provisional application of certain UPCA provisions) for the provisional application phase to start, and final preparations for the introduction of the UPC and unitary patent system can start in earnest. # ⚓ Pinsent_Masons_life_sciences_team_grows_again_with six_CMS_hires [Ed: Amy Sandys continues to publish SPAM/PR/marketing as "news"; when not too busy reprinting lies for gangsters who infiltrated EPO she also spreads classic fake news for Team UPC. Journalism isn't dying, it's dead in the area of patents]⠀⇛ # ⚓ UPC_Preparatory_Committee’s_October_optimistic_for the_UPC_becoming_a_reality_in_2022 [Ed: Convicted corrupt ‘law’ firm Marks & Clerk is spreading fake_news about_UPC, which they hoped would usher in illegal patents by corrupting the EU’s court system]⠀⇛ The report of the October 2021 meeting of UPC Preparatory Committee provides some further support for the slow, but increasingly sure progress regarding the steps required for the Unified Patent Court to become a reality. First, the report confirms that the Protocol on Privileges and Immunities entered into force on 27 October 2021. This is a rather technical development but it is a forerunner for the entry into force of the Protocol on Provisional Application, which requires just one more participating country to deposit its instrument of ratification in order to come into force. That will then allow the final preparations for the United Patent Court to be completed. # § Software Patents⠀➾ # ⚓ Sound_View_Patent_Narrowed_After_Ex_Parte Reexamination⠀⇛ In 2020, Unified filed an ex parte reexamination (Reexam) request against patents owned by Sound View Innovations, a non-practicing entity (NPE) that has sued various companies for their use of widely-adopted Internet technologies. In early October 2021, the Reexam of U.S. Patent 6,725,456 concluded with a “Notice of intent to issue a Reexamination Certificate” (Notice of Intent) that highlights a problematic habit of NPEs like Sound View: reading a patent broadly when accusing others of infringing and narrowly when its validity is in question. The Notice of Intent casts serious doubt on Sound View’s infringement theories and still leaves open future questions about validity. The examiner narrowed claims that Sound View has asserted repeatedly were much broader in court complaints. The Reexam (and every ex parte reexamination since 2000) can be found on Unified’s Portal here. Challenged claim 13 of the ’456 patent relates to a method of ensuring a particular quality of service for an application in a computer system. The claim recites a “resource reservation” and the examiner credited Sound View’s arguments that the claim required “two separate and distinct values to be associated with each resource reservation[.]” Notice of Intent, p. 6; see Office Action Response, p. 19. In particular, the examiner took the position that the resource reservation must specify both a “weight” and a “minimum amount of resources.” Id. The examiner held that specifying a minimum amount of resources in a resource reservation, which results in a weight being associated with that resource reservation, is not sufficient to read on the claim. Conversely, specifying a weight in a resource reservation, which results in a minimum amount of resources being allocated, is also not sufficient to read on the claim. Rather, as Sound View argued, allocating both a weight and a minimum amount of resources was needed according to the examiner. See Office Action Response, p. 23. # ⚓ Proven_Networks_patent_has_all_claims_cancelled —_Unified_Patents⠀⇛ On November 3, 2021, the USPTO filed a notice of intent to cancel claims 1-18 of U.S. Patent 8,018,852, owned by Proven Networks, LLC. The ‘852 patent relates to a port selection technique used in a network switching environment where there are multiple equal-cost paths between two nodes. ䷩ 𝚕𝚒𝚗𝚎 4321 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_5/11/2021:_LibreOffice_7.3_Alpha_1_and_“Red_Hat_Forced_to_Hire Cheaper”⠀✐ Posted in News_Roundup at 6:24 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⠀➾ # ⚓ Going_Linux_#414_·_Listener_Feedback⠀⇛ This episodes includes discussions about key bindings, Mastadon, Virtual Box, the Framework laptop, file permissions, astronomy programs, printers, Win-Kex, and App Outlet. There’s even more! # ⚓ Three_HUGE_Mistakes_New_Emacs_Users_Make_–_Invidious⠀⇛ It’s a common story. A person hears about Emacs and wants to give it a try, but their initial experience is usually pretty bad. Why? Well, I think a lot of it has to do with three HUGE mistakes that new Emacs users tend to make. # ⚓ Hackaday_Podcast_143:_More_Magnesium_Please,_Robot_Bicep Curls,_Malamud’s_General_Index,_And_Are_You_Down_With_EMC?_| Hackaday⠀⇛ Hackaday editors Mike Szczys and Elliot Williams catch up on a week’s worth of hacks. Get a grip on robot hands: there’s an eerily human one on offer this week. If you’re doing buck/boost converter design, the real learning is in high-frequency design patterns that avoid turning your circuits into unintentional radiators. Those looking for new hobbies might want to take up autonomous boat racing. We saw a design that’s easy enough to print on the average 3D printer — and who doesn’t want to build their own jet boat? We’ll wrap up the episode by digging into magnesium sources, and by admiring the number of outfits who are rolling their own silicon these days. # ⚓ Video_Editing_with_Linux:_5_Basic_Techniques_You_Should Know_–_Purism⠀⇛ Next in our video editing series for the Librem 14, Gardiner Bryant explains how to use various kinds of cuts. In this video you’ll learn about J-cuts, L-cuts, Jump cuts, and Action/Motivated cuts. While this will apply to Kdenlive, a free software video editing solution, it will also generally apply to video editing. This video will help those looking to level up their overall video production. We hope to do similar projects like this in the future, so if you have ideas for topics you’d like us to cover, please let us know! # ⚓ Alex_Deletes_it_All_|_Self-Hosted_57⠀⇛ Troubleshooting goes very wrong for Alex, and he puts his backups to the ultimate test. Plus, monitoring your freezer in Home Assistant, building a self-hosted Notion alternative, and more. # ⚓ Is_elementary_OS_REALLY_user_friendly?_–_Invidious⠀⇛ o § Kernel Space⠀➾ # ⚓ Bcachefs_Gets_“Bad@$$”_Snapshots,_Still_Aiming_For_Mainline Linux_Kernel_Integration⠀⇛ Kent Overstreet who has been working relentlessly on Bcachefs for over a half-decade now issued his latest status update on this Linux file-system born out of the kernel’s block cache code. Bcachefs continues making progress with ambitions still to be mainlined in the kernel and being capable of competing ultimately with the likes of Btrfs and XFS. Today’s mailing list post offers a fresh look at the current happenings around this file-system. The core B-Tree code has been undergoing improvements with interior nodes now journalled, updating parent B-Tree node pointers on every B-Tree write, and other optimizations. # ⚓ Ryabitsev:_lore+lei:_part_1,_getting_started_[LWN.net]⠀⇛ Konstantin Ryabitsev introduces the “local email interface” (lei) functionality for the lore archive of kernel mailing lists… # ⚓ Konstantin_Ryabitsev_on_lore+lei:_part_1,_getting_started⠀⇛ One of kernel developers’ perennial complaints is that they just get Too Much Damn Email. Nobody in their right mind subscribes to “the LKML” (linux- kernel@vger.kernel.org) because it acts as a dumping ground for all email and the resulting firehose of patches and rants is completely impossible for a sane human being to follow. # ⚓ Nintendo_Switch_Controller_Driver,_Sony_PS5_Controller Improvements_Come_For_Linux_5.16_–_Phoronix⠀⇛ The HID subsystem updates have been sent in for the ongoing Linux 5.16 merge window with some notable improvements for Linux gamers. As written about at the end of last month, the Nintendo Switch controller driver is finally landing! This kernel driver enables the Nintendo Switch Pro and Nintendo Switch Joy-Con controllers to now work with the mainline kernel. Both USB and Bluetooth connectivity is supported. Features like rumble mode, LEDs, and other functionality is working for these Joy-Cons / Pro controllers. # ⚓ Linux_5.16_Drops_Support_For_MIPS_Netlogic_SoCs_– Phoronix⠀⇛ he Linux 5.16 kernel is doing away with hardware support for the MIPS-based Netlogic Microsystems SoCs, the network processors developed prior to being acquired by Broadcom a decade ago. The Linux kernel has supported the more than decade old Netlogic XLR/XLS and XLP processors used in the company’s former high-end network gear. However, as no current Linux kernel developers have access to Netlogic hardware and no clear signs there still are users out there with Netlogic SoCs and running up-to-date kernels, that Netlogic Microsystems support is being cleared out from the Linux kernel. # § Graphics Stack⠀➾ # ⚓ What_do_you_know_about_video_decoding/encoding?⠀⇛ A few weeks ago I watched Victor’s excellent talk on Vulkan Video. This made me question my skills in this area. I’m pretty vague on video processing hardware, I really have no understanding of H264 or any of the standards. I’ve been loosely following the Vulkan video group inside of Khronos, but I can’t say I’ve understood it or been useful. radeonsi has a gallium vaapi driver, that talks to firmware driver encoder on the hardware, surely copying what it is programming can’t be that hard. I got an mpv/ vaapi setup running and tested some videos on that setup just to get comfortable. I looked at what sort of data was being pushed about. The thing is the firmware is doing all the work here, the driver is mostly just responsible for taking semi-parsed h264 bitstream data structures and giving them in memory buffers to the fw API. Then the resulting decoded image should be magically in a buffer. I then got the demo nvidia video decoder application mentioned in Victor’s talk. I ported the code to radv in a couple of days, but then began a long journey into the unknown. The firmware is quite expectant on exactly what it wants and when it wants it. After fixing some interactions with the video player, I started to dig. Now vaapi and DXVA (Windows) are context based APIs. This means they are like OpenGL, where you create a context, do a bunch of work, and tear it down, the driver does all the hw queuing of commands internally. All the state is held in the context. Vulkan is a command buffer based API. The application records command buffers and then enqueues those command buffers to the hardware itself. # ⚓ RADV_Seeing_Early_Experimenting_With_Vulkan_Video Capabilities⠀⇛ As another “first on RADV” for this Mesa Radeon Vulkan open-source driver compared to AMD’s official Vulkan Linux driver options, there is an early branch providing primitive, experimental support for Vulkan Video acceleration. Earlier this year the Vulkan Video extensions were published in provisional form. When it comes to Linux support so far there has just been the NVIDIA Vulkan beta driver exposing the video extensions, but now with a branched, not-yet-mainlined set of patches there is initial RADV support too. # ⚓ AMDVLK_2021.Q4.1_Released_As_First_Code_Drop_In_Over A_Month_–_Phoronix⠀⇛ AMD traditionally has been updating its AMDVLK official open-source Vulkan driver sources publicly on a (bi)weekly basis, but that went off the wagon recently with not seeing any updates since the end of September. That changed this morning with the publishing of AMDVLK 2021.Q4.1. While more than one month has passed since the last AMDVLK code drop, AMDVLK 2021.Q4.1 isn’t all that exciting. AMDVLK 2021.Q4.1 updates against the Vulkan 1.2.195 headers, limits the memory size of the pipeline cache for 32-bit systems, and improves the shader cache hit rate. There are also a few fixes primarily about the Vulkan memory handling. o § Benchmarks⠀➾ # ⚓ Intel_UHD_Graphics_770_/_Alder_Lake_GT1_Linux_Graphics Performance⠀⇛ Published yesterday was the Core i5 12600K / Core i9 12900K Linux review looking at the exciting performance uplift provided by Alder Lake. One of the areas only talked about briefly in yesterday’s article were the UHD Graphics 770 found with these new desktop processors, due to time constraints with only having a few days so far for carrying out tests. Today the initial batch of UHD Graphics 770 / ADL-S GT1 Linux graphics/gaming benchmarks have wrapped up to show how the Intel graphics performance compares to prior generation Rocket Lake as well as AMD’s Ryzen 7 5700 o § Applications⠀➾ # ⚓ Create_your_own_private_Google_Photo_alternative_with PhotoPrism⠀⇛ If you are a professional or a hobby photographer, certainly you are using Google Photos or similar services to back up, organize and share your photo collections. Many open-source tools and self-hosted solutions can help you to achieve that, but today, we bring you the best there is: PhotoPrism. Let’s know why! PhotoPrism is a free open-source solution that helps you browse, organize and share your photo collection. PhotoPrism comes with built-in search support, RAW file format conversion, duplicate finder support, many videos, and file formats, and automatic image classification and location visualization support. While using PhotoPrism, you don’t need to worry about your data being collected or sent to big firms. o § Instructionals/Technical⠀➾ # ⚓ How_to_Upgrade_Fedora_Linux_to_Latest_Version⠀⇛ Being able to upgrade Fedora from one version to the next is one of Fedora’s best features. Here’s how to do it easily. Fedora brings two major stable releases every year. If you’re using an older version, you can easily upgrade to the latest desktop or server edition. You benefit from getting the latest software, including new security patches, and all the upgraded technology that comes with a new release without having to resort to reinstalling and reconfiguring your system. There are two ways to upgrade to a new Fedora version, graphically or by using command line, and I will show you both ways here. # ⚓ How_To_Install_Nano_Text_Editor_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install Nano Text Editor on Debian 11. For those of you who didn’t know, GNU nano is one of the popular and easiest command line text editors used on many operating systems including Unix-based systems and BSD variants. Nano text editor supports syntax highlighting, spell checking, justifying, completion, undo/redo, 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 nano text editor on a Debian 11 (Bullseye). # ⚓ How_to_Install_GitLab_on_Rocky_Linux_8⠀⇛ GitLab is a free git repository management tool that allows you to create and manage git repositories. It provides tools for everything an open-source developer would need. Gitlab has everything that allows a developer to manage their project easily. You can create issues, track your bugs or comments related to your project, keep releases organized, and have much more useful features than the ones you find on GitHub. It integrates perfectly with other development tools like CodeShip, which makes deployments easy and fast. The difference between GitLab and GitHub is: GitHub is a web-based application while GitLab is an open- source application. GitHub is currently the most popular choice among developers. Both services are popular for hosting projects of any kind. However, GitHub is more popular among open-source projects. If you search on Google with “GitHub” or “GitLab”, GitLab will return almost four times fewer results than GitHub. This doesn’t mean that GitLab is not good. GitLab is the better choice for self-hosted private repositories. # ⚓ How_to_Start_a_Horizon_Session_from_a_Linux_Command_Line_— Virtualization_Review⠀⇛ This is the third and final article in a series on starting the Horizon Client from the command line. In the first article, I walked through how to launch the Horizon Client to a Horizon desktop using a .bat file. In the second article, I showed how I added a .bat file to the taskbar and Start menu which could automatically log me in to a Horizon streaming application. Being that I was already down this rabbit hole, I figured it would be worthwhile to go one step further; in this article, I will go over how to start a Horizon session from the Linux command line, even if you are not on the GUI. If you are not familiar using the vmware-view command, I highly recommend first reading the articles mentioned above. # ⚓ How_to_create_and_attach_an_EBS_(Elastic_Block_Storage) Volume_to_an_EC2_Instance_on_AWS⠀⇛ Elastic Block Storage (EBS) is a high-performance block storage service. It is designed for use with Elastic Cloud Compute i.e. EC2 for transactions and intensive workload. Relational and non-relational databases, enterprise applications, containerized applications, big data analytics engines, file systems, and media workflows are widely deployed on Amazon EBS. We can change types of EBS Volume, increase volume size without disrupting our applications. Amazon EBS volumes are easy to create, use, encrypt, and protect. Amazon EBS architecture offers reliability for mission- critical applications. Each volume is designed to protect against failures by replicating data on it within the Availability Zones. Amazon EBS enables us to increase storage without any disruption to our critical workloads. EBS is built to be secure for data compliance. Newly created EBS volumes can be encrypted by default with a single setting in our account. # ⚓ How_to_Install_and_Configure_Ansible_on_Fedora_35⠀⇛ Ansible is an open source IT automation engine that automates provisioning, configuration management, application deployment, orchestration, and many other IT processes. It enables infrastructure as code. Ansible automates and simplifies repetitive, complex, and tedious operations. It runs on many Unix-like systems, and can configure both Unix-like systems as well as Microsoft Windows. Ansible itself is written in Python and has a fairly minimal learning curve. Ansible follows a simple setup procedure and does not depend on any additional software, servers or client daemons. It manages nodes over SSH and is parallel by default. In this guide, we are going to learn how to Install and Configure Ansible on Fedora 35. # ⚓ How_to_Install_Python_2_and_Python_3_on_Fedora_35⠀⇛ Python is among the most popular programming languages. Because of this, most scripts and tools used in linux are written on python. It iss often described as easy to learn and therefore often recommendd for beginners. In this guide, we are going to learn how to install Python 2 and python 3 in Fedora 35. # ⚓ pa-applet_volume_control_for_system_tray⠀⇛ o § Games⠀➾ # ⚓ Liftoff:_Micro_Drones_races_off_into_Early_Access_on November_30⠀⇛ Get ready for a race around various indoor arenas in the upcoming Liftoff: Micro Drones, as it’s now confirmed to be releasing in Early Access on November 30 with Linux support. This is the fifth game from LuGus Studios and their fourth to officially support Linux too. o § Desktop Environments/WMs⠀➾ # ⚓ LXQt_1.0_Released_For_Lightweight_Qt5_Desktop_–_Phoronix⠀⇛ After eight years in development, the LXQt desktop that was created by the merging of the LXDE and Razor-qt open-source desktop projects is celebrating its v1.0 release. LXQt 1.0 targets the Qt 5.15 LTS toolkit and hasn’t yet been ported to Qt 6. LXQt 1.0 prides itself on improvements to its file manager and image viewer, a do-not-disturb mode for its desktop notifications, two new desktop themes, updated translations, and more. # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Accent_Color_Folders_in_Plasma_and_Dolphin!_– Kockatoo_Tube⠀⇛ # ⚓ A_Whole_New_KDE_Bug_Reporting_Page!_–_Kockatoo_Tube⠀⇛ # § GNOME Desktop/GTK⠀➾ # ⚓ #17_Hourly_Backups_·_This_Week_in_GNOME⠀⇛ Update on what happened across the GNOME project in the week from October 29 to November 05. o § Distributions⠀➾ # ⚓ How_Open_Source_Operating_Systems_Can_Be_Ideal_For_Your Business⠀⇛ In a world where Windows has become synonymous with PCs in the minds of the public, is there room for Open Source Operating Systems in your business? What many business leaders don’t realize is that even companies like Microsoft themselves are adopting Open Source technologies, mostly in a bid to tempt diehard Linux users to Microsoft. There’s many reasons that an Open Source operating system might be good for your business, however. Today we will take a look at a few of them. # § New Releases⠀➾ # ⚓ New_LinDoz_Dev_Build_05/11-2021⠀⇛ We have just sent out a new Stable Development build of MakuluLinux LinDoz to testers, this ISO has also been shared with our Patreon Members. There have been significant updates to this new build, which has been marked as a stable build. You can read the Dev logs by Clicking here, We are one step closer to release. Additionally, should you wish to get access to early builds, you can always sign up to become a patreon member to help support the project, to sign up Click here to our Patreon page, and follow the sign up links. # § BSD⠀➾ # ⚓ Project_Trident,_a_Linux_Distribution_with_BSD_Roots, Shuts_Down⠀⇛ Project Trident, the Linux distribution that started life as a BSD operating system, is calling it quits, bringing to an end a desktop operating system saga that began with PC-BSD during the first decade of the 21st century. Some might remember that PC-BSD was an attempt to develop a GNU-based desktop oriented BSD operating system as an alternative to GNU/Linux. Based on FreeBSD, the OS even went so far as to develop its own desktop environment, Lumina, and for many years maintained booths at various Linux and open source conferences, where it handed out installation CDs of the operating system, hoping to get Linux users to give it a try. In 2016, the company that had owned PC-BSD since 2006, iXsystems, changed the OS’s name to TrueOS, and two years later dropped the desktop version to focus on servers and the enterprise, with the desktop being spun-off under a new moniker, Project Trident, that continued to produce a desktop distribution, but now based on TrueOS. This lasted for about a year, until in 2019 problems such as hardware compatibility and software availability (issues that were also once a roadblock to Linux desktop adoption) moved Project Trident’s developers to move the project away from BSD to adopt Void Linux, a scratch-built and systemd-free distro, as its base. # § Screenshots/Screencasts⠀➾ # ⚓ Linux_overview_|_Fedora_35_–_Invidious⠀⇛ In this video, I am going to show an overview of Fedora 35 and some of the applications pre-installed. # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾ # ⚓ Kernel_Updates_Available_»_PCLinuxOS⠀⇛ The following kernels are available for PCLinuxOS. Kernel LTS 5.4.157. Kernel LTS 5.10.77 and Kernel 5.14.16. # ⚓ KDE_Plasma_Applications_»_PCLinuxOS⠀⇛ KDE Plasma Applications updated to 21.08.3 which is a service release to address a few bugs to the KDE Plasma programs. # § SUSE/OpenSUSE⠀➾ # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2021/44_– Dominique_a.k.a._DimStar_(Dim*)⠀⇛ The weather is getting colder, days shorter, motivation to go outside is shrinking. Which leaves more time in front of the computer, helping Tumbleweed roll. And roll it did during the last week! We have published 6 snapshots (number 7 needed to be discarded due to vi installation issues). The snapshots released were numbered 1028, 1029, 1030, 1031, 1101, and 1102. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Red_Hat_Enterprise_Linux_9_Beta_—_more_features_for users,_fewer_headaches_for_admins⠀⇛ The launch of Red Hat Enterprise Linux (RHEL) 9 Beta today marks a bit of a change from previous releases. While it has many improvements and enhancements that customers have asked for, there are fewer changes that require admins and IT Ops to learn new ways of doing things. This means anyone already familiar with RHEL 8 should feel at home. Among new features are enhanced web console performance metrics, kernel live patching via the web console, and streamlined image building. Security and compliance improvements include smart card authentication via the web console so users can make use of smart card authentication to access remote hosts, additional security profiles to help compliance with standards like PCI-DSS, HIPAA, and others. There’s also detailed logging of SSSD — the built-in enterprise single-sign-on framework — and integrated OpenSSL 3 cryptographic framework support. # ⚓ DSE_measures_and_improves_DevOps⠀⇛ Davie Street Enterprises is our fictional Red Hat customer that is working its way through real-world digital transformation problems, and this time around, it’s tackling measurement. Newly-promoted Director of Security Engineering Zachary L. Tureaud knew that Monique Wallace, Davie Street Enterprises’ (DSE) CIO, was impressed with the work he had led on solution design, but he still needed to ensure his DevSecOps vision was working. It wasn’t enough to just point to all the new tooling his team had put together. He needed to be able to demonstrate, quantifiably, that the changes were having the desired effect. Let’s see how he led DSE toward a DevSecOps practice using measured approaches from Google’s DevOps research and assessment team. # ⚓ 4_soft_skills_for_successful_sysadmins_|_Enable Sysadmin⠀⇛ To move up the IT ladder, it helps to be aware of where you need to improve. Half the battle is acknowledging your weaknesses, and the other half is looking for ways to improve them. Coachable people typically have a better chance to succeed in their careers. Most successful professionals do not do it alone; they have mentors to give them constructive feedback. Being coachable means you will never stop learning and improving. This article does not talk about coaching and mentorship, rather it highlights four soft skills I think help sysadmins further their IT careers. As a sysadmin, I use these skills almost daily to help me become a better communicator at work and make my professional life easier and more enjoyable. # ⚓ Red_Hat_Forced_To_Hire_Cheaper,_Less_Senior_Engineers Amid_Budget_Freeze⠀⇛ Next year, IBM’s Red Hat plans to cut back on hiring senior engineers in an effort aimed largely at controlling costs. # ⚓ Red_Hat_to_hire_fewer_senior_engineers_after_budget frozen_•_The_Register⠀⇛ # ⚓ 5_must-read_Harvard_Business_Review_articles⠀⇛ Each month, through our partnership with Harvard Business Review, we refresh our resource library with five new HBR articles we believe CIOs and IT leaders will value highly. Check out the curated pieces below, available to readers through the end of the month. # ⚓ 3_skills_of_teams_that_succeed_with_containers_|_The Enterprisers_Project⠀⇛ Container adoption is a common step in the DevOps journey for many organizations. But as the number of containerized applications increases, teams become unable to manually sustain the operational processes required to manage and deploy them. Container orchestration via a Kubernetes platform enables them to automate many of these processes. After an organization adopts a container orchestration approach, human skills still play an important role in container success. At enterprise organizations, teams require specific skills to ensure that they can effectively problem-solve, make improvements, scale, monitor, maintain security, and more. # § Debian Family⠀➾ # ⚓ Tails_4.24_Anonymous_Linux_OS_Switches_to_Tor_Browser 11,_Improves_Tor_Connection_Wizard⠀⇛ After a two-day delay, Tails 4.24 is now available for download and ships with the latest and greatest Tor Browser 11.0 anonymous web browser, which is based on the Mozilla Firefox 91 ESR series and brings numerous new features and improvements. In fact, Tor Browser 11 has not even been officially released, it’s still in alpha development at the moment of writing, but the Tails developers decided to include it as the default web browser in this new release of their amnesic incognito live system. o § Devices/Embedded⠀➾ # ⚓ AGX_Xavier_powers_railway_and_self-driving_car_computers⠀⇛ Adlink unveiled two edge AI systems that run Linux on a Jetson AGX Xavier: a rugged “AVA-RAGX” railway PC with 4x GbE with PoE, 4x USB, 2x M.2, and 2x CAN, and an “AVA-XV-V1” system for autonomous vehicles with 10GbE, GbE, and 8x GMSL2 camera ports. Adlink has been keeping us busy this week with new edge AI products that run Linux. After rolling out its Coffee Lake based AVA-3501 and AVA-3510 systems for autonomous vehicles, the company announced two new ROSCube-branded robotics controllers: a ROSCube Pico NPN equipped with a Jetson Nano or Jetson Xavier NX and a ROSCube Pico TGL built around Intel’s 11th Gen Tiger Lake Core processors. # § Open Hardware/Modding⠀➾ # ⚓ Raspberry_Pi_DAQ_HATs_focus_on_analog⠀⇛ Contec has added three new RPi HATs to it DAQ-oriented CPI Series for 12-bit, 8-ch. isolated analog in, 16-bit, 2-ch. isolated analog out, and 32-bit Up/Down counter. There is also a DIN-rail kit for its HATs and some recent “DX” Jetson edge AI systems. We missed Contec’s April announcement of its CPI Series HAT Size Cards for digital acquisition (DAQ), having forgotten entirely about the Japanese embedded firm, which was founded in 1975. We had to go back to our LinuxDevices archives for our last Contec report from 2011, about an Atom D510 based BX-956 embedded computer. We heard about their latest round of CPI Series Raspberry Pi HATs from this Nov. 1 MarketScreener announcement. Farther below, we also look at some recent DX-branded embedded computers based on Jetson Nano and Xavier NX. # ⚓ TQ_Embedded_launches_NXP_i.MX_RT1170_SoC_module_and SBC_–_CNX_Software⠀⇛ TQ Embedded (aka TQ) has just announced the availability of the TQMa117xL system-on-chip module based on NXP i.MX RT1170 crossover processor family, and as well as MBa117xL single board computer (SBC) based on the 31×31 mm module. TQMa117xL’s small size has been achieved thanks to a 277-pad LGA design, with the module still integrating LP-SDRAM, Quad-SPI NOR flash and EPROM, a PMIC, as well as an optional security chip. # ⚓ Ubuntu_Desktop_and_Raspberry_PI_4:_fast_Home_Computer Booting_From_SSD⠀⇛ With remote activities increased due to pandemic, a lot of families needed more home computer to manage smart working, school sessions and family meetings. Ubuntu on Raspberry PI can be a fast solution for your cheap desktop computer, but only adopting certain tricks # ⚓ Prepare_For_Wildfire_Season_With_an_Air_Quality Monitor⠀⇛ For some reason, wildfire seasons in Australia, North America, and other places around the world seem to happen more and more frequently and with greater and greater fervor. Living in these areas requires special precautions, even for those who live far away from the fires. If you’re not sure if the wildfires are impacting your area or not, one of the tools you can build on your own is an air quality meter like [Costas Vav] shows us in this latest build. The air quality indicator is based around an Adafruit Feather RP2040 which is in turn based on the 32-bit Cortex M0+ dual core processor. This makes for a quite capable processor in a small package, and helps accomplish one of the design goals of a rapid startup time. Another design goal was to use off-the-shelf components so that anyone could easily build one for themselves, so while the Feather is easily obtained the PMS5003 PM2.5 air quality sensor needed to be as well. From there, all of the components are wrapped up in an easily-printed enclosure and given a small (and also readily-available) OLED screen. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Google_Pixel_6_Pro_vs_Samsung_Galaxy_S21_Ultra:_Which Android_phone_wins?_|_Tom’s_Guide⠀⇛ # ⚓ Some_Google_Pixel_phones_suffer_from_battery_drain with_Android_12⠀⇛ # ⚓ 5_Android_12_features_you_can_bring_to_any_phone today_|_Computerworld⠀⇛ # ⚓ Moto_E30_unveiled:_a_Moto_E40_but_with_Android_11_Go Edition_–_GSMArena.com_news⠀⇛ # ⚓ The_7_Best_Mileage_Tracker_Apps_for_Android⠀⇛ # ⚓ The_most_entertaining_basketball_games_for_your Android_device⠀⇛ # ⚓ Android_Circuit:_Stunning_Galaxy_S22_Ultra_Leaks, Powerful_Pixel_6_Pro_Tensor_Benchmarks,_Surface_Duo_2 Surprise⠀⇛ # ⚓ Xiaomi_12_Leak_Could_Pioneer_the_Snapdragon_898_in Next_Android_Flagship_Smartphone_|_Tech_Times⠀⇛ # ⚓ Android:_how_to_find_your_cell_phone_by_clapping_– Market_Research_Telecast⠀⇛ # ⚓ How_to_Print_Wirelessly_on_Android_with_Mopria_Print Service_–_Phandroid⠀⇛ # ⚓ Portugal:_NOS_launches_Android_NVIDIA_Shield_TV_|⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ 16_Top_Open-source_web-based_photo_manipulation_and_image editors [Ed: Some of these are proprietary, so this title is misleading]⠀⇛ Photo manipulation and image editing programs like Photoshop, and GIMP are often desktop applications. However, photo editing can also be done through the web browser. Many web-based services offer photo editing for a price, which requires only an internet connection, a web browser, and an account. Although they seem limited compared to desktop programs, web-based image editing programs have proven to be reliable for many users. In this article, we present a collection of free web-based open-source image editing solutions that you can download, install and run on your local machine or server. # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Firefox_Makes_Changes_to_Add-on_Policy_to Better_Protect_Users⠀⇛ No big deal, Philipp Kewisch, the add- ons product operations manager at Firefox’s parent Mozilla, said in a blog announcing the upcoming changes on Wednesday. The organization is mostly clarifying their add-on policies to make them easier for developers to understand — although there are a few small changes in the works. “While this has resulted in a substantially rewritten and reorganized document, the policy changes are modest and unlikely to surprise anyone,” he said. # ⚓ Firefox_91-94_&_Additional_visual_and_ergonomic tweaks⠀⇛ Every morning, I wake up, look in the mirror, and ask myself: Am I a hipster? And since the answer is always categorically no, I know that my choices in life will be superior, aesthetically and functionally. Which meant that when I saw my Firefox 78 ESR transform into Firefox 91 ESR with its pointless Proton interface, I knew it was going to be a bad day. Now, Firefox is my default browser of choice on any platform, has always been and hopefully will always be, but I refuse to succumb to hipsterology trends. I’m neither a child nor do I live near the Pacific Ocean coast. Hence, clarity, contrast, good clear colors. I’ve already shown you how to undo most of Proton nonsense in a dedicated tutorial, now I’d like to give you a few more tips. Follow me. # ⚓ Linux_Release_Roundup_#21.45:_Linux_Kernel 5.15,_Fedora_35,_Firefox_94,_and_More_Releases⠀⇛ The well-known open-source web browser has received yet another update that contains some major features. Notable features include tweaks for faster performance, improved warnings on exit, and a bug fix for Ubuntu. Most importantly, the OpenGL EGL backend is now enabled by default. You should find all the technical details in the official release notes. # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ LibreOffice_7.3_Alpha1_is_ready_for_testing⠀⇛ LibreOffice 7.3 will be released as final at the beginning of February, 2022 ( Check the Release Plan ) being LibreOffice 7.3 Alpha1 the first pre-release since the development of version 7.3 started in mid June, 2021. Since then, 4764 commits have been submitted to the code repository and more than 760 bugs were set to FIXED in Bugzilla. Check the release notes to find the new features included in this version of LibreOffice. LibreOffice 7.3 Alpha1 can be downloaded from here for Linux, MacOS and Windows, and it can be installed alongside the standard version. In case you find any problem in this pre- release, please report it in Bugzilla ( You just need a legit email account in order to create a new account ). # ⚓ Nine_more_videos_from_the_LibreOffice_Conference 2021⠀⇛ Here are some more videos from the LibreOffice Conference 2021! Check out the playlist, using the button in the top-right – or scroll down for links to individual videos: Please confirm that you want to play a YouTube video. By accepting, you will be accessing content from YouTube, a service provided by an external third party. # § FSF⠀➾ # § Licensing/Legal⠀➾ # ⚓ Luis_Villa:_Editing_a_background_check_policy⠀⇛ A legal document is, in many cases, a part of a company’s user experience. As such, it needs to be vetted for consistency with the rest of the software, just as you’d vet any other part of the UX. This is hard, and easy to screw up, because let’s face it—who likes reading and re-reading legal documents? Not even lawyers, if we’re being honest. This particular document screws this up in two ways. First, the tool (very correctly!) encourages companies not to do a background check for every position, since that introduces a significant bias against people who may have been rehabilitated and should have a fair chance at employment. But the legal document says very plainly that “all offers of employment are contingent on … a background check” (emphasis mine). The legal terms must be brought into alignment with the software’s reality. Similarly, one of the benefits of this tool is that it takes care of the paperwork for you—without pens and paper. And yet the legal document says that a “signed, written consent will be obtained … in compliance with … law”. Now, good American lawyers know that under the E-SIGN Act of 2000, lots of digital things are “signatures” for the purposes of American law, but most people don’t know that. Good drafting will avoid confusing these non-lawyers by simply saying the consent will be “explicit” and recorded by the service. [...] I continue to believe that many legal documents should at least be edited (not necessarily finalized) in a Q&A style—in other words, changing each section header to a question, and making sure the section actually answers the question. I talked a bit more about that in this post about doing it for a draft of the Mozilla Public License. # § Programming/Development⠀➾ # ⚓ PHPStan_Reached_Version_1.0_After_6_Years_of Development⠀⇛ PHPStan is a static analyzer for PHP focused on finding bugs in your code without actually running it. PHPStan 1.0 finally has been released, so let’s see what’s new. Introducing static code analysis into your process should improve the quality of your code and make the QA process more efficient due to finding errors earlier on. PHPStan is an open source tool with 10.4K GitHub stars and 737 GitHub forks. It is probably the most popular static analysis system for PHP projects, which finds bugs in your codebase by inspecting the source files. In other words, you don’t need to run your code or manually write tests to discover issues. # ⚓ Dark_theme_for_Qt_online_documentation⠀⇛ Out of all Qt’s subdomains, https://doc.qt.io sees the most views and time spent browsing. Many users find a darker color scheme easier on eyes, especially during late-night coding sessions. # § Perl/Raku⠀➾ # ⚓ My_Favorite_Modules:_Term::ReadLine::Perl_|_Tom Wyant_[blogs.perl.org]⠀⇛ Term::ReadLine is a core module (since Perl 5.002) that provides an extremely limited text interface of the prompt- and-type variety. Its main virtue is that you can add a back end which gives it things like command history, editing, and completion. The back ends live in the Term:: ReadLine::* name space, and you can control which one you get by defining the PERL_RL environment variable as documented at Term::ReadLine. If this is not defined, various undocumented things are tried; if none works you get the bundled minimal interface, Term:: ReadLine::Stub. The preferred back end (at least, according to Bundle::CPAN as of this writing) is Term::ReadLine::Perl. This is a shy, retiring module, with no POD documentation at all, which provides readline-style history, editing, and completion. By default the only completion you get is file name completion, but with some work you can expand this to do whatever you can figure out. # ⚓ Should_it_mutate_or_not?_YES!_|_Playing_Perl 6␛b6xA_Raku⠀⇛ On Discord Hydrazer was looking for a list concatenation operator. That leaves the question if it should mutate like Array.push or return a new list of Slips. # ⚓ TIMTOWTDItime_|_Playing_Perl_6␛b6xA_Raku⠀⇛ On Discord flirora wished for a way to merge list elements conditional. In this instance the condition is that any element that starts with a space is part of a group. # § Rust⠀➾ # ⚓ View_types_for_Rust⠀⇛ I wanted to write about an idea that’s been kicking around in the back of my mind for some time. I call it view types. The basic idea is to give a way for an &mut or & reference to identify which fields it is actually going to access. The main use case for this is having “disjoint” methods that don’t interfere with one another. * § Leftovers⠀➾ o § Science⠀➾ # ⚓ Brain_Implant_Offers_Artificial_Vision_To_The_Blind_| Hackaday⠀⇛ Nothing makes you appreciate your vision more than getting a little older and realizing that it used to be better and that it will probably get worse. But imagine how much more difficult it would be if you were totally blind. That was what happened to [Berna Gomez] when, at 42, she developed a medical condition that destroyed her optic nerves leaving her blind in a matter of days and ending her career as a science teacher. But thanks to science [Gomez] can now see, at least to some extent. She volunteered after 16 years to have a penny-sized device with 96 electrodes implanted in her visual cortex. The research is in the Journal of Clinical Investigation and while it is a crude first step, it shows lots of promise and uses some very novel techniques to overcome certain limitations. # ⚓ Luster_Lost⠀⇛ There’s this effect I often refer to when talking about digital photography. Old photographs, for whatever reason, tend to age themselves significantly over time, as the formats reflect older processes for making pictures, as well as the general effects of age. But digital photos, while not nearly as high a resolution as a modern pro- quality camera can take, do not age themselves quite so quickly. So as a result, pictures on Flickr that are nearly 20 years old at this point often manage to look like they were, for all intents and purposes, taken yesterday. As time goes on, the baseline for quality improves. Same with music: A pop song from 1998 generally doesn’t draw too much attention to its age on modern radio compared to a song from 1988, in part because digital recording formats like ProTools had become common by that point. o § Hardware⠀➾ # ⚓ Back-to-the-Office_Ergo_Brings_A_Bit_Of_Home_Sweet_Home_| Hackaday⠀⇛ We sure do love a good one-piece split keyboard, and it’s not just because you never have to worry about the halves drifting too far apart throughout the day, though that’s a big plus. For one thing, the angles are always just right without having to mess with anything, so muscle memory gets you back to the home row every time. Usually, the only thing missing from these mono-block splits is the num pad. Well, not on the SuperLyra. This is [Malevolti]’s back-to-the-office build, and it’s sure to start a few conversations. While we don’t have a lot of details, there will be plenty forthcoming on the Black Cat Plasticworks website. As soon as next year, [Malevolti] plans to sell fully-assembled SuperLyras, kits, and bare-bones PCBs. We really appreciate that it allows for either MX-type switches or Chocs, depending on the hot swap sockets installed. # ⚓ Pulp-Molding:_A_Use_For_Cardboard_Confetti_|_Hackaday⠀⇛ We’re pretty sure that we don’t have to tell you how great cardboard is. You probably sing the praises yourself and use it for everything from a work surface protective layer to a prototype of your next amazing build. But if you still find yourself flush with cardboard even after all that, here’s one thing you can do with all those pieces that are too small to use for anything else– chuck them in an old blender, whip up some cardboard pulp, and press that gunk into some 3D-printed molds. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ Security_updates_for_Friday⠀⇛ Security updates have been issued by Debian (python3.5, redis, and udisks2), Fedora (rust), openSUSE (binutils, java-1_8_0-openj9, and qemu), Oracle (firefox and httpd), Red Hat (thunderbird), Scientific Linux (thunderbird), and SUSE (binutils, qemu, and systemd). # ⚓ John_the_Ripper:_Penetration_Testing_Tool Review⠀⇛ Passwords are a weak link in enterprise security. As users struggle with requirements for complex passwords and password managers, bad habits multiply: post-it notes on screens, Word docs with passwords listed, retaining default passwords, reused passwords, and other workarounds. That’s why cyber criminals go after passwords so often. Once a hacker steals credentials, they can enter sensitive systems or wait in ambush to stage a devastating attack against a prized asset. And because users tend to reuse passwords, they attempt to crack other systems and websites with them too in password spraying and credential stuffing attacks. It’s enough to make you want to go passwordless. Penetration testing, therefore, pays close attention to password cracking. John the Ripper is a free, easy-to-use, open-source tool that takes the best aspects of various password crackers and unites them into one package. As such it can be harnessed by pen testers to detect weak passwords and find a way into a system or database. # ⚓ Reproducible_Builds_(diffoscope):_diffoscope 190_released⠀⇛ The diffoscope maintainers are pleased to announce the release of diffoscope version 190. This version includes the following changes: [ Chris Lamb ] * Don't raise a traceback if we cannot de-marshal Python bytecode to support Python 3.7 loading newer .pyc files. (Closes: reproducible-builds/ diffoscope#284) * Fix Python tests under Python 3.7 with file 5.39+. [ Vagrant Cascadian ] * Skip Python bytecode testing when "file" is older than 5.39. [ Roland Clobus ] * Detect whether the GNU_BUILD_ID field has been modified. ⚓ Vulnerability_in_Linux_kernel_could_let_hackers_remotely_take_over_systems⠀⇛ Security researchers have discovered a heap overflow vulnerability in the Transparent Inter-Process Communication (TIPC) module of the kernel of Linux operating systems. Hackers could exploit the vulnerability locally or remotely within a network to gain kernel privileges. ⚓ This_Week_in_Security:_The_Battle_Against_Ransomware,_Unicode,_Discourse,_and Shrootless [Ed: Microsoft Windows TCO]⠀⇛ We talk about ransomware gangs quite a bit, but there’s another shadowy, loose collection of actors in that arena. Emsisoft sheds a bit of light on the network of researchers and law enforcement that are working behind the scenes to frustrate ransomware campaigns. Darkside is an interesting case study. This is the group that made worldwide headlines by hitting the Colonial Pipeline, shutting it down for six days. What you might not realize is that the Darkside ransomware software had a weakness in its encryption algorithms, from mid December 2020 through January 12, 2021. Interestingly, Bitdefender released a decryptor on January 11. I haven’t found confirmation, but the timing seems to indicate that the release of the decryptor triggered Darkside to look for and fix the flaw in their encryption. (Alternatively, it’s possible that it was released in response the fix, and time zones are skewing the dates.) Emsisoft is very careful not to tip their hand when they’ve found a vulnerability in a ransomware. Instead, they have a network of law enforcement and security professionals that they share information with. This came in handy again when the Darkside group was spun back up, under the name BlackMatter. § Privacy/Surveillance⠀➾ * ⚓ Homebrewed_Voice_Assistant_Keeps_An_Eye_On_Air_Quality_|_Hackaday⠀⇛ The system had limited goals compared to commercial competitors. [7402] was more than happy to deal with a limited vocabulary of understanding as a trade off for privacy. It’s all built around a Raspberry Pi Zero, which runs the Julius speech recognition library. Ultrasonic sensors are used to only activate the device when a person leans in and directly addresses the system. § Defence/Aggression⠀➾ * ⚓ Statement_on_the_implications_of_the_ongoing_situation_in_the_Sudan_– Invidious⠀⇛ ORAL STATEMENT 32nd Special Session of the U.N. Human Rights Council on the implications of the ongoing situation in the Sudan Delivered by: Marwa Fatafta, MENA Policy Manager, Access Now § Environment⠀➾ * ⚓ Biden_announces_new_methane_rules_and_launches_global_pledge_to_slash planet-warming_emissions⠀⇛ President Joe Biden targeted planet-warming methane emissions on Tuesday from the UN climate summit, announcing strong new US regulations from the Environmental Protection Agency and launching a Global Methane Pledge, in partnership with the European Union, that has been signed by around 100 countries. At the center of Biden’s US methane strategy is a rule from the EPA that would push oil and gas companies to more accurately detect, monitor and repair methane leaks from new and existing wells, pipelines and other equipment. The agency estimates the rule would cut 41 million tons of methane emissions from 2023 to 2035 — more greenhouse gas than all the carbon dioxide emitted by all US passenger cars and commercial planes in 2019. § Finance⠀➾ * ⚓ How_a_Squid_Game_Crypto_Scam_Got_Away_With_Millions_|_WIRED⠀⇛ On the front lines of the $SQUID “rug pull” that left investors in the lurch. * ⚓ Squid_Game_Cryptocurrency_Scammers_Make_Off_With_$2.1_Million⠀⇛ * ⚓ UN-Backed_Banker_Alliance_Announces_“Green”_Plan_to_Transform_the Global_Financial_System⠀⇛ On Wednesday, an “industry-led and UN-convened” alliance of private banking and financial institutions announced plans at the COP26 conference to overhaul the role of global and regional financial institutions, including the World Bank and IMF, as part of a broader plan to “transform” the global financial system. The officially stated purpose of this proposed overhaul, per alliance members, is to promote the transition to a “Net-Zero” economy. However, the group’s proposed “reimagining” of international financial institutions (IFIs), according to their recently published “progress report”, would also move to merge these institutions with the private banking interests that compose the alliance; create a new system of “global financial governance”; and erode national sovereignty among developing countries by forcing them to establish business environments deemed “friendly” to the interests of alliance members. In other words, the powerful banking interests that compose this group are pushing to recreate the entire global financial system for their benefit under the guise of promoting sustainability. This alliance, called the Glasgow Financial Alliance for Net Zero (GFANZ), was launched in April by John Kerry, US Special Presidential Envoy for Climate Change; Janet Yellen, US Secretary of the Treasury and former chair of the Federal Reserve; and Mark Carney, the UN Special Envoy for Climate Action and Finance and former chair of the Bank of England and Bank of Canada. Carney, who is also the UK Prime Minister’s Finance Advisor for the COP26 conference, currently co-chairs the alliance with US billionaire and former Mayor of New York City, Michael Bloomberg. [...] With the UN now essentially a vehicle for the promotion of stakeholder capitalism, it is only fitting that it would “convene” and support the efforts of a group like GFANZ to extend that stakeholder capitalist model to other institutions involved in global governance, specifically global financial governance. Allowing GFANZ members, i.e. many of the largest private banks and financial institutions in the world, to fuse with MDBs, remake the “global financial governance system” and gain increased control over political decisions in the emerging world is a banker’s dream come true. To get this far, all they have needed is to convince enough of the world’s population that such shifts are necessary due to the perceived urgency of climate change and the need to rapidly decarbonize the economy. Yet, if put into practice, what will result is hardly a “greener” world, but a world dominated by a small financial and technocratic elite who are free to profit and pillage from both “natural capital” and “human capital” as they see fit. Today, MDBs are used as “instruments of power” that utilize debt to force developing nations to implement policies that benefit foreign interests, not their national interests. If GFANZ gets their way, the MDBs of tomorrow will be used to essentially eliminate national sovereignty, privatize the “natural assets” (e.g. ecosystems, ecological processes) of the developing world and force increasingly technocratic policies designed by global governance institutions and think tanks on ever more disenfranchised populations. Though GFANZ has cloaked itself in lofty rhetoric of “saving the planet,” their plans ultimately amount to a corporate-led coup that will make the global financial system even more corrupt and predatory and further reduce the sovereignty of national governments in the developing world. ䷩ 𝚕𝚒𝚗𝚎 6061 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.05.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_5/11/2021:_LXQt_1.0.0_and_GNOME_41.1⠀✐ Posted in News_Roundup at 10:45 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Why_I_use_Linux_to_manage_my_yoga_studio⠀⇛ When I started my first yoga studio in 2000, computer technology was way out of my wheelhouse. In fact, for the first two years, I didn’t even have a website. I did everything from scratch, including collecting emails, sending newsletters, marketing events, and corresponding with my student base. I was extremely content operating my business that way; my focus was on teaching yoga and creating community. Since then, I have gone on quite a journey in learning to use the right technology to support my business goals. In this article, I want to give you real-life evidence that Linux is a viable operating system (OS) and share some of the ways that switching to Linux has helped my business thrive. I’m here to testify how much easier Linux has made my work life and my personal life. o § Applications⠀➾ # ⚓ Best_Free_and_Open_Source_Alternatives_to_Microsoft_Visio⠀⇛ Microsoft’s stance for decades was that community creation and sharing of communal code (later to be known as free and open source software) represented a direct attack on their business. Their battle with Linux stretches back many years. Back in 2001, former Microsoft CEO Steve Ballmer famously tarnished Linux “a cancer that attaches itself in an intellectual property sense to everything it touches”. Microsoft also initiated its “Get the Facts” marketing campaign from mid-2003, which specifically criticized Linux server usage, total cost of ownership, security, indemnification and reliability. The campaign was widely criticized for spreading misinformation. However, in recent years, there has been a partial shift by Microsoft to embrace the open source software paradigm. For example, some of their code is open sourced. Examples include Visual Studio Code, .NET Framework, Atom, and PowerShell. They have also made investments in Linux development, server technology and organizations including the Linux Foundation and Open Source Initiative. They have made acquisitions such as Xamarin to help mobile app development, and GitHub a hugely popular code repository for open source developers. And they have partnered with Canonical, the developers of the popular Ubuntu distro. But many developers remain hugely sceptical about Microsoft and their apparent shift to embrace open source. # ⚓ HP_Linux_Printer_Driver_HPLIP_3.21.10_Adds_Debian_11,_Zorin OS_16_&_Ubuntu_21.10_Support⠀⇛ HPLIP, HP’s inkjet and laser printers Linux driver, released version 3.21.10 with new devices and Linux distributions support. Zorin OS, the modern Ubuntu-based Linux distribution, is finally supported by HPLIP’s official .run installer. And, it also adds Debian 11 and Ubuntu 21.10 support. o § Instructionals/Technical⠀➾ # ⚓ Hairsplitting_the_Pseudo-Element_Syntax⠀⇛ Fast forward a few years, I remember reading an article stating that single-colon notation was some kind of backwards-compatibility artifact of the standardization process. Both were valid, but double-colon was “more right”. # ⚓ Ansible_“pull_mode”_or_“Runner”_as_fail-safe_rollback methods⠀⇛ Recall that “pull mode” means a local installation of Ansible on each node. Each node subscribes to a “repository” (of any type) and periodically pulls configuration files and playbooks from that repository, and runs them locally, as in ansible-playbook -c local playbook.yml Thanks to the fact that “pull mode” is less of a product but more of a concept everything can be fine-tuned however I wish to do this. # ⚓ How_To_Install_EPrints_on_Ubuntu_20.04_LTS_–_idroot⠀⇛ In this tutorial, we will show you how to install EPrints on Ubuntu 20.04 LTS. For those of you who didn’t know, EPrints is a free and open-source software for document management systems, which are more commonly implemented as university repositories that store scientific work documents such as theses, theses, dissertations, and research journals. 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 EPrints 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_RabbitMQ_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install RabbitMQ on Debian 11. For those of you who didn’t know, RabbitMQ is a free, open-source, and one of the most popular message broker software. It supports multiple messaging protocols and uses plugins to communicate with popular messaging solutions like MQTT. RabbitMQ supports multiple messaging protocols. RabbitMQ can be easily deployed in distributed and federated configurations to meet high-scale, high- availability requirements. 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 RabbitMQ on a Debian 11 (Bullseye). # ⚓ How_To_Install_Ubuntu_21.10_Impish_Indri_to_USB_Flash_Drive with_Dualboot,_BIOS_and_UEFI_Methods⠀⇛ This tutorial will explain how to install Ubuntu 21.10 into your computer. The result of this tutorial is your computer will run Ubuntu operating system and can be viewed as alternative to Windows or macOS. This installation is flexible, as you may choose to install normally (to the internal hard disk) or externally (to USB flash drive or external HDD) in either BIOS Legacy-MBR or UEFI-GPT mode, for either dualboot or singleboot purpose. You will start everything by downloading the operating system itself, make required preparations, make a bootable medium, then booting and finishing the installation procedures step by step. Good luck! # ⚓ How_To_Upgrade_To_Fedora_35_From_Fedora_34_–_OSTechNix⠀⇛ After months of development, Fedora 35 final version has been released on November 2, 2021. If you’re already using Fedora 34, you can now safely upgrade to Fedora 35 desktop or server edition for latest features, performance and stability improvements as described in the following steps. # ⚓ How_to_Install_FTP_Server_With_ProFTP_on_Ubuntu_20.04_– ByteXD⠀⇛ ProFTPD is a highly enriched flavor of FTP server. It is available on Linux and Unix-like machines but can also be used in Windows via Cygwin. It is free and open-source software. Its environment exposes a person to many configuration options and a person who has used FTP before on Unix system will learn this version very easily. It was released and distributed under the GNU Public License. This FTP version is very versatile because it can support TLS (SSL) for a secure connection. # ⚓ How_to_Install_Prometheus_on_Ubuntu_20.04⠀⇛ Prometheus is a free and open-source monitoring and alerting tool that was initially used for monitoring metrics at SoundCloud back in 2012. It is written in Go programming language. Prometheus monitors and records real-time events in a time-series database. Since then it has grown in leaps and bounds and had been adopted by many organizations to monitor their infrastructure metrics. Prometheus provides flexible queries and real-time alerting which helps in quick diagnosis and troubleshooting of errors. # ⚓ How_to_Install_Puppet_7_Server_on_Rocky_Linux/Centos_8⠀⇛ In this guide, we are going to install Puppet 7 Server Open Source in Rocky Linux/Centos 8 Server. We will set up a Puppet server and an agent and install nginx using puppet manifests. Puppet is a software configuration management tool which includes its own declarative language to describe system configuration. It is a model-driven solution that requires limited programming knowledge to use. Puppet operates in an agent- master architecture, in which a master node controls configuration information for a fleet of managed agent nodes. Puppet is distributed in several packages. These include puppetserver, puppet-agent and puppetdb. Puppet Server controls the configuration information for one or more managed agent nodes. PuppetDB is where the data generated by Puppet is stored. # ⚓ How_to_Install_and_Use_Docker_on_AlmaLinux_8_–_VITUX⠀⇛ Docker is a powerful platform for developers and sysadmins that simplifies the process of deploying applications inside software containers. Containers allow you to package up an application with all its parts (code, runtime, system tools, system libraries – anything that would usually go in /usr/ bin, or /usr/lib) so it will run consistently on any Linux machine. This includes the operating system kernel and other shared resources such as memory and disk space. Docker provides a portable environment for both development and production environments. You can create a container from one set of files that works anywhere else without having to worry about dependencies being different on each new server. Docker CE is useful for Linux users because it helps them in creating their own environments without affecting other users on the system. It also automates deployment, which eliminates configuration errors and makes it easy to manage projects across teams of developers who are working together on software applications. In this guide, we will take a look at how we can install Docker CE to create and manage development environments on an AlmaLinux 8 system. # ⚓ How_to_install_aapanel_6_on_Fedora_34_–_NextGenTips⠀⇛ In this tutorial guide we will learn how to install aapanel in Fedora 34. Aapanel is a free open source hosting control panel, it manages the servers through graphical user interface. It is an international version of BAOTA. aapanel provides one click function such as one click LAMP install, one click deployment of SSL, remote backup etc. It is a server software system that offers ideal support for Linux systems. # ⚓ Improve_UDP_performance_in_RHEL_8.5_|_Red_Hat_Developer⠀⇛ If you have ever tested throughput performance in a container deployment, you know that the UDP protocol is (a lot) slower than TCP. How can that be possible? After all, the TCP protocol is extremely complex, whereas UDP is simple and carries less per-packet overhead. This article will explain the not-so-dark magic beyond the superior TCP throughput performance and how recent improvements in the Linux kernel can close that gap. You’ll also learn how to use all these shiny new features in the upcoming version 8.5 of Red Hat Enterprise Linux to boost UDP throughput in container deployments by a factor of two or more. # ⚓ Convert_Audio_File_Formats_on_Ubuntu_with_SoundConverter_– Technastic⠀⇛ In this tutorial, we discuss how you can convert audio files into different formats on Ubuntu with a neat tool called SoundConverter. Before the rise of music streaming services, people bought their music DRM-free. # ⚓ Proxmox_VE_Full_Course:_Class_16_–_High_Availability_– Invidious⠀⇛ In the final episode of LearnLinuxTV’s Proxmox VE tutorial series, we explore the concept of high availability. This will ensure that our most important virtual machines are always running, even if one of the nodes in our cluster stops responding. # ⚓ Fedora_Post_Install_Setup_Util_–_Security_and_Linux⠀⇛ A number of years ago I shared a script to help with getting your system up and running with software and tweaks when you had freshly installed Fedora (F27 I think it was at the time) Looking around on the internet I found that a lot of Fedorians were asking the same questions “How do I install this?” “How do I get that?” So I thought to myself I’d create a revamped version to help with this so it’s all in one place. I mainly use it for myself but I thought I’d release it to the public with the hope that some of you also find it useful. So here it is. o § Games⠀➾ # ⚓ Watch_this_before_you_buy_your_Steam_Deck._–_Invidious⠀⇛ # ⚓ Total_War:_WARHAMMER_III_launches_February_17_–_2022,_Linux port_soon_after_|_GamingOnLinux⠀⇛ Creative Assembly has now confirmed that Total War: WARHAMMER III will be officially launching on February 17, 2022 but if you’re waiting on the Linux port it will be a little after. This was confirmed yesterday, with their official FAQ being updated to note it will “also be available as close to launch day as possible on macOS and Linux thanks to our friends at Feral Interactive – we’ll be confirming exactly when closer to release day”. # ⚓ Discover_the_Top_14_New_Games_to_Play_on_Linux_With_Proton Since_October_2021_–_Boiling_Steam⠀⇛ We are back with our usual monthly update! Boiling Steam looks at the latest data dumps from ProtonDB to give you a quick list of new games that work (pretty much?) perfectly with Proton since October 2021 – all of them work out of the box or well enough with tweaks… # ⚓ OpenMW_brings_many_new_features_for_Morrowind_in_the_new 0.47.0_release_|_GamingOnLinux⠀⇛ Rejoice RPG fans! There’s a fresh and fancy new release of OpenMW, the free and open source game engine reimplementation for The Elder Scrolls III: Morrowind. One of the best around, this enables you to play Morrowind on modern platforms (like Linux!) easily with many enhancements over the original while still keeping the original gameplay. Over a year since the last release this brings with it absolutely tons of bugs solved for the game and the editor, while also bringing with it brand new features. A fair amount of the game engine features improved and background things, some of which users won’t directly notice but keep OpenMW running smoothly. # ⚓ Proton_Experimental_gets_Disgaea_4_&_Mafia_II_working_plus CEG_startup_improvements_|_GamingOnLinux⠀⇛ More quick fixes coming in recently for Proton Experimental to get even more Windows games to play nicely on Linux with this compatibility layer. Note: to play games using CEG DRM, you should opt into the Steam Client Beta. Released November 4, the latest update to Proton Experimental added in improved support for Mafia II (Classic), Disgaea 4 Complete+ and Ghostbusters: The Video Game Remastered. On top of that, work more went into improving the new support for CEG DRM on Linux with Proton. Now you should see an improvement to the startup time of games using it, pushing it another step forwards towards being ready to roll out in a stable version of Proton. o § Desktop Environments/WMs⠀➾ # ⚓ LXQt_1.0.0_Desktop_Environment_Released_After_8_Years_of Development,_This_Is_What’s_New⠀⇛ After more than eight years of development and six months after LXQt 0.17.0, LXQt 1.0.0 is here as the first mature version of the Lightweight Qt Desktop Environment, the successor of the lightweight LXDE desktop environment, but written in Qt rather than GTK. As you can imagine, LXQt 1.0.0 is packed with numerous new features, such as a Do-Not-Disturb mode in LXQt Desktop Notifications, a new LXQt Panel plugin called “Custom Command” that lets you run a custom command, as well as the ability to save and load Qt palettes in LXQt Appearance Configuration. # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ KDE_Gear_21.08.3_Released_as_the_Last_in_the_Series, KDE_Gear_21.12_Arrives_December_9th⠀⇛ KDE Gear 21.08.3 is here about a month after KDE Gear 21.08.2 and it brings one last batch of bug fixes and improvements for those of you using the KDE Gear 21.08 software suite. A total of 74 changes are included in this last KDE Gear 21.08 point release across several KDE apps and core libraries. # § GNOME Desktop/GTK⠀➾ # ⚓ GNOME_41.1_Improves_the_New_Calls_and_Connections Apps,_Nautilus,_Software,_and_More⠀⇛ GNOME 41.1 is the first point release of the GNOME 41 desktop environment, which introduced a new Calls and Connections apps, a redesigned Software app, new multitasking and mobile connection settings, and enhanced power management features. Now, GNOME 41.1 builds on these changes and brings a first batch of improvements that update the GNOME Software package manager to allow searching for GNOME extensions, improve codec installation process, add the new GNOME Circle apps to the featured carousel, improve metadata support for Snap apps, and much more. o § Devices/Embedded⠀➾ # § Open Hardware/Modding⠀➾ # ⚓ The_Raspberry_Pi_Build_HAT_and_LEGO®_components_at our_CoderDojo⠀⇛ # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Google_sets_the_record_straight_on_which_Pixel_phones will_get_the_Android_12L_beta⠀⇛ # ⚓ OnePlus_OxygenOS_12_(Android_12)_update_tracker: Eligible_devices,_release_date⠀⇛ # ⚓ Samsung_One_UI_4.0_(Android_12)_update_tracker: Eligible_devices_&_more⠀⇛ # ⚓ How_To_Add_&_Customize_Widgets_To_Your_Home_Screen_On Android_12⠀⇛ # ⚓ Google_lets_Android_apps_use_third-party_payments_in South_Korea⠀⇛ # ⚓ 10_Top_Educational_Android_Apps_in_2021_|_LMSPulse⠀⇛ # ⚓ Best_Android_Phones_for_2021_|_Popular_Science⠀⇛ # ⚓ Best_Black_Friday_Android_smartwatch_deals_|_Android Central⠀⇛ # ⚓ Best_Android_app_deals_of_the_day:_Vandals,_QR_and Barcode_Scanner_PRO,_more_–_9to5Toys⠀⇛ # ⚓ 7_Best_Android_Icon_Packs_to_Customize_Your_Android Experience_in_2021_–_TechPP⠀⇛ # ⚓ How_to_create_a_signature_for_PDF_documents_on_an Android_phone_–_The_Verge⠀⇛ # ⚓ The_Latest_Android_Malware_is_Extremely_Dangerous, Here’s_Why_/_Digital_Information_World⠀⇛ # ⚓ Do_Beats_Fit_Pro_Work_With_Android?_What_You_Need_To Know⠀⇛ # ⚓ Backbone_One’s_Gaming_Controller_Now_Supports Android⠀⇛ # ⚓ Android_Auto_does_not_appear_in_the_Pixel_6′s_app launcher_–_9to5Google⠀⇛ # ⚓ Android_Users_Alert!_Delete_THESE_151_apps_from_your phones_immediately:_Here’s_why_|_Technology_News_|_Zee News⠀⇛ # ⚓ Netflix’s_mobile_games_for_Android_users:_Here’s_how it_works_|_Technology_News,The_Indian_Express⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # ⚓ Why_browsers_are_driven_to_offer_some_degree_of remote_control⠀⇛ The bigger problem is your web browser profile, which almost always contains things that your browser will want to update (such as your history and your current cookies). If there are multiple copies of your browser running they all need to coordinate access to your profile; they need to carefully lock it for updates, and probably to notify each other that important things have been updated. Essentially it’s a shared database, and shared databases are pain points. Given the locking, it’s also a fine way for one copy of the browser to cause another copy to perform badly, as the other copy waits for an update lock or to pick up new things or whatever. # § Mozilla⠀➾ # ⚓ Thunderbird_Email_Client_»_PCLinuxOS⠀⇛ Mozilla Thunderbird is a standalone mail and newsgroup client. Updated to version 91.3.0. # ⚓ Firefox_Browser_»_PCLinuxOS⠀⇛ Mozilla Firefox is a free and open source web browser descended from the Mozilla Application Suite and managed by Mozilla Corporation. Updated to version 94.0.1. # ⚓ Firefox_fixed_with_patch_for_libdrm⠀⇛ For EasyOS 3.x there is a firefox SFS, which runs real nice. Running the latest Easy 3.1.7 (not released) with pulseaudio, starting firefox from a terminal… [...] This build of EasyOS is using pulseaudio. Although there is only the one instance of the daemon, running as root, it is still usable by non-root users (if they belong to ‘audio’ group), via the socket /tmp/pulse- socket… # ⚓ New_Release:_Tor_Browser_11.0a10_(Windows/ macOS/Linux)⠀⇛ Tor Browser 11.0a10 is now available from the Tor Browser download page and also from our distribution directory. Note: This is an alpha release, an experimental version for users who want to help us test new features. For everyone else, we recommend downloading the latest stable Windows/macOS/Linux release instead. # § FSF⠀➾ # § Licensing/Legal⠀➾ # ⚓ Breaking_down_Apollo_Federation’s_anti-FOSS corporate_gaslighting⠀⇛ Gather around, my friends, for there is another company which thinks we are stupid and we enjoy having our faces spat in. Apollo Federation has announced that they will switch to a non-free license. Let’s find out just how much the Elastic license really is going to “protect the community” like they want you to believe. Let’s start by asking ourselves, objectively, what practical changes can we expect from a switch from the MIT license to the Elastic License? Both licenses are pretty short, so I recommend quickly reading them yourself before we move on. # § Programming/Development⠀➾ # § Python⠀➾ # ⚓ An_oral_history_of_Bank_Python⠀⇛ Today will I take you through the keyhole to look at a group of software systems not well known to the public, which I call “Bank Python”. Bank Python implementations are effectively proprietary forks of the entire Python ecosystem which are in use at many (but not all) of the biggest investment banks. Bank Python differs considerably from the common, or garden-variety Python that most people know and love (or hate). Thousands of people work on – or rather, inside – these systems but there is not a lot about them on the public web. When I’ve tried to explain Bank Python in conversations people have often dismissed what I’ve said as the ravings of a swivel-eyed loon. It all just sounds too bonkers. I will discuss a fictional, amalgamated, imaginary Bank Python system called “Minerva”. The names of subsystems will be changed and though I’ll try to be accurate I will have to stylise some details and – of course: I don’t know every single detail. I might even make the odd mistake. Hopefully I get the broad strokes. # ⚓ Python_3_forced_its_own_hand_so_that_standard input_had_to_be_Unicode⠀⇛ All of this fits with Python 3′s general philosophy, of course. Python 3 really wants the world of text to be Unicode, and that includes input and output. Providing standard input as bytes and making it easy to process those bytes without ever turning them into Unicode would invite a return to the Python 2 world where people processed text in non-Unicode ways. Arguably, Unicode text processing is the reason for Python 3 to exist, so it’s not surprising that the Python developers were so strongly against anything that smelled like it. # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ Understanding_Bash_Variables⠀⇛ So let me walk you through how variables work in bash, starting with local shell variables and then covering special and environment variables. I think you’ll find understanding the basics to be extremely helpful. * § Leftovers⠀➾ o ⚓ Welcome_to_the_American_Century…Even_If_It_is_Hell_on_Earth⠀⇛ And he wasn’t wrong, was he?  Eight decades later, who would deny that we’ve lived through something like an American century? After all, in 1945, the U.S. emerged triumphant from World War II, a rare nation remarkably unravaged by that war (despite the 400,000 casualties it had suffered). With Great Britain heading for the imperial sub-basement, Washington found itself instantly the military and economic powerhouse on the planet. As it turned out, however, to “exert upon the world the full impact of our influence,” one other thing was necessary and, fortunately, at hand: an enemy. From then on, America’s global stature and power would, in fact, be eternally based on facing down enemies.  Fortunately, in 1945, there was that other potential, if war-ravaged, powerhouse, the Soviet Union. That future “superpower” had been an ally in World War II, but no longer. It would thereafter be the necessary enemy in a “cold war” that sometimes threatened to turn all too hot. And it would, of course, ensure that what later came to be known as the military-industrial complex (and a nuclear arsenalcapable of destroying many planets like this one) would be funded in a way once historically inconceivable in what might still have passed for peacetime. o ⚓ A_Very_Special_Operator:_the_Eddie_Gallagher_Story⠀⇛ In the not-always secretive world of special operations, few post 9/11 warriors have become better known than Navy Seal Eddie Gallagher, a chief petty officer much beloved by former President Trump. When Gallagher faced a 2019 court-martial for allegedly killing a wounded ISIS prisoner in Iraq and committing other war crimes, Trump assured his supporters that “I will always stick up for our great fighters.” True to his word, after Gallagher was acquitted of all but a lesser charge (taking a trophy shot of the dead Iraqi teenager), Trump blocked a Navy attempt to demote him and take away his Trident Pin, the coveted symbol of SEAL Team membership. Among those joining the “Free Eddie” campaign was former Marine Duncan Hunter, a Republican Congressman from San Diego who stole $250,000 in campaign funds and then avoided jail only thanks to a Trump pardon. As Hunter argued on Fox News, Gallagher “is the kind of guy we want out there killing for us, killing bad guys. He shouldn’t be going to court at all for doing his job.” o ⚓ What_Passing_Can_Still_Teach_Us_About_Identity⠀⇛ Whenever talking about Nella Larsen’s classic 1929 novel, Passing, I often confuse the names of its main characters. When I mean to refer to the Black woman who grows up in Chicago’s South Side and then decides to pass as white, I rarely identify her as Clare. I regularly mistake her for Irene, the Black woman who is Clare’s childhood friend and who encounters Clare as an adult. I may just be bad with names, but I think that this mistake stems, in part, from the novel. Both light-skinned, raised in Chicago, and relatively wealthy, Clare and Irene are foils. They blur together even as each character distinguishes herself from the other. o ⚓ What_Saul_Alinsky_Learned_from_His_“Mentor”,_Al_Capone⠀⇛ A central tenet of neoliberalism—a political theory of governmental administration—is a tendency to view the purpose of government and public processes in strictly economic terms, and to ascribe the cause of most problems to market inefficiencies and too little competition. Under this approach, all conflict is resolved by using rational, professional problem solving to find win-win, job-creating solutions. A defining characteristic of this approach is a reluctance to ascribe the cause of any problem to pervasive and systematic corruption, or to the ability of the rich and the strong to take advantage of the poor and the weak. This theory is in sharp contrast to what activists have learned from decades of experience—a world view best summed up by Saul Alinsky (probably the 20th century’s best grassroots community organizer) who said, “We live in a world of unbelievable deceit and corruption…Giant corporations are unbelievably oppressive and follow a win-lose philosophy…. [and] will go to any length to make more money.” * o ⚓ 640%_Kickstarter,_Sponsorships,_and_Shipping⠀⇛ When it comes to shipping books internationally, the US post office provides three options. 1. Media Mail. I can get it just about anywhere in the world for less than $10. No international tracking. No guarantee of delivery. Might take months or years. Those container ships moored outside every port in the world, waiting months for an opportunity to unload? There are Media Mail packages adrift in every one. 2. First class mail. Costs $25 +/- $5-ish. Delivery guaranteed, eventually. Might take months. I can complain to the post office, and they’ll fill out a form. What they’ll do with that form is another issue. 3. International Priority Mail. Costs about $40 ($30 to Canada). Ouch. Delivers within a week or two, sort of guaranteed. Insured. Complaints are taken mostly seriously. o § Hardware⠀➾ # ⚓ Tencent_Developing_Three_SoCs_Set_to_Replace_Western Processors⠀⇛ Chinese Internet conglomerate Tencent offers dozens of various cloud services and operates massive datacenters in China. Just like other cloud giants, Tencent has been developing its own datacenter infrastructure for a while. Now, in in a bid to increase performance, cut power consumption, reduce costs, and get a complete control over its software and hardware, Tencent has ventured into chip design. o § Health/Nutrition⠀➾ # ⚓ Biden_Gives_January_4_Deadline_to_Employers_for_New_OSHA Vaccine_Requirements⠀⇛ # ⚓ ‘Historic_Moment’_as_NYC_Taxi_Drivers_Win_Major_Debt_Relief Following_Hunger_Strike⠀⇛ “By going on a hunger strike in front of City Hall, there was no way you could ignore what we were doing to our bodies in the service of this fight.” “Next time folks wonder why I’m stubborn, it’s because we’re constantly told our requests are impossible or unreasonable until we wind up accomplishing it anyway through hard work and organizing,” tweeted Ocasio-Cortez. “When we organize people, the people win!” # ⚓ A_COVID_Memorial_Mixtape_Revisited⠀⇛ # ⚓ COVID_Vaccine_Rollout_for_Children_Ages_5_to_11_Comes_With Familiar_Challenges⠀⇛ # ⚓ Here’s_Why_Rapid_COVID_Tests_Are_So_Expensive_and_Hard_to Find⠀⇛ A few weeks ago, a ProPublica reporter decided to test his kids for COVID-19. They had the sniffles, and with a grandparent set to visit he wanted to minimize the risk that they were infectious. This was the problem that quick, cheap COVID-19 tests were supposed to help fix. No need to go to a clinic or wait days for results. Just pick up a pack of tests at a local pharmacy whenever you want, swab your nose and learn within 15 minutes if you’re likely to pass the virus along. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ ‘Tis_the_Season_for_the_Wayward_Package_Phish⠀⇛ The holiday shopping season always means big business for phishers, who tend to find increased success this time of year with a lure about a wayward package that needs redelivery. Here’s a look at a fairly elaborate SMS-based phishing scam that spoofs FedEx in a bid to extract personal and financial information from unwary recipients. # ⚓ Facebook_skirts_Apple’s_App_Store_fees_with_custom subscription_links_for_creators⠀⇛ Facebook is operating in a gray zone under Apple’s rules for the App Store, though a spokesperson said the social network believes its approach has always been allowed on iOS. The App Store currently forbids iOS apps from offering alternative payment options for purchasing digital goods, but in this case, it’s the creator, not Facebook, the app developer, that will be sending people to pay for a subscription on the web. The spokesperson for Facebook confirmed the social network isn’t removing the ability for users to sign up for a creator subscription using Apple’s native payments system. # ⚓ Sinclair_Broadcast_Group_says_ransomware_incident_not ‘fully_resolved’_weeks_after_breach⠀⇛ Employees of the Maryland-based company — which is the second-largest broadcast company in the U.S., owning or operating 185 television stations in 85 markets, multiple national networks, and 21 regional sports network brands — reported at the time that the attack had caused “major technical problems” and made it difficult for some stations to get on the air. The company also reported that [crackers] had taken data in the attack. # § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ Seventh_Circuit_Says_Riley_Doesn’t_Apply To_Searches_Of_Parolees’_Phones⠀⇛ In 2014, the Supreme Court extended Fourth Amendment coverage to the contents of cell phones. Prior to that ruling, cops had successfully argued that searching the contents of someone’s cell phone was no different than searching the contents of their pockets when arresting them. Claims — bad ones — were made about “officer safety” and, for the most part, courts tended to agree. If the pants pocket argument didn’t work, cell phones — with their wealth of personal information and private communications — were analogized as the digital equivalent of car trunks or address books. # ⚓ Document_Freed_By_FOIA_Shows_How_Much Data_The_FBI_Can_Obtain_From_Cellphone Service_Providers⠀⇛ An internal FBI document shared with Joseph Cox of Motherboard by Ryan Shapiro of Property of the People gives a little more insight into law enforcement’s data grabs. The Third Party Doctrine — ushered into law by the Supreme Court decision that said anything voluntarily shared with third parties could be obtained without a warrant — still governs a lot of these collections. # ⚓ The_Metaverse:_Gateway_to_Unanimous Consent_and_Panarchy?⠀⇛ The metaverse is a decades-old concept. Neal Stephenson coined the term in his 1992 novel Snow Crash, but versions of it appear in much earlier speculative fiction. Think of it as virtual reality on steroids, a computer/ Internet environment into which humanity could, and might, effectively move most of its social activities. To some, this sounds utopian. Others (especially writers of fiction) treat it as at least potentially dystopian. Either way, it’s coming, and the political possibilities are intriguing. # ⚓ Planned_regulation:_EU_Commission postpones_mandatory_screening_of_encrypted chats⠀⇛ Providers of messengers and cloud services will be allowed to voluntarily screen for child abuse content worthy of prosecution, which is to become mandatory across the EU. The Council and Commission are pushing for an extension to other crime areas. Next week, the EU interior ministers will publish a declaration on this. # ⚓ “Complexity_is_Fraud”:_Why_We_Must_Drop Micro-Targeted_Ads_to_Help_Publishers_and to_Protect_Online_Privacy⠀⇛ Against those massively well- financed and well-connected groups, the fight to rein in micro-targeted advertising might seem hopeless. Nonetheless, there are efforts to counter those powers. Privacy News Online wrote about one of them back in July. The Tracking-Free Ads Coalition is “a coalition of political leaders, civil society organisations and companies from across the EU that are committed to put an end to the pervasive tracking advertising industry that dominates the internet today.” It includes 24 Members of the European Parliament from a range of parties. Recently, they took the unusual step of writing to leading businesses that use targeted advertising: # ⚓ Data_Privacy_Is_The_Price_Of_The_Latest Antitrust_Proposals⠀⇛ In the wake of data breaches at Target and Equifax where hackers compromised the personal information of millions of Americans and the Cambridge Analytica scandal, customers and policymakers are increasingly worried about the privacy and security of our personal information online. Unfortunately, policymakers often confuse these privacy and data security concerns with broader anti-tech fervor against America’s leading technology businesses. But simply put, kitchen-sink anti-tech responses could exacerbate, not ease, concerns regarding data privacy and security. # ⚓ Open-source_browser_fingerprinting startup_FingerprintJS_raises_$32M⠀⇛ Open-source browser fingerprinting startup FingerprintJS Inc. said today it has raised $32 million in new funding to accelerate the development of additional developer tools, including a JavaScript bot detection application programming interface. Craft Ventures led the Series B round. Also participating in the round were Nexus Venture Partners and Uncorrelated Ventures. # ⚓ Digital_privacy_of_correspondence: ePrivacy_Regulation⠀⇛ Because of the very sensitive nature of personal communications, location and internet usage data, the 2002 ePrivacy Directive guaranteed special data protection for telephone and internet communications, which goes far beyond the GDPR (General Data Protection Regulation). The ePrivacy Regulation is intended to replace this 2002 Directive, for better or for worse. Mass intelligence surveillance, the Cambridge Analytica scandal, and potentiallywrongful convictions based on false telecommunications data inDenmark show how urgently better protection of our telephone and [Internet] use is needed. # § Confidentiality⠀➾ # ⚓ Thinking_through_the_threat_models when_encrypting_your_backups⠀⇛ Here is a simple seeming question you might wind up asking someday. Suppose that for some reason you need to keep encrypted copies of your backups. Does it matter if you use symmetric encryption for this (where the encryption key is also the decryption key), or do you need some form of asymmetric encryption (where the encryption key is not the decryption key)? Well, it depends on what your threats are (a threat model, in the jargon). # ⚓ [Crackers]_are_stealing_data_today so_quantum_computers_can_crack_it_in a_decade⠀⇛ Faced with this “harvest now and decrypt later” strategy, officials are trying to develop and deploy new encryption algorithms to protect secrets against an emerging class of powerful machines. That includes the Department of Homeland Security, which says it is leading a long and difficult transition to what is known as post- quantum cryptography. # ⚓ Tens_of_thousands_of_medical_school records_found_on_misconfigured_cloud storage⠀⇛ The student data was found on a single, open Amazon Web Services Inc. S3 storage bucket. The 157 gigabytes of student data covered an estimated 27,000 to 50,000 students and included personally identifiable information, national ID cards, academic records and more. o § Defence/Aggression⠀➾ # ⚓ Denial_of_Wrongdoing_in_Deadly_Kabul_Strike_Reveals ‘Systemic_Problem’_at_Pentagon:_Critics⠀⇛ Following a Pentagon official’s assertion Wednesday that the August 29 airstrike in a Kabul neighborhood that killed 10 innocent Afghan civilians, including seven children, was not the result of misconduct or negligence, human rights advocates reiterated that the United States’ remote-controlled assassination program is “rotten” from top to bottom and called for a moratorium on drone warfare. “We need to shut down these strikes until we figure out what the hell is going on.” # ⚓ Opinion_|_In_Praise_of_People_(Even_Me)_Who_Were_Right About_the_Failed_Afghan_War_From_the_Beginning⠀⇛ I waited almost three months for some acknowledgement, but it never came. Not a bottle of champagne. Not a congratulatory note. Not an email of acknowledgement. Not one media request. # ⚓ It_is_Time_For_General_Mark_Milley_to_Step_Aside⠀⇛ The real “Sputnik moment” in 1957, when the Soviet Union was the first to launch a vehicle into space, had international and national consequences for American national security policy.  Physicists and engineers around the world know that hypersonic weapons do not represent a revolution in the strategic arsenal.  Writing in “Scientific American” in August 2021, David Wright and Cameron Tracy noted that many of the claims regarding hypersonic weapons are exaggerated or simply false.  They are not game-changers.  The Pentagon and the Congress should not be allowed to use this canard to drive a new arms race and escalate the chances of conflict. Over the past year or so, the Department of Defense has delivered a series of statements that exaggerate the power and influence of China in order to increase U.S. defense spending and to “strengthen deterrence” against China.  Assistant Secretary of Defense for East Asia and the Pacific Ely Ratner outlined a plan in June 2021 to deploy a permanent naval squadron to waters surrounding Taiwan that would include an aircraft carrier task force. # ⚓ Citing_Failure_to_Prosecute_Trump_and_Cronies,_Legal_Group Calls_On_AG_Garland_to_Resign⠀⇛ Frustrated by the U.S. attorney general’s failure to investigate or take legal action against former President Donald Trump and his associates for various potential crimes, Free Speech for People argued Thursday that because Merrick Garland “is unwilling to step up, it is time for him to step down.” “Garland is no longer fit to serve as attorney general.” # ⚓ What_the_CIA_is_Hiding_in_the_JFK_Assassination_Records⠀⇛ To understand what they are still hiding and why they are still hiding it, it’s necessary to go back to the 1990s during the era of the Assassination Records Review Board — and even further back than that to November 22, 1963 — the day that Kennedy was assassinated.  People often say that if the CIA and the Pentagon had orchestrated the assassination of President Kennedy, someone would have talked by now.  # ⚓ “I_Would_Like_to_See_The_New_York_Times_Wash_the_Blood_Off Its_Hands”⠀⇛ Mohammed El-Kurd is a Palestinian poet, writer, and activist who grew up in the East Jerusalem neighborhood of Sheikh Jarrah. When he was 11 years old, settlers carrying rifles and backpacks, and supported by the Israeli army, took over half his house. # ⚓ Controversial_term:_German_Ministry_of_the_Interior_sneaks „Gefährder“_into_the_EU⠀⇛ In order for state protection departments to be able to cooperate better at EU level in the area of politically motivated crime, they need common definitions of the persons to be prosecuted. A corresponding initiative to this end comes from Germany. This way, threats are prosecuted that have not even occurred yet. # ⚓ The_Supreme_Court_Is_Poised_to_Give_a_Giant_Gift_to_Gun Nuts⠀⇛ On a winter night in 1984, Bernhard Goetz brought his handgun on the New York City subway and shot four young unarmed black men he claimed were trying to rob him. The people he shot were never charged with attempted robbery, which they would have been had Goetz had any evidence of the crime. Goetz claimed he had bought the gun for self-defense after being attacked on the subway three years earlier. The story drew national attention. Some people hailed him as a hero, others damned him as a villain. Goetz was eventually charged with assault and attempted murder but was only convicted on one count of carrying an unlicensed firearm. He served eight months in prison and, as far as I know, is still out there somewhere in the world, armed and dangerous. # ⚓ Former_Maldives_President_Mohamed_Nasheed_on_Climate_Risk_& Surviving_Assassination_Attempt⠀⇛ We speak to Mohamed Nasheed, the former president of the low-lying island nation of the Maldives, at the U.N. climate summit in Glasgow. Nasheed is one of the world’s leading climate advocates, who once held a cabinet meeting underwater to bring attention to the threat of global warming, pledged to make the Maldives the first carbon-neutral country and installed solar panels on the roof of his presidential residence. Now serving as speaker of parliament, Nasheed survived an assassination attempt earlier this year that required 16 hours of surgery. As a result of the sea level rising four millimeters a year in the Maldives, Nasheed says the country faces devastating consequences such as contaminated water, loss of biodiversity, inclement weather and coastal erosion. “We want to see countries agree that this is an emergency, and we want to see countries do things that they do in an emergency,” he says. # ⚓ Dems_Urge_Biden_to_‘Reduce_Nuclear_Weapons_Risks’_in_Summit With_Chinese_President⠀⇛ Four congressional Democrats on Thursday urged U.S. President Joe Biden to make reducing nuclear weapons risks a “top priority” in his upcoming virtual summit with Chinese President Xi Jinping, emphasizing the important context of the United States’ huge arsenal. The message to Biden from Sens. Ed Markey (D-Mass.) and Jeff Merkley (D-Ore.) as well as Reps. Don Beyer (D-Va.) and John Garamendi (D-Calif.) came a day after the Pentagon projected that China’s cache of deliverable nuclear warheads could increase fivefold to 1,000 by 2030. # ⚓ Warnings_of_‘More_Death_and_Suffering’_in_Yemen_as_US_Moves to_Sell_Saudis_Missiles⠀⇛ Anti-war activists on Thursday accused the Biden administration of throwing fuel on the flames of the Saudi-led war in Yemen after the U.S. State Department notified Congress it approved a new $650 million missile sale to the repressive Middle Eastern monarchy. Defense News reports the Pentagon said the Saudi government requested to purchase 280 AIM-120C-7/C- 8 advanced medium-range air-to-air missiles and 596 LAU-128 missile rail launchers in a deal that would also include spare parts, support, and logistical services. The missiles would be fitted to Saudi warplanes including Eurofighter Typhoons and McDonnell-Douglas F-15s. # ⚓ Israel_Dossier_on_Palestinian_“Terror”_Groups_Offers_No Proof⠀⇛ A SECRET DOCUMENT distributed by Israel to justify its terrorist designations of six prominent Palestinian human rights groups shows no concrete evidence of involvement in violent activities by any of the groups. The designation of the Palestinians groups, which was met by international outrage from defenders of human rights, was announced on October 22 by Israeli Defense Minister Benny Gantz. Gantz cited alleged links between the groups and the Popular Front for the Liberation of Palestine, or PFLP, a left-wing Palestinian political party with its own military wing. Despite the severity of the declaration, Israel has yet to publicly present any documents directly or indirectly linking the six groups to the PFLP or to any violent activity. o § Environment⠀➾ # ⚓ Biden_keeps_pressure_on_OPEC+_to_boost_output,_citing inflation⠀⇛ The pressure on OPEC+ is unusually strong. U.S. Secretary of State Antony Blinken spoke with Sheikh Abdullah Bin Zayed, the foreign minister of the United Arab Emirates on Tuesday to press for increased production. Other oil-consuming nations are pushing hard as well, with Japan and India wanting more production as the energy crisis threatens to undermine the economic recovery in Europe and Asia. As gasoline prices pose increasing domestic political risks, the issue came up on the sidelines of the Group of 20 meeting over the weekend in Rome, with Biden administration officials calling for more production when producers meet on Thursday. Members including Kuwait, Iraq, Algeria, Angola and Nigeria have indicated that they want OPEC+ to stick with its current plan to increase output gradually. # ⚓ COP26:_The_Clock_Is_Ticking⠀⇛ # ⚓ More_Than_20_Nations_Vow_to_End_Funding_for_Overseas_Fossil Fuel_Projects⠀⇛ # ⚓ Climate_Change_and_the_Limits_of_Economic_Growth⠀⇛ Not all ecologists or economists are enthusiastic about this “green growth” alternative. According to these critical views, which have now begun to move into the mainstream, the planet simply can’t sustain the current pace of growth and even renewable energy sources like solar hit up against significant resource limits. The only effective way to control carbon emissions, as well as related problems of pollution and biodiversity loss, is to address “overshoot,” the unconstrained use of energy and material resources well beyond planetary limits, particularly in the richer parts of the world. These arguments pick up from some of the earliest computer modeling of resource limits highlighted in the Club of Rome’s Limits to Growth report in 1972, but now with a climate crisis twist. With the fiftieth anniversary of the Club of Rome report approaching, a number of scientists and economists gathered in early October to assess the current state of play of the zero-growth argument, its traction in the mainstream, and how best to call attention to the data supporting these positions. They looked at this question from various angles—physics, geology, biology, economy, ecology—and discussed the major obstacles to greater acceptance of more critical approaches to economic growth as well as ways of overcoming these obstacles. # ⚓ ‘Global_warming_is_not_a_problem’_says_Net_Zero_Watch_Board Member_Lord_Lawson_During_COP26⠀⇛ A board member of a new MP-backed ‘Net Zero Watch’ campaign group has said today that “global warming is not a problem”, defended burning fossil fuels, and said carbon dioxide’s “principal effect” is the growth of plants.   Net Zero Watch (NZW), which launched last month, presents itself as a reasonable campaign to scrutinise the impact and cost of the UK government’s net zero policies. The group has been quoted in the media and retweeted by prominent anti-net zero MPs Steve Baker and Craig Mackinlay.   # ⚓ Italy’s_First_Climate_Lawsuit_Seeks_Bold_Emissions_Target in_Effort_to_Protect_the_Planet_and_Human_Rights⠀⇛ Martina Comparelli’s pollen allergies have been getting worse. Sometimes it’s so bad that she has to spend whole afternoons in bed with her windows closed. As the planet heats up, allergy seasons are getting longer and the climate crisis is “violating” her “right to health” said Comparelli, a climate activist in her 20s with Fridays for Future Italy. Above all, though, Comparelli is afraid. She is afraid that when her parents are older, they will be subjected to the tremendous heat waves climate scientists say are already becoming more common. She is afraid for her own future. And her country isn’t doing anything to protect them. That is why Comparelli is suing.  # ⚓ Kick_Fossil_Fuel_Interests_Out_of_Climate_Policy_Process, Campaigners_Urge⠀⇛ World leaders must bring in stricter criteria to exclude fossil fuel companies from decision-making, campaigners have urged, as talks at the crucial COP26 summit enter their fifth day. A broad coalition of 138 green groups submitted an open letter in Glasgow on Wednesday, calling for decision-makers to address the “elephant in the room holding back global climate ambition: the fossil fuel industry and its lobbying”. The letter calls on leaders including UK Prime Minister Boris Johnson, COP26 President Alok Sharma and head of the UN Framework Convention on Climate Change (UNFCCC) Patricia Espinosa to revoke the sponsorship of two of the companies officially partnering the event – National Grid and Scottish energy provider SSE.  # ⚓ Just_Two_Countries_Mention_Need_to_Cut_Fossil_Fuel Production_at_COP26_‘Greenwashing’_Stands⠀⇛ GLASGOW, SCOTLAND – Only two of the 35 stalls lauding countries’ green credentials at the COP26 UN climate summit mention the need to cut fossil fuel production — the chief cause of the carbon emissions driving climate change.  The summit’s official “blue zone” includes large corporate-style pavilions run by some of the world’s leading producers of oil, gas, and coal, including the United States, Australia, Indonesia, Saudi Arabia, Russia, United Arab Emirates, Germany, and Qatar. They highlight the countries’ environmental efforts while failing to mention their massive and ongoing trade in fossil fuels. # ⚓ Activists_Push_for_World_Leaders_to_Join_Fossil_Fuel_Non- Proliferation_Treaty⠀⇛ # ⚓ ‘Enough_Is_Enough’:_Sunrise_Movement_Confronts_Manchin_on Climate_Policy_Outside_His_Yacht⠀⇛ Over a hundred climate activists confronted Sen. Joe Manchin outside his Washington, D.C. houseboat on Thursday to protest the West Virginia Democrat’s obstruction of climate policy in the Build Back Better Act. The activists from the youth climate group Sunrise Movement, some who have been participating in a hunger strike to demand a $3.5 trillion climate and jobs package, corralled around Manchin as he walked to his parking garage from his yacht to leave for a committee meeting. # ⚓ ‘The_Big_Tobacco_of_Our_Generation’:_Study_Shows_Huge_Scale of_Facebook_Climate_Lies⠀⇛ A new study published Thursday by a pair of watchdog groups shows Facebook is allowing climate misinformation to proliferate widely—and profiting from it—even as its newly rebranded parent company vows to curb such lies on the massive social media platform. “Facebook cannot and will not police themselves. We need real, independent, transparent outside oversight and regulation.” # ⚓ US_Lawmakers_Praised_for_Pushing_Sanctions_to_‘Crack_Down Climate-Destroying_Activities’⠀⇛ A quartet of congressional progressives was applauded by the nonprofit EarthRights International on Thursday for urging members of President Joe Biden’s Cabinet to use “targeted sanctions as a method of deterring reckless, climate-destroying behavior.” “Those who destroy the planet for profit, such as fossil fuel companies, need to face the consequences.” # § Energy⠀➾ # ⚓ Ruralist_Lament:_The_Ghost_(and)_the_Machine⠀⇛ While they burn gas or off-road diesel, their castings were forged many decades ago. Their life cycle contributions to today’s “carbon budget”are (I think) fairly modest——especially compared to the much larger machines manufactured today using fracked fossil energy products pulled out of the Earth’s crust at great financial/ environmental cost. Most every calorie of food energy in America has long come at the cost of  fossil energy, As Michael Pollan pointed out in his 2008 public “(Letter) To the Farmer-in-Chief,”  we now have. “…. transformed a system that in 1940 produced 2.3 calories of food energy for every calorie of fossil-fuel energy it used into one that now takes 10 calories of fossil-fuel to produce a single calorie of supermarket food. Put another way, when we eat from the industrial-food system, we are eating oil and spewing greenhouse gasses.” # ⚓ Shell_CEO:_We_Need_to_Keep_Extracting_Oil_to_Stop Extracting_Oil⠀⇛ Declaring that “cash comes from our legacy business,” the CEO of Royal Dutch Shell has asserted that continuing the company’s oil operations is necessary to help it transition away from non-oil energy operations. Ben van Beurden made the remarks in an interview with the BBC published online Thursday. # ⚓ Energy_Ministers_To_Mingle_With_CEOs_of_High-Carbon Companies_at_COP26_Business_Dinner⠀⇛ UK energy ministers attending the COP26 climate summit will tonight socialise with the CEOs of highly-polluting companies, including HSBC and Heathrow Airport. Business secretary Kwasi Kwarteng and Scotland secretary Alister Jack are among the 600 expected attendees at the Confederation of Business Industry (CBI) event in Glasgow, Politico reported earlier today. # ⚓ Experts_Sound_Alarm_as_Coal_and_Gas_Surge_Pushes Emissions_Close_to_Pre-Pandemic_Levels⠀⇛ After falling in 2020 due to coronavirus- related shutdowns, global carbon dioxide emissions are on pace to nearly reach pre- pandemic levels this year as powerful nations—including the United States—continue to burn fossil fuels at a dangerous clip. “To stop further global warming, global CO2 emissions must stop or reach net-zero.” # ⚓ ‘Welcome_Progress’:_20+_Nations_Vow_to_End_Funding for_Overseas_Fossil_Fuel_Projects⠀⇛ More than 20 countries across the globe—including the U.S., Canada, Finland, Portugal, and Ethiopia—vowed Thursday to cut off public financing for international fossil fuel projects by the end of next year, a pledge climate campaigners hailed as a positive step that must be accompanied by action. “All governments need to urgently end all support for fossil fuels and ensure a just transition.” # ⚓ Court_Suspends_‘Copyright_Troll’_Lawyer_From Practicing_Law_in_New_York⠀⇛ Due to repeated misconduct, copyright lawyer Richard Liebowitz is suspended from practicing law in the State of New York, effective immediately. The Appellate Division of the New York Supreme Court took this drastic decision following a similar order from the Southern District of New York last year, which has since spilled over to other states too. # ⚓ Police_Arrest_Six_in_Connection_With_Private_Torrent Sites_&_Seedboxes⠀⇛ Following criminal referrals by anti-piracy group Rights Alliance, authorities in Denmark have arrested six men believed to be “ringleaders” or central staff at torrent sites including DanishBytes and ShareUniversity. Police have seized computers and other IT equipment plus money claimed to be profits from the supply of seedboxes. # ⚓ How_a_Fossil_Fuel_Non-Proliferation_Treaty_Can_Guide a_Global_Just_Transition_&_Emission_Cuts⠀⇛ We speak with Harjeet Singh, senior adviser with the Climate Action Network, who is at the U.N. climate summit in Glasgow. Activists like Singh are pressuring world leaders to join the Fossil Fuel Non-Proliferation Treaty, which would supplement the Paris Agreement by directly targeting the fossil fuel industry and outlining clear actions that every country could take to drastically decrease carbon emissions. “This treaty talks about ending fossil fuel expansion, phasing out, and also just transition,” says Singh. He also speaks about his home country of India, which has only recently become one of the world’s largest emitters of greenhouse gases and has fewer resources to adapt while “rich countries have been polluting for more than 100 years.” # ⚓ Meet_the_Climate_Lawyer_Who_Helped_Write_2015_Paris Agreement_&_Superglued_Herself_at_Shell’s_U.K._HQ⠀⇛ We speak to Farhana Yamin, one of the most prominent climate lawyers in Britain, who has been deeply involved in international climate negotiations for decades, including the landmark 2015 Paris Agreement, and has also engaged in direct action to effect change. Yamin is currently working with the Climate Vulnerable Forum, a group that represents 48 of the countries most threatened by the climate crisis, at the U.N. climate summit in Glasgow. We last spoke with Farhana in 2019 after she was arrested for supergluing her hands to the ground outside Shell’s headquarters in London as part of an Extinction Rebellion action. She applauds the demonstrators outside the conference who are bringing political pressure on those inside. She says the net zero emissions goal that many global leaders are discussing “has to have emissions that are real, and those emissions cannot be bought at the expense of vulnerable people and countries.” # ⚓ 100+_Peace,_Green_Groups_Back_Barbara_Lee’s Resolution_to_Cut_Pentagon’s_Climate_Impact⠀⇛ More than 100 peace and environmental groups are supporting a resolution issued Wednesday by U.S. Congresswoman Barbara Lee demanding that the U.S. military account for its carbon impact, and establish targets for reducing its emissions in line with the Paris climate agreement. “The climate crisis is past the point where the U.S. can just take symbolic action, nor can we accept military greenwashing.” # ⚓ If_Fighting_Climate_Crisis_Is_the_Goal,_Critics_Say COP26_Coal_Reduction_Deal_‘Falls_Spectacularly_Short’⠀⇛ COP26 officials on Thursday are heralding developments they say signal that “the end of coal is in sight”—but advocates for strong climate action suggest holding the applause. “An agreement that only tackles coal doesn’t even solve half the problem.” o § Finance⠀➾ # ⚓ Progressives_to_Biden:_If_You_Want_to_Be_Popular,_Take_On Corporate_Greed⠀⇛ Following Terry McAuliffe’s Tuesday night loss in Virginia’s gubernatorial election and amid the White House’s ongoing failure to enact redistributive legislation due to obstruction from Republicans and right-wing Democrats in Congress, progressives are urging President Joe Biden to fully embrace and use his executive authority to challenge corporate power, which they say might give people a reason to vote for his party in next year’s midterms. “If… Democrats refuse to fight for the people, the people will seek fighters elsewhere.” # ⚓ Opinion_|_A_World_Without_Money⠀⇛ And climate change begins . . . # ⚓ American_Tax_Policy_in_the_Age_of_Trillionaires⠀⇛ # ⚓ With_Only_23_Percent_of_Rental_Aid_Distributed,_Warren_and Bush_Demand_Answers⠀⇛ # ⚓ Opinion_|_The_United_States_of_Tax_Havens⠀⇛ # ⚓ For_Migrant_Families,_COVID-19_Made_Precarious_Housing_Much Worse⠀⇛ As the national lockdown went into effect in March 2020, Susana, a Latina woman in her early 60s, was living alone on the Northside of Minneapolis. She had been getting by as a childcare provider for an affluent family. But when her employer began working from home, that source of income became impromptu at best—and, more importantly, unsustainable. Susana’s decade-long source of income came to a close.  With living expenses rising and few job opportunities, Susana, her two adult daughters, and four grandchildren doubled up in a three-bedroom apartment to cut costs. A new routine developed: Susana’s daughters would go to work, regardless of COVID surges, and she would stay with the grandkids while they tried to make the most of online schooling.  # ⚓ How_These_Ultrawealthy_Politicians_Avoided_Paying_Taxes⠀⇛ As a member of Congress, Jared Polis was one of the loudest Democrats demanding President Donald Trump release his tax returns. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ “We’re_Going_to_Win”:_Charles_Booker_Officially_Files Campaign_to_Oust_Rand_Paul⠀⇛ # ⚓ Opinion_|_No_Time_to_Lose:_Why_Democrats_Should_Include Voting_Rights_In_Their_Build_Back_Better_Compromise⠀⇛ It seems like “last minute” negotiations about President Biden’s “Build Back Better” legislative agenda have been dragging on for months. Even now, after Biden outlined his “bottom line” before heading for Rome, disagreements persist, about details and about the timing of a vote. Each time it appears that a common understanding has been reached, Joe Manchin recoils. # ⚓ Corporate_News_Conveniently_Piles_Blame_for_Virginia_on Progressives⠀⇛ # ⚓ Opinion_|_Is_There_a_Republican_Alive_Who_Still_Believes_in Democracy?⠀⇛ Investigative accounts of the Trump administration, like the recent Washington Post feature on the January 6 insurrection, routinely write about three kinds of conservatives. # ⚓ Schumer_Suggests_Filibuster_Reform_After_GOP_Blocks_John Lewis_Voting_Rights_Act⠀⇛ # ⚓ Kristof’s_Moralistic_Journalism_Was_Often_Full_of_Holes⠀⇛ New York Times columnist and two-time Pulitzer Prize–winner Nicholas Kristof has ended a four- decade career of globe-trotting and covering poverty, war and strife. He is choosing to return to his native Oregon, where he grew up on a farm, with an eye toward running for governor as a Democrat (New York Times, 10/14/21). o § Censorship/Free Speech⠀➾ # ⚓ Content_Moderation_Case_Study:_Facebook_Struggles_To Correctly_Moderate_The_Word_‘Hoe’_(2021)⠀⇛ Summary: One of the many challenges with content moderation is the flexibility of language. When applying blocklists — a list of prohibited terms considered not appropriate for the platform — moderators need to consider innocuous uses of words that, when removed from their context, appear to be violations of the platform’s terms of use. # ⚓ Throwing_gas_on_the_fire_of_Iranian_internet_suppression⠀⇛ In reality, the bill’s goal is to increase state control over cyberspace by further localizing services and platforms that Iranian users rely on. It would allow the Iranian government to place bandwidth restrictions on any international services that do not comply with authorities’ demands (namely, to localize their data in Iran). By making it even harder for ordinary Iranians to use common international messaging apps, social media platforms, and other communication tools, lawmakers hope to drive users onto state-controlled Iranian alternatives like local cloud services and messaging apps, thus, making future shutdowns of communication even easier. The bill would also place full control of the internet gateway into the hands of the General Staff of the Armed Forces–Iran’s version of the Joint Chiefs of Staff—turning Iranian cyberspace into an extension of the police state. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ WikiLikes:_Writers_Association_Honors_Julian_Assange_And Calls_For_His_Release⠀⇛ “Assange has been in solitary confinement in London’s maximum security prison in Belmarsh since April 2019, after applying for asylum at the Ecuadorian embassy in London in 2012 and living there as a political refugee for almost seven years,” the German PEN Centre said. # ⚓ WikiLeaks:_To_obtain_the_extradition_of_Julian_Assange,_the United_States_seeks_to_reassure_his_fate⠀⇛ At a hearing scheduled until Thursday, the United States hopes to convince the High Court of London to overturn the decision rendered last January by Vanessa Baraitser. The magistrate had rejected the American request for extradition, putting forward a risk of suicide. U.S. government attorney James Lewis insisted on assurances from Washington that Julian Assange would not be subject to special measures or be held in the dreaded ADX super- security prison in Florence, Colo. nicknamed the “Alcatraz of the Rockies”. o § Civil Rights/Policing⠀➾ # ⚓ Opinion_|_How_I_Triggered_Bill_Maher_by_Writing_About_White Supremacy_and_Standardized_Tests⠀⇛ Bill Maher is mad at me. # ⚓ Culture_Wars:_“The_Great_Male_Renunciation”⠀⇛ The issue posed a critical question: “Freed from the binary of boy and girl, gender identity is a shifting landscape. Can science help us navigate?” Provocatively, a number of articles profiled male gender identity in the U.S., including a trans boy, a gun-toting youth and a father raising two newborns. These stories suggest the range of maleness beginning to reshape masculine identity in a traditionally patriarchal society. # ⚓ Democrats’_Paid_Family_Leave_Plan_‘Keeps_Getting_Worse,’ Policy_Expert_Warns⠀⇛ “The Democrats modified the eligibility rule to ensure that the lowest earners in the workforce cannot claim benefits from the program.” # ⚓ Cleo_Smith_and_the_Lost_Child_Syndrome⠀⇛ For eighteen days, four-year old Cleo Smith could not be found.  She had gone missing from the Quobba Blowholes Shacks campsite north of Carnarvon in Western Australia, “last seen,” according to a notice, “at 1.30 am on 16thOctober 2021”.  The Western Australian government had promised a $1 million reward for information on her disappearance. There was a feast of coverage.  Google’s search engine was cluttered (the latest search reveals some 85.5 million results).  Bounty hunters, melting at the prospect of a reward, moved in.  There were stretched claims that 65,000 “average Aussies” were deployed in the search effort.  That number was taken from the Bring Cleo Smith HomeFacebook group, established to drum up publicity for the cause.  In the social media age, such voyeuristic engagement can count as physical participation.  The administrators of the group were keen that only acceptable members join: anyone questioning holes in the account, inconsistencies and motives (the Daily Mail charmingly called them “liars and trouble-makers”) were blocked. # ⚓ The_Confederacy_Votes_for_A_White_Supremacist—Is_That News?⠀⇛ It’s not the end of democracy. That ended years ago. Like George Bush’s hanging chad victory in 2000 and Donald Trump’s electoral but not popular vote win in 2016, it’s just another nail in the coffin. Or like Joe Biden’s win in 2020, where the corporate leadership of the Democratic Party twisted arms, promised paydays to politicians and otherwise forced the left-leaning primary candidates into a line behind Joe. Just like it is doing now in Congress as it morphs a bill designed to help working people into one that will mostly help the corporations that give most people in Congress their true payday. Columnists fret, progressives fret, even leftists who focus on electoral politics fret. How can we stop the reactionaries from taking over everything? How can we stop the US fascists—the Trumpists and their allies—from total victory? While I don’t have the answer to that, I do know that it’s not by trying to be more like them. Fascism is a real possibility in the United States. It always has been. Wall Street knows this better than most liberals do. Wall Street would ultimately have no problem with a fascist regime in DC. Like German capital in the 1930s, US capital understands that an authoritarian state run for the benefit of profiteers is a great way to make money. The fact that so many of the Democrats in power are part of the same economy that would easily lie with the fascists compromises their opposition. They put their bank accounts and their potential for cashing in ahead of their commitment to the people who elected them and the democracy they claim to live in. Their party cannot overcome the fascists as long as it serves the same masters. # ⚓ ‘Outrageous’:_Nearly_All-White_Jury_Chosen_for_Ahmaud Arbery_Murder_Trial⠀⇛ Relatives of Ahmaud Arbery, their attorneys, and racial justice advocates expressed shock and indignation Thursday following the selection of a nearly all-white jury—even after the presiding judge accused the defense of “intentional discrimination”—in the trial of three men accused of murdering the unarmed Black jogger in Glynn County, Georgia last year. “Is the KKK serving as jury consultants in the Ahmaud Arbery murder trial?” # ⚓ Gun_Rights_at_the_Supreme_Court⠀⇛ The crux of the issue before the court is captured by a debate that Thomas Jefferson had with himself at the time of the founding. When Jefferson was drafting a proposed constitution for his home state of Virginia in June 1776, he suggested a clause that read “No freeman shall ever be debarred the use of arms.” # ⚓ “There_Should_Be_No_Statute_of_Limitations_on_Stolen Land”⠀⇛ On September 30, the California legislature passed Senate Bill 796, which made it possible for a government entity to return property that had been unjustly taken from Black property owners. At issue was a former Black-owned resort in Manhattan Beach in Los Angeles County. In 1912, Black entrepreneurs Charles and Willa Bruce opened Bruce’s Beach on two previously undeveloped waterfront lots. Black Americans from California as well as around the country soon flocked to the resort, because it was one of the few beaches in the United States that Black people could legally patronize. Not surprisingly, the white Manhattan Beach community resented the success of Bruce’s Beach. In 1924, the City used eminent domain to force Charles and Willa Bruce and other nearby Black property to sell their beachfront land for a fraction of its value on the pretense that it was needed for a public park. # ⚓ The_Working_Class_Is_on_Strike⠀⇛ Across the country we are witnessing a historic strike wave, with over 22,000 US union members on strike right now. From our BCTGM Local 374G right here in Lancaster, Pa., on strike against the greed of Kellogg’s, to the 10,000 UAW workers at John Deere plants walking off the factory floor, the Ironworkers Regional Shop Local 851 on strike against Erie Strayer Company in northwestern Pennsylvania, or the 24,000 health care workers at Kaiser Permanente on the west coast who have overwhelmingly authorized a strike, workers have had enough, and they are taking action. # ⚓ Voters_Reject_Policing_Overhaul_in_Minneapolis_—_But Activists_Aren’t_Deterred⠀⇛ # ⚓ Abortion_Rights_‘In_Peril’_as_Ohio_GOP_Proposes_Total_Ban Modeled_on_Texas_Law⠀⇛ “The future of reproductive freedom is in peril.” “It is past time to pass the Women’s Health Protection Act and safeguard the legal right to abortion.” o § Internet Policy/Net Neutrality⠀➾ # ⚓ The_GOP_Is_Mad_Because_New_FCC_Appointment_Gigi_Sohn Actually_Defends_Broadband_Consumers⠀⇛ So after the longest (and completely unexplained) delay in FCC and NTIA history, last week the Biden administration finally got around to fully staffing the nation’s top telecom regulator. While the selection of fairly centrist Jessica Rosenworcel is expected to make it through the confirmation process, the same can’t be said of Gigi Sohn, a popular consumer advocate: o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ Moderna_Reports_‘Obscene’_Profits_From_Covid_Vaccine Funded_by_US_Taxpayers⠀⇛ After Moderna announced Thursday that it expects to deliver up to 300 million fewer coronavirus vaccine doses this year than previously anticipated despite posting large profits, public health campaigners ramped up pressure on President Joe Biden to force the U.S.-based pharmaceutical giant to share its recipe with the world. Despite the lower delivery forecast, Moderna said it still expects to rack up between $15- 18 billion in sales this year from its vaccine, which was largely funded by the U.S. government and developed in partnership with the National Institutes of Health (NIH). # § Software Patents⠀➾ # ⚓ Senators_Push_To_Study_“Unstable”_Patent_Law, While_Patent_Trolls_Cheer_Them_On⠀⇛ That would be Alice v. CLS Bank, the Supreme Court case that made it clear you can’t get a patent on an abstract idea just by adding in generic computer language. As we’ve told Congress before, the only ones experiencing “uncertainty” because of the Alice precedent are people and companies using weak software patents to demand money from others. For people who actually work with and on software, the Alice precedent has produced more certainty than ever before. Software innovation in the past seven years has been extraordinary. In the U.S., since Alice, the software industry is experiencing record profits and levels of employment. It certainly helps that more baseless patent lawsuits are being thrown out by courts. Truly innovative companies that build stuff—rather than rely on software patents—are thriving. # § Trademarks⠀➾ # ⚓ King.com_Opposes_‘Candy_Crunch’_Trademark Application…_From_Actual_Fruit_Varietal_Maker⠀⇛ King.com and its flagship product, mobile game Candy Crush, have made it onto our pages several times in the past. The most common reason for that is that King appears to enjoy playing trademark bully. Fighting with the folks behind hit game Banner Saga, not to mention picking fights with any other game maker that uses the word “candy” in their titles, have become the norm. Notably, some of the time, when there is a severe public backlash over its antics, King has also shown that it is capable of running away from such disputes. # ⚓ Facebook_Stole_Our_Name_and_Livelihood⠀⇛ For the last three months, Facebook lawyers have been hounding us to sell our name to them. We refused their offer on multiple bases. Namely, the low offer wouldn’t cover the costs of changing our name, and we insisted on knowing the client and intent, which they did not want to disclose. At least two law firms were involved: One in the USA that requested our trademark and domains (Kilpatrick, Townsend & Stockton), and the other in Europe aggressively contacting trying to get us to sell our domain registrations (Hogan Lovells). On October 20th, 2021, during a phone call with Facebook attorneys, we declined their low offer and maintained our requirements. At this point, we presumed it was Facebook and identified them on the call. The attorney representing Facebook declared they would respect our existing right and registration. On October 28th, 2021, Facebook decided to commit trademark infringement and call themselves “Meta”. # § Copyrights⠀➾ # ⚓ Internet_Archive_Would_Like_To_Know_What_The Association_Of_American_Publishers_Is_Hiding⠀⇛ Last year when a bunch of the biggest publishing houses sued the Internet Archive, in the midst of a pandemic, over their digital library program, I was a bit surprised that the announcement about the lawsuit came not from any of the publishers themselves directly, but rather from the Association of American Publishers (AAP), which is officially not a party in the lawsuit. That alone felt a bit… sketchy. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 8629 ➮ Generation completed at 02:41, i.e. 85 seconds to (re)generate ⟲