𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, December 07, 2021 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Wed 8 Dec 02:41:23 GMT 2021 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2021/12/07/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmcNLdXKwxdD6cLvdgRCUDzCTD4PfjtBzdq6btKA1VdHeD QmXkgs6nUp2YxKaphy2EXnEaHqcAAagQyA5Z44RUfN2uvD QmdGDdRX8ZuGj76UZ5fvhjBZ81N9v4RyisduQDvtX5i4bQ QmXUd8Sk2pSNG2yA8y1Ddfd7zDgDgQCfztF4s5mGnkZKin QmeDHFuwxMuWGXnXY8ELJ4X5fk6wWvRiyFNXRQ9noLwTQw Qma6fG1kUmKGPn5zAHpVWkUoTsUNdRgGNmFYPmFKcxGEHK QmcehsKRe5D9pD1MUq2cbSWmBriwyeQoqZP3fXiJWEjy4z QmSWwJ7eRdx1kz73nTFtXRp2vF9nhTnV7sYYZVwuM6t9c5 QmWM7VYrVdqPgZh8JgwKyiXxRcVGNjoM8cBVEUyQXKcR5T QmWSgWCNaXdj4bqpVXJtFwGUpuJtUjJhMJNpvzpyfvb343 QmcVbvyKViSMyKpSnvawYzxL7fTBuhBFrU1Qs3vw1Dka8p QmUKBswRXMsDq5RCK5eUe68NysKpHtQ9EhcoUWes6WJbtG QmUS4fYkvuMboBGcVkEMNHsnTxKWQm7WKvLr6wGqwSsgk1 QmWxGDdEJSbvkgneVRR2pbXgmVk3pi5U6cgy64gq54Dsi7 QmThpqmVrTBjQ3aKEp3yrZKJUdKapNAGts5Lu3eYkGeBwf QmQPL4aU5VkHzGprihFtysZx7tMGqLPQa11SU2s4ao6H6r QmWDLoPpML1exaPTP8wfzYiKd4whiRGaCCqWNHJQ8Tgfgg QmXP9uUCLGPXq5XphWSHwKkEcNvzBUFmcGuun1rgVhDoMf QmbcSKJZiufM2XfxxnB92wQE323m9MsiAMo5YFmwFPu8VN QmWmC3AgPDFykej4Jpay8nnpKKVGMMEfv8MjggJ9Qw5Lm9 QmNPpiGqWGFQNEECwNKt72LSricBeH2VuxSzamtqTrESHV ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ All IRC Logs Now Available as GemText Over Gemini Protocol | Techrights ⦿ Clare Daly (GUE/NGL) Does What Every Public Official in Europe Should Have Done About EPO Shenanigans | Techrights ⦿ [Meme] EU Assurances | Techrights ⦿ IRC Proceedings: Monday, December 06, 2021 | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2021/12/07/all-irc-logs-now-available-as-gemtext-over-gemini-protocol/#comments http://techrights.org/2021/12/07/clare-daly-on-epo/#comments http://techrights.org/2021/12/07/epo-eu-assurances/#comments http://techrights.org/2021/12/07/irc-log-061221/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2021/12/07/easyos-3-1-13/#comments http://techrights.org/2021/12/07/firefox-96-beta/#comments http://techrights.org/2021/12/07/tails-4-25/#comments ䷩ 𝚕𝚒𝚗𝚎 58 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/07/all-irc-logs-now-available-as-gemtext-over-gemini-protocol/#comments Gemini version at gemini://gemini.techrights.org/2021/12/07/all-irc-logs-now-available-as-gemtext-over-gemini-protocol/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.07.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ All_IRC_Logs_Now_Available_as_GemText_Over_Gemini_Protocol⠀✐ Posted in Site_News at 9:13 am by Dr. Roy Schestowitz Video_download_link | md5sum ac65a720a06526f9422c3088d7902b49 http://techrights.org/videos/irc-gemtext-indexed.webm Summary: Today we’ve completed the transition from plain text over gemini:// to GemText over gemini:// for IRC logs LATELY we’ve been working to enhance the capsule and increase adoption of GemText/gemtext/gmi, the HTML equivalent of Gemini Protocol. We’ve focused more on converting our IRC logs (static/daily and scrollback) into proper GemText [1, 2] and as of today the job is nearly done. We shall do some further testing and link to the new pages in the coming days (IRC, blog posts etc.); with that little project out of the way we’ll certainly be able to focus more on articles. Eventually we want the same experience in Gemini that we already have on the Web. Sure, there are technical limitations, but many can be overcome with a little creativity. What matters the most is the content, not the presentation. █ ䷩ 𝚕𝚒𝚗𝚎 103 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/07/clare-daly-on-epo/#comments Gemini version at gemini://gemini.techrights.org/2021/12/07/clare-daly-on-epo/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.07.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Clare_Daly_(GUE/NGL)_Does_What_Every_Public_Official_in_Europe_Should_Have Done_About_EPO_Shenanigans⠀✐ Posted in Deception, Europe, Patents at 6:13 pm by Dr. Roy Schestowitz Written question recently submitted to the EU Council of Ministers (see date at the bottom) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Clare Daly (GUE/NGL) Question for written answer⦈ Summary: There’s another (new) push to hold the EPO accountable, seeing that the_overseers_clearly_do_not_do_their_job and instead_cover_up_the_abuses IN THE NEXT batch of Daily Links (due in about an hour) we’ll include the latest criticisms of the EPO and the_lies_from_the_EPO (hard to keep track of it all anymore) will be mentioned. German politicians don't_seem_to_care. Or maybe if they do care, they’re not ‘supposed’ to talk about it. There’s a lack of journalism, there’s virtually no oversight and public interest in politics, but Clare Daly (GUE/NGL) should be commended for the effort she has put into holding the EPO accountable, as we noted_here_before (she_was_obstructed by friends and allies of Benoît_Battistelli, who had taken over positions of power in the EU). Even the EPO itself is still governed by Battistelli_in_absentia. It’s grotesque and it must be stopped. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Clare Daly (GUE/NGL); CC BY-SA 2.0⦈ Here’s the latest, dated today (for the update or the listing): Parliamentary questions 16 November 2021 E-005130/2021/rev.1 Question for written answer E-005130/2021/rev.1 to the Council Rule 138 Clare Daly (The Left) Subject: Development of a common position on reform of European Patent Office governance, in particular the system of legal protection for staff Long-standing, serious labour disputes persist at the European Patent Office (EPO) due to, inter alia, management‑imposed restrictions on fundamental rights, including the right to strike. The EPO, which is headquartered in Munich with offices in Berlin, The Hague and Vienna, is an international organisation established by the European Patent Convention (EPC), and therefore enjoys extraterritoriality and jurisdictional immunity from national courts. The Administrative Tribunal of the International Labour Organization has jurisdiction over employment disputes, but the procedure is slow and inefficient, with decisions poorly implemented by EPO management. EPO staff living and working on EU territory therefore suffer from a de facto legal vacuum, lacking an effective, accountable system of legal protection to safeguard their rights. Despite having observer status at the EPO, the Commission denies standing to intervene in its affairs. 1. What is the Council’s position on the ongoing deprivation of staff rights at the EPO? 2. All EU Member States are EPC contracting states. Will the Council take action to develop a common position among Member States on the reform of EPO governance, in particular to promote coordinated action to provide EPO staff with an effective system of legal redress for safeguarding their labour and fundamental rights? Last updated: 7 December 2021 It’s going to be interesting to see 1) who answer/s this and 2) what they say. As we saw before, there’s a collusion among the overseer and those whom the overseer is supposed to oversee. It is the hallmark of the world’s worst ‘banana republics’. █ 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Breton-Battistelli relationship⦈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⠔⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠀⠅⠢⠐⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠄⡁⠠⠌⣐⠂⠀⠭⠅⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠒⠤⠌⢬⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠀⠀⠘⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠁⢿⡇⠂⢿⡏⠂⢿⡇⠡⢿⡇⠁⢿⡇⠃⢿⡏⠈⢿⠀⠀⢸⡇⠧⢿⡏⠠⢿⠏⠁⢿⡿⠇⢿⠇⠈⢿⠇⠂⢿⠏⠉⢿⠯⠁⢿⠇⠈⢿⠇⠝⢿⠇⠅⢿⠇⠁⢿⠇⠉⢿⠏⠛⣿⠇⠾⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⡙⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢛⢿⢿⣿⡟⢻⠿⡿⢿⢿⠿⡿⢿⠿⡿⡿⠿⡿⣿⠿⠿⡿⡿⢿⠿⡿⣟⡿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢿⣿⣿⣿⣿⠛⠉⠻⣿⣿⣿⣿ ⣿⣿⣴⣮⣧⣷⣧⣼⣢⣧⣷⣼⣴⣧⣧⣼⣴⣤⡷⣱⣿⣼⢠⣧⣶⣾⣮⣧⣧⣜⣤⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣀⣸⣼⣸⣽⣿⣤⣀⣣⣆⣬⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣘⣇⣁⣉⣝⣯⣍⣉⣯⣉⣉⣿⣢⣀⣣⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣏⣉⣩⣺⣟⣉⣋⣧⣱⣷⣏⣛⣭⣝⣽⣹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠭⡿⡟⡛⡏⢛⢿⡟⣯⡿⣟⣿⡻⣿⡏⣻⢻⣿⡟⠛⣿⢻⡻⡟⣿⣿⠙⣿⢍⢍⠙⠽⠍⣉⡩⢉⠭⢹⠟⣿⢛⣻⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⢻⣻⡿⢛⡟⣽⠛⢻⣟⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⣿⣿⢻⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣛⣿⣿⡿⢿⢛⣿⣿⠿⡟⡛⣿⠿⢿⢻⣿⣟⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⣿⣾⣷⣿⣶⣷⣾⣽⣷⣷⣿⣶⣾⣶⣷⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢹⣿⣛⠉⡏⢹⠹⣿⡙⠙⢛⠛⠙⠛⢻⡏⠍⠛⠙⠛⢿⠟⢛⣿⡏⠉⣹⠭⣿⢟⢟⣿⣿⠛⠿⢿⡟⠟⡟⠿⠛⠛⠛⢿⣏⡹⣽⢹⢻⣟⣿⡯⢝⢟⢿⣟⠟⢹⠹⠋⠛⢻⠟⠻⠙⠻⢛⡟⡻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⠙⡻⣛⣻⡻⡛⣟⢻⢛⡛⡛⢛⠛⠛⠛⡟⡛⣛⠛⠛⠛⠛⡟⠛⢛⢛⢛⢛⣿⢛⣟⣟⡻⡛⣚⣻⣻⢟⠛⠛⣛⢻⠛⡛⡟⢙⢛⡟⣟⣿⡛⡛⠛⡟⡛⣿⣿⢻⣿⣿⣟⢛⠻⣛⣟⡛⠛⡛⢛⣛⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⡿⠿⠿⠻⢿⠿⠻⠿⣿⣿⣿⡿⡿⠿⠷⠿⠻⢿⢿⢿⢿⢿⣿⣿⡿⣿⠿⣿⡿⢿⣿⣿⢿⣿⣿⢿⠿⠿⡿⠿⠟⠿⡟⢿⠛⢿⣻⡿⢻⢟⣻⡿⡿⠛⣿⡿⣿⣿⠿⣛⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣷⢷⢶⣾⣶⣷⡶⣲⡶⠿⠷⢿⡾⠷⠶⢶⣶⡾⣾⢷⣷⣷⢾⡾⡻⠷⢿⠾⠾⠷⠲⠿⢷⠿⡿⡶⢾⣶⣾⡾⡶⡶⢶⠷⠾⠿⡷⢾⣷⢾⣾⣿⣷⣾⡿⣿⢷⡾⠻⠞⠿⠾⡚⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣿⣾⣿⣿⣿⣷⣿⣷⣧⣴⣾⣿⣾⣶⣾⣿⣿⣿⣾⣿⣿⣷⣷⣷⣧⣴⣶⣾⣶⣶⣧⣼⣶⣷⣿⣾⣿⣷⣷⣷⣷⣿⣶⣾⣶⣷⣿⣿⣾⣾⣿⣿⣿⣿⣿⣾⣿⣦⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⡿⢻⠛⡟⠛⠛⠛⠛⠛⠛⣻⢿⡟⡿⡻⡻⡛⣛⢛⠟⢻⣿⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⠛⠻⠛⡟⠻⣻⡻⣻⢻⣿⡿⡛⠛⠛⠛⣛⢻⠛⢟⣿⢟⡻⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣷⣿⣿ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢨⣿⠁⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⡇⠀⠀⠀⠀⠀⣀⣤⣶⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⣿⣿⣿⣻⣿⢛⣮⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠇⠀⠀⠀⠀⠰⣯⣿⣿⣿⣿⣿⣯⡲⣶⣽⣷⣴⣶⣾⣿⣷⡀⠱⡿⣿⣇⣿⣽⣖⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣱⢿⣯⣳⡙⢿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⡄⠙⡛⢮⢹⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠸⣷⣬⣬⡅⠀⠹⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣷⡰⠈⠀⣿⡟⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣟⠀⠀⠙⠻⣿⣿⣿⣮⣝⢿⣿⣿⣿⣿⣧⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡙⠛⠷⡤⠀⠀⠀⠈⠻⣿⣿⣿⣶⠝⠗⢻⣿⡿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣖⠚⠈⠀⠀⠀⠀⠒⠝⠛⠟⠁⢀⡀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢁⣤⣾⣷⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠑⣀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠾⠶⠿⣿⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⡶⢋⣥⣶⣶⣶⣿⢻⣿⡭⡁⢀⡠⡶⠾⢉⡩⣟⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠚⠋⠛⠛⠛⠛⠋⠈⠉⠉⠎⠁⠀⠀⠈⠉⠄⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾ ⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⡟⡟⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠭⣇⣿⣆⠿⣯⣿⣿⣧⢰⣿⢮⡷⢾⢸⡱⢸⡱⢿⢰⣾⡰⣿⡇⠥⣏⠶⡇⣶⣏⠶⡇⣇⢾⣿⠨⢼⡲⢻⡰⡶⠆⡧⢞⡶⣏⠶⡇⡇⣿⣿⡞⡼⣸⢰⠶⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⢿⠿⣟⣿⣿⢻⣿⣿⣿⣟⣻⢻⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣇⣮⣆⣇⣕⣿⣸⣾⣫⣸⣭⣭⣼⣸⣨⣼⣿⢸⣨⣼⣭⣸⣸⣸⣻⣿⣾⣹⣨⣼⣸⣿⣸⣩⣭⣸⣏⣅⣇⣿⣉⣾⣧⣻⣏⣭⣭⣷⣏⣅⣥⣷⣟⣅⣇⣿⣇⣗⣇⣿⣿⣿⣸⣾⣨⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣛⣿⠿⠿⠿⡿⢿⡿⠿⡿⡿⢿⡿⢿⠻⡿⡿⢿⡿⢿⣿⡿⡿⢿⠿⢿⠿⡿⢿⠿⣿⠿⣿⠻⣿⡿⢿⠿⢿⡿⢿⢹⡿⢿⣿⡿⢿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⣛⣷⣸⣿⡃⣏⣋⣇⣇⣇⣗⣫⣝⣻⣜⣇⣟⣣⣿⣇⣿⣇⣿⣇⣟⣣⣛⣇⣿⣸⣸⣙⣸⣘⣿⣜⣻⣸⣿⣝⣻⣸⣜⣻⣿⣜⣻⣜⣳⣿⣿⣝⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⣿⡿⣿⡿⡿⡿⡿⣿⡿⡿⡿⡿⡏⡿⡿⡿⡿⡿⡯⡿⡿⣿⣿⣿⡿⡿⡿⡿⡿⣿⡿⡿⣿⣿⢿⢿⢿⣿⢻⣿⡿⡿⣿⣿⣿⡿⡿⡿⡿⣿⡿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⣿⣿⣯⣦⣧⣿⣧⣿⣯⣧⡇⣧⣧⣧⣧⣯⣧⣧⣧⣧⣶⣯⣿⣯⣦⣧⣿⣧⣯⣿⠏⣷⣯⣿⣿⢏⣾⣿⣼⣿⣿⣧⣷⣦⣿⣿⣧⣧⣿⣯⣦⣧⣿⣿⣿⣿⣿⣿⣼⣷⣶⣦⣿⣼⡧⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 357 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/07/epo-eu-assurances/#comments Gemini version at gemini://gemini.techrights.org/2021/12/07/epo-eu-assurances/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.07.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_EU_Assurances⠀✐ Posted in Deception, Europe, Patents at 6:56 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇The EPO is totally accountable⦈ This harms the EU’s image (complicity) as well as the EPO’s Summary: The EPO‘s staff cannot be blamed for losing patience as elected public representatives completely fail to do their job (with_few_exceptions) ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣯⣹⣧⣽⣽⣯⣿⣽⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢫⠅⠛⠙⠋⠛⠇⠀⠈⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠸⢹⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢁⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠝⠻⠿⠟⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠩⠭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠍⢻⣿⣿⡿⠛⠛⠙⢿⣿⣿⠿⢿⢿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣺⣛⣛⣛⡀⠀⠀⠀⢀⡀⢀⣀⣶⣶⠆⢀⣜⣻⠆⢧⣿⣿⣿⣿⣿⣿⠃⠤⠿⡿⣦⡋⢿⣿⣿⣿⣿⣿⣿⣿⣧⣧⠿⠿⠿⠐⠿⠿⡇⠸⠿⠿⠿⠿⠿⠭⠽⠿⠯⠦⠼⢿⣿⣿⣿⣿⠿ ⡌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⢿⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⢿⡿⠃⠀⣼⣿⣿⣿⣿⣿⠀⢶⣶⣶⣶⡇⢸⣿⣿⣿⣿⣿⣿⣿⡆⣀⣄⡀⢸⡛⢻⣿⣿⠇⠀⠀⡀⢀⠀⠀⠀⠀⡧⣤⢐⢋⣠⣶⡆⠙⣧ ⣇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠹⡷⢶⡟⠀⠀⢶⣶⣿⣿⣤⠄⡔⠀⠀⠀⣤⠀⠀⠰⣿⣿⣿⣿⣿⣿⡦⠘⠿⢿⡏⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠉⠛⠀⠉⠉⠁⠐⠂⠴⣾⣿⠀⠀⢀⣶⣷⡩⢸⡉⣩⣻⣷⣤⣿ ⢻⣿⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⣸⠀⠀⠀⠹⣿⡿⠋⠉⠀⠀⣼⣦⣴⡏⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣬⠀⠀⣻⣿⣿⡎⠸⠷⠉⡹⠿⠏⠛ ⠑⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⢳⣀⣛⡿⡿⠇⢤⡤⢶⡆⢻⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⢸⠾⣿⠟⠁⠀⠀⠀⠀⡴⠀⢀ ⠀⢻⣿⣿⡿⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠁⠀⠀⠈⡟⣛⡇⠀⠀⠀⠑⠀⢀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠿⠂⠀⠠⠄⠀⠀⠀⠀⠘ ⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⣀⣤⡜⠓⠂⣟⠉⠛⣿⣶⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⢸⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⡆⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⠸⠏⠸⢿⣿⢿⣿⠁⠀⠉⠀⢤⣰⣎⠁⣄⠹⣷⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡄⢸⣀⢀⣀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢨⣧⣼⣧⠈⠻⢦⣤⣤⡄⠠⡾⠟⠛⢁⣿⡇⢸⣿⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠻⢿⠿⣯⠻⠟⣿⠃⠀⢠⣶⣶⣿⠂⢀⡀⠀⠀⢀⡠⡴⠀⠀⠀⢠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠀⠀⠈⠉⠉⠓⠄⠀⠀⠀⠈⠛⢧⣼⣿⡿⡆⠉⠛⢳⣶⣶⣶⣴⡾ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣽⢿⣷⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠿⠞⠉⠉⢡⣤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠁⠀⠀⠈⠃⢠⡀⠀⠀⠀⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠂⠀⠀⠀⠀⠀⠘⣲⣿⠆⠀⠀⠀⣜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠁⠁⠰⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⢀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⡶⠁⠀⠀⠀⠀⢐⣆⠀⠀⠀⢿⣿⡿⢿⣿⡇⣿⡇⣿⡿⠟⠀⢸⣿⡿⠃⣿⡟⣿⣦⣿⡟⣿⡆⠀⢸⣿⢰⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⡱⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡇⣿⣷⡆⠀⢸⣿⣷⠀⣿⣷⡿⢻⣿⡇⣿⡇⠀⢸⣿⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠌⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⡇⣿⣷⣤⠀⢸⣿⣧⡄⣿⡇⠀⠸⣿⣧⣿⠇⠀⢸⣿⠸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣶⣶⣶⣠⣶⣶⣄⣶⣶⣶⡆⣶⣶⡆⢰⣶⡆⢰⣶⡖⣶⣄⣶⡆⠀⢰⣶⣶⠀⣠⣶⣶⣄⢠⣴⢶⣦⣀⣴⣶⣦⡀⣶⡆⣶⡆⢰⣦⢰⣶⢴⣶⣶⣶⣶⣶⣦⢠⣶⡶⣦⡄⣶⡆⠀⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⣿⡇⣽⣿⠀⣿⣿⢠⣿⢻⣿⢸⣿⡇⢸⣿⡇⢹⣿⡿⠀⠀⣼⡿⣿⡇⣿⡏⠹⠿⢸⣿⠸⠿⢻⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⣾⣿⠀⣿⣿⠀⣿⣿⣿⢸⣿⣧⣿⠃⣿⡇⠀⣿⣧⡄⠀⠀⢠⣤⣤⣀⡀⠀ ⠀⠀⣿⣿⠀⣿⣇⣾⣿⠀⣿⣿⢸⣿⣾⣿⣼⣿⣇⣸⣿⣇⡀⣿⡇⠀⠀⣿⣷⣿⡇⣿⣧⣴⣶⢸⣿⣰⣶⢾⣿⣿⣿⡇⣿⡇⣿⡇⢸⣏⣿⣿⠀⣿⣿⢰⣿⣿⣿⣸⣿⣇⣿⡇⣿⣇⡀⣿⣏⣁⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠴⠛⠻⢠⠘⠛⠛⠡⠠⠻⠛⠜⠛⠙⠟⠛⠛⠛⠛⠛⠛⠃⠛⠃⠀⠘⠛⠃⠛⠛⠘⠛⠛⠁⠈⠛⠛⠋⠀⠙⠛⠋⠀⠙⠛⠛⠁⠘⠛⠙⠛⠀⠛⠛⠘⠛⠙⠛⠛⠛⠛⠛⠁⠛⠛⠃⠛⠛⠛⠀⠀⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣯⣽⣧⣽⣽⣿⣿⣽⣷⣻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣫⠍⠹⠉⠋⠛⠇⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠸⢹⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢁⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠻⠿⠛⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠩⠹⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⢻⣿⣿⡿⠛⠛⠙⢿⣿⣿⠿⢿⢿⢿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣚⣛⣛⣛⡀⠀⠀⠀⢀⡀⢀⣀⣦⣶⠆⢀⣞⣻⠆⢧⣿⣿⣿⣿⣿⣿⠃⢤⢴⣿⣎⠋⣿⣿⣿⣿⣿⣿⣿⣿⣧⡧⠾⠿⠿⠐⢿⠿⡧⠸⠿⠿⠿⠿⠿⠭⠽⠿⠿⠦⠼⢿⣿⣿⣿⣿⠿ ⡍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⢿⠁⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠙⢿⡿⠃⠀⣼⣿⣿⣿⣿⣿⠀⡦⡤⣤⣬⡇⢸⣿⣿⣿⣿⣿⣿⣿⣆⣀⣄⡀⢸⠛⠻⣿⣿⠇⠀⠀⣀⠀⠀⠀⠀⠀⣇⣤⢐⢋⣠⣶⡆⠙⣧ ⣇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠑⡶⢶⡟⠀⠐⢶⣶⣿⣿⣦⠄⡔⠀⠀⠀⣤⠀⠀⠰⣿⣿⣿⣿⣿⣿⡦⠹⣭⣽⡟⠱⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠀⠈⠁⠁⠐⠂⠤⣶⣿⠀⠀⣠⣶⣷⣉⢸⡈⣭⣿⣷⣤⣿ ⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⣸⠀⠀⠀⠹⣿⡿⠋⠉⠀⠀⣼⣠⣼⡇⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣭⠀⠀⢽⣿⣿⢞⠸⠧⠀⠹⠿⠏⠋ ⠹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⢻⣀⣛⡿⡿⠇⢤⡤⢶⡆⢻⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⢸⢿⣿⡟⠁⠀⠀⠀⠀⡴⠀⢀ ⠀⢻⣿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠁⠀⠀⠈⠟⣛⡇⠀⠀⠀⠑⠀⢀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠿⠂⠀⠠⠄⠀⠀⠀⠀⠈ ⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⣠⣤⡜⠓⠂⣟⠉⠛⣿⣶⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⢸⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⢸⣿⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⠸⠍⠸⢿⣿⢿⣿⠁⠀⠉⠀⢤⣰⣎⠁⣄⠹⣷⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡄⢸⣀⣀⣀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣼⣧⠈⠹⢦⣤⣤⡄⠤⡾⠟⠛⢁⣷⡇⢸⣯⡙⢿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠻⢿⠛⣯⠻⠛⢿⠁⠀⢠⣶⣶⣿⠂⢀⠀⠀⠀⢠⢠⡴⠀⠀⠀⢠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠋⠀⠀⠀⠉⠉⠓⠄⠀⠀⠀⠈⠛⢧⣼⣿⠷⠆⠉⠛⠻⣶⣶⣶⣶⡾ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣝⢿⣷⣾⣿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⡿⠿⠟⠋⠉⢠⣤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠁⠀⠀⠈⠂⢠⡀⠐⠀⠀⠝⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠀⠂⠀⠀⠀⠀⠀⠘⣶⣾⠂⠀⠀⠀⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠁⠁⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⢀⠀⢍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⢐⣆⠀⠀⠀⢿⣿⡿⢿⣿⡇⣿⡇⣿⡿⠟⠀⢸⣿⡿⠃⣿⡟⣿⣦⣿⡟⣿⡆⠀⢸⣿⢰⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡇⣿⣷⡆⠀⢸⣿⣷⠀⣿⣷⡿⢻⣿⡇⣿⡇⠀⢸⣿⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢾⠔⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⡇⣿⣷⣤⠀⢸⣿⣧⡄⣿⡇⠀⠸⣿⣧⣿⠇⠀⢸⣿⠸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣶⣶⣶⣠⣶⣶⣄⣶⣶⣶⡆⣶⣶⡆⢰⣶⡆⢰⣶⡖⣶⣄⣶⡆⠀⢰⣶⣶⠀⣠⣶⣶⣄⢠⣴⢶⣦⣀⣴⣶⣦⡀⣶⡆⣶⡆⢰⣦⢰⣶⢴⣶⣶⣶⣶⣶⣦⢠⣶⡶⣦⡄⣶⡆⠀⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⢠⣿⢻⣿⢸⣿⡇⢸⣿⡇⢹⣿⡿⠀⠀⣼⡿⣿⡇⣿⡏⠹⠿⢸⣿⠸⠿⢻⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⣾⣿⠀⣿⣿⠀⣿⣿⣿⢸⣿⣧⣿⠃⣿⡇⠀⣿⣧⡄⠀⢠⣶⣶⣶⣶⣶⣶ ⠂⠀⣿⣿⠀⣿⣇⣿⣿⠀⣿⣿⢸⣿⣾⣿⣼⣿⣇⣸⣿⣇⡀⣿⡇⠀⠀⣿⣷⣿⡇⣿⣧⣶⣶⢸⣿⣰⣶⢾⣿⣿⣿⡇⣿⡇⣿⡇⢸⣏⣿⣿⠀⣿⣿⢰⣿⣿⣿⣸⣿⣇⣿⡇⣿⣇⡀⣿⣏⣁⠀⢸⣿⣿⣿⣿⣿⣿ ⣇⡴⠛⠻⢠⠘⠛⠛⠥⠠⠻⠛⠜⠛⠙⠟⠛⠛⠛⠛⠛⠛⠃⠛⠃⠀⠘⠛⠃⠛⠛⠘⠛⠛⠁⠈⠛⠛⠋⠀⠙⠛⠋⠀⠙⠛⠛⠁⠘⠛⠙⠛⠀⠛⠛⠘⠛⠙⠛⠋⠛⠛⠛⠁⠛⠛⠃⠛⠛⠛⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣽⣧⣽⣽⣿⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢯⠅⠹⠉⠋⠻⠇⠀⠈⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠸⢹⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢁⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢿⠻⠿⠟⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣽⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡙⣻⣿⣿⡿⠛⠛⠙⢯⣿⣿⡏⢿⢿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣛⣛⣛⡂⠀⠀⠀⢀⡀⢀⣂⣲⣶⠆⢀⣞⣻⠆⢷⣿⣿⣿⣿⣿⣿⠃⣤⣤⣶⣎⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⡾⠿⠿⠐⢿⠿⣇⠸⠿⠿⠿⠿⠿⠭⠭⠿⠿⠦⠼⢿⣿⣿⣿⣿⠿ ⡍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⢿⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⢿⡿⠃⠀⣼⣿⣿⣿⣿⣿⠀⣤⣤⣤⣼⡇⢸⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⡀⢐⡛⢻⣿⣿⠇⠀⠀⠀⢀⠀⠀⠀⠀⠁⣤⢐⢋⣠⣶⡆⠙⣧ ⣇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⡷⢶⡟⠀⠒⢴⣶⣶⣿⣖⠄⡔⠀⠀⠀⣤⠀⠀⠰⣿⣿⣿⣿⣿⣿⡦⠩⣥⣿⡟⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠛⠀⠉⠁⠁⠀⠒⠴⣾⣿⠀⠀⠀⣢⡐⠏⢸⡌⣭⣽⣷⣴⣿ ⢻⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⣺⠀⠀⠀⠹⣿⡿⠋⠉⠀⠀⣤⣠⣼⡏⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣭⠀⠀⠀⣺⣷⡆⠸⠷⠀⠩⠿⠏⠋ ⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⢣⣀⣛⡿⡿⠇⢤⡤⢶⡆⢻⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⠀⠄⣿⠟⠁⠀⠀⠀⠀⡴⠀⢀ ⠀⢻⣿⣿⡿⠿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠁⠀⠀⠈⡟⣛⡇⠀⠀⠀⠑⠀⢀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠸⠂⠀⠠⠄⠀⠀⠀⠀⠈ ⠀⢸⣿⣿⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⣠⣤⡜⠓⠂⣟⠉⠛⣿⣶⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⢨⠊⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⢸⣿⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠘⠏⠸⢿⣿⢿⣿⠁⠀⠉⠀⢤⣰⣎⠁⣅⠹⣷⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⣀⢀⣀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠟⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣾⣧⠈⠻⢦⣤⣤⡄⠤⣾⠿⠛⢁⣿⡇⢸⣟⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠻⢿⠿⣯⠹⠛⣿⠀⠀⢠⣶⣶⣿⠂⢀⡀⠀⢀⢈⢦⡴⠀⠀⠀⢠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠋⠀⠀⠀⠉⠉⠓⠄⠀⠀⠀⠈⠛⢧⣼⣿⠷⠆⠉⠛⢻⣶⣶⣶⣶⣾ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣝⢿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⡿⠿⠟⠉⠉⢠⣤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠉⠀⠀⠈⠂⢠⡀⠀⠀⠀⠨⡅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠀⠂⠀⠀⠀⠀⠀⠸⣲⣾⠂⠀⠀⠀⡘⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠁⠁⢰⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⢀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠁⠀⠀⠰⠃⠀⠀⠀⠀⢒⡖⠀⠀⠀⢿⣿⡿⢿⣿⡇⣿⡇⣿⡿⠟⠀⢸⣿⡿⠃⣿⡟⣿⣦⣿⡟⣿⡆⠀⢸⣿⢰⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣰⡇⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡇⣿⣷⡆⠀⢸⣿⣷⠀⣿⣷⡿⢻⣿⡇⣿⡇⠀⢸⣿⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠔⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⡇⣿⣷⣤⠀⢸⣿⣧⡄⣿⡇⠀⠸⣿⣧⣿⠇⠀⢸⣿⠸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣶⣶⣶⣠⣶⣶⣄⣶⣶⣶⡆⣶⣶⡆⢰⣶⡆⢰⣶⡖⣶⣄⣶⡆⠀⢰⣶⣶⠀⣠⣶⣶⣄⢠⣴⢶⣦⣀⣴⣶⣦⡀⣶⡆⣶⡆⢰⣦⢰⣶⢴⣶⣶⣶⣶⣶⣦⢠⣶⡶⣦⡄⣶⡆⠀⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⣿⡇⣽⣿⠀⣿⣿⢠⣿⢻⣿⢸⣿⡇⢸⣿⡇⢹⣿⡿⠀⠀⣼⡿⣿⡇⣿⡟⠹⠿⢸⣿⠸⠿⢻⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⣾⣿⠀⣿⣿⠀⣿⣿⣿⢸⣿⣧⣿⠃⣿⡇⠀⣿⣧⡄⠀⢀⣶⣶⣶⣶⣶⣶ ⠀⠀⣿⣿⠀⣿⣇⣿⣿⠀⣿⣿⢸⣿⣾⣿⣼⣿⣇⣸⣿⣇⡀⣿⡇⠀⠀⣿⣷⣿⡇⣿⣿⣴⣶⢸⣿⣰⣶⢾⣿⣿⣿⡇⣿⡇⣿⡇⢸⣏⣿⣿⠀⣿⣿⢰⣿⣿⣿⣸⣿⣇⣿⡇⣿⣇⡀⣿⣏⣁⠀⢸⣿⣿⣿⣿⣿⣿ ⣇⡴⠛⠻⢠⠘⠛⠛⠡⠠⠻⠛⠜⠛⠙⠟⠛⠛⠛⠛⠛⠛⠃⠛⠃⠀⠘⠛⠃⠛⠛⠘⠛⠛⠁⠈⠛⠛⠋⠀⠙⠛⠋⠀⠙⠛⠛⠁⠘⠛⠙⠛⠀⠛⠛⠘⠛⠙⠛⠛⠛⠛⠛⠁⠛⠛⠃⠛⠛⠛⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣽⣧⣽⣽⣿⣿⣽⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⢯⠅⠙⠙⠋⠛⠇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⢿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢁⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠟⠿⠋⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⢻⣿⣿⡿⠛⠛⠙⢿⣿⣿⡟⢿⢿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣛⣛⣛⡀⠀⠀⠀⢀⡀⢀⣀⣢⣶⠆⢀⣞⣻⠆⢧⣿⣿⣿⣿⣿⣿⠃⣀⣤⣶⣊⠟⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⠿⠿⠿⠐⢿⠿⣧⠸⠿⠿⠿⠿⠿⠭⠽⠿⠿⠦⠼⢿⣿⣿⣿⣿⠿ ⡍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠅⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⢿⡿⠃⠀⣼⣿⣿⣿⣿⣿⠀⣤⢨⣥⣽⡆⢸⣿⣿⣿⣿⣿⣿⣿⣆⣀⣄⡀⢸⡛⢻⣿⣿⠇⠀⠀⣀⣀⠀⠀⠀⠀⣧⣤⢰⢋⣠⣶⡆⠙⣧ ⣇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠹⡷⢶⡟⠀⠒⢴⣶⣶⣿⣄⠆⡔⠀⠀⠀⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⡦⠉⣭⣿⡟⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠀⠉⠉⠁⠀⠂⠶⣾⣿⠀⠀⣠⣶⣷⢯⢸⡌⣭⣽⣷⣴⣿ ⢻⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⣸⠀⠀⠀⠹⣿⡿⠋⠉⠀⠀⣴⣠⣼⡏⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣭⠀⠀⣽⣿⣿⣾⠸⠷⠀⠩⠿⠏⠋ ⠐⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⢻⣀⣛⡿⡿⠇⢤⡤⢶⡆⢻⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⢸⢿⣿⡟⠁⠀⠀⠀⠀⡴⠀⢀ ⠀⢻⣿⣿⣿⠿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠁⠀⠀⠈⡟⣛⡇⠀⠀⠀⠑⠀⢀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠃⠀⠠⠄⠀⠀⠀⠀⠈ ⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⣠⣤⡜⠓⠂⣟⠉⠛⣿⣶⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⢸⠞⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡆⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⠸⠏⠸⢿⣿⢿⣿⠁⠀⠉⠠⢤⣰⣎⠁⣄⠹⣷⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⣀⢀⣀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣾⣧⠈⠻⢶⣤⣤⡄⠤⣾⠟⠛⢁⣽⡇⢸⣿⡈⢿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠻⣿⠟⣯⠻⠛⣿⠃⠀⢠⣶⣶⣿⠂⢀⡀⠀⢀⢀⢢⡴⠀⠀⠀⢠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠋⠀⠀⠀⠉⠉⠓⠄⠀⠀⠀⠈⠛⢧⢼⣿⠿⠆⠉⠛⠻⣶⣶⣶⣶⣾ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣝⢿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⡿⠿⠞⠋⠉⢥⣴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠁⠀⠀⠈⠃⢐⡀⠀⠀⠀⣹⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠀⠀⠀⠀⠀⠀⠀⠘⣶⣾⠃⠀⠀⠀⣌⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠁⠁⢐⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⢀⠀⢏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⢒⣖⠀⠀⠀⢿⣿⡿⢿⣿⡇⣿⡇⣿⡿⠟⠀⢸⣿⡿⠃⣿⡟⣿⣦⣿⡟⣿⡆⠀⢸⣿⢰⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢹⣕⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡇⣿⣷⡆⠀⢸⣿⣷⠀⣿⣷⡿⢻⣿⡇⣿⡇⠀⢸⣿⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠗⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⡇⣿⣷⣤⠀⢸⣿⣧⡄⣿⡇⠀⠸⣿⣧⣿⠇⠀⢸⣿⠸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣶⣶⣶⣠⣶⣶⣄⣶⣶⣶⡆⣶⣶⡆⢰⣶⡆⢰⣶⡖⣶⣄⣶⡆⠀⢰⣶⣶⠀⣠⣶⣶⣄⢠⣴⢶⣦⣀⣴⣶⣦⡀⣶⡆⣶⡆⢰⣦⢰⣶⢴⣶⣶⣶⣶⣶⣦⢠⣶⡶⣦⡄⣶⡆⠀⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⢠⣿⢻⣿⢸⣿⡇⢸⣿⡇⢹⣿⡿⠀⠀⣼⡿⣿⡇⣿⡟⠹⠿⢸⣿⠸⠿⢻⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⣾⣿⠀⣿⣿⠀⣿⣿⣿⢸⣿⣧⣿⠃⣿⡇⠀⣿⣧⡄⠀⢀⣶⣶⣶⣶⣶⣶ ⠀⠀⣿⣿⠀⣿⣇⣿⣿⠀⣿⣿⢸⣿⣾⣿⣼⣿⣇⣸⣿⣇⡀⣿⡇⠀⠀⣿⣷⣿⡇⣿⣿⣴⣶⢸⣿⣰⣶⢾⣿⣿⣿⡇⣿⡇⣿⡇⢸⣏⣿⣿⠀⣿⣿⢰⣿⣿⣿⣸⣿⣇⣿⡇⣿⣇⡀⣿⣏⣁⠀⣸⣿⣿⣿⣿⣿⣿ ⣇⡰⠛⠻⢠⠘⠛⠛⠡⠠⠻⠛⠼⠛⠙⠟⠛⠛⠛⠛⠛⠛⠃⠛⠃⠀⠘⠛⠃⠛⠛⠘⠛⠛⠁⠈⠛⠛⠋⠀⠙⠛⠋⠀⠙⠛⠛⠁⠘⠛⠙⠛⠀⠛⠛⠘⠛⠙⠛⠛⠛⠛⠛⠁⠛⠛⠃⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣯⣽⣧⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⠗⠻⠙⠫⠛⠇⠈⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⢻⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢁⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠿⠉⠿⠛⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⣩⡩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢻⣿⣿⡿⠛⠛⠙⢿⣿⣿⡟⢟⢿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣺⣛⣛⣛⡀⠀⠀⡀⠀⡀⣀⣀⣶⣶⠆⢠⣞⣿⠆⢧⣿⣿⣿⣿⣿⣿⠃⣀⣤⣤⣘⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⡮⠼⠿⠿⠀⢻⡿⣧⠸⠿⠿⠿⠿⠿⠭⠽⠿⠯⠦⠼⢿⣿⣿⣿⣿⠿ ⡍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⣿⠁⠀⠀⠀⢠⡤⢀⠀⠀⠀⠀⠙⢿⡿⠃⢀⣼⣿⣿⣿⣿⣿⠀⣤⣨⣡⣽⡄⢹⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⡀⠂⠻⢻⣿⣿⠇⠀⠀⠀⡀⠀⠀⠀⠀⠁⣤⢰⣋⣠⣶⡆⠈⢧ ⣇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠱⡶⢶⡟⠀⠘⢷⣶⣾⣿⣷⠋⠆⠀⠀⠀⣤⠀⠀⠸⣿⣿⣿⣿⣿⣿⡤⢩⣙⣾⡏⠱⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠒⠀⠈⠉⠁⠐⠚⠰⢶⣟⠀⠀⠀⢠⡁⠏⢸⡍⣭⣭⣷⣶⣾ ⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⣸⠀⠀⠀⠹⣿⡿⠋⠉⠀⠀⣰⣁⣼⡏⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣄⠀⠀⠀⢻⣗⡂⠸⠿⠀⠽⠻⠿⠉ ⠚⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⢃⣀⣛⡿⠿⠇⢤⡤⢶⡆⢻⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⠀⠀⢿⡏⠁⠀⠀⠀⠀⠴⠀⢀ ⠀⢻⣿⣿⣿⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠁⠀⠀⠈⡟⣛⡇⠀⠀⠀⠑⠀⢀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠸⠂⠀⠠⠄⠀⠀⠀⠀⠈ ⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣤⡔⠓⠂⣟⠉⠛⣿⣶⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⢀⡆⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠘⠇⠸⢿⣿⢿⣿⠁⠀⠁⠀⢠⣰⣌⠁⣄⠹⣷⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⣀⢀⣀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣼⣧⠈⠹⢦⣤⣤⡄⠠⡾⠟⠛⢀⣽⡇⢸⣟⡈⢿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠻⢿⠻⣯⠻⠛⢿⠂⠀⢠⣶⣶⣿⠂⢀⠀⠀⠀⢀⣦⣴⠀⠀⠀⢠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠋⠀⠀⠀⠉⠙⠓⠄⠀⠀⠀⠈⠛⠧⡜⣿⡿⠆⠉⠛⠻⣶⣶⣶⣶⣾ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣉⣻⣷⣾⣿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⡿⠿⠞⠉⠉⠁⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⡀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠀⠂⠀⠀⠀⠀⠀⢐⣴⣗⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠑⠁⢈⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠈⠀⠀⠶⠇⡀⠀⠀⠀⠐⠂⠀⠀⠀⢿⣿⡿⢿⣿⡇⣿⡇⣿⡿⠟⠀⢸⣿⡿⠃⣿⡟⣿⣦⣿⡟⣿⡆⠀⢸⣿⢰⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡇⣿⣷⡆⠀⢸⣿⣷⠀⣿⣷⡿⢻⣿⡇⣿⡇⠀⢸⣿⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⡇⣿⣷⣤⠀⢸⣿⣧⡄⣿⡇⠀⠸⣿⣧⣿⠇⠀⢸⣿⠸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣶⣶⣶⣠⣶⣶⣄⣶⣶⣶⡆⣶⣶⡆⢰⣶⡆⢰⣶⡖⣶⣄⣶⡆⠀⢰⣶⣶⠀⣠⣶⣶⣄⢠⣴⢶⣦⣀⣴⣶⣦⡀⣶⡆⣶⡆⢰⣦⢰⣶⢴⣶⣶⣶⣶⣶⣦⢠⣶⡶⣦⡄⣶⡆⠀⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⢠⣿⢻⣿⢸⣿⡇⢸⣿⡇⢹⣿⡿⠀⠀⣼⡿⣿⡇⣿⡏⠹⠿⢸⣿⠸⠿⢻⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⣾⣿⠀⣿⣿⠀⣿⣿⣿⢸⣿⣧⣿⠃⣿⡇⠀⣿⣧⡄⠀⢠⣶⣶⣶⣶⣶⣶ ⡂⠀⣿⣿⠀⣿⣇⣿⣿⠀⣿⣿⢸⣿⣾⣿⣼⣿⣇⣸⣿⣇⡀⣿⡇⠀⠀⣿⣷⣿⡇⣿⣧⣶⣶⢸⣿⣰⣶⢾⣿⣿⣿⡇⣿⡇⣿⡇⢸⣏⣿⣿⠀⣿⣿⢰⣿⣿⣿⣸⣿⣇⣿⡇⣿⣇⡀⣿⣏⣁⠀⢸⣿⣿⣿⣿⣿⣿ ⣇⡴⠛⠻⢠⠘⠛⠛⠥⠠⠻⠛⠼⠛⠙⠟⠛⠛⠛⠛⠛⠛⠃⠛⠃⠀⠘⠛⠃⠛⠛⠘⠛⠛⠁⠈⠛⠛⠋⠀⠙⠛⠋⠀⠙⠛⠛⠁⠘⠛⠙⠛⠀⠛⠛⠘⠛⠙⠛⠛⠛⠛⠛⠁⠛⠛⠃⠛⠛⠛⣀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣽⣧⣽⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡏⣽⣿⠇⠛⠙⠋⠛⠇⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⢻⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢁⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠻⠉⠿⠋⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⣫⡫⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢻⣿⣿⡿⠛⠛⠙⢿⣿⣿⡟⢛⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣺⣛⣛⣛⡀⠀⠀⠀⡀⠀⣀⣀⣲⣶⠆⢠⣞⣿⠆⠧⣿⣿⣿⣿⣿⣿⠃⣀⣤⣤⣘⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⡮⠾⠿⠿⠠⢻⡿⣧⠸⠿⠿⠿⠿⠿⠭⠽⠿⠿⠦⠼⢿⣿⣿⣿⣿⠿ ⡍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠿⣿⠁⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠙⢿⡿⠃⢀⣼⣿⣿⣿⣿⡇⠀⣤⣨⣡⣽⡄⢹⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⢠⡿⣻⣿⣿⠇⠀⠀⠀⡀⠀⠀⠀⠀⠃⢤⢸⣋⣠⣶⡆⠈⢧ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢱⡶⢶⡟⠀⠐⢶⣶⣾⣿⣮⡋⡖⠀⠀⠀⣤⠀⠀⠰⣿⣿⣿⣿⣿⣿⡤⢩⣝⣿⡏⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠚⠀⠉⠉⠁⠐⠒⠶⣾⣿⠀⠀⠀⣀⡀⠎⢸⡍⣭⣭⣿⣶⣦ ⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⣺⠀⠀⠀⠹⣿⡿⠋⠉⠀⠀⣴⣅⣸⡏⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣎⠀⠀⠁⣺⡦⡆⠸⠿⠀⠭⠻⠿⠉ ⠚⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⢃⣀⣛⡿⠿⠇⢤⡤⢶⡆⢻⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⠀⠆⢿⡏⠁⠀⠀⠀⠀⠴⠀⢀ ⠀⢻⣿⣿⣿⠿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠁⠀⠀⠈⡟⣛⡇⠀⠀⠀⠑⠀⢀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠸⠂⠀⠠⠄⠀⠀⠀⠀⠈ ⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠁⢀⣠⣤⡔⠓⠂⣟⠉⠛⣿⣶⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⢠⡖⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠘⠏⠸⢿⣿⣿⣿⠁⠀⠉⠠⢤⣰⣎⠁⣄⠹⣷⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⣀⢀⣀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠛⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣾⣧⠈⠻⢶⣤⣤⡄⠠⡾⠟⠛⢁⣽⡇⢸⣟⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠻⢿⠻⣯⡻⠛⢿⠂⠀⢠⣶⣶⣿⠂⢀⡀⠀⠠⢀⣢⣼⠀⠀⠀⢠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠋⠀⠀⠀⠉⠙⠛⡄⠀⠀⠀⠈⠛⠧⣼⣿⡿⠆⠉⠛⢳⣶⣶⣶⣶⣶ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣍⣿⣷⣿⣿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⠻⡿⠿⠞⠉⠉⠡⠔⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠉⠀⠀⠈⠀⢤⡀⠐⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠂⠀⠀⠀⠀⠀⢠⣶⣮⠁⠀⠀⠀⣐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠠⢻⡿⠀⠑⠁⢐⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⢀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⢾⠎⡀⠀⠀⠀⠐⢂⠀⠀⠀⢿⣿⡿⢿⣿⡇⣿⡇⣿⡿⠟⠀⢸⣿⡿⠃⣿⡟⣿⣦⣿⡟⣿⡆⠀⢸⣿⢰⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡇⣿⣷⡆⠀⢸⣿⣷⠀⣿⣷⡿⢻⣿⡇⣿⡇⠀⢸⣿⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢿⠊⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⡇⣿⣷⣤⠀⢸⣿⣧⡄⣿⡇⠀⠸⣿⣧⣿⠇⠀⢸⣿⠸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣶⣶⣶⣠⣶⣶⣄⣶⣶⣶⡆⣶⣶⡆⢰⣶⡆⢰⣶⡖⣶⣄⣶⡆⠀⢰⣶⣶⠀⣠⣶⣶⣄⢠⣴⢶⣦⣀⣴⣶⣦⡀⣶⡆⣶⡆⢰⣦⢰⣶⢴⣶⣶⣶⣶⣶⣦⢠⣶⡶⣦⡄⣶⡆⠀⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⢠⣿⢻⣿⢸⣿⡇⢸⣿⡇⢹⣿⡿⠀⠀⣼⡿⣿⡇⣿⣏⠻⠿⢸⣿⠸⠿⢻⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⣾⣿⠀⣿⣿⠀⣿⣿⣿⢸⣿⣧⣿⠃⣿⡇⠀⣿⣧⡄⠀⢠⣶⣶⣶⣶⣶⣶ ⠂⠀⣿⣿⠀⣿⣇⣿⣿⠀⣿⣿⢸⣿⣾⣿⣼⣿⣇⣸⣿⣇⡀⣿⡇⠀⠀⣿⣷⣿⡇⣿⣯⣴⣶⢸⣿⣰⣶⢾⣿⣿⣿⡇⣿⡇⣿⡇⢸⣏⣿⣿⠀⣿⣿⢰⣿⣿⣿⣸⣿⣇⣿⡇⣿⣇⡀⣿⣏⣁⠀⢸⣿⣿⣿⣿⣿⣿ ⣇⡰⠛⠻⢠⠘⠛⠛⠥⠠⠻⠛⠜⠛⠙⠟⠛⠛⠛⠛⠛⠛⠃⠛⠃⠀⠘⠛⠃⠛⠛⠘⠛⠛⠁⠈⠛⠛⠋⠀⠙⠛⠋⠀⠙⠛⠛⠁⠘⠛⠙⠛⠀⠛⠛⠘⠛⠙⠛⠛⠛⠛⠛⠁⠛⠛⠃⠛⠛⠛⣀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣿⣽⣧⣽⣽⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣽⣯⠇⠛⠙⠋⠛⠇⠈⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⢻⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢁⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠫⢉⠿⠋⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⢫⡫⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⡿⠛⠛⠙⢿⣿⣿⣟⢻⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣚⣛⣛⣛⡀⠀⠀⠀⢀⠀⣀⣀⣦⣶⠆⢠⣞⣿⠆⢧⣿⣿⣿⣿⣿⡿⠁⣀⣠⣤⣘⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⠾⠿⠿⠀⢻⡿⣧⠸⠿⠿⠿⠿⠯⠭⠼⠿⠿⠦⠼⢿⣿⣿⣿⣿⠿ ⡍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⣿⠁⠀⠀⠀⢀⡄⠄⠀⠀⠀⠀⠹⢿⡿⠃⠀⣼⣿⣿⣿⣿⡧⠀⣤⣨⣡⣽⡄⢻⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⠚⡿⢫⣿⣿⠇⠀⠀⠀⣀⠀⠀⠀⠀⣧⣤⢸⣋⣠⣶⡆⠈⠧ ⡆⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠹⡶⢶⡞⠀⠐⢶⣶⣾⣿⣾⠁⡔⠀⠀⠀⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⡤⢫⣍⣾⡏⠱⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠀⠈⠉⠁⠐⠚⠶⣿⣿⠀⢀⢄⣶⡿⢮⢸⡍⣭⣭⣿⣦⣦ ⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⢹⠃⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⣺⠀⠀⠀⠹⣿⡿⠋⠉⠀⠀⣴⣁⣸⡏⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣌⠀⢠⢿⣿⣿⡳⠸⠷⠀⠭⠻⠿⠉ ⠚⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⢫⣀⣛⡿⠿⠇⢤⡤⢶⡆⢻⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠴⠀⢀ ⠀⢻⣿⣿⣿⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠁⠀⠀⠈⡟⣛⡇⠀⠀⠀⠑⠀⢀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠾⠃⠀⠤⠤⠀⠀⠀⠀⠈ ⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠁⢀⣠⣤⡜⠓⠂⣟⠉⠛⣿⣶⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⢨⡜⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀⢀⡀⠘⠏⠸⢿⣿⣿⣿⠁⠀⠉⠠⢤⣰⣌⠃⣄⠹⣷⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⣀⢀⣀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠻⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣾⣧⠈⠻⢶⣤⣤⡄⠠⡾⠿⠛⢁⣽⡇⢸⣿⡈⠿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠻⢿⠻⣯⡻⠛⢿⠂⠀⢠⣶⣶⣿⠂⢀⡀⠀⢀⢀⣢⣼⠀⠀⠀⢠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠋⠀⠀⠀⠉⠙⠛⡄⠀⠀⠀⠈⠛⠇⣼⣿⡿⡆⠉⠛⠳⣶⣶⣶⣶⣶ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣍⢻⣷⣿⣿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠿⠞⠉⠉⠥⢔⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠈⠀⠀⠈⠁⢠⡀⠐⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠂⠀⠀⠀⠀⠀⢠⣴⣢⠃⠀⠀⠀⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠐⢹⡿⠄⠑⠁⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⢀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠁⠀⠀⢼⠎⡀⠀⠀⠀⢐⢒⠀⠀⠀⢿⣿⡿⢿⣿⡇⣿⡇⣿⡿⠟⠀⢸⣿⡿⠃⣿⡟⣿⣦⣿⡟⣿⡆⠀⢸⣿⢰⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡇⣿⣷⡆⠀⢸⣿⣷⠀⣿⣷⡿⢻⣿⡇⣿⡇⠀⢸⣿⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢿⠕⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⡇⣿⣷⣤⠀⢸⣿⣧⡄⣿⡇⠀⠸⣿⣧⣿⠇⠀⢸⣿⠸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣶⣶⣶⣠⣶⣶⣄⣶⣶⣶⡆⣶⣶⡆⢰⣶⡆⢰⣶⡖⣶⣄⣶⡆⠀⢰⣶⣶⠀⣠⣶⣶⣄⢠⣴⢶⣦⣀⣴⣶⣦⡀⣶⡆⣶⡆⢰⣦⢰⣶⢴⣶⣶⣶⣶⣶⣦⢠⣶⡶⣦⡄⣶⡆⠀⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⢠⣿⢻⣿⢸⣿⡇⢸⣿⡇⢹⣿⡿⠀⠀⣼⡿⣿⡇⣿⡏⠹⠿⢸⣿⠸⠿⢻⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⣾⣿⠀⣿⣿⠀⣿⣿⣿⢸⣿⣧⣿⠃⣿⡇⠀⣿⣧⡄⠀⢀⣶⣶⣶⣶⣶⣶ ⠂⠀⣿⣿⠀⣿⣇⣿⣿⠀⣿⣿⢸⣿⣾⣿⣼⣿⣇⣸⣿⣇⡀⣿⡇⠀⠀⣿⣷⣿⡇⣿⣧⣴⣶⢸⣿⣰⣶⢾⣿⣿⣿⡇⣿⡇⣿⡇⢸⣏⣿⣿⠀⣿⣿⢰⣿⣿⣿⣸⣿⣇⣿⡇⣿⣇⡀⣿⣏⣁⠀⢸⣿⣿⣿⣿⣿⣿ ⣇⡴⠛⠻⢠⠘⠛⠛⠡⠠⠻⠛⠜⠛⠙⠟⠛⠛⠛⠛⠛⠛⠃⠛⠃⠀⠘⠛⠃⠛⠛⠘⠛⠛⠁⠈⠛⠛⠋⠀⠙⠛⠋⠀⠙⠛⠛⠁⠘⠛⠙⠛⠀⠛⠛⠘⠛⠙⠛⠛⠛⠛⠛⠁⠛⠛⠃⠛⠛⠛⣀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣯⣽⣧⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⠇⠻⠛⠋⠛⠇⠈⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⢹⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢁⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠝⠿⠛⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⢭⡋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢻⣿⣿⠿⠛⠛⠙⢯⣿⣿⡟⢻⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣚⣛⣛⣛⡀⠀⠀⡀⠀⡀⣀⣀⣶⣶⠆⢠⣞⣿⠆⠧⣿⣿⣿⣿⣿⡿⠁⣀⣠⣤⣛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠼⠿⠿⠐⢻⡿⣧⠸⠿⠿⠿⠿⠿⠭⠤⠿⠿⠦⠼⢿⣿⣿⣿⣿⠿ ⡍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⣿⠁⠀⠀⠀⢀⣤⠄⡀⠀⠀⠀⠙⢿⡿⠃⠀⣼⣿⣿⣿⣿⡇⢠⣤⣨⣁⣽⡄⢻⣿⣿⣿⣿⣿⣿⣿⡆⣀⣀⣀⠐⠿⣫⣿⡿⠇⠀⠀⠀⡀⠀⠀⠀⠀⠃⣤⢸⣋⣠⣶⣆⠈⢧ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢱⡶⢶⡞⠀⠐⢶⣶⣾⣿⣾⡍⡄⠀⠀⠀⣤⠀⠀⠰⣿⣿⣿⣿⣿⣷⡤⢫⣈⣮⡏⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠚⠀⠈⠉⠀⠐⠚⠰⢼⣟⠀⠀⠀⢀⡂⠌⢸⡍⣭⣭⣿⣶⡦ ⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡆⢹⠁⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⣸⠀⠀⠀⠹⣿⡿⠋⠉⠀⠀⣶⣈⣱⡇⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣄⠀⠀⠠⢿⡶⡆⠸⠷⠀⠽⠻⠿⠉ ⠚⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⢃⣀⣛⡿⠿⠇⢤⡤⢶⡆⢻⣿⣿⣿⡿⠃⠀⠀⠂⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⠀⢂⢿⡏⠁⠀⠀⠀⠀⡴⠀⢀ ⠀⢻⣿⣿⣿⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠁⠀⠀⠈⡟⣛⡇⠀⠀⠀⠑⠀⢀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠼⠂⠀⠠⠤⠀⠀⠀⠀⠘ ⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⣠⣤⡔⠓⠂⣏⠉⠛⣿⣶⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡀⢨⡗⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠿⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠈⠇⠸⢿⣿⢿⣿⠁⠀⠁⠀⢠⣰⣌⠁⣄⠹⣷⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⣀⢀⣀⠀⠀⢼⡿⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠟⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣾⣧⠈⠛⢶⣤⣤⡄⠠⡾⠿⠛⢁⣵⡇⢸⣟⠈⠿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠻⢿⠛⣯⠹⠛⢿⠂⠀⢠⣶⣶⣿⠂⢀⡀⠀⠠⢀⣢⣼⠀⠀⠀⢠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠃⠋⠀⠀⠀⠉⠙⠛⡄⠀⠀⠀⠈⠛⠇⣜⣿⡿⡦⠉⠛⢳⣶⣶⣦⣶⣶ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣍⢻⣷⣿⣿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠑⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⠻⡿⠿⠞⠉⠉⠁⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠁⠀⠀⠈⠀⠄⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⢠⣧⣖⠃⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠑⠁⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⢀⠀⢎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⡀⠀⠀⠀⢐⠂⠀⠀⠀⢿⣿⡿⢿⣿⡇⣿⡇⣿⡿⠟⠀⢸⣿⡿⠃⣿⡟⣿⣦⣿⡟⣿⡆⠀⢸⣿⢰⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣹⡆⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡇⣿⣷⡆⠀⢸⣿⣷⠀⣿⣷⡿⢻⣿⡇⣿⡇⠀⢸⣿⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⡇⣿⣷⣤⠀⢸⣿⣧⡄⣿⡇⠀⠸⣿⣧⣿⠇⠀⢸⣿⠸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣶⣶⣶⣠⣶⣶⣄⣶⣶⣶⡆⣶⣶⡆⢰⣶⡆⢰⣶⡖⣶⣄⣶⡆⠀⢰⣶⣶⠀⣠⣶⣶⣄⢠⣴⢶⣦⣀⣴⣶⣦⡀⣶⡆⣶⡦⢰⣦⢰⣶⢴⣶⣶⣶⣶⣶⣦⢠⣶⡶⣦⡄⣶⡦⠀⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⢠⣿⢻⣿⢸⣿⡇⢸⣿⡇⢹⣿⡿⠀⠀⣼⡿⣿⡇⣿⣯⠹⠿⢸⣿⠸⠿⢻⣿⣿⣿⡇⣿⡇⣿⡇⢸⣿⣾⣿⠀⣿⣿⠀⣿⣿⣿⢸⣿⣧⣿⠃⣿⡇⠀⣿⣧⡄⠀⢠⣶⣶⣶⣶⣶⣶ ⠂⠀⣿⣿⠀⣿⣇⣿⣿⠀⣿⣿⢸⣿⣾⣿⣼⣿⣇⣸⣿⣇⡀⣿⡇⠀⠀⣿⣷⣿⡇⣿⣿⣶⣶⢸⣿⣰⣶⢾⣿⣿⣿⡇⣿⡇⣿⡇⢸⣏⣿⣿⠀⣿⣿⢰⣿⣿⣿⣸⣿⣇⣿⡇⣿⣇⡀⣿⣏⣁⠀⢸⣿⣿⣿⣿⣿⣿ ⣇⡴⠛⠻⢠⠘⠛⠛⠥⠠⠻⠛⠜⠛⠙⠟⠛⠛⠛⠛⠛⠛⠃⠛⠃⠀⠘⠛⠃⠛⠛⠘⠛⠛⠁⠈⠛⠛⠋⠀⠙⠛⠋⠀⠙⠛⠛⠁⠘⠛⠙⠛⠀⠛⠛⠘⠛⠙⠛⠛⠛⠛⠛⠁⠛⠛⠃⠛⠛⠛⣀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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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 3083 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/07/irc-log-061221/#comments Gemini version at gemini://gemini.techrights.org/2021/12/07/irc-log-061221/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.07.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Monday,_December_06,_2021⠀✐ Posted in IRC_Logs at 2:13 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights- 061221.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-061221.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-social-061221.txt * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes- 061221.txt Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmNp48GX6FvdXru2tSAbPLB2t7y1U1qgMiXnDdxsamEGg8 #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmRrpn5m47yebfkV4LcXkybLotpjJGjbwdADVFEUbvK2Ae (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  Qme5Jsw7HW7rTGBowPfhBgRAVaSgPE9CVdWBDHeWBa8sRy social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  Qmb8ndGihmFqNffYeC3jihABcddf6nx1ctKQsjCorFG9SM social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  Qmc24mjWBuxBRetubYQRCfe4uhVSuDbPmx2CCjZ7thBQrh #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmaajcdiFAzR29ya7XxJVsw6MMgstqpbFKkdHg1AHdGst7 (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmfFjg7qTgrK9fFJPt1UEnfvDmy9B7DB96UR6dYLbs5xMu #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmaXQqtCe6qPYQW6Vk9p44PLDjzY68i5u1U6zNUGBjtGfj (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmNPpiGqWGFQNEECwNKt72LSricBeH2VuxSzamtqTrESHV ䷩ 𝚕𝚒𝚗𝚎 3212 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.07.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_8/12/2021:_FreeBSD_12.3,_EasyOS_3.1.13,_and_WordPress_5.9_Beta_2⠀✐ Posted in News_Roundup at 7:29 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Why_The_Librem_14_with_QubesOS_Exceeded_My_Expectations_– Purism⠀⇛ If you face extreme threats, or even if you are just looking for a high-security operating system for peace of mind, it’s hard to beat QubesOS. While it’s not as easy to use as our default PureOS, it offers a lot of advanced security features that, when combined with the advanced hardware and firmware security features of the Librem 14, makes for one of most secure computers out there. I have been using QubesOS as my primary OS for many years now, starting with the 3.x release on both my work (Thinkpad X230) and personal (Librem 13v1) computers. Over the last couple years my primary work machine has been a Librem 13v4 running Qubes with 16Gb RAM and solid-state storage. Starting this summer I moved to a Librem 14 for my work computer, our dream laptop that we designed (at least in part) to run Qubes well by adding a fast, 6-core/12-thread CPU and expansion up to 64GB RAM. I’ve been using this laptop constantly over the past few months and I’m convinced that the Librem 14 is the best laptop for Qubes. In this post I wanted to offer a brief retrospective on my experience running Qubes as my primary OS on my Librem 14 compared to past computers. [...] I admit I had high expectations for running Qubes on the Librem 14 before I got it. After all, we did design it at least partially with running Qubes in mind. Having now used it for a number of months, I can say that it’s met and exceeded my expectations (and based on some of the feedback I’ve gotten from customers, I’m not the only one). It’s really nice to run Qubes on a machine not only with full hardware support, but also with horsepower to spare. Now that we are almost at shipping parity, and it’s a supported, pre-installed option here at Purism, if you have been curious to try Qubes out, I think the Librem 14 is the ideal platform. o § Audiocasts/Shows⠀➾ # ⚓ One_Month_with_GNOME_Web_/_Epiphany_was_NOT_FUN_– Invidious⠀⇛ # ⚓ Wayland_Is_Forever_Years_Away:_Pipewire_Is_Today_– Invidious⠀⇛ Pipewire and Wayland are 2 massive changes happening in the Linux desktop but one of these is seeing vastly quicker adoption than the other and it’s for good reason # ⚓ Live_–_Building_ISO_Images_for_Projects_–_Invidious⠀⇛ # ⚓ 255:_Lutris_Interview_with_Mathieu_Comandon_–_Destination Linux⠀⇛ This week’s episode of Destination Linux, we have an interview with the creator of Lutris, Mathieu Comandon. Then we’re going to discuss KDE appealing to a wider audience. Plus we’ve also got our famous tips, tricks and software picks. All of this and so much more this week on Destination Linux. So whether you’re brand new to Linux and open source or a guru of sudo. This is the podcast for you. o § Kernel Space⠀➾ # ⚓ Intel_Posts_Updated_Driver_&_Sample_Code_For_“Software Defined_Silicon”_–_Phoronix⠀⇛ Back in September Intel originally posted Linux patches for “Software Defined Silicon” for being able to activate extra CPU features present in the processor’s silicon but not exposed by default unless the cryptographically secure process with this SDSi driver was performed. Intel appears to be moving toward allowing licensable processor features that can be activated after the fact and today a new version of that SDSi Linux driver appeared. o § Instructionals/Technical⠀➾ # ⚓ Install_ownCloud_Server_on_Debian_11_–_kifarunix.com⠀⇛ In this guide, we are going to learn how to install ownCloud Server on Debian 11. If you need to have your own self-hosted cloud storage that provides a safe, secure, and compliant file synchronization and sharing solution, try ownCloud. # ⚓ How_to_Manage_Packages_on_RPM-Based_Linux_Distros_With DNF⠀⇛ Knowing how to install and remove packages is a rudimentary task you should be accustomed to. Here’s how to manage packages on Linux with DNF. # ⚓ 2_ways_to_Install_PyCharm_Python_IDE_on_Debian_11_Bullseye Linux⠀⇛ Here is the guide to learn the simple steps for the installation of PyCharm on Debian 11 Bullseye Linux using command terminal. PyCharm is a Python development environment with code completion, code analysis, refactorings, and debuggers. It is open-source and distributed under the Apache license. Apart from the free community edition, there is also a paid Professional Edition. The latter (paid one) also supports the web frameworks Django, Pyramid, Flask, and web2py, Google’s Platform as a Service App Engine, and the object-relational mapper SQLAlchemy. # ⚓ How_to_install_Moshi_Monsters_Rewritten_Desktop_on_a Chromebook⠀⇛ Today we are looking at how to install Moshi Monsters Rewritten Desktop on a Chromebook. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ How_to_install_Moshi_Monsters_Rewritten_Desktop_on_a Chromebook⠀⇛ o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ EasyOS_version_3.1.13_released⠀⇛ Version 3.1.13 does not have SeaMonkey, instead has BlueGriffon HTML editor and Balsa email client. Let me know how they go. If any problems, they can be changed. I am planning to create Claws and Sylpheed email client PETs for comparison, as Balsa spam filtering seems a bit weak. I received an email that samba is still broken in 3.1.11. I didn’t get time to check that one. So that is something we need to look at. I tested booting up in RAM (& optionally disable drives). Works fine, there is one error message during bootup about a missing file, but that doesn’t matter. Getting closer to the next major release, that will be 3.2. # § BSD⠀➾ # ⚓ FreeBSD_12.3-RELEASE_Announcement_|_The_FreeBSD Project⠀⇛ The FreeBSD Release Engineering Team is pleased to announce the availability of FreeBSD 12.3-RELEASE. This is the fourth release of the stable/12 branch. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Fedora_Linux_35_Release_Party_Recordings_Available Now!_–_Fedora_Community_Blog⠀⇛ The Fedora community celebrated the release of Fedora Linux 35 in the third installment of our virtual Release Parties on 12–13 November 2021. A big thank you to everyone who helped to build Fedora Linux 35 as well as the organizers, participants, and attendees at the event! The recordings are now available for viewing in a YouTube Playlist. We had 12 info sessions, 3 socials, and the Fedora Museum WorkAdventure for the “Hallway Track”. We also had a session of the virtual team building event “Beat the Bomb“—a collaborative gaming activity that resulted in hilarity and chaos! # ⚓ Fedora_36_Planning_To_Run_Wayland_By_Default_With NVIDIA’s_Proprietary_Driver_–_Phoronix⠀⇛ While all of the software components are out there now for being able to run NVIDIA’s proprietary driver stack with modern (GBM- based) Wayland compositors by default, including XWayland support, Fedora Workstation currently defaults to using an X.Org based session with the green binary blob. However, for Fedora 36 next spring they are planning on using the Wayland-based desktop here too. Fedora Workstation for a while now has defaulted successfully to using the Wayland- based GNOME Shell desktop but with the NVIDIA proprietary driver they have kept to using the X.Org session. Thanks to the NVIDIA 495 series driver introducing GBM support and other improvements made to accelerated XWayland, etc, running NVIDIA’s proprietary driver stack for daily Wayland-based desktop use is becoming viable. # ⚓ Kafka_Monthly_Digest:_November_2021⠀⇛ This 46th edition of the Kafka Monthly Digest covers what happened in the Apache Kafka community in November 2021, including the imminent release of Apache Kafka 3.1.0, notable Kafka Improvement Proposals (KIPs), community project releases for Jikkou 0.7 and AKHQ 0.19.0, and more. For last month’s digest, see Kafka Monthly Digest: October 2021. # ⚓ Red_Hat’s_CentOS_Stream_9_Linux_arrives_|_ZDNet⠀⇛ Almost a year ago to the day, Red Hat changed CentOS from being a Red Hat Enterprise Linux (RHEL) clone to being a developmental rolling Linux distribution, CentOS Stream. Many users weren’t happy. As a result, several replacement CentOS/RHEL clones, such as AlmaLinux and Rocky Linux, got their start. But, Red Hat continued with its plans to use CentOS to foreshadow the next edition of RHEL. Now, the new CentOS project is showing off its latest and greatest in its first totally new release: CentOS 9. o § Devices/Embedded⠀➾ # ⚓ Compute_module_and_Hummingboard-T_SBC_showcase_safety- conscious_TI_AM64x⠀⇛ TI’s headless, 16nm FinFET fabricated AM64x runs Linux on 1x or 2x 1GHz Cortex-A53 cores and offers up to 4x 800MHz Cortex-R5F cores for real-time duty. The SoC also supplies up to 2x programmable real-time units (PRUs) for managing up to 4x GbE ports with time-sensitive networking (TSN) and fieldbus protocols. o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Firefox_Nightly:_These_Weeks_in_Firefox:_Issue 105⠀⇛ # ⚓ New_JavaScript_syntax_support_in_add-on developer_tools_|_Mozilla_Add-ons_Community Blog⠀⇛ It’s been a year since we last added support for new JavaScript syntax to the add-ons linter. In that time we’ve used it to validate over 150,000 submissions to AMO totalling hundreds of millions of lines of code. But it has been a year, and with both Javascript and Firefox are constantly and quickly evolving, the list of JavaScript features Firefox supports and what the AMO linter allows have drifted apart. This drift is not an accident; Firefox and AMO don’t keep the same cadence on supported features, and this is deliberate. Upcoming JavaScript features are spread across different EcmaScript proposal stages, meaning different features are always in different stages of readiness. While Firefox often trials promising new JavaScript features that aren’t “finished” yet (stage 4 in the ECMAScript process) to better test their implementations and drive early adoption, the AMO team takes a different approach intended to minimize friction developers might face moving their addons between browsers. To that end, the AMO team only adds support for “finished”, stage 4 features to the linter. # § Content Management Systems (CMS)⠀➾ # ⚓ WordPress_5.9_Beta_2⠀⇛ WordPress 5.9 Beta 2 is now available for testing! This software version is still under development. Please do not run this software on a production site. Instead, install it on a test site, where you can try out the newest features to get a feel for how they will work on your site. You can test the WordPress 5.9 Beta 2 in three ways: Option 1: Install and activate the WordPress Beta Tester plugin (select the “Bleeding edge” channel and “Beta/RC Only” stream). Option 2: Direct download the beta version here (zip). Option 3: When using WP-CLI to upgrade from Beta 1 to Beta 2 on a case-insensitive filesystem, please use the following command sequence: Command 1: wp core update –version=5.9-beta1 # § Funding⠀➾ # ⚓ VR_Platform_‘Decentraland’_Now_a_Patron_Level ‘Blender’_Member⠀⇛ Remember Second Life? Evidently virtual worlds are still a thing, and one of them, Decentraland, is now funding Blender, the popular open-source 3D computer graphics software used for creating everything from animated films to computer games (and yes, virtual reality), to the tune of $135,000 over the next two years. The cryptocurrency/blockchain based Decentraland platform, in which virtual real estate is acquired through blockchain-based purchases and deeded as non-fungible tokens, announced on Monday that it’s signed up to be a top level Patron sponsor of Blender for a two year period. In doing so, they join such A-list Patron level contributors as Unity, AMD, Facebook, NVIDIA, Amazon Web Services, Epic Games, and Apple. # § FSF⠀➾ # ⚓ Support_the_FSF_through_the_GNU_Press_shop_with_great holiday_picks⠀⇛ Greetings from the GNU Press shop! My name is Davis Remmel, and I am excited to introduce myself as the new operations assistant at the Free Software Foundation (FSF). These past few weeks I’ve been working through our backlog of orders, and I’m pleased to say that we are just about caught up and processing new orders on our normal timeline. If you were thinking about getting a gift for that GNU-loving friend or family member, now is the time to place that order! If you’re in the US, and if you place your order by Friday, December 17, there’s a good chance that package will arrive on, or before, December 24. [...] For privacy lovers (or those who have ever uttered the word, “cryptography”), we have a NeuG USB True Random Number Generator (RNG). Your cryptographic keys will be stronger than an ox, without any need to trust your CPU’s definition of “random.” I recommend this RNG in conjunction with our anti-surveillance webcam stickers, which don’t leave residue and can also cover microphone holes. # § Programming/Development⠀➾ # ⚓ The_Mocking_will_continue,_until_CI_improves_|_die- welt.net⠀⇛ One might think, this blog is exclusively about weird language behavior and yelling at computers… Well, welcome to another episode of Jackass! Today’s opponent is Ruby, or maybe minitest , or maybe Mocha. I’m not exactly sure, but it was a rather amusing exercise and I like to share my nightmares 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇;)⦈ It all started with the classical “you’re using old and unmaintained software, please switch to something new”. The first attempt was to switch from the ci_reporter_minitest plugin to the minitest- ci plugin. While the change worked great for Foreman itself, it broke the reporting in Katello – the tests would run but no junit.xml was generated and Jenkins rightfully complained that it got no test results. While investigating what the hell was wrong, we realized that Katello was already using a minitest reporting plugin: minitest- reporters. Loading two different reporting plugins seemed like a good source for problems, so I tried using the same plugin for Foreman too. Guess what? After a bit of massaging (mostly to disable the second minitest-reporters initialization in Katello) reporting of test results from Katello started to work like a charm. But now the Foreman tests started to fail. Not fail to report, fail to actually run. WTH‽ # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ Gremlin_detection_bigly_improved_and_a_NUL problem_avoided⠀⇛ Gremlin” is my name for an invisible character other than a plain whitespace, a linefeed or a horizontal tab. Gremlins can cause errors in data processing and can also make it harder to detect duplicate records in a data table. A few years ago I wrote a gremlin- detector script (called “gremlins”) for A Data Cleaner’s Cookbook that works on UTF-8-encoded plain text files. The script has since had a few minor updates, but I’ve now rewritten “gremlins” from scratch to make it faster and more informative. This post explains the new script, which is presented in full at the bottom of this webpage. * § Leftovers⠀➾ o § Science⠀➾ # ⚓ Jonathan_Dowland:_Cost_models_for_evaluating_stream- processing_programs⠀⇛ As I wrote, last week I attended the UK Systems Research 2021 and gave two (or 2½, or 3) talks. my PhD talk is entitled “Picking a winner: cost models for evaluating stream-processing programs”. o § Censorship/Free Speech⠀➾ # ⚓ What_Turkmenistan_internet_shutdowns_tell_us_about_digital repression_in_Central_Asia_–_Access_Now⠀⇛ Turkmenistan internet shutdowns are extreme. Today, any social media platform, foreign media outlet, or website that provides information criticizing the current regime is shut down. Not only are sites like Facebook, YouTube, and Wikipedia banned, the government also blocks sites that offer circumvention tools like Virtual Private Networks (VPNs). What’s more, Turkmenistan residents are asked to swear on the Quran not to use the circumvention tools while signing up for a home internet connection, while students are asked to make declarations pledging to use the internet only for “educational purposes.” Unfortunately, we are seeing a similar pattern of disproportionate online censorship in Uzbekistan and Tajikistan. In response to protests, authorities have cut internet access for 13 days in the Tajik town of Khorog, forcing locals to travel hundreds of kilometers to neighboring cities to get connected. Deprived of their ability to continue their studies online, do business, or communicate with loved ones, people are experiencing stress and frustration while getting no answers from local telecommunication companies about when the situation will improve. In extremely restrictive environments like these, ordinary citizens, activists, and journalists are sharply limited in their possibilities to speak freely. The Tajikistan and Turkmenistan internet shutdowns are a sign of growing digital repression in Central Asia. The international community must speak out for those denied internet access, free use of VPNs to seek information, and the ability to share critical thoughts online. o § Civil Rights/Policing⠀➾ # ⚓ Looking_for_Work?_Electronic_Frontier_Foundation_Has_a $100,000_Job_Opening⠀⇛ “This is a two-year fellowship with the potential to be extended for one to two additional years,” EFF said in a job posting on its website. “The ideal candidate will act as a public advocate helping establish EFF as a leader in the civil liberties implications of decentralizing the Internet. You’ll help chart a course for EFF to have a big impact in the public conversations about decentralization of the Internet and how it fits into our mission of ensuring technology supports freedom, justice, and innovation for all people of the world.” # ⚓ ‘It_took_only_four_false_witnesses_to_ruin_my_life’:_In_an open_letter_from_jail,_blogger_Yuri_Khovansky_shares_how investigators_are_pressuring_his_loved_ones⠀⇛ Blogger Yuri Khovansky, currently in pre-trial detention on charges of justifying terrorism, penned an open letter from jail, where he has been since June. In the text, Khovansky says investigators threatened him with serious prison time when he refused a plea bargain. Officers also allegedly promised “problems” for his girlfriend, Maria Nelyubova (who spoke about this before). Khovansky says the authorities suggested that they would plant drugs on her. Meduza is publishing a translation of Khovansky’s letter.  o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ EPO_President_meets_the_Commissioner_of_the_Korean Patent_Office [Ed: This is false. He did not meet him. They had a webchat. EPO_“news”_section_is_a_stream_of lies and notice how he promotes software_patents in Korea]⠀⇛ Today, EPO President António Campinos met online with Dr Kim Yong Rae, Commissioner of the Korean Patent Office (KIPO). Mr Campinos and Dr Kim took stock of the fruitful collaboration between the two offices and launched the first EPO-KIPO study, a comparative study on computer-implemented inventions (CIIs). The publication aims to provide applicants and practitioners with clear and useful insights into each office’s examination practices in this rapidly growing area. The study first outlines and compares the respective approaches to examining CIIs. It then focuses on ten example cases that have been analysed in parallel by experts from the EPO and KIPO. These examples were carefully selected by both offices to reflect the range of CIIs for which patent applications are often filed. The cases therefore span areas such as artificial intelligence, graphical user interfaces, speech processing, e- commerce and telecommunications. As shown in the study, the EPO and KIPO use overlapping yet different sets of criteria to assess the patentability of CIIs. In practice, this leads to outcomes which are largely comparable, but not always completely aligned. Therefore, when drafting CII-related patent applications, applicants and practitioners may benefit from taking into consideration the two offices’ different approaches. # ⚓ EPO_user_survey:_ViCo_oral_proceedings_continue_(to divide_opinion) [Ed: EPO produces lies to ‘legitimise’ utterly_illegal_policies]⠀⇛ Following the decision of the EBA in G 1/21 on the legality of mandatory ViCo oral proceedings, the EPO has continued with ViCo proceedings before the Boards of Appeal. The EPO has also now released a report of the user survey of the opposition division (OD) ViCo pilot program. As with the EBA decision in G 1/21, both supporters and critics of ViCo oral proceedings will find evidence in the report to bolster their position. Nonetheless, the user survey results are broadly positive, even if they are not quite the unequivocally glowing endorsement of ViCo that the EPO, with its usual positivity, has concluded. [...] The EBA decision in G 1/21 was presented in such a way that both sides of the debate on ViCo were able to claim a victory of sorts. Proponents of ViCo were able to point to a clear order by the EBA that ViCo proceedings were permitted, at least during the pandemic. Critics of ViCo seized on the EBA language that in-person proceedings should be preferred in the absence of a general emergency and in view of the current limitations in ViCo technology. Notably, whilst the EBA decision in G 1/21 did not explicitly address the legality of mandatory ViCo proceedings in Opposition, the advantages and disadvantages of ViCo highlighted by the EBA appear as applicable to the OD as they do to the Boards of Appeal. [...] Even the most ardent supporters of ViCo would probably admit that the EPO report glosses over some of the legitimate criticisms of ViCo. The direct quotes of user feedback provided in the report are all positive and this Kat finds it hard to believe that there was no negative feedback that could have been quoted for balance. Nonetheless, however much it may be argued that the EPO report sugar- coated the data, it is undeniable that the majority of users responding to the survey were in favour of ViCo. Particularly, it is clear from the report that there is a good deal of support for the continuation of ViCo proceedings even after the state of general emergency impairing parties ability to attend in-person proceedings has passed. It would have been interesting to see the breakdown of responses to the survey by country. Anecdotally, representatives of German patent firms have been particularly vociferous in their objection to ViCo. A cynic might say that this is unsurprising, given that a move to ViCo removes some of the competitive advantage these firms have for being located within striking distance of the EPO. On the flip side, UK professional representatives (including CIPA itself) have come out broadly in favour of ViCo. Was the positive feedback on ViCo driven by the majority UK respondents? Interestingly, in its conclusion, the report took pains to highlight that the reasoning in G 1/21 on the primacy of in-person proceedings only explicitly applies to Boards of Appeal proceedings and not to opposition proceedings. The report also noted that the reasons for which the EBA found that in- person proceedings should be the default, namely the current limitations of ViCo technology, may be overcome both by improvements in technology as well as the increased familiarity of parties with the technology. Here we see how the EPO might seek to overcome the EBA’s clear direction that in-person proceedings should be the default post-pandemic, e.g. by citing an improvement in the technology. Nonetheless, as Germany begins suffering a fourth wave of coronavirus infections, we can be confident that ViCo proceedings are here to stay for the immediate future. The results of the user survey at least provide comfort that the majority of users haven’t found ViCo to be a barrier to justice. # ⚓ DLA_Piper_hires_life_sciences_partner_in_London [Ed: JUVE continues with faker and faker news or ads/spam disguised as reporting, as if hiring one ‘low-level’ worker is “news” and mentioning that is “journalism”]⠀⇛ Rebecca Lawrence (47) will expand the firm’s life sciences litigation practice in London. She brings more than 20 years of experience to the firm, but has not worked in patent law for the past four years. Rebecca Lawrence has a background in biological science. She began her career in 1998 at Linklaters, where she was active in IP in the life sciences sector from a very early stage. During her time in the full- service firm’s IP team, she played a role in the high-profile patent litigation between Linklaters client American Home Products and Bristows client Novartis. The case concerned rapamycin, a drug used to suppress transplant rejection. In 2000, Lawrence joined the renowned IP boutique Bristows, then moved to competitor Powell Gilbert in 2007. She became partner in 2008. Her work there included acting for Monsanto in its dispute against Cargill over glyphosate-resistant enzymes in plants. In addition to litigation for other well-known clients, including Boehringer Ingelheim, Krka and Dr. Reddy’s, she also advised on biosimilars. # ⚓ EPO,_JPO,_USPTO_discuss_co-operation_in_the_digital environment [Ed” Notice the EPO’s greenwashing_of monopolies such as “IP and environmental issues.” Lots more can be said about this typical EPO ‘fluff’; PR on overdrive this past fortnight… maybe because of the impending AC meeting]⠀⇛ The heads of the European Patent Office (EPO), Japan Patent Office (JPO) and United States Patent and Trademark Office (USPTO), known as the Trilateral offices, held their 39th annual meeting in the form of videoconference today (7 December), hosted by the JPO. At the meeting, EPO President António Campinos, JPO Commissioner MORI Kiyoshi, and USPTO (Performing the functions and duties of the Under Secretary of Commerce for Intellectual Property and Director of the USPTO, Office of the Under Secretary and Director) Drew Hirshfeld, discussed the outcome of their recent meeting with the Trilateral industry associations, reviewed the digitalisation of procedures at each office and spoke about the possibility of future Trilateral co-operation on Intellectual Property (IP) and environmental issues. ䷩ 𝚕𝚒𝚗𝚎 4125 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.07.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_7/12/2021:_Firefox_96_Beta_and_Fedora_37_Abandons_ARMv7⠀✐ Posted in News_Roundup at 3:51 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ The_9_Best_Linux_Distros_for_Windows_Users⠀⇛ Windows has evolved over the years, and there is no denying how Windows users are spoilt for options. Multiple OS versions rolled out at regular intervals, making it one of the best operating systems in the market. Nevertheless, people are on the lookout for open- source options for their systems. Windows, being a closed-source OS, is not suitable for every computer user out there. Alternatively, Linux is an open-source operating system, and this Linux distro list is ideal if you are looking to switch from Windows to Linux. Rest assured, you won’t have to stay away from your Windows favorites for very long. # ⚓ 5_Honest_Reasons_To_Avoid_Switching_To_Linux⠀⇛ Linux has been a wonderful operating system for many people. It’s free, it’s open source, it’s customizable, secure and much more. We, like many other open source enthusiasts around the world as well, have been trying to convince people to switch to Linux from Windows for many reasons. These reasons should be all known for you by now. But we have to be honest and admit that Linux is not for everybody. There are some specific cases where staying as an avid Windows user could be better for you than switching to Linux, and we’ll be seeing some of these in today’s article. # ⚓ What_Is_a_Physical_Kill_Switch,_and_Does_Your_PC_Need One?⠀⇛ Purism is a company founded on the idea of having strict privacy and security features built into its computers. The Librem 14 is a prime example of this philosophy, and its hardware, firmware, and operating system have been designed with a significantly higher level of paranoia than typical computers. The Librem 14 Linux laptop features multiple physical kill switches, which the company claims absolutely disables the related hardware. There are switches for the webcam and microphone as well as WiFi and Bluetooth. When it comes to the Librem 14 in particular, there are so many additional privacy features that the kill switches really are the least of it, but there are examples of such kill switches in regular laptops that don’t go to such extremes. All the way back in 2018, HP was already shipping laptops with physical kill switches for the webcam. Their Specter laptops included these switches, so hopefully the chances of a hacked webcam recording you when you don’t want it to are virtually zero. Kill switches may not always take the form of a traditional sliding switch on the side of a laptop. It’s entirely possible to integrate the kill switch with a physical, built-in camera shutter. # ⚓ Partaker_Intel_Core_i3-8130U_fanless_mini_PC_Win_10_Linux supported_$423⠀⇛ Partaker have created a new fanless mini PC equipped with a wealth of connectivity and capable of supporting both the Microsoft Windows 10 and operating system most Linux distributions depending on your preference. Pricing starts from $423 for the Intel Core i3-8130U processor version although a more affordable Intel Celeron 3865u/3867u/3965u processor version is also available with prices starting from $246. Both are barebone systems meaning that you will need to provide your own memory, storage and operating system, enabling you to tailor the system to your exact requirements. # ⚓ IGEL_Releases_Support_for_VMware_Workspace_ONE_Intelligent Hub_for_Linux⠀⇛ o § Audiocasts/Shows⠀➾ # ⚓ AlmaLinux_OS_8.5_Quick_overview_#Shorts_–_Invidious⠀⇛ A Quick overview of AlmaLinux OS 8.5 # ⚓ Proxmox_Backup_Server:_Full_Getting_Started_Guide!_– Invidious⠀⇛ Proxmox Backup Server is a custom Linux distro that you can run on your server to have it serve as a backup endpoint. It integrates quickly and easily with Proxmox Virtual Environment, making it a great solution to back up your virtual machines and containers. In addition to that, it can also be used to store non-VM backups too, so running Proxmox Virtual Environment is NOT a requirement. In this video, I’ll teach you everything you need in order to get started with Proxmox Backup Server. # ⚓ Working_on_Xmonad,_Emacs_and_DTOS_(DT_LIVE!)_–_Invidious⠀⇛ Today’s live stream event will be working on some of my GitLab projects. This may involve some chasing bugs, doing some scripting, spinning up a virtual machine to test things on, etc. # ⚓ Late_Night_Linux_–_Episode_154⠀⇛ Nextcloud and friends go after Microsoft, modern packaging comes under fire, whether we should be targeting less advanced users, a new old Raspberry Pi OS, KDE Korner, and more. # ⚓ KDE_Dev_Reacts_To_Linus’_New_Linux_Video!_And_tries_some_of the_challenges!_–_Kockatoo_Tube⠀⇛ o § Kernel Space⠀➾ # ⚓ Custom_Linux_allows_Raspberry_Pi_to_drive_ADI_peripherals⠀⇛ Called Kuiper Linux, it incorporates Linux device drivers for ADI products, and supports other hardware including Digilent Zedboard, TerASIC DE10- Nano and Digilent Cora “The reasoning behind creating this distribution is to minimise the barriers to integrating ADI hardware devices into a Linux-based system,” according to the company. “When starting with a generic Linux distribution, the kernel typically would have to be rebuilt with the desired drivers enabled. While this is not difficult for an engineer that is familiar with the process, it can be a daunting task even when everything goes right. ADI Kuiper Linux solves this problem, and includes a host of additional applications, software libraries, and utilities.” # ⚓ Rust_takes_a_major_step_forward_as_Linux’s_second_official language_|_ZDNet⠀⇛ It wasn’t that long ago that the very idea that another language besides C would be used in the Linux kernel would have been laughed at. Things have changed. Today, not only is Rust, the high- level system language moving closer to Linux, it’s closer than ever with the next “patch series to add support for Rust as a second language to the Linux kernel.” # ⚓ Apple_SoC_PMGR_driver_for_5.17⠀⇛ Hi SoC folks, Please merge the new PMGR driver for 5.17. This should not have any hard deps with the previous pulls. The MAINTAINERS change already rode along the DT pull, for simplicity. # ⚓ More_Apple_Silicon_M1_Bring-Up_On_The_Way_For_Linux_5.17_– Phoronix⠀⇛ The enablement work for supporting Apple’s M1 SoC under Linux continues and with the v5.17 kernel next year will be yet more additions. Among the new driver activity for Linux 5.17 is an Apple PMGR driver for controlling the power states. The Apple PMGR block on their SoC has high-level power state controls for SoC devices. At the moment not all features are supported but important step forward for power management with Apple Silicon on Linux. # § Graphics Stack⠀➾ # ⚓ Intel’s_SWR_Removed_From_Mainline_Mesa,_More_Classic Code_Cleaning_Continues_–_Phoronix⠀⇛ Last Friday Mesa classic drivers were removed from the mainline code-base and punted off to an “Amber” code branch where they will receive whatever attention moving forward. With that classic Mesa code removed, more code cleaning is now happening on top of the tens of thousands of lines of code already removed. Intel’s OpenSWR driver has also now been removed from mainline. Since the original classic Mesa drivers consisting of Radeon R100/R200, original Nouveau, and Intel i915 / i965 drivers were removed, more code cleaning can now happen on mainline for code that was just sticking around for these old, rather unmaintained drivers. # ⚓ XWayland_Lands_DRM_Leasing_Support_To_Handle_VR Headsets_–_Phoronix⠀⇛ Along with XWayland touchpad gestures, another shiny feature was merged this week into X.Org Server Git for XWayland: DRM leasing support! XWayland now has mainline support for the DRM leasing (drm-lease-v1) protocol for allowing X11 clients running through XWayland to lease non-desktop connectors/outputs from the underlying Wayland compositor. This is particularly useful and designed around the needs of virtual reality (VR) head-mounted displays. o § Benchmarks⠀➾ # ⚓ Amazon_Linux_2022_Performs_Well,_But_Intel’s_Clear_Linux Continues_Leading_In_The_Cloud ⠀⇛ AWS recently introduced Amazon Linux 2022 in preview form as the latest iteration of their Linux distribution now based on Fedora with various alterations to catering to their customers running it on EC2. Last week were benchmarks looking at Amazon Linux 2022 compared to Amazon Linux 2 and other distributions like CentOS and Ubuntu. In this article we are seeing how Amazon Linux 2022 can compete with Intel’s own Clear Linux performance- optimized distribution. o § Applications⠀➾ # ⚓ Quickly_Create_And_Run_Optimized_Linux,_macOS_And_Windows Virtual_Machines_With_Quickemu_(With_Auto_ISO_Download)_– Linux_Uprising_Blog⠀⇛ Quickemu is a command line wrapper for QEMU that can be used to quickly create and run highly optimized Linux, macOS, *BSD and Windows desktop virtual machines. It’s currently only intended for use on Linux hosts (it also works on WSL), but in the future it might also support macOS hosts. Instead of expecting an exhaustive list of configuration options, Quickemu tries to automatically “do the right thing” and creates the VM configuration automatically for you. Besides this, the tool also automatically downloads the Linux, macOS or Windows image, so all you have to do is run and install the OS in the virtual machine. Even though using Quickemu you don’t need to configure anything, e.g. it automatically calculates the number of CPU cores and RAM it should allocate to a VM based on the host computer specifications, you can still use custom config options in the .conf file. What’s more, if using the command line is not your thing, there’s also a third-party GUI for Quickemu written in Flutter, called Quickgui: # ⚓ Weekly-ish_recap_—_7_December_2021:_Blender_3.0⠀⇛ This is one of the most exciting releases in 2021. I wholeheartedly recommend watching the “Every new feature in 6 minutes” video, it provides a pretty good summary of the most important changes. # ⚓ 4_Best_Free_and_Open_Source_DVD_Authoring_Tools⠀⇛ DVD authoring is the process of creating a DVD video capable of playing on a DVD player. DVD authoring software must conform to the specifications set by the DVD Forum. DVD videos are logically divided into a first-play section, a set of top-level menus (called VMGM for Video Manager Menus) and one or more video title-sets (VTSs). Each title-set is logically divided into menus and titles, meaning the main content of the disc. DVD authoring is the second step in the process of producing finished DVDs. The first step is the creation of the movie and the second, the authoring, is the creation of artwork, user menus, insertion of chapter points, overdubs/commentaries, setting autoplay and/or repeat options, etc. The final step is the manufacturing (replication) process to mass-produce finished DVDs. This article showcases the best free and open source DVD authoring tools that run under Linux. o § Instructionals/Technical⠀➾ # ⚓ SSH_Key_Rotation_with_the_POSIX_Shell_–_Sunset_Nears_for Elderly_Keys_|_Linux_Journal⠀⇛ OpenBSD has recently stressed to us the value of key rotation by their use of “Signify” distribution release signatures. We have realized that SSH keys should also rotate, to reduce the risk of powerful keys that fall into the wrong hands which become “the gift that keeps on giving.” There have always been open questions on the retirement of SSH keys. These questions have grown in volume and many are joining the advocacy for SSH certificate authorities. To “rotate” an SSH key is to replace it, in such a way that it is no longer recognized, requiring removal from the authorized_keys file. SSH rotation is commonly addressed with Ansible, but this leaves many users on smaller systems or lacking privilege without recourse. A more basic and accessible method to migrate SSH keys is sorely lacking. Below is presented an SSH key rotation script written in nothing more than the POSIX shell. There is palpable danger in the misuse of such a tool. Many administrators control inaccessible systems that entail massive inconvenience in a loss of control. Demonstrated here are rotation schemes of increasing risk, for any holder of a key to choose, to their own tolerance. Hopefully, I have not made grave mistakes in the design. The most conservative users of this approach should tread with extreme caution, test carefully, and ensure alternate means of access prior to any deployment. As the author, I have no desire to assume any responsibility for a failed rotation, and its consequences. I especially disavow the “wipe” option below to remove entries from authorized_keys. It is presented as commentary, not working code. In any case, we foolishly rush in where the more prudent fear to tread. # ⚓ Replicating_Slow_Latency_on_Linux_—_Virtualization_Review⠀⇛ I recently found that, in order to demonstrate some monitoring software, I needed to replicate a slow network that was being used in a VDI environment. Using the Linux Traffic Control (tc) command, which is found on most modern Linux systems, I was able to easily accomplish this. I used it on a virtual machine (VM), but I have also used it on physical systems with the same results. In two previous articles, I showed you how I installed Ubuntu on older equipment and on a virtual machine (VM), and then how I installed the VMware Horizon Client on it and was able to use it to connect to a Horizon desktop. I decided to focus on this topic as I have found that, due to the current chip shortage, many people are having to repurpose older systems because they simply cannot find new devices to use to attach to remote desktops. I logged into my Linux system and was able to launch the Horizon Client and connect to a Horizon desktop without any issues. # ⚓ Best_Tools_to_Install_on_Fresh_Linux_Mint_Installation [Ed: Horrible advice; lots of spyware, DRM, and proprietary software, even Microsoft's; this is the way to ruin the whole OS]⠀⇛ So, you have just installed a fresh copy of Linux Mint 20 and are ready to make the most of your new system. How do you move forward? In this guide, we will highlight some of the useful tools to consider installing which will enhance your user experience in Linux Mint. Note that this is not a comprehensive list of the tools you need to install, but a collection of some of the most popular tools that will considerably enhance your experience. # ⚓ Anyone_can_draw_on_Linux_with_Inkscape_|_Opensource.com⠀⇛ Inkscape is an illustration application, and it works in vectors to ensure limitless resolution for your drawings. Vector illustration is different from freehand illustration. If you’re used to drawing freehand, vectors may at first feel restrictive, but once you get used to how vectors get created and how you can use them to construct an image, it’s a powerful way to build visuals of all sorts. And if you’re not much of an illustrator at all, you might just find that the hands-off approach of vectors means you can draw in Inkscape even though you can’t draw with pen and paper. # ⚓ EasyOS:_All_downloads_now_to_/files_folder⠀⇛ As you can see in the photo in above link, there is /files, with sub-directories such as ‘downloads’, ‘media’, etc. Folder /files is no longer a symlink. Up to the current release of EasyOS, /files is a symlink to the actual /files folder at /mnt/wkg/ files, that is, on the working-partition. # ⚓ EasyOS:_File_/etc/fstab_is_now_empty⠀⇛ For a very long time I have considered this file to be deprecated. The time has now come to retire that file completely. # ⚓ Install_WebVirtCloud_KVM_Management_on_CentOS_8_–_Unixcop the_Unix_/_Linux_the_admins_deams⠀⇛ WebVirtCloud the (virtualization web interface for admins and users). So, WebVirtCloud is a virtualization web interface for admins and users.It can delegate Virtual Machine’s to users. A noVNC viewer presents a full graphical console to the guest domain. KVM is currently the only hypervisor supported. # ⚓ How_to_install_Python_pip_21_on_Ubuntu_21.10_– NextGenTips⠀⇛ Pip is a package management system written in Python and is used to install and manage software packages. It connects to an online repository of public packages called the Python Package Index. It can also be configured to connect to other package repositories. Usually, Pip is automatically installed while working in a virtual environment, and also if you are using Python that has not been modified by the redistributor to remove ensure pip. Pip is recommended tool for installing Python packages. For you to start using pip, you need to have python installed on your system. # ⚓ How_To_Install_Podman_on_AlmaLinux_8_–_idroot⠀⇛ In this tutorial, we will show you how to install Podman on AlmaLinux 8. For those of you who didn’t know, Podman is a daemon-less container engine for developing, managing, and running OCI Containers on your Linux System. Containers can either be run as root or in rootless mode. Podman provides a Docker- compatible command-line front end that can simply alias the Docker CLI. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the Podman container on an AlmaLinux 8. You can follow the same instructions for CentOS and Rocky Linux. # ⚓ How_to_mirror_your_Android_device_on_Linux,_macOS_and Windows_–_TechRepublic⠀⇛ Sometimes it’s nice when those devices can be consolidated. So, when I discovered a little tool called scrcpy, I was thrilled. Why? Because I could easily mirror my Android phone on my desktop and interact with it without having to always be picking up the device. Now, there are a couple of caveats to this. I can’t unlock my Pixel 6 phone from the desktop (because it requires a fingerprint). Nor can I take calls from the desktop. I can answer calls from the mirrored version of Android, but I have to immediately switch to speakerphone or pick up the device to actually speak to the caller. Unless said caller is spam … then I can just block ‘em from within the mirrored window (which I always do). o § Games⠀➾ # ⚓ Bridging_Game_Worlds_With_The_‘Impossible’_Pokémon_Trade_| Hackaday⠀⇛ Transferring hard-earned Pokémon out of the second generation GameBoy game worlds into the ‘Advance Era’ cartridges (and vice versa) has never been officially supported by Nintendo, however [Goppier] has made these illicit trades slightly easier for budding Pokémon trainers by way of a custom PCB and a healthy dose of reverse engineering. Changes to the data structure between Generation II on the original GameBoy (Pokémon Gold, Silver and Crystal) and Generation III on the GameBoy Advance (Pokémon Ruby, Sapphire, FireRed, LeafGreen and Emerald) meant that trades between these cartridges was never a possibility – at least not through any legitimate means. In contrast, Pokémon trades are possible between the first and second generation games, as well as from Generation III and beyond, leaving the leap from Gen II to Gen III as an obvious missing link. # ⚓ Punk_Wars,_Axis_&_Allies_1942_Online,_Melvor_Idle, Unpacking_…_–_itsfoss.net⠀⇛ One more to liven up the December bridge, and that is that there is nothing more entertaining to pass the time than to play a game and that is partly Linux Play, our premiere native games section for Linux with this, its monthly edition with the best that came out in November. Including construction and survival title and Punk wars, the classic war strategy of Axis & Allies 1942 Online, the RPG hardcore Melvor idle… And a lot more, without forgetting the free title with which we close the list and that this time transfers the television phenomenon of The Squid Game to PC controls under the name of Crab Game. Linux Play! # ⚓ NeuroNet:_Mendax_Proxy_gets_some_first_footage,_mixing elements_of_Your_Grace_&_Reigns_|_GamingOnLinux⠀⇛ NeuroNet: Mendax Proxy is an upcoming adventure that the developer claims blends together elements found in the likes of Your Grace, Reigns and Astrologaster into something new. Set to launch in 2022, NeuroNet sees you take control of an AI charged with managing a city called Catena. You will need to make quick-fire decisions that impact the future and the prosperity of its citizens, with every choice and decision taken having a lasting effect on those you meet and the city’s status. Lots of cyberpunk theming going on here with a new trailer giving a look into what to expect you can see below. # ⚓ The_Jackie_and_Daria_update_for_Spiritfarer_lands_December 13_|_GamingOnLinux⠀⇛ The biggest update yet for the award-winning Spiritfarer lands on December 13, with plenty of new content. Spiritfarer is a casual thoughtful experience about being a ferrymaster for the deceased. You build up a boat, explore and care for various spirits before letting them go. With the new update coming the developer said it is the biggest yet with a new island to explore, there’s two new spirits to make friends with and a hospital to bring back from the brink. On top of that there’s also some sort of new platforming event and new upgrades for your ferry. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Plasma_Mobile_Gear_21.12_Released_for_Linux_Phones with_ModemManager,_Improved_Apps⠀⇛ Packing three months worth of improvements since the Plasma Mobile Gear 21.08 update, Plasma Mobile Gear 21.12 is the first release of the software suite to switch its telephony stack from oFono to ModemManager. As you may know, ModemManager integrates with the NetworkManager network management daemon, which is currently being used by many popular GNU/Linux distributions for network connectivity of all sorts, including but not limited to Wi-Fi, wired and mobile connections, as well as for telephony functions. # § GNOME Desktop/GTK⠀➾ # ⚓ Enable_This_Cool_3D_Cube_Desktop_Effect_on_Ubuntu 21.10⠀⇛ Now the 3D cube effect is back thanks to Simon Schneegans (of GNOME Pie/Fly Pie fame). Much like the original Compiz cube it’s inspired by, this marvellous re-make isn’t masquerading under any pretence. The GitHub project description even states: “indulge in nostalgia with useless 3D effects”. Fancy giving it a go? This 3D Cube GNOME extension requires GNOME 40 or above. So to use the Desktop Cube GNOME extension on Ubuntu you need to be using Ubuntu 21.10 or later (or a Linux distribution with GNOME 40 or above). The add-on also requires the default horizontal workspace switcher to be present, so be sure to disable any workspace-altering extensions prior to this one. o § Distributions⠀➾ # § IBM/Red Hat/Fedora⠀➾ # ⚓ Fedora_36_Establishing_ELN-Extras,_Fedora_37_To Retire_ARMv7_–_Phoronix⠀⇛ he Fedora Engineering and Steering Committee (FESCo) has signed off on more feature work for the current Fedora 36 cycle as well as Fedora 37 due out toward the end of next year. Arguably most interesting from the latest batch of approved changes is Fedora 36 establishing ELN-Extras. ELN as “Enterprise Linux Next” continues going strong with the various Fedora / Red Hat / CentOS organizational changes. ELN-Extras now is a new build target similar to ELN but closer in function to Extra Packages for Enterprise Linux (EPEL). ELN-Extras will be the target for preparing and maintaining packages that are planned for EPEL N+1 while ELN is still targeting RHEL N+1. # ⚓ [Solved]_Error_rpmdb_damaged_header_in_Fedora,_RHEL_– OSTechNix⠀⇛ Today I tried to update all packages with sudo dnf –refresh upgrade command in my Fedora 35 desktop. During the package update, I encountered with this issue – error: rpmdb: damaged header #5904 retrieved — skipping. I kept getting this error a lot. I couldn’t update the Fedora system. After a couple web searches, I found that the RPM database is corrupted for some reason. If you ever stuck into a situation like mine, you can easily solve the “rpmdb damaged header” error by rebuilding the RPM database as shown in the following steps. # ⚓ Visualize_your_Apache_Kafka_Streams_using_the_Quarkus Dev_UI⠀⇛ This article shows how you can visualize Apache Kafka Streams with reactive applications using the Dev UI in Quarkus. Quarkus, a Java framework, provides an extension to utilize the Kafka Streams API and also lets you implement stream processing applications based directly on Kafka. # ⚓ Digital_transformation:_4_strategies_to_set_the_right goals⠀⇛ Digital transformation initiatives should be comprehensive and defined by a vision that leads organizations toward more efficient, data-driven, and goal-oriented performance. Digital transformation requires a clear end goal as well as detailed benchmarks to help lead teams in the right direction. The more specific and considered the goals and benchmarks, the more likely the organization is to see progress and ultimate success. As your organization establishes its digital transformation vision, the most important question may be whether it is goal-oriented or outcome-oriented. While a goal-based perspective considers the big picture and long-term priorities, focusing on outcomes will prioritize steady progress and finding opportunities for incremental improvement on existing processes. The outcomes of that progress – cost savings or reduced workload, for example – help to build buy-in and momentum for the broader transformation. Regardless of your overall approach, it’s important to use frequent, consistent measurements to ensure that work is moving forward. Regular measurement helps you identify your most successful efforts, which you can then replicate in other areas of the business. It’s also essential to not only review your goals regularly but also refine them. Benchmarks that made sense in January may no longer be ambitious enough after review in July. # ⚓ Automation_strategy:_6_key_elements⠀⇛ IT automation often occurs organically – a sysadmin writing Bash scripts to simplify redundant tasks in their day-to-day job, for example. This kind of incremental automation doesn’t preclude big-picture vision and planning, however. Automation strategies should be incremental. As recently noted by Red Hat technology evangelist Gordon Haff, incremental progress is part of the attraction. It’s in automation’s DNA. “This is automation through the lens of traditional system admins and even site reliability engineers in many cases,” Haff says. “Do something manually more than once and automate it so that you don’t have to, ever again.” This is a perfectly reasonable progression that can also be aligned with a higher-level strategy. # ⚓ Tech_careers:_Hiring_tips_for_candidates_and_leaders |_The_Enterprisers_Project⠀⇛ Tech careers are hotter than ever these days, but candidates still need to stand out in this competitive field. According to the Bureau of Labor Statistics, technology- related jobs will grow much faster than jobs in most other fields over the next decade. So, what does an ideal candidate look like at a startup or a large established corporation? # ⚓ AS400_–_Russell_Coker⠀⇛ The IBM i operating system on the AS/400 is a system that runs on PPC for “midrange” systems. I did a bit of reading about it after seeing an AS/400 on ebay for $300, if I had a lot more spare time and energy I might have put in a bid for that if it didn’t look like it had been left out in the rain. It seems that AS/400 is not dead, there are cloud services available, here’s one that provides a VM with 2GM of RAM for “only EUR 251 monthly” [1], wow. I’m not qualified to comment on whether that’s good value, but I think it’s worth noting that a Linux VM running an AMD64 CPU with similar storage and the same RAM can be expected to cost about $10 per month. # ⚓ Single_Node_OKD_(OpenShift)⠀⇛ Everytime I get to use Red Hat’s Open Shift I think to myself: “I should use OpenShift more”. It is a really great tool not just for high availability clusters but for general software development also. Its Web interface is super intuitive and nice to use, and you can provision all sorts of stuff in minutes. And everything is open source. Its really great. So naturally I decided to run it locally, especially after the news that starting from version 4.8 you can use it on single node architecture also. I decided to run it virtualized in libvirt so I can destroy it if I no longer needed. Hooray! # ⚓ Fedora_on_NVIDIA_Jetson_Xavier_–_nullr0ute’s_blog⠀⇛ The last two years or so I’ve been working with NVIDIA on general distro support including UEFI and ACPI for their Jetson Xavier platforms. Their Xavier platform, except a few quirks, are mostly SystemReady- ES compliant, so having a SBBR compliant firmware goes quite some way to having a widely available, relatively affordable, platform that “just works” for the arm ecosystem. I was very excited to finally have NVIDIA finally release the first version in March this year. This firmware is a standard UEFI firmware based on the open source TianoCore/EDK2 reference firmware, it allows booting in either ACPI or Device-Tree mode and supports all the basic things needed. The ACPI mode is not as fully featured as the Device-Tree mode as yet. In ACPI you get compute (cpu/memory/virt etc), PCIe, USB, network, which is just fine if you’re just looking for standard server or for testing a SystemReady system but there’s no display or accelerator support as yet. The Device-Tree mode is more feature full but both work pretty well with upstream kernels and NVIDIA are improving and upstreaming more things regularly. For flashing with the latest Fedora releases you’ll want the Linux for Tegra (L4T) R32.6.1 release and the latest UEFI firmware (1.1.2 ATM). The R32.6.1 release fixes issues with python3.9 and later so you’ll need that for Fedora. The following will extract everything into a directory called Linux_for_Tegra. Note the release for Xavier is different to the L4T for the TX1/TX2 series of devices such as the nano. # ⚓ An_introduction_to_Red_Hat_Insights_for_Red_Hat Ansible_Automation_Platform⠀⇛ Red Hat Ansible Automation Platform is a framework for building and operating IT automation at scale. The platform includes many of the tools you’ll need to implement automation across your organization, allowing you to simplify and centralize control of your infrastructure. Ansible Automation Platform includes a visual dashboard, role-based access control (RBAC) and automation tools, including Red Hat Insights for Red Hat Ansible Automation Platform. # ⚓ 20_years_of_Red_Hat_Product_Security:_The_rise_of branded_exploits_(Part_2)⠀⇛ In part 1 of this story we traced the history of Red Hat Product Security from its inception in 2001 through to its shift into the Customer Experience and Engagement (CEE) team in 2013. But that was just the beginning…security was always important, of course, but it was about to become front-page news. # ⚓ CentOS_Community_Newsletter:_December_2021⠀⇛ As we approach the end of 2021, I wanted to thank all of you who have worked so hard this year towards the betterment of the project. This year we’ve made governance more transparent, welcomed several new SIGs, made big strides in consolidating infrastructure with Fedora where it made sense, and begun to return to in-person events. We could not have done this without the passion and hard work of the project community. Thank you. # § Canonical/Ubuntu Family⠀➾ # ⚓ Pop!_OS_is_Moving_PPA_Repositories_to_its_Own_System: Is_System76_Considering_to_Switch_its_Ubuntu_Base?_– It’s_FOSS_News⠀⇛ Pop!_OS has been making news for some of its recent development decisions. For instance, they introduced a customized GNOME-based desktop environment experience with COSMIC. Moving forward, they decided to create their desktop environment from scratch based on Rust. Overall, Pop!_OS has been putting a lot of effort into providing a unique desktop experience keeping all the essential factors in mind like user-friendliness, resource efficiency, and security. Now, in a tweet, a Pop!_OS user noticed that System76 had replaced the PPA repositories with its self-hosted APT system in Pop!_OS 21.10 beta, instead of Canonical’s launchpad. And, to that, System76’s Principal Engineer, Jeremy Soller, responded with a confirmation sharing more details. # ⚓ Freespire_8.0_Comes_Tightly_Integrated_with_Google Services⠀⇛ The developers behind Freespire 8.0 have decided to put strong focus and take full advantage on Google’s services with this release. For those of you unfamiliar with what Freespire is, let’s start with some history. Freespire started off under the name Lindows twenty years ago as an easy-to-use Linux- based operating system with great Wine integration and easy application support, but then changed to Linspire following a Microsoft lawsuit. Nowadays, Freespire is a desktop oriented Ubuntu-based Linux distro powered by Xfce. It’s the open source equivalent of Linspire, but containing mostly FOSS components. Freespire is sponsored by Linspire, a commercial, desktop-oriented Linux distrio based on Debian and Ubuntu and owned by PC/ OpenSystems LLC. A couple of days ago the Freespire development team announced the release of Freespire 8.0, so let’s take a brief look at it. o § Devices/Embedded⠀➾ # § Open Hardware/Modding⠀➾ # ⚓ Retro_Reproduction_Captures_The_Style_Of_The_Sol-20_| Hackaday⠀⇛ In the early years of the computer revolution, a machine like the Sol-20 really stood out. Where most hobbyist machines had front panels that bristled with toggle switches and LEDs, the Sol-20 was a sleek, all-in-one that looked like an electric typewriter in a walnut-trimmed box. Unfortunately, it was also quite expensive, so not that many were sold. This makes them hard enough to find 40 years later that building his own reproduction Sol-20 is about the only way for [Michael Gardi] to have one of his own. # ⚓ Imagination_Catapults_into_RISC-V⠀⇛ Imagination unveiled four RISC-V-based “Catapult” CPU cores: two 32-bit MCU cores and two 64-bit designs that run Linux, including an automotive functional safety core. The big news on the first day of the RISC- V Summit in San Francisco was the announcement from Imagination Technologies that it was launching four RISC-V core designs under a Catapult brand. This summer, Imagination revealed it was building RISC- V CPU cores, and it has now announced four Catapult CPU designs. The in-order cores include two 32-bit MCU- like cores and two 64-bit models that run Linux. The UK-based company refers to the four core categories as “dynamic microcontrollers; real-time embedded CPUs; high-performance application CPUs; and functionally safe automotive CPUs.” # ⚓ Adding_Optical_Audio_to_the_Raspberry_Pi_with_One Chip⠀⇛ In the home theater space most people would tell you the age of optical audio, known officially as TOSLINK, is over. While at one time they were the standard for surround sound systems, the fiber cables with their glowing red tips have now been largely supplanted by the all-in-one capabilities of HDMI on new TVs and audio receivers. But of course, that doesn’t mean all that TOSLINK- compatible hardware that’s in the field simply disappears. If you’re looking to connect a Raspberry Pi to the optical port of your AV system, [Nick Sayer] has you covered. His “TOSLINK Transceiver Hat” utilizes a WM8804 chip from Cirrus Logic to go from the Pi’s I2S audio output to S/PDIF. From there the signal goes directly into the TOSLINK input and output modules, which have the appropriate fiber optic hardware and drivers built-in. All you have to do from a software standpoint is enable a boot overlay intended for a digital- to-analog converter (DAC) from HiFiBerry. # ⚓ Guitar_Pickguard_Adds_MIDI_Capabilities⠀⇛ For a standard that has been in use since the 1980s, MIDI is still one of the most dominant forces on the musical scene even today. It’s fast, flexible, and offers a standard recognized industry-wide over many different types of electronic instruments. Even things which aren’t instruments can be turned into musical devices like the infamous banana keyboard via the magic of MIDI, and it also allows augmentation of standard instruments with other capabilities like this guitar with a MIDI interface built into the pick guard. [Ezra] is the creator of this unique musical instrument which adds quite a few capabilities to his guitar. The setup is fairly straightforward: twelve wires run to the pick guard which are set up as capacitive sensors and correspond with a note on the chromatic scale. Instead of using touchpads, using wires allows him to bend away the “notes” that he doesn’t need for any particular piece of music. The wires are tied back to an Adafruit Feather 32u4 microcontroller behind the neck of the guitar which also has a few selectors for changing the way that the device creates tones. He can set the interface to emit single notes or continuously play notes, change the style, can change their octave, and plenty of other features as well. o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ Firefox_96_Enters_Public_Beta_Testing_with_More Performance_and_Security_Improvements⠀⇛ Firefox 96 isn’t a major update, but it’s the first release of the open- source web browser in 2022 and it introduces several performance and security improvements to make your browsing experience more enjoyable, more reliable, and much safer. For example, the upcoming Firefox release significantly reduces the main thread load, significantly improves noise-suppression and auto-gain- control, slightly improves echo- cancellation, and enforces the Cookie Policy: Same-Site=lax option by default to protect users against Cross-Site Request Forgery (CSRF) attacks. # ⚓ Firefox_95_Released!_Available_in_Microsoft Store_&_New_Sanboxing_Technology⠀⇛ # ⚓ Firefox_95.0,_See_All_New_Features,_Updates_and Fixes⠀⇛ RLBox — a new technology that hardens Firefox against potential security vulnerabilities in third-party libraries — is now enabled on all platforms. We’ve reduced CPU usage on macOS in Firefox and WindowServer during event processing. You can now move the Picture-in-Picture toggle button to the opposite side of the video. Simply look for the new context menu option Move Picture-in- Picture Toggle to Left (Right) Side. # ⚓ Firefox_95.0_and_Firefox_ESR_91.4.0⠀⇛ Firefox 95.0 is now available. With this version the RLBox sandboxing technology is enabled on all platforms, as is the Site Isolation security architecture, which protects against side-channel attacks. # ⚓ Firefox_ESR_91.4.0⠀⇛ # § SaaS/Back End/Databases⠀➾ # ⚓ MySQL_a_‘pretty_poor_database’_says_departing_Oracle engineer⠀⇛ You’ve collected your leaving card, novelty presents, and perhaps a bottle of wine – what’s next on the list for the departing developer? For one, it’s a blog rubbishing the technology he’s been working on for five years. That was the choice of Steinar Gunderson, a former principal software engineer at Oracle and member of the MySQL optimiser team. In an online missive, the engineer, who has now taken up a role in Google’s Chrome team, left no reader in doubt of his views on MySQL. With the caveat that his reasons for leaving were complex, he went on to say: “MySQL is a pretty poor database, and you should strongly consider using Postgres instead. “Coming to MySQL was like stepping into a parallel universe, where there were lots of people genuinely believing that MySQL was a state-of-the-art product.” # ⚓ PostgreSQL:_MySQL-to-PostgreSQL_v5.5_has_been released⠀⇛ New version of MySQL-to-PostgreSQL, a program to migrate MySQL, MariaDB or Percona databases to PostgreSQL, has been released. # ⚓ PostgreSQL:_check_pgbackrest_2.2_has_been_released⠀⇛ check_pgbackrest is designed to monitor pgBackRest backups from Nagios, relying on the status information given by the info command. It allows to monitor the backups retention and the consistency of the archived WAL segments. # ⚓ Learn_more_about_distributed_databases_with ShardingSphere⠀⇛ Apache ShardingSphere is an open source distributed database, plus an ecosystem users and developers need for their database to provide a customized and cloud-native experience. In the three years since it joined the Apache Foundation, the ShardingSphere core team has worked hard with the community to create an open source, robust, and distributed database and a supporting ecosystem. ShardingSphere doesn’t quite fit into the usual industry mold of a simple distributed database middleware solution. ShardingSphere recreates the distributed pluggable system, enabling actual user implementation scenarios to thrive and contributing valuable solutions to the community and the database industry. # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ Winners_in_the_Month_of_LibreOffice,_November_2021!⠀⇛ At the start of November, we revved up a new Month of LibreOffice, celebrating community contributions all across the project. We do these every six months – so how many people got sticker packs this time? Check it out… # § Programming/Development⠀➾ # ⚓ Rblpapi_0.3.12:_Fixes_and_Updates⠀⇛ The Rblp team is happy to announce a new version 0.3.12 of Rblpapi which just arrived at CRAN. Rblpapi provides a direct interface between R and the Bloomberg Terminal via the C++ API provided by Bloomberg (but note that a valid Bloomberg license and installation is required). This is the twelveth release since the package first appeared on CRAN in 2016. Changes are detailed below and include both extensions to functionality, actual bug fixes and changes to the package setup. Special thanks goes to Michael Kerber, Yihui Xie and Kai Lin for contributing pull requests! # ⚓ LLVM_Now_Has_“Official”_Support_For_Targeting_NEC’s Vector_Engine_(VE)_–_Phoronix⠀⇛ The LLVM compiler infrastructure supports not only a growing number of CPU architectures but continues to lead when it comes to its support for different accelerators. Back in 2019 NEC was working to upstream their SX- Aurora VE “Vector Engine” Accelerator and now as of this week that target is considered officially supported upstream. NEC originally launched the SX-Aurora Vector Engine (VE) back in 2018 as a PCI Express accelerator card and supporting up to eight vector processors per server. The NEC SX- Aurora has its own architecture for the “VE” and is backed by HBM2 memory. The current VE processor is rated for 1.53 TB/s of memory bandwidth and a double precision peak performance of 3.07 TFLOPS or 4.91 single precision TFLOPS. # ⚓ 5_Excellent_Free_Books_to_Learn_CSS_–_LinuxLinks⠀⇛ Web pages are built with HTML, which specifies the content of a page. CSS (Cascading Style Sheets) is a separate language which specifies a page’s appearance. CSS code is made of static rules. Each rule takes one or more selectors and gives specific values to a number of visual properties. Those properties are then applied to the page elements indicated by the selectors. Here’s our recommended books to learn CSS. # § Perl/Raku⠀➾ # ⚓ Day_7:_Neural_Nets_in_Raku_(Part_1)_–_Raku Advent_Calendar⠀⇛ Thinky the Elf was sitting in his office, it had been a closet but he’d been given it as his office after the great baked beans incident. It wasn’t his fault. He was right that feeding the reindeer beans would give them a jet boost but Santa had not been all that happy about it. And his tendency to stare of into space while suddenly having a thought wasn’t great while working on the shop floor meant it was safer to put him out of the way to do some thinking. Recently he’d been thinking about how to sort children into naughty or nice. This was Santa’s big job all year and Thinky thought that there must be a way to simplify it, he’d spent some time watching videos on YouTube and there was one that gave a brilliant description of Neural Networks (jump to 20 minutes for that bit but it’s an interesting video). As Thinky watched this he couldn’t help thinking about Raku and how the connections between nodes felt like Supplies. * § Leftovers⠀➾ o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Pseudo-Open Source⠀➾ # § Openwashing⠀➾ # ⚓ AWS_DocumentDB_not_MongoDB-compatible, says_MongoDB_Inc⠀⇛ # § Privatisation/Privateering⠀➾ # § Linux Foundation⠀➾ # ⚓ Linux_Foundation_Expects_Revenues Of_$177_Million_This_Year⠀⇛ Once again they are facing some criticism for the Linux Foundation’s annual report being made on macOS using Adobe software products. They’ve done that in the past and in public settings pre-pandemic it hasn’t been uncommon to find Linux Foundation directors and other stakeholders running Apple MacBook products with macOS. # ⚓ Daniel_Lange:_Gradual_improvements at_the_Linux_Foundation⠀⇛ After last year’s blunder with trying to hide the Adobe toolchain and using hilarious stock photos, the Linux Foundation did much better in their 2021 annual report published Dec. 6, 2021. # ⚓ A_2021_Linux_Foundation_Update_from the‭_‬Executive_Director_–_Linux Foundation⠀⇛ In 2021 the Linux Foundation (“LF”) emerged from the worst pandemic in a century and embraced new horizons. The collaborative activities in our project communities weathered the COVID-19 crisis exceptionally well, and many communities are now pushing forward with a renewed sense of purpose. # ⚓ The_Cyber-Investigation_Analysis Standard_Expression_Transitions_to Linux_Foundation_–_Linux_Foundation⠀⇛ The Linux Foundation, the nonprofit organization enabling mass innovation through open source, today announced the Cyber- investigation Analysis Standard Expression (CASE) is becoming a community project as part of the ​​Cyber Domain Ontology (CDO) project under the Linux Foundation. CASE is an ontology-based specification that supports automated combination and intelligent analysis of cyber-investigation information. CASE concentrates on advancing interoperability and analytics across a broad range of cyber- investigation domains, including digital forensics and incident response (DFIR). # ⚓ The_Cyber-Investigation_Analysis Standard_Expression_Transitions_to Linux_Foundation⠀⇛ # § Security⠀➾ # ⚓ A_mysterious_threat_actor_is_running_hundreds of_malicious_Tor_relays⠀⇛ Since at least 2017, a mysterious threat actor has run thousands of malicious servers in entry, middle, and exit positions of the Tor network in what a security researcher has described as an attempt to deanonymize Tor users. Tracked as KAX17, the threat actor ran at its peak more than 900 malicious servers part of the Tor network, which typically tends to hover around a daily total of up to 9,000-10,000. Some of these servers work as entry points (guards), others as middle relays, and others as exit points from the Tor network. Their role is to encrypt and anonymize user traffic as it enters and leaves the Tor network, creating a giant mesh of proxy servers that bounce connections between each other and provide the much-needed privacy that Tor users come for. Servers added to the Tor network typically must have contact information included in their setup, such as an email address, so Tor network administrators and law enforcement can contact server operators in the case of a misconfiguration or file an abuse report. # ⚓ Someone_Is_Running_Lots_of_Tor_Relays⠀⇛ Since 2017, someone is running about a thousand — 10% of the total — Tor servers in an attempt to deanonymize the network… # ⚓ Security_updates_for_Tuesday_[LWN.net]⠀⇛ Security updates have been issued by CentOS (nss), Debian (roundcube and runc), openSUSE (aaa_base, brotli, clamav, glib-networking, gmp, go1.16, hiredis, kernel, mozilla-nss, nodejs12, nodejs14, openexr, openssh, php7, python-Babel, ruby2.5, speex, wireshark, and xen), Oracle (kernel and nss), Red Hat (kpatch-patch, nss, rpm, and thunderbird), SUSE (brotli, clamav, glib-networking, gmp, kernel, mariadb, mozilla-nss, nodejs12, nodejs14, openssh, php7, python-Babel, and wireshark), and Ubuntu (busybox, mariadb-10.3, mariadb-10.5, python- django, and samba). # ⚓ Hitachi_Energy_RTU500_OpenLDAP_|_CISA⠀⇛ All information products included in https://us-cert.cisa.gov/ics are provided “as is” for informational purposes only. The Department of Homeland Security (DHS) does not provide any warranties of any kind regarding any information contained within. DHS does not endorse any commercial product or service, referenced in this product or otherwise. Further dissemination of this product is governed by the Traffic Light Protocol (TLP) marking in the header. For more information about TLP, see https://us-cert.cisa.gov/tlp/. # ⚓ Hitachi_Energy_XMC20_and_FOX61x_|_CISA⠀⇛ All information products included in https://us-cert.cisa.gov/ics are provided “as is” for informational purposes only. The Department of Homeland Security (DHS) does not provide any warranties of any kind regarding any information contained within. DHS does not endorse any commercial product or service, referenced in this product or otherwise. Further dissemination of this product is governed by the Traffic Light Protocol (TLP) marking in the header. For more information about TLP, see https://us-cert.cisa.gov/tlp/. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Digital_Transparency:_A_Right_to_Information_Report_for November_2021⠀⇛ Since our last report for the month of November, IFF has filed 37 RTI requests and 1 first appeal. Here, we give you an overview of the requests filed and an analysis of the responses we have received from the different public authorities. This report highlights why demanding transparency and accountability from Government authorities is one of the key elements in our fight to protect digital rights. [...] The Right to Information (RTI) Act is thus one of the most important tools at the disposal of the public to engage with, and demand transparency and accountability from, the Government. We use the Act to routinely extract information about various ongoing policies and projects that the Government launches. In the month of November, we have filed 37 RTI requests and 1 First Appeal electronically with authorities at the Central level as well as through speed posts with relevant authorities at the States’ levels, concerning the various issues on which we engage with the Government. Note: The number of RTI requests are calculated from the date of the previous report. While we try to make this a monthly report, some RTI requests from the previous month that were filed after that month’s report may be included in the present report. o § Digital Restrictions (DRM)⠀➾ # ⚓ Cracking_the_Spotify_Code⠀⇛ Spotify offers a little picture that, when scanned, opens almost anything searchable with Spotify. Several lines are centered on the Spotify logo with eight different heights, storing information in octal. Many visual encoding schemes encode some URI (Uniform Resource Identifier) that provides a unique identifier for that specific song, album, or artist when decoded. Since many URIs on Spotify are pretty long (one example being spotify :show: 3NRV0mhZa8xeRT0EyLPaIp which clocks in at 218 bits), some mechanism is needed to compress the URIs down to something more manageable. Enter the media reference, a short sequence encoding a specific URI, generally under 40 bits. The reference is just a lookup in a database that Spotify maintains, so it requires a network connection to resolve. The actual encoding scheme from media reference to the values in the bars is quite complex involving CRC, convolution, and puncturing. The CRC allows the program to check for correct decoding, and the convolution enables the program to have a small number of read errors while still having an accurate result. Puncturing is just removing bits to reduce the numbers encoded, relying on convolution to fill in the holes. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ All_Sound_Recordings_Prior_to_1923_Will_Enter_the_US Public_Domain_in_2022_–_The_Public_Domain_Review⠀⇛ Thanks to the Music Modernization Act passed by US Congress in 2018, all sound recordings prior to 1923 will have their copyrights expire in the US on January 1st. ䷩ 𝚕𝚒𝚗𝚎 5997 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.07.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_7/12/2021:_Plasma_Mobile_Gear_21.12_and_Tails_4.25⠀✐ Posted in News_Roundup at 9:57 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ The_9_Best_Linux_Distros_for_Windows_Users⠀⇛ Linux can be hard to adapt to for first-time users, but only if you install the wrong distro. Here are the best Linux distros for Windows users. Windows has evolved over the years, and there is no denying how Windows users are spoilt for options. Multiple OS versions rolled out at regular intervals, making it one of the best operating systems in the market. Nevertheless, people are on the lookout for open- source options for their systems. Windows, being a closed-source OS, is not suitable for every computer user out there. Alternatively, Linux is an open-source operating system, and this Linux distro list is ideal if you are looking to switch from Windows to Linux. o § Kernel Space⠀➾ # ⚓ ADI_grows_Linux_device-driver_lineup⠀⇛ Analog Devices (ADI) expands it Linux distribution with over 1000 in-kernel drivers for devices from both ADI and Maxim Integrated Products. These open- source drivers streamline the software development process by providing access to tested code and preventing hardware lock-in. # § Graphics Stack⠀➾ # ⚓ Nvidia_card_in_eGPU_and_NixOS⠀⇛ Nvidia made work in their proprietary driver to allow a program to have its OpenGL/Vulkan calls to be done in a GPU that is not the one used for the display. This allows to throw optirun/primerun for this use case, which is good because they added performance penalty, complicated setup and many problems. o § Instructionals/Technical⠀➾ # ⚓ Simple_Raspberry_Pi_powered_SMS_Gateway:_make_your_projects send_SMS_with_a_simple_REST_API⠀⇛ TL;DR Install gammu-smsd, get the API code from github and you’ll be able to send and receive SMS via API. # ⚓ Use_dmseg_to_check_your_Linux_system’s_kernel_message buffer_|_Network_World⠀⇛ The dmesg command displays the content of the kernel’s message buffer since the system’s most recent boot. It displays a lot of details on how the system is working and problems it might be running into that you won’t normally see. That can be a lot of data, but there are several tricks for paring it down. For example, Even though the system queried below has only been up a little more than three days, it’s collected more than a thousand lines of data. # ⚓ Working_with_gnome-boxes_–_Unixcop_the_Unix_/_Linux_the admins_deams⠀⇛ In my PC I’ve worked with Virtual box for years. Then virtual box, for some reason, was removed from the Debian repository. As I wasn’t using those VMs for something critical I’ve just didn’t bother to find out why or to search some alternate repo. Few months ago I need some virtual machines on my PC, so I began working with gnome-boxes. # ⚓ How_To_Install_Terminalizer_on_Ubuntu_20.04_LTS_–_idroot⠀⇛ In this tutorial, we will show you how to install Terminalizer on Ubuntu 20.04 LTS. For those of you who didn’t know, Terminalizer is a very useful terminal recording tool designed for different distributions of the Linux operating system. Terminalizer works in the same way as a desktop screen recorder but instead runs in your terminal. It has the capability to record all the activities that you perform on the Linux terminal and then save them in the form of an animated GIF. 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 Terminalizer on Ubuntu 20.04 (Focal Fossa). You can follow the same instructions for Ubuntu 18.04, 16.04, and any other Debian-based distribution like Linux Mint. # ⚓ How_To_Install_Yunohost_on_Debian_10_Buster_Made_Simple⠀⇛ This tutoriall will explain how one can install Yunohost based on Debian 10 with examples in step by step. This tutorial is practiced locally in a virtual machine and you can practice later on a real computer once you understood how to play it. Now let’s start practicing! # ⚓ How_to_Change_User_Passwords_in_Linux_–_ByteXD⠀⇛ In this tutorial we’ll explain how to change user passwords in Linux using the passwd command, from the command-line. We’ll show you how to change your current user’s password, as well as changing, expiring, or locking passwords for other users. These commands should work on any Linux distribution, such as Ubuntu, Debian, Linux Mint, CentOS, Rocky Linux, etc. # ⚓ How_to_Install_Telegraf_Configure_InfluxDB2_output_in Debian_11⠀⇛ In this guide we are going to learn how to install Telegraf and configure InfluxDB v2 output on a Debian 11. Telegraf is a plugin-driven server agent for collecting & reporting metrics, and is the first piece of the TICK stack. Telegraf has plugins to source a variety of metrics directly from the system it’s running on, pull metrics from third- party APIs, or even listen for metrics via a statsd and Kafka consumer services. It also has output plugins to send metrics to a variety of other datastores, services, and message queues, including InfluxDB, Graphite, OpenTSDB, Datadog, Librato, Kafka, MQTT, NSQ, and many others. # ⚓ How_to_Install_and_Configure_InfluxDB2_in_Debian_11⠀⇛ InfluxDB is the database in which we will store the metrics sent from the agent. This database is designed to withstand high write and read loads. InfluxDB is an open source time series database. It has everything you need from a time series platform in a single binary – a multi-tenanted time series database, UI and dashboarding tools, background processing and monitoring agent. All this makes deployment and setup a breeze and easier to secure. The InfluxDB Platform also includes APIs, tools, and an ecosystem that includes 10 client and server libraries, Telegraf plugins, visualization integrations with Grafana, Google Data Studio, and data sources integrations with Google Bigtable, BigQuery, and more. # ⚓ How_to_Install_and_Use_Ping_Command_in_Linux⠀⇛ PING is undoubtedly a millennial word. It’s rooted in quotidian life and henceforth has become a concept to be unveiled. Many of us might be known of the fact that the word ‘ping‘ is not actually a word but an acronym. PING stands for Packet Internet Groper. The meaning says it all. Pinging is a notion to observe the connectivity between two systems, to check whether the remote system is online. Technically, the word ping lies in the domain of network communication. It deals with the notion of transferring and accepting the packets from source to destination system. # ⚓ How_to_install_system_updates_using_Webmin_–_Unixcop_the Unix_/_Linux_the_admins_deams⠀⇛ Hello, friends. We continue with Webmin and now we will explain very briefly how to install system updates using Webmin. This post is part of our series dedicated to this tremendous application. # ⚓ How_to_use_monitoring_to_troubleshoot_Ansible_Automation Platform_|_Enable_Sysadmin⠀⇛ Running an Ansible automation controller in OpenShift provides an easy way to scale an Ansible automation controller. However, as with any virtualization platform, you need to enable the Ansible automation controller to run as efficiently as possible. Often, OpenShift runs on top of another virtualization platform, and understanding how resources are used at the various virtualization levels is essential. Overcommitting CPU and memory resources in your virtualization platform can impact OpenShift performance. Therefore, it is important to have a 1:1 commit ratio for CPU and memory in your virtualization platform and let OpenShift manage resource overcommitment. In addition to looking at CPU and memory overcommitment, you need to understand what other pods are running on the OpenShift instances in order to prevent resource conflicts. Proper management of OpenShift guarantees the availability of the Ansible automation controller and other applications running in the OpenShift environment. Quotas on namespaces set the maximum amount of CPU and memory resources a project can consume, limiting the impact one project can have on other projects. In addition, the request and limit settings for the task container set the CPU and memory resources the Ansible automation controller has for running jobs. By default, the Ansible automation controller installer sets the CPU request to 1,500 millicores and the memory request to 2GBs. You can use the task_cpu_request and task_mem_request variables to set request sizes for the task container in the Ansible automation controller installer inventory. These settings directly impact the number of forks an Ansible automation controller instance has available for running jobs. # ⚓ What_Is_’Sudo’_In_Linux?⠀⇛ If you’re new to Linux, you might have seen the word “sudo” being thrown in Linux commands, and you may be wondering what it does. In this article, let’s look at Sudo in Linux, what it means, and how to use it to get specific work done. The word Sudo stands for “Superuser Do” and is pronounced as “Sue Dough.” By using sudo in command in the terminal, you ask your computer to run commands with root privileges. Now, if you ask, “But why do I need superuser permission when I’m already the superuser.” That’s a good question. You’ll need superuser permissions to get that stuff done, which the average user wouldn’t know about. # ⚓ What_is_a_Cron_Job_in_Linux?_How_to_Use_it?⠀⇛ Cron is a command line utility to run small and quick commands on a scheduled basis. This is a handy, classic sysadmin tool for automating various tasks by combining it with othe tools. For example, some people combine rsync and cron to automatically create a daily or weekly backup at a certain time. Some people use it to analyze server logs and combine it with mail function to send an email if there is certain kind of error detected in the logs. Cron is like the Swiss army knife. It can be used for a variety of use cases. It’s really up to your imagination on what to use it for. Getting started with cron is super easy, and only takes a matter of seconds to get started. But before I show you that, I’ll discuss something else that often confuses Linux users. o § Games⠀➾ # ⚓ My_Major_Is_Gaming…_|_Hackaday⠀⇛ Times have changed. You can now take a university class in writing games. In fact, YOU can now take a university class about writing games because [Dave Churchill] of Memorial University has put all 22 of his lectures up for your enjoyment. [Dr. Churchill] isn’t planning on releasing the assignment files, but you can still get a lot from watching the videos. Apparently, the classes were also live streamed on Twitch. The games build on SFML so the resulting games can be portable. The library abstracts input, graphics, sound, and networking. # ⚓ RetroArch_1.9.14_out,_with_more_emulator_cores_landing_on Steam_|_GamingOnLinux⠀⇛ The RetroArch team have released RetroArch 1.9.14, and recently they’ve been expanding what emulator cores are available on the Steam version with 26 now available. Cores are what RetroArch runs to do pretty much anything. They can be emulators, entire games and more. # ⚓ Survival-horror_deck-builder_Draft_of_Darkness_adds_gamepad support_ready_for_Steam_Deck_|_GamingOnLinux⠀⇛ The Steam Deck will be a great device for many things, and one genre we’re excited to play on the go (or in bed) are deck-builders and it sounds like Draft of Darkness will be a lot easier to play now. “Draft of Darkness is a survival horror deck builder with roguelike dungeon exploration. Recruit allies, synergize their decks to create powerful card combos, manage your resources, explore procedurally generated maps and determine the outcome of the story.” # ⚓ 7_Days_to_Die_gets_Alpha_20_out_in_Experimental,_lots_of shiny_new_additions_|_GamingOnLinux⠀⇛ 8 years of Early Access and 7 Days to Die shows no signs of slowing down on the major upgrades, with Alpha 20 Experimental out now on Steam. It’s opt- in, so you need to select it from the Beta menu for the game on Steam, and once it’s stable enough it will be out for everyone. This version is another huge change for the game with lots of new character / enemy models that look and perform better, along with some massive world- building upgrades to the whole experience. # ⚓ Decentraland_is_the_latest_to_help_fund_Blender_development |_GamingOnLinux⠀⇛ Decentraland joins a long list of companies and individuals helping to fund Blender, the excellent free and open source 3D creation suite that just recently released the big 3.0 version. Becoming a Patron member for at least two years, Decentraland will be providing at least €120,000 to Blender per year along side NVIDIA, Epic Games, AWS, Facebook, Unity and AMD. # ⚓ New_Patron_member:_Decentraland⠀⇛ Decentraland is the first fully decentralized virtual world. Its vision is to hand over control to the people who create and play in this virtual space. The DAO (“Decentralized Autonomous Organization”) behind Decentraland decided in a recent community town hall meeting to join the Blender Development Fund for a period of two years, as Patron Member. # ⚓ The_amusing_Rain_on_Your_Parade_to_get_a_DLC_on_December_15 |_GamingOnLinux⠀⇛ Rain on Your Parade is a little gem that released back in April, a game where you fly around as a little cloud and mess things up for everyone and now it’s set for an expansion. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Top_10_Linux_Distributions_for_KDE_Plasma_ [Compared]⠀⇛ Planning to adapt a stable KDE Plasma based desktop in Linux and thinking about as a daily driver? Well, here we present top 10 Linux distributions that are better integrated with KDE Plasma. # ⚓ Plasma_Mobile_Gear_21.12_is_Out⠀⇛ The Plasma Mobile team is happy to introduce the Plasma Mobile updates for September to December 2021 Since its inception, Plasma Mobile has used the oFono stack for telephony functions (mobile data, calling, SMS), but with this Plasma and Gear release, we are transitioning our telephony stack to ModemManager. oFono is a Nokia/Intel project started in 2009 with the Nokia N900. It integrates with the higher-level ConnMan connection manager, and is currently used by projects like Ubuntu Touch and Sailfish, which maintain their own series of patches on top of the stack in order for it to work for their use cases. ModemManager is a FreeDesktop project started in 2008 with the goal of providing USB dongle support for desktops. It integrates with the higher-level NetworkManager network management daemon. It is currently used on Plasma Desktop and the GNOME desktop to provide support for USB modems, as well as on Phosh for telephony functions. o § Distributions⠀➾ # ⚓ SteamOS-like_Linux_distribution_ChimeraOS_28_is_out_now_| GamingOnLinux⠀⇛ ChimeraOS is a Linux distribution aimed at gamers who primarily want a more console-like big-screen experience. A new release with ChimeraOS 28 is now available. With this fresh upgrade it comes with some freshened up internals like Linux Kernel 5.15.5, Mesa 21.2.5, NVIDIA 495.44, RetroArch 1.9.13 and updates to their own built-in apps and tooling. Additionally there’s now improved support for Xbox controllers connected via Bluetooth, an issue with the chimera app server crashing under certain conditions when loading MangoHud configuration files was solved and they also fixed an issue with the system updater which could result in an unbootable system under certain conditions. # ⚓ My_VR_Hell_on_NixOS⠀⇛ Recently I got a new VR setup that uses my tower directly instead of the wifi streaming catastrophe. I have a Valve Index and an AMD RX6700XT GPU. Some huge advantages of this setup include: [...] # § BSD⠀➾ # ⚓ Using_awk_to_pretty-display_OpenBSD_packages_update changes⠀⇛ You use OpenBSD and when you upgrade your packages you often wonder which one is a rebuild and which one is a real version update? The packages updates are logged in / var/log/messages and using awk it’s easy to achieve some kind of report. # ⚓ Supporting_a_new_C_compiler_for_oksh_and_review_of the_vbcc_C_compiler⠀⇛ Today, I added support for the vbcc compiler to oksh, my portable version of the in-base OpenBSD Korn shell. I will discuss how I got vbcc running on OpenBSD, how I got oksh building and working with vbcc, and my overall review of using the vbcc compiler. # ⚓ Battery_status_in_tmux_status_bar_in_FreeBSD⠀⇛ I don’t need much information to be shown in the status bar. When the charger is connected, I want to know how far the charging is. When on battery, I want to know what the remaining battery time is. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Fedora_on_NVIDIA_Jetson_Xavier⠀⇛ The last two years or so I’ve been working with NVIDIA on general distro support including UEFI and ACPI for their Jetson Xavier platforms. Their Xavier platform, except a few quirks, are mostly SystemReady- ES compliant, so having a SBBR compliant firmware goes quite some way to having a widely available, relatively affordable, platform that “just works” for the arm ecosystem. I was very excited to finally have NVIDIA finally release the first version in March this year. This firmware is a standard UEFI firmware based on the open source TianoCore/EDK2 reference firmware, it allows booting in either ACPI or Device-Tree mode and supports all the basic things needed. The ACPI mode is not as fully featured as the Device-Tree mode as yet. In ACPI you get compute (cpu/memory/virt etc), PCIe, USB, network, which is just fine if you’re just looking for standard server or for testing a SystemReady system but there’s no display or accelerator support as yet. The Device-Tree mode is more feature full but both work pretty well with upstream kernels and NVIDIA are improving and upstreaming more things regularly. # § Debian Family⠀➾ # ⚓ Tails_4.25_Anonymous_Linux_OS_Released_with_New Backup_Tool_for_Persistent_Storage⠀⇛ The monthly Tails releases continue, and Tails 4.25 is here to introduce a brand-new and simple backup utility to help users backup their Persistent Storage from the USB flash drive where they run Tails to another Tails USB stick. Contributed by David A. Wheeler, the new backup tool offers a graphical interface and automates the process described in the official Tails documentation on how to make a backup of your Persistent Storage via the command line. You can find it under System Tools > Back Up Persistent Storage. # § Canonical/Ubuntu Family⠀➾ # ⚓ Linux_Mint’s_(Ace)_Sticky_Notes_App_Works_Great_on Ubuntu⠀⇛ I used to use real post-it notes in real life. A ton of them. I’d use them remind me to buy cat food, put the bins out, and unclog the sink. But most of my sticky notes ended up face down on my desk, dog eared and ignored (or, on more than one occasion stuck to the back of the cat). These days I keep on top of my to-do list using desktop (and mobile) apps. The latest version of Linux Mint comes with a standout one preinstalled called Sticky. # ⚓ Ubuntu-based_Freespire_8.0_Linux_distribution_focuses heavily_on_Google_services⠀⇛ Guess what, folks? Freespire 8.0 is available to download immediately. This version of the Ubuntu-based operating system utilizes Linux kernel 5.4.0-91 LTS while using Xfce 4.16 as its desktop environment. This no-nonsense distribution is fairly lightweight and easy to use, making it a good choice for Linux newbies; particularly with aging (not obsolete) hardware. Surprisingly, the developers have decided to focus heavily on Google with this release. This includes the search giant’s services (Translate, News, etc.) and the Chrome browser. Apparently, this new focus is a result of reading user feedback. While this may scare some privacy-zealots away, it should make the operating system more appealing to the average home computer user. Let’s be honest, shall we? Google services are rather essential for many people. o § Devices/Embedded⠀➾ # ⚓ Jetson_carrier_can_stream_four_Flir_USB3_cameras⠀⇛ The 138 x 92 x 18.2mm Quartet TX2 runs Arch Linux and is available with the cross-platform Flir Spinnaker SDK. Applications include robotics, metrology, ADAS, and 3D scanning. # ⚓ Teledyne_FLIR_Quartet_Jetson_TX2_carrier_board_supports_up to_four_USB_3.0_cameras⠀⇛ There are already plenty of NVIDIA Jetson-based camera solutions from carrier boards to IP67 rugged cameras, but Teledyne FLIR has decided to launch its own with the Quartet carrier board for the Jetson TX2 module. The Quarter board is not designed to work with the thermal cameras the company is known for, but instead FLIR Blackfly S USB3 cameras designed for machine vision. Besides four TF38 USB 3.0 connectors, the carrier board also offers a SATA storage interface, HDMI video output, and extra USB Type-A ports for other peripherals. # ⚓ Variscite_and_ICS_Team_Up_to_Offer_Complete_Hardware_and Software_Solution_for_High-Performing_Embedded_Devices⠀⇛ Variscite, a leading System on Module (SoM) provider and Integrated Computer Solutions, Inc. (“ICS”), creators of sophisticated embedded software solutions, today announced their collaboration to offer a complete hardware and software solution to customers in the embedded market. # § Open Hardware/Modding⠀➾ # ⚓ Imagination_introduces_Catapult_RISC-V_CPU_cores_– CNX_Software⠀⇛ As expected, Imagination Technologies is giving another try to the CPU IP market with the Catapult RISC-V CPU cores following their previous unsuccessful attempt with the MIPS architecture, notably the Aptiv family. Catapult RISC-V CPUs are/will be available in four distinct families for dynamic microcontrollers, real-time embedded CPUs, high-performance application CPUs, and functionally safe automotive CPUs. # ⚓ AS5600_support_for_moteus_auxiliary_encoders⠀⇛ The initial implementation of auxiliary encoders for moteus supported exactly one encoder, the AS5048B. The hardware can support any I2C based encoder, so supporting additional encoders has always been on the TODO list. I’m excited to announce, that as of firmware release 2021-12-03, AS5600 encoders are now supported as well. They are a lot cheaper than the AS5048 as they have a much lower update rate and resolution, but that isn’t necessarily a problem if it is only used to disambiguate a modest gear reduction. # ⚓ Fixing_the_Logitech_MX_Ergo_Trackball_mouse_buttons⠀⇛ In this 27 minute video, you can look over my shoulder as I swap out the worn-out Omron mouse buttons with Kailh replacement mouse buttons: [...] # ⚓ Imagination_launches_RISC-V_CPU_family_– Imagination⠀⇛ Based on RISC-V, the open-source CPU architecture, which is transforming processor design, Imagination’s Catapult CPUs can be configured for performance, efficiency, or balanced profiles, making them suitable for a wide range of markets. # ⚓ Imagination_Announces_“Catapult”_RISC-V_CPU_Family_– Phoronix⠀⇛ With Imagination Technologies having sold off what was MIPS Technologies several years ago and that CPU architecture having been abandoned now, Imagination today announced “Catapult” as their new family of RISC- V processor IP. Imagination’s Catapult is a line of RISC- V CPUs designed for heterogeneous compute and are offered in different versions to fit varying performance / efficiency needs. Catapult CPUs are also available in different families for dynamic microcontrollers, real- time embedded CPUs, high performance application CPUs, and automotive CPUs. # ⚓ This_system_classifies_different_types_of_clouds using_tinyML_|_Arduino_Blog⠀⇛ At the basis of each weather forecast is data — and a lot of it. And although the vast majority of atmospheric data collection is fully automated, determining cloud volumes and types are still done manually. This problem is what inspired Swapnil Verma to create a project that utilizes machine learning to categorize six different classes of clouds. The hardware for this system consists of an Arduino Portenta H7 due to its powerful processor and array of connectivity features, along with a Portenta Vision Shield for the camera. Both of these boards were mounted to a custom base on top of a tripod and powered by a battery bank over USB-C. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Paranoid_Android_Sapphire_Alpha_is_now_available_for more_devices⠀⇛ # ⚓ Google_aware_of_Android_apps_not_loading_on_Chrome_OS 96⠀⇛ # ⚓ Android_TV_update_bringing_a_Google_TV_style_user interface⠀⇛ # ⚓ Samsung_One_UI_4.0_(Android_12)_update_tracker: Eligible_devices_&_more⠀⇛ # ⚓ LG_is_killing_its_only_remaining_connection_to Android_enthusiasts⠀⇛ # ⚓ How_to_speed_up_your_Android_phone_or_tablet_|_Tom’s Guide⠀⇛ # ⚓ Moto_Edge_30_Ultra_camera_samples_and_battery_specs revealed,_may_launch_with_Android_12_–_PhoneArena⠀⇛ # ⚓ Download:_OnePlus_9_and_OnePlus_9_Pro_receive_stable Android_12_with_OxygenOS_12_update⠀⇛ # ⚓ Samsung_launches_Galaxy_Z_Fold_3_stable_Android_12 update_–_9to5Google⠀⇛ # ⚓ Nearly_100_Android_12,_Pixel_6_issues_fixed_by December_update_–_9to5Google⠀⇛ # ⚓ Pixel_6_owners_are_reportedly_facing_connectivity issues⠀⇛ # ⚓ OnePlus_9_gets_Android_12_update_starting_today_– 9to5Google⠀⇛ # ⚓ Google_Pixel_Android_12_bugs,_problems,_&_issues tracker⠀⇛ # ⚓ Samsung_shames_Chinese_smartphone_makers_with_Android 12_rollout_–_SamMobile⠀⇛ # ⚓ Three_Android_web_browsers_where_you_can_install extensions_from_the_Chrome_Web_Store_–_How_smart Technology_changing_lives⠀⇛ # ⚓ How_to_factory_reset_your_Android_phone_remotely_– 9to5Google⠀⇛ # ⚓ How_to_Delete_Unwanted_Apps_on_Your_Android_Phone_| Screen_Rant⠀⇛ # ⚓ How_to_clear_your_cache,_cookies_on_your_Android phone’s_web_browser_–_CNET⠀⇛ # ⚓ Android_Tips_and_Tricks:_How_to_boost_mobile performance⠀⇛ # ⚓ The_Best_Android_Apps_You_Haven’t_Installed⠀⇛ # ⚓ LG_closing_bootloader_unlock_program_for_its_Android phones_–_9to5Google⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # ⚓ Goodbye_WordPress,_I’ve_Switched_To_Jekyll_(Again)⠀⇛ I’ve decided to leave WordPress behind and switch to Jekyll…for a second time. This post explains why. # ⚓ Cross-platform_package_building:_Pkgsrc_vs._Ravenports_(2/ 2)⠀⇛ Part 2 discusses two package building frameworks that were developed to allow for a cross-platform solution. It contains a short introduction of both, a somewhat detailed elaboration of how they compare as well as information on the test scenario and of course the results. It ends with a conclusion. # § FSF⠀➾ # § Licensing/Legal⠀➾ # ⚓ The_EUPL_is_a_“Legal_Licence”_in_France⠀⇛ This omission is now repaired by a Décret n° 2021-1559 of 1st December 2021 adding the EUPL as a “Legal licence” in the Code of Relationship between the Public and the Administrations (CRPA). Before this Décret, French public administrations wanting to make use of the EUPL had to justify it case by case in a long administrative process. Since the EUPL is a reciprocal licence stating that derivatives of the covered software must be distributed under the EUPL too, this was a barrier for sharing and reusing software between European institutions, France and the rest of EU. # § Programming/Development⠀➾ # § Python⠀➾ # ⚓ Install_Python_3.9_on_Raspberry_Pi_OS_or_Debian 10_(for_Ansible_or_other_uses)⠀⇛ The problem is Ansible 2.12 has a new hard requirement for Python 3.8 or newer. And Ansible 2.12 is included in Ansible 5.0.0, which was recently released. Raspberry Pi OS, which was based on Debian 10 (“Buster”) until recently, includes Python 3.7, which is too old to satisfy Ansible’s installation requirements. And there was recently a fix that makes it so Ansible 5.x won’t get installed on these older systems, but who wants to get stuck on old unsupported Ansible versions? There are three options: [...] * § Leftovers⠀➾ o ⚓ Port_Arthur_and_the_Sublime⠀⇛ The most amazing place I saw during a recent tour of flood damaged towns and cities on the Gulf Coast, was Port Arthur, Texas. The ruin of its downtown, combined with the fury of its petrochemical infrastructure, can only be called sublime. That’s not a good thing. The vacant lots and gutted buildings downtown — which recall Pompeii after Vesuvius — are tokens of a vicious system of racial capitalism. The oil refineries — a tentacular network of pipes, distilleries, smoke stacks, and storage tanks — leak so many cancer-causing pollutants that adjacent residential areas are sometimes called “sacrifice zones.” The ruin and fury that characterizes Port Arthur today is so overwhelming, that it seems timeless and impervious to change. Breaking the spell of the sublime is therefore one of the most important tasks of environmental justice activists in Port Arthur. And as I learned, that’s precisely what they’re doing. o ⚓ The_Question_Dave_Hickey_Dared_to_Ask⠀⇛ What are critics good for? There’s certainly no lack of commentary today; if anything, the current online environment is a flowering of critical prose. On platforms like Twitter, the shorthand of “the discourse” (trickled down from Foucault, but never applied with so much seriousness as to seem uncool) is pervasive. We’re having a conversation out here, and it would behoove you to pay attention, subject aside—perhaps there is a much- hyped novel or a possibly offensive artwork you need to become aware of (or, just as often, something even more fleeting: an image, a meme). “Takes,” hot or cold, follow; if we’re analyzing television, where the real man-hours are spent consuming culture, “recaps” regurgitate screen time into the following day: Writers are hard at work extending, reiterating, dissenting, providing nuance and context. o ⚓ Donald_Trump’s_Media_&_Tech_Company_Facing_SEC_Investigation⠀⇛ Former President Donald Trump’s media company thinks it can attract 10 million paying subscribers to a new streaming service, and that users will be willing to pay a monthly fee “closer to that of Netflix given President Trump’s highly-enthused base.” But first, it will have to navigate a federal investigation. According to documents filed by Digital World Acquisition Company (the SPAC Trump’s company intends to merge with) Monday, both firms are facing investigations by the SEC and FINRA. o ⚓ ‘Nobody_Is_Above_the_Law’:_Elizabeth_Warren_Applauds_SEC_Probe_of Trump’s_Social_Media_Venture⠀⇛ Garnering praise from progressives including Sen. Elizabeth Warren, U.S. federal regulators have launched investigations into the proposed merger of a special purpose acquisition company with a budding social media company backed by former President Donald Trump. Ongoing probes conducted by the Securities and Exchange Commission (SEC) and the Financial Industry Regulatory Authority (FINRA) were revealed on Monday in an SEC filing by Digital World Acquisition Corporation, a “so-called blank-check company that raised nearly $300 million in an initial public offering in September” and intends to merge with Trump Media Technology Group, the New York Times reported. o § Science⠀➾ # ⚓ Actegories_and_Lenses⠀⇛ A lens is a reification of the concept of object composition. In a nutshell, it describes the process of decomposing the source object s into a focus a and a residue c and recomposing a new object t from a new focus b and the same residue c. The key observation is that we don’t care what the residue is as long as it exists. This is why a lens can be implemented, in Haskell, as an existential type: [...] o § Hardware⠀➾ # ⚓ Sony_cameras_are_getting_harder_to_buy_due_to_the_chip shortage⠀⇛ The global chip shortage has claimed yet another camera from Sony’s lineup. This time, Sony is suspending orders for the ZV-E10, a mirrorless vlogging camera that the company released in August, as reported by Digital Photography Review. Sony announced the camera’s suspension in a post on its website, noting that it will no longer sell the ZV-E10 on its store or through any of its distributors for the time being. “With regard to digital imaging products, parts procurement is delayed due to the effects of global semiconductor shortages,” a translation of Sony’s notice reads. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Antivaxxers_vs._FDA’s_VRBPAC_and_CDC’s_ACIP.⠀⇛ Sometimes the long Thanksgiving holiday weekend delays my writing about something that caught my interest (that, and my wife and I agreeing to foster a litter of puppies for a local animal shelter). Before the holiday, I had seen a rather long post over on Children’s Health Defense (CHD), the website of one of the oldest and most influential antivaxxers out there, Robert F. Kennedy, Jr., and I knew I had my topic. The article was published the day before Thanksgiving and is titled “14 ACIP Members Who Voted to Jab Your Young Children — and Their Big Ties to Big Pharma“. Unlike most articles on CHD, it was not credited to any single author, but rather to the Children’s Health Defense Team. Whenever I see that credit, I can’t help but speculate that maybe no one wanted to take personal credit for this article because it’s so misleading and bad, but then I remember: This is RFK Jr.’s website. Misleading is his business model. # ⚓ Continuing_Vaccine_Apartheid_Could_Herald_“Wave_After_Wave of_Variants”⠀⇛ # ⚓ COVID-19_Hit_This_County_Hard._A_Weakened_Health_Department Still_Can’t_Get_People_Vaccinated.⠀⇛ Most people told her the COVID-19 vaccine helped them feel safer, but Barbara Hawkins worried it would make her sick. Uninsured and without a regular doctor, she feared that side effects could aggravate her heart condition. Her friends and family, mostly vaccinated, reassured her that they wouldn’t. # ⚓ Campaigners_Warn_of_‘Wave_After_Wave_of_Variants’_as_Long as_Vaccine_Apartheid_Remains⠀⇛ A coalition of humanitarian groups warned Sunday that the world could face “wave after wave of variants” unless rich countries stop blocking a proposed patent waiver for coronavirus vaccines and immediately distribute the technology needed to mass-produce the lifesaving shots. “Pharmaceutical monopolies and profiteering have prevented vaccination in Africa and the rest of the developing world.” o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Better.com_CEO_fires_900_employees_over_Zoom⠀⇛ The Softbank-backed mortgage lender announced in May it was going public through an SPAC and last week received $750 million in cash as part of the deal. The company is prepared to have more than $1 billion on its balance sheet. # § Pseudo-Open Source⠀➾ # § Privatisation/Privateering⠀➾ # § Linux Foundation⠀➾ # ⚓ Linux_Foundation_Hosts_Project_for Container_Collaboration_Between Enterprise_and_HPC⠀⇛ # ⚓ Linux_Foundation_2021_annual_report [Ed: Corbet from Linux Foundation is shilling Linux Foundation PR/ marketing in LWN]⠀⇛ For those who would like to catch up on what the Linux Foundation has been doing, the 2021 annual report is available as an 87-page PDF file. # ⚓ The_Linux_Foundation_Annual_Report 2021:_New_Horizons_in_Open_Source [Ed: Made_on_an_Apple_Mac_using proprietary_software]⠀⇛ # § Security⠀➾ # ⚓ Announcing_Istio_1.10.6⠀⇛ This release contains bug fixes to improve robustness. This release note describes what’s different between Istio 1.10.5 and Istio 1.10.6. # ⚓ CISA_Releases_Security_Advisory_on_WebHMI Vulnerabilities⠀⇛ CISA has released an Industrial Controls Systems (ICS) advisory detailing vulnerabilities in Distributed Data Systems WebHMI products. A remote attacker could exploit these vulnerabilities to take control of an affected system. # ⚓ Zoho_Releases_Security_Advisory_for ManageEngine_Desktop_Central_and_Desktop_Central MSP⠀⇛ Zoho has released a security advisory to address an authentication bypass vulnerability in ManageEngine Desktop Central and Desktop Central MSP. An attacker could exploit this vulnerability to take control of an affected system. According to Zoho, this vulnerability is being actively exploited in the wild. # § Privacy⠀➾ # ⚓ What_is_the_Surveillance_State?⠀⇛ Surveillance and crime prevention At the present time, in the US, the focus of surveillance has become the “crime problem.” On the lookout for the incipient evil-doer, surveillance rationalizes itself through technological silence, while depending on sociological explanations. It is supposed to help prevent crime. But that just makes it more mysterious. Does it stop corporate crime? Does it rescue us from administrative corruption? These crimes reside in the domain of brave investigative journalism. When nine different people observed a woman being sexually assaulted on a train (Philadelphia, 10/13/21), all they could think of to do was record the event on their nine separate cellphones – thinking, perhaps, that that act of surveillance would stop the crime they were witnessing. Remaining in the hands of the police, will the technology of surveillance stop the crimes committed by the police? # ⚓ NSO_Spyware_Used_To_Snoop_On_US_State Department_Employees_Stationed_In_Uganda⠀⇛ Israeli exploit seller NSO Group has long past reached the limits of its non-denials and deflection attempts. There’s only bad news on the horizon for the tech company, which would be a lot less disheartening for the company if it hadn’t been preceded by months of bad news. # ⚓ Clearview’s_Facial_Recognition_AI_One_Of The_Best_In_The_Business,_Says_NIST⠀⇛ Some good news for Clearview, the bottom dweller of the facial recognition field. The prodigious scraper of web content has finally submitted its algorithm (the one it actually sells to government agencies) to the National Institute of Science and Technology (NIST) and has obtained a score that justifies its frequent blustering about how accurate its AI is. Here’s Kashmir Hill with the details for the New York Times. # ⚓ The_Open_Technology_Fund_That_Makes_All Your_Favorite_Privacy_Apps_is_Staffed_Full of_Spies⠀⇛ The Open Technology Fund (OTF) is one of the most influential and celebrated organizations in the hacking and internet freedom communities. Well over two billion people globally use OTF- produced software, including communications app Signal and web browser Tor, services that are specifically marketed to privacy- conscious consumers looking to circumvent government censorship and surveillance. Yet its close links to the U.S. national security state raise many worrying questions about whether the world is making a mistake by trusting the organization and its products. # ⚓ Chinese_Government_Is_Building_A Surveillance_System_That_Will_Target,_Track Foreign_Journalists,_Students⠀⇛ The Chinese government is truly, undeniably, utterly evil. Anyone saying otherwise has something to sell (most likely to the Chinese people or their government). Private companies and public entities alike have kowtowed and capitulated rather than face the ferocity of the easily angered government and/or risk losing access to a marketplace containing a few billion people. # ⚓ Interview_With_Nathan_Collins_– PAVilion⠀⇛ Nathan Collins: In the late ‘90s I was an economics graduate from UCW Aberystwyth and determined not to go anywhere near IT. IT had been the profession that my father had chosen, and I wanted to go a different way. Alas, I failed spectacularly in this endeavor with a 20+ year career involving technical direction, consulting services, support services, and everything else associated with technology. However, in the last 5 years I have broken free a little becoming a sales director. # ⚓ TikTok_considers_monetization_and_creator retention_in_judging_recommendation algorithm⠀⇛ To keep users watching and coming back, TikTok considers four main objectives, according to the Times: user value, long-term user value, creator value, and platform value. One way that plays out is the algorithm prioritizing a diversity of content rather than overwhelming users with one single topic they might love. # ⚓ Rise_in_employee_monitoring_prompts_calls for_new_rules_to_protect_workers⠀⇛ “We have seen a significant increase of interest in employee monitoring technology through the pandemic,” said Helen Poitevin, VP analyst at Gartner focusing on human capital management technologies. “This continues as organizations plan for hybrid work environments, with employees working more flexibly from home and at the office.” Technological innovation has largely outpaced existing employment and equality legislation, said Andrew Pakes, director of communications and research at UK union Prospect. (Pakes contributed to a recent cross-party government report on AI monitoring and management in the workplace.) # ⚓ Ransomware_attacks_soar,_[attackers]_set to_become_more_aggressive_–_Canada_spy agency⠀⇛ Global ransomware attacks increased by 151% in the first half of 2021 compared with 2020 and [attackers] are set to become increasingly aggressive, Canada’s signals intelligence agency said on Monday. The Communications Security Establishment (CSE), citing attacks on North American health facilities and a U.S. pipeline, said the scale and scope of ransomware operators represented both security and economic risks to Canada and its allies. # ⚓ Personal_Data_Protection_Bill_report likely_to_be_tabled_in_Parliament_on_Dec 21⠀⇛ The bill that seeks to provide protection of personal data of individuals and establish a Data Protection Authority for the same, was brought in Parliament in 2019 and was later referred to the Joint Committee for further scrutiny on the demand of opposition members. # ⚓ noyb’s_Second_“Advent_Reading”:_How_the Irish_DPC_tried_to_lobby_Facebook’s_“GDPR bypass”_into_European_Guidelines.⠀⇛ This week, noyb published two rounds of documents as part of their “Advent Readings” from DPC and Facebook documents: A letter from Facebook to the Irish DPC confirms that the DPC had ten meetings with Facebook where they discussed and agreed on Facebook’s GDPR bypass. The second round of documents shows that the DPC tried to push this bypass for “Social Media” into Guidelines of the European Data Protection Board (EDPB) but was met with harsh criticism from other European Data Protection Authorities (DPAs), going all the way with comments like “We think that this interpretation undermines the system and spirit of the GDPR“ or “This reduces the GDPR to a pro-forma instrument.” The DPC’s attempt to include the GDPR bypass into the guidelines took place, while it was tasked with being an indepent decision maker in a pending case on Facebook’s “GDPR bypass”. # ⚓ Digital_surveillance_/_Pegasus:_Civil society_calls_for_EU_sanctions_against_NSO Group⠀⇛ In a letter published today to the EU’s foreign affairs commissioner Josep Borrell and the foreign ministers of EU member states, the coalition summarises the growing number of allegations against the company and calls for action under the EU’s human rights sanctions regime. The EU must take appropriate steps to ban the use and trade of NSO technology until effective human rights protections are in place. More than 220 journalists have been identified as targeted or confirmed targets of state spying attacks using the spyware since the first Pegasus Project revelations in July. The German government has so far maintained its use of Pegasus, including by the Federal Intelligence Service. The US Department of Commerce, on the other hand, took concrete steps in November and placed NSO Group and another Israeli surveillance technology company on a sanctions list. o § Defence/Aggression⠀➾ # ⚓ U.S._Opposes_a_Ban_on_Killer_Robots–A_New_Autonomous_Form of_Warfare–Ahead_of_U.N._Weapons_Summit⠀⇛ Human rights activists and dozens of countries are calling for an all-out ban on the use of lethal autonomous weapons, also known as “killer robots” that can make the final order to kill without a human overseeing the process. The robots will be coming under review next week during high-level talks on the Convention on Certain Conventional Weapons. So far, the Biden administration has rejected calls to ban the weapons, instead proposing the establishment of a “code of conduct” for their use. “This is not just a new weapon, it’s a new form of warfare,” says Steve Goose, director of Human Rights Watch’s arms division and co- founder of the Campaign to Stop Killer Robots, says. “The majority of countries want to see a legally binding instrument — a new treaty — that would have prohibitions and regulations on fully autonomous weapons.” # ⚓ Gun_Control_Advocates_Demand_New_Regulations_After_Michigan School_Shooting⠀⇛ # ⚓ “Systemwide_Failure”:_Gun_Control_Advocates_Demand_New Regulations_After_Michigan_School_Shooting⠀⇛ Funerals have begun in Oxford, Michigan, for the four students killed when their 15-year-old classmate opened fire in a rampage that also injured seven others. Ethan Crumbley has been charged with terrorism and first-degree murder, and his parents have also been charged with involuntary manslaughter for allegedly giving him access to a firearm even as he displayed obvious signs he was thinking about committing violent crimes. We’re joined by Nicole Hockley, whose 6-year-old son Dylan was killed in the Sandy Hook Elementary School shooting, prompting her to found Sandy Hook Promise; and Kris Brown, president of Brady, one of the oldest gun violence prevention organizations in the country. “We have an epidemic of gun violence in this country,”says Brown. “This was an absolutely preventable act of violence,” adds Hockley, who also discusses her organization’s anonymous reporting system called “Say Something” for students to use if they see a classmate who is at risk of harming themselves or others. # ⚓ Corrupting_science:_Shunning_forensic_expertise,_OPCW_left Douma,_Syria_murders_unsolved⠀⇛ # ⚓ “Crisis_of_Accountability”:_Pentagon_Reopens_Probe_of Syrian_Airstrike_That_Killed_Dozens_of_Civilians⠀⇛ Defense Secretary Lloyd Austin has ordered a new investigation into one of the deadliest U.S. airstrikes in recent years after the New York Times exposed an orchestrated cover-up by U.S. military officials to conceal the attack. The March 2019 airstrike killed dozens of women and children during a bombing of one of the last strongholds of the Islamic State of Syria. Evidence has shown that U.S. military officials spent two-and-a-half years covering up the attack by downplaying the death toll, delaying reports, and sanitizing and classifying evidence of civilian deaths. “This is not the case of one little mistake,” says Priyanka Motaparthy, director of the Counterterrorism, Armed Conflict and Human Rights Project at Columbia Law School. “This really points to a crisis of accountability in the Pentagon.” # ⚓ Breaking_China:_There_Won’t_be_Anything_Left⠀⇛ But this was all intentional misdirection, because the “War on Terror” was a handy diversion from the real intent of the folks pulling the strings of the Military Industrial Complex. The WOT was a very effective way to a inculcate a permanent sense of terror at home, provide a vehicle to strip away constitutional rights and the checks and balances of our federal system, eviscerate the last shreds of the constitutional duty for congress to declare war, and work to develop a cadre of volunteer troops who would be primed to redirect their racist brainwashing from denigrating sand-monkeys to demonizing slope-heads, or other natives, as needed. Some of you may remember how well that worked out, the last time we went to Asia to fight the domino- flipping commies. # ⚓ Chris_Hedges:_The_Ghislaine_Maxwell_Trial_Is_an_American Satyricon⠀⇛ The trial of Ghislaine Maxwell which began this week in Manhattan will not hold to account the powerful and wealthy men who are also complicit in the sexual assaults of girls as young as twelve Maxwell allegedly procured for billionaire Jeffrey Epstein. # ⚓ Sham_GOP_Election_‘Auditors’_Want_to_See_Your_Ballot_—_But Hide_Their_Own_Work⠀⇛ Vos’s comparison was farcical on its face, likening alleged election-related fraud with the search for a killer. But it also revealed a key dynamic of Wisconsin’s GOP-driven audit, showing how the same lawmakers signing off on subpoenas and demanding extraordinary access to election records sought to keep the public in the dark about the inner workings of their “audit.” # ⚓ American_Oversight_Files_Motion_to_Hold_Speaker_Vos_in Contempt_for_Failure_to_Comply_with_Wisconsin_Public_Records Law⠀⇛ On Nov. 5, the court ordered the Wisconsin Assembly and Vos to release records in response to American Oversight’s lawsuit, giving Vos and the Assembly 10 days to release certain records held by the contractors hired to conduct the inquiry. Almost two weeks have passed since that Nov. 19 deadline, and Vos and the Assembly have not produced the records. # ⚓ A_gathering_storm:_why_did_Japan_attack_Pearl_Harbor_in 1941?⠀⇛ With a dwindling supply of petroleum, Japan faced the appalling prospect of having to give up its ambitions for a ‘Co-Prosperity Sphere’. In reaction to the US’s financial freeze and de facto oil embargo, on 3 September 1941, Prime Minister Konoe’s cabinet convened to discuss the ‘Outline Plan for the Execution of the Empire’s National Policy’, produced by Imperial General Headquarters, a council of top-ranking army and navy officers. Unless the western powers backed down, the cabinet resolved “… to go to war with the United States, Great Britain and the Netherlands if necessary”. The accepted strategy for combating the west was for Japan to move rapidly to secure the oil-rich Dutch East Indies and the Philippines, a US colonial depen­d­ency. The supposedly formidable British military and naval garrison at Singapore would be taken, along with commodity-rich Malaya and Burma. Meanwhile, the main body of the Japanese navy would wait for the approach of the US fleet as it sailed to relieve the Philippines – which was indeed the proposal of ‘War Plan Orange’, as con­c­eived by the joint US Army and Navy Board in the 1920s. Here, at the Marshall Islands, in the western approaches of the Pacific Ocean, the Japanese navy would annihilate the US navy, just as the legendary Admiral Tōgō had decimated the Russian navy at the battle of Tsushima in the Russo-Japanese War in 1905. However, Admiral Isoroku ­­Yama­moto, who as commander-in-chief of its Combined Fleet held the pivotal role in Japan’s war strategy against the United States, had other ideas. He turned conventional wisdom on its head by planning a surprise attack on the US’s key Pacific naval base, located in Hawaii. By sinking America’s Pacific Fleet in a surprise attack – particularly its flotilla of aircraft carriers, which Yamamoto had identified as the key sea weapons of the coming war – he would seek to delay a US naval advance. This would give time for Japan to build up defences in the Pacific islands, and secure its resource supply lines within its newly acquired south-east Asian empire. At best, Yamamoto surmised that, after the destruction of the US navy at Pearl Harbor, Washington might even offer a truce. # ⚓ 101-year-old_returns_to_Pearl_Harbor_to_remember_those lost⠀⇛ In 2015, the Defense POW/MIA Accounting Agency exhumed 388 sets of these remains in hopes of identifying them with the help of DNA technology and dental records. They succeeded with 361. # ⚓ America_Learned_the_Wrong_Lessons_From_Pearl_Harbor—And_the World_Is_Still_Living_With_the_Consequences⠀⇛ World War II was an aberration in so many ways: the existential threat posed by fascism, the unequivocal necessity of our participation, and the decisiveness of Allied victory are only the most obvious. When we remember Pearl Harbor, we find ourselves in the position of Orpheus, suddenly mistrusting Hades’ bargain, compelled to look back, only to discover that Eurydice has vanished. Betrayed by the last twenty years, we grasp in vain to retrieve an elusive glory. Our tragic postwar mistake was in thinking that the consequences of World War II could be endlessly duplicated. Over the years we have somehow developed a capacity to be surprised when American military might doesn’t establish, as it once helped to do, a new world but instead, after twenty wasteful years of occupation, fitful nation-building, and unfounded confidence, are left right back where we started. There is a cruel and particular irony in the paradox that a country the imagination of which has always been knit so tightly to the future—to the seductive dream of beginning anew—now finds itself in the position of hoping that history will miraculously repeat itself. # ⚓ US_Remembers_Pearl_Harbor_on_80th_Anniversary_of_Attack⠀⇛ Tuesday marks the 80th anniversary of the surprise strike on the U.S. Pacific Fleet that killed more than 2,400 service members and civilians, wounded about 1,000 people, and damaged or destroyed almost 20 ships and more than 300 aircraft in less than two hours. The next day, Roosevelt asked Congress to declare war on Japan, and the lawmakers approved the move. Just three days later, Germany and Italy, Japan’s allies, declared war on the U.S. The U.S. reciprocated, entering World War II, which had been raging in Europe for more than two years. # ⚓ War_in_Ukraine?_NATO_expansion_drives_conflict_with Russia⠀⇛ # ⚓ Europe’s_future_will_be_decided_in_Ukraine⠀⇛ My appointment as Ukraine’s new Minister of Defense in early November coincided with a wave of mounting international concern over Russia’s latest military build-up along the Ukrainian border. This concentration of troops and armor is consistent with preparations for a large-scale invasion of Ukraine in the coming months. As the international community began to raise the alarm over Russia’s menacing military activity, it was noted that Ukraine seemed to be reacting in a far calmer manner than many in the US or European capitals. This was an entirely accurate observation. # ⚓ Han_Chinese_now_hold_most_government_posts_in_Tibet_as Beijing_extends_control⠀⇛ Han Chinese now outnumber Tibetans in top government posts in Tibet by more than 2-to-1, an indication, Tibetan sources say, of China’s push to dominate the region. Following Beijing’s installation of Wang Junzheng as Tibet’s party secretary on Oct. 19, only four out of fifteen chief and vice-chief administrative positions in the capital Lhasa are now held by Tibetans, according to Chinese government figures. This lack of representation in government shows that Tibet’s status as an Autonomous Region of China has no meaning for Beijing, a Tibetan living in Lhasa told RFA. # ⚓ The_Taliban_are_losing_the_fight_against_Islamic_State⠀⇛ Deborah Lyon, the UN secretary-general’s special representative for Afghanistan, recently told the UN Security Council, ‘Once limited to a few provinces and the capital, [IS-K] now seems to be present in nearly all provinces, and increasingly active’. Indeed, there’s been a marked increase in attacks across the country since 2020. US Under Secretary of Defense for Policy Colin Kahl similarly testified to Congress, ‘We could see [IS- K] generate that capability [for foreign attacks] in somewhere between six or 12 months’, adding that the Taliban’s ability to combat the group ‘is to be determined’. The US recently identified and sanctioned senior officials of IS-K, including its leader. # ⚓ US_and_EU_condemn_Taliban_over_‘summary_killings’_and demand_investigation⠀⇛ Early this week Human Rights Watch (HRW) released a report that it says documents the summary execution or enforced disappearance of 47 former members of the Afghan National Security Forces, other military personnel, police and intelligence agents “who had surrendered to or were apprehended by Taliban forces” from mid-August through October. # ⚓ Salah_Abdeslam_and_the_Banality_of_Terror⠀⇛ Abdeslam is the most prominent defendant, and the one that bears the greatest burden of guilt. French newspapers printed his photo when the trial kicked off in September, presenting him as the incarnation of evil. The other defendants stand accused of having participated in preparations for the attack – arranging fake documents, for example, or obtaining vehicles and apartments for the conspiracy. Two of them had been on their way to Europe, hoping to join in on the attack, but didn’t make it in time. Still others helped Salah Abdeslam escape after Nov. 13. Abdeslam, though, is the only one who was there and was supposed to have blown himself up, and he’s the only one who could provide answers to a number of open questions. Thus far, though, he has remained silent about the background of the attacks. # ⚓ Two_soldiers_killed_in_Islamist_militant_attack_in_northern Benin,_army_says⠀⇛ # ⚓ West_Africa:_Explosions,_attacks_in_Mali,_Niger_kill_over 100⠀⇛ Both Niger and Mali are struggling to contain an Islamist insurgency that started in 2012 in northern Mali. The federal government in both West African nations has little control outside cities in the vast deserts that comprise the countryside. Additionally, both countries are desperately poor, ranking at the very bottom and near the bottom of the UN’s Development Index. # ⚓ Former_D.C._Guard_official_accuses_Army_generals_of_lying to_Congress_about_Jan._6_response⠀⇛ The officer, Col. Earl Matthews, wrote in a 36-page memo to the House committee investigating the attack that Gen. Charles Flynn, who was the deputy chief of staff for operations on Jan. 6, and Lt. Gen. Walter Piatt, the director of the Army staff, “repeatedly misrepresented, understated, or misled” the House Oversight Committee and the Defense Department’s inspector general. o § Environment⠀➾ # ⚓ How_China_wrested_control_of_the_Congo’s_critical minerals⠀⇛ Despite an avowed concern to end the US dependence on China for supplies of critical minerals, both the Obama and Trump administrations stood aside, allowing Freeport to hand control of the world’s largest cobalt mine to China Molybdenum with the sale of its nickel and cobalt operations in the DRC. The Chinese were assisted in their purchase by President Joe Biden’s son Hunter. # ⚓ How_the_U.S._Lost_Ground_to_China_in_the_Contest_for_Clean Energy⠀⇛ Not only did the Chinese purchase of the mine, known as Tenke Fungurume, go through uninterrupted during the final months of the Obama administration, but four years later, during the twilight of the Trump presidency, so did the purchase of an even more impressive cobalt reserve that Freeport-McMoRan put on the market. The buyer was the same company, China Molybdenum. China’s pursuit of Congo’s cobalt wealth is part of a disciplined playbook that has given it an enormous head start over the United States in the race to dominate the electrification of the auto industry, long a key driver of the global economy. But an investigation by The New York Times revealed a hidden history of the cobalt acquisitions in which the United States essentially surrendered the resources to China, failing to safeguard decades of diplomatic and financial investments in Congo. The sale of the two mines, also flush with copper, highlights the shifting geography and politics of the clean energy revolution, with countries rich in cobalt, lithium and other raw materials needed for batteries suddenly playing the role of oil giants. # ⚓ A_Future_With_Little_to_No_Snow?_What_That_Means_for_the West⠀⇛ # § Energy⠀➾ # ⚓ ‘We_Won’t_Stop_Fighting,’_Vow_South_African_Activists After_Judge_OKs_Shell_Seismic_Blasting_at_Sea⠀⇛ South African activists on Monday vowed to keep fighting after a court ruling allowing fossil fuel giant Shell to proceed with massive underwater explosions off the ecologically sensitive Wild Coast, a move environmentalists say would cause “irreparable harm” to marine life. “Our ancestors’ blood was spilled protecting our land and sea, and we now feel a sense of duty to protect it for future generations.” # ⚓ Big_Oil_Profits_Surge_to_$174_Billion_in_2021_Amid Rising_Gas_Prices:_Report⠀⇛ While rising gasoline prices have adversely affected millions of working people in the U.S., the world’s biggest fossil fuel corporations have benefited immensely, raking in a combined $174 billion in profits during the first nine months of this year. “Oil corporations are reveling in their massive profits and using that money for their real priorities: stock buybacks and lining shareholders’ pockets.” # ⚓ Oil_and_Gas_Industry_Profits_Climbed_as_Americans Faced_High_Gas_Prices_in_2021⠀⇛ # ⚓ ‘It’s_a_Proud_Day’:_Oregon_Landowners_Celebrate Demise_of_LNG_project,_Even_as_Legal_Questions_Go Unanswered⠀⇛ Oregon’s 15-year battle against the Jordan Cove LNG project quietly came to an end on December 1, bringing relief to dozens of landowners that live in the path of the proposed project.  It was an anti-climactic end to one of the most controversial fossil fuel projects ever proposed in the Pacific Northwest. Pembina, the backer of Jordan Cove LNG and the Pacific Connector gas pipeline that would have fed the export terminal, submitted a request to the Federal Energy Regulatory Commission (FERC) to cancel its authorization, citing the company’s inability to obtain state environmental permits.  # ⚓ Biden_Administration_Is_Approving_Oil_and_Gas Drilling_at_Faster_Rate_Than_Trump⠀⇛ # ⚓ Biden_Continues_Drilling_Boom_on_Public_Lands_Despite Campaign_Pledge,_Analysis_Shows⠀⇛ Despite pledging as a presidential candidate that he would allow “no ability for the oil industry to continue to drill, period,” President Joe Biden’s White House has approved more drilling permits for public lands each month than the Trump administration, a new analysis shows. In a report titled Biden’s Oil Letdown, released Monday, Public Citizen showed that since Biden took office, the Interior Department’s Bureau of Land Management (BLM) has approved an average of 333 oil and gas drilling permits per month this year—40% more than it did in the first three years of Trump’s presidency. # ⚓ South_African_environment_groups_demand_an_end_to Shell_exploration⠀⇛ Royal Dutch Shell’s plans to explore for oil along a stretch of pristine coastline raised the ire of local activists on Sunday as hundreds gathered on beaches around South Africa, calling for the oil giant to stop prospecting. Demonstrators are worried about the effect seismic blasting — a prospecting method based on emitting powerful sound waves — will have in a 6,000 square kilometer (2316 square mile) area. # ⚓ The_price_of_electricity_around_the_world⠀⇛ This data might be of some interest to bitcoin miners and owners of data centres in their decision-making process to determine suitable locations, although typically, ‘big- pipe’ access to the [Internet] is poor in the cheapest countries, thereby limiting interest. # ⚓ Why_have_prices_of_cryptocurrencies,_such_as_Bitcoin, fallen—again?⠀⇛ The effect of all this on cryptocurrencies has been particularly pronounced. They are consistently volatile. Though they are billed as digital currencies, their holders treat them not as means of payment but as financial assets. Most are thinly traded in comparison to shares, with a few big investors holding significant sway. About 2% of bitcoin accounts hold 95% of the available coins, according to Flipside, a crypto-analytics firm. Last year, less than 20% of bitcoin supply was actively traded—most is held in long-term accounts. That means trades do not have to be very large to shift prices dramatically. Crypto exchanges are numerous: the fragmentation of trading increases volatility, as a few trades on a given exchange can have a significant effect. Prices are also affected by a massive market for derivatives (contracts based on the price of an underlying asset, in this case a cryptocurrency): there are on average five times more bitcoin derivative trades than spot trades of the coin itself. These bets, which are usually made on unregulated offshore exchanges, can shift the price of cryptocurrencies, adding to volatility. # ⚓ Ethereum_Emissions⠀⇛ After reading a paper by Jonathan Koomey that encourages taking a bottom-up approach to energy estimates instead of Alex’s top-down approach, I looked for some bottom-up estimates. When I couldn’t find one I was happy with, I did some research and built a new Ethereum emissions tracker. This is the part where I am supposed to say “what I found will shock you”, but perhaps what is most surprising is that the previous attempts at answering this question seem to have been basically correct in their conclusions. # ⚓ A_Bitcoin_Boom_Fueled_by_Cheap_Power,_Empty_Plants and_Few_Rules⠀⇛ But the surge of activity has also prompted a growing outcry over the amount of electricity and pollution involved in mining for Bitcoin. Globally, cryptocurrency mining is said to consume more electricity annually than all of Argentina. China, once home to perhaps two- thirds of all crypto mining, banned the practice this year to help achieve its carbon-reduction goals, driving some miners to New York. As a result, environmental groups say, the Wild West-style scramble, coupled with a lack of restrictions on Bitcoin mining, is threatening the state’s own emission- reduction goals, which call for more renewable power and rapid reductions in fossil-fuel emissions. o § Finance⠀➾ # ⚓ Inside_the_November_Jobs_Numbers⠀⇛ The 210,000 job growth in the establishment survey is slower than generally expected, but it is important to note that it went along with an increase in the average workweek. The index of aggregate hours in the private sector increased by 0.5 percent in November. This would be the equivalent of more than 630,000 new jobs, with no change in the workweek. This fits a story where employers are increasing hours since they are unable to hire new workers. We are seeing a reshuffling of the labor market where workers are looking for better jobs and employers are competing to attract workers, especially in lower paying sectors. # ⚓ Concentration_of_Power⠀⇛ Well, it is nice to be free again, though as I said on release, I shall never really feel free while Julian is still imprisoned and while Scotland is still part of an imperialist United Kingdom. I expect most of you have seen my release, but for those who have not… # ⚓ “Unregulated_Capitalism_is_a_Suicide_Pact”:_Noam_Chomsky Talks_Climate,_China,_and_More_with_Lowkey⠀⇛ # ⚓ Opinion_|_With_Maxwell_Sacrificed,_the_Ruling_Oligarchs Will_Once_Again_Escape_Justice⠀⇛ The trial of Ghislaine Maxwell which began this week in Manhattan will not hold to account the powerful and wealthy men who are also complicit in the sexual assaults of girls as young as twelve Maxwell allegedly procured for billionaire Jeffrey Epstein. # ⚓ WATCH:_Sanders_Hosts_‘Solidarity_Brewing’_Town_Hall_With Starbucks_Workers_Amid_Union_Push⠀⇛ Sen. Bernie Sanders on Monday night will host a town hall with Buffalo, New York Starbucks workers as they attempt to form the first-ever union at the company, whose management has turned to well-worn corporate tactics in its campaign to stamp out the historic organizing drive. “Young workers are struggling with low wages, high rents, student debt, lack of healthcare, etc. Some of them are fighting back,” Sanders (I-Vt.) wrote in a tweet promoting the event, slated to begin at 8 pm ET. # ⚓ Opinion_|_The_First_Corporate-Owned_Starbucks_in_the Country_to_Unionize?⠀⇛ The cream always rises to the top. Howard Schultz must love this folk maxim. And well he should. Understanding the ways of cream has helped make Schultz—the two-time former CEO and current chairman emeritus of Starbucks—a billionaire almost five times over. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Opinion_|_In_Buffalo_and_After:_Democratic_Socialists_Vs. Republican_Democrats⠀⇛ Two weeks ago, with the final ballots counted in Buffalo’s mayoral race, India Walton acknowledged her loss. She also looked ahead: “This election was not an end, but a beginning,” she told reporters. “The new ideas we articulated, the new energy we inspired, the new volunteers we trained, and the new relationships we built will only grow in the coming years. This campaign planted many seeds. The blossoms are inevitable.” # ⚓ A_Litmus_Test_for_Democracy?_Democratic_Deficits_at_the Summit_for_Democracy⠀⇛ There are, of course, many manifestations or “models” of democracy, exercised nationally as well as locally in provinces and communities. The spectrum of democratic governance goes from direct democracy by way of citizen power of initiative and the possibility to challenge legislation by way of referenda, to participatory democracy through public meetings and voting on specific issues by ballot (or even show of hands!), to representative democracy through the election of parliamentarians with specific mandates, to presidential democracy by electing a president with wide-ranging powers. As a Swiss citizen, I recognize the benefits of the semi-direct democracy practised in Switzerland. Indeed, I vote in every single election and referendum, and actively participate in the public debate that precedes them, and in this way I feel that my opinion counts. As an American citizen I vote in every congressional and presidential election every two years. However, on the important issues I feel that there is no genuine choice given to the electorate, because the two parties converge precisely on those issues where there must be change. Because there is hardly a possibility to influence domestic or international policy, I and many other Americans feel disenfranchised. We suffer from endemic democratic deficits. # ⚓ Rights_Groups_Decry_‘Farcical_and_Corrupt’_Verdict_as Myanmar’s_Suu_Kyi_Sentenced_to_Four_Years_in_Prison⠀⇛ A Myanmar court on Monday sentenced the nation’s ousted civilian leader Aung San Suu Kyi to four years in prison on charges that human rights groups and the United Nations condemned as “politically motivated” and “corrupt.” The verdict—under which the former leader was convicted of incitement and violating Covid-19 restrictions—came more than 10 months after Myanmar’s armed forces arrested Suu Kyi and took control of the country’s government, imperiling the nation’s recent, tenuous steps toward democracy after decades of military dictatorship. # ⚓ DOJ_Lawsuit_Challenging_Texas_Gerrymandering_Met_With Applause,_Calls_for_Action_in_Congress⠀⇛ Following the lead of a number of voters and rights organizations, the U.S. Department of Justice on Monday filed a legal challenge to Texas’ newly drawn, “discriminatory” congressional district map, while noting that action by federal lawmakers could keep states from imposing racial and partisan gerrymandering on constituents. The DOJ filed its lawsuit under Section 2 of the Voting Rights Act, which bars legislators from denying equal access to voting on the basis of voters’ race or ethnicity. # ⚓ Justice_Department_Sues_Texas_Over_Racist_Congressional Maps⠀⇛ # ⚓ Opinion_|_GOP_Is_Launching_a_Mechanical_Attack_to_Steal_the Next_Election⠀⇛ The insurrection at the U.S. Capitol on January 6  demonstrated exactly how little the United States has progressed since the civil rights era. The right, still battling against the foundation and promise of a multiracial democracy, has demonstrated its willingness to use violent means to preserve political control. But, beyond the desire of some to literally murder their opponents, Republican leaders are also launching a less obvious and more mechanical attack on the idea of a fairly elected government.  # ⚓ Proud_Boy⠀⇛ # ⚓ Honduras_Elects_a_Socialist—but_Will_She_Be_Allowed_to Govern?⠀⇛ Tegucigalpa, Honduras—You could hear the shouting inside the Buenos Aires voting center from almost a block away. It was nearing 6 pm on November 28, and arguments began spilling out from the school- turned-polling-place onto the street. In this poor neighborhood in Tegucigalpa, the vote facilitators, who belonged to the ruling right-wing National Party, were preventing voters from casting their ballots. Just minutes remained before the cutoff for the presidential elections. Many had been waiting in line since the morning. # ⚓ Omas_Gegen_Rechts—Grannies_Against_the_Right!⠀⇛ The first time I saw Omas gegen Rechts (Grannies Against the Right) in action at a demonstration in Berlin, I was startled, then thrilled. Here was a group of older women bringing attention to the fact that they were older women, distinct from yet allied with other protesters on the street. Simply by being there, by carrying signs that said Omas gegen Rechts, they seemed to be confronting the dismissal of older women while also drawing on the mythologies of grandmothers who sort things out. And they explicitly identified which side they were on: countering the far right. # ⚓ Opinion_|_Must_Reads:_Critical_Exposés_Abound_But_American Fascism_Marches_On⠀⇛ Franklin Delano Roosevelt in his 1938 message to Congress warned that when private power becomes stronger than the democratic state itself, we have Fascism. There are many ways to witness the intensifying domination toward a corporate state. One way is to compare exposé books in the 1960s and the present. # ⚓ Human_Rights_Groups_Condemn_Sentencing_of_Myanmar’s_Suu_Kyi as_“Farcical”⠀⇛ # ⚓ Critical_Exposés_Everywhere_as_the_Corporate_State Worsens⠀⇛ Within a span of five years, there were three books in the sixties that put forces in motion leading to significant reordering of our society’s priorities. They were Silent Spring by Rachel Carson (1962), my Unsafe at Any Speed (1965), and The Other America by Michael Harrington (1962). The message of these bestselling books was expanded by authors going on national TV and radio shows. They spoke around the country, before large audiences at colleges/universities and even high schools. An aroused citizenry prompted congressional hearings, legislation, and the establishment of federal agencies to deal with the problems of toxic chemicals, unsafe motor vehicles, and deep poverty in the U.S. # ⚓ On_the_Origins_of_Neoliberalism⠀⇛ The second problem is that while neoliberalism can be traced back to to old-school market liberalism of the Republican type, it is not the same thing, but something new and different — thus the “neo”. Neoliberals do hold many points in common with the anti-tax, anti-regulation, anti-union, little- government conservatism we know all too well, but their ideas about the political history and the role of government are entirely different. Most of what I will say here comes from The Road from Mont Pelerin: The Making of the Neoliberal Thought Collective, ed. Mirowski and Plehwe (Harvard , 2009), which I think is the best single source on the topic. I will only discuss what I think are the main points, with special emphasis on the American-based neoliberals Friedman, Hayek, and Buchanan and will mostly draw from Plehwes’s introduction, Mirowski’s two contributions, and the chapter on neoliberalism in Chile. # ⚓ Opinion_|_How_Congress_Loots_the_Treasury_for_the_Military- Industrial-Congressional_Complex⠀⇛ Despite a disagreement over some amendments in the Senate, the United States Congress is poised to pass a $778 billion military budget bill for 2022. As they have been doing year after year, our elected officials are preparing to hand the lion’s share—over 65%—of federal discretionary spending to the U.S. war machine, even as they wring their hands over spending a mere quarter of that amount on the Build Back Better Act. # ⚓ Devin_Nunes_Retires_From_Congress_To_Spend_More_Time Banning_Satirical_Cows_From_Trump’s_New_Social_Network⠀⇛ In a bit of a Monday afternoon surprise, Rep. Devin Nunes has announced that he’s retiring from Congress this month to become the CEO of Trump’s new media company, Trump Media & Technology Group — a company which apparently now has tons of money in the bank (even if from sketchy sources) but also is facing a newly revealed SEC investigation that might require someone who actually understands this stuff, rather than a very thin-skinned politician who sues people who criticize him. # ⚓ Donald_Trump_Taps_Congressman_Devin_Nunes_as_CEO_of_His Media_and_Tech_Company⠀⇛ Nunes will retire from Congress and start as CEO of TMTG in January. He was one of Trump’s closest allies in Congress during his presidency, and was a frequent critic of tech companies. The hiring of Nunes comes as Trump’s company faces an investigation from the SEC over its talks with Digital World Acquisition Company, the SPAC that TMTG is planning to merge with in order to go public. # ⚓ Trump_Just_Wanted_to_Remind_America_that_He_Committed Obstruction_of_Justice⠀⇛ Former President Trump went on Mark Levin’s show on Sunday to promote his new picture book, a MAGA holiday essential you can get your hands on for a mere $74.99 (or $229.99 if you want one autographed by the “author” himself). The provides a glossy overview of Trump’s four years in office, which might not have been possible, Trump told Levin, if he hadn’t fired James Comey as FBI director in May 2017. # ⚓ NSA_leaker_Reality_Winner_says_she_acted_in_‘service_to_the American_people’⠀⇛ “She actually stood up and worked for the American people to give us the truth about an attack on our vote, an attack on our democracy, an attack on our country.” # ⚓ Reality_Winner_and_the_debate_over_the_Espionage_Act⠀⇛ But there had been another [attack] that targeted the state and local officials who managed voter registration systems. The NSA — and by extension, the White House — had evidence the attack had been carried out by Russian military intelligence. Winner, then an intelligence contractor at the NSA, saw the classified report on an in-house newsfeed in early May 2017. # ⚓ 60_Minutes_speaks_with_ex-NSA_contractor_Reality_Winner about_leaking_documents_to_the_press⠀⇛ Former Air Force linguist and NSA contractor Reality L. Winner made headlines in 2017 for her arrest on charges of leaking classified information to the media. After her case dragged on for more than year, Winner pleaded guilty and was handed the longest sentence ever on a civilian for releasing unauthorized government documents to the press. She was sentenced to five years and three months behind bars for releasing a classified report that alleged the Russian military “executed cyber espionage” against local U.S. election officials in 2016. o § Misinformation/Disinformation⠀➾ # ⚓ Belarusian_KGB_accused_of_using_fake_social_media_accounts to_inflame_migrant_crisis⠀⇛ People posing as journalists and activists from Poland, Lithuania, and elsewhere in the European Union used the fake profiles to post “criticism of Poland in English, Polish, and Kurdish”, the company said in a report issued late on December 1. The West accuses Belarusian strongman Alexander Lukashenko of waging “hybrid war” by allowing migrants to fly into the country and then funneling them to the borders of EU members Poland, Lithuania, and Latvia. # ⚓ New_Greek_law_against_disinformation_endangers_press freedom⠀⇛ Under article 191 of the Penal Code, the dissemination, in public or online, of any information that “causes concern or fear among citizens” or “disturbs public confidence in the national economy, defence or public health” is now punishable by a prison sentence ranging from three months to five years. If the offence is committed repeatedly in the media or online, the minimum sentence increases to six months in prison. These penalties are not limited to the person who is the source of the information. They also apply to the owners and directors of the media that publish it, or simply publish links to it. The previous version of the Penal Code provided for a prison sentence ranging from six months to three years for disseminating false information that had “the effect of causing fear” or entailed “a risk of harm” to society. Public health was not included in the list of sensitive sectors. # ⚓ “Powered_by_AI”_has_become_a_marketing_gimmick:_Zerodha CTO⠀⇛ “Anecdotally, pretty much every single instance of “Al-first mindset” that I have seen in the industry have been strong cases of misguided assumptions, outright delusions, and often, intellectual dishonesty. “Al-first mindset” tends to fall into the solution looking for a problem category so much that personally, I am highly sceptical of anything labelled “powered by Al”.” o § Censorship/Free Speech⠀➾ # ⚓ Twitter_Admits_It_Messed_Up_In_Suspending_Accounts_Under Its_New_Policy,_But_Policies_Like_This_Will_ALWAYS_Lead_To Overblocking⠀⇛ Last week, we called out a questionable move by Twitter to put in place a new policy that banned images or videos that included someone without their permission. The company claimed that this was to prevent harassment and also (for reasons I still don’t understand) buried the fact that this was not supposed to apply to public figures or newsworthy media. However, as we pointed out at the time, the standard here was incredibly subjective, and wide open to abuse. Indeed, we pointed out examples in that article of the policy clearly being abused. And even as Fox News talking heads insisted the policy would only be used against conservatives, in actuality, a bunch of alt right/white nationalists/ white supremacists immediately saw this as the perfect way to get back at activists who had been calling out their behavior, leading to a mass brigading effort to “report” those activists for taking pictures and videos at white nationalist rallies and events. # ⚓ Sialkot_no_surprise⠀⇛ With that out of the way, I’m sure the official condemnation will be even more vociferous now, due also in no small part to the fact that this time the blasphemy brigade has claimed the life of a foreign national from a friendly country. After all there’s this geo-economic reset to think about. We’ll see the truth of this soon enough when the next Pakistani — be he or she Muslim, Hindu, Christian or otherwise — is lynched in the name of blasphemy. Because that’s going to keep happening no matter what becomes of those arrested in the Sialkot lynching. You know it, and I know it too. And if you believe otherwise, you may as well try to cure cancer with dispirin. Make no mistake; there will be several thousand more Kumaras and Mashals before this runs its course, if it ever will. And let’s face another fact. It won’t end. Why should it? # ⚓ Peng_Shuai_and_the_Real_Goal_of_Chinese_Censorship⠀⇛ “Even if I court disaster like an egg against stone or a moth to a flame, I will tell the truth about you and me.” So wrote Chinese doubles tennis star Peng Shuai. Her post lasted 30 minutes on Weibo before it was censored, and her name rendered unsearchable. # ⚓ My_Take:_Ways_you_or_your_gamer_kids_can_help_battle censorship_in_China⠀⇛ Even the Internet browser the Chinese populace is forced to use is of China’s own creation, controlling the narrative by altering facts, adding propaganda, and omitting any hint of troubling conditions. Hence, freedom of speech is almost entirely stifled, which creates nearly insurmountable challenges for those wanting to create change through political or nonviolent means. # ⚓ ‘Eating_melons’:_Chinese_people_dodge_censors_to_discuss Peng_Shuai_sexual_assault_allegations⠀⇛ When Peng last month posted that former Chinese vice-premier Zhang Gaoli forced her to have sex, censors were quick to scrub the message and obvious discussion of Peng from social media. # ⚓ Facebook_removes_accounts_targeting_critics_of_Vietnam’s government⠀⇛ Facebook’s parent company removed a network of accounts on the platform that coordinated attacks against Vietnamese activists who criticized the government, but Hanoi said the removed accounts belonged to “anti-state” elements. In its Adversarial Threat Report published Wednesday, Meta said users of the accounts abused Facebook policy by “mass reporting,” which is an organized effort to flag content with the intent of getting its author’s account suspended. The accounts in this case targeted anti-government posts. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ Australia_Has_Sacrificed_Julian_Assange_to_the_United States⠀⇛ The US is fighting tooth and nail to get Julian Assange extradited to an American prison. Ever the dutiful ally, the Australian government is effectively giving over Assange, and flouting any commitment to human rights, freedom of the press, and democracy in the process. # ⚓ Mauritian_parliament_imposes_tougher_regulations_on broadcast_media⠀⇛ “Wake for freedom of expression,” was the front- page headline in the Mauritian newspaper L’Express yesterday morning, a few hours before the national assembly approved the Independent Broadcasting Authority (Amendment) Bill, giving the authorities extensive powers to penalise the island nation’s very popular privately-owned radio stations and jeopardising the confidentiality of journalists’ sources. The law would enable the director of the Independent Broadcasting Authority (IBA), the national broadcast media regulator, to ask a judge to order journalists to reveal their sources or “produce any record, document or article needed for the exercise, by the Authority, of its regulatory powers.” And it establishes no legal safeguards for this practice. # ⚓ After_targeting_journalists,_Russian_authorities_now targeting_their_lawyers⠀⇛ “These proceedings and this use of the ‘foreign agents’ label against media lawyers is designed solely to put additional pressure on the journalists they defend, to isolate these journalists and to deter those who could assist them,” said Jeanne Cavelier, the head of RSF’s Eastern Europe and Central Asia desk. “We urge the Leningrad region bar association and the Russian justice ministry not to yield to the FSB’s pressure and to drop all the baseless proceedings against lawyers who defend journalists, so that they can practice their profession in the manner prescribed by the law.” The authorities began a year ago to place media outlets, journalists and now lawyers on the “foreign agents” list. The two Komanda 29 lawyers were preceded by the head of the Mass Media Defence Centre (MMDC), a leading source of expertise and legal assistance for media in difficulty, who became the first lawyer to be placed on this denigratory register on 8 October. There were 11 media entities on the list in December 2020 but another 85 entities and journalists have been added in the past year. o § Civil Rights/Policing⠀➾ # ⚓ How_US_Guns_Destabilize_Latin_America_and_Fuel_the_Refugee Crisis⠀⇛ # ⚓ Opinion_|_UK_Police_Bill_Is_an_Attack_on_the_Rights_of Everyone_Who_Has_a_Cause_They_Believe_In⠀⇛ Just over a year ago, disturbing reports began trickling out: the British government was preparing an attack on the right to protest. The right through which we won many of the things we take for granted today—from voting rights to marriage equality—which allows all of us to stand up against injustice. Now we know the government is taking a sledgehammer to this right, smashing everyone’s ability to stand up to power. # ⚓ Urging_Dems_to_‘Fight_for_Justice,’_Progressives_Launch ‘Pass_the_PRO_Act_Holiday_Tour’⠀⇛ Declaring that “workers are under attack,” Our Revolution—the progressive advocacy group born from Sen. Bernie Sanders’ 2016 presidential campaign—Communications Workers of America, and the Worker Power Coalition on Monday rallied outside the Phoenix office of Sen. Kyrsten Sinema to kick off the “Pass the Pro Act Holiday Tour.” “We have a chance to pass the most important labor law since FDR, since the 1930s.” # ⚓ Prison_Officials_Punished_Me_With_Solitary_—_Against_Their Own_Rules⠀⇛ # ⚓ Why_Amazon_Is_Terrified_of_Its_U.S._Workers_Unionizing⠀⇛ Stuart Appelbaum, president of RWDSU, accused Amazon of engaging in “efforts to gaslight its own employees,” and filed a petition in April to nullify the vote. After investigating the union’s assertion, the NLRB decided that Amazon interfered so blatantly in its workers’ ability to vote that a second election is now in order. The ruling detailed how, in spite of the NLRB denying Amazon’s request to install a mail collection box right outside the warehouse entrance, the company did so anyway, giving workers the impression that it was involved in the vote counting. Additionally, the company distributed “vote no” paraphernalia to workers in the presence of managers, forcing them to declare their support of or opposition to the union. And, Amazon held what the NLRB called “captive audience meetings” with small groups of workers, “six days a week, 18 hours a day,” in order to blast the approximately 6,000 employees who were eligible to vote with anti-union messaging over the course of the voting period. # ⚓ Opinion_|_The_Donald_Also_Rises?⠀⇛ What alt-right guru Steve Bannon failed to create, German taxpayers have just stepped in to revive: a Nationalist International. Thanks to the German government, the far right is about to get its own well-heeled global think tank, complete with the sort of political academy that was so dear to Bannon’s plan for world domination. # ⚓ The_Far_Right_Continues_to_Build_Its_International⠀⇛ Germany’s gift to the far right is the Desiderius Erasmus Foundation, the public-policy arm of the country’s most prominent extremist party, the Alternative für Deutschland (AfD). Erasmus, a Dutch humanist of the Renaissance best known for his ironic essay “In Praise of Folly,” would have been appalled at such a grotesque misappropriation of his name. The AfD, after all, has built its political base on a series of follies diametrically opposed to humanism, from its initial anti- immigration screeds to its current overtures to the anti-vaccination crowd. Strangely enough, the AfD underperformed in the recent German elections, its parliamentary delegation losing 11 seats. Still, by capturing a little more than 10% of the vote, the party made it into parliament a second consecutive time. As a result, it qualifies for what all other major parties also receive: government support of its foundation. Unless legal efforts to block this largesse succeed, the Erasmus foundation will soon enjoy the equivalent of tens of millions of taxpayer dollars a year. # ⚓ Dems_Mark_Anniversary_of_13th_Amendment_With_Calls_to ‘Close_the_Slavery_Loophole’⠀⇛ Congressional Democrats on Monday marked the 156th anniversary of the ratification of the 13th Amendment to the U.S. Constitution by calling on federal lawmakers to end a form of slavery that has been allowed to persist in the United States. “Abolishing slavery can’t come with a loophole.” # ⚓ Opinion_|_Bracing_for_a_Post-Roe_South_in_the_Region’s_Last Three_Abortion-Safe_States⠀⇛ The U.S. Supreme Court this week heard oral arguments in Dobbs v. Jackson Women’s Health Organization, a high-profile case about the constitutionality of Mississippi’s ban on abortions after 15 weeks of pregnancy. The state’s Republican-controlled legislature passed the law, which has no exceptions for rape or incest, in 2018, with the intention that it would take effect if Roe v. Wade were overturned. That landmark 1973 case set out a legal framework that protected the right to an abortion until fetal viability at 24 weeks of pregnancy. # ⚓ If_Roe_v_Wade_Ends,_So_Will_Easy_Re-Elections_for_Right- Wing_Republicans_and_Neoliberal_Dems⠀⇛ Such a decision in the current case before the High Court, which involves Mississippi’s recently passed ban on the abortion of any fetus where a “heartbeat” can be detected, would be a major loss for women’s rights, particularly in the Republican Party-dominated states that can be expected to push rapidly for bans on abortion if they haven’t passed such laws already (some 21 such states are said to be preparing legislation to outlaw abortions like Mississippi and Texas have done if the High Court overturns its long-standing ruling denying states the right to ban abortions outright). But I would argue that in the long run this legal U-turn, if it happens, may prove to be a  Pyrrhic victory for the reactionaries and the white fundamentalist Christian zealots whom the Republican Party has been pandering to for decades over this issue of “reversing Wade.” # ⚓ Why_Women_Will_be_Collateral_Damage_in_the_Abortion_War: the_View_of_a_Former_State_Supreme_Court_Justice⠀⇛ It goes without saying that Judges should be immune from partisan and sectarian pressures when deciding cases involving a woman’s right to make decisions about her own body and her private reproductive choices free from government interference. Notwithstanding, however, it appears that a majority of the Court has adopted Republican and religious right conservative ideology; and that will likely result in a decision against these women’s rights. Recall that, historically, abortion has been a part of American history since its inception. States began to criminalize it the 1870s, with the result that by the 1960s there were hundreds of thousands of illegal abortions a year endangering women. Based on sound medical practice, states began to de-criminalize pregnancy terminations, leaving the matter to the woman and her doctor. By 1972, (the year Roe v. Wade was handed down) 64% of Americans (59% of Democrats and 68% of Republicans) agreed with this medical model. # ⚓ How_a_Supreme_Court_Decision_Limiting_Access_to_Abortion Could_Harm_the_Economy_and_Women’s Well-Being⠀⇛ But reproductive health isn’t just about abortions, despite all the attention the procedures get. It’s also about access to family planning services, contraception, sex education and much else – all of which have also been under threat in recent years. Such access lets women control the timing and size of their families so they have children when they are financially secure and emotionally ready and can finish their education and advance in the workplace. After all, having children is expensive, typically costing almost US$15,000 a year for a middle-class family. For low-income working families, child care costs alonecan eat up over a third of earnings. # ⚓ Unapologetic_Support_for_Abortion_Rights_Must_Be_a_Pillar of_the_Left⠀⇛ # ⚓ Deutsche_Welle_halts_cooperation_with_Jordanian broadcaster⠀⇛ Deutsche Welle (DW), Germany’s international broadcaster, has established an independent investigation into a press report on antisemitic remarks made by some members of the editorial staff at DW’s Arabic service. Director General Peter Limbourg has emphasized that there is a zero-tolerance policy toward antisemitism at DW. # ⚓ Here’s_Why_Movie_Dialogue_Has_Gotten_More_Difficult_To Understand_(And_Three_Ways_To_Fix_It)⠀⇛ This problem indeed goes far beyond simply flipping a switch or two on a mixing board. It’s much more complex than I anticipated, and it turns out there isn’t one simple element that can be singled out and blamed as the primary culprit. “There are a number of root causes,” says Mark Mangini, the Academy Award-winning sound designer behind films like “Mad Max: Fury Road” and “Blade Runner 2049.” “It’s really a gumbo, an accumulation of problems that have been exacerbated over the last 10 years … that’s kind of this time span where all of us in the filmmaking community are noticing that dialogue is harder and harder to understand.” Join me and these industry experts as we sort through that “gumbo” and identify some of the most prominent reasons it has become more difficult to, in the paraphrased words of Chris Tucker’s Detective Carter in “Rush Hour,” understand the words that are coming out of characters’ mouths. # ⚓ Police_raid_home_of_Human_Rights_Association_head_Eren Keskin’s_mother_at_midnight⠀⇛ “But what does it mean to come to my home at this hour? A statement at this hour? I would go to testify had they summoned me verbally. Moreover, my lawyer friends got power of attorney,” said the lawyer. “Call me and I’ll come. They called me after raiding the home.” o § Internet Policy/Net Neutrality⠀➾ # ⚓ The_Law_Bytes_Podcast,_Episode_111:_The_Story_Behind JusTech_–_How_Three_University_of_Ottawa_Law_Students_Created a_Technology_Compliance_Solution_for_Privacy_Breach_Rules⠀⇛ CBC News, How to Keep Your Information Secure Amid Data Breaches # ⚓ GOP_Claim_That_Biden_FCC_Nom_Gigi_Sohn_Wants_To_‘Censor Conservatives’_Is_AT&T_&_Rupert_Murdoch_Backed_Gibberish⠀⇛ We’d already noted how telecom and media giants are hard at work trying to scuttle the nomination of consumer advocate Gigi Sohn to the FCC. Sohn is not only a genuine reformer, she’s broadly popular on both sides of the aisle in telecom and media circles. So companies like AT&T and News Corporation, which enjoyed no limit of ass kissing during the Trump era, are working overtime to come up with some feeble talking points loyal politicians can use to oppose her nomination. It’s not going well. # ⚓ DNS_doesn’t_“propagate”⠀⇛ This came up because I was showing a friend a demo of how DNS caching works last week, and he realized that what was happening in the demo didn’t line up with his mental model of how DNS worked. He immediately brought this up and adjusted his mental model (“oh, DNS records are pulled, not pushed!“). But this it got me thinking – why did my very smart and experienced friend have an inaccurate mental model for how DNS works in the first place? First – I’m very tired of posts that complain about how people are “wrong” about how a given piece of technology works without explaining why it’s helpful to be “right”. So here’s why I like knowing how DNS works. o § Monopolies⠀➾ # ⚓ Dems_Urge_DOJ_Antitrust_Probe_Into_$43_Billion_Discovery- WarnerMedia_Merger⠀⇛ Nearly three dozen congressional Democrats revealed Monday that they are calling on the Biden administration to investigate the proposed $43 billion merger of Discovery and WarnerMedia for antitrust law violations and whether it will reduce diverse content. “Corporate consolidation and monopolistic practices come at the direct expense of workers, consumers, competition, innovation, fairness, and equity.” # ⚓ Why_Apple_may_be_planning_life_after_Arm⠀⇛ Like so many companies, Apple is a licensee of Arm, which means it very likely shares competitively sensitive information with Arm, which is seen as a neutral partner. In the event Nvidia took possession of Arm, that neutral status would be in doubt, and the chip development company might become less likely to innovate in ways challenging to Nvidia’s interests. Nvidia could also gain access to historically confidential data from Apple and other competitors. # ⚓ AT&T_CEO_Calls_Congressional_Letter_Opposing_Discovery- WarnerMedia_Merger_“Unfounded”⠀⇛ As the deal to create the newly-titled WarnerMedia Discovery company awaits regulatory approval, the pending mega-merger of Discovery and AT&T’s WarnerMedia is set to close during the first half of 2022. While insisting the antitrust review process was going according to expectations, Stankey discounted the overture from the Democratic Congressional members. # § Patents⠀➾ # ⚓ Steely_Dan,_The_CIA_and_the_acid_anthem_of_‘Kid Charlemagne’⠀⇛ It seems very un-1960s-like to mention admin, but in 1963, the patent for LSD expired, and a lot of the culture thereafter spun out from that tie-dye three years where mind-bending was basically legalised. It wasn’t just the hippies at it either. The CIA, an organisation that has seemingly welcomed more well-manicured arseholes than every one of Hugh Hefner’s pool parties combined, were dabbling in its kaleidoscopic properties to no end. Somewhere from this melee of psychedelic mania derives the Steely Dan acid anthem ‘Kid Charlemagne’. Be forewarned before you trip down this rabbit hole things get fairly strange, dude. # ⚓ Feds_Uncover_Alleged_$20_Million_Music_Royalty_Scam_— 50,000+_Songs_Illegally_Claimed⠀⇛ The Department of Justice just recently shed light upon the shocking indictment, which alleges that a 36-year-old Arizona resident named Jose Teran and a 38-year-old Florida resident named Webster Batista established a company called MediaMuv. Via MediaMuv – the web presence of which looks to have been scaled back dramatically, currently consisting of a few inactive social-media accounts – the defendants are alleged to have collected north of $20 million, as mentioned at the outset. This alleged scam kicked off in 2016, according to the government agency’s release, and Teran and Batista are said to have “first claimed they had the legal right to monetize over 50,000+ songs” back in mid-February of 2017. Then, the royalty-minded crooks allegedly inked “contractual agreements” with “two third party companies,” the names of which aren’t disclosed in the text, maintaining that they possessed “legal rights over the music they claimed to control.” # § Copyrights⠀➾ # ⚓ Hollywood,_Netflix,_Amazon_&_Apple_Sue_Two_Pirate IPTV_Providers_in_the_US⠀⇛ A coalition of Hollywood studios plus Amazon, Netflix and Apple have sued two IPTV providers in the US. Targeting AllAccessTV and Quality Restreams, which are allegedly operated by the same person, the complaint claims that sales take place through a fake VPN website and a large network of resellers who funnel customers and revenue to the platforms. # ⚓ DNS-Resolver_Quad9_Loses_First_Pirate_Site_Blocking Appeal_in_Germany⠀⇛ DNS-resolver Quad9 has lost its appeal against Sony Music’s pirate site-blocking order at the Regional Court in Hamburg. The non-profit Quad9 Foundation is disappointed with the outcome but isn’t giving up the legal battle just yet, noting that various Internet services are at risk if the order isn’t successfully challenged. # ⚓ Public_Fallout_Over_Take-Two_Playing_IP_Troll Begins⠀⇛ Take-Two Interactive continues to find itself in the news for all the wrong reasons. The game publisher and parent company of Rockstar Games, the studio behind the Grand Theft Auto franchise, had a reputation built for itself for making great AAA video game titles. More recently, its reputation centers more on its aggressive actions on all things intellectual property. The company has gone after its own modding community, seeing it as a threat to its release of a shitty anthology of past GTA games. The company has also found itself going after companies in totally unrelated industries over the silliest of trademark concerns. And, most recently, there was speculation that there was a threatened opposition to the trademark application filed by Hazelight Studios for its indie hit game It Takes Two, as though anyone were going to take that common phrase and confuse it with the much larger game publisher. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 9420 ➮ Generation completed at 02:42, i.e. 52 seconds to (re)generate ⟲