𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, November 19, 2021
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Sat 20 Nov 02:40:34 GMT 2021
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2021/11/19/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
  Previous bulletins in IPFS (past 21 days, in chronological order):

QmR26bCkmAgeJHsLEpDDduxsZtvTiPxLdppYuH4w8mzfdo
Qmex86DPLV4yK5WC34kReVXbdEtRT7fvt7mBVzMTGbSCct
QmUF9ey4dzyvtaKZQVc5QTVyN1uh5C8nqhzm5bDtAjMpUH
QmQQsCU87GH58r3ULuJPn4a3DUUCqjRgtvTnrTgEzE32uB
QmXo7j8hPUpwapnbFNNyHpSzJw8jxwrfGCZfVzhG6m46Fc
QmWRUGR4iW5rnmLQnw9FgqKFSzKTya3pneRJvmK2VknwKJ
QmRj8aGQBLtRqtiYJQreD9xtEMzqDcpaLPjFYLoe48xgQ5
QmceuRQeatSitbW6vADhod8yMXLWphJhT1uYZmcy4rjm6f
QmewryoNvgmB7zLqV7RQ2PTLYkagYXvBASicFQi1ESPiHm
QmViJLHdiRf7wrstUaHcTaXuiWpGyTkptFkDjYAFoJBJoj
QmVzPu6Qip7yK3FGSsrMzEt3zNmqWufLFF5CZNmsVbHZLd
QmYTFyk7SSEVeJPYyyFr91pb7fbKnpS4kiFjty9U136upV
QmYKBd728JBm11x2JbtET9sF2KJXtKjGPDD1jVnpt7fLqz
QmQba8m7JeAYTn4JDwkhe5nDZfnw9TnSASsQqLF7LBYEg2
QmT9Hh5LgzS2eg26pkvFLpdGLNAEURRLod8DffDCczhxy1
QmdEutfCAc7HzKtnLt7k7b2dajGSqfBSGnEPAuD2bontJM
QmSuWrcnwPk5e1gVWiJbTq7uxUkNn8DzRVm659JmGTFR5W
QmRDvU3Bb1mJHK7qGvaLg5kKvJ9tXx4qDntaaZU2EPXgnr
QmXnPPSuiAbypBs2W4Hu14xEgjjptzNmzCptadFdRv7xt5
Qmed7VnZALGrUYrCRnPW72Zg4XmWFjZQUFe7BHLQ4EWp12
Qmak6N1wRPKAPf9DxMtCC9P4rZVS2rKi58Zcinr7iLRtd5


╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ 32,000 Blog Posts | Techrights

⦿ For the Second Month in a Row, Almost Half a Million Page Requests Over Gemini Protocol (gemini://) | Techrights

⦿ IRC Proceedings: Thursday, November 18, 2021 | Techrights

⦿ EPO: We Support Women and Gay People, But We Also Support People Who Behead Them (in the Interest of Patent Profits) | Techrights

⦿ Techrights is for Whistleblowers and Suppressed Information Which Other Sites Refuse (or Are Afraid/Shy) to Publish | Techrights

⦿ [Meme] Patent Searches and Examinations Without Colleagues to Help (and Line Managers You Cannot See) | Techrights

⦿ New Ways of Working for António Campinos, Even From One’s Own Home During a Crisis | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/11/19/32000-blog-posts/#comments
		http://techrights.org/2021/11/19/gemini-protocol-usage-is-growing/#comments
		http://techrights.org/2021/11/19/irc-log-181121/#comments
		http://techrights.org/2021/11/19/ksa-patent-profits/#comments
		http://techrights.org/2021/11/19/on-suppressed-information/#comments
		http://techrights.org/2021/11/19/patent-examination-pandemic/#comments
		http://techrights.org/2021/11/19/working-peasants-for-campinos/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/11/19/freebsd-12-3-rc2/#comments
		http://techrights.org/2021/11/19/pureos-10-released/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 66

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/19/32000-blog-posts/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/19/32000-blog-posts/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.19.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ 32,000_Blog_Posts⠀✐


Posted in Site_News at 10:02 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇wordpress-techrights⦈_


Summary: Depending on whether one counts all posts, including drafts (or only
published ones), this week we cross another important threshold and mark a
milestone


THE site turned 15 earlier this month and around the same time our Gemini
capsule exceeded_38,000_pages. We’re growing at a fast pace, owing to the hard
work of sources and activists. We have some important revelations in the
pipeline and we aren’t releasing them as fast as possible, mostly in the
interest of impact (giving people time to catch up and digest material never
seen elsewhere).


On the coding_side, the past week has been eventful and this morning we came
under a DDOS attack lasting about 10 minutes. We already have mitigation code
in place — programs that improve over time to secure uptime/availability. █


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⡦⡀⠀⠀⠀⠀⣀⠀⢀⡄⣀⠀⢀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠁⠉⠀⠀⠈⠀⠁⠀⠈⠁⠈⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣾⣸⣇⣿⣽⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⢾⠛⠀⠸⠛⠞⠞⠼⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⢋⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 115

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/19/gemini-protocol-usage-is-growing/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/19/gemini-protocol-usage-is-growing/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.19.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ For_the_Second_Month_in_a_Row,_Almost_Half_a_Million_Page_Requests_Over
Gemini_Protocol_(gemini://)⠀✐


Posted in Site_News at 12:29 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 1d7923ae1c2b91270f1899ddf9d294e2


http://techrights.org/videos/stats-gemini-november.webm


Summary: Based on the latest stats (see below or the video above), we’re steady
at around 15,000 page requests per day (on average) over gemini://, which is a
new but very exciting protocol for hypertext on the Net


AROUND the same time last month we noted that we had reached the point where
almost 500,000 pages are requested (per month) over gemini://, which is a new
and simplified Internet protocol for pages (alternative to the bloated World
Wide Web).


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Bortzmeyer's Gemini stats⦈ As I show in the video above,
this month is similar and we’ve implemented improvements to the means of
tracking traffic (the underlying code is in_our_self-hosted_Git_server and is
freely available).


Earlier this week we pondered setting up our very own gemini:// -> https:/
/ gateway. For practical reasons we gave up on it for the time being. Instead
we encourage readers to download a proper Gemini client and access the capsule
in the intended way, basically navigating to gemini://gemini.techrights.org,
which is still considered the biggest capsule in Gemini space (the screenshot
on the right is new).


There will soon be 1,800 known (to Lupa at least) capsules. “There are 1783
capsules,” it says at this moment. “We successfully connected recently to 1450
of them.”


Less_than_11_months_ago_it_was_506_and_many_of_the_today’s_“top”_capsules_did
not_even_exist_back_then. The third-biggest capsule (by Lupa’s metrics/reach)
was fewer than 3,000 URLs in total. For comparison’s sake, today’s tenth-
biggest is 5,711 URLs in total. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠈⣿⣆⢠⣿⢁⣤⣄⢠⣤⣠⣦⠀⢀⣤⡄⣤⣄⢠⣤⣤⣤⣠⣤⣤⣤⡄⣠⣤⣠⣤⣄⠀⢀⣤⣤⣤⣤⢤⣤⣄⣠⣤⣤⢠⡌⣿⢀⣤⡀⣤⡄⠀⢹⣤⡤⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⢀⣿⣻⡞⣿⡸⣇⣸⢸⣻⢾⣇⠀⢺⣄⡹⣇⣸⣸⣇⣿⣸⣿⣇⣿⣸⣇⣇⣸⢿⣇⣿⠀⠸⣇⣈⣞⣻⣸⣇⡿⣝⣷⢸⣀⣇⣿⣸⣟⡃⣟⡦⠀⢸⣀⡿⠹⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣤⠄⢤⡤⣤⣤⣄⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠈⣿⢻⢸⡇⣿⢹⠛⡟⢻⢸⡟⣷⣾⣿⣾⡟⠃⢠⡟⢳⡜⡟⠀⠘⣏⣶⣹⢳⡟⣷⢻⠛⣿⣼⠋⡇⢻⠛⡇⣾⣻⠇⠀⣿⠀⢸⡇⣿⢴⡟⠀⡇⠀⡰⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠐⠛⠚⠊⠓⠛⠚⠒⠓⠚⠚⠓⠋⠙⠒⠚⠓⠀⠈⠓⠚⠐⠓⠀⠀⠙⠈⠃⠘⠓⠋⠚⠂⠛⠙⠓⠓⠚⠒⠓⣟⣻⡆⠀⠘⠓⠚⠑⠛⠂⠛⠒⠓⠒⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢠⣤⣦⣤⣤⢤⢤⣼⣧⡤⡤⡇⠠⡦⣤⣄⡤⣼⣧⣤⣤⣧⡤⣴⣿⢤⣶⣤⡄⢀⡤⡤⡤⣤⢴⢠⠀⠐⡇⢸⢹⣾⢹⣶⢻⣶⢻⡆⢸⡇⢹⢹⣏⡷⢹⠁⢠⣤⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣛⡟⠛⠚⠚⠚⠛⠛⠓⠓⠓⠆⠓⠛⠋⠳⠚⠛⠛⠃⠛⣟⣳⠛⠚⠻⠛⠃⠎⠳⠛⠓⣾⣻⠴⠀⠐⠓⠚⠚⠙⠚⠙⠚⠙⠚⠃⠈⠓⠚⠘⠛⠓⠚⠒⠛⠟⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⡄⡄⡀⡀⢀⡀⠀⠀⠀⡀⢀⡀⠀⡀⡀⢀⠀⣠⢤⢠⢤⣠⢤⣠⢤⡀⢤⡄⢤⢤⡤⡄⢤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⢸⣯⣿⣏⣏⣏⣏⣿⣛⣏⣡⢿⣙⣏⣿⣿⣿⣹⢨⠀⢹⣺⢻⣺⢿⣺⢿⣺⠇⠸⣇⣸⢸⡿⣇⣸⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⢠⣶⣦⣶⣴⢶⢶⣼⣷⡶⡞⡇⠐⡶⣴⢦⣿⢶⣀⣸⡷⣤⠶⣼⣷⡷⡶⣦⡶⣦⠀⡴⢦⡶⣆⠐⡖⡎⣧⡖⠆⠀⣯⣷⣯⣷⣯⣿⡿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠞⠓⠚⠚⠚⠛⠛⠓⠓⠓⠓⠓⠙⠚⠛⠚⠀⠘⠛⠋⠓⠛⠛⠓⠓⠋⠓⠛⠓⠓⠊⠓⠃⠃⠓⠓⠛⠓⠃⠀⠓⠋⠓⠋⠓⠋⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⢤⣤⡄⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⢸⣷⣏⣸⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢠⣤⣾⣧⡦⠀⣤⢤⣤⢤⡤⣤⢤⢦⠀⢸⢠⣴⡤⠄⠰⣏⡷⣟⣗⣯⡷⣏⡇⠈⡏⠈⡏⣏⡿⢸⡇⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣛⡞⠋⠓⠓⠚⣇⡏⠘⠛⠛⠘⢺⡘⠚⠚⠛⠓⠂⠘⠒⠛⠒⠛⠓⠃⠒⠃⠀⠛⠚⠑⠓⠙⠚⠓⠃⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀⣀⢀⣀⣀⢠⣄⣀⢀⡄⠀⣀⢀⣀⢀⡀⣀⣀⣀⠀⣀⡀⢀⣀⣀⣀⡠⡄⡀⣀⢀⠀⢠⢤⣠⢤⣠⢤⣄⡤⡄⢠⡤⢤⢤⡤⣄⢤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢸⣿⣻⣟⣻⣹⣹⣿⣿⣏⣏⣇⣬⣻⢼⣹⢿⣻⣹⣹⣹⣠⠘⡾⡾⢺⣹⣺⣁⣿⣽⣻⢬⠀⢸⣺⢿⣻⢇⡞⢸⣽⡇⠸⣇⣸⢸⣟⣧⣸⣀⣼⣻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⢠⣶⣦⣶⣶⢶⢶⡄⢸⠲⣤⣶⣶⢶⢰⣲⡶⠖⡶⣖⡆⣿⢻⠂⢸⢰⣶⡔⡟⡖⣦⠶⠀⢯⣿⢿⣽⣾⢭⣾⢭⠀⢹⠁⣿⢹⣽⠏⣿⢀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⠓⠚⠚⠚⠛⠛⠚⠙⠓⠚⠚⠚⠛⠛⠒⠓⠛⠓⠛⠘⠚⠚⠚⠛⠓⠓⠓⠋⠛⠀⠓⠋⠓⠋⠙⠚⠙⠚⠀⠘⠛⠃⠚⠊⠓⠛⠚⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⡆⢀⣔⣆⡀⣀⣀⣀⡀⣀⢀⣀⠀⣀⣀⢀⣀⣄⣀⠀⣤⢦⣤⢦⢠⠶⠰⢦⠀⢰⠆⢶⢲⡦⡄⣶⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢸⣿⡿⣿⢻⣸⣼⣿⣿⣯⣧⣇⡄⣧⣇⣿⢿⡇⣧⣯⣿⢾⣿⢤⣿⣸⢿⡿⣧⢬⠀⢩⡿⢾⣽⠹⣽⢶⣯⠄⠸⣦⡼⣸⡟⣧⣿⣤⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⡀⢀⣀⠀⣀⡀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⢰⣶⣷⣶⣶⢲⢲⣾⣷⡖⡖⡇⢠⡖⢶⠖⣶⡖⣶⡖⡖⡆⣶⣶⣶⡆⢠⡖⣶⡶⣶⣾⠒⠀⠿⢽⣿⢾⠈⡇⠨⢾⡀⢸⡀⢸⢸⢼⡇⣿⢀⢰⣖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃⠙⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠋⠙⠉⠉⠿⠿⠉⠀⠙⠉⠉⠋⠈⠉⠈⠋⠀⠈⠙⠁⠉⠁⠉⠉⠉⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸

                    ䷩ 𝚕𝚒𝚗𝚎 227

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/19/irc-log-181121/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/19/irc-log-181121/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.19.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Thursday,_November_18,_2021⠀✐


Posted in IRC_Logs at 2:21 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      181121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-181121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-181121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      181121.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
 QmNsm6rr8kkCAADrJsmMJbHui77PRgj6KX4KVqXpazu53n #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmWzrrjs55j8QPmu5Kg1bVdsws9SKyPmwdEvGEGFqVpZ9B (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmNa2FBX6FT3wTvTkM844zbHiygk8dzV4rrFi6H8EM37do social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmeCaXTu7MkcgShGaoSzGo5ikBdRnJxCzV528jAPfJxLuu social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmRRQwL8T1sTYToaphTLVMBgpePwBWWTybKS47HbPKD35j #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmNzhMS9fnpr4JqbCYapYWrX6i24D5ZDRcTjUSYyJookum (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmbM1T8LjML1kjbQx7RHdFvdYBECke6Axys7kUgxxJzMpn #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmX3DfyHM6Ht5oAqYd3BNHHLjgisj1CiNqa8eeTs7tbAQA (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmdGDdRX8ZuGj76UZ5fvhjBZ81N9v4RyisduQDvtX5i4bQ



                    ䷩ 𝚕𝚒𝚗𝚎 356

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/19/ksa-patent-profits/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/19/ksa-patent-profits/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.19.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EPO:_We_Support_Women_and_Gay_People,_But_We_Also_Support_People_Who_Behead
Them_(in_the_Interest_of_Patent_Profits)⠀✐


Posted in Deception, Europe, Patents at 1:09 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 019a36a4fb36c48d082312ce7219d1b8


http://techrights.org/videos/epo-ksa.webm


Summary: Misogynists and infamous abusers of human rights are partners of the
EPO’s regime, serving to remind us that the EPO’s management cares about
absolutely nothing but money


JUST a_few_months_ago_we_responded to the EPO‘s persistent and repeated
pinkwashing. Autocrats who crush people of all races and sexes (remember that
Benoît_Battistelli crushed two unionists who were female, one male, before
proceeding to more staff representatives getting crushed psychologically and
morally; António_Campinos hires based on friendship and kinship, not diversity)
love pinkwashing PR because them helps distract from what they really are.


“What message does that send to women and LGBT folks working for the
EPO?”Earlier today the EPO published (warning: epo.org link) the item which I
respond to in the video above. What are the ‘unwashed masses’ supposed to think
if the EPO is bows down to regimes that barely matter to the EPO (in terms of
number of European Patents pursued)? What message does that send to women and
LGBT folks working for the EPO? █



                    ䷩ 𝚕𝚒𝚗𝚎 404

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/19/on-suppressed-information/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/19/on-suppressed-information/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.19.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Techrights_is_for_Whistleblowers_and_Suppressed_Information_Which_Other_Sites
Refuse_(or_Are_Afraid/Shy)_to_Publish⠀✐


Posted in Free/Libre_Software, GNU/Linux, Site_News at 11:21 am by Dr. Roy
Schestowitz


Video_download_link | md5sum 7aa038459e0ccd86155b67511e793914


http://techrights.org/videos/the-need-for-scoops.webm


Summary: We strive to publish material that other sites cannot or would not;
our focus is software patents and Free software, but we’re open to anything
else in the realms of tech, rights, and law


AT the start of this year we published Intel_leaks, some EPO_leaks (on the very
first day of the year) and right now we do a series about GitHub_leaks,
refuting revisionism by the mainstream media (parroting Microsoft instead of
actually investigating the facts).


What’s particularly interesting about these GitHub leaks is that some
mainstream sites turned down the source, for reasons we’ll show in the coming
months (we shall also name the culprits). The Web needs a place that’s willing
to protect sources and publish what they have to say, even in the face of
incredible pressure, including threats. Having successfully_published_32,000
blog_posts (and retracted not a single one in_15_years; also, no source was
compromised) we’re probably well equipped to do more of the same. We’ve made
ourselves relatively robust to censorship or takedown requests (related to
pressure from hosters, including ‘Clown Computing’ providers).


As people can see in our IRC channels, we shun ClownFlare and aren’t interested
in CDNs. They come at a (hidden) cost. In the video above I meant to refer to a
company that’s not actually Singaporean but also operates in Singapore
(notorious for oppressive Internet censorship). Well, the company I wanted to
allude to is Imperva, which is connected to Incapsula and is generally “dodgy”
for a number of reasons (many so-called ‘security’ companies are connected to
states).


If you have something to send us discreetly, we do have encrypted means of
communications, albeit some aren’t publicly advertised (it’s not just PGP, we
can do voice as well). Get in touch with us. IRC is typically a good start
(direct message or public). █



                    ䷩ 𝚕𝚒𝚗𝚎 469

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/19/patent-examination-pandemic/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/19/patent-examination-pandemic/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.19.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Patent_Searches_and_Examinations_Without_Colleagues_to_Help_(and_Line
Managers_You_Cannot_See)⠀✐


Posted in Europe, Patents at 7:21 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_prior_art_search⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Trying_to_get_back_to_the_office⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_Line_Managers⦈_


Summary: The EPO is transforming into a patent ‘production line’ (or pipeline)
which lacks many of the safeguards that used to exist, including real-time
collaboration among examiners and a work environment designed for the task;
António_Campinos does not care how staff feels or thinks, he just wants to
‘produce’ as many monopolies as possible for his ‘clients’


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢦⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡟⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣿⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣕⣶⠾⣶⣾⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡮⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⢼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⣿⣿⣿⣿⣿⣿⠟⢁⣀⠆⠀⠀⣤⣭⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⡀⠀⢁⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⡿⢻⣿⡧⣼⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⢇⣿⣿⠛⣻⢿⡿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠉⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢙⡁⡅⣜⢰⣪⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢠⣏⠹
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣋⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢟⣀⣀⣀⣤⣥⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣿⣿⣟⢿⡿⢿⣿⢽⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠴⢮⠽⣻⣿⣿⣿⣿⣿⣟⣻⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣷⡇⡃⢢⡻⠽⠛⠁⠀⢀⣀⣈⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣶⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠛⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣲⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠤⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⡿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣿⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡳⣶⣶⣛⣀⣳⣶⣞⣁⣳⣶⠾⣶⣾⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢺⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⡇⣿⣿⣿⣿⣿⣿⠟⢁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠂⠄⠂⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢺⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢹⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠠⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⡿⢻⣿⡧⣼⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⡛⣻⢿⡿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢾⠿⢻⡯⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠓⠎⠉⠉⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢙⡉⡁⣜⢰⣪⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⢹
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣵⣾⣭⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢟⣀⣀⣠⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣾⣯⣽⣟⣿⣿⡟⢿⡿⠟⠻⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠴⢮⠽⣻⣿⣿⣿⣿⣿⣟⣻⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣷⡆⡃⢪⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⢿⣿⣶⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣲⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠘⠑⠋⠉⣀⣠⣤⣤⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢦⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣿⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣷⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⢤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠂⢀⠀⣤⣭⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣤⣨⠿⣿⣿⣿⣿⢹⣿⡧⣼⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⡛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⡟⣻⢿⡿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢻⡯⠝⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠉⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣦⠀⠐⢩⡉⡁⣜⢰⣸⡸⠸⠼⠜⢘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣩⣿⣓⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⢹
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣟⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣋⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣟⣿⣿⡿⢿⡿⠟⠻⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠽⢿⠛⣻⣿⣿⣿⣿⣿⣟⣛⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣷⡇⡃⢢⡛⠽⠛⠋⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣶⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣶⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣄⣰⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠴⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⡿⠀⢸⠀⢸⠀⠀⣇⠀⠸⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣯⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣷⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⡶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠂⠀⠀⣤⣭⣽⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⡐⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠠⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⡿⢹⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⡛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⠟⣻⢿⣿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠉⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢩⡉⡃⣜⢸⣨⡸⠨⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⢹
⢄⣀⠰⠬⠉⠝⠛⡿⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣛⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣽⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣋⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢿⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣿⣟⣿⣿⡿⢿⡿⠟⢿⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠩⠿⢮⠽⣻⣿⣿⣿⣿⣿⣟⣻⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡇⡃⢪⡻⠽⠛⠉⠀⢀⣀⣈⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣶⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣲⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢦⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⡿⠀⢸⠀⢸⠀⠀⣇⠀⠸⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣿⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣗⣶⠾⣶⣾⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠂⠀⠀⣤⣭⣽⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣹⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⡿⢻⣿⣧⣼⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⡟⣻⢻⡿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⡿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⢻⡯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠉⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢹⡉⡅⣜⢰⣺⡸⠸⠼⠜⢘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣐⣴⣶⢨⣏⠹
⢄⣀⠰⠬⠉⠝⠛⡿⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣻⣹⣟⣻⣿⢿⣿⣟⣿⣿⣶⣿⣿⣿⣿⣾⣿⣽⣟⣶⣈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢟⣀⣀⣠⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⡿⠟⢿⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠴⢮⠽⣻⣿⣿⣿⣿⣿⣟⣻⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡇⡃⢢⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣷⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣲⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣀⣠⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢦⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣯⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣷
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣓⣶⣞⣁⣷⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⡶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢿⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⢀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠠⠄⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⢀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠠⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⣿⢹⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⡛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⡿⣻⢻⡿⡁⣀⠀⠀⠀⠀⣠⣾⣛⣧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠾⠷⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡽⢿⡯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠉⠀⠀⠀⠀⢀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢹⡉⡁⣜⢰⣪⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣐⣴⣶⢨⣏⢹
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣹⣟⣻⣿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣾⣿⣽⣟⣶⡈⠭⣛⡻⠇⢀⡿⢈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣶⣯⢲⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⡿⠟⢿⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠴⢮⠽⣻⣿⣿⣿⣿⣿⣟⣻⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡆⡃⢪⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⢿⣿⣶⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣰⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠤⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠸⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣷⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡳⣶⣶⣛⣀⣳⣶⣞⣁⣳⣶⠾⣶⣾⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠟⢁⣀⠂⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠈⠀⣀⡂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣺⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠠⠂⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⣿⢹⣿⡧⣼⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⡛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⡟⣻⢻⣿⡁⣀⠀⠀⠀⠀⣠⣾⣛⣧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠾⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡽⢿⡯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠓⠎⠉⠉⠀⠀⠀⠀⢀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢹⡉⡁⣜⢰⣨⡸⠸⠼⠜⢘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⢹
⢄⣀⠰⠬⠉⠝⠛⡿⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣟⣻⣿⢿⣿⣟⣿⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣶⡈⠭⣛⡻⠇⢀⡿⢈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢟⣀⣀⣠⣤⣥⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⡿⠟⠻⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠶⢮⠽⣻⣿⣿⣿⣿⣿⣟⣛⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣷⡇⡃⢢⡛⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣷⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣬⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣰⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣁⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠤⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⡿⠀⢸⠀⢸⠀⠀⣇⠀⠸⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣿⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣷
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣵⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⡶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢺⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠂⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⡿⢹⣿⡧⣼⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⠿⣻⢿⣿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠬⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⡯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠉⠀⠀⠀⠀⢀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢩⡁⡁⣜⢰⣚⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⠹
⢄⣀⠰⠬⠉⠝⡛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣶⡈⠭⣛⡻⠇⢀⡿⢈⣛⣛⣋⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢟⣀⣀⣠⣤⣥⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⣯⣟⣛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣏⣿⣟⣿⠿⠿⠟⢻⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠴⢮⠽⣻⣿⣿⣿⣿⣿⣟⣛⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⣷⡇⡂⢪⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣷⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣲⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⡿⠀⢸⠀⢸⠀⠀⣇⠀⠸⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣿⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣷
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣓⣶⣞⣁⣷⣶⠾⣶⣾⣶⣶⣿⣶⣶⣶⣿⡶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⡛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⣿⢹⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⢇⣿⣿⡟⣻⢿⡿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⢶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⢻⡯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠓⠎⠉⠉⠀⠀⠀⠀⢀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢹⡉⡁⣜⢰⣪⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⢹
⢄⣀⠰⠬⠉⠝⡛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣽⣛⣻⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣟⣶⣈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢰⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⣭⣝⣛⡛⠿⠿⠟⠻⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣾⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠖⢮⠽⣻⣿⣿⣿⣿⣿⣟⣻⠿⣿⣿⡿⣿⣿⣿⣿⣶⣶⣷⣶⡆⡃⢪⡛⠽⠛⠋⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣷⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣿⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣲⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣁⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢦⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣯⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣷
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣓⣶⣞⣁⣵⣶⠾⣶⣾⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡅⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⣻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠨⠀⠠⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣹⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢻⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⡿⢻⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⡛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⠟⣿⢻⡿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⡿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠓⠎⠉⠁⠀⠀⠀⠀⢀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢹⡉⡁⣜⢰⣊⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⢹
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣋⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢟⣀⣀⣠⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣟⣻⣭⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣷⣶⣮⣭⣝⣛⡛⠿⠿⠟⢻⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠶⢮⠽⣻⣿⣿⣿⣿⣿⣟⣛⠻⢿⣿⡿⣿⣿⣿⣿⣶⣶⣲⣶⡆⡃⢢⡛⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣷⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣿⣬⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣰⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣀⣠⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢦⣀⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠸⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣿⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣓⣶⣞⣁⣳⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⢤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠀⡊⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢽⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⣿⢻⣿⣧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⡛⠃⠀⠻⢿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⡟⣿⢿⣿⡁⣀⠀⠀⠀⠀⣠⣾⣛⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⠮⣭⣛⡿⠭⣽⣛⣾⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠁⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢩⡉⡁⣜⢰⣚⡸⠸⠼⠜⢘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣟⣛⣛⣻⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⢱
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣹⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣋⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣶⣯⢲⠚⢻⠉⠉⢟⣀⣀⣀⣤⣥⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⡿⣿⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⣮⣍⣝⣛⡛⠿⠿⠟⠻⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠶⢮⠽⣻⣿⣿⣿⣿⣿⣟⣛⠻⢿⡿⠿⣟⣿⣭⣿⣷⣷⣲⣶⡆⡃⢢⡻⠽⠛⠉⠀⢀⣀⣈⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⢿⣿⣶⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣰⣶⢀⡰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢦⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠸⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣿⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡌⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣓⣶⣞⣁⣕⣶⠾⣶⣾⣶⣶⣿⣶⣶⣶⣿⡶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠂⠀⠀⣤⣭⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⡛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠠⠀⠀⠀⠀⠀⣿⣿⡿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣤⣨⠿⣿⣿⣿⡿⢹⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣝⣛⠃⠀⠻⢿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⡛⣻⢿⡿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣭⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⡿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠓⠎⠉⠁⠀⠀⠀⠀⢀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢩⡉⡁⣜⢴⣊⡸⠸⠼⠜⢘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⢹
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣶⣈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣶⣯⢲⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⡿⣿⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⣾⣍⣝⣛⡛⠿⠿⠟⢻⢿⣿⣯⣭⣭⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠶⢮⠽⣻⣿⣿⣿⣿⣿⣟⣛⠻⢿⡿⠿⣟⣿⣭⣿⣷⣷⣳⣶⡆⡃⢢⡻⠽⠛⠁⠀⢀⣀⣈⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⢿⣿⣷⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣿⣬⣵⣘⣩⣽⣽⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣰⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠑⠋⠉⣁⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣯⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣓⣶⠾⣶⣾⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠴⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡅⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣭⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠠⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⣿⢻⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⡟⣛⢿⣿⡁⣀⠀⠀⠀⠀⣠⣾⣛⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠓⠎⠉⠁⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢩⡉⡁⣜⢰⣘⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣧⣭⣛⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢠⣏⢹
⠄⣀⠐⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣿⣿⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣿⣿⡟⠿⠿⢿⣿⢽⣿⣯⣭⣽⣥⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠲⢮⠽⣿⣿⣿⣿⣿⣿⣟⣛⠻⢿⡿⠿⣟⣿⣭⣿⣷⣷⣿⣷⡆⡃⢢⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣶⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠛⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣰⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠛⠑⠋⠉⣁⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠤⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣿⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣳⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠈⠀⠂⡈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢸⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠠⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠻⣿⣿⣿⣿⢻⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⢇⣿⣿⡻⣟⢿⡿⡁⣀⠀⠀⠀⠀⣠⣾⣛⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣭⣛⡻⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣯⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠓⠎⠉⠉⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣦⠀⠐⢩⡁⡁⣜⢰⣘⡸⠸⠼⠜⢘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢠⣏⢸
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣋⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢰⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣭⣟⣏⣻⠿⢿⡿⠿⢿⢿⣿⣯⣭⣭⣭⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠲⢮⠽⣻⣿⣿⣿⣷⣾⣟⣛⠻⢿⡿⠿⣟⣿⣭⣿⣷⣶⣷⣶⡆⡃⢢⡻⠽⠛⠉⠀⢀⣀⣁⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⢿⣿⣷⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣰⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠛⠑⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠤⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣷⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣷
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣳⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠻⣿⣿⣿⣿⢻⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⠇⣿⣿⡿⣛⢿⣿⡁⣀⠀⠀⠀⠀⣠⣾⣛⡥
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣭⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⡿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⢿⡯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠈⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢹⡉⡁⣜⢰⣨⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣋⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢠⣏⢸
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣶⣿⣍⣟⣿⡯⢿⡿⠿⢿⢿⣿⣯⣭⣭⣭⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠻⠋⢽⠭⣿⣿⣿⣿⣿⣿⣟⣛⠻⢿⡿⠿⣟⣿⣭⣿⣷⣷⣷⣷⡆⡃⢢⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣷⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣾⣭⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠛⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣲⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠛⠑⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠤⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣯⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣷
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡳⣶⣶⣛⣀⣳⣶⣞⣁⣑⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢥⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⡛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⡿⢻⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⢇⣿⣿⡟⣛⢿⣿⡁⣀⠀⠀⠀⠀⣠⣾⣛⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⡿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣽⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠁⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢩⡉⡁⣝⣰⣺⡸⠸⠼⠜⢘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣛⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢠⣏⢹
⠄⣀⠐⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣟⣿⣿⣿⣿⣯⣽⡿⣿⣽⣿⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢰⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣿⣿⣯⣯⣿⣿⣿⣿⣽⣿⣶⣿⣍⣟⣿⡿⢿⡿⠿⢿⢿⣿⣯⣭⣭⣭⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⠋⢯⠽⣻⣿⣿⣿⣿⣿⣟⣛⠻⢿⡿⠿⣟⣿⣭⣿⣷⣶⣷⣷⡆⡃⢢⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⢿⣿⣶⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣿⣭⣵⣘⣩⣽⣽⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣄⣲⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠙⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣯⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣷
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣳⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢽⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣭⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠻⣿⣿⣿⣿⢻⣿⡧⣼⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⢿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⢇⣿⣿⡿⣛⢿⣿⡁⣀⠀⠀⠀⠀⣠⣾⣛⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠓⠎⠉⠉⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣦⠀⠐⢩⡁⡁⣜⣰⣸⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣛⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢨⣏⢸
⢄⣀⠐⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣏⣻⣽⣟⣻⡿⢿⣿⣟⣿⣿⣿⣿⣿⣽⡿⣿⣽⣿⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢰⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡽⣿⣽⣟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣯⣍⣟⣟⡿⢿⡿⠿⢿⣿⣿⣯⣭⣭⣭⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠛⠶⢮⠽⣻⣿⣿⣿⣿⣿⣟⣛⠻⢿⡿⠿⣟⣿⣭⣿⣷⣶⣿⣶⡆⡃⢢⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣶⣶⣤⣄⣀⡁⠘⠉⠹⠛⡿⢿⣷⣭⣵⣘⣩⣽⣽⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣲⣶⢀⣴⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠛⠁⠋⠉⣁⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⣿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣯⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣿
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣳⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡅⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⢽⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⡛⢿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠻⣿⣿⣿⣿⢻⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⢇⣿⣿⡟⣛⢿⡿⡁⣀⠀⠀⠀⠀⣠⣾⣟⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣭⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⡿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣽⢿⡯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠉⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣦⠀⠐⢹⡁⡁⣝⢰⣨⡸⠸⠼⠜⢘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣛⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢠⣏⢹
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣯⣿⣿⣟⣿⣿⣽⡿⣿⣽⣿⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢲⠚⢻⠉⠉⢿⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣶⣮⣍⣟⣟⠭⢟⢿⠿⢿⣿⣿⣯⣭⣭⣭⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡩⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⠿⢿⠟⣻⡻⣿⣿⣿⣿⣿⣛⠻⢿⡿⠿⣟⣿⣭⣿⣷⣷⣷⣶⡆⡃⢪⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣶⣶⣤⣤⣀⡁⠘⠉⠸⠛⡿⢿⣾⣭⣵⣘⣩⣽⣽⠿⠿⠛⠛⠛⠛⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣰⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠙⠙⠋⠉⣁⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⡿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣯⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣷
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣛⣀⣳⣶⣞⣁⣳⣶⠾⣶⣾⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡍⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⡛⢿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⢺⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⡨⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠿⣿⣿⣿⣿⢻⣿⡧⣼⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⢇⣿⣿⠿⣛⢿⡿⡁⣀⠀⠀⠀⠀⣠⣾⣛⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣽⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢿⡯⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠁⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣦⠀⠐⢩⡁⡁⣜⢰⣸⡸⠸⠼⠜⣘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣙⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢠⣏⢸
⢄⣀⠐⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣭⣭⣗⣻⡿⢿⣿⣭⣿⣿⣟⣿⣿⣽⡿⣿⣽⣿⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢰⠚⢻⠉⠉⢿⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⣶⣿⣝⣿⣛⠟⠿⣿⠿⢿⢿⣿⣯⣭⣭⣭⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡉⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣟⣿⣭⣿⣷⣶⣶⣶⡆⡃⢢⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣷⣾⣭⣝⣛⡛⠛⠿⢿⣿⣿⣿⣿⣿⣵⣘⣩⣽⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣲⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣶⣶⣤⣄⣈⡁⠛⠙⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠦⢤⣄⣄⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣧⣇⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣀⡇⠀⢠⠀⠙⠀⢠⠀⠸⣿⡇⠀⢠⠀⢹⠀⢠⠀⢸⠀⠀⡏⠀⢠⠀⢹⠀⠀⡀⠈⣿⣿⠇⠀⠀⢻⠀⠀⡄⠈⣇⡀⠀⣀⣼⡟⠀⢠⠀⢸⠀⠀⣀⣿⠀⠀⠈⡇⠀⢠⠀⢸⠃⠀⡄⠀⠇⠀⢸⠀⠀⣿
⣿⣿⣿⠀⠀⠉⡇⠀⠈⢀⡀⠀⢸⠀⠀⣿⡇⠀⠈⠀⣸⠀⢈⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠠⣿⣿⠀⢠⠀⢸⠀⠀⡁⠀⣿⡇⠀⣿⣽⣿⣄⠀⠉⢻⠀⠀⠉⡇⠀⡀⠀⠇⠀⢈⠀⢸⠀⠀⣧⣤⡆⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠛⠃⠀⢸⣿⣇⠀⠸⠀⢠⣿⡇⠀⢸⣿⡿⠀⢸⠀⢸⠀⠀⣇⠀⠘⠀⢸⠀⠀⡇⠀⣿⡿⠀⢀⠀⠀⠀⠀⡇⠀⣿⡇⠀⣿⣿⣯⠀⠸⠀⢸⠀⠀⠛⠇⠀⡀⠀⠀⠀⢸⠀⢸⡀⠀⠇⠀⡄⠀⢸⠀⠀⣷
⣿⣿⣿⣲⣶⣶⣶⣶⣾⣿⠘⡷⣶⣶⣋⣀⣳⣶⣞⣁⣳⣶⠾⣶⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣷⣶⣿⣷⣶⣾⣶⠶⣶⣶⣷⣶⣿⣷⣶⣿⣿⣿⣷⣶⡶⣾⣶⣶⣶⣶⣶⡷⣶⣶⣶⣾⡶⠺⠷⠶⠶⠾⠷⠶⠺⠶⠶⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡤⡅⡯⠤⡬⢤⠍⠉⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢺⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⠫⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⣀⠆⠀⠀⣤⣬⣽⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⠛⠛⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⠀⢸⠟⠃⠀⠘⠿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠳⣿⣿⣿⣿⡿⠿⠿⢺⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠂⡀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⣿⣿⣿⣿⣿⣿⣽⣆⠀⢠⣿⣿⣿⣿⡇⠀⠰⢸⣿⡇⣿⣿⣿⣿⣿⣿⣷⠤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣤⣨⠻⣿⣿⣿⣿⢻⣿⡧⣼⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡿⣿⣿
⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⠿⢇⣿⣿⡟⣟⢿⡿⡁⣀⠀⠀⠀⠀⣠⣾⣛⡧
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣿⣿⣿⣿⣿⠮⣭⣛⡿⠭⣽⣛⣿⣿⣻⣼⣿⣿⠿⠿⠶⠾⠝⠛⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢻⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣌⣉⠙⠒⠎⠉⠁⠀⠀⠀⠀⠀⣀⣀⢀⠀⢄⠠⢀
⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣦⠀⠐⢹⡉⡁⣜⢰⣸⡸⠸⠼⠜⢘⠒
⣿⣿⣿⣿⣋⣁⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣧⣭⣛⡋⠀⣌⢈⣉⠁⢀⣀⣤⣀⣴⣶⢠⣏⢸
⢄⣀⠰⠬⠉⠝⠛⡻⠿⣿⣷⣾⣿⣿⠿⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣷⣻⣿⣿⣿⣭⣿⣿⣟⣿⣿⣽⡿⣿⣽⣿⣿⣶⡈⠭⣛⡻⠇⢀⡿⣈⣛⣛⣛⣬⣭⣥⣤⣶⣾⣿⣿
⣿⣿⣾⣯⢰⠚⢻⠉⠉⢟⣀⣀⣀⣤⣤⣼⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣝⣟⣿⡟⢿⣿⠿⢿⢿⣿⣯⣭⣭⣭⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⡩⣭⣼⣶⣾⠿⠿⣿⠛⡟⣋⣏⣉⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣭⣿⣷⣷⣳⣶⡆⡃⢢⡻⠽⠛⠉⠀⢀⣀⣉⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡿⢿⠿⣸⠤⢼⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⠿⠿⠛⠛⠛⠋⠁⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣇⣀⣰⣶⢀⣰⢌⣡⣠⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣬⣭⣹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⣀⣀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣛⣛⣛⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠂⠒⠀⠀⡀⠀⠢⠀⠀⠁⠀⠀⢀⠀⠀⠨⠀⠀⠀⠀⠀⠁⠁⠂⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣤⣤⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣠⣴⣷⣴⣤⣦⣦⣤⣤⣄⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⢉⠀⠒⠀⡀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡟⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠙⣷⣿⠉⣯⠹⣿⠉⣽⣯⡍⣩⣿⠇⠉⠀⢀⢀⠀⠀⠀⡂⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡀⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡅⣽⡧⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣇⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣅⣸⠇⠀⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣶⣿⣿⣏⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣒⣶⡆⡄⢼⡇⢰⡆⣿⡇⣠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⠀⣴⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠀⣶⠈⣷⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⢼⡇⢰⡎⢻⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢻⣧⣿⠀⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣿⢠⣾⡏⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣽⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣥⣿⢿⣦⣥⣾⠏⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣯⣬⣿⣧⣼⣿⣧⣼⣧⣬⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣻⡇⡇⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣛⡿⣾⣿⡷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣿⡿⠿⣟⣛⣯⣽⣷⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠛⠒⠚⠛⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣻⡓⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠲⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠂⠂⠐⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⡀⠀⠈⠀⠂⠀⠁⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣤⣥⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣤⣤⣦⣴⣦⣤⣦⣤⣤⣄⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠙⣷⣿⠉⣯⠹⣿⠉⣽⣯⡉⢭⣿⠇⠈⠀⢀⠀⠀⠀⠀⠂⠁⠂⠠⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡈⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡆⢻⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡂⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⣿⣄⣻⣄⣿⣀⣉⣿⣇⣹⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣾⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣲⣶⡆⡄⢼⡇⢰⡆⣻⡇⢠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⠄⣶⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣶⠈⣷⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⢻⡇⢰⡎⢻⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢿⣧⣿⡂⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣇⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣽⢽⣯⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣾⠟⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣯⣼⡿⣧⣼⣿⣧⣼⣷⣬⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣻⡇⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣛⡿⣾⣿⣷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣿⡿⠿⣟⣛⣯⣽⣷⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠛⠒⠚⠛⠻⠿⠿⠿⢧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣻⡓⠓⢺⣀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢰⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠉⠉⠉⠛⠃⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠲⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠂⢀⠂⢒⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠂⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣤⣤⣅⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣤⣤⣥⣴⣦⣤⣤⣤⣤⣄⠀⠀⠀⢀⠀⠀⠐⠀⠤⠀⠄⠀⠀⡀⠀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠹⣷⣿⠉⣯⠹⣿⠉⣽⣯⡉⣭⣿⠃⠈⠀⢀⠀⡀⠀⡀⠂⠁⢀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡌⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡇⣼⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠦⠄⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣇⣹⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣼⣿⣿⣏⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣲⣶⡆⡄⢼⡇⢰⡆⣿⡇⢠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⠀⣶⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣶⠈⣿⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⣿⡇⢰⡎⢻⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢿⣧⣿⠀⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣽⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡟⢿⣥⣿⢿⣦⣥⣼⠟⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣿⣼⡿⣧⣼⣿⣧⣼⣧⣬⣴⣿⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⢽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣿⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣛⡿⣾⣿⣷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣿⡿⠿⣟⣛⣯⣽⣷⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⣀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠛⠒⠚⠛⠛⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡃⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠉⠉⠉⠛⠃⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠁⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠈⠲⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢒⠐⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⡁⢀⢠⡄⠀⠀⠀⠂⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣤⣤⣅⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣡⣭⣦⣤⣤⣤⣤⣤⣬⣤⠀⠀⠀⠄⡀⡐⠠⠄⠦⠀⠀⢀⠀⠀⠀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠹⣷⣿⠉⣯⠹⣿⠉⣽⣯⡉⣭⣿⠇⠀⠀⠐⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡄⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡇⢸⡧⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠰⠂⠀⢈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣃⣹⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣾⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣲⣶⡆⡄⢼⡇⢰⡆⣿⡇⢠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⡄⣶⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣶⠈⣷⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⣾⡇⢰⡎⢻⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢻⣧⣿⠂⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣽⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣥⣿⢿⣦⣥⣾⠟⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣯⣼⣿⣧⣼⣿⣧⣼⣧⣬⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⢻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣛⡿⣾⣿⣷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣿⡿⠿⣟⣛⣯⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠛⠒⠚⠛⠛⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡓⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠁⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠲⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠄⡀⠀⡂⠀⠂⢒⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠂⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣠⣤⣤⢀⣠⣤⣤⣤⣤⣤⣄⡀⢈⣠⣤⣦⣴⣦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠅⠀⡀⠤⠀⠂⠀⠀⡄⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠙⣷⣿⠉⣯⠹⣿⠉⣽⣯⡉⣭⣿⠇⠈⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡌⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡇⢹⡧⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠄⠂⠠⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣆⣾⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣴⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣒⣶⡆⡄⢼⡇⢰⡆⣿⡇⢠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⡄⣶⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣶⠈⣷⢠⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⣿⡇⢰⡎⢻⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢿⣧⣿⠆⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣥⣿⢿⣦⣥⣾⠏⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣯⣼⣿⣧⣼⣿⣧⣼⣷⣬⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⢽⣣⡏⣿⣿⣻⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠿⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣛⣿⣾⣿⡷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣿⡿⠿⣟⣛⣭⣽⣷⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠘⠛⠒⠚⠛⠛⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡃⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠘⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢰⣶⣶⣶⣦⣤⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠲⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⡀⡀⠀⠂⠀⠐⢒⠐⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⡁⢀⢠⡄⠀⠀⠀⠈⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣠⣤⣅⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠂⢀⠀⡄⠀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠹⣷⣿⠉⣯⠹⣿⠉⣽⣯⡉⢩⣿⠇⠁⠀⠘⠀⡀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡌⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡇⢸⡧⠂⠀⠀⠀⠈⠁⠘⠁⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣇⣹⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣾⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣷⣖⣶⡆⡄⢼⡇⢰⡆⣿⡇⢠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⠀⣶⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣷⠈⣷⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⢿⡇⢰⡎⢻⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢿⣧⣿⠄⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣽⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣾⠏⢻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣯⣼⣿⣧⣼⣿⣧⣼⣷⣬⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⢽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⣿⣾⣿⣷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣿⡿⠿⣟⣛⣯⣽⣷⡆⡇⠀⠀⠀⣾⣿⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠘⠛⠒⠚⠛⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡓⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠘⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢰⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠉⠉⠙⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠲⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢒⠐⠀⢀⠈⠂⠐⠀⠀⠀⠀⡁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣤⣬⣥⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣤⣤⣶⣤⣤⣦⣤⣤⣤⣤⡀⠀⠀⠄⠀⠉⠂⠀⠄⠀⠀⢀⠀⡄⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠹⣷⣿⠉⣯⠹⣿⠉⣽⣯⡉⣩⣿⠇⠈⠄⠐⠀⠅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡄⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠅⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂⠄⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⣿⣄⣻⣄⣿⣀⣉⣿⣇⣻⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣴⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣲⣶⡆⡄⢼⡇⢰⡆⣽⡇⣠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⡀⣴⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣶⠈⡷⢠⣶⡇⢰⣾⡇⢸⡇⢰⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⢾⡇⢰⡎⢹⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢻⣧⣿⡃⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣭⢽⣯⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣾⠟⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣼⣯⣼⡿⣧⣼⣿⣧⣼⣷⣬⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣻⡇⡇⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣛⡿⣾⣿⣷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣿⡿⠿⣟⣛⣯⣽⣷⡆⡇⠀⠀⠀⣾⣿⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠛⠒⠚⠛⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡓⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢰⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠲⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⡀⠀⡂⠀⠂⢒⠀⠀⠀⠈⠆⢀⠀⠀⠈⠀⡀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠂⠀⠁⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣤⣤⣥⢀⣠⣤⣤⣤⣤⣤⣄⡀⢈⣤⣤⣦⣴⣦⣤⣤⣤⣤⣤⠀⠀⠀⠄⢀⠁⠐⠀⠄⠀⠀⠀⠀⡀⠠⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣭⠙⣷⣿⠉⣯⠙⣿⠉⣽⣯⡉⣩⣿⠇⠈⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡈⢸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡇⢻⡧⠂⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠐⠂⠄⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⣿⣄⣻⣄⣿⣀⣉⣿⣁⣻⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣶⣿⣿⣏⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣿⣷⣖⣶⡆⡄⣼⡇⢰⡆⣻⡇⣠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⠄⣶⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣶⠈⡗⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⢿⡇⢰⡎⢻⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢿⣧⣿⠂⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣾⠏⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣿⣼⡿⣧⣼⣿⣧⣼⣷⣬⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⢽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣛⡿⣾⣿⡷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣿⡿⠿⣟⣛⣯⣽⣷⡆⡇⠀⠀⠀⣾⣿⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠙⠒⠚⠛⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡓⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢰⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠈⠲⠄⠰⠲⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⡀⠀⡂⠀⠂⢒⠀⠀⠀⠈⠆⢀⠀⠀⠈⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣤⣤⣥⢀⣠⣤⣤⣤⣤⣤⣄⡀⢈⣤⣤⣦⣴⣦⣤⣤⣤⣤⣤⡀⠀⠀⢔⠀⠐⠠⠀⠄⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠙⣷⣿⠉⣯⠙⣿⠉⣽⣯⡉⣭⣿⠇⠈⠀⢐⠀⡄⢐⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡈⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡇⢻⡧⠂⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠄⠀⠆⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣘⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⣿⣄⣻⣄⣿⣀⣉⣿⣃⣿⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣶⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣲⣶⡆⡄⢼⡇⢰⡆⣿⡇⢠⢸⣿⠀⣶⠘⣿⠀⡇⣼⣿⣷⡄⣶⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣶⠈⣷⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⣾⡇⢰⡎⢹⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢻⣧⣿⠆⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣼⠏⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣿⣼⡿⣧⣼⣿⣧⣼⣷⣬⣴⣿⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢰⣿⣶⣶
⢼⣛⣿⣾⣿⣷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣿⡿⠿⣟⣛⣯⣽⣷⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠛⠒⠚⠛⠛⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡓⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣦⣤⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠲⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⡀⠀⡂⠀⠂⢒⠀⠀⠀⠈⠆⢀⠀⠀⠈⠀⣀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠂⠀⠁⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣤⣤⣅⢀⣠⣤⣤⣤⣤⣤⣄⠀⢈⣠⣤⣦⣴⣦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⡠⠐⡀⠀⠀⠄⠀⠀⡀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠹⣷⣿⠉⣭⠙⣿⠉⣽⣯⡉⣭⣿⠇⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡌⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡇⣻⡧⠂⠀⠀⠀⠈⠀⠈⠀⠀⠀⢀⠀⠐⠐⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣃⣽⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣶⣶⣿⣿⣶⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣷⣒⣶⡆⡄⢼⡇⢰⡆⣿⡇⢠⢸⣿⠀⣶⠈⣿⠀⠇⣼⣿⣷⠄⣶⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣶⠈⡷⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⢾⡇⢰⡎⢹⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢿⣇⣿⠂⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣾⠏⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣼⣯⣼⣿⣧⣼⣿⣧⣼⣧⣬⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⢽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣛⡿⣾⣿⡷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⣟⣛⣯⣽⣷⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠛⠒⠚⠛⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡓⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠈⠁⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠁⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡆⠲⣶⠉⠲⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠡⠀⠀⠀⠀⠀⣀⠉⠉⠁⠀⠀⠐⠀⠂⠀⠀⢠⠐⠂⢄⠄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠉⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣤⣬⣄⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣥⣵⣦⣼⣦⣤⣦⣤⣬⣤⡀⠀⠀⠀⠠⠠⠀⠀⠁⠦⠈⠀⠀⠁⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡟⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠙⣷⣿⠉⣯⠹⣿⠉⣽⣯⡉⣭⣿⠗⠴⠐⠀⠀⠁⠀⠀⡂⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡌⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡇⢹⡧⠂⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠀⠀⠤⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣃⣽⠇⠀⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣾⣿⣿⣏⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣒⣶⡦⡄⣾⡇⢰⡆⣻⡇⣠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⠀⣶⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣷⠈⣷⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⢹⡇⢰⡎⢻⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢿⣇⣿⠀⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣽⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣾⠏⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣿⣼⡿⣧⣼⣿⣧⣼⣷⣬⣴⣿⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣽⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⣿⣾⣿⡷⣿⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⣟⣻⣯⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⡀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠘⠛⠒⠚⠛⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡓⠓⢺⣀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⡀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠘⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠐⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠈⠉⠁⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠰⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⣀⠉⠉⠁⠀⠀⠐⠀⠂⠀⠀⠀⠐⠂⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⣬⣄⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣥⣤⣦⣤⣤⣦⣤⣤⣬⣤⡀⠀⠄⠀⠠⠀⠤⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣭⠙⣷⣿⠉⣯⠙⣿⠉⣽⣯⡉⢩⣿⠇⠬⠍⢀⣀⡂⠐⠀⠀⠀⠈⠠⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡈⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡅⢸⡧⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣇⣸⠇⠀⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣶⣿⣿⣏⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣒⣶⡦⡄⢸⡇⢰⡆⣿⡇⢠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⠀⣶⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣷⠈⣷⢰⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣿⣿⣿⣿⡿⣿⡇⡇⢺⡇⢰⡎⢹⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢻⣇⣿⠀⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣿⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣽⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣼⠏⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣿⣼⣿⣧⣼⣿⣧⣼⣷⣬⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⣽⣣⡏⣿⣿⣿⡇⡇⠀⠀⠀⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣿⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⣿⣾⣿⡷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⣟⣻⣯⣽⣶⡆⡇⠀⠀⠀⣾⣿⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⡀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠘⠛⠒⠒⠛⠿⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡛⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⡀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠘⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠈⠉⠁⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠲⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⣀⠉⠉⠁⠀⠀⠰⠈⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⣬⣄⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣥⣴⣦⣤⣤⣤⣤⣤⣤⣤⡀⠀⠄⠀⠀⡠⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠹⣷⣿⠉⣯⠹⣿⠉⣽⣯⡉⣩⣿⠇⠣⠅⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡌⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⡇⢽⡧⠂⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣇⣿⣿⣀⣿⣀⣧⣸⣷⣜⣣⣸⡿⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣇⣹⠇⠀⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣴⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣶⣶⣿⣿⣤⣿⣿⣏⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣲⣶⡦⡄⣼⡇⢰⡆⣿⡇⢠⢸⣿⠀⣷⠘⣿⠀⠇⣼⣿⣷⠄⣶⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠁⣷⠈⣷⢠⣶⡇⢰⣾⡇⢸⡇⢸⡆⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣿⣿⣿⣿⡿⣿⡇⡇⢺⡇⢰⡎⢻⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢿⣇⣿⠄⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣟⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣽⢽⣏⡇⣿⡇⡇⠸⣧⣬⣥⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣾⠏⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣯⣼⡿⣧⣼⣿⣧⣼⣷⣬⣴⣿⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⢽⣣⡏⣿⣿⣽⡇⡇⠀⠀⠀⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣿⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣛⣿⣾⣿⡷⣿⣧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⣟⣻⣯⣽⣶⡆⡇⠀⠀⠀⣾⣿⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠘⠛⠒⠒⠛⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡛⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⡀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠘⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣈⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠠⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠰⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣤⣬⣌⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡿⢩⡏⢹⣿⣯⡍⢩⣿⠉⣯⠙⣷⣿⠉⣯⠙⣿⠉⣽⣯⠉⣩⣿⠇⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡀⣸⣿⠀⣿⠀⡌⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢿⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣸⣿⣗⣾⣿⣀⣿⣀⣧⣸⣷⣈⣣⣸⡟⢿⣇⣸⣿⣄⣛⣴⡿⢿⣄⣻⣄⣿⣀⣉⣿⣂⣺⠇⠀⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣤⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣩⣽⣿⣿⣷⣶⣿⣿⣶⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣒⣶⡆⡄⢸⡇⢰⡆⣿⡇⢠⢸⣿⠀⣷⠘⣿⠀⠇⣼⡿⣷⠀⣴⣿⠀⡇⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠀⣷⠈⡷⢠⣶⡇⢰⣾⡇⢸⡇⢸⡄⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣿⣿⣿⣿⡿⣿⡇⡇⢼⡇⢰⡎⢹⠇⠿⠈⣿⠀⣿⠛⣿⠀⡄⢿⣧⣿⠀⣿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡷⢠⣾⡇⢰⣾⡇⢸⡇⢸⡟⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣭⣼⣿⣤⣧⣼⡿⢿⣤⣿⢿⣦⣥⣾⠏⠻⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣯⣼⡿⣧⣼⣿⣧⣼⣧⣬⣴⣿⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣿⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⣿⣾⣿⡷⣿⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⣟⣛⣯⣽⣶⡆⡇⠀⠀⠀⣾⣿⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠘⠛⠒⠒⠛⠿⠿⠿⠽⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣿⡓⠓⢺⣈⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⡀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣶⡀⠰⣆⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢿⡿⢸⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠐⠉⠁⠂⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣄⣴⣿⣽⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠰⣶⣶⣶⣦⣤⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠙⠃⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣶⠉⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣤⣤⣄⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣯⢹⠏⣿⠉⣿⠉⣿⢹⡟⢩⡌⢹⣿⣯⡍⢩⣿⠉⣭⠙⣷⣿⠉⣭⠙⣿⠉⣭⣯⠉⢩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣥⢺⣿⡀⢸⣿⠀⣿⠀⡈⢘⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣘⣿⣇⣸⣿⣀⣿⣀⣇⣸⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣛⣰⡿⢿⣄⣛⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣤⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣯⣿⣿⣯⣭⣿⣿⣿⣶⣶⣿⣿⣶⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣽⣖⣒⣶⡆⡄⢸⡇⢰⡆⣹⡇⢠⢸⣿⠀⣶⠈⣷⠀⠇⣼⡿⣷⠀⢴⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠠⣶⡇⢰⣾⡇⢸⡇⢰⠀⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣷⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡎⢹⠇⠻⠀⣿⠀⣿⠛⣿⠀⡄⢻⣇⣿⠀⢺⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡧⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⣿⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣯⣤⣧⣼⡟⢿⣤⣼⢿⣤⣥⣼⠏⠻⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣥⣴⣧⣤⡿⣧⣼⣿⣧⣼⣧⣬⣤⣿⣤⣤⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣿⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡽⣾⣿⡷⢯⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⢟⣛⣯⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⣀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠘⠚⠒⠒⠛⠻⠿⠿⠽⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⢠⣟⡓⠓⢸⣀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡄⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠸⣻⡧⠀⠢⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⡇⠈⢱⠀⢻⣄⠀⠀⠀⠀⣀⣴⣀⣀⠀⠀⠀⠀⠀⠀⢘⣿⠀⢷⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡆⠀⠀⠊⣦⡸⣿⣶⣶⡆⣿⣿⣿⣿⡭⠀⠀⠀⠀⠀⠀⠘⠊⠀⠉⠁⠀⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣟⣀⣀⣾⣿⣷⣹⣿⣿⣓⣛⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢶⣶⣶⣶⣦⣤⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠙⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⣯⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠰⣶⠈⠲⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⠿⢿⣿⡿⠿⣿⢿⡿⢿⡟⢿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣤⣤⣄⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣏⢹⠏⣿⠉⣿⠉⣿⢹⡟⢩⡌⢹⣿⣯⡍⢩⣿⠉⣭⠙⣷⣿⠉⣭⠙⣿⠉⣭⣯⠉⢩⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡀⢸⣿⠀⣿⠀⡈⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣘⣿⣇⣸⣿⣀⣿⣀⣇⣸⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣛⣰⡿⢿⣄⣛⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣤⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣯⣿⣿⣯⣭⣿⣿⣿⣶⣶⣿⣿⣴⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣽⣶⣲⣲⡆⡄⢸⡇⢰⡆⣹⡇⢠⢸⣿⠀⣶⠈⣷⠀⠇⣼⡿⣷⠀⣴⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⣿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡧⠠⣶⡇⢰⣾⡇⢸⡇⢰⠀⣿⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣷⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡎⢹⠇⠻⠈⣿⠀⣿⠛⣿⠀⡄⢻⣇⣿⠀⢿⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⣿⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣯⣤⣧⣼⡟⢿⣤⣼⢿⣤⣥⣼⠏⠻⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣭⣴⣧⣤⡿⣧⣼⢿⣧⣼⣧⣬⣤⣿⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡿⣾⣿⡷⢯⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⢟⣛⣯⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⡶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠛⠒⠒⠛⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⡿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣻⡃⠓⢺⣀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡯⠃⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡄⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣻⠧⠀⠢⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⡇⠈⢱⠀⢿⣆⠀⠀⠀⠀⣀⣴⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⡆⠀⠀⠋⣦⡸⣿⣶⣶⡆⣿⣿⣿⣿⡭⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣟⣀⣀⣾⣿⣷⣹⣿⣿⣓⣛⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢰⣶⣶⣶⣦⣤⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠰⣶⠉⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡿⠿⢿⡿⢿⡿⠿⣿⣿⡿⠿⡯⢿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣠⣤⣠⣤⣤⣤⣤⣠⣄⣀⣤⣤⣄⢀⣠⣤⣤⣠⣤⣤⣄⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣏⢹⠋⣿⠉⣿⠉⣿⢹⡟⢩⡌⢹⣿⣯⡍⢩⣿⠉⣬⠙⣷⣿⠉⣬⠙⣿⠉⣭⣯⠉⢩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣭⢺⣿⡀⢸⣿⠀⣿⠀⡈⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣈⣿⣇⣸⣿⣀⣿⣀⣇⣸⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣋⣰⡿⢿⣄⣛⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣤⣶⣾⣿⣽⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⢿⣯⣉⣽⣿⣿⣶⣶⣿⣿⣴⣿⣿⣍⣠⣴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣽⣶⣒⣒⡂⡄⢸⡇⢰⡆⣹⡇⢠⢸⣿⠀⣶⠈⡇⠀⠇⣼⡿⣷⠀⢰⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠀⣶⡇⢰⣾⡇⢸⡇⢰⠀⣻⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣷⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡎⢹⠇⠻⠀⣿⠀⣿⠛⡇⠀⡄⢻⣇⣿⠀⢸⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣧⣤⣧⣼⠟⢿⣤⣼⢿⣤⣥⡼⠏⠸⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣥⣴⣧⣤⡿⣧⣼⢿⣥⣼⣧⣬⣤⣿⣤⣤⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢼⢻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡽⣾⣿⡷⢯⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⢟⣛⣯⣽⣶⡆⡇⠀⠀⠀⣾⣶⣶⣶⢶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠙⠒⠒⠛⠛⠻⠿⠿⠧⠃⠀⠀⠀⣿⣿⡿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣛⡃⠓⢸⣀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠐⡸⣿⣿⡿⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢸⣿⡿⠃⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠀⠉⠘⢿⣿⠀⠈⠈⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣻⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢈⣤⠄⣘⣷⣽⠀⠀⠟⡀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣶⣿⣿⣿⣧⠀⠀⣼⣷⠈⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠁⠀⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣿⣿⣿⣯⣭⣴⣀⣀⣸⣿⣿⣘⣿⣿⣇⣴⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣴⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢰⣶⣶⣶⣦⣤⣀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠁⣯⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⢲⠈⠐⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⡿⡿⠿⢿⣿⠿⢿⠿⠏⠟⢿⠿⢿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⣤⣄⣤⣤⣤⣄⣄⣠⣄⣀⣤⣤⣄⢀⣠⣤⣤⣤⣤⣤⣄⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣏⢹⠋⣿⠉⣿⠉⣿⢹⡟⢩⡌⢹⣿⣯⡍⢩⣿⠉⣬⠙⣷⣿⠉⣬⠙⣿⠉⣭⣯⠉⢩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣥⢺⣿⡀⢸⣿⠀⣿⠀⡈⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣸⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣋⣰⡿⢿⣄⣛⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣶⣾⣿⣿⢿⣿⣽⣿⣿⣯⣭⣿⣿⣿⣿⣿⢿⣯⣉⣽⣿⣿⣶⣶⣿⣿⣴⣿⣿⣍⣠⣴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣽⣶⣒⣒⡂⡄⢸⡇⢰⡆⣹⡇⢠⢸⣿⠀⣶⠈⡇⠀⠇⣼⡿⣷⠀⢰⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠀⣶⡇⢰⣾⡇⢸⡇⢰⠀⢻⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣷⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡎⢹⠇⠻⠀⣿⠀⣿⠛⡇⠀⡄⢻⣇⣿⠀⢸⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣧⣤⣧⣼⠟⢿⣤⣼⢿⣤⣥⡼⠏⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣥⣴⣧⣤⡿⣧⣼⢿⣧⣼⣧⣬⣤⣿⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣿⢾⢻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡿⣾⣿⡷⢯⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⢟⣛⣭⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⢶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠑⠒⠒⠛⠛⠻⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢠⣋⡃⠓⢸⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢸⣿⠠⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡐⠰⡹⣿⣿⡟⠙⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢸⡿⡻⠃⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣷⠀⠉⠙⢿⣿⠀⢿⠈⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠸⣻⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠿⠋⣠⠀⣸⣬⡟⠀⠀⡝⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢐⡀⢽⣾⣿⣿⣿⣧⠀⠀⣴⣷⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣸⣵⣶⣿⣿⣏⣥⣶⣀⣀⣻⣿⣧⣘⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢲⣶⣶⣶⣶⣤⣤⣄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠈⠟⡿⡇⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠁⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠰⢲⠈⠐⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢿⠿⠿⠿⠿⠿⠏⠟⢿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣠⣤⣤⣤⣤⣤⣤⣠⣀⣀⣠⣤⣄⢀⣠⣤⣤⣠⣤⣤⣄⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣏⢹⠋⣿⠉⣿⠉⣿⢹⡟⢩⡌⢹⣿⣯⡍⢩⣿⠉⣬⠙⣷⣿⠉⣬⠙⣿⠉⣭⣯⠉⢩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣥⢺⣿⡀⢸⣿⠀⣿⠀⡈⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣘⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣋⣰⡿⢿⣄⣛⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣤⣶⣼⣿⣿⣿⣯⣽⣿⣿⣯⣭⣽⣿⣿⣿⣿⢿⣯⣉⣽⣿⣿⣶⣶⣿⣿⣴⣿⣿⣍⣠⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⡶⣶⣤⣴⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣭⣶⣒⣲⡂⡄⢸⡇⢰⡆⣹⡇⢠⢸⣿⠀⣶⠈⡇⠀⠇⣼⡿⣷⠀⢰⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠀⣶⡇⢰⣾⡇⢸⡇⢰⠀⢻⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣷⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡎⢹⠇⠻⠀⣿⠀⣿⠛⡇⠀⡄⢻⣇⣿⠀⢸⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⣇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣧⣤⣧⣼⡟⢿⣤⣼⢿⣤⣥⡼⠏⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⢿⣦⣥⣴⣧⣤⡿⣧⣼⢿⣧⣼⣧⣬⣤⣿⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⢻⡿⡇⣿⣿⣾⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡿⣾⣿⡷⢭⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⢟⣛⣯⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠓⠒⠒⠛⠛⠻⠿⠽⠧⠃⠀⠀⠀⣿⣿⡿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣫⡃⠓⢸⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡐⠰⡹⣿⣿⡟⠙⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⢸⣿⡻⠃⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⠀⡁⠙⢿⣿⠀⢿⠈⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⠸⣻⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡟⠋⣰⠀⣸⣬⡟⠀⠀⡟⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⡀⢴⣾⣿⣿⣿⣧⠀⠀⣴⣷⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣸⣵⣶⣿⣿⣯⣥⣶⣀⣀⣿⣿⣧⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣤⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢲⣶⣶⣶⣶⣤⣤⣄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠉⠟⡿⡇⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠁⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠰⣲⠈⠐⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢿⠿⠿⠿⢿⠿⠏⠟⢿⢿⡿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣀⣄⣠⣄⣀⣤⣬⣄⢀⣠⣤⣤⣤⣤⣤⣄⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣏⢹⠋⣿⠉⣿⠉⣿⢹⡟⢩⡌⢹⣿⣯⡍⢩⣽⠉⣬⠙⣷⣿⠉⣬⠙⣿⠉⣭⣯⠉⢩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣥⢺⣿⡀⢸⣿⠀⣿⠀⡈⢨⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣘⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣋⣰⡿⢿⣄⣛⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣶⣾⣿⣿⢿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⢿⣯⣉⣽⣿⣿⣶⣶⣿⣿⣴⣿⣿⣍⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡶⣦⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣭⣶⣒⣒⡂⡄⢸⡇⢰⡆⣹⡇⢠⢸⣿⠀⣶⠈⡇⠀⠇⣼⡿⣷⠀⢴⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠀⣶⡇⢰⣾⡇⢸⡇⢰⠀⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣟⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡎⢹⠇⠻⠀⣿⠀⣿⠛⡇⠀⡄⢻⣇⣿⠀⢸⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣧⣤⣧⣼⠟⢿⣤⣼⢿⣤⣥⡼⠋⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⣿⢿⣦⣥⣴⣧⣤⡿⣧⣼⢿⣧⣼⣧⣬⣤⣿⣤⣤⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣻⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢼⢻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡽⣾⣿⡷⢯⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⢟⣛⣭⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠑⠒⠒⠚⠛⠻⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣛⡓⠓⢸⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢠⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠠⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⣈⢿⣿⣿⠟⠹⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡿⠃⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⣾⣿⡧⠘⠊⢻⣿⡇⠐⡯⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣾⠸⣫⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⡿⡿⢃⣞⠸⠷⡙⡇⠀⠁⡆⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣄⠀⣺⣭⣶⣿⣿⣱⠀⠀⣴⣆⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣸⣿⣫⣾⣿⣿⣿⣟⣛⣭⣀⣈⣿⣿⣆⣫⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣍⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣴⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢶⣶⣶⣶⣶⣤⣄⠀⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠉⠛⠶⡇⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠁⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⢲⠈⠐⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⡿⡿⠿⠿⠿⠿⡿⠿⠏⠟⢿⠿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⣠⣤⣠⣤⣤⣤⣤⣠⣀⣀⣤⣬⣄⢀⣠⣤⣤⣤⣤⣤⣄⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣏⢹⠋⣿⠉⣿⠉⣿⢉⡟⢩⡌⢹⣿⣯⡍⢩⣿⠉⣬⠙⣷⣿⠉⣬⠙⣿⠉⣭⣯⠉⢩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣥⠺⣿⡀⢸⣿⠀⣿⠀⡈⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣘⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣋⣰⡿⢿⣄⣛⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⢀⣾⣿⣿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣤⣶⣾⣿⣿⢿⣿⣽⣿⣿⣿⣭⣿⣿⣿⣿⣿⢿⣯⣉⣽⣿⣿⣶⣶⣿⣿⣤⣿⣿⣍⣠⣴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡶⣾⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣽⣶⣒⣒⡆⡄⢸⡇⢰⡆⣹⡇⢠⢸⣿⠀⣶⠈⡇⠀⠇⣼⡿⣷⠀⣴⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠀⣶⡇⢰⣾⡇⢸⡇⢰⠀⢻⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣟⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡆⢹⠇⠻⠀⣿⠀⣿⠛⡇⠀⡄⢻⣇⣿⠀⢸⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡾⢻⣷⣭⢽⢏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣧⣤⣧⣼⠟⢿⣤⣼⢿⣤⣥⡼⠋⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⡿⣧⣼⢿⣧⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣿⢹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⣻⡿⡇⣿⣿⣾⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡿⣾⣿⡧⢭⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⢟⣛⣭⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⡀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠑⠒⠒⠛⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢠⣛⡃⠓⢸⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡽⣿⣿⣿⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⢸⣿⠠⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣤⣶⣿⡄⠷⠝⢿⣿⡄⢨⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡻⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⣿⣿⣿⣿⠃⡔⠀⣮⠻⡇⠀⠇⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⠸⣛⠧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⣿⣿⣿⠉⢁⡾⢟⣠⣭⣥⣄⠀⠀⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠹⣿⣿⣟⣧⣴⣿⣿⣿⣿⣿⡿⠀⠠⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣈⣾⣿⣿⣿⣿⣏⣭⣴⣦⣤⣄⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣮⣉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣦⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠉⠛⠃⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠁⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⢲⠈⠀⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⢿⣿⢿⠿⡿⣿⠯⠏⢿⠿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣠⣄⣤⣤⣤⣄⣀⣠⣀⣀⣠⣬⣄⠀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⢹⣏⢹⠋⣿⠉⣿⠉⣿⠩⡟⢡⡌⢹⣿⣯⡍⢩⣿⠉⣬⠙⣷⣿⠉⣬⠙⣿⠉⣭⣯⠉⢩⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣥⢺⣿⡀⢸⣿⠀⣿⠀⡈⢸⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣋⣰⣿⣿⣄⣋⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣤⣶⣼⣿⣿⢿⣯⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⢿⣯⣉⣽⣿⣿⣶⣶⣿⣿⣴⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡶⣦⣤⣴⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣭⣶⣒⣒⡀⡄⢸⡇⢰⠆⣹⡇⢠⢸⣿⠀⣶⠈⡇⠀⠇⣸⡿⣷⠀⢰⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠀⣶⡇⢰⣾⡇⢸⡇⢰⠀⢹⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣗⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡆⢹⠇⠻⠀⣿⠀⣿⠛⡇⠀⡄⢻⣇⣿⠀⢸⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣧⣤⣧⣼⡟⢿⣤⣼⢿⣤⣥⡼⠏⠸⣧⣼⣿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⠿⣧⣼⢿⣧⣼⣧⣬⣤⣿⣤⣤⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣿⢹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⢻⡿⡇⣿⣿⣿⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡿⣾⣿⡷⢭⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⢟⣛⣯⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠑⠒⠒⠚⠛⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⢠⣻⡃⠓⢸⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⢸⣮⢿⣿⣿⠁⢹⡇⡀⠀⠀⠀⠀⠀⠀⠀⢸⣫⢸⣿⠠⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠂⡉⢡⡹⣿⡇⠸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠐⣻⢸⡯⡿⠃⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⣿⣿⡿⠻⢣⣶⣦⡙⠿⠌⠁⠀⠃⠆⠀⠀⠀⠀⠀⠀⠀⢨⢻⠸⣓⡧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⣿⣿⣿⣷⣀⣻⣭⣵⣾⣿⣿⡇⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⢘⣾⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⠙⢫⣿⣿⣿⣿⣿⠿⠿⣟⡋⠀⡘⣿⣿⣧⠀⠀⠀⠀⠀⠈⠋⠀⠉⠀⠀⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣉⣻⣿⣿⣿⣋⣴⣿⣿⣿⣿⣇⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣤⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢶⣶⣶⣶⣶⣤⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠙⠛⠃⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠁⣯⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣲⠈⠐⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⡿⠿⠿⡿⠿⠿⠿⠿⢿⡿⢿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣠⣄⣤⣤⣤⣄⣤⣠⣀⣀⣠⣬⣄⠀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⠹⣏⢹⠋⣿⠉⣿⠉⣿⢉⡟⢡⡌⢹⣿⣯⡍⢩⣿⠉⣬⠙⣷⣿⠉⣬⠙⣿⠉⣭⣯⠉⢩⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣥⠺⣿⡀⢸⣿⠀⣿⠀⡈⢘⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣘⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣋⣰⣿⣿⣄⣋⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣤⣶⣼⣿⣽⢿⣯⣽⣿⣿⣯⣭⣿⣿⣿⣿⣿⢿⣯⣉⣽⣿⣿⣶⣶⣿⣿⣦⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡶⣶⣤⣴⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣭⣭⣽⣶⣒⣒⡀⡄⢸⡇⢰⡆⣹⡇⢠⢸⣿⠀⣶⠈⡇⠀⠇⣼⡿⣷⠀⢰⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠀⣶⡇⢰⣾⡇⢸⡇⢰⠀⢹⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣟⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡆⢹⠇⠻⠀⣿⠀⣿⠛⡇⠀⡄⢻⣇⣿⠀⢸⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣧⣤⣧⣼⡟⢿⣤⣼⢿⣤⣥⡼⠏⠸⣧⣼⣿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⠿⣧⣼⢿⣧⣼⣧⣬⣤⣿⣤⣤⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣿⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣾⢾⢻⡿⡇⣿⣿⣾⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡽⣾⣿⡷⢭⡥⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣹⣿⣿
⢿⣾⡿⠿⢟⣛⣯⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠑⠒⠒⠚⠻⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⣟⡓⠓⢸⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⢸⣮⢿⣿⣿⠁⢹⡇⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⡉⢀⡹⣿⡇⠸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠰⣿⢸⣧⡻⠃⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣾⣿⣿⡿⠻⢃⣴⣦⡙⠿⠌⠁⠀⠃⠆⠀⠀⠀⠀⠀⠀⠀⢘⣾⠸⣻⠧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⣿⣿⣿⢧⣀⣻⣭⣴⣾⣿⣿⡗⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⢐⣿⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⠙⢫⣿⣿⣿⣿⣿⠿⠿⢟⡋⠀⡈⣿⣿⣧⠀⠀⠀⠀⠀⠘⠉⠀⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣉⣻⣿⣿⣿⣛⣼⣿⣿⣿⣿⣇⣽⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢶⣶⣶⣶⣶⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠙⠛⠃⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠁⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⣲⠈⠀⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠿⠿⠿⢿⠿⠿⡯⠟⢿⡿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣠⣤⣤⣤⣤⣤⣄⣠⣀⣀⣠⣤⣄⠀⣠⣤⣤⣤⣤⣤⣄⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡍⢩⣿⠉⣭⠹⣏⢹⠋⣿⠉⣿⠉⣿⢩⡟⢩⡌⢹⣿⣯⡍⢩⣿⠉⣬⠙⣷⣿⠉⣬⠙⣿⠉⣭⣯⠉⣩⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣥⠺⣿⡀⢸⣿⠀⣿⠀⡈⢐⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣘⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣋⣰⡿⢿⣄⣋⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣶⣼⣿⣿⢿⣯⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⢿⣯⣉⣽⣿⣿⣶⣶⣿⣿⣴⣿⣿⣍⣠⣴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡶⣶⣤⣶⣶⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣽⣶⣒⣒⡀⡄⢸⡇⢰⡆⢹⡇⢠⢸⣿⠀⣶⠈⡇⠀⠇⣼⡿⣷⠀⢰⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠀⣶⡇⢰⣾⡇⢸⡇⢰⠀⢹⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣯⣗⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡆⢹⠇⠻⠀⣿⠀⣿⠛⡇⠀⡄⢻⣇⣿⠀⢸⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣶⠀⣿⠀⣶⣿⣿⠀⣿⠀⡇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣷⣭⢽⣏⡇⣿⡇⡇⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣧⣤⣧⣼⡟⢿⣤⣼⢿⣤⣥⡼⠏⠸⣧⣼⣿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⣿⣧⣼⢿⣧⣼⣧⣬⣤⣿⣤⣤⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣿⣹⡇⡇⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣵⣿⢼⢻⡿⡇⣿⣿⣾⡇⡇⠀⠀⠀⠛⠻⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶
⢼⣚⡿⣾⣿⡷⢭⡧⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⢟⣛⣯⣽⣶⡆⡇⠀⠀⠀⣾⣷⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠑⠒⠒⠚⠛⠿⠿⠿⠧⠃⠀⠀⠀⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢸⣿⢠⣻⡃⠓⢸⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣦⢸⣘⣿⣿⣿⠁⢹⡇⡀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠠⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⡈⣨⢿⣿⡇⠸⣇⠁⠀⠀⠀⠀⠀⢨⣿⢸⣿⡿⠃⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣰⣿⣿⣿⠟⠟⣡⣶⣄⠻⠷⠝⠃⠀⠃⡆⠀⠀⠀⠀⠀⢸⣾⠸⣟⠧⠀⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣇⣈⣭⣽⣯⣶⣶⣖⠆⠀⠀⣰⣄⠀⠀⠀⠀⢸⣻⠀⢳⣶⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⢙⣿⣿⣿⣿⣿⣿⣿⠿⠟⠓⠀⠰⣿⣿⣧⠀⠀⠀⠈⠉⠀⠉⠁⠀⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣃⣴⣿⣿⣿⣾⣄⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣶⣤⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠙⠛⠁⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠁⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠲⢲⠈⠀⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⠿⢿⠿⡿⡿⠿⢿⢿⠿⠛⢿⡿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣤⣄⣤⣤⣤⣄⣤⣤⣄⣀⣠⣥⣄⢀⣠⣤⣤⣤⣤⣤⣀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣯⡍⢩⣿⠉⣭⠹⣏⢹⠋⣿⠉⣿⠉⣿⠩⡟⢡⡌⢹⣿⣯⡍⢩⣽⠉⣬⠙⣿⣿⠉⣤⠙⣿⠉⣭⣯⠉⢩⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⡇⢸⣿⠀⣥⠺⣿⡀⢸⣿⠀⣿⠀⡈⠐⡇⢸⡟⢻⣿⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⣿⠀⣽⣿⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣺⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣷⣈⣣⣸⡿⢿⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣿⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣶⣿⣯⣽⢿⣯⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⢿⣯⣉⣽⣿⣿⣶⣶⣿⣿⣴⣿⣿⣍⣠⣴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡶⣶⣤⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⣶⣶⣯⣭⣭⣵⣖⣒⣶⢀⠀⢸⡇⢰⡆⣹⡇⢠⢸⣿⠀⣶⠈⡇⠀⠇⣸⡿⣷⠀⢰⣿⠀⡆⢸⣿⣷⡆⢰⣾⠀⡿⠀⣿⠀⣶⣿⣿⠀⣶⠈⡇⠀⣶⡇⢰⣾⡇⢸⡇⢰⠀⢹⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢻⣽⣾⣿⣿⡿⢿⣿⢸⠀⢸⡇⢰⡆⢹⠇⠻⠀⣿⠀⣿⠛⡇⠀⡄⢻⣇⣿⠀⢸⣿⠀⡇⢸⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⣿⠀⡇⠀⣾⡇⢰⣾⡇⢸⡇⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠟⣽⣯⡾⣾⣻⣸⣿⢸⠀⠸⣧⣬⣤⣾⣤⣿⣤⣿⣦⣥⣼⣧⣤⣧⣼⠟⢿⣤⣼⢿⣤⣥⡼⠇⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⣿⣦⣥⣴⣧⣤⣿⣧⣼⡿⣧⣼⣧⣬⣤⣿⣤⣤⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⠫⢟⣔⢇⣽⡇⣿⢸⠀⠀⠀⢸⣿⣛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⣼⣦⣿⣿⣯⢸⣿⡇⣿⢸⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣾⣷⣾⣿
⢓⢯⢷⣿⣾⡨⣭⢵⣿⢿⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⣿⣿
⢿⣿⠿⠿⣛⣛⣭⣽⣶⢸⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿
⠈⠃⠒⠒⠛⠻⠻⠯⠽⠌⠀⠀⠀⢸⣿⣿⣿⢷⣽⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠰⡆⣜⣙⠚⠒⣇⡀⠀⠀⠀⠈⠼⠟⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⢡⡹⣿⣿⣿⠉⢹⡇⡀⠀⠀⠀⠀⢸⡇⣿⡇⠇⠂⡌⡇⠀⠀⠀⠀⠀⠀⠐⠟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⠈⠓⠉⢿⣿⡆⢰⣷⠃⠀⠀⠀⠀⢸⠆⣿⣿⠟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡿⠃⣤⠁⠺⣮⠻⠇⠀⠿⡄⠀⠀⠀⠀⢈⡆⢟⣻⠄⠀⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⡀⢰⠿⢙⣳⣤⣼⡵⡄⠀⠀⢁⣄⠀⠀⠀⢰⠅⢸⣶⣶⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⢿⣿⣟⣭⣶⣿⣿⣿⣿⣿⣿⡯⠀⠀⣿⣿⣄⠀⠀⠈⠁⠈⠉⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣨⣿⣿⣿⣿⣿⣟⣫⣭⣴⣶⣤⣄⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣴⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢴⣶⣶⣶⣶⣤⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠉⠛⠃⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⢯⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠰⢲⠈⠐⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⠿⠿⠿⡿⢿⠹⠟⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⠀⣠⣤⣤⣀⣠⣤⣀⠀⢀⣠⣤⣄⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣴⠺⣯⡉⢩⣽⠉⣍⠙⣏⢹⠋⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣤⠙⣯⠉⣭⣯⠉⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣏⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡿⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⠀⢻⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣷⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣏⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣼⣿⣵⣤⣤⣽⠿⣮⣽⣿⣯⣤⣭⣿⣾⣿⣯⣿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣿⣤⣿⣿⣅⣤⣶⠿⣿⣿⣽⣿⣿⣿⣿⣧⣤⣤⡶⣦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⣬⣭⣤⣐⣒⣒⢀⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⡇⢸⠃⢰⠀⢹⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣿⡿⣿⣿⢠⡀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠺⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠇⢸⠀⢸⠛⢻⠀⣴⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣜⡾⣼⢷⣿⣿⡏⠉⢀⡀⢰⣿⣧⣬⣤⣼⣤⣿⣤⣿⣤⣥⣴⣧⣤⣧⣬⠟⠻⣤⣼⠿⣤⣥⡼⠃⠸⢧⡼⠿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⣿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢟⣑⡇⣭⡅⣿⡇⠀⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⢀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣏⣇⣯⡇⣿⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⣿⠟⠁⠀⠀⠀⠙⠀⠀⠀⢾⣿⣶⣶⡄⢠⣶
⣾⣾⡨⢭⢅⢿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⣻⣿⣿⣿⣿⣿
⠿⢛⣛⣭⣥⣷⠀⠉⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠛⠛⠉⠭⠭⠄⢾⡿⠁⢸⣿⣿⣿⣿⣿⣿⢿⠿⣦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⢿⡆⠀⠀⠀⠀⠀⢈⢀⠃⠀⠆⠀⠀⠀⠀⠈⠼⠿⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⣿⠛⣿⢿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⡀⢸⣗⠀⠀⠀⠀⠀⠈⡆⠆⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠙⠁⢸⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠘⣿⠀⠀⠀⠀⠀⢸⢨⠟⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠐⡠⠄⠀⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⣶⢀⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣤⣀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣴⣶⣦⣤⣤⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠹⣿⣿⣿⣿⢿⣿⣿⣿⠟⡟⡿⣯⡉⠁⢩⢿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣤⣤⣀⣄⣠⣤⣤⣀⣀⣤⣄⠀⢀⣠⣤⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣤⡆⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣾⠁⣤⠙⡏⠉⣭⣯⠉⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⠁⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣧⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⣿⣿⡇⠀⠀⢻⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⣟⣿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣥⣤⣴⣤⣤⣽⠿⣬⣽⣯⣽⣯⣭⣽⣾⣿⣭⣿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⣤⣄⣒⣒⡀⡀⠀⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠘⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⡆⢸⠁⢰⠀⢹⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⣿⡇⣀⠀⠀⠀⠀⣤⣼⡇⢰⡆⢹⠃⠺⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣾⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠃⢸⠀⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢵⣟⡇⣿⡇⠋⢀⣀⠀⣶⣿⣿⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⣧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠋⠹⢧⡼⠿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⣿⢧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡺⢨⣽⢸⡇⠀⠈⠻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⡇⢨⣽⢸⡇⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⠿⠋⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶⣄⢀⣴⣿⡿
⣇⠭⡭⣾⡇⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀
⣛⣩⣭⣴⡆⠉⣠⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠘⠉⠉⠍⠅⠰⡿⠋⢀⣿⣿⣿⣿⣿⣿⣟⡿⣷⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠛⠻⣷⠀⠀⠀⠀⠀⢃⡓⠒⢲⠀⠀⠀⠀⠀⠡⠿⠛⢻⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢀⠀⢠⣾⠟⣻⠿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡆⠠⣿⠀⠀⠀⠀⠘⠃⠸⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⣿⣿⣿⠇⠀
⠀⠀⠀⠀⠀⠟⠀⠈⠋⠀⣿⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⢻⠀⠀⠀⠀⠀⡖⠛⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡁⠀⠀⠀⠀⠀⠀⠠⢀⠧⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣿⣿⣿⣣⠀⠀⠀⠀⠀⠀⠀⣷⣶⡆⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠙⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠠⣴⣶⣦⣤⣤⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠁⠀⠹⢿⣿⣿⢻⣿⡿⠟⠿⢫⣟⢛⠋⡉⠁⠭⠿⠿⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣤⣤⣄⡀⣀⣤⣄⣀⣠⣤⣀⠀⢀⣠⣤⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣤⣴⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣾⠉⡄⠙⡏⠉⣭⣯⠉⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣿⣷⠀⠀⠀⠀⢻⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⣿⣿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣤⣤⣤⣤⣤⣤⣽⠿⣬⣽⣿⣿⣧⣭⣥⣶⣿⣭⣿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣿⣿⣿⠿⣿⣿⣽⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀
⣐⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⢿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡆⣿⠀⢸⡇⠀⡇⠀⣿⣽⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⢸⣿⢸⠀⠀⠀⢰⣾⣷⣲⣿⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⣧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠋⠹⢧⡼⠿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⣿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢉⡉⣿⢸⠐⠿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣟⣁⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿
⢠⢦⣿⢸⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣾⣷⣴⣦⡀⣠⣾⣿⠟⠀
⠬⢸⣿⠸⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀
⢭⣵⣶⠐⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠈⠩⠭⣴⣿⠟⠉⣹⣿⣿⣿⣿⣿⣿⠙⢿⡄⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠁⠘⣿⠀⠀⠀⠀⠈⢙⠀⠂⠇⠀⠀⠀⠀⠉⠾⠟⠛⣿⣿⣿⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠈⠁⠀⣰⣿⢻⣿⣿⣿⣿⡿⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⣿⠀⠀⠀⠀⠂⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠟⣿⣿⣿⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠁⢸⣿⣿⣿⡟⠁⠀⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⡷⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠇⠀⣾⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢻⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⣶⣶⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣀⠈⠉⠁⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠠⣤⣶⣤⣤⣤⣀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠻⠁⠀⠻⠿⢿⢿⠿⠿⠻⠻⠿⠛⡛⠛⡋⠉⠀⠩⠋⠛⠹⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣄⣀⣀⣀⣠⣄⣀⣠⣄⣠⣤⣀⣤⣤⣀⢀⣀⣤⣤⣀⣠⣤⣀⠀⢀⣠⣤⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⡆⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣃⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⣿⣿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⣤⣶⣤⣤⣤⣤⣤⣤⡽⠿⣯⣽⣿⣭⣤⣭⣥⣾⣿⣯⡿⠿⣭⣈⣽⣿⣿⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣴⣶⣦⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⠿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⢰⡆⢹⠃⠘⠀⣿⠀⡟⠛⡇⠀⡀⢻⣇⣿⠀⢸⡇⠀⡇⠀⣿⣻⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⠀⠀⠀⠀⣶⣶⡖⢦⣿⣧⡀⢸⣧⣬⣤⣼⣤⣾⣤⣽⣤⣥⣴⣧⣤⣧⣬⠇⠻⣤⡼⠿⣤⣥⡼⠋⠹⣧⣼⢿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⢀⡀⢘⡍⠀
⠀⢰⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠁⠘⠋
⠀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠰⣿⣶⣶⣦⠀⣴⣾⡿⠏⠀⠀⠠⠀
⠘⢛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠙⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢙⣿⣿⣿⣿⣿⣿⠁⠀⠀⡯⣹⢍
⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠼⠀⠊
⣼⡿⠃⠹⣿⣿⣿⣿⣿⣿⣿⠻⣿⡈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠉⢿⡇⠀⠀⢁⡘⠁⠒⠀⠀⠀⠀⠀⠡⠿⠟⢻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀
⠛⠀⠀⣴⡿⢻⣿⣿⡿⣿⠏⠀⢸⡇⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⢾⡧⠀⠀⠀⠱⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡟⠁⣼⡇⡿⠀⢸⡆⠀⢸⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡇⠀⠀⠀⡴⡤⡦
⠀⠀⢸⠇⠀⣿⠀⡇⠀⠘⠃⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⣇⠀⠀⠀⠿⠟⠛
⠀⠀⢸⠀⠀⡇⠀⠇⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣷⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣯⣍⠉⠉⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣶⣶⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠿⠀⠀⠻⢿⠿⠌⠹⠛⡿⠻⠛⠛⠿⠿⠯⠁⠀⢩⡿⠿⡟⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣠⣤⣀⣠⣤⣀⣤⣄⣄⣀⣤⣤⣀⠀⣀⣤⣤⣀⣠⣤⣀⠀⢀⣠⣤⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣄⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣄⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠰⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣽⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⣺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣃⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢹⣇⣸⣿⣄⣋⣠⣿⣿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⢀⣤⣦⣤⣤⣤⣤⣤⣤⣽⠿⣯⣭⣯⣭⣤⣭⣥⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣽⣿⣿⣿⣿⣿⣥⣤⣤⠶⢤⣤⣴⣶⣤⠀⠀⢀⠀⠀⠐⠀⠀⠀⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⠿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠘⠀⣿⠀⡟⠛⡇⠀⡀⢻⣆⣿⠀⢸⡇⠀⡇⠀⣿⢻⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⠀⠀⢰⣶⣖⠲⣾⣿⣄⠀⣀⣼⣧⣤⣤⣼⣤⣾⣤⣽⣤⣥⣴⣧⣤⣧⣬⠇⠻⣤⡼⠿⣤⣥⡼⠏⠹⢧⣼⢿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⣀⠀⣋⠁⠀⠀
⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⡟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠁⠋⠀⠀
⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣾⣷⣶⣦⡀⣠⣾⣿⠟⠁⠀⠀⠤⣀⣀
⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀⠺⣝⠽⠋⠎
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠰⠊⠂⠘⡘
⠋⠘⢿⣿⣿⣿⣿⣿⣿⡟⢿⡆⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠋⢻⣿⠀⠀⠈⢙⠂⠂⡇⠀⠀⠀⠀⠈⠼⠟⠛⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣿⠟⣿⣿⡿⢿⡿⠁⠈⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⢸⣿⠀⠀⠀⠀⠇⠀⠈⠆⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⣿⣿⡿⠀⠀⠀⠠⠀⠀⠀⣀
⠀⣿⠁⢰⡿⢸⠁⠈⣇⠀⠀⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠁⠈⡿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⠀⠀⠀⠠⡮⢆⢴⡴
⠀⡟⠀⢸⠇⣸⠀⠀⠛⠀⠀⡇⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣿⠀⠀⠀⠺⠟⠚⠛⠓
⢀⡇⠀⢸⠀⠻⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣿⣿⣿⣯⣉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣴⣶⣦⣤⣤⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠀⠀⠻⠻⠫⠉⠻⠛⠛⢛⠛⠟⠿⠛⠏⠈⠁⢩⡟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣤⣠⣀⣀⣠⣤⣠⣤⣠⣀⣀⣀⣠⣤⣀⢀⣀⣤⣤⣀⣀⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⡏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⡄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣻⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⣟⢿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⢀⣤⣴⣤⣤⣤⣴⣤⣤⣿⠷⣬⣽⣯⣭⣤⣭⣵⣾⣿⣭⡿⠿⣭⣈⣽⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣧⠿⣯⣽⣿⣿⣿⣿⣽⣷⣤⣤⠶⢶⣤⣦⣦⣄⠀⡀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡄⢹⠃⠘⠀⣿⠀⡟⠛⡇⠀⡀⢻⣆⣿⠀⢸⡇⠀⡇⠀⣿⢿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⣶⣶⡒⢦⣤⣤⡀⠀⣀⠀⠸⣧⣬⣤⣼⣤⣾⣤⣽⣤⣥⣴⢧⣤⣧⣬⠏⠹⣤⡼⠿⣤⣥⡼⠃⠸⣧⣼⠿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⣀⠀⢸⠉⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠈⠘⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣴⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣠⡠⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶⣄⢀⣴⣿⡿⠃⠀⠀⠠⢄⣀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢛⣤⣶⣾⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⡟⠀⠀⢸⢫⡏⠿⢹⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⢀⣿⣿⣿⣿⣿⣿⣗⠀⠐⠻⠏⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠆⠙⠀⠃⢃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠛⠹⣿⣿⠀⠀⠀⠃⠐⠰⠀⠀⠀⠀⠈⠰⠿⠛⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣴⡿⣿⣿⣿⠿⣿⡟⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀
⠛⠀⣿⢿⡇⠀⢸⡇⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠆⠀⠀⢸⢴⠴⡴⣦⡆⠀
⠀⢰⡏⢸⡇⠀⢸⣷⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣿⡆⠀⠀⠸⠿⠛⠛⡛⠛⠀
⠀⢸⡇⢸⠃⠀⠈⠋⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠂⢸⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣿⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣴⣶⣶⣦⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠿⠀⠀⠛⠿⢿⡈⢛⠿⣿⠿⠟⠻⠛⠏⣯⡁⠁⠉⠛⠿⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠰⠄⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣄⣀⣀⣀⣠⣤⣤⣤⣠⣀⣀⣀⣠⣤⣀⢀⣀⣤⣤⣀⣠⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣻⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢹⣇⣸⣿⣄⣋⣠⣿⣿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⢀⣤⣶⣤⣤⣤⣴⣤⣤⡿⠷⣮⣽⣿⣿⣤⣭⣵⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣭⣿⣿⣿⣿⣿⣷⣤⣤⠶⢶⣤⣦⣶⣄⠀⡀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⣆⣿⠀⢸⡇⠀⡇⠀⣿⢿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⣶⣶⡒⢦⣤⣤⡀⠀⣀⠀⠸⣧⣤⣤⣼⣤⣾⣤⣽⣤⣥⣴⢧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⡼⠇⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⣀⠀⢸⠉⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠈⠘⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶⣄⢀⣴⣿⡿⠃⠀⠀⠠⣄⣀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⡟⠀⠀⢸⢫⡏⠿⢹⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⡿⣹⣿⣿⣿⣿⣿⣿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠇⠙⠀⢃⢃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⠻⣿⣿⠇⠀⠈⠃⠒⠰⠀⠀⠀⠀⠈⠰⠿⠛⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⠿⣿⡟⠀⢹⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⠃⠀⠀⠠⠀⠀⠀⢀⡀⠀
⠏⢁⣿⢹⡇⠀⢸⡇⠀⢸⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠆⠀⠀⢸⢴⠴⡴⣦⡆⠀
⠀⢸⡇⢸⡇⠀⢸⣇⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣿⡆⠀⠀⠸⠿⠓⢛⠛⠛⠀
⠀⢸⠇⢸⡇⠀⠸⡟⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠀⢸⡇⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣸⣀⣸⣇⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣟⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣶⣶⣶⣤⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠛⠟⢛⠉⠛⠛⠿⠿⠟⠛⠛⠛⣯⡉⠁⠩⠟⠿⠻⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠄⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣤⣀⣄⣀⣠⣤⣠⣤⣠⣀⣀⣀⣠⣤⣀⢀⣠⣤⣤⣀⣠⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣻⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢹⣇⣸⣿⣄⣋⣠⣿⣿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⢀⣤⣶⣤⣤⣤⣶⣤⣤⣽⠷⣮⣽⣿⣽⣤⣭⣵⣾⣿⣭⡽⠿⣭⣉⣽⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣽⣿⣿⣿⣿⣽⣷⣤⣤⠶⢶⣦⣦⣶⣄⠀⡀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⣆⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⣶⣶⡒⢦⣦⣤⡀⠀⠀⠀⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⡼⠇⠸⣧⡼⢿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⣀⠀⢘⠉⠀⠀⠀⠀
⠀⣶⣿⣿⣿⣿⣿⣧⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠈⠘⠁⠀⠀⠀
⣷⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶⣄⢀⣴⣿⡿⠃⠀⠀⠠⣄⣀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⢸⢫⡯⠿⠑⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⣿⠁⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠇⠛⠀⢃⢃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠇⢸⣟⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠰⠿⠛⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⠿⣿⡏⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⢼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⠃⠀⠀⠀⠄⠀⠀⢀⠀⠀
⠛⢻⡿⢹⡟⠀⢸⡇⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠆⠀⠀⢸⢴⠴⡴⣦⡆⠀
⠀⢸⡇⢸⡇⠀⢸⡇⠀⢸⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣿⡇⠀⠀⠸⠿⠛⠛⢛⠛⠀
⠀⢸⠁⢸⡇⠀⢸⡇⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠀⢸⡇⠀⠀⠁⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣸⣀⣸⣇⣀⣀⣀⣀⣈⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢶⣶⣶⣦⣄⣤⣄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠽⠻⢿⠇⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠿⠀⠀⠛⢿⠟⡈⠛⡛⡻⠿⠿⠻⠻⠟⣯⡁⠁⠉⠟⠻⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠰⠄⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣤⣀⣀⣀⣠⣄⣠⣤⣠⣀⣀⣀⣠⣤⣀⢀⣠⣤⣤⣀⣠⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⡄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣻⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⣿⣿⣄⣋⣀⣏⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⢀⣤⣶⣤⣤⣤⣶⣤⣤⣽⠷⣮⣽⣿⣯⣤⣭⣥⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣭⣿⣿⣿⣿⣿⣷⣤⣤⠶⢶⣤⣦⣶⣄⠀⡀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢼⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⣆⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⣶⣶⡒⢦⣦⣤⡀⠀⠀⠀⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⡼⠃⠸⣧⡼⢿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⣀⠀⢸⠉⠀⠀⠀⠀
⠀⣶⣿⣿⣿⣿⣿⣧⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠈⠘⠁⠀⠀⠀
⣷⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶⣄⢀⣴⣿⡿⠃⠀⠀⠠⢄⣀⣐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⢸⢫⡯⠿⢙⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⣿⠁⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠆⠙⠀⣃⢃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠇⢸⣟⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠰⠿⠛⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⠿⣿⡏⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⢼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⠃⠀⠀⠠⠀⠀⠀⢀⡀⠀
⠛⢻⡿⢹⡟⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠆⠀⠀⢸⢴⠴⡴⣦⡆⠀
⠀⢸⡇⢸⡇⠀⢸⡇⠀⢸⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣿⡆⠀⠀⠸⠿⠛⠛⡛⠛⠀
⠀⢸⠁⢸⡇⠀⢸⡇⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠀⢸⡇⠀⠀⠁⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣸⣀⣸⣇⣀⣀⣀⣀⣈⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣶⣶⣶⣦⣄⣦⣄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠹⠻⠿⠇⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠽⠿⠀⠀⠛⣿⢻⢉⢛⡛⡛⠿⠻⠟⠻⠟⣯⡉⠁⠉⠛⠿⡻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠰⠄⠠⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣤⣠⣀⣀⣠⣄⣠⣤⣠⣀⣀⣀⣠⣤⣀⢀⣀⣤⣤⣀⣠⣤⣄⠀⢀⣠⣤⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣻⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢹⣇⣸⣿⣄⣋⣠⣿⣿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⢀⣤⣦⣤⣤⣤⣴⣤⣤⣽⠷⣬⣽⣿⣿⣤⣭⣽⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⠿⣿⣭⣿⣿⣿⣯⣯⣷⣤⣤⠶⢶⣤⣤⣦⣄⠀⡀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠘⠀⣿⠀⡟⠛⡇⠀⡀⢻⡆⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⣶⣶⣒⢦⣦⣤⡀⠀⠀⠀⠸⣧⣤⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⣼⠇⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⣿⣿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⣀⠀⢸⠉⠀⠀⠀⠀
⠀⣶⣿⣿⣿⣿⣿⣧⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠈⠘⠁⠀⠀⠀
⣷⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶⣄⢀⣴⣿⡿⠃⠀⠀⠠⣠⣀⣐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⡟⠀⠀⢸⢫⡯⠿⢙⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⡟⠙⣿⠻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠈⠇⠙⠀⣃⢃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢸⠃⠠⠃⢀⣿⣿⠿⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠰⠿⠛⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⠿⣿⡇⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠟⢻⡏⢹⣿⠀⢹⡇⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠆⠀⠀⢸⢴⠴⡴⣦⡆⠀
⠀⢸⠇⢸⡏⠀⢸⡇⠀⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣿⡆⠀⠀⠸⠿⠛⠛⡛⠛⠀
⠀⢸⠀⢸⡇⠀⢸⡇⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⠀⢸⡇⠀⠸⡇⠀⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣿⣀⣸⣇⣀⣀⣀⣀⣸⣀⣷⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢀⣾⣿⣿⣶⣶⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠿⠀⠀⠛⠿⠻⠉⠛⠻⡿⠿⠿⠛⠛⠏⡯⡁⠁⠩⢛⠟⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠰⢠⠀⠰⠄⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣤⣄⣀⣀⣠⣤⣠⣤⣠⣀⣀⣀⣠⣤⣀⢀⣀⣤⣤⣀⣠⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣻⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⣏⣽⣇⣸⣿⣄⣋⣠⠿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⢀⣤⣶⣤⣤⣤⣴⣤⣤⣽⠷⣬⣽⣿⣽⣤⣭⣵⣾⣿⣭⡿⠿⣭⣉⣽⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣦⣴⠿⣯⣽⣿⣿⣿⣿⣿⣷⣤⣤⠶⢶⣦⣤⣶⣄⠀⡀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⣆⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⣶⣖⣒⠦⣦⣤⡀⠀⠀⠀⠸⣧⣬⣤⣼⣤⣾⣤⣽⣤⣥⣴⢧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⡼⠇⢸⣧⣼⣿⣤⣿⣤⣿⣤⣤⣿⠻⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⣀⠀⢘⠉⠀⠀⠀⠀
⠀⣶⣶⣿⣿⣿⣿⣧⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠈⠘⠁⠀⠀⠀
⣷⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶⣄⢀⣴⣿⡿⠃⠀⠀⠠⢄⣀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⡟⠀⠀⢸⢫⡏⠿⠹⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⣿⣿⣿⣿⣿⠟⠁⢹⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠇⠙⠀⠃⢃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢁⠀⢸⣿⣿⠟⠁⠀⠀⠀⠁⠀⠁⡃⠐⢰⠀⠀⠀⠀⠈⠰⠿⠛⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⣿⣿⠿⣿⡇⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⠃⠀⠀⠠⠀⠀⠀⢀⡀⠀
⠿⣿⡏⢻⣿⠀⢻⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠆⠀⠀⢸⢴⠴⡴⣦⡆⠀
⠀⣸⠁⢸⣿⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠘⣿⡆⠀⠀⠸⠿⠛⠛⠛⠛⠀
⠀⢸⠀⢸⡟⠀⢸⡇⠀⢸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡆⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⢸⡇⠀⢸⡇⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣿⣀⣸⣇⣀⣸⣇⣀⣸⣘⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣮⣍⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣴⣶⣶⣤⣤⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠿⠁⠀⠛⠿⢿⡘⠛⠿⠿⡟⠟⠛⠛⠛⣯⡁⠁⠉⠛⠻⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠰⠄⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣤⣄⣀⣀⣠⣤⣠⣤⣠⣀⣀⣀⣠⣤⣀⢀⣠⣤⣤⣀⣠⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣄⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⣏⣽⣇⣸⣿⣄⣋⣠⠿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⢀⣤⣴⣤⣤⣤⣶⣤⣤⡽⠷⣬⣽⣿⣽⣤⣭⣵⣾⣿⣯⡿⠿⣭⣉⣽⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣦⣴⠿⣯⣭⣿⣿⣿⣯⣿⣷⣤⣤⠶⢶⣤⣤⣶⣄⠀⡀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⣆⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⣶⣖⣒⠦⣦⣤⡀⠀⠀⠀⠸⣧⣬⣤⣼⣤⣾⣤⣽⣤⣥⣴⢧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⡼⠃⢸⣧⣼⣿⣤⣿⣤⣿⣤⣤⣿⠻⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⣀⠀⢘⠉⠀⠀⠀⠀
⠀⣶⣶⣿⣿⣿⣿⣧⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠈⠘⠁⠀⠀⠀
⣷⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶⣄⢀⣴⣿⡿⠃⠀⠀⠠⢄⣀⣐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⡟⠀⠀⢸⢫⡯⠿⢹⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⣿⣿⣿⣿⣿⠟⠁⢹⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠇⠛⠀⠃⢃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢁⠀⢸⣿⣿⠟⠁⠀⠀⠀⠁⠀⢁⡃⠀⢰⠀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⣿⣿⠿⣿⡇⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⠃⠀⠀⠀⠠⠀⠀⢀⡀⠀
⠿⣿⡏⢻⣿⠀⢻⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠆⠀⠀⢸⢴⠴⡴⣦⡎⠀
⠀⣸⠁⢸⣿⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠘⣿⡇⠀⠀⠸⠿⠛⠛⣛⠛⠀
⠀⢸⠀⢸⡟⠀⢸⡇⠀⢸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡆⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⢸⡇⠀⢸⡇⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣿⣀⣸⣇⣀⣸⣇⣀⣸⣘⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣮⣍⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣴⣶⣦⣤⣤⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠀⠀⠛⠿⢟⡍⠙⠿⠿⠟⠻⠛⠛⠛⣯⡁⠁⠉⠛⠿⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠄⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣤⣀⣀⣤⣄⣠⣤⣀⣀⣠⣤⣀⠀⣀⣤⣤⣀⣠⣤⣀⠀⢀⣠⣤⣀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣠⣤⡆⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⡏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣄⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⢹⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠐⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢸⣇⣸⣿⣄⣋⣠⡿⢿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢀⣤⣶⣤⣤⣤⣦⣤⣤⡽⠿⣮⣭⣿⣭⣤⣭⣵⣾⣿⣯⡽⠿⣭⣉⣽⣿⣿⣤⣶⣭⣥⣤⣿⣿⣅⣀⣴⠿⣯⣽⣿⣿⣿⣿⣯⣭⣤⣤⠶⢤⣤⣴⣦⣤⠀⠀⠀⡀⠀⠀⠒⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⠿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠘⠀⣿⠀⡟⠛⡇⠀⡀⢻⣇⣿⠀⢸⡇⠀⡇⠀⣿⣼⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⣶⣶⣒⠶⢤⣤⡀⠀⠸⣧⣬⣤⣼⣤⣾⣤⣽⣤⣥⣴⣧⣤⣧⣬⠇⠻⣤⡼⠿⣤⣥⡼⢿⣿⣧⣼⣿⣤⣿⣤⣿⣤⣤⠿⢻⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⢀⡀⢘⡍⠀⠀
⣀⣀⠀⣶⣶⣿⣿⣿⣿⣇⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⣤⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠘⠁⠀
⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣶⣶⣄⠀⣴⣿⡿⠋⠀⠀⠠⢄⣀
⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⡆⡯⡻⠝⠱
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⢿⣿⠟⣿⡟⢻⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠇⠴⠃⠀⡃
⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⠋⠉⠁⠀⠘⡏⠀⢸⡇⢸⡇⠀⣁⡐⠀⠰⠀⠀⠀⠀⠀⠡⠿⠛⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⣹⣿⣿⣿⣿⡿⣿⡏⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⢸⡇⠀⠈⠰⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⣾⡿⣿⡿⢹⣿⠃⢻⡇⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠊⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡇⠀⠀⠆⢴⠵⡤⢦
⢸⡟⠀⢸⡇⠈⣿⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠂⡠⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⡇⠀⠀⠑⠿⠗⠛⠚
⢸⡇⠀⢸⠃⠀⣿⠀⢸⡇⠀⢸⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣷⣶⡆⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⢸⠀⠐⣿⠀⠰⡇⠀⢸⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣂⣀⣾⣀⣀⣧⣀⣀⣇⣀⣸⣇⣿⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣶⣶⣦⣤⣄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠿⠀⠀⠻⠟⠛⠈⠛⠛⡛⣛⠛⠹⠻⠿⠯⠉⠀⠉⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣄⣀⣀⣀⣀⣤⣤⣀⣄⣀⣠⣤⣤⣄⣀⠀⣀⣤⣤⣄⣠⣤⣀⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⠀⠀⠀⠀⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣧⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣃⣸⣿⣀⣟⣀⣿⣃⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⣤⣶⣤⣄⣤⣴⣤⣤⡽⠷⣮⣽⣿⣿⣤⣭⣵⣾⣿⣭⡽⠿⣭⣈⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣤⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠴⢤⣤⣤⣶⣤⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⠿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠘⠀⣿⠀⡟⠛⡇⠀⡀⢻⡆⣿⠀⢸⡇⠀⡇⠀⣿⣻⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⠁⠀⠀⠀⣰⣶⣒⠶⢴⣤⣼⢧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⣧⣤⣧⣬⠇⠻⣤⡼⠿⣤⣥⡼⠋⢹⣧⣼⣿⣤⣿⣤⣿⣤⣤⣿⠻⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢘⡏
⣿⠀⣀⣀⠀⣶⣶⣾⣿⣿⣿⣿⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠉
⣿⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠠⣿⣷⣶⣦⠀⣰⣾⡿⠏⠀⠀⠀
⣿⢠⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢉⣿⣿⣿⣿⣿⣿⠃⠀⠀⡏⣹
⢰⠘⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⡿⢿⡿⢻⡿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠽⠀
⢀⣴⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠟⠛⠉⠉⠈⠀⢸⣿⠀⠘⡇⢸⡿⠀⢀⡘⠀⠒⠀⠀⠀⠀⠀⠡⠾⠟⢛⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀
⣾⣿⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡇⠈⡇⠀⠈⠰⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀
⢹⡏⠀⣼⡿⣿⣿⠛⣿⡏⢸⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠇⠀⡇⠀⠀⠠⠐⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⡗⠀⠀⠀⡵⡤
⢸⡇⠀⣿⠁⢸⡿⠀⣿⡇⠸⡿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡟⠀⠀⠠⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⣇⠀⠀⠁⠿⠟
⢸⡇⢀⡇⠀⢸⡇⠀⣿⠁⠀⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⠀⡆⣶⣶⢸⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠏⠀⠀⠀⠀⠀
⠈⠁⢸⡇⠀⢸⡇⠀⣿⠀⠀⣷⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣤⣤⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣸⣇⣀⣸⣇⣀⣿⣀⣀⣿⣀⣀⣇⣿⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣰⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠈⠈⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣵⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⢰⠀⠀⠴⠀⠀⠀⠀⠀⠆⢰⢠⣤⣤⣤⡄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣶⣶⣦⣤⣀⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣹⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠿⠀⠀⠹⢿⠿⠟⠈⠹⠛⠛⡛⠋⠛⠿⠋⠉⠀⠉⠋⠿⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠰⢠⠀⠀⠀⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣤⣤⣀⣀⣀⣠⣀⣀⣀⣀⣀⣤⣀⣠⣤⣀⣀⣄⣤⣀⣀⣀⣤⣀⠀⢀⣠⣤⣀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣤⣴⠀⠸⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⡏⠀⠀⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣏⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢺⣿⣿⠀⠀⢻⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣾⣏⣤⣶⣤⣤⡽⠿⣬⣽⣯⣭⣮⣭⣽⣾⣿⣯⡽⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⣤⣤⣀⣒⣂⢀⠀⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⡿⢿⣿⢸⠀⠀⠀⠀⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣾⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠬⣼⣳⢸⣿⢸⠀⠀⠀⢰⣶⣾⣧⣬⣤⣼⣤⣾⣤⣽⣤⣥⣴⣧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠃⠹⢧⡼⢿⣤⣿⣤⣿⣤⣤⣿⠻⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢔⡇⣭⡅⣿⢘⠀⣀⡀⢰⣶⣾⣿⣿⣿⣿⣀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣦⣴⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢫⢁⣭⡇⣿⢸⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣾⣷⣶⣦⡀⢠⣾⣿
⣾⡨⢭⢥⣿⢐⣴⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⡯⢾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷
⢛⣋⣭⣥⣶⢰⠛⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⡿⣿⡟⢻⣿⡿⠿⣿⠛⣿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠛⠩⠩⠍⣸⣾⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⢀⡿⠀⢻⡇⠈⣿⠁⠀⣿⠀⣿⠀⡈⢀⠂⠀⠆⠀⠀⠀⠀⠈⠼⠟⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⠏⠀⢨⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠉⠁⠀⠀⢸⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⠆⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠟⣿⠀⣰⣿⣿⣿⡿⣿⣿⠹⣿⡇⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⣿⠀⣿⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⣿⠇⠘⣿⠃⢸⡏⠀⣿⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⣿⠀⠄⠀⠄⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢻⠁⢸⣶⣶⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡟⠀⣿⠀⢰⣿⠀⢸⡇⠀⢿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣩⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠘⠀⠈⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠙⠛⠻⣿
⣀⣀⣀⣀⣀⣀⣀⣿⣀⣸⣷⣀⣸⣇⣀⣸⣀⣀⣿⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣌⣉⣙⣻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠈⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠤⠀⠀⠆⠀⢰⠀⠀⢰⢠⣤⣶⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣤⣶⣶⣤⣤⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠁⠀⠻⣿⢿⠿⠿⠿⠿⠿⠻⠏⠿⠿⠏⠉⠁⠉⠛⠏⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⠀⣠⣤⣤⣄⣠⣤⣀⠀⢀⣠⣤⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣟⢿⡇⢸⣿⠀⣅⠰⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⢿⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢹⣇⣸⣿⣄⣋⣠⡿⢿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣼⣿⣥⣤⣽⠿⣬⣽⣯⣽⣤⣭⣽⣾⣿⣯⡿⠿⣭⣈⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣽⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣬⣭⣭⣥⣀⣐⣂⠀⠀⠀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣽⣿⣿⡿⣿⣿⡇⠀⠀⠀⢸⡇⢰⡆⢹⠃⠘⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣓⡬⣼⢧⡿⣿⡇⠀⠀⠀⢸⣧⣬⣤⣼⣤⣾⣤⣽⣤⣥⣴⣧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⡼⠃⠸⣧⡼⠿⣤⣿⣤⣿⣤⣤⣿⡿⣦⣥⣴⢧⣤⡿⣧⣼⣿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⢿⣑⡇⣭⡅⣿⡇⠀⣀⡀⢰⣶⣾⣿⣿⣿⣿⣇⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠰⣶⣿⣿⣿⣧⣴⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣹⣹⣏⡇⣥⡄⣿⡇⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢼⣿⣶⣶⡄⢀
⢅⣾⣾⡧⢭⢅⣿⡇⣤⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⣹⣿⣿⣿⣿
⠿⠿⢛⣛⣭⣥⣶⡆⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⢿⡿⢻⣿⡿⠿⣿⠟⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠒⠛⠉⠉⠭⢡⣾⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⡾⠁⢸⡇⠀⣿⡇⠀⢹⠀⣿⡇⠀⢀⠃⠐⠂⢀⠀⠀⠀⠈⠴⠿⠛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠟⠛⠛⠻⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⠀⢹⠀⠠⠋⠆⠀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠾⣿⠁⢠⣿⣿⣿⣿⢿⣿⠛⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠀⣾⠀⢸⡄⢀⠁⡖⠃⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⠈⣿⡇⢸⣿⠀⢿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠉⠀⢸⡇⠀⠀⠄⠀⠠⢲⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⣿⠁⢸⡇⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⢸⡇⢸⢰⣶⡆⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠀⠀⠁⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣿⣀⣸⣇⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡶⠀⢰⠆⢠⣴⣦⣤⣴⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠠⣶⣶⣶⣤⣤⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠿⠁⠀⠿⠿⢿⠙⠿⠿⡿⠿⠿⠿⠟⠛⠋⠉⠀⠍⠛⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣠⣤⣤⣠⣤⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣤⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠰⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⡇⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡏⢻⣇⣸⣿⣄⣋⣠⡿⢿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣼⣿⣽⠿⣮⣽⣿⣭⣤⣭⣥⣾⣯⣭⡿⠿⣯⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣥⣤⣤⠶⢦⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣤⣄⣐⣒⡀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⠀⢸⡇⢰⡄⢹⠃⠘⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣤⢽⢇⡇⣿⡇⠀⠸⣧⣤⣤⣼⣤⣾⣤⣽⣤⣥⣴⢧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⡼⠏⠹⣧⣼⠿⣤⣿⣤⣿⣤⣤⠿⠻⣦⣥⣴⢧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣉⣙⢹⡇⠁⢀⡀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠰⣶⣶⣾⣿⣷⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⣾⢸⢻⡟⡇⡤⠄⣾⡇⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢘⣃⢠⣾⣿⣿⣷⣶
⢼⡚⡝⣾⣿⡧⢭⠅⣿⡇⣠⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣠⣶⣾⣯⣿⣿⣿⡿⣿⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⠻⣿⣿⠿⣿⡟⢿⡟⠀⡀⠀⣰⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷
⠀⠀⠀⠐⠂⠋⠉⠉⠉⢡⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⠏⢸⡟⠀⣿⡏⠀⢸⡇⢸⡇⢀⠁⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠈⣽⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢸⠃⢸⡇⢸⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⢀⣾⣿⣿⣿⢿⣿⡟⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⢸⡇⠀⢸⠀⢸⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡿⠀⣿⡟⠈⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠘⠀⢸⡇⠘⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇⠀⠀⠀⢸⡇⠀⢱⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢸⡇⠀⣿⡃⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠈⡗⠀⠁⠀⠀⠹⠯⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣸⣂⣀⣿⣀⣀⣿⣀⣸⣇⣀⣸⣟⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣈⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣻
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠈⠉⠉⠉⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠴⠀⢰⣶⣤⣤⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢤⣶⣶⣦⣤⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠀⠀⠿⠿⣿⠁⠿⠿⡿⠿⣿⠛⠿⠿⡯⠉⠁⠍⠟⠻⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣀⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⡏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⢻⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢸⣇⣸⣿⣄⣋⣠⡿⢿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣦⣼⣿⣽⠿⣮⣽⣿⣭⣤⣭⣥⣾⣯⣭⡽⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣤⣥⣄⣐⣒⡀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⡂⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣬⢽⢇⡇⣿⡇⡂⠸⣧⣤⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠹⣧⣼⢿⣤⣿⣤⣿⣤⣤⠿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣉⣙⢹⡇⠃⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⠀⠀⠀⠀⠠⣶⣾⣿⣿⣷⣴⣶⣿⡟⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡟⡇⡯⠄⣼⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣦⡄⠀⠀⣾⣵⣟⣀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣿⡧⢭⠅⣿⡇⣀⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⡟⠁⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⢛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠁⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣏⣿⣻⣿⣿⣿⣿⣿⣦⣸⣿⣿⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠉⠉⠉⢡⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⠱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣻⣿⣿⣿⣿⠟⠃⢹⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣾⣹⣽⣿⣿⣿⣿⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣽⣷⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣦⢀⣀⣠⣄⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠁⠀⣿⠁⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠒⠊⠻⢿⣿⣿⣿⣿⠿⠁⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣾⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣻⣿⣟⣙⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣘⣿⣿⣛⣁⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠈⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠴⠀⢰⣶⣤⣤⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣶⣶⣶⣦⣀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠿⠁⠀⠟⡻⣿⠍⠿⠿⠿⠿⠿⠝⠿⠿⠯⠉⠁⠩⠟⠋⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⠀⣀⣤⣤⣠⣤⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡇⢸⣇⣸⣿⣄⣋⣠⡿⢿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣼⣿⣽⠿⣬⣭⣿⣽⣤⣭⣽⣾⣿⣭⡽⠿⣭⣀⣿⣿⣿⣦⣴⣯⣧⣤⣿⣿⣅⣠⣴⠿⣯⣽⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣥⣤⣄⣀⣒⡂⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⠀⢸⡇⢰⡆⢹⠃⠘⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣣⣬⢽⢇⡇⣿⡇⡀⠸⣧⣬⣤⣼⣤⣾⣤⣽⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠹⣧⣼⣿⣤⣿⣤⣿⣤⣤⠿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠏⠽⣣⡏⣍⣙⢹⡇⠀⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣾⣿⣿⣴⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣾⢸⢻⡟⡇⡧⡄⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠅⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⠿⣾⡿⠿⢛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣿⣿⣿⣿⡿⢿⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠀⠀⠂⠙⠉⠉⠉⢡⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢹⡿⠀⢻⡏⠀⢸⢇⣼⣷⣤⣌⣃⠀⢰⠀⠀⠀⠀⠈⠰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⡇⠀⢸⣧⡴⣿⣿⣿⣿⣿⣿⣿⡇⠀⢪⠀⠀⠀⣠⢖⡄⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣥⡀⠠⠀⣀⣼⣿⡿⠖⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣷⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣽⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠠⢴⢤⣦⣤⣄⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠁⠀⠻⢿⢿⡏⠿⠿⡿⠿⠿⢿⠿⠿⡯⠉⠁⢭⠿⢿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣤⣤⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣧⣿⡇⢸⣿⠀⡿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡏⢸⣇⣸⣿⣄⣋⣠⡿⢿⣀⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣼⣿⡽⠿⣬⣭⣿⣭⣤⣭⣽⣾⣿⣭⡿⠿⣭⣀⣽⣿⣿⣦⣴⣯⣧⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣥⣤⣄⣐⣒⡂⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣁⣗⣿⣿⣿⡿⣿⡇⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣬⢽⢇⡇⣿⡇⡀⠸⣧⣬⣤⣼⣤⣾⣤⣽⣤⣥⣴⢧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⡼⠏⠹⣧⣼⢿⣤⣿⣤⣿⣤⣤⠿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠏⠽⣣⡏⣍⣙⢹⡇⠀⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣿⣴⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣾⢸⢻⡟⡇⡦⡆⣾⡇⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠅⣿⡇⣠⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⢛⣛⣩⣭⣶⡆⠛⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣿⣿⣿⣿⡿⢿⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠙⠉⠍⠉⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢹⡿⠀⢻⡏⠀⢸⢇⣼⣷⣤⣌⣃⠀⢰⢀⠀⠀⠀⠈⠰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⡇⠀⢸⣧⡴⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⠀⠀⠀⣠⢖⡄⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣧⡀⠰⠀⣀⣼⣿⡿⠖⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡟⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣽⣷⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣽⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣷⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢶⣤⣦⣤⣄⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠀⠀⠻⣿⣿⡍⠿⠿⡿⠿⠿⢿⡿⠿⡯⡉⠀⢭⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣶⣼⣿⣽⠿⣬⣭⣿⣯⣤⣭⣵⣾⣿⣭⣽⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣽⣿⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣥⣥⣄⣐⣒⡀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣥⣗⣽⣿⣿⡿⣿⡇⡂⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢠⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣬⢽⢇⡇⣿⡇⡁⠸⣧⣤⣤⣼⣤⣾⣤⣽⣤⣥⣴⢧⣤⣧⣬⠏⠻⣤⡼⠿⣤⣥⡼⠏⠹⣧⣼⢿⣤⣿⣤⣿⣤⣤⠿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠏⠽⣣⡏⣍⣙⢹⡇⠀⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣾⢸⢻⡟⡇⡥⡆⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣿⡧⠭⠅⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠛⠉⠉⠩⢡⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⠠⠋⠃⠀⢰⠀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢸⠰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠸⠀⡌⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡟⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢀⡼⣤⣴⣿⣿⣶⣤⡀⠀⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣣⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣷⣏⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢶⠀⢰⣦⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢠⣤⣶⣤⣄⠠⣄⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠨⠃⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠀⠀⠿⢿⣿⡍⠿⠿⠿⠿⠿⠿⠿⠿⠯⠉⠁⠯⠿⢿⡻⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣤⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣧⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣶⣼⣿⣽⠿⣬⣭⣿⣽⣤⣭⣵⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣥⣤⣄⣐⣒⡂⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣅⣗⣽⣿⣿⡿⣿⡇⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣤⢽⢇⡇⣿⡇⡁⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠸⣧⣼⣿⣤⣿⣤⣿⣤⣤⠿⠿⣦⣥⣴⢧⣤⠿⣧⣼⠿⣤⡼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣙⢹⡇⠃⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣾⢸⢻⡟⡇⡯⡦⣾⡇⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣿⡧⢭⠅⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⢛⣛⣩⣭⣶⡆⠛⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠐⠒⠛⠩⠉⠩⢡⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⠠⠃⠃⠁⢰⢀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢰⠐⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠈⠠⠈⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡟⠈⣿⡟⠈⣿⠀⢻⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠸⡀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠁⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣻⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣷⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣴⣶⣷⣴⣾⣷⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣤⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠤⣤⣦⣤⣄⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠱⠿⠄⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠁⠀⠿⢿⣿⡟⢿⡿⣿⠿⠿⠿⢿⠿⡯⠉⠁⠯⠿⠟⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣤⣤⣤⣄⠀⢀⣠⣤⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣤⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣴⣼⣿⣽⠿⣬⣽⣿⣿⣤⣭⣽⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣴⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣥⣤⣄⣒⣒⡂⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣽⣿⣿⡿⣿⡇⠂⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⣆⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣤⢽⢇⡇⣿⡇⡃⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠹⣧⣼⢿⣤⣿⣤⣿⣤⣤⠿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣙⢹⡇⠁⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣾⢸⢻⡟⡇⡯⡦⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣿⡧⢭⠅⣿⡇⣢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠀⠐⠂⠛⠉⠉⠉⢡⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⢠⠃⠃⠀⢰⠀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢹⡇⠀⢸⠀⢸⡇⢸⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠀⠀⠊⠃⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠸⡈⠀⠀⠠⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠁⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣴⣶⣷⣴⣾⣷⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠈⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣤⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢠⣴⣦⣤⣄⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠱⡿⠄⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠁⠀⠻⢿⣿⡟⠿⠿⣿⠿⠿⠿⠿⠿⣯⠉⠁⢯⠿⠿⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣤⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⡄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣏⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣼⣿⣽⠿⣬⣽⣿⣿⣦⣭⣵⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣦⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣥⣤⣄⣒⣒⡂⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⠆⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣬⢽⢇⡇⣿⡇⡃⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠹⣧⣼⢿⣤⣿⣤⣿⣤⣤⠿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠏⠽⣣⡏⣯⣙⢹⡇⠁⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣾⢸⢻⡟⡇⡥⡆⣾⡇⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠅⣿⡇⣢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⢛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠛⠙⠍⠩⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⠠⠃⡃⠀⢰⠀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⠰⠐⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠀⠀⠈⠃⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡟⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠠⡀⠀⠀⠀⢝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠁⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢤⡤⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠁⠀⠿⢿⣿⡯⡿⣿⣿⡿⢿⠿⠿⠿⡯⠉⠁⢯⠿⢿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣄⣠⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣤⣤⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣴⣼⣿⣽⠿⣮⣽⣿⣽⣦⣭⣽⣾⣿⣯⣿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣽⣿⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣥⣤⣄⣒⣒⡂⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣥⣗⣿⣿⣿⡿⣿⡇⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠁⢸⠀⢸⠛⢻⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣬⢽⢇⡇⣿⡇⡀⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠇⠹⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣙⢹⡇⠀⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣾⢸⢻⡟⡇⡯⡆⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠅⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠀⠀⠂⠛⠩⠍⠩⢡⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⢠⠃⡃⠁⢰⠀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢸⠰⠀⠀⠀⠪⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠀⠀⠉⠃⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠰⡚⠀⠀⠠⢝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠁⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠁⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣸⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣴⣶⣤⣄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠀⠀⠿⣿⣿⡏⣿⡿⣿⣿⢿⠿⣿⢿⣯⡉⠁⠭⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣏⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣶⣼⣿⣽⠿⣮⣽⣿⣽⣤⣭⣽⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣽⣿⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣄⣒⣒⡂⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣥⣗⣿⣿⣿⡿⣿⡇⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣬⢽⢇⡇⣿⡇⡀⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⠿⣦⣥⣴⢧⣤⠿⣧⣼⠿⣤⡼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠏⠽⣣⡏⣯⣙⢹⡇⠃⣀⣀⠀⣿⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣾⢸⢻⡟⡇⡯⡆⣾⡇⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠅⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠀⠀⠒⠛⠉⠍⠉⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⠠⠋⠃⠁⢐⠀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⠀⠀⠠⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠀⠀⠀⠁⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡟⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠠⡀⠀⠀⠠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠉⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠠⢴⣦⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠁⠀⠿⣿⣿⡿⠿⢿⠿⣿⢿⠿⢿⠿⡯⡉⠁⢭⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣧⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣶⣼⣿⣽⠿⣮⣽⣿⣭⣤⣭⣽⣾⣿⣭⡽⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣄⣒⣒⡂⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣥⣗⣿⣿⣿⡿⣿⡇⠀⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣬⢽⢇⡇⣿⡇⡀⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⣼⠿⣤⣥⡼⠏⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠏⠽⣣⡏⣭⣙⢹⡇⠂⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣥⣾⢺⢻⡟⡇⡧⡆⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠅⣿⡇⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠐⠂⠂⠛⠩⠍⠍⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⢠⠋⡃⠁⠰⠀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⠐⠀⠠⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠀⠀⠀⠁⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡟⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠰⡀⠀⠀⠀⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠁⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠁⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣦⣦⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠁⠀⠿⣿⣿⡟⠿⡿⠿⣿⢿⠿⣿⡿⡯⠉⠁⠭⠿⠿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣄⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣴⣼⣿⣽⠿⣮⣽⣿⣽⣤⣭⣵⣾⣿⣯⣿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣽⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣾⣭⣭⣤⣄⣒⣒⡀⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠘⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣣⣗⣿⣿⣿⡿⣿⡇⠆⢸⡇⢰⡄⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⣇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣭⢽⢇⡇⣿⡇⡁⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣭⣙⢹⡇⠇⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡟⡇⣯⡧⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠥⣿⡇⣢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠐⠂⠒⠉⠋⠉⠍⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⠠⠋⠃⠀⠘⢀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢸⠰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠈⠀⠍⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠰⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠁⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠁⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣶⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠁⠀⠿⢿⣿⡽⠿⠿⣿⢿⢿⠿⠿⣿⡯⠉⠁⢭⣿⢿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣄⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣧⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣼⣿⣽⠿⣬⣽⣿⣿⣤⣭⣭⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣀⣐⣒⡀⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⠇⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣤⢽⢇⡇⣿⡇⡁⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠇⠸⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⠻⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣭⣙⢹⡇⠀⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡟⡇⣭⡇⣾⡇⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠇⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣭⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠐⠂⠚⠙⠋⠉⠙⢧⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⠠⠋⡃⠁⠘⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⠀⠰⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠈⠀⠉⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠀⡀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠉⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣶⣦⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠀⠀⠿⢿⣿⡯⢿⣿⠿⣿⣿⠿⡿⠿⡯⠉⠁⠯⠿⠿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣀⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣦⣼⣿⣽⠿⣬⣽⣿⣽⣤⣭⣥⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣀⣐⣒⡀⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⠇⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⣇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣤⢽⢇⡇⣿⡇⡀⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠸⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣯⣉⢹⡇⡂⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡟⡇⣯⡟⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⣚⡝⣾⣷⡧⢭⠥⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣭⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠂⠂⠙⠋⠉⠉⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⠠⠋⠃⠀⠘⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢹⡇⠀⢸⠀⢸⡇⢸⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠈⠀⠈⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠠⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠉⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠈⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣶⣦⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠁⠀⠿⢿⣿⡿⢿⡿⠿⣿⣿⠿⣿⠿⡯⠉⠁⢭⠿⠿⡿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣇⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣟⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣦⣼⣿⣽⠿⣯⣽⣿⣽⣤⣭⣵⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣀⣐⣒⡀⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⠆⢸⡇⢰⡆⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⣇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣥⢽⢇⡇⣿⡇⡅⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⣼⠿⣤⣥⡼⠇⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣭⣙⢹⡇⠇⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡟⡇⣯⡇⣾⡇⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠥⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠀⠂⠂⠙⠋⠉⠉⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⠠⢋⠃⠐⠘⢀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢨⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠈⠀⡉⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡟⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠠⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠉⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠈⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣦⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠿⢿⣿⡝⠿⠿⢿⢿⣿⠻⣿⠿⣯⠉⠁⠭⡿⠿⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣧⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣦⣼⣿⣽⠿⣬⣭⣿⣽⣤⣭⣭⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣀⣐⣒⡀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⠃⢸⡇⢰⡄⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⣇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢫⣳⣤⢽⢇⡇⣿⡇⡀⠸⣧⣤⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⣼⠿⣤⣥⡼⠏⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣭⣙⢹⡇⠇⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡟⡇⣯⡇⣾⡇⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠅⣿⡇⢢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣭⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠀⠀⠐⠒⠚⠙⠉⠉⠙⢧⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⢠⠋⠃⠀⠘⢀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠈⠀⠍⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠰⡂⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠉⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠈⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢤⣶⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠿⢿⣿⡿⢿⡿⡿⣿⠿⠿⣿⢿⠯⠉⠁⢭⠿⢿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡄⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣦⣼⣿⣽⠿⣮⣽⣿⣽⣤⣭⣥⣾⣿⣯⡿⠿⣭⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣭⣿⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣀⣒⣒⡀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⡇⢸⡇⢰⡄⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣤⢽⢇⡇⣿⡇⡁⠸⣧⣤⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠸⣧⣼⣿⣤⣿⣤⣿⣤⣤⡿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣭⣙⢹⡇⠅⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡟⡇⣯⡇⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⣚⡝⣾⣷⡧⢭⠅⣿⡇⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣭⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠈⠀⠀⠒⠚⠋⠋⠉⠉⢧⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⢠⢃⠃⠀⠘⠀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢸⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠈⠀⠌⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠠⡀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠉⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣴⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠿⣿⣿⡿⣿⠿⣿⢿⢿⠿⣿⣿⡯⡉⠁⠭⠿⢿⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣦⣼⣿⣽⠿⣮⣽⣿⣿⣤⣭⣭⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣴⣿⣯⣤⣿⣿⣅⣠⣤⠿⣯⣭⣿⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣀⣒⣒⡀⠀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⡆⢸⡇⢰⡄⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣥⢽⢇⡇⣿⡇⡂⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠇⠹⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⡼⢧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣭⣙⢹⡇⠆⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡟⡇⣯⡧⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠥⣿⡇⣢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠒⠚⠋⠋⠉⠉⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⢠⠋⡃⠀⠘⢀⠀⠀⠀⠈⢱⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢰⠘⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠈⠀⡍⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠠⡐⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠁⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠉⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣾⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣶⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠀⠀⠿⣿⣿⡯⢿⢿⠿⣿⣿⠿⢿⢿⡯⡉⠁⢭⠿⢿⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠉⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣧⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣼⣿⣽⠿⣮⣽⣿⣽⣤⣭⣽⣾⣿⣯⡿⠿⣯⣉⣽⣿⣿⣤⣤⣿⣯⣤⣿⣿⣅⣠⣤⠿⣯⣭⣿⣿⣿⣿⣿⣧⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣀⣒⣒⡀⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡏⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣡⣗⣿⣿⣿⡿⣿⡇⠆⢸⡇⢰⡄⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢫⣳⣤⢽⢇⡇⣿⡇⡆⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠏⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⡿⠻⣦⣥⣴⢧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣭⣙⢹⡇⠃⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡟⡇⣯⡇⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠅⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⠛⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠂⠚⠙⠋⠉⠉⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⢠⢋⠃⠀⠘⢀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢰⠀⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠈⠀⠌⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡿⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠁⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠁⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠈⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣶⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠁⠀⠿⢿⣿⡿⢿⠿⢿⡿⠿⣿⢿⠿⣯⡉⠁⢭⡿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⠀⣀⣤⣤⣠⣤⣤⣀⠀⢀⣠⣤⣄⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣯⡉⢩⣽⠉⣍⠙⣏⢹⠉⣿⠉⣿⠉⢿⠉⡟⠁⡌⢹⣿⣯⡉⢩⣽⠉⣤⠙⣷⣿⠁⣄⠙⡏⠉⣭⣯⠉⢩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⢸⣿⠀⣅⠸⣿⡀⢰⣿⠀⣿⠀⡈⠀⡇⠀⡟⢻⣯⣿⡇⢸⣿⠀⣿⠀⣿⣿⠀⣟⠛⡇⠀⣭⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣇⣸⣿⣀⣿⣀⣿⣇⣸⣿⣀⣿⣀⣇⣀⣧⣀⣣⣸⡟⢻⣇⣸⣿⣄⣋⣠⡿⢿⣄⣋⣀⣇⣀⣉⣿⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣼⣿⣽⠿⣮⣽⣿⣿⣤⣭⣵⣾⣿⣭⡿⠿⣭⣉⣽⣿⣿⣤⣴⣿⣯⣤⣿⣿⣅⣠⣴⠿⣯⣽⣿⣿⣿⣿⣿⣷⣤⣤⠶⢦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣭⣭⣤⣀⣐⣒⡀⡀⢸⡇⢰⠆⢹⡇⢠⠸⣿⠀⡆⠈⡇⠀⠃⣸⡿⣷⠀⢰⡟⠀⡆⠈⣿⣷⡆⢰⣾⠀⠿⠀⣿⠀⣶⣿⣿⠀⡆⠈⡇⠀⣶⡇⢰⣾⠀⢸⠁⢰⠀⢹⠀⢴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣝⣁⣗⣿⣿⣿⡿⣿⡇⠄⢸⡇⢰⡄⢹⠃⠸⠀⣿⠀⡟⠛⡇⠀⡀⢻⡇⣿⠀⢸⡇⠀⡇⠀⣿⣿⡇⢸⣿⠀⣦⠀⣿⠀⣶⣿⣿⠀⡇⠀⡇⠀⣶⡇⢰⣾⠀⢸⠀⢸⠛⢻⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠾⢻⣳⣤⢽⢇⡇⣿⡇⡁⠸⣧⣬⣤⣼⣤⣾⣤⣿⣤⣥⣴⢧⣤⣧⣬⠟⠻⣤⡼⠿⣤⣥⡼⠇⠸⣧⣼⢿⣤⣿⣤⣿⣤⣤⠿⠿⣦⣥⣴⣧⣤⠿⣧⣼⠿⣤⣼⣧⣬⣤⣿⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣷⠟⠽⣣⡏⣭⣙⢹⡇⠆⣀⣀⠀⣷⣾⣿⣿⣿⣿⣇⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣿⣷⣴⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⢸⢻⡿⡇⡯⡕⣾⡇⡿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢰⣿⣦⣶
⢼⡚⡝⣾⣷⡧⢭⠅⣿⡇⢢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣿⣿
⢿⣾⡿⠿⢟⣛⣩⣭⣶⡆⠟⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿
⠀⠀⠂⠂⠐⠛⠋⠉⠏⢥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡿⠀⣿⡏⠀⢸⠇⢸⡇⢠⢋⠃⠁⢸⠀⠀⠀⠀⠈⢰⠿⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠀⢸⡇⠀⢸⠀⢸⡇⢈⠰⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⣾⣿⣿⣿⣿⣿⡿⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢸⠀⢸⡇⠀⠀⠉⠃⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡟⠈⣿⡟⠈⣿⠀⢹⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⢸⡇⠠⡀⠀⠀⠠⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠸⠀⢸⡇⠀⢱⣶⡆⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⣿⠀⠀⣿⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⡇⠀⠁⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣹⣀⣀⣿⣀⣀⣧⣀⣸⣇⣀⣹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣀⣸⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢶⠀⢰⣶⣤⣴⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢴⣦⣶⣤⣄⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠙⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠁⠀⠿⣿⣿⡽⣻⠿⠿⣿⠿⠿⡿⠿⡯⠉⠁⠭⠿⣿⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⢠⠀⠀⠀⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣛⣛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡏⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡏⠉⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢭⣭⣭⣥⣭⣭⢭⣭⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⡄⣤⣴⡶⠒⠒⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢰⠀⣶⣶⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣟⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⣛⣛⡛⣛⣛⣀⣋⣛⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣆⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣀⠈⠉⠀⠘⠛⠉⠻
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠾⣯⢿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣧⠀⠀⠀⣀⣀⣀
⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⣀⣀⣀⣀⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣇⢽⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢘⣻⡿⣿⣿⣿⠿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⡏⠀⢹⣿⣇⠸⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣶⣶⣶⣿⣿⣿⣷⣐⣶⣶⣶
⣿⣿⣿⣇⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣫⣿⣿⣿⣿⣇⠀⠈⣿⣿⡂⢿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢘⣿⣭⣿⣿⣿⣿⡿⢰⣿⣿⣇⣦⢙⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣿⣭⣿⣷⣾⣿⡇⣸⣿⣿⣿⣿⢱⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⢿⣿⣿⣥⣾⣿⣿⣿⣏⣿⣿⣿⣿⣿⢸⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠫
⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⡛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄
⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⠿⢛⣛⠭⢒⣊⣥⣦⣌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⡇
⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢸⡿⠿⠀⠀⠀⣀⣭⣷⣶⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣿⡆
⣿⣿⣿⣿⣇⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⣥⣤⣭⣭⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣶⣾⣶⣶⣶⣶⣷⣤⣤⣴⣮⣭⣭⣭⣭⣭⣭⣽⣯⣭⣙⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⡘⣛⠻⢿⣿⣿⣿⣿⠿⣟⢫⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣼⣿⣷⣿⣌⡀⢀⠀⣶⣼⣧⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⠙⠛⠛⠋⠉⠁⠈⢿⣯
⠀⠀⠀⠀⠀⠈⢿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣇⣘⣿⣿⣿⣿⣿⣿⣿⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⢀⣨⡵⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⢃⣾⣿⣿⣿⢻⣿⠟⣃⣤⣭⡙⣿⣿⣿⡟⠛⡿⡆⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀
⣶⣶⣴⣶⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡿⠿⡹⠻⠻⢘⡭⢏⡻⢹⠈⠏⡄⠟⠛⢟⣻⢈⢻⣿⡏⢩⣤⡏⠸⡹⠻⣻⠸⡹⢹⡛⢿⡛⡏⣹⣿⣿⣿⢹⣷⣤⣀⠀⠀⠀⢀⣼⣿⣿⣄⠀⠀⠀⠀⣀
⣿⣿⣿⣿⢛⣟⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⢠⣶⢶⣶⡶⣷⡀⣶⣷⣶⣷⣒⣊⣸⡆⣿⣷⣾⣿⣶⣸⣶⣾⢷⣾⣶⣿⣶⣶⣶⡶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣨⡏⢿⠥⢯⠿⡎⡟⢡⣾⠀⡇⠨⡿⠹⠿⠿⡟⠷⢻⡸⣾⢰⣧⣴⠃⣹⠾⣡⣾⡇⣾⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿
⣿⣿⣿⣿⠇⠨⠉⠉⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣩⣤⣍⣴⠨⣀⣯⣡⡿⢉⣁⣍⣩⣤⣾⣿⣿⣥⣦⠨⣥⣭⣌⡇⢠⣭⣩⣤⣯⣭⣥⣭⣸⣯⣥⣿⣿⡿⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿
⣿⣿⣿⣿⣆⣠⢀⠀⠀⠀⠀⠠⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠉⠙⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠉⠁⠈⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠂⠁⠐⠙⢡⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡿
⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⣀⣀⣀⠠⠤⠄⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⣀⣀⣀⣀⣈⡹⣿⣿⣿⣿⣯⡀⠈⠐⠀⠈⠉⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢻⣿⣿⣿⣿⡟⣛⣛⣛⣛⣛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠟⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡯⠉⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⠈⠀⢩⣭⣭⣥⣭⣭⢩⣭⣭⣥⣼⣿⣿⣿⣿⣿⣿⣿⡋⢁⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣧⠀⢸⣿⣿⣿⣿⣿⢁⣀
⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣀⡆⢰⣶⣤⡆⣴⣶⣶⠖⠒⠒⠘⠛⠻⣿⣿⣿⣿⣿⡇⣼⣹⠃⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⠸⢿⣿⠀⢸⣿⣿⣿⣿⣿⢻⣿
⣿⣿⣿⣿⣿⣿⢟⣛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣷⡈⢿⣿⣷⣶⣶⢆⣤⣤⣄⣀⠀⠀⠀⢹⣿⣿⣿⠇⣿⡿⢸⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣺⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢻⣿⣿
⣿⣿⣿⣿⣿⡟⡛⣋⣹⣁⣩⣉⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣷⡈⢿⣿⣿⠇⢨⣽⣭⣭⣟⡻⢷⡄⢸⣿⣿⡿⢠⣿⡇⣼⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢿⣿⠟⣵⣶⣶⣶⣶⣄⠀⠈⠉⠹⠟⢸⣿⣿
⣿⣿⣿⣿⣿⣗⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣷⡀⢻⡏⣶⢿⣿⣿⣿⣿⡇⠀⠀⣾⣿⡿⢁⣿⣿⠁⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⢱⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡟
⣿⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⣿⣿⣆⠊⢴⣿⢻⣿⣷⣾⣀⡀⢰⣿⣿⠃⣼⣿⡟⢰⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡯⣾⣿⣿⣿⣿⣿⣿⢁⠀⠀⠀⠀⣼⣿⣿⠇
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⠏⣵⣶⢶⣿⢿⢿⣿⡗⣂⣼⢋⡅⣾⣿⣿⢡⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⡟⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣾⣷⣿⣿⡿⣿⣿⣿⠁⠟⣱⣿⣿⣝⠿⢁⣾⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣾⣿⣿⣿⠄⠰
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣇⣿⣿⣟⣜⣼⣿⣿⣿⣿⡿⣡⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣿⣿⣿⣿⣟⣿⡇⠸
⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣼⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣷⣶
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣿⣿⣾⣾⡧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢛⠫⠉⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣇
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⠿⢟⣛⠭⢐⣢⣭⣶⣞⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⡏
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⢸⣿⠿⠀⠀⠀⢀⣬⣿⣶⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿
⡮⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣴⣦⣤⡥⢠⣾⣸⡟⠻⠿⠿⠿⢿⣿⣿⡉⢠⣶⣶⣶⣶⣶⣶⣷⣤⣤⣤⣮⣭⣭⣭⣭⣭⣭⣭⣭⣭⡃⠙⠿⠿⢿⣿⣿⣿⣿⣿⠿⣿⣘⣿⣛⣛⣛⣋
⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣟⣵⣿⣷⣜⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⢿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⢂⡌⢿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⠏⣴⣿⣿⡘⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣾⣿⣧⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⡏⣸⣿⣿⣿⣇⢹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿
⢿⡟⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⣿⣿⣿⢿⡿⢰⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⡇⣿⡟⡛⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡿⠻⡹⠺⠻⢙⡥⢏⡻⢻⠈⠏⡁⠞⠫⢟⣻⢻⡇⣿⡏⢩⣤⡏⠹⡹⠻⣻⠸⡹⢹⡛⢿⡛⡏⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿
⠿⢿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠀⠀⢐⠘⢀⢶⣶⡶⣷⣶⣶⣷⣶⡔⢒⢊⣸⠃⣿⣷⣾⣿⣶⣾⣶⣾⢷⣾⣶⣿⣶⣶⣶⡂⣴⣿⡿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⣿
⠠⢶⡶⡷⡬⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡇⠈⡇⢤⠥⢧⠼⡎⡟⢡⢾⠀⡇⠈⡿⠁⠀⠀⡟⠶⢻⡘⢾⢰⡧⣴⠃⣹⠾⣡⣴⡇⢺⢳⣾⡇⠳⠫⠙⠐⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⢺⠳⠞⠎⣙⢿⣿
⣿⣷⣶⣶⣶⣺⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⣭⣤⣍⣴⣼⣠⣯⣁⣿⣏⣡⣍⣩⣤⣾⣿⣶⣥⣤⣌⣁⣈⡈⢇⣤⣭⣩⣤⣯⣭⣥⣬⣄⣬⣥⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠑⠠
⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶
⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣭⣭⣥⣭⣭⢩⣭⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠀⢸⣿⣿⣿⣿⣿⠁⠈⠀⣥⣠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡆⢠⣶⣶⡶⠂⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠀⢸⣦⡈⠻⠀⠀⠀
⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⣲⣶⡶⣶⣤⡀⠀⠀⢿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣤⣤⣤⣤⡀⠈⢿⣿⣿⣿⡆⢸⣿⣿⣶⠀⠀⠀
⡛⣛⣛⣃⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣿⣿⣿⣿⣮⠙⢷⠄⣾⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⡷⠀⠈⠙⠟⠉⠀⠈⠉⠹⠿⠀⠀⠀
⣷⣾⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⣼⣿⣿⣿⣿⣿⠖⣰⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣵⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣿⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣽⣟⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⠀⠀⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣶⣶⣾⣶⣾⣾⣿⣷⣿⣶⣷⣶⣾⣭⣛⡿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣛⣛⣛⣛⣣⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣫⣥⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡘⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣶⣾⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⣥⣶⣿⣿⡿⠿⣃⣻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣟⡻⣿⣿⣦⣌⠻⠀⠀⠀⣿⣿⢟⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣶⣿⡿⢟⣉⣵⣶⣾⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣶⣮⣝⠿⣿⣷⡄⠀⣀⣭⣾⣿⣿⣿⣿⣿⣿⣿⣶⣯⣷⢸⣿⣿⣿⣿⣿⣿⣿⡿⣦⣝⡿⠟⡻⢿⣿⣿⣿⣟⠇⠀⠀
⣿⣾⣟⣻⢿⣿⣿⣾⡀⣋⣏⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣬⣙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢛⡻⠍⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⡻⣿⣿⣷⣄⡀
⣿⣿⣿⣿⣷⣻⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣽⠿⠛⣿⣿⠈⢟⣛⠭⢕⣒⣭⣶⣾⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣶⣝⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣄⣭⡛⢛⠻⠿⡿⣟⣻⢱⣿⣿⣿⣿⣿⣿⡇⣿⠿⠀⠀⠀⢀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇⢻⠟
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣬⣽⣭⢸⣿⣷⣢⣶⡑⣶⣿⣿⣿⢠⣷⣶⣿⣷⣿⣷⣶⣶⣿⣦⣤⣤⣾⣮⣭⣭⣭⣭⣭⣭⣯⣭⡍⠉⠛⠻⠿⠿⠿⠿⠿⢻⣿⣛⣿⣿⣿⣿⣛⣛⣛⣿⣿⣃⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣬⣛⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⠸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠟⠛⢻⣿⠇⠀⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠼⡿⠿⡹⠰⢱⢹⡭⢏⡻⢻⠈⡏⡅⠟⠛⢟⣻⢻⣿⣿⡏⢩⣤⡏⣹⡹⠻⣻⠸⡹⢹⣋⢯⡛⡏⣹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣷⣶⣾⡆⣴⣶⣀⣶⣶⡶⣇⡶⣶⣷⣶⣷⣒⣊⣸⣿⣿⣷⣾⣿⣶⣾⣶⣾⢶⣾⣶⣿⣖⣿⣶⣷⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⡇⠈⡇⢴⠥⢯⠟⡎⡝⠁⢸⠀⡇⢨⡿⢻⣿⣿⡟⠿⢻⡘⣾⢐⡧⣴⠃⣹⠾⡡⢒⡇⢺⢻⣿⡇⠘⣿⣿⢈⣽⣻⣿⠝⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⣀⣤⣅⣭⣤⣍⣴⣾⣀⡌⣁⡀⠈⠁⠁⠩⣤⣾⣿⣿⣥⣶⣮⣥⣭⣬⣇⣤⣭⣩⠀⠬⠍⠁⠈⠀⣉⣡⣤⣿⣿⡈⠛⠋⠰⣾⣦⡙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣵⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⣿⣿⡍⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⣭⣭⣭⣬⣭⣩⣭⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⠀⠀⠀⢠⣤⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⢸⣦⡈⠛⠀⠀⠀⢸⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠖⠒⠒⠲⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣶⡄⠀⠀⠸⠿⠇⠀
⣙⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣤⣤⣤⣀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠉⠀⠀⠛⠉⠙⠿⠉⠀⠀⠈⠹⠿⠃⠀⠀⠐⠋⠁⠀
⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣶⣷⣏⣽⣿⠷⣦⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣤⣤⣤⣄⡀⠀⠀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⢿⣿⡇⠀⠈⣸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣛⣿⣿⣿⣷⡔⢰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⡿⠿⢿⣻⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣿⣿⣿⣿⣿⣿⣿⠀⠀⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⡆⠀⠀⢰⣶⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡌⢿⣿⡇⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⣛⠻⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⡇⠀⠀⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣜⣟⣧⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡇⠀⠀⢐⣾⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣟⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⡯⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣷⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢟⠋⢍⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡇⠀⠀⠀⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⠀⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⣿⡿⢿⣛⠯⢟⣲⣭⣶⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⣿⣿⣿⣿⣿⡇⣿⠿⠀⠀⠀⢐⣬⣽⣶⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⣿⣿⣯
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣧⣤⡄⠀⣋⣛⠿⠿⠿⠿⡿⠿⣟⢿⣿⠁⣶⣾⣾⣷⣶⣶⣶⣿⣦⣤⣤⣶⣮⣭⣭⣭⣭⣭⣭⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣛⣿⣿⣛⣛⣿⣃⣀⣀⣀⣻⣟⣓
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣧⡄⢀⣸⣷⣿⣿⡟⣼⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣇⣸⣿⣿⣿⣿⡇⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠟⠻⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣟⠿⣿⣿⣿⣿⡿⠰⢻⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⣮⢹⣿⣿⣿⡞⠈⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠞⠻⢻⣿⣿⡇⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡿⣿⣿⣿⣿⣶⢠⣤⣤⣤⣀⣀⣀⣀⣸⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢴⡿⠻⡹⠻⠳⢹⡭⢏⡻⢻⢈⡏⡅⠟⡛⢟⣻⢻⣿⣿⡏⢩⣤⡏⣹⡹⠻⣻⠸⡹⢻⣛⢯⡛⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣖⣶⣾⣶⣶⢀⣶⣶⣷⡶⣷⣶⣶⣷⣶⣷⣒⣊⣸⣿⣿⣷⣿⣿⣶⣾⣶⣾⢷⡾⣿⣿⣶⠆⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⡇⢬⡏⢿⠧⢯⠿⡌⡟⢡⣾⠀⡇⢨⡿⢹⣿⣿⡟⠿⢻⡸⣿⢰⡧⣴⠃⣹⠾⡡⣾⡇⣿⠳⣿⡇⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠘⠻⠿⠁⠩⠤⠍⢀⣾⣠⣯⣡⣶⣬⣥⣍⣩⣤⣾⣿⣿⣥⣶⣮⣥⣭⣬⣇⣴⣭⣭⣤⡏⣭⣥⣯⠀⣿⣥⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠡⠉⡽⡉⠀⠉⠝⠛⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣶⣶⣶⣶⣶⣶⣧⣦⠄⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠂⠐⠀⣁⣀⠀⠘⠀⠽⠆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣛⣛⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣬⣭⣭⣭⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⠀⠀⠀⢠⣤⡄⠀⡀⢠⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣴⣶⢠⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⢸⣦⡈⠙⠀⠀⠀⢸⣿⡇⠀⡇⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⡄⠀⠀⠘⠿⠇⠀⠃⠀⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠋⠀⠀⠛⠉⠙⠟⠉⠀⠀⠈⠹⠿⠃⠀⠀⠘⠋⠁⠀⠁⠀⣿⣿⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⡶⢶⣶⣦⣀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇⣀⣀⠀⡀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀⡀⠀⢈⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⣷⣯⠛⠿⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣳⣶⣶⣶⣶⣶⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣿⣿⣿⡗⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⡿⠁⠀⠂⣶⣶⡆⠀⣶⣶⣶⣶⣶⣆⢐⣶⣶⣶⡆⠀⠀⠰⣶⡆⠀⠆⠀⢰⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠺⢛⠻⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣷⣤⠀⠀⣸⣿⡇⠀⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⡇⠀⠀⠈⣿⡇⠀⠀⡜⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⡿⣨⣝⡻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡧⠀⠀⢰⣿⡇⠀⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣾⣿⣿⣿⣿⣿⣿⣶⣭⡻⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⣽⣭⣛⡿⢿⣿⣿⣷⠻⡇⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⡧⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣥⣉⣑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣿⣿⣿⡇⣿⣿⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠿⣟⠛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⣿⣿⡿⣟⣻⣭⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣉⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣫⣾⣆⢻⣿⣿⡇⣿⣿⠀⠀⠀⢺⡿⢿⣛⡯⣟⣺⣭⣶⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡈⣿⣿⡇⣿⠿⠀⠀⠀⢐⣯⣽⣶⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣭⣭⣭⣭⣭⣭⣯⣯⡅⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⣿⣿⡇⣴⣶⣶⣶⣿⣶⣤⣤⣶⣯⣿⣯⣭⣭⣭⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣛⣃⣀⣀⣀⣿⣛⣿⣟⣻⣟⣿⣿⣗
⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⡗⢠⣯⢹⢛⠿⢿⣟⣻⣭⣵⡆⡇⣻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢇⣿⣿⣿⡀⡄⣄⣻⣿⣿⣿⡇⠁⢿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢸⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⢰⣿⠘⠋⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⠉⠉⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾⣿⣿⣯⣛⠿⣿⣿⣿⣿⣿⢸⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢁⢹⣿⣿⣿⣿⠖⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠒⡄⠀⠀⠀⠀⢠⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⢤⡿⠿⡹⠻⢻⢻⡭⢏⡻⢻⢈⡏⡅⠟⡻⢟⣻⢻⣿⣿⡏⣩⣴⡖⣴⡱⠲⣺⢰⡰⢰⡒⢿⡛⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣭⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⠘⢸⣿⣿⣿⡿⣲⣶⣾⣶⣾⣾⣶⣶⣷⡶⣷⡾⣶⣷⣶⣷⣒⣊⣸⣿⣿⣧⣿⣿⣷⣿⣶⣾⢾⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣇⣼⣿⣿⣿⢃⡇⢬⡟⢿⠧⢯⠿⡌⡟⢡⣾⠀⡇⢨⡿⢻⣿⣿⡟⠿⢻⡸⣼⢰⣧⣶⠃⣻⠾⣥⣾⡇⣾⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠛⠻⠿⠇⠻⡿⠿⠏⣼⣅⣭⣴⣏⣴⣾⣠⣯⣡⣿⣭⣥⣍⣩⣤⣾⣿⣿⣥⣶⣮⣥⣭⢸⣧⣶⣭⡍⣼⣿⣽⣡⣭⣼⣯⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⠁⢯⣭⡕⠀⠚⠉⢃⢬⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣖⣲⣾⣷⣦⠤⢄⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠚⠙⠀⠈⣉⣁⣄⡀⠘⠋⠿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⣭⣭⣭⣭⣭⡍⣭⠭⠭⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⡇⠀⠀⢤⣤⡄⠀⠀⢠⣤⡄⠀⡄⠀⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀
⣿⣿⣷⣬⣥⣬⣤⣴⢀⣀⣀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⣶⣄⠙⠇⠀⠀⢸⣿⡇⠀⡇⠀⣿⣿⣿⣿⣿⣿⡿⠃⣠⠀
⣿⣿⣿⣿⣿⣿⣷⢀⣿⣿⣻⣿⣶⣤⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠁⠙⢿⡇⠀⣿⣿⣿⣿⣿⡇⠀⣿⣿⣷⡄⠀⠀⠘⠿⠇⠀⠃⠀⠹⠿⠿⠿⠿⠿⠋⠚⠻⠀
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⡏⠙⠓⣰⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣤⣤⣤⣤⣤⡀⠁⠀⠛⠋⠉⠿⠋⠀⠀⠀⠉⠿⠃⠀⠀⠀⠋⠁⠀⠀⠀⢸⣿⡿⠛⠛⠃⠺⡿⠟⠀
⣿⣿⣿⣿⣿⣿⠋⣾⣿⣿⣿⣾⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⣀⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⢈⣁⣀⣀⣀⣀⠀⠀⡀⠀
⣿⣿⣿⣿⣿⠏⣴⣿⣾⣿⣿⣿⡟⣣⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣽⣽⢻⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠿⠾⡿⣿⣿⢧⣽⠿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣕⡿⠿⢿⣿⣿⣿⣿⣿⣷⡆⠀⢰⣶⣶⣶⣶⣖⡀⣶⣶⣶⣶⠀⠀⠀⣶⣶⠀⠀⠀⢰⣶⣶⣶⣶⣶⣴⣶⣶⠦
⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢞⣻⣿⣿⣿⣿⡇⣀⣸⣿⣿⣿⣿⣿⠁⣿⣿⣿⣏⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣿⠟⣁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡙⠇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⠀⠀⠀⣾⣿⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣵⣾⣿⡎⢛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⢟⠱⣿⣿⣦⡙⢿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⢏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⢸⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢛⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣦⣙⢿⣿⣄⠃⠀⠀⢸⣿⣿⣿⢟⣯⣾⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣾⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣝⢿⣷⣄⠀⢸⢿⣯⣾⣿⣿⣿⡿⣿⡓⢄⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡻⣿⣿⣿⣏⠀⠀⠀⣿⣿⣿⣿⣼⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣿⡆⠟⠻⠇⢨⣿⣿⣿⡿⢼⣲⣭⣷⣾⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣮⡝⣿⣿⣷⣦⠀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆
⣿⣿⣿⣿⣿⡏⣽⢻⡿⣿⣿⣿⣿⣿⠿⡿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠀⠸⣿⣫⣼⣼⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⡏⠻⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⢡
⣭⣭⣭⣭⣭⢱⣿⣿⣷⡗⢋⡉⣾⣾⣷⣷⢠⣾⣿⣿⣿⣶⣶⣶⣾⣷⣤⣤⣶⣶⣿⣯⣭⣭⣭⣭⣭⣭⣭⡅⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣂⣀⣉⣀⣺⣟⣛⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣟⣸
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⢨⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿
⣿⣿⣿⣿⡇⣿⣿⣿⣿⣛⠿⠿⣟⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠇⢹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢠⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⡘⢸⣿⣿⣿⡿⣸⣿⣿⣿⣿⠟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⠛⡿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⡇⣸⣿⣿⣿⢃⣿⣿⣿⣿⣿⢴⡿⠿⡹⠻⢻⢻⡭⢏⡻⢻⢈⡏⡅⠟⡛⢟⣻⢻⣿⣿⡏⢩⣤⡎⣽⡹⠳⣻⠸⡹⢹⡛⢿⡛⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣌⠻⠟⠿⠋⠻⠻⠻⠏⣼⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣾⣶⣶⣷⡶⣷⣾⣶⣷⣶⣷⣒⣊⣠⠻⣿⣿⣮⡯⣷⣿⣷⣾⢶⣾⣶⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠋⠀⠀⠀⣀⢄⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⢬⡏⢿⠥⢯⠿⡌⡟⢡⣾⠀⡇⢨⡿⢹⣿⡿⡟⠶⢻⠰⢾⠀⡧⣴⠋⢸⠾⣡⡶⡇⣾⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣷⣿⣿⡿⠿⠿⢿⠟⠁⠀⠉
⣿⣿⣿⣁⣀⣤⣤⣶⣿⣿⣿⣿⣖⣤⣀⠀⠀⣻⣿⣿⣿⣅⣭⣴⣏⣴⣾⣠⣯⣡⣿⣭⣥⣍⣩⣤⣾⠋⠤⠁⠒⣈⣡⣭⣤⣇⡀⠩⠭⡤⢫⣭⣥⣭⣼⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⣌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⣛⣛⣛⣛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡏⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣥⣭⡍⣭⡍⠉⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣗⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠟⠃⠀⠙⠻⣿⣿⣿⡏⠀⠀⢤⣤⡄⠀⠀⢠⣤⡄⠀⡄⠀⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⢤⣤⣤⣤
⣭⣭⡍⣭⣥⣼⢁⣿⣿⡶⣦⣀⠀⠀⢹⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢫⣤⣤⣤⣤⡀⠈⢿⣿⡇⠀⣷⣄⠙⠇⠀⠀⠘⣿⣇⠀⠇⠀⢿⣿⣿⣿⣿⣿⡿⠫⣠⠀⢸⣿⣿⣿
⣿⣿⣷⣶⣶⣤⣾⣿⣿⣿⣷⠉⢳⡄⣠⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣵⣿⣿⣿⣿⣿⣇⠀⠘⣿⡇⠀⣿⣿⣷⡆⠀⠀⠀⠿⠟⠀⠀⠀⠸⠿⠿⠿⠿⠟⠃⠚⠛⠀⠘⠿⠿⠛
⣿⣿⣿⣿⡿⣩⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠀⠀⠀⠉⠿⠃⠀⠀⠀⠋⠁⠀⠀⠀⢸⣿⡿⠛⠛⠃⠸⡿⠟⠀⠈⠉⠹⢡
⣿⣿⣿⡟⢡⣾⣿⣿⣿⣿⣷⡥⢠⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⣿⣿⣿⣿⣿⣷⣆⠀⠀⣀⣀⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⢈⣁⣀⣀⣀⡀⠀⣀⡀⠀⢀⣀⣀⢸
⣿⣿⣿⣦⣝⣻⣿⣿⣿⣿⢏⣴⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣛⡿⢿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⡿⣟⣻⣿⣿⣛⢸⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣽⣭⣷⣧⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⣭⣷⣶⣶⣶⣍⣿⣿⣿⣇⣐⣶⣶⣶⣶⣶⠀⣶⣶⣶⣶⠀⠀⠀⣶⣶⠀⠰⠀⢰⣶⣶⣶⣶⣶⢴⣶⣶⡦⢰⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣉⠃⢿⣿⡇⠀⠀⢸⣿⡿⢿⣛⣯⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿
⣝⣻⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠹⣿⣿⣶⣌⠁⠀⠀⢸⣵⣾⣿⣿⣿⣿⣿⣛⣻⣿⡿⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⠀⠀⠀⣾⣷⠀⢰⡶⢞⢷⣾⣿⣿⣿⣿⣿⣿⣷⣿⡿⢿⣟
⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣭⣾⣿⣶⣝⢻⡿⣿⡦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⡻⣿⢿⣽⣿⠿⣿⣿⣿⣤⡀⠀⣿⣿⠀⢸⡽⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿
⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⢿⣿⡆⠺⠿⣿⡀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣛⢻⣿⣷⣿⣿⣷⣿⣞⣫⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢹⣿⡇⠀⠀⢰⣄⠀⠙⣿⣿⣿⡿⢟⣛⠩⡑⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠀⠙⠏⠛⢿⣿⣿⣿⣿⣿⣶⣍⣛⣻⠿⠿⠿⠿⣿⣿⣿⣿
⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⢸⣿⠿⣒⣯⠭⣒⣯⣵⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⣿⣇⣼⣯⣿⣻⡿⠿⢿⢿⢟⠋⣾⣿⣿⣿⣿⣿⣿⢸⡿⠇⠀⠀⠐⣢⣭⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣇⣿⣿⣿⣿
⣭⣭⣿⣿⣿⣿⡍⣸⢸⣾⣾⡆⣾⣿⣿⣿⣿⣿⣷⣶⣾⣷⣤⣤⣴⣮⣭⣭⣭⣭⣭⣭⣭⣭⣭⡏⠈⠉⠙⠛⠛⠛⠛⠋⢻⣷⣿⣿⣿⣟⣛⣛⣛⣛⣻⣛⣀⣀⣀⣚⣛⣛⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣟⢸⣿⣿⣿⣿
⣿⢻⣿⣿⣿⠿⣇⡜⣿⠿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⡦⢹⣶⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣦⣤⣤⣤⣤⣤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣯
⣿⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⢿⠿
⣿⣸⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡟⣛⡟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⡻⣿⣿⣿⡇⣾⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⡿⠿⡹⠻⢻⢻⡭⢏⡻⢻⢈⡏⡅⠟⡃⢟⣻⢿⣿⢿⡏⣭⣤⡎⣹⡹⠻⣻⢸⡹⢹⡛⢿⡛⡏⣹⣿⣿⣿⣿⡿⢿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⡟⠈⠈⠉⠠⠀⠉⠉⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣾⣶⣶⣷⡶⣷⣾⣶⣷⣶⡷⣒⣊⣸⡋⡘⣻⣟⡋⣶⣿⣶⣾⢷⣾⣶⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠅
⣿⡟⠀⠀⠀⡤⠄⠠⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢬⡏⢿⠥⢯⠿⡜⡟⢡⣾⠀⡇⢨⡿⢁⠛⠻⡟⠶⢻⡸⢾⠰⡧⣴⠃⢹⠾⣡⣶⡇⣾⢻⣿⡇⣿⣿⣿⣿⣿⡿⣵⣾⣿⠿⠿⠿⠿⠟⠁⠂⠈⠁⠁⠀⠀
⣿⠀⠀⣠⣶⣾⣿⣿⣿⣦⡀⠀⠰⣿⣿⣾⣿⣿⣿⣿⣿⣅⣭⣤⣍⣴⣾⣠⣯⣡⣿⣯⣥⣍⣩⠀⢬⠏⢀⣥⣶⣮⣅⠉⢈⡇⣰⣭⣬⣤⣯⣭⣥⣭⣼⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⣠⣴⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣥⣴⣿⣿⣿⣿⣿⣷⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣛⡛⣹⣿⣽⣿⣿⣟⣿⢿⣿⡋⣿⣿⡏⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⣿⡏⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠿⣿⡿
⠭⣭⣥⣽⡿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⡇⠀⠀⠈⣿⣟⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⠀⠠⣤⡄⠀⠀⠀⣤⡄⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⢠⣤⣤⣤⣤⡄⠀⠠⣤⠤
⣤⠄⠂⠈⠉⠛⠛⠻⣟⣻⣿⣿⡁⣿⣿⡇⠀⠀⠀⣿⣏⢽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡿⠃⠀⠘⠻⣿⣿⣿⡇⠀⣶⣄⠈⠃⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⢀⠀⢸⣿⣿⣿⣿⡅⢀⣀⣀⣀
⠂⣤⣤⣤⡀⠀⠀⠀⠉⢛⣿⣻⡇⡜⣝⡇⠀⠀⢘⣽⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣯⣿⣟⡧⠸⣠⣠⣄⣀⡀⠈⢿⣿⡇⠀⣿⣿⣷⡄⠀⠀⠀⠛⠓⠀⠀⠀⠘⠛⠛⠛⠛⠛⠃⠐⠛⠀⠘⠛⠛⠛⢫⣾⣿⣿⣿⣿
⣀⢶⣶⣦⢈⠙⠲⡀⠀⢸⣿⣿⡇⣻⣿⡇⢀⠀⠘⠿⣫⣿⡿⣿⣿⣿⣿⣿⢿⡿⣽⣯⣿⠟⣣⣼⣿⣿⣿⣿⣷⠀⠘⠉⠀⠀⠀⠈⠿⠃⠀⠀⠀⠊⠀⠀⠀⠀⠰⣿⡿⠛⠛⠁⠘⠿⠛⠀⠈⠉⠙⠆⣾⣿⣿⣿⣿⣿
⢁⣾⡸⠿⠇⠀⠀⠀⣠⣿⣿⣿⡇⣽⣿⠩⣿⣿⣶⣿⣜⠛⠻⣭⡿⣯⣯⣾⢿⣏⣿⣽⠍⣼⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⢘⣻⣿⣾⣧⡀⠀⢸⣿⣿⣿⣿⡇⣿⣿⡇⠈⠛⠿⣿⣿⣶⣤⣘⢿⣿⣾⣻⣿⣿⢾⡻⠶⣋⣽⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠐⣚⣿⣿⡿⠁⢰⣿⣿⣿⣿⣿⠇⠛⠋⣁⠠⠴⠋⣀⣈⣻⣿⣿⣷⣮⣕⡚⠿⣿⡻⡀⣙⡻⠿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⡂⢸⣿⣿⠁⣾⣿⢿⣟⡙⢉⣠⣤⠖⠛⠊⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣴⣶⣬⣊⠿⡖⠘⣿⣿⣿⢳⣶⣶⣶⡶⣶⠀⢶⣶⣶⣴⣶⣿⡿⠿⠛⠋⠀⠀⠀⠶⣶⣶⣶⡆⠰⣶⡶⠆⠀⣶⣶⡆⠀⣾⡿⠛⠉⠛
⣷⢤⣽⣯⡄⣨⣶⣿⣿⣿⡌⠛⠋⢠⣴⡅⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣷⣮⣀⣿⣿⣿⢘⣫⣽⣿⣿⣤⣶⣿⣿⣿⠿⠛⠉⠀⠐⠂⠀⠀⠀⢨⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣷⠆⠜⣿⣶⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣜⡅⢸⣿⡇⠀⠀⠀⣿⣿⣷⣿⣽⣿⣷⡿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣽⣶⣶⠀⠀⠀⢲⣶⠀⢰⣶⣶⣶⣶⣿⣿⣾⣿⣾⣶⣶⠶⣂⣴⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⡿⢛⢭⣶⣷⣟⣇⢸⣿⡇⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡲⡈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠫⠾⣿⣿⣿⡿⠀⠀⠀⠿⡿⠀⠸⠿⠿⢿⣿⡿⠿⠿⠿⢟⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠄⢻⣗⣿⣿⣿⣷⢸⣿⡇⠀⠀⠀⢿⡧⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡧⣸⢓⢕⣾⣿⣿⡇⠀⠀⠀⠠⢶⡶⠀⠻⣷⣮⣽⣫⣬⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣗⢸⣿⡇⠀⠀⠀⠛⣿⣿⣯⣿⣿⠿⠛⠛⠉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣷⣟⣻⣿⡇⠀⠀⠀⠠⣺⣇⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⡿⣷⣿⣿⣿⣷⢸⣿⡇⠀⠀⠀⡙⠟⢛⠩⠁⢒⣀⠀⢂⢀⠦⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣪⣿⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⢨⢿⠖⣀⡛⠛⠻⠿⢿⣿⣿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⢿⢸⠹⠅⠀⠀⠀⠀⠠⠄⠤⣶⣟⣿⡄⢝⠧⡁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢱⣿⣿⣿⣿⣿⡿⠛⠇⠀⠀⠀⠐⣻⣿⣿⣿⣾⣶⣦⣤⡢⠐⢀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⡛⠛⠛⠁⣤⣤⣤⣤⣴⣴⣶⣶⣷⣤⣤⣴⣤⣤⣤⣭⣭⣭⣬⣭⣭⣭⣈⠈⠿⠿⠿⠿⠿⠿⠿⠿⣿⣅⣈⣭⣍⣉⣉⣙⣙⣉⣀⣀⢀⣀⣀⣚⣙⣛⣛⣛⣉⣙⣛⣛⣃⣂⣂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⣀⣷⣷⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⢩⣶⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢫⣿⣛⣿⣛⣛
⣾⡇⢸⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡷⣶⣶⣷⣄⢠⣤⣴⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠍⣁⣻⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿
⣿⣿⠘⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢻⣿⣿⣿⣿⣿⢸⣿⣿⠇⣿⣿⣿⣿⢸⣿⣿⡇⣿⡟⠛⡟⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣥⣾⣿⡟⣿⣿⣿⣿⣿⣿⣤⣭⣽⣿⣿⡿
⣿⣿⡆⢿⣿⣿⣿⡇⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢴⡽⠻⡹⠹⠱⢙⡍⢍⡛⢻⠈⠏⡁⠟⠛⢒⣻⢻⣇⣯⡏⢉⣄⡎⡹⡹⠻⢻⠸⡹⢹⡋⢿⡛⡏⣙⣻⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⣿⣿⣿⠘⢿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⢾⣶⠆⣿⡶⣿⡐⣶⣷⣶⣶⡒⢊⣼⣿⡹⣷⣞⡿⣶⣶⣶⣾⢶⡾⣶⣾⣶⣶⣶⡔⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀
⠿⠿⠿⠇⠈⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠨⡏⢽⠥⢯⠟⡄⡟⠀⢻⠀⡇⢈⡿⢹⠟⠘⡟⠿⢻⠈⢾⠐⡧⣤⠃⢹⠾⣡⡔⡇⢺⠻⣿⡇⣴⣾⠿⠿⠿⠿⠿⡟⠛⠛⠉⠉⠻⠿⠿⠿⠃⠀⠀⠀⠀
⣿⣿⣿⣦⣦⣀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣩⣤⣍⠀⠈⠀⠈⠁⠀⣈⣁⣅⣉⣤⣾⣃⠀⠁⠀⠈⢁⠉⢠⣁⣠⣭⣩⣤⣯⣬⣁⣬⣤⣭⣥⣾⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣵⣒⣠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⡇
⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣉⡛⣟⠉⠛⠝⢟⡿⡏⠉⠉⡉⠉⠉⠉⣋⠹⣩⣍⣛⣉⣛⢽⣽⣉⣿⣋⣏⣭⡩⠩⣿⣿⡏⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⢿⡏⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠿⡿⠿⢿⣿⢿⡿
⣳⠽⠁⠀⠀⠀⠽⡈⡅⠀⢵⡇⠀⠀⠠⠸⠤⢻⣫⠹⣯⡯⣹⠘⣙⢬⡉⠮⣖⣕⠆⢻⣿⡇⠀⢸⡿⣏⣿⣭⠁⠀⠀⠀⣠⡀⠀⠀⠀⣤⡄⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⠄⠀⢠⣤⣤⣤⣤⡄⠀⢀⡀⠄⠀⠀⠀⢰
⠌⠀⠀⠀⠀⢀⢀⣝⡆⢠⡭⠅⠀⠀⠀⠬⢈⠾⠹⣁⣰⠵⡳⢗⡵⡱⠤⣸⠘⡬⡄⢸⣿⡇⠀⠸⣱⣿⣿⣿⠀⠀⣶⣄⠈⠃⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⢀⠀⢸⣿⣿⣿⢏⠄⣠⣤⣴⣶⣬⡿⠀⢸
⡞⠀⠀⠀⠀⢺⢿⣯⡂⢸⠷⠀⠀⠀⠐⠹⡚⠂⢚⠵⠳⠿⠾⢕⢷⠛⢗⢣⡻⡧⡄⢸⣿⡇⠀⣰⣿⣿⣿⡇⡆⠀⣿⣿⣷⡄⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠛⠛⠻⠛⠃⠐⠛⠀⠘⠛⠛⠋⢡⣾⣿⣿⣿⣿⣿⣿⡄⠸
⠀⠀⠀⠀⠀⣨⣿⣿⡃⢘⣠⡄⠀⠀⠀⣘⠻⢄⠂⢲⣔⣯⡜⢐⢆⡳⠡⠋⣀⠹⡅⠀⠘⠁⠰⣿⣿⣿⣿⠁⠀⠀⠀⠈⠿⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⣷⡾⠛⠛⠁⠐⠿⠟⠀⠈⠉⠘⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢹⣿⣿⡇⢘⢺⡂⠀⠀⠀⢟⢮⢔⢐⣲⠏⡩⢌⠈⣑⠭⢬⠙⢸⣓⡇⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠦⠀⠀⠀⠀⣸⣿⣿⡆⢘⣾⡇⠀⠀⠀⢒⡳⢡⢹⣪⢅⢀⠢⠁⣠⠘⡨⠘⡨⡈⠁⣠⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⢀⣿⣿⡇⠐⣷⡄⠀⠀⠀⣢⡾⢦⣅⡍⡽⣨⠤⠓⢊⢌⡧⣚⣽⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡿⢿⣿⣿⣿
⠉⠀⠀⠀⠀⢀⣿⣿⡇⠰⠿⡇⠀⠀⠀⠌⠶⠔⡴⣤⣇⠮⡷⠨⠐⡆⣌⠆⠱⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⠀⢶⣶⣶⣶⠀⠀⠀⠶⠶⠀⠀⠀⠀⠶⣶⣶⣶⡆⠠⡶⡶⠆⠠⣶⣶⡆⢠⣿⣿⣯⣀⣀⣀⣾⣿⣿
⠀⢀⣀⣀⣀⠈⢛⣿⡇⠈⡂⡆⠀⠀⠀⠒⢸⢙⣻⢒⠳⠚⡃⠄⠡⠾⡚⠄⠐⠿⢿⢿⣿⣿⣿⣟⣻⣿⣿⣷⡅⠀⠸⠿⠿⠏⠀⠀⠀⠐⠀⠀⠀⠀⠀⡂⠉⢙⣿⣛⣠⣩⣟⠀⠀⠐⣪⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⣿⣿⣿⣿⣿⠂⣛⡃⠈⠀⠆⠀⠀⠀⢨⢜⠸⢩⠊⢽⠯⡖⡽⠨⣁⠈⠄⠄⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⢧⣶⣶⣶⣶⣶⠀⠀⠀⢰⣶⠀⢠⣴⣶⣶⣶⣶⣶⣾⣾⣶⣾⠆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶
⠀⣿⣿⣿⣿⡟⣐⠛⠃⠸⡀⠅⠀⠀⠀⢚⣚⡓⢂⢃⢎⡪⡹⠗⡁⢐⠀⡀⠀⣿⣿⢟⣻⣿⣿⣿⣿⣿⣿⡟⢾⣿⣿⣿⣿⡿⠀⠀⠀⢼⡿⠀⠸⢿⡿⢿⣿⣿⡿⣿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛
⣶⣿⣿⣿⡿⢡⡐⣺⠃⢐⡇⡁⠀⠀⠀⢆⠈⡩⢐⣐⠬⡁⠉⡁⢈⢂⠀⠁⠁⢻⣿⣿⢿⣿⣧⣿⣿⣿⣿⠁⠀⠀⠀⡀⡇⠂⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠚⠉⠋⠙⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣛⡟⠁⠪⡐⣊⡀⢨⠑⠁⠀⠀⠀⠀⠐⢧⠣⢆⢲⠀⠀⠂⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠠⢔⣳⣎⡀⠀⢠⣀⡂⠀⠀⠀⠂⠄⢐⡀⠁⠀⠀⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⡢⡸⣏⠒⢄⠸⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⢠⠊⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠈⣤⣭⣥⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣄⣠⣀⣀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣁⣐⣀⣈⣃⣀⣀⡀⠀⢀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣁⣀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⢟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠀⠉⠀⠀⠀⠀⠉⠉⠱⣅⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣔⣾⣾⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⡛
⣾⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⣩⣭⣭⣽⣶⣾⣿⣿
⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠍⣛⡃⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣧⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢢⠄⣰⣦⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⡟⠛⡟⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⡿⣛⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⣿⣿⡿⠓⠘⠂⠀
⠷⣽⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⡯⠹⡱⠻⢹⢻⡅⢆⡐⢸⠈⠏⡀⠖⡂⢔⣲⢻⣿⣿⡏⢉⣄⡎⠹⡹⠻⢻⠰⡹⠹⡋⢯⡋⡆⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀
⢻⣾⢿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣶⢠⣶⣿⣿⢂⢶⣶⡶⣶⡲⣶⣆⢿⣿⣗⣊⣸⣿⡿⣷⣞⡿⣶⣺⣶⣾⢶⡾⣶⡜⢲⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠈⢿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⢈⡟⢿⠥⢧⠞⡄⡟⠀⢸⠀⡇⢈⡻⢻⣿⣿⡟⠿⢻⠈⢼⠐⡇⣤⠃⢹⠾⣡⡦⡇⣼⢻⣿⡄⠿⠿⠿⠟⠛⠛⠉⠉⠹⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⡦⡈⢻⣿⢷⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠁⣭⣴⣯⢀⣨⣀⣭⣁⣠⣈⣁⣅⣉⣤⡘⣿⣿⣥⡄⢪⣥⣉⣀⣅⣠⣭⣩⣤⣭⣬⣁⣬⣤⣭⣥⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣦⡆
⣟⣗⡄⠀⠁⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠛⠛⠁⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡗
⢢⡿⠷⣶⢥⣶⣄⣰⣶⢶⣆⡘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⡿⠀⠀⠀⠀⠀⠀⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢽⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⢿⡏⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⠉⠹⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⣀⡀⠀⠀⠀⣤⡀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠤⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⢰⣄⠈⠁⠀⠀⠀⢿⡗⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⢀⠀⢘⣿⣿⣿⣿⡇⠀⣀⣠⣤⣤⣄⡀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⢸⣿⣷⡆⠀⠀⠀⠛⠛⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠉⠀⠈⠛⠛⠛⠉⠀⣼⣿⣿⣿⣿⣿⣿⣆⠻⠛⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⠁⠀⠈⠋⠀⠹⠋⠀⠀⠀⠀⠻⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⣿⡿⠛⠛⠀⠐⠿⠛⠀⠀⠉⠙⠆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠠⠤⠄⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⣶⣶⣿⣿⣿⣷⡀⣴⣶⣶⣶⣶⠀⢰⣶⣶⣶⠀⠀⠀⠲⠶⠀⠀⠀⠀⠶⠶⠶⠶⠆⠀⠶⢦⣆⡀⠶⠶⠖⠀⠛⢛⠛⠛⠛⢻⣿⣿⠀⢶⣶⣶⣶⣶⣶
⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⠀⠸⠿⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣷⣶⣶⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿
⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣇⢻⣿⣿⣿⣦⣶⣶⣶⣶⠀⠀⠀⢀⣦⠀⠀⠤⢒⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡿⠿⣿⡿⢿⣿⣿⡿⠀⠀⠀⠰⠿⠀⠀⠴⢿⣿⣿⣿⣿⠟⠻⠭⠭⠍⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⣩⣽⣶⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⡿⠿⠿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠙⠿⢿⢿⣿⣿⣿⣿⣿⣛⣏⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠈⢻⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⠟⣩⣭⣭⣭⣩⣩⠈⢻⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⠀⣿⣿⣿⣿⣿⣿⣿⡏⢚⣿⣿⣿⣿⣯⣿⣿⠆⣿⣿⣿⣿⣿⣿⡿
⠄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢠⠔⠂⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠹⣷⢽⣿⣿⣿⣿⣿⡿⡟⠛⡟⣿⣿⣿⣿⣿⠻⣛⣥⣾⣻⣿⣿⣿⣿⣿⣿⣿⣦⣭⣽⣿⣷⡶⠒⠀⢀⣿⣿⣿⣿⣿⣿⠃
⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣷⣤⡀⠸⢄⡠⠰⡰⠘⠱⢐⡅⢄⡐⢸⢀⠇⡄⠎⠋⢛⣻⢹⣿⡯⡏⠉⠀⡎⠹⡹⠻⢻⠰⠹⢹⡋⢯⡋⡏⣹⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⠇⠼⣓⣲⣢⣶⣔⠲⣖⢲⣶⡂⣿⣾⣷⣷⢠⣀⡒⠊⣘⣿⡃⢳⣊⡽⣐⣘⡳⣿⠶⡾⣶⣿⣶⣶⣶⣶⣻⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⡿⠑⠃
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢠⡓⡇⠈⡇⢶⠥⢧⠟⡄⡞⠀⢸⢰⡇⣬⡱⠈⢿⠏⡟⠿⢻⠈⢸⠀⡇⣤⠃⣺⠾⡡⠾⡇⢿⠻⣿⡄⠏⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀
⠠⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠀⢿⣿⣿⢘⣇⠁⢉⡀⢉⢀⣈⠀⣉⢁⣀⢨⣭⣧⣭⢠⣨⣭⣽⣅⣄⣌⣁⣉⡀⡁⡀⣉⢈⣄⣨⣌⣁⣈⣀⣈⠁⠀⠀⠀⠀⠀⠀⣀⣶⣶⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠘⠋⠫⣙⢽⣿⣟⣿⢻⠜⠋⠀⠀⠀⠀⠀⠁⠀⠡⣦⡪⡆⢹⣕⣅⠘⣽⣵⣍⠈⠛⠛⠉⠀⠀⠛⠙⢿⢱⡇⢙⣿⡿⣽⣽⣽⣿⣿⣷⣿⣯⣿⣿⣿⣄⢀⣀⣠⣤⣴⣾⣿⢾⣿⣿⣿⡷⣧⣴⣶⣤⣠⣤⣤⣄⠀
⣀⡆⠲⣶⣌⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠯⠁⢤⠃⢼⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⣿⣿⣷⠿⣿⣽⣿⣿⣟⣽⣛⣽⣽⣿⣝⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⣿⣯⡿⢿⣿⣾⡄
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⢿⠏⠉⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠿⠿⠿⠏⠉⠹⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣇⣀⡀⠀⣀⡀⠀⠀⠀⣀⡄⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⠄⠀⢠⣤⣤⣤⣤⡄⠀⠠⠠⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⠀⠀⠀⠀⠸⢿⡇⠀⢸⣿⣿⣿⣿⡇⣿⣿⡇⠈⠃⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⢀⠀⢸⣿⣿⣿⣿⡇⠀⢀⣀⣤⣤⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣿⣿⣿⢡⣷⡄⠀⠀⠀⠛⠛⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠛⠀⠘⠛⠛⠛⠋⠀⣰⣿⣿⣿⣿⣿⣿⣦⠛⠛⠿⠛⠛⠁⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣴⣶⣶⣶⣶⡄⠀⠀⠁⠹⠋⣼⣿⡏⠀⠻⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⣷⡿⠛⠓⠁⠀⠿⠛⠀⠀⠈⠉⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⢠⣿⣿⡇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠠⠤⠤⠤⠄⠤⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⡴⣾⣿⣿⣿⣿⣿⡟⣀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣽⣿⣿⣿⣷⣿⡏⠀⢀⣦⣾⣿⣿⠟⠀⢰⣶⣶⣶⠀⠀⠀⠰⠶⠀⠀⠀⠀⠖⣢⣴⣾⣿⣿⣿⣿⣷⣶⣦⣔⡂⠛⠻⠿⠿⠿⠿⣿⣿⡏⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⣿⠃⣰⣿⣿⣿⡻⡋⢮⠀⠸⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡰⣧⣤⣤⣿⣿⣷⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⡿⢻⣾⣶⣶⣶⣶⣶⠀⠀⠀⢠⣶⠀⠀⣄⣻⣿⡿⣿⡟⣵⣶⣶⣯⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣾⣾⣿⣯⣿⠿⠿⠫⠴⠿⢿⡿⢿⣿⣿⣿⠀⠀⠀⠸⠿⠀⠀⠿⠿⠬⠴⠼⠾⠿⠿⠿⠿⠿⠷⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⠿⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠙⠛⠻⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠐⠀
⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠘⠻⠿⣿⣿⣿⣿⣿⡿⠿⣧⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣷⡖⣠⣤⣴⣿⣠⡄⣴⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⡿⣫⣴⣬⣭⣭⣭⡍⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⢱⣿⣿⣿⣿⣿⣧⢸⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡅⢸⣿⣿⣿⣿⣿⣿⡏⠼⢿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⠇⢸⣿⣻⣿⠟⠛⠻⠈⣿⣿⣿⢸⣿⣿⢿⠻⠿⣿⣿⣿⣿⡿⣿⣿⡿⡟⠛⡟⣿⡿⣋⣥⣾⢿⣿⣿⣿⣿⣿⣿⣿⡧⣭⣽⣿⣶⡶⠒⠀⢹⣿⣿⣿⣿⣿⡟⠈⠙⢻⣿⣗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⢀⣿⣷⣿⡿⠄⡥⠹⡱⠛⢹⢻⡅⢏⡙⢸⠈⠏⡀⠏⠋⢛⣺⢹⣿⡗⡏⢉⣀⡎⡰⡹⠻⢻⠸⠹⢹⡋⢯⡛⡏⡽⠁⠀⠙⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡃⣠⣴⣾⣿⡧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠛⠛⠛⠘⢿⣿⣿⣟⣒⣶⣆⣖⢸⣿⣾⠆⢶⡀⣒⡶⣖⣶⣶⣖⡒⢊⣸⠟⣻⡐⣻⣿⣷⣿⣶⣿⣷⣾⣶⣿⣶⠾⢒⡓⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⡟⠀⢻⡿⣿⣿⡇
⢹⣿⣿⣿⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠢⡇⢈⡇⢰⠥⢦⠜⡄⡞⠀⢸⠀⡇⠨⡷⢉⣞⡆⡟⠿⢻⠀⢼⢰⡇⣶⠋⢽⠾⡁⠚⡇⢿⠳⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⢸⣿⣿⣿⡇
⠘⣿⣿⣿⣿⡟⣿⢇⣀⣀⣀⠀⣀⣄⠀⣀⣴⣿⣿⢹⣃⠁⠉⠀⠍⢀⣈⠀⠉⠁⠀⠈⠁⢁⣉⢤⣦⣿⣿⣥⡐⢮⣡⣉⣀⡁⣀⣉⣨⢀⣨⣬⣁⣈⠀⠈⠁⠀⣀⣶⣶⣿⣖⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⠇
⢄⣿⣿⢿⣿⣮⣻⢟⣯⢽⢿⣿⣿⣿⣿⣗⣿⣼⠋⡎⠀⠀⢾⡆⢢⡔⡓⠁⠀⢠⣠⣔⣦⣮⡧⣿⣿⣿⢻⣿⠗⣣⢙⢿⣯⣿⣿⣟⣽⣾⣿⣿⣯⣽⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣠⣤⣤⣄⣻⣿⣿⡇
⠠⠿⢿⣿⡿⢿⡿⠿⢿⠿⠿⢛⠄⠿⡨⢞⢴⣻⡅⠈⠀⠀⢀⡅⠑⠘⡨⢸⠯⡿⠧⢿⢝⣿⡿⢿⣻⣿⣿⣿⣛⣻⣿⣿⡿⠟⣿⣾⣿⣿⡿⣵⢯⣿⣿⣷⢿⣿⣿⣿⣿⠿⣜⣿⣿⣷⣿⣷⣿⢮⢬⣿⣿⣿⣿⣿⡿⡆
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠿⡿⠉⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⢿⠏⠉⠹⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠉⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⣤⣤⣤⣤⣄⠀⢠⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⢰⣄⠈⠃⠀⠀⠀⢸⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠠⠦⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠈⢿⣿⣿⣿⠀⢸⣿⣷⣦⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⠚⠀⠀⠛⠛⠋⠋⠁⢀⣶⣿⣿⣿⣿⣷⣄⠻⠛⠻⠛⠛⠁⠀⠀⠿⠇⠀⠀⠀⠀⢸⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⣿⣿⠇⠀⠈⠙⠏⠁⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠚⠓⠁⠀⠺⠛⠀⠀⠁⠉⠇⠀⠅⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⠤⠠⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢯⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⣴⣶⣶⣶⣶⠀⢰⣶⣶⣶⠀⠀⠀⠰⠶⠀⠀⠀⠀⠰⠶⠶⠶⡆⠀⠴⠶⠄⠀⠴⠶⠶⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⢶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣐⣁⣿⣿⣷⣤⣀⣙⣟⠿⣿⣿⠀⠸⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠈⠙⡇⠐⢐⢀⠀⠀⠀⠀⠀⠀⠈⠉⠩⢬⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣛⣻⣿⣾⣿⣿⣿⣿⣿⣷⣮⠀⣴⣶⣶⣦⠀⠀⠀⢠⣶⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⣒⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿
⣠⣴⣾⣿⣿⣿⡽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⣷⣾⣿⠿⡿⠀⠀⠀⢨⠿⠀⠀⠿⠿⠿⠿⠿⠿⣿⣛⣯⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⢻⡛⠀⠀⠀⠀⣀⣛⡿⠿
⣿⣿⡿⠿⠋⠁⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠿⠟⠻⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡪⡁⠀⠀⠀⠀⢻⡿⣿⡆
⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣄⠀⠀⠀⡄⠄⠈⠉⣹⠿⢿⣿⣿⣿⣿⠿⠿⠿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠠⢨⡿⠿⠃
⠀⠀⠄⠀⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠠⡊⡄⠀
⠀⠀⠀⠀⠀⠄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠰⠗⠀⠑⠀⠀⠀⠀⠈⠀⠿⠛⢿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠄⣉⠅⠀
⣤⣄⣀⣀⣀⣀⣀⡀⠈⠛⠛⠿⠽⠿⠿⠟⢻⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢈⡀⢿⣿⡿⣿⡇⢀⣀⣀⣀⣒⣃⣀
⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠸⣟⣷⣘⣇⣾⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣦⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣷⢆⠆⣶⣶⣶⡆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⢸⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⠅⢸⣿⣿⣿⣿⣿⣿⡟⢰⣾⣿⣿⣿⣿⣿⠕⣂⡈⠻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⡇⣾⡇⢿⣿⣿⡇⣿⣿⣿⣿⠟⠛⢻⠿⣿⣿⡿⢿⣿⣿⢿⠻⠿⣿⣿⣿⣿⠿⢛⣬⣾⡟⣛⡿⣿⣿⣿⣿⣿⠳⣬⣽⣷⣶⡶⠒⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣽⣿⣿⣿⣿⣏⠁⣿⣿⣿⠇⣿⡇⢸⣿⣿⡆⢹⣿⡿⠿⠤⡽⠹⡱⠘⢹⢙⡍⢏⡙⢸⠈⠏⡀⠏⡋⢓⣲⢿⣿⣿⡏⢭⣤⡏⡹⠹⠻⢻⢨⠹⢹⡋⢯⡂⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢟⣿⣿⣿⣿⡿⡀⣿⣿⣿⠠⠻⣇⢸⣿⣿⡇⢼⣿⣿⣷⣒⣶⢂⣶⣴⡒⣂⠒⣶⡆⣲⡶⣶⣀⡻⣿⡖⣊⣼⣿⣿⣷⣿⣿⣷⣿⣶⣿⣷⣾⣷⡋⢀⠀⢀⡀⠀⠀⠀⠀⠈⠛⠛⠉⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⡘⣿⣿⡿⠃⠀⠀⠈⠉⠉⠀⢒⡇⠈⠉⠋⠁⠘⠛⠿⠷⡇⢈⡇⢵⠥⢧⠜⡄⡞⠀⢸⠀⡇⠈⡳⢺⡿⠿⡟⠿⢻⠙⢺⠀⡧⣴⠋⢿⠾⡁⠀⡆⢸⠳⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢘⣟⠁⠀⠀⠀⠀⠀⠀⢀⢀⣰⣇⠀⠀⠀⠀⠈⠀⠀⢀⡁⠉⣀⢉⢀⣈⣀⣉⢁⣀⠈⡁⣁⣉⢠⣤⣆⣤⣁⢶⠈⠁⠈⠀⠁⠀⠉⠈⠀⠈⠀⣁⣈⣀⣨⣡⣤⣄⣶⣦⣤⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⡺⣿⣲⣦⣦⣤⣦⡵⣲⣴⣿⣿⣷⣯⢤⣴⣤⣀⠀⠀⠄⠮⣭⣖⣕⠵⣟⣟⡻⣿⣿⣼⣏⣿⣶⣾⣿⣿⣻⠟⣿⣷⣦⣤⣠⣠⣤⡤⠄⡤⣴⣶⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠢⠿⢿⣿⣿⢿⣿⣿⠿⣿⠿⠋⠭⠿⣮⡬⡧⣄⢂⢠⠥⠽⢠⡴⡐⢮⠒⠺⡿⣼⡿⣿⣹⠽⡿⣿⢻⡿⣿⣿⣿⠿⣟⣿⡿⡿⢿⣿⠿⡿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣟⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠹⡿⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⡿⠉⠩⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿
⠠⠠⠁⠈⢀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⣠⣤⣤⣤⣤⠀⢀⣤⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠈⢁⠀⡀⠈⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⢀⣤⡈⠓⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⠠⠴⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⡠⢄⡨⡀⠱⠨⡓⠄⢈⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣦⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠚⠃⠀⠛⠛⠛⠛⢁⠀⣠⣶⣿⣿⣿⣶⣄⠿⠟⠻⠟⠛⠁⠀⠀⠿⠇⠀⠀⠀⠀⢸⠿⢿⣿⣿⣿⣿⠟
⠤⠉⠌⡀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠛⠉⠙⠟⠁⠀⠀⠀⠹⠟⠀⠀⠀⠐⠀⠀⠀⠀⠀⣶⡶⠗⠚⠃⠀⠾⠟⠁⠀⠉⠉⠇⠀⡮⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀
⠈⡨⢓⢁⠀⠀⣢⣤⣤⣤⣄⠀⠀⠀⢀⣀⣀⣀⣀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠴⣶⠀⠂⣶⣿⣿⡿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠩⣿⢫⣵⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣻⣿⠧⢈⣽⣿⣿⣿⣿⣿⡿⠀⠀⣴⣶⣶⣶⣶⡄⠰⣶⣶⣶⠀⠀⠀⠰⡶⠆⠀⠀⠀⠰⠶⢶⣶⡶⠀⠴⠶⠆⠀⠶⢶⡶⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠠⣿⣿⣿⣿⣶⣾⣶
⠠⢪⣇⡘⠛⠛⠻⣽⣷⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠽⣿⣿⣑⣐⡔⠀⠀⠐⠧⠃⠀⠈⠛⠛⢽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠈⣺⣳⣯⡌⠬⠁⠀⣾⣿⡇⣿⠀⠀⣽⣿⣿⣿⣿⣷⣶⣶⣶⣶⡄⠀⠀⠠⣶⡄⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢖⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣾⠮⢥⣵⢳⠂⣿⣿⣧⣝⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⣿⠇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡛⠀⠀⠀⠀⢀⣻⠿⢿⣿⣿⣿⣿
⢀⠘⡿⠚⡜⢋⣠⣾⣿⣿⣿⣿⣷⣆⠁⠀⠙⢻⠯⣿⡍⢝⡡⠄⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⡈⠘⠈⠄⠀⣀⣀⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢋⡇⠀⠀⠀⠐⣿⣿⣿⣷⣾⣿⣭⡉
⠐⠈⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠠⡤⢠⢁⠈⢁⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⡜⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠁⠋⠀⠄⠐⠄⠀⠀⠀⠀⠐⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣿⡇⡄⠀⠀⠀⠀⢻⣿⣻⣿⣿⣿⣿⡇
⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⢘⡓⠊⠀⠀⠒⠀⠀⠀⠈⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢧⡄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇
⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣑⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣐⣀⣀⣀⣀⣀⣉⣙⣙⣛⣛⣛⣛⣃
⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⠏⠻⠟⣿⣿⣿⣿⠿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⢠⣿⣿⣿⣿⣿⣿⣿⠋⣶⣿⣿⣿⣷⣿⣿⣿⣷⣦⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣦⢠⣤⣀⣀⠀⣀⣀⣀⡘⣃⣠⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⢿⠻⣿⡿⢟⣭⣼⣿⣿⣿⣿⡟⣛⡿⣿⣷⣬⣭⣷⢶⡶⠖⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢴⡽⠹⡹⠹⠹⢙⡍⢏⡙⢸⢈⠏⡅⠏⡛⢛⣻⢻⣿⣿⡏⢭⣤⡎⣹⡹⢻⢻⠸⠰⢰⡂⢦⡂⡆⠘⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⠼⣿⣿⣿⠀⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣶⣶⠶⣶⡄⣻⣾⣶⣷⣾⣿⣗⣊⣼⣿⣿⣷⣿⣿⣷⣿⡷⢟⠀⡀⢀⡀⢀⠀⢀⡀⠀⠀⠙⠏⠁⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⣿⣿⣿⡅⣿⣿⣿⠀⣿⣿⣿⢠⣿⣿⣿⣿⠿⢿⣿⣿⣷⡇⢈⡇⢿⠥⢯⠝⡄⡞⠀⢸⢰⡇⠬⡿⠻⠿⠿⡟⠿⢻⠙⢿⠸⡧⣤⠃⢸⠶⡁⠀⡇⢸⠳⣼⡇⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⢾⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿⠰⣿⣿⣿⣿⣶⣾⣿⣿⣿⣅⣩⣤⣍⣠⣬⣀⣍⣁⣦⣌⣁⣅⣩⣤⣶⡗⠀⠁⠀⠈⠁⠈⠀⠁⠀⠉⣨⣤⣭⣬⣁⣨⣀⣬⣥⣶⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠜⠟⠋⠁⠉⠙⠉⠀⠉⠉⠁⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠖⠶⣶⠟⢷⠆⠰⠶⠶⠶⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣛⣻⣿⢿⣿⠉⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⢹⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠹⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣿⠆⣿⣿⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⣀⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣾⣿⣻⠁⣿⣿⠀⠀⣿⣿⣿⣿⣿⡀⢰⣦⡈⠛⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠀⡀⠀⣿⣿⣿⣿⣿⠀⠀⠁⠠⣄⣐⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣻⣿⡄⣿⣿⠀⠀⣿⣿⣿⣿⣿⠄⢸⣿⣿⣦⠀⠀⠀⠘⠟⠃⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⠚⠃⠀⠛⠛⠛⠛⢁⠀⠀⣴⣿⣿⣿⣿⣿⣮⠛⠿⠟⠛⠉⠀⠀⠿⠇⠀⠀⠀⠀⢸⠿⢿⣿⣿⣿⣿⠟⠛⠛⠛⠛
⣿⣿⣿⣿⣿⡇⠀⠛⠀⠀⠛⠉⠙⠟⠉⠀⠀⠈⠹⠟⠀⠀⠀⠐⠀⠀⠀⠀⠀⢴⣶⠟⠛⠛⠀⠾⠿⠃⠀⠉⠉⠷⠀⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣦⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠁⠀⠀⢶⣶⠀⠀⣶⣶⣶⣶⣶⡆⠀⣶⣶⣶⡆⠀⠀⠠⣶⠆⠀⠀⠀⢴⣄⣹⣷⡤⠀⢴⡶⠦⠀⠶⣶⣶⠀⣶⡆⢰⣿⣿⣿⣿⣿⣿⣧⣴⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣄⠀⠀⣈⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⠿⡿⣻⠇⠀⠀⠀⣚⡀⠀⠀⠠⢤⣿⣿⣿⣿⣷⣴⣟⣂⣀⣈⣛⣀⣀⣀⣁⠀⠻⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⢰⡄⣾⣿⡄⠀⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⠀⠀⢠⣶⡆⠀⣶⣶⣶⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣷⠸⡇⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⡇⠀⢿⠿⢿⠿⠮⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠌⢻⣿⣿⣿⣥⣉⣁⠶⠐⣬⣭⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⣷⣶⣬⣯⢽⡿⡻⣿⣓⣦⣉⡙⢛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣷⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠿
⣾⣿⣿⣿⣿⣿⣿⣿⣷⣌⢛⢣⡞⣹⣿⣿⣿⣛⣻⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣻⣲⡯⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⢧⣦⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⡵⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢢⡓⣟⡿⢷⡻⢟⠯⠿⠀⠀⠀⠀⢺⣿⢿⢯⣿⣿⡿⣿⣿⠗⢛⠗⠐⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢈⣁⣀⣙⣛⣚⣑⣋⣐⣀⣀⢀⣀⣐⣋⣉⣉⣛⣛⣃⣁⣘⣋⣉⣈⣀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣛⣀⣀⣀⣈⣛⣛⣛⣛⣻⣿⣛⣛⣿⣻⣿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠻⣿⣉⠻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠉⠉⠉⠁⢸⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣝⣛⣛⡿⣿⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⠁⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⢿⢣⡼⣿⣿⣿⣿⣿⣿⣿⣿⡗⣛⡭⣿⣶⡶⠖⢢⠀⣰⣿⣿⣿⣿⣿⣿⠁⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡄⣤⣤⢠⣤⣤⣴⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⡿⠻⡹⠹⠻⢙⡍⢏⡁⢺⢈⠏⡅⠏⡛⢟⣻⢿⡿⠿⡏⣭⣴⡏⠹⡱⠰⢺⢸⠹⢻⡋⣯⡛⡏⡝⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣆⢺⢶⣿⡶⣿⣾⣷⣷⠛⠛⠓⠊⣀⠀⡀⠰⣿⠟⣁⣀⡀⢈⠀⣾⣿⣿⣷⣿⣶⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⣿⣧⢿⡿⣾⣿⣿⡇⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢨⡏⢿⠥⢯⠽⡔⡟⢠⢿⠰⡇⠈⡷⠀⠀⠀⡟⠶⢻⠀⢸⠀⡧⣤⠃⢸⠶⡁⠈⡇⢸⠳⣼⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡞⡁⣿⣿⣿⠣⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣅⣩⣤⣍⣴⣬⣀⣭⣡⣛⣍⣡⣅⣉⣤⣤⣤⣤⣥⣤⣮⣥⣌⣠⣅⣠⣭⣈⡀⠈⠈⠁⠈⠀⠈⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠉⠉⠁⠀⠉⠉⠁⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠖⠲⣶⠯⢶⠶⠰⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡏⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣿⣿⡇⠀⣿⣿⣿⣿⣿⡏⠀⠀⣀⣀⠀⠀⠀⢀⣠⡄⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⣤⡀⠀⣤⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⣦⡈⠛⠀⠀⠀⢸⣿⡇⠀⠆⠀⣿⣿⣿⣿⣿⣿⡟⠁⡀⠀⣿⣿⣿⣿⣿⡆⠀⠉⠀⣀⣚⣂⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⣿⣿⣶⡄⠀⠀⠸⠿⠇⠀⠂⠀⠛⠟⠻⠟⠛⠛⠂⠘⠃⠀⢛⡛⠛⠛⢉⡀⠀⣴⣿⣿⣿⣿⣿⣿⡝⠻⠿⠛⠋⠀⠀⠻⠿⠀⠀⠀⠀⢀⡿⠿⣿⣿⣿⢿⡿⠛⠻⠛⠛⠻⣿⣿⣿
⣿⡇⠉⠙⠁⠀⠛⠋⠙⠿⠋⠁⠀⠉⠙⠿⠃⠀⠀⠐⠂⠀⠀⠀⠀⢸⣿⠟⠛⠛⠀⢰⠞⣶⡄⣸⣧⠻⠀⢾⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠿⡿⠋
⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⢈⣀⣀⣀⣀⠀⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠄⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣻⢰⣶⡆⠀⢰⣶⣶⣶⣶⡆⠀⣶⣶⣶⡆⠀⠀⠀⣶⡆⠀⠄⠀⢰⣶⣶⣶⣶⠄⠴⣶⠸⣿⣿⣿⣿⣿⣦⡂⠀⢀⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠚⠿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣇⠀⡿⣿⣿⡇⠀⠀⠀⣟⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⢾⢹⣿⡇⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣿⡅⠀⠀⠀⣾⣇⠀⢰⣶⣾⣾⣿⣿⣿⣿⣿⣿⣷⣶⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⢻⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠮⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⡋⢊⣭⣶⣿⣿⣭⣿⣿⣿⣿⣿⣾⣿⣿⡆⠀⠀⠀⢾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣮⡻⢿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡳⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀⣀⣀⣐⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢛⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣛⢃⣀⣀⣸⣟⣿⣟⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣾⣽⣛⣿⠿⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡛⣭⣶⣿⣿⣷⣿⣭⣽⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿⣧⣛⡿⠿⠿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣷⣹⣿⣿⣿⢿⣿⣿⠇⠙⢻⣿⣭⣭⣿⡟⣳⡗⣂⠀⣿⣿⣿⢿⣿⣿⣿⠩⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⢀⣀⣀⣀⣨⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⡿⠻⡹⠛⣹⢺⡭⢯⡛⢹⠨⠏⡁⠎⡂⣾⣻⢿⣿⣿⡏⠉⠀⡎⢸⡹⢻⣻⢸⡿⢻⡋⢮⡒⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣹⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡛⢷⣿⣿⣿⣶⣿⡄⣀⡀⣀⣀⣰⣷⣖⣊⣾⠟⣁⠀⣀⠀⣀⣾⣿⣿⣿⣿⣿⡟⢒⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢇⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⡏⢶⠧⢿⠿⡽⡟⠀⢸⠀⡀⠾⡿⠛⠋⠁⡟⠶⢻⠀⢸⠀⡧⣤⠋⢻⠾⡁⠀⡇⢸⠻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⡟⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣭⣴⣍⣴⣾⣀⣭⣡⣿⣍⣡⣥⣩⣤⣾⣿⣿⣥⣶⣮⣥⣭⣀⡁⠀⠉⠈⠀⠈⠈⠁⠈⠀⣯⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠖⠶⣶⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⢿⣿⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⢹⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡿⠛⠀⠀⠛⠿⣿⣿⣿⠁⠀⠀⣀⣀⠀⠀⠀⢠⣀⠀⠀⠀⢠⣤⣤⣤⣄⣤⣤⣤⡄⠀⠀⣤⣤⣤⣤⣤⠀⢀⣀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣣⣤⣤⣄⡀⠀⠹⣿⣿⠀⢰⣄⠈⠻⠀⠀⠀⢸⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠏⠀⡀⠀⣿⣿⣿⣿⣿⠀⢀⣀⣤⣄⣐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⠀⠀⢻⣿⠀⢸⣿⣿⣦⠀⠀⠀⠸⠟⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠚⠁⠀⠛⠛⠛⠋⢁⣾⣿⣿⣿⣿⣿⣷⡘⡿⠛⠿⠟⠛⠁⠀⠀⠿⠇⠀⠀⠀⠀⢸⠿⢿⣿⣿⡿⢿⠟⠛⠛⠛⠙⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠁⠀⠀⠀⠹⠟⠀⠀⠀⠐⠀⠀⠀⠀⠀⣶⡶⠒⠒⠂⠀⠾⠟⠂⠀⠉⠉⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀
⣿⣿⣿⣿⣿⣶⠀⠀⠀⣀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⢀⣐⣢⣶⣶⣶⠄⢰⣶⣶⣶⠀⠀⠀⠰⣶⠆⠀⠀⠀⠰⠶⠶⢶⡦⠀⠶⠶⠆⠀⢶⣶⡶⠀⠆⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⠿⢿⣿⠀⠀⠀⠀⡒⠀⠛⢷⣶⣤⣛⣲⣒⣒⣐⣃⣺⣥⣤⣴⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⡀⠀⠀⢠⣶⡜⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡯⡟⢿⡿⣫⣛⡿⢿⣿⣿⣦⣄⠀⢸⣿⠘⠛⠻⢿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠿⣿⠿⠛⠛⢿⠟⠛⠛⠟⠛⠻⠟⠛⠛⠉⠉⠀⠀⠀⠀⢀⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠘⠂⢂⣌⣙⠛⣿⣿⣦⣀⠄⠀⠉⠒⠈⠁⠿⢿⣿⡿⠇⣿⣿⡇⣿⣿⢸⣿⣿⠿⠇⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣧⢸⣿⡇⣿⣿⡿⠇⠀⢨⣿⣿⣿⣿⣶⣶⣭⣝⠛⣻⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⣉⠋⢁⠀⠈⠻⠙⠻⣧⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⣶⣿⣿⢸⣿⣿⣤⡜⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣾⣿⡇⣿⣿⣥⡄⠀⠀⣿⣿⣿⣿⣿⣽⣧⣾⣾⠽⣿⣿⣿⣟⣿⣿⡟
⣿⣿⣿⣿⣿⣇⠐⠀⠁⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⡄⡁⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⡏⣿⣿⢸⣿⣿⠉⢱⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡏⠁⠀⠘⣗⡧⡑⢓⢛⣍⠨⡔⠐⢀⠒⠿⣿⣏⣿⣿⡇
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⢀⠀⠈⢀⠀⢸⣿⡇⠀⣿⣿⡇⣿⣿⢸⣿⣿⣶⡇⣿⢸⣿⣿⣶⢸⣿⣿⢸⣿⡇⢿⣿⡇⣿⣿⣷⣶⢰⠀⣯⣤⡈⣀⣘⣭⣒⣧⣋⢵⣮⣡⣕⣾⣿⣿⡇
⠛⠛⠛⠛⣿⡇⣉⣀⣀⣀⣀⣐⣂⣊⣁⣀⠀⠀⣀⣀⣀⣀⣉⠐⠂⠒⠀⠀⠀⠀⠀⠀⠠⠤⣦⣴⡶⢦⣤⡴⣶⣿⣷⠦⠤⢴⣶⡤⠴⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣑⣉⣙⣳⣛⣛⣙⣉⣑⣋⣋⣛⣻⣿⣿⡃
⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⡆⣰⣶⣶⠀⢰⣶⣶⡆⠀⣶⣶⡀⣶⣶⠀⣶⣶⣶⡆⠉⣴⣶⣶⣦⡀⢰⣶⣶⣶⢰⣶⣶⣶⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⠀⣿⡿⣿⣇⢸⣿⣿⠸⠿⠇⢸⣿⣇⣀⢸⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⢿⣿⠀⣿⣿⣹⣿⡄⣿⣿⣿⣿⣿⢸⣿⣇⣿⣿⢸⣿⣿⢶⣶⡆⢸⣿⡿⠿⢸⣿⣿⢻⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⣤⣤⣤⡄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡿⣾⣿⢸⣿⡿⢻⣿⡇⣿⣿⢹⣿⣿⣸⣿⡟⣿⣿⡜⣿⣿⣸⣿⡇⢸⣿⣧⣤⢸⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠉⠁⠉⠁⢉⣉⣈⣉⣁⣌⣉⡁⠉⠉⠀⠉⠉⠉⠉⠁⠉⠉⠁⣈⣛⣋⣉⣁⣈⣉⠉⠉⠈⠉⠉⠈⠉⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣾⣿⣿⣿⣿⣿⣿⣿⣻⣷⣭⣭⣿⣶⡶⠓⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣩⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠛⠿⠟⠛⠃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠛⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⢹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢡⣶⣿⠿⠿⠿⠿⠿⠛⠛⠉⠙⠿⠿⠛⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣷⡀⠀⠐⠀⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣷⡦⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⣤⣤⣤⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⢪⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⢹⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⣿⡏⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡇⠀⢸⣿⣿⣿⣿⡏⠀⠀⢀⣀⡀⠀⠀⠀⣄⡀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⡤⠄⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡿⠇⠀⠘⠿⣿⣿⣿⡇⠀⣦⣄⠙⠃⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⢠⠀⢸⣿⣿⣿⣿⠇⣀⣨⣤⣔⣀⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣁⣀⣀⣀⡀⠈⢿⣿⡇⠀⣿⣿⣷⡄⠀⠀⠀⠛⠃⠀⠀⠀⠘⠛⠛⠛⠛⠛⠁⠐⠛⠀⠘⠛⠛⠛⢡⣿⣿⣿⣿⣿⣿⣷⠀⢸⠟⠛⠿⠛⠋⠀⠀⠸⠿⠀⠀⠀⠀⠀⡿⠿⢿⣿⣿⠿⡿⠋⠙⠛⠋⠛⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣧⠀⠸⠋⠀⠀⠀⠈⠿⠃⠀⠀⠀⠂⠀⠀⠀⠀⢰⣶⡶⠚⠛⠁⠰⠿⠋⠀⠈⠉⠙⠄⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠀⠉
⣿⣿⣿⣿⣿⠋⠀⠀⢀⡀⠀⣀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⣿⣿⣿⢧⣤⣴⣶⢶⣶⠀⢶⣶⣶⣤⣶⣿⣿⠿⡛⠋⠀⠀⠀⢶⣶⣶⣶⠆⠰⠶⠶⠀⠰⣶⣆⠿⠿⣿⡿⣿⣿⣿⣿⠇⢀⣐⣒⣲⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣿⣿⣿⠸⣛⣭⣶⣿⣬⣶⣿⣿⣿⠿⠛⠉⠀⠘⣛⠀⠀⠀⠐⠿⣿⣿⣿⣿⣽⣿⣛⠀⠀⣛⣭⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣶⣴⠀⠀⠀⣶⣶⠀⢰⣶⣶⣶⣷⣿⣷⣿⣶⢶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢟⢻⣽⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠸⠿⠿⠿⠟⠋⠉⠉⠐⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠿⣿⡿⠛⠛⠿⠟⠛⠛⠛⠛⠻⠟⠛⠻⠛⠃⠀⠀⠀⠀⣘⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣤⣮⡿⣿⣿⣿⣿⣶⣦⠀⠀⠀⢠⣿⣧⣾⣷⠄⣁⡀⠿⢿⣿⡿⠇⣿⣿⡇⣿⣿⢸⣿⣿⠿⢇⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣧⢸⣿⡇⣿⣿⡿⠇⠀⣾⣿⣿⣿⣿⣶⣿⣭⣝⢛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⢾⣻⡽⣛⣛⣻⣿⡗⠀⠀⠀⢨⣧⣫⣵⢾⣿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣷⣿⣿⢸⣿⣿⣤⡜⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣾⣿⡇⣿⣿⣧⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⡇⣽⠿⣿⣛⣯⣿⣵⢯⠧⠀⠀⠀⠀⣾⠂⣤⡾⢿⣿⣿⡇⢸⣿⡇⠀⣿⣿⡏⣿⣿⢸⣿⣿⠉⢱⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡏⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣾⡿⡳⢯⣟⡿⡷⠻⡯⠀⠀⠀⠰⠼⢦⣥⡀⠾⡋⠁⠀⢸⣿⡇⠀⣿⣿⡇⣿⣿⢸⣿⣿⣶⡇⣿⢸⣿⣿⣶⢸⣿⣿⢸⣿⡇⢿⣿⡇⣿⣿⣷⣶⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣇⣉⣐⣘⣊⣛⣓⣛⣛⣃⡀⠀⢀⣀⣒⣛⣑⣋⠛⠛⠛⠂⠀⠀⠀⠀⠀⠰⠶⣦⣶⣶⣦⣤⣴⣶⣿⡷⠦⠤⣤⣦⣤⠴⠦⣶⣶⣤⠄⠀⠀⠀⠀⠀⠀⠬⣟⣛⣛⣿⣿⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⡆⣰⣶⣶⠀⢰⣶⣶⡆⠀⣶⣶⡀⣶⣶⠀⣶⣶⣶⡆⠋⣴⣶⣶⣦⡈⢰⣶⣶⣶⢰⣶⣶⣶⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⠀⣿⡿⣿⣇⢸⣿⣿⠸⠿⠇⢸⣿⣇⣀⢸⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⢿⣿⢀⣿⣿⣹⣿⡄⣿⣿⣿⣿⣿⢸⣿⣇⣿⣿⢸⣿⣿⢶⣶⡆⢸⣿⡿⠿⢸⣿⣿⢻⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡿⣾⣿⢸⣿⡿⢻⣿⡇⣿⣿⢹⣿⣿⣸⣿⡟⣿⣿⡌⣿⣿⣸⣿⡇⢸⣿⣧⣤⢸⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣄⢀⣤⣤⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⠉⠁⠉⠁⢉⣉⣈⣉⣡⣌⣉⣁⠉⠉⡀⠉⠉⠉⠉⢁⡉⠉⠁⠈⣛⣋⣉⣡⣈⣉⠉⠉⡈⡉⢉⡈⠉⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣿⣶⣶⠖⠂⠀⠀⠀⠀⠈⠛⠿⠋⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⢿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣫⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠘⠿⠟⡘⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣾⠿⠿⠿⠿⠿⢟⠛⠋⠉⠻⠿⠟⠛⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣿⣇⠀⠀⠀⠈⢀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣿⣿⣷⣦⣄⣀⠀⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣴⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢢⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⡍⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⠀⠀⣿⡿⣹⣯⣝⡇⠀⠀⢀⣀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⡤⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡀⠀⠻⣽⣿⣿⡿⡇⠀⣤⡀⠙⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⡀⠀⣿⣿⣿⣿⠿⣀⣤⣤⣤⣄⡚⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡄⠀⣸⣿⣿⣿⢡⡇⠀⣿⣿⣶⡄⠀⠀⠘⠿⠇⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠘⠃⠀⠙⠛⠛⢋⣾⣿⣿⣿⣿⣿⣿⣦⠀⡿⠟⠻⠿⠛⠋⠀⠀⠹⠿⠀⠀⠀⠀⠀⡿⠿⣿⣿⣿⢿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿
⠀⠙⠁⣼⣿⣿⣿⣿⠈⠀⠀⠀⠉⠿⠃⠀⠀⠀⠂⠀⠀⠀⠀⢰⣶⠖⠛⠛⠀⠸⠿⠃⠀⠈⠉⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠈⠉
⠀⠀⠀⠀⠀⢹⣿⣿⢀⡀⠀⣀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⣠⣾⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢰⡆⠀⣶⣶⣶⡆⠀⠀⠀⣶⡆⠀⠀⠀⠰⣶⣶⣶⡶⠄⠰⠶⠶⠀⠰⣬⠛⢛⣿⣿⣿⣿⣿⣿⣇⣢⣤⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢛⣿⣿⣿⣬⡇⠀⠿⠿⣿⡇⠀⠀⠀⠐⠂⠀⠀⠀⠠⢿⣿⣿⣿⣷⣮⣶⠃⠀⠀⣋⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣝⣿⣿⣿⣸⣿⣿⣿⣿⣳⣶⣶⣿⣿⡅⠀⠀⠀⣶⡆⠀⢰⣶⣶⣶⣾⣿⣿⣿⣶⡶⢂⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⢸⡿⠿⠿⠟⠋⠉⠉⠉⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⡿⠛⠛⠟⠉⠁⠀⠂⠈⠻⠟⠛⠻⠛⠛⠃⠀⠀⠀⡛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣻⣿⣿⣿⡟⠀⢒⣿⣿⣶⣶⠆⠀⠀⠀⠰⡖⣰⡖⣚⠾⠅⠀⠿⢿⣿⡿⠇⣿⣿⡇⣿⣿⢸⣿⣿⠿⢇⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣧⢸⣿⡇⣿⣿⡿⠇⠀⣿⣿⣿⣿⣷⣶⣯⣭⣛⣛⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⡁⢢⡂⡝⣓⣰⡾⡇⠀⠀⠀⢀⣕⢗⡽⡣⡠⢀⣤⡆⢸⣿⡇⠀⣿⣿⣶⣿⣿⢸⣿⣿⣤⡜⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣾⣿⡇⣿⣿⣥⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⢐⢯⠆⠹⣳⡍⢜⠌⠁⠀⠀⠀⠀⠿⠄⠆⣠⣴⣿⣿⡇⢸⣿⡇⠀⣿⣿⡏⣿⣿⢸⣿⣿⠉⢱⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡏⠁⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⡏⠰⠁⢂⢑⠼⢠⠝⠛⠀⠀⠀⠀⠘⢵⡡⠞⢋⣿⣿⣿⡇⢸⣿⡇⠀⣿⣿⡇⣿⣿⢸⣿⣿⣶⡇⣿⢸⣿⣿⣶⢸⣿⣿⢸⣿⡇⢿⣿⡇⣿⣿⣷⣶⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣷⣁⣐⣀⣀⣓⣓⣃⣈⣀⡀⠀⢀⣀⣑⣒⣀⠟⠉⠽⠟⠁⠀⠀⠀⠀⠠⠴⠶⣦⣴⣶⣦⣤⡴⣶⣿⠷⠦⠤⢦⣦⣤⠶⠶⢴⣶⣶⠶⠶⡄⠀⠀⠀⠀⠌⣛⣛⣻⣟⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⡃
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⡆⣰⣶⣶⠀⢰⣶⣶⡆⠁⣶⣶⡀⣶⣶⠀⣶⣶⣶⡎⠋⣴⣶⣶⣦⡈⢰⣶⣶⣶⢰⣶⣶⣶⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⢺⡡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⠀⣿⡿⣿⣇⢸⣿⣿⠸⠿⠇⢸⣿⣇⣀⢸⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⢿⣿⠀⣿⣿⣹⣿⡄⣿⣿⣿⣿⣿⢸⣿⣇⣿⣿⢸⣿⣿⢶⣶⡆⢸⣿⡿⠿⢸⣿⣿⢻⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡿⣸⣿⢸⣿⡿⢻⣿⡇⣿⣿⢹⣿⣿⣸⣿⡟⣿⣿⡜⣿⣿⣸⣿⡇⢸⣿⣧⣤⢸⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠉⠁⠉⠁⠉⣉⣈⣉⣡⣌⣉⣁⠉⠉⡀⠉⠉⠉⠉⠁⠉⠉⠁⠈⠛⠋⣉⡁⠈⠉⠉⠉⠈⠉⠉⠈⠉⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣐⡀⠀⠀⠀⠀⠀⠘⠛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣵⣟⣿⣿⣿⣿⣿⣿⣿⣿⣬⣬⣷⣶⣾⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣷⣀⢀⣀⣤⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡜⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⡘⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣶⣿⠿⠿⠿⠿⠿⠛⠛⠉⠉⠻⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣹⣿⣿⣿⣇⠹⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣾⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣻⣿⣿⣿⣿⡧⠙⠛⠛⠁⠍⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣠⣠⣄⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣢⡿⢿⣿⣿⣷⠔⠰⠶⠶⠶⠀⠀⠀⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⠀⣿⣿⣿⣿⣿⡇⠀⠀⢀⣠⠀⠀⠀⢀⣤⡄⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡁⠀⣿⣿⣿⣿⣿⡇⠀⣦⡀⠙⠁⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⡀⠀⣿⣿⣿⣿⣿⠀⣀⣥⣤⣤⣋⠅⠀⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⣿⣿⣶⡄⠀⠀⠘⠟⠃⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠘⠃⠀⠛⠛⠛⠛⢡⣿⣿⣿⣿⣿⣿⣷⡄⡿⠛⠻⠟⠛⠋⠀⠀⠹⠿⠀⠀⠀⠀⠀⡿⠿⢿⣿⣿⠿⠟⠋⠙⠛⠉⠛⣿⣿⣿⣿⣿
⠀⠙⠁⠀⠛⠋⠉⠿⠉⠀⠀⠀⠉⠿⠃⠀⠀⠐⠋⠀⠀⠀⠀⢰⣾⠟⠛⠛⠀⠺⠿⠃⠀⠈⠉⠻⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠉⠀⠉
⣿⡆⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠁⠠⠠⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣆⢰⣶⣶⣶⣶⡆⠀⣶⣶⣶⡆⠀⠀⠀⣶⡆⠀⠀⠀⠰⣶⣶⣶⣶⠄⠰⢶⠶⠀⠰⢦⡽⠛⠛⡛⠛⠻⣿⣿⣿⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⢿⣿⣿⣿⡇⠀⠿⢿⣿⡇⠀⠀⠀⢙⡃⠀⠀⠀⣒⢿⣿⣿⣿⣷⡿⢻⣂⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⢀⣠⣭⣭⣿⣭⣭⣿⣻⡿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⣘⣿⣿⣿⣼⣿⣿⣿⣷⣶⣾⣿⣿⡇⠀⠀⠀⣾⣆⠀⢰⣶⣶⣶⣿⣿⢿⣣⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡟⠀⢸⣿⠿⠿⠟⠑⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⠿⠛⠛⢿⠿⠛⠛⠟⠛⠻⠟⠛⠻⠛⠛⠛⠻⣦⡀⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣷⣶⣶⡆⠀⠀⠀⣘⢷⣴⣞⡿⣡⣾⡇⠿⢿⣿⡿⠇⣿⣿⡇⣿⣿⢸⣿⣿⠿⢇⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣧⢸⣿⡇⣿⣿⡿⠇⣸⡟⢻⣻⣿⣷⣶⣯⣭⣟⣛⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠡⣟⣻⣻⣿⣛⣻⣿⠇⠀⠀⠀⢤⣿⣿⣿⠾⡟⣽⣿⡆⢸⣿⡇⠀⣿⣿⣶⣿⣿⢸⣿⣿⣤⡜⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣾⣿⡇⣿⣿⣧⡄⠙⣗⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⡿⠡⣻⣻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢠⣿⣒⣺⣽⡧⢋⢀⠃⢸⣿⡇⠀⣿⣿⡏⣿⣿⢸⣿⣿⠉⢵⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡏⠁⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣷⢉⣽⢯⣿⣿⣿⣟⡽⠯⡇⠀⠀⠀⠉⣿⣴⡿⣿⣿⣧⣺⠀⢸⣿⡇⠀⣿⣿⡇⣿⣿⢸⣿⣿⣶⡇⣿⢸⣿⣿⣶⢸⣿⣿⢸⣿⡇⢿⣿⡇⣿⣿⣷⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣈⣉⣛⣒⣋⣓⣊⣉⣛⣁⡀⠀⢀⣀⣛⣘⣊⣚⠐⠛⠓⠂⠀⠀⠀⠀⠀⠰⠶⣶⣶⣶⣦⣤⣴⣶⣿⣷⠦⠤⣴⣶⣤⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣻⣛⣛⣿⣟⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣶⣶⡆⣰⣶⣶⠀⢰⣶⣶⡆⠁⣶⣶⡀⣶⣶⠀⣶⣶⣶⡎⠉⣴⣶⣶⣦⡀⢰⣶⣶⣶⢰⣶⣶⣶⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⠀⣿⡿⣿⣇⢸⣿⣿⠸⠿⠇⢸⣿⣇⣀⢸⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⢿⣿⠀⣿⣿⣹⣿⡄⣿⣿⣿⣿⣿⢸⣿⣇⣿⣿⢸⣿⣿⢶⣶⡆⢸⣿⡿⠿⢸⣿⣿⢻⣿⡄⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠋⠉⠁⠘⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡿⣿⣿⢸⣿⡿⢻⣿⡇⣿⣿⢹⣿⣿⣸⣿⡟⣿⣿⡜⣿⣿⣸⣿⡇⢸⣿⣧⣤⢸⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠉⠁⠉⠁⢉⣉⣈⣉⣡⣌⣉⡁⠉⠉⣀⠉⠉⠉⠉⢁⠉⠉⢁⣌⣛⣋⣉⣁⣈⠉⠉⠉⣈⠉⢉⣈⢉⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⠀⠀⠀⠀⠀⠀⠈⢿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣷⣶⣶⠖⠂⠀⣠⣿⣿⣿⣿⣿⣿⠏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⡀⠀⠀⠀⠀⣀⣤⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣫⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⢣⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⡜⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⠋⠙⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡗⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣶⣿⠿⠿⠿⠿⠿⡛⡛⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠛⠛⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⢻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⢀⢀⣶⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡷⠘⠛⠛⠃⡍⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡿⢿⣿⣿⣷⠔⠰⠶⠶⠶⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⠏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡃⠀⣿⣿⣿⣿⣿⡇⣀⠀⢠⣄⡀⠀⠀⢀⣤⡄⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠤⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⠄⠀⣿⣿⣿⣿⣿⢿⣿⣿⠀⠙⠇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⡀⠀⣿⣿⣿⣿⣿⠀⠀⣁⣠⣴⣒⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⣼⣶⡄⠀⠀⠘⠿⠃⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠘⠃⠀⠛⠛⠛⠛⠉⢀⣾⣿⣿⣿⣿⣿⣷⡹⠟⠻⠟⠛⠋⠀⠀⠹⠿⠀⠀⠀⠀⠀⡿⠿⣿⣿⣿⢿⠟⠋⠙⠛⠉⠛⣿⣿⣿⣿⣿
⣤⣴⣤⠀⠀⠋⠉⠿⢋⣿⣿⠃⠙⠿⠃⠀⠀⠐⠃⠀⠀⠀⠀⢰⣶⠟⠛⠛⠀⠸⠿⠃⠀⠈⠉⠻⠀⠟⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠉⠀⠉
⣿⣿⣿⠆⠀⠀⠀⠀⣼⣿⣿⢀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠇⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⣠⣴⣿⣿⣿⡃⠀⣶⣶⣶⡆⠀⠀⠀⣶⡆⠀⠄⠀⠰⢖⣠⣴⣾⣿⣿⣿⣿⣷⣦⣤⣲⠘⠿⠿⠿⠿⠿⣿⣿⣿⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢁⣼⣿⣿⣿⢟⣹⡇⠀⠿⢿⣿⡇⠀⠀⠀⢓⡃⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⢾⣤⣤⣾⣿⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⣿⣿⡿⣻⣷⣶⣶⣿⣿⡆⠀⠀⠀⣾⡇⠀⢰⣼⣿⣿⢿⣿⢫⣷⣶⣿⣝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣭⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡷⠀⢸⡿⠿⠷⠎⠁⠉⠉⠉⠉⠉⠉⠈⠛⠛⠛⠛⠛⠛⠿⣿⡿⠛⠛⢿⠿⠛⠛⠟⠊⠙⠛⠉⠛⠋⠀⠀⠀⠀⢀⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⢺⣿⣶⣿⣿⣿⡏⠀⠿⢿⣿⡿⠇⣿⣿⡇⣿⣿⢸⣿⣿⠿⢇⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣧⢸⣿⡇⣿⣿⡿⠇⣀⣛⣛⣛⡻⣷⣶⣯⣭⣟⣛⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣛⣻⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⠀⢸⣿⡇⠀⣿⣿⣷⣿⣿⢸⣿⣿⣤⡜⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣾⣿⡇⣿⣿⣧⡄⢿⣿⣿⣍⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⠀⢸⣿⡇⠀⣿⣿⡏⣿⣿⢸⣿⣿⠉⢱⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡏⠡⠿⣿⣯⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣜⣾⣿⣿⣿⣿⣿⠟⠻⡇⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⣿⣿⡇⣿⣿⢸⣿⣿⣶⡇⣿⢸⣿⣿⣶⢸⣿⣿⢸⣿⡇⢿⣿⡇⣿⣿⣷⣶⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⢿⣌⣛⣛⣛⣛⣓⣛⣛⣓⣁⣀⠀⢀⣀⣛⣉⣛⣋⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣦⣤⡴⣶⣿⣷⠦⢤⣴⣶⣦⠶⠶⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣻⣙⣛⣿⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣃
⠉⠉⠀⠀⠀⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣶⣶⡆⣰⣶⣶⠀⢰⣶⣶⡆⠀⣶⣶⡀⣶⣶⠀⣶⣶⣶⡎⠉⣴⣶⣶⣦⡀⢰⣶⣶⣶⢰⣶⣶⣶⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⠀⣿⡿⣿⣇⢸⣿⣿⠸⠿⠇⢸⣿⣇⣀⢸⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠈⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⢿⣿⢀⣿⣿⣹⣿⡄⣿⣿⣿⣿⣿⢸⣿⣇⣿⣿⢸⣿⣿⢶⣶⡆⢸⣿⡿⠿⢸⣿⣿⢻⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣠⣠⣴⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡿⣿⣿⢸⣿⡿⢻⣿⡇⣿⣿⢹⣿⣿⣸⣿⡟⣿⣿⡌⣿⣿⣸⣿⡇⢸⣿⣧⣤⢸⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠉⠁⠉⠁⣉⣉⣈⣉⣡⣌⡉⠉⠉⢉⣀⠉⠉⠉⠉⡁⢉⣉⣡⣌⣛⣋⣉⡁⣈⠉⠉⠉⣈⠉⢉⣈⠉⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣿⣷⣶⠗⠂⠘⣿⣿⣿⣿⣿⣿⠁⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡜⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣫⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠻⠏⠁⠀⠀⢸⣿⣿⣿⣿⣿⣟⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡅⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⠇⠀⠀⠀⠲⢈⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣶⣿⠿⠿⠿⠿⢿⣛⣛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣆⣀⣀⠈⠀⠉⠛⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣠⣶⣶⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠻⠿⠏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⡿⡿⠉⠉⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣤⣤⣤⣤⣤⠀⠀⠠⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⠀⠈⣿⣿⣿⡇⠀⣤⡀⠙⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⡀⠀⢸⣿⣿⣿⣟⠀⢀⣠⣤⣤⣬⣃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⡿⠃⠀⠘⢻⣿⡇⠀⣿⣿⣦⡄⠀⠀⠘⠛⠃⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠘⠃⠀⠘⠛⠛⠛⢁⢰⣿⣿⣿⣿⣿⣿⣧⠻⠟⠻⠟⠛⠋⠀⠀⠹⠿⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⠿⠟⠋⠙⠛⠉⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣇⡀⠀⠀⠻⠋⠀⠀⠀⠉⠿⠃⠀⠀⠀⠂⠀⠀⠀⠀⢰⣶⠖⠒⠛⠀⠸⠿⠃⠀⠈⠉⠳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠉⠀⠉
⣿⣿⣿⡿⠃⠀⠀⠀⢀⡀⠀⣀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⡿⣿⡆⠀⠠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣶⣿⣿⣿⣿⣿⣇⣀⣶⣶⠶⡆⠀⠀⠀⢶⣢⣴⣶⣤⡄⠶⠦⣶⡶⠄⠰⠶⠦⠀⠰⠶⠶⠄⢰⠸⣿⣉⣁⣈⣉⣿⡇⣠⣴⣾⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠘⡯⡿⣿⣷⠐⠀⣃⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢋⣭⣭⣛⣛⣽⣭⣿⣭⣭⡍⠉⠉⠉⣭⡅⠀⢠⣤⣶⣶⣶⠶⣖⣢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣯⣭⣭⣟⠿⣿⣿⠟⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⢸⠿⣛⣭⡷⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⠿⠛⠛⠿⠟⠁⠈⠉⠉⠙⠉⠉⠁⠋⠁⠀⠀⠀⠀⢛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠐⠀⠀⡀⠚⣻⣿⡃⠿⢿⣿⡿⠇⣿⣿⡇⣿⣿⢸⣿⣿⠿⢇⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣧⢸⣿⡇⣿⣿⡿⠇⠀⣺⣿⣷⣿⣶⣶⣮⣭⣛⣛⡻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡆⡠⠀⠀⠀⠀⠀⣀⡨⠞⠀⠀⠀⠀⠀⠀⠀⠁⡈⠉⠽⠋⠀⢸⣿⡇⠀⣿⣿⣶⣿⣿⢸⣿⣿⣤⡜⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣾⣿⡇⣿⣿⣤⡄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⣛⡿⠿
⣿⣿⣿⣿⠃⠩⣛⣓⠮⣆⡂⠄⣾⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⡏⣿⣿⢸⣿⣿⠉⢱⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⠋⠁⠀⣞⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠛⠛⠉⢹⣷⠐⣂⢀⠈⠴⢇⡀⠌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⡇⣿⣿⢸⣿⣿⣶⡇⣿⢸⣿⣿⣶⢸⣿⣿⢸⣿⡇⢿⣿⡇⣿⣿⣷⣶⠀⢼⣽⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣄⣀⣐⣀⣀⣀⣀⣀⣂⣀⡀⠀⠀⣀⣀⣀⣀⡈⠐⠈⠒⠀⠀⠀⠀⠀⠠⠴⠶⣦⣴⣶⢦⣤⡴⣶⣿⡷⠦⢤⣴⣶⡦⠴⠶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣘⣉⣓⣉⣋⣛⣛⣛⣛⣛⣛⣻⣿⣿⣛⣃
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⡆⣰⣶⣶⠀⢰⣶⣶⡆⠁⣶⣶⡀⣶⣶⠀⣶⣶⣶⡆⠉⣴⣶⣶⣦⡀⢰⣶⣶⣶⢰⣶⣶⣶⣦⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣶⣆⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⠀⣿⡿⣿⣇⢸⣿⣿⠸⠿⠇⢸⣿⣇⣀⢸⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⢿⣿⠀⣿⣿⣹⣿⡄⣿⣿⣿⣿⣿⢸⣿⣇⣿⣿⢸⣿⣿⢶⣶⡆⢸⣿⡿⠿⢸⣿⣿⢻⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡞⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡿⣼⣿⢸⣿⡿⢻⣿⡇⣿⣿⢹⣿⣿⣸⣿⡟⣿⣿⡌⣿⣿⣸⣿⡇⢸⣿⣧⣤⢸⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⢻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠉⠁⠉⠁⢉⣉⣈⣉⣡⣌⣉⣁⡉⠉⠀⠉⠉⠉⠉⠁⠉⠉⠁⣈⣛⣋⣉⣁⣈⡉⠉⠉⠈⠉⠉⠈⠉⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢿⡸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣫⣵⣿⣷⢿⣿⣿⣿⣿⣿⣿⣬⣭⣷⣶⣶⠖⠂⠀⠀⢰⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣇⢿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣫⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠈⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⢿⣧⣤⣄⣀⠀⠀⠈⠂⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⣶⣿⠿⠿⠿⠿⠿⡛⠛⠛⠉⠙⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⣹⣿⣿⣿⣿⣾⣄⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣶⣖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣶⣦⣶⣶⣲⣦⣄⣀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣥⣤⣀⡄⣀⣤⣤⣤⣤⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣢⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⠿⢞⣽⣿⣿⣿⣝⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⡍⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠿⠉⠉⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠄⠀⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣤⣤⣤⣤⣤⠀⠀⠤⠤⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⣦⡀⠙⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⡀⠀⣻⣿⣿⡟⢋⠀⣀⣤⣤⣤⣜⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⡀⠀⢻⣿⣿⣿⡇⠀⣿⣿⣶⡄⠀⠀⠘⠿⠇⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠘⠃⠀⠙⠛⠑⠒⢡⣿⣿⣿⣿⣿⣿⣿⡄⡿⠟⠻⠟⠛⠋⠀⠀⠹⠿⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⠿⠟⠋⠛⠛⠉⠛⣿⣿⣿⣿⣿
⡿⣿⣿⡷⠀⠀⠉⠿⠋⠀⠀⠀⠉⠿⠃⠀⠀⠐⠂⠀⠀⠀⠀⢰⣶⠗⠛⠛⠀⠸⠿⠃⠀⠈⠉⠻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠉⠀⠉
⣿⣿⣿⠁⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠃⠀⢠⣴⣶⣶⣶⡆⠀⣶⣶⣶⡆⠀⠀⠀⣶⡆⠀⠀⠀⠰⣶⣴⣶⣶⠄⠰⠶⠶⠀⠰⢶⡶⠄⠀⣿⣿⣏⣉⠀⠩⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣄⣘⣿⡿⣿⣿⡇⠀⠿⢿⣿⠅⠀⠀⠀⢜⡁⠀⠀⠀⠲⠿⣿⣿⣿⣷⣿⣿⣠⠀⠀⢓⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣷⣶⣶⣿⡿⣳⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⡕⣶⣶⣷⣿⡆⠀⠀⠀⣾⡆⠀⢰⣶⣾⣶⣿⣿⣷⣿⣶⡶⢖⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣟⠿⣿⡇⠀⠀⠀⣿⡇⠀⠸⠿⠿⠿⠟⠋⠉⠉⠉⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⡿⠛⠛⠁⠋⠉⠙⠋⠉⠛⠋⠉⠛⠉⠀⠀⠀⠀⢀⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢐⡍⠻⠿⠛⢿⣿⣿⣷⣄⠂⠀⠀⠀⢸⣷⣦⣲⠼⠾⢟⡀⠿⢿⣿⡿⠇⣿⣿⡇⣿⣿⢸⣿⣿⠿⢇⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣧⢸⣿⡇⣿⣿⡿⠇⠀⣿⣿⣿⣿⣷⣶⣯⣭⣛⣛⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢸⣿⣽⣾⣶⣤⣌⠛⢿⣿⣷⣤⡀⠀⢨⣾⣿⠱⠾⣿⣿⣿⡆⢸⣿⡇⠀⣿⣿⣶⣿⣿⢸⣿⣿⣤⡜⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣾⣿⡇⣿⣿⣥⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⡜⠿⣟⣷⣿⣿⢞⣭⣧⡍⠿⣿⣿⣦⡘⢿⢆⡐⠞⣻⣿⣿⠇⢸⣿⡇⠀⣿⣿⡏⣿⣿⢸⣿⣿⠉⢱⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡏⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⢣⢾⣿⢝⣽⡿⣯⡵⠝⠫⡁⠹⠟⢿⡷⠈⡶⡫⣤⢭⣡⡶⠀⢸⣿⡇⠀⣿⣿⡇⣿⣿⢸⣿⣿⣶⡇⣿⢸⣿⣿⣶⢸⣿⣿⢸⣿⡇⢿⣿⡇⣿⣿⣷⣶⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠿⠿⢿⣿⣐⣐⣊⣊⣚⣓⣑⣑⣛⣓⣁⡀⠀⢀⣁⣀⣒⣒⣙⠒⠛⠓⠂⠀⠀⠀⠰⣶⠴⠶⣶⣶⣶⣦⣤⣴⣶⣿⣷⠦⢤⣶⣶⡤⠴⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣻⣃
⠀⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⡆⣰⣶⣶⠀⢰⣶⣶⡆⠁⣶⣶⡀⣶⣶⠀⣶⣶⣶⡆⠁⣴⣶⣶⣦⡀⢰⣶⣶⣶⢰⣶⣶⣶⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⠀⣿⡿⣿⣇⢸⣿⣿⠸⠿⠇⢸⣿⣇⣀⢸⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⢿⣿⢀⣿⣿⣹⣿⡄⣿⣿⣿⣿⣿⢸⣿⣇⣿⣿⢸⣿⣿⢶⣶⡆⢸⣿⡿⠿⢸⣿⣿⢻⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⡿⣿⣿⢸⣿⡿⢻⣿⡇⣿⣿⢹⣿⣿⣸⣿⡟⣿⣿⡜⣿⣿⣸⣿⡇⢸⣿⣧⣤⢸⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠉⠁⠉⠁⢉⣉⣈⣉⣡⣌⣉⣁⣉⠉⡀⠉⠉⠉⠉⢁⡉⠉⢁⢈⣛⣋⣉⣁⣈⣉⡉⠉⠈⠉⢉⡈⢉⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣷⣶⣶⠖⠂⠀⠂⢀⣼⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣫⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⢿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠛⠛⠈⠻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣶⣿⠿⠿⠿⠿⠿⡛⠛⠛⠛⠛⠿⠿⠿⠿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣽⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣷⣷⣶⣶⣶⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣵⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⡀⣀⣄⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢦⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⠀⢠⣤⡀⠀⠀⢠⣤⡄⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣤⣤⣤⣤⣤⡀⠀⡤⠤⠄⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⣦⣀⠙⠃⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⡀⠀⣿⣿⣿⣿⣿⠄⠀⢁⣠⣤⣥⣥⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠐⣿⣿⣷⡄⠀⠀⠘⠿⠇⠀⠃⠀⠙⠛⠛⠛⠛⠛⠀⠚⠃⠀⠛⠛⠛⠛⢉⡀⣴⣿⣿⣿⣿⣿⣿⣟⠟⠻⠟⠛⠋⠀⠀⠹⠿⠀⠀⠀⠀⠐⡿⠿⣿⣿⣿⢿⠟⠋⠻⠛⠉⠻⣿⣿⣿⣿⣿
⠀⠙⠁⠀⠛⠋⠉⠿⠋⠁⠀⠀⠙⠿⠃⠀⠀⠐⠋⠁⠀⠀⠀⢸⣿⠟⠛⠛⠀⠺⠿⠃⠀⠉⠉⠻⠀⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠉⠀⠉
⠀⣀⡀⠀⢀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠈⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠧⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⡆⠀⢰⣶⣶⣶⣶⡆⠀⣶⣶⣶⡆⠀⠀⠠⣶⡆⠀⠄⠀⠰⣶⣴⡶⣶⠆⢰⣶⡶⠀⢰⣶⣶⠆⢰⡖⣾⣿⣿⣿⣿⣿⣿⣿⠷⠶⢶⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⣟⡇⠀⠘⠻⣷⣿⣿⣿⣷⣯⣭⣿⣯⣤⣬⣭⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡇⠀⢸⣿⣿⣿⣿⣷⣶⣿⣿⣿⡆⠀⠀⠀⣾⣧⠀⢐⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡿⠀⢸⣿⡿⢾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢿⣿⡿⠛⠻⢿⠿⠛⠛⠟⠛⠻⠟⠛⠻⠛⠛⠓⠠⣤⣀⠛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣌⣩⢶⣾⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣶⣿⣿⣿⣇⠀⠿⣿⣿⡿⠇⣿⣿⡇⣿⣿⢸⣿⣿⠿⢇⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣧⢸⣿⡇⣿⣿⡿⠇⣸⣿⡛⢺⣿⣷⣶⣿⣽⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⢸⣿⣿⣤⡜⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣾⣿⡇⣿⣿⣧⡌⠻⣯⢙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⠀⣿⣿⡇⠀⣿⣿⡏⣿⣿⢸⣿⣿⠉⢵⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡏⠁⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⢸⣿⣿⣶⡇⣿⢸⣿⣿⣶⢸⣿⣿⢸⣿⡇⢿⣿⡇⣿⣿⣷⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣈⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀⣀⣀⣐⣛⣙⣛⣛⠛⠛⠛⠂⠀⠀⠀⢠⠰⠴⡶⢶⣶⣶⣶⣤⣴⣾⣿⣷⠶⢤⣶⣶⣶⠶⠦⠀⣤⠀⠀⠀⠀⠀⠀⠀⠠⠟⣻⣻⣛⣿⣿⣛⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣶⣶⡆⣴⣶⣶⠀⢰⣶⣶⣆⠀⣶⣶⡀⣶⣶⠀⣶⣶⣶⡎⠋⣴⣶⣶⣦⡀⢰⣶⣶⣶⢰⣶⣶⣶⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⢀⣿⡿⣿⣇⢸⣿⣿⠸⠿⠇⢸⣿⣇⣀⢸⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⢸⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⣿⣿⢀⣿⣿⣹⣿⡄⣿⣿⣿⣿⣿⢸⣿⣇⣿⣿⢸⣿⣿⢶⣶⡆⢸⣿⡿⠿⢸⣿⣿⢻⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⢻⣿⡇⣿⣿⢹⣿⣿⣸⣿⡟⣿⣿⡜⣿⣿⣸⣿⡇⢸⣿⣧⣤⢸⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⠉⣁⡉⠁⢉⣉⣈⣉⣡⣌⣉⣉⠉⢉⣈⣉⢉⡉⠉⣁⡉⠉⢁⣌⣛⣋⣉⣡⣌⠉⠉⢉⣈⣉⣉⣈⣉⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣷⣶⠗⠂⠐⣂⣾⣿⣿⣿⣿⣿⠏⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣻⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⢿⣿⣿⣿⣿⣿⠋⠀⠘⠛⠋⠁⠀⠈⠟⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣶⣿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠙⠋⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢏⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣤⣀⣤⣤⣶⣾⣿⣿⣶⣶⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⢀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠿⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢿⢿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⣿⣿⣿⣿⣿⡏⠁⠀⣀⣀⡀⠀⠀⢀⣤⡄⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⣤⠄⠀⣤⡤⠄⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⣦⡈⠙⠇⠀⠀⢸⣿⡇⠀⡆⠀⣿⣿⣿⣿⣿⣿⡿⠁⡀⠀⣿⣿⣿⣿⣿⡅⠀⠉⢀⣐⣓⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠐⣿⣿⣶⡄⠀⠀⠸⠿⠇⠀⠃⠀⠹⠿⠿⠿⠿⠛⠃⠚⠃⠀⠛⠛⠛⠛⠋⡀⢀⣶⣿⣿⣿⣿⣿⣿⠿⠻⡿⠛⠋⠀⠀⢻⠿⠀⠀⠀⠀⢸⡿⠿⣿⣿⣿⢿⡿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿
⠉⠙⠁⠀⠻⠋⠙⡿⠋⠁⠀⠉⠹⡿⠇⠀⠀⠐⠂⠀⠀⠂⠀⢰⣿⠟⠛⠛⠀⠾⡿⠃⠀⠉⠉⠿⠀⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠿⡿⠋⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⢈⣁⣀⣀⢠⡀⢀⣀⡀⠀⢀⣀⢀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⡆⠀⢴⣶⣶⣶⣶⡆⠀⣶⣶⣶⡆⠀⠀⠠⣶⡦⠀⠄⠀⢰⣶⣦⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⠆⢰⡆⠀⣼⣿⣿⣿⣿⣿⣿⣯⣿⣷⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡇⠀⢸⣿⣿⣿⣿⡧⠀⣿⢿⣿⡇⠀⠀⠀⣟⡇⠀⠀⠀⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣿⡇⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⣾⣧⠀⢴⣴⣿⣾⣿⣿⣿⣷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠀⢸⣿⣿⣿⠟⠛⠛⠙⠙⠛⠃⠉⠛⠛⠛⠿⠛⠛⠛⢿⣿⡿⠛⠻⢿⠿⠛⠻⠟⠛⠻⠛⠛⠛⠛⠁⠀⠀⠀⣀⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⣿⣷⣶⣿⣿⣿⣿⠀⠿⣿⣿⡿⠇⣿⣿⡇⣿⣿⢸⣿⣿⠿⢇⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣧⢸⣿⡇⣿⣿⡿⠧⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣯⣻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⢸⣿⣿⣤⡜⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣾⣿⡇⣿⣿⣧⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⣿⣿⡟⣿⣿⢸⣿⣿⠉⢵⣿⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡏⠡⣤⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⢸⣿⣿⣾⡇⣿⢸⣿⣿⣾⢸⣿⣿⢸⣿⡇⢿⣿⡇⣿⣿⣷⣷⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣙⣛⣛⣛⣛⣛⣻⣓⣃⡀⠀⣀⣒⣛⣻⣛⣛⠛⠛⠛⠷⠀⠀⠀⠀⠀⠰⠶⣤⣶⣶⣶⣶⣶⣾⣿⣷⠶⣶⣶⣶⣶⠶⠆⠠⣄⠀⠀⠀⠀⠀⠀⠐⠦⢚⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣶⣶⡆⣴⣶⣶⠀⢰⣶⣶⣆⠁⣶⣶⡀⣶⣶⠀⣶⣶⣶⡎⠋⣴⣶⣶⣦⡄⢰⣶⣶⣶⢰⣶⣶⣶⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⢀⣿⡿⣿⣧⢸⣿⣿⠸⠿⠇⢸⣿⣇⣀⢸⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠋⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⣿⣿⢀⣿⣿⣹⣿⡄⣿⣿⣿⣿⣿⢸⣿⣇⣿⣿⢸⣿⣿⢶⣶⡆⢸⣿⡿⠿⢸⣿⣿⢿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⣿⣿⣿⢸⣿⣿⢻⣿⡇⣿⣿⢹⣿⣿⣸⣿⡟⣿⣿⡜⣿⣿⣸⣿⡇⢸⣿⣧⣤⢸⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⡉⣁⡉⣁⣉⣉⣈⣉⣁⣨⡉⠉⠉⢉⣈⡉⢉⡉⠉⣁⣉⢉⣡⣌⣛⣋⣉⣡⡈⣉⣉⣉⣈⣉⣉⣈⣉⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣾⣭⣿⣿⣿⢟⡃⠶⣸⣿⣿⣿⣿⣿⣿⠏⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣻⣭⣾⣿⣿⣾⡿⠿⢿⣿⠿⠋⠀⠘⣿⣿⣿⠟⠁⠉⠻⢄⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⠁⢄⠈⠨⠉⣼⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣶⣿⣿⡿⠿⠿⠿⠀⠀⠀⠀⠴⠟⠋⠑⠀⠀⠀⠀⠀⠂⠀⠈⠙⠛⠋⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣽⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣦⣶⣶⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⣃⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠿⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3411

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/19/working-peasants-for-campinos/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/19/working-peasants-for-campinos/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.19.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ New_Ways_of_Working_for_António_Campinos,_Even_From_One’s_Own_Home_During_a
Crisis⠀✐


Posted in Europe, Patents at 9:26 am by Dr. Roy Schestowitz


Video_download_link | md5sum 2c262586c7d77d6801a59b7498527bf3


http://techrights.org/videos/epo-work-changes.webm


Summary: The European Patent Office (EPO) is taking advantage of a pandemic to
take away basic rights of staff; in the video above, which is based on the
document below, I give my personal views/thoughts


The Central Staff Committee (CSC) of the EPO wrote to António_Campinos about
his proposal for the pandemic, seeing that Europe is again the “epicenter” of
the COVID-19 health crisis, with Germany on exceptionally high alert at the
moment.


On “New ways of working,” the CSC wrote (alluding to something published by
Team Battistelli/Campinos), much needs to be said. They were preparing for a
meeting when they wrote it. “Proposal in preparation of the GCC meeting” was
the title circulated with this open letter. “In a meeting with the President on
16 November,” they noted, “the Central Staff Committee (CSC) addressed some
problematic aspects of “New ways of working”. We are now making concrete
proposals in order to address the issues of core time and flexi-hours.”


That was 3 days ago. I’ve converted the letter into HTML and decided to record
a quick video, seeing that this is a very “tech rights” issue, especially at
times of significance change and when self-serving management exploits the
pandemic the tilt the systems in their own favour at workers’ expense, often
discarding basic rights, e.g. extensively spying on employees. A week ago the
EPO’s President was promoting European_software_patents under the guise of “Hey
Hi” (in relation to JPO), but today’s issue is less technical and more to do
with human rights.


Here’s the open letter in full:


     European Patent Office | 80298 MUNICH | GERMANY


     Mr António Campinos
     President of the EPO


     By email


     OPEN LETTER


     Reference: sc21133cl
     Date: 18/11/2021


     Preparation of the consultation on GCC/DOC 24/2021 (CA/77/21): “New
     ways of working”


     Dear Mr President,


     The topic of “New ways of working” is of interest to all staff and is
     essential for the performance and future of our Organisation. The
     Central Staff Committee believes that a jointly agreed text should be
     possible. Compared to the current applicable statutory regulations
     (especially on Part-Time Home Working), we appreciate your intention
     to extend geographical flexibility for all staff.


     First, we take note that the period of notice according to Article 7
     (5) will be aligned with the current Part-Time Home Working provision
     and set at two months. Second, we welcome your willingness to extend
     the transitional provisions (Article 17) to children under the age of
     4. Third, we understand that the entry into force (and presumably the
     period of the transitional measures) will be extended in accordance
     with the development of the pandemic.


     There are however still some issues which need to be resolved and
     reflected in an amended version of the Circular for consultation in
     the General Consultative Committee (GCC). Our proposals are the
     following:


     1. Core-time and flexi-hours


     Current_proposal:


     Article 15(1): “All provisions of the Guidelines on arrangements for
     working hours concerning the accrual of flexi-hours and the
     establishment of core time are suspended by the Circular.”


     Argument:
     Flexi-hours (as they are called) are a means for flexibility in
     managing one’s working time/schedule, when working on the Office
     premises. Teleworking is actually a means for flexibility in working
     location. Hence, the two concepts are entirely different. Creating
     one and removing the other does not mean increasing flexibility,
     rather it removes one form of flexibility and introduces another,
     where the beneficiaries are not the same.


     A group of at least 25% of staff declared that they are not
     interested in geographical flexibility and others might not be
     allowed to make use of it due to the nature of their tasks. This
     group would be negatively affected by the reform as well as all
     others planning to work partly in the Office’s buildings.


     In the current proposal, the Working time framework (Article 3 of the
     guidelines on arrangement for working hours, PART 4j CODEX) still
     sets the working day at a minimum of six hours (maximum ten hours)
     and the minimum working week at 35 hours (maximum 48 hours). The
     abolition of accrual of flexi-hours would remove any possibility for
     staff to deviate from this framework. In addition, flexi-hours
     accrual is very simple to administrate and gives visibility and
     predictability for management, while helping staff to manage their
     work-life balance.


     The New Normal staff survey results show that 82% of staff want
     flexibility in working times and 73% are interested in the removal of
     core-hours. We understand that, for the Human Resources Department,
     both are linked. In order to meet both ends, we propose to abolish
     accrual of flexi-hours only on days of teleworking and to change the
     purpose of core-hours to define them as a preferred timeslot for
     joint meetings, thus also for strengthening the “sense of belonging”.


     Our_proposal:
     Article 15(1): “All provisions of the Guidelines on arrangements for
     working hours concerning the accrual of flexi-hours on_days_of
     teleworking and the establishment of core time are suspended by the
     Circular. Core-time as set out in the Guidelines on arrangements for
     working hours should be the preferred timeslot for the purpose of
     Article 7(1)(b) and Article 8(1)(d).”


     2. Fast joint conflict resolution panel


     Argument:
     The Circular does not define clear procedures and steps for negative
     decisions on teleworking, and the criteria remain vague. Teleworking
     has a significant impact on personal and family planning which cannot
     be reconciled with long delays incurred by the management review and
     internal appeal systems, let alone the AT-ILO as the ultimate end of
     any dispute.


     We understand that the administration is currently reluctant to set
     up a fast joint conflict resolution panel.


     In order to move forward, we propose that this topic be revisited at
     the time of the review. We also understand that in the meantime the
     staff and Office will try to solve arising conflicts expeditiously,
     using the existing internal means of redress.


     Our_proposal:
     An addition in Article 16(1): “The review shall involve the
     monitoring of cases of conflict arising from the implementation of
     the Circular and an evaluation of the suitability of the existing
     means of redress on this topic.“


     3. Health & Safety


     We are still waiting for the opinion of the COHSEC with respect to
     Health & Safety matters on the document.


     We are looking forward to a fruitful discussion in the GCC. We would
     appreciate receiving an amended text reflecting our proposals above
     and would of course agree to waive our right to the deadline for
     submission to the GCC.


     Yours sincerely,


     Alain Dumont
     Chairman of the Central Staff Committee


The short story is, there is an ongoing inquiry (survey) about how staff feels
after more than a year working from home, at least part of the time. Expect
more of this in light of the Austrian news.


As we’ve seen many times before, ILO-AT (or AT-ILO, same thing) is clearly too
slow to react to abuses against staff, especially a new modality of abuse (off-
site labour). Working from home isn’t as simple as it sounds. It’s not like
being “on holiday”; there are health implications, lack of access to various
facilities that are expected in an organised and centralised workplace, and no
access to supportive supervisors (yes, some do exist and a good supervisor can
provide help and comfort, not fear). █



                    ䷩ 𝚕𝚒𝚗𝚎 3638

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.19.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_19/11/2021:_Arcan_0.6.1_and_FreeBSD_12.3_RC2⠀✐


Posted in News_Roundup at 5:38 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⠀➾


                # ⚓ Arcan_0.6.1⠀⇛


                       Time for another fairly beefy Arcan release. For
                       those thinking in semantic versioning still
                       surprised at the change-set versus version number
                       here (‘just a minor update?’) do recall that as per
                       the roadmap, disregarding the optimistic timeline,
                       we work with release-rarely-build-yourself thematic
                       versions until that fated 1.0 where we switch to
                       semantic and release-often.


                       On that scale, 0.5.x was the display server role,
                       0.6.x is focused on the networking layer as the
                       main feature and development driver. 0.7.x will be
                       improving audio and some missing compatibility/3D/
                       VR bits. Then it gets substantially easier/faster –
                       0.8.x will be optimization and performance. 0.9.x
                       will be security — hardening attack surface,
                       verification of protections, continuous fuzzing
                       infrastructure and so on.


          o § Server⠀➾


                # ⚓ Istio_1.12_Upgrade_Notes⠀⇛


                       When you upgrade from Istio 1.10.0 or 1.11.0 to
                       Istio 1.12.0, you need to consider the changes on
                       this page. These notes detail the changes which
                       purposefully break backwards compatibility with
                       Istio 1.10.0 and 1.11.0. The notes also mention
                       changes which preserve backwards compatibility
                       while introducing new behavior. Changes are only
                       included if the new behavior would be unexpected to
                       a user of Istio 1.12.0.


                # ⚓ Istio_1.12_Change_Notes⠀⇛


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_use_DD_command_and_how_to_burn_ISO_using_it_–
                  Unixcop_the_Unix_/_Linux_the_admins_deams⠀⇛


                       Copying your data as well as backing them up is a
                       day-to-day tasks that we perform regularly. Thus we
                       need a utility to perform these tasks. And as in
                       case of Linux, we can do what we want in various
                       ways using different utilities. Then, our utility
                       today is dd command. As we know everything in Linux
                       is a file and is treated according to this rule
                       even block devices. Which makes dd is useful to
                       copy and backup our data.


                # ⚓ How_To_Install_Mono_on_Linux_Mint_20 [Ed: Very bad idea.
                  This is a Microsoft pandemic, trying_to_infect_everything_in
                  order_to_undermine_it.]⠀⇛


                # ⚓ How_to_Upgrade_to_Ubuntu_22.04_–_Linux_Nightly⠀⇛


                       This guide will show how to upgrade to Ubuntu 22.04
                       Jammy Jellyfish, which is the latest LTS version of
                       the operating system.


                       Canonical releases new LTS (long term support)
                       versions of Ubuntu every two years, in April. They
                       also release interim editions every six months.


                       It’s always recommended that you keep Ubuntu up to
                       date with the latest LTS release. Interim versions
                       are okay to skip, unless you want to get a sneak
                       preview on new features to come.


                # ⚓ Remove_an_expired_key_in_APT_–_Unixcop_the_Unix_/_Linux_the
                  admins_deams⠀⇛


                       Hello, dear friends. Although it is not always
                       recommended, many times to get recent versions of a
                       package or a whole program, we need to add external
                       repositories. Usually, these repositories have a
                       GPG key that allows us to secure the installation.
                       What happens when these GPG keys expire? Well, it
                       is no longer possible to use the repository. So in
                       this post, you will learn how to remove an expired
                       key in APT.


                # ⚓ How_to_Install_Rundeck_on_Ubuntu_20.04⠀⇛


                       Rundeck is a free open-source software for
                       automation services. It gives self-service access
                       to the processes and tools they need to get their
                       job done. Using Rundeck you can create automation
                       workflows from existing tools or scripts. It
                       provides a web console, CLI tools, and a Web API to
                       run automation tasks.


                       In this tutorial, we learn how to install the
                       Rundeck community on Ubuntu 20.04.


                # ⚓ How_to_Install_AlmaLinux_8.5_Step_by_Step⠀⇛


                       As CentOS 8 draws steadily to End of Life on
                       December 31st, 2021, efforts have been made to come
                       up with centos alternative distributions which will
                       fill in the big shoes left by CentOS 8. This comes
                       following RedHat’s decision to dump CentOS 8 in
                       favor of CentOS Stream, something which has
                       elicited mixed reactions.


                       Many users have felt betrayed by RedHat’s move to
                       cut short the life of CentOS 8 by 9 years. A good
                       number have also expressed their concerns about the
                       stability and security that CentOS Stream will
                       provide.


                # ⚓ Using_MangoHud_to_check_FPS,_CPU_&_GPU_usage_on_a
                  ‘hackendeck’_–_CNX_Software⠀⇛


                       Previously I followed Valve’s documentation to
                       build a ‘hackendeck’ using a mini PC to emulate
                       their highly anticipated Steam Deck. Interestingly
                       the ‘hackendeck’ uses a Linux OS, specifically
                       Manjaro, as whilst Valve based their earlier
                       version of Steam OS on Debian, they have now
                       switched to being based on Arch.


                       If the ‘hackendeck’ had just been Steam on Windows
                       then to review gaming performance I’d just use MSI
                       Afterburner. Until now, however, for Linux, I’ve
                       always had to estimate the average FPS as I’ve not
                       been aware of a good reliable equivalent.


                       Fortunately several ‘commenters’ recommended using
                       MangoHud, a Linux open-source Vulkan/OpenGL overlay
                       for monitoring FPS, CPU/GPU usage, and temperatures
                       similar to MSI Afterburner. So now I’ve been able
                       to capture the average frame rate for the games I
                       previously tested and I’ll present them below.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ On_(hopefully)_taming_Webkit_and_getting_better
                        privacy_in_GNOME_Web_with_Privoxy.⠀⇛


                             Really, it would be nicer if Apple would just
                             double the amount of filter rules allowed in
                             Content Blockers, but it seems they really
                             can’t do much about users who take Privacy
                             matters into their own hands, even on Mac OS,
                             as Privoxy apparently works on Mac OS too!


                             Privoxy has been around for 20 years or so
                             and previously went under the name Internet
                             Junkbuster. In fact, it was one of my ad
                             blocking Hosts files that was used as the
                             basis for the early Junkbuster list.


                             I got fed up with ads and Windows adware in
                             the late 90s and felt like I could take on
                             the problem of blocking it, and for a while I
                             was correct. However, HOSTS files are no
                             answer for today’s problems on the Web, and
                             Windows will try to revert any changes you
                             make to it with “Defender” anyway if you use
                             Windows.


                             And if you successfully make it ignore that
                             and allow the modifications, Windows
                             Telemetry spyware is IMPOSSIBLE to block with
                             the HOSTS file because it will ignore you if
                             you ad their telemetry sites to it!


                             You really should not use Windows….


                             Back to Privoxy…. It will not interfere with
                             your VPN software, or at least it shouldn’t
                             (it doesn’t with my setup, using NordVPN),
                             because it is a local proxy. It should
                             enhance the privacy your VPN gives you. In
                             fact, it used to be part of the Tor Browser
                             Bundle.


          o § Distributions⠀➾


                # § BSD⠀➾


                      # ⚓ FreeBSD_12.3-RC2_Now_Available⠀⇛



                             The second RC build of the 12.3-RELEASE
                             release cycle is now available.

                             Installation images are available for:

                             o 12.3-RC2 amd64 GENERIC
                             o 12.3-RC2 i386 GENERIC
                             o 12.3-RC2 powerpc GENERIC
                             o 12.3-RC2 powerpc64 GENERIC64
                             o 12.3-RC2 powerpcspe MPC85XXSPE
                             o 12.3-RC2 sparc64 GENERIC
                             o 12.3-RC2 armv6 RPI-B
                             o 12.3-RC2 armv7 BANANAPI
                             o 12.3-RC2 armv7 CUBIEBOARD
                             o 12.3-RC2 armv7 CUBIEBOARD2
                             o 12.3-RC2 armv7 CUBOX-HUMMINGBOARD
                             o 12.3-RC2 armv7 RPI2
                             o 12.3-RC2 armv7 WANDBOARD
                             o 12.3-RC2 armv7 GENERICSD
                             o 12.3-RC2 aarch64 GENERIC
                             o 12.3-RC2 aarch64 PINE64
                             o 12.3-RC2 aarch64 PINE64-LTS

                             Note regarding arm SD card images: For
                             convenience for those without
                             console access to the system, a freebsd user
                             with a password of
                             freebsd is available by default for ssh(1)
                             access.  Additionally,
                             the root user password is set to root.  It is
                             strongly recommended
                             to change the password for both users after
                             gaining access to the
                             system.

                             Installer images and memory stick images are
                             available here:

                             https://download.freebsd.org/ftp/releases/
                             ISO-IMAGES/12.3/

                             The image checksums follow at the end of this
                             e-mail.

                             If you notice problems you can report them
                             through the Bugzilla PR
                             system or on the -stable mailing list.

                             If you would like to use SVN to do a source
                             based update of an existing
                             system, use the "releng/12.3" branch.

                             A summary of changes since 12.3-RC1 includes:

                             o Updates to the igc(4) driver.

                             o BEAGLEBONE and RPI3 SoC images have been
                             removed, due to late
                               discovered issues.

                             A list of changes since 12.2-RELEASE is
                             available in the releng/12.3
                             release notes:

                             https://www.freebsd.org/releases/12.3R/
                             relnotes/

                             Please note, the release notes page is not
                             yet complete, and will be
                             updated on an ongoing basis as the 12.3-
                             RELEASE cycle progresses.

                             === Virtual Machine Disk Images ===

                             VM disk images are available for the amd64,
                             i386, and aarch64
                             architectures.  Disk images may be downloaded
                             from the following URL
                             (or any of the FreeBSD download mirrors):

                             https://download.freebsd.org/ftp/releases/VM-
                             IMAGES/12.3-RC2/

                             The partition layout is:

                                 ~ 16 kB - freebsd-boot GPT partition type
                             (bootfs GPT label)
                                 ~ 1 GB  - freebsd-swap GPT partition type
                             (swapfs GPT label)
                                 ~ 20 GB - freebsd-ufs GPT partition type
                             (rootfs GPT label)

                             The disk images are available in QCOW2, VHD,
                             VMDK, and raw disk image
                             formats.  The image download size is
                             approximately 135 MB and 165 MB
                             respectively (amd64/i386), decompressing to a
                             21 GB sparse image.

                             Note regarding arm64/aarch64 virtual machine
                             images: a modified QEMU EFI
                             loader file is needed for qemu-system-aarch64
                             to be able to boot the
                             virtual machine images.  See this page for
                             more information:

                             https://wiki.freebsd.org/arm64/QEMU

                             To boot the VM image, run:

                                 % qemu-system-aarch64 -m 4096M -cpu
                             cortex-a57 -M virt  \
                             	-bios QEMU_EFI.fd -serial telnet::
                             4444,server -nographic \
                             	-drive if=none,file=VMDISK,id=hd0 \
                             	-device virtio-blk-device,drive=hd0 \
                             	-device virtio-net-device,netdev=net0 \
                             	-netdev user,id=net0

                             Be sure to replace "VMDISK" with the path to
                             the virtual machine image.
          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ 5750_Scottish_children_code_to_raise_awareness_of
                        climate_change_with_Code_Club⠀⇛


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Should_you_clear_your_app_cache_on_Android?⠀⇛


                      # ⚓ Best_Android_app_deals_of_the_day:_Exploding_Kittens,
                        Despotism_3k,_KORG_Kaossilator,_more_–_9to5Toys⠀⇛


                      # ⚓ How_To_Connect_An_Xbox_Wireless_Controller_To_Your
                        Android_Phone⠀⇛


                      # ⚓ 2022_Android_flagships_are_tipped_to_upgrade_to_~150W
                        charging_speeds_thanks_to_new_Qualcomm_technology_–
                        NotebookCheck.net_News⠀⇛


                      # ⚓ Samsung_brings_Android_12_privacy_to_Galaxy_S21
                        series⠀⇛


          o § Free, Libre, and Open Source Software⠀➾


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Mozilla_loading_full_page_ads_for_their_VPN_
                              (they_just_resell_Mulvad_VPN).⠀⇛


                                   This behavior is beyond annoying and
                                   not at all welcome on the part of the
                                   user. Not only does Mozilla do this
                                   over and over again (I had it happen
                                   more than once), but they load it in
                                   your private windows too.


                                   This time, there’s two more checkboxes
                                   to find (good luck). Hint: “recommend
                                   extensions as you browse” and
                                   “recommend features as you browse”. But
                                   this shouldn’t be necessary and using
                                   Mozilla software is becoming the
                                   literal….Look, next year Webster’s
                                   English Dictionary is going to have to
                                   put the Firefox logo as the definition
                                   of “annoying”.


                                   Brave, a competing web browser, has a
                                   regular “private” window which just
                                   means no history logging on your
                                   device, but also Private Windows with
                                   Tor. It also works atop your VPN if you
                                   want to access Tor hidden services.


                            # ⚓ Ring_doorbells_no_longer_support_Firefox_for
                              live_view._Recommend_Google_Chrome,_Microsoft
                              Edge.⠀⇛


                                   Mozilla could probably hack their way
                                   around this one with a UA quirk, but
                                   will just let company after company
                                   keep destroying what’s left of their
                                   browser business while they send “Web
                                   Compat” emails that go right into the
                                   trash to outfits like Facebook,
                                   Microsoft Skype, and now Amazon.


                # § FSF⠀➾


                      # ⚓ FSF_Giving_Guide:_Freedom_is_the_greatest_gift_of
                        all⠀⇛


                             It seems like the usual holiday sales just
                             get earlier and earlier. Not content with
                             just hammering us with ads, certain
                             megalithic companies named after large rivers
                             or fruits try to foist their “deals” on us as
                             soon as they can. Given the degree to which
                             our lives are mediated by technology, it’s no
                             surprise that so many holiday sales focus on
                             “devices,” that catch-all name we’ve given to
                             those computers that run in our pockets,
                             laps, and living rooms. Yet before you cave
                             to pressure, you should make sure that gift
                             isn’t putting your friend or family member
                             under unjust control.


                             For the last twelve years, the Free Software
                             Foundation (FSF) has published our Ethical
                             Tech Giving Guide as a way to help concerned
                             individuals make sure that the gift they
                             might plan on giving their loved ones doesn’t
                             deprive them of their freedom. It’s natural
                             to want the very best gift for that special
                             person in your life. It’s also natural to
                             want that gift to last them as long as
                             possible. But if you plan on giving any
                             devices, it’s important to carefully consider
                             the gift that you choose and the message it
                             sends. The Amazon Echo or Chromebook that
                             you’re buying today has a good chance of
                             being obsolete in the next few years, and
                             more importantly, could set your friend or
                             family member’s digital freedom back even
                             longer.


                             Freedom is the best gift you can give, and
                             the one that keeps on giving. Rather than
                             purchasing that new gadget, we encourage you
                             to take the time to explore installing free
                             software on one your friend or family member
                             already owns. Taking your first steps to
                             freedom often doesn’t just help you win back
                             your digital autonomy: it provides an
                             opportunity for you to deepen your
                             relationship with the ones you care about
                             through a shared learning experience, and
                             inaugurates you into a worldwide community of
                             users.


                # § Programming/Development⠀➾


                      # ⚓ Intel_Releases_ControlFlag_1.0_For_AI-Driven
                        Detection_Of_Bugs_Within_C_Code_–_Phoronix⠀⇛


                             Intel last month open-sourced “ControlFlag”
                             for finding bugs within source code by using
                             AI with training off more than a reported one
                             billion lines of code. Intel has said they
                             have successfully been using it within their
                             software from applications down to firmware.
                             The new milestone today is ControlFlag 1.0
                             being released.


                      # ⚓ Display_Git_Configuration⠀⇛


                             From time to time I tend to forget what’s my
                             effective Git configuration, so I have to
                             check it somehow. Most of the time I’d simply
                             do the following: [...]


          o § Standards/Consortia⠀➾


                # ⚓ XMPP,_A_Comeback_Story:_A_20_Year_Old_Messaging_Protocol
                  For_Robust,_Private_and_Decentralized_Communications⠀⇛


                       XMPP has a huge potential to replace platforms like
                       Telegram, Signal, and WhatsApp, although its use
                       hasn’t reached mass consciousness. Rather then
                       spread awareness of friendly and open technologies
                       like these, big tech companies preferred to build
                       their proprietary solutions ontop of XMPP and
                       market those instead – so you may have been using
                       XMPP this whole time without even knowing it.


                       Instead of depending on proprietary centralized
                       chat platforms like Telegram, WhatsApp and Signal
                       we believe that truly decentralized platforms like
                       XMPP can achieve and surpass our needs.


    * § Leftovers⠀➾


          o ⚓ Surveying_the_Wreckage_of_the_World_and_Wondering_Where_Habermas
            Fits_in_These_Days⠀⇛


                 A military rife with sexual abuse, universities that lack
                 courage to defend freedom of inquiry, a healthcare system
                 that is crumbling beneath too heavy loads, violence
                 against stressed-out and fearful healthcare workers,
                 governments that reek of incompetence of stupid decision-
                 making, a culture that denies science and evidence,
                 churches that advocate reconciliation without justice.
                 God, is every institution, the NHL included, covering up
                 bad and dirty deeds, demeaning some members of our
                 society or sweeping the dirt under some grimy rug
                 somewhere? An inquisitorial and accusatory spirit is
                 roaming the land. Who and what might be next?


                 Watched the news this morning, O boy, and learned that
                 some healthcare workers don’t want to be vaccinated.
                 What? The stability and surety of daily life is eroding
                 before my eyes. Marx’s words in The Communist Manifesto
                 of 1848 – “All that is solid melts into the air, all that
                 is holy is profaned and man is at last compelled to face
                 with sober sense, his real conditions of life, and his
                 relation to his kind” – capture our dreadful time of
                 troubles.


          o ⚓ Inside_the_Hell_That_Is_The_Many_Saints_of_Newark⠀⇛


                 The long-running HBO series The Sopranos often ventured
                 into Hell—or, more narrowly defined, into realms beyond
                 death where things feel bad and very little changes. The
                 Many Saints of Newark, a feature film prequel released
                 this year, begins in Hell, with a snaking shot through a
                 graveyard and, in voiceover, Christopher Moltisanti
                 (Michael Imperioli), a central character in the original
                 series, explaining how he died in the monotone of a man
                 who has told this story many times before. “I met death
                 on Route 23, not too far from here,” he says. Then we see
                 a young Tony Soprano, in 1967, rushing down a pier in
                 bright sunlight: “That’s my uncle.… He choked me to
                 death.”


          o ⚓ Reassessing_the_Legacy_and_Power_of_DC_Hardcore_–_Censored
            Notebook⠀⇛


                 Premised on the idea that the development, experience,
                 and messaging of music are indivisible from geography and
                 chronology, Shayna L. Maskell, professor in the College
                 of Humanities and Social Sciences at George Mason
                 University, interprets a lesser known version of
                 Washington, DC history via “DC hardcore;” harDCore, as it
                 was known in the vernacular. Politics As Sound examines
                 this music as “a performance of self…complicated and
                 contradictory,” as well as a presentation of the politics
                 of its circumstances (3).


          o § Education⠀➾


                # ⚓ Vilnius_library_builds_book_pickup_lockers_throughout_city
                  to_stay_contactless⠀⇛


                       According to the library’s press release, the new
                       service allows readers to order library books
                       online and pick them up at a chosen locker at any
                       time of the day.


                       “The idea of book pickup lockers came during the
                       quarantine when libraries were closed. At the time,
                       we were looking for ways to keep in touch with
                       readers and issue books in a secure contactless
                       way,” said Rima Gražienė, head of Vilnius Central
                       Library.


                # ⚓ A_Note_About_Recruiters⠀⇛


                       Most people, including me, hate LinkedIn and are
                       there just out of necessity. You’re simply expected
                       to have a LinkedIn profile these days. What’s also
                       true is that most people have turned off any form
                       of emails and notifications from LinkedIn and visit
                       it very rarely (unless actively looking for a job).


          o § Hardware⠀➾


                # ⚓ Isolated_Oscilloscope_Design_Process_Shows_How_It’s_Done_|
                  Hackaday⠀⇛


                       [Bart Schroder] was busy designing high voltage
                       variable speed motor drives and was lamenting the
                       inability of a standard scope to visualise the
                       waveforms around the switch transistors. This is
                       due to the three phase nature of such motors being
                       driven with three current waveforms, out of phase
                       with each other by 120 degrees, where current flows
                       between each pair of winding taps, without being
                       referenced to a common notion of ground. The
                       average scope on your bench however, definitely is
                       ground-referenced, so visualising such waveforms is
                       a bit of a faff. Then there’s the fact that the
                       motors run at many hundreds of volts, and the
                       prospect of probing that with your precious bench
                       instrument is a little nerve-wracking to say the
                       least. The solution to the issue was obvious, build
                       your own isolated high voltage oscilloscope, and
                       here is the Cleverscope CS448 development journey
                       for your viewing pleasure.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Americans_Want_Tougher_Controls_on_Drug_Prices_Than_What
                  Democrats_Are_Offering⠀⇛


                # ⚓ 60_US_Health_Groups_Urge_Companies_to_Voluntarily_Implement
                  Blocked_Vaccine_Rule⠀⇛


                       With the Biden administration’s effort to require
                       workers at companies with 100 or more employees to
                       be vaccinated against Covid-19 or tested weekly now
                       stalled due to right-wing legal challenges, dozens
                       of healthcare experts and associations on Thursday
                       urged businesses to swiftly implement the contested
                       rule on a voluntary basis ahead of the busy holiday
                       season, which epidemiologists fear will coincide
                       with a surge in cases.


                       “Businesses have wanted to vanquish this virus. Now
                       is their chance to step up and show they are
                       serious.”


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Mexican_Businessman_Arrested_For_Using
                                    NSO_Spyware_To_Target_A_Journalist⠀⇛


                                         No news is the only good news for
                                         Israeli tech company NSO Group.
                                         The problem is it’s impossible to
                                         generate no news when you can’t
                                         go more than a few days without
                                         generating more bad news.


                                  # ⚓ From_Pegasus_to_Blue_Wolf:_How_Israel’s
                                    ‘Surveillance’_Experiment_in_Palestine_Went
                                    Global⠀⇛


                                         The revelation, a few years ago,
                                         that the US National Security
                                         Agency (NSA) has been conducting
                                         mass surveillance on millions of
                                         Americans has reignited the
                                         conversation on governments’
                                         misconduct and their violation of
                                         human rights and privacy laws.


                                  # ⚓ Who_chose_your_vacation?_The_dangers_and
                                    pitfalls_of_surveillance_advertising⠀⇛


                                         We may like that we could see an
                                         ad that is relevant for us.
                                         However, precise targeting is
                                         redeemed by our privacy. The
                                         problem is in the amount of data
                                         that these tech giants collect
                                         about us. They track our every
                                         click. Surveillance advertising
                                         not only violates our privacy,
                                         but also leads to manipulation
                                         and discrimination. Let’s take it
                                         point by point: [...]


                                  # ⚓ Vizio’s_profit_on_ads,_subscriptions,_and
                                    data_is_double_the_money_it_makes_selling
                                    TVs⠀⇛


                                         It’s been less than a year since
                                         Vizio became a publicly traded
                                         company, and one consequence of
                                         that is we know more about its
                                         business than ever before. The TV
                                         maker released its latest
                                         earnings report on Tuesday and
                                         revealed that over the last three
                                         months, its Platform Plus segment
                                         that includes advertising and
                                         viewer data had a gross profit of
                                         $57.3 million. That’s more than
                                         twice the amount of profit it
                                         made selling devices like TVs,
                                         which was $25.6 million, despite
                                         those device sales pulling in
                                         considerably more revenue.


                                  # ⚓ NordVPN_follows_up_its_GNU/Linux_client
                                    breakage_by_also_breaking_their_Windows
                                    client.⠀⇛


          o § Defence/Aggression⠀➾


                # ⚓ Will_You_Storm_the_Capitol_if_the_2024_Election_is
                  Stolen?⠀⇛


                       This is not a call to “understand” or “have
                       compassion” for Trump voters.  Instead, it’s a call
                       for a wholesale political and social indictment of
                       Trump’s Big Lie, along with every elected
                       Republican politician or media member who knows
                       Trump lost but keeps perpetuating that Lie.


                       If we fail, history may repeat itself and — this
                       time — the result will be far worse than Bush’s
                       lying us into two wars and privatizing Medicare.


                # ⚓ Court_Cases_Show_Colombian_Government_Role_in_Paramilitary
                  Killings,_US_Implicated⠀⇛


                       The 2016 agreement ending 50 years of armed
                       conflict between the Revolutionary Armed Forces of
                       Colombia (FARC) and Colombia’s government might
                       have brought peace. Since the accord was signed,
                       however, killers, presumably paramilitaries, have
                       taken the lives of  292 former FARC combatants and
                       1241“social leaders.”


                       Special Forces General William Yarborough,
                       reporting on a U.S advisory mission to Colombia in
                       1962, recommended “a civil and military structure …
                       [that could] execute paramilitary, sabotage and/or
                       terrorist activities against known communist
                       proponents.” Even so, paramilitary activities
                       remained quiescent until the 1980s. From then on,
                       paramilitary assaults multiplied in rural areas,
                       leaving deaths, destitution and displacement in
                       their wake.


                # ⚓ The_Pentagon_and_the_Washington_Post:_Cold_War_Brothers-in-
                  Arms⠀⇛


                       One of the reasons why President Harry S. Truman
                       created the Central Intelligence Agency, also in
                       the National Security Act, was to have an
                       independent civilian agency challenging the
                       Pentagon’s self-serving briefings on Capitol Hill
                       for increased defense spending.  The imperative for
                       the military is to ensure the continued flow of
                       funding for its arsenal.  To this end, it will
                       always posit the worst case possible that it must
                       defend against.


                       The mainstream media should be well aware of the
                       dangers of relying on military briefings and
                       assessments when editorializing about the
                       capabilities and intentions of putative adversaries
                       such as Russia and China.  But the Washington Post,
                       which has been beating the editorial drums for
                       challenging Beijing, is currently using the
                       Pentagon’s latest report to the Congress on China’s
                       military strength to promote increased U.S. defense
                       spending and additional military deployments in
                       East Asia.  The Post and the New York
                       Times regularly cite the U.S. Cold War with China,
                       a very dangerous self-fulfilling prophecy if there
                       ever was one.


                # ⚓ Cubans_More_Excited_About_School_Reopening_Than_Regime
                  Change⠀⇛


                       Even after the Cuban government denied the
                       protesters a permit on the grounds that they were
                       part of a destabilization campaign led by the
                       United States, anti-government forces insisted that
                       they were undeterred and were ready to take the
                       risks. But in the end, their Field of Dreams turned
                       out to be an illusion. What happened?


                       Intimidation of dissidents was certainly a key
                       factor. The leader of the Facebook group
                       Archipelago, Yunior Garcia, was kept under virtual
                       house arrest. Other leaders were threatened with
                       arrest and repudiated by their pro-revolution
                       neighbors.


                # ⚓ The_Fiscal-Military-Corporate_State_We_Cannot_Sustain⠀⇛


                       A parade of weapons manufacturers is plying members
                       of Congress with arguments for new weapons
                       technologies and dollars for the next election
                       cycle. Leading the way: Lockheed Martin, Boeing,
                       Northrup Grumman, General Dynamics and Raytheon
                       Technologies.


                       The top 20 Defense contractors contributed $47
                       million to federal candidates in 2020.  Lobbying
                       efforts of defense contractors totaled more than
                       $87 million in 2021.


                # ⚓ Kyle_Rittenhouse_Is_on_Trial_for_Murder._Matt_Gaetz_Says
                  He’d_Be_a_Good_Intern.⠀⇛


                # ⚓ In_Charlottesville,_Rittenhouse_and_Arbery_Cases,_White
                  Supremacy_Is_on_Trial⠀⇛


                # ⚓ Censure_Is_“Not_Enough”:_Rights_Groups_Call_for_Expulsion
                  of_Paul_Gosar⠀⇛


                # ⚓ Ed_Dept._Opens_Inquiry_on_District_That_Wanted_“Opposing”
                  Lessons_on_Holocaust⠀⇛


                # ⚓ US_Policy_on_Taiwan_is_a_False_and_Dangerous_Two-Step⠀⇛


                       Biden, however, managed to score a double own goal
                       on the subject of Taiwan by simultaneously
                       justifying bad US foreign policy and endorsing
                       Beijing’s false “One China” claim.


                       On one hand, the US has neither any obligation nor
                       any good reason to continue guaranteeing Taiwan’s 
                       de facto independence from the mainland regime.


                # ⚓ Gosar_Censured_Over_AOC_Murder_Video,_As_AOC_Slams_GOP:
                  “What_Is_So_Hard_About_Saying_This_Is_Wrong?”⠀⇛


                       Republican Congressmember Paul Gosar is the first
                       lawmaker to be censured in more than a decade for
                       posting an animated video on social media where he
                       murders Congressmember Alexandria Ocasio-Cortez and
                       attacks President Biden. The U.S. House of
                       Representatives also voted Tuesday to censure Gosar
                       and strip him of committee assignments. He has
                       refused to apologize and after the vote he
                       retweeted the video. Speaking from the House floor
                       before the vote Congressmember Ocasio-Cortez said:
                       “This is not about me. This is not about
                       Representative Gosar. This is about what we are
                       willing to accept.” The co-sponsor of the censure
                       vote, Congressmember Jackie Speier of California,
                       said “Congressmember Ocasio-Cortez has become the
                       go-to subject of the radical right to stir up their
                       base, as too often is the case for women of color.”


                # ⚓ Three_White_Supremacy_Trials:_Dahlia_Lithwick_on
                  Charlottesville,_Rittenhouse_&_Arbery_Murder_Case⠀⇛


                       Jurors in Charlottesville, Virginia, are hearing
                       closing arguments today in a civil trial that seeks
                       to hold white supremacists accountable for
                       organizing the deadly “Unite the Right” rally there
                       in 2017, and conspiring to commit racially
                       motivated violence. Two of the white supremacists
                       have been defending themselves in the courtroom:
                       Richard Spencer and Christopher Cantwell. They took
                       the stand Tuesday, and tried unsuccessfully to have
                       the judge dismiss the case for lack of evidence,
                       even as they used racial slurs during the trial.
                       Jurors are expected to begin deliberations Friday.
                       Both Spencer and Cantwell have “failed utterly to
                       take responsibility for the roles they played,”
                       says Slate legal correspondent Dahlia Lithwick, who
                       lived in Charlottesville during the 2017 rally and
                       is reporting on the trial, which is not being
                       broadcast. She also discusses the homicide trial of
                       white teenage gunman Kyle Rittenhouse and the broad
                       use of the “self defense” argument by white
                       supremacists on trial.


                # ⚓ The_Latest_Round_of_Protests_in_Cuba_Are_a_Bust—for_Now⠀⇛


                       Havana—After weeks of media hype, planned anti-
                       government demonstrations that had been billed here
                       as a nationwide March for Change fizzled out on
                       Monday. Around the country, at least 11 protesters
                       that did come out were arrested. In downtown
                       Havana, handfuls of university students wearing
                       white walked around looking for a march to join—but
                       found only throngs of police and plainclothes state
                       security officers.


                # ⚓ Sanders_Says_Deficit_Concerns_‘Seem_to_Melt_Away’_When_It’s
                  Time_to_Fill_Pentagon_Coffers⠀⇛


                       Sen. Bernie Sanders of Vermont noted in a floor
                       speech Wednesday that concerns about the deficit
                       curiously disappear on Capitol Hill when it’s time
                       to authorize the annual U.S. military budget, which
                       lawmakers are preparing to boost to $778 billion
                       for fiscal year 2022.


                       “All of this money is going to an agency, the
                       Department of Defense, that continues to have
                       massive cost overruns.”


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Data_Shows_LA_Sheriff’s_Department_Is_Stopping_Tons_Of
                  Latino_Bicyclists,_Rarely_Finding_Anything_Illegal⠀⇛


                       Law enforcement doesn’t just engage in pretextual
                       stops of cars. Bicyclists are on the radar as well,
                       especially if they happen to be minorities. That’s
                       according to data obtained by the Los Angeles
                       Times, which shows the LA Sheriff’s Department
                       (which has buried the needle on the far end of
                       “problematic” for years) is targeting bike riders
                       with tactics that fall somewhere between pretextual
                       stop and stop-and-frisk.


          o § Environment⠀➾


                # ⚓ ‘Encouraging’:_Unlike_Trump,_Biden_Backs_Global_Treaty_for
                  Plastic_Pollution⠀⇛


                       In stark contrast to the U.S. position under former
                       President Donald Trump, the Biden administration on
                       Thursday signaled support for developing a global
                       treaty to tackle marine plastic pollution, winning
                       swift applause from environmental campaigners.


                       “As a major producer and exporter of plastic, the
                       U.S. has a responsibility to take a leadership
                       role.”


                # ⚓ Dem_Lawmakers,_Climate_Groups_Urge_Biden_Administration_to
                  Support_Kids_Climate_Case⠀⇛


                       Four dozen federal lawmakers and scores of advocacy
                       groups on Thursday sent President Joe Biden and
                       other leaders within his administration letters in
                       support of the yearslong climate case that accuses
                       the U.S. government of violating young Americans’
                       constitutional rights to life, liberty, and
                       property, and failing to protect essential public
                       trust resources.


                       “We urge the DOJ to reverse its position, stop
                       fighting the youth, and bring to the settlement
                       table tangible ideas to significantly address the
                       youth’s concerns for a safe environment.”


                # ⚓ Opinion_|_Bipartisan_American_Empire_and_Catastrophic
                  Climate_Change⠀⇛


                       When the leaders of more than 100 nations gathered
                       in Glasgow for the U.N. climate conference last
                       week, there was much discussion about the
                       disastrous effect of climate change on the global
                       environment. There was, however, little awareness
                       of its likely political impact on the current world
                       order that made such an international gathering
                       possible.


                # ⚓ Markey_Amendment_Would_Redirect_1%_of_Funds_From_‘Bloated’
                  Pentagon_to_Address_Climate_Crisis⠀⇛


                       Democratic Sen. Ed Markey of Massachusetts filed an
                       amendment Thursday that would cut the Senate’s
                       proposed $768 billion Pentagon budget by 1% and
                       invest the resulting savings in global programs
                       aimed at helping low-income nations build
                       resilience against the climate crisis.


                       “Unfettered military spending will not protect us
                       from the destruction of the environment and
                       worsening climate chaos.”


                # ⚓ Opinion_|_Big_Oil,_Lurking_in_Shadows,_Continues_to_Call
                  Shots_on_Climate⠀⇛


                       During the Second World War, no Canadian would have
                       been satisfied to learn that, while the Allies were
                       making progress, their efforts wouldn’t be enough
                       to stop Hitler. Any possibility of Hitler winning
                       was unacceptable; accordingly, the Canadian
                       government devoted itself unwaveringly to
                       mobilizing a national war effort against him.


                # ⚓ Opinion_|_World_Leaders_Failed_Us_at_COP26,_but_Change
                  Always_Comes_From_the_Power_of_People⠀⇛


                       If it wasn’t for the greenhouse effect, the Earth
                       would be as cold and dead as the far side of the
                       moon.


                # ⚓ Imagine_If_Stopping_Climate_Change_was_More_Important_Than
                  Creating_More_Climate_Change_Billionaires⠀⇛


                       On the other side, some people did manage to get
                       enormously rich from the pandemic. Specifically,
                       those who had patent monopolies on the mRNA
                       vaccines did very well, as the stock prices of both
                       Pfizer and Moderna soared during the pandemic. Back
                       in April, Forbes identified 40 people who became
                       billionaires as a direct result of their ownership
                       of stock in companies that were profiting off the
                       pandemic. Three of these were from Moderna alone.
                       The number has surely grown, as the stock market
                       has gone up further in the last seven months.


                       The reason why the Moderna billionaires might be
                       especially upsetting is that so much of what they
                       did was with government funding. The development of
                       mRNA technology, beginning in the early 1980s, was
                       accomplished almost entirely on the government’s
                       dime. While Moderna did do further research to
                       develop a foundation for producing vaccines, the
                       money to actually develop and test Moderna’s
                       vaccine came entirely from the government through
                       Operation Warp Speed. The government also signed a
                       large advance purchase agreement, which would have
                       required it to pay for several million Moderna
                       vaccines, even if other vaccines were superior.


                # ⚓ COP26:_Capitalism_=_Death⠀⇛


                       For many, the U.S.-China deal, like much of the
                       other proclamation made by government leaders at
                       the conference, exemplified what Swedish climate
                       activities Greta Thunberg dubbed the great “blah,
                       blah, blah.”  As she said at the Youth4Climate
                       summit in Milan (Italy) in September:


                       Looking critically at COP26, Thunberg argued, “It
                       is not a secret that COP26 is a failure. It should
                       be obvious that we cannot solve the crisis with the
                       same methods that got us into it in the first
                       place.” She added, “The COP has turned into a PR
                       event, where leaders are giving beautiful speeches
                       and announcing fancy commitments and targets, while
                       behind the curtains governments of the Global North
                       countries are still refusing to take any drastic
                       climate action.”


                # § Energy⠀➾


                      # ⚓ This_City_in_Oregon_is_Making_Moves_to_Ban_Natural
                        Gas_in_New_Homes_and_Buildings⠀⇛


                             The City of Eugene, Oregon, initiated a
                             process on November 17 that could lead to a
                             ban on new natural gas hookups in residential
                             and commercial buildings, following in the
                             footsteps of dozens of other cities around
                             the country. The move would be the first in
                             Oregon, and activists believe it could set
                             off a domino-like trend in the state and more
                             broadly across the Pacific Northwest. 


                             The Eugene City Council approved a process in
                             which they would consider a ban on new gas
                             hookups in the coming months, with the ban
                             tentatively planned to take effect in January
                             2023. Wednesday’s vote did not immediately
                             approve the prohibition, but the apparent
                             strong support from a majority of the City
                             Council suggested that there is considerable
                             momentum in that direction. 


                      # ⚓ Gulf_Coast_Tribe_Vows_to_Resist_Enbridge’s_New
                        Pipeline_Expansion_Plans⠀⇛


                      # ⚓ Applause_for_‘All_Who_Fought’_as_Boston_City_Council
                        Votes_to_Divest_From_Fossil_Fuels⠀⇛


                             Progressives praised the Boston City Council
                             after its members voted unanimously Wednesday
                             to divest city funds from the fossil fuel
                             industry, a major endorsement of clean energy
                             investment that came as Massachusetts
                             lawmakers prepare to debate how to allocate
                             the state’s financial resources.


                             “The climate crisis requires us to take
                             immediate steps toward a cleaner future.”


                      # ⚓ From_Glasgow_to_Gulf_of_Mexico,_Fossil_Fuel_Industry
                        Shows_Us_Who’s_in_Charge⠀⇛


                      # ⚓ HS:_Peat_has_lost_its_significance_for_security_of
                        supply_in_Finland⠀⇛


                             It is important to distinguish between the
                             use and production of peat, reminded
                             Helsingin Sanomat. Production, in particular,
                             can fluctuate noticeably based on demand and
                             weather conditions: heat production plants
                             are this winter expected to burn through
                             reserves left over from the good peat year
                             that was 2018.


                             Salo also pointed out that the production of
                             energy peat has fallen from about 15–16
                             million cubic metres in the 2010s to about
                             6.5 million cubic metres in 2020 and possibly
                             as low as two million cubic metres in 2021.


                             Energy peat has typically made up 85–90 per
                             cent of all peat produced in Finland. The
                             other types of peat include white peat, which
                             is used in greenhouses and livestock farming.


          o § Finance⠀➾


                # ⚓ Elizabeth_Warren_Releases_Blueprint_to_End_‘Free_Ride’_for
                  Tax-Dodging_US_Billionaires⠀⇛


                       “While these companies report billions in profits,
                       they often pay no income tax to the IRS and leave
                       hardworking families holding the bag.”


                # ⚓ Opinion_|_Making_the_Holidays_Happier_for_the_Postal
                  Service⠀⇛


                       Last year’s holiday season was not exactly a merry
                       one for the U.S. Postal Service. In the lead-up to
                       Christmas, overwhelmed postal workers had to leave
                       gifts sitting in sorting facilities for weeks. They
                       delivered just 38 percent of greeting cards and
                       other nonlocal first-class mail on time.


                # ⚓ How_Did_Fiscal_Scorekeepers,_like_the_CBO,_Become_So
                  Powerful_in_Congress?⠀⇛


                       This is certainly the case in the current debate
                       over President Joe Biden’s proposed Build Back
                       Better legislation, which rarely makes the news
                       without mention of its estimated US$1.75 trillion
                       cost.


                       There is one overriding reason for this: the
                       Congressional Budget Office, known popularly as the
                       CBO. The CBO is tasked with “scoring” legislation
                       by estimating the impact that it would have on both
                       revenue and spending. But as a scholar who
                       investigates CBO score controversies, I know that
                       the office’s figures are often used for partisan
                       reasons.


                # ⚓ Agency_Tasked_by_Trump_With_$100M_to_Boost_Supply_Chain
                  Hasn’t_Spent_a_Penny⠀⇛


                # ⚓ John_Deere_Strike_Ends_as_Workers_Win_Higher_Wages,_Bonus
                  and_Better_Pension⠀⇛


                # ⚓ ‘Sacrifice_and_Solidarity’_Pay_Off_as_Striking_John_Deere
                  Workers_Win_Bigger_Wage_Hike⠀⇛


                       Factory workers at John Deere officially ended
                       their historic month-long strike late Wednesday by
                       approving a six-year contract that includes an
                       immediate 10% wage increase, reinstatement of a
                       cost-of-living adjustment, and an $8,500
                       ratification bonus—provisions the United Auto
                       Workers hailed as a major victory.


                       “They have started a movement for workers in this
                       country by what was achieved here today.”


                # ⚓ Opinion_|_Inflation_Is_Complicated,_But_the_Solution_Is
                  Simple⠀⇛


                # ⚓ Opinion_|_The_New_Inflation_Scare_Is_Dumb—Don’t_Fall_for
                  It⠀⇛


                       After years of hypocrisy and bungled forecasts of
                       doom, the budget deficit no longer provokes panic.
                       The elites need a new bogeyman, otherwise Congress
                       might actually spend us into happiness. Now, the
                       new monster in the closet is Inflation. The great
                       prognosticators Sen. Joe Manchin (D‑W.V.) and CNN’s
                       Wolf Blitzer have weighed in, and we are officially
                       advised to be afwaid, vewy afwaid.


                # ⚓ ‘Let’s_Get_It_Done’:_House_Set_to_Vote_on_Build_Back_Better
                  Act_After_CBO_Score_Released⠀⇛


                       Progressive U.S. lawmakers on Thursday evening
                       looked forward to an imminent vote on President Joe
                       Biden’s flagship Build Back Better reconciliation
                       bill after the Congressional Budget Office released
                       its estimates for the sweeping package—an analysis
                       that a few conservative Democrats demanded before
                       they would support the legislation.


                       The nonpartisan Congressional Budget Office said
                       Thursday that it “estimates that enacting this
                       legislation would result in a net increase in the
                       deficit totaling $367 billion over the 2022-2031
                       period, not counting any additional revenue that
                       may be generated by additional funding for tax
                       enforcement.”


                # ⚓ Not_The_Onion:_Bloomberg_–_Americans_with_no_money_“opt-
                  out”_of_holiday_spending.⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ How_Progressives_Can_Mobilize_to_Win⠀⇛


                       This is a pivotal moment. In recent years we’ve
                       witnessed the awakening and uprising of creative,
                       courageous people demanding justice and
                       equality—from #BlackLivesMatter to
                       #protecttranskids, #LandBack to #MeToo and
                       disability justice to immigrant rights.
                       Politically, these movements have spurred
                       progressive candidates at every level of
                       government, from new members of the “Squad” in
                       congress to diverse and bold progressive candidates
                       winning at every level. Our multicultural and
                       participatory democracy is within reach.


                # ⚓ Finnish_Democracy_Is_on_the_Brink⠀⇛


                       Last week, a noose and an unprintably racist
                       message were delivered to a Muslim lawmaker. The
                       target wasn’t Minnesota Representative Ilhan Omar,
                       as you might well have imagined,
                       but—shockingly—Suldaan Said Ahmed, a first-term
                       member of the Finnish Parliament. “This repulsive
                       act is only part of the racist feedback and
                       harassment I’ve faced during my time in politics,”
                       said Ahmed. “I thought it was important to show
                       what it’s like also publicly. This is what people
                       still have to face in Finland in the 2020s. I want
                       to work to make sure no child has to face anything
                       like this in the future.”


                # ⚓ Sunrise_Endorses_Cisneros_Over_Corporate-Backed_Cuellar_in
                  Texas_Democratic_Primary_Fight⠀⇛


                       The Sunrise Movement announced Thursday its
                       endorsement of progressive Jessica Cisneros in her
                       primary challenge to oust Democratic Congressman
                       Henry Cuellar and represent Texas’ 28th
                       Congressional District.


                       “She knows that it takes bold solutions to solve
                       the crises we face.”


                # ⚓ Opinion_|_Was_Frederick_Hayek_a_Bernie_Sanders_Socialist?⠀⇛


                       Of course not! 


                # ⚓ Texts_Show_Kimberly_Guilfoyle_Bragged_About_Raising
                  Millions_for_Rally_That_Fueled_Capitol_Riot⠀⇛


                       Kimberly Guilfoyle, a top fundraiser for former
                       President Donald Trump and the girlfriend of his
                       son Donald Trump Jr., boasted to a GOP operative
                       that she had raised $3 million for the rally that
                       helped fuel the Jan. 6 Capitol riot.


                       In a series of text messages sent on Jan. 4 to
                       Katrina Pierson, the White House liaison to the
                       event, Guilfoyle detailed her fundraising efforts
                       and supported a push to get far-right speakers on
                       the stage alongside Trump for the rally, which
                       sought to overturn the election of President Joe
                       Biden.


          o § Misinformation/Disinformation⠀➾


                # ⚓ High_Profile_Commission_On_Disinformation_Unable_To_Solve
                  Disinformation_Despite_Having_Prince_Harry_On_Board⠀⇛


                       Dealing with disinformation is not an easy problem
                       to solve. Part of the problem is that very few
                       people even agree how to define disinformation, or
                       how subjective it is. Indeed, as we’ve noted, most
                       of the reporting on disinformation itself is
                       misinformation (or, at the very least misleading).
                       That said, I still had decently high hopes for the
                       Aspen Institute’s “Commission on Information
                       Disorder.” The Aspen Institute tends to do more
                       credible and serious work on tech policy issues
                       than many other groups. And the project was
                       supported by Craig Newmark, who has been funding a
                       bunch of important research over the past few
                       years. And, while some of the choices for who was
                       on the Commission struck me as odd (Prince Harry?!?
                       Katie Couric?!?), there were some very serious and
                       very thoughtful participants on the Commission
                       itself, acting as “advisors” to the group, and who
                       participated in the various discussions they held.


          o § Censorship/Free Speech⠀➾


                # ⚓ ‘You’re_already_in_the_authoritarian_state’:_Chinese
                  dissident_Ai_Weiwei_criticizes_US_‘woke’_culture⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ Opinion_|_John_Oliver_Just_Aired_the_Best_Anti-Union
                  Busting_Segment_We’ve_Ever_Seen⠀⇛


                       October saw the largest number of workers on strike
                       in years, and 2021 has seen a dramatic rise in
                       coverage of unionization efforts. John Oliver, host
                       of Last Week Tonight, took aim on his show at the
                       efforts by companies to keep unions out. Whether or
                       not you are likely to see a union drive at your
                       workplace, it matters that more Americans
                       understand how union busting and corporate pressure
                       tactics work; the more you know, the better you can
                       push back against their deceitful propaganda.


                # ⚓ Only_Democracy_Can_Save_One_of_America’s_Greatest_Unions⠀⇛


                       Last month was Striketober. Fueled by historic
                       labor shortages, 100,000 workers either went on
                       strike or prepared to strike, in some of the
                       largest coordinated labor actions in recent US
                       history. This is encouraging. With gridlock in
                       Congress holding up a social safety net bill, the
                       United States needs strong unions more than ever.
                       The trends are very clear: When unions are weak,
                       the highest incomes go even higher, but when unions
                       are strong, middle and lower incomes go up.


                # ⚓ We_Need_Barcelona’s_Hidden_Radical_History_Now_More_Than
                  Ever⠀⇛


                       In the United States, there is a mighty and deeply
                       reactionary movement for historical erasure. Its
                       aims are nothing less than to prevent teaching the
                       truth about the ugliest parts of the history of
                       this country. The bewitching, paradoxical city of
                       Barcelona presents a vision of what it could look
                       like if such a movement were to reach its goals.


                # ⚓ Uncivil_War_on_Democracy⠀⇛


                # ⚓ Morality_Plays:_When_Entertainers_Draw_the_Line⠀⇛


                       Our ethics, however capricious they’ve become,
                       evolve largely from the mega entertainment
                       industry. Authors and athletes, singers and poet-
                       rappers, television hosts and comedians, even
                       though they sometimes do so unwittingly, guide our
                       choices, consequently our values as well. Today’s
                       A-list stars —oh, how we adore them—they are who
                       pronounce what’s good and right, bad and wrong. At
                       least we endow them with that power. Even when they
                       don’t intend their statements to be a moral
                       judgement, even after they’ve moved beyond whatever
                       they’re charged with.


                       Columnist Paul Street, addressing the weakening
                       role of journalism, hints at the moral implications
                       of that slide: “In the name of political
                       neutrality”, he writes, “‘the news’ often produces
                       moral (my emphasis) and intellectual paralysis in
                       its consumers…”.


                # ⚓ ‘Morally_Repugnant’:_Video_Shows_Israeli_Troops_Waking,
                  Photographing_Palestinian_Kids⠀⇛


                       Human rights groups this week reacted with outrage
                       to video footage showing Israeli troops forcing
                       Palestinian children from their slumber and
                       photographing them outside their family home—an act
                       that Israel’s military admits was “not proper.”


                       “It seems that for the army, all Palestinians,
                       including boys and girls of elementary school age,
                       are potential criminals.”


                # ⚓ ‘Drop_the_Charges’:_Greece_Delays_Trial_of_Humanitarians
                  Who_Aided_Refugees_at_Sea⠀⇛


                       Human rights defenders expressed renewed demands on
                       Thursday for charges to be dropped against a group
                       of humanitarian activists now facing trial in
                       Greece for aiding refugees at sea off the country’s
                       coast.


                       “All we have done is assist people seeking safety
                       at a time of need.”


                # ⚓ Yes,_Even_If_You_Think_Project_Veritas_Are_A_Bunch_Of
                  Malicious_Grifters,_FBI_Raid_Is_Concerning⠀⇛


                       I am no fan of Project Veritas. They appear to be a
                       group of malicious grifters, deliberately
                       distorting things, presenting them out of context
                       to fit (or make) a narrative. Even so (or perhaps,
                       especially so), we should be extremely concerned
                       about the FBI’s recent raid on Project Veritas’
                       founder James O’Keefe and two of his colleagues.


                # ⚓ ‘Solidarity_Forever’:_40,000_Kaiser_Workers_Set_to_Strike
                  to_Defend_700_Fellow_Union_Members⠀⇛


                       “It’s so important for working people to stand
                       together, and we hope that with the nurses by their
                       side, Kaiser engineers will win meaningful change
                       for working people, and for safe patient care
                       conditions.”


                # ⚓ “The_Dawn_of_Everything”:_David_Wengrow_&_the_Late_David
                  Graeber_On_a_New_History_of_Humanity⠀⇛


                       In an extended interview, we speak with
                       archeologist David Wengrow, who co-authored the new
                       book “The Dawn of Everything: A New History of
                       Humanity” with the late anthropologist David
                       Graeber. The book examines how Indigenous cultures
                       contributed greatly to what we have come to
                       understand as so-called Western ideas of democracy
                       and equality, but argues these contributions have
                       been erased from history. “What the broad sweep of
                       history shows is that living in large-scale,
                       densely populated, technologically sophisticated
                       societies really doesn’t require people to simply
                       give up social freedoms,” says Wengrow. The two
                       completed the book just weeks before Graeber died
                       unexpectedly last year at the age of 59. Graeber is
                       credited with helping to coin the phrase “We are
                       the 99%.” His book “Debt: The First 5,000 Years”
                       made the case for sweeping debt cancellation.


                # ⚓ Julius_Jones_Will_“Fight_Another_Day”_—_Death_Sentence
                  Commuted⠀⇛


                # ⚓ There’s_Still_Time_to_Save_Julius_Jones⠀⇛


                       UPDATE: Oklahoma Governor Kevin Stitt commuted
                       Julius Jones’s death sentence to life without
                       parole just hours before Jones was scheduled to be
                       executed for a murder that he says he did not
                       commit. Read more about the Justice for Julius
                       movement here.


                # ⚓ ‘Hallelujah!’:_Justice_Advocates_Rejoice_at_11th-Hour_Halt
                  to_Julius_Jones_Execution⠀⇛


                       Human rights advocates rejoiced Thursday after
                       Oklahoma Gov. Kevin Stitt heeded the advice of his
                       state’s pardon board—which found compelling
                       evidence of the condemned man’s innocence—and
                       commuted the death sentence of Julius Jones to life
                       imprisonment without parole with just hours to go
                       before his scheduled execution.


                       “Now we organize to get Gov. Stitt out of office so
                       Julius Jones can gain his full freedom back.”


                # ⚓ IFF_releases_Legislative_Brief_on_Digital_Rights_for_Winter
                  Session_2021⠀⇛


                       Before the commencement of the Winter Session of
                       the Indian Parliament, we have prepared our second
                       Legislative Brief on Digital Rights. In our brief,
                       we highlight some of the focus areas within the
                       larger issues of data protection and digital rights
                       that call for the extensive deliberation in the
                       houses of the Parliament.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ The_FCC_Ponders_A_Hugely_Problematic_Tax_On_WiFi⠀⇛


                       For years, we’ve noted how telecom and media giants
                       have been trying to force “big tech” to give them
                       huge sums of money for no reason. The shaky logic
                       usually involves claiming that “big tech” gets a
                       “free ride” on telecom networks, something that’s
                       never actually been true. This narrative has been
                       bouncing around telecom policy circles for years,
                       and recently bubbled up once again thanks to FCC
                       Commissioner Brendan Carr.


                # ⚓ .net_Forever⠀⇛


                       Let’s talk a bit about .net. No, not Microsoft’s
                       .NET, but the other .net – one of the original top-
                       level internet domains. Given how popular .com has
                       become, I find it really strange that .net failed
                       to reach such prominence. Even .org is more popular
                       than .net!


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Windows_Store_causes_errors_in_Firefox,_makes_Accessibility
                  unusable.⠀⇛


                       They shilled Microsoft’s new DRM store, and all
                       they got were more bugs to fix, Edge using nasty
                       tricks to steal their users from them, and this
                       lousy T-shirt.


                # ⚓ Apple’s_Self_Service_Repair_Program_Must_Live_Up_To_Its
                  Promises⠀⇛


                       This is a major shift for the company, which has
                       fought for years against movements to expand
                       people’s right to repair their Apple products.
                       Right-to-repair advocates have not only pushed the
                       company to move on this issue, but also to get
                       regulators and lawmakers to acknowledge the need to
                       protect the right to repair in law. Apple’s
                       announcement is only one illustration of how far
                       the advocacy on the right to repair has come; in
                       just the past two years, advocates have won at the
                       ballot box in Massachusetts, received a
                       supportive directive from the Biden Administration,
                       changed policy at Microsoft, and made some gains at
                       the Library of Congress to expand repair
                       permissions.


                       The Self Service Repair Program could be another
                       feather in that cap. But now that Apple has
                       announced the program, we urge them to roll it out
                       in ways that truly expand their customers’ access
                       and choice.


                       It’s important that Apple’s program, or any
                       program, does not come with strings attached that
                       make it unworkably difficult or too expensive for a
                       normal person to use. In the past, Apple has done
                       both—as YouTuber and professional repairer Louis
                       Rossman pointed out.


          o § Monopolies⠀➾


                # ⚓ [Old] How_Piracy_Opens_Doors_for_Windows⠀⇛


                       “The first dose is free,” said Hal Varian, a
                       professor of information management at UC Berkeley,
                       facetiously comparing Microsoft’s anti-piracy
                       policy to street-corner marketing of illicit drugs.
                       “Once you start using a product, you keep using
                       it.”


                # § Trademarks⠀➾


                      # ⚓ EFF_Tells_Court_to_Protect_Anonymous_Speakers,_Apply
                        Proper_Test_Before_Unmasking_Them_In_Trademark
                        Commentary_Case⠀⇛


                             EFF filed its brief in the U.S. Court of
                             Appeal for the Second Circuit after several
                             anonymous defendants in a case brought by
                             Everytown for Gun Safety Action Fund appealed
                             a district court’s order that mandated the
                             disclosure of their identifying information.
                             Everytown’s lawsuit alleges that the
                             defendants used its trademarked logos in 3-
                             D printed gun part plans and sought the order
                             to learn the identities of several online
                             speakers who printed them.


                             Unmasking can result in serious harm to
                             anonymous speakers, exposing them to
                             harassment and intimidation, which is why the
                             First Amendment offers strong protections for
                             such speech. So courts around the country
                             have applied a now well-established three-
                             step test when parties seek to unmask Doe
                             speakers, to ensure that the litigation
                             process is not being abused to pierce
                             anonymity unnecessarily. But in granting the
                             order in this case, the district court
                             instead applied a looser test that is usually
                             used only in P2P copyright cases. The court
                             then ruled that the online speakers could not
                             rely on the First Amendment here because
                             “anonymity is not protected to the extent
                             that it is used to mask the infringement of
                             intellectual property rights, including
                             trademark rights.”


                             That ruling cannot stand. As we explained in
                             our friend-of-the-court brief, “Although the
                             right to speak anonymously is not absolute,
                             the constitutional protections it affords to
                             speakers required the district court to pause
                             and meaningfully consider the First Amendment
                             implications of the discovery order sought by
                             Plaintiffs, applying the correct test
                             designed to balance the needs of plaintiffs
                             and defendants in Doe cases such as this
                             one.”  By choosing to apply the wrong test,
                             and even then in the most cursory way, the
                             district court fell far short of its
                             obligations.


                # § Copyrights⠀➾


                      # ⚓ Is_Protecting_Copyright_More_Important_Than_Saving
                        Lives_During_The_COVID-19_Pandemic?⠀⇛


                             Although the COVID-19 pandemic has wreaked
                             terrible suffering across the world, we are
                             fortunate that we already have several
                             vaccines that have been shown to be highly
                             effective in reducing the number of deaths
                             and hospitalization rates. Discovering
                             vaccines proved easier than expected, but
                             ensuring that everyone – including people in
                             developing countries – has access to them has
                             proved much harder. The main reason for that
                             is an intellectual monopoly: patents. Even
                             though at least two of the main vaccines were
                             developed almost entirely using public funds,
                             which ought by rights to mean that the
                             results are in the public domain, companies
                             have obtained exclusionary patents on them.
                             This has led to calls for a patent waiver of
                             some kind to allow countries to produce their
                             own supplies of medicines, without needing to
                             pay licensing fees.


                      # ⚓ “The_NFT_Bay”_Shares_Multi-Terabyte_Archive_of
                        ‘Pirated’_NFTs⠀⇛


                             NFTs are unique blockchain entries through
                             which people can prove that they ‘own’
                             something. However, the underlying images can
                             be copied with a single click. This point is
                             illustrated by The NFT Bay which links to a
                             19.5 Terabyte collection of ‘all NFTs’ on the
                             Ethereum and Solana blockchains. And it comes
                             with an important warning message too.


                      # ⚓ YouTubers_Who_Uploaded_Movie_Edits_Receive_Suspended
                        Prison_Sentences⠀⇛


                             After being arrested earlier this year, three
                             people have been handed suspended prison
                             sentences and fines for uploading so-called
                             “fast movies” to YouTube. Their trial, which
                             took place in Japan, heard that the
                             defendants uploaded minutes-long movie
                             summary edits to YouTube with accompanying
                             commentary. All three pleaded to criminal
                             breaches of Japan’s copyright law.


                      # ⚓ CC_Certificate_Alumnus,_Mostafa_Azad_Kamal_on_his
                        work_with_open_education_policies_and_practice⠀⇛


                             After launching in 2018, and certifying
                             approximately 1000 graduates from 56
                             countries, Creative Commons (CC) is taking
                             stock of the incredible community of
                             Certificate participants and alumni. We are
                             particularly interested in learning about
                             local “case studies” of open licensing in
                             local country contexts, and asking alumni
                             about their experiences. CC Certificate
                             alumni have used the certificate course in a
                             number of ways—read about alumni testimonials
                             here, and an in-depth adaptation one alumnus
                             made of course content here. In this
                             interview, we highlight one Certificate
                             graduate’s work in Bangladesh, and celebrate
                             the momentum he’s built in open education. 


                      # ⚓ ‘GTA’_Modding_Group_Doesn’t_Fold,_Fights_Back_In
                        Court_Against_Take-Two,_Rockstar [Ed: Delete Microsoft
                        GitHub]⠀⇛


                             We’ve been talking a great deal about Take-
                             Two Interactive and Rockstar Games lately as
                             it relates to their aggressive actions on
                             modding communities for the Grand Theft Auto
                             series. This new war on modders really kicked
                             off over the summer, with the companies
                             looking to shut down a bunch of mods that
                             mostly brought old GTA content into newer
                             games for retro fans. Then came one modding
                             group managing to reverse engineer the game
                             to create its own version of the source code,
                             which it posted on GitHub. Rockstar DMCA’d
                             that project, but at least one modder managed
                             to get GitHub to put it back up. That project
                             was called “GTA RE3″ and was supposed to be
                             the basis to let other modders do all sorts
                             of interesting things with the game from a
                             modding standpoint, or to forklift the game
                             onto platforms it wasn’t designed for, say on
                             a Nintendo console. Take-Two and Rockstar
                             then cried “Piracy!” and filed a lawsuit.



                    ䷩ 𝚕𝚒𝚗𝚎 5612

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.19.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_19/11/2021:_Ubuntu_Touch_OTA-20,_Wine_6.22,_and_PureOS_10_Released⠀✐


Posted in News_Roundup at 6:51 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⠀➾


                # ⚓ A_German_State_Is_Saying_Goodbye_Windows,_Hello_Linux⠀⇛


                       The state parliament of Schleswig-Holstein in
                       Northern Germany has already produced plans to make
                       the state government almost 100% open source by the
                       end of 2026.


                       Schleswig-Holstein, the northernmost state in
                       Germany, has plans to move almost entirely open
                       source. By the time the dust settles, the regional
                       government will have all but dropped Windows,
                       Microsoft Office, Zoom and other proprietary
                       software for Linux, LibreOffice, OnlyOffice, and
                       Jitzi.


                       FOSS Force first learned of the plans from a post
                       by Mike Saunders, a marketing assistant for the The
                       Document Foundation, the organization behind the
                       open source office suite LibreOffice.


                # ⚓ Change_Desktop_Environments_on…_iOS?⠀⇛


                       While Apple’s modern operating systems may seem
                       like they exist independently of the rest of the
                       computing world, they are actually close cousins of
                       modern versions of Linux. The primary link between
                       the two is that Apple’s offerings are Unix-based
                       and even though Linux isn’t Unix in the strict
                       sense, it’s built to be extremely Unix-like. Plenty
                       of Linux software is POSIX-compliant, meaning it is
                       effectively compatible with true Unix. But what can
                       we do with that information? Well, to start, we can
                       run Linux desktop environments on top of an iOS
                       install on your favorite iPhone or iPad.


                       To be sure, we will be filing this hack in the
                       “because you can” category. [Torrekie], the creator
                       of this project, has plenty of builds (Google
                       translate from Chinese) where the boundaries
                       between things like Linux and Unix are either
                       blurred or nonexistant. In this particular project,
                       a jailbroken iOS device is essentially gifted a
                       ported version of XFCE which is able to run fairly
                       well on iOS thanks to its compatibility with Unix
                       environments. Details on how this was accomplished
                       are sparse without a full investigation of the
                       source code right now, but you can head over to the
                       repository if you are curious enough to try this
                       for yourself. [Torrekie] does note that this will
                       only work with iOS devices that have been
                       jailbroken using the “unc0ver” jailbreak only
                       though.


          o § Audiocasts/Shows⠀➾


                # ⚓ KDE_Floating_Panels:_ALMOST_THERE!_–_Kockatoo_Tube⠀⇛


                # ⚓ Pi_Server_Upgrade_|_Self-Hosted_58⠀⇛


                       This week we unlock the Pitential of the Compute
                       Module 4 and turn it into a dual gigabit router and
                       Jellyfin server.


                       How far can we push it?


                       Plus, Alex shares his thoughts on the state of
                       mobile operating systems and the challenges they
                       are imposing on DIYers.


                # ⚓ Emacs_Is_A_Gaming_Platform_for_Windows,_Mac_and_Linux_–
                  Invidious⠀⇛


                       Emacs is much more than a text editor. It is its
                       own complete environment


                # ⚓ Hackaday_Podcast_145:_Remoticon_is_On,_Movie_FX,_Cold
                  Plasma,_and_The_Purest_Silicon⠀⇛


                       With literally just hours to go before the 2021
                       Hackaday Remoticon kicks off, editors Tom Nardi and
                       Elliot Williams still managed to find time to talk
                       about some of the must-see stories from the last
                       week. There’s fairly heavyweight topics on the
                       docket this time around, from alternate methods of
                       multiplying large numbers to the incredible
                       engineering that goes into producing high purity
                       silicon. But we’ll also talk about the movie making
                       magic of Stan Winston and some Pokemon-themed
                       environmental sensors, so it should all balance out
                       nicely. So long as the Russian’s haven’t kicked off
                       the Kessler effect by the time you tune in, we
                       should be good.


                # ⚓ How_to_install_Lubuntu_21.10_–_Invidious⠀⇛


                       In this video, I am going to show how to install
                       Lubuntu 21.10.


                # ⚓ How_Apple’s_self-service_repair_program_reveals_that
                  they’ve_lost_their_way._–_Invidious⠀⇛


                       Apple revealed their Self Service Repair program
                       allowing their i̶n̶m̶a̶t̶e̶s̶ users to purchase
                       replacement parts for their iPhones and
                       (eventually) their M1-based Macs. I hope they prove
                       me wrong on this, but I find this to be a cynical
                       step on their part. But what I really want to talk
                       about is the design of the artwork on their
                       announcement post. It follows the “Big Tech” art
                       style called “Corporate Memphis” (also referred to
                       as “globohomo,” among other terms). Apple’s now
                       chasing design trends rather than progressing them.
                       If I didn’t know any better I would think this was
                       just another phone manufacturer’s website.


          o § Kernel Space⠀➾


                # ⚓ Collabora_Brings_Flicker-Free_Multi_GPU_Boot_and_Rockchip
                  H.264_Decoder_to_Linux_5.15⠀⇛


                       Linux kernel 5.15 arrived on Halloween with many
                       great new features, such as a brand new NTFS file
                       system implementation contributed by Parangon
                       Software to finally provide Linux users with fully
                       functional NTFS support, realtime preemption
                       locking, in-kernel SMB3 server, as well as DAMON
                       (Data Access MONitor).


                       On top of all that, Linux 5.15 is an LTS (Long-Term
                       Support) kernel branch, which will be supported for
                       at least a couple of years. As usual, Collabora
                       have made some important contributions themselves
                       to the Linux 5.15 LTS kernel series.


                # ⚓ Linux_ITMT_Patch_Fixes_Intel_“Alder_Lake”_Hybrid_Handling
                  For_Some_Systems_–_Phoronix⠀⇛


                       There is a patch pending that improves the Linux
                       kernel’s dealing with the hybrid P and E cores
                       found with Intel’s new Alder Lake processors that
                       will benefit some systems/motherboards.


                       For those with Intel 12th Gen Core “Alder Lake”
                       systems, one of the important tidbits of
                       information I recently learned is that while Thread
                       Director is hardware-based, the hybrid P/E core
                       selection under Linux does depend upon the working
                       Intel TurboBoost Max 3.0 / ITMT code path working.
                       The CPU selection within Linux for Alder Lake
                       relies on that ITMT (Intel Turbo Boost Max
                       Technology) scheduling.


                # ⚓ Updated_AMD_P-State_Driver_Posted_For_Improving_Linux_Power
                  Efficiency_–_Phoronix⠀⇛


                       A fourth iteration of the AMD P-State CPU frequency
                       scaling driver patches for Linux have been sent out
                       for review and testing.


                       This is the amd-pstate driver aiming for better
                       power efficiency on Linux by leveraging ACPI CPPC
                       found with Zen 2 and newer processors. Valve
                       collaborated with AMD on the creation of this new
                       driver that aims to be superior to the generic ACPI
                       CPUFreq driver currently used by AMD processors.
                       This driver has been undergoing public review since
                       September with aims to make it to the mainline
                       kernel.


                # § Graphics Stack⠀➾


                      # ⚓ Mike_Blumenkrantz:_The_Finale⠀⇛


                             It’s been a wild year for zink. Does anybody
                             even remember how many times I finished the
                             project? I don’t, but it’s been at least a
                             couple. Somehow there’s still more to do
                             though.


                             I’ll be updating zink-wip one final time
                             later today with the latest Copper snapshot.
                             This is going to be crashier than the usual
                             zink-wip, but that’s because zink-wip doesn’t
                             have nearly as much cool future-zink stuff as
                             it used to these days. Nearly everything is
                             already merged into mainline, or at least
                             everything that’s likely to help with general
                             use, so just use that if you aren’t
                             specifically trying to test out Copper.


                             One of those things that’s been a thorn in
                             zink’s side for a long time is PBO handling,
                             specifically for unsupported formats like
                             ARGB/ABGR, ALPHA, LUMINANCE, and InTeNsItY.
                             Vulkan has no analogs for any of these, and
                             any app/game which tries to do texture upload
                             or download from them with zink is going to
                             have a very, very bad time, as has been the
                             case with CS:GO, which would take literal
                             days to reach menus due to performing
                             fullscreen GL_LUMINANCE texture downloads.


                             This is now fixed in the course of landing
                             compute PBO download support, which I blogged
                             about forever ago since it also yields a 2-
                             10x performance improvement for a number of
                             other cases in all Gallium drivers. Or at
                             least the ones that enable it.


                             CS:GO should now run out of the box in Mesa
                             22.0, and things like PCSX3 which do a lot of
                             PBO downloading should also see huge
                             improvements.


          o § Applications⠀➾


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Microsoft_To_Do⠀⇛


                       Microsoft’s stance for decades was that community
                       creation and sharing of communal code (later to be
                       known as free and open source software) represented
                       a direct attack on their business. Their battle
                       with Linux stretches back many years. Back in 2001,
                       former Microsoft CEO Steve Ballmer famously
                       tarnished Linux “a cancer that attaches itself in
                       an intellectual property sense to everything it
                       touches”. Microsoft also initiated its “Get the
                       Facts” marketing campaign from mid-2003, which
                       specifically criticized Linux server usage, total
                       cost of ownership, security, indemnification and
                       reliability. The campaign was widely criticized for
                       spreading misinformation.


                # ⚓ vifm:_A_Terminal_File_Browser_for_Hardcore_Vim_Lovers⠀⇛


                       When it comes to navigating through the Linux
                       directory structure in the command line, people
                       often rely on the cd command.


                       And nothing wrong with it because you’ll get the cd
                       command on any Linux system you log in.


                       However, if the system is maintained by you and you
                       want to have a better view of the directories, a
                       file manager does a lot better than the cd or tree
                       command.


                       Yes, you can get file managers in the terminal as
                       well. They may not be as good as the GUI ones like
                       Nautilus but still better than the plain old
                       commands.


                # ⚓ Ubuntu_PPA_for_Annotator_–_Elementary_OS_Image_Annotation
                  Tool_|_UbuntuHandbook⠀⇛


                       Linux has quite a few image annotation tools.
                       “Annotator” is the one designed for Elementary OS
                       with specific features. Here’s how to install it in
                       Ubuntu 20.04, Ubuntu 21.10, Ubuntu 22.04 via PPA.


                       Without using GIMP image editor, I sometimes uses
                       Shutter to annotate image quickly. As well, Ksnip
                       has some useful tools (e.g., drop shadow, invert
                       color and add border) that I use regularly.


                       Annotator is an app looks kinda like MacOS Preview.
                       Like other tools, it allows to add text, rectangle,
                       ellipse, sequence number, line, arrow, blur effect,
                       crop and resize image. What makes it different is
                       the “Magnifier” tool. It adds a circle on your
                       image and enlarge the area inside. By right-
                       clicking on the circle, it offers option to change
                       magnification.


                # ⚓ Ubuntu_Blog:_Top_10_apps_to_boost_your_productivity⠀⇛


                       Winter is rolling in (for those in the Northern
                       Hemisphere at least). Long summer evenings are on
                       hold for now. In these colder months, it can be
                       difficult to get back into work and feel efficient.
                       But whether you are feeling tired, unorganised, or
                       demotivated, there may be an application here to
                       help you refocus and re-energise. Here are a few
                       that have given us the boost we needed to get back
                       on track. There are note-taking apps, habit
                       trackers, calendar organisers, jira editors,
                       drawing tools and even a snap to remind you to take
                       regular breaks. Let’s look back at some of the top
                       productivity-related applications from this year.


                # ⚓ Firebird_3.0.8_Docker_image_is_released⠀⇛


                       Firebird 3.0.8 Docker image is released and the
                       following tags can be used : 3.0, v3.0, v3.0.8 .


                # ⚓ FWUPD_1.7.2_Released_With_Fixes,_Faster_&_Smaller_Daemon_–
                  Phoronix⠀⇛


                       FWUPD 1.7.2 is out as the latest release of this
                       leading open-source solution for handling firmware
                       updates under Linux for devices from motherboard
                       UEFI to peripheral firmware.


                       FWUPD 1.7.2 adds support for handling exported MTD
                       block devices, tweaking the compiler flags to
                       reduce the install size by around 300 Kb, speeding
                       up the FWUPD daemon startup by ~40% by postponing
                       some work, and a variety of fixes. The fixes range
                       from a possible DFU crash to DLI download troubles
                       and other device-specific corrections.


          o § Instructionals/Technical⠀➾


                # ⚓ How_To_Install_Apache_with_Let’s_Encrypt_SSL_on_Ubuntu
                  20.04_LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Apache with Let’s Encrypt SSL on Ubuntu 20.04 LTS.
                       For those of you who didn’t know, Let’s Encrypt is
                       a certificate authority that provides free SSL
                       certificates for websites. All SSL certificates
                       provided by Let’s Encrypt can be used for
                       production/commercial purposes without any costs or
                       fees. This guide will tell you about installing the
                       Apache web server, installing the Certbot,
                       generating an SSL certificate with Certbot, and
                       creating additional SSL configuration to get the A+
                       from the SSL test SSL Labs.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the Apache with free SSL 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_and_use_the_HTTP_prompt_in_Linux⠀⇛


                       In this article, we are going to discuss the
                       installation process and use cases of HTTP Prompt.
                       HTTP Prompt is an interactive command-line HTTP
                       client which is used for testing and debugging
                       purposes and built on HTTPie and HTTP Toolkit. It
                       has a special feature of auto-complete,
                       interactive, and syntax highlighting. It has other
                       features as well such as auto cookies, Unix-like
                       pipelines, OpenApi/Swagger Integration, and HTTpie
                       compatibility.


                # ⚓ How_to_run_RethinkDB_with_Docker_and_Docker-Compose⠀⇛


                       In this guide we are going to explore how to run
                       RethinkDB locally with docker and docker compose.
                       This can be helpful if you want to run RethinkDB
                       locally without installing it in your machine or if
                       you want to run multiple versions of RethinkDB
                       seamlessly.


                # ⚓ How_to_play_Super_Nintendo_games_on_Linux_with_Higan⠀⇛


                       Higan is a multi-system emulator. Previously, Higan
                       was known as Bsnes, a super Nintendo emulator.
                       However, Higan still supports Super Nintendo roms,
                       and in this guide, we’ll show you how to play them
                       with this app.


                       Note: AddictiveTips in no way endorses using Higan
                       to play Super Nintendo ROMS that have been
                       illegally downloaded. Please only play games you’ve
                       backed up from your collection.


                # ⚓ How_to_Install_VirtualBox_on_Linux_and_Create_Your_First
                  Virtual_Machine⠀⇛


                       Setting up a virtual machine can be a great way to
                       test software or alternative operating systems on
                       your computer without altering or putting your
                       current system at risk.


                       Follow along to install VirtualBox on Linux and
                       create your very first virtual machine.


                # ⚓ How_to_customize_VM_and_cloud_images_with_guestfish_|
                  Enable_Sysadmin⠀⇛


                       Most sysadmins are used to dealing with base,
                       guest, or gold images to provision new virtual
                       machines (VM) or cloud instances in their
                       traditional virtualization or cloud environments.
                       The appeal of using these images is their slim
                       size, standardization, simplicity, and basic
                       configurations, from which it is possible to
                       perform pre- or post-provisioning customization.
                       Much of the customization takes place post-
                       provisioning.


                # ⚓ How_to_install_and_configure_Redis_6_on_FreeBSD_13⠀⇛


                       Redis is an in-memory data structure store, used as
                       a distributed, in-memory key–value database, cache
                       and message broker, with optional durability. Redis
                       supports different kinds of abstract data
                       structures, such as strings, lists, maps, sets,
                       sorted sets, HyperLogLogs, bitmaps, streams, and
                       spatial indices.


                # ⚓ Container_Layer_Analyzer_–_openQA_bites⠀⇛


                       Today I’d like to point out an amazing new tool:
                       The Container Layer Analyzer, written by Dan
                       Čermák. Dan also wrote a comprehensive blog post
                       about it, which explains it much better than what I
                       do here.


                # ⚓ How_To_Install_cPanel_on_AlmaLinux_8_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       cPanel on cPanel 8. For those of you who didn’t
                       know, cPanel is a commercial enterprise-grade web
                       hosting control panel. It is designed for hosting
                       needs and used by most of the hosting companies for
                       dedicated hosting, semi-dedicated hosting, shared
                       hosting as well as cloud VPS hosting providers.
                       This is one of the best control panels for every
                       web hosting service.


                       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 cPanel on an AlmaLinux 8. You
                       can follow the same instructions for Fedora, RHEL,
                       CentOS, and Rocky Linux distributions.


                # ⚓ How_to_Install_Discord_on_Fedora_Linux⠀⇛


                       It is a boon to several communities, which helps
                       them to expand their projects, reach out to more
                       people, and maintain a community of fans and
                       followers. It’s surprising considering that Discord
                       was originally meant for gamers.


                       Discord is available for various platforms,
                       including Linux. In this tutorial, I’ll walk you
                       through the steps for installing Discord in Fedora.


                # ⚓ How_to_Install_GlassFish_Java_Server_with_Nginx_as_a
                  Reverse_Proxy_on_Debian_11⠀⇛


                       GlassFish is an open-source application server used
                       for deploying Java applications. It supports
                       different Java-based technologies including, JPA,
                       JavaServer Faces, JMS, RMI, as well as many other
                       Java-based technologies. It provides a web-based as
                       well as a command-line interface for managing Java
                       applications and their components. GlassFish allows
                       you to create portable and scalable applications
                       that can be easily integrated with legacy
                       technologies.


                       In this tutorial, I will show you how to install
                       the Glassfish server with Nginx as a reverse proxy
                       on Debian 11.


                # ⚓ How_to_Install_Nethogs_on_Centos_8_–_ByteXD⠀⇛


                       Nethogs is a small, free, open-source utility used
                       to monitor network traffic for Linux. Nethogs
                       behaves differently from other traffic monitoring
                       tools, as it groups the bandwidth per process,
                       instead of breaking the traffic down per subnet or
                       a protocol. It doesn’t rely on kernel modules to be
                       loaded. Therefore, Linux administrators using
                       Nethogs can easily identify which program is
                       generating utilization spikes.


                       Nethogs relies on /proc, so most of the features
                       are only available on Linux therefore, it doesn’t
                       work well for other operating systems such as
                       FreeBSD and Mac OS X. Nethogs tool will only
                       display the connections on these systems without
                       displaying the processes. Nethogs program is useful
                       for monitoring real-time network traffic. Moreover,
                       you can track a specific network interface or all
                       network interfaces using this utility on your
                       system.


                       This article will show how to install nethogs on
                       CentOS 8 and we will also explain how to monitor or
                       track network traffic using the nethogs tool.


                # ⚓ How_to_Install_VirtualBox_Guest_Additions_on_Rocky_Linux_8
                  –_VITUX⠀⇛


                       Running any operating system on a virtual box takes
                       experience. You have to figure out various issues
                       like connectivity issues and performance issues but
                       out of all of them, the graphical issues is an
                       exercise in patience. Not having fullscreen, shared
                       clipboard, and file sharing limit your efficiency
                       but also destroys the whole experience.


                       VirtualBox Guest Additions is a beautiful piece of
                       software that solves these issues in a single shot
                       and ensures better display, performance, and
                       overall functionality. Adding Virtualbox Guest
                       Additions used to be very easy but there are a few
                       errors and issues that are coming up with new
                       versions of the operating systems. you have to
                       ensure all the package dependencies are fulfilled.
                       In this article, You will learn how to install
                       VirtualBox Guest Additions in the up-and-coming
                       Rocky Linux.


                # ⚓ How_to_Install_XanMod_Kernel_on_Linux_Mint_20_–
                  LinuxCapable⠀⇛


                       XanMod is a free, open-source general-purpose Linux
                       Kernel alternative to the stock kernel with Linux
                       Mint 20. It features custom settings and new
                       features and is built to provide a responsive and
                       smooth desktop experience, especially for new
                       hardware. XanMod is popular amongst Linux Gaming,
                       streaming, and ultra-low latency requirements and
                       often boasts the latest Linux Kernels, having
                       multiple branches to choose from the stable, edge,
                       and development.


                       For users seeking to have their system kernel up to
                       date and not wanting to manually install kernels or
                       use the testing/unstable repositories, installing a
                       third-party kernel may be for you.


                       In the following tutorial, you will learn how to
                       import the XanMod repository and install the latest
                       Linux Kernel on your Linux Mint 20.xx operating
                       system.


                # ⚓ How_to_Install_osTicket_on_Debian_11_Bullseye_–_Linux
                  Shout⠀⇛


                       Here in this tutorial, we will install the OSTicket
                       open source support ticketing system on Debian 11
                       Bullseye using Apache, PHP, and MySQL, or MariaDB.


                       osTicket offers free, open-source ticket management
                       and customer care solutions for businesses of all
                       sizes, especially small and medium-sized
                       businesses. The software can be used to capture
                       tickets and assign custom fields to each ticket,
                       creating a list of data associated with each ticket
                       that can be shared with customers in the knowledge
                       base. You can create automatic reply templates for
                       incoming email tickets, and rich text HTML lets you
                       add your logo, images, and videos to tickets.


                       With the ticket filter tool provided by osTicket,
                       you can define routing rules for tickets so that
                       tickets are sent to the correct person or
                       department. Tickets can also be reassigned if not
                       received by the correct person, and notes on all
                       actions are logged in the ticket thread. The
                       ticketing software helps to further streamline
                       operations by preventing agent collisions using the
                       ticket lock tool. Other features include an
                       autoresponder, customer portal, and dashboard
                       reports.


                # ⚓ How_to_install_Erlang_on_FreeBSD_13–_Citizix⠀⇛


                       Erlang is a functional, general-purpose, concurrent
                       programming language and garbage-collected runtime
                       environment built for concurrency, fault tolerance,
                       and distributed application architectures. It is
                       supported and maintained by Ericsson OTP product
                       unit.


                # ⚓ How_to_install_pgAdmin_4_version_6.2_on_Ubuntu_21.10⠀⇛


                       In this tutorial guide I will be taking through the
                       installation of pgAdmin 4 version 6.2 on Ubuntu
                       21.10.


                       pgAdmin 4 is free and opensource management tool
                       for Postgres. Its desktop runtime written in NWjs
                       allows it to run standalone for individual users,
                       or the web applications code may be directly
                       deployed on a web server for use by the web
                       browser.


                       pgAdmin 4 is a complete rewrite of pgAdmin, built
                       using Python and Java


                # ⚓ How_to_install_and_configure_Redis_6_on_Ubuntu_20.04⠀⇛


                       Redis is an in-memory data structure store, used as
                       a distributed, in-memory key–value database, cache
                       and message broker, with optional durability. Redis
                       supports different kinds of abstract data
                       structures, such as strings, lists, maps, sets,
                       sorted sets, HyperLogLogs, bitmaps, streams, and
                       spatial indices.


                       In this tutorial we are going to learn how to
                       install Redis 6 on Ubuntu 20.04.


                # ⚓ How_to_install_RabbitMQ_in_FreeBSD_13_–_Citizix⠀⇛


                       In this guide we will explore how to install the
                       latest release of RabbitMQ On a FreeBSD Server or
                       Workstation


                       RabbitMQ is an open source message broker software
                       that implements the Advanced Message Queuing
                       Protocol (AMQP). RabbitMQ works by receiving
                       messages from publishers (applications that publish
                       them) and routes them to consumers (applications
                       that process them).


          o § Wine or Emulation⠀➾


                # ⚓ Wine_6.22_Announcement⠀⇛


                       The Wine development release 6.22 is now available.

                       What's new in this release (see below for details):
                         - Mono engine updated to version 7.0.0.
                         - Exception unwinding on ARM.
                         - More improvements to HID joystick support.
                         - WoW64 thunks in a number of Unix libraries.
                         - Beginnings of moving USER32 to Win32u.
                         - Various bug fixes.

                       The source is available from the following
                       locations:

                       https://dl.winehq.org/wine/source/6.x/wine-
                       6.22.tar.xz


                       http://mirrors.ibiblio.org/wine/source/6.x/wine-
                       6.22.tar.xz

                       Binary packages for various distributions will be
                       available from:

                       https://www.winehq.org/download

                       You will find documentation on https://
                       www.winehq.org/documentation

                       You can also get the current source directly from
                       the git
                       repository. Check https://www.winehq.org/git for
                       details.

                       Wine is available thanks to the work of many
                       people. See the file
                       AUTHORS in the distribution for the complete list.
                # ⚓ Wine_6.22_Released_With_Mono_7.0,_Joystick_Improvements⠀⇛


                       Wine 6.22 is out as the latest bi-weekly
                       development release of this open-source software
                       for running Windows games and applications on Linux
                       and other platforms like macOS and FreeBSD. Wine
                       6.22 brings more improvements while the Wine 7.0
                       stable release is inching closer.


                       We’ll likely see the freeze begin in December for
                       Wine 7.0. In fact, last year at this time down to
                       the very week after Wine 5.22 the Wine 6.0 release
                       preparations began in working towards its January
                       release. The same dance will likely begin soon for
                       Wine 7.0.


          o § Games⠀➾


                # ⚓ Seek_the_truth⠀⇛


                       After more than 10 years of development, the
                       ScummVM Team is pleased to announce support for the
                       psychological-horror adventure game Sanitarium.


                # ⚓ Proton_Experimental_update_fixes_up_DEATHLOOP,_Forza
                  Horizon_5_and_more_|_GamingOnLinux⠀⇛


                       More fixes made their way into Proton Experimental
                       yesterday, with Valve / CodeWeavers fixing up some
                       issues in a few different games. What is Proton?
                       It’s a compatibility layer designed to run Windows
                       games from Steam on Linux. See more about it in our
                       full guide.


                # ⚓ Deck-building_RPG_Xenotheria_looks_like_it’s_worth_keeping
                  an_eye_on_|_GamingOnLinux⠀⇛


                       Ganymede Games have announced Xenotheria, a story-
                       driven deck-building RPG with turn-based combat
                       with plans to support Linux at the full release.


                       “Xenotheria takes place on Wolf Prime, a sprawling
                       desert planet that’s home to the galaxy’s most
                       important trading port. A seemingly ordinary day
                       quickly turns chaotic after a mysterious,
                       cataclysmic event. What follows can only be
                       described as a shower of spaceships, satellites and
                       orbital stations raining down havoc on the innocent
                       souls of Wolf Prime. One of those souls is
                       Squiggles, a hard-working spaceship construction
                       yard worker with a heart of gold.


                # ⚓ Kingdom_Two_Crowns:_Norse_Lands_expansion_is_out_now_|
                  GamingOnLinux⠀⇛


                       Kingdom Two Crowns: Norse Lands is a brand new
                       expansion for the popular mix of strategy and
                       exploration from publisher Raw Fury and developers
                       Stumpy Squid / Fury Studios.


                       This expansion brings with it a new land to
                       explore, inspired by Norse Viking culture with a
                       whole new campaign to expand the world. In Norse
                       Lands, players can look forward to unleashing
                       abilities drawn upon from Norse gods, commanding
                       mighty units, building Viking- inspired armaments,
                       solving challenging puzzles, and facing a new enemy
                       Greed.


                # ⚓ Nobodies:_After_Death_is_a_point_&_click_where_you_clean_up
                  after_assassins_|_GamingOnLinux⠀⇛


                       Nobodies: After Death is another point & click game
                       where you’re part of the cleaning crew for a top-
                       secret intelligence agency from developer Blyts.
                       The second game of its kind from Blyts, following
                       on from Nobodies: Murder Cleaner released in 2019
                       which was actually pretty good.


                       “You are a ‘cleaner’ for a top-secret intelligence
                       agency. Your mission is to hide all evidence of
                       carefully planned murders, leaving no sign that you
                       or the target were ever there.


                # ⚓ Set_off_chain_reactions_in_the_explosive_upcoming_Bomb_Club
                  Deluxe_|_GamingOnLinux⠀⇛


                       Bomb Club Deluxe is an upcoming casual comedy game
                       about setting off many explosions across hundreds
                       of levels from Antoine Latour and Lozange Lab (Swim
                       Out / Rip Them Off).


                       Looking over the details, it plays out like a
                       puzzle game with you need to place the right type
                       of bomb in the right location, to set off a chain
                       reaction of all the other bombs going off to
                       complete a level and it sure does look fun.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ 15_Best_GNOME_Extensions_for_Ubuntu_(2021_Edition)⠀⇛


                             Well, how about here, with this list of the
                             best GNOME Shell extensions for Ubuntu.


                             This roundup makes an ideal starting point
                             for anyone looking to experiment with GNOME
                             extensions on their Ubuntu install,
                             regardless of which version it is.


                             Better yet, this roundup is fully up-to-date
                             for 2021 and only includes GNOME extensions
                             that are actively maintained and work with
                             Ubuntu 20.04 LTS (and up).


                             Read on to discover some truly great add-ons!


                      # ⚓ Emmanuele_Bassi:_Fair_Weather_Friends⠀⇛


                             Today I released libgweather-3.90.0, the
                             first developers snapshot of GWeather 4….


                      # ⚓ Felix_Häcker:_#19_Updated_Calculations⠀⇛


                             Update on what happened across the GNOME
                             project in the week from November 12 to
                             November 19.


          o § Distributions⠀➾


                # ⚓ Discover_Slitaz,_a_50MB_Lightweight_Desktop_Operating
                  System⠀⇛


                       Slitaz GNU/Linux is an Swiss computer operating
                       system that is user-friendly, super lightweight and
                       very fast to install, with a spider logo, for both
                       desktop and server. It can run on a quarter of a GB
                       memory. Its installation image is only fifty
                       megabytes, full desktop included, with LiveCD
                       capability. We overview Slitaz in this article with
                       short highlights on where you can get it, available
                       versions and how its desktops and applications are.
                       Happy discovering!


                # ⚓ What_is_Clear_Linux?_—_Most_Powerful_Operating_System_in
                  2022⠀⇛


                       The most powerful Operating and Best Kept Secret of
                       2021. There is a new kid on the block, Clear Linux
                       by Intel.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ Ruby,_Plasma,_GTK_Update_in_Tumbleweed⠀⇛


                             There were a total of four openSUSE
                             Tumbleweed snapshots released this week.


                             Snapshot 20211117 gave KDE users the Plasma
                             5.23.3 update. The bug-fix release had
                             changes for the systemsettings5 package,
                             which had a fix for a touchscreen click. The
                             plasma-desktop had a fix involving drag and
                             drop that reset a position and overlap; the
                             package also had a fix showing an inactive
                             kwin console. The kwin package also made some
                             fixes that prevented crashing of
                             screencasting and provided a couple fixes for
                             Wayland. The update of kplotting was the
                             single KDE Frameworks 5.88.0 package updated
                             in the snapshot; the rest came in the
                             previous day’s snapshot. Xfce users also had
                             an update in the snapshot with xfce4-
                             whiskermenu-plugin 2.6.2, which provided a
                             fix for the menu not toggling after pressing
                             escape. The package also fixed shifting the
                             background when showing the menu. Other
                             packages to update in the snapshot were
                             fribidi 1.0.11 and restorecond 3.3, which is
                             a daemon that watches for file creation.


                      # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2021/46⠀⇛


                             Dear Tumbleweed users and hackers,


                             This week, we had a little bit of a fight
                             with our snapshots in openQA: not because of
                             openQA, but actually because some issues
                             could not have been in staging but became
                             visible in the full product tests (e.g.
                             ncurses memory leak, which manifested while
                             installing a full Tumbleweed fro the net
                             installer). So, out of the 7 snapshots
                             produced and tested, we only managed to
                             publish 3 (1111, 1116, and 1117).


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Dynamic_scheduling_of_Tekton_workloads_using_Triggers
                        |_Opensource.com⠀⇛


                             Tekton is a Kubernetes-native continuous
                             integration and delivery (CI/CD) framework.
                             It allows you to create containerized,
                             composable, and configurable workloads
                             declaratively through Kubernetes Custom
                             Resource Definitions (CRD).


                      # ⚓ Improve_multicore_scaling_in_Open_vSwitch_DPDK⠀⇛


                             A new feature in version 2.16 of Open vSwitch
                             (OVS) helps developers scale the OVS-DPDK
                             userspace datapath to use multiple cores. The
                             Data Plane Development Kit (DPDK) is a
                             popular set of networking libraries and
                             drivers that provide fast packet processing
                             and I/O.


                             After reading this article, you will
                             understand the new group assignment type for
                             spreading the datapath workload across
                             multiple cores, how this type differs from
                             the default cycles assignment type, and how
                             to use the new type in conjunction with the
                             auto load balance feature in the poll mode
                             driver (PMD) to improve OVS-DPDK scaling.


                      # ⚓ Hybrid_work_model:_3_ways_to_simplify_yours⠀⇛


                             Last year’s expedited shift to remote work
                             did not give business leaders much time to
                             map out a thoughtful out-of-office setup for
                             employees. But the challenges leaders have
                             faced over the past year and a half have led
                             to a better understanding of how to lead a
                             hybrid workforce – and how to simplify the
                             hybrid work model.


                      # ⚓ Remi_Collet:_PHP_version_7.3.33,_7.4.26_and_8.0.13⠀⇛


                             RPMs of PHP version 8.0.13 are available in
                             remi repository for Fedora 35 and remi-php80
                             repository for Fedora 33-34 and Enterprise
                             Linux (RHEL, CentOS).


                             RPMs of PHP version 7.4.26 are available in
                             remi repository for Fedora 33-34 and remi-
                             php74 repository Enterprise Linux (RHEL,
                             CentOS).


                             RPMs of PHP version 7.3.33 are available in
                             remi-php73 repository for Enterprise Linux
                             (RHEL, CentOS).


                      # ⚓ Red_Hat_Satellite_6.10.1_has_been_released⠀⇛


                             We are pleased to announce that Red Hat
                             Satellite 6.10.1 is generally available as of
                             November 18, 2021.


                             Red Hat Satellite is part of the Red Hat
                             Smart Management subscription that makes it
                             easier for enterprises to manage patching,
                             provisioning, and subscription management of
                             Red Hat Enterprise Linux infrastructure.


                      # ⚓ Putting_security_into_DevOps_is_tougher_than_it_looks
                        [Ed: Red Hat fluff. The_Register_is_dead. “PAID
                        FEATURE” it discloses at the top… so they’ve quit
                        journalism and are just posting junk for deep-pocketed
                        companies/people who pay them to do it; The Register
                        has been increasingly compromised this past year.]⠀⇛


                             If software development has absorbed a single
                             lesson in the last two decades it’s that
                             there’s an urgent need to integrate security
                             at an early stage rather than leaving flaws
                             to rot dangerously inside compiled code.
                             Optimistically, dubbed shift left, the trick
                             has been working out what this means in an
                             era undergoing an historic transformation of
                             development models.


                             In monolithic, linear development,
                             implementing shift left was about adding a
                             security checking stage earlier in the coding
                             lifecycle. This was never easy and, the
                             complaint went, slowed everything down, but
                             the pileup of vulnerability disasters told
                             the industry something had to change. One
                             case study was Microsoft’s then novel
                             Security Development Lifecycle (SDL) of the
                             early 2000s.


                             Today, however, coding is increasingly
                             defined by cloud native applications, agile
                             development, and infrastructure as code
                             (IaC), coordinated using continuous
                             deployment platforms such as Kubernetes. In
                             this world of high-velocity DevOps, the idea
                             of early intervention is stretched to
                             breaking point. Code is created, tested, and
                             deployed at incredible speed.


                      # ⚓ Fedora_Community_Blog:_Friday’s_Fedora_Facts:_2021-
                        46⠀⇛


                             Here’s your weekly Fedora report. Read what
                             happened this week and what’s coming up. Your
                             contributions are welcome (see the end of the
                             post)!


                             Fedora Linux 33 will reach end of life on
                             Tuesday 30 November. The F35 retrospective
                             survey is open through 4 December.


                             I have weekly office hours on Wednesdays in
                             the morning and afternoon (US/Eastern time)
                             in #fedora-meeting-1. Drop by if you have any
                             questions or comments about the schedule,
                             Changes, elections, or anything else. See the
                             upcoming meetings for more information.


                      # ⚓ Near_Zero_Downtime_maintenance_with_RHEL_for_SAP
                        Solutions [Ed: IBM Red Hat -- like SUSE -- is shilling
                        SAP's proprietary software again, as if for GNU/Linux
                        to win this is what's required]⠀⇛


                # § EasyOS Development⠀➾


                      # ⚓ Home_button_fixed_in_ROX-Filer⠀⇛


                             At the top of a ROX-Filer window, there is an
                             icon of a house, mouseover shows “Change to
                             home directory”. Clicking that icon changes
                             the window to the /root folder.


                      # ⚓ Mesa_now_has_r600_and_radeonsi_drivers⠀⇛


                             Folder /usr/lib/dri has drivers that provide
                             hardware acceleration for libGL.


                      # ⚓ Package_libxres_compiled⠀⇛


                             I was recently compiling a source package,
                             forget what it was, might have been xfce, it
                             required a dependency ‘libxres”. OK, it is a
                             small library, might as well include it in
                             the build, so now compiled in OpenEmbedded
                             and added to the EasyOS package-list.


                # § Debian Family⠀➾


                      # ⚓ True_Convergence_is_Here:_PureOS_10_is_Released_for
                        all_Librem_Products⠀⇛


                             Purism has released its latest version of its
                             convergent operating system (OS), PureOS 10,
                             code named Byzantium. PureOS is a freedom
                             respecting, free software OS that is neither
                             based on Android nor iOS. Endorsed by the
                             Free Software Foundation it is now the
                             default operating system installed on all
                             Librem products, including the


                             PureOS is the first truly convergent
                             operating system, where the same OS is used
                             for laptops, desktops, and mobile.


                             The new version, PureOS 10, is now the
                             default for Purism’s Librem laptops, phones,
                             and mini-computers. “Making the same OS
                             convergent across mobile, laptop, and desktop
                             computers is a dream many big technology
                             companies have, but so far none have
                             achieved. It’s taken a lot of investment and
                             work to make PureOS 10 an OS with true
                             convergence, and now it’s a dream come true.”
                             said Kyle Rankin, Chief Security Officer at
                             Purism.


                      # ⚓ Purism’s_Librem_5_Linux_smartphone_costs_$1199_after
                        the_latest_price_hike⠀⇛


                             The Purism Librem 5 was one the most powerful
                             smartphone capable of running mainline Linux
                             software when the first units began shipping
                             in limited quantities a few years ago. But
                             it’s also one of the most expensive – and
                             that’s even more true after a price hike that
                             took effect this month.


                             When Purism launched a crowdfunding campaign
                             for the Librem 5 in 2017, backers could pre-
                             order the phone for $599. The price has gone
                             up several times since then, and now the
                             Librem 5 costs twice as much.


                      # ⚓ Raven_Reader⠀⇛


                             There is a new application available for
                             Sparkers: Raven Reader


                      # ⚓ Neil_Williams:_git_worktrees⠀⇛


                             You could go to the trouble of making a new
                             directory and re-cloning the same tree.
                             However, a local commit in one tree is then
                             not accessible to the other tree.


                             You could commit everything every time, but
                             with a dirty tree, that involves sorting out
                             the .gitignore rules as well. That could well
                             be pointless with an experimental change.


                             Git worktrees allow multiple filesystems from
                             a single git tree. Commits on any branch are
                             visible from other branches, even when the
                             commit was on a different worktree. This
                             makes things like cherry-picking easy,
                             without needing to push pointless changes or
                             branches.


                             Branches on a worktree can be rebased as
                             normal, with the benefit that commit hashes
                             from other local changes are available for
                             reference and cherry-picks.


                             I’m sure git worktrees are not new. However,
                             I’ve only started using them recently and
                             others have asked about how the worktree
                             operates.


                      # ⚓ Bits_from_Debian:_New_Debian_Developers_and
                        Maintainers_(September_and_October_2021) [Ed: GNU/Linux
                        is now used more than ever before, much of it in use is
                        Debian-based distros, yet Debian got only one new
                        developer (DD) per month lately]⠀⇛


                             The following contributors got their Debian
                             Developer accounts in the last two months:


                             Bastian Germann (bage)
                             Gürkan Myczko (tar)


                             The following contributors were added as
                             Debian Maintainers in the last two months:


                             Clay Stan
                             Daniel Milde
                             David da Silva Polverari
                             Sunday Cletus Nkwuda
                             Ma Aiguo
                             Sakirnth Nagarasa


                             Congratulations!


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Lilbits:_A_smartphone_with_a_smartwatch_on_the_back,
                        mini_PCs,_and_Linux_for_phones,_PCs,_and_servers⠀⇛


                      # ⚓ Ubuntu_Touch_OTA-20_Release_|_UBports⠀⇛


                             Ubuntu Touch is the privacy and freedom-
                             respecting mobile operating system by
                             UBports. Today we are happy to announce the
                             release of Ubuntu Touch OTA-20, our twentieth
                             stable update to the system! OTA-20 will
                             become available for the following supported
                             Ubuntu Touch devices over the next week:


                             BQ E4.5 Ubuntu Edition
                             BQ E5 HD Ubuntu Edition
                             BQ M10 (F)HD Ubuntu Edition
                             BQ U Plus
                             Cosmo Communicator
                             F(x)tec Pro1
                             Fairphone 2
                             Fairphone 3
                             Google Pixel 2XL
                             Google Pixel 3a
                             Huawei Nexus 6P
                             LG Nexus 4
                             LG Nexus 5
                             Meizu MX4 Ubuntu Edition
                             Meizu Pro 5 Ubuntu Edition
                             Nexus 7 2013 (Wi-Fi and LTE models)
                             OnePlus 2
                             OnePlus 3 and 3T
                             Oneplus 5 and 5T
                             OnePlus 6 and 6T
                             OnePlus One
                             Samsung Galaxy Note 4 (910F, 910P, 910T)
                             Samsung Galaxy S3 Neo+ (GT-I9301I)
                             Sony Xperia X
                             Sony Xperia X Compact
                             Sony Xperia X Performance
                             Sony Xperia XZ
                             Sony Xperia Z4 Tablet (LTE or Wi-fi only)
                             Vollaphone
                             Vollaphone X
                             Xiaomi Mi A2
                             Xiaomi Mi A3
                             Xiaomi Mi MIX 3
                             Xiaomi Poco F1
                             Xiaomi Redmi 3s/3x/3sp (land)
                             Xiaomi Redmi 4X
                             Xiaomi Redmi 7
                             Xiaomi Redmi Note 7 and 7 Pro
                             Xiaomi Redmi 9 and 9 Prime
                             Xiaomi Redmi Note 9, 9 Pro, 9 Pro Max and 9S


                      # ⚓ UBports_releases_its_twentieth_stable_update_of
                        Ubuntu_Touch⠀⇛


                             Do you remember several years ago when all
                             the tech firms wanted in on the mobile space
                             but were more or less forced out due to
                             Apple’s and Google’s market dominance? One of
                             the players was Canonical which was aiming
                             for true convergence across desktop, tablets,
                             and phones. Canonical ended up shelving that
                             ambitious goal but its mobile operating
                             system, Ubuntu Touch, was picked up by the
                             UBports Foundation and that organisation has
                             just published OTA-20, the twentieth stable
                             release of Ubuntu Touch.


                             Building and maintaining an operating system
                             is no easy job which explains why Ubuntu
                             Touch OTA-20 is still based on the archaic
                             Ubuntu 16.04 which came out more than five
                             years ago. Nevertheless, the team is still
                             working away on improvements. In this update,
                             LED notification support was added for
                             devices with the Halium 9 base. If your
                             device is newer and doesn’t have an LED
                             light, vibration support for incoming
                             notifications has also been added. Other new
                             features include support for Khmer and
                             Bengali fonts and the ability to define a
                             custom notification sound by picking any
                             audio file.


                      # ⚓ Ubuntu_Touch_OTA-20_Released_for_Linux_Phones,_Here’s
                        What’s_New⠀⇛


                             Still based on the Ubuntu 16.04 LTS (Xenial
                             Xerus) operating system series, Ubuntu Touch
                             OTA-20 is a maintenance update that
                             introduces support for the notification LED
                             and vibration for incoming notifications on
                             Halium 9 devices, such as OnePlus 6, OnePlus
                             6T, Xiaomi Mi A2, Xiaomi Mi 6, and others.


                             However, the devs note the fact that some
                             recent devices with a Halium 9 base do not
                             have a notification LED, so this new feature
                             doesn’t apply to them. These include the
                             Volla Phone and Google Pixel 3a.


                      # ⚓ Distrowatch_Top_5_Distributions_Review:_Linux_Mint⠀⇛


                             Besides the couple of negatives I listed
                             earlier, I really don’t have much negative to
                             say about Linux Mint. It’s got graphical
                             tools for driver installations, it’s got
                             great support, it’s based on one of the most
                             commonly used OS’s in the Linux World, and
                             it’s a system that even first-time users can
                             enjoy. Cinnamon is a gorgeous Desktop
                             Environment for those who enjoy more
                             traditional layouts similar to Windows, and
                             it’s highly customizable too. I highly
                             recommend anyone who hasn’t used it yet,
                             check this OS out.


          o § Devices/Embedded⠀➾


                # ⚓ 10.1-inch_Raspberry_Pi_All-in-One_touchscreen_display
                  review_–_Part_1:_Unboxing_and_installation⠀⇛


                       I’ve just received a 10.1-inch touchscreen display
                       designed for Raspberry Pi model B boards with
                       1920×1080 resolutions from the EVICIV store on
                       Amazon that also offers models with 1366×378 and
                       1280×800 resolutions, and allows users to create an
                       All-in-One computer based on the popular SBC.


                       The product can also be used as a standalone
                       display connected to an HDMI or USB-C (via
                       DisplayPort Alt mode) source, so it could be
                       interesting for all sorts of projects and not only
                       ones relying on Raspberry Pi boards. In the first
                       part of the review, I’ll check out the hardware,
                       install a Raspberry Pi 4, and boot it to check out
                       whether it works, before going into more details in
                       the second part of the review.


                # ⚓ Jetson_powered_systems_offer_dual_GbE_and_a_256GB_SSD⠀⇛


                       Seeed’s Xavier NX based “Jetson EX1 Mini PC-Ubuntu”
                       and 2.5-inch equipped “Jetson SUB Mini PC-Black”
                       systems offer 2x GbE, 2x HDMI, 4x USB, and 256GB
                       storage. There is also a metal-clad “Silver”
                       variant of the earlier Jetson SUB Mini PC Kit.


                       Last month, Seeed launched a $799 Jetson SUB Mini
                       PC Kit. The kit is almost identical to Nvidia’s
                       Jetson Xavier NX Developer Kit but is based on
                       Leetop’s A206 Jetson carrier board equipped with a
                       Jetson Xavier NX module. Seeed has now launched two
                       more Xavier NX-based systems: a Jetson EX1 Mini PC-
                       Ubuntu and a larger Jetson SUB Mini PC-Black, which
                       is equipped with a 2.5-inch SATA bay.


                # ⚓ Jetson_EX1_and_SUB_mini_PCs_put_Xavier_NX_SoM_into_metal
                  enclosures⠀⇛


                       Seeed Studio has just unveiled another Jetson
                       Xavier NX mini PC with the Jetson EX1, plus some
                       metal enclosures for the Jetson SUB mini PC
                       announced last month with the official NVIDIA
                       Jetson Xavier NX developer kit, a 128GB SSD, and
                       the Re_Computer case comprised of an aluminum frame
                       and a plastic cover.


                       The Jetson EX1 mini PC has a different design with
                       a custom carrier board offering dual Gigabit
                       Ethernet and support for four MIPI CSI cameras, a
                       256GB NVMe SSD, and an aluminum enclosure designed
                       to help with cooling, albeit the computer is not
                       completely fanless since a 5V fan is included in
                       the design as well.


                # ⚓ Linux-on-NXP_boards_from_Kontron_and_SolidRun_gain_Arm
                  SystemReady_compliance⠀⇛


                       Kontron and SolidRun have each announced several
                       NXP-based embedded products that have achieved Arm
                       SystemReady certification for interoperable Linux
                       stacks and boot systems.


                       Following Arm’s formal announcement of its Arm
                       SystemReady initiative in Oct. 2020, support for
                       the interoperability program has begun to
                       accelerate. Yesterday, Kontron announced three
                       embedded Linux products based on NXP processors
                       that have received Arm SystemReady certification
                       for standardized firmware and hardware running on
                       Arm-based CPUs. The products include its pITX-iMX8M
                       Pico-ITX SBC and sandwich-style BL i.MX8M Mini, as
                       well as a new KBox A-203-LS networking box with an
                       NXP LS1028A.


                # § Open Hardware/Modding⠀➾


                      # ⚓ This_Portal_fan_brought_Wheatley_to_life_as_his_own
                        personal_assistant [ed: This is a listening device of
                        (or for) Amazon]⠀⇛


                             The video game Portal 2 is widely regarded as
                             a classic that introduced players to several
                             memorable characters, including one of the
                             main protagonists-turned-antagonists,
                             Wheatley. This anthropomorphized personal
                             assistance robot was able to move, speak, and
                             listen/respond to speech from a user, which
                             is exactly what Steve Turner was trying to
                             recreate when he built his own version of
                             Wheatley. His animatronic device starts by
                             waking up, and from there it selects a folder
                             of audio files to play at random.
                             Additionally, its AI-powered interactivity is
                             provided by an Amazon Echo Dot via Alexa and
                             the Arduino Cloud.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ The_Android_12_Quick_Settings_trick_you’ve_been
                        missing_|_Computerworld⠀⇛


                      # ⚓ How_to_install_Android_12_Beta_on_Samsung_phones_–
                        9to5Google⠀⇛


                      # ⚓ Samsung_Galaxy_A13_5G_user_manual_confirms_key_specs
                        and_Android_11_onboard_–_GSMArena.com_news⠀⇛


                      # ⚓ The_Best_Games_on_Sale_for_Android_This_Week_–_Donut
                        County,_Tempest,_Deemo_Reborn_and_More_–_Droid_Gamers⠀⇛


                      # ⚓ AetherSX2:_A_promising_PS2_emulator_for_Android_–
                        Android_Authority⠀⇛


                      # ⚓ Xiaomi_12X_leak_reveals_a_Snapdragon_870-powered
                        compact_Android_‘flagship’_|_Android_Central⠀⇛


                      # ⚓ YouTube_on_Android_TV_tests_autoplay_videos_on
                        homepage_–_9to5Google⠀⇛


                      # ⚓ A_new_Lenovo_Tab_P12_Pro_on_Android_12L_has_a_new
                        Google-generated_discount_code_–_NotebookCheck.net
                        News⠀⇛


                      # ⚓ How_to_Check_Screen_Time_on_Android⠀⇛


                      # ⚓ AetherSX2:_A_promising_PS2_emulator_for_Android_–
                        Android_Authority⠀⇛


                      # ⚓ Android_Engg_Team_In_India_Will_Look_At_Developing
                        Devices_Beyond_Smartphones:_Google_India_GM⠀⇛


                      # ⚓ DuckDuckGo_Privacy_Tool:_App_Tracking_Protection_for
                        Android⠀⇛


                      # ⚓ When_is_Android_12_coming_to_Samsung_phones?⠀⇛


                      # ⚓ [Update:_Nov._19]_Xiaomi_Android_11_update_bugs_&
                        issues_tracker:_Here’s_the_current_status⠀⇛


                      # ⚓ What_are_Android_security_updates,_and_why_do_they
                        matter?⠀⇛


                      # ⚓ Google_Finally_Has_a_Solution_For_iMessage_Reactions
                        on_Android⠀⇛


                      # ⚓ Lost_your_Android_phone?_Here’s_how_to_remove_or
                        block_Google_Pay_and_Paytm_account_|_Technology
                        News,The_Indian_Express⠀⇛


          o § Free, Libre, and Open Source Software⠀➾


                # ⚓ Open-Source_Apache_CloudStack_4.16_Improves_Cloud_IaaS⠀⇛


                       The Apache CloudStack project’s second major
                       milestone release of 2021 improves storage and
                       Kubernetes integration for the cloud platform.


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ Thousands_of_Firefox_users_accidentally_commit
                              login_cookies_on_GitHub [Ed: Microsoft_just
                              doesn’t_care_about_security_and_the_media_is_paid
                              to_blame_the_victims_for_Microsoft’s_own
                              problems]⠀⇛


                                   Thousands of Firefox cookie databases
                                   containing sensitive data are available
                                   on request from GitHub repositories,
                                   data potentially usable for hijacking
                                   authenticated sessions.


                                   These cookies.sqlite databases normally
                                   reside in the Firefox profiles folder.
                                   They’re used to store cookies between
                                   browsing sessions. And they’re findable
                                   by searching GitHub with specific query
                                   parameters, what’s known as a search
                                   “dork.”


                                   Aidan Marlin, a security engineer at
                                   London-based rail travel service
                                   Trainline, alerted The Register to the
                                   public availability of these files
                                   after reporting his findings through
                                   HackerOne and being told by a GitHub
                                   representative that “credentials
                                   exposed by our users are not in scope
                                   for our Bug Bounty program.”


                                   [...]


                                   “I’m frustrated that GitHub isn’t
                                   taking its users’ security and privacy
                                   seriously,” Marlin told The Register in
                                   an email. “The least it could do is
                                   prevent results coming up for this
                                   GitHub dork. If the individuals who
                                   uploaded these cookie databases were
                                   made aware of what they’d done, they’d
                                   s*** their pants.”


                            # ⚓ Mozilla_Performance_Blog:_Upgrading_Page_Load
                              Tests_to_Use_Mitmproxy_7⠀⇛


                                   mitmproxy is a third-party tool that we
                                   use to record and play back page loads
                                   in Firefox to detect performance
                                   regressions.


                                   The page load is “recorded” to a file:
                                   the page is loaded while mitmproxy is
                                   running, and the proxy logs all
                                   requests and responses made and saves
                                   them to a file.


                                   The page load can then be played back
                                   from this file; each response and
                                   request (referred to as a “flow”) made
                                   during the recording is played back
                                   without accessing the live site.


                                   Recorded page load tests are valuable
                                   for detecting performance regressions
                                   in Firefox because they are not
                                   dependent on changes to the site we are
                                   testing. If we tested using only live
                                   sites, it would be much more difficult
                                   to tell if a regression was caused by
                                   changes in Firefox or changes in the
                                   site being tested.


                                   So, as we run these tests over time, we
                                   have a history of how Firefox performs
                                   when replaying the same recording again
                                   and again, helping us to detect
                                   performance regressions that may be
                                   caused by recent changes to our code
                                   base.


                            # ⚓ When_you_use_Bing_to_search_for_Chrome_or
                              Firefox,_this_is_what_happens_instead.⠀⇛


                                   Microsoft can’t just put on their big
                                   boy pants and admit that people don’t
                                   like Edge and don’t want to use Edge.


                                   This reeks of desperation. But then, we
                                   didn’t suspect it would end with the
                                   paid shitposting about Edge on GNU/
                                   Linux or with the million ways you can
                                   accidentally launch Edge in Windows
                                   Vista SP11. Did we?


                # § Programming/Development⠀➾


                      # ⚓ Mike_Hommey:_Announcing_git-cinnabar_0.5.8⠀⇛


                             Git-cinnabar is a git remote helper to
                             interact with mercurial repositories. It
                             allows to clone, pull and push from/to
                             mercurial remote repositories, using git.


                      # ⚓ Evgeni_Golov:_A_String_is_not_a_String,_and_that’s
                        Groovy!⠀⇛


                             Halloween is over, but I still have some
                             nightmares to share with you, so sit down,
                             take some hot chocolate and enjoy 🄸🄼🄰🄶🄴
                             🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈


                             When working with Jenkins, there is almost no
                             way to avoid writing Groovy. Well, unless you
                             only do old style jobs with shell scripts,
                             but y’all know what I think about shell
                             scripts…


                             Anyways, Eric have been rewriting the jobs
                             responsible for building Debian packages for
                             Foreman to pipelines (and thus Groovy).


                      # ⚓ Looking_for_Qt_Champions_–_2021!⠀⇛


                             Who do you think should be a Qt Champion?
                             Nominate the champions you know right now!


                      # § Perl/Raku⠀➾


                            # ⚓ Perl_Weekly_Challenge_139:_JortSort_and_Long
                              Primes⠀⇛


                      # § Rust⠀➾


                            # ⚓ Rebecca_Rumbul_named_new_CEO_of_The_Rust
                              Foundation_•_The_Register⠀⇛


                                   The Rust Foundation – the US non-profit
                                   behind the programming language since
                                   Mozilla let the team go – has picked a
                                   new CEO: Rebecca Rumbul, formerly
                                   director of research and engagement at
                                   digital democracy charity mySociety,
                                   and before that the Privacy Collective.


                                   Dr Rumbul’s appointment at the
                                   relatively new foundation reflects the
                                   growing importance of the Rust language
                                   – which can be seen from the
                                   foundation’s list of members. Facebook
                                   is using it, as is Google, Microsoft,
                                   various Linux kernel developers, and
                                   Linux lappy vendor System76. There are
                                   even a couple of Rust-based OSes, Redox
                                   and Theseus.


          o § Standards/Consortia⠀➾


                # ⚓ OpenCL_3.0.10_Brings_A_Handful_Of_New_Extensions_–
                  Phoronix⠀⇛


                       OpenCL 3.0.10 has been tagged as the newest
                       revision to the OpenCL 3.0 API.


                       One month since OpenCL 3.0.9, v3.0.10 is now
                       available with several new extensions added along
                       with some cosmetic documentation updates.


    * § Leftovers⠀➾


          o ⚓ Popsicle-Stick_Piano_Sounds_Sweet_|_Hackaday⠀⇛


                 Technically, this is a kalimbaphone, and not a piano or
                 even a chordophone since there are no strings. But this
                 handcrafted instrument doesn’t just sound sweet, it’s
                 also mellow, and it’s much nicer than you’re probably
                 imagining. Go check out the short build video, which
                 starts with a demo.


          o ⚓ Electric_Mini_Rat_Rod_Starts_‘Em_Young_|_Hackaday⠀⇛


                 These days, a lot of people barely even say hello to
                 their neighbors. But not [dewey302]. They’re so tight
                 with the people next door that they built this bad-ass
                 electric mini rat rod for the neighbors’ five-year-old
                 kid. Talk about community!


                 Nearly every bit of this rod is recycled — the body is a
                 wheelbarrow, the transaxle is from a mobility scooter,
                 and the frame was welded together from scrap tubing
                 including the wheelbarrow itself, and old bike or two,
                 and some broken lawn chairs. The rear wheels are also
                 from the ‘barrow, though the front ones were purchased
                 (one of few new parts. Power comes from a pair of 18 V
                 tool batteries wired in series and running through the
                 Curtis controller from the scooter. Depending on the
                 weight of the driver, this baby will do 10-12 MPH.


          o § Science⠀➾


                # ⚓ There_were_Almost_Jet_Packs_on_the_Moon⠀⇛


                       Here it is almost 2022 and we still don’t have our
                       jet packs. But don’t feel bad. NASA astronauts
                       wanted a lunar jetpack, but they didn’t get one
                       either. [Amy] at The Vintage Space has an
                       interesting video about what almost was, and you
                       can see it below.


                       Of course, a jet pack on the moon would be easier
                       than an Earthbound one. The goal was to allow the
                       crew to range further from their lander since they
                       couldn’t carry very much and the lander didn’t have
                       a lot of consumables, either. In addition, if you
                       lost sight of the lander, getting back could be a
                       problem since navigating on the moon was an unknown
                       skill.


                       In 1969 awarded exploratory contracts for lunar
                       personal flying vehicles including one to Bell who
                       had their Earth-bound jet pack that shows up every
                       so often for example in Bond movies.


          o § Hardware⠀➾


                # ⚓ Cheap_Big_Servo_For_Robot_Arm_|_Hackaday⠀⇛


                       [Skyentific] is looking to push the hobbyist
                       robotics state of the art. Motors and their gears,
                       the actuators, are typically the most expensive
                       part. For his build, he realised he needed big
                       servos capable of delivering plenty of torque.
                       Thus, he set about creating a 3D-printed design to
                       get the job done on a budget. (Video, embedded
                       below.)


                       Stepper motors are the order of the day here,
                       chosen for their low cost compared to brushless
                       solutions, particularly when taking control
                       hardware into account. In this design, the stepper
                       motor drives a sun gear as part of a bigger
                       planetary gearbox with a high gear ratio. Cross-
                       roller bearings are used to allow the servo to
                       effectively handle both radial and axial loads. The
                       servo as a whole is designed to fit neatly into the
                       joints of the robot arm itself, and has external
                       mounting points provisioned as such.


                # ⚓ N64_Mini_PC_Conversion_Includes_All_The_Trimmings_|
                  Hackaday⠀⇛


                       We’ve seen quite a few retro gaming consoles
                       physically modded to house modern emulation
                       hardware, but the NUC-64 by [RetroModder] stands
                       out as one of the most impressive Nintendo 64
                       guttings that we’ve seen to date.


                       Observed from the front, the NUC-64 almost
                       resembles a stock Nintendo console. The project’s
                       name is printed across the vestigial cartridge
                       slot, and two suspiciously modern wireless
                       networking antennas can be seen poking out from the
                       back. The console’s modifications are fully
                       revealed when looking at it from the rear – gone is
                       the power brick socket, which now houses the I/
                       O for the replacement motherboard. A custom 3D
                       printed I/O shield keeps everything looking neat
                       and tidy.


                # ⚓ Pushing_Photos_Through_Wires⠀⇛


                       In some ways, when I became a graphic designer in
                       the newspaper industry, I had it easy. By that
                       time, wire photos were already being transmitted
                       primarily over the internet, and those that weren’t
                       could quickly be scanned into a digital format via
                       a flatbed scanner. To place those images on the
                       page, all I had to do was hit a key command, and
                       suddenly, I was ready to paste an image in. A lot
                       of things had to happen to get us to that point,
                       and one of those things was a process called
                       phototelegraphy. This concept, essentially, refers
                       to the process of distributing images via wires or
                       through the radio, something that we’ve covered in
                       other ways previously, but not directly. In many
                       ways, it cuts to the heart of why we call wire
                       services wire services. And because I love
                       newspapers, I’m going to tell you all about them.
                       Today’s Tedium talks about formative efforts to
                       spread photographs far and wide.


                # ⚓ The_Silent_Dripper_Dispenses_Water_Without_Making_Any_Sound
                  |_Hackaday⠀⇛


                       Engineering is all about making a design that
                       conforms to a set of requirements. Usually those
                       are boring things like cost, power consumption,
                       volume, mass or compatibility with existing
                       systems. But sometimes, you have to design
                       something with restrictions you might have never
                       considered. [Devon Bray] was tasked with designing
                       a system that could dispense single drops of water,
                       while making absolutely no noise. [Devon]’s blog
                       describes in detail the process of making The
                       Silent Dripper, which was needed for an art
                       installation called The Tender Interval by [Sara
                       Dittrich].


                       The design process started with picking a proper
                       pump. Centrifugal pumps can be very quiet due to
                       their smooth, continuous motion, but are not
                       suitable for moving small quantities of liquid.
                       Peristaltic pumps on the other hand can generate
                       single drops of liquid very accurately, but their
                       gripping-and-squeezing motion creates far more
                       sound. [Devon] still went for the latter type, and
                       eventually discovered that filling up the pumping
                       mechanism with lithium grease made it quiet enough
                       for his purpose.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Dynatrace_:_Managed_release_notes_version_1.230⠀⇛


                      # § Security⠀➾


                            # ⚓ SkyFail._6_million_routers_left_exposed⠀⇛


                                   DNS rebinding is a technique that
                                   allows an attacker to bypass the Same-
                                   origin policy, a defence implemented in
                                   web browsers to prevent web
                                   applications interacting with different
                                   domains without the user’s consent.


                                   This can be exploited when a user
                                   visits a malicious web page under the
                                   control of the attacker.


                            # ⚓ diffoscope_193_released⠀⇛


                                   The diffoscope maintainers are pleased
                                   to announce the release of diffoscope
                                   version 193. T


                            # ⚓ Security_updates_for_Friday⠀⇛


                                   Security updates have been issued by
                                   Arch Linux (chromium, grafana, kubectl-
                                   ingress-nginx, and opera), Debian
                                   (netkit-rsh and salt), Fedora (freeipa
                                   and samba), Mageia (opensc, python-
                                   django-filter, qt4, tinyxml, and
                                   transfig), openSUSE (opera and
                                   transfig), Red Hat (devtoolset-11-
                                   annobin, devtoolset-11-binutils, and
                                   llvm-toolset:rhel8), SUSE (php72 and
                                   php74), and Ubuntu (mailman and
                                   thunderbird).


                            # ⚓ This_new_Linux_malware_targets_ecommerce_sites
                              ahead_of_Black_Friday [Ed: Mayank Sharma should
                              know better; this isn't the fault of Linux and
                              moreover he has added the smear against Go just
                              because people can write malicious programs in Go
                              (as they can in any other language)]⠀⇛


                                   The malicious agent, dubbed linux_avp
                                   is written in Golang, and was
                                   discovered by researchers at Sansec,
                                   who were approached by an affected
                                   merchant who couldn’t seem to get rid
                                   of malware from his store.


                            # ⚓ New_Rowhammer_Technique [Ed: We have states and
                              so-called 'tech' companies putting back doors in
                              all their stuff and yet we're meant to focus on
                              theoretical attacks of this oddball nature]⠀⇛


                                   Rowhammer is an attack technique
                                   involving accessing — that’s
                                   “hammering” — rows of bits in memory,
                                   millions of times per second, with the
                                   intent of causing bits in neighboring
                                   rows to flip. This is a side-channel
                                   attack, and the result can be all sorts
                                   of mayhem.


                            # ⚓ DDR4_memory_protections_are_broken_wide_open_by
                              new_Rowhammer_technique⠀⇛


                                   Rowhammer exploits that allow
                                   unprivileged attackers to change or
                                   corrupt data stored in vulnerable
                                   memory chips are now possible on
                                   virtually all DDR4 modules due to a new
                                   approach that neuters defenses chip
                                   manufacturers added to make their wares
                                   more resistant to such attacks.


                            # ⚓ This_Week_in_Security:_Intel_Atoms_Spill
                              Secrets,_ICMP_Poisons_DNS,_and_The_Blacksmith⠀⇛


                                   Intel has announced CVE-2021-0146, a
                                   vulnerability in certain processors
                                   based on the Atom architecture, and the
                                   Trusted Platform Module (TPM) is at the
                                   center of the problem. The goal of the
                                   system around the TPM is to maintain
                                   system integrity even in the case of
                                   physical access by an attacker, so the
                                   hard drive is encrypted using a key
                                   stored in a secure chip on the
                                   motherboard. The TPM chip holds this
                                   encryption key and provides it during
                                   the boot process. When combined with
                                   secure boot, this is a surprisingly
                                   effective way to prevent tampering or
                                   data access even in the case of
                                   physical access. It’s effective, at
                                   least, when nothing goes wrong.


                                   Earlier this year, we covered a story
                                   where the encryption key could be
                                   sniffed directly from the motherboard,
                                   by tapping the traces connecting the
                                   TPM to the CPU. It was pointed out that
                                   TPM 2.0 can encrypt the disk encryption
                                   key on the traces, making this attack
                                   impossible.


                                   The entire Trusted Compute Model is
                                   based on the premise that the CPU
                                   itself is trustworthy. This brings us
                                   back to Intel’s announcement that a
                                   debug mode could be enabled via
                                   physical access. In this debug mode,
                                   the CPU master key can be extracted,
                                   leading to complete compromise. The
                                   drive encryption key can be recovered,
                                   and unsigned firmware can be loaded to
                                   the Management Engine. This means data
                                   in the TPM enclave and the TPM-stored
                                   encryption key can be compromised.
                                   Updated firmware is rolling out through
                                   motherboard vendors to address the
                                   problem.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Privacy_legislation_reform:_Bill_64_has
                                    now_been_passed⠀⇛


                                  # ⚓ Amazon_reportedly_gave_employees_access
                                    to_practically_all_customer_data⠀⇛


          o § Environment⠀➾


                # § Wildlife/Nature⠀➾


                      # ⚓ Abundance_decline_in_the_avifauna_of_the_European
                        Union_reveals_global_similarities_in_biodiversity
                        change:_Input_datasets_&_species_results⠀⇛


                             This archive contain the two input datasets
                             of bird population estimates and trend
                             estimates underpinning the journal article:
                             Abundance decline in the avifauna of the
                             European Union reveals global similarities in
                             biodiversity change. It also contains the
                             species level results obtained from the
                             Bayesian hierarchical model described in
                             section 2.2.1 of the paper.


                      # ⚓ Eerie_video_captures_elusive,_alien-like_squid
                        gliding_in_the_Gulf_of_Mexico⠀⇛


          o § Finance⠀➾


                # ⚓ The_Zero_Hour_with_RJ_Eskow⠀⇛


                       Whitney joins RJ Eskow of the Zero Hour to discuss
                       the efforts of Wall Street banks and Central banks
                       to monetize and take ownership of the natural world
                       through the recently created Natural Asset
                       Corporations and the UN-backed Glasgow Financial
                       Alliance for Net Zero


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ From_Myanmar_to_Sudan,_autocratic_regimes_have_weaponised
                  internet_shutdowns._Time_to_fight_back.⠀⇛


                       Internet censorship is nearly as old as the
                       internet itself. While much of the theorizing about
                       the early internet viewed it as a free and open
                       space for the exchange of new ideas, a number of
                       governments had different ideas about its
                       potential.


                       While China is well-known for its sophisticated
                       internet censorship apparatus, several governments
                       across the Middle East and North Africa — including
                       Tunisia, Saudi Arabia, and Syria—were early
                       adopters of certain censorship tactics such as
                       keyword filtering and DNS tampering. Similar to
                       China, these countries targeted a range of content,
                       including sites that offered information about
                       human rights violations, sex, and certain
                       religions, as well as those that encouraged
                       political opposition.


                       But in recent years, governments have taken the
                       more decidedly extreme tactic of cutting off
                       internet access entirely, depriving their citizens
                       of a lifeline to the world…and each other, a tactic
                       that Human Rights Watch has rightly called
                       “collective punishment.”


                # ⚓ Ideas_|_Facebook_is_bad_at_moderating_in_English._In
                  Arabic,_it’s_a_disaster._–_Rest_of_World⠀⇛


                       For many, the Facebook Papers come as no surprise.
                       As a Palestinian digital rights advocate, the
                       recent revelations perfectly describe and validate
                       the archetypal experience of Palestinians and
                       millions of others generating daily content outside
                       the U.S.


                       For years, activists and civil society
                       organizations have warned of Facebook’s negligence
                       of non-English speaking regions, and its deeply
                       discriminatory content moderation structure which
                       have served to silence globally marginalized
                       voices, not empower them. Yet Facebook, at every
                       ebb and flow, has chosen profit over people.


                       The thousands of pages of leaked documents now
                       provide incontestable evidence, finally laying to
                       rest one of the biggest claims repeatedly made by
                       Facebook and its leadership since the heyday of the
                       Arab Spring: Safety and freedom of expression are
                       not afforded to all users equally, but are rather
                       dictated by the company’s market interests and
                       bottom line.


                # ⚓ Digital_world_seen_moving_into_‘authoritarian_space’_|
                  Reuters⠀⇛


                       From blocking websites to forcing companies to
                       share user data, governments – including
                       democracies – are increasingly resorting to
                       “authoritarian” methods to control the internet,
                       tech experts warned on Thursday.


                       Governments like China and Russia are blocking
                       social media content, requiring firms to submit to
                       data surveillance, and silencing journalists and
                       activists online, panelists told the Thomson
                       Reuters Foundation’s annual Trust Conference.


                       “The digital world is increasingly moving into an
                       authoritarian space,” said Alina Polyakova, head of
                       the Center for European Policy Analysis, a U.S.-
                       based think-tank.


                # ⚓ Web_trust_dies_in_darkness:_Hidden_Certificate_Authorities
                  undermine_public_crypto_infrastructure⠀⇛


                       Security researchers have checked the web’s public
                       key infrastructure and have measured a long-known
                       but little-analyzed security threat: hidden root
                       Certificate Authorities.


                       Certificate Authorities, or CAs, vouch for the
                       digital certificates we use to establish trust
                       online. You can be reasonably confident that your
                       bank website is actually your bank website when it
                       presents your browser with an end-user or leaf
                       certificate that’s linked through a chain of trust
                       to an intermediate certificate and ultimately the
                       X.509 root certificate of a trusted CA.


                       Each browser relies on a trust store consisting of
                       a hundred or so root certificates that belong to a
                       smaller set of organizations. Mozilla’s CA
                       Certificate List for example currently has 151
                       certs representing 53 organizations.


                       Some of the more well-known CAs in the US include
                       IdenTrust, DigiCert, Sectigo, and Let’s Encrypt.


          o § Monopolies⠀➾


                # ⚓ Naked_Capitalism’s_Private_Equity_Trust-Busting⠀⇛


                # § Trademarks⠀➾


                      # ⚓ Streamlabs_shamed_into_dropping_‘OBS’_from_product
                        name_after_open-source_OBS_Project_wades_into_Twitter
                        spat⠀⇛


                             One of the few virtues of Twitter is that if
                             someone makes a complaint to a big
                             corporation, it’s public. Everyone can see
                             it, which sometimes means you get a rapid
                             escalation and result. Just ask the OBS
                             Project, which this week shamed Logitech
                             subsidiary Streamlabs into changing the name
                             of a product.


                             The clash started when cloud-based streaming
                             tools vendor Lightstream pointed out the very
                             conspicuous resemblance between Streamlabs’
                             website and its own. That led to
                             Lightstream’s co-founder namechecking the
                             open-source OBS Project, on which Streamlabs
                             is based.


╘══════════════════════════════════════════════════════════════════════════════╛
                       ¶ Lines in total: 8054
    ➮ Generation completed at 02:42, i.e. 110 seconds to (re)generate ⟲