𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Sunday, October 02, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Mon 3 Oct 02:42:30 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/2022/10/02/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmSSVivjsb74DwAwvNFUWiXAExS8esEHiJBzykMK9Da4BW QmYr91F9jQ6C4UgdRQqHE5QbcXGHYUcZYCYnigDogJGkyy QmVMkxTFB9LnSNGEQQ9wHzrmgcc9R1GBBrkXQwesnZn9sF QmVp5xT7mzD29ygLxoepcfrYB5u4Vyc9cndBz66AV7cb69 QmYPR3iBujyTHUCpxPHwsMNXJiNSLgfQa4AuzchgiUJ3M8 QmWTRh2ZdgwUGq9b4v8Cnv5g51yvN18PNFNC89vkDa478d QmQCpGVvMV5EduUzKqAToqKEmsDN4YWubH4KwPsA11BkFL Qmac6ycg4HgCXK32zmYm12JDmDQfL8BtJPF89Q129UbkCn QmTscUZbUfSgcCFNAKKV4rEvAsHABZ2Ct9K7RCSGGzRRDT QmcB3PmzUDz4gMMbVfzAbgcnKwRGZjhaY7foe2B7ox9dZW QmPRWZzVkej6AaPT8ApKxMdBRNbW94Cun6NRXmgn86A4C6 Qmey3FmUxZfMChKk9iWk1mHUB4Ymv2HgjzsQvr46EWDcdK QmesUFpQsQz19kHzMA7tU1y4kQBAYsznybzsWwLBxiEGvf QmUNJbX6AjW7qRrRLEqvkvgYaXD8vF7JZ7MVUdUWWqFEWb QmaxL9evVXo6gdQbWEnxs6y6kbCqGpRDiMGpi9NzXpjWN6 QmWVv1HPWfKNdq4B1hsdKRUksjQbdu793jr8mx3togTQqd QmPKM7UPv2eUYm1VWHrWhpB7k57bm5wSRaYyKhQ6Ck6Pfj QmenFrYXbGBu2iTqkM1ZVF7uotUuiMKBWQgMwjKRxvNmog QmYa74Gwhe1CXD1aRApxCZPiNvwqHtoaRNRJYUXXzTAzcC QmR2u26QZwYsd8Gmx2PtKEkxWiRY7DBNoBnQ9eCG6wYxoB QmVLjiRjCRwAgqnB8rLKTYXEMmL6cgQMvDGgKZemCXwyc4 ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ GNU/Linux and the GPL in Particular Are Under Attack Because They Spread Fast (Like a ’Cancer’) | Techrights ⦿ IRC Proceedings: Saturday, October 01, 2022 | Techrights ⦿ Windows Majority in Asia Down to Just Three Countries, All-time Low for Windows Worldwide This Month | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/10/02/gnu-and-gpl-spread-fast/#comments http://techrights.org/2022/10/02/irc-log-011022/#comments http://techrights.org/2022/10/02/microsoft-windows-new-low/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/10/02/djangocon-europe-2022/#comments http://techrights.org/2022/10/02/postgresql-15-rc-1/#comments ䷩ 𝚕𝚒𝚗𝚎 54 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/10/02/gnu-and-gpl-spread-fast/#comments Gemini version at gemini://gemini.techrights.org/2022/10/02/gnu-and-gpl-spread-fast/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ GNU/Linux_and_the_GPL_in_Particular_Are_Under_Attack_Because_They_Spread_Fast (Like_a_‘Cancer’)⠀✐ Posted in GNU/Linux, GPL, Microsoft at 6:08 pm by Dr. Roy Schestowitz Is the “cancer” Microsoft? Buying GitHub was all about control, not freedom, and curtailing the GPL by sabotaging it. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Steve Ballmer... Checking his men for cancer of the thigh... Who said sit down?⦈ Summary: The good news is that GNU/Linux continues to expand (widespread usage); the bad news is, it has come under a sheer magnitude of attacks and the media barely bothers to mention the obvious We’ve just shown that according this month’s figures (so far), based on data from about 3 million sites’ logs, Windows_reached_another_all-time_low, whereas GNU/Linux continues to make gains. On desktops and laptops, GNU/Linux_rose_to_10%_in_India_this_month and in general Windows_went_down_sharply_to_17%_in_India_this_month (it’s at 9% in Turkey, it cannot exceed single-digit territories for months already). Turns out people either cannot afford or don’t want to buy some Vista 11 laptop these days. Sales measurably plunged. In Nigeria, GNU/Linux rose_to_5.13%_this_month. It’s a very large population overall. Some very large populations (the above- mentioned 3 countries are almost 2 billion people) are steering away from Microsoft, but the media just isn’t reporting on it. Why? Follow the money. Instead of reporting such facts, the media attacks GNU/Linux and defames key people. There_have_been_no_"Linux"_posts_from_ZDNet_in_11_days_already and ZDNet’s Liam Tung persists with his — i.e. Microsoft’s – propaganda (“Microsoft: Hackers are using open source software and fake jobs in phishing…”). Microsoft_is_just_using_its_media_moles_to_blame_the competition_for_its_own_failures. It is noteworthy that ZDNet staff was reduced to very few parrots of companies like IBM and Microsoft. In the areas of interest it’s just Steven Vaughan-Nichols (SJVN), Liam Tung, and Jack Wallen. SJVN is mostly being assigned puff pieces for corporations (and their_front_groups which attack_the_GPL), whereas Liam Tung is little but a Microsoft mouthpiece. As for Wallen, he was ‘borrowed’ from a sister site (TechRepublic, mostly_a_spamfarm_of_diplomas_mills_these_days) to help pretend ZDNet isn’t a sinking ship. “Some very large populations (the above-mentioned 3 countries are almost 2 billion people) are steering away from Microsoft, but the media just isn’t reporting on it. Why? Follow the money.”To a certain extent, GNU/Linux scares Microsoft a lot more than the BSDs because of the licence. Accordingly, Microsoft wages a war on GPL complaince and enforcement. We wrote about this last night and the topic came up in_IRC, the plagiarism aspect in particular. Projects need to move away from GitHub. The sooner, the better. “I have a person working on adding more features to Gitea,” our_sysadmin_wrote, separately noting “the reality is that an ML model is *not* code, at least not in the sense that normal software is code…” A reader has meanwhile contacted us. He wrote to say (regarding the Software Freedom Conservancy (SFC), which seems to be doing what OSI did in 1998): I read your latest blog about the total corporate takeover of Linux [...] This has been going on for a decade or more by lwn.net, Linux Foundation, Microsoft, etc. It’s time to take back Linuxf rom these corporate paid idiots! lwn.net editor Corbet is #1! I’ve been censored and blocked by him for years for commenting on how Firefox is spyware! Any comments against the Google spy machine have also been censored by Corbet for years! This reader argues that “lwn.net Corbet is “#1 enemy of FOSS!” We mentioned some days ago how had admitted (openly) the financial relationship with the Linux Foundation, his role inside the Linux Foundation notwithstanding. “LWN never writes about the gross media bias, the growth of GNU/Linux, or anything of that sort.”Judging by the editorial policies and choices, LWN is strongly in favour of the corporate takeover. There’s a “token” mention of FSF statements and resistance from community actors; but it’s in the tiny minority. Anyway, Linux 6.0 has_just_been_released and LWN will mention this soon. LWN never writes about the gross media bias, the growth of GNU/Linux, or anything of that sort. It’s focused on corporations and their kernel-level work. That’s unlikely to change due to reductions in staffing, which followed many cancellations by longtime LWN subscribers. Maybe they deserved that. █ ⣿⣿⡟⠛⠃⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠛⠋⠀⠀⠀⠀⢸⣿⣿⣶⣦⣤⣤⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠛⠁⢹⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋ ⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠾⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢢⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⣀⠀⠐ ⠁⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⢹⣿⣿⣿⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡜⢸⣿⡇⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣿⣧⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⠤⠴⠾⢿⣿⣿⣯⣟⡃⠀⣦⡀⠀⠀⢀⣶⣾⣿⣿⡿⠉⠇⠀⣿⡇⠀⠀⠰⣿⣶⣤⣤⡀⠀⠀⠀⣴⣾⣿⡟⢻⣿⣿⣿⣿⣿⣷⣀⣀⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀ ⠠⠶⠶⠛⠛⠛⠀⠀⣀⣀⣦⣤⣴⣿⣿⣿⣿⣿⣿⠟⠀⠘⠿⣧⣤⣾⣿⣿⣬⣥⣤⣤⣄⣀⠘⠃⠀⠀⣠⣿⣿⣿⣿⣿⣦⡄⢰⣿⣿⠿⠇⠸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⠉⢉⣁⣧⣶⣶⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⡀⠀⣻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡿⠿⠛⠋ ⠉⠀⠀⠀⠘⢿⢀⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠛⠙⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣧⣿⣿⠁⠀⠀⠙⣿⣿⢿⣿⣿⣿⣿⣿⣷⣤⡝⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠻⠛⠻⠛⠿⠿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⣹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⣿⣿⣿⣿⡏⠈⠊⠉⢠⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⠟⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⠅⠉⣍⣵⣯⢝⡾⡋⡉⠉⠉⠉⠩⠻⠟⢿⢧⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠦⠀⠀⢸⣛⠁⠀⠀⣀⣀⡀⠀⠈⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⢃⣂⣀⣀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡆⠿⢿⣿⡿⢿⢿⣿⣿⠿⢸⣿⣿⢠⣿⣿⢹⣿⣿⠿⠟⠛⠛⣿⣿⡿⣿⣿⠀⢸⣿⣿⣿⣄⣸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣷⢸⣿⣿⡇⢸⣿⣿⠿⠿⣿⣿⡿⣿⣦⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⣼⣿⡇⠐⢸⣿⣧⣤⠀⣿⣿⢸⣿⣿⢸⣿⣿⣤⠀⠀⠀⣿⣿⣧⣿⡿⠀⣾⣿⢿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⡇⢸⣿⣿⣤⢀⣿⣿⣧⣿⡿⠀⠀⠀⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠀⢀⣈⣛⢿⣿⣦⣴⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣷⠀⣿⣿⣸⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⡇⣿⣿⣿⣿⡇⢸⣿⣿⠛⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⡿⣽⣿⣿⡇⠀⢸⣿⣿⣽⡿⢹⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢰⣿⣿⢻⣿⣿⢹⣿⣿⣤⢸⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠛⠩⠉⠁⠀⠈⠉⠉⠉⠁⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠉⠉⠈⠉⢉⣭⡬⠉⠍⢩⣿⣿⠿⠉⠛⠋⠉⠁⠈⠉⠉⠉⠁⡉⣭⠁⠉⠉⠀⠀⠀⠀⠀⠠⡄ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠨⠡⠦⢤⣶⣶⠀⠀⠀⠀⣤⣶ ⣿⣿⠛⠋⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠟⠀⠀⠀⠀⠀⢘⣿⣿⣧⣤⣤⣤⣿⣿⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠟⠟⠋⢹⣿⣿⣿⡿⠻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠿⠻⠿⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒ ⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢿⣿⣿⣿⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡈⢹⣿⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣇⣀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣤⠐⠃⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠤⠶⠿⢿⣿⣿⣯⣿⡋⢐⣄⠀⠀⠀⠀⣠⣶⣿⣿⣿⣻⡇⠘⣿⡇⠀⠀⢠⣦⣄⣀⡀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄ ⠐⠒⠒⠛⠋⠉⠀⠀⠀⠀⢀⣀⣀⣼⣾⣿⣿⣿⡿⠃⠈⣿⣷⣄⣀⣾⣿⣿⣿⣯⣽⡟⠀⠀⠈⠃⠀⠀⣸⣿⣿⣿⣿⣦⣀⠀⢸⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⢀⣁⡀⣄⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣦⣾⡟⠛⠋⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⣿⣿⣿⣿⠿⠃ ⠀⠀⠀⠀⠐⠆⣤⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⡶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀ ⠦⠄⢀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣧⣄⣨⣿⣿⣿⣿⣿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣧⣿⣿⠁⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⢼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⠿⠿⢿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⠟⠁⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣏⠘⠀⠀⢸⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀ 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⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⣿⣿⣿⣿⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣧⠁⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣤⣤⣀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠐⠿⢿⣿⣿⣿⠉⠻⣀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⠀⠻⢿⡏⠀⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄ ⠀⠒⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠈⠲⡄⠀⣰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠁⠀⠀⣾⣿⣿⣷⣦⣄⠀⠀⣴⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣦⢀⣀⣠⣾⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓ ⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣰⣦⣀⠄⢸⣿⣿⣿⡁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣩⣂⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣸⣿⡟⠛⠛⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠀⠙⠻⠿⠻⣿⣿⣿⣿⣷⣶⠆ ⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣗⢀⣺⣿⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠁⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⡄⡀⣰⣿⣿⣿⣿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⣶⣿⣿⣿⣿⠟⠙⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠺⢿⡿⢿⣿⣿⡿⠿⠟⠻⠿⠿⡿⡿⠟⢋⣿⣿⣿⡟⠓⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠸⣿⣧⣦⣤⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡛⠀⠀⠀⣰⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠉⠉⠻⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠁⠠⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢀⣀⣀⠀⢸⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⡆⠿⢿⣿⡿⠿⣸⣿⣿⠿⢿⣿⣿⢠⣿⣿⢹⣿⣿⣿⠟⠛⠛⣿⣿⡿⣿⣿⠀⣼⣿⣿⣿⣴⢼⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣷⢸⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⡿⣿⣧⠰⠒⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⣶⣿⣿⣿⣤⠈⣿⣿⢸⣿⣿⢸⣿⣿⣿⠀⠀⠀⣿⣿⣧⣿⡿⠀⣿⣿⣿⣿⣷⣼⣿⣿⢀⣸⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⣿⢹⣿⣿⣭⠉⣿⣿⣧⣿⡿⠀⠀⠀⠀⠀⣤⣶ ⠀⠀⠀⠀⠀⠀⢀⣈⣛⢿⣿⣆⠀⣾⣿⣧⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⡏⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⠀⢸⣿⡏⣿⣿⣿⣿⡟⢸⣿⣿⠛⠾⣿⣿⣟⣿⣷⠁⠀⠀⠀⠀⠈⢿ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⡿⣸⣿⣿⡇⠉⢹⣿⣿⣿⡇⢸⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⢻⣿⣿⢿⣿⣿⣤⢸⣿⣿⣤⣼⣿⣿⣿⣿⢹⣿⡇⢸⣿⣿⣦⣼⣿⣿⣿⣿⣿⠀⠀⠴⠶⠂⠐⠘ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⢹⣿⡯⠁⠀⠈⠉⣽⡯⠁⢨⡍⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠈⠉⠉⠈⠉⠉⠉⠈⢉⠉⣿⣿⣿⣿⣿⣿⠌⠉⠁⠈⠉⢭⣭⣽⣭⣭⢿⡍⠉⠀⠀⠀⠀⠀⢀⢀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⠀⠊⠉⠀⠀⠀⠀⠀⠈⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠀⠀⠀⠋⠉⠉⠁⠁⠁⠀⠄⠀⠀⠀⠈⡈⣿⣿⣿⣦⢠⣤⡤⢀⣤⣤⣾⣿⣷ ⣿⠟⠛⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠃⠀⠀⠀⠀⠀⣸⣿⣿⣶⣦⣦⣴⣶⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⢻⣿⣿⣿⡏⠸⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠟⠀⠀ ⣶⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⢉⣉⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⢀⣈⣛⢿⣿⡆⠀⢸⣿⣧⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⡏⢸⣿⣿⠛⠁⠀⠀⣿⣿⡟⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⠈⢹⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢻⣶⣿⣿⡟⣿⣷⠒⠀⠀⠀⠀⠻⣿ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⡟⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⢻⣿⣿⢻⣿⣿⣤⢸⣿⣿⣤⣽⣿⣿⣿⣿⢹⣿⣿⢺⣿⣿⣶⣼⣿⣿⣿⣿⣿⠀⠀⣶⣶⣤⠤⡿ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢁⢽⣿⣯⠭⠏⠈⠉⣽⡯⠁⣿⡍⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠈⠉⠉⠈⠉⠉⠉⠈⠉⢩⣿⣿⣿⣿⣿⣯⠈⠉⠉⠈⢩⣽⣿⣿⣯⣭⣿⡍⠉⠀⠀⠈⠉⠀⠃⠀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⢈⡈⣻⠋⠀⠀⠀⠀⠛⠁⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠀⠁⠘⠛⠛⠛⠉⠉⠉⠀⡀⠀⠀⠀⠉⣿⣿⣿⣿⣤⣲⣄⣤⣤⣤⣤⣶⣿⣿ ⡀⠀⠁⠀⠀⠀⠀⠀⢠⣾⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠿⠛⠉⢿⢿⣿⣿⡏⠛⢿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠁⠐⠀⠀⠀⠤⣤⠃⠙⠈⠛⠛⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠐⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⡻⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡾⠀⠀⠐⠁⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⣀⣀⠠⠒⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣹⣿⣿⠇⠸⠆⠀⠀⢠⣶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⣀⠀⠀⠀⠀⣠⣶⣿⣿⠿⣿⣿⣿⣷⣴⣄⡀⠀⠀⠀⠛⠉⢀⡄⠀⠀⢀⣾⣯⣥⣤⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣷⣄⠀⣼⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣛⣀⣀⣤⣤⣴⠋⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⢀⡀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡷⠀⠀⢸⣿⣿⠀⠀⠀⢠⣴⣿⣿⣿⠕⠻⣿⣿⣿⣷⡀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⠏⠉⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠀⢀⣀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⠀⠀⠐⢿⣿⠀⠀⠀⣸⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⡆⢸⠀⠀⣽⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣷⣦⣀⣤⣤⣶⡾⠿⠿⠛⣿⣿⣏⠁⠀⠀⠀⠀⠈⠃⠀⠘⠻⠿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠿⠶⠆⢸⣿⡿⠿⠃⠀⠀⠀⢸⣷⣿⣿⡇⠰⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠘⣻⠿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠆⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠤⠢⠪⡟⢿⣿⣤⣀⠀⠀⠀⠘⣿⣾⣶⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⣁⠀⠀⢀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠁⠀⠀⠀⣤⠀⠼⣿⣿⣿⣷⣤⣿⣿⡿⠿⣫⣻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⣄⡀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⢿⣧⠄⠈⠉⢁⣴⣿⠃⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⣀⡀⢰⣯⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡆⠿⢿⣿⡿⠿⣿⣿⣿⠿⢿⣿⣿⢸⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣹⣿⣿⣿⣴⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⡿⣿⣦⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⠀⣹⣿⣿⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⢸⣿⣿⣿⣿⡏⢿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⣧⢸⣿⣿⣿⡿⣿⣿⣧⣿⡿⢩⡀⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⣇⣿⣿⣿⣿⠛⠀⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣴⣿⣿⣿⣿⣷⣼⣿⣿⠾⢿⣿⣿⠀⢸⣿⡏⣿⣿⣿⣿⣟⢸⣿⣿⣛⣀⣿⣿⡟⣿⣷⠄⠀⠀⠀⠸⣿⣿ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣧⡄⢸⣿⣿⣿⡇⢸⣿⣿⣿⡟⠛⠋⣿⣿⣧⣿⣿⢻⣿⣿⢻⣿⣿⢿⣿⣿⣤⢸⣿⣿⣴⣾⣿⡇⢻⣿⢹⣿⣷⣼⣿⣿⣿⣽⣿⣿⡇⣿⣿⠀⢀⣀⣀⠀⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⢨⣭⣿⣿⣿⣿⣿⠭⣿⣮⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠈⠩⣯⠈⠉⠩⠍⠈⠉⢉⣭⣉⣿⣿⣌⠉⠈⠉⠭⣯⣭⣭⣽⣿⣩⣭⣧⠉⠉⠀⠈⠛⠃⠈⠈⠙ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠶⢠⣾⣿⣿⣿⣿⠟⣿⡿⠀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡀⢶⠆⢸⣿⣿⡿⠻⠿⠂⠀⠀⠀⢸⣿⣿⣷⢿⣿⣏⠟⡄⠀⠀⠀⠀⠀⢀⣄⣶ ⡦⠀⠉⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣦⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⡿⣿⡿⠿⣿⣿⣿⣿⡿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠲⠦⠀⠀⠀⣀⣀⡤⠸⠿⢟⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠉⠁⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠛⠙⠉⢿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⡤⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠹⣿⣿⡿⠷⠀⠀⠀⣠⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣦⣸⣦⡤⠀⠀⠀⠀⢀⣠⣤⡿⠀⠀⠀⠀⣀⣤⡶⠒⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣤⡀⠀⢠⣾⣿⣿⡟⠉⣿⣿⣿⣿⣾⣶⣀⣠⣤⣰⡾⠁⠀⠤⠒⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣷⣶⣶⣶⣤⡄⠀⢰⣿⣿⠃⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣴⣿⣿⣿⣿⢿⣿⣿⣿⣷⣤⣿⠟⠛⠙⠁⠀⠘⣿⣿⣿⣿⣿⣿⠛⠉⠉⠀⠁⠀⠀⠀⠀⠈⣈⣡⣿⣿⣶⣦⣤⣴⠆⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠘⣿⣿⠀⠀⢀⣾⣿⣿⣿⠏⠰⣿⣿⣿⣿⡇⠠⣦⣮⣿⣿⣿⣿⣿⣾⡿⢿⣿⣿⣿⣿⣦⡀⢀⣤⣤⡤⠻⠿⠛⣩⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠷⠶⣤⣾⣿⣿⣿⡏⠀⠀⢹⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠸⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠨⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠘⡽⣿⢿⣿⣷⣄⣀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡏⠀⠀⠀⣀⠐⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡛⣿⡿⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⢿⣿⣷⣄⡀⠀⠹⢿⣷⣆⠀⠀⠀⠀⠀⠀⢠⣤⣤⠾⠿⢿⡿⢣⣤⡄⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⢸⣇⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣸⣿⣿⣆⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠈⠻⠟⠰⠯⠀⣀⠙⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢻⣿⡆⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢺⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣠⢸⣿⣿⠀⢸⣿⣿⠀⢹⣿⣿⣿⣼⣿⣿⡇⢸⣿⣿⠿⠇⣿⣿⡿⣿⣦⠸⠿⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡿⣿⣿⣿⣿⣿⠘⣿⣿⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⢻⣿⡷⣾⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⣶⣦⣿⣿⣧⣿⡿⠒⠒⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⣷⣿⣿⣿⣿⠛⠀⢿⣿⣿⣿⡇⢸⣿⣿⠛⢿⣿⡿⣿⣿⡟⣿⣿⣜⣿⣿⣿⣿⣧⢽⣿⣿⣤⣼⣿⣿⠀⢸⣿⣯⣿⣿⣿⣿⡇⢸⣿⣿⠛⠙⣿⣿⠛⣿⣷⠘⠂⠀⠀⢡⣤⣤ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣤⡌⠀⠀⣿⣿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣤⢻⣿⣿⣤⣼⣿⡇⢿⣿⢹⣿⡇⢸⣿⣿⣶⣶⣿⣿⡇⣿⣿⠁⠀⠀⠀⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⢈⣿⣿⣿⣿⣿⡿⣭⣅⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⢽⣿⣯⠸⢯⡍⠉⠈⠉⠉⠉⢯⡍⠉⠈⠉⠈⣭⣭⣌⠉⢉⣿⣿⣿⣿⡇⠉⠉⡀⢰⣶⣶⡶⡿⣿ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⣴⣿⣿⣿⡿⣿⣿⠃⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠁⢀⣄⠀⣾⣶⣮⣿⣆⠀⠀⠈⣿⣿⣿⣧⡀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠃⠀⠀⠼ ⣶⡆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠛⠙⢿⠿⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣦⡄⠀⠀⠀⠀⡀⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠰⠶⠞⠁⠉⠛⠷⠍⣻⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠘⠀⠹⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣠⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠⣿⣿⣿⣇⡆⠀⠀⢀⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣭⡛⠛⡇⠀⠀⠀⠀⠀⢐⡅⠀⡀⠠⠔⠀⠀⠀⠀⣀⣅⠀⠒⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢹⣿⠛⠁⠁⣰⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣰⣾⣿⣿⠿⣿⣴⣷⣦⣆⣤⣾⡿⠟⠻⠋⠁⠀⠀⣀⠀⠴⠛⠋⠁⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⢠⣾⣿⣿⡿⢈⣿⣿⣿⣿⡆⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣾⠿⠿⠿⠃⠀⠹⣾⣿⡿⠿⣿⢃⡀⣀⡀⠠⠐⠀⠉⠀⠀⠐⠠⠆⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡶⣦⠀⠀⠀⢳⠇⢀⣾⣿⣿⣿⡗⠀⠿⣿⣿⣿⣿⡌⢙⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠛⠉⢱⣿⣿⣌⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣴⣶⠿⠛⠋⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁⠀⠈⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠘⢻⣿⣿⣿⣿⣿⣶⡁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⣀⣠⣤⣤⣤⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠀⠀⠰⣿⣿⣿⡿⢸⣆⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠶⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠐⠿⠿⢿⠿⡿⠿⠟⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠀⠀⠀⢘⣿⣿⣿⣧⢸⣿⣴⣿⣿⣿⣿⡟⢿⠇⠀⠀⠀⠙⠛⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠸⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⠆⠀⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠐⢲⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣾⡿⢻⣿⡆⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⢿⣿⣿⣿⣷⢸⣿⣿⡇⢸⣿⣿⠿⠆⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠁ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⣿⣿⣿⣿⣿⠟⣿⣿⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠰⣿⣿⢻⣿⣏⣸⣿⣿⠀⢸⣿⣿⠀⢹⣿⣿⣿⣼⣿⣿⡇⢸⣿⣧⣀⡀⣿⣿⣤⣿⡿⢈⣉⡉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⡇⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⡇⢸⣿⣿⠛⠁⠀⠉⣿⣿⡟⣿⣷⣼⣿⣿⣼⣿⣏⢻⣿⣿⡀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠿⣿⣿⣿⠛⣿⣷⢈⡁⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣸⣿⡇⠀⢸⣿⣷⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣾⣿⣿⣤⢸⣿⡟⢻⣿⣿⣿⡇⢸⣿⣷⣤⣄⣿⣿⠀⣿⣿⣀⠉⠀⠀⠠⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠈⣩⣿⣿⣿⣿⣿⣯⠁⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⢻⣿⡍⣿⣍⠉⠉⠈⠉⠉⢭⡈⠉⠁⠈⠉⣯⣏⠁⠈⠉⢹⣟⣻⣿⣯⡅⠉⠉⠀⠀⠀⠀⠀⣸⣿ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠹⡷⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⣜⣿⣆⠀⠀⢸⡿⠛⣿⣿⣧⠀⠀⠀⠀⠿⣿⣗⠋⠻ ⣤⣤⡀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣤⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠙⠻⠿⣿⠋⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠃⠂⠀⠀⢤⣤⠴⠐⠻⡿⠘⠛⢿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣿⠉⠀⠀⠀⠀⠀⣀⣠⠴⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣸⣿⣿⣟⢆⠀⠀⣀⣴⣶⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡿⠿⡇⠀⠀⠀⢀⣤⣴⡏⠀⠀⢀⡠⠀⠈⠉⠁⠀⠀⠀⠠⠴⠒⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠏⠙⣿⣿⣿⣖⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣀⣠⣄⣠⣶⡿⠛⠙⠓⠒⠃⠀⠀⠀⠀⢀⡴⠞⠋⠁⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣦⠀⢀⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣴⣿⠿⣿⡏⠁⠹⣿⣿⡿⣻⣋⣁⠀⠀⠀⠀⡠⠄⠒⠈⠁⠀⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⣤⣀⡀⠀⠀⠀⣽⣿⣿⣿⣿⣿⠃⠀⢿⣿⣿⣿⣇⠉⢻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡄⠀⢀⠀⠄⠀⠉⠉⢸⣿⣿⣟⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⣷⡈⠁⠀⠀⣾⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠈⢻⣿⣿⣿⣿⣿⣶⣅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⡀⠈⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⢿⣿⣿⣿⣿⠀⡈⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⢿⣿⣷⡀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡴⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡀⠀⢺⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠉⠉⠀⠀⠈⢿⣿⣿⣄⠀⠀⠀⢸⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⡙⠛⠋⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣧⡐⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣶⠀⠘⣿⣶⣶⣄⠀⠀⠀⢀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⡿⢻⣿⡆⠿⢿⣿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣧⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢼⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡇⢸⣿⣿⠿⠄⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠀⣿⣿⢻⣿⣶⣸⣿⣿⠀⢸⣿⣿⠙⣿⣿⣿⣿⣼⣿⣿⡇⢸⣿⣧⣀⠀⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣷⣀⣿⣿⣸⣿⡏⢿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢿⣷⣿⣿⠛⣿⣿⠁⠒⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣸⣿⡇⠀⢸⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⢹⣿⣿⣷⣾⣿⣿⣤⢸⣿⣿⢿⣿⣹⣿⡇⢸⣿⣷⣬⡍⣿⣿⠀⣿⣿⠀⠐⠷⠀⠀⢁⣀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠈⠉⢱⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⢿⣿⡹⣮⡍⠉⠉⠉⠛⠍⡍⠈⠉⠁⠈⠉⣿⣍⠁⠈⠉⢩⣿⣷⣿⣯⠀⠉⠙⠒⠂⠀⠀⠀⠙⣿ ⠀⠆⠲⣶⠇⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠙⢿⣦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⢸⣷⣾⣿⣿⣷⠀⠀⠀⠀⢰⣤⣶⡆⠻ ⣄⣀⡙⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠟⠛⠙⠿⠿⣿⡿⠻⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠖⠒⠂⠂⠀⢀⣠⣄⡄⠸⠻⣿⠉⠻⢿⠿⠿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠹⠟⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠉⠁⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⡄⠀⡄⠀⠀⠀⠀⠀⣀⣤⠄⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⠧⠀⠀⢀⣴⣶⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⠀⠀⠀⢀⣤⣤⡏⠀⠀⠲⠄⠀⠰⠖⠋⠉⠀⠀⠀⢀⡠⠴⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⠛⢻⣿⣿⣷⣶⣿⣿⡿⣿⣦⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢀⣤⣤⣼⣿⠉⡉⢀⣠⣶⡿⠛⢉⣡⠤⠆⠀⠂⠀⠀⠐⢀⣤⡶⠖⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡏⢲⢿⣿⣷⡄⢀⣦⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣴⣿⣿⣿⠋⠹⣿⣿⡿⣟⡋⡁⠀⠈⠀⠀⠀⡀⠠⠄⠒⠀⠉⠀⡀⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢋⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣇⠀⠀⣀⠈⠀⠉⠁⢸⣿⣿⡿⢧⠶⠖⠀⠉⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⣀⣀⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢾⡿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⠀⠸⣿⣿⣿⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠘⠛⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⡄⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⡈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⠿⠿⢿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⠀⠀⢻⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⣡⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⡙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠖⠀⢸⣿⣥⣀⡀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⡿⢻⣿⡆⠿⢿⣿⡿⠿⢸⣿⡿⠿⢾⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⠀⢸⣿⣧⣤⠀⣿⣿⣸⣿⣿⢻⣿⣿⣿⠛⠛⠿⣿⣿⣧⣿⡿⠀⣿⣿⢻⣿⡦⣸⣿⣿⠀⢸⣿⣿⢿⣿⣿⣿⣿⣼⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⡇⠀⢸⣿⡿⠛⠀⢿⣿⣿⣿⡇⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣷⡀⣿⣿⣺⣿⡏⢿⣿⣿⠀⢸⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⡇⢸⣿⡟⣿⣤⣿⣿⠛⣿⣷⠀⠠⠤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣸⣿⡇⠀⢸⣿⡇⣀⢺⣿⣷⣤⡄⢸⣿⣿⣿⠇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⢺⣿⣿⣤⣼⣿⣿⣤⢸⣿⣿⣿⣿⣹⣿⡇⢸⣿⣷⣬⡟⣿⣿⠀⣿⣿⠀⠐⣤⡄⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠈⠉⢡⣿⣿⣿⣯⠉⠁⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⣿⣿⣽⣮⠏⠉⠉⠛⠭⣉⠉⠈⠉⠉⠋⠩⣿⡍⠁⠈⠉⡉⣩⣥⣭⣉⠀⠉⢉⣤⠤⠈⠀⠀⠰⣶ ⠀⠆⠲⣶⠇⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⣿⣿⣿⠙⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⢸⣿⣭⣿⣿⣶⠀⠀⠀⠀⠀⢀⣀⣀⠹ ⣀⡀⠘⠻⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠇⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠿⠿⠿⠿⠿⣿⣿⣿⡿⢿⢿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠴⠞⠓⠒⠂⠀⢀⣤⣤⠆⠾⢿⣧⠟⠿⣿⠿⠟⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⢡⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⢿⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠈⠉⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣄⠀⣤⠀⠀⠀⠀⠀⠀⣀⡀⠀⠖⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⢰⣿⣿⣿⠆⠀⢀⣴⣶⣿⣿⣿⣿⣶⡆⠀⢿⣿⣿⣿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣼⠃⠀⠰⢶⠀⠀⣤⠶⠊⠉⠀⠀⠀⠀⣀⡤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠿⣹⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣀⣀⣸⣾⡝⠙⣁⠀⣠⣾⡿⠛⢯⣤⣤⠀⠂⠀⠀⠀⠄⢀⣤⡴⠄⠘⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠛⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣤⣾⣿⣿⡟⠛⢻⣾⣿⡿⠟⠛⠀⠀⠉⠁⠀⠀⠀⠠⠤⠂⠘⠉⠁⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣟⡍⠉⠻⣿⣿⣿⣿⣿⣿⣧⡀⣈⡈⠋⠉⠉⠁⣾⣿⣿⣶⣠⡴⠆⠈⠉⠀⠀⠀⠐⠀⠑⠋⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⡎⢡⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠶⠶⠿⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠆⠀⠈⣿⣿⣿⣿⣻⣿⣿⡟⠀⠀⠀⠈⠻⠋⠋⢿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⠃⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣽⣧⣾⣿⣿⣿⣿⣿⣝⣿⠀⠀⠀⠀⠀⣼⠀⠀⠘⣿⣿⣿⣧⣀⡀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡶⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣟⠃⠀⢻⣿⣯⣿⡄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⡿⢻⣿⡆⠿⢿⣿⡿⠿⢸⣿⡿⠿⢾⣿⣿⢠⣿⣿⢹⣿⣿⠿⠏⠻⢿⣿⣿⣿⣿⣷⠀⢻⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠃⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⠀⢸⣿⣧⣠⠈⣿⣿⣸⣿⣿⢸⣿⣿⣤⠀⠀⠉⣿⣿⣧⣿⡿⠀⣿⣿⢻⣿⣦⢼⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⢸⣿⣿⣍⠉⣿⣿⣿⣿⡿⠛⠿⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⡇⠀⢸⣿⣿⠛⠀⢿⣿⣿⣿⡇⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣷⡔⣿⣿⣺⣿⡇⢿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡟⣛⣀⣿⣿⠛⣿⣷⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣸⣿⡇⠀⢸⣿⡇⣠⣻⣿⣿⣴⡄⢸⣿⣿⣿⠇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⢺⣿⣿⣤⣸⣿⣿⣬⢽⣿⣿⣿⣿⣹⣿⡇⢸⣿⣷⣭⡿⣿⣿⡀⣿⣿⠀⠈⡌⡉⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠈⠉⠁⣿⣿⣿⣯⠉⠁⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠩⣿⣿⣿⣬⠍⠉⠉⠿⣭⡉⠉⠈⠉⠹⠏⠩⣿⡍⠁⠈⠩⠉⠉⣁⣉⠉⠁⠉⠉⠀⠀⠙⠛⠀⠀⣤ ⠀⠖⠲⣶⠇⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢻⣷⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⢼⣿⢛⣻⣿⣧⡀⠈⠉⠉⠀⠀⠀⠀⠙ ⣿⣀⢀⡻⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠚⠛⠛⠛⠂⠀⢤⣤⠔⠃⠛⢿⡀⠈⢙⡿⠿⠋⠀⠀⠀⠀⣶⣿⡟⠻⢛⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢴⣿⠃⠀⠀⠀⠀⠀⢸⡿⠿⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⢀⣄⣤⡀⠀⢀⣾⡧⠂⠀⣀⣼⣿⢗⣻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⢰⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠂⠀⠀ ⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣀⣠⡤⠾⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⠁⢀⣠⡀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⣀⣨⣷⣿⠛⢇⠀⠀⠀⢀⣠⣶⣶⣷⠀⠢⠒⠀⠉⠁⠀⠀⣀⣄⡀⠰⠓⠋⠉ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠁⠈⠙⠿⠿⢿⡿⢿⣿⣿⣿⣿⣷⣦⣀⣾⣿⣿⣿⢟⢿⣿⣷⣯⣵⣶⣿⣿⠋⠉⠀⠀⠀⠀⣀⡠⠄⠒⠛⠉⠁⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⡀⢸⡟⠈⢀⣠⣷⣦⣶⣄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣅⣀⣠⠿⠿⠿⠿⢿⣿⣿⣦⣄⣤⣤⠀⠒⠂⠀⠀⠀⠄⠐⠤⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢁⠀⠉⠀⣾⣿⣿⣷⣿⡟⠀⠀⠀⠀⠀⠈⠻⠫⠀⢹⣿⣿⣿⡅⠀⠀⠀⠀⣼⣿⣿⣷⢉⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⣤⣤⣶⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣼⣿⣿⣫⠉⠀⠀⠐⠂⠀⠀⠀⠀⠀⠸⢿⣿⣿⣷⡀⠀⠀⠀⢹⣿⣿⣿⠧⠁⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⣾⣿⣿⣿⣾⡈⠈⣴⠀⠀⠀⠀⠀⠤⠂⠀⠘⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⡆⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣷⡦⠿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⡀⠀⣿⣿⣿⣿⣇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⡿⢻⣿⡆⠿⢿⣿⡿⠿⢸⣿⡿⠿⢹⣿⣿⢠⣿⣿⢹⣿⣿⠿⠏⠻⢿⣿⣿⣿⣿⣷⠀⢿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⢹⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡼⠇ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⠀⢸⣿⣧⣤⠈⣿⣿⣼⣿⣿⢸⣿⣿⣤⡀⠀⠀⣿⣿⣧⣿⡿⠀⣿⣿⢻⣿⣦⢼⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⢸⣿⣷⣤⠀⣿⣿⣧⣿⡿⠙⠢⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⡇⠀⣸⣿⡿⠛⠀⣿⣿⣿⣿⡇⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣷⣤⣿⣿⣻⣿⡇⢻⣿⣿⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡟⠛⠀⣿⣿⡟⣿⣷⠀⠀⠘⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⡇⠀⢸⣿⡇⣰⣿⣿⣷⣤⡍⢸⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⢺⣿⣿⣤⣸⣿⣿⣤⢹⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⣽⣿⣿⣿⡅⣿⣿⠀⠐⡒⠒⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠈⠉⠁⣿⣿⣿⣿⣏⠁⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠩⣿⣿⣿⣌⠍⠉⠉⠿⣍⠉⠉⠈⠉⠉⠉⠉⢿⣍⠁⠈⣯⠉⠉⠁⠉⠉⠁⠉⠉⠀⠀⠘⠾⠆⠀⠲ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⢸⣿⣿⠏⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⢿⣧⣆⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⢻⣆⠀⠸⣷⣴⠶⠶⣶⣆⠀⠐⠖⠒⠂⠀⠀⠀⠸ ⣿⣧⣔⣟⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⢿⣿⣿⠟⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠚⠋⠉⠉⠉⠀⠀⠶⠖⠉⠈⠛⠧⣀⠨⣿⠛⠛⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠐⠿⠃⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡿⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢀⣤⣴⣶⣤⡐⢿⣿⣿⣿⡐⠀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢠⣿⣿⣿⠛⠻⣿⣿⣿⡛⠁⠀⠀⠘⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢀⣀⣤⠶⠞⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠻⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢀⣠⣤⣽⣿⡍⢋⠀⠀⠀⠀⠀⢀⣀⣸⠇⠠⠀⠀⠈⠁⠀⠀⢀⣀⣀⠀⠶⠚⠉ ⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠛⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣴⣿⣿⣿⠟⢻⣯⣿⣷⣅⣀⣠⣶⣿⠟⠿⠃⠀⠀⢀⣀⠄⠰⠚⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⢠⣤⣀⣀⢀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣧⡀⣈⢼⣿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠀⠐⠂⠀⠁⠀⠠⠀⠠⠴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡃⠘⠇⠀⠀⢻⣿⣿⣿⣾⠀⠀⠀⠀⠀⠈⠙⠋⠀⢸⣿⣿⣿⣏⠀⠀⠀⠀⢠⣼⣿⣧⣉⡀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡄⠀⠀⠀⣀⣤⣴⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠲⡺⡻⣗⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡤⠀⠀⢸⣿⣿⣿⡧⠈⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡄⠀⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⣾⣿⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠘⢿⣿⣿⣿⣦⣤⡀⢸⣿⣿⣿⡇⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢻⣿⡆⠿⢿⣿⡿⠿⢸⣿⡿⠿⢸⣿⣿⢠⣿⣿⢹⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣷⠈⢻⣿⣿⣿⠀⢸⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⢸⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⡿ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⠀⢸⣿⣧⣤⠈⣿⣿⣾⣿⣿⢸⣿⣿⣤⡀⠀⠉⣿⣿⣧⣿⡿⢀⣿⣿⣿⣿⣦⢼⣿⣿⠀⢸⣿⣿⢻⣿⣿⣿⣿⣼⣿⣿⡇⢸⣿⣷⣴⠀⣿⣿⣧⣿⡿⠛⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⡇⠀⢸⣿⡿⠛⣀⣿⣿⣿⣿⡇⢸⣿⣿⠛⠁⠀⠀⣿⣿⡟⣿⣿⣜⣿⣿⣻⣿⣇⢻⣿⣿⠀⢸⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⡇⢸⣿⡟⠛⠀⣿⣿⡟⣿⣷⠀⠀⠐⠛⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣸⣿⡇⠀⢸⣿⡇⢰⣾⣿⣷⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⢺⣿⣿⣤⣸⣿⣿⣤⢸⣿⡟⢻⣿⣿⣿⡇⢸⣿⣷⣼⣿⣿⣿⡇⣿⣿⠀⠀⢒⠒⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠈⠉⠁⢸⣿⣿⣿⣯⡁⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⢹⣿⣿⣿⣮⠍⠉⠉⠿⣍⡉⠉⠈⠉⠁⠈⠉⠩⣭⠁⠈⢯⡉⠉⠁⠉⠉⠁⠉⠉⠀⠀⠘⢶⡆⠀⠐ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⢸⣿⣿⠋⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⣷⣦⠀⠀⠀⠙⢲⣄⠀⠀⠀⠀⠀⠈⡷⡀⠘⣷⣶⡶⢶⣶⣆⠀⠐⠶⠶⠆⠀⠀⠀⠀ ⣿⣧⣄⣨⡛⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠛⠛⠛⠟⠿⠿⣿⣿⠻⠿⠿⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⠀⣿⣿⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠐⠋⠉⠉⠉⠁⠀⠶⠖⠈⠀⠉⠫⠄⢀⣽⠛⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⢸⡿⠛⠿⢿⡿⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣴⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠂⠀ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⣿⣿⣿⣿⣷⣀⡄⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣴⠖⠛⠋⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠙⠛⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣷⣧⢉⠀⠀⠀⠀⠀⠀⠀⣀⣼⠇⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠒⠛⠉ ⠉⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣴⣿⣿⣿⠟⢉⣿⣿⣿⣬⠠⡄⢀⣾⣯⣿⡇⠀⠀⢀⡠⠤⠀⠚⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣶⣶⣶⣆⣀⠓⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⢿⣿⣿⣿⣷⣾⣿⣏⠁⠉⠀⢀⣙⣿⣿⣿⣷⣿⣿⠟⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⠁⠀⠸⠅⠀⠀⠠⢢⡛⢛⠅⠀⠀⠀⠀⠀⠈⠁⠁⠀⢩⣿⣿⣿⣶⡟⠛⠛⠿⠛⢋⣽⣯⡁⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣤⣴⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠒⠝⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣷⣶⣄⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠛⠛⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣮⡶⣪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣈⣐⣾⣿⣿⣿⣷⣤⣄⡀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠁⠈⠻⣿⣿⣿⣿⣿⣿⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⡆⠿⢿⣿⡿⠿⢸⣿⡿⠿⢸⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠊⣼⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⢿⣿⣿⡇⢸⣿⣿⠿⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠼ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⠀⢸⣿⣧⣤⠈⣿⣿⣼⣿⣿⢸⣿⣿⣤⡉⠛⠿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣦⢼⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⡇⢸⣿⣿⣤⡄⣿⣿⣯⣿⡿⠛⠀⠄⠀⡀⠁⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⡇⠀⢸⣿⡿⠛⢀⣿⣿⣿⣿⡇⢸⣿⣿⠛⠃⠀⠀⣿⣿⡟⣿⣷⡘⣿⣿⣿⣿⣇⢸⣿⣟⠀⢸⣿⣿⠀⢸⣿⡏⣿⣿⣿⣿⡇⢸⣿⡟⠛⠀⣿⣿⡟⣿⣷⠀⠀⠀⠚⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣸⣿⡇⠀⢸⣿⡇⠀⣿⣿⣷⣤⡄⢸⣿⣿⣿⠇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⢸⣿⣿⣴⣼⣿⣿⣤⢸⣿⡇⢻⣿⢻⣿⡇⢸⣿⣷⣬⡿⣿⣿⡇⣿⣿⠀⠀⠐⡐⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠈⠉⠁⠀⣿⣿⣿⢿⣅⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⢹⣿⣿⣿⣿⡹⠉⠉⠙⠯⣍⢉⠈⠉⠁⠈⠉⠈⠩⣧⠈⠹⠍⠉⠁⠉⠉⠉⠉⠉⠀⠀⠀⠳⡶⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠛⣿⣶⡀⠀⠀⠈⠙⣦⡄⠀⠀⠀⠀⠀⠉⡓⠀⢁⣶⡾⠿⢿⣶⠀⠐⠲⠒⠒⠀⠀⠀⠀ ⣿⣿⣿⣿⣛⡿⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⡿⠛⠛⠿⢿⠏⠙⠿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣿⣿⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡏⠀⠐⠚⠋⠉⠉⠓⠀⠶⠒⠀⠈⠙⠿⡤⣨⡿⠛⠋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠘⠉⠁⠀⢀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⢰⣿⣶⣿⣦⡀⠀⠛⠉⠛⠿⠿⣿⢿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠐⠊⠁ ⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⣿⣿⡿⢷⡀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠞⠋⠉⠀⠠⠀⠀⣠ ⣋⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⣶⣄⡀⠀⠀⠀⣀⣀⡤⡀⠀⠀⠀⠀⠀⠐⢀⣤⡴⠶⠂⠈⠉ ⠉⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⠀⠀⠸⡏⠀⠀⡈⠛⣏⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣿⣿⣿⣿⣋⣿⣿⣿⣿⣦⡒⠂⠈⠉⠀⣼⠃⠀⠀⠤⠔⠒⠀⠉⠀⠀⠀⠀⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡧⠉⠀⠀⠀⠀⠀⠈⠁⠀⢵⣿⣷⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⣠⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⢰⣤⠞⡡⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣏⠀⣸⣿⣿⣿⣿⣿⣿⠛⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⢸⡿⠀⣪⣿⣥⣤⣟⠻⡟⠍⠀⠉⠉⠉⠛⠙⢿⡿⠏⠉⠩⡿⠿⠟⠛⠻⠿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣿⡟⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠇⠀⠐⠛⠉⠉⠙⠒⠲⠖⠂⠀⠉⠻⢧⢠⣼⠟⠉⠁⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠉⠉⠀⠀⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠁⠀⠀⠀⣀ ⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠠⣾⣿⣿⣷⣄⠀⠀⢸⣿⠛⠛⡿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠛⠀ ⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⡿⠿⢧⡀⣀⠀⠀⠀⠀⠉⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣽⡛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠛⠉⠀⠀⠀⠀⣀ ⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣶⣤⡄⠀⠀⠀⣀⣠⡤⠆⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠟⠀⠀ ⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣦⣄⠀⠈⡟⠀⠀⢀⡿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠂⠀⠉⠀⠀⠀⠀⠀⠀⠔⠒⠉⠀⡀⠀⠀⠰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡄⢀⡈⠉⠀⠀⠃⠀⠀⠉⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢸⣿⣿⣿⣿⣿⠉⢙⣿⣿⣿⣿⣷⠀⠶⠖⣿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⣠⣄⡀⢀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣴⣿⡿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣦⣶⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⣽⣿⣿⡏⠉⠉⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⣿⡿⠿⠃⠽⣷⣷⣤⣾⣿⣿⣿⣿⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⡻⡫⡋⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⣼⠟⠁⠉⠀⠉⠁⢸⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠀⢸⣿⣿⡄⢊⢻⣿⡿⣿⣿⣟⠁⢡⢁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢰⣶⣾⣾⣿⣿⡇⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡆⠿⢿⣿⡿⠿⢸⣿⣿⠿⢾⣿⣿⣶⣿⣿⢻⣿⣿⣿⣧⣃⡃⣿⣿⡿⣿⣷⣺⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⢸⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⠀⣼⣿⣿⣦⢸⣿⣿⣸⣿⣿⢸⣿⣿⣿⣿⣿⣷⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡆⢼⣿⣿⣇⢸⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠇⣠⡀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⡇⣰⣿⣿⣿⡛⠂⢿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡙⣿⣿⣿⣿⡇⢸⣿⣿⠇⢸⣿⣿⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⠛⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠉⠁ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣸⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⢸⣿⣿⣽⡿⣿⣿⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⢸⣿⣿⣤⢸⣿⡇⢻⣿⢹⣿⣿⣿⣿⣿⣤⡄⣿⣿⡿⣿⣿⠀⠀⠀⠀⢩⡉⠉ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⣰⣿⣿⣿⣿⣯⣿⣿⣿⡟⣿⡍⠉⠉⠀⠈⠉⠉⠉⠁⠘⠿⠿⠉⠉⠉⠉⠈⣯⣽⣿⣿⣿⣿⣿⣍⢉⠈⠉⠙⠫⣬⣍⠁⠈⠉⠈⠉⠉⠉⢽⣯⠉⠡⢉⣉⣁⡉⠉⠀⠀⠀⠀⠀⠛⠇ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠶⣰⣿⡯⢿⡿⠟⠙⢻⣿⣿⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⡯⢻⣿⣆⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠀⢻⣧⡰⠿⣛⣛⣿⣇⡀⠈⠙⠛⠃⠐⠀ ⠀⠀⣶⣾⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⠇⠙⠂⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠛⠁⠀⠀⠀⠀⠀ ⣄⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣂⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠉⠉⠉⠛⠇⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠏⠀⢀⣀⣀⡀⠀⠀⠀⠀⡀⣿⣿⡟⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡏⠀⠐⠋⠉⠉⠙⠓⠒⠛⠀⠀⠉⠻⢶⣦⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠈⠉⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢠⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠀⠀⠉ ⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡿⣿⣿⡿⢿⣧⣄⣤⣴⣶⣿⠉⠁⠀⠙⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣯⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⠚⠋⠉⠀⠀⠀⠂⠀ ⠈⣭⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⢠⣾⣿⣿⣿⣿⡗⠀⠀⠀⠀⠈⢿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⡂⡀⠀⢀⣤⡴⠶⠂⠈⠁⠀⠀⠀⠀⢁⡴⠶⠛⠋⠀ ⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣦⣄⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣴⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⡀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣮⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣤⠠⢰⣿⡿⢿⣿⣿⡟⣿⣿⡿⣿⣿⣿⡇⠰⠚⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⣀⣠⣤⣸⣿⣿⣿⣿⣿⠋⣿⣿⣿⣷⣌⠋⣀⣸⣿⣿⣗⠜⢿⡿⣿⣿⣿⣿⡀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⣿⣿⣿⠁⢰⣿⣿⣿⣿⣟⣻⣿⣏⣹⠀⠘⠛⠛⠿⢿⣷⣿⣿⣿⣿⣗⢀⠀⢀⣀⣸⣿⣿⣷⣶⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣷⡎⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⣿⠛⠿⠿⠿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠄⢀⣼⣿⣿⣿⡇⢸⠿⣿⣿⡋⠙⢿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⢠⣀⣀⣀⣠⣦⣄⣀⣀⡀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡆⠿⢿⣿⡿⠿⢸⣿⣿⠿⢺⣿⣿⢾⣿⣿⣻⣿⣿⣿⢏⢁⠀⣿⣿⡿⣿⣷⡐⣹⣿⣿⣿⡀⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣷⢸⣿⣿⣧⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⠛⢻⣻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⢠⣾⣿⣿⣤⠈⣿⣿⣸⣿⣿⢸⣿⣿⣿⣿⣿⣧⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡧⢸⣿⣿⣽⢼⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢁⣤ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢸⣿⣧⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣉⣿⣿⣿⣿⣧⣸⣿⣿⠟⢸⣿⣿⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣤⢸⣿⡇⢻⣿⢸⣿⡗⢸⣿⣿⣬⡟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢡⠉ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠱⣿⣿⣭⣽⣿⣯⠉⣿⣿⣿⠉⠉⠉⠉⠀⠈⠉⢹⣿⣿⣿⡗⠉⠉⠉⠉⠉⢨⣯⣽⣿⣿⣿⣿⣯⣿⣍⡈⠉⠉⠉⠪⣿⣥⠈⠉⠈⠉⠁⠈⠉⠭⣿⡅⣍⣉⣁⣉⡉⠀⠀⠀⠀⠀⠈⠓ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠾⠀⠉⠙⠟⠉⠉⢹⠘⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠈⠻⡿⠄⠀⠀⠀⡈⠻⣷⣦⠀⠀⠀⠀⠀⠀⢹⣷⡾⢏⣝⣻⣿⣧⠀⠉⠉⠉⠁⣀ ⠀⠀⢠⣶⣾⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡿⠉⠓⠀⠀⠀⠀⠀⠀⣰⣿⣟⡋⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀ ⣶⣄⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠈⠘⠛⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶ ⣿⣿⣿⣿⡿⠁⢀⣀⣀⣀⣀⠀⠀⠀⡠⢸⣿⡟⢹⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀ ⣿⣿⣿⣿⠃⠀⠉⠉⠉⠉⠙⠛⠛⠃⠀⠀⠘⠻⣾⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠁⠠⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢰⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠓⠀⠀ ⠲⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠼⣿⢿⡿⡿⠟⢿⣦⣴⣶⣿⣿⣿⣿⠏⠁⠀⠙⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣦⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠙⠋⢁⠀⠀⠀⣀⣀ ⠀⢨⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠐⢹⣿⣷⣦⣀⠀⠀⠀⠀⠐⠀⣠⣾⣿⣿⣿⣻⣿⣿⣿⣇⢀⠀⠀⡤⠶⠚⠋⠀⠀⠀⠀⠀⣀⠀⠴⠖⠛⠉⠁ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⣀⠀⠀⠀⠀⠀⢀⡾⢿⣿⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⡀⠀⠀⣰⣿⣿⣿⣿⠁⠉⢿⣿⣿⣿⣷⣅⠀⠀⣀⣀⠀⠤⠄⠀⠈⠉⠀⡀⠠⣀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠉⠙⠁⠁⠀⠀⠀⠀⠈⠈⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠐⣿⡿⠛⠻⡿⣤⣶⣾⣿⣿⣿⣿⣿⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡗⠀⣤⣤⣶⣷⣿⣿⣿⣿⡿⠛⣿⣿⣿⣷⡌⠀⠀⠀⢸⣿⣿⣿⡟⠛⢿⣿⣿⣧⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠍⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⠸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣯⢯⠀⠙⠛⠿⠿⢿⣶⣾⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⡀⠀⠀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⣙⣟⠋⣻⡿⠷⢶⣶⣶⣾⣿⣿⣿⣿⠾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢶⠶⣀⣴⣾⣿⣿⣯⣕⣠⣿⣻⣫⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠉⠉⠛⠻⢿⡟⠁⠀⣠⣤⣤⣤⣴⣶⣄⣠⣤⡀⠀⠀⠤ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡆⠿⢿⣿⡿⢿⣼⣿⣿⠿⢸⣿⣿⢸⣿⣿⣻⣿⣿⣿⣿⣧⣤⣿⣿⡿⣿⣿⠀⣸⣿⣿⣿⣀⢸⣿⣿⡀⢸⣿⣿⠀⢸⣿⣿⣷⢸⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠿⠥⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⣷⣿⣿⣿⣿⣤⣈⣿⣿⣸⣿⣿⢹⣿⣿⣼⣿⣿⣿⣿⣿⣧⣿⡿⣺⣿⣿⣿⣿⡷⢸⣿⣿⣿⣼⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⣤ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⣸⣿⣿⣿⢿⣿⣿⣿⣯⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡟⣿⣿⡟⣿⣿⡈⣿⣿⣾⣿⣷⣾⣿⣿⡝⢸⣿⣿⠀⢸⣿⡇⣿⣿⣿⣿⡏⢹⣿⣿⠛⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⣿⣾⣿⣿⣿⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠏⠀⣿⣿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢸⣿⣿⣦⣸⣿⡇⢻⣿⢸⣿⡇⢸⣿⣿⣦⡌⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠻⣿⣯⣭⣭⣿⡌⠉⣿⣿⣿⡏⠉⠉⠉⠀⠈⣿⣿⣿⡟⠀⠀⠉⠉⠉⠉⠉⢨⣽⣿⣿⣿⣿⣿⣿⣽⣿⣨⠉⠉⠉⠙⢽⣷⡈⠉⠈⠉⠁⠈⠉⠉⣽⣧⢩⣩⣥⣭⣍⡀⠀⢀⣀⣀⣀⠈ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⠀⠈⠑⠁⠉⠘⡃⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⠁⠙⠿⠗⠀⠀⠀⠠⡙⣻⣿⣄⠀⠀⠀⠀⠀⢨⣿⣿⣛⣭⣭⣿⣿⣄⠀⠈⠉⠉⠠ ⠀⠀⠀⣴⣶⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⠏⠙⠂⠀⠀⠀⠀⠀⢠⣾⣿⣋⡁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠍⠉⠈⠀⠀⠀⠀⠀⠀ ⣿⣦⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣵⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠿⠿⢿⠿⢿⣿⣿⣿⡿⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾ ⣿⣿⣿⣿⣿⠏⠀⣠⣤⣤⣤⣀⢀⣀⠠⠄⣿⣿⡏⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠀⠉⠉⠀⠀⠉⠋⠉⠃⠀⠀⠈⠛⢿⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠈⣀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣿⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡼⣻⣿⣿⣷⣄⠀⠀⠀⣀⣀⣀⣀⣀⣻⣿⡿⠛⢿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠾⠛⠀⠀ ⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠻⠿⠿⠛⠻⣷⣶⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣷⣼⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠤⠀⠈⠉⠀⡀⠀⠀⣀⣀ ⠀⠀⢤⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣻⣷⣤⣀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢻⣿⣿⣿⣷⣤⢄⠀⠴⠶⠛⠋⠀⠀⠀⠀⢀⣀⠄⠰⠞⠛⠉⠁ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⢀⡀⠀⠀⠀⠀⣹⣿⣿⠿⣿⠿⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣷⣄⠀⠀⣰⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣷⠀⠀⣀⣀⡀⠠⠖⠀⠉⠁⠀⠀⠐⢀⠤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡿⠟⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣧⠄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄⢻⡿⠋⠉⠛⠀⠀⠀⣿⣿⣿⣿⣿⡆⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠅⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⢿⡃⢹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⡿⠏⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⠷⡄⠀⠀⠀⠛⠛⠷⢶⣦⣤⣴⣤⣿⣿⣿⡏⠉⢻⣿⡆⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⣾⣿⣿⣿⡿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣶⣦⣴⡾⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⢻⢓⣆⣤⣴⣿⣿⣿⣶⡇⢰⣿⣿⡏⠓⠋⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠉⠙⠛⠛⠋⠁⠈⣙⣿⣿⣿⣿⣿⣿⣢⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡆⠿⢿⣿⣿⣿⣾⣿⣿⠿⢸⣿⣿⢸⣿⣿⣻⣿⣿⣿⣿⣿⣷⣿⣿⡿⣿⣷⠉⣺⣿⣿⣿⣀⢸⣿⣿⣄⣸⣿⣿⠀⢸⣿⣿⣷⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠵⠄⢀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⣿⣿⢿⣿⣧⣤⣈⣿⣿⣸⣿⣿⢸⣿⣿⣼⣿⠿⠟⣿⣿⣧⣿⡿⠀⣿⣿⢿⣿⡿⢺⣿⣿⣷⣿⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⡇⢸⣿⣿⣤⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢠ ⠀⠀⠀⠀⠀⠀⢀⣈⣛⢿⣿⡆⢀⣾⣿⡇⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠛⠋⠀⠀⣿⣿⡟⣿⣷⣄⣿⣿⣾⣿⣿⣿⣿⣿⢭⢹⣿⣿⡀⢸⣿⡇⣿⣿⣿⣿⡇⢸⣿⣿⡛⢺⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⣿⣿⣿⣿⡇⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢸⣿⣿⣧⣼⣿⡇⢻⣿⢸⣿⡇⢸⣿⣿⣷⡄⣿⣿⡏⣿⣿⠣⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⢽⣭⠩⠵⣷⠈⠉⣽⣿⣿⡏⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⢭⣽⣿⣿⣿⣿⣿⡏⣿⣬⡉⠉⠉⠈⠙⣿⣎⡉⠈⠉⠁⠈⠉⠉⢹⣷⡍⣭⣤⣭⣭⣄⠀⢀⣀⣀⣀⡀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠾⠀⠀⠀⠀⠀⠘⠁⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠈⠙⠃⣀⠀⢀⣀⣊⢻⣿⣧⠀⠀⠀⠀⠀⠈⣿⣿⣿⣵⣮⣿⣿⣶⠀⠀⠀⠀⠰ ⠀⠀⠀⣴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀ ⣆⡀⠀⢿⣿⣿⣿⣿⡏⠙⠃⠀⠀⠀⠀⠀⢀⣾⣿⣯⣅⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠟⠟⠛⠻⠿⠛⢿⡿⠛⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⢀⣠⣤⣤⣤⣤⣀⣤⠠⠖⠼⣿⣏⠈⢻⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠀⠀⠙⢹⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣁⣢⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠛⠉⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⡼⠛⣿⣿⣿⣦⡀⠀⣀⣤⣤⣴⣦⣤⣤⣤⣤⣿⠟⠉⠙⠿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⣏⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠁⠀ ⠀⠀⠙⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠚⠛⢋⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡀⠀⠄⠂⠀⠉⠀⠠⠀⢀⣀⣤ ⠀⠀⠠⠶⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠈⠻⣿⣿⣿⣿⣅⠀⠰⠚⠋⠉⠁⠀⠀⠀⣀⡠⠄⠐⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡟⠁⠀⢈⣿⣿⣧⣽⡄⠀⠀⠀⠀⣰⣿⣿⣿⣶⡀⠀⢸⣿⣿⢿⣿⠇⠀⠀⢻⣿⣿⣿⣿⡄⢀⣠⣤⡄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⣤⠀⠀⠀⢸⣿⣿⡧⠝⠋⠻⠟⠃⠀⠀⢀⣸⣿⣿⣿⣿⣿⠆⢀⣀⣼⣿⣿⣿⠟⣿⣿⣦⡘⠛⠀⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠻⣏⣻⠃⢀⣿⣿⣿⣿⡟⠃⠀⠺⠿⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⣸⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠉⠀⣀⣀⣀⣀⠀⠀⠀⣠⣄⣨⣿⣷⣶⣶⣶⢿⣁⣀⣀⣀⣤⣾⣿⣷⠀⠀⠀ ⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣠⣾⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡿⢟⣁⣧⣶⣿⣿⡿⢿⣿⠇⠑⠂⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⠟⠛⠀⣩⣽⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⡿⣿⠿⠏⠀⠀⠀⠀⠀⠉⢻⣧⣴⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠻⠿⣿⣿⣿⠋⠁⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢻⣿⡆⠿⣿⣿⣿⣿⢸⣿⣿⠿⢸⣿⣿⢸⣿⣿⢹⣿⣿⠿⠿⠻⡟⣿⣿⡿⣿⣷⠀⣸⣿⣿⣿⣠⢼⣿⣿⠤⣼⣿⣿⠀⢸⣿⣿⣿⢹⣿⣿⡇⢸⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⢀⣿⣿⡏⠋⢸⣿⣷⣤⣼⣿⣿⣼⣿⣿⢸⣿⣿⣤⠀⠀⠀⣿⣿⣧⣿⡿⢀⣿⣿⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⡇⢸⣿⣧⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠁ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⣦⠾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⠲⢹⣿⣿⡄⢸⣿⡇⣿⣿⣿⣿⡇⢸⣿⣿⡟⠘⣿⣿⡿⣿⣷⡀⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⡿⠀⣿⣿⣇⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣸⣿⣿⣿⢼⣿⣇⢻⣿⢸⣿⡇⢸⣿⣿⣿⡄⣿⣿⠁⣿⣿⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠉⠉⠁⠷⠈⠉⣽⣿⡿⠏⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠩⣿⣿⣿⣿⣿⣯⠹⣿⣏⠉⠉⠈⠉⢹⣯⣉⡈⠉⠁⠈⠉⠉⠩⣿⣭⣹⣶⣿⣿⣤⡀⠀⠤⠤⠤⠤ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⡇⠀⠈⠁⣠⡀⢀⣤⣥⣽⣿⣷⡀⠀⠀⠀⠀⠈⢿⣿⣯⣵⣶⣾⣿⣷⡄⠀⠀⠀⠈ ⠀⠀⠀⣶⣶⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠛⠀⠀⠀⠀ ⣦⡀⠀⣿⣿⣿⣿⣿⠏⠙⠂⠀⠀⠀⠀⠀⢀⣼⣿⣯⣅⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠋⠛⠛⠛⠛⠛⠛⢿⣿⠉⠛⠟⠻⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⢀⣠⣤⣤⣤⣤⣀⣤⠠⠒⠺⣿⣿⣉⣻⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⢻⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢭⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⣀⣢⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠖⠀⠀⠀⣀⣀⠀ ⠋⠋⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⡾⠙⠋⣻⣟⣷⡀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠛⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣽⣿⣯⡉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⡤⠶⠚⠉⠁⠀ ⠀⠀⠙⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠙⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠑⣿⠁⠀⠀⠀⢀⣴⣾⣿⣿⢿⣿⣿⣿⣷⣀⠀⠀⠀⠀⢀⣀⡄⠀⠖⠂⠀⠀⠀⠀⠀⣀⣠⣤ ⠀⠀⠀⠴⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡯⠋⠀⠀⠀⠀⠀⠀⢨⡁⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠙⣿⣿⣿⣿⣦⡀⠐⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢈⣿⣿⣧⣆⠀⠀⠀⠀⢀⣴⣿⣿⣶⡀⠀⢸⣿⠟⠛⠛⠃⠀⠀⢹⣿⣿⣿⣿⣇⢀⣠⣤⠤⠀⠊⠁⠀⠀⠀⠀⠀⠁⠐⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣤⣤⠀⢀⣀⣰⣿⣿⣿⡷⠘⠋⠀⠀⠁⠀⠀⠀⢠⣿⣿⢿⠿⠶⠂⢀⣤⣾⣿⣁⠟⢿⣿⣦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⢿⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀ ⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠄⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡤⠀⠈⣿⣿⣿⡿⠉⠀⠀⠘⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣧⣤⣤⣴⣴⣾⣀⣀⣤⣤⣴⣿⣿⣿⣄⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⢛⣼⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡇⠀⣾⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠻⡿⢿⣿⡿⠁⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣧ ⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣼⣿⣿⣿⡿⠃⠀⠀⠀⠀⢀⣼⠀⠀⢀⣠⣼⣿⣿⣿⣿⣷⣾⣿⣿⠟⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⡿⢿⢿⣿⠁⠀⠀⠀⠀⠹⢹⣿⢆⣀⣴⣿⢿⣿⣿⣿⣿⣿⣿⡟⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣧⣀⣀⢀⣀⣀⣀⣤⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡆⠿⣿⣿⣿⣿⢸⣿⣿⠿⢸⣿⣿⢸⣿⣿⢹⣿⣿⠿⠇⠂⠗⣿⣿⡿⣿⣿⠀⣸⣿⣿⣿⣀⢼⣿⣿⠒⣼⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⢿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⢀⣿⣿⣿⡟⢸⣿⣧⣤⣼⣿⣿⣼⣿⣿⢸⣿⣿⣀⠀⠀⠀⣿⣿⣧⣿⡿⢀⣿⣿⣻⣿⣿⣹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣧⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣛⢿⣿⣮⠛⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⠒⢸⣿⣿⡄⢸⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⢻⣿⣿⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣸⣿⡿⠀⣿⣿⡇⢢⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣽⢻⣿⣧⣻⣿⢹⣿⡏⢸⣿⣿⣿⣮⣿⣿⡄⣿⣿⠉⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠈⠉⠁⠈⠉⠉⠩⠿⠿⠏⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⢩⣿⣿⣿⣿⣿⡯⠙⢿⡯⠉⠉⠈⠉⡙⣿⣭⡈⠉⠁⠈⠉⠉⠉⣽⣯⣭⡶⠿⣿⣶⡄⠀⠐⠶⠶⠄ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡿⡿⣿⠃⠀⠀⠁⢠⡄⠀⣶⣶⣞⢿⣷⡄⠀⠀⠀⠀⢘⣿⣿⣇⠶⠿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⣤⣶⣾⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀ ⣦⣤⣿⣿⣿⣿⣿⡿⠙⠂⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠙⠉⠉⠉⠁⠹⠟⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠋⠀⢠⣤⣤⣤⣤⣠⡄⠰⠂⢾⣿⣁⠈⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠉⢻⠾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡻⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⣠⣤⣦⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣻⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀ ⠀⠀⢻⣿⣿⡿⠶⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⠏⠉⠉⢻⠛⢷⣄⣤⣴⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣼⣿⣷⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠛⠋⠁⠀⠀ ⠀⠀⠈⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⢩⡿⠀⠀⡀⢠⣾⣿⣿⡿⠻⣿⣿⣿⣿⣅⠀⠀⠀⠀⣀⣤⡤⠀⠂⠉⠀⠀⠀⠀⠀⠀⠠⠶ ⠀⠀⠀⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠋⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣷⡄⠘⠉⠁⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⠛⠉⠙⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⡀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⢠⡤⠶⠖⠀⠉⢀⣠⡴⠃⣀⣴⣿⣿⣧⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡷⣠⣴⠄⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⡿⣽⠿⠀⠀⠀⢀⣠⣾⡟⠙⠿⣿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡶⢿⣏⣠⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠆⢠⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣭⣾⡂⠀⠀⠀⣾⣿⡿⠋⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⠿⣿⣿⣿⠏⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⠿⠋⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⠀⢀⣠⣴⣾⣿⣿⣿⠇⠀⠀⢘⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠀⢀⣀⣰⡿⠁⠀⠋⠙⠟⠿⠛⢉⣡⣵⣶⣿⣿⡋⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀⠈⣋⣿⣿⣀⣀⣀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠂⠈⢛⠛⠻⠿⢿⠿⠉⠁ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡆⠿⢿⣿⡿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣿⣿⢹⣿⣿⠿⠇⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣤⣸⣿⣿⡒⣾⣿⣿⠀⢸⣿⣿⣿⣼⣿⣿⡇⢸⣿⣿⠿⠀⣿⣿⡿⣿⣯⠀⠀⠀⠟⠉⠀⠠ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⣽⣹⣿⣿⣧⣼⣿⣿⣼⣿⣿⢸⣿⣿⣀⠀⠀⠀⣿⣿⣧⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣤⣀⣿⣿⣧⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣙⢿⣿⡆⠀⢾⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⡉⢺⣿⣿⣶⣸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠟⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⡇⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⢹⣿⣧⣿⣿⢹⣿⡟⢻⣿⣿⣿⣷⣿⣿⠆⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠈⠉⠁⠀⠈⠉⠹⠿⠿⠋⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠩⣿⣿⣿⣿⣿⣯⠉⠹⣿⠍⠉⠈⠉⠩⢿⣭⣨⠉⠁⠈⠉⠉⢉⣽⣯⣭⠿⣛⢿⣿⣆⡀⠐⠒⠒⠒ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⡿⠟⠻⠋⠀⠀⠀⠰⣦⠀⣶⣶⣶⡻⣧⠀⠀⠀⠀⠀⠘⣿⣿⣧⠚⠻⢿⣿⣿⣗⠀⠀⠀⠀ ⠀⢠⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀ ⣷⣾⣿⣿⣿⣿⣿⠏⠙⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⠿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠁⠀⢤⣴⣶⣶⣤⣠⡄⠐⠀⢿⣿⣆⢌⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠉⠿⠿⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣤⣤⣷⣷⣦⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⢿⣹⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠀ ⠀⠀⢻⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡘⠃⠉⢀⣟⣋⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣦⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠞⠋⠁⠀⠀⠀ ⠀⠀⠘⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠟⠛⠉⠉⠹⢿⡟⠀⠀⠀⣰⣿⣿⣿⣿⢫⣿⣿⣿⣿⣆⡀⠀⠀⣀⣠⡤⠶⠀⠉⠁⣀⠀⠀⠀⣀⣤⠴⠖ ⠀⠀⠀⠠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢰⣿⠟⠙⠛⠃⠀⠈⣿⣿⣿⣿⣿⡆⠈⣉⣀⣤⣤⣀⣴⣾⡿⠃⠀⣰⣿⣿⣷⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠉⠉⠀⠀⠸⣿⠿⠄⠀⠀⠀⠀⠀⠀⣠⣿⣦⡀⠀⠈⡛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⠁⡤⣤⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣓⣾⡆⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠖⢼⣶⡀⠀⠀⠀⠀⣾⠿⠉⠿⢿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢛⣿⣿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠐⠿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⡧⠀⠀⠀⢾⣷⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠁⠀⠀⠀⠀⣽⣿⣿⣿⣿⠀⠀⢀⡗⠀⠲⣿⣿⣿⣿⣿⡟⠁⠀⠸⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣀⣀⣾⡇⠀⠀⠈⠛⠁⠐⠈⣗⣠⣶⣶⣿⠇⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠇⠀⠀⠀⠀⠀⢀⠀⢀⠀⢙⠛⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣹⣿⣧⡆⢀⠀⠀⠀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⢰⠀⡀⠛⣿⣓⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⡆⠿⢿⣿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠿⠇⠀⠀⣿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣦⣼⣿⣿⣈⣸⣿⣿⠀⢹⣿⣿⣷⣼⣿⣿⡇⢸⣿⣿⠿⠀⣿⣿⡿⣿⣷⠀⠀⠀⠋⠉⠀⠰ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣬⡉⠁⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⢸⣿⣿⣀⠀⠀⠀⣿⣿⣧⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠹⢿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣤⣀⣿⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⣛⢿⣿⡆⠀⢸⣿⡇⠀⢸⣿⣿⠛⣿⣿⣿⣿⣿⡇⢸⣿⣿⠛⠀⠀⠀⣿⣿⡟⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣌⢻⣿⣿⣷⣼⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⠟⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣸⣿⡏⠀⢸⣿⡇⠀⢸⣿⣿⣬⣽⣿⣿⣿⣿⡇⢸⣿⣿⣤⡄⠀⠀⣿⣿⣧⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢹⣿⣷⢿⣿⢹⣿⡿⢿⣿⣿⣿⣷⣿⣿⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠈⠉⠁⠀⠈⠉⠉⠉⠙⠋⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠩⣿⣿⣿⣿⣿⣿⠉⠙⠟⠋⠉⠈⠉⠉⠻⣍⠈⠉⠁⠈⠉⠉⢉⣽⣿⡿⠿⣙⣻⣿⣷⡀⠈⠉⠉⠉ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠉⠛⠁⠀⣀⡀⠐⣶⠀⣾⣿⣷⡿⢷⠀⠀⠀⠀⠀⠠⣿⣿⣷⡙⠛⢻⣿⣿⣷⠀⠀⠀⣀ ⣰⣶⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⡟⠋⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠀⠀⠰⠴⢶⣶⣤⡴⠄⠋⠀⠿⣿⣤⢬⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠛⠉⠓⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⡿⠶⠾⠿⠶⣀⣀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⢻⣽⡟⠻⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢀⣤⣄⡤⠶⠂ ⠀⠀⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡌⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣶⣧⣂⠀⠀⠀⠀⠀⢀⣀⡀⢠⣴⣾⡿⠀⠘⠋⢁⡀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠈⠉⠁⠀⠈⠉⠉⠉⠙⠋⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⣿⣿⣿⣿⣿⣯⠉⠉⠿⠋⠉⠈⠉⠑⠙⣯⡈⠉⠁⠈⠉⠉⠉⣹⣽⣽⢛⣩⣭⣿⣿⣄⠈⠉⠉⠉ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⠉⠉⠀⠀⣀⡄⠀⢷⠀⣸⣿⣿⣞⢿⡄⠀⠀⠀⠀⠐⢽⣿⣿⡌⠉⢻⣿⣿⣯⠀⠀⠀⣀ ⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣶⣦⡉⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠟⠠ ⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠒⠀⢠⣿⣿⣿⣿⣿⡟⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡀⠀⠀⣀⠀⣸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣩⣭⣠⠀⠀⠈⠘⠛⠆⠀⠑⠑⣿⣿⣿⣿⠏⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡏⠀⠀⠻⠻⠿⠿⠿⠟⢀⠀⠘⠿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣀⣠⣬⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣄⠀⠀⡀⠔⡤⣴⣴⠂⢸⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⣤⣤⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣄⣀⣴⣾⣶⣦⣤⣀⣠⣿⣿⣿⣿⣿⣿⣆⠉⠀⠀⠊⠛⠁⠀⠈⣹⣿⣿⠿⣟⠀⣠⣴⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢠⣄⣀⣴⣿⠗ ⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠇⠉⠉⠀⠀⢀⣠⡄⠀⠙⣸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣤⣴⠶⠒⠀⠈⠀⠀⣠⣿⣿⣿⣿⣿⣿ ⠛⠛⠉⠉⠛⠢⠦⠄⠀⠀⠀⠀⠀⣼⣴⣄⣠⣴⠂⣾⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣄⡀⠀⠀⢸⣿⠃⠀⣴⣿⣿⣿⠏⠉⠹⣿⣿⣮⡻⣧⣀⣀⠀⢠⡦⠀⠀⠉⠉⠋⠉⠻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⢹⣭⣴⠀⠙⠋⠈⠋⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣠⣾⣿⣿⣿⣦⣄⡌⠋⠀⠀⠿⠿⠅⠁⠀⢰⣶⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠒⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠘⠟⠡⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⡡⠀⠀⠀⠀⠀⠛⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⣾⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠤⣀⣾ ⠢⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠨⠻⢗⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⠀⠀⢀⡘⠀⡉⣀⣈⡉⠀⠀⠐ ⠷⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠠⠄⠩⠻⢻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⠆⠐⠀⣈⣛⣼⡏⣻⣍⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⡀⣠⣀⡀⣰⣴⠌⢞⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠻⡟⢹⡇⠬⠛⣿⣿⡇⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣀⣼⣿⣹⣿⡿⡟⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣾⣿⣿⡿⣟⣯⣿⣿⡶⠛⠻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠋⠀⠀⠈⠛⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠋⠉⣧⣶⣿⣿⣿⣿⣦⣧⣘⡿⠃⣀⣀⠀⠀⠉⠻⢿⣿⣿⣷⣤⣄⣀⠀⣿⣧⠀⣤⣶⣤⡀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⠀⠙⠿⢿⡄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡹⣿⠀⠘⠻⢿⢿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠙⠷⣷⣤⣀⣨⣿⠿⣿⣿⣿⣷⣿⣤⣤⣤⣤⣤⣀⢀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠻⣿⠅⠀⠀⠀⠀⢅⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠙⠻⠃⡀⠁⣐⣉⣙⣿⣿⣿⡇⣠⣶⣤⣾⣿⣿⣿⣻⣿⣿⣿⣿⣶⠁⠉⠉⠉ ⠀⠶⠶⣶⠿⢷⠖⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡩⠁⠴⠶⠈⣿⠀⣿⣿⣿⣿⢻⣿⠀⠹⠛⢻⣿⣿⣿⣿⣏⠹⣿⣿⣿⣿⡀⠀⣴⣦ ⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣄⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠀ ⣿⣿⣿⣿⣿⣿⠁⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠏⠂⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠩⠑⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠇⠀⠀⣀⣀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢈⣽⣯⣥⠀⠀⠋⠰⠙⠛⠛⢹⣿⣿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡏⠀⠀⠋⠉⠛⠛⠛⠋⣤⠀⠈⠙⠟⠛⠻⢯⡀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠠⣷⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣦⣀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣉⣤⣶⣶⣶⣤⡆⠀⠆⠢⢠⣆⣤⣾⡴⢹⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⡿⠉⠀⠀⢠⡄⠀⠀⠀⠀⠀⡀ ⣿⣿⣿⣿⣷⣶⣦⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⡿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠉⠉⠉⠀⢈⣹⣿⣿⠻⣿⣠⣼⣿⠿⠏⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⡀⠀⠀⠀⠀⠀⢀⣠⠄⠀⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⣀⣀⠄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠐⣾⣿⠟⠛⢻⣿⣿⣿⠋⢈⣿⣿⢿⣿⣦⣶⠿⠟⠂⠈⠁⠀⣴⣿⣿⡿⠿⣿⣿ ⠛⠃⠋⠉⠙⠛⠒⠂⠀⠀⠀⠀⢠⣿⣿⣿⣾⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠉⠙⠻⠟⣿⣿⣿⣦⣄⠀⠀⠀⣿⡿⠀⢠⣿⡿⠿⠏⠀⠈⣿⣿⣷⣝⣿⣦⣤⠀⠀⠛⠀⠀⠀⠀⢀⠀⢀⣀⣍ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⠀⢾⣿⢿⠻⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣶⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣤⠄⠘⠁⠰⠼⠿⠅⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁ ⠿⠿⣿⣤⣤⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠙⠙⠓⠀⠀⠉⠙⠉⠉⠀⡐⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣄⡀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⡾⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⣨⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡳⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡯⠟⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠛⠻⡀⠀⣀⣀⣀⡀⠀⠀⠦ ⠃⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠑⠒⠿⡿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⢀⣈⣻⣾⣿⣻⣇⣨⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣲⡆⣀⣴⣷⡦⠖⠻⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠉⠁⠀⠀⠈⠻⣟⣻⡏⠬⠛⣿⣿⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣦⣼⣿⣼⣿⣿⠟⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⣏⢿⣿⣿⡖⠀⠈⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⡀⠀⠠⡄⠈⠛⠉⠀⠈⠛⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠙⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠉⢀⣿⣿⣿⣿⣿⣿⣷⣷⣬⡟⠁⣀⣄⣀⠀⠀⠈⠻⣿⣿⣿⣷⣶⣤⠈⣿⣧⢀⣴⣶⣤⡀⠀⠁⠀⠀⠁⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠻⢿⣄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⣿⣿⠀⠘⠻⣿⢿⣶⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡀⠀⠀⠘⣿⣿⣶⣤⣼⣍⡙⠻⠿⣿⣿⣿⣷⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⡇⠀⠂⠈⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠈⠙⢱⣀⠀⣼⣯⣍⣿⣿⣯⠁⢺⣾⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣷⠉⠉⠉⠉ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⠾⠷⢈⣿⠀⣿⣿⣿⣯⢻⣿⠀⡥⡟⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⡀⠀⣴⣾ ⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟ ⣿⣿⣿⣿⣿⣿⡿⠿⠆⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠋⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢁⡀⡀⠄⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢈⣽⣶⣦⡀⠈⠀⠉⠉⠛⠉⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⠁⠀⠘⠉⠉⠛⠛⢛⡷⠀⠀⠈⠀⠀⣉⣻⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛ ⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣷⣄⠓⠂⠠⠾⢿⣶⣦⣾⡕⢸⣿⣿⣿⣿⣿⠇⠀⢀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⡄⢀⢤⣤⣤⣠⣀ ⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠨⠙⣿⣿⣿⣿⠋⠉⠙⠓⢠⣤⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠉⠙⠉⢁⣀⣸⣿⣿⡻⣿⢀⣰⣿⣿⣟⠻⠛⠛⠀⠀⠀⠀⠀⠀⣰⣽⣿⣿⣿⣿ ⠉⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢀⣿⣿⣿⣿⣤⣤⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣿⣿⣿⣿⣿⣿ ⠀⠸⡿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣾⣤⣤⣤⣤⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⢿⣿⣿⣿⣿⣄⡠⠀⠀⠀⠐⢰⣿⣿⠿⢿⣟⣿⣿⣿⠛⢻⣿⡻⣿⣷⣶⠾⠟⠃⣀⡀⠀⠛⠛⠋⠨⠿⠿⠻ ⠀⠈⠁⠐⠁⠉⠙⠒⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠋⣻⣿⣿⣿⣿⣶⣄⠀⠀⢸⣿⠇⠀⠀⣼⣿⠿⣟⠀⢸⣿⣷⣮⣻⡷⠒⠂⠀⠉⠀⠀⠀⠀⠀⡀⠠⡀⣠ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡄⠠⠛⣡⢴⡆⣿⣿⠁⠀⠰⡀⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁ ⠿⠟⠀⠀⣠⣤⠄⠀⠀⠀⠀⠉⠛⠿⠿⠟⠁⠀⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢼⡄⠘⠛⠃⠀⠀⠀⠀⠹⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠉⠈⠉⠉⠁⣽⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻ ⡙⠂⡀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⠀⠀⠀⢀⣄⠀⣄⣀⣠⣀⠀⠀⠒ ⠁⠀⠰⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⡘⣭⠁⠸⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⣀⣙⣴⣿⢹⣧⣨⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣀⣰⣦⣀⣤⣾⡀⠀⠛⢿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢙⡏⠱⠟⣿⣿⣧⣀ ⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣦⣼⣿⣤⣼⣿⡿⠋⠉⠉⠻⢿⣿⣿⣿⣿⣿⠟⢻⣙⣛⣹⣿⣿⡟⣯⢾⣿⡿⠇⠀⠀⠉⠻⢿⣿⣿⣷⣦⣤⠀⠀⢀⣀⡀⠐⠆⠀⠙⠉⠀⠀⠉⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡬⡟⠁⣠⣴⣶⠆⠀⠀⠻⣿⣿⣿⣿⣷⠀⢸⣿⣧⡀⣴⣶⣶⣄⠀⠀⠀⠀⠁⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠉⠙⠻⣧⣀⣀⣴⡿⠛⠻⠿⣿⣧⣠⣿⣿⡇⠈⠛⠿⠿⠷⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡻⣿⠛⡁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⢀⠀⢈⣛⣿⣾⣇⡤⢢⣷⣿⣿⣷⣿⣿⣷⣤⣤⣤⣤⣄⣀⣀⣤⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠋⠻⠛⠀⠛⠀⠈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠉⠱⣀⠀⣾⣶⣮⣿⣯⡤⠱⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⣿⣿⣿⠈⠀⠀⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢨⣚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡳⢿⡛⢀⣿⠀⠿⠿⣿⣿⠹⡷⢸⠽⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⡄⠀⣰⣾ ⣿⣿⣿⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣭⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠉⠳⠼ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⡚⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡕⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠋⠙⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠽⡟⣿⢻⣿⣿⣿⣿⠛⢿⠛⢿⢟⣿⠟⢻⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⡄⠁⠉⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠛⠀⠀⠀⠀⢀⠀⠀ ⠀⣽⣿⣿⣿⡏⠀⠀⠚⠛⠛⠛⢿⡗⠀⠀⣀⣀⣠⣴⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠀⠀ ⠀⣽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⡄⠠⠐⠐⠠⠰⢀⣢⣴⡄⠰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣶⣿⣿⣿⡆⠀⠀⠤⠠⣄⣤⣤⣤⣀ ⠀⣻⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⣑⣿⣝⠁⠀⠀⠀⠈⣩⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠉⠑⢀⣀⣠⣿⣿⣛⣿⣠⣀⠀⣠⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡆⠀⣿⣏⠉⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡛⠛⠉⢉⠀⢠⣤⠤⠀⣼⣿⣿⣿⣿⣿ ⠀⠀⢹⢚⡿⠟⠉⠀⠀⠀⠀⠀⢠⣿⣧⣴⣼⡿⠁⠨⠿⢭⡆⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠋⠉⠙⠻⢿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢿⣿⣶⠾⠛⠃⣀⠀⠀⠘⠛⠁⡌⠿⠿⠛ ⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃⠀⠀⠈⠈⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡁⡀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣷⣦⠀⠀⢸⣿⡟⠁⠀⢀⣼⣿⡟⠛⢙⣾⣿⣷⣿⡟⠒⠂⠀⠈⠁⠀⠀⠀⠀⡀⠀⢄⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠟⢣⡀⡀⢸⣿⡿⠀⠀⠀⣹⣿⡿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠿⠟⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢼⣇⠀⣿⠿⠁⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠁⠀⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡙⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠙⠻⡿⢻⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⣀⠀⣠⣀⣠⡀⠀⠀⠀ ⠁⠀⠐⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣿⣿⣿⣿⣿⠇⠀⠀⡶⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠤⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⢀⣈⡲⢿⡇⣧⣤⣥⡀⠀ ⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⢃⣶⢴⣿⣾⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣠⣧⢀⣰⣶⣄⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⢈⣯⠘⠋⣿⣿⣿⣠ ⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣤⣿⣿⣿⠇⠁⠀⠈⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡟⢻⠸⣿⣿⠇⠀⠀⠀⠙⢻⣿⣿⣿⣿⣄⠀⠀⢀⣀⡀⠀⠺⠀⠈⠉⠀⠀⠉⠁⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡿⠟⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣤⢽⠁⣠⣼⣿⡆⠀⠀⣽⠿⣿⣿⣿⡄⠀⠸⣿⣷⡀⢴⣶⣶⣤⡀⠀⠀⠀⠈⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠟⠋⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠙⠛⢦⣀⠀⠛⠀⠈⣙⣿⣿⡄⠀⢻⣿⡁⠈⠙⠿⠻⠷⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠿⣿⣿⣿⡟⢿⣿⡋⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⢿⣾⣆⠀⠀⢀⠽⢿⣄⡨⣾⣿⣿⣿⣿⣷⣺⣿⣿⣤⣶⣦⣤⣤⣀⣀⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠛⠋⠀⠉⠃⠁⠱⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⢀⣀⠐⣤⡀⣾⣿⣧⣽⣶⢙⣽⣿⣿⣿⣿⣿⣿⣯⢩⣾⣶⣿⣿⣿⠄⠀⠀⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⢀⠡⠀⣾⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡛⣛⣛⡀⡿⠁⠿⠿⢿⣷⠟⠆⢙⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⡆⠀⢰⣷ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡏⠉⠙⠋ ⣿⣿⣿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡋⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠋⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⢀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠹⠿⢿⣿⣿⡿⡿⠛⠛⠻⢿⠿⠿⠿⠹⠟⠛⠙⡛⠟⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣿⣿⣿⣿⣿⡟⠉⠉⠛⢿⣿⠀⠀⠿⡿⠿⠿⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣖⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⢘⣿⣿⣿⣿⠋⠀⠀⠒⠚⠻⣿⠃⠀⠠⢄⣤⣴⣶⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡄⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⣶⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⡿⠛⠛⠻⣦⣀⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠂⠀⠀⠠⠀⠈⠀⣰⣴⣆⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⡤⣀⣀⣀⣠⣀⡀ ⠉⠛⣿⣿⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠨⣯⣿⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣤⣿⣿⣛⣻⡤⣄⠀⠀⠀⠀⢀⣤⣴⣿⣿⡂⠀⠀⢠⣹⣿⣿⣿⣿ ⠀⠀⢿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⠀⣯⣿⡂⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣧⣠⣾⣿⣿⣿⣿⣿⣆⠤⠀⣼⣿⣿⣿⣿⣿ ⠀⠀⠐⠘⢿⡿⠃⠀⠀⠀⠀⠀⣼⣿⣦⣴⣿⡇⠀⠈⢧⣷⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠉⠉⠙⠻⢿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⣃⠀⠀⠛⠛⠫⡟⠛⠟⠻ ⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣾⣿⣿⣿⣿⣯⠀⠀⠀⠀⠈⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠸⣿⣿⠁⠀⠈⢨⣿⣿⣿⣿⡿⣿⣿⣽⡿⠖⠂⠀⠉⠀⠀⠀⠀⠀⠄⠀⢤⣤ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠘⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠐⠛⢧⠀⠀⢀⣾⣿⠯⠈⠈⢸⣿⣿⠻⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⡃⠀⢀⣤⡤⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⢫⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣸⠀⠀⣸⣿⠃⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣄⡀⠉⠉⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠉⠉⠀⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⢠⡀⢠⣀⣠⡀⣀⠀⠀ ⠀⠀⠐⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠀⠀⠲⣶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠂⠀⠀⠈⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⢀⣈⣱⢾⡇⣿⣤⣬⣄⠐ ⠀⣰⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⡏⠀⣴⡴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣰⣿⣂⣰⣿⣅⡀⠀⠈⠛⢿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡻⢈⣹⠀⠚⣩⡿⠿⠤ ⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣧⣿⣿⣿⠇⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⢻⠸⣿⣿⠇⢀⡀⠀⠀⠙⣿⣿⣿⣿⡆⠀⠀⢠⣠⡄⠀⠹⠀⠈⠁⠀⠀⠈⠁⢀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⠁⢠⣼⣿⠇⠀⠀⡿⠛⠿⣿⣿⡀⠀⠸⣿⣿⡄⠰⣿⣷⣦⡀⠀⠀⠀⠈⠤ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⠿⠟⠉⠁⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠙⠷⣄⡈⠂⠀⣾⣿⣿⣿⡄⠀⢻⣿⡧⠀⠉⠻⠟⠿⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⢿⣿⣿⡇⢻⣿⣏⠇⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⣿⣦⠀⠄⠀⡬⢿⣦⣠⣿⣿⣿⣿⣿⣶⡨⣿⣿⣶⣶⣶⣶⣦⣄⡤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⠋⠀⠈⠉⠁⠁⠀⠃⢐⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣀⣀⠀⣧⡀⢸⣿⣿⡿⡄⢹⣿⣿⣿⣿⣿⣬⣿⣿⢹⣾⣷⣿⣿⣿⡆⠀⠒⠀ ⠀⠶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠈⠈⣻⣿⡇⣠⡀⠀⠄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣛⣛⣁⠚⠁⠛⠻⠿⠿⠆⠏⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⠀⢠⣾ ⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⠿⣿⣿⣿⡿⠿⣿⡻⢿⣿⣿⣿⠿⡻⠟⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠈⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠘⠿⠋⠙⠛⠻⣿⣥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⠿⣿⡏⢉⡏⠀⠀⠀⠀⢰⣟⣻⣻⣿⠟⢿⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣿⣿⣿⠋⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⡛⠀⠀⠈⠁⠀⠀⠀⠀⠈⠓⠄⣄⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠿⣟⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠘⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣤⣽⣖⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣾⣯ ⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠋⠁⠉⠹⢟⡻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⢧⡄⠀⠀⠀⢀⣀⣤⡄⠀⠀⣀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⢀⣼⣿⣷⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣄⠀⠀⠀⢠⣿⣿⣿⣿⠔⠙⣿⣿⣿⣿⣿⣿⡙⢿⡾⠛⠋⣽⣟⠁⠀⣴⠟⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⢿⣿⡄⣤⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠸⣿⡏⠉⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣿⣅⠀⠀⠀⠀⠀⠠⠉⠑⡽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣅⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⡛⠁⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠃⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡝⠻⠃⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠟⠉⠙⠛⠛⢿⣿⠿⠋⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⠀⠀⠀⠘⠙⠙⠙⢹⣶⣦⡍⠁⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣿⠇⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣶⣦⡀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⡄⢠⡄⢀⠀⠴⠀⠀ ⠀⢰⡆⠒⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⢘⢻⡖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣶⣄⡀⠀⠀⠉⠉⠀⠀⠀⠀⢄⠀⠻⡇⢸⣶⣶⣦⡘ ⢀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⢟⡁⣠⡄⢻⣾⣿⣿⢿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣯⡀⣀⢠⣄⣄⢀⣰⢶⣄⢀⣀⠀⡀⢀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡄⠀⠥⠀⠉⢸⡿⠿⠂ ⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⡟⣿⣾⢻⣿⣿⣿⡟⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣽⣿⣿⠨⡏⠙⠿⣿⡆⠀⠀⢀⡀⡤⠄⠘⠃⠀⠀⠀⠀⠀⠀⢀⠀ ⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⢠⠀⣾⡇⠀⠀⠈⣿⣿⠇⠐⣿⣿⣷⣄⠀⠀⠀⠀⠐ ⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⡿⣟⣋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⢀⣀⡛⢿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⢈⡙⣆⢀⡀⣠⣶⣿⣿⣦⡀⠀⢸⣿⡟⠀⠀⠉⠉⠙⠛⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⡇⣿⣿⡏⢹⣿⠿⢿⣿⣷⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⣿⣿⣿⣿⣿⣉⠻⢿⡏⢹⣧⣿⣿⣷⣿⣿⣿⣿⣿⣷⡄⠈⣿⣿⣷⡿⠿⢶⣶⣆⡀⠒⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢿⡇⠸⣿⣾⢾⡿⣿⣿⢿⣿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⣟⣿⣿⡏⣿⣥⣤⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣧⠐⠿⣿⣿⣿⣿⡇⠀⡙⠀ ⠀⠶⠶⣶⠿⢶⠖⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡆⠀⠀⠀⠀⢸⣿⣿⠠⠤⠀⠺⠇⠀⠀⠀⠀⠀⢸⣷⡁⡈⠁⣭⣭⣥⡈⠁⣈⠉⠛⠛⠃⠀⠐⣿⣿⣿⣿⣿⡙⣿⡀⠀⢿⣿⣿⣿⣷⠀⠀⠿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠫⠿⡟⢿⣟⢿⡿⡿⢯⠛⠛⠿⠟⠙⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣫⣝⡋⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⣀⣀⠀⠛⠉⠀⢈⣍⣻⣧⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⣼⣟⠁⠀⠀⠀⢀⠿⠍⠡⠁⠀⠄⠀⠉⠙⢶⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣶⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠉⣻⣿⠿⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤ ⠀⠀⠀⣿⣿⣿⡿⠋⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⠟⠟⢙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣶⣶⣧⣕⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠾⠛⠋⠁ ⠀⠀⠀⠈⠹⣿⣿⠀⠀⠀⢀⣆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡇⠀⠀⠀⠈⠩⠛⣿⠻⣿⣿⣄⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣷⣦⡀⢀⣀⣠⣤⠄⠰⠈⠁⠀⠲⣶⣦⣀⣤ ⠀⠲⠀⠀⠀⠻⠇⠀⠀⢀⣾⣿⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⣿⣿⣿⠛⠙⢿⣿⣿⣿⣿⣿⣌⢻⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠐⢲⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠫⣿⣿⣾⣷⣤⢠⣐⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠘⣿⠁⠀⠀⠀⠀⠘⣿⣿⣿⢻⣿⣿⣿⣧⣴⠶⣶⡇⠀⠀⠀⠀⣀⣴⣾⣿⣿ ⠀⢀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⠏⠀⠸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡍⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⣿⣿⠀⠃⠀⣾⠋⠀⠀⠀⠀⠀⠙⠛⠛⢻⣿ ⠛⠟⠂⠀⠀⢤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⠏⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠟⢿⣿⣿⡧⣀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⠀⠀⠀⠀⠈⠙ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⠋⠈⠁⠈⣹⣷⣶⣟⠋⠉⠈⠉⠉⠛⣿⡟⠙⠛⠋⠉⠁⠀⠐⠚⠛⠉⠁⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣇⠀⠀⠀⠈⠀⠀⠀⠈⠙⠿⣿⣦⣤⣀⡀⠀⠀⠘⢿⣷⠃⠀⠀⠀⠀⠐⠆⢰⡖⢶⡆⠀⠀⠀ ⠀⢀⡚⠉⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠁⠀⠀⠘⡻⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢦⠂⠈⠋⣸⠿⣿⣷⡆ ⣠⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣷⢀⣀⣠⡄⢙⣻⣾⣏⢛⡉⣉⢻⣿⣿⣿⣿⣿⡿⣛⣿⡇⣠⣰⣦⣶⣤⣄⣻⣦⣀⣀⠀⡀⢀⢀⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⠀⢠⡏⠀⠚⠀⠀⠺⠟⠛⠁ ⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢻⣿⣿⣿⡏⣿⢹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣻⣿⣿⢸⠇⠀⠙⣿⠂⠀⠀⢠⣦⣼⡇⢈⣣⣄⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠘⠐⢀⣾⣿⣤⠀⠀⠈⢿⣿⣧⠀⠿⢿⣿⣷⣄⠀⠀⠀⠈ ⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⢛⣋⠁⣀⣀⠾⢿⣿⣿⣿⣿⣿⣻⣿⣿⢊⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢙⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⢀⡈⣳⣆⡀⣶⣿⣿⣿⣧⠀⠀⢸⣿⣿⣀⣀⣀⣁⡈⠁⠀⠀⠀⠀ ⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡇⢰⣿⠿⢿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⣿⣿⣿⡿⣿⣉⠉⢻⡏⢹⣯⣿⣿⣷⣿⣿⣿⣿⣿⣧⡀⢘⣿⡿⠿⣻⣿⣿⣿⣧⡈⠉⣙⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡇⠘⣿⣿⢾⡗⣿⣿⣻⣿⢿⣼⡇⣿⣵⣿⣿⡇⠀⣿⣿⢿⣿⠁⠀⣿⡏⣿⣿⡇⣿⣵⣶⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠱⣿⣇⠈⠛⣿⣿⣿⣿⣇⠀⠊⣠ ⠀⠶⠶⣶⠿⢷⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⡶⢾⡟⠀⠀⠀⠀⢸⣿⣿⠐⠛⠃⠘⣛⡀⠀⠀⠀⠀⠈⢱⡄⡒⠆⣴⣶⣶⡆⠀⣤⡄⠈⠉⠀⠐⢺⣿⣿⣿⣿⣧⠘⣿⠀⠀⠹⣿⣿⣿⣿⡄⠈⠛ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠯⠆⡈⠅⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⢿⡿⠁⠀⠀⠀⠀⣀⣠⣀⠀⠉⠀⠀⣠⣤⡬⠁⠉⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡛⠁⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⢀⣀⣀⣀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣠⣿⣯⣉⣻⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡼⠟ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⠃⠀⠀⠈⠟⡝⣿⣟⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠀⡀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣧⣤⣿⣿⣷⣄⠀⠀⠀⠀⢤⣿⣿⣿⣿⡉⠿⣿⣿⣿⣿⣿⣞⢷⣄⣠⣤⠶⠛⠀⠀⠀⠀⠀⢤⠃⠀⠷⠟ ⠶⠴⠀⠀⠘⠿⠟⠉⣽⣿⣿⣣⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⢿⣿⣿⢀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢿⡿⠛⠛⠛⠃⠀⢻⣿⣿⣿⣿⣿⣷⣙⡅⠀⢀⠀⠀⠀⠀⠀⠐⠀⣀⡀⢢⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡿⠃⠀⢻⣿⣂⣿⣕⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⡇⠀⠀⠀⠀⠀⠈⣿⡿⠙⢻⣿⣿⠿⡟⠟⢉⡁⠀⠀⠀⢀⣴⣿⣿⣷⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⠟⠁⠀⠀⢾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⣿⣿⠀⠀⢀⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠚⠿⠇⠀⠀⢠⣄⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠘⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣹⣿⠟⠻⣦⣀⠐⣿⡇⠠⠰⢾⣿⣿⣿⣿⣿⣿⣾⣷⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠈⠛⠂⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠉⠛⣿⡟⠉⠙⠉⠉⠁⠀⠀⡀⠀⢼⣿⣿⣿⣿⣿ ⠙⠃⠀⠀⠀⠠⠄⡶⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⣤⣦⣄⠀⠀⠈⠚⠇⠀⠀⠀⠀⠀⠀⠑⢼⣷⢸⣯⣹⣿⡿ ⠆⢀⡀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢹⡏⢱⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠏⢿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠁⠀⣻⣿⣿⠇ ⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣁⣠⣦⣀⡀⣀⡄⢈⣛⣿⣯⢀⡀⡀⢈⢿⣿⢿⣟⠁⠀⣀⢸⣇⣀⣿⣿⣾⡆⣀⣽⣿⣴⣀⡀⡀⢀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠘⡇⠀⠀⠀⠀⠈⣁⣀⡀ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢻⣿⣿⣿⡇⣿⣹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢴⣿⣇⣀⣽⡏⠀⠀⠀⣶⣶⡷⠀⣶⣶⣦⣄⠀⠈⠛⠛⣇ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠛⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⠀⠉⢡⣿⣿⣧⡀⠀⠀⠺⣙⡿⡀⠈⠛⠛⠻⠷⠀⠀⠀⠀ ⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⠀⣀⠀⣀⣀⠻⠿⣿⣿⠿⣿⣿⣗⣿⣿⢁⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢀⣹⣿⣿⣿⣿⣿⣿⢷⣦⣀⢀⡀⣘⢇⡀⣹⣿⣿⣿⣧⠀⠀⠀⣿⣷⣧⣶⣶⣶⣦⡄⠠⠤⠤⠤ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⠇⢰⣿⠿⢾⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡿⣿⣿⡿⣿⣉⠀⢹⣟⣹⣧⣿⣿⣷⣿⣿⣿⣿⣿⣷⣄⠀⣿⡏⠉⣷⣷⣾⣿⣿⡆⠀⢲⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡇⠘⣿⣾⢾⡗⣿⣿⣻⣿⢿⣼⡇⣿⣽⣿⣿⣇⡀⣿⣿⣿⣿⠁⠀⣿⡇⣿⣿⡇⣿⣽⠿⢿⡏⢿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣷⠀⠀⢻⣿⣿⣿⣷⠀⠡⣶ ⠀⠶⠶⣶⠿⢷⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠾⠿⠿⠀⠀⠀⠀⠱⣿⡏⢈⣛⡋⠀⣩⣥⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⣿⣿⡷⡠⣾⣧⡀⢀⡀⠀⣻⣿⣿⣿⣿⣧⠀⢿⣄⠀⠀⢙⣿⢿⢿⣇⠀⣀ ⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢛⣿⣿⣿⡿⢿⡿⠿⡿⠿⢿⢿⣿⣿⠟⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⠿⠿⢿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠻⢿⡟⠀⠀⠀⠀⣀⣀⡀⠀⠘⠃⠀⢀⣤⣤⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠁⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣟⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣧⣠⣼⣄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠷⠛⠉ ⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⡏⠀⠀⠀⠀⠙⠻⣿⠝⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀ ⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣿⣿⣿⣤⠀⠀⠀⠀⣼⣿⣿⣿⣿⡩⠻⣿⣿⣿⣿⣿⣎⢳⣴⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉ ⠤⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⠛⣿⣇⣤⡀⣀⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣿⡟⠛⠛⠛⠀⠀⢹⣿⣿⣿⣿⣿⣷⡝⡄⣀⣤⡀⠀⠀⠀⠀⠉⠀⠀⠀⠱⠤ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠏⠁⢀⢿⡇⢹⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣨⡇⠀⠀⠀⠀⠀⠈⠿⠟⠘⢹⣿⡿⠻⡌⠋⣩⡟⠀⠀⠀⣀⣴⣦⡀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⠿⠟⠃⠀⠄⠀⣺⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠿⡿⣿⣿⣿⣧⠀⠀⠀⣤⡀⠀⠀⢀⣀⣘⣿⣷⣤⣄⣰⣿⠀⣠⣴⣾⣿⣿⣿⣤⡀⠀⠀ ⠶⣶⠆⠀⠀⢀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢂⠘⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠻⣿⠟⠛⣢⣄⡐⢿⠇⠀⠀⠻⢿⣿⣿⣿⣿⢿⣿⠿⠆⠈⣿⣿⣿⣿⣿⣿⣿⣦⣤ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣺⣅⠕⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⠾⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⠉⣿⢯⡀⠈⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠂⠀⠀⠀⢀⡀⣴⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠄⠘⣿⣿⣿⣿⣿⣿⣿⡿⠿⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣶⣿⣦⡀⠀⠘⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟ ⠆⠀⠀⠒⢰⣶⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢻⡛⢰⣟⠁⠉⠛⢿⣿⣿⣿⣿⡿⠛⠋⠻⠛⠁⠀⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢀⡅⠿⣿⣿⣿⣿⣿⠿⠁ ⢠⣿⣷⠄⠁⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⢀⣀⢠⣦⣀⡀⣀⡄⢈⣓⢽⣿⢀⡀⡀⢀⢿⡿⢋⣁⠀⠀⣀⢺⣧⣀⣻⣿⣾⡆⣀⣿⣿⣼⣀⡀⡀⢀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⡆⠈⠇⠀⠀⠙⠿⠛⠁⠀⠀ ⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠿⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢻⣿⣿⣿⡇⣿⣹⡇⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣧⣬⡿⠀⠀⠀⣶⣾⣇⠀⢿⣿⣷⣦⡀⠀⠀⠀⠀ ⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⣿⠀⠀⢉⣿⣿⣷⠀⠀⠀⠺⣩⡏⡆⠀⠙⠋⠙⠛⠀⠀⠀⠀ ⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣀⠻⠿⢿⣿⠿⣿⣿⣇⣻⣿⢃⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢀⣸⣿⣿⣿⣿⣿⣟⠻⣶⣀⢀⡀⣀⣂⡀⣼⣿⣿⣿⣷⠀⠀⢀⣿⣿⣷⡿⡿⢿⣷⣆⠐⠒⠒⠒ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡇⢰⣿⠿⢶⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⡟⣿⣿⡟⣿⣉⣀⣹⣿⣹⣧⣿⣿⣷⣿⣿⣿⣿⣿⣧⠀⠈⣿⡇⠂⠿⢿⣿⣿⣿⡇⠀⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡇⠘⣿⣾⢾⡗⣿⣿⣿⣿⢿⣼⡇⣿⣽⣿⣿⣇⣀⣿⣿⣿⣿⠁⠀⣿⡇⣿⣿⡇⣿⣽⣛⣻⡏⢻⣟⣿⢿⡟⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⠀⠀⠘⣿⣿⣿⣿⡄⠀⠛ ⠀⠶⠶⣶⠿⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠇⠀⠀⠀⠰⣿⡏⠀⣉⣉⠀⣉⣥⡄⠀⠀⠀⠀⠀⣷⠀⠀⠀⡿⠿⣟⠀⣿⣷⣀⣀⡀⠀⣿⣿⣿⣿⣿⡄⠀⢹⣷⠀⠀⣨⣿⣟⣿⣷⣤⣤ ⣿⣶⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠿⢿⠻⢿⢿⠿⢿⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⢿⣿⡿⠿⣿⣿⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⣿⡟⠀⠀⠀⠀⣀⣀⠀⠘⠋⠀⠀⣠⣤⡤⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠁⢰⠇⠀⠀⠀⢀⠜⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⠦⣤⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠻⠙⢿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣧⣤⣽⣄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠖⠋⠉ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⠃⠀⠀⠀⠀⠛⢿⣟⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣜⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠠⣾⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣜⣷⣴⡶⠞⠛⠁⠀⠀⠀⠀⠐⠀⠀⠐⠛⠉ ⠀⠀⢀⣼⡋⣰⣶⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⠟⠹⣿⡄⣆⠀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⣿⡟⠛⠛⠋⠀⠀⢻⣿⣿⣿⣿⣯⣮⣡⠀⣀⣠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠢⠴ ⠀⠀⠘⠟⠛⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡿⠙⠀⠀⠻⡅⢙⣥⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⡇⠀⠀⠀⠀⠀⠀⠿⠟⠈⣿⣿⡿⣇⠛⠉⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡟⠃⠀⠀⣤⣶⣶⣿⣿⣿⣿⡿⠟⠛⠫⠁⠠⠀⠀⢹⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⢿⣿⣿⣿⣆⠀⠀⠀⣤⣄⠀⠀⢀⣤⣼⣿⣷⣾⣿⣿⣿⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⢶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠇⡼⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣿⠛⣻⣤⣤⡐⢿⠟⠋⠉⠙⠛⠿⣿⣿⠟⠉⠋⢡⣀⣀⣴⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡅⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⣀⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⣻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠶⠀⠀⠀⠀⢀⡀⣤⠀⠀⢀⣴⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⣀⡤⠀⠀⠀⠀⠿⠗⠀⠀⠈⠻⣿⣾⣷⣦⡀⠀⠙⠟⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⠀ ⣀⠀⠀⠠⣶⣶⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠘⠛⡟⢐⠂⠀⠀⠀⢿⣿⣿⣿⡿⠿⠛⠉⢺⠛⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀ ⣿⣿⣦⠀⠉⠉⠁⠀⠀⠘⣿⣿⠟⠉⠉⠛⣧⠀⠀⣀⢠⣤⢀⡀⣠⡄⢀⣑⢿⣿⢄⡀⡀⢀⠈⡈⢉⣀⠀⠀⣀⢾⣧⣀⣺⣿⣾⡆⣠⣿⣿⢄⣀⡀⡀⢀⠀⢸⣿⣿⣿⣿⣦⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠠⠄⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠏⠁⠀⠀⠀⠀⠛⠗⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⢻⣿⣿⣿⡇⣿⣹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢠⣀⣿⣇⡈⠙⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀ ⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣽⡿⣿⠀⠈⣿⣿⣿⣆⠀⠀⠀⠉⡽⡟⠀⠀⠉⠉⠙⠋⠀⠀⠀⠀ ⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣀⠿⣿⣿⣿⡿⣿⣿⣇⣿⣿⢁⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⢀⣀⡀⢀⣹⣿⣿⣿⣿⣿⡟⠳⣶⣀⢀⡀⣀⢀⡰⣹⣿⣿⣿⣄⠀⠀⢸⣿⣷⣷⡿⡿⣿⣷⣆⠐⠒⠒⠚ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⠇⢰⣿⠿⢷⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⡏⣿⣿⡟⣿⣉⣀⣹⣿⣹⣧⣿⣿⣷⣿⣿⣿⣿⣿⡀⠀⠀⣿⡇⠐⠿⣿⣿⣿⣿⡇⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢿⡇⠘⣿⣾⢾⡗⣿⣿⣻⣯⢿⣼⡇⣿⣽⣿⣿⣇⣀⣿⣿⣿⣿⠁⠀⣿⡇⣿⣿⡟⣿⣽⣿⣿⣏⢻⣏⣿⢿⡟⣿⣿⣿⣿⣿⣷⠀⠀⢻⣷⠀⠀⠹⣿⣿⣿⣿⡄⠀⠛ ⠀⠶⠶⣶⠿⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠾⠿⠇⠀⠀⠀⠀⠚⠅⠈⣛⣋⠀⣉⣁⡀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡿⠿⢻⢀⢿⣷⣀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⢻⣦⠀⢀⣨⣿⣟⣿⣧⣤⣤ ⣿⣶⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⢿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⢿⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠆⠀⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠁⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣿⡟⠀⠀⠀⠀⣀⡀⠀⠙⠋⠀⠀⣠⣤⣭⠀⠀⠈⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠈⠀⡴⠀⠀⠀⠀⠀⠏⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⠷⢤⣄⣀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠟⣻⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣦⣈⣻⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠛⠋ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣽⣿⣿⡟⠀⠀⠀⠉⠛⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⣀ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣾⣿⣿⣿⣯⠻⢿⣿⣿⣿⣿⣷⣹⣦⣠⣴⠾⠞⠂⠀⠀⠀⠀⠔⠀⠀⠴⠛⠉ ⠀⠀⣰⡟⠁⠀⢀⣀⣤⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⡿⢿⣿⡀⣄⠀⠀⢀⣔⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠸⣿⡟⠛⠛⠋⠀⠀⢻⣿⣿⣿⣿⣿⡙⡁⠀⢀⣀⣰⠄⠀⠀⠀⠀⠀⠀⠐⢄⢴ ⠀⠰⠿⠿⠶⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⡿⠋⠀⣫⣿⣗⠋⣸⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣹⡇⠀⠀⠀⠀⠀⠈⣿⠿⠈⣿⣿⣿⢴⠟⠋⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⠿⠛⠛⠁⢀⠀⠨⢿⠽⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⢿⣿⣿⣿⡆⠀⠀⠀⣤⡄⠀⠀⣀⣤⣿⣿⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⢀⣻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢈⡼⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠚⢿⡿⠿⢇⣄⣀⠀⣿⠗⠙⠀⠘⠛⠿⣿⣿⠏⠁⠉⡉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠃⠀⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⢸⣿⣴⣶⣿⣿⠆⡀⠀⠀⠀⠀⠀ ⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠣⠁⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣄⠀⠀⠀⠀⠷⠂⠀⠙⠛⢿⣷⣶⣦⡀⠀⠈⠽⠏⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⣰⣦⣤⣄⠀ ⡀⠀⠀⢤⣤⡭⠈⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠛⠗⠰⠀⠀⠀⠴⣿⣿⣿⣿⣿⡿⠛⠻⢿⠳⠚⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣦⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠠⣽⠿⠷⠀ ⣿⣷⣄⠈⠈⠁⠀⠀⡠⢧⣿⣿⠿⠛⠛⣿⡀⠀⠀⣀⢠⣄⢀⡀⣀⡀⢀⣱⣿⣷⢀⡀⡀⢈⠉⡉⢉⣀⠀⠀⣀⢾⡄⣀⣸⣿⣾⡏⣸⣿⣷⣄⣀⠀⡀⢀⠀⢸⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠠⠀⠀ ⣿⣿⣏⠀⠀⠀⠀⠐⠽⠿⠋⠀⠀⠀⠀⠘⠿⠆⣿⣿⣿⣿⣿⣷⣿⣯⣿⣽⡟⣿⣾⢻⣿⣿⣿⡇⣿⣹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣻⣿⣿⢀⣸⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀ ⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣟⣿⣿⣿⡄⠙⠿⠟⣿⣻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀ ⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⢉⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⢀⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⢷⣦⣀⢀⡀⣀⢀⡈⣿⣿⣿⣿⣄⠀⠀⢸⣿⣷⣶⡶⢶⣶⣶⡄⠐⠲⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡇⢰⣿⠿⢷⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⡟⣿⣿⡿⣿⣉⠀⢹⣿⣹⣧⣿⣿⣷⣿⣿⣿⣿⣿⡀⠀⠘⣿⡉⠰⠾⣿⣿⣿⣿⡆⠀⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢿⡇⠘⣿⣾⢾⡟⣿⣿⢻⡟⢿⣼⡇⣿⣽⣿⣿⡇⠀⣿⣿⣿⣿⠁⠀⣿⡇⣿⣿⡏⣿⣽⠿⢿⡟⢻⡿⣿⣿⡟⣿⣿⣿⣿⣿⣷⡀⠈⢻⣧⠀⠀⢿⣿⣿⣿⣧⠀⠐⠿ ⠀⠖⠶⣶⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⠀⠀⠀⠀⠀⠙⠇⠘⠛⠛⠀⣛⣯⡀⠀⠀⠀⠀⠀⡀⠰⠂⠸⣿⣿⠷⢠⣿⣦⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⢿⣄⠀⢀⣙⣿⣿⣻⣧⣀⣀ ⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠘⢿⡛⠿⢉⠁⠉⠁⠙⠛⠛⡛⠛⠛⠋⠉⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠀⠀⠀⠀⣀⠀⠀⠛⠋⠀⠀⣀⣉⣉⠈⠉⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⡞⠉⠉⠁⠀⢀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠭⣿⣿⡿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣉⣉⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠟⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣻⣿⣿⣿⠋⠀⠈⠋⠉⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣌⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⡀⠀⢀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⢽⣿⣿⣿⣿⣿⣧⢳⣄⣀⣠⡶⠶⠀⠘⠀⠀⠀⣠⠀⠀⡶⠞⠛ ⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣇⣄⠀⠀⢀⣀⣶⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢸⣿⡿⠿⠿⠋⠀⠘⣿⣿⣿⣿⣿⣬⢻⠉⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⣀⣠ ⠀⢾⣿⣶⣶⣤⣶⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⢫⣿⣿⣿⠉⣶⣧⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢻⡃⠀⠀⠀⠀⠀⠸⣿⡟⠹⣿⣿⣿⣷⡶⠛⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠏⢀⡀⢿⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣿⣷⣿⡁⠀⠀⠀⣀⡀⠀⠉⢀⣀⣿⣿⣭⣿⣶⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡆⢠⣤⣤⡀⠘⠿⠿⠿⠿⠟⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢉⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⣿⣿⣿⣿⣧⡀⠀⢰⣿⡷⠖⠋⠙⠿⣿⣿⣿⠏⠋⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢸⢷⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠋⠉⠙⣿⣿⣮⡉⠀⠀⠀⠀⠀⢸⣿⡇⠀⠠⣿⡀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣧⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣷⣦⣤⡀⠀⠀⠘⣿⠇⠀⠀⢿⣿⣿⣿⣿⡡⣾⠀⣰⣄⣤⡀⠀ ⠀⠀⠄⠀⣴⣂⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠐⠀⠀⠴⣶⠖⣥⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⣿⠧⠰⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣄⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠰⠘⠁⢉⣿⣿⡧⠀ ⣿⣦⡀⠋⠜⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡀⠀⠀⣀⣀⣀⢀⡀⣀⡂⢘⣲⣶⣧⢀⡻⣟⢛⠛⡛⢛⣉⠀⠀⣀⢾⡄⡀⢠⣶⣶⡄⣰⣿⣦⢄⣀⠀⡀⢀⠈⢹⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⢫⣪⢹⠛⠋⠁⠀⠙⣿⡀⣿⣿⣿⣿⣿⣷⣿⣯⣿⣹⡟⣿⣾⢻⣿⣿⣿⡇⣿⣹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠐⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⠿⢿⠛⠻⠆⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣹⣿⡿⢋⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢘⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⢀⡀⣀⢀⣿⣿⣿⣿⣿⣄⠀⠀⢹⣼⣿⣤⣶⣶⣶⣤⡄⠤⠤⠤⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡏⢹⣿⠿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡟⣿⣿⣿⣿⣉⠈⢹⡏⢹⣧⣿⣿⣷⣿⣿⣿⣿⣿⡄⠀⢸⣿⠉⢩⣷⣶⣿⣿⣷⡆⠀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢿⡇⠸⣿⣾⢾⡟⣿⣿⢻⣿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠁⠀⣿⡇⣿⣿⣇⣿⣷⣿⢿⡿⢿⡿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡄⠀⢿⣇⠀⠐⣿⣿⣿⣿⣇⠀⠠⠾ ⠀⠖⠶⣶⠿⢶⠖⠰⠶⠶⠶⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠀⠀⠀⠀⠀⠛⠀⠲⠾⠇⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⣷⣾⡦⢠⣶⣆⠀⠀⠀⢱⣿⣿⣿⣿⣷⠀⠀⣿⣄⠀⠘⠻⢿⠿⢿⣆⣀⣀ ⣷⣦⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠻⠋⠛⠛⠛⠛⠿⠟⠻⠛⠿⠛⠙⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⣀⠀⠀⠻⠟⠉⠉⠉⠙⠛⠊⠙⠒⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠁⠀⠀⠀⠀⢱⠆⠀⠀⠀⠀⢠⠎⠛⠛⠀⠀⡀⠀⠀⠙⠢⣄⠀⠀⠀⢰⣶⠤⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣶⣶⣶⣶⣿⣿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣽⣿⡉⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⠁⠈⠁⠋⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣦⡑⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠞⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡂⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠈⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡝⢿⣿⣿⣿⣿⣿⡄⣄⠀⠀⣀⣤⡤⠀⠘⠉⠀⠀⠀⠀⢨⣴⡶⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧⢀⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⢸⣿⡿⢿⡿⠇⠀⠹⣿⣿⣿⣿⣿⡽⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⠀⣀ ⠀⣿⣷⣄⡀⡤⣀⠀⣀⣀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡛⣽⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠘⢿⠀⠀⠀⠀⠀⠀⢹⣿⡏⢻⣿⣶⣽⣤⣶⠾⠟⣤⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉ ⠀⠀⠈⠻⣿⣿⣷⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠿⠛⠹⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠿⣿⣿⣿⣦⣍⠀⠀⠀⠀⠀⠀⠈⠛⠁⠸⣿⡟⠉⠃⠀⢠⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⡯⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠸⢿⣿⣿⣿⣀⠀⠀⣠⣶⡀⠀⠀⣤⣤⣿⣿⣶⣶⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⣶⢊⢥⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⠟⠙⢻⣷⣤⡙⠛⠀⠀⠉⠛⢿⣿⣿⡟⠛⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣴⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣆⡀⠀⠀⠀⠀⢸⣟⠀⠀⢼⣦⣶⣷⣆⢰⢀⣾⣆⣿⣾⣿⣤⠤ ⠀⢀⡀⠀⠟⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠤⣤⠤⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣿⢇⠀⡾⠂⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠀⠿⠋⢛⣹⣿⣿⠶ ⣶⣄⠸⠄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⠀⠀⣀⠀⣀⢻⡇⣀⡤⢻⣠⣿⣾⢿⡿⣿⢛⠿⡿⢿⣛⠁⠀⣀⢼⡄⡀⢀⣦⣤⡀⣰⣾⣄⢀⣀⠀⡀⢀⠙⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⡆⠀⠃⠀⠀⠉⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠿⠻⣿⠀⣾⣿⣿⣿⣾⣧⣿⡏⣿⣹⡟⣿⣿⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣻⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⠀⠀⠀⠀⠠⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠨⠚⠉⠀⠀⠀⠀⠻⡦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢷⡄⠀⠀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟⢁⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣆⣄⣀⣀⡀⣀⢸⣿⣿⣿⣿⣿⣿⠋⠉⢩⣝⣛⣯⣥⣤⣤⣄⡀⢀⣀⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡟⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⡿⣿⣿⣿⣿⣉⠉⢹⡏⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⠛⢛⣿⣯⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡇⠸⣿⣾⢾⡿⣿⣿⢻⣿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⡏⣿⣵⣶⣾⡷⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣧⠀⠀⢿⣇⠀⠉⢿⣿⣿⣿⣧⠀⢀⣴ ⠀⠖⠶⣶⠏⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⢀⡀⠀⢠⣴⡆⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⢾⠂⢸⣭⣤⡄⠀⣤⡄⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⢿⡄⠀⠈⢿⣿⣿⣿⡆⠀⠀ ⣾⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣻⠟⢿⡿⠛⠿⠛⠿⠻⣿⣿⡿⢿⠿⠛⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⣯⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠀⠀⠀⠀⣀⠈⠀⠹⠿⠟⠋⠛⠛⠷⠆⠒⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠻⠃⠀⠀⠀⠀⢉⡆⠀⠀⠀⠀⠀⠔⠻⠿⠂⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡄⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⢳⣶⣤⣤⣤⣤⣾⣿⡿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⣹⣟⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣠⣴⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⣿⣿⣿⣿⡏⠀⠀⠙⢻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣶⣷⣔⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⡭⣄⠀⠀⢀⣄⣤⠀⠐⠊⠀⠀⠀⠀⠈⢀⠴⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆⣀⠀⣠⣠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣼⣿⣿⣿⣿⠇⠈⢹⣿⣿⣿⣿⣿⡽⣷⠚⠋⠉⠀⠀⠀⠀⠀⠀⠒⠋⠀⣀⠀⢀ ⠀⢨⣿⣆⠀⣤⣀⠀⢀⣀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠹⡿⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⣿⣷⢻⣤⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉ ⠀⠈⠛⢿⣿⣦⣄⣀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣦⡏⠀⠀⠀⠀⠀⠀⠈⠉⠁⠘⣿⡿⠀⠃⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⠿⠂⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠁⠀⢈⡿⠻⠋⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣷⡀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠁⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⡿⣦⠀⠀⠀⣸⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⢰⣥⣭⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⢿⠏⠻⣿⣦⡈⠻⢿⡇⠀⢠⣿⣿⣷⣶⣾⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⢿⠷⠄⠀⣰⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⠿⣿⣿⣦⣀⠀⠀⠀⠉⠻⣿⣿⠟⠉⢿⣿⣿⣦⡀⠴⢀⢾⡆⣟⢹⡇⠀⠀ ⠁⠀⣀⣠⠥⠀⠀⠀⠀⠈⠀⢀⣠⣤⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⣠⠆⠀⠀⠏⠉⠀⠀⠈⠛⢿⣷⣶⣄⡀⠀⠈⠉⠀⢀⣼⣿⣿⣿⣿⣷⠌⠿⠃⠘⢻⣿⡇⠀ ⣦⣄⢹⡟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⣀⢀⡀⣀⡄⢻⣀⣽⣿⢿⡛⣛⢛⠛⡛⢛⣉⠉⠀⣀⢸⡆⡀⢀⣤⣠⠀⣤⣶⣄⢀⣀⠀⡀⢙⢿⣿⣿⣄⡀⣀⣴⣿⣿⣿⣿⣿⢯⡄⠠⠇⠀⠀⠛⠉⠁⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠟⠛⣿⡇⣾⣿⣿⣿⣼⣇⣿⡏⣿⣹⣟⣿⣿⢻⣿⣿⣿⡇⣿⣹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠀⠀⠀⠈⢀⡀ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⡁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣷⣄⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⢀⡀⣐⢹⣿⣿⣿⣿⣿⣿⠛⠛⢻⡿⣟⣟⣋⣀⣀⣀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡯⣿⣿⣿⣿⣉⠙⢻⡏⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠿⠿⣻⣽⣿⣿⣧⡌⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡏⣿⣿⡇⠸⣿⣾⢿⡿⣿⣿⢿⣿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠁⠀⣿⡇⣿⣿⡇⣿⣥⣤⣼⣿⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⡆⠀⠀⢸⣧⠀⠉⢻⣿⣿⣿⣧⠀⠀⣠ ⠀⠖⠶⣶⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠰⠀⠀⢠⣤⡄⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⡄⠁⣨⡉⠉⠀⠀⢼⣿⣿⣿⣿⡄⠀⠀⢻⡆⠀⠀⢹⣿⣿⣿⡆⠀⠉ ⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠟⢿⠿⡿⠿⡿⢿⠿⠿⢿⣿⠿⠿⠿⠟⠽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠛⠻⠿⠦⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⢿⡟⠀⠀⠀⠀⠉⢳⡆⠀⠀⠀⠀⢠⡔⢶⣶⢄⠈⠉⢹⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢠⡞⠁⠀⢱⣿⣿⣿⠏⠁⠀⠙⠲⣦⣤⣤⣤⣤⣸⣿⠏⠏⢿⣿⣿⠁⠀⠀⠃⢀⣠⢠⠀⠀⠀⠀⠀⠀⠙⢻⡟⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠⠿⢿⣿⣿⣿⣿⡏⠀⠀⠀⠙⢻⣦⡀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣤⣴⣶⣿⣷⣦⣬⣷⡂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣦⣙⡀⠀⠀⠀⢀⣀⠀⠰⠐⠂⠀⠀⠀⠀⢂⣠⣴ ⠀⠀⠀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⣤⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣼⣿⣿⣿⣿⠇⠈⢻⣿⣿⣿⣿⣷⡹⡶⠶⠚⠋⠉⠀⠀⠀⠀⣠⠤⠒⠂⠀⠀⠀ ⠐⠂⢒⣿⡁⢀⡀⠀⠀⣴⣧⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠹⡏⠀⠀⠁⠀⠀⠈⢿⣿⡙⣿⣿⣧⢹⡄⣀⡤⠄⠀⠂⠀⠀⠀⠉⠀⠀⣈⠷⠾ ⠀⠀⠙⢿⣿⣦⡌⠁⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⠟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣦⠆⠀⠀⠀⠀⠀⠀⠘⠛⠀⠹⣿⡿⠀⠿⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⢻⣿⣿⣷⣮⣿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠰⢺⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢺⣿⣿⣿⣦⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠛⠓⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⠻⠛⣿⣷⣄⢸⣿⡷⣀⢀⣠⣀⡀⣀⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠿⣿⣄⠀⠉⠀⠘⢿⣿⣿⣿⣿⣿⣷⣾⣧⣤⣤⡀⠀⠄⢰⣆⢰⠂⠄⠀⠀ ⠁⠀⠀⠀⢀⠀⠀⠀⠀⠹⡋⠙⠛⠿⣿⣿⣿⣿⡏⠀⠀⠀⢀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠛⠻⠃⠀⣠⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣄⠀⠈⠿⣿⠟⠁⠙⣋⣻⣿⣿⣯⣤⡀⢠⡟⠸⠷⣿⣖⠀ ⣦⣀⠁⢾⠇⠀⠀⠀⠀⠀⢀⣤⣴⣾⡿⠿⢿⣿⠀⣀⠀⣀⢀⡀⣀⡈⢅⣀⣌⣄⢈⡉⡉⢉⠉⡁⢀⣀⠀⠀⡀⢀⣦⡀⢀⣀⢀⠀⣀⣤⣀⠀⣀⠈⣻⣿⣿⣿⣦⡄⠀⠀⣠⣴⣿⣿⣿⣿⣿⣍⠀⠐⠀⠀⠚⠛⠋⠀ ⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠟⣾⣿⣗⣿⣼⡇⣿⡏⣿⠹⡟⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⣿⣽⣿⡗⣿⣿⣿⣾⣿⣹⣿⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣯⣀⡀⠀⠀⠀⠀⠂⡀ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣿⣼⡿⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣯⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠉ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢈⣻⣛⣿⣿⣿⣿⣿⡇⣀⣀⢀⡀⣰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠋⠁⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣉⠙⢿⣏⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢻⣷⣶⣶⡿⣛⣟⣿⣷⣀⠈⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡇⠸⣿⣾⢾⡿⣿⣿⢿⣿⢿⣴⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⡇⣿⣥⣀⣸⡟⣼⡏⣿⣿⡟⣿⣿⣿⣿⣿⠀⠀⠀⢿⣆⠀⠘⠛⣿⣿⣿⣿⠀⠀⠀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⡀⠀⠀⠉⠁⠀⢰⣿⣿⣿⣿⣆⠀⠀⠈⢻⡄⠀⠈⠹⣿⣿⣿⣇⠀⠀ ⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠃⠛⠛⠛⠟⢿⢿⡛⠛⠿⠿⢿⣿⠿⠟⠻⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⠿⠿⢿⣧⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠛⢿⣿⠁⠀⠀⠀⠐⠒⣦⠀⠀⠈⠁⠀⣠⢤⣤⡄⠈⠉⠉⣲⣤⣤⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣠⠋⠀⠐⣾⣿⣾⡮⠁⠀⠙⠶⣤⣤⣀⣠⣤⣀⣿⠅⠚⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⠽⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢹⣧⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣷⣤⣤⣷⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠚⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⣸⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⣾⣿⣿⡿⢻⣿⣿⣿⣿⣿⣦⡙⡀⠀⠀⠀⢀⣀⡀⠠⠔⠂⠀⠀⠀⠀⠂⢀⣠ ⠀⠀⠀⠀⣄⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣶⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣸⣿⣿⣿⣿⠆⠈⢻⣿⣿⢿⣿⣷⠹⣶⠴⠖⠛⠋⠁⠀⠀⣀⣀⡤⠔⠂⠙⠀⠀ ⠀⠂⠀⢼⣿⣏⠀⠀⠀⠀⣽⣷⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠙⠏⠀⠀⠁⠀⠀⠘⣿⣿⠋⣿⣿⣧⢸⡀⣀⣀⠄⠀⠘⠛⠉⣀⡀⠀⠀⠀⠐⠖ ⠀⠀⠀⠺⣿⣿⣦⡉⠀⢠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⠏⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢸⣿⣿⡆⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⠃⠀⠀⢰⣾⣿⣿⣿⣿⣿⠿⠿⠃⠀⢸⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⢿⣿⣿⣄⠀⠀⣀⣀⠤⠀⠀⠀⠀⣨⣿⣧⠀⠀⠀⢀⡀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀ ⠐⠒⠂⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤⣶⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠻⠿⣿⣶⡄⢿⡿⠂⠀⣀⣀⣀⣿⣧⡁⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠛⠻⣷⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣿⣠⣤⣴⣤⡀⡄⠐⣦⢰⡖⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⣙⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣰⡿⢿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠛⠉⠙⠃⠀⠀⡄⠀⠀⠀⠀⠈⠻⣷⣦⣤⡀⠀⠹⠿⠿⠋⠁⠙⢛⣿⣿⣿⣿⣧⡀⠀⣼⠀⠵⢶⣶⠀ ⣧⣀⠐⠀⣿⠀⠀⠀⠀⠀⠀⠀⠿⠿⠳⠛⠛⠛⣿⣀⠀⢀⢀⡀⣀⡘⢉⣉⣀⣤⢀⡀⡀⢀⠀⡀⢀⣀⠀⠀⡀⢀⣶⡄⢀⣀⠀⡀⣀⢠⣀⠀⣀⣹⣿⣿⣿⣷⣦⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣯⡃⠠⠀⠀⠠⠞⠛⠀ ⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣇⣿⣼⡇⣿⡏⣿⠹⡿⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⣿⣝⣻⡿⣿⣿⣿⣼⣟⣹⣿⣿⣿⣿⣿⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣿⣼⡇⣿⢿⣾⣿⣿⢹⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⣽⡿⣿⢿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣝⣻⣿⣿⣿⣿⣇⣀⣀⢀⡀⣀⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⢿⡿⠿⠿⠛⠋⠉⠙⠃⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣉⠛⢿⡏⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⣧⣤⣷⣶⡿⠿⢿⣶⣆⠀⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢿⡇⠘⣿⣾⢾⡿⣿⣿⢿⣿⢿⣴⡆⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⡏⣿⣤⠀⣸⡗⣺⡏⣿⢿⡟⣿⣿⣿⣿⣿⠀⠀⠹⣿⡄⠀⠀⠿⣿⣿⣿⣿⡇⠀⠀ ⠀⠖⠶⣶⠏⢶⠶⠰⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠈⠁⠀⠀⡲⢿⣿⣿⣿⣷⡀⠀⠀⠘⢿⡀⠀⠀⠀⣿⣿⣿⣿⡀⠀ ⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣬⡰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠚⠙⠛⠉⢛⠛⠙⠫⠻⠋⢻⢿⡿⠻⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠼⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣿⢿⣿⣧⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠘⢿⣿⡇⠀⠀⠀⠠⠤⠤⡀⠀⠉⠉⠀⢀⡤⣤⣤⠀⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⣸⠁⠈⠩⣶⣾⣶⠎⠀⠙⠶⢤⣄⣀⣀⣀⣀⣿⠃⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠽⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠ 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⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡖⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣁⣻⣿⣿⣿⣿⣿⣀⣀⢀⡀⣀⢾⣿⣿⣧⣸⣿⣿⣿⣿⣿⠿⠿⠿⡟⠛⠛⠋⠉⠓⠀⠀⠀ ⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣏⠛⢿⡏⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣷⣦⣤⣤⣤⣶⠶⢶⣶⣦⠀⠀⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢿⡇⠘⣿⣾⢾⡷⣿⣿⢿⡿⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⡟⣿⣥⠀⢸⡇⢺⡏⣿⢿⡟⣿⣿⣿⣿⣿⠀⠀⢹⣿⡤⠉⠁⠶⢿⣿⣿⣿⣿⠀⢀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠿⠇⠈⠃⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⢹⣷⠂⠀⠀⠀⠻⣿⣿⣿⣆⠀ ⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣾⣿⣰⡰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠙⠛⠛⠋⠙⠙⠛⠙⢿⣿⠟⠛⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣾⣿⣿⣿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠻⣿⡿⠀⠀⠀⠀⢀⡀⠀⠀⠉⠙⠉⠀⢀⣀⣩⡄⠉⠙⠓⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⠀⠀⠀⠒⠀⣸⠀⠀⠀⠀⠀⡸⠀⠉⣱⣶⣶⠄⠀⠉⠳⢄⣀⣀⢦⣀⡀⢸⣿⠀⠀⠛⣿⣿⠁⠀⠀⠳⣶⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠃⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠈⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣷⣤⣄⣧⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠙⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⢀⣽⣿⣿⣷⣦⣀⠀⠀⠀⠀⣾⣿⣿⠟⣯⣿⣿⣾⣿⣿⣦⡘⡁⠀⠀⠀⠀⠀⠀⠀⢠⠴⠀⠀⠁⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠂⠀⠀⣴⣿⣿⡿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢸⣿⣿⣿⠆⠀⠈⣿⣿⣿⣿⣿⣷⠙⠷⣤⡴⠖⠛⠉⠀⠀⠀⠀⣀⡠⠤⠂⠛⠃ ⠀⠠⠄⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣤⣠⣠⣀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⠋⠀⠀⠀⠀⠀⢹⣟⠀⢻⣿⣿⣷⣄⠇⠀⠀⠀⠀⠀⠖⠒⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣴⡂⠀⠀⢠⣿⣿⣾⣿⣦⠀⠀⠀⠀⢀⣠⣿⣿⣿⠯⠁⢀⢸⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⢺⣿⣿⣿⢿⠘⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣤⣈⣿⣿⣿⣿⡿⠀⠀⣠⣴⣿⣿⣿⣿⠏⠀⠀⢸⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣯⣅⠀⣠⣿⣿⣿⣿⡟⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠋⣶⡄⠘⠀⠀⢀⣤⣄⣀⣼⣿⣧⣴⡏⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠛⢃⡀⠀⠀⠘⠿⣿⣿⡿⠿⣿⣿⣶⡆⠀⠀⠘⢻⣿⣿⣿⣿⣆⣄⢠⠄⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣯⣹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⠿⠿⢿⡿⢿⡿⠿⠿⠛⠁⠀⠛⠀⠀⠀⡀⠀⠀⠀⠙⢷⣤⣤⣀⠉⠉⠀⠀⠀⠈⠉⠃⠀⣠⣴⣿⣿⣿⣿⣿⣿⠱⠈⠡⢤⣤ ⣭⣧⣀⢀⣶⠀⠀⠇⠀⠀⠀⠀⠀⣰⣿⠿⠿⠿⠛⣿⡇⢀⢀⡀⣀⡀⢉⣯⣁⣠⢀⡀⡀⢀⠀⡀⠀⡀⠀⠀⠀⢀⠴⣆⢀⣀⠀⠁⣀⠀⡀⠀⢀⠻⣿⣿⣿⣶⡄⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠸⠟ ⣿⣿⣿⡇⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣾⡿⠇⣿⣼⡇⣿⣫⣿⠻⠏⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⣿⣝⣃⡐⣿⣿⣿⣼⣟⣹⣿⣿⣿⣿⣧⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣿⣿⣿⣿⣿⣿⣴⡆⣿⢿⣾⣿⣿⢹⡇⢿⣽⡇⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢻⣯⣽⡟⣿⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣀⣈⢿⣿⣿⣿⣿⣂⣀⢀⡀⣀⢘⣿⣿⣦⠀⡀⣉⠛⢿⣿⡏⠉⠩⠉⠀⠈⠉⠉⠻⠆⠀⠀ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⠛⢿⣏⢹⣧⣿⣿⣷⣿⣿⣿⣿⣿⠀⠘⣿⣄⣀⣀⣀⣰⣶⣶⣶⣤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣿⡇⣿⢹⡇⠘⣿⣾⢺⡷⣿⣿⢿⣿⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠃⣿⢿⡟⣿⣷⠀⢸⡇⢸⡏⣿⢽⡟⣿⣿⣿⣿⣿⠀⠀⢹⣷⠉⠉⠉⠩⣷⣶⣾⣿⣷⣦⠀ ⠀⠶⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠾⠿⠀⠙⠀⠀⠀⠰⣿⣿⣿⡆⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀ ⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣸⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⠿⠿⠿⢿⠛⠻⠿⠟⢿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠡⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣷⣽⣿⣿⣿⣿⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢿⣿⠁⠀⠀⠀⢀⣤⡀⠀⠉⠙⠋⠀⠀⣀⣈⣄⠙⠉⠓⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⢸⠃⠉⠉⣶⣶⡦⠀⠈⠛⢤⣀⡀⣠⣄⠀⠀⣿⡏⠈⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠐⢿⣻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠛⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣧⣄⣠⣧⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⡴⠞⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢘⣿⣷⣶⣤⡀⠀⠀⠀⠀⣼⣿⣿⢿⣯⣽⣿⣿⣿⣷⣦⡘⡇⠀⠀⠀⠀⠀⠀⠀⢠⠠⠄⠀⠉⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣴⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⠄⠈⢻⣿⣿⣿⣿⣿⣷⠙⠷⣦⣤⠶⠚⠋⠀⠀⠀⠀⢀⣀⡤⠄⠚⠋ ⠀⠀⠤⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⠋⠉⠁⠀⠀⠈⣿⣿⠉⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠈⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠸⣿⣿⣤⡖⠀⠀⠀⢀⣼⣿⣽⣿⡄⠀⠀⠀⠀⣰⣾⣿⣿⠿⠉⢀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠺⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠁⠁⣿⣿⣿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣤⣀⣸⣿⣿⣿⣿⠇⠀⣀⣴⣿⣿⣿⣿⡟⠀⠀⢸⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠉⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⡃⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⣧⡄⠠⠀⠀⣄⣤⣀⣀⣠⣿⡏⠀⣀⡀⠀⠀⠀⢠⣤⣤⣾⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢇⡀⠀⠀⠹⣿⣿⠿⠿⢿⣷⣾⣿⣷⠀⠀⠀⢈⣿⣿⣿⣿⣿⣷⡀⡤⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⣿⡟⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⡀⠀⣿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠟⠀⠀⠀⢀⠀⠀⠈⠻⢦⣤⣄⡈⠁⠀⠀⠀⠈⠉⠉⠉⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⢡⣤⣤ ⣭⣽⣀⡀⣆⠀⠀⠼⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⢀⢀⡀⣀⡀⢋⣯⢁⣤⢀⡀⡀⢈⠉⡉⠈⡉⠉⠀⡀⢀⡠⣄⢀⣀⠀⠈⣀⠀⣀⠀⣀⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠿ ⣿⣿⣿⡧⠘⠷⠶⠀⠀⠀⠀⠀⠿⠿⠟⠛⠋⠉⣿⡿⠇⣿⣼⡇⣿⣯⣿⠻⠏⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⢿⣝⣃⡀⣿⣿⣿⣼⣟⣹⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⣿⣿⣿⣿⣿⣴⡆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣯⣽⡿⣿⠈⢿⣿⣷⠀⠀⠸⣿⣿⣿⢿⣿⠿⠿⠿⢿⣿⣿⡿⠟⠀⠀ ⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣈⣉⢿⣿⣿⣿⣷⣆⣀⢀⡀⣀⢐⡿⣿⣿⠀⡀⣀⠀⢻⣿⡆⠀⠠⠀⠀⠀⠙⠛⠻⠦⠀⠀ ⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡿⢿⣯⢹⣧⣿⣿⣷⣿⣿⣿⣿⣿⠀⠠⣿⣦⣀⣀⣀⣠⣤⣤⣤⣤⣀⠀⠀ ⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣿⡇⣿⢹⡇⠘⣿⣿⣿⣷⣿⣿⣿⣿⢿⣴⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⡟⣿⣷⠇⢸⡇⢸⡏⣿⢿⡟⣿⣿⣿⣿⣿⠀⠀⢺⣿⡉⠙⠛⠉⣭⣶⣾⣿⣿⣦⠀ ⠀⠿⠶⣶⠏⢶⠆⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠰⠾⠿⠀⠙⠀⠀⠀⠈⢷⣿⣿⡆⠀⠀⠀⠙⣧⠤⠀⠀⠀⠈⣿⣿⣿⣿⡀ ⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⣇⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠛⠛⠋⠹⠉⠋⠻⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢱⣦⣿⣿⣿⣿⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⢿⣿⠃⠀⠀⠀⣀⣐⣀⣀⠈⠉⠋⠁⠀⢀⣀⣠⠈⠉⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠛⢿⠀⠀⠀⠀⠀⡇⠈⠉⠀⢠⣤⠀⠀⠙⠧⣄⣀⠀⠀⠀⠀⠘⣿⡏⠉⠻⣿⣿⡗⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⢿⣟⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣾⣿⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣧⣀⣀⣱⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣦⣄⠀⠀⠀⠀⠀⣠⣿⣿⢿⣯⣽⣿⣽⣿⣿⣄⠑⡆⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠉⠁⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⡀⠀⢠⣿⣿⣿⠀⠉⢻⣿⣿⣿⣿⣿⣷⠙⠂⠀⠀⠐⠒⠛⠁⠀⠀⠀⠀⣀⡠⠤⠘⠛ ⠀⠀⠰⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⢀⣠⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄⠸⡿⠛⠁⠀⠀⠸⣿⡏⢹⡯⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠒⠂⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣆⠒⠂⠀⠀⠀⣤⣾⣯⣿⣦⠀⠀⠀⣠⣼⣿⣿⣿⣿⠿⠏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠟⠃⠸⣿⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣤⣀⠀⠀⢿⣿⣿⣿⣿⣠⣤⣿⣿⣿⣿⠟⡟⠁⠀⢸⡀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣗⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⣜⡋⠛⢹⣿⣿⣿⣿⣿⣿⠝⠀⠀⠀⠀⢘⡇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣾⣿⣿⣴⣿⣿⣧⡀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣦⡀⠀ ⠼⠛⡁⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠻⣿⣿⣿⣿⣷⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡀⠀⠀⠃⠀⠀⣶⣄⠀⠀⠀⠀⠀⠉⠉⠛⠋⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣬⣆⣀⢸⣇⡀⠾⠃⠀⣼⣿⣿⣿⢻⣿⣿⠉⠀⣀⠀⠀⠀⠀⣀⡀⢈⣩⢉⣿⢟⡀⡙⢿⠿⡿⢿⣛⠿⠿⡟⢁⠈⡃⠀⣀⠀⠀⣀⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠻⠿⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⠀⣾⡿⠇⣿⣼⡇⣿⣩⣿⣿⡏⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣼⣿⣿⢿⣝⢃⡀⣿⣿⣿⣸⣏⣹⣿⣿⢻⣿⣷⣤⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣄⠀⠀⠀⠀⠐⠛⠋⠉⠀⠀⠸⣿⠀⢿⣷⡆⣿⣿⣿⣿⣷⣿⣶⡆⣿⢿⣾⣿⣿⢹⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣽⡟⣿⢸⣿⣿⣿⣿⠂⠀⠀⢘⡏⠋⠭⡝⠋⠀⢶⣶⣦⡀⠀⠀⠀ ⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣉⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣛⣻⣿⣿⣿⣿⣷⣇⣀⢁⡀⣀⢘⡛⢉⡛⣿⡀⣀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠘⠛⠛⠦⠀⠀ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⠋⣿⣿⣿⣿⣿⡟⢿⣯⣹⣧⣿⢹⣷⣿⣻⣿⣿⣿⠀⠀⠘⣧⡀⢀⢀⣀⣤⣤⣤⣤⣀⠀⠀ ⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢿⣿⡇⣿⢸⡇⠘⣿⣶⢾⡗⣿⣿⢽⣿⢿⣴⡆⣿⣤⣿⣿⡇⠈⣿⣿⢿⣿⠀⠀⣿⠆⣿⣿⣿⣿⣿⡇⢸⡇⢸⡏⣿⢾⡟⣿⣿⣿⣿⣿⠀⠀⠀⢻⣏⠙⠛⠛⣭⣤⣽⣿⣿⣦⡀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢶⠿⠆⠘⠀⠀⠀⠀⢀⣮⣿⣇⠀⠀⠀⠀⠹⡄⠄⠀⠀⠉⣿⣿⣿⣿⡄ ⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣷⣤⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠉⠛⠛⠙⠛⠟⠁⠘⢿⡿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢛⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣦⣼⣿⡿⠿⣿⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⣶⣦⣤⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠻⣿⡏⠀⠀⠀⠀⢀⣀⢀⡀⠉⠙⠉⠀⢀⣀⣠⡀⠉⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⢹⠃⠀⠀⠀⠀⡘⠈⠉⠁⢀⠁⠆⠀⠈⠙⢤⣀⡀⠀⠀⠀⠀⢹⣿⠉⢩⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣾⡿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣾⡏⠀⠈⠉⢿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢈⣯⣉⡉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⠶⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣿⣷⣤⡀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣻⣿⣶⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠈⠉⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⡀⠀⠀⣾⣿⣿⡇⠉⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⢀⣀⠤⠀⠛ ⠀⠀⠰⠀⠀⢠⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣆⠰⣿⠟⠛⠀⠀⠀⢸⣿⠉⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⡀⠠⠔⠂⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⠀⠑⠒⠀⠀⠀⣤⣾⣦⣽⣤⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠟⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⣿⣧⠁⠀⠀⠀⠀⠀⢸⣿⡄⣿⣿⣿⢀⠀⣶⡿⠟⠉⠀⠀⠀⠀⠀⣠⣶⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⡀⠀⠀⠠⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⡿⠛⠟⠋⠀⠀⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠙⠻⡀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣦⣄⠀⠛⠙⠛⣿⣿⣿⣿⣿⢿⡯⠀⠀⠀⠀⠀⠀⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠻⠿⠋⠈⢉⣿⣿⣿⣷⡀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣠⣴⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⢀⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠆⠀⠁⠀⣀⣼⣦⡀⠀⠀⠀⠀⠘⠛⠛⠛⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣧⣀⠀⣼⣷⠠⠃⢤⣿⣿⡻⣿⣿⣿⠋⠀⠀⣀⠀⢀⠀⠀⡀⡀⢺⣭⣉⣿⢟⡛⡻⢿⣿⣿⣿⣿⣿⡿⣿⢋⠉⡃⠀⣀⠀⠀⣀⠀⣀⠀⠀⠈⡻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⠀⠸⠿⠀⠘⣾⣿⣿⣴⣿⣿⣿⠀⠀⣾⡿⠇⣿⣼⡇⣿⣩⣿⣻⡏⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣼⣿⣿⢿⣝⢃⡀⣿⣿⣿⢸⣏⣹⣿⣿⠛⣿⣿⣦⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛ ⣼⣿⣿⣿⣆⡀⠀⠀⠐⠟⠋⠉⠀⠀⠘⣿⠀⠀⢿⣷⡆⣿⣿⣿⣿⣷⣿⣷⡆⣿⢿⣾⣿⣿⢹⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⡟⣿⠀⣿⣿⣿⣿⣷⠀⠀⠀⢄⠀⠨⡜⠋⠀⢶⣶⣦⡀⠀⠀⠀ ⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠉⣀⣀⠀⠀⣰⣿⣿⣿⣿⣿⢿⡧⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣙⣻⣿⣿⣿⣿⣷⣇⣀⢁⡀⣀⢀⣹⢋⡙⢻⣏⣀⠀⠀⢸⡤⠀⠀⠀⠀⠀⠘⠛⠛⠶⠀⠀ ⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⣿⣾⣿⡁⠈⣿⠋⣿⣿⣿⣿⣿⡟⢿⣯⣹⣧⣿⢿⣷⣿⣻⣿⣿⣿⠀⠀⠈⣧⡀⠀⡀⠀⣤⣤⣤⣤⣀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣿⡇⣿⢸⡇⠘⣿⣶⢾⡷⣿⣿⢿⣷⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠀⣿⢿⣿⣿⣿⠇⢸⡇⢸⡏⣿⢸⡟⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⠙⠛⠛⢻⣭⣭⣿⣿⣦⡀ ⠀⠖⠶⣶⠏⢶⠆⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢶⠷⠆⠘⠂⠀⠀⠀⠀⠠⢐⢾⡄⠀⠀⠀⠘⡇⠀⠀⠈⠉⢻⣿⣿⣿⣇ ⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠟⠿⠻⠿⠿⠿⠟⠛⠛⠻⣿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣛⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠙⢿⡟⠀⠀⠀⠀⢀⣀⠀⡀⠀⠙⠋⠀⢀⢀⣤⡄⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⢻⠇⠀⠀⠀⠀⡜⠀⠉⠁⠀⠀⠀⠀⠀⠈⠷⣤⣀⡀⠀⠀⠚⠀⣿⡟⠉⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠉⣳⡛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠠⣀⣠⡶⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣶⣄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣾⣷⣀⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠈⠉⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⣿⣿⣿⣷⡀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⠀⠀⣰⣿⣿⣟⠛⢿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠠⠤⠞⠃⠀⠀⠀⠀⠀⣀⡠⠄⠚ ⠀⠀⠐⠂⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⡿⠁⢹⣿⣿⣿⡇⡀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⠿⠃⠀⠀⠙⣿⡿⣿⣿⣿⣿⠀⡀⠀⠀⠀⣀⡀⠀⠴⠒⠀⠉⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⢸⣿⣿⡇⠙⠒⠀⠀⢠⣴⣿⣤⣤⡆⠀⠀⣀⣴⣿⣿⣿⣿⣿⠟⠋⠁⠀⠘⠸⣍⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣷⠙⠁⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⣾⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣷⡀⡀⠀⠀⠸⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⡿⠋⠋⠁⠀⠀⢀⠀⠀⠰⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠉⠹⣷⡀⠁⠀⠀⠄⠀⢠⣴⣿⣿⣿⣿⣿⣷⣦ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⣸⠀⠀⢀⣿⣿⣿⣿⣿⣿⡻⣻⣿⣿⡟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣤⣿⣿⣿⣄⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣄⣠⣾⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢨⣿⣿⣿⣿⣿⣿⣶⣿⡿⣟⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣦⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⡂⢀⡁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠋⠀⠀⠀⢀⠀⠀⠀⡃⠀⣰⣦⡄⠀⠀⠈⠉⠙⠿⠟⠛⠋⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣾⣤⡀⣸⣤⠃⠀⣨⣿⣿⣿⡿⠛⣿⠁⠀⠀⣀⠀⢀⠀⡀⣀⡀⢛⣯⣍⣻⢏⡀⣰⣿⣿⣿⣿⣿⣿⡿⣿⢗⠃⡆⢀⣀⠀⠀⣈⠀⣀⠀⣀⠀⡸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣽⣿⠛⠃⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⡀⠀⠀⢠⣿⣿⣿⣿⣿⢿⡇⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣻⣿⣿⣿⣿⣿⣿⣷⣇⣀⢘⡃⣀⢈⡁⣂⣿⣿⡇⣀⠀⠀⠈⢿⡀⠛⠄⠀⠘⠻⢻⠿⢦⣄⠀ ⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⣿⢿⣯⣹⣧⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠘⢧⠀⠰⠀⢀⣀⣀⣀⡀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⡇⣿⢹⡇⠸⣿⣾⢾⡗⣿⣿⢿⣿⢿⣴⡆⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⣿⣿⣿⡇⢸⡟⢻⡏⣿⢹⡟⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣷⠾⠿⠾⣿⣋⣻⣿⣷⡀ ⠀⠖⠶⣶⠏⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⣤⣶⡄⠰⠆⢰⡆⠀⠀⠰⣿⣿⣿⡀⠀⠀⠀⢻⣧⠀⠘⠛⢿⣿⣿⣿⣿ ⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣄⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⡿⠿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⠁⠁⠀⠀⠀⠀⠀⠀⠀ ⣛⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠈⠉⠃⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⣍⣽⣿⣿⣿⣏⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠻⢿⣿⠃⠀⠀⠀⠀⣀⣀⢀⡀⠘⠛⠁⠀⠀⣀⣉⠀⠀⠉⠉⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠐⠒⠿⠁⠀⠀⠀⠀⠃⠘⠉⠀⠀⠀⠀⠀⠈⠙⠢⣄⣀⣀⠀⠀⠀⢀⣿⣿⠻⠟⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠻⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢸⣿⣦⣄⠀⠀⠀⠀⠀⣠⣤⣴⣿⣶⣶⣾⣇⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠘⠛⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⣿⣿⣧⡀⠀⠀⣾⣿⣿⡟⢿⣿⣿⣾⣿⣷⣦⣧⣀⠀⣀⣠⣤⠶⠂⠀⠉⠀⠀⠀⠀⣀⡀⠰ ⠀⠀⠒⠆⠀⣤⣀⣀⣿⡏⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⣻⣿⣿⣿⣿⡅⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⠿⠇⠂⠀⣿⣿⡟⣿⣿⣿⡟⣷⠉⠁⠀⠀⠀⠀⠀⠤⠀⠊⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⡀⠀⠀⢸⣷⣦⣽⣥⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠀⢱⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣷⠸⠏⠀⠀⠀⠀⠀⢸⡟⠀⣿⣿⣿⣷⡼⣦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⠀⢿⣿⣿⣿⡿⠇⢰⣶⣿⣿⣿⣿⣿⠁⠀⠀⠄⢸⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⣹⠆⠀⠀⠀⠀⠀⢠⣶⣶⣄⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠠⠈⠻⣿⣿⣷⣤⣟⣿⠿⠋⠀⣰⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⣾⢁⣼⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿ ⠷⠄⢀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠋⠀⠀⢴⠄⠀⠀⢠⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠿⢿⣿⣿⣿⣦⡀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢛⡀⣿⠟⠃⠹⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠙⠁⠀⠀⠼⠿⠛⠋⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣾⣗⣸⣇⢠⣬⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣇⠀⢀⢀⡀⣀⡀⢈⣿⣩⣿⢀⡀⡀⢀⠛⡋⢛⣻⠿⠿⣟⢛⠁⡀⢀⣀⠀⠀⣀⠃⣀⠀⣀⠀⡻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿ ⠿⣿⢿⣿⡟⠻⠿⠟⠃⠀⠀⠀⠀⠼⠏⠉⠉⠈⣿⡿⠇⣿⣼⡇⣿⣫⣿⣿⡟⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⢿⣝⡳⠀⣿⣿⣿⣾⣟⣹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣿⠛⠻⠿ ⣄⣿⣿⣿⣇⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⣿⣿⣿⣷⣿⣿⡇⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢿⣯⣼⡟⣿⢿⣋⣿⣿⣆⠀⠀⠀⠀⢰⡄⢄⣠⡷⠄⣤⣤⣄⡉⠀⠀⠁ ⣿⣿⣽⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⢀⣀⠀⣀⣀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣻⣿⣿⣿⣿⣿⣿⣷⣇⣀⢚⡀⣀⢘⡽⣿⣿⣏⡀⣀⠀⠀⠘⣿⠀⠛⡄⠀⠘⠿⣿⠿⢦⣄⠀ ⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⣿⢿⣯⣹⣧⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠘⣇⠀⠳⠁⢀⣀⣀⣀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢿⣿⡇⣿⢹⡧⠸⣿⣾⢾⡗⣿⣿⢿⣿⢿⣴⡆⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⣿⣿⣿⡏⢸⡟⢻⡏⣿⢸⡟⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣶⠾⠷⠾⢟⣟⣻⣿⣖⡀ ⠀⠶⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠃⢠⣶⡄⠶⠆⢰⡀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠈⣿⣆⠀⠘⠻⣿⣿⣿⣿⣟ ⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠞⠁⠁⠀⠀⠀⠀⠀⠀ ⣛⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠛⠊⠈⠁⠁⠈⠛⠟⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣆⣯⣿⣿⣿⣏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠻⣿⣿⠀⠀⠀⠀⠠⠤⠤⢀⡀⠈⠛⠋⠀⠀⢀⣉⡁⠈⠉⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠿⠁⠀⠀⠀⠀⠏⠈⠛⠁⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⣀⡀⠀⠀⣨⣿⣿⠋⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠻⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣶⣤⡀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣶⣶⣼⣧⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠚⠉⠁⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣦⡀⠀⠀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣷⣮⢷⡀⠀⢀⣀⣤⡴⠆⠀⠉⠀⠀⠀⠀⢀⡀⠤ ⠀⠀⠐⠂⠀⣤⣄⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡆⣸⣿⣿⣿⡇⠈⠙⣿⣿⣿⣿⣿⣿⡿⣧⠍⠁⠀⠀⠀⠀⣀⠄⠀⠒⠉⠁⠀⠠ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⢀⣤⣀⣤⣤⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡟⠁⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⡹⠟⠀⠀⠀⠀⠀⢿⡟⠉⣿⣿⣿⣷⡘⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⠄⢀⣤⣤⣿⣿⣿⣿⠛⠁⠀⠤⢸⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠤⠈⠿⣿⣿⣧⣄⡛⠉⠿⠏⠀⠰⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⡅⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣦⣤⡀ ⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣶⣤⣤⣿⣿⣿⡟⠁⠰⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣄⣤⣶⣄⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠁⠀⠀⠀⠀⡀⢀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡀⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠈⠻⠋⠉⠋⠻⣿⠿⠿⠟⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣿⣿⣷⣄⣠⣄⡘⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⠀⢀⢀⡀⣀⡀⢙⣿⣯⣿⢀⡀⡀⢘⠛⡛⢿⣿⢿⠿⣿⢛⠁⡠⢀⣀⠀⠀⣀⠒⣀⠀⣀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢹⣿⣿⣿⣿⣿⣿⣿ ⠿⣿⣿⣿⡟⠻⠿⠛⠀⠀⠀⠀⠀⢜⣿⡿⠟⠟⣿⡿⠇⣿⣼⡇⣿⣫⣿⣿⡟⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⢿⣝⣷⠀⣿⣿⣿⣸⣟⣹⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢠⣿⠋⠹⣿ ⣠⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢿⣷⡆⣿⣿⣿⣿⣿⣿⣽⡆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣯⣼⡿⣿⣿⢿⣿⣿⠀⠀⠀⠀⢠⣄⣀⣀⣸⣦⠄⣀⣄⣈⠛⠀⣠⠁ ⣿⣯⣿⡟⠛⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣀⠀⠀⢀⣶⣿⣿⣿⣿⢿⡂⢀⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢐⣻⣿⣿⣿⣿⣿⣿⣶⣇⣀⢒⡀⣐⢿⣾⣿⣿⠇⡀⣀⠀⠘⢿⡄⠘⠷⠁⠀⠻⣿⣿⣷⣤⡀⠀ ⣿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡿⣿⣏⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣷⡀⠈⢃⠀⠀⠀⠁⠀⠉⠁⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣿⡇⣿⢿⡇⠼⣿⣾⢾⡷⣿⣿⣿⣿⢿⣴⡆⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⣿⣿⣿⡇⢸⡟⢹⡏⣿⢻⡟⣿⣿⣿⣿⣿⠀⠀⠀⢺⣷⠶⣾⣶⠿⢿⣟⣿⣷⣖⠂ ⠀⠶⠶⣶⠏⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡿⡁⠀⣴⡀⠶⠄⢀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⢻⣇⠀⠈⠚⠿⣿⣿⣿⣿⣧ ⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣦⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⠿⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⡛⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠡⠝⠋⠛⠉⠈⠈⠈⢹⠟⠋⠛⠛⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣞⣸⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⠿⣿⡟⠀⠀⠀⠠⠤⠤⣦⣀⡄⠀⠙⠋⠀⠀⢀⣈⡁⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠃⠀⠀⠀⠀⠎⠈⠛⠃⠀⠀⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡿⠋⠉⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣷⣿⣿⣿⣿⣿⣾⣿⠉⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠻⠿⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣶⣶⣾⣧⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⠚⠋⠁⡀ ⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⣿⣿⣷⣦⡀⠀⢀⣾⣿⣿⢿⣿⣿⣿⣿⣿⣷⣬⢧⡀⠀⢀⣀⣤⡴⠆⠐⠋⠁⠀⠀⠀⢀⡀⣵ ⠀⠀⠐⠀⠠⣤⣀⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⠄⠈⢻⣿⣿⢿⣿⣿⣿⠛⠀⠉⠁⠀⠀⠀⢀⣀⠄⠀⠒⠈⠁⠀⠠ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣀⠀⠀⠀⢀⣀⣀⣠⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠟⠁⠀⠀⠀⢘⡿⠋⢺⣿⣿⡏⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⠀⠀⣿⣿⣿⣿⣷⠀⢀⣀⣶⣿⣿⣿⣿⠻⠛⠁⠀⢤⡤⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀⠘⠟⠻⠛⠀⢀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣿⣿⣿⣿⡟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣶⣄⠀⠀ ⠒⢀⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⣀⣀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣶⣿⣿⣶⡀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣷⣤⣄ ⠀⠈⠁⠀⠀⠀⠀⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⡀⣀⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣿⣧⣿⣄⣠⣜⠇⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣋⠀⢀⢀⡀⣀⡀⢹⣿⣯⣿⢀⡀⡀⢛⠿⡿⢿⣿⣿⡿⣿⢛⠋⡋⢉⣀⠀⠀⣀⠘⣀⠀⣁⣰⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⡟⠿⠟⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠇⣿⣼⡇⣿⣯⣿⣿⡟⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⢿⣝⣷⠀⣿⣿⣿⢸⣟⣹⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⠛⢿⣿⣿⣿⣿ ⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠻⠛⠉⠛⣿⢿⣷⡆⣿⣿⣿⣿⣿⣿⣽⡆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣯⣼⡟⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⡀⣀⣀⣸⣤⢀⣈⣀⣈⠋⠹⣿⠋ ⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⣈⣉⠀⣀⠀⣀⣻⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⢀⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⢀⣀⡀⢐⣻⣿⣿⣿⣿⣿⣿⣾⣆⣀⢂⡀⣀⢿⡉⣻⣿⣇⣀⣀⠀⠘⣷⣄⠘⢷⠁⠀⠿⣿⣿⣷⣄⡀⠀ ⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡿⣿⣏⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣇⡀⠈⠇⠀⠀⠀⠀⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣿⡇⣿⣿⡇⠸⣿⣾⢾⡿⣿⣿⣿⣿⢿⣴⡆⣿⣥⣿⣿⡇⠈⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⣿⣿⣿⠃⢹⡟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣷⠶⣾⣷⠿⣿⣿⣿⣷⣖⠂ ⠀⠶⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠉⣋⢠⡄⢤⠀⣶⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⡀⠀⠁⠻⠿⣿⣿⣿⣿⡇ ⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠻⠿⢿⠯⡓⠹⠛⢿⢿⣿⢿⡿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⢰⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⢿⣿⠇⠀⠀⠀⢀⠤⢤⣤⢀⣤⡀⠈⠁⠀⠀⠀⣀⡀⠀⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠀⠀⠀⠀⠘⠀⠛⠃⠀⠀⠀⠀⠉⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠋⠁⠻⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣤⣤⣤⣤⣤⣽⣿⠟⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣷⣶⣬⣇⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠶⠚⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣴⣶⣦⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣯⣿⣿⣷⣬⠣⠀⠀⠀⠀⢠⡤⠀⠘⠁⠁⠀⠀⠀⢀⠀⠤ ⠀⠀⠒⠀⠠⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣬⣿⣿⣿⣿⣷⡀⣼⣿⣿⣿⠀⠙⢸⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠒⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣇⠐⠒⠀⠀⣠⣥⣼⣶⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠛⠋⠀⠀⣼⣿⡿⣿⣿⡇⠀⠀⠀⠀⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⡇⠀⢀⣤⣾⣿⣿⡿⠿⣿⠿⠿⠅⠀⠀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⡁⠀⠀⠧⠀⠿⡿⠧⣿⣿⣿⠀⠀⢠⡄⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠹⣿⣿⣿⣧⡤⠀⢿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠙⠇⠀⣤⠀⠀⠀⣀⣀⣿⣿⣿⣧⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀ ⠂⠀⡀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠁⠀⣼⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢰⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣏⣧⣿⣿⣇⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⣿⡟⠛⢿⣿⣿⣧⡀⠀⠀⠀⠋⣶⣶⣶⣿⣿⣿⣿⡀⠀ ⠀⠀⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⣦⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣦ ⠴⣦⣾⣧⡀⣧⣠⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣀⠀⠀⠀⡀⣀⡀⠈⣿⠡⣿⢟⡀⣙⢟⠿⡿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⠛⠃⣀⠀⣀⠀⣀⡀⣰⣿⣆⠀⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⣿⢿⣿⡏⠛⠉⠀⠀⣈⣿⣿⣿⣿⡽⠟⠁⠀⣾⡿⠇⣿⣼⡇⣿⣩⣿⢹⡏⣿⣾⠫⣿⣿⣿⡇⣿⢹⡟⠛⣿⣿⣿⣿⢿⣝⣷⡄⣿⣿⣿⢸⣏⣹⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣷⡆⣿⣿⣿⣿⣷⣿⣼⡆⣿⢿⣞⣿⣿⢹⡇⢿⣼⡇⠀⣿⢿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣯⣼⡏⣿⠙⢿⣿⣷⣄⠀⠀⠀⢀⠀⣀⡀⣠⠀⢼⣿⣿⣿⣿⣿⣿⠛ ⣿⣿⡿⠟⠀⠀⠀⠀⠀⠙⠜⣋⣁⠀⣘⣷⣀⡀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡀⢀⣀⠀⣀⡀⣀⡀⠀⠀⢀⡀⠀⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⢂⡀⣀⢀⣽⣿⣿⣿⣿⣀⠀⠈⣧⡀⠘⠃⠀⠀⠻⣿⣿⣿⣅⠀⠀ ⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣾⣿⡏⣿⣽⠇⢰⣿⣿⣿⣿⣿⣿⣿⡇⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡿⣿⡏⢹⣧⣿⣸⣿⣿⣻⣿⣿⣿⠀⠀⢻⡇⠀⠀⠆⠀⠀⠈⠉⠉⠉⠁⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⢿⣿⡇⣿⢸⡇⠸⣿⣶⢾⡷⣿⣿⢽⡇⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⣿⣿⣿⡇⢹⡟⢸⡏⣿⢸⡟⣿⣿⣿⣿⣿⠀⠀⠀⢿⡷⠴⣾⣶⠿⣿⣻⣿⣶⡂⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡧⡄⠠⠀⢦⠀⣄⡀⡀⢻⣿⣷⠀⠀⠀⠀⠈⣷⠀⠀⠀⠻⠿⣿⣿⣿⣿⠀ ⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣥⣤⣜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⡴⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠻⠛⠿⠿⠟⢛⠖⠨⠻⢿⣿⣿⡿⡯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠿⢿⣿⠇⠀⠀⠀⢀⣠⣤⣶⢄⣠⡀⠉⠀⠀⠀⠀⣀⠉⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠛⠛⠛⢻⠟⠃⠀⠀⠀⠘⠀⠙⠋⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠁⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⣤⣀⣀⣀⣀⡀⣸⣿⣿⠟⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠸⢿⡻⠿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣷⣦⣤⣆⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢂⠀⠀⠀⠀⢠⡤⠀⠐⠃⠁⠀⠀⠀⠀⠀⡤ ⠀⠀⠐⠀⠠⢀⣿⣿⡿⠀⠀⠀⠀⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣾⣿⣿⣿⣦⡀⢰⣿⣿⣿⠃⠘⢻⣿⣿⢿⣿⣿⣾⢿⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠒⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⡅⠐⠒⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠛⠛⠀⠀⢸⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣿⣿⣿⣿⣿⠃⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⡁⠀⣠⠆⠀⢸⣿⡟⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⣠⣾⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⡋⠋⠛⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠀⢿⣿⡇⠀⣠⠀⠀⠀⢀⣀⣻⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⡀⠀⠀⢸⣿⣿⣿⣷⡄⠈⠉⠉⠁⣽⣿⣿⣿⣿⣿⣿⡿⠟⠒⠀⠀⠀⠀⠀⠆⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⠽⠁⠀⠀⣻⡷⠀⠁⠀⠀⠀⠈⣿⣿⡟⠻⣿⣿⣇⠀⠀⠀⠐⢚⣤⣤⣤⣶⣿⣿⡷⠀⠀ ⠀⠀⠁⠀⠀⠈⢻⣿⣿⣿⣿⣶⣦⣠⣶⣿⣿⣿⣿⠿⠯⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⡄⠀⠉⠁⠀⠀⡀⠀⠀⠀⠈⠋⠀⠀⠸⣿⣿⡇⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣆⠀ ⢤⣄⣶⣇⣠⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣀⠀⠀⠀⠀⠀⠀⠈⣻⢉⣷⢄⡀⡐⢻⡿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣆⠀⣀⠀⣀⠀⡰⣾⣦⡀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⠿⣾⢿⣿⡟⠛⠉⣉⣿⣿⣿⣟⣿⣿⠟⠁⠀⠀⣾⡿⠇⣿⣼⡇⣿⣩⣿⠹⠏⣿⣾⠻⣿⣿⣿⡇⣿⢽⡿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣿⣿⢸⣏⣹⣿⣿⢻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⣿⣿⣿⡁⠀⠀⣿⣿⣿⢿⣯⣻⣿⡄⠀⠀⠀⢿⣷⡆⣿⣿⣿⣿⣧⣿⣴⡆⣿⢻⡄⣿⢽⢹⡇⢿⣹⡇⠀⣿⢹⣿⣿⣶⣿⣿⣶⣿⣿⣿⣿⣯⣼⡏⣿⠈⠛⢿⣿⣦⣀⠀⠀⢀⠀⢀⡀⣠⠀⣿⣿⣿⣿⣿⣿⣿⠿ ⣿⣫⣿⡿⠁⠀⠀⠘⢿⡿⠋⢛⣛⢿⣇⠀⣀⡀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⢀⣀⠀⣀⡀⣀⡀⠀⠀⢀⡀⠀⣀⡀⢀⣾⣿⣿⣿⣿⣿⣿⣦⣀⣀⢂⡀⣀⢀⡀⢼⣿⣿⣿⣶⠀⠈⣧⡀⠘⠃⢠⣿⣿⣿⣿⣿⡏⠁⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠈⠀⠀⣿⣍⣾⣿⡇⣿⣹⠇⣴⣿⣿⣿⣿⣿⣿⣿⡇⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⣻⣾⣿⡁⠈⣿⠋⣿⣿⣿⣿⣿⡿⣿⡏⢹⣧⣿⢸⣧⣿⣻⣿⣿⣿⠀⠀⠸⣇⠀⠀⠆⠙⠿⠿⠛⠁⠉⠀⠀ ⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⡇⣿⢸⡇⠹⣿⣾⢿⣷⣿⣿⣽⡇⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠀⣿⢿⣿⣿⣿⡇⢸⡏⢸⡏⣿⢸⡟⣿⣿⣿⣿⣿⠀⠀⠀⢻⣶⠤⣾⣦⠿⠟⠻⣿⣶⡀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣇⡄⢠⠀⢤⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⢻⡄⠀⠀⠺⠿⢿⣿⣿⣿⠂ ⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣥⣶⣄⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠻⠻⣛⡟⠛⠻⣿⣿⢿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⣿⣿⣿⣿⡇⠀⠀⠀⠠⣄⣀⠀⠀⠀⠀⣭⡉⢽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⢿⣿⠇⠀⠀⠀⠀⢛⣛⣁⣀⣀⠀⠘⠃⠈⠀⠀⠈⠙⠀⠀⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠻⠛⠛⠻⠿⠃⠀⠀⠀⠐⠀⠙⠛⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣻⣿⡿⠁⠀⠀⠟⣫⡙⠿⣛⣿⣷⣀⠀⢀⡀⠀⠀⢰⣾⣿⣿⣿⣿⣷⡄⢀⣀⠀⣀⡀⣀⡀⠀⠀⢀⡀⠀⣀⡀⢀⣺⣿⣿⣿⣿⣿⣿⣦⣆⣀⢒⡀⣀⢀⡀⢀⣿⣿⣿⣷⡄⠀⢰⡀⠀⠧⣿⣿⣿⣿⣿⣿⡁⠀⠀ ⣿⣿⠏⠁⠀⠀⠀⠒⠀⠀⠀⣿⣍⣿⣿⡇⣿⣹⠇⣰⣿⣿⣿⣿⣿⣿⣿⡇⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⢹⣾⣿⡁⠈⣿⡋⣿⣿⣿⣿⣿⡿⣿⡏⢹⣧⣿⢸⣇⣿⣻⣿⣿⣿⠀⠀⠘⣧⠀⠀⠋⠿⣿⣿⠇⠀⠉⠀⠀ ⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⡇⣿⢸⡇⠙⣿⣾⢿⣷⣿⣿⣽⡇⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣼⢿⣿⠀⠀⣿⠇⣿⣿⣿⣿⣿⡇⢸⡏⢸⡏⣿⢸⡏⣿⣿⣿⣿⣿⠀⠀⠀⠹⣶⠤⣶⣦⡿⠿⠛⢿⣷⡀⠀ ⠀⠶⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢍⢿⣿⡇⣀⠀⠀⢤⠀⠀⠀⠀⠐⣿⣿⣷⡀⠀⠀⠀⢹⡆⠀⠀⠘⠿⠿⣿⣿⣿⠆ ⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣤⣦⣨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠯⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠻⠻⡿⠟⠉⠉⠛⠻⣿⣿⡿⡿⠗⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠛⠈⠀⠀⠈⠉⠓⠈⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⢈⠙⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠃⠀⠀⠀⠰⠀⠙⠛⠁⠀⠀⠀⠈⠛⢦⡀⠐⠒⠶⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠾⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⢲⣤⣀⡀⠀⠀⠀⢰⣿⣿⣟⠉⠛⠻⠿⣷⠀⠀⠀⠀⠀⠀⠸⣿⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠀⠀⠀⠀⠀⢀⣠⡤ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣴⣿⡟⠋⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⣀⣼⣦⣤⣼⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠚⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣻⣿⣷⣜⣂⠀⠀⠀⣀⣠⡤⠀⠘⠁⠁⠀⠀⠀⢀⠀⡤ ⠀⠀⠀⠀⢀⣀⡀⣴⣿⠃⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⣠⣾⣷⡄⠀⢠⣿⣿⣿⡇⠉⠋⣿⣿⢻⣿⣿⣿⢿⡆⠉⠉⠀⠀⠀⠀⣀⠀⠀⠒⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠉⣸⣿⡇⠀⠀⠀⣀⣄⡀⣄⠀⠀⠀⠀⠀⢠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢾⣿⣿⣿⣿⣦⣼⣿⠟⠛⠁⡄⠀⣿⡿⠐⣿⣿⣿⣦⢃⡤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣾⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣀⠀⠹⠿⠀⢻⣿⣿⡿⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⢸⣿⣿⣿⣿⣟⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢹⣿⣷⠀⠈⠉⠁⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⡁⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠛⠏⠀⠀⠀⠷⠆⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⣻⣿⣿⣿⣷⣄⣀⣤⣾⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⣀⣀⠙⡏⠁⠀⠀⠀⠀⠀⠱⢶⣶⣾⣿⣿⠆⠀⠀⠀ ⢤⣥⢤⣶⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⣀⠀⠀⠀⠀⡀⠀⠘⣻⠋⣸⣇⡸⡿⢻⠿⡿⣿⣿⣿⣿⣿⢿⡿⣿⡍⣀⠀⣠⣄⠀⣀⠀⣀⠀⡀⢀⠉⠻⡿⠟⠷⢧⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣇⠀⠀⣾ ⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⣾⡿⠇⣿⣼⡇⣿⡉⣿⢹⠇⣿⣿⢻⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⢸⣏⣹⣿⣿⠀⠀⠀⢀⠀⠈⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀ ⠀⣽⣾⣿⡇⠀⠙⣻⣯⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣷⡆⣿⣿⣷⣿⣵⣿⣴⡆⣿⢻⡾⣿⣿⢹⡇⢿⣽⡏⡿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣯⣼⡏⣿⠀⠀⠀⢿⣷⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⣻⣟⣿⣿⠃⠀⣢⡄⣿⠿⢿⣿⣿⠀⣀⠀⣀⡀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣦⢀⣀⠀⣀⡀⣀⡀⠀⠀⢀⡒⠉⣀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣆⣀⢒⡂⣀⢀⡀⢀⡨⣿⣿⣷⠄⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⢿⣉⠀⠀ ⣿⣿⡏⠀⠀⠀⠟⠛⠀⠀⠀⣿⣿⣿⣿⡇⣿⣽⢇⣴⣿⣿⣿⣿⣿⣿⣿⡏⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⢻⣾⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣧⣿⢸⡧⣿⣻⣿⣿⣿⠂⠀⠀⢸⠻⢿⣿⣿⠉⠀⠀⠀⠉⠀⠀ ⣿⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⣿⠛⢿⣿⡇⣿⣸⣿⡟⣿⣿⢿⡟⣿⣿⣿⡇⢿⣴⠆⣿⣤⣿⣿⡇⠀⣿⣼⢿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⢹⡏⢸⡏⣿⢸⡇⣿⣿⣿⣿⣿⠃⠀⠀⠘⣶⡦⣽⣧⡼⠟⠛⢿⣷⡄⠀ ⠻⠷⠲⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣇⣀⠀⠀⢠⠀⢠⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠸⣧⠀⠀⠐⠿⠿⣿⣿⣿⡇ ⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣤⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣯⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠻⠿⢿⠋⠹⠻⠛⠻⣿⣿⡿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⢿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠀⠈⠀⠀⠀⣀⡈⠉⠁⠛⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣄⣤⣬⡙⠁⠀⠀⠀⠀⠀⠈⠛⠛⡟⠋⠀⠀⢀⡰⠁⠙⠛⠁⢀⠄⠀⠀⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠋⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠀⠀⠀⣠⣿⣿⡿⠛⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠺⣿⠻⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤ ⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣶⣾⣿⡿⠇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣀⣀⣼⣦⣤⡼⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⣿⣿⣷⣌⣂⠀⠀⠀⣀⣠⡤⠀⠘⠁⠀⠀⠀⠀⢀⡀⡤ ⠀⠀⠀⠀⢀⣀⡀⣰⣿⠃⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣶⡄⠀⢰⣿⣿⣿⠁⠙⠛⣿⣿⢻⣿⣿⣿⢧⡄⠉⠀⠀⠀⠀⠀⣀⠀⠀⠒⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⣡⣾⡯⠀⢀⣠⣶⣠⣴⡇⠀⠀⠀⠀⠀⢠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣴⣿⣿⣿⣷⣄⣾⣿⠿⠛⠉⠀⠀⣿⣿⠘⣿⣿⣟⣦⢣⡤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⠄⣠⣴⣸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠻⢿⠀⢿⣿⣿⡿⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠿⢿⣿⣿⣿⣁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣟⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠛⠛⠉⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⠁⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠃⠀⢸⣿⣿⣿⣿⣆⣀⣠⣼⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠱⢶⣶⣾⣿⣿⠆⠀⠀⢀ ⢠⣤⠤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⣀⠀⠀⠀⠀⢀⠀⢸⣻⠛⣸⣇⡀⡀⢀⠽⡿⣿⣿⣿⡿⣿⢷⡿⡆⢷⣀⠀⠀⣀⠀⣀⠀⣀⠀⡀⢀⠛⢿⡿⠷⠾⣀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣇⠀⠈⣿ ⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⣾⡿⠇⣿⣼⡇⣿⣉⣿⠹⠇⣿⣿⢻⣿⣿⣿⡇⣿⢹⡏⡧⣿⣿⣿⣿⢿⣝⣳⣶⣿⣿⣿⢸⣟⣹⣿⣿⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⣸⣷⣿⡏⢹⡿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⣿⣷⣿⣷⣿⣴⡆⣿⢿⣾⣿⣿⢹⡇⢿⣽⡇⡧⣿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣯⣼⡏⣿⠀⠀⠰⣷⣧⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⣿⣟⣿⣿⠃⢀⣗⣵⣿⣿⣿⣷⣀⠀⣀⠀⣀⡀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡆⢀⣀⠀⣀⡀⣀⡀⠀⠐⢒⡚⠁⣂⡀⢀⣾⣿⣿⣿⣿⣿⣿⣧⣆⣀⢒⡂⣀⢀⡀⢀⡸⣿⣿⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀ ⣿⣿⡟⠀⠀⠘⠛⠃⠀⠀⠹⣿⣏⣾⣿⡇⣿⣹⢧⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⢻⣾⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣧⣿⢸⣧⣿⣿⣿⣿⣿⡆⠀⠙⢿⡿⠿⠋⠁⠀⠀⠀⠀⠉⠁⠀ ⣿⣿⠇⠀⠊⠀⠀⠀⠀⠀⠀⣿⠿⢿⣿⡇⣿⣸⣿⣿⣿⣿⢿⡟⣿⣿⣿⡇⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⢹⡏⢸⡏⣿⢸⡏⣿⣿⣿⣿⣿⢷⠀⠀⠘⣷⠦⢶⣦⡼⢟⠛⢿⣷⣆⠀ ⠿⠿⠶⣶⠏⢶⠴⠰⠶⠶⠶⠀⠀⠀⠀⠀⠐⠻⠋⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⡇⣀⠀⠀⢠⠀⢰⡄⠀⠀⠘⣿⣿⣿⡀⠀⠀⢸⣆⠀⠀⠘⠿⠿⣿⣿⣿⡇ ⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣤⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⡿⢿⣿⣿⢿⢿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠀⠈⠙⠋⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡄⠀⠁⠀⡀⣀⣀⠀⠁⠉⠘⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣾⣟⠁⠀⠀⠀⠀⠀⠊⢉⣩⡟⠉⠀⠀⣀⠞⠀⠉⠉⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣄⠀⠐⠶⣆⡀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁ ⡿⠏⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠻⣯⠟⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣶⣿⣿⣿⠅⠀⠀⠉⣻⠃⠀⠀⠀⠀⠀⣀⣰⣿⣶⣶⣽⣄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠶⢤⣤⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣽⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠈⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣃⠀⠀⠀⣀⠠⠤⠀⠘⠉⠀⠀⠀⠀⣀⠠⡴ ⠀⠀⠀⠀⢀⣀⣀⣼⣿⡏⢀⣀⣀⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⢸⣦⡀⠀⣾⣿⣿⣿⠉⠹⢻⣿⣿⢿⣿⣿⣞⢿⡄⠉⠀⠀⠀⠀⢀⠠⠄⠐⠂⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣴⣿⣿⣿⡲⣿⡿⠟⠟⠀⠀⠘⣿⣿⢹⣿⣿⣿⣆⢣⡤⠄⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠉⢙⣿⣿⣿⣿⣿⡂⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢿⠿⢸⣿⣿⡿⠟⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠃⠀⣿⣿⣿⣿⠛⠛⠛⠛⠉⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⡍⠀⠀⠀⠀⢵⣿⣿⣿⣿⣿⣷⡀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡿⠆⠙⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⣶⡮⢺⣿⣿⣿⣿⣿⣿⠂⢩⣿⣿⣿⣿⠁⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣶⣄⠀⠀ ⠀⠀⠃⢀⣿⣿⣿⣿⣿⠀⣀⣠⣷⣿⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⢿⣿⣿⣿⣿⡟⣿⡇⠈⢻⣿⣿⡟⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⣤⣤⣼⣿⣏⣀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⡏⠀⢈ ⣤⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⣀⠀⢀⢀⡀⣀⡀⢘⣻⠃⣰⣆⡀⣀⢀⠻⡿⣿⣿⠟⡤⣽⢗⠀⡀⢜⣟⠀⠀⣒⠀⣀⢀⣀⠀⡀⢀⠀⠀⠀⠈⠉⢸⠟⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⣿ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⣾⡿⠇⣿⣼⡇⣿⣉⣿⢹⠇⣿⣿⢻⣿⣿⣿⡟⣿⣹⡏⣦⣿⣿⣿⣿⢿⣝⣳⣴⣿⣿⣿⢹⣟⣹⣿⣿⣿⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀ ⣀⣿⣿⣿⣿⡇⠈⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆⣿⣿⣿⣿⣿⣿⣼⡆⣿⣿⣾⣿⣿⢻⡇⢿⣽⡇⠸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣯⣼⡟⣿⠻⣿⣿⣦⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀ ⣿⣿⣿⣿⠋⠉⠂⢻⣿⣿⡇⢀⣀⠀⣀⠀⣀⡀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣆⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⣤⢥⣀⡀⢀⣹⣿⣿⣿⣿⣿⣿⣦⣀⣀⢒⡂⣀⢀⡈⢻⣿⣿⣦⣀⠀⠀⠀⢩⠉⠛⠉⠉⠛⠿⢿⣿⣇⡀⠀ ⣿⣿⡟⠁⣀⡠⠚⠋⠘⠻⣿⣿⣏⣾⣿⡇⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣧⣿⢾⣧⣿⣻⣿⣿⣿⡄⠀⠀⢸⡀⠀⢀⠀⠀⣀⠀⠀⠉⢠⠀ ⣿⣿⠁⠀⠙⠀⠀⠀⠀⠀⠈⣿⠇⢿⣿⡇⣿⣾⣿⡿⣿⣿⢿⡿⣿⣿⣿⡇⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⣷⣿⣿⣿⣿⣷⡏⢹⡟⢸⡏⣿⢸⡟⣿⣿⣿⣿⣿⣇⠀⠀⢸⣷⠶⢾⡶⠿⢿⣛⣿⣷⣂⠀ ⠿⠿⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠉⠋⢁⣤⠀⠀⣶⠀⣴⡀⠈⠀⣰⣶⣻⣿⠀⠀⠀⢹⡇⠀⠈⠚⠻⣿⣿⣿⣿⡃ ⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⣸⣷⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⠐⠊⠀⠀⠘⠟⠉⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣠⣀⣠⡄⠀⠁⠀⡀⣀⣀⠀⠁⠈⠘⠒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣦⠶⣾⣏⠀⠀⠀⠀⠀⠀⠚⢉⣩⠏⠉⠀⠀⣠⠎⠀⠉⠉⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣦⡀⠀⠀⠀⢀⣀⡀⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠻⠃⠘⠻⡟⠻⠿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣶⣿⣿⣿⠂⠀⠉⠙⣿⠀⠀⠀⠀⠀⢀⣀⣴⣷⣷⣶⣿⣔⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠋⠉⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣶⠤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣽⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠘⠌⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣜⣅⠀⠀⢀⣀⠤⠤⠀⠈⠀⠀⠀⠀⠀⣀⠠⡶ ⠀⠀⠀⠀⢀⣀⣀⣾⠟⢯⣽⣯⣤⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⣿⣿⣿⣧⠉⠿⢿⣿⣮⣿⣿⣿⡞⢿⡄⠁⠀⠀⠀⠀⢀⠠⠄⠐⠊⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣀⡀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⢀⣴⣿⣿⣷⣺⣿⡿⠿⠏⠀⠀⢸⣿⣿⢻⣿⣿⣿⡌⠃⠀⠂⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠋⢿⣿⣿⣿⣿⣷⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⢿⡿⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠃⠀⣿⣿⣿⡏⠉⠉⠉⠉⠀⠀⠀⣰⣶⣾⣿⣿⣿⣿⣿⣯⣽⣿⡟⠉⠁⠀⠀⠀⣽⣿⣿⣿⣿⣿⣆⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀ ⠄⠀⠀⠀⣴⣿⣿⣿⠁⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⡉⢿⠿⠿⣿⠿⠟⠛⠁⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣇⠐⢻⣿⣿⣿⣿⠏⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠀⠀⠀⠀⣀⣀⣀⣀⣲⣿⣿⣿⣿⣿⡃⢀ ⢀⠈⠁⢰⣿⣿⣿⣿⡀⠀⢀⣨⣼⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢩⣿⣿⣿⣿⣿⣿⣿⠀⠘⢻⣿⣿⡿⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠻⠟⠛⠉⠉⣷⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣈ ⣼⣤⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠟⠋⠁⠀⣀⠀⢀⢀⡀⣀⡀⢚⣿⠃⣀⣀⡀⡀⢀⠿⡿⣿⣿⣿⡲⣿⢂⠀⡀⢻⣟⠁⠀⣀⠀⣀⢀⣀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿ ⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⣾⡿⠇⣿⣼⡇⣿⣉⣿⣹⠏⣿⣿⢻⣿⣿⣿⡟⣿⣽⡇⣹⣿⣿⣿⣿⢿⣝⣷⣴⣿⣿⣿⢺⣿⣹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀ ⣠⣿⣿⣿⣗⠘⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆⣿⣿⣿⣿⣿⣿⣼⣦⣿⣿⣾⣿⣿⢻⡇⢿⣽⡇⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢸⣯⣼⡟⣿⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣀⣸⡟⢻⣿⣿⣿⢁⠀⠀⠀ ⣿⣻⣿⠙⢻⣶⣿⣿⣿⣷⠀⢀⣀⠀⣀⠀⣀⣀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⢈⣁⠀⣀⡀⣀⣀⠀⠀⢀⣰⣤⣀⡀⢀⣻⣿⣿⣿⣿⣿⣿⣦⣄⣀⢒⡀⣀⢈⡹⢿⣿⣷⣄⣀⠀⠀⠀⠇⠈⠁⠀⠀⠉⠿⡿⣿⣆⠀⠀ ⣿⣿⠋⠀⠀⣧⠟⠛⢿⣿⣄⣿⣏⣾⣿⡇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣧⣿⢸⣧⣿⣻⣿⣿⣿⡀⠀⠀⢸⡀⠀⠃⠀⢀⣀⡀⠀⠉⠄⠀ ⣿⠏⠀⠀⠛⠀⠀⠀⠀⠈⠻⣿⡇⢿⣿⡇⣿⣾⡿⠻⣿⣿⢿⡿⣿⣿⣿⡿⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢻⡟⢸⡏⣿⢹⡟⣿⣿⣿⣿⣿⣿⠀⠀⢸⣷⠶⠾⠶⠿⣿⣛⣿⣷⣂⠀ ⠑⠷⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⢈⠉⠋⠑⢠⣤⠀⠀⡶⠀⣦⠀⣾⠋⢁⢩⣿⣿⠀⠀⠀⢹⣗⠀⠀⠛⠻⣿⣿⣿⣿⡂ ⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⠩⠫⠃⠁⠉⠙⠛⠉⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⢿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣀⣤⣄⣠⡄⠀⠁⠀⡀⣀⣀⠀⠉⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⣾⡏⠀⠀⠀⠀⠀⠀⠊⢉⣭⠏⠉⠀⠀⣠⠚⠀⠉⠉⠀⠀⠀⠀⠀⠈⠹⢦⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣜⢻⡞⠻⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣶⣼⣿⣿⡿⠀⠀⠉⡹⡟⠀⠀⠀⠀⠀⣀⣨⣾⣷⣷⣦⣷⡐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠋⠉⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⡶⡦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣽⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠁⡅⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡜⣄⠀⠀⢀⣀⡠⠄⠀⠂⠀⠀⠀⠀⠀⣀⢠⠶ ⠀⠀⠆⠀⢠⣀⣀⣾⣿⣿⣿⣦⣤⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⠀⠀⠀⠀⠀⠀⣷⣄⠀⢠⣿⣿⣿⡇⠉⠛⣿⣿⣾⣿⣿⣿⡝⢿⡄⠁⠀⠀⠀⠀⢀⡠⠄⠐⠊⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣮⣿⣿⣷⣾⣿⠿⠿⠛⠀⠀⢸⣿⣿⢻⣿⣿⣷⡌⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣷⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠸⣿⠿⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠘⠛⠁⠀⣿⣿⣿⠁⠈⠉⠉⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣟⣿⣿⣿⠟⠋⠀⠀⣨⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠐⠂⠀⠀⣤⣤⣴⣾⣿⣿⣗⠀ ⠈⠛⠆⠀⣰⣿⣿⡿⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⠟⣿⣿⣿⡇⠀⠀⠀⠀⢠⣤⣤⣿⢿⠿⣤⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⢀⠘⠀⣰⣿⣿⣿⣿⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣇⠀⠿⢿⣿⣿⡏⠀⠈⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡ ⣾⣤⣶⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⡿⠿⠛⠁⣀⠀⢀⢀⡀⣀⡀⢛⣿⠃⣀⢀⡀⣀⢀⠿⡿⣿⣿⢿⡿⣷⢀⠀⣘⢿⣟⠀⠀⣀⠀⣀⢀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡃⢹⣿ ⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⣾⡿⠇⣿⣼⡇⣿⣋⣿⣿⣗⣿⣾⢻⣿⣿⣿⡟⣿⣿⡏⣿⣿⣿⣿⣿⢿⣝⣷⣦⣿⣿⣿⣿⣟⣹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠙⠻⠿⣿⣿⣿⡇⠀⠀ ⣠⣿⣿⣿⡇⢹⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣿⣿⣿⣿⣿⣿⣼⣾⣿⣿⣾⣿⣿⢻⡇⣿⣽⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣯⣽⡟⣿⢻⣿⣧⡀⠀⠀⠀⠀⠀⢀⣀⣀⣼⠀⢀⣤⣄⣀⡀⠀⠀⠀ ⣿⣿⡏⠘⣿⣼⣿⣿⣿⡄⠀⣀⣀⠀⣀⠀⣀⣀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⢌⣀⠀⣀⡀⣀⣀⠀⠀⢀⣾⢇⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⢒⡀⣀⢈⡻⣿⣿⣆⡀⣀⠀⠀⠈⡆⠘⠂⠀⠈⠹⢿⣿⣷⣄⠀⠀ ⣿⠟⠁⠀⣹⣙⣿⠿⣿⣧⡀⣿⣏⣾⣿⡇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣧⣿⢸⣷⣿⣿⣿⣿⣿⠀⠀⠀⣧⠀⠀⡄⠀⣀⣀⠀⠈⠁⠄⠀ ⡏⠀⠀⠘⠿⠋⠀⠀⠈⠙⢿⣿⠇⢿⣿⡇⣿⣿⡿⠹⣿⣿⢿⡿⣿⣿⣿⡿⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⢹⡇⢸⡏⣿⢸⡟⣿⣿⣿⣿⣿⣦⡀⠀⢹⣷⠶⠷⠾⠿⣟⣻⣿⣖⡀⠀ ⠀⠶⠶⣶⠏⢶⠄⠰⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⡌⠛⠉⠛⢠⣤⠀⠐⡦⠀⣆⠀⢀⣾⣿⣿⣿⣿⡇⠀⠈⣿⡂⠀⠁⠛⢿⣿⣿⣿⣿⠀ ⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠅⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠩⠛⠉⠋⠈⠀⠉⠛⠋⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣠⣤⣄⣤⡄⠀⠁⠀⠀⣀⣀⠈⠉⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠐⢶⣾⡏⠀⠀⠀⠀⠀⠀⠋⢩⣭⠏⠁⠀⠀⣀⠘⠁⠙⠛⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣄⡀⠀⠀⠀⢸⣿⣿⡿⠟⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠛⣿⠛⠻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⣤⣤⣿⣿⠿⠁⠀⠀⠠⠹⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣶⣾⣇⡒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠛⠁⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣳⣄⠀⠀⢀⣀⣤⠄⠀⠂⠀⠀⠀⠀⠀⡀⣤⠴ ⠀⠐⠀⠀⣤⣀⣠⣿⣿⣿⣿⣿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣟⣧⠁⠀⠀⠀⠀⠀⣼⣶⡀⠀⣼⣿⣿⣿⡉⠙⠿⣿⣿⣽⣿⣿⣷⠻⣝⠋⠉⠁⠀⠀⠀⣀⣀⠀⠒⠊⠉⠀⠀⢀ ⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⣿⣿⡿⣿⣿⣿⣷⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⠉⢣⣿⣿⣿⣿⣿⡧⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠻⠿⠗⢿⣿⣿⣻⠗⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣦ ⠀⠙⠋⠀⠀⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⠀⡘⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⡆⠀⠀⠀⠐⠶⠾⡾⠋⠉⢹⠖⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠉⠀⢠⣼⣿⣿⣿⣇⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣿⣿⣿⣿⣧⠀⢹⠻⣿⣿⣿⠃⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⣶⣦⣴⣾⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⠿⠛⣁⠀⢀⢀⡀⣀⡀⢛⣟⠃⣤⢀⡀⣀⢀⠿⡿⣿⣿⢿⡿⣀⢀⠀⣽⢟⣇⠀⠀⣀⠀⣀⢀⣀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⡿⠿⠿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⣾⡿⠇⣿⣼⡇⣿⣏⣿⣻⣿⣿⣾⢻⣿⣿⣿⡟⣿⣽⡏⣿⣿⣿⣿⣿⢿⣝⣷⣆⣿⣿⣿⢹⣟⣹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠈⠠⡄⠀⠁⠀⠀⠀⠈ ⣴⣿⣿⢿⣿⠘⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⢿⣷⣶⣿⣿⣿⣿⣿⣿⣴⣿⣿⢿⣾⣿⣿⢻⡇⣿⣽⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣯⣽⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⡶⠀⣀⣤⣀⣀⠀⠀⠀⠀ ⣟⣿⠟⠀⣿⣦⣿⣿⣿⣇⠀⢀⣀⠀⣀⠀⣀⣀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⣀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡄⣀⣐⢒⡀⣀⢻⣿⣿⣦⡀⡀⣀⠀⠀⢨⠀⠙⠀⠀⠈⠹⣿⣿⣧⡀⠀⠀ ⡿⠋⠀⠀⠐⡕⢾⣿⣿⣿⡄⣿⣏⣾⣿⡇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡏⢹⣧⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⡆⠀⠰⠀⠀⣀⠀⠀⠈⠡⠀⠀ ⠁⠀⠀⠀⣹⠓⠋⠀⠉⠻⢷⣿⡇⢿⣿⡇⣿⣿⡯⠹⣿⣾⢿⡿⣿⣿⣿⡟⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣷⠉⢹⡇⢸⡏⣿⢿⡟⣿⣿⣿⣿⣿⠀⠀⠈⣿⡶⢶⠷⠾⢿⣟⣻⣿⣆⡀⠀ ⠀⠶⠶⣿⠟⢷⠄⠰⠶⠶⠾⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠻⠃⠀⢀⣤⠀⢱⡆⢀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠹⣗⠀⠀⠘⠻⢿⣿⣿⣿⣇⠀ ⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠽⠓⠀⠀⠀⠀⠀⠀ ⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠙⠿⠛⠛⠓⠁⠉⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠾⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠄⠈⠁⠀⠀⣀⢀⠈⠁⠀⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠰⢷⣿⡍⠀⠀⠀⠀⠀⠀⠉⢭⡽⠉⠁⠀⠀⡀⠜⠁⠙⠛⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⠀⠀⠀⠀⣾⣿⣿⠟⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⠈⠻⡟⠛⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣶⣤⣄⣿⡿⠋⠀⠀⠀⠐⠙⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣦⣿⣖⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠛⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣧⡀⠀⠀⢀⣀⣤⠄⠐⠂⠀⠀⠀⠀⠀⡀⣥⠶ ⠀⠐⠀⠀⣤⣀⣴⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣅⡷⠀⠀⠀⠀⠀⣀⣿⣦⡀⢀⣿⣿⣿⣧⠉⠹⢿⣿⣯⣿⣿⣿⣯⠳⡀⠉⠉⠁⠀⠀⠀⣀⡀⠀⠒⠊⢉⣀⡀⠀ ⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣰⣿⣿⣿⣿⣾⣿⠟⠛⠋⠀⠀⢸⣿⣿⣽⣿⣿⣿⣆⠙⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⣴⣿⣿⣷⣤ ⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣑⣿⣿⣿⣿⣿⣧⠀⣲⣤⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠰⢿⠿⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⠃⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣹⢽⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⡿⣿⠿⠿⠟⠻⠙⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⡟⠈⢿⣿⡇⠀⠀⠀⠀⢶⡶⠾⠟⠛⠻⣶⠀⠀⠀⠀⣠⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠃⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡇⠀⠞⠸⣿⣿⡟⠁⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣦⡄⣤⣶⣿⣿⣿⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⠿⠟⣁⠀⢀⢀⡀⣀⡀⢛⣟⢣⣷⢀⡀⣀⢘⠿⡿⣿⣿⣿⡧⣀⢀⡀⡛⢋⣂⠀⠀⣀⠀⣀⢀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠉⠛⣿⣧ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⣾⡿⠇⣿⣼⡇⣿⣯⣿⡽⣿⣿⣾⢻⣿⣿⣿⡏⣿⣹⡟⣿⣿⣿⣿⣿⢿⣝⣧⣄⣿⣿⣿⢿⣟⣹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⠠⡀⠀⠁⠀⠀⠈⠉ ⣾⣿⣿⡿⢿⡏⠹⣿⣽⣿⠿⠛⠁⠀⠀⠀⠀⠀⢿⣷⣶⣿⣿⣷⣿⣷⣿⣴⡿⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢹⣯⣽⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡆⠀⣠⣄⣀⡀⠀⠀⠀⠀ ⣿⣿⠏⠀⠀⣷⣴⣿⣿⣿⡄⢀⣀⠀⣀⠀⣀⣀⠀⣴⣿⣿⣿⣿⣿⣿⣦⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⣀⠀⣠⣶⣶⣿⣻⣿⣿⣿⣿⣷⡀⣀⣐⢂⡀⣘⢿⣿⣷⣄⠀⡀⣀⠀⠀⣜⠀⠛⠀⠀⠈⠿⣿⣿⣦⠀⠀⠀ ⡿⠃⠀⠀⢀⡓⠤⢾⢿⣿⣿⣿⣏⣾⣿⡇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣹⡏⢹⣧⣿⢹⣿⣿⣿⣾⣿⣿⠀⠀⢿⠀⠀⢀⠀⢀⣀⠀⠀⠉⡄⠀⠀ ⠀⠀⠀⠀⠀⣱⠔⠁⠀⠈⠻⣿⣇⢿⣿⡇⣿⣾⡏⠻⣿⣿⢿⡷⣿⣿⣿⣿⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢻⡇⢸⡏⣿⢸⡟⣿⣿⣿⣿⣿⠀⠀⠸⣷⠶⢾⠷⠿⢿⣛⣿⣷⣂⠀⠀ ⠀⠖⠶⣾⠿⢷⠄⠰⠶⠶⠖⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠻⠛⠿⠫⠛⠀⢀⣤⠀⢲⡄⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⢻⡆⠀⠈⠘⠻⢿⣿⣿⣿⡃⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠊⠀⠀⠀⠀⠀⠀ ⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠙⠛⠛⠋⠉⠁⠻⠛⠛⠛⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠽⠿⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋ ⠙⠿⣿⣿⣿⠀⠀⠀⠀⠀⢠⠶⠒⣶⣶⣶⠀⠈⠁⠀⠀⣀⢀⠉⠉⠃⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠘⢶⣿⠁⠀⠀⠀⠀⠀⠀⠀⢩⡬⠁⠀⠀⠀⢀⠐⠁⠙⠛⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠛⠿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⠀⠀⠀⠀⣻⡿⠟⠀⠀⠀⠏⠿⠀⠀⠀⠀⠀⠀⠸⢿⡟⠻⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣦⣤⡿⡃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⣤⣾⣿⣷⣾⣷⡖⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠞⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡽⣤⠀⠀⠀⠀⣠⣤⠄⠐⠀⠀⠀⠀⠀⠀⢀⣥⠶ ⠀⠂⠀⢀⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣷⣤⢰⣿⣿⣿⡇⠉⠛⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠖⣺⣿⣷⣆⡀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣴⣿⣿⣿⣿⣿⣿⠝⣿⣿⣿⣿⣿⣿⡇⠀⣴⣦⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠀⢻⣿⣯⣿⣿⣿⡃⠀⠀⠀⠤⠰⠒⢃⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠘⠟⠋⢽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿ ⠈⠻⠃⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⢿⣿⣿⣿⣿⣿⣧⢈⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⡀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⢽⣿⣿⣿⣿⡉⢘⣿⣿⣿⣿⣿⠀⠀⠈⢿⠿⠀⠀⠀⠀⠀⠛⠛⠉⠀⣼⣭⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣗⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⢺⣿⣿⡿⣿⢃⠈⢟⣿⣯⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠁ ⣦⣀⣶⣾⡀⢸⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣾⠿⠛⣉⠁⢀⢀⡀⣀⡀⢛⣟⣸⣏⢀⡀⣀⢺⠿⡿⢿⣿⣷⡤⣰⢝⡽⡛⢁⣀⠀⠀⣀⠀⣀⢀⣰⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠙⠛⠙⢻⣿⣄ ⢿⣿⣿⣿⠟⠸⣿⡿⢻⣿⣿⣿⣿⣿⡿⠋⠁⠀⣾⡿⠇⣿⣼⡇⣿⣏⣿⣿⣿⣿⣾⢻⣿⣿⣿⡇⣿⢹⣯⣿⣿⣿⣿⣿⢿⣽⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠀⠀⢤⠀⠈⠀⠀⠀⠉⠉ ⣾⣿⣿⠏⠀⠀⠙⣷⣸⣿⣿⣿⡟⠋⠀⠀⠀⠀⢿⣷⣶⣿⣿⣷⣿⣷⣿⣼⡏⣿⢿⣾⣿⣿⢻⡇⢿⣽⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢸⣯⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡆⢀⣠⣀⣀⡀⠀⠀⠀⠀ ⣿⣿⠇⠀⠀⠀⢀⡛⢻⣿⣿⣿⣧⠀⣀⠀⣀⣀⠀⢠⣿⣿⣿⣿⣿⣷⣦⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣀⣀⢀⡈⣻⣿⣿⣷⡄⠀⣀⣀⠀⢸⣵⠈⠳⠀⠀⠙⢿⣿⣿⣄⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠘⣽⣿⣿⡿⣿⣿⣾⣿⡇⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⢹⡏⢹⣧⣿⢿⣿⣿⣿⣾⣿⣿⠀⠐⣗⠀⠀⢇⠀⢀⣀⠀⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡿⠈⠁⠀⣿⡟⢿⣿⡇⣿⢹⡏⠹⣿⣿⢾⣷⣿⣿⣿⣿⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠙⠉⣿⣿⣿⣿⣿⣿⣥⠉⢻⡇⢸⡏⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⢻⣷⠶⡾⠶⠿⣿⣻⣿⣷⡀⠀⠀ ⠀⠖⠶⣶⠿⢿⠗⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠉⠛⠈⢀⣠⡀⠀⢶⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⠀⠈⢿⡂⠀⠈⠛⠿⣿⣿⣿⣿⡀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠩⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠛⠿⠿⠛⠋⠉⠙⠿⠿⠿⠿⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠿⣿⣿⠇⠀⠀⠀⠀⠀⠜⠋⣩⣤⣷⡾⠄⠀⠉⠀⠀⢀⣀⡈⠉⠙⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠛⢿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠈⢿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⢀⡐⠋⠘⠛⠋⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢘⣿⡿⠃⠀⠀⠘⠹⠁⠀⠀⠀⢴⣤⡀⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣤⣄⣤⣄⣸⣿⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⠻⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣶⣿⣦⡒⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠚⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⡟⢀⣤⣦⣶⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣷⣤⠀⢀⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣿⠀⠀⠀⠀⣀⣤⡤⠀⠐⠀⠀⠀⠀⢠⣤⣤⡴⠶ ⠀⠂⠀⢠⣴⣿⣿⣿⣧⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠀⣤⣶⣼⣿⣿⣿⣿⣧⣾⣿⠿⣿⠇⠈⠹⣿⣷⣿⣿⣿⣿⣿⣷⣼⡏⠉⠀⠀⢀⣀⣀⠀⠰⣶⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⡿⢋⢽⣿⣿⢳⠉⠂⠒⠋⠻⠉⠁⠐⠛⢿⣿⣿⣿⣿⣿ ⠀⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡄⠀⠀⠀⠀⠛⠛⢋⣤⣿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⠙⠛⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⣾⣿⣿⣿⠛⠻⠛⠉⠉⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠀⠀⢽⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢠⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⡆⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠛⢻⣿⣿⣿⣿ ⠙⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢸⡿⠀⠀⠐⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠈⠉⠘⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠣⡜⢿⣿⣿⡿ ⣦⣀⣶⣿⡀⠀⠂⠀⠀⠻⢟⡿⣿⣿⣿⣿⣿⡿⠋⣁⠀⢀⢀⡀⣀⡈⢻⣛⣿⣧⢀⡀⣀⢉⠁⣩⣿⣿⣯⣾⣿⢿⡟⡀⢀⣀⠀⠀⣀⠀⣨⣿⣿⣦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⠘⢿⣷⡀ ⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⡟⠛⠀⣾⡿⠇⣿⣼⡇⣿⣯⣿⣻⠏⣿⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣧⣥⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⣄⠁⠈⠀⠀⠀⠉⠁ ⣾⣿⣿⠏⠀⠀⠀⠀⠀⣀⣄⣵⣿⣿⣿⡄⠀⠀⢿⣷⣦⣿⣿⣿⣿⣷⢿⣽⡆⣿⢿⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⣄⡄⣀⣼⠦⢠⣤⣤⣄⠀⠀⠀⠀⠀ ⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⡧⣀⣀⠀⠀⣾⣿⣿⣿⣿⣷⠂⡀⢀⣀⠀⣀⡀⣀⣀⠛⠛⢿⣿⢿⣃⡀⢻⣿⣿⣿⣿⣿⣿⣯⠀⣀⣀⢀⡻⣿⣿⣿⢀⡀⠀⡀⣀⠀⢳⣇⠘⢃⠀⠀⠹⢿⢿⣷⡄⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠠⢭⡿⣿⣏⣿⣿⣿⣿⣿⠇⣰⣿⣿⣿⣿⣧⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣧⢹⡏⢹⣷⣿⣿⣿⣿⣿⣾⣿⣿⠀⢸⣇⠀⠀⡆⢀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⠇⢿⣿⡏⣿⢹⡇⠸⣿⣾⢿⡷⣿⣿⣿⡿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡿⣿⣿⣿⣿⣥⠉⢺⡇⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⡿⠾⠿⠿⣿⣟⣻⣿⣯⡁⠉⠉ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⠃⢠⣴⡆⠀⡦⠀⠸⡟⡿⠿⣿⡇⠀⠀⠀⠀⠘⣷⢀⠀⠈⠛⠻⣿⣿⣿⣏⠀⠀ ⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⠀⠀⠀⠀⣀⠀⠀⠈⠻⠛⢝⣿⠿⠟⣿⣙⣙⠻⠿⠿⠿⠿⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢀⣀⠄⢀⠀⠀⠀⠹⣿⡿⠿⠿⣿⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢴⣾⠆⠀⠈⠀⠀⠀⣀⡈⠉⠓⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠈⢙⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⣽⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠁⠀⠀⢀⡤⠋⠀⠛⠋⠀⠀⠀⠀⠘⠳⣄⣀⣀⣀⣀⣀⣹⡗⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠚⢻⡟⠛⠻⡏⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠦⠀ ⠀⠀⠀⠀⢀⣶⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣷⣤⡀⠀⠀⣀⣤⣴⣾⣿⣿⣶⣷⣴⣿⣿⡻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣽⣷⣆⡀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣅⡀⢠⣶⣶⣶⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣶⣿⣾⣿⣿⣿⣿⣷⣄⣰⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⡀⣀⣀⡴⠆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷ ⠐⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠁⠈⠛⠛⠋⠁⢸⣿⣿⣯⣳⣎⣿⣯⠁⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡎⠿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⢀⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣠⣿⣿⡿⠿⠿⠿⠫⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⠃⠀⠀⠀⢰⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢸⠁⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠛⠁⢀⣴⡀⠀⠀⠀⠀⢿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⡛⠂⡀⠀⠈⢻⣿⣿ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⣠⣿⡆⠀⠐⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⣸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠐⠀⠀⠱⠎⢣⠺⣆⣠⡀⠉ ⣶⣰⣾⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠛⣁⠀⢀⢀⡀⣀⡘⣹⣯⡇⣀⢀⡀⡀⢿⣿⣿⣿⣿⣿⠿⣛⢃⠀⡀⢀⣀⠀⠀⣀⠘⣿⣿⣿⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⠠⠀⡀⠐⠉⢿⣧⠀ ⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣏⣾⡿⠇⣿⣼⡷⣿⣯⣿⡿⠇⣿⣾⢻⣿⣿⣿⡟⣿⢻⡇⠀⣿⣿⣿⣿⢿⣿⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠰⡄⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢿⣷⡆⣿⣿⣿⣿⣧⢿⣵⡆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣤⣲⠤⣤⢿⠦⣤⣦⣤⣄⠀⠀⠀⠀⠰ ⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠋⣉⣻⡇⠀⢀⣿⣿⣿⡟⣟⠀⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢀⣾⣿⣿⣿⣿⣿⣦⠀⣀⣀⢀⣿⣿⣿⣆⢀⡀⠀⣀⣈⢻⣾⡄⠙⢃⠄⠀⠛⠿⠿⣷⠄⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⡇⣿⣿⠇⢰⣿⣿⣿⣿⣧⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣇⢹⡏⢹⣿⣿⣿⣿⣿⣻⣾⣿⣿⠸⣿⣀⠀⢙⣤⢠⣤⣤⣤⣀⣀⢀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢹⡇⠸⣿⣿⢾⡷⣿⣿⢿⡿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⣿⣿⣥⠉⢸⡇⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡽⣿⠛⠛⠛⢛⣿⣭⣿⣿⣤⡀⠀⠀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠴⢶⡆⠀⠀⠀⠰⣶⣾⢛⢷⠀⠀⠀⠀⠀⢹⣇⡄⠀⠈⠙⣿⣿⣿⣿⣅⠀⠀ ⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠟⠛⠿⣿⣿⣋⠛⠻⢛⠟⠻⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡠⣠⠤⠠⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣼⠃⠀⠈⠁⠀⠀⠀⠉⠉⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠸⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⣠⠜⠁⠙⠿⠃⠀⠀⠀⠙⣳⣤⣤⣤⣤⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⢠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠙⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣧⣤⡀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠻⢿⢃⣾⣿⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡴⠆⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣷⠂⢠⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣴⣶⣿⣿⣿⣿⣷⣄⠀⢀⣤⣶⣶⣿⣿⣷⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿⣿⡿⢿⠿⠛⠉⠀⢻⣿⣿⣿⠦⣤⣀⣠⡤⠶⠆⠀⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿ ⠂⠀⠀⠛⠟⠋⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣷⣼⡟⢧⡀⣀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢺⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠙⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡯⠉⠙⠁⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠠⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠽⣿⡗⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⠀⠀⠀⢀⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠊⢠⣾⣿⣆⠀⠀⠀⠸⣿⠿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠆⠀⢒⠀⢀⡀⣀⠀⢈⠉⠉ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠃⠀⡈⠷⠚⡯⢺⣆⣌⠀⠀ ⣾⣶⣾⣧⣼⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣏⠀⢀⢀⡀⣀⡙⣽⣭⠃⣀⢀⡀⡈⢉⠉⡉⢙⣁⠈⠉⡀⢀⡀⣀⢀⣀⠀⡀⣀⠘⣻⢿⣿⣿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠙⠠⠚⠀⠙⠹⠿⠦⠀ ⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠇⣿⣼⡇⣿⣏⣿⠹⠇⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⢿⣷⡆⣿⣿⣿⣿⣧⢿⣴⡆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣤⣄⢾⠧⣴⠟⠢⣶⣶⣶⣄⠀⠀⠀⠀⠐ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢻⣿⠋⣁⣀⠀⠙⢃⣰⣿⣿⡟⣇⠀⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢀⣸⣿⣿⣿⣿⣿⣦⠀⣀⣀⣿⣿⣿⣿⣧⢀⡀⠀⣀⣹⣿⣾⠄⠙⡀⠀⠀⠻⠛⠻⠷⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⡇⣿⣽⡇⢰⣿⣿⣿⣿⣧⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡿⣿⣿⣿⣿⣿⣆⢹⡟⢿⣿⣿⣿⣷⣿⣻⣾⣿⣿⣿⣧⣀⣀⣱⣄⣤⣤⣤⣤⣄⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢻⡇⠸⣿⣿⢾⡷⣿⣿⢿⣿⢿⣴⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⣿⣿⣥⠉⢸⡇⢸⡿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣟⠛⠛⠛⣫⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠂⢢⠶⠶⠆⠀⠀⢀⣺⣿⣟⠛⠄⠀⠀⠀⠀⢸⣿⡤⠄⠀⠀⢙⣿⣿⣿⣷⡄⠀⠀ ⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀ ⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠩⠛⠐⠓⠻⠿⢿⣿⣿⣯⢟⡿⠟⠛⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢰⠃⠀⠀⠉⠋⠉⠉⠙⠛⠒⠶⢦⡀⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⢹⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⣀⠊⠀⠿⠏⠀⠀⠀⢙⣶⣶⣶⣿⣶⣶⣿⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀⣰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠛⠀⡀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣌⣀⠀⠀⢀⡔⠃⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀⢀⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⣿⢣⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣴⣦⣀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣗⣠⣾⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢠⣴⣶⣶⣿⣿⣾⣿⠿⠿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣠⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⡿⠿⠿⠛⠋⠀⢀⣾⣿⣷⣾⢶⣄⣀⣤⡴⠶⠀⠈⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠛⠉⠀⢙⢻⣿⣿⣿⣿⣿⣿⣿⡟⠉⠿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣯⣽⣦⣿⡿⠧⠠⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠿⠿⠿⠃⠀⠀⠀⠙⠹⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡉⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⠟⠛⣠⡄⠀⠀⠀⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠃⠀⠀⣰⡦⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠾⣿⣿⣷⡀⠀⠈⣿⣿⠿⢿⣿⣿⠆⠀⠀⠀⠀⠰⠆⠀⣀⠀⣀⣀⡀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠀⠀⠀⠀⢸⠀⠀⠀⠙⠛⠛⠟⠻⠿⠿⠟⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠁⢀⡉⠷⢙⡛⣶⣠⡄⠀⠀ ⣿⣶⣿⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣁⢀⡀⣀⡩⢿⣉⠀⣀⢀⡀⡀⢀⠀⡀⢀⣀⠀⠀⣀⢠⣄⣀⢀⣀⠀⠀⣀⠀⣛⢿⣿⣦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⠔⠚⠉⠋⠻⠿⠆⠀ ⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣼⣇⣿⡋⣿⠹⠇⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⣿⣿⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠢⠈⠀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣥⢿⣴⡆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⢀⣤⡀⡼⢧⣼⠟⠰⣶⣶⣦⡄⠀⠀⠀⠀⠐ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠿⣋⣁⠀⠀⢀⣀⣿⣿⡟⢀⠀⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⣀⢀⣀⡀⢀⣘⣿⣿⣿⣿⣿⣄⠀⣀⣿⢻⡿⣿⣇⡀⢀⡀⢀⣐⣿⣿⣿⠀⠙⡄⠀⠘⠛⠛⠻⠦⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⢿⣿⣿⣧⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡯⣿⣿⣿⣿⣿⡆⢹⡯⣹⣿⣿⣿⣧⣿⣻⣾⣿⣿⣿⣄⣄⣈⣣⣦⣬⣤⣤⣤⡀⠀⡠⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣿⡇⣿⢹⡇⠸⣿⣾⢾⡷⣿⣿⢿⣿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⣿⣿⣥⠉⢸⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠛⠛⣽⣿⣾⣿⣷⣆⠀⠀⠀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠶⠾⠀⠀⠠⣽⣿⣿⣮⠋⠀⠀⠀⠀⠈⣿⣇⠤⠄⠀⠈⢹⣿⣿⣿⣷⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠉⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠟⠿⠿⠛⢃⣙⣻⡟⠛⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠄⠀⠀⠀⠛⠒⠒⡎⠉⠅⠤⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⠀⠀⠀⠀⠀⠠⠎⠁⠀⠀⠀⠀⢀⡀⠀⠀⠈⠙⠛⠋⠑⠓⠀⣤⣄⠀⠀⠀⠀⠀⠀⣸⡧⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⣨⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠊⠁⠀⠀⠀⠀⢠⠖⠸⣶⠆⠰⠼⣷⣶⣿⣿⣿⣿⣯⠁⠀⠀⠀⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀ ⠀⠈⠃⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢿⡿⠿⢿⡿⠀⢀⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣠⣤⣤⣴⣷⣶⣶⣧⢀⣾⣿⡟⠻⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⣀⣀⣀⣠⣤⡤⠀⠘⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⠤⣤⣤⡀⠘⠉⠛⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⢸⡿⠛⠉⠉⣾⣿⣿⣹⣷⣼⣿⢿⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣼⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠂⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠿⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠃⠀ ⠟⠁⠀⠀⠘⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣷⣦⣤⡄⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⢀⣀⡲⣾⣇⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠈⠙⠃⠀⠙⠤⠙⠀⣦⣠⡀⠀⠀ ⢀⣬⣿⡀⢰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⣘⡻⢋⣀⠀⣀⢀⡀⡀⢀⠀⡀⢀⣀⠀⠀⣀⢀⡀⡀⢀⣀⠀⠀⣀⠀⣀⢿⣿⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠁⠐⠃⠀⠉⠻⠷⠀⠀ ⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⡋⣿⠹⠇⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⢿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠆⠈⠀⠀⠀⠀⠀⠄⠀ ⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⣿⢹⣿⣿⣥⢿⣴⡆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣯⣽⡟⣿⠀⠀⠀⠀⠀⣤⣤⡀⠤⢤⡼⠗⠠⣶⣶⣤⡁⠀⠀⠀⠀⠃ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⡀⠀⠀⢀⡀⢸⣿⡃⢀⠀⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣻⣿⣿⣿⣷⣀⠀⣀⣀⣴⡄⣀⢀⡀⢀⡀⢀⣿⣿⣷⣤⠈⠑⠀⠀⠘⠛⠛⠻⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⠿⢾⣿⣧⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡀⢹⡯⣽⣿⣿⣾⡧⣿⣻⣾⣿⣿⣍⣀⣀⣀⣢⣠⣤⣤⣤⣄⡀⠀⠀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⢿⣿⡇⣿⢹⡇⠘⣿⣾⢾⡗⣿⣿⢹⡿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⡿⣿⣥⠁⢸⡇⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣉⠙⠛⠛⢛⣽⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⢶⠀⠀⠀⢹⣿⣾⣦⠀⠀⠀⠀⠈⣿⣿⠀⠠⠀⠀⠈⢹⣿⣿⣿⣆⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠹⠯⠿⠟⠛⠛⠻⡿⠟⠻⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠐⠸⣿⣿⣿⣿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠁⠉⠁⠀⠀⠀⡾⠉⠀⠀⠀⡀⠀⠆⠀⠀⠈⠙⠻⠿⠛⠶⠤⢄⡀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶⣶⠾⠿⣶⣾⣿⣿⣿⣿⣆⠀⠀⠀⢠⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⣿⠃⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀ ⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡲⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣾⣿⣼⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢿⡿⠿⣿⠇⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⣴⣾⣷⣶⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⠀⠈⠀⠀⢠⣤⣤⣤⣀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣤⣤⣶⣶⣶⣾⣆⢀⣀⢀⣀⣼⣿⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⢿⡿⣿⣿⣿⣿⣿⣶⣼⣿⡟⣿⡿⠇⠀⣀⣤⡤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⣀⣀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠍⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠟⠀⣦⣸⣶⡏⠉⠀⠂⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⡟ 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⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆⣴⣶⡦⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠹⠃⠀⠀⠀ ⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠻⢻⣿⢿⣿⠟⠿⢻⣿⣿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣠⣀⠀⠀⠠⠺⣷⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⢾⣿⠏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢠⡏⠀⠀⠀⠀⠈⠻⢿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣷⣴⣶⣶⣶⣶⣾⡄⣀⡀⢀⣨⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣀⠀⠀⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⢸⣿⣻⣿⣿⠇⠀⠀⠀⠀⠀⠘⠛⠀⠘⠃⠀⠀⠀⠀⢀⣤⠀⠀⠀⣀⣄⠀⠈ ⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣠⣤⣤⣾⣶⣦⣼⡀⢀⠀⠀⠀⣀⡄⠀⠘⠀⠀⣰⣶⣶⣿⣿⣿⣿⣷⣿⡍⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢿⣿⣿⣿⣿⣿⣿⣷⣬⣹⣦⣤⡿⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⣡⣤⠶⠚ ⠀⠀⣀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣤⣀⠀⠀⠙⠻⢿⣿⣇⠀⠀⠀⠀⠠⣿⡋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢸⡇⠀⠀⠀⠀⠈⢻⣿⡿⣿⣿⣿⣿⣿⣇⣀⠀⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣦⣄⡀ ⠀⠀⠈⠉⠛⠓⠒⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣈⣉⣀⠀⠀⠀⢸⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡇⠀⠀⠀⣠⣀⣀⣃⣵⣿⡿⣿⠿⢿⣿⣿⡗⠀⠀⠀⠈⠉⠛⢿⢿⣿⣿⣿⣿⣿⣿⡿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠉⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣾⣿⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠁⠀⠀⠈⠉⠀⠛⠿⠿⠟⠀⢁⣠⠄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀ ⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⠃⠀⠸⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠘⠛⠻⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⠸⡶⢤⣀⡀⠀⠀ ⠟⣻⣿⠁⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀⡀⣀⡠⣿⣿⣿⣿⣿⡆⡀⢀⠀⡀⢀⣀⠀⠀⣀⢀⠀⡀⢀⣀⠀⠀⣪⣿⣿⣿⣀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢃⠠⠰⠓⠉⠻⠷⠄⠀ ⣶⣿⣿⡆⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⣿⣼⡇⣿⡋⣿⠿⡿⣿⣿⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⢿⣽⣃⠀⣿⣿⣿⣿⣿⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠠⠄ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⢹⣧⣿⣥⢿⣴⡆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⢶⣿⣿⣆⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣠⡶⢄⣤⣤⣄⠃⠀⠀⠀⠀⠐ ⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⡀⠀⠀⢀⡀⠀⣾⡿⢀⠀⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣈⣿⣿⣿⣶⣀⠀⣲⣿⣶⡦⣄⢀⡀⢀⡀⢀⣿⣿⣷⣔⡀⠛⡀⠀⠙⢿⡿⢷⣤⠂⠀⠀⠀ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⠿⢶⣿⣧⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡀⢹⣿⣽⣿⣿⣿⣧⣿⣻⣿⣿⣿⠙⠋⠁⠀⢧⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣿⣿⡇⣿⢽⡇⠸⣿⣾⢾⡷⣿⣿⢻⡿⢿⣴⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⣿⣿⣭⠓⢸⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠿⠷⢟⣟⣻⣿⣯⣄⠈⠉⠉ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⣤⣤⠀⠀⠀⢛⣿⣿⣿⣷⡀⠀⠀⢻⣿⣿⠀⢀⡀⠀⠙⠛⣿⣿⣿⣯⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⣄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠇⠀⠀⠀ ⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⡟⠟⢿⣿⣿⣿⡿⠿⢻⣿⡿⠿⠿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⢠⡏⠀⠉⠉⠈⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠛⠋⢉⣹⣦⣀⣠⣤⣶⣶⣾⡍⣀⡀⠀⣸⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⡾⠒⠀⠀ ⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⠀⠀⠀⠀⠀⠘⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣀⠀⠐ ⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢀⣠⣤⣤⣾⣶⣤⣶⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣤⠶⠞⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣷⣌⣷⣠⡄⠀⠀⠀⢀⣤⣄⣠⣴⣾⣧⣦⣶⣄⡀⠄⢈⣠⡴⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⢸⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡇⠀⠙⠃⠘⠙⢿⣿⡿⣿⣿⣿⣿⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠉⠈⢁⠀⢀ ⠀⠀⠈⠛⠛⠶⠤⠤⣿⣿⢿⣿⣿⣿⣿⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣺⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⠃⠀⠀⠀⠀⠀⠈⠉⣩⣻⣿⣿⣧⣀⣼⣧⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠈⠁⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠛⠛⠉⠛⢛⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢐⠦⢴⣶⣿⣿⣿⢿⣿⣿⡿⠟⠛⠋⠈⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠉⠙⠿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢡⣤⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠀⠈⠀⠀⠴⠟⠛⢿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠲⠀⠀⠀⠀⠀⠘⣿⠟⠢⢄⡀⢀⣀⣤⣤⣴⣛⠀⠀⠀⢐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀ ⠻⠿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢶⡞⢿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣀⣀⣠⣷⣴⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣴⠞⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⣿⣿⣧⡙⠂⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠀⠈⠁⠀⠄⢀⣂⣤⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠁⠉⠇⠈⠛⠙⢿⣿⣿⣿⣧⠀⠀⠈⠀⢀⠀⠶⠖⠋⢉⣤⣤⣀⣀⡁⡤⠖⠒⠈⠉⠀⢀ ⠀⠀⠀⠓⠶⠶⠤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠀⠀⠀⠀⠀⠀⠉⠟⠠⣿⡇⠀⠀⡀⢄⣴⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠑⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠙⠛⠏⠽⠻⢿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣼⣦⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣾⣧⣴⣾⣿⣎⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠉⠉⠙⠻⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠱⢻⣿⣿⠟⠙⢿⣿⣿⣿⣇⠈⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠈⠁⠀⠉⠉⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡇⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡉⣿⣟⡛⠀⠀⠀ ⠀⠀⣤⠄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀⡐⣿⣿⣿⣿⣷⣀⢀⡀⡀⢀⠀⡀⢀⣀⠀⠈⣂⢀⠀⡀⢀⣀⠀⠀⣰⣿⣿⣿⣄⣀⡀⢀⠀⠛⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢤⣶⠀⠡⣿⡦⠓⠿⣆⠀ ⣧⣿⣿⣇⣉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⣿⣼⡇⣿⡻⣿⣿⣿⣿⣾⢻⣿⣿⣿⡇⣿⣹⡇⠀⣿⣿⣿⣿⢿⣝⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠉⠂⠀⠀⠀⠀⠀⠠ ⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⢹⡇⣿⣧⢿⣴⡆⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⢶⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⢈⣁⣀⣸⠇⠀⠀⠀⠀ ⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣀⠀⠀⢀⡀⠀⣸⣿⣆⠀⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⣀⢀⣀⡀⢀⣀⣀⣿⣿⣿⣦⡀⠀⣐⣴⣿⡿⣦⢀⡀⢀⡀⢀⣸⣿⣿⣄⠍⠹⣏⠀⠙⢿⣿⣷⣤⡐⡀⠀⠀ ⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⠿⢶⣿⣯⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⢀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡄⢹⣯⣽⣿⣿⣿⣷⣿⣻⣿⣿⣿⠟⠿⠟⠀⠸⡀⠀⠀⠈⠉⠉⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣿⣿⡇⣿⢹⡇⠘⣿⣾⢾⡿⣿⣿⢻⣿⢿⣴⡇⣿⣥⣿⣿⡇⠘⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⣿⣿⣽⢷⣸⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⣤⣤⣶⣷⣿⠿⢷⣶⡖⠒⠒⠒ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠀⢀⡀⠀⠀⠻⣿⣿⣿⣿⡄⠀⠀⠹⣿⣷⡴⠠⠀⠀⠀⠶⣿⣿⣿⣿⡷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠓⠀⠀⠀⠀ ⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⢀⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠿⢿⢿⣿⠿⠿⠟⣿⣿⢿⠿⡿⠿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣰⣿⡏⠉⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠀⠀⢀⣼⣿⡉⢻⣿⣿⠿⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠁⠀⠀⠀⠀⢰⠇⠀⠈⢲⣿⡏⠀⠀⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠐⣆⣠⣶⣾⣿⣿⣷⣤⣤⣤⣤⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠛⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣀⣅⣤⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣶⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⡿⠿⠿⣿⣿⡿⠇⠐⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠈⠉⠀⢀⠀⢀⣠⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠑⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⠞⠛⠁⠀⠀⠀⠀⣀⡤⠔⠂⠉⠉⠀ ⠀⠀⠀⠰⠦⣤⣄⣀⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡟⠁⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠈⠛⠀⠀⠀⠀⣿⡀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⣀⢠⡤⠀⠐⠉⠁⠀⠀⠀⠀⠀⠘⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠿⠛⠛⠛⠉⠛⠿⢿⣿⣿⣷⣶⣦⣤⣤⣀⣰⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠁⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣠⣴⣶⡝⣶⠖⠒⠉⠉⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣾⠄⠀⠀⣾⣿⣿⡙⠓⢸⣦⣤⣤⣤⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⠀⠉⠀⠟⠉⠉⠙⠻⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⢶⣿⠿⠿⢿⠷⠀⠀⢸⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢉⠉⠙⣋⣀⣀⣀⠀⣀⢂⡀⡀⢀⠀⡀⢀⣶⠈⠖⣲⢀⠀⡀⠀⣀⠀⠀⣀⣾⣦⣀⣀⠀⡀⢀⠸⣿⣿⣿⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠑⣶⡀ ⣶⣰⣾⣇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⣿⣼⡇⣿⡉⣿⠹⠇⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⢿⣝⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠇⠀⠀⠀ ⣿⣿⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⢹⡇⣿⣧⢿⣴⡆⣿⢿⣾⣿⣿⢹⡇⢿⣽⡇⠀⣿⣿⣿⣿⢶⣽⡇⠀⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⠀⣀⠲⠀⠀⠀⠀ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⡀⠀⠀⢀⡀⠀⣀⣾⣇⠀⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣀⣘⣿⣿⣦⡀⠀⣸⣿⢿⡿⣀⢀⡀⢀⡀⠀⣀⣶⣶⣄⢀⠐⢾⠋⠀⠻⣿⣿⣦⡀⠀⠀⠀ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⠿⢶⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡄⢹⡯⢽⣿⣿⣿⡇⣿⣻⣾⣿⣿⣿⢿⡷⠄⠀⠁⠀⠀⠈⠉⠉⠛⠂⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⡇⣿⢸⡇⠘⣿⣶⢺⣗⣿⣿⢹⡿⢿⣴⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⣿⣿⣽⢿⣸⡇⢸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⣬⣄⣰⣶⣶⣶⣤⡀⠠⠤ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠁⠀⢘⣿⣿⣿⣿⣆⠀⠀⠀⠀⢻⣿⣄⡀⠉⠉⠉⢩⣶⣶⣿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠙⠙⠃⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠿⡻⠛⠛⠛⠿⣿⠿⠿⠿⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢀⣾⡿⠛⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠀⠀⠀⢀⣿⣏⠻⢿⣿⣿⠇⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⢨⡍⠉⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢀⣽⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠸⠇⠠⡀⢀⣠⣤⣤⣤⣼⣅⣀⡀⢀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠔⣾⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⣱⣤⣌⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠲⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣿⣷⠿⣿⣿⣆⡉⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠉⠁⠀⠀⠀⢀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠲⣦⠀⠀⠀⢠⡤⠶⠛⠁⠀⠀⠀⠀⢀⡠⠤⠒⠈⠉⠀ ⠀⠀⠀⠢⣤⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠿⠇⢠⣀⡉⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⠃⠊⠀⠀⠀⢀⣠⡤⠀⠐⠈⠁⠀⠀⠀⠀⠀⠐⠂ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠐⠾⠿⠿⠟⠛⠛⠿⢿⣿⣿⣷⣦⣤⣤⣀⡀⢀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣧⠙⡤⠴⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⢿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⣿⣿⣿⡿⠇⠐⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠐⠻⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣤⣶⣶⣿⣄⠀⠀⠀⢻⣿⣿⣧⠀⠀⢀⣀⣀⣠⣤⣴⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠘⠿⠈⠛⠋⠉⠀⠀⠀⠈⣿⣿⣿⡂⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⡃⡀⣀⣀⠀⣀⢀⡀⡀⢀⠀⡀⢀⣀⠀⠀⣀⢀⠀⡀⠀⣀⠀⠀⣀⣴⣄⠀⠀⠀⠀⠀⢻⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠰⢰⠄ ⣤⣠⣴⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⣿⣼⡇⣿⡉⣿⠹⠇⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠘⣿⣿⣿⣿⢿⣝⠃⠀⣿⣿⣿⣿⣿⣹⣿⣿⠘⠿⠿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀ ⣿⣿⣿⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⢹⡇⣿⣧⢿⣴⡆⣿⢿⣾⣿⣿⢹⡇⢿⣽⡇⠀⣿⣿⣿⣿⢶⣽⡇⠀⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⡀⠀⠀⢀⡀⠀⣀⣾⣇⠀⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣁⣀⢷⣶⣆⡀⠀⣙⣿⣿⣿⣿⢀⡀⢀⡀⠀⣀⣤⣤⣄⠀⠀⢶⠋⠀⠺⢿⣿⣧⡀⠀⠀⠀ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣾⣿⡇⣿⣽⠇⢰⣿⠿⢶⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡅⢹⡏⢹⣿⣿⣿⡇⣿⣻⣿⣿⣿⣿⠿⣷⠆⠀⠡⠀⠀⠈⠙⠛⠛⠆⠈⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⡇⣿⢸⡇⠘⣿⣶⢺⣗⣿⣿⣽⡇⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⢿⣿⣿⣽⢷⣸⡇⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⢿⣤⣅⣀⣀⣀⣂⣠⣴⣤⣤⣤⡀⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠁⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⣿⣏⡉⠉⠛⠛⠋⣭⣬⣾⣿⣷⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠟⠃⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⣀⢄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠻⠻⢿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⢿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⣸⣿⡿⢿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⢉⡛⠋⠀⣻⡿⠋⠀⠀⠀⠀⠀⠘⢿⠃⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢉⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠨⣆⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣁⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⡈⡀⢀⣶⣿⣿⣿⣿⣷⣴⣦⣀⣴⣿⣷⣶⣦⡀⠀⠀⠀⠀⠈⣭⣨⣉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠞⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣾⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣤⣤⡶⠈⠛⠛⠛⠂⠈⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠉⠉⠀⠀⠀⢀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣴⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢀⡶⠀⠀⢀⡻⣶⡄⠀⠀⢠⡤⠶⠚⠃⠀⠀⠀⠀⢀⣠⠤⠒⠈⠉⠁ ⠀⠀⠀⠠⣤⣀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠻⡛⠂⠁⠀⠀⢀⣀⣤⠄⠀⠂⠉⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠉⠈⠉⠒⠒⠚⠛⠙⠙⠛⠛⠿⣿⢿⣿⣶⣄⡀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⠀⠀⠀⠄⠀⠀⠀⣼⣿⣿⣿⣧⠙⠄⠤⠖⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠻⢿⣿⣿⣷⣶⣶⡍⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠘⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠻⠿⠃⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣤⣶⣿⣿⡷⡆⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠠⢀⣀⣤⣴⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠛⠉⠛⠃⠀⠀⠀⠀⠈⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢠⣾⣇⡀⣀⣀⠀⣀⢀⠀⡀⢀⠀⠈⠁⡈⠀⠀⡀⢀⠀⡀⠀⣀⠀⠀⢀⢰⣶⡀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣷⡀⠈⠑⠒⠂ ⣤⡄⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣿⣿⡇⣿⡉⣿⣻⠇⣿⣾⢻⣿⣿⣿⡇⣿⢹⡇⠀⣿⣿⣿⣿⢿⣝⠃⠀⣿⣿⣿⣿⣏⣹⣿⣿⠀⢻⣿⠄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⣿⣿⡇⣿⣧⢿⣽⡆⣿⢿⣾⣿⣿⢹⡇⢿⣽⡇⠀⣿⢿⣿⣿⢶⣽⣇⠀⣿⣿⣿⣿⣿⣿⣯⣿⠀⠀⠀⠰⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀ ⣽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠘⣟⡉⠀⠀⢠⡟⠀⣀⣴⣧⠄⡀⢀⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢀⣀⣀⣘⣿⣄⣀⣾⠃⣈⣻⣿⣿⣷⣄⡀⢀⡀⢻⣿⣿⣿⣿⣿⣿⢿⡛⠛⠛⢿⣿⣿⡀⠀⠠⠀ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣾⣿⡇⣿⣹⠇⢰⣿⠿⢶⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⠇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⡆⢹⡏⢹⣿⣿⣿⡇⣿⣻⣿⣿⣿⣿⣿⣿⣄⠀⠑⠀⠀⠀⠋⠛⠛⠦⠀⠈ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⡇⣿⢸⡇⠘⣿⣶⢺⡗⣿⣿⣿⣿⢿⣴⡆⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⣿⣿⣵⢻⣸⡇⣸⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣤⣈⢀⣀⠀⣀⠀⣤⣤⣤⣤⣀⠀⠀ ⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠁⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠻⣿⣏⢉⠉⠛⠛⠛⢛⣭⣭⣿⣿⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠛⠋⠟⠁⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠟⡛⠻⠿⠟⠛⠛⢟⣿⡿⠟⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢠⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⡏⠁⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠙⡛⠓⠄⣙⣻⠟⠁⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣙⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⡼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠑⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⣵⠀⠃⠀⠂⢀⣴⣶⣶⣿⣿⣧⠀⠀⠀⢀⣴⣦⣤⣄⡀⠀⠀⠀⠀⠉⣯⡉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⣾⣿⣿⣿⣿⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣆⢀⣠⣤⣶⣍⠀⠀⠀⢠⡄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠉⠉⠀⠀⠀⣀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠉⠀⠀⡰⣶⡄⠀⠀⢀⣤⠶⠚⠋⠀⠀⠀⠀⢀⣠⠤⠒⠂⠉⠁ ⠀⠀⠀⠠⣤⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⢠⣾⣿⡻⡟⠒⠁⠀⠀⠀⣀⣤⠄⠀⠒⠉⠀⠀⠀⠀⠀⠀⠓ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠂⠈⠁⠀⠈⠙⠻⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⣀⠀⣰⣿⣿⣿⣷⡘⠂⠤⠖⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢰⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢠⣤⣀⡀⣀⣀⡀⣸⢿⡛⣿⢿⡿⡿⣿⣿⣿⣿⣿⢿⠋⡀⠀⣀⠀⠀⣀⠀⣀⢿⣄⠀⡀⢀⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠰⡖⠛ ⣤⣄⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣿⣿⡏⣿⡉⣿⣻⡇⣿⣾⢻⣿⣿⣿⡇⣿⢹⡏⠉⣿⣿⣿⣿⢿⣝⠃⠀⣿⣿⣿⢿⣿⣿⣿⣿⠀⠈⢿⣧⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀ ⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⢻⡇⣿⣷⢿⣽⡇⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⢶⣽⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⡀⠀⠀⠘⢷⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⢀⣈⡟⠂⠀ ⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣼⣿⣿⣿⠿⠿⣿⣏⠀⣠⣾⣷⣄⡀⢀⣀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢀⣀⣨⣻⣿⣷⣄⡀⡀⣠⣾⢟⡻⣿⣿⣄⢀⡀⢘⣿⣷⣤⣾⣿⣿⣿⣿⠃⠀⢶⣶⣾⣍⠀⠀⢠ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡏⣿⣽⠇⢰⣿⡿⢶⣿⣿⣿⣿⣷⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡏⣿⣿⣿⣿⣿⣆⣽⡟⢹⣯⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣯⠀⠉⡂⠀⠀⠉⠛⠛⠿⠦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣿⡇⣿⢸⡇⠘⣿⣾⢺⣷⣿⣿⣿⡿⢿⣴⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⣿⣿⣿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣅⣀⣀⣐⣀⢠⣤⣤⣤⣄⡀⠀ ⠀⠖⠶⣶⠟⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⠀⠉⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠉⢻⣿⡟⠉⠛⠛⠛⢛⣫⣭⣽⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀ ⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣖⠂⠀⢾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⢿⠿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣶⣸⠇⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠘⢣⣄⠀⠀⠀⠁⠈⠈⠏⠛⠁⠀⠀⠉⠋⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠤⡀⡀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠈⢏⠉⠛⠿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣿⡿⠟⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣻⣻⡿⠁⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠣⢤⡀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠶⠿⠿⣿⡧⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠈⣻⡄⠃⠄⠀⠀⢀⣠⣤⣤⣤⣮⠁⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣅⡉⣭⠀⢀⡄⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠟⠋⠀ ⠂⠂⠐⠽⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣶⣦⢀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣼⣿⣿⣶⣤⣀⠀⣀⣠⣴⣬⣻⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠤⠀⠈⠉⠀⡀⠀⢀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠛⣿⣷⣝⣿⣿⣿⣿⣰⣶⣦⠀⠀⠀⣦⠶⠚⠋⠀⠀⠀⠀⠀⣠⠤⠖⠂⠉⠁ ⣤⠄⠀⢠⣤⣀⣀⠀⠀⠀⠀⠻⠛⢿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠿⣿⡄⠐⠻⠟⠻⣿⣿⣿⣿⣿⣿⢿⡞⠁⠀⠀⢀⣀⣦⠤⠀⠒⠉⠀⠀⠀⠀⠀⠀⠨ ⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠂⠀⠀⠀⠁⠉⢻⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣾⡿⠛⠛⣻⣿⣿⣧⠻⡴⠖⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣦⣄⠀⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡸⠿⠛⠁⠀⠸⣿⣿⣿⡟⠂⠑⠂⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣶⠄⠀⠀⠀ ⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⡿⣥⡞⢿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⠏⠀⢠⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣤⡤⣀⡀⣀⣀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⡀⢀⣀⠀⠀⣀⠀⣀⢀⣰⣄⡀⢀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠷⠏ ⣤⣄⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⡇⣿⡉⣿⣿⡇⣿⣿⢻⣿⣿⣿⡟⣿⢿⡟⠛⣿⣿⣿⣿⢿⣝⠃⠀⣿⣿⣿⢹⣿⣻⣿⣿⠀⠀⠸⠿⣀⠀⠀⠀⠀⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⢹⣇⣿⣷⣿⣽⡇⣿⢿⣾⣿⣿⢻⡇⢿⣽⡇⠀⣿⣿⣿⣿⢷⣿⣿⣷⣿⣿⣿⢸⣯⣼⣿⣿⣦⠀⠀⠀⠿⣷⡄⠈⠉⠙⣿⣿⣿⡿⠉⠉⠈⠉⣉⡛⠛⠀ ⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⣿⣿⣿⣿⣿⣿⡀⠀⣴⣾⣿⣄⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⣀⣻⣿⣿⣿⣷⣀⡀⣀⣀⣴⡿⣿⣿⣿⣆⡀⠀⣘⣿⣶⣶⣦⣿⠻⣿⠂⠀⢶⣶⣶⣯⡀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡿⣿⣿⠏⣿⣿⠿⢶⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⡿⣿⣿⣿⣿⣿⣦⣹⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡆⠉⣃⠀⠀⠙⠛⠛⠻⠦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⢿⣿⡇⣿⢹⡇⣿⣿⣾⢾⣿⣿⣿⣿⡿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⠇⣿⣿⣿⣿⣿⠿⣿⡇⢸⡯⣿⣿⣿⣿⣿⣿⣿⣿⠘⢽⣮⣅⣀⣀⣈⣄⢠⣤⣤⣤⣄⡀⡀ ⠀⠶⠶⣶⠯⢷⠴⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠍⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠉⠛⠀⠐⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⡋⠛⠛⠛⢛⣫⣭⣽⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀ ⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠂⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠁⠛⠋⠋⠉⠀⢀⠙⠛⠉⠁⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣝⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠛⠒⠄⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠃⠀⠀⠀⠀⢿⠉⠛⠛⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⠿⣿⠏⠀⠀⠀⠀⠀⢀⣾⣿⣧⣤⣄⡀⠀⠀⠀⠀⠃⢤⡄⢨⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⡇⠀⠀⢸⣇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⠻⠛⠿⠿⣷⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣆⠀⠄⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣉⣹⡄⠀⠀⢈⣷⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡶⠛⠋⠁ ⠀⠂⠀⠀⠜⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠈⢻⣿⣶⣆⠀⢀⣤⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⣶⣤⣤⣀⠀⠀⢀⣠⣤⣾⣼⣿⣿⣿⣶⣹⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⠀⢠⡴⠄⠈⠉⠀⠀⠀⢀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠹⠿⠁⣐⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⢠⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣟⠋⣿⡀⠀⠀⡤⠶⠚⠋⠁⠀⠀⠀⠀⢠⠤⠖⠊⠈⠁ ⣤⠀⠀⠠⢤⣄⣀⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⠿⠇⠛⠛⠿⠋⠈⠛⣿⣿⣿⢫⣿⣷⣟⢿⡍⠀⠀⠀⣀⣠⡤⠀⠐⠉⠁⣠⣤⣄⠀⠀⠈ ⠁⠀⠀⠀⠀⠀⠈⠉⠉⠓⠂⠀⠀⠀⠀⠨⠹⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣶⢓⠉⠉⠸⣿⣿⣿⣿⣯⠹⣖⠓⠉⠉⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣄⡀⢀⢄⢙⣽⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠹⣿⣿⣿⡉⠀⠀⠀⠐⠂⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣾⣿⠁⠸⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠀⠀⢉⣿⡉⠉⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣤⡄⣀⡀⢀⣀⣀⣸⣿⣿⣷⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⢂⣀⠀⠀⣀⠀⣀⢀⣀⡰⣶⣄⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⣤⣤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣿⡉⣿⣿⣏⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠃⠀⣿⣿⣿⢸⣟⣹⣿⣿⣧⡀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠹⣿⣿⣿⣿⣿⡋⠀⣤⠀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⣿⢹⣇⣿⣷⣿⣽⡟⣿⢿⣾⣿⣿⢻⡿⢿⣽⡇⠀⣿⣿⣿⣿⣶⣽⣿⣷⣿⣿⣿⢸⣯⣼⡟⣿⢸⣿⣶⡄⠀⠙⠠⠀⠈⠉⠉⠀⠀⠈⠉⠙⠀⠘⢁⣈⠛⠃ ⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣤⣶⣿⣿⣿⡟⢀⣀⠀⣶⣶⣿⣤⡄⢀⣀⠀⣀⡀⣀⣀⠀⠀⢀⣀⠀⣀⡀⢀⣀⣿⣿⣿⣿⣿⡕⠂⣀⣀⢀⡤⣴⣾⣿⣿⣿⣆⣀⣀⠈⢶⣦⣄⡒⣶⡲⠀⢴⣶⣾⣯⡁⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣿⣿⣿⣷⣿⠿⢶⣿⣿⣿⣿⣿⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⡯⣿⣿⣿⣿⣿⣧⢹⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⡇⠈⣣⠀⠀⠙⠛⠛⠻⠦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⣿⣿⡟⣿⢿⣿⡟⣿⣾⢺⣿⣿⣿⣿⣿⢿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣧⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣯⣀⣀⣀⣇⣀⣤⣤⣤⣄⣀⠀ ⠀⠖⠶⣶⠏⢶⠖⠰⠶⠶⠖⠀⠈⠘⠃⠀⠀⠀⣿⡇⠀⠀⠀⢛⣋⠀⣸⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠙⠛⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⠛⠛⠻⠛⣛⣭⣭⣿⣿⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠑⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀ ⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣟⣤⣔⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠋⠉⠀⢹⣷⣙⠋⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⣻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠻⠛⠂⢀⣸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢈⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⠿⠉⠁⠀⠀⠀⠘⢧⠉⠙⠛⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⡀⢸⠿⢿⡿⠁⠀⠀⠀⠀⣼⣿⣿⣿⣶⣦⣤⠀⠀⠀⠈⠙⣶⡄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⡇⠀⠀⠀⣤⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠛⠻⢿⡿⢿⡧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠘⣿⣿⣆⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣯⣉⣹⡅⠀⠀⢠⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉ ⠐⠂⠀⠠⠤⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣠⠁⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣷⣼⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⡀⢀⣤⠆⠀⠉⠁⠀⡀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠨⠿⣿⠁⠀⣠⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣶⣤⡀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⢿⣿⣧⡀⠀⣤⡴⠖⠛⠁⠀⠀⠀⢠⣿⣿⣷⣶⣃⣉ ⣴⡤⠀⠀⠤⣤⣄⣀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠋⠀⣤⣾⣿⣿⣿⣿⣿⣿⣧⢀⣀⡀⣼⣿⣿⣿⣿⣿⣿⣾⣿⠟⠛⠛⠙⣿⡿⠟⠋⠁⢻⣷⣽⣿⡅⠀⠀⢀⣀⣤⠄⠀⢺⣿⣿⣿⣿⣿⣿⣿ ⠛⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢿⣿⣿⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⠋⡿⡂⠀⠀⠀⠈⠋⠀⠀⠀⢠⣿⣿⣿⣷⠻⣞⠈⠉⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⠀⠀⢀⢠⣿⣿⣿⣿⣷⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣾⣿⠋⢻⣿⣿⡿⠈⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠀⠀⠉⢹⣿⠈⠃⠉⢈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⢀⠀⠸⣿⣿⣿⣿⡿⠿ ⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡀⣈⡁⢀⣀⣀⣀⣿⣿⣤⢀⠀⡨⣿⣿⣿⣿⣿⢿⣿⣿⣇⣀⠀⠀⣀⠀⣀⢀⣀⡘⡻⣷⣄⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣄⠙⠻⢿⡟⠋⠠ ⣤⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣿⡉⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡃⠀⣿⣿⣿⢸⣟⣹⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢀⡀⢤⣾⠁⢀⣀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡟⣿⢻⣇⣿⣷⣿⣽⡏⣿⢿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣷⣿⣿⣿⣿⣸⣯⣼⡟⣿⠀⠙⢿⣷⣦⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⠙⠇⠀⠛⢀⣈⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣼⣿⣿⡟⠁⣀⣀⠀⣶⣾⣿⣷⣤⢀⣴⡿⣂⡀⣀⣀⠈⠻⣿⣿⢿⣀⡀⢀⣀⣿⣿⣿⣿⣿⣟⣛⣶⣀⢀⡀⣲⣶⣶⣾⣿⣿⣷⣀⠀⢸⣶⣤⡐⢶⣖⠄⠠⣶⣶⣿⣟⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⠿⢶⣿⣿⣿⣿⣧⣿⠹⠇⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣷⣹⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⢿⣷⠈⢻⣤⠀⠈⠛⠿⠿⢷⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⡇⠸⣿⣾⢾⣿⣿⣿⣿⣿⣿⣼⡇⣿⣤⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣧⣼⡯⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⣥⣀⡈⢽⣁⣀⣠⣀⣀⣀⠀ ⠀⠶⠶⣶⠿⢶⠦⠰⠶⠶⠖⠀⣺⣿⠋⠀⠀⣾⣿⠀⠀⠀⠀⢿⣟⠁⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠈⠛⠓⡀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⢿⣟⠻⠿⠿⠿⣛⣟⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋⠀⠀⠀⠀⠀⠀ ⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣥⣤⣺⣻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⠉⠨⣿⣿⡚⠉⠉⠈⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣙⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠋⠑⣄⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠘⣤⡈⠉⠛⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠃⠉⠻⣿⣿⠃⠀⠀⠀⢀⣾⣿⣷⣶⣤⣄⡀⠀⠀⠀⠈⢹⣷⡄⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠿⠿⡿⠿⢿⣶⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠸⣿⣿⣆⣈⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣏⣉⣽⠀⠀⠀⣾⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⠶⠟⠋ ⠀⠑⠀⠀⢀⠙⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠙⢻⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣷⣟⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⠀⣠⠴⢠⣾⣧⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠘⠿⣿⠃⠀⠀⢀⣤⣶⣶⣶⣿⡇⠀⠀⠀⠀⢸⣦⣤⣄⣀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢿⣷⣄⠀⢠⡤⠶⠛⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿ ⣀⣀⠀⠀⠠⣤⣤⣀⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⠛⠀⢀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣤⣾⣿⣿⠉⠉⠉⢻⠛⠉⠀⠀⣼⣯⣿⣧⡀⠀⢀⣀⣤⠤⠀⠀⠈⣿⣿⣿⣿⣿⣿ ⠋⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠠⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣤⡤⣾⣿⣿⣿⣿⣿⡿⣿⣿⡿⠃⠀⠀⠀⠈⠀⠀⠀⢰⣿⣿⣿⣎⠳⡋⠉⠁⠉⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣷⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣷⣤⣴⣷⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢵⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿ ⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⡿⠛⠛⠋⢉⣼⡚⠿⠻⢿⠏⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠀⠠⠦⠄ ⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡈⣉⡉⢀⣀⣀⣀⢸⡿⣃⢀⠀⡠⢧⣼⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⣀⠀⣀⢀⣀⡘⣿⣿⣷⣄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠈⢀⣤⡀⠀⠳⡆⠻⣦ ⢤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⡇⣿⡉⣿⣿⣏⣿⣿⣿⣿⣿⣿⣇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣝⡃⠀⣿⣿⣿⢸⣟⣹⣿⣿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣺⡋⠀⣠ ⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡟⣿⢻⣇⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣽⣷⣿⣿⣿⣿⣿⣯⣼⡟⣿⠀⠉⢿⣿⣶⡄⠀⠀⠀⠀⠀⣀⠀⢀⣄⠈⠫⠀⠛⠃⣈⣛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣼⣿⣿⡟⠉⢀⣀⠀⣾⣶⣿⣿⣿⣯⣿⢿⣗⣀⣀⣀⠀⢻⣿⣿⣿⣿⡇⢀⣐⣿⣾⣾⣿⣿⣿⢛⣓⣀⢀⡀⣀⢤⣤⣬⣿⣿⣿⣆⠀⠀⣷⣦⡟⢤⣾⠆⠀⢤⣶⣽⣗⠋⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⠿⢶⣿⣿⣿⣿⣿⣿⢹⡇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣽⡏⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢿⣿⡆⠙⣏⡄⠈⠛⢿⠿⢿⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⡘⣿⣾⢾⣿⣿⣿⣿⣿⣿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡏⣿⣿⣿⣿⣿⣿⣿⡇⣼⡟⣿⣿⡿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢹⣅⡀⠼⡄⢀⣀⣀⣀⣀⠀ ⠀⠖⠶⣶⠿⢷⠖⠰⠶⠶⠖⠀⣸⣿⠋⠀⠀⢸⣿⡆⠀⠀⠀⣿⣿⡃⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠉⠛⠓⢂⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠸⣿⡻⠿⠿⠿⠟⣛⣛⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣵⣤⣭⣿⣧⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠛⠋⢩⣯⣯⠉⡙⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢉⣛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣠⣾⡟⠋⠉⠈⢢⣄⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⢿⣤⡀⠉⠙⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣆⠀⠀⠈⣻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⢀⡹⢿⣿⡟⠀⠀⠀⢠⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣀⢻⢰⣿⠆⠀⠀⠈⠁⠀⠀⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⠄⠀⢠⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⡿⢷⣶⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣟⡛⣏⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⣴⣾⣛ ⠉⠀⠀⠀⠀⡉⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠹⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠏⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣼⣾⡟⠃⠀⠀⠀⠀⠀⠀⢀⠀⢠⡴⢾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡇⠀⠀⠀⠀⣀⣤⣤⣤⡟⠀⠀⠀⠀⢸⣅⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⠋⠑⠀⣤⡀⢠⣤⠶⠚⠋⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⡀⠀⠀⢤⣤⣄⣀⠈⠉⠛⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠍⠀⠀⠀⣶⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⢘⣿⣿⣿⣿⣶⣄⠀⢼⣿⣿⠀⠀⢠⣿⣿⡇⠀⠀⣿⣜⣿⣆⠀⠀⣀⣠⣄⠀⠀⠀⠀⠹⢿⣿⣿⣿ ⠐⠊⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⢹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⠏⠀⠀⠚⠋⠁⠁⠀⠸⣿⣿⣿⡜⢗⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣤⡀⠀⠀⠘⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⠟⣨⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣶⣤⣤⣾⣿⡿⣿⡿⠀⣺⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⢿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠋⠉⠀⠀⠀⠸⠟⢻⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⢿⠃⠠⣤⣤⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⡀⠀⢠⣄⠀⣤⣤⡤ ⠀⠈⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡘⣟⡛⢁⣀⣀⣀⢀⣦⣄⢀⠈⡿⣿⣇⢀⡿⣿⢿⣿⣿⣿⣇⠀⠀⣀⠀⣀⢀⣀⠺⣿⣿⣿⣦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⣀⡀⣀⠿⢿⠿⣿ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⡿⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣯⣿⣿⣿⣿⣿⣿⣝⡃⠀⣿⣿⣿⣿⣟⣹⣿⣿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⡀⣒⣟⡓⢀ ⡠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢻⣇⣿⣷⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢷⣽⡇⣿⣿⣿⣿⣿⣯⣼⡟⣿⠀⠙⢿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢹⢿⣇⣟ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣤⣾⣿⣿⣿⣇⣀⠀⣾⣷⣶⣿⣶⣤⣤⠤⣷⣋⣉⣉⠀⠀⢳⣿⣿⣿⣿⣏⣀⣽⣶⣶⣾⣿⣿⠻⣛⣖⢀⡀⣀⢀⣠⣤⣿⣿⣿⣆⠀⠀⠰⣶⣄⠷⣾⡤⠀⢠⣤⣽⣶⡘⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⠿⢶⣿⣿⣿⣿⣧⣿⠹⣧⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣽⡏⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⣿⣗⠘⢧⢀⠈⠹⢿⡿⢿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⡏⣻⣿⣾⢾⣿⣿⣿⣿⣿⣿⣼⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⢸⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣧⡀⠈⣏⠆⣀⣀⣀⡀⠈ ⠀⠖⠶⣶⠿⢷⠖⠰⠶⠶⠖⠀⡆⣹⣿⠟⠁⠀⠀⠈⠛⠟⠈⢿⣻⣛⠀⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠉⠻⠿⢂⠀⠀⠐⢶⣷⣲⣿⣿⣿⣧⠀⠀⠀⣿⣿⢿⣿⡿⠿⢟⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⡀⠀⠐⣠⣄⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⣽⣿⠗⠶⠂⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⡀⠀⠂⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣙⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣴⠛⠋⠁⠐⣶⣄⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⢙⣿⣿⣿⣿⡿⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠸⣿⣦⣀⠀⠉⢻⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣶⡄⠈⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠗⠙⠿⣿⣿⠃⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣤⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤ ⡿⠿⠃⠂⠴⣾⣦⠀⠀⢠⣯⣥⣤⣀⣀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣿⠏⠉⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⣿⣿⣿⠇⠀⢠⣦⡀⠀⣤⠴⠖⠛⠁⠀⢰⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠤⣤⣤⣀⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠀⣤⣶⣿⣿⣿⣯⠀⠀⠀⠀⠈⣿⣶⣶⣤⣄⡀⠀⠀⠸⣿⣿⠀⢸⣿⣿⣿⠁⠀⣾⣿⣯⣶⡄⠀⣀⣠⣤⠀⠀⠀⠀⠉⠈⠉⠉⣷ ⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣄⠴⢼⡏⠀⠈⠉⠉⠁⠀⠀⠙⢿⣿⣷⡵⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⣿⣿⡟⡟⠿⣿⣿⣿⣿⣿⠀⣀⡠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣼⣀⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣶⣤⣤⣤⣿⣿⣿⡿⠛⠁⢻⡿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏⠈⠿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢐⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠘⠛⢿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⠄⠀⠀⠈⠻⠿⡿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢀⠀⠀⣤⠀⢤⡄⠠ ⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀⡈⣛⡛⢛⣃⣠⣀⢀⣤⣀⢀⠀⡻⣿⣿⣿⡆⣾⢿⣿⣿⣿⣿⠀⠀⣀⠀⣀⢀⣀⡘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⢈⠐⢢⡅⠀ ⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⣿⣿⣿⣿⡟⣿⢻⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⣿⣿⣿⣿⣟⣹⣿⣿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣐⣼⡛⠂ ⡠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣿⡷⣿⣿⣿⣿⣿⢶⣿⡇⢶⣿⣿⣿⣾⣯⣼⡟⣿⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡇⢸⣿⣿⣄ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⡷⢤⣤⠴⣿⣟⣻⣟⠙⡿⣿⣿⢿⣿⣿⣿⣖⣴⣷⣶⣾⣿⣿⡿⣛⣿⢀⡀⣀⢀⣀⣄⣹⣿⣿⣷⡀⠀⠀⢰⣦⡶⣾⡤⠠⢠⣤⣬⣷⡖⠺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠹⣇⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣽⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢹⣷⡈⠿⡰⠀⠙⢿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⢿⣿⡇⣿⣿⡿⠛⣿⣾⢾⣿⣿⣿⣿⣿⣿⣴⣏⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⡏⣿⢹⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⡀⠂⢳⢣⠀⠀⠀⠀⠈ ⠀⠖⠶⣶⠏⢷⠆⠰⠶⠶⠖⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⢿⡟⠀⢼⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡿⠿⠶⠀⠀⠀⢺⣷⢒⢾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠨⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⡌⢠⣶⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠑⠀⠀⠀⠀ ⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠃⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠿⣿⣿⣿⣿⣭⣌⡁⠉⠉⠉⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢙⣻⣿⣿⣿⣷⠀⠀⠀⢀⣴⡿⠋⠉⠹⣶⣦⢠⡼⡿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠘⣿⣿⣿⣿⣿⠀⠀⢠⣿⡏⠀⠀⠀⠀⠻⣷⣮⣄⣀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣤⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠏⠩⠿⣿⣿⠏⠀⢠⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⣽⣿⣷⣆⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀ ⡿⢿⣿⠷⠰⣾⣿⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿ ⠀⠀⠘⠃⠀⢠⠊⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⠟⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣶⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣻⡯⠈⠽⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⢻⣿⣿⣿⠁⢠⣮⡣⣀⠀⣴⠴⠖⠛⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡀⢀⠀⠰⢤⣤⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⣀⣀⡀⠀⣀⣴⣶⣾⣿⣿⠁⠀⠀⠀⠈⣷⣦⣤⣄⡀⠀⠀⠀⠀⣿⣿⡇⠀⠉⠉⠀⠀⠈⣿⣿⣯⡷⡄⠀⣀⣐⣤⠄⠘⠉⠛⠋⠙⠟⣯⣷ ⠀⠀⠇⠀⠀⠀⠀⠀⠈⠉⠏⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣦⣄⠤⢿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢈⢉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠽⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣯⣀⣀⣀⠀⠀⠀⠀⠘⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣶⣦⣤⣼⣿⣿⣟⣻⠽⡿⢻⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⡏⠉⢿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢸⢟⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠙⠿⠿⠿⣿⣿⣧⣀⡀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢀⠀⠀⣤⠀⢤⣄⠠ ⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀⡀⣈⡹⣿⣃⣄⣤⣠⣤⣌⢂⠈⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⣿⠀⠀⣀⠀⣀⢀⣀⠀⣽⣿⣿⣿⣿⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣤⢈⡰⢂⡇⠠ ⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣿⣿⣿⣿⣟⣹⣿⣿⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢒⣾⣟⠂ ⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⢾⣿⡧⢾⣿⣿⣿⣿⣿⣼⡟⣿⠀⠀⠉⢻⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢸⣿⢿⡇ ⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⡷⢤⣔⠒⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⡿⣛⣿⢀⡀⣀⢀⣤⣦⣶⣿⣿⣿⣧⡀⠀⠐⣦⡴⣾⡤⡤⢠⣤⣬⣿⡖⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⣿⣿⣿⠿⢷⣿⣿⣿⣿⣷⣿⠹⣧⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢻⣷⡤⢹⡱⡀⠙⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡏⠙⣿⣾⢾⣿⣿⣿⣿⣿⣿⣼⣿⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡏⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⡇⠀⣷⢣⠀⠀⠁⠀⠈ ⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⠁⣽⣿⡯⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠈⠻⠿⠖⠀⠀⠀⠸⣿⣻⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠫⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣠⣘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠃⠀⠀⠀⠀ ⣶⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⡿⠋⠄⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣾⣿⣿⣿⣿⣿⣶⡀⠈⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢉⣻⣿⣿⣿⣿⠀⠀⠀⣠⠞⠟⠉⠉⢗⣆⠄⡴⡿⠿⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⡈⢿⣿⣿⣿⣿⠀⠀⣰⡟⠀⠀⠀⠀⠘⠿⠶⣤⣄⣀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠨⠻⣿⣿⠟⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡌⠟⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣶⣿⣿⡄⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿ ⠉⠉⠙⠛⠀⢨⡍⠀⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡤⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠫⠯⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡇⠈⠛⠛⠁⠀⢸⣦⣇⣀⠀⣴⠶⠚⠋⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⠀⠐⠤⣤⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⢀⣠⣴⣶⣶⣿⠋⠀⠀⠀⠘⣧⣤⣠⣀⡀⣠⡤⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠘⢻⣿⣿⡓⠀⢀⣀⣠⣤⠄⠀⠿⠛⠿⣿⣿⣿⣿ ⠀⠀⠛⠁⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣦⣤⠴⢾⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡭⡉⠑⠇⠀⠀⠀⠀⠀⠀⠘⠙⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣦⣴⣦⡀⠀⠀⠀⠈⢿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⢿⡟⠿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⡟⠉⠁⠀⠀⢘⠿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠙⠻⡿⠟⣿⣿⣷⣤⣄⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⠤⣄⠰ ⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀⡴⣿⣿⣿⣳⣤⣤⣤⣤⣼⢦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⠀⣀⢀⣀⠀⡸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⣈⡰⢣⡇⢨ ⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣿⣾⣿⣿⡏⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣃⠀⣿⣿⣿⣿⣿⣹⣿⣿⠉⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣾⣟⠃ ⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡧⣿⢿⣿⣿⣿⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⢷⣿⡟⢻⣿⣿⣿⣿⣿⣼⡟⣿⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⢿⠇ ⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣾⣿⣿⣿⣿⡟⣿⣿⣾⣿⡿⢦⣔⠒⣿⣿⣿⣟⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⡟⣛⣿⢀⡀⣀⢀⡀⣦⣿⣿⣿⣿⣷⣄⠀⠀⢶⡶⣿⣤⡦⢠⣤⣾⣷⣆⠺ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⣿⢿⣿⠿⢿⣿⣿⣿⣿⣷⣿⠹⣧⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⣷⡤⠻⡴⡀⠙⠿⣿⡿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡇⠸⣿⣾⢾⣿⣿⣿⣿⣿⣿⣼⣿⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠁⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⣇⠤⢷⢣⢀⣀⣈⡀⠈ ⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⡅⢼⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠉⠛⠛⢓⠀⠀⠀⠈⣉⠿⣽⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠍⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣷⣿⣄⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠉⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⡿⠫⠟⢿⣿⡿⡿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣟⣿⣿⣿⣿⡀⠀⢠⠞⠛⠋⠈⠂⠀⠀⢰⠿⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⢹⣿⣿⣿⣿⠃⣰⡆⠀⠀⠀⠀⠈⠓⠛⠣⣦⣤⡄⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠁⠙⠿⣿⠏⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣧⣭⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⣿⣿⣿⠆⠰⠿⡿⣇⣿⣃⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣷⣽ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⠀⣀⡄⠀⢶⣶⣶⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⠣⡽⠻⣿⡧⠀⠀⠀⠠⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⢰⣾⣿⣯⣠⡀⠸⠞⠋⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⡄⠀⢀⣠⣤⣶⣶⣿⠇⠀⠀⠀⠘⣧⣤⣤⣀⡀⠀⠀⠀⠀⢐⣿⣿⠋⠀⠀⠀⠈⠋⠹⣿⣿⣿⣦⣀⣤⡤⡶⠂⢸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⣀⣿⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣦⣦⠒⠚⣿⣿⣇⢀⣀⡀⠀⠀⠀⠈⣿⣿⡷⡎⠀⣀⡀⠀⠈⠛⠛⠛⠟⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣀⣼⣿⣿⣿⣿⣿⠿⣿⣿⣷⣶⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⠙⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⠏⠀⠛⠿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡟⠉⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣷⡽⣿⣿⣿⣿⣿⡃⠀⠀⠀⠈⠉⠉⠉⣿⣿⣿⣿⣦⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⢶⠀⠲⡦⠒ ⠀⠀⢐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡛⣿⡿⢏⣥⣤⣴⣶⣤⣤⢃⠘⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⠃⠀⣀⠀⣀⢀⣀⠀⡙⢿⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠠⡘⢱⣆⠸ ⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣿⣿⣿⣿⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⣀⣿⣿⣿⣿⣿⣹⣿⣿⠀⠉⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣿⣭⡁ ⣤⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⢿⣿⣿⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣗⠻⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⢀⣈⣿⣿⣿⣄⠀⠀⠀⠀⠀⡀⠀⠀⠐⠆⢸⡟⠻⠇ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣸⣿⣿⣿⣃⠀⣿⣿⣿⣿⡟⢓⣒⠉⣿⣿⣿⣓⠈⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣏⣭⣟⢀⣀⣀⢀⡀⢩⣻⣿⣿⣿⣿⣷⠀⠀⣻⣟⠷⣖⡓⠰⣶⣾⣿⣇⡸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡇⢰⣿⠿⢷⣿⣿⣿⣿⣿⣿⠹⣧⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⢿⡆⢙⡼⡀⠈⠻⠿⠿⢿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢿⡇⠸⣿⣾⢾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣸⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣧⣈⣹⣡⣠⣤⣤⣄⣀ ⠀⠖⠶⣶⠯⢶⠶⠰⠶⠶⠖⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠃⢺⣿⣷⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⠉⠋⢉⡀⠀⢀⡀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⣿⣿⠿⠿⢟⣻⣟⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀ ⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣿⣿⣿⣿⣿⡟⠉⠁⠉⠛⠟⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠾⣿⣿⣿⣿⣧⠀⠀⠀⣀⣤⢄⡀⠀⠀⠀⢈⣿⣟⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⡇⣀⠚⠉⠀⠀⢀⠈⠁⠀⠉⠁⠉⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⠠⢿⣿⣿⣿⡗⠉⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⣤⡈⠿⠟⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡟⠁⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣉⣭⣉⠀⠀⠙⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣶⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠ ⠈⠀⠁⠀⠀⠀⣩⣷⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣟⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠞⠋⠉ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣧⡀⠀⠀⢿⣿⣿⣶⢄⠀⠀⠀⠀⣀⣤⡆⠀⠚⠉⠀⠀⢀⣀⢀⣂ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣁⣠⣲⣄⠀⠀⠀⠀⠀⠀⢿⣿⠙⠻⠿⣿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⢻⣿⣿⣿⣷⣴⣄⠚⠋⠉⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣀ ⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠿⢿⣿⣿⣷⣀⣤⣴⣶⣶⣾⠁⠀⠀⠀⠙⣧⣄⣄⣀⡀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⡀⢩⠉⠈⢿⣿⣯⣇⣤⡤⠖⠚⠃⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣶⣓⠘⠉⣿⣿⣿⣾⣿⣧⠈⠀⠀⠘⣿⣿⣿⣶⠆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣙⠛⠋⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠚⠀⠀⠈⠙⠛⠻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⡿⢿⣿⠘⠋⢹⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⡏⠉⠟⠻⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣿⣿ ⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢘⠿⢿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠠⠀⠀⠶⢀⡸⠏⢛ ⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⢈⣿⣿⡿⢁⣴⣿⣿⢿⡷⣄⢠⠘⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⣀⠀⣠⣇⣄⠀⡀⢙⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢠⢌⣰⣧⠙ ⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⡏⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣷⢠⣿⣿⣿⣿⣿⣹⣿⣿⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢲⣿⣦⡈ ⠀⠸⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢻⣿⣿⣧⣿⣿⡏⣿⣿⣿⣿⣿⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣯⣜⣿⣿⣿⣿⣿⣽⡟⣿⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⠀⠘⠃⢾⣟⠛⣁ ⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⣀⠉⠉⢀⣀⠀⣿⣿⣿⣿⣏⢉⣁⠀⣻⣛⣛⣃⠀⠿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣒⣏⢀⣤⣤⢀⡀⢀⣻⣿⣿⣿⣿⠃⠀⠀⢹⣏⠋⣏⡇⠘⢿⣿⣿⣦⡈ ⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡇⢰⣿⠿⢶⣿⣿⣿⣿⣿⣿⠹⣷⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡁⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⣧⣿⢿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⢿⡇⠙⡵⡀⠈⠙⠛⠛⠿ ⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣿⡇⣿⢹⡇⠘⣿⣶⢾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣾⣏⣿⢼⡟⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣷⣤⣽⣧⣶⣶⣶⣤⣤ ⠃⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⠿⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣄⠀⣰⡆⠀⠀⠸⣿⣿⣷⡀⠀⠀⠀⣿⣿⠛⠋⣭⣽⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⣿⠅⠈⠉⠙⠻⠿⢿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢯⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣛⣿⣿⣿⣿⡆⠀⠴⠶⠂⠀⠀⠠⠤⠞⠛⠿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⢙⣿⣿⣿⣿⠷⠋⠀⠀⠀⠀⠂⠂⠤⣤⣀⣀⠘⠿⠿⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠟⠁⠘⠿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⣷⣶⣶⣦⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢀⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠎⠂⠀⠀⢀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⠀⠀⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠛⠋⠉⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣀⣠⣼⣷⣄⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⣿⡀⠀⣷⣿⣿⣿⣿⣵⠆⠀⢀⣠⣤⠶⠞⠀⠉⡀⠀⠀⠀⢀⣀⠤ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⡏⠀⠈⠉⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⡈⠉⢿⣿⡿⣿⣮⣶⠈⠁⠀⠀⢀⣀⡀⠤⠖⠂⠉⠁⠀⠀ ⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢸⣶⣤⣤⣤⣀⡀⣀⣀⢠⣤⣿⣿⣷⣾⣿⣄⣾⣇⡀⢹⣿⣧⣴⠲⠚⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⣿⠿⠿⠟⠛⠉⠙⠉⠁⠸⣿⣿⠻⠟⠆⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣦ ⠀⠀⠀⠈⠙⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⡆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠛⠋⠀⠀⣹⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⠀⠈⠉⠛⠿⠿⠿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠘⢿⠇⠐⢄⠂⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⠿⢃⣀⣀⣄⣀⡼⢏⢿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠙⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡏⢀⣸⣿⣭⣿⣏⣯⢜⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⣠⢀⣾⣿⣇⠀⡀⢈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣿⣿⣿⣿⣿ ⠀⠸⡿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡻⣿⡿⠏⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢺⣿⣿⣿⣿⣿⣹⣿⣿⠀⠘⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢙⣿⣿⡿⠟ ⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡇⣿⣻⣿⣿⣿⣿⣿⡦⣿⢿⣿⣿⣿⣻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⢿⣿⣿⣿⣿⠃⠀⠀⢱⣤⣤⣤⣤⠀⣠⣼⣿⡌⠱⣶ ⣀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⣀⠀⠀⢀⣀⠀⣿⣿⣿⣿⣿⣆⣀⢠⣾⡀⣀⣀⠀⠉⢛⣛⠛⣛⡋⢀⣻⣿⣿⣿⣿⣿⣿⣿⣌⣄⢀⡻⣷⣄⡀⢈⣟⢹⣿⣇⠀⠀⠀⠀⢿⣮⠙⡾⡀⠘⢿⣿⣿⣦⣼ ⠃⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣽⣧⣿⣹⣷⣿⣿⣿⣿⣿⣄⠀⠀⠀⠈⣿⡀⢸⣡⢀⡀⢀⠀⠉⠉ ⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⣿⡇⣿⢽⡇⠸⣿⣾⢾⡗⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⢸⡟⢻⣏⣿⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢹⣿⣿⡿⠿⢿⡿⣿⣿⣆ ⠀⠖⠶⣶⠯⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠛⣿⣿⡇⢠⣶⡄⢸⡆⠰⣿⣇⠀⠈⣿⣿⣿⣷⠀⠀⠀⢸⣿⣇⠀⠺⠿⣿⣿⣿⣿ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠉⠛⠀⠀⠀⠀⠀⠀⠍⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠳⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⡆⡀⠒⠒⠒⠐⠀⠀⠙⠁⠉⠻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⠈⢿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠉⠓⠀⠐⣦⣈⣀⣀⣤⣴⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣭⣍⠉⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⡿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠐⠀⠀⠀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠶⠚ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠉⣰⣦⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⢨⣟⢿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⣠⠀⣤⠴⠀⠈⠉⠀⠀⠄ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠰⣿⣟⡿⢿⣿⣗⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣷⠀⠀⠘⢿⣿⣿⣿⣧⢃⠀⠠⠴⠖⠛⠋⠀⠀⠄⠀⠀⢀⠤⠔⠒ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⠈⠹⠿⣿⣿⣿⣷⣶⡟⠁⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣴⣤⣽⣿⣿⠿⣿⣿⠳⡄⠀⣀⣀⣤⠤⠀⠒⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠛⠛⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣶⣶⣶⣤⣄⣠⣤⠤⠰⠶⣿⣿⣿⠿⠿⠿⢿⠿⠂⢸⣿⣇⡾⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡟⠙⠛⣻⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣥⣄⡐⠋⠁⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡄⢴⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣄⠀⠀⠀ ⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⡇⠈⠉⠁⠀⣻⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⡏⠀⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠟⠀⠈⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶ ⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠟⢭⣤⣤⣦⣤⣻⠝⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣀⠀⠙⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣶⣿⣦⣗⢀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣰⢦⣿⢿⣇⠀⡀⢀⠛⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠟⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣿⣷⣿⣟⣿⣿⠏⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿ ⠀⢠⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⣿⣿⣿⣿⣿⣿⡗⣿⢿⣿⣿⣿⢻⡇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣽⣿⣿⠀⠀⢿⠿⢿⣿⠁⠀⠀⠀⠸⣖⠒⢒⠗⠐⣾⣿⣿⣿⡛⠛ ⣀⢼⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣀⠀⠀⢀⣀⠀⣿⣿⣿⣿⣹⣧⣀⣰⣗⡀⣀⣀⠀⠀⢉⣉⠁⣀⡀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣧⣄⢀⡘⣛⢂⡀⣼⣢⣾⣿⣄⠀⠀⠀⠀⢻⡗⠘⡼⡀⠈⠛⠛⠛⠷⠦ ⠉⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⠿⢶⣿⣿⣿⣿⣿⣿⣿⣯⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡁⠿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣯⣿⣧⣿⣸⣷⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣷⣀⣹⣡⣤⣤⣤⣤⣄⠀ ⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢽⡇⠸⣿⣾⢾⡗⣿⣿⢿⡿⢿⣿⡏⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣯⣿⢹⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⣿⣿⠛⠛⣯⣿⣭⣿⣿⣷ ⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⠘⣻⣿⣧⠻⠛⠁⠈⠁⠹⠿⠯⠀⢿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣇⠀⠉⢹⣿⣿⣿⣿ ⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠉⠙⠽⠟⠛⠟⠿⠿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⢿⣿⣿⣿⣿⣠⡔⠃⠀⠀⠀⡁⡂⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡶⠚⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⣶⣴⣶⣾⣿⣿⣷⣄⣀⡀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⠀⠀⣠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰ ⠈⠉⠀⠀⠀⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡏⠋⠁⣤⡀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢿⣿⣿⣽⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠾⠟⠋ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⠀⠀⠀⣀⣠⣶⣶⣦⣤⣀⠀⠀⣿⣿⣿⣷⠀⢸⣿⣿⣷⣦⣄⡀⢀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠰⢯⣭⣽⣿⣶⡦⣀⠀⠀⠀⣀⣀⡔⠀⠖⠛⠀⠀⠀⠀⠀⣂ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣾⣿⣿⣿⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⡏⠛⠟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣠⣤⣸⣿⣿⣿⣿⣷⣩⡄⠘⠛⠋⠁⠀⠀⠀⣀⣠⠄⠐⠒⠉⢁ ⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⡿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣉⣛⣟⠋⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠘⣿⣧⢹⣆⣠⣤⠶⠶⠊⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠁⠉⢿⡟⠟⡃⠀⢀⣴⣾⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣶⣶⣦⣤⣰⠶⠂⠚⠛⠛⠛⠛⠉⠉⠉⠙⠛⠀⢿⣿⡿⢿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠈⣿⡇⢸⡄⣀⠀⠀⣀⣠⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⣟⠉⠋⠉⠈⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⠀⠀⠻⠀⢰⣿⣿⣿⣿⣿⠓⠀⠐⠶⠂ ⠀⠀⢀⣶⣶⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⢻⡶⠶⢶⣶⡿⢟⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣷⡄⠀⠀⢀⢀⣶⣠⠀⠉⠛⢿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣶⣷⡆⠀⠂ ⠀⠀⣼⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣷⣿⣔⢀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣼⣿⣿⢿⣄⠀⡀⢀⢹⣿⣿⣿⣶⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣧⣾⣷ ⠀⠀⠏⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠏⣿⣿⣿⣿⣯⣿⣿⣏⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡟⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣋⣀ ⠀⢰⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⣿⣿⣿⣿⣿⣿⡏⣿⢿⣿⣿⣿⢻⡏⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⠀⠨⣇⣸⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣙⠋ ⣦⠾⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣀⠀⠀⣀⣀⢰⣿⣿⣿⣿⣹⣿⣀⣼⣇⣀⣀⣀⠀⠀⢀⣀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⣉⢀⡸⣷⣿⣿⣿⣄⠀⠀⠀⠈⣿⡿⠿⡿⡟⠉⠉⠉⠙⠋⠁ ⢉⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⡇⢰⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣉⣿⣿⡇⠀⣿⣿⣾⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⡏⢻⡿⢻⣧⣿⢻⣷⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣶⣿⣿⣿⡿⢿⣷⣦⡀ ⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢿⡇⠸⣿⣿⢾⡗⣿⣿⢻⡟⢿⣽⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠀⣿⣿⣿⣿⡟⣿⣷⠇⣼⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠐⣿⣷⠀⠰⠿⢿⣿⣿⣿⣷ ⠀⠖⠶⣶⠟⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡆⠀⣿⡇⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠠⣻⣿⣇⢸⠹⣿⣆⣩⣩⣀⠀⠀⠉⠉⠀⠀⣻⣿⣿⣿⡇⠀⠀⠀⢹⣿⣇⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⡛⠋⠁⠙⠉⠛⢿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠤⠿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣙⣿⣿⣿⣿⡇⡰⠶⠶⠶⠶⢶⠀⠀⢀⣉⣁⣀⣀⣤⣤⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡛⠛⠁⠈⠻⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠿⡿⠟⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣷⣦⡀⠀⠀⠀⢻⣿⣿⡿⠁⠙⢂⣄⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶ ⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⡏⠀⠀⢸⣿⣿⣷⣶⣦⣤⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢻⡿⢿⣸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠋⠉⢀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠿⠿⠟⠿⠃⠀⠀⣿⣿⣿⡇⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣿⡀⢠⣿⣿⣿⣿⣿⣿⡻⡦⠀⣠⣤⡤⠖⠁⠈⢁⠀⠀⠀⢀⣀⡬⠄ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠁⠉⠉⣿⣿⣿⡆⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⢻⣦⡉⠀⠀⠀⣀⡀⠠⠔⠒⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠏⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠐⠂⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠟⠿⠉⠀⠀⠀⠀⠀⢀⠀⣀⣼⣿⣿⠟⠛⠿⣿⠿⠿⢻⣿⣧⡿⡷⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡻⠄⠀⠀⣀⣴⣾⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣀⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠾⠷⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣃⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⣧⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⡟⠻⡿⣿⣿⡿⢿⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠹⠇⢿⠀⠀⠉⢶⣾⣿⣿⣿⣇⠀⣀⣀⣀⠀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡇⣻⣟⡛⢙⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⠘⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⡟⡶⠐⠫⢹⣀ ⠀⠀⢰⣶⣂⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠃⢟⣛⡛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣀⣀⠀⣠⣸⢦⠀⠀⠉⠛⣿⣿⣿⣦⣄⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⡯⢯⣿⡉⢠⣬⣻ ⠀⠠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⣿⢟⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣻⣿⣿⣿⣿⣯⣽⣧⡀⡐⢼⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣼⣿⠿⣿⣿⠋ ⠀⠐⣫⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣻⣯⣻⣿⡇⠻⢿⡿⠿⠿⢟⠻⣿⣿⣿⣶⣿⣷⣀⠈⡷⠶ ⣀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢻⡇⢿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⣿⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⡆⠘⡏⡀⠙⠻⠿⠿⡿⠇⠀ ⡿⣹⣿⣿⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣷⣶⣄⣀⠀⠀⢀⣀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣠⣀⡀⣀⢛⣿⣿⣿⣿⣧⣀⠀⠀⠀⢻⣧⣀⣻⣣⣤⣤⣤⣤⣀⠀⠀ ⣰⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡇⢰⣿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣉⣿⣿⡇⠀⣿⣿⣿⣿⡉⢹⣿⣿⣿⣿⣿⣿⣿⠀⢹⡏⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢺⣿⣿⠛⢛⣿⣿⣽⣿⣿⣶⠀ ⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⢿⡇⠸⣿⣾⢾⡗⣿⣿⢹⣿⣿⣼⣏⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣵⠲⢿⡷⢸⡟⣿⢿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣆⠀⠉⢹⣿⣿⣿⣿⡄ ⠀⠶⠶⣶⠯⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠿⠿⠀⠐⣟⠐⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⢸⣿⣿⡇⢈⠝⠙⠇⣷⣾⡆⠀⣶⡆⠀⣸⣿⣿⣿⣿⣧⠀⠀⠀⠈⢿⣿⡀⠀⠀⠻⣿⣿⢿⣿ ⢿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠽⠋⠁⠀⠈⠁⠙⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠐⠺⠿⢿⠟⠛⠛⠃⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡶⠚⢿⣿⣿⡿⠁⠠⠲⢿⣿⣿⣶⣤⡀⢦⣀⠠⣰⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⡆⠀⠀⠉⠛⠃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣮⠛⠃⠙⢿⣿⣿⣿⣿⡟⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠋⠅⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢹⣶⣮⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⠴⠛ ⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣿⣿⡿⣿⣦⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠉⠁⣀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⡀⠀⠀⠀⠄⢸⣷⣀⣴⣿⣿⣿⣿⣿⣷⣻⣆⠄⣴⣶⠶⠚⠀⠀⠀⠀⠀⢀⣀⣤⠴⠀ ⠀⠀⠀⠀⠘⢿⡿⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠈⠉⠹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⠀⠄⢀⣀⣤⡄⠴⠒⠂⠈⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠈⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠐⠶⢆⣀⣀⣀⣈⡇⠀⠀⠀⢀⠉⠉⠀⠀⠀⠀⠀⣀⣀⠀⡶⣾⣿⡿⠛⠙⠻⠛⠛⠻⣿⣿⢿⠹⣷⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠻⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⣼⣿⣿⣷⣶⣦⣄⡀⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⠀⠁⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠛⠃⠀⠀⣠⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣻⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣀⠀⠀⠀⣦⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⠀⠀⠀⠀⠀⠘⠃⠉⣠⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣤⡄⠀ ⠀⠀⠰⠁⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣟⣻⣿⡉⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣘⠻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⣆⡉⠹⣤⣤ ⠀⢠⣿⣯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠉⣻⣯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⡄⣀⣶⣿⣆⡀⠀⠉⢻⣿⣿⣿⣦⡄⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡉⣿⣯⣀⣶⣾⡟ ⠀⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠛⣿⢿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣧⣿⣷⡀⡸⣿⡿⢿⣿⡇⠀⠀⠀⠁⠉⠈⠻⣿⣿⡏⠘⢷⣿⠻⢿⣿⡟⠀ ⠀⣨⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣷⣼⣿⡇⠀⠀⠀⠀⢸⣷⡤⢹⣿⠛⢻⣿⣿⣦⣄⣻⡿⠃ ⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⢻⡏⢿⣽⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⡏⠀⢹⣣⠀⠉⠻⠛⠿⠓⠀⠀ ⠋⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣀⠀⠀⣈⣛⠛⣻⣿⣿⣡⣿⣷⣾⣿⣷⣦⣆⣀⠀⠀⢀⣀⢀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⣶⣀⡀⣻⣿⣿⣿⣿⣷⣀⣀⠀⠈⢻⣿⣶⣾⣿⣶⣶⣶⣶⣦⡀⠀⠀ ⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡇⢰⣿⠿⢷⣿⣯⣿⣿⣿⣿⣿⡯⣿⣽⣿⣿⡇⠀⣿⣿⣿⣿⡉⣿⣿⣯⣿⣿⣿⣿⣏⢀⣹⡏⢻⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⡉⠩⢿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡇⠸⣿⣾⢾⡗⣿⣿⣿⣿⢿⣿⡇⣿⣥⣿⣿⡇⠀⣿⣿⢿⣿⠁⠹⣿⣿⣿⣿⣿⣿⣵⢛⣻⡇⣸⡏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣧⠀⠀⠐⣿⣿⣿⣿⡇⠀ ⠀⠶⠶⣶⠿⢷⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⢸⣿⠀⠀⠀⣶⣾⣧⣤⠀⠀⠀⠀⢸⣿⣿⣿⣦⡐⣃⣐⣼⣿⣿⣧⢸⣿⡆⢾⣿⣿⣿⣿⣷⠀⠀⠀⠀⢙⣿⡇⠀⠀⠈⢿⣿⠿⣿⣇ ⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠈⠀⠀⠀⠀⠀⠛⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⢛⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⢿⣿⣿⣿⣇⠀⣠⣤⣴⣶⣦⣀⠛⠛⠋⠁⠀⢉⣀⣰⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠃⠘⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣦⠀⠰⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠛⠛⠃⠀⠀⠀⣽⣿⣿⣿⣿⣿⠿⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠹⣿⣿⡽⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠚⠛ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠀⠀⠈⠛⠛⢿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⠀⢀⣟⣯⣀⣿⣴⡲⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠈⠉⠁⠀⡀⢈ ⠀⠀⠀⠀⠹⠻⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣾⣿⣿⣿⣿⣿⣷⢸⣶⣤⡶⠖⠛⠃⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈ ⠀⠀⠀⠰⠄⠀⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⠉⠙⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⠀⣀⣀⣤⠄⠀⠒⠉⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠙⠃⠀⠀⠀⠀⢀⣀⠀⣸⠁⠀⠀⠀⡈⠉⠀⠀⠀⠀⠀⢀⣤⣤⠰⠶⠿⠿⠉⠉⠻⠟⠉⠙⢿⣿⣿⡆⢻⣮⠉⠁⠀⢀⣠⣶⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⠀⢒⣠⣴⣾⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⣴⠍⠀⠀⢠⠀⠀⠀⢸⣿⣷⠃⠀⠁⠀⣤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠙⠛⠀⠀⠀⠶⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣠⡀⠌⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⡄⢀⣤⣾⣿⣿⣿⣿⣿⣥⠋⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡯⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣄⠶⠀⠀ ⠀⢈⡛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣅⢈⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇⠀⡈⠀⠀⠉⠈⠻⢿⡿⣿⣿⣿⣦⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡴⠙⢿⣴⣦ ⠀⣼⣿⣦⣤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠄⢸⢶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣆⣀⠶⣷⣄⣀⠀⡸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⢠⣾⣧⣼⣷⣿⡃ ⠠⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣿⢿⣿⣿⣿⣗⣸⡂⣹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣗⣳⡿⣿⠻⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⣂⠀⢙⣾⣟⠛⢿⣿⣏⣀ ⡘⣦⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠧⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣧⠀⠀⠀⠀⢘⣿⡾⡉⠹⠫⠀⢿⣿⣿⣦⣀⠽⠛⠂ ⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⢻⡏⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⡀⠀⢣⠄⠀⠈⠛⠉⠋⠀⠀⠀ ⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣀⠀⠀⢈⣉⠉⣹⣿⣏⣀⣻⢿⣿⣷⣶⣶⣦⣀⠀⠀⢀⣀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣃⣡⣀⡸⣿⣿⣿⣿⣿⣄⣀⣀⠀⠙⣿⣷⣶⣾⣾⣿⣿⣿⣿⣦⡀⠐⠒ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡗⢰⣿⠿⢶⣿⣷⣿⣿⣿⣿⣿⡏⣿⣽⣿⣿⡇⠀⣿⣿⣿⣿⡑⣿⣿⡏⣿⣿⣟⣿⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣇⠀⠘⠛⢿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡇⠘⣿⣾⢾⡷⣿⣿⣿⣿⢿⣿⡇⣿⣽⣿⣿⡇⠀⣿⣿⢿⣿⠁⣿⣿⣿⣿⣿⡇⣿⣥⣉⣹⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⡄⠀⠀⠸⣿⣿⣿⣿⡄⠀ ⠀⠿⠶⣶⠿⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣉⣉⣉⡁⠀⣸⡇⠈⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠉⣿⣿⣿⣤⣤⣤⣤⣿⣿⣿⣿⣿⡦⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠻⣧⣄⣀⠤⣬⣭⣍⣽⣷⣤ ⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣽⣿⣿⣿⣷⢀⣠⣴⣦⣤⡀⠈⢻⣿⣿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠌⡉⠁⠀⣀⣰⣶⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠰⣆⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⡟⠛⠛⠃⠹⠖⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⣟⣽⣿⣿⣿⠁⠀⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠻⣿⡷⠘⡅⠀⠀⠀⠀⠀⠀⢠⣶⡶⠆⠀⠀⠀⣠⣤⠷⠞⠋⠉ ⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣸⢷⣶⣼⣿⣿⡙⡤⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢨ ⠀⠀⠀⠀⠘⠉⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⡀⠀⠀⠀⡀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠠⠀⠀⠀⠈⠀⣿⣦⣾⣿⣾⣿⣿⣿⣿⣧⣿⣿⣶⠖⠛⠉⠀⡀⠀⢀⣶⣶⡤⠒⠊⠁⠀ ⠀⠀⠀⠷⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠻⢿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢹⣿⣀⣠⡤⠶⠀⣼⣿⣿⣿⣇⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠈⠉⣁⠀⠀⠀⠀⢠⠤⠦⠲⠚⣍⠋⠀⠀⠉⠁⠀⢹⣿⣿⣿⠄⢻⠟⠐⢀⣴⣿⣿⣿⣿⣿⣉⠀⠀⠀⠀ ⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡏⠉⠀⣁⣠⣴⣾⣿⣿⣿⣿⣿⠀⠀⠀⢸⣶⣾⣿⣤⣤⡀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠂⠀⠀⢸⣿⣿⣧⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⠀⠰⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣠⣶⡐⢀⠀⠀⠀⠁⠀⠀⠸⣿⡟⠻⢿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢷⡆⠀⠀ ⠀⣀⡃⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⣿⣿⣿⣿⣿⣍⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠉⠉⠙⠟⠛⠻⢿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠏⢻⣿⠏⣙⢿⣿⡶ ⢠⣿⣿⣶⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣶⣷⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣶⣤⣤⣻⣷⢦⣤⣔⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠘⢽⣇⣾⣿⣶⣿⣿⡿⠀ ⢸⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⣿⣿⣿⣿⣿⣟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣹⣿⣧⣼⣿⡀⠀⠀⠀⠀⠀⣦⣼⣷⣄⣨⡆⢀⣭⣿⡏⠘⣿⣿⡦⠀ ⣹⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣷⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣭⣷⡃⠐⠿⣿⡿⣶⠜⠉⠉⣀ ⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣆⣿⣿⣾⣿⣿⢻⡇⢿⣽⡇⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣀⣤⣨⣀⣀⠀⠀⣈⣋ ⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣀⠀⠀⢀⡀⠀⣺⣿⣗⠀⡿⢿⣿⣿⣶⣷⣆⣀⠀⠀⢀⣀⢀⣀⣿⣿⣏⣻⣿⢿⣿⣿⡀⠀⣁⣲⣀⡹⣿⣿⣿⣿⣧⠀⣀⣀⠀⢻⣿⡿⠟⠛⣻⣿⣿⣿⣿⣧⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣿⡇⢰⣿⠿⢶⣿⣧⣿⣿⣿⣿⣻⡏⣿⣽⣿⣿⡇⠀⣿⣿⣿⣿⣽⣿⣿⡯⣿⣿⡏⣿⣽⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣷⡄⠀⠈⠹⣿⣿⣿⣿⡂⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡇⣿⣿⡇⠸⣿⣾⢾⣷⣿⣿⣿⡿⢿⣽⡇⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⢹⣿⣿⣿⣿⣿⡏⣿⣥⣴⣾⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣷⠀⠀⠀⠻⣿⣿⣿⣷⠀⠀ ⠀⠿⠶⣶⠿⢷⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⣠⣤⣤⣤⡄⢠⣦⠀⠙⣿⣿⣿⣿⠷⠆⠀⠀⠀⠀⠉⣿⣿⣿⠶⢶⣶⣶⣿⣿⣿⣿⣷⡾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢻⡦⠤⣶⣲⣾⣾⣿⣿⣷⣶ ⠻⢿⣿⣿⣷⣀⣀⣀⠀⠀⠀⠙⢿⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣷⠦⠛⠉⠙⠃⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⡿⣿⣿⠿⠻⣆⢠⣄⢀⢠⣤⠂⠛⠿⢿⣿⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣷⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣧⠹⠟⠀⠀⠀⠀⠿⠄⢿⣇⡀⠀⠀⠈⣿⣿⡇⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠶⢆⣾⣿⣄⡀⢠⣿⣿⡇⠀⠀⠈⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⠹⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀ ⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠽⣿⣿⣷⠀⠀⠠⠼⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⢸⡿⠳⣶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠶⠘⠉⠁ ⠀⠀⠀⠈⠋⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⠏⠀⠀⢹⣿⡟⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⢵⣶⡸⣿⣷⣼⣆⡀⠀⠀⠀⣀⠀⠠⠀⣠⣿⣿⣿⣆⠀⠀⣥ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣙⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣠⣿⠅⢼⣿⣦⣿⣿⡟⠻⣝⢷⠚⠉⠉⠀⠀⣸⣿⣿⣿⣿⣿⠉⠀⠀ ⠀⠀⠈⠋⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣯⡹⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠀⣾⠟⠝⣿⣿⣿⣏⠛⣾⠇⣤⠴⢦⣾⣿⣿⣿⣿⣿⣿⣷⡄⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠉⠀⠈⢉⠀⢙⣀⠀⠀⠀⠀⠰⠶⠂⠒⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠃⠈⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡋⠀⢀⢀⣠⣴⣶⣶⣶⣶⣾⠂⠀⠀⠀⣿⣤⣬⣬⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢸⣿⣿⣿⣿⣦⣄⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠈⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣰⣿⣿⣿⣿⣿⣿⣶⣤⣄⣠⣀⣂⣀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠛⢿⣾⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠉⠀ ⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡯⣾⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⡏⡀⣀⠀⠉⠉⠉⠉⠈⠉⢻⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠇⠀⣀⢲⣷⠀ ⢸⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⠑⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣉⣒⣠⣤⣤⣠⣀⣀⠀⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠾⠷⣶⣿⡇⠉⠀ ⠈⠉⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⢇⣀⡀⣻⣿⣿⡄⠀⠀⠀⣰⢐⣄⠀⢀⣀⣠⠀⢠⣬⣶⡀⠀⠛⠀⠀⠀ ⢸⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡏⣿⣼⡟⣿⡯⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⢾⣿⣿⣇⠀⠈⠂⠀⠀⠙⠻⠿⠆⠀⠀⠀⠀ ⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡇⣿⢹⡟⣿⣧⢿⣿⣾⣿⢿⣾⣿⣿⢻⡏⢿⣽⡇⠉⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣿⣸⣯⣿⣿⣿⣿⣿⡆⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⣤⣤⣤⣄⡀⠀⠀⣀⣀ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⠀⡁⢹⣧⣤⣤⣤⣀⣀⠀⠀⢀⣀⢀⣀⡀⢁⣀⣉⣒⢙⡉⣀⡀⣀⣀⣆⢀⡚⣿⣿⣿⣿⡄⠀⣀⣹⣿⣿⣧⠈⠛⠛⣭⣾⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⠿⢦⡿⣇⣹⣿⡇⣿⠹⡇⣿⣽⣿⣿⡇⠀⣿⣿⣿⣿⡁⡌⣿⡋⣿⣿⡇⣿⣿⠿⢿⡏⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⠻⣿⣿⡦⠀⠀⠀⠈⢹⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⡇⣿⢹⡇⠘⣿⣶⢺⣿⣿⣿⣿⡇⢿⣼⡇⣿⣽⣿⣿⡇⠀⣿⣿⢿⣿⠙⠿⣿⡇⣿⣿⡇⣿⣤⠒⢺⡇⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⢿⣷⠀⠀⠀⠀⠈⠻⠿⢻⡄⠀⠀ ⠀⠶⢾⣷⠿⢷⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⢠⠶⠶⠶⠀⢀⠀⣶⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿⡿⣀⠀⠀⠀⠀⣘⣿⡄⠐⠒⠠⠼⣿⣶⣶⣿⣿⣟ ⠈⠙⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠻⡛⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠛⠊⠁⠀⠀⣅⣤⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⠉⣩⣉⠁⠀⠀⠀⣶⣤⣦⢿⠿⠃⠉⠛⣿⣿⣿⣿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⣷⡾⠏⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠀⠈⠙⠈⠁⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣧⣽⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡦⠀⠀⠀⣿⣷⡀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⣿⡝⡻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣤⣀⣀⣀ ⠀⠀⠀⠛⠙⢿⣧⡀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠈⣿⣿⡧⠀⠀⠰⠞⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠘⠿⠻⣿⣄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢹⣿⣏⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⣸⣿⣧⣼⣥⣀⡀⠀⠀⣀⠀⢠⢀⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣯⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣴⡆⠀⣀⣾⣿⣿⣿⣿⣿⣯⠻⠞⠋⠉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠉⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠻⣿⡄⠀⠀⠀⠤⠄⠀⠀⠀⠀⣿⣿⠿⢷⣾⣿⠿⠟⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡿⠛⣿⣿⢇⣀⠀⠀⠀⠀⠰⠶⠂⠒⠱⣧⢠⣴⣿⣇⡄⢸⣿⣿⢿⣿⠿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋ ⠀⠀⣶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⡀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣿⠋⠀⠀⢀⣀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣗⣾⣿⣿⣿⣿⢸⣿⣿⣽⠿⣶⣄⠀⠀⠀⢿⣿⡿⠿⠿⠋⠉⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣀⣸⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣂⣻⣿⣿⣿⣿⣿⠿⠿⢿⡿⠀⠀⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠐⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⢿⠋⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀ ⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⠛⠻⠋⠋⠉⠸⣿⣿⣿⣏⠀⡀⠀⣹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢸⠂⢀⡐⣶⣆⠀ ⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣁⣠⣄⣤⣦⣠⣄⣾⡿⣿⣿⣿⣦⡅⠀⠿⢿⣿⣷⣀⣤⠠⠤⠀⠀⠀⢴⠀⠿⢷⣶⣿⠏⠉⠀ ⡄⢀⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⢿⣿⣿⡿⣙⣃⠀⣶⢄⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣯⣿⣿⣿⣷⠀⢀⢽⣿⣿⣧⡀⠀⣀⣀⡄⠀⣤⣼⣖⠀⠈⠋⠀⠀⠀ ⢣⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⣿⣼⣿⣿⡋⣿⡿⢧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣿⣷⡄⠀⠙⠀⠀⠈⠻⠻⠷⠄⠀⠀⠀⠀ ⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⣿⢹⡏⣿⣥⢿⣷⣾⣿⢿⣿⣿⣿⣿⡟⢿⣽⡏⠛⣿⣿⣿⣿⣿⣽⣿⡟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢰⠙⣿⣿⣿⣿⡄⠀⠀⠀⢠⣤⣤⣤⣄⠀⠀⢀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣀⡀⠀⠀⢀⡀⠀⣀⡀⢀⠀⡀⢸⣦⣤⣤⣄⣀⣀⠀⠀⢀⣀⢀⣀⡀⢀⣀⣹⣿⣿⣿⣦⣀⣄⣀⣚⢒⡛⣻⢿⣿⣿⡀⢸⣿⣿⣿⣷⡀⠙⠛⢩⣵⣾⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⡇⣿⣽⠇⢰⣿⠿⢦⣿⣧⣼⣿⡷⣿⢹⣯⣿⣽⣿⣿⠇⠠⣿⣿⣿⣿⡽⣬⣿⣿⣿⣿⣿⣿⣿⠿⢿⡏⢹⣷⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠉⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⡇⣿⢸⡇⠘⣿⣶⢺⡟⣿⣿⢻⡇⢿⣼⡇⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⠳⠟⣿⣿⣿⣿⣿⣿⣶⣄⣸⣇⢸⡏⣿⢿⣟⣿⣿⣿⣿⣿⣻⢿⣿⡄⠀⠀⠀⠀⠘⠟⠻⢧⠀⠀⠀ ⠀⡖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠟⠀⢀⣴⠷⢈⣿⠇⣴⠸⣻⣿⣿⣿⣷⡖⠒⠒⠬⢿⣷⣶⣿⣿⣟⠯ ⢶⢼⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⠉⣡⣤⡆⣦⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣿⡞⠻⠿⠏⠉⠛⠿⣿⣿⣿⡿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣴⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⢽⣿⣿⣿⣿⠿⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⢘⣿⣿⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⠄⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿ ⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⠀⠀⢀⣴⣛⣻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠙⣿⣿⣇⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠘⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠐⠛⠛⢻⣦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⢟⣶⣾⣿⣷⣸⣷⣤⣀⠀⠀⢀⠄⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⣤⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣸⣷⣾⣿⣄⣴⣟⡇⣿⣿⣟⠻⣿⣿⣿⣿⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣷⡤⠤⠀⠀⠀⠀⠠⠦⠀⠀⠀⣿⣿⠿⠯⣾⠿⠿⢿⣿⣿⡿⡇⠌⠻⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠿⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣷⡄⠀⡀⠀⢀⠀⢀⠀⢀⣿⣿⠿⣿⣿⣿⣷⢀⣄⠀⠀⠀⠀⠰⠶⠂⠛⡧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠘⡿⠃⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠑⢲⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣶⣶⣶⣷⣶⣾⣷⠀⠀⠀⣸⣶⣶⣦⣤⣤⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠇⠀⠀⠀⠈⠱⠀⠀⠀⠫⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠟⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣿⣿⣿⣿⡟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠀⢠⣴⡒⠀⠀⠀ ⣷⣄⣀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⠀⠀⠀⠉⠻⠿⠿⠟⠉⠘⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢀⣼⡟⢈⣻⣾⣦⣀ ⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣿⣿⣿⣿⠿⠁⠀⣽⣿⣿⣿⣿⡿⢊⣿⣿⣿⣿⣷⣤⣤⣶⣶⣿⣿⣿⣖⣿⣿⣿⢹⣇⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠄⠀⠉⣾⣸⣿⣿⣿⣿⣿⣿⣷ ⣇⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣯⣄⢠⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣿⣾⣿⣷⡄⠀⠀⠀⠀⣸⣄⡀⣠⣀⣀⣷⢀⣬⣿⣿⢿⣿⣿⣿⣿⡍ ⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣏⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣻⣿⣿⣿⡟⢿⡕⠘⠿⣿⣿⡟⢻⣿⣿⣿⣧ ⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡇⣿⣿⡟⣿⣷⢿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢿⣿⣿⣇⣠⠀⢧⣤⣤⣬⣤⣀⡀⢿⣿⣿⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣀⠀⠀⢀⡀⠀⣀⡀⢀⠀⡀⣰⣿⣿⣿⣎⣀⣀⠀⠀⢀⣀⢉⣀⣀⢀⣰⣿⣿⢿⣿⣇⣠⣤⣸⣿⣿⣿⣿⣿⣿⣦⡀⢀⣀⣻⣿⣷⣙⡛⠛⣿⣿⣿⣿⣿⣶⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣿⣷⣿⣿⡇⢰⣿⠿⢶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⡿⠷⠀⠉⣿⣿⣿⣿⣿⣷⣄⠀⣤ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⡟⣿⣿⡇⠸⣿⣾⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⢿⣿⢻⢿⣿⣿⣿⣿⣧⣿⣵⣶⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠿⣿⢰⠂⠀⠸⣿⣿⣿⣿⣿⣿⠥⠉ ⣰⡶⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠈⠋⡆⢀⢠⡤⣶⣶⣦⠄⠘⠋⠋⠀⠠⠞⠁⠘⠛⠛⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠛⠛⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⢇⡄⠀⠀⠀⠈⢸⣾⡗⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠋⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⢈⣩⣥⣶⣖⣴⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾ ⣼⣿⣿⣿⣿⣿⣿⠆⠀⠐⠰⣼⡿⠿⠟⠻⠉⠛⠙⠛⢿⣿⣿⡿⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠅⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠹⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿ ⠘⠿⣿⣿⣿⡏⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣧⠀⠀⠈⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⣰⣾⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿ ⠀⠀⠈⠻⣿⣷⣀⡠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠘⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢛⠛⢻⣷⡖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⢿ ⠀⠀⠀⠀⢻⣿⣿⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠸⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡓⠀⠀⠀⠽⣿⡿⣿⣿⣾⣿⣷⣶⡄⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⠀⠀⢠⣤⣄⡩⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣻⣿⣿⠀⠂⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣸⣿⣾⣿⣆⣾⣿⣇⣿⣿⣿⡛⠻⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠗⠒⠁⠈ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢿⣿⡟⣿⣿⡇⠸⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⢿⣿⠻⠟⣿⡿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣶⡇⠀⠀⠙⣿⣿⡿⣿⣇⡀⢀ ⣤⡷⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⣣⣄⡴⠶⣾⣷⣶⠆⣠⡿⠉⠀⠀⠀⠀⠈⠁⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⢏⣴⠀⠀⠀⢈⣈⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⢸⣿⠟⠛⠛⠿⢧⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢠⣷⣿⣿⣿⣿⡇⠋⠑⠁⠋⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿ ⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⣠⣦⣤⣀⣠⣈⣠⣶⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿ ⣾⣿⣿⣶⠉⠙⠃⠀⠀⠒⠛⣻⠿⠿⠿⠟⠛⠋⠉⠉⢻⣿⣿⡟⠁⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠘⣷⣄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠄⠠⠀⠀⢀⣀⣠⣾⣿⠏⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⠹⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡆⠀⢀⣹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠋⠀⠀⠀⡘⢿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⣤ ⣿⣿⣿⣿⣿⠟⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣿⣿⣿⡇⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡧⠀⠀⢠⣼⣟⣿⣿⡙⣿⣦⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀ ⠀⠙⠛⠻⣿⣷⣶⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠸⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠤⠊⢀⠀⠀⠀⠀⣀⢏⣐⡀ ⠀⠀⠀⣤⣽⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡹⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀ ⠀⠀⠀⠘⠋⠙⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⢿⣿⠿⠿⢿⣿⣿⣷⠙⠗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⣧⠄⣠⠀⠀⡀⡀⡀⢀⣾⣿⣿⣿⣧⣤⡄⠀⡤⠄⠀⠀⠀⠀⠛⠛⢸⣿⣿⡟⠀⢨⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⣠⠃⠀⠀⡄⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣸⣿⣿⣿⣀⡀⠀⠀⠀⢀⣀⣀⣸⣿⣿⠟⠁⣤⣤⣀⡀⣠⣤⡤⠀⠀⠀⢠⣶⣼⠟⠁⠀⠛⢀⡀⡾⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⣀⡀⠀ ⠀⠀⠰⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣧⠀⢠⣾⣿⣿⣿⣿⣿⣏⣤⣶⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠉⣿⣿⣔⡄⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠙⣫⣿⣿⣿⣧⡞ ⠀⣾⣆⣘⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡝⠁⠟⠋⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢿⣿⣿⣯⣐⣿⣿⣿ ⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢯⣿⣆⣤⣤⣴⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⣤⡄⠴⠶⣶⡒⠚⣍⠙⢿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣽⣿⣶⣶⣿⣷⣦⣿⢖⣾⣿⣿⣭⡟⠻⣿⣯ ⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⡟⣻⣾⠀⠙⠻⠿⠛⠃⠺⢿⣿ ⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⡿⠟⠁⠀⠀⠘⠻⡿⠛⠻⠋⠻⣿⡟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣉⣻⣿⣿⣿⣿⣿⡇⠉⠃⢻⣿⣿⣿⣿⣿⡄⠀⠀⠈⣿⣿⣿⣯⣿⣬⣿⣷⣶⣶⣶⣶⣤⣴⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣴⣿⣷⣦⡀⠀⠀⠘⢿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠹⣿⣿⣿⡴⡯⠐⠶⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠛⠛⠓⠀⠐⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⡃⣨⣿⣿⣿⣿⣿⣥⡀⠀⠀⠚⢿⣿⣟⠉⡀⠀⢹⣿⣿⣿⣿⣷⡀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢏⠛⠛⠀⠈⠁⠈⢉⣉⣛⡉⣹⡿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠿⣿⠟⠈⠁⠁⠉⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢙⣿⣿⣿⣧⡤⣈⣭⣿⣿⣿⣿⣧⣄ ⣴⣶⣾⣶⠿⢷⠶⠴⠶⠶⠶⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣣⣼⠟⠁⠀⠀⠀⠀⠀⠈⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠂⠿⠟⠁⠉⣙⣛⣷⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡸⢿⣏⣿⣯⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⣲⣶⣶⣶⣦⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⡷⠂⠉⠋⠀⠀⢐⣺⣿⠿⠛⠛⠛⠋⠉⠁⠀⠙⢻⣿⣿⠉⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠿ ⠿⠿⣿⣁⣄⣤⣶⣶⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠻⠇⠐⡆⠦⡀⣀⣠⣤⣸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠘⠋⠛ ⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣿⣿⣿⣧⠀⠀⣠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢻⣿⣿⣿⣿⣿⠋⠀⠀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⣤ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⠀⠀⠉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠃⠀⠀⣰⣿⣧⣹⣧⣦⣤⣄⠀⠀⠀⢀⣤⡿⠀⠀⠀⠀⡠⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡄⠁⠀⠀⠀⢰⡿⣻⣿⣿⣿⣿⣿⣿⣦⡤⠖⠰⠻⠃⠀⠀⠀⣼⣃⡤ ⠙⠋⠛⠛⠟⢻⣿⡿⠂⠰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⠐⠀⠀⠀⠀⠻⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⣄⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣧⣀⠀⠒⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⠿⠿⣿⣿⣿⡇⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣷⣿⣿⣿⠄⠤⡄⠀⣠⠀⢀⢀⣿⣿⣿⣿⣷⣤⡤⠀⠴⠦⠀⠀⠀⠀⠙⠉⠑⣿⣿⣿⠃⢀⡀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢰⣿⣿⠁⢀⣼⠋⠀⢀⢼⣿⡿⠃⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⣠⣤⣿⣿⣿⠏⣾⣤⣤⣤⣀⣴⡶⠦⠀⠀⠫⠼⣿⣟⡋⠀⠈⠋⢀⣠⡿⢿⠟⠁⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⡀ ⠀⠀⠀⣺⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⡟⠉⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣼⣿⡂⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⣈⢫⣿⣿⣿⣿⣿ ⠀⢰⣿⣯⣽⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⡧⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣿⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⢿⣿⣧⣼⣿⣿ ⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢠⣦⡴⠖⢲⣟⠋⢹⡉⠙⠟⣿⣿⣟⣿⣿⣿ ⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣷⣶⣾⣿⣶⣾⡟⢿⣿⣿⣯⣭⡽⠿⣿ ⡿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⢿⣿⡛⣿⡇⠈⠙⠿⠛⠛⠃⠐⠻ ⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠈⠙⠻⠟⠟⠃⠸⢿⡉⠉⠙⠛⠻⠿⣿⣿⢻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⠈⠉⢸⣿⣿⣿⣿⣿⣧⡀⠀⠀⠹⣿⣿⣿⣿⣯⣽⣿⣾⣿⣿⣿⣶⣶⡶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡯⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣿⣿⣷⣦⡀⠀⠀⠈⠩⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣎⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢿⣿⣿⣶⠶⡂⠒⠿⣿⣿⣿⣿⣿⠀⢀ ⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠛⠛⠑⢒⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠻⣿⣿⣿⡿⠛⠛⠛⢿⡻⣿⣛⣛⣛⣀⣿⣿⣿⣿⣿⣧⣤⠀⠀⠈⢻⣿⣿⠉⣁⠀⠀⢿⣿⣿⣿⣿⣦⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢟⣉⣁⣈⣉⡉⠉⣩⣭⡉⠽⠛⠙⠛⠛⠿⣿⣿⠇⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⣿⣿⣿⣿⣤⣤⣤⣭⣿⣿⣿⣿⣦ ⣶⣶⣿⣿⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠒⢻⣿⣿⣿⣿⣿⣯⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣷⣟⣿⡿⢿⣿⣿⣿⣿ ⠉⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠁⢀⣤⣽⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠙⠋⢘⣰⣛⣯⡽⠀⢀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢰⣿⣿⣿ ⣿⣿⣿⣿⢿⣿⣿⣇⠀⠀⠈⣾⣿⣿⣯⣼⡷⣶⣿⠿⠿⣿⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣗⣤⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⠄⠀⠉⠀⠀⠀⠚⠑⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⡿⣿⣿⠇⠀⠀⠀⣠⣴⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⣖⠂⡀⣄⢀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠻⠍ ⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⠀⠀⢠⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠠⠄⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠉⢉⣦⣽⣶⣦⣤⡀⠀⠀⠀⣀⡀⢿⠀⠀⠀⠀⢀ ⠀⣠⣤⣤⣀⣹⣿⣿⣿⣿⣟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⢿⣿⣿⣿⠟⠁⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⠾⠞⠟⠷⠒⠀⠀⣠⣤⠤ ⠐⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠂⠁⠀⠀⠀⠀⠛⠻⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⣿⣉⡀⠀⠀⠀⢶⣿⣿⣿⣿⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠿⠿⠿⠟⠋⠀⠀⠀⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣦⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⢀⣿⣿⣿⣿⡇⢀⠄⠀⢛⣿⣿⡿⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⣿⣿⣿⠦⠠⠤⠀⠠⠄⠠⠀⣾⣿⣿⣿⣿⡧⠴⠀⠰⠶⠀⠀⠀⠀⠈⠉⠁⣻⣿⡟⠁⠀⢠⡀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⣠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢀⡚⠁⠀⢠⣸⡿⠃⠀⠀⠀⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣦⣬⣿⣿⡿⠀⢠⠀⠀⣀⣤⣤⣤⣾⣧⣿⣿⣿⣷⣶⣤⣄⢂⠀⠀⠀⠀⠒⠀⠈⣻⠁⠀⠀⠈⠀⢀⣰⠿⠿⠁⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⣀⡀⢠⣤⣤⡄ ⠀⠀⠀⡈⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠁⠀⠈⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣀⣈⣹⣵⠿⢿⣧ ⠀⠀⣾⣧⣤⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⢀⣼⣿⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⡿⣿⣿⣦⣽⣿ ⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣶⣄⠒⠛⣿⡋⠉⣏⠁⠻⢱⣿⣯⣽⣿⣿ ⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢐⣿⣿⣷⣾⣿⣷⣶⢿⠋⣿⣿⣿⣦⣰⠙⠻ ⠿⠿⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⡄⠀⠀⠈⣿⣿⣿⠿⢿⣟⢿⣿⡀⠈⠛⠋⠙⠋⠀⠐ ⠾⠾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠟⠀⠀⠈⣿⣿⣿⣿⣿⡈⣛⣍⣋⠙⠛⠋⠉⠛⠛⠡⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠏⢀⡀⣠⣿⣿⣿⣿⣷⡀⠀⠀⠘⢿⣿⣿⣿⣿⣯⣿⡿⢿⣿⣿⣿⣦⡰⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣀⠀⠀⠀⣿⢿⣟⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠠⣶⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣾⣿⣷⣹⣹⣿⣿⣿⣿⣯⠀⠀⠀⠉⢻⣿⣷⠲⣖⠈⠺⢿⣿⣿⣿⣿⡇⠀ ⠀⠈⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣛⠉⣉⣀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠹⣿⣿⡿⠃⠀⠀⠀⠈⢙⣟⣛⣿⣭⣉⣼⣿⣿⣿⣿⣧⣤⡄⠀⠀⠘⣿⣿⡏⣁⡄⠀⠸⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣆⣤⣤⣤⡀⣨⣭⡭⠈⠁⠀⠈⠀⠈⠻⢿⠟⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⢹⣿⣷⣿⣷⣀⣠⣬⣽⣿⣿⣿⣷ ⣶⣿⣿⣿⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣟⣿⡆⠀⠀⢈⣿⣿⣿⣿⣶⢾⣿⣿⣿⣿⣿⣿ ⠀⠘⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣀⠀⠀⠉⠀⠀⠀⣤⣤⣽⡿⠛⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⠀⠀⠀⢀⣤⣤⣼ ⠟⠷⠀⠙⠿⠿⣿⡇⠀⠀⠀⠸⣿⠿⠃⠀⠀⠀⠀⠀⠈⠉⠋⠹⡆⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⢀⣠⣾⣿⣿⣿⠂⠀⠀⢸⣿⣿⣿ ⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡿⠀⠀⠀⣼⣿⣿⣿⣿⡿⠂⠀⠀⠸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣿⣿⡏⠙⠉⠁⠀⢠⣼⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⣿⠋⠉ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡧⠀⠀⠀⢠⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣤⣒⣶⣶⣿⣿⡿⠟⠀⠒⠂⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⡀⢀⠀⠒⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⢶⣶⣿⣿⣿⠏⠋⠁⣀⡉⠿⣿⣿⣷⣶⡾⠂⠈⠀⠀⠀⠀⢀⣠⠤ ⠀⠀⢀⢆⠤⠀⠘⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣼⣦⣹⣿⡿⠋⠁⠀⠀⢸⣿⣧⢄⡈⢻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠣⠈⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣟⣼⣷⡄⠈⠉⠉⠀⠀⠀⠀⠀⠀⣉⣀⢠⠿⡿⣿⠏⠀⠀⠀⠀⠠⣿⣿⡿⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣤⠦⠠⠤⠀⠠⠤⠀⠀⣸⡿⠹⢿⣿⡷⠶⠀⠐⠒⠀⠀⠀⠀⠈⠉⠁⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⣥⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣀⣠⣤⣤⣾⣅⢸⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠛⢿⠇⠀⠀⠀⠀⢈⡀⠀⢀⢀⡄ ⠀⠀⠀⠀⠙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡀⠱⣢⡶⠒⣷ ⠀⠀⣸⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⣀⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣷⣆⣀⣀⣀⠀⣴⣦⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡹⢠⣿⣷⣤⣿ ⠀⢰⣿⡻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠀⠀⢀⠀⠘⣃⡸⢯⣤⡝⠛ ⣾⣿⡷⢷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣦⣴⡲⣶⣿⠀⢿⣿⣿⣷⡄⠀⠀ ⠟⠉⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣿⡿⠁⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⠉⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣿⡄⠀⠀⠀⠘⣿⣿⠟⠛⠇⠈⢟⠀⠀⠈⠉⠉⠉⠀⠀ ⠀⠰⣿⡅⣠⣤⡀⣤⣤⣠⣤⢠⣤⡄⢀⣤⣤⣄⠀⠀⣠⣤⣤⣄⢸⣿⣿⣿⣿⣤⣭⣠⣭⣭⣍⡉⠁⠀⣠⣤⣾⣿⣿⣷⣶⣿⣿⣿⣿⡿⢣⣤⣤⣤⡻⢿⣿⣿⣷⢀⣤⡄⣠⣬⣿⣷⣦⣾⣤⢼⣾⢿⣿⣿⣿⣶⡀⠀ ⠀⠀⣿⣇⣿⣿⡇⣿⡏⣿⣿⣸⣿⡇⣿⣿⢹⣿⠀⠀⣿⣿⡹⠿⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡿⢿⢿⣿⡏⢹⣿⡟⠙⢂⢸⣿⣿⣿⣧⣿⣿⣿⣿⣯⣿⡇⣿⣿⣿⣿⣿⣿⣿⣼⣿⠻⢿⣿⣿⣿⣗⠀ ⠀⠀⢿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⢸⣿⡄⠀⣉⣻⣿⣷⣰⣿⣿⣿⡏⣿⣿⢻⣿⣿⣿⣿⠀⠀⣙⡻⣿⣯⢸⣿⡇⢸⣿⡇⠀⠀⣸⣿⣯⣿⣧⣿⣿⣿⣿⣧⣿⣷⣿⢿⣿⣿⡿⣿⣿⣿⣿⠀⣶⣿⣿⣿⣿⡄ ⠀⠀⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⢠⣿⣿⣼⣿⣻⣿⡟⣿⣧⣿⣿⢸⣿⣷⣿⡿⠀⠀⢿⣧⣿⡿⢸⣿⡇⢸⣿⡇⠘⠻⢿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠁⣿⣯⣿⣿⣀⣿⣧⣭⣭⣼⣷ ⣳⣿⣾⣿⡿⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠈⠉⠀⠀⢰⣷⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠄⠀⠈⢿⣿⣿⣿⠋⣰⠀⠀⠀⠀⠀⣸⣷⣞⡥⠤⣭⣽⢿⣿⣿⣿ ⣀⣀⡘⢿⣿⣿⣿⡇⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠰⣶⣾⣿⡋⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⢃⣴⣾⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠙⠈⠛⠛⠿⠇⠀⠀⠀⠈⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⢻⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⣿⣿ ⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⢺⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⢮⣉⠳⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⡿ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⠻⠿⠯⢃⡔⣀⣿⣤⣿⣶⣄⡀⠀⣸⣿⢠⣤⣤⠀⠈⠉⠋⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠀⠀⠀⠀⣨⠟⢻⣿⣿⡟⣿⣿⣿⣶⣿⣿⣾⡏⠒⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣦⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣠⣤⣤⣤⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠶⣴⣆⠀⠉⠻⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣾⣷⡄⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⢀⠼⠗⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠿⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⠔⠀⠐⠀⠀⠂⠀⠀⢰⡿⠉⠛⣿⣿⣷⠂⠀⠚⠃⠀⠀⠉⠁⠁⠀⢀⠀⠀⠙⠛⠛⠋⠀⠀⠀⢀⣾⠟⠁⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⣮⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣄⣸⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⢿⢿⠀⠀⠀⠀⠀⣀⠀⢠⡀⣤ ⠀⠀⠀⣀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⢖⣴⠖⢾ ⠀⠀⢠⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⣁⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣄⣀⣀⣀⡀⢰⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡉⢇⣼⣿⣦⣼ ⠀⢠⣿⢯⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⡀⠐⠒⠐⠀⠀⢀⡀⠈⣋⣀⠿⣤⣬⠛ ⣾⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣿⣷⣴⡶⢶⡞⡏⠹⣿⣿⣷⣦⡀⠀ ⡾⠁⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⣿⡇⣬⠿⣿⣿⣿⣿⠿⠿⢿⠿⠟⣁⣀⠙⣿⣿⣿⣿⣿⣿⡟⠻⠿⠟⣿⣿⣿⣿⡆⠀⠀⠀⠐⢿⣿⡙⠛⠓⠀⢹⠃⠀⠀⠉⠁⠈⠁⠀ ⠀⠐⣯⡄⢠⣤⡀⣤⣤⣠⣤⢠⣤⡄⢀⣤⣤⣀⠀⠀⣠⣤⣤⣄⠀⣿⣿⣿⣿⣿⣤⣤⣤⣤⣭⡉⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢡⣤⣤⣤⡟⢿⣿⣿⣿⣠⣤⡄⣤⣤⣻⣿⣧⣼⣦⢴⣷⢿⣻⣿⣿⣷⣆⠀ ⠀⠀⣿⣇⣿⣿⡇⣿⡏⣿⣿⣸⣿⡇⣿⣿⢹⣿⠀⠀⣿⣿⡹⠿⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡿⣿⢹⣿⡏⢹⣿⡏⠁⠀⢸⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣼⣿⠹⢿⣿⣿⣿⣿⡀ ⠀⠀⢿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⢸⣿⠀⠀⣈⣻⣿⣷⣴⣿⣿⣿⡇⣿⣿⢹⣿⡿⣿⣿⠀⠀⣙⡻⣿⣧⢸⣿⡇⢸⣿⡇⢀⣀⣸⣿⣯⣿⣧⣿⣿⣿⣿⣧⣿⣷⣿⢿⣿⣿⡿⣿⣿⣿⣿⠀⣶⣾⣿⣿⣿⣧ ⣀⠀⢸⣿⣿⢾⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⠀⢿⣿⣾⣿⣻⣿⡟⣿⣧⣿⣿⢸⣿⣧⣿⡿⠀⠀⢿⣧⣿⡿⢸⣿⡇⢸⣿⡇⠈⠛⢻⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠁⣿⣇⣿⣿⣀⣿⡧⣬⣭⣥⣿ ⣿⣿⣿⣿⣿⢷⠄⠰⠶⠶⠖⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠀⠀⣻⣿⣿⣿⡉⢰⡆⠀⠀⠀⠀⣸⣿⣾⣺⠤⢬⣭⡽⣿⣿⣿ ⣶⣶⣶⠸⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⠿⠇⠀⠀⠀⠀⠀⠘⠿⢿⣿⣄⡉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠇⠀⠀⠀⠈⠋⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠅⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠻⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣧⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠉⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤ ⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠡⣴⣿⣿⣿⣆⣼⣷⣄⠀⠀⠀⠀⢀⡤⠦⠀⠈⠉⣵ ⠀⠀⠀⠀⠀⠈⠙⠛⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢃⠀⠀⠀⠀⡀⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠉⠉⠛⠓⠀⠿⣿⣿⣿⣿⣿⣿⣿⡷⠞⠛⠀⠀⠀⠀⠀⠀⣴⣿ ⠀⠀⠀⠀⠀⠘⠛⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⣳⣄⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣤⠈⣿⣿⣆⣀⣤⢶⠶⠒⠋⢸⣿⣿ ⠀⠀⠀⠀⠀⣠⡼⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣿⣿⡅⠀⠈⠉⠉⠁⠀⠀⢠⣤⠔⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠘⠃⠙⠋⠉⠁⠀⠀⠀⠀⠀⠘⠻⣿ ⠀⠀⠀⠀⠀⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡖⠀⠀⠁⠀⠐⠀⠐⠀⣿⠏⠉⠻⣿⣿⡟⠀⠈⠉⠀⠀⠀⠀⠀⠀⣠⠄⠠⣶⣶⣶⣶⠖⠀⠀⠀⢰⡟⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣿⣿⣿⣿⣄⣠⣀⣠⣼⠀⠀⣀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣧⣬⣽⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉⠁⠙⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⢠⡤⠀⢀⣤ ⠀⠀⠀⢠⣄⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠻⠿⠛⠁⠀⠀⠁⣠⡄⢰⠂⣲⡟ ⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣦⣤⣤⣤⣸⣶⣶⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡙⢠⣾⣿⣷ ⢀⣤⣿⣯⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣷⣶⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⣆⠀⢘⣃⣘⠿⠤⠬ ⣿⣿⠛⢋⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢟⣿⠿⠝⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣻⣿⢛⠉⢿⣿⣿⣷⣄⠀ ⠛⠃⢠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠿⠀⠀⠀⠙⠿⣿⣿⡿⠿⠟⢿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠈⠉⢙⢿⣿⣿⣿⣧⠀⠀⠀⠀⠹⣿⡉⠛⠛⠁⠙⣿⡀⠀⠈⠉⠀⠉⠁ ⠀⠀⣤⡄⢠⣤⡄⣤⣤⣠⣤⢠⣤⡄⢀⣤⣤⣄⠀⠀⢀⣤⣤⣄⠀⣠⣤⣤⠀⣤⣤⣶⣷⣦⣤⡀⠀⠀⣠⣤⣿⣿⢫⣥⣤⣤⣼⣥⡝⠙⢠⣤⣤⣤⡾⢿⣿⣿⣿⣦⣤⡄⣤⣤⣹⣿⣿⣴⣷⢶⣾⢾⣿⣿⣿⣿⣷⡀ ⠀⠀⣿⣇⣿⣿⣧⣿⡏⣿⣿⣸⣿⡇⣿⣿⢹⣿⠀⠀⣿⣿⣿⠿⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⡿⢸⣿⡏⢹⣿⡏⠁⠠⢸⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣽⣿⠘⠿⣿⣿⣿⣿⣯ ⠀⠀⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⢸⣿⠀⠀⣈⣻⣿⣷⣹⣿⣟⣿⡇⣿⣿⢸⣿⡟⣿⣿⠇⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⢤⣤⣼⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⠀⣶⣾⣿⣿⣿⣿ ⣶⣦⣼⣿⣿⣿⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣾⡿⠀⠀⢿⣿⣿⣿⣿⣿⡟⣿⣧⣿⣿⢸⣿⣷⣿⡿⠀⠀⢿⣧⣿⡿⢸⣿⡇⢸⣿⡇⠀⠈⢹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠃⣿⣧⣿⣿⣀⣿⡧⢤⣬⣿⣽ ⣿⠿⠿⣿⠿⢿⠕⠰⠶⠶⠶⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠖⠒⠀⠀⢿⣿⣿⣿⡄⢰⡆⠀⠀⠀⠀⣼⣿⣿⣷⡤⢴⣯⣭⣿⣿⣿ ⣿⡿⠿⠒⠻⠿⢿⣿⠀⠀⠀⠀⠚⢻⠋⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣧⣄⠁⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⢀⣿⣷⣠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣿⣿⣿⠐⢀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⣷⣄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤ ⠀⠀⠀⠀⠈⠻⠿⠟⠛⢉⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⠀⠠⣾⡞⣽⣿⣧⣿⣷⡄⠀⢀⡀⠀⠴⠖⠂⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠄⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢿⣿⠟⠛⠛⠛⠁⠀⠀⣿⣃⣿⣿⡯⠿⣿⣿⠛⠋⠁⠀⠀⠀⠀⣀⠀⠤ ⠀⠀⠀⠀⠀⠀⠛⢳⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⣰⣷⣠⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢯⡀⢸⣿⣇⣤⠴⠾⠂⠘⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣧⠀⢀⣀⠀⠀⠀⠀⠠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠘⠇⠈⠉⠉⠀⠀⠀⠀⠀⠀⢠⣴⣿ ⠀⠀⠀⠀⠀⠘⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠂⠀⠁⠁⠈⠁⠈⠁⢸⡟⠉⠙⣿⣿⣿⠁⠈⠉⠀⠀⠀⠀⠀⠀⠤⠀⣤⣤⣤⣀⡀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢹⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿ ⠀⠀⠀⠀⠺⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⣠⣶⣶⣶⣿⣶⣤⣷⣿⣿⣶⣶⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠀⢤⣦⣤⣀⡀⠀⠀⠀⠀⢀⣴⡆⠀⠀⣀⠀⠀⣄⠘⠿⣿ ⠀⠀⠀⢠⣦⣄⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠺⠇⠀⠈⠿⠇⠀⠀⢀⣀⣤⣠⡟⢰⣿ ⠀⠀⢰⣾⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣔⣶⡖⡶⢦⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠃⠀⠀⠀⣀⠀⠈⠋⣄⠋⣵⣿⡿ ⢀⣴⣿⣿⣾⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠸⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢠⡀⣀⣙⣀⡙⠷⠦ ⣿⣿⠏⢋⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⡀⡄⠀⠋⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⣦⣹⣻⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣶⡏⣿⡟⡁⠹⢿⣿⣿⣦⣄ ⠉⠁⠰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠻⠿⣿⣿⣷⡿⠿⠿⢿⣿⡿⣿⡟⠀⠀⢀⢙⣿⣿⣿⣿⡀⠀⠀⠀⠈⢻⣏⠙⠛⢃⠀⢳⣃⣀⣀⣉⣀⠈⠉ ⠀⠀⣤⡄⣠⣤⡀⣤⣤⣠⣤⢠⣤⡄⢀⣤⣤⣀⠀⠀⢀⣤⣤⣄⠀⣠⣤⣤⣀⣤⣴⣾⣿⣷⣦⡀⠀⠀⣠⣤⣽⡿⢡⣤⣤⣤⣤⣭⡄⠊⢡⣤⣶⣶⡎⢙⣿⣿⣿⣧⣤⡄⣠⣤⡈⣿⣿⣴⣟⢲⣾⠻⣻⣿⣿⣿⣿⣧ ⠀⠀⣿⡇⣿⣿⣷⣿⡏⣿⣿⣸⣿⡇⣿⣿⣿⣿⠀⠀⣿⣿⡹⠿⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⡿⠿⢸⣿⡏⢹⣿⡏⠁⠐⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⣿⣿⣿⣿⣿⣿⠰⠿⢿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⢿⣿⠀⠀⣈⣻⣿⣷⣠⣿⣟⣿⡇⣿⣿⢸⣿⡏⣿⣿⠟⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠰⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣿⣿⣿⣿⠀⣶⣾⣿⣿⣿⣿ ⣶⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣿⡿⠀⠀⢿⣿⣼⣿⣿⣿⡟⣿⣧⣿⣿⢸⣿⣧⣿⡿⠀⠀⢿⣧⣿⡿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠁⣿⡷⣿⣿⠤⣿⣇⣲⣶⣦⣤ ⠿⠿⠿⣿⠿⢷⠗⠰⠶⠶⠶⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣉⣁⣠⡄⠀⠀⠀⠀⠀⠶⠶⢒⣒⠒⢊⠀⠀⠈⠛⣿⣿⡄⢀⡇⠀⠀⠀⠀⢸⣿⡿⢿⣶⣷⣶⣟⣻⣿⣿ ⠿⠻⠟⠁⠙⠛⠿⣿⠀⠀⠀⠀⠚⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢷⣄⡈⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⣷⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⢀⣿⣿⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⡀⠀⠖⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⢿⢿⡾⣷⠀⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶ ⠀⠀⠀⠀⠀⠛⠛⠋⠉⢉⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡋⠀⠀⡾⡮⣽⣿⡇⣾⣿⣆⠀⣀⣀⠂⠰⠚⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⢦⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⠛⠛⠛⠀⠀⢀⣀⣰⣿⣿⣿⠻⣿⣿⡋⠉⠁⠀⡀⠀⣀⣤⡴⠶ ⠀⠀⠀⠀⠀⠀⠛⠓⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣼⣿⢤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⣿⣿⢿⡆⢈⣿⣧⣤⠶⠞⠃⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣇⠀⢀⣀⡀⠀⠀⠀⠠⠴⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠸⠇⠈⠫⠥⠄⠀⠂⠀⠀⠀⠀⠠⢾ ⠀⠀⠀⠀⠀⠀⠻⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠉⠀⠈⠉⠀⠁⢸⡟⠁⠈⣿⣿⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠰⢀⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⣀⠀⠀⠀⠀⣤⣄⣀⣀⣀⣤⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⠿⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⠀⠀⠀⠀⠸⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣀⣠⣶⣶⣾⣿⣷⣿⣿⣿⣿⣷⣶⣦⡀⠀⣀⣀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠤⣤⣀⠀⠀⠀⠀⠀⠀⢠⣶⡦⠀⠀⢀⠀⠀⢿⣿⣿⣿ ⠀⠀⠀⠀⣶⣤⣐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣶⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⡖⠶⠀⠀⠀⠿⠇⠀⠀⢀⣠⣶⣼⣿⣿⣿ ⠀⠀⢰⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣮⣿⣾⣿⣂⡀⠀⠀⠀⠀⠉⠉⠀⠀⠑⠀⠀⠀⠀⡀⠀⠀⠉⣴⠈⢿⣿⣿ ⢀⣴⣿⣿⡿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠛⢫⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⢿⡏⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⣀⣘⣄⣀⣬⣤⣄⠛⢿ ⣿⣿⡟⠉⣱⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣄⠀⠈⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣄⣵⣿⣿⣿⣿⡿⠟⠈⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⠿⣏⡇⠘⠿⣿⡿⠷⣾ ⠉⠉⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠛⠏⢻⣿⣿⠿⠛⠛⠻⢿⡟⢿⡟⠀⠀⢀⣘⣻⣿⣿⣿⡆⠀⠀⠀⠀⢹⣧⣉⡉⢉⡀⠸⡧⣀⣤⣀⣀⣀⠀ ⠀⢀⣤⣄⣠⣤⡀⣤⣤⣠⣤⢠⣤⡄⢀⣤⣤⣄⠀⠀⢀⣤⣤⣄⠀⣠⣤⣤⣠⣤⣴⣿⣿⣿⣦⡄⠀⠀⣠⣤⣼⡟⢡⣤⣤⣤⣤⣤⡄⢀⢱⣴⣶⣶⡿⢁⣽⣿⣿⣿⣤⡄⣠⣤⡀⣽⣿⣵⣝⣻⣿⠛⣿⣭⣿⣿⣿⣯ ⠀⠀⣿⡏⣿⣿⣗⣿⡏⣿⣿⣸⣿⡇⣿⣿⣿⣿⠀⠀⣿⣿⡹⢿⠂⣿⣿⣿⡟⣿⣿⢿⣿⣿⣿⣿⣦⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡿⣿⣇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⣿⡟⣿⣿⣽⣿⠐⠿⠏⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⣹⣿⠀⠀⣈⣻⣿⣿⣷⣿⣟⣿⡇⣿⣿⢸⣿⡇⣿⣿⠋⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠐⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⣿⣿⠀⣶⣶⣿⣿⣿⡿ ⣿⣷⣿⣿⣿⣿⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣿⣿⠀⠀⢻⣿⣽⣿⣿⣿⡟⣿⣧⣿⣿⢸⣿⣧⣿⡿⠀⠀⢿⣧⣿⡿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⣿⡟⢻⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⠁⣿⣧⣿⣿⢀⣿⣧⣓⣶⣶⣶ ⠛⠿⠿⣿⠿⢷⠆⠰⠶⠶⠶⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣄⣀⣉⠥⣤⡤⠀⠀⠀⠀⠀⠐⠒⢒⣛⡋⠉⠁⠀⠈⢻⣿⣿⣯⢡⣿⠀⠀⠀⠀⠩⣿⣟⣿⣷⣷⣿⣿⣿⣿⣿ ⡿⠿⠟⠀⠙⠛⠻⠿⠀⠀⠀⠀⠙⠋⡙⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⢶⣀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡭⢿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣤⣤⣤⣴⣶⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⡗⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⣼⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣅⠀⡀⠀⠲⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⠛⠛⠻⣿⣿⣆⠀⣴⡄⠀⠀⠀⢀⠀⣀⣀⠀⠀⠛ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠈⠙⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣸⣿⣿⣤⣤⠶⠈⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄⠀⠀⠀⠠⠀⠀⠀⠹⠿⠟⢳⣄⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠸⠟⠉⠉⠛⠋⠀⠀⠀⠀⠀⣿⣿⣿⠉⢻⣦⡅⠀⠀⢀⣤⠀⣤⠴⠂⠀ ⠀⠀⠀⠀⠀⠀⠘⠓⢶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⡰⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠈⢻⠷⠖⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣀⡀⠀⣤⡄⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠘⠃⠀⠠⣄⡀⠀⠀⠀⠒⠛⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠨⢿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣦⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣀⠀⠀⢀⣼⣶⡀⣠⣀⡀⠀⠀⠀⣠⣀⡀⠀⠀⠄⠀⠹⠿⠿⠿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⢀⠀⠈⠓⠠⣤⣀⣀⣠⣤⣤ ⠀⠀⠀⠀⠘⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡞⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣀⡀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠉⢁⡀⠀⠀⠙⠿⠄⢀⣴⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⣾⣾⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡇⠀⢼⣿⣷⣾⡧⣚⣲⣀⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⢦⣾⣿⣿⣿⣿⣿⣿⣿ ⢀⣴⣾⣿⣷⢷⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠉⢹⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣈⠻⠃⢀⣾⣿⣿⣿⡿⠛⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢴⣦⣤⣄⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⡟⠉⣡⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣹⣷⣶⣿⣿⣿⣿⡟⠃⢀⡘⢿⣿⣿⣿⡄⠀⠀⠀⠀⠺⣿⠿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠏⠉⠁⠀⠀⠀⢀⣀⣙⠛⠛⠛⠛⠋⠀⠉⣽⡷⠚⠉⠉⠛⠿⠯⠙⠟⠁⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢿⣦⡄⢀⣄⣿⣿⣿⣿⣿⣿⣿⣾ ⠀⢤⣤⣄⣠⣤⡀⣤⣤⣠⣤⢠⣤⡄⢀⣤⣤⣄⠀⠀⢀⣤⣤⣄⠀⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣦⠀⠀⣠⣤⣤⡇⢠⣤⣤⣤⣤⣤⡄⠀⢠⣤⣿⣿⡿⣿⣿⣿⣿⣿⣧⡄⣠⣤⡀⣤⣿⣧⣤⢤⣭⠛⣻⣿⣿⣿⣿⣿ ⠀⠀⣿⡇⣿⣿⡗⣿⡏⣿⣿⣸⣿⡇⣿⣿⢹⣿⣯⠀⣿⣿⡹⠿⠀⣿⣿⣿⡟⣿⣿⢻⣿⣿⣿⣿⣷⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⣟⣿⣧⣿⣿⣿⣿⣿⣿⣇⣿⣿⣧⣿⡏⣿⣿⣼⣿⠀⠿⠏⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⣼⣿⠉⠀⣈⣻⣿⣷⣺⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠙⢻⣿⡿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⣿⣿⠀⣶⣦⣿⡿⣻⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣿⡿⠀⠀⢻⣿⣼⣿⢻⣿⡟⣿⣧⣿⣿⢸⣿⣧⣿⡿⠀⠀⢿⣧⣿⡿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣷⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠁⣿⣿⣿⣿⣉⣿⣟⣛⣿⣿⣿ ⠛⠿⠿⣿⠏⢷⠔⠰⠶⠶⠖⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠴⠤⠽⠓⠲⠒⠂⠀⠀⠀⠀⠈⠉⠩⠭⠅⠐⠂⠀⠈⠉⢩⣼⣿⢂⣾⡇⠀⠀⠀⠀⢹⣿⣭⠿⢛⢿⣿⣿⣿⣿ ⠉⠭⠁⠀⠈⠉⠙⠟⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠶⢿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠄⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠻⡿⠿⠿⠿⠿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠟⠛⠛⢻⢣⣿⡄⢀⣷⡄⠀⠀⢀⡀⣀⠤⠄⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⠀⠀⠈⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠠⢠⣾⣿⢁⣾⡿⣧⠴⠞⠃⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣥⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠋⠀⠉⠙⠋⠀⠀⠀⠀⡀⣽⣿⣿⠋⠛⣷⣦⠀⢀⣀⣴⠀⠰⠒⠋⠀ ⠀⠀⠀⠀⠀⠀⠘⠛⢲⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⢿⡀⠀⠸⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀⠀⡀⠀⣼⣿⣿⣿⣧⣤⠄⠀⠴⠆⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠁⠀⠀⣀⠀⠀⠀⠒⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣤⣤⣤⡀⠀⠿⡏⠉⠀⠃⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⡾⠙⣛⣹⣇⣀⣴⣿⣤⣰⣦⣄⣀⡀⢻⣿⣿⣷⠀⠐⠆⠀⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⣘⢁⡀⠀⠀⣿⡆⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠹⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣾⠟⢀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠿⠛⢿⡦⠀⢹⣿⣦⢀⣾⣶⣦⣤⣴⣯⣤⣀ ⠀⠀⠀⠀⢸⣦⣤⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣿⣿⣿⣿⡿⢿⠛⣿ ⠀⠀⢸⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠙⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣿⡇⠀⢼⣿⣿⣾⡆⢀⣤⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠷⠀⠙⠻ ⢀⣴⣿⣿⣿⢻⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢈⣧⡀⠸⠇⢘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣜⣁⣠⣾⣿⣿⣿⣿⠹⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣶⣄ ⣿⣿⡟⠁⢠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡇⠀⠀⠀⠀⠀⠀⢼⢿⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⠿⠿⡿⢟⢀⣸⣿⣿⣿⣿⣿⣿⡏⠙⣷⣜⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠙⠋⠙ ⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠚⠀⠀⠀⢀⣠⣤⣤⣌⠉⠋⠉⠁⠀⠀⢰⠟⠋⠀⠀⠉⠙⠛⠋⠋⠁⢀⣹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⣿⣿⣿⣿⡿⢿⣿⣯⣵⡶⠶⢶⣶⣦ ⠀⠤⣤⣤⣤⣤⡄⣤⣤⣠⣤⢠⣤⡄⢀⣤⣤⣄⣄⠀⢀⣤⣤⣄⠀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣷⡀⠀⣠⣤⣤⡄⢠⣤⣤⣤⣤⣤⡄⠀⢠⣤⣿⣿⡟⢿⣿⣿⣿⣿⣷⡄⣠⣤⡀⣬⣭⣷⣦⢶⣶⠀⣠⣿⣿⣿⣿⣿ ⠀⠀⣿⡇⣿⣿⡏⣿⡏⣿⣿⣸⣿⡇⣿⣿⢹⣿⣿⠄⣿⣿⡹⠿⠀⣿⣿⣿⡟⣿⣿⢹⣿⡿⣿⣿⠿⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⢀⣸⣿⣟⣿⣧⣿⣿⣿⣿⣿⣿⣧⣿⣿⣧⣿⡟⣿⣿⣼⣿⠀⠿⠇⣿⣿⣿⣿ ⣀⣀⣿⣿⣿⣿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⣼⣿⠅⠀⣈⣻⣿⣷⣸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢹⣿⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⣿⣿⢀⣶⣦⣿⣿⣛⣛ ⣿⣿⣿⣿⣿⢿⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣿⡿⠒⠒⢿⣿⣼⣿⢻⣿⡟⣿⣷⣿⣿⢸⣿⣧⣿⡿⠀⠀⢿⣧⣿⡿⢸⣿⡇⢸⣿⡇⠀⣀⣸⣿⣷⣿⡧⢻⣿⣽⣿⣿⣿⣿⣿⣼⣿⣿⠁⣿⣿⣿⣿⣤⣿⣯⣭⣶⣿⣿ ⠉⠿⠿⣷⠿⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⢒⡙⠛⠉⠙⡃⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠁⠀⠈⢩⢿⣿⡿⢃⣿⡇⠀⠀⠀⠀⢩⡭⢞⣛⠽⣻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠠⡀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠟⠛⠛⠛⣻⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠙⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⡗⣿⣧⠀⣠⣄⠀⠀⠀⡀⢀⡤⠄⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠘⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣴⣿⠇⠀⠉⠟⠶⠖⠃⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣄⣀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠙⠋⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⣠⠄⢀⣀⣠⠆⠀⠒⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⡄⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡇⠀⠀⠐⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠠⠄⢠⣴⣶⣾⠾⣿⣿⠟⠛⢿⠤⠆⠀⣶⣆⡀⠀⠀⠀⠉⠉⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣷⣾⠎⠀⠙⣇⠀⠀⠈⠀⠀⠰⣿⣿⣿⣧⠀⠀⠀⠀⣿⠿⠋⠁⠀⠀⢴⣾⣿⣿⣿⡯⠿⣿⡏⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠏⢀⣉⣥⣤⣤⣼⣿⣶⣶⣯⣤⣤⣄⡈⠛⣫⣽⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠁⠀⠈⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡘⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣶⣄⡀⠀⠚⠀⡀⠈⢠⣀ ⠀⠀⢀⣤⣼⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⡷⠾⠿⠩⠚⣽ ⠀⠀⣸⣿⣿⣿⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢈⡁⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⢿⡇⠀⢸⣿⣿⣷⡄⢀⣤⣤⣤⣄⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⠏⢩⠀⠀⠷⠀⠙⠛ ⣴⣿⣿⠿⠿⣹⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⠇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢴⣾⣤⣶⣾⣿⣿⣿⣿⢾⣿⣿⣿⣿⣆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢾⠇⠐⣿⣷⣶⣄ ⠿⠿⠇⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⡿⠟⠿⠟⢛⣄⣈⠿⣿⢿⣿⣿⣿⡏⠁⣾⣿⣿⣿⣿⣿⡆⠛⠿⠿⣿⣿⣿⣿⣿⡿⠀⠙⣇⠀⠀⠈⠙⠋⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⣀⣤⣶⣶⣶⣬⠉⠉⠉⠁⠀⠀⠀⠛⠁⠀⠀⠀⠈⠁⠁⠈⠀⣀⣽⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢹⣿⡍⠁⠧⣤⣼⣴⡶⠶⠶⣶⣦ ⠀⠫⣤⡔⣲⣤⣄⣤⣤⣠⣤⢠⣤⡄⢀⣤⣴⣤⣤⠀⢀⣤⣤⣄⠀⣤⣥⣶⣾⣿⣿⣿⣿⣿⣿⣓⡀⠀⣠⣤⣤⡀⢠⣤⣤⣤⣤⣤⡄⠀⢠⣤⣿⣿⡟⢻⣿⣿⣿⣿⣷⡄⣠⣤⠀⣤⣭⣷⣦⢶⣶⠀⣠⣿⣿⣿⣿⣿ ⠀⠀⣿⣇⣿⣿⡇⣿⡏⣿⣿⣸⣿⡇⣿⣿⢹⣿⡿⠆⣿⣿⡹⠿⠀⣿⣿⣿⡍⣿⣿⢸⣿⣟⣿⣿⠛⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡧⣿⣿⣧⣿⡟⣿⣿⣼⣿⠀⠿⠇⣿⣿⣿⣿ ⣤⣦⣿⣿⣿⣿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⣾⣿⡀⠀⣈⣻⣿⣷⣰⣿⣟⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡟⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⣿⣿⣀⣶⣦⣿⣿⣛⣛ ⣿⡿⢿⣿⣿⢻⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣿⡿⠃⠀⢻⣿⣼⣿⢹⣿⡟⣿⣧⣿⣿⢸⣿⣧⣿⡿⠀⠀⢿⣧⣿⡿⢸⣿⡇⢸⣿⡇⠀⣀⣸⣿⣷⣿⡗⢻⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠁⣿⣿⣿⣿⣤⣿⣯⣭⡶⣿⣿ ⠀⠖⠶⣶⠿⢶⣴⣴⠶⠶⠖⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢘⣚⣀⣛⣉⡉⠉⠈⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠹⣿⣿⣿⢡⣿⡇⠀⠀⠀⠈⣫⡭⢶⣫⡭⣻⣿⣯⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡿⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠁⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠷⠾⢿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠈⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⠛⠋⣿⣿⣯⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠘⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⠛⠻⠿⡆⣠⠀⠀⢨⣄⠀⠀⠀⠀⢀⡤⠤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⠀⠈⠻⣟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣵⡏⠀⠀⠀⢿⡗⠖⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠉⠃⠀⠀⠀⠀⠀⢸⣿⣇⠀⠈⠆⢸⠇⢀⣀⣠⠆⠀⠖⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣶⣄⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣤⡄⠀⠖⠛⠉⠁⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⠆⣰⣟⣟⢫⣟⣻⡿⠋⠉⢻⠶⠆⠠⣶⣶⣤⡀⠀⠀⠈⠁⢀⣀⡶⠗⠀⠀⣤⣶⣿⣿⣿⣿⠙⣿⣿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠛⢿⣿⠋⠀⠘⣧⡀⠀⡈⠀⠀⠀⠿⠿⠿⣷⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠛⠿⠛⠻⠿⠃⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡏⣠⣤⣤⣶⣶⣾⣿⣿⣷⣿⣦⣤⣤⣀⠀⣹⣿⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢩⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⠀⠀⠀⠐⠀⣀⠈⢡⠀ ⠀⠀⣠⣶⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢠⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢡⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣷⡆⠂⠼⠯⠄⠚⠉ ⠀⣠⣿⣿⣯⣿⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⢿⡏⠀⢸⣿⣿⣿⡄⢀⣤⣤⣤⣆⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡟⠉⠉⢀⡀⠀⠷⠀⠑⠉ ⣾⣿⣿⠟⠚⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣹⠀⠘⠃⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢶⣷⣶⣶⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣆⢰⣿⣿⣿⣿⣿⣿⣿⣿⣥⢤⣤⢾⠂⠐⣿⣷⣶⣄ ⠛⠛⠋⠠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠋⠛⢿⣿⣿⣿⣿⡿⠟⠻⠟⢋⣀⣸⣿⢿⣿⢿⡿⣿⡇⠉⣷⣿⣿⣿⣿⣿⡆⠉⠉⠻⠿⣿⣿⡿⠿⠿⠂⠙⣆⡄⠀⠈⠙⠛⠻ ⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣠⣴⣶⣿⣷⣤⡉⠉⠉⠀⠀⠀⠀⠛⠁⠀⠀⠀⠉⠉⠁⠈⠀⣀⣼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠻⣧⡤⠠⢧⣤⣼⣴⡶⠶⣶⣶⣦ ⠀⠀⣤⡄⣡⣥⡤⣤⣤⣠⣤⢠⣤⡄⢀⣤⣼⣤⡥⠤⢀⣤⣤⣄⠀⣤⣤⣾⢿⣿⣿⣿⣿⣿⣯⣣⠀⠀⣠⣤⣤⡀⢠⣤⣤⣤⣤⣤⡄⠀⢠⣤⣾⣿⡟⢿⣿⣿⣿⣿⣷⡄⣠⣤⡀⣤⣼⣷⣦⢶⣶⠀⣰⣿⣿⣿⣿⣿ ⠀⠀⣿⣇⣿⣿⣇⣿⡏⣿⣿⣸⣿⡇⣿⣿⢹⣿⡿⠆⣿⣿⡹⠿⠀⣿⣿⣿⡎⣿⣿⢹⣿⡿⣿⣿⠂⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⣼⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⡧⣿⣿⣷⣿⡏⣿⣿⣼⣿⠀⠿⠇⣿⣿⣿⣿ ⣶⣶⣿⣿⣿⣿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⣿⣿⣇⠀⣈⣻⣿⣷⢠⣿⣟⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡏⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣗⣿⣿⣿⣿⣀⣶⣦⣿⣿⣛⣛ ⠿⠟⢻⣿⣿⢹⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣿⡿⠁⠀⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣧⣿⡿⠀⠀⣿⣧⣿⣿⣸⣿⡇⢸⣿⡇⠀⠤⢸⣿⣷⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠉⣿⣿⣿⣿⣤⣿⣯⣽⡺⣿⣿ ⢀⣶⣶⣶⡿⢶⣶⢴⠶⠶⠖⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣙⣋⣠⠭⢭⡍⠉⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⠁⠀⠈⢻⣿⣿⡿⢡⣿⡇⠀⠀⠀⠈⣻⣍⣾⣫⣭⣻⣿⣭⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣼⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠏⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⣿⠟⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡟⠚⠋⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠀⠀⠀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣿⣿⠟⠃⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠀⠀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠛⣹⣿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠘⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠛⠻⠟⣧⣠⣿⣀⣀⣤⡄⠀⠀⠠⢀⡤⠶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⣹⣿⣧⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢹⡷⠛⠋⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠲⢦⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⣿⣿⡿⠃⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠈⠁⠀⠀⣠⣴⣾⣿⣿⣿⣿⠿⠁⠈⠃⢀⣠⣤⠆⠀⠒⠋⠁ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢀⣴⣾⣿⡿⠛⣵⣿⣿⣦⠀⠉⠀⣤⣤⣀⠀⠀⠀⣀⡀⠀⠀⣰⠖⠂⠄⣾⣿⣿⣿⢿⢿⣿⣿⣿⠀⠰⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠒⠂⣾⣿⣿⡿⠟⢸⣿⠋⠉⢹⡒⠓⠐⠻⣿⣿⣧⠀⠀⠀⠀⠴⠟⠃⠀⠀⠀⠉⠉⠀⠁⠀⣸⡿⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣾⣿⡿⠁⠀⠀⢈⣿⡄⠀⣀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣷⣶⣶⣦⣤⠀⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣄⡀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠷⠀⠀⠀⠈⠿⢃⣀⠀⢡⣀ ⠀⢀⣾⣷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣶⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢱⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣤⡀⣾⣿⣾⣶⠀⠀⠐⠲⠚⠛⠀⠉⢉ ⣀⣼⣿⣿⣷⢷⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢺⠁⢱⡄⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⡿⠟⢀⣸⣿⣿⣷⣄⢀⣀⣀⣠⣄⣴⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⢤⡀⠀⠷⠀⠙⠁ ⣿⣿⡟⠁⣡⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠀⠀⠀⠀⠀⠀⠀⣾⠀⠘⠁⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣦⣐⢒⣲⢿⠃⢘⣿⣿⣷⣄ ⠉⠉⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠻⡟⠿⠿⣿⣿⣿⠟⠛⠛⠛⣋⣤⣬⣿⣿⣿⡿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⡀⠈⠻⣿⣿⣿⣿⡛⠛⠛⠀⠙⠆⠀⠀⠈⠙⠋⠙ ⢀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡶⢀⣀⣤⣶⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⣤⣾⣿⣿⣿⣿⣿⣷⡀⠀⠈⠉⠀⠙⣷⡄⠠⠧⠤⠼⠵⠿⣿⣿⣿⣶ ⠀⠀⣤⡄⢠⣤⡖⣶⣦⣠⣤⢠⣤⡄⢀⣤⣤⣔⣒⠊⢀⣤⣤⣄⠀⣤⣼⣿⢿⣿⣿⣿⣿⣿⣯⡡⠀⠀⣠⣤⣤⡀⢠⣤⣤⣤⣤⣤⡄⠀⢠⣤⣿⣿⡝⣿⣿⣿⣿⣿⣷⡄⣠⣤⡀⣤⣼⣿⣇⢲⣶⠀⣸⣿⣿⣿⣿⣿ ⠀⠀⣿⣧⣿⣿⣇⣿⡏⣿⣿⣸⣿⡇⣿⣿⢹⣿⠛⠃⣿⣿⡹⠿⠀⣿⣿⣿⡅⣿⣿⢸⣿⡿⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡷⣿⣿⣷⣿⡟⣿⣿⣼⣿⠀⠿⠇⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⣿⣿⡅⢠⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡏⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⢀⣶⣦⣿⣿⣽⣋ ⠛⠋⢹⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⠀⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣧⣿⣿⠀⣀⣿⣧⣿⣿⣸⣿⡇⢸⣿⡇⠀⠤⢼⣿⣷⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠉⣿⣿⣿⣿⣦⣿⣿⣭⣽⣿⣿ ⠤⠶⠶⣶⠿⢷⠶⠶⠶⠶⠶⠀⠀⠀⠀⠈⠉⣀⠀⢀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠥⠤⠭⠠⠍⠁⠀⠤⠂⠀⠀⠀⠀⠀⠀⡈⣉⡀⣀⠀⠀⠈⢿⣿⣿⡟⢰⣿⡇⠁⠀⠀⠈⣷⣊⣽⣒⣫⣽⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⠃⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⣿⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠉⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠓⠲⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠀⠀⠐⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⠟⠀⠀⢀⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⢿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠿⠛⠛⣸⣿⣿⣿⣿⣿⣿⡟⣀⣀⠐⠰⠖⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⣠⣿⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠛⠟⠁⠀⣠⣴⣶⣿⣿⣿⡛⠓⠀⢻⡟⠋⠁⠀⠀⠀⠀⢀⡀ ⠀⠀⠀⠀⠁⠀⣻⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⠿⠃⠀⢀⣀⠀⠀⣤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣴⠾⠷⠒⠺⠿⠿⠋⢩⣿⣿⣿⠀⠀⢀⣁⣠⡤⠶⠃⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⢰⣿⣿⡅⠀⢀⣾⣿⣿⣷⠀⠀⠀⣀⣿⣷⣤⠀⠀⢤⠤⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠉⢀⣿⣿⡿⠃⠀⢺⣟⠁⠀⠙⠉⠉⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⡿⠀⠀⠀⢠⢿⣄⡀⡤⠀⠀⠀⠀⠈⣿⣿⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡀⣿⣿⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠠⣦⡄⠀ ⠀⠀⠐⠆⣲⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⢀⢹⡄⠀⠀⠀⠀⠛⣡⡄⠉⣴⣴ ⠀⣰⣿⣿⢿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢿⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡀⢰⣶⣆⡀⠀⠀⠀⠀⠀⣴⣶⣶⣷⣦⣤⠀⣿⣶⣮⣿⠂⠀⠀⠈⠉⠉⡀⠀⣀⣀ ⣤⣿⣿⡿⡿⣳⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⣺⠀⣶⡀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣘⣛⣛⣠⣼⣿⣿⣷⣤⣀⡀⡀⣶⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠋⠁⠁⠀⣶⠀⢀⣃⣀⠈⠀ ⣿⢿⠋⠈⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢱⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣿⣿⡟⠿⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⣜⠉⣽⠋⠀⠨⣿⣿⣿⣦ ⠉⠈⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠈⢻⣿⠿⠻⠿⠿⠿⠛⠋⠛⠛⠁⠀⠨⠿⣿⣿⡿⠟⠟⠃⠀⣿⣜⣿⣿⣿⣿⡉⢛⣿⡿⠛⢿⣿⡉⠛⠋⡀⠈⡆⠀⣀⣀⣀⡀⠈ ⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣴⣿⣷⣾⣿⣿⣿⣷⡌⠉⠀⠀⠀⠙⣿⣆⡐⠓⠒⠚⢚⣛⣟⣻⣿⣷ ⠀⠀⣤⡄⢠⣤⡖⣯⣥⣠⣤⢠⣤⡀⢀⣤⣤⣽⣯⡀⢀⣤⣤⣄⠀⣤⣾⣿⡿⣿⣿⣿⣿⣿⣥⡀⠀⠀⣠⣤⣤⡀⢠⣤⣤⣤⣤⣤⡄⠀⢠⣤⣿⣿⡈⣿⣿⣿⣿⣿⣿⡆⣠⣤⡀⣤⣬⣿⣅⢩⣥⠀⣸⣿⣿⣿⣿⣿ ⠀⠀⣿⣇⣿⣿⣧⣿⡏⣿⣿⣸⣿⡇⣿⣿⣹⣿⠉⠁⣿⣿⡹⠿⠀⣿⣿⣿⡄⣿⣿⢹⣿⡟⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⣿⣿⣇⣿⣿⣿⣿⡿⣿⣏⣿⣿⣷⣿⡏⣿⣿⣼⣿⠀⠿⠇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⣿⣿⠆⠄⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡇⣿⡇⣿⣿⣿⣿⣇⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠤⣶⣶⣿⣿⣮⣤ ⠉⠉⢹⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⠀⢻⣿⣼⣿⢸⣿⡟⣿⣷⣿⣿⢸⣿⣧⣿⡿⠀⣤⣿⣧⣿⡿⢼⣿⡇⢸⣿⡇⠀⠐⢺⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠁⣿⣿⣿⣿⢶⣿⣿⡶⣾⣿⣿ ⠤⠶⠶⣶⠿⢶⠖⠲⠶⠶⠖⠀⠀⠀⠀⠈⣉⣀⣀⠠⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠲⠖⠒⠒⠉⠁⠐⠒⠂⠀⠀⠀⠀⠀⠀⣄⣤⠠⡄⠀⠀⠈⠽⣿⣿⡆⢾⣿⡄⠀⠀⠀⠀⣿⣥⢶⣬⡤⠾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⣿⣿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠓⠿⠿⠿⢿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡗⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣼⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠛⠋⢋⣴⣿⣿⣿⡿⠿⠋⣁⣀⣄⠀⠐⠋⠉⠀⠀ ⠀⠀⠀⢀⠀⠀⢰⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⣿⠏⠀⣬⡍⠁⠠⢴⣾⡿⠿⣛⣽⣯⠀⠀⠰⠏⠉⠀⠀⡀⠀⣀⣠⠄ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⣿⡟⠛⠃⠀⠀⣀⣀⠀⠀⠤⠤⠤⣤⣄⠀⠀⠀⠀⠀⠘⠋⠀⠘⠋⠀⠀⠀⠀⠁⠁⢸⣿⣿⡏⠀⠀⣀⣤⣴⠖⠞⠃⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⢿⠟⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⢀⠀⢸⣿⣷⡄⠀⢀⣾⡿⢿⣷⣀⡀⠀⣠⣿⣿⣧⠀⠀⠴⠖⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠈⢠⣿⣿⡟⠁⠀⢸⡟⠁⠀⠸⠉⠁⠀⠈⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠃⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠁⣀⣀⣠⢿⣄⢀⡄⠀⠀⠀⠀⠀⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠺⠊⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠰⣶⠄⢀ ⠀⠀⡐⠒⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⣁⣤⡄⠁⠷⠾ ⢀⣾⣿⣷⣾⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⠿⠟⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠄⣸⣶⣄⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣦⡀⢠⣤⣤⣻⣇⣀⡀⠀⠀⠀⢁⡀⠡⣤⠤ ⣴⣿⣿⣟⢟⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠚⠀⣿⢰⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣽⣽⣭⣴⣿⣿⣿⣷⣄⠀⠀⠠⣴⣶⣿⣿⣿⣿⣿⣼⡿⠿⠟⠁⢀⠀⢀⣶⠀⣀⣣⣀⡀⠀ ⣿⣿⠁⢀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢻⣿⣿⣿⣿⣿⣿⡟⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⣶⣿⣷⣌⠹⣿⠃⠀⠘⠿⣿⣿⣦ ⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⣻⣟⡛⠛⠿⠿⠿⠛⠉⠙⠉⠁⠀⠠⢴⣾⣿⡏⠻⠛⠁⠀⣷⡙⣿⣿⣿⣿⡉⢹⣿⡟⠙⠿⣿⣌⠉⠁⠀⠈⡮⢀⣀⣀⣀⣀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣗⣿⣿⣿⣿⣿⡎⠉⠀⠀⠀⠈⢿⣇⣈⣙⡛⠛⣻⣭⣭⣿⣿⣿ ⠀⠀⣤⡄⢠⣤⡔⣭⣤⣠⣤⢠⣤⡀⢀⣤⣤⣭⣭⠀⢀⣤⣤⣄⠀⣠⣾⣿⠿⣿⣿⣿⣿⣯⣤⡀⠀⠀⣠⣤⣤⡀⢠⣤⣤⣤⣤⣤⡄⠀⢠⣼⣿⣿⡀⣿⣿⣿⣿⣿⣭⡄⣠⣤⡀⣤⣬⣿⣅⢡⣤⠀⣨⣽⣿⣿⣿⣿ ⠀⠀⣿⣧⣿⣿⣧⣿⡏⣿⣿⣸⣿⡇⣿⣿⣹⣿⠉⠀⣿⣿⡹⠿⠀⣿⣿⣿⡀⣿⣿⢹⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡿⣿⣇⣿⣿⣿⣿⡿⣿⣯⣿⣿⣷⣿⡏⣿⣿⣼⣿⠀⠿⠇⣿⣿⣿⡿ ⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⢿⣿⡆⠀⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡇⣿⡇⣿⣿⣿⣿⡇⣿⣿⣿⢿⣿⣿⡧⣿⣿⣿⣿⢂⣶⣶⣿⣿⣶⣶ ⠉⠉⢹⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⠀⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣧⣿⡿⠀⡤⣿⣧⣿⡿⢼⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⣿⡇⢻⣿⣿⣿⣷⢿⣿⣿⢸⣿⣿⠁⣿⣿⣿⣿⠶⣿⣿⣯⣽⣿⣿ ⠠⠶⠶⣶⠿⢷⠗⠳⠶⠶⠖⠀⠀⠀⠀⠈⣉⣀⣀⠠⣤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠘⠉⠁⠐⠊⠁⠀⠀⠀⠀⠀⠀⣤⡤⠠⠄⠀⠀⠈⠻⣿⣿⣀⣻⣷⡆⠀⠀⠀⠀⣷⠷⠶⠶⣗⠺⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣧⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢈⣛⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡄⠀⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠛⠲⢿⣿⠟⠋⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣾⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢿⣿⡇⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣼⣿⣦⠸⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⡿⠿⠹ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠉⠙⣿⣿⣿⠿⠦⠆⢀⣴⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀ ⠀⠰⠢⢦⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠐⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⠟⠀⢀⠼⠋⠈⠀⠀⠀⠀⠀⠉⠉⠉⠀⠒⠀⠀⠀⢀⠀⢀⡠⠤⠀ ⠀⠀⠀⠀⢿⣿⣿⡿⠯⠹⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢩⣅⠀⠀⠀⠀⢀⣠⣄⠀⠐⠒⠒⠂⣿⣷⡄⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢀⣤⠤⠶⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⣿⣿⣤⣀⠀⣰⣿⠿⠻⣷⣤⡄⠀⣤⣿⣿⣿⠀⠀⠒⠛⠈⣁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⠀⠀⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢀⣾⣿⡟⢡⠀⠽⡏⠀⠀⠘⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠿⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠐⣿⣿⣿⣧⣄⣀⣴⣿⣦⢠⣆⡀⠀⠀⠀⠀⣿⣿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠈⠁⠀⠀⠠⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⠘⠋⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠖⠀⢲ ⢀⣤⡛⠩⣷⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⡠⣄⣶⢀⢘⠿⠷ ⣿⣿⣿⣿⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⡉⣩⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⢨⣿⣷⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣀⠀⢀⣀⠀⢸⣿⣥⠤⠤⠀⠀⠀⢤⠀⢢⡶⠖ ⣿⣿⡿⠟⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠀⠀⠀⠀⠀⠀⠀⢸⠇⢹⣧⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣀⣤⣤⣿⣿⣄⣼⣿⣿⣦⣅⠰⣦⣀⣸⣇⠠⣬⣤⣤⠀⠀ ⣽⡃⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⠛⢿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⢿⣷⡄⠿⠏⡀⠀⠛⠻⠿⠿⣦ ⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⣈⣻⣿⡛⠛⠛⠛⠛⠉⠉⠉⠉⡀⠀⣠⣴⣿⣿⣿⡟⠋⠀⢸⣷⣿⣿⣿⣿⣿⡉⣿⣿⠟⠀⠻⣿⣄⠀⣤⣀⣸⣁⣤⣤⣤⣤⣄⠀ ⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠉⠉⠁⠋⠀⠀⢸⣿⡿⢿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠘⣿⣤⣨⡍⠉⢩⣽⣿⣾⣿⣿⣧ ⠀⠀⣤⡄⢠⣬⡉⣤⣤⣠⣤⢠⣤⡄⢀⣤⣴⣷⣦⠀⢀⣤⣤⣄⠀⣤⣿⣿⠟⣿⣿⣿⣿⣧⣤⡀⠀⠀⣠⣤⣤⡀⢠⣤⣤⣤⣤⣤⡄⠀⢠⣼⣿⣿⣸⣿⣿⣿⣿⣯⣭⡄⣠⣤⡀⣤⣬⣿⣄⢲⣤⠀⣨⣿⣿⣿⣿⣿ ⢀⣀⣿⣧⣿⣿⣷⣿⡏⣿⣿⣸⣿⡇⣿⣿⢹⣿⠀⠀⣿⣿⡹⠿⠀⣿⣿⣿⡄⣿⣿⢻⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡿⣿⡗⣿⣿⣿⣿⡟⣿⣧⣿⣿⣷⣿⡟⣿⣿⣼⣿⠀⠿⠏⣿⣿⠿⢿ ⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⢿⣿⠆⠄⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣇⣿⡇⣿⣿⣿⣿⡇⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠰⣶⣿⣿⣿⣿⣿ ⠉⠀⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⠀⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣧⣿⡿⠰⠶⢿⣷⣿⡿⢺⣿⡇⢸⣿⡇⠀⠈⢹⣿⣷⣿⡇⢻⣿⣿⣿⡿⢿⣿⣿⢸⣿⣿⠁⣿⣟⣿⣿⢻⣿⣿⣿⣿⣿⣿ ⠐⠶⠶⣶⠿⣿⠗⠰⠶⠶⠖⠀⠀⠀⠀⢨⣭⡤⠄⠤⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠙⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠶⠆⠒⠀⠀⠀⠈⢿⣿⣧⣬⢿⣿⠀⠀⠀⠀⢸⣟⡚⠛⠿⠿⣛⠻⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢺⣧⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠀⠀⢀⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠓⠿⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶ ⠀⠀⠀⠀⠀⠀⣰⣿⠁⠙⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠃⠀⢺⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿ ⠀⠀⠀⢀⣤⣼⣿⣿⣦⡀⠹⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⡿⡟⠀⣴⣿⡿⠻⢿⠻⠗⠀⢰⣾⣿⣿⣿⣿⣿⣿⡿⠟⠙⠂ ⠀⠒⠒⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⢠⠆⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠟⠛⣛⠋⢀⡤⠄⠀ 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⣀⣀⣿⣧⣿⣿⡗⣿⡏⣿⣿⣸⣿⡇⣿⣿⢽⣿⠀⠀⣿⣿⡹⠿⠀⣿⣿⣿⡄⣿⣿⢻⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢹⣿⡿⣿⡧⣿⣿⣿⣿⡏⣿⣧⣿⣿⣷⣿⡏⣿⣿⣼⣿⠀⠿⣏⣿⣿⠛⣿ ⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⢿⣿⠆⠀⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⢀⣸⣿⣇⣿⡏⣿⣿⣿⣿⡇⣿⣿⣿⢿⣿⣿⣧⣿⣿⣿⣿⣭⣷⣾⣿⣿⣿⣿ ⠁⠀⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⠀⢻⣿⣼⣿⢸⣿⡟⣿⣷⣿⣿⢸⣿⣷⣿⡿⠐⠶⢿⣷⣿⣿⣸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣷⣿⡇⢻⣿⣿⣿⡟⢻⣿⣿⢸⣿⣿⠁⣿⣟⣿⣿⢒⣿⣯⣿⣿⣿⣿ ⠐⠶⠶⣾⢟⣿⠇⠰⠶⠶⠖⠀⠀⠀⠄⠬⠭⠤⠤⠤⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠀⠀⠉⡉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠲⠶⠂⠐⠀⠀⠀⠈⢻⣿⡧⠼⠿⡇⠀⠀⠀⠀⣿⣟⡛⠛⠫⢭⣛⡻⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠐⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⡇⠀⢀⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠏⠛⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⢰⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣀⣠⣴⣿⣿⣿ ⠀⠈⠿⡿⢿⠛⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣿⣿⢿⢿⣿⠟⢋⣀⣭⣶⣿⣿⣦⣠⣿⣦⠶⣞⣀⣿⣿⣿⣿⣿⣿ ⠈⠉⠃⠀⠰⢤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⢀⣀⠀⠀⣤⡀⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⣀⣲⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⢻ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⠄⠀⠀⣤⡀⠀⠴⠖⠀⣠⣤⣤⠀⠈⠉⠉⠁⢀⣿⣿⡀⢀⣀⣠⣤⣿⠁⠀⠀⠀⠀⠟⠛⠁⠀⠀⠀⠉⠉⠁⣿⣿⣿⡿⠿⢿⠟⠉⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⠖⠂⠀⠻⣿⣿⣦⢀⣾⣿⠟⠛⡷⠒⠀⠐⠚⢺⣿⡿⠀⠈⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢀⣿⣿⣯⠀⢻⡄⠀⠀⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢂⣲⡶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠀⠀⠀⣹⣿⣿⣿⣴⣿⣷⣦⣴⣀⣀⣀⠀⠀⢸⣿⣷⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⣄⣈⣀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠙⣄⣸⢿ ⣶⣍⣀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡀⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠶⠿⠃⠀⢋⠛⢿ ⣿⣿⣿⣿⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⠀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠺⣶⣦⡀⠀⠀⡀⠀⢰⣿⠗⠲⠒⠀⣀⠀⠘⡇⠈⠿⠋⠉ ⡿⠟⠏⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡆⠀⠀⠀⠀⠀⠀⠀⡟⠈⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⢀⣀⣽⣿⣿⡀⣸⣿⣷⣶⣶⣄⠿⢦⣴⡿⠂⣺⣿⣶⣦⠀⠀ ⠃⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠻⢿⣿⣿⣿⣿⡗⠙⢤⠀⣰⣿⣿⣿⣿⣿⣿⣿⠛⢻⣾⡟⠿⠟⠈⠿⣠⠀⠀⠉⠛⠛⠛⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣀⣬⣽⣾⡃⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⣈⣿⡛⠛⠃⠀⣀⣸⣿⣿⣿⣿⣿⣧⣽⣿⡿⠀⠀⠛⣿⣤⠴⢤⣤⣯⣾⢿⠶⣶⣶⡄⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⡄⠀⠀⠀⠀⠀⠀⢤⣤⣾⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠧⠀⠀⣾⣿⡟⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠈⠿⡶⠶⡂⠀⠿⢿⣿⣿⣿⣿⡆ ⠀⠀⣤⡄⢠⣤⡀⣤⣤⣤⣤⢠⣤⡄⢀⣴⣿⣿⠄⠀⢀⣤⣤⣄⠀⣼⣿⣿⢻⣿⣿⣿⣿⣤⣤⡀⠀⠀⣠⣤⣤⡀⢠⣤⣤⣤⣤⣤⡄⠉⣠⣭⣭⣵⣿⣿⣿⣿⣿⣠⣤⡄⣠⣤⡀⣤⣤⣿⣍⣠⣤⠀⣸⣿⣿⣿⣿⡇ ⣀⢀⣿⣧⣿⣿⡇⣿⡏⣿⣿⣸⣿⡇⣿⣿⢿⣿⠄⠀⣿⣿⡹⠿⠀⣿⣿⣿⡄⣿⣿⣿⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡟⣿⣗⣿⣿⣿⣿⡟⣿⡗⣿⣿⣷⣿⡏⣿⣿⣼⣿⣰⡿⢯⣿⣿⣹⣧ ⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡇⣿⣿⢾⣿⠇⠀⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⣸⣿⡧⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⢿⣿⣿⡧⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿ ⠁⠀⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⠀⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣷⣿⡿⠐⠒⣿⣷⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⣿⡇⢻⣿⣿⣿⡏⣽⣿⣿⢸⣿⣿⠁⣿⣯⣿⣿⣽⣿⣷⣿⣿⣿⣿ ⠰⠶⠶⣶⣟⢷⠄⠰⠶⠶⠖⠀⠀⠠⡤⠬⠵⠦⠤⠖⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠉⠀⢉⠀⠀⢁⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠋⠀⠀⠀⠈⠻⠿⣖⠚⠻⡇⠀⠀⠀⠀⣿⣥⣌⡉⠒⠮⢭⣛⣿⢿⣿ ⣰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣀⣾⣿⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣍⣿⣿⣜⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⠿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⣴⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⠿⠃⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣿⠯⠏⢻⣿⣿⠋⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⠀⠀⠀⠀⠒⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠇⢠⣦⠀⣀⡄⠀⢀⣤⠀⣀⣀⠐⣤⡾⠀⠀⠀⠀ ⣀⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣿⣿⠿⠿⠿⠿⠃⠀⢸⣿⣾⣿⡇⠀⢾⣿⡟⠛⠉⢀⣾⡇⠀⢀⡀⠀ ⠉⠉⠀⠀⠲⠆⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣤⡤⡀⠀⢸⣧⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢀⣰⣿⣾⣿⣿⠃⠐⠀⢿⣆⣤⣤⣿⣿⣿⣿⣁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⣿⣿⣥⣀⢉⣵⣶⣤⠀⠀⠀⢀⣀⢠⣿⡿⠀⢠⡤⠴⢾⡟⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠘⠀⠀⠒⠉⠹⣿⣿⣿⡿⠛⠛⡟⠉⠀⠈⠉⣿⣿⠁⠀⠀⠀⠀⠸⠃⠀⢠⣧⣾⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⣿⣿⣄⠀⡀⠀⠀⠀⠀⠀⠈⠿⠋⠁⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠛⠛⠁⠈⠀⠀⠀⠀⠀ ⠉⢡⣶⡶⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣾⣤⣀⣀⠀⢠⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣤⠠⣤⣄ ⢰⣄⣠⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⣠⠀⠁⣶⣾⣹ ⣦⣁⣘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣤⣄⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠈⠙⢋⡓⢨⣵⣠⣿ ⣿⡯⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣆⡈⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⢀⣄⡀⠸⠿⢉⣭⠁⠐⣦⠀⣈⣃⡸⠋⠀⠀ ⡿⠳⢉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⣠⣤⣬⣿⣿⣄⣼⣿⣿⢿⣿⣾⡏⢿⣿⡏⠁⠿⣿⣿⣷⡀⠀ ⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⠈⠛⢻⣿⣿⣿⣿⠗⠉⢠⠀⣴⣿⣿⣿⣿⣿⣿⣿⡉⠙⣿⣯⠛⢉⠈⢻⢠⢀⣀⣈⣁⡈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣀⣠⣬⣷⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢘⠟⣿⡏⠏⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠉⢿⣏⠚⠒⠚⠻⣛⣿⣿⣿⣿⣆⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⣶⠀⠀⠀⠀⠀⠀⠈⣷⣶⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣄⠀⠀⣿⣿⡏⢿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠻⣿⠿⠄⠀⠛⢿⣿⣿⣿⣿⠀ ⠀⠀⣤⡄⢠⣤⡄⣤⣤⣠⣤⢠⣤⡄⢀⣼⣿⣟⠀⠀⢀⣤⣤⣄⠀⣽⣿⣿⠿⣿⣿⣿⣿⣦⣤⡀⠀⠀⣠⣤⣤⡀⢠⣤⣤⣤⣤⣭⡅⢲⣤⣴⣤⣤⣾⣿⣿⣿⣿⣴⣶⡆⣠⣤⡀⣤⣤⣿⣤⢦⣤⠀⣸⣿⣿⣿⣿⡆ ⡀⢀⣿⣧⣿⣿⡇⣿⡏⣿⣿⣸⣿⡇⣿⣿⣿⣿⠄⠀⣿⣿⡹⠿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡟⣿⣗⣿⣿⣿⣿⡟⣿⣇⣿⣿⣷⣿⡏⣿⣿⣾⣿⠴⢿⣿⣿⣿⣾⣷ ⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡯⣿⣿⢿⣿⠇⠀⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡇⣿⡇⣿⣿⣿⣿⣧⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿ ⠉⠁⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⡀⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣷⣿⡿⠀⠒⣿⣿⣿⡿⢹⣿⡇⢸⣿⡇⠀⠀⣸⣿⣿⣿⡇⢻⣿⣿⣿⡇⢿⣿⣿⢸⣿⣿⠁⣿⡷⢿⣿⡾⣿⣿⣿⣿⣿⣿ ⠤⠶⠶⣶⠿⢷⠄⠰⠶⠶⠖⠀⠀⠠⠤⠬⠭⠤⠠⠖⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢉⡀⠀⠀⣬⠭⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠻⣯⣉⠉⠃⠀⠀⠀⠀⢿⣷⣶⣤⣈⡉⠒⠮⢭⣿⣿ ⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢀⣠⣴⣿⣇⠀⣀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⢧⣿⣿⣢⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣷⣶⣿⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣾⣿⣿⣿⣷⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡿⠛⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡿⠿⠋⠁⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶ ⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠃⢸⣷⢀⣠⣴⠀⢀⣤⡀⣠⣤⠈⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⢀⣼⣟⣾⣿⡇⠀⠺⣿⡏⠉⠀⢀⠀⠀⢀⣀⠄⠀ ⠀⠉⠀⠀⠓⠒⠦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⢠⣤⣤⠀⡀⠀⠀⠀⢤⠤⠤⠀⠀⣸⣧⠀⠀⠀⠀⢸⣿⠟⠉⠈⠁⠀⢀⣼⣿⣿⣿⣿⠑⠆⠀⠘⣭⣤⣔⡟⠁⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡇⠀⠀⠀⠀⠀⠘⢻⣿⣷⣵⣶⣦⣀⡀⠀⢀⣀⣼⣿⠃⠀⠠⠶⠖⣺⠟⠀⠀⠀⠀⢀⣼⣍⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣾⠗⠀⠀⠀⠀⠀⣀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠉⠉⠀⠉⠁⠉⠀⢸⣿⣿⡿⠛⡏⠉⠀⠈⢹⣿⡇⠀⠀⠀⠀⠀⠛⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⡇⢀⣠⣤⣴⣶⣾⣿⣷⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠃⠀⠁⠀⠀⠀⢸⣿⣿⣄⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀ ⠉⣥⣯⠗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣾⣤⣄⣀⡀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠋⢀⣀⠀⠠⣶⠤⢶⣤ ⢸⣄⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣁⣤⡔⠠⡷⣿⣽ ⣦⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣗⣀⣀⠀⠉⠙⢩⡅⢨⣵⡤⠿ ⣿⡏⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣭⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⣤⣤⢘⣿⢉⣄⡀⢀⣶⠀⣈⣃⣘⠋⠀⠀ ⡟⠽⢩⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣄⠀⠀⠀⢀⣤⣶⣿⣿⣇⣰⣿⣿⣿⣿⣷⣏⢻⣟⡏⠀⠺⢿⣿⣷⡀⠀ ⠀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠟⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⡿⠘⠛⢻⣿⣿⣿⣿⠇⠉⢠⡀⢰⣿⣿⣿⣿⣿⣿⣿⡅⠉⢾⣆⠋⢩⠀⢙⢀⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣀⣠⣬⣷⣾⡉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⣀⣘⠻⢿⡏⠋⠀⣤⣼⣷⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⢻⣯⣙⣛⠛⠛⣻⣿⣭⣿⣿⣥⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠘⣷⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⣤⡀⠀⠿⠿⠏⢿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠻⣯⠭⠀⠀⠉⣿⣿⣿⣿⣯⠀ ⠀⠀⣤⡄⢠⣤⡀⣤⣤⣠⣤⢠⣤⡄⢀⣼⣿⣛⠀⠀⢀⣤⣤⣄⠀⣿⣿⣿⡿⣿⣿⣿⣿⣥⣤⡀⠀⠀⣠⣤⣤⡄⢠⣤⣤⣭⣬⣥⡅⠳⣤⣴⣶⣶⣿⣿⣿⣿⣿⢦⣶⡆⣠⣤⡀⣤⣤⣿⣤⢢⣤⠀⣸⣿⣿⡿⢿⡆ ⣀⠀⣿⣷⣿⣿⡇⣿⡏⣿⣿⣸⣿⡇⣿⣿⣿⣿⠀⠀⣿⣿⡹⠿⠀⣿⣿⣿⡆⣿⣿⣿⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⡏⣿⣇⣿⣿⣧⣿⡗⣿⣿⣾⣿⣺⠿⢿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡷⣿⣿⢿⣿⠇⠀⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⢿⣿⣿⡟⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿ ⠉⠁⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⣿⢀⡀⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣷⣿⣿⠀⠙⣿⣯⣿⡿⢹⣿⡇⢸⣿⡇⠀⠀⣸⣿⣿⣿⡏⢻⣿⣿⣿⣇⣻⣿⣿⢸⣿⣿⠁⣿⡿⢿⣿⣛⣿⣿⣿⣿⣿⣿ ⠴⠶⠶⣶⠿⢷⠄⠰⠶⠶⠖⠀⠀⠠⠤⠬⠭⠤⠰⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢠⡀⠀⠠⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠛⠧⣄⡉⠁⠀⠀⠀⠀⢿⣿⣶⢦⣤⣉⠙⠒⠿⣿⣿ ⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣶⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠛⠺⢾⣿⡼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡞⣿⣿⣿⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⠈⠉⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣾⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠘⢿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠟⠿⠁⠀⠀⠈⢻⣿⡿⠿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡯⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠃⠀⣿⡇⣴⣶⠃⠀⣴⣦⣴⡶⠀⠀⠉⢀⠀⠀⠀ ⠦⠤⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡄⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⢀⣴⣿⣿⣿⡿⠀⡈⠙⡏⠀⠀⢀⣀⠀⢠⠤⠖⠀ ⠀⠀⡀⠈⠉⠙⠛⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⠉⠻⠏⠀⢸⣿⣿⣿⣿⡇⠈⠀⠀⠴⠶⠟⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⡇⣀⣀⠀⣀⡀⣀⠀⢀⣠⣶⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠋⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀ ⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠠⣿⠿⢫⣿⣿⡿⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡇⠀⠀⠀⠀⣀⣀⣀⣈⣽⣿⣿⣿⠏⠀⠀⢽⣿⣧⡠⠄⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣾⣿⡿⠃⠀⠀⠙⠋⠀⢠⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣻⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⡿⠟⠏⠀⠀⠀⠀⠀⠀⣴⡾⠀⠀⡤⠀⠐⠶⡀⣲⣶ ⠸⠶⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠛⠙⠉⠉⠉⠀⠐⢦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣤⣤⣶⣎⣴⡟⠿⢰ ⣷⣴⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣄⠀⢭⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣶⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠘⠻⢿⣿⣿⠿⠿⠿⠿⠏⠀⠈⢠⡄⢰⣾⠖⠛ ⣿⣿⣟⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣦⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⢠⣿⣇⣀⠀⣶⣄⣨⣿⠀⣤⣥⣬⡁⠀⠀ ⡏⢊⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⣼⡁⠘⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣆⠀⠀⠀⢀⣴⣴⣾⣿⣿⣆⣿⣿⣿⢻⣿⣇⢹⣯⡇⠀⠛⠻⠿⢷⡄⠀ ⢠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠃⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⣿⠿⠟⣿⣿⣿⠿⣿⡿⠿⠿⢿⠟⠈⠉⢻⣿⣿⣿⡿⠃⠈⢠⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⡁⣠⣀⣹⣀⣤⣤⣤⣤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣀⣠⣤⣶⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⠿⠿⠿⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⢻⣧⢩⡍⠉⢍⣽⣿⣾⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⣿⡦⡀⠈⠛⠛⠊⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠈⠹⣗⠓⠀⠀⠠⣿⣿⣿⣿⣷⠀ ⠀⠀⣤⡄⣠⣤⡀⣤⣤⣠⣤⢠⣤⡄⢀⣬⣭⣍⠀⠀⢀⣤⣤⣄⠀⣿⣿⣿⢿⣿⣿⣿⣿⣧⣦⡀⠀⠀⣠⣤⣤⡄⢠⣤⣤⣤⣤⣤⡄⠀⢶⣶⣶⣶⣿⣿⣿⣿⣿⢾⣿⡇⣠⣤⡀⣤⣤⣿⣼⢠⣤⢀⣸⣿⣿⡟⣿⡀ ⣤⣤⣿⣿⣿⣿⡇⣿⡏⣿⣿⣸⣿⡇⣿⣿⣿⣿⠀⠀⣿⣿⡹⠿⠀⣿⣿⣿⡌⣿⣿⣿⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⡟⣿⣧⣿⣿⣷⣿⡏⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡟⣿⣿⢿⣿⠃⠀⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⠀⣙⣻⣿⣦⣸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣇⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⢿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⠄⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣯⣿⡿⠉⠉⣿⣯⣿⡿⢸⣿⡇⢸⣿⡇⠀⠀⣸⣿⣷⣿⡏⢻⣿⣿⣿⣧⣿⣿⣿⢸⣿⣿⠁⣿⡟⢿⣿⢍⣿⡿⠿⣿⣿⡿ ⠒⠶⢶⣾⡿⢶⠔⠰⠶⠶⠶⠀⠀⠐⠒⠚⠛⠒⠒⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠀⠀⠐⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢤⣈⠁⠀⠀⠀⠀⢻⣿⣿⠶⢤⣄⣉⠙⣾⣿⣿ ⢻⡿⠏⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠙⠿⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡿⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠉⢿⠿⠿⠛⠛⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡠⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠁⢸⣿⢃⣼⡾⠀⠀⣾⡶⠟⠃⠀⠀⠀⠄⠀⠀ ⠉⠃⠀⠰⢦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣿⣿⡇⢀⠀⠙⠁⠀⢀⣠⠄⠠⠖⠚⠁ ⠀⠀⠂⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⡉⠁⠀⠀⠀⠀⢀⣀⣀⣘⣿⠏⠛⠻⢿⡟⠀⠀⣾⣿⣿⣿⣿⠁⠊⠀⠐⠿⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣿⠆⠐⠀⠀⠤⠀⠠⠀⠠⣤⣾⣿⣿⣿⢿⣿⣿⡖⠀⠀⠀⠀⠈⠉⠁⣼⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠠⠶⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠃⢹⣇⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⣒⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠄⠀⠀⠀⠀⣠⣤⣤⣤⣼⣷⣤⣾⣿⣿⣿⢿⣿⣆⡄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠛⣏⣹⣿ ⡜⠉⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠉⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡠⣶⢶⣾⣆⠼⢟⠛⢊ ⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡄⠸⢿⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠉⠁⠀⠀⠀⣤⣤⣤⣤⣤⣤⣾⣃⠤⠖⢐⣀⠀⠰⡆⢰⣿⠟⠛ ⡿⡾⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢿⣷⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⢿⣿⡽⣤⣴⡿⡄⢴⣶⣮⡀⠀⠀ ⠁⣡⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡗⠄⠀⠀⠀⣀⣤⣶⣿⣿⣿⣻⣻⠉⣱⣿⣿⡷⢿⣯⡇⠀⠙⠻⠟⠻⠀⠀ ⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠻⠟⠀⠉⠹⣿⣿⣿⡿⠁⠀⢤⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣶⣀⣸⣠⣴⣶⣤⣤⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣼⠀⣀⣠⣴⣶⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢴⣶⣶⣏⡹⠟⢹⢀⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠘⢿⣧⠠⠭⠉⠩⣿⣿⣶⣿⣿⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⡿⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⢷⣄⠀⠩⠍⢙⣿⣿⣿⣿⣿⢉⣀⠀⠀⠀⠀⠈⠻⡖⠛⠀⠀⠀⣿⣿⣿⣿⣷⠀ ⠀⢠⣤⣤⣠⣤⡀⣤⣤⣠⣤⢠⣤⡄⢀⣤⣤⣄⠀⠀⢀⣤⣤⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⣠⣤⣤⡄⢠⣤⣤⣤⣤⣤⡄⠘⢶⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡇⣠⣤⡀⣤⣤⣷⣌⣠⣤⢀⣨⣿⣿⣛⣿⣀ ⣶⣾⣿⣿⣿⣿⡇⣿⡏⣿⣿⣸⣿⡇⣿⣿⣿⣿⠀⠀⣿⣿⡹⠿⠀⣿⣿⣿⡏⣿⣿⣿⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣷⣿⣿⣷⣿⡏⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿ ⠿⠿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡏⣿⣿⢻⣿⠃⠀⣈⣻⢿⣷⢠⣿⣏⣿⡇⣿⣿⢸⣿⡇⣿⣿⣀⣀⣙⣻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⡿⠀⠀⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣯⣿⡿⠀⠀⢿⣧⣿⡿⢺⣿⡇⢸⣿⡇⠀⠀⢼⣿⣷⣿⡏⢻⣿⣿⣿⠯⢿⣿⣿⢸⣿⣿⢡⣿⣏⣿⣿⢭⣿⡿⠿⣿⣿⡟ ⠉⠿⣷⣶⠿⢷⠆⠰⠶⠶⠶⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡩⠛⠓⢦⣄⠀⠀⠀⠀⠘⣿⣿⣻⠶⣦⣄⣉⠙⣻⣿⣿ ⠋⠘⠁⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠙⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⠻⠛⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠀⣄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠠⢀⡤⠶⠀⠀ ⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠿⠋⠀⣿⣇⣴⣿⠃⠀⢴⡷⠟⠋⠀⡀⠀⠀⠀⠀ ⠈⠁⠀⠘⠶⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡋⠀⠀⠀⣴⣿⣿⣿⣿⢀⡌⠀⠃⣀⣀⣤⠄⠀⠒⠋⠁ ⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣬⣥⣀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣿⡟⠿⠿⣿⡷⠀⠀⢰⣿⣿⣿⣿⡇⠘⠀⠐⠻⠏⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣷⣿⠆⠐⠒⠂⠒⠀⠒⠀⠐⢶⣾⣿⣿⣿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠁⠀⣾⠏⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⢨⣅⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⣂⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠄⠀⠀⠀⢀⣤⣶⣦⣤⣾⣷⣤⣾⣾⣿⣿⢻⣿⣗⡆⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡀⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡆⠀⣀⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⡛⣯⣹⣿ ⡌⠉⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣀⣀⠀⠀⣶⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⡾⢧⡜⠟⠛⢋ ⣿⣮⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⠘⢻⣿⣅⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢽⣿⣿⣿⣿⣷⠀⠀⠉⠛⠛⠛⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⢠⠖⠒⠂⣄⠀⠐⡆⠈⡿⠟⠛ ⡿⡾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣯⣶⣄⡿⢦⣴⡿⠆⣶⣶⣶⡄⠀⠀ ⠁⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣤⣶⣿⣿⣟⠿⠏⢡⣿⣿⣿⠿⠹⣿⢃⠀⠉⠛⠟⠛⠀⠀ ⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⢿⣟⣿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠟⠀⠈⢹⣿⣿⣿⣿⡁⠀⢠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣁⣾⣀⣺⣼⣴⣶⣶⣶⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⣿⢀⣀⣤⣴⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠔⢶⣶⣶⣯⡿⠃⠛⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢿⣦⠠⠬⠀⠋⠶⣿⣿⣿⣿⡷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡷⣦⠀⠩⡭⢩⣿⣿⣿⣿⣿⢉⣀⠀⠀⠀⠀⠈⢻⡖⢉⠀⠀⠀⢿⣿⣿⣿⣿⠀ ⠀⢠⣤⣄⣠⣤⡄⣤⣤⣠⣤⢠⣤⡄⢀⣴⣴⣆⠀⠀⢀⣤⣤⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⣠⣤⣤⡄⢠⣤⣤⣤⣥⣥⡄⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡆⣠⣤⡀⣤⣤⣷⣬⣠⣤⣠⣬⣽⣿⣛⣿⣄ ⣶⣬⣿⣿⣿⣿⡇⣿⡏⣿⣿⣸⣿⣇⣿⣿⣿⣿⠀⠀⣿⣿⡹⠿⠀⣿⣿⣿⡏⣿⣿⣿⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣷⣿⡏⣿⣿⣼⣿⣽⣿⣿⣿⣿⣿⣿ ⠿⠟⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡏⣿⣿⢻⣿⠃⠀⣈⣻⢿⣷⢠⣿⣟⣿⡇⣿⣿⢹⣿⣇⣿⣿⣀⣀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡯⣿⡿⣿⣿⣿⣿⣇⣿⣿⣿⢿⣿⣿⡏⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣾⡿⢐⡂⢻⣿⣼⣿⢻⣿⡟⣿⣷⣿⣿⢸⣿⣧⣿⡿⠀⠀⢿⣧⣿⡿⢺⣿⡇⢸⣿⡇⠀⠀⢼⣿⣷⣿⡇⢻⣿⣿⣿⠷⢿⣿⣿⢸⣿⣿⢡⣿⣏⣿⣿⠭⣿⣟⠿⣿⣿⣛ ⠀⠶⠶⣶⠿⢷⠆⠰⠶⠶⠶⠀⠀⠀⠀⠈⠉⠁⣈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠓⠦⣄⠀⠀⠀⠀⠘⣿⣿⣟⡻⣶⣤⣍⡹⣿⣿⣿ ⠉⠙⠁⠈⠻⣿⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⡟⠋⢿⣿⠀⠀⢼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡟⠀⠙⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⢠⣄⡀⠀⣠⠀⠀⢠⣀⣤⡄⠁⠚⠉⠁⠀ ⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠠⠀⠈⠛⠟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⠛⠁⢸⣿⢠⣾⡿⠀⡠⣿⠉⠁⠀⠠⠀⠀⣀⣠ ⠀⠁⠀⠘⠛⠲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⠀⠀⢐⣾⣿⣿⣿⡇⣴⠄⢀⣤⡤⠶⠖⠀⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠳⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠤⠴⢶⣼⡟⠻⢿⣿⣷⠀⠀⠀⣾⣿⣿⣿⣿⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢿⣿⠃⠈⠁⠁⠉⠁⠈⠁⠀⢻⣿⣿⣿⣿⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠙⠁⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡯⠋⠀⠷⣰⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⣩⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⢀⣴⣶⣶⣶⣾⣿⣶⣶⣾⣿⣿⣯⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠈⠉⠀⠀⠀⠀⡀⠀⢀⣤⣀⣤ ⢀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣀⡼⣯⣧⣿ ⣶⠉⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣇⣀⣀⣄⠀⢰⣿⣿⣿⡷⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠿⢛⣆⣙⣭⣡ ⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡈⢻⣷⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠀⠀⠙⠛⠛⠃⠀⠀⠀⣀⣘⣀⡀⣀⠀⠀⠀⣾⡉⠁⣦⡄⠀⠻⠀⠼⠋⠀ ⡿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢹⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠏⣴⣶⣶⣾⢳⣶⢿⠓⢸⣿⣿⣷⡀⠀ ⠃⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠈⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿⢏⣨⣤⣿⣿⣿⣿⠊⣿⡼⠀⠀⠈⠙⠉⠁⠀ ⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⢻⣿⣿⠧⠿⠿⠿⠟⠛⠋⠉⠙⠛⠁⠀⠘⣿⣿⡟⡿⠃⠀⢠⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠻⢶⡾⢿⡶⢿⡿⣿⣷⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⠄⠀⠀⠀⠀⠀⠀⣼⢀⣀⣤⣴⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠠⠲⣶⣿⣶⣦⣈⠇⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⠋⠻⣿⡐⢒⠀⠀⠚⢿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⢿⣸⣿⣿⣿⣿⣿⣿⣿⣟⠿⠆⠀⠀⠀⠀⢀⠠⠈⠉⠛⢿⣿⣿⣷⣤⠀⣰⣶⣨⣿⣿⣿⣿⣿⣁⣤⡄⠀⠀⠀⠀⠙⣷⢉⡄⠀⠀⠘⣿⣿⣿⣿⡇ ⠀⢀⣤⣄⣠⣤⡀⣤⣤⣠⣤⢠⣤⡄⢀⣼⣿⣇⠀⠀⢀⣤⣤⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⣠⣤⣴⣄⢠⣤⣤⣤⣬⣭⡅⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣤⣤⡀⣤⣤⣿⣤⣤⣤⣠⣴⣬⣿⣯⣽⣧ ⣶⣾⣿⣿⣿⣿⡇⣿⡏⣿⣿⣸⣿⣷⣿⣿⣿⣿⡀⠀⣿⣿⡹⠿⠀⣿⣿⣿⡍⣿⣿⣿⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡏⣿⣷⣿⣿⣿⣿⣏⣿⣷⣿⣿⣷⣿⣟⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿ ⠿⠿⢿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡟⣿⣿⢻⣿⠃⠀⣈⣻⣿⣷⢠⣿⣏⣿⡇⣿⣿⢹⣿⣇⣿⣿⠀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡧⣿⡿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣽⣷⣾⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⣿⠀⡀⢻⣿⣼⣿⢹⣿⡟⣿⣷⣿⣿⢸⣿⣧⣿⡿⠀⠀⢿⣧⣿⡿⢹⣿⡇⢸⣿⡇⠀⠀⢸⣿⣷⣿⡇⢻⣿⣿⣿⡗⢻⣿⣿⢸⣿⣿⠁⣿⣧⣿⣿⠒⣿⣯⣛⣿⣿⣿ ⠀⠶⠶⣾⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠈⠉⠁⣀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠐⠂⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢙⠙⠓⢦⠀⠀⠀⠀⠀⢻⣿⣿⣟⡳⣶⣤⣈⡻⣿⠿ ⠉⠙⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡜⠉⢻⡿⠀⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣄⠀⣠⡄⠀⢠⣤⣴⠆⠈⠘⠁⠀⠀ ⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠈⠛⠋⠄⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠀⠐⠀⠀⠀⠀⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠻⠛⠉⠀⣿⣇⣾⣿⠃⢠⢾⠇⠀⠀⠐⠂⢀⣀⠤ ⠀⠀⠀⠘⠛⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣾⣿⡿⢰⡆⠀⣤⠶⠚⠟⠁⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠶⠖⢺⣾⠏⠻⠿⣿⣷⠀⠀⠀⣸⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⠁⠈⠁⠁⠉⠉⠈⠁⠀⢩⣿⣿⣿⣿⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡯⠉⠀⠷⣤⣿⣿⣿⣯⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⣫⣼⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⠀⠀⠀⠀⢀⣴⣶⣶⣤⣾⣿⣷⣶⣾⣿⣿⣏⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠀⠀⠀⠈⠁⠀⠀⢀⣀⠀⠀⣤⡤⢤ ⠀⣮⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣤⡴⢀⣷⣾ ⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣤⠀⠰⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢀⡀⠛⠋⠛⣛⡿⢩⣥⡠ ⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡈⢻⣷⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣨⣿⣿⣿⣿⠀⠀⠉⠛⠙⠁⠀⠀⢀⣀⣸⣋⡀⣀⠀⠀⠀⢸⣯⠀⢰⣆⠀⠘⠃⠸⠋⠁ ⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡇⠏⣴⣶⣷⣾⡟⣿⣿⠛⠨⣿⣿⣿⡆⠀ ⠃⢃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⠀⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⢀⣠⣤⣴⣿⣿⡟⠏⣩⣴⣟⣿⣿⣿⡧⢻⡇⡆⠀⠀⠘⠉⠀⠀ ⠠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⣻⢿⣿⠯⠼⠟⠛⠛⠟⠛⠉⠙⠁⠀⠀⠈⣿⣿⣿⣟⡁⠀⣰⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢹⠷⠶⠿⠿⣿⣿⣻⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⣿⢀⣀⣤⣴⣾⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⣶⣦⣙⡛⠛⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠻⣿⡍⣉⠁⠀⠛⢛⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠃⠀⠀⠀⠀⠀⠀⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⠻⠦⠀⠀⠀⠀⠀⣀⠂⠉⠹⢿⣿⣿⣿⣦⡀⢰⣷⣠⣿⣿⣿⣿⣿⣅⣤⡄⠀⠈⠀⠀⠙⣿⢀⡄⠀⠀⠀⢻⣿⣿⣿⣧ ⠀⢠⣤⡄⣠⣤⡀⣤⣤⣠⣤⢠⣤⡄⣀⣴⣿⣆⠀⠀⢀⣤⣤⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⡀⠀⠀⣠⣤⣴⡶⢠⣤⣤⣤⣭⣥⡍⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⣤⣤⡀⣤⣤⣽⣦⣤⣤⢤⣶⣾⣿⣿⣼⣿ ⣶⣿⣿⣧⣿⣿⡇⣿⡏⣿⣿⣸⣿⣇⣿⣿⣿⣿⠀⠀⣿⣿⡹⠿⠀⣿⣿⣿⡅⣿⣿⣿⣿⡏⣿⣿⠀⠀⣿⣏⡿⠿⢸⣿⡏⢹⣿⡏⠁⠀⢸⣿⡏⣿⣷⣿⣿⣿⣿⣇⣿⣷⣿⣿⣷⣿⡟⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿ ⡿⠿⣿⣿⣿⢿⣿⣿⡇⣿⣿⢿⣿⡏⣿⣿⢻⣿⠃⠀⣈⣻⢿⣷⢠⣿⣟⣿⡇⣿⣿⢸⣿⣇⣿⣿⡀⠀⣙⡻⣿⣦⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⡇⣿⡟⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⢸⣿⣿⠃⣿⣿⢸⣿⡇⢿⣿⣼⣿⠀⡀⢻⣿⣼⣿⢻⣿⡟⣿⣷⣿⣿⢸⣿⣧⣿⡿⠂⠀⢿⣧⣿⡿⢹⣿⡇⢸⣿⡇⠀⠀⢸⣿⣷⣿⡇⢻⣿⣿⣿⣟⢻⣿⣿⢸⣿⣿⠁⣿⣷⣿⣿⠙⣿⡯⣭⣻⣿⣯ ⠀⠶⠶⣶⠿⢷⠖⠰⠶⠶⠶⠀⠀⠀⠀⠈⠉⠉⢀⡁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠙⠲⡄⠀⠀⠀⠀⢹⡿⠿⣭⣛⢿⢧⣤⣝⠿⡿ ䷩ 𝚕𝚒𝚗𝚎 2813 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/10/02/irc-log-011022/#comments Gemini version at gemini://gemini.techrights.org/2022/10/02/irc-log-011022/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Saturday,_October_01,_2022⠀✐ Posted in IRC_Logs at 2:37 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-011022.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-011022.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-011022.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-011022.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  QmUBhD9k5nPvKBLrPLsLd168Sb1AssSLViLxrWYr4tFx2g #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmUzYsJYHSi1cgug1LNEKVPKR2Nuh2BWidZYo4wmyXEvvm (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  QmVK5C2hJ2q8pj5NoqLRFRUN2x9xgm7EuEfkUQHQiaXgdm social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  Qmb5vsrDE1Ywr2AVzYjTKanFArhEPDswEj5gKq21zwXyjS social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmP2AmKwM4wyVE7otVh4xJeHyxyesfa3cwh8a8AsiBJUHH #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmXEmPpX1pEThHNr7zewyTCLnoaUWNJciJPhHbAr2kC9bV (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmZoANBMC1bacA49E66hGcacbCKsPBGV1T3iHTBJXZqDc2 #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmSPCETbcFyjjhKZLmqMas59Lpad2aqd15oyQ6d7nV9Peh (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmVLjiRjCRwAgqnB8rLKTYXEMmL6cgQMvDGgKZemCXwyc4 ䷩ 𝚕𝚒𝚗𝚎 2940 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/10/02/microsoft-windows-new-low/#comments Gemini version at gemini://gemini.techrights.org/2022/10/02/microsoft-windows-new-low/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Windows_Majority_in_Asia_Down_to_Just_Three_Countries,_All-time_Low_for Windows_Worldwide_This_Month⠀✐ Posted in Asia, Microsoft, Windows at 4:42 pm by Dr. Roy Schestowitz Last month it was four_countries and now this: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Asia_usage_for_Windows⦈_ All-time low for Windows: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇All-time_low_for_Windows⦈_ Summary: The decline of Microsoft Windows continues; sooner or later Android (Linux inside) will be dominant in almost every country in terms of its market share or number of users ⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢿⣿⡿⠿⢿⠛⢟⣻⣿⣿⡿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣤⣀⣄⣮⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣟⣷⠲⠅⠩⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣾⣿⠛⠿⠙⠛⠁⠀⠀⠀⠀⠐⠛⠛⠛⠛⣿⡵⠐⠷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠉⠁⠀⠈⠉⠛⠟⠏⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠋⠀⢠⠌⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠍⢹⣿⡔⢄⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡞⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⡦⠀⠃⠀⠀⠙⠛⠀⠀⠀⠀⠀⢀⣤⣤⣼⣿⣿⣾⣤⡄⠀⣀⣀⣄⣀⣀⡀⢠⣶⣀⠀⠀⡀⣿⣿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢻⡃⣠⡄⡐⠄⠊⠍⠴⡴⠄⠀⠰⣁⢑⠩⡻⠟⡛⢋⣶⣿⣬⣙⣛⢟⣋⣵⡾⡿⠟⣁⣴⢃⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣭⣭⣿⣿⣿⣿⣿⣿ ⡷⣈⢱⣭⡅⠭⣾⠦⣠⣭⡉⢍⣥⢦⣥⣶⢙⣤⢄⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡬⡴⡈⠛⣉⣸⣟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸⣙⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿ ⢉⠲⣿⣿⣇⢿⣶⣾⢰⣶⣈⠀⠈⠐⢙⢻⡎⡵⠫⣼⣦⣈⡋⠫⡉⣿⣿⣿⣿⠇⠭⣫⣿⣿⣿⡟⠵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣩⣙⣟⣿⣿⣛⣻⣿⣿⣿⣿ ⠿⢸⡶⠝⣵⡾⣰⡭⢰⣶⡶⢣⠀⣀⢠⣢⣿⣿⣶⢿⡿⣻⣷⡖⠟⣀⠰⣱⣶⡇⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿ ⠈⣅⠀⢡⡶⢆⠻⣣⢛⣋⢡⣶⣐⠮⣿⣿⣿⣿⣿⣏⡛⣿⣿⣿⡇⢦⣢⣿⣿⣳⠊⣿⡿⣿⡿⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢟⠻⠿⠿⠿⠿⣟⣻⢿⣿⣿ ⣷⣶⣾⣿⡄⠉⢍⣶⣶⠪⠳⡅⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠄⢿⢋⡳⡚⠛⠻⠾⡿⡿⣿⣿⣾⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡆⣜⡝⢿⢘⠿⠼⣿⢿⣯⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢬⣗⣘⡑⣾⣂⣴⣎⣐⣋⠭⣟⡻⣿⣿⣿⣷⣿⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿ ⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣶⡌⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣴⣶⣶⡄⠀⠀⠀⠀⢰⣿⣶⠈⡉⡉⢈⣉⠛⡛⢻⠁⣛⡿⠛⡛⡿⢛⠛⢿⠛⡟⠛⡟⠛⠛⣟⠀⣻⠟⡛⢻⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⡿⠢⠈⣇⠘⢻⠁⠀⢈⡀⠙⠃⠸⠟⣇⠸⠃⣸⠀⠃⠀⡇⢸⠀⣿⠀⠻⡀⠰⠲⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠉⠉⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠟⢛⣉⠛⣻⣿ ⠀⠀⠀⠀⠀⢠⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣬⠉⠉⠉⠉⢡⣤⡍⠉⠉⠭⠍⠥⣤⣤⡄⠩⠍⠭⠍⠉⢉⣭⣤⣤⣤⣍⣉⡉⠉⣉⡉⠍⣡⣤⣬⣤⣤⣤⣤⣍⣉⣩⣤⣬⣭⣭⣭⣽⣿ ⣦⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠟⣡⣾⣿⣿⣶⣶⣤⣶⣾⣶⣶⣶⣶⣶⣶⣶⣆⢠⣤⣾⣿⣦⣬⣥⣭⣍⣤⣬⣉⣴⣦⡤⠤⠭⠭⠭⣭⢭⡭⠭⠭⣭⠭⢭⠭⠭⢭⣭⣭⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠛⢋⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣀⣀⣉⣈⣉⣀⣀⣉⣀⣈⣀⣀⣈⣉⢉⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣋⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠀⠀⠈⢉⣽⣿ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⢂⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢲⡖⡖⣶⡶⠖⡶⢶⠶⣶⢶⣶⡖⣶⢶⢶⣶⣶⡶⠲⣶⣶⣶⡶⠶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠂⡀⢒⡒⣸⣿ ⣿⣿⣿⣿⣿⠟⢛⣋⣡⠴⠾⠛⠛⠛⠿⠿⢿⠿⠿⢿⡿⠿⠿⠿⠿⠟⠛⠛⠛⢛⣛⣋⣉⣉⣉⣙⢃⣁⠃⡁⣉⡂⠂⡁⡀⣀⣅⠤⣍⡁⡁⢄⡌⣀⢠⣴⡃⠀⠀⢀⣀⣠⣤⣴⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠛⠋⠉⠁⠨⠤⠤⠴⠶⠿⠿⠿⠿⠿⠷⠶⠶⢿⣶⣶⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠹⠿⠟⠛⠻⠿⠿⠛⡛⣋⣉⣁⣈⣙⣉⣉⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿ ⠼⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠀⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠐⠒⠒⠂⠒⠒⠒⠒⠁⠂⠠⠘⠛⠋⠁⠙⠻⠿⠿⠿⠿⠿⠟⠻⠛⠙⠟⠛⠛⠉⠉⠛⠛⠋⠛⠛⠓⠒⠒⠒⢺⣿ ⣶⣶⣶⣶⣶⡶⢒⣶⣶⣶⣶⣶⣶⡖⣒⣶⣶⣶⣶⣶⣶⡶⢒⣶⣶⣶⣶⣶⣶⡖⢰⣶⣶⣶⣶⣶⣶⡖⢐⣶⣶⣶⣶⣶⣶⡶⢐⣶⣶⣶⣶⣶⣶⡶⢐⣶⣶⣶⣶⣶⣶⡶⢒⣶⣶⣶⣶⣶⣶⡶⠐⣶⣶⣶⣶⣶⣾⣿ ⣿⣿⣿⣿⡯⢀⣿⣿⣿⣿⣿⣿⡯⢀⣿⣿⣿⣿⣿⣿⡯⢀⣿⣿⣿⣿⣿⣿⡯⢀⣿⣿⣿⣿⣿⣿⡯⢀⣿⣿⣿⣿⣿⣿⡯⢀⣿⣿⣿⣿⣿⣿⡿⢄⣾⣿⣿⣿⣿⣿⡿⢄⣾⣿⣿⣿⣿⣿⡿⢄⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣯⣀⣿⣿⣿⣿⣿⣿⣯⣄⣿⣿⣿⣿⣿⣿⣯⣄⣿⣿⣿⣿⣿⣿⣯⣄⣿⣿⣿⣿⣿⣿⣯⣄⣿⣿⣿⣿⣿⣿⣯⣄⣿⣿⣿⣿⣿⣿⣯⣄⣿⣿⣿⣿⣿⣿⣯⣄⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 3015 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_02/10/2022:_KStars_3.6.1_and_DjangoCon_Europe_2022⠀✐ Posted in News_Roundup at 3:25 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Server o Instructionals/Technical o Desktop_Environments/WMs # K_Desktop_Environment/KDE_SC/Qt * Distributions_and_Operating_Systems o Canonical/Ubuntu_Family o Open_Hardware/Modding * Free,_Libre,_and_Open_Source_Software o Web_Browsers/Web_Servers o Education o Programming/Development # TeX # Java * Leftovers o Education o Hardware o Health/Nutrition/Agriculture o Proprietary o Security # Privacy/Surveillance o Defence/Aggression o Environment # Energy 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 * § GNU/Linux⠀➾ o § Server⠀➾ # ⚓ GNU World Order (Audio Show) ☛ GNU_World_Order_480⠀⇛ **kldap** , **kleopatra** , **klickety** , **klines** , and **kmag** from the KDE software series of Slackware. # ⚓ Video ☛ Google_Assimilates_Your_Heath_Data_–_Invidious⠀⇛ This week in the Weekly News Roundup, Google will start Assimilating Your FitBit Data, 2FA is falling apart, and more IT work is being done by non-IT employees. o § Instructionals/Technical⠀➾ # ⚓ [Old] CSS_Fundamentals⠀⇛ My team recently recruited 6 new grads. As part of their onboarding they were going to tackle CSS. I wanted to give them my take on what’s important to know in CSS. # ⚓ Linux Capable ☛ How_to_Install_Plex_Media_Server_on_Ubuntu 22.04_LTS⠀⇛ Plex Media Server is a widely used software to store all your digital media content and access it via various client applications. It is popular among users for its ability to store TV Shows and Movie Libraries and share content with friends and family members. Plex Media Server has continuously grown in popularity and now supports many platforms. Some of the most popular client applications for accessing content from a Plex Media Server include NVIDIA Shield, Roku, Mobile App, and many more. The software organizes your files and content into categories, making it easy to find and use. In addition, the Plex Media Server provides security and privacy features that allow you to control who can access your content and when. The Plex Media Server is a great way to store and share your digital media content with others. In the following tutorial, you will learn how to install Plex Media Server on Ubuntu 22.04 LTS Jammy Jellyfish by securely importing the GPG key and official Plex repository and some tips on basic sets creating a reverse proxy with Nginx. # ⚓ Data Swamp ☛ My_NixOS_workflow_after_migrating_from OpenBSD⠀⇛ After successfully switching my small computer fleet to NixOS, I’d like to share about the journey. # ⚓ Linux Capable ☛ How_to_Install_qBittorrent_on_Raspberry_Pi OS⠀⇛ qBittorrent is a cross-platform free and open- source BitTorrent client. qBittorrent is a native application written in C++ which uses Boost, Qt 5 toolkit, and libtorrent-rasterbar library.qBittorrent aims to meet the needs of most users while using as little CPU and memory as possible. The program also has a built-in search engine with support for healthy trackers and mirrors. You can create torrents through the interface or by passing parameters to qBittorrent on the command line. qBittorrent is very popular amongst torrent users as the main alternative to UTorrent due to its lightweight footprint, lack of intrusive advertising, and additional features such as an integrated search engine, remote control via the Web user interface, IP filtering, sequential downloading, etc. In the following tutorial, you will learn how to install qBittorrent on Raspberry Pi desktop GUI and qBittorrent-nox, which can be installed on a desktop or headless server using the command line terminal to access the WEB UI. # ⚓ Linux Hint ☛ How_to_Install_Roblox_on_Linux_Mint_21⠀⇛ The developers of Roblox introduced their tool as an “Imagination Platform” where people can play millions of games. Not only this, but it’s also a game creation platform used by game lovers to create their own games. This online game platform Roblox is growing rapidly and getting popular among users. They made millions of worldwide users in a small period. Developers can create games by making use of language Lua. Roblox is a Windows/macOS application and cannot run on a Linux system directly. In the below- mentioned process, you will see Roblox platform running on Linux Mint 21 system. # ⚓ Linux Hint ☛ How_To_Read_exFAT_Partitions_in_Linux⠀⇛ This tutorial explains how to mount and read exFAT partitions in Linux. After reading this tutorial, you will be able to read the content within exFAT (Extended File Allocation Table) partitions. After the practical instructions, I briefly introduced the different Microsoft partition types, which will also help you understand the possible reasons behind your difficulty reading the exFAT file systems. Basic mount commands are also described at the end of this document. All instructions in this tutorial include screenshots, making it easy for every Linux user to understand and apply them. # ⚓ Linux Hint ☛ Docker_Commands⠀⇛ Are you new to Docker? Are you struggling with the Docker commands? Are you curious about how Docker works and how do Docker container images build? Well, luckily, you have reached the right place! In this hands-on, brief, and self-paced tutorial, we will help you use the Docker commands in the Ubuntu operating system. This guide will provide a brief overview of what Docker is and how it works, how to install Docker on Ubuntu, and how to use Docker commands in Dockers. We will demonstrate the primarily used Docker command and present some quick examples to enable you to use the Docker commands in your applications. # ⚓ Linux Hint ☛ AutoSSH_Command_in_Linux⠀⇛ Working with Ubuntu allows you to use all essential applications like email, Office Suite, browsers, media, or social apps. Most applications required to run an organization, home, school, or enterprise come pre-installed, and thousands more are available in the Ubuntu software center. The Ubuntu operating system is very simple and easy to use and clean. In fact, it is way simpler than any other mainstream competition. Windows and Mac operating system users may experience some differences in the Ubuntu operating system, but they certainly will not feel any difficulty using it. This article is designed around using the AutoSSH command in Ubuntu operating system. We will define the basic meaning of the AutoSSH command and how to use it in the Ubuntu 22.04 operating system. # ⚓ Linux Hint ☛ How_to_Install_TimeShift_on_Raspberry_Pi⠀⇛ Having your data backed up can really save you a lot of trouble in case of any unexpected error that causes your system to not function properly. Though reinstalling the Linux operating system is not much of a big deal, you must install all the applications again and most importantly you might lose some of your important data. TimeShift is one of the free tools that can create a backup for your Linux operating system and in case of something goes wrong, you can restore your system. So read this guide to go through the procedure of installing TimeShift on Raspberry Pi. # ⚓ Linux Hint ☛ How_to_Install_Raspup_Puppy_Linux_OS_on Raspberry_Pi⠀⇛ Raspup, a port of Puppy Linux, is a lightweight, easy-to-use operating system designed for low- powered devices like Raspberry Pi. You can run this entire operating system on RAM. Its latest version takes hardly 600MB of memory, making it an ideal operating system to run even on old Raspberry Pi models. Several lightweight applications are already installed, such as the Midori browser, Abiword, Mplayer, and more. You can install other applications from the built-in Puppy Package Manager. # ⚓ Linux Hint ☛ How_to_Find_Hardware_Details_Raspberry_Pi GUI⠀⇛ Getting hardware details about your Raspberry Pi device through commands is a hectic task for most users. You will need to search for commands; each command will provide different results. You won’t get all your system hardware information with a single command. However, there is a GUI-based application designed especially for Linux users that provides them the freedom to get real-time system information. If you are a Raspberry Pi user and want to find hardware details, follow this article to install the GUI application and get the information onto your system desktop. # ⚓ Linux Hint ☛ Three_Ways_to_Delete_the_Partitions_Under Linux⠀⇛ This tutorial explains how to remove the partitions under Linux using different tools including fdisk, cfdisk and gparted. After reading this article, you will be able to delete the partitions in Linux by applying a few steps. The command line techniques that are shared in the following examples are valid for all the Linux distributions. In some cases, some additional packages need to be installed. Additionally, we also included the steps for the users who are looking for a graphical method. All the instructions in this document contain screenshots to make it easy for every Linux user to understand and implement them independently of their experience level. # ⚓ Linux Hint ☛ How_to_Place_the_Brave_Browser’s_Cache_in RAM⠀⇛ Your web browser cache stores images, HTML, and JavaScript from the sites that you visit in a local cache. This allows for much faster page loading and less bandwidth usage. Basically, once an asset is saved to the cache, it is reread locally unless there has been some sort of change remotely. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ KStar Development ☛ KStars_v3.6.1_Released⠀⇛ KStars v3.6.1 is released on 2022.10.02 for MacOS, Linux, and Windows. It’s a bi-monthly bugfix release with a couple of exciting features. Due to major changes in this release, we are releasing it as Early Preview. We hope to release final stable release in a few weeks given the user feedback. * § Distributions and Operating Systems⠀➾ o § Canonical/Ubuntu Family⠀➾ # ⚓ Tom’s Hardware ☛ Ubuntu_22.10_Arrives_For_Beta_Testing⠀⇛ New features in 22.10 include a new Quick Settings menu that lets you toggle changes rather than flying out a whole menu, including quickly changing an audio device. There’s been a revamp of the Nautilus file manager, which now uses the GTK4 toolkit and has tabs, a pop-out sidebar, redesigned spacing and icons, and generally a fresh new modern look that’s (whisper it) somewhat Mac-like. You can also finally use your mouse to select multiple files by dragging a box around them. o § Open Hardware/Modding⠀➾ # ⚓ [Old] ElectroDacus⠀⇛ Due to semiconductor shortages products are out of stock until around November 2022. # ⚓ Adafruit ☛ The_Most_Legendary_Arcade_In_North_America⠀⇛ I had never heard of the fighting game community before but somehow watching this video made me feel nostalgic for it. [...] * § Free, Libre, and Open Source Software⠀➾ o § Web Browsers/Web Servers⠀➾ # ⚓ How_much_time_do_we_waste_waiting_for_websites_to_load?⠀⇛ After all, a slow website leads to a lower ranking on Google which can cost a website dearly. In 2013 a case study found that an extra 2 seconds of load time resulted in 87% less conversions on an e- commerce website. This often cited number tells us that speed matters. Yet website speeds clearly haven’t improved. o § Education⠀➾ # ⚓ Introduction_to_the_Theory_of_Programming_Languages:_full book_now_freely_available⠀⇛ Short version: the full text of my Introduction to the Theory of Programming Languages book (second printing, 1991) is now available. This page has more details including the table of chapters, and a link to the PDF (3.3MB, 448 + xvi pages). The book is a survey of methods for language description, particularly semantics (operational, translational, denotational, axiomatic, complementary) and also serves as an introduction to formal methods. Obviously it would be written differently today but it may still have its use. # ⚓ Paolo Melchiorre ☛ DjangoCon_Europe_2022⠀⇛ A lightning talk on the history of the documentation full-text search function on the djangoproject.com site, a report on the latest implemented features and an invitation to contribute. o § Programming/Development⠀➾ # ⚓ Ruben Schade ☛ Do_I_need_line_numbers?_Yes⠀⇛ I’ve been having fun lately challenging assumptions about my operating environment. I’ve got into the habit of blindly enabling settings without stopping to think if I need them, or for what reason. I’ve been surprised how much stuff was either built on sand, or that have been held over by sheer inertia and force of habit. Line numbers are one of these. No matter if I’m starting with Vim, Kate, or a code repository site, I instinctively reach for the tool’s respective line number setting or dotfile config, and everything is right in the world. But… why? What use are they? # ⚓ Daniel Lemire ☛ A_review_of_elementary_data_types_:_numbers and_strings⠀⇛ Computer programming starts with the organization of the data into data structures. In almost all cases, we work with strings or numbers. It is critical to understand these building blocks to become an expert programmer. # ⚓ My_Developer_Setup_in_2022⠀⇛ Getting to know the vast ecosystem around Developer Experience made me more passionate about the open source community and led me ultimately to even build my own OSS project that helps other developers. I believe that “optimizing” my setup sparked renewed interest in development for me. Working on a Developer Experience product could be my next passion. And there are many companies that work on tools to help developers and non-developers alike that I might be interested in exploring as future job candidates. Companies that develop things like IDEs (replit, VSCode), or others that write an app launcher (Raycast), Calendar (Cron) or maybe a better tool for work messaging (Slack 😠). Hopefully I gave you some motivation to work on your dev setup, but let’s look at the more concrete reasoning. # ⚓ The_Renaissance_of_the_Command_Line⠀⇛ Recently, I’ve been falling in love with the CLI. I went through a rabbit hole of trying to make my developer experience better and found that a lot of stuff are snappier to do on the terminal. On top of that, there have been a lot of innovation surrounding the terminal. So hopefully I can convince you to give the terminal more attention and that you find it rewarding. # ⚓ Linux Hint ☛ Function_Pointers_in_C⠀⇛ “Whenever we declare any variable in the program, it allocates some memory for itself, and we can access the values stored in this variable by pointing to the address of the memory location of the variable. Likewise, whenever we make a function in the program, some memory size also gets allocated for that function, and if, at any point in the program, we want to access that function, we may simply point towards the memory address of that function. This is done by the function pointers; the function pointers in the programming language C simply make the call to the function for which they are appointed as a pointer, just as a normal type of function. The declaration of the function pointer is represented with the symbol “*” and it has the same parameters of the function, just like the same function to which it points.” # ⚓ Linux Hint ☛ How_to_Reverse_a_String_In_C⠀⇛ “We use the reverse string function whenever we are required to change or reverse the order of string in a program. For example, if we have initially declared a char string of memory size 5 as “cloth”, now if we want to apply the string reversal operation on this string, then we will get the output string as “htolc”. There exist several methods to perform the string reversal in the C, and they are strev func (), recursion func (), and string reversal using the pointers. We can also verify the palindrome string using the string reversal methods. A palindrome is a string whose order of the characters remains unchanged even after the implementation of the string reversal operation on it.” # ⚓ Mandell_O_Mandell,_Please_Grant_Me_Some_Insight!_|_Everyday Is_A_School_Day⠀⇛ Bring a textbook to life by Using a simple Natural Language Processing method (Ngram) to guide focused reading and build a robust differential diagnosis # ⚓ Nicholas Tietz-Sokolsky ☛ RC_Week_1:_Getting_Unexpected Extrovert_Energy_|_nicholas@web⠀⇛ Pair programming is hard. It’s really freaking hard. If you’re not careful (and, reader, I’m not careful) it can turn into performance, and that is not what it’s supposed to be! I’m working through some feelings of needing to be right, needing to not flail around or be ignorant when I’m the driver. Fellow Recursers have given me some really great advice on how to work on this. Next week, pairing will be a focus, and I am looking forward to the practice! # § TeX⠀➾ # ⚓ Linux Hint ☛ How_to_Write_and_Use_a_Derivative_Symbol in_LaTeX⠀⇛ There is a fundamental approach to calculus known as derivatives. Calculating the derivative of a real variable function involves measuring how sensitive a change in the input value (the argument) is to a change in the output value (the function value). While calculating any mathematical number or question of derivatives, it is essential to write a derivative symbol. That’s why document processors like LaTeX provide simple source codes to write derivative symbols. So in this tutorial, we will give you some brief information on how to write and use a derivative symbol in LateX. # ⚓ Linux Hint ☛ How_to_Create_and_use_summation_symbol in_LaTeX⠀⇛ In mathematics, summation refers to adding a series of any type of digits. We can easily perform summation on other forms of values along with the new numbers. In mathematics, we express summation with the sigma symbol, “∑,” which is a Greek capital letter. An index accompanies this symbol that encompasses all the essential terms to be considered in the sum. Hence, the summation symbol has a vital role in mathematical expressions. So, let’s look at the methods for creating and using summation in LaTeX. # ⚓ Linux Hint ☛ How_to_Add_a_Line_Break_in_LaTeX⠀⇛ A document may include a long paragraph, so it is good to break the paragraph into short ones to make it more readable. A line break or paragraph break helps writers to create clean documents. Breaking a paragraph or line also helps readers read long sentences. That’s why document processors like LaTeX contain various source codes to add a line break in the document. However, many new users don’t know how to create the line break in the LaTeX document page. So, in this tutorial, we will show different ways to add the line break in LaTeX. # ⚓ Linux Hint ☛ How_to_Wrap_a_Text_Around_Figures_in LaTeX⠀⇛ Sometimes, it is essential to wrap text around a figure to maintain the flow of the information in the document. Usually, wrapping text stands for the figure caption and the context of the images. Many document processors support the text wrapping feature to create clean research papers. LaTeX also has the same feature, but many users don’t know how to do it. So if you are also interested in learning, this tutorial is for you. In this tutorial, we’ll show you how to wrap text around figures in LaTeX. # ⚓ Linux Hint ☛ How_to_Write_and_Use_an_Angstrom_Symbol in_LaTeX⠀⇛ An angstrom symbol is a unit of length that equals 0.1 nanometres. This symbol is mainly used in physics to measure wavelengths, including their compound structures and microscopic components. The angstrom symbol is also abundantly used in chemistry and natural sciences to measure atoms, molecules, and other chemical bonds. In LaTeX, you can write an angstrom symbol, but it requires the correct source code. So, in this tutorial, we will give you a complete brief on the source codes to write an angstrom symbol in LaTeX. # § Java⠀➾ # ⚓ Matt Rickard ☛ The_Promise_of_Write_Once,_Run Anywhere⠀⇛ The idea can be traced all the way back to the 1960s with the start of virtualization (the IBM M44/44X that emulated multiple IBM 7044 mainframes). The catchy slogan wouldn’t come around until 1995 when Sun Microsystem was marketing Java and the JVM. While Java had many advantages, its portability was instrumental to its success. # ⚓ Linux Hint ☛ Fibonacci_Numbers_in_Java_Language⠀⇛ The Fibonacci numbers is a particular sequence of positive (whole) integers, beginning from zero to positive infinity. The current Fibonacci number is obtained by adding the immediate previous two Fibonacci numbers. The immediate previous two Fibonacci numbers are not just any numbers. * § Leftovers⠀➾ o ⚓ New York Times ☛ The_Long_Road_to_Driverless_Trucks⠀⇛ Companies like Kodiak know the technology is a long way from the moment trucks can drive anywhere on their own. So they are looking for ways to deploy self-driving trucks solely on highways, whose long, uninterrupted stretches are easier to navigate than city streets teeming with stop-and-go traffic. “Highways are a more structured environment,” said Alex Rodrigues, chief executive of the self-driving-truck start-up Embark. “You know where every car is supposed to be going. They’re in lanes. They’re headed in the same direction.” Restricting these trucks to the highway also plays to their strengths. “The biggest problems for long- haul truckers are fatigue, distraction and boredom,” Mr. Rodrigues explained on a recent afternoon as one of his company’s trucks cruised down a highway in Northern California. “Robots don’t have a problem with any of that.” o § Education⠀➾ # ⚓ Hackaday ☛ DIY_Wind_Tunnel_Aims_To_Educate_The_Youth⠀⇛ Typically, when we talk about wind tunnels, we think of the big facilities in use by the aerospace and motorsports industries. However, there’s nothing stopping you building a wind tunnel of your very own, and it may even be easier than you think! [Jude Pullen] has whipped up just such a design with DIY in mind. o § Hardware⠀➾ # ⚓ Hackaday ☛ Building_A_Tessellated_NeoPixel_Clock⠀⇛ Anyone can buy a clock, but building your own lets you express your creative flair along the way. [Edison Science Corner] did just that with this neat sci-fi looking design. # ⚓ Hackaday ☛ DREEMWORK_Lets_You_Code_Morse_From_Inside_Your Dream⠀⇛ Lucid dreaming fascinates hackers. Every few years for over a decade now, we’ve seen a serious project dedicated to studying or taking advantage of this phenomenon, and the interest in this topic hasn’t faded still. [Michael] has contacted us to tell about a small and unconventional breakthrough that a few lucid dream hackers have accomplished — communicating in Morse code from their dream using eye movements. # ⚓ Hackaday ☛ 2022_Cyberdeck_Contest:_A_Chorded-Keyboard Wearable_Cyberdeck⠀⇛ Those of us who are unreformed hunt-and-peck typists are often baffled by the keyboard skills of those with more formal training. Home row? Specific fingers for specific keys? The mind boggles. And chorded keyboards? That’s straight-up witchcraft! # ⚓ Hackaday ☛ Lamp_Flashing_Module_Is_Perfect_For_Automotive Use⠀⇛ Modern cars tend to have quite advanced lighting systems, all integrated under the control of the car’s computer. Back in the day, though, things like brake lights and indicators were all done with analog electronics. If your classic car needs a good old-fashioned flasher module, you might find this build from [DIY Guy Chris] useful. # ⚓ Hackaday ☛ DVD_Drives_Turned_Into_Microscopes⠀⇛ With the advent of streaming services, plenty of people are opting to forego the collection of physical media. In turn, there are now a lot of optical drives sitting unused in parts bins and old computers. If you’d like something useful to do with this now-obsolete technology, you can have a try at turning one into a laser microscope. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Bridge Michigan ☛ Dana_Nessel_sues_former_west_Michigan company_over_PFAS,_other_pollution⠀⇛ FKI is the latest in a host of companies sued by the state for their alleged role in Michigan’s PFAS contamination crisis. In 2020, Nessel announced a sweeping lawsuit against 17 companies, including 3M and DuPont, alleging the PFAS manufacturers knew for decades their products posed health risks, but “intentionally hid” those concerns from the public. # ⚓ Scheerpost ☛ Denial_of_Mental_Healthcare:_‘Your_Therapist Will_See_You_Now_or_Will_They?’⠀⇛ The denial of timely mental health care is immoral and unethical and it’s the reason why therapists employed by Kaiser are on strike in Northern California and Hawai’i. # ⚓ TruthOut ☛ Abled-Bodied_Leftists_Cannot_Abandon_Disabled Solidarity_to_“Move_On”_From_COVID⠀⇛ o § Proprietary⠀➾ # ⚓ India Times ☛ Here’s_why_Apple_has_fired_its_vice_president of_procurement⠀⇛ The TikTok interview that got Blevins sacked was taken by TikTok creator Daniel Mac who he asked Blevins what he does for a living, to which the Apple executive’s answer was: “I race cars and play golf and fondle big-breasted women. But I take weekends and major holidays off.” The interview was taken earlier this month and went viral. o § Security⠀➾ # § Privacy/Surveillance⠀➾ # ⚓ Make Use Of ☛ Why_Google_Is_Banned_From_Danish Classrooms⠀⇛ However, data protection concerns mean that the tech giant could be expelled from parts, or potentially all, of the EU. Here’s what you need to know. # ⚓ The Hill ☛ A_year_after_bombshell_Facebook disclosure,_fight_for_kids’_online_safety_forges ahead⠀⇛ The documents released by Haugen and her wide-ranging testimony to U.S. and global lawmakers dealt with a range of topics, from the spread of misinformation to human exploitation. But her accusations about how the company, especially through Instagram, negatively impacted teen mental health made the most waves. # ⚓ EFF ☛ California_Leads_on_Reproductive_and_Trans Health_Data_Privacy⠀⇛ EFF encourages other states to consider passing similar bills adapted to their own state civil and criminal laws. o § Defence/Aggression⠀➾ # ⚓ Damaged_cultural_sites_in_Ukraine_verified_by_UNESCO⠀⇛ UNESCO is conducting a preliminary damage assessment for cultural properties* by cross- checking the reported incidents with multiple credible sources. These published data which will be regularly updated do not commit the Organization. UNESCO is also developing, with its partner organizations, a mechanism for independent coordinated assessment of data in Ukraine, including satellite image analysis, in line with provisions of the 1954 Hague Convention for the Protection of Cultural Property in the Event of Armed Conflict. # ⚓ Medforth ☛ Islamic_headscarf:_for_the_European_Union “freedom_will_be_found_by_wearing_the_hijab”⠀⇛ The campaign, which initially went relatively unnoticed and was co-financed by the European Union, eventually aroused the ire of [Internet] users and numerous politicians such as Nadine Morano, who wrote to Ursula von der Leyen. “Madam President of the European Commission, I call on you to put an immediate end to this scandal of using EU funds for scandalous Islamist propaganda. This campaign is an insult to Iranian women who are dying for their freedom,” she tweeted on Wednesday September 28. # ⚓ Meduza ☛ Ukrainian_forces_enter_Lyman_—_Meduza⠀⇛ Ukrainian forces have entered Lyman. A video appeared on social media showing the Ukrainian military raising a flag on a monument at the entrance to the city. Witnesses confirm that Ukrainian forces are in the western part of the city. The Russian Ministry of Defense has announced that “in connection with a developing threat of encirclement” Russian troops have been withdrawn from Lyman “to more advantageous lines.” # ⚓ Meduza ☛ 20_civilians_killed_by_shelling_in_Kupiansk_— Meduza⠀⇛ A convoy of cars carrying civilians was hit by shelling in the Kupiansk area of Kharkiv. Regional Governor Oleh Synehubov reported on Telegram that 20 people were killed. # ⚓ Meduza ☛ Russia_limits_trucking_for_companies_from_the_EU, Ukraine,_Norway,_and_UK_—_Meduza⠀⇛ The Russian government will ban truck transport through Russia for companies from countries which have previously taken analogous measures against Russian freight carriers. The decree was published on October 1. # ⚓ Meduza ☛ Ramzan_Kadyrov_calls_for_drastic_measures_in Ukraine_—_Meduza⠀⇛ Ramzan Kadyrov, head of Chechnya, reacted to Russia’s loss of Lyman with a Telegram post full of harsh criticism of the commander of the Central Military District, Colonel General Alexander Lapin. # ⚓ Meduza ☛ Poland_completes_wall_on_its_border_with_Belarus_— Meduza⠀⇛ Poland has completed construction of fences on its border with Belarus, says Stanislaw Zaryn, a representative of Poland’s public security services. # ⚓ Meduza ☛ Poet_Boris_Bulgakov_was_handed_a_draft_summons_as he_walked_out_of_jail_—_Meduza⠀⇛ The poet Boris Bulgakov, who took part in the Mayakovsky Readings, an anti-draft demonstration with roots in Soviet dissident movements, told Mediazona that he was handed a summons as he was released from detention. o § Environment⠀➾ # ⚓ The Hill ☛ UN:_Nord_Stream_pipeline_rupture_largest_single release_of_methane_recorded⠀⇛ Methane has more than 80 times the warming power of carbon dioxide over the first 20 years in the atmosphere, although carbon dioxide has a longer lasting effect, according to the Environmental Defense Fund. # ⚓ Reuters ☛ Nord_Stream_rupture_may_mark_biggest_single methane_release_ever_recorded,_U.N._says⠀⇛ Researchers at GHGSat, which uses satellites to monitor methane emissions, estimated the leak rate from one of four rupture points was 22,920 kilograms per hour. That is equivalent to burning about 630,000 pounds of coal every hour, GHGSat said in a statement. # ⚓ Hackaday ☛ Unintentional_Emissions⠀⇛ First, it was the WiFi router: my ancient WRT54G that had given me nearly two decades service. Something finally gave out in the 2.4 GHz circuitry, and it would WiFi no more. Before my tears could dry, our thermometer went on the fritz. It’s one of those outdoor jobbies that transmits the temperature to an indoor receiver. After that, the remote for our office lights stopped working, but it was long overdue for a battery change. # ⚓ Common Dreams ☛ Opinion_|_Climate_Extremes_and_a_Democracy Under_Threat⠀⇛ The hurricane season and the election season have converged in the United States. The prospect of catastrophic, irreversible climate change and the potential demise of democracy are both very real. The fate of these essential pillars of our society hinge largely on what we all do in the coming weeks and months. # ⚓ TruthOut ☛ California_Gov._Newsom_Proposes_Windfall_Profits Tax_on_Big_Oil⠀⇛ # ⚓ Common Dreams ☛ California_Gov._Newsom_Proposes_Windfall Profits_Tax_on_Big_Oil⠀⇛ While crude oil prices are down nationally, big oil companies have increased gas prices in California by a record 84 cents per gallon in just the last 10 days.  # § Energy⠀➾ # ⚓ Björn Wärmedal ☛ Just_Happy_For_Bike_Lanes⠀⇛ It’s about 8 km from my home to the airport, a little longer by car I believe. Taking the bike is actually quite a breeze, because there’s a protected bike lane all the way. While I do cross some roads it’s really just streets with very little traffic. And bikes have the right of way in almost all of those places. The airport even has dedicated bike parking, with a somewhat protective roof. # ⚓ Bitcoin ☛ SEC_Charges_2_Firms_and_4_Individuals_in_ [Cryptocurrency]_Pump-and-Dump_Scheme⠀⇛ The U.S. Securities and Exchange Commission (SEC) said Friday that it has filed charges against two firms and four individuals allegedly perpetrating a cryptocurrency pump- and-dump scheme. The two companies are Bermuda-based Arbitrade Ltd. and Canadian firm Cryptobontix Inc. The other defendants are their principals — Troy R. J. Hogg, James L. Goldberg, and Stephen L. Braverman — and Max W. Barber, founder and sole owner of SION Trading. SION is named a relief defendant in the case. o § Finance⠀➾ # ⚓ CoryDoctorow ☛ Twitch_does_a_chokepoint_capitalism⠀⇛ When Amazon bought Twitch, the story was that the new conglomerate would be more efficient and that would benefit everyone – streamers and audiences. That’s the story we hear about every anticompetitive merger, and it’s always a lie. [...] But for Twitch’s most valuable streamers – the ones it courted most aggressively – there’s a better revenue split: 70/30 (the worker gets 70%, while Amazon takes 30%). These are the deals that Clancy is unilaterally cancelling. Clancy says it’s not fair that the company’s favored streamers should be earning more than the majority of streamers, which is a pretty good point. What he doesn’t explain is why the solution to that unfairness isn’t to just give all the streamers a 70/30 split – especially in light of all the new revenue he boasts about. After all, nearly all of Twitch’s costs are fixed – adding a new monetization feature costs the same whether there are a million Twitch streamers or just two of them. That means that every streamer boosts the dividends from new monetization features. The major variable cost for Twitch – the cost that changes based on the number of streamers on the service – is bandwidth, which may be why Clancy blames the clawback on it. But this is weird. As Sam Biddle wrote, “Amazon is charging Amazon so much money to run the business via Amazon that it has no choice but to take more money from streamers.” # ⚓ TruthOut ☛ Corporations_Are_Spending_a_Ton_to_Stop_Low-Wage Workers_From_Unionizing⠀⇛ # ⚓ TruthOut ☛ GEICO_Is_Trying_to_Crush_Workers’_Attempts_to Form_an_Independent_Union⠀⇛ # ⚓ Common Dreams ☛ ‘Enough_is_Enough’:_Hundreds_of_Thousands March_Across_the_UK⠀⇛ The organizers of the ‘Enough is Enough’ campaign lists their five demands as: o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ New York Times ☛ Big_Tech_Should_Support_the_Iranian People,_Not_the_Regime⠀⇛ For Twitter, there’s one initial easy step: making #MahsaAmini and #مهسا_امینی “official.” Despite the record-breaking number of #MahsaAmini tweets, the hashtag remains flagless. Hashflags are custom emojis specific to Twitter that help boost a particular hashtag on the platform and draw attention to a movement. By introducing a hashflag, Twitter would also make it less likely that misleadingly similar hashtags for #MahsaAmini will divert attention. Whether just an accidental typo, or an effort ​​by pro- government or government-owned accounts to reduce engagement, similar hashtags can divert attention and cause confusion. The latest protests have once again highlighted the dangers of Telegram’s lack of effective content moderation policies and practices. This has endangered vulnerable users, especially activists targeted by authoritarian states. Telegram channels associated with or supporting the Islamic Republic’s security forces have sprung up to identify protesters. We do know that in the past Telegram has responded to pressure to protect their users: They banned Russian state media accounts following the invasion of Ukraine. It’s past time for Telegram to commence dialogue with civil society and experts to proactively put in place basic human rights standards. # ⚓ MIT Technology Review ☛ The_EU_wants_to_put_companies_on the_hook_for_harmful_AI⠀⇛ The new bill, called the AI Liability Directive, will add teeth to the EU’s AI Act, which is set to become EU law around the same time. The AI Act would require extra checks for “high risk” uses of AI that have the most potential to harm people, including systems for policing, recruitment, or health care. The new liability bill would give people and companies the right to sue for damages after being harmed by an AI system. The goal is to hold developers, producers, and users of the technologies accountable, and require them to explain how their AI systems were built and trained. Tech companies that fail to follow the rules risk EU-wide class actions. # ⚓ Common Dreams ☛ Opinion_|_Climate_Idiocy_of_DeSantis Exposes_Him_as_Threat_to_Entire_Nation⠀⇛ Florida Governor Ron DeSantis has abruptly been handed an honest-to-God crisis that may distract him from his usual antics of trolling Venezuelan asylum-seekers, firing elected prosecutors who disagree with him on coerced childbirth, and firing scientists who wouldn’t manipulate state COVID statistics for him. # ⚓ Common Dreams ☛ Opinion_|_Fascist_Victory_in_Italy_a Setback_for_the_Future⠀⇛ In any unequal society becoming substantially more unequal, democratic forces better directly address that growing inequality. Or else get prepared to face the consequences. # ⚓ Common Dreams ☛ Opinion_|_New_GOP_Agenda_Proves_These People_Are_Just_Plain_Nuts⠀⇛ Let me say one word to you: Nuts. # § Misinformation/Disinformation/Propaganda⠀➾ # ⚓ Scoop News Group ☛ Nord_Stream_pipeline disinformation_fits_pattern_of_Russian_information warfare⠀⇛ Cyber scholar Thomas Rid, who has written extensively on Russian disinformation, said Sikorski’s tweet did something “very important,” in part because it “predictably got lots of engagement, most interestingly by the Russian Foreign Ministry pointing the finger at us.” (On Tuesday, Russian official and United Nations representative Dmitry Polyanskiy retweeted Sikorski’s now deleted message, thanking him for “making it crystal clear who stands behind this terrorist-style targeting of civilian infrastructure!”) o § Censorship/Free Speech⠀➾ # ⚓ Static Media ☛ Censorship_Was_The_Spark_That_Sent_Rod Serling_To_The_Twilight_Zone⠀⇛ Serling was expecting to deal with a lot of pushback and censorship with his script, but was still surprised by how extreme it all turned out to be. He later claimed the story was “gone over with a fine-tooth comb by 30 different people,” and that by the time it aired it was basically unrecognizable from the story Serling was trying to tell. As Smithsonian Magazine put it, “Any hint of the South was removed from the plot; not even a Coca-Cola bottle could appear, lest viewers invoke the idea of the region.” The whole thing made Serling rethink his approach to social commentary, and soon after he had the idea for “The Twilight Zone,” a show that was about apolitical sci-fi/fantasy concepts on the surface, but often used them as an avenue to explore more controversial ideas. It was through the “Twilight Zone” that Serling managed to get his Emmett Till- inspired story aired on TV: the aforementioned episode “I Am the Night,” which is still one of the most memorable episodes of the series. # ⚓ Frontpage Magazine ☛ Christians_‘Face_Routine_Torture’_in Afghanistan⠀⇛ The estimated 15,000-20,000 Christians who remain in Afghanistan after the Taliban takeover “face routine torture and persecution from both the government and their own friends, families and communities,” a new report finds. This is not a new development. From the start, matters significantly worsened for Christians on August 15, 2021, following the Biden administration’s abrupt and poorly-planned withdrawal of U.S. troops, which caused the Central Asian nation to fall right back into the grips of the Taliban, an Islamic terrorist group complicit in the 9/11 attacks on the U.S. # ⚓ Scheerpost ☛ The_Hill_Cancels_Katie_Halper_for_Telling Truth_About_Israel⠀⇛ Katie Halper recorded a segment for The Hill’s Rising defending Congresswoman Rashida Tlaib from attacks over calling Israel an apartheid state. The Hill presents itself as a channel that opposes cancel culture and censorship. Halper says she was told that The Hill has a ban on opinion videos about Israel. When she pushed to have it aired as a show segment, she says she was fired. o § Freedom of Information / Freedom of the Press⠀➾ # ⚓ Iranian_journalist_seized_after_reporting_on_Mahsa_Amini funeral⠀⇛ Elahe Mohammadi (pictured) – a reporter for the pro-reform Hammihan newspaper – had been summoned to face the judicial authorities. But she was arrested on the way there on Thursday, 29 September, according to the newspaper. # ⚓ uni Michigan ☛ Here’s_how_journalism_could_work_better_for all_of_us⠀⇛ It’s a well-established truth that one of the greatest indicators of a healthy and functioning democracy is the ability to disseminate accurate and accessible journalism to the general public. And, as midterm elections loom right around the corner, journalism could not be more crucial right now: the continuation of democratic backsliding, economic turmoil and deep political divisions are some of our most obvious challenges as a country. On the surface, not much is different from the American political landscape of the ’60s and ’70s. And yet, in living rooms and handheld devices across the country, our reality is much more stark: whether a fact is in fact a fact is being contested, misinformation runs rampant and common ideals such as democracy, citizenry and voting have become foundations for contentious debate. # ⚓ CPJ ☛ Zambian_officials_threaten_journalist_Wellington Chanda_over_reporting⠀⇛ At least four officials with Zambia’s ruling political party, United Party for National Development (UPND), threatened Wellington Chanda, a reporter for the privately owned City TV broadcaster in the northeastern town of Kasama, during two separate phone calls on August 7 and 8, 2022, over a City TV report, according to news reports, a statement by the Zambia chapter of the Media Institute of Southern Africa press freedom group, the journalist, and recordings of the calls. # ⚓ CPJ ☛ Khashoggi’s_legacy_will_forever_haunt_his_killers, says_CPJ’s_Sherif_Mansour⠀⇛ Washington, D.C., September 30, 2022 — The four years that have passed since Washington Post columnist and Saudi journalist Jamal Khashoggi was murdered and dismembered underscores the global failure to punish the killers of journalists around the world, the Committee to Protect Journalists said Friday. o § Civil Rights/Policing⠀➾ # ⚓ France24 ☛ How_China_uses_zero-Covid_policy_to_crack_down on_Tibetans⠀⇛ There has been a widespread outcry from the residents of Lhasa, the capital of the Chinese autonomous region of Tibet, about how local authorities are managing a Covid-19 lockdown, instated on August 9. Many people have gone online to post videos showing crowded quarantine centres, which they have nicknamed pigsties. When the videos were quickly censored, locals said it was another example of the Chinese government silencing Tibetan voices. # ⚓ ‘You_do_not_automate_people_out_of_their_jobs’:_Data journalism_bosses_on_the_rise_of_robots⠀⇛ Deepna Devkar, vice president of data science and engineering at CNN, said: “It’s actually the exact opposite. We’re here to enable journalists to do what they do best… # ⚓ Hindustan Times ☛ Iran:_Woman_arrested_for_eating_at restaurant_without_hijab,_says_report⠀⇛ Donya Rad was arrested after a photo of her and another woman eating at a Tehran restaurant without their headscarves was widely circulated online, reported CNN. # ⚓ CNN ☛ Iranian_security_forces_arrest_a_woman_for_eating_at restaurant_in_public_without_her_hijab,_family_says⠀⇛ Iranian security forces arrested a woman after a photo of her and another woman eating at a Tehran restaurant without their head scarves was widely circulated online, her family said Friday. The photo emerged Wednesday showing the two women having breakfast at a cafe that, like most coffeehouses in Iran, is traditionally patronized by men. One of the women in the photo, Donya Rad, was arrested shortly after the photo was published online. CNN spoke with her sister who said security agencies contacted Donya and summoned her to explain her actions. # ⚓ Saudi Arabia ☛ Iran_arrests_woman_for_eating_in_restaurant without_headscarf:_Sister⠀⇛ “Today, after going where she was told, she was arrested. After a few hours of silence, Donya told me in a short call that she was transferred to ward 209 of Evin prison,” she said, referring to a notorious wing of the Tehran jail which is reputedly run by the intelligence ministry. # ⚓ The Straits Times ☛ Iran_arrests_woman_for_eating_out without_hijab:_Sister⠀⇛ Persian media outside Iran have over the last days pointed to growing images of civil disobedience, with women in Iran sharing images of themselves walking, shopping or in cafes without headscarves. “They just went to get breakfast without headscarves. They were arrested. This is how brutal/sick the hijab policy is in Iran,” commented prominent US-based campaigner and journalist Omid Memarian on Twitter. # ⚓ TruthOut ☛ Protests_Against_Compulsory_Hijab_Sweep_Iran, With_Spotlight_on_Bodily_Autonomy⠀⇛ o § Internet Policy/Net Neutrality⠀➾ # ⚓ The Register UK ☛ UN’s_ITU_election_may_spell_the_end_of our_open_[Internet]⠀⇛ Speaking of Huawei, in 2019 it and China Mobile, China Unicom, and China’s Ministry of Industry and Information Technology (MIIT), did something unexpected: submit a proposal to the ITU for a standard called New IP (as in, Internet Protocol, the standard that helps glue our modern communications together). The entities behind New IP claimed it is needed because existing protocols don’t include sufficient quality-of-service guarantees, so netizens will struggle to handle latency-sensitive future applications, and also because current standards lack intrinsic security. New IP is controversial for two reasons. One is that the ITU does not oversee IP. That’s the IETF’s job. The IETF is a multi-stakeholder organization that accepts ideas from anywhere – the QUIC protocol that’s potentially on the way to replacing TCP originated at Google but was developed into a standard by the IETF. The ITU is a United Nations body so represents nation-states. The other is that New IP proposes a Many Networks – or ManyNets – approach to global internetworking, with distinct, individual networks allowed to set their own rules on access to systems and content. Some of the rules envisioned under New IP could require individuals to register for network access, and allow central control – even shutdowns – of traffic on a national network. # ⚓ Internet Society ☛ Sender_Pays:_What_Lessons_European Policy_Makers_Should_Take_From_The_Case_of_South_Korea⠀⇛ As proponents of new interconnection rules in Europe champion a new settlement regime, based on a model of “sending party pays”, there is one important question looming over the debate: why are proponents not championing the case of South Korea, where similar rules were implemented? The simple answer: it’s not a favorable example. o § Monopolies⠀➾ # ⚓ Stacey on IoT ☛ Podcast:_The_FTC_eyes_Amazon’s_iRobot_buy_– Stacey_on_IoT_|_Internet_of_Things_news_and_analysis⠀⇛ The Federal Trade Commission is looking into Amazon’s decision to purchase the maker of Roomba vacuum cleaners for $1.7 billion. The agency this week asked Amazon and iRobot for more information about the deal, so Kevin and I took a moment to explain exactly what the FTC should worry about. Then we talk about Wi-Fi sensing showing up in Signify’s WiZ lightbulbs, and a wireless power provider paired with smart tags enabling a new retail experience — all without batteries. We touch on Nvidia’s continued forays into the metaverse and its plans to create digital twins for retailers with its new Omniverse services. We also cover two surveys this week from MachineQ and Hitachi Vantara. Those surveys focus mostly on enterprise IoT adoption and things that stand in the way of them. We also cover Helium’s new deal to bring its decentralized 5G wireless network to T-Mobile and then discuss Tile’s new QR code stickers to create a tech-savvy label for your stuff that might get lost. It’s better than sewing your name in your underwear. Kevin then discusses his review of a LoRa-based IoT development kit from Blues Wireless. We end by answering a listener question about leak monitoring and water shut off tools. # § Copyrights⠀➾ # ⚓ Torrent Freak ☛ DNS_Providers_as_Piracy_Fighters? Enforcement_Groups_Weigh_Options⠀⇛ The World Intellectual Property Organization’s Advisory Committee on Enforcement recently heard how DNS providers have the ability to fight online piracy but could also face liability as secondary infringers. Veiled warnings like these are nothing new, but with piracy colossus Fmovies cited as a primary example, pressure on DNS entities is building once again. # ⚓ Final_Space_and_the_(sweet)_path_to_the_Torrent⠀⇛ Final Space has been removed from the face of the earth and has kind woke some people up regarding digital ownership of items, this is not something new, of course. Think about your Spotify library, if at some point Spotify kills your account, you’d loose [sic] everything in a heartbeat. Same with Netflix and all of the other services. # ⚓ Digital Music News ☛ Ed_Sheeran_‘Thinking_Out_Loud’ Copyright_Lawsuit_to_Proceed,_Federal_Judge_Rules⠀⇛ Back to the newest development in Structured Asset Sales’ copyright complaint against Ed Sheeran, though, the Halifax, West Yorkshire- born artist had been seeking a summary judgement dismissal of the infringement claim, which the litigants agreed involves elements (related to the aforementioned chord progression) that are “commonplace and unprotectable” when considered on their own. * § Gemini* and Gopher⠀➾ o § Personal⠀➾ # ⚓ Re:_Regarding_Life_Beyond_Earth⠀⇛ Ah, that’s not a good fit for how I see things. I’ve messed around enough with emergent systems to not presuppose a pre-existing blueprint or fully formed Intelligence. Great things can grow out of simple things, as you might remember from Luke (13: 18–19) (and in the parallel gospels). In the legendary book, we saw a story about God coming to Earth as a human form and learning things, experiencing things from a new point-of-view. (Hebrews 5 for an explicit example.) There’s no reason to diminish and shrink down God to a particular image or icon, to this one-week, one-planet, static, unyielding picture frame, when our own senses and hearts and minds show us aeons and galaxies and this unfolding, learning, teaching, listening resounding symphony. =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It’s like the World Wide Web but a lot lighter. ䷩ 𝚕𝚒𝚗𝚎 4737 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_02/10/2022:_Debian_on_Firmware_Policy_and_PostgreSQL_15_RC_1⠀✐ Posted in News_Roundup at 2:37 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Desktop/Laptop o Server o Audiocasts/Shows o Applications o Instructionals/Technical o Games o Desktop_Environments/WMs # K_Desktop_Environment/KDE_SC/Qt * Distributions_and_Operating_Systems o BSD o Arch_Family o Debian_Family o Devices/Embedded * Free,_Libre,_and_Open_Source_Software o Events o SaaS/Back_End/Databases o Content_Management_Systems_(CMS) o Programming/Development * Leftovers o Science o Hardware o Health/Nutrition/Agriculture o Proprietary o Security # Integrity/Availability/Authenticity # Privacy/Surveillance o Defence/Aggression o Transparency/Investigative_Reporting o Environment # Energy # Wildlife/Nature o Finance o AstroTurf/Lobbying/Politics o Censorship/Free_Speech o Freedom_of_Information_/_Freedom_of_the_Press o Civil_Rights/Policing o Internet_Policy/Net_Neutrality o Digital_Restrictions_(DRM) * Gemini*_and_Gopher o Personal o Technical # Internet/Gemini # Announcements * § GNU/Linux⠀➾ o ⚓ Linux Links ☛ Linux_Around_The_World:_USA_–_Vermont_– LinuxLinks⠀⇛ We cover events and user groups that are running in the US state of Vermont. This article forms part of our Linux Around The World series. o ⚓ Linux Links ☛ Linux_Around_The_World:_Slovakia_–_LinuxLinks⠀⇛ We cover events and user groups that are running in Slovakia. This article forms part of our Linux Around The World series. o § Desktop/Laptop⠀➾ # ⚓ Linuxiac ☛ TUXEDO_Computers_Released_TUXEDO_OS_1_to_the Mass_Public⠀⇛ TUXEDO Computers, a Linux-focused computer manufacturer, has made its in-house operating system, TUXEDO OS, available to all Linux users. In the Linux community, TUXEDO Computers is a well- known name. The company has gained the attention of Linux supporters due to its strong focus on manufacturing notebooks and PCs specifically built and further tuned to work with Linux. Users can choose between Ubuntu and some of its flavors for the operating system or the in-house developed TUXEDO OS, with the latter being the company’s recommended choice. o § Server⠀➾ # ⚓ Toolbx_—_running_the_same_host_binary_on_Arch_Linux, Fedora,_Ubuntu,_etc._containers_|_Debarshi’s_den⠀⇛ This is a deep dive into some of the technical details of Toolbx and is a continuation from the earlier post about bypassing the immutability of OCI containers. # ⚓ Andre Franca ☛ How_to_self-host_Vaultwarden_with_Podman_on a_VPS⠀⇛ I would say that one of the most important things in our digital life is to have good passwords, then to have a proper way to secure and manage those passwords. Thankfully, we have different solutions. Today I’m going to show you how to self-host Vaultwarden with Podman. # ⚓ Earthly ☛ Comparison:_Flux_vs_Argo_CD⠀⇛ Since February we have been working on adopting Kubernetes and cloud-native technologies for our cell simulation platform at Turbine.ai. Part of my job entailed figuring out how to onboard developers who didn’t practice DevOps before. # ⚓ Earthly ☛ How_to_use_ReplicaSets_in_Kubernetes_and_Why_You Should_Know_About_Them_–_Earthly_Blog⠀⇛ Kubernetes is a container orchestration system. This means that it manages the lifecycle of containers and allows you to deploy applications in a scalable way, with high availability and fault tolerance. Kubernetes is also a cluster manager, which means that it can manage multiple hosts or VMs on your behalf so you don’t have to worry about them (or their resources) going down. o § Audiocasts/Shows⠀➾ # ⚓ Video ☛ My_First_Look_At_SpiralLinux_(From_the_Creator_of GeckoLinux)_–_Invidious⠀⇛ SpiralLinux is a rather new Linux distro that is built from Debian, with a focus on simplicity and out-of-the-box usability across all the major desktop environments. SpiralLinux was created by the creator of GeckoLinux, and like GeckoLinux, SpiralLinux offers a number of different desktop editions. # ⚓ Jon Udell ☛ Curating_the_Studs_Terkel_archive_–_Jon_Udell⠀⇛ I heard these words on an episode of Radio OpenSource about the Studs Terkel Radio Archive, an extraordinary compilation of (so far) about a third of his 5600 hours of interviews with nearly every notable person during the latter half of the twentieth century. # ⚓ E54:_Learn_Open_Source_Tools_–_Frameworks_on_CoRise_by_Open Source_Startup_Podcast⠀⇛ Sourabh Bajaj is Cofounder & CTO of CoRise, the technical up-skilling platform with courses taught by industry experts. They have courses focused on open source projects such as DBT that use real- world projects to teach industry skills. In this episode, we discuss how technical learners are different, the opportunity for education to be a third-party tool, why industry professionals can make the best teachers, assessing your own founder- market fit, and more! # ⚓ E53:_Bringing_Data_Science_Projects_to_Production_with Linea⠀⇛ Doris Xin is Cofounder & CEO of Linea, the platform to bring data science projects to production. The company’s open source project, LineaPy, helps remove engineering bottlenecks for data science teams. o § Applications⠀➾ # ⚓ DebugPoint ☛ 5_Great_GUI_Apps_for_Visual_Disk_Usage_in Linux,_Ubuntu_[With_Bonus]⠀⇛ Filelight, a GUI-based KDE app, provides a sunburst representation of disk usage. Instead of showing a tree view & list view of directories/files, it shows the usage in a concentric pie chart view representing each directory. You can mouse over to a specific colour/pie to get the information about that specific segment. It also provides a way to dive deep into a particular segment to a single file level to analyze! This feature is pretty neat. o § Instructionals/Technical⠀➾ # ⚓ LinuxTechi ☛ How_to_Install_HAProxy_on_Ubuntu_20.04_LTS_ (Focal_Fossa)⠀⇛ In this guide, we will cover how to install latest version of HAProxy on Ubuntu 20.04 LTS (Focal Fossa) step-by-step. HAProxy is a free & open source solution for High availability and load balancing, it can also be used for proxying TCP & HTTP based applications. HAProxy can be installed and configured on Linux, Solaris & FreeBSD. HAProxy is best recommended solution for the websites which has huge traffic as it improves performance & reliability of the server by means of load balancing the servers & using its high availability capabilities. HAProxy is used by a number of most popular websites including GitHub, Bitbucket, Stack Overflow, Reddit, Tumblr, Twitter and it is also used in the OpsWorks product from Amazon Web Services. # ⚓ ID Root ☛ How_To_Install_Kate_Text_Editor_on_Ubuntu_22.04 LTS_–_idroot⠀⇛ In this tutorial, we will show you how to install Kate Text Editor on Ubuntu 22.04 LTS. For those of you who didn’t know, Kate (KDE Advanced Text Editor) is a source code editor developed by the KDE-free software community. It comes with plugins that boast the Kate editor functionality. The clean interface of Kate editor helps the developer to maximize their productivity. 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 KDE Kate Text Editor on Ubuntu 22.04 (Jammy Jellyfish). You can follow the same instructions for Ubuntu 22.04 and any other Debian- based distribution like Linux Mint, Elementary OS, Pop!_OS, and more as well. # ⚓ DebugPoint ☛ String_Processing_in_LibreOffice_Calc_Macro with_Examples⠀⇛ This tutorial will show how to do various common string processing using macro in LibreOffice. We will use LibreOffice Calc cells to use the strings for this tutorial. These processes are essential for any macro development. # ⚓ Make Use Of ☛ Get_HDMI_Audio_Working_on_Ubuntu_for Raspberry_Pi⠀⇛ On a Raspberry Pi, the Ubuntu Desktop and Ubuntu MATE operating systems output audio to the 3.5mm audio port by default. For the audio to be carried over an HDMI cable, the audio output device needs to be manually selected every time the Pi boots. The issue persists even in the latest version of the Ubuntu flavored OS for the Pi, 22.04. If your Raspberry Pi is connected to a television or a monitor with built-in speakers, it is wise to transmit the audio over HDMI. It reduces cable clutter and also the need for additional external speakers. # ⚓ Citizix ☛ How_to_Install_and_set_up_PHP_and_Nginx_(LEMP)_on Ubuntu_22.04⠀⇛ # ⚓ Citizix ☛ How_to_install_and_configure_NextCloud_on_Ubuntu 22.04_and_LEMP⠀⇛ o § Games⠀➾ # ⚓ Boiling Steam ☛ Best_Steam_Deck_Games_Released_in_the_Past Week_–_2022-10-02_Edition_–_Boiling_Steam⠀⇛ Between 2022-09-25 and 2022-10-02 there were 149 new games validated for the Steam Deck. We have developed a series of filters to help you find the Best Steam Deck Games in those, based on the available Steam Ratings, their respective popularity, and a few other criteria. We hope it can help you find games that you would have otherwise never known, so that you won’t be running out of games to play on your Steam Deck anytime soon! o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Jonathan Riddell ☛ Akademy_2022_in_Barcelona_Day_1 Talks_–_Jonathan_Esk-Riddell’s_Diary⠀⇛ Niccolo and The Dawn of Consistency. He gives the example of KHamburgerMenu which should have a similar widget which is a panel, having a common component was something he kept talking of but it was never done. App redundancy, one part of the goal was removing multiple applications. This depends if KDE is an umbrella for any app or if it’s a brand that promotes a set of apps. For example Maui is very much doing the wrong thing with their own design with their own Kit and they have their own shell but MauiShel isn’t part of KDE even though MauiKit is. Maybe we should have a requirement for KDE look and feel as part of being KDE. Some apps are a bit stagnant, in general I’d like to move them to Kirigami because that helps consistency. Kate and KWrite use the same code so congratulations. Band consistency, many apps had their own website, there has been a lot of improvement for this. Consistency within applications has improved. Mevin talks about Wayland goal. In Plasma 5.24 we got the Overview Effect, improved NVidia support (where the distro uses the patches), improved stability too. In Plasma 5.25 we got touch mode for better tablet support and a tonne of stability improvements. In Plasma 5.26 we got improved virtual keyboard support, improved graphical tablet support, xwayland and DPI improvements and a lot of stability improvement. But showstoppers are still missing colour profiles, blurry rendering with fractional scaling and many more. Virtualisation and screen recording still needed before people can switch from X. # ⚓ Akademy_2022_–_Sunday_2nd_October_–_Room_1_–_Kockatoo Tube⠀⇛ # ⚓ Akademy_2022_–_Sunday_2nd_October_–_Room_2_–_Kockatoo Tube⠀⇛ * § Distributions and Operating Systems⠀➾ o § BSD⠀➾ # ⚓ DragonFly BSD Digest ☛ Lazy_Reading_for_2022/10/02⠀⇛ o § Arch Family⠀➾ # ⚓ Arco Linux ☛ Everything_you_need_to_know_about_keys_| ArcoLinux⠀⇛ The package manager from Arch Linux aka pacman works with signed packages. To sign a package you need key. To be able to install a package you need a key. o § Debian Family⠀➾ # ⚓ Debian ☛ Results_for_non-free_firmware⠀⇛ Greetings, This message is an automated, unofficial publication of vote results. Official results shall follow, sent in by the vote taker, namely Debian Project Secretary This email is just a convenience for the impatient. I remain, gentle folks, Your humble servant, Devotee (on behalf of Debian Project Secretary) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Starting results calculation at Sun Oct 2 06:33:53 2022 Option 1 "Only one installer, including non-free firmware" Option 2 "Recommend installer containing non-free firmware" Option 3 "Allow presenting non-free installers alongside the free one" Option 4 "Installer with non-free software is not part of Debian" Option 5 "Change SC for non-free firmware in installer, one installer" Option 6 "Change SC for non-free firmware in installer, keep both installers" Option 7 "None of the above" In the following table, tally[row x][col y] represents the votes that option x received over option y. Option 1 2 3 4 5 6 7 === === === === === === === Option 1 158 206 270 72 129 264 Option 2 170 235 286 121 75 291 Option 3 144 99 294 127 84 306 Option 4 80 64 53 74 55 135 Option 5 229 219 229 279 169 289 Option 6 216 253 266 298 163 311 Option 7 91 63 51 197 63 42 Looking at row 2, column 1, Recommend installer containing non-free firmware received 170 votes over Only one installer, including non-free firmware Looking at row 1, column 2, Only one installer, including non-free firmware received 158 votes over Recommend installer containing non-free firmware. Option 1 Reached quorum: 264 > 45.8911756223351 Option 2 Reached quorum: 291 > 45.8911756223351 Option 3 Reached quorum: 306 > 45.8911756223351 Option 4 Reached quorum: 135 > 45.8911756223351 Option 5 Reached quorum: 289 > 45.8911756223351 Option 6 Reached quorum: 311 > 45.8911756223351 Option 1 passes Majority. 2.901 (264/ 91) >= 1 Option 2 passes Majority. 4.619 (291/ 63) >= 1 Option 3 passes Majority. 6.000 (306/ 51) >= 1 Dropping Option 4 because of Majority. (0.6852791878172588832487309644670050761421) 0.685 (135/197) < 1 Option 5 passes Majority. 4.587 (289/ 63) >= 3 Option 6 passes Majority. 7.405 (311/ 42) >= 3 Option 2 defeats Option 1 by ( 170 - 158) = 12 votes. Option 1 defeats Option 3 by ( 206 - 144) = 62 votes. Option 5 defeats Option 1 by ( 229 - 72) = 157 votes. Option 6 defeats Option 1 by ( 216 - 129) = 87 votes. Option 1 defeats Option 7 by ( 264 - 91) = 173 votes. Option 2 defeats Option 3 by ( 235 - 99) = 136 votes. Option 5 defeats Option 2 by ( 219 - 121) = 98 votes. Option 6 defeats Option 2 by ( 253 - 75) = 178 votes. Option 2 defeats Option 7 by ( 291 - 63) = 228 votes. Option 5 defeats Option 3 by ( 229 - 127) = 102 votes. Option 6 defeats Option 3 by ( 266 - 84) = 182 votes. Option 3 defeats Option 7 by ( 306 - 51) = 255 votes. Option 5 defeats Option 6 by ( 169 - 163) = 6 votes. Option 5 defeats Option 7 by ( 289 - 63) = 226 votes. Option 6 defeats Option 7 by ( 311 - 42) = 269 votes. The Schwartz Set contains: Option 5 "Change SC for non-free firmware in installer, one installer" -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-=-=-=-=-=-=-= The winners are: Option 5 "Change SC for non-free firmware in installer, one installer" -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-=-=-=-=-=-=-= -- The voters have spoken, the bastards... --unknown DEbian VOTe EnginE digraph Results { ranksep=0.25; "Only one installer, including non-free firmware\n2.90" [ style="filled" , fontname="Helvetica", fontsize=10 ]; "Only one installer, including non-free firmware\n2.90" -> "Allow presenting non-free installers alongside the free one\n6.00" [ label="62" ]; "Only one installer, including non-free firmware\n2.90" -> "None of the above" [ label="173" ]; "Recommend installer containing non-free firmware\n4.62" [ style="filled" , fontname="Helvetica", fontsize=10 ]; "Recommend installer containing non-free firmware\n4.62" -> "Only one installer, including non-free firmware\n2.90" [ label="12" ]; "Recommend installer containing non-free firmware\n4.62" -> "Allow presenting non-free installers alongside the free one\n6.00" [ label="136" ]; "Recommend installer containing non-free firmware\n4.62" -> "None of the above" [ label="228" ]; "Allow presenting non-free installers alongside the free one\n6.00" [ style="filled" , fontname="Helvetica", fontsize=10 ]; "Allow presenting non-free installers alongside the free one\n6.00" -> "None of the above" [ label="255" ]; "Installer with non-free software is not part of Debian\n0.69" [ style="filled" , color="pink", shape=octagon, fontname="Helvetica", fontsize=10 ]; "None of the above" -> "Installer with non-free software is not part of Debian\n0.69" [ label="62" ]; "Change SC for non-free firmware in installer, one installer\n4.59" [ style="filled" , color="powderblue", shape=egg, fontcolor="NavyBlue", fontname="Helvetica", fontsize=10 ]; "Change SC for non-free firmware in installer, one installer\n4.59" -> "Only one installer, including non-free firmware\n2.90" [ label="157" ]; "Change SC for non-free firmware in installer, one installer\n4.59" -> "Recommend installer containing non-free firmware\n4.62" [ label="98" ]; "Change SC for non-free firmware in installer, one installer\n4.59" -> "Allow presenting non-free installers alongside the free one\n6.00" [ label="102" ]; "Change SC for non-free firmware in installer, one installer\n4.59" -> "Change SC for non-free firmware in installer, keep both installers\n7.40" [ label="6" ]; "Change SC for non-free firmware in installer, one installer\n4.59" -> "None of the above" [ label="226" ]; "Change SC for non-free firmware in installer, keep both installers\n7.40" [ style="filled" , fontname="Helvetica", fontsize=10 ]; "Change SC for non-free firmware in installer, keep both installers\n7.40" -> "Only one installer, including non-free firmware\n2.90" [ label="87" ]; "Change SC for non-free firmware in installer, keep both installers\n7.40" -> "Recommend installer containing non-free firmware\n4.62" [ label="178" ]; "Change SC for non-free firmware in installer, keep both installers\n7.40" -> "Allow presenting non-free installers alongside the free one\n6.00" [ label="182" ]; "Change SC for non-free firmware in installer, keep both installers\n7.40" -> "None of the above" [ label="269" ]; "None of the above" [ style="filled" , shape=diamond, fontcolor="Red", fontname="Helvetica", fontsize=10 ]; } # ⚓ Steve McIntyre ☛ Steve’s_blog:_Firmware_vote_result_–_the people_have_spoken!⠀⇛ It’s time for another update on Debian’s firmware GR. I wrote about the problem back in April and about the vote itself a few days back. Voting closed last night and we have a result! This is unofficial so far – the official result will follow shortly when the Project Secretary sends a signed mail to confirm it. But that’s normally just a formality at this point. # ⚓ LWN ☛ Debian’s_firmware_vote_results_[LWN.net]⠀⇛ The results are in on the Debian project’s general- resolution vote regarding non-free firmware in the installer image. o § Devices/Embedded⠀➾ # ⚓ Ruben Schade ☛ Raspberry_Pis_in_racks_or_PCI_slots⠀⇛ I’ve seen the Raspberry Pi Compute Modules and their boards mounted in racks for ARM development, but the idea of mounting regular Raspberry Pis into racks tickles me. # ⚓ SparkFun Electronics ☛ Amp_Up_Your_Audio_With_Qwiic_–_News –_SparkFun_Electronics⠀⇛ This small board has been designed from the ground up to easily take in audio input and output to speakers all via Qwiic. * § Free, Libre, and Open Source Software⠀➾ o § Events⠀➾ # ⚓ Rlang ☛ Leading_the_Way_for_New_R_useRs_with_Strong Connections_To_Local_Universities_|_R-bloggers⠀⇛ The R Consortium recently spoke with Ryan Benz, one of the organizers for the Southern California R Users Group which covers Los Angeles and Orange County, CA. Ryan shares more about how the R Community in SoCal continues to grow by forming partnerships with local universities to offer students workshops. The SoCal R useR Group is also committed to offering a valuable learning environment and resources for those who are both new and have more experience with R. o § SaaS/Back End/Databases⠀➾ # ⚓ PostgreSQL ☛ PostgreSQL:_PostgreSQL_15_RC_1_Released!⠀⇛ The PostgreSQL Global Development Group announces that the first release candidate of PostgreSQL 15 is now available for download. As a release candidate, PostgreSQL 15 RC 1 will be mostly identical to the initial release of PostgreSQL 15, though some more fixes may be applied prior to the general availability of PostgreSQL 15. The planned date for the general availability of PostgreSQL 15 is October 13, 2022. Please see the “Release Schedule” section for more details. # ⚓ PostgreSQL ☛ PostgreSQL:_pg_dbms_job_v1.5.0_released⠀⇛ pg_dbms_job is a PostgreSQL extension to create, manage and use Oracle-style DBMS_JOB scheduled job. The use and behavior is just like with the DBMS_JOB Oracle package. It allows to manage scheduled jobs from a job queue or to execute immediately jobs asynchronously. A job definition consist on a code to execute, the next date of execution and how often the job is to be run. A job runs a SQL command, plpgsql code or an existing stored procedure. o § Content Management Systems (CMS)⠀➾ # ⚓ Kev Quirk ☛ My_Blogging_Utopia_–_Kev_Quirk⠀⇛ I personally think the admin UI of WordPress is stuck firmly in 2004. It can also be slow and clunky to navigate around. Then there’s hosting. It’s not difficult to host a WordPress site, but I’d rather not have to put up with it. o § Programming/Development⠀➾ # ⚓ August_2022:_“Top_40″_New_CRAN_Packages_–_R_Views⠀⇛ One hundred ninety-four new package made it to CRAN in August. Here are my “Top 40” picks in thirteen categories: “Computational Methods, Data, Epidemiology, Genomics, Insurance, Machine Learning, Mathematics, Medicine, Pharmaceutical Applications, Statistics, Time Series, Utilities, and Visualization. # ⚓ Recent_challenges_in_model_specification_testing_based_on different_data_structures_|_YoungStatS⠀⇛ Model specification testing is one of the essential methodological tasks in statistics. Recently, with the development of different data structures, envisioning concepts from classical data setups to other environments becomes very important. # ⚓ R_tips_and_tricks_–_get_the_gist⠀⇛ In scientific programming speed is important. Functions written for general public use have a lot of control-flow checks which are not necessary if you are confident enough with your code.To quicken your code execution I suggest to strip run-of-the- mill functions to their bare bones. You can save serious wall-clock time by using only the laborers code lines. Below is a walk-through example of what I mean. # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppArmadillo 0.11.4.0.1_on_CRAN:_Updates⠀⇛ Armadillo is a powerful and expressive C++ template library for linear algebra and scientific computing. It aims towards a good balance between speed and ease of use, has a syntax deliberately close to Matlab, and is useful for algorithm development directly in C++, or quick conversion of research code into production environments. RcppArmadillo integrates this library with the R environment and language–and is widely used by (currently) 1023 packages other packages on CRAN, downloaded 26.4 million times (per the partial logs from the cloud mirrors of CRAN), and the CSDA paper (preprint / vignette) by Conrad and myself has been cited 497 times according to Google Scholar. # ⚓ Buttondown ☛ Snippet_Praxis_•_Buttondown⠀⇛ Oh no, it’s the dreaded Copy-and-paste programming! I regularly see old-timers complain about how modern programming isn’t about “understanding” things anymore, people just copy code from Stackoverflow. This is seen as a bad thing. # ⚓ 5_New_books_added_to_Big_Book_of_R⠀⇛ The Big Book of R has just had 5 new additions to the collection! Thanks to Gary and Adejumo for some of them! PS for those who may be interested, I have posted my replies to some great questions about cleaning a messy dataset. # ⚓ Housing_Markets_Down:_Hierarchical_Time_Series⠀⇛ For a long time, everybody in Turkey complains about how far the house and rent prices are up. It seems the same situation is true all over the world. This is called the pandemic housing boom in the USA. But this might’ve been coming to the end, according to some authorities. # ⚓ age_and_Authenticated_Encryption⠀⇛ age is a file encryption format, tool, and library. It was made to replace one of the last remaining GnuPG use cases, but it was not made to replace GnuPG because in the last 20 years we learned that cryptographic tools work best when they are specialized and opinionated instead of flexible Swiss Army knives. # ⚓ How_to_Use_Italic_Font_in_R_–_Data_Science_Tutorials⠀⇛ How to Use Italic Font in R, to create an italic typeface in R plots, use the basic syntax shown below. # ⚓ Frederic Cambus ☛ Toolchains_adventures_–_Q3_2022_| Frederic_Cambus⠀⇛ This is the sixth post in my toolchains adventures series. Please check the previous posts in the toolchains category for more context about this journey. In Pkgsrc land, I updated binutils to the 2.39 version, mold to the 1.3.1, 1.4.0, 1.4.1, and 1.4.2 versions, patchelf to the 0.15.0 one, and finally pax-utils to the 1.3.5 one. Regarding OpenBSD, we imported llvm-profdata into the base system in early July, so I took the opportunity to propose importing llvm-cov as well. This was accepted and is now committed, which will allow producing reports from coverage data without having to install the devel/llvm port. * § Leftovers⠀➾ o ⚓ Nicholas Tietz-Sokolsky ☛ [Repost]_I’m_taking_a_sabbatical_and attending_Recurse_Center!_|_nicholas@web⠀⇛ It’s been almost a decade since I graduated from college. In that time, I’ve worked at three startups, co-founded a non-profit immigration tech company, consulted for the United Nations, and noped out of grad school after one semester (twice!). I’ve also struggled with depression and anxiety, had three different therapists, and tried multiple different anxiety and depression medications. And I’ve adopted three cats, met and married my wife, and had two kids with her. During that decade, I’ve kept learning. On the job. On the weekends. In my evenings. I’m tired. During that decade, I’ve not had time to sit down and really dive deep into becoming a better programmer, a better software engineer. I’ve done a lot I’m proud of, but I haven’t had the chance to dive deep since college. It’s time to do that. I’m going to take a sabbatical from work to spend dedicated time becoming a better programmer and software engineer. This is a great privilege, and not one I’m taking lightly. Many people do not have this opportunity for myriad reasons, and I’m grateful. o ⚓ Ruben Schade ☛ Blander_logos_are_good,_via_@NeilIreland⠀⇛ Last year I wrote about MediaWiki’s new logo, and talked of the general trend among logo designers towards bland, dull, uninteresting, unoriginal, and largely interchangeable marks. o ⚓ Tim Bray ☛ ongoing_by_Tim_Bray_·_Luxury_media⠀⇛ Wait, am I saying that the Web was a mistake, that we should all go back to dead trees? Not at all. I couldn’t tap on the pretty-decent Jack White article and watch a YouTube of the songs. I couldn’t share a particularly tasty written morsel on Twitter. I had to go to a store to get it. I couldn’t read it in bed without turning a lamp on. I probably could have paid for a couple months’ online subscription to The Atlantic for the newsstand price. But on balance I was left thinking “This feels like a luxury product.” I can’t think of an obvious analogy… Perhaps the enveloping, focusing hands-on experience of putting a record on the turntable as opposed to a streaming service on the earbuds? Except for, magazines are more convenient, once you’ve gone to the trouble of going to the store for them. Hmmm, I hear rumors you can arrange to have them delivered to your home at regular intervals; must check that option out. o ⚓ Engadget ☛ AI_is_already_better_at_lip_reading_than_we_are⠀⇛ They Shall Not Grow Old, a 2018 documentary about the lives and aspirations of British and New Zealand soldiers living through World War I from acclaimed Lord of the Rings director Peter Jackson, had its hundred-plus-year- old silent footage modernized through both colorization and the recording of new audio for previously non- existent dialog. To get an idea of what the folks featured in the archival footage were saying, Jackson hired a team of forensic lip readers to guesstimate their recorded utterances. Reportedly, “the lip readers were so precise they were even able to determine the dialect and accent of the people speaking.” o ⚓ Matt Rickard ☛ What’s_an_MVP_in_2022?⠀⇛ One piece of advice I think still holds is picking one thing and executing flawlessly on it. Getting the core experience correct – you can rapidly iterate on the market, the customer, and the go-to-market strategy, but it’s much more challenging to build a completely different product. o ⚓ Ruben Schade ☛ A_great_relationship_with_his_garbage_contractor⠀⇛ Someone with a private account on Mastodon shared a lovely story about how he has the mobile number of his garbage collector, and could easily arrange to have his garbage bin replaced. He surmised this sort of relationship must be a rural Australian thing, because people in the city would be unlikely to know their collector by name and number. He’s right. I don’t know our garbage or recycling collectors. I’m even a step removed living in an apartment building; we also have sanitation workers who maintain the chutes and take out the skips, in addition to the people who operate the trucks and align the bins. But that’s not from avoiding them, I simply never see them. [...] The old joke among New York City taxi drivers was that they could tell if an Australian was hailing them, because we get into the front seat to talk with them instead of the back. I did this all the time in Singapore too. o ⚓ James Brown ☛ roguelazer’s_website:_What’s_Next?⠀⇛ In retrospect, seven years is probably too long to stay at a startup… We built a bunch of neat stuff, but at some point every startup either fails or lives to see itself become an enterprise. Anyhow, I’m off to another very small company where I can learn some new things and build some new products. I’m sure you’ll hear about it here soon. o § Science⠀➾ # ⚓ ACM ☛ Neural_Networks_Predict_Forces_in_Jammed_Granular Solids⠀⇛ A team of researchers from Germany’s Göttingen University and Belgium’s Ghent University used machine learning and computer simulations to create a tool for predicting force chains within granular solids. The researchers showed that graph neural networks can be trained in a supervised manner to anticipate the position of force chains that manifest while deforming a granular system, provided an undeformed static structure. # ⚓ Preparing_You_with_Future_Skill_Sets_with_EmpowerME_– Chulalongkorn_University⠀⇛ Developed by lecturers of the Faculty of Education, Chulalongkorn University. EmpowerMe is a Chatbot- based career coach that enables learners to become digital citizens by developing future skill sets and suggests the right jobs needed by the market. The application has received a gold medal award in an innovation contest in South Korea. # ⚓ Economic_Development_Administration_Awards_Georgia_Tech_$65 Million_for_AI_Manufacturing_Project_|_News_Center⠀⇛ The Georgia Institute of Technology has been awarded a $65 million grant from the U.S. Department of Commerce’s Economic Development Administration (EDA) to support a statewide initiative that combines artificial intelligence and manufacturing innovations with transformational workforce and outreach programs. The grant will increase job and wage opportunities in distressed and rural communities, as well as among historically underrepresented and underserved groups. # ⚓ Princeton_Engineering_–_Why_’erasure’_could_be_key_to practical_quantum_computing⠀⇛ A team led by Jeff Thompson, associate professor of electrical and computer engineering, pioneered an approach to more efficient error correction in quantum computers. # ⚓ Forbes ☛ Why_Don’t_You_Have_A_Self-Driving_Car_Yet?_This_2- Part_Series_Explains_The_Big_Remaining_Problems⠀⇛ People often ask, “Where’s my self-driving car?” “Why don’t I have one and when will it come?” A lot of people feel they were promised a car by the late 20-teens and it’s late, and perhaps isn’t coming, like the flying cars talked about decades ago. In this two-article series (with accompanying videos) let’s look at the core reasons you probably aren’t riding in a robocar today, and when it might happen. What are the core technological, legal and social issues standing in the way, and, and what issues actually aren’t blockers? # ⚓ The Wall Street Journal ☛ Deere_Invests_Billions_in_Self- Driving_Tractors,_Smart_Crop_Sprayers⠀⇛ For decades, Deere & Co. has dominated the hardware that powers the American farm industry with tractors, harvesters and other machinery used to plant seeds and reap crops. # ⚓ Sci Tech Daily ☛ Uncovering_Hidden_Patterns:_AI_Reduces_a 100,000-Equation_Quantum_Physics_Problem_to_Only_Four Equations⠀⇛ # ⚓ Interesting Engineering ☛ IBM_builds_the_world’s_largest dilution_refrigerator_for_quantum_computers⠀⇛ IBM has built a super-fridge known as project Goldeneye that is capable of cooling future generations of quantum experiments and that surpasses the issues found in today’s dilution refrigerators, according to a blog published by the firm on Thursday. # ⚓ Sabine Hossenfelder ☛ [Reposted]_Sabine_Hossenfelder: Backreaction:_I’ve_said_it_all_before_but_here_we_go_again⠀⇛ For reasons I don’t fully understand, particle physicists have recently started picking on me again for allegedly being hostile, and have been coming at me with their usual ad homimen attacks. What’s going on? I spent years trying to understand why their field isn’t making progress, analyzing the problem, and putting forward a solution. It’s not that I hate particle physics, it’s rather to the contrary, I think it’s too important to let it die. But they don’t like to hear that their field urgently needs to change direction, so they attack me as the bearer of bad news. o § Hardware⠀➾ # ⚓ Liam Proven ☛ The_pivotal_importance_of_IBM’s_PS/2_range_on computers,_even_today⠀⇛ A HN poster questioned the existence of 80286 computers with VGA displays. In fact the historical link between the 286 and VGA are significant and represent one of the most important events in the history of x86 computers. The VGA standard, along with PS/2 keyboard and mouse ports, 1.4MB 3.5″ floppies, and even 72-pin SIMMs, was introduced with IBM’s PS/2 range of computers in 1987. # ⚓ Kev Quirk ☛ The_Casio_F-91W_Is_the_Best_Smartwatch⠀⇛ A little over a week ago, Joel posted a picture of his watch on Fosstodon and it opened a MAHOOSIVE can of worms. People started posting photos of their Casio watches and I just had to get involved. I’ve had a number of Casio watches over the years, from really cheap ones that my parents bought me as a kid, to rather expensive G-Shock watches that survived deployments to both Iraq and Afghanistan with the Army. I’ve always had a couple of Casio watches knocking around the house. When Joel published his post, I had 2. A G-Shock M5610 and a Green W-218H. But for the most part, I was rocking a series 5 Apple Watch. # ⚓ dwaves.de ☛ GNU_Linux_–_hardware_review_–_Wifi_WLAN_USB Stick_Edimax_N300_(EW-7612UAn_V2_802.11n_Wireless_Adapter_ [Realtek_RTL8192CU])_(also_works_with_ODROID_XU4_(Armbian))⠀⇛ o § Health/Nutrition/Agriculture⠀➾ # ⚓ A_New_Tool_for_Discovering_Cancer-Driving_Structural Variations_|_Newsroom_|_Weill_Cornell_Medicine⠀⇛ An advanced software tool for analyzing DNA sequences from tumor samples has uncovered likely new cancer-driving genes, in a study led by Weill Cornell Medicine researchers. # ⚓ How_a_Methodist_Preacher_Became_a_Champion_for_Black-Led Sustainable_Agriculture_–_YES!_Magazine⠀⇛ In 1979, an idealistic 44-year-old Black woman named Nettie Mae Morrison moved with her husband to Allensworth, 75 miles south of Fresno, in California’s Central Valley. “She wanted to be a part of history,” said her son, Dennis Hutson, who was in his mid-20s at the time. The town had a distinctive past. It was founded in 1908 by Allen Allensworth, a man born into slavery who became the first African American to reach the rank of lieutenant colonel in the U.S. Army. About 3 square miles in size, Allensworth was the first town in California founded and governed by Black people—and it served as a beacon of possibility for Black people all over the nation, its population growing to around 1,200 people. But the community soon fell on hard times. # ⚓ Lee Yingtong Li ☛ The_urea:creatinine_ratio_in_SI_units⠀⇛ It is said that a high urea:creatinine ratio is an indicator of a pre-renal cause of acute kidney injury [1]. This is usually discussed in United States units, where urea is measured as blood urea nitrogen (BUN) in mg/dL, and creatinine in mg/dL. The cut-off for a high BUN:creatinine ratio is usually given as >20 (mg/mg) [1–3]. Outside of the United States, urea is usually expressed in SI units mmol/L, and creatinine in μmol/L. The cut-off for a high urea:creatinine ratio is usually given in SI units as >100 (mmol/ mmol) [1]. However, these cut-offs are not equivalent. The molar mass of (molecular) nitrogen is 28.014 g/ mol [4], so a BUN of 1 mg/dL is equivalent to a urea of $\frac{1\ \text{mg/dL}}{28.014\ \text{g/ mol}} = \frac{10\ \text{mg/L}}{28.014\ \text{mg/ mmol}}$ = 0.357 mmol/L. o § Proprietary⠀➾ # ⚓ The Verge ☛ Google_is_shutting_down_Stadia ⠀⇛ Google is refunding all Stadia purchases — hardware, software, and DLC. Members of the Stadia team will be “carrying this work forward” in other departments at Google. # ⚓ John Gruber ☛ Daring_Fireball:_Shocker:_Google_Is_Shutting Down_Stadia⠀⇛ A lot of the speculation around Stadia was focused on the technology — streaming. But put that aside, and what to me has seemed clear all along is that Google was never particularly invested in making Stadia a serious platform. If you’re committed to the platform, the underlying technology doesn’t matter. And there’s a “Boy Who Cried Wolf” factor — except instead of a little boy who lacks credibility, it’s one of the five largest corporations in the world. When Google next launches a platform, how much does this affect their credibility? Frankly, their credibility was already shit on this front. o § Security⠀➾ # ⚓ IT Wire ☛ iTWire_–_O’Neil_hammers_Coalition_over_‘useless’ cyber-security_laws⠀⇛ The Morrison Government has been raked over the coals for passing laws that claimed to be of little use in the area of cyber security, with Home Affairs Minister Clare O’Neil telling a media conference on Sunday that the laws in place were “absolutely useless to me when the Optus matter came on foot”. She was referring to the data breach that Optus announced through the media on 22 September. O’Neil addressed the media along with Government Services Minister Bill Shorten. Asked about the possibility of reforming laws about data security, she did not hold back. # ⚓ IT Wire ☛ iTWire_–_Govt_says_Optus_dragging_its_feet_on providing_data_breach_details⠀⇛ The federal government has accused telco Singtel Optus of dragging its feet on providing full details of users whose data was compromised in a data breach which the telco reported on 22 September. Government Services Minister Bill Shorten told a media conference in Melbourne on Sunday morning that a request on 27 September had sought more details about the Medicare and Centrelink data that had been leaked in the data breach. # ⚓ Mandiant ☛ Elevating_Women_in_Cyber_Security_to_Highest Positions_of_Impact⠀⇛ Mandiant Cyber Defense Summit (CDS) 2019 in Washington, D.C. was a fantastic event, but like so many other cyber security events, only a small percentage of registrants were women. # ⚓ Mandiant ☛ Bad_VIB(E)s_Part_One:_Investigating_Novel Malware_Persistence_Within_ESXi_Hypervisors⠀⇛ As endpoint detection and response (EDR) solutions improve malware detection efficacy on Windows systems, certain state-sponsored threat actors have shifted to developing and deploying malware on systems that do not generally support EDR such as network appliances, SAN arrays, and VMware ESXi servers. # ⚓ Mandiant ☛ Bad_VIB(E)s_Part_Two:_Detection_and_Hardening within_ESXi_Hypervisors⠀⇛ In part one, we covered attackers’ usage of malicious vSphere Installation Bundles (“VIBs”) to install multiple backdoors across ESXi hypervisors, focusing on the malware present within the VIB payloads. In this installment, we will continue to elaborate further on other attacker actions such as timestomping, describe ESXi detection methodologies to dump process memory and perform YARA scans, and discuss how to further harden hypervisors to minimize the attack surface of ESXi hosts. For more details, VMware has released additional information on protecting vSphere. # ⚓ Mandiant ☛ Hardening_the_Electoral_Process:_Supply_Chain, Zero_Trust_and_Insider_Threats⠀⇛ Some people envision election-related cyber attacks as a threat actor sitting in front of a keyboard in a windowless room trying to infiltrate voting machines while elections are happening. But, the reality is that election security is much deeper and more complex than protecting voting infrastructure. Ensuring the integrity of our electoral system is not “questioned” is a tall order as it may come down to small details like verifying that enough paper ballots are printed and mailed out or that everyone working in our elections has been adequately trained and vetted. Regardless of the scale or type of election—local, state, or even national- local and state officials bear the responsibility to secure this democratic process, making it more challenging to implement and enforce standardized security measures and procedures. Despite the effort it entails, we understand the importance of protecting the integrity of our electoral process and how cybercriminals or state-sponsored actors can disrupt our way of life by discrediting our elections. # § Integrity/Availability/Authenticity⠀➾ # ⚓ Atlantic Council ☛ Security_in_the_billions:_Toward_a multinational_strategy_to_better_secure_the_IoT ecosystem_–_Atlantic_Council⠀⇛ The explosion of Internet of Things (IoT) devices and services worldwide has contributed to an explosion in data processing and interconnectivity. Simultaneously, this interconnection and resulting interdependence have amplified a range of cybersecurity risks to individuals’ data, company networks, critical infrastructure, and the internet ecosystem writ large. Governments, companies, and civil society have proposed and implemented a range of IoT cybersecurity initiatives to meet this challenge, ranging from introducing voluntary standards and best practices to mandating the use of cybersecurity certifications and labels. However, issues like fragmentation among and between approaches, complex certification schemes, and placing the burden on buyers have left much to be desired in bolstering IoT cybersecurity. Ugly knock-on effects to states, the private sector, and users bring risks to individual privacy, physical safety, other parts of the internet ecosystem, and broader economic and national security. # ⚓ ACM ☛ Security_by_Labeling⠀⇛ Empowering consumers to make risk-informed purchasing decisions when buying Internet-of- Things (IoT) devices or using digital services is a principal thrust to advance consumer cybersecurity. Simple yet effective labels convey relevant cybersecurity information to buyers at the point of sale and encourage IoT vendors to up their cybersecurity game as they now can recoup their security investments from risk-aware buyers. These dynamics benefit consumers and the industry alike, resulting in better, more resilient cybersecurity for all. Consumers are insufficiently aware of risks emanating from IoT and are ill-equipped to manage them. For all the much-heralded benefits of consumer IoT to come true, the industry must ensure all the smart home appliances, connected thermostats, and digital services are secure and can be trusted. The industry has for long been criticized for not paying sufficient attention to the cybersecurity of its products. Concerns over security were pushed aside, yielding precedence to shorter time- to-market and higher corporate profits. Less time for testing translates into insecure products in residential homes. # ⚓ ACM ☛ Securing_the_Enterprise_When_Employees_are Remote⠀⇛ Permitting workers to split their time between their home and office can improve job satisfaction and, in some cases, productivity. However, hybrid work arrangements can introduce additional layers of complexity and risk to an organization’s technology systems and data. As such, IT departments need to consider several security technologies, processes, and policies to guard against cybersecurity threats that can be more easily exploited by workers that are on the go, or are working in unsecure environments. For starters, security experts interviewed for this article highlight the importance of insisting that hybrid workers utilize virtual private networks (VPNs), which allow a direct, secure connection between their device and a corporate system, as well as virtual desktops (which ensures all activity and data remain within a corporate, secure environment) when accessing company information offsite. # ⚓ Ruben Schade ☛ how.complexsystems.fail⠀⇛ See also: James T. Reason’s Swiss cheese model of accident causation. You can blame the human involved in the last slice, but you’re neglecting the rest of the stack that should never have let such a failure result in a catastrophe. # § Privacy/Surveillance⠀➾ # ⚓ Stacey on IoT ☛ What_smoke_alarm_systems_can_send phone_notifications?⠀⇛ On a recent IoT Podcast episode, we took a question from Ryan on our Voicemail hotline. Ryan wants to get notifications from smart smoke alarms on his farm. He looked into these a few years back but only found limited options. So he wants to know what smoke alarm systems today can send phone notifications. Luckily, the number of available connected smoke detectors is much higher today than it was a handful of years ago. The challenge here is that Ryan needs phone alerts in case of a fire, given that he’s not just trying to protect his home, but his farm buildings too. We’re assuming that Ryan’s farm has network connectivity in all of the places he wants to install a smart smoke alarm system. Surprisingly, not every connected smoke detector sends mobile notifications. Some simply announce alerts throughout the home. This makes sense if you’re actually at home but if not, you may not be aware of a potential disaster. Some systems also require a subscription for advanced features such as notifications. # ⚓ Stacey on IoT ☛ Podcast:_Amazon’s_turning_Alexa_into the_brains_of_the_home [Ed: Next-generation mass surveillance in people's private space; can they sell that as a "hip" thing?]⠀⇛ This week’s show focuses on Amazon’s new devices and services launched Wednesday. Kevin and I talk about Amazon’s direction with Alexa as the manager of your life. We also gawp at the price iRobot is charging for its latest iteration of the Roomba robotic vacuum, although Kevin convinces me it’s not too crazy. Then we move into a discussion of the energy grid, sharing data from Itron on how utilities are thinking about the future electric grid, and how a partnership between Itron and Samsung SmartThings is an example of long-term thinking. Then I talk about the latest reporting from Forbes on Helium, and apologize for not being more wary about the chicanery that went on in the beginning by Helium’s executives. We then talk about my experience with the latest Yale lock. We end by answering a listener question about Ecobee thermostats that start heating or cooling before you intended. o § Defence/Aggression⠀➾ # ⚓ imetatronink:_The_Mostly_Forgotten_1857_Utah_War⠀⇛ A scarcely remembered and yet very significant event that occurred in the years leading up to the US Civil War was the so-called “Utah War”, which took place from the latter half of 1857 into the first half of 1858. Frequently referred to as “Buchanan’s Blunder” (after then-US President James Buchanan), it was one of the most notorious examples in US history of a president ginning up a “rally ’round the flag” war to distract the populace from domestic strife. The so-called “Mormons” (members of the Church of Jesus Christ of Latter-day Saints) had been driven from Missouri to Illinois, and following the assassination of their founding prophet Joseph Smith, were compelled to leave the United States altogether to escape persecution. # ⚓ Medium ☛ Roger_Waters_added_to_Ukrainian_Hit_List⠀⇛ “Pink Floyd” star declared “Enemy of Ukraine” # ⚓ Michael West Media ☛ AUKUS_was_a_tough_sell_already,_and now_it_seems_local_industry_will_miss_out_–_Michael_West⠀⇛ When Australia signed up to the AUKUS pact, it committed to enormously expensive nuclear-powered submarines. And if rumours of the US taking over their construction are true, there will be little if any benefit to Australian workers, writes Rex Patrick. As for strategic benefits … o § Transparency/Investigative Reporting⠀➾ # ⚓ Michael West Media ☛ NACC_or_SNACC?_Labor_delivers_its anti-corruption_body_but_will_we_get_to_hear_about_it?_– Michael_West⠀⇛ The day has finally arrived: an Australian government today made good on its commitment to legislate an integrity watchdog, the National Anti- Corruption Commission (NACC). But there is one major bone of contention … secrecy. Callum Foote reports on the spectre of a Secret National Anti- Corruption Commission (SNACC). The actual legislation is yet to be revealed; the devil in the detail if you like, and there will be much in that. Yet, Attorney-General Mark Dreyfus has unveiled the broad remit for Australia’s National Anti-Corruption Commission (NACC). In a speech to parliament and follow-up media release Labor detailed the broad points of its proposed anti-corruption body and for a party that ran on an integrity campaign, the plans appear to tick all the boxes, save one. o § Environment⠀➾ # ⚓ TomDispatch ☛ The_Nightmare_of_Military_Spending_on_an Overheating_Planet_–_TomDispatch.com⠀⇛ In so many ways, you still wouldn’t know it — not, that is, if you focused on the Pentagon budget or the economic growth paradigm that rules this country and our world — but this planet is in a crisis of a sort humanity has never before faced. Whether you’re considering heat in the American West, floods in Pakistan, the drying up of the Yangtze River in China, record drought in Europe, or the unparalleled warming of the Arctic, we are, as scientists have been pointing out (and ever more of us ordinary people have noted), in an increasingly “uncharted territory of destruction.” In the process, ever more climate “tipping points” stand in danger of being passed as the overheating of this planet becomes the stuff of everyday life. # ⚓ Andre Franca ☛ Hurricane_Ian⠀⇛ This is one of those moments where we have to embrace ourselves and wish for hope for our fellows from Cuba and Florida. # § Energy⠀➾ # ⚓ New Scientist ☛ Too_many_electric_cars_charging_at night_may_overload_electrical_grid⠀⇛ The growth in electric car ownership could strain power grids if most drivers continue charging primarily at home overnight. Investment in daytime charging options will be crucial to help the western US power grid handle the demand with an estimated 50 per cent of drivers using electric vehicles by 2035. That finding comes from computer models looking at how driver charging behaviours and available charging station infrastructure at home and in public places could impact peak net electricity demand – the highest electrical power demand minus power provided by solar and wind power. If drivers primarily charge vehicles at home during the night, that could lead to a 25 per cent surge in peak net electricity demand when states reach 50 per cent electric vehicle ownership, and possibly surpass grid capacity at even higher levels of ownership. But expanding daytime charging opportunities could reduce that increase in peak net electricity demand to just 7.5 per cent and help reduce the costs of expanding grid capacity. # ⚓ As_drought_dries_up_the_Yangtze_river,_China_loses hydropower_|_Grist⠀⇛ A historic drought in the southwest of China is drying up rivers, intensifying forest fires, damaging crops, and severely curtailing electricity in a region highly dependent on hydropower. The Yangtze River, the third largest in the world, has dropped to half its average water levels, affecting shipping routes, limiting drinking water supplies, causing rolling blackouts, and even exposing long-submerged Buddhist statues. Some 66 rivers across 34 counties in Chongqing were dried up as of last week, Reuters reported. Also last week, the province of Sichuan, which gets more than 80 percent of its energy from hydropower, cut or limited electricity to thousands of factories in an effort to “leave power for the people.” Poyang Lake, the largest freshwater lake in China, is just a quarter of its normal size for this time of year. # § Wildlife/Nature⠀➾ # ⚓ The Wall Street Journal ☛ AI,_GPS_Technology_Could Help_Save_Lives_in_Wildfires_and_Floods⠀⇛ New technology is on the way to assist in a growing public-safety problem: How to get people out of the way of wildfires, floods and other natural disasters. o § Finance⠀➾ # ⚓ Michael West Media ☛ Worker_Hit:_fuel_excise_relief_gone with_low_income_tax_breaks_–_atop_rising_rates_and_prices_– Michael_West⠀⇛ It’s a grim time for ordinary workers. Tax cuts for high income earners are still in the pipeline but today the fuel excise cuts end, and that’s on top of vanishing (LAMITO) tax breaks for low income workers. Employers have probably decided by now whether to fork out for the rise in super to 10.5%, or take the super increase out of wages (see story below). It was missed by the media in the Coalition’s March Budget but most Australian workers are probably $50 a week worse off from July as the LAMITO tax offset was removed. That’s Low And Middle Income Tax Offset. Add to that the cost of living pressures from the removal of the temporary cut to petrol excise which cuts in this week. Then there’s the big one: rising interest rates. # ⚓ Michael West Media ☛ High_income_earners_oppose_tax_cut plan_–_Michael_West⠀⇛ Australians, including those set to benefit most, overwhelmingly support scrapping tax cuts for high income earners, new research shows. # ⚓ Project Syndicate ☛ Time_to_Blow_Up_Electricity_Markets_by Yanis_Varoufakis_–_Project_Syndicate⠀⇛ The European Union’s power sector is a good example of what market fundamentalism has done to electricity networks the world over. With the end of cheap natural gas, retail consumers and businesses are paying the price for their governments’ embrace of a shoddy theory. ATHENS – The blades of the wind turbines on the mountain range opposite my window are turning especially energetically today. Last night’s storm has abated but high winds continue, contributing extra kilowatts to the electricity grid at precisely zero additional cost (or marginal cost, in the language of the economists). But the people struggling to make ends meet during a dreadful cost-of-living crisis must pay for these kilowatts as if they were produced by the most expensive liquefied natural gas transported to Greece’s shores from Texas. This absurdity, which prevails well beyond Greece and Europe, must end. # ⚓ 9_Myths_About_Gentrification_–_YES!_Magazine⠀⇛ Gentrification is natural. Neighborhoods change over time. Different groups move in and out, businesses change hands, land uses shift. But just because change is normal doesn’t mean it’s natural. What drives middle-class residents into working- class and minority communities? What policies, economic forces, and cultural dynamics propel these changes? What makes it profitable and desirable? The answers lie everywhere from city zoning practices to historic redlining and racial segregation policies to a capitalist system of private property where housing is an investment and an asset. There may be a wide array of forces that encourage gentrification, but they are all human- made. Gentrification is good for the city. It’s hard to argue with some of the changes that come with gentrification: renovated housing, clean parks, cute local businesses. A darker reality lurks under the surface. Those renovations may have begun with reno-victions, booting people out of their homes to allow landlords to jack up rents. The clean park might have been home to unhoused people, who were rounded up with heavy-handed policing and forced into crowded, unsafe shelters or out of the city altogether. A charming new café may have displaced a low-cost diner where locals have gathered for decades. While many welcome the sanitized, homogeneous face of the gentrified city, this change comes with a tremendous cost paid by the city’s most vulnerable communities. # ⚓ TomDispatch ☛ No_More_Sacrifices_–_TomDispatch.com⠀⇛ In today’s piece, TomDispatch regular Liz Theoharis, co-chair of the Poor People’s Campaign, explores the Biden administration’s recent surprising successes in passing the Inflation Reduction Act (IRA) and cancelling significant student loans. She also focuses on the deeper failure that underlies our American world, leaving it filled with “sacrifice zones” of the poor and underpaid. Thought of a certain way, all of us now live in sacrifice zones. In a sense, thanks to climate change, this whole country — in fact, our whole world from Europe to Africa, China to Pakistan — is now a sacrifice zone. After all, while I was writing this introduction, the Northeast was experiencing devastating flash floods and the West, already embroiled in years of a historic megadrought, was suffering through soaring temperatures, breaking hundreds of heat records, that don’t faintly fit this end-of-summer season. Some temperatures in California were expected to rise 20-30 degrees above the early September norm. And despite the way the IRA genuinely took us forward on the issue of climate change, as Theoharis suggests, the Biden administration also made painful — in the sense that, in the years to come, we’ll all feel the pain — concessions to fossil-fuel companies and Joe Manchin as well as Kyrsten Sinema, the two Democratic senators who have received such copious financial support from that industry. # ⚓ The Conversation ☛ The_Queen_has_left_her_mark_around_the world._But_not_all_see_it_as_something_to_be_celebrated⠀⇛ From the very beginning, Queen Elizabeth II’s reign was deeply connected to Britain’s global empire and the long and bloody processes of decolonisation. Indeed, she became Queen while on a royal visit to Kenya in 1952. After she left, the colony descended into one of the worst conflicts of the British colonial period. Declaring a state of emergency in October 1952, the British would go on to kill tens of thousands of Kenyans before it was over. Is it possible to disentangle the personal attributes of a gentle and kindly woman from her role as the crowned head of a declining global empire that waged numerous wars and resisted those demanding independence across the globe? Even though she was a constitutional monarch who generally followed the lead of her parliament, many of Britain’s ex-subjects don’t think so, and some historians agree, with one commenting that “Elizabeth II helped obscure a bloody history of decolonisation whose legacies have yet to be adequately acknowledged”. # ⚓ Caitlin Johnstone ☛ Our_Entire_Civilization_Is_Fake_And Stupid_–_Caitlin_Johnstone⠀⇛ That’s why the more you learn about the world, the more fake and stupid our civilization looks. It’s because it is fake and stupid. Our news, our entertainment, our jobs, our legal systems, our political systems, our education systems, our financial, monetary, economic and commercial systems; the way our entire civilization is structured and organized has nothing to do with what’s true and good and everything to do with keeping human organisms compliantly turning the gears of capitalism and empire. [...] So mainstream culture presents a fraudulent image of reality. It’s written into the code of everything that’s mass produced — not just in Prager University lectures on the evils of socialism or propagandistic news stories about weapons of mass destruction, but in sitcoms, in advertisements, in clothing brands, in pop music, in textbooks, in trends. When it’s not constant messaging that capitalism is totally working and the world is ordered in a more or less sane and truth-based way, it’s manipulations designed to shape our values and measures of self-worth to make us into better gear-turners. If you’re noticing this ubiquitous fraudulence, it’s not because you’re becoming distant from the rest of society, it’s because you’re becoming more intimate with it. You’re getting in real close, so close you can see the nuts and bolts of it, see how the sausage is made. # ⚓ Matt Rickard ☛ Startup_Ideas_I’ve_Considered⠀⇛ After I graduated last year, I evaluated different startup ideas for a few months. Here’s a list of ideas I ultimately didn’t end up pursuing, with varying levels of research and prototyping. # ⚓ CoryDoctorow ☛ Billionaire_grifters_hate_her⠀⇛ A billionaire’s crime spree has come to an end: a federal judge held that Fleetcor was running a fraudulent, predatory business, and found that the company’s billionaire owner, Ron Clarke, was personally responsible for the company’s offenses. [...] It was her careful, dogged reporting that unraveled Fleetcor’s scam and established Clarke’s personal culpability in it. She’s a hero – and she’s part of a glorious American tradition of muckraking women journalists who devoted their lives to bringing down the billionaires who preyed on them and their families. Reading about Epstein, I was immediately reminded of Ida B. Tarbell, who brought down John D. Rockefeller and triggered the breakup of his juggernaut, the Standard Oil Company. Rockefeller was the most powerful businessman in the world and Standard Oil was the most powerful company in the world, and Tarbell took them on – and won. It’s an amazing story. Tarbell was the daughter of a small-time Pennsylvania oilman who had been crushed by Rockefeller’s cartel. # ⚓ Das_U-Blog_by_Prashanth:_Book_Review:_“From_the_War_on Poverty_to_the_War_on_Crime”_by_Elizabeth_Hinton⠀⇛ I’ve recently read the book From the War on Poverty to the War on Crime by Elizabeth Hinton. This book is a history of the progression through the titular subjects in the US, starting with the Kennedy presidency and ending with the Reagan presidency. It shows how while some problems associated with the war on poverty did come from good but conflicting intentions when implementing social welfare programs, many more problems came from halfhearted implementation of social welfare programs with the intent & through the lens of fighting crime leading ultimately to replacement of those programs with more explicit expansions of policing to fight crime especially in response to high-profile riots in large cities in the 1960s & 1970s. # ⚓ Antipope ☛ I_can’t_even_–_Charlie’s_Diary⠀⇛ The reason there was no new blog entry earlier this week is the same reason I’ve been unable to write (or edit) all week: my brain tends to freeze when the wrong kind of history is happening. And it is now very clear that the wrong kind of history is happening in the UK. Seriously, I had no idea it was possible to crash a G7 economy in less than a week! But it looks like only a Bank of England intervention in the gilts market averted a run—followed by the collapse of the nation’s largest pension funds. 40% of mortgage products have been withdrawn by banks and lending institutions, the housing market is expected to fall 10% in the next six months, Sterling is heading below US dollar parity for the first time ever, the BoE is inevitably going to have to raise the base rate (crashing the finances of a huge proportion of the mortgage-holding public) … it beggars belief. [...] Fuck Around and Find Out time: as of Monday, Labour were polling 17 points ahead of the Conservative (per YouGov). That was bad enough, but by Thursday 29th, a new poll gave Labour a stunning 33 point lead in the polls as Conservative voter support imploded. It seems that tanking the currency, the pension system, the housing market, and the national debt in just one week is slightly unpopular. Who could possibly have seen that coming? [...] Speculation: the Conservative Party conference begins on Monday 3rd, and is going to be an epic drama. Either the party will double down and drink the poisoned Kool-Aid or (I think this is more likely) they will go backstabby on La Trussterfuck, possibly lining up behind Rishi Sunak, who is currently pulling no punches (and who was absolutely right when he warned about the effects of her policies on the economy before he lost the leadership election). [...] If Truss somehow survives, we’re fucking doomed. When someone tells you who they are, you should generally believe them, and Truss has been shouting through a megaphone that she’s a deeply stupid Thatcher cosplayer in the pocket of dogmatic libertarian ideologues who I assume were hired to felate billionaire oligarchs… [...] What other options are there? Who knows. But I think we can say for certain that the crisis is not over, there is scope for it to get much worse … and this is the sort of thing that breaks political parties, breaks nations, and if the UK was a developing world country I’d be getting worried about a military coup round about now. # ⚓ Michael West Media ☛ The_monster_that_ate_hope:_Robodebt was_a_tragedy_40_years_in_the_making_–_Michael_West⠀⇛ Even by the miserable standards set during nine years of Coalition government, Robodebt was one of its worst scandals. #Mate examines the scheme’s genesis and its disastrous fallout. The royal commission into the illegal Robodebt scheme that ruined the lives of countless Australians opened in Brisbane this week. The commission is chaired by Catherine Holmes, a former Queensland Supreme Court chief justice. Inaugurated in 2015, the scheme falsely accused welfare recipients of owing money to the government and issued debt notices to people identified through a process called income averaging, which compared their reported income with Tax Office figures. More than $750 million was wrongfully recovered from 381,000 people. # ⚓ Michael West Media ☛ Run_of_Luck:_systemic_money- laundering,_disgrace,_then_pay_rises_for_Star_casino directors_–_Michael_West⠀⇛ The directors of one of Sydney’s two Tweedledee and Tweedledum casinos are desperate to keep the roulette wheels spinning, the blackjack dice rolling, and the poker machines humming. In other words, to keep the money flowing to the decision- making tables of the discredited enterprise, writes Michael Sainsbury. Star Entertainment has this week prostrated itself. The company grovelled to maintain its licence to operate its Sydney casino and with it, official permission to keep inflicting untold misery on the families of gambling addicts. This was after it was found unfit to hold a licence and asked to show cause why it should by Adam Bell, SC. Yet its directors and executives appear to be getting off not just scot free – but with the bank balances enhanced. # ⚓ Bloomberg ☛ NFT_Trading_Volumes_Collapse_97_Percent_From Peak_Earlier_This_Year⠀⇛ Trading volumes in nonfungible tokens — digital art and collectibles recorded on blockchains — have tumbled 97% from a record high in January this year. They slid to just $466 million in September from $17 billion at the start of 2022, according to data from Dune Analytics. The fading NFT mania is part of a wider, $2 trillion wipeout in the crypto sector as rapidly tightening monetary policy starves speculative assets of investment flows. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Michael Geist ☛ The_Law_Bytes_Podcast,_Episode_140:_Anthony Housefather_Reflects_on_the_Fight_Against_Anti-Semitism Online_and_the_Laith_Marouf_Incident_–_Michael_Geist⠀⇛ The Law Bytes podcast returns with a special episode focused on combatting online anti-semitism with a particular emphasis on an incident involving the department of Canadian Heritage and Laith Marouf, a well known anti-semite. As part of Heritage’s anti-hate program, the government had provided funding to the Community Media Advocacy Centre (CMAC), led by Marouf, to develop an anti- racism strategy for Canadian broadcasting. While there was years of evidence of Marouf’s anti- semitism, the department didn’t look or didn’t find it. The contract was cancelled after a public outcry, but even that led to concerns as it was left to Jewish MPs such as Anthony Housefather, Ya’ara Saks, and Melissa Lantsman to say something while many others remained silent. Anthony Housefather, a Liberal MP from Montreal, not only spoke out on the Marouf situation but also called on all MPs to become more vocal. Housefather has been working on the online anti-semitism issue with politicians from around the world as part of an Inter-Parliamentary Task Force on Online Antisemitism and he joins me on the Law Bytes podcast to talk about the work of the task force and its recent hearing in Washington, DC, the Marouf incident, and the urgency for all to speak out more aggressively against anti-semitism. # ⚓ Michael West Media ☛ Labor_surprises_nobody_with_first_big diplomatic_appointment_–_Michael_West⠀⇛ ”Mr Smith goes to Washington,” journalists mused with amusement when Labor’s foreign minister began his northern hemisphere wanderings as our chief diplomat under the first government of Kevin Rudd. Now Mr (Stephen) Smith, former Labor MP for Perth, has been tapped as our high commissioner to the UK. Labor fiercely rejects the notion this is a job for the boy, but it certainly is a job for a Labor mate. Smith, 66, spent 20 years in federal parliament, and certainly put up with the rough as well as smooth. In 2010 he was moved into the political graveyard of defence when Labor gave his job to Kevin Rudd. The thinking was that Rudd, a disgruntled deposed PM, would do the least damage if he was sent as far away as possible. If this pattern continues, the UK will eventually be rewarded with the appointment of Kevin 07 as high commissioner. Not soon, hopefully – they are suffering enough. # ⚓ Andre Franca ☛ Brazilian_elections⠀⇛ With elections in Brazil around the corner, my concerns about how the current President will behave in relation to the results becomes more latent. Jair Bolsonaro commits several atrocities daily, such as attacking the country’s institutions, offending women, and accusing the same electoral system that elected him in 2018 as fraudulent, threatening with the use of military force not to surrender office in the event of defeat next Sunday. # ⚓ Michael West Media ☛ “Massive_achievement”_but_is_the_NACC anti-corruption_commission_missing_some_teeth?_–_Michael West⠀⇛ A federal integrity body is finally to become a reality. While it’s a significant achievement, there are shortfalls and political hurdles. Callum Foote garners expert opinion on Australia’s National Anti-Corruption Commission (NACC) draft legislation. Whistleblower protections and secret hearings are the two big issues. On Wednesday, Attorney-General Mark Dreyfus released the legislation which will power the promised National Anti-Corruption Commission (NACC). While a Labor government has carriage of the body, it has long been a policy plank of the expanding cross-bench of the Greens and Teal independents, particularly the MP for Indi, Helen Haines. # ⚓ Michael West Media ☛ Pokies_Thuggery:_ClubsNSW_lobbyists hammer_critics,_hide_their_own_dirty_laundry_–_Michael_West⠀⇛ ClubsNSW is dragging a dying man through the courts, and media identity Friendly Jordies too, but its own house is hardly in order. Michael West reports. The people from ClubsNSW are such sticklers for the law, at least in their own opinion, that they have anointed themselves public prosecutors to drag their critics through the courts. They are suing a whistleblower dying of cancer, Troy Stolz, and popular YouTube investigator and comedian Jordan Shanks. Not just suing but bringing private criminal prosecutions. Punishment? Gaol- time. They have anointed themselves as police and the Directors of Public Prosecution to boot. # § Misinformation/Disinformation/Propaganda⠀➾ # ⚓ Associated Press ☛ ‘Pre-bunking’_shows_promise_in fight_against_misinformation_|_AP_News⠀⇛ Soon after the Russian invasion, the hoaxes began. Ukrainian refugees were taking jobs, committing crimes and abusing handouts. The misinformation spread rapidly online throughout Eastern Europe, sometimes pushed by Moscow in an effort to destabilize its neighbors. # ⚓ Ruben Schade ☛ Rubenerd:_The_sham_referendums_in Ukraine⠀⇛ These numbers look North Korean. They’re so ridiculous, and so divorced from reality, that no rational person would take them seriously. Even in the most unified and functional of democracies, a 60% win is seen as a landslide. # ⚓ Russia_declares_annexation_of_4_Ukrainian_oblasts after_staged_referendums⠀⇛ The announcement comes after Russia’s proxies held sham referendums in the occupied parts of these regions and, on Sept. 27, declared nearly 100% of people living in the occupied territories of Ukraine “voted” to join Russia. # ⚓ Positech Games ☛ This_article_is_too_long_for_you_– Cliffski’s_Blog⠀⇛ I made the mistake today of reading some social media comments (twitter, reddit, arstechnica, slashdot) on a topic I know a bit about and have read a lot of the background on. As you might guess it was an IQ-barren tirade of abuse, uninformed hot- takes and absolutely baseless bullshit. [...] The reason I take you on this tedious heroes journey about me learning C++ is this: Learning C and C++ on your own, with just one book and 3 floppy disks, and nobody to ask questions…is fucking hard. I remember struggling and getting very confused, and thinking it was all gibberish, but persevering, and persevering and struggling and trying again and again and again until finally I started to understand how it all works. 30 years later and it turns out doing that made me millions and millions of dollars, financial freedom, my own business and lots of stuff to be proud of. In many ways, struggling alone with a seriously complex and hard task, and no distractions was the making of me. (In many ways…not just career. For someone like me who is clearly on the autistic spectrum developing expertise in an absolutely clear definite and logical language that isn’t English is very very comforting). o § Censorship/Free Speech⠀➾ # ⚓ CoryDoctorow ☛ Book-banning_wingnuts_are_a_tiny,_vocal minority⠀⇛ “The Moral Majority” is a stupendous marketing gimmick: it allowed a small minority of vicious, paranoid, hateful creeps to brand themselves as a “silent majority” who were all around us, afraid to speak their minds. The impact of this wasn’t merely in convincing politicians and the press that the views of these unhinged, fringe conspiratorialists should be taken seriously – just as important is the zap it put on the heads of their enemies, the people who wanted to love whom they loved, take care of one another, and let folks be themselves. For these people, the Moral Majority created the impression that they themselves were the minority. These people were convinced that their broadly shared, commonsense values – entiirely compatible with the Christian gospels, as it happens – made them outliers. o § Freedom of Information / Freedom of the Press⠀➾ # ⚓ The Wire ☛ Warrant_Issued_Against_Journalist_Ravi_Nair_in Defamation_Suit_Filed_by_Adani_Group⠀⇛ The journalist, who has extensively written on BJP’s economic policies and the business dealings of the Adani Group, has said that he wasn’t served any prior summons nor was he given any copy of the complaint against him. o § Civil Rights/Policing⠀➾ # ⚓ Literary Hub ☛ A_Pig_and_a_Locust_Get_Into_Serious_Trouble With_the_Law:_On_Justice_in_Medieval_Europe_‹_Literary_Hub⠀⇛ Arran Lomas Details The Gruesome Methods of Proving Guilt or Innocence in the Middle Ages Curiously trial by jury was voluntary in medieval England. However, if you did refuse to stand trial, the authorities would crush you between two heavy stones until you either acquiesced or died. In despotic feudal kingdoms “voluntary” was often about as voluntary as Janice from work’s wedding invitation, whom ironically you also wish you could crush between two heavy stones. More serious crimes such as murder, assault and treason were dealt with in the king’s court. If you ended up here and were found guilty, you could be sure of severe punishment. Murderers were hanged or beheaded. Those convicted of treason were hung, drawn and quartered. So you don’t lose sleep over it, I should explain that being ‘hanged’ stipulated until dead, whereas to be “hung” meant you would be let down before death. As in “I hanged my cat; now it’s dead” compared to “I hung my cat on the wall, then fed it dinner.” However, being hung was usually far worse than a quick hanging, because the executioner would have a delightful basket of torture lined up for you. Starting with the next step, being “drawn.” o § Internet Policy/Net Neutrality⠀➾ # ⚓ Michael Geist ☛ Bill_C-11_Goes_Off_The_Rails_Amid_Charges of_Witness_Intimidation_and_Bullying_by_Government_MPs_– Michael_Geist⠀⇛ The Senate Bill C-11 hearings have provided a model for the much-needed, engaged, non-partisan inquiry that was largely missing from the House committee’s theatrics in which the government cut off debate on over 150 amendments. But this week those hearings attracted attention for another reason: serious charges of witness intimidation and bullying by government MPs, most notably Canadian Heritage Parliamentary Secretary Chris Bittle (yes, the same Bittle who last month suggested I was a racist and a bully for raising concerns about Minister Pablo Rodriguez silence over Canadian Heritage funding of an anti-semite as part of its anti-hate program). The Globe and Mail reported late on Tuesday night that Bittle – together with his colleague, Liberal MP Lisa Hepfner – had sent a letter to the Lobbying Commissioner to seek an investigation into the funding of Digital First Canada, a group representing digital first creators. The letter may have been shopped around to other MPs as Liberal MP Anthony Housefather has told the Globe he did not sign it. DFC’s Executive Director, Scott Benzie, had appeared before the Heritage committee months ago and Bittle used his time to focus on the organization’s funding. Leaving aside the fact that government MPs reserve these kinds of questions only for critics of Bill C-11 (there were no similar questions this week from Ms. Hepfner to the Director of Digital Content Next, whose organization supports Bill C-18 and counts Fox News among its members), the timing of Globe story was incredibly troubling. The Lobbyist Commissioner letter was apparently filed nearly two months ago and Benzie had been assured that he was compliant with the law. Yet the story was presumably leaked to coincide with Benzie’s appearance before the Senate committee last night. o § Digital Restrictions (DRM)⠀➾ # ⚓ Das_U-Blog_by_Prashanth:_Technological_Restrictions_on_E- Books_and_Culture_Wars_on_Books_in_2022⠀⇛ Despite the long title, this post will be fairly short. This blog used to publish a lot more often (I had a lot more free time in high school & college) and focus a lot more on issues related to free software, free culture, and things like that, yet even after looking through posts on this blog from its early years (which, aligning with the stereotype of an adult looking through essays written in high school, made me cringe at the quality of writing even if I agreed with some of the basic opinions), I actually couldn’t find any posts specifically about the effects of so-called digital rights management (DRM) on E-books. * § Gemini* and Gopher⠀➾ o § Personal⠀➾ # ⚓ SpellBinding:_ALMOPXS_Wordo:_WHACK_–_2014_SMALLPOX_scare⠀⇛ This is a wordlog for the SpellBinding puzzle (in which you construct words using the specified letters; each word must contain the anchor letter). o § Technical⠀➾ # ⚓ Comparing_with_the_worst⠀⇛ Often I see people comparing their situation with the worst possible situation in order to convince themselves they’re fine and not change. This is usually the case with addictions. “I don’t drink much because I only drink 2 beers a day, I know people that drink 5!” “I’m not a social media addict because I only spend 3 hours a day, others spend 8!” # ⚓ Extending_fail2ban_on_NixOS⠀⇛ Fail2ban is a wonderful piece of software, it can analyze logs from daemons and ban them in the firewall. It’s triggered by certain conditions like a single IP found in too many lines matching a pattern (such as a login failure) under a certain time. What’s even cooler is that writing new filters is super easy! In this text, I’ll share how to write new filters for NixOS. # ⚓ Hello_call_center_agent,_I_found_a_bug_in_your_website⠀⇛ The other night the wife was baby sitting for some friends of ours. The kid went to sleep and she turned on Apple TV and started watching Ted Lasso to see what all the hype was. After half a dozen episodes she was hooked and talked me into getting the service for a month so that we could watch the rest of the season (also I kind of want to see how badly Foundation ruins Asimov’s masterpiece). So tonight she installs the app on our TV and it turns out Samsung gives you 3 months free of Apple TV. 3D barcode, sign up for an Apple account, give them my CC info and Bob’s your uncle… # ⚓ WHY_I_SWITCHED_TO_PRUSASLICER⠀⇛ I have a general aversion to installing new apps, and try to have as few onto my devices as possible. This is even more pronounced when the apps have not been developed well for the OS, leading to unintuitive keystroke shortcuts and other confusing behaviours. # § Internet/Gemini⠀➾ # ⚓ Hello,_World!⠀⇛ Hello, fellow capsuleers! I just discovered Gemini a couple days ago, and I finally got around to securing a domain and server so I could join in. I find the ideas behind Gemini pretty interesting (obviously, or why would I be here?), and I’d love to see the community grow and continue to play with what can be done over the protocol. I think if we put our minds to it, we can come up with some pretty interesting ideas that will work surprisingly well despite the limitations. I’ve looked around a little bit and seen some cool things so far, but there’s definitely still some untapped potential. # ⚓ colorOberon⠀⇛ Since there are no colors in gemini markup, I can’t quite do this topic justice. And also, it’s a fairly vague idea to begin with. Let’s see how it shakes out. Stacksmith kindly replied to some posts I’ve made about Oberon. He and I have some things in common, it turns out, such as having enjoyed other languages over time. In particular, I first encountered Forth in 1983 or thereabouts, having used an Osborne I computer to plot to an HP plotter over the parallel port. The language I used for that was Forth. I worked at an electronics store in West LA at the time, and we had that equipment for sale, and it was just sitting there, so when it was quiet in the store… Anyway, I’ve long enjoyed Forth, and was an avid reader of things Forth around the time that colorForth came out. Somehow or another the little ‘Game of Life’ app I wrote in colorForth made it into a later re-release of colorForth by a guy from England somewhere. # ⚓ Decentralized_Gemini⠀⇛ I love decentralization: the freedom for individuals to establish a presence in a society, online or in the real world, on equal terms with everyone else, and to not be beholden to large corporations or government entities to provide a place and a space for them. It’s one of the things I loved about the early days of the Internet, and it’s one of the things I currently love about Gemini so much. To that end, I always want to encourage the adoption of decentralized tools as much as I can, from Mastodon to PeerTube to Tox, and even self-hosting on Gemini. [...] The biggest problem with reversing this trend is that most people don’t care about it. They say they’re worried about privacy invasions and aren’t comfortable with government surveillance, but they don’t take any active steps to mitigate it. Why? [...] One is the convenience of centralization: any content you could ever want to find is on YouTube, Amazon, Google, Reddit, and all the rest. One no longer has to keep a lost of bookmarks, as was so common twenty years ago; one of my friends recently commented that he hasn’t used bookmarks outside of a work context in over a decade. Now, simply go to one page, type in what you want, and voilà! Everything is one click or tap away. [...] In fairness, some security know-how is required to self-host Internet services safely. Most people don’t understand what it takes, and most people don’t care. But that apathy is a killer to decentralized projects in the long run. [...] The problem with an approach like this is that it would require so many additions and extensions to a Gemini client that it would essentially no longer be running the Gemini protocol. Certainly a viable decentralized network could be built this way, but other tools already operate under this paradigm far more effectively, and they don’t use Gemini either. # ⚓ The_top_10_things_about_blog_and_IT_you_should_know⠀⇛ 1. clicking on click bait titles should be avoided at best, this gives credit to such titles and authors will continue to publish them # § Announcements⠀➾ # ⚓ plass(1)_first_public_release⠀⇛ Many many moons ago, so many that I don’t remember the details, I was trying to hack something with pass(1) and got really fed up with it. It was my second password manager, with keepassxc being the first, and I really loved the idea behind it but I started to hate the interface. I remember that I found the output of the various pass commands difficoult to parse programmatically; having to bypass it (for example by means of find(1) seems wrong.) When I’m using a CLI tool, I want a good output I can further hack on. [...] I remember that I found the output of the various pass commands difficoult to parse programmatically; having to bypass it (for example by means of find(1) seems wrong.) When I’m using a CLI tool, I want a good output I can further hack on. For those who don’t know, pass(1) is a simple password manager. It stores passwords in a directory tree rooted at ‘~/.password-store’ where the passwords are files encrypted with GPG. How to organize things is up to you; for example if I have to save the password for the website ‘example.com’ where my username is ‘foo’ I’d probably persist it as ‘www/ example.com/foo’. So, dirven by my scriptability problem (and also the fact that I wanted to use got(1) instead of git(1)) I wrote mine. The name? It’s a “perl pass”, so “plass”! (God, I’m awful at picking names…) =============================================================================== * Gemini_(Primer) links can be opened using Gemini_software. It’s like the World Wide Web but a lot lighter. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 7635 ➮ Generation completed at 02:43, i.e. 48 seconds to (re)generate ⟲