𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, April 06, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Thu 7 Apr 02:43:42 BST 2022 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2022/04/06/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmUPqrHFRdqGwBx8p2FCLNocU3kbtbteb4MYP57ypavVZB QmYvgv9zmTR2cBLvzpLNvAdsLo7iFFrWKJtu79JkWKTaRZ QmQNiNjPkABhPdvb5wDciDcpwJ6XNWjUQ6er2que9tMRLG QmYTPvdifyTSUV9CuZ5gpuZVC7pHshJvZhZ5niheQb2vzE QmZkDEgYNnUUQtaGwFdmteyZ5W9URPTE1mBXTnYquZ1fsa QmYDUiQWeiJU7WCsdP3xeCnELkr2V2Y9aQVLP4Z8n6efVs QmVmhebNywnTu6B8SmaNwvmpQrK5uGfyPHsAeM383HwKRx QmbtCnKikT7Qr6XTD9CLjRmtU6T3bRTyVqgASiAa1S3VBY QmZAPYrP7hETWM5jGJE8DCf5TgW4hE1qdRnTa5DiwUyy2i QmbZUGxupu36yFf72bxj4yCNrYAfeMKD4kf3TzSvrLqGkT QmfLQGVUofEiaUy33j7d2fYbyaYzAQJvw2ZWN6FztbPGc6 QmRLV4LzQCcbGE4VJXvT8zja7a8Ehkc6z5ALTVvwBbNgA7 QmVsotEYMNPE1dyPEZpAQ81YQFtSrxNxJNRyba9tPacbNr Qma6RvSv1ESUzDxUh7arsCZmoLXUaaSzK11P7gLczW1TKT QmcKAXzUKRMGp3YdQETGwbF7nS2hNTSzE84u2fb9P3tEDf QmYX7yxkzNPmi6NC3UHnNT3dqZ5FfkpgUrstQa95hPuvgt Qmc3h1ndVkwPrqkr5MwUe6DdA5S7dDpBHt61UHELCc9ewf QmTQQuAATQ3bx7aaCvuFeFsB7QuviwS2MdAiz9SW34tZeV QmanAKUKZgCyqdLttoPwN8UdE5JSFDVuH8vEncfJwtmqZ9 QmPA9baiheMyYvoirRpVxfonAnbATaW9SCDexu9yzCdwpR QmPP37AxLbRc3k9bp8hVPgJLkqdNKMo4NwWGy77QCsCNmS ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ EPO.org is a Fake News Site Which Promotes and Glorifies Illegal Behaviour and Unlawful Policies | Techrights ⦿ Just 2³² IPv4 Addresses for a Planet With Almost 2³³ People | Techrights ⦿ IRC Proceedings: Tuesday, April 05, 2022 | Techrights ⦿ Waiting for the Boat to Sink or Disembarking Early | Techrights ⦿ [Meme] It’s All Connected (and Wired) | Techrights ⦿ Thoughts on Quitting Social Control Media, One Month Later... | Techrights ⦿ Musk’s Bubble: Twitter Notifications Turned Into SPAM and Recommendations (to Drive Up ’Engagement’ by Adding Noise) | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/04/06/epo-org-illegal-content/#comments http://techrights.org/2022/04/06/ipv4-limits/#comments http://techrights.org/2022/04/06/irc-log-050422/#comments http://techrights.org/2022/04/06/no-free-lunch/#comments http://techrights.org/2022/04/06/social-control-media-and-apps/#comments http://techrights.org/2022/04/06/social-control-media-is-junk/#comments http://techrights.org/2022/04/06/twitter-is-spam/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/04/06/linux-mint-21-is-named/#comments http://techrights.org/2022/04/06/nutyx-22-04-1/#comments http://techrights.org/2022/04/06/snap-to-flatpak-bridge/#comments ䷩ 𝚕𝚒𝚗𝚎 67 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/06/epo-org-illegal-content/#comments Gemini version at gemini://gemini.techrights.org/2022/04/06/epo-org-illegal-content/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ EPO.org_is_a_Fake_News_Site_Which_Promotes_and_Glorifies_Illegal_Behaviour and_Unlawful_Policies⠀✐ Posted in Europe, Patents at 12:23 pm by Dr. Roy Schestowitz Video_download_link | md5sum aac067cc5f166ca7ae74d84a4b61780f EPO Management Legitimising Crimes? Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/epo-lies-and-hogwash.webm Summary: EPO.org — the official Web site of Europe’s second-largest institution — has become an insanely dishonest propaganda outlet which incites to break the law and violate constitutions; it’s not forgivable that other European authorities are tolerating this TODAY the EPO‘s management issued several more lies. It’s important to always correct the lies and rebut false claims. The moment you no longer bother the liars can win, as they can repeat the same lies over and over again, unchallenged. To an oursider and bypasser/observer it might even seem like the lies are “truth”; if they’re false, after all, why isn’t anyone saying so? Fighting back against well-connected liars such as Benoît_Battistelli and António_Campinos can be mentally exhausting and demoralising. Staff representatives have done this for years and they must persist. It’s the only way to get things done; persistence and patience are the only way because charlatans and liars rely on the other side surrendering or giving up due to resources running out. It’s a political modus operandi. “We invite EPO staff (such as examiners) to help oppose the liars. Their agenda is very ruinous to all of us.”This past weekend we finished a long series focusing on the failure of the media, which is very much complicit in all this. When it comes to patent news, European press is like Chinese state media. It never wants to even touch EPO scandals and instead it gets paid to lie, as per the “official” lies from EPO management, as told hours ago [1, 2] (warning: epo.org link). We intend to issue rebuttals more frequently than before. More posts, shorter videos. There might be another video coming later today. Compensating for such utter lies by endless repetition means that quality of lies was abandoned in favour of sheer quanitity. But lying over and over again (like a thousand times about the UPC) does not make a falsehood suddenly “true”. We invite EPO staff (such as examiners) to help oppose the liars. Their agenda is very ruinous to all of us. When I started writing about patents about 20 years ago I focused on technical aspects. In the EPO, as the EPO’s management repeatedly demonstrates, technicalities don’t matter anymore. It’s all about revenue maximisation and pedantic examiners are a barrier to it; the very purpose of the EPC was to prevent such a situation and at the moment it seems like the EPO’s response isn’t an attempt to become compliant with the law but to change the law (they’ve said this shamelessly in their own site, EPO.org) while vigorously silencing staff and censoring publications. █ ䷩ 𝚕𝚒𝚗𝚎 145 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/06/ipv4-limits/#comments Gemini version at gemini://gemini.techrights.org/2022/04/06/ipv4-limits/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Just_2³²_IPv4_Addresses_for_a_Planet_With_Almost_2³³_People⠀✐ Posted in Free/Libre_Software at 2:38 am by Dr. Roy Schestowitz Video_download_link https://media.libreplanet.org/mgoblin_media/media_entries/2617/jupiter-sunday- 1525.webm Summary: This talk was uploaded eight_days_ago. “This talk is about the IPv4 Unicast Extensions Project, which is proposing software and standards changes to eventually make reserved addresses usable. Some of our changes have been accepted in systems, including GNU/Linux and FreeBSD. This presentation will describe what has been done and what still needs to happen.” Licence: CC_BY_4.0 ䷩ 𝚕𝚒𝚗𝚎 182 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/06/irc-log-050422/#comments Gemini version at gemini://gemini.techrights.org/2022/04/06/irc-log-050422/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Tuesday,_April_05,_2022⠀✐ Posted in IRC_Logs at 2:31 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-050422.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-050422.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-050422.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-050422.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  Qmd8evj8h7nePdTRHYtDM6D4yMFbzffiuooraRFMQbUCTW #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmfFT77hZekp8z1Dmk5kFLydDYStxwiaEcRGg1Qh6WdmfG (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  QmVvhVwwQEMfJyZVdpJ5CCQmLVvTDaGaiEw6uUDszDc8mD social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmcGFdrbYEBwce7UsnwMDkzUGnwuaFoShqmYeyAXwosCgV social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmeGJWaEZSSu5MsZMMEv1qoJ4J5iisWawar9oqgmbYm3Xv #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmSZ8Uc6qTnhzGPeSf6tDu7vJyqhg6sjxnoocJ2tSMnf5p (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmRqJUcWCYy1dC78958Y2jfyR7t6ZtuicjcQiDfgbeTF1m #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmdmDC5cGVXj39nLTZ7LYfyr4NengxJSUZqEVDq7ZQAbqV (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmPP37AxLbRc3k9bp8hVPgJLkqdNKMo4NwWGy77QCsCNmS ䷩ 𝚕𝚒𝚗𝚎 309 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/06/no-free-lunch/#comments Gemini version at gemini://gemini.techrights.org/2022/04/06/no-free-lunch/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Waiting_for_the_Boat_to_Sink_or_Disembarking_Early⠀✐ Posted in Deception at 4:12 am by Dr. Roy Schestowitz Video_download_link | md5sum 6d898a5792a43fdbb981d418c7cc445e Self-Host or Perish Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/the-bubble-is-busting.webm Summary: The ‘free’ platforms one can sign up for online (GitHub, Twitter, YouTube and so on) aren’t free at all; their true cost is becoming more apparent over time THIS MORNING we published_a_few_rants_about_social_control_media, with an example_specific_to_Twitter. The bubble_is_bursting and oligarchs step in to pick up the pieces. “They just try to earn as much money as possible on their way out.”I personally think people need to distance themselves from centralised platforms as soon as possible. The sooner, the better. Derek Taylor, who knows Google’s YouTube very well, has just produced_a_video_that_explains_what_'free'_video_hosting_turned into. I personally can speak about a dozen or so social control media platforms; they’re all a waste of time and they get worse over time. They won’t last. They just try to earn as much money as possible on their way out. █ ䷩ 𝚕𝚒𝚗𝚎 356 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/06/social-control-media-and-apps/#comments Gemini version at gemini://gemini.techrights.org/2022/04/06/social-control-media-and-apps/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_It’s_All_Connected_(and_Wired)⠀✐ Posted in Deception at 11:15 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Social_control_media,_Apps,_Intelligence_agencies⦈_ Social control media and the “apps” it imposes (typically on so-called ‘phones’) are part of an extensive package you don’t always see (not fully) Summary: A kind and gentle reminder is in order as “smart” things are better described as spy things; Social control media and ‘phones’ are no exception to this ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢔⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠻⡿⠁⠈⠁⠀⠀⠀⠈⣿⠿⢰⣿⣀⣾⣿⣿⣿⣿⣿⣿⣿⣶⡰⢠⣤⣿⣦⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣄⣠⠌⠁⠄⢀⡀⠀⠀⠀⠀⠀⠭⠄⠠⣴⣠⣠⡾⠷⣶⢀⣀⢠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠸⠌⠀⠀⠀⠀⠒⠨⠀⠀⣀⠀⠂⠈⠠⣾⠿⢻⡇⣠⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔ ⠀⠀⠀⠀⠀⠀⠀⢹⣄⡰⠀⠀⢀⠀⠈⠀⢀⠠⢂⠁⢀⠀⢀⣸⠀⠀⠂⠀⠀⡼⠩⠍⠱⣗⠀⠐⢬⡏⢸⣿⣃⢐⣉⠀⠁⠠⣶⣿⣷⠴⠶⠷⠿⠶⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⡆⠸⡊⠀⠀⠀⣀⣀⣴⣎⣁⠀⠀⡀⠜⢀⡈⠋⢀⠀⢤⢄⠀⠀⠘⠂⠀⠁⠩⡦⠌⠁⢿⠧⠽⠀⢈⣤⣄⡀⠿⣋⣤⣶⣶⣦⡀⠀⠀⠀⠀⠉⢻⣿⣿⡿⢟⣯⣭⡻⣶⢾⣿⣿⠭⣟⢻⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⠁⠀⢀⣠⣶⠿⠿⠻⣿⣿⣿⣿⣿⣷⣤⡷⠀⠲⡟⠁⠘⠹⠀⠀⠀⢀⡄⢀⣤⡄⠀⠀⠉⠀⠀⡀⠀⠭⠘⠁⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⣿⣗⣿⣬⣭⡅⣿⠙⣓⢿⢯⣟⢺⣿⣿⣿⣿⣿ ⠀⢄⠀⣀⢤⣴⣑⢤⡞⠉⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣧⡀⡄⠀⢤⠀⠉⠀⠀⠈⠁⠈⠎⢀⠀⠀⠀⠀⠐⠋⣠⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣴⣄⣸⢣⣿⣤⣿⢸⣷⣹⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣸⠗⣻⣇⣾⡇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⠿⠀⠀⠀⣀⡄⠀⠀⠀⠈⠁⠩⠀⠀⠂⢸⡟⠀⡾⠿⢾⣿⣿⣟⣛⣛⡻⡇⠀⠀⠀⠀⠀⠀⠈⣿⣩⣽⣷⣾⡿⢿⣿⣷⢶⣿⣿⣿⣿⣿⣿⣿ ⠰⢰⣁⠘⠄⠁⠘⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠣⠄⠀⠀⣹⣿⣶⣆⣛⡡⢤⠀⠀⠀⠈⠁⠁⣼⣷⣶⣾⣿⣿⣿⡟⠛⠛⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⠀⠀⣀⠠⣀⡿⢘⢿⣿⣿⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠘⣾⣿⣿⣿⣿⣷⣻⣿⣇⢀⣴⣦⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⠿⣾⣝⣛⢻⢿⣿⣿⣿⣿⣿⣿⡏ ⠀⢸⠒⠉⢀⠈⠁⡇⠘⠋⣿⣷⣦⣄⣠⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣟⡿⠝⠋⠉⡭⣾⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠑⠈⠦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⠀⢠⣿⣟⢿⢸⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣇⡄⣰⣿⣿⠿⣿⣿⣷⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟ ⢀⣄⠀⠸⣿⣿⠁⠀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡄⠈⡿⣿⣿⣿⣿⡏⢹⣿⢟⣭⣭⡿⢭⣿⣏⡀⢠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⠷⣆⠀⠈⣋⢀⣰⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠘⣿⣿⣿⣿⡈⢳⣿⣫⣿⣧⣼⣿⣿⣿⣿⢛⣾⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣯⠀⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⡿⠟⠁⢀⣧⠀⢨⣿⣿⣿⣧⣾⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⡿⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⣸⣿⠀⠘⠚⢻⣿⣿⣿⠈⠛⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠸⡿⢿⣿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢻⣇⠀⠀⠈⢻⣿⣿⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿ ⣿⠇⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠘⢻⡳⢦⣤⠴⣿⣿⡇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⢸⠗⠀⣰⠃⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠈⠲⣶⣤⣤⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠿⣛⠛⠛⠛⠛⢻⣿⣿⣿⣿ ⣿⣷⡄⠀⠀⠀⠀⣼⡀⢘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠋⠁⠀⠀⢀⣜⣿⣿⣿⣿ ⣿⣿⣷⣶⣦⠀⣾⣿⣿⣤⡀⣶⣶⣶⣤⡀⣤⣶⣶⣤⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠛ ⣿⣿⣿⣿⣿⡿⣿⣿⣟⣿⡇⣿⣿⢹⣿⡇⣿⣿⡸⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠃⣠⡄⠀⣀⣴⣿⣿⠏⠹⠖⠛⠒ ⣿⣿⣿⣿⣿⡇⣿⣿⡿⠿⠃⣿⣿⠿⠿⠃⣙⡻⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠋⣽⣿⡿⠃⠀⠀⠀⢠⣤ ⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿⣸⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠄⠀⠀⠀⠀⠸⣿ ⣿⣿⣿⣿⡿⠉⠉⠉⠁⠀⣀⠉⠉⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠈⣼⣿⣿⣿⡿⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄⢀⣽⠀⠀⠈⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿ ⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⡿⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠟⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣽⣿⡿⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⠋⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣦⣄⡀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⢠⠠⠀⣀⠀⠄⠀⢠⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠚⠒⢚⣒⣒⣒⣒⣒⣲⣼⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢔⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠻⣿⠉⠀⠁⠀⠀⠀⠀⣿⡿⢰⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣐⢀⣦⣿⣷⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠀⢀⣄⣠⠌⠁⠄⢀⡄⠀⠀⠀⠀⠀⠭⠆⢠⣶⣢⣠⡾⠿⣾⢀⣀⢠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣴⣄⠸⠎⠀⠀⠀⠀⡒⠬⠄⠀⣄⠀⠂⠀⠠⢾⡟⢻⡇⣠⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖ ⠀⠀⠀⠀⠀⠀⠀⢹⣦⡰⠀⠀⢀⠀⠈⠀⣀⠄⠂⠁⢀⠀⢀⣸⠀⠠⠃⠀⠀⡼⠡⠌⠱⡗⢄⠉⢬⡇⢰⣻⣳⢀⣉⡀⠁⠠⣶⣿⣿⡶⠷⠾⠿⢷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠂⠀⠀⠀⢠⡆⠸⠎⠀⠀⠀⣀⣀⣴⣎⣀⠀⠀⡀⠜⢠⡈⠋⢠⠀⢤⢤⠀⠀⠘⠂⠀⠑⠉⠧⠌⠁⢸⡿⠽⠈⠈⣤⣄⡀⠿⢋⣡⣴⣾⣿⣄⠀⠀⠀⠀⠉⢻⣿⣿⣿⣟⣯⣭⡹⣶⢾⣿⣿⡿⣽⢻⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠁⠀⢘⣤⣶⠿⠿⠿⣿⣿⣿⣿⣿⣷⣤⡷⠂⠲⠟⠁⠘⠹⢀⠀⠀⢀⡄⢀⣤⡄⢀⠀⠉⠀⠀⣀⡄⠹⠘⠋⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⢿⣯⣭⡅⣿⢘⣿⣿⡿⣝⣿⣿⣿⣿⣿⣿ ⠀⢤⠀⣂⢦⣴⣑⢴⡟⠉⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡄⠀⣤⠀⠁⠀⠀⠈⠁⠀⡎⢁⡀⠀⠀⠀⠐⠋⣠⡤⠀⣼⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣿⢰⣆⣸⢧⣿⣭⣿⣿⣧⣽⡏⣿⣿⣿⣿⣿ ⠀⠀⢀⣼⠖⣻⢇⣾⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⡿⠀⠀⠀⣀⡄⠀⠀⢀⠈⠁⠩⠀⠀⠚⢸⣿⠁⡼⠻⢿⣿⣿⣿⣛⣛⣻⠿⠀⠀⠀⠀⠀⠀⠀⢹⣨⣽⣷⣿⣿⢿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿ ⠔⢰⡁⠘⠄⠁⠘⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠣⠄⠀⠀⣹⣿⣶⣖⣛⡥⢤⠀⠀⠀⠈⠅⠈⣰⣿⣿⣾⣿⣿⣿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⠀⢸⠀⢀⡠⢠⡀⡿⢘⢿⣿⣿⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠘⣾⣿⣿⣿⣿⣷⣻⣿⣧⣠⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣶⣍⣚⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⠒⠁⢀⠘⠁⡇⠘⠋⣿⣷⣦⣄⣠⣾⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⠀⠀⢰⢿⣿⣿⣿⡿⠝⠋⢉⡭⢾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡎⢹⢯⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠸⠀⢠⣿⣟⢿⢸⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣯⡆⣸⣿⣿⠿⣿⣿⣷⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣼⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⣄⠀⢸⣿⣿⠁⠀⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⡇⠈⡿⣿⣿⣿⣿⣏⢹⣿⢟⣯⣽⡿⢯⣿⣿⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⢷⣆⠀⠈⣋⠀⣰⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠸⢻⣿⣿⣿⡀⢳⣿⣫⣿⣧⣼⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣯⠀⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⡿⠁⢠⣷⠀⢸⣿⣿⣿⣷⣾⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠁⠀⠀⣼⣿⡀⠈⠛⢿⣿⣿⣿⡝⠟⠁⣀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠿⠿⠿⣿⣿⣿⣿⣿⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣇⠀⠀⠈⢻⣿⣿⠇⠀⠀⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿ ⣿⠀⠀⠀⠈⠻⢿⣿⣿⠋⠀⡀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡳⠦⣤⠴⣿⣿⣇⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿ ⠃⠀⠀⠀⠀⠀⠀⢿⠅⠀⣰⠃⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠈⠲⣶⣦⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⣛⡛⠛⠛⠛⠻⣿⣿⣿⣿ ⣷⡀⠀⠀⠀⠀⠀⣾⡀⢘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⠁⠀⠀⠀⣤⣿⣿⣿⣿ ⣿⣷⣶⣶⣦⢀⣾⣿⣿⣤⡀⣶⣶⣶⣤⡀⣤⣶⣶⣤⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⡿⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⡇⣿⣿⢹⣿⡇⣿⣿⡸⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⣠⣄⠀⣀⣤⣿⣿⠟⠙⢝⠛⠛ ⣿⣿⣿⣿⣿⡇⣿⣿⡿⠿⠃⣿⣿⠿⠿⠃⣙⡻⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢿⠟⠋⣹⣿⣿⠏⠀⠀⠀⣴⣶ ⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿⣸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡤⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⡿⠉⠉⠉⠁⠀⣀⠉⠉⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠉⣼⣿⣿⣿⣿⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠈⡆⠀⠀⠙⠁⠀⠀⠀⠀⢸⣿ ⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⡄⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠐⠏⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣜⢿⣿⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠤⠃⠀⠀⣿ ⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣦⣄⡀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⢠⡠⠀⣤⠄⠄⠀⢠⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠚⠒⠚⠓⣒⣒⣒⣒⣒⣚⣣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢜⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠘⠻⣿⠉⠀⠁⠀⠀⠀⠀⣿⡿⢳⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣾⣄⣂⣦⣼⣿⣿⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠆⠀⠀⠀⢀⣄⣰⠌⠁⠄⢠⡄⠀⠀⠀⠀⠀⢙⠁⢠⣶⣶⣢⡿⠿⣾⢀⣠⣠⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣴⣌⠸⡎⠀⠀⠀⣀⡒⠯⠄⠀⣄⠀⠂⠀⠠⢾⣟⢿⡇⣰⣤⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⡻⣆⡔⠀⠀⢀⠀⠈⠀⣀⠔⢊⠁⢠⠀⢀⣼⠀⠠⠃⠀⠀⡾⠡⠊⠱⡗⢄⠉⢬⡇⢸⣻⣳⢀⢍⡀⠁⠠⣶⣿⣿⣶⡷⢾⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⠂⠀⠀⠀⢰⡆⢸⠈⠀⠀⠀⣀⣀⣴⣪⡀⠀⠀⡠⠘⢠⡈⠃⢤⠀⢤⢦⠀⠀⠘⠃⠀⠑⠉⠷⠌⠑⢘⠿⠽⠈⠈⣤⣤⣀⠻⠟⣉⣴⣶⣿⣦⡀⠀⠀⠀⠙⠻⣿⣿⣿⣟⣯⣭⡝⣶⢾⣿⣿⡿⣽⣻⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠁⠀⢘⣤⣶⠿⠿⠿⣿⣿⣿⣿⣿⣷⣴⡷⠂⠲⠏⠁⠘⠹⢀⠀⠀⢀⡄⢀⣤⡄⢀⠀⠉⠀⠀⣀⡄⠹⠚⠋⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⢻⣯⣭⡅⣿⣬⣻⣛⡷⣽⡃⣿⣿⣿⣿⣿ ⠀⢄⠐⣀⢦⣶⣣⣴⡿⠉⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡄⠀⢤⠀⠁⠀⠀⠈⠁⠈⡎⢀⡀⣀⡀⠀⠐⠋⣠⣴⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢹⢰⣆⣸⢧⣼⣯⣽⣟⣧⣿⡇⣿⣿⣿⣿⣿ ⠀⠀⢀⣼⠖⣽⣆⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⡿⠀⠀⠀⣀⡄⠀⠀⢀⡈⠁⠩⠀⠀⠘⢸⣿⠇⣰⠛⠿⣿⣿⣿⣟⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣨⣽⣷⣿⣿⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿ ⠔⢸⡁⠘⠄⠁⠙⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠣⠄⠀⠀⣹⣿⣶⣖⣫⡥⢤⡀⠀⠀⠀⠅⠈⣰⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⠀⢸⠀⢀⡠⢠⡀⡿⢛⢿⣿⣿⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣧⣀⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⢶⣏⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⠚⠁⢀⠘⠁⡇⠙⠋⣿⣷⣤⣄⣠⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡀⠀⢰⢿⣿⣿⣿⣻⠝⠋⢉⡭⣾⣿⣿⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⢫⡷⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⠀⢠⣿⣟⢿⢹⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣯⡆⣼⣿⣿⠿⣿⣿⣷⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⣄⠀⢸⣿⣿⠁⠈⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇⠈⡿⣿⣿⣿⣿⣯⢹⣿⢿⣯⣽⡿⣯⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⢷⣆⠀⠈⣃⠀⢠⣿⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⡇⠈⡇⠸⢻⣿⣿⣿⡄⢳⣿⣫⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⡿⠃⢠⣿⠀⢸⣿⣿⣿⣷⣾⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠁⠀⠀⣾⣿⡀⠈⠛⢻⣿⣿⣿⡟⠟⠁⣴⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣇⠀⠀⠈⠻⣿⣿⡇⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⠋⠀⠉⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿ ⣿⡟⠛⠿⢿⣿⣿⣿⣿⠋⠁⡀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠘⢻⡻⠦⣤⠼⣿⣿⣇⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿ ⠿⠁⠀⠀⠀⠈⠛⢿⠻⠄⣰⠃⠀⠙⠛⠒⠀⠀⠀⠀⠀⠀⠀⠈⠲⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⢿⠿⠿⠛⠛⠟⣿⣿⣿⣿ ⣦⠀⠀⠀⠀⠀⠀⣸⡈⢐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿ ⣿⣷⣶⣶⣦⠀⣶⣿⣿⣥⡀⣶⣶⣶⣤⡀⣤⣶⣶⣤⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟ ⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⡇⣿⣿⢹⣿⡇⣿⣿⡸⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⣄⠠⢀⣤⣿⣿⡟⠙⣿⡿⠛ ⣿⣿⣿⣿⣿⡇⣿⣿⡿⠿⠃⣿⣿⠿⠿⠃⣙⡿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢿⡿⠛⢹⣿⣿⡟⠀⠀⠁⣿⣿ ⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿⣸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⢁⡠⠀⠀⠀⠀⢻⣿ ⣿⣿⣿⣿⣿⠉⠉⠉⠁⠀⡀⠉⠉⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠙⣼⣿⣿⣿⣿⠟⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⣦⠀⠀⠙⠁⠀⠀⠀⠀⠸⣿ ⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡧⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢿⣷⠀⠀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿ ⣿⡅⠀⠀⠀⠀⠀⠀⠀⠘⡏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣀⢿⣷⣿⡏⠀⠀⠀⢸⣷⠀⠀⠀⠀⢀⢠⠂⠀⠀⣿ ⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣤⣀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⢠⡠⠀⣤⠄⠄⠀⢠⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠒⠒⠚⠒⠒⠒⣒⣒⣒⣚⣃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢪⡄⠀⠀⠀⠒⠂⠀⠀⠀⣀⡈⠙⠿⠁⠀⠀⣀⢀⠀⠀⠿⣿⢻⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⣼⣶⣿⣿⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠆⠀⠀⠀⢠⢦⡴⠒⠀⠆⠠⢄⠀⠀⠀⠀⠀⢸⠂⠀⣺⣵⣥⠿⠛⢿⢀⣤⣲⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⡀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠄⠀⠀⠉⢀⠀⠀⠀⠀⡠⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⣶⣦⡸⡆⠀⠀⠀⣀⠘⣛⡀⠀⣤⠀⠁⠀⠠⢾⣿⢻⡏⢰⣶⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡿⣧⠂⠀⠀⡀⠀⠀⢀⡠⠒⠡⠀⢠⠀⢠⡼⠀⠸⠀⠀⠀⠞⢐⠂⠸⡯⣀⠈⣶⠁⢸⣿⣽⢠⢥⠄⠀⠐⣿⣿⣿⣿⣿⣻⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⠀⠿⡀⠀⠀⣀⣠⣤⣶⣥⣀⠀⢀⠄⠊⣠⠌⠁⣄⠀⢶⣂⠀⢀⡈⠁⠀⠈⠉⠷⠝⠀⣻⠟⠾⠀⠀⣶⣦⣄⠛⣿⢿⣻⣿⣿⣿⣯⡁⠙⠛⠛⠻⣿⣿⣿⣿⣯⣿⡟⢻⣟⣿⣿⣾⣿⡽⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠀⠀⣧⣴⠿⠿⠻⣿⣿⣿⣿⣿⣿⣧⣼⡟⣈⠻⠏⠀⠉⠙⣀⡀⠀⢠⠄⢀⣴⡤⢀⠀⠀⠀⠀⣀⠄⠒⠚⠛⠋⣡⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⢹⣧⣿⣧⢺⡇⣟⡛⣻⢮⣟⣿⣿⣿⣿⣿ ⠰⢆⠒⣔⢶⣾⡭⣾⠋⢁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⡆⠀⣦⠀⠀⠀⠀⠈⠀⠀⡏⢁⡄⣀⡀⠀⠀⠋⣠⣶⡆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⢸⢰⣆⣼⠏⠼⠷⠾⠇⣿⣬⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⣟⠊⡿⣰⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠀⠀⠀⣀⣄⠀⠀⢀⡀⠀⠰⠀⠀⢈⣸⣿⡟⢀⣟⠻⢿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢩⣽⣿⣿⣯⢿⣯⣽⡿⣿⣿⣿⣿⣿⣿⣿ ⠂⡾⠄⠘⠀⠀⢹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠧⢤⠀⠀⣼⣿⣿⣗⣭⡥⣤⡀⠀⠀⠀⠄⠘⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣇⠀⣀⠄⣒⣼⠟⡻⣿⣿⣧⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢙⣾⣿⣿⣿⣿⣿⣿⣿⣧⣠⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣈⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣯⣛⣻⡿⣿⣿⣿⣿⣿⣿⣿ ⠀⢱⠋⠀⡤⠉⣹⠀⠛⢹⣿⣷⣤⣀⣴⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣷⡀⠀⣶⣿⣿⣿⣿⣟⡛⠉⠩⠴⣺⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡋⠟⡽⣘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠸⠀⣼⣿⣝⠷⢇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣻⣿⣿⣷⣄⣀⠀⢹⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢤⠤⠀⢻⣿⡿⠀⢸⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢿⣿⣿⣿⣿⡏⢹⡿⣿⣽⣿⡿⢿⣽⣿⣿⣷⣾⣿⠟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⣿⣆⢀⠈⡇⠀⣼⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠙⣿⣿⣿⣿⡀⢱⣿⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⡀⠀⠻⠿⠿⠿⠿⠿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⢨⣿⣿⣿⡄⠀⣸⣿⣿⣿⣿⣿⣿⠁⡸⡇⠀⣿⣿⣿⣿⣧⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡛⠛⣿⣿⣿⣿⠟⠁⠠⣧⣇⠀⠑⠙⢿⣿⣿⣿⠹⠟⠁⢻⢿⣿⣿⣿⣿⠟⠛⠛⠛⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⣿⣿⡿⠟⠋⠀⠀⠀⠀⢏⣿⣆⠀⠀⠘⢿⣿⣿⠇⢀⣴⣾⣿⣾⣿⡿⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡳⢤⡤⠾⢿⣿⣇⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿ ⠃⠀⠉⠉⠛⢿⣿⣿⠀⢀⡼⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢻⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠈⣗⠁⡪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣆⣀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠋⠀⠀⠀⣠⣾⣿⣿⣿ ⣿⣠⣶⣶⣦⢀⣾⣿⣿⣤⡀⣶⣶⣶⣤⡀⣤⣶⣶⣤⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠘⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣿⣿⣟⣿⡇⣿⣿⢹⣿⡇⣿⣿⡹⠿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣠⠀⢤⣠⣾⣿⣿⠋⢻⣿⣯ ⣿⣿⣿⣿⣿⡇⣿⣿⡿⠿⠃⣿⣿⠿⠿⠃⣙⡿⣿⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠀⠀⠾⡿⠿⢻⣿⣿⣿⠃⠀⠘⣿⣿ ⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿⣸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠉⣀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⡏⠉⠉⠉⠁⠀⠀⠉⠉⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠉⣼⣿⣿⣿⣿⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢲⠀⠀⠙⠋⠀⠀⠀⠀⠰⣿ ⣿⣿⠿⠛⠀⠀⠀⠀⠀⢸⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠰⡸⣦⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣿⣿⣆⠑⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⡬⠁⠀⢿ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⢺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣗⡋⠁⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣦⣄⠀⠀⢀⣤⣶⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⢠⠠⠀⣤⠄⠄⠀⢠⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠒⠓⠚⠓⠒⠒⠒⠒⠒⠚⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡂⢀⠀⠀⠊⠁⠀⠀⠀⢠⡄⠈⠹⠃⠀⢀⣀⣀⡀⠀⠘⠟⠏⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣵⣾⣿⠿⢿⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠐⡲⡼⠋⠁⠂⠠⣦⡀⠀⠀⠀⠀⠀⠍⠀⣯⣿⣷⠞⠛⠛⣇⣤⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⣀⠤⠀⠀⠀⢠⠀⢀⠀⠀⠀⢠⡾⢧⡟⣃⠀⣀⡀⡀⠌⣛⣒⠀⢰⡄⠈⠀⠀⣚⣿⣍⣿⠰⣷⡷⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣟⢧⠃⠀⠀⠄⠀⠀⣀⠔⠊⠠⠀⢰⠀⢠⡾⠀⠘⠀⠀⠀⠞⢘⢁⠘⢖⣂⡀⡗⠀⢰⣽⣽⣄⢖⠖⠀⠀⢻⣿⣿⣿⣿⡉⠛⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⢸⠄⠻⡄⠀⢀⣠⣤⣤⣯⣴⣄⣀⣠⡔⠈⡴⠄⠀⣄⡀⢺⣳⠀⠀⠠⠁⠀⠈⠀⠛⠛⠀⢨⠟⠛⠃⠀⢲⠿⣶⡌⣛⡿⢿⣫⣿⣿⣿⡟⠻⠿⠿⢿⣿⣿⣿⣿⣽⢷⣶⣹⣿⢿⣿⣿⡿⣾⣻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣴⡟⡉⠙⠃⠀⠈⠈⡠⠀⠀⠀⣆⠠⢶⡦⠠⠀⠀⠀⠀⢠⡦⠀⠋⠙⠟⢋⣴⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⢻⣿⡏⠿⠶⣷⡔⣿⠿⣿⢻⣻⣮⣿⣿⣿⣿⣿ ⠐⠢⠨⣞⢷⣿⠕⣿⠉⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡆⠀⣲⠀⠀⠀⠀⠀⠀⠀⡇⢀⡄⣤⡄⠁⠀⠉⣤⣶⡿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⡇⣾⣤⠟⠰⣿⣶⣿⣸⠷⣽⣿⣿⣿⣿⣿ ⠀⢀⠤⣟⠉⡾⣴⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠂⠀⠀⢤⣆⡀⠀⢀⡄⠀⠀⠂⠀⠈⣰⢿⡿⢁⡞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣷⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⡯⠄⠐⠀⠀⢹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠷⢶⣀⠀⣸⢿⣿⣿⡩⡔⣲⣄⠀⠀⠀⠀⠈⢱⣿⣿⣷⣾⣿⣿⣿⣾⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡇⢀⡠⠆⣢⣼⢟⡿⣿⣿⡇⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣄⣶⣶⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣟⠻⣿⣝⣟⣻⣿⣿⣻⣿⣿⣿⣽ ⠀⡟⠁⠀⣤⣉⣸⠈⠛⢹⣿⣷⣦⣄⣴⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣷⡀⢰⣿⣛⣿⣿⣯⣿⡚⠉⠀⠴⢻⣿⣿⡏⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣕⠩⠛⠇⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣼⣿⣝⠧⣇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⣿⡆⣴⣿⣿⣻⣿⣿⣿⣦⡀⠀⢸⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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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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═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/06/social-control-media-is-junk/#comments Gemini version at gemini://gemini.techrights.org/2022/04/06/social-control-media-is-junk/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Thoughts_on_Quitting_Social_Control_Media,_One_Month_Later…⠀✐ Posted in Site_News at 12:14 am by Dr. Roy Schestowitz Speaking from personal experience, with and without it… 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Let's pose for a photo to improve our social status; I got no 'likes'⦈ Social control media is not (and was never) a substitute for real social life; it’s a mostly meaningless time drain Summary: Social control media is generally a waste of time; no president (or state leader) was ousted because of the number of “likes” (they’re not even a currency) and all Social Control Media Web sites are short-lived bubbles of disorganised (mis)information DEPENDING on what one deems “social [control] media”, I’ve probably been ‘on it’ since 2005 with Digg.com, where I was ranked 17th overall (nearly 200 promotions to the front page). As one LibrePlanet talk explained last month, one might consider USENET a “form” of “social [control] media”, but I’d not go that far because it’s more like E-mails and if newsgroups count as “social [control] media”, then “social [control] media” goes back to the early 1980s. Social control media — no matter if federated, or decentralised, or peer to peer, or “open source”, or free/libre — is generally a waste of time. Hard to maintain, distracting, and totally not worth it. People should set up blogs, then use RSS feeds to ‘federate’. Vastly better from a free speech point of view among many other aspects. Too much of people’s communications has been centralised this past decade and even E-mail has been centralised (many conflate E-mail with GMail). “Too much of people’s communications has been centralised this past decade and even E-mail has been centralised (many conflate E-mail with GMail).”A month ago I left all social control media. It wasn’t a staged exit and it was immediate, ‘cold turkey’. Looking back, I realise that I miss none of that. Moreover, I’ve since then seen two articles about people who did the same thing and had no regrets. We’ve mentioned their experiences in Daily Links. Remember that those things being centralised isn’t really their main problem (or the main downside). I used to think that it was, but over the years I’ve used about a dozen different social control media sites, most of them decentralised, and the main concern was uptime, including long-term commitment. Many sites just shut down with barely a prior warning or contingency. A lot of history was lost. “Spend not a moment longer on “social [control] media”; emancipate yourself from that.”If you care about the past and if you value your work, focus on self-hosting blogs, or Gemini capsules, or something along those lines (Gemini lowers the technical debt considerably). The future of the Internet and the future of the Web (I reckon it will last only another decade before it warps into something totally different; Chrome is the new Adobe Flash) will be shaped by those who thought ahead, exercising caution and foresight. The future of the Web isn’t Twitter or Facebook. “Apps” too are a passing fad. A lot of ‘free’ video hosting will shut down or become like television (broadcast conglomerates with advertising). Spend not a moment longer on “social [control] media”; emancipate yourself from that. Nobody in the future will cherish a “like” or a one-sentence “shitpost” (or shower thought). Nobody will care or even remember. █ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢤⣄⣀⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠀⠘⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣈⠉⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣽⡤⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣫⣾⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣟⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡯⣅⣄⠄⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠸⠀⢠⣿⣿⣿⣿⣿⣿⣋⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠰⡟⡯⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⢠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⣄⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⢸⠀⢸⣿⠿⠟⠛⠉⠉⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⠟⢁⣤⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢜⡸⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡸⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⡿⠻⠿⣿⣿⣿⣿⡿⠟⢁⣤⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⣛⠈⢼⣿⣿⣿⣿⣿⣿⣿⣿⠩⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣀⣀⣀⡀⠈⠛⠛⠓⠀⣼⣿⣿⣀⣤⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡂⢼⣿⣿⣿⣿⣿⣿⣿⣿⢰⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⡛⠫⡶⠲⢆⡠⢠⣿⣿⣿⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣼⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⢿⡿⢿⣶⡆⠘⣡⣾⡅⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠟⠷⠞⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡷⠂⠙⣿⣷⣦⡘⣿⣿⣿⣿⣿⣿⣿⣇ ⣿⢿⣿⣿⡿⣿⡖⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⣿⣾⣿⣭⣯⣿⢥⣾⣿⣿⡿⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠁⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣠⣴⣦⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣧⡟⣟⢣⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠹⣿⢟⣙⣁⣲⣶⣾⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⠉⠀⢰⢳⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⠛⠈⠻⡽⣿⣵⣧⣠⣮⣗⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⡍⣿⣿⣿⣿⣿⣿⣿ ⡇⠱⣂⠀⢰⣻⢿⢿⠀⡀⠻⡻⣿⣿⣿⣿⠄⠀⣹⣵⡿⠛⠉⠉⠉⠁⠛⠿⠿⣿⣻⡿⢻⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠈⠻⠿⠃⣹⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣦⠄⠓⣼⣿⣿⣻⠿⠂⠹⣿⣿⣿⣴⣖⣿⣿⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢳⠎⡘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟ ⣟⣏⠙⢿⣿⣘⣒⣸⠟⢁⣀⡤⠀⠈⠉⡉⢨⠃⠁⠉⠿⢰⣀⠀⢤⠦⠄⠀⠀⠀⠀⢻⠃⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡄⡀⢈⡨⠀⠆⠀⠀⠀⠀⠀⣮⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿ ⣧⡩⢇⣈⢺⠧⣿⠇⣴⣿⣿⡅⣠⣴⣀⢠⠃⠀⠀⠀⠀⠀⠀⠁⠸⠒⠆⠂⠀⠀⠀⢘⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡃⣉⣀⠉⠁⠸⡄⠀⠀⠀⠀⡿⠀⠾⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⡈⠙⠚⠘⠯⢸⢃⣾⣿⣿⣿⢰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣿⣿⣿⣿⢿⢀⠀⠀⠀⠀⢿⣿⣤⣼⣶⣶⣿⣄⢮⡳⣤⣷⣶⠄⠄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿ ⣀⣅⢸⠀⠂⢸⢸⠛⢿⣿⡇⢺⠏⡁⢀⡎⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⣿⣿⣿⣿⣸⢠⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⢸⣀⡐⢺⠀⠀⢸⣿⣇⣳⣭⡶⣿⣿⡄⡀⢠⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡇⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠛⠫⠻⠋⢡⣾⡄⠀⢸⣿⢹⣶⣿⣾⣿⣿⣷⣷⣼⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⣿⣿⣿⢹⡇⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣇⡄⣨⡴⠀⠘⡇⠀⠸⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⢠⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣿⣿⣿⢸⡇⡇⠀⡄⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣽⣿⣭⣿⣿⡟⣫⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣧⣽⠀⠀⠀⠀⡇⠀⠀⠁⠁⢻⣿⣿⣿⣿⣿⣿⠋⢰⣾⣾⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⢸⡅⣿⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡾⠟⢛⣏⣷⣼⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣿⣿⠹⣿⣿⡀⠸⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠇⣿⣼⡗⠰⠀⠀⠀⠀⣐⣲⣶⡿⢭⣭⣻⣷⣶⣭⡵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠁⣮⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⣠⣤⣄⣀⠀⠈⢿⣿⣿⣦⠜⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣱⣿⣷⡀⢳⢀⡤⣾⢶⣿⣭⠛⣿⣾⣿⣿⡿⣟⡷⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠘⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣾⣧⢣⣿⣷⢿⣿⣿⣭⣟⢻⣿⡟⣛⣛⠉⡉⡖⠔⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⣿⣿⣿⣿⣟⢿⡇⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢡⡿⠿⣿⡮⠻⠿⢟⣩⡜⢋⠇⣿⡇⠸⡇⡇⠦⠹⡄⠀⠀⡠⠊⠀⠀⢀⡆⠀⢰⢷⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣗⠁⢰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣫⣾⣟⣛⣷⣾⡇⣿⡇⢸⡗⠂⠄⠱⠃⢀⠊⠀⠀⠀⢀⡞⠁⠀⡸⣾⣿⣿⣿⣿⣿⣿ ⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿⣿⣷⠻⠚⢿⣿⡿⠛⠇⠿⡇⢸⡇⡇⠀⠄⢰⠀⠄⠖⠒⠊⠁⠀⣠⠶⠇⠿⠿⠿⠿⢿⣿⣿ ⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢏⣿⣿⣿⣿⡟⣩⣭⣅⠊⢀⣀⣉⠁⣀⣀⣘⡀⠘⠃⠃⠀⠂⠁⠀⠀⠀⠀⠀⠀⠉⠁⠄⠀⣴⣶⠶⠒⠒⠀⠀ ⣿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣾⣿⣿⡿⣿⢱⣿⡇⠿⠇⣿⡏⣿⡇⠛⣿⡟⣣⡄⢸⣿⢸⣿⢰⣿⢻⣷⠀⠀⠀⠀⡌⠀⠀⠈⠉⠀⠀⠀⠀⠀ ⡟⠀⣸⣿⣿⣿⣿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢋⣴⣿⢸⣿⢸⣿⡇⣿⡇⣿⡇⠀⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⢸⣿⠀⡀⠀⡜⠀⠀⣠⣤⣤⣤⣦⣤⣤⣄ ⡇⢀⣿⣿⣿⣿⣿⠀⠀⠀⢠⡄⢠⣤⡤⣤⡤⣬⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⣿⣿⣿⣿⣿⣷⣿⣿⣿⣜⠿⠾⠿⠁⠻⠷⠿⠃⠠⣿⡇⢿⡇⣿⡇⣿⡇⢸⣿⣸⣿⢠⣻⡞⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⣾⣿⣿⣿⣿⠇⠀⠀⠀⢸⣇⢸⣷⠆⢸⡇⣰⢙⣳⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⢉⡃⣀⡀⠀⣀⡀⢀⣀⠀⠒⠸⠷⠶⠀⠀⠀⠀⠉⠉⠰⢸⡟⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⠟⠀⢤⣤⣭⣼⣿⣚⣛⣃⣜⣣⣿⡜⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠸⠇⣿⡇⠀⣿⡇⣾⣿⣼⡟⢸⣿⠻⢰⣿⢻⣷⢸⡇⣶⠈⢀⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠿⣿⣿⢫⣤⣄⣠⣭⡝⣭⢿⡍⣿⠏⡏⣶⠶⣴⢲⡆⣶⢲⡆⠀⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣻⢱⣶⡿⠀⣿⡇⠀⣿⡇⣿⣿⣿⡀⢸⣿⠶⠘⠿⣷⣄⢀⠅⠉⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠒⠀⠀⢸⣷⠿⢻⣿⣿⣙⢷⡄⣿⠂⠀⣿⠛⣿⣾⡇⣿⢹⡇⠀⣿⢿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣩⡠⠿⠷⠦⣿⡇⣿⡇⣿⣇⣿⣿⣤⢸⣿⣸⣿⠈⠀⠀⠀⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⠀⢸⢟⢸⣜⣛⢋⣙⡛⢣⣛⣛⠀⠛⠁⠈⠉⠁⠉⠉⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢃⢠⣼⣿⣿⡆⠀⠐⠆⠒⠂⠆⠀⣤⣤⠤⠀⠀⠈⠉⠁⠀⠀⠀⠀⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⡏⣶⣶⡍⣶⢰⡆⣶⢶⡔⣶⡞⣴⣿⡆⠀⢻⡟⢹⡏⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣰⣾⣿⣿⣿⣿⡄⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣧⢻⡟⡃⣿⢻⡇⣿⢸⡇⢹⡇⢹⣿⡿⠀⢸⡇⠸⣇⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⢘⣣⡇⣛⡘⠃⠉⡉⠁⠨⠅⠈⠉⠁⠀⠈⢁⣀⠼⣒⢂⡀⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠜⠁⢠⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⡆⣶⣆⣶⣶⣶⣶⢰⡞⣦⢼⣿⣧⣿⣸⡏⣿⣉⠀⣿⢹⡇⣿⢸⡇⣿⣽⡃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⢷⣦⡀⠀⠀⠀⣀⡠⡖⠂⠀⡁⠔⠁⠀⠀⠈⢆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⡇⣿⣿⢻⡇⣿⢛⢸⡏⣷⢸⣟⣿⢸⣿⡇⣿⣥⠀⢿⣿⡇⢿⣼⠇⠿⠸⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠻⣿⣿⣄⠀⠀⠉⠛⠦⡀⡀⠿⠭⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⠀⠐⢜⡃⠛⠈⠌⠁⠉⠺⠮⠁⠉⠦⠍⠓⠀⣀⡀⢀⣀⡀⣀⣀⢀⣀⣀⣠⢠⡄⣠⣤⡀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣬⣿⣿⡇⠄⠀⠀⠈⢷⡙⢿⡖⣖⠶⡄⠀⠀⠀⢀⣀⣤⣤⣤⣙⡄⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⣶⠶⢠⣞⣷⢰⡟⣷⢸⡇⣼⣿⡈⣿⠀⠸⣯⣛⠈⣿⠁⣿⣿⠀⣿⡁⣿⢸⡇⠻⣮⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡆⣷⣦⡈⢷⡄⠀⠉⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿ ⠀⣽⢻⡾⣿⣿⢸⣇⣶⢸⣧⣿⢾⡇⣿⡄⠀⣾⣿⠀⣿⠀⠿⠻⠇⠿⠇⠻⠿⠇⠻⠾⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣿⣿⣿⣿⣟⣦⡀⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣍⡉⠱⣭⣭⣦⡍⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠻⢹⣿⣿⣿⣿⠻⣛⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⡿⠿⠿⠿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⢿⣿⡇⢤⡞⣿⣿⣿⣟⣀⡙⠣⠆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⢁⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣶⣤⣤⠐⡶⢰⣶⣶⣶⠠⡂⠀⠀⠀⠀⢀⠀⠀⠀⢻⣿⡿⠛⢹⣿⣿⣿⣿⣿⣿⣿ ⣧⣯⠓⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⢈⠙⠻⢿⣿⣿⣿⣿⣿⣆⠡⣧⢻⣿⡿⡇⣯⢇⡖⢇⡆⠜⠰⠐⠊⠉⠀⠀⠀⢸⠽⣿⣿⣿⣿⣿⣿ ⣿⡐⠀⠄⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⢸⣷⠀⠀⢀⠉⠉⠛⠛⠛⠀⠉⠈⠛⠉⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢿⣿⣿⣿⣿⣿ ⣙⣿⠈⢻⠷⠅⢴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠈⣿⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠉⠀⠀⠀⠀⠀⠌⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⠀⣿⡇⠀⠈⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠢⠄⢐⢳⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⡇⢻⣧⠀⠀⢷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2323 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/06/twitter-is-spam/#comments Gemini version at gemini://gemini.techrights.org/2022/04/06/twitter-is-spam/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Musk’s_Bubble:_Twitter_Notifications_Turned_Into_SPAM_and_Recommendations_(to Drive_Up_‘Engagement’_by_Adding_Noise)⠀✐ Posted in Deception at 12:52 am by Dr. Roy Schestowitz Stop feeding Musk’s graft 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Twitter_is_spam:_Twitter_Spam;__What_does_that_have_to_do with_me?_So_what?_Pushing_stuff;_Nothing_to_do_with_me...⦈_ Notifications used to mean things that happen which relate to you! Not anymore… Summary: Twitter isn’t means of communication; Twitter looks like a dying platform desperate for attention; the above is an annotated screenshot of my notifications bar this morning (there’s more noise than signal); Twitter is advertising things to me instead of presenting actual notifications and this keeps getting worse over time (they only prioritise what makes them more money; same as YouTube) ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 2510 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_07/04/2022:_Emacs_28.1_and_Linux_Mint_21_is_Named⠀✐ Posted in News_Roundup at 7:23 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⠀➾ # ⚓ Video ☛ How_To_Install_GE-Proton_in_2022_|_Works_on_Linux Distros_+_Steam_Deck!_–_Invidious⠀⇛ The Linux gaming world moves FAST. Since my last guide about installing the “glorious” custom version of Valve’s Proton, things have become MUCH easier. # ⚓ Video ☛ Kubuntu_22.04_Beta_Run_Through_–_Invidious⠀⇛ In this video, we are looking at Kubuntu 22.04 Beta. Enjoy! For the links and more, # ⚓ Linux Made Simple ☛ Kubuntu_22.04_Beta⠀⇛ Today we are looking at Kubuntu 22.04 Beta. It comes with KDE 5.24.3, Linux kernel 5.15, and uses about 1GB of ram when idling. Enjoy! # ⚓ FLOSS_Weekly_675:_The_Plausible(.io)_Alternative_to_Google Analytics_–_Plausible,_Adblocking,_Open_Source_Analytics⠀⇛ Marko Saric of Plausible joins Doc Searls and Shawn Powers to unpack the challenges and rewards of dropping Google Analytics and using an open source alternative such as Plausible.io. This conversation is especially timely given a shifting regulatory environment in which—among other developments—Google Analytics has lately been declared illegal in France and Austria. o § Kernel Space⠀➾ # ⚓ Update:_A_smol_kernel_hack⠀⇛ On a previous gemlog, I described how I prefer to use my electronics device in a greyscale (desaturated) mode for accessibility and anti- doomscrolling reasons, as colour processing is nontrivial. Since I daily drive an Apple M1 machine running Linux with a display driver I co-authored, I added a kernel hack to do the desaturation in the display controller. This avoids any overhead from desaturating on the CPU or GPU, which is much more efficient. o § Applications⠀➾ # ⚓ Medevel ☛ Sigil_is_a_free,_open-source_eBook_and_ePUB editor_for_Windows,_Linux,_and_macOS⠀⇛ Sigil is an outstanding EPUB editor and creator for book authors, publishers, and anyone who writes and self-publish books. Furthermore, it is a totally, free, open-source solution that works on all popular desktop operating systems. [...] Sigil is an open-source software that is released under the GPL-3.0 License. # ⚓ Download_and_Test_Inkscape_1.2_Beta⠀⇛ It has been almost a year since the last major Inkscape release, and the time is approaching to launch version 1.2! This “Beta” release comes with many performance tweaks, new features (such as the clipart importer) and user interface improvements (see the Release Notes for more details). Before we share Inkscape 1.2 with the world, we need help testing the “Beta” version. If you are confident using Inkscape and you would like to support us in refining it, please follow the instructions below. # ⚓ Medevel ☛ Atom:_Access_to_Memory._The_Web_Catalog⠀⇛ Atom is an open-source web-based self-hosted cataloging and archiving system that helps collectors, and museums catalog and keep track of their items. Atom is compliant to International Council on Archives, so public, private, cultural centers, and NGOs, can use without worrying about international standards. Atom is powered and maintain by a strong community of developers, users, archivers, and museum experts. o § Instructionals/Technical⠀➾ # ⚓ Install_Thunderbird_Mail_Client_on_Rocky_Linux_– kifarunix.com⠀⇛ In this guide, we are going to walk you through steps required to install Thunderbird mail client on Rocky Linux system. Thunderbird is a free and opensource cross-platform email application that was developed by Mozilla Foundation. It can be used as a mail client, chat client, RSS and news client. # ⚓ UNIX Cop ☛ How_to_Install_Roxy-WI_on_Ubuntu,_A_GUI management_server_for_HA_Proxy,_Nginx,_and_keepalived_–_Unix /_Linux_the_admins_Tutorials⠀⇛ This post is about Install Roxy-WI on Ubuntu- Roxy-WI server manages HA Proxy, Nginx, and Keepalived servers from a centralized location. It will create servers on AWS, Digital Ocean, and G- Core Labs, install HA-Proxy, Nginx, and Keepalived, and carry out the initial configuration for the service to start. # ⚓ UNIX Cop ☛ Switching_to_virt-manager⠀⇛ Ever since I got into the world of Linux, I have realised that there exist these various “rabbit holes” (as I like to call it) that I could get myself into. I define these “rabbit holes” as the period when you spend your time into adopting a certain technology into your workflow. Most of these workflows are sometimes very uncommon. For example one of my first “rabbit holes” was switching to a tiling window manager. There already isn’t a big percentage of people who use Linux on their desktops let alone having a tiling window manager setup. One of the “rabbit holes” that I have recently gotten into – hence the title of this article – is switching away from VirtualBox to virt-manager. I had already seen a lot of videos and articles about this QEMU/KVM thingy already. So it was predictable for me to eventually pick this up. # ⚓ Linux Made Simple ☛ How_to_install_FL_Studio_20_on_a Chromebook_in_2022⠀⇛ Today we are looking at how to install FL Studio 20 on a Chromebook. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ How_to_use_MystiQ_video_converter_on_Linux_|_FOSS_Linux⠀⇛ Open-source media file converter MystiQ or MystiQ Video Converter enables you to convert video and audio files into various popular formats. For its backend, it employs FFmpeg and C++. MystiQ can run on Linux, Windows, and Mac OS X. Various techniques of encoding these audio and video data into efficient and portable formats have been developed due to advancements in audio and video capture technology. In some circumstances, you may be obliged to save a file in a specific format to send it over the internet. As a result, you may have to convert the media file into a compressed format. In addition, the material must be converted into a format that will not be corrupted upon access to the file. Using only a few clicks, you can change the format of your media files with MystiQ. It contains a simple, graphical user interface that makes it simple to operate. This tutorial will teach us how to set up and use MystiQ on Linux. # ⚓ ID Root ☛ How_To_Install_MATE_Desktop_on_Fedora_35_– idroot⠀⇛ In this tutorial, we will show you how to install MATE Desktop on Fedora 35. For those of you who didn’t know, The MATE Desktop Environment is the continuation of GNOME 2. It provides an intuitive and attractive desktop environment using traditional metaphors for Linux and other Unix-like operating systems. MATE is also an excellent choice for a lower-end system or those looking to remain efficient on system resources. 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 MATE Desktop environment on a Fedora 35. # ⚓ Network World ☛ 2_ways_to_remove_duplicate_lines_from_Linux files⠀⇛ There are many ways to remove duplicate lines from a text file on Linux, but here are two that involve the awk and uniq commands and that offer slightly different results. # ⚓ TechRepublic ☛ How_to_add_a_data_source_to_Redash_| TechRepublic⠀⇛ Redash can create dashboards from various data sources that display charts, pivot tables, cohorts, boxplots, counters, funnels, maps, sankeys, sunbursts and word clouds. Here’s how to use it. # ⚓ ID Root ☛ How_To_Install_PowerShell_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install PowerShell on Debian 11. For those of you who didn’t know, PowerShell is Microsoft’s automation platform with an interactive command-line shell and scripting language that allows administrators to simplify and automate administrative tasks. PowerShell runs on Windows, Linux, macOS, and other platforms. 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 PowerShell on a Debian 11 (Bullseye). # ⚓ Video ☛ How_to_install_deepin_20.5._–_Invidious⠀⇛ In this video, I am going to show how to install deepin 20.5. # ⚓ Ubuntu Handbook ☛ How_to_Install_Latest_Firefox_as_classic Deb_in_Ubuntu_22.04_|_UbuntuHandbook⠀⇛ Ubuntu 22.04 finally removed the .deb package for Firefox web browser from it’s repository! Here’s how to install it back. As you may know, Firefox in Ubuntu 22.04 is a Snap package that runs in sandbox. It’s easy to remove it. But when you try installing the deb package via apt, it just install the Snap version back!! Like Chromium, the Firefox deb in Ubuntu 22.04 is an empty package that links to the Mozilla’s official Snap. # ⚓ Install_Thunderbird_Mail_Client_on_Debian_11/Debian_10_– kifarunix.com⠀⇛ In this guide, we are going to walk you through steps required to install Thunderbird mail client on Debian 11/Debian 10 system. Thunderbird is a free and opensource cross-platform email application that was developed by Mozilla Foundation. It can be used as a mail client, chat client, RSS and news client. # ⚓ Install_Thunderbird_mail_client_on_Ubuntu_22.04/Ubuntu 20.04_–_kifarunix.com⠀⇛ In this guide, we are going to walk you through steps required to install Thunderbird mail client on Ubuntu 22.04/Ubuntu 20.04 system. Thunderbird is a free and opensource cross-platform email application that was developed by Mozilla Foundation. It can be used as a mail client, chat client, RSS and news client. # ⚓ Install_DBeaver_on_Ubuntu_22.04/Ubuntu_20.04_– kifarunix.com⠀⇛ Follow through this tutorial to learn how to install DBeaver on Ubuntu 22.04/Ubuntu 20.04. DBeaver is free and open source universal database tool for developers and database administrators. o § Games⠀➾ # ⚓ GamingOnLinux ☛ GOG_attempt_to_bring_customers_back_with_a revival_of_Good_Old_Games_|_GamingOnLinux⠀⇛ GOG aren’t having the best of times recently, with details about their financial troubles painting a bleak picture, although it seems they have something of a plan. Later they announced some changes, including a tweak to what they mean by DRM free. # ⚓ GamingOnLinux ☛ Toasty:_Ashes_of_Dusk_confirm_a_Native Linux_build_is_planned,_shown_off_on_Steam_Deck_| GamingOnLinux⠀⇛ Toasty: Ashes of Dusk is an upcoming action RPG that honestly looks great, and now Pocket Llama has issued an update to confirm they will be doing Native Linux support. It’s currently crowdfunding on Kickstarter, with a little publishing hand from Top Hat Studios (who reached out to use about this) and it’s managed to be successfully funded with 22 still to go on the campaign. # ⚓ Godot Engine ☛ Godot_Engine_–_Dev_snapshot:_Godot_4.0_alpha 6⠀⇛ We’re continuing on our fortnightly release schedule for alpha snapshots of Godot 4.0 – this time with 4.0 alpha 6. See past alpha releases for details (alpha 1, 2, 3, 4, 5). Be aware that during the alpha stage the engine is still not feature-complete or stable. There will likely be breaking changes between this release and the first beta release. Only the beta will mark the so-called “feature freeze”. As such, we do not recommend porting existing projects to this and other upcoming alpha releases unless you are prepared to do it again to fix future incompatibilities. However, if you can port some existing projects and demos to the new version, that may provide a lot of useful information about critical issues still left to fix. Most importantly: Make backups before opening any existing project in Godot 4.0 alpha builds. There is no easy way back once a project has been (partially) converted. # ⚓ Boiling Steam ☛ New_Steam_Games_with_Native_Linux_Clients_– 2022-04-05_Edition_–_Boiling_Steam⠀⇛ Between 2022-03-29 and 2022-04-05 there were 26 New Steam games released with Native Linux clients. For reference, during the same time, there were 293 games released for Windows on Steam, so the Linux versions represent about 8.9 % of total released titles. Here’s a quick pick of the most interesting ones: o § Desktop Environments/WMs⠀➾ # ⚓ RE:_Lightweight_GUIs,_TUIs⠀⇛ I’ve always admired fast an efficient software. This is probably from my upbringing. The first computer I got in my own room was running at 996MHz, which was way slower than any other computer at that time. I was running Windows XP on it and it was painful slow! So the first thing I did when the computer had started was to kill explorer.exe. That made things a little better. I installed linux, Red Hat 5.2 and was happy, until I upgraded to Fedora and my computer got painful slow again! I had to switch to Ubuntu. After that I started to experiment. I continued to replace applications with more lightweight ones that was harder to learn ut easier to use. o § Distributions⠀➾ # § IBM/Red Hat/Fedora⠀➾ # ⚓ Running_a_Container_off_the_Host_/usr/⠀⇛ Apparently, in some parts of this world, the /usr/-merge transition is still ongoing. Let’s take the opportunity to have a look at one specific way to take benefit of the /usr/ -merge (and associated work) IRL. I develop system-level software as you might know. Oftentimes I want to run my development code on my PC but be reasonably sure it cannot destroy or otherwise negatively affect my host system. Now I could set up a container tree for that, and boot into that. But often I am too lazy for that, I don’t want to bother with a slow package manager setting up a new OS tree for me. So here’s what I often do instead — and this only works because of the /usr/-merge. # ⚓ Red Hat Official ☛ Innovation_and_flexibility_in_an open_design_approach_to_Cloud_RAN_and_access_networks⠀⇛ Cloud radio access networks (RANs), virtual RANs (vRANs), and open RANs are seen as ways for telecommunication operators to incorporate flexibility in how they design, build, and operate their access networks. # ⚓ Business Wire ☛ CIQ_and_Google_Cloud_to_Provide Optimized_Experience_for_Rocky_Linux_|_Business_Wire⠀⇛ Rocky Linux is a community-maintained and freely available enterprise Linux distribution founded and led by Gregory M. Kurtzer, one of the original founders of CentOS. Since the project was launched, there have consistently been over a quarter of million downloads and installs per month. Rocky is rapidly growing, and many large organizations have partnered and joined the community. # ⚓ Linuxiac ☛ GitLab_Switched_from_Centos_8_to_AlmaLinux as_a_Supported_Platform⠀⇛ AlmaLinux supporters have reason to rejoice after the distro was chosen to replace CentOS 8 in the GitLab infrastructure. As you know, CentOS itself reached End-of- Life (EOL) on December 31, 2021, due to which corporate users across many industries are looking for alternatives. # § Debian Family⠀➾ # ⚓ Thorsten_Alteholz:_My_Debian_Activities_in_March 2022⠀⇛ This month I accepted 332 and rejected 15 packages. This ratio gives a reason to hope. The overall number of packages that got accepted was 342. # § Canonical/Ubuntu Family⠀➾ # ⚓ Beta News ☛ Linux_Mint_21_is_named_‘Vanessa’⠀⇛ Linux Mint is a very popular operating system, so any news surrounding upcoming versions is highly sought after by members of the open source community. Today, the developers of that operating system have shared some very interesting information — the name of Linux Mint 21! The Linux Mint developers always use female names (alphabetically) as codenames, and version 21 is no different. You see, following version 19 (“Tara”) and version 20 (“Ulyana”), version 21 of Linux Mint is named “Vanessa.” According to Think Baby Names, it is a Greek name meaning “butterfly.” # ⚓ 9to5Linux ☛ Linux_Mint_21_“Vanessa”_Will_Be_Based_on Ubuntu_22.04_LTS,_New_Upgrade_Tool_in_the_Works⠀⇛ First and foremost, Linux Mint 21 has been dubbed “Vanessa” and it will come with the same three editions that you’ve been used to, featuring the Cinnamon, Xfce, and MATE desktop environments. Second of all, as you might have expected, Linux Mint 21 will be based on the next major Ubuntu LTS (Long Term Support) series, Ubuntu 22.04 LTS (Jammy Jellyfish), which means that it will also be supported for a long period of time and that it will be powered by its Linux 5.15 LTS kernel series. # ⚓ Linux_Mint_21_Code_Name_Announced_with_New_Upgrade Utility_and_More⠀⇛ The Mint team announced the upcoming Linux Mint 21 codename, a utility for easy upgrade and Warpinator use cases that stuns the team. # ⚓ Linux Mint ☛ Monthly_News_–_March_2022⠀⇛ Many thanks to all of you for your support and your generous donations. Slow download speeds We are observing heavy load on our main repositories. If you are experiencing slow download speeds when updating large packages (Firefox and Chromium in particular), launch the Software Sources and click on the “Main” repository… [...] It’s funny to see how Warpinator became a solution to something we never actually envisioned. In this video Windows users are looking for a way to share files with their Steam Deck. I find this really cool personally, not just to see developers build on top of what we made, but to see software reach new audiences and let completely different devices interoperate like this. Now, before people ask, no, it’s not “coming on Switch” 🙂 # ⚓ Ubuntu ☛ The_State_of_Robotics_–_February_&_March 2022⠀⇛ When you use open source software, you establish a connection with its maintainers, contributors, and users. You join a community, leveraging code and knowledge. You share bugs, solutions, recommendations, and challenges. Open source accelerates innovation while uniting us all under the same cause. Today, millions of open source contributors are being affected, fighting for their survival. Members of your community, my community. And while a blog can’t stop the ongoing war, it can honour those who are suffering. It can also show you how close we are to them, in our work, in our field, and in our passion. It shows who we want to help, who we care about, because today, we all share the same pain. [...] We can’t feature them all, and I do apologize for those who were not mentioned, but I will promise you this: if you send us an email to robotics.community@canonical.com, I will add them, and keep updating this blog for as long as needed. These are some of the organisations, robotics companies, and communities in Ukraine that have contributed to open source robotics in different ways. o § Devices/Embedded⠀➾ # ⚓ CUPS_and_Raspberry_Pi_AirPrinting_|_Developer.com⠀⇛ While printing to paper perpetually seems to be “going the way of the Dodo,” the need to print something on an actual piece of paper nonetheless has a way of showing up when we least expect (or desire) to see it. Naturally, no one who encounters this need on a mobile device really wants to get up and print the same document from a traditional computer. As anyone who frequently uses the AirPrint feature on an iPhone can attest, most consumer-grade printers’ support for AirPrint is sketchy at best. For most, all it takes is for the printer to go into an extended sleep and it is no longer available for AirPrint until it is manually woken up by a human. # ⚓ Introducing_the_Wind_River_Linux_Binary_Distribution⠀⇛ Wind River is proud to announce a new member of the commercially supported Wind River Linux family, Wind River Linux Distro. Distro is a binary Linux distribution created from our source code–based Linux product. Wind River, the leader in the IoT and embedded operating systems, has long provided customers with the ability to create their own purpose-built Linux operating system from source. Wind River starts with the Yocto Project and adds a significant amount of integration with semiconductor vendor SDKs to provide a commercially supportable Linux distribution builder for intelligent edge solution developers. # ⚓ Linux Gizmos ☛ INNOTECH_reveals_the_AX-1020_Atom_x6000E Elkhart_Lake_SBC⠀⇛ Recently, INNOTECH announced the introduction of their AX-1020 which integrates Intel’s Atom x6000E Elkhart Lake high performance SoCs. This SBC provides high performance and flexibility due to its support of different Elkhart Lake Series SoCs. The AX-1020 might be integrated with the Atom x6245E (2GHz, 12W TDP), the Atom x6413E(1.5GHz, 9W TDP) or the Atom x6211E (1.3GHz, 6W TDP). All of the listed SoCs have a max frequency of 3GHz.The display interfaces include a 1x Display port, 1x Analog RGB and 1x LVDS. The board has DDR4 SO-DIMM support that ranges from 4GB to 16GB. It has a SATA port, a M.2 socket for NVMe storage and a socket for CFast cards. # § Open Hardware/Modding⠀➾ # ⚓ Joystick_with_Arduino:_How_to_Interface_with_Code Explained⠀⇛ To deal with the control of the robotic movement in directions joystick is the best choice, as it has the ability to control four directions In this tutorial, we’ll interface the joystick with Arduino Uno including code, connection diagram, and component list. # ⚓ Arduino ☛ Reset_your_Canon_printer’s_maintenance cartridge_with_this_hack_|_Arduino_Blog⠀⇛ Printers are notorious for high operating costs. Usually those come in the form of expensive ink cartridges, which require replacement even when they still contain some ink. But some printers, including Canon Pixma G models, take this a step further with a maintenance cartridge. A new MC-G02 maintenance cartridge only costs around $10, but that adds up if you need to replace yours often. To eliminate that cost, Yancey Wang developed a hack that only requires an Arduino Uno and some wire. Canon printers use the MC-G02 maintenance cartridge to store waste ink after some operations, such as print head cleaning. The cartridge will soon fill up and Canon expects you to purchase a new cartridge. If you don’t, the printer will stop working. But users can empty and reuse the maintenance cartridge, making a new cartridge unnecessary. The problem is that the cartridge has a built-in “counter” chip, which will tell the printer that the cartridge is full — even if the user emptied it. # ⚓ CNX Software ☛ Antmicro_releases_open-source_hardware Snapdragon_845_baseboard_designed_with_KiCad_–_CNX Software⠀⇛ Antmicro team has released an open-source hardware baseboard for Quectel SA800U-WF System-on-Module powered by Qualcomm Snapdragon 845 octa-core processor, which they designed with KiCad open-source EDA tool. The baseboard supports NVMe storage and offers Micro HDMI and MIPI DSI video interfaces, Gigabit Ethernet with PoE support, USB 3.1 Type-C interfaces, and other I/Os, plus three separate power inputs. The company expects the design to serve as a starting point for building portable smart assistants, kiosks, VR/AR or smart screens, and more. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Android Authority ☛ We_asked,_you_told_us:_Most_of you_don’t_care_for_Android_chat_bubbles⠀⇛ # ⚓ Android Central ☛ Poll:_How_would_you_prefer_to unlock_your_Android_smartphone?_|_Android_Central⠀⇛ # ⚓ HowTo Geek ☛ How_Much_Storage_Space_Do_You_Need_on_an Android_Phone?⠀⇛ # ⚓ [Guide]_How_to_enable_Face_Detection_for_Autorotate in_Android_12_–_TalkAndroid.com⠀⇛ # ⚓ 9to5Google ☛ Google_Play_will_hide_outdated_Android apps_for_new_users_–_9to5Google⠀⇛ # ⚓ 9 to 5 Toys ☛ Android_app_deals_of_the_day:_Gunslugs 3,_Space_Grunts_2,_Ashworld,_and_more_–_9to5Toys⠀⇛ # ⚓ CNX Software ☛ Antmicro_releases_open-source_hardware Snapdragon_845_baseboard_designed_with_KiCad_–_CNX Software⠀⇛ # ⚓ Phone Arena ☛ America’s_top_Android_chipset_maker MediaTek_may_wiggle_into_the_Galaxy_S22_FE_and_the flagship_S23_series_–_PhoneArena⠀⇛ # ⚓ How_to_rename_Bluetooth_devices_on_Android_– Phandroid⠀⇛ # ⚓ Gizmodo ☛ How_To_Hack_the_Android_Status_Bar⠀⇛ # ⚓ Top_6_Ways_to_Fix_Discord_App_Crashes_on_Android_– Guiding_Tech⠀⇛ # ⚓ iToolab_RecoverGo:_The_Android_data_recovery_software that_you_must_try⠀⇛ # ⚓ Make Use Of ☛ What_Is_Android_TV?⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ Economic_Woes_and_FOSS⠀⇛ Many people seem reluctant to invoke the term, but with rising unemployment, stagnant wages, runaway inflation, and significant shortages in all kinds of goods, I can only describe the current economic situation around the world as a recession. The lack of electronics supplies is particularly notable in a hyper-digital global civilization. In an age where almost everyone in the first world and an increasing percentage of the third world communicate, get news, make purchases, and even handle finances online, access to digital services is more than a luxury–it is fast becoming a right, and one that needs protection. Outside the realm of necessary interactions, the Internet is also where we often find entertainment and relaxation, in the form of videos, articles, video games, and even VR and AR spaces. Most companies develop these services and spaces with the unspoken assumption that their customers will access them using the latest technology available. In the case of video games in particular, devices more than a few years old are often unable to run the software at all, either due to a lack of horsepower or an intentional lack of compatibility. Web sites implement new designs that require newer technologies and heavier processing. Smartphone apps become bigger, more processor- intensive, and increasingly reliant on device optimizations. Older computers, consoles and smartphones are left in the dust. [...] Of course, such a transition in the way we think about technology can’t happen overnight. Profit- driven companies will always fight to villainize technology they can’t profit from, while simultaneously attracting people into their walled gardens through endless dopamine triggers and FOMO. We also need to make the case for FOSS clearly and articulately, emphasizing its economic benefits and demonstrating its penchant for bringing people together in constructive ways. We can introduce people to the topic via FOSS frontends for existing platforms, such as NewPipe for YouTube and Nitter for Twitter. # § Web Browsers⠀➾ # § Chromium⠀➾ # ⚓ Eric Hameleers ☛ Chromium_100_out-of-band security_update_addresses_(again)_a_single vulnerability_|_Alien_Pastures⠀⇛ What’s with all these updates that follow rapidly on each others’ heels? Just like the recent Chromium 99 security update which addressed a single critical vulnerability, last monday Google announced on their official blog the immediate availability of Chromium 100.0.4896.75. This hotfix release plugs a single hole which Google deemed serious enough to warrant the update. See CVE-2022-1232. The difference with last week is that no known exploit of this vulnerability is reported yet. # ⚓ USCERT ☛ Google_Releases_Security_Updates_for Chrome⠀⇛ This version addresses vulnerabilities that an attacker could exploit to take control of an affected system. # § Mozilla⠀➾ # ⚓ Mozilla ☛ A_glossary_of_terms_about cyberattacks,_from_ransomware_to_DDoS⠀⇛ If you read news about technology, you’re bound to run into some jargon. Here at Mozilla, we believe that information should be as accessible as possible regardless of your level of expertise. We want to help you approach stories about technology with more curiosity and with a little less head- scratching involved. We’ll break down headline-making topics through a glossary of terms often used to discuss them. Consider it your cheat sheet to all things tech. # ⚓ Mozilla ☛ What_is_a_cyberattack_and_what_can_we do_to_protect_ourselves_online?⠀⇛ Cyberattacks are nothing new. According to the FBI, the first major “attack on the internet” predated even the web — a self-replicating malicious program created by a grad student who shortly apologized with instructions to remove it. While the software didn’t damage or destroy any files, it spread, within 24 hours, to about 6,000 of the 60,000 computers that were connected to the internet at the time. It slowed down university and military operations and delayed email for days. The apology that contained the fix reached few people in time. To say that our lives have become more dependent on the internet since the Morris worm of 1988 would be an understatement. A cyberattack can disrupt fuel supplies by shutting down the largest pipeline in the U.S. It can cut electricity for entire regions. It can disable computers at hospitals. No wonder cyberattacks have become destructive tools during international conflicts like the Russia-Ukraine war. With cyberattacks making headlines, we turned to Mozilla’s chief security officer to shed some light on the role of cybersecurity during the Russia- Ukraine war. Marshall Erwin has worked in cybersecurity for two decades, spending the first five years of his career in the CIA’s counterterrorism center. He also spent some time working on cybersecurity policy issues in the U.S. Congress before taking the lead on trust and security at Mozilla seven years ago. # ⚓ USCERT ☛ Mozilla_Releases_Security_Updates_for Firefox,_Firefox_ESR,_and_Thunderbird⠀⇛ Mozilla has released security updates to address vulnerabilities in Firefox, Firefox ESR, and Thunderbird. An attacker could exploit some of these vulnerabilities to take control of an affected system. CISA encourages users and administrators to review the Mozilla security advisories for Firefox 99, Firefox ESR 91.8, and Thunderbird 91.8 and apply the necessary updates. # § FSF⠀➾ # § GNU Projects⠀➾ # ⚓ LWN ☛ Emacs_28.1_released⠀⇛ Hi! Version 28.1 of Emacs, the extensible text editor, should now be available from your nearest GNU mirror: https://ftpmirror.gnu.org/emacs/emacs- 28.1.tar.xz https://ftpmirror.gnu.org/emacs/emacs- 28.1.tar.gz The tarballs are signed; you can get the corresponding PGP signature files at: https://ftpmirror.gnu.org/emacs/emacs- 28.1.tar.xz.sig https://ftpmirror.gnu.org/emacs/emacs- 28.1.tar.gz.sig You can choose a mirror explicitly from the list at: https://www.gnu.org/prep/ftp.html Mirrors may take some time to update; the main GNU ftp server is at: https://ftp.gnu.org/gnu/emacs/ To verify that the downloaded tarball is intact, download both the tarball and the corresponding .sig file, and run this command: gpg --verify emacs-28.1.tar.xz.sig (and similarly for emacs-28.1.tar.gz, if you download that format). If the GPG command fails because you don't have the required PGP public key, run this command to import the key: gpg --keyserver keyserver.ubuntu.com --recv-keys \ 17E90D521672C04631B1183EE78DAE0F3115E06B Alternative keyservers to try are pgp.mit.edu and keys.openpgp.org. You can also run sha1sum or sha256sum and confirm that these checksums match: SHA1 emacs-28.1.tar.gz 7af2566ff1d2a1b9b3c70e9517fa02a7137ad835 SHA1 emacs-28.1.tar.xz a198d69dfa5a42c30cabe9a82edb101ac5ee423c SHA256 emacs-28.1.tar.gz 1439bf7f24e5769f35601dbf332e74dfc07634da6b1e9500af67188a92340a28 SHA256 emacs-28.1.tar.xz 28b1b3d099037a088f0a4ca251d7e7262eab5ea1677aabffa6c4426961ad75e1 For a summary of changes in Emacs 28.1, see the etc/NEWS file in the tarball; you can view it from Emacs by typing 'C-h n', or by clicking Help->Emacs News from the menu bar. For the complete list of changes and the people who made them, see the various ChangeLog files in the source distribution. For a summary of all the people who have contributed to Emacs, see the etc/AUTHORS file. For more information about Emacs, see: https://www.gnu.org/software/emacs # ⚓ LWN ☛ Emacs_28.1_released⠀⇛ Version 28.1 of the Emacs editor has been released. The announcement says little about what’s in this release, but there are a lot of details in the NEWS file. Significant changes include native compilation of ELisp files, support for running the editor in a seccomp() sandbox, improved emoji support, and much more. Wayland support did not make it into this release, but is already merged for version 29. # § Programming/Development⠀➾ # ⚓ GamingOnLinux ☛ Open_source_XR_runtime_Monado_adds initial_6DoF_‘inside-out’_tracking_support⠀⇛ It’s been a little while since we heard progress on Monado, the free and open source XR (VR / AR) runtime for Linux but it has been progressing nicely with a big new feature added. Developer Mateo de Mayo had a six-month internship at Collabora, and decided to do a write up on this exciting enhancement for Monado. Pretty tech-heavy stuff here, and not something for regular consumers to read through and think “ah yes, I understood all that”. The basic gist is that Monado, on Linux, can now support XR devices that have cameras and an IMU (Inertial measurement unit) to provide 6DoF (inside-out) tracking utilizing other open source projects like Kimera-VIO, ORB-SLAM3, and Basalt. # ⚓ Another_new_project⠀⇛ I started this project to make searching easier. Currently, I mainly just go to my preferred search engine and type in what I want. The main disadvantage with this approach is that for most searches, only a few websites are relevant, for example if I am currently programming, it seems that 90% of all searches lead me directly to StackOverflow (which has some horrible themes now by the way, but that is a topic for another blog) or directly to the documentation of some library. I therefore decided that I could just query all these sites directly and forward me to the site I am actually looking for. To further enhance the searching, I decided that I needed some profiles, which decide which sites should be queried. If I am looking for documentation of a Rust module, I can therefore activate the Rust profile and just receive information from Rust documentation (e.g. doc.rust-lang.org, maybe crates.io) but not some random StackOverflow questions that are irrelevant. [...] This project will of course be open-source in the future, but as this is still completely unusable (I have just started on the project yesterday), this will have to wait a little bit. # ⚓ Monado_accepted_in_GSoC_2022!⠀⇛ We’re proud to announce that Monado, the free and open source XR platform, has been accepted for the first time as a mentoring organization for the 2002 Google Summer of Code (GSoC)! Collabora will be providing three mentors to support contributors who want to work on Monado-related projects. For 17 years, GSoC has focused on bringing new open source contributors into open source communities. GSoC has brought over 18,000 university students from 112 countries together with over 17,000 mentors from 746 open source organizations! Head to their website to learn more. Beginning in 2022, GSoC is opening the program up to all newcomers of open source that are 18 years and older. The program will no longer focus solely on university students or recent graduates! If you’re new to open source and want to learn more about Monado OpenXR runtime, check out the Monado webpage on freedesktop and our 2022 GSoC Project Ideas here to get you inspired. Then join GSoC to submit your proposal, and if accepted, you’ll get a mentor from Collabora to guide you on your journey! # ⚓ Medevel ☛ WeasyPrint_converts_any_HTML_webpage_into_a rich_PDF_document⠀⇛ From a technical point of view, WeasyPrint is a visual rendering engine for HTML and CSS that can export to PDF. It aims to support web standards for printing. WeasyPrint is free software made available under a BSD license. It comes with a developer-friendly documentation to help developers integrate it into their projects. # ⚓ Medevel ☛ Add_a_Full-Text_Search_to_your_PHP_Projects with_TNTSearch⠀⇛ # ⚓ APIs:_The_Building_Blocks_of_Modern_Software Development⠀⇛ APIs are the foundation of modern software development in 2022, but what are the keys to success? # ⚓ Qt ☛ Commercial_LTS_Qt_5.15.9_Released [Ed: When Qt says "Commercial" is actually means proprietary]⠀⇛ We have released Qt 5.15.9 LTS for commercial license holders today. As a patch release, Qt 5.15.9 provides important bug fixes and security updates. One highly requested improvement is support for macOS on ARM and universal builds. # § Perl/Raku⠀➾ # ⚓ Perl ☛ The_ordering_operators_|_Aristotle_ [blogs.perl.org]⠀⇛ Perl has two operators, cmp and <=>, which are basically never seen outside of sort blocks. That doesn’t mean you can’t use them elsewhere, though. Certainly sort and these operators were designed to work seamlessly together but there isn’t anything sort-specific about the operators per se, and in some contexts they can be the most appropriate solution. # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ HowTo Geek ☛ How_To_Validate_the_Syntax_of_a Linux_Bash_Script_Before_Running_It [Ed: GNU Bash, not Linux bash. Linux is a kernel.]⠀⇛ Bugs and typos in Linux Bash scripts can do dire things when the script is run. Here are some ways to check the syntax of your scripts before you even run them. # ⚓ What_is_Bash_shell,_and_know_its_importance_in Linux_|_FOSS_Linux [Ed: GNU, not Linux]⠀⇛ If you have ever seen any movie or series with a “hacker” character (a genuinely good example would be Mr. Robot), you have seen this scene. There is a bunch of random text on the screen, the hacker puts in some command, and the screen pours out more information. So what’s that all about? Why are there no icons or anything graphical? Well, I am here with an answer. What is being shown in a scene like this is a Command Line Interface (CLI). The CLI of any operating system makes it possible for mere mortals like us to interact with the complex systems of our machines. We enter commands in the form that we understand them. Next, they are sent to the shell, the software that makes sense of the commands, variables, and names that we put in. Finally, the command is executed, and we are provided with the results. # § Rust⠀➾ # ⚓ Lang_team_April_update⠀⇛ Today, the lang team held its April planning meeting. We hold these meetings on the first Wednesday of every month, and we use them to schedule design meetings for the remainder of the month. * § Leftovers⠀➾ o ⚓ Everywhere⠀⇛ As the time for bording aproached, the gate agent announced that, “we do not have a captain or first officer for this flight.” o ⚓ Tedium ☛ FAQ:_The_Difference_Between_Centralized_and Decentralized⠀⇛ Today in Tedium: Recently, a reader asked me to lay out the concerns about centralization and decentralization in relation to the internet, having had questions about it in response to a recent piece of mine on my sister newsletter, MidRange, about Jack Dorsey. It’s a debate that constantly comes up, and if you’re not in the know, it can feel like it’s passing you by. In many ways, it’s about who controls the keys of digital culture, what rooms you can go in, and what you can say. It is the difference between public property and carefully curated environments. It is also the difference between you being completely responsible for your screw-ups and someone else doing something that can negatively affect you—or, depending on the situation, not doing something. Given a decision by a PayPal Mafia alum/rocket man/satellite internet guru/electric car maven/digital edgelord to acquire a significant stake in the social network Twitter this week, this conversation is going to become more important in the coming years. So, let’s have it. Today’s Tedium offers an FAQ on the centralization question. o § Science⠀➾ # ⚓ The_Automation_Myth⠀⇛ In 1963, the Black working-class revolutionist James Boggs wrote of a coming cataclysm in American industrial production. As an autoworker at Chrysler in Detroit, Boggs had an intimate knowledge of the changes introduced on the shop floor and the impacts that reverberated from them across the city, seeing the ways in which these shifts in the technical aspects of the labor process came to affect the prospects for radical organizing. He saw one particular harbinger of this coming utter devastation of the working class, and especially the Black working class—automation. It makes sense that a Detroit autoworker would find himself especially attuned to this phenomenon. The contemporary usage of the word *automation* has its origins in the Automation Department at Ford Motor Company set up by vice president of manufacturing Delmar Harder in 1947—even though Harder’s actual proposals for the reorganization of work in Ford’s factories primarily relied on nineteenth-century technologies designed simply to speed up the production line. Throughout “The American Revolution: Pages from a Negro Worker’s Notebook”, Boggs speaks of automation in apocalyptic terms, issuing the grave pronouncement that “America is headed toward full unemployment, not full employment.” By the early 1960s when Boggs wrote of this fast-approaching wave of automation, the term had come to mean the replacement of jobs once done by human laborers, now performed by an integrated system of machines that themselves come to regulate the pace of production for the smaller number of workers on the line. # ⚓ The Register UK ☛ UC_Berkeley_ML_pioneer_wins_top_computing gong_•_The_Register⠀⇛ This year’s ACM Prize in Computing is going toward a machine learning specialist whose work, even if you haven’t heard of him, is likely to be familiar. Pieter Abbeel, UC Berkeley professor and co-founder of AI robotics company Covariant, was awarded the prize and its $250,000 bounty, which is given to those in the machine learning field “whose research contributions have fundamental impact and broad implications.” o § Hardware⠀➾ # ⚓ Public Knowledge ☛ Public_Knowledge_Urges_Congress_To_Pass Bill_Providing_Veterans,_Students_With_Refurbished_Computers –_Public_Knowledge⠀⇛ Today, the House Oversight Committee marked up the “Computers for Veterans and Students (COVS) Act,” a bill introduced by Representative Abigail Spanberger (D-VA) to direct hundreds of thousands of out-of-service computers from the federal government to nonprofit refurbishers for repair and distribution to veterans, students, and low-income consumers. Participating refurbishers would also provide digital literacy training. Public Knowledge urges Congress to pass this bipartisan bill to help close the nation’s device divide. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Video ☛ Has_Windows_11_Adoption_Really_Stopped?_– Invidious [Ed: It_really_is_bad; If Brodie Robertson gets his ‘info’ from Reddit, sooner or later he’ll be repeating Microsoft shills and trolls]⠀⇛ Based on some random data a bunch of news outlets started saying that nobody is adopting Windows 11 and microsoft is dissapointed but looking at prior Windows releases tells a very different story. # § Pseudo-Open Source⠀➾ # § Privatisation/Privateering⠀➾ # § Linux Foundation⠀➾ # ⚓ Linux Foundation’s Site/Blog ☛ Automotive_Grade_Linux_Announces IndyKite,_Marelli_and_Red_Hat_as_New Members⠀⇛ # ⚓ PR Newswire ☛ IndyKite,_Marelli_and Red_Hat_Join_Automotive_Grade_Linux⠀⇛ Automotive Grade Linux (AGL), a collaborative cross-industry effort developing an open source platform for all connected car technologies, announces IndyKite, Marelli and Red Hat as new Bronze members. “Our active community of automakers and suppliers continues to expand and invest resources in AGL, demonstrating the value of participating in the AGL ecosystem,” said Dan Cauchy, Executive Director of Automotive Grade Linux at the Linux Foundation. “We are excited to welcome our new members to the AGL community, and we look forward to working with them as we continue to expand and enhance the AGL platform.” # § Security⠀➾ # ⚓ LWN ☛ Security_updates_for_Wednesday_ [LWN.net]⠀⇛ Security updates have been issued by Arch Linux (rizin), Fedora (fish, gdal, mingw-fribidi, mingw-gdal, mingw- openexr, mingw-python-pillow, mingw- python3, and python-pillow), Mageia (chromium-browser-stable), Oracle (Extended Lifecycle Support (ELS) Unbreakable Enterprise kernel and kernel), Red Hat (kernel, kernel-rt, and Red Hat OpenStack Platform 16.2 (python-waitress)), Scientific Linux (kernel), Slackware (mozilla), SUSE (mozilla-nss), and Ubuntu (h2database). # ⚓ IT World CA ☛ Cyber_Security_Today,_April_6, 2022_–_Patch_Linux_fast,_secure_your_Totolink routers,_news_on_the_new_Borat_trojan_and_more Russia-Ukraine_cyberwar⠀⇛ # ⚓ FOSSLife ☛ Free_Cybersecurity_Resources_for Protecting_Your_Organization⠀⇛ Information is power, and staying informed about the latest cybersecurity threats and mitigation techniques is crucial for protecting your organization. This article looks at key agencies and organizations offering an array of free resources and guidance to help you stay informed of the latest threats, implement best practices, and strengthen your cybersecurity approach. # ⚓ USCERT ☛ CISA_Adds_Three_Known_Exploited Vulnerabilities_to_Catalog [Ed: 66.6% of that is Microsoft]⠀⇛ CISA has added three new vulnerabilities to its Known Exploited Vulnerabilities Catalog, based on evidence of active exploitation. These types of vulnerabilities are a frequent attack vector for malicious cyber actors and pose significant risk to the federal enterprise. Note: to view the newly added vulnerabilities in the catalog, click on the arrow on the of the “Date Added to Catalog” column, which will sort by descending dates. # § Privacy/Surveillance⠀➾ # ⚓ Bruce Schneier ☛ Cyberweapons_Arms Manufacturer_FinFisher_Shuts_Down [Ed: Probably just changes names, goes under some other shell, carries on as usual without the burden of lawsuits]⠀⇛ FinFisher has shut down operations. This is the spyware company whose products were used, among other things, to spy on Turkish and Bahraini political opposition. # ⚓ AccessNow ☛ India’s_Criminal_Procedure_ (Identification)_Bill_jeopardizes_privacy_— it_must_not_be_enforced_–_Access_Now⠀⇛ In a blow for human rights, the Parliament of India has today, April 6, passed the Criminal Procedure (Identification) Bill, which will severely jeopardize people’s privacy and expand the scope for surveillance. Once the bill receives the president’s assent, it will turn into law — it must not be enforced. “The Criminal Procedure (Identification) Bill fundamentally contravenes the Supreme Court’s rulings on the fundamental right to privacy guaranteed by the Indian Constitution,” said Raman Jit Singh Chima, Senior International Counsel and Asia Pacific Policy Director at Access Now. “Instead of responding to the need of the hour and propelling reforms over government surveillance and databases, the Indian government has fast-tracked a bill through parliament that exacerbates the threat of mass surveillance, and attacks people’s fundamental rights and freedoms. This bill must not be enforced in its current form.” The contentious bill empowers the police, and any agency notified by the government, to collect, retain, and share an alarming range of personal information. This includes biometric data such as fingerprints, palm prints, footprints, photographs, iris and retinal scans, and other physical and biological samples. This data can be collected from people who have been convicted, arrested, or merely detained under India’s preventive detention laws, and can be retained in digital forms for at least 75 years. In doing so, the bill goes far beyond the 1920 colonial era law it claims to replace, with no meaningful oversight mechanisms or guarantees on remedy for individuals facing abuse by authorities. Resisting the collection of information under the bill would amount to an offense. o § Finance⠀➾ # ⚓ Buzz Feed ☛ Sam_Altman’s_Worldcoin_Promised_Them_Free Crypto_For_An_Eyeball_Scan._Now_They_Feel_Robbed.⠀⇛ The Sam Altman–founded crypto startup has said it aims to alleviate global poverty, but so far it has angered the very people it claims to be helping. o § Misinformation/Disinformation⠀➾ # ⚓ France24 ☛ ‘TikTok_is_having_a_bad_war,’_say_disinformation experts [Ed: Was this article sponsored by Mark Zuckerberg and Facebook?]⠀⇛ The war in Ukraine has rapidly positioned TikTok as the number one source of misinformation thanks to its gigantic number of users and minimal filtering of content, experts say. Every day, Shayan Sardarizadeh, a journalist with the BBC’s disinformation team, ploughs through a hallucinatory mix of fake and misleading information about the war being spewed out on the video-sharing site. “TikTok is really not having a good war,” he told AFP. “I haven’t seen another platform with so much false content,” he added. o § Internet Policy/Net Neutrality⠀➾ # ⚓ MakeTech Easier ☛ 7_of_the_Best_USENET_Newsgroups_Still Active_Today_–_Make_Tech_Easier⠀⇛ USENET is arguably the oldest online network alive today. It was first developed in the late 1970s and has since been a part of internet culture. USENET has also been a witness to historical events such as the announcement of Linux and the first spam message. With modern websites and social media, most people think that USENET is a dead place. This is not the case. Over the decades, hundreds of communities have continued to use USENET to discuss their interests. This article aims to show 7 USENET groups that are still alive and kicking today. o § Monopolies⠀➾ # ⚓ Regulatory_Competition:_Where_the_UK_Stands_on_Tech_– Disruptive_Competition_Project⠀⇛ Under the French Council presidency, European lawmakers reached a political agreement on the Digital Markets Act (DMA) at “the speed of lightning” (and just in time for the upcoming French Presidential Election). But will this lead to a wave of copy-cat legislation, or will the UK take a different approach? The DMA is set to introduce new rules that will change the design and delivery of the world’s most popular digital services. Critics are concerned that the DMA’s rules could degrade service quality, expose users to security risks, or break services altogether. Pro-DMA forces are now putting pressure on policy makers in the UK to follow suit. But what approach should UK lawmakers follow if they want to secure UK leadership in tech innovation, not just tech regulation? # § Copyrights⠀➾ # ⚓ Public Domain Review ☛ A_Vanishing_Nova: *Uranographia_Britannica*_(ca._1749)_–_The_Public Domain_Review⠀⇛ In 1748, scientific instrument maker John Neale advertised the sale by subscription of a new “exact Survey of the Heavens”. It would offer not only “all the fix’d Stars hitherto observed in any Part of the World”, but also two planispheres of the Ptolemaic constellations and a historical account of the asterisms, “from the earliest Antiquity to the present Time”. The atlas relied on the work of Dr. John Bevis (1695–1771), a London physician who had devoted a year of his life to recording the nightly transits of stars from his observatory in Stoke Newington. Documenting faintly luminous entities down to the eighth magnitude, he added to those already cataloged — by John Flamsteed’s 1729 Atlas Coelestis and Edmond Halley’s southern hemisphere observations — for a total of 3550 stars. Best known to historians of astronomy for discovering the Crab Nebula (depicted in Taurus), Bevis contributed papers on eclipses and comets to the Philosophical Transactions of the Royal Society, making strides toward establishing the configuration and scale of the solar system, and helping to account for apparent irregularities in the motions of the moon and planets. At a time when the accurate measurement of longitude was of paramount importance to imperial British navigation, Bevis played a prominent role in the assessment of contending claims. ䷩ 𝚕𝚒𝚗𝚎 4410 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_05/04/2022:_NuTyX_22.04.1_and_Ghostscript_9.56.1⠀✐ Posted in News_Roundup at 4:21 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Server⠀➾ # ⚓ Docker_founder_launches_Dagger,_a_new_DevOps_platform_– TechCrunch⠀⇛ It’s been almost exactly four years since Docker founder Solomon Hykes left the company that kickstarted the container revolution. Docker has gone through its share of ups and downs since then, including selling its enterprise business to Mirantis in 2019, but Hykes, who was long the public face of Docker, mostly stayed on the periphery, with the exception of his participation in a few funding rounds. For a while now, though, he’s been quietly working on his next startup, Dagger, which is launching into public beta today and announcing a $20 million Series A funding round. o § Audiocasts/Shows⠀➾ # ⚓ Video ☛ Ubuntu_Budgie_22.04_Beta_Run_Through_–_Invidious⠀⇛ In this video, we are looking at Ubuntu Budgie 22.04 Beta. # ⚓ Linux Made Simple ☛ Ubuntu_Budgie_22.04_Beta⠀⇛ Today we are looking at Ubuntu Budgie 22.04 Beta. It comes with Gnome 42, Linux kernel 5.15, and uses about 1.2 GB of ram when idling. Enjoy! # ⚓ Video ☛ Xubuntu_22.04_Beta_Run_Through_–_Invidious⠀⇛ In this video, we are looking at Xubuntu 22.04 Beta. # ⚓ Linux Made Simple ☛ Xubuntu_22.04_Beta⠀⇛ Today we are looking at Xubuntu 22.04 Beta. It comes with XFCE 4.16, Linux kernel 5.15, and uses about 800MB of ram when idling. Enjoy! # ⚓ Video ☛ 3D_printing_a_bunch_of_community-made_Steam_Deck models._Any_you’d_recommend?_–_Invidious⠀⇛ # ⚓ Video ☛ STEAM_DECK_Gameplay_|_LEGO_Star_Wars:_The_Skywalker Saga_–_Invidious⠀⇛ # ⚓ Video ☛ “Hey,_DT!_What’s_Your_Thoughts_On_Elementary_OS?”_ (And_Other_Questions)_–_Invidious⠀⇛ On this episode of Hey, DT: 0:00 Intro 0:19 Are you finally gonna do a true review about ChromeOS? # ⚓ Video ☛ Gitlab_Ships_Critical_Account_Takeover_Bug_– Invidious⠀⇛ So a gitlab dev made a pretty big mistake and pushed a hardcoded password into production code, the results are as you’d expect. o § Applications⠀➾ # ⚓ Istio_/_Announcing_Istio_1.12.6⠀⇛ This release contains bug fixes to improve robustness. This release note describes what’s different between Istio 1.12.5 and Istio 1.12.6 # ⚓ Medevel ☛ Shaarli_is_a_free_open-source,_self-hosted Bookmarking_solution⠀⇛ If you are an active internet users, or on a self- education path, surly you collect dozens of links and web pages every day. You most likely need a software to collect, record, organize your links. So, here we introduce you to Shaarli. # ⚓ Ghostscript_9.56.1_Released_with_Apple_Raster_Support⠀⇛ The team announced the release of Ghostscript 9.56.1 with a couple of new features. Read what’s new. o § Instructionals/Technical⠀➾ # ⚓ HowTo Forge ☛ How_to_Install_TeamSpeak_Server_on_Debian 11⠀⇛ # ⚓ Linux Made Simple ☛ How_to_install_Anime_Tournament_HD Reborn_on_a_Chromebook⠀⇛ Today we are looking at how to install Anime Tournament HD Reborn 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. # ⚓ TecAdmin ☛ How_To_Install_LAMP_Stack_on_Ubuntu_22.04_– TecAdmin⠀⇛ The LAMP (Linux, Apache, MySQL, and PHP) stack is wildly used for deploying PHP-based applications on Linux systems. The LAMP server installation is pretty easy and straightforward. You need some basic knowledge of the Linux package manager to complete this setup. This tutorial will help you to install PHP, Apache & MySQL on Ubuntu 22.04 LTS Linux system. # ⚓ Linux Hint ☛ Xrdp_on_CentOS_8⠀⇛ The Xrdp protocol is an open-source remote desktop protocol for Linux and BSD. By using Xrdp server one can remotely log into the machine to perform various operations on the local machine. The Xrdp comes up with a graphical interface, thus making it suitable for novice Linux users as well. Keeping the importance of Xrdp in mind,this guide intends to provide a step-by-step installation and configuration of Xrdp on CentOS 8. # ⚓ OpenSource.com ☛ My_guide_to_understanding_Git_rebase_-i_| Opensource.com⠀⇛ Git is a free and open source distributed version control system designed to handle everything from small to very large projects with speed and efficiency. It is an essential tool in an open source developer’s toolkit. This article covers why and how to use the git rebase –interactive (-i for short) command. This is considered an intermediate Git command, but it can be very useful once you start working with large teams. # ⚓ Linux_Virtual_Machine:_a_Step-By-Step_Guide_to_Increase Your_Company’s_Flexibility⠀⇛ Every operating system (OS) has its pros and cons. Linux, for example, is an open-source operating system, well-known for its speed and configurability. Windows on the other hand, costs a business money, but is easier to use and has enterprise level support offerings. What if you can combine both? You can, with a Linux Virtual Machine. After today’s technological advancements, you no longer have to stick to one OS. You can create a virtual machine with any OS on one computer, regardless of its underlying OS. In any case, this helps you to easily switch back and forth between operating systems. This is great for software development and running older software versions. # ⚓ UNIX Cop ☛ Using_Runit_on_Devuan⠀⇛ Devuan and various systemd-free Linux distributions provide alternative init systems. runit is among the most barebones and lightest. Having a small code base makes it easier to maintain and also audit for bugs and security issues. It is able to run on other Unices like *BSD, MacOSX, etc., as well. In this article, I am going to cover the basics of the runit init scheme with Devuan as a base. However, most concepts and commands should be the same for other distributions. You may refer to the references at the end for learning in more detail. # ⚓ Linux Capable ☛ How_to_Install_Showfoto_on_Ubuntu_22.04 LTS⠀⇛ Showfoto is an Image Editor that has powerful tools for editing photographs. You can view your photos and improve them using this program’s standalone image editor from the digiKam project! One of the features that similar tools like is their versatility with tools dedicated to importing and exporting content to remote web services, like Flickr, GPhoto, Imgur, Facebook, etc. In the following tutorial, you will learn how to install Showfoto on Ubuntu 22.04 LTS Jammy Jellyfish and update and remove the image editing software using the APT package manager with the command line terminal. # ⚓ Building_Emacs_28.1⠀⇛ # ⚓ How_to_Change_the_Root_Password_in_Linux_Mint_20⠀⇛ Occasionally, we have so many things on our minds that we might forget the password of a social network or even a system user. That’s why today, I will help you to change the root password in Linux Mint 20. The procedure is easier than you think. # ⚓ UNIX Cop ☛ Install_Navidrome_using_Docker⠀⇛ We recently told you about Navidrome, and it is a marvel that allows us to deploy our personal streaming platform similar to Spotify. Navidrome has such good support for Linux that we can even install it via Docker. That’s the aim of our post, to help you install Navidrome using Docker. # ⚓ Linuxiac ☛ How_to_Install_Discord_on_Linux:_A_Step_by_Step Guide⠀⇛ This guide will demonstrate how to install Discord, a free voice, video, and text chat app, on different Linux distros. Discord runs natively on all major operating systems, including Windows, macOS, and Linux. Debuted in 2015, it quickly became the communication platform of choice for gamers. Although it was designed with gamers in mind, the application’s versatile features found a home in other communities, and many Open Source organizations began to take an interest in it. # ⚓ UNIX Cop ☛ Ceph_Storage_Centos⠀⇛ All types of Linux can install ceph on any Linux distribution, but it requires the recent kernel and other up-to-date libraries to be appropriately executed. But, here in this tutorial, we will be using CentOS with minimal installation packages on it. # ⚓ UNIX Cop ☛ Create_Files_of_Custom_Size_in_Linux⠀⇛ In this article we will learn to Create Files of Custom Size in Linux. You can create files with your own specific size in linux using different methods. It is very useful when you perform testing of some sorts and you need files with a specific size. We will not be using any external commands. Built in commands will be used to perform this task so that you may not download any external package. # ⚓ Vitux ☛ How_to_Uninstall_Programs_from_your_Ubuntu_System_– VITUX⠀⇛ This article describes removing software from your Ubuntu system that you do not need anymore. We are describing software removal both through the graphical user interface (Ubuntu Software Manager) and the command line-the (Terminal). Please note that you need administrative privileges in order to install/uninstall software from Ubuntu. We have run the commands and procedures mentioned in this article on Ubuntu 20.04 LTS. # ⚓ UNIX Cop ☛ How_to_Install_Diffgram_using_ubuntu,_Docker, and_GCP_Storage⠀⇛ In this post, you will learn how to install Diffgram. Complete training data platform for machine learning delivered as a single application. Open Source Data Labeling, Workflow, Automation, Exploring, Streaming, and more! # ⚓ UNIX Cop ☛ Setup_Network,_System,_and_Datacenter Documentation_Server.⠀⇛ Management of your infrastructure documentation is not an easy job. An application is designed to keep 80% of infrastructure documentation called NET BOX. Being a System Network guy, I always wondered about such an app/server that could manage my infrastructure documentation. Let me tell you more about this application. o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ NuTyX_22.04.1_available_with_cards_2.5.0⠀⇛ The NuTyX team is happy to announce the new version of NuTyX 22.04.1 and cards 2.5.0. New toolchain gcc 11.2.0, glibc 2.35 and binutils 2.38. The xorg-server graphics server version 21.1.3, the Mesa 3D library in 22.0.1, Gtk4 4.6.2 and Qt 6.2.4. The python interpreters are en 3.10.4 et 2.7.18. The XFCE desktop environment is updated to version 4.16.0. The MATE desktop environment is a 1.26.0 version . The GNOME desktop environment is also updated to version 41.5 The KDE desktop environment is available in Plasma 5.24.4, Framework 5.92.0 and applications in 21.12.3. Available browsers are: Firefox 99.0, Chromium 100.0.4896.60, Epiphany 41.3, etc Many desktop applications have been updated as well like Telegram-desktop 3.6.1, Thunderbird 91.7.0, Scribus 1.5.8, Libreoffice 7.3.2.2, Gimp 2.10.30, etc. Core NuTyX ships with Long Term Support (LTS) kernels: 4.9.309, 4.14.274, 4.19.237, 5.4.188 et 5.10.109 and 5.15.32 and the latest stable version 5.17.1 . # § IBM/Red Hat/Fedora⠀➾ # ⚓ Red Hat ☛ A_developer’s_guide_to_using_Kafka_with Java,_Part_1_|_Red_Hat_Developer⠀⇛ Apache Kafka is a distributed, open source messaging technology. It’s all the rage these days, and with good reason: It’s used to accept, record, and publish messages at a very large scale, in excess of a million messages per second. Kafka is fast, it’s big, and it’s highly reliable. You can think of Kafka as a giant logging mechanism on steroids. # ⚓ Red Hat ☛ Automate_CI/CD_on_pull_requests_with_Argo CD_ApplicationSets_|_Red_Hat_Developer⠀⇛ The ongoing quest for greater and greater automation of building, testing, and deployment has recently inspired several new features in Argo CD, Kubernetes, Red Hat OpenShift, and other tools. This article shows how to improve feature testing by automating builds and the creation of Kubernetes environments. Red Hat OpenShift GitOps includes an opinionated deployment of Argo CD that provides a way to manage continuous development or delivery cluster-wide, or even in a multi-tenant cluster configuration. This Operator also provides many toolsets that can help you fit your GitOps workflows into your CI/CD (continuous integration/continuous delivery) processes. One of these tools is called ApplicationSets. ApplicationSets mass-produces Argo CD applications and deploys them onto a cluster or multiple clusters. ApplicationSets accomplishes this task by using generators. Generators vary from use case to use case and depend on things like the Git repository structure, configuration files, key/value lists, and cluster names. # ⚓ Enterprisers Project ☛ Want_to_build_a_relationship with_your_CIO?_5_things_you_shouldn’t_do⠀⇛ Don’t stand out for the wrong reasons. To showcase your ability to handle responsibility and become a trusted partner to the CIO, avoid these five mistakes How you approach your job matters, and CIOs are looking for people who promote a spirit of collaboration and teamwork within IT. Equally important is building a positive reputation within the business as someone who takes a solution-oriented approach. On the flip side, here are five characteristics that will make you stand out to your CIO – for the wrong reasons. # ⚓ PHP_version_8.0.18RC1_and_8.1.5RC1_–_Remi’s_RPM repository_–_Blog⠀⇛ Release Candidate versions are available in testing repository for Fedora and Enterprise Linux (RHEL / CentOS) to allow more people to test them. They are available as Software Collections, for a parallel installation, perfect solution for such tests, and also as base packages. # ⚓ Fedora ☛ Contribute_at_the_Fedora_Linux_36_Test_Week for_Kernel_5.17_–_Fedora_Community_Blog⠀⇛ The kernel team is working on final integration for Linux kernel 5.17. This version was just recently released, and will arrive soon in Fedora. As a result, the Fedora kernel and QA teams have organized a test week now through Sunday, April 10, 2022. Refer to the wiki page for links to the test images you’ll need to participate. Read below for details. # ⚓ Red Hat Official ☛ Automating_Red_Hat_Identity Management_installation⠀⇛ All system admins should be lazy. Not as in not doing their job, but as in doing it as efficiently as possible. Why do you have to do things manually when you can automate them? The more complicated a task, the more reason for automation. Identity Management is an application that makes sense to automate when rolling it out. Red Hat Identity Management (IdM) is fairly easy to install, but the larger your environment, the more machines you need. In a typical datacenter you would probably have an intranet and a DMZ, and you would probably have your servers divided into development and production. The people that should access your servers will probably be divided up into groups as well, consisting of database, web and application administrators. Not to mention your system admins that need access to everything. # ⚓ Working_with_gradient_meshes_in_Inkscape_&_Scribus_to produce_print-ready_artwork_–_Máirín_Duffy⠀⇛ I recorded a ~20-minute video tutorial demonstrating how to work with mesh gradients in Inkscape, importing them into Scribus and producing print-ready CMYK artwork. You can watch it above embedded from YouTube or on my personal LinuxRocks PeerTube channel. # § Debian Family⠀➾ # ⚓ Beta News ☛ Privacy-focused_Linux_distro_Tails_5_Beta now_available_for_download_with_many_critical_security bug_fixes⠀⇛ If you’re worried about your privacy, there’s plenty you can do to secure it. Tails, The Amnesiac Incognito Live System, is a live Linux-based operating system that you can boot into on any computer. Once running it can be used to encrypt your files, emails and instant messaging chats. Today, the developers release a beta version of Tails 5.0, and this is the first version of the distro based on Debian 11 (Bullseye). It offers new versions of most of the software included in Tails, as well as some important usability improvements. # § Canonical/Ubuntu Family⠀➾ # ⚓ The_Call_For_Participation_Is_Now_Open_For_Ubuntu 22.04_Release_Party⠀⇛ To celebrate the new release of the popular free and open source GNU/Linux distribution, Ubuntu 22.04, we are going to hold a release party. The event will take place on the 1st of May. Due to continued COVID uncertainties, the event will be held in a live virtual format with moderated Q&A. The Call for Participation is now open for Ubuntu 22.04 Release Party. There will be 2 session types this year, General session and Workshop session. For the general session each speaker will be allowed 30 minutes to speak on the topic and an extra 15 minutes for discussion/Q&A. For the workshop session each speaker will be allowed 45 minutes for the topic and to do hands-on with the participants together and an extra 15 minutes for discussion/Q&A. o § Devices/Embedded⠀➾ # ⚓ Purism ☛ Purism:_A_Vision_in_Focus⠀⇛ It’s important to understand how we view who are customers and competitors are, because it helps explain how we make decisions, how we prioritize our projects, and why we take such a long-term view on our goals. Because Purism is a strong supporter of free software, many people pigeon-hole us into the “Linux market” and assume our target customer is the hardcore Linux geek. For the same reasons, people often assume our competitors are other companies selling hardware that runs free software and that somehow our or their success is at each others’ expense. While it’s true that we’ve always had a strong core of Linux geeks in our customer base (I’m one of them), I think many people would be surprised to discover just how diverse our customers are. I often say that we sit on a three-legged stool of freedom, privacy and security. Everyone, not just Linux geeks, deserve those things yet each of our customers prioritizes those three values differently. Our core Linux geek audience prioritizes freedom and picks us because of our goal to build hardware that runs 100% free software. Security experts pick us because of our unique security features like our hardware kill switches, auditable firmware, PureBoot, and our Qubes support. Our customers who prioritize privacy pick us because they want an alternative to Big Tech that doesn’t spy on them, and many of these customers have never used something like PureOS before. # ⚓ CNX Software ☛ Bee_Motion_Mini_board_combines_ESP32-C3_with PIR_sensor⠀⇛ Designed by Smart Bee Designs, the tiny Bee Motion Mini combines an ESP32-C3 wireless RISC-V SoC with a PIR sensor for motion detection reporting over WiFi, Bluetooth LE, or Bluetooh Mesh. The board was designed to be as small as possible to fit into a 3D printed case with a LiPo battery and placed/hidden anywhere you want. Motion detection range is up to 5 meters, and the Bee Motion Mini can connect to services like MQTT, ITTT, or NodeRed to trigger other devices upon motion. # § Open Hardware/Modding⠀➾ # ⚓ Jeff Geerling ☛ New_Raspberry_Pi:_Compute_Module_4S⠀⇛ The CM4S mashes a BCM2711 SoC into the Compute Module 1, 3, and 3+ form factor—which was used for years until the switch to 2x 100-pin board-to-board connectors on the CM4 (pictured on the left): [...] # ⚓ Arduino ☛ This_DIY_coop_controller_makes_caring_for chickens_a_much_easier_task_|_Arduino_Blog⠀⇛ Chickens, like most other livestock, require consistent care including access to fresh water, plenty of food, and space to roam around until sheltering throughout the night. For the hobbyist farmers who run the YouTube channel East x West Farms, they needed a simple way to automatically regulate their chicken coop without having to constantly visit it in person, especially while away doing other things during the day. In response, they created a chicken coop controller that is able to reduce the amount of direct care required. # ⚓ Arduino ☛ The_Arduipiano_is_an_Arduino-powered_floor piano_that_lets_you_play_music_with_your_feet_|_Arduino Blog⠀⇛ The typical piano consists of an array of keys that, when struck by a finger, cause a note to play either from a digital circuit or a vibrating string. But to change this design up a bit and introduce some additional fun, a team of students from the Marie Noel college in Joigny, France set out to create a larger version that could be played using feet instead of hands just like Tom Hanks in the 1988 classic film “Big.” The aptly named Arduipiano is based around an Arduino Mega 2560 owing to its large number of GPIO pins. After cutting out piano “keys” from large sheets of aluminum foil, each piece was glued to a cardboard base and wired to the Mega via a single 4.7Mohm resistor on each receive pin. Pin 2 acts as the capacitive send pin, which lets the microcontroller measure the change in capacitance for every key in order to determine if it is currently being touched. At the end of each iteration of the main loop, all of the pressed keys are converted to notes and sent through a serial port to a MIDI receiver. # ⚓ Arduino ☛ The_O-Clock_is_a_fun_way_to_check_the current_time_|_Arduino_Blog⠀⇛ After coming to the conclusion that the traditional analog clock just isn’t enough and the digital clock is too boring, Hans Andersson decided to make his own version that integrates both RGB LEDs and fiber optics to show the current time in a far more entertaining manner. Rather than moving a set of three hands around in a circle or toggling a bunch of digits, the “O-Clock” lights up a series of 60 slits in a hollow ring in red, green, and blue, as well as many other colors, to indicate the hour, minute, and second. o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Firefox_99_Brings_New_ReaderMode_Feature_and Security_Fixes⠀⇛ Mozilla announced the release of Firefox 99 across all stable channels, and soon, it will be available for all the official Linux distribution repo. # ⚓ Extensions_for_cleaning_up_a_chaotic_desktop _– Firefox_Add-ons_Blog⠀⇛ Clutter isn’t just material stuff scattered about your floor and shelves. Clutter can consume us in digital form, too — from an overabundance of browser bookmarks and open tabs to navigating a world wide web that’s littered with junk. The right browser extension, however, can really help clean things up… # ⚓ Mozilla ☛ Mozilla_Open_Policy_&_Advocacy_Blog: Philippines’_SIM_Card_Registration_Act_will expose_users_to_greater_privacy_and_security risks_online⠀⇛ While well-intentioned, the Philippines’ Subscriber Identity Module (SIM) Card Registration Act (2022) will set a worrying precedent for the privacy and anonymity of people on the internet. In its current state, approved by the Philippine Congress (House of Representatives and Senate) but awaiting Presidential assent, the law contains provisions requiring social media companies to mandatorily verify the real names and phone numbers of users that create accounts on their platform. Such a move will not only limit the anonymity that is essential online (for example, for whistle blowing and protection from stalkers) but also reduce the privacy and security they can expect from private companies. # § Content Management Systems (CMS)⠀➾ # ⚓ WordPress_5.9.3_Maintenance_Release_–_WordPress News⠀⇛ WordPress 5.9.3 is now available! This maintenance release features 9 bug fixes in Core and 10 bug fixes in the block editor. WordPress 5.9.3 is a short-cycle maintenance release. The next major release will be version 6.0. # § Programming/Development⠀➾ # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ The_Day_of_a_new_Command-Line_Interface: Shell⠀⇛ This article continues the long-lost series on how to migrate away from terminal protocols as the main building block for command-line and text- dominant user interfaces. The previous ones (Chasing the dream of a terminal- free CLI (frustration/idea, 2016) and Dawn of a new Command-Line Interface (design, 2017)) might be worth an extra read afterwards, but they are not prerequisites to understanding this one. The value proposition and motivation is still that such a critical part of computing should not be limited to device restrictions set in place some 50-70 years ago. The resulting machinery is inefficient, complex, unreliable, slow and incapable. For what is arguably a strong raison d’être for current day UNIX derivates, that is not a strategic foundation to neither rely nor expand upon. The focus this time is about the practicalities of the user facing ‘shell’ — the cancerous and confused mass that hides behind the seemingly harmless command-line prompt. The final article will be about the developer facing programming interfaces themselves as application building blocks, how all of this is put together, and the design considerations that go into such a thing. # ⚓ Mapping_with_gnuplot,_part_3⠀⇛ In the last post I explained how I built a base map of Tasmania (coastline plus main roads) with a lat/lon grid using gnuplot. Here I describe how the base map was used to generate GIF animations. # § Java⠀➾ # ⚓ TecAdmin ☛ Java_–_Get_Value_from_Key_in_HashMap –_TecAdmin⠀⇛ Write a Java program to get keys from the hashmap using the value. The HashMap class is available under the java.util package. It is pretty similar to HashTable, but the HashMap is unsynchronized and also allows to stole one null key. In this tutorial, you will learn Java examples to get keys from a HashMap based on a defined value. o § Standards/Consortia⠀➾ # ⚓ Samsung_devices_incorrectly_handle_CSS_@media_hover queries⠀⇛ The hover @media feature query lets you check if a device’s primary input device supports hovering interactive elements. It became part of the web platform as of CSS Media Queries Level 4. The hover: hover query should match on devices with a mouse cursor (e.g. a touchpad), and hover: none should match touchscreens (mobile devices). Unfortunately, Samsung devices say their touchscreens are touchpads. The media feature query let you detect and apply different styling when a device supports hover interactions. For example, you can collapse an expandable menu when the device supports hovering and expand it by default when it doesn’t. * § Leftovers⠀➾ o § Science⠀➾ # ⚓ Matt Rickard ☛ Zero_Knowledge_Proofs⠀⇛ How do you prove that you know something secret without revealing the secret? # ⚓ Vice ☛ Sound_on_Mars_Has_a_‘Unique’_And_Extremely_Trippy Property,_Recordings_Reveal⠀⇛ The new audio confirms that the speed of sound is slower on Mars than on Earth, a result that was expected since the motion of acoustic waves is modulated by the density of substances they occupy. For instance, here on Earth, the speed of sound is faster in the dense medium of water than it is in the air. o § Hardware⠀➾ # ⚓ Hackaday ☛ Fix_Every_Broken_Via_To_Return_This_Game_To Life⠀⇛ We all know the havoc that water in the wrong place can do to a piece of electronics, and thus we’ve probably all had devices damaged beyond repair. Should [Solderking] have thrown away the water- damaged PCB from a Nintendo Pokemon Ruby cartridge? Of course he should, but when faced with a board on which all vias had succumbed to corrosion he took the less obvious path and repaired them. # ⚓ Hackaday ☛ RC_Car_Test_Tether_Takes_Car_Testing_To_New Lengths⠀⇛ It’s fascinating to see what happens when a creative hacker is given a set of constraints to work within. [rctestflight] found themselves in a very specific set of circumstances: Free RC cars from sponsors, and no real purpose for them. Instead of just taking them apart to see what made them tick (itself the past time of many a beginning hacker), [rctestflight] decided to let the RC cars disassemble themselves, destructively, on their way to 100,000 (scale) RC Car Miles, tallying up the distance (and the carnage) in the end as you see in the video below the break. # ⚓ Hackaday ☛ A_3D_Printed_35mm_Movie_Camera⠀⇛ Making a camera can be as easy as taking a cardboard box with a bit of film and a pin hole, but making a more accomplished camera requires some more work. A movie camera has all the engineering challenges as a regular camera with the added complication of a continuous film transport mechanism and shutter. Too much work? Not if you are [Yuta Ikeya], whose 3D printed movie camera uses commonly-available 35 mm film stock rather than the 8 mm or 16 mm film you might expect. # ⚓ Hackaday ☛ LED_Filaments_Make_A_Retro_Clock_Without_Any Retro_Parts⠀⇛ We love clock projects here at Hackaday, and we’ve seen many beautiful designs based on a wide variety of display technologies. There are various types of glass tubes like Nixies, Numitrons and classic VFD displays, all of which have that warm “retro” glow to them. Then there’s LEDs, which are useful for making cool pixel-based timepieces and easy to drive with low-voltage electronics. So how about combining the best of both worlds, by using LEDs to make a Numitron-like display? That’s exactly what [Jay Hamlin] did when he built a digital clock based on LED filaments. # ⚓ Hackaday ☛ Solder_Pot_From_The_Kitchen⠀⇛ We aren’t shy of dangerous projects, but, then again, a large cooking pan full of lead solder might be a bit much, even for us. It goes without saying that you should be extremely careful and you won’t want to use any of the cookware again for any other purpose. You can see the build in the video below. # ⚓ Hackaday ☛ Magpies_Help_Each_Other_Escape_Tracking_Devices With_This_One_Weird_Trick⠀⇛ Scientists who work with animals love to track their movements. This can provide interesting insights on everything from mating behaviour, food sources, and even the way animals behave socially – or anti-socially, as the case may be. # ⚓ Hackaday ☛ A_Simple_Linear_Power_Supply,_Done_Well⠀⇛ When reaching for a power supply design it’s normal here in 2022 to reach for a switching design. They’re lightweight, very efficient, and often available off-the-shelf at reasonable prices. Their benefits are such that it’s become surprisingly rare to see a traditional linear power supply with a mains-frequency transformer and rectifier circuit, so [ElectroBoy]’s dual voltage PSU board for audio amplifiers is worth a second look. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Democracy Now ☛ A_Poor_People’s_Pandemic:_Report_Reveals Poor_Died_from_COVID_at_Twice_the_Rate_of_Wealthy_in_U.S. [Ed: Patents are again killing millions of people to increase profit]⠀⇛ The newly released “Poor People’s Pandemic Report” shows poor people died from COVID at twice the rate of wealthy Americans and that people of color were more likely to die than white populations. “Our country has gotten used to unnecessary death, especially when it’s the death of poor people,” says Rev. Liz Theoharis, co-chair of the Poor People’s Campaign. # ⚓ WHO_launches_guidance_on_digitally_documenting_SARS-CoV- 2_test_results⠀⇛ interoperability standards, facilitated by a common digital architecture, for a digitized test result certificate which can be used as proof of negative test results or proof of previous SARS-CoV- 2 infection for international travel, or as a means for protection policies that reduce public health risk in public or private venues – in accordance with individual Member States’ public health policy and their risk-based approach to addressing COVID- 19. Additional technical details to support the adoption of open standards for interoperability and approaches for implementing a DDCC:TR solution can be found in the WHO DDCC Health Level Seven (HL7) Fast Healthcare Interoperability Resources (FHIR) implementation guide. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ IT Wire ☛ Google_blames_Microsoft_‘monoculture’_for govt_security_problems [iophk: Windows TCO]⠀⇛ Google has taken a potshot at Microsoft, something it does occasionally, using a survey conducted by Public Opinion Strategies — and paid for by its own cloud business — to ventilate the concerns of government users who are mostly locked into a Microsoft environment. # § Pseudo-Open Source⠀➾ # § Openwashing⠀➾ # ⚓ OpenSource.com ☛ 4_questions_about_the essence_of_openness⠀⇛ Despite some quibbles I voiced in the first part of my review of Johan Norberg’s Open: The Story of Human Progress, the author’s argument remains engaging—especially at this historical juncture, as the world witnesses Russia’s invasion of Ukraine, and authoritarian movements around the world are threatening the sustainability of the liberal democracies Norberg identifies as bastions of openness. But if the world were to somehow make a transformational leap towards more global openness, what would actually be required? The conceptual challenge of that is daunting—but a first step might begin simply by articulating some of the unexplored questions that follow from Open’s overall vision. These are meaty questions, to be sure—about the actual “performance gains” more openness will deliver, about design considerations that any community would need to make if to pursue open transformation, and about how, precisely, that work would have to be undertaken in different contexts. # § Security⠀➾ # ⚓ Transparency_initiatives_in_the_DSA:_An Exciting_Step_Forward_in_Transparency_Reporting⠀⇛ In January 2022, the European Parliament voted in favor of the Digital Services Act (DSA), a horizontal legislation for the EU’s digital single market that seeks to define platforms’ responsibility regarding user content. The draft law also contains several concrete provisions aimed at mitigating certain harms of online advertising, including imposing a ban on ‘dark patterns’ when getting consent from users (Article 13a), a behavior that recently led to the French DPA imposing fines of over $200 million on Facebook and Google. While the DSA seeks to promote a more free internet in numerous ways, this article focuses on its transparency mandates for content moderation decisions and the provisions mandating researcher access to data. # ⚓ SUSE’s Corporate Blog ☛ Reinforcing_Open_Source Security_with_SUSE_and_the_new_IBM_z16 [Ed: What does this have to do with security? When "Senior Product Manager" with "a wide breadth of technical marketing expertise" writes stuff...]⠀⇛ If the last two years have taught us anything, they’ve taught CIOs how to be resilient. Resiliency comes in the form of being agile, adaptable, and the right security. And the ability to thrive in unforeseen circumstances. # ⚓ Fixing_Dirty_Pipe:_Samsung_rolls_out_Google code_faster_than_Google_|_Ars_Technica⠀⇛ Dirty Pipe is one of the most severe vulnerabilities to hit the Linux kernel in several years. The bug lets an unprivileged user overwrite data that is supposed to be read-only, an action that can lead to privilege escalation. The bug was nailed down on February 19, and for Linux flavors like Unbuntu, a patch was written and rolled out to end users in about 17 days. Android is based on Linux, so Google and Android manufacturers need to fix the bug, too. # ⚓ 9to5Google ☛ Dirty_Pipe:_Pixel_6_&_Galaxy_S22 affected_by_major_exploit_–_9to5Google⠀⇛ The security world has been abuzz about a new Linux exploit called “Dirty Pipe,” which also affects Android 12 devices like Galaxy S22 and Pixel 6. Here’s everything you need to know about “Dirty Pipe,” which devices it affects, and how best to avoid it. # ⚓ Qt ☛ Security_advisory:_Recently_reported_zlib compression_issue_impacts_Qt⠀⇛ zlib has recently reported that it has a security issue when deflating which could cause memory corruption if the input has many distant matches. This is reported in a bit more detail here: https://github.com/madler/zlib/issues/ 605 and has been assigned the CVE id CVE-2018-25032. This has been fixed in an update to zlib 1.2.12 # § Privacy/Surveillance⠀➾ # ⚓ Tails ☛ Tails_4.29_is_out⠀⇛ Have a look at our roadmap to see where we are heading to. # ⚓ IT Wire ☛ News_media_code_review_will_go easy_on_Facebook_again⠀⇛ Australia’s news media bargaining code is being reviewed after its first year of operation, but the Federal Government has signalled that it will not force any company that has not adhered to the requirements of the code to do so. o § Defence/Aggression⠀➾ # ⚓ Site36 ☛ Ukraine_war:_The_age_of_loitering_warheads_is dawning⠀⇛ Initially, the Ukrainian military dominated the drone war against the Russian attackers, who are now striking back unmanned. Both sides are relying on a new weapons system. # ⚓ Site36 ☛ „Thin_Blue_Line“:_German_police_divided_on extremist_iconography⠀⇛ An internal paper of the Bavarian Police problematises a symbol which stands for a conspiratorial community of solidarity. According to the paper, it is widespread in right-wing police circles and could violate the principle of neutrality and lead to disciplinary consequences. Not all police officers see it that way. # ⚓ RTL ☛ Tigrayans_subjected_to_‘war_crimes’_in_Ethiopia⠀⇛ Amnesty International and Human Rights Watch (HRW) said Tigrayan civilians had been targeted in “a relentless campaign of ethnic cleansing” in the long-contested western Tigray region since the outbreak of Ethiopia’s war in November 2020. Over the ensuing months, several hundred thousand Tigrayans were forcibly expelled from western Tigray in a “coordinated” manner by security forces and civilian authorities through ethnically- motivated rape, murder, starvation, and other serious violations. # ⚓ Jerusalem Post ☛ Suspected_Islamists_kill_21_civilians_in eastern_Congo⠀⇛ Fighters believed to be from the Allied Democratic Forces (ADF) attacked the village of Masambo on Sunday night, said Ricardo Rupande, president of the group, the Ruenzori Sector Civil Society. # ⚓ MEMRI ☛ Egyptian_Writer_Following_Killing_Of_ISIS_Operative Who_Was_Nephew_Of_Hamas_Leader_Yahya_Al-Sinwar:_There_Is_No Difference_Between_ISIS,_Hamas_And_Muslim_Brotherhood⠀⇛ Following the report of his killing, Egyptian journalist Amira Khawasek published an article in the daily Al-Yawm Al-Sabi’, in which she mentioned other terrorist attacks against Egypt that some Egyptian elements had attributed to Hamas. She stated that Mus’ab Mutawa’s ties to both Hamas and ISIS prove that “ISIS, Hamas and the Muslim Brotherhood (MB) are equal in their depravity and crimes, and do not differ in any way.” # ⚓ Antipope ☛ Behind_the_Ukraine_war⠀⇛ It’s a lot less morally questionable than my grim speculation about geolocation/social media apps mediating intra-community genocide, but it’s still appalling by implication. The Ukrainians are justified in doing this, but sooner or later someone is going to turn this into a tool for genocide. What is funny, in the sense of funny-peculiar, not funny-humorous, is the war of the cellular networks. It turns out the Russian field units are using 1980s analog radios and cellphones to communicate. A lot of them got lost because after commanders confiscated all the troops’ smartphones, they issued paper maps which nobody knows how to use any more. Meanwhile the Russian commanders were using an end-to-end encrypted secure messaging app … that required cellphone service, and by shelling the Ukrainian cellphone base stations they were disrupting their own secure comms. It’s an absolute clusterfuck, and if it wasn’t combined with atrocities and war crimes it would be hilarious. o § Transparency/Investigative Reporting⠀➾ # ⚓ IT Wire ☛ WikiLeaks_marks_12_years_since_release_of Collateral_Murder_video⠀⇛ As WikiLeaks founder and publisher Julian Assange remains in the UK’s Belmarsh Prison, waiting for the next move in the US bid to extradite him, WikiLeaks has released long and short versions of the Collateral Murder video that shows unprovoked killings by US forces in Iraq in 2010. o § Environment⠀➾ # ⚓ Times Higher Education ☛ Fossil_fuel_research_ties undermine_universities’_climate_change_response⠀⇛ Let’s be clear. Industry executives have known about the devastating climate impacts of their business for more than 50 years. Instead of acting on the science, however, they spent millions of pounds spreading climate disinformation and expanded their fossil fuel operations. They continue to engage in extensive anti-climate political lobbying and resolutely focus the overwhelming majority of their business on fossil fuels, including building new infrastructure and exploring for new reserves. Meanwhile, the world’s top scientists and energy experts are clear that no new fossil fuel infrastructure can be built if the world is to reach net zero emissions by 2050 and avoid runaway climate breakdown. # ⚓ DeSmog ☛ ExxonMobil_Announces_$10_Billion_Oil_Investment the_Same_Day_IPCC_Signals_End_for_Fossil_Fuels⠀⇛ “Investing in new fossil fuel infrastructure is moral and economic madness,” UN Secretary-General António Guterres said as the Intergovernmental Panel on Climate Change (IPCC) released part of its latest report on Monday. This scientific summary, focused on how the world can cut greenhouse gas emissions, warns of the extraordinary harm to all of humanity caused by fossil fuels and the need for a rapid energy transition away from oil, gas, and coal, calling for meaningful changes over the next three years. “Such investments will soon be stranded assets, a blot on the landscape, and a blight on investment portfolios.” That same day, oil giant ExxonMobil made an announcement of its own: a $10 billion final investment decision for an oil and gas development project in the South American nation of Guyana that the company said would allow it to add a quarter of a million barrels of oil a day to its production in 2025. # ⚓ The Economist ☛ A_new_IPCC_report_says_the_window_to_meet UN_climate_targets_is_vanishing⠀⇛ THE WINDOW for limiting global warming to relatively safe levels is rapidly closing, according to the Intergovernmental Panel on Climate Change (IPCC). On April 4th the body released a new report, of nearly 3,000 pages. It appeared after two weeks of wrangling by representatives from 195 governments over how best to present the “state of the union” of climate science. Its conclusion is hardly cheering. To meet the goals of the Paris agreement, to limit the average global temperature rise to 1.5°C above pre-industrial levels—and failing that, to below 2°C—will take immediate and unprecedented action from every country. The IPCC, a UN-backed body, releases a new “assessment report” every eight years or so. Each cycle is a mammoth undertaking, culminating in a trio of reports that comprehensively examines the science of climate change. Hundreds of scientists from around the world plough through thousands of peer-reviewed papers, and then collate their findings into a door-stopping tome. # ⚓ Teen Vogue ☛ Fossil_Fuel_Divestment:_Students_Are_Filing Complaints_to_Force_Change_on_Campus⠀⇛ Throughout the process of filing these complaints, we engaged in conversations with people in the highest positions of administrative power on convoluted topics like institutional asset management. After our Vanderbilt Divestment group presented in front of the faculty senate, we received dozens of messages from faculty members applauding our presentation and ability to synthesize these complex subject matters. Long-gone is the stereotype of unmotivated college students focused on partying more than anything else. When our future is at stake, we step up. # ⚓ [Old] The Washington Post ☛ Student_climate_activists_from Yale,_Stanford,_Princeton,_MIT_and_Vanderbilt_file_legal complaints_to_compel_divestment⠀⇛ Now, frustrated by the response from some school officials, a coalition of student groups working with the nonprofit Climate Defense Project has escalated the fight. Instead of just trying to convince university leaders that their investments are immoral for contributing to global warning, the groups argue that the investments are also illegal. Student-led campaigns at Yale, Princeton, Stanford and Vanderbilt universities and the Massachusetts Institute of Technology filed complaints Wednesday with their respective state attorneys general in a bid to compel schools to divest. The campaigns have requested an investigation into whether the schools have violated a state law related to investments by nonprofit institutions. # ⚓ Vice ☛ ‘They_Are_Lying’:_Companies_and_Governments_Must Decarbonize_Now_to_Avert_Disaster,_UN_Report_Says⠀⇛ The world must achieve “deep and rapid” emissions reductions across all sectors in order to skirt the worst effects of the climate crisis, according to the latest report from the Intergovernmental Panel on Climate Change (IPCC). The United Nations body responsible for advancing knowledge on climate change urged multiplying the speed of the global shift to renewable energy by ending subsidies for fossil fuels and reinvesting those funds in wind and solar in the latest report from the Working Group III on Mitigation of Climate Change, released on Monday. # ⚓ RTL ☛ Major_lifestyle_changes_are_required_to_stop_global warming,_says_Andrew_Ferrone⠀⇛ The goal is clear, Ferrone stressed, namely to reduce CO2 emissions, “preferably to zero”. Fossil fuels currently account for 64% of carbon emissions. Ferrone explained that in practice, this means limiting CO2 emissions to what can be naturally re- absorbed. To limit global warming to 1.5 degrees, “net zero” must be reached by 2050. Global warming could still be limited to 2 degrees by reaching net zero by 2070. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Hungary ☛ Szijjártó_summons_Ukraine’s_ambassador⠀⇛ # ⚓ Hungary ☛ The_five_important_lessons_to_learn_from_Fidesz’ latest_two-thirds_win⠀⇛ # ⚓ Democracy Now ☛ Poor_in_El_Salvador_Face_Brunt_of_Crackdown on_Gang_Violence_as_Gov’t_Suspends_Rights,_Arrests_6,000+⠀⇛ We go to El Salvador for an update on how the government under President Nayib Bukele has arrested over 6,000 people since a 30-day state of emergency was imposed following a wave of violence. The state of exception has suspended freedom of assembly and weakened due process rights for those arrested, including an extension of how long people can be held without charge. Nelson Rauda, a journalist at the newspaper El Faro who has been a target of harassment and surveillance by the Salvadoran government, says the impact of the state of exception has a class divide. “If you have resources … you might go about the state of exception as if nothing is happening,” he says. “For the majority of the country which comes from the lower-income population, it’s been difficult. It’s military checkpoints and police checkpoints and stop-and-frisk.” # ⚓ Democracy Now ☛ Pakistan_in_Crisis_After_PM_Imran_Khan Dissolved_Parliament_&_Accused_U.S._of_Plotting_Regime Change⠀⇛ Pakistan is facing a constitutional crisis after Prime Minister Imran Khan dissolved the country’s National Assembly and called for new elections in an effort to block an attempt to remove him from power. Khan was facing a no-confidence vote in Parliament that would have unseated him, but his allies blocked the vote from happening. Pakistan’s Supreme Court is now hearing a pivotal case on whether it was within the authority of the speaker of the National Assembly to reject the motion for a vote of no confidence, says Pakistani journalist Munizae Jahangir. # ⚓ Copenhagen Post ☛ The_latest_Henley_Passport_Index_shows_a new_Iron_Curtain_forming⠀⇛ The impact of the conflict on travel freedom and mobility has been more important than first imagined. With millions of Ukrainians fleeing their home, Europe is witnessing its worst refugee crisis since World War II. But where it became easier for Ukrainians to cross borders – thanks to the EU emergency plan that allows them to live and work in any of the 27 member states – it has become much more difficult for Russians. # ⚓ CNN ☛ UK_government_will_sell_public_service_broadcaster Channel_4⠀⇛ The British government has decided to sell Channel 4, the publicly-owned but commercially funded broadcaster founded nearly 40 years ago as an edgy alternative to the BBC and ITV (ITVPF), the company said on Monday. Ministers said last year that privatization would help secure Channel 4′s future as a public service broadcaster. The broadcaster, however, has fought such a move, saying there was no evidence to show that a privatized Channel 4 would be able to better fulfill its remit to provide challenging and distinctive programming for audiences under-served by rivals. # ⚓ Digital_Markets_Act:_Dispute_over_press_publishers_shows what’s_wrong_with_EU_legislation⠀⇛ Last week, the EU reached an agreement on a core piece of platform regulation, the Digital Markets Act. The Digital Markets Act contains rules for digital companies with high market power, so-called gatekeepers. These are large companies that provide an exceptionally widely used platform service, for example a smartphone operating system, a social network, a messenger service or a search engine. Unlike traditional competition law, which mainly intervenes after the fact, the Digital Markets Act is intended to prevent market abuses and make it easier for smaller competitors to enter platform markets. # ⚓ Ali Reza Hayati ☛ Give_Amazon_and_Facebook_more_power? Human_idiocy_has_no_limit_whatsoever!⠀⇛ A Bloomberg opinion suggested we give Amazon and Facebook a seat at the United Nations as commercial superpowers so we can force them to behave as we wish to benefit people! What about no? o § Misinformation/Disinformation⠀➾ # ⚓ The Atlantic ☛ Stop_Saying_Ukraine_Is_Winning_the Information_War⠀⇛ Despite this, it’s far too early to declare information victory. If anything, this apparent consensus—that Ukraine has won the online war—might be obscuring where battles over the invasion are really raging. # ⚓ The Verge ☛ Elon_Musk_tweeted_his_way_onto_Twitter’s_board —_now_what?⠀⇛ If Musk is trolling, though, this is sharp. Like, maybe he’ll get a fine or something, but the SEC’s job is to protect shareholders, right? It’s why Musk and Tesla got fined for his “funding secured” tweets but Musk remained as CEO — removing him would arguably harm shareholders more than letting Musk yolo his little heart out. Musk is valuable! The disclosure of his stake in Twitter sent shares up 27 percent, a cute lil pop for a social media company that’s getting absolutely clobbered by TikTok and the company formerly known as Facebook. So if the SEC is like, “haha, you are definitely not going to be on the board of Twitter,” it’s probably wise to assume the stock will fall! And shareholders will get hurt! # ⚓ Salon ☛ Elon_Musk_blows_up_Twitter_with_board_of_directors announcement⠀⇛ While Musk has indicated he will be making “significant improvements” to Twitter it is unclear what those improvements will be. On Monday he tweeted out a poll asking if people wanted an edit feature added to the platform. # ⚓ IT Wire ☛ Twitter_shares_soar_after_Elon_Musk_9.2%_stake revealed⠀⇛ On 27 March, he wrote: “Given that Twitter serves as the de facto public town square, failing to adhere to free speech principles fundamentally undermines democracy. What should be done?” # ⚓ Screen Rant ☛ Did_Elon_Musk_Buy_His_Way_Into_Twitter_For Its_Crypto_Project?⠀⇛ As reported by Wired, Twitter is shifting the way it does business, moving away from ad-generated revenue and into the crypto and NFT world as part of its diversification of revenue strategy. According to the report, Twitter has a solid crypto future in full development. Twitter Crypto, a unit within the social media giant, works to massify crypto and digital assets. While digital wallets and online crypto trading sites face the challenge of attracting millions of users, Twitter already has plenty, 396.5 million of them. Now the company is developing crypto technology and moving fast into a trend which Musk publicly supports. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ VOA News ☛ From_Exporting_Goods_to_the_News:_Ukrainians Swap_Day_Jobs_for_Journalism⠀⇛ In journalism-speak, fixers are local people who work closely with foreign reporters on everything from securing interviews, translating, and booking hotels to more crucial work including advising on possible threats and no-go areas. Often these are journalists already established in their home country. But some like Zubova are new to the profession — and learning on the job while navigating a war zone. o § Civil Rights/Policing⠀➾ # ⚓ NPR ☛ Supreme_Court_makes_it_easier_to_sue_the_police_for malicious_prosecution⠀⇛ On Monday, the Supreme Court sided with Thompson in declaring that he did not have to show an “affirmative indication of innocence.” The vote was 6-to-3, with three conservative justices — Chief Justice John Roberts and Justices Brett Kavanaugh and Amy Coney Barrett — joining the courts three liberals in the majority. # ⚓ uni Michigan ☛ Organ_trafficking_is_not_getting_the attention_it_deserves_—_here’s_why⠀⇛ [...] Because the human organ market is an underground market, it is difficult to make any definitive estimates of its value. Journalist Scott Carney supposes it could be worth billions of dollars. There are estimates that 10% of all organ transplants are performed using trafficked organs. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ Public Domain Review ☛ Knowledge_by_the_Pound:_*The Renowned_History_of_Giles_Gingerbread*_(1768)_–_The Public_Domain_Review⠀⇛ As Giles learns how to read, in this 18th- century children’s book, he consumes an alphabet baked from gingerbread, literally becoming “A little Boy who lived upon Learning”. # ⚓ Torrent Freak ☛ Music_Industry_Flags_Discord_and Reddit_as_Primary_Piracy_Threats⠀⇛ International music industry group IFPI has submitted its recommendations for the EU’s upcoming ‘Counterfeit and Piracy Watch List’. As expected, the report flags YouTube rippers, cyberlockers and torrent sites. However, messenger platforms and social media sites such as Discord, Reddit, Telegram and Twitter, are also seen as top enforcement priorities. ䷩ 𝚕𝚒𝚗𝚎 6308 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.06.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_06/04/2022:_Snap_to_Flatpak_Bridge⠀✐ Posted in News_Roundup at 9:19 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Applications⠀➾ # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to Apple_Logic_Pro⠀⇛ Apple, Microsoft, Alphabet (Google’s parent), Amazon and Facebook dominate the tech landscape. Their dominance is so broad they account for more than 20% of the S&P 500. There are many things to admire about Apple’s hardware and software. Apple make great looking (albeit expensive) hardware. Over the years key successes include the iPhone, iPad, iPod, and the MacBook Air. The company designs its own hardware and software. This gives them the power to make an operating system and suite of apps that are tailor- made and optimized for their hardware. Apple also operates the Apple Music and Apple TV media distribution platforms. Mac OS X is Apple’s proprietary operating system for its line of Macintosh computers. Its interface, known as Aqua, is highly polished and built on top of a BSD derivative (Darwin). There’s a whole raft of proprietary applications that are developed by Apple for their operating software. This software is not available for Linux and there’s no prospect of that position changing. o § Instructionals/Technical⠀➾ # ⚓ ID Root ☛ How_To_Install_Ristretto_on_Ubuntu_20.04_LTS_– idroot⠀⇛ In this tutorial, we will show you how to install Ristretto on Ubuntu 20.04 LTS, as well as some extra required packages by Ristretto # ⚓ TecAdmin ☛ Install_MySQL_Server_on_Ubuntu_14.04,_12.04_and Debian_7⠀⇛ MySQL is the most popular Open Source SQL database management system. It is developed and supported by Oracle Corporation. MySQL is widely used on Linux systems. Now MySQL providers also provide their own apt repository for installing MySQL on Ubuntu systems. This tutorial will help you to install the MySQL server on Ubuntu 22.04 Jammy Jellyfish Linux systems. # ⚓ Packaging_for_Arch_Linux_|_SleepMap⠀⇛ In Arch, a recap I elaborated a bit on my reasons for getting involved with Arch Linux. In this post I would like to highlight a few technical details and give a “behind the scenes” when it comes to packaging on and for Arch Linux. This post is written from the viewpoint of a distribution packager, but it is likely to contain information also useful to people packaging on different distributions or for private purposes. Arch Linux is a Linux distribution, that offers binary packages in software repositories (aka. repos). To achieve this, packages are built from source files using tooling that is developed by the distribution and various volunteers. The resulting binary packages are then provided to users on mirrors of the distribution (i.e. package files and their cryptographic signatures are provided by web servers) and are downloaded, verified, validated and installed using a package manager. # ⚓ Have_a_smile_Using_printf⠀⇛ # ⚓ uni Toronto ☛ Things_I_needed_to_change_for_HiDPI_on_Linux that_weren’t_in_my_X_settings⠀⇛ I use a very custom desktop which requires me to do a lot of stuff by hand that’s probably covered automatically (or with a general setting) by more standard desktops. With that said, the three big areas that I had to change were font selections, window sizes, and window positions. A subsidiary area has been tweaking the size of interface elements that are sized in pixels, like the width of xterm scroll bars. # ⚓ MWL ☛ Kickstarter_and_Blockchain⠀⇛ The first step is to see if you’re already technically buzzword compliant. Do you have an existing system or product that fits that buzzword? # ⚓ Those_HTML_Attributes_You_Never_Use⠀⇛ My answer was easy: HTML. And I wasn’t being sarcastic or mocking in the least. Sure, I pretty much know which tags to use in which instances and how to keep my HTML mostly semantic and accessible. But there is a whole bunch of lesser-used attributes that I was sure I’d forgotten about, and probably a whole bunch of attributes I didn’t even know existed. This post is the result of my research, and I hope you’ll find some of these useful to you, as you build HTML pages in the coming months. # ⚓ OpenSource.com ☛ 10_Git_tips_we_can’t_live_without_| Opensource.com⠀⇛ Git tips are a dime a dozen, and it’s a good thing because you can never get enough of them. If you use Git every day, then every tip, trick, and shortcut you can find is potentially time and effort saved. I asked Opensource.com community members for their favorite Git hacks. Here they are! # ⚓ OpenSource.com ☛ Make_your_own_Git_subcommands_| Opensource.com⠀⇛ Git is pretty famous for having lots of subcommands, like clone, init, add, mv, restore, bisect, blame, show, rebase, and many more. In a previous article, I wrote about the very useful rev-parse subcommand for Git. Even with all of these subcommands available, users still come up with functions to improve their Git experience. While you’re free to create Git-related commands and run them as scripts, it’s easy to make your own custom Git subcommands. You can even integrate them with Git through rev-parse. # ⚓ ID Root ☛ How_To_Install_TeamSpeak_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install TeamSpeak on Debian 11 (Bullseye), as well as some extra requirements for TeamSpeak # ⚓ ID Root ☛ How_To_Install_Shotwell_on_Ubuntu_20.04_LTS_– idroot⠀⇛ In this tutorial, we will show you how to install Shotwell on Ubuntu 20.04 LTS, as well as some extra required packages by Shotwell # ⚓ Install_nopCommerce_on_Ubuntu_20.04,_MySQL,_Nginx,_SSL_– Cloudbooklet⠀⇛ nopCommerce is a free open-source e-commerce web application built with ASP.NET. It is a high performance application with multi-store, multi- vendor and a user-friendly web interface. In this guide you are going to learn how to install nopCommerce in Ubuntu 20.04 with MySQL, Nginx and secure the setup with Let’sEncrypt SSL. # ⚓ Linux Shell Tips ☛ How_to_Install_AnyDesk_Remote_Desktop_in Ubuntu⠀⇛ AnyDesk meets the qualifications of reputable remote desktop software for your Ubuntu Linux distribution. AnyDesk attributes to easy and stable operation, simple administrative tools, user- friendly setup, seamless & smooth remote access from other Linux-powered machines, stable and powerful remote connectivity (Linux-based), and continuous connection (uninterrupted). It uses encryption mechanisms like RSA 2048 asymmetric key exchange and military-grade TLS 1.2 to guarantee user safety while making remote desktop connections. # ⚓ Vitux ☛ Two_ways_to_Flush_the_DNS_Cache_on_Debian_11_– VITUX⠀⇛ The DNS or the Domain Name Server can be characterized as the most essential part of your link to the internet. The DNS translates the domain names to and from the IP addresses so that we don’t need to remember or keep a list of all the IP addresses of the websites we ever want to access. Our systems also maintain a list of DNS records so that we can access our frequently visited websites faster through a quick resolution of IP addresses. This cache on our system needs to be flushed from time to time. This flushing is required because websites may change their addresses time and again, so it is a good idea to avoid IP conflict by clearing the cache. Flushing the cache is also a good way to clear unnecessary data residing on our systems. # ⚓ Vitux ☛ 5_Commands_to_Check_Swap_space_in_Linux_–_VITUX⠀⇛ When the physical memory or RAM on our system is full, we end to make use of the swap space on our systems. In this process, the inactive pages of our memory are moved to the swap space, creating more memory resources. This space is especially useful when a system is down on RAM; however, swap space is located on the hard drive and hence slower to access. Therefore, it should not be considered an appropriate alternative to RAM. In this article, we will describe a few ways to check for available swap space on your Ubuntu system. The commands and procedures described in this article have been run on an Ubuntu 20.04 LTS system. # ⚓ Vitux ☛ Four_Ways_to_Empty_the_Trash/Recycle_Bin_in_Ubuntu –_VITUX⠀⇛ When we delete a file or folder from our system, it moves to the Trash folder(Linux) or the Recycle Bin (Windows). Time and again, we need to get rid of these mostly useless files and folders residing in our system trash in order to vacate space for other important data. In this article, we will describe several ways to empty your system trash, both through the UI and the command line. # ⚓ Vitux ☛ How_to_use_apt_to_install_programs_from_command line_in_Debian_11_–_VITUX⠀⇛ If you are a Linux user, you might be well aware of the apt and apt-get commands with the most common option apt install. Apt is a powerful package management tool that can be used to search, install, update, upgrade, and manage the packages in a Linux operating system. It is a command-line- based tool that is preferred by most system administrators and users. This article shows how to use the apt-get command for installing programs from the command line in Debian OS. We have used Debian 11 OS for running the commands and procedure mentioned in this article. The same commands will work on Debian-based distributions like Ubuntu and its derivates as Kubuntu and Linux Mint too. # ⚓ Vitux ☛ How_to_Check_the_User_Group(s)_an_Ubuntu_User Belongs_To_–_VITUX⠀⇛ As an Ubuntu system administrator, you can create and manage groups for the user accounts on your system. This way you can assign administrative & configurations rights, files & folder access permissions to an entire group rather than a single user at a time. Sometimes we need to know which user group a user belongs to in order to verify or perform group management operations or for assigning/de-assigning user rights. This Group Management on Ubuntu 20.04 only through the command line. In this article, we will describe the simple commands used to perform this effortless check. Open the Ubuntu Terminal through Ctrl+Alt+T or through the Dash. # ⚓ Install_WordPress_on_OpenLiteSpeed_Ubuntu⠀⇛ WordPress is a well-known content management system (CMS) on the Internet. Almost all large and small hosting providers offer several solutions for easily hosting WordPress, and OpenLiteSpeed is one of those solutions. OpenLiteSpeed is a popular open-source free web server that is renowned for responding to user requests faster than Apache, Nginx, and other web servers. OpenLiteSpeed is a free and open-source web server with a simple user interface. When compared to Apache and Nginx, it enables caching out of the box. The OpenLiteSpeed interface allows for the easy creation of virtual hosts for hosting multiple sites on the same server, the installation of SSL certificates, and it supports latest PHP versions. In this tutorial, I will walk you through the entire process of installing WordPress on OpenLiteSpeed. This tutorial will teach you how to configure OpenLiteSpeed to function with the most recent PHP version, how to create virtual hosts, and how to install SSL certificates for sites. # ⚓ Import_Multiple_SQL_Files_In_MySQL⠀⇛ If you are manually migrating your website or simply need to import certain SQL files into your database, this article will show you how to import multiple SQL files in mySQL. We will use both a graphical interface and MySQL command-line. To begin with, it is strongly advised not to import a database onto a live website. Before attempting to import any SQL file, stop the web server and make a backup of your database. # ⚓ Red Hat ☛ Linux_bridging_commands_and_features:_An introduction_|_Red_Hat_Developer⠀⇛ A Linux bridge is a kernel module that behaves like a network switch, forwarding packets between interfaces that are connected to it. It’s usually used for forwarding packets on routers, on gateways, or between VMs and network namespaces on a host. # ⚓ Red Hat ☛ Configure_CodeReady_Containers_for_AI/ML development_|_Red_Hat_Developer⠀⇛ Machine learning and artificial intelligence applications require substantial resources to run in production scenarios. But you can develop and test these applications on a cluster environment that runs on your laptop. In this article, you’ll learn how to properly customize Red Hat OpenShift and Red Hat CodeReady Containers so that you can quickly set up a clustering environment where you can run open source machine learning tools from Open Data Hub. # ⚓ Medium ☛ 7_Uses_of_grep_Commands_in_Linux⠀⇛ To say the grep command is a useful tool for Linux administrators is still an understatement. The grep command is a must-know command for all backend developers. o § Games⠀➾ # ⚓ GamingOnLinux ☛ LEGO_Star_Wars:_The_Skywalker_Saga_runs_on Steam_Deck_and_Linux_with_GE-Proton_|_GamingOnLinux⠀⇛ LEGO Star Wars: The Skywalker Saga has rolled out today, and thankfully for fans of these LEGO games you can get it working on Steam Deck and Linux thanks to Proton. In this case, specifically you need GE-Proton, the community-built version. Valve have given it an “Unsupported” rating on Steam Deck and it’s not surprising for now. With the current Proton 7, even the intro movies are a mess of stuttering and out of sync audio. Proton Experimental is better but performance is still not great. GE-Proton 7.14 seems to work the best for now, although the game (even on Windows) has some performance problems overall it appears. # ⚓ GamingOnLinux ☛ Steam_Deck_improves_Offline_Mode_switching, looks_like_a_lock_screen_is_coming_|_GamingOnLinux⠀⇛ Valve has updated the Steam Deck software again, this time giving a little improvement to the way they handle Offline Mode, plus a bunch of other improvements. Before getting into what’s available now though, how about something else that’s exciting? It seems Valve are preparing to have a lock screen on the Steam Deck. This is something I’ve seen people mention as an issue on Reddit, as the Deck isn’t just like a console, it’s also a PC too with a full desktop mode where you can have more sensitive info. So, a little security makes sense. # ⚓ Liliputing ☛ Lilbits:_Another_AMD_handheld_gaming_PC,_Volla Phone_22_(with_Android_or_Ubuntu),_and_Asus_Tinker_Edge_R single-board_computer_–_Liliputing⠀⇛ The ONEXPLAYER Mini is a handheld gaming PC with a 7 inch display, built-in game controllers, and a choice of processors – a model with an 11th-gen Intel processor launched in January, and a new model with a 12th-gen Intel chip is coming soon. Last month One Netbook introduced a version with an AMD Ryzen 7 5800U processor, but it was only available in China at launch. This week it goes on sale globally. Pricing hasn’t been revealed yet though. In other recent tech news from around the web, Valve says it’s ramping up Steam Deck shipments, Google is cracking down on apps that had allowed you to make in-app purchases for things like eBooks without using Google Play billing (so some app makers are dropping in-app purchases altogether), there’s a new model of the Asus Tinker Edge R single-board computer that’s (a little) cheaper, and phone maker Volla has a new model coming soon that will be able to run Android-based Volla OS or the Linux-based Ubuntu Touch software. # ⚓ GamingOnLinux ☛ GPD_are_getting_quite_desperate_against_the Steam_Deck_|_GamingOnLinux [Ed: GNU/Linux is already killing Windows in games... in some sense]⠀⇛ I’ve never personally used one of their devices, and would have happily taken a look at any point with Linux installed onto one. Even some direct Steam Deck comparisons. Now though? This is not painting a good picture of GPD as a company. # ⚓ GamingOnLinux ☛ Space_Haven_adds_gamepad_support,_gets Steam_Deck_Verified_|_GamingOnLinux⠀⇛ Good news space sim colony-building fans, as Space Haven just got a fresh upgrade and now it’s Steam Deck Verified. Previously, it was given a Playable rating and it was tested with Proton. As of today, the developer released a new update adding in Steam Deck and Gamepad support directly. Seems they got a lightning fast turnaround on retesting, as it’s now fully Verified with the Native Linux build, it’s likely they sent Deck Verified their build before release to test to enable it to be Verified as it’s released. # ⚓ GamingOnLinux ☛ Factorio_improves_low_resolutions_for_Steam Deck_|_GamingOnLinux⠀⇛ Playing Factorio on Steam Deck and low screen resolutions gets better, with a fresh update out now for all players. One of the problems a lot of developers face with the Steam Deck, is the screen size and resolution. A lot of games have quite a small interface, and text that cannot scale — an area that will be a constant improvement for games. Factorio being the latest that’s tweaked it. # ⚓ GamingOnLinux ☛ Humble_Choice_for_April_gives_Ghostrunner, Destroy_All_Humans!_|_GamingOnLinux⠀⇛ As usual, here’s our run over what a new month of Humble Choice brings and the expected compatibility across Linux and Steam Deck for you. This is the bundle where each month Humble give a list of games for subscribers to claim, a good way to build up your collection. o § Distributions⠀➾ # ⚓ Unicorn Media ☛ Elementary_OS_Faces_Uncertain_Future_After Co-Founder_Split⠀⇛ It seems that a business downturn at Elementary, Inc, the company behind the Elementary OS Linux distribution, has led to a partnership breakup. This has left one partner in sole custody of the company, with the other leaving to take a position at a commercial open source company. Also gone is Elementary Inc’s CFO, which has some questioning whether the project can survive with only one person running a company with ailing financials. # § BSD⠀➾ # ⚓ Tachyum_Successfully_Runs_FreeBSD_in_Prodigy Ecosystem;_Expands_Open-Source_OS_Support_|_Tachyum⠀⇛ Tachyum™ today announced it has completed validation of its Prodigy Universal Processor and software ecosystem with the operating system FreeBSD, and completed the Prodigy instruction set architecture (ISA) for FreeBSD porting. FreeBSD powers modern servers, desktops, and embedded platforms in environments that value performance, stability, and security. It is the platform of choice for many of the busiest websites and the most pervasive embedded networking and storage devices. # § EasyOS⠀➾ # ⚓ Barry Kauler ☛ Attempting_fix_Xorg_horiz_and_vert sync_limits⠀⇛ Reading the posts, you will get to a fix. Pemasu commented out the “HorizSync 35-81″ in /etc/X11/xorg.conf and X started OK. Those horiz and vert limits were put in way back when we had cathode-ray-tube monitors. It constrained Xorg so it didn’t try to run the monitor with some insane horiz and vert rates. # ⚓ Barry Kauler ☛ Automatic_popup_of_drives_menu_fixed⠀⇛ It is intended also, that the drives menu will popup automatically, whenever there is some change to the drives, for example, a USB-stick plugged in or removed, or a partition mounted or unmounted. However, that is not happening in Easy 3.4.4. What is supposed to happen is that the ‘xdotool’ utility is used to move the mouse pointer over the drives icon in the tray, then a middle-mouse-button click simulated. This was not happening, the mouse pointer was not getting moved correctly. # ⚓ Barry Kauler ☛ Grub4dosconfig_startup_fixed⠀⇛ Forum member ‘shinobar’ is the author of Grub4dosconfig PET package. It goes way back, and is no longer maintained, as shinobar is now developing Grub2config, that supersedes Grub4dosconfig, and supports both UEFI and traditional BIOS based computers. I will probably update to Grub2config someday, but for now EasyOS has Grub4dosconfig, with some fixes for EasyOS. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Fedora ☛ Contribute_at_the_Fedora_36_CoreOS_Test Week⠀⇛ The Fedora CoreOS team released the first Fedora CoreOS next stream release based on Fedora Linux 36. They expect to promote this to the testing stream in two weeks, on the usual schedule. As a result, the Fedora CoreOS and QA teams have organized a test week. It is underway now and runs through the end of the week. Refer to the wiki page for links to the test cases and materials you’ll need to participate. Read below for details. # ⚓ Enterprisers Project ☛ 4_IT_leadership_tips_for collaborating_with_the_CEO⠀⇛ Establishing a productive working relationship between yourself as an IT leader and your CEO is foundational to your ability to succeed. No matter what company you’re at, there will inevitably be a dichotomy between the two roles at one point or another, and it’s crucial to establish a good rapport to collaborate effectively. # ⚓ Enterprisers Project ☛ New_job_remorse:_3_tips_for handling_struggles_with_a_new_position⠀⇛ You open your brand-new laptop, register your new email address, and update your LinkedIn profile. You introduce yourself to coworkers and try to get acquainted with everyone. You’re navigating the maze called “onboarding,” slowly figuring out your place in the new environment. Then anxiety creeps in: “Did I do the right thing in taking this new job? I feel like a fish out of water. What if this wasn’t the right move?” # § Debian Family⠀➾ # ⚓ Bits_from_Debian:_Infomaniak_Platinum_Sponsor_of DebConf22⠀⇛ We are very pleased to announce that Infomaniak has committed to support DebConf22 as a Platinum sponsor. This is the fourth year in a row that Infomaniak is sponsoring The Debian Conference with the higher tier! Infomaniak is Switzerland’s largest web- hosting company, also offering backup and storage services, solutions for event organizers, live-streaming and video on demand services. It wholly owns its datacenters and all elements critical to the functioning of the services and products provided by the company (both software and hardware). # § Canonical/Ubuntu Family⠀➾ # ⚓ Its FOSS ☛ Ex-Snap_Advocate_at_Ubuntu_Creates_a_Tool to_Help_You_Migrate_from_Snap_to_Flatpak⠀⇛ Don’t like using Snap? Well, you can always stick to the traditional binary packages (deb/rpm) or opt for Flatpak. But, what if you already rely on apps from the Snap store? It will be time-consuming to manually remove the apps, get rid of Snap, install Flatpak, and install all the Flatpak packages. That’s where “Unsnap” comes to the rescue. Unsnap is an open-source utility developed by a former Snap advocate at Canonical, Alan Pope to help you quickly migrate from using snap packages to Flatpaks. o § Devices/Embedded⠀➾ # § Open Hardware/Modding⠀➾ # ⚓ CNX Software ☛ Arducam_Pi_Hawk-eye_is_a_64MP_camera for_Raspberry_Pi_4/CM4_–_CNX_Software⠀⇛ Arducam Pi Hawk-eye is a 64MP “ultra-high resolution” camera for Raspberry Pi 4 or CM4 with built-in autofocus following the company’s 16MP autofocus camera introduced at the end of last year. The new camera module will allow you to take still images at up to 9152 x 6944 resolution, but videos will still be limited to 1080p30 on the Raspberry Pi 4. The Pi Hawk-eye is also compatible with the official Raspberry Pi v1/v2 cameras, meaning you can reuse your enclosures/mounts, and keep on using the same software, for instance, libcamera. # ⚓ CNX Software ☛ RoenDi_is_a_rotary_encoder_with_a color_display_(Crowdfunding)_–_CNX_Software⠀⇛ RoenDi is a rotary encoder with an integrated round color display. Based on an STM32L4 MCU, it can be programmed with the STM32CubeIDE or the Arduino IDE, and be used as an information display, an IoT controller, a locking mechanism, as well as in audio applications. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ 9 to 5 Toys ☛ Android_app_deals_of_the_day:_DRAW CHILLY,_ProCam_X,_Braveland_Wizard,_and_more_– 9to5Toys⠀⇛ # ⚓ 5_Great_Android_Apps_for_Video_Content_Creators_– Phandroid⠀⇛ # ⚓ Android Headlines ☛ Having_An_Android_Phone_Comes With_These_8_Risks_—_How_To_Avoid_Them?⠀⇛ # ⚓ Android Authority ☛ How_to_scan_a_document_on_Android –_Android_Authority⠀⇛ # ⚓ 9to5Google ☛ Rename_your_Bluetooth_devices_on_Android –_Here’s_how_–_9to5Google⠀⇛ # ⚓ MakeTech Easier ☛ How_to_Install_Apps_from_Unknown Sources_on_Android_–_Make_Tech_Easier⠀⇛ # ⚓ 9to5Google ☛ How_to_join_and_leave_Android_app_beta programs_–_9to5Google⠀⇛ # ⚓ Phone Arena ☛ If_your_Samsung_phone_is_running Android_9-12,_it_might_have_been_hijacked_– PhoneArena⠀⇛ # ⚓ GSM Arena ☛ Samsung_Galaxy_Tab_Active3_gets_Android 12-based_One_UI_4.1_update_–_GSMArena.com_news⠀⇛ # ⚓ TechRadar ☛ LG’s_phone_business_is_dead,_but_its phones_are_still_getting_Android_12_|_TechRadar⠀⇛ # ⚓ Ghacks ☛ Vivaldi_5.2_launches_for_the_desktop_and Android_–_gHacks_Tech_News⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ Thoughts_dereferenced_from_the_scratchpad_noise._|_ASUS KGPE-D16_Dasharo_testing_update⠀⇛ Software testing is very important in every type of project to ensure the quality reaches the desired level and the product is in a production state. Unlike software testing, firmware testing does not only verify whether the code behaves as it is supposed to, but also covers functional verification if the hardware works as it should. It makes firmware validation much harder than any software application as we may face many unexpected and not always reproducible issues. The firmware industry constantly tries to improve itself in the field of validation and quality assurance, so is Dasharo. This time we made a huge leap in ASUS KGPE-D16 testing. # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Ghacks ☛ Mozilla_Firefox_99.0:_here_is_what_is new⠀⇛ Mozilla released Firefox 99.0 Stable, Firefox 91.8.0 ESR and Firefox 99.0 for Android on April 5, 2022 to the public. The new release includes security fixes, sandbox strengthening on Linux devices, and support for autofill and capture of credit card data in Germany and France. # § SaaS/Back End/Databases⠀➾ # ⚓ PostgreSQL ☛ PostgreSQL:_PGConf_NYC_2022_(Sep_22_– 23)_–_Call_for_Papers_Now_Open!⠀⇛ PGConf NYC 2022 is a PostgreSQL community conference that will be held on September 22 – 23, 2022 at Convene, 237 Park Avenue, New York City. Come join us for two days packed with talks, demos, and use cases, about PostgreSQL and related technologies. Stay for the fantastic hallway and social track where you can interact with other PostgreSQL users and open source contributors! # ⚓ PostgreSQL ☛ PostgreSQL:_Database_Lab_Engine_3.1: pgBackRest,_timezones_for_CLI,_DLE_community⠀⇛ The Postgres.ai team is happy to announce the release of version 3.1 of Database Lab Engine (DLE), the most advanced open-source software ever released that empowers development, testing, and troubleshooting environments for fast-growing projects. The use of Database Lab Engine 3.1 provides a competitive advantage to companies via implementing the “Shift-left testing” approach in software development. Database Lab Engine is an open-source technology that enables thin cloning for PostgreSQL. Thin clones are exceptionally useful when you need to scale the development process. DLE can manage dozens of independent clones of your database on a single machine, so each engineer or automation process works with their own database provisioned in seconds without extra costs. # § Content Management Systems (CMS)⠀➾ # ⚓ The_Month_in_WordPress_–_March_2022_–_WordPress News⠀⇛ We hope that you and your beloved ones are staying safe during these difficult times. If you’re looking for a way to help support the humanitarian crisis in Ukraine, a list of Non-Governmental Organizations (NGOs) was shared earlier last month in the 26th episode of WP Briefing, Matt Mullenweg on Ukraine, Community, and WordPress. In parallel to the work the community is doing in preparation for the next major release, WordPress 6.0, March has seen the launch of some exciting new projects and proposals. Read on to find out more about the latest updates and how to get involved. # § Programming/Development⠀➾ # ⚓ Medevel ☛ Deployd:_The_REST-API_toolkit_is_not_active anymore.⠀⇛ Deployd is a free, open-source platform for quickly building a REST-API on top of MongoDB. It is an easy-to-use system, as the user does not require any boilerplate, and dive directly into a user-friendly dashboard and start creating and testing your DB collections and API. Deployd comes with dozens of useful features which speeds up the production time. Moreover, it comes with a set of examples, guides, and a developer-friendly rich documentation. # ⚓ Using_the_regexp-parser_of_syslog-ng_–_Blog_–_syslog- ng_Community_–_syslog-ng_Community⠀⇛ For many years, you could use the match() filter of syslog-ng to parse log messages with regular expressions. However, the primary function of match() is filtering. Recent syslog-ng versions now have a dedicated regular expression parser, the regexp-parser(). So, you should use match() only if your primary use case is filtering. Otherwise, use the regexp-parser for parsing, as it is a lot more flexible. # ⚓ Automating_my_home_network_with_Salt_–_Federico’s Blog⠀⇛ In my mind there exists this whole universe of scary power tools for large-scale sysadmin work. Of course you would want some automation if you have a server farm to manage. Of course nobody would do this by hand if you had 3000 workstations somewhere. But for my puny home network with one server and two computers? Surely those tools are overkill? Thankfully that is not so! My colleague Richard Brown has been talking about the Salt Project for a few years. It is similar to tools for provisioning and configuration management like Ansible or Puppet. What I have liked about Salt so far is that the documentation is very good, and it has let me translate my little setup into its configuration language while learning some good practices along the way. I started with the Salt walkthrough, which is pretty nice. TL;DR: the salt-master is the central box that keeps and distributes configuration to other machines, and those machines are called salt-minions. You write some mostly- declarative YAML in the salt-master, and propagate that configuration to the minions. Salt knows how to “create a user” or “install a package” or “restart a service when a config file changes” without you having to use distro-specific commands. # ⚓ Visual-inertial_tracking_for_Monado⠀⇛ Monado now has initial support for 6DoF (“inside-out”) tracking for devices with cameras and an IMU. Three free and open source SLAM/VIO solutions were integrated and adapted to work on XR: Kimera-VIO, ORB-SLAM3, and Basalt. Thanks to this, the RealSense and WinMR (Linux only) drivers in Monado were extended to support this type of tracking. During my six-month internship at Collabora, I had the opportunity to gain firsthand experience on this project. Let me walk you through the concepts, the type of work, and exposure I attained while working remotely as an intern in the XR team for Monado. If any of this has piqued your interest, be sure to check out our careers page. # ⚓ Launch_Your_First_Jenkins_Server_in_a_Single_Command |_by_Vladimir_Mukhin_|_Apr,_2022_|_Medium⠀⇛ Jenkins is one of the oldest and most popular CI/CD tools. It dominates the market and is a requirement for more than 50% of job positions. However, Jenkins is a complicated solution, installing it requires a lot of heavy lifting and can become a pain. In this article, I will uncover the fastest way to deploy Jenkins using only one command. # § Python⠀➾ # ⚓ Red Hat Official ☛ How_to_write_a_Python_script to_create_dynamic_Ansible_inventories_|_Enable Sysadmin⠀⇛ In my last article, I used the host_list and Nmap plugins to generate a dynamic inventory to cover that gap. This article covers how to write your own dynamic inventory script using Python while following good practices for packaging tools, using virtual environments, and unit testing your code. * § Leftovers⠀➾ o ⚓ Counter Punch ☛ Facts_Without_Consequences⠀⇛ What is far more worrisome is the phenomenon that there are “real facts” that cry out for our attention, that demand urgent action, and that our politicians and media treat as non-existent or marginal, e.g. exorbitant military expenses, skewed national budgets, xenophobic war-mongering, structural violence, military aggression, unilateral coercive measures, financial blockades, the homologation of the media, manifestly unjust laws, the corruption of the “rule of law” through legal scams and “lawfare”, the penetration of public institutions by intelligence services, the “weaponization” of human rights, the imprisonment of whistleblowers like Julian Assange, unjust taxation, tax havens, tax evasion, corporate bribery, economic exploitation, ecocide, extreme poverty, man-made famine, social exclusion, etc. Now pause, take a breath and ask yourself why these facts are largely ignored or trivialized by politicians and media alike.  Why are these “inconvenient” facts shoved aside, as if they were only of marginal importance or as if they did not exist?  Without a doubt these facts engender short-term, medium-term and long-term consequences, create or perpetuate imbalances and spread a vague, destabilizing sense of incoherence and cognitive dissonance. o ⚓ Counter Punch ☛ Give_Me_that_Flipper_Shane⠀⇛ In the early 1990s, one figure broke through the stuffiness of willow bats, pads, leather balls and white flannel.  When life left the overly worked body of Australia’s Shane Warne, who expired in Thailand at 52, the reaction was global.  In India and Pakistan, hundreds of millions mourned.  This most celebrated of error-prone buffoons was, as the emperor Vespasian might have said, becoming a god. The Melbourne Cricket Ground, on March 30, became the venue for one such occasion: a state memorial service held in honour of the cricketer.  For a brief spell, a sporting stadium had become a cathedral, the occasion heavy with solemnity.  In it, Warne’s followers and admirers communed. o ⚓ The Nation ☛ Another_World⠀⇛ Niki de Saint Phalle could be iconic even anonymously. In a 2014 interview, Gloria Steinem recalled passing the French American artist on the street in New York City “a long time ago” without knowing who she was. “She was walking on 57th Street and she had on one of those Australian raincoats…it was flowing out behind her,” Steinem said. “She had a cowboy hat and cowboy boots and no purse…. And I thought, ‘That is the first free woman I have ever seen in real life. I want to be just like her.’” o ⚓ The Nation ☛ Green_Tomatoes_in_Fire_Season⠀⇛ There is smoke in the air when I go pick them. I go despite panic, also because inside I’ll make chutney. o ⚓ The Nation ☛ Home_Movie⠀⇛ Strewn across the floors their toys and things, a video cassette the dadhad written “We used to have more of these” on, the kitchen in a state of high party, boxed cakes half eaten, cannoli and rows and rows of drinks were pastries brimming with cream along the broken ramparts of the countertops, we noticed blue carpet but hardwood elsewhere, no choice had been right the house abandoned in haste if in triumph or terror, just abandoned, a family photo on the wall when the twins were babies dad diminutive and round, pale as batter, mom had great bones and a vanity he subsidized while the babies grew through that disorder into us and as we toured the house accepting slowly even this we can’t afford I’d love to steal the plants but how to get them home the towering ficus and an actual tree I can’t name and others they lived at least on a larger scale, they reached for things, these half-wits o § Health/Nutrition/Agriculture⠀➾ # ⚓ Common Dreams ☛ Aid_Groups_Warn_‘More_Variants_Will_Emerge’ If_Congress_Kills_Global_Covid_Funds⠀⇛ An international coalition of humanitarian groups warned Tuesday that “more variants will emerge” if Congress fails to approve new money for the global coronavirus response, a message delivered after senators announced a Covid-19 funding package without any money to fight the pandemic beyond the borders of the United States. “We are deeply disappointed by the Senate’s short- sighted decision to cut off all global Covid funds.” # ⚓ Common Dreams ☛ As_Global_Food_Crisis_Looms,_Groups_Blast Proposed_$1.65_Billion_USDA_Cut⠀⇛ More than 160 advocacy groups on Monday sent letters to President Joe Biden and congressional leaders decrying a proposal to slash up to $1.65 billion in U.S. Department of Agriculture funding, a move that comes during a pandemic-driven global hunger crisis. “Ultimately, the $1.65 billion proposed rescission will impact the most vulnerable among us.” # ⚓ Project Censored ☛ Child_Safety_Concerns_Drive_Potential Pesticide_Ban_–_Validated_Independent_News⠀⇛ On April 29, 2021, the U.S Court of Appeals for the 9th Circuit gave the federal government 60 days to either pull the chemical from all forms of use or prove it was safe for public health. # ⚓ Project Censored ☛ How_Mask-Wearing_to_Prevent_Spread_of COVID-19_Impacts_Children_in_Speech_Therapy_–_Validated Independent_News⠀⇛ “He would just completely disengage, lie on the floor, start playing with the toys, literally turn his back to the computer, try to close it,” said mother Julia Toof of her son, who, at the time, was just shy of 3-years-old. “It just didn’t work.” # ⚓ Project Censored ☛ Biden_Administration’s_Pandemic_Testing Board_Remains_a_Mystery_More_than_One_Year_After Implementation_–_Validated_Independent_News⠀⇛ By that time, tests were in short supply following a rejected proposal to send rapid tests to every American household. As the Omicron variant reached its peak, lack of access to free testing options disproportionately affected communities of color. # ⚓ Pro Publica ☛ The_Invisible_Hand_of_Steve_Twist⠀⇛ When Josh Tate was sentenced in 2017 to 10 years in prison for getting caught with drugs multiple times, his wife, Claire Tate, tried not to dwell on the moments he would miss with their two young kids. She didn’t see the purpose in sending Josh — who had struggled with a meth addiction for years but never been convicted of a violent crime — away for so long. “You can’t punish a drug addiction out of somebody,” Claire Tate said recently. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Pseudo-Open Source⠀➾ # § Privatisation/Privateering⠀➾ # § Linux Foundation⠀➾ # ⚓ PR Newswire ☛ CIP_Expands_Work_on SLTS_Kernel_Maintenance [Ed: For a change, Linux Foundation does something related to Linux]⠀⇛ In December 2021, the Civil Infrastructure Platform (CIP) project (cip- project.org) released the first 5.10-based version of its super-long-term stable (SLTS) kernel. The 5.10- based release made official the third CIP kernel series available after 4.4-cip and 4.19-cip. It demonstrates how CIP remains committed to maintaining all SLTS versions for a minimum of 10 years after the original release. # § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ Techdirt ☛ Clearview_AI_Walks_Back Earlier_Claims,_Is_Now_Willing_To_Sell_Its Sketchy_Product_To_Anyone_With_Money_And_A Pulse⠀⇛ If only Clearview had managed to remain under the radar. If it had, it could have been the stealth privacy assassin multiple entities (both public and private) desire, but are unwilling to admit to using publicly. Even the rest of the facial recognition tech field wants nothing to do with Clearview and the billions of images/data points it has scraped from the public web. Clearview remains alone in its extreme odiousness — a villain rising head and shoulders above its already questionable competition. # ⚓ EFF ☛ Google_Fights_Dragnet_Warrant_for Users’_Search_Histories_Overseas_While Continuing_to_Give_Data_to_Police_in_the U.S.⠀⇛ Keyword search warrants like the one in Brazil are far broader than traditional search warrants described in the Fourth Amendment to the U.S. Constitution. The Fourth Amendment requires police to establish probable cause to search a particular place or seize a particular person or thing before the court authorizes the warrant. But keyword search warrants don’t start with a suspect person or device. Instead, they require Google to comb through the search histories of all of its users, including users who are not logged into a Google account when they search. Keyword warrants allow the police to learn anyone and everyone who may have searched for particular terms on the off-chance one of those people could have been involved with the crime. Like better-known geofence warrants, keyword warrants allow police to conduct a fishing expedition and sweep up data on innocent people, turning them into criminal suspects. Police are using both types of expansive, suspicionless searches with increasing frequency. The Brazilian case arises out of the assassination of Rio de Janeiro City Councilor Marielle Franco. Franco was murdered, along with her driver, Anderson Gomes, near Rio de Janeiro in 2018. It was a terrible crime that stirred up public outcry. o § Defence/Aggression⠀➾ # ⚓ Common Dreams ☛ Opinion_|_Will_the_Wasteful_Pentagon_Budget Ever_Shrink?⠀⇛ I have a question for you: What would it take in today’s world for America’s military spending to go down? Here’s one admittedly farfetched scenario: Vladimir Putin loses his grip on power and Russia retrenches militarily while reaching out to normalize relations with the West. At the same time, China prudently decides to spend less on its military, pursuing economic power while abandoning any pretense to a militarized superpower status. Assuming such an unlikely scenario, with a “new cold war” nipped in the bud and the U.S. as the world’s unchallenged global hegemon, Pentagon spending would surely shrink, right? # ⚓ Common Dreams ☛ Opinion_|_For_War_Crimes_There_Must_Be Accountability⠀⇛ The mass graves of civilians murdered and mutilated in Bucha, Ukraine, are stark evidence of the horrors of war—and of war crimes. Putin’s invasion of Ukraine—itself a violation of international law—raises a profound challenge to the world. How can a dictator armed with nuclear weapons be held accountable for the crimes of war? # ⚓ Common Dreams ☛ Russian_Artist_Depicts_Bucha_Victims_in Photos_Staged_Around_Moscow⠀⇛ As Moscow residents went about their morning early this week, they may have come across an artist laying face-down in front of government buildings and landmarks, recreating widely-seen images of the alleged massacre of civilians in Bucha, Ukraine which have sparked international outrage in recent days. Wearing a brown jacket with their hands tied behind their back with white fabric, the artist appeared on a staircase outside the Kremlin, two streets crowded with pedestrians, and a bridge outside the Cathedral of Christ the Savior, according to images posted Monday by independent Russian media outlet Holod. # ⚓ Common Dreams ☛ Opinion_|_From_Korea_to_Libya:_On_the Future_of_Ukraine_and_NATO’s_Neverending_Wars⠀⇛ Much has been said and written about media bias and double standards in the West’s response to the Russia-Ukraine war, when compared with other wars and military conflicts across the world, especially in the Middle East and the Global South. Less obvious is how such hypocrisy is a reflection of a much larger phenomenon which governs the West’s relationship to war and conflict zones. # ⚓ Mint Press News ☛ The_Ukraine_Conflict_Lays_Bare_the_Myth of_a_More_Civilized_Europe⠀⇛ When a gruesome six-minute video of Ukrainian soldiers shooting and torturing handcuffed and tied up Russian soldiers circulated online, outraged people on social media and elsewhere compared this barbaric behavior to that of Daesh. # ⚓ Mint Press News ☛ On_Its_Seventh_Anniversary,_Yemen_Seeks to_End_a_War_the_World_Has_Forgotten⠀⇛ Seven years have passed since the brutal war against Yemen, a ship-shaped country located on the southern Arabian Peninsula, began in March 2015. The war has been acknowledged as one the bloodiest in modern history and called the “world’s worst humanitarian disaster” by human rights groups. Yet, rather than breaking Yemeni resolve, the Saudi-led war backed by the collective military might of the world’s most powerful nations has only strengthened the poorest country in the Middle East; and Ansar Allah, its underdog combatant, is now stronger and more united than it has ever been. # ⚓ The Nation ☛ Ukraine_Tragedy⠀⇛ # ⚓ The Nation ☛ Tucker_Carson_on_the_War_in_Ukraine⠀⇛ There are no autocrats he can’t abide, So Carlson seems to be on Putin’s side. Thus, Russian television runs his shows. He’s sort of like a preppie Tokyo Rose. # ⚓ Meduza ☛ New_footage_shows_Russian_troops_sending_stolen Ukrainian_items_home_through_Belarus_Russian_soldiers_have been_stealing_Ukrainian_goods_since_the_start_of_the_war.⠀⇛ In early April, the Telegram channel Belaruski Gayun, which has been monitoring military activity in Belarus since February, reported that Russian soldiers were sending large packages to Russia through a courier service. Journalists from the project believe the packages contain items the soldiers stole in Ukraine. In an effort to help hold Russian soldiers “responsible for stealing from and murdering people in Ukraine,” the channel published the names and phone numbers of 16 Russian soldiers. # ⚓ Meduza ☛ ‘We_live_in_a_closet_stuffed_with_skeletons’_Maxim Trudolyubov_on_how_Russians’_inability_to_condemn_the_crimes of_the_past_has_led_them_to_war⠀⇛ Nearly six weeks ago, on February 24, 2022, Russia launched a full-scale invasion of Ukraine. From that moment, the history of the Russian state’s past crimes ceased to be history, argues Meduza’s Ideas editor, Maxim Trudolyubov. Russia’s shared present once again includes a fight against the country’s own population, the trials of “enemies of the people,” deportations, occupations of neighboring countries, and “cleansing operations” in countries that were once part of the Soviet bloc. In the war against Ukraine, all of the Russian state’s worst facets in its Imperial, Soviet, and post-Soviet guises have coalesced. This war is a living indictment that brings together all the things Russian society can no longer ignore. # ⚓ Meduza ☛ ‘A_mockery_of_the_law_and_common_sense’_Meduza translates_Ivan_Safronov’s_remarks_from_the_first_day_of_his closed-door_treason_trial⠀⇛ On Monday, April 4, the Moscow City Court began to review the case of Ivan Safronov on its merits. The former defense reporter and Roscosmos communications advisor stands accused of treason; therefore, his trial is taking place behind closed doors. Meduza has translated the text of the appeal Ivan Safronov made to the court on the first day of the proceedings. Our newsroom received a copy of these remarks from human rights lawyer Ivan Pavlov, who was involved in Safronov’s defense.  # ⚓ FAIR ☛ Western_Sahara_Overlooked_in_Israel/Arab_Summit Reporting⠀⇛ Israeli officials recently hosted representatives of Morocco, Egypt, Bahrain and the United Arab Emirates. For US media, this meant many things, but one thing that didn’t make the papers was that Israel and Morocco share a common goal: maintaining military occupations that are widely condemned throughout the world. # ⚓ Project Censored ☛ Ukraine’s_Women_Warriors_–_Validated Independent_News⠀⇛ In addition to civilian women acting in defense, Ukrainian women also make up fifteen percent of the nation’s soldiers, Kaufman reported. They are “frontline warriors,”  Kaufman wrote, serving as snipers and in other combat roles, not just “logistical support roles or other rear guard jobs.” # ⚓ Counter Punch ☛ Don’t_Let_a_Mountain_in_Montenegro_Be_Lost to_a_War_in_Ukraine⠀⇛ By undeveloped we should not understand uninhabited. Sheep, cattle, dogs, and pastoral people have lived on Sinjajevina for centuries, apparently in relative harmony with — indeed, as part of — the ecosystems. About 2,000 people live on Sinjajevina in some 250 families and eight traditional tribes. They are orthodox Christians and work to maintain their holidays and customs. They are also Europeans, engaged with the world around them, the younger generation tending to speak perfect English. # ⚓ Counter Punch ☛ Where_the_Nuclear_Weapons_Are_and_Who_Has Them⠀⇛ NATO countries have been taken aback by Russian President Vladimir Putin’s implied threats to use nuclear weapons against “whoever interferes with us” in Ukraine, and his placement of additional nuclear officers on shifts under a “special regime of combat duty.” Both Russia and the U.S. have thousands of nuclear weapons, most of which are five or more times more powerful than the atomic bombs that leveled Hiroshima and Nagasaki in 1945. These include about 1,600 weapons on standby on each side that are capable of hitting targets across the globe.Those numbers are near the limits permitted under the 2011 New Strategic Arms Reduction Treaty, often called “New START,” which is the only currently active nuclear arms control treaty between Russia and the U.S. Their arsenals include intercontinental ballistic missiles, better known as ICBMs, and submarine-launched ballistic missiles, as well as missiles launched from specialized aircraft. Many of those missiles can be equipped with multiple nuclear warheads that can independently hit different locations. # ⚓ Counter Punch ☛ War_Crimes_Will_Only_Make_Things_Worse_for Russia_as_Ukrainians_Prepare_for_a_Fight_to_the_Bitter_End⠀⇛ Massacres are the all-important staging posts of history – their influence often greater than that of famous battles – because they send a message to whole communities that their existence is threatened by a common enemy. If the aim of a mass killing is to intimidate a whole population, then experience from Amritsar to My-Lai shows that it usually has precisely the opposite effect. The death of 410 civilians at the hands of the Russian army in the town of Bucha outside Kyiv may well join the grisly list of massacres that permanently shape relations between nations. Why did the Russian army carry out these crimes? They are much against the interests of the Kremlin, which five weeks ago had persuaded itself that part of the Ukrainian population would welcome Russian intervention with open arms. The atrocities were the more-or-less inevitable outcome of this ill- conceived invasion plan, rooted in wishful thinking and carried out by ill-disciplined and ill-trained troops. Poor-quality soldiers like this facing a hostile population are particularly dangerous in my experience, because they quickly come to believe that they are being spied on, sniped at and generally betrayed by the local population. # ⚓ Counter Punch ☛ Albright_and_Clinton:_Two_Peas_in_the_Pod of_“Liberal_Interventionism”⠀⇛ Obituaries for Albright in the mainstream media described the expansion of the North Atlantic Treaty Organization as her “greatest diplomatic achievement.”  At the ceremony in 1999 for the signing of the expansion of NATO into the Czech Republic, Poland, and Hungary), she shouted “To quote an old Central European expression: ‘Hallelujah!’” NATO expansion was the return of the United States to the Cold War policy of containment; it played a major role in destabilizing the balance of power in Europe.  We will never know the full impact of this expansion as well as the flirtation of membership for Ukraine and Georgia, but there is ample evidence of Russian anxieties over the new balance of power.  Putin’s wanton destruction of Ukraine suggests that the expansion of NATO does not fully explain the Russia invasion of Ukraine, but the provocations of Presidents Bill Clinton and George W. Bush must be part of any discussion of today’s war. # ⚓ Counter Punch ☛ Why_Russia_Fumbled_in_Ukraine,_China_Lost Its_Way,_and_America_Should_Exercise_Restraint⠀⇛ That notion differs from the “balance of forces” by placing greater weight on intangible factors. It stipulates that the weaker of two belligerents, measured in conventional terms, can still prevail over the stronger if its military possesses higher morale, stronger support at home, and the backing of important allies. Such a calculation, if conducted in early February, would have concluded that Ukraine’s prospects were nowhere near as bad as either Russian or Western analysts generally assumed, while Russia’s were far worse. And that should remind us of just how crucial an understanding of the correlation of forces is in such situations, if gross miscalculations and tragedies are to be avoided. The Concept in Practice Before Ukraine # ⚓ Counter Punch ☛ What_Would_It_Take_for_Military_Spending_in America_to_Go_Down?⠀⇛ Well, I wouldn’t count on it.  Based on developments after the Soviet Union’s collapse three decades ago, here’s what I suspect would be far more likely to happen.  The U.S. military, aided by various strap-hanging think tanks, intelligence agencies, and weapons manufacturers, would simply shift into overdrive.  As its spokespeople would explain to anyone who’d listen (especially in Congress), the disappearance of the Russian and Chinese threats would carry its own awesome dangers, leaving this country prospectively even less safe than before. You’d hear things like: we’ve suddenly been plunged into a more complex multipolar world, significantly more chaotic now that our “near-peer” rivals are no longer challenging us, with even more asymmetrical threats to U.S. military dominance.  The key word, of course, would be “more” — linked, as I’m sure you’ve guessed, to omnipresent Pentagon demands for yet more military spending.  When it comes to weapons, budgets, and war, the military-industrial complex’s philosophy is captured by an arch comment of the legendary actress Mae West: “Too much of a good thing can be wonderful.” o § Environment⠀➾ # ⚓ Project Censored ☛ Special_Guest_“Coyote”_From_“Defend_the Atlanta_Forest”_and_Under-Reported_Climate_Crisis_Stories_– The_Project_Censored_Show⠀⇛ # ⚓ Common Dreams ☛ Opinion_|_Appalachia_Knows_There’s_a Climate_Crisis._Does_President_Biden?⠀⇛ As an Army veteran who served in Desert Storm and a frontline organizer in the fight to stop the Mountain Valley Pipeline, I am certain that a transition to renewable energy is what our world needs right now. We can’t keep watching as fossil fueled wars displace and kill thousands of people around the world, from Ukraine to Iraq. Not only are these wars inhumane; they threaten the possibility of a livable future for everyone on this planet. They underscore the need to stop projects like MVP and transition to renewable energy. # ⚓ Common Dreams ☛ Opinion_|_Time_to_Put_Charles_Koch_Under Oath_for_His_Climate_Lies⠀⇛ The US House Oversight and Reform Committee kicked off its investigation of the fossil fuel industry’s decades-long climate change disinformation campaign last fall by inviting top executives from BP, Chevron, ExxonMobil and Shell to testify about their role and subpoenaing their companies for internal documents. # § Energy⠀➾ # ⚓ Common Dreams ☛ 120+_Groups_Urge_Pelosi_and_Schumer to_Embrace_Windfall_Tax_on_Big_Oil⠀⇛ More than 120 advocacy groups on Tuesday urged Democratic congressional leaders to support proposed legislation that would levy a new tax on Big Oil “to provide relief to consumers from rising prices and prevent fossil fuel corporations from exploiting the current energy crisis for profit.” “Consumers need relief from price gouging—relief that a windfall profits tax can provide.” # ⚓ Common Dreams ☛ New_Analysis_Details_‘Master_Class_in War_Profiteering’_by_US_Oil_Giants⠀⇛ An analysis released Tuesday by a trio of groups highlights how Big Oil has cashed in on various crises over the past year—including the Covid-19 pandemic, Russia’s war on Ukraine, and the global climate emergency—while enriching wealthy shareholders. “Big Oil is living the second half of their unspoken mantra ‘socialize losses, privatize gains.’” # ⚓ Common Dreams ☛ Federal_Court_Rejects_Coal_Mine Expansion_Unlawfully_Authorized_by_Trump⠀⇛ Environmental defenders on Tuesday urged the Biden administration to take advantage of a federal court ruling which declared that the U.S. Interior Department under former President Donald Trump had wrongly allowed the expansion of a coal mine in Montana—one that would have resulted in the largest coal mine in the U.S. and hundreds of millions of tons of fossil fuel emissions over a decade. With the question of the expansion of Signal Peak Energy’s Bull Mountain Coal Mine now headed back to the Interior Department, said Jeremy Nichols of WildEarth Guardians, which joined other groups in suing over the expansion, “this is now a huge opportunity for the Biden administration to get it right on coal and climate.” # ⚓ Counter Punch ☛ Court_Strikes_Down_Montana_Coal_Mine Expansion⠀⇛ HELENA, MONTANA—A Ninth Circuit Court of Appeals’ panel has just ruled that Trump’s Office of Surface Mining (OSM) wrongly approved an expansion of Signal Peak’s Bull Mountains coal mine located north of Billings, Montana. OSM largely ignored the fact that the proposed 175 million ton expansion would release 240 million tons of greenhouse gas pollution over 11 years. The court ruled OSM “hid the ball” about the climate and environmental impacts of expanding the mine. The proposed expansion would make this the largest underground coal mine in the U.S. based on annual production. It would also result in more greenhouse gas emissions than any point source in the country. # ⚓ Counter Punch ☛ Large-Scale_Logging_Project_in_Castle Mountains_Sent_Back_to_Drawing_Board⠀⇛ The Alliance for the Wild Rockies and Native Ecosystems Council are extremely pleased the Court halted this clearcutting and road bulldozing project and sent it back to the drawing board to force the Forest Service to follow the law. Public lands must be managed for the public and for our wildlife, not for the private profit of a few logging companies.  Legal protections are meaningless if the Forest Service is free to simply ignore them when it plans logging projects on our public lands. The Castle Mountains get their name from the numerous 50-foot high igneous rock spires on the western slopes that look like castle turrets. The range is located about 65 miles northeast of Bozeman and is characterized by peaks over 8,000 feet with numerous grassy parks surrounded by Douglas fir, lodgepole, and limber pine forests.“ # § Overpopulation⠀➾ # ⚓ The Nation ☛ Let’s_Start_Charging_Men_to_Have Babies⠀⇛ Women had a good pandemic the last time around—something actually came of it!—compared with this one, which is total shit. Just over a century ago, the 1918 flu pandemic may have vanquished a decent chunk of the global population, but after witnessing mass death, plus the loss of their children from other preventable diseases like diphtheria and meningitis, women decided to actually do something about it. When (white) American women got the vote two years later, they used their newfound political power to immediately pressure local and federal governments into action, resulting in the largest expansion of public health spending in US history up until that point. It was wildly successful, fueling later large-scale door-to-door household hygiene campaigns and driving an 18 percent decline in childhood infectious diseases, with 20,000 fewer annual deaths compared with pre-suffrage mortality rates. Then, as now, women were overwhelmingly the early adopters of that revolution—washing their hands, boiling milk to kill bacteria, and refrigerating meat—while men generally resisted even the most basic public health directives, much as they’ve resisted wearing masks today. Quite simply: More children lived because politicians actually responded to the flush of new female voters and their demand for less death.1 o § Finance⠀➾ # ⚓ Counter Punch ☛ Strong_Job_Growth_in_March,_But_Some Evidence_of_Slowing_Wage_Growth⠀⇛ Employment Closes in on Pre-Pandemic Levels The rise in employment in March left total employment at 1.6 million jobs below its pre- pandemic level, less than three months of growth at its recent pace. Private sector employment is down by just 870,000 jobs from its February 2020 level. # ⚓ Common Dreams ☛ Millionaires_for_Humanity_Calls_Forbes_List ‘A_Slap_in_the_Face_of_Society’⠀⇛ In response to Tuesday’s publication of Forbes’ annual compendium of billionaire wealth, critics of skyrocketing inequality denounced the list as “a slap in the face of society” and called for hiking taxes on the super-rich around the globe. “The time for a wealth tax on people like me is long overdue. Inequality is bad for everyone.” # ⚓ Common Dreams ☛ ‘Pausing_a_Crisis_Doesn’t_End_It’:_Biden_to Extend_Student_Loan_Payment_Freeze_Again⠀⇛ President Joe Biden is reportedly planning to keep the moratorium on student loan repayments in place through August 31, an extension that progressives criticized as inadequate as they continued pressuring the White House to fully cancel all outstanding federal student loan debt. “We have to keep pushing. This isn’t enough,” the Debt Collective tweeted in response to reports Tuesday that the Biden administration intends to announce its fourth extension of the payment freeze as soon as Wednesday. # ⚓ TruthOut ☛ AOC_Calls_for_Student_Loan_Cancellation_as_Biden Is_Expected_to_Extend_Freeze⠀⇛ # ⚓ The Nation ☛ The_Real_Numbers_Behind_the_Labor_Movement⠀⇛ On March 8, 2021, 700 nurses launched what would become the nation’s longest strike of the year. They were demanding better staffing and working conditions at Saint Vincent Hospital in Worcester, Mass., and they picketed for nearly 10 months as the hospital, owned and operated by Tenet Healthcare, hired permanent replacements. The two sides reached an agreement on most issues in August, but the work stoppage continued for four more months until the Massachusetts Nurses Association members could ensure that striking workers could keep their jobs. # ⚓ The Nation ☛ As_Prices_Soar,_We_Need_Action—Not_Spin⠀⇛ As the midterm elections loom, Americans feel worse about the economy than they have in a decade. Inflation is at a 40-year peak. Gas prices are soaring. And the situation is unlikely to improve anytime soon, as Russia’s invasion of Ukraine rages on. # ⚓ Counter Punch ☛ Housing_is_a_Human_Right,_Here’s_How_to Make_It_a_Reality⠀⇛ Or is it a privilege affordable only to those who have made it under our unfair system of market capitalism? If you read CNBC’s recent financial advice column, you may come away believing the latter to be true. Economist and CNBC contributor Laurence J. Kotlikoff said Americans “are wasting too much money on housing,” and in order to be more financially savvy about housing he offered such innovative ideas as moving in with one’s parents, renting out part of one’s home to visitors through Airbnb, selling one’s home altogether in favor of a smaller, cheaper one, or—and this is my favorite—moving to a cheaper state. # ⚓ Counter Punch ☛ Grocery_Workers_Who_Are_Food_Insecure⠀⇛ In California, some 48,000 grocery workers in 540 stores stretching from central California to the Mexican border authorized a strike on March 27 against two major chains, Kroger and Albertsons. Whether or not the strike is now in effect as you read this column, or whether it’s been averted (or is still pending the outcome of bargaining), the strike authorization itself represents a powerful response to untenable conditions for workers. These conditions underscore the deep inequality continuing to erode the quality of life for millions of people. This past year, financial stresses impacting grocery workers have drawn increasing attention. A recent survey of workers employed by Kroger-owned supermarkets found that almost two-thirds of the workers surveyed reported being unable to meet basic monthly expenses, and of this group, a significant number (39 percent) indicated that they were unable to pay for groceries and 44 percent reported being unable to pay rent. Fourteen percent said that they were either currently homeless, or had been homeless in the preceding year. A New York Times account began with the story of one young worker at a Kroger-owned store who has been selling blood plasma to make ends meet. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Common Dreams ☛ AOC_Gets_Official_to_Admit_USPS_Leaders Don’t_Care_About_Sending_Truck_Work_to_Anti-Union_State⠀⇛ While much of the criticism of a U.S. Postal Service deal with Oshkosh Defense for a new fleet has focused on the fact that most vehicles will be gas-guzzling versus electric, Rep. Alexandria Ocasio-Cortez on Tuesday got a USPS official to admit the agency isn’t concerned the Wisconsin- based firm plans to build the trucks in notoriously anti-union South Carolina. Near the end of a U.S. House Committee on Oversight and Reform hearing, the New York Democrat questioned Victoria Stephen, executive director of the Postal Service’s Next Generation Delivery Vehicle (NGDV) Program, about whether the USPS considered Oshkosh’s unionized workforce in Wisconsin and when the agency knew about the company’s location decision. # ⚓ Common Dreams ☛ Opinion_|_State_Candidates_and_the_‘Trump Ticket’—He_Said_the_Quiet_Part_Out_Loud_Again⠀⇛ As he plants the seeds of democracy’s destruction, former President Donald Trump is open and notorious about his plan. Most recently, at an April 2 rally in Washington Township, Michigan, he exhorted the crowd to ask each candidate at the state’s upcoming Republican convention “if they will support the Trump ticket.” # ⚓ The Nation ☛ Kathy_Hochul_Is_the_Un-Cuomo⠀⇛ “What a celebration this is!” Kathy Hochul kvelled in mid-February as she accepted the New York State Democratic Party’s nomination for governor, a job she’d been doing ably for six months. A parade of powerful New York women preceded her at the podium: US Senator Kirsten Gillibrand, state Attorney General Letitia James, state Senate majority leader Andrea Stewart-Cousins, US Representative Carolyn Maloney, and, finally, the woman who introduced Hochul, former US senator (and so much more) Hillary Clinton. The message: While the state has never elected a woman governor, it has nonetheless elevated some badass female leadership. The steely, diminutive Hochul stepped up to the microphone beaming. # ⚓ The Nation ☛ Don’t_Be_Fooled_by_the_2022_Congressional Map⠀⇛ Redistricting for the next decade is nearly complete, with a whole new set of gerrymandered legislative maps. State and federal courts, governors, and some modicum of legislative self- restraint have prevented gerrymandering for the sort of extreme Republican advantage we saw a decade ago, with a map poised to produce a balanced Congress. Yet I can hardly call this result fair. While appellate courts can sometimes lend their blessing to the right result supported by the wrong reasoning, we should not accept a broken and antidemocratic process just because it yields a false sense of balance. # ⚓ TruthOut ☛ Study:_Fox_Viewers_More_Likely_to_Have_Factual Opinions_If_They_Switch_Networks⠀⇛ # ⚓ TruthOut ☛ Senate_Advances_Jackson’s_Nomination_After Republicans_Force_Committee_Deadlock⠀⇛ # ⚓ TruthOut ☛ Pakistan’s_Prime_Minister_Dissolves_Parliament to_Prevent_His_Removal_From_Power⠀⇛ # ⚓ TruthOut ☛ Former_Trump_Aide_Running_for_Congress_in_NH Voted_in_2_States_in_2016⠀⇛ # ⚓ TruthOut ☛ Federal_Judge’s_Opinion_May_Compel_DOJ_to_Bring Criminal_Charges_Against_Trump⠀⇛ o § Censorship/Free Speech⠀➾ # ⚓ Common Dreams ☛ Opinion_|_Why_the_GOP_Is_Very_Afraid_of Students_Learning_the_Real_History_of_Reconstruction⠀⇛ According to the state of Georgia’s Standards of Excellence for teaching the Reconstruction era to eighth-graders, students ought to “compare and contrast the goals and outcomes of the Freedmen’s Bureau and the Ku Klux Klan.” That side-by-side framing of the federal agency tasked with supporting formerly enslaved people in the years after the Civil War with a group of White supremacist terrorists has two problems: It is not only an unsettling echo of the “both sides” language mobilized by then-President Donald Trump following the 2017 deadly white supremacist rally in Charlottesville, but is also an example of how state standards fail to help educate young people about one of the most important eras in U.S. history. # ⚓ Common Dreams ☛ Library_Group_Launches_Anti-Censorship Campaign_to_Combat_GOP_Book-Banning_Wave⠀⇛ The American Library Association on Monday marked the start of National Library Week with a new report documenting a record-high number of attempts to ban books and a new campaign “to empower readers everywhere to stand together in the fight against censorship.” Reading—especially books that extend beyond our own experiences—expands our worldview. Censorship, on the other hand, divides us and creates barriers. o § Civil Rights/Policing⠀➾ # ⚓ Common Dreams ☛ Reproductive_Rights_Advocates_Brace_for Oklahoma’s_Near-Total_Abortion_Ban⠀⇛ Reproductive rights advocates on Tuesday braced for Kevin Stitt, Oklahoma’s Republican governor, to sign what’s been described as a “worse than Texas” abortion ban that would make performing the medical procedure at any stage of pregnancy a felony punishable by up to a decade in prison. “These extremist politicians are willing to turn their own constituents into medical refugees.” # ⚓ TruthOut ☛ Tennessee_Republicans_Push_a_Bill_That_Would Circumvent_Marriage_Age_Limits⠀⇛ # ⚓ The Nation ☛ Where_Is_the_Women’s_Movement?⠀⇛ In 1980, my first book, The Rising of the Women: Feminist Solidarity and Class Conflict 1880–1917, was published. In it, I used the term “united front of women” to mean a broad women’s movement of different classes within which progressives must fight for leadership without destroying the unity needed to move forward. The suffrage movement in the early part of the 20th century was like that, drawing in everyone from millionaire J.P. Morgan’s daughter Anne to radical union organizer Clara Lemlich. While anarchists and syndicalists saw the vote as a bourgeois distraction, most socialists recognized it was a basic democratic right; the Socialist Party’s founding program in 1901 included equal rights for men and women. When the party did nothing to put this position into practice, socialist feminists around the country organized local women’s groups and, in 1908, submitted two resolutions to the party convention: one to set up a Women’s National Committee, the other for a women’s suffrage campaign. Within a year, the party had increased its female membership 10 times over. This essay was adapted from the introduction to the third edition of The Rising of the Women: Feminist Solidarity and Class Conflict 1880–1917, published today in Verso’s Feminist Classics series. # ⚓ The Nation ☛ In_Criminalizing_Error,_We_Are_Doomed_to Repeat_Our_Mistakes⠀⇛ Two weeks ago in Nashville, a jury found former Vanderbilt University Medical Center nurse RaDonda Vaught guilty of criminally negligent homicide and abuse of an impaired adult for unintentionally giving her patient, 75-year-old Charlene Murphey, the wrong medication. Murphey died; Vaught faces up to six years in prison for the abuse charge and up to two years for homicide. # ⚓ Techdirt ☛ Law_Prof_Suggests_Geofence_Warrants_Are_A_Net Gain_For_The_Public,_Even_If_They_Invert_The_Probable_Cause Standard⠀⇛ On March 9th, we covered a Virginia court’s decision to reject a geofence/”reverse” warrant as unconstitutional. This was brought to our attention by FourthAmendment.com. Roughly a month later, it’s suddenly news. # ⚓ Project Censored ☛ Injustice_for_Incarcerated_Women_in Maryland_after_State_Cuts_Funds_for_Prerelease_Facility_– Validated_Independent_News⠀⇛ In 2021, Congress appropriated $1.5 million for the Department of Public Safety and Correctional Services (DPSCS) to construct a women’s prerelease facility. However, in an interview with The Real News Network, Executive Director of Out For Justice Nicole Hanson-Mundell shared that DPSCS have yet to spend one dime of the allocated $1.5 million toward meeting this goal. Hanson-Mundell and other advocates are now attending numerous budget hearings involving the Department of Corrections in order to ensure adequate funding is guaranteed toward the creation of a prerelease facility for incarcerated women in Maryland. # ⚓ Project Censored ☛ Youth_Activists_in_El_Salvador_Take Stand_against_Street_Harassment_–_Validated_Independent News⠀⇛ The teenage girls, ranging in age from 12-16, who started the campaign in 2020 are from San Ramón, El Salvador. Sandoval wrote, “Like other communities, San Ramón has been classified by the government as ‘zona roja’ (red zone) because of ongoing gang violence.” With high levels of violence and “street harassment being one of the most pressing problems affecting them in their community,” the girls saw an opportunity to speak up and make a difference. Sandoval interviewed one of the activists who said, “… We seek to make visible that street harassment is violence, which adolescents experience daily.” Unwanted gestures, comments, or in some cases invasions of personal space have become a normal, daily encounter for girls. According to Sandoval, “For many of them, street harassment is something they experience walking to school, taking the bus, or in other parts of their daily lives.” The campaign has allowed these girls to voice their opinions, but it has also been a learning experience for them as well. # ⚓ TruthOut ☛ Bernie_Sanders_Hails_Growing_Union_Movement_as an_Antidote_to_Oligarchy⠀⇛ # ⚓ Common Dreams ☛ CEO_Howard_Schultz_Ripped_for_Saying Starbucks_‘Being_Assaulted’_by_Unionization⠀⇛ On his first day back as chief executive of Starbucks, billionaire Howard Schultz said during a town hall Monday that the coffee giant and other U.S. companies are “being assaulted” by unionization drives, a comment that workers took as a signal of his union-busting intentions as he takes the helm amid a nationwide wave of organizing. “It doesn’t matter what industry: corporations are terrified of what happens when workers organize.” # ⚓ TruthOut ☛ Amazon_Will_Ban_Words_Like_“Union,”_“Living Wage”_in_Worker_App,_Documents_Find⠀⇛ # ⚓ Counter Punch ☛ The_Growing_Union_Movement⠀⇛ Amazon spent over $4 million in trying to defeat the union drive. The independent union, the Amazon Labor Union, had almost no money at all for their grassroots campaign but ended up with 55% of the vote. Congratulations Amazon Labor Union. I also want to congratulate the workers at Starbucks for their incredible union organizing efforts. Starbucks has coffee shops in some 15,000 locations all across the country and, until a few months ago, none of them were organized. Then, in December, workers in 2 shops in Buffalo, New York voted to join a union and that union organizing effort is now spreading like wildfire all across the nation. In fact, last Friday workers in New York City successfully voted to form the first Starbucks union roastery and tenth union Starbucks coffee shop in America. And, in the coming weeks and months, Starbucks workers in some 170 other coffee shops in 27 states will be holding union elections. # ⚓ TruthOut ☛ Amazon_Workers_at_Over_50_Buildings_Have Contacted_the_Union_About_Organizing⠀⇛ # ⚓ Common Dreams ☛ Sanders_Hails_Growing_Union_Movement_as Threat_to_‘Oligarchy_and_Corporate_Greed’⠀⇛ Sen. Bernie Sanders delivered a floor speech on Monday hailing the growing wave of union victories across the United States, including high-profile wins by Amazon and Starbucks workers, as an essential challenge to the country’s vastly unequal political and economic status quo. “It is that growing trade union movement that makes me so very hopeful for the future of this country.” # ⚓ Techdirt ☛ Florida_Has_Already_Wasted_Over_$700k_Of Taxpayer_Funds_Defending_Its_Unconstitutional_Content Moderation_Bill⠀⇛ We’ve already talked about how Georgia looks to be moving forward with its clearly unconstitutional content moderation bill. Back when Florida signed its content moderation bill into law (which actually put in a few things to pretend to appear more constitutional, unlike Georgia’s…), we noted that the state was going to waste a ton of taxpayer funds before losing. And, that’s exactly what’s happened. Florida’s bill was tossed out as unconstitutional, fairly easily. While an appeal on that ruling will be heard soon, all this is doing is racking up Florida’s expensive legal bills. # ⚓ Techdirt ☛ Louisiana_Supreme_Court_Says_Anonymous_Cop_Can Continue_To_Sue_Activist_Over_Injuries_Caused_Another Protester⠀⇛ Well, this is a mess. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Counter Punch ☛ Three_Internet-Creating_Ideologies⠀⇛ At its origins, we were promised the entry to The Golden Age of Computer Networks. Instead, what emerged under capitalism was the Internet becoming, rather quickly, a vastly profitable gold mine for a handful of corporations. Today, there are a few companies that have taken very profitable advantage of the original collective enthusiasm for a new creation of a computerized network system that started to emerge during the 1990s. Today, the Internet and the World Wide Web (www) are the commanding signifiers of social and political – but even more so – for corporate information, control. In short, the much-trumpeted Internet Revolution announced by some intellectuals, a substantial entourage of business writers, all too many politicians, and even several counter-cultural movements, has turned into a domain for a few corporate players furnished with the power to centralize information based on their corporate power. o § Monopolies⠀➾ # ⚓ Techdirt ☛ Rep._Ken_Buck_Threatens_To_Use_Antitrust_To Attack_‘Woke’_Apple⠀⇛ We’ve noted for a while that DC, and particularly the GOP’s, interest in “antitrust reform” is somewhat hollow. For one, while the United States is rife with heavily monopolized business sectors (insurance, health care, telecom, banking, airlines), this recent batch of “reform” only specifically targets large technology companies. It’s as if these other sectors (most notably telecom) simply… don’t exist. # ⚓ The Nation ☛ Big_Tech_Is_Making_an_Investment_in_Congress⠀⇛ While a bipartisan antitrust bill targeting Big Tech makes its way through Congress, industry giants have been showering both Democrats and Republicans with tens of thousands of dollars in contributions. Their political action committees, executives, and lobbyists have targeted both critics and supporters of the legislation, which is aimed at reining in some of the most powerful tech companies in the world. # § Trademarks⠀➾ # ⚓ Techdirt ☛ Monster_Energy_Suing_A_Fishing_Gear Company_Claiming_Customer_Confusion⠀⇛ Normally when discussing a company that has appeared on our pages before for being a trademark bully, I like to list off and link to a few examples. Monster Energy, the company that makes fizzy caffeine bombs in liquid form, makes that all very silly. You need only look at all the stories we’ve done on the company to see why: there are simply too many of them from which to choose. I could be convinced that the company was, in fact, doing some kind of avant-garde art piece highlighting the horrors of the trademark bully were I not so well informed of Monster’s ridiculous behavior overall. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 8897 ➮ Generation completed at 02:45, i.e. 122 seconds to (re)generate ⟲