𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, August 29, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Tue 30 Aug 02:41:38 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/2022/08/29/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmQeorfyCyeAdMaNzuRmrXYgrqiqrzPKP9SHtd6mCKWrFe QmUiMdJ65F7h2Cxy54N5XhhxXLLQwtpgk8b6bvC942r2xY QmNb2ydzs2uqBuBowYxV8oB66PL2Ed3KkRKEaU3DCDTSZ9 QmQe9CSmi7hJdXsrLQALzxjVKn6GwdcmeGuS1KbgZg6DfD QmY8oB1Qg87HBxwHopNxS6LMozLiwmSxad31Ttse73Fh2q QmXt1BammAJUuBrf4QPcungjNg2ePnbbrjoTfCoibP7XTL QmdDSQKaZJPnyDHFjeXTz7ZrVGb39ksdMdmtNhpx75EgdH QmZ7mLY8uo6YvRrfUTtX3hPHDhQgDNyt4AB4fPvzYWrcC4 QmTZezLwd5vekievmKZscKgr1hkxvuHoSSsWhkA4iTy7Tu QmNWKKu3gEEUM8UjAb868zLoy5CP9rUmyUWSSFH78F7ZGy Qmc1hpdpKJMrmE55WT3tg3aQBqe3inuQhnbsjTc8RVVKFq QmZNGE6NoRBC2J66AEvKbXxsP9j48e5nLCkLncW2SuYUD5 Qmd1qRcbFUvYnekMd31x6KbniK82hv6mEweUfvuLLLU3Dn QmPGPjyuWmmi4WH1Pm1qxX7pzZhtRC3umeb4DmdE7NfXdU QmbvCLhKBwB76DsbrKx6Pq16KSvtb9sW8UKVXj9v1pDgCv QmcoFCaZUJmzby8Vb2wg8PBXe6VR8hW77edQo1u3NsCJ3Q QmT4B1hoouASzbTAnEZbb6oYbbFnicQpd6JXDB5iwP9Y91 QmZeoDeQynAEb5Yhp8urADxooTvcjp93jYM7aoGTReoxAm QmUR5BqkVtBjeM3RbDysVaCrQyP93xoRwDKU5C1u5XZdyR QmS9E4XW4XZrtmFNP12pX65zisQkFTw7frAgGwhna5Fz9m Qmdj75rdsbiWjm4ms8CTMfcbYno6Pw9hH66AytZ3Hs3qV7 ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ Your Bank and Other Web Sites Are Running Creepy JavaScript That Records Your Every Action | Techrights ⦿ [Meme] Bringing Cheeks Together | Techrights ⦿ IRC Proceedings: Sunday, August 28, 2022 | Techrights ⦿ The ’Linux’ Foundation is Working Against Linux for People Who Reject Linux | Techrights ⦿ Linux Foundation Drowning in Grift and 7-Figure Salaries (Awarded to People Who Never Created Anything) | Techrights ⦿ EPO Management Trying to Make EPO Staff Miserable and Isolated | Techrights ⦿ The Inquisition of Norbert Preining is a Cautionary Tale About the Clique That’s Killing Debian From the Inside | Techrights ⦿ ZDNet’s Exit Strategy: Ugly/Cheap Redesign, Infinite Scroll for Fake ’Traffic’ (‘Engagement’), and Hardly Any New ‘Content’ | Techrights ⦿ Echoes of Narcissism: How Jim Zemlin Views Himself | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/08/29/creepy-javascript/#comments http://techrights.org/2022/08/29/epo-staff-slapped/#comments http://techrights.org/2022/08/29/irc-log-280822/#comments http://techrights.org/2022/08/29/lf-rejects-linux/#comments http://techrights.org/2022/08/29/lf-still-no-pdf/#comments http://techrights.org/2022/08/29/making-epo-staff-miserable/#comments http://techrights.org/2022/08/29/norbert-preining-canary/#comments http://techrights.org/2022/08/29/zdnet-exit-strategy/#comments http://techrights.org/2022/08/29/zemlin-narcissism/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/08/29/canonical-helping-microsoft/#comments http://techrights.org/2022/08/29/general-resolution-firmware/#comments http://techrights.org/2022/08/29/mx-21-2/#comments ䷩ 𝚕𝚒𝚗𝚎 73 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/creepy-javascript/#comments Gemini version at gemini://gemini.techrights.org/2022/08/29/creepy-javascript/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Your_Bank_and_Other_Web_Sites_Are_Running_Creepy_JavaScript_That_Records_Your Every_Action⠀✐ Posted in Free/Libre_Software, Protocol, Security, Standard at 2:51 pm by Guest Editorial Team Reprinted with permission from Ryan Your bank and other Web sites are running creepy “Session-Replay” JavaScript that follows you around the site recording your every movement. You’re not “supposed to know” about this, but NoScript can block that from running. I had a conversation with Matthew Garrett (alleged security person, actual drama bomb thrower) on IRC the other day about the “security” of JavaScript. He had previously promoted it as a “great way of running untrusted code”. Unfortunately, there’s just nothing secure about JavaScript. It’s the most widely abused platform in all of computing because almost everyone ends up running it without thinking of the consequences, and browsers which are instructed to do so, do it without bothering to allow any user control over the process in their default state. If you can’t trust code, it’s better to not have it running at all. Especially if it’s not doing anything to help you, and is proprietary. Garrett said that “total sandbox escapes” where the program gets out of your browser sandbox and starts interfering with another tab or running arbitrary malicious code outside of any sort of confinement is “rare” to the point where someone would need to be “targeting you” and willing to blow a Zero Day exploit to do it. That’s not exactly true as we see time and time again in the real world. But let us not hang ourselves up too long on what the Dalek of Social Justice has said. If you drop a copy of O’Reilly’s book on Sixth Edition JavaScript from the kitchen counter, you’ll be walking with a limp for a while. Far from something that adds a little bit of “interactivity” to a Web page, JavaScript is a full blown computer programming language, Turing-complete, that can be used to write and run almost anything. (I laughed the other day when I noted that someone had ported all of the LAME MP3 Encoder to JavaScript. It’s like, you could. But why? This is even dumber than online Office suites. People have spent years and lots of effort writing high performance encoding routines in C. Let’s make things worse and shove it to a Web server!) Very little of what I do on the Web calls for something like JavaScript. Nobody asked me if I wanted applications that run best on my computer, where I control them, where Big Brother is not looking over my shoulder replaced by some online version on someone else’s computer that I may or may not be able to access, and if I can, it’s watching what I do with it. I don’t use Services_as_a_Software_Substitute where I can avoid it, and the ones I do use tend to be licensed under the GNU Affero General Public License, which makes them Free and Open Source Software. If I don’t like someone’s Searx search engine, I can use someone else’s. If I don’t like a Matrix (protocol) chat server’s moderation, I can go use another one. If anyone wants to know what the source code does, or make their instance work differently, they can! Web applications don’t have to be malicious. It’s just that many of them are. In general, every way that Microsoft’s proprietary software could hurt you before is wrong with their Web applications, and then they’ve invented new ways of being nasty as well. So thanks, no thanks. The people who invented the Web and the earliest browsers (such as Marc Andreeson, who said as much in 1994) wanted to keep it lightweight. The idea of JavaScript and even Cascading Style Sheets were controversial. They knew that if these “features” were added, the consequences would be severe. And they are severe! The Web has basically become Microsoft Windows. Bloated, fat, slow, and requiring a new computer every 4-5 years because of how painful things get. Features that are only useful to advertisers and marketers and spyware and other parasites being bolted on with no debate by Google and Microsoft, and tossed in by Mozilla and Apple “for compatibility”. Worse, it’s all impossible to secure and it’s rather embarrassing how complicated the standards are to get it to do much at this point. (There are starting to be chat servers implemented in GeminiSpace. But on the Web, you need to run a 600 MB tab for that!). Worse, the Web rots. It’s become mostly a spam farm. Things disappear. Domain squatters come in. All your links go to a scam now. The entire thing has become so balkanized by megacorporations that come and go that if you use those “services”, every 10 years you have to figure out where all the people you used to talk to are. We have to start backing away from standards that are hacked together by companies that won’t exist in a few years based on speculative business plans, many of which ought to be criminal. Attackers take advantage of whatever they can. They take advantage of poorly coded applications, gaps in security policy whether deliberate or accidental (some Windows malware includes the calculator from Windows 7 to get past User Account Control and evade virus scanners, for example), or software distributors like Apple which do not ship Web browser security updates quickly (giving the attackers time to study the fix and start exploiting a long time before most users are patched), or users who do not apply fixes. Recently, Apple had to rush two emergency fixes for the kernel in Mac and iOS and for Webkit (Safari) for zero day vulnerabilities, and it’s hardly even like it’s rare for in-the-wild attack code to be targeting these platforms. A while back, China_attacked_and_targeted_Uyghurs_using_a_Safari_vulnerability in_the_JavaScript_engine. They’re not the only nation state that hoards software vulnerabilities. The US FBI and NSA are known to do it. But aside from the sandbox escapes and arbitrary code execution are privacy problems that Tracking and Session-Replay scripts cause. According_to_an_article_from_VICE_from_2017 (compacted with NewsWaffle and archived), at that time, 482 of the top 50,000 Web sites had JavaScript programs that followed the user around and recorded things that can even include keystrokes that aren’t “submitted” yet, and mouse movement patterns, and some even tie your activity to your real identity. This is….super creepy and super sketchy! Richard Stallman’s JavaScript_Trap essay pointed out that many users end up running non-Free JavaScript programs without thinking much about it. I pointed out in an earlier post about how much I like the add-on NoScript. In many cases, JavaScript is bloated, it’s spyware, it’s proprietary, and at the very least, it does something unwanted and aggravating, such as powering news site paywalls. Firefox, some time ago, joined the majority of Web browsers in removing the user’s ability to turn off JavaScript globally, but NoScript can add this back. You can do whatever you want to. You can whitelist domains that are “Just Enough” to make the site work. Even browsing in the non-default mode of “Temporarily Allow All Top-Level Domains” would provide a lot of protection from malicious, annoying, and bloated third-party scripts without forcing you to do too much manual intervention. But it isn’t even like JavaScript engines really are that secure. By the time Mozilla finally does declassify security hole fixes for a Firefox release, you can go back and easily see that the majority of really nasty ones involved JavaScript, so the more domains you have it coming in and executing from, the more likely one is to come in and do _something_ nasty. Odds approach 100% very quickly that your browser is running some kind of malware without telling you. It’s bad enough when programs are “legitimate” in the sense that they are what they say they are, do something useful, and just won’t tell you how they do it. That’s what Stallman’s complaints were in The JavaScript Trap. Unfortunately, there’s never been a more useful language to abuse the user with, or a better place to run it, than JavaScript in a Web browser. Admitting defeat and turning it all on out of laziness simply ensures that you will be encountering serious malware at some point. Unfortunately, the JavaScipt Problem is bigger yet than proprietary software and malware running behind-the-scenes. Some site owners set their Web sites to simply lock out people who are using Tor Browser, a VPN, or just simply have JavaScript turned off. CloudFlare, a Web cancer that just keeps growing bigger, now hosts about 1/5th of major Web sites and about as many smaller ones too, and has convinced site owners to set “security” settings high to bounce people who fit these categories. I’m a VPN and Tor user with NoScript, so I run into problems with those “Checking your browser” pages somewhat frequently. The other day, I was trying to look at an article on Bleeping Computer, and CloudFlare blocked me for using my VPN. So I opened up Opera, which I only occasionally use because CloudFlare blocks their Opera “VPN” (proxy) except in the EU for some reason, so I had to view the article in Opera and then close Opera. JavaScript is a major annoyance on banking Web sites. One of the advantages of running NoScript and just whitelisting the top domain for the bank is that I use 6 banks, and they all work with just first party scripting turned on. The rest is Session-Replay, data analytics, and other crap and garbage. Why do I want some creepy third-party script looking over my shoulder while I’m banking or using any Web site for that matter? When I went to the United States Social Security Administration and the Internal Revenue Service, I even found Session-Replay scripts that they were attempting to load from third-party domains! Once again, with these scripts excised from the site, the functionality I wanted to use still worked. With your Web browser’s default settings, spyware companies are recording your actions even on government Web sites that you have to use! I counted at least six tracking companies monitoring your usage of the Social Security Administration’s site. They’ve even outsourced compliance with the Americans With Disabilities Act to a tracking company that records your session! On top of the security and privacy concerns are more practical ones. Some JavaScript malware is designed to commit theft of utilities. Some sites resort to “mining” cryptocurrency with JavaScript and WebAssembly (which NoScript also handles). This runs your CPU hard and causes your power bills to rise as your battery life falls. Firefox, indeed most major Web browsers, now have some sort of anti- cryptomining feature, but nothing’s perfect. The less sites even have the permission the less chance they’ll get one of these loaded. Tracking scripts also take resources to run. They slow down page loads and instruct your computer to do things. That’s not “free”. The Web site owners don’t want to make a big fuss about all of this crap that they load, because when you investigate what the companies are telling them, it’s usually like, “We can help you monetize your site and optimize your search engine results and tell you all of these things about your visitors and what they do.”. Stealing your resources to benefit themselves is what they do. How does this compare with ad blocking, or running add-ons such as Decentraleyes? Ad blocking and Decentraleyes (which hosts commonly used Web frameworks locally to avoid Content Delivery Network requests) compliment NoScript and add to the privacy you can expect to gain from it. uBlock-Origin (an ad and tracking blocker) is already a pretty big hammer. It will block ads and tracker lookups completely if they’re in your blacklists. Unfortunately, many things are not included for whatever reason. They tend to give priority to not breaking anything on a site you could conceivably want to use, and there have been cases where tracking companies used the US DMCA to be removed from ad blocking lists. So it’s not bulletproof. There are too many things that slip past them, and that’s where NoScript comes in. Between these things, you should be able to reduce your browsing data usage by about half. There are a few other extensions I really like, such as Google Container. I don’t use Google very much (preferring the Free and Open Source Searx instances) and I’d like to stay logged in, but not outside that container (so Google can’t easily track me in general across the Web). As I’ve increasingly focused on Gemini (such as Chilly Weather and the NewsWaffle on Gemi.dev) instead of the Web, I’ve found few cases where I actually need JavaScript to run to power something I want or need to do on the Web. Ironically, writing this blog post about JavaScript requires me to run some JavaScript. Even then, not all of the domains that the WordPress.com editor wants to load are necessary, and when I go to read blogs, I don’t need JavaScript at all. You don’t even need a graphical Web browser to read this. You can load it in text browsers that don’t even support JavaScript, with cookies turned off. You should block most of WordPress’s JavaScript. I think most of it comes from analytics sites. As I continue looking into an escape from the Web for most activities, I still occasionally need to watch a video or refill a prescription or make appointments with my doctor, or use some dumb banking site, and pay my taxes. Unfortunately, thanks to JavaScript being as widely abused as it now is, you need NoScript to make sure that these creepy programs can’t run. I’m considering moving to a Gemlog instead of WordPress, but I’m going to have to learn how to do that so it may be a while. Eventually, I would like to leave an “I’m not here anymore. Use Gemini.” message on WordPress. We’ll see when I manage to get around to this. Until then, turn off your JavaScript, mostly. The Web is more pleasant when there’s less of it. Although I mostly read news in the NewsWaffle, most of the annoyances and slowdowns (bloated JavaScripts, annoying videos, tracking) are gone from news sites with NoScript. Even when I load a CNN article with uBlock-Origin and NoScript, it comes up instantly. CNN is infamous for its terrible page load performance. You can get NoScript here: Firefox_Add-Ons / Homepage License: GNU General Public License Version 2 There is also a port of the extension available for Firefox on Android. Unfortunately, iOS users will just have to live with JavaScript. The version of Firefox on iOS isn’t the real Firefox with Gecko. It’s a neutered version that has to use the same engine as Safari by diktat of Apple. Unfortunately, this means Web browsers on iOS are insecure and impossible to fix, and issues such as the one Apple rushed an emergency fix for cannot be user-mitigated by blocking active content. █ ䷩ 𝚕𝚒𝚗𝚎 463 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/epo-staff-slapped/#comments Gemini version at gemini://gemini.techrights.org/2022/08/29/epo-staff-slapped/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Bringing_Cheeks_Together⠀✐ Posted in Europe, Patents at 9:24 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_Staff;_The_'f***ing_president'⦈_ António_Campinos refers to himself as the “f***ing president” Summary: EPO staff continues to be abused and its patience is being tested ⣿⠀⠀⣾⠀⠀⢠⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀ ⣿⠀⠀⡗⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀ ⣿⡇⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄ ⣿⡇⠀⣿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⠿⢛⣳⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧ ⣿⢇⠀⢹⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⢿⣿⣿⣛⠿⣻⣴⠞⡚⠉⠊⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣷⡀⢸⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢁⣸⣿⣿⣿⣫⠭⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⢹⡟⣧⠸⡀⢪⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⠠⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⢇⠘⣇⡇⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⣿⣿⡿⢿⠟⢀⡤⠤⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣀⠸⡄⠹⡇⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⣇⠀⢷⠀⢳⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢻⠀⢸⡀⠘⡇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣿⢿⡟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣟⠀⠀⡇⠀⢹⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣾⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⠀⠀⢱⠀⠘⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⢹⣶⢠⢸⡄⠀⡇⢡⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⡸⣿⣿⣄⡇⣶⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⣰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⡇⣿⣿⣇⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⣰⣿⣿⣿⣷⠀⢀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⢨⣿⣿⢸⣿⣿⢀⣴⣿⣿⣿⣿⣿⣦⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡘⠛⠃⠀⠀⠀⠙⠛⠛⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⠃⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⡀⢸⣿⣿⠿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉ ⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣴⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣦⣤⣤ ⣿⣾⣿⣷⣿⣶⣶⣯⣟⡛⠛⠛⣿⣿⡿⣿⣿⣏⢉⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠀⠉⠉⠀⠈⠉⠙⡁⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠶⠶⠛⠛⠉⢉⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠿⠿⠟⠃⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⣀⣒⣢⣤⣤⣤⣤⣤⣶⣶⠶⣶⣖⣛⣻⠃⠀⠀⠀⠀⢠⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠤⣾⣿⣿⣿⣿ ⣻⣟⣻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⢶⣶⠆⠀⠀⠂⡛⠛⠛⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣯⣭⣿⣿⣿⣿⣿⣶⣶⣶⣾⠊⠛⠈⢽⣿⣁⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣼⡏⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⠛⠻⠟⠛⠛⠛⠛⠉⠉⠉⠉⠁⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠠⠄⠒⢺⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⠀⠀⠀⣾⣿⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⢻⣿⠿⠟⠋⠉⠁⠀⠀⠀⢀⣀⣀⣼⣿⠿⠿⠛ ⣤⣄⣤⣤⣤⣶⣿⣤⣴⣴⣤⣤⣤⣤⣤⣵⣥⣵⡶⡦⠀⣿⣿⣾⣿⣿⣆⣀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⣤⣤⣤⠶⠶⠶⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⡿⢿⣿⣿⣷⣶⣶⣞⣛⣛⣿⣿⣿⣿⣿⡟⠛⠻⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠰⢾⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠭⠉⠙⠛⡃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣷⣦⣌⡉⠙⠳⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣯⣟⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠈⠉⠉⢻⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠉⠙⠛⣶⣶⣤⣶⣖⠛ ⣿⠀⠀⣿⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀ ⣿⠀⠀⡏⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀ ⣿⡇⠀⣷⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀ ⣿⡇⠀⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⠛⣑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷ ⣿⢇⠀⢹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⢻⣿⣿⢛⠿⣛⡵⠖⠛⠉⠶⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣷⡀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢁⣸⣿⣿⣶⣻⠭⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⢹⡟⣧⠸⠀⢪⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⢇⠘⣇⡇⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⣿⣿⡿⠿⡟⠠⡤⠤⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣀⠸⡄⠹⡆⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⣇⠀⣷⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢻⠀⢸⡀⠘⡇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣿⢿⡟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⠀⠀⡇⠀⢹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⠀⠀⢹⠀⠘⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⢹⣶⣠⢸⡀⠀⡇⢡⣤⣶⣶⣶⣶⣶⣶⣶⣶⣖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⡸⣿⣿⡀⡇⣦⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⣰⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⡇⣿⣿⣇⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⣰⣿⣿⣿⣧⠀⢀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⠐⣿⣿⢸⣿⣿⢀⣴⣿⣿⣿⣿⣿⣆⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠿⠻⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠃⠀⠀⠀⠙⠛⠛⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⠃⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉ ⣿⣿⣿⡿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣴⠿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣦⣤⣤ ⣿⣾⣿⣷⣿⣶⣦⣭⣛⠛⠛⠛⣿⣿⡟⣿⣿⣟⠩⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠉⠉⠀⠈⠉⠙⠀⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠶⠶⠛⠛⠉⢉⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡭⠭⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠻⠟⠛⠃⠀⠀⠀⠸⣾⣿⡄⠀⠀⠀⣀⣒⣠⣤⣤⣤⣤⣤⣶⣶⠶⣶⣖⣛⣻⠃⠀⠀⠀⠀⢠⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⣾⣿⣿⣿⣿ ⣻⣟⣻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠶⣶⠆⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣭⣽⣿⣿⣿⣿⣷⣶⣶⣶⣾⠊⠛⠈⢿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⣼⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⡿⠛⠛⠟⠛⠛⠛⠋⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠐⢺⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⣾⣿⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⢻⣿⠟⠟⠋⠉⠁⠀⠀⠀⢀⣀⣀⣼⣿⠿⠿⠛ ⣀⣠⣤⣤⣤⣼⣶⣤⣦⣤⣤⣤⣤⣤⣤⣭⣭⣵⡶⡆⠀⣿⣿⣾⣿⣿⣄⣀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⠆⠀⠀⠀⠀⣤⣤⣤⠴⠶⠶⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⠿⢿⣿⣿⣷⣶⣶⣞⣛⣛⣿⣿⣿⣿⣿⡟⠛⠻⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠰⢮⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠭⠉⠙⠛⢃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣷⣦⣌⡉⠙⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣮⣟⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠈⠉⠉⢻⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠉⠙⠛⣶⣶⣤⣶⣖⠛ ⣿⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀ ⣿⡄⠀⢸⠀⠀⠸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀ ⣿⡇⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆ ⣿⡇⠀⣼⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠟⢛⣁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏⢙⢿⠿⣛⠿⣋⡴⠾⠛⠉⠤⠂⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⡀⢸⠀⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠙⣿⣿⣿⣿⣗⣫⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠸⡟⣷⡸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⡏⣀⡤⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⠀⢳⠘⣧⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⠇⢰⣶⣦⠤⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⡄⠘⡆⠸⣇⢸⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⢃⠀⢻⠀⢹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣸⠀⠸⡆⠈⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣿⢿⡟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿ ⣿⡄⠀⣇⠀⢸⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⠀⠀⢸⠀⠈⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⢸⣷⣰⠘⡆⠀⡇⢰⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠈⣿⣿⡄⣇⢰⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⣰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⣇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⢠⣿⣿⣿⣷⠀⢀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⠘⣿⣿⢸⣿⣿⠀⣰⣿⣿⣿⣿⣿⣇⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿ ⠿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠃⠀⠀⠀⠙⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣀⣀⣀⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉ ⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⣿⣴⠿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣤ ⣿⣾⣿⣿⣾⣷⣶⣭⣛⠛⠛⠛⣻⣿⡿⣿⣿⣿⡪⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣦⣹⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠉⠉⠀⠈⠉⠙⡁⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠶⠶⠛⠛⠉⠉⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡀⠀⠀⠀⠠⠶⠶⠚⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠛⠟⠿⠃⠀⠀⠀⠰⢿⣿⡆⠀⠀⠀⣀⣒⣲⣤⣤⣤⣤⣤⣶⡶⠶⣶⣶⣻⠂⠀⠀⠀⠀⣾⣯⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠤⣴⣿⣿⣿⣿ ⣛⣿⣻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠶⣶⡶⠀⠀⠐⠘⠛⠛⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣭⣭⣿⣿⣿⣿⣾⣷⣶⣶⣾⠙⠋⠉⢿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⢠⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠠⠄⠒⠺⣿⣿⣿⣿ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡀⠀⠀⠀⣾⣿⣷⣶⣶⣶⣶⠆⠀⠀⠀⢻⣿⡿⠿⠟⠋⠉⠁⠀⠀⠀⢀⣀⣀⣴⣿⠿⠿⠛ ⣄⣠⣤⣤⣤⣶⣦⣴⣦⣤⣤⣤⣴⣤⣤⣿⣷⣶⣶⡦⡄⢰⣿⣿⣿⣿⣇⣀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣤⣤⣤⡴⠶⠶⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⡿⢿⣿⣿⣷⣶⣶⣞⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠺⢿⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠉⠉⠋⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢘⣷⣶⣬⡉⠙⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣟⡉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉⠉⢻⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣄⡀⠉⠙⠛⣶⣶⣤⣴⣖⠚ ⣿⠀⠀⢸⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀ ⣿⡄⠀⢸⠀⠀⠸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⠀ ⣿⡇⠀⣺⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆ ⣿⡇⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠿⠋⣙⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢹⠿⡻⡟⠿⣹⣷⠾⠛⠩⡱⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⡄⢸⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠙⣿⣿⣿⣷⢟⣫⠅⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⠸⡟⣷⡸⡆⢸⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⡏⣀⡤⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⠀⢳⠘⣧⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠯⣴⣶⣶⠤⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⡅⠘⡇⠸⣇⢸⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⢣⠀⢻⠀⢹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣸⠀⠸⡆⠈⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣿⢿⡟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⠄⠀⣇⠀⢸⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⠅⠀⢸⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⢸⣿⣠⠘⡆⠀⡇⢰⣶⣶⣶⣶⣶⣶⣶⣷⣿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠘⣿⣿⡆⡇⢰⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⣰⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢸⣿⡇⣸⣿⢀⣿⣿⢻⣿⣿⠀⠀⢠⣿⣿⣿⣧⠀⢀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⢸⣿⣿⢸⣿⣿⠀⣰⣿⣿⣿⣿⣿⣇⣸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⡿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠃⠀⠀⠀⠙⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣄⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉ ⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣴⠿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣤ ⣿⣿⣿⣿⣿⣷⣶⣿⣛⡛⠛⠛⣿⣿⡿⣿⣿⣿⢭⣿⣿⡇⠀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣽⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣯⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠉⠉⠀⠈⠉⠹⡁⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠶⠶⠟⠛⠉⠉⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡀⠀⠀⠀⠠⠶⠶⠚⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠋⠀⠀⠠⠲⣿⣿⡆⠀⠀⠀⣀⣂⣢⣤⣤⣤⣤⣤⣶⣶⠶⣶⣶⣻⠂⠀⠀⠀⠀⣾⣯⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠤⣾⣿⣿⣿⣿ ⣛⣿⣻⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠶⣶⡶⠀⠀⠐⠚⡛⠛⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣭⣭⣿⣿⣿⣿⣿⣶⣶⣶⣾⠛⠛⠩⠽⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠟⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⢠⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿ ⣿⡛⠻⡛⠛⠛⠛⠛⠋⠉⠉⠁⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠄⠒⢚⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⠀⠀⣾⣿⣷⣶⣶⣶⣶⠆⠀⠀⠀⢻⣿⡿⠿⠟⠋⠉⠁⠀⠀⠀⢀⣀⣀⣴⣿⠿⠿⠛ ⣀⣠⣤⣤⣤⣶⣦⣶⣦⣤⣤⣴⣶⣤⣾⣿⣶⣶⣶⣦⡄⢰⣷⣿⣿⣿⣇⣀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣤⣤⣤⡶⠶⠶⠖⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⠿⣿⣿⣷⣶⣶⣞⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠺⠿⣥⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠿⠿⠿⠟⠛⠭⠉⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢘⣷⣶⣬⣉⠙⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣟⡉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉⠉⢻⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣄⡀⠉⠙⠛⣷⣶⣤⣴⣖⡛ ⣿⡄⠀⢸⠀⠀⠀⠇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀ ⣿⡇⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀ ⣿⡇⠀⢸⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇ ⣿⣧⠀⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣑⣂⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⠀⢸⡇⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠙⠻⣿⣛⢿⣫⡵⠶⠛⠉⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⣿⣿⡄⢈⡇⢰⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⣶⣞⣫⡥⠂⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⠘⡏⢷⡄⡇⢸⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣧⢸⡛⣠⡤⠄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⢹⡈⢿⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠛⠀⠐⣶⣶⡶⠤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⠀⡇⠘⣧⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢫⠀⢸⠀⢸⣾⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⡾⡃⠈⡇⠀⢿⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⣿⢿⡟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⠆⠀⢳⠀⠘⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⢻⣏⠀⢸⡀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⢸⣿⣴⡄⣇⢁⡻⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠁⣿⣿⡇⣿⢸⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣧⢹⣿⣿⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⢀⣿⣿⣿⣿⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡿⠿⠟⠘⣿⣿⢸⣿⣿⠀⣰⣿⣿⣿⣿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⣀⣀⣄⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⣿⣿⣿⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢻⣿⡇⢸⣿⣿⣤⠿⣿⣿⣿⡟⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦ ⣿⣾⣿⣿⣿⣷⣶⣮⣍⣋⠙⠛⢻⣿⡿⣿⣿⣿⣋⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣽⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⢻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣭⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠉⠉⠀⠈⠉⠉⡍⠉⠉⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡶⠶⠞⠛⠛⠉⠁⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠿⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠤⠶⠶⠖⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠻⠃⠀⠀⠐⣾⣿⣗⠀⠀⠀⣀⣦⣤⣤⣤⣤⣤⣶⡶⢶⣶⣾⣛⠂⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⠴⢾⣿⣿⣿⣿ ⣹⣿⣽⣿⣿⣿⣿⣧⣤⣤⣤⣴⡶⠶⠶⠶⠶⠶⠶⣶⠂⠀⠀⠀⠛⠛⠛⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣞⢙⢙⡛⣿⣿⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⡿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠔⠒⠚⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⣠⣤⣦⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡀⠀⠀⢠⣿⣿⣷⣶⣶⣶⣷⠀⠀⠀⠻⣿⣿⠿⠿⠟⠋⠉⠀⠀⠀⠀⣀⣀⣀⣤⡿⠿⠿⠛ ⣤⣤⣤⣤⣬⣤⣤⣤⣤⣭⣥⣤⣥⣶⣶⣶⣶⣶⣶⣶⣶⠀⣾⣿⣿⣿⣧⣀⡀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⢀⣤⣤⣴⠶⠶⠶⠒⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⡿⠿⠿⢿⣿⣶⣶⣾⣙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢛⠿⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⠟⠛⠋⠙⠋⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⢰⣽⣿⣶⣦⣌⡉⠛⠳⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⣿⣉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⠇⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡈⠉⠛⢻⣶⣶⣶⣖⣛ ⣿⠄⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀ ⣿⡇⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀ ⣿⡇⠀⢸⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧ ⣿⣷⠀⢸⡄⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣩⣦⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⠀⢸⡇⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣟⣏⡈⠻⡿⣛⠿⣙⡴⠾⠛⠉⠒⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⢿⣿⡆⢀⡆⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡅⠀⢷⣞⣯⠵⠂⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⠘⡏⢿⡄⡇⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠸⠑⣀⠤⠔⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⢹⡈⢷⡇⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠍⠁⠀⠶⣶⣶⡶⠄⠀⠈⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⣠⠀⣇⠈⣧⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢫⠀⢸⡀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⡞⡁⠈⡇⠀⢿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⢿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⠅⠀⢹⠀⠘⡆⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⢻⣖⠀⢸⡆⡀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡸⣿⣴⡀⡇⢀⢛⢰⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡀⣿⣿⣇⣿⢰⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣷⢸⣿⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⡇⣸⣿⢀⣿⣿⢻⣿⣿⠀⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⡿⠿⠟⠸⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿ ⣀⣀⣤⣀⣰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣷⣿⣿⣿⣿⠿⠃⠠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣤⠿⣿⣿⣿⡟⠈⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶ ⣿⣾⣿⣿⣿⣿⣷⣬⣍⡉⠙⠛⣻⣿⡿⣿⣿⣿⣭⣿⣿⡇⢀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠉⠉⠀⠈⠉⠩⠁⠉⠉⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠶⠶⠟⠛⠋⠉⠁⣽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠛⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠠⠶⠶⠶⠖⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠻⠇⠀⠀⠰⢿⣿⣇⠀⠀⠀⣠⣤⣤⣤⣤⣤⣴⣶⠶⢶⣶⣟⡓⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠴⠾⣿⣿⣿⣿ ⣽⣿⣽⣿⣿⣿⣿⣦⣤⣤⣴⡶⠶⠶⠶⠶⠶⠾⢿⡛⠓⠀⠀⠈⠛⠛⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣏⡉⣉⡉⣿⣿⣄⡀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⣟⠛⢛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠐⠒⠛⣿⣿⣿⣿ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡄⠀⠀⠀⣿⣿⣿⣶⣶⡆⠀⠀⠻⣿⣿⣿⠿⠿⠟⠟⠛⠁⠀⠀⢀⣀⣀⣀⣤⡤⠿⠿⠟⠛ ⣤⣤⣤⣤⣴⣬⣤⣤⣭⣿⣯⣴⣷⣶⣶⣶⣶⣶⣶⣶⢶⠄⢾⣿⣿⣿⣧⣄⣀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢉⣥⣤⣤⣶⠶⠶⠶⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⡿⠿⠿⠿⣿⣷⣾⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⢀⣀⣩⣛⡛⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠟⠛⠋⠙⠋⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀⢀⣼⣿⣷⣿⣿⣷⣶⣤⣉⠙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣷⣿⣉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⡿⠁⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠉⠉⢻⣷⣶⣶⣿⣋ ⣿⡆⠀⢸⠀⠀⠀⠇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀ ⣿⡇⠀⢸⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀ ⣿⡇⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧ ⣿⣷⠀⢸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣩⡆⢄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⠀⢸⡇⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣟⣏⡉⠛⡿⣟⠿⣻⡴⠞⠛⠉⠂⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⢿⣿⡆⢀⡆⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⢳⣚⣫⡵⠂⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⠈⣏⢿⡄⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠸⠁⣠⠤⠔⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⢹⡈⢿⡇⢸⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠍⠁⠀⠶⢶⣶⡶⠔⠀⠈⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⣄⠀⣇⠈⣧⢸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢣⠀⢸⡀⠸⣾⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⡞⡃⠈⡇⠀⢻⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡇⠀⢻⠀⠘⡆⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⢹⣖⠀⢸⡆⠀⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⡸⣿⣶⡀⣇⠁⡹⢰⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡀⣿⣿⣇⣿⢰⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣷⢸⣿⣿⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⡇⣸⣿⢰⣿⣿⢻⣿⣿⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⡿⠿⠟⢸⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠈⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠃⠀⠀⠀⠘⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⣀⣀⣤⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⣷⣿⣿⣿⣿⠿⠋⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣤⠿⣿⣿⣿⡏⠊⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶ ⣿⣾⣿⣿⣿⣿⣶⣬⣍⡉⠙⠛⣻⣿⡿⣿⣿⣿⣭⣿⣿⡇⠀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣺⣿⣧⣿⣿⠏⠉⣿⣿⡇⢸⣿⣿⢻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣭⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠉⠉⠀⠈⠉⠉⠇⠉⠉⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠶⠶⠛⠛⠋⠉⠁⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠿⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠠⠶⠶⠶⠖⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⠻⠛⠃⠀⠀⠙⢿⣿⣇⠀⠀⠀⣠⣦⣤⣤⣤⣤⣶⡶⠶⢶⣶⣟⡓⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⠴⠾⣿⣿⣿⣿ ⣽⣿⣽⣿⣿⣿⣿⣤⣤⣤⣴⠶⠶⠶⠶⠶⠶⠶⢿⡛⠃⠀⠀⠂⡛⠛⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣾⣶⣶⣾⣿⣿⣿⣿⣿⣋⢉⣉⢙⣯⣽⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿ ⣟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠄⠒⠒⠛⣿⣿⣿⣿ ⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡀⠀⠀⠀⣿⣿⣿⣶⣶⡆⠀⠀⠻⣿⣿⣿⠿⠿⠿⠟⠛⠁⠀⠀⢀⣀⣀⣀⣠⡤⠿⠿⠟⠛ ⣤⣤⣤⣤⣵⣤⣤⣬⣭⣽⣯⣦⣶⣷⣶⣶⣶⣶⣶⣶⢶⠄⢾⣿⣿⣿⣧⣄⣀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢉⣥⣤⣤⡶⠶⠶⠶⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⡿⠿⠿⠿⣿⣶⣶⣿⣝⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⢀⣀⣉⣛⡛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠋⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀⢀⣼⣿⣷⣿⣿⣷⣶⣄⣉⠙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⢿⣷⣯⣉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠙⢿⡿⠁⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠉⠉⢻⣷⣶⣶⣿⣋ ⣿⡆⠀⢸⠀⠀⠀⠇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀ ⣿⡇⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀ ⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧ ⣿⣷⠀⢸⡄⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⢋⣩⡦⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⠀⢸⡇⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣟⡈⠻⡟⣟⢿⣩⡴⠾⠋⠉⠒⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⢿⣿⡆⢀⡆⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡅⠀⢳⢟⣫⠵⠂⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠈⣏⢿⡄⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠄⠸⠁⣠⠤⠔⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⢸⡈⢿⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠉⠁⠀⠶⣶⣶⡦⠤⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⣄⠀⣇⠈⣷⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢹⠀⢸⡄⠸⣾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠵⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣞⡃⠈⡇⠀⢻⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⠅⠀⢹⠀⠈⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⢻⣇⠀⢸⡄⡀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡸⣿⣴⡄⣇⢀⡹⢠⣶⣶⣶⣶⣶⣶⣶⣷⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡀⣿⣿⣇⣿⢰⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣷⢸⣿⣿⣹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⡇⣸⣿⢠⣿⣿⢻⣿⣿⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⡿⠿⠟⢸⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠈⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⣤⣀⣤⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⡿⠿⠿⠿⣿⣷⣷⣶⣝⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⢀⣀⣍⣛⡛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠋⠉⠋⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀⢀⣼⣿⣷⣿⣿⣷⣶⣤⣉⠙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣾⠿⠿⢿⣷⣿⣉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠙⢿⡿⠁⠙⠛⠛⢿⣿⣿⣿⣾⣿⣿⣿⣶⣤⣄⣀⠈⠉⢻⣿⣶⣶⣿⣋ ⣿⡆⠀⢸⠀⠀⠀⠇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀ ⣿⡇⠀⢸⠀⠀⢰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀ ⣿⡇⠀⢸⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷ ⣿⣿⠀⢸⡄⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣭⣗⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⣿⣿⠀⢸⡇⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣯⡈⠹⡿⡫⣍⣣⠴⠟⠋⠐⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⢿⣿⡆⢠⡇⢸⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⣷⣚⣭⠖⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠈⣏⢻⡆⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢹⣅⡤⠤⠒⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⢸⡄⢻⡇⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠻⠻⠂⠈⡷⣶⣷⠷⠒⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⡠⠀⣇⠈⢷⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⢸⠀⢸⡀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠵⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡅⠈⣇⠀⢻⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡇⠀⢹⠀⠈⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⢹⣧⡀⠸⡆⡀⣇⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠜⣿⣿⡆⣧⠀⢸⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡆⣿⣿⣧⣿⢸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⢹⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⡇⣸⣿⢀⣿⣿⢻⣿⣿⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⠿⠟⠰⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢘⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿ ⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠂⢀⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⢷⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣤⠟⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣶⣶ ⣿⣿⣿⣿⣿⣿⣷⣾⣬⡍⠉⠉⣹⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣼⣿⣧⢸⣿⣿⠉⠀⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣠⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣧⣿⣿⠇⠉⣿⣿⡇⢸⣿⣿⣻⣿⣿⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠉⠉⠀⠈⠉⠉⣅⠉⠉⠈⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⠶⠶⠞⠛⠛⠉⠁⠀⣻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠟⠟⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠴⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠻⠃⠀⠀⠙⢜⣿⣇⠀⠀⠀⣠⣤⣤⣤⣴⣶⢶⣶⣶⣶⣟⣛⠁⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠒⠺⣿⣿⣿⣿ ⣭⣽⣭⣽⣿⣿⣿⣷⠶⠶⠶⠶⠶⢶⠶⢿⣿⣛⣛⣛⠋⠀⠀⠀⠍⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿ ⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⠘⠿⣿⠦⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⣟⠉⠙⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠔⠀⠒⠈⠙⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⠻⠛⠛⠉⠀⠀⠀⣀⣀⣀⣤⣤⠶⠿⠟⠛⠋ ⣤⣤⣤⣤⣭⣭⣭⣽⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠷⠆⢸⣿⣿⣿⣧⣤⣀⡀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡏⠀⠀⠘⣛⡋⣉⣭⣤⣤⣴⡶⠶⠞⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢹⠏⠁⠀⠀⠀⣿⣿⣦⣦⣨⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠉⠙⠛⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣤⣔⡐⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡉⠛⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣾⣍⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠉⠛⠿⠲⠀⠀⠉⠉⠙⠻⠿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠉⢹⣿⣷⣾⣯⣍ ⣿⡄⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣗⠀ ⣿⡇⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀ ⣿⡇⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷ ⣿⣿⠀⢸⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠟⢋⣭⣦⣆⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⣿⣿⠀⠘⡇⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣟⣯⡈⠹⡿⠻⣍⣣⠴⠟⠋⠑⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⢿⣿⡆⢀⡇⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆⠀⣷⣚⣭⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⠘⣏⢻⡆⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢹⣅⡤⠄⠒⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⢸⡄⢻⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠻⠻⠀⠈⠿⣶⡷⠷⠒⠀⢀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⡠⠀⣇⠈⢷⢸⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠈⢀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⢸⠀⢸⡀⠘⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠽⠗⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡃⠈⣇⠀⢻⠠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡇⠀⢹⠀⠈⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿ ⢹⣧⠀⠸⡆⡀⣇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠜⣿⣾⡆⣇⢀⣼⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡆⣿⣿⣧⣿⢰⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⣴⣿⣿⣷⣆⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⢹⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⡇⣸⣿⢀⣿⣿⢻⣿⣿⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⠿⠟⢸⣿⣿⢸⣿⣿⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣸⣿⡿⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⠃⠀⠀⠀⠈⠛⠛⠛⠁⢸⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿⣿⣿⠀⢸⣿⣿⠿⢷⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⡇⢸⣿⣿⣤⠟⣿⣿⣿⡟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣷⣶ 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⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣾⣍⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠉⠛⠿⠲⠀⠀⠉⠉⠙⠻⠿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠉⢹⣿⣷⣾⣯⣍ ⣿⡇⠈⢸⠇⠀⢠⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀ ⣿⡧⠀⢸⡀⠀⢸⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇ ⣿⣗⠀⣸⡆⠂⡾⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⢿⡇⠀⣧⠤⣞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⡄⢸⡇⢸⡏⢀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡟⢻⣿⣿⣿⣿⡿⣟⣿⠿⡿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⣿⣿⣷⣼⡇⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⣿⣛⣽⡿⣟⡋⣈⣤⠴⠒⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠘⣯⢻⣧⣇⢸⡄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⣶⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢻⣿⣾⠿⢞⣛⣁⣠⣴⣿⠿⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⡠⢸⡄⢿⣿⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢟⣿⣿⠇⠈⣿⣿⣿⡿⠟⢋⣩⣥⣶⡶⠿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⣿⡀⣧⠈⢿⢹⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⢄⠔⡼⠛⠀⠀⡃⢿⣷⠾⠛⠛⣉⣁⣤⡮⢃⣋⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⡧⢹⡆⠸⣿⠇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠡⠈⠠⠀⠁⡠⠀⢀⡅⠂⠀⣹⣿⠿⠿⠛⠋⠉⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣇⠈⣧⠀⢻⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⢿⠿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡐⠔⢶⠀⠀⠀⠀⠀⣀⠠⠀⠂⠒⠀⠀⠨⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⢄⢻⡀⠘⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢐⢂⠀⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⢹⣿⣿⣸⡇⡇⣿⣿⣠⣀⣄⣤⣆⣠⣠⣠⣠⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⡾⣿⣿⣏⣷⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣒⡒⠀⠌⠅⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿ ⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⣤⣤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠀⠐⡣⣒⣾⠀⠀⠀⠀⠐⠿⢿⣿⣿⡿⠿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣄⡀⠀⣀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⠻⠿⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠠⠿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⣿⣶⣷⣾⣵⣾⣆⣤⣦⣀⠀⠀⢀⡴⠤⢿⣿⣿⣿⣿⣿⣿ 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⣿⡅⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀ ⣿⡇⠀⢸⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆ ⣿⡇⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷ ⣿⣿⠀⢸⡆⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢋⣭⣦⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⣿⣿⠀⠘⡇⢰⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣯⠀⠹⡏⠫⣍⣡⠴⠞⡉⠁⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⢿⣿⣇⠀⡇⢸⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⣿⣚⣭⠖⠊⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠈⣏⢻⡆⡇⢸⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣁⡤⠔⠂⠈⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⢸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠻⠻⠀⠀⢿⣶⣿⠷⠖⠀⣀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣀⠀⣇⠈⢷⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⢹⠀⢸⡄⠘⣟⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠽⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡁⠀⣇⠀⢻⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠾⠻⠁⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡅⠀⢹⠀⠈⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⢹⣧⢀⠸⡆⠀⢇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡚⣿⣾⡆⣧⢠⣾⢨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⡀⢀⠀⠉⠉⠀⠉⠀⠀⠀⢀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡄⣿⣿⣷⣿⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢀⡀⣠⣿⣿⣦⡀⢴⡦⢤⣶⢸⣿⣸⣿⣆⣿⡞⣿⡏⣟⡃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣼⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⣿⣿⡟⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣧⢿⡇⠿⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡄⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣧⣤⣄⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⣿⣿⣽⣷⠀⣿⡇⠀⢀⡄⢠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⢿⣿⣿⣿⣿⣿⡟⠃⣤⡏⣿⡇⣿⣧⢹⣿⣼⡿⠸⠿⠿⠾⠿⠼⠿⢤⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⠀⠀⢿⣿⠀⠛⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣷⣶ ⣿⣿⣿⣿⣿⣿⣿⣶⣭⣍⡉⠉⠛⠛⠛⠛⠿⠿⣇⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣠⡄⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠶⠟⠛⠛⠉⠁⠀⣽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠻⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠴⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿ ⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠃⠀⠀⠐⢞⣿⣗⠀⠀⠀⣠⣤⣤⣤⣤⣶⠶⣶⣶⣶⣛⣛⠃⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠒⠺⣿⣿⣿⣿ ⣭⣽⣭⣽⣿⣿⣿⣷⠶⠶⠶⠶⠶⡶⠶⢶⣞⣛⠛⡛⠋⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣁⡉⢉⡐⠾⣧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⣿⠛⠋⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠐⠒⠉⠉⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠀⠀⠀⣀⣀⣀⣠⡤⠴⠿⠟⠛⠉ ⣤⣤⣤⣬⣥⣭⣬⣵⣾⣷⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⠷⠆⢸⣿⣿⣿⣧⣤⣀⡀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⡏⠀⠀⠘⣛⡋⣩⣭⣤⣤⣤⡶⠶⠖⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢹⠏⠁⠀⠀⠀⣿⣿⣦⣤⣨⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣤⣔⡘⠛⠿⢿⣿⣿⣿⣿⣿⣷⣤⣈⠉⠙⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⢀ ⣿⣿⣷⣿⣿⣷⣿⡿⠿⠿⠿⣿⣾⣅⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠉⠛⠿⠂⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠉⢹⣿⣷⣾⣯⣍ ⣿⡇⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀ ⣿⡇⠀⢸⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄ ⣿⡇⠀⢸⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷ ⣿⣿⠀⢸⡆⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠛⣋⣡⣶⣐⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⠀⠘⡇⢰⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠙⣿⠫⣙⣧⠾⠛⠉⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⢿⣿⣇⠀⡇⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⢹⣋⡽⠖⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠈⢇⢻⡆⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢸⡇⠤⠔⠂⠁⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⠸⡄⢻⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠻⠻⠇⠀⢻⣾⡾⠷⠂⠀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣤⠀⢇⠀⢷⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠀⡀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⢱⠀⢸⡀⠘⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡭⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡇⠀⣇⠀⢻⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠿⠿⠻⠁⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⡇⠀⢹⠀⠈⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢹⣧⢀⠘⡆⠀⠃⠂⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡞⣿⣿⡇⣧⢀⣼⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⡀⡀⠀⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣄⣿⣿⣷⣿⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢀⡀⣠⣿⣿⣠⡀⢴⡤⢠⣶⢸⣿⣸⣿⣏⣿⡎⣿⡏⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⣿⣏⠈⠁⠈⠈⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡋⢀⣤⠀⠀⠀⠀⠀⣿⣇⢿⡇⠿⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠋⠿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⣿⣿⣽⣷⠀⣿⡇⠀⢀⡤⠶⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣧⣿⣧⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⠃⣤⡏⣿⡇⣿⣧⢻⣿⣼⡿⠸⠿⠿⠾⠿⠸⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠸⠀⠀⢻⣿⠀⠛⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⣸⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣷⣯⣍⠉⠉⠉⠛⠋⠛⠻⠿⣅⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠠⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠋⠉⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⠶⠶⠶⠞⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿ ⣿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠃⠀⠀⠀⣛⣛⣃⠀⠀⠀⢠⣤⣤⣶⣶⣶⢶⣶⣞⣛⣻⣏⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠒⠻⢿⣿⣿⣿ ⣭⣽⣿⣿⣿⣿⡿⡷⠶⠶⠶⢶⢶⣾⣛⡛⡛⠛⠛⠛⠋⠀⠀⠀⠍⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⢁⠈⠠⠾⠷⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⣟⠋⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠤⠀⠒⠂⠈⠉⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣦⠀⠀⠀⠠⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠁⠀⠀⣀⣀⣀⣠⣤⠴⠶⠿⠛⠛⠉ ⣤⣤⣴⣤⣽⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠿⠆⢸⣿⣿⣿⣷⣤⣄⣀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡿⠁⠀⠀⢙⣟⡉⢩⣥⣤⣤⣶⠶⠶⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣶⣤⡨⣭⣛⡛⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠋⠛⠛⠛⠉⠑⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣌⠛⠛⠛⢿⣿⣿⣿⣿⣷⣦⣄⡉⠙⠛⠲⠶⣤⣄⣀⡀⠀⠀⠀⣀ ⣿⣿⣶⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣅⡈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⠳⠤⡄⠀⠉⠉⠛⠿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠈⢹⣿⣿⣿⣯⣭ ⣿⡅⠀⢸⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀ ⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄ ⣿⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⢸⡅⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⠀⠈⡇⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠁⠘⠿⠩⣉⣧⠶⠛⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⢿⣿⣇⠀⡇⢰⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣇⠀⢰⣋⡭⠖⠈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠈⣧⢻⡆⡇⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠸⡇⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⠸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠻⢿⡆⠀⠙⠲⡶⠶⠒⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣀⠀⢧⠀⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣤⣤⠐⠉⠀⠀⡀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⣹⠀⠸⡄⠘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠁⣒⣠⡤⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣯⡇⠀⡇⠀⢹⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠟⠿⠻⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣏⠀⠀⠀⠀⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⡆⠀⢸⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢹⣧⣀⠘⡆⠀⠁⠀⠀⠀⢀⡀⡀⠀⢀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡜⣿⣿⡇⣇⠀⠘⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⢀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡆⢿⣿⣿⣿⣸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢀⡀⣠⣿⣿⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡆⣿⡏⣿⡇⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⣿⣋⣈⡁⠈⠈⠀⠀⠸⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣇⢿⠇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣿⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠛⠻⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡄⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⢿⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣷⢹⣿⣾⡿⢸⡿⠾⠾⠟⠸⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⠀⠀⢻⣿⠀⠙⣿⣿⢿⠷⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣶⣬⣄⠉⠉⠉⠉⠉⠉⠛⠻⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⠁⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠋⠉⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⠿⠙⠋⠋⠛⠛⠛⠛⠛⠻⠟⠛⠻⣿⣿⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠶⠶⠶⠞⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿ ⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⢘⣛⣃⠀⠀⠀⢠⣤⣤⣴⣶⣶⣶⣖⣛⣛⣛⡏⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿ ⣬⣽⣿⣿⣿⣿⠿⠶⠶⠶⠶⠶⠶⡿⢟⢛⡛⠛⠛⠛⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢀⢀⠀⠸⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⣿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠀⠐⠂⠉⠉⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣶⣷⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣦⠀⠀⠀⢸⣿⣿⡆⠀⠘⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠁⠀⠀⣀⣀⣀⣠⡤⠤⠶⠿⠛⠛⠉ ⣤⣤⣴⣤⣶⣾⣷⣶⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣷⣤⣄⣀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⡿⠁⠀⠀⢙⣟⡋⢩⣭⣤⣤⣶⠶⠶⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣟⣛⣛⣛⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄⡨⣭⣛⠓⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⠉⠙⠛⠋⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣴⣦⣌⠙⠛⠛⠻⣿⣿⣿⣿⣷⣦⣄⡉⠙⠛⠲⠶⣤⣄⣀⡀⠀⠀⠀⣀ ⣿⣿⣶⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣥⡈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⠳⠤⡄⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠈⢹⣿⣿⣿⣯⣭ ⣿⡅⠀⢸⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀ ⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄ ⣿⣇⠀⢸⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟ ⣿⣿⠀⢸⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣥⣖⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⠀⠘⡇⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣻⣿⠁⠙⡿⢫⣉⣧⠶⢛⠋⠀⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⢻⣿⣇⠀⡇⢰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣇⠀⢸⣋⡭⠖⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠈⢯⠻⡆⡇⢸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⢸⡧⠠⠖⠂⠁⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⠸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠹⣿⡆⠀⣿⣶⣿⠶⠒⢀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢀⠀⢧⠀⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢿⣿⣿⠷⠒⠉⠀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⣹⡄⢸⡀⠘⣟⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠙⠙⣷⣒⣦⡭⠶⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡅⠀⣇⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⠿⠻⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣏⡀⠀⠀⠀⠀⠘⠋⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿ ⣿⡇⠀⢸⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⢈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢸⣷⢀⠘⡇⠀⢁⠀⠀⠀⡀⠀⡀⠀⢀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠠⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡏⣿⣿⡆⣧⠐⢔⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⢀⣀⡀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡆⣿⣿⣷⣿⢰⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⢀⡀⣠⣿⣿⣣⡀⢴⡤⢤⣶⢸⣿⣸⣿⣎⣿⡆⣿⡏⣿⡇⠒⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢿⣿⣿⣿⣾⡅⠈⠈⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⣇⢿⡇⠿⠿⠘⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣭⡍⣿⣷⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠛⠻⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡤⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣦⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⢟⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⡿⢸⣿⠿⠾⠟⠸⠿⠦⠮⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⢻⣿⠀⠙⣿⣿⢿⠷⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣾⣥⣉⠉⠉⠉⠉⠉⠛⠛⠿⣅⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢈⠄⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠋⠉⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠟⠿⠿⢿⣿⣿⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿ ⣿⣿⣿⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⢘⣛⣃⠀⠀⠀⢠⣤⣤⣶⣶⣶⣶⣖⣛⣛⣻⡏⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠒⠻⢿⣿⣿⣿ ⣭⣽⣿⣿⣿⣿⠿⠶⠶⠶⠶⠶⣶⡿⠛⣛⢛⡛⠛⠛⠃⠀⠀⠀⠉⠉⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢀⣀⠀⠠⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⣿⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⠀⠒⠂⠉⠉⣿⣿⣿⣿ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⡄⠀⠀⠀⣿⣿⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛⠉ ⣤⣤⣴⣼⣿⣿⣶⣶⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣷⣤⣄⣀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡿⠃⠀⠀⠈⣛⡉⠩⣭⣤⣴⣶⠶⠶⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⣶⣤⡨⣭⣛⡛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠉⠛⠛⠋⠉⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⢰⣷⣶⣦⣶⣶⣌⠙⠛⠙⠻⣿⣿⣿⣿⣷⣦⣄⡉⠙⠛⠲⠶⣤⣄⣀⡀⠀⠀⠀⣀ ⣿⣿⣷⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣥⡈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠈⠙⣛⠳⠤⠀⠀⠀⠉⠛⠿⣿⣾⣿⣿⣷⢶⣤⣄⣀⠈⢹⣿⣿⣿⣯⣭ ⣿⡅⠀⢸⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀ ⣿⡇⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄ ⣿⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟ ⢻⣿⠀⢸⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⣥⣶⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⠀⠘⡇⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣻⣿⠁⠘⢟⠫⣉⣭⠶⢛⠉⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⢻⣿⣇⠀⡇⢠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⡇⠀⢸⣋⡭⠖⠉⠁⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠈⢯⠻⡆⡇⢸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⢸⡧⠤⠖⠂⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⠸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠹⣿⡆⠀⣿⣶⡿⠖⠒⢀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⡤⠀⢧⠀⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⡗⠚⠉⠀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⣹⡀⢸⡀⠘⣟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠙⠙⢶⣲⣬⡭⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⡅⠀⣇⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⠿⠻⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣏⡀⠀⠀⠀⠀⠘⠋⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⡆⠀⢸⠀⠈⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢸⣧⢀⠘⡆⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡞⣿⣿⡇⣧⠐⣤⢠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⢀⣀⡀⠉⠉⠀⠁⠀⠀⠀⢀⣀⢀⣀⠀⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡆⢿⣿⣷⣿⢸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⢀⡀⣠⣿⣿⣣⡀⢴⡤⢠⣶⢸⣿⡸⣿⣎⣿⡎⣿⡏⣿⡇⠒⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢿⣿⣿⣿⣾⡅⠈⠈⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣇⢿⠇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣷⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠟⠛⠻⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡄⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣦⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⢏⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⡿⢸⣿⠿⠾⠟⠘⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⠀⠀⢻⣿⠀⠘⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠈⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠉⠉⠉⠉⠛⠛⠻⠿⣯⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠋⠉⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢻⣿⣿⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿ ⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢘⣛⣃⠀⠀⠀⢠⣤⣴⣶⣶⣶⣶⣖⣟⣛⣻⡋⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠄⠒⠻⢿⣿⣿⣿ ⣭⣽⣿⣿⣿⣿⢿⠶⠶⠶⠶⠶⣶⡿⢛⡛⠛⡛⠛⠛⠋⠀⠀⠀⠉⠉⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡇⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢀⢀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⣿⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠤⠀⠀⠂⠉⠉⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⣶⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⡄⠀⠀⠀⣿⣿⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠁⠀⠀⢀⣀⣀⣠⡤⠤⠶⠟⠛⠛⠉ ⣤⣤⣴⣬⣿⣷⣶⣷⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣷⣤⣄⣀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡿⠃⠀⠀⠈⣟⡉⠩⣭⣤⣴⣶⠶⠾⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⣶⣤⡈⣭⣛⡛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣷⣶⣦⣶⣶⣌⠙⠛⠙⠻⣿⣿⣿⣿⣷⣦⣄⡉⠙⠛⠲⠶⣤⣄⣀⡀⠀⠀⠀⣀ ⣿⣿⣾⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣥⡈⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠈⠙⣛⠳⠤⠀⠀⠀⠉⠛⠿⣿⣾⣿⣿⣷⣶⣤⣄⣀⠈⢹⣿⣿⣿⣯⣭ ⣿⡇⠀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀ ⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆ ⣿⣧⠀⢸⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⢸⣿⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠛⣉⣡⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⡀⠀⡇⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⡀⠘⡏⠩⣙⣤⠖⠛⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⢻⣿⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢠⣉⠵⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⠀⢿⠹⣆⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠘⡤⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⠘⡄⢹⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠈⠻⡇⠀⢰⠶⠦⠑⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣠⠀⢣⠀⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠐⠈⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿ ⣸⡀⠘⡆⠈⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⠋⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⡷⢄⣐⣤⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣇⡆⠀⢧⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⡋⠹⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⠀⠀⠀⡀⠀⠛⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⣿⡇⠀⢸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣠⣶⣶⣾⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⢸⣧⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢸⣷⣄⡈⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠻⣿⣿⠟⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠅⣿⣿⡇⣷⠀⡰⢀⣾⣿⣷⣷⣷⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⢸⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣇⢻⣿⣷⣼⢨⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⢀⡀⣀⣴⣷⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡟⣿⡏⣻⡇⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣇⢿⡇⠻⠿⠘⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣷⡾⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠟⠛⠻⠟⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣦⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣼⡿⠸⢿⠿⠾⠟⠸⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⣿⠀⠈⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⣬⣀⠉⠉⠉⠉⠉⠉⠛⠿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡴⠶⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⠛⠋⠉⠙⠛⠛⠛⠛⠛⠟⠟⠿⣿⣿⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⠀⠲⠖⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿ ⣿⣿⣿⣿⣿⣡⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⢀⣛⣃⡀⠀⠀⢠⣤⣤⣶⣶⣶⣶⣚⣛⣛⠁⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠐⠛⢿⣿⣿⣿ ⣭⣽⣿⣿⣿⠿⠿⠶⠶⠶⠶⢶⠶⡞⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠰⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⠀⠀⠰⠷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⡟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡶⠶⠦⠄⠂⠒⠀⠈⠉⢹⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⡿⠿⠛⠛⠋⠁⠀⠀⣀⣀⣀⣠⡤⠤⠶⠛⠛⠋⠉ ⣤⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣿⣤⣄⣀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡈⠉⢥⣤⣶⣶⠶⠾⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣛⣛⣛⣛⣿⣿⣿⣿⣯⣭⣭⣿⠿⠋⠁⠀⢀⡀⢀⣼⣿⣿⣿⡋⠀⠀⠀⠀⠀⣀⣿⣷⣶⣀⢬⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣶⣾⣷⣦⣄⡈⠈⠙⠿⣿⣿⣿⣿⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⢀⣀ ⣿⣿⣶⣾⣿⣿⣿⠿⠿⠿⠿⢿⣷⣧⣀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠉⠛⠛⠛⠤⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣶⣦⣤⣀⡀⢩⣿⣿⣿⣿⣯ ⣿⡇⠀⢸⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀ ⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆ ⣿⣧⠀⢸⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⢸⣿⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠛⣉⣠⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⡀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⡀⠈⣍⠯⣋⣤⠖⠛⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⢻⣿⣧⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢸⣩⠵⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⠀⢿⠹⣆⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠘⡅⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⠘⡆⢹⡆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠈⠻⡇⠀⢸⠴⠮⠐⠂⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣠⠀⢣⠀⢻⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠉⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿ ⣸⡄⠘⡆⠈⣿⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠘⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⡷⢀⣐⣦⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣇⡄⠀⢧⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⡋⠹⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⡀⠀⠀⡀⠀⠛⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⣿⡇⠀⢸⡄⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣠⣶⣶⣾⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⢸⣧⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢸⣷⣤⡈⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠹⣿⣿⠟⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠅⣿⣿⡇⢷⢀⡸⠀⣾⣷⣿⣿⣿⣿⣿⣷⣿⣷⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⢸⣿⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡇⢹⣿⣷⣼⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⢀⡀⣀⣶⣷⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡟⣿⡏⣻⡗⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣇⢿⡇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣷⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠟⠛⠻⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣦⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⡿⠸⢿⠿⠾⠟⠸⠿⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠃⠀⢿⣿⠀⠈⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⣤⣁⠉⠉⠉⠉⠉⠉⠛⠻⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣄⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡴⠶⠶⠚⠛⠛⠉⠉⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠛⠉⠋⠛⠛⠛⠛⠛⠻⠿⠟⠿⣿⣿⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⠀⠲⠖⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿ ⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣛⣃⡀⠀⠀⢠⣤⣴⣶⢶⣶⣶⣚⣛⣛⠁⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠐⠛⢿⣿⣿⣿ ⣬⣽⣿⣿⣿⠿⠿⠶⠶⠶⠶⠶⣶⠞⡛⠛⠛⡛⠛⠛⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠠⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠰⠦⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿ ⣏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡶⠶⠤⠄⠒⠒⠂⠉⠉⢹⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣶⣶⣀⠀⠀⠀⠀⢀⣠⣀⣀⣤⣤⣤⣤⣄⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⠿⠟⠛⠛⠋⠁⠀⢀⣀⣀⣀⣠⡤⠤⠶⠛⠛⠋⠉ ⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣿⣤⣤⣀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡈⠉⢥⣴⣶⣶⡶⠾⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣟⣛⣛⣛⣻⣿⣿⣿⣯⣭⣭⣿⠿⠋⠁⠀⢀⡀⠀⣼⣿⣿⣿⡋⠀⠀⠀⠀⠀⡀⣿⣶⣶⣄⢬⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣶⣾⣷⣦⣄⡈⠈⠙⠿⣿⣿⣿⣿⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⢀⣀ ⣿⣿⣶⣾⣿⣿⣿⠿⠿⠿⠿⢿⣷⣧⣀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠉⠛⠛⠛⠤⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⢶⣦⣤⣀⡀⢩⣿⣿⣿⣿⣯ ⣿⡇⠀⢸⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀ ⣿⡇⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆ ⢿⣷⠀⢸⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⢸⣿⠀⠘⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⠛⣉⣤⣄⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⣿⣿⡀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⣿⣿⣿⠀⠈⠯⠩⣛⣤⠖⠛⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⢻⣿⣷⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣧⠀⢸⣉⡥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⢻⠹⣆⢱⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡀⠈⡇⠠⠔⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⠘⡆⢹⡾⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠏⠉⠻⠇⠀⢸⣶⠮⠕⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢀⠀⢱⠀⢻⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠈⣷⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣜⡂⠈⡇⠈⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣷⢤⣶⣦⠥⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣷⡇⠀⢳⠀⠸⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣷⠶⢺⣿⢹⣿⢸⣿⣏⡀⠀⠀⡀⠀⠛⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⢿⣆⠀⠸⡄⠀⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠈⠙⠛⢻⣿⡇⢸⣿⣿⣿⡜⣿⡟⠃⠀⢸⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠸⣯⣆⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⢸⣿⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡇⣿⣷⣇⢿⢀⢸⢀⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⢀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⢸⣿⣦⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣇⢹⣿⣿⣾⣸⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢀⡀⣠⣾⣿⣠⡀⢴⡤⢤⣶⢸⣿⡸⣿⣆⣿⡞⣿⡏⣛⡓⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿ ⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠁⠈⠈⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣇⢿⡇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣷⡾⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠿⠟⠻⠟⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣶⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣦⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠰⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢻⣿⠛⢸⣿⣿⣿⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠇⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣼⡿⠸⣿⡿⠾⠟⠘⠻⠦⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⢿⠿⠿⠿⠟⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⣽⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣤⣥⣉⠉⠉⠉⠉⠋⠉⠛⠻⢍⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡴⠶⠶⠚⠛⠛⠉⠉⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⡗⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⡄⠀⠀⠀⠲⠖⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿ ⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣛⣃⡀⠀⠀⢠⣤⣤⣶⣶⣶⢶⣖⡂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠐⠛⢻⣿⣿⣿ ⣬⣽⣿⣿⣿⠿⠿⠷⠶⠶⠶⡶⣶⠞⠛⡛⡛⡛⠛⠛⠋⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣾⣿⣿⣿⣻⣿⣋⠀⠀⠀⠀⠀⠨⣿⣿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿ ⣿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡶⠶⠦⠄⠒⠒⠂⠉⠉⢹⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣶⣶⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠉⠀⠀⣀⣀⣀⣠⡤⠴⠶⠛⠛⠛⠉ ⣥⣤⣤⣶⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠷⠆⢸⣿⣿⣿⣿⣦⣤⣀⡀⠀⠉⣽⣿⣿⣿⡿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠩⢭⣴⣶⣶⡶⠞⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣟⣛⣛⣛⣻⣿⣿⣿⣯⣭⡉⠁⠀⠀⣤⣶⣤⣶⣾⣿⣿⣿⣿⣟⠉⠁⠀⠀⢀⣀⣰⣶⣤⣀⢬⣍⣛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⠉⠉⠙⠋⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣦⣤⡈⠈⠙⠻⢿⣿⣿⣿⣶⣤⣀⠉⠙⠛⠶⢦⣤⣀⣀⠀⠀⢀⣀ ⣿⣿⣶⣾⣿⣿⣿⡿⠿⠿⠿⢿⣷⣧⣀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠈⠁⠙⠛⠛⠛⠶⣤⠀⠀⠉⠛⠿⣿⣿⣿⣿⡷⣶⣤⣀⡀⢩⣿⣿⣿⣿⣯ ⣿⡇⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀ ⢻⡇⠀⢐⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡥⢽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣄ ⢹⣿⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⢸⣿⠀⠀⡇⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⠿⠛⢉⣡⠄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⣾⣟⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣽⣿⣯⡀⠈⣯⠭⣉⣭⠶⢚⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⢹⣿⣧⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢸⣎⡭⠖⠋⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⢻⠹⣇⢱⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠈⣏⠴⠔⠂⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠈⡆⠹⣮⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠹⢻⣿⣿⣿⠿⠃⠀⢸⣶⣾⠗⠒⢀⠀⠠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⢠⠀⢹⠀⢹⡀⠄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⢤⣿⡿⠋⠀⠀⠀⠀⠈⣟⠂⠒⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⡄⡄⠈⡇⠀⢷⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠋⡂⢀⣀⣀⠀⠀⠀⠀⠀⢻⠖⣲⣢⡬⠴⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⣷⡇⠀⢹⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⣹⣿⣇⠀⠀⠀⠀⢀⡠⠄⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣏⠀⠀⠀⠀⠀⠛⠋⠉⣁⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢻⡄⠀⠘⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣷⣾⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡞⣿⡟⠃⠀⠀⣀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡘⣷⡀⡀⣇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⢰⣿⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡇⣿⣧⡧⢸⠠⣀⠀⣶⣿⣶⣿⣶⣿⣷⣾⣶⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⣀⢀⣀⣿⣿⣦⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⡇⢸⣿⣷⢸⡄⣇⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣷⣦⡄⢴⡦⢤⣶⢸⣿⡸⣿⣆⣿⡟⣿⡏⣛⡳⠐⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣼⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣇⠈⠈⠀⠀⠸⣿⡇⣿⣿⣿⡇⣿⣯⢿⣿⠀⠀⠄⠀⠂⠀⠨⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣇⢿⠇⠻⠷⠘⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠿⠟⠸⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣥⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣧⠀⣿⡇⠀⠀⣤⠠⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣤⣀⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⠀⠀⠀⠰⣶⡾⣶⣸⣿⣿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⡿⣿⣿⠿⠾⠟⠸⠿⠦⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⢿⠧⠿⠿⠟⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷ ⣶⣶⣿⣿⣿⣿⣿⣷⣤⣌⡈⠉⠉⠙⠉⠻⠻⠟⢄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠴⠶⠖⠛⠛⠋⠉⠀⠀⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠿⠿⠛⠙⠛⠻⠿⠟⠛⠛⠛⠛⠿⠻⣷⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡀⠀⠀⠀⠰⠶⠶⠖⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢠⣤⣤⣶⠶⠶⠀⠀⠀⠀⠀⠈⣭⣭⣭⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠚⢻⣿⣿⣿ ⣭⣭⣭⣭⣽⣽⣿⣷⠶⠶⠶⠶⠶⠶⠶⠶⡛⡛⠛⠛⠛⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣾⣾⣿⡶⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⣿⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠀⠒⠂⠈⠉⢹⣿⣿⣿ ⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⣶⣆⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄⡀⠀⠀⠀⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛⠉ ⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡖⠦⢸⣿⣿⣿⣿⣤⣤⣀⡀⠀⠉⠹⣿⣿⡿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⢭⣥⣤⣶⡶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣟⣛⣛⣻⣿⣿⣶⣮⡉⠻⠀⠀⢠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⢀⡄⣴⣶⣤⣤⣬⣝⣛⠳⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⠙⠛⠷⠒⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣠⣈⠈⠙⠻⠿⣿⣿⣿⣶⣤⣀⡉⠙⠛⠶⠦⣤⣄⣀⡀⠀⠀⢀ ⣽⣿⣿⣿⣿⣷⣿⣿⠿⠿⠿⢿⣿⣯⣀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠉⠉⠙⠛⠛⠻⠶⡀⠀⠀⠈⠙⠿⣾⣿⣿⣿⣷⣶⣤⣄⡀⠈⣿⣿⣿⣿⣯ ⢸⣯⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀ ⢸⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧ ⢸⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⢸⣿⡄⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠙⢿⣿⣿⣿⣿⠿⠛⢋⣡⡄⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣻⣿⣿⡀⠘⣿⠍⣍⣠⡴⢚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠸⣿⣷⠀⢹⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠘⣟⡭⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⢻⠙⣧⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡆⠀⢿⠶⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⣇⠸⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⣿⣿⣿⣿⣿⣧⠀⠸⣷⢶⠿⠖⠀⡈⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿ ⢰⠀⢸⡀⠹⡄⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣰⣿⣿⠟⠋⠁⠀⠀⣟⠕⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⡆⡆⠀⣇⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢟⣋⣀⠀⠀⠀⠀⠀⢹⡖⣖⣲⣬⠭⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣷⠇⠀⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⠀⠀⠀⠀⠀⠚⠋⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢹⡆⠀⠈⡇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣴⣿⣿⡀⠀⠀⠀⠀⠀⣠⣴⡋⠀⢸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⢸⣯⠉⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿ ⡈⣷⡀⡀⢣⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⣤⣶⣿⣿⣿⡇⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⢠⣿⡆⠈⡿⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⡆⢻⣷⣷⢸⡀⡀⠀⣴⣾⣿⣷⣿⣷⣶⣶⣶⣶⣾⡆⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠈⠉⠉⠉⠉⢁⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣠⣾⣿⣧⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣧⢸⣿⣿⡞⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⢀⡀⣠⣾⣷⣠⡄⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡿⣿⡏⣟⡗⠒⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⡇⣿⣿⣷⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⡇⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⣷⣿⣯⢿⣿⠀⠀⠀⠀⠂⠠⠬⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣇⢿⠇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠿⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣧⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣿⡃⢿⣿⣽⣷⠀⣿⡇⠀⠀⣤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣤⣀⣀⣤⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠐⣶⡾⣶⣸⣿⡿⣿⣿⣿⣿⡟⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⡟⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⡟⣿⣿⣿⣟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣿⣿⡿⠾⠿⠘⠿⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⠿⠿⠿⠟⠘⠛⠛⠁⠈⠉⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷ ⣿⣶⣾⣿⣿⣿⣿⣶⣮⣭⢉⠉⠙⠛⠻⠿⠻⠟⠋⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠃⢀⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⠀⠀⠀⠈⠁⠀⠀⣀⣀⣀⣠⣤⡴⠶⠶⠚⠛⠛⠉⠁⠀⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠻⠿⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠟⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠘⠷⠶⠶⠶⠒⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿ ⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣂⠀⠀⠀⣤⣤⣤⠶⠶⠶⠆⠀⠀⠀⠀⠙⣭⣭⣭⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⣿⣿⣿ ⣭⣭⣿⣯⣽⣿⣿⣶⣶⡶⠶⠶⠶⠶⠶⣶⣶⣚⢛⡛⡛⠛⠁⠀⠐⠈⠉⠉⠉⠀⠀⠀⢠⣿⣿⣾⣿⡧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠠⢠⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿ ⣿⡟⠛⠛⠋⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠀⠂⠀⠀⠉⢉⣿⣿⣿ ⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣦⣤⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⢻⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⢀⣀⣀⣀⣠⡤⠴⠾⠛⠛⠋ ⣧⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⢶⠀⣿⣿⣿⣿⣧⣤⣄⡀⠀⠉⠙⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢨⣭⣤⣴⡶⠶⠶⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣻⣿⣿⣿⣶⣾⣉⠛⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⢀⣀⣰⣶⣦⣤⣬⣝⣛⠳⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡋⠉⠛⢷⣶⣦⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣷⣶⣿⣷⣄⠀⠈⠉⠙⠿⣿⣿⣿⣶⣤⣈⠉⠙⠛⠶⢶⣤⣄⣀⡀⠀⠀⢀ ⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣯⣀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠛⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠉⠙⠿⠿⠧⠀⠀⠀⠀⠀⠙⠿⣾⣿⣿⣿⣷⣶⣤⣄⡀⠈⣽⣿⣿⣿⣿ ⢸⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀ ⢸⣷⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧ ⢸⣿⠀⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⢸⣿⡄⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠛⢿⣿⣿⣿⣿⡿⠛⢋⣡⡄⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⣧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣻⣿⣿⠀⠘⣿⢭⣍⣠⡵⢚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠸⣿⣧⠀⢹⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠘⣞⡭⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⢻⠙⣧⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡆⠀⢿⠔⠶⠒⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⣇⠸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⢿⣿⣿⣿⣿⣧⠀⢸⣶⣶⠿⠖⠂⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿ ⢰⠀⢸⡀⠸⡄⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣰⣿⣿⠟⠋⠁⠀⠈⣿⡖⠖⠛⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⡆⡆⠀⣇⠀⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢟⣋⣀⠀⠀⠀⠀⠀⢹⡶⣶⣲⣭⠭⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⠇⠀⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣏⠀⠀⠀⠀⠀⠚⠋⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢹⡆⠀⠘⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣴⣿⣿⡀⠀⠀⠀⠀⠀⣠⣴⡋⠁⢸⣿⡆⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠸⣇⠉⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿ ⡈⣷⡀⠀⢧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⣤⣶⣿⣿⣿⡇⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⢠⣿⡆⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⡆⢻⣷⣿⢸⡐⠀⠀⣴⣾⣷⣷⣷⣿⣾⣷⣶⣾⣾⡆⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠈⠉⠉⠉⠉⢁⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⣀⢀⣠⣾⣿⣧⣤⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⡇⢸⣿⣿⡎⡇⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⢀⡀⣠⣾⣷⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡿⣿⡏⣛⡷⠐⠒⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⡇⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⡇⠈⠀⠀⠀⠸⣿⡇⣿⣿⣿⣷⣿⣯⣿⣿⠀⠀⠀⠀⠒⠠⠬⠥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣇⢿⡇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠿⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣧⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣿⡃⢿⣿⣽⣷⠀⣿⡇⠀⠀⣤⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣤⣀⣀⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠐⣶⡾⣶⣸⣿⡿⣿⣿⣿⣿⡿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⡟⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⡟⣿⣿⣿⡟⠁⣤⡏⣿⡇⣿⣧⢹⣿⣼⣿⣿⣿⡿⠾⠟⠘⠿⠦⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⠿⠿⠿⠟⠘⠛⠛⠁⠈⠉⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣷ ⣿⣶⣾⣿⣿⣿⣿⣶⣮⣍⡉⠉⠉⠛⠛⠻⠿⠿⢍⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠁⢀⡀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠈⠁⠀⠀⣀⣀⣀⣠⣤⡴⠶⠶⠛⠛⠛⠉⠁⠀⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠻⠿⠿⠿⠿⠿⠿⠻⠛⠛⠷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠘⠷⠶⠶⠶⠚⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣐⣀⠀⠀⠀⣤⣤⣤⠶⠶⠶⠆⠀⠀⠀⠀⠙⣭⣭⣭⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⣿⣿⣿ ⣭⣭⣿⣭⣽⣿⣿⣿⣷⡶⠶⠶⠶⠶⠶⠶⢶⡖⡛⣛⡛⠛⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠰⣾⣷⣶⣾⡧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿ ⣿⡟⠛⠛⠋⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠀⠂⠂⠈⠉⢉⣿⣿⣿ ⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⢤⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⢻⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⢀⣀⣀⣀⣠⡤⠴⠾⠛⠛⠋ ⣧⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡗⢶⠀⣿⣿⣿⣿⣧⣤⣄⡀⠀⠉⠙⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢩⣭⣤⣴⡶⠶⠶⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣟⣿⣿⣿⣶⣶⣉⠛⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⢀⣀⣰⣶⣦⣤⣬⣝⣛⠳⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠙⠛⢷⣶⣦⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣷⣶⣿⣷⣄⠀⠉⠉⠛⠿⣿⣿⣿⣶⣤⣈⠉⠙⠛⠶⢶⣤⣄⣀⡀⠀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣯⣀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠛⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠉⠙⠿⠿⠷⠀⠀⠀⠀⠀⠙⠿⣾⣯⣿⣿⣷⣶⣤⣄⡀⠈⣽⣿⣿⣿⣿ ⢸⣿⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇ ⢸⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣏⡘⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⠀⣿⡆⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⡄⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡻⠻⣿⣿⣿⣿⡿⠿⠛⣉⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⢻⣿⣷⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⣭⣿⣿⡅⠀⢿⢭⣭⣁⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠈⣿⣿⡄⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⣗⣫⠽⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠸⡟⢿⡘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣇⠀⢻⡥⠦⠖⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿ ⠀⠀⢣⠘⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⣷⣦⡶⠤⠒⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⡀⠀⠘⡇⠘⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠋⠙⠃⠀⢿⡦⠤⠒⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣇⢁⠀⢻⠀⢹⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡈⢿⣿⣏⠀⠀⠀⠀⠀⠘⠷⢔⣶⣤⡬⠕⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢿⣼⠀⠘⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠾⢺⣿⢻⣿⣼⣿⣏⡀⠀⠀⠀⠀⠐⠛⠋⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠘⣧⡀⠀⢇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⡆⢻⣄⢀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠉⠉⠁⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⣿⡇⠘⣿⡏⣿⡟⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿ ⣧⢸⣿⣾⡄⡇⠀⠀⢠⣴⣶⣶⣶⣶⣷⣶⣶⣶⣶⣇⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣬⣧⡄⠀⣩⠉⠀⠁⠀⠀⠀⠀⣉⢛⣃⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡄⣿⣿⣧⣿⢰⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⣸⡋⢴⡤⢠⣶⢸⣿⠘⣿⣆⣿⡆⣿⡏⣛⡃⠀⠀⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣧⢿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⣿⣿⣿⣿⣏⢈⣁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡏⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢻⣿⠛⣿⣿⣇⠀⠀⠀⠀⣿⣇⢿⡇⠻⠷⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢳⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣤⡄⣤⡌⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⠿⠇⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣿⡏⢿⣿⣽⣷⠀⣿⡇⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿ ⣤⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠆⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⣿⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⣿⣷⣿⠏⣿⡟⣿⣾⣿⣟⠏⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣿⣿⣿⠞⠿⠘⠿⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷ ⣿⣿⣾⣿⣿⣿⣷⣶⣮⣉⡍⠉⠙⠛⠛⠻⠟⠿⢿⢭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⠁⠠⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡠⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⠈⠁⢀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠈⠁⠀⠀⢀⣀⣀⣀⣤⣤⠴⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⠹⠿⠻⠿⠿⠿⠿⠿⠿⠯⠛⠻⢷⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠘⢷⠶⠶⠶⠖⠒⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿ ⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⣂⡀⠀⠀⢠⣤⣤⡶⠶⠶⠖⠀⠀⠀⠀⢉⣭⣭⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢿⣿⣿ ⣉⣩⣿⣿⣿⣿⣷⣶⣤⣤⣤⣴⠶⠶⠶⠶⠶⠶⠶⣖⡛⡛⠛⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢠⣶⣶⣶⣿⣿⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣵⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣁⡈⠁⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⣿⡿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠀⠀⠀⠉⠉⣽⣿⣿ ⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣆⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠛⠛⠃⠀⠀⢀⣀⣀⣠⡤⠤⠶⠟⠛⠛ ⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣷⣶⣶⣶⣶⠰⡄⢺⣿⣿⣿⣿⣧⣤⣀⠀⠈⠙⢻⣿⣿⣿⠟⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣭⣭⣤⣶⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⡿⠿⠿⠿⣿⣿⣿⣷⣞⠿⠛⠁⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⡛⠛⠉⠀⢠⠴⢿⣿⣶⣤⣬⣭⣛⡓⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠷⢶⣿⣿⣦⠀⠀⠈⠉⠻⠾⣽⣿⢷⣦⣄⡉⠙⠛⠳⠶⣤⣄⣀⡀⠀⠀⠀ ⣭⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣷⣯⣍⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣽⣿⢿⣶⣤⣄⣀⠀⢹⣿⣿⣿⣿ ⢸⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇ ⠀⣿⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣏⡹⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⡆⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠟⠛⢉⡄⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿ ⢻⣿⣷⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⣽⣿⣿⡅⠀⢻⡻⣯⣹⡦⠖⠛⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠈⣿⣿⡄⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⣟⣫⠽⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠹⡟⢿⡘⠅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⠀⢻⣤⠦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿ ⠀⠀⢳⠈⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠐⣷⣶⡿⠤⠂⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⡀⡁⠘⡇⠘⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠏⠙⠃⠀⢻⡵⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣇⢀⡀⢻⠀⢹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡈⣿⣿⣏⠀⠀⠀⠀⠀⠸⠧⢶⣶⣶⡭⠕⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿ ⢿⣼⠀⠘⡆⠀⢧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠾⢺⣿⢻⣿⣼⣿⣏⡀⠀⠀⠀⠀⠐⠛⠋⠉⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠘⣧⡀⠀⢧⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠊⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⡄⢻⣄⢀⢸⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠉⠋⠁⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣿⡇⠈⣿⡏⣿⡟⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⡧⠸⣿⣾⡌⡇⠀⠁⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣧⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣬⣧⡄⠀⣩⠉⠀⠁⠀⠀⠀⠀⣉⢛⣃⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡄⣿⣿⣷⣿⢰⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⣸⡋⢴⡤⢠⣶⢸⣿⠘⣿⣆⣿⡆⣿⡏⣛⡃⠀⠀⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣷⢿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⣿⣿⣿⣿⣯⢈⣁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡏⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠤⠬⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢻⣿⠛⣿⣿⣇⠀⠀⠀⠀⣿⣇⢿⠇⠻⠷⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢳⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⡿⠿⠇⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣶⣤⢰⣶⡔⣿⡟⣿⡆⣿⣿⡏⢿⣿⣽⣷⠀⣿⡇⠀⠀⢠⣤⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⣤⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣷⣿⣿⣿⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣥⡀⠀⠀⠀⠀⠀⣿⣷⣿⠏⣿⡟⣿⣾⣿⣟⠏⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣿⣿⣿⠞⠿⠘⠿⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⢹⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷ ⣿⣿⣿⣿⣿⣿⣷⣶⣶⣩⣍⡉⠙⠛⠛⠻⠻⠟⢯⣩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠁⢨⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠘⠁⢀⡀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠈⠃⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠚⠛⠛⠉⠉⠀⠀⣸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠿⠿⠿⠿⢿⠟⠿⠟⠻⠷⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠿⠶⠶⠶⠖⠒⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿ ⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣂⡀⠀⠀⢠⣤⣤⡶⠶⠶⠖⠀⠀⠀⠀⠉⣭⣭⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢿⣿⣿ ⣍⣩⣿⣿⣿⣿⣯⣶⣤⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⣖⣛⠛⠓⠀⠀⠀⠈⠙⠉⠉⠁⠀⠀⢠⣾⣶⣿⣿⣿⠀⠀⠀⠀⠀⢐⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣯⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡉⠉⠁⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⣿⣿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠐⠀⠈⠉⠉⣹⣿⣿ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣦⣄⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣤⣤⣴⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢿⣿⣿⣿⡿⠿⠛⠛⠃⠀⠀⣀⣀⣀⣠⡤⠤⠶⠟⠛⠛ ⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣶⣶⣶⣶⣶⠲⡆⢸⣿⣿⣿⣿⣧⣤⣀⠀⠈⠙⢻⣿⣿⣿⠟⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣭⣥⣤⣴⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣴⣿⣿⡿⠿⡿⠿⣿⣿⣿⣷⣾⠿⠋⠁⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⡛⠛⠉⠀⢠⠰⢿⣿⣶⣤⣤⣭⣙⡓⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠷⢶⣿⣿⣦⠀⠀⠉⠉⠛⠾⣽⣿⣷⣦⣄⡈⠉⠛⠳⠶⢤⣄⣀⡀⠀⠀⠀ ⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⣯⣍⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣻⣿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⣽⣿⢿⣶⣦⣤⣀⠀⢹⣿⣿⣿⣿ ⠀⣿⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷ ⠀⣿⡅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⡇⣿⣇⠀⢸⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢿⣿⣿⣿⣿⡿⠿⠛⣉⡤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⢹⣿⣿⠀⢸⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⣻⣿⣿⣷⠀⢹⡿⣭⣙⡾⠖⠋⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⣿⣿⡅⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣹⣿⡆⠀⣿⣫⠽⠖⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⠀⠘⡟⢿⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣥⠤⠖⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⢹⠈⢷⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣶⡷⠤⠒⠀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⡄⡄⠈⣇⠈⣇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠙⠃⠀⠹⡶⠶⠒⠁⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣧⢀⠀⢸⡄⠸⣾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡐⢾⣿⣿⠃⠀⠀⠀⠀⠀⠀⢶⣶⣴⡭⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢻⣾⡀⠈⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣶⣶⣶⣤⡄⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⠶⢺⣿⢻⣿⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠈⣿⡅⠀⢹⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢸⣿⡇⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿ ⡀⢹⣇⠀⠘⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠻⠛⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣷⡘⣿⣿⡆⡇⠀⠀⢠⣶⣾⣶⣶⣶⣶⣴⣶⣶⣦⣇⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣨⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡃⣿⣿⣿⢻⢸⣾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠿⣿⣧⠀⠀⠀⠀⠀⠀⠘⢿⣞⣡⣤⣄⣠⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡞⣿⣿⣿⣧⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣷⣸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣉⠈⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠤⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡉⠀⢀⣀⠀⠀⠀⠀⣿⡇⢻⠇⠻⠷⠘⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠿⣷⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣤⡄⣤⡌⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⠿⠟⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣨⣿⣿⣿⣷⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣿⣷⠀⣿⡇⠀⠀⢠⡤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣤⣄⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⡿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢿⣿⡟⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⣿⣧⣿⠇⣿⡟⣿⣾⣿⣟⡟⣥⡏⣿⡇⣿⣧⢹⣿⣼⣿⣿⣿⣿⠞⠿⠘⠿⠦⠬⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠘⣿⣿⣿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿ ⣿⣿⣶⣿⣿⣿⣷⣶⣦⣍⣉⡉⠙⠛⠛⠛⠿⠻⢿⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠘⠃⢀⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠋⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠿⠽⠻⠿⠿⠿⠿⠿⠿⠿⠿⠻⠟⡷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠿⠷⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿ ⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⣤⣤⣶⠶⡶⠶⠒⠀⠀⠀⠀⢨⣭⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⢿⣿⣿ ⣉⣉⣿⣿⣿⣿⣵⣶⣤⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⣖⣛⠛⠃⠀⠀⠀⠉⠋⠩⠉⠉⠀⠀⠀⣾⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⠚⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣴⣶⣶⣶⣶⣶⣷⣶⣾⣿⣷⡉⠁⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⣿⡿⠛⠛⠛⠛⠙⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠐⠐⠂⠈⠉⣹⣿⣿ ⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⢶⣆⣀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⠠⠈⠻⣿⣿⣿⡿⠿⠛⠛⠃⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛ ⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣶⣶⣶⣶⣶⠶⡆⢰⣿⣿⣿⣿⣿⣿⣧⣀⡀⠉⣿⣿⣿⣿⠟⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⡀⠀⣬⣭⣤⣴⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⡟⠋⠉⠀⠠⠜⠿⢿⣷⣦⡤⣭⣙⡛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠀⠐⠠⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⠀⠀⠀⠉⠙⠲⣽⣿⣿⣶⣤⣈⠉⠛⠳⠶⢦⣤⣀⣀⠀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣾⣏⡉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠁⠈⠁⠻⣶⡄⠀⠀⠀⠀⠀⠈⠻⢷⣾⣽⣿⣿⣶⣦⣤⣀⡀⢉⣿⣿⣿⣿ ⠀⣿⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷ ⠀⣿⡇⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⡀⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⡇⣿⣇⠀⢸⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠻⣿⣿⣿⣿⡿⠟⠛⣉⡤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⢹⣿⣿⠀⢸⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣿⣿⣿⣷⠀⢻⡯⣭⣉⡤⠶⡊⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⢿⣿⡆⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣹⣿⡆⠈⣿⣫⡽⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠘⡟⢿⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣧⠴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⢸⠈⢷⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡆⠀⣷⣾⡾⠤⠀⠈⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⡄⡀⠈⣇⠈⣇⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠛⠃⠀⢹⠧⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣷⢀⠀⢸⡀⠸⣾⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢾⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣶⣻⡯⠔⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢹⣿⡄⠈⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣶⣶⣤⡄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣟⡀⠀⠀⠀⠀⠀⠀⠉⠉⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠈⣿⡇⠀⢳⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣿⡇⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿ ⡁⢹⣇⠀⠘⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠻⠏⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⠘⣿⣾⡆⣇⢀⠀⢰⣶⣶⣾⣶⣶⣶⣶⣶⣶⣦⣇⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡐⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣨⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡆⣿⣿⣿⣻⢸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠿⣿⣧⠀⠀⠀⠀⠀⠀⠘⢿⣞⣡⣤⣤⣠⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡞⣿⣿⣿⣧⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣸⣿⣿⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣉⠈⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⡆⠀⠀⠐⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡉⠀⢀⣀⠀⠀⠀⠀⣿⡇⢿⠇⠻⠷⠘⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠙⠿⣷⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣤⡄⣤⡍⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⠿⠟⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠀⢀⣨⣿⣿⣿⣷⣤⢰⣶⡔⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⢠⣤⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣤⣄⣀⣀⣀⣠⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⡿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢿⣿⡟⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⡿⣿⣾⣿⣟⡟⣤⡏⣿⡇⣿⣧⢹⣿⣼⣿⣿⣿⣿⠞⠟⠘⠿⠤⠬⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣷⢿⠿⠿⠿⠿⠘⠛⠛⠁⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿ ⣿⣿⣶⣿⣿⣿⣷⣶⣦⣭⣍⣉⠛⠙⠛⠻⠿⠻⠿⢟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠋⠀⡀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡂⠀⠀⠈⠋⠀⠀⢀⣀⣀⣠⣤⣤⠴⠶⠚⠛⠛⠉⠉⠀⠀⣸⣿⣿ ⣿⣿⣿⣿⣿⡿⠿⢿⠿⠛⠛⠿⠿⠿⠿⠿⠟⠟⠙⠿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠿⠷⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿ ⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣀⠀⠀⠀⣤⣤⣶⡶⠶⠶⠒⠀⠀⠀⠀⢨⣭⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢿⣿⣿ ⣍⣹⣿⣿⣿⣿⣿⣦⣴⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⢛⣛⠛⠃⠀⠀⠀⠈⠉⠉⠍⠉⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣽⣿⣽⣶⣶⣶⣶⣶⣿⣿⣿⣿⣯⣉⠁⡀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⣿⣿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠐⠂⠀⠉⠉⣹⣿⣿ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣴⣆⣀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⠠⠈⠻⣿⣿⣿⣿⠿⠛⠛⠃⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛ ⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣷⣾⣶⣶⣶⣶⣷⠶⡆⢰⣿⣿⣿⣿⣿⣿⣧⣄⣀⠈⣿⣿⣿⣿⠟⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢀⡀⠀⣬⣥⣤⣴⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠁⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⡟⠋⠉⠀⠠⠼⠿⢿⣷⣦⡤⣭⣙⡛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠂⠐⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠛⠲⣽⣿⣷⣶⣤⣈⠉⠛⠻⠶⣦⣤⣀⣀⠀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣍⡉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠁⠈⠀⠻⣶⡄⠀⠀⠀⠀⠀⠈⠻⢷⣾⣽⣿⣿⣶⣦⣤⣀⡀⢩⣿⣿⣿⣿ ⠀⣿⠅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿ ⠀⣿⡆⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⡀⣿⡇⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⡇⣿⣇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⢟⠛⣉⡤⠐⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⢹⣿⣿⠀⢸⡂⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣛⣿⣿⣷⠀⢹⣿⣭⣉⣿⠶⡚⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⢿⣿⡆⠈⡅⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⡆⠈⣷⣫⡽⠞⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⠀⠘⡟⢿⡄⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣧⡶⠖⠂⡀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⢸⡈⢷⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣷⣶⡿⠥⠐⢈⣀⡤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⡄⡀⠀⣇⠈⣇⢸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠛⠇⠀⢹⠧⠴⠖⠋⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣧⢀⠀⢸⠄⠸⣾⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⢰⣴⣾⡭⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢹⣿⡄⠘⡇⠀⢻⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣶⣶⣤⡄⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⠶⢺⣿⢻⣿⢸⣿⣟⡀⠀⠀⠀⠀⠀⠈⠉⠉⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠈⣿⡆⠀⢳⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢸⣿⡇⢸⣿⣿⣿⡜⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿ ⣁⢹⣇⢀⠘⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠿⠏⢙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣷⠘⣿⣾⡇⣇⢀⠀⢠⣶⣶⣾⣶⣶⣷⣾⣷⣶⣦⣇⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡄⣿⣿⣿⢻⢸⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⢿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣷⣂⣧⣤⣄⣠⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡆⣿⣿⣟⡻⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣽⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣉⠈⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⠀⣀⣀⠀⠀⠀⠠⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡋⠀⢀⡀⠀⠀⠀⠀⣿⡇⢻⠇⠻⠷⠘⠻⠛⢻⣷⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡜⣽⡿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⠿⠟⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⠀⢈⣹⣿⣿⣿⣷⣤⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⢠⣤⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⡿⣿⣼⣿⣿⣿⣿⣮⣍⠈⣿⡇⣿⣇⣿⣧⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⣿⣧⣿⠇⣿⡟⣿⣾⣿⣟⡏⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣾⣿⣿⠞⠟⠘⠿⠤⠬⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠉⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣷⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠈⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿ ⣿⣿⣶⣿⣿⣿⣷⣷⣦⣭⣍⡉⠉⠛⠛⠻⠿⠻⠻⢭⣅⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⢠⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠈⠁⠄⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠐⠀⠀⠉⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠉⠉⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠿⠷⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿ ⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣐⣐⣒⣀⠀⠀⠀⣤⣤⣶⠶⠶⠶⠖⠀⠀⠀⠀⠈⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢿⣿⣿ ⣍⣉⣿⣿⣿⣿⣿⣿⣤⣤⣤⣶⠶⠶⠶⠶⠶⡶⠶⣚⡛⠛⠃⠀⢀⠀⠙⠛⠉⠍⠉⠀⠀⠠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣽⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡉⡁⡁⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⣿⣿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠐⠒⠀⠉⠉⣹⣿⣿ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣶⣦⣀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⠠⠀⠹⣿⣿⣿⣿⠿⠟⠛⠂⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛ ⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣶⣶⣶⣶⣷⠶⡆⢸⣿⣿⣿⣿⣿⣿⣧⣄⣀⠈⢿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡀⠀⢨⣭⣤⣶⠶⠶⠾⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣴⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣟⠋⠉⠁⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⡟⠋⠉⠀⠠⠼⠿⣿⣷⣦⣤⣭⣝⡛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠃⠒⠂⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠛⠲⣽⣿⡷⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣏⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⠃⠙⠉⠻⣿⣦⠀⠀⠀⠀⠀⠈⠻⢷⣾⣽⣿⡿⣶⣦⣤⣀⡀⢉⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⡀⣿⡇⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⡇⣿⣇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠛⣉⣴⠦⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⢻⣿⣿⠀⢸⡆⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣷⠀⢻⣿⣿⣙⣿⠶⠛⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⢿⣿⡆⠈⡇⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⣦⣾⣿⣿⣿⡆⠈⣿⣫⡿⢞⠋⠀⣀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠘⡟⢿⡄⡇⢸⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣷⣶⢖⢂⡀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⢹⡀⢷⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⣾⣿⠧⠒⢊⣁⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⡄⡄⠀⣇⠈⣇⢸⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⡿⠻⠇⠀⢹⡷⠶⠞⠋⣉⣀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣷⢠⠀⢸⡀⠸⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠇⠀⠀⠀⠈⠀⢶⣶⣿⡿⠾⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢹⣿⡄⠈⡇⠀⢻⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⡄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠉⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠈⣿⡇⠀⢻⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡞⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿ ⡅⢹⣏⢀⠸⡄⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠛⠋⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣷⠘⣿⣿⡆⣇⢀⢸⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠀⢠⡼⣇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠇⠀⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡇⣿⣿⣿⢸⢸⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⢧⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣠⣬⣤⣠⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡎⣿⡏⣟⡛⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣼⣿⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣉⠘⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠩⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⡏⠀⠆⠀⠀⠀⠀⠀⣿⡇⢻⠇⠻⠷⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣬⡍⣿⣿⡿⢾⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⣿⣿⣿⣿⣧⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣿⣷⠀⣿⡇⠀⠹⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠈⣿⡇⣿⣇⣿⣷⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣧⡿⠏⣿⡿⣿⣿⣿⣿⡿⣥⡏⣿⡇⣿⣧⢻⣿⣾⣿⣼⣿⣿⠞⠿⠘⠿⠦⠬⠭⠀⠀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠘⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿ ⣿⣿⣷⣿⣿⣿⣿⣶⣦⣭⣍⡉⠛⠛⠛⠿⠿⠿⠿⣿⣉⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⣰⡀⠀⢀⡠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡁⠈⠃⠁⡀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠆⠐⢀⠠⠋⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⣿⣿⣿⠿⠿⣿⣷⡆⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⡿⠷⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿ ⣿⣿⣿⣿⣿⣇⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢄⣟⣒⣐⣕⣀⠀⠘⢥⣤⣤⣶⣶⣶⠶⠖⠀⠀⠀⠀⢈⣭⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠒⠚⢿⣿⣿ ⣟⣛⣿⣿⣿⣿⣿⣿⣬⣦⣶⣶⡶⠶⠶⠶⠶⢶⡶⡶⣛⡛⠀⠀⣉⠛⠋⠭⠭⠭⠍⠀⠈⢸⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣽⣿⣭⣽⣶⣶⣶⣶⣿⣿⣿⣿⣿⣯⣉⣀⠁⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⣿⣿⠛⠛⠛⠛⠛⠋⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠐⠒⠀⠉⠉⢹⣿⣿ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣶⣶⣀⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣷⠀⠀⠠⠀⠹⣿⣿⣿⣿⠿⠟⠛⠂⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛ ⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣷⣿⣶⣶⣶⣶⠷⡆⢰⣿⣿⣿⣿⣿⣿⣿⣅⣀⠈⢿⣿⣿⣿⡿⠁⠀⠀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡀⠀⢨⣭⣤⣶⠶⠶⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣴⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠁⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⣟⠋⠉⠀⢠⠴⠿⢿⣷⣦⣄⣭⣝⣛⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⢿⡗⠒⠂⠀⠀⠀⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠙⠲⣽⣿⡿⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣾⣏⡉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠏⠉⠋⠻⣿⣦⠀⠀⠀⠀⠀⠈⠛⢿⣾⣭⣿⣿⣷⣦⣤⣀⡀⠉⣿⣿⣿⣿ ⠀⣿⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣚⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⡆⣿⡇⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⡇⢻⣷⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠛⣉⣤⠖⢂⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⠹⣼⣿⠀⢸⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⢻⣿⣯⣉⣭⠶⢛⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⠀⢻⣿⡆⠈⡇⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣶⣿⣿⣿⡆⠈⣿⣯⡽⢞⡋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⠀⠈⣟⢻⡄⡇⢸⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣗⣿⣿⠀⢸⣷⠶⠖⠒⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⠀⠀⢸⡀⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡿⠧⠒⢈⣁⠤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡆⢴⠀⢇⠈⢧⢸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠷⠀⢸⣷⠶⠚⠋⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿ ⣷⢠⠀⢸⡄⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠇⠀⠀⠀⠀⠈⢧⣖⣾⡿⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢸⣿⡆⠀⣧⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣦⠀⡦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢹⣿⢸⣿⣿⡋⠀⠀⠀⠀⠀⠀⠉⠉⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⡄⣿⡇⠀⢹⠀⠈⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡞⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣇⢸⣏⠀⠈⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡊⣿⣶⣇⢇⠀⠈⢀⣤⣶⣶⣶⣾⣶⣶⣶⣶⣶⣷⠀⣰⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡇⢻⣿⣿⢸⢀⣧⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣀⣤⣤⣠⡀⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡆⣿⡏⣟⡋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣸⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣉⠈⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣿⠀⠀⢀⠀⠀⠀⠀⠨⠬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡋⠀⢰⡄⠀⠀⠀⠀⣿⡇⢻⠇⠻⠷⠘⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢾⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣶⣶⣶⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⠰⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠈⣿⡇⣿⣇⣿⣧⢿⣿⡛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⡿⠇⣿⣿⣿⣿⣿⣿⡟⣤⡏⣿⡇⣿⣧⢹⣿⣾⣿⣸⣿⣿⠞⠿⠘⠿⠦⠬⠭⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣿⢿⠿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠈⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿ ⣿⣿⣷⣿⣿⣿⣷⣶⣦⣬⣍⠉⠉⠛⠛⠿⠿⠿⠯⣯⣍⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⢀⣀⠀⡀⢀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠸⠉⢀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⠐⡀⠠⠛⠀⠀⢀⣀⣀⣀⣤⣤⠴⠶⠞⠛⠛⠉⠉⠀⠀⣸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡯⡿⠛⢿⣿⣿⡿⣿⠿⠷⠿⡿⠷⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⡿⠿⠶⠶⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿ ⣿⣿⣿⣿⣿⣇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⣂⣓⣀⣓⡀⠀⠰⣴⣤⣴⣶⣶⢶⡶⠞⠂⠀⠀⠀⠈⣭⣄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠒⠒⠚⢿⣿⣿ ⣭⣉⣿⣿⣿⣿⣿⣦⣥⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⢾⣛⠓⠀⠀⡛⠟⠉⠭⠭⠭⠁⠀⠈⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⠛⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣽⣿⣭⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⡍⣉⣉⠈⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿ ⣿⣿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠄⠐⠂⠀⠉⠉⢹⣿⣿ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣴⣶⣶⣄⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⡷⠀⠀⠠⠀⠹⣿⣿⣿⣿⠿⠟⠛⠂⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛ ⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣶⣶⣶⣶⣶⣾⠶⠂⢸⣿⣿⣿⣿⣿⣿⣿⣅⣀⠈⢻⣿⣿⣿⡿⠁⠀⠀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢀⡀⠀⢨⣭⣤⣴⠶⠶⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣴⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠁⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⣟⠋⠉⠀⢠⠶⠿⢿⣷⣦⣤⣭⣝⣛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⢻⡗⠒⠀⠀⠀⠀⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠙⠳⣿⣿⡿⣶⣤⣈⠉⠙⠛⠶⢦⣤⣀⣀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣏⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⠙⠋⠻⢿⡆⠀⠀⠀⠀⠀⠈⠛⢿⣾⣽⣿⣿⣶⣦⣤⣀⡀⠉⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⡂⣿⡇⠀⢸⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⡄⢿⣧⠀⢸⠇⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣇⢸⣿⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡛⣋⣴⠶⢒⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠸⣾⡿⠀⠘⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢹⣿⣿⣝⣿⠷⢚⠋⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⢻⣿⣦⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣼⣿⣿⣿⣇⠈⢻⣻⡽⠿⡛⠁⣀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⠀⠈⣿⢻⡆⡇⢰⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠀⠸⣷⣶⠶⢒⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⠀⠀⠸⡄⢻⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠧⠒⢉⣁⡠⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡆⠶⠀⢷⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⢿⠀⢸⣿⠶⠖⠋⣁⣀⡀⠤⢆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⢿⣰⡀⢸⡆⠘⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿⠅⠀⠀⠀⠉⢱⣶⣿⡿⠿⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠸⣿⡇⠈⣧⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢺⣿⢻⣿⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠉⣀⡀⠄⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⡆⢿⣇⠀⢸⡀⠈⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡼⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠉⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣇⢸⣿⡀⠐⡇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡎⣿⣿⣇⢷⠀⢘⢠⣴⣾⣾⣷⣿⣶⣶⣿⣾⣶⣦⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿ ⣿⣇⢻⣿⣿⣸⡮⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣀⣤⣤⣡⡀⢴⡤⢠⣶⢸⣿⠸⣿⣆⣿⡆⣿⡏⣟⡃⡷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣉⠘⠁⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⣿⣿⡄⠀⢀⠀⠀⠀⠀⠩⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⡄⠀⠀⠀⠀⣿⡇⢻⠇⠿⠿⠘⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡍⣿⣿⡿⢾⡇⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡿⠿⢽⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣷⣶⣶⣶⣶⢰⣶⡜⣿⡟⣿⡆⣿⣏⡁⣿⣿⣿⣷⠀⣿⡇⠀⠀⠰⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣤⣄⣀⣀⣀⣀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠈⣿⡇⣿⣇⣿⣷⢿⣿⣛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡿⠇⣿⣿⣿⣿⣿⣿⡿⣷⡏⣿⡇⣿⣷⢻⣿⣾⡿⢸⣿⣿⡟⠟⠘⠿⠦⠮⠽⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿ ⣿⣿⣷⣿⣿⣿⣿⣿⣷⣭⣍⡉⠙⠛⠛⠻⠿⠿⠿⣿⣍⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⢡⡄⠀⣀⡄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠉⠃⢀⣀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢟⠀⡂⠨⠋⠀⠀⢀⣀⣀⣀⣤⣤⠴⠶⠖⠛⠛⠋⠉⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⡿⠿⠶⠶⠖⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿ ⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⣖⣒⣓⡀⠀⠸⣤⣤⣶⣶⣶⣶⣶⠞⠂⠀⠀⠀⠀⣭⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠚⢿⣿⣿ ⣭⣙⣿⣿⣿⣿⣿⣯⣦⣤⣴⡶⠶⠶⠶⢶⣶⣶⠶⢞⠛⠃⠀⢰⣽⠟⠩⠭⠭⠍⠁⠀⢀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣽⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣯⢈⡁⡁⠀⣠⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿ ⣿⣿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠔⠒⠂⠉⠉⢹⣿⣿ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣴⣶⣆⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⡷⠀⠀⠠⠈⠻⣿⣿⣿⣿⢿⠟⠛⠃⠀⠀⣀⣀⣀⣠⣤⠤⠶⠟⠛⠛ ⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣷⣷⣶⣶⣶⣶⣿⣾⠷⠂⢸⣿⣿⣿⣿⣿⣿⣿⣅⣀⠈⢻⣿⣿⣿⡿⠁⠀⠀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⡀⠀⢭⣭⣤⣴⠶⠶⠾⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠁⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⣿⠛⠋⠁⠀⢤⠾⠿⢿⣷⣶⡤⣭⣝⣛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⢿⡗⠲⠆⠀⠀⠀⠁⠀⠀⠛⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⠀⠀⠀⠉⠙⠲⣽⣿⡿⣶⣤⣈⠉⠛⠛⠶⢦⣤⣀⣀⠀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣯⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣭⣿⣿⣷⣶⣤⣀⡀⠉⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⡄⣿⣇⠀⢸⡃⠄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣇⢸⣿⠀⠸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡛⢛⣡⡴⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⠹⣼⡿⠀⠐⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⢹⣿⣯⣝⣿⠷⡟⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⠀⢻⣿⣆⠀⡇⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡌⢙⣿⣿⠅⠈⢿⣿⡽⠿⡛⠁⣀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⠀⠈⣿⢻⡆⡇⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠸⣷⣶⠶⠒⡉⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⠀⠀⠸⡄⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⣿⣿⡇⠀⣿⣾⣾⠧⠖⢊⣉⣠⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡆⢤⠀⢷⠀⢷⢰⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣷⠀⢸⣷⡴⠶⠊⠁⣀⡀⠤⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿ ⣿⢰⠀⢸⡆⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⠇⠀⠀⠁⠹⣶⣾⣿⠿⠗⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢸⣿⡆⠈⣧⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣛⣿⣿⠃⠀⠀⠀⠀⠈⠉⢁⣀⠤⠄⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿ ⡄⣿⣇⠀⢹⠀⠈⡇⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡞⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⡇⢸⣿⠀⠈⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡎⣿⣷⣆⣧⠀⢈⢀⣴⣷⣿⣾⣶⣷⣾⣶⣷⣦⣄⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡇⢿⣿⣿⣸⣐⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⢿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⣀⣤⣄⣠⣤⢴⡤⢠⣶⢸⣿⡸⣿⣆⣿⡏⣿⡏⣟⡃⠖⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣁⠘⠉⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣷⠄⠀⢀⠀⠀⠀⠀⠠⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⣿⣇⢻⠇⠿⠿⠘⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡜⣿⣿⡷⢾⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣁⣤⣶⣶⣶⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⢰⣾⣧⣄⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⡇⣿⣧⣿⣧⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠇⣿⣿⣿⣿⣿⣟⡿⣷⡏⣿⡇⣿⣧⢻⣿⣾⡿⠸⣿⣿⠞⠿⠘⠿⠦⠬⠍⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠀⠀⠀⠀⢠⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿ ⣿⣿⣷⣿⣿⣿⣿⣿⣶⣮⣍⡉⠉⠛⠛⠿⠿⠿⠿⢛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⢤⠀⠀⠀⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠉⠁⠀⡁⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠗⠀⡀⠀⠛⠀⠀⢀⣀⣀⣀⣤⣤⡴⠶⠶⠛⠛⠋⠉⠁⠀⣸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⣿⠷⠶⠶⠶⠒⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿ ⣿⣿⣿⣿⣿⣏⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⢲⣞⣳⣜⣐⣖⡀⠠⣯⣥⣤⣴⣶⣶⣶⣶⡶⠓⠀⠀⠀⠀⢨⣥⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠐⠚⢿⣿⣿ ⣭⣹⣿⣿⣿⣿⣿⣦⣶⣤⣶⡶⠶⠶⠶⠶⣶⢶⡶⣾⡛⠃⠀⢘⢿⠟⠭⠭⠭⠭⠁⠈⡉⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣧⡀⠀⠀⠀⠀⠈⠨⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣽⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣭⡁⣉⠉⠀⣀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢨⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿ ⣿⣿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠄⠒⠒⠈⠉⢹⣿⣿ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣶⣶⣤⣴⣶⣄⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠛⣿⣿⣿⣿⣿⡿⡿⠛⠃⠀⠀⠀⣀⣀⣀⣤⡤⠴⠿⠛⠛ ⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣷⣶⣾⣾⣷⣶⣷⣾⠶⠀⣾⣿⣿⣿⣿⣿⣿⣿⣅⡀⠈⢿⣿⣿⣿⡿⠁⠀⢀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠀⠈⣭⣭⣥⣤⡶⠶⠾⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣙⠉⠉⠁⠀⠀⠀⠈⠉⠀⣿⣿⣿⣿⣟⠋⠋⠁⠀⣤⠶⠆⢶⣶⣤⣬⣭⣙⡛⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⢿⠟⠲⠀⠀⠀⠈⠁⠀⠀⠻⣿⣿⣿⣿⣿⣶⣾⣿⣿⣷⠀⠀⠀⠉⠛⠾⣿⣿⡷⣶⣤⣉⠉⠛⠳⠶⣤⣤⣀⣀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣍⡉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠋⠙⠛⠿⣿⣶⣤⡀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣶⣦⣄⣀⠀⢉⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⣿⡇⠀⢸⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⡄⣿⣇⠀⢸⠃⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣇⢺⣿⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢛⣵⡤⢆⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⢹⣼⣿⠀⠘⡇⠀⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⢻⣿⣿⣝⣯⠷⣚⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⠀⢿⣿⣆⠀⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⢉⣻⣿⠄⠈⣿⣿⣽⠿⡛⠉⣀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⠀⠈⣿⢿⡆⡇⢸⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢸⣿⣴⠷⡒⡁⠀⠀⢀⡔⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⠀⠀⠸⡈⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⠧⠔⢂⣁⣠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⡆⣴⠀⢧⠈⣿⢸⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡄⠸⣿⣴⠶⠋⠁⣀⡀⠤⢤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿ ⣿⢠⠀⢸⡆⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⡿⠂⠀⠘⠹⣶⣾⣿⠿⠗⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢸⣿⡆⠀⣧⠀⢻⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣟⣿⣿⡟⠁⠀⠀⠀⠀⠉⠁⣀⠠⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⡌⣿⡇⠀⢹⡀⠈⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡞⣿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣇⢹⣷⠀⠸⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡜⣿⣷⡦⣧⠀⢸⢰⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⡀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣇⢿⣿⣿⢹⡼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⣤⣄⣰⣤⢴⡦⢠⣶⢸⣿⡸⣿⣆⣿⡆⣿⡏⣟⡃⠰⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣁⠘⠉⠈⠀⠀⠀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣷⠀⠀⠀⠀⠀⠀⠀⠠⠤⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡉⠀⠀⣀⠀⠀⠀⠀⣿⣇⢻⠇⠿⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡌⣿⣷⡶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢉⣿⣿⣿⣿⣥⣶⣤⣶⣶⡜⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⢀⣤⣤⣠⣤⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣤⣄⣀⣀⣀⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡇⣿⣧⣿⣧⢿⣿⠛⢸⣿⣿⣿⠀⢿⣿⠘⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⣿⡿⣷⡏⣿⡧⣿⣧⢻⣿⣾⡿⠸⠿⠿⠞⠿⠸⠿⠤⠬⠭⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⢿⡿⠿⠿⠿⠘⠛⠛⠁⠈⠉⠈⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿ ⣿⣿⣷⣿⣿⣿⣿⣿⣷⣯⣍⡉⡛⠛⠛⠻⠿⠿⣿⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⡠⠀⠀⠢⣢⣔⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡅⠈⠸⠉⡀⠁⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣵⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⡀⢐⠛⠁⠠⠀⣀⣀⣀⣤⣤⡴⠶⠶⠛⠛⠋⠉⠁⠀⣸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢿⡿⠾⠶⠶⠖⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿ ⣿⣿⣿⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⢊⣭⣿⣷⣚⣗⡀⠠⠿⣧⣤⣤⣶⣶⣶⣶⡶⠟⠀⠀⠀⠀⢀⣭⡄⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠄⠒⠺⢿⣿⣿ ⣯⣹⣿⣿⣿⣿⣿⣿⣦⣤⣶⣶⠶⠶⠶⠶⠶⣶⠶⠾⡛⠂⠀⣟⣟⡟⠯⡭⠭⠭⠁⢠⡍⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠸⠟⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣽⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣯⣉⣉⣉⠉⣤⡀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢨⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⣿⣿⡛⠛⢛⠛⠋⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠀⠒⠒⠈⠉⢹⣿⣿ ⣿⠟⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣶⣶⣦⣴⣶⣄⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠟⠛⠃⠀⠀⠀⣀⣀⣀⣤⡤⠴⠿⠟⠛ ⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣾⣶⣷⣶⣾⣾⠲⠀⢾⣿⣿⣿⣿⣿⣿⣿⣅⣀⠈⢿⣿⣿⣿⠟⠁⠀⢀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠐⠂⠈⣭⣭⣥⣤⡶⠶⠾⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⣙⠉⠉⠀⠀⠀⠀⠈⠉⠀⣿⣿⣿⣿⡟⠋⠉⠉⠀⢤⡤⠄⢠⣤⣤⣬⣭⣙⡓⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⠿⣿⠗⠂⠀⠀⠀⠈⠁⠀⠀⢻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⠀⠀⠀⠉⠛⠾⣿⣿⣷⣦⣄⣉⠙⠛⠳⠶⣤⣄⣀⡀⠀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣏⡉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⠏⠛⠛⠿⣿⣶⣤⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣷⣶⣦⣄⣀⠈⢉⣿⣿⣶⣿ ⠀⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷ ⠀⣿⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⡄⣿⡇⠀⢸⡁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⣇⢸⣿⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⣥⡴⠆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⢹⣼⣿⠀⠘⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠂⢿⣿⣿⣏⣻⡵⠞⡋⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⢿⣿⣆⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣿⡶⠀⣿⣟⣿⠿⡟⠉⢀⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⠀⠘⣿⢿⡄⡇⢸⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⠄⠸⣿⣶⡷⠖⣀⠀⠀⢀⡀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⢸⡈⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⡄⣯⣶⣿⡯⠔⠂⣉⣡⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⡆⣀⠀⢧⠈⣧⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⢹⣿⣷⠶⠞⠉⠁⣀⠤⢤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣷⢡⠀⢸⡄⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢩⣿⣿⣿⣿⠀⠈⠓⠶⣶⣿⡿⠷⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢹⣿⡆⠈⣇⠀⢻⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢸⣿⢹⣿⢸⣿⣏⠀⢿⣿⡿⠁⠀⠀⠀⠀⠁⠀⡠⠄⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⡌⣿⡇⠀⢹⠀⠘⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣿⣿⣿⡼⣿⡟⢃⠘⠻⠅⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿ ⡇⢸⣿⠀⠸⡆⠀⢣⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡏⣿⡇⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡞⣿⣷⡆⣧⠀⠀⢰⣴⣷⣿⣿⣾⣿⣷⣿⣶⣄⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⣀⢀⣀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⠇⢿⣿⣿⢹⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠿⣿⣿⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣄⣤⣄⣰⣤⢴⣦⢤⣶⢸⣿⠸⣿⣆⣿⡆⣿⡏⣟⡃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣁⠘⠿⠈⠈⠀⡀⠘⣿⡇⣿⣿⣿⡇⣿⣯⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠀⠀⠀⢀⣾⡇⠀⣿⣇⢿⠇⠻⠿⠙⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣮⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄⣤⡄⣶⣶⡶⢾⡇⠈⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣛⡛⣿⣿⣿⣿⣿⣿⣿⢰⣶⡔⣿⡟⣿⡆⣿⣏⡁⢿⣿⣽⣷⠀⣿⡇⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣤⣄⣀⣀⣀⣀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡼⣿⡇⣿⣇⣿⣷⢿⣿⠛⢸⣿⣿⣿⠀⢻⣿⣶⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠏⣿⣿⣿⣿⣿⣿⡿⣿⡏⣿⣇⣿⣧⢻⣿⣾⡿⠸⠿⠿⠞⠟⠘⠿⠤⢬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠟⠂⠀⠀⠀⠈⠁⠀⠘⠻⣿⣿⣿⣿⣷⣶⣶⣶⣿⣶⣄⠀⠀⠉⠻⠿⣻⣿⣶⣦⣌⠉⠛⠳⠶⢦⣤⣀⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣋⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡋⠛⠻⠿⣿⣿⣷⣤⡀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣦⣤⣀⡀⠉⢙⣿⣷⣶⣿ ䷩ 𝚕𝚒𝚗𝚎 1645 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/irc-log-280822/#comments Gemini version at gemini://gemini.techrights.org/2022/08/29/irc-log-280822/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Sunday,_August_28,_2022⠀✐ Posted in IRC_Logs at 2:51 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-280822.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-280822.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-280822.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-280822.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  Qmc9CFRLenFK2RwWG9geCXFX5mSZaoYnzhcwUzk8sWMUuN #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmdvdufFvS6VcJGSysyPxvUVmgaAMex619fH94FBS6PH1U (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  QmamuW1aeLr8gp7CtGMKiYBy6uErey3NKjAirNYJ5dVfB4 social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmXgUndwsLst1ZwdrYP6aj1dWwpM71GLpBLvkzp4DA2vGZ social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmbeY1t3e66MQjVZuFm78tAPuoaaScgLJjtthoRE5wCHzg #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmQBd8GcjZiABHWZJ5FDCkSkA32c3vtdsEPLHoWhd22dUu (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmcwbaedQvFSEDYMZrUC4KMnEK7xvgoS2FPZUhnXzyuaJV #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmXRU9RGGogqni4oiJGin9Qfi5QnFpkaKva2Y5kocauXdP (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): Qmdj75rdsbiWjm4ms8CTMfcbYno6Pw9hH66AytZ3Hs3qV7 ䷩ 𝚕𝚒𝚗𝚎 1772 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/lf-rejects-linux/#comments Gemini version at gemini://gemini.techrights.org/2022/08/29/lf-rejects-linux/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_‘Linux’_Foundation_is_Working_Against_Linux_for_People_Who_Reject_Linux⠀✐ Posted in Deception, Kernel at 8:10 am by Dr. Roy Schestowitz Video_download_link | md5sum e97cad80e2343157a0717981e1ed2aef LF is Run by Charlatans and Liars Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/lf-acting-dodgy.webm Summary: Corporations that reject_Linux_and_the_GPL have managed to position themselves above Linus Torvalds; due to the name (“Linux Foundation”) a lot of people cannot realise that this rogue organisation is run by Linux-hostile people, who don’t even use the “product” named in their payslip (now exceeding 6 figures; some are netting 7-figure salaries despite the revenue shrinking) LAST night and this morning we posted three articles (about 3 in 12 hours [1, 2, 3]) regarding the so-called ‘Linux’_Foundation. Not only has it gotten increasingly rogue; it also lost 18 million dollars in revenue (in just one year!) and its chief’s wife seems to be running a fraud, which was recently sued — a class action lawsuit — for securities fraud. “The trademark “Linux” is under attack and Linus (Torvalds) is under the influence… of frauds.”Not too long ago we mentioned how the so-called ‘Linux’ Foundation is also defrauding_companies with clickfarms. It sells_"tweets"_in clear_violation_of_Twitter's_rules. It also fails_to_defend_the_founder_of Linux (which it is called after); instead it is promoting_Microsoft, which involves a_conflict_of_interest (the chief’s wife). The trademark_"Linux"_is under_attack and Linus (Torvalds) is under the influence… of_frauds. █ ䷩ 𝚕𝚒𝚗𝚎 1823 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/lf-still-no-pdf/#comments Gemini version at gemini://gemini.techrights.org/2022/08/29/lf-still-no-pdf/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Linux_Foundation_Drowning_in_Grift_and_7-Figure_Salaries_(Awarded_to_People Who_Never_Created_Anything)⠀✐ Posted in Deception, GNU/Linux at 3:16 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇LF IRS 2020⦈ New screenshot from here, but no further details for now. Regarding the scale and currency, it is US dollars. Summary: The cookie jar associated with exploitation (or dilution) of the brand “Linux” is being opened and emptied by people who don’t use Linux and don’t contribute anything to it, instead selling control over it to hostile companies — i.e. opponents — like Microsoft (classic, textbook sellout) MANAGERS of the Linux_Foundation, i.e. the bosses of the person who actually made Linux, are parasitic and greedy. As we noted last_night, it’s hard to find any IRS filing later than 2018. This isn’t normal. For other institutions we can download the 2020 filings already. It’s hard to tell what’s going on or why it’s taking so long, but we’ve managed to get the above sneak peek this past weekend. Now compare it to the prior year. We’ve uploaded a locally-hosted HTML version, but we’ll carry on pursuing the original PDF. Revenue nosedived. Salaries, on the other hand, soared. Are they rewarding themselves for failure? “Revenue nosedived. Salaries, on the other hand, soared.”Compare 2019 to 2020; 27.1% to 35.4% of the money is spent on salaries — an increase of 8.3% in just one year! A decade ago that was 19%-22%, so clearly something has changed. Executive compensation leaped from 5% to almost 7%, so that’s like 40% increase, relatively speaking, in just one year. One year! But let’s ask the more important question, as it was posed by an associate yesterday. Who nets that money? Not people who make Linux (or very few who do): 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇lf-deadweights⦈_ The deadweights Only about 2 of these people actually code Linux. Only one of them gets paid by the so-called ‘Linux’ Foundation and he_gets_treated_rather_poorly. “It is very useful to point out the salaries of the coders versus the dead wood,” an associate noted. “It might be also useful to point out that the former are mostly at the bottom of the list.” (Many unpaid, except by corporations like Oracle) “Also,” this associate added, “is Brescia the only director representing Microsoft? I thought there was at leastone other, not to mention all the partners and license infringers there, too.” This is from 2019. At least two more have been added since (the Board and the management team). Some have been identified before (by name), but more have been recruited. One friend brings another… and another. It’s seen_as_desirable, not just acceptable. “Of the fourteen salaried positions listed, only four (29%) are programmers,” the associate said, “according to your annotations. Except for LT himself, they are at the bottom of the list and even LT is a distant second to JZ.” There’s money on top of that. Here’s a screenshot from the HTML_version: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇zemlin-totals⦈_ Over a million a year. No tax to pay. █ ⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿ ⣿⣉⢉⠛⢛⠛⣯⠩⡉⡍⡏⡟⠛⠟⠛⠛⡏⠙⡛⠛⣏⠉⠙⢻⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣼⣤⣤⣤⣯⣤⣧⣤⣥⣥⣤⣀⣠⣤⣷⣤⣇⣼⣿⣤⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡍⢙⠛⡏⠉⠉⡏⡙⠛⠛⢻⠉⠉⠩⣿⠛⡏⣟⡿⠛⡛⠛⠟⠋⡏⣛⡙⢛⠛⠛⠋⠙⠛⢻⠛⠋⠻⢛⣻⡙⡙⠉⢻⣛⠛⠛⣹⠛⣛⠹⢹⡛⠛⠛⠉⠛⠛⢻⡏⠙⠋⠛⠋⡛⠛⡏⠛⠋⠛⡛⠋⡏⠛⢛⣻⣿⣿ ⣿⠿⠿⠿⠿⠿⠟⡿⠟⠿⠻⠿⣿⠟⣿⠿⢻⠛⠻⢿⠿⠻⠻⠟⢿⡟⠻⠿⠟⢻⠛⠿⢿⡟⡟⢻⡿⠿⠻⢿⠿⠿⠿⠿⠿⡟⠿⢿⡟⠛⢞⢻⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣶⣶⣶⣷⣦⣶⣷⣶⣶⣶⣶⣿⣿⣷⣶⣾⣾⣶⣾⣼⣶⣶⣿⣶⣷⣶⣶⣶⣾⣾⣶⣾⣿⣶⣾⣿⣶⣶⣷⣶⣶⣶⣾⣶⣿⣶⣿⣷⣶⣷⣾⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⡿⠿⢿⢿⠿⠿⠿⠿⠟⠿⠿⢿⢿⢿⡿⠿⠿⡟⢻⠿⢿⡿⡿⣿⠿⠿⠿⠿⠟⠿⠟⡿⠿⠿⣿⠿⣿⡿⣿⠿⡿⠿⡿⠿⠿⡟⠿⢿⠿⠟⠻⠿⠿⠿⠟⡟⠿⡿⠻⠿⡿⠻⠿⠿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⣾⣶⣾⣶⣦⣴⣶⣶⣶⣶⣾⡶⣷⣿⡶⡶⢷⣾⣶⣾⣷⣿⣷⢶⣾⣶⣶⣶⣶⣶⣷⣶⣶⣾⡿⣿⣿⢿⣿⢶⣷⣷⣶⣶⣷⣶⣾⣶⣶⣶⢶⣶⣶⣶⣷⣶⣷⣶⣶⣷⣶⣷⣶⣷⣶⣶⣶⡶⣾⣿⣿⣿⣿⣿⣿ ⣿⣯⣮⣄⣼⣤⣤⣦⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣧⣷⣧⣤⣷⣤⣤⣸⣤⣤⣧⣼⣥⣼⣤⣼⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣼⣤⣾⣼⣦⣤⣴⣤⣴⣦⣤⣶⣤⣷⣤⣯⣼⣾⣤⣤⣨⣼⣮⣤⣤⣤⣤⣦⣤⣿⣿⣿⣿ ⣿⣉⣩⡉⣏⣝⣹⣏⣉⣭⣻⣭⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢫⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿ ⣿⢸⣿⣿⢿⢿⢿⢿⣿⠿⢿⠿⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⠚⠔⠵⠶⠽⡜⠄⢆⣼⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⠶⢶⠶⢷⡶⢷⡶⠶⣾⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⠄⢸⠰⠆⠄⠀⠁⠆⢸⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣷⣶⣾⣶⣾⣶⣶⣷⣶⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⢩⠛⡋⠛⠋⣿⠉⠛⠛⠟⠛⢛⠛⡟⠛⢻⣿⣿⣿⣿⣿⠁⢉⢹⠉⠋⢹⡟⢹⠉⠋⢹⡏⢙⡍⢩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣾⣶⣷⣶⣶⣿⣷⣶⣾⣾⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣦⣾⣾⣶⣷⣶⣾⣾⣶⣷⣶⣶⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣍⣉⣁⣏⣉⣉⣉⣉⣉⣉⣹⣉⣉⢉⣉⣉⣉⣉⣿⣿⣿⣿⣿⢉⣉⡙⣉⣉⡙⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣏⣉⣉⣏⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣉⡙⣉⣩⡙⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⢠⣀⣀⡠⣄⣇⢅⣀⣀⣀⣅⣇⣴⣠⣀⣄⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣧⣄⣠⣀⣤⣄⣄⣸⣀⣄⣀⣇⣀⣠⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡧⠥⢤⢦⠦⢤⣥⠤⡴⡤⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⡿⠿⠿⡿⡧⡬⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠶⡴⠼⠦⠤⠼⠤⡖⠤⠤⠤⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣮⡆⠥⡆⠆⡝⠇⠖⣿⣧⠠⡄⠠⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣾⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⠻⠖⠖⡶⠶⠶⠳⠷⠗⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⡖⢒⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⠒⠺⠒⢓⠚⢲⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⠙⢓⠙⠋⠛⢛⠛⠛⢛⠛⡏⡛⠛⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣏⣉⠉⣯⢋⣉⢉⢹⡉⣩⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⣈⣉⣉⣏⣡⣏⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⢈⣁⣿⣦⣄⣠⣈⣁⣱⣉⣀⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡇⡔⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣤⣴⣤⣼⣦⣬⣤⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣥⣥⣤⣿⣿⣤⣭⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠿⠿⠿⠻⠿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢻⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⡲⠶⠶⡶⠲⠷⡶⠴⠶⠶⠶⠶⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⡟⠛⠟⡟⠟⠟⣿⡗⡶⢲⠒⠚⣶⣶⣾⣶⣶⣶⣷⣶⣴⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡗⢒⠒⠐⠚⠒⠳⡓⠒⣚⠗⠒⢚⠲⠒⠒⠒⡏⠻⠛⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣶⡆⢓⣿⣧⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⢝⢛⠓⢻⠚⠛⠛⠙⠛⡟⢛⠋⡟⠛⠛⠒⢻⣾⣿⣿⣿⣿⣿⡏⠋⠋⠯⡉⠋⠯⡁⡋⣿⡏⠉⠉⠉⢹⠉⠙⠏⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣏⣈⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡷⣄⣈⣹⣣⣉⣈⡁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡰⣕⣀⣃⣀⣅⣳⣇⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡷⢤⡤⡼⣯⣤⡧⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⡥⡤⡥⡡⡤⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣧⣤⣤⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣥⣵⣧⣤⣥⣤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⠛⠛⢛⡟⣿⣟⠛⡛⠟⢻⣿⣿⣿⣿⣿⠛⠻⢿⠿⠿⡟⣿⠛⠿⢿⠿⡿⢿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⠛⡿⢻⣿⠛⠟⠿⠛⣿⠟⠟⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⢻⠓⡓⠚⠒⢻⣗⠚⢒⢾⣿⣿⣿⣿⣿⣇⣇⣠⣌⣀⣄⣿⣠⣁⣠⣄⣄⣠⣀⣇⣠⣀⣼⣿⣿⣿⣿⣿⣧⣀⣿⣘⣀⣥⣸⣡⣄⣄⣌⣀⣫⣄⣄⣠⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⠾⠿⡾⠿⣾⠾⡷⠷⢷⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⡿⠿⠿⠿⠟⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠻⠿⠿⢿⠿⠿⠿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⠖⠠⡀⠷⢰⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⠿⡶⢶⠶⢷⣶⡶⣶⢶⣶⣶⣶⣿⣶⣦⣶⣶⣶⣶⣶⣿⣿⣿⣷⡼⠾⠾⢦⠶⠶⠶⡶⠶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣶⣶⣷⣶⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣤⣬⣤⣤⣤⣵⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠿⠿⡿⠿⢿⠿⠿⢿⢿⠿⢻⠿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⡿⠟⡿⠿⠿⠟⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿ ⢸⣿⣿⠿⠿⠾⠽⠿⠧⠧⠵⠯⠿⠿⢿⣿⣿⣿⢖⠦⠦⢴⠔⠦⡧⠦⠦⠶⢴⣴⣼⣴⣾⣶⣶⣦⣶⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡻⣿⣶⣶⣶⣴⣶⣦⣷⣶⣧⣶⣤⣶⣷⣴⣶⣴⣶⣶⣼⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⠿⠿⢿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⠒⠶⠶⠾⠷⠶⢶⠶⠶⠷⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⡟⡟⡿⡟⠛⢻⠻⠰⢲⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⢻⡛⠛⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⠶⠶⠾⡵⠶⡷⠶⠾⢶⣿⣿⣿⣿⣿⠺⠶⠦⠴⠲⠶⠾⠶⢶⠷⠶⠶⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣶⡖⢚⠓⠒⢲⡒⠲⢲⣿⣤⣠⡄⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⠛⠒⠒⠒⠓⠒⠓⠒⠒⠊⠛⢿⣿⣿⣿⠒⠶⠷⠖⡶⠶⠶⠷⠺⠺⠲⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⠒⡲⣿⣿⣶⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠒⠒⠖⢲⢓⠞⢲⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⠒⠒⡚⡚⢶⢒⠚⡛⡻⠛⣛⢿⠛⠛⢛⢟⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⠘⠚⢻⢰⠟⠒⠙⠒⠘⠚⠛⢺⣶⣶⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⠛⠛⠛⡟⢋⡟⠛⠛⠛⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠹⠝⠜⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⠙⠛⢹⠙⠛⠛⢛⠙⠛⡛⡟⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⡟⠻⠛⠛⣟⢻⠛⣿⣿⣿⣿⣿⣿⣿⠩⡉⣙⢛⣻⡛⡛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠩⠹⠉⠩⢙⣿⣿⢽⡫⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⠛⠓⠒⠚⠛⠓⠒⠛⠓⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⡉⡉⢙⢉⡉⡏⢉⠍⡋⣉⡋⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⠉⢉⠉⠉⠉⡏⡁⡏⠉⠉⠉⡏⠉⠉⡉⠉⢉⢙⢹⣿⣿⣿⣿ ⢸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣠⣉⣉⣉⣉⣈⣉⣏⣉⣉⣉⢉⣉⣉⣉⣉⣈⣉⣹⣿⣿⣿⣿⣿⣿⣿⡃⣁⢃⣈⣉⣙⣈⣨⢘⣿⠸⣇⣟⣪⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣉⣁⣉⣉⣁⣉⣍⣁⣇⣉⣉⣁⣉⣁⣁⣉⠉⣇⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣍⣍⣉⣽⣉⣉⣉⣍⣉⣹⣉⣍⣹⣉⣉⡉⣉⣉⣿⣿⣿⣿⣿⣿⣁⣃⣐⣫⣇⣀⣘⣊⣸⣼⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣄⣈⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣢⣂⣼⣡⣀⣨⡀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣄⣄⣃⣰⣄⣘⣾⣬⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⣦⣤⡼⣼⣤⣷⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⡵⡤⣣⢤⠤⢽⢴⢾⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣡⣤⣤⣬⣤⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⠿⠿⠿⡿⠿⢿⢿⢿⢿⢿⠿⠿⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⢿⣿⢿⢿⠿⢿⠿⢿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣤⣵⣦⣤⣤⣶⣤⣤⣼⣤⣤⣤⣮⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿ ⢸⣿⣿⣿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣋⣘⣀⣀⣀⣃⣂⣂⣘⣃⣈⣃⣀⣐⣀⣒⣘⣒⣀⣀⣚⣂⣀⣀⣒⣂⣖⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣧⣙⣀⣀⣸⣿⣿⣿⣿ ⢸⣿⣿⣿⣇⣻⣐⣕⣸⣀⣷⣂⣿⣿⣿⣿⢸⣿⠹⢉⠉⠉⢹⣭⠍⠉⡙⠋⠹⠉⠉⡏⢉⠩⠿⠏⢝⠛⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⡏⠻⠹⠙⢹⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⢉⠍⠩⢩⢉⣭⠉⡉⠩⠉⢩⡉⡭⡉⢍⢭⠉⣉⠍⢩⢉⡭⠩⠹⣛⠻⡻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣟⠟⢿⠻⠻⢻⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⡶⠾⢶⢾⢶⡶⠾⣾⣾⢶⣶⠶⠶⢶⡷⡿⠾⣾⠶⠶⠶⢶⢾⡷⡶⠶⢾⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⡶⡷⣶⠶⢶⢾⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣬⣤⣤⣼⣤⣤⣿⣤⣾⣠⣥⣦⣤⣤⣧⣤⣤⣤⣤⣤⣿⣤⣤⣼⣬⣤⣷⣥⣥⣬⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣧⣬⣽⣴⣼⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣠⣠⣾⣈⣈⣘⣅⣁⣝⣁⣉⣹⢌⣈⣈⣉⣈⣘⣈⣻⣈⣉⣣⣈⣉⣈⣈⡘⣇⣉⣀⣎⣨⣈⣁⣉⣁⡡⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣁⣇⣝⣙⣈⣸⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠛⠟⢛⡟⠻⣿⠛⢛⠛⠛⠟⠛⢻⡙⠛⡛⠻⣙⠛⠛⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⡟⡻⡻⢻⢻⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⡷⠷⢷⠿⣿⠿⡿⢷⠿⢿⠷⢷⠿⠷⠿⠿⠷⠷⠿⡿⠾⡾⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠷⠷⡿⢿⢾⠿⢿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣴⣾⣬⣽⣤⣴⣮⣮⣶⣼⣿⣥⣵⣤⣮⣮⣦⣿⣼⣼⣬⣦⣦⣴⣵⣴⣵⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣦⣿⣴⣬⣼⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣀⣈⣘⣀⣁⣂⣙⣘⣈⣐⣓⣑⣐⣑⣀⣊⣐⣀⣂⣀⣈⣐⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣅⣹⣨⣀⣸⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠉⠉⠉⠋⢻⠉⠉⢙⠹⠉⠉⠩⡫⠉⠉⣽⡍⠍⠍⠩⡹⡉⣭⠫⢹⠩⠙⠉⠉⢽⡉⠝⡹⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⣯⡿⠙⠉⢹⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⠍⠉⠉⠩⢩⢩⡍⡉⠉⠍⠉⠍⢩⠉⠉⡉⢉⡉⢍⡉⠉⠉⣍⠉⠉⠉⣉⢉⡉⠉⣩⣭⣭⣭⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⣟⣿⠻⢛⢻⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⣶⡶⣶⢶⡶⡶⠶⠶⠶⠶⠶⡶⡶⡶⡶⢶⡶⠶⠶⣶⠶⠶⠶⠶⢶⣶⢶⠶⣶⢶⠶⡶⠶⡶⢶⠶⠶⠶⣶⢸⣿⣿⣿⣿⣿⣿⣿⡷⠶⡶⡿⣷⢶⢶⢾⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣴⣧⣽⣬⣥⣵⣤⣤⣤⣥⣬⣼⣬⣿⣤⣾⣤⣿⣦⣤⣼⣤⣥⣬⣼⣤⣤⣬⣯⣥⣼⣤⣤⣥⣥⣦⣤⣬⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣮⣬⣤⣬⣼⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⣀⣐⣀⣐⣂⣲⣀⣀⣂⣠⣤⣰⢀⣀⣀⣠⣐⣀⣐⣲⣀⣀⣢⣀⣀⣀⣐⡐⣆⣀⣄⣢⣐⣆⣀⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⣐⣁⣅⣙⣈⣨⣸⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠫⠻⠋⠙⠉⠏⠋⠋⠉⠉⠙⠙⠛⠙⠟⠋⠏⠟⠉⠋⠋⠿⠏⠋⠻⠙⠏⠋⠋⠋⠿⠍⠙⠻⠉⠛⠙⠫⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠋⡏⢻⠹⠙⢹⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⠶⠶⠶⡶⡶⢶⡶⠶⠶⣶⢶⠶⡖⡶⠶⠶⠶⣶⠶⠶⢶⢶⠶⡶⠶⢶⡶⠶⠶⠶⠶⠶⠶⢶⠶⠖⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⡿⣿⠿⠿⢿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠶⠶⠶⠶⠷⠾⠾⠿⠶⠷⠷⠶⠶⠿⠾⠾⠾⠶⠿⠿⠷⠶⠾⠷⠷⠶⠶⠷⠶⠶⠷⠶⠶⠶⠶⠶⠶⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣷⢶⣾⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣘⣤⣨⣧⣢⣋⣤⣴⣼⣀⣠⣠⣀⣔⣶⣔⣤⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣸⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠉⠉⠋⠙⠩⠉⠉⠻⠏⠉⠙⠉⠻⠭⠉⠩⠩⠍⠩⠍⠉⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢉⢽⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠻⡟⣿⠻⣟⠟⠻⡛⠻⡟⡿⢛⠛⠻⠛⡛⠛⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣻⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠒⠛⠛⠚⠚⠓⠓⠚⠒⠒⠚⠒⠒⠓⠓⠚⠚⠚⠒⠓⠚⠛⠛⢛⣛⣛⣛⣛⣛⣛⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⢾⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣈⣐⣓⣙⣀⣃⣀⣂⣐⣁⣂⣃⣈⣀⣀⣀⣙⣃⣁⣊⣛⣛⣛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣽⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣩⣇⣻⣈⣇⣋⣚⣘⣁⣊⣀⣃⣑⣂⣐⣁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣺⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⠏⠙⢹⠩⢿⢉⠹⡙⠫⡏⠝⣍⠉⠭⠉⠩⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢽⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡟⠻⠛⢻⠻⠻⠟⠛⢻⠛⠛⠛⠛⠟⣛⢟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⢻⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣶⣶⠶⣾⣶⣶⡶⡶⣾⣵⢶⡶⡶⡶⡿⡶⡶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢴⢾⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣀⣁⣀⣀⣘⣀⣀⣀⣀⣘⣀⣀⣀⣐⣈⣃⣈⣀⣀⣛⣛⣛⣛⣛⣛⡛⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣼⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣉⣉⣹⢙⡩⣙⣉⣉⢍⢩⢿⢉⠉⢍⢉⡙⢭⣍⣋⣍⢽⣿⣿⣿⡇⣿⣿⣿⡿⣿⣿⢈⢣⢸⡏⠬⢩⡏⠌⡇⢸⠥⢩⢨⠠⣿⣿⣿⣿⣿⣿⣿⣏⢈⢹⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⣭⣭⣥⠟⠋⠁⠀⠛⢻⣾⣿⣾⣿⣶⣿⣿⣾⣷⣾⣷⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠤⠤⢤⢤⠤⠤⠤⠤⠤⢤⢤⠤⢤⠤⠤⠤⠤⠤⡤⢤⡄⠀⠛⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢾⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠈⠀⠀⠈⠀⠈⠀⠈⠀⠁⠀⠀⠈⠉⠈⠀⠉⠁⠀⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣽⣿⣿⣿⣿ ⣿⠿⣿⣿⡿⢿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠁⢠⡄⠁⠀⠠⠀⠉⠉⠍⢍⠉⠉⠉⢩⠉⢭⠉⠉⠩⠉⠩⠉⢩⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⢩⠉⢩⠩⠉⠍⠩⠭⠉⠍⡭⠉⠉⠉⡍⠩⠭⢩⠉⠉⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭ ⣿⠤⠤⠤⠤⠤⡤⢤⠤⠤⡤⢄⢤⠤⡤⠦⠤⠤⡦⢤⠤⡤⠤⠤⠤⢤⠶⢤⠤⡄⠤⡤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣈⣉⣀⣉⣉⣋⣉⣈⣉⣃⣀⣃⡀⠙⠉⠘⡉⢙⠁⢉⣉⣋⣉⣋⣉⣃⣁⣉⣈⣉⣉⣃⣈⣉⡃⠈⠈⠐⠈⠈⠁⠙⠘⠈⠋⠉⠉⠈⠀⡋⠉⠉⠁⠈⢁⠀⡋⠉⠉⠁⠙⠈⡋⢈⠉⠙⠛⠛⣛⡛⢛⠛⠛⢛⣛⠛⣛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠰⠀⠒⠶⣶⡶⠶⠶⡀⠶⠶⢶⣶⡶⠀⠀⠐⣶⣶⣾⠭⠭⠭⠭⠭⣿⣷⣿⣭⣭⣽⡿⠛⣁⠠⢤⠈⣉⠹⣾⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⢷⡄⠄ ⣿⣑⣒⣚⣒⣒⣚⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣓⣲⣾⣟⣻⣿⣿⣯⣭⣽⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣭⣭⡅⢸⣿⣿⣭⣭⣭⣿⣿⡇⣸ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠼⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠻⠾⠌⠻⠿⠿⠻⠷⠿⠛⠠⠿ ⣿⣠⣀⣁⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣗⣶⣾⣿⣻⣿⣿⣓⣳⣾⣟⣻⣿⣿⣓⣲⣾⣟⣻⣿⣟⣓⣳⣾⣛⣻⣿⣟⣓⣶⣾⣛⣷⣦⣄⣀⣤⣔⣾⣻⣿ ⣿⠿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣾⣿⣿⡿⠽⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣰⣾⣿⣿⣿⣿⣽⣶⣿⣻⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2036 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/making-epo-staff-miserable/#comments Gemini version at gemini://gemini.techrights.org/2022/08/29/making-epo-staff-miserable/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ EPO_Management_Trying_to_Make_EPO_Staff_Miserable_and_Isolated⠀✐ Posted in Europe, Patents at 9:42 am by Dr. Roy Schestowitz Video_download_link | md5sum 8bcdadc32da94f7f1f7fa378c73b1402 EPO Breaking Teams Apart Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/epo-teams-apart.webm Summary: The siege against EPO examiners carries on; the sole goal is to turn educated, motivated, principled people into demoralised serfs who just grant as many patents as possible in order to fake_so-called_'production' (in effect, bypassing the safeguards against fake and invalid patents which beget frivolous threats and litigation) THE END of August is imminent. Today is Bank Holiday here in England and September soon commences. Expect our EPO coverage to be back in “full swing”, exposing the crimes of António_Campinos, the successor of his_corrupt compatriot_aand_close_friend. Truth and justice can catch up with them, however belatedly. The EPO isn’t saying much at the moment, mostly because people are on vacation (some physically away from work). We’ve meanwhile spoken to the EFF, trying to figure out the EFF’s silence on these matters in spite of the EFF’s focus on patents and on Europe (lots about copyright law in the EU). Don’t they show interest in European_software_patents? If not, then why not? They ought to explain and we’ll keep pressing. “Maybe union-busting consultants suggested this to EPO managers.”The letter below concerns a meeting that actually took place last month. That’s when the EPO last issued a statement (regarding Montenegro) — no less than 33 days ago! The message to staff covers “the project to reshuffle office spaces and introduce an “office for a day”. [Euphemism]” Ignore terms like “bringing teams together” as “Breaking Teams Apart” (the title of the video above) seems to be the real goal, as we_noted_here_back_in June. It’s a strike-breaking strategy — akin to those which discourage any other industrial actions, even merely a protest of solidarity. Maybe union- busting consultants suggested this to EPO managers. Here’s the message in full: Bringing teams together – Report on the meeting of the LSCTH with VP1 on 13 July 2022 “The present publication emanates from Local Staff Committee the Hague which does not have access to mass email. It is re-published via SUEPO in order to reach a larger number of colleagues.” Dear colleagues, your Local Staff Committee The Hague met with VP1, VP4 and a member of facility management on 13 July 2022 regarding “bringing teams together”, i.e. the project to reshuffle office spaces and introduce an “office for a day”. Main_points: - The lack of consultation before the decision was taken does not seem to comply with the requirements of the CODEX and iso 45001 certification; - LSCTH is concerned about the prominence of managerial discretion in the attribution of assigned individual offices; - Decision to assign individual offices to be based on a mature dialogue with staff; - Staff can change their minds at any stage; - Input from colleagues welcome: direct feedback, questions, tips and ideas relating to the project can be sent by email to Frédéric Brunelle and Edda Franz, possibly with staff representation (DHSTCOM for TH, MNSTCOM for MU) in cc. - Concerns or questions related to managerial discretion should be addressed to staff representation directly; - Bona fide consultation on contingency plan was requested. Conclusions: The plethora of recent changes will “make the EPO great again” according to the members of management, while staff representation pointed to the fact that they are more likely to have far reaching negative consequences on the wellbeing and social fabric of the EPO, potentially leading to an increase of psychosocial risks. See the full report [...] for more details. Kind regards, Your Local Staff Committee The Hague (LSCTH) The video above goes through the original full report, which we’re reproducing as HTML for Gemini, IPFS, and plain text. It’s a longer version of the above, bearing the date of last Monday: Staff Committee The Hague Comité du personnel de La Haye Personalausschuss Den Haag 22 August 2022 Bringing teams together Report on the meeting of the LSCTH with VP1 on 13 July 2022 Dear colleagues, Members of the LSCTH met Steve Rowan (VP1), Nellie Simon (VP4) and Frédéric Brunelle (Facility management) on 13th of July 2022. The administration stated that the purpose of the meeting was to collect The Hague site specific issues related to the implementation of the “Bringing Teams Together” project. While the Staff Representation expressed its appreciation for the opportunity to exchange on the matter, it noted that the present meeting could not be considered a consultation. It further noted that a decision on “Bringing Teams Together” had already been taken without prior consultation of the Staff Committees and of the Health & Safety statutory bodies, which goes against the CODEX1 and does not comply with the requirements for ISO 45001 certification2. The LSCTH referred to the opinion of the CSC (central staff committee) members of the GCC on GCC/DOC 13/2022, and added that the project appears to be rushed, premature and seems to steer staff away from coming into the buildings. It also noted that no prior consultation took place for the contingency plan which determines building temperatures in view of the energy crisis. The LSCTH indicated its sensitivity to the energy crisis and pointed out that consultation with the relevant committees should be carried out to ensure the legality, legitimacy, and acceptance amongst staff of any contingency measure that may be taken. The members of the administration insisted that no consultation would be required since neither the “Bringing teams together” project nor the contingency plan would change our working conditions. The LSCTH expressed its disagreement, insisting that both matters quite obviously concern aspects of health, safety, and ergonomics, which are part and parcel of our working conditions. The LSCTH expressed concerns on the implementation of “Bringing teams together”, in particular on the prominence of managerial discretion in the attribution of assigned individual offices and insisted that staff be treated equitably. The administration answered that the basis of this concept would be flexibility and ______ 1 Art. 37(1)(a) Service Regulations: the Local Staff Committee “shall be consulted on any proposal [...] which concerns the conditions of employment of the whole or part of the staff at the place of employment concerned”. 2 ISO 45001 certification requires consultation including engaging health and safety committees and workers’ representatives ===================================================================== that it would be possible for staff to change their minds at any stage, even after the planning and implementation phases. There would be no fixed rules on which staff and line management could rely, everything will be at the discretion of line management and should be based on a mature dialogue with staff. F. Brunelle from facility management stated that all input from colleagues is welcome, and it was agreed that staff could send direct feedback, questions, tips and ideas relating to the project by email to Frédéric Brunelle and Edda Franz, possibly with staff representation (DHSTCOM for TH, MNSTCOM for MU) in cc. Concerns or questions related to managerial discretion should be addressed to staff representation directly. The LSCTH concluded that the perpetual changes which have been taking place during and since the heights of the pandemic (for example, the series of reorganisations, the implementation of the new ways of working, the “Bringing teams together” initiative and the contingency plan) may have far reaching negative consequences on the wellbeing and social fabric of the EPO, potentially leading to disengagement, a loss of cohesion and sense of belonging as well as to an increase of psychosocial risks. The members of management, on the other hand, closed the meeting with an optimistic outlook, in that all the changes and permanent reforms would “make the EPO great again” in an energetic, vibrant, collaborating and connecting environment. Let’s see what the future brings. Your Local Staff Committee The Hague (LSCTH) [...] Among the references they’ve added to the bottom (redacted) we have “What is wrong with hot- desking?” and “Appalling lack of consultation are the “New Ways of Working”?” (Munich) Workers are clearly unhappy about this. Maybe making them unhappy is a side goal. █ ䷩ 𝚕𝚒𝚗𝚎 2285 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/norbert-preining-canary/#comments Gemini version at gemini://gemini.techrights.org/2022/08/29/norbert-preining-canary/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_Inquisition_of_Norbert_Preining_is_a_Cautionary_Tale_About_the_Clique That’s_Killing_Debian_From_the_Inside⠀✐ Posted in Debian, GNU/Linux at 7:18 am by Dr. Roy Schestowitz Video_download_link | md5sum d532ecde5c79535bae77b762cab6a6ee Passive Bullies Disguised as Victims Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/debian-mob.webm Summary: This morning Norbert Preining, a veteran GNU/Linux developer (maintaining key packages including KDE and widely-used LATEX stuff), indicated that he was still being harassed by the same people who had pushed him out of Debian, where his volunteering track record is decades long and highly productive EARLIER this year we did a video_about_Norbert_Preining and how he had been (mis)treated by a vocal, abusive minority inside Debian. Dr. Preining isn’t new to Debian or to GNU/Linux. The thought police probably deemed him a “high- profile” target and having been put in positions of unjust power (like the so- called ‘anti-harassment’ team) mischief was likely imminent, firing the first shot over the word “it”. To make matters worse, the same incompetent fools are still chasing and mobbing him. They want nothing short of destruction/end to his career. Maybe they derive pleasure from causing the downfall of very productive developers. Maybe this is a mental sickness akin_to_the_Zemlins'. Who knows… Dr. Preining has already attempted to just go along, sucking up to the mob that ousted/demoted him from the “DD” status. It didn’t work; nothing would ever please them, so he just left Debian completely, but they_still_chase_him, just like FSFE autocrats chased Daniel Pocock after he had exposed to FSFE members (who elected him!) some of the dirty laundry from inside the FSFE. I end the video above by commenting on Debian_selling_out_to_a_Microsoft_front not too long after Microsoft had paid DebConf. There’s a whole bunch of stuff happening inside Debian that causes my wife and I to reassess our choice of Debian (for 4 of our computers, which still run Debian for the time being). █ ䷩ 𝚕𝚒𝚗𝚎 2348 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/zdnet-exit-strategy/#comments Gemini version at gemini://gemini.techrights.org/2022/08/29/zdnet-exit-strategy/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ ZDNet’s_Exit_Strategy:_Ugly/Cheap_Redesign,_Infinite_Scroll_for_Fake ‘Traffic’_(‘Engagement’),_and_Hardly_Any_New_‘Content’⠀✐ Posted in GNU/Linux at 7:54 am by Dr. Roy Schestowitz 10 days ago: ZDNet_Turns_Ugly._Really,_Really_Ugly. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇ZDNet on Linux⦈ ZDNet has hardly mentioned “Linux” in a long time (nothing in 6 days); then again, the site in general is barely active Summary: It’s truly noteworthy that in the past 13 days only three “Linux” stories were published in ZDNet; the one at the bottom is actually_about Microsoft promotion, not Linux ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣛⣙⣋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿ ⣿⣷⣶⠶⠖⠒⠀⠀⢸⠀⢰⣶⣶⣦⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢭⠤⣬⣨⣥⣼⣤⣭⣬⣭⣥⣭⣭⣥⣬⣥⣭⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠅⣸⣿⣿ ⣿⡇⠀⠀⠤⠴⠶⠿⢿⠀⠸⠿⠿⠟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⢿⡇⠀⢸⠀⢀⣀⣀⣀⣀⣸⣀⣀⡀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⡻⡛⠛⠛⢻⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡟⠛⠛⠛⠛⡟⢻⠛⠛⠛⡛⢻⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛ ⣿⡇⠀⢸⡀⠈⡇⠀⢸⠀⠈⠉⠉⠉⢹⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾ ⣿⡇⠀⢸⣧⠀⠀⠀⢸⠀⠘⠛⠛⠛⠛⢻⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣶⣾⣿⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡏⢰⣿⢸⠀⡟⢋⠻⠛⣿⢻⡛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣀⣿⣿⣸⣀⣇⣿⣀⣄⣋⣸⣁⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣟⣛⣛⣛⣛⣛⣛⣛⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣟⣼⣏⣰⣃⣁⣇⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⣿⣿⣿⢍⣝⠛⡋⢛⢻⢫⠙⠉⢿⢛⠟⠋⡛⢻⢟⠛⡛⡟⢻⡟⢛⠛⠻⠛⢙⠛⢟⢛⡋⠛⡟⠛⢻⡋⢛⠛⣛⠛⠋⡻⠛⡋⡟⠛⡟⡻⠛⡛⠋⢛⡛⡛⢛⢿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⢷⣾⣾⠶⢾⣶⣿⣴⣷⣶⣶⡾⣷⣶⣷⢷⣾⡷⣾⡶⣶⣶⢶⢶⡿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣿⣾⣶⣷⣶⣷⣷⣶⣷⣾⣶⣷⣶⣶⣶⣾⣴⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣄⣤⣠⣴⣠⣆⣤⣦⣀⣸⣄⣊⣦⣴⣧⣠⣤⣦⣧⣠⣦⣄⣄⣤⣄⣼⣧⣠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣿⣿⣿⡿⠿⡿⡿⠿⠿⠿⢿⠿⢿⠿⢿⠿⢿⠿⡿⠿⠿⢿⠿⠿⡿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⡿⢿⠿⠿⢿⠿⠿⠿⡿⠿⣿⠿⠿⡿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠛⣿⣿⣿⣿⣿⣿⡶⡶⢶⢷⠶⣖⡶⠿⢶⢲⠲⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣷⣶⣶⣷⣶⣶⣶⣶⣷⣾⣶⣶⣾⣿⣶⣿⣷⣶⣾⣶⣶⣷⣶⣶⣷⣶⣷⣷⣾⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣴⣶⣶⣶⣿⣿⣿⣶⣬⣴⣤⣥⣬⣧⣴⣬⣧⣶⣵⣤⣦⣶⣦⣤⣶⣷⣦⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠩⠝⠝⠋⠋⡏⠍⠉⡏⠙⠍⠋⣿⢋⠋⠋⢹⠋⠛⠙⢉⣟⠉⠋⢻⠉⢋⠉⠉⢹⠩⠉⠋⢹⡿⠏⢩⠋⢻⠋⡟⠍⠋⠋⠉⠫⠙⠙⠩⢻⢹⠉⠏⠋⣽⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⡿⡿⢿⠿⠿⠟⢳⠶⠻⠿⡾⠿⠻⠛⠿⡟⠟⠻⢿⠿⢟⡻⠛⢻⠿⡿⢟⠟⠟⠻⢿⠟⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣠⣬⣤⣥⣧⣥⣤⣼⣼⣼⣬⣤⣥⣧⣦⣼⣤⣧⣧⣴⣤⣤⣬⣮⣵⣤⣼⣬⣦⣿⣴⣼⣤⣴⣥⣮⣤⣤⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⡿⠿⠿⡿⠿⠿⡿⠿⡿⢿⠿⠿⢿⡿⠟⠿⣿⠿⡿⢿⡿⢿⡿⢻⠿⠟⠛⠿⢿⡟⠿⡿⡿⠻⠿⢻⣿⢿⣿⠻⢿⢻⡛⠻⠟⠿⣿⠿⣿⠿⠿⢿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⡞⢚⠛⠓⠛⡛⠛⢛⡟⠺⡗⠓⠛⠓⠛⠛⢳⠛⠺⢾⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣷⣿⣷⣶⣾⣷⣷⣿⣿⣷⣿⣾⣿⣷⣿⣷⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠿⡿⣿⡿⠿⢿⠿⠿⡿⠿⠿⠿⠿⠿⠿⡿⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣷⣶⣶⣷⣶⣶⣶⣶⣷⣶⠶⠾⠷⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠓⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡰⡊⠉⠉⡉⠉⡍⢈⢍⠉⣹⡏⢉⠁⡩⠀⢸⡿⢈⠀⠤⡆⣾⢈⠍⣇⠇⡇⢉⠏⢩⠁⡙⢹⠂⠔⢸⠇⢊⡁⣻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢶⣭⣭⣽⣭⣯⣼⣭⣯⣭⣽⣍⣭⣽⣵⣬⣝⣧⣼⠝⠛⠉⠉⠒⠙⠁⠀⠐⠈⠀⠒⠩⣭⣿⣧⣤⣦⣧⣤⣤⣼⣭⣼⣥⣬⣧⣥⣭⣽⣧⣿⣭⣉⣿⣿⣿⣿ ⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣤⣴⣶⣧⣤⣤⣤⣤⣦⣶⣤⣦⣤⣤⣧⣾⣤⣤⣥⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣍⣉⣉⣉⣏⣹⣫⣛⣋⣏⣹⣉⣉⣉⣉⣍⣉⣉⣉⣩⣏⣉⣉⣉⣉⣏⣉⣋⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2423 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/08/29/zemlin-narcissism/#comments Gemini version at gemini://gemini.techrights.org/2022/08/29/zemlin-narcissism/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Echoes_of_Narcissism:_How_Jim_Zemlin_Views_Himself⠀✐ Posted in Kernel, Videos at 4:49 am by Dr. Roy Schestowitz The Elizabeth_Holmes of Linux? Watch this: http://techrights.org/wp-content/uploads/2022/08/zemlin-pride.mp4 Compare to this: http://techrights.org/wp-content/uploads/2020/08/What-the-Tech-Industry-Has- Learned-from-Linus-Torvalds_-Jim-Zemlin-at-TEDxConcordia-U-Portland.mp4 Summary: This older_talk shows a familiar pattern of megalomania (and an often- repeated_talking_point), derived by gaining leverage over people who actually accomplished something, then controlling_them 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Zemlin on humility⦈ Slide he presented only months ago ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⣷⣶⣶⣷⣿⡇⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⢀⡤⣤⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣚⣳⣛⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⠍⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⣀⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠰⠟⢀⠀⠀⢀⠰⢀⢚⠳⡐⡀⢀⠀⠀⡀⡀⠀⠀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠲⠴⠋⠀⠉⠘⠘⠊⠘⠘⠃⠁⠘⠊⠂⠓⠃⠉⠘⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 2486 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_29/08/2022:_Canonical_Helping_Microsoft_Again⠀✐ Posted in News_Roundup at 5:25 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Audiocasts/Shows o Kernel_Space o Applications o Instructionals/Technical o Games o Desktop_Environments/WMs # K_Desktop_Environment/KDE_SC/Qt # GNOME_Desktop/GTK * Distributions_and_Operating_Systems o Reviews o New_Releases o Fedora_Family_/_Red_Hat o Debian_Family o Canonical/Ubuntu_Family o Mobile_Systems/Mobile_Applications * Free,_Libre,_and_Open_Source_Software o Web_Browsers # Mozilla o Productivity_Software/LibreOffice/Calligra o Programming/Development # Perl_/_Raku * Leftovers o Hardware o Security o Internet_Policy/Net_Neutrality * Gemini*_and_Gopher o Technical # Programming * § GNU/Linux⠀➾ o § Audiocasts/Shows⠀➾ # ⚓ Video ☛ Linux_Wayland_Screen_Lockers_Are_Simply_Better_– Invidious⠀⇛ While Wayland has a lot of issues in many areas there’s one thing that Wayland especially wlroots do objectively better is screenlockers especially with the way the new screenlocking protocol works # ⚓ Video ☛ Manjaro_21.3.7_Gnome_Edition_overview_|_OS_FOR EVERYONE_–_Invidious⠀⇛ In this video, I am going to show an overview of Manjaro 21.3.7 Gnome Edition and some of the applications pre-installed. # ⚓ Episode_3:05:_How_to_Exit_Vim⠀⇛ # ⚓ Jupiter Broadcasting ☛ End_of_the_Road_|_LINUX_Unplugged 473⠀⇛ We’ve reached the end of the road in our immutable Linux series, and an old friend stops by to give us the inside scoop on Endless OS. # ⚓ Video ☛ Steam_Deck_2_—_CONFIRMED._But_also_a_new_Steam Controller_(plus_other_Steam_Deck_News)_–_Invidious⠀⇛ o § Kernel Space⠀➾ # ⚓ LWN ☛ Linux_5.19.5⠀⇛ I'm announcing the release of the 5.19.5 kernel. All users of the 5.19 kernel series must upgrade. The updated 5.19.y git tree can be found at: git://git.kernel.org/pub/scm/linux/kernel/ git/stable/linux-stable.git linux-5.19.y and can be browsed at the normal kernel.org git web browser: https://git.kernel.org/?p=linux/kernel/git/stable/ linux-s... thanks, greg k-h # ⚓ LWN ☛ Linux_5.10.139⠀⇛ # ⚓ Techgage ☛ SPECviewperf_2020:_GPU_Viewport_Performance_In Linux_&_Windows_–_Techgage⠀⇛ We’re taking a fresh look at viewport performance in popular design software with the help of SPECviewperf 2020. With 21 gaming and workstation GPUs in-hand, we’re testing not just the performance in Windows, but also Linux – which has made for some interesting comparisons. It’s been nearly a year since we last took an in- depth look at viewport performance with the help of SPEC’s SPECviewperf, and with the recent release of its 2020 v3.1 update, we felt now was a good time to generate some fresh numbers. As an added bonus, this article marks the first time we’ve run the same tests under Linux. That proved to be a good move, as it gave this article’s results more flavor. For those not familiar with SPECviewperf, it’s important to note the fact that it is not the benchmark. It’s instead the tool for benchmarking viewports in individual applications, like 3ds Max, SolidWorks, and Siemens NX. To make the magic happen, SPEC captures API traces of the full versions of said applications, and creates viewsets that replicate playback – without the native application needing to be installed. # ⚓ WCCF Tech ☛ AMD_Zen_4_Last_Branch_Record_Extension_version 2_queued_for_Linux_6.1⠀⇛ The Last Branch Record functionality, or LBR, is “used for determining and analyzing the control flow of software by logging branch information to registers in real-time.” The branch information will allow the system to decide what paths “hot code” should be directed to, such as optimizations to profile-specific compilers or other optimizations seen active in applications # ⚓ Neowin ☛ You_can_soon_daisy_chain_three_4K_60Hz_monitors_on your_Intel_Arc_laptop_running_Linux_–_Neowin⠀⇛ Previously, Intel’s Linux drivers allowed only connecting two monitors, without daisy chaining, including Intel’s integrated graphics solutions. Intel will be pushing this feature out to its open- source driver stack for Arc GPUs. But whether or not it will work on the cheaper options like the Arc A380, which just arrived in the US, remains to be seen. # ⚓ PC Perspective ☛ Intel_Arc_A380_On_Linux_–_PC_Perspective⠀⇛ If you need an accelerator on a PC running Linux that works for a living, this is a decent choice if you can’t afford a higher end card. o § Applications⠀➾ # ⚓ DebugPoint ☛ Scrivano:_Fascinating_Whiteboard_App_For Handwritten_Notes⠀⇛ Scrivano is a new whiteboard application which recently getting some attention for its unique features and “ease of use”. It has some seriously cool feature which I will talk about shortly. When I write about the top Whiteboard applications for taking hand written notes using touch devices, I was not aware of this application since it was probably under development. In that article, I mentioned about the major apps which you all know about. For example, Xournal++ is probably the most used and “go to” app for taking quick notes using stylus in supported devices. Another GTK & Rust based app which recently became famous is Rnote. It also has some excellent features. Now, you can try out another cool app – Scrivano. It is a Qt based application and comes with a simple user interface for utmost productivity. # ⚓ Ubuntu Handbook ☛ Pano_–_Manage_Clipboard_History_in_Ubuntu 22.04_/_Fedora_36_in_New_Style_|_UbuntuHandbook⠀⇛ Need to access your copy & paste history quickly? Forget about GPaste or CopyQ, try Pano! It’s a cool new clipboard manager for Ubuntu, Fedora, and other Linux with GNOME Desktop, such as Arch and Manjaro. No system tray indicator or app window, just press your custom keyboard shortcut will bring up the bottom bar with all recent clipboard histories. # ⚓ Linux Shell Tips ☛ Stig_–_A_TUI_and_CLI_Client_for BitTorrent_Transmission⠀⇛ The BitTorrent client Transmission application is becoming a must-have for a growing number of Linux users. The features of this app have more to say about what it has to offer than the name itself. For instance, it is resource-friendly since it uses minimal system resources during its application runtime. Also, its full support for Magnet Link, PEX, DHT, µTP, and DHT are some prime features associated with the BitTorrent client transmission application. However, to use this app, you will need to install it from the default repositories. [...] The following are some prime features that Stig CLI and TUI-based client applications have to offer for your BitTorrent client Transmission endeavors. o § Instructionals/Technical⠀➾ # ⚓ ID Root ☛ How_To_Install_Chromium_Browser_on_Linux_Mint_21 –_idroot⠀⇛ In this tutorial, we will show you how to install Chromium Browser on Linux Mint 21. For those of you who didn’t know, Chromium is an open-source browser project that aims to build a safer, faster, and more stable way for all users to experience the web. Google’s Chromium browser is an open-source project. The Chromium codebase is also used by many other browsers, including Microsoft Edge, Opera, and Vivaldi. 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 a Chromium web browser on Linux Mint 21 (Vanessa). # ⚓ OSNote ☛ UUID_in_Linux_–_OSNote⠀⇛ The UUID refers to a Universally Unique Identifier that consists of 128-bit numbers that have the probability of having duplicates close enough to zero but not zero in the local system. It was originally used in the Networking Computing System and then, later standardized by the Open Software Foundation. The UUID is divided into five groups separated by hyphens (-) consisting of 8-4-4-4-12 characters in each group. In total it consists of 36 characters. You can see the UUID string like the string shown below. # ⚓ Investigating_database_replication_in_different availability_zones_–_formicapunk⠀⇛ In regards to safety of data, it looks similar to the raft algorithm used by etcd with three members as a write is only ack’ed if it has been fsynced by two servers, the difference is that raft has a leader election, whereas in PostgreSQL the leader is set at startup and you have to build yourself the election mechanism. # ⚓ LinuxTechi ☛ How_to_Setup_EKS_Cluster_along_with_NLB_on AWS⠀⇛ Are looking for an easy guide for setting up EKS cluster on AWS? The step-by-step guide on this page will show you how to setup EKS cluster along with NLB (Network Load Balancer) on AWS from the scratch. # ⚓ HowTo Forge ☛ How_to_Mount_an_NTFS_Drive_on_CentOS_/_RHEL_/ Rocky_Linux⠀⇛ This tutorial will show you how to mount an NTFS drive ina read/write mode on CentOS and other RHEL based Linux operating systems with ntfs-3g driver. NTFS-3G is a stable Open Source NTFS driver that supports reading and writing to NTFS drives on Linux and other operating systems. The ntfs-3g driver is available in the EPEL repository, it is available for all RHEL-based systems like AlmaLinux, CentOS, Rocky Linux, and also RHEL itself from version 6 to 9. The first step is to install and activate EPEL on your Linux system. # ⚓ HowTo Forge ☛ How_to_Enable_HTTP/2_in_Apache_Web_Server_on Ubuntu_and_Debian⠀⇛ Hypertext Transfer Protocol Version 2 (HTTP/2) is the latest version of the HTTP protocol, published as an IETF standard in RFC 7540 in 2015. The focus of the protocol is on performance; specifically, end-user perceived latency, network, and server resource usage. One major goal is to allow the use of a single connection from browsers to a Web site. The protocol is backward compatible, so HTTP methods, status codes, and semantics are the same as for previous versions of the protocol. Apache has HTTP/2 support since version 2.4.17. In this tutorial, I’m going to assume that you already have a working TLS configuration, and that you have the required Apache version installed on your Linux distribution of choice, and that you know how to use Let’s Encrypt, or you know how to issue a self- signed certificate. This tutorial has been tested on Debian 10, Debian 9, Ubuntu 20.04 LTS, and Ubuntu 18.04 LTS. # ⚓ Vitux ☛ How_to_Install_and_Use_Snapd_on_Debian_11⠀⇛ Snap packages are widely used all across different Linux distributions. These packages are easier to create, install, and manage and they are there to keep all of your applications updated. However, to use these packages, you need to have an API installed which is known as Snapd. This API is responsible for managing snap packages on your Linux system. It communicates with the Snap Store to download and install snap packages on your Linux system. Most of the flavors of Linux have this API installed on them by default. However, on some distributions of Linux like Debian, you have to install this API manually so that you can conveniently deal with the snap packages. Therefore, in this article, we will explain to you the method of enabling Snapd on Debian 11. # ⚓ LinuxConfig ☛ Introduction_to_the_dconf_configuration system⠀⇛ Dconf is the low-level configuration system used by the GNOME desktop environment. It is basically a database, where the various configuration are stored as keys together with their values. The keys in the database can be inspected, changed, or dumped with the dconf utility or by using the dconf-editor graphical tool. In this tutorial we see how manage dconf keys, how to backup and restore them and how to keep the database status in sync with a configuration file. # ⚓ LinuxConfig ☛ How_to_remove_unnecessary_files_with BleachBit_on_Linux⠀⇛ BleachBit is a free and open source application available on Linux and Windows, which can be used, among the other things, to remove unnecessary files and directories from a filesystem. BleachBit can be used to free the caches of many applications, remove cookies and browsers history, but also to shred (secure delete) files and directories. In this tutorial we see how to install and use BleachBit on the major Linux distributions. # ⚓ UNIX Cop ☛ How_to_deploy_GLPI_using_Docker⠀⇛ Docker is a software development platform for virtualization with multiple operating systems running on the same host. This is made possible by containers that are distributed as images. The system is very lightweight because it does not incorporate an operating system, which also allows for better use of resources. Docker also allows applications to be isolated, which is very useful for testing without bringing down the client’s production server. Meanwhile, GLPI is a web application that allows us to deploy a fleet management system. It has also evolved and with it, you can also manage hardware, software, and data centers by linking the asset inventory to the helpdesk. # ⚓ Linux.org ☛ LFCS_–_Network_Management⠀⇛ These days, we connect nearly all computers to a network in some manner. Whether the connection is Ethernet (hard-wired) or Wi-Fi, there is a method of sharing data or accessing shared data. When dealing with TCP/IP for the Internet, these commands can come in handy when there are connection issues. # ⚓ Unix Men ☛ Bash_While_Loop_Examples:_For_Loops,_Until Loops,_And_More⠀⇛ Bash programming comprises three kinds of loops: the for loop, the while loop, and the until loop. The idea of all the loops is to repeatedly execute some code as long as some specific parameters are met. The Bash for loop operates differently from the for loops in other programming languages you may be familiar with. With it, you can iterate over a series of “words” in a string. On the other hand, the while loop executes the code under it if the control expression (or simply, the “condition”) is true. The loop stops executing the code when the condition becomes false, or there is an explicit break in the code. The until loop is comparable to the while loop, with the only difference being that the code keeps executing while the control expression is deemed false. In this post, we discuss how to use the Bash while loop with examples. # ⚓ ZDNet ☛ How_to_kill_a_process_in_Linux_|_ZDNET⠀⇛ Every application and service on your Linux machine runs as a process. And, for the most part, those processes run fairly smoothly. Every so often, however, you might find a process (an application or a service) that goes astray and either slows down your system or causes other problems (such as a locked-up desktop). # ⚓ TechRepublic ☛ How_to_install_the_Redis_in-memory_database server_on_Ubuntu_22.04⠀⇛ Redis is an open-source, in-memory key-value store that can be used as a powerful database server. Redis supports numerous data structures, such as strings, hashes, lists, sets, bitmaps, sorted sets and much more. And given that Redis stores everything in-memory, it’s blazingly fast. The one caveat to this is you’ll want to install it on a server with a fairly large amount of RAM. What I’m going to do here is walk you through the process of getting a single node Redis server up and running. In a later tutorial, we’ll discuss setting up a Redis cluster, so you can gain high availability with your server. Until then, let’s get that single instance server up and running. # ⚓ Linux Made Simple ☛ How_to_install_Teamspeak_on_a Chromebook_in_2022⠀⇛ Today we are looking at how to install Teamspeak 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. o § Games⠀➾ # ⚓ Boiling Steam ☛ Transform_your_Steam_Deck_into_a_Steering Wheel,_with_Sol_Wheel’s_Clever_New_Model_–_Boiling_Steam⠀⇛ Not long after the first iteration was shared on Reddit and on Boiling Steam, Ethan from Sol Designs has made progress with their second iteration of the Sol Wheel, an accessory that can turn your Steam Deck into a Steering Wheel. Now there are massive improvements in usability. The previous iteration could only make the Steam Deck turn very slightly left and right, but this new one makes it possible to do much more drastic wheel turns, along with rubber bands to give some pull back from the more extreme positions on the side. Very clever. # ⚓ Video ☛ How_to_install_Steam_on_Pop!_OS_22.04_–_Invidious⠀⇛ In this video, we are looking at how to install Steam on Pop!_OS 22.04. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Volker Krause ☛ 20_Years_of_KDE_Contributions⠀⇛ On this day twenty years ago I wrote and submitted by very first patch to a Free Software project, KDE. What basically started with changing a single number got slightly out of control and had consequences my younger self wasn’t even remotely able to imagine. [...] But in 2000 and 2001 when KDE 2 came out I was doing my mandatory civil service which gave me access to “infinite” Internet (10Mbit/s). So I could download all the updates and carry them home on floppy disks and CD-RWs. The step from KDE 1 to 2 was huge, I wanted more of that. # § GNOME Desktop/GTK⠀➾ # ⚓ Linux Magazine ☛ GNOME_Project_Releases_a_New Telemetry_Data_Collection_Tool⠀⇛ Although telemetry (the collection of data and measurements for the purpose of monitoring) is a rather touchy subject, especially for those who value their privacy), the GNOME foundation has announced it will be adding a telemetry data collection tool to the desktop environment. Before anyone panics, this data will be 100% anonymous and will be used only to improve the GNOME desktop environment by informing various decisions for the future of the software. Those decisions will help to inform the GNOME Foundation where resources should be best used and how to better help users. * § Distributions and Operating Systems⠀➾ o ⚓ Make Use Of ☛ Is_Linux_Lite_the_Simple,_Fast,_and_Lightweight Linux_Distro_You_Need?⠀⇛ Linux Lite is one of the many lightweight Linux distros that run seamlessly on older hardware. But is it the best operating system for your computer? Linux is a highly customizable and open-source operating system kernel. This is why you’ll find tons of Linux distros out there to choose from, making it pretty hard to make a choice. However, if you are looking for a simple, fast, and lightweight distro, Linux Lite might be the one for you as it offers a great balance between performance and functionality. So, let’s look at what Linux Lite is along with a rundown of its notable features. [...] To test it, we used a 2005 Dell laptop. The system specifications included 2GB of RAM, a 1GHz processor, 250GB HDD storage, and Intel VGA 1280×768. o ⚓ ZDNet ☛ Want_to_save_your_aging_computer?_Try_these_Linux distributions_|_ZDNET⠀⇛ On top of this, several modern operating systems aren’t exactly friendly to older hardware. If you’ve found yourself in such a situation, there’s hope by way of a handful of Linux distributions that have been designed specifically for older hardware. With these operating systems, you can revive old hardware and make it run as though it were new. Let me introduce you to five such Linux distributions, each of which is perfectly at home on new and older hardware. o § Reviews⠀➾ # ⚓ FOSS Post ☛ Linux_Mint_21_Review:_A_Considerable_Upgrade⠀⇛ Linux Mint 21, which is based on Ubuntu 22.04 LTS, has been released less than a month ago with a number of considerable changes. [...] The Linux Mint 21 distribution contains considerable improvements, and it should definitely be recommended over a plain Ubuntu 22.04 LTS installation. It will remain supported with updates until 2027, which is a good support period for any desktop user. Still, compared to previous releases, not much was added in this release. Mostly, developers focused on backend improvements and cleaning old chunks of code which will enable them to add more features in the future. o § New Releases⠀➾ # ⚓ Linuxiac ☛ MX_Linux_21.2_Is_Here_as_a_Bugfix_Release,_Based on_Debian_11.4⠀⇛ MX Linux 21.2, the second refresh of the MX Linux 21 “Wildflower” release, consists of bug fixes and application updates. MX Linux is a desktop-oriented Linux distro based on Debian’s Stable branch, including the Xfce as a default desktop. However, the desktop environment has a slightly modified layout, with the main panel moved to the left side. o § Fedora Family / Red Hat⠀➾ # ⚓ Make Use Of ☛ What_Is_Fedora?_Everything_You_Need_to_Know⠀⇛ Alongside Arch and Debian, Fedora is one of “the big three” Linux distributions. It traces its lineage back to Red Hat Linux, the original RPM- based distro. Fedora is known for its cutting-edge technologies, the latest software, and frequent updates. It’s also one of the few major distros to embrace stock GNOME. Lately, the distribution has become more user-friendly, with a welcome screen, Flatpak support, and the ability to enable third-party repositories in setup. # ⚓ Fedora Magazine ☛ Fedora_Linux_editions_part_2:_Spins_– Fedora_Magazine⠀⇛ One of the nice things about using Linux is the wide choice of desktop environments. Fedora Linux official Worksation edition comes with GNOME as default desktop environment, but you can choose another desktop environment as default via Fedora Spins. This article will go into a little more detail about the Fedora Linux Spins. You can find an overview of all the Fedora Linux variants in my previous article Introduce the different Fedora Linux editions. # ⚓ Red Hat Official ☛ Preview_the_new_system_role_support_for Microsoft_SQL_Server_Always_On_availability_groups [Ed: Red Hat is helping its own competition, which ruthlessly blocks GNU/Linux from even booting!]⠀⇛ # ⚓ Red Hat Official ☛ Red_Hat_Summit:_Connect_2022_lab sessions_and_topics⠀⇛ Red Hat Summit: Connect 2022 is kicking off in September. Learn about our self-paced and instructor-led labs here. # ⚓ Red Hat ☛ Containers_and_container_images_101_for developers_|_Red_Hat_Developer⠀⇛ Containers are the backbone of modern development. Learn the basics of how the components of a container interact. # ⚓ Enterprisers Project ☛ Agile:_Starting_at_the_top⠀⇛ Change management can be the hardest part of any transformation. While you may quickly get people on board with the idea of change, it can be a long time before behaviors start to shift. We are all creatures of habit, after all. When the IT organization at Thales North America wanted to transform product and service delivery from waterfall to agile, they took a radical approach: Instead of simply talking about what they wanted to achieve – squads, operating using agile methods driven by user stories, and ultimately delivering incremental value – they decided to show the organization by walking the walk themselves. “The only way we could truly be effective in leading the organization through an agile transformation is if we transformed our leadership team first,” says Kevin Neifert, CIO of Thales North America. o § Debian Family⠀➾ # ⚓ Make Use Of ☛ MX_Linux_21.2_“Wildflower”_Lands,_Keeping Things_Simple⠀⇛ The Debian-based distribution MX Linux has announced the release of MX Linux 21 version 21.2, dubbed “Wildflower.” The update continues MX’s tradition of simplicity. The developers stressed that all that existing users of the distro had to do was run the package manager to obtain the latest version. o § Canonical/Ubuntu Family⠀➾ # ⚓ Ubuntu ☛ Ubuntu_Blog:_Canonical_Ubuntu_now_available_on Ampere®_Altra®_Arm-based_Azure_virtual_machines [Ed: Microsoft_bought_Canonical. It_does_not_seem_to_bother Canonical_that_Ubuntu_users_are_being_obstructed_from_booting because_of_Microsoft.]⠀⇛ # ⚓ Paul Thurrott ☛ Canonical,_Microsoft_Bring_Ubuntu_on_Arm_to Azure [Ed: Microsofters like Paul Thurrott cannot contain their excitement; Canonical now works for the company that's attacking GPL, Linux, Free software...]⠀⇛ o § Mobile Systems/Mobile Applications⠀➾ # ⚓ 9to5Google ☛ Android_14_Developer_Preview_–_9to5Google⠀⇛ # ⚓ Android Headlines ☛ ASUS_ZenFone_9_Gets_Android_13_Beta Program,_And_You_Are_Invited⠀⇛ # ⚓ Android_12L_is_making_its_way_onto_Samsung_Galaxy_Tab_S8 devices_–_Phandroid⠀⇛ # ⚓ 9to5Google ☛ Samsung_Galaxy_Tab_S8_gets_Android_12L_and_the taskbar⠀⇛ # ⚓ The Verge ☛ Android_12L-based_update_is_arriving_on_the Galaxy_Tab_S8_–_The_Verge⠀⇛ # ⚓ How_to_translate_text_on_your_Android_smartphone⠀⇛ # ⚓ Android Central ☛ How_to_add_videos_to_your_Strava_posts_on Android_|_Android_Central⠀⇛ # ⚓ Giz China ☛ Stolen_or_lost_Android_smartphone:_What_to_do? –_Gizchina.com⠀⇛ # ⚓ Giz China ☛ 10_tips_to_improve_the_security_of_your_Android smartphone⠀⇛ # ⚓ 9to5Google ☛ AAWireless_is_soon_to_graduate_from_Indiegogo –_9to5Google⠀⇛ # ⚓ 9to5Google ☛ Android_Auto_7.8_causing_‘phone_not compatible’_error_–_9to5Google⠀⇛ * § Free, Libre, and Open Source Software⠀➾ o ⚓ diaspora*'s_10_years_in_community_hands_–_The_diaspora* Project⠀⇛ This weekend marked the 10th anniversary since the diaspora* project was handed over by its founders to the community. Ten years – time really does fly! During that time we’ve made many fundamental improvements to the software that this network runs on, from standardizing the process of making improvements to the code to completely rewriting the federation protocol on which communication between pods is based. We’ve also stabilized performance in many ways, and we’ve added many improvements to the user interface and new features. Over the past couple of years things have been a bit quieter as our team of volunteer developers has been hard at work on some really huge and complex tasks. The most fundamental of these have been creating a feature to allow members to move their account from one pod to another, and creating an API to allow apps to interact with diaspora* more easily and in more interesting ways. o § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ SpiderMonkey_Newsletter_(Firefox_104-105)_| SpiderMonkey_JavaScript/WebAssembly_Engine⠀⇛ SpiderMonkey is the JavaScript engine used in Mozilla Firefox. This newsletter gives an overview of the JavaScript and WebAssembly work we’ve done as part of the Firefox 104 and 105 Nightly release cycles. o § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ Document Foundation ☛ Live_town-hall_meetings_with_the Membership_Committee_candidates_–_The_Document_Foundation Blog⠀⇛ The Document Foundation is the non-profit home of LibreOffice, and its Membership Committee (MC) administers membership applications and renewals following the criteria defined in the Foundation’s Statutes. The election process for a new MC is underway, and we’ll have live Q&A sessions with the candidates! o § Programming/Development⠀➾ # ⚓ Barry Kauler ☛ ui_GUI_toolkit_for_Nim⠀⇛ # ⚓ The_Ultimate_List_of_Open_Source_Cloud-Native_Tools_– Container_Journal⠀⇛ There are so many great open source cloud-native tools for nearly everything you want to do. And they’re all in one place—look no further than the Cloud Native Computing Foundation (CNCF). This Linux Foundation body has become a locus of some stellar cloud-native open source projects. The CNCF now hosts an array of helpful packages, spanning container scheduling, observability, persistent storage, container runtime and other areas. # ⚓ DEV Community ☛ Enable_Gitsign_Today_and_Start_Signing_your Commits_–_DEV_Community⠀⇛ I have been meaning to write this post for some time already, but the extra motivation came after looking at the recent news of PyPI phishing attacks that have compromised several Python library maintainers and their packages. The issue of code provenance is ultimately an industry-wide threat that needs to be addressed sooner rather than later. In this post, I will address something rather simple you can do today if you are an open source maintainer and/or contributor, and it can help you attest that the code pushed to a repository really comes from where it’s supposed to come: from you. # ⚓ FOSSLife ☛ Start_Signing_your_Commits_with_Gitsign⠀⇛ The issue of code provenance is an industry-wide threat that needs to be addressed, says Erika Heidi. “We need additional layers of security to prove the provenance of code that is committed to a repository, especially when it comes to libraries that are used as dependencies by hundreds or thousands of other projects.” # ⚓ LinuxTechLab ☛ A_Complete_Guide_On_Open_Source_Linux Software_Development_–_LinuxTechLab⠀⇛ There are several important steps, factors, and elements to know about the world of Linux software development. Linux can be thought of an operating system (OS), ecosystem, build environment, platform, and culture. It supports our tech infrastructure, stock exchanges, business servers, and some of the world’s largest supercomputers. In fact, the entire Android OS is built on Linux kernels. One of the most interesting facts about Linux is that the actual OS is open source. Even if it can be frustrating and time-consuming at first, learning to develop applications with Linux is certainly a rewarding process. Learning these skills, you can take advantage of one of the most secure, dependable, stable, and scalable operating systems. # ⚓ Search_API_Endpoints,_Fully_Documented_–_Open_Build Service⠀⇛ Here we come again, with another piece of the API documentation rework. This time we fully documented the search endpoints. # § Perl / Raku⠀➾ # ⚓ Rakulang ☛ 2022.35_Reworkout_–_Rakudo_Weekly_News⠀⇛ Mitarashi Dango reports that all of the Raku exercises at exercism.org have been reworked, and mentions there are some Raku exercises that need an example solution. Consider yourselves invited! # ⚓ Perl ☛ Perl_Weekly_Challenge_180:_First_Unique Character_and_Trim_List⠀⇛ * § Leftovers⠀➾ o ⚓ Ruben Schade ☛ Rubenerd:_Cane_toads,_the_“seenzone”_and_message state⠀⇛ Except, this technocratic solution introduces a new social issue: the removal of plausible deniability. And it turns out, humans like having this. o § Hardware⠀➾ # ⚓ CNX Software ☛ SyncBot_educational_mobile_robot_supports NVIDIA_Xavier_NX_or_Intel_Tiger_Lake_controller [Ed: Why are they assuming people still want or need Windows in 2022?]⠀⇛ It runs Windows 10 IoT Enterprise by default, but Linux is available upon request. # ⚓ The Next Platform ☛ Details_Emerge_On_Nvidia’s_“Grace”_Arm CPU⠀⇛ Imagine, if you will, that Nvidia had launched its forthcoming “Grace” Arm server CPU three years ago instead of early next year. How much better would Nvidia be fairing in the gaming and cryptocurrency downdraft that is impacting its sales today? o § Security⠀➾ # ⚓ Send_Alert_When_ClamAV_Finds_Infected_Files_on_Linux Systems_–_kifarunix.com⠀⇛ In this tutorial, you will learn how to send alert when ClamAV finds infected files on Linux systems. ClamAV is an opensource antivirus engine for detecting trojans, viruses, malware & other malicious threats. It is a good idea to sent alerts whenever a malicious file is detected on the system. This enables you to take actions of analyzing the files and probably removing them from the system based on the results of the analysis. # ⚓ LinuxSecurity ☛ BlackHat_USA_2022:_Return_to_Sender_– Detecting_Kernel_Exploits_with_eBPF⠀⇛ Let’s take a brief look at what Guillaume Fournier from Datadog presented at Blackhat USA 2022: “One of the fastest growing subsystems in the Linux Kernel is, without any doubt, eBPF (extended Berkeley Packet Filter).” # ⚓ Michael West Media ☛ Click,_collect_and_regret:_how scammers_made_a_lazy_$8k_out_of_a_$189_fridge_–_Michael West⠀⇛ In our embrace of online shopping, we have become prime targets for scammers. And when bank accounts are emptied, Australians have to jump through hoops to get their money back, if at all, writes James Fitzgerald Sice. Mike Daws was finally able to visit his mother-in- law for her 101st birthday in the US in May 2022 after two years of Covid border restrictions, only for the trip to be ruined by an online scam that almost cost him $8000. o § Internet Policy/Net Neutrality⠀➾ # ⚓ The Anarcat ☛ How_to_nationalize_the_internet_in_Canada⠀⇛ Rogers had a catastrophic failure in July 2022. It affected emergency services (as in: people couldn’t call 911, but also some 911 services themselves failed), hospitals (which couldn’t access prescriptions), banks and payment systems (as payment terminals stopped working), and regular users as well. The outage lasted almost a full day, and Rogers took days to give any technical explanation on the outage, and even when they did, details were sparse. So far the only detailed account is from outside actors like Cloudflare which seem to point at an internal BGP failure. Its impact on the economy has yet to be measured, but it probably cost millions of dollars in wasted time and possibly lead to life-threatening situations. Apart from holding Rogers (criminally?) responsible for this, what should be done in the future to avoid such problems? It’s not the first time something like this has happened: it happened to Bell Canada as well. The Rogers outage is also strangely similar to the Facebook outage last year, but, to its credit, Facebook did post a fairly detailed explanation only a day later. The internet is designed to be decentralised, and having large companies like Rogers hold so much power is a crucial mistake that should be reverted. The question is how. Some critics were quick to point out that we need more ISP diversity and competition, but I think that’s missing the point. Others have suggested that the internet should be a public good or even straight out nationalized. I believe the solution to the problem of large, private, centralised telcos and ISPs is to replace them with smaller, public, decentralised service providers. The only way to ensure that works is to make sure that public money ends up creating infrastructure controlled by the public, which means treating ISPs as a public utility. This has been implemented elsewhere: it works, it’s cheaper, and provides better service. * § Gemini* and Gopher⠀➾ o § Technical⠀➾ # ⚓ Thoughts_on_sandman_and_my_feelings_on_‘wokeness’⠀⇛ What sparked this log is just how often I see the term ‘woke’ be used now in general discussion on the internet. It seems you cant go into a comment section for a new show, movie, or game without seeing the term thrown around followed by very heated rants between random people. Modern ntertainment seems to be fundimentally changing in reaction to various social pressures and movements in real life. Also Recently I watched ‘the sandman’ on netflix with my mom and she made the remark after a few episodes ‘why does every show now have lesbians in it?’ Its a fair question, and I have never really thought about it. So here are some of my opinions on the matter that im sure all of you will unanimously agree with and there will be no controversal statements or conflicting feelings between us. # ⚓ My_BTRFS_cheatsheet⠀⇛ I recently switched my home “NAS” (single disk!) to BTRFS, it’s a different ecosystem with many features and commands, so I had to write a bit about it to remember the various possibilities… BTRFS is an advanced file-system supported in Linux, it’s somehow comparable to ZFS. # § Programming⠀➾ # ⚓ Do_not_let_MinuzSopht_making_free-software_illegal⠀⇛ I promised myself to not write anything about “Copilot” but when you are not a developer or a person involved into coding and licensing, it easier — or at least I find it easy — to have a different approach about such topics and to be concerned about all the possible incoming scenarios, especially the ones you think are going to affect your daily relationship with these technologies. The point is the following one: end-users, without coding skills, can just observing the evolution of the opensource and freesoftware landscape but anything else; We can only decide which tools to use but we can’t influence which tools will be available for us. I think this is the main reason why, many of us, are sincerely concerned when Tech Corporations use their weight to alter the balance, and start dragging resources and development toward them rather than toward us. # ⚓ Trying_rust⠀⇛ Rust is not easy to learn for beginner programmers. I suggest beginner programers start learning python or javascript then C and then rust. Learning C helps understanding the kind of issues that are detected by the rust compiler. There are tools for C for detecting the memory issues but they run in the tests (CI) but they don’t detect all issues. Rust shows the issues earlier at compile time when the program is under development. =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It’s like the World Wide Web but a lot lighter. ䷩ 𝚕𝚒𝚗𝚎 3811 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_29/08/2022:_Debian’s_General_Resolution_on_Non-free_Blobs⠀✐ Posted in News_Roundup at 12:56 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Applications o Instructionals/Technical o Desktop_Environments/WMs # GNOME_Desktop/GTK * Distributions_and_Operating_Systems o New_Releases o Debian_Family o Canonical/Ubuntu_Family o Devices/Embedded o Open_Hardware/Modding o Mobile_Systems/Mobile_Applications * Free,_Libre,_and_Open_Source_Software o Web_Browsers # Mozilla o GNU_Projects o Programming/Development o Standards/Consortia * Leftovers o Science o Education o Hardware o Health/Nutrition/Agriculture o Proprietary o Security # Integrity/Availability/Authenticity # Privacy/Surveillance o Defence/Aggression o Environment # Energy # Overpopulation o Finance o AstroTurf/Lobbying/Politics o Censorship/Free_Speech o Freedom_of_Information_/_Freedom_of_the_Press o Civil_Rights/Policing o Internet_Policy/Net_Neutrality o Monopolies # Copyrights * Gemini*_and_Gopher o Personal o Technical * § GNU/Linux⠀➾ o § Applications⠀➾ # ⚓ Linux Links ☛ ncspot_–_ncurses_Spotify_client⠀⇛ We’ve recently reviewed spotify-qt and Spotify TUI, third party-clients which let you enjoy Spotify without needing to use the semi-official bloated Spotify app. ncspot is a command-line Spotify client that’s written in Rust. It’s published under an open source license. Like the other third-party clients, you’ll need a Spotify premium subscription to use it. o § Instructionals/Technical⠀➾ # ⚓ Dan Langille ☛ Adding_an_SSL_certificate_to_HomeAssistant⠀⇛ In my previous blog post, I got homeassistant up and running, but without a TLS connection. Let’s fix that. # ⚓ TecMint ☛ 3_Ways_to_Install_Skype_in_Fedora_Linux [Ed: This is malicious spyware, controlled by an anti-Linux company]⠀⇛ Skype is a popular proprietary communication application well known for its voice calls, chats, VoIP-based video telephony, and video conferencing functionalities. It helps people stay connected regardless of their geographical location; from colleagues within an organization to family and friends. Skype works across a wide range of devices including smartphones (iOS and Android) PCs, and tablets. You can also log in to Skype on the browser to stay in touch with all your contacts. # ⚓ OpenSource.com ☛ 4_ways_to_use_the_Linux_tar_command⠀⇛ When you have a lot of related files, it’s sometimes easier to treat them as a single object rather than 3 or 20 or 100 unique files. There are fewer clicks involved, for instance, when you email one file compared to the mouse work required to email 30 separate files. This quandary was solved decades ago when programmers invented a way to create an archive, and so the tar command was born (the name stands for tape archive because back then, files were saved to magnetic tape.) Today tar remains a useful way to bundle files together, whether it’s to compress them so they take up less space on your drive, to make it easier to deal with lots of files, or to logically group files together as a convenience. I asked Opensource.com authors how they used tar, and related tools like zip and gzip, in their daily work. Here’s what they said. # ⚓ OpenSource.com ☛ Clean_up_unwanted_files_in_your_music directory_using_Groovy⠀⇛ In this series, I’m developing several scripts to help in cleaning up my music collection. In the last article, we used the framework created for analyzing the directory and sub-directories of music files, checking to make sure each album has a cover.jpg file and recording any other files that aren’t FLAC, MP3, or OGG. I uncovered a few files that can obviously be deleted—I see the odd foo lying around—and a bunch of PDFs, PNGs, and JPGs that are album art. With that in mind, and thinking about the cruft removal task, I offer an improved script that uses a Groovy map to record file names and counts of their occurrences and print that in CSV format. # ⚓ ID Root ☛ How_To_Install_Java_on_Linux_Mint_21_–_idroot⠀⇛ In this tutorial, we will show you how to install Java on Linux Mint 21. For those of you who didn’t know, Java is the most popular programming language, and many applications require Java JRE (Java Runtime Environments) to execute programs. Java can be used on different platforms such as Linux, macOS, Windows, Raspberry Pi, and many others. 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 Java programming languages on Linux Mint 21 (Vanessa). # ⚓ OSTechNix ☛ Manage_Docker_Containers_Using_Portainer_In Linux_–_OSTechNix⠀⇛ In this tutorial, we will learn what is Portainer, how to install Portainer and how to manage docker containers using Portainer in Linux. # ⚓ Linux Shell Tips ☛ How_to_Block_User-Agents_in_Nginx_Web Server⠀⇛ Suppose you are after infinite power and control in web administration. In that case, you have no choice but to consult Nginx, which is a reputable web server and is attributed to have almost infinite configuration footprints, high performance, and component adaptability in modern stacks. That said, if you are dealing with a high-traffic website and need a web server that is lightweight and fast, you should consider implementing Nginx. On the other hand, a user agent is simply a software package with the responsibility of retrieving, rendering and interacting with end users’ web content. Popular examples of user agents known to the Linux ecosystem include Curl and Wget. Sometimes the access that these user agents have to a web server can compromise its integrity. In this case, you need a way of blocking/restricting their access. This article will walk us through valid Nginx configurations for blocking user agents from having access to your web server data/information. # ⚓ HowTo Forge ☛ How_to_Install_Focalboard_on_Ubuntu_22.04⠀⇛ Focalboard is an open-source and self-hosted project management tool. It is multilingual and an alternative to Asana, Trello, and Notion that can be used by developers to track and manage work across teams. It is based on kanban and is available for desktops and servers. It can be used as a stand-alone personal server for testing and development. Focalboard helps developers stay aligned to complete tasks, reach milestones, and achieve their goals. In this post, we will show you how to install Focalboard with Nginx as a reverse proxy on Ubuntu 22.04. # ⚓ Linux Handbook ☛ How_to_Ping_an_IPv6_Address_in_Linux Command_Line⠀⇛ Using the ping command is perhaps the most common way to check if a remote server is reachable or not. By default, the ping command works on the IPv4 address. But what if you need to ping an IPv6 address? The answer is that you still use the ping command. Yes, the newer versions of the ping command support IPv6 addresses. # ⚓ AddictiveTips ☛ How_to_play_Halo_Infinite_on_Linux⠀⇛ Halo Infinite is the sequel to Halo 5, released in 2021 on PC and Xbox platforms. The games multiplayer is free, although the campaign costs money. Unfortunately, the game was never released on Linux. Thanks to the hard work of Valve and other Proton developers in the Linux community, a blockbuster game like Halo is now available to play on Linux. If you’re dying to try out the new Halo on Linux, follow this guide to get it working. # ⚓ HowTo Forge ☛ How_to_Setup_Kubernetes_Cluster_with_Kubeadm on_Debian_11⠀⇛ Kubernetes or k8s is an open-source platform for container orchestration that automates deployments, management, and scaling of containerized applications. Kubernetes is a container orchestration created by Google, and now become an open-source project and become standard for modern application deployment and computing platforms. Kubernetes is the solution for the modern container deployment era. It provides service discovery and load-balancing, storage orchestration, automated rollout and rollback, self-healing service, secret and configuration management. Kubernetes enables cost-effective cloud-native development. # ⚓ Red Hat Official ☛ How_to_use_variables_as_arguments_in Ansible_|_Enable_Sysadmin⠀⇛ When you write an Ansible playbook, you sometimes need to pass data into your play at runtime. To do that, you can use a variable, a sort of placeholder for data that’s meant to be determined at some point in the future. There are lots of places to create variables for your playbooks, such as an inventory file, included files, or even dynamically in your playbook itself. However, you can also pass variables in the terminal when you launch your playbook. # ⚓ LinuxOpSys ☛ Rsync_Command_in_Linux_–_Options_+_Examples⠀⇛ As a system administrator or Linux power user, how do you transfer files from your local system to a remote? To synchronize folders or files to another machine we need a fast and reliable tool. In this tutorial, we learn about rsync command in Linux with some useful examples. o § Desktop Environments/WMs⠀➾ # § GNOME Desktop/GTK⠀➾ # ⚓ Its FOSS ☛ 5_GNOME_43_Features_to_Keep_an_Eye_On⠀⇛ GNOME 43 is due for release on September 21, 2022. As of now, GNOME 43’s beta build is available to test. The features/changes that we find with GNOME 43 beta should arrive with the final release. So, what are the best GNOME 43 features that you should look forward to? * § Distributions and Operating Systems⠀➾ o § New Releases⠀➾ # ⚓ 9to5Linux ☛ MX_Linux_21.2_Released_with_Linux_Kernel_5.18, Based_on_Debian_GNU/Linux_11.4⠀⇛ Coming almost five months after MX Linux 21.1, the MX Linux 21.2 release is here as an updated installation medium for those who want to deploy the lightweight Debian-based distribution on new computers. MX Linux 21.2 is based on Debian GNU/Linux 11.4, which introduced 79 security fixes and 81 miscellaneous bugfixes, and bumps the kernel to Linux 5.18, despite it reaching end of life earlier this month, for the AHS (Advanced Hardware Support) edition. The standard editions stay with Debian’s Linux 5.10 LTS kernel. o § Debian Family⠀➾ # ⚓ DebugPoint ☛ Debian_Proposes_Better_Discovery_of_non-free Firmware_Images⠀⇛ Debian Linux provides two major installer images based on the firmware type. The “free” images contain the “open-source” drivers and packages, whereas the “non-free” images are for proprietary firmware packages. If you tried downloading the “non-free” version from the official website, you might have spent some time locating the installer images. Because the “non-free” images are kind of “hidden” and buried under several directory structures in the official Debian download server. # ⚓ Its FOSS ☛ Debian_Finally_Starts_a_General_Resolution_to Consider_a_Non-Free_Firmware_Image⠀⇛ Debian is one of the most loved Linux distributions for its approach to stability and a balance between new features. But, it does not come with any non-free firmware. And, that is becoming an issue for users who want to use Debian on newer hardware. Most of the latest devices and configurations need non-free firmware to make things work, which includes Wi-Fi, graphics, and more. To address that, Steve McIntyre, a Debian developer and a former Debian project leader, has been actively discussing the issue for a while. At the DebConf 22 conference, Steve recently talked about fixing the firmware mess to highlight this better to users and developers, as spotted by Geeker’s Digest. As an update to the discussion among the community: it looks like Debian has started a general resolution to let its stakeholders vote what to do with non-free firmware. o § Canonical/Ubuntu Family⠀➾ # ⚓ IT Pro Today ☛ 3_Ubuntu_Commands_for_Monitoring_System Resource_Use⠀⇛ Here are three basic Ubuntu commands that will let you monitor system resource use in Ubuntu and other Linux distributions. # ⚓ Ubuntu ☛ Meet_Canonical_at_Hannover_Messe_2022⠀⇛ Hannover Messe USA is almost here! With a 114,000+ net sq. ft exhibition area, 500+ companies, 129400+ registrants and 100+ countries represented, Hannover Messe USA is the largest gathering of industrial manufacturing in North America. Join Canonical, the company behind Ubuntu, at Hannover Messe USA to discuss open source innovation in industrial technology. You can meet with the Canonical team on-site in Chicago and pick our technical experts’ brains about your industrial use case.  o § Devices/Embedded⠀➾ # ⚓ CNX Software ☛ Pine64_Star64_SBC_to_feature_StarFive_JH7110 quad-core_RISC-V_processor_with_Imagination_GPU_–_CNX Software⠀⇛ Pine64 Star64 is an upcoming single board computer (SBC) powered by StarFive JH7110 quad-core 64-bit RISC-V processor equipped with an Imagination BXE- 4-32 GPU, and in a form factor similar to the earlier Pin64 model B boards such as the Quartz64 Model A. The Star64 SBC will be offered with either 4GB or 8GB of RAM, an HDMI 2.0 video output connector, two Gigabit Ethernet ports, a WiFi 6 and Bluetooth 5.2 module, USB 3.0 ports, a PCIe slot, and a GPIO header for expansion. # ⚓ Linux Gizmos ☛ Pine64_reveals_the_Star64_RISC-V_based Single_Board_Computer⠀⇛ Yesterday, Pine64 made an announcement about the Star64 Single Board Computer (SBC) prototype. The company mentioned this SBC will be powered with the RISC-V based StarFive JH7110 64-bit processor. The processor integrated on the Star64 is the same one found on the recently launched StarFive VisionFive 2 board.  # ⚓ CNX Software ☛ StarFive_JH7110_RISC-V_processor specifications_released⠀⇛ Some documentation for the StarFive JH7100 processor has been released and answers some of those questions. It’s actually an SoC with six RISC-V cores, of which four 64-bit RISC-V cores run the main OS, plus a 64-bit RISC-V monitoring core, and a 32-bit RISC-V real-time core. The AI accelerators found in the JH7100 (Neural Network Engine and NVDLA) appear to be gone for good, and there are two 1-lane PCIe 2.0 interfaces up to 5 Gbps each. Target applications for the StarFive JH7110 processor include single board computers, home NAS, routers with software routing, Smart Home appliances, industrial robots, drones, and video surveillance applications. Right now, the documentation website only comes with a product brief, but the datasheet is coming soon, and a hardware design reference plus a software developer guide are also in the works. # ⚓ Hackaday ☛ A_Pi_Camera_To_Be_Proud_Of⠀⇛ Inside the box is a Waveshare touchscreen that fits on the GPIO header, and a NanoWave 5000 mAH USB battery pack. The camera module fits on the front of the unit, with the C-mount ready to take a lens. Software is still a work in progress and is promised to be a Python script controlling the various camera programs. There are enough Pi camera projects for software to be a matter of choice and taste. We like the form factor and we like the use of the very compact NanoWave battery, so we think this is a design with some possibilities. Perhaps a cover over the Pi ports might be of use though for general robustness in the face of everyday photography. The question remains though, whether it can come close to the performance of even a budget mirror-less compact camera, and we’re guessing that will depend as much on the operator skill, lens quality, and software capabilities as it does on the Pi HQ module. We look forward to seeing what comes of this project, but meanwhile you can see a video with all the details below the break. o § Open Hardware/Modding⠀➾ # ⚓ Arduino ☛ Monitoring_the_force_of_a_20-ton_hydraulic_press |_Arduino_Blog⠀⇛ Material testing often comes down to breaking stuff and measuring how much force it took to do so. How a thing breaks is a result of different strength properties. There are many different types of strength, but mechanical engineers are most concerned with tensile, compressive, shear, and torsional strength. The easiest way to test compressive strength is to squish something with a very powerful press. Element14 Presents’ Clem Mayer purchased a 20-ton hydraulic press for that purpose and used an Arduino to measure its force. Even if you don’t have any shop experience, you’ve probably seen a hydraulic press in action in one of those YouTube videos where they squeeze household objects until they explode in an entertaining way. This particular press can exert up to 20-tons of force, which is about as heavy as three elephants. The actual pressure depends on how much area that force applies to. To calculate the pressure at the time of failure, Mayer needs the contact area (which is easy to measure ahead of time) and the current amount of force that the press is applying. He collected the pressure data using an Arduino Leonardo and a load cell. # ⚓ Raspberry Pi ☛ Remotely_open_your_garage_door_with Raspberry_Pi_Pico_W⠀⇛ The best part about this creation being controllable via mobile phone is that you don’t need a bulky garage door remote on your keychain. You’ve already got your car key (hence the garage), your front door key, back door key, gym locker key, barcode thing you scan at the supermarket to collect points that never really get you anything. You get the picture. Also, have you ever tried to find a replacement battery for an old-fashioned garage door remote control? Skip the hassle and keep your keychain slimline with Michael’s Pico W- based solution. # ⚓ Hackaday ☛ Share_Screen_To_RGB_Panel_With_Pi_Pico_W⠀⇛ RGB LEDs are great for adding a bit of color to your life, and it’s even more satisfying to use a matrix of them as a graphic display. [bitluni] built an RGB LED display with Pi Pico to which you can share a pixelated version of your PC’s screen. o § Mobile Systems/Mobile Applications⠀➾ # ⚓ Google_Pixel_Buds_Pro_review:_Best_Android_AirPod alternative?_|_NextPit⠀⇛ # ⚓ HowTo Geek ☛ How_to_Split_the_Screen_on_Android⠀⇛ # ⚓ Pixel_7_buyers_in_for_a_treat_if_Android_13_is_as_good_as on_Pixel_6⠀⇛ # ⚓ Android Police ☛ Some_Pixel_6_users_are_reporting_increased idle_battery_drain_on_Android_13⠀⇛ # ⚓ SamMobile ☛ Galaxy_Tab_S8_gets_Android_12L_(One_UI_4.1.1) update_with_better_multitasking_–_SamMobile⠀⇛ # ⚓ 9to5Google ☛ Google_Assistant_tests_Search_this_screen_Lens button_–_9to5Google⠀⇛ # ⚓ Android Authority ☛ You_told_us:_Over_half_of_you_have received_storage_alerts_on_Android_TV⠀⇛ # ⚓ 5_Ways_To_Silence_All_Notifications_On_Android_For Sometime⠀⇛ # ⚓ Make Use Of ☛ How_Many_Phones_Does_Apple_Sell_Compared_to Android?⠀⇛ * § Free, Libre, and Open Source Software⠀➾ o § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Mozilla ☛ Merging_two_GitHub_repositories_without losing_commit_history [Ed: Mozilla is outsourced to proprietary software of Microsoft, betraying both standards and Free software]⠀⇛ We are in the process of merging smaller example code repositories into larger parent repositories on the MDN Web Docs project. While we thought that copying the files from one repository into the new one would lose commit history, we felt that this might be an OK strategy. After all, we are not deleting the old repository but archiving it. # ⚓ Mozilla ☛ The_Truth_is_Out_There [Ed: Mozilla continues to push for Web censorship under the guise of battling misinformation]⠀⇛ Murky political groups are exploiting social media systems to spread disinformation. With important elections taking place around the world this year, who is pushing back? We meet grassroots groups in Africa and beyond who are using AI to tackle disinformation in languages and countries underserved by big tech companies. o § GNU Projects⠀➾ # ⚓ DebugPoint ☛ GIMP_2.99.12_Released_with_Huge_Updates,_But No_Date_of_v3.0_Yet⠀⇛ The free and open source drawing program brings the latest point release (development) in the 2.99 series with a list of new features and updates. GIMP’s point releases are not minor ones. They often bring several new features and improvements. Although, in the official release announcement, the team did not say specifically when the much- anticipated GIMP 3.0.0 will be released. As it is a community project and a complex one, we can guess it will be released when ready. o § Programming/Development⠀➾ # ⚓ Everything_markdown_with_pandoc⠀⇛ o § Standards/Consortia⠀➾ # ⚓ Matt Rickard ☛ Timeline_of_Early_Email⠀⇛ The first version of a computer email system that resembles anything like what we have today showed up around 1965. Computers had been primitively networked a few years earlier, and you could technically send and receive content. * § Leftovers⠀➾ o ⚓ Counter Punch ☛ Stop_Using_Thermobaric_Flame-Throwers!⠀⇛ o § Science⠀➾ # ⚓ NPR ☛ NASA_is_set_to_return_to_the_moon._Here_are_4_reasons to_go_back⠀⇛ A 2013 study commissioned by NASA estimates that commercial products emerging from the space agency’s research return between $100 million and $1 billion annually to the U.S. economy. Many of those “spinoffs” had their origin in the Apollo program. # ⚓ Site36 ☛ US_military_test_flight:_Zephyr_solar_glider crashed⠀⇛ Airbus‘ high-flying drone has crashed in the desert just hours before setting a record for the longest flight ever recorded by an aircraft. o § Education⠀➾ # ⚓ Ruben Schade ☛ Handwritten_HTML_sites⠀⇛ Mine answer is the same, though like him I don’t run modern Windows. The tool might have changed, but I still write basic HTML sites by hand. It has to span dozens of pages, need editing by other people, or require interactive features for me to do it any other way. # ⚓ Data Swamp ☛ My_blog_workflow⠀⇛ I rarely spend more than 40 minutes for a blog post, the average blog post takes 20 minutes. Most of them are sharing something I fiddled with in the day or week, so the topic is still fresh for me. The content of the short articles often consists of dumping a few commands / configuration I used, and write a bit of text around so the reader knows what to expect from the article, how to use the content and what’s the point of the topic. It’s important to keep track of commands/ configuration beforehand, so when I’m trying something new, and I think I could write about it, I keep a simple text file somewhere with the few commands I typed or traps I encountered. o § Hardware⠀➾ # ⚓ Hackaday ☛ Giant_3D_Printer_Aims_To_Produce_Life-Sized Boat⠀⇛ As 3D printers become more ubiquitous, the number of custom designs and styles of printers has skyrocketed. From different printing materials and technologies to the movements of the printing head, we’ve seen all kinds of different takes on these tools. But one thing that has been largely limited to commercial and industrial use has been large print sizes —  leaving consumer level prints to be split into several pieces to fit together later. Not so with this giant 3D printer from [Ivan], though. # ⚓ Hackaday ☛ Automate_Your_Desk_With_The_Upsy_Desky⠀⇛ It might be surprising for some, but humans actually evolved to be long-distance runners. We aren’t very fast comparatively, but no other animal can run for as long or as far as a human can. Sitting at a desk, on the other hand, is definitely not something that we’re adapted to do, so it’s important to take some measures to avoid many of the problems that arise for those that sit at a desk or computer most of the day. This build takes it to the extreme, not only implementing a standing desk but also a ton of automation for that desk as well. # ⚓ Hackaday ☛ Sleep_Posture_Monitor_Warns_You_Away_From Dangerous_Positions⠀⇛ Age, we’re told, is just a number, but that number seems to be the ever-increasing count of injuries of a ridiculous nature. Where once the younger version of us could jump from a moving car or fall out of a tree with just a few scrapes to show for the effort, add a few dozen trips around the sun and you find that just “sleeping funny” can put you out of service for a week. o § Health/Nutrition/Agriculture⠀➾ # ⚓ SUVs_‘eight_times_more_dangerous’_to_kids_walking_or cycling_than_smaller_cars_are⠀⇛ A recent study from the US has found that children are eight times more likely to be killed in a collision involving an SUV or pick-up truck than they are in a crash in which a standard passenger car is involved. # ⚓ Helsinki Times ☛ Instagram_rolls_out_update_to_change default_content_settings_for_teens⠀⇛ Instagram is also testing prompts for teens that suggest limiting who can interact with their content. The test will ask them to review privacy and security settings related to who can re-share their content, who can message them, the type of content they can see, and time management, as per The Verge. # ⚓ Is_TikTok_or_Instagram_worse_for_teen_mental_health?:_A therapist_vs._psychologist_perspective⠀⇛ Although teens think TikTok may be the most harmful social media platform, therapists and psychologists disagree. Instagram perpetuates additional issues due to the fact that users can alter their public image. Regardless, this is nothing new. Media has shaped the body standard for decades. Therapists and psychologists also harp on the benefits of social media platforms, as they often provide community to those struggling. # ⚓ Effects_of_Social_Media_on_Teens:_Understanding_the Headlines⠀⇛ Social media plays a powerful role in connecting with others, getting information and expressing ourselves. But over the past year, the impact of social media, particularly Instagram, has made headlines for its negative effects on teens, especially girls. Concerns around social media’s impact on self- esteem adds to national conversations around the ongoing youth mental health crisis. It’s more important than ever that parents, caregivers, educators and youth development professionals guide young people in having safe experiences online that support their wellbeing and success. # ⚓ Counter Punch ☛ The_UN_Proved_Its_Usefulness_in_Crafting Ukraine_Grain_Deal⠀⇛ Before the war, Ukraine exported more than 45 million metric tons of grain annually to the global market. The war has caused grain prices to rise dramatically. o § Proprietary⠀➾ # ⚓ YLE ☛ Police_solve_4%_of_internet_crime [iophk: Windows TCO]⠀⇛ A decade ago, police managed to solve more than 30 percent of data breach cases. Police told Yle that the shrinking percentage of solved cases reflects the explosion of this type of crime. In 2012, for example, police said they dealt with fewer than 500 cyber crime cases. o § Security⠀➾ # ⚓ LWN ☛ Security_updates_for_Monday_[LWN.net]⠀⇛ Security updates have been issued by Debian (curl, exim4, maven-shared-utils, ndpi, puma, webkit2gtk, and wpewebkit), Fedora (dotnet3.1, firefox, and webkit2gtk3), Mageia (clamav, mariadb, net-snmp, postgresql, python-ldap, and thunderbird), SUSE (freeciv, gnutls, keepalived, libyang, nim, python- Django, and varnish), and Ubuntu (schroot). # § Integrity/Availability/Authenticity⠀➾ # ⚓ SequoiaPGP ☛ sq_User_Testing_Results⠀⇛ I did some user testing of sq with five volunteers. This blog post is a report of what I learned. Good news: everyone did get all the tasks done successfully and within the one hour I had allocated, with plenty of time left over. Of course, there were a few things that could be improved. # § Privacy/Surveillance⠀➾ # ⚓ Scoop News Group ☛ Most_top_mobile_carriers_retain geolocation_data_for_two_years_on_average,_FCC_findings show⠀⇛ Ten of the top 15 mobile carriers collect geolocation data and provide no way for consumers to opt-out, according to information from the telecom companies the Federal Communications Commission published Thursday. The carriers’ answers to questions about data collection and retention from the FCC come in response to a July request from the agency seeking information on geolocation practices in light of concerns about how law enforcement could use phone data to arrest abortion-seekers in states where the procedure is now illegal or will soon be outlawed. # ⚓ Silcon Republic ☛ Norway_reportedly_wants_to_fine Meta_for_illegal_data_transfers⠀⇛ While Norway is not a member of the EU, it is part of the European Economic Area which has incorporated GDPR. The proposal was a response to a draft ruling issued by the Irish Data Protection Commission (DPC) to other EU regulators last month, following an investigation into whether Meta’s transatlantic data-sharing practices comply with EU rules. A final ruling could force Meta to halt data transfers between the EU and US. # ⚓ DaemonFC (Ryan Farmer) ☛ Your_bank_and_other_Web sites_are_running_creepy_JavaScript_that_records_your every_action._NoScript_can_block_that_from_running. Bonus:_“Web_Rot”_|_BaronHK’s_Rants⠀⇛ Your bank and other Web sites are running creepy “Session-Replay” JavaScript that follows you around the site recording your every movement. You’re not “supposed to know” about this, but NoScript can block that from running. I had a conversation with Matthew Garrett (alleged security person, actual drama bomb thrower) on IRC the other day about the “security” of JavaScript. He had previously promoted it as a “great way of running untrusted code”. Unfortunately, there’s just nothing secure about JavaScript. It’s the most widely abused platform in all of computing because almost everyone ends up running it without thinking of the consequences, and browsers which are instructed to do so, do it without bothering to allow any user control over the process in their default state. If you can’t trust code, it’s better to not have it running at all. Especially if it’s not doing anything to help you, and is proprietary. Garrett said that “total sandbox escapes” where the program gets out of your browser sandbox and starts interfering with another tab or running arbitrary malicious code outside of any sort of confinement is “rare” to the point where someone would need to be “targeting you” and willing to blow a Zero Day exploit to do it. o § Defence/Aggression⠀➾ # ⚓ ABC ☛ Bali_bombmaker_Umar_Patek_records_on-camera_interview from_Indonesian_jail⠀⇛ Patek was filmed in recent days walking through the jail grounds at Porong in East Java, chatting with the prison governor, both men smiling and laughing together on camera as he casually discusses his role in the terror attacks, which killed more than 200 people. # ⚓ Nature ☛ Global_food_insecurity_and_famine_from_reduced crop,_marine_fishery_and_livestock_production_due_to_climate disruption_from_nuclear_war_soot_injection⠀⇛ In conclusion, the reduced light, global cooling and likely trade restrictions after nuclear wars would be a global catastrophe for food security. The negative impact of climate perturbations on the total crop production can generally not be offset by livestock and aquatic food (Fig. 5a). More than 2 billion people could die from a nuclear war between India and Pakistan, and more than 5 billion could die from a war between the United States and Russia (Table 1). The results here provide further support to the 1985 statement by US President Ronald Reagan and Soviet General Secretary Mikhail Gorbachev and restated by US President Joe Biden and Russian President Vladimir Putin in 2021 that ‘a nuclear war cannot be won and must never be fought’. # ⚓ New York Times ☛ The_Zaporizhzhia_nuclear_plant_was_cut_off from_Ukraine’s_grid,_leading_to_outages,_officials_say.⠀⇛ An off-site power supply from the electricity grid is essential for ensuring nuclear safety, the director, Rafael Marino Grossi, said in a statement. The plant has diesel generators and a separate coal-fired plant to provide backup power if it loses external power, he noted. Backup power is required to ensure the continued operation of cooling systems that remove heat from the reactors. Without cooling, the nuclear fuel could overheat and melt down, potentially releasing radiation. # ⚓ BBC ☛ How_many_people_cross_the_Channel_in_small_boats?⠀⇛ As at 22 August, 22,557 migrants had made the crossing in small boats since the start of the year. [...] The government wants to send to Rwanda those who arrive in the UK through “illegal, dangerous or unnecessary methods”, such as on small boats or hidden in lorries, when they could have claimed asylum in another safe country such as France. # ⚓ The Telegraph UK ☛ Dozens_more_Channel_migrants_land_in Kent_as_total_this_year_nears_25,000⠀⇛ It comes as people smugglers are offering “TikTok Black Friday” cut-price Channel deals to Albanians to beat a Government crackdown ahead of the bank holiday. Gangs are advertising on the social media platform with offers as low as £3,000 per migrant to cross the Channel, at least 40 per cent cheaper than the “standard” rates of around £5,000 to £5,500. # ⚓ ABC ☛ New_Mexico_man_charged_with_supporting_Islamic_State group⠀⇛ Federal prosecutors believe Wilson was trying to establish an “Islamic State Center” in New Mexico that would teach Islamic State group ideology, provide martial arts training and serve as a haven for people preparing to fight for the group in the U.S. and abroad. # ⚓ Scheerpost ☛ Why_the_US_and_Israeli_Right_Really_Hate_the Iran_Nuclear_Deal⠀⇛ Juan Cole explores what right-wingers in both countries actually want to happen in Iran. # ⚓ Common Dreams ☛ Opinion_|_Will_Six_Months_of_War_in_Ukraine Turn_Into_Six_Years?⠀⇛ President Joe Biden announced Wednesday that Washington will fund an additional $3 billion in military aid for Ukraine. On the surface, this may seem like business as usual. After all, the United States has sent 19 separate tranches of military support since the war began, and Congress has already approved funding for at least another $10 billion worth of arms. # ⚓ Counter Punch ☛ The_Death_of_Daria_Dugina:_Moscow’s Invocation_of_Terrorism_is_More_Than_Chutzpah⠀⇛ Russian state television called the incident a “terrorist attack.” That terminology implies an act in violation of existing rules. A dictionary definition of terrorism is “The unlawful use of violence and intimidation, especially against civilians, in the pursuit of political aims.” o § Environment⠀➾ # ⚓ BBC ☛ Tyre_Extinguishers:_Activists_deflate_SUV_tyres_in Leeds_in_climate_protest⠀⇛ The group left leaflets on windscreens telling owners their “gas guzzler kills” and “SUVs and 4x4s are a disaster for our climate”. # ⚓ [Old] Tyre_Extinguishers_target_SUVs_on_home_turf_of_the ‘Chelsea_Tractor’⠀⇛ Tyre Extinguishers, the direct action group calling for SUVs to be banned from cities, have struck again, targeting 30 vehicles in London’s upscale Cheyne Walk area in the district of the capital that gave 4x4s their ‘Chelsea Tractor’ nickname. # ⚓ TruthOut ☛ The_Inflation_Reduction_Act_Is_a_Disappointing Act_of_Federal_Greenwashing⠀⇛ # ⚓ TruthOut ☛ Climate-Fueled_Wildfires_Are_Depleting_the_Ozone Layer,_New_Study_Shows⠀⇛ # ⚓ TruthOut ☛ Poor_Countries_Are_Suffering_the_Worst_Climate Woes_But_Getting_the_Least_Help⠀⇛ # ⚓ Counter Punch ☛ America’s_Summer_of_Floods⠀⇛ Floods are complex events, and they are about more than just heavy rain. Each community has its own unique geography and climate that can exacerbate flooding, so preparing to deal with future floods has to be tailored to the community. # ⚓ Counter Punch ☛ How_Drought_and_Growth_Threaten_the_Waters of_the_Northern_Rockies⠀⇛ The government spends millions on studies while avoiding decisive action. In Utah, ten million to study why the isolated Great Salt Lake is turning into a puddle. Hundreds of millions to figure out how to stop the Lake Mead and Powell reservoirs from becoming dead pools. The answers are clear. Forty million people rely on the Colorado system along with 10 million cows and there isn’t enough water to go around. Yet states and cities promote more growth. The water subsidy required would put other areas of the country at risk of more impoundments, mega-pipelines and shipments of water. Action is needed now to protect our water at its source as part of an interconnected ecological system. # § Energy⠀➾ # ⚓ JURIST ☛ California_approves_regulation_phasing_out gasoline-powered_car_sales_by_2035⠀⇛ The California Air Resources Board (CARB) approved Advanced Clean Cars II rule on Thursday making California the first state to prohibit sales of new gasoline-powered cars. The rule sets out a roadmap whereby 100% of new cars and light trucks sold in the state will be zero emission vehicles (ZEVs), including plug-in hybrids. The regulation codifies Governor Gavin Newsom’s light-duty vehicle goals set forth in Executive Order N-79-20 and requires automobile manufacturers to deliver an increasing number of ZEVs and plug-in hybrid vehicles (PHEVs) each year beginning in 2026. Specifically, sales targets of new ZEVs and PHEVs are set at 35% in 2026, increasing to 68% in 2030 and ultimately 100% in 2035. # ⚓ Hackaday ☛ Hackaday_Prize_2022:_Compact_Solar Tracking_System_Doesn’t_Break_The_Bank⠀⇛ If you need to squeeze every available watt out of a solar panel, you’ll probably want to look into a solar tracking system. Unfortunately, they are usually quite large, heavy, and expensive. As an alternative, [JP Gleyzes] has put together a DIY solar tracking system that aims to address these issues. # § Overpopulation⠀➾ # ⚓ JURIST ☛ Bangladesh_dispatch:_‘A_silent_famine_is prevailing_across_Bangladesh_as_food_and_commodity prices_soar_to_record_highs.’⠀⇛ Many of us may have heard about the so-called domino effect in which one event causes a series of like events to happen one after another. Currently, we hear talk of a domino effect in South Asian countries. After the dreadful economic and political crisis in Sri Lanka, experts fear that other countries in this region may face a similar situation. Unfortunately, Bangladesh is on this list of countries. Why do experts fear this? The question is even more interesting because South Asian country’s $416 billion economy has been one of the fastest-growing in the world for years. In fact, in November 2021, the United Nations decided to strike Bangladesh off its list of the world’s least developed nations. # ⚓ The Daily Star ☛ Bringing_population_back_into_the conversation⠀⇛ At present, the country has more than 167 million people, but strangely, the topic of “overpopulation” or “population explosion” receives little attention. Moreover, some quarters in our country tend to see this large population as an economic asset. There is no denying the fact that the population of a country is the greatest social capital a nation can have, but unchecked population growth can be detrimental to economic development. Some empirical studies have found that an unchecked rising population comes with several economic and social challenges. It diminishes the availability of capital per head by limiting access to food, housing, sanitation, healthcare, education and employment, which in turn reduces the productivity of its labour force. It often has devastating effects on the environment as well. # ⚓ Climate_Change:_Are_we_heading_towards_extinction?⠀⇛ Dire environmental consequences are happening in Africa and measures and initiatives are being attempted in this regard by the United Nations Environmental Programme (UNEP) within the theme ‘Only One Earth’. Communities around the globe have observed World Environment Day on June 5 by putting environmental concerns in the spotlight. This effort is now considered as the UN’s primary platform to promote action for the protection of the environment by raising awareness on issues such as human overpopulation, marine pollution, global warming, wildlife crime and sustainable consumption. Celebrated annually by more than 150 countries worldwide, the day is a global platform for environmental outreach, to also showcase initiatives at the country and global level in the promotion of environmental health. # ⚓ Chatham Asset Management ☛ Letter:_Overpopulation_is cause_of_every_environmental_problem_we_face⠀⇛ As any good doctor can tell you, treating symptoms can make you feel good for a while, but if you don’t treat the disease it will eventually kill you. o § Finance⠀➾ # ⚓ Common Dreams ☛ Opinion_|_Organizers_Have_Fought_for_Debt Cancellation_for_Over_a_Decade—and_Their_Work_Is_Far_From Finished⠀⇛ Following over a decade of activism against the United States’ massive student debt crisis, President Biden announced a plan on Wednesday to cancel a significant amount of student loan debt for tens of millions of low and middle-income Americans. # ⚓ Counter Punch ☛ Biden’s_Student_Debt_Forgiveness_Plan:_Good Enough_for_Government_Work?⠀⇛ To clarify, the plan gives $10,000 of student loan forgiveness to people earning less than $125,000 a year. That probably excludes our Harvard Business School graduate. # ⚓ Common Dreams ☛ Sanders_Derides_GOP_for_‘Squawking’_About Debt_Relief_But_Not_Handouts_to_Billionaires⠀⇛ In response to GOP claims that forgiveness of $10,000 in student debt for most borrowers would be “unfair,” the Vermont senator told ABC’s George Stephanopoulos that “60% of the benefits go to people who are on Pell Grants” and “87% of the benefits go to people making $75,000 a year [or less].” # ⚓ Counter Punch ☛ Can_a_Deeply_Unequal_Nation_Totally_Reverse Course?⠀⇛ # ⚓ Telex (Hungary) ☛ The_number_of_Hungarians_working_in Austria_reaches_historic_high⠀⇛ o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ ‘You_are_next’:_Twitter_ignores_sick_death_threat_against JK_Rowling_from_Islamic_extremist⠀⇛ Afterward, Rowling shared an update from Twitter expressing that no standards had been broken corresponding to Aziz’s message after it had inspected the realities accessible. “[email protected] These are your principles, right? Rowling created. Savagery: You are not permitted to take steps to utilize viciousness against a particular individual or gathering of people. The advancement of savagery is additionally taboo. “Psychological warfare/fierce fanaticism: You may not compromise or supporter illegal intimidation,” it peruses. # ⚓ Consortium News ☛ JOHN_KIRIAKOU:_Don’t_Charge_Trump_With Espionage⠀⇛ Nobody should be charged with espionage unless they are working for a foreign power and mean harm to the United States. The Espionage Act, which was written 105 years ago to combat German saboteurs, is rarely used now to target spies and traitors. Instead, it’s used as a cudgel to silence whistleblowers, journalists, and occasionally a stupid former president. To understand the damage that this deeply flawed law has done, and will continue to do, we have to look at its origins. The Espionage Act was written in 1917, at the height of World War I. The U.S. was panicked at the thought of German spies working undercover to steal its secrets and to disrupt its ability to produce war materiel and support its allies. # ⚓ Salon ☛ Truth_Social_is_headed_for_bankruptcy⠀⇛ As the report points out, Truth Social has not been paying for web-hosting fees to the point where attorneys are now involved, traffic is collapsing, the value of stock in the company is plunging and money is running out. # ⚓ TruthOut ☛ Dark_Money_Groups_Are_Scheming_to_Bring_Down Biden’s_Student_Debt_Relief_Plan⠀⇛ # ⚓ Common Dreams ☛ Republican_AGs,_Dark_Money_Groups_Scheme_to Sue_Over_Student_Debt_Relief⠀⇛ “Conservative jurists, and ultimately the justices themselves, will be eager to shred the new program.” # ⚓ Counter Punch ☛ Will_the_Democrats_Manage_to_Help_Re-Elect Trump?⠀⇛ I learned about this furious row because I knew a Canadian paper magnate who had bought a house close to Mar-a-Lago at about the same time as Trump. My friend was bitter that the agency that sold him the property had carefully timed his visit for a moment in the afternoon when there were no planes flying directly overhead. # ⚓ Counter Punch ☛ Weaponizing_Charity_to_Advance_a_Political Agenda⠀⇛ # ⚓ Counter Punch ☛ Could_Liz_Cheney_Initiate_a_New Conservative_Party?⠀⇛ Elie Mystal of the Nation points out that Republicans rejected Cheney because “white conservative voters trash everything to keep themselves in power.” In other words, the core Republican base will not support any candidate who fails to address their fears of being replaced by others. # § Misinformation/Disinformation⠀➾ # ⚓ Gannett ☛ Michigan_students_connected_to_TikTok, Snapchat_—_and_learning_is_suffering,_teachers_say⠀⇛ Saidi, a teacher at Salina Intermediate in Dearborn, started to notice students becoming less engaged in school long before the pandemic, particularly with the rise of smartphones and social media. # ⚓ New York Times ☛ A_Journey_Into_the_Misinformation Fever_Swamps⠀⇛ Several of my colleagues here at The New York Times track the trends and shifting tactics of these fraudsters on their daily beats. So I exchanged messages this week with Sheera Frenkel, Tiffany Hsu and Stuart A. Thompson, all three of whom spend their days swimming in the muck brewed by fake news purveyors here and abroad. Our conversation, lightly edited for length and clarity: [...] o § Censorship/Free Speech⠀➾ # ⚓ BBC ☛ Google_‘airbrushes’_out_emissions_from_flying,_BBC reveals⠀⇛ Flights now appear to have much less impact on the environment than before. That’s because the world’s biggest search engine has taken a key driver of global warming out of its online carbon flight calculator. # ⚓ JK_Rowling_compared_to_murderer,_Nazi_collaborator_and creepy_cult_leader_by_woke_website⠀⇛ Rowling, 57, has been a strong supporter of women’s rights and has rallied against the use of terms that excludes ‘female’ or ‘women’. She has also criticised the Scottish Government’s Gender Recognition Reform Bill, which has been heavily criticised by women’s rights groups. The Bill will make it easier for people to legally change gender. # ⚓ Modern Ghana ☛ Ordering_Oyerepa_FM/TV_to_shut_down_an_act of_censorship_–_Sulemana_Braimah⠀⇛ The Executive Director of the Media Foundation for West Africa (MFWA), Sulemana Braimah does not side with an order for Kumasi-based Oyerepa FM and TV to temporarily shut down over comments made by the founder of the United Progressive Party, Akwasi Addai Odike on the platform. Mr. Braimah argued that the order forms part of attempts to muzzle the independence of the media house in question. # ⚓ Gannett ☛ Critics_of_Larry_Arnn_should_oppose_laws censoring_Tennessee_educators_|_Opinion⠀⇛ Now, Tennesseans should do even more to defend their educational professionals. Arnn may be the only person who’s called Tennessee educators “dumb,” but he’s not the only one insulting them. As part of my job, I talk to teachers in Tennessee and across the United States. Right now, many of them feel hurt, insulted and afraid because of the avalanche of educational gag orders sweeping the country. # ⚓ Gannett ☛ A_Michigan_town_may_lose_its_only_library_after its_staff_refused_to_remove_an_LGBTQ_book⠀⇛ When a library staff in a west Michigan township refused to remove its books containing LGBTQ themes, residents voted to defund their only library. # ⚓ Ex-Iran_vice-president_living_in_UK_says_‘I’m_not_to_blame for_Rushdie_stabbing’⠀⇛ In his 1989 book backing Rushdie’s death sentence over his “blasphemous” novel, Mohajerani wrote “whoever insults the prophet deserves to be killed”. # ⚓ Facebook_Tells_Moderators_to_Allow_Graphic_Images_of Russian_Airstrikes_but_Censors_Israeli_Attacks⠀⇛ # ⚓ The Guardian UK ☛ How_to_shut_down_the_internet_–_and_how to_fight_back [Ed: The Guardian does a lot of censorship for the British government and rich "sponsors" like Bill Gates, so that's rich]⠀⇛ # ⚓ The Guardian UK ☛ Flicking_the_kill_switch:_governments embrace_internet_shutdowns_as_a_form_of_control [Ed: The Guardian shows its sheer hypocrisy, posting as champion of free speech whilst attacking it]⠀⇛ # ⚓ The Guardian UK ☛ When_internet_shutdowns_spill_over borders [Ed: NSA took down the Internet in the whole of Syria]⠀⇛ o § Freedom of Information / Freedom of the Press⠀➾ # ⚓ Counter Punch ☛ It’s_All_Political:_Julian_Assange_Appeals his_Extradition⠀⇛ Along this potted judicial road, Assange chalked up a qualified success before District Court Judge Vanessa Baraitser on January 4, 2021, who held that he would be at serious risk of suicide occasioned by the effects of Special Administrative Measures and confinement in the ADX Florence supermax facility in Colorado.  This was deemed oppressive within the meaning of the US-UK Extradition Treaty.  The most obvious aspect of the prosecution – its self-evidently political nature – was given little thought. o § Civil Rights/Policing⠀➾ # ⚓ Six_Months_with_Android:_A_journey_from_a_blind perspective⠀⇛ During the last six months, I’ve used Android exclusively as my primary device. I made calls with it, texted with it, read emails with it, browsed the web, Reddit, Twitter, and Facebook with it, and played games on it. Now, I’m going to express my thoughts on it, its advancements, and its issues. This will contain mostly opinions, or entirely opinions, depending on whether you really love Android or not. But whatever your stance, these are my experiences with the operating system. My issues may not be your issues, and so on. # ⚓ JURIST ☛ Former_Kentucky_police_detective_pleads_guilty_to falsifying_warrant_affidavit_that_led_to_death_of_Breonna Taylor⠀⇛ The US Department of Justice announced Tuesday that a former Louisville, Kentucky detective has pleaded guilty to two separate federal charges. Detective Kelly Goodlett admitted that she conspired to falsify an affidavit to obtain a warrant to search Breonna Taylor’s home without probable cause and that, after the search resulted in Taylor’s death, she also conspired to cover up the illegal warrant by lying to investigators. According to her plea agreement, Goodlett acknowledged that she assisted another LMPD detective and their unit supervisor in efforts to obtain a warrant to search Taylor’s home despite knowing that they lacked any probable cause to do so. In order to establish probable cause for the affidavit, the group knowingly created information that was false, misleading, and stale. # ⚓ ABC ☛ Fanta_Bility’s_family_reflects_on_grief_1_year_after 8-year-old_was_fatally_shot_by_police⠀⇛ Fanta was shot while exiting a football game with her family at Academy Park High School on Aug. 27, 2021, when officers Brian Devaney, Devon Smith and Sean Dolan fired their weapons toward the crowd after two teens opened fire in a personal dispute close to the high school, according to Delaware County District Attorney Jack Stollsteimer. # ⚓ TruthOut ☛ Disappointed_in_Biden’s_Inaction,_Immigrant Rights_Advocates_Look_to_the_States⠀⇛ # ⚓ TruthOut ☛ UPS_Workers_Say_Union_Activists_Are_Being Targeted_Amid_Contract_Negotiations⠀⇛ # ⚓ Counter Punch ☛ To_Democrats:_Make_Labor_Day_A_Workers’ Action_Day⠀⇛ Never mind the dwindling Labor Day parades. Instead, organize rallies and assemblies in neighborhoods around real reforms, redirections and respect that all workers (regardless of their political labels) want for themselves and their families. # ⚓ Common Dreams ☛ Opinion_|_With_Rights_Under_Assault,_We Must_Create_a_Feminism_That_Promotes_Egalitarian_Values⠀⇛ One of the most liberating moments of my young life was when, at age 14, the school dress code finally loosened to the point where it ceased to exist (this was 1968.) I had always hated the compulsory skirts and knee socks that allowed the cold wind to freeze us girls as we walked to and from school. I definitely felt more comfortable in every way in my ratty, ripped jeans that I wore to school the minute I was able. # ⚓ Counter Punch ☛ Life_Isn’t_Fair._Get_Over_It.⠀⇛ Wolf starts with a cynical view of the American people: “But the overriding question for a lot of people who didn’t go to college, those who already paid off their loans or folks who make more than $125,000 (or more than $250,000 if they’re married couples or heads of households) is this: What about me?” How disgusting. Only Wolf is this selfish. The American people love one another and we love when our neighbor is helped. Fuck your fairness. # ⚓ AccessNow ☛ Saudi_authorities_must_release_women’s_rights activist_Salma_al-Shehab⠀⇛ We, the undersigned NGOs, call on the international community to press Saudi Arabian authorities to immediately and unconditionally release women’s rights activist and academic Salma al-Shehab, who was recently sentenced to 34 years in prison based on tweets in support of women’s rights and for the respect of basic rights. It is the longest known prison sentence handed down against a peaceful activist for their free speech in Saudi Arabia, signalling an alarming deterioration of the human rights situation in the country. Al-Shehab, a 34-year-old mother of two children, is a dental hygienist and PhD student at Leeds University in the United Kingdom, where she was residing before her detention. She was arrested on 15 January 2021 while on holiday in Saudi Arabia, and subjected to solitary confinement and lengthy sessions of questioning over a period of nine and a half months before being brought before the Specialised Criminal Court (SCC), a court used as an instrument of repression to silence dissent in the kingdom. Al-Shehab belongs to the country’s Shi’a Muslim minority, who have long suffered from the government’s repression. # ⚓ AccessNow ☛ Free_Salma_al-Shehab,_Saudi’s_Twitter_activist! Even_Big_Tech_has_a_role_to_play⠀⇛ Saudi Arabian authorities must immediately and unconditionally release women’s rights activist and academic Salma al-Shehab — and all other prisoners locked up for free expression — and put an end to their oppressive regime of human rights abuses. Big Tech must play its part by ensuring human rights are at the core of any business dealings in the kingdom. In a joint statement, Access Now and civil society organizations from across the globe strongly condemn the arbitrary arrest and unlawful sentencing of Salma al-Shehab — “the longest known prison sentence handed down against a peaceful activist for their free speech in Saudi Arabia, signalling an alarming deterioration of the human rights situation in the country.” “A woman born into a totalitarian landscape dared to speak out — via Twitter. Now Saudi authorities plan on snatching the rest of her life away. Civil society says, unequivocally, no to this,” said Marwa Fatafta, MENA Policy and Advocacy Manager at Access Now. “We demand the Saudi Crown Prince Mohammed bin Salman immediately release Salma al- Shehab, and put an end to persecuting all activists.” o § Internet Policy/Net Neutrality⠀➾ # ⚓ Moving_blog_from_blogger.com_to_wordpress.com_– formicapunk⠀⇛ I switched from blogger.com the Google Blog platform to the hosted wordpress.com of Automaticc, the WordPress blog engine main authors. [...] On the personal side, I also intend to pause twitter activity, as I notice current microblogging platforms tend to mostly contain flame wars, self promotion, or shared links I could find anyway with a good feed reader. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ Torrent Freak ☛ YouTube_Holds_Licenses_For_Copyright Lawsuit_Plaintiff’s_“Entire_Back_Catalog”⠀⇛ YouTube says it will seek summary judgment to shut down a lawsuit headed by musician Maria Schneider which alleges mass copyright infringement. YouTube’s motion reveals that Schneider’s publisher granted YouTube a blanket license covering the musician’s entire back catalog, but that’s just the beginning. # ⚓ Torrent Freak ☛ Dash_the_Iranian:_Busted_Pirate_IPTV Kingpin_Allegedly_Owns_RapidIPTV⠀⇛ In June 2020, a massive international law enforcement operation targeted an IPTV provider servicing two million subscribers. Millions of euros in assets were seized and authorities arrested the alleged kingpin. Known to colleagues as “Dash the Iranian” the businessman faces a legal nightmare. But what about the fate of the giant piracy service at the center of his prosecution? * § Gemini* and Gopher⠀➾ o § Personal⠀➾ # ⚓ The_disease_called_“Perfection”⠀⇛ This post is by Single Dad Laughing. I found it in 2010 (or thereabouts) and it was transformative in helping me be more at peace with myself and the world around me. He gives permission to share it, so I wanted to preserve it here in the smolweb because it feels important and evergreen. [...] We live in communities where people feel unconquerable amounts of pressure to always appear perfectly happy, perfectly functional, and perfectly figured. “Perfection” is much different than perfectionism. The following examples of “Perfection” are all real examples that I have collected from experiences in my own life, from confidential sources, or from my circle of loved ones and friends. If you actually stop to think about some of these, you will probably cry as I admittedly did while writing it. If you don’t, maybe you’re infected with a little too much of this “Perfection” infection. “Perfection” is a wife who feels trapped in a marriage to a lazy, angry, small man, but at soccer practice tells the other wives how wonderful her husband always is. “Perfection” keeps people from telling the truth, even to themselves. My husband is adorable. He called me a whore this week because I smiled at a stranger. When I started crying, he said he had a game to go watch. I love him so much. # ⚓ Verstappen_makes_everyone_look_foolish⠀⇛ Verstappen qualified with a huge advantage, got put back to 15th with penalties, and still had an easy win. Everything was working for him this weekend. He could have won if he’d started last. It was quite impressive. It doesn’t really matter what happened to the others. # ⚓ AUMORTI_Wordo:_BRIDE⠀⇛ # ⚓ Ancom_2022?⠀⇛ This is a follow-up to Ancom 2020? where I argued that the 2007 IPCC shook my ancom foundations. There’s another problem that’s come up more and more these last few years: the tension between autonomy and human rights. The federalism component of ancom was that every workplace, every village, every city block should be autonomous. The drawback of that view is that the bar for how humans treat each other can get placed a li’l too low and things like systematic racism can thrive. We’ve all seen the old “states rights” arguments that tramples human dignity in the name of autonomy. o § Technical⠀➾ # ⚓ Why_Not_Oberon?⠀⇛ OberonStation was a tiny computer with a VGA output and ports for keyboard and mouse. It booted into Oberon in under a second, and featured an SD-card slot and ton of ports. It seemed like an ideal computer, the kind I always blab about. Not a trace of Intel inside – just a simple (too simple, perhaps) RISC CPU, fully described in the documentation, designed for the sole purpose of running compiled Oberon. But then I tried to write some simple code. =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It’s like the World Wide Web but a lot lighter. ䷩ 𝚕𝚒𝚗𝚎 5869 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 08.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_28/08/2022:_Linux_6.0_RC3_and_MX-21.2⠀✐ Posted in News_Roundup at 2:07 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Audiocasts/Shows o Kernel_Space o Instructionals/Technical o WINE_or_Emulation o Desktop_Environments/WMs # GNOME_Desktop/GTK * Distributions_and_Operating_Systems o Reviews o New_Releases o Red_Hat_/_Fedora_/_IBM o Debian_Family o Devices/Embedded o Open_Hardware/Modding o Mobile_Systems/Mobile_Applications * Free,_Libre,_and_Open_Source_Software o Web_Browsers # Mozilla o Programming/Development # Perl_/_Raku * Leftovers o Science o Health/Nutrition/Agriculture o Security # Privacy/Surveillance o Environment # Energy o Finance o AstroTurf/Lobbying/Politics o Civil_Rights/Policing o Internet_Policy/Net_Neutrality * Gemini*_and_Gopher o Personal o Politics o Technical # Science # Internet/Gemini # Programming * § GNU/Linux⠀➾ o ⚓ 9to5Linux ☛ 9to5Linux_Weekly_Roundup:_August_28th,_2022_– 9to5Linux⠀⇛ The 9to5Linux Weekly Roundup for August 28th, 2022, brings news about Linux’s 31st birthday, Firefox 104, new Linux computers, NetworkManager 1.40, KDE Plasma 5.25 in Kubuntu 22.04 LTS, as well as all the latest distro and software releases. o ⚓ Linux Made Simple ☛ Linux_Weekly_Roundup_#197⠀⇛ Welcome to this week’s Linux weekly roundup. We had a peaceful week in the world of Linux distro and application releases, with no major release. I see it as the “calm before the storm”. May you have a wonderful week and see you in the Autumn. o ⚓ Linux Links ☛ Linux_Around_The_World:_Finland_–_LinuxLinks⠀⇛ We cover events and user groups that are running in Finland. This article forms part of our Linux Around The World series. o § Audiocasts/Shows⠀➾ # ⚓ Adafruit ☛ Receiving_Weather_Satellites_on_a_Raspberry_Pi or_Linux_«_Adafruit_Industries_–_Makers,_hackers,_artists, designers_and_engineers!⠀⇛ This NOAA Weather satellite setup on a Raspberry PI 4 using Raspberry OS either 32 or 64 bit was shared by TekMaker on Youtube! # ⚓ Video ☛ Valve_are_cool,_Janet_kills_hard_drives,_Bug zappers_and_BeReal_app_–_A_Trendy_Talk_–_Invidious⠀⇛ # ⚓ Video ☛ LastPass_Password_Manager_|_Security_Breach_– Invidious⠀⇛ # ⚓ Video ☛ Neovim_112:_Command-T_–_Invidious⠀⇛ # ⚓ Open Source Security (Audio Show) ☛ Episode_338_–_The government_didn’t_make_vulnerabilities_illegal._Yet._–_Open Source_Security⠀⇛ Josh and Kurt talk about the recent National Defense Authorization Act that requires security vulnerabilities to be fixed. What does this mean for us, is it as bad as some people are claiming it is? It’s actually not a huge deal, for most of us it’s really just time to deal with product security. # ⚓ Linux Made Simple ☛ How_to_install_Shadow_PC_on_a Chromebook⠀⇛ Today we are looking at how to install Shadow PC 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. # ⚓ Video ☛ How_to_install_FreeOffice_on_Pop!_OS_22.04_– Invidious⠀⇛ In this video, we are looking at how to install FreeOffice on Pop!_OS 22.04. # ⚓ GNU World Order (Audio Show) ☛ GNU_World_Order_475⠀⇛ **kile and LaTeX** , **killbots** , **kimageformats** from the Slackware **kde** package set. o § Kernel Space⠀➾ # ⚓ Linux_6.0-rc3⠀⇛ So as some people already noticed, last week was an anniversary week - 31 years since the original Linux development announcement. How time flies. But this is not that kind of historic email - it's just the regular weekly RC release announcement, and things look pretty normal. We've got various fixes all over the tree, in all the usual places: drivers (networking, fbdev, drm), architectures (a bit of everythinig: x86, loongarch, arm64, parisc, s390 and RISC-V), filesystems (mostly btrfs and cifs, minor things elsewhere), and core kernel code (networking, vm, vfs and cgroup). And some tooling support (perf and selftests). We've got a few known issues brewing, but nothing that looks all that scary. Knock wood. Please give it a go, Linus # ⚓ LWN ☛ Kernel_prepatch_6.0-rc3_[LWN.net]⠀⇛ The 6.0-rc3 kernel prepatch is out for testing. o § Instructionals/Technical⠀➾ # ⚓ Data Swamp ☛ Solene’%_:_Using_nix_download_bandwidth_limit feature⠀⇛ I submitted a change to the nix package manager last week, and it got merged! It’s now possible to define a bandwidth speed limit in the nix.conf configuration file. # ⚓ 15+_RPM_Commands_with_Examples_in_Linux_–_LinuxWizardry⠀⇛ The RPM Package Manager (RPM) is an open packaging system used in Red Hat Linux and its distributions such as CentOS and Fedora. An RPM Package contains archive files and metadata including dependencies and installs location. An RPM package has a .rpm file format. rpm command is used to install, update, remove, verify, query, and manage RPM packages. This tutorial will demonstrate different examples of rpm commands in RHEL-based Linux systems. # ⚓ How_to_Install_Chrome_on_Ubuntu_–_Linux_Stans⠀⇛ In this tutorial, we’re going to show you how to install Chrome on Ubuntu. This tutorial was tested on Ubuntu 22.04, but it will work on other Ubuntu releases and Ubuntu derivatives. Google Chrome is one of the most popular browsers for all OSes, including Linux. Firefox is pre- installed by default on Ubuntu. If you want to install Chrome, you’ll have to do it manually, it’s not available in the Ubuntu Software center. If you need other recommendations for browsers on Linux, check out The 4 Best Linux Browsers I’ve Used in 2022 and Top 5 Most Secure Browsers for Linux # ⚓ ID Root ☛ How_To_Install_Telegram_on_Linux_Mint_21_– idroot⠀⇛ In this tutorial, we will show you how to install Telegram on Linux Mint 21. For those of you who didn’t know, Telegram is the free instant messaging application that can be used to connect to friends, family, and relatives. With Telegram you can send and receive text & voice messages, multimedia files like images and videos, as well as make and receive video calls. Telegram is available for Linux, Android, Windows Phone, iOS, and macOS. 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 Telegram messenger on Linux Mint 21 (Vanessa). # ⚓ XDA ☛ How_to_install_Python_on_Windows,_Linux,_and_macOS⠀⇛ If you want to get into development, one of my favorite programming languages that I’ve learned is Python. It’s a multi-paradigm language, supporting imperative, functional, procedural, and object- oriented programming. It’s wide open and can be used for practically anything, and is a go-to language for many when working in artificial intelligence or machine learning. I use it for a lot of automation, and it’s even the language that some of the testing tools that we’ve used are written in. Python is a powerful language, and if you want to get started with it, this guide will teach you the basics. Not only will you need to install the Python binaries and ensure that it’s in your PATH, but you’ll also need something to actually write code in. You could use a full-fledged IDE (Integrated Development Environment) like PyCharm, or you could lean towards a text editor such as the pre-installed IDLE or Sublime Text 3. There are a lot of options, but this guide should kick-start you on the basics. # ⚓ 10+_Seq_Commands_with_Examples_in_Linux_–_LinuxWizardry⠀⇛ seq command prints a sequence of numbers in Linux. It is super-fast in generating a list of sequential numbers. The output of seq command can be piped to various other commands for additional functionality. The seq command is also useful in for loops and bash scripts. This article will discuss different examples of the seq command to print a sequence of numbers in the Linux system. o § WINE or Emulation⠀➾ # ⚓ Neowin ☛ Wine_7.16_arrives_two_days_late,_brings_game enhancements_–_Neowin⠀⇛ In a world where Valve’s Proton dominates gaming headlines, it’s hard to remember that it would be nothing without the forward progress of Wine. Wine 7.16 was released this morning, breaking with its tradition of releasing every other Friday. It’s the latest on the march toward 8.0 which is due out later this year. Thankfully, we don’t have to wait for version 8.0 to benefit from lots of meaningful fixes. o § Desktop Environments/WMs⠀➾ # § GNOME Desktop/GTK⠀➾ # ⚓ OMG Ubuntu ☛ ‘Nephrite’ is_a_Classy_New_GTK_Theme_for Linux_Desktops_–_OMG!_Ubuntu!⠀⇛ One of Linux desktop’s most prolific — not to mention best, imo — theme makers has released a brand new GTK theme for us all to go gaga over. Designer Vince Liuice’s latest creation is called Nephrite, and it was made available to download from Pling and from GitHub this weekend. Nephrite maintains the high quality this theme maker is famed for, and the theme looks pixel perfect on my high resolution display, i.e. no blurry corners or pixelated edges some themes inadvertently offer. Always one for options, Vince has made the Nephrite theme available in light, dark, and mixed versions. All come paired with a calming teal accent colour by default, making it the ideal compliment to Vince’s Colloid icon theme. * § Distributions and Operating Systems⠀➾ o § Reviews⠀➾ # ⚓ Distro Watch ☛ Review:_Qubes_OS_4.1.1_and_Alchg_Linux⠀⇛ Qubes OS is an unusual project which strives to perform two difficult tasks in parallel. First, it attempts to isolate various tasks and elements of the operating system to prevent the compromising of one component from affecting other components. Second, it attempts to make this experience virtually seamless for desktop users. The idea here is that the user should be able to use their applications in a way which allows each application (or a group of applications) to be isolated from the rest of the system. If our web browser is hijacked it shouldn’t give access to our office documents, for example. I downloaded the latest version of Qubes OS, which is provided as a 5.4GB ISO for 64-bit (x86_64) computers. Booting from this ISO displays a boot menu where we can immediately launch the system installer or run a self-check on the media and then start the install process. There is no option to launch a live desktop environment. By default, Qubes runs Fedora software. This includes getting up and running using the Anaconda system installer. The installing experience is virtually identical to setting up Fedora 36 Workstation with the exception the default software selection uses the Xfce desktop instead of GNOME. The Anaconda installer presents the steps we take to set up the operating system as a series of modules we can access in the order of our choosing from a hub screen. After going through the modules and (mostly) taking the defaults, the installer refused to continue. At the bottom of the page a message informed me that I’d need to complete all the steps currently marked with an alert icon. The problem was none of the modules was marked with an icon. I went through the modules again and ran into the same warning without the ability to continue. I restarted the computer and tried again. This time I took all the defaults. This caused the partitioning module to complain, saying the automated partition layout wouldn’t work. I set up partitions for booting, swap, and root. Then returned to the hub screen where I was shown the same warning about completing all marked modules before continuing, despite no modules being marked. o § New Releases⠀➾ # ⚓ MX Linux ☛ MX-21.2_“Wildflower”_released!_–_MX_Linux⠀⇛ We are pleased to offer MX-21.2 for your use. MX-21.2 is the second refresh of our MX-21 release, consisting of bugfixes, kernels, and application updates since our original release of MX-21. If you are already running MX-21, there is no need to reinstall. Packages are all available thru the regular update channel. o § Red Hat / Fedora / IBM⠀➾ # ⚓ Kubernetes Blog ☛ Red_Hat_on_Kubernetes_1.25:_CSI_Inline Volumes_have_graduated_to_GA_|_Kubernetes⠀⇛ CSI Inline Volumes were introduced as an alpha feature in Kubernetes 1.15 and have been beta since 1.16. We are happy to announce that this feature has graduated to General Availability (GA) status in Kubernetes 1.25. CSI Inline Volumes are similar to other ephemeral volume types, such as configMap, downwardAPI and secret. The important difference is that the storage is provided by a CSI driver, which allows the use of ephemeral storage provided by third- party vendors. The volume is defined as part of the pod spec and follows the lifecycle of the pod, meaning the volume is created once the pod is scheduled and destroyed when the pod is destroyed. # ⚓ Video ☛ Flathub_Is_Introducing_Paid_Apps!?!?_–_Invidious⠀⇛ Flathub is the main place that you acquire Flatpaks on Linux and soon a big change is coming to the service, allowing developers to to have paid apps if they choose to do so. # ⚓ IBM’s_Competitive_Analysis_For_The_Power10_Midrange_Machine [Ed: This publisher fails to properly disclosure that it is funded by IBM to publish such puff pieces. Same for the ones below.]⠀⇛ # ⚓ Moving_To_The_Cloud_Should_Be_Easier_Than_Switching_Homes⠀⇛ # ⚓ Kisco_Makes_Moves_In_the_IBM_i_Security_Business⠀⇛ # ⚓ Two_Weeks_Of_Webinars_On_IBM_i_Security⠀⇛ # ⚓ IBM_i_PTF_Guide,_Volume_24,_Number_35⠀⇛ o § Debian Family⠀➾ # ⚓ Slashdot ☛ Debian_Replaces_Google_with_DuckDuckGo_as Chromium’s_Default_Search_Engine [Ed: There’s this discussion now in Slashdot. DuckDuckGo_is_a_Microsoft_front basically.]⠀⇛ # ⚓ Norbert Preining ☛ Debian_complaining_to_KDE_…_|_There_and back_again⠀⇛ So now some Debian boohoos are complaining about my blog which is aggregated at Planet KDE, directly to KDE, how nice. [...] Funny that those few ….. over at Debian cannot get a grip on reality and continue to witch hunt me. # ⚓ Andrew_Cater:_Debian_Barbeque,_Cambridge_2022⠀⇛ And here we are: second day of the barbeque in Cambridge. Lots of food – as always – some alcohol, some soft drinks, coffee. Lots of good friends, and banter and good natured argument. For a couple of folk, it’s their first time here – but most people have known each other for years. Lots of reminiscing, some crochet from two of us. Multiple technical discussions weaving and overlapping o § Devices/Embedded⠀➾ # ⚓ MakeTech Easier ☛ Battle_of_Android_Desktops:_Android_x86_v Bliss_v_Phoenix_OS_v_PrimeOS⠀⇛ The Android desktop scene is relatively new, with a handful of distributions like in the early days of Linux. In theory, Android desktops should provide a new way of using your PC, with a conventional desktop harnessing the enormous Android ecosystem. That’s the idea at least. But how do they stack up really? We put the four main players to the test to decide which Android desktop is the best. o § Open Hardware/Modding⠀➾ # ⚓ Andrew Hutchings ☛ Australian_Commodore_64:_Keyboard_Repair –_LinuxJedi’s_/dev/null⠀⇛ In my previous post about the repair of my Australian C64 I got as far as diagnosing that I needed a new CIA chip. The CIA chip has arrived so I thought I would try it out and see how far I get. The CIA chip arrived and I popped it straight into the socket where the dead one originally was (the U2 socket). o § Mobile Systems/Mobile Applications⠀➾ # ⚓ GSM Arena ☛ Weekly_poll_results:_Most_of_you_are_excited about_Android_13_as_long_as_your_phone_gets_it_–_GSMArena.com news⠀⇛ # ⚓ XDA ☛ How_to_check_Android_13_bootloader_version_on_the Google_Pixel_6_series⠀⇛ # ⚓ Android Police ☛ How_to_take_better_photos_with_your Android_phone⠀⇛ # ⚓ CNET ☛ Take_Control_of_Your_Data:_How_to_Manage_Android_App Permissions_–_CNET⠀⇛ # ⚓ Hectic Geek ☛ Best_10_Tech_News_Top_Apps_for_Android_in 2022⠀⇛ Time changes, and with it, technology is evolving with swift changes with every passing day. If you are in the tech industry, you must stay in touch with all these rapid changes and the coming trends to stay up to date. * § Free, Libre, and Open Source Software⠀➾ o § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ James G ☛ Is_Firefox_a_search_engine?⠀⇛ After sharing this with others, I was informed this is not the first time Firefox has been referred to as a search engine. o § Programming/Development⠀➾ # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_littler_0.3.16_on CRAN:_Package_Updates⠀⇛ The seventeenth release of littler as a CRAN package just landed, following in the now sixteen year history (!!) as a package started by Jeff in 2006, and joined by me a few weeks later. littler is the first command-line interface for R as it predates Rscript. It allows for piping as well for shebang scripting via #!, uses command- line arguments more consistently and still starts faster. It also always loaded the methods package which Rscript only started to do in recent years. littler lives on Linux and Unix, has its difficulties on macOS due to yet-another- braindeadedness there (who ever thought case- insensitive filesystems as a default were a good idea?) and simply does not exist on Windows (yet – the build system could be extended – see RInside for an existence proof, and volunteers are welcome!). See the FAQ vignette on how to add it to your PATH. A few examples are highlighted at the Github repo, as well as in the examples vignette. # ⚓ Barry Kauler ☛ Commandline_and_file_IO_in_Nim⠀⇛ This post explains some more code fragments; concerning reading parameters from the commandline and file reading and writing. Also, some notes on string manipulation. # ⚓ Jim Nielsen ☛ Re:_“The_web_is_a_harsh_manager”,_Pt._II_– Jim_Nielsen’s_Blog⠀⇛ It would be easy to conclude that, since you’re not sure what a “front-end engineer” is — The person who styles the page or queries the data layer? The person who animates things on screen or keeps the bundler and tooling humming along? — you can’t consider yourself a “real” front-end engineer. # ⚓ Matt Rickard ☛ Webhooks_Aren’t_So_Bad⠀⇛ Webhooks are the ultimate escape hatch to systems integration. Event publishing that doesn’t require you to know much about who is listening on the other end. It’s trivial to create a publisher or consumer (bring your own HTTP server/client). On the surface, Webhooks seem antithetical to the rise of the cloud native – it’s easier than ever to set up servers that long-poll, managed pub/sub infrastructure, or simple event queues. But the opposite might be happening. # ⚓ Matt Rickard ☛ The_Issues_with_Buildpacks⠀⇛ Buildpacks promise source-to-image generation. No need to write a Dockerfile or maintain dependencies. Get started with golden configurations for languages, frameworks, and more. [...] The trade-off between Dockerfiles and buildpacks is challenging for many developers to assess. We’re usually much better at identifying upfront costs rather than future costs. And Dockerfiles have an initial learning curve. # ⚓ Bozhidar Batsov ☛ OCaml_Tips:_Multiple_Let_Bindings_–_ (think)⠀⇛ One thing that was a bit weird for me in OCaml early on was how to introduce multiple let bindings (e.g. in the body of a function definition). # ⚓ Rlang ☛ the_Kelly_criterion_and_then_some_|_R-bloggers⠀⇛ The Kelly criterion is a way to optimise an unlimited sequence of bets under the following circumstances: a probability p of winning each bet, a loss of a fraction a of the sum bet, a gain of a fraction b of the sum bet, and a fraction f of the current fortune as the sum bet. # ⚓ Rlang ☛ Surprising_Things_You_Can_Do_With_R_|_R-bloggers⠀⇛ If you are interested to learn more about data science, you can find more articles here finnstats. Surprising Things You Can Do With R, R has changed the way we think about data. R has had a significant impact on a wide range of data science fields, from machine learning and artificial intelligence to data visualization and analysis. As a result, a large number of academic experts, data scientists, and analysts employ the incredibly flexible R programming language. R, a long-standing participant in the TIOBE index that gauges the popularity of several programming languages, is utilized by individuals from all occupational fields. # ⚓ Barry Kauler ☛ debdb2pupdb.nim_cross-compiled_in_OE⠀⇛ # § Perl / Raku⠀➾ # ⚓ @data».sparkle_|_Playing_Perl_6␛b6xA_Raku⠀⇛ While reading solutions to the PWC, I spotted a pattern. There where plenty of .map-calls that contained only simple maths. It must not be so! Task 179-2 leans itself to use vector operations. * § Leftovers⠀➾ o § Science⠀➾ # ⚓ Matt Rickard ☛ r/K_Startup_Theory⠀⇛ In ecology, r/K selection theory relates to the tradeoff organisms make between quantity and quality of offspring. Some organisms choose K- selection, i.e., to have few offspring but offer them substantial parental investment (e.g., humans, whales, elephants). Others choose r-selection, having many offspring with low probabilities of reaching adulthood (dandelions, rodents, bacteria). o § Health/Nutrition/Agriculture⠀➾ # ⚓ High_incarceration_rates_fuel_COVID-19_spread_and_undermine U.S._public_safety_–_Northwestern_Now⠀⇛ Extremely high rates of incarceration in the U.S. undercut national public health and safety. The overcrowded, tight quarters in jails fuel constant risks of outbreaks. Add to that the daily movement of 420,000 guards in and out of the facilities and 30,000 newly released people who are likely to inadvertently carry the virus back to communities. o § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ No_Days_Off_|_Matt_Murphy⠀⇛ Workplace surveillance goes mobile [...] Time off task is a perverse little metric; a product of run-amok capitalism’s fetishization of productivity, efficiency, and other quantifications. It’s the kind of policy that was only a dream for burgeoning companies of the industrial revolution, as they clawed for more time and yield from laborers. Now though, calculating time off task can be fully realized by using the right technologies to scrupulously track workers. For Amazon, those handheld scanners are the perfect gadgets to facilitate workplace surveillance because they are essential tools that are built into the infrastructure of the work itself: the workers must use them to scan packages. The scanners are also, conveniently, extensions of workers’ physical bodies, making the data they collect a reliable depiction of physical locations and movements—or inactivity. o § Environment⠀➾ # § Energy⠀➾ # ⚓ Price Of Oil ☛ Calls_grow_for_a_U.S_windfall_tax after_Exxon_makes_USD_$2,245.62_every_second⠀⇛ The amounts are obscene. They are mind- boggling. This is profit-making like you have never seen it before. It is also profiteering from war and price gouging at our expense. Big Oil is making billions of the misery of millions. On Friday, oil giants Exxon and Chevron reported record second quarter profits, a day after Shell’s results. First, let’s look at Exxon. The company made USD 17.9 billion in net profit in the 2nd quarter of 2022. We should call it out for what it is. This is blood money. This is crude capitalism at its worse. o § Finance⠀➾ # ⚓ WSWS ☛ Poverty_in_Germany:_Food_banks_count_2_million people_seeking_help_–_World_Socialist_Web_Site⠀⇛ Social inequality in Germany continues to rise at an alarming rate. As a result of the pandemic, war and high inflation, the official poverty rate climbed to 16.6 percent last year, which corresponds to 13.8 million people living in poverty. This means that for ever more people—the unemployed, single parents, low-wage workers, poor pensioners—they no longer have the resources to live on. [...] “The food banks are at their limit and report to us that many people are coming to them who have previously managed to make ends meet and need help for the first time,” Brühl said. Since the food banks can barely, or no longer can, meet the demand, every third food bank has had to stop accepting entrants, according to his data. There is a shortage of food and volunteers to help everyone who asks for support. Tafel Deutschland surveyed 962 of its member food banks in June and July, 603 of which responded. According to the results, 60 percent of the food banks have seen their customer load increase by up to 50 percent since the beginning of the year. Just under a quarter (22.6 percent) of respondents said they were now supporting 50 to 100 percent more people than before. At 16 percent of the food banks, the number of people seeking help had doubled or more than doubled. # ⚓ The_Future_of_Work_Is_No_Work_–_YES!_Magazine⠀⇛ Activists have long suggested that oppressive institutions should be abolished rather than reformed. The same could be said about labor. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Mark Curtis ☛ ‘CIA_sidekick’_gives_£2.6m_to_UK_media_groups –_Mark_Curtis⠀⇛ A US government-funded agency that claims to promote democracy but which helps undermine governments independent of Washington has moved decisively into Britain’s media space since 2016. # ⚓ How_the_American_Legislative_Exchange_Council_Turns Disinformation_Into_Law⠀⇛ In June 2021, Texas Governor Greg Abbott signed into law a bill banning the state from contracting with or investing in businesses that divest from coal, oil or natural gas companies. For Texas Railroad Commissioner Wayne Christian—one of the state’s top energy regulators—the message was clear: “Boycott Texas, and we’ll boycott you.” Since the beginning of this year, lawmakers in Indiana, Oklahoma and West Virginia have introduced bills that read a lot like the Texas anti- divestment law, and legislators in a dozen other states have also expressed support for the legislation’s objective. o § Civil Rights/Policing⠀➾ # ⚓ New York Times ☛ Pope_Francis_Will_Travel_to_Canada_to Apologize_to_Indigenous_Community_–_The_New_York_Times⠀⇛ Pope Francis is traveling to Canada this week to ​apologize to ​Indigenous communities for the Roman Catholic Church’s role in ​the country’s notorious residential school system, ​​where thousands of Indigenous children died, and countless others were sexually and physically abused. The visit comes after years of pleas from Indigenous leaders and leading politicians for a Vatican apology about the schools, which were designed to erase Indigenous culture and language by forcibly separating children from their families to assimilate them into Western ways. And some Indigenous leaders say it will fill in one of the biggest remaining pieces in Canada’s efforts at reconciliation over a brutal education system that a national commission declared to be a form of “cultural genocide.” # ⚓ The Toronto Star ☛ Another_pope’s_apology_isn’t_enough_when Church’s_shameful_acts_continue_|_The_Star⠀⇛ The truth is, there have been many apologies issued by many popes. [...] The Catholic Church and its officials have directed, authorized, counselled and/or were complicit in the horrific physical and sexual abuse of children; subjugation, vilification and violence against women; and the deaths of millions of Indigenous peoples in Canada, the United States, Australia, New Zealand, South America and the African continent. According to recent inquiries, that abuse has continued into the present. For some First Nation, Inuit and Métis survivors, this papal visit to Canada that begins this weekend in Alberta is an important part of their healing journey. For others, the Pope is the last person they want on their territories, as he represents a religious organization that has caused much misery around the world. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Patrick Louis ☛ Ten_Years⠀⇛ Writing. Ten years ago I had an inner urge to lay my ideas on the web, on a place I owned. The page was initially hosted on 1.ai, a now- defunct free platform that existed way before any similar service surfaced (resurfaced). I was immensely thrilled to design everything from scratch and to add Easter eggs. Hence, the blog became my medium of expression, my badge, an integral part of my journey and progress as I joined different online communities, looking to bond over shared interests. A blog is a persona, a blog is a canvas, a blog is a series of sketches that are often seen only by the author. As the brainstorming gets less rigid and conventional, the more enthralled and absorbed by the sentences we are. These days blogs have changed but I try to keep mine unaltered: each piece is uniquely me, not a pastiche or the echo of someone else. # ⚓ Data Swamp ☛ My_blog_workflow⠀⇛ I rarely spend more than 40 minutes for a blog post, the average blog post takes 20 minutes. Most of them are sharing something I fiddled with in the day or week, so the topic is still fresh for me. The content of the short articles often consists of dumping a few commands / configuration I used, and write a bit of text around so the reader knows what to expect from the article, how to use the content and what’s the point of the topic. * § Gemini* and Gopher⠀➾ o § Personal⠀➾ # ⚓ Reactionaries⠀⇛ I still think that intersectional feminism has a bigger kernel of truth than its enemies: anti-PC, gamergaters, anti-SJW, anti-woke… an old movement with many names that’s founded on misrepresentations and second-hand accounts. # ⚓ There’s_a_Monster_in_Your_Room⠀⇛ There’s a monster in your room. It stays awake while you sleep; it can feel you when you move; it listens to you while you dream. The monster speaks in a language you cannot see, nor hear, nor sense. Indeed, the monster speaks faster than you can comprehend. It can make strange noises and sound exactly like your friend. This creature can and will interrupt your deep slumber. During the day it will surely make you dumber. You cannot stop checking to see if it is there. When it disappears then you might be given a scare. Though ’tis small in scale it will perform endless deeds. At half past nine you find your mind inside its hold. Your attention is its desired feast upon which it feeds. It does not matter if it can or cannot fold. # ⚓ We’re_Going_the_Wrong_Way:_Childhood_Exploration_in_Video Games⠀⇛ If you aren’t able to read it right now, the (overly) short summary is that she discusses playing video games as a child, ignoring the rules and intended gameplay in favour of exploring and observing the worlds they portrayed. Reading this essay resonated strongly with my own childhood computer experiences. I’ll talk about this more generally later on, but the first thing it brought to mind was the 1999 PC game “Mobil 1 Rally Championship”, so I want to focus on that. # ⚓ Catacombs_of_the_Crazy_Cat_Conjurers⠀⇛ I ran the 39th installment of my quarterly old school tabletop rpg convention yesterday. It was absolutely lovely. Without question the most fun I’ve had on the con this year. For this one I had taken the time to properly prepare a dungeon of the type I typically like. A mix of puzzles, a lot of danger which is avoidable, a fun magic item or two, and some gonzo elements. As you may guess from the title there’s also a fair bit of humour involved. I’m hoping to do a little write-up about the dungeon and the process of writing it, but for now I just want to share my joy over how well the two sessions played out. o § Politics⠀➾ # ⚓ Three_stories_about_appeal_to_authority ⠀⇛ Who do you like? Earlier this summer, I was having dinner with some friends and to my surprise, they started speaking positively about some fairly well-known reactionary public voices. I didn’t wanna start a whole thing but I didn’t wanna say nothing either so I tried clearing out what I thought were misconceptions. They listened but then they asked me a question I couldn’t answer. “Sandra, who do you like? Which public figure do you approve of?” I’m right because he says so There’s another friend of mine who always has had a kind of “appeal to authority”–based reasoning. He’d latch on to such-and-such book or writer. We were in an argument about a project and a lot of his arguments were based around his judgments of the people involved. He’d be like: this is good because these guys are the only one in the field who can think about this stuff, that other project is bad because the people working on it are futzes who don’t know what they’re doing. o § Technical⠀➾ # ⚓ Make_HAM_video_on_Ubuntu_22.04_from_MP4_files⠀⇛ There is a script to convert mp4 files to .hv. It ran on 32-bit linux and won’t work by default on 64-bit linux. Below are the steps I took to get it working. # ⚓ Preliminary_Job_Reflections⠀⇛ My position is full-time remote–the company is located in a different part of the country from where I live. That is going to be a challenge for me. I worked remote for several months during the height of the COVID-19 pandemic, but I found that I was more susceptible to distractions and less productive at home. This is the first time I’ve ever accepted a position knowing ahead of time that I would not have an office to work at. The company is located in the America/New York time zone, while I’m located in the America/Chicago time zone. That means I’ll have to log into my work PC an hour earlier than I would at my previous job. Working from home is a benefit there–I don’t have to factor in travel time when considering what time to wake up. # ⚓ Reinstalling_from_backups⠀⇛ Now that we have a working backup setup, the only thing left to try is to test a restore (and more dangerously, a reinstallation). I planned on doing a reinstall anyway, so this is a good exercise to make sure my backups work as expected. # ⚓ Farewell_to_Arm⠀⇛ It’s been a good three years at least since I gave up my last desktop PC in favor of a cluster of Raspberry Pi’s running various small services. I still have some x86_64 machines in the form of two laptops, but they run when needed rather than 24/ 7 like the Pi’s. In that time I’ve discovered that provided you keep the expectations reasonable a Pi makes for a great little home server. My little cluster until today consisted of Frodo, Samwise, Gimli and Legolas. Frodo a Caldav and Carddav service as well as serving my ebook library via Calibre. Samwise is a torrent box and sometime DNS cache. Gimli runs this capsule over both Gemini and Spartan, a Finger service and a Gitea instance. Finally, Legolas runs a web server which also proxies a few of the other services on the network. Since yesterday after an upgrade and reboot Legolas has been offline, and today I tracked the problem down to a failed ethernet connection. # § Science⠀➾ # ⚓ Scientific American ☛ Eating_Too_Much_Protein_Makes Pee_a_Problem_Pollutant_in_the_U.S._–_Scientific American⠀⇛ Protein-packed diets add excess nitrogen to the environment through urine, rivaling pollution from agricultural fertilizers # § Internet/Gemini⠀➾ # ⚓ The_most_popular_Gemini_hosting⠀⇛ # ⚓ Create_a_Custom_Filter_for_Antenna⠀⇛ I remembered how I had to do some digging and experimentation before I got a working filter for antenna. My personal reason for filtering or excluding content was because there are frequent posts in languages that I do not know and wanted a way to view the list of recent posts of only the languages that I do know. # § Programming⠀➾ # ⚓ In_“Why_Not_Oberon?”,_I_mentioned_I_had_a_project_in mind._This_is_it.⠀⇛ The board is 15×15, represented in simple ascii originally. It’s now using unicode characters for special squares. The board is still way too busy, and something will need to be done about that (more/better use of unicode might be the answer to that issue). Next major “game play” step is adding turn- taking and the handling of the bag of tiles and user racks. And then I might have to hook it up to gemini. Still need a better board display, imho, for that, though. # ⚓ Enjoying_Lisp⠀⇛ About a year and a halve ago I decided to look for a way to explore coding in Forth and Lisp. This was the main incentive to make a serious start to learn to use Emacs. Also the fact that support for things like the GNU recutils and ledger in Emacs is much better than in Vim, helped. Now, one and a halve year later, I am using Emacs on a daily basis. Still I am not as efficient with Emacs as I am with Vim, but having a few decades of Vim under my belt, this is to be expected. =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It’s like the World Wide Web but a lot lighter. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 7234 ➮ Generation completed at 02:43, i.e. 113 seconds to (re)generate ⟲