𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, June 30, 2022
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Gemini index for the day: gemini://gemini.techrights.org/2022/06/30/


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⦿ [Meme] EPO Election (Auction) | Techrights

⦿ IRC Proceedings: Wednesday, June 29, 2022 | Techrights

⦿ Published 10 Minutes Ago: IRCNow by Aaron Lin | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/06/30/epo-rigged-election/#comments
		http://techrights.org/2022/06/30/irc-log-290622/#comments
		http://techrights.org/2022/06/30/ircnow-by-aaron-lin/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/06/30/condres-os-1-0/#comments
		http://techrights.org/2022/06/30/pico-w-introduced/#comments
		http://techrights.org/2022/06/30/postgresql-15-beta-2/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 55

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/30/epo-rigged-election/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/30/epo-rigged-election/

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✐ [Meme]_EPO_Election_(Auction)⠀✐


Posted in Europe, Fraud, Patents at 8:34 pm by Dr. Roy Schestowitz


Bought outcome


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I am the f***ing president, Josef; The delegates really
                           appreciated 'mobility'⦈
   Lucky for António_Campinos that the EPO is above the law; don’t want any
                investigation into what_happened_on_Wednesday…


Summary: The corruption at the EPO did not end with Benoît_Battistelli‘s
departure; it’s still deepening


New_comment from “Experienced Examiner”:


     The situation at the EPO was bad and is worsening.


     The money discussion overlooks a huge number of facts:
     – the salaries paid in any international organisation have to be
     competitive with the highest salary of a member state. Otherwise,
     persons from this state will not apply. Local salaries will normally
     be lower.


     – the salaries paid have to provide the same standard of living
     regardless of the location. This goes back to the League of Nations,
     the predecessor of the United Nations. Some countries have higher
     expenses than others. This is where inflation kicks in. The point is
     not whether EPO employees have their salaries adjusted in line with
     inflation. The point is why inflation is ignored for national civil
     servants and also for subsidies paid (e.g. Hartz IV in Germany) or
     when determining how much tax you have to pay.
     Law Sniffer & Bitter Worker: You have your real income nibbled away
     by inflation, and you seem to believe this is ok and should be done
     everywhere.


     – The EPO has a huge surplus, see the blog. And if there still were a
     shortage, one may reasonably ask why the EPO share of post-grant
     renewal fees is only at 50%. Article 39 EPC allows to go up to 75%.
     The EPO share was at 60% until 1984. But the national offices want to
     keep this free money, and their heads are sitting in the
     Administrative Council.


     – employees of an international organisation give up their rights.
     There is no fast track route involving an independent decision making
     body. The only such body is ILO-AT in Geneva, you get a decision
     roughly 6 to 8 years after the dispute has started. Justice delayed
     for this amount of time is justice denied.
     Law Sniffer & Bitter Worker: You think it is ok to get sacked while
     holding a position as elected staff representative, and then you have
     to wait for about 5 (FIVE) years for a decision from an independent
     court?


     – It seems to have been completely forgotten that EPO employees for
     about 8 (EIGHT) years were allowed to strike only after approval of
     the EPO President. It also seems to have been forgotten that the same
     President interfered with a decision from the Enlarged Board of
     Appeal, see G2301/16, headnote “threat of disciplinary measures
     against the members of the Enlarged Board”.


     Whatever a President of the EPO does, the signals are clear: it will
     not have consequences. We see this not only in the past, but also in
     ongoing developments: forcing applicants and parties to opposition
     proceedings into video conferences – the emphasis is on “forcing”:
     whoever wants life oral proceedings should simply get them, for all
     others, video is fine.


     My higher layers – as far as I can judge – live in blissed ignorance
     on what a patent application is, what a “search” is and how a search
     can and should be done (that depends on the case). The recent
     developments focus on machine based searches providing many
     documents, you have to apply some filters to reduce the number, you
     browse them and then you stop. This is a paradigm shift from a
     “finder” – someone who knows the area of technology and keeps hunting
     until something is found – to a “searcher” – someone who follows a
     predefined approach and stops regardless of the result.


     Typcially, a “searcher” does not have in-depth experience in the area
     of technology and lacks the needed gut feeling. It takes about a
     decade to build this gut feeling. Frequent changes of the area of
     technology are not supportive. I recall a management meeting where
     the work of a substantive examiner was compared to the work of a post
     office: weighing letters, selling stamps, and so on. This comparison
     left me flabbergasted and insulted.


     My Vice President is not technically skilled (DG1 – Steve Rowan,
     legally skilled, a bachelor, if I remember correctly). The person in
     charge of search and examination lacks the qualification necessary to
     understand an application. We are getting more and more instructions
     on procedure, probably because that is what Steve feels comfortable
     with. I personally disagree with this approach. Procedure is
     important, yes, but applicants do not file to have a good procedure.
     They file to have a good search and then a thorough examination.
     Procedural violations are very rare.


     Last, if want to learn where a major problem is, please move to the
     EPO intranet site, “about us”-> “our leadership and management” -
     > “the management advisory committee”. There are way too many chiefs
     who do not have any purpose enshrined in Articles 10, 11 or 15 EPC.
     Thorsten touched on this topic in an earlier blog.
     I am a member of an examining division, enshrined in Article 15 and
     18 EPC. I do not need any of those chiefs to carry out my tasks. I
     believe we could with a quarter of those chiefs without even noting
     that the others have gone.


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⠀⠖⠶⣶⠿⢷⠷⠰⠶⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢿⣃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⣶⡿⠃⠀⠀⠀⠀⣶⣶⣶⣶⠶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⡆⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠒⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣴⣧⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣉⣠⣤⣼⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡄⠀
⠙⡛⣛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠀⣈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⣴⣶⣦⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⡿⠻⢿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⢠⣾⣿⡿⠛⠟⠶⢤⡀
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡍⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠉⣡⣤⣀⣈⣿⣿⣿⣿⣿⣿⣆⠀⢀⣼⣿⠋⠀⠀⠀⢠⣿⡅
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⡇⠀⢠⣾⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⡀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⣰⣶⣿⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠇⠀⠸⣿⣿⣿⡿⠀⢀⣰⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⢛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣾⣿⣷⣦⣤⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣿⣿⡇
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠋⢳⣶⣾⣿⣿⣿⣯⠐⠺⠾⠟⠉⠹⣿⣿⡇⠀⠀⠀⠀⠈⠆⠀⠙⣿⣿⣿⣿⣿⣿⡏⠀⠿⢿⣿⣿⣿⢿⣧⠈⠉⠁⠀⠙⣿⣿⡇⠉⠁⠘⣿⣿⡿⠻⣿⣿⣇⣉⣻⡇
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠿⢿⠁⠀⠀⠀⠀⠀⠀⠆⠀⠈⢻⣿⣿⣿⣿⣷⡀⠰⠆⠙⠁⠀⠀⠈⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠛⠋⠀⠀⠈⠻⠛⠿⣿⡇
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠺⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⡶⠀⠿⢶⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣿⣿⣿⣿⠟⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣠⣠⣠⣤⣤⣼⡇⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡇⠁⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣿⡾⣿⠟⠿⠿⠿⠻⠿⠛⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠷⠴⠶⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢛⣁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢐⣶⣶⡿⠛⠀⠀⠀⠀⢶⣶⣶⣶⠶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⡆⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠒⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣴⣶⣾⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣁⣤⣶⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡄⠀
⠙⡛⢛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠀⣈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⢠⣾⣿⡿⠛⠻⢶⢤⡀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⠛⠛⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠉⣡⣤⣀⣍⣿⣿⣿⣿⣿⣿⣆⠀⢀⣼⣿⠋⠀⠀⠀⢠⣿⡅
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢿⡇⠀⢀⣾⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣷⠀⠀⣰⣶⣿⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡇⠀⠘⣿⣿⣿⣿⠁⠀⢐⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣷⣤⣠⢿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢀⣴⣿⣿⣿⣿⡇
⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠙⠛⢳⣶⣾⣿⣿⣿⣷⠀⠽⠿⠓⠈⠹⣿⣿⡃⠀⠀⠀⠀⠀⠆⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠿⠿⣿⣿⣿⠟⠀⠈⠉⣁⣀⠙⣿⣿⠀⠉⠉⠈⣿⣿⠕⠘⣿⣿⣇⣈⣻⡇
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠿⢿⠃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⣿⣿⣿⣿⣷⡀⢰⠀⠉⠁⠀⠀⠈⠀⠈⡿⣿⣷⡸⠟⠀⠀⠀⠀⠛⠃⠀⠀⠈⠻⠛⠿⣿⡇
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣏⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠺⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⣿⡶⠀⠿⢦⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣿⣿⣿⣿⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣠⣠⣠⣤⣤⣼⡇⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣿⡾⣿⠟⠿⠿⠿⠻⠿⠛⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢷⠷⠰⠶⠿⠿⢉⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⣁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⣶⡿⠃⠀⠀⠀⠀⢶⣶⣶⣶⠶⠾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⢲⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣴⣦⣾⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣀⣴⣧⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀
⠙⠛⢛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⣈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⡟⠻⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⢠⣼⣿⡟⠻⠶⢶⣤⡀
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡏⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⣤⣄⣀⣙⣿⣿⣿⣿⣿⣿⣆⡀⢠⣼⡿⠋⠀⠀⠀⣼⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⡇⠀⢠⣾⣿⣿⣿⡿⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠸⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⣴⣿⣿⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠇⠀⠸⣿⣿⣿⡟⠀⠀⢀⡿⠻⣿⣧⡀⠀⠀⠀⠀⠀⢹⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⣿⣿⣤⣠⡿⢿⣿⣿⣾⣿⣿⣿⠟⣿⣿⡿⣿⣿⡿⢀⣴⣿⣿⣿⣿⡇
⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠋⢳⣶⣾⣿⣿⣿⣇⠀⠹⠚⠁⠈⢻⣿⣷⠀⠀⠀⠀⠀⠀⠃⠀⠙⠿⣿⣿⣿⣿⣿⡟⠀⠹⠉⣿⣿⠟⠀⠉⠈⢉⣁⡀⠙⣿⣿⠀⠈⠉⠀⣿⣿⠁⠘⣿⣿⣷⣿⣿⡇
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠸⣿⣿⣿⣿⣷⡄⠆⠀⠋⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⠏⠀⠀⠂⠀⠘⠃⠀⠀⠈⠿⠛⢿⣿⡇
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢟⣀⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⢳⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⡶⠸⠿⢠⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⣿⣻⣿⣿⠟⠙⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣼⡇⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠛⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡏⠃⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠝⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⡾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠰⠶⠿⠿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⣶⡿⠃⠀⠀⠀⠀⢶⣶⣶⣶⡶⣾⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢲⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣴⣦⣾⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣀⣤⣥⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀
⠙⠛⢛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⣈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⢀⣼⣿⡟⠻⠷⢶⣤⡀
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠉⠃⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠈⠉⣤⣄⠀⡙⣿⣿⣿⣿⣿⣿⣆⡀⢠⣽⡿⠃⠀⠀⠀⣼⣿⡇
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡁⠀⢠⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣇⠀⠀⠀⠀⠀⠘⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣦⠀⠀⢸⣿⣿⣿⢟⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⠀⠀⣴⣿⣿⣿⡇
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠁⠀⢸⣿⣿⣿⡏⠀⠀⠀⠟⢿⣿⣅⡀⠀⠀⠀⠀⠀⢹⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣾⣿⣿⣤⢠⡿⢿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⢀⣴⣿⣿⣿⣿⡇
⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠋⢳⣶⣾⣿⣿⣿⡇⠀⠐⠊⠀⠘⢿⣿⣷⠀⠀⠀⠀⠀⠀⠁⠀⠙⠿⣿⣿⣿⣿⣿⡟⠀⠹⠙⣿⡿⠟⠀⠉⠈⠉⣀⠀⠘⢿⣿⠀⠈⠉⠁⢹⣿⠁⠘⣿⣿⣿⣿⣿⡇
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠸⢿⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠨⣿⣿⣿⣿⣷⡄⠆⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠃⠀⠀⠐⠀⠘⠃⠀⠀⠘⠿⠛⢿⣿⡇
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⢳⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⡶⠰⠿⢠⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⣿⣻⣿⣿⠟⠙⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣼⡇⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠾⣿⣿⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡏⠃⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠝⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⡾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠰⠶⠿⠿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢉⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⡶⠞⠀⠀⠀⠀⠀⢶⣶⣶⣶⠶⢶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣴⣦⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⣿⡓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⣉⣙⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀
⠙⠛⣛⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣀⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣴⣶⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣤⣶⣦⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠠⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⠀⣴⣿⠿⠿⠶⠦⣠⡀
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠉⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⣤⡄⠀⠙⣿⣿⣿⣿⣿⣿⣦⡀⢀⣽⡿⠋⠀⠀⠀⣰⣿⡇
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡏⠀⢀⣾⣿⣿⣿⣿⠆⠀⠉⣻⣿⣿⡄⠀⠀⠀⠀⠀⠘⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⢠⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣴⣶⣿⣿⡇
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡏⠀⠈⣿⣿⣿⣿⠁⠀⠀⢀⠽⢿⣿⣁⠀⠀⠀⠀⠀⠀⢹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⠏⣿⣷⣤⠰⡿⢿⣿⠷⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⢀⣴⣿⣟⢿⣿⡇
⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠋⠹⣶⣾⣿⣿⣿⣿⡄⠀⠠⠞⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠈⠃⠈⠻⢿⣿⣿⣿⣿⣿⡿⠃⠻⠀⣿⠿⠟⠀⢹⠈⠁⠀⠀⠘⢿⣿⠀⠈⠉⠁⢸⣿⠇⠘⣿⣿⣄⣈⣿⡇
⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢻⣿⡯⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠻⣿⣿⣿⣿⣷⡀⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠐⠀⠘⠋⠀⠀⠀⠻⠛⢿⣿⡇
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣤⣤⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⡷⠲⠿⢠⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢿⣿⣹⣿⣿⠟⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣿⡇⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣼⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣿⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡿⠃⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢶⠟⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⡾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠸⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢉⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢐⣶⠖⠀⠀⠀⠀⠀⠀⠰⣶⢶⠶⠶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣴⣦⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣯⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⣉⣉⣻⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀
⠙⠛⣛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣶⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣶⣶⣶⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣽⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⣀⣄⠀⠀⠀⠀⣴⣿⠷⠿⠶⠦⣠⡀
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡍⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⣠⡄⠀⠙⢿⣿⣿⣿⣿⣿⣦⡀⢀⣽⡿⠋⠀⠀⠀⣴⣿⡇
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡁⠀⢰⣿⣿⣿⣿⡿⠀⠀⠉⢻⣿⣿⠀⠀⠀⠀⠀⠈⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⢀⠀⠀⠀⢠⣿⣿⣶⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣴⣶⣿⣿⡇
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⡃⠀⢸⣿⣿⣿⡿⠆⠀⠀⠀⠈⢹⣿⣀⠀⠀⠀⠀⠀⠈⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡿⢿⣦⣵⣄⠰⡿⢿⡿⠷⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⢀⣴⣿⠛⢻⣿⡇
⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠉⢻⣿⣾⣿⣿⣿⣷⠀⠀⠒⠂⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠉⠃⠘⠿⣿⣿⣿⣿⣿⣿⣿⠃⠿⠀⣿⠿⠟⠀⠛⠈⠁⠀⠀⠘⢿⣿⠀⠈⠉⠁⢸⣿⠁⠘⣿⣿⣄⣈⣿⡇
⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠻⣿⣿⣿⣿⣷⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠐⠀⠘⠋⠀⠀⠀⠻⠛⢿⣿⡇
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⣠⣭⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⡷⠖⠿⢤⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢿⣧⣹⣿⣿⠟⠙⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣿⡇⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣼⣿⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡿⠃⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢦⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⡾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠆⠸⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢁⣁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠰⠶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⣉⣉⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀
⠙⠛⢛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣴⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣤⣄⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⢀⣴⣿⠟⠿⠶⢶⣠⡀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣊⡁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣤⡄⠈⠙⢿⣿⣿⣿⣿⣿⣦⣀⢠⣼⡟⠃⠀⠀⠀⣴⣿⡇
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡅⠀⢰⣿⣿⣿⣿⡿⠁⠀⠀⠉⢻⣿⣇⠀⠀⠀⠀⠀⠹⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣄⡀⡀⠀⢠⣿⣿⣷⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⣾⣿⣿⡇
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⢘⣿⣿⣿⣿⡵⠦⠀⠀⠀⠀⠻⣟⣀⠀⠀⠀⠀⠀⠉⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡞⠿⣧⣥⣄⢰⡟⣻⣿⠷⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⡇⢀⣾⣿⠛⢻⣿⡇
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠉⢻⣿⣾⣿⣿⣿⣿⣇⡀⠀⠀⠁⠀⢼⣿⣿⡆⠀⠀⠀⠀⠀⠘⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠛⡆⠀⣿⠿⠇⠀⠁⠈⠀⠀⠀⠙⣿⣿⠀⠈⠉⠁⢸⣿⠀⠘⢿⣏⣀⣈⣿⡇
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠻⣿⣿⣿⣿⣷⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠒⠀⠘⠁⠀⠀⠀⠻⠛⢿⣿⡇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢀⣨⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠘⣿⣿⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠆⠿⣤⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⢿⣧⡹⣿⣿⠟⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣿⡇⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣼⣿⣷⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡟⠃⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡩⠻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⠝⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⡾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢶⠔⠺⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢉⣁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⢾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠙⠇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣤⣭⣽⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀
⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⣷⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣤⣤⣀⣀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡅⣀⣀⠀⠀⠀⢀⣴⣿⠟⠿⠶⢦⣀⡀
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⣤⡄⠈⠙⢿⣿⣿⣿⣿⣿⣷⣄⣠⣾⡟⠁⠀⠀⢠⣴⣯⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⠀⠀⢾⣿⣿⣿⣿⡟⠉⠉⠉⠉⠙⢻⣿⡇⠀⠀⠀⠀⠀⠈⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⡇⢀⠀⢠⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣄⣿⣿⣿⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠘⣿⣿⣿⣿⣇⡴⠄⠀⠀⠀⠀⢸⣖⡀⠀⠀⠀⠀⠀⠈⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠸⣧⣬⡄⢰⠟⣿⡿⣿⣿⣿⣿⣿⠛⣿⣿⡿⣿⣿⠀⢠⣿⠟⠛⣻⣿⡇
⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢾⣿⣿⡄⠀⠀⠀⠀⠀⠈⠀⠉⠙⢿⣿⣿⣿⣿⣿⣻⣿⠄⠀⠿⠿⠃⠀⠁⠉⠀⠀⠀⠻⣿⣇⠀⠀⠁⠀⣹⡿⠀⠘⢻⣄⣀⣘⣿⡇
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠒⠀⠛⠁⠀⠀⠀⠹⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⢀⣨⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⣀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣶⣿⣿⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⠈⢿⣿⡯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠸⠿⣤⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢿⣷⡘⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣿⡇⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣼⣿⣷⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡟⠃⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⡼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠏⢶⠷⠾⠿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⣁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⣶⠾⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡓⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⣋⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⢀⣈⣉⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣤⣴⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⣠⣴⣿⠟⠶⠶⢄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣠⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⠁⣤⡄⠈⠙⣿⣿⣿⣿⣿⣿⣦⣠⣴⣿⡟⠁⠀⠀⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣋⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠉⠻⣿⣇⠀⠀⠀⠀⠀⠈⢿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⢸⣿⣿⣷⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣤⣄⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⣀⢀⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠸⣟⡀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣀⡀⢀⣥⣄⡀⢸⠿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⢿⣿⡏⠀⣸⡿⠟⢛⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠈⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢾⣿⣷⡀⠀⠀⠀⠀⠀⠈⠀⠉⠙⢿⣿⣿⣿⣿⣿⡄⢻⣦⣿⣿⡿⠃⠀⠁⠀⠀⠀⠈⢻⣿⡇⠀⠈⠀⠀⣿⡇⠀⠛⢈⠀⢀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠸⠗⠀⠛⠁⠀⠀⠈⠟⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣈⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡀⠀⠘⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⣷⣴⣿⣶⣾⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⠘⢿⣿⠃⠀⠬⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠸⢿⣤⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡌⣿⣿⠏⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣿⠀⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣤⣿⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡟⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⡾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠿⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠉⣁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡖⢾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣩⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⢉⠉⣙⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣤⣤⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⣠⣾⣿⠷⠶⠤⣄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣤⠄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠻⢿⣯⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⢀⡀⠀⠉⢡⣤⡄⠉⠻⣿⣿⣿⣿⣿⣧⣄⣤⣴⣿⡿⠃⠀⢀⣤⣤⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣹⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠉⠛⢿⣧⠀⠀⠀⠀⠀⠀⢻⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠁⠀⠀⢸⣿⣿⣷⣓⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⣤⡄⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢧⣀⣀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣤⣀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⠟⠛⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣿⣿⣿⣿⣿⠀⠀⣾⡿⡿⠿⠃⠈⠁⠈⠀⠀⠈⢻⣿⠀⠈⠉⠀⢸⣿⡇⠀⠛⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠲⠂⠘⠛⠀⠀⠀⠈⠞⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡤⠄⠀⣀⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡀⢀⢸⣿⣿⣿⡏⠙⠻⢿⣿⣿⣿⣿⣶⣷⣶⣾⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⠛⢿⠟⠀⠀⠀⠀⢳⣻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠐⢿⡄⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⣿⣿⠏⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣾⣿⠀⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⣀⣸⣷⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡟⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠯⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⡼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢿⠿⠿⠷⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡆⢾⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⢀⠉⣉⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣠⣤⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣠⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⣀⡀⠀⠀⠀⣠⣾⣿⡷⠦⠤⢠⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣠⡄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⢿⣯⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⢠⡀⠀⠉⢡⣤⣄⠉⠻⣿⣿⣿⣿⣿⣦⣀⣤⣴⣿⡿⠃⠀⢠⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣹⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠉⠻⣿⣷⠀⠀⠀⠀⠀⠀⢻⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⠁⠀⠀⢰⣿⣿⣷⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣀⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢧⣀⢀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣟⡀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣸⣤⣀⠐⠸⠿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⣿⣿⣿⠃⣿⣿⠟⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠀⠀⣿⢿⡿⠟⠃⠀⠁⠈⠀⠀⠈⢻⣿⠀⠈⠉⠀⢹⣿⡇⠀⠛⠀⠀⠀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⡀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠒⠂⠘⠋⠀⠀⠀⠈⠟⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠄⠀⣀⣬⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⢀⢸⣿⣿⣿⡏⠉⠉⠻⡿⣿⣿⣿⣷⣷⣶⣾⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⢿⡿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠀⢿⡄⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⣿⡿⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣿⣷⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠁⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢀⣸⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡟⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠿⠾⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣤⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⣠⣀⣭⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣤⣤⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⢰⣿⣿⠷⠀⠤⢤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⣧⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⠀⠀⠙⠡⣤⣴⡍⠛⢿⣿⣿⣿⣿⣄⣰⣶⣤⣾⡏⠀⠀⣤⣴⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠈⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠹⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⣿⠀⠀⠀⢠⣿⣿⣿⣗⣼⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣦⢰⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣯⡀⠀⠀⠀⠀⠀⠀⠻⠟⡿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣿⣄⣀⠂⢻⠿⣿⣿⣿⣿⣿⣿⠻⣿⡿⢻⣿⣿⣿⢟⣿⡟⠛⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⣿⣿⢿⠿⠋⠀⠀⠀⠈⠉⠀⠈⢻⣏⠀⠀⠀⠀⣿⣿⠁⠈⠃⠀⢀⣀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⡛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠃⠀⠈⠛⠁⠛⠋⠀⠀⠀⠐⠏⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣀⣤⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⡀⣀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣿⣿⣿⠉⠉⠉⠻⢿⣿⣿⣿⣦⣤⣾⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⢷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠀⠿⡄⠀⠀⠀⠘⠃⠛⠛⠙⠛⠣⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢹⡏⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢿⠷⠾⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣶⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⣠⣀⣭⣿⡿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣤⣀⣀⣀⣤⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⡀⠀⠀⠀⢰⣿⣿⠷⠠⠄⣤⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠙⠛⣷⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⡀⠀⠛⠡⣤⣶⣉⠛⢿⣿⣿⣿⣿⣄⣰⣶⣤⣾⠏⠀⠀⣤⣴⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣿⣿⡟⠉⠉⠁⠈⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠹⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⣿⠁⠀⠀⢠⣾⣿⣿⡷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣰⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣯⡀⠀⠀⠀⠀⠀⠀⠻⠛⠿⢿⣿⣿⣿⣿⣿⣿⡏⢀⣠⣷⣄⡀⠖⢻⢿⣿⣿⣿⣿⣿⣿⠻⣿⡿⢻⣿⣿⣿⢿⣿⡿⠻⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⢰⣿⡿⣿⡿⠋⠀⠀⠀⠉⠉⠀⠈⢻⡇⠀⠀⠀⠀⣿⣿⠃⠈⠃⠀⢀⣐⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⡛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠈⠛⠉⠛⠋⠀⠀⠀⠰⠏⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⣴⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⡀⣀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⣿⣿⠉⠉⠁⠙⢿⣿⣿⣿⣤⣤⣾⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⡘⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⡷⠀⠿⡄⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⢿⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢹⡏⠀⠸⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢿⠷⠾⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡤⠘⢀⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⢀⡈⣉⣿⡿⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣀⣤⣤⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣰⣶⣶⣶⣤⣤⣀⣄⣠⣤⣠⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⣄⠀⠀⠀⢸⣿⣿⠷⠤⠄⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠉⠙⣷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠀⠙⠟⠃⣤⣼⡏⠛⢿⣿⣿⣿⣭⡀⣳⣶⣦⣾⠏⠁⠀⣤⣴⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣿⣿⣿⡟⠉⠉⠁⠉⠙⢻⣿⣿⠀⠀⠀⠀⠀⠀⠹⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣾⣿⠁⣴⠀⠀⣾⣿⣿⢆⣠⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣄⣼⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠻⠻⡿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣧⣘⠁⠰⢺⢿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⢿⣿⡟⠻⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⠉⠋⣹⣿⣗⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠉⠀⠈⠉⠀⢈⢻⡇⠀⠀⠀⢸⣿⡿⠁⠘⠃⠀⢀⣰⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠋⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠊⠁⠀⠀⠉⠸⠟⠃⠀⠀⠀⠰⠋⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣠⣴⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⡀⡀⣀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠉⠉⠁⠙⣿⣿⣿⣷⣠⣤⣾⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⡘⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⡷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢹⣁⢀⣀⣀⣀⢀⣀⣠⣠⣤⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢹⡇⠀⠸⣿⣿⣿⣯⣿⣷⣿⣉⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠐⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠛⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢿⠷⠾⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡤⠘⢠⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⢈⠉⣙⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣤⣤⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣼⣷⣶⣤⣤⣤⣀⣄⣤⣤⣤⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣗⣠⣄⠀⠀⠀⢸⣿⣿⠷⠤⠄⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⠙⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⠀⢹⡿⠃⣦⣬⡉⠙⢻⣿⣿⣿⣍⠈⣷⣶⣤⣾⠏⠀⠀⣤⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠁⠀⠙⢿⣿⡃⠀⠀⠀⠀⠀⠀⠹⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣾⣿⣄⣶⠄⠀⣼⣿⣿⠂⢠⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣄⣼⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣿⣿⣿⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠻⠽⡿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⣧⣙⠛⠰⠒⡿⣿⣿⣷⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣧
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣿⣯⡈⢛⣹⣿⣇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠺⠃⠈⠉⠁⠈⢻⡇⠀⠀⠀⢸⣿⡟⠉⠘⠃⠀⢀⣸⣿⣿⡟
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠁⠀⠀⠛⠹⠟⠁⠀⠀⠀⠰⠋⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⡀⡀⣀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠉⠉⠹⣿⣿⣿⡇⢀⣤⣾⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠀⠀⠀⠀⠀⡘⣿⣿⡟⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⡷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠹⣁⢀⣀⣀⣀⢀⣀⣠⣠⣤⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢹⡇⠀⠸⣿⣿⣿⣯⣿⣷⣿⣍⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠛⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢿⠷⠿⠾⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⡤⠘⢠⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣀⣉⣽⣿⡿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣠⣴⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣼⣶⣶⣤⣤⣤⣄⣀⣤⣤⣤⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣇⣠⣄⠀⠀⠀⣼⣿⣿⠷⠤⠄⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠉⠛⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣀⠈⢻⡿⠃⢤⣄⠉⠛⢿⣿⣿⣿⣍⠈⣷⣶⣤⣾⠋⠀⢠⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⣿⣿⠟⠉⠉⠁⠉⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣤⣾⡇⠀⢰⣿⡆⠀⢰⣿⣿⣾⣿⣿⣿⣟⣿⣿⣤⡄⣾⣿⣿⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣛⠻⠁⠂⢻⣿⣿⣶⣿⣿⣿⢻⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡋⠛⢺⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠁⠀⠀⢘⠈⠉⠁⠀⢹⡇⠀⠀⠀⢹⣿⡇⠉⠘⠃⠀⢈⢿⣿⣿⡟
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⡉⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⣫⠄⠀⠀⠀⠉⠹⠟⠁⠀⠀⠀⠰⠋⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀⡀⣀⣀⣀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠉⠉⠉⠹⣿⣿⣿⡆⢀⣄⣾⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⢶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠸⣿⣿⡇⣸⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⡷⠀⢿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢹⡇⠀⠸⣿⣿⣿⣯⣿⣷⣿⣍⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠛⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢿⠷⢿⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢠⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⣠⣀⣭⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢤⣽⣿⣶⣶⣤⣤⣄⣠⣠⣤⣴⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡏⣡⣄⠀⠀⠀⣼⣿⡿⠷⠠⢤⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣻⣇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠛⠻⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠈⢿⣿⠃⢠⡄⠙⠛⢿⣿⣿⢿⣍⠈⣿⣦⣤⣾⠋⠀⢠⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣾⣿⣿⣿⠟⠉⠉⠀⠉⠹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠹⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣧⣴⣾⡇⠀⢀⣾⠀⠀⢸⣿⣿⣾⣿⣿⣿⣟⣿⣯⣤⣄⣾⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⣿⣿⣿⢟⡻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⢿⣿⣿⣿⣿⣿⣿⣏⣾⣷⣼⡿⠟⡁⠀⡘⣿⣿⣶⣿⣿⡿⢻⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣄⣈⣡⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⢿⠿⠃⠀⠀⠀⠀⠎⠋⠁⡀⠙⠇⠀⠀⠀⢹⣿⡏⠉⠙⠃⠀⣈⢻⣿⣿⡟
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⡅⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠉⠘⠟⠁⠀⠀⠀⠸⠋⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⡀⡀⣀⣀⣀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠉⠉⠉⠻⣿⣿⣿⡄⢀⣤⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣷⢶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠀⠀⠀⠀⠹⣿⣿⡇⣺⣿⡿⠋⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠀⢿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠄⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠰⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢹⡇⠀⠸⣿⣿⣿⣯⣿⣷⣿⣍⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠛⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠄
⠀⠖⠶⣾⠿⢷⠷⠼⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣄⣘⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡤⠘⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⢀⣀⣩⣿⣿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⣴⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣶⣶⣶⣤⣤⣤⣄⣄⣀⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⣾⣿⠿⠷⠠⢠⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣷⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠛⢻⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠈⢿⣿⠃⠠⡄⠙⠛⢿⣿⣿⢯⣄⠈⣿⣶⣴⡿⠁⠀⢠⣤⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡦⠹⣿⣿⣿⡟⠉⠁⠀⠀⠹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠻⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣾⣧⣶⣾⡇⠀⠀⣶⠀⠀⢸⣿⣿⣾⣿⣿⣿⣟⣻⣧⣤⣀⣿⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢿⣿⠟⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠟⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⠿⠿⣡⠀⡀⣿⣷⣶⣿⣿⡏⢹⣿⠟⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⣿⣷⣶⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⢿⠿⠃⠀⠀⠀⠀⠸⠋⣁⠀⠈⠀⠀⠀⠀⢹⣿⡀⠈⠙⠀⠀⣀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡁⢰⡆⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠉⠈⠛⠁⠀⠀⠀⠸⠋⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠗⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡀⡀⣀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠉⠉⠉⠻⣿⣿⣿⡇⢀⣀⣴⣿⡯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠹⣿⣿⡇⢸⣿⡿⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⡷⠀⢿⡄⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢰⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢹⡇⠀⠸⣿⣿⣿⣯⣿⣷⣿⣍⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠛⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠆
⠀⠖⠶⣶⠿⢿⠷⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡀⣀⠀⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣤⣹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡤⠘⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⢀⣀⣉⣽⡿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣤⣤⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⣶⣶⣶⣤⣤⣤⣄⣠⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣀⣄⠀⠀⠀⣾⣿⡿⠷⠠⢠⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⡆⠙⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⠟⠛⠉⠛⢿⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠈⢿⣿⠃⠀⠄⠙⠻⢿⣿⣿⢟⡉⠸⣿⣶⣴⡿⠁⠀⢠⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⢻⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣴⣯⣴⣾⡇⠀⠀⣶⠀⠀⢘⣿⣷⣼⣿⣾⣿⣟⢻⣧⣤⡄⣾⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⣿⡿⠃⠀⠀⢸⣿⣿⡇⠀⣾⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⡟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⠿⠿⣡⡀⠀⣿⣷⣶⣾⣿⡟⢹⣿⠟⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⣿⣿⣷⣾⣿⣿⣿⣿⡁⠀⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠻⡿⠂⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⢸⣿⡁⠉⠙⠀⠀⣀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣿⣿⣿⡇⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡀⠀⡶⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠒⠘⠟⠁⠀⠀⠀⠸⠛⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⣿⣿⣿⣷⣤⣌⡻⠿⠃⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠉⠉⠙⣿⣿⣿⣧⠀⣷⣤⣴⣿⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠈⢿⣿⣿⠀⢽⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⡷⠀⠿⡀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠄⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠁⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢰⡀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢹⡇⠀⠸⣿⣿⣿⣯⣿⣷⣿⣉⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠛⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠐⠄
⠀⠖⠶⣶⠿⢿⠷⠼⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⣀⠀⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣤⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡤⠘⢠⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣀⣀⣭⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⣴⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣠⣶⣷⣶⣤⣤⣤⣄⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣇⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡏⣠⣄⠀⠀⠀⣾⣿⡿⠷⠠⢠⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⡿⠿⠛⠛⠙⠛⢿⣧⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⠋⠀⠀⠙⠻⣿⣿⡿⢋⠉⢹⣿⣶⣤⡿⠁⠀⢠⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠻⣿⣿⣿⣿⠛⠉⢀⣀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣴⣟⣶⣾⡇⠀⢠⡆⠀⠀⢸⣿⣷⣼⣿⣾⣿⣟⢻⣧⣤⣄⣾⣿⣿⣿⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⣿⡟⠁⠀⠀⣿⣿⣿⠃⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠟⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣟⠿⠿⣡⠀⠘⣿⣷⣶⣿⣿⠏⢿⣿⠿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣨⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠻⡿⠇⠀⠀⠀⠀⠈⠉⡀⠀⠈⠀⠀⠀⠀⢹⣿⠀⠉⠙⠀⠀⣀⣸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠙⠟⠀⠀⠀⠀⠹⠛⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⣿⣿⣿⣤⣀⠀⠙⠻⡟⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡀⡀⣀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠈⠙⢿⣿⣿⣧⠀⢸⣿⣶⣴⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠻⣿⣿⣧⡀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⡷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠄⠀⠀⠀
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢦⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢹⡇⠀⠸⣿⣿⣿⣯⣿⣷⣿⣉⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠐⠄
⠀⠖⠶⣶⠿⢿⠷⠼⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢰⣾⣷⡂⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣠⣀⣬⣽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣤⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣴⣷⣶⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠠⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⣾⣿⡿⠗⠀⢠⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⠟⠛⠛⠛⠛⠻⢿⣷⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⢻⣿⠁⠀⠀⠙⠻⣿⣿⡿⢃⡈⢹⣿⣶⣤⡿⠁⠀⢠⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠄⠀⠘⣿⣿⣿⣿⡿⠛⠁⣀⣤⣤⠘⠉⠀⠀⠀⠀⠀⠀⠈⢻⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣿⣶⣾⡇⠀⣸⣷⠀⠀⣸⣿⣷⣼⣿⣾⣿⣟⢛⣇⣤⣄⣾⣿⣿⣿⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⣿⣏⣀⣀⣤⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣝⠿⠟⢁⡀⢻⣿⣷⣶⣿⣿⠋⢿⣿⠿⣿⣿⡿⣿⣽⣿⠟⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⣿⣿⣿⣿⢹⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠛⠿⠛⠀⠀⠀⠀⠈⠉⡀⠀⠉⠀⠀⠀⠀⢹⣿⠀⠉⠘⠀⠀⣀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡷⠀⣿⣿⡇⠀⠀⠛⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠻⠛⠟⠀⠀⠀⠀⠸⠋⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⣿⣿⡇⠀⣀⠀⠀⢽⣿⠉⠀⠘⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠙⢻⣿⣆⠀⠀⠀⢸⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⢷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣶⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⢀⠀⠀⠀⡇
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠠⡄⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢹⡇⠀⠸⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢿⠷⠾⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⢶⣾⣷⡆⣾⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⢀⣄⣨⣽⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⢿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⣴⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣴⣷⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡄⠸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡏⣀⣀⠀⠀⠀⣾⣿⡿⠖⠀⠠⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣿⠀⠹⣿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⣿⠛⠛⠛⠛⠻⢿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⢻⣿⠉⠀⠀⠙⠻⣿⣿⡿⢣⡈⢹⣿⣶⣤⡿⠁⠀⢠⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⡿⠛⠁⣠⣤⣄⠀⠛⠉⠀⠀⠀⠀⠀⠈⢻⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣾⣴⣾⡇⠀⣼⣷⠀⠀⣸⣿⣷⣼⣿⣾⣿⣟⢛⣇⣤⡄⣾⣿⣿⣿⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠙⣿⣇⣀⣠⣤⣿⣿⣿⡏⠀⠀⣾⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⣟⠋⠟⢿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡟⠿⠛⢁⡀⢿⣿⣷⣶⣿⣿⠋⢿⣿⢿⣿⣿⠿⣿⣽⣿⠛⠻⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢨⣿⣿⣿⣿⡿⠹⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠨⠄⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠛⠿⠋⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⢹⣿⠀⠀⠘⠀⠀⢀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⠀⠻⣿⣿⣿⣿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⡁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠿⠻⠟⠀⠀⠀⠀⠸⠋⠻⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠈⣿⣿⡁⠀⠘⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃⠀⠉⢿⣷⣄⠀⠀⠀⣹⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⢷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡗⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣶⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠠⡄⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢿⠷⠾⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⢐⣶⣿⣿⡆⣾⣿⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣀⢉⣹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⣿⣿⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣀⣤⣶⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣾⣷⣶⣦⣤⣄⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣷⡄⠹⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⣶⣿⡿⠗⠀⠠⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠹⣿⢓⣿⣿⣿⣿⣿⡿⠿⠛⢿⣿⣿⣿⣿⡟⠛⠻⠿⣿⣿⠄⠀⣻⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⢀⠀⢻⣿⠉⢀⡀⠙⠿⣿⣿⡟⢱⣌⢹⣷⣶⣤⡟⠁⠀⢀⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⠀⠀⠘⣿⣿⣿⣿⠟⠉⣠⣤⣤⡀⢹⣿⣿⡿⠁⠀⠀⠀⠀⠹⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⣾⣴⣾⡏⢀⣿⣿⡄⠀⣹⣿⣷⣾⣿⣿⣿⣟⢛⣧⣠⣆⣼⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢹⣿⣥⣤⣴⣶⣿⣿⣿⠁⠀⢸⣿⣿⣿⣷⣰⣿⣿⣧⠀⠀⠀⠀⠀⠀⢿⠏⠿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣷⡝⠛⠛⠁⡀⣿⣿⣷⣶⣿⡿⠉⣿⡿⠻⣿⣿⠿⣿⣿⣿⠟⠙⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣻⣿⣿⡟⢻⣿⡿⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⢨⡇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠻⠇⠀⠀⠀⣄⠉⠉⡀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠘⠁⠀⢀⣐⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡇⠀⣿⣇⠀⠀⠛⢿⣿⣿⣿⣟⠙⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡃⠀⠰⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠿⠹⠟⠀⠀⠀⠀⠸⠋⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⠀⢹⣿⣿⣄⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠁⠀⠉⢿⣄⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣿⣷⣤⣶⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠀⣿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠹⣁⢀⣀⣀⣀⢀⣀⣠⣠⣤⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢠⠈⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢹⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠿⠾⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣶⣿⣿⡄⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣀⢉⣙⣟⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣀⣤⣦⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣶⣷⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣿⡀⠻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⣾⣿⠿⠗⠀⠠⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠻⣿⣅⣿⣿⣿⣿⣿⡿⠿⠻⢿⣿⣿⣿⣿⡏⠛⠻⠿⣿⣿⠄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⠁⢀⡀⠙⠻⣿⣿⡟⢱⣆⣹⣿⣶⣴⡟⠁⠀⠀⣴⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠹⣾⣿⣿⡿⠟⠁⣠⣤⣄⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠹⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣾⣰⣾⡟⢠⣿⣿⣶⣦⣿⣿⣷⣾⣿⣿⣿⣿⠋⣇⢠⣤⣸⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⢹⣿⣅⣤⣤⣦⣿⣿⡿⠁⠀⢸⣿⣿⣿⣷⣱⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣇⣰⣷⣽⠛⠛⠀⣸⣿⣿⣿⣿⣿⡿⠉⣿⡿⠻⣿⣿⠿⢿⢸⡿⠟⠛⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⣿⣻⣿⣿⡟⢹⣿⡇⠀⠀⢹⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠨⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠇⢼⣿⠀⣴⠉⠉⣤⡀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠘⠀⠀⢀⣐⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⣿⡇⠀⠀⠻⣿⣿⣿⣿⡇⠙⢛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡏⠀⠠⠀⠀⠘⢷⠇⠀⠀⢹⡇⠀⠀⠀⠸⠿⠻⠟⠀⠀⠀⠀⠸⠋⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⣿⣇⠀⠀⠀⠈⢻⣿⣿⣀⣰⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠁⠀⠙⣧⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣷⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⣿⣦⣴⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠀⣿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠹⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣾⢶⣿⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢀⠈⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢹⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠾⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⢐⣾⣿⣿⡆⣾⣿⣾⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣄⣈⣭⣟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣠⣴⣶⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣶⣷⣶⣤⣤⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣿⡄⢻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⣿⣿⡿⠆⠀⠀⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⡇⠀⠻⣿⢥⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⠛⠛⠻⠿⢿⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⢻⣿⠁⣠⡀⠙⢿⣿⣿⡟⣿⣎⢻⣿⣶⣴⡿⠁⠀⠀⣤⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠘⣾⣿⣿⡿⠛⠁⣠⣤⣄⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠹⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣼⣰⣾⡿⢰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⠋⣇⢠⣤⣰⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⢙⣿⣅⣤⣤⡦⣿⣿⡿⠁⠀⣾⣿⣿⣿⣷⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⢿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣇⣨⣷⡽⠛⠛⠀⢸⣿⣿⣿⣿⣿⡿⠉⣿⣿⠟⣿⣿⠿⣿⢸⡿⠟⠛⠛⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⢻⣿⣿⡟⢹⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⡆⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠇⠾⢿⡄⣤⠉⣿⣶⡄⠀⠀⠀⠀⠀⢹⣯⠀⠀⠈⠀⠀⢀⣀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠘⣿⠆⠀⠈⠿⣿⣿⣿⣿⠇⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣿⣿⣿⣿⣿⡟⠃⢠⠀⠀⠈⠣⠇⠀⣿⣿⣟⠀⠀⠀⠸⠿⠛⠟⠀⠀⠀⠀⠰⠋⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⣿⡇⠀⠀⠀⠈⣿⣿⣯⣠⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⣀⡀⡀⡀⣀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠀⢹⣇⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢹⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⢿⣿⣦⣼⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠘⣿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣴⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⣿⢹⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠛⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠿⠾⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⢐⣶⣿⣿⡆⣾⣿⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣠⣤⣠⣭⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣶⣶⣶⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡀⢹⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⢰⣾⣿⣷⠆⠀⣤⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠻⣿⢄⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⠛⠛⠛⠿⢿⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⢻⣿⡁⣠⡀⠙⢿⣿⣿⡟⣿⣌⣻⣷⣶⣴⡿⠉⠀⠀⣶⣷⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠘⣿⣿⣿⡿⠟⠉⣀⣤⣄⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠹⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⣾⣠⣾⡿⣻⣿⣿⣿⣧⣿⣿⣷⣽⣿⣿⣿⣟⠉⣇⠀⣴⣶⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣿⣧⣀⣤⣤⣿⣿⡿⠁⠀⣾⣿⣿⣿⣧⠁⣿⣿⣆⠀⠀⠀⠀⠀⠀⢻⠏⠛⢿⣿⣿⣿⣿⣿⣿⣇⣨⣿⣯⠛⠛⠀⢸⢿⣿⣿⣿⣿⡿⠉⣿⣿⠟⣿⣿⠿⡿⠀⣿⠿⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣿⣿⣿⣿⡿⢹⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠆⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠀⠀⠀⠀⠉⣿⣦⡄⠀⠀⠀⠀⠀⢹⣿⠀⠀⠈⢿⣦⣈⣛⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠈⣿⡀⠀⠘⠿⣿⣿⣿⣿⠇⠸⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠨⣿⣿⣿⣿⣿⡿⠃⢰⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠸⠿⠛⠟⠀⠀⠀⠈⠻⠏⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⣿⡇⠀⠀⠀⠉⣿⣿⣏⣀⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡄⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⢙⣇⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢹⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⡦⡀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⣿⣦⣼⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠘⣿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠙⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣠⣠⣠⣴⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠘⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡯⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠏⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠾⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢰⣾⣿⣿⣆⣾⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⣤⣠⣭⣏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣶⣶⣶⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡁⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡆⣀⣀⠀⠀⢠⣾⣶⣶⠄⠀⢄⣤⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢿⣿⣃⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠿⠟⠛⠛⠿⢿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⢹⣿⣉⣠⡈⠛⢿⣿⣿⡟⣿⣏⣻⣿⣶⣼⣿⠋⠀⠀⢠⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠹⣾⣿⣿⣿⠟⠋⢀⣠⣀⠀⢹⣿⠗⠀⠀⠀⠀⠀⠀⢻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣾⠀⣴⡿⣿⣿⣿⡆⢨⣿⣿⣷⣿⣿⣿⣿⡟⠉⣿⠀⢠⣶⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⢿⣿⣧⣀⣠⣤⣿⣿⣿⠃⠀⢸⣿⣿⣿⣷⡈⣸⣷⣄⠀⠀⠀⠀⠀⠈⢿⠏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣀⣽⣇⠘⠛⠀⢸⣿⣿⣿⣿⣿⡿⠉⣿⡿⠻⣿⣿⢻⣿⠁⣨⣿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡇⢿⣿⣿⡄⠀⠀⠀⠀⠀⡸⠇⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠆⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠀⢻⣿⣦⡛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⡇⠸⣿⡇⠀⠀⢿⣿⣿⣿⣿⡇⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⠿⠉⠀⠀⠈⠻⠟⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡗⠀⣿⣷⠀⠀⠀⠉⢻⣿⣿⣀⣴⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠹⣿⣄⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡿⣿⣿⣿⣿⡇⡦⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⠀⠀⠻⣿⣷⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠸⣿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⢹⠂⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣠⣠⣠⣴⣿⣧⠀⢠⣦⣴⣶⣴⣶⡦⣶⢶⣾⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢠⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡏⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠼⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⢲⣿⣿⣿⣆⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣤⣈⣭⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣶⣶⣶⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣟⣿⣈⢿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣽⣿⣿⠿⢿⣿⣿⣿⣿⣿⡆⣀⣀⠀⠀⢠⣾⣿⣿⠦⠀⠀⢄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⠿⠛⠛⠛⠻⢿⣿⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣀⠀⢹⣿⣁⣀⡈⠛⢿⣿⣿⡟⣿⣏⣻⣿⣶⣶⣿⠏⠀⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⡿⠛⢁⣀⣀⡀⢈⣿⠃⠀⠀⠀⠀⠀⠈⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠀⣴⡿⣿⣿⣿⡆⢨⣿⣿⣷⣿⣿⣿⣿⣟⣉⣽⡀⠀⣠⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣻⣿⣧⣤⣴⣾⣿⣿⣿⡏⠀⢰⣿⣿⣿⣿⡆⣸⣷⣄⠀⠀⠀⠀⠀⠈⣿⠏⠛⢿⣿⣿⣿⣿⣿⣿⡿⢀⣽⣇⠈⠙⠀⢸⣿⣿⣿⣿⣿⡿⠉⣿⡿⠻⣿⣿⣿⡿⠁⣠⣾⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣷⢻⣿⣿⣇⠀⠀⠀⠀⠀⣻⡆⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠆⠀⠀⠀⠈⠉⠁⠀⠀⠆⠀⠀⠀⠀⢻⣿⡿⠃⠀⠋⢣⣀⠀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠂⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠿⠁⠀⠀⠀⠈⠏⠻⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⢻⣿⣿⡁⣰⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠛⣿⣧⡀⠀⢀⣸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠺⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠩⢟⠀⠀⠘⣿⣿⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠸⣿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⢨⠿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣠⣠⣠⣴⣿⣧⠀⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢤⣀⠀⢰⡜⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡏⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠛⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⣲⣿⣿⣿⣆⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣤⣠⣭⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣶⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣰⣶⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣰⣶⣶⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣟⣿⡌⡿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠠⣾⣿⣷⠦⠀⠀⠄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⡇⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⠿⠛⠛⠛⠻⣿⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⠀⢸⣿⣉⣀⡈⠛⢿⣿⣿⡟⣿⣏⢻⣿⣶⣴⣿⠏⠀⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠙⣿⣿⣿⣿⡿⠛⢉⣀⣀⡀⢈⣿⠃⠀⠀⠀⠀⠀⠈⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⡿⠀⣴⡿⣿⣿⣿⡆⢠⣿⣿⣷⣾⣿⣿⣿⣟⣉⣽⡀⠀⢠⣴⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣧⣤⣴⣶⣿⣿⣿⡟⠀⢰⣿⣿⣿⣿⡄⣠⣷⣄⡀⠀⠀⠀⠀⠙⣿⠏⠛⣿⣿⣿⣿⣿⣿⣿⡟⢀⣹⣇⠈⠉⠀⠼⢿⣿⣿⣾⣿⡿⠉⣿⡿⠻⣿⣿⡿⠛⠁⣠⣾⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣟⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡷⢿⣿⣿⣧⠀⠀⠀⠀⠸⣻⡀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠆⠀⠀⠀⠈⠉⠁⠀⠀⠄⠀⠀⠀⠀⢻⣿⣇⠀⠀⠋⢳⢀⠀⣙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⡇⠘⣿⣿⡿⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠈⣿⣿⣿⣿⣿⡽⠃⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠻⠿⠋⠀⠀⠀⠈⠏⠹⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⢻⣿⣿⡁⣰⣦⣿⣧⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠉⠛⢿⣷⣄⠀⠀⣘⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣾⡆⠺⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠩⠿⠀⠀⠘⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⢿⠷⠰⣿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠿⢿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣠⣠⣠⣴⣿⣧⠀⢠⣦⣴⣶⣴⣶⡆⣶⠶⣾⡃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢴⣎⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣿⣿⣻⣿⣿⣿⣿⣿⢿⣿⡇⢸⡏⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣿⡾⠿⠟⠿⠿⠿⠛⠿⠟⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠴⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣾⣿⣿⣆⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣀⣀⣴⣦⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣷⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣤⣶⣦⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⢼⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⢰⣿⣶⣶⡄⠀⠀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⠿⠛⠛⠛⠿⢿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⠀⠈⣿⡁⣀⡈⠛⢿⣿⣿⡿⣿⣏⢹⣿⣶⣾⣿⠟⠁⠀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡷⠀⠈⢿⣿⣿⣿⣿⠟⢋⣀⣀⡀⠘⠿⠁⠀⠀⠀⠀⠀⠀⣿⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⡷⠀⢴⡿⣿⣿⣿⣧⠀⣿⣿⣷⣼⣿⣿⣿⣿⣉⣽⡀⠀⢠⣴⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣁⣀⣀⣸⣿⣿⣿⡏⢰⣿⣿⣿⣿⠀⣸⣷⣦⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠀⣨⣇⠀⠈⠠⠼⣿⣿⣿⣆⣿⣿⠉⢿⣿⠿⣿⣿⠟⠛⠁⣠⣾⠿⠟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡖⣿⣿⣿⣧⠀⠀⠀⠀⠸⣣⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛⠷⠀⠀⠀⠈⠉⠁⠀⠈⣉⠀⠀⠀⠀⢻⣿⠀⠀⠀⠛⢳⡀⠀⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⠀⠸⣿⣿⣿⣿⠂⢸⣿⣿⣿⠀⠀⠀⠀⠀⠁⠐⠀⠀⠈⠻⣿⣿⣿⣿⣿⡼⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠟⠻⠟⠀⠀⠀⠀⠀⠟⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⣿⣿⣿⠀⠂⠙⢿⣿⣿⡄⣠⣬⣭⣧⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠘⢿⣿⣿⣧⡀⠀⣀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣷⣿⡇⠺⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠡⠀⠀⠀⠘⢿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣧⣤⣿⢸⣿⣿⢿⠷⠰⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⢿⣿⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣋⠉⠙⢻⣏⢛⣻⣝⣀⢀⣠⣠⣠⣬⣶⣦⠀⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢶⣮⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⢿⣿⡇⣿⡏⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢾⠟⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⣿⣿⣿⣿⡿⣿⠟⠿⠿⠿⠻⠿⠟⠛⠛⠙⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠷⠴⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣾⣿⣿⣆⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣀⣠⣴⣶⣽⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣴⣶⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢼⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⢴⣿⣷⣶⡄⠀⠀⢄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⠿⠛⠛⠛⠿⢿⣿⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⠀⠀⣿⣁⣀⡈⠛⢿⣿⣿⡿⣷⣎⡹⣿⣶⣾⣿⠟⠁⠀⠀⢠⣾⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⡿⢋⣁⣀⡀⠈⠻⠁⠀⠀⠀⠀⠀⠈⣿⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⡿⠀⢠⡿⣿⣿⣿⣦⠀⣿⣿⣿⣾⣿⣿⣿⣿⣉⣹⡀⠀⣠⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣅⣀⣀⣸⣿⣿⣿⡟⠀⣿⣿⣿⣿⠀⣸⣿⣦⠀⠀⠀⠀⠀⠈⠃⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⠀⣨⣇⠀⠈⠡⢼⣿⣿⣿⣦⣿⣿⠉⢿⣿⠟⣿⣿⠟⠛⠁⣠⣾⠿⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⣿⣿⣿⣿⡖⣿⣿⣿⣧⠀⠀⠀⠀⠀⠺⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠷⠀⠀⠀⠈⠉⠁⠀⠈⣻⠀⠀⠀⠀⢹⣿⠀⠀⠀⠛⠷⡀⠀⠙⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣿⣿⣿⠇⠘⣿⣿⣿⣿⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠟⠻⠿⠀⠀⠀⠀⠀⠟⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢼⣿⣿⣿⡇⠂⠙⢿⣿⣿⣄⢀⣭⣭⣥⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠘⢿⣿⣿⣷⡄⠀⣀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠈⣿⣿⣷⣷⣿⡆⠺⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⠡⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣇⠀⣿⢸⣿⣿⢿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⢴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡿⢿⣿⣿⣿⠟⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⡫⠉⠉⢻⣇⢁⣀⣀⣀⢀⣠⣠⣠⣤⣶⣧⠀⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢾⣶⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⣿⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⠿⠇⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣿⡾⣿⠟⠿⠿⠿⠛⠿⠛⠛⠛⠻⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢿⣿⡾⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣾⣿⣿⣆⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⣠⣦⣽⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣦⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⣼⣶⣶⣦⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⠟⠛⠛⠛⠿⢿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠀⠀⢹⡇⣠⡈⠛⠻⣿⣿⡿⣷⣎⠙⣷⣶⣿⣿⠟⠁⠀⠀⢠⣬⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡷⠀⠈⢿⣿⣿⣿⣿⡿⢟⣁⣀⡀⠈⢛⠁⠀⠀⠀⠀⠀⠀⣿⢰⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⡿⠀⢠⡾⢻⣿⣿⣶⠀⣿⣿⣿⣼⣿⣿⣿⣿⣋⣹⡄⢠⣶⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣅⣀⣀⣸⣿⣿⣿⣿⠁⣿⣿⣿⣿⠀⣸⣷⣆⠀⠀⠀⠀⠀⠉⠃⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⠇⣈⣧⡀⠀⠀⢸⣿⣿⣿⣆⣿⣿⡟⢹⣿⠿⣿⣿⡿⠋⠁⣰⣿⠟⠛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣿⣿⣿⣿⢿⣿⣿⣿⡇⢰⣿⣿⣿⣿⠞⣿⣿⣿⡄⠀⠀⠀⠀⠀⠺⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⠀⠀⠀⠈⠉⠁⠀⠘⣿⠃⠀⠀⠀⢻⣿⠀⠀⠀⠻⣿⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢾⣿⣿⣿⡇⠸⣿⣿⣿⣿⠂⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠻⣿⣿⣿⣿⣿⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠿⠻⠿⠀⠀⠀⠀⠀⠞⠹⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢾⣿⣿⣿⣧⡀⠙⢿⣿⣿⡄⢀⣭⣍⣥⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠸⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠈⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣟⢻⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣶⣦⠀⢠⣦⣴⣶⣴⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠈⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢾⠿⣇⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠻⣿⡇⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢿⣿⡾⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣾⣿⣿⣆⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡉⡀⣀⢀⣬⣽⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣶⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠚⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣤⣶⣤⣤⣄⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⣼⣶⣶⣦⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⠟⠛⠛⠛⠿⢿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣄⠀⠀⢉⣠⣤⡈⠛⠿⣿⣿⡿⣷⣎⠘⣷⣶⣿⣿⡟⠁⠀⠀⢠⣼⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣿⡿⢟⣁⣀⡀⠈⢛⠁⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⠀⠠⡞⢻⣿⣿⣶⠀⣿⣿⣿⣾⣿⣷⣿⣿⡋⣹⡄⢠⣶⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣁⣀⣀⣸⣿⣿⣿⣿⠃⣿⣿⣿⣿⠀⣸⣷⣆⠀⠀⠀⠀⠀⠈⠃⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⡇⣈⣧⡀⠀⠀⢸⣿⣿⣿⣆⣿⣿⡟⢹⣿⠿⣿⣿⡿⠛⠁⣰⣿⡿⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣹⣿⣿⣿⣿⢿⣿⣿⣿⡇⢰⣿⣿⣿⣿⠞⣿⣿⣿⡄⠀⠀⠀⠀⠀⠺⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⠀⠀⠀⠈⠋⠁⠀⠘⣿⡇⠀⠀⠀⢹⣿⠀⠀⠀⠻⣿⠁⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠿⣿⣿⣿⣿⣿⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠻⠻⠿⠀⠀⠀⠀⠀⠊⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢼⣿⣿⣿⣷⣀⠙⠿⣿⣿⡄⢀⣭⣉⣥⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠸⢿⣿⣿⣿⣿⡄⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠀⠀⠀⠀⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠈⠿⡀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⣷⠹⣿⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣾⣧⠀⢠⣦⣴⣶⣴⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠈⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⣏⣿⣿⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⢿⣧⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠛⣛⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢿⣿⣿⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣾⣿⣿⣦⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⣤⣝⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⣼⣿⣷⣶⡄⠀⠀⢀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⠟⠛⠛⠛⢿⣿⣟⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⠀⠀⢋⣤⣠⣈⠛⠻⣿⣿⡿⢷⣆⠈⣿⣶⣿⣿⠟⠁⠀⠀⣠⣼⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠘⢿⣿⣿⣿⣿⣿⢿⣋⣀⡀⠀⠛⠁⠀⠀⠀⠀⠀⠈⣿⢠⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⠀⠀⡜⢻⣿⣿⣶⠀⣻⣿⣿⣾⣿⣿⣿⣿⡋⣹⡄⢠⣶⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣅⣀⣀⣸⣿⣿⣿⣿⠇⣾⣿⣿⣿⠀⣸⣷⣆⠀⠀⠀⠀⠀⠈⠇⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢈⣧⡀⠀⠀⢸⡿⣿⣿⣦⣿⣿⡿⢹⣿⠿⣿⣿⡿⠟⠁⣸⣿⡿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣽⣿⣿⣿⣿⢿⣿⣿⣿⡏⢰⣿⣿⣿⣿⠞⣿⣿⣿⡄⠀⠀⠀⠀⠀⠻⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⠀⠀⠀⠀⠉⠁⠀⠘⣿⡇⠀⠀⠀⢹⣿⠀⠀⠀⠻⣿⡁⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢻⣿⣿⣿⡏⠸⣿⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠀⠀⠀⠀⠀⠋⠘⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢽⣿⣿⣿⣿⣇⢙⣿⣿⣿⡄⢀⣍⣉⣥⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠈⢿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣯⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢾⠀⠀⠀⠀⢨⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠈⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⠹⣿⣿⣿⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣴⠀⢠⣦⣴⣶⣰⣶⡆⣶⢶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡟⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⢿⣧⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠛⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠟⢷⠖⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢐⣾⣿⣿⣦⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣄⣤⣀⣶⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⣶⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢺⣿⠿⠿⣿⣿⣿⣿⣿⣿⡇⢀⢀⠀⠀⣴⣿⣷⣶⡄⠀⠀⢀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠟⠛⠛⠛⠿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⠀⠀⢃⡄⣀⣄⠙⠻⣿⣿⡿⢷⣆⠈⣿⣶⣿⣿⠟⠁⠀⠀⣠⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠂⠈⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⠀⠛⠀⠀⠀⠀⠀⠀⠙⢿⠰⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠀⠘⢻⣿⣿⣦⠀⣹⣿⣿⣾⣿⣿⣿⣿⣋⣹⡀⢠⣦⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣤⣤⣼⣿⣿⣿⣿⠏⣾⣿⣿⣿⠄⣸⣷⣆⠀⠀⠀⠀⠀⠨⣧⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣀⣵⡀⠀⠀⢸⡿⣿⣿⣦⣿⣿⡿⢹⣿⠟⣿⣿⡿⠟⠁⣸⣿⣿⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠉⠁⠀⠀⢿⡇⠀⠀⠀⢹⣿⠀⠀⠀⠻⣿⡇⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢸⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠛⠛⠿⠀⠀⠀⠀⠀⠚⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢙⢿⣿⣿⡀⢀⣍⣉⣥⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠈⢿⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠁⠀⠀⢀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠈⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⠹⣿⣿⣿⠿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡏⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⢿⣇⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠴⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠂⣾⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⣤⣤⣤⣾⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⡿⠿⠿⣿⣿⣿⣿⣿⣿⡆⢀⢀⠀⠀⣼⣷⣷⣦⡀⠀⠀⢀⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠟⠛⠛⠛⢿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣀⠀⠀⠀⡀⣀⣄⠙⠻⣿⣿⡿⠷⡀⠈⣷⣶⣿⣿⠟⠁⠀⠀⣤⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠗⡈⢿⣿⣿⣿⣿⣿⡿⣟⣅⣀⠀⠋⠀⠀⠀⠀⠀⠀⠹⣿⡸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⠀⠀⠀⢻⣿⣿⣷⠀⣸⣿⣿⣾⣿⣷⣿⣿⡏⣩⡀⢠⣤⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣤⣥⣸⣿⣿⣿⣿⠟⢸⣿⣿⣿⡄⣾⣶⣆⠀⠀⠀⠀⠀⠸⣷⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⢀⣹⡄⠀⠀⢴⡿⣿⣿⣦⣿⣿⣿⢹⣿⠿⣿⣿⡿⠟⠁⢨⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠠⠀⠀⠀⠀⠉⠁⠀⠀⢻⡇⠀⠀⠀⢹⣿⠀⠀⠀⢹⣿⡏⠉⣙⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢿⣿⣿⣿⢻⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠀⠀⠀⠀⠉⠟⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢾⣿⣿⣿⣿⣧⠙⢻⣿⣿⡀⢀⣉⣉⣥⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠈⣿⣿⣿⣿⣿⣄⣀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢰⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠀⠀⠀⢨⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠈⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣯⠹⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢹⣷⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡏⠀⠘⣿⣿⣻⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⢿⣇⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣭⣤⣤⣤⣤⣾⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⣦⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⡿⠿⣿⣿⣿⣿⣿⣿⡆⢀⡀⠀⠀⣴⣶⣷⣦⠀⠀⠀⠀⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠟⠛⠛⠻⢿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⠀⠀⠀⠀⣠⣄⠙⠻⣿⣿⡿⠳⡀⠈⢳⣦⣿⣿⠟⠁⠀⠀⣴⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡎⢻⣿⣿⣿⣿⣿⡿⣟⣅⡀⠀⠃⠀⠀⠀⠀⠀⠀⢹⣿⡖⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⠀⠀⠀⠻⣿⣿⣷⡄⢘⣿⣿⣾⣿⣷⣿⣿⣏⢉⡄⢠⣤⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣅⣈⣀⣿⣿⣿⣿⠟⢸⣿⣿⣿⡄⣿⣶⣄⠀⠀⠀⠀⠀⢹⣷⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⠀⠦⠿⣿⣿⣷⢿⣿⣿⢻⣿⠿⣿⣿⣿⠿⠁⢨⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠿⡆⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠴⠂⠀⠀⠀⠉⠁⠀⠀⢻⡿⠀⠀⠀⢹⣿⠁⠀⠀⠸⣿⣿⡛⣙⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡅⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠛⠛⠿⠀⠀⠀⠀⠉⠻⠉⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣆⠙⢿⣿⣿⡀⢀⣉⣉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠈⢿⣿⣿⣿⣷⡀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢰⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠁⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠈⢿⡄⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣯⠹⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣿⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡟⠀⠈⣿⣿⣽⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⢿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢶⠶⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣶⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢩⣤⣠⣤⣤⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣴⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⠿⠿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣴⣶⣷⣦⠄⠀⠀⠠⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⠛⠛⠿⢿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⣰⣌⠙⠻⣿⣿⡿⠷⡀⠈⣷⣦⣿⣿⠟⠁⠀⠀⣴⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠜⠻⣿⣿⣿⣿⣿⡿⣟⣁⡀⠀⠃⠀⠀⠀⠀⠀⠀⢹⣿⡖⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⠀⠀⠀⠻⣿⣿⣷⡀⢘⣿⣿⣾⣿⣶⣿⣿⡏⢉⡀⢀⣤⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣅⣈⣀⣿⣿⣿⣿⡟⢹⣿⣿⣿⡀⣿⣶⣄⠀⠀⠀⠀⠀⢹⣿⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⡿⣿⣿⣧⣻⣿⣿⠿⣿⠟⣿⣿⡿⠿⠁⢠⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⢿⠆⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠴⠆⠀⠀⠀⠉⠉⠀⠀⢻⡿⠀⠀⠀⢹⣿⠀⠀⠀⠸⣿⣿⠛⢉⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠻⣿⣿⣿⣿⣿⡅⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠛⠛⠿⠀⠀⠀⠀⠉⠻⠉⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣿⣿⡀⣀⣉⣉⣥⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠈⢿⣿⣿⣿⣧⡀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢴⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠀⠀⠀⢸⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠈⢿⡄⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⠹⣿⣿⣿⠿⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣿⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡟⠀⠈⣿⣿⣻⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⢿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠴⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣾⣿⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣷⣶⣶⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⣠⣶⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⣿⡿⠿⣿⣿⣿⣿⣿⣿⡇⢀⢀⠀⠀⣼⣿⣿⣦⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⠛⠛⠿⢿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⠀⠀⠀⣴⣎⠙⠻⢿⣿⣿⠳⡀⠀⣿⣶⣿⣿⠟⠀⠀⠀⢠⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠗⠻⣿⣿⣿⣿⣿⡿⣟⣁⡀⠀⠃⠀⠀⠀⠀⠀⠀⢹⣿⡔⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠻⣿⣿⣷⡄⢘⣿⣿⣾⣿⣷⣿⣿⣟⠁⠀⠀⣠⣦⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣇⣈⣀⣿⣿⣿⣿⠟⣽⣿⣿⣿⡀⣿⣶⣆⠀⠀⠀⠀⠀⢹⣿⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣁⣧⠀⠀⠰⠀⠿⣿⣿⣷⣻⣿⣿⠹⡿⠻⣿⣿⡿⠿⠀⢀⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⣿⡿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⢿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠶⠂⠀⠀⠀⠉⠉⠀⠀⠹⡇⠀⠀⠀⢹⣿⠇⠀⠀⠸⣿⣿⣟⣋⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠛⠛⠿⠃⠀⠀⠀⠘⠿⠋⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣿⣿⡀⣈⣉⣙⣧⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠈⢿⣿⣿⣿⣇⡀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢵⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡏⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠈⠿⡄⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⠹⣿⣿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣥⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡏⠀⠈⣿⣿⣻⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⢿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠟⢶⠶⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣷⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⣶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⣿⡿⠿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠀⠀⣼⣿⣷⣦⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⠛⠛⠻⢿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⠀⠁⠀⣴⣮⠙⠛⢿⣿⣿⠻⡀⠀⣷⣶⣿⣿⠟⠀⠀⠀⢀⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠷⠻⣿⣿⣿⣿⣿⡿⣟⣁⡀⠀⠃⠀⠀⠀⠀⠀⠀⠹⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠻⣿⣿⣷⡄⢘⣿⣿⣶⣿⣷⣿⣿⣟⠉⠀⠀⢠⣦⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣈⣀⣿⣿⣿⣿⠿⣼⣿⣿⣿⡀⣿⣶⣦⠀⠀⠀⠀⠀⢹⣿⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⣥⡀⠀⠆⠠⠿⣿⣿⣷⣻⣿⡿⢹⠿⠻⣿⣿⡿⠿⠀⢀⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⣿⡿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⢿⣿⣿⣿⡆⠀⠀⠀⠀⠈⢿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠶⠒⠀⠀⠀⠈⠉⠀⠀⢹⡇⠀⠀⠀⢹⣿⠁⠀⠀⠸⣿⣿⣿⣋⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠻⠛⡿⠃⠀⠀⠀⠙⠿⠋⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⣿⣿⣿⢿⣿⣿⣿⣿⡄⠙⢿⣿⣿⡀⣈⣉⣙⣧⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠈⢿⣿⣿⣿⣇⡀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢰⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠉⠀⠀⢸⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⡀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⠹⣿⣿⣿⠿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣥⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡏⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⢿⣏⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠟⢶⠶⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢹⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣾⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣿⠿⠿⣿⣿⣿⣿⣿⣿⡁⠀⡀⠀⠀⣾⣾⣷⣤⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⠛⠛⠻⢿⣿⣿⡀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⣶⣮⠙⠛⢿⣿⡿⠷⠀⠀⣷⣦⣿⣿⠟⠁⠀⠀⠀⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢟⠹⣿⣿⣿⣿⣿⡿⣟⣁⡀⠀⠓⠀⠀⠀⠀⠀⠀⠹⣿⣇⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣷⡆⢘⣿⣿⣶⣿⣾⣿⣿⣟⠁⠀⠀⠀⣴⣎⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣈⣡⣿⣿⣿⣿⠿⣾⣿⣿⣿⡄⣿⣷⣦⠀⠀⠀⠀⠀⢹⣿⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣠⡀⠀⠆⢶⠿⣿⣿⣷⢸⣿⡟⢹⡿⠻⣿⣿⡿⡿⠀⢀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣇⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡧⠿⠿⠃⠀⠀⠀⠈⠉⠀⠀⠹⡇⠀⠀⠀⢹⣿⠁⠀⠀⠸⣿⣿⣿⣟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠻⣿⣿⣿⣿⣿⡅⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠻⠛⡿⠁⠀⠀⠀⠘⠿⠋⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⣿⣿⣿⢿⣿⣿⣿⣿⡆⠙⢿⣿⣿⡀⣀⣉⣉⣯⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠈⢻⣿⣿⣿⣧⡄⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡏⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⢸⡩⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⢹⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣷⠀⢠⣦⣴⣶⣰⣶⡆⣶⠖⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡏⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⢿⣯⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠿⢷⠶⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣶⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣰⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⡿⠿⣿⣿⣿⣿⣿⣿⡀⢀⣀⠀⠀⣾⣾⣷⣤⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⠛⠛⠻⢿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣡⢄⣶⣮⡙⠛⢿⣿⡟⠷⠀⠈⣷⣦⣿⣿⡟⠁⠀⠀⠀⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⣟⣁⡀⠀⠛⠀⠀⠀⠀⠀⠀⠹⣿⣧⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣷⡄⢘⣿⣿⣼⣿⣾⣿⣿⣟⠉⠀⠀⠀⣴⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣬⣥⣼⣿⣿⣿⠿⣿⣿⣿⣿⡄⣿⣷⣦⠀⠀⠀⠀⠀⢹⣿⡆⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣀⡁⠰⠆⣦⠿⢿⣿⣷⢺⣿⡟⢽⡿⠛⣿⣿⡿⠿⠀⢀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⠛⢻⣿⢿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠷⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⡇⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠃⠀⠀⠀⠘⠉⠀⠀⠹⠇⠀⠀⠀⢹⣿⠀⠀⠀⠸⣿⣿⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠻⣿⣿⣿⣿⣿⡛⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣿⠃⠀⠀⠀⠙⠿⠋⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢿⣿⣿⣽⣿⣿⣿⣿⡄⠙⢿⣿⣿⡀⣀⣉⣉⣯⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠉⣻⣿⣿⣿⣷⡄⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⢶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠉⠀⠀⢹⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠈⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⢻⣿⣿⣿⠿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣷⠀⢠⣤⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡏⠀⠈⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⢿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠟⢷⠶⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢻⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢁⣴⣾⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⣿⡿⠿⣿⣿⣿⣿⣿⣿⠁⢀⣀⠀⠀⢰⣾⣷⣦⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⠛⠛⠛⠿⣿⣿⡇⠀⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠈⣩⢄⣶⣮⡙⠛⢿⣿⡟⠷⠀⠈⣷⣦⣿⣿⡿⠁⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣟⣁⡀⠀⠙⠀⠀⠀⠀⠀⠀⠙⣿⣷⡹⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠋⠻⣿⣿⣷⡄⢘⣿⣿⣼⣿⣾⣿⣿⣿⡉⠀⠀⠀⣠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣭⣼⣿⣿⣿⡿⣿⣿⣿⣿⡆⢺⣿⣶⠀⠀⠀⠀⠀⢹⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠁⠰⠄⣆⠿⣿⣿⣷⣸⣿⡟⢹⣿⠟⣿⣿⡿⠿⠀⢀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡾⡟⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⡷⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⡇⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠘⠋⠁⠀⠘⠃⠀⠀⠀⢸⣿⠁⠀⠀⠘⣿⣿⣿⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡃⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡆⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⠀⠀⠈⠻⣿⣿⣿⣿⣿⡟⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⡿⠃⠀⠀⠀⠈⠿⠋⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠈⣿⣿⣿⣿⣿⣿⣿⡆⠘⠻⣿⣿⡄⣀⣍⡉⣿⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⡀⡀⢀⢀⣀⣄⣤⣠⣤⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⢻⣿⣿⣿⣷⡄⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⢲⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⢸⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⢹⣿⣿⣿⠿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣧⠀⢠⣤⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡏⠀⠈⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⢿⣯⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢷⠷⠸⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢱⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣰⣿⡿⠿⣿⣿⣿⣿⣿⣿⡂⢀⡀⠀⠀⢰⣶⣷⣦⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⣿⣿⡇⢀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠘⣧⢠⣶⣮⠛⢛⣿⣿⡟⠳⠀⠈⣿⣦⣼⣿⡿⠁⠀⠀⠀⢰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣁⣀⠀⠙⠀⠀⠀⠀⠀⠀⠘⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠟⠻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣾⣿⣿⣿⣋⡀⠀⠀⣰⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣬⣉⣿⣿⣿⡿⢿⣿⣿⣿⡇⢸⣿⣦⠀⠀⠀⠀⠀⠸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣌⡀⣶⡰⡄⢹⣿⣿⣿⣽⣿⠟⣿⣿⠟⣿⣿⡿⠿⠁⠀⣴⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⡷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠻⣇⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠸⣿⡆⠀⠈⠙⣭⣭⡉⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⣿⣿⣿⢋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⡏⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⡇⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠸⠿⠻⣿⠃⠀⠀⠀⠈⠻⠃⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢸⣿⣿⣿⣿⣿⣿⡇⠘⠻⣿⣿⣇⣀⣍⣉⢻⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⢿⣏⡿⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢻⣿⣿⣿⣿⡄⢀⣽⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢰⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⢸⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⡀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣯⢻⣿⣿⣿⠿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣧⠀⢠⣤⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡏⠀⠈⣿⣿⣻⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⣿⣯⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠇⢶⠄⠸⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣻⣿⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠁⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⡿⠿⣿⣿⣿⣿⣿⣿⡀⢀⡀⠀⠀⢰⣶⣶⣦⡀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠟⠛⠛⠋⠛⢿⣿⣇⢀⣤⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢈⣧⢠⣶⡚⠛⢻⣿⣿⡟⠷⠀⠘⣷⣦⣼⣿⡿⠋⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠁⢿⡆⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣁⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢻⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡟⠻⣿⣿⣿⣿⣟⣿⣷⣾⣿⣾⣿⣿⣟⣉⡄⠀⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣼⣿⣿⣝⡛⣿⣿⠿⢸⣿⣿⣿⡆⢰⣶⣄⠀⠀⠀⠀⠀⠀⢿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢠⣤⢲⠀⢻⣿⣿⣿⣜⣿⠏⣿⣿⠟⣿⣿⠿⠿⠋⠀⣴⣾⣿⣿⣿⡇
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣼⡿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⡿⢾⣿⣿⣆⠀⠀⠀⠀⠀⠈⠃⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠸⣷⠀⠀⠉⠙⣯⣭⡉⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⣿⣿⣿⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⡇⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠻⠟⠻⣿⠃⠀⠀⠀⠈⠿⠋⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⢻⣿⣿⣿⣿⣿⣆⠈⠻⣿⣿⣇⣀⣬⣉⢩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣏⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡄⢀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⢰⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠁⠉⢸⡟⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣾⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⡀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⢻⣿⣿⣿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣧⠀⢠⣤⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢿⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡏⠀⠈⣿⣿⣻⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠸⠾⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣻⣿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⢱⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⡶⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⡿⠿⣿⣿⣿⣿⣿⣿⡀⢀⣀⠀⠀⣶⣶⣶⣦⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⣧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠻⡿⣿⢀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢈⣧⢠⡶⠊⠻⢿⣿⣿⡿⠧⠀⢸⣷⣦⣿⣿⡿⠁⠀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣉⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣼⡿⢿⣶⣶⣤⡄⢙⣿⣷⣼⣷⣾⣿⣿⣛⣿⡄⠀⠀⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣾⣿⣿⡆⠀⣤⣄⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠂⠀⠿⣿⣿⣿⣼⡿⠋⣿⣿⠟⣿⣿⢿⠟⠋⠀⣠⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠁⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠊⠁⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⣿⣿⣷⡛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠻⣿⠃⠀⠀⠀⠈⠻⠋⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣦⡈⠻⣿⣿⣿⣿⣿⣿⣆⠄⠙⢿⣿⣿⣀⣤⣉⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠙⢿⣿⣿⣿⣿⣷⡄⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⢶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠐⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡻⣿⣿⣿⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣦⠀⢠⣤⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⢿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡏⠀⠈⣿⣿⣻⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⢿⣯⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠋⢠⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣾⠆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⣿⡿⠿⣿⣿⣿⣿⣿⣿⡀⢀⣀⠀⢠⣶⣶⣶⣤⠀⠀⠀⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣻⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠻⢿⣿⢀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣧⢠⠶⠊⠻⠿⣿⣿⡿⢧⠀⢸⣷⣦⣿⣿⡿⠁⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣉⣁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣾⡿⢿⣶⣶⣤⡀⢙⣿⣷⣿⣷⣾⣿⣿⣋⣫⡄⠀⠀⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣾⣿⣿⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢿⣿⣿⣷⣼⡿⠋⣿⣿⠟⣿⣿⢿⠟⠁⠀⣠⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣠⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠚⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⣿⣿⣶⢙⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⡅⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠻⣿⠃⠀⠀⠀⠈⠻⠋⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣆⠻⣿⣿⣿⣿⣿⣿⡤⠄⠙⢿⣿⣿⣀⣠⣈⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠙⢿⣿⣿⣿⣿⣿⣆⢀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⢶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡅⣹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⠻⣿⡻⣿⣿⣿⠟⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣦⣴⣶⣴⣶⡆⣶⠖⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⢻⣷⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢾⢿⣧⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠃⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠔⠰⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠈⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⢁⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣤⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡗⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⡿⠿⣿⣿⣿⣿⣿⣿⡄⣀⣀⠀⣀⣶⣶⣦⣄⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣷⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠻⣿⣇⢀⣤⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣰⠶⠂⠻⠿⠻⢿⠿⣧⠀⢹⣷⣾⣿⣿⡟⠁⠀⠀⠀⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣉⠀⠏⠀⠀⠀⠀⠀⠀⠀⠡⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣾⡟⢿⣶⣶⣤⡀⠀⢸⣷⣿⣷⣾⣿⣿⣩⣭⡄⠀⢠⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠒⠀⠀⠀⢿⣿⣿⣷⣾⠿⠋⣿⣿⠛⣿⣿⣿⠋⠁⢀⣈⠙⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⡀⣼⣷⡄⠀⠀⠀⠀⠀⠠⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠈⠋⠀⢀⣘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⡇⠉⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⢹⡿⠋⠀⠀⠀⠀⠀⠋⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⠄⠈⠻⣿⣿⣇⣠⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠙⢿⣿⣿⣿⣿⣿⣦⡀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⣷⣶⣶⡆⠺⣿⢻⣿⣿⣿⣏⢸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡘⣿⣿⣿⠟⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣦⣴⣶⣴⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢿⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠙⢾⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⡾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠃⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠇⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡴⣦⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⢡⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡷⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⡿⠿⣿⣿⣿⣿⣿⣿⡄⣀⣀⠀⣀⣶⣶⣦⣄⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠈⠙⢿⣇⢀⣤⣀⣨⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢸⣿⣰⡖⠂⠛⠿⠛⠿⠟⣧⠀⢹⣿⣿⣿⣿⠟⠁⠀⠀⠀⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣾⡿⢿⣶⣶⣤⡄⠀⢸⣷⣿⣷⣾⣿⣿⣩⣩⡄⠀⢠⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠐⠀⠀⠀⢿⢿⣿⣷⣾⠾⠋⣿⡿⠟⣿⣿⣿⠋⠁⢀⡈⠛⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⠀⣾⣿⣿⣿⣄⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠋⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠘⠃⠀⢀⣘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⡏⠉⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢻⡿⠋⠀⠀⠀⠀⠀⠋⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡟⢿⣿⣿⣿⣿⣿⣷⠄⠈⠻⣿⣿⣇⣀⣌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢓⣘⣿⣿⣿⣿⣿⣿⣧⡀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⣷⣶⣶⡆⠺⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢹⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠻⣿⡈⣿⣿⣿⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢙⣇⢀⣀⣀⣀⢀⣠⣠⣠⣤⣤⣤⠀⢠⣦⣴⣶⣴⣶⡆⣶⠖⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⣀⠀⢿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡇⠀⠈⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠙⠛⢺⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⡾⢿⠟⠿⠿⠿⠻⠿⠚⠛⠓⠘⠃⠃⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠇⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠉⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⡿⠿⣿⣿⣿⣿⣿⣿⡀⢀⣀⠀⣠⣶⣶⣦⡄⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠉⠉⠉⠙⣿⢀⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣰⡶⠋⠻⢿⡿⠟⠛⢦⠀⢹⣷⣿⣿⣿⠟⠁⠀⠀⢠⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣉⡁⠀⠛⠃⠀⠀⠀⠀⠀⠀⢿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣾⡿⢿⣴⣶⣤⡀⠀⠀⢠⣿⣷⣾⣿⣿⣩⣭⡄⠀⢠⣶⣺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢀⣾⣿⣿⣦⣠⣤⠀⠀⠀⠀⠀⠀⠸⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⢿⢿⣿⣷⣾⡿⠉⣿⡿⠛⣿⡿⣿⠋⠁⢀⡸⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⣼⣿⣿⣿⡟⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠘⠁⠀⣶⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⣘⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⠀⢿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢻⡿⠋⠀⠀⠀⠀⠰⠋⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⣿⣿⣿⣿⣿⣿⡴⠈⠻⣿⣿⣇⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⢛⣿⣿⣿⣿⣦⡀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣷⣶⣶⡆⠺⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠙⠛⠃⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡌⣿⣿⣿⠟⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⢹⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣦⣴⣶⣴⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣽⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣾⣿⣻⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢺⢿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣿⡾⣿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠃⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠇⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠐⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⣰⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣆⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⣿⣿⠿⢿⣿⣿⣿⣿⣿⡄⣀⣀⠀⣰⣶⣶⣦⣄⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠉⠀⠈⠉⣿⢀⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣰⡶⠋⠻⢿⣿⠿⠛⢧⠀⢹⣿⣿⣿⣿⠟⠁⠀⠀⢰⣶⣾⡇
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠁⠙⠏⠀⠀⠀⠀⠀⠀⢸⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣾⡿⢿⣶⣶⣤⡀⠋⠀⢠⣿⣿⣾⣿⣟⣩⣧⡄⠀⣰⣦⣿⣿⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣾⣿⣿⣦⣠⣶⡄⠀⠀⠀⠀⠀⠘⠃⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠐⠀⠀⠀⢿⢿⣿⣷⣾⡿⠁⣿⡿⠋⣿⣿⣿⠋⠁⢀⡸⠿⢿⣿⣿⡇
⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⡟⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠘⠁⠀⣶⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢹⡿⠋⠀⠀⠀⠀⠰⠋⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢿⣿⣿⣿⣿⣷⡶⠈⠻⣿⣿⣯⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡄⠀⠀⠀⠀⠀⠙⠛⠋⢻⣿⣿⣿⣿⣧⣄⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⢸⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠷⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⡙⣿⣿⣿⠟⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢹⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣤⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢻⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡇⠀⠈⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢺⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠃⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⣿⣿⠛⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⢠⣶⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⣿⣿⠿⣿⣿⣿⣿⣿⣿⡆⣀⣀⠀⣠⣶⣶⣦⡄⠀⠀⠀⢠⣤⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⠉⢿⢀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣰⡶⠃⠛⢿⣿⡿⠛⢧⠀⢹⣷⣿⣿⣿⠟⠀⠀⠀⢰⣶⣾⡇
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠙⠛⠀⠀⠀⠀⠀⠀⢸⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡿⢻⣶⣶⣦⡌⢛⠃⢀⣾⣿⣾⣿⣟⣉⣧⡄⠀⣴⣶⣿⣿⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠃⣾⣿⣿⣦⡀⣴⡄⠀⠀⠀⠀⠀⠈⠃⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠐⠀⠀⠀⢿⢿⣿⣿⣿⡿⠃⣿⡿⠏⣿⡿⡿⠋⠁⢀⡽⠿⣿⣿⣿⡇
⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠘⠁⠀⣾⣛⣿⡇
⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣀⣻⣿⣿⣿⣿⣿⠃⢻⣿⣿⣿⣿⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡏⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢻⡿⠋⠀⠀⠀⠀⠸⠋⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢿⣿⣿⣿⣿⡶⠈⠻⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠙⠛⠋⢻⣿⣿⣿⣦⣄⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⣿⣿⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡏⣿⣿⣿⣿⡇⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡆⠀⠀⠀⠀⠀⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠶⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⠛⠓⣿⡽⣿⣿⣿⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢹⣃⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣤⣴⣶⣴⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣄⡀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢺⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠇⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠸⣿⣿⠛⠹⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⢡⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢀⣴⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⠿⣿⣿⣿⣿⣿⣿⡄⣀⣀⠀⡠⣦⣶⣦⡄⠀⠀⠀⢠⣄⠀
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠉⣿⢀⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣠⡶⠂⠛⢿⣿⣿⡟⢧⠀⢙⣷⣿⣿⣿⠏⠀⠀⠀⣰⣶⣾⡇
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⡿⠿⣶⣶⣦⡄⢛⣿⠀⣼⣿⣾⣿⣏⣝⣿⡀⠀⣤⣄⣿⣿⣿⡇
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⠿⠂⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠾⢿⣿⣿⣿⡿⠉⣿⣿⠟⣿⣿⡟⠋⠁⢀⡿⠿⣿⣿⣿⡇
⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⢿⣿⣿⠉⢹⣿⣿⣿⣿⡀⣼⣿⣿⣿⣿⡀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠘⠁⢠⣾⣻⣿⡇
⠀⠹⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⢸⣿⣿⣿⣿⠃⢹⣿⣿⣿⣿⡇⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡏⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⢹⡿⠋⠀⠀⠀⠀⠸⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⣿⣿⣿⡶⠈⠻⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⣿⣿⣯⣯⣄⣠⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⣿⣷⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠶⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⣿⡽⣿⣿⣿⠟⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢙⣇⢀⣀⣀⣀⢀⣀⣠⣠⣤⣤⣤⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢸⣿⣿⣿⡇⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠃⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠸⣿⣿⠛⠻⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠲⠤⠀⠀⠺⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⣦⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣆⣠⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⢀⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⠀⠀⣤⣴⣤⣄⠀⠀⠀⢀⣄⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠀⠀⠉⣇⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠘⣁⢀⡴⠋⠛⢿⣿⣿⡿⢧⠈⠹⣷⣿⣿⣿⡟⠁⠀⠀⣤⣤⣿⡇
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠙⠿⠃⠀⠀⠀⠀⠀⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣼⡿⢿⣷⣾⣶⣄⢻⣿⡇⣸⣿⣾⣿⣟⣻⣿⡄⢠⣄⢸⣿⣿⣿⡇
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣿⣿⣿⠇⢠⣾⣿⣷⣦⠀⣠⣄⠀⠀⠀⠀⠀⠘⠆⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠿⣿⣿⣿⣿⡟⠁⣿⣿⠟⣿⣿⡿⠟⠁⢸⣿⢿⣿⣿⣿⡇
⠙⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠿⣿⣿⡿⠛⣿⣿⣿⠀⣾⣿⣿⣿⣿⠃⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠇⠀⠀⠀⠀⠉⠉⠁⢀⠀⠀⠈⠁⠀⢸⣿⠀⠀⠀⠘⠀⢠⣝⣿⣿⡇
⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⡇⠀⣿⣿⣿⡄⢿⣿⣿⣿⣿⡇⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡋⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢺⡿⠃⠀⠀⠀⠀⠿⠛⠿⠛⠃
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡆⠘⢿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢸⣿⣷⣀⣠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠙⣿⣿⣶⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡏⣿⣿⣿⣿⡇⠀⠠⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠶⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢻⣁⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣤⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⡇⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⡼⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠃⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠇⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣶⣶⠾⠟⠛⠛⠀⠀⠀⢺⣓⠀⠺⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡆⣀⣠⣤⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣠⣤⣤⣄⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⠀⣀⣶⣶⣦⣄⠀⠀⠀⠠⣀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠀⠀⠈⣇⢀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⣡⢠⡎⠙⠛⠿⣿⣿⡿⢧⡌⢹⣷⣿⣿⣿⡟⠁⠀⢀⣤⣤⣿⡇
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠻⠿⠃⠀⠀⠀⠀⠀⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⣴⡿⢿⣿⣿⣧⣄⢛⣿⣷⣸⣿⣾⣿⣿⣻⣿⡄⣤⡄⣾⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣷⣾⣷⣶⡄⠀⣠⣤⠀⠀⠀⠀⠀⠘⠆⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠻⣿⣿⣿⣿⡟⠉⣿⣿⠟⣿⣿⠟⠏⠁⢹⣿⣿⣿⣿⣿⡇
⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠈⠁⠀⢸⣿⠀⠀⠀⠛⠀⣀⣻⣿⣿⡇
⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⡿⠃⠀⠀⠀⠀⠿⠛⠿⠛⠇
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣿⣿⠙⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣽⣿⣀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠙⣿⣿⣴⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡏⣿⣿⣿⣿⡇⠀⡰⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠶⠀⢿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢻⣁⢀⣀⣀⣀⢀⣀⣠⣠⣤⣾⣧⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣻⣿⣻⣿⣿⣿⣿⣷⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡼⡆⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠃⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⠾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⠿⠿⠛⠛⠀⠀⢺⣗⡂⠺⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡆⠀⢀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀
⣻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⠀⢀⣶⣶⣦⣤⠀⠀⠀⠀⣄⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠀⠀⠈⣯⢀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣀⢠⡾⠙⠛⠻⣿⣿⡿⢷⡌⠙⣿⣾⣿⣿⡿⠉⠀⢀⣤⣤⣽⡇
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠛⠉⠉⠙⠻⣿⠃⠀⠀⠀⠀⠀⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⢠⡿⣿⣷⣿⣶⣄⢛⣿⣷⣼⣿⣿⣿⣿⣿⣿⣆⣤⡄⣾⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣶⣦⡄⠀⣰⣦⠀⠀⠀⠀⠀⠘⠆⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠋⣿⣿⡿⣿⣿⠿⠟⠁⢹⣿⢿⣿⣿⣿⡇
⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠉⠉⠁⣀⠀⠀⠈⠁⠀⢸⣿⠀⠀⠀⠘⠀⣀⢻⣿⣿⡟
⠀⠀⠹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢹⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠛⠿⠋⠀⠀⠀⠀⠿⠛⠿⠻⡇
⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣼⣿⣿⡿⣿⣿⣿⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡀⢀⢀⣀⡄⣤⣠⣤⡀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣽⣿⡇⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠙⣿⣿⣴⣶⣶⡆⠚⣿⢻⣿⣿⣿⣏⠸⣿⡝⠃⠉⠉⢸⡟⣿⣿⣿⣿⡇⠠⣰⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⠀⣿⢸⣿⣿⠿⠶⠀⠿⠀⠀⠀⠀⠘⠃⠛⠛⠘⠛⠃⠀⠈⢁⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⢻⣁⢀⣀⣀⣀⢀⣀⣠⣠⣤⣼⣧⠀⢠⣦⣴⣶⣰⣶⡆⣶⠶⣾⡃⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⢾⣿⣺⣿⣻⣿⣿⣿⣿⣿⢼⣿⡇⢸⡇⠀⠘⣿⣿⣿⣯⣿⣷⣿⣁⣿⠁⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⣿⠉⣿⣿⣿⣷⠾⠿⠟⠿⠿⠿⠛⠿⠚⠛⠓⠘⠃⠃⠈⠉⠈⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⡿⠿⠿⠿⠿⠿⢶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡆⠀⠀⣠⣤⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠙⢛⣂⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡤⠘⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⡄⠀
⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣷⣶⣤⣤⣄⣀⣀⣀⣤⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣁⣀⠀⠀⣼⣷⣷⣦⡀⠀⠀⢠⣄⡀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠀⠀⠈⣇⣀⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠉⣽⡿⠟⠛⠻⣿⣿⡿⢷⡍⢹⣿⣶⣿⣿⣿⠋⠀⢀⣤⣦⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣿⣿⣿⣿⣿⡟⠉⠉⠛⢿⣿⡇⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⢀⡿⣿⣿⣿⣿⣦⣻⣿⣷⣼⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢛⠿⣿⣿⣿⣿⣿⣶⣦⡄⠀⣿⣷⠀⠀⠀⠀⠀⠈⠆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⢻⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⢿⠟⠉⢻⣿⣿⣿⣿⣿⡇
⠛⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠐⢿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠃⠀⠀⠸⠋⠉⢉⣀⠀⠀⠈⠉⠀⢹⣿⠀⠀⠀⠺⢟⣍⣻⣿⣿⡿
⠀⠀⠙⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡟⣹⣄⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠸⠿⠛⣿⠏⠀⠀⠀⠀⢿⠻⠿⠿⡇
⠀⠀⠀⠸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡗⠈⠉⠉⠀⠀⢀⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣧⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢠⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠑⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢐⣶⣶⣿⣿⣿⣿⠿⠿⠿⠿⠿⢶⣾⣿⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡆⠀⢀⣠⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠛⣂⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⡄⠀
⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣾⣿⣶⣤⣤⣤⣤⣀⣠⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣫⣀⠀⠀⣴⣿⣿⣶⡄⠀⠠⢠⣄⠀
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠀⠀⠘⡇⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠉⣵⡿⠟⠛⠻⣿⣿⣿⢷⡍⢹⣿⣶⣿⣿⣿⠋⠀⢀⣤⣦⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣿⣿⣿⣿⡟⠉⠉⠛⢿⣿⠃⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⣼⣿⣿⣿⣷⣦⣻⣿⣷⣼⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡿⣿⣿⣿⣿⣿⣶⣦⡆⠀⣿⣧⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⣿⣿⡿⣿⣿⡿⡟⠉⢹⣿⣿⣿⣿⣿⡇
⠙⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠏⠀⠀⠸⠏⠉⢉⣀⠀⠀⠈⠉⠀⢹⣿⠀⠀⠀⠺⠟⣄⣻⣿⣿⡿
⠀⠀⠘⢿⣿⣿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡟⣱⣄⠀⠀⠀⠀⠀⠀⠀⠸⡻⠀⠀⠀⠸⠿⠻⡿⠋⠀⠀⠀⠀⢿⠛⠿⠿⡇
⠀⠀⠀⠘⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡗⠈⠉⠁⠀⠀⢀⣀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣠⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⡆⣀⣀⣀⣀⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠘⠛⠿⠍⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡄⠒⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⡄⠀
⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣴⣾⣷⣶⣤⣤⣤⣀⣠⣴⣴⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣃⣀⠀⠀⠀⣾⣿⣿⡷⠀⠠⣠⣄⠀
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⢸⡇⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⣹⡿⡿⠟⠿⣿⣿⡿⣷⣍⣻⣿⣶⣤⣾⣿⠋⠀⢠⣤⣶⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣿⣿⣿⠉⠉⠻⡿⡆⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠀⢰⣿⣿⣿⣿⡄⣻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⣿⣿⣿⣿⣿⣶⣄⠐⠀⣀⠀⠀⠀⠀⠀⠀⠘⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⢿⠟⠙⣿⣿⣿⣿⣿⣿⡇
⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣭⣼⣾⣿⣿⣿⣿⣿⣿⠀⠠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁⠀⠹⠋⠛⢩⣄⠀⠀⠉⠁⠀⣿⣿⠀⠐⠓⠻⠟⠋⣁⣿⣿⡟
⠀⠈⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠋⣻⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠺⠿⢿⡿⠃⠀⠀⠀⠀⠾⠻⠿⣿⡇
⠀⠀⢸⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣤⣀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡆⠈⠉⠀⠀⠀⢀⡀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃
⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡆⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠰⣂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠩⡆⠀⠀⠀⢼⣵⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣆⣀⣀⣀⣀⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠐⠻⠿⡏⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡄⠓⢠⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠩⣤⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠛⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⡄⠀
⣻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣰⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣧⣄⠀⠀⠀⣶⣿⣿⡷⠀⠤⣠⣄⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⢹⡇⢁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠈⠉⣠⣿⡿⠛⠿⣿⣿⡿⣷⣍⣻⣿⣦⣤⣼⣿⠋⠀⢠⣤⣼⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣿⣿⣿⣿⣿⠉⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⢰⣿⣿⣿⣷⣤⣹⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣅⠀⠀⠈⣿⣿⣿⣷⣿⣿⠿⣿⣿⢿⣿⣿⠿⠟⠉⣿⣿⣿⣿⣿⣿⡇
⠛⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣼⣿⣿⣿⣿⣿⣿⣿⡀⠠⣿⣷⡄⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠸⠃⠛⢡⡄⠀⠀⠈⠀⠀⣿⣷⠀⠐⠛⠛⠛⠉⢘⣿⣿⡟
⠀⢹⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⢿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠉⣻⡄⠁⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠻⠿⢿⡿⠋⠀⠀⠀⠀⠼⠻⠿⣿⡇
⠀⠀⢻⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣤⣀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡆⠈⠉⠀⠀⠀⣀⡀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⡆⠀⠀⠀⠀⠐⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢾⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣦⣤⣤⣤⣠⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠒⠛⢻⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠓⢠⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠩⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣰⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣣⣄⠀⠀⠀⢰⣿⣿⡿⠆⠤⣠⣄⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠈⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⡀⠈⠉⠈⠹⠻⠛⠿⣿⣿⡿⣷⡍⣻⣿⣦⣤⣼⣿⠋⠀⢠⣤⣴⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⣿⣿⣿⣿⡏⠉⠉⠻⢷⡄⠀⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡏⠀⢠⡆⣾⣿⣷⡄⣸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢿⣿⣿⣿⣿⣿⣶⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢿⣇⡀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⠿⠟⠋⣿⣿⣿⣿⣿⣿⡇
⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣭⣴⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠁⠀⠸⠋⠛⢩⣀⠀⠀⠈⠀⠀⣿⣷⠀⠐⠛⠻⠟⠋⣉⣾⣿⡗
⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣇⠀⣻⡄⠁⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠻⠿⢿⡿⠋⠀⠀⠀⠀⠾⠻⣿⣿⡇
⢸⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣤⣀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡆⠈⠉⠂⠀⠀⣀⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡇⠀⠀⠀⠀⠀⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣶⣤⣤⣤⣤⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⢻⣃⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⢠⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣡⣼⣽⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⡄⠀
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣰⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣣⣄⠀⠀⠀⢠⣾⣿⣿⠦⠤⢠⣄⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠈⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⡀⠀⠀⠀⠉⠛⠛⠻⣿⣿⡿⣧⡉⢻⣿⣦⣤⣤⣿⠋⠀⢠⣤⣴⣿⡇
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣿⣿⣿⣿⣿⠋⠉⠉⠻⢷⠄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠇⠀⠀⡄⣾⣿⣧⣤⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠻⣿⣿⣿⣿⣿⣿⣶⡄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⠟⠉⣽⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣧⡀⠠⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠁⠀⠙⠃⠙⢫⣀⠀⠀⠈⠀⠈⣿⣯⠀⠀⠛⠛⠛⠉⢉⣻⣿⡇
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣯⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠻⠿⢿⡿⠋⠀⠀⠀⠀⠾⠻⣿⣿⡇
⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣤⣀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠈⠉⠀⠀⠀⣀⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣇⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣷⣖⠀⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿⠏⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡤⠓⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣉⣭⣽⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠋⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄⠀
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣾⣷⣦⣤⣤⣤⣤⣤⣤⣤⠲⠀⠀⠀⠀⢀⡀⣀⠀⠈⠙⠁⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⣾⣿⣿⠿⠦⢤⣄⡀
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣀⠀⠀⠀⠈⠉⣛⠛⠻⣿⣿⡿⣧⡉⢻⣿⣦⣤⣴⣿⠋⠀⢀⣤⣶⣿⡇
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⢀⡹⠿⠆⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⡀⠀⠀⡄⣾⣿⣿⣶⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⡇
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⢀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⢉⣹⣿⣿⣿⣿⣿⡗
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣧⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠋⠀⠛⠉⠙⢫⣅⠁⠀⠉⠀⢸⣿⣇⠀⠛⠛⠻⣿⠟⢉⣻⣿⡗
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣿⣏⢸⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⡇⠀⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣇⠀⣭⡘⠁⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠘⠿⠿⣿⡟⠋⠀⠀⠀⠈⠿⠻⣿⣿⡇
⡿⠟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣆⠻⢿⣿⣿⣧⣄⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⠆⠈⠉⠀⠀⠀⣀⣀⡀⠀⠸⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢿⣿⣿⣿⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆⡀⣸⣿⣿⣿⡇⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡾⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡀⢀⠲⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⢉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡤⠓⣠⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⣉⣉⣻⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢀⣴⣦⣶⣤⣤⣤⣤⣤⣤⣴⡦⣤⡀⠀⠀⠀⡀⣀⠀⠈⠙⠁⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣄⠀⠀⠀⠀⣾⣿⣿⠿⠦⣤⣤⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⠀⠈⠉⠉⠉⣛⡛⠻⣿⣿⡿⣧⡉⢻⣿⣶⣤⣴⣿⠋⠀⠀⣤⣴⣿⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⢀⡙⠻⠿⠀⠀⠀⠀⠀⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡀⠀⠀⡤⣼⣿⣿⣦⢺⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢠⣦⡀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⢀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⢋⣹⣿⣿⣿⣿⣿⡿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣧⡀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⡿⠟⠁⠀⠙⠉⠙⣭⣤⠁⠀⠉⠀⣸⣿⣏⠀⠈⠛⠻⣿⣿⣎⣹⣿⡷
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⡄⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡇⢀⣥⡞⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠸⠿⠿⣿⡟⠋⠀⠀⠀⠉⠿⠻⣿⣿⡇
⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⢿⣿⣿⣧⣀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡀⠀⠁⠀⠀⠀⣀⣀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⣿⣿⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢸⣿⣿⣿⡇⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⡏⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣄⢀⠒⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢋⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⢀⡤⠓⣠⣤⡤⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣉⣉⣛⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡆⠀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⡲⠄⠀⠀⠀⢀⣀⡀⠀⠀⠉⠁⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣀⠀⠀⠀⠀⣾⣿⣿⠿⢦⣤⣄⡀
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⡀⠀⠉⠉⠉⠉⣙⡛⠻⣿⣿⡿⣧⠉⢻⣿⣦⣤⣴⡿⠋⠀⠀⣠⣴⣿⣧
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣀⡈⠻⣿⠇⠀⠀⠀⠀⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣇⡀⠀⠀⡴⣼⣿⣿⣦⢾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣴⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⣿⣄⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧⣄⡀⢠⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⣉⣩⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣷⡄⠘⣿⣿⡆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢿⡿⠟⠁⠀⠙⠁⠙⢭⣄⠀⠀⠉⠀⣸⣿⣏⠈⠉⠛⠻⣿⣿⣝⣹⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⣇⡈⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⡆⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣇⢠⣭⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠹⠿⠿⣿⡿⠛⠀⠀⠀⠘⠿⠻⣿⣿⡇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⠿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⢶⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⢻⣿⣿⣿⣿⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢰⣦⠀⠠⣿⣿⣿⣇⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⠀⠀⠀⠀⠀⠸⠿⡿⡾⠿⢿⣿⡿⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠿⠀⠙⣟⡆⠀⠀⠀⠀⠀⠀⢠⡇⠀⣹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣀⣀⣈⣽⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⡀⠀⠀⠀⠀⣾⣿⣿⠷⠦⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡉⠁⠀⠀⠈⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠁⠀⠀⣉⠛⠛⢿⣿⠿⣤⠉⢻⣷⣦⣤⣠⡿⠋⠀⠀⢀⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣀⣀⣀⠙⠟⠁⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⡄⠀⠀⠀⡤⣸⣿⣧⣄⢸⣿⣦⣿⣷⣼⣿⣟⢿⣿⣇⠀⣠⣤⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⢀⣶⣄⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⠆⣿⣇⡀⠀⢀⣽⣿⣿⣿⣾⡿⢹⣿⡿⢿⣿⣿⠿⠟⠉⢀⣽⣿⠿⢻⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠸⣿⣿⣿⣿⣿⣿⣿⣯⢠⣿⣿⣿⣿⠄⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡼⠡⡼⢿⠿⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⢘⣿⡇⠀⠀⠈⠹⣿⡇⠀⠈⢿⡇
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣏⠈⢿⣿⣿⣿⠄⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣇⢠⣁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⣿⡟⠃⠀⠀⠀⠈⠱⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⡀⢙⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠻⢿⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣏⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡄⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠈⠉⠉⠋⠛⠃⠘⠛⠻⠷⠿⠾⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣼⣿⣿⢸⡏⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣴⡖⣶⣦⣶⣠⣄⣬⣤⣤⣼⣿⣿⣿⣿⣛⣿⠉⠉⠉⠉⠛⠛⠛⠛⠓⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⣿⣿⡽⣿⡶⣿⣿⣿⣼⣧⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣶⢲⡶⣶⢶⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠛⠛⣿⠟⠛⠛⠻⠋⠿⠟⠿⠿⢼⡇⣿⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⣷⣴⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢀⣠⣄⣩⣽⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⡀⠀⠀⠀⠀⣾⣿⣿⠷⠦⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠉⠁⠀⠀⠈⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣉⠛⠛⢿⣿⠿⣤⠉⠻⣷⣤⣤⣠⡿⠋⠀⠀⢀⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣀⣀⣀⠙⡟⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⠀⠀⠀⠀⡤⣸⣿⣧⣄⢸⣿⣦⣿⣷⣼⣿⣟⢿⣿⣇⠀⣠⣤⣸⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠉⢠⣷⣄⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⠇⢿⣄⡀⠀⢀⣿⣿⣿⣿⣾⡟⢹⣿⡿⣿⣿⣿⠿⠏⠉⢀⣼⣿⠿⢛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣯⡾⢡⡬⠾⠿⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⢘⣿⡇⠀⠀⠈⠸⣿⡟⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣇⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⣿⡟⠂⠀⠀⠀⠈⠠⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⡈⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠻⢿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣏⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠈⠉⠉⠋⠛⠃⠘⠛⠻⡷⠿⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣼⣿⣿⢸⡇⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣾⣿⣿⣿⣿⣶⣴⡖⣶⣦⣶⣠⣄⣬⣤⣤⣴⣿⣿⣿⣿⣛⣛⠉⠉⠉⠉⠛⠛⠛⠛⠓⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⡿⢿⡽⣿⡶⣿⣿⣿⣼⣧⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣶⢲⡶⣶⢶⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠛⠛⢿⠟⠛⠛⠻⠋⠿⠟⠿⠿⢼⡇⣿⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠔⠰⠶⠶⠿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⡄⠀⡀⣤⣤⣄⣤⠄⠰⠤⠄⣀⣀⣀⠀⠀⡠⢀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣶⣶⣿⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣂⣸⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿
⣿⣿⣿⡟⠋⢰⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀
⣿⣿⣿⠀⢀⣤⣌⠀⠀⢺⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀
⢹⣿⡏⠀⠀⢁⢹⣤⣤⣾⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡏⣼⣿⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡀⠀⠘⢿⣿⣿⠀⠀⠀
⢸⣿⠁⠀⣶⣶⣾⣿⣿⣿⣿⣿⣶⠀⣼⣿⣿⣿⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⡟⢀⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢸⣷⣴⡷⢸⣿⣿⡆⠀⠀
⣾⡇⠀⠀⠈⢿⣿⣿⣿⣿⠟⠛⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣮⠅⠀⠀⠀⠀⢹⠀⠀⠀
⠈⠀⠀⠀⢀⣼⣿⣿⡿⠀⠀⢀⣠⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣤⣤⣤⣴⡾⠟⠁⠀⠀⢴⣿⡿⡟⠀⠀⠀⠀⠀⣿⠇⠀⠀
⠀⠀⠀⠀⣾⠋⠉⠁⠀⠀⠀⠈⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⢀⣲⣶⣾⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⣿⠀⠀⠀
⣘⣧⣄⡀⠀⠀⣤⣤⣀⣀⣀⣀⢀⡀⠘⠻⠛⠻⠿⠟⠋⣽⣿⣿⡷⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣴⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠉⠀⠀⠀
⣿⣿⡿⠁⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣿⣿⣿⣿⣷⣶⣶⣼⣧⣦⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⠀⠀⢀⡀⠈⠁⠉⠛⠛⠃⠛⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡿⣿⣫⣿⡏⢹⣿⣿⡷⣾⣿⣿⣸⣇⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢉⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⢀⣀⣉⡁⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⡰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣼⣧⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⢿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠼⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⠏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⡄⠀⣀⣤⣤⣄⣤⡄⠰⠤⠄⣀⣀⣀⠀⣀⣠⣦⣤⣦⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣿⣿⠀⠀⠀⠰⣶⣶⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿
⣿⣿⣿⡿⠉⠀⢾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠁⠀⠀
⣿⣿⣿⡇⠀⣠⣬⠁⠸⠻⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢾⠏⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀
⣿⢹⣿⠇⠀⠈⣴⣷⣦⣾⣿⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡀⠀⠘⢻⣿⣿⠀⠀⠀
⠏⣼⡏⠀⠰⣶⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⣿⣿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⡟⢀⣿⡏⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢸⣷⣴⡗⢸⣿⣿⡆⠀⠀
⣸⡿⠁⠀⠀⠙⣿⣿⣿⡿⠿⠛⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⠍⠀⠀⠀⠀⢹⡀⠀⠀
⠛⠁⠀⠀⠀⣰⣿⣿⡿⠀⠀⢀⣠⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⣤⣤⣤⣴⡾⠟⠁⠀⠀⢰⣿⡿⡟⠀⠀⠀⠀⠀⣿⠄⠀⠀
⠀⠀⠀⠀⣼⠋⠉⠀⠀⠀⠀⠈⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⢀⣢⣶⣶⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⣿⠀⠀⠀
⢸⣷⣄⡀⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠈⠻⠛⠻⠿⠟⠋⣹⣿⣿⡷⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠈⠀⠀⠀
⣿⣿⡿⠁⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢹⣟⣶⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⢾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⠀⠀⢀⡀⠈⠁⠉⠛⠛⠃⠛⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡿⣿⣫⣿⡏⢹⣿⣿⡷⣾⣿⣿⣹⣇⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢩⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⢀⣀⣉⡁⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⡰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣧⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⢿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠸⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣦⡄⠀⣤⣴⣤⣤⣤⣀⠂⠤⢄⣀⡀⢂⢂⣂⣠⣦⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣿⣷⣿⣿⠀⠀⢀⡶⣴⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⣿⣿⣿⣷⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿
⣿⣿⣿⠟⠋⠁⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠁⠀⠀
⢽⣿⣿⠀⠀⢀⢰⣿⣿⣿⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀
⢹⣿⣧⠀⠀⠸⣾⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡀⠀⠸⢿⣿⣿⠀⠀⠀
⣼⣿⡯⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⡀⣼⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⡏⠀⣿⡏⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⣴⡷⢸⣿⣿⡆⠀⠀
⣿⣿⣇⠀⠀⠀⠺⣿⣿⡿⠟⠛⠛⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⠍⠀⠀⠀⠀⢹⡀⠀⠀
⣿⣿⣿⡧⠀⠀⢰⣿⠏⠀⠀⢀⣠⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣤⣾⠿⠋⠀⠀⢰⣿⡿⡟⠀⠀⠀⠀⠀⣿⡅⠀⠀
⢹⣿⣤⡀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠟⠀⢀⣤⣤⣤⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⣿⠀⠀⠀
⢾⣿⣿⡷⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠈⠻⠛⠻⠿⠟⠋⣵⣿⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⣠⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠉⠀⠀⠀
⣿⣿⡿⠁⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣿⣿⣿⣿⣷⣶⣶⣾⣿⣶⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⢸⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠏⠀⠀⢀⡀⠈⠉⠉⠛⠛⠃⠚⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡿⣿⣫⣿⡟⢻⣿⣿⡷⣾⣿⣿⣹⣇⣻⡟⠀⠀⠀⠀⠀⠸⠃⠀⠀⠈⢿⡇⠈⢉⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⢀⣀⣉⡁⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣼⣧⣿⣺⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⢿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠼⠾⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠏⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣦⡄⠀⣠⣴⣤⣤⣤⣀⡀⠤⢄⣀⣀⣀⣀⣀⣀⣤⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣿⣷⣿⣿⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿
⣿⣿⡏⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠁⠀⠀
⣿⣿⣀⠾⠃⠀⠀⣿⣿⣿⣿⣿⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⣴⡿⠉⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀
⣿⡟⠉⠁⠀⠀⠀⣹⣿⣿⣿⡿⠂⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⣼⣿⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡀⠀⠸⣿⣿⣿⡀⠀⠀
⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀⣸⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢙⡇⠀⣿⡏⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⣴⡷⢸⣿⣿⡆⠀⠀
⣿⡟⠀⠀⠀⠀⠀⣻⣿⣿⣿⠟⠛⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⠍⠀⠀⠀⠀⢹⡀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⣽⣿⣿⠈⣀⢠⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⡅⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣀⣀⣤⣶⠟⠋⠀⠀⠰⣿⠿⡟⠀⠀⠀⠀⠀⣿⡄⠀⠀
⢺⣧⣀⣠⡦⠀⠀⠈⠉⠈⠀⠉⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠿⣿⣿⠟⠀⢀⣤⣤⣤⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣿⠁⠀⠀
⣿⣿⣿⣿⠃⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠻⠛⠻⠿⠟⠋⣵⣿⣿⡧⠀⢀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠉⠀⠀⠀
⣿⣿⡿⠁⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣿⣿⣿⣿⣷⣶⣶⣼⣿⣶⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⠀⠀⢀⡀⠈⠉⠉⠛⠛⠃⠚⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡿⣿⣫⣿⡏⢹⣿⣿⡷⣾⣿⣿⣹⣇⣻⡟⠀⠀⠀⠀⢿⡄⠀⠀⠀⠈⢻⣅⠙⢉⣹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⢀⣀⣉⡁⠈⠉⠉⠙⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡟⠁⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣧⣿⣺⣿⡇⠘⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⢿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠼⠾⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠏⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣶⣶⣾⠀⠀⠀⠰⣶⣶⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⣿⣿⣿⣇⣀⢀⣴⣥⠼⡥⠔⢐⠉⠨⠀⢁⠨⠡⣒⣷⣻⣶⣰⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣷⣥⣤⣦⣴⣿⣷⣿⣿⣛⣫⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿
⣿⣿⣿⠇⢀⡈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀
⢿⣿⣿⣴⠟⠁⠀⢈⣿⣿⣿⣿⠟⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢺⠿⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀
⢸⣿⡏⠁⠀⠀⠀⢨⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠻⡏⣸⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡀⠀⢸⣿⣿⣿⡀⠀⠀
⢸⣿⣿⠆⠀⢠⠀⢸⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠉⠇⠀⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⣴⡯⢸⣿⣿⡅⠀⠀
⠸⠋⠉⠀⠀⠸⠀⠀⢻⣿⣿⠟⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⠀⠀⢀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣇⣤⠀⠀⠀⠀⠀⢹⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⢠⡌⢻⣿⠀⢀⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣰⣶⣶⣤⣴⡾⠛⠁⠀⠀⠠⣿⠿⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⣀⡸⠀⠀⠈⠁⠀⠉⠁⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠙⠿⠟⠁⠀⣀⣖⣶⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⢀⣠⣼⣿⠃⠀⣤⣤⣀⣀⣀⣀⢀⡀⠀⠻⠿⠻⠿⠿⠋⣽⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠈⠀⠀⠀
⣿⣿⡿⠁⠀⠀⢸⡇⣿⣿⣿⠇⣸⣿⣿⣿⣿⢹⣟⣶⣿⣿⣿⣿⣷⣶⣶⣤⣴⣶⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠀⠀⢀⡀⠈⠁⠉⠛⠛⠃⠛⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡟⣿⣫⣿⡇⢸⣿⣿⡷⣾⣿⣿⣼⣇⣻⡟⠀⠀⠘⣿⡀⠀⠀⠀⠀⠘⡷⣰⠋⣩⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠏⠀⣼⢀⣾⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣰⣤⣤⣤⣤⣤⣄⡀⣀⣀⣉⡁⠈⠉⠉⠙⠛⣿⣿⣿⣿⡿⠇⠀⠀⠀⠹⠇⠀⠀⠀⠀⠰⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⡞⣾⣿⣿⣿⣿⣿⣿⠿⠿⣿⡽⣿⡶⣿⣿⣿⣼⣷⣿⣾⣿⡇⠙⣿⣿⣷⣿⣿⣿⣷⣿⣾⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⢿⣿⡿⢿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⢾⣿⣿⣿⣿⣿⡿⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⠋⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⡄⠀⠀⢀⢀⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣶⣶⣾⠀⠀⠀⣴⣴⣾⣷⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⣿⣿⣿⣇⡠⢀⣴⠦⣬⣤⣅⣉⠍⡂⠀⠃⠄⡆⢂⣑⣶⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣦⣧⣶⣶⣷⣿⣿⣿⣿⡛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿
⣿⣿⣿⠁⢀⡈⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀
⢿⣿⣧⣼⠟⠁⠀⢸⣿⣿⣿⣿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⢶⡿⠁⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀
⢸⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠻⡏⣸⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡀⠀⢸⣿⣿⣿⡀⠀⠀
⢺⣿⣿⠀⠀⢰⠀⢸⣿⣿⣿⣷⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠉⠃⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⣴⡿⢹⣿⣿⡇⠀⠀
⠹⠋⠁⠀⠀⢸⠀⠈⢻⣿⣿⠟⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠻⣿⠀⠀⢠⠀⢸⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣏⣬⠀⠀⠀⠀⠀⢻⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡌⣿⣿⠀⢀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣄⣤⣤⣤⣴⡾⠛⠁⠀⠀⠠⣿⡿⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠉⠁⠈⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠁⠀⠻⠿⠿⠃⠀⣠⠀⣤⣶⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⢀⣠⣼⡗⠀⠀⣤⣤⣀⣀⣀⣀⢀⡀⠀⠀⠈⠛⠋⠙⢿⣿⣿⣿⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⡆⠈⠀⠀⠀
⣿⣿⡿⠁⠀⠀⢸⡇⣿⣿⣿⠏⢸⣿⣿⣿⣿⢹⣟⣶⣿⣿⣿⣿⣷⣶⣶⣴⣷⣶⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⣰⠀⢀⡀⠈⠁⠉⠛⠛⠃⠚⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡟⣿⣫⣿⡇⢸⣿⣿⡷⣾⣿⣿⣼⣇⣻⡟⠀⠀⠘⣿⡄⠀⠀⠀⠀⠈⢿⡠⠈⢨⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⢠⣿⢠⣾⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣰⣤⣤⣤⣤⣤⣄⡀⣀⣀⣉⡁⠉⠉⠉⠙⠛⣿⣿⣿⣿⡿⠇⠀⠀⠀⠹⠷⠀⠀⠀⠀⠰⠃⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠏⣿⣟⣻⠿⢉⣿⠁⠿⠿⣿⡽⣿⡶⣿⣿⣿⣼⣷⣿⣾⣿⡇⠙⣿⣿⣷⣿⣿⣿⣷⣿⣾⣿⣿⣿⣷⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⣿⣿⣷⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⢿⣿⡿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⢾⣿⣿⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⡄⠀⠀⣀⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⢐⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣷⣷⣶⣾⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⣿⣿⣿⣧⣠⣥⣿⣦⣧⣥⣥⣦⣽⡆⢀⢶⡶⢵⣿⣳⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣬⣾⣿⣿⣿⣿⣿⣟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿
⣻⣿⡿⠁⢀⡉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀
⢻⣿⣧⣾⠟⠁⠀⢿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⣶⡟⠁⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀
⢸⣿⡏⠁⠀⠀⠀⢸⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠻⡏⣼⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡀⠀⢸⣿⣿⣿⡀⠀⠀
⣾⣿⣿⠀⠐⢰⠀⣾⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠉⡇⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⣴⡿⢹⡿⣿⡇⠀⠀
⢹⠋⠁⠀⠀⠳⠀⠉⣿⣿⣿⠛⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠛⣿⠀⠀⢠⠀⢸⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⣤⠁⠀⠀⠀⠀⢿⡆⠀⠀
⠀⠀⠀⠀⢀⠀⠀⣠⡙⣿⣇⠀⢀⣀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣀⣤⣀⣠⣤⡾⠟⠁⠀⠀⠠⣿⣿⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠈⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠻⣿⡿⠟⠀⢀⠀⣠⣤⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⢀⣤⣼⡇⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠙⠻⠿⠻⣿⣿⣿⠂⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⡆⠈⠀⠀⠀
⣿⣿⡟⠁⠀⠀⢸⡇⣿⣿⣿⠏⢸⣿⣿⣿⣿⢹⣟⣶⣿⣿⣿⣿⣶⣶⣶⣼⣿⣦⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡏⠀⠀⢀⡀⠈⠉⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡟⣿⣫⣿⡏⢸⣿⣿⡷⣾⣿⣿⣽⣇⣻⡿⢀⠀⠘⣿⣆⠀⠀⠀⠀⠈⢿⣄⠈⢩⡽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣴⡶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⣀⣀⣉⡁⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⠿⠀⠀⠀⠀⠠⠏⠀⢀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣼⣷⣿⣾⣿⡇⠙⣿⣿⣷⣿⣿⣿⣷⣿⣾⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⣿⣿⡿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣾⠿⢷⠷⠼⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣴⣤⠀⣀⢠⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣤⣲⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣷⣷⣾⣾⠂⠀⠀⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶
⣿⣿⣿⣿⣠⣌⣿⣿⣿⣿⣿⣷⣿⡆⢰⣽⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⠉⢁⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⢿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⡿
⣻⣿⡿⠉⢈⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⡄⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀
⢻⣿⣧⣾⠟⠁⠀⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⡿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠐⣾⡿⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀
⢸⣿⡏⠁⠀⠀⠀⢸⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡏⣸⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⢸⣿⣿⣿⡇⠀⠀
⣾⣿⣿⠀⠠⣤⢠⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⡏⠀⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠸⣿⣴⣿⢽⣿⣿⡇⠀⠀
⠹⠏⠉⠀⠀⢹⠀⠹⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⠀⠀⢠⠀⢸⡿⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⠀⠀⠀⠀⠀⢺⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⡙⣿⣇⠀⢀⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣠⣤⣤⣤⣤⣾⠟⠁⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⣾⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⠁⠀⠻⣿⡿⠟⠀⢠⣠⣤⣶⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀
⣀⣠⣤⠀⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠁⠀⠠⣀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠀⠈⠀⠀⠀
⣽⣿⠇⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣿⣿⣿⣿⣶⣶⣶⣿⣿⣦⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠃⠀⠀⢀⡀⠈⠉⠉⠛⠛⠃⠚⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡟⣿⣻⣿⡏⢹⣿⣿⡷⣾⣿⣿⣽⣇⣿⡟⢠⣄⣀⢿⣿⡀⠀⠀⠀⠘⢿⣤⠊⢩⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⣀⣀⣉⡁⠈⠉⠉⠙⠛⣿⣿⣿⣿⣿⠇⠈⠀⠉⠈⢻⠇⠀⠀⠀⢠⠟⠁⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣼⣷⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠛⠛⠋⠻⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠼⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣴⣤⠀⣄⣠⣤⣴⣤⢤⠴⠄⠄⡀⠀⣀⡄⠠⣦⡤⢤⣤⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣷⣷⣾⣾⠂⠀⠀⣴⣶⣶⣾⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⣿⣿⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⡿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢉⣉⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⢿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿
⣻⣿⣿⠉⢉⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⡄⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀
⢻⣿⣧⣶⠟⠁⠀⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⡿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀
⢸⣿⡏⠉⠀⠀⠀⢸⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⣸⣿⠃⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⢀⡀⠀⢰⣿⣿⣿⡇⠀⠀
⢸⣿⣷⡀⠐⢶⢒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⡏⠀⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⣿⣶⣿⢿⡿⣿⡇⠀⠀
⠸⡏⠉⠀⠀⠸⠀⢙⣿⣿⣿⠛⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⠀⠀⢠⠀⢸⡿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣤⠈⠀⠀⠀⠀⢺⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡉⣿⣇⠀⡀⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⣰⣶⣶⣤⣴⡾⠟⠁⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⣼⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡏⠀⠀⠻⠿⠿⠏⠀⢠⣠⣴⣾⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀
⡀⣠⣤⠀⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠉⠑⠠⣀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠈⠀⠀⠀
⣹⣿⠃⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢹⣟⣶⣿⣿⣿⣿⣶⣶⣾⣿⣿⣶⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠁⠀⠀⢀⡀⠈⠉⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡟⣿⣫⣿⡟⢹⣿⣿⡷⣾⣿⣿⣽⣇⣿⡿⢠⡄⣠⣹⣿⡆⠀⠀⠀⠘⣿⣤⠂⣩⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⣀⣀⣉⡁⠉⠉⠉⠛⠛⣿⣿⣿⣿⣿⠇⠈⠉⠉⠀⢹⡇⠀⠀⠀⢰⠏⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣼⣷⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠼⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⢶⣶⣶⣶⢰⣶⠆⠀⠀⢠⢶⣴⣶⣿⣿⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣼⣿⣿⡿⢸⢸⡟⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯
⣿⣿⣿⣿⣷⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⢛⠻⢿⣿⣿⣿⡟⣿⣿⣿⠇⣾⢸⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⢀⣀⢀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡿⠿
⠛⡙⡿⠀⠀⠈⠉⢹⣿⣿⢷⣷⣾⣷⣦⣶⣿⡿⠀⠀⢀⣴⣿⣷⣿⣶⣔⠀⠠⣿⣿⢷⣷⣿⡟⢠⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣼⣿⣿⣿⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀
⠘⠛⠃⣠⡖⠀⠀⢸⣿⣿⢾⣿⠏⠁⠈⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠸⡿⣿⠃⣾⡿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀
⠀⡴⠃⠉⠀⠀⠀⠀⣿⣿⣾⣿⠀⠀⣸⣿⣿⣷⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠛⢠⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣷⣶⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⣷⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠁⠉⠀⢸⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠩⠄⠼⠁⠟⠻⡇⠀⠀
⠀⠘⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⢙⠁⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣠⣾⣿⣿⣿⣷⣄⢀⣀⣀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⠁⠠⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠻⡿⠋⠈⣿⣿⣿⣿⡿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡀⠀⠙⠿⠿⠋⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠈⠙⠛⢛⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠈⠁⠀⠀
⠟⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢱⣟⣲⣶⢶⣿⣷⣷⣶⣦⣤⡄⢠⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠈⠁⠉⠋⠛⠃⠘⠛⠛⠷⠿⠾⠷⠻⢿⣿⢿⣿⡿⣿⣫⣿⡆⢸⣿⣿⡷⣼⣿⣿⣸⣇⣻⡟⠀⡄⣀⡀⠀⠙⠃⠀⠀⠈⢿⣿⠿⢉⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣴⡖⣶⣦⣶⣠⣄⣤⣤⣤⣤⣄⡀⢀⣀⣉⡀⠈⠉⠉⠙⠛⢻⣿⣿⣿⣿⠇⠀⠀⠉⠀⠑⠄⠀⠀⠀⠀⠉⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠻⠀⠿⠀⠿⠿⢿⡽⣿⡶⣿⣿⣿⣸⣇⣿⢺⣿⡇⠈⣿⣿⣇⣿⣿⣿⡷⣿⣾⣿⣿⣿⣿⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠋⢿⣿⡿⢿⣿⣿⣿⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⠶⣬⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣶⣶⢲⣶⣶⣶⢰⣶⠆⠀⠀⢠⣖⣶⣶⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣩⣶⣵⣿⣼⣷⣿⣿⢸⢸⡟⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯
⣿⣿⣿⣿⢷⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣿⡟⣿⣿⣿⠇⣼⢸⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣀⢀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⠿
⠋⠙⠿⠀⠀⠀⠉⢹⣼⣷⢴⣶⣦⣶⣦⣴⣾⡿⠃⠀⠀⣤⣾⣿⣾⣶⣄⠀⠀⢸⣿⢷⣇⣿⡏⢠⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⣽⣿⣿⣿⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀
⠘⠛⠀⢀⡖⠁⠀⢸⣿⣿⢓⣿⠋⠁⠀⣹⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⡿⠸⡻⣽⠃⣼⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢨⣿⠇⠀⠀
⠀⢰⠂⠈⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢰⣿⣿⣶⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠛⢠⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣷⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⡷⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠁⠉⠀⢸⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣽⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠩⠄⠰⠅⠟⠻⡇⠀⠀
⠀⠘⠀⠀⠀⠀⠀⠀⠘⣿⣿⡉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⢈⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣷⣄⡀⣀⣀⡀⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢻⡿⠋⠈⣿⣿⣿⣿⣿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⠀⠘⢿⠿⠟⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠈⠛⠿⠻⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠄⠀⠁⠀⠀
⡾⠁⠀⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢱⣟⣲⢶⣶⣿⣷⣷⣶⣦⣤⡄⢠⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠈⠁⠉⠋⠛⠃⠘⠛⠛⠷⠿⠾⠷⠻⢿⣿⢿⣿⡿⣿⣫⣿⡆⢸⣿⣿⡷⣼⣿⣿⣸⣇⣻⡟⠀⡄⢀⣀⡀⠀⠁⠀⠀⠈⣿⣿⡿⢋⣽⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣴⡖⣶⣦⣶⣠⣄⣤⣤⣤⣤⣄⡀⢀⣀⣉⡀⠈⠉⠉⠙⠛⢻⣿⣿⣿⣿⠃⠀⠀⠈⠙⠁⠀⠀⠀⠀⢰⡿⠋⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠻⠀⠿⠀⠿⠿⢿⡽⣿⡶⣿⣿⣿⢸⣇⣿⢺⣿⡇⠈⣿⣿⡇⡿⣿⣿⡷⣿⣾⣿⣿⣿⣿⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠋⠛⠃⠻⠋⢿⣿⡿⠿⣿⣿⣿⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢳⠂⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⢲⣶⣶⣶⢰⣶⡆⠀⠀⢠⠖⣆⣤⣤⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣰⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⢹⣷⣿⣿⢹⢸⡟⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⣿⣿⣿⣿⠷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⣀⠀⠀⠉⠛⠿⢿⣿⡟⣿⣿⣿⡇⣸⠸⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⡁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠿
⠉⠉⠻⠁⠀⠀⠈⢹⣴⣷⡀⣤⣄⣤⣤⣀⣴⣿⡿⠉⠀⣠⣶⣿⣷⣿⣦⡄⠀⠐⣾⠇⣧⢻⡏⢀⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢀⡒⣸⣿⡟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀
⠀⠉⠁⢀⡄⠀⠀⠘⣿⣿⢃⣽⠋⠁⠀⢨⣿⣿⣷⣆⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⠀⡍⢸⠇⣸⣿⠁⠀⢠⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣄⣤⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀
⠀⠠⠂⠀⠀⠀⠀⠀⣻⣿⣿⡿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢛⢀⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⡿⣾⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⢠⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⠉⠀⢸⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⡆⠠⠁⠛⠙⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠁⠀⠀⠀⠀⡾⠁⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⣿⣿⣿⣷⣀⠀⢀⣀⠀⠀⠀⠘⠁⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⢀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁⠈⣿⣿⣿⣿⣿⡟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠸⣿⣿⡿⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⡄⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄⠀⠁⠀⠀
⡶⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢱⣟⢲⠶⢴⣶⣿⣿⣶⣦⣤⡄⢠⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠈⠁⠉⠋⠛⠃⠙⠛⠛⠷⠿⠾⠷⠻⠿⣿⢿⢿⡿⣿⣫⣿⡆⢸⣿⣿⡷⣼⣿⣾⣸⣇⣻⣟⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢏⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣴⡖⣶⣦⣴⣠⣄⢤⣤⣤⣤⣄⡀⢀⣀⣉⡀⠈⠉⠉⠙⠛⠻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢁⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠻⠀⠿⠀⠿⠿⢿⡵⣿⡶⣿⣿⣿⢸⣇⣿⢺⣿⡇⠈⣿⣿⡇⡿⣷⣿⡷⣿⣾⣿⣿⣿⣿⣦⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁⠀⠋⠛⠃⠻⠋⠿⣿⡿⠿⣿⣿⣿⢋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⢃⠆⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣶⣶⣶⣾⡶⢰⣶⡆⠀⠀⣠⣶⣦⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⢰⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣻⣿⣿⣿⢡⣾⡿⠀⠀⠀⠛⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣾⣿⣿⣿⠿⢷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⣀⡀⠈⠛⠻⢿⣿⡿⣿⣿⣿⡏⣸⡛⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡾⠿
⠛⡉⠻⠇⠀⠀⠀⢸⣦⣷⡄⣤⣤⣤⢀⢀⣠⣶⣿⠟⠀⠀⣠⣴⣿⣷⣿⣦⣄⠠⣿⡇⣷⢹⡟⠀⣿⡅⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⣰⡃⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀
⡆⠛⠁⠀⡴⠀⠀⠈⣿⣿⢃⣉⠛⠁⠀⠈⣻⣿⡿⣦⡀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣿⠑⡋⢸⡇⢸⣿⠁⢴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀
⠀⠀⠆⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⢛⢀⣿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⣾⣾⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⢠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠁⠉⠀⢸⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠙⣦⠠⠇⠘⠙⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⢿⣿⣿⣿⣿⠏⢿⣿⣿⣿⣿⣿⣿⡿⠀⣠⣿⣿⣿⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠓⠀⠀⣀⣤⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣟⣄⠈⣿⣿⣿⣿⣿⠟⢱⣾⣿⣿⣿⣿⣿⣿⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀
⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠋⠀⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⡇⠀⠀
⠀⢀⣾⡇⠀⠀⣤⣤⣀⣀⣀⣀⢀⣸⡟⠀⠀⠀⠀⠀⠙⠿⢿⣿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠀⢠⣤⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⠀⠁⠀⠀
⡴⢣⣿⠃⢸⣅⢸⡇⣿⣿⣿⠏⣾⣿⣿⣿⣿⢱⣟⢲⠶⢴⣶⣴⣷⣾⣦⣤⡄⢠⣤⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡏⠀⣾⣉⢙⣉⠉⠟⢻⣿⣿⠟⠛⠷⠿⠾⠷⠻⠿⢿⢿⣿⡿⣿⣫⣿⡆⢸⣿⣿⡷⣼⣿⣾⣼⣇⣻⣟⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠏⣩⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠁⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣶⣦⣶⣠⣄⣤⣤⣤⣤⣄⡀⢀⣀⣉⡀⠈⠉⠉⠙⠛⠻⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠻⢿⠁⢿⣿⣿⣿⣿⡽⣿⡶⣿⣿⣿⣸⣇⣿⢺⣿⡇⠈⣿⣿⣇⡿⣷⣿⡷⣿⣶⣿⣿⣿⣿⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣹⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁⠀⠋⠛⠃⠻⠋⠿⢿⡿⠿⣽⣿⣿⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣾⢿⢿⠿⠼⣿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡄⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⡾⣶⣶⡗⠀⠀⢀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⣿⣿⣿⣿⣆⡀⢀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢐⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⠃⠀⠀⠈⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⣆⣀⡀⠀⠀⢠⡀⢀⣀⣴⣠⣽⣿⠉⠁⠈⠉⠉⠻⣿⣿⣿⣿⣿⣿⡟⣸⡟⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠿
⣿⣿⣿⣿⠀⣀⡄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣷⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡦⠀⠀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠀⠀
⣿⣿⣿⣷⡾⠏⠁⠀⢹⣿⡏⣹⣿⣿⠋⠙⢿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣋⣀⣀⣤⣄⡀⠘⣿⣿⣿⣿⣿⣿⣷⡄⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀
⣿⣿⣿⡟⡀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠈⣿⣿⣿⣷⣴⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣏⢻⢁⣿⡟⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⣼⣿⣿⣿⠀⠀
⣿⠿⢿⡿⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⡆⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⢸⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢿⣿⣶⡿⠿⠻⣿⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠋⠁⡀⠉⠀⠀⠀⠀⣿⠀⠀
⢿⠃⠀⠀⣠⠀⠀⠀⠈⠉⠙⠛⠓⠐⠛⠋⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⡿⠀⠀⠀⠏⠀⠀⠸⠿⣿⣿⣿⡿⢿⣤⣌⣿⣿⣿⣿⡟⠀⢀⣼⣿⣿⣿⣷⣄⣠⣴⠶⠊⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⣿⠀⠀
⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢸⣿⣿⣿⣿⣿⡏⠀⠐⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠛⠀⠀
⣿⣦⣾⣿⠇⠀⣤⣤⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢿⣿⡿⣿⡟⣡⣶⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀
⣿⠟⣿⣿⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢱⣟⣶⣶⢶⣶⠰⣾⣿⣿⣿⡟⣩⣦⣄⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢟⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠋⢠⣟⠈⠁⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠻⢿⢿⢿⢼⡿⣿⣿⣿⡇⢸⣿⣿⡷⣾⣿⣿⣼⣇⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⡭⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣰⣤⣤⣤⣤⣤⣄⡀⣈⣙⣟⡁⠉⠉⠉⠙⠛⠻⣿⣿⣿⣿⡟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣇⣿⣺⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⡾⣶⣶⡗⠀⠀⢠⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⣿⣿⣿⣿⣆⣀⣀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠂⠒⢖⣲⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⠃⠀⠀⢺⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⡀⠀⠀⢀⡀⢀⣀⣖⣄⣶⣿⡏⠁⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⡟⣸⡟⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡿⠿
⣼⣿⣿⣿⠁⣀⡤⠈⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠟⠁⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣷⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣴⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀
⣿⣿⣿⣿⡾⠟⠀⢀⢸⣿⡏⣽⣿⡟⠉⠙⢿⣿⣿⣿⣿⡧⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣏⣀⣠⣤⣀⡀⢹⣿⣿⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀
⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⣿⣿⡟⠁⠀⠀⠘⣿⣿⣿⣿⣶⣶⣀⣼⣿⣿⣿⣿⣿⣿⣿⣏⢻⢀⣿⡟⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⡀⠀⣼⣿⣿⣿⠀⠀
⣿⡟⠻⡿⠉⠀⠀⠈⠻⣿⣿⣿⣷⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠁⢸⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢾⣿⣶⡿⠿⠻⣿⠀⠀
⣿⡅⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠉⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⣿⠃⠀⣿⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⠋⠀⣀⠉⠀⠀⠀⠀⣿⠀⠀
⠻⠃⠀⠀⣠⠂⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⠃⠀⠀⡏⠀⠀⠹⠿⣿⣿⣿⡿⣡⣤⣬⣿⣿⣿⣿⡿⠁⢠⣾⣿⣿⣿⣷⣄⣤⣴⠶⠛⠁⠀⠀⠀⠀⠀⠇⠀⠄⠀⢀⡀⣿⠀⠀
⢀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢻⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠋⠀⠀
⣿⣷⣾⣿⡇⠀⣤⣤⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠻⢿⣿⡿⣿⠿⢃⣤⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀
⣿⠿⣿⣿⠁⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢱⣟⣶⣶⢶⣶⠰⣿⣿⣿⣿⣿⢿⣶⣤⣀⢀⣀⢀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡟⢀⣾⠈⠁⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠻⢿⣿⢿⢼⡿⣿⣿⣿⡇⢸⣿⣿⡿⣾⣿⣿⣾⣇⣿⣿⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠬⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣰⣄⣤⣤⣤⣤⣄⡀⣀⣙⣿⡃⠉⠉⠉⠙⠛⠻⣿⣿⣿⣿⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣇⣿⣺⣿⡇⠘⣿⣿⣷⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠶⠸⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡾⣶⣶⡗⠀⠀⣠⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⣿⣿⣿⣿⣄⣀⣀⣀⠀⠀⢂⠠⠄⠀⡀⠀⠀⠁⠀⠀⠔⣔⣢⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⠁⠀⠀⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣄⣄⡀⡀⢢⣄⡀⢀⣰⣤⣾⣿⣿⠉⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⡟⣸⡟⡏⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿
⣼⣿⣿⣿⠃⣀⡴⠉⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠃⠀⢤⣴⣿⣿⣾⣾⣿⣿⣿⣿⢁⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣄⠀⠀⣤⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀
⣿⣿⣿⣿⡿⠟⠁⢠⢸⣿⣏⣽⣿⡟⠉⠙⣿⣿⣿⣿⣿⣿⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣏⣠⣴⣦⣤⡈⢿⣿⣿⣿⣿⣿⣿⡀⠀⣹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀
⣿⣿⣿⡟⡀⠀⠀⢈⣿⣿⣿⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⣧⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣏⠻⢀⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⠛⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⡀⠀⣼⣿⣿⣿⠀⠀
⣿⡟⠻⠿⠉⠀⠀⢨⢿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⢸⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢿⣿⡾⠿⠿⠻⣿⠀⠀
⣿⡅⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠛⣷⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣿⠃⠀⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠉⠀⣄⡉⠀⠀⠀⠀⣿⠀⠀
⠻⠁⠀⠀⣠⠆⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⡏⠀⠀⠸⠿⣿⣿⣿⡟⣡⣶⣼⣿⣿⣿⣿⣿⠀⢠⣶⣿⣿⣿⣷⣤⣤⣴⠶⠋⠁⠀⠀⠀⠀⠀⠇⠀⠄⠀⢀⡀⣿⠀⠀
⢀⡀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡇⠹⣿⣿⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠀⠀
⣿⣷⣾⣿⡏⠀⣤⣤⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠙⢻⡿⠿⠿⠟⢣⣄⣸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀
⣿⡿⣿⣿⠃⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢹⣟⣶⣶⢶⣶⢰⣾⣿⣿⣿⡿⢻⣷⣤⣀⢀⣀⢀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⢺⡿⢀⣾⠈⠁⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠻⢿⣿⢿⢼⡇⣿⣿⣿⡇⢸⣿⣿⡿⣾⣿⣿⣾⣧⣿⣿⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠬⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⣼⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣰⣄⣤⣤⣤⣤⣄⡀⣈⣉⣿⡃⠉⠉⠉⠙⠛⠻⣿⣿⣿⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣇⣿⣺⣿⡇⠘⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⠀⠀⠀⠀⠀⢤⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡐⠀⠶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡶⣶⣷⡇⠀⠀⢠⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⣿⣿⣿⣿⣆⣰⢯⣡⡡⡀⣨⡀⢀⠀⣀⡀⡈⠀⠀⡮⢅⣠⠰⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠁⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣤⣼⣥⣬⣁⣤⡌⠀⣁⣂⣭⣿⣿⠟⠉⠀⠉⠉⠛⠿⣿⣿⣿⣿⡟⣸⡿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠟
⣿⣿⣿⣿⢃⣠⡾⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⠀⠠⣤⣾⣿⣿⣿⣿⣿⣿⣿⢁⣿⣷⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⠀⠠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⢣⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀
⣿⣿⣿⣿⡿⠟⠁⣠⣻⣿⢋⣿⣿⠉⠀⠉⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣧⣴⣿⣿⣶⣄⢹⣿⣿⣿⣿⣿⣿⣆⣀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠀
⣿⣿⣿⡏⡀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⣿⣿⣿⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⡹⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣠⡀⠀⣾⣿⣿⣿⠀⠀
⣿⡏⠉⠏⠀⠀⠀⢺⣿⣿⣿⣿⣷⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢿⣿⡾⠿⠻⠻⣿⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠃⠀⢻⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⠃⠀⣀⣼⣿⣧⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀
⠙⠁⠀⠀⣀⡎⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡇⠀⠀⠀⠛⠛⣿⣿⣿⠀⣶⣿⣿⣿⣿⣿⡿⢠⣾⣿⣿⣿⣿⣷⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⢠⡀⣿⠀⠀
⣴⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠹⣿⣿⣿⣿⣿⡀⠉⢿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠟⠀⠀
⣿⣷⣾⣿⣿⠀⣤⣤⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⠙⠻⠟⣡⣤⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀
⣿⡿⢿⣿⡇⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢹⣟⣶⣶⢶⣶⢰⣶⣾⣿⣽⣿⢿⣿⣤⣄⢀⣀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⢸⣿⢁⣴⠋⠁⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠻⢿⣿⢿⢼⡏⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⣿⣧⣿⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢴⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⣾⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣰⣤⣤⣤⣤⣤⣄⡀⣀⣁⣻⡟⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⡏⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣧⣿⣺⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠸⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡟⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡶⣶⣷⡇⠀⠀⢠⣾⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⣿⣿⣿⣿⡅⡠⠤⣈⡘⠏⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠂⣅⣹⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⢥⣺⣤⣄⣀⣔⣤⣐⣊⡀⣈⣶⣽⣿⡟⠁⠀⠀⠉⠛⠻⣿⣿⣿⣿⡏⣸⡿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠟
⣿⣿⣿⣿⠃⣉⡽⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⠟⠀⠠⢄⣾⣿⣿⣿⣿⣿⣿⣿⢁⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⠱⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀
⣿⣿⣿⣴⡾⠟⠁⣤⢿⣿⢋⣿⣿⠋⠀⠉⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣧⣴⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠀
⣿⣿⣿⡃⠀⠀⠀⢻⣿⣿⣾⣿⡃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣤⣤⡄⣠⣿⣿⣿⣿⣿⣿⣿⡹⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣠⡀⠀⣾⣿⣿⣿⠀⠀
⣿⠏⠉⠃⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⢻⣿⡿⠟⠛⠛⣿⠀⠀
⣿⡅⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠃⠀⠸⣿⣿⣿⣿⣿⡟⠀⢹⣿⣿⣿⣿⣿⠃⢀⣠⣾⣿⣷⡀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀
⠟⠀⠀⠀⣠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠇⠀⠀⠀⠙⠙⢿⣿⣿⠇⣴⣿⣿⣿⣿⣿⡿⣴⣿⣿⣿⣿⣿⣷⣶⣷⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡄⣿⠀⠀
⣠⡀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠙⣿⣿⣿⣿⣿⡌⠙⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠟⠀⠀
⣿⣶⣾⣿⣿⠀⣤⣤⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠉⠙⠛⠛⣡⣶⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀
⣿⡿⢿⣿⡇⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢹⣟⣶⣶⢶⣶⢰⣶⣾⣿⣿⣿⢿⣿⣤⣄⢀⣀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⢸⣿⢃⣴⠏⠁⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠻⢿⣿⢿⢼⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⢶⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠋⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣰⣤⣤⣤⣤⣤⣄⡀⣀⣈⣙⡟⠉⠉⠉⠛⠛⠻⣿⣿⣿⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣧⣿⣺⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠟⠿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠼⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡏⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣲⣶⣶⣶⣶⣶⣶⣶⣶⣾⡶⣶⣷⡇⠀⠀⢠⣶⣶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣷⣦⣴⣦⡀⠀⢀⠀⠀⡀⠀⣀⠀⠀⠁⢀⡀⣤⣽⣾⡇⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⡏⣸⡿⠇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠛
⣿⣿⣿⡿⠛⢛⣿⣿⣿⣯⢶⣿⣿⣶⣿⣿⣿⣾⣶⣶⣿⣿⣿⠟⠀⠀⠄⣰⣿⣿⣾⣿⣿⣿⣿⢁⣿⣷⠀⣀⣀⣠⣸⣿⣿⣿⣿⣿⣿⣷⡄⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠠⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀
⣿⣿⣏⣤⣾⠟⢡⣸⣿⣿⢉⣿⡿⠁⠀⠈⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⡇⠀⠀
⣿⣿⡿⠉⠀⠀⢸⣿⣿⣧⣿⣿⡁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣄⣠⡄⢀⣾⣿⣿⣿⣿⣿⣿⡹⢀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⡀⠀⣾⣿⣿⣿⠀⠀
⠋⠁⠻⠈⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠺⡿⠞⠟⠛⠙⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣿⣿⣿⣆⠀⠀⠀⣀⣠⠤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⠀⠀⠀⠀⠉⠉⣻⣿⣿⠟⢿⣿⣿⣿⡿⣳⣾⣿⣿⣿⣿⣿⣷⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀
⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠘⢿⣿⣿⠀⠙⢿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣿⠀⠀
⢀⣤⣾⣿⣿⠀⣤⣤⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⣠⣦⣸⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠷⠁⠀⠀
⣿⡿⢿⣿⡇⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢹⣟⣶⣶⢶⣶⢰⣾⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⢀⣼⣆⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⢏⡿⠟⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠁⢸⣿⢁⣰⡏⠁⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠿⢿⣿⢿⢼⡇⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⢶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠋⣾⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣰⣤⣤⣤⣤⣤⣄⡀⢀⣁⣙⣟⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣇⣿⣺⣿⡇⠘⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠟⠿⣿⣽⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠼⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠏⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣾⡶⣶⣷⡇⠀⠀⢠⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⣿⣿⣿⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠁⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣷⣦⣤⣤⡡⡀⠢⣐⣀⣀⣀⣀⠀⣀⠀⠀⣀⣤⣼⣿⡟⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⡏⣸⡯⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠟
⣿⣿⣿⠿⠋⢹⡿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣿⠟⠁⠀⣄⣰⣿⣿⣾⣿⣿⣿⣿⢁⣿⣷⠀⣀⣀⣤⣸⣿⣿⣿⣿⣿⣿⣶⡤⠴⣿⣿⣿⣿⡇⠠⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀
⣿⣿⣯⣤⣾⠟⢡⢸⣿⡏⢈⣿⡿⠁⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣟⠀⠀
⣿⣿⠟⠁⠀⠀⢾⣿⣿⣧⣿⣿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣄⣤⡀⢀⣿⣿⣿⣿⣿⣿⣿⡻⢀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⡀⠀⣼⣿⣿⣿⠀⠀
⠉⠀⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠘⠿⠚⠟⠙⠉⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⠃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⣿⣿⣿⣆⠀⠀⢀⣀⣠⡤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠇⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿⡿⣿⣿⣿⣿⡿⢱⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀
⠀⠀⢀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠘⢿⣿⠟⠀⠐⢿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣿⠀⠀
⣀⣴⣿⣿⣿⠀⣤⣤⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⣠⣦⡨⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠀⠀⠀
⣿⡿⢻⣿⡇⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣶⢶⣶⢰⣶⣿⣿⣿⣿⣿⣿⣤⣄⢀⣀⢚⠙⡓⠂⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⢋⡿⠟⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠁⢸⣿⢇⣰⡏⠁⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠿⢿⣿⢿⢼⡏⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⢒⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠋⣾⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⢀⣀⣙⣿⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠻⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣧⣿⣺⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠟⠿⣿⣽⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣶⠿⢷⠷⠼⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠏⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣦⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣶⣶⣶⣶⣶⣶⣶⣶⣾⡶⣶⣷⡇⠀⠀⣴⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⣿⣿⣿⣿⠀⠀⠕⠀⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠁⠀⠰⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣶⣴⣿⣤⣿⣖⣶⢆⡀⣀⠀⡀⡀⠠⢀⣀⣼⣴⣿⣿⠋⠀⠀⠉⠙⠻⣿⣿⣿⣿⡏⣸⡏⠏⠀⠀⠀⣼⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠟
⣿⣿⣿⠟⠉⣹⡿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠃⠀⢀⢠⣶⣶⣴⣿⣿⣿⣿⢁⣿⣷⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⣤⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠇⠄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀
⣿⣿⣥⣴⡿⠋⣤⢹⣿⡏⢩⣿⡿⠁⠀⠙⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠀
⣿⠿⠟⠁⠀⠀⣿⣿⣿⣇⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⡻⢀⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⡀⠀⣸⣿⣿⣿⠀⠀
⠉⠙⠄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣿⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠘⠿⠀⠋⠉⠉⣿⠀⠀
⠀⠀⠀⠀⠀⢀⡈⠿⢿⣿⣿⣇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⠃⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣰⣿⣿⣷⡄⠀⠀⢀⣀⣠⡴⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀
⠀⠀⣀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⠙⠻⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣿⠀⠀
⢠⣼⣿⣿⣿⠀⣤⣤⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⣠⣤⡸⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠀⠀⠀
⣿⡿⢫⣿⡇⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢹⣟⣶⣷⢶⣶⢰⣶⣿⣿⣿⣿⣿⣿⣦⣄⣀⣈⢉⠉⠀⠀⠀⠀⠀⠒⠒⠀⠉⠀⠀⠀⠀⢋⡽⠛⠿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠁⠸⣿⣇⣰⡏⠁⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠻⢿⣿⢿⢾⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢒⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⣀⣈⣹⡿⠋⠉⠉⠛⠛⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠻⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣧⣿⣺⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠟⠿⣿⣼⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢿⠷⠼⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣦⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⡶⣶⣷⡇⠀⠀⢠⣾⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢶⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣷⣶⣴⣦⣤⡂⣠⣔⣆⣤⢀⠀⢀⢀⡀⡀⠀⣤⣬⣿⡿⠉⠁⠈⠉⠙⠿⣿⣿⣿⣿⡏⣸⡏⠏⠀⠀⠀⢠⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠛
⣿⣿⣿⠟⠉⣹⡿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠃⠀⣀⢠⣶⣶⣶⣾⣿⣿⣿⢁⣿⣷⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠛⡆⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠀⠀
⣿⣿⣥⣴⡿⠏⢠⢹⣿⡏⢨⣿⡟⠁⠀⠙⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⠃⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⡟⠀⠀
⣿⠿⡏⠀⠀⠀⢿⣾⣿⣇⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣀⣀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡻⢀⣿⡏⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢠⡀⠀⢸⣿⣿⣿⠀⠀
⠉⠑⡇⠁⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⡀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠘⠟⠀⠀⠀⠀⢹⠀⠀
⠀⠀⠀⠀⠀⠀⡨⠿⣿⣿⣿⣇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⠀⢀⠀⣀⣤⡴⠂⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⡀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⡟⠀⠈⠙⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⢀⣾⣿⣿⣿⠀⣤⣤⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣿⡏⠀⠀⣴⣶⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀
⣿⡿⠋⣿⡇⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢹⣟⣶⣶⢶⣶⢰⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣠⣶⡶⠒⠀⠀⠀⠠⠤⠿⠀⠉⠀⠀⠀⢯⡟⠛⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠁⢰⣿⣇⣰⡏⠉⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠿⢿⣿⢿⢼⡏⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⣺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢘⣟⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣰⣤⣤⣤⣤⣤⣄⡀⣀⣉⣹⣟⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠓⠀⣿⣿⣿⣿⣿⠀⢿⣿⣿⣽⣿⡶⣿⣿⣿⣸⣧⣿⣺⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⡏⢠⣿⣿⣿⡇⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠟⠿⣿⣼⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣾⣿⣿⣿⣿⡿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣦⠄⠠⣴⡶⠴⣤⡤⡤⣤⣠⡀⠀⠀⠀⢀⠀⠀⣀⢀⣀⣰⣶⣴⣶⣶⣶⣶⣶⣶⣾⣶⣾⡾⣶⣷⡗⠀⠀⠀⣾⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣿⣿⣿⣿⡆⠨⣩⣿⣷⣓⣿⡿⣸⣻⡁⢠⢨⡎⣀⣵⣜⣳⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣧⣽⣾⣿⣿⡟⠁⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⡟⣸⡏⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⣀⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠁
⣿⣿⣿⡿⠛⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣇⣩⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀
⣿⣿⣯⣥⣶⠟⢉⠸⣿⣿⢿⣿⣿⠁⠀⠙⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⣿⣿⣿⡉⠁⠀⢼⣿⣿⣿⣼⣿⡏⠀⠀⠀⢸⣿⣿⣿⣬⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡹⢁⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠹⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠘⠀⠛⠃⠀⠀
⠛⢿⡟⠋⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠁⢸⣿⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⡇⣀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠘⠿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⠉⠉⢡⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⣀⣄⣤⠖⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠙⠛⠛⠛⠛⠂⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⣄⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⣿⡿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀
⢠⣼⣿⣿⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢉⣵⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀
⣿⠏⢸⡟⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣷⢶⣶⢹⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢿⡟⠻⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠸⠃⢠⡂⠈⠁⠉⠛⠛⠃⠘⠛⠻⠷⠿⠾⠷⠿⢿⣿⢿⣾⣿⣿⣿⣿⡇⢻⣿⣿⡿⣿⣿⣿⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠐⣫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⣙⣇⣉⡁⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣸⣧⣿⣺⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠿⠿⣿⣼⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠸⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⡯⠿⡏⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⠄⢠⣴⡤⡤⠀⣰⣤⡀⢀⠀⢀⠐⠀⢀⡠⡄⠀⣤⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⡾⣶⣷⡗⠀⠀⢲⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣿⣿⣿⣿⠇⠰⠿⣗⣿⣺⡾⣿⡪⣍⡁⣰⣯⣻⣆⡮⠿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣻⣿⣿⣿⣾⣾⣾⣿⣿⣿⣷⣿⣿⣷⣾⣭⣿⣿⣿⣿⣿⡿⠋⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡟⠏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠋
⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣠⣼⡿⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀
⣿⣿⣯⣥⣶⡿⢃⠸⣿⣿⣿⣿⣿⠏⠉⠉⣿⣿⣿⣯⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⣿⣿⣿⠋⠁⠀⣸⣶⣿⣿⣼⣿⡏⠀⠀⠀⣿⣿⣿⣾⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢁⣿⡏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠸⠀⠛⠃⠀⠀
⠻⢿⡾⠟⠀⠀⢼⣿⣿⣿⣿⣿⣧⣾⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠁⢸⣿⠁⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠸⠷⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⡎⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠇⠀⣠⣾⣿⣆⢀⠀⣀⣠⡤⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠂⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠘⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡑⣁⣴⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⠁⠀⢊⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀
⣀⣼⢤⡆⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣷⣌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠖⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀
⣿⠏⢸⠇⠀⠀⢸⡇⣿⣿⣿⠏⢸⣿⣿⣿⣿⢻⣟⣶⣷⢶⣶⣼⣿⣿⣿⣿⣿⣿⣷⣤⣄⢀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠁⠀⢿⡿⠛⡿⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠨⠀⢀⡀⠈⠉⠉⠛⠛⠃⠛⠛⠻⠷⠿⠾⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣾⣿⣿⣿⣯⣿⣿⠀⠀⠀⣤⢀⣀⠀⠀⠀⠀⠀⠟⠊⠀⢲⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣌⡙⣿⣁⣉⡁⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⡿⣿⡽⣿⡶⣿⣿⣿⣼⣧⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠿⠿⣿⣼⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠾⠶⣶⠿⢷⠷⠼⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⣶⡇⠹⠏⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⠄⢠⣴⣶⡶⣤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣾⣶⣷⡗⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣿⣿⣿⣿⠇⢰⣽⣿⣿⢛⣟⣿⡟⡾⠀⠰⣻⣷⡅⢗⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠁⠀⢀⣀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡟⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛
⣿⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀
⣿⣿⣯⣤⣶⡿⠃⢸⣿⣿⣿⣿⡿⠋⠁⢹⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⣿⣿⣿⠉⠁⠀⢸⣼⣿⣿⣼⣿⡇⠀⠀⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢁⣿⡟⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡤⠁⢼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠸⠀⠺⠃⠀⠀
⠻⣿⡿⠃⠀⠀⣽⣿⣿⣿⣿⣿⣧⣼⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠁⢸⣿⠁⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⠆⠀⠈⠉⠙⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⢷⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠈⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠘⣇⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⠀⣸⣿⣦⣴⣶⠆⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠂⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠐⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⠀⢰⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠁⢁⣤⣴⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀
⣀⣶⠀⠀⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣧⣌⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠁⠀⠀
⣿⠏⠀⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣷⢶⣶⣿⣿⣿⣿⣼⣿⣿⣷⣤⣄⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢿⣿⠿⠿⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠠⠀⢀⡀⠈⠉⠉⠛⠛⠃⠛⠛⠻⠷⠿⠾⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠰⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡘⣟⣁⣉⡁⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⣶⣿⣿⣿⣼⣧⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠛⠻⠟⠿⠿⠿⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠾⠶⣶⠿⢷⠷⠼⠾⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⣶⡦⢸⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⠀⠠⠰⠖⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣔⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣾⣶⣷⡗⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⠇⠨⠵⣭⡝⠳⠀⠀⠀⠀⠀⠀⡀⡐⢀⣀⠐⠲⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⣻⣿⣿⣿⣦⣶⣷⣾⣿⣶⣶⣶⣖⣖⣟⣣⣷⣿⣿⠃⠀⢀⣀⣀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡟⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢧⣄⣤⡀⠀⠀⠀⠀⠀⠀⣤⡄⠈⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠃
⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⢤⣾⣿⣿⣿⣿⣿⣦⣤⣴⡶⢶⣠⣿⠇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀
⣿⣟⣏⣴⣶⠟⠁⢻⣿⣿⣿⣿⡿⠋⢸⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠙⠋⠀⠈⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⣷⣿⠏⠉⠁⠀⢠⢸⣿⣿⣼⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢁⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⢿⣿⣿⣿⣦⠉⠙⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠸⠀⠘⠃⠀⠀
⢳⣿⠶⠀⠀⠀⣽⣿⣿⣿⣿⣿⢧⣴⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢹⠁⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⠇⠘⠷⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⡇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠄⢠⣾⠟⠉⠙⣿⣿⣧⣶⡦⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠧⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⠀⠀⠁⠀⠀⢠⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠋⣠⣤⣀⣀⣠⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀
⣀⣦⠀⠀⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⠿⢷⣦⣌⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣼⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠁⠀⠀
⣿⠏⠀⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣷⣶⣿⣿⣿⣶⣶⣿⣿⣿⣷⣤⣄⢀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⡿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢀⡀⠈⠉⠉⠛⠛⠃⠚⠛⠻⠷⠿⠾⠷⠿⣿⣿⣿⣿⣿⣿⣫⣿⡿⢻⣿⣿⡿⣾⣿⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣤⡛⣀⣀⣉⡁⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⣶⣿⣿⣿⣼⣧⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⢿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠛⠻⠛⠿⠿⠿⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠸⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⣶⠆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣴⠀⠠⡤⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣰⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣾⣶⣷⡗⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⠀⠀⠶⡭⡏⠁⡀⠀⠀⠀⠁⠀⠀⡀⠀⣀⠀⠀⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⣻⣿⣿⣿⣶⣾⣷⣾⣿⣷⣤⣳⣤⣀⣂⣴⣿⣿⡟⠁⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡟⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣤⣤⣄⠀⠀⠀⠀⠀⠀⣠⣄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠞⠃
⣿⣿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣷⠀⠀⠀⠀⠀⢹⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣷⣤⣴⣶⢶⢠⣼⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀
⡿⢟⣡⣴⣾⠟⠀⢿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠛⠋⠀⠀⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⣿⣿⠏⠉⠁⠀⢀⢸⣿⣿⣼⣿⡇⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢁⣿⡏⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠟⢻⣿⣿⣿⣯⠌⠉⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠸⠀⠘⠁⠀⠀
⢲⣿⠷⠂⠀⢀⣽⣿⣿⣿⣿⣿⣧⣴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢹⠁⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣾⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⠇⠘⡷⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⡇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⢿⠟⠉⠈⣿⣿⣷⣴⣶⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣀⣻⣿⠿⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⣠⣤⣆⣀⣠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀
⢀⣧⠀⠀⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⠛⢷⣦⣌⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠁⠀⠀
⣿⠟⠀⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣷⣾⣿⣿⣷⣶⣾⣿⣿⣿⣷⣤⣀⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣿⡿⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⢀⡀⠈⠁⠉⠛⠛⠃⠛⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⣿⣿⣫⣿⡿⢻⣿⣿⡷⣾⣿⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣼⡋⣀⣀⣉⡁⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⠿⠀⠿⠿⣿⡽⣿⡶⣿⣿⣿⣼⣧⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⢿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉⠁⠀⠛⠛⠛⠻⠛⠿⠿⠿⣿⣼⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣶⠿⢷⠷⠸⠶⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢄⣶⡆⠈⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣶⣶⣶⣶⣶⣶⣾⣶⣾⣾⣶⣷⡗⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠈⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢅⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⣿⣿⣿⣿⣦⣼⣦⣧⣶⣤⣤⡀⠀⠄⢀⣴⣶⡿⠀⠀⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡟⠏⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠁
⣿⣿⣿⡟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣷⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⣀⣼⠇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀
⠿⢛⣡⣴⡾⠃⠀⣿⣿⣿⣿⣻⠟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠻⠿⢿⣿⣷⡆⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⢸⣿⠋⠉⠀⠀⠀⣹⣿⣧⣹⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢁⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣟⣉⣹⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠘⠀⠘⠁⠀⠀
⢸⣿⠖⠀⠀⠀⢵⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢹⠁⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠻⠉⠹⣿⣆⠀⠀⠀⠀⠀⠀⣿⠇⠐⡦⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⡆⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣀⣿⣿⣷⣶⠦⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⣈⢚⣚⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠘⠋⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠅⠀⣱⣴⣷⣶⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀
⢀⣦⠀⠀⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⠀⢹⣷⣦⣌⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠁⠀⠀
⣿⡟⠀⠀⠀⠀⢸⡇⣿⣿⣿⠏⢸⣿⣿⣿⣿⢻⣟⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣷⣤⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢻⣿⠿⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⢀⡀⠈⠁⠉⠛⠛⠃⠛⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢻⣿⣿⡷⣾⣿⣿⣽⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠰⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⣀⣀⣉⡁⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠿⠀⢿⣀⡿⡿⣿⡽⣿⡶⣿⣿⣿⣼⣷⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣾⢿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠿⠿⣿⣼⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣾⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⣖⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣾⣶⣾⡾⣶⣷⡗⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣿⣿⣿⣤⣤⣷⣶⣦⣄⣀⣀⣀⡀⢀⣠⣶⡾⠀⠀⣤⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡏⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠀
⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣷⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⣠⣸⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠛⣛⣁⣴⡾⠃⠀⣿⣿⣿⣟⣿⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣷⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠘⣟⠁⠁⠀⠀⠀⣽⣿⣧⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⢁⣿⡏⠀⠀⠀⠀⠀⠀⠀⠿⣯⣉⣹⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠘⠀⠘⠀⠀⠀
⢰⣷⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠹⠁⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠁⢹⣿⣆⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⡇⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⠆⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⣀⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣢⣠⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀
⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠘⠟⠁⠀⠙⠻⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⣴⣿⣷⣾⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀
⠀⣁⠀⠀⠀⠀⣤⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⠀⠈⣶⣦⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠁⠀⠀
⣿⡟⠀⠀⠀⠀⢸⡇⣿⣿⣿⠇⢸⣿⣿⣿⣿⢻⣟⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⣤⣀⢀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢻⣿⠟⠿⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠏⠀⠀⠀⢀⣀⡉⠉⢉⣛⣛⣣⠛⠛⠻⠷⠿⠾⠷⢿⣿⣿⣿⣿⡟⣿⣿⣿⡟⢹⣿⣿⡷⣾⣿⣿⣽⣇⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠰⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣶⣴⣤⣤⣤⣤⣤⣄⡀⣀⣀⣉⡁⠉⠉⠉⠙⠛⠛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡽⣿⡶⣿⣿⣿⣼⣿⣿⣾⣿⡇⠙⣿⣿⣿⣿⣿⣿⣷⣿⣶⢿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠛⠛⠋⠻⠛⠿⠿⠿⣿⣼⣿⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⢾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1840

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✐ IRC_Proceedings:_Wednesday,_June_29,_2022⠀✐


Posted in IRC_Logs at 2:56 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-290622.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-290622.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-290622.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-290622.gmi
Over HTTP:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 QmR2ppvL2a31JDkFUcxPBoMqKn28t6gwV13CHCBjSrxXyv #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 Qmd9oJa3JZC2YAW3N9dFZ4ykLgdhFRCT8Y2KpstDWh1wwu (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmVxoydf7Cv6Hk57v6BQh6QiGVAAwzareiRFeXTisnM9aa social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 Qmah6v9P2oPGRQ3e9DPiG5PBbjjM1AJ7d8PqKKfoMPrBn5 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmPp5eGTNEzLm4umewBi3wRYJ2sESbC3WgheZgiwW1jAzP #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmQkPjyZ6mXLLdQ35nDELtFQZj8LyXajjaH8QthuobzfYH (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmTdqV3WHcZbmVf2gjwaq1SzM7jt6WWpMs6ehWYN7R3aPr #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmddbxFq3AYG39rsfUQP7HRN7W2CtNvQNkAPisnaZKTzWC (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmSGNyqayw9Kb8GtH2D4DicRMEG9NuJ9kQEJo4KgFc1NeH



                    ䷩ 𝚕𝚒𝚗𝚎 1967

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/30/ircnow-by-aaron-lin/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/30/ircnow-by-aaron-lin/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Published_10_Minutes_Ago:_IRCNow_by_Aaron_Lin⠀✐


Posted in Free/Libre_Software, FSF at 1:54 pm by Dr. Roy Schestowitz


Video_download_link


https://media.libreplanet.org/mgoblin_media/media_entries/2747/libreplanet2022-
workshop-IRCNow-Of-the-users-by-the-users-for-the-users.webm


Summary: This talk was uploaded moments_ago. “Of the users, by the users, for
the users…”


Licence: CC_BY_SA_4.0



                    ䷩ 𝚕𝚒𝚗𝚎 2001

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_01/07/2022:_Condres_OS_1.0_and_Microsoft_Losing_More_Share_in_Web
Servers⠀✐


Posted in News_Roundup at 6:55 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o New_Releases
          o Canonical/Ubuntu_Family
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o Productivity_Software/LibreOffice/Calligra
          o FSF
    * Leftovers
          o Entrapment_(Microsoft_GitHub)
          o Security
                # Privacy/Surveillance
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o ⚓ Linux Links ☛ Linux_Around_The_World:_Canada_–_LinuxLinks⠀⇛


                 Canada is a country in North America sharing a land
                 border with the United States in the south and in the
                 northwest. It borders the Atlantic Ocean in the east, the
                 Pacific Ocean in the west and the Arctic Ocean in the
                 North.


          o § Server⠀➾


                # ⚓ Netcraft ☛ June_2022_Web_Server_Survey [Ed: Microsoft is
                  down even further, as usual]⠀⇛


                       In the June 2022 survey we received responses from
                       1,146,976,964 sites across 273,010,403 unique
                       domains and 12,224,786 web-facing computers. This
                       reflects a loss of 8.75 million sites and 583,000
                       domains, but a gain of 155,000 computers.


                       Cloudflare experienced strong growth this month,
                       gaining 2.99 million sites and 85,000 domains,
                       representing a 4.64% growth in its number of sites.
                       Cloudflare experienced a significant outage on 21
                       June, impacting around half of the total requests
                       made to its network. The outage lasted around an
                       hour and a half and affected a significant number
                       of popular sites. 20.2% of the million most visited
                       sites rely on Cloudflare (up 1,400 sites since last
                       month).


                       The three largest vendors by the million most
                       visited sites metric—Apache, nginx, and
                       Cloudflare—all have similar market share, though
                       only Cloudflare gained market share this month.
                       Apache saw the largest loss, dropping 2,190 sites
                       (-0.96%), while nginx lost 280 sites (-0.13%).


                       LiteSpeed gained a significant number of sites with
                       an addition of 2.96 million (+5.89%), and gained
                       171,000 (+2.21%) domains – the second largest
                       increase this month. The number of web-facing
                       computers using LiteSpeed also showed strong
                       growth, increasing by 4,460 (+3.44%) to a total of
                       134,000.


                       nginx and Apache remain the two largest server
                       vendors, though both saw similar losses of 6.52
                       million (-1.84%) and 6.18 million (-2.33%) sites
                       this month. Despite this, nginx gained 795,000
                       (+1.06%) domains and saw continued growth in the
                       number of web-facing computers with 158,000
                       (+3.44%) computers. Conversely, Apache lost 1.07
                       million domains (-1.71%) and 25,700 (-0.74%) web-
                       facing computers.


                # ⚓ The Next Platform ☛ So,_You_Think_You_Can_Design_A_20
                  Exaflops_Supercomputer?⠀⇛


                       The US Department of Energy has a single 2 exaflops
                       system up and running – well, most of it anyway –
                       and that of course is the “Frontier” system at Oak
                       Ridge National Laboratory and two more slated for
                       delivery, and that is the “Aurora” system at
                       Argonne National Laboratory supposedly coming
                       sometime this year and the “El Capitan” system at
                       Lawrence Livermore National Laboratory, which is
                       due next year. It took a lot of money and sweat to
                       get these machines into the field – in Intel’s
                       case, the sweat to money ratio has been pretty high
                       given the four-year delay and massive architectural
                       changes involved the latest and final incarnation
                       of Aurora.


          o § Audiocasts/Shows⠀➾


                # ⚓ Jupiter Broadcasting ☛ Linux_Action_News_247⠀⇛


                       Fedora gets serious about its server editions, our
                       thoughts on Valve’s increased Steam Deck
                       production, and the surprising results of booting
                       Linux on the Apple M2 SoC.


                # ⚓ Video ☛ KaOS_2022.06_overview_|_KaOS_is_an_independent
                  distribution_focused_on_Qt_and_KDE._–_Invidious⠀⇛


                       In this video, I am going to show an overview of
                       KaOS 2022.06 and some of the applications pre-
                       installed.


                # ⚓ Video ☛ Thunderbird’s_huge_update_and_Google’s_new
                  antitrust_issues_–_Linux_and_open_source_news_–_Invidious⠀⇛


                # ⚓ Video ☛ Enterprise_Linux_Security_Episode_34_–_How_one
                  business_lost_Everything_–_Invidious⠀⇛


                       What would it be like to suffer a cyberattack
                       event, that literally closes down an entire
                       business? That’s exactly what happened to United
                       Structures of America, a steel manufacturing
                       company. In this episode, Jay and Joao discuss what
                       happened, and some of the lessons learned that
                       should cause other organizations to take a hard
                       look at how insecure their own systems are.


                # ⚓ Video ☛ Why_Do_I_Choose_Emacs_Over_Vim?_It_Looks_Better!_–
                  Invidious⠀⇛


                       I spent a couple of hours today playing with my
                       Doom Emacs config. In particular, I focused on some
                       font settings which I think help with aesthetics
                       and with readability. In fact, I think one of the
                       biggest reasons that I use Emacs over Vim is how
                       Emacs renders fonts.


                # ⚓ Video ☛ Biggest_Problem_With_Wayland_Desktop_Capture_–
                  Invidious⠀⇛


                       Wayland is continually imporving and one aspect of
                       that is with desktop capture but right now there’s
                       a pretty annoying design flaw with the way this
                       system functions but it can certainly be fixed


          o § Kernel Space⠀➾


                # ⚓ Gradual_Explorations_of_Filesystems,_Paging_and_L4Re_«_Paul
                  Boddie’s_Free_Software-related_blog⠀⇛


                       A surprising three years have passed since my last
                       article about my efforts to make a general-purpose
                       filesystem accessible to programs running in the L4
                       (or L4Re) Runtime Environment. Some of that delay
                       was due to a lack of enthusiasm about blogging for
                       various reasons, much more was due to having much
                       of my time occupied by full-time employment
                       involving other technologies (Python and Django
                       mostly, since you ask) that limited the amount of
                       time and energy that could be spent focusing on
                       finding my way around the intricacies of L4Re.
                       In fact, various other things I looked into in 2019
                       (or maybe 2018) also went somewhat unreported. I
                       looked into trying to port the “user mode” (UX)
                       variant of the Fiasco.OC microkernel to the MIPS
                       architecture used by the MIPS Creator CI20. This
                       would have allowed me to conveniently develop and
                       test L4Re programs in the GNU/Linux environment on
                       that hardware. I did gain some familiarity with the
                       internals of that software, together with the Linux
                       ptrace mechanism, making some progress but not
                       actually getting to a usable conclusion.
                       Recommendations to use QEMU instead led me to
                       investigate the situation with KVM on MIPS, simply
                       to try and get half-way reasonable performance:
                       emulation is otherwise rather slow.
                       You wouldn’t think that running KVM on anything
                       other than Intel/AMD or ARM architectures were
                       possible if you only read the summary on the KVM
                       project page or the Debian Wiki’s KVM page. In
                       fact, KVM is supported on multiple architectures
                       including MIPS, but the latest (and by now very old
                       3.18) “official” kernel for the CI20 turned out to
                       be too old to support what I needed. Or at least, I
                       tried to get it to work but even with all the
                       necessary configuration to support “trap and
                       emulate” on a CPU without virtualisation support,
                       it seemed to encounter instructions it did not
                       emulate. As the hot summer of 2019 (just like 2018)
                       wound down, I switched back to using my main
                       machine at the time: an ancient Pentium 4 system
                       that I didn’t want heating the apartment; one that
                       could run QEMU rather slowly, albeit faster than
                       the CI20, but which gave me access to Fiasco.OC-UX
                       once again.


          o § Applications⠀➾


                # ⚓ Linuxiac ☛ Vim_9.0_Released,_Introduces_the_New_Vim9
                  Scripting_Language⠀⇛


                       After two and a half years of development, Vim 9.0
                       is now available, firmly focused on the new Vim9
                       scripting language capabilities.


                       In its 30-year history, the terminal-based text
                       editor Vim has been one of the most recognizable
                       names in the open-source world, loved by some and
                       disliked by others. Using it has put Unix/Linux
                       users to the test more than once.


                       However, Vim sticks to its original path, as
                       evidenced by the recently released version 9.0.
                       With that said, let’s take a look at the highlights
                       of it.


                # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Software_–
                  Utilities⠀⇛


                       
                       Let’s kick off with a collection of detailed
                       reviews highlighting 31 essential utilities. They
                       are small, indispensable tools, useful for anyone
                       running a Linux machine. They cover a wide spectrum
                       of utilities.


                       The following articles focus on specific topics.


                # ⚓ Make Use Of ☛ Vim_9.0_Drops_Linux_Editing_Bombshell_With
                  New_Scripting_Language⠀⇛


                       The popular Linux text editor Vim has a new version
                       available, version 9.0. The new version debuts a
                       revamped scripting language, dubbed Vim9 Script.


                       Vim 9.0 “Takes a Big Step”


                       Vim creator Bram Moolenaar announced the new
                       version in a post on Vim’s official website. “After
                       many years of gradual improvement Vim now takes a
                       big step with a major release,” Moolenaar wrote.


                       While Vim already had a scripting language, Vim9
                       Script makes some changes to how comments,
                       functions, and variable assignments work. While
                       most users will want to wait until their
                       distribution’s package manager updates Vim, Unix/
                       Linux users eager to try the new version can
                       download the source code from the download pageand
                       compile it.


          o § Instructionals/Technical⠀➾


                # ⚓ OMG Ubuntu ☛ How_to_Enable_Nautilus_Typeahead_Search_in
                  Ubuntu_–_OMG!_Ubuntu!⠀⇛


                       In this post I show you how to get the Nautilus
                       typeahead feature back on all supported versions of
                       Ubuntu.


                       GNOME developers retired Nautilus’ type ahead
                       functionality back in 2013. Ubuntu devs continued
                       to patch the feature back in until 2017 when they
                       decided to switch to a more ‘vanilla’ GNOME desktop
                       experience.


                       Chances are you’ve long-since adapted to life
                       without it.


                       However, in the world of open source anything is
                       possible; if you have an itch, you can scratch it
                       yourself — and one fervent fan of Nautilus
                       typeahead search has done just that.


                # ⚓ ID Root ☛ How_To_Install_Terraform_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Terraform on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, Terraform is an open-source
                       infrastructure as a code software tool that enables
                       you to safely and predictably create, change, and
                       improve infrastructure. With Terraform you can
                       manage Cloud Compute, Networking, Load Balancers,
                       DNS, and so on using simple Declarative Programming
                       Language.


                       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 Terraform on Ubuntu 22.04
                       (Jammy Jellyfish). You can follow the same
                       instructions for Ubuntu 22.04 and any other Debian-
                       based distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ Video ☛ How_to_install_Toontown_Rewritten_on_Pop!_OS_22.04
                  –_Invidious⠀⇛


                       In this video, we are looking at how to install
                       Toontown Rewritten on Pop!_OS 22.04.


                # ⚓ Linux Made Simple ☛ How_to_install_WPS_Office_2019_on_a
                  Chromebook_–_June_Update⠀⇛


                       Today we are looking at how to install WPS Office
                       2019 on a Chromebook and some core fonts like Arial
                       and New Times Roman. Please follow the video/audio
                       guide as a tutorial where we explain the process
                       step by step and use the commands below.


                # ⚓ Citizix ☛ How_to_create_a_Kubernetes_TLS/SSL_Secret⠀⇛


                       A Secret is an object that contains a small amount
                       of sensitive data such as a password, a token, or a
                       key. Such information might otherwise be put in a
                       Pod specification or in a container image. Using a
                       Secret means that you don’t need to include
                       confidential data in your application code.


                       Because Secrets can be created independently of the
                       Pods that use them, there is less risk of the
                       Secret (and its data) being exposed during the
                       workflow of creating, viewing, and editing Pods.
                       Kubernetes, and applications that run in your
                       cluster, can also take additional precautions with
                       Secrets, such as avoiding writing secret data to
                       nonvolatile storage.


                       Secrets are similar to ConfigMaps but are
                       specifically intended to hold confidential data.


                # ⚓ UNIX Cop ☛ lftp._How_to_“rsync”_with_ftp⠀⇛


                       I’ve always been in complete control of my own
                       servers¹, this mean they have all the tools I need.
                       Recently they got me in charge of regularly backup
                       a large site. This usually mean that I’m taking
                       filesystem ‘snapshots’. But I’ve only have access
                       to this large site via ftp, and my script needs
                       rsync (and/or ssh). I need a way to do (almost) the
                       same, after a research I’ve found lftp; this
                       article will show you how to “rsync” with ftp.


                # ⚓ TechRepublic ☛ How_to_add_and_manage_groups_in_SFTPGo_|
                  TechRepublic⠀⇛


                       After deploying a platform for the storing and
                       sharing of files and directories, one of the first
                       things you’ll want to do is start adding and
                       managing groups. With groups, you can better
                       control who has access to what without having to
                       take care of it on a user-by-user basis. By
                       employing groups, you can add users who will
                       inherit the permissions found within the group so
                       it’s more efficient.


                       But not every platform is the same and some do
                       require a bit of extra attention to get right. One
                       such platform is SFTPGo. Although on the surface,
                       it looks as though it should be very simple to
                       manage users and groups, you do have to go the
                       extra mile to make sure it all works.


                       Let me show you what I mean by walking you through
                       the process of adding a group and then adding a
                       user to that group.


                # ⚓ TechRepublic ☛ How_to_deploy_CouchDB_as_a_cluster_with
                  Docker_|_TechRepublic⠀⇛


                       Recently, I showed you how to deploy CouchDB as a
                       standalone NoSQL database server, which could serve
                       you well in small instances. This time around, I
                       want to show you a neat trick for deploying CouchDB
                       as a cluster using Docker. Although this method
                       might not be ideal for production usage, it’s a
                       great way for developers to be able to work with
                       CouchDB in a test environment.


                # ⚓ ID Root ☛ How_To_Install_Neofetch_on_CentOS_9_Stream_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Neofetch on CentOS 9 Stream. For those of you who
                       didn’t know, Neofetch is a free and open-source
                       command-line tool that displays system and hardware
                       information in a visually appealing manner.
                       Neofetch displays an ASCII logo of your Linux
                       distribution along with information related to your
                       system in the terminal such as OS type, kernel
                       version, CPU, RAM, and others.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the Neofetch command-line tool that
                       displays the system on CentOS 9 Stream.


                # ⚓ H2S Media ☛ 4_Ways_to_install_GIMP_on_Ubuntu_22.04_LTS
                  Jammy_–_Linux_Shout⠀⇛


                       Install free and open-source GIMP editor on Ubuntu
                       22.04 Jammy JellyFish Linux for editing,
                       retouching, or optimizing your images.


                       The free image editor “GIMP” offers professional
                       tools and retouching functions forIts name is
                       actually an acronym for GNU Image Manipulation
                       Program and it is one of the best free alternatives
                       to Adobe Photoshop for private and semi-
                       professional use.


                # ⚓ H2S Media ☛ 3_Ways_to_install_Pinta_image_editing_tool_on
                  Ubuntu_22.04_or_20.04_LTS [Ed: Warning for Microsoft Mono]⠀⇛


                       Have Microsoft Paint open-source alternative Pinta
                       on Ubuntu 22.04 Jammy JellyFish or 20.04 Focal
                       Fossa for image drawing and editing images.


                       Inspired by Paint.NET, Pinta is another open-source
                       program for Linux users with features similar to
                       Microsoft Paint software. It is not just limited to
                       Linux, instead, Pinta is a cross-platform that can
                       be installed on Windows, FreeBSD, and macOS


                       This bitmap image drawing tool is very
                       straightforward and also offers drawing tools,
                       image filters, and color adjustment tools but fewer
                       feartures as compared to GIMP. However, GIMP is a
                       little complicated for new users whereas this one
                       is easy and focuses on usability which can be seen
                       in its offerings. Such as unlimited undo history;
                       Multiple language support; flexible toolbar
                       arrangement, including floating as windows or
                       docking around the image edge; also supports for
                       image layers.


                # ⚓ Composable_tools_for_disk_images_|_Richard_WM_Jones⠀⇛


                       Over the past 3 or 4 years, my colleagues and I at
                       Red Hat have been making a set of composable
                       command line tools for handling virtual machine
                       disk images. These let you copy, create,
                       manipulate, display and modify disk images using
                       simple tools that can be connected together in
                       pipelines, while at the same time working very
                       efficiently. It’s all based around the very
                       efficient Network Block Device (NBD) protocol and
                       NBD URI specification.


                # ⚓ Ubuntu Handbook ☛ Deluge_BitTorrent_Client_2.1.0_Released!
                  How_to_Install_in_Ubuntu_|_UbuntuHandbook⠀⇛


                       The free cross-platform Deluge BitTorrent client
                       released version 2.1.0 one day ago. Here’s how to
                       install it in Ubuntu 18.04, Ubuntu 20.04, Ubuntu
                       22.04.


                       Deluge is a fully-featured torrent downloading app
                       with GTK, web UI, and command line interfaces. The
                       app features protocol encryption, DHT, Local Peer
                       Discovery (LSD), Peer Exchange (PEX), UPnP/NAT-PMP,
                       web seeds, stream torrent and more.


                       The new 2.1.0 was released with minimum libtorrent
                       requirement increased to v1.2. Python 2 is no
                       longer supported! And, Python 3.6 is the minimum
                       requirement of the programming language.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ OMG Ubuntu ☛ New_Effect_Added_to_‘Burn_My_Windows’
                        GNOME_Extension_–_OMG!_Ubuntu!⠀⇛


                             Why settle for merely burning application
                             windows on close when you could totally
                             incinerate them instead?


                             Yes, everyone’s1 favourite over-the-top
                             desktop effect extension is back with an
                             update, and it adds yet another epically
                             excessive window closing animation to its
                             pool: Incinerate.


                             As you can probably imagine the new
                             Incinerate effect takes your app windows and…


    * § Distributions and Operating Systems⠀➾


          o § New Releases⠀➾


                # ⚓ Condres_OS_Plasma_1.0⠀⇛


                       With great pleasure we announce the release of
                       Condres Plasma 1.0 based on Debian 11.


                       This first release will be followed by a full
                       online calamares based installer, we will integrate
                       the Control Center that was previously available in
                       the old releases on the new Debian based version.


                       The new implementations will be available (some) in
                       September / October 2022.


                # ⚓ Second_Point_Release:_Univention_Corporate_Server_5.0-2⠀⇛


                       With the Point Release UCS 5.0-2, another important
                       step has been taken for further developing
                       Univention Corporate Server towards more
                       accessibility, better usability, as well as the
                       integration of services and their central
                       management. In this blog article, I would like to
                       give you an overview of the most important new
                       features and improvements, such as the integration
                       of Self Services into the UCS Portal, the
                       introduction of service-specific passwords or
                       various performance improvements in the use of DNS
                       and LDAP, as well as an overview of the apps made
                       available for UCS 5.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ 9to5Linux ☛ Unity_7.6_Desktop_Released_as_the_First_Major
                  Update_to_Ubuntu’s_Unity7_in_6_Years⠀⇛


                       
                       The last release of the Unity7 desktop environment
                       was back in May 2016, when Ubuntu was still using
                       Unity, but the community never let it die. Rudra
                       Saraswat, who is known for many Open Source
                       projects, as well as the maintainer of the
                       unofficial Ubuntu Unity Remix flavor, is also
                       involved in keeping Unity7 alive.


                       Since this is the first major release in the last
                       six years, you can imagine that it packs a bunch of
                       new features, starting with a redesigned dash (app
                       launcher) and HUD to look more modern and slick
                       featuring a flat style, improved dash rounded
                       corners, as well as support for accent colors to
                       Unity and Unity Control Center.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Sportskeeda ☛ 5_best_Android_gaming_devices_to_play_single-
                  player_games_in_2022⠀⇛


                # ⚓ 5_Best_Sticker_Apps_for_Android_in_[2022]_–_TechPP⠀⇛


                # ⚓ Android Police ☛ Android_14:_The_top_features_we_want_to
                  see_in_2023⠀⇛


                # ⚓ Digital Trends ☛ Android_13:_Everything_we_know_about
                  Google’s_big_OS_update_|_Digital_Trends⠀⇛


                # ⚓ Giz China ☛ Beware_of_this_Android_banking_malware_and
                  here’s_how_to_protect_yourself⠀⇛


                # ⚓ Geeky Gadgets ☛ Tecno_Pova_3_Android_smartphone_unveiled_–
                  Geeky_Gadgets⠀⇛


                # ⚓ Google_Pixel_7_suddenly_looks_an_even_more_appealing
                  Android_phone_|_T3⠀⇛


                # ⚓ PR Newswire ☛ RuggON_Rugged_Android_Tablet,_SOL_PA501,
                  Earns_FirstNet®_Certification⠀⇛


                # ⚓ The Verge ☛ Google’s_Android_Automotive_OS_is_coming_to_BMW
                  cars_next_year_–_The_Verge⠀⇛


                # ⚓ Android Police ☛ Google_Password_Manager_for_Android_and
                  Chrome_is_getting_a_new,_more_consistent_UI⠀⇛


                # ⚓ Make Use Of ☛ How_to_Customize_the_Google_Search_Widget_on
                  Your_Android_Phone⠀⇛


                # ⚓ Make Use Of ☛ How_to_Share_Your_Android_Clipboard_With_All
                  Your_Other_Devices⠀⇛


                # ⚓ GO Media ☛ You_Should_Use_These_Hidden_Chrome_‘Flags’_to
                  Make_It_a_Better_Android_Browser⠀⇛


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


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Firefox_Nightly:_These_Weeks_In_Firefox:_Issue_119⠀⇛


                             The Firefox Profiler can now sort roots in
                             alphabetical order with a flamgraph. This is
                             especially useful when comparing profiles
                             with the JavaScript filter, as this ensures
                             that the order is consistent.


                      # ⚓ SpiderMonkey_Newsletter_(Firefox_102-103)_|
                        SpiderMonkey_JavaScript/WebAssembly_Engine⠀⇛


                             SpiderMonkey is the JavaScript engine used in
                             Mozilla Firefox. This newsletter gives an
                             overview of the JavaScript and WebAssembly
                             work we’ve done as part of the Firefox 102
                             and 103 Nightly release cycles.


                      # ⚓ Mozilla ☛ A_Pocket_collection_for_your_wellness
                        journey,_as_curated_by_the_team_behind_‘The_Science_of
                        Happiness’_podcast⠀⇛


                             Want to live a more fulfilling life? The
                             internet gives plenty of advice. But finding
                             guidance backed by research can get tricky.


                             That’s where The Science of Happiness podcast
                             comes in. Co-produced by PRX and UC
                             Berkeley’s Greater Good Science Center, the
                             popular podcast explores science-backed
                             strategies to cultivate a happier life. Its
                             new series, Happiness Break, guides listeners
                             through a practice they can follow for a few
                             minutes during their day.


                             Podcast host and psychologist Dacher Keltner
                             is curating Pocket reading lists in hopes of
                             encouraging listeners to go deeper on
                             subjects like fear of failure, gratitude and
                             optimism. We chatted with him about what
                             motivated the Happiness Break, why he thinks
                             wellness audio content have become so popular
                             and how he makes time for his own reading
                             list.


                      # ⚓ Rust Blog ☛ Announcing_Rust_1.62.0_|_Rust_Blog⠀⇛


                             The Rust team is happy to announce a new
                             version of Rust, 1.62.0. Rust is a
                             programming language empowering everyone to
                             build reliable and efficient software.


                      # ⚓ LWN ☛ Rust_1.62.0_released⠀⇛


                             Version 1.62.0 of the Rust language has been
                             released. Changes include a new cargo add
                             command, default enum variants, an improved
                             Linux mutex implementation, a number of
                             stabilized APIs, and more.


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ Stuff_Michael_Meeks_is_doing⠀⇛


                       Really pleased to see so much work from the team,
                       and the wider community released as Collabora
                       Online 22.05 – a first cut of our next round of
                       development work around the next-generation
                       Collabora Online – quicker, slicker, better,
                       prettier and more.
                       Today Collabora’s app-store experiment with
                       LibreOffice Vanilla was ended. In time we will
                       write up and publish the data more widely, make
                       final donations to TDF and as/when sensible finish
                       up some Mac work in due course. Many thanks to all
                       those who worked hard over the years to get
                       LibreOffice into many app-stores – you rock. Of
                       course – you can still get Collabora Office for
                       your Mac, and help to support FOSS development that
                       way.


          o § FSF⠀➾


                # ⚓ FSF ☛ Fresh_in_the_LibrePlanet_archives:_LibrePlanet_2022
                  workshop_videos⠀⇛


                       In the lead-up to LibrePlanet 2022, the Free
                       Software Foundation (FSF) received more workshop
                       submissions than ever before. And because our
                       LibrePlanet schedule is often chock full of
                       splendid talks already, we thought it best to
                       present the workshops in our very first LibrePlanet
                       workshop series, which ran after LibrePlanet so
                       that they would not conflict with any talks.


                # ⚓ Translators_and_free_software,_a_practical_introduction_to
                  OmegaT⠀⇛


                       Professional translators are more than often taught
                       to use proprietary tools in universities and
                       professional groups. OmegaT has existed for 20
                       years as a professional Computer Aided Translation
                       tool (CAT) and is used all around the world. This
                       workshop will introduce participants to the
                       concepts behind CATs and especially how they are
                       practically put into use in OmegaT: translation
                       memories, segmentation, exchange formats,
                       collaborative work, etc.


                # ⚓ Software_localization_(translation)_of_Web-based_projects⠀⇛


                       Software localization (translation) of Web-based
                       projects could be a nightmare for many developers.
                       However, this time-consuming process can be solved
                       easily thanks to the free software tool Tolgee. Jan
                       Cizmar will guide you through with his workshop
                       named Web Application Localization Without Tears.
                       He will show you how to manage localization texts
                       in simple UI or how to take the advantage of the
                       in-context localization feature, so you can just
                       click & translate the text easily.


                       “The more languages your software knows, the more
                       of a satisfied users you have”. However, current
                       software localization in modern JS frameworks and
                       other software is complicated and fairly time-
                       consuming for all involved participants. Thanks to
                       the in-context localization feature of free
                       software project Tolgee, this tool offers easier
                       localization process, more relevant translations
                       delivery and finally less work for developers.


                # ⚓ Installing_Ourselves_into_LibrePlanet⠀⇛


                       Hosted by Cristina Cochior, Karl Moubarak, and Jara
                       Rocha of The Cell for Digital Discomfort


                       A workshop session to map out each of our current
                       conditions of connecting and being together, the
                       physical-political, and technological conditions
                       using a diagrammatic methodology.


                       The workshop is geared towards installing ourselves
                       into the conference’s infrastructural spectralities
                       by sharing, learning from and attuning to each
                       others’ conditions for connectivity, online
                       participation and basic computer-mediated mundane
                       day-to-day life. We want to pose this affirmation
                       as an initial trigger: installing is about
                       situating — attuning to our network of (inter-
                       )dependencies and attuning to the dependencies with
                       our local and vernacular but also standardized and
                       planetary networks.


    * § Leftovers⠀➾


          o § Entrapment (Microsoft GitHub)⠀➾


                # ⚓ LWN ☛ Software_Freedom_Conservancy:_Give_Up_GitHub:_The
                  Time_Has_Come!⠀⇛


                       The Software Freedom Conservancy (SFC) has issued a
                       strong call for free software projects to give up
                       GitHub and to move their repositories elsewhere.
                       There are a number of problems that SFC has
                       identified with the GitHub code-hosting service
                       and, in particular, with its Copilot AI-based code-
                       writing tool that was trained on the community’s
                       code stored in the company’s repositories. Moving
                       away from GitHub will not be easy, SFC said, but it
                       is important to do so lest the free-software
                       community repeat the SourceForge mistake.


          o § Security⠀➾


                # ⚓ USCERT ☛ #StopRansomware:_MedusaLocker [Ed: Should stop
                  Windows then, as that's by far the biggest ransomware
                  magnet]⠀⇛


                       CISA, the Federal Bureau of Investigation (FBI),
                       the Department of the Treasury (Treasury), and the
                       Financial Crimes Enforcement Network (FinCEN) have
                       released a joint Cybersecurity Advisory (CSA),
                       #StopRansomware: MedusaLocker, to provide
                       information on MedusaLocker ransomware.
                       MedusaLocker actors target vulnerabilities in
                       Remote Desktop Protocol (RDP) to access victims’
                       networks. Note: this joint #StopRansomware CSA is
                       part of an ongoing #StopRansomware effort to
                       publish advisories for network defenders that
                       detail various ransomware variants and ransomware
                       threat actors.


                # ⚓ eSecurity Planet ☛ Nearly_a_Million_Kubernetes_Instances
                  Exposed_on_Internet⠀⇛


                       Cybersecurity researchers have found more than
                       900,000 instances of Kubernetes consoles exposed on
                       the internet.


                       [...]


                       Kubernetes is a very popular container
                       orchestration system. The name comes from the Greek
                       word for “helmsman.” The term “K8s” or “K-eights”
                       is also used to refer to this technology.


                       Many organizations manage their applications with
                       Kubernetes using self-contained units called
                       “pods,” which share common resources with other
                       units without being aware of each other. For
                       example, “npm start” or “go run” processes can be
                       managed in pods and share some CPU and RAM.


                       K8s is helpful to deploy, manage, and scale
                       containers, which often consist of micro-services
                       and their configuration files. When the workload
                       increases or decreases, Kubernetes can handle the
                       situation automatically.


                       As a result, an important security aspect of
                       Kubernetes is access control. Any misconfiguration
                       can lead to unwanted disclosures and attackers
                       could even use them to escape containers and
                       escalate privileges. Besides, Kubernetes provides
                       APIs, CLI commands, and user interfaces that could
                       be attractive for hackers.


                       Cyble explained its scan “does not necessarily
                       imply that all exposed instances are vulnerable to
                       attacks or will lead to the loss of sensitive
                       data,” but “emphasizes the existence of seemingly
                       simple misconfiguration practices that might make
                       companies lucrative targets for TAs in the future.”


                # ⚓ eSecurity Planet ☛ Hacking_Linux_is_Easy_with_PwnKit [Ed:
                  This is patched, unlike the dozens of Microsoft actively-
                  exploited vulnerabilities that are not even patched;
                  selective media slant]⠀⇛


                       The U.S. Cybersecurity and Infrastructure Security
                       Agency (CISA) has added PwnKit as a high-severity
                       Linux vulnerability to its list of actively
                       exploited bugs.


                       Recorded as CVE-2021-4034, with a CVSS score of
                       7.8/10, PwnKit was discovered by Qualys in November
                       2021 and can be used by hackers to gain full root
                       control over major Linux distributions.


                # ⚓ Wired ☛ A_New,_Remarkably_Sophisticated_Malware_Is
                  Attacking_Routers_|_WIRED⠀⇛


                       AN UNUSUALLY ADVANCED hacking group has spent
                       almost two years infecting a wide range of routers
                       in North America and Europe with malware that takes
                       full control of connected devices running Windows,
                       macOS, and Linux, researchers reported on June 28.


                # ⚓ Bruce Schneier ☛ ZuoRAT_Malware_Is_Targeting_Routers⠀⇛


                # § Privacy/Surveillance⠀➾


                      # ⚓ AccessNow ☛ Why_Kenyans_should_say_no_to_biometrics
                        for_SIM_card_registry_–_Access_Now⠀⇛


                             “Avoid disconnection, update your SIM
                             registration details.” This is the message
                             that Kenyans have been seeing for months.
                             Kenyan telcos have been threatening to
                             disconnect people from mobile phone and
                             internet services if they do not provide new
                             data, including facial images — part of their
                             personal, unchangeable biometrics. The
                             companies claimed it was required under the
                             Kenya Information and Communications
                             (Registration of SIM-Cards) Regulations,
                             2015. In fact, that’s a gross
                             misrepresentation of the law. Collecting
                             biometric data for a SIM card puts people at
                             risk of privacy violations, data breaches and
                             abuse, and even identity theft. Kenyans must
                             say no, and oppose any new regulations to
                             authorize it.


                             Privacy violations are not new in Kenya. As
                             Access Now has previously highlighted,
                             companies like Safaricom have not only failed
                             to protect subscribers’ personal information,
                             but also refused to take accountability for
                             data breaches. Here’s a look at what’s
                             happened so far in Kenya, details on the push
                             to authorize biometric data collection, and
                             what Kenyans can do now to oppose it.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Public Knowledge ☛ Marking_A_Win_for_Free_Expression
                        Online,_Copyright_Office_Finds_that_New_Forms_of
                        Copyright_Would_Not_Benefit_Journalism_–_Public
                        Knowledge⠀⇛


                             Today, the U.S. Copyright Office published
                             its report on “Copyright Protections for
                             Press Publishers,” concluding that the
                             publishing industry already benefits from
                             significant protections under existing law
                             and does not require any new copyright
                             protections, including a new ancillary
                             copyright like the one currently implied in
                             the “Journalism Competition and Preservation
                             Act.” Public Knowledge applauds the Copyright
                             Office for conducting a robust inquiry into
                             the questions and providing balanced, nuanced
                             insights into the issue.


                             The following can be attributed to Meredith
                             Rose, Senior Policy Counsel at Public
                             Knowledge:


                             “The Copyright Office’s report today made one
                             thing crystal clear: Copyright law is neither
                             the source of, nor the solution to, the
                             crisis facing journalism in the United
                             States. The Office also helpfully notes that
                             creating an ancillary right (such as a right
                             to prevent outside linking to content) would
                             go far beyond the bounds of existing
                             copyright law, would likely be unable to
                             accommodate basic free speech protections,
                             and would otherwise raise constitutional
                             concerns.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ SpellBinding:_GINOYWR_Wordo:_GRAFT⠀⇛


                # ⚓ Modern_Art⠀⇛


                       So the fash are on their “modern art is bad” spree
                       again and I’m seeing a lot of comrades speaking out
                       in defense of modern art and that’s great because I
                       love modern art but two things:


                       First, the fascists started out rejecting but ended
                       up coopting modern art (Hartwig comes to mind).
                       Second, let’s be careful so we don’t make
                       aesthetics education a shibboleth for gatekeeping.
                       Uh, that came out a li’l bit jargony but what I
                       mean is I don’t want “lol those grobians don’t get
                       this stuff, we’re so clever” because then people
                       who don’t get modern art will be like “oh ok I
                       guess the left is not for me, bye“.


                       [...]


                       Like these days when we have Frozen and Doom and
                       Jimi Hendrix and pop rocks and acid and Glass Teeth
                       and Adventure Time and Tetris and the Monkees, now
                       maybe cubism and modernism and neoplasticism don’t
                       look so special but back in the day we were
                       dropping our jaws down to the god damned basement
                       seeing this stuff.


                       Haussmann’s boulevards had just obliterated Paris
                       and subjected us to the modern city. It was an era
                       of spirits and aliens and evolution and evil
                       flowers and Little Nemo in Dreamland and our brains
                       were on the god damned floor seeing this stuff.


          o § Technical⠀➾


                # ⚓ On_choosing_a_text_editor⠀⇛


                       When I was young, I read an excerpt from a book
                       about a child who was becoming a pearl diver. I
                       can’t find its source (it turns out that there are
                       many children’s books about pearl divers), but the
                       scene has stuck with me with a dreamlike
                       combination of haziness and crystal-clarity.


                       A child (or young man?) had to choose between
                       donning a hooded suit of cotton or covering himself
                       with hot oil to protect himself (from what?) in the
                       water while diving for pearls (or maybe something
                       else?). This was presented as a momentous decision:
                       you were either a cotton suit diver, or a hot oil
                       diver, and whatever you picked for your first dive
                       decided which it was going to be. I think the
                       protagonist chose oil?


                # ⚓ Behind_The_Scenes⠀⇛


                       Today we’ll talk about the Gemini server that
                       powers this capsule and runs on an ESP32
                       development board. (All code is simplified and some
                       uninteresting parts are omitted.)


                # ⚓ Mobile_Musings⠀⇛


                       It occurred to me today that as of Monday, I’ve
                       been using my current smartphone–the Samsung Galaxy
                       Note 8–for four and a half years. That is quite a
                       bit longer than I expected to use it; I’d used my
                       previous smartphone for three and a half years, and
                       it was in pretty bad shape by the time I retired
                       it. My Note 8 certainly isn’t in mint condition:
                       its battery life has been reduced to about 24 hours
                       of standby time, its body has many scratches and
                       scuffs, and its screen has noticeable burn-in from
                       the keyboard and on-screen navigation buttons (a
                       featured I always disliked). The software on the
                       phone, however, runs quite well, and the phone
                       shows no apparent slowdown.


                # § Internet/Gemini⠀➾


                      # ⚓ Bombo_fork_cert_skipping,_and_TLS_critique⠀⇛


                             The host is Sean, and
                             I presume he the father of Gemini. This is a
                             worrying development
                             in light of the fact that his capsule says:
                             I’m no longer involved with the Gemini
                             development, so
                             all the tests and tools that were here are
                             have been re-
                             moved. Why doesn’t matter. I’ve been told to
                             shut up,
                             sit down, and let the adults in the room
                             talk. You have
                             been warned.
                             Ouch.


                # § Programming⠀➾


                      # ⚓ FBInfer_reduced_our_product_crash_by_50%⠀⇛


                             Just want to share how powerful this tool is.
                             Infer[1], or FBInfer (since it’s written by
                             Facebook), is a static analyzer that can
                             detect cross-function logic errors and
                             potential data race in C, C++ and Objective-
                             C. Which is just amazing.


                      # ⚓ How_to_host_git_repos⠀⇛


                             In honor of World Give Up GitHub day, here’s
                             a quick guide to how to serve up your own git
                             repos.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.



                    ䷩ 𝚕𝚒𝚗𝚎 3289

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.30.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_30/06/2022:_Pine64_Has_RISC-V-Based_Raspberry_Pi_Rival,_Pico_W
Introduced⠀✐


Posted in News_Roundup at 7:24 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Debian_Family
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o SaaS/Back_End/Databases
          o Openness/Sharing/Collaboration
                # Open_Access/Content
          o Programming/Development
                # Rust
    * Leftovers
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Science
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o ⚓ CNX Software ☛ tio_is_a_serial_device_I/O_tool_for_Linux_targeted
            at_embedded_developers⠀⇛


                 There are already several serial terminal programs such
                 as Putty and minicom, and in recent times, I’ve been
                 using Bootterm myself. But that does not mean there isn’t
                 room for more and Martin Lund has developed tio serial
                 device I/O tool for Linux.


                 Martin found out many of the existing tools are very
                 modem focused or a bit cumbersome to use, so he developed
                 tio as the simpler alternative which puts less focus on
                 classic terminal/modem features and more focus on the
                 needs of embedded developers and hackers.


          o § Audiocasts/Shows⠀➾


                # ⚓ The BSD Now Podcast ☛ BSD_Now_461:_Persistent_Memory
                  Allocation⠀⇛


                       Q1 FreeBSD Quarterly Status Report 2022, Nginx on
                       OpenBSD 7.1, Persistent Memory Allocation, Colorize
                       your BSD shell, cgit With Gitolite and Nginx on
                       FreeBSD 13, and more


                # ⚓ mintCast Pocast ☛ 390_–_This_is_the_Way(land)_–_mintCast⠀⇛


                       1:20 The News
                       15:47 Security and Privacy
                       21:07 Bi-Weekly Wonderings
                       35:42 The Linux Innards
                       56:58 Vibrations from the Ether
                       1:03:45 Check This Out
                       1:04:20 Announcements


                       First up in the news, Gnome wins Microsoft money,
                       Firefox translates offline, Rocky overtakes the Red
                       Hat pack, apps on KDE look more klear, Debian gets
                       the Gecko treatment, Zoom gets Wayland screen
                       sharing, Photoshop is kind-of–but not-really coming
                       to Linux, and Nvidia contributes.


                       In security and privacy, Hertzbleed is coming for
                       your CPU, and the EU is going after deepfakes.


                       Then in our Wanderings, Moss goes Custom, Norbert
                       emerges, and Joe is Florida Man
                       In our Innards section we discuss the various
                       licenses in the world of open source software


                # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_960⠀⇛


                       Joel cannot get pizza hut delivered. Little ceasars
                       is too far away now.


          o § Kernel Space⠀➾


                # ⚓ Getting_Started_at_the_Linux_Kernel_–_Maíra_Canal⠀⇛


                       I started my journey with the Linux Kernel in
                       October 2021. At that time, I thought it was
                       impossible for a 19-year-old Brazilian girl to have
                       an approved commit at the kernel. Then, I find out
                       about an extracurricular group at Campinas, LKCAMP.
                       And I found out that undergraduate students were
                       able to contribute to the kernel. Although I
                       couldn´t go to the LKCAMP meetings, this really
                       push me forward, cause I saw that I was able to be
                       a part of the kernel community.


                       I was a Linux user for about two years, and I
                       became passionate about the system. I was eager to
                       contribute to the community and improve the kernel.
                       But, I was in doubt about where to start.


                # ⚓ Linux_Kernel_Developing_with_Fedora_–_Maíra_Canal⠀⇛


                       I’m a Fedora fan. I mean: I have two laptops for
                       development, and all of them run Fedora. I also
                       have a deployment machine. Guess what? It runs
                       Fedora. Stickers? The Fedora Logo sticked forever
                       on my laptop.


                       So, by now, you know: I’m really a Fedora fan.


                       So, when I started working with Linux Kernel, I
                       really wanted to develop in a Fedora environment.
                       But, without any kind of script, the work of a
                       Linux Kernel developer is ungrateful. I mean, do
                       you want to deploy to a remote machine? Be ready
                       for network configurations, grub configurations,
                       generate initramfs image, and tons of commands. Do
                       you want to manage your config files? Basically,
                       you are back to the ancient times when many save
                       tons of config files on folders.


          o § Graphics Stack⠀➾


                # ⚓ My_experience_as_a_Google_Summer_of_Code_Contributor_–
                  Introduction⠀⇛


                       With some pushes and pulls from friends, I’ve been
                       studying the Linux Graphical stack for some time
                       now. After some minor patches to both Mesa and the
                       Linux Kernel, I followed the instructions
                       thoroughly and landed a successful Google Summer of
                       Code proposal…


                # ⚓ An_introduction_to_the_Linux_graphics_stack⠀⇛


                       As you can probably imagine, the Linux graphics
                       stack comprises many layers of abstractions, from
                       the pretty little button from which you open your
                       Proton-able AAA Steam title to the actual bytecode
                       that runs on whatever graphics card you have
                       installed.


                       These many abstractions are what allow us to have
                       our glorious moments of being a hero (or maybe a
                       villain, whatever you’re up to…) without even
                       noticing what’s happening, and – most importantly –
                       that allow game devs to make such complex games
                       without having to worry about an awful lot of
                       details. They’re really a marvel of engineering
                       (!), but not by accident!


                       All of those abstraction layers come with a history
                       of their own, and it’s kinda amazing that we can
                       even have such a smooth experience with all of
                       those, community-powered, beautifully thought-out,
                       moving pieces, twisting and turning in a life of
                       their own.


                       But enough mystery! Let’s hop into it already,
                       shall we?


                       Though in most cases we start from the bottom of
                       the stack and build our way towards the top, here I
                       think it makes more sense for us to build it upside
                       down, as that’s what we’re used to interacting
                       with.


          o § Instructionals/Technical⠀➾


                # ⚓ Tips On UNIX ☛ Install_HPLIP_3.22.6_On_Ubuntu_/_Fedora_|
                  Tips_On_UNIX⠀⇛


                       This tutorial will be helpful for beginners to
                       download and install HPLIP 3.22.6 on Ubuntu 22.04
                       LTS, Fedora 36, and other Linux distributions.


                       HPLIP – HP Linux Image and Printing, developed by
                       HP for Printing, scanning, and faxing with HP
                       inkjet and laser-based printers on Linux platforms.


                       The latest version of HPLIP 3.22.6 contains new
                       Distro support and added support to the new
                       printers.


                # ⚓ UNIX Cop ☛ Nginx_–_Using_HTTP2⠀⇛


                       There goes a lot more behind the scenes between a
                       browser and a server than we might think. Our
                       browser may be handed a index.html but on
                       processing, it (the browser) may need to get
                       additional documents such as style sheets,
                       JavaScript files, etc. This requires multiple
                       connections to the server. Making a connection
                       requires performing the TCP three-way handshake,
                       exchanging headers, etc. all of which introduces
                       unnecessary overhead, as well as latency to the
                       client. It is in this context that the need for a
                       better way to serve documents become apparent.


                       It wasn’t until the publication of the HTTP/
                       2 protocol that the issue could be solved. HTTP/
                       2 protocol, officially RFC 7540 or more recently
                       RFC 9113, is a replacement for the older HTTP/1.1
                       which provides an optimized method for
                       transportation of documents over TCP. It allows
                       multiplexing connections so that multiple documents
                       can be sent over the same stream. It also allows
                       compressing the headers and many requests into a
                       single packet. Furthermore, it provides an optional
                       feature called server push whereby a server can
                       send additional documents that the client may need
                       along side the response for the document that was
                       actually requested. For example, a server may send
                       the style sheets and JavaScript files along side
                       the response for the request to an HTML file.


                # ⚓ Linux Shell Tips ☛ How_to_Install_Latest_Linux_Kernel_in
                  RHEL_8⠀⇛


                       A Kernel is somewhat the soul of an operating
                       system since it exists at its core. Once you start/
                       boot your machine, the Kernel takes control of the
                       entire system. Each RHEL 8 distribution is shipped
                       with a custom-built kernel.


                       Since a Kernel is the primary bridge of
                       communication between the hardware and software
                       components of an entire computer system, it is
                       responsible for such a system’s integrity and
                       supported hardware compatibility. Also, it is the
                       kernel that provides an interfacing link between
                       system processes and computer hardware.


                # ⚓ Trend Oceans ☛ dnf-automatic:_Enable_Automatic_Updates_for
                  RHEL-based_distributions_–_TREND_OCEANS⠀⇛


                       There are new vulnerabilities being disclosed every
                       day that put your server at a security risk. This
                       stress of updating your system for the latest
                       security patch or application update can be
                       relieved by automating the update process using the
                       dnf-automatic command.


                       The dnf-automatic is a command-line tool for RHEL-
                       based distributions such as Fedora, AlmaLinux,
                       Rocky Linux, etc., for automating the update
                       process using systemd timers. It will periodically
                       check the system for the latest release or security
                       update and update them without your interaction as
                       a background process.


                # ⚓ H2S Media ☛ Install_Python_3.9_or_3.8_on_Ubuntu_22.04_LTS
                  Jammy_JellyFish⠀⇛


                       Learn how to use the PPA repository to install
                       Python’s old versions such as 3.9. 3.8, 3.7, and
                       more on Ubuntu 22.04 Jammy JellyFish using the
                       command terminal.


                       Python is freely available for the common operating
                       systems. The programming language is standard
                       equipment in many Linux distributions. Python can
                       also be used on many mobile operating systems. For
                       web servers, WSGI (Web Server Gateway Interface) is
                       a universal interface between the server and
                       Python.


                       It offers clear syntax and good readability. It is
                       considered easy to learn and can be interpreted in
                       the common operating systems. Python supports
                       several programming paradigms such as functional,
                       object-oriented, or aspect-oriented programming and
                       can also be used as a scripting language.


                       Since Python is a so-called multiparadigm language,
                       programmers are not tied to a specific programming
                       style. The optimal programming style can be
                       selected for the various tasks. Python allows
                       Python programs to be embedded in other languages
                       ​​as individual modules.


                # ⚓ UNIX Cop ☛ How_to_Install_Darktable_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       Darktable (stylized as darktable) is a free and
                       open-source photography application program and raw
                       developer. Rather than being a raster graphics
                       editor like Adobe Photoshop or GIMP, it comprises a
                       subset of image editing operations specifically
                       aimed at non-destructive raw image post-production.
                       It is primarily focused on improving a
                       photographer’s workflow by facilitating the
                       handling of large numbers of images. It is freely
                       available in versions tailored for most major Linux
                       distributions, macOS, Solaris and Windows and is
                       released under the GPL-3.0-or-later.


                # ⚓ UNIX Cop ☛ How_to_Install_Pinta_on_Ubuntu_20.04_|_22.04_LTS
                  [Ed: Microsoft Mono warning]⠀⇛


                       Pinta is an open-source, cross-platform bitmap
                       image drawing and editing program inspired by
                       Paint.NET, a similar image editing program which is
                       limited to Microsoft Windows. Pinta has more
                       features than Microsoft Paint. Compared with open-
                       source image editor GIMP, Pinta is simpler and has
                       fewer features.


                # ⚓ Linux Capable ☛ How_to_Install_MariaDB_10.9_on_Ubuntu_22.04
                  LTS_–_LinuxCapable⠀⇛


                       MariaDB is one of the most popular open-source
                       databases next to its originator MySQL. The
                       original creators of MySQL developed MariaDB in
                       response to fears that MySQL would suddenly become
                       a paid service due to Oracle acquiring it in 2010.
                       With its history of doing similar tactics, the
                       developers behind MariaDB have promised to keep it
                       open source and free from such fears as what has
                       happened to MySQL.


                       MariaDB has become just as popular as MySQL with
                       developers, with advanced clustering with Galera
                       Cluster 4, faster cache/indexes, storage engines,
                       and features/extensions that you won’t find in
                       MySQL.


                       In the following tutorial, you will learn how to
                       install or upgrade MariaDB 10.9 on Ubuntu 22.04 LTS
                       Jammy Jellyfish using the command line terminal and
                       some tips on how to upgrade your existing database
                       if needed one exists.


                # ⚓ Linux Capable ☛ How_to_Install_Sublime_Merge_on_Ubuntu
                  22.04_LTS_–_LinuxCapable⠀⇛


                       Sublime Merge is a git client software that comes
                       with various features to help make working with git
                       repositories easier. One of its most valuable
                       features is the syntax highlighting engine, which
                       makes it easier to read code. The custom high-
                       performance Git reading library is also helpful,
                       allowing you to stage changes line-by-line.


                       Additionally, the build-in git search function lets
                       you quickly find commits, and the themes allow you
                       to customize the look of the software to match your
                       preferences. The Command Palette and Commit Editing
                       functions are also helpful, letting you quickly
                       execute git commands and edit commits. Finally, the
                       Submodule Management and Git Flow Integration
                       functions make it easy to work with submodules and
                       manage branches. Overall, Sublime Merge is a
                       powerful git client that can significantly improve
                       your workflow.


                       In the following tutorial, you will learn how to
                       install Sublime Merge on Ubuntu 22.04 LTS using the
                       official Sublime APT repository using the command
                       line terminal, along with how to launch the
                       software and remove it in the future if required.


                # ⚓ Linux Capable ☛ How_to_Install_SQLite_3_on_CentOS_9_Stream
                  –_LinuxCapable⠀⇛


                       SQLite is a free, lightweight relational database
                       management system (RDBMS) in a C library. SQLite is
                       not a client-server database engine. Instead, it is
                       embedded into the end program. Primarily all
                       programming languages support SQLite, which how
                       languages embed the program is with a file with
                       .sqlite3/.sqlite/.DB extension. The software is
                       popular for local/client storage such as web
                       browsers, Android devices, etc. The list is quite
                       extensive.


                       The following tutorial will teach you how to
                       install SQLite 3 with CentOS 9 Stream using the
                       command line terminal using the standard DNF
                       package manager or manually installing straight
                       from the project’s Git.


                # ⚓ Red Hat Official ☛ Linux_superuser_access,_explained_|
                  Enable_Sysadmin⠀⇛


                       Here’s how to configure Linux superuser access so
                       that it’s available to those who need it—yet well
                       out of the way of people who don’t need it.


                # ⚓ Its FOSS ☛ Hide_Files_and_Folders_in_Linux_[With_and
                  Without_Renaming]⠀⇛


                       This beginner-focused article discusses how you can
                       hide files and folders from normal view in Linux.
                       Both GUI and command-line methods have been
                       discussed.


                       There will be times when you need to hide files in
                       Linux.


                       No, I am not talking about those ‘special files’
                       that you don’t want your family to see. Although
                       you can hide these special files, it is better to
                       lock them with a password for an extra layer of
                       protection.


                       Back to hiding files. Any file or folder whose name
                       begins with a . (dot) is “hidden” in Linux.


                # ⚓ TecMint ☛ How_to_Install_Fedora_36_XFCE_Desktop_Edition⠀⇛


                       Many Fedora users are unaware of the fact that you
                       do get an option to choose other Desktop
                       Environments apart from the default GNOME which we
                       are used to downloading directly from their
                       download page.


                       Apart from the default GNOME, you do get an option
                       of KDE Plasma, Xfce, LXQT, MATE, Cinnamon, LXDE,
                       SOAS, and even i3.


                       So through this guide, we will be showing you how
                       you can install XFCE Fedora spin on your system in
                       the easiest way possible but before that, let’s
                       discuss why you should even consider using XFCE
                       instead of GNOME.


                # ⚓ Linux Handbook ☛ Show_Only_Hidden_Files_in_Linux_Command
                  Line⠀⇛


                       Displaying hidden files in Linux is quite easy. You
                       use the ls command in this manner:


                       ls -a
                       That’s fine. You can see the hidden files with
                       their names starting with a dot (.).


                       But you see all the files in the current directory,
                       the hidden ones and the regular ones.


                       What if you want to ONLY see the hidden files, not
                       the regular ones?


                       There is no ready-to-use option like -a and -A.
                       However, you can always find a way to achieve
                       things by combining a few commands through the
                       wonderful pipe redirection.


                # ⚓ UNIX Cop ☛ How_to_Install_PlayOnLinux_on_Ubuntu_20.04_|
                  22.04_LTS⠀⇛


                       In this article, we will show you how to install
                       PlayOnLinux on Ubuntu systems.


                       PlayOnLinux is a graphical frontend for the Wine
                       software compatibility layer which allows Linux
                       users to install Windows-based video games,
                       Microsoft Office (2000 to 2010), Microsoft Internet
                       Explorer, as well as many other applications such
                       as Apple iTunes and Safari.


                       While initially developed for Linux-based systems,
                       it is also used on macOS and FreeBSD under the
                       names PlayOnMac and PlayOnBSD, respectively. It can
                       also be used on other operating systems supported
                       by Wine.


                # ⚓ Jim Nielsen ☛ Notes_From_“In_And_Out_Of_Style”⠀⇛


                       I watched Jeremy’s talk at CSS Day 2022 titled “In
                       And Out Of Style” and, as always, I had my notepad
                       ready. Here are a few points that stood out to me.


                # ⚓ uni Toronto ☛ What_symmetric_and_asymmetric_IP_routing
                  are⠀⇛


                       However, if you have a multi-homed host, a host
                       with multiple interfaces and IP addresses, this
                       approach to routing outgoing traffic can create a
                       situation where outgoing and incoming packets for
                       the same connection (or flow) use different
                       interfaces. To have this happen you normally need
                       at least two of your networks to be routable, which
                       is to say that hosts not on those networks can
                       reach them and hosts on those networks can reach
                       other networks.


                # ⚓ Undeadly ☛ (Almost)_0_Dependency_Websites_with_OpenBSD_&
                  AsciiDoc⠀⇛


                       Courtney Allen has published a blog post about how
                       to run a website and blog almost exclusively on
                       things that are in the OpenBSD base system already,
                       only adding AsciiDoc to the mix.


                # ⚓ Naman Sood ☛ Implementing_RSS_for_my_blog_(yes,_this
                  one!)⠀⇛


                       A few months ago, a friend of mine mentioned that
                       they still, in the year 2021, used RSS feeds to
                       subscribe to the blogs they liked. I was
                       incredulous? RSS? That orange button I used to see
                       on websites years ago? The one that returned XML if
                       you accidentally clicked it? People still used
                       that? People still provided that?


                       Apparently the answer was yes. My friend also said
                       that if I implemented RSS on my blog, they would
                       subscribe to it. So I thought about it, and decided
                       to do it. I forgot about it until today, but when I
                       did remember it didn’t take long to implement at
                       all.


                # ⚓ RandomNixFix ☛ 0_Dependency_Websites_with_OpenBSD_&
                  AsciiDoc⠀⇛


                       I have fallen in love with a recent combination of
                       software to make good looking websites, and having
                       an easy to manage web server. I’m a minimalist in
                       many ways. Really, I find that it makes my life
                       easier. I like to keep my blog up here and don’t
                       want to deal with database updates, language
                       exploits, weird migrations, and so on. I also
                       manage my church’s website. I can’t be having
                       complex solutions that require large amounts of
                       maintenance at multiple times a month because of a
                       dozen pieces of software requiring version upgrades
                       or what have you. Sure, some people have needs for
                       elaborate content management systems, but sometimes
                       you only need a simple site too, and why
                       overcomplicate it?


                       This is why I like my current combo:


                       1. OpenBSD


                       2. AsciiDoc


          o § Games⠀➾


                # ⚓ HowTo Geek ☛ “Atari_Was_Very,_Very_Hard”_Nolan_Bushnell_on
                  Atari,_50_Years_Later⠀⇛


                       It’s been 50 years since Nolan Bushnell co-founded
                       Atari, which brought video games to the mainstream.
                       To celebrate, we asked Bushnell what he learned
                       during the early years—and what we’ve lost sight of
                       since then.


                # ⚓ GamingOnLinux ☛ Some_Steam_Decks_ship_with_an_x2_SSD
                  instead_of_an_x4_SSD⠀⇛


                       Valve made a change to the specifications of the
                       top two versions of the Steam Deck last month,
                       which it seems plenty of people (including me)
                       completely missed. It’s not a massive change but
                       still one to be aware of as not all Decks are the
                       same.


                # ⚓ GamingOnLinux ☛ AOKZOE_are_the_latest_to_attempt_a_Steam
                  Deck_rival_with_the_AOKZOE_A1⠀⇛


                       AOKZOE will be jumping in the handheld ring with
                       their upcoming AOKZOE A1 AMD Ryzen 7 6800U portable
                       that will offer either Windows 11 or SteamOS to
                       perhaps rival the Steam Deck. They’re a rather new
                       company, so everything they’re talking about and
                       showing off should be taken with a rather large
                       pinch of salt.


                # ⚓ TecMint ☛ How_to_Change_and_Reset_Forgotten_Root_Password
                  in_RHEL_9⠀⇛


                       While installation of RHEL 9, the installer
                       recommends we choose a complex password and while
                       making the password complex enough, the chances of
                       forgetting our password are quite high. And things
                       get even more complex when your user is not even
                       added to the wheel group (which allows a normal
                       user to elevate root privileges for a small amount
                       of time).


                       This tutorial will guide you on how you can change
                       your forgotten root password in 3 scenarios and we
                       are quite sure that you’ll be able to recover your
                       forgotten password at the end of this guide.


                # ⚓ Linux Handbook ☛ How_to_Cut,_Copy_and_Paste_Text_in_Nano
                  editor?⠀⇛


                       GNU Nano is an editor that has a minimal learning
                       curve and hence is widely used for beginner-level
                       guides.


                # ⚓ Linux Links ☛ 10_Fun_Free_and_Open_Source_Action-Adventure
                  Games⠀⇛


                       The action-adventure genre is a video game genre
                       that combines core elements from both the action
                       game and adventure game genres. They engage both
                       reflexes and problem-solving in both violent and
                       non-violent situations.


                       There are many games that can fall into this genre
                       given that the action genre, itself, is very wide
                       encompassing. Other games that can fit into this
                       genre are covered in the series.


                       There is an eligibility criteria that needs to be
                       met to be included in this round up (see below).


                       Let’s explore the 10 games. For each game we have
                       compiled its own portal page, a full description
                       with an in-depth analysis of its features, a screen
                       shot of the game in action, together with links to
                       relevant resources.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Its FOSS ☛ With_Extensions,_GNOME_Web_is_Slowly
                        Becoming_an_Attractive_Option_on_Desktop_Linux⠀⇛


                             GNOME Web (Epiphany) is one of the best
                             browsers available for Linux users.


                             It offers a minimal, and a unique user
                             experience.


                             Unfortunately, the uniqueness does not
                             incentivize users to use it as their primary
                             web browser.


                             But, it looks like that could change soon…


                             GNOME Web is finally adding support for
                             WebExtensions, as revealed by one of the
                             developers (Patrick a.k.a TingPing).


                             This is all a part of the GNOME 43 feature
                             set.


    * § Distributions and Operating Systems⠀➾


          o § Debian Family⠀➾


                # ⚓ Daniel Pocock ☛ Retrofitting_Jonathan_Cohen’s_house_for
                  energy_efficiency⠀⇛


                       Personally, I’ve done an enormous amount of work
                       promoting Debian over more than 25 years without
                       receiving any payment in return. I couldn’t help
                       noticing the news that Debian is now paying a
                       lawyer to silence critics, in other words,
                       contradicting the Debian Social Contract. The
                       lawyer’s west London mansion in Pinner has really
                       emphasized the injustice of this situation.


                       News today tells us the UK is planning to cut off
                       gas supplies to some European countries so that
                       traditional British mansions like this can stay
                       warm. This could be avoided if Mr Cohen used some
                       of his Debian money to insulate his house.


                       I had a quick look at the pictures that have been
                       circulating online, they provide valuables lessons
                       for all homeowners in the UK and Ireland.


                       [...]


                       With all the money he has received from Debian in
                       the last year, this type of deep retrofit will be
                       easily within reach for Mr Cohen.


          o § Open Hardware/Modding⠀➾


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Robot_Maps_Its_World_with
                  LiDAR⠀⇛


                       Autonomous Raspberry Pi robots navigate their
                       environment without bumping into things. Using an
                       ultrasonic sensor, such as the HC-SR04, to detect
                       obstacles is a fairly common tool for Pi-based
                       robots and cars but this robot car project, created
                       by maker and developer エス ラボ (S Lab), is going even
                       further by mapping out a room with the help of a
                       LiDAR sensor.


                       The car has a Raspberry Pi 4 4GB at its core and as
                       it drives around, LiDAR sensor data is transmitted
                       from the Pi to a nearby PC which uses a SLAM-based
                       (simultaneous localization and mapping) system to
                       create a virtual, 3D replica of the room
                       surrounding the Raspberry Pi. The program also
                       provides a virtual representation of the car in
                       Unity to estimate its position in the room.


                # ⚓ Tom’s Hardware ☛ Pine64_Teases_RISC-V_Based_Raspberry_Pi
                  Alternative⠀⇛


                       Pine64, maker of many fine SBCs including the
                       Rock64 and Quartz64 (opens in new tab), is
                       preparing to dip its toe into the choppy waters of
                       RISC-V, including news of an upcoming “powerful,
                       yet affordable” board based on the versatile open-
                       source architecture in its most recent product
                       update (opens in new tab).


                # ⚓ SparkFun Electronics ☛ All_Aboard_the_mikroBUS⠀⇛


                       Hello and welcome, everyone! We are back, yet
                       again, with a handful of new products here at
                       SparkFun Electronics! We’ve heard your requests for
                       kits for our mikroBUS boards to include a few
                       hookup accessories (specifically Click boards™) so
                       we took both of our boards and made them easier to
                       get started with! Following that, we have a new
                       WiFi HaLow HAT from ALFA Network that we expect to
                       really help your Raspberry Pi get connected to a
                       new type of IoT network. Now, let’s jump in and
                       take a closer look at all of this week’s new
                       products!


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Pico_W_Review:_Built-in_Wi-Fi
                  Comes_to_Pico⠀⇛


                       Solid hardware, good software, and Wi-Fi access see
                       this incremental update elevate the Raspberry Pi
                       Pico to a truly versatile development board.


                # ⚓ Raspberry Pi ☛ Raspberry_Pi_Pico_W:_your_$6_IoT_platform_–
                  Raspberry_Pi⠀⇛


                       New product alert! In January last year, we
                       launched the $4 Raspberry Pi Pico, our first
                       product built on silicon designed here at Raspberry
                       Pi. At its heart is the RP2040 microcontroller,
                       built on TSMC’s 40nm low-power process, and
                       incorporating two 133MHz Arm Cortex-M0+ cores,
                       264kB of on-chip SRAM, and our unique programmable
                       I/O subsystem.


                # ⚓ CNX Software ☛ Raspberry_Pi_Pico_W_–_A_$6_Raspberry_Pi_Pico
                  board_with_WiFi_4_–_CNX_Software⠀⇛


                       I was expecting the next official Raspberry Pi
                       board to be either an update of Raspberry Pico with
                       WiFi and Bluetooth or with a machine learning
                       accelerator and the new $6 Raspberry Pi Pico W
                       delivers that wish through the addition of 2.4GHz
                       WiFi 4.


                       Having said that, I was actually expecting a
                       competitor to ESP8266 or ESP32 with a new Raspberry
                       Pi wireless microcontroller, but it did quite
                       happen that way as the Raspberry Pi Pico W features
                       the same Raspberry Pi RP2040 dual-core Cortex-M0+
                       microcontroller found in Raspberry Pi Pico board
                       coupled with an Infineon CYW43439 chip that’s
                       supposed to support both 2.4 GHz WiFi 4 and
                       Bluetooth LE 5.2. Bluetooth is not enabled right
                       now, but may be at a later stage.


                # ⚓ The DIY Life ☛ What_Makes_TMC2208_Stepper_Motor_Drivers
                  Silent_–_The_DIY_Life⠀⇛


                       A while ago I did a bit of an experiment to compare
                       the sound level between TMC2208 and A4988 stepper
                       motor drivers. At the time, A4988 drivers were more
                       commonly used on 3D printers and other hobby CNC
                       devices. Since then, most 3D printer and CNC laser
                       manufacturers have moved towards replacing at least
                       the X and Y axis motors with the silent TMC2208
                       stepper motor driver or some other variant of
                       silent motor driver. A question that has come up
                       quite a lot in the video’s comments was how these
                       drivers manage to drive the motors with such a
                       significant sound reduction and if there was any
                       trade-off.


                # ⚓ Ken Shirriff ☛ X-ray_reverse-engineering_a_hybrid_module
                  from_1960s_Apollo_test_equipment⠀⇛


                       In this blog post, I reverse-engineer a hybrid
                       module that was used for ground-testing of
                       equipment from the Apollo space program. But first,
                       some background. During the Apollo missions to the
                       Moon, NASA could send digital messages to the
                       spacecraft from the ground. These data messages
                       could perform specific tasks: control spacecraft
                       equipment by activating relays, send commands
                       directly to the Apollo Guidance Computer, or even
                       set the spacecraft’s clock. Onboard the Command
                       Module, these messages were decoded by the Up-Data
                       Link, a drab bluish box (below) mounted in the
                       equipment bay.


                # ⚓ Arduino ☛ Building_a_simple_USB_adapter_for_the_Logitech
                  Driving_Force_Shifter_with_Arduino_|_Arduino_Blog⠀⇛


                       Logitech’s Driving Force Shifter is a very common
                       piece of kit for those who enjoy racing games, as
                       it connects to a Logitech Racing Wheel and allows
                       the player to control their car in a more realistic
                       fashion. However, this accessory’s DB-9 connector
                       must be connected to a proprietary base within the
                       racing wheel or else it fails to work. So as a way
                       to circumvent this annoying problem, Parts Not
                       Included’s Dave Madison created his own custom
                       adapter, which translates the signals from the
                       shifter into commands over a USB port on the host
                       PC.


                       To begin this endeavor, Madison purchased a DB-
                       9 connector with the rear leads exposed, and after
                       quickly modifying them, plugged the X/Y axis wires
                       into analog input pins and connected the binary
                       reverse pin into a digital input pin on the Arduino
                       Leonardo. In terms of software, this setup requires
                       both the Arduino Joystick library and the Sim
                       Racing library. The latter converts X/Y values into
                       shifter positions in order to determine the current
                       gear, while the former communicates with the host
                       as an emulated HID device.


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


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ PC World ☛ This_new_privacy_feature_in_Firefox_strips
                        tracking_info_from_links⠀⇛


                             With the update to version 102, Firefox now
                             automatically strips tracking parameters from
                             some URLs, including those shared on
                             Facebook. However, as reported by Bleeping
                             Computer, it’s just a handful, and in some
                             light, quick testing, it won’t cover all the
                             sites you might visit during the normal
                             course of a day.


          o § SaaS/Back End/Databases⠀➾


                # ⚓ Twilio Inc ☛ SQLite_or_PostgreSQL?_It’s_Complicated!⠀⇛


                       I chose SQLite for the database that supports this
                       dashboard, which in early 2021 when I built this
                       system, seemed like a perfect choice for what I
                       thought would be a small, niche application that my
                       teammates and I can use to improve our blogging.
                       But almost a year and a half later, this
                       application tracks daily traffic for close to 8000
                       articles across the Twilio and SendGrid blogs, with
                       about 6.5 million individual daily traffic records,
                       and with a user base that grew to over 200
                       employees.


                       At some point I realized that some queries were
                       taking a few seconds to produce results, so I
                       started to wonder if a more robust database such as
                       PostgreSQL would provide better performance. Having
                       publicly professed my dislike of performance
                       benchmarks, I resisted the urge to look up any
                       comparisons online, and instead embarked on a
                       series of experiments to accurately measure the
                       performance of these two databases for the specific
                       use cases of this application. What follows is a
                       detailed account of my effort, the results of my
                       testing (including a surprising twist!), and my
                       analysis and final decision, which ended up being
                       more involved than I expected.


          o § Openness/Sharing/Collaboration⠀➾


                # § Open Access/Content⠀➾


                      # ⚓ Techdirt ☛ Enjoy_Digital_Ownership_And_Public
                        Libraries_While_You_Still_Can⠀⇛


                             Michael E. Karpeles, Program Lead on
                             OpenLibrary.org at the Internet Archive,
                             spotted an interesting blog post by Michael
                             Kozlowski, the editor-in-chief of Good e-
                             Reader. It concerns Amazon and its audiobook
                             division, Audible:


          o § Programming/Development⠀➾


                # ⚓ Finding_bugs_using_IGT_and_git_bisect⠀⇛


                       The first step to eliminate bugs is to find a way
                       how to reproduce them consistently. Wait… what?


                       Test suites are great for that, since they can
                       simulate very specific behavior in a timely manner.
                       IGT GPU Tools is a collection of tools for
                       development and testing of the DRM drivers, and, as
                       such, it can help us to find and reproduce bugs.


                # ⚓ Real_contributions_with_real_money⠀⇛


                       Recently I’ve heard from a friend that his
                       professor simply doesn’t believe that free software
                       should be profitable, so I’m making this blog post.


                # ⚓ Reviewing_patches⠀⇛


                       Being part of the community, is more than just
                       writing code and sending patches, it is also
                       keeping track of the IRC discussions and reading
                       the mailing lists to review and test patches sent
                       from others whenever you can.


                       Both environments are not the most welcoming, but
                       there are plenty of tools from the community to
                       help parsing them. In this post I’ll talk about b4,
                       suggested by my GSOC mentor André, a tool to help
                       with applying patches.


                # ⚓ J Pieper ☛ Flexible_I/O:_Source_configuration⠀⇛


                       Each “source” in the above diagram represents a
                       single encoder. To the sinks it provides a position
                       and velocity, along with various validity
                       indications for that data. Each has three basic
                       configuration components: where to get the raw
                       data, how to transform that raw data, and the low-
                       pass filter configuration. We’ll cover each in
                       turn.


                # ⚓ Mark Dominus ☛ Things_I_wish_everyone_knew_about_Git_(Part
                  I)⠀⇛


                       The command set wasn’t always well thought out, and
                       then over the years it grew by accretion, with new
                       stuff piled on top of old stuff that couldn’t be
                       changed because Backward Compatibility. The
                       commands are non-orthogonal and when two commands
                       perform the same task they often have inconsistent
                       options or are described with different
                       terminology. Even when the individual commands
                       don’t conflict with one another, they are often
                       badly-designed and confusing. The documentation is
                       often very poorly written.


                # § Rust⠀➾


                      # ⚓ Rust Weekly Updates ☛ This_Week_In_Rust:_This_Week_in
                        Rust_449⠀⇛


    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Odd_Inputs_And_Peculiar_Peripherals:_Miniature_Steel
            Drums_Become_Rotary_Mouse_Controllers⠀⇛


                 When [bornach] browsed through his office’s free-cycling
                 box he found an old novelty toy that lets you play simple
                 tunes on miniature steel drums. Such a thing is probably
                 fun for about five minutes – if it’s working, which this
                 one wasn’t. But instead of throwing it away, [bornach]
                 spotted an opportunity in the capacitive touch pads on
                 top of those little drums: they looked perfect to be
                 modified into an unusual mouse cursor controller.


          o ⚓ The Nation ☛ The_Hunted⠀⇛


                 Over the past two decades, Pierre Senges has emerged as
                 one of France’s most important and celebrated writers. At
                 the age of 54, Senges has published 16 novels, mostly
                 with Éditions Verticales, an experimental imprint of
                 Gallimard, the most storied publishing house in France,
                 as well as some two dozen radio plays. Since his 2000
                 debut, Veuves au Maquillages, a dark comedy about a man
                 with a fetish for women who have murdered their husbands,
                 he has won a number of prestigious literary prizes. Yet
                 despite the efforts of a handful of devoted translators
                 and small presses, he remains little-known among
                 Anglophone readers.


          o ⚓ Scheerpost ☛ Steve_Wasserman:_Turn_of_the_Screw⠀⇛


                 Cuban rapper Maykel Castillo and visual artist Luis
                 Manuel Otero who helped compose and record last year’s
                 Latin Grammy-winning “Patria y Vida,” a bitter viral rap
                 song that gave voice to the accumulated rage and
                 resentment of some disaffected Cubans, received harsh
                 prison sentences last Friday.


          o ⚓ Wesley Aptekar Cassels ☛ How_Websites_Die⠀⇛


                 I think a lot about the lifecycle of websites. I’m
                 frustrated by so much of the short-term thinking I see in
                 the world today, and the way we think about websites is a
                 part of that: it’s “normal” for them to just go up in
                 smoke as soon as their authors stop paying attention.
                 People switch platforms and providers and break links
                 without a second thought. It pains me to see people build
                 websites with no feeling of obligation to them — when you
                 put something out into the world, it is your
                 responsibility to care for it.


          o ⚓ Michał Woźniak ☛ The_Outrage_Dividend⠀⇛


                 I would like to propose a new term: outrage dividend.


                 Outrage dividend is the boost in reach that content which
                 elicits strong emotional responses often gets on social
                 media and other content sharing platforms.


                 This boost can be related to human nature — an outrage-
                 inducing article will get shared more. It can also be
                 caused by the particular set-up of the platform a given
                 piece of content is shared on — Facebook’s post-promoting
                 algorithm was designed to be heavily biased to promote
                 posts that get the “angry” reaction.


          o ⚓ The Verge ☛ Substack_CEO_says_he’s_‘very_sorry’_about_laying_off
            13_people⠀⇛


                 According to The New York Times, some of the employees
                 laid off were involved in human resources and writer
                 support. The report also says that Substack recently
                 halted efforts to secure funding from investors, but that
                 its revenue is still growing.


          o ⚓ The Nation ☛ Harlem_Renaissance!⠀⇛


          o § Education⠀➾


                # ⚓ [Old] Code Like A Girl ☛ 5_Things_Steve_Jobs_Taught_Me⠀⇛


                       I’m not here to defend him but it appeared to me
                       that he wasn’t necessarily looking to attack or
                       hurt his team (I could be wrong) but to stop them
                       from limiting themselves, to prevent them from
                       settling for less, to force them to push themselves
                       to think outside of the box, to “think
                       differently”.


                # ⚓ Pro Publica ☛ How_Idaho’s_Boise_State_University_Is_Bowing
                  to_a_Conservative_Ideological_Crusade⠀⇛


                       In August 2020, Boise State University chose a
                       doctoral student in public policy, Melanie
                       Fillmore, to deliver what is called a “land
                       acknowledgment” speech at a convocation for
                       incoming freshmen. Fillmore, who is part
                       Indigenous, would recognize the tribes that lived
                       in the Boise Valley before they were banished to
                       reservations to make way for white settlers.


                       Fillmore considered it an honor. She was devoted to
                       Boise State, where she had earned her bachelor’s
                       and master’s degrees, taught undergraduate courses
                       and served on job search committees. She also
                       admired Marlene Tromp, a feminist literary scholar
                       who came from the University of California, Santa
                       Cruz, in 2019 to become Boise State’s first female
                       president. Tromp had been hired with a mandate to
                       promote diversity, and including an Indigenous
                       speaker in the ceremony marking the start of
                       students’ higher education would advance that
                       agenda.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Hackaday_Prize_2022:_The_Baffatari_2600_Adds
                  Atari_Compatibility_To_Retrocomputers⠀⇛


                       Like today’s Intel-AMD duopoly, the market for home
                       computer CPUs in the 1970s and ’80s was dominated
                       by two players: Zilog with their Z80, and MOS
                       Technology with their 6502 processor. But unlike
                       today, even if two computers had the same CPU, it
                       didn’t mean the two were software compatible:
                       differences in memory layout, video interfaces, and
                       storage media meant that software developed for an
                       Atari 2600 wouldn’t run on an Apple I, despite the
                       two sharing the same basic CPU architecture.


                # ⚓ Hackaday ☛ Bare-Metal_STM32:_Adding_An_Analog_Touch_With
                  ADCs⠀⇛


                       An Analogue to Digital Converter (ADC) is at its
                       core a straight-forward device: by measuring an
                       analog voltage within a set range and converting
                       the measured level to a digital value we can use
                       this measurement value in our code. Through the use
                       of embedded ADCs in microcontrollers we can address
                       many essential use cases, ranging from measuring
                       the setting on a potentiometer, to reading an
                       analog output line on sensors, including the MCU’s
                       internal temperature and voltage sensors.


                # ⚓ Hackaday ☛ A_Home_Made_Laser_Cutter_For_$700⠀⇛


                       While some decent lasers are out there for under
                       $400 USD, they tend to be a little small. What if
                       you wanted something a little nicer but didn’t want
                       to jump to the $2,000 category? The answer for
                       [Owen Schafer] was to build it with parts he had
                       lying around and a few strategic purchases.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Counter Punch ☛ How_Polio_Shaped_My_Life⠀⇛


                       The number of new infections declined as herd
                       immunity was established, marking a turning point
                       in the effort to stop epidemic polio. The success
                       of this decades-long campaign was one of the
                       greatest US achievements in the 20th century. Not
                       that it did me any good at the time as I was
                       admitted to St Finbarr’s fever hospital in Cork
                       city on 30 September.


                       When I was released three months later, I was at
                       first confined to bed or was in a wheelchair and
                       learned to walk again with metal callipers on my
                       legs and wearing a plastic waistcoat to keep my
                       back straight. Though my mobility improved markedly
                       over the years, I could not run and have always
                       walked with a severe limp.


                # ⚓ Orac ☛ Peter_Doshi_vs._COVID-19_vaccines,_the_latest
                  round⠀⇛


                       From time to time, there are dubious studies that
                       pop up that I mean to discuss and, for whatever
                       reason, never get around to or, having failed to
                       discuss them in a timely fashion, decide that no
                       one cares any more and don’t come back to. On the
                       other hand, sometimes there are studies like what I
                       just described that keep bugging me, that keep
                       coming back in a niggling fashion in such a way
                       that eventually I just say, “WTF?” and discuss
                       them, even though I probably should have done so a
                       week or two ago. A new study by Peter Doshi and
                       colleagues that purports to be a reanalysis of the
                       adverse events data from the original phase 3
                       clinical trials of the Pfizer and Moderna mRNA-
                       based COVID-19 vaccines that the companies used to
                       gain Emergency Use Authorizations (EUAs) for their
                       products over a year and a half ago is one such
                       study, and last night I just gave in.


                # ⚓ Common Dreams ☛ Flint_Residents_‘Disgusted’_After_Court
                  Throws_Out_Indictments_of_Top_Officials⠀⇛


                       Flint residents expressed disappointment and
                       disgust after the Michigan Supreme Court on Tuesday
                       determined former state officials were not indicted
                       properly—yet again delaying accountability for the
                       city’s water crisis.


                       “No more excuses. No more delays.”


                # ⚓ Counter Punch ☛ “The_Famine_is_Coming”⠀⇛


          o § Proprietary⠀➾


                # ⚓ Daniel Miessler ☛ The_Cybersecurity_Skills_Gap_is_Another
                  Instance_of_Late-stage_Capitalism⠀⇛


                       I think what we’re facing is an instance of the
                       Two-Worlds Problem that’s now everywhere in US
                       society. It’s where the vast majority of people are
                       feeling pain from an issue, but there’s an elite
                       that lives in a reality where the problem doesn’t
                       exist.


                # ⚓ The Hill ☛ Norway_hit_with_cyberattack,_temporarily
                  suspending_service⠀⇛


                       Norway’s public and private sector websites were
                       temporarily down on Wednesday following a
                       cyberattack that targeted the country’s national
                       data network, forcing it to suspend online services
                       for several hours.


                # ⚓ Associated Press ☛ Cyberattack_hits_Norway,_pro-Russian_
                  [cracker]_group_fingered⠀⇛


                       The distributed-denial-of-service (DDOS) attack
                       targeted a secure national data network forcing the
                       temporary suspension of online services for several
                       hours, the Norwegian National Security Authority
                       said.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Earthly ☛ Programmatic_Multi_Factor_Auth_and_Time
                        Based_One_Time_Passwords⠀⇛


                             Now if I break another YubiKey, or brick my
                             phone, I can always generate codes using the
                             secret key, or easily re-add it to my new
                             phone. But also, now a new option is open for
                             me: I can programmatically generate the OTP
                             tokens.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Techdirt ☛ NSO_Lawyer_Tells_Lawmakers_Company_Can
                        Count_To_Five,_Will_Need_More_Time_To_Count_Higher_Than
                        That⠀⇛


                             Israeli phone malware manufacturer NSO Group
                             has plenty of customers. Or at least it did
                             until the Israeli government edited the
                             company’s list of approved customers and the
                             US government slapped sanctions on it.


                      # ⚓ Hollywood Reporter ☛ FCC_Commissioner_Calls_On_Apple,
                        Alphabet_to_Ban_TikTok⠀⇛


                             According to the Republican FCC commissioner,
                             TikTok violates policies dictating the app
                             stores of Apple and Google covering user
                             data. He cites Apple’s guidelines stating
                             that an app developer “must provide access to
                             information about how and where the data [of
                             an individual] will be used” and “data
                             collected from apps may only be shared with
                             third parties to improve the app or serve
                             advertising.” Of Google’s app store, Carr
                             argues that TikTok violated rules requiring
                             developers to disclose an app’s access,
                             collection, use and sharing of data.


                      # ⚓ Broadband Breakfast ☛ TikTok_Data_Concerns,_Broadband
                        Data_Collection_System,_Internet_Access_on_COVID-19
                        Mortality⠀⇛


                             The app is run by ByteDance, a company that
                             is “beholden to the Communist Party of China
                             and required by Chinese law to comply with
                             the PRC’s surveillance demands,” read the
                             June 24 letter to Apple CEO Tim Cook and
                             Google CEO Sunder Pichai.


                             “It is clear that TikTok poses an
                             unacceptable national security risk due to
                             its extensive data harvesting being combined
                             with Beijing’s apparently unchecked access to
                             that sensitive data,” said Carr, calling it a
                             wolf in sheep’s clothing. “At its core,
                             TikTok functions as a sophisticated
                             surveillance tool that harvests extensive
                             amounts of personal and sensitive data” such
                             as search histories, keystroke patterns and
                             biometric identifies.”


                      # ⚓ Tor ☛ Network_DDoS⠀⇛


                             This issue is not resolved yet


          o § Defence/Aggression⠀➾


                # ⚓ Scheerpost ☛ Foreign_Policy:_The_Warmonger’s_Game⠀⇛


                       Any honorable foreign policy dedicated to the
                       betterment of the human condition must begin by
                       wresting control of the policy process, from
                       inception to execution, away from the elites who
                       now control it.


                # ⚓ Counter Punch ☛ An_Open_Letter_to_Biden_on_Using_Okinawa_as
                  an_Attack_Base_Against_China⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Our_Life_Spaces_Have_Become
                  Danger_Zones:_Reflections_on_Gun_Violence_in_America⠀⇛


                       The spate of mass shootings we’ve witnessed over
                       the past few weeks has jolted our minds and broken
                       our hearts. The killings come in rapid-fire
                       sequence, leaving us hardly a pause to catch our
                       breath. In May alone, ten people at a Tops
                       supermarket in Buffalo, New York; nineteen children
                       and two teachers at an elementary school in Uvalde,
                       Texas; four at a hospital in Tulsa, Oklahoma; and
                       three at a church in Ames, Iowa. Over the first
                       weekend of June, a medley of gun deaths dotting the
                       country’s landscape. Mass shootings, it seems, have
                       become an American pastime.


                # ⚓ Common Dreams ☛ Opinion_|_We_Have_a_Smoking_Gun—Trump_Must
                  Be_Indicted_for_Sedition⠀⇛


                       Mitchell Zimmerman’s June 22, 2022 column explored
                       a similar theme. This newer column contains
                       significant new information.


                # ⚓ TruthOut ☛ Did_a_White_House_Aide_Just_Pierce_the_Seemingly
                  Impenetrable_Trump_Bubble?⠀⇛


                # ⚓ TruthOut ☛ Trump_Defended_“Hang_Mike_Pence”_Chants,_Witness
                  Cassidy_Hutchinson_Says⠀⇛


                # ⚓ TruthOut ☛ Cheney_Alleges_Trump_Allies_Are_Intimidating
                  Some_Jan._6_Committee_Witnesses⠀⇛


                # ⚓ Counter Punch ☛ Brace_for_Impact⠀⇛


                       No one who watched, listened to, or read about the
                       Jan. 6 committee’s most recent hearing could
                       possibly believe Trump’s big lie of a stolen
                       election for one second. The Attorney General,
                       acting Attorney General, and the entire top echelon
                       of the U.S. Department of Justice did their jobs,
                       investigated the potential for voter fraud across
                       the nation and came to a unanimous agreement on one
                       thing — there was no evidence of any actions by any
                       individuals in any state, county, or municipality
                       that could possibly affect the reality that Donald
                       Trump simply lost his re-election bid.


                       Despite threats of physical violence — including
                       intrusions into the homes of voting election
                       officials — the witnesses at the hearing bravely
                       told the nation that they stood their ground,
                       followed the law, and did their jobs. Hardcore
                       Republican conservatives — who admitted they wanted
                       Trump to win — testified that they could not and
                       would not break their oaths to uphold the
                       constitution to cast doubt on the integrity of the
                       American election system for Donald Trump. Even
                       when threatened with dismissal and replacement they
                       refused to claim there was a shred of truth in
                       Trump’s Big Lie — despite his demand that they
                       “just say that the election was corrupt and leave
                       the rest to me and the Republican congressmen.”


                # ⚓ The Nation ☛ Mark_Meadows_Is_the_Biggest_January_6_Coward.
                  Also,_Perhaps,_a_Criminal.⠀⇛


                       As my friend and colleague John Nichols wrote right
                       after Tuesday’s shattering January 6 Committee
                       testimony, Donald Trump assaulted his security
                       detail as he was trying to illegally hold on to the
                       presidency. Trump said, “I’m the fucking president.
                       Take me up to the Capitol now!” when he was told he
                       could not personally lead the insurrectionists into
                       the seat of government. Trump then attempted to
                       grab the steering wheel of the presidential
                       limousine and, when he was stopped by Bobby Engel,
                       the leader of his Secret Service detail, Trump
                       tried to strangle Engel.


                # ⚓ Common Dreams ☛ Jan._6_Panel_Subpoenas_Trump_White_House
                  Counsel_Pat_Cipollone⠀⇛


                       A day after a key witness dropped “bombshell after
                       bombshell” during a surprise hearing of the panel
                       probing last year’s insurrection at the U.S.
                       Capitol, the committee on Wednesday subpoenaed
                       former White House Counsel Pasquale “Pat” Cipollone
                       for “on-the-record testimony.”


                       Cassidy Hutchinson—an ex-special assistant to Mark
                       Meadows, former President Donald Trump’s last chief
                       of staff—testified Tuesday that Cipollone urged her
                       to prevent Trump from joining a violent mob of his
                       supporters at the Capitol on January 6, 2021.


                # ⚓ Democracy Now ☛ After_Jan._6,_Meadows_&_Giuliani_Sought
                  Pardons;_Cheney_Says_Trump_Allies_Tampering_with_Witnesses⠀⇛


                       Former aide to White House Chief of Staff Mark
                       Meadows, Cassidy Hutchinson, revealed Tuesday to
                       the House January 6 committee that Meadows and
                       Trump lawyer Rudy Giuliani both sought pardons
                       after the insurrection. Meanwhile, in a video
                       deposition with Trump’s former national security
                       adviser Mike Flynn, who supported Trump’s efforts
                       to overturn the election, Flynn repeatedly refused
                       to answer questions from committee Vice Chair Liz
                       Cheney. Cheney concluded the hearing by presenting
                       evidence of possible witness tampering by allies of
                       Trump.


                # ⚓ Meduza ☛ ‘Your_compatriots_are_real_terrorists’_Shura
                  Burtin_reports_from_Kremenchuk_in_the_aftermath_of_the
                  shopping_mall_missile_strike⠀⇛


                       A Russian missile strike hit the Amstor shopping
                       center in Kremenchuk, Ukraine, late in the
                       afternoon on Monday, June 27. According to the
                       latest reports, the attack killed up to 20 people
                       and injured 59 others; at least 21 people are still
                       missing. Ukrainian Interior Minister Denys
                       Monastyrsky said on Wednesday that rescue workers
                       are still recovering body parts from the wreckage,
                       but there is no longer any hope of finding
                       survivors. Journalist Shura Burtin, who is
                       reporting for Meduza from Ukraine, traveled to
                       Kremenchuk on Monday to cover the immediate
                       aftermath of the strike. Here’s what he saw.


                # ⚓ The Economist ☛ Donald_Trump’s_shameful_role_in_the
                  storming_of_the_Capitol⠀⇛


                       Members of the president’s cabinet were so
                       disgusted with his actions that they seriously
                       contemplated invoking the 25th Amendment, which
                       would have removed the president from power. The
                       next day, Mr Trump had to be dissuaded from
                       mentioning the possibility of pardons for those who
                       had taken part in the attempted insurrection. Mr
                       Meadows and Rudy Giuliani, the president’s lawyer
                       (who filed frivolous lawsuits about voter fraud and
                       put pressure on state legislators to decertify
                       lawful election results), would later both seek
                       presidential pardons.


                # ⚓ Taipei Times ☛ China_destroys_education_in_Tibet⠀⇛


                       An April circular by the Chinese Ministry of
                       Education on student admission criteria at Tibetan
                       universities has been harrowing and discriminating
                       to say the least.


                       The circular said that prospective students must
                       state their “political attitude and ideological
                       morality” to be considered for admission.


                       It also said that students should not be involved
                       in religious movements and students who are
                       proficient in Marxist theory should be preferred.


                       Since Beijing started occupying Tibet, it has
                       meticulously introduced policies to dismantle the
                       Tibetan education system, which is closely tied to
                       its rich monastic tradition, and has even pulled
                       students from Afghanistan and eastern Europe to
                       Tibet.


                # ⚓ Tibet ☛ Chinese_government_to_force_more_than_100,000
                  Tibetans_out_of_their_homes⠀⇛


                       While Chinese-state propaganda says the reason for
                       the move is to get the people away from “harsh
                       weather and relatively backward production and
                       living conditions”, the real consequences would be
                       the end of the traditional Tibetan way of life.
                       Farmers and nomads have made a sustainable way of
                       life high on the Tibetan plateau for centuries and
                       those being relocated are often not given an
                       opportunity to stay or even given full information
                       about what will happen to them as they are forced
                       into a completely alien way of life.


                # ⚓ The Baltic Times ☛ Lithuania_fixing_cybersecurity_gaps,_not
                  surprised_by_Russia’s_hostile_rhetoric_–_PM⠀⇛


                       Lithuania’s National Cyber Security Centre said on
                       Monday afternoon that the most serious incidents
                       had been brought under control, but warned that
                       attacks might continue.


                # ⚓ The Washington Post ☛ Cassidy_Hutchinson_could_read_the
                  ketchup_on_the_wall⠀⇛


                       Contrast that with the cowardice of retired Gen.
                       Michael Flynn, one of the insurrection schemers,
                       whose testimony the committee aired, to chuckles:


                       “Do you believe the violence on January 6 was
                       justified morally?”


                       “Take the Fifth.”


                       “Do you believe the violence on January 6th was
                       justified legally?”


                       “Fifth.”


                       “Do you believe in the peaceful transition of
                       power?


                       “The Fifth.”


                # ⚓ Salon ☛ Melania_Trump_gave_a_one-word_response_to_the
                  option_of_promoting_peace_on_Jan._6⠀⇛


                       According to ex-aide Stephanie Grisham, she
                       personally sent a text to Melania on Jan. 6 asking
                       “Do you want to tweet that peaceful protests are
                       the right of every American, but there is no place
                       for lawlessness & violence?”


                       Melania’s response was a simple “No.”


                # ⚓ Scheerpost ☛ NATO_and_a_War_Foretold⠀⇛


                       Instead of exploiting this crisis to expand even
                       further, NATO should suspend all new or pending
                       membership applications until the current crisis
                       has been resolved.


                # ⚓ Counter Punch ☛ NATO_and_a_War_Foretold⠀⇛


                       Stoltenberg could have looked all the way back to
                       when the U.S.S.R. was dissolving, and highlighted a
                       1990 State Department memo warning that creating an
                       “anti-Soviet coalition” of NATO countries along the
                       U.S.S.R’s border “would be perceived very
                       negatively by the Soviets.”


                       Stoltenberg could have reflected on the
                       consequences of all the broken promises by Western
                       officials that NATO would not expand eastward.
                       Secretary of State James Baker’s famous assurance
                       to Soviet President Gorbachev was just one example.
                       Declassified U.S., Soviet, German, British and
                       French documents posted by the National Security
                       Archive reveal multiple assurances by Western
                       leaders to Gorbachev and other Soviet officials
                       throughout the process of German unification in
                       1990 and 1991.


                # ⚓ Scheerpost ☛ Growing_Hope_for_Humanity:_65_Countries_in
                  Vienna_Say_No_to_Atomic_Weapons_in_TPNW_Declaration⠀⇛


                       In Vienna, a total of 65 countries with many others
                       as observers and a large number of civil
                       organisations…


                # ⚓ Scheerpost ☛ Turkey_Lifts_Objection_to_Sweden,_Finland
                  Joining_NATO⠀⇛


                       Sweden and Finland agreed not to support Kurdish
                       militant groups and to lift export controls on
                       Turkey.


                # ⚓ The Nation ☛ How_Will_the_War_in_Ukraine_End?⠀⇛


                       When Russia invaded Ukraine on February 24, I was
                       easing my way into a new job and in the throes of
                       the teaching year. But that war quickly hijacked my
                       life. I spend most of my day poring over multiple
                       newspapers, magazines, blogs, and the Twitter feeds
                       of various military mavens, a few of whom have been
                       catapulted by the war from obscurity to a modicum
                       of fame. Then there are all those websites to check
                       out, their color-coded maps and daily summaries
                       catching that conflict’s rapid twists and turns.


                # ⚓ Scheerpost ☛ The_Angry_Arab:_Iran_Losing_Info_War⠀⇛


                       The repercussions of the open sectarian war sparked
                       by the U.S. invasion of Iraq can still be felt
                       throughout the region, says As`ad AbuKhalil, partly
                       because of Iran’s inaction.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Project Censored ☛ Whistleblowers_–_The_Project_Censored
                  Show⠀⇛


          o § Environment⠀➾


                # ⚓ Pro Publica ☛ Congress_Investigates_Portable_Generator
                  Manufacturers_Following_Carbon_Monoxide_Deaths⠀⇛


                       A congressional committee is investigating whether
                       portable generator manufacturers have done enough
                       to protect the public from deadly levels of carbon
                       monoxide emitted by their products.


                       Rep. Carolyn B. Maloney, D-N.Y., who leads the
                       House Committee on Oversight and Reform, sent
                       letters to top executives at four major generator
                       companies on Tuesday requesting copies of records
                       documenting why they have not implemented
                       potentially lifesaving safety upgrades in many
                       generator models for sale. Maloney also asked for
                       messages sent or received by officials at the
                       companies — Generac Power Systems, DuroMax Power
                       Equipment, Firman Power Equipment and Champion
                       Power Equipment — related to any injuries or deaths
                       connected to their products.


                # ⚓ Counter Punch ☛ Incident_at_Santa_Susana:_A_Meltdown,_a
                  Fire_and_a_Cover-Up⠀⇛


                       Just about the time that this half-century-long
                       campaign to enshrine the right to a safe
                       environment kicked off, a story about the horrific
                       violation of this same human right and its cover-up
                       emerged in a community near my own childhood home
                       in Southern California. In 1979, a UCLA student
                       named Michael Rose uncovered evidence of a partial
                       nuclear meltdown at the Santa Susana Field Lab
                       (SSFL) in the Simi Hills outside of Los Angeles.
                       The SSFL, formerly known as Rocketdyne, played key
                       government roles throughout the Cold War,
                       developing and testing rocket engines and
                       conducting experiments with nuclear reactors.
                       Today, as the result of a recently published peer-
                       reviewed study that represents the dogged efforts
                       of both professional researchers and a team of
                       specially trained citizens, we have solid evidence
                       of the spread of dangerous contamination from that
                       site.


                       Working with nuclear safety expert and then-UCLA
                       professor Daniel Hirsch, Rose discovered
                       documentation that the partial nuclear meltdown had
                       occurred at SSFL twenty years earlier in 1959,
                       releasing up to 459 times more radiation into the
                       environment than the infamous meltdown at the Three
                       Mile Island nuclear reactor in Pennsylvania. Unlike
                       the Three Mile Island facility, the SSFL reactors
                       lacked containment structures—those tell-tale
                       concrete domes that surround commercial nuclear
                       power plants to prevent radiation spread in case of
                       a nuclear accident.


                # § Energy⠀➾


                      # ⚓ Counter Punch ☛ OPEC_Plus’s_Accelerated_Oil
                        Production_Pales_in_Comparison_to_Lost_Output_from_US
                        Sanctions⠀⇛


                             Higher energy prices are a significant
                             political problem for US president Joe Biden
                             and many other world leaders, who face
                             strikes and protests. One way world leaders
                             might seek to lower prices is work to
                             increase the global supply of oil. Biden
                             especially has a significant opportunity in
                             his hands to boost global production by
                             breaking with Trump’s failed “maximum
                             pressure” campaigns, and ending unilateral —
                             and likely illegal — sanctions against Iran
                             and Venezuela. These potential increases in
                             oil production amount to about 2.6 million
                             extra barrels per day, which dwarfs increases
                             Biden is likely to get directly from the
                             Organization of the Petroleum Exporting
                             Countries (OPEC), the cartel that coordinates
                             oil production in many countries.


                             To show the potential benefits of abandoning
                             the Trump administration’s failed policies
                             toward Venezuela and Iran, it is useful to
                             compare their potential oil production to
                             that from OPEC Plus, an expanded and loosely
                             organized group of oil-producing countries.
                             Biden, along with other world leaders, have
                             been extensively lobbying OPEC Plus to
                             increase production. A recent announcement
                             from the group included an agreement to
                             accelerate planned increases in oil
                             production for July and August. For these
                             months, the total production increase will
                             now be 648,000 barrels per day — but this
                             does not represent a new commitment to
                             increase total supply. Rather, increases
                             scheduled for over three months have been
                             condensed into two months, meaning that
                             production levels in July and August will be
                             about 200,000 barrels above what they would
                             have been. The increase represents 0.4
                             percent of global demand for these months.


                      # ⚓ Common Dreams ☛ ‘Flies_in_the_Face_of_Science’:_Biden
                        Sued_for_Restarting_Oil_Leasing_on_Public_Lands⠀⇛


                             Several environmental groups sued the Biden
                             administration on Tuesday for resuming oil
                             and gas leasing on public lands despite ample
                             evidence that doing so will exacerbate the
                             fossil fuel-driven climate crisis.


                             “Our climate can’t afford any new fossil fuel
                             developments.”


                      # ⚓ Hackaday ☛ Gym_Equipment_Converted_To_Generator⠀⇛


                             Energy cannot be created or destroyed, but
                             the most likely eventual conclusion of
                             changing it from one form or another will be
                             relatively useless heat. For those that
                             workout with certain gym equipment, the
                             change from chemical energy to heat is direct
                             and completely wasted for anything other than
                             keeping in shape. [Oliver] wanted to add a
                             step in the middle to recover some of this
                             energy, though, and built some gym equipment
                             with a built-in generator.


                      # ⚓ The Revelator ☛ Regulators_Have_a_Big_Chance_to
                        Advance_Energy_Equity⠀⇛


                      # ⚓ DeSmog ☛ Will_Reforms_to_Carbon_Markets_Better
                        Protect_the_Climate?⠀⇛


                             To advocates, scaling up the markets where
                             companies go to offset their greenhouse gas
                             emissions will unlock billions of dollars to
                             plant forests, restore ecosystems, and spur a
                             global roll-out of machines to scrub carbon
                             dioxide (CO2) from the sky. 


                             To critics, a long history of failed projects
                             suggests that the chief beneficiary may not
                             be the climate — but the bankers and brokers
                             betting that carbon trading is on the cusp of
                             exponential growth. 


                      # ⚓ Copenhagen Post ☛ EU_climate_ministers_agree_to_halt
                        sale_of_fossil-fuel_cars_in_2035⠀⇛


                             Ultimately, the climate ministers hope their
                             proposed package of laws will help the EU
                             meet its target of a 55 percent greenhouse
                             gas emissions reduction by 2030.


                      # ⚓ Malaysia ☛ 25_km/h_limit_for_micro-mobility_vehicles
                        in_Malaysia?⠀⇛


                             Plans are being made to adapt micro-mobility
                             vehicles to suit existing laws and
                             regulations under the aegis of local
                             governments and the Road Transport Department
                             (JPJ). Upon finalisation, the plan will be
                             forwarded to the Housing and Local Government
                             Ministry (KPKT) as well as the MOT.


                             Such micro-mobility devices are currently
                             banned from use on Malaysian public roads,
                             gazetted under the Road Traffic (Prohibition
                             of Use of Certain Microbility Vehicles) Rules
                             2021 and in effect since December 17, 2021.
                             The ban covers mopeds, personal mobility aids
                             (i.e. motorised wheelchairs, mobility
                             scooters) and personal mobility devices (i.e.
                             e-scooters, hoverboards, skateboards, kick
                             scooters).


                      # ⚓ DeSmog ☛ Industry_Insiders_Question_Louisiana
                        Regulators_Over_Cleanup_on_ExxonMobil_Land,_Amid
                        Corruption_Claims_and_Pollution_Fears⠀⇛


                             If you had ventured down a dirt road running
                             through remote marshland along the Gulf Coast
                             in Vermilion Parish, Louisiana, at just the
                             right time back in late February, you might
                             have come across a pit of gray muck. Down in
                             that pit, you’d find a contractor welding a
                             steel cap about the size of a dinner plate
                             onto a stub of pipe jutting up from the mud
                             below. 


                             That pipe was the last visible sign of an old
                             oil and gas wastewater well that once dropped
                             over a half-mile deep into the earth, now
                             plugged up and sealed by contractors hired by
                             the state.


                # § Wildlife/Nature⠀➾


                      # ⚓ Counter Punch ☛ Does_the_Amazon_Now_Have_a_Shot_at
                        Survival?⠀⇛


          o § Finance⠀➾


                # ⚓ The Nation ☛ Food_Prices_Are_Up._A_“Bean_New_Deal”_May_Be
                  the_Answer.⠀⇛


                # ⚓ TruthOut ☛ With_Food_Prices_Up,_a_“Bean_New_Deal”_May_Be
                  Part_of_the_Answer⠀⇛


                # ⚓ Scheerpost ☛ VIDEO:_Ask_Prof_Wolff:_What_the_NYTimes_Gets
                  Wrong_About_Inflation⠀⇛


                # ⚓ Scheerpost ☛ Thousands_Protest_Against_G7_Summit_in
                  Germany⠀⇛


                       The leaders of the seven most powerful imperialist
                       countries are meeting in the Alps. These seven men
                       stand for environmental destruction and militarism
                       like no one else. That’s why protests were g…


                # ⚓ Counter Punch ☛ The_Great_White_West_Aims_to_Crush_the
                  Slavs_and_Chinese⠀⇛


                       It truly is astonishing to watch the G-7 and NATO
                       summits which are theaters of the absurd; meetings
                       of rouge bandits laughing away while their policies
                       lead to death and destruction on a global scale.
                       Highway robbery does not describe adequately what
                       the US-Europe have done with Russian foreign assets
                       or those of other nations (Iran, Venezuela,
                       Afghanistan) at the receiving end of the US
                       sanctions regime. Further, as the United States and
                       its NATO puppets continue to punish Russia for its
                       military activities in Ukraine, the end result of
                       the deadly gambit is to send to the slaughter more
                       Ukrainians as Russia methodically moves to liberate
                       Luhansk and Donetsk, and fortify its gains in the
                       south of Ukraine.


                       Arsenal of Stupidity


                # ⚓ Counter Punch ☛ G7_and_the_Desperation_Stage_of_Russian
                  Sanctions⠀⇛


                       Like most of the previous six phases of sanctions
                       the purpose of the latest is to deprive Russia of
                       revenues from exports. So far sanctions haven’t
                       been all that successful in that regard, at least
                       in the shorter term. While the USA has banned
                       Russian oil and gas imports to the USA, those
                       amounts and their respective revenue impact on
                       total Russian export revenue is insignificant.
                       Moreover, the ban on Russian oil exports to Europe
                       do not begin until December 2022, while there’s no
                       ban on Russian natural gas imports whatsoever. So
                       little net impact on Russian energy export revenues
                       from Europe either.


                       The sanctions on oil & gas Russian exports to
                       Europe have been quite minimal to date. Meanwhile,
                       Russia’s exports to China, India and rest of the
                       world have been rising. As have global energy
                       prices in general.  With accelerating global prices
                       for oil and gas, and an increase in Russian energy
                       exports to India, China and elsewhere, Russia’s
                       revenues have been actually rising.


                # ⚓ Common Dreams ☛ Sanders,_Fetterman_Urge_Buttigieg_to_Fine
                  Airlines_Over_Flight_Cancellations⠀⇛


                       Sen. Bernie Sanders and Democratic U.S. Senate
                       candidate John Fetterman on Wednesday urged the
                       Department of Transportation to levy hefty fines
                       against airlines that schedule flights they’re
                       unable to adequately staff, causing the kinds of
                       mass cancellations that have thrown travelers into
                       chaos in recent months.


                       “Government has a responsibility to hold these
                       airlines accountable.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_Are_Democrats_Really_Clueless
                  About_Impending_Election_Doom?⠀⇛


                       Armageddon comes November 8. Pundits and
                       progressives have been warning Democrats for months
                       that if they don’t change course and achieve
                       significant legislation promised in 2020, they will
                       go down in flames on election day, along with our
                       democracy. The tone of these warnings is imbued
                       with the implication that the party, and especially
                       President Biden, either doesn’t believe this or
                       that it is flummoxed on how to avoid the calamity.
                       But is this case?


                # ⚓ Counter Punch ☛ Maybe_It_Is_The_Right’s_Fault⠀⇛


                       —Kendrick Lamar, N95


                       Beware of those saying Putin is a communist. Beware
                       of those saying Putin is fighting Nazis. Beware of
                       those cancelling Amber Heard. Beware of those
                       telling you they are cancelled when you give them a
                       monthly subscription. There is some very spooky
                       shit going on. Socially distance for clarity when
                       necessary. Socially distance for health when
                       necessary. Thank your friends. Thank your enemies
                       but only on the inside.


                # ⚓ Meduza ☛ Going_home_—_to_Europe_Georgians_are_calling_for
                  their_government_to_resign_after_it_failed_to_receive_EU
                  candidate_status._Meduza_reports_from_Tbilisi⠀⇛


                       In mid-June, the European Commission voted against
                       recommending that Georgia receive EU candidate
                       status, recommending instead that it be granted the
                       “European perspective.” Now, if Georgia wants to
                       join the EU, it will have to take specific steps
                       that, according to the EU, will strengthen its
                       democracy. After the announcement, protesters from
                       Georgia’s Sirtskhvilia (“Shame”) movement led
                       thousands of people in a rally they called Going
                       Home — to Europe. Another rally followed the
                       European Parliament’s official refusal to grant the
                       country EU status. That time, the protesters
                       demanded the resignation of the government — and
                       gave them an ultimatum.


                # ⚓ Craig Murray ☛ Don’t_Look_Back_in_Anger⠀⇛


                       The new bid for Scottish Independence is started.
                       It does not matter how each of us got here, who had
                       which idea first, what might be a better plan, who
                       stabbed who in the back. It is gone. Let it be.


                # ⚓ Democracy Now ☛ Jan._6_Witness_Says_Trump_Was_Warned_of
                  Potential_Violence,_Didn’t_Care:_“They’re_Not_Here_to_Hurt
                  Me”⠀⇛


                       In explosive testimony Tuesday, Cassidy Hutchinson,
                       former aide to White House Chief of Staff Mark
                       Meadows, revealed new details to the January 6
                       select committee about the events leading up to the
                       “Stop the Steal” rally. She indicated then-
                       President Donald Trump and his inner circle, that
                       included personal lawyer Rudy Giuliani, expected
                       the event to grow violent and did little to stop
                       it. Hutchinson described how Trump demanded that
                       the Secret Service allow his supporters wielding
                       weapons to enter the Ellipse in order to make his
                       rally seem better attended. “They’re not here to
                       hurt me,” Trump said in dismissing safety concerns,
                       Hutchinson testified. We feature her extended
                       remarks.


                # ⚓ Democracy Now ☛ “Hang_Mike_Pence!”_As_Armed_Mob_Threatens
                  VP_on_Jan._6,_Witness_Says_Trump_“Thinks_Mike_Deserves_It”⠀⇛


                       Minutes after rioters stormed the Capitol on
                       January 6, 2021, White House Chief of Staff Mark
                       Meadows seemed unperturbed and reluctant to act,
                       according to live testimony from his former aide,
                       Cassidy Hutchinson, at the public hearing on
                       Tuesday. Then-President Donald Trump, rather than
                       calling off his supporters, defended their chants
                       to hang Vice President Mike Pence for validating
                       the election results. “I remember thinking in that
                       moment, Mark needs to snap out of this,” recalled
                       Hutchinson. “I don’t know how to snap him out of
                       this, but he needs to care.” Hutchinson also notes
                       Meadows and Rudy Giuliani both sought pardons after
                       the insurrection. Committee Vice Chair Liz Cheney
                       presented evidence of possible witness tampering by
                       allies of Trump. Meanwhile, in a video deposition
                       with Trump’s former national security adviser Mike
                       Flynn, who supported Trump’s efforts to overturn
                       the election, Flynn repeatedly refused to answer
                       questions from Cheney.


                # ⚓ Democracy Now ☛ Jan._6_Bombshell:_Trump_Physically_Attacked
                  Secret_Service_Agent,_Demanded_to_Join_Mob_at_Capitol⠀⇛


                       In one of the most dramatic revelations at
                       Tuesday’s hearing of the House committee
                       investigating the January 6 attack, star witness
                       Cassidy Hutchinson described how then-President
                       Trump intended to join his supporters in the march
                       to the Capitol and lunged at his Secret Service
                       agent, who tried to prevent him from doing so, and
                       grabbed the steering wheel of the presidential
                       limousine, before he was driven back to the White
                       House. Hutchinson was aide to White House Chief of
                       Staff Mark Meadows at the time. She also describes
                       another temper tantrum by the president weeks
                       earlier, after Attorney General Bill Barr said
                       publicly there was no election fraud, saying Trump
                       threw a plate of food, leaving “ketchup dripping
                       down the wall.”


                # ⚓ TruthOut ☛ Progressive_Delia_Ramirez_Wins_Illinois_Primary,
                  Defeating_Billionaire_PAC_Money⠀⇛


                # ⚓ Common Dreams ☛ Progressive_Delia_Ramirez_Defeats
                  Billionaire_PAC_Money_to_Win_Illinois_Primary⠀⇛


                       State Rep. Delia Ramirez trounced Chicago Alderman
                       Gil Villegas in the Democratic primary for
                       Illinois’ newly drawn and solidly blue 3rd
                       Congressional District, besting an influx of
                       spending by billionaire-backed organizations
                       working to defeat progressive candidates
                       nationwide.


                       “Tonight, the Illinois 3rd Congressional District
                       has spoken—we are rooted and we are ready,” Ramirez
                       said after she was officially declared the winner.
                       As of this writing, Ramirez leads Villegas by a
                       margin of 65.8% to 23.7%.


                # ⚓ Common Dreams ☛ Opinion_|_Uncertainty_and_Hope_Set_the
                  Stage_for_Colombia’s_Future_Leftist_Government⠀⇛


                       A former leftwing guerrilla—Gustavo Petro—has been
                       elected to Colombia’s highest office.  


                # ⚓ Counter Punch ☛ Petro’s_Victory_Brings_an_Opportunity_to
                  Reverse_Inequality_in_Colombia⠀⇛


                       One does not need to look very far into the past to
                       find evidence of collective targeting of known
                       political detractors. For example, over 4,000
                       activists, leaders, and presidential candidates of
                       the first openly leftist and oppositional party,
                       Unión Patriótica, were systematically assassinated
                       after achieving some initial electoral success at
                       the local and regional level in the mid-1980s.
                       Supporters, too, were targeted. Civilians were
                       forcibly displaced or killed by illegal armed
                       groups with the explicit goal of violently
                       reorganizing districts and municipalities to deny
                       Unión Patriótica a local or regional base of
                       support. Traditional political elites and their
                       wealthy patrons made it clear that alternative
                       political projects grounded in social justice were
                       not to be tolerated even in a competitive
                       democracy.


                       And while the threat of political violence has not
                       ceased, analyst and current Colombian Senator Ariel
                       Ávila recently remarked that the struggle to create
                       a political space for the excluded and marginalized
                       has resulted in the ascendancy of Petro and
                       Márquez. As an Afro-Colombian environmental
                       activist, Márquez and her connections to grassroots
                       social movements increased Afro-Colombian and
                       indigenous voter participation in the Pacific
                       region of the country, ensuring a strong base of
                       support for an egalitarian political program, that
                       guaranteed their victory.


                # ⚓ Common Dreams ☛ In_Blow_to_Voting_Rights,_SCOTUS_Saves
                  Louisiana’s_Racially_Rigged_Electoral_Map⠀⇛


                       Civil rights advocates on Tuesday decried the U.S.
                       Supreme Court’s reinstatement of Louisiana’s
                       Republican-drawn congressional map, which a federal
                       judge said will cause “irreparable harm” to Black
                       voters in the 2022 midterm elections and likely
                       violates the Voting Rights Act.


                       “We won’t stop fighting in court until Louisiana
                       has a fair congressional map.”


                # ⚓ Common Dreams ☛ ‘Lunacy’:_Democrats_Risk_Running_Out_of
                  Time_to_Confirm_Federal_Judges⠀⇛


                       Warning that U.S. President Joe Biden may lose his
                       chance to confirm more circuit and district court
                       nominees after the midterm elections if Republicans
                       win a Senate majority, legal scholars are calling
                       on Democratic lawmakers to immediately ramp up
                       confirmations of federal judges.


                       “It’s lunacy not to fill [judicial seats]
                       immediately and by any means necessary.”


                # ⚓ Common Dreams ☛ Sanders_Pushes_Back_Against_AIPAC_Super_PAC
                  With_Endorsements_of_Tlaib_and_Levin⠀⇛


                       U.S. Sen. Bernie Sanders on Wednesday endorsed a
                       pair of House Democrats in their primaries against
                       challengers backed by the nation’s most powerful
                       pro-Israel lobby—which is spending heavily to
                       defeat progressive candidates who advocate for
                       Palestinian rights.


                       Sanders (I-Vt.) endorsed Reps. Rashida Tlaib and
                       Andy Levin, both of Michigan, tweeting that the
                       former “has taken on powerful special interests and
                       fought for working people” while the latter “is a
                       strong labor voice” who is “taking on right-wing-
                       funded super PACs.” 


                # § Misinformation/Disinformation⠀➾


                      # ⚓ Rolling Stone ☛ Herbal_Abortions_Are_Going_Viral_on
                        TikTok._They_Could_Kill_You⠀⇛


                             Such herbs have become the focal point of a
                             new wave of discourse on TikTok focusing on
                             herbs that can induce abortion. In the wake
                             of Roe v. Wade being overturned last Friday —
                             prompting an onslaught of terror and protests
                             from reproductive rights advocates across the
                             country — people on social media are taking
                             matters into their own hands by offering
                             grassroots solutions to those seeking
                             abortions. Some of these solutions, such as a
                             TikTok trend set to the Chainsmokers’
                             “Paris,” with women in blue states offering
                             to help people in red states procure
                             abortions, have been helpful; yet medical
                             experts are concerned about the growing trend
                             of TikTok creators promoting these herbal
                             abortifacients — some of which can also have
                             devastating health effects.


                      # ⚓ Teen Vogue ☛ Social_Media_Influencers_Get_Media
                        Attention_on_Climate_Change_—_Grassroots_Activists
                        Don’t⠀⇛


                             However, social media is structured in a way
                             that encourages one’s interactions with an
                             issue to awareness alone. It is designed to
                             encourage users to spend hours scrolling
                             through automated feeds. Users can like a
                             single post from an eco-influencer and feel
                             the gratification of having taken a stand
                             against climate change, then move on to
                             watching cat videos.


          o § Censorship/Free Speech⠀➾


                # ⚓ NBC ☛ What_Facebook_and_Instagram’s_restricting_abortion
                  pills_posts_so_fast_should_tell_us⠀⇛


                       And the ease with which Meta seems to have simply
                       flipped a switch to block information about
                       abortion pills reminds us that the company can
                       effectively cut off access to harmful postings if
                       it wants to — like, for example, expressions of
                       hate. Over 40% of Americans have been victims of
                       online harassment, according to a 2021 Pew Research
                       survey. So what seems to be missing here is the
                       will to better protect users from abuse. (Meta, for
                       its part, claims to work hard to remove such
                       content.)


                # ⚓ Techdirt ☛ Facebook_Bans_People_For_Simply_Saying_Abortion
                  Pills_Exist⠀⇛


                       On the one hand, content moderation at the scale
                       modern social media companies operate at is an
                       impossible nightmare. Companies are always going to
                       lack the staff and resources to do it well (raising
                       questions about the dangers of automation at
                       scale), and they’re always going to screw things up
                       for reasons well discussed.


                # ⚓ Tibet ☛ China_jails_Tibetan_university_student_for_contact
                  with_exile_fellows⠀⇛


                       “He could be seen sharing Tibet’s history and
                       authentic Tibetan culture with the tourists, so I
                       think that may be the reason for his arrest. His
                       family has no idea where he is imprisoned at the
                       moment,” the source has said, requesting anonymity
                       for safety reasons.


                       His persecution is seen as arbitrary and in keeping
                       with China’s ongoing crackdown on intellectuals,
                       artists, critics, and activists who are seen as
                       antithetical to President Xi Jinping’s sweeping
                       Sinicization drive being implemented across the
                       Tibetan Plateau.


          o § Freedom of Information / Freedom of the Press⠀➾


                # ⚓ Techdirt ☛ Clarence_Thomas_REALLY_Wants_To_Make_It_Easier
                  For_The_Powerful_To_Sue_People_For_Criticizing_Them⠀⇛


                       As we’ve discussed before, Supreme Court Justice
                       Clarence Thomas really does not like the “actual
                       malice” standard required to make a defamation
                       claim against a public figure, as laid out in the
                       extremely important NY Times v. Sullivan case. The
                       actual malice standard confuses many people,
                       because it’s not actually about malice. The
                       standard is that for there to be defamation of a
                       public figure, it needs to be expressed while the
                       speaker knows that the claims are false, or with
                       “reckless disregard” for whether it’s true. And
                       even the “reckless disregard” part is often
                       misunderstood. It’s a much higher bar than simply
                       being negligent. It means that that the speaker had
                       serious doubts at the time of expression that the
                       speech was false.


                # ⚓ TruthOut ☛ Petition_Calling_for_Impeachment_of_Clarence
                  Thomas_Nears_500,000_Signatures⠀⇛


                # ⚓ Counter Punch ☛ Damning_Americans’_Freedom⠀⇛


                       Bottom line: You cannot trust its future rulings to
                       be based on neutrality. Respect for it, chiefly
                       among the most vulnerable and who conservatives
                       sneeringly describe as “libs,” has vanished.


                       The court has been slip-sliding in the direction of
                       extremist Republican conservatism since its opening
                       in October with a new 6-3 right-wing majority,
                       three of the six appointed by Trump, the
                       disgraceful and disgraced nemesis of most
                       Americans.


                # ⚓ RTL ☛ Journalist_murdered_in_Mexico,_12th_this_year⠀⇛


                       A Mexican reporter was shot dead on Wednesday in
                       the violence-plagued northeastern state of
                       Tamaulipas — the 12th journalist killed so far in a
                       particularly bloody year for the country’s press.


                # ⚓ FAIR ☛ Depp/Heard_Verdict_a_Loss_for_Violence_Survivors—and
                  a_Free_Press⠀⇛


                       The high-profile Johnny Depp/Amber Heard defamation
                       trial ended with what seemed like a split decision:
                       Both were found to have defamed each other. But
                       with the jury awarding millions more in damages to
                       Depp than to Heard, the outcome suggests that she
                       defamed him more. The chilling effect of the ruling
                       on survivors of domestic violence who want to speak
                       out against their abusers is clear, but the damage
                       from the case extends to all issues that depend on
                       unfettered discussion in a free press.


                # ⚓ EFF ☛ The_Journalism_Competition_and_Preservation_Act_Will
                  Produce_Neither_Competition_Nor_Preservation⠀⇛


                       The way the JCPA is supposed to work is by giving
                       an antitrust exemption to news sites, allowing them
                       to negotiate as a bloc with sites like Google and
                       Facebook, with the goal of getting paid every time
                       those sites link to news articles. There are a few
                       major, fundamental problems with that premise. For
                       one, creating a new cartel to deal with existing
                       monopolists is not competition, it’s the opposite.
                       For another, creating an implicit right to control
                       linking in any context won’t preserve journalism,
                       it will let it rot away. Finally, the focus on
                       getting paid for links makes even less sense when
                       the problem, historically, has been the domination
                       of the digital ad market by a few huge players. The
                       Competition and Transparency in Digital Advertising
                       Act actually targets that specific problem much
                       more effectively than the JCPA.


                       As mentioned above, competition doesn’t flourish
                       when a group—even one of smaller newsrooms—are
                       allowed to form a cartel. It just means that both
                       sides of this fight are now huge. Proposed changes
                       to the bill will limit the organizations that could
                       get compensation under this scheme to publications
                       with 1,500 employees or fewer. But that won’t
                       preserve competition, because the loss of local and
                       independent news has already happened. Many smaller
                       publications are now owned or backed by large
                       corporations and venture capital funds. And the
                       industry is consolidating at a rapid rate.


                       The large corporations and investment vehicles that
                       dominate online journalism took advantage of the
                       mess created by Facebook and Google’s ad
                       domination. And the JCPA would allow them to reap
                       the rewards of buying up, laying off, and click-
                       baiting these newsrooms. That’s infuriating.


          o § Civil Rights/Policing⠀➾


                # ⚓ NBC ☛ Medieval_Times_theater_plans_union_vote_over_pay_and
                  safety_concerns⠀⇛


                       “We are the actors, stunt performers, and stable
                       hands of Medieval Times in Lyndhurst, New Jersey
                       joining together in union to create a fairer,
                       safer, and more enjoyable workplace,” the group
                       said in a statement. “With a supermajority of
                       support, we are excited to be forming our union
                       with the American Guild of Variety Artists (AGVA).”


                       The American Guild of Variety Artists, which is
                       affiliated with the AFL-CIO, represents live act
                       performances at theaters and theme parks across the
                       country. Notable performers they represent include
                       entertainers at Disneyland and the Radio City
                       Rockettes.


                # ⚓ BBC ☛ Bruce’s_Beach_returned_to_family_nearly_a_century
                  after_seizure⠀⇛


                       Bruce’s Beach was purchased in 1912 to create a
                       beach resort for black people at a time of racial
                       segregation in southern California.


                       Located in the desirable city of Manhattan Beach,
                       it was forcibly taken by the local council in 1924.


                       But on Tuesday, Los Angeles officials voted to
                       return the land to the family.


                # ⚓ Shadowproof ☛ Protest_Song_Of_The_Week:_‘We_Won’t_Go_Back’
                  By_MILCK⠀⇛


                # ⚓ TruthOut ☛ Treatments_for_Ectopic_Pregnancies_in_Missouri
                  Are_Delayed_Due_to_“Trigger_Law”⠀⇛


                # ⚓ Common Dreams ☛ Missouri_Hospital_System_Resumes_Providing
                  Plan_B_After_‘Shameful’_Ban⠀⇛


                       A Kansas City hospital system on Wednesday reversed
                       its decision to stop providing emergency
                       contraceptives like Plan B following assurances
                       from Missouri’s top elected officials that the
                       morning-after pill does not violate the state’s
                       restrictive abortion ban.


                       “First it’s abortion. Next it’s contraception.”


                # ⚓ TruthOut ☛ Contraception_Could_Be_at_Risk_Next_—_Especially
                  IUDs_and_Plan_B,_Experts_Say⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_This_Right-Wing_Attack_on
                  Abortion_Rights_Is_a_Direct_Attack_on_Liberal_Democracy⠀⇛


                       Roe v. Wade is now history, and with it the U.S.
                       constitutional protection of a woman’s right to
                       choose whether or not to carry a pregnancy to term.
                       A half century of medical practice, normative
                       evolution, and legal precedent has been overturned
                       by a Supreme Court stacked with conservative,
                       Trump-appointed judges who have long made clear
                       their opposition to the idea that reproductive
                       freedom is a fundamental right.


                # ⚓ Counter Punch ☛ Hard-Fought_Freedoms_on_the_Line⠀⇛


                       Make no mistake. This Supreme Court decision is a
                       huge disaster for women, minorities, and all those
                       who want a freer and more democratic society.


                       The wording of the ruling, penned by the fanatic
                       Federalist Society Catholic theocrat Samuel Alito,
                       makes it clear that it is based upon an “original
                       intent” concept of the Constitution where laws are
                       evaluated for their constitutionality on the basis
                       of what the white property-owning, and in many
                       cases slave-owning founding men of the
                       Constitutional Assembly believed to be the natural
                       order of things. That so-called natural order
                       included slavery, the genocide of North America’s
                       Indigenous people, second-class status of women and
                       freed blacks, the denial of voting rights to people
                       — even white people — who owned no property, and
                       the right to a public trial by a jury of one’s
                       peers (except to those excluded populations, who
                       weren’t even allowed in courtroom public galleries,
                       much less in a jury box).


                # ⚓ Common Dreams ☛ Watching_US_With_Horror,_European_Groups
                  Push_Leaders_to_Strengthen_Abortion_Rights⠀⇛


                       Appalled by the U.S. Supreme Court’s decision to
                       strike down Roe v. Wade and concerned about the
                       dark money-fueled global assault on abortion
                       rights, advocacy groups from 28 European countries
                       demanded Tuesday that their leaders take immediate
                       steps to shield and strengthen access to
                       reproductive care throughout the continent.


                       Expressing “profound solidarity” with people across
                       the U.S. who will be or already have been harmed by
                       the right-wing high court’s unpopular ruling, the
                       groups noted in an open letter that several
                       European countries—including Liechtenstein, Malta,
                       Monaco, and Poland—also have in place “highly
                       restrictive laws in disregard of international
                       human rights obligations and public health
                       evidence.”


                # ⚓ Common Dreams ☛ Women_Face_Chaos,_Torment_as_Abortion
                  Clinics_Shutter_Across_US⠀⇛


                       Less than a week after the U.S. Supreme Court
                       overturned Roe v. Wade, women across the United
                       States are facing the painful chaos and confusion
                       of a new reality in which they are being forced to
                       continue unwanted pregnancies as clinics end
                       abortion services and struggle to help patients get
                       the care they need.


                       The court’s ruling last Friday immediately
                       triggered abortion bans in nine states that are
                       home to 16 million women of reproductive age. Lower
                       courts have blocked the bans for now in two of
                       them, Louisiana and Utah, but several more states
                       are expected to impose bans soon.


                # ⚓ Common Dreams ☛ Opinion_|_Alito’s_Bad_History_Meets_the
                  Vendetta_of_Clarence_Thomas⠀⇛


                       The Dobbs opinion overturning Roe. v. Wade is
                       another marker on the road to where Republicans and
                       the U.S. Supreme Court’s conservative super-
                       majority are taking the country. Millions of
                       Americans cheer the journey. But a lot of them
                       won’t like the final destination.


                # ⚓ The Nation ☛ Life_After_Roe_Will_Be_Worse_Than_We_Feared⠀⇛


                       Let’s not kid ourselves. The decision in Dobbs v.
                       Jackson Women’s Health Organization, overturning
                       Roe v. Wade, is going to be a catastrophe. There’s
                       a German proverb that translates roughly as “the
                       soup is never eaten as hot as it’s cooked,” meaning
                       things won’t be as bad as you fear. Sometimes
                       that’s true, but it wasn’t for the Germans, and it
                       won’t be for us.


                # ⚓ The Nation ☛ “I_Called_Jane”_for_a_Pre-Roe_Illegal
                  Abortion⠀⇛


                       Now that the Supreme Court has overturned Roe vs.
                       Wade, I want to share my experience as a woman who
                       had to turn to an illegal abortion to end a
                       pregnancy. The experience was frightening,
                       degrading, and painful. It was frightening because
                       I was not sure who would be preforming the
                       abortion. Degrading because I was blindfolded
                       during the procedure. Painful because the abortion
                       was performed with very little anesthesia. No woman
                       should have to go through what I went through, and
                       no woman should have to overcome barriers to obtain
                       a safe abortion.


                # ⚓ The Nation ☛ 48_Hours_on_the_Abortion_Hotline_After_Roe
                  Fell⠀⇛


                       Less than three hours after the Supreme Court
                       overturned Roe v. Wade, Elyssa Klann sat down at
                       her kitchen table, her phone plugged into the wall,
                       two laptops open in front of her. Klann is a
                       psychologist who has volunteered for the All-
                       Options Talkline for seven years, supporting
                       callers who are making decisions about their
                       pregnancies and connecting them to resources when
                       they ask for them.


                # ⚓ The Nation ☛ It_Should_Become_Standard_for_Women_to_Freeze
                  Their_Eggs⠀⇛


                       In November of last year, I froze 16 eggs. I had
                       met the man I now plan to marry a few months
                       earlier, but if the relationship hadn’t worked out,
                       I was prepared to become a solo parent. I was tired
                       of feeling like I’d fucked up by failing to find a
                       suitable romantic partner during my peak
                       childbearing years. The women of my generation have
                       more education and workforce participation (pre-
                       pandemic) than at any time in history, but none of
                       the social affirmation or infrastructure to support
                       our ambitions. Even the heterosexual millennial men
                       who are our peers aren’t necessarily interested in
                       a financially or professionally successful partner
                       if she doesn’t put his career first. And I wasn’t
                       terribly interested in doing that.1


                # ⚓ Scheerpost ☛ Why_Roe_v._Wade’s_Demise—Unlike_Gay_Rights_or
                  Ukraine—Isn’t_Getting_Corporate_America_to_Speak_Up⠀⇛


                # ⚓ TruthOut ☛ US_Immigration_Policy_Is_to_Blame_for_the
                  Horrific_Mass_Death_in_San_Antonio⠀⇛


                # ⚓ Common Dreams ☛ ‘An_Act_of_Conquest’:_Native_Americans
                  Condemn_SCOTUS_Tribal_Sovereignty_Ruling⠀⇛


                       Indigenous leaders on Wednesday condemned a U.S.
                       Supreme Court ruling that allows authorities in
                       Oklahoma and other states to prosecute certain
                       crimes on sovereign tribal land, a narrowing of a
                       landmark 2020 decision affirming Native treaty
                       rights.


                       “The right and power of tribes to rule themselves
                       is being dismissed in favor of state power.”


          o § Internet Policy/Net Neutrality⠀➾


                # <
                  ⚓ Techdirt ☛ California_Legislators_Seek_To_Burn_Down_The
                  Internet_—_For_The_Children⠀⇛


                       I’m continuing my coverage of dangerous Internet
                       bills in the California legislature. This job is
                       especially challenging during an election year,
                       when legislators rally behind the “protect the
                       kids” mantra to pursue bills that are likely to
                       hurt, or at least not help, kids. Today’s example
                       is AB 2273, the Age-Appropriate Design Code Act 
                       (AADC),


                # ⚓ Techdirt ☛ Trump’s_Truth_Social_Big_Payday_May_Be_Falling
                  Apart⠀⇛


                       Donald Trump promised to take the social media
                       world by storm with his Truth Social Twitter-clone
                       for the MAGA world. “Free speech!” he claimed as he
                       banned anyone who criticized him. Of course, from
                       the beginning, many suspected that this was all a
                       very sketchy grift, using a SPAC to try to cash in
                       on gullible MAGA folks willing to pump up a shell
                       company stock well beyond what it could possibly be
                       worth.


                # ⚓ Techdirt ☛ How_The_Internet_Enabled_A_Mariners_Fan_And
                  DoorDash_Driver_To_Connect_And_Do_Something_Cool⠀⇛


                       The world can be an awful, horrible place. Lately,
                       it feels like, in America, things are only getting
                       more difficult. And, because my country loves its
                       scapegoats, the internet has been routinely blamed
                       for all the country’s, perhaps the world’s, ills.
                       Insurrections, political radicalization, obesity,
                       poor socialization, literally any sub-optimal thing
                       to do with children: blame the internet.


                # ⚓ Techdirt ☛ Please_Take_A_Moment_To_Celebrate_How_A_Very
                  Different_Supreme_Court_Saved_The_Internet_25_Years_Ago⠀⇛


                       The terrible, awful, no good, horrible plans to
                       regulate the internet keep coming faster and
                       furiouser these days. So, it’s worth remembering a
                       time back when Congress passed one of the worst
                       laws about the internet: the Communications Decency
                       Act. Yes, these days we talk about the CDA more
                       reverently, but that’s only because we’re talking
                       about the one part of it that wasn’t declared
                       unconstitutional: Section 230. Section 230, of
                       course, was never even supposed to be a part of the
                       CDA in the first place. It was crafted by then
                       Representatives Chris Cox and Ron Wyden as an
                       alternative approach to the ridiculousness that was
                       coming out of Senator James Exon in the Senate.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ Kim_Dotcom_Not_Happy,_Says_‘Mega_Mass
                        Piracy_Report’_is_On_the_Way⠀⇛


                             Megaupload founder Kim Dotcom does not seem
                             like a happy man right now. After accusing
                             two of his former colleagues of facilitating
                             Chinese spying, Dotcom says that a report is
                             being produced to show that mass infringement
                             is taking place on Mega, a company he co-
                             founded. Surprisingly, he says it will
                             include live pirate links to content posted
                             by Mega users.


                      # ⚓ Torrent Freak ☛ ACE_Anti-Piracy_Alliance_Expands_Into
                        Asia_to_Disrupt_Illegal_Streaming⠀⇛


                             The Alliance for Creativity and
                             Entertainment, the world’s most powerful
                             anti-piracy coalition, has announced further
                             expansion. ACE/MPA chief Charles Rivkin says
                             the addition of two new members – Hong Kong-
                             based streaming platform Viu and Thailand’s
                             leading cable satellite TV provider True
                             Visions – will strengthen ACE’s global reach.
                             But the coalition doesn’t plan to stop there.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ 2022/0629/1600_—_cockies⠀⇛


                       There’s a small patch of grass alongside the
                       Djerring trail just after the Huntingdale station
                       car park, almost every time I ride past during the
                       day I can see a couple of pairs of Galahs[1]
                       foraging around, probably digging up the roots of
                       the grass. Sometimes just a pair, other times one
                       or two groups of three or four, today was a small
                       flock of nine, and the closest less than a metre
                       from the path. They look up when I ride past, but
                       barely stop feeding . I guess they’d pay more
                       attention if I stopped


                # ⚓ emotions_#0⠀⇛


                       The moment when someone asks me for how I’m
                       feeling, and then it’ll take me serveal minutes to
                       figure out how I’m actually feeling, and to think
                       about if I’m ok to express how I’m fine with
                       expressing for some other minutes.


                # ⚓ 2022/0624/0700_—_morning_noises⠀⇛


                       Only a couple of days after the winter solstice and
                       its still very dark when we get up in the morning,
                       the sun doesn’t rise until after 7.30.


          o § Technical⠀➾


                # ⚓ Berty,_A_New_Offline-First_Messenger⠀⇛


                       I just discovered the Berty messengers. It’s an
                       open-source (Apache 2.0 & MIT) offline-first
                       messenger that looks like it has a lot more
                       potential and polish than others. A messenger
                       designed to function even without an internet
                       connection, falling back to Blutooth to connect
                       devices directly.


                # ⚓ “These_are_not_the_child_processes_you_are_looking_for.”⠀⇛


                       At The Enterprise, QA (Quality Assurance) asked if
                       they could have a tool that starts all our stuff up
                       so they can do some performance tests (there are
                       reasons they’re asking for this, and why I agree
                       with them that go beyond the scope of this entry).
                       I replied I would see what I could do—it can’t any
                       harder than what I’ve done so far [1]. And I came
                       across an interesting bug.


                # ⚓ Cleaning_cobwebs_off_the_web_browse⠀⇛


                       Firefox [1] was giving me fits. It would work fine
                       except when I quit the application, then it would
                       just sit there consuming over 100% of the CPU
                       (Central Processing Unit) (not hard given I have
                       multiple CPUs on the machine).


                # ⚓ trickle-down_tech⠀⇛


                       Whenever someone uses the term “trickle-down” in a
                       performative (usually economic) sense it invokes a
                       feeling of warm apathy, like a high profile
                       politician promising the passive benefits of his
                       high nutrient diet as he smiles and pisses against
                       your leg.


                       That being said, there is one instance of trickle-
                       down theory where I do believe that that the
                       benefits are actually passed on from the top to the
                       bottom – and that’s: technology.


                # § Science⠀➾


                      # ⚓ Hackaday ☛ A_GPS_Frequency_Standard_For_When_The
                        Timing_Has_To_Be_Right⠀⇛


                             A metrology geek will go to extreme lengths
                             to ensure that their measurements are the
                             best, their instruments the most accurate,
                             and their calibration spot-on. There was a
                             time when for time-and-frequency geeks this
                             would have been a difficult job, but with the
                             advent of GPS satellites overhead carrying
                             super-accurate atomic clocks it’s
                             surprisingly easy to be right on-frequency.
                             [Land-boards] have a GPS 10 MHz clock that’s
                             based around a set of modules.


                      # ⚓ Hackaday ☛ Record-Setting_Jumper_Tosses_Biomimicry
                        Out_The_Window⠀⇛


                             How can a few grams of battery, geared motor,
                             and some nifty materials get a jumping robot
                             over 30 meters into the air? It wasn’t by
                             copying a grasshopper, kangaroo, or an easily
                             scared kitty. How was it done, then?


                # § Internet/Gemini⠀➾


                      # ⚓ A_Story_About_the_Evolution_of_a_New_Web_Framework⠀⇛


                             The original web was a revelation. It may be
                             lo-fi compared to what we know today, but it
                             was a dream for academics, scientists, and
                             indie hobbyists. The Internet connected
                             computers and people around the world.


                             [...]


                             Libraries helped normalize programming for
                             the web. Then the frameworks had frameworks.
                             And configuration of configuration. Soon
                             frameworks rewrote browser mechanics inside
                             the browser instead of dealing with browser
                             compatibility and shortcomings.


                             [...]


                             While we were waiting on our test suites,
                             browser vendors worked together and got their
                             act together. Performance gains, standardized
                             APIs, increased user security and privacy,
                             and native components. The sun rises on the
                             platform.


                # § Programming⠀➾


                      # ⚓ coexist_with_AI⠀⇛


                             algorithms, machine learning or not, are
                             already better than people at many things.
                             the main problem is that the current machine
                             learning algorithms are limited to pretty
                             specific domains and it’s a pain to teach
                             them how to learn new things unless you have
                             lots and lots of data. the next big leap for
                             AI would be creating an algorithm that learns
                             how to learn. this means that AI entities
                             would eventually be able to replace all the
                             engineering jobs that were used to create the
                             itself as well as continue to progress at a
                             much faster rate than humans due to various
                             advantages computers have over human
                             intellect.


                             so what will you do with your life if AI
                             powered algorithms and robots can do anything
                             you can do but better?


                      # ⚓ Emacs_Basics⠀⇛


                             Emacs is a Lisp machine. Lisp is a
                             programming language from the 1950s but it’s
                             good. It looks different from C or JavaScript
                             or shell scripts but just like them, you can
                             make functions, and functions can be marked
                             as interactive so they can be called as
                             commands. Don’t worry, it comes with a huge
                             amount of ready-made commands.


                      # ⚓ Learning⠀⇛


                             I can see how that might work. But I’m too
                             lazy to read a whole book to find out how to
                             use soure control because I came to git
                             simply as another replacement for the (many)
                             previous source control things. Conceptually,
                             though, I was reading from chapter 1, but
                             pretty soon with git I found myself thinking
                             “that can’t possibly work” and having to find
                             out some of the chapter 10 stuff. So… I want
                             to read both ends??


                             I think there may be a pre-book stage that’s
                             important but often ignored. I knew what git
                             was before I used it, but often that’s not
                             the case. For example, today I saw a mention
                             of Jupyter notebooks.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.



                    ䷩ 𝚕𝚒𝚗𝚎 6597

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Gemini_version_available_♊︎


✐ Links_30/06/2022:_PostgreSQL_15_Beta_2⠀✐


Posted in News_Roundup at 10:51 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o SaaS/Back_End/Databases
          o FSF
          o Licensing_/_Legal
          o Programming/Development
                # Python
    * Leftovers
          o Hardware
          o Security
                # Fear,_Uncertainty,
                  Doubt/Fear-mongering/Dramatisation
                # Privacy/Surveillance
          o AstroTurf/Lobbying/Politics
                # Misinformation/Disinformation
          o Internet_Policy/Net_Neutrality
    * Gemini*_and_Gopher
          o Technical
                # Programming
    * § GNU/Linux⠀➾


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ Disabling_an_extent_optimization_[LWN.net]⠀⇛


                       In the final filesystem session at the 2022 Linux
                       Storage, Filesystem, Memory-management and BPF
                       Summit (LSFMM), David Howells led a discussion on a
                       filesystem optimization that is causing various
                       kinds of problems. Extent-based filesystems have
                       data structures that sometimes do not reflect the
                       holes that exist in files. Reads from holes in
                       sparse files (i.e. files with holes) must return
                       zeroes, but filesystems are not obligated to
                       maintain knowledge of the holes beyond that, which
                       leads to the problems.


                       Howells began by describing the problem, which he
                       first encountered with files cached using FS-Cache,
                       but he has found that it is actually more
                       widespread. When there is a file on an extent-based
                       filesystem (which is ext4, XFS, and Btrfs for
                       Linux) that has a small gap between two extents,
                       the filesystem will sometimes merge the extents,
                       filling in the gap with zeroes. That is done to
                       reduce the extent list for the file, though it
                       increases the amount of storage used on the disk.
                       The opposite can also happen, when the filesystem
                       sees a huge block of zeroes in a file, it can save
                       disk space by creating two extents with a gap
                       between them, though that is seemingly less of a
                       problem for Howells.


                # ⚓ LWN ☛ NFS:_the_early_years_[LWN.net]⠀⇛


                       I recently had cause to reflect on the changes to
                       the NFS (Network File System) protocol over the
                       years and found that it was a story worth telling.
                       It would be easy for such a story to become swamped
                       by the details, as there are many of those, but one
                       idea does stand out from the rest. The earliest
                       version of NFS has been described as a “stateless”
                       protocol, a term I still hear used occasionally.
                       Much of the story of NFS follows the growth in the
                       acknowledgment of, and support for, state. This
                       article looks at the evolution of NFS (and its
                       handling of state) during the early part of its
                       life; a second installment will bring the story up
                       to the present.


                       By “state” I mean any information that is
                       remembered by both the client and the server, and
                       that can change on one side, thus necessitating a
                       change on the other. As we will see, there are many
                       elements of state. One simple example is file
                       content when it is cached on the client, either to
                       eliminate read requests or to combine write
                       requests. The client needs to know when cached data
                       must be flushed or purged so that the client and
                       server remain largely synchronized. Another obvious
                       form of state is file locks, for which the server
                       and client must always agree on what locks the
                       client holds at any time. Each side must be able to
                       discover when the other has crashed so that locks
                       can be discarded or recovered.


          o § Applications⠀➾


                # ⚓ Vim_9.0_is_Available_on_Arch_Linux_–_Fasterland⠀⇛


                       Vim is a free and open-source, screen-based text
                       editor program. The program is designed for use
                       both from a command-line interface and as a
                       standalone application in a graphical user
                       interface. Vim is released under the Vim license,
                       which includes some charityware clauses that
                       encourage users who enjoy the software to consider
                       donating to children in Uganda.


                       The Vim license is compatible with the GNU General
                       Public License through a special clause allowing
                       distribution of modified copies under the GNU GPL
                       version 2.0 or later.


                       Since its release for the Amiga, cross-platform
                       development has made it available on many other
                       systems.


                # ⚓ The Register UK ☛ Old_school_editor_Vim_hits_version_9_with
                  faster_scripting_language⠀⇛


                       Old school editor fans, rejoice: some two and a
                       half years after version 8.2, Vim 9 is here with a
                       much faster scripting language.


                       Vim 9 has only a single big new feature: a new
                       scripting language, Vim9script. The goal is to
                       “drastically” improve the performance of Vim
                       scripts, while also bringing the scripting language
                       more into line with widely used languages such as
                       JavaScript, TypeScript, and Java.


                       The existing scripting language, Vimscript, remains
                       and will still work. Only scripts beginning with
                       the line vim9script will be handled differently.
                       The syntax changes are relatively modest; the
                       important differences are in things like local
                       versus global variables and functions, and that
                       functions defined with :def will be compiled before
                       they are run. This allows many errors to be caught
                       in advance, but more significantly, compiled
                       functions execute from 10× to 1000× faster.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Capable ☛ How_to_Install_Xfce_Desktop_on_CentOS_9
                  Stream_–_LinuxCapable⠀⇛


                       Xfce is a lightweight free, open-source desktop
                       environment for UNIX-like operating systems. It is
                       designed to be fast and light on system resources
                       while visually appealing to the default desktop
                       environments that ship with most operating systems.
                       Xfce is very popular with older systems, with
                       hardware as a key feature in its design to conserve
                       memory and CPU cycles. For example, the desktop
                       panel will not hog resources by constantly polling
                       for changes, and the file manager has been designed
                       to use minimal memory and CPU cycles. In addition,
                       Xfce includes several power management features
                       that can help reduce your carbon footprint.
                       Overall, Xfce is an excellent choice for users who
                       want a fast and stable desktop environment without
                       sacrificing visual appeal or functionality.


                       In the following tutorial, you will learn how to
                       install Xfce on your CentOS 9 Stream desktop using
                       the command line terminal, along with some basic
                       tips on running an update and removing the Xfce
                       desktop environment.


                # ⚓ OSNote ☛ How_to_Install_Apache_Cassandra_NoSQL_Database_on
                  Rocky_Linux_8_–_OSNote⠀⇛


                       Apache Cassandra is an open-source NoSQL database
                       management system. It is designed to handle large
                       amounts of data across many servers and to survive
                       the loss of any server.


                       Cassandra’s architectural model is quite different
                       from relational database systems. Cassandra stores
                       non-relational data in row key-value pairs in a
                       distributed set of nodes so that no single point of
                       failure exists and scales linearly by adding more
                       nodes as necessary to meet the demands on capacity,
                       request throughput, and storage capacity for an
                       increasing number of users or client applications.


                # ⚓ OSNote ☛ How_to_Install_Nginx,_MariaDB,_and_PHP_(LEMP
                  Stack)_on_AlmaLinux_8_and_Rocky_Linux_8_–_OSNote⠀⇛


                       LEMP is a popular web hosting stack used by
                       developers and web hosting companies to test and
                       host web applications. It comprises 3 components:
                       the Nginx ( pronounced as Engine-X) webserver,
                       MariaDB, and PHP which is a server-side scripting
                       language.


                       In this walkthrough, you will learn how to install
                       the LEMP stack on AlmaLinux and Rocky Linux 8.4.


                # ⚓ Make Use Of ☛ How_to_Open_ISO,_TAR,_ZIP,_and_7z_Files_on_a
                  Chromebook⠀⇛


                       While you may think of Chromebooks as devices for
                       accessing the web, they’re increasingly capable of
                       managing local files. Chromebooks with Chrome OS
                       versions 101 and higher can now open several common
                       Linux file formats: ISO, TAR, and ZIP.


                       Here’s how you can open and use such files on your
                       Chromebook.


                # ⚓ Linux Capable ☛ How_to_Install_UNRAR_on_CentOS_9_Stream_–
                  LinuxCapable⠀⇛


                       UNRAR is a powerful tool for extracting compressed
                       files, and it is widely used amongst Windows users.
                       RAR files are much smaller archives and compress
                       better than ZIP for most files by compressing files
                       “together,” saving more space. UNRAR does not come
                       pre-installed natively on CentOS Stream and is not
                       featured in its repositories, but it can be easily
                       installed from a third-party repository. Once
                       installed, UNRAR can be used to extract RAR files
                       with a simple command. In addition, UNRAR offers a
                       number of features for manipulating archives, such
                       as the ability to list the contents of an archive
                       or extract only certain files. As a result, UNRAR
                       is a valuable tool for anyone who needs to work
                       with compressed files.


                       The following tutorial will show you how to install
                       UNRAR on CentOS 9 Stream workstation or server with
                       EPEL, along with the most commonly used commands.


                # ⚓ Linux Capable ☛ How_to_Import_Remi_Repository_on_CentOS_9
                  Stream_–_LinuxCapable⠀⇛


                       REMI is a third-party repository that provides us
                       with the latest PHP versions on RHEL-derived
                       systems. However, it is not only limited to PHP but
                       also many of its modules. If you are an active PHP
                       developer, you must enable this repository almost
                       mandatory. An excellent aspect of the repository
                       and its creator is that it is very well documented,
                       so even a newbie can set it up and update their
                       system in a matter of minutes following the
                       repository documentation.


                       Another significant advantage of using REMI over
                       other third-party repositories or compiling PHP
                       from the source is that it keeps the RPM packaging
                       consistent with the official repositories. As a
                       result, you will not have any issues when trying to
                       install other software that has dependencies on PHP
                       from the official repositories. All in all, REMI is
                       an essential repository for anyone running an RHEL-
                       derived distribution who wants to stay up-to-date
                       with the latest version of PHP.


                       In the following tutorial, you will learn how to
                       import the Remi Repository on CentOS 9 Stream for
                       users who would prefer to install the latest
                       version of the PHP branch they have installed on
                       their system using the command line terminal.


                # ⚓ Trend Oceans ☛ How_to_fix_file_size_limit_exceeded_–_TREND
                  OCEANS⠀⇛


                       Linux provides you with options to limit hardware
                       resources as per users and groups to manage optimal
                       performance all around users, and it is common to
                       find limitations in shared hosting to prevent heavy
                       usage by other tenants.


                       In almost every shared hosting situation, you will
                       see the resources available to the account
                       (bandwidth, disk space, CPU power) getting capped
                       off by an application that was installed on the
                       account.


                       A similar kind of incident happened to me a few
                       days back when I was downloading the AlmaLinux 8.6
                       DVD release using the wget command. All of a
                       sudden, files got stopped, and when I checked the
                       reason for stopping, I found “File size limit
                       exceeded.” Then I remembered I had added a limit
                       for file sizes that should not exceed more than 4GB
                       to save some space on my 250 GB SSD.
                       If your system also has a file size limit that you
                       want to remove or want to extend, then this article
                       is enough for you.


                # ⚓ Why_&_How_to_change_Swappiness_in_Ubuntu?⠀⇛


                       After installing any Linux distribution, such as
                       Ubuntu, there are basic things that you need to do:
                       one of them is to change the value of Swappiness.
                       But what is Swappiness, why should you change it,
                       and how do you do it? Your time is precious (isn’t
                       it?), so I will try to make it simple and short.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Its FOSS ☛ 6_New_Changes_Coming_to_Nautilus_File
                        Manager_in_GNOME_43_–_It’s_FOSS_News⠀⇛


                             We have a few months to go before the GNOME
                             43 release, but the development activity for
                             GNOME applications is in full swing.


                             For instance, the support for extensions in
                             GNOME Web 43 alpha version.


                             Similarly, there are a few exciting changes
                             coming to GNOME Files (Nautilus), especially
                             for the list view.


    * § Distributions and Operating Systems⠀➾


          o § SUSE/OpenSUSE⠀➾


                # ⚓ OpenSSL,_Squid,_Dracut_Update_in_Tumbleweed_–_openSUSE
                  News⠀⇛


                       Five openSUSE Tumbleweed snapshots have been
                       released since last Friday.


                       The snapshots had a small amount of packages in
                       each release.


                       The 20220629 snapshot updated OpenSSL to version
                       1.1.1p. This newer version fixed CVE-2022-2068
                       affecting the c_rehash script, which was not
                       properly sanitizing the shell metacharacters to
                       prevent command injection. The script, which is
                       distributed by some operating systems in a manner
                       where it is automatically executed, could give an
                       attacker execute arbitrary commands with the
                       privileges of the script. Another package updated
                       in the snapshot was perl-JSON 4.07, which provided
                       some backport updates from 4.10 version. New memory
                       device types, processor upgrades, slot types,
                       processor characteristics and more came in the
                       update of dmidecode 3.4. There were also several
                       table engine updates in the snapshot like ibus-
                       table 1.16.9, ibus-table-chinese 1.8.8 and more.


                       A single package was updated in snapshot 20220628.
                       The update of mpg123 1.30.0 has a new network
                       backend using external tools/libraries to support
                       HTTPS and the terminal control keys are now case-
                       sensitive.


          o § Fedora Family / IBM⠀➾


                # ⚓ Red Hat Official ☛ Harvard_Business_Review_Analytics
                  Services_Report_–_Digital_Transformation_Refocused:_New_Goals
                  Require_New_Strategies⠀⇛


                       The Covid-19 pandemic has been a catalyst for many
                       organizations in their digital transformations,
                       leading companies to expedite technology
                       initiatives, design dramatic changes to processes
                       and reexamine culture and the role it plays in
                       today’s new business world. As some organizations
                       find success in their digital transformation
                       strategies, they are able to provide additional
                       bandwidth to their teams to focus on improving
                       customer experience through the collection and
                       analysis of data.


                # ⚓ IBM Old Timer ☛ Irving_Wladawsky-Berger:_The_Impressive
                  Scope_of_the_Linux_Foundation_in_the_21st_Century_Digital
                  Economy [Ed: Irving Wladawsky-Berger on IBM's (and now
                  Microsoft's) sham marketing (e.g. openwashing, greenwashing)
                  front, misleadingly labeled "Linux Foundation"]⠀⇛


                       Last week, the Linux Foundation held its North
                       America Open Source Summit in Austin. The week-long
                       summit included a large number of breakout sessions
                       as well as several keynotes. Open Source Summit
                       Europe will take place in Dublin in September and
                       Open Source Summit Japan in Yokohama in December.


                       I’ve been closely involved with open, collaborative
                       innovation and open source communities since the
                       1990s. In particular, I was asked to lead a new
                       Linux initiative that IBM launched in January of
                       2000 to embrace Linux across all the company’s
                       products and services.


                       At the time, Linux had already been embraced by the
                       research, internet, and supercomputing communities,
                       but many in the commercial marketplace were
                       perplexed by IBM’s decision. Over the next few
                       years, we spent quite a bit of effort explaining to
                       the business community why we were supporting
                       Linux, which included a number of Linux commercials
                       like this one with Muhammad Ali that ran in the
                       2006 Super Bowl. IBM also had to fight off a multi-
                       billion dollar lawsuit for alleged intellectual
                       property violations in its contributions to the
                       development of Linux. Nevertheless, by the late
                       2000s, Linux had crossed the chasm to mainstream
                       adoption, having been embraced by a large number of
                       companies around the world.


                # ⚓ LWN ☛ Fedora,_FFmpeg,_Firefox,_Flatpak,_and_Fusion_
                  [LWN.net]⠀⇛


                       Fedora’s objective to become the desktop Linux
                       distribution of choice has long been hampered by
                       Red Hat’s risk-averse legal department, which
                       strictly limits the type of software that Fedora
                       can ship. Specifically, anything that might be
                       encumbered by patents is off-limits, with the
                       result that much of the media that users might find
                       on the net is unplayable. This situation has
                       improved over the years as the result of a lot of
                       work within the Fedora project, but it still puts
                       Fedora at a disadvantage relative to some other
                       distributions. A recent discussion on video
                       support, though, shines a light on how some
                       surprising legal reasoning may be providing a way
                       out of this problem; that way may not be pleasing
                       to all involved, however.


                # ⚓ Enterprisers Project ☛ IT_hiring:_5_challenges_with
                  emerging_technologies⠀⇛


                       As the pace of innovation quickens, companies of
                       all sizes are racing to adopt the latest emerging
                       technologies. IT teams are the technical
                       trailblazers within most firms, making them the
                       first to leverage new technologies. However, we
                       face an ongoing and potentially prolonged talent
                       shortage, both in IT and beyond, which threatens to
                       leave our technical teams depleted for years to
                       come.


                       Already, we only have 23 unemployed workers for
                       every 100 job openings in the United States,
                       according to Lightcast, and some of the most severe
                       talent shortages are in emerging technical fields.
                       This lack of human capital spills over to
                       technological capital, hindering the adoption of
                       emerging technologies and limiting the ability of
                       organizations to extract value out of new
                       innovations.


                       Here are five key challenges associated with
                       emerging technologies that companies are facing due
                       to the talent shortage.


                # ⚓ Enterprisers Project ☛ 3_ways_CIOs_should_approach_IT_team
                  accountability⠀⇛


                       Holding people accountable is one of the most
                       important – and sometimes one of the most
                       challenging – aspects of a leader’s job. For CIOs,
                       the success of a project intended to propel a
                       company forward often depends on how well they hold
                       their IT teams accountable.


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


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ The Register UK ☛ Thunderbird_102:_A_compelling
                        facelift_•_The_Register⠀⇛


                             Open-source cross-platform email and
                             messaging client Thunderbird has hit version
                             102, with a new look and improved
                             functionality, including Matrix chat support.


                             The latest release is the first major upgrade
                             since version 91, which The Reg looked at
                             last August. This is normal for the app – it
                             follows the same approximately annual release
                             cycle as Firefox’s Extended Support Releases,
                             the most recent of which was also version 91.
                             From now until the next major release,
                             Thunderbird 102 will get a regular stream of
                             minor updates and bug fixes.


                             102 has a modernized look and feel. There’s a
                             new “Spaces” toolbar, which appears
                             vertically on the left of the app window and
                             lets users quickly flip between inbox,
                             address book, calendar, task list, and chat
                             tabs. All of these are built-in features –
                             the former Lightning calendar add-on is now
                             an integral part of the app, as is PGP
                             support, which used to be an add-on called
                             Enigmail. Thunderbird can talk to various
                             groupware calendar and contact servers,
                             including both private and corporate Google
                             Mail accounts, Microsoft Exchange and Office
                             365, and others.


                      # ⚓ Thunderbird ☛ Mozilla_Thunderbird:_Are_Your_Favorite
                        Thunderbird_Add-ons_Compatible_With_Thunderbird_102?⠀⇛


                             Thunderbird 102 is here! Our annual release
                             is full of highly-requested features,
                             beautiful new visuals, and quality-of-life
                             upgrades. We’re also working hard to ensure
                             that your favorite Thunderbird add-ons are
                             compatible. In fact, we expect the majority
                             of add-ons to be updated within a few weeks
                             of Thunderbird 102’s release.


                             We understand that certain add-ons are
                             invaluable to your workflow. So, to help you
                             decide the best time to update your version
                             of Thunderbird, here’s a simple way to
                             discover if the extensions you currently have
                             installed are compatible with Thunderbird
                             102.


          o § SaaS/Back End/Databases⠀➾


                # ⚓ PostgreSQL ☛ PostgreSQL_15_Beta_2_Released!⠀⇛


                       The PostgreSQL Global Development Group announces
                       that the second beta release of PostgreSQL 15 is
                       now available for download. This release contains
                       previews of all features that will be available
                       when PostgreSQL 15 is made generally available,
                       though some details of the release can change
                       during the beta period.


          o § FSF⠀➾


                # ⚓ FSF ☛ Free_Software_Directory_on_IRC:_Friday,_July_1
                  starting_at_12:00_EDT_(16:00_UTC)⠀⇛


                       Join the FSF and friends Friday, July 1, from 12:00
                       to 15:00 EDT (16:00 to 19:00 UTC) to help improve
                       the Free Software Directory.


          o § Licensing / Legal⠀➾


                # ⚓ Give_Up_GitHub:_The_Time_Has_Come!_–_Conservancy_Blog_–
                  Software_Freedom_Conservancy⠀⇛


                       Those who forget history often inadvertently repeat
                       it. Some of us recall that twenty-one years ago,
                       the most popular code hosting site, a fully Free
                       and Open Source (FOSS) site called SourceForge,
                       proprietarized all their code — never to make it
                       FOSS again. Major FOSS projects slowly left
                       SourceForge since it was now, itself, a proprietary
                       system, and antithetical to FOSS. FOSS communities
                       learned that it was a mistake to allow a for-
                       profit, proprietary software company to become the
                       dominant FOSS collaborative development site.
                       SourceForge slowly collapsed after the DotCom
                       crash, and today, SourceForge is more advertising
                       link-bait than it is code hosting. We learned a
                       valuable lesson that was a bit too easy to forget —
                       especially when corporate involvement manipulates
                       FOSS communities to its own ends. We now must learn
                       the SourceForge lesson again with Microsoft’s
                       GitHub.


          o § Programming/Development⠀➾


                # ⚓ Make Use Of ☛ The_Basics_of_Coding_and_Programming_That_You
                  Need_to_Know⠀⇛


                       Considering picking up some programming skills?
                       Great idea!


                       Programming is a popular and rewarding career path,
                       especially when you get the fundamentals right.
                       Whether you’re considering picking it up as a
                       hobby, or you’re eyeing up a potential job, it pays
                       to understand the basics. Find out a bit more about
                       what programming involves, and whether it might be
                       for you.


                # ⚓ TecAdmin ☛ What_is_difference_between_var,_let_and_const_in
                  JavaScript?_–_TecAdmin⠀⇛


                       A variable declaration is simply telling the
                       computer that a variable exists and what value it
                       should start with. Similar to other programming
                       languages JavaScript also allows for the
                       declaration of variables.


                       There are three keywords in JavaScript that can be
                       used to declare variables: let, var, and const.
                       Each keyword has different rules and implications
                       for how the variables they create can be used.


                # ⚓ Red Hat ☛ Red_Hat_Developer_roundup:_Best_of_June_2022_|
                  Red_Hat_Developer⠀⇛


                       Security, code tracing, SaaS, and more: Get the Red
                       Hat Developer highlights for the month.


                # ⚓ InfoQ ☛ The_Compounding_(Business)_Value_of_Composable
                  Ecosystems⠀⇛


                       In the finance department, they say compounding
                       interest is the eighth wonder of the world because
                       your money makes money. In software, IT, and open
                       source, composability is the first wonder of the
                       world because it allows innovation to build on
                       innovation. This is what we mean when we say we are
                       standing on the shoulders of giants.


                # ⚓ Barry Kauler ☛ Blocking_web-page_adverts_in_a_container⠀⇛


                       The “dunfell” icon runs a full isolated desktop,
                       and Pup-Advert-Blocker should work there.
                       I have fixed so that /etc/hosts gets copied into
                       every container at startup.That will be in the next
                       release.
                       But, as I mentioned in the forum, replying to
                       Tenoch’s post, The “Mvps.org” choice in Pup-Advert-
                       Blocker doesn’t work.
                       Pup-Advert-Blocker is a very old application,
                       created by sc0ttman, found it in the old forum:


                       https://oldforum.puppylinux.com/
                       viewtopic.php?t=59290


                       I will need to fix the PET, either take out
                       “Mvps.org” or find a replacement.


                # ⚓ LWN ☛ A_new_LLVM_CFI_implementation_[LWN.net]⠀⇛


                       Some kernel features last longer than others.
                       Support for forward-edge control-flow integrity
                       (CFI) for kernels compiled with LLVM was added to
                       the 5.13 kernel, but now there is already a
                       replacement knocking on the door. Control-flow
                       integrity will remain, but the new implementation
                       will be significantly different — and seemingly
                       better in a number of ways.


                       The kernel makes extensive use of indirect function
                       calls; they are at the heart of its internal object
                       model. Every one of those calls is a potential
                       entry point for an attacker; if the target of the
                       call can be somehow changed to an address of the
                       attacker’s choosing, the game is usually over.
                       Forward-edge CFI works to thwart such attacks by
                       ensuring that every indirect function call sends
                       control to a code location that was actually
                       intended to be a target of that call. Specifically,
                       an indirect function call should only go to a known
                       function entry point, and the prototype of the
                       function should match what is expected at the call
                       site.


                       The CFI implementation merged for 5.13 works by
                       creating “jump tables” containing all of the
                       legitimate targets of indirect function calls in
                       the kernel; there is one jump table for each
                       observed function prototype. Actual indirect calls
                       are replaced with a jump-table lookup to ensure
                       that the intended target meets the criteria; the
                       target should be found in the jump table
                       corresponding to the intended function prototype.
                       If that test fails, a kernel panic results. See
                       this article for a more detailed description of how
                       this mechanism works.


                # § Python⠀➾


                      # ⚓ TecAdmin ☛ How_to_accept_user_input_in_Python_–
                        TecAdmin⠀⇛


                             In Python, there are a few ways to accept
                             user input. In this blog post, we will
                             explore three different ways to do so. We
                             will start with the simplest way and work our
                             way up to the more complex methods. By the
                             end of this post, you should have a good
                             understanding of how to accept user input in
                             Python. Let’s get started!


                             Python 3 provides a built-in function called
                             input() that allows you to take user input.
                             Where Python 2.x uses the raw_input()
                             function is used to accept user input. Python
                             2.7 also has a function called input().
                             However, this function takes only one
                             argument: the prompt string.


                      # ⚓ OpenSource.com ☛ Package_a_new_Python_module_in_4
                        steps_|_Opensource.com⠀⇛


                             When you install an application, you’re
                             usually installing a package that contains
                             the executable code for an application and
                             important files such as documentation, icons,
                             and so on. On Linux, applications are
                             commonly packaged as RPM or DEB files, and
                             users install them with the dnf or apt
                             commands, depending on the Linux
                             distribution. However, new Python modules are
                             released virtually every day, so you could
                             easily encounter a module that hasn’t yet
                             been packaged. And that’s exactly why the
                             pyp2rpm command exists.


                      # ⚓ LWN ☛ Introducing_PyScript_[LWN.net]⠀⇛


                             In a keynote at PyCon 2022 in Salt Lake City,
                             Utah, Peter Wang introduced another entrant
                             in the field of in-browser Python
                             interpreters. The Python community has long
                             sought a way to be able to write
                             Python—instead of JavaScript—to run in web
                             browsers, and there have been various efforts
                             to do so over the years. Wang announced
                             PyScript as a new framework, built atop one
                             of those earlier projects, to allow Python
                             scripting directly within the browser; those
                             programs have access to much of the existing
                             Python ecosystem as well as being able to
                             interact with the browser document object
                             model (DOM) directly. In addition, he gave
                             some rather eye-opening demonstrations as
                             part of the talk.


                             Wang began by introducing himself and the
                             company that he runs, Anaconda, which he co-
                             founded with Travis Oliphant ten years ago.
                             Oliphant was the creator of NumPy and one of
                             the founders of SciPy, both of which are
                             cornerstones of the Python scientific-
                             computing ecosystem. Anaconda has created a
                             number of different tools that are used
                             widely in the community, as well as founding
                             the NumFOCUS non-profit and the PyData
                             conferences.


                             There were a number of reasons why he and
                             Oliphant chose to focus their efforts around
                             Python, including that the language is
                             approachable, even by those who lack a
                             computer-science background. Another point in
                             its favor is that the Python community is
                             generally welcoming and pleasant to work in.
                             That is a “really big deal if you want to
                             keep growing the user base”.


                             But there is another aspect of the language
                             that makes it so desirable from his
                             standpoint: it can be extended with binary
                             extensions that use an API that is written in
                             C, but can be accessed from other languages.
                             He likens Python to “a Honda Civic with
                             mounting bolts for a warp drive”. So the
                             language can be picked up by kids who can
                             then pop open the trunk “and bolt on warp
                             nacelles” that allows the code to run faster
                             than C or C++ in some cases, Wang said.


                             That aspect is sometimes overlooked, but it
                             means that Python can be used in ways that
                             other, similar languages cannot. “It’s not
                             just like Node, it’s not just an alternative
                             to Ruby”. The reason Python was picked up by
                             Wall Street firms ten or 15 years ago was
                             because of this warp-drive capability, he
                             said.


    * § Leftovers⠀➾


          o § Hardware⠀➾


                # ⚓ Linux Gizmos ☛ Vecow_introduces_SOM_line_based_on_MediaTek
                  Genio_1200/500/350_processors⠀⇛


                       Vecow presented their new line of System on Module
                       devices (SoM) at Embedded World 2022. The latest
                       SoMs integrate MediaTek’s Genio 1200, Genio 500 and
                       Genio 350 processors. Additionally, the company has
                       developed carrier boards for quick product
                       development.


          o § Security⠀➾


                # ⚓ LWN ☛ Security_updates_for_Thursday_[LWN.net]⠀⇛


                       Security updates have been issued by Debian
                       (firefox-esr, firejail, and ublock-origin), Fedora
                       (chromium, firefox, thunderbird, and vim), Mageia
                       (kernel and kernel-linus), Oracle (389-ds-base and
                       python-virtualenv), SUSE (chromium), and Ubuntu
                       (cloud-init).


                # ⚓ Google ☛ 2022_0-day_In-the-Wild_Exploitation…so_far [Ed: A
                  lot of Windows]⠀⇛


                       This blog post is an overview of a talk, “ 0-day
                       In-the-Wild Exploitation in 2022…so far”, that I
                       gave at the FIRST conference in June 2022. The
                       slides are available here.
                       For the last three years, we’ve published annual
                       year-in-review reports of 0-days found exploited in
                       the wild. The most recent of these reports is the
                       2021 Year in Review report, which we published just
                       a few months ago in April. While we plan to stick
                       with that annual cadence, we’re publishing a little
                       bonus report today looking at the in-the-wild 0-
                       days detected and disclosed in the first half of
                       2022.
                       As of June 15, 2022, there have been 18 0-days
                       detected and disclosed as exploited in-the-wild in
                       2022. When we analyzed those 0-days, we found that
                       at least nine of the 0-days are variants of
                       previously patched vulnerabilities. At least half
                       of the 0-days we’ve seen in the first six months of
                       2022 could have been prevented with more
                       comprehensive patching and regression tests. On top
                       of that, four of the 2022 0-days are variants of
                       2021 in-the-wild 0-days. Just 12 months from the
                       original in-the-wild 0-day being patched, attackers
                       came back with a variant of the original bug.


                # § Fear, Uncertainty,
                  Doubt/Fear-mongering/Dramatisation⠀➾


                      # ⚓ ZDNet ☛ Microsoft_warning:_This_malware_that_targets
                        Linux_just_got_a_big_update [Ed: With help from
                        Microsoft operatives in ZDNet (Tung), anti-Linux FUD is
                        being broadcast and the issue isn't Linux itself but
                        some malware]⠀⇛


                      # ⚓ Computing UK ☛ CISA_issues_warning_on_active
                        exploitation_of_PwnKit_Linux_vulnerability⠀⇛


                      # ⚓ TechRadar ☛ CISA_sounds_the_alarm_over_high-severity
                        bug_in_all_major_Linux_distros [Ed: CISA mostly warns
                        about Microsoft holes; this selective coverage comes
                        from publishers funded by Microsoft]⠀⇛


                # § Privacy/Surveillance⠀➾


                      # ⚓ TechCrunch ☛ [Older]_Wow,_Facebook_really_knows_how
                        to_give_someone_a_send-off!⠀⇛


                             So much for that touching goodbye post to
                             Sheryl Sandberg that Mark Zuckerberg posted
                             just 9 days ago, when after a 14-year run at
                             Facebook — now Meta Platforms — Sandberg said
                             she was resigning from her post as COO. At
                             the time, Zuckerberg called Sandberg’s
                             planned departure the “the end of an era” and
                             spoke glowingly of her as an “amazing person,
                             leader, partner, and friend.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # § Misinformation/Disinformation⠀➾


                      # ⚓ MakeTech Easier ☛ FCC_Urges_Apple_and_Google_to_Ban
                        TikTok_as_Security_Threat⠀⇛


                             While it’s much beloved by its users, TikTok
                             has been much maligned by U.S. government
                             officials since it picked up popularity
                             during the pandemic. The latest hit is from
                             the Federal Communications Commission. The
                             FCC commissioner sent a letter to Apple and
                             Google, asking them to ban TikTok, believing
                             the social app is a “national security
                             threat.”


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Internet Freedom Foundation ☛ CIC_orders_MeitY_to_respond
                  to_IFF’s_RTI_seeking_information_on_Non-Personal_Data
                  Governance_Framework_Policy-Process⠀⇛


                       In November 2020, we filed an RTI application
                       requesting the Ministry of Electronics and
                       Information Technology to provide copies of all
                       public consultation responses received by the
                       Committee constituted for deliberation on a Non-
                       Personal Data Governance Framework. This
                       information was refused on the ground that the
                       Ministry was not the custodian of any information
                       relating to internal functioning of the Committee.
                       When the first appeal filed against this response
                       was also rejected, we filed a second appeal with
                       the Central Information Commission. The matter was
                       heard on June 23, 2022 where the CIC directed MeitY
                       to respond to the RTI application afresh after
                       taking certain corrective steps.


                       [...]


                       We found that the Committee’s revised report did
                       not contain any information on the suggestions and
                       public feedback received by them during the first
                       round of consultation. So, we filed an RTI
                       application on November 2, 2020 requesting MeitY to
                       provide copies of all responses received by the
                       Committee during the public consultation process.


                       When MeitY refused to provide us with this
                       information by stating that it was “not the
                       custodian of any information relating to internal
                       functioning of the Committee,” despite the fact
                       that the Committee was constituted and funded by
                       MeitY, we filed a first appeal before the First
                       Appellate Authority (‘FAA’). When the FAA found
                       that the CPIO, MeitY’s response was “appropriate,”
                       and called for no interference, we filed a Second
                       Appeal before the Central Information Commission
                       (‘CIC’) on February 6, 2021.


    * § Gemini* and Gopher⠀➾


          o § Technical⠀➾


                # § Programming⠀➾


                      # ⚓ The_pre-book_learning_stage_and_awk⠀⇛


                             I wholeheartedly agree, before starting to
                             learn something a general overview of what it
                             is, what it can do, what it’s useful for, is
                             needed. One great example of this is in my
                             opinion “The AWK Programming Language” (1988)
                             by A. V. Aho, B. W. Kernighan and P. J.
                             Weinberger.


                      # ⚓ Curiouser_and_Curiouser:_How_I_found,_and_what_you
                        can_learn,_from_gemserv’s_Directory_Transversal
                        vulnerabilities⠀⇛


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.


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