𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, May 27, 2023
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Generated Sun 28 May 02:53:04 BST 2023
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2023/05/27/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ European Patent Office (EPO) Management Not Supported by the EPO’s Applicants, So Why Is It Still There? | Techrights

⦿ Geminispace Continues to Grow Even If (or When) Stéphane Bortzmeyer Stops Measuring Its Growth | Techrights

⦿ HMRC: You Can Click and Type to Report Crime, But No Feedback or Reference Number Given | Techrights

⦿ One Week After Sirius Open Source Was Reported to HM Revenue and Customs (HMRC) for Tax Fraud: No Response, No Action, Nothing... | Techrights

⦿ IRC Proceedings: Friday, May 26, 2023 | Techrights

⦿ Social Control Media Needs to be Purged and We Need to Convince Others to Quit It Too (to Protect Ourselves as Individuals and as a Society) | Techrights

⦿ Anonymously Travelling: Still Feasible? | Techrights

⦿ German Media About Industry Patent Quality Charter (IPQC) and the European Patent Office (EPO) | Techrights

⦿ EPO Applicants Complain That Patent Quality Sank and EPO Management Isn’t Listening (Nor Caring) | Techrights

⦿ With EUIPO in Focus, and Even an EU Kangaroo Tribunal, EPO Corruption (and Cross-Pollination With This EU Agency) Becomes a Major Liability/Risk to the EU | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2023/05/27/european-patent-office-ga-de/#comments
		http://techrights.org/2023/05/27/geminispace-growing/#comments
		http://techrights.org/2023/05/27/hmrc-you-can-click-and-type-to-report-crime-but-no-feedback-or-reference-number-given/#comments
		http://techrights.org/2023/05/27/hm-revenue-and-customs-mum/#comments
		http://techrights.org/2023/05/27/irc-log-260523/#comments
		http://techrights.org/2023/05/27/social-control-networks-need-to-be-purged/#comments
		http://techrights.org/2023/05/27/some-privacy-still-feasible/#comments
		http://techrights.org/2023/05/27/stuttgarter-zeitung-epo/#comments
		http://techrights.org/2023/05/27/stuttgarter-zeitung-thomas-magenheim-on-epo/#comments
		http://techrights.org/2023/05/27/suepo-and-epo-articles/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2023/05/27/40th-anniversary-gnu/#comments
		http://techrights.org/2023/05/27/goodbyes-to-tina-turner/#comments
		http://techrights.org/2023/05/27/new-wine-and-more/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 76

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/european-patent-office-ga-de/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/european-patent-office-ga-de/

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Gemini_version_available_♊︎


✐ European_Patent_Office_(EPO)_Management_Not_Supported_by_the_EPO’s
Applicants,_So_Why_Is_It_Still_There?⠀✐


Posted in Europe, Patents at 5:57 am by Dr. Roy Schestowitz


More translations (with more languages) available in the site of the EPO‘s
union, SUEPO


                       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_pathway⦈_
    The European Patent Office in Munich. Experts criticise the practice of
                         granting inventor protection.
                             Photo: dpa/Sven Hoppe


Summary: This third translation in the batch is an article similar to the prior
one, but the text is a bit different (“Patente_ohne_Wert”)


A BIT less than a week before the EPO wanted (or merely hoped) to open an
illegal and unconstitutional kangaroo court, in violation of international
conventions, some condemnation came from the German press. This project will
destabilise the EU by discrediting the EU, so Germany’s government needs to
sober up and listen to the warning signs. EPO corruption is highly contagious
and it has been left to flourish for over a decade already. Here’s the latest
of the batch from SUEPO:


     § Criticism of the European Patent Office Patents without value⠀➾


     Munich – To increase its revenues, the European Patent Office grants
     questionable patents, say critics. Transparency International sees
     structures that favour corruption.


     By Thomas Magenheim-Hörmann


     The example described by the Munich patent attorney makes it clear
     what is at stake. A pharmaceutical company developed a pill against
     infertility, had it protected at the European Patent Office (EPO) and
     invested in its marketing. Then a rival entered the market with an
     alleged plagiarism. The patent holder went to court and lost. The
     alleged imitator was able to show a US patent that Epa examiners had
     overlooked. This rendered their property right worthless. “In extreme
     cases, this can cause millions in damages,” explains the patent
     attorney, who wishes to remain anonymous. He works for one of the
     largest patent law firms in Europe. Patenting for several countries
     alone consumes a six-figure sum, and many times that amount is
     invested in production in reliance on the patent.


     There is a system of lame searches, the expert complains. Examiners
     are encouraged to grant more and more patents because they maximise
     the office’s income. Quality research falls by the wayside. Michael
     Heisel puts the grievances even higher. “We see structural problems
     at the EPO that facilitate corruption,” says the Bavarian head of the
     anti-corruption organisation Transparency International.


     39 countries represented in the Council


     An element of this is the Epa Board of Directors, in which 39
     European countries are represented and which is supposed to control
     the management of the office. But this is called into question by a
     conflict of interests, warns Heisel. On the one hand, the office
     takes over the patent examination for many countries. On the other
     hand


     the states shares of the Office’s income for granted patents. “The
     Administrative Council is not independent of the party being
     controlled, and that can’t be good,” Heisel criticises. Epa service
     instructions support this view. “Productivity has to improve, very
     soon, … because productivity is the only thing that guarantees that
     our payroll will be paid on the 26th. of each month,” writes an Epa
     director. The clarity of a patent is not a priority, the inventive
     step is not to be examined in depth, it continues. It is to be
     examined quickly, decided positively and recognised a lot, it means.


     This practice is also a thorn in the side of Siemens patent chief
     Beat Weibel. His company is the largest German patent applicant and
     the initiator of an industry initiative with the abbreviation IPQC.
     20 major international companies such as Siemens, Bayer and Nokia,
     but also smaller firms, have joined forces because they fear for
     effective patent protection. “We have nothing if patent examiners
     can’t find the state of the art and can only do incomplete research
     due to internal time pressure,” complains Weibel. Siemens has also
     had similar experiences with Epa patents. Representatives of IPQC and
     Office 2023 have met twice to discuss and resolve problems. But that
     already fails in terms of awareness. “The Office’s management has
     denied that there are any quality deficiencies,” says the Siemens
     expert regretfully. The
     Critics, meanwhile, remain silent. “We ask for your understanding
     that Epa does not wish to comment on this,” a spokesperson explains
     succinctly when asked. Data speak a clear language.


     For example, Siemens has documented an increase in the time spent on
     patent applications by one third in the last decade. At the same
     time, according to internal EPO statistics, the time available to
     examiners per patent search has almost halved. As a result, those who
     challenge patents are becoming more successful. From 2015 to 2021,
     the revocation rate climbed from 41 to 46 per cent, according to
     Siemens.


     For 2022, a study by the Chair of Intellectual Property at the
     University of Osnabrück has determined a revocation rate of the Epa
     Board of Appeal of almost 50 percent. A further almost 40 percent of
     contested patents were marginally to substantially restricted. It is
     striking that not even one in ten revocations was based on documents
     that could not be found in the Epa patent database, the study authors
     write. In nine out of ten contested cases, the
     We need reliable patents, and examiners need enough time and
     experience for this,” emphasises a patent expert from the Roche
     pharmaceutical company in Switzerland. He too is a member of th IPQC.
     Epa staff representatives support the accusations from industry and
     research. To the outside world, the management claims that everything
     is fine and plays down or completely ignores quality deficiencies,
     they explain. Only four out of five examiners who leave the office
     are replaced, despite an increase in work. “The Office must provide
     more examiners and more examination time,” the Munich patent attorney
     also demands. A few years ago, several large patent law firms wrote
     an incendiary letter to the Office criticising the declining patent
     quality. This has been negated by the office. “Nothing happened,”
     regrets the expert. Like Tranparency International, he sees the Epa
     Board of Directors as problematic. “There are States, for them this
     is a significant source of income,” Weibel also criticises.


     Patent trolls have also recognised this and use it for themselves.
     These are applicants who apply for protective rights for superficial
     patents, which are also granted if the examination is inadequate,
     explains Heisel. These patents then block competitors. “China in
     particular applies for a large number of patents, and if they are not
     carefully examined, this can deprive German companies of innovation
     opportunities,” warns Heisel.


     Patents: More and more applications from China


     The European Patent Office, with its headquarters in Munich, is a
     supranational organisation and not an EU organisation. The management
     of the Office, under President Antonio Campinos, is controlled by the
     EPO Administrative Council. It is made up of representatives of the
     39 European states that have acceded to the European Patent
     Convention. Germany is represented by a State Secretary for Justice.
     In particular, patent applications from China have been on the rise
     at the European Patent Office for years . In 2022, the increase on
     this basis was a good 15 percent to more than 19,000 requests for
     protection by Chinese inventors. mho


All of a sudden all those EPO photo ops with China don’t quite look the same.
And much can be said about the EPO doing so much business with Belarus
(outsourcing_parts_of_the_EPO_to_Vladimir_Putin's_'oblasts'). █


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣀⣸⣀⣄⣀⣀⣸⣿⣯⣭⣽⠓⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣀⣤⣤⣤⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⠤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⡟⠅⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠿⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 277

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/geminispace-growing/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/geminispace-growing/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Geminispace_Continues_to_Grow_Even_If_(or_When)_Stéphane_Bortzmeyer_Stops
Measuring_Its_Growth⠀✐


Posted in Protocol at 4:30 am by Dr. Roy Schestowitz


Video_download_link | md5sum f726c3cf0bd8fe90ec207a68fa9544b8
Gemini is Growing, But Growth Not Measured
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/tracking-size-of-gemini.webm


Summary: A Gemini crawler called Lupa (Free/libre software) has been used for
years by Stéphane Bortzmeyer to study Gemini and report on how the community
was evolving, especially from a technical perspective; but his own instance of
Lupa has produced no up-to-date results for several weeks


THE work of Stéphane_Bortzmeyer, notably Lupa, has helped us estimate the
growth of Gemini in general (as a protocol). But the Botond/Bortzmeyer-led
capsules (the former charts the latter) stopped updating their numbers that
track Gemini’s growth; maybe it’s just too big and expensive for Stéphane to
track all the time, as it’s not 2020 anymore and many thousands of capsules
exist, counting subsites (in the domain sense) too.


“It’s perfectly plausible and possible that Bortzmeyer isn’t aware of the issue
and has just accidentally let the job fail (Botond uses a cron job at 1AM UTC
since last year).”The video above explains that, based on our own experience,
Gemini continues to grow. Even in the absence of crawlers estimating and
reporting this growth, we’re optimistic and last month was record_traffic_for
us. We’re talking about lots and lots of Gemini pages (about half a million
pages in one month). It’s perfectly plausible and possible that Bortzmeyer
isn’t aware of the issue and has just accidentally let the job fail (Botond
uses a cron job at 1AM UTC since last year). radia.bortzmeyer.org is definitely
active this month. Either way, tracking the growth of Geminispace has become a
computationally expensive (and thus financial burdensome) task. It did help a
lot — a very positive contribution. █


                   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Stéphane_Bortzmeyer⦈_
Stéphane_Bortzmeyer (see image licence in Wikipedia). One of the more essential
       voices of Gemini, up there with "Skyjake", Sean, and Solderpunk.


⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠋⠙⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶
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⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
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⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿⣿⣿⣿⡿⠿⠿⣿⠛⠉⠉⠁⠀⢙⠛⠃⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠺⠟⠋⠁⠀⠀⠀⠈⠀⠀⠀⠀⣀⣈⢃⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢀⠀⠀⠠⣀⡄⣸⣿⣌⠲⠦⠬⢿⣛⣼⣷⠀⠀⠀⠉⢱⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠉⠉⣉⣉⣉⣉⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣁⠀⠀⠀⢠⡠⠶⠶⠛⠋⢰⠿⠛⠻⠷⡀⠲⣶⣿⣿⣿⡇⠀⠀⢀⣙⣋⣉⣙⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠁
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠘⢿⣇⣴⣶⣣⣦⣀⠀⠀⣴⣿⣷⡌⢹⣿⣿⣷⡆⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⡀⠀⠉⠉⠙⠿⠿⠻⠐⠚⠛⠙⠋⠉⣾⣿⣿⡟⠁⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣀⣀⣠⣤⣤⣤⣤⣤⣬⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣆⠀⠀⣦⠀⢀⣤⠶⠒⠺⢿⣿⣆⠋⠻⣿⡇⣀⣨⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀
⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡆⠈⠀⠀⠀⠀⢠⣿⣧⣀⣀⣠⣾⣿⣿⡆⠀⠛⡔⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⢻⣿⠿⠿⠛⠛⠿⠏⠁⢀⣼⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣛⣛⣛⣛⣿⣛⣛⣿⣛⣛⣛⣛⣛⣻⣛⣛⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣽⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢠⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣩⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤
⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⡟⢿⣿⡟⢭⡏⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣰⣍⣇⣿⣿⣧⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⢻⡿⡻⡟⣟⠿⣧⡍⣯⣯⡎⡆⡗⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣧⠣⢸⣿⡆⣺⣧⡷⣵⣷⡿⢿⢿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⣼⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛
⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⢻⣿⣿⡿⣇⡻⣸⢸⣸⣹⣸⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣷⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⡟⣿⣿⣿⣿⣿⣿⡟⠂⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄
⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠖⢉⡏⣿⣿⣿⣿⣿⣧⠸⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉
⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠮⠤⠛⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛

                    ䷩ 𝚕𝚒𝚗𝚎 370

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/hmrc-you-can-click-and-type-to-report-crime-but-no-feedback-or-reference-number-given/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/hmrc-you-can-click-and-type-to-report-crime-but-no-feedback-or-reference-number-given/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ HMRC:_You_Can_Click_and_Type_to_Report_Crime,_But_No_Feedback_or_Reference
Number_Given⠀✐


Posted in Finance, Fraud, Free/Libre_Software at 2:38 am by Dr. Roy Schestowitz


Video_download_link | md5sum 3658fca2df7acb84de0dde460f814926
HMRC Useless UI, No Reference
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/sirius-hmrc-inaction.webm


Summary: The crimes of Sirius_‘Open_Source’ were reported 7 days ago to HMRC
(equivalent to the IRS in the US, more or less); but there has been no visible
progress and no tracking reference is given to identify the report


THE system of accountability (“checks and balances” is the motto) isn’t
working. The matter is now being escalated to a political level.


“…HMRC inaction would say a lot about the system and reinforce the widespread
belief that enforcement is done only/mostly against foes of “the system”.”The
video above deals with HMRC. I don’t have much to say about the progress; I
have received no reference code/number, they did not get in touch (phone, E-
mail, post), and it’s not clear if they’re doing anything at all to hold Sirius
accountable. As noted earlier, HMRC inaction would say a lot about the system
and reinforce the widespread belief that enforcement is done only/mostly
against foes of “the system”. Irrespective of severity, scale, and strength of
evidence.


Setting up a UI in a Web page is only the first step; does HMRC do anything
with what’s collected in this UI? it’s certainly not designed for anonymous
reporting. █



                    ䷩ 𝚕𝚒𝚗𝚎 424

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/hm-revenue-and-customs-mum/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/hm-revenue-and-customs-mum/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ One_Week_After_Sirius_Open_Source_Was_Reported_to_HM_Revenue_and_Customs_
(HMRC)_for_Tax_Fraud:_No_Response,_No_Action,_Nothing…⠀✐


Posted in Deception, Finance, Fraud, Free/Libre_Software at 12:01 am by Dr. Roy
Schestowitz


It’s like writing to zombie agencies that exist only on paper or selectively
enforce (based on special interests)


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Regulators_and_enforcers_asked_to_tackle_the_crimes;_No
                                 action....⦈_


Summary: One_week_ago we reported tax_abuses of Sirius_‘Open_Source’ to HMRC;
we still wait for any actual signs that HMRC is doing anything at all about the
matter (Sirius has British government clients, so maybe they’d rather not look
into that, in which case HMRC might be reported to the Ombudsman for
malpractice)


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣤⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢤⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠒⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣿⣿⡇⣿⣯⢘⣳⣤⣤⣿⣷⣿⣿⣧⣿⣿⠀⣺⡗⣹⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠛⠙⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠖⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⣾⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⡀⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠉⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⡿⠁⠀⠈⠉⠙⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣟⣿⠟⠉⠀⠀⠀⠀⣿⡏⣿⡅⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡇⠀⠀⠀⠀⠀⠀⣼⠓⠛⣿⣄⡀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡀⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣣⠀⠀⠀⠀⠀⣰⠃⠐⠀⠘⣿⣿⣶⣶⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠻⡛⣛⠀⠀⠀⠀⠀⠉⡇⠀⠀
⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣄⣀⣴⣿⣿⣄⣀⣤⣡⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⢀⡏⠙⢷⣦⣄⡀⣀⣴⣧⠀⠀
⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⢀⣴⣿⡅⢀⣄⣿⣿⣿⣿⣏⠈⠀⠀
⣷⣶⣶⣶⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⣿⣯⣿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⣿⣿⠿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡯⣿⠾⠿⠿⠿⠋⠋⠉⢸⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡹⠋⠟⠋⠋⠉⠁⠉⠉⢿⡇⠀⠀
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣻⣷⡄⠀⠈⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⡀⠀⢀⣀⣤⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⣀⠀⠀⢠⣼⡇⠀⠀
⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠹⢿⣿⣿⡶⣾⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⣟⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀⠔⠀⠀⣿⡇⠀⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⣿⣽⠋⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⡿⠛⣁⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⠤⠀⣀⡀⣤⣾⣿⣿⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣏⣥⠀⠀⠀⠀⣠⣿⣿⣟⠿⣷⣤⣤⡀⠀⣀⣀⣀⡀⠀⠀⠚⠭⠷⠿⠛⢹⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣯⣿⣿⣿⡿⢻⡆⣀
⠈⠙⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡶⠃⠀⠀⢰⣿⣿⣿⣿⡄⠈⢿⣿⣿⣿⠛⠉⣉⣉⡉⠒⠂⠀⠀⠀⠀⠟⣿⠨⠿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣛⣿⣷⣦⠄⠀⠀⢀⣤⣽⠟⠋⢉⣑⠴⢿⣛⣿
⣤⣤⣾⣿⣿⣿⠿⠿⠿⠿⣿⣶⣦⣄⣴⣿⡿⠷⠀⣀⡀⠒⠀⠀⣿⣿⣿⣿⣧⠀⣼⣿⣿⣇⣤⣀⣀⣀⣈⠙⠀⣀⣀⣀⡀⢀⣠⣤⣶⡿⠟⠛⣉⣭⣵⣶⣾⣿⣿⣿⠀⢩⠀⢺⣿⣶⣶⣟⠋⠁⠀⠀⢢⣤⣾⣿⣿⠿
⠛⠛⢩⣿⡷⠀⠀⠀⠀⢀⣬⣽⣿⡅⠉⣩⣤⡀⣀⣀⣀⡤⠔⢻⣿⣿⠟⠙⠉⠀⣿⣿⡛⣩⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⠛⠉⠁⠐⠚⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠋⠀⠘⣿⣷⡯⡻⡇⣠⣤⣤⣶⡿⠉⠀⠀⢀
⣀⣴⣿⡿⠃⠀⠀⠀⢠⢾⣿⣿⣿⠇⠀⢿⡿⠗⠈⠉⠀⣶⣶⣿⣿⣧⠀⠀⡠⢊⠽⣿⡆⠿⣿⣿⣿⣿⣿⠿⠋⠋⠉⠀⠀⠀⠐⠊⠁⣠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣸⣿⠹⣿⣿⢰⣿⣿⣿⣿⢀⣤⣤⣶⡿
⠙⠁⠹⣿⠄⠀⢀⡴⠟⡛⢸⣿⣟⠐⠂⣶⡆⠒⠒⠶⠒⢛⣿⣿⢻⣿⣷⣾⠁⠀⠀⠙⢿⡀⠹⢿⠛⠛⢁⣾⣷⣶⣶⣶⣶⣶⣶⠾⠿⠿⠛⠁⣸⣿⣿⣿⣿⣿⠟⣻⡇⠀⢀⣿⣏⡄⠈⠉⠁⠉⠛⠛⠁⠈⠋⠉⠀⠀
⣐⣦⣼⡿⠀⡴⠁⠀⢠⣿⣾⣿⡿⠤⠤⣤⡀⠠⢤⣤⣤⣿⣿⣯⡾⢻⣿⣿⣿⣤⣶⣶⣾⣷⣤⣄⡀⠐⠻⠛⠉⠉⠉⠀⠁⠀⠀⣀⡄⠚⠓⢲⣿⣿⣿⣿⡿⠋⠀⡍⡿⠀⠘⣿⡇⢷⣤⣤⣀⢺⣿⣿⣿⠂⠀⠀⠀⠀
⠛⠛⢻⣧⠞⠁⠀⠀⢸⣿⣧⣿⣷⠀⠀⠉⠇⠠⠀⠀⣾⣿⡟⠙⣿⢼⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡛⠁⢸⣿⠀⠀⠀⠀⠀⠐⠈⠁⣀⣼⣶⣿⣿⣿⣿⣿⠃⠀⠀⢨⣿⡇⠀⢻⣿⠀⠛⠛⠻⢿⣿⣥⣤⠐⠾⠿⢿⠿
⠀⣦⣾⣷⠯⢶⠄⠰⣾⠷⢿⣿⣿⢀⠀⠉⠁⠀⠀⢸⣿⡿⠹⠟⡟⢸⣿⣿⣷⣿⣝⠻⢿⣈⡙⠛⠃⠀⢿⣿⣦⣤⣤⣤⣤⣶⣾⣿⣿⣿⠿⠟⠋⠈⣿⣿⡆⠀⠀⣾⣿⠇⠀⠀⣿⣦⣀⣀⡀⠘⠲⠽⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢠⡤⣠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠒⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⣤⣤⣿⣷⣿⣿⣧⣿⣿⠀⣻⡗⢼⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠛⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠉⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⡿⠁⠀⠈⠉⠙⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣟⣿⠟⠁⠀⠀⠀⠀⣿⡍⣭⡅⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⣼⠓⠛⣿⣄⡀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡀⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⣼⠇⠐⠀⠘⣿⣿⣶⣤⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠻⡛⣛⠀⠀⠀⠀⠀⠉⡇⠀⠀
⠀⠀⠀⠙⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣄⣀⣴⣿⣿⣄⣀⣤⣡⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⢀⡏⠙⢷⣦⣄⡀⣀⣴⣧⠀⠀
⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⢀⣴⣿⡁⢀⣄⣿⣿⣿⣿⣏⠈⠀⠀
⣷⣶⣶⣶⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⣿⣯⣿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⣿⣿⠿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⠾⠿⠿⠿⠋⠋⠉⢸⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⠋⠟⠋⠋⠉⠁⠉⠉⢿⡇⠀⠀
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢻⣷⡄⠀⠈⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⡀⡀⠀⢀⣀⣤⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⣀⣀⠀⠀⢠⣼⡇⠀⠀
⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠹⢿⣿⣿⡶⣾⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⣟⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀⠔⠀⠀⣿⡇⠀⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⣿⣽⠋⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⠿⠛⣁⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠤⠀⣀⡀⣤⣾⣿⣿⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣏⣥⠀⠀⠀⠀⣠⣿⣿⣟⠿⣷⣤⣤⡀⠀⣀⣀⣀⡀⠀⠀⠈⠭⠷⠿⠛⢹⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣯⣿⣿⣿⡿⢻⡆⣀
⠈⠙⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡶⠃⠀⠀⢰⣿⣿⣿⣿⣄⠈⢿⣿⣿⣿⠛⠉⣉⣉⡉⠒⠂⠀⠀⠀⠀⠟⡿⠨⠿⣿⣿⣶⣤⣶⣶⣿⣿⣿⣿⢿⢛⣿⣶⣦⠄⠀⠀⢀⣤⣽⠟⠋⢉⣑⠴⢿⣛⢿
⣤⣤⣾⣿⣿⣿⠿⠿⠿⠿⣿⣶⣦⣄⣴⣿⡿⠷⠀⣀⡁⠒⠀⠀⣿⣿⣿⣿⣧⠀⣼⣿⣿⣇⣤⣀⣀⣀⣈⠙⠀⣀⣀⣀⡀⢀⣀⣤⣶⡿⠿⠋⣉⣭⣽⣶⣶⣿⣿⣿⠀⢩⠀⣺⣿⣶⣶⣟⠋⠉⠀⠀⠢⣤⣾⣿⣿⠿
⠛⠛⢩⣿⡷⠀⠀⠀⠀⢀⣬⣭⣿⡅⠉⣩⣤⡀⣀⣀⣀⡤⠔⢻⣿⣿⠏⠙⠉⠀⣿⣿⡛⣩⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⠛⠉⠁⠐⠚⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠋⠀⠘⣿⣷⡟⡻⠇⣠⣤⣤⣦⡿⠋⠀⠀⢀
⣀⣴⣿⡿⠃⠀⠀⠀⢠⣾⣿⣿⣿⠇⠀⢿⡿⠗⠈⠉⠀⣶⣶⣿⣿⣧⠀⠀⡠⢊⠽⣿⡆⠻⣿⣿⣿⣿⣿⠿⠉⠋⠉⠀⠀⠀⠐⠚⠀⣠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣸⣿⠹⣿⣿⢠⣿⣿⣿⣿⢀⣤⣤⣶⡿
⠙⠁⠹⣿⠄⠀⢀⡴⠟⡛⢸⣿⣟⠐⠂⣴⡄⠒⠒⠶⠒⢻⣿⣿⢻⣿⣿⣾⠁⠀⠀⠙⢿⡀⠹⢿⠛⠛⢁⣾⣷⣶⣶⣶⣶⣶⣶⠾⠿⠿⠛⠁⣸⣿⣿⣿⣿⣿⠟⣻⡇⠀⢀⣿⣏⡄⠈⠉⠁⠙⠙⠛⠁⠈⠋⠉⠀⠀
⣐⣦⣼⡿⠀⡴⠁⠀⢠⣿⡾⣿⣿⠤⠤⣤⡀⠤⢤⣤⣤⣿⣿⣯⡾⢻⣿⣿⣿⣤⣶⣶⣾⣷⣤⣄⡀⠐⠻⠛⠉⠉⠉⠀⠁⠀⠀⣀⡄⠚⠓⢲⣿⣿⣿⣿⡿⠋⠀⣎⡿⠀⠘⣿⡇⢷⣤⣤⣀⢸⣿⣿⣿⠂⠀⠀⠀⠀
⠛⠛⢻⣧⠞⠁⠀⠀⢸⣿⣷⣿⣿⠀⠀⠉⠇⠠⠀⠀⣾⣿⡟⠙⣿⢼⣿⣿⠻⣿⣿⣿⣿⢿⣿⣿⡛⠁⢸⣿⠀⠀⠀⠀⠀⠐⠈⠁⣀⣼⣶⣿⣿⣿⣿⣿⠃⠀⠀⢨⣿⡆⠀⢻⣿⠀⠛⠛⠻⢿⣿⣤⣤⠰⠾⠿⠿⡿
⠀⣦⣾⣷⠏⢶⠄⠰⣾⠷⢾⣿⣿⢀⠀⠉⠁⠀⠀⢨⣿⡿⠹⠟⡟⢸⣿⣿⣷⣾⣝⠻⢿⣈⡙⠛⠃⠀⢿⣿⣦⣤⣤⣤⣤⣶⣾⣿⣿⣿⠿⠟⠋⠈⣻⣿⡆⠀⠀⣿⣿⠇⠀⠀⣿⣦⣀⣀⡀⢘⠣⠽⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣠⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠒⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣿⣿⡇⣿⣿⢘⣳⣄⣠⣯⣷⣿⣿⣧⣿⣿⠀⣹⡗⢾⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡛⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⣶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⢈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠉⠀⠉⠈⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠟⠉⠉⠙⠛⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣻⡿⠛⠁⠀⠀⠀⢹⣯⢩⣭⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⠁⠀⠀⠀⠀⠀⢨⡟⠘⢿⣦⡀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⣿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡄⠀⠀⠀⠀⢠⡿⠀⠆⠀⢿⣿⣶⣤⣤⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⡿⠟⠛⠛⠟⢛⠋⠀⠀⠀⠀⠉⢻⠀⠀
⡁⠀⠀⠙⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣀⣀⣶⣿⣧⡀⣠⣄⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⣸⠛⠻⣶⣄⡀⠀⣠⣾⡄⠀
⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣠⣾⡟⠀⣀⣹⣿⣿⣿⣿⠉⠁⠀
⣿⣦⣤⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡓⢾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀
⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢀⠼⠿⣿⣿⡿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢯⣩⣽⡿⣿⠿⠟⠛⠉⠁⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠟⢻⠛⠛⠉⠉⡉⠙⠻⣿⠀⠀
⣿⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⢹⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⠀⡀⣀⣠⣴⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⢀⣀⡀⠀⠀⣤⣿⠀⠀
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠙⢿⣿⣿⣦⣴⣎⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠉⠀⡠⠖⠀⢸⣿⠀⠀
⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠟⢰⣯⡾⠁⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⠿⣿⣿⣿⣿⠿⠋⣡⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⡀⠀⣀⢀⣠⣾⣿⡆⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⡅⠀⠀⠀⠀⣸⣿⣿⡿⣿⣦⣤⡀⠀⠀⢀⣀⠀⠀⠀⠚⠋⠽⠷⠶⠋⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣤⣼⣽⣿⣿⣿⠟⣷⠄
⠉⠙⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢭⡔⠀⠀⠀⣾⣿⣿⣿⣯⡈⢻⣿⣿⣿⡟⠛⠋⢉⠋⠒⠲⠀⠀⠀⠀⠰⢿⡏⠻⢿⣿⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⢿⣶⣦⣤⠀⠀⠀⢀⣭⡿⠛⢛⣩⢡⠾⣟⠿
⣀⣤⣤⣿⣿⣶⣶⣶⡶⠿⣷⣶⣦⣤⣠⣶⣾⡾⠍⠁⠒⠁⠤⠀⢹⣿⣿⣿⣿⡅⢀⣿⣿⣿⣀⣀⡀⠈⠉⠙⠂⠀⣀⣀⠀⠀⢀⣀⣤⣴⡿⠟⠋⣉⣭⣽⣿⣿⣿⣿⡖⠈⡁⠀⣿⣶⣠⣴⠟⠋⠁⠀⠀⠤⣵⣾⣿⣿
⠿⠟⠛⣻⣿⡇⠀⠀⠀⠀⢨⣿⣿⣟⡈⣉⣭⣄⢀⡈⢉⣀⣠⠖⣾⣿⣿⠏⠛⠃⢸⣿⣟⢛⣽⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠛⠉⠁⠰⢆⣾⣿⣿⣿⣿⣿⣿⣿⠁⠸⠃⠀⢻⣿⣿⡛⢿⠀⣀⣀⣴⡾⠟⠉⠀⠀
⠀⣀⣴⣿⡟⠀⠀⠀⠀⣤⣿⣿⣿⡿⠀⠸⣿⡿⠊⠉⠉⢡⣶⣶⣿⣿⣉⠀⢀⡔⠉⢿⣧⠸⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠁⠀⠀⠐⠊⢀⣤⣿⡿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⡯⢿⣷⣆⣸⣿⣿⣿⡇⣀⣤⣤⣶
⠛⠛⠉⢿⣧⠀⠀⣠⡴⠿⠏⣿⣿⡗⠲⢠⣭⠠⠄⠤⠤⠾⣿⣿⡿⣿⣿⣦⡟⠀⠀⠘⢿⣇⠈⢿⡿⠿⠛⣡⣾⣶⣶⣶⣶⣶⣶⣶⣾⣿⠿⠋⠀⣿⣿⣿⣿⣿⣿⠟⣿⠀⠀⢸⣿⢣⠀⠉⠉⠘⠛⠛⠛⠀⠛⠋⠉⠁
⠀⣢⣠⣾⡏⢀⡞⠁⠀⣸⣷⣿⣿⡧⠤⣬⣥⠀⢤⣤⣤⣰⣿⣿⣡⡿⣿⣿⣷⣦⣤⣴⣶⣾⣤⣄⡀⠀⠴⠿⠛⠛⠉⠁⠉⠉⠁⠀⣠⠐⠒⠶⣼⣿⣿⣿⣿⠟⠁⢰⢻⡇⠀⢺⣿⢸⣦⣄⣀⡀⣷⣶⣿⡷⠀⠀⠀⠀
⠛⠿⠟⢯⣠⠎⠀⠀⠀⣿⡿⣼⣿⡇⡀⠈⠙⠂⠀⠈⢩⣿⣿⠟⢻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⣾⡆⠀⠀⠀⠀⠀⠐⠊⠁⣀⣶⣾⣿⣿⣿⣿⡿⠀⠀⠀⣿⣷⠀⠘⣿⡇⠙⠛⠿⠿⣿⣯⣭⡄⠴⡶⢶⣶
⠀⠆⣲⣾⠿⢶⠄⠠⢶⡿⠷⢿⣿⡇⢀⠀⠈⠀⠀⠈⣽⣿⡟⠶⢾⠃⣿⣿⣿⣿⣯⡻⢿⣇⡙⠻⠛⠀⠰⣿⣷⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⡿⠟⠋⢙⣿⣷⠀⠀⢰⣿⡿⠀⠀⢸⣷⣄⡀⠀⠀⠗⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢠⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠢⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣽⣿⡇⣿⣯⢘⣳⡄⣠⣏⣷⣿⣿⣧⣿⣿⠀⣽⡗⣽⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⢛⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡛⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⡄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠛⠛⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣷⣶⣤⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⡿⠋⠁⠀⠀⠙⣿⡛⣛⡃⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⣿⠏⠀⠀⠀⠀⠀⠀⣿⠇⢿⣧⡀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡄⠀⠀⠀⠀⠀⣰⠇⠠⠀⢻⣿⣶⣤⣀⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⡿⠿⠿⢿⠿⠟⠉⠀⠉⠉⠉⠻⡆⠀
⡟⠀⠈⠙⢿⣿⣿⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⠀⠀⣤⣴⣿⡀⠀⣐⢀⣿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠏⠁⠀⠀⠀⢀⡗⠻⣦⣄⡀⠀⠀⣰⣇⠀
⣿⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⣠⣿⠁⠀⣘⣿⣿⣷⣿⡟⠙⠀
⣿⣤⣀⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⢤⣾⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⠿⣿⡟⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣛⣟⣿⣿⣿⣿⠿⠟⠛⢹⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⢛⡿⠟⠛⠛⠋⠛⢻⣿⠃⠀
⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠘⢿⣏⠀⠈⠛⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⠈⠀⠀⣀⣠⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀
⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⣶⣾⣿⣧⣠⣴⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡗⡷⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠉⢉⡤⠂⠈⣿⡇⠀
⢛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⠋⡿⣢⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⣿⣿⣿⣿⣿⠿⠋⣡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠈⠀⣀⣴⣿⣷⠀
⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢟⠀⠀⠀⠀⢀⣾⣿⡿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣯⣷⠶⢺⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣈⣟⣿⣿⣿⡿⢻⡄
⠒⠒⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣾⣿⣫⠄⠀⠀⢠⣿⣿⣿⣿⡈⠻⣿⣿⣶⣶⠿⠟⠛⠓⠢⠤⠄⠀⠀⠀⠀⣺⣿⢛⣿⣿⣶⣄⣀⣤⣤⣶⣾⣿⣿⣶⡶⢶⣤⣄⡀⠀⠀⠀⣉⣿⡿⠛⠛⠋⣠⣾⢷
⠀⣀⣀⣹⣿⣤⣤⣤⣤⣶⣶⣦⣤⣀⡀⣠⣤⣿⣏⠒⠡⠐⢀⡀⠘⣿⣿⣿⣿⣏⠀⣹⣿⣿⡏⠀⠀⠉⠉⠒⠢⠀⠀⠀⠀⠀⠀⠁⣀⣤⣿⣿⠿⠛⢛⣻⣭⣭⣿⣿⣿⠉⢛⠀⣽⣶⣤⣤⠾⠛⠋⠀⠀⢌⢑⣤⣾⣿
⣿⣿⠿⠿⣿⣿⠉⠁⠀⠀⠈⣻⣻⣿⠋⠚⢛⣁⠀⠀⠒⠁⠀⣠⢦⣿⣿⡿⠻⠻⠀⣿⣿⠿⢛⣿⣿⣷⣶⣶⣦⣴⣿⣿⣿⣶⣾⠿⠟⠋⠡⠴⢰⣿⣿⣿⣿⣿⣿⣿⡟⠀⡟⠀⠸⣿⣯⡿⢿⡆⢀⣀⣀⣤⣿⠛⠉⠁
⠀⠀⢀⣾⣿⠏⠀⠀⠀⢀⣼⣿⣿⣿⡇⠈⣿⣿⡇⠛⠚⠋⣩⣤⣾⣿⠏⠁⠀⢀⠔⣻⣿⡀⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⠉⠉⠀⠠⠴⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⢻⣿⣶⢡⣿⣿⣿⣿⠀⣀⣀⣤
⠶⠾⠟⢻⣷⡀⠀⠀⣀⣼⠿⢻⣿⡿⠤⡄⣈⡋⡀⢀⣀⣤⣿⣿⣿⣿⣿⣦⣴⠃⠈⠀⢿⣷⠈⢻⣿⠿⡿⠋⣴⣦⣤⣤⣤⣤⣤⣤⣤⣶⣿⠿⠃⢸⣿⣿⣿⣿⣿⡿⢿⡆⠀⠀⣿⡏⡀⠙⠛⠈⠛⠿⠿⠋⠘⠟⠛⠉
⠀⠠⡀⣠⣿⠃⢠⠞⠁⠀⣷⣼⣿⣿⣀⣀⣛⠁⢀⣀⣀⣀⣼⣿⣟⣸⣿⣿⣿⣤⣀⣠⣤⣭⣧⣀⠉⠀⠠⢾⠿⠟⠛⠛⠙⠛⠉⠉⠁⡉⠤⢤⣤⣿⣿⣿⣿⣿⠟⠀⡟⣷⠀⢰⣿⡏⣧⣀⣀⠀⢰⣶⣶⣶⡄⠀⠀⠀
⠶⠾⠿⢿⡋⡠⠋⠀⠀⢰⣿⣿⣿⣿⠀⠈⠛⡇⠀⠉⠛⣻⣿⡿⠿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠆⢰⣶⠀⠀⠀⠀⠀⠠⠔⠊⠁⣰⣤⣾⣿⣿⣿⣿⠇⠀⠀⢱⣷⡄⠀⢿⣿⠘⠿⠿⢿⣾⣿⣋⣉⡠⣶⠶⣶
⠀⠆⠲⣶⡿⢶⠄⠠⠴⣾⠿⢻⣿⣿⠈⠀⠀⠂⠀⠁⢲⣿⣿⢣⣤⡿⢹⣿⣿⣾⣽⡿⣿⣿⠙⠻⠿⠇⠀⣼⣿⣄⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⠟⠙⣿⣿⡄⠀⠀⣼⣿⡇⠀⠈⣿⣄⠀⠀⠀⠸⢿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⣄⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣼⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣛⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⣾⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠉⠀⠉⠈⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣾⣶⣤⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⡿⠟⠉⠀⠀⠈⣿⡟⣛⡋⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣷⡟⠁⠀⠀⠀⠀⠀⢸⡿⠿⣷⣀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢧⠀⠀⠀⠀⠀⢀⡟⠀⠀⠘⣿⣷⣤⣀⣠⣴⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠿⠻⠿⡿⠿⠋⠀⠈⠉⠉⠙⢇⠀
⠛⠁⠈⠙⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡄⠀⢠⣴⣾⡅⠀⢀⠂⣽⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⠉⠀⠀⠀⠀⡸⠛⢶⣤⣀⠀⠀⢀⣿⠀
⣿⡆⠀⠀⠀⠘⣿⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⣾⡇⠀⣀⣻⣿⣿⣿⡿⠉⠃
⣿⣧⣀⣀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣦⣶⣿⣿⣷⣾⡿⣿⣿⣿⣿⣿⣦⠀
⣿⣿⡿⢿⣿⠛⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⣟⣿⣻⣿⣿⣿⡟⠟⠛⢫⣷⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠹⠟⣿⠿⠛⠛⢋⠛⠛⣿⡏⠀
⣿⣿⣳⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠻⣿⡁⠈⠙⢿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠁⠀⢀⣀⣤⡼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀
⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠢⠾⢶⣶⣿⣷⣄⣠⡎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢾⢶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠀⠀⠉⠉⣡⠔⠀⢹⣿⠀
⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⠻⡟⢹⢷⡿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⢾⣿⣿⣿⣿⣿⡿⠟⣩⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⡁⢀⣠⣾⣿⡄
⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⡁⠀⠀⠀⠀⣰⣿⡿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢟⣻⣵⡶⠶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣅⣹⣻⣿⣿⣿⠿⣦
⠗⠒⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⡥⠀⠀⠀⣼⣿⣿⣿⡇⠙⢿⣯⣷⣶⡶⠿⠛⠓⠒⠤⠤⠀⠀⠀⠀⢰⣿⡏⣻⣿⣶⣦⣀⣤⣤⣴⣶⣿⣿⣷⣶⢶⣦⣤⣀⠀⠀⠀⢈⣹⣿⠛⠛⠛⢁⣼⡿
⠀⠀⢀⣘⣿⣧⣤⣤⣤⣤⣶⣦⣤⣀⡀⢀⣤⣼⣿⡐⠊⠄⠂⣀⠀⢿⣿⣿⣿⣗⡀⢈⣿⣿⣿⠁⠀⠈⠉⠓⠲⠄⠀⠀⠀⠀⠀⠈⢀⣠⣼⣿⠿⠛⠛⣛⣯⣭⣽⣿⣿⡏⠙⠋⢨⣷⣦⣤⡴⠟⠛⠁⠁⠠⡁⣠⣶⣿
⣾⣿⡿⠿⢿⣿⡋⠉⠉⠀⠀⢙⣿⣿⡟⠙⠛⣋⠀⠀⠐⠂⠀⢀⡴⣼⣿⣿⠟⠿⠇⢸⣿⡿⠟⣻⣿⣷⣶⣶⣶⣤⣾⣿⣿⣶⣶⡿⠿⠛⠉⠤⠆⣾⣿⣿⣿⣿⣿⣿⣿⠁⠸⠃⠈⣿⣿⣽⠿⣷⠀⣀⣀⣠⣽⡟⠋⠉
⠁⠀⢀⣰⣿⡿⠀⠀⠀⠀⣠⣿⣿⣿⣿⠈⢹⣿⣷⠚⠒⠚⢉⣭⣴⣿⡿⡁⠀⠀⡠⠺⣿⡇⢸⣿⣿⣿⣿⣿⣿⡟⠿⠛⠋⠉⠁⠀⠤⠂⠀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣟⣿⣾⡎⣼⣿⣿⣿⡇⢀⣀⣤
⠴⠶⠿⠻⣿⡆⠀⠀⢀⣠⡿⠛⣿⣿⠧⢠⣈⣛⢁⢀⣀⣀⣼⣿⣿⣿⣿⣷⣠⡞⠀⠁⠸⣿⡄⠹⣿⡿⡿⠟⢡⣶⣤⣤⣤⣤⣤⣤⣤⣴⣿⡿⠟⠀⣿⣿⣿⣿⣿⣿⠿⣣⠀⠀⢸⣿⣃⠈⠛⠓⠹⠻⠿⠟⠁⠻⠛⠉
⠀⠀⢀⢀⣼⡟⠀⡴⠋⠁⢸⣤⣿⣿⣄⣀⢘⡋⠀⣀⣀⣀⣠⣿⣿⣃⣿⣿⣿⣧⣄⣀⣠⣬⣵⣀⡈⠁⠀⢴⡿⠿⠟⠛⠋⠛⠋⠉⠉⢈⠡⠤⣤⣼⣿⣿⣿⣿⡿⠃⢸⢿⡄⠀⣿⣿⢻⣄⣀⡀⢰⣶⣶⣶⡦⠀⠀⠀
⠶⢶⣾⡿⣟⢁⠜⠁⠀⠀⣿⣿⣿⣿⡀⠀⠙⢳⠀⠈⠙⢻⣿⣿⠿⢿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠀⣶⠆⠀⠀⠀⠀⠀⠤⠚⠉⢀⣤⣴⣿⣿⣿⣿⡿⠀⠀⠈⣾⣧⠀⠸⣿⡏⠛⠿⠿⣷⣿⣟⣉⣁⣴⣶⣶
⠀⠆⠲⣶⣿⢷⠄⠠⠴⢶⡿⠹⣾⣿⡏⠁⠀⠐⠀⠀⠐⣾⣿⣟⣤⣼⠇⣿⣿⣷⣭⡿⠿⣿⡟⠛⠿⠿⠀⢸⣿⣧⣀⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⡿⠋⢻⣿⣧⠀⠀⢨⣾⣿⠀⠀⢻⣧⡀⠀⠀⠀⠿⣿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣽⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⢛⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⢐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣷⣦⣤⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⣿⡿⠋⠁⠀⠈⢻⣿⢛⣛⠁⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⠋⠀⠀⠀⠀⠀⠈⣿⡾⣿⣆⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡽⡀⠀⠀⠀⠀⠀⣼⠃⠀⠈⢿⣷⣦⣄⣀⣤⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡿⠿⠿⢿⠿⠟⠁⠀⠉⠉⠉⢻⡀
⠛⠟⠉⠉⠻⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡄⠀⠀⢤⣴⣏⠀⠀⡐⢸⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋⠁⠀⠀⠀⢀⠞⢷⣦⣄⠀⠀⠀⣼⡅
⣿⣧⠀⠀⠀⠈⢻⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣽⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣴⣿⠀⢀⣙⣿⣿⣶⣿⠏⠑
⣿⣿⣀⣀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡶⢴⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⠀
⣿⣿⣿⠿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣻⣟⣿⣿⣿⣿⠿⠟⠛⣿⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⡿⢻⡿⠿⠛⠛⠙⠛⢻⣿⠀
⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠸⣿⡏⠈⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠉⠉⠀⠀⢀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀
⣤⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠦⣶⣾⣿⣆⣀⣴⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠶⡶⣶⣾⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠈⠉⢉⡤⠀⠸⣿⡆
⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠩⠭⠿⢿⠋⡿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣷⣿⣿⣿⣿⣿⣿⠿⢛⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⢀⠀⢈⠀⣀⣼⣿⣇
⣶⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠏⠀⠀⠀⠀⠠⣾⣿⣷⣶⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠩⠝⣛⣯⣥⠶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣬⣘⣟⣿⣿⣿⡿⢷
⡿⠒⠢⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⣾⣗⣫⠄⠀⠀⢠⣿⣿⣿⣷⠉⢻⣿⣽⣦⣶⠶⠾⠓⠲⠤⢤⡀⠀⠀⠀⠀⣿⡿⠻⣿⣷⣦⣄⣀⣠⣤⣴⣶⣿⣷⣶⡶⣦⣤⣀⠀⠀⠀⠀⣉⣿⡛⠛⠛⠋⣠⣿
⠀⠀⠀⠀⣻⣷⣄⣤⣤⣤⣤⣤⣤⣀⡀⠀⣠⣤⣿⣇⠐⠡⠀⣀⡀⢸⣿⣿⣿⣿⢀⠀⢻⣿⣿⡋⠀⠐⠒⠒⠒⠤⠀⠀⠀⠀⠀⠀⠁⣀⣨⣽⣿⠿⠛⢛⣻⣿⣭⣿⣿⣯⠙⠛⠉⣽⣦⣤⣤⠾⠟⠃⠀⠀⠍⣁⣴⣾
⣶⣾⣿⣿⠿⣿⣟⠛⠉⠉⠉⠉⡿⠿⣿⠓⠻⠟⠋⠀⠀⠒⠀⠀⣠⣤⣿⣿⡟⠿⠿⢠⣧⡿⡿⢛⣿⣷⣶⣶⣶⣆⣴⣿⣿⣷⣶⣾⠿⠟⠋⢡⡤⢰⣿⣿⣿⣿⣿⣿⣿⡏⠀⡟⠀⢹⣿⣿⠿⢷⡆⢀⣀⣀⣤⣿⠛⠉
⠉⠁⠀⢀⣼⣿⠇⠀⠀⠀⢀⣸⣿⣿⣿⡇⠐⣿⣿⡖⠒⠒⠚⣩⣅⣾⣿⠏⠀⠀⢀⠜⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⠋⠉⠀⠠⠤⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣷⣖⢡⣿⣿⣿⣿⠀⣀⣀
⡤⠦⣶⠿⢿⣯⠀⠀⠀⢀⣼⣿⢻⣿⡿⢄⣀⣙⠋⡀⣀⣀⣠⣿⣿⣿⣿⣾⣅⣴⠃⠈⠈⢿⣧⠈⢿⣿⣿⡿⠋⣵⣦⣤⣤⣤⣤⣤⣤⣤⣶⣿⡿⠃⣻⣿⣿⣿⣿⣿⡿⢿⡄⠀⢀⣿⣇⠀⠙⠛⠈⠟⠿⠿⠋⠸⠟⠋
⠀⠀⢀⠀⢸⣿⠀⢠⠞⠉⢁⣦⣼⣿⣇⠀⠀⢛⠁⠀⣀⠀⢀⣼⣿⡟⣸⣿⣿⣿⣤⢀⣀⣠⣽⣄⡈⠉⠀⢠⣾⠿⠿⠟⠛⠙⠛⠋⠉⠉⡉⠤⢤⣄⣿⣿⣿⣿⣿⠟⠀⣿⣧⠀⢸⣿⡟⣆⣀⣀⠀⣶⣦⣶⣶⠄⠀⠀
⠶⠶⣶⣿⣿⡋⣠⠏⠀⠀⢸⣿⣿⣿⡇⠀⠉⠟⡆⠈⠙⠛⣿⣿⡿⢿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⢠⡦⠀⠀⠀⠀⠀⠀⠤⠊⠁⣠⣤⣾⣿⣿⣿⣿⠇⠀⠀⢹⣿⡄⠈⢿⣷⠙⠿⠿⣿⣿⣿⣛⣉⢠⣴⣶
⠀⠆⠲⣶⢿⣿⠇⠠⠴⠶⣾⡟⢿⣿⣿⠉⠀⠤⠃⠈⠀⠰⣿⣿⣧⣤⡿⢸⣿⣿⣮⣿⢿⣿⣿⠛⢿⡿⠆⠀⣿⣿⣄⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⠟⠛⣿⣿⡄⠀⠀⣾⣿⡇⠀⠘⣿⣄⠀⠀⠀⠸⢿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣤⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⢛⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠙⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⡄⢐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣷⣦⣤⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⣿⡿⠋⠁⠀⠈⢻⣿⢛⣛⠁⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣾⠋⠀⠀⠀⠀⠀⠈⣿⡾⣿⣆⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⡀⠀⠀⠀⠀⠀⣼⠃⠀⠈⢿⣷⣦⣄⣀⣤⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡿⠿⠿⠿⠿⠟⠁⠀⠉⠉⠉⢻⡀
⠛⠟⠉⠉⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡄⠀⠀⢤⣴⣏⠀⠀⡐⢸⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋⠁⠀⠀⠀⢀⠞⢷⣦⣀⠀⠀⠀⣼⡅
⣿⣧⠀⠀⠀⠈⢻⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣽⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣴⣿⠀⢀⣙⣿⣿⣶⣿⠏⠱
⣿⣿⣀⣀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡶⣴⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⠀
⣿⣿⣿⠿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣻⡛⣿⣿⣿⣿⠿⠟⠛⣿⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⡿⢻⡿⠿⠛⠛⠙⠛⢻⣿⠀
⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠸⣿⡏⠀⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠉⠉⠁⠀⢀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀
⣤⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠦⣶⣾⣿⣆⣀⣴⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⡶⡶⣶⣾⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠈⠉⢉⡤⠀⠸⣿⡆
⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠩⠭⠿⢿⠋⡿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣵⣿⣿⣿⣿⣿⣿⠿⢛⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⢀⠀⢈⠀⣀⣼⣿⣇
⣶⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠏⠀⠀⠀⠀⠠⣾⣿⣷⣶⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠩⠝⣛⣯⣥⡶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣬⣜⣿⣿⣿⣿⡿⢷
⡿⠒⠲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⣾⣗⣫⠄⠀⠀⢠⣿⣿⣿⣷⠉⢻⣿⣽⣦⣶⠶⠶⠓⠲⠤⢤⡀⠀⠀⠁⢀⣿⡿⠻⣿⣶⣦⣄⣀⣤⣤⣶⣶⣿⣷⣶⡶⣦⣤⣀⠀⠀⠀⠀⣉⣿⡛⠛⠛⠏⣠⣿
⠀⠀⠀⠀⣻⣷⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⣀⣤⣿⣗⠐⠡⠀⣀⠀⢸⣿⣿⣿⣿⢀⠀⢻⣿⣿⡋⠀⠐⠒⠒⠒⠤⠀⠀⠀⠀⠀⠀⠁⣀⣨⣽⣿⠿⠛⢛⣻⣿⣭⣿⣿⣯⠑⠛⠉⣽⣦⣤⡤⠾⠟⠃⠈⠀⠍⣁⣴⣾
⣶⣾⣿⣿⠿⣿⣛⠛⠉⠉⠉⠉⡿⠿⣿⠓⠛⠟⠋⠀⠀⠒⠀⠀⣠⣤⣿⣿⡟⠿⠿⢠⣷⣿⡿⢛⣿⣷⣶⣶⣶⣦⣴⣿⣿⣶⣶⣾⠿⠟⠋⢩⡤⢰⣿⣿⣿⣿⣿⣿⣿⡏⠀⡟⠀⢹⣿⣿⡿⢷⡆⢀⣀⣀⣤⣿⠛⠉
⠉⠉⠀⢀⣼⣿⠏⠀⠀⠀⢀⣸⣿⣿⣿⡏⠐⣿⣿⡖⠒⠒⠚⣩⣅⣾⣿⠏⠀⠀⢀⠜⢿⣿⠠⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⠋⠉⠀⠠⠤⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣷⣖⢩⣿⣿⣿⣿⠀⣀⣀
⣤⠦⣾⠿⢿⣯⠀⠀⠀⢀⣼⣿⢿⣿⡿⢄⣀⣙⠋⣀⣀⣀⣠⣿⣿⣿⣿⣾⣅⣴⠃⠈⠈⢿⣇⠈⢿⣿⣿⡿⠋⣵⣦⣤⣤⣤⣤⣤⣤⣤⣶⣿⡿⠃⣻⣿⣿⣿⣿⣿⡿⢿⡄⠀⢀⣿⣇⠀⠙⠛⠉⠟⠿⠿⠋⠸⠟⠋
⠀⠀⢀⠀⢸⣿⠀⢠⠞⠉⠁⣦⣼⣿⣇⠀⠀⢛⠁⠀⣀⠀⠀⣼⣿⡟⣸⣿⣿⣿⣤⢀⣀⣠⣽⣄⡈⠉⠀⢠⣾⠿⠿⠟⠛⠙⠛⠋⠉⠉⡉⠤⣤⣄⣿⣿⣿⣿⣿⠟⠀⣿⣧⠀⢸⣿⡟⣆⣀⣀⠀⣶⣤⣶⣶⠄⠀⠀
⠶⢶⣶⣿⣿⡋⣠⠏⠀⠀⢸⣿⣿⣿⡇⠀⠉⠟⡆⠈⠙⠛⣿⣿⡿⢿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⢠⡦⠀⠀⠀⠀⠀⠀⠤⠊⠁⣠⣤⣾⣿⣿⣿⣿⠇⠀⠀⢸⣿⡄⠀⢿⣷⠙⠿⠿⣿⣿⣿⣛⣉⢠⣴⣶
⠀⠆⠲⣶⢿⣿⠅⠠⠲⠶⣾⡟⢿⣿⣿⠉⠀⠠⠃⠈⠀⢠⣿⣿⣧⣤⡿⢸⣿⣿⣮⣿⢿⣿⣿⠛⢿⡿⠆⠀⣿⣿⣄⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⠟⠛⣿⣿⡄⠀⠀⣾⣿⡇⠀⠘⣿⣄⠀⠀⠀⠸⢿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣠⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣿⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⣈⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣰⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣹⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣾⣶⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠟⠉⠀⠀⠙⣿⡟⣛⡋⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣷⡟⠁⠀⠀⠀⠀⠀⢹⢧⢿⣧⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⢠⡟⠠⠀⠹⣿⣦⣄⣀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⡿⠿⠿⠿⡿⠿⠋⠀⠉⠉⠉⠙⣇
⡙⠟⠏⠉⠛⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⣤⣾⡁⠀⠀⠂⣿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠉⠀⠀⠀⠀⡰⠻⣶⣄⡀⠀⠀⢠⣯
⢰⣿⡄⠀⠀⠀⠹⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢠⣾⡇⠀⣈⣻⣿⣷⣾⡿⠉
⢸⣿⣇⡀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣗⢦⣶⣿⣿⣷⣾⣻⣿⣿⣿⣿⣿⡆
⣼⣿⣿⣿⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⣟⣛⣻⣿⣽⣿⡿⠿⠛⢻⣧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠻⠟⣿⠿⠟⠛⢋⠛⠛⣿⡇
⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠊⠉⡉⢿⣿⠉⠉⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠈⠉⠁⠀⠀⣀⣠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⣤⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⡴⢴⣴⣿⣧⣀⣠⡎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣶⢶⣴⣶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠉⠉⣡⠄⠀⢿⣷
⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠭⠿⢿⡟⢹⢧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⣾⣿⣿⣿⣿⣿⡿⠟⣋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⡀⠀⡁⢀⣠⣾⣿
⣥⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠃⠀⠀⠀⠀⢰⣾⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⢛⣻⣭⡤⢶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣅⣻⣻⣿⣿⣿⠿
⣿⠿⠥⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⣿⣚⡅⠀⠀⠀⣴⣿⣿⣿⡎⠙⣿⣯⣶⣤⡶⠶⠖⠲⠦⠤⣄⠀⠀⠀⠁⢰⣿⠟⢿⣷⣶⣤⣀⣀⣤⣤⣶⣾⣿⣶⣶⢶⣤⣄⡀⠀⠀⠀⢈⣹⣿⠛⠛⠛⢁⣼
⡆⠀⠀⠀⢙⣿⣆⣀⣠⣤⣤⣤⣤⣀⣀⠀⢀⣠⣴⣿⡉⠛⠠⢀⡀⠀⣿⣿⣿⣿⡇⡀⠘⣿⣿⣟⠁⠀⠒⠒⠒⠢⠄⠀⠀⠀⠀⠀⠈⢀⣀⣭⣿⡿⠟⠛⣛⣿⣭⣽⣿⣿⡅⠙⠋⢩⣷⣤⡤⠴⠿⠛⠁⠀⠀⢁⣠⣶
⣴⣶⣾⣿⣿⢿⣿⡛⠋⠉⠉⠉⠻⠿⠿⡿⠺⠿⠛⠉⠁⠐⠒⠀⢀⣤⣼⣿⣿⢟⠿⠇⣸⣿⣿⡟⢿⣿⣶⣶⣶⣶⣠⣾⣿⣷⣶⣶⣾⠿⠛⠉⣥⠄⣾⣿⣿⣿⣿⣿⣿⣿⠁⢸⠀⠈⣿⣿⣿⠿⣶⢀⣀⢀⣠⡸⡟⠋
⠛⠉⠉⠀⢠⣿⣿⠁⠀⠀⠀⢀⣾⣿⣿⣷⠀⢺⣿⣷⠒⠶⠒⢚⣉⣠⣿⡿⠉⠀⠀⡠⠻⣿⡇⢼⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠀⠠⠄⠀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⡿⣿⣶⡀⣾⣿⣿⣿⡇⢀⣀
⣤⡤⢴⡾⠿⣿⡅⠀⠀⠀⣀⣿⡛⣻⣿⣇⣀⡈⡛⢁⣀⣀⣀⣸⣿⣿⣿⣷⣧⣀⡞⠀⠁⠹⣿⡌⠹⣿⣿⣿⠟⢉⣶⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⠟⠈⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀⢸⣿⣁⠈⠛⠓⠙⠻⠿⠟⠁⠿⠛
⠀⠀⠀⡀⠀⣹⡗⠀⣠⠚⠉⢰⣀⣻⣿⡀⠀⠸⠛⠀⠀⠀⠀⢠⣿⣿⢃⣿⣿⣿⣇⡄⢀⣀⣭⣷⣀⠉⠁⠀⣠⣿⠿⠿⠛⠛⠛⠛⠋⠉⢉⠩⢤⣄⣸⣿⣿⣿⣿⡿⠃⢸⣿⡄⠀⣿⣿⢻⣀⣀⠀⠠⣶⣴⣶⣦⠀⠀
⠤⢤⣴⣾⣿⣿⠃⡴⠁⠀⠀⣾⣿⣿⣿⡁⠈⠻⢷⠈⠙⠛⢻⣿⣿⡿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠀⣤⠄⠀⠀⠀⠀⠀⠠⠔⠉⠀⣤⣴⣿⣿⣿⣿⡿⠀⠀⠘⣶⣧⠀⠹⣿⡆⠻⠿⠿⣷⣿⣟⣋⡁⣤⣶
⠀⠆⠲⣶⠋⣿⠎⠠⠰⠶⢶⣿⠻⣿⣿⡇⠀⠠⠬⠀⠁⠀⢼⣿⡿⣤⣼⠇⣿⣿⣧⣽⡿⣿⣿⡟⠻⣿⠷⠀⢸⣿⣆⣀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⡿⠛⢻⣿⣧⠀⠀⢸⣿⣿⠀⠀⢹⣧⡀⠀⠀⠀⠿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⢤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⢿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⢈⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣷⣦⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⠿⠋⠁⠀⠉⢻⣿⢛⣛⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣼⣿⠃⠀⠀⠀⠀⠀⢘⣿⡸⣿⣄⠀⠀⠀⠀⠀⢀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⠀⠀⠀⠀⠀⠀⣼⠃⠄⠈⣿⣷⣤⣀⣀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠿⠿⠏⠀⠀⠉⠉⠉⢻
⣘⠻⠿⠉⠛⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⢠⣼⣇⠀⠀⠐⢸⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠋⠀⠀⠀⠀⢀⠟⢳⣦⣄⠀⠀⢀⣼
⠃⣾⣇⠀⠀⠀⠈⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣷⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣴⣿⠀⢀⣹⣿⣿⣿⣿⡏
⠀⣿⣿⣀⠀⠀⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⢴⣿⣿⣿⣶⣟⣿⣿⣿⣿⣿⣷
⣤⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢛⣛⣿⣿⣿⣿⠿⠛⠋⣿⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠿⢻⡿⠛⠛⠙⡉⠙⢻⣿
⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠹⣿⡏⠉⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠀⠀⢀⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⡀⠀⠀⠀⢀⣸
⣤⣭⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣦⣼⣿⣄⣀⣰⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣦⣶⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠉⢉⡤⠀⠸⣿
⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠽⠿⣿⠛⡿⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣴⣿⣿⣿⣿⣿⣿⠿⢛⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢄⢀⠀⢀⠀⣀⣼⣿
⣭⣴⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠏⠀⠀⠀⠀⠠⣾⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢙⣛⣯⣥⡴⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣬⣜⣿⣿⣿⣿⡿
⣿⡿⠭⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣾⣷⣋⠀⠀⠀⢠⣾⣿⣿⣷⠙⢿⣿⣵⣦⣶⠶⠶⠒⠶⠤⢤⡀⠀⠀⠁⢀⣿⡟⠻⣿⣶⣦⣄⣀⣤⣤⣶⣶⣿⣷⣶⡶⣦⣤⣀⠀⠀⠀⠀⣉⣿⡟⠛⠛⠋⣠
⣶⡀⠀⠀⠈⢻⣷⣀⣀⣀⣠⣤⣤⣄⣀⡀⠀⣀⣄⣾⣏⠙⠋⠄⣀⠀⢸⣿⣿⣿⣿⢀⠀⢻⣿⣿⡋⠀⠐⠒⠒⠒⠤⠀⠀⠀⠀⠀⠀⠁⣀⣨⣽⣿⠿⠛⢛⣻⣿⣭⣿⣿⣯⠙⠋⠉⣽⣦⣤⡤⠾⠟⠋⠈⠀⢈⣉⣴
⣡⣴⣶⣿⣿⣿⣿⣟⠛⠋⠉⠉⠙⠿⠿⣿⠒⠿⠿⠋⠉⠀⠒⠂⠀⣠⣤⣿⣿⡟⡿⠿⢠⣯⣿⡿⠻⣿⣷⣶⣶⣶⣆⣴⣿⣿⣶⣶⣶⡿⠟⠋⢩⡤⢰⣿⣿⣿⣿⣿⣿⣿⡏⠀⡟⠀⢹⣿⣿⡛⢷⡆⢀⣀⣀⣤⣿⠋
⠏⠋⠉⠉⠀⣸⣿⡏⠀⠀⠀⠀⣰⣿⣿⣿⡆⠐⣾⣿⡖⠶⠶⠒⣋⣁⣾⣿⠏⠀⠀⢀⠜⢿⣿⠠⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠁⠀⠤⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣸⣿⢻⣷⣶⢠⣿⣿⣿⣿⠀⣀
⣤⣤⠤⣶⡿⢿⣯⠀⠀⠀⢀⣸⣿⣿⣿⣿⣀⣀⠙⠋⡁⣀⣀⣀⣿⣿⣿⣿⣾⣄⣰⠋⠈⠈⢿⣇⠈⢿⣿⣿⡿⠛⣱⣦⣤⣤⣤⣤⣤⣤⣤⣶⣿⡿⠃⢸⣿⣿⣿⣿⣿⡿⢿⡀⠀⠀⣿⡏⡀⠙⠛⠋⠟⠿⠿⠋⠘⠟
⠀⠀⠀⢀⠀⢈⣿⠆⢀⡴⠋⠉⣦⣨⣿⣧⠀⠀⠿⠃⠀⠀⠉⠀⣼⣿⡟⣸⣿⣿⣿⣠⠀⣀⣨⣽⣆⡈⠉⠀⢀⣼⡿⠿⠟⠛⠛⠛⠛⠉⠉⡉⠤⢤⣄⣿⣿⣿⣿⣿⠟⠀⡿⣧⠀⢸⣿⡟⣧⣀⣀⠀⢴⣦⣶⣶⡆⠀
⡤⣤⣤⣴⣿⣿⠟⢀⠞⠀⠀⢰⣿⣟⣿⣯⠉⠙⠿⡆⠉⠛⠛⣻⣿⣿⢿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⢠⡤⠀⠀⠀⠀⠀⠀⠤⠚⠁⢠⣤⣾⣿⣿⣿⣿⠇⠀⠀⢰⣿⡄⠀⢿⣿⠙⠻⠿⢿⡾⣿⣛⣉⢠⣴
⠀⠆⠲⣶⠉⢾⣷⠣⠰⠶⠆⣸⡟⢻⣿⣿⠀⠀⠠⠅⠈⠀⠠⣿⣿⢧⣤⡿⢹⣿⣿⣮⣿⢿⣿⣿⠙⢿⣿⠆⠀⣾⣿⣄⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⠟⠛⢿⣿⡄⠀⠀⣼⣿⡇⠀⠈⣿⣄⠀⠀⠀⠸⢿⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢠⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢻⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⢹⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⢛⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠀⠉⠈⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣷⣦⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⠿⠋⠁⠈⠙⣿⡿⣟⡛⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣾⣿⠁⠀⠀⠀⠀⠀⢸⣷⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣃⠀⠀⠀⠀⠀⢀⣾⠀⡀⠹⣿⣶⣄⣀⣀⣤⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠿⠿⠿⠿⠿⠋⠀⠈⠉⠉⠉
⠀⠿⢿⡿⠛⠻⢿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⡀⠀⠀⣠⣾⡇⠀⠀⠄⢹⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠺⠋⠀⠀⠀⠀⢸⠛⢷⣦⣀⠀⠀⢀
⡾⠇⣶⡆⠀⠀⠀⠙⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣱⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣴⡯⠀⢀⣹⣿⣿⣿⣿
⠀⠀⣿⣇⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡲⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣤⣠⣿⣿⣿⣷⣾⣿⠟⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣿⢟⣛⣿⣭⣿⣿⠿⠻⠋⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠙⡿⢻⠿⠛⠛⠙⡉⠙⢻
⣿⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⢻⣿⡏⠉⠻⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠘⠉⠉⠉⠀⠀⢀⣀⣴⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⣀
⣌⣉⣉⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣷⡀⢀⡸⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⢴⣴⣴⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⠉⢁⠴⠀⢸
⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢙⡛⢿⣿⢛⡷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣾⣶⣿⣿⣿⣿⣿⠟⢋⣵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⡀⠀⢀⢀⣠⣾
⣛⣋⣥⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⢠⣶⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢛⣯⣤⡴⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣜⣻⣿⣿⣿
⣿⣿⣿⠥⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡶⢇⠀⠀⠀⢠⣾⣷⣿⡎⠙⢿⣯⣷⣤⣴⡶⠶⠲⠦⠤⣤⠀⠀⠀⠀⢠⣿⡟⠻⣷⣶⣤⣀⣀⣠⣤⣶⣶⣿⣷⣶⡶⣦⣤⣀⠀⠀⠀⠀⣙⣿⡟⠛⠛⠍
⣭⣭⠁⠀⠀⠉⣿⣦⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣿⡏⠽⡋⠄⡀⠀⢸⣿⣿⣿⣿⠂⠈⢿⣿⣿⠋⠀⠐⠒⠒⠢⠄⠀⠀⠀⠀⠈⠈⠁⣀⣩⣽⣿⠿⠛⢛⣻⣯⣽⣿⣿⣯⠘⠋⠉⣽⣦⣠⡤⠾⠟⠃⠈⠀⢉⣡
⣿⣩⣤⣴⣶⣾⣿⡿⠿⠟⠛⠛⠙⠛⢿⣿⣿⠶⠿⠿⠋⠁⠀⠤⠀⠉⣁⣨⣿⣿⡟⡿⠟⢠⣿⢿⡿⠻⣷⣶⣶⣶⣶⣄⣴⣾⣶⣶⣶⣶⡿⠟⠋⢩⡤⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⢻⣿⣿⡻⢷⡆⣀⣀⣀⣄⣿
⣿⠟⠛⠋⠉⠁⣸⣿⡇⠀⠀⠀⠀⣰⣿⣾⣿⠂⠰⣾⣷⡤⠦⠤⠖⣚⣁⣾⣿⠟⠁⠀⢀⠼⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠁⢀⠤⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⢿⣿⣗⢸⣿⣿⣿⣿⠁
⣀⣀⣀⣤⣴⡾⣿⣏⠀⠀⠀⠀⣸⣿⣿⣿⣿⡀⠀⠻⠟⡁⠀⠀⣰⣿⣿⣿⣿⣾⡀⣰⠃⠈⠈⣿⣆⠙⣿⣿⣿⡿⠋⣱⣄⣠⣤⣀⣀⣀⣠⣤⣶⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢟⡀⠀⢀⣿⣇⠀⠙⠛⠈⠟⠻⠿⠋⠸
⠉⠉⠀⠀⠈⠀⢸⣿⠀⢀⡴⠛⠉⡇⣸⣿⡇⠀⠙⠿⠀⠁⠉⠉⠉⣼⣿⡟⣸⣿⣿⣿⣀⠀⣀⣈⣻⣀⠈⠋⠀⢀⣼⡿⠿⠟⠛⠛⠛⠛⠉⠉⡩⠥⣤⣀⣿⣿⣿⣿⣿⠟⠀⣿⣇⠀⢸⣿⡟⣦⣀⣀⠀⢴⣦⣶⣶⠄
⣤⣤⣤⣤⣬⣷⣾⠟⢀⠞⠀⠀⢸⣿⣿⣿⡏⠉⠓⠿⡄⠘⠛⠿⣿⣿⣿⣿⣏⢹⣿⡻⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄⢠⡤⠀⠀⠀⠀⠀⠀⠤⠊⠁⢠⣤⣾⣿⣿⣿⣿⠃⠀⠀⢹⣿⡄⠈⢿⣧⠙⠻⠿⢿⣞⣿⣙⣉⢠
⠀⠆⠲⣶⠋⢿⠽⡷⠿⠶⠆⠀⢸⡟⣿⣿⣿⠒⠀⠀⠇⠀⠀⢤⣿⣿⢇⣠⣿⢸⣿⣿⣝⣿⢿⣿⣿⠹⢿⣿⠆⠀⣿⣧⡀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⠟⠛⣿⣿⡀⠀⠀⣿⣿⡇⠀⠘⣿⣄⠀⠀⠀⠸⠿⣿⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢤⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣸⡗⣼⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⢛⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡘⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠀⠉⠈⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣷⣦⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⠁⠈⠙⣿⡿⣟⡛⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⠁⠀⠀⠀⠀⠀⢸⣷⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢀⡾⠀⠀⠹⣿⣶⣄⣀⣀⣤⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠿⠿⠿⠿⠿⠋⠀⠈⠉⠉⠉
⠀⠻⢿⡿⠛⠻⢿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⡀⠀⠀⣠⣾⡇⠀⠀⠄⢹⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠋⠀⠀⠀⠀⢸⠛⢷⣦⣀⠀⠀⢀
⠾⠇⣶⡆⠀⠀⠀⠙⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣵⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣴⡯⠀⢀⣹⣿⣿⣿⣿
⠀⠀⣿⣧⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡲⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣤⣠⣿⣿⣿⣷⣾⡿⠟⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣟⣟⣻⣿⣽⣿⡿⠿⠻⠋⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠙⡿⢻⠿⠛⠛⠙⡉⠙⢻
⣿⣿⣿⣿⢿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⢻⣿⡏⠉⠻⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠘⠉⠉⠉⠀⠀⢀⣀⣴⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⣀
⣌⣉⣉⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣷⡀⢀⡸⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⢴⣴⣴⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠉⢁⠴⠀⢸
⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢙⡛⢿⣿⢛⡷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣾⣾⣿⣿⣿⣿⣿⠟⢋⣵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢄⠀⠀⢀⢀⣠⣾
⣛⣋⣥⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠏⠀⠀⠀⠀⢠⣶⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡻⣛⣯⣤⡴⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢶⣤⣜⣻⣿⣿⣿
⣿⣿⣿⠥⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡶⢇⠀⠀⠀⢠⣾⣿⣿⡎⠙⢿⣯⣷⣤⣴⡶⠶⠒⠦⠤⣤⠀⠀⠀⠀⢠⣿⡟⠻⣶⣶⣦⣀⣀⣠⣤⣶⣶⣿⣷⣶⠶⣦⣤⣀⠀⠀⠀⠀⣉⣿⡟⠛⠛⠍
⣭⣭⠁⠀⠀⠉⢿⣦⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣿⡏⠽⡋⠄⠀⠀⢸⣿⣿⣿⣿⠂⠈⢿⣿⣿⠋⠀⠐⠒⠒⠢⠄⠀⠀⠀⠀⠈⠈⠁⣀⣨⣽⡿⠿⠛⢛⣻⣿⣽⣿⣿⣯⠙⠋⠉⣿⣦⣤⣤⠾⠟⠃⠈⠀⢉⣡
⣿⣩⣤⣴⣶⣾⣿⣿⠿⠟⠛⠛⠛⠛⢿⣿⣿⠶⠿⠿⠋⠁⠀⠤⠀⠉⣁⣬⣿⣿⡿⡿⠟⢠⣟⣿⡿⠻⣷⣶⣶⣶⣤⣄⣴⣾⣷⣶⣶⣶⡿⠟⠋⢩⡤⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⢻⣿⣿⡿⢷⡆⣀⣀⣀⣄⣿
⣿⠟⠛⠋⠉⠉⣰⣿⡇⠀⠀⠀⠀⣰⣿⣾⣿⠀⠲⣾⣷⡤⠦⠤⠖⣚⣁⣾⣿⠟⠁⠀⢀⠼⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠁⢀⠤⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣷⡗⢸⣿⣿⣿⣿⠀
⣀⣀⣀⣤⣴⡾⣿⣏⠀⠀⠀⠀⣸⣿⣿⣿⣿⡀⡀⠻⠟⠁⠀⠀⣰⣿⣿⣿⣿⣶⡀⣰⠃⠈⠘⣿⣆⠙⣿⣿⣿⡿⠋⣱⣄⣠⣤⣄⣀⣀⣠⣤⣶⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢟⡀⠀⢀⣿⣇⠀⠙⠛⠛⠟⠿⠿⠋⠸
⠉⠁⠀⠀⠉⠀⢸⣿⠀⢀⡴⠛⠉⣅⣹⣿⡇⠀⠘⠿⠀⠁⠉⠉⠉⣽⣿⡟⣹⣿⣿⣿⣀⠀⣀⣈⣻⣀⠈⠃⠀⢀⣼⡿⠿⠟⠛⠛⠛⠛⠉⠉⡩⠥⣤⣀⣿⣿⣿⣿⣿⠟⠀⣿⣇⠀⢸⣿⡟⣦⣀⣀⠀⢲⣶⣶⣶⡄
⣤⣤⣤⣤⣬⣷⣾⠟⢀⠞⠀⠀⢸⣿⣿⣿⡏⠉⢓⠿⡄⠘⠛⠿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄⢠⡤⠀⠀⠀⠀⠀⠀⠤⠚⠁⢠⣤⣾⣿⣿⣿⣿⠃⠀⠀⢻⣿⡄⠈⢿⣷⠙⠿⠿⢿⣾⣿⣋⣉⢠
⠀⠆⠲⣶⠋⢿⠽⡷⠿⠶⠆⠀⢼⡟⣿⣿⣿⠐⠀⠀⠃⠀⠀⢤⣿⣿⢇⣠⣿⢸⣿⣿⣝⣿⢿⣿⣿⠻⢿⣿⠆⠀⣿⣷⡀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⠟⠛⣿⣿⡄⠀⠀⣾⣿⡇⠀⠘⣯⣄⠀⠀⠀⢸⢿⣿⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢻⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣻⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⢁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣷⣦⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⠉⠉⠙⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⣷⡿⠁⠀⠀⠀⠀⠀⢹⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⢀⡿⢀⠀⢹⣿⣦⣄⣀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠿⠿⠿⡿⠿⠋⠀⠀⠉⠉
⠀⠀⠿⣿⡿⠻⠿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣄⠀⠀⢀⣠⣾⡃⠀⠀⠄⣻⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⠉⠀⠀⠀⠀⡸⠛⢷⣦⣀⠀⠀
⣠⣼⢇⣾⡄⠀⠀⠈⠻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣷⣶⣿⣿⣿⣷⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢠⣼⡇⠀⣀⣻⣿⣿⣿
⠋⠀⠈⣿⡇⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠲⣶⣿⣿⣿⣾⡿⣿⣿⣿⣿
⣤⣄⣀⣿⣿⣷⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⣿⣿⣿⣿⣿⡿⠿⠻⢻⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠟⢻⠿⠛⠛⢉⡉⠛
⣿⣿⣿⣿⣿⣯⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢿⣿⠛⠛⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠈⠉⠉⠈⠀⢀⣠⣼⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡀⠀⠀⠀
⣉⣉⣉⣛⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣌⣿⣧⠀⠀⡸⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⢴⣤⣴⣶⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠈⠉⢡⠔⠀
⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢛⣿⣿⣿⢻⣧⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣾⣾⣿⣿⣿⣿⣿⠿⢋⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄⡀⠀⢀⢀⣠
⠿⠿⣛⣩⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣷⠏⠀⠀⠀⠀⢠⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡿⣿⣯⣥⡴⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣜⣻⣿⣿
⣿⣿⣿⣿⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣿⡴⢆⠀⠀⠀⣠⣾⣿⣷⡍⠻⣿⣿⣦⣤⣤⣶⠶⠶⠤⢄⣀⠈⠉⠉⠀⢠⣿⡟⢿⣶⣶⣤⣀⣀⣠⣤⣴⣶⣿⣷⣶⡶⣦⣄⣀⠀⠀⠀⢀⣹⣿⡛⠛⠛
⣉⣉⣽⠁⠀⠈⠙⣷⣦⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣠⣿⡏⠽⢋⠄⠀⠀⢿⣿⣿⣿⣷⠆⠘⣿⣿⣿⠃⠀⠀⠒⠢⠤⡄⠀⠀⠀⠀⠈⠈⠁⢈⣩⣽⣿⠿⠛⢛⣛⣿⣿⣿⣿⡭⠘⠋⠉⣿⣦⣤⡤⠿⠛⠃⠁⠀⢉
⣿⣿⣋⣤⣤⣶⣶⣿⣿⡿⠿⠛⠛⠛⠻⣿⣿⣷⠴⣿⡿⠛⠃⠀⠤⠀⠉⣀⣸⣿⣿⡿⡿⡇⢰⣟⣿⣿⢶⣶⣶⣤⣤⣤⣀⣴⣶⣶⣶⣴⣶⡿⠟⠛⣩⡤⣰⣿⣿⣿⣿⣿⣿⣿⡇⠐⠇⠀⢻⣿⣟⠻⢷⡆⣀⣀⣀⣬
⣿⣿⠿⠟⠛⠋⠉⣹⣿⡇⠀⠀⠀⠀⣰⣶⣾⣷⠀⢠⣶⣶⡠⢤⠤⠴⢒⣉⣿⣿⠟⠀⠀⢀⠸⣿⣗⢰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁⢀⡤⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⣿⢿⣿⡅⢰⣿⣿⣿⣿
⣉⠁⡀⣀⣀⣠⣶⣿⣟⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠿⠟⠁⠀⠀⢰⣿⣿⣿⣿⣦⡀⣰⠋⠀⠹⣿⡄⠙⣿⣿⣿⡿⠟⣵⣄⣀⣀⣀⣀⣀⣀⣤⣶⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⢀⣿⣇⠀⠙⠛⠊⠟⠿⠿⠋
⠛⠛⠉⠉⠀⠉⠀⢸⣿⠀⠀⡠⠞⠋⡁⢻⣿⡇⠉⠨⠿⠀⠉⠉⠉⠉⣽⣿⡟⣹⣿⣿⣯⡀⠀⢀⣉⣻⡀⠉⠋⠀⢀⣼⣿⠿⠿⠿⠛⠛⠛⠋⠉⡩⢥⣤⣀⣿⣿⣿⣿⣿⠟⠀⣿⡇⠀⢸⣿⡿⣆⣀⣀⠀⢶⣶⣶⣶
⣀⣀⣀⣀⣀⣨⣶⣾⡟⢀⡜⠀⠀⢸⣿⣿⣿⡇⠀⢲⡾⡀⠒⠳⠶⣾⣿⣿⣾⣏⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⣩⡄⠀⠀⠀⠀⠀⢀⠠⠚⠁⢤⣠⣾⣿⣿⣿⣿⠁⠀⠀⢸⣷⡄⠀⢿⣿⠙⠿⠿⢿⣞⣿⣏⣉
⠀⠆⠲⣾⠛⢿⠟⠹⡷⠾⠆⠀⠀⢸⡟⣿⣿⣷⠐⠀⣀⠃⠐⠀⢠⣿⣿⣇⣨⣿⢸⣿⣿⣝⣿⣿⣿⡿⠻⣿⣿⠀⠀⣿⣧⡀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⠟⠻⣿⣿⡀⠀⠀⣿⣿⡇⠀⠘⣿⣄⠀⠀⠀⠸⢿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡇⣿⣿⠀⣼⡗⢾⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⣘⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡂⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣻⠇⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣶⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠟⠋⠉⠙⢿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣹⣾⠋⠀⠀⠀⠀⠀⠘⣿⣻⣿⡀⠀⠀⠀⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠀⠀⠀⠀⠀⠀⣸⠃⡀⠘⣿⣶⣄⡀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠿⠿⠿⠿⠿⠟⠁⠀⠈⠉
⠀⠀⠸⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣧⡀⠀⠀⣀⣴⡏⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠏⠁⠀⠀⠀⢀⡟⠻⣦⣄⡀⠀
⢀⣤⣶⣰⣅⠀⠀⠀⠙⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣶⣿⣿⣿⣶⣾⣷⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⣴⣿⠀⢀⣘⣿⣿⣿
⡿⠋⠀⢹⣿⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣖⢶⣾⣿⣿⣶⣿⢿⣿⣿⣿
⣧⣀⡀⣸⣿⣷⣶⣶⣾⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢿⡿⣿⣿⣿⣿⢿⠿⠟⣿⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠻⠻⡿⠟⠛⠋⣉⠉
⣿⣿⣿⣿⣿⣿⣭⣿⠃⠀⠀⠀⠀⠀⠀⠀⠜⠛⢻⣿⡿⠛⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠋⠉⠉⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢀⠀⠀⠀
⢉⣉⡙⢛⣛⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⣀⣹⣿⡄⠀⢀⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡶⣦⣤⣶⣾⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠉⢉⡤⠂
⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠙⣻⣿⣿⡞⣿⣔⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣵⣷⣿⣿⣿⣿⣿⡿⠟⣩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠠⣀⠀⠀⡀⣀
⠿⠿⠿⢛⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⡾⠁⠀⠀⠀⠀⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⢿⣻⣭⣤⢾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣄⣛⣿⣿
⣭⣿⣿⣿⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⣧⡶⡀⠀⠀⠀⣴⣿⣿⣿⠙⢿⣿⣷⣤⣤⣴⡶⠶⠤⢄⣀⡈⠉⠉⠉⠀⣼⣿⠻⣷⣶⣦⣄⣀⣀⣤⣤⣶⣾⣿⣶⣶⣶⣤⣄⡀⠀⠀⠀⣉⣿⡟⠛⠛
⣉⣉⣛⡛⠀⠀⠉⢻⣦⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣼⣿⠛⠟⠁⠀⠀⠸⣿⣿⣿⣿⡖⠀⢻⣿⣿⡟⠀⠀⠐⠒⠤⢄⠀⠀⠀⠀⠀⠁⠋⠀⣉⣭⣿⡿⠟⠛⣛⣻⣿⣿⣿⣯⡍⠛⠉⢹⣷⣤⣠⠼⠿⠛⠀⠀⠈
⣿⣿⡟⣃⣠⣤⣴⣾⣿⣿⡿⠿⠛⠛⠛⢿⣿⣷⡦⣾⣿⠟⠛⠀⠠⠄⠈⢁⣀⣿⣿⣿⢿⣿⠀⣾⣿⣿⡷⣶⣶⣤⣤⣤⣄⣠⣶⣶⣶⣤⣴⣾⠿⠛⢋⣥⢄⣾⣿⣿⣿⣿⣿⣿⣿⠀⠸⠀⠸⣿⣿⡛⠿⣶⢀⣀⣀⣤
⣿⣿⣿⡿⠟⠛⠛⢉⣿⣿⠀⠀⠀⠀⢀⣶⣶⣿⡧⠀⣴⣶⣄⢤⣤⠤⠖⡊⣹⣿⡿⠇⠈⠀⢀⢿⣿⡆⣼⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠀⣠⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣾⠀⣿⣿⣿⣿
⠛⠉⠁⠀⢀⣀⣴⣾⣿⡋⠀⠀⠀⠀⣾⢿⣿⣿⡇⠀⠸⡿⠋⠀⠀⠀⣾⣿⣿⣿⣷⣔⢀⡔⠁⠈⢻⣧⠈⢿⣿⣿⣿⠿⢋⣄⣀⣀⣀⣀⣀⣀⣠⣴⣾⣿⠟⢸⣿⣿⣿⣿⣿⣿⢿⣇⠀⠀⣸⣿⡄⠉⠛⠓⠹⠻⠿⠟
⠝⠛⠛⠉⠉⠉⠉⠈⢻⡇⠀⢀⡴⠚⢋⠘⣿⣿⠉⠁⢶⠆⠈⠉⠙⠉⢉⣿⣿⠋⣿⣿⣿⣇⠀⠀⢈⣛⣇⠈⠙⠁⠀⣠⣿⡿⠿⠿⠟⠛⠛⠛⠉⢉⠭⣤⣀⣸⣿⣿⣿⣿⡿⠃⢸⣿⠄⠀⣿⣿⢳⣄⣀⡀⠐⣶⣶⣶
⣀⣀⣀⣀⣀⣀⣱⣴⣿⠇⣠⠋⠀⠀⣾⣾⣿⣿⠐⠒⢶⣆⠐⠲⠶⢶⣾⣿⣿⣾⡋⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣦⡄⢈⣥⠀⠀⠀⠀⠀⠀⡀⠴⠋⠀⣄⣴⣿⣿⣿⣿⡯⠀⠀⠀⣿⣧⠀⠹⣿⡞⠻⠿⠿⣷⣻⣯⣉
⠀⠆⠺⣿⠏⢿⠟⠻⢷⡶⠗⠀⠀⠀⣿⢿⣾⣿⡆⠀⢀⣘⠀⠂⠀⣸⣿⣿⣀⣹⡇⣿⣿⣏⣻⣿⣿⣿⡟⢿⣿⣧⠀⢸⣿⣄⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⠟⢿⣿⣇⠀⠀⠀⣿⣿⠀⠀⢻⣧⡀⠀⠀⠀⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⢤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢿⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣇⣿⣿⠀⣿⡗⣻⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⢘⣫⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣼⣃⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡆⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣼⠇⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣾⣿⣿⣶⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⣿⣿⠿⠛⠉⠉⠻⣿⠿⠿⠇⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⣿⡟⠁⠀⠀⠀⠀⠀⣿⣟⣿⣇⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡇⠀⠀⠀⠀⠀⢀⡟⢀⠈⢻⣷⣤⣀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⣿⡿⠿⠿⠿⠿⠿⠋⠀⠀⠀
⠀⠀⠈⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣠⣾⠁⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠉⠀⠀⠀⠀⡘⠛⢶⣦⣀⠀
⠀⣀⣴⣆⣮⡀⠀⠀⠉⢿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⣾⣿⣿⣷⣴⣿⣶⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣠⣾⡇⠀⣀⣻⣿⣿
⣾⠟⠁⠘⣿⡇⠀⠀⠀⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠢⣶⣿⣿⣷⣾⣿⣿⣿⣿
⣿⣀⡀⢀⣿⣿⣶⣤⣴⣿⡏⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⡿⣿⢿⣿⣿⣿⡿⡿⠿⢻⣥⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⠟⢿⠿⠛⠋⢉⡉
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠠⠛⠛⣿⣿⠛⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠘⠉⠉⠉⠀⢀⣠⣼⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀
⡈⢉⡙⠛⠛⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣂⣈⣿⣆⠀⠀⡹⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣶⣤⣴⣶⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠈⠉⣡⠔
⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠻⣿⣿⣷⢿⣇⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣬⣼⣾⣿⣿⣿⣿⣿⠿⢋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢄⡀⠀⢀⢀
⠿⠿⠿⠟⣋⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣷⠏⠀⠀⠀⠀⢠⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣯⣥⠴⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣘⣻⣿
⣍⣽⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⢆⠀⠀⠀⢠⣾⣿⣿⡍⠻⣷⣟⣦⣠⣤⣤⡶⠦⠤⣀⣀⠈⠉⠉⠀⢠⣿⡟⢿⣶⣦⣤⣀⣀⣠⣤⣴⣶⣿⣷⣶⢶⣦⣤⣀⠀⠀⠀⢀⣹⣿⠟⠛
⣉⣉⣛⣛⠋⠀⠈⠻⣶⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣿⠟⠻⠋⠀⠀⠀⢿⣿⣿⣿⣷⠄⠘⣿⣿⣿⠃⠀⠀⠐⠤⠤⡈⠀⠀⠀⠀⠈⠘⠁⢉⣩⣿⣿⠿⠛⢛⣻⣿⣿⣿⣿⣭⠙⠋⠉⣿⣦⣠⣤⠾⠟⠃⠈⠀
⣿⣿⣿⢛⣀⣠⣤⣴⣿⣿⣿⠿⠿⠿⠻⠿⣿⣷⣶⢤⣿⣿⠟⠃⠀⠤⠀⠁⢀⣸⣿⣿⡿⣿⡇⢰⣿⣿⣿⢶⣶⣦⣤⣤⣤⣀⣴⣶⣶⣦⣤⣶⡿⠟⠛⣩⡤⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⢿⣿⣟⡻⢷⡆⣀⣀⣀
⣿⣿⣿⣿⠿⠟⠛⠋⢹⣿⡇⠀⠀⠀⠀⢠⣾⣿⣿⠀⢠⣶⣦⣠⣤⣤⠤⠖⠋⣿⣿⠟⠀⠁⠀⡸⣿⣷⢠⣿⣿⣿⣿⣿⣿⣿⢿⠿⠟⠛⠋⠁⢀⡤⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⡿⢿⣷⡇⢸⣿⣿⣿
⠛⠛⠉⠀⠀⣀⣠⣴⣿⡿⠁⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⢿⠟⠁⠀⠀⢰⣿⣿⣿⣿⣦⡀⣠⠊⠐⠙⣿⡄⠹⣿⣿⣿⡿⠟⣡⣀⣀⣀⣀⣀⣀⣀⣤⣶⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⠀⣿⣇⠀⠙⠛⠊⠟⠿⠿
⣿⠛⠛⠛⠋⠉⠉⠁⠙⣿⠀⠀⣠⠶⠛⡉⢸⣿⡏⠉⠑⣶⠀⠁⠙⠛⠉⣹⣿⡟⢻⣿⣿⣿⡀⠀⠀⣙⣻⡀⠙⠋⠈⢀⣼⣿⡿⠿⠿⠻⠛⠛⠋⠉⡉⢥⣄⣀⣿⣿⣿⣿⣿⠟⠀⣿⣇⠀⢸⣿⡟⣧⣀⣀⠀⢰⣦⣶
⢀⣀⣀⣀⣀⣀⣀⣦⣼⡿⠀⡼⠁⠀⢰⣷⣿⣿⡗⠒⠲⣶⡀⠒⠶⠶⣶⣿⣿⣷⣟⢻⣿⣿⣿⣾⣿⣿⣿⣿⣷⣦⣤⠈⣩⡄⠀⠀⠀⠀⠀⢀⠠⠞⠁⢠⣠⣾⣿⣿⣿⣿⠇⠀⠀⢹⣿⡄⠀⢿⣷⠝⠿⠿⢿⣞⣿⣏
⠀⠖⠺⣿⠛⢿⠟⠻⠻⣶⠞⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢀⡇⠀⠀⢀⣿⣿⣇⣈⣿⢸⣿⣿⣹⣿⣿⣿⣿⠻⣿⣿⡅⠀⣿⣧⡀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠿⠻⣿⣿⡀⠀⠀⢻⣿⡇⠀⠈⣿⣄⠀⠀⠀⠸⠽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢻⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⣋⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣇⠛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢰⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣷⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⡿⠛⠋⠉⠛⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣾⣿⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢏⠀⠀⠀⠀⠀⠀⣼⠃⡀⠹⣿⣦⣄⡀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠟⠻⠿⠿⠋⠀⠀⠀
⠀⠀⠀⢹⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⣀⣼⡏⠀⠁⠄⢹⣿⣿⣟⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠋⠀⠀⠀⠀⢨⠛⠳⣶⣄⡀
⠀⠀⣠⡶⣨⡅⠀⠀⠈⠻⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣿⣿⣷⣦⣾⣷⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣴⣿⠀⢀⣘⣿⣿
⣶⡿⠋⠁⣿⣿⠀⠀⠀⠀⣹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡲⢶⣿⣿⣿⣶⣿⣿⣿⣿
⣿⣅⣀⠀⣸⣿⣶⣦⣤⣶⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⢿⡿⣿⣿⣿⣿⢿⠿⠟⣯⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠿⢻⡿⠟⠛⠉⣉
⣿⣿⣿⣿⣿⣿⣿⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠼⠛⢻⣿⡟⠛⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠋⠋⠉⠉⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀
⣈⠉⠛⠛⠻⢟⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣀⣻⣷⡀⠀⢈⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠈⠉⢉⡤
⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⡾⣿⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣥⣷⣿⣿⣿⣿⣿⡿⠟⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠤⣀⠀⠀⡀
⡿⢿⣿⠿⢛⣩⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠀⣯⡿⠁⠀⠀⠀⠀⣤⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡻⢿⣿⣭⣤⢾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣄⣛⣿
⣌⣹⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡴⠀⠀⠀⢀⣴⣿⣿⣯⠛⢿⣾⣲⣄⣤⣤⣤⠦⠤⢄⣀⡈⠉⠉⠁⠀⣼⣿⠻⣶⣶⣤⣄⣀⣀⣤⣤⣶⣾⣷⣶⣶⢶⣤⣄⡀⠀⠀⠀⣉⣿⡿⠛
⣈⣉⠛⢛⡛⠉⠉⠙⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢓⠞⠁⠀⠀⢸⣿⣿⣿⣿⡄⠀⢻⣿⣿⡟⠀⠀⠄⠢⠤⢄⠁⠀⠀⠀⠀⠁⠋⠈⣉⣽⣿⡿⠟⠛⣛⣻⣿⣿⣿⣯⠍⠛⠉⢹⣷⣤⣠⠼⠿⠛⠀⠁
⣿⣿⣿⡟⢃⣀⣤⣤⣼⣿⣷⣿⡿⠿⠿⠿⣿⣷⣶⣤⣼⣿⡿⠓⠀⠈⠄⠘⠀⣀⣿⣿⣿⢿⣿⠀⣾⣿⣿⡷⣶⣶⣤⣤⣤⣄⣠⣶⣶⣶⣤⣴⣾⠿⠛⢋⣥⢤⣾⣿⣿⣿⣿⣿⣿⣿⠀⡾⠀⠸⣿⣿⡛⠿⣶⢀⣀⣀
⣿⣿⣿⣟⡿⠿⠟⠛⠋⣿⣷⠀⠀⠀⠀⠀⣼⣽⣿⡅⠤⣴⣶⡄⣤⣤⡤⠴⠚⢹⣿⡿⠇⠈⠀⢀⢿⣿⠋⣴⣿⣿⣿⣿⣿⣿⡿⡿⠿⠛⠛⠉⠀⣠⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣿⠿⣿⣶⠀⣿⣿⣿
⡛⠛⠋⠁⠀⠀⣀⣠⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠸⡿⠋⠀⠀⠀⣾⣿⣿⣿⣷⣄⢀⡔⠁⠊⣻⣧⠙⢿⣿⣿⣿⠿⢋⣄⣀⣀⣀⣀⣀⣀⣠⣴⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣇⠀⠀⢸⣿⡀⠈⠛⠃⠙⠻⠿
⣿⡟⠛⠛⠛⠋⠙⠋⠉⣿⡇⠀⢀⡴⠞⢋⠘⣿⣿⠉⠁⢶⡆⠈⠐⠒⠋⢉⣿⣿⠛⣿⣿⣿⡃⠀⠀⠈⣛⡆⠈⠛⠉⠁⣠⣿⣿⠿⠿⠟⠟⠛⠛⠉⢉⠩⣤⣀⣸⣿⣿⣿⣿⡿⠃⠘⣿⡀⠀⣿⣿⢳⣀⣀⡀⠰⣶⣶
⠁⣀⣀⠀⠀⣀⣀⣢⣤⣿⠇⢠⠏⠀⠀⣾⣾⣿⣿⠒⠲⢶⣆⠐⠲⠶⣶⣾⣿⣿⣾⠛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣤⡄⠉⣡⠀⠀⠀⠀⠀⠀⡀⠴⠋⠠⣄⣴⣿⣿⣿⣿⡿⠀⠀⠀⣽⣧⠀⠸⣿⡾⠻⠿⠿⣷⣻⣿
⠀⠖⠳⣿⠟⢿⠟⠻⠻⢿⡶⠃⠀⠀⠀⣿⣿⣿⣿⡆⠀⠁⣸⠀⠀⢀⣸⣿⣿⣈⣹⡇⣿⣿⣟⢿⣿⣿⣿⡿⢿⣿⡯⠀⢸⣿⣄⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⠟⢿⣿⣇⠀⠀⢰⣿⣿⠀⠀⢹⣧⡀⠀⠀⠀⠽⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢽⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⢼⡗⣹⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡗⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⣛⣿⣼⣿⣿⣿⣿⣿⣿⣿⣾⣧⣛⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣶⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠋⠉⠻⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⣝⣿⠋⠀⠀⠀⠀⠀⢹⣷⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⣼⠉⠈⠹⣷⣦⣀⠀⢀⣠⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⠿⠛⠻⠿⢿⠋⠀⠀
⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣄⠀⠀⠀⢀⣼⡇⠀⠁⠄⢹⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡪⠋⠀⠀⠀⠀⢨⠛⠻⣶⣤
⠀⠀⠀⢀⡌⣩⡋⠀⠀⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⣶⣿⣿⣷⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢀⣴⣿⠀⢀⣘⣿
⣤⣴⣾⠟⠁⣿⣷⠀⠀⠀⠀⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣲⢶⣿⣿⣿⣶⣿⣿⣿
⣿⣿⡇⠀⠀⢻⣿⣦⣤⣤⣴⣿⠁⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⢿⡿⣿⣻⣿⣿⣿⠿⠟⣯⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠿⢻⡿⠛⠋⠉
⢻⣿⣿⣿⣿⣿⣿⣿⣻⣿⠏⠉⠀⠀⠀⠀⠀⠀⠼⠟⢿⣿⡿⠿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠛⠛⠛⠉⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣀⡀
⢀⠉⠛⠛⠿⠿⠿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⣻⣧⠀⠀⢘⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠈⠉⠉
⣼⣿⣶⣿⣷⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠉⠿⢿⣿⣷⡶⣿⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣷⣿⣿⣿⣿⣿⡿⠟⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠁⣀⠀⠀
⠻⣿⣿⣿⣿⠟⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⣯⡿⠁⠀⠀⠀⠀⣤⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⢻⠿⣟⣩⣤⢾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣤⣛
⣦⣉⢒⣶⣶⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣏⡵⠀⠀⠀⠀⣴⣿⣿⣯⠻⣿⣶⣦⣄⣠⣤⣤⠤⢤⣀⣀⡈⠉⠉⠁⠀⣼⣿⠻⣶⣶⣤⣀⣀⣀⣤⣤⣶⣾⣿⣶⣶⢶⣤⣄⡀⠀⠀⠀⣈⣽⣿
⣈⠉⠛⠛⠿⠿⠉⠉⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣒⠶⢁⠀⠀⢸⣿⣿⣿⣿⡀⠈⢿⣿⣿⡟⠁⠀⠤⠤⠤⣈⠁⠀⠀⠀⠀⠁⠋⠀⣈⣽⣿⡿⠟⠛⣛⣻⣿⣿⣿⣯⡍⢛⠉⢹⣷⣤⣠⠴⠟⠋⠀
⣿⣿⣿⣿⡿⠇⢀⣀⣤⣬⣿⣷⣶⣶⠾⠿⠿⣷⣶⣶⣄⣼⣿⡿⠓⠀⣈⡀⠐⠂⡀⣿⣿⣿⣿⣷⠀⣾⣿⣿⡷⣶⣦⣤⣤⣤⣄⣠⣴⣶⣦⣤⣴⣶⡿⠟⢋⣡⠄⣾⣿⣿⣿⣿⣿⣿⣿⠀⠸⠀⠘⣿⣿⣟⠿⣶⠀⣀
⣿⣿⣿⣿⣷⡿⡿⠿⠿⠛⣿⣿⠀⠀⠀⠀⠀⣬⣭⣿⡅⠀⣡⣦⡄⣀⣀⣠⠤⠞⢹⣿⣿⠛⠈⠈⢀⣿⣿⠏⣴⣾⣿⣿⣿⣿⣿⡿⡿⠿⠟⠛⠉⠀⣠⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣾⡄⣾⣿
⡉⠻⠿⠛⠋⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠸⣿⠟⠀⠀⠀⣾⣿⣿⣿⣧⡤⢀⡴⠁⠊⣻⣧⠙⢿⣿⣿⣿⡿⢋⣄⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⠟⢸⣿⣿⣿⣿⣿⣿⠿⣃⠀⠀⢸⣿⢅⠈⠛⠋⠙⠻
⣿⣿⣶⠶⠲⠒⠒⠛⠛⠉⢿⣇⠀⠀⣠⠾⢛⠚⣿⣿⠋⠂⣶⡆⠐⠒⠒⠚⢛⣿⣿⠟⣿⣿⣾⡇⠀⠀⠈⠻⡆⠈⠛⠋⠁⣠⣿⣿⡿⠿⠟⠿⠛⠛⠋⢉⢩⣤⣀⣸⣿⣿⣿⣿⡿⠃⠸⣿⡀⠀⣿⣿⢹⣄⣀⣀⠀⣶
⠿⠋⠁⠀⠀⠀⠀⠀⢢⣠⣾⡏⢀⡞⠁⠀⣸⣶⣿⣿⠂⠠⢤⣆⠀⠶⣶⣦⣾⣿⣿⣾⠛⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣤⣀⠉⣁⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣄⣴⣿⣿⣿⣿⣿⠀⠀⠀⣏⣧⠀⠸⣿⣯⠛⠿⠿⢷⣿
⠿⠖⠻⣿⠿⢿⠟⠻⠿⠿⢿⣠⠎⠀⠀⠀⣿⣿⣿⣿⡆⠀⠈⠸⠀⠀⢀⣸⣿⣿⠉⣹⡇⣿⣿⣟⠻⣿⣿⣿⡿⣿⣿⣯⠁⢰⣿⣄⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⠟⢻⣿⣧⠀⠀⢀⣿⣿⠁⠀⢸⣧⣀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣼⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⢛⣻⣼⣿⣿⣿⣿⣿⣿⣿⣾⣧⣟⠀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⣴⣶⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣿⣿⠟⠛⠉⠛⢿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢻⣽⠟⠁⠀⠀⠀⠀⠘⣿⣼⣿⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠀⠀⠀⠀⠀⠀⢰⠏⡁⠙⣿⣦⣄⡀⠀⣀⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡿⠟⠛⠿⠿⠟⠁⠀
⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⠀⠀⠀⠀⣠⡿⠀⠀⠠⠸⣿⣿⣿⣿⣿⣿⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠟⠁⠀⠀⠀⠀⡟⠛⢶⣤
⠀⠀⠀⠀⣠⢭⣝⠁⠀⠉⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣗⣤⣴⣾⣿⣿⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⣠⣿⡇⢀⣈⣿
⣤⣤⣴⡿⠋⢸⣿⡄⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⢶⣾⣿⣿⣷⣿⣿⣿
⣿⣿⣏⠀⠀⢸⣿⣧⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⢿⡿⣿⣻⣿⣿⣿⡿⠿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠻⠟⣿⠟⠛⠉
⢛⣿⣿⣿⣷⣾⣿⣿⡟⣿⡿⠉⠁⠀⠀⠀⠀⠀⡠⠿⠿⣿⣿⠿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠟⠛⠙⠋⠉⠀⢀⣠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⢀⡀
⠀⠉⠛⠻⠻⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢹⣿⡄⠀⠈⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⣤⣴⣴⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡥⠀⠀⠉⠉
⣶⣿⣷⣶⣶⣶⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠹⠿⣿⣿⡶⢾⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣣⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡨⢀⡀⠀
⠻⢿⣿⣿⣿⡿⢟⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⣺⣼⠏⠀⠀⠀⠀⢠⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⡻⡿⢿⣋⣥⡴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣘
⢠⣉⠒⣶⣶⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⣩⠄⠀⠀⠀⢠⣾⣿⣯⡛⢿⣷⣶⣄⣀⣤⣤⡤⢤⣄⣀⡀⠉⠉⠉⠁⢨⣿⡿⢷⣶⣤⣄⣀⣀⣠⣤⣴⣶⣿⣶⣶⣶⣦⣄⣀⠀⠀⠀⢀⣹⣿
⠈⠉⠛⠛⠿⠿⠟⠉⠓⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣷⠊⠀⠀⠀⣿⣿⣿⣿⣇⠀⠹⣿⣿⡿⠋⠀⠤⠤⠤⢄⡉⠀⠀⠀⠀⠈⠘⠉⢁⣹⣿⣿⠿⠛⢛⣛⣿⣿⣿⣿⡭⠙⡋⠉⣿⣦⣄⡤⠿⠛⠁
⣿⣿⣿⣿⣾⠿⠀⢀⣀⣠⣿⣿⣶⣶⡶⠾⠿⢿⣶⣦⣤⣠⣾⣿⠿⠂⢀⣉⠐⠒⠀⢹⣿⣿⡿⣷⡆⢰⣿⣿⡿⣶⣶⣤⣤⣤⣤⢀⣤⣶⣶⣤⣤⣶⡾⠿⠛⣉⡄⣴⣿⣿⣿⣿⣿⣿⣿⠇⠐⠇⠀⢿⣿⣟⠻⢷⡆⣀
⣿⣿⣿⣿⣿⣾⣿⡿⠿⠟⢻⣿⡏⠀⠀⠀⠀⢨⣭⣽⣯⠀⢉⣥⣄⢀⣀⣀⣤⠴⠋⣿⣿⠟⠀⠁⠁⣸⣿⡏⢡⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⢀⡤⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣼⣿⣿⣷⡇⢸⣿
⡉⠻⠿⠿⠛⠁⠀⠀⢀⣠⣾⡿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠀⠈⣿⡿⠃⠈⠀⢰⣾⣿⣿⣿⣄⠀⣠⠎⠐⢛⣷⡌⢻⣿⣿⣿⣿⠟⣡⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⣟⡀⠀⠀⣿⣧⠀⠙⠛⠉⠛
⣿⣿⣶⠶⠶⠶⠒⠛⠛⠋⢻⣷⠀⠀⢀⡴⠞⠃⢻⣿⡏⠒⢰⣶⠀⠒⠒⠒⠚⣻⣿⡟⢻⣿⣷⣏⠀⠀⠀⠙⢷⠀⠛⠏⠉⢁⣼⣿⣿⠿⠿⠿⠟⠛⠛⠉⡉⣥⣀⣀⣿⣿⣿⣿⣿⠟⠀⢻⣇⠀⢸⣿⡟⣦⣀⣀⠀⢰
⠿⠟⠉⠀⠀⠀⠀⠀⠀⣄⣴⣿⠀⣰⠋⠀⢰⣷⣾⣿⡇⠄⢤⣵⠀⠤⣤⣤⣴⣿⣿⣷⡟⢻⣿⣿⣷⣶⣿⣿⣿⣷⣶⣤⣄⡈⢉⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⢀⣠⣾⣿⣿⣿⣿⠅⠀⠀⢨⣽⡄⠈⢿⣿⡟⠿⠿⢿⣾
⡾⠷⠺⣿⠿⢿⠿⠻⠿⠿⠿⣇⡴⠁⠀⠀⢸⣿⣿⣿⣧⠀⠈⠉⠇⠀⠀⣀⣿⣿⡏⢙⣿⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡍⠀⣿⣇⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⡿⠻⣿⣿⡀⠀⠀⣾⣿⡇⠀⠀⣿⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣺⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⣛⣼⣷⣿⣿⣿⣿⣿⣿⣾⣷⣿⡀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡆⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣶⣶⣾⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠛⠋⠛⢻⣿⡿⠿⠏⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⣯⡿⠋⠀⠀⠀⠀⠀⢿⡿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⢀⡾⢁⠈⢻⣷⣤⣀⠀⢀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⠿⠛⠻⠿⢛⠋⠀
⠛⠛⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢀⣼⠃⠀⠀⠄⢿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⠉⠀⠀⠀⠀⣸⠛⢻⣶
⠀⠀⠀⠀⢀⡭⣛⡋⠀⠉⠛⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣾⣿⣿⣧⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⢠⣼⣇⠀⣀⣹
⣤⣤⣤⣶⠟⠁⣿⣇⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⣶⣿⣿⣿⣾⣿⣿
⣹⣿⣿⡃⠀⠀⣿⣿⣤⣀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡿⣿⢿⣿⣿⣿⣿⣿⠿⢟⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢉⠟⢻⡿⠛⠋
⠙⣿⣿⣿⣿⣶⣿⣿⣿⢟⣿⠟⠉⠀⠀⠀⠀⠀⢀⠼⠿⢿⣿⡿⠿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠛⠋⠛⠉⠁⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⠀⣀
⠀⠈⠙⠛⠿⠿⢿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣆⠀⠀⢹⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣤⣠⣤⣦⣶⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠉
⣿⣾⣿⣶⣶⣶⣶⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠿⣿⣿⣷⢶⣿⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣜⣸⣿⣿⣿⣿⣿⣿⡿⠟⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⣀⠀
⠛⢿⣿⣿⣿⣿⠿⢋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢐⣯⡿⠁⠀⠀⠀⠀⣠⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⣿⠿⣟⣩⣤⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤
⠀⣌⡑⢺⣯⣶⣾⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣏⡥⠀⠀⠀⠀⣬⣿⣽⣝⠻⣷⣶⣦⣀⣀⣤⣤⠤⣄⣀⣀⠀⠉⠉⠛⠀⣿⣿⠿⣶⣦⣤⣀⣀⣀⣤⣤⣶⣾⣷⣶⣶⣶⣤⣄⡀⠀⠀⠀⣈⣽
⠀⠉⠛⠛⠿⠿⠿⠛⠓⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡶⢁⠀⠀⢸⣿⣿⣿⣿⠀⠘⢿⣿⣿⡟⠁⠠⠤⠤⠤⣈⠁⠀⠀⠀⠈⠉⠃⠉⣈⣿⣿⡿⠟⠛⣛⣻⣿⣿⣿⣯⠁⢛⠉⢹⣷⣄⣤⡞⠟⠋
⣸⣿⣿⣿⣶⡿⠇⠀⣀⣀⣸⣿⣧⣶⣶⣶⠾⢿⣶⣶⣤⣄⣴⣾⡿⠷⠀⣀⡁⠒⠀⠘⣿⣿⣿⣿⣴⠀⣾⣿⣿⢷⣶⣤⣤⣤⣤⡄⣠⣴⣶⣦⣤⣤⣶⡿⠟⢋⣡⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠾⠀⠸⣿⣿⣟⠿⡶⢀
⣿⣿⣿⣿⣿⣷⣾⣿⡿⠿⠟⣿⣿⠁⠀⠀⠀⠀⣹⣿⣿⣅⢉⣩⣤⡀⣀⣀⣀⡤⠜⢻⣿⡿⠋⠈⠉⢀⣿⣿⠍⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⣀⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⡿⣿⣾⡀⣾
⠉⠛⠿⠿⠟⠋⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⢹⣿⠟⠈⠁⠀⣴⣷⣿⣿⣧⡀⢀⡴⠁⠚⣿⣇⠙⢿⣿⣿⣿⡿⢋⣄⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⠟⢸⣿⣿⣿⣿⣿⣿⠿⣇⠀⠀⣸⣿⡄⠈⠛⠓⠙
⣿⣿⣷⣶⠶⠶⠶⠶⠻⠟⠛⣿⡆⠀⠀⣠⡴⢟⠙⣿⣿⠓⠒⣦⡄⠐⠒⠒⠒⢛⣿⣿⠟⣿⣿⣾⡁⠀⠀⠈⠻⡆⠘⠻⠉⠁⣠⣿⣿⡿⠿⠿⠿⠟⠛⠋⢉⢩⣅⣀⣸⣿⣿⣿⣿⡿⠃⢸⣿⡄⠀⣿⣿⢹⣄⣀⣀⠀
⠻⠿⠟⠁⠀⠀⠀⠀⠀⢠⣀⣼⡇⢀⡞⠁⠀⣼⣶⣿⣿⠤⠠⣬⡄⠠⢤⣤⣤⣾⣿⣿⣼⠛⣿⣿⣿⣷⣾⣿⣿⣿⣷⣦⣤⣀⠉⣁⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⣴⣿⣿⣿⣿⡯⠀⠀⠘⣽⣧⠀⠘⣿⣯⠛⠿⠿⣷
⣶⣶⠶⣿⠿⢿⠾⠿⠿⠿⠿⢿⣁⠞⠀⠀⠀⣿⣿⣿⣿⡄⠀⠈⠹⠀⠄⠀⢸⣿⣿⠉⣻⡇⣿⣿⣟⢿⣿⣿⣿⡿⣿⣿⣯⠁⢸⣿⡄⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠟⢿⣿⣧⠀⠀⠀⣿⣿⠀⠀⢸⣧⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢠⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣿⢘⣳⡄⢀⣏⣷⣿⣿⡇⣿⣿⠀⣾⡗⣾⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⢛⣸⣧⣿⣿⣾⣿⣿⣿⣾⣷⣿⣀⠙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⠿⠛⠙⠛⣿⣿⠿⠿⠀⠀⠀⠀⠀⠈⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿
⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⣿⠟⠁⠀⠀⠀⠀⢸⣷⢾⣷⡀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⠀⠀⠀⠀⠀⠀⣰⠏⠈⠹⣿⣦⣀⠀⠀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠿⠟⠛⠿⠟⡛⠁
⠞⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⣠⡟⠀⠁⠠⢹⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠋⠁⠀⠀⠀⢀⡟⠛⣶
⠀⠀⠀⠀⠀⢨⢝⡛⠃⠈⠙⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣴⣾⣿⣷⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣴⣿⡁⢀⣈
⣆⣀⣠⣴⡾⠛⢸⣿⠀⠀⠀⠀⢹⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⢶⣾⣿⣿⣷⣿⣿
⢈⣿⣿⡟⠀⠀⢸⣿⣦⣀⣀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢿⣿⡿⣿⣟⣿⣿⣿⡿⠿⣻⣄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠌⣻⠛⡿⠟⠛
⠈⢻⣿⣿⣾⣷⣾⣿⣿⡟⣿⡿⠋⠁⠀⠀⠀⠀⠀⣠⠾⢿⣿⣿⠿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠟⠛⠛⠋⠉⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠀⠀⢀
⠀⠀⠉⠻⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣷⡀⠀⠈⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣄⣤⣤⣴⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠉
⣿⣦⣿⣦⣶⣶⣶⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠻⣿⣿⣷⣤⣾⡅⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣣⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⢀⡀
⠙⠿⣿⣿⣿⣿⣿⠟⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠇⣾⣽⠏⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⡻⡿⢿⣋⣥⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤
⠀⢠⣑⠻⢭⣭⣶⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣫⠄⠀⠀⠀⢠⣽⣯⣽⠛⢿⣶⣶⣄⣀⣠⣤⣤⢤⣀⣀⡀⠈⠉⠙⠁⢸⣿⠿⢷⣶⣤⣄⣀⣀⣠⣤⣴⣶⣿⣶⣶⣶⣦⣤⣀⠀⠀⠀⢀⣩
⠀⠈⠙⠛⠿⠿⠿⠟⠒⠒⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣷⠆⠀⠀⠀⣿⣿⣿⣿⡇⠀⢻⣿⣿⡿⠋⠀⠤⠤⠤⣀⡉⠀⠀⠀⠀⠈⠙⠈⢁⣹⣿⣿⠿⠛⢛⣛⣿⣿⣿⣿⡍⠛⡋⠉⣿⣦⣤⣴⠿⠛
⢀⣽⣿⣲⣶⣶⡿⠀⠀⣀⣀⣿⣷⣤⣶⣶⣶⣶⣶⣶⣤⣄⣀⣶⣾⠿⠌⠀⣈⠐⠂⠀⢻⣿⣿⣿⣧⡆⢰⣻⣿⡷⣶⣤⣤⣤⣤⣄⢀⣤⣶⣦⣤⣤⣴⣾⠿⠛⣉⡄⣴⣿⣿⣿⣿⣿⣿⣿⠇⢰⠇⠀⢿⣿⣟⡻⢿⠆
⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠿⢻⣿⡏⠉⠀⠀⠀⢈⣿⣿⣟⣈⣉⣥⣄⢀⣀⣀⣠⠴⠛⣿⣿⠿⠋⠉⠁⣸⣿⡏⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⢀⡠⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⡿⢿⣷⣄⢀
⠉⠛⠻⣿⠿⠟⠋⠀⠀⠀⣀⣾⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠀⠘⣿⡿⠋⠉⠁⢠⣾⣾⣿⣿⣄⠀⣠⠎⠐⢻⣷⡘⠻⣿⣿⣿⣿⠟⣡⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢿⠀⠀⢀⣿⣇⠀⠙⠛⠊
⣿⣿⣷⣶⣶⠶⠴⠶⠲⠿⠟⢻⣷⡀⠀⢀⣠⠾⡟⢿⣿⡟⠒⠂⣬⠀⠒⠲⠶⠚⣻⣿⡟⢿⣿⣷⡏⠀⠀⠈⠛⢷⠀⠛⠏⠉⢁⣼⣿⣿⡿⠿⠿⠿⠛⠛⠉⡋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⣿⣇⠀⠸⣿⡟⣧⣀⣀⠀
⠙⠿⠿⠋⠀⠀⠀⠀⠀⠠⣀⣠⣿⠁⢰⠋⠀⢠⣷⣾⣿⡇⠄⢤⣭⠀⠤⣤⣤⣴⣿⣿⣥⡟⢿⣿⣿⣷⣶⣾⣿⣿⣷⣶⣤⣄⠈⢉⣁⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⣠⣾⣿⣿⣿⣿⠇⠀⠀⢻⣿⡄⠀⢿⣿⡝⠿⠿⢿
⣶⣶⡶⣶⠿⢷⠶⠶⠶⠿⠿⠿⡏⡰⠃⠀⠀⢸⣿⣿⣿⣧⡀⠀⠉⠇⠀⠀⠀⣿⣿⡏⠙⣿⢸⣿⣿⢻⣿⣿⣿⣿⢿⣿⣿⠉⠀⣿⣇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠻⣿⣿⡄⠀⠀⢸⣿⡇⠀⠀⣿⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣠⡤⣠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣻⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⢛⣘⣧⣿⣿⣾⣿⣿⣿⣾⣷⣿⣄⡙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠈⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠋⠛⢿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿
⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠹⣿⡿⠋⠀⠀⠀⠀⠈⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⡁⠀⠀⠀⠀⠀⢀⡟⠉⠉⢿⣶⣄⡀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⡿⠟⠛⠻⠟⢛⠁
⡴⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⢀⣾⠁⠈⠀⠌⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠁⠀⠀⠀⠀⣸⠙⠻
⠀⠀⠀⠀⠀⠀⡍⡛⠛⠈⠉⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣤⣤⣾⣿⣿⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢠⣾⡿⠀⣀
⢷⣀⣀⣠⣴⠝⠃⣿⡇⠀⠀⠀⠈⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⢶⣿⣿⣿⣾⣿
⠀⣹⣿⣿⠃⠀⠀⣿⣷⣄⣀⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⡿⢿⣿⣿⣿⣿⣿⠿⢟⣧⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢙⠟⢻⠿⠛
⠀⠙⢿⣿⣷⣶⣴⣿⣿⣿⢿⣿⠟⠋⠀⠀⠀⠀⠀⢀⡴⠿⣿⣿⡿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠻⠛⠛⠛⠉⠁⠀⢀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀
⡄⠀⠙⠻⠿⠿⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣆⠀⠈⢹⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣠⣤⣦⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠈
⣿⣶⣼⣶⣴⣶⣶⣴⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠛⢿⣿⣿⣦⣴⣏⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣜⣼⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠄⣀
⠈⠻⢿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠿⢰⣯⡿⠁⠀⠀⠀⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣿⢿⣟⣉⣤⣾⣯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦
⠀⠀⣔⠛⢭⣭⣥⣶⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⡥⠀⠀⠀⠀⣬⣿⣭⡟⠻⣷⣶⣤⣀⣀⣤⣤⠤⣄⣀⢀⠐⠉⠉⠋⠀⣿⡿⠿⣶⣦⣤⡀⣀⣀⣤⣴⣶⣿⣷⣶⡶⣶⣤⣤⡀⠀⠀⠀⣈
⠀⠀⠙⠛⠾⢿⣿⡿⠒⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⡷⠀⠀⠀⢸⣿⣿⣿⣷⠀⠘⣿⣿⣿⠟⠁⠠⠤⠤⢄⣉⠀⠀⠀⠀⠈⠉⠃⠉⣉⣿⣿⡿⠟⠛⣛⣻⣯⣿⣿⣿⠅⢛⠁⢹⣷⣤⣤⡴⠟
⡀⣸⣧⣶⣶⣶⣶⡆⠀⢀⣀⣸⣿⣦⣤⣶⣶⣶⣶⣶⣤⣤⡄⣴⣶⡿⠧⠁⢀⡁⠒⠀⠘⣿⣿⣿⣿⣴⠀⣞⣿⣿⢶⣤⣤⣤⣤⣤⡈⣠⣴⣶⣤⣤⣴⣶⠿⠛⢋⣡⢠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠺⠀⠸⣿⣿⣟⠿⢷
⣺⣿⣿⣿⣿⣿⣧⣶⣿⣿⡿⠿⣿⣿⠉⠁⠀⠀⠀⣹⣟⣿⣃⣉⣩⣤⡀⣀⣁⣀⡠⠜⢻⣿⡿⠇⠈⠉⢀⣿⣿⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⣀⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⡿⣿⣿⡆
⡟⠛⠛⣿⣿⠿⠛⠀⠀⠀⢀⣰⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⢻⣿⠟⠉⠉⠁⣴⣶⣿⣿⣧⡀⢀⡴⠁⠘⣿⣆⠙⣿⣿⣿⣿⡿⢋⣄⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⢿⣃⠀⠀⣸⣿⡂⠈⠙⠛
⣿⣿⣿⣶⣦⣤⣤⠤⠶⠲⠿⠛⣿⡆⠀⠀⣀⣴⠿⠹⣿⣿⠓⠆⣤⡅⠐⠒⠶⠖⢛⣿⣿⠟⣿⣿⣾⠁⠀⠀⠙⠻⡆⠘⠻⠉⠉⣠⣿⣿⣿⠿⠿⠿⠟⠛⠋⢙⢩⣁⣀⣸⣿⣿⣿⣿⡿⠃⠘⣿⡀⠀⢿⣿⢻⣄⣀⣀
⠉⢻⣿⠟⠃⠀⠀⠀⠀⠀⢄⣀⣼⡏⠀⡜⠁⠀⣸⣶⣿⣿⠤⠤⣭⡅⠠⢤⣤⣤⣾⣿⣿⣼⠿⣿⣿⣿⣶⣶⣿⣿⣿⣶⣦⣤⣀⠉⣁⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⣴⣿⣿⣿⣿⣿⠀⠀⠘⣟⣧⠀⠸⣿⣿⠛⠿⠿
⠶⣶⣶⣶⠿⢷⠶⠶⠶⠶⠿⠿⢿⢁⠞⠀⠀⠀⣿⣿⣿⣿⣄⡀⠊⠹⠀⠀⠀⢸⣿⣿⠉⢻⡇⣿⣿⣟⢿⣿⣿⣿⡿⢿⣿⣏⠁⢸⣿⡄⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠟⢿⣿⣧⠀⠀⠀⣿⣿⠀⠀⢸⣧⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣠⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⣘⣣⣿⣿⣶⣿⣿⣿⣾⣷⣿⣤⡙⠋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⠿⠛⠛⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿
⢰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡿⣿⠟⠁⠀⠀⠀⠀⢹⣷⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⣸⠋⠉⠻⣷⣤⣀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠛⠿⡛⡋
⢀⠾⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡄⠀⠀⠀⢀⣰⡏⠀⠁⡀⢹⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠋⠀⠀⠀⠀⢀⡏⠛
⠀⠀⠀⠀⠀⠀⣘⠛⠿⠋⠉⠛⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢦⣤⣼⣿⣿⣷⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣴⣿⠀⢀
⠿⣄⣀⣀⣠⡾⠛⢼⣷⠀⠀⠀⠀⢻⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣗⠶⣾⣿⣿⣷⣿
⡀⢉⣿⣿⡟⠀⠀⢸⣿⣄⣀⣀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠟⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢻⠛⡿⠟
⡇⠘⠿⣿⣿⣶⣦⣼⣿⣿⡿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢠⡾⢿⣿⣿⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠾⠟⠛⠛⠋⠉⠀⠀⣀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠀⠀
⣧⠀⠈⠛⠿⢿⣿⣿⣿⣟⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣧⠀⠀⠙⡟⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣄⣄⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀
⢹⣷⣤⣶⣦⣤⣤⣤⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⢻⣿⣿⣷⣤⣾⡁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣣⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠠⢀
⠈⠻⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠻⠇⣿⣵⠏⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⣿⣋⣡⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷
⠀⠀⢀⠋⠭⣭⣭⣵⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣫⠄⠀⠀⠀⢀⣿⣿⣿⠻⣿⣦⢦⣀⣀⣠⣤⣤⣄⣀⡀⡁⠊⠙⠛⠁⢸⣿⠿⣷⣦⣤⣄⢀⣀⣠⣤⣴⣶⣿⣶⣶⢶⣦⣤⣄⠀⠀⠀⢀
⠀⠀⠘⠛⠶⢿⣿⣿⡗⠒⠢⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⢭⠆⠀⠀⠀⣿⣿⣿⣿⣆⠈⢻⣿⣿⡿⠋⠁⠤⠤⠤⣈⠁⠀⠀⠀⠀⠉⠙⠀⢈⣻⣿⣿⠿⠻⢛⣛⣿⣿⣿⣿⡏⠛⠋⠉⣷⣦⣀⣴⠾
⣄⢀⣵⣶⣶⣶⣴⣦⠀⠀⠀⣈⣿⣷⣤⣤⣤⣶⣶⣶⣤⣤⣄⢠⣶⣾⠿⠍⠑⠂⠐⠀⠀⢿⣿⣿⣿⣧⡆⢠⢿⣿⣷⣤⣤⣤⣤⣀⣀⢁⣤⣶⣦⣤⣤⣴⣾⠿⠛⣉⡄⣴⣿⣿⣿⣿⣿⣿⣿⠇⢰⠇⠀⣿⣿⣿⡻⠿
⢩⣿⣿⣿⣿⣿⣿⣴⣶⣿⣿⠿⢿⣿⡏⠉⠀⠀⠀⢙⣛⣛⣟⢉⢙⣭⡀⢀⡈⢁⣀⡤⠛⣿⣿⠿⠙⠉⠁⣻⣿⡍⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⢀⡠⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⢿⣿⣆
⣮⠛⠛⢻⣿⡿⠿⠋⠉⠁⠀⢀⣾⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠀⠸⣿⡿⠋⠉⠉⢠⣶⣾⣿⣟⡄⠀⢠⠎⠌⢿⣷⡘⢿⣿⣿⣿⣿⠟⣡⠀⠀⣀⣀⣀⣀⣀⣠⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⢀⣿⣿⠀⠙⠛
⢻⣾⣷⣶⣦⣤⣤⡤⠤⠶⠾⠟⢿⣧⠀⠀⠀⣠⡿⠏⢿⣿⡟⠢⢠⣭⠀⠄⠤⠴⠞⣿⣿⡿⢿⣿⣷⡏⠀⠀⠈⠻⢧⠀⠻⠟⠉⠁⣼⣿⣿⡿⠿⠿⠿⠟⠛⠙⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⢿⣇⠀⠸⣿⡏⣧⣀⣀
⠉⠛⣿⣿⠛⠁⠀⠀⠀⠀⠀⡀⣨⣿⠀⢠⠎⠁⢀⣷⣾⣿⡧⠀⣈⣭⠀⢠⣤⣤⣤⣿⣿⣧⡿⣿⣿⣿⣷⣴⣶⣿⣿⣷⣶⣤⣀⠈⢋⡁⠀⠀⠀⠀⠀⠀⣠⠜⠁⢀⣈⣽⣿⣿⣿⣿⠇⠀⠀⢲⣿⡄⠀⢿⣿⡝⠻⠿
⣶⣶⣶⣶⠿⢶⠶⠶⠶⠶⣶⣿⢿⡋⣠⠋⠀⠀⢸⣿⣿⣿⣇⣀⠐⠋⡇⠀⠈⠉⣿⣿⡏⠛⣷⢸⣿⣿⠻⣿⣿⣿⣿⢿⣿⣿⡉⠀⣿⣇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠻⢿⣿⡄⠀⠀⢸⣿⡏⠀⠀⣿⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣠⡤⢤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡅⣿⠢⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣿⢘⣳⡄⢠⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣹⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡟⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⣃⣻⣿⣶⣿⣿⣿⣾⣷⣿⣤⣝⡋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣟⣿⠏⠁⠀⠀⠀⠀⢿⡦⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⡇⠀⠀⠀⠀⠀⠀⡼⠉⠉⢻⣷⣄⡀⠀⠀⣠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⠟⠛⠛⠟⠛
⠀⢀⡾⠿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢳⡀⠀⠀⠀⠀⣴⡇⠀⠀⡄⢻⣿⣿⣿⣿⣿⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠋⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⢘⠿⠿⠋⠙⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⣿⣿⣧⣤⣴⣦⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣴⣿⠀
⠰⢷⡀⠀⢀⣠⣶⠟⣼⣧⠀⠀⠀⠈⢿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣒⠶⣿⣿⣿⣷
⠀⠀⢙⣿⣿⡟⠁⠀⢸⣿⣀⠀⠀⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠟⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠛⡿
⢀⡇⠘⢿⣿⣷⣴⣤⣼⣿⣿⡿⣿⡿⠟⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠟⠛⠛⠋⠉⠀⠀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀
⢸⣦⠀⠘⠛⠿⣿⣿⣿⣿⡟⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⠘⢿⣇⠀⠈⠙⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⣄⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀
⠀⢹⣦⣤⣰⣄⣤⣤⣬⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⢾⣾⣿⣧⣤⣾⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣭⣿⣿⣿⣿⣿⣿⣿⠿⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠡
⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠛⠿⠃⣿⣳⠏⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⡿⣿⣋⣡⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠫⢟⣛⣫⣥⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣋⠀⠀⠀⠀⢠⣿⣿⣿⠿⣷⣤⣤⣀⣀⣠⣤⣤⣄⣀⠀⠁⠊⠙⠋⠁⢸⣿⠿⣷⣦⣤⣄⢀⣀⣠⣤⣶⣶⣿⣶⣶⢶⣦⣤⣀⠀⠀⠀
⠀⠀⠀⠘⠳⢶⣿⣿⣿⡿⠥⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⠿⢭⠆⠀⠀⠀⣿⣿⣿⣿⣄⠈⢿⣿⣿⡿⠉⠉⠠⠤⢀⣉⠁⠀⠀⠀⠀⠉⠛⠀⢉⣻⣿⣿⠿⠻⢛⣛⣿⣿⣿⣿⡏⠛⠋⠈⣷⣦⣠⣤
⣤⣀⠀⣲⣦⣤⣤⣤⣆⠀⠀⠀⢈⣿⣧⣤⣤⣤⣤⣶⣦⣤⣄⣀⢠⣴⣾⣿⠌⠁⠂⠠⠄⠀⢿⣿⣿⣿⣧⡄⢨⢿⣿⣧⣤⣤⣤⣀⣀⣀⢁⣤⣦⣤⣤⣤⣴⣾⠿⠛⣉⡄⣶⣿⣿⣿⣿⣿⣿⣿⠃⢰⠇⠀⢿⣿⣟⣻
⠈⢉⣾⣿⣿⣿⣿⣿⣥⣶⣾⣿⣿⢿⣿⡛⠋⠉⠀⠈⢙⣻⣿⡟⠙⢛⣉⡀⠀⠈⢁⣀⡤⠞⣿⣿⠿⠙⠉⠁⣿⣿⡝⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⢀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣼⣿⢿⣿
⣶⣬⠻⠿⢿⣿⣿⡿⠛⠉⠉⠀⢀⣾⣿⠇⠀⠀⠀⢀⣿⣿⣿⣿⠀⠸⣿⡿⠍⠉⠉⢡⣶⣾⣿⣟⡄⠀⢠⠎⠈⢿⣧⠘⢿⣿⣿⣿⣿⠟⣡⠀⠀⢀⠀⠀⠀⣀⣠⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⢀⣿⣷⡀⠉
⠙⢻⣶⣶⣦⣭⣤⣤⢤⣤⠤⣶⠿⢿⣧⠀⠀⠀⣀⣽⢟⢿⣿⡧⠤⢠⣭⠀⠤⠤⠤⠾⣿⣿⡿⢿⣿⣶⡏⠀⠀⠈⠻⣧⠀⠿⠏⠋⢁⣼⣿⣿⡿⠿⠿⠿⠟⠛⠙⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⢿⣇⠀⠸⣿⡟⣧⣀
⠀⠘⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⡀⢨⣿⠀⢠⠞⠉⢠⣦⣼⣿⡇⠀⣈⣩⠀⣀⣤⣤⣤⣿⣿⣥⡿⣿⣿⣿⣧⣴⣶⣿⣿⣶⣦⣄⣀⠈⢋⡁⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣨⣽⣿⣿⣿⣿⠇⠀⠀⢻⣿⡄⠀⢿⣷⡜⠻
⠳⢶⣶⣶⣯⢶⠶⠶⠶⠶⢶⣶⣿⣿⡏⣠⠏⠀⠀⢸⣿⣿⣿⣇⠀⠘⠛⡆⠀⠉⠉⣿⣿⡟⠻⣷⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⠋⠀⣿⣇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠻⣿⣿⡀⠀⠀⢺⣿⡏⠀⠀⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡆⢠⣏⣷⣿⣿⡇⣿⣿⠀⣽⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⢃⣛⣯⣴⣿⣿⣿⣾⣷⣿⣦⣽⣋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿
⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⣿⡟⠉⠀⠀⠀⠀⠸⣷⢾⣿⡀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⠀⠀⠀⠀⠀⠀⢰⠏⠈⠹⣷⣦⣀⠀⠀⣀⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠿⠛⠛⠻⠛
⠀⠀⣰⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣆⠀⠀⠀⠀⣠⡿⠀⠁⢠⠸⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠟⠁⠀⠀⠀⢀⡘
⠀⠀⠁⠀⠀⠀⠀⠀⡟⢿⠟⠙⠻⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣤⣿⣿⣿⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣰⣿⡇
⠀⢾⣄⠀⠀⢀⣤⡾⢷⣿⡄⠀⠀⠀⠹⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⡲⢾⣿⣿⣿
⠀⠀⠘⢻⣿⣿⠋⠀⠈⣿⣇⡀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⢿⣿⣿⣿⣿⡿⠿⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⡟⠻
⠀⣰⠀⢿⣿⣿⣦⣤⣠⣿⣿⣿⢿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠿⠛⠛⠛⠉⠁⠀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀
⠀⣿⡄⠀⠺⢻⢿⣿⣿⣿⣿⢧⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠻⣿⡀⠀⠉⢿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣄⣀⣠⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄
⠀⠈⣷⣄⣢⣤⣠⣤⣅⣭⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠲⣶⣿⣿⣤⣤⡆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣽⣿⣿⣿⣿⣿⣿⡿⠟⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠛⠻⠟⢸⣟⡾⠁⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣿⣟⣉⣤⣾⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠨⠿⣛⣛⣫⣥⡖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢛⡁⠀⠀⠀⠀⣸⣿⣿⡻⢿⣦⣤⣄⠀⣀⣤⣤⣤⣀⡀⢈⠑⠉⠛⠉⢀⣿⡿⢿⣶⣤⣄⡀⣀⣀⣤⣴⣶⣿⣷⣶⡶⢶⣤⣤⡀⠀⠀
⠀⠀⠀⠀⠻⠦⣴⣿⣯⣿⠭⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⡿⢯⡵⠀⠀⠀⢼⣿⣿⣿⣧⡄⠹⣿⣿⣿⡟⠉⠁⠤⢄⣈⡉⠀⠀⠀⠀⠈⠙⠃⠈⣙⣿⣿⡿⠟⠟⣛⣻⣿⣿⣿⣿⠉⢛⠉⢹⣶⣤⣤
⣤⣀⡀⢠⣶⢤⣤⣤⣽⡁⠀⠀⠀⢹⣷⣄⣤⣤⣤⣤⣤⣤⣤⣀⡀⣤⣴⣿⡧⠈⠐⠀⠤⠀⠸⣿⣿⣿⣿⣤⠀⡽⣿⣿⣤⣤⣤⣀⣀⣀⡈⣠⣴⣤⣤⣤⣤⣶⡿⠟⢋⣡⢠⣾⣿⣿⣿⣿⣿⣿⡿⠀⡾⠀⠸⣿⣿⣟
⠈⠉⢱⣿⣿⣿⣿⣿⣯⣥⣶⣾⣿⡿⣿⣟⠛⠉⠉⠉⠉⣛⣿⣿⠋⠛⢛⣁⠀⠀⠉⢀⣀⡴⢲⣿⡿⠏⠋⠉⢸⣿⣯⠋⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⡿⣿
⣶⣤⡟⠿⠿⣿⣿⣿⠿⠛⠉⠉⠀⣠⣿⡿⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⢿⣿⡿⠙⠋⠉⣴⣶⣿⣿⣧⠀⠀⡴⠂⠽⣿⡄⠻⣿⣿⣿⣿⡿⢋⡄⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣇⠀⠀⢸⣿⣂⠈
⠙⠿⣳⣶⣶⣬⣭⣤⣀⣀⣤⣤⡾⠿⣿⡅⠀⠀⢀⣠⡿⠻⣿⣿⠧⠄⣈⡏⠠⠤⠤⠴⢿⣿⣿⠿⣿⣿⣾⠁⠀⠀⠙⢿⡄⠘⠿⠛⠋⣠⣿⣿⣿⠿⠿⠿⠿⠟⠋⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⣿⡄⠀⢿⣿⢸⣤
⡀⠀⠚⢿⣿⡿⠟⠉⠀⠀⠀⠀⡀⠀⣹⡇⠀⡴⠋⠁⣰⣤⣿⣿⣀⢀⣙⡁⢀⣀⣀⣀⣼⣿⣟⣴⠿⣿⣿⣷⣤⣶⣾⣿⣷⣶⣤⣀⡀⠙⣉⠁⠀⠀⠀⠀⠀⢀⡤⠊⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠈⣿⣧⡀⠘⣿⣿⠙
⠛⠶⣶⣶⣯⣶⠶⢶⣶⣶⣶⣤⣾⣿⣿⠃⡴⠁⠀⠀⣿⣿⣾⣿⡀⠀⠙⢳⠀⠈⠉⢹⣿⣿⠛⢿⡆⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢸⣿⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠟⠻⣿⣧⠀⠀⠀⣿⣿⠁⠀⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣿⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣻⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡷⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⣛⣫⣤⣿⣿⣿⣾⣷⣿⣶⣽⣋⠘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⣖⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣲⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠹⣿⣿⠏⠁⠀⠀⠀⠈⣿⡶⣾⡇⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿
⠀⠀⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡇⠀⠀⠀⠀⠀⠀⡾⠉⠉⢿⣶⣄⡀⠀⢀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡿⠟⠛⠛⠟
⠀⠀⢀⣼⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⠀⠀⠀⠀⢀⣼⠇⠈⠀⡌⣿⣿⣿⣻⣿⣿⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⠀⠀⠀⠀⣠
⠀⠀⠈⠀⠀⠀⠀⠀⠸⠿⠿⠛⠛⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣠⣤⣿⣿⣦⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣼⣿
⠀⠰⣧⠀⠀⠀⣀⣴⠿⣾⣦⠀⠀⠀⠙⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣒⠶⣿⣿⣿
⠀⠀⠈⠻⣿⣿⡟⠁⠀⢹⣿⡀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢻⠛
⠀⢀⡇⠸⣿⣿⣧⣤⣄⣼⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠞⠟⠛⠛⠉⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠂
⠀⢸⡤⠀⠘⠿⣿⣿⣿⣿⣿⣿⣥⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⢀⠘⣿⣏⠀⠈⠻⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠈⢻⣄⣠⣤⣄⣀⣉⣉⣩⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⣶⣾⣿⣦⣠⣴⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣭⣿⣿⣿⣿⣿⣿⣿⠿⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠛⠿⠇⣿⣻⠏⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣋⣁⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠽⣛⣛⣛⣩⣴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢋⠀⠀⠀⠀⢀⣿⣿⣟⠿⣷⣤⣤⡀⢀⣀⣀⣀⣀⣀⠀⠙⠚⠙⠋⠉⢸⣿⠿⣷⣦⣤⣄⠀⣀⣠⣤⣶⣾⣿⣶⣶⢶⣦⣤⣄⠀⠀
⠀⠀⠀⠀⠸⢶⣤⣾⣿⣿⡯⠥⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⣿⣯⠆⠀⠀⠠⣿⣿⣿⣿⣄⠈⢿⣿⣿⣿⠋⠉⠀⢤⣈⣉⠁⠀⠀⠀⠀⠉⠛⠀⢉⣻⣿⣿⠿⠻⢛⣛⣿⣿⣿⣿⡍⠙⡋⠉⣷⣦⣤
⣤⣀⡀⠀⣤⣤⣤⣤⣭⣍⠀⠀⠀⠙⣿⣦⣀⣠⣤⣤⣤⣤⣤⣀⣀⢀⣤⣼⣿⠀⠁⠀⠠⠄⠀⢿⣿⣿⣿⣧⡄⢨⣿⣿⣧⣤⣤⣀⣀⣀⣀⢁⣤⣤⣤⣄⣤⣴⣾⠿⠛⣉⡄⣴⣿⣿⣿⣿⣿⣿⣿⠇⠰⠇⠀⢿⣿⣿
⠀⠉⢙⣾⣿⣿⣿⣿⣿⣩⣤⣶⣾⣿⣿⣿⡟⠛⠉⠉⠉⠙⡿⢿⡟⠙⠛⣋⡀⠀⠈⠉⢀⣠⠶⣾⣿⡿⠛⠋⠁⣿⣿⡟⢡⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⣿⢻
⣶⣤⣴⠿⠿⢿⣿⣿⣿⠟⠛⠋⠉⠀⣼⣿⠇⠀⠀⠀⢀⣾⣿⣿⣿⠀⠹⣿⣿⠎⠛⠉⢩⣶⣾⣿⣿⡄⠀⢀⠔⡩⢿⣧⠘⢿⣿⣿⣿⣿⠟⣁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⠀⣿⡿⡄
⠉⠻⢿⣴⣶⣬⣍⣁⣀⣀⣀⣤⣴⡿⢿⣯⠀⠀⠀⢀⣼⡟⢿⣿⡿⠤⢄⣙⢁⠤⠤⠤⠼⢿⣿⡿⣿⣿⣶⡏⠀⠀⠈⠻⣧⠀⠿⠟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⣿⣧⠀⠸⣿⡇⢧
⣀⠀⠘⠿⣿⣿⡿⠋⠉⠉⠁⠀⠀⠀⢈⣿⠀⢀⠞⠉⢀⣦⣼⣿⣇⣀⣈⣛⠀⣀⣀⣀⣠⣿⣿⣣⡿⣿⣿⣿⣦⣤⣶⣾⣿⣶⣤⣄⣀⠈⢛⣉⠀⠀⠀⠀⠀⠀⣀⠔⠃⢀⣈⣽⣿⣿⣿⣿⡇⠀⠀⢹⣿⣆⠀⢻⣿⡟
⠛⠷⢶⣶⣯⣷⠤⣴⣴⣶⣦⣤⣤⣷⣿⡟⢀⠞⠀⠀⢰⣿⣷⣿⣇⠀⠈⠛⡆⠀⠉⠉⣿⣿⡟⠻⣷⢸⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡋⠀⣾⣧⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡿⠛⢿⣿⡄⠀⠀⢸⣿⡟⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⢠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣺⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡏⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⣋⣠⣽⣿⣿⣾⣷⣿⣶⣿⣯⣘⠛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⡿⠋⠁⠀⠀⠀⠘⣷⣴⣶⡀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿
⠀⠀⠀⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⠃⠀⠀⠀⠀⠀⢀⡿⠉⠙⣿⣦⣄⠀⠀⢀⣠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⠟⠛⠛
⠀⠀⠀⢀⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⣼⠃⠈⠀⡈⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⠁⠀⠀⠀⠀
⠀⠀⠀⡏⠀⠀⠀⠀⠀⢹⣿⣿⠛⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣠⣴⣿⣿⣦⣠⣶⣴⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢠⣾
⠀⠀⢠⣆⠀⠀⠀⢀⣴⡿⣼⡆⠀⠀⠀⠙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⢶⣿⣿
⠀⠀⠀⠙⠷⣶⣾⡟⠁⠀⣿⣿⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣿⣿⣿⡿⣿⣿⣿⣿⢿⠟⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿
⠀⠀⢀⡇⠼⣿⣿⣧⣠⣀⣼⣿⣿⣷⣶⣿⠿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠾⠾⠟⠛⠛⠁⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⢸⡇⠀⠹⠿⣿⣿⣿⣿⣿⣿⣹⡿⠁⠀⠀⠀⠀⠀⠀⠐⠉⢁⠹⣿⡇⠀⠉⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣠⣀⣀⣤⣴⣾⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠈⢿⣄⣠⣠⣀⣉⣉⣙⣫⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣶⣾⣿⣄⣠⣼⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣘⣿⣿⣿⣿⣿⣿⣿⠿⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠭⠿⢿⠋⣿⣾⠇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⢿⣿⣿⣋⣁⣴⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⢛⣿⠿⢟⣋⣵⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢋⠀⠀⠀⠀⢀⣿⣿⣻⢿⣶⣤⣄⡀⢀⣀⣀⣀⣀⡀⠈⠑⠚⠛⠋⠁⣸⣿⠿⣶⣦⣤⣀⠀⣀⣠⣤⣶⣾⣿⣶⣶⢶⣦⣤⣄⠀
⠀⠀⠀⠀⠀⠺⣶⣤⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣾⣿⣯⠆⠀⠀⢠⣿⣿⣿⣿⣀⠙⣿⣿⣿⡿⠋⠉⣀⣀⣈⡉⠁⠀⠀⠀⠀⠉⠛⠀⢉⣻⣿⣿⠿⠻⢛⣛⣿⣿⣿⣿⡍⠛⡋⢈⣷⣦
⢦⣄⣀⠀⠀⣠⣤⣈⣉⣉⡍⠁⠀⠀⠙⣿⣆⣀⣀⣀⣤⣤⣤⣀⣀⡀⢠⣤⣾⣿⠐⠡⠐⠠⠀⠀⣿⣿⣿⣿⣧⡄⣸⣿⣿⣧⣤⣤⣀⣀⣀⣈⢀⣤⣤⣤⣤⣤⣴⣾⠿⠛⣉⡄⣶⣿⣿⣿⣿⣿⣿⣿⠃⢸⠇⠀⢿⣿
⡀⠉⠛⠛⣶⣿⣿⣿⣿⣿⣋⣤⣴⣶⣾⣿⡿⠟⠛⠋⠉⠉⠻⠿⣿⡟⠛⠟⣋⠀⠀⠀⠁⢀⣠⠶⣿⣿⡟⠙⠙⠁⣿⣿⡟⢡⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⢀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿
⢿⣦⣤⣰⠿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⣼⣿⠇⠀⠀⠀⢀⣾⣿⣿⣿⠈⢸⣿⣷⠚⠛⠋⢩⣤⣼⣿⣟⡀⠀⢀⠔⡙⢿⣇⠹⢿⣿⣿⣿⣿⠟⣃⠁⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠉⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⢀⣿⡟
⠀⠉⠻⣿⣤⣤⣬⣙⣉⣀⣀⣀⣠⣴⡾⣿⣏⠀⠀⠀⢀⣿⣿⣿⣿⡯⢤⣌⣛⢁⠀⣀⣤⠼⣿⣿⡿⣿⣿⣴⡏⠀⠀⠘⠿⣇⠈⠿⠟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⡿⣧⠀⠸⣿⣇
⣄⡀⠀⠰⢿⣿⣿⡿⠋⠉⠉⠉⠁⠉⠀⢸⣿⠂⢀⡴⠋⢁⣌⣼⣿⡇⠀⠘⣛⠀⣀⣀⣀⣰⣿⣿⣃⡿⣿⣿⣷⣦⣤⣶⣶⣿⣶⣤⣄⡀⠘⢋⡉⠁⠀⠀⠀⠀⠀⣀⠔⠃⢀⣉⣽⣿⣿⣿⣿⡇⠀⠀⢹⣿⣄⠀⠿⣿
⠛⠿⠷⣶⣧⣿⣏⠠⣴⣶⣦⣤⣤⣤⣷⣾⡟⢀⡞⠀⠀⢸⣿⣿⣿⡇⠀⠩⠛⡆⠀⠉⠉⣿⣿⡟⠻⣷⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣇⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡿⠻⣿⣿⡄⠀⠀⢸⣿⡟⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡟⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⢋⣀⣽⣿⣾⣾⣷⣿⣶⣿⣯⣜⡛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣿⣿⠟⠁⠀⠀⠀⠀⢿⣦⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠸⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⡟⠀⠀⠀⠀⠀⠀⣸⠛⠉⢻⣷⣤⡀⠀⠀⣀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡿⠟⠛⠛
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⣰⡏⠀⠂⡀⢻⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠋⠀⠀⠀⠀
⠀⠀⠀⠰⠉⠀⠀⠀⠀⠘⣿⣿⡟⠻⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⣤⣿⣿⣧⣀⣴⣦⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢀⣴
⠀⠀⠀⣴⡀⠀⠀⠀⣠⣾⣷⣦⠀⠀⠀⠘⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠶⣿⣿
⠀⠀⠀⠈⠳⣶⣶⣿⠟⠀⢸⣿⡇⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹
⠀⠀⠀⢸⠠⣿⣿⣿⣀⣄⣀⣿⣿⣶⣶⣾⡿⠇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠷⠿⠛⠛⠋⠀⠀⣀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⣟⠀⠈⢿⣿⣿⣿⣿⣿⣿⣯⣿⠏⠀⠀⠀⠀⠀⠀⠀⠊⠉⡈⢿⣟⠁⠉⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣄⣀⣠⣴⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣧⡀⣄⣈⢈⣉⣉⣛⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠤⡼⢴⣶⣿⣧⣀⣤⡇⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣃⣿⣿⣿⣿⣿⣿⣿⡿⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠽⠿⡟⢹⢳⡿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⣛⣁⣤⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⣿⠿⠿⢛⣩⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⡁⠀⠀⠀⠀⣺⣿⣟⡿⣷⣦⣤⣀⠀⣀⣀⣀⣀⣀⠀⠉⠓⠛⠛⠉⢀⣿⡿⢷⣦⣤⣄⡀⣀⣀⣤⣴⣶⣿⣷⣶⠶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢶⣤⣽⣿⣿⣿⣓⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣿⣟⡥⠀⠀⠀⣾⣿⣿⣿⣇⡈⢻⣿⣿⣿⠟⠉⢁⣀⣁⣉⠉⠀⠀⠀⠀⠈⠙⠃⠀⣙⣿⣿⡿⠟⠟⣛⣻⣿⣿⣿⣿⠉⢛⠁⢹⣷
⠷⣤⣀⡀⠀⢠⣄⣀⣉⣉⣩⠋⠀⠀⠉⢻⣶⣀⣀⣀⣀⣤⣤⣄⣀⡀⠀⣤⣼⣿⡗⠊⠄⠂⠄⠀⢹⣿⣿⣿⣿⣤⢀⣿⣿⣿⣤⣤⣄⣀⣀⣀⡁⣠⣤⣤⣤⣤⣤⣶⡿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⡿⠀⠾⠀⠸⣿
⡄⠈⠛⠛⢣⣾⣿⣿⣿⣿⣟⣡⣤⣶⣶⣾⣿⡿⠟⠛⠋⠉⠛⠿⠿⢿⠛⠻⢟⡁⠀⠀⠊⠀⣀⡴⢾⣿⣿⠏⠏⠋⢸⣷⣿⠋⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿
⢻⣶⣤⣀⡾⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⢡⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⡏⠁⣿⣿⡖⠛⠛⠉⣥⣤⣿⣿⣧⡄⠀⡰⢊⠻⣿⡈⠿⣿⣿⣿⣿⡿⢛⡈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢹⣿⣿⣿⣿⣿⣿⢿⣇⠀⠀⢸⣿
⠀⠈⠙⢿⣧⣤⣤⣉⣋⣉⢀⣀⣀⣤⣴⣿⣿⡁⠀⠀⠀⣰⣿⢿⣿⣿⠥⣀⣘⡋⡀⢀⣠⡤⢿⣿⣿⢿⣿⣶⣾⠁⠀⠀⠻⢷⡀⠹⠿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣋⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢿⡄⠀⢿⣿
⣤⣀⠀⠀⠻⣿⣿⣿⠿⠋⠉⠉⠉⠉⠁⠀⢻⡇⠀⣠⠞⠉⢨⣤⣿⣿⠀⠀⢛⡃⢀⣀⣀⣀⣼⣿⣟⣸⢿⣿⣿⣶⣤⣴⣶⣾⣷⣦⣄⣀⠐⠛⣋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣈⣩⣿⣿⣿⣿⣿⠀⠀⠈⣿⣧⡀⠘⣿
⠙⠟⠿⣶⣯⣾⣟⡡⣴⣶⣦⣀⣠⣤⣼⣶⣿⠇⣰⠃⠀⠀⣿⣿⣿⣿⠀⠈⠝⢳⠀⠈⠉⢻⣿⣿⠻⢷⡆⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⠟⠿⣿⣧⠀⠀⠀⣿⣿⠇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢠⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣸⣿⡇⣿⣿⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡷⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⣀⣹⣿⣾⣾⣷⣿⣶⣿⣯⣜⡛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣴⢸⡿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⡿⠋⠀⠀⠀⠀⠸⣷⣲⣶⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⠁⠀⠀⠀⠀⠀⢠⡟⠋⠙⣷⣦⣀⠀⠀⢀⣴⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⠿⠛⠛
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⠀⠀⠀⠀⢀⣾⠁⠐⢀⠘⣿⣿⣟⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠁⠀⠀⠀
⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⢿⣿⣿⠻⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⣄⣠⣼⣿⣿⣤⣠⣶⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣠
⠀⠀⠀⢠⣄⠀⠀⠀⢀⣰⡞⣼⡅⠀⠀⠈⠻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡳⢾⣿
⠀⠀⠀⠈⠙⢶⣶⣶⡿⠉⠀⣿⣧⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣇⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈
⠀⠀⠀⢀⡆⢾⣿⣿⣅⣀⠀⣽⣿⣷⣶⣶⣿⡿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠿⠺⠟⠛⠛⠁⠀⢀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣹⡿⠁⠀⠀⠀⠀⠀⠀⠐⠉⢉⠻⣿⡋⠉⠙⢿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣠⣀⣠⣤⣶⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⡄⠠⣀⡉⣉⡛⠛⣛⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⣤⣧⣦⣿⣷⣄⣀⣜⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣜⣸⣿⣿⣿⣿⣿⣿⡿⠟⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠩⠽⠿⣿⠉⡟⣾⠇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣋⣠⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⣻⠿⠿⠿⣛⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢏⠀⠀⠀⠀⢐⣿⣿⡿⢿⣦⣤⣄⠀⢀⣀⣀⣀⣀⡀⠈⠑⠚⠛⠋⠁⣸⣿⢿⣶⣤⣤⣀⢀⣀⣤⣤⣶⣾⣿⣶⡶⢶⣦⣤⣄
⢀⠀⠀⠀⠀⠀⠶⣤⣌⣽⣿⣿⣟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣾⣿⣫⠄⠀⠀⢰⣿⣿⣿⣿⠀⠙⣿⣿⣿⡿⠋⠉⣀⣈⣉⡉⠁⠀⠀⠀⠀⠉⠛⠀⢉⣻⣿⡿⠿⠿⢛⣛⣿⣿⣿⣿⡇⠙⡃⠀⣿
⠻⣦⣀⡀⠀⠀⣤⣀⣉⣉⣙⡟⠁⠀⠈⠻⣷⡄⢀⣀⣀⣀⣤⣄⣀⡀⠀⢀⣤⣾⣟⠒⠡⠐⢠⠀⠈⣿⣿⣿⣿⣧⡀⣸⣿⣿⣧⣤⣄⣀⣀⣀⡈⢀⣤⣤⣤⣤⣤⣴⡾⠿⠛⣉⡄⣶⣿⣿⣿⣿⣿⣿⣿⠃⠸⠃⠀⢿
⣧⠈⠙⠿⠷⣴⣿⣿⣿⣿⣿⣛⣠⣤⣶⣶⣿⣿⠿⠛⠛⠛⠙⠻⠿⢿⡗⠻⠿⡋⠀⠀⠒⠂⠀⣠⠶⣿⣿⡿⠙⠛⠀⣿⣾⡛⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢀⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣼
⠻⣷⣤⣄⣰⣿⣿⣿⣿⣿⣿⠻⠟⠛⠉⠉⣼⣿⡇⠀⠀⠀⢀⣾⣿⣿⣷⠈⢸⣿⣷⠞⠒⠛⢩⣤⣼⣿⡟⣄⠀⢀⠔⡙⢿⣇⠻⣿⣿⣿⣿⣿⠟⣁⠁⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠉⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⣿
⠀⠈⠙⢿⣿⣤⣤⣈⣛⣋⠁⠀⣀⣀⣤⣾⣿⣏⠀⠀⠀⢀⣾⡿⣿⣿⡏⣀⣈⣛⢁⣀⣀⣠⡼⣿⣿⡿⣿⣷⣶⡏⠀⠀⠘⢿⣆⠈⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⡯⣧⠀⠸⣿
⣦⣄⡀⠀⠸⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠀⢸⣿⠀⢀⡴⠛⢉⣄⣽⣿⡇⠀⠘⣛⠀⢀⣀⣀⣠⣿⣿⣃⡿⣿⣿⣷⣦⣤⣶⣶⣿⣶⣤⣀⡀⠚⢛⡉⠀⠀⠀⠀⠀⠀⣠⠔⠁⢀⣉⣽⣿⣿⣿⣿⡇⠀⠀⢡⣿⣆⠀⢻
⠙⠟⠿⣷⣯⣶⣟⣻⠰⣶⣦⣀⣀⣀⣠⣷⣾⡿⢀⡞⠀⠀⢸⣿⣿⣿⣇⠀⠹⠟⡆⠈⠙⠛⣿⣿⡟⠿⣦⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡛⠀⣿⣇⠀⠀⠀⠀⠀⠁⣀⣠⣴⣿⣿⣿⡿⠛⣿⣿⡄⠀⠀⢸⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⢤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⢀⣙⣿⣽⣾⣷⣿⣶⣿⣯⣼⣛⠃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⠟⠁⠀⠀⠀⠀⣿⡶⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡏⠀⠀⠀⠀⠀⠀⣼⠛⠉⢻⣶⣄⡀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡿⠟⠛
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣳⡀⠀⠀⠀⠀⣰⡇⠀⠂⡀⢻⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠋⠀⠀⠀
⠀⠀⠀⠀⠰⠋⠉⠉⠀⠀⠹⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣀⣤⣿⣿⣧⣄⣴⣦⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢀
⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣴⢺⣯⠀⠀⠀⠙⢿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠲⢿
⠀⠀⠀⠀⠙⠳⣶⣶⣾⠟⠁⢸⣿⡆⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠠⣾⣿⣿⣀⡀⢈⣿⣷⣶⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠷⠿⠛⠛⠋⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⣿⣿⠉⠉⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣄⣀⣠⣴⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣧⡀⡄⣈⠙⠛⠛⠛⣻⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣼⣿⣧⣀⣠⡇⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣿⣿⣿⣿⣿⣿⣿⡿⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⢿⡟⢹⢷⡿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣟⣉⣠⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⢙⣿⠿⠿⢟⣋⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⡃⠀⠀⠀⠀⣸⣿⣿⡿⣷⣦⣤⣀⠀⣀⣀⣀⣀⣀⠀⠉⠒⠛⠛⠉⢀⣿⡿⣿⣶⣤⣄⡀⣀⣠⣤⣴⣶⣿⣿⣷⢶⣶⣦⣤
⡀⢀⠀⠀⠀⠀⠀⢦⣬⣽⣿⣿⣿⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣿⣞⡡⠀⠀⠀⣼⣿⣿⣿⣇⡈⢻⣿⣿⣿⡟⠉⢁⣀⣁⣉⠙⠀⠀⠀⠀⠈⠙⠃⠀⣙⣿⣿⡿⠟⢛⣛⣻⣽⣿⣿⣷⠈⢉⠀⢸
⠛⢦⣄⡀⠀⠀⢀⣀⣈⣉⣙⣛⠋⠀⠀⠉⢻⣦⡀⢀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣤⣿⡇⠚⠥⠂⣄⡀⢹⣿⣿⣿⣿⣤⢀⣿⣿⣿⣤⣤⣀⣀⣀⣀⡁⣠⣤⣤⣤⣤⣤⣶⡿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⡿⠀⠺⠀⠈
⣿⡆⠉⠛⠿⢦⣼⣿⣿⣿⣿⡟⣃⣠⣴⣶⣾⣿⣿⠿⠟⠛⠛⠛⠿⣿⣿⠞⠿⠟⠃⠀⠀⠒⠀⢀⡴⢶⣿⣿⠟⠟⠋⢸⣿⣿⠋⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀
⠘⢿⣦⣄⣀⣸⣿⣿⣿⣿⣿⣿⠛⠟⠛⠉⢉⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⣿⣿⡶⠓⠒⠋⣩⣤⣾⣿⢇⠀⠀⣠⢊⠻⣿⡈⠿⣿⣿⣿⣿⣿⢛⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀⢸
⠀⠀⠉⠻⣿⣷⣠⣈⣙⠛⠋⠁⠀⢀⣀⣴⣾⣿⡃⠀⠀⠀⢀⣿⣿⣿⣿⢇⡀⢘⡋⢀⣀⣀⣤⠿⣿⣿⣿⣿⣷⣼⠃⠀⠀⠻⢿⡄⠸⠿⠛⠋⢀⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣋⣁⣀⣸⣿⣿⣿⣿⡿⠃⢰⢹⡇⠀⢸
⣦⣄⣀⠀⠀⠿⣿⣿⣿⡿⠛⠛⠋⠉⠉⠉⠀⢹⣷⠀⢠⠞⠋⢩⣉⣿⣿⠀⠀⠙⡃⠀⣀⣀⣀⣼⣿⣿⣠⠿⣿⣿⣶⣤⣤⣶⣶⣷⣦⣤⣀⡀⠛⢋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠀⣪⣿⡄⠈
⠉⠟⠻⣿⠿⣶⣌⢻⡻⢶⣦⣀⣀⣀⣀⣸⣶⣿⠏⢠⠏⠀⠀⣼⣿⣿⣿⡅⠈⠻⢳⠀⠉⠛⢻⣿⣿⠿⢿⡆⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢠⣿⡅⠀⠀⠀⠀⠀⢁⣀⣤⣶⣿⣿⣿⠿⠻⣿⣷⡀⠀⠀⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⢙⣛⣽⣼⣷⣿⣶⣿⣿⣾⣿⣃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⠟⠁⠀⠀⠀⠈⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿
⠀⠀⠀⠀⠀⡸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⡇⠀⠀⠀⠀⠀⠀⡿⠋⠉⢿⣦⣄⡀⠀⠀⣠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⡿⠟
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⠀⠀⠀⠀⠀⣼⠇⠈⠀⡈⢿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⠀
⠀⠀⠀⠀⠀⢰⠛⠉⠉⠉⠈⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆⣀⣤⣿⣿⣦⣀⣴⣦⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣴⢩⣍⠀⠀⠈⠹⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠲
⠀⠀⠀⠀⠈⠙⢷⣤⣤⣾⠟⠁⢹⣿⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⢰⢠⣿⣿⣯⠀⡀⢸⣿⣷⣦⣤⣶⣿⠁⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠖⠟⠛⠛⠋⠀⠀⣀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⠀⠀⠀⠀⡿⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏⣿⠟⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⣿⣟⠉⠙⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣔⠀⠀⠀⠈⢻⣆⠀⡀⡙⠙⠛⠛⠿⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⣼⣿⣆⣀⣠⠃⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣃⣿⣿⣿⣿⣿⣿⣿⠿⢛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠻⢿⡏⣻⢧⡿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣛⣁⣤⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠿⢛⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠁⠀⠀⠀⠀⣺⣿⣿⠿⣷⣤⣤⡀⠀⣀⣀⣀⣀⡀⠀⠉⠓⠛⠛⠉⢀⣿⡿⢷⣶⣤⣄⡀⣀⣠⣤⣶⣾⣿⣿⡷⢶⣶⣦
⣄⠀⢀⠀⠀⠀⠀⠠⣤⣉⣲⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣞⡡⠀⠀⠀⣼⣿⣿⣿⣇⠈⢿⣿⣿⣿⡟⠉⢁⣀⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⠀⣙⣿⣿⠿⠛⢛⣛⣿⣿⣿⣿⣶⠉⢛⠁
⠉⠳⢧⣀⠀⠀⠀⢀⣈⣉⡛⠛⢛⠛⠉⠉⠙⢷⣦⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣴⣿⡇⠛⠡⠂⣀⡀⢻⣿⣿⣿⣿⡄⢀⣿⣿⣿⣤⣤⣀⣀⣀⣀⠁⣠⣤⣤⣤⣤⣤⣶⡿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⣿⠀⠚⠀
⠀⣶⡄⠙⠻⠷⢆⣼⣿⣿⣿⣿⡿⢃⣀⣤⣴⣾⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⠖⠿⠿⠋⠁⠀⠒⠀⢀⡴⣼⣿⣿⠏⠟⠋⢸⣿⣿⠛⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⠀⠸⢿⣦⣀⡀⣸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢉⣿⣿⠀⠀⠀⠀⢠⣶⣿⣿⡆⠀⣾⣿⣶⠒⠒⠛⣩⣤⣿⣿⢇⡀⠀⡠⢊⢻⣿⡈⠿⣿⣿⣿⣿⡿⢛⡈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀
⠀⠀⠀⠙⠻⣿⣿⣈⣉⡛⠟⠛⠁⠀⠀⣀⣤⣾⣿⡋⠀⠀⠀⢀⣿⣿⣿⣿⣇⣀⠙⡋⢁⣀⣀⣠⣿⣿⣿⣿⣿⣦⣼⠃⠀⠀⠻⣿⡀⠹⢿⠛⠋⢀⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣋⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢹⡆⠀
⣷⣦⣄⡀⠀⠈⣽⣿⣿⣿⣿⠟⠓⠛⠛⠛⠋⠀⢻⣷⠀⢀⠴⠋⢩⣈⣿⣿⠀⠈⠻⠃⠀⠀⠀⠀⣸⣿⣿⣰⡿⣿⣿⣶⣤⣤⣶⣶⣷⣤⣄⣀⠀⠛⢋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⡄
⢀⡟⠻⣿⢿⢶⣄⡹⠿⠿⢆⣀⣀⣀⣀⣀⣱⣤⣾⡏⢠⠏⠀⠀⢸⣿⣿⣿⡉⠉⠻⢧⠈⠙⠛⢻⣿⣿⠿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢠⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⠻⣿⣧⡀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢾⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⢙⣛⣼⣼⣷⣿⣶⣿⣿⣾⣿⣃⠙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⠟⠁⠀⠀⠀⠈⣿⡷⣶⡆⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⡸⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⡇⠀⠀⠀⠀⠀⠀⡿⠋⠉⢿⣦⣄⡀⠀⠀⣠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⣿⡿⠟
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢧⠀⠀⠀⠀⠀⣼⠇⠈⠀⡈⢿⣿⣿⣻⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⠀
⠀⠀⠀⠀⠀⢰⠛⠉⠉⠉⠉⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆⣀⣤⣿⣿⣦⣀⣴⣤⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣴⢩⣍⠀⠀⠈⠹⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠲
⠀⠀⠀⠀⠈⠛⢷⣤⣤⣾⠟⠉⢹⣿⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡀⠀⠀⠀⠀⢰⢠⣿⣿⣯⢀⡀⢸⣿⣷⣦⣤⣶⣿⠅⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠖⠟⠛⠛⠋⠀⠀⣀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⠀⠀⠀⢀⡗⠀⠹⣿⣿⣿⣿⣿⣿⣿⣏⣿⠟⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⣿⣟⠉⠙⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣔⠀⠀⠀⠈⢻⣆⠀⡀⡙⠙⠛⠛⠿⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣼⣿⣆⣀⣠⠃⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢇⣿⣿⣿⣿⣿⣿⣿⠿⢛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠻⢿⡏⣻⢧⡿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⢿⣿⣿⣛⣁⣤⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠿⢛⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠁⠀⠀⠀⠀⣺⣿⣿⠿⣷⣤⣤⡀⠀⣀⣀⣀⣀⡀⠀⠉⠒⠛⠛⠉⢀⣿⡿⢷⣶⣤⣄⡀⣀⣠⣤⣶⣾⣿⣿⣷⢶⣶⣦
⣄⢀⠀⠀⠀⠀⠀⠠⣤⣉⣳⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣞⡡⠀⠀⠀⣼⣿⣿⣿⡇⠈⢻⣿⣿⣿⡟⠉⢁⣀⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⠀⣙⣿⣿⠿⠛⢛⣛⣿⣿⣿⣿⣶⠉⢛⠁
⠉⠳⢧⣀⠀⠀⠀⢀⣈⡉⠛⠛⢛⠛⠉⠉⠙⢷⣦⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣴⣿⡇⠚⠡⠂⣀⠀⢻⣿⣿⣿⣿⡄⢀⣿⣿⣿⣤⣤⣀⣀⣀⣀⠁⣠⣤⣤⣤⣤⣤⣶⡿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⣿⠀⠚⠀
⠀⣶⡄⠙⠻⠷⢆⣼⣿⣿⣿⣿⡿⢃⣀⣤⣴⣾⣿⣿⠿⠟⠛⠛⠻⢿⣿⣿⠖⠿⠿⠋⠁⠀⠒⠀⢀⡴⣾⣿⣿⠏⠟⠋⢸⣿⣿⠛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⠀⠸⢿⣦⣀⡀⣸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢉⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⡆⠀⣾⣿⡶⠒⠒⠛⣩⣤⣿⣿⢏⡀⠀⡠⢊⢻⣿⡈⠿⣿⣿⣿⣿⡿⢛⡈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀
⠀⠀⠀⠙⠻⣿⣿⣈⣉⡛⠟⠛⠁⠀⠀⣀⣤⣾⣿⡋⠀⠀⠀⢀⣿⣿⣿⣿⢃⣀⠙⡋⢁⣀⣀⣠⣿⣿⣿⣿⣿⣦⣼⠃⠀⠀⠻⣷⡀⠹⢿⠛⠋⢀⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣋⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢻⡆⠀
⣷⣦⣄⡀⠀⠈⡽⣿⣿⣿⣿⠛⠓⠛⠛⠛⠋⠀⢻⣷⠀⢀⠴⠋⢩⣈⣿⣿⠀⠀⠻⠃⠀⢀⠀⠀⣼⣿⣿⣰⠿⣿⣿⣶⣤⣤⣶⣶⣷⣤⣄⣀⠀⠛⢋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠀⣺⣿⡄
⣀⡟⠻⣿⢿⢶⣄⡹⠿⠿⢆⣀⣀⣀⣀⣀⣱⣤⣾⡏⢠⠏⠀⠀⢸⣿⣿⣿⡉⠉⠻⢧⠈⠙⠛⢻⣿⣿⠿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢠⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⠻⣿⣧⡀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣤⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡏⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⣹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⣛⣹⣼⣷⣿⣶⣿⣿⣾⣿⣇⡙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⢂⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⣇⣿⣴⢸⡿⣇⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠛⠁⠀⠀⠀⠘⣿⣴⣶⡀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⣿⣿
⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⠃⠀⠀⠀⠀⠀⢀⡿⠋⠙⣿⣦⣀⠀⠀⢀⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⠿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⣼⠃⠘⠀⡈⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣀⣀⣤⣿⣿⣦⣠⣴⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣬⢹⡋⠀⠀⠉⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣶⠟⠉⢻⣿⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⢠⢠⣿⣿⣏⠀⠀⢸⣿⣶⣤⣤⣴⣿⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠾⠟⠛⠛⠋⠀⠀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣆⠀⠀⠀⠀⡇⠈⢻⣿⣿⣿⣷⣿⣿⣿⣟⣿⠏⠉⠀⠀⠀⠀⠀⠀⠚⠉⡻⣿⡟⠉⠛⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡜⠀⠀⠀⠈⢿⡄⠀⡉⠛⠛⠻⠿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣤⣽⣿⣄⢀⣠⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣋⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠁⠀⠀⠀⠀⠘⣿⣷⣿⣷⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⣛⠻⣿⡟⣿⢦⡟⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⢿⣿⣿⣛⣁⣴⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡈⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⢛⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠁⠀⠀⠀⠀⣾⣿⣿⢶⣶⣤⣄⡀⠀⣀⣀⣀⣀⡀⠈⠉⠒⠛⠛⠁⢸⣿⡿⣷⣶⣤⣄⣀⣀⣠⣤⣶⣾⣿⣿⣿⢿⣶
⣤⣀⡀⠀⠀⠀⠀⠀⢰⣬⣙⣲⣶⣾⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣞⡅⠀⠀⠀⣾⣿⣿⣿⡄⠙⢿⣿⣿⣿⠟⠉⣁⣈⣉⣉⠁⠀⠀⠀⠀⠊⠙⠃⠈⣛⣿⣿⠿⠛⢛⣻⣿⣭⣿⣷⣶⠉⢉
⠉⠙⠷⣅⡀⠀⠀⠀⢀⡉⠙⠛⠛⢻⠋⠉⠉⠻⣶⣄⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣰⣿⡋⠛⠡⢀⣀⠀⢿⣿⣿⣿⣿⡄⢈⣿⣿⣿⣤⣄⣀⣀⣀⣈⠁⣠⣤⣤⣤⣠⣴⣶⠿⠟⢋⣡⢰⣾⣿⣿⣿⣿⣿⣿⡟⠀⠟
⠀⠀⣶⡌⠛⠿⣶⣄⣴⣿⣿⣿⣿⡿⢆⣀⣤⣤⣾⣿⣿⠿⠿⠟⠛⠻⣿⣿⣿⠶⠿⠿⠋⠁⠀⠒⠀⢀⣴⣼⣿⣿⠏⠟⠃⢸⣿⣟⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⠀⠀⠹⣷⣄⣀⠀⣹⣿⣿⣿⣿⣿⣿⢿⠿⠟⠛⢋⣿⣷⠀⠀⠀⠀⢠⣶⣿⣿⡖⠒⣾⣷⡔⠶⠖⠚⣩⣤⣿⣿⢋⠀⠀⡠⢊⢻⣿⡘⢿⣿⣿⣿⣿⡿⢋⡈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠇⢹⣿⣿⣿⣿⣿⣿⠿⣇⠀
⣄⠀⠀⠈⠛⠿⣿⣧⣉⣉⠻⠿⠛⠉⠀⠀⢀⣤⣾⣿⠃⠀⠀⠀⢰⣿⣿⣿⣿⣃⣀⠻⠟⣁⣀⣀⣠⣿⣿⣿⣿⣿⣦⣼⠁⠀⠀⠻⣷⡀⠻⢿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢹⡆
⠻⣷⣤⣀⠀⠀⠉⣿⣿⣿⣿⣿⠷⠒⠛⠛⠛⠋⠈⢿⡇⠀⢀⡴⠋⣩⣉⣿⣿⠀⠉⠿⠃⠁⠀⠀⠀⣸⣿⡟⣸⢿⣿⣿⣶⣠⣤⣶⣾⣷⣤⣄⣀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡤⠚⠀⣀⣩⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿
⣀⣎⠻⣿⠿⣶⠆⡰⠻⠿⠟⢁⣀⠀⠀⢀⣀⣰⣤⣾⡇⢠⠏⠀⠀⣿⣿⣿⣿⠉⠙⠻⢧⠈⠙⠛⢻⣿⣿⠿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠟⠻⣿⣷⡀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣤⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⡟⣿⣿⠀⣿⡗⣻⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⢛⣙⣼⣧⣿⣶⣿⣿⣾⣿⣧⣙⠋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣾⠇⠀⣿⢸⣿⣇⣿⣴⢸⡿⣇⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⣿⡿⠋⠀⠀⠀⠀⢿⣷⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣿⡟⠀⠀⠀⠀⠀⠀⣸⠛⠙⢻⣶⣄⡀⠀⠀⣀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢰⡟⠀⠂⠀⢻⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⠀
⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣀⣠⣼⣿⣧⣄⣠⣦⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡭⣟⠁⠀⠈⠻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿
⠀⠀⠀⠀⠀⠀⠚⢧⣄⣠⣤⡾⠟⠹⣿⡆⠀⠀⠀⢘⣿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⡿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⡀⠀⠀⠀⠀⠀⡄⣽⣿⣿⠁⠀⠀⣿⣷⣤⣤⣤⣾⡏⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⡷⠿⠻⠛⠛⠁⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣷⡀⠀⠀⠀⢸⠁⠙⣿⣿⣿⣿⣶⣿⣿⣿⢻⡿⠉⠁⠀⠀⠀⠀⠀⠰⠛⠛⣿⣿⠋⠙⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣠⠃⠀⠀⠀⢻⣦⠀⢈⠙⠛⠿⠿⠿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣣⣬⣿⣦⡀⣀⡜⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣹⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡟⠀⠀⠀⠀⠀⢻⣿⣾⣿⣶⣶⣶⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⢛⣻⣿⣿⢻⡷⣼⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣟⣋⣠⣾⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⠇⠀⠀⠀⠀⢰⣿⣿⣷⣶⣦⣤⣀⠀⢀⣀⣀⣀⣀⠀⠉⠑⠚⠛⠋⠁⣿⣿⢿⣶⣦⣤⣀⢀⣀⣤⣴⣶⣿⣿⣿⡿⣷
⣮⣄⡀⠀⠀⠀⠀⠀⠀⣦⣉⡒⣶⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣋⠀⠀⠀⢰⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⠋⢉⣀⣉⣉⡉⠂⠀⠀⠀⠐⠉⠛⠀⢉⣻⣿⡿⠟⠛⣛⣻⣭⣽⣿⣷⡎⠉
⠈⠙⠳⢦⣁⠀⠀⠀⠀⡈⠙⠛⠛⠿⡿⠋⠉⠑⢶⣦⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⣾⡿⠙⠋⠄⣀⡀⠸⣿⣿⣿⣿⣧⠀⣸⣿⣿⣇⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣄⣤⣴⣾⠿⠛⣉⡄⣶⣿⣿⣿⣿⣿⣿⣿⠃⠰
⠀⠀⢰⣄⠙⠻⣶⣦⣠⣿⣿⣿⣿⣿⠷⠀⣀⣤⣤⣿⣿⣿⠿⠿⠟⠛⢿⣿⣿⡷⠾⠿⠟⠉⠀⠐⠂⠀⢠⣤⣿⣿⡿⠹⠛⠀⣿⣿⡟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⢀⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⡄⠀⠈⢿⣦⣀⠀⢀⣿⣿⣿⣿⣿⣿⣾⣿⠿⠟⠛⢻⣿⡆⠀⠀⠀⠀⣴⣾⣿⣷⠐⢰⣿⣦⡶⠶⠖⢋⣥⣼⣿⡟⡁⠀⢀⠔⡙⣿⣇⠻⣿⣿⣿⣿⣿⠟⣃⠁⠀⠀⠀⠀⠀⢁⣠⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⡿⢿⡄
⣧⡀⠀⠀⠙⠿⣿⣿⡍⠉⠛⠿⠿⠛⠁⠀⠀⣀⣴⣿⡿⠁⠀⠀⠀⣺⣿⣿⣿⣟⡀⠈⠿⠋⢀⣀⣀⣼⣿⣿⣿⣿⣯⣤⡏⠀⠀⠘⢿⣆⠘⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣛⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⣮⣿
⠻⢿⣦⣀⠀⠀⠈⢹⣿⣿⣿⣷⡶⠶⠖⠚⠛⠛⠋⠹⣿⡀⠀⣠⠞⠛⣍⣹⣿⡇⠈⠹⠿⠈⠀⠈⠁⢀⣿⣿⢇⣿⣿⣿⣷⣄⣠⣤⣶⣿⣦⣤⣀⡀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠃⢀⣈⣽⣿⣿⣿⣿⡇⠀⠀⢸⣿
⣀⣎⠻⣿⢿⣷⣦⢸⠻⠿⠿⠋⠀⠀⠀⠀⠀⢀⣦⣴⣿⠁⡸⠁⠀⢀⣿⣿⣿⡏⠀⢒⠿⡄⠉⠛⠛⣿⣿⡿⢿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⣿⣏⠀⠀⠀⠀⠀⠈⣀⣠⣴⣾⣿⣿⡿⠟⢿⣿⣇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣤⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⣿⣿⡇⣿⣿⢘⣳⡄⢠⣟⣷⣿⣿⣟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣏⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⢙⣸⣧⣿⣶⣿⣿⣾⣿⣧⣝⡋⠘⠛⠛⠃⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⣶⡄⠐⣶⢲⣶⡆⣶⣶⣰⣦⡖⣶⠀⣶⠂⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡾⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣾⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣾⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⡿⠋⠁⠀⠀⠀⢹⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿
⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣼⣿⠁⠀⠀⠀⠀⠀⢠⡟⠋⠻⣷⣤⣀⠀⠀⢀⣴⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⢀⣾⠁⠐⢀⠸⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠟⠛⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣶⣀⣀⣶⣿⣿⣄⣠⣶⣴⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣼⣿⡛⠀⠈⠙⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠘⠿⣄⣀⣠⣴⡿⠉⣿⣷⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⣿⣿⣿⡿⣿⣿⣿⣿⢿⠿⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠀⠀⠀⠀⠀⣀⣸⣿⣿⡏⠀⠀⢸⣿⣦⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢷⠾⠟⠟⠛⠃⠁⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⡆⠀⠀⠀⢀⡇⠈⢻⣿⣿⣿⣷⣿⣿⣿⡟⣿⠏⠉⠀⠀⠀⠀⠀⠀⠞⠛⢻⣿⡟⠙⠛⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⢀⡜⠀⠀⠀⠘⣷⡄⠀⠉⠛⠿⠿⠿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣤⣽⣷⣄⢀⣨⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣛⣯⣿⣿⣿⣿⣿⣿⠿⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⠃⠀⠀⠀⠀⠸⣿⣶⣿⣷⣶⣶⣶⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠜⠑⠛⣻⣿⣿⡟⣿⢼⡟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⢿⣿⣿⣛⣁⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡜⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⢟⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡿⠀⠀⠀⠀⠀⣾⣿⣿⣶⣦⣀⣄⠀⠀⢀⣀⣀⣀⠀⠈⠙⠒⠛⠛⠉⣸⣿⠿⣷⣶⣤⣄⣀⣀⣠⣤⣶⣾⣿⣿⡿⢿
⣶⣅⣀⠀⠀⠀⠀⠀⠀⢰⣌⠛⢿⣷⣶⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣞⡄⠀⠀⠀⣾⣿⣿⣿⡀⠙⢿⣿⣿⣿⠟⠉⣁⣈⣉⡉⠃⠀⠀⠀⠀⠊⠛⠀⠉⣻⣿⣿⠿⠛⢛⣛⣯⣽⣿⣷⣶⠉
⠈⠉⠛⢶⣄⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠟⠉⠙⠲⣶⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣰⣿⠉⢛⠡⢀⡀⠀⢿⣿⣿⣿⣟⡄⢈⣿⣿⣯⣀⣀⣀⣀⣀⣈⠁⣠⣤⣤⣤⣠⣴⣶⠿⠟⣋⣥⢰⣾⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⣦⡉⠻⣶⣦⣄⣼⣿⣿⣿⣶⡿⠆⢀⣠⣤⣽⣿⣶⣿⡿⠿⠟⠿⣿⣿⣷⠶⢿⠿⠋⠁⠀⠒⠀⠀⣤⣼⣿⣿⠟⠟⠃⢸⣿⣟⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⣤⠀⠀⢻⣷⣄⠀⠁⣻⣿⣿⣿⣿⣿⣷⣿⡿⠿⠛⢛⣿⣷⠀⠀⠀⠀⢠⣶⣿⣿⡄⠲⣾⣷⡴⠶⠶⠚⣩⣤⣿⣿⢋⠀⠀⡠⢊⢿⣷⡘⢿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⠈⣀⣤⣾⣿⠇⢹⣿⣿⣿⣿⣿⣿⢿⣧
⣾⣄⠀⠀⠈⠻⢿⣷⣟⠙⠛⠿⠿⠟⠋⠁⠀⢀⣠⣾⣿⠏⠀⠀⠀⢰⣿⣿⣿⣿⣁⠀⠻⠟⡁⣀⣀⣰⣿⣿⣿⣿⣿⣇⣼⠁⠀⠀⠻⣷⠀⠻⢿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿⠃⢸⢿
⠙⢿⣦⣄⡀⠀⠀⠙⣿⣿⣿⣿⣶⠶⠶⠖⠛⠛⠛⠙⢿⡇⠀⢀⡴⠟⣫⣟⣿⣿⠈⠉⠿⠇⠁⠈⠉⠀⣼⣿⡟⣸⢿⣿⣿⣴⣀⣤⣴⣾⣷⣤⣄⣀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣈⣩⣿⣿⣿⣿⣿⠀⠀⠀⣿
⣀⣆⡻⣿⠿⣷⣦⠰⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⢢⣤⣾⡇⢠⠏⠀⠀⣿⣿⣿⣿⠀⠐⡾⢧⠈⠛⠛⢻⣿⣿⠿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⠀⠀⠀⠀⠀⠀⢁⣀⣤⣶⣿⣿⣿⠟⠻⣿⣷⡀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣠⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⢙⣘⣧⣿⣶⣿⣿⣾⣿⣧⣽⣋⠘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⢐⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⣿⠟⠁⠀⠀⠀⠈⣿⣵⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⡏⠀⠀⠀⠀⠀⠀⣿⠓⠛⢿⣦⣄⠀⠀⠀⣠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⠀⠀⠀⠀⠀⣰⡇⠈⠀⡈⢿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣀⣠⣾⣿⣧⣀⣴⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⣠⣟⡛⠁⠀⠉⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠻⢆⣀⣀⣠⣾⠛⢸⣿⡄⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⡿⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠈⣿⣧⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡿⡶⠿⠻⠛⠛⠈⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⠀⠀⠀⠀⢸⠀⠛⣿⣿⣷⣷⣾⣿⣿⣿⢿⡿⠋⠁⠀⠀⠀⠀⠀⠰⠛⠛⣿⣿⠋⠛⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢦⡀⣨⠃⠀⠀⠀⢿⣆⠀⠉⠙⠻⠿⠿⣿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡀⣠⣠⣨⣿⣆⠀⣀⡏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢉⣻⣿⣿⣿⣿⣿⣿⡿⠟⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⡟⠀⠀⠀⠀⠀⣿⣷⣾⣿⣴⣶⣶⣶⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠚⢛⣻⣿⣿⢻⣧⣿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⣿⣿⣟⣋⣠⣾⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠃⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⠇⠀⠀⠀⠀⢸⣿⣿⣷⣶⣄⣄⡀⠀⢀⣀⣀⣀⡀⠀⠉⠓⠚⠛⠋⢀⣿⡿⢿⣶⣦⣤⡀⣀⣠⣤⣴⣾⣿⣿⣿⡿
⣶⣮⣀⠀⠀⠀⠀⠀⠀⠀⣌⡙⠻⣭⣶⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡶⣣⠀⠀⠀⢰⣿⣿⣿⣇⠈⠻⣿⣿⣿⡿⠋⢉⣀⣉⣉⠙⠀⠀⠀⠀⠘⠙⠃⠀⢙⣿⣿⡿⠟⠛⣛⣯⣭⣿⣿⣶⡆
⠀⠉⠛⠷⣵⡁⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠋⠉⠓⢶⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣾⡏⠝⡋⠄⣀⠀⢸⣿⣿⣿⣿⣃⠀⣹⣿⣿⣅⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣄⣤⣶⡾⠟⢛⣡⡄⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢠⣌⠙⢷⣶⣤⢀⣿⣷⣾⣶⣾⠧⠀⣀⣀⣤⣿⣷⣶⡿⠿⠿⠿⣿⣿⣾⡶⢾⡿⠟⠉⠀⠐⠂⠀⢠⣤⣿⣿⡿⠽⠛⠀⣿⣟⡛⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁⢀⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆
⢀⡄⠀⠘⣿⣦⡀⠈⢀⣿⣿⣿⣿⣿⣷⣾⣿⠿⠿⠛⣻⣿⡆⠀⠀⠀⠀⣴⣿⣿⣧⠒⢶⣷⣦⠶⠶⠖⢊⣥⣼⣿⣟⡁⠀⢀⠔⡻⣿⡆⠻⣿⣿⣿⣿⣿⠟⡁⠁⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠀⣿⣿⣿⣿⣿⣿⡿⢻
⣺⣧⠀⠀⠀⠙⠿⣿⣾⡉⠛⠻⠿⠿⠛⠉⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣟⡀⠘⠿⠋⠀⡀⣀⣾⣿⣿⣿⣿⣯⣠⡏⠀⠀⠸⣿⡆⠘⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠿⠛⠛⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀⠏
⠘⠻⣷⣄⣀⠀⠀⠈⢻⣿⣿⣿⣶⡶⠶⠶⠶⠛⠛⠋⠹⣷⠀⠀⣠⠶⢛⣅⣻⣿⡇⠉⠸⠿⠈⠀⠉⠁⢀⣿⣿⢃⡿⣿⣿⣧⣆⣠⣤⣶⣷⣤⣤⣀⡀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠃⢀⣈⣽⣿⣿⣿⣿⡇⠀⠀⢸
⣀⣆⡺⣿⠿⢿⣶⡴⠾⠿⠿⠿⠋⠀⠀⠀⠀⠀⠐⣤⣴⣿⠀⡼⠁⠀⢸⣿⣿⣿⡇⠀⢒⡿⡄⠙⠛⠛⣿⣿⡿⢿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣇⠀⠀⠀⠀⠀⠈⣀⣠⣴⣾⣿⣿⡿⠛⢿⣿⣆⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢺⣿⡇⣿⣯⢘⣳⡄⢠⣟⣷⣿⣿⣿⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠋⠛⠋⠀⠙⠛⠙⢘⣃⣿⣤⣽⣿⣾⣿⣧⣽⣏⡘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠟⠁⠀⠀⠀⠘⣿⣴⣶⡆⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣿⡇⠀⠀⠀⠀⠀⠀⡿⠃⠙⢿⣦⣀⠀⠀⢀⣠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⣼⠇⠈⠀⡈⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣀⣀⣠⣿⣿⣄⣀⣴⣤⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⣸⢟⡟⠁⠉⠙⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⢆⣀⣀⣠⣾⠟⢺⣿⠀⠀⠀⠀⢹⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⢀⢈⣽⣿⣿⠁⠀⠸⣿⣦⣄⣀⣠⣾⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡽⡶⠿⠿⠛⠛⠈⠀⣀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⠀⠀⠀⠀⣸⠈⠻⣿⣿⣶⣶⣴⣿⣿⡿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠴⠛⠻⣿⡿⠛⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⣀⣠⣤⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢅⠀⢉⠂⠀⠀⠀⢯⡆⠀⠙⠻⠿⠿⡿⣿⣿⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣹⣿⣄⠀⢀⡏⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢏⣿⣿⣿⣿⣿⣿⣿⡿⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠾⣿⡟⠀⠀⠀⠀⠈⣿⣶⣮⣶⣴⣶⣶⣶⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠙⢻⣿⣿⡿⢻⣧⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⣿⣿⣟⣉⣠⣾⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⢨⠃⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⢋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣾⠇⠀⠀⠀⠀⢰⣿⣿⢶⣶⣄⣄⡀⠀⠀⣀⣀⣀⡀⠀⠉⠑⠛⠛⠋⢀⣿⡿⢿⣶⣦⣤⡀⣀⣠⣤⣶⣾⣿⣿⣿
⣶⣦⣎⡀⠀⠀⠀⠀⠀⠀⠐⣀⡚⠭⣭⣵⣾⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⢃⠀⠀⠀⣰⣿⣿⣿⣇⠉⢿⣿⣿⣿⡟⠋⢉⣀⣉⣉⠙⠀⠀⠀⠀⠘⠙⠃⠈⢙⣿⣿⡿⠟⠛⣛⣿⣿⣿⣿⣶
⠈⠉⠙⠻⢧⣔⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠓⠓⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡏⠽⣋⠄⣀⠀⢸⣿⣿⣿⣿⣁⠀⣹⣿⣿⣄⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣀⣤⣶⡿⠟⢋⣡⠄⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⡍⠻⢶⣤⣄⢀⣷⣶⣶⣶⣶⡧⠀⢀⣀⣬⣿⣷⣶⣶⠿⠿⠿⣿⣿⣶⡶⣾⣿⠟⠉⠀⠤⠂⠀⢠⣤⣿⣿⡟⡿⠛⠠⣿⣿⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁⢀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⠘⣿⣄⠀⠁⢑⣿⣿⣿⣿⣿⣷⣶⣿⡿⠿⠟⣻⣿⡅⠀⠀⠀⠀⣼⣿⣿⣧⠀⣴⣷⣦⠴⠴⠖⢚⣁⣼⣿⡏⠁⠀⢀⠔⡻⣿⡄⢿⣿⣿⣿⣿⣿⠟⡁⠁⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠀⣿⣿⣿⣿⣿⣿⡿
⠀⢜⣧⠀⠀⠈⠻⢿⣶⣾⡟⠛⠻⣿⠿⠟⠉⠀⠀⢀⣠⣿⡿⠁⠀⠀⠀⣶⣿⣿⣿⣏⠀⠸⠿⠋⠀⠀⣀⣿⣿⣿⣿⣿⣾⣠⡏⠀⠀⠸⣿⡄⠘⢿⡟⠛⠁⣼⣿⣿⣿⡿⡿⠿⠿⠛⠙⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟⠀
⠀⠘⠾⣷⣄⡀⠀⠀⠈⢻⣿⣿⣷⣶⡶⠶⠶⠶⠞⠿⠋⢻⣷⠀⠀⣠⠶⢛⡩⢿⣿⡏⠉⠻⠿⠈⠉⠉⠉⢠⣿⣿⢃⣿⣿⣿⣧⣄⣠⣤⣶⣿⣤⣤⣀⠀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠁⢀⣨⣽⣿⣿⣿⣿⡇⠀⠀
⣀⠆⠲⣾⠿⢿⣷⣶⡶⠾⠿⢻⡿⠏⠁⠀⠀⠀⠀⠀⣄⣰⣿⠀⡰⠁⠀⢸⣿⣿⣿⡇⠂⢲⡿⡀⠙⠛⠿⣿⣿⡿⢿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⣿⣇⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⡿⠛⢿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢾⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⣃⣻⣤⣽⣿⣾⣿⣷⣽⣯⣘⠛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣰⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣼⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡿⣿⡿⠋⠀⠀⠀⠀⢿⣷⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠀⠀⠀⠀⠀⠀⢸⠟⠙⢻⣷⣄⡀⠀⠀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢠⡿⠀⠃⢀⢹⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣀⣼⣿⣷⣄⣠⣦⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣹⡿⠟⠈⠉⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⢀⣀⣴⡾⠃⣿⡇⠀⠀⠀⠈⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣇⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⡏⠀⠀⢿⣿⣄⣀⣀⣴⣿⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢯⢷⠾⠿⠟⠛⠃⠁⢀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⡄⠀⠀⠀⠀⡇⠙⢿⣿⣷⣶⣤⣾⣿⣿⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠞⠛⢿⣿⠟⠛⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⢀⣀⣤⣴⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠩⡀⠈⡱⠀⠀⠀⠸⣥⠀⠈⠛⠿⠿⣿⣿⣿⣟⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣈⣿⣧⡀⠀⣸⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡹⣙⣿⣿⣿⣿⣿⣿⣿⠿⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡶⣿⣿⠇⠀⠀⠀⠀⢹⣶⣤⣴⣦⣤⣦⣴⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⣿⣿⣿⠟⣿⣼⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣿⣋⣁⣴⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠹⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⠟⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣷⡿⠀⠀⠀⠀⠀⣾⣿⢷⣶⣦⣀⣀⠀⠀⢀⣀⣀⣀⠀⠈⠉⠚⠛⠛⠉⣸⣿⠿⣷⣶⣤⣄⣀⣀⣤⣴⣶⣿⣿⣿
⣶⣤⣤⡃⠀⠀⠀⠀⠀⠀⠀⢀⡘⠫⢭⣭⣶⣾⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣸⣧⠞⡀⠀⠀⠀⣾⣿⣿⣿⡈⠙⣿⣿⣿⣿⠟⠉⣁⣈⣉⡉⠃⠀⠀⠀⠀⠋⠛⠀⠈⣻⣿⣿⠿⠛⢛⣻⣭⣿⣿⣷
⠉⠉⠉⠛⠿⣦⡔⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⠟⠒⠒⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠭⢟⡡⢀⡀⠀⣿⣿⣿⣿⣏⡀⢈⣿⣿⣯⣀⣀⣀⣀⣀⣈⠁⣠⣤⣤⣤⣠⣴⣾⠿⠛⣉⣤⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣌⠙⢷⣦⣤⡀⣰⣶⣶⣶⣶⣾⡄⠀⣀⣀⣽⣿⣶⣶⡶⠿⠿⢿⣿⣶⣶⢴⣿⡿⠛⠁⠠⠔⠀⠀⣠⣼⣿⣿⣿⠿⠃⢸⣿⣟⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⢻⣧⡀⠈⠉⢻⣿⣿⣿⣿⣿⣷⣾⣿⡿⠿⠛⣿⣿⠀⠀⠀⠀⢠⣯⣿⣿⡄⢠⣶⣶⡤⠤⠴⠒⣋⣡⣿⣿⢋⠀⠀⡠⢚⢿⣷⠘⢿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⢸⣿⣿⣿⣿⣿⣿
⠀⠀⣾⡄⠀⠀⠙⠿⣷⣶⣿⠛⠛⢿⣿⠿⠛⠉⠀⠀⢀⣼⣿⠏⠀⠀⠀⢠⣾⣿⣿⣿⡃⠀⠻⠟⠁⠀⠀⣰⣿⣿⣿⣿⣿⣇⣼⠁⠀⠀⢿⣷⠀⠻⣿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠟⠛⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿⠃
⠀⠀⠙⢿⣦⡀⠀⠀⠀⠛⣿⣿⣷⣶⣶⣶⡶⠶⠶⠾⠟⠙⢿⣆⠀⠀⣤⠞⢻⢽⣿⣿⠉⠙⣾⠇⠉⠉⠉⠁⣸⣿⡿⣸⣿⣿⣿⣤⣀⣤⣴⣾⣧⣤⣄⣀⠐⠛⠋⠉⠁⠀⠀⠀⠀⢀⡠⠚⠀⣀⣠⣿⣿⣿⣿⣿⠀⠀
⣷⠆⠲⣶⠿⢿⣿⣶⣶⠶⠟⠻⣿⡿⠋⠀⠀⠀⠀⠀⠠⣀⣼⡟⢀⡞⠀⠀⣿⣿⣿⣿⠒⠒⢶⢇⠀⠛⠿⢿⣿⣿⠿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡁⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟⠻⣿⣿⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣿⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⢃⣛⣤⣽⣿⣾⣿⣷⣿⣯⣜⡛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⣖⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣴⣶⡀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢽⣿⠃⠀⠀⠀⠀⠀⠀⡟⠋⠛⣷⣦⣀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡆⠀⠀⠀⠀⠀⣾⠃⠐⠀⡘⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣀⣢⣿⣿⣄⣀⣴⣤⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣸⣻⠿⠉⠉⠛⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢀⣠⣶⠟⢾⣷⠀⠀⠀⠀⢻⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡿⠁⠀⢸⣿⣆⣀⣀⣠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢽⡶⠿⠿⠛⠋⠈⠀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣆⠀⠀⠀⠀⣸⠘⢿⣿⣿⣶⣦⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠴⠛⠻⣿⡿⠛⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⣍⠈⢙⠄⠀⠀⠀⣿⡆⠀⠛⠻⢿⣿⣿⣿⣿⣳⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣹⣷⡄⠀⢀⠏⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⢏⣿⣿⣿⣿⣿⣿⣿⡿⢛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣾⣷⡿⠀⠀⠀⠀⠈⣷⣦⣦⣶⣤⣤⣤⣴⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠙⢿⣿⣿⡟⣿⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣟⣁⣤⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⣾⠃⠀⠀⠀⠀⢰⣿⣿⣶⣶⣄⣀⡀⠀⠀⣀⣀⣀⡀⠀⠉⠓⠛⠛⠋⢁⣿⡿⢿⣶⣦⣤⡀⣀⣠⣤⣶⣾⣿⣿
⣶⣤⣤⣜⠀⠀⠀⠀⠀⠀⠀⠀⣐⠻⢭⣭⣥⣶⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⢃⠀⠀⠀⣰⣿⣿⣿⣇⠙⢿⣿⣿⣾⡟⠋⢉⣉⣉⣉⠙⠀⠀⠀⠀⠘⠙⠃⠀⣙⣿⣿⡿⠟⠛⣻⣯⣽⣿⣿
⠉⠉⠉⠛⠻⢷⣴⠂⠀⠀⠀⠀⠙⠻⠾⢿⣿⣿⠒⠒⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡏⠽⣋⠄⠀⠀⢹⣿⣿⣿⣿⣃⠀⣻⣿⣿⣁⣀⣀⣀⣀⣀⠉⢀⣤⣤⣤⣀⣤⣶⡿⠟⢋⣡⠄⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡙⠳⣶⣤⣄⢀⣶⣶⣶⣶⣶⡇⠀⢀⣀⣨⣿⣷⣶⣶⡶⠿⠿⣿⣷⣶⡦⣾⣿⠟⠋⠀⠤⠀⠉⢠⣬⣿⣿⡿⡿⠟⠠⣿⣿⠟⣩⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⠿⠋⠁⢀⠄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠸⣿⣄⠀⠉⠉⣿⣿⣿⣿⣿⣷⣶⣾⣿⠿⠿⢻⣿⡅⠀⠀⠀⠀⣼⣽⣿⡥⠄⣴⣶⣄⠤⠤⠖⢚⣁⣼⣿⡏⠁⠀⢀⠔⡻⣿⡄⢿⣿⣿⣿⣿⣿⠟⡁⠁⠀⠀⠀⠀⠀⣀⣠⣶⣿⡿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣇⠀⠀⠉⠻⣿⣶⣾⡟⠻⢿⣿⡿⠿⠋⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⣴⣿⣿⣿⡇⠀⠸⠿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣠⡏⠀⠀⠺⣿⡄⠘⢿⡟⠛⠁⣼⣿⣿⣿⡿⡿⠿⠿⠛⠙⣋⣉⣀⣀⣿⣿⣿⣿⣿⠟
⠀⠀⠘⢿⣷⣀⠀⠀⠀⠙⢻⣷⣶⣶⣦⣴⣦⡴⠶⠶⠿⠛⢻⣷⠀⠀⢠⡴⢛⡣⣿⣿⡏⠙⢳⡷⠈⠉⠉⠉⢡⣿⣿⢃⣿⣿⣿⣧⣆⣠⣤⣶⣷⣤⣄⣀⠀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠜⠃⢀⣀⣼⣿⣿⣿⣿⡇⠀
⢰⡇⠲⣶⠿⢿⢿⣶⣶⡶⠾⠛⢿⣿⠟⠁⠀⠀⠀⠀⠀⣄⣸⣿⠀⣰⠃⠀⢸⣿⣿⣿⡗⠂⢲⣶⡀⠚⠿⠿⣿⣿⡿⢿⣅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣇⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⡿⠛⢿⣿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣿⢘⣳⡄⢠⣟⣷⣿⣿⡟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⣛⣠⣽⣿⣾⣿⣷⣿⣯⣼⣛⠛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣽⠇⠀⣿⢸⣿⣇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⢻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⡿⠋⠀⠀⠀⠈⢿⣧⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡏⠀⠀⠀⠀⠀⠀⣸⠛⠙⢻⣶⣄⡀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⢰⡟⠀⠂⠀⢻⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣀⣐⣾⣿⣧⣀⣠⣦⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡻⠿⠏⠉⠙⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⢀⣤⡾⠣⣿⡆⠀⠀⠀⠘⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⠏⠀⠀⣿⣧⣀⣀⣀⣴⡟⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠯⣷⠾⠻⠟⠛⠁⠁⢀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡇⠻⣿⣿⣷⣴⣤⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠞⠛⢿⣿⠟⠛⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⢀⣠⣤⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢉⢩⡉⠉⠣⠀⠀⠀⢸⣥⠀⠘⠛⠿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⣿⣦⠀⠀⡸⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡹⣹⣿⣿⣿⣿⣿⣿⣿⠟⣃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣷⣦⣿⣶⠇⠀⠀⠀⠀⢻⣦⣤⣰⣦⣤⣤⣤⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠿⢿⣿⣿⢻⣷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⢿⣿⣿⣋⣡⣴⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⣷⡿⠀⠀⠀⠀⠠⣾⣿⣷⣶⣤⣀⣀⠀⠀⢀⣀⣀⣀⠀⠈⠉⠚⠛⠛⠉⣸⣿⠿⣷⣶⣤⣄⢀⣀⣤⣴⣾⣿⣿
⣤⣤⣤⣤⡂⠀⠀⠀⠀⠀⠀⠀⢄⡈⠻⣟⣭⣵⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠾⡀⠀⠀⢀⣾⣿⣿⣿⡈⠻⣿⣿⣷⣿⠛⠉⣁⣉⣉⡉⠃⠀⠀⠀⠀⠋⠛⠀⢁⣻⣿⣿⠟⠛⢛⣿⣽⣿⣿
⠉⠉⠉⠛⠻⢿⣆⡄⠀⠀⠀⠀⠘⠛⠶⢾⣿⣿⡷⠒⠲⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠩⠟⡁⠀⠀⠀⣿⣿⣿⣿⣟⡀⢘⣿⣿⣯⣀⣀⣀⣀⣀⣈⠁⣠⣤⣤⣄⣠⣴⣾⠿⠛⣉⣤⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣈⠻⢶⣤⣄⡀⢰⣶⣶⣶⣤⣶⡀⠀⢀⣀⣻⣷⣴⣶⣶⡾⠿⢿⣷⣶⣶⢤⣿⡿⠛⠁⠠⠄⠈⠉⣠⣽⣿⣿⢿⠿⠃⢸⣿⡻⢋⣽⣿⣿⣿⣿⣿⣾⣿⣿⡿⠿⠟⠉⠀⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⢿⣧⡀⠈⠛⢻⣿⣿⣿⣿⣿⣧⣶⣾⣿⠿⠿⣿⣭⠁⠀⠀⠀⢠⣭⣽⣿⡤⢤⣶⣦⡠⠤⠴⠖⣋⣡⣿⣿⠉⠀⠀⡠⢚⢿⣧⠸⣿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⠇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⣾⡀⠀⠈⠙⢿⣶⣦⣾⠻⠿⣿⣿⡿⠟⠉⠁⠀⢀⣼⣿⠏⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⠿⠟⠁⠀⠀⣰⣿⣿⣿⣿⣿⣅⣼⠁⠀⠀⢿⣧⠀⠻⣿⠛⠋⢠⣾⣿⣿⣿⢿⠿⠿⠟⠋⢛⣉⣁⣀⣸⣿⣿⣿⣿⡿
⠀⠀⠀⠫⣿⣄⡀⠀⠀⠈⠛⣻⣶⣶⣶⣤⣤⣤⡤⠶⠾⠟⠛⣿⡆⠀⠀⣠⠾⢛⢹⣿⣿⠉⠻⣶⠆⠉⠉⠉⠉⣼⣿⡟⣸⣿⣿⣿⣤⣀⣠⣴⣾⣧⣤⣄⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣠⣿⣿⣿⣿⣿⠀
⠐⢷⠲⣶⠛⢿⠿⣷⣶⣶⠶⠛⠻⣿⡿⠋⠀⠀⠀⠀⠀⢠⣀⣼⡏⢀⡞⠁⠀⣿⣷⣿⣿⠒⠒⣶⣆⠐⠻⠿⢷⣿⣿⠿⣯⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡯⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡷⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⢛⣀⣽⣯⣼⣿⣷⣿⣿⣼⣿⣛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠖⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⠟⠉⠀⠀⠀⠈⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⡏⠀⠀⠀⠀⠀⠀⣿⠛⠙⢿⣶⣄⡀⠀⠀⣠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⣰⡇⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⣀⣀⣰⣾⣿⣧⣀⣰⣤⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡿⣿⠏⠉⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⠀⢀⣤⡾⢳⣿⡄⠀⠀⠀⠹⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⠏⠀⠀⣿⣧⣀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡿⣷⠿⠻⠟⠛⠁⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣾⣿⣿⣿⣦⡀⠀⠀⠀⢀⡇⠻⣿⣿⣦⣴⣤⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⢠⠾⠻⣿⣿⠟⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠉⠉⢛⠉⠙⠣⠀⠀⠀⢸⣥⠀⠐⠿⡿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣘⣿⣆⠀⠀⡹⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣹⣿⣿⣿⣿⣿⣿⡿⠟⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣴⣦⣬⣷⣶⠇⠀⠀⠀⠀⢻⣤⣤⣤⣄⣤⣤⣬⣵⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠿⢿⣿⣷⢻⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣋⣠⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠀⠉⠁⠈⡻⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢸⣷⡟⠀⠀⠀⠀⠠⣾⣿⣷⣶⣤⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠚⠛⠋⠁⣸⣿⠻⣷⣶⣤⣄⣀⣠⣤⣶⣾⣿
⣤⣤⣤⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⢄⠩⠟⣛⣫⣥⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠖⡀⠀⠀⢀⣾⣿⣿⣿⡈⠻⣿⣿⣷⣿⠛⠉⣉⣉⣉⡉⠃⠀⠀⠀⠀⠋⠛⠈⢁⣩⣿⡿⠟⠛⣛⣯⣽⣿
⡛⠋⠛⠛⠛⠿⢶⣄⠄⠀⠀⠀⠀⠘⠻⢶⣿⣿⣿⡿⠓⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠟⡡⠀⠀⠘⣿⣿⣿⣿⣏⡀⢘⣿⣿⣇⣀⣀⣀⣀⣀⣈⠀⣠⣤⣤⣄⣤⣴⣾⠿⠛⣉⡤⢰⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⣉⠳⣦⣤⣀⡀⢰⣶⣤⣤⣤⣶⡀⠀⠀⣀⣻⣷⣤⣶⣶⡶⠿⣿⣶⣶⣦⣴⣿⡿⠛⠀⠠⠄⠈⠉⣠⣽⣿⣿⢿⠿⠃⣾⣿⡿⢋⣽⣿⣿⣿⣿⣿⣾⣿⣿⡿⠿⠛⠉⢀⡠⠀⠀⣰⣿⣿⣿⣿⣿⣿
⠟⠀⠀⠀⢀⠀⠀⢿⣇⠀⠙⠛⢳⣿⣿⣿⣿⣿⣥⣶⣾⣿⡿⠿⣿⣯⠉⠀⠀⠀⢨⣭⣿⣯⠤⢤⣶⣦⡠⠤⠴⠖⣋⣠⣿⣿⠉⠀⠀⡠⢚⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⠇⢸⣿⣿⣿⣿
⠀⠀⠀⠀⣾⡀⠀⠈⠛⢷⣶⣤⣾⠿⠿⣿⣿⡿⠟⠉⠁⠀⢀⣼⣿⠏⠀⠀⠀⢠⣾⣿⣿⣿⠀⠈⠿⠟⠁⠀⠀⣸⣿⣿⣿⣿⣷⣅⣼⠁⠀⠐⢿⣧⠀⠻⣿⠛⠋⢠⣿⣿⣿⣿⠿⠿⠿⠟⠋⢛⢩⣤⣀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠉⠻⢿⣶⣶⣦⣥⣤⣤⣤⡴⠶⠿⠛⣿⡆⠀⠀⣠⠾⢛⢿⣿⣿⠉⠛⣶⠆⠉⠉⠉⠉⣹⣿⡟⣸⣿⣿⣿⣴⣀⣠⣤⣾⣦⣤⣀⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣠⣿⣿⣿⣿⣿
⠐⠖⠾⣶⠋⢿⠿⢿⣶⣶⣦⠀⠛⠿⣿⣿⠛⠈⠀⠀⠀⠀⢄⣀⣼⡇⢀⡞⠁⠀⢾⣷⣿⣿⠒⠲⢶⣆⠐⠺⠾⢷⣿⣿⣿⣯⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢸⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⠟⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣤⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⣿⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡷⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⢛⣀⣽⣯⣼⣿⣷⣿⣿⣾⣿⣛⠃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠖⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⢰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⠟⠉⠀⠀⠀⠈⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⡏⠀⠀⠀⠀⠀⠀⣾⠛⠙⢿⣶⣄⡀⠀⠀⣠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⣰⡏⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⣀⣀⣰⣾⣿⣧⣀⣰⣤⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡿⢿⠏⠉⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⠀⢀⣤⡾⢿⣿⡄⠀⠀⠀⠹⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⠏⠀⠀⣿⣧⣀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡿⡶⠿⠻⠟⠛⠁⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣾⣿⣿⣿⣦⠀⠀⠀⠀⢀⡇⠿⣿⣿⣦⣴⣤⣿⣿⣿⢿⣿⠟⠃⠀⠀⠀⠀⠀⢠⠾⠻⣿⣿⠟⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⢀⣠⣤⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠉⠙⢛⠉⠙⠣⠀⠀⠀⢸⣇⠀⠘⠿⡿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣘⣿⣆⠀⠀⡙⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣹⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣴⣦⣤⣷⣶⠇⠀⠀⠀⠀⢻⣤⣠⣤⣄⣤⣤⣬⣵⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠿⢿⣿⣷⢻⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣋⣠⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠉⠁⠈⡻⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢸⣷⡟⠀⠀⠀⠀⠀⣾⣿⣷⣶⣤⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠚⠛⠛⠁⣸⣿⠿⣷⣶⣤⣄⣀⣠⣤⣶⣾⣿
⣤⣤⣤⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⢄⠩⠟⣛⣫⣥⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠖⡀⠀⠀⢀⣾⣿⣿⣿⠈⠻⣿⣿⣷⣿⠛⠉⣉⣉⣉⡉⠃⠀⠀⠀⠀⠋⠛⠈⢉⣩⣿⡿⠟⠛⣛⣭⣽⣿
⡛⠛⠉⠛⠛⠿⢶⣄⠄⠀⠀⠀⠀⠘⠻⢶⣾⣿⣿⡿⠒⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠻⠟⡁⠀⠀⠘⣿⣿⣿⣿⣏⡀⢘⣿⣿⣇⣀⣀⣀⣀⣀⣈⠀⣠⣤⣤⣄⣤⣴⣾⠿⠛⣩⡤⢰⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⣉⠳⣦⣤⣀⡀⢰⣶⣤⣤⣤⣶⡀⠀⠀⣀⣻⣷⣤⣶⣶⡾⠿⣿⣶⣶⣦⣼⣿⡿⠛⠀⠠⠄⠈⠉⣠⣽⣿⣿⢿⠿⠃⣾⣿⡿⢋⣽⣿⣿⣿⣿⣿⣾⣿⣿⡿⠿⠛⠉⢀⡠⠀⠀⣰⣿⣿⣿⣿⣿⣿
⠟⠀⠀⠀⢀⠀⠀⢿⣇⠀⠙⠛⢳⣿⣿⣿⣿⣿⣧⣶⣾⣿⡿⠿⣿⣯⠉⠀⠀⠀⢨⣭⣿⣯⠤⢤⣶⣦⡤⠤⠤⠖⣋⣡⣿⣿⠉⠀⠀⡠⢚⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⠇⢸⣿⣿⣿⣿
⠀⠀⠀⠀⣼⡀⠀⠈⠛⢷⣶⣤⣾⠿⠿⣿⣿⡿⠟⠋⠁⠀⢀⣼⣿⠏⠀⠀⠀⢠⣾⣿⣿⣿⠀⠈⢿⠟⠁⠀⠀⣸⣿⣿⣿⣿⣧⣆⣼⠁⠀⠐⢿⣧⠀⠻⣿⠛⠋⢠⣿⣿⣿⣿⠿⠿⠿⠟⠋⢛⢩⣤⣀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠉⠻⢿⣶⣶⣦⣥⣤⣤⣤⠴⠶⠿⠛⣿⡆⠀⠀⣠⠾⢛⠿⣿⣿⠉⠓⣶⠆⠉⠉⠉⠉⣹⣿⡟⣸⣿⣿⣿⣴⣀⣠⣴⣾⣦⣤⣀⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡠⠚⠀⣀⣠⣿⣿⣿⣿⣿
⠐⠖⠾⣶⠉⢿⠿⢿⣶⣶⣦⠀⠛⠿⣿⣿⠛⠉⠀⠀⠀⠀⢄⣀⣼⡗⢀⡞⠁⠀⣼⣷⣿⣿⠐⠲⢶⣆⠐⠺⠾⢷⣿⣿⣿⣯⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢸⣿⡁⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⠟⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢼⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⣟⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢸⡗⢸⡗⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠋⠛⠋⠀⠙⠛⠙⠘⠃⠛⢀⣹⣯⣼⣿⣷⣿⣿⣾⣿⣿⣃⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣼⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣴⣶⡆⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣿⡇⠀⠀⠀⠀⠀⠀⡿⠉⠙⢿⣦⣄⡀⠀⢀⣤⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⣼⡇⠈⠄⡈⢿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣀⣰⣾⣿⣦⣀⣴⣤⣾⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠿⢿⠏⠛⠻⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⣠⡾⢿⣷⡀⠀⠀⠀⢹⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠟⠀⠀⣿⣇⡀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡽⡶⠿⠻⠛⠛⠁⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣶⣾⣿⣶⣦⠀⠀⠀⠀⠀⡇⢿⣿⣿⣦⣤⣠⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⢠⠿⠿⣿⣿⠛⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⢛⠛⠛⠇⠀⠀⠀⢸⣁⠀⠹⠿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣙⣿⣆⠀⠀⡙⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢩⣻⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⣦⣬⣷⣴⡇⠀⠀⠀⠀⢿⣤⣴⣤⣄⣤⣭⣩⣵⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠍⠿⢿⣿⣷⢿⣧⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣋⣤⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠁⠉⠉⠉⠻⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢸⣷⡏⠀⠀⠀⠀⠠⣾⣿⢷⣶⣤⣀⡀⠀⠀⢀⣀⣀⣀⠀⠈⠙⠚⠙⠋⠁⣸⣿⠻⣷⣶⣶⣤⣀⣤⣤⣶⣿
⢀⣠⣤⣄⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠽⢟⣛⣛⣥⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠖⡀⠀⠀⢠⣾⣿⣿⣿⠈⠻⣿⣿⣷⣿⠛⠉⣁⣈⣉⡉⠃⠀⠀⠀⠀⠉⠛⠀⢉⣭⣿⡿⠟⠛⣻⣭⣽
⣟⡛⠛⠛⠛⠻⠷⣶⡀⡄⠀⠀⠀⠀⠘⠷⣶⣾⣿⣿⡿⠷⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠟⡡⠀⠀⠘⣿⣿⣿⣿⣏⡀⢘⣿⣿⣇⣀⣀⣀⣀⣀⣈⠁⣠⣤⣤⣄⣤⣴⣾⠟⠋⣩⡤⣸⣿⣿⣿⣿
⣿⣿⡀⠀⠀⠀⠀⠀⠙⠳⣦⣄⣀⠀⢰⣦⣤⣤⣤⣾⡀⠀⠀⢈⣻⣷⣤⣴⣶⣶⡾⣷⣶⣶⣦⣼⣿⡿⠛⠀⠠⠄⠈⠉⣠⣽⣿⣿⢻⠿⠇⣼⣿⡿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢀⡠⠀⢀⣰⣿⣿⣿⣿⣿
⣿⠿⠁⠀⠀⠀⠀⠀⢿⣆⠈⠙⠛⢳⣿⣿⣿⣿⣿⣭⣴⣾⣿⡿⠿⣿⣯⠉⠀⠀⠀⢨⣭⣿⣯⠤⢤⣶⣤⡤⣤⠤⠖⣚⣡⣿⣿⠉⠀⠀⡠⢚⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⠈⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⠇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣼⡀⠀⠈⠻⣷⣦⣤⣼⠿⠿⣿⣿⣿⠿⠋⠉⠀⢀⣼⣿⡏⠀⠀⠀⢠⣾⣿⣿⣿⠀⠈⢿⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣆⣼⠁⠀⠐⢿⣧⠀⠻⢿⠛⠋⢠⣾⣿⣿⣿⠿⠿⠿⠛⠋⢉⢩⣤⣄⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠉⠻⢿⣶⣶⣬⣭⣤⣤⣤⡴⠶⠿⠻⣿⡆⠀⠀⣠⡾⢏⢻⣿⣿⠉⠰⣶⠆⠉⠉⠉⠉⣽⣿⡿⢹⣿⣿⣿⣤⣀⣠⣤⣾⣧⣤⣄⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡰⠛⠀⣄⣤⣿⣿⣿⣿
⠰⠖⠲⣾⠟⢶⠞⠻⢿⣶⣦⣀⠀⠛⠿⣿⣿⠟⠉⠀⠀⠀⠀⢀⣀⣸⡟⠀⡞⠁⠀⣻⣷⣿⣿⠒⠰⢶⣆⠐⠲⠶⢶⣿⣿⣿⣯⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢠⣿⡅⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⣄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⣙⣯⣼⣿⣷⣿⣿⣾⣿⣿⣇⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⣷⣶⣦⠀⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣾⡿⠀⠀⠀⠀⠀⠀⢸⠏⠉⠻⣷⣤⣀⠀⠀⣠⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢀⣿⠀⠁⢀⠹⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣀⣀⣶⣿⣷⣄⣠⣦⣴⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⠿⡿⠛⠛⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⢀⣤⠿⣴⣆⠀⠀⠀⠙⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣾⡿⠃⠀⢸⣿⡀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⢿⠾⠟⠟⠛⠃⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣶⣶⣶⣦⡄⠀⠀⠀⠀⣰⠸⣿⣿⣧⣤⣄⣸⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⡴⠿⢿⣿⡿⠛⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠛⠻⠛⠛⠻⡀⠀⠀⠀⣿⡀⠈⠿⢿⣿⣿⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢻⣧⡀⠀⢈⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢏⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣴⣄⣹⣦⣾⠀⠀⠀⠀⠙⣧⣀⣄⣤⣈⣈⣉⣩⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠻⢿⣿⣿⡾⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣛⣡⡴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠋⠉⠉⠉⠻⡇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠃⣿⣾⠃⠀⠀⠀⠀⢴⣿⣿⣶⣦⣄⣀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠓⠉⠙⠃⢀⣿⡟⠿⣶⣶⣦⣄⣠⣤⣶⣾
⠀⢀⣀⣀⣀⣀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⣟⣛⣫⣵⡖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⢂⠀⠀⠀⣰⣿⣿⣿⡆⠙⢿⣿⣿⣾⡟⠋⢉⣀⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⠉⣉⣽⣿⠿⠛⣛⣭⣭
⣐⡛⠛⠛⠛⠻⠿⣶⣦⢀⡀⠀⠀⠀⠀⠳⢶⣶⣿⣿⣿⠯⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⢋⠀⠀⠀⢻⣿⣿⣿⣿⣅⠀⣻⣿⣿⣀⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣤⣤⣶⡿⠟⠋⣥⠄⣿⣿⣿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⣠⣤⣤⣬⣥⣇⠀⠀⠀⢙⣿⣦⣤⣴⣶⣶⣾⣶⣶⣴⣤⣾⣿⠟⠓⠀⠤⠀⠉⢁⣬⣿⣿⡿⡿⠿⠀⣿⣿⠟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⠄⠀⢀⣾⣿⣿⣿⣿
⣿⣿⠟⠀⠀⠀⠀⠀⠸⣷⡀⠉⠹⠻⣾⣿⣿⣿⣿⣿⣭⣶⣾⣿⡿⢿⣿⡍⠉⠀⠀⠀⣹⣿⣿⡥⠤⣵⣶⣄⣤⣤⠴⢒⣋⣸⣿⡟⠁⠀⢀⠔⡻⣿⡄⠿⣿⣿⣿⣿⣿⠟⣁⠁⠀⠀⠀⠀⣀⣀⣠⣶⣿⡿⠁⣿⣿⣿
⠁⠀⠀⠀⠀⢀⣎⠀⠀⠙⢿⣶⣤⣤⡿⠿⢿⣿⣿⣿⠟⠉⠉⠀⢀⣾⣿⠃⠀⠀⠀⣴⣿⣿⣿⡿⠀⠸⣿⠋⠀⠀⠀⣾⣿⣿⣿⣿⣯⣠⡏⠀⠀⠸⣿⡆⠘⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠟⠛⠉⡉⢥⣤⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠉⠙⠿⣧⣦⣤⣭⣡⣤⣀⣠⣤⣾⠟⢿⣧⠀⠀⢀⣤⠿⡟⢿⣿⡏⠓⢰⣶⠘⠉⠙⠉⢉⣿⣿⠇⣿⣿⣿⣧⣄⣀⣤⣴⣿⣤⣤⣀⡀⠘⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠃⠠⣠⣼⣿⣿⣿
⠀⠶⠶⣶⠿⢷⠄⠻⢿⣶⣶⣄⡀⠘⠻⢿⣿⡿⠋⠉⠉⠀⠀⠀⡀⢀⣿⠇⢠⠏⠀⠀⣿⣿⣿⡗⠀⠤⣶⡀⠒⠶⠶⣾⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⣸⣯⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⡿⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢠⣏⣷⣿⣿⡗⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⣙⣫⣼⣿⣷⣿⣿⣾⣿⣿⣇⡋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢰⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠖⣶⣶⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⠃⠀⠀⠀⠀⠀⢀⡟⠋⠙⣿⣦⣄⡀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⡄⠀⠀⠀⠀⠀⣼⠃⠈⠀⡈⣿⣿⣿⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣀⣴⣾⣿⣦⣀⣴⣤⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠸⣿⣿⠛⠛⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⣠⡾⢻⣷⠀⠀⠀⠈⢻⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣻⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣿⠟⠀⠸⣿⣇⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⡼⡷⠿⠛⠛⠋⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⢠⠇⢿⣿⣿⣄⣤⣠⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⢠⠿⠿⣿⣿⠟⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠚⠛⠛⠿⠛⠻⠆⠀⠀⠀⣼⣀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢙⣿⡄⠀⠀⡛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢝⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣆⣘⣦⣤⡇⠀⠀⠀⠈⣿⣄⣠⣤⣀⣉⣉⣉⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠙⠿⣿⣿⣶⢿⣇⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⣿⣿⣟⣉⣤⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠉⠋⠉⠙⠿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢸⣷⡏⠀⠀⠀⠀⢠⣾⣿⣶⣶⣄⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠛⠛⠉⠀⣼⣿⠻⣶⣶⣶⣤⣀⣤⣴⣶
⠀⠀⣀⣀⣀⣂⣀⠇⠀⠀⠀⠀⠀⠀⠀⡉⠿⣿⣿⣛⣫⣴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣥⠖⡀⠀⠀⢠⣾⣿⣿⣧⠈⠻⣿⣿⣷⣿⠛⠉⣁⣈⣉⡉⠃⠀⠀⠀⠀⠉⠛⠈⢁⣭⣿⡿⠟⢛⣫⣭
⣀⣻⠟⠛⠛⠛⠿⣶⣦⣄⡠⠀⠀⠀⠀⠸⢶⣤⣾⣿⣿⡯⠥⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠟⡠⠀⠀⠸⣿⣿⣿⣿⣇⡀⢹⣿⣿⣇⣀⣀⣀⣀⣀⣈⢀⣠⣤⣤⣤⣤⣶⡾⠟⠋⢩⡤⣸⣿⣿⣿
⣿⣿⣷⡀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⢠⣤⣤⣤⣩⣽⠁⠀⠀⠈⣿⣷⣤⣤⣴⣶⣶⣶⣶⣦⣤⣴⣿⡿⠛⠀⠠⠄⠈⠁⣠⣿⣿⣿⢻⠿⠃⣿⣿⡿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⢀⡠⠀⢀⣴⣿⣿⣿⣿
⣿⣿⡿⠁⠀⠀⠀⠀⠀⢿⣆⠈⠙⠟⢲⣿⣿⣿⣿⣿⣭⣤⣶⣿⣿⢿⣿⡛⠉⠁⠀⠀⢉⣿⣿⣯⠨⢭⣶⣤⣤⣤⡤⠖⣚⣡⣿⣿⡃⠀⠀⡠⢚⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⡈⠀⠀⠀⠀⣀⣀⣠⣴⣿⡿⠏⢸⣿⣿
⡏⠀⠀⠀⠀⠀⣼⠀⠀⠘⠻⣷⣤⣄⡼⠿⣿⣿⣿⣿⡿⠙⠉⠁⠀⣼⣿⡇⠀⠀⠀⢠⣾⣿⣿⣿⠀⠈⢿⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣅⣼⠁⠀⠘⢿⣧⠀⠿⣿⠛⠋⢠⣿⣿⣿⣿⠿⠿⠿⠛⠋⢉⠩⣤⣄⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠈⠙⠿⣿⣤⣤⣭⣉⣀⣀⣠⡤⣴⡿⠿⣿⡄⠀⠀⣠⡼⢿⢿⣿⣿⠓⠲⣶⡆⠃⠉⠋⠉⣹⣿⡟⢹⣿⣿⣿⣤⣀⣠⣤⣾⣦⣤⣀⡀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⡰⠋⠀⣄⣤⣿⣿⣿
⠀⠶⠶⣶⢿⢷⠄⠹⠿⣷⣶⣄⣀⠀⠻⢿⣿⣿⠿⠉⠉⠁⠀⠀⢀⠀⣸⡇⠀⡼⠁⠀⣸⣷⣿⣿⠀⠠⢴⣆⠐⠲⠶⢶⣿⣿⣿⣯⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢰⣿⡁⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡗⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⢙⣋⣼⣿⣷⣿⣿⣾⣿⣿⣧⣋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡆⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠁⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⡿⠋⠀⠀⠀⠀⢿⣷⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡟⠀⠀⠀⠀⠀⠀⣸⠛⠉⢻⣷⣤⣀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⢰⡟⠀⠂⢀⢹⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣠⣶⣿⣧⣀⣠⣦⣾⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⢿⢿⡿⠛⠻⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⢀⣴⡟⣶⡄⠀⠀⠀⠙⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣶⣶⡿⠃⠀⢻⣿⡀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢯⢿⠾⠟⠟⠛⠁⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⣠⣶⣶⣶⣦⡀⠀⠀⠀⠀⡴⠸⣿⣿⣧⣠⣀⣸⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⡼⠿⣿⣿⡿⠻⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠛⠿⠿⠛⠷⠀⠀⠀⠀⣇⠀⠨⢿⣿⣿⣿⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢻⣧⠀⠀⢸⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣙⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣤⣀⣳⣤⣴⠀⠀⠀⠀⠹⣧⡀⣄⣌⣉⣉⣉⣉⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠻⢿⣿⣷⡾⣿⣐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⢿⣿⣿⣋⣡⡴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠋⠛⠛⠙⠻⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⣿⣾⠁⠀⠀⠀⠀⣴⣿⣷⣶⣦⣀⣀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠛⠛⠉⠁⢠⣿⡟⠿⣶⣶⣦⣄⣠⣤⣶
⠀⠀⠀⣀⣀⣐⠀⢸⠀⠀⠀⠀⠀⠀⠀⢈⠙⢿⡿⢿⣛⣥⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⣴⢂⠀⠀⠀⣴⣿⣿⣿⡀⠙⢿⣿⣿⣾⡟⠋⢉⣀⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⠁⣩⣽⣿⠿⠛⣛⣭
⣀⣰⡿⠿⠻⠿⠿⢷⣦⣤⣀⠀⠀⠀⠀⠀⠶⣦⣼⣿⣿⣿⠭⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠻⢋⠀⠀⠀⢻⣿⣿⣿⣿⣁⠈⣿⣿⣿⣀⣀⣀⣀⣀⣀⡉⢀⣤⣤⣤⣤⣴⣶⡿⠛⠉⣥⢄⣿⣿⣿
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⣤⣤⣨⣍⣩⡏⠀⠀⠀⢹⣿⣦⣤⣤⣶⣶⣶⣶⣶⣤⣤⣾⣿⠟⠃⠀⠤⠀⠉⢀⣼⣿⣿⡟⡿⠟⢸⣿⣿⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⠄⠀⣠⣾⣿⣿⣿
⣿⣿⣿⠟⠀⠀⠀⠀⠀⠸⣷⡀⠙⠻⠷⣴⣿⣿⣿⣿⣿⣩⣴⣶⣿⣿⢿⣟⡋⠉⠀⠀⠀⣹⣿⣿⡅⠍⣵⣦⣄⣤⣤⠤⠖⣋⣼⣿⡟⠀⠀⢀⠔⣻⣿⡄⢿⣿⣿⣿⣿⣿⠟⣁⠁⠀⠀⠀⢀⣀⣀⣤⣾⣿⡿⠁⣿⣿
⣿⠃⠀⠀⠀⠀⢀⡆⠀⠀⠛⢿⣦⣄⣠⡿⣿⣿⣿⣿⣿⠏⠛⠉⠁⢀⣾⣿⠁⠀⠀⠀⣤⣿⣿⣿⡇⠀⠹⣿⠛⠀⠀⠀⣾⣿⣿⣿⣿⣯⣠⡏⠀⠀⠺⣿⡄⠘⠿⡟⠛⠁⣴⣿⣿⣿⡿⠿⠿⠟⠛⠉⡉⢥⣤⣀⣿⣿
⠇⠈⢁⡀⠀⠀⠈⢿⣦⠀⠀⠀⠉⠻⣿⣧⣤⣤⣍⣉⣀⣀⣀⣤⣶⠿⢿⣧⠀⠀⢀⣤⠿⣿⢿⣿⡟⠒⢶⣶⠐⠈⠛⠉⢉⣿⣿⠇⣿⣿⣿⣧⣄⣀⣤⣴⣿⣤⣤⣀⡀⠚⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠃⠠⣤⣼⣿⣿
⠀⠖⡶⣶⠿⢷⠆⠸⠿⢿⣶⣤⣀⠀⠸⢿⣿⣿⡿⠏⠉⠉⠁⠀⠀⡀⢀⣿⠇⢠⠏⠀⢀⣿⣾⣿⡇⠀⠤⣶⡀⠒⠶⠶⣾⣿⣿⣿⣅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⣸⣯⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡄⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡗⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⠙⢋⣘⣿⣧⣿⣿⣾⣿⣿⣷⣯⣙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⣰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⢰⣖⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡶⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⡟⠉⠀⠀⠀⠈⣿⣶⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣿⡏⠀⠀⠀⠀⠀⠀⣼⠛⠉⢻⣷⣤⣀⠀⢀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⣰⡏⠀⠂⡀⢻⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣰⣾⣿⣧⣄⣰⣦⣾⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠀⠀⠈⢿⣿⡿⠛⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣴⡟⣶⡄⠀⠀⠈⠻⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣧⣽⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣶⡿⠋⠀⣿⣧⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢯⢷⠾⠟⠛⠉⠁⠀⢀⣼⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣾⠁⠀⠀⢠⣤⣶⣤⣤⠀⠀⠀⠀⠀⡄⢰⣿⣿⣇⣀⡀⣹⣿⣿⣷⣿⡿⠗⠀⠀⠀⠀⠀⠀⡼⠿⣿⣿⠿⠻⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠰⠿⠿⠿⠿⠿⢧⠀⠀⠀⢀⣇⠀⠩⣿⣿⣿⣿⣿⣿⣿⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣦⠀⠀⢹⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣙⣿⣿⣿⣿⣿⣿⣿⠟⣁⡦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣀⣳⣄⣼⠀⠀⠀⠀⢻⣆⠀⣄⡉⢉⣉⣙⣋⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠿⣿⣿⣷⡶⣿⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⢿⣿⣿⣋⣤⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠟⠛⠛⠛⠿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⣯⣿⠁⠀⠀⠀⠀⣾⣿⣷⣶⣦⣀⣀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠛⠉⠉⠁⢠⣿⡟⢿⣶⣶⣦⣄⣤⣴
⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⠿⠿⣛⣡⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣯⡴⢂⠀⠀⠀⣼⣿⣿⣿⡀⠙⢿⣿⣿⣾⡟⠋⣉⣈⣉⣉⠙⠀⠀⠀⠀⠈⠙⠃⢀⣩⣽⣿⠟⠋⣉
⠀⠀⣰⠾⠿⠿⠿⠿⣷⣤⡄⡀⡀⠀⠀⠀⠀⢷⣤⣭⣿⣿⣿⠭⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⡲⠋⠀⠀⠀⢿⣿⣿⣿⣿⡀⠈⣿⣿⣿⣀⣀⣀⣀⣀⣀⡉⣀⣤⣤⣤⣤⣴⣾⠿⠛⠉⡤⢆⣿⣿
⣾⣿⣿⣿⣆⠀⠀⠀⠀⠈⠙⠿⣤⣀⠀⠀⠀⣤⣈⣉⣉⣩⡏⠀⠀⠀⠹⣷⣄⣤⣤⣴⣶⣶⣶⣦⣤⣤⣾⣿⠟⠃⠀⠤⠀⠉⢀⣸⣿⣿⡿⡿⠟⢸⣿⣟⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⣠⠄⠀⣠⣾⣿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣷⠈⠙⠿⠷⣴⣿⣿⣿⣿⣿⣩⣤⣶⣿⣿⣿⣟⡛⠉⠉⠀⠈⣙⣿⣿⣁⠩⣥⣦⣀⣤⣤⠤⠖⣋⣼⣿⣏⡁⠀⢀⠔⣻⣿⡄⢿⣿⣿⣿⣿⣿⠟⣁⠁⠀⠀⢀⣀⣀⣀⣤⣾⣿⠟⠀⣿
⣿⣿⠋⠉⠀⠀⠀⠀⡆⠀⠀⠻⢷⣤⣄⣀⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⢀⣾⣿⠀⠀⠀⠀⣤⣿⣿⣿⡇⠀⠹⣿⠟⠀⠀⠀⣾⣿⣿⣿⣿⣧⣠⡏⠀⠀⠺⣿⡄⠘⢿⡟⠛⠁⣼⣿⣿⣿⠿⠿⠿⠟⠛⠉⡉⠥⣤⣄⣿
⣿⡏⠀⠁⠀⠀⠀⠘⣿⣆⠀⠀⠈⠙⠻⣿⣧⣤⣬⣙⣉⣁⣀⣀⣤⣴⡿⢿⣧⠀⠀⠀⣠⡿⣿⢿⣿⡟⠒⢲⣶⠐⠈⠛⠋⢉⣿⣿⠏⣿⣿⣿⣧⣄⣀⣤⣴⣿⣤⣤⣀⡀⠚⠛⠉⠁⠀⠀⠀⠀⠀⡀⠔⠁⠠⣤⣼⣿
⡿⠖⠳⣶⠯⢷⡶⠲⠺⠿⣷⣦⣄⣀⠀⠘⢿⣿⣿⣿⠏⠉⠉⠉⠀⠀⡀⢈⣿⠆⢠⠞⠁⠀⣿⣾⣿⡧⠀⠤⣶⡀⠲⠶⠶⣾⣿⣿⣿⣅⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⢸⣯⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣤⠄⣤⣤⢠⣤⡄⣤⠀⣤⣄⢤⡤⢠⣤⡄⣤⣤⢠⣤⡄⠀⣤⡄⣤⣠⡤⣤⣤⠀⣤⡤⣤⣠⡄⣤⠄⣤⣤⢠⣤⡄⣤⣤⢠⡤⢠⣤⡄⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡅⣿⠂⣿⣿⢸⣿⡇⣿⠀⣿⣿⢸⡇⢸⣿⡇⣿⣯⢘⣳⡄⢀⣏⣷⣿⣿⡇⣿⣿⠀⣿⡗⣿⣿⡇⣿⢺⣿⣿⢸⣿⡅⣿⣩⢹⡗⢸⡿⣇⣙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠃⠛⠃⠙⠙⠈⠛⠁⠛⠃⠛⠛⠘⠃⠈⠛⠁⠛⠛⠈⠛⠁⠘⠋⠛⠛⠘⠃⠛⠋⠀⠙⠛⠙⠘⠃⠛⠀⠙⠋⣘⣿⣧⣽⣿⣾⣿⣿⣷⣯⣝⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⢴⡶⠆⣶⡶⢰⡖⢰⣶⡆⠐⣶⠖⣶⢶⡄⠐⣶⢲⣶⡆⣶⣶⢰⣦⡖⣶⠀⣶⠂⠐⣶⠒⣶⣶⢰⡖⣢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣿⡦⣿⣷⢸⣏⢸⣿⡇⠀⣿⠀⣿⣸⠇⠀⣿⢸⣿⡇⣿⣴⢸⡿⣇⣿⡀⣿⡁⠀⣿⠀⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠈⠉⠀⠀⠈⠀⠈⠁⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠉⠉⠁⠉⠁⠀⠈⠀⠉⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢷⣿⡿⠋⠀⠀⠀⠀⢻⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣾⣿⠁⠀⠀⠀⠀⠀⢸⡟⠉⠙⣷⣦⣄⡀⠀⣠⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⢀⣾⠀⠁⢀⠘⣿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⣀⣀⣶⣿⣿⣤⣠⣶⣴⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠀⠀⢹⣿⣿⠟⠿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⣀⣾⢻⣧⠀⠀⠀⠙⢿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠟⣻⣬⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣾⠟⠁⢸⣿⡀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠾⡶⠿⠛⠋⠉⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣶⡞⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⠀⢀⠄⣾⣿⣿⣀⣀⢈⣿⣿⣷⣶⣿⠿⠂⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠋⠁⠀⠀⠼⠿⠿⡿⠿⠿⡄⠀⠀⠀⣸⡀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⣷⡀⠀⠈⡏⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢉⣻⣿⣿⣿⣿⣿⣿⡿⢋⣱⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣄⠰⣄⣠⡆⠀⠀⠀⠘⣿⣀⢠⣈⠉⣉⣋⣛⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⠞⠻⢿⣿⣿⣶⢾⣇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣟⣡⡤⣾⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠛⠛⠛⠻⢿⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠙⠛⢸⣿⡏⠀⠀⠀⠀⢰⣾⣿⣶⣶⣄⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠋⠉⠉⠀⣼⣿⠻⢷⣶⣶⣤⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⠙⢻⡿⠿⢿⣋⣵⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣭⠖⠀⠀⠀⢠⣾⣿⣿⣇⠉⠻⣿⣿⣷⣿⠛⢉⣀⣉⣉⡉⠃⠀⠀⠀⠀⠁⠋⠀⣀⣭⣿⡿⠛⣉
⠀⠀⠀⠶⠿⠿⠿⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠸⣦⣬⣽⣿⣿⣿⠧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣓⠞⠠⠀⠀⠸⣿⣿⣿⣿⣇⠀⢹⣿⣿⣇⣀⣀⣀⣀⣀⣈⢁⣠⣤⣤⣤⣤⣶⡿⠟⠋⢡⠴⣸⣿
⣠⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⠳⣧⣀⡀⠀⠀⢀⣀⣉⣉⣉⣽⠁⠀⠀⠉⣿⣦⣠⣤⣤⣴⣶⣶⣦⣤⣤⣴⣾⣿⠛⠀⢨⠄⠈⠁⣀⣿⣿⣿⡿⠿⠃⣿⣿⡻⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢀⡤⠀⢀⣴⣿⢿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣶⡆⠉⠻⠿⢦⣾⣿⣿⣿⣿⣋⣥⣴⣶⣿⣿⣿⣛⠋⠉⠁⠀⢙⣛⣿⣏⠈⢉⣤⣄⣠⣤⡤⠴⢚⣡⣿⣿⠉⠀⠀⡠⢚⣿⣧⠸⢿⣿⣿⣿⣿⡿⢋⡈⠀⠀⢀⣀⣀⣀⣠⣴⣿⡿⠏⠘
⣿⣿⡿⠉⠁⠀⠀⠀⢠⠀⠀⠘⢿⣦⣄⣀⣸⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⣰⣿⡟⠀⠀⠀⢀⣼⣿⣿⣿⠀⠈⣿⡿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣆⣼⠁⠀⠐⢿⣧⠀⠻⢿⠛⠋⢠⣿⣿⣿⡿⠿⠿⠟⠛⠉⢉⠩⠤⣤⣸
⣿⣿⠁⠈⠁⠀⠀⠀⢿⣧⡀⠀⠀⠉⠛⢿⣿⣤⣤⣙⣛⣉⣀⣀⣠⣤⣾⠿⣿⡄⠀⠀⢀⣼⢿⣿⣿⣿⠒⠲⣶⡆⠒⠚⠚⠉⣹⣿⡿⢹⣿⣿⣿⣤⣀⣠⣤⣾⣧⣤⣄⣀⠐⠛⠋⠉⠀⠀⠀⠀⠀⢀⠠⠊⠀⢤⣤⣿
⣿⡟⠲⣶⠿⢷⠶⠶⠲⠿⢿⣶⣤⣀⠀⠀⠿⣿⣿⣿⡿⠛⠉⠉⠁⠀⣀⠀⢹⣿⠀⡴⠋⠀⢸⣷⣿⣿⠤⠠⢤⣆⠐⠶⠶⢶⣿⣿⣷⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⡅⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿⣷⣾⡆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡏⠀⠀⠀⠀⠀⠀⣿⠃⠉⢿⣷⣤⣀⣀⣀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⣼⡇⠈⠀⡄⢻⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣀⣰⣾⣿⣧⣄⣴⣦⣾⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠉⠉⠀⠘⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⡆⠀⠀⠀⠀⠀⠀
⠉⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣴⣟⣿⡅⠀⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣧⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⣤⣶⣿⠋⠈⣿⣇⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⢿⠾⠟⠛⠉⠁⠀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣶⣶⠋⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⣴⣾⣿⣿⣇⣀⡀⣹⣿⣿⣶⣾⡿⠇⠀⠀⠀⠀⠀⢀⣾⠿⣿⣿⡿⠿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣠⣀⣠⣤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠛⠋⠀⠀⢰⠿⠿⣿⡿⠿⣧⠀⠀⠀⢀⣿⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⣿⣦⠀⠀⢹⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⠂⢦⣀⣼⠀⠀⠀⠈⢿⣧⡀⣄⡉⢙⣙⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⡾⠻⠿⣿⣿⣷⡾⣿⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⢿⣿⣿⣋⣤⣴⣿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡟⠿⠟⠻⢿⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠛⠃⣿⣿⠁⠀⠀⠀⠀⣾⣿⣷⣶⣦⣀⣀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠛⠉⠉⠃⢠⣿⡟⢿⣿⣷⣶⣤⣤
⠀⠀⠀⠀⠀⠁⠀⠠⠀⢰⠁⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⠿⣟⣩⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣯⣵⠂⠀⠀⠀⣴⣿⣿⣿⣟⠛⣿⣿⣿⣿⡟⠋⣉⣈⣉⣉⠙⠀⠀⠀⠀⠈⠙⠋⢀⣨⣿⣿⠟⠋
⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⣤⣀⡀⡀⠀⠀⠀⠈⣷⣭⣽⣿⣿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⡳⠋⠄⠀⠀⣿⣿⣿⣿⣿⡄⠈⣿⣿⣿⣀⣀⣀⣀⣀⣀⡉⣀⣴⣶⣤⣤⣴⣾⠿⠛⠩⡤⢆⣿
⢀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠉⠛⢿⣄⡀⠀⠀⠀⣄⣈⣉⣙⣋⡏⠀⠀⠈⢻⣷⣄⣤⣤⣤⣶⣶⣶⣦⣤⣤⣶⣿⡿⠃⠀⣡⠀⠉⢀⣼⣿⣿⣿⡿⠟⢸⣿⣿⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⣠⠄⠀⣠⣾⡿
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣦⠉⠻⢿⣷⣴⣿⣿⣿⣿⣿⣫⣤⣶⣾⣿⣿⣿⡛⠋⠉⠉⠉⣻⣿⣿⣇⣍⣩⣦⣄⣤⣤⠤⠖⣋⣼⣿⣿⡃⠀⢀⠔⣻⣿⡄⢿⣿⣿⣿⣿⣿⠟⣁⠁⠀⣀⣀⣀⣀⣀⣤⣾⣿⠿⠁
⣿⣿⣿⠟⠉⠁⠀⠀⢀⣾⠁⠀⠻⣷⣤⣀⣀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⢀⣿⣿⠃⠀⠀⠀⣠⣿⣿⣿⡏⠀⢹⣿⠟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣠⡏⠀⠀⠻⣿⡆⠸⢿⡟⠛⠁⣼⣿⣿⣿⠿⠿⠿⠟⠋⠉⡩⠥⢤⣤
⢸⣿⡟⠐⠋⠀⠀⠀⢸⣿⣄⠀⠀⠈⠙⠿⣿⣇⣬⣌⣛⣋⣁⣀⣀⣤⣴⡿⣿⣯⠀⠀⠀⣠⣿⣿⣿⣿⡟⠒⢶⣶⠘⠒⠛⠋⢉⣿⣿⠏⣿⣿⣿⣧⣄⣀⣤⣴⣿⣦⣤⣀⡀⠚⠛⣉⠁⠀⠀⠀⠀⠀⡠⠞⠁⠠⣤⣾
⣾⣿⠳⣿⢿⢿⢷⣶⠾⠿⠿⣷⣤⣄⡀⠀⢸⣿⣿⣿⣿⠟⠛⠛⠉⠉⢉⡀⠈⣿⡇⢠⡞⠁⢀⣿⣿⣿⡧⠤⢬⣴⡀⠲⠶⠶⣾⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⢿⣿⣶⣷⠀⠀⠀⠀⠀⠀⢸⣿⣅⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣿⡿⠀⠀⠀⠀⠀⠀⣸⡟⠉⠻⣷⣦⣄⣀⣀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⢠⣿⠀⠡⢠⠹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣆⣀⣀⣶⣿⣿⣄⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠉⠁⠀⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⣷⠀⠀⠀⠀⠀⠀
⠋⠉⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣠⣾⣿⣇⠀⠀⠀⠙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣼⡏⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣴⣾⠟⠁⢹⣿⡀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⡿⠟⠛⠋⠉⠀⢀⣤⣿⣿⡀⠀⠀⠀⠀⠀⠀
⣷⣶⡞⠁⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣀⡀⢸⣿⣿⣶⣶⣿⠿⠀⠀⠀⠀⠀⠀⣰⠿⢿⣿⡿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠟⠛⠁⠀⠀⡾⠿⢿⣿⠿⢿⡀⠀⠀⠀⣼⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠁⢀⠊⢻⣧⡀⠀⢈⡟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡄⠰⣄⣠⡇⠀⠀⠀⠻⣿⣠⢀⣈⠉⣛⠛⣛⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢲⠟⢿⢿⣿⣿⣶⢿⣄⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣟⣥⣴⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⠿⠿⠛⠿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠙⠃⢸⣽⡏⠀⠀⠀⠀⢰⣿⣿⣶⣶⣄⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⠙⠋⠉⠙⠀⣽⣿⢻⣿⣿⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⠿⢿⣋⣵⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣭⣆⠀⠀⠀⢠⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⠛⢉⣁⣉⣉⡉⠃⠀⠀⠀⠀⠉⠋⠁⣀⣽⣿⡿⠛
⠀⠀⠀⢀⣶⣿⣿⣿⣷⣿⣦⣄⣀⢀⠀⠀⠀⠀⢹⣦⣭⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣓⠞⡀⠀⠀⢸⣿⣿⣿⣿⣇⠀⣹⣿⣿⣇⣀⣀⣀⣀⣀⣈⢀⣤⣶⣦⣤⣤⣶⡿⠟⠋⠥⠶⣸
⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠉⠙⠿⣧⣀⠀⠀⠀⣀⣈⣉⣉⣛⣻⠁⠀⠀⠙⣿⣦⣀⣤⣤⣴⣶⣶⣤⣤⣤⣴⣿⣿⠗⠀⣈⠄⠉⠁⣠⣿⣿⣿⣿⠿⠀⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢀⡤⠀⢀⣼⣿
⢘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣶⡌⠛⠿⣷⣦⣾⣿⣿⣿⣿⣛⣤⣴⣶⣾⣿⣿⡟⠛⠉⠉⠈⢙⣿⣿⣏⣈⣩⣥⣄⣠⣤⡤⠴⣚⣩⣿⣿⣏⠀⠀⡠⢻⣿⣧⠸⣿⣿⣿⣿⣿⡿⢋⡈⠀⣀⣀⣀⣀⣀⣠⣴⣿⡿⠋
⢸⣿⣿⡿⠛⠉⠀⠀⠀⢰⡍⠀⠸⢿⣦⣀⣀⣹⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⣸⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⠀⠘⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣇⣼⠁⠁⠘⢿⣧⠈⠿⣿⠛⠋⢠⣿⣿⣿⡿⠿⠿⠟⠛⠉⢉⠭⠤⣤
⠀⣿⣿⠃⠒⠁⠀⠀⠀⣿⣧⡀⠀⠀⠙⠻⣿⣿⣠⣁⣛⣛⣉⣀⣀⣀⣤⣾⢿⣿⡄⠀⠀⢀⣼⣿⣿⣿⣿⠓⠶⣶⡆⠓⠚⠛⠉⣽⣿⡿⢹⣿⣿⣿⣤⣀⣠⣤⣾⣷⣤⣄⣀⠐⠛⢋⠉⠀⠀⠀⠀⠀⢀⡴⠋⠀⢤⣴
⢸⣿⡿⣶⠿⢿⣏⣲⡶⠾⠿⣿⣦⣄⣀⠀⠀⣿⣿⣿⣿⣿⠛⠛⠋⠉⠉⡁⠀⣹⡷⠀⡴⠋⠀⣾⣿⣿⣿⠤⠤⣥⣆⠐⠶⠶⢶⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⡅⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠉⠀⠀⠀⠘⣿⣷⣾⣇⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⡏⠀⠀⠀⠀⠀⠀⣼⠛⠉⢻⣷⣦⣀⣀⣀⣤⣾⣿⣿⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⣰⡟⠀⠃⢀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⣄⣀⣰⣾⣿⣷⣄⣴⣶⣾⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠉⠉⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀⠀
⣿⠟⠉⠻⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⣾⣿⡅⠀⠀⠈⠻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣷⣼⠇⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣤⣾⠟⠁⢻⣷⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⢿⢿⠾⠟⠛⠋⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣷⣤⡖⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣯⢀⡀⢸⣿⣷⣶⣶⣿⠿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⡿⠿⠛⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⣾⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠁⢠⠚⢿⣧⠀⠀⢙⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⣿⣿⣿⣿⣿⠿⢋⣴⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⢢⣀⣠⠃⠀⠀⠀⢿⣧⡀⣈⡙⠙⠛⠛⠛⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⢿⣿⣿⣷⣶⣾⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣛⣥⣴⣿⣷⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⢿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠚⠉⠙⠃⣿⣽⠏⠀⠀⠀⠀⣴⣿⣷⣶⣦⣄⣀⠀⠀⢀⣀⣀⣀⣀⠀⠈⠛⠉⠉⠉⢠⣿⣿⢿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠿⣛⣥⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣭⢆⠀⠀⠀⢰⣿⣿⣿⣏⠟⢿⣿⣿⣿⣿⠛⢉⣀⣉⣉⡉⠀⠀⠀⠀⠈⠉⠋⢁⣨⣽⣿⠿
⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣾⣄⣀⡀⢀⠀⠀⠀⠀⢷⣬⣿⣿⣿⣿⣟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣳⠞⡀⠀⠀⢹⣿⣿⣿⣿⣇⠀⣻⣿⣿⣅⣀⣀⣀⣀⣀⡉⢀⣤⣶⣦⣤⣴⣾⡿⠟⠋⠤⠶
⠀⠀⣠⣶⣾⣿⣦⠀⠀⠀⠈⠉⠛⢿⣇⡀⠀⠀⠀⣀⣉⣙⣛⢛⣛⠁⠀⠈⠻⣷⣄⣀⣤⣤⣤⣶⣦⣤⣤⣄⣴⣾⣿⠗⠀⣉⠄⠉⠀⣈⣿⣿⣿⣿⠿⠀⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣀⡤⠀⢀⣼
⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣶⡈⠻⢿⣶⣄⣿⣿⣿⣿⣿⣛⣠⣴⣶⣾⣿⣿⡟⠛⠉⠉⠉⢻⣿⣿⣏⣉⣩⣥⣄⣠⣠⣤⠴⢚⣹⣿⣿⡏⠀⠀⡠⢻⣿⣇⠹⣿⣿⣿⣿⣿⡿⢋⠁⠀⣀⣀⣀⣀⣀⣤⣶⣿⡿
⠀⢸⣿⣿⡿⠛⠋⠀⠀⠀⢠⠀⠀⠹⣷⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⣼⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⠀⠸⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣄⣾⠁⠁⠘⢿⣇⠈⠿⣿⠛⠋⣰⣿⣿⣿⡿⠿⠿⠟⠛⠉⢉⠥⠤
⣰⠀⣿⣿⠃⠒⠀⠀⠀⠀⣿⣦⠀⠀⠀⠙⠿⣿⣿⣉⣉⣛⠛⣋⠁⣀⣀⣤⣾⣿⣿⡀⠀⠀⢀⣼⣿⣿⣿⡿⠒⢶⣼⡄⠒⠒⠚⠋⣽⣿⡟⣹⣿⣿⣿⣤⣀⣠⣤⣿⣦⣤⣄⣀⠐⠛⢋⠁⠀⠀⠀⠀⠀⣀⠴⠋⠀⣤
⡿⢾⣿⣿⠿⢿⠏⢳⣶⡶⠿⢿⣷⣦⣀⡀⠀⠈⣿⣿⣿⣿⣿⠛⠛⠛⠉⠉⠁⠀⣿⡇⠀⡴⠋⠁⣿⣿⣿⣿⠤⢤⣭⡄⠴⠶⣶⣶⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⡅⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⡟⠉⠀⠀⠀⠈⣿⣶⣶⣇⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣿⡏⠀⠀⠀⠀⠀⠀⣼⠛⠉⠻⣷⣦⣀⡀⣀⣠⣾⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⣰⡏⠀⠂⠀⢹⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣀⣰⣾⣿⣧⣄⣰⣶⣾⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠉⠉⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀⠀
⣿⠋⠉⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡆⣮⡅⠀⠀⠈⠻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣧⣼⠇⠀⠀⠀⠀⠀
⣻⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣤⣤⣾⠟⠁⢻⣷⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣄⣀⣠⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠨⠿⢷⠾⠟⠛⠋⠁⠀⢀⣤⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣧⣤⡖⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢠⢠⣿⣿⣇⢀⡀⢸⣿⣷⣶⣶⣿⠿⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⡥⣶⣶⢶⣾⠟⢿⡟⠛⠸⠀⠀⠀⢡⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⡿⠿⠛⠀⠀⠀⣾⣿⣿⣿⢿⣧⠀⠀⠀⠀⣼⠀⠙⣿⣿⣿⣿⣿⣿⣿⣯⣿⠷⠶⠞⢛⣛⣏⡉⣽⣷⣶⣮⣿⣿⠟⢿⣿⣿⣿⢹⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⢮⢏⣿⣿⣿⣿⣿⣿⣿⠟⢋⣴⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢢⡀⣠⠃⠀⠀⠀⢻⣇⠀⠈⣻⠙⣻⣿⢻⣿⣿⣿⡿⢿⣦⣿⡿⠙⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⢹⣿⠁⠀⠀⠀⣿⠄⠀⢷⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣋⣥⡴⣿⣷⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⠿⠿⠟⢿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠈⣻⣿⣧⠀⣿⣯⣿⡍⢻⣿⣿⡿⠻⣿⣿⠿⠿⣛⣙⣛⣴⣿⣷⣶⣶⣟⣛⠙⠀⠀⣀⣀⣀⣀⠀⠈⠑⠉⠉⠁⠀⣿⣿⠻⢿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣶⣶⠀⣶⣶⢛⣿⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⣾⣿⣿⡟⣩⣿⣿⣷⣿⣿⣶⣾⣿⣶⣿⣾⡟⠛⢉⣀⣉⣉⡉⠀⠀⠀⠀⠈⠁⠋⠀⣠⣽⣿⠟
⠀⠀⠀⠀⠀⣴⣶⣿⣷⣶⣾⣄⣀⠀⣿⣿⣇⣿⣿⢽⣿⣿⣾⣿⣿⣟⣋⣤⣿⣿⣿⣷⠒⣿⣿⠙⣿⣿⡇⠀⣿⣿⣿⡗⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣅⣀⣀⣀⣀⣀⡉⢀⣤⣶⣤⣤⣤⣶⡿⠛⠉⠤⠖
⠀⠀⣠⣶⣾⣶⣤⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣸⣿⣿⣻⣿⣿⠉⠀⢸⣿⣷⣿⣿⣠⣿⣿⣶⣦⣤⣤⣄⣿⣿⡿⠗⣿⣿⡇⣿⣿⣇⣿⣿⡿⣿⣿⣿⣿⣿⠹⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⢀⡤⠀⢀⣼
⠀⢰⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⣶⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣠⣤⣾⣿⡿⣿⣿⡟⣿⣿⣁⣿⣿⣿⣏⣿⣿⣧⣄⣿⣿⡧⢿⣿⣿⣿⣿⡇⣿⣿⣸⣿⣿⣇⣙⣻⣿⣿⣿⣿⣛⣃⠀⠀⢀⣀⣀⣀⣀⣠⣶⣿⡿
⠀⠈⣿⣿⡿⠛⠋⠀⠀⠀⢠⠀⠀⠹⣿⣇⣘⠛⣛⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⣻⣿⡟⠃⠈⠛⢻⣿⣿⣿⣿⠛⠛⣻⡿⠛⠛⠃⢸⣿⣿⣿⣯⣷⣛⣿⠀⠛⠛⢿⣟⠛⠛⣛⠛⠛⢻⣿⣿⣿⠿⠿⠿⠟⠛⠉⢉⠡⠤
⠀⠀⣿⣿⠃⠒⠀⠀⠀⠀⢿⣆⠀⠀⠀⠙⠿⣿⣏⣉⣉⣛⠛⠉⠀⠀⣀⣠⣾⢿⣿⡀⠀⠀⢀⣼⠿⢿⣿⡟⠒⠲⣤⡀⠒⠒⠚⠋⣽⣿⡟⢹⣿⣿⣷⣤⣀⣠⣤⣾⣦⣤⣀⣀⠐⠛⠋⠁⠀⠀⠀⠀⠀⢀⠴⠋⠀⢤
⡇⢾⣿⣿⠿⢿⠏⠰⠶⠶⠞⠹⣷⣤⣀⡀⠀⠈⣿⣿⣿⣿⣿⠛⠛⠋⠉⠉⠁⠀⢿⡇⠀⡴⠋⠀⣾⣿⣿⣿⠤⢠⣭⡄⠰⠶⣶⣶⣿⣿⣷⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢀⣿⡅⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣷⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠿⠟⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⠟⠁⠀⠀⠀⠘⣿⣶⣶⣇⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣽⡏⠀⠀⠀⠀⠀⠀⣼⠉⠉⢻⣷⣦⣀⣀⣀⣴⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢇⠀⠀⠀⠀⠀⣰⡇⠀⠂⡀⢻⣿⣿⣿⣿⣿⣿⣭⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣄⣀⣠⣾⣿⣷⣄⣴⣶⣾⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠉⠙⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠀⠀⠀
⣿⣿⠟⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⢠⡿⣭⡁⠀⠀⠉⠻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣷⣼⠇⠀⠀⠀⠀
⠛⢳⠀⠀⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣀⣤⣾⠟⠁⢿⣷⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣀⣠⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠨⠿⢷⠾⠟⠛⠉⠁⠀⣀⣤⣿⣿⠀⠀⠀⠀⠀
⠀⣿⣦⣤⡴⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢠⢨⣿⣿⣇⠀⠀⢸⣿⣶⣶⣶⣿⡿⠀⠀⢀⣀⣠⣄⣴⣿⣿⣿⣿⡿⢿⣿⣿⣯⡥⣶⡶⢶⣾⠿⢿⡟⠛⠸⠀⠀⠀⠀⢠⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⡿⠟⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⡞⠈⢙⣿⣿⣿⣷⣿⣿⣿⣯⣿⠷⠖⢛⣛⣏⡉⣽⣿⣷⣦⣻⣿⣿⣿⣾⣿⡟⣿⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⢌⢏⣿⣿⣿⣿⣿⣿⣿⠟⢋⣴⠀⠀⠀⠀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⢈⠂⠀⠀⠀⢻⡇⠀⢻⠙⣻⣿⢻⣿⣻⣿⡿⢿⣦⣿⡿⠙⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢹⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠈⠛⠛⠛⠿⣿⣿⣋⣥⠴⣿⣷⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠲⠿⡷⠾⢿⣿⠀⠀⠀⠀⠀⢻⣷⣿⣿⣾⣿⣿⣿⣿⣿⡇⠈⣻⣿⣧⠀⣿⣯⣿⡏⢻⣿⣿⡯⠻⣿⣿⣿⠿⣛⣙⣛⣤⣴⣿⣷⣶⣿⣟⣙⠀⠀⠀⣀⣀⣀⣀⠀⠈⠘⠉⠉⠁⠀⣿⣿⢻⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⣶⠀⣶⣶⠙⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣿⣿⣷⣶⡝⣿⣶⣻⣾⡟⠋⢉⣀⣁⣉⡉⠀⠀⠀⠀⠀⠁⠉⢀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣾⣅⣀⣿⣿⣇⣿⣿⢸⣿⣿⣹⣿⣿⣿⣿⣤⣿⣿⣿⣷⠒⣿⣿⠙⣿⣿⡆⠀⣿⣿⡇⣸⣿⣿⡟⣿⣿⡇⣿⣿⣿⣿⣿⣧⣿⣿⢿⣿⣅⣀⣀⣀⣀⣀⡈⢀⣤⣶⣦⣤⣴⣾⠿⠛⠉⠤
⣷⠀⠀⢀⣴⣶⣾⣄⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⣛⠁⢸⣿⡟⣿⣿⣀⣿⣿⣤⣴⣤⣤⣤⣿⣿⣷⡿⣿⣿⣏⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⢀⠄⠀⢀
⣿⠀⠀⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣿⡟⢻⣿⣿⣼⣿⣿⣿⣿⣿⠛⣀⣼⣿⣿⣿⣿⡟⣿⣿⣏⣿⣿⣿⣿⣿⣿⣏⣤⣿⣿⣇⣿⣿⣟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣇⣘⣻⣿⣿⣿⣿⡛⢃⠀⠀⣀⣀⣀⣀⣀⣤⣶⣿
⡿⠀⠀⣿⣿⣿⠛⠋⠀⠀⠀⢀⠀⠀⠻⣿⣌⡛⠛⢸⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⣹⣿⡇⠈⠛⠛⢛⣿⣿⣿⣿⠛⠛⣿⡟⠛⠃⠈⢻⣿⣿⣿⣿⣛⣛⣼⠛⠛⠘⢿⣟⠛⠛⢛⠛⠛⢣⣿⣿⣿⠿⠿⠿⠛⠛⠉⢉⠡
⣿⢀⠀⣿⣿⠇⠐⠂⠀⠀⠀⢼⣆⠀⠀⠀⠛⠿⣿⣿⣉⣉⡛⠛⠋⠁⠀⣀⣠⣴⣿⣿⡀⠀⠀⢀⣼⡿⢿⣿⣿⠒⠶⣤⡄⠒⠒⠚⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣠⣤⣾⣦⣤⣀⣀⠀⠛⢋⠁⠀⠀⠀⠀⠀⢀⠴⠋⠀
⣿⡿⢲⣿⡿⢶⠖⠲⠲⠶⠶⠂⠻⣷⣤⣀⠀⠀⠈⣿⣿⣿⣿⣿⠛⠛⠛⠉⠉⠁⠀⢻⡇⠀⡴⠋⠁⣸⣿⣿⣿⠄⠠⣭⡄⠠⠶⣶⢶⣿⣿⣷⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⣿⡅⠀⠀⠀⠀⠀⢀⣠⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⣷⢾⣿⡀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣿⣿⠁⠀⠀⠀⠀⠀⢰⡏⠈⠙⢿⣶⣤⣀⣀⣠⣾⣿⣿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⢀⣾⠀⠐⢀⠈⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⣀⣀⣴⣿⣿⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⡟⣇⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠛⠉⠉⢻⣿⣿⡿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀⠀⠀
⣰⣿⡿⠛⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⣰⢏⣝⠀⠀⠈⠙⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⢹⣦⡿⠀⠀⠀⠀
⠛⠛⡇⠀⠀⠀⢹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣀⣤⡾⠋⠸⣿⡆⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣠⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠽⠶⠿⠿⠛⠋⠉⠀⢀⣠⣼⣿⡇⠀⠀⠀⠀
⠀⢸⣷⣤⣤⠆⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡈⣽⣿⣿⠀⠀⠀⣿⣷⣶⣶⣶⣿⠇⠀⢀⣀⣠⣄⣤⣾⣿⣿⣿⡿⢿⣿⣿⣿⡥⣶⡶⢶⣾⠟⢿⡟⠛⠸⠀⠀⠀⠀⠀⢤⣄⣄⣀⣠⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⠿⠟⠀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⡇⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠞⢛⣛⣏⡉⣽⣷⣾⣦⣻⣿⣿⣿⣾⣿⡻⢻⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠰⡙⣹⣿⣿⣿⣿⣿⣿⡿⠛⣡⡆⠀⠀⠀
⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⣅⠀⡹⠀⠀⠀⠘⣷⡀⢾⠉⣻⣿⢻⣿⢛⣿⣿⢿⣦⣿⡿⠛⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⢹⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⡿⣟⣭⡤⢾⣿⣾⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠶⢿⠶⢿⣿⡟⠀⠀⠀⠀⠘⣿⣾⣾⣿⣿⣿⣿⣿⣿⡟⠈⣻⣿⣧⠀⣿⣯⣿⡉⢿⣿⣿⡗⠹⣿⢽⣿⣿⣛⣙⣛⣤⣤⣾⣿⣷⣿⣿⣙⣀⠀⠀⢀⣀⣀⣀⣀⠀⡉⠉⠉⠉⠀⢸⣿⡟⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣶⣶⠀⣶⣶⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡿⣩⣿⣿⣶⣾⣿⣾⣶⡌⣿⣿⣽⣿⣿⠟⠉⣁⣀⣀⣉⡁⠀⠀⠀⠀⠀⠈⠁⣀⣤⣾
⡆⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣮⣀⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣿⣿⣧⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡄⠀⣿⣿⡇⢀⣿⣿⡷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣯⣀⣀⣀⣀⣀⣀⡁⣠⣶⣶⣦⣤⣶⡿⠟⠋⠁
⣼⡆⠀⠀⣠⣶⣾⣯⡀⠀⠈⠉⠉⠛⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⢛⡋⢸⣿⡟⣿⣿⣀⣿⣿⣤⣤⣦⣤⣤⣿⣿⣷⣿⣿⣿⣇⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⡠⠆⠀
⣿⡟⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣾⣿⣿⣿⣿⣿⡟⢃⣸⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣟⣿⣿⣿⣏⣡⣿⣿⣇⣿⣿⣗⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣀⣛⣻⣿⣿⣿⣿⠛⣁⠀⢀⣀⣀⣀⣀⣠⣴⣾
⣿⡇⠀⢸⣿⣿⡟⠛⠃⠀⠀⠀⠰⠐⠛⢿⣾⣛⠛⠀⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠙⣻⣿⠈⠛⠛⠛⣻⣿⣿⣿⡟⠃⢻⣻⠟⠃⠈⠛⣿⣿⣿⣿⣛⣛⣠⡟⠛⠈⠻⣿⡛⠛⠛⡛⠛⠃⣼⣿⣿⡿⠿⠿⠟⠛⠋⠁⣉
⣿⡇⠀⢸⣿⡿⠀⠐⠀⠀⠀⠠⣷⡀⠀⠀⠘⠻⢿⣿⣏⣉⣙⠻⠛⠉⠀⠀⣀⣠⣾⣿⣏⠀⠀⠀⣀⣿⠿⣿⣿⡗⠲⣤⣤⠐⠒⠒⠛⢉⣿⣿⠏⣿⣿⣿⣧⣄⣀⣤⣴⣿⣤⣤⣀⣀⠘⠛⣉⠀⠀⠀⠀⠀⠀⡠⠞⠁
⣿⣿⠷⣾⣿⢷⠖⠲⠲⠶⡶⠀⠛⢿⣦⣄⡀⠀⠀⢩⣿⣿⣿⣿⡿⠛⠛⠋⠉⠉⠀⠈⣿⡆⢀⡞⠉⠀⣦⣾⣿⡧⠀⢬⣥⠀⠴⢶⣶⣾⣿⣿⣾⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⢸⣿⠀⠀⠀⠀⠀⢀⣀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⢿⣿⠟⠁⠀⠀⠀⠘⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⣾⠃⠀⠀⠀⠀⠀⠀⡿⠁⠉⢿⣷⣦⣀⣀⣠⣴⣿⣿⡟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⣸⡇⠈⠀⡄⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⢀⣠⣾⣿⣧⣄⣴⣶⣾⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠛⠋⠉⠙⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀
⢀⣿⣿⠟⠛⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢠⡟⣽⡁⠀⠀⠙⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠻⠋⣷⣼⠇⠀⠀⠀
⠟⠛⣧⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣄⣀⣤⣾⠟⠙⣿⣇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣠⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠨⠦⠿⠾⠛⠛⠉⠁⠀⣀⣴⣿⣿⠀⠀⠀⠀
⠀⠀⣿⣤⣀⡤⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣩⣿⣿⡇⠀⠀⢻⣿⣶⣶⣶⣿⡏⠀⢀⣀⣠⣄⣤⣴⣿⣿⣿⡿⢿⣿⣿⣿⡥⣶⡶⢶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⢠⣤⣠⣀⣀⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣾⣿⣿⠿⠀⠀⠀⣼⣿⣿⣿⣿⣦⠀⠀⠀⠀⣾⠈⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⠟⢛⢛⣏⡉⣽⣷⣾⣦⣻⣿⢿⣿⣾⣿⣻⢻⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⢎⣙⣿⣿⣿⣿⣿⣿⣿⠟⣡⡶⠀⠀⠀
⠻⠿⠁⠀⠀⠀⠀⠀⠁⠀⠈⢅⠀⢉⠂⠀⠀⠀⢿⡆⢾⡉⣻⣿⢻⣿⠿⣿⣿⣿⣦⣿⡿⠙⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⢹⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⡿⢿⣫⣤⠴⣿⣷⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⡶⠾⣿⣿⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋⣻⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡗⠻⣿⠟⣿⣿⣛⣙⣛⣤⣤⣴⣿⣷⣿⣿⣙⣀⠀⠀⢀⣀⣀⣀⣀⠀⢈⠊⠉⠉⠁⠀⣿⣿⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⣶⣶⠀⣶⣶⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⣿⣯⣿⣿⣶⣶⣿⣾⣷⡄⣾⣿⣿⣿⣾⡟⠋⢉⣀⣀⣉⡉⠀⠀⠀⠀⠈⠀⠉⢀⣠⣴
⣷⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣼⣁⣿⣿⣇⣿⣿⢸⣿⣿⣹⣿⣿⣿⣿⣷⣿⣿⣿⣷⠒⣿⣿⠙⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣄⣀⣀⣀⣀⣀⡈⢀⣴⣶⣶⣤⣴⣾⠿⠛⠉
⣠⣦⠀⠀⢀⣤⣶⣯⣍⠈⠉⠉⠉⠛⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⠛⡛⢹⣿⡏⣿⣿⡄⣿⣿⣤⣤⣤⣤⣤⣿⣿⣷⣶⣿⣿⡇⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠀⠠⠔⠀
⣿⣿⠀⠀⣾⣿⣿⣿⣿⠆⠀⠀⠀⠀⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⠗⣸⣿⣿⣿⣿⡿⣿⣿⣋⣿⣿⢻⣿⣿⣿⣏⣉⣿⣿⣇⣿⣿⣷⣿⣿⣿⣿⣿⢹⣿⣿⢛⣿⣇⣙⣛⣿⣿⣿⣿⠟⢁⡀⢀⣀⣀⣀⣀⣠⣤⣶
⣿⡏⠀⠀⣿⣿⣿⠛⠋⠀⠀⠀⢀⠒⠛⢻⣿⣟⡛⠀⢹⣿⣿⣿⣿⣿⣿⠛⠛⠛⠙⣻⣿⡏⠛⠛⠛⢋⣾⣿⣿⣿⠃⠸⣛⡟⠃⠈⠛⢻⣿⣿⣿⣟⣛⣀⡿⠛⠘⠛⢿⣟⠛⠛⠛⠛⠋⢠⣿⣿⣿⠿⠿⠿⠛⠛⠉⢉
⣿⣿⠀⠀⣿⣿⠇⠤⠀⠀⠀⠀⣿⣆⠀⠀⠈⠻⢿⣿⣿⣉⣉⠻⠟⠋⠁⠀⢀⣠⣴⣿⣿⠀⠀⠀⢀⣼⣿⣿⣿⡿⠒⢦⣬⡀⠒⠒⠚⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣠⣴⣾⣦⣤⣄⣀⠀⠛⣋⡁⠀⠀⠀⠀⠀⢀⠴⠋
⣿⣿⡿⣶⣿⣿⠶⠲⠶⠶⢶⠀⠀⢻⣷⣄⡀⠀⠀⠉⣿⣿⣿⣿⣿⠏⠛⠛⠉⠉⠁⠀⢻⡇⠀⡰⠋⠁⣶⣾⣿⣿⠠⢠⣭⡄⠠⠶⣶⣶⣿⣿⣷⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⣿⡅⠀⠀⠀⠀⠀⣀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠻⠿⣿⣿⡇⠀⠀⠀
⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⡿⠋⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣿⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣿⡟⠀⠀⠀⠀⠀⠀⢸⠏⠉⠹⣿⣶⣤⣀⣀⣴⣾⣿⣿⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⢠⡿⠀⠁⢠⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣀⣠⣼⣿⣷⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠛⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣿⠀⠀⠀
⠀⣸⣿⡿⠛⠻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⢫⡏⠀⠀⠈⠻⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠟⢽⣦⡟⠀⠀⠀
⡿⠛⠿⡅⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣆⣀⣀⣴⡾⠋⢹⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠽⠾⠿⠟⠛⠋⠉⠀⣀⣠⣾⣿⡇⠀⠀⠀
⠀⠀⢸⣧⣀⣠⠄⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡈⣽⣿⣿⠀⠀⠈⣿⣷⣶⣴⣾⣿⠇⢀⣀⣠⣄⣤⣤⣾⣿⣿⣿⢿⣿⣿⣿⣷⣶⡶⢶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⣤⣄⣄⣀⣰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣶⣿⣿⡿⠇⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⠉⠙⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⢛⣛⣏⡉⣽⣷⣶⣮⣻⣿⢿⣿⣾⣿⡈⣿⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠰⣹⣽⣿⣿⣿⣿⣿⣿⠟⢋⣴⠆⠀⠀
⠿⠿⠏⠀⠀⠀⠀⠀⠈⠉⢈⠩⡁⠈⡱⠀⠀⠀⠸⣶⢻⠉⣩⣿⢻⣿⠿⣿⣿⣿⣧⣿⡿⠙⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠙⠋⠛⠛⢿⢿⣿⣥⡴⢾⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⣷⣶⢿⣿⡇⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⣻⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡗⠺⣿⠟⢿⣿⣟⣙⣛⣤⣤⢴⣾⣿⣿⣿⣽⣀⡀⠀⠀⣀⣀⣀⣀⣀⢀⡈⠉⠉⠉⠀⢸⣿⡏⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⠀⣶⣶⠀⣽⣿⣿⣿⣿⣿⡿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⣟⣿⣿⣿⣶⣦⣾⣶⣿⣷⣶⣿⣿⣿⣷⣿⠋⠉⣀⣠⣀⣉⡁⠀⠀⠀⠀⠀⠈⠁⣀⣤
⣶⡆⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⣤⣎⣿⣿⣇⣿⣿⢸⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⣟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣯⣀⣀⣀⣀⣀⣀⡁⣠⣶⣶⣶⣴⣶⡿⠟⠉
⣃⣱⡄⠀⠀⣠⣤⣾⣭⡉⠉⠉⠉⠙⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⠛⢛⢻⣿⡏⣿⣿⣦⣿⣿⣀⣤⣤⣤⣤⣿⣿⣧⣶⣿⣿⡇⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣟⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠤⠂
⣿⣿⡟⠀⠰⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠛⣻⣿⣿⣏⣉⣿⣿⣇⣿⣿⣧⣿⣿⣿⣿⣿⢹⣿⣿⢜⣻⣿⣈⣛⣿⣿⣿⣿⣿⠛⣄⣀⣀⣀⣀⣀⣠⣤⣴
⣿⣿⡇⠀⢸⣿⣿⡿⠟⠃⠀⠀⠀⠐⠛⠛⢿⣟⡛⠈⠙⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠛⣿⣿⠛⠛⠛⠋⣰⣿⣿⣿⡇⠀⢛⣻⠛⠈⠛⠛⣿⣿⣿⣿⣛⣤⣻⡟⠘⠛⠻⣿⡛⠛⠛⡛⠋⢁⣼⣿⣿⠿⠿⠻⠛⠛⠉⠁
⢿⣿⡆⠀⢸⣿⣿⠁⠄⠀⠀⠀⢰⣷⡀⠀⠀⠙⠿⣿⣿⡏⣉⠙⠿⠛⠋⠀⠀⣀⣠⣾⣿⣏⠀⠀⠀⣠⣿⣿⣿⣿⠗⠶⣤⣥⠐⠒⠒⠛⢉⣿⣿⠋⣿⣿⣿⣧⣄⣀⣤⣶⣿⣤⣤⣀⣀⠈⢋⣁⠀⠀⠀⠀⠀⠀⠠⠞
⠸⣿⣿⣶⢿⣿⡧⠴⠶⠶⠶⡀⠀⠹⣿⣦⣀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠀⠘⣿⠄⢀⡞⠉⢀⣿⣿⣿⡇⠀⣬⣥⠀⠴⢶⣶⣾⣿⣿⣾⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⡀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠻⠿⣿⣿⡇⠀⠀
⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⡟⠁⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⡟⠀⠀⠀⠀⠀⠀⣸⠋⠉⠹⣿⣶⣤⣀⣠⣴⣿⣿⣿⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⢠⡯⠀⠁⠠⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣀⣠⣼⣿⣷⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠟⠛⠛⠛⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⠀⠀
⠀⠀⢸⣿⣿⠿⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣬⢙⡋⠀⠀⠉⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣻⣿⣿⠿⠟⠋⢽⣶⡟⠀⠀
⣶⡶⠿⢿⡁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣴⡾⠋⢻⣿⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠺⠾⠟⠛⠛⠉⠁⠀⣀⣤⣿⣿⡇⠀⠀
⡏⠀⠀⢸⣧⣀⣠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⠀⠀⠘⣿⣷⣦⣤⣾⣿⢀⣀⣠⣄⣤⣤⣴⣾⣿⣿⣿⣿⢿⣿⣿⣶⣶⢶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⣤⣄⣄⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣶⣾⣿⣿⠇⠀⠀⢠⣾⣿⣿⣿⣧⡀⠀⠀⠀⢰⠎⣛⣿⣿⣿⣷⣾⣿⣿⣿⣿⣟⣛⣟⡉⣽⣷⣶⣦⣻⣿⠟⣿⣿⣿⡀⢹⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠰⣙⣽⣿⣿⣿⣿⣿⣿⠟⢋⣴⠃⠀
⠻⠿⠿⠟⠁⠀⠀⠀⠀⠈⠉⢉⢩⡉⠉⡣⠀⠀⠀⠸⣿⠋⣩⣽⢻⣿⠿⣿⣿⣿⣿⣿⡿⠛⣿⣽⣷⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠁⠀⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣿⢿⣫⣥⡶⢾⣿⣿⣄
⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣦⣿⣾⠇⠀⠀⠀⠀⢹⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠝⠿⢿⣿⣟⣛⣤⣤⢤⢶⣾⣿⣿⣿⣤⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⡈⠉⠉⠁⠀⢸⣿⡏⠛
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠀⣶⣶⠀⣴⣿⣿⣿⣿⣿⣿⢿⣿⣶⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⣿⣯⣿⣿⣶⣦⢀⣶⣶⣿⣶⣶⠹⣿⣿⣷⣿⠋⠉⣀⡠⢄⣈⡁⠀⠀⠀⠀⠀⠈⠁⣠
⣤⣶⣆⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣿⣿⣷⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣇⣿⣿⡏⣿⣿⣿⣿⣿⡀⢈⣿⣿⣧⣠⣤⣀⣀⣀⣀⡀⣠⣶⣶⣶⣶⣾⡿⠟
⠻⣏⣹⡄⠀⠀⢀⣤⣼⣭⡉⠉⠉⠉⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⠛⠛⢻⣿⡏⣿⣿⣷⣿⣿⣀⣀⣤⣤⣤⣿⣿⣇⣀⣿⣿⡿⣿⣿⡇⣿⣿⣇⣿⣿⣿⣿⣿⠇⢸⣿⣿⠛⣭⣿⣿⣿⣿⣿⣿⡿⣿⠿⠛⠋⠁⠀⠤
⢼⣿⣿⡿⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⣿⡇⢻⣿⣿⢾⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⠋⠙⣿⣿⣟⡉⣿⣿⣇⣿⣿⣧⣿⣿⠏⣿⣿⢹⣿⣿⢀⣜⣻⣿⣀⣛⣻⣿⣿⣿⣿⠋⣄⣀⣀⣀⣀⣀⣠⣤
⠀⣻⣿⡇⠀⢸⣿⣿⡿⠿⠋⠀⠀⠀⠛⠓⠘⣿⣟⡀⠙⠛⣿⣿⣿⣿⣿⣟⣛⠻⠛⠛⠋⣿⣿⠛⠛⠋⠀⣰⣿⣿⣿⡇⠛⢛⣻⠟⠛⠛⠛⣿⣿⣿⣿⣴⣛⣻⡟⠛⠛⠻⣿⡟⠛⠛⡛⠋⠁⣼⣿⣿⠿⠿⠻⠛⠛⠉
⣾⣿⣿⡇⠀⢸⣿⣿⠁⠠⠀⠀⠀⠠⣦⡀⠀⠈⠙⠿⣿⣶⡏⠙⠻⠿⠟⠋⠀⠀⣀⣠⣾⣿⣏⠀⠀⠀⣀⣿⣿⣿⣿⠗⠲⣦⣥⠐⠒⠒⠛⢉⣿⣿⠃⣿⣿⣿⣧⣄⣀⣤⣶⣿⣦⣤⣀⣀⠈⢋⣁⠀⠀⠀⠀⠀⠀⠠
⠑⠾⣿⣿⡿⢾⣿⡷⠶⠶⠶⠀⠀⠀⠹⣿⣦⣀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠗⠛⠛⠉⠉⠁⠘⣿⠄⢀⡞⠉⠀⣷⣿⣿⡇⠀⣬⣥⠀⠴⢶⣶⣾⣿⣿⣾⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⢿⣿⡟⠀⠀
⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⡿⠋⠀⠀⠀⠀⠹⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣿⣿⠁⠀⠀⠀⠀⠀⢠⡏⠉⠉⢿⣷⣦⣄⣀⣤⣾⣿⣿⠏⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢀⣾⠁⠈⠀⠄⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣀⣀⣤⣿⣿⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⢳⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣾⡇⠀
⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣝⣟⠁⠀⠈⠙⢿⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⣿⣿⢿⣿⣿⣿⡿⠿⠛⠩⣶⣾⠃⠀
⣤⣶⡾⠿⣏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣠⣶⠟⠙⣿⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠘⠶⠿⠛⠛⠋⠉⠀⢀⣠⣶⣿⣿⠀⠀
⣿⠉⠀⠀⣿⣀⣀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡃⠀⠀⢿⣿⣦⣤⣴⣿⣇⣀⣠⣄⣤⣤⡴⣶⣿⣿⣿⣿⠿⣿⣿⣷⣶⢶⣮⠟⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠠⣤⣠⣠⣤⣶⣾⣿⣿⣿⣿⣿⠀⠀
⣿⣷⣶⣶⣿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⡏⢙⣻⣿⣷⣾⣶⣿⣿⣿⣿⣿⣛⣟⡉⣽⣷⣶⣦⣻⣿⠿⣿⣿⣿⡀⢹⣿⣿⣷⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢎⣩⣿⣿⣿⣿⣿⣿⡿⠛⣡⡞⠀
⠛⢿⢿⡿⠋⠁⠀⠀⠀⠀⠉⠉⠙⣋⠉⠙⠄⠀⠀⠀⣿⡟⣩⣿⢻⡿⠿⣿⡿⣿⣿⣿⡿⠛⣿⣽⣷⣴⣿⣻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠁⠀⠀⠀⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⢻⠿⣿⣭⡴⠖⣿⣿⣧
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣥⣼⣷⣾⠀⠀⠀⠀⠸⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠟⠿⠿⣿⣽⣛⣤⣤⢤⠶⣶⣿⣿⣿⣦⣄⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠉⠉⠉⠀⠀⣿⣿⠙
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⠀⣶⣶⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⣟⣿⣿⣿⣶⣦⠀⣶⣶⣿⣷⣶⠙⢿⣷⣿⣾⡟⠉⢁⣀⠤⣄⣉⠀⠀⠀⠀⠀⠀⠉⣀
⣠⣴⣦⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣻⣿⣶⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⡟⣿⣿⡇⣿⣿⣿⣿⣿⢀⠀⣹⣿⣿⣤⣤⣄⣀⣀⣀⣀⢀⣴⣶⣶⣶⣶⡿⠟
⠟⢿⡉⣦⠀⠀⠀⣠⣤⣿⡋⠉⠉⠉⣿⣿⣿⣿⣿⢸⣿⣿⢺⣿⣿⠛⠻⢿⣿⡏⣿⣿⠻⣿⣿⣀⣀⣀⣤⣤⣿⣿⣇⡀⣿⣿⡿⣿⣿⣏⣿⣿⣇⣿⣿⣿⣿⣿⠸⠀⣿⣿⡟⢫⣽⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠠
⠤⣾⣿⣿⠇⠀⣼⣿⣿⣿⣿⡆⠀⠀⣿⡇⢻⣿⣿⢾⣿⣿⣸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠋⠉⣿⣿⣟⡏⣿⣿⣧⣿⣿⣇⣿⣿⠟⣿⣿⣿⣿⣿⢀⣀⣛⣿⣇⣘⣛⣿⣿⣿⣿⡟⢡⣀⣀⣀⣀⣀⣀⣤
⠀⠘⣿⣿⠀⠀⣻⣿⣿⡿⠟⠁⠀⠀⠛⠓⠈⢻⣿⣀⠙⠛⢻⣿⣿⣿⣿⣿⣛⡻⠟⠛⠋⢹⣿⡟⠛⠋⠀⢀⣻⣿⣿⣿⠛⠛⣻⡿⠛⠛⠛⢻⣿⣿⣿⣷⣛⡛⣼⠛⠛⠛⢿⣿⠛⠛⢻⠛⠉⢠⣿⣿⡿⠿⠟⠟⠛⠋
⣶⣾⣿⣿⠀⠀⣽⣿⡟⠀⠄⠀⠀⠀⣰⣆⠀⠀⠉⠻⣿⣶⣿⠙⠛⠿⠿⠛⠁⠀⠀⣀⣴⣿⣿⠁⠀⠀⠀⣸⣿⢿⣿⡿⠦⢤⣬⡄⠒⠒⠒⠋⣹⣿⡿⢹⣿⣿⣿⣤⣀⣠⣴⣶⣷⣤⣄⣀⡀⠙⣉⡀⠀⠀⠀⠀⠀⠀
⠘⠆⢿⣿⣿⢷⣿⣿⠷⠶⠶⠀⠀⠀⠘⢿⣶⣄⡀⠀⠀⠙⣻⣿⣿⣿⣶⠷⠾⠛⠛⠉⠉⠀⢻⣧⠀⣠⠟⠁⣶⣾⣿⣿⠀⢀⣩⡄⠠⠶⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣇⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠿⣿⣿⠂⠀
⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣿⡏⠀⠀⠀⠀⠀⠀⣼⠉⠈⠹⣿⣶⣤⣀⣠⣴⣿⣿⡿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢧⠀⠀⠀⠀⠀⣰⡏⠀⠁⠠⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣠⣾⣿⣷⣤⣴⣷⣾⣿⣿⣿⣿⣿⣿⠟⡆⠀
⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⠀
⠀⠀⠀⢹⣿⣿⠿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣬⣻⡋⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⣿⣿⡿⣿⣻⣿⣿⠿⠛⠋⣽⣾⡟⠀
⣤⣴⣶⠿⢿⠁⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣤⡾⠋⢻⣷⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣦⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠳⠿⠟⠛⠛⠉⠁⠀⣀⣴⣿⣿⡇⠀
⣿⡏⠁⠀⢸⣇⡀⣀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⠁⠀⠸⣿⣦⣤⣤⣾⣿⣀⣠⣄⣤⣤⡴⣶⣾⣿⣿⣿⠿⣿⣿⣿⣶⢶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀
⣿⣷⣶⣦⣾⣿⣿⡏⠀⠀⢀⣶⣿⣿⣿⣦⠀⠀⠀⠀⢸⣈⣻⣿⣿⣶⣷⣾⣿⣿⣟⣿⣟⣟⡉⣽⣷⣶⣦⣻⣿⢟⣿⣿⣿⡀⢹⣿⣿⣿⣾⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠰⣁⣽⣿⣿⣿⣿⣿⣿⠟⢉⣴⠃
⠻⠿⣿⣿⡟⠉⠁⠀⠀⠀⠘⠉⠙⢛⡉⠉⠣⠀⠀⠀⢾⣿⣩⣽⢻⡿⠿⣿⡿⢿⣿⣿⡿⠛⣿⣽⣷⣴⣿⣻⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⠁⠀⠀⠀⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⡿⢿⣯⣥⠶⢻⣿⣿
⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣦⣤⣿⣾⠇⠀⠀⠀⠸⣿⣾⣿⣾⣿⣷⣿⣷⣿⣿⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⣇⠸⣿⠟⠿⠿⣻⣿⣟⣤⣤⢤⠶⢶⣿⣿⣿⣷⣄⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⡈⠁⠀⠁⠀⣸⢿⡏
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣿⠁⣶⣶⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣹⣿⣿⣶⣦⠀⣶⣶⣿⣿⣶⠈⠻⣿⣿⣿⣿⠋⠉⣀⠤⠤⣀⡁⠀⠀⠀⠀⠀⠈⢀
⣀⣠⣴⡄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣬⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣛⣿⣷⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⡷⣿⣿⡇⣿⣿⣿⣿⣿⠘⡀⢈⣿⣿⣧⣤⣤⣀⣀⣀⣀⡀⣤⣶⣶⣶⣶⣾⠿
⡿⢻⡛⢱⡄⠀⠀⢀⣠⣬⣟⠉⠉⠉⣿⣿⣿⣿⣿⢸⣿⣿⢺⣿⣿⠛⠛⢻⣿⡏⣿⣿⠙⣿⣿⠀⣀⣀⣠⣤⣿⣿⣇⣀⣿⣿⣿⣿⣿⣇⣿⣿⡇⣿⣿⣿⣿⣿⠸⠇⢸⣿⣟⠋⣭⣿⣿⣿⣿⣿⣿⡿⡿⠟⠛⠋⠁⠀
⣤⢼⣿⣿⡿⠀⢠⣿⣿⣿⣿⣷⠀⠀⣿⡇⢻⣿⣿⠻⣿⣿⣼⣿⣿⣿⣿⣾⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⠋⠉⣿⣿⣿⣟⣿⣿⣧⣿⣿⣇⣿⣿⠗⣿⣿⣿⣿⣿⢀⣀⣈⣻⣿⣀⣛⣻⣿⣿⣿⣿⠋⣤⣀⣀⣀⣀⣠⣤
⠀⠀⢻⣿⡇⠀⢘⣿⣿⡿⠿⠏⠀⠀⠛⠓⠘⠛⣿⣄⠙⠛⠻⣿⣿⣿⣿⣿⣟⣻⠟⠛⠛⠉⣿⣿⠛⠋⠀⠀⣛⣿⣿⣿⡟⠛⢻⣿⠟⠛⠛⠋⣿⣿⣿⣿⣛⣛⣸⡟⠛⠛⠻⣿⡟⠛⠻⡟⠋⠀⣼⣿⣿⠿⠟⠛⠛⠛
⢲⣶⣿⣿⡇⠀⢸⣿⣿⢃⡀⠀⠀⠀⢠⣶⡀⠀⠈⠙⢿⣷⣾⡏⠛⠻⠿⠟⠋⠀⠀⢀⣠⣾⣿⣏⠀⠀⠀⢀⣿⣿⣿⣿⠗⠤⣤⣅⠐⠒⠒⠚⢉⣿⣿⠋⣿⣿⣿⣧⣄⣀⣤⣶⣾⣦⣤⣀⣀⠈⢋⣁⠀⠀⠀⠀⠀⠀
⠀⠿⠺⣿⣿⣷⢾⣿⡿⠶⠶⠀⠀⠀⠀⠻⣷⣤⡀⠀⠀⠈⢛⣿⣿⣿⣷⡶⠶⠾⠛⠋⠉⠁⠘⣿⡄⢀⡴⠋⠠⣾⣼⣿⡇⠀⣈⣥⠀⠴⢶⣶⣾⣿⣿⣾⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⢿⣿⡇⠀
⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⡿⠋⠀⠀⠀⠀⢹⣿⢿⣿⡀⠀⠀⠀⠀⠀⢀⣿⣷⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣿⣿⠀⠀⠀⠀⠀⠀⢸⡏⠁⠉⢿⣷⣦⣤⣠⣴⣾⣿⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⡄⠀⠀⠀⠀⢀⣿⠀⠈⠀⠌⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣶⣀⣀⣼⣿⣿⣦⣤⣾⣶⣿⣿⣿⣿⣿⣿⡿⢳⠀
⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⡆
⠀⠀⠀⠈⣿⣿⡿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣨⢟⣟⠀⠀⠉⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢹⣷⣿⠀
⣠⣤⣴⡾⢿⡏⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⣀⣠⣾⠟⠹⣿⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠚⠾⠿⠛⠛⠉⠀⠀⢀⣤⣾⣿⣿⠀
⣿⣿⠉⠀⠀⣿⣀⢀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⡃⠀⠀⣿⣷⣤⣤⣴⣿⣇⣠⣄⣤⣤⡴⣶⣾⣿⣿⣿⡿⣿⣿⣿⣷⣶⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⣠⣤⣶⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣶⣦⣴⣿⣿⣿⠁⠀⠀⣰⣾⣿⣿⣷⡄⠀⠀⠀⠀⣇⣙⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣟⡉⣽⣷⣶⣦⣻⣿⠟⣿⣿⣿⣄⢹⣿⣿⣿⣿⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢌⣼⣿⣿⣿⣿⣿⣿⡿⠋⣡⡞
⠛⠿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠋⠉⠛⡋⠉⠛⠄⠀⠀⢸⣿⣩⣭⢫⣿⠿⣿⡿⢿⣿⣿⡿⠛⣿⣿⣷⣴⣿⡻⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣛⠿⣿⣥⡴⠞⣿⣿
⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⢶⣤⣼⣶⡾⠀⠀⠀⠸⡟⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣧⠀⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠟⠿⠿⣛⣿⣿⣥⣤⢤⠶⠶⣿⣿⣿⣷⣦⣄⣀⡀⠀⢀⣀⣠⣤⣀⣀⣀⠉⠀⠀⠀⠀⡿⣿
⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣶⣾⡇⣶⣶⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣧⣰⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣶⣿⣾⣷⠀⠙⢿⣿⣿⣿⡟⠉⠁⡤⠤⠤⣈⠀⠀⠀⠀⠀⠀⠁
⣄⣀⣤⣤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣙⣻⣥⣿⣿⣿⣷⠒⣿⣿⠉⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⢿⢃⠀⣹⣿⣿⣤⣤⣄⣀⣀⣠⣄⢠⣶⣶⣶⣶⣶⡿
⣿⠟⢟⢛⣧⠀⠀⠀⣀⣠⣿⡋⠉⠛⣿⣿⣿⣿⣿⣾⣿⣿⢺⣿⣿⠛⠛⢻⣿⡿⣿⣿⠙⣿⣿⡄⣀⣀⣀⣤⣿⣿⣇⣀⣿⣿⣷⣿⣿⡇⣿⣿⡏⣿⣿⣿⣿⣿⠸⠿⠀⣿⣿⡟⢩⣽⣿⣿⣿⣿⣿⣿⢿⠿⠛⠛⠁⠀
⣯⣠⣾⣾⣿⡇⠀⣴⣿⣿⣿⣿⡄⠀⣿⡇⢻⣿⣿⠻⣿⣿⣼⣿⣿⣿⣾⣿⣿⡿⢿⣿⣧⣿⣿⣿⣿⣿⠛⠉⣿⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⠷⣿⣿⣿⣿⣿⠀⣀⣐⣙⣿⣇⣘⣛⣿⣿⣿⣿⠟⢡⣄⣀⣀⣀⣠⣤
⠁⠀⠘⣿⣿⠀⠀⣿⣿⣿⡿⠿⠁⠀⠛⠓⡘⠛⢻⣧⡙⠛⠛⢻⣿⣿⣿⣿⣿⣻⡟⠛⠛⠋⢻⣿⡟⠋⠀⠀⢛⣻⣿⣿⣿⠛⠻⣿⡿⠛⠛⠋⢸⣿⣿⣿⣟⣛⣐⣿⠛⠛⠛⠻⣿⠛⠻⠿⠙⠁⣠⣿⣿⡿⠿⠛⠛⠋
⠲⣶⣾⣿⣿⠀⠀⣿⣿⡟⣀⠀⠀⠀⠀⣼⣆⠀⠀⠉⠿⣷⣶⣯⠛⠛⠿⠿⠟⠃⠀⠀⣀⣴⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠢⢤⣬⡄⠒⠒⠒⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣠⣴⣶⣷⣤⣤⣀⡀⠙⣉⡀⠀⠀⠀⠀⠀
⠀⠞⢷⣿⣿⣷⠆⣾⣿⠷⠶⠀⠄⠀⠀⠘⢿⣦⣀⠀⠀⠀⠙⣻⣿⣿⣿⣶⠶⠲⠞⠛⠉⠉⠈⢻⣧⠀⣠⠟⠁⣼⣷⣿⣿⠀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣧⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠛⠛⠛⠻⢿⣿⡇
⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠈⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⡿⣿⡟⠁⠀⠀⠀⠀⢻⣿⢿⣧⡀⠀⠀⠀⠀⠀⢀⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣷⡟⠀⠀⠀⠀⠀⠀⢸⠏⡀⠙⢿⣷⣦⣤⣤⣴⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡵⡀⠀⠀⠀⠀⢠⣿⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿⡆
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣶⣀⣠⣼⣿⣿⣦⣤⣿⣾⣿⣿⣿⣿⣿⣿⡟⣷
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠉⣿⣿⣿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⢛⡛⠀⠀⠉⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡿⢿⣿⡿⣿⣻⣿⣿⡿⠟⠛⢹⣷⡿
⣀⣀⣤⣤⣶⣿⡏⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⢀⣠⣶⠟⢸⣿⡄⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠚⠾⠿⠛⠉⠉⠀⠀⢀⣴⣾⣿⣷
⣿⣿⣿⠋⠀⠀⣷⡀⠀⣀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠃⠀⠀⣿⣷⣤⣤⣴⣿⣧⣄⣤⣤⡴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⡿
⢻⣿⣿⣶⣦⣴⣿⣿⣿⠁⠀⠀⣰⣶⣿⣷⣶⡀⠀⠀⠀⢀⣇⣛⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡉⣽⣷⣶⣦⣻⣿⠟⢿⣾⣿⣿⣽⣿⣿⣿⣿⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣨⣿⣿⣿⣿⣿⣿⠟⠋⣴
⡘⠻⠿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠛⠛⠛⡋⠉⠳⠀⠀⢸⠹⣿⣭⢩⣿⠿⣿⡿⢿⣿⣿⣿⡟⣿⣿⣷⣴⣿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣛⣿⣿⣥⡶⠞⣿
⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣤⣽⣶⡾⠀⠀⠸⡆⣾⣿⣾⣿⣷⣿⣷⣾⣿⣿⣿⠁⣿⣯⣿⡉⢻⣿⣿⡇⠹⣿⠝⠿⠿⣻⣙⣿⣿⣥⢤⠶⠖⠛⣿⣿⣷⣶⣦⣄⣄⠀⠀⣀⣀⣤⣤⣀⣀⣀⠁⠀⠀⠀⢀⠿
⣷⡶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠙⣷⣶⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣷⣦⠀⣶⣶⣼⣶⣿⣿⡄⠙⢿⣿⣿⣿⡏⠉⠠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀
⠯⣀⢀⣠⣤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣷⣿⣿⢸⣿⣿⢸⣿⣿⣜⣻⣭⣿⣿⣿⣷⠖⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡏⣿⣿⡟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢁⠀⣹⣿⣿⣤⣤⣄⣀⣠⣤⣄⣠⣶⣶⣶⣶⣶
⣴⣿⡿⣟⠛⣄⠀⠀⠀⢀⣀⣟⡛⠛⣿⣿⣿⣿⣿⣾⣿⣿⢺⣿⣿⠙⠛⢻⣿⡿⣿⣿⠉⣿⣿⣦⣀⣀⣀⣀⣿⣿⣧⣄⣿⣿⣷⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠙⡿⠿⠀⣿⣿⡛⢩⣽⣿⣿⣿⣿⣿⣿⢿⠿⠛⠋⠁
⣿⣏⣀⣼⣽⣿⡆⠀⣼⣿⣿⣿⣿⡄⣿⡇⢻⣿⣿⣹⣿⣿⣼⣿⡿⣼⣶⣾⣿⣿⢿⣿⣧⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⣧⣿⣿⢹⣿⣿⢀⣀⣀⣐⣙⣿⣇⣘⣻⣿⣿⣿⣿⠟⢡⣀⣀⣀⣤⣤
⣿⠁⠀⠘⣿⣿⠀⠀⣿⣿⣿⣿⠿⠁⠛⠃⠘⠛⠛⢻⣿⡛⠛⠛⣹⣿⣿⣿⣿⣿⣟⣛⠛⠛⠛⢻⣿⡏⠀⠀⠛⢛⣻⣿⣿⣿⠃⠸⣿⡿⠛⠋⠀⢻⣿⣿⣿⣛⣘⣛⣿⠛⠛⠛⠻⣿⠃⠻⠿⠉⠁⣠⣿⣿⠿⠿⠛⠛
⣿⠶⣶⣶⣿⣿⠀⠀⣿⣿⡟⢀⠀⠀⠀⠀⣼⡅⠀⠀⠙⠿⣷⣶⣿⠛⠛⠿⡿⠟⠃⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⣸⡿⢿⣿⡿⠲⢤⣬⡀⠒⠒⠒⠋⣹⣿⡿⢹⣿⣿⣿⣤⣀⣤⣴⣶⣷⣤⣤⣀⣀⠉⣁⡀⠀⠀⠀⠀
⡿⠆⠺⣿⢿⣿⣷⠶⣿⣿⢷⠀⠀⠄⠀⢀⠙⢻⣦⣀⠀⠀⠀⠙⣻⣿⣿⣷⣶⠶⠶⠖⠛⠛⠋⠈⢻⡇⠀⣠⠞⠁⣴⣽⣿⣿⠀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣧⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠛⠛⠛⠻⢿⣿⡇
⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠈⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⡿⣿⡟⠁⠀⠀⠀⠀⢻⣿⢿⣧⡀⠀⠀⠀⠀⠀⢀⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣷⡟⠀⠀⠀⠀⠀⠀⢸⠏⡀⠙⢿⣷⣦⣤⣤⣴⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡵⡀⠀⠀⠀⠀⣠⣿⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿⡆
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣶⣀⣠⣼⣿⣿⣦⣤⣿⣾⣿⣿⣿⣿⣿⣿⡟⣷
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠉⣿⣿⣿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⢛⡛⠀⠀⠉⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⡿⣿⣻⣿⣿⡿⠟⠛⢹⣷⡿
⣀⣀⣤⣤⣶⣿⡏⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⢀⣠⣶⠟⢺⣿⡄⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⠴⠦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠚⠾⠿⠛⠉⠉⠀⠀⢀⣴⣾⣿⣷
⣿⣿⣿⠋⠀⠀⣷⡀⠀⣀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠃⠀⠀⣿⣷⣤⣤⣴⣿⣧⣄⣤⣤⡴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠟⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⣠⣴⣶⣿⣿⣿⣿⣿⡿
⢻⣿⣿⣶⣦⣴⣿⣿⣿⠁⠀⠀⣴⣶⣿⣿⣶⡀⠀⠀⠀⢀⣇⣛⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡉⣽⣷⣶⣦⣻⣿⠟⢿⣾⣿⣿⣹⣿⣿⣿⣿⡿⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣬⣿⣿⣿⣿⣿⣿⠟⠋⣴
⡘⠻⠿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠛⠛⠛⡋⠉⠳⠀⠀⢺⠹⣿⣭⢩⣿⠿⣿⡿⢿⣿⣿⣿⡟⣿⣿⣷⣴⣿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣻⣿⣿⣥⡶⠞⣿
⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣽⣶⡾⠀⠀⠸⡆⣾⣿⣾⣿⣷⣿⣷⣾⣿⣿⣿⠁⣿⣯⣿⡉⢻⣿⣿⡇⠹⣿⠝⠿⠿⣻⣙⣿⣿⣥⢤⠶⠖⠛⣿⣿⣷⣶⣦⣄⣄⡀⠀⣀⣀⣤⣤⣀⣀⣀⠉⠀⠀⠀⢀⠿
⣷⡶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠙⣷⣶⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣷⣦⠀⣶⣶⣼⣷⣿⣿⡄⠙⢿⣿⣿⣿⡟⠉⠀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀
⠿⣄⢀⣠⣤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣧⣿⣿⢸⣿⣿⢸⣿⣿⣘⣛⣭⣿⣿⣿⣷⠖⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡏⣿⣿⡟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢁⠀⣹⣿⣿⣤⣤⣄⣀⣠⣤⣄⣠⣶⣶⣶⣶⣶
⣴⣿⡿⣟⠛⣄⠀⠀⠀⢀⣠⣿⡛⠛⣿⣿⣿⣿⣿⣾⣿⣿⢺⣿⣿⠙⠓⢻⣿⡿⣿⣿⠉⣿⣿⣦⣀⣀⣀⣀⣿⣿⣧⣄⣿⣿⣷⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠙⡿⠿⠀⣿⣿⡛⢩⣽⣿⣿⣿⣿⣿⣿⢿⠿⠛⠋⠁
⣿⣏⣀⣼⣽⣿⡆⠀⣼⣿⣿⣿⣿⡄⣿⡇⢻⣿⣿⣹⣿⣿⣼⣿⡿⣿⣶⣾⣿⣿⢿⣿⣧⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⣧⣿⣿⢹⣿⣿⢀⣀⣀⣐⣙⣿⣇⣘⣻⣿⣿⣿⣿⠟⢡⣄⣀⣀⣤⣤
⣿⠁⠀⠘⣿⣿⠀⠀⣿⣿⣿⣿⠿⠁⠛⠃⠘⠛⠛⢻⣿⡛⠛⠛⣹⣿⣿⣿⣿⣿⣞⣛⠛⠛⠛⢻⣿⡏⠀⠀⠛⢛⣻⣿⣿⣿⠃⠸⣿⡟⠛⠋⠀⢻⣿⣿⣿⣛⣘⣛⣿⠛⠛⠛⠻⣿⠃⠻⠿⠉⠁⣠⣿⣿⡿⠿⠛⠛
⣿⠶⣶⣶⣿⣿⠀⠀⣿⣿⡟⢀⠀⠀⠀⠀⢼⡄⠀⠀⠙⠿⣷⣶⣯⠛⠛⠿⠿⠟⠃⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⣸⣿⢿⣿⡿⠲⢤⣬⡀⠒⠒⠒⠋⣹⣿⡿⢹⣿⣿⣿⣤⣀⣤⣴⣶⣷⣤⣤⣀⣀⠉⣁⡀⠀⠀⠀⠀
⡿⠆⠺⣿⢿⣿⣷⠶⣿⣿⢧⠀⠀⠄⠀⠀⠙⢿⣦⣀⠀⠀⠀⠙⣻⣿⣿⣷⣶⠶⠶⠖⠛⠛⠋⠈⢻⣇⠀⣠⠞⠁⣶⣽⣿⣿⠀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣧⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⠛⠛⢿⣿
⢀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⢠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣿⡇⠀⠀⠀⠀⠀⠀⣼⠋⡀⠙⢿⣷⣦⣤⣤⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⣰⡟⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣀⣠⣾⣿⣿⣦⣴⣿⣾⣿⣿⣿⣿⣿⣿⡏
⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢘⢛⡟⠀⠈⠙⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⡿⠿⣿⣻⣿⣿⠿⠋⠋⢸⣷
⣀⣀⣀⣀⣤⣴⣿⡏⠀⠀⠙⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⣀⣶⠟⢺⣿⠀⠀⠀⠀⢹⡗⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣴⠦⠾⣖⣛⡋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠞⠟⠛⠉⠁⠀⢀⣠⣴⣾⣿
⣿⣿⣿⣿⠋⠀⠀⣧⠀⠀⣀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⠃⠀⠘⣿⣧⣤⣤⣴⣿⣇⣤⣤⡴⣶⣶⣓⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿
⢈⣿⣿⣿⣤⣄⣤⣿⣿⣿⠁⠀⠀⣰⣶⣶⣶⣦⡀⠀⠀⠀⣀⣇⣻⣿⣿⣷⣶⣶⣿⣿⣿⣿⡿⣽⣷⣶⣦⣻⣿⠟⢿⣿⣿⡻⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣎⣼⣿⣿⣿⣿⣿⣿⠟⠉
⠆⠘⠻⣿⣿⣿⣿⠟⠉⠁⠀⠀⠘⠛⠛⠛⡛⠙⢣⠀⢸⠉⣹⣯⢩⣿⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣻⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣇⢸⡇⠀⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣛⣟⣿⣵⠶⠛
⣀⠀⠀⢀⠃⠈⠁⠀⠀⠀⠀⠀⠀⣠⣤⣤⣹⣦⣾⠀⠸⡆⣾⣿⣾⣿⣷⣿⣷⣾⣿⣿⣿⡿⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣻⣻⣯⣿⢤⠶⠖⠛⠛⣿⣿⢷⣶⣦⣄⣄⡀⠀⣀⣠⣤⣤⣄⣀⣀⠀⠀⠀⠀⢀
⣿⣷⡶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣶⣿⠉⣿⣷⠀⣴⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣿⣧⠀⣶⣶⡄⣶⣶⣿⣿⡄⠙⢿⣿⣿⣿⡏⠉⠠⠤⠤⠤⣀⠀⠀⠀⠀⠀
⠿⢿⣁⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣻⣯⣿⣿⣿⣿⠷⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣷⣿⣿⣿⣿⣿⢀⠀⣻⣿⣿⣤⣤⣤⣤⣤⣤⣄⣠⣶⣿⣿⣶
⢀⣰⣿⡿⣟⠟⣄⠀⠀⠀⢀⣀⣿⠛⣿⣿⣿⣿⣿⣾⣿⣿⢻⣿⣿⠈⠙⢻⣿⡿⣿⣿⠉⣿⣿⢷⣦⣀⡀⣀⣿⣿⣧⣤⣿⣿⣇⣿⣿⡿⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⡿⠿⠀⣿⣿⡛⣩⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉
⣿⣿⣏⣀⣼⣾⣿⡆⠀⣰⣿⣿⣿⣿⣿⡇⢻⣿⣿⠸⣿⣿⣾⣿⣿⠀⣶⣾⣿⣿⣿⣿⣇⣿⣿⣶⣿⣿⠿⠟⣿⣿⡏⢻⣿⣿⡏⣿⣿⣧⣿⣿⣇⣿⣿⢻⣿⣿⣟⣁⣀⣀⣔⣙⣿⣇⡙⢿⣿⣿⣿⣿⠟⣡⣄⣀⣠⣤
⣿⣟⠁⠀⠹⣿⣿⠁⠀⣻⣿⣿⣿⡿⠛⠃⠘⠛⠛⠀⢿⣿⡛⠛⠋⣿⣿⣿⣿⣿⣿⣛⣻⠿⠟⠛⢻⣿⡇⠀⠛⠛⢃⣾⣿⣿⣿⠈⠛⣿⡿⠋⠀⠛⢻⣿⣿⣿⣟⣛⣛⣿⠛⠛⠛⠻⣧⠀⠹⠿⠉⠁⣠⣿⣿⠿⠟⠛
⣿⣿⠶⣤⣴⣿⣿⠀⠀⣿⣿⡟⢀⡀⠀⠀⠀⢸⡄⠀⠈⠙⢿⣶⣦⣞⠛⠛⠿⡿⠟⠋⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠶⢤⣭⡀⠒⠒⠚⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣤⣴⣶⣷⣤⣤⣀⣀⠉⣁⡀⠀⠀⠀
⣿⣿⠲⣿⠟⢿⣿⣶⠶⣿⣿⣃⠀⠤⠄⠀⠀⡙⣿⣦⡀⠀⠀⠈⠛⢿⣾⣿⣶⣶⠶⠶⠶⠛⠛⠋⠈⢻⡇⠀⣠⠞⠁⣶⣼⣿⣿⠀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣧⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠛⠻⣿
⠀⢀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⡿⢿⡿⠀⠀⠀⠀⠀⠀⠀⢻
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⡿⠋⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣼⣿⠁⠀⠀⠀⠀⠀⢠⡟⢀⠈⠻⣿⣶⣦⣤⣴⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⢀⣼⠇⠀⠀⠆⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆⣠⣴⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡄⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡛⣻⠃⠀⠉⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⢿⣿⢿⢿⣿⣿⣿⡿⠛⠙⠁⣿
⡃⠀⠀⢀⣠⣤⣾⣿⠋⠀⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⢀⣠⡾⠓⣿⡆⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣴⡦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⠻⠛⠋⠉⠁⠀⣀⣤⣾⣿
⣻⣿⣿⣿⡟⠋⠀⢸⡆⠀⠀⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⡟⠀⠀⢻⣿⣤⣤⣤⣾⣿⣤⣤⡴⣶⣶⡒⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣤⣶⣾⣿⣿⣿⣿
⠀⣹⣿⣿⣧⣤⣀⣼⣿⣷⡏⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⣀⣸⣘⣿⣿⣷⣶⣶⣾⣿⣿⣟⣿⣿⣷⣶⣦⣻⣿⠟⢿⣿⣿⡚⢿⣿⣿⣷⣿⡿⣿⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣡⣿⣿⣿⣿⣿⣿⡿⠋
⠰⠀⠻⢿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠚⠛⠛⠟⠛⠛⠄⢺⠉⣩⣿⣭⣧⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣻⣿⣾⣿⣯⣿⣷⣾⣿⣿⣿⣿⡀⣿⠀⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣻⣻⣯⣶⠞
⣄⡀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⣄⣈⣶⣴⡇⠸⡆⣾⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣛⣟⣾⣽⣿⠶⠖⠛⠛⢹⣿⣿⣶⣶⣤⣠⣀⠀⢀⣠⣤⡤⢤⣀⣀⡀⠀⠀⠀⠀
⣿⣿⣶⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠉⣾⣿⠀⣴⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣾⣯⡄⣶⣶⡄⣶⣾⣿⣿⣧⠈⠻⣿⣿⣿⣿⠉⠁⠤⠤⠤⠤⡀⠀⠀⠀⠀
⠿⢿⣏⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣻⣮⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⣿⣿⣿⡟⣿⣿⣧⣿⣿⣿⣿⣿⡏⡀⢈⣿⣿⣧⣤⣤⣤⣤⣤⣤⣄⣴⣿⣿⣿
⠀⢀⣼⣿⢿⡿⢣⡀⠀⠀⠀⣀⣸⡿⣿⣿⣿⣿⣿⢾⣿⣿⢻⣿⣿⠈⠈⢻⣿⡿⣿⣿⠟⣿⣿⠳⣶⣄⡀⢀⣿⣿⣧⣤⣿⣿⣇⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⢸⣿⣟⠋⣼⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉
⣿⣿⣿⣇⣀⣷⣾⣷⠀⢀⣾⣿⣿⣿⣿⡇⢻⣿⣿⠸⣿⣿⣾⣿⣿⡀⢰⣾⣿⣿⣿⣿⡇⣿⣿⣤⣿⣿⣿⠿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣧⣿⣿⣇⣿⣿⢾⣿⣿⣿⣋⣀⣀⣀⣊⣻⣿⡀⠻⢿⣿⣿⣿⡿⠋⣤⣀⣠⣤
⢿⣿⡟⠉⠈⢻⣿⡟⠀⢸⣿⣿⣿⣿⠟⠃⠘⠛⠛⠀⠙⣿⣟⠛⠙⠛⣿⣿⣿⣿⣿⣟⣛⡿⠟⠛⠛⣿⣿⠀⠛⠛⠃⣰⣿⣿⣿⡏⠛⢟⣿⠏⠀⠛⠛⣿⣿⣿⣿⣛⣛⣻⡟⠛⠛⠛⢿⣆⠈⠛⠏⠉⢀⣼⣿⡿⠿⠛
⣿⣿⣿⣤⣤⣼⣿⡇⠀⠘⣿⣿⡏⢀⠀⠀⠀⢀⣼⠀⠀⠉⠻⣷⣶⣴⡟⠛⠻⣿⠿⠟⠁⠀⠀⣠⣾⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠷⠤⣤⣥⠐⠒⠒⠚⢉⣿⣿⠋⣿⣿⣿⣧⣄⣠⣴⣶⣾⣶⣤⣤⣀⡈⢉⣠⠀⠀⠀
⣿⣿⡷⣾⠿⢿⣿⣿⡶⠶⣿⣿⢀⠁⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠉⠻⣷⣿⣷⣶⣶⠶⠶⠞⠛⠛⠉⠙⣿⡄⢀⡴⠋⠁⣧⣿⣿⡇⠀⣈⣥⠀⠤⢶⣶⣾⣿⣿⣾⣧⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠁⢸⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⠉⠛⠛⢿
⠀⠀⣀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⠟⠛⠛⢿⡿⠿⣟⡃⠀⠀⠀⠀⠀⠀⢸
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⣿⠟⠁⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣸
⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⣾⡇⠀⠀⠀⠀⠀⠀⣾⠁⡀⠙⢿⣿⣦⣤⣤⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⣰⡏⠁⠀⠰⢈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⣤⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⣘⢛⡟⠀⠉⠙⢿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⡿⣿⣯⣿⣿⠻⠋⠋⢸
⢣⠀⠀⠀⣀⣠⣼⣿⡟⠁⠈⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⣠⣴⠟⢾⣷⠀⠀⠀⠀⣻⡗⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⠾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠞⠟⠛⠉⠁⠀⢀⣠⣴⣿
⠛⣿⣿⣿⣿⠟⠁⠉⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠃⠀⠸⣿⣦⣤⣤⣴⣿⣥⣤⡴⣶⣶⡒⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣤⣤⣴⣶⣿⣿⣿⣿
⠀⢙⢿⣿⣿⣤⣄⣠⣿⣷⣾⠁⠀⠀⣠⣶⣶⣶⣤⡀⠀⠀⣀⣀⣗⣻⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣻⣿⠟⢿⣿⣿⡈⢿⣿⣿⣷⣾⡿⢿⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⣼⣿⣿⣿⣿⣿⣿⠟
⠀⠄⠘⠿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠰⠟⠛⠿⠛⠛⢧⢺⠉⣩⣽⣯⣧⠘⣿⡿⣿⣿⣿⡿⣿⣿⣿⣷⣴⣿⣻⣿⣾⣿⣯⣿⡷⣾⣿⣿⣿⣿⣇⢼⡇⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣛⣟⣫⣵⡶
⣤⡀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⣀⣳⣤⣾⠸⡆⣾⣿⣿⣿⣷⣿⣧⣼⣿⣿⣿⣿⣿⣯⣿⡍⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣛⣿⣼⣯⣿⠶⠖⠛⠛⠙⣿⣿⣷⣶⣦⣤⣄⡀⠀⣀⣤⣤⠤⣄⣀⣀⠁⠀⠀⠀
⣿⣿⣧⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠋⣾⣿⡇⣴⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⡿⣶⣯⣵⣶⣶⡄⣶⣶⣿⣿⣿⡄⠙⢿⣿⣿⣿⠏⠉⠠⠤⠤⠤⣄⠀⠀⠀⠀
⠿⢿⣟⡁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣫⣤⣿⣿⣿⣿⣾⣿⣿⠉⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⣇⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣷⣀⠀⣽⣿⣿⣤⣤⣤⣤⣤⣤⣄⣠⣾⣿⣿
⠀⠀⣠⣿⡿⡿⠿⡄⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⢾⣿⣿⢿⣿⣿⠈⠀⢻⣿⡿⣿⣿⡿⣿⣿⠓⣶⣦⡀⠀⣿⣿⣧⣤⣿⣿⣇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣿⣿⡛⣠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋
⣿⣿⣿⣟⠀⣹⣶⣿⡆⠀⣰⣿⣿⣿⣿⡇⢻⣿⣿⠸⣿⣿⣿⣿⣿⣀⠀⣾⣿⡿⣿⣿⡧⣿⣿⣤⣿⣿⣿⠿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⢼⣿⣿⣿⣟⣁⣀⣀⣔⣙⣿⣇⠙⠿⣿⣿⣿⣿⠟⢡⣄⣠⣤
⠻⣿⣿⠋⠉⠹⣿⣿⠁⠀⣿⣿⣿⣿⣿⠃⠈⠛⠛⡀⠙⢿⣟⠛⠙⠛⣿⣿⣿⣿⣿⣿⣓⣿⡿⠟⠛⢻⣿⡇⠛⠛⠃⢀⣿⣿⣿⣿⠛⠻⣿⡿⠀⠛⠛⢸⣿⣿⣿⣛⣛⣛⣿⠛⠛⠛⠻⣧⡀⠙⠿⠉⠁⣰⣿⣿⠿⠟
⣾⣿⣿⣧⣤⣤⣿⣿⠀⠀⣿⣿⣿⠁⢀⠀⠀⠀⣼⡇⠀⠈⠛⢿⣶⣤⣿⠛⠿⣿⣿⠿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⢿⣿⡿⠦⢤⣭⡀⠒⠒⠚⠋⣹⣿⡟⢹⣿⣿⣿⣤⣀⣤⣶⣶⣷⣦⣤⣀⣀⠉⣁⡀⠀⠀
⣿⣿⣿⣾⠿⢿⢿⣿⣶⠶⣿⣿⠇⣉⣀⣀⠀⠀⣹⣿⣦⡀⠀⠀⠈⠛⣿⣾⣷⣶⣶⣶⠶⠶⠞⠛⠋⠉⢿⣇⠀⣠⠞⠉⣸⣽⣿⣿⡀⢀⣩⡄⠠⠴⣶⣶⣿⣿⣷⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠙⢻
⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⣿⠿⢟⣛⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡟⣿⡟⠁⠀⠀⠀⠀⠹⣿⣿⣿⣄⡀⠀⠀⠀⠀⢀
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣷⣿⠀⠀⠀⠀⠀⠀⢰⡇⢀⠈⠻⣿⣷⣦⣤⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⠀⠀⠀⠀⢀⣿⠀⠀⠀⠆⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣠⣼⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠇⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢈⡻⡻⠃⠈⠙⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⢿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁
⠻⠄⠀⠀⢀⣀⣠⣿⣿⠋⠀⠙⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⢀⣤⡿⠳⣿⡆⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣦⡾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠉⠀⢀⣀⣤⣿
⠛⢿⣿⣿⣿⡿⠋⠉⢹⡀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡏⠀⠀⢿⣷⣤⣤⣤⣾⣯⣤⡴⣶⣶⡒⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣴⣤⣤⣾⣿⣿⣿⣿
⠀⠘⠻⣿⣿⣧⣤⣀⣼⣿⣶⡏⠀⠀⢀⣴⣶⣶⣦⡄⠀⠀⣀⣀⣘⣸⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⣻⣿⠟⢿⣾⣿⡀⢻⣿⣿⣷⣾⣿⠻⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣡⣿⣿⣿⣿⣿⣿⡿
⠀⠠⠀⠿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠾⠛⠛⠿⠛⠻⣾⠉⣩⣭⣿⣷⠈⣿⡿⢿⣿⣿⣿⢿⣿⣿⣷⣴⣿⣻⣿⣾⣿⣯⣿⣷⢾⣿⣿⣿⣵⣿⡠⣿⣿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠿⣛⣧⣶
⣦⣄⠈⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⣄⣘⣦⣴⡽⡆⣾⣿⣾⣿⣿⣿⣷⣬⣿⣿⣷⣿⣿⣯⣿⡉⢻⣿⣿⡇⠸⣿⠟⠿⠿⣛⣛⣻⣧⣿⣽⠷⠖⠛⠛⠙⢲⣿⣿⣶⣶⣤⣤⣀⠀⣀⣠⣤⡤⠤⢄⣠⡀⠀⠀⠀
⣿⣿⣿⣴⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠛⣿⣿⢿⣴⣷⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧⣰⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣾⣩⣶⣶⡄⣶⣶⣿⣿⣿⣇⠈⠻⣿⣿⣿⡿⠉⠀⠤⠤⠤⠤⡀⠀⠀⠀
⠿⠿⣿⣋⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⣼⣿⣿⢸⣿⣿⣘⣋⣤⣿⣿⣿⣿⣾⣿⣿⠙⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣗⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⣧⣤⣤⣤⣤⣤⣤⣀⣴⣿⣿
⠀⠀⠀⣼⣿⣿⠿⢧⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢿⣿⣿⢾⣿⣿⠉⠀⢸⣿⡿⣿⣿⡿⣿⣿⠛⣲⣶⣄⠀⣿⣿⣇⣤⣿⣿⣇⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣹⣿⣿⣻⠟⠃⢸⣿⣟⠃⣼⣿⣿⣿⣿⣿⣿⡿⠿⠛
⣿⣿⣿⣿⡏⢈⣷⣾⣷⠀⢀⣾⣿⣿⣿⣧⢻⣿⣿⠸⣿⣿⣻⣿⣿⣄⡀⣸⣿⡿⣿⣿⡿⣿⣿⣤⣿⣿⣿⡿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣟⣿⣿⣇⣿⣿⢼⣿⣿⣿⣿⣋⣀⣀⣠⣊⣻⣿⡄⠛⢿⣿⣿⣿⡿⢋⣤⣠⣤
⠘⢿⣿⡟⠉⠉⢿⣿⡟⠀⢸⣿⣿⣿⣿⡟⠈⠛⠛⢀⠙⠻⣿⡛⠉⠛⢻⣿⣿⣿⣿⣿⣗⣿⣿⠿⠛⠋⣿⣿⠛⠛⠃⠀⢻⣿⣿⣿⡟⠛⢟⣿⠇⠛⠛⠀⣿⣿⣿⣟⣛⣛⣻⡟⠛⠛⠛⢿⣆⠈⠛⠏⠉⢀⣾⣿⠿⠟
⣰⣿⣿⣿⣤⣤⣼⣿⡇⠀⠸⣿⣿⡏⠀⡀⠀⠀⢀⣧⠀⠀⠙⠻⣷⣦⣼⡟⠻⢻⣿⡿⠟⠁⠀⠀⣀⣼⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠷⠤⣤⣅⠐⠒⠒⠋⢉⣿⣿⠃⣿⣿⣿⣧⣄⣠⣴⣶⣾⣶⣶⣤⣄⡈⢉⣤⠀⠀
⣿⣿⣿⣿⠟⢿⠏⣿⣿⣾⠶⣿⣿⠉⣁⣀⡀⠀⢈⣿⣷⣄⠀⠀⠀⠙⠻⣷⣶⣶⣶⣶⡶⠶⠾⠛⠛⠉⠙⣿⡄⢀⡴⠋⢁⣦⣿⣿⣇⡀⣈⣥⠀⠤⢶⡶⣾⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⠁⢸⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠙
⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⠟⠋⠛⠻⣿⣿⣛⡃⠀⠀⠀⠀⠀⠀
⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⡟⣿⠟⠁⠀⠀⠀⠀⢹⣿⢻⣿⣄⡀⠀⠀⠀⠀
⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⡟⠀⠀⠀⠀⠀⠀⣸⠇⢀⠈⠻⣿⣷⣶⣴⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡄⠀⠀⠀⠀⣠⣿⠀⠀⠀⠂⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠜⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣤⣼⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣻⠻⠉⠉⠙⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠿⣿⣿⣯⣿⣿⠟⠛⠉
⢻⠿⠀⠀⠀⠀⣀⣠⣿⣿⠋⠉⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⢀⣴⡟⢻⣿⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣶⣾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠀⢀⣠⣤
⣿⠾⣿⣷⣾⣿⡿⠋⠉⢻⡀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⡏⠀⠀⣿⣧⣤⣤⣤⣾⣧⡴⣶⣶⡓⢛⣿⣽⣿⣿⣿⣿⢿⣿⣿⣿⡟⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡴⣦⣶⣿⣿⣿⣿
⠁⠀⠜⢻⣿⣿⣇⣀⣀⣼⣷⣶⡞⠀⠀⢀⣤⣶⣶⣦⡀⠀⣀⣀⣀⣬⣽⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⠟⢿⣾⣿⡁⢹⣿⣿⣷⣾⡿⢹⢻⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠁⠿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠾⠿⠻⠿⠛⢿⡉⣩⣭⢩⣿⡠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣻⣿⣾⣿⣏⣿⣧⢿⣿⣿⣿⣷⡴⣿⡸⣿⠄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢟⡛⢵
⣀⣦⡄⠈⠀⠀⠨⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣄⣘⣦⣼⡇⣾⣿⣾⣿⣿⣿⣗⣾⣿⣿⣧⣶⣿⣿⣿⡍⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣛⣛⣿⣧⣿⣿⠷⠛⠛⠙⠀⢴⣿⣿⣶⣶⣤⣤⣀⠀⣀⣤⣤⠤⠤⠤⢤⡀⠀⠀
⣿⣿⣿⣷⣤⣤⠇⠀⠀⠀⠀⠀⠀⠀⣶⣶⠛⣾⣿⠛⣿⣷⣿⣿⡿⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⣿⣷⣶⡄⣶⣶⢰⣿⣿⣿⣇⠈⠻⣿⣿⣿⡿⠁⠀⠤⠤⠤⠤⠀⠀⠀
⠿⠿⢿⣿⡟⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡏⣿⣿⣿⣿⣿⣷⣿⣿⠸⣿⣿⣿⣿⣤⡀⢨⣿⣿⣧⣤⣤⣤⣤⣤⣤⣄⣶⣿
⡀⠀⠀⠀⣽⣷⣿⡿⢷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠉⠀⢸⣿⡟⣿⣿⡿⣿⣿⠋⣑⣲⣦⣄⣿⣿⣇⣀⣿⣿⣇⣿⣿⣧⣿⣿⡷⣿⣿⣿⣿⣿⣀⣽⣿⣿⠿⠟⠃⢸⣿⣟⠃⣼⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣶⣿⣿⡏⢈⣷⣾⣷⠀⢀⣴⣿⣿⣿⣿⣿⣿⠸⣿⣿⣹⣿⣿⣤⣀⣸⣿⡿⣿⣿⣷⣿⣿⣀⣿⣿⣿⣿⣿⣿⡟⠋⣿⣿⣿⣿⣿⣏⣿⣿⣇⣿⣿⣸⣿⣿⢁⣿⣿⣃⣀⣀⣠⣊⡻⣿⡄⠛⢿⣿⣿⣿⡿⢋⣤⣤
⠀⠘⣿⣿⡟⠉⠙⢿⣿⡟⠀⢸⣿⣿⣿⣿⡟⠛⠛⠀⢙⠛⠻⣿⡁⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⠛⠃⠀⠛⣻⣿⣿⣿⡟⠛⢿⣿⠛⠛⠀⠛⣿⣿⣿⣿⣛⣛⣻⡟⠛⠃⠙⢿⣆⠀⠛⠏⠁⢀⣾⣿⠿
⣤⣠⣾⣿⣷⣤⣀⣼⣿⡇⠀⠸⣿⣿⡏⠁⠀⠀⠀⢠⣟⠀⠀⠙⠻⣷⣦⣼⡿⠿⢿⣿⡿⠟⠀⠀⠀⣀⣾⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠷⠤⣤⣥⠐⠒⠒⠋⢩⣿⣿⠃⣿⣿⣿⣧⣄⣠⣴⣶⣾⣶⣶⣤⣤⡈⢉⣤⠀
⢰⣿⣿⣿⡿⢿⠿⠻⣿⣷⣾⢀⣿⣿⠉⣉⣀⡀⠀⠈⣿⣧⣄⠀⠀⠈⠙⢿⣷⣶⣶⣶⣶⣶⠶⠶⠛⠛⠉⠹⣿⡄⢀⡴⠋⢡⣾⣿⣿⣇⡀⣈⣥⠀⠤⢶⡶⣾⣿⣿⣿⣧⢸⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣯⠁⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⡿⠛⠙⠛⢿⣿⣛⣛⠀⠀⠀⠀⠀⠀
⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⢻⡿⠋⠀⠀⠀⠀⠈⣿⡟⢿⣧⣀⠀⠀⠀⠀
⣴⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢼⣿⠁⠀⠀⠀⠀⠀⢀⡿⠀⡀⠙⣿⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⢀⣼⡇⠀⠀⡐⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣠⣴⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣻⢿⠏⠉⠉⠛⢿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⢿⣿⣿⣽⣿⠿⠛⠋
⣛⡿⢇⠀⠀⠀⠀⣀⣼⣿⡟⠉⠙⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⣠⣾⠟⣿⣧⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣾⣖⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠈⠀⠀⣀⣤
⣿⡿⠿⣷⣶⣿⣿⠟⠉⠉⣇⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠁⠀⢸⣿⣦⣤⣤⣴⣿⡶⣶⣶⡓⢛⣟⢉⣿⣿⣿⣿⢿⣿⣿⣿⣿⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣦⢶⣴⣾⣿⣿⣿
⡟⠁⠀⠛⢿⣿⣿⣀⡀⣀⣿⣶⣶⠃⠀⠀⣠⣴⣶⣦⣄⠀⣀⣀⣀⣠⣼⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⠟⢿⣾⣿⡋⢹⣿⣿⣷⣾⡿⠈⣿⣿⡆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠰⠿⠿⠿⠟⢻⢏⣩⣭⢩⣿⣧⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣻⣿⣾⣿⣏⣿⡧⣼⣿⣿⣿⣿⣦⢾⣇⣿⡇⠀⢳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⣟⠿
⣀⢠⣤⠈⠀⠀⠉⠝⠙⠋⠀⠀⠀⠀⠀⢀⢀⣠⣀⣳⣼⣮⣾⣿⣾⣿⢿⣿⣷⣸⣿⣿⣧⣴⣿⣿⣿⡏⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣿⣿⢼⣿⡿⠛⠛⠙⠀⠀⣾⣿⡷⣶⣦⣤⣤⣀⢀⣠⣤⡤⠤⠤⠤⣤⠀⠀
⣿⣿⣿⣿⣦⣤⡴⠀⠀⠀⠀⠀⠀⠀⣶⣶⡙⣶⣿⠙⣿⣿⣿⣿⡿⣿⡿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⢸⣿⣶⡄⣶⣶⠀⣼⣿⣿⣿⡄⠉⢿⣿⣿⣿⠏⠀⠠⠤⠶⠤⠤⠀⠀
⠾⠿⠿⣿⣿⠃⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡄⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣷⣿⣿⠀⢿⣿⣿⣿⣷⣄⠀⡽⣿⣿⣦⣤⣤⣤⣤⣤⣤⣰⣾
⣀⡀⠀⠀⢈⣿⣶⣿⡿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠉⠀⢸⣿⡟⣿⣿⡿⣿⣿⠋⣉⣒⣶⣦⣿⣿⣇⣀⣿⣿⣧⣿⣿⡇⣿⣿⡿⣿⣿⣿⣿⣿⢀⣬⣿⣿⣟⠿⠛⠀⣿⣯⡟⢠⣿⣿⣿⣿⣿⣿⣿⠻
⣿⣿⣷⣶⣿⣿⠁⢹⣦⣿⡆⠀⢠⣾⣿⣿⣿⣿⣿⠸⣿⣿⣸⣿⣿⣤⣄⣸⣿⡿⣿⣿⣷⣿⣿⣄⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⡿⣿⣿⣏⣿⣿⣧⣿⣿⣸⣿⣿⢋⣹⣿⣟⣁⣀⣀⣔⡙⢿⣧⡘⠻⣿⣿⣿⣿⠟⣡⣦
⠉⠀⢻⣿⣿⠟⠉⠹⣿⣿⠇⠀⣿⣿⣿⣿⣿⠛⠛⠀⠙⣛⠛⢿⣇⠈⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⡟⠃⠀⠛⢛⣿⣿⣿⣿⠛⠻⣿⡟⠛⠀⠛⢻⣿⣿⣿⣟⣛⣛⣿⠛⠃⠈⠻⢷⡄⠘⠻⠉⠁⣠⣿⡿
⣤⣄⣰⣿⣿⣧⣄⣠⣿⣿⠀⠀⢹⣿⣿⠁⠁⠀⠀⠀⣸⡇⠀⠈⠛⢿⣶⣤⣿⠿⠿⣿⣿⠿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠦⢤⣬⡄⠒⠒⠚⠉⢹⣿⡿⢸⣿⣿⣿⣶⣀⣤⣶⣾⣿⣶⣶⣤⣄⠉⢡⣤
⠀⣾⣿⣿⣿⢿⠿⠿⢿⣿⣷⡆⢸⣿⡏⠉⣁⣀⡀⠀⢹⣿⣦⡀⠀⠀⠉⠻⣿⣶⣶⣶⣶⣶⣶⠶⠞⠛⠛⠉⢻⣧⠀⢠⠞⠉⢼⣾⣿⣿⣀⢀⣩⡄⠠⠴⣶⢶⣿⣿⣷⣿⣌⢿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⡍⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⠟⠉⠉⢻⣿⣟⣛⡃⠀⠀⠀⠀⠀
⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⡿⣿⣄⡀⠀⠀⠀
⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣿⡇⠀⠀⠀⠀⠀⠀⣼⠃⠄⠈⢻⣿⣷⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⣰⣿⠀⠀⢀⢀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣄⣤⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠁⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⠿⠉⠉⠙⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⠿⠟⠋
⣙⣿⣿⡀⠀⠀⠀⢀⣠⣿⡿⠋⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⢀⣴⡿⢸⣿⡀⠀⠀⠀⢹⡷⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣾⣶⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⢀⣠
⣿⣿⢿⣿⣶⣾⣿⡿⠋⠉⣻⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡿⣾⣿⠏⠀⠀⣿⣧⣤⣄⣤⣾⡷⣶⣶⡓⢛⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣴⣶⣶⣿⣿⣿
⣼⠋⠀⠜⣿⣿⣿⣅⣀⢀⣿⣷⣶⡞⠀⠀⢀⣤⣴⣶⣤⡀⣀⣀⣀⣀⣦⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⠟⢿⣾⣿⡊⢹⣿⣿⣿⣾⡿⠈⢹⣿⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿
⡇⠀⠀⢄⠁⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠾⠿⠿⠿⢿⠿⣩⣭⢩⣶⣷⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣏⣿⡧⣼⣿⣿⣿⣿⣶⣶⣿⣿⡟⠀⢳⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⢝⡟
⣃⣀⣄⡀⠁⠀⠈⠹⠋⠛⠁⠀⠀⠀⠀⠀⣀⣀⣄⣱⣾⣶⣿⣿⣾⣿⢿⣿⣧⣎⣿⣿⣧⣤⣿⣿⣿⡏⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣿⣿⢷⣿⣿⠛⠛⠙⠀⠀⣾⣿⣿⢶⣶⣤⣤⣄⣀⣠⣤⣤⠤⠤⠤⠤⡄⠀
⢻⣿⣿⣿⣷⣤⣤⠇⠀⠀⠀⠀⠀⠀⣶⣶⢸⣶⣾⠋⣿⣿⣿⣿⡿⣿⡿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣿⣷⣆⣶⣶⠀⢰⣿⣿⣿⣇⠈⠻⣿⣿⣿⡿⠁⠀⠤⠒⠒⠤⠄⠀
⠶⢿⡿⣿⣿⠟⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣏⣿⣿⣸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣤⡀⢸⣿⣿⣧⣤⣤⣤⣤⣤⣤⣄⣶
⣄⡀⠀⠀⠀⣹⣷⣾⡿⢇⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠊⠀⢸⣿⡟⣿⣿⡿⣿⣿⠟⣊⣓⡶⣦⣿⣿⣇⣀⣿⣿⣧⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣿⣿⣿⠿⠟⠃⢸⣿⣿⢃⣼⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣷⣶⣾⣿⡏⢈⣷⣾⣧⠀⢀⣴⣿⣿⣿⣿⣿⠸⣿⣿⣸⣿⡿⣦⣄⣸⣿⡿⣿⣿⣷⣿⣿⣄⣿⣿⣥⣿⣿⣿⡿⠟⣿⣿⡿⣿⣿⣟⣿⣿⣧⣿⣿⣸⣿⣿⢚⣁⣿⣿⣋⣀⣀⣠⣊⠻⣿⣄⠻⢿⣿⣿⣿⡿⢃⣶
⠈⠁⠘⣿⣿⡿⠋⠙⢿⣿⡟⠀⢸⣿⣿⣿⣿⡟⠛⠀⠙⢛⡛⠻⣷⡀⠙⠛⢛⣿⣿⣿⣿⣿⣟⣿⣿⠿⠟⠛⣿⣿⠃⠀⠛⠛⣻⣿⣿⣿⡟⠋⢿⣿⠛⠀⠛⠛⣿⣿⣿⣟⣛⣛⣻⡟⠋⠀⠙⠿⣆⠈⠛⠏⠉⢀⣾⣿
⣤⣤⣠⣾⣿⣿⣀⣀⣸⣿⡇⠀⢸⣿⣿⡏⠉⠀⠀⠀⢀⣿⠀⠀⠙⢿⣶⣦⣼⡿⠿⢿⣿⡿⠟⠁⠀⠀⣠⣾⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠷⠦⣬⣅⠐⠒⠒⠋⢉⣿⣿⠃⣿⣿⣿⣷⣆⣠⣴⣶⣿⣷⣶⣦⣤⡀⠉⣤
⠉⢷⣿⣿⣿⣿⠟⢿⠿⣿⣷⣬⠀⣿⣿⠁⣉⣀⡀⠀⠘⣿⣧⣀⠀⠀⠈⠙⢿⣷⣶⣶⣶⣶⣶⡶⠾⠛⠛⠋⠹⣿⡄⠀⡴⠋⢱⣶⣿⣿⣇⠀⣬⣥⠀⠴⢶⠶⣾⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⣿⣿⣛⣛⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⡿⢿⣦⣀⡀⠀⠀
⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⠀⠀⠀⠀⠀⠀⢠⡏⠠⠀⠙⣿⣿⣶⣶
⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⣀⣾⡇⠀⢀⡂⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣴⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣿⠿⠏⠉⠉⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠽⣿⣿⣛⣿⣿⡿⠿⠛
⢙⣻⣿⡇⠀⠀⠀⠀⣀⣼⣿⠟⠉⠙⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⣠⣾⠓⣿⣇⠀⠀⠀⠈⣿⠆⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣾⣶⣟⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⣀
⢸⣿⡾⣿⣶⣶⣾⣿⠟⠋⢛⡆⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⡿⠁⠀⢸⣿⣤⣄⣤⣼⣿⣶⣶⡓⢛⣟⠉⣽⣿⣿⣿⣿⣿⢿⣿⣿⣟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⢶⣶⣾⣿⣿
⢠⡟⠁⠈⠻⣿⣿⣧⣀⡀⢸⣿⣦⣶⠃⠀⠀⣠⣤⣴⣤⣄⣀⣀⣀⣀⣼⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠟⢿⣾⣿⡀⢹⣿⣿⣿⣿⡿⠀⢹⣿⣿⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⣾⣿⣿⣿⣿
⣿⠀⠀⠀⡈⠸⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠰⠿⠿⠿⢿⠿⣯⣭⢩⣦⢸⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣏⣿⡇⢼⣿⣿⣿⣿⣷⣶⢾⣿⣿⠃⢷⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⣿
⣿⣀⣠⣀⠀⠀⠀⠉⠟⠛⠋⠀⠀⠀⠀⠀⢀⢀⣠⡈⣾⣦⣾⣿⣾⣿⢿⣿⣧⣸⣿⣿⣧⣤⣿⣿⣿⡟⢻⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣿⣿⠿⢾⣿⡟⠛⠙⠀⠀⠠⣿⣿⡷⢶⣶⣤⣤⣀⣀⣤⣤⠴⠦⠤⠤⠤⠀
⠹⣿⣿⣿⣷⣆⣤⡴⠀⠀⠀⠀⠀⠀⣶⣶⠀⣶⣶⠛⣿⣿⣿⣿⡿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣾⣿⡴⣶⣶⠀⠀⣾⣿⣿⣿⡄⠉⢿⣿⣿⣿⠏⠀⠀⠒⠒⠒⠤⠀
⠶⠾⣿⣿⣿⣿⠋⠀⠀⡀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣇⣿⣿⣷⣿⣿⠀⠀⢿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣶⣶⣦⣤⣤⣶⣦⣴
⣄⣀⠀⠀⠈⢉⣷⣶⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡌⠀⢸⣿⡇⣿⣿⡔⣿⣿⡿⣒⣙⡲⢶⣿⣿⡇⢀⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⠉⢀⣬⣿⣿⡟⠿⠛⠀⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣶⣶⣿⣿⠁⢹⣤⣿⡄⠀⣠⣿⣿⣿⣿⣿⠸⣿⣿⣸⣿⡿⢶⣤⣼⣿⡿⣿⣿⣷⣿⣿⣧⣿⣿⣥⣼⣿⣿⡿⠟⣿⣿⡟⣿⣿⣿⣿⣿⣯⣿⣿⣸⣿⣿⢖⣋⣸⣿⣟⣁⣀⣀⡔⡹⠿⣧⡘⠻⣿⣿⣿⡿⠏⣰
⠀⠉⠁⢻⣿⣿⠟⠋⠻⣿⣿⠇⠀⣟⣻⣿⣿⣿⠛⠀⠙⠛⣻⠛⢿⣆⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⡇⠀⠛⠛⢃⣿⣿⣿⣿⠋⠹⣻⡟⠀⠛⠛⢸⣟⣿⣿⣛⣛⣛⣿⠃⠀⠈⠻⠷⡄⠘⠛⠁⠀⣰⣿
⣀⣤⣄⢴⣿⣿⣆⣀⣀⣿⣿⠀⠀⣻⣿⣿⠋⠁⠀⠀⠀⣸⡇⠀⠈⠛⣷⣦⣤⣿⠿⠿⣿⣿⠿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠦⢤⣬⡄⠒⠒⠚⠉⣹⣿⡟⣸⣿⣿⣿⣶⣤⣴⣶⣿⣿⣷⣶⣤⣤⠀⢡
⠉⠗⣿⣿⣿⣿⠟⠻⡿⢿⣿⣧⡆⢸⣿⡏⢈⣁⣀⠀⠀⢻⣿⣄⠀⠀⠀⠉⠻⣿⣶⣶⣶⣦⣶⡶⠶⠞⠛⠛⠉⢻⣧⠀⢠⠞⠉⣴⣾⣿⣿⣀⢀⣭⡄⠠⠶⡶⢶⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡅⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⠟⠉⠉⠙⣿⣟⣛⣭⠀⠀⠀⠀
⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⠟⠁⠀⠀⠀⠀⠘⣿⠽⠿⣦⣄⡀⠀
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⠀⠀⠀⠀⠀⠀⢰⡇⠠⠀⠙⣿⣿⣷
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣠⣿⡀⠀⢀⣃⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⢈⣿⢿⠏⠉⠙⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠹⣿⣿⣿⣯⣿⡿⠟
⠙⢛⡻⣿⡇⠀⠀⠀⠀⠀⣸⣿⠟⠋⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⣠⡾⠇⣿⡆⠀⠀⠀⠈⣿⠂⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣾⣶⣿⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠁⠀⠀⢀
⠀⢸⣿⡿⣾⣶⣶⣶⣿⡿⠋⢻⡆⠀⠀⠀⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⣶⣿⡿⠁⢀⣻⣿⣤⣤⣤⣾⣿⣶⡓⢛⣟⠉⣭⣵⣿⣿⣿⣿⠿⢿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⢶⣶⣾⣿
⠀⢰⡟⠁⢈⠿⣿⣿⣯⣀⠀⢸⣷⣤⡴⠂⠀⠀⣀⣤⣤⣤⣄⣀⣀⣀⣤⣴⠼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⡀⢹⣿⣿⣿⣿⣿⠀⢸⣿⠏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⣾⣿⣿⣿
⢀⣾⠀⠀⠀⡘⢹⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⢸⠿⠿⣿⠿⣿⣯⢩⡦⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣏⣿⡇⢘⣿⣿⣿⣿⣿⣷⣶⣿⣆⣿⢷⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽
⢸⣿⢀⣠⣀⠀⠂⠈⠉⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⣸⣦⣾⣿⣾⣿⢷⣿⣿⣬⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣴⣾⠿⠿⢾⣿⡟⠙⠀⠀⠀⢰⣿⣿⡿⢿⣶⣤⣤⣀⣀⣤⣴⠶⠲⠦⠤⠤
⠀⠻⣿⣿⣿⣷⣆⣀⣰⠀⠀⠀⠀⠀⣶⣶⠀⣶⣶⠻⣿⣿⣿⣿⡿⣿⡿⠿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣾⣯⣶⣶⠀⠀⢀⣾⣿⣿⣿⡄⠈⢻⣿⣿⣿⠃⠀⠐⠒⠒⠒⠤
⠒⣶⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣘⣋⢤⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣯⣄⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣦⣄⣀⠀⠀⠈⢉⣳⣶⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣉⡄⢸⣿⡇⣿⣿⠴⣿⣿⣷⣿⣚⠚⠲⣿⣿⡇⠀⣿⣿⣧⣿⣿⣇⣿⣿⣷⣿⣿⣿⣿⣿⠈⠉⢠⣬⣿⣿⡿⠟⠛⠀⣿⣿⡍⢰⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣷⣶⣶⣾⣿⠋⢹⣤⣿⡄⠀⣿⣿⣿⣿⣿⡸⣿⣿⣸⣿⡿⠻⢦⣼⣿⡿⢿⣿⣷⣿⣿⣶⣿⣿⣁⣠⣿⣿⣿⡿⣿⣿⡏⢿⣿⣿⣿⣿⣟⣿⣿⣸⣿⣿⢤⣖⣋⣸⣿⣏⣁⣀⣀⡜⡉⠿⣷⡈⠻⢿⣿⣿⡿⠟
⠀⠈⠉⠁⢻⣿⣿⠟⠒⠻⣿⣿⠇⠀⣛⣻⣿⣿⣿⠇⠙⠛⠛⣛⠁⢿⣄⠛⠛⠋⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⡇⠛⠛⠃⢈⣿⣿⣿⣿⠀⠛⣻⡟⠛⠛⠐⢻⣿⣿⣿⣛⣛⣛⣿⠀⠀⠈⠛⠿⡄⠈⠛⠁⠀⣰
⣀⣀⣠⡄⣠⣿⣿⣆⣀⣀⣿⣿⠀⠀⢿⣿⣿⠋⠉⠀⠀⠀⣸⡇⠀⠘⠻⣷⣦⣤⣿⠿⠿⣿⣿⠿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠖⢦⣬⡀⠒⠒⠛⠉⣹⣿⡟⣸⣿⣿⣿⣶⣤⣴⣶⣿⣿⣷⣶⣤⣤⠀
⠙⠟⠻⣿⣿⣿⣿⠻⠿⡿⢿⣿⣇⡆⢸⣿⡏⠐⢉⣀⠀⠀⢻⣿⣄⠀⠀⠀⠉⠻⣿⣶⣶⣶⣤⣤⠶⠶⠞⠛⠛⠉⢿⣧⠀⢠⠞⠉⣼⣼⣿⣿⡀⢠⣭⣄⠐⠶⠶⢶⣿⣿⡿⣿⣄⢿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⣿⣟⣛⣭⠀⠀⠀⠀
⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⣿⠿⠿⣦⣄⡀⠀
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠙⣿⣿⣷
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⣠⣿⡇⠀⢀⣃⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⢈⣿⢿⠏⠉⠙⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⣿⣿⣻⣯⣿⡿⠿
⠙⢛⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⠟⠋⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⣠⡾⠇⣿⡆⠀⠀⠀⠈⣿⠆⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣾⣶⣿⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⢀
⠀⢸⣿⡿⣾⣶⣶⣶⣿⡿⠋⢻⡆⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣶⣿⡟⠁⢀⣻⣿⣤⣤⣤⣾⣿⣶⡓⢛⣟⠉⣭⣵⣿⣿⣿⣿⠿⢿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⢶⣶⣾⣿
⠀⢸⡟⠁⢈⠿⣿⣿⣯⣀⠀⢸⣷⣤⡴⠂⠀⠀⣀⣤⣤⣤⣄⣀⣀⣀⣤⣼⠼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⡀⢹⣿⣿⣿⣿⣿⠀⢸⣿⠏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣾⣿⣿⣿
⢀⣾⠀⠀⠀⡘⢹⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⢸⠿⠿⣿⠿⣿⣯⢩⡦⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣏⣿⡇⢘⣿⣿⣿⣿⣿⣷⣶⣿⣆⣿⢷⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽
⢸⣿⣀⣠⣀⠀⠂⠈⠉⡟⠛⠋⠀⠀⠀⠀⠀⠀⢀⣠⣹⣦⣾⣿⣾⣿⢷⣿⣿⣬⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣴⣿⢿⠿⢾⣿⡟⠙⠀⠀⠀⢰⣿⣿⣿⢿⣶⣤⣤⣀⣀⣤⣴⠶⠲⠦⠤⠤
⠀⠻⣿⣿⣿⣷⣆⣀⣰⠀⠀⠀⠀⠀⣶⣶⠀⣶⣶⠻⣿⣿⣿⣿⡿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣾⣯⣶⣶⠀⠀⢀⣾⣿⣿⣿⣄⠉⢻⣿⣿⣿⠃⠀⠐⠒⠒⠒⠢
⠒⣶⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣘⣋⢤⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣤⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣦⣄⣀⠀⠀⠈⢉⣳⣶⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣉⡀⢸⣿⡇⣿⣿⡴⣿⣿⣷⣿⣚⡚⠲⣿⣿⡇⠀⣿⣿⣧⣿⣿⣇⣿⣿⣷⣿⣿⣿⣿⣿⠈⠉⢡⣼⣿⣿⡿⠟⠛⠀⣿⣿⡍⢰⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣷⣶⣶⣾⣿⠋⢻⣦⣿⡄⠀⣿⣿⣿⣿⣿⡸⣿⣿⣸⣿⡿⠻⢦⣼⣿⡿⢿⣿⣷⣿⣿⣶⣿⣿⣁⣠⣿⣿⣿⡿⣿⣿⡏⢿⣿⣿⣿⣿⣟⣿⣿⣸⣿⣿⢤⣖⣋⣸⣿⣏⣁⣀⣀⡜⡩⠿⣷⡘⠻⣿⣿⣿⡿⠟
⠀⠈⠉⠉⢿⣿⣿⠟⠒⠻⣿⣿⠇⠀⣛⣻⣿⣿⣿⠇⠙⠛⠛⣛⠁⢿⣄⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⡇⠛⠛⠃⢈⣿⣿⣿⣿⠀⠛⣻⡟⠛⠛⠘⢻⣟⣿⣿⣛⣛⣛⣿⠀⠀⠈⠛⠿⡄⠘⠛⠁⠀⣰
⣀⣀⣠⡄⣤⣿⣿⣆⣀⣀⣿⣿⠀⠀⣿⣿⣿⠋⠉⠀⠀⠀⣸⡇⠀⠈⠻⣷⣦⣤⣿⠿⠿⣿⣿⠿⠋⠁⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠶⢦⣬⡀⠒⠒⠛⠉⣹⣿⡟⣸⣿⣿⣿⣶⣤⣴⣾⣿⣿⣷⣶⣤⣤⠀
⠙⠟⠻⣿⣿⣿⣿⠻⠿⡿⢿⣿⣇⡆⢸⣿⡟⠒⣉⣀⠀⠀⢻⣿⣄⠀⠀⠀⠉⠻⣿⣶⣶⣶⣦⣦⣶⠶⠞⠛⠛⠉⢿⣧⠀⢠⠞⠉⣽⣽⣿⣿⣄⢠⣭⣄⠐⠶⠶⢶⣿⣿⣿⣿⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠛⠉⠉⠙⣿⣟⣫⣭⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⡟⣿⠏⠀⠀⠀⠀⠀⠘⡿⠿⠿⣦⣄⡀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⣸⡇⠠⠀⠙⣿⣿
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⣠⣿⡀⠀⢀⣃⣼⣿
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣾⣿⣿⣿⣷⣿⣿⣿⣿
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⡟⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠀⠀⢘⣿⢿⠏⠉⠙⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣻⣿⣾⠿
⠀⠙⠻⢿⣿⡇⠀⠀⠀⠀⠀⣸⣿⠟⠛⠻⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⣠⡾⠧⣿⡆⠀⠀⠀⠘⣿⠀⠀⢀⣀⣠⣤⣤⣤⣴⣶⣾⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⢀
⠀⠀⢸⣿⣿⣷⣦⣤⣶⣾⡿⠛⢻⡄⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢶⣶⣾⡿⢁⣀⣿⣷⣤⣤⣴⣾⣿⡗⢛⣟⠉⣭⡥⣶⣿⣿⣿⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⣷⣶⣾
⠂⠀⢸⡿⠃⠙⢿⣿⣿⣏⠀⠀⢸⣷⣤⡴⠂⠀⠀⣀⣤⣤⣤⣀⣀⣀⣤⣤⢼⠾⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⠟⣿⣾⣿⡀⢹⣿⣿⣷⣿⣿⣇⢸⣿⢙⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⢀⣾⠁⠀⠀⠘⢹⣿⣿⣿⣷⣿⣿⠿⠃⠀⠀⢸⡿⢿⣿⣿⣿⣯⡦⠀⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣿⡇⢘⣿⣽⣿⣿⣾⣿⣿⣿⣿⣄⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠀⣀⢀⠑⠀⠉⠛⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⣸⡖⣾⣿⣾⣿⢷⣿⡟⢿⣿⣿⣧⣤⣿⣯⣿⣿⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣤⣴⠿⠿⠿⢻⣿⡟⠀⠀⠀⠀⢰⣿⣿⣿⢿⣶⣴⣦⣀⣀⣤⡶⠶⠒⠖⠤
⠒⠊⢻⣿⣿⣿⣶⣄⣀⣰⠀⠀⠀⠀⣶⣶⠀⣶⣶⣟⣿⣿⣿⣿⡿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣶⣼⣿⣶⠀⠀⠀⢀⣿⣿⣿⣿⣄⠈⢻⣿⣿⣿⠃⠀⠐⠒⠒⠒
⠀⠰⣦⣽⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⣿⣿⣇⣿⣿⢻⣿⣿⢸⣿⣿⣘⣋⢤⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣇⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⢁⠀⠀⠀⢿⣿⣿⣿⣿⣤⠀⣿⣿⣿⢶⣶⣶⣶⣶⣶
⣶⣤⣀⡀⠈⠀⠉⠙⣶⣴⣾⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣭⢀⣸⣿⡇⣿⣿⠽⣿⣿⣿⣷⣿⡒⠓⣿⣿⣇⠀⣿⣿⣇⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⡠⠈⠉⢡⣼⣿⣿⡿⠟⠛⠀⣿⣿⡍⢰⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣷⣦⣤⣾⣿⠋⢻⣥⣷⡄⣿⣿⣿⣿⣿⣾⣿⣿⣸⣿⡿⠉⠻⣾⣿⣿⣿⣿⣷⣿⣿⣦⣿⣿⠁⣀⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⡏⣿⣿⣽⣿⣿⣠⣴⣒⣋⣸⣿⣟⣁⡀⢀⠜⡨⠿⣷⡈⠛⣿⣿⣿⡿
⠀⠀⠉⠉⠋⢻⣿⣿⡿⠒⢺⣿⣿⡇⠛⣛⣿⣿⣿⣿⠟⠛⠛⠛⢁⠀⣿⣟⠛⠻⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⡟⠛⠃⠈⢛⣿⣿⣿⣿⠛⠛⣿⡟⠛⠘⠛⢻⣟⣿⣿⣛⣛⣣⣾⠀⠀⠀⠙⠿⡄⠘⠛⠁⠀
⠀⢀⣀⣀⡀⢨⣿⣿⣆⣀⣀⣿⣿⠀⠀⢿⣿⣿⠛⠉⠀⠀⠀⣰⡇⠀⠘⠿⣷⣦⣤⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⡿⠶⢦⣬⡄⠒⠒⠛⠉⣽⣿⡟⣸⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣶⣦⣤
⠛⠟⠻⣿⣿⣿⣿⣿⠿⠿⡿⢿⣿⣧⡆⢸⣿⡟⠒⠊⠁⠀⠀⢹⣷⣄⠀⠀⠈⠉⠻⣿⣶⣶⣶⣤⣤⣤⡶⠾⠛⠛⠉⢻⣧⠀⢠⠞⠉⣾⣽⣿⣿⣄⢠⣭⣄⠠⠶⠶⢶⣿⣿⡿⣿⣄⢿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠋⠈⠉⢻⣿⣫⣭⡄⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢿⢹⡟⠁⠀⠀⠀⠀⠀⣿⠿⠿⢿⣦⣀
⠀⠀⠀⣠⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⢀⡿⠀⠄⠈⢻⣿
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⣠⣼⣇⠀⠀⣈⣠⣿
⠀⢰⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⠛⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⢻⡿⡟⠉⠉⠛⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⡿
⠀⠘⠛⠿⣿⣿⠀⠀⠀⠀⠀⢀⣿⡿⠛⠛⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⣴⡿⢼⣧⠀⠀⠀⠀⣻⡗⠀⢀⣀⣠⣤⣤⣤⣴⣶⣾⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⣿⣟⣿⣦⣤⣴⣶⣿⠟⠛⣧⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣶⣿⢋⣀⣸⣿⣦⣤⣴⣶⣿⡟⢛⣿⠉⣭⡥⣶⣾⣿⣿⣿⢿⡿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠾⣾⣿
⠐⠀⠀⣽⠟⠀⡻⣿⣿⣿⡁⠀⠀⣿⣦⣤⡖⠀⠀⢀⣠⣤⣤⣄⣀⣀⣤⣤⠴⡷⢿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⠟⣿⣾⣿⡀⢹⣿⣿⣷⣾⡿⣿⣼⣿⠈⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿
⠀⠀⢰⡏⠀⠀⠈⠊⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⣿⣿⣿⣿⣿⢯⣦⠀⣶⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣿⡇⢘⣿⢽⣿⠿⣷⣿⣿⣿⡾⣧⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡇⠀⡀⠈⠂⠈⠙⢻⠻⠿⠃⠀⠀⠀⠀⠀⠀⢸⡆⣾⣿⣾⣿⢷⣿⡇⢻⣿⣿⣧⣄⣿⣯⣿⣿⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣤⣤⠶⠿⠿⠛⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⡿⣿⣶⣶⣤⣀⣤⣴⠶⠒⠒⠒
⠒⠒⠛⢿⣿⣿⣷⣦⣀⣀⡆⠀⠀⠀⣶⣶⠀⣶⣶⢸⣿⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⣄⣿⣷⢂⠀⠀⠀⣸⣿⣿⣿⣧⡀⠙⣿⣿⣿⡟⠀⠀⠒⠚⠒
⠀⠀⢶⣬⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⣯⡀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠏⡀⠀⠀⠸⣿⣿⣿⣿⣦⡄⢸⣿⣿⣷⢶⣶⣶⣶⣶
⣷⣦⣄⡀⠈⠉⠉⠙⢳⣦⣴⣿⣧⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣭⡄⣸⣿⡇⣿⣿⠘⣿⣿⣿⣿⣾⡗⠚⣿⣿⣧⡄⣿⣿⣇⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⠨⠄⠈⢁⣤⣽⣿⣿⠿⠛⠃⢸⣿⣯⠁⣾⣿⣿⣿⣿
⠻⢿⣿⣿⣿⣶⣤⣴⣿⡿⠉⣏⣽⣦⣿⣿⣻⣿⣿⣿⣿⣿⣸⣿⡟⠉⠛⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⠅⠀⣿⣿⣿⣿⣿⣿⡟⢿⣿⣟⣿⣿⣟⣿⣿⣽⣿⣿⣠⣤⣖⣊⣁⣿⣿⣋⡀⠀⣠⠃⠝⢿⣦⠙⢻⣿⣿⣿
⠀⠀⠈⠙⠛⠙⣿⣿⣿⠗⠒⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⠛⠛⠛⠁⡀⢸⣿⡛⠛⠟⢛⣿⣿⣿⣿⣿⣿⣾⣿⠻⠛⠛⣿⣿⠛⠃⠈⠛⣻⣿⣿⣿⡟⠛⢿⣿⠛⠘⠛⠛⣿⣻⣿⣿⣛⣳⣴⡇⠀⠀⠈⠻⢷⠀⠙⠋⠀
⠀⠀⢀⣀⣀⠀⣽⣿⣷⣀⡀⢸⣿⣏⠀⠸⣿⣿⡿⠋⠁⠀⠀⢀⣾⠀⠀⠛⢿⣶⣤⣼⡿⠿⢿⣿⣿⠿⠉⠀⠀⢀⣼⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⡗⠶⣤⣥⠐⠒⠛⠉⢉⣿⣿⢇⣿⣿⣿⣷⣶⣤⣶⣿⣿⣿⣿⣶⣶
⠙⠟⠻⣿⢿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣠⠀⣿⣿⠓⠒⠉⠀⠀⠘⣿⣧⡀⠀⠀⠉⠙⢿⣷⣶⣶⣦⣤⣤⣴⠶⠛⠛⠋⠙⣿⡄⠀⡴⠋⠁⣿⣾⣿⣧⡠⢬⣥⡀⠲⠶⠶⢾⣿⣿⠿⣷⡜⣿⣿⡿⣿⣿⣿⣿⡿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⠁⠉⠙⣿⣯⣭⣧⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⡏⣿⠋⠀⠀⠀⠀⠀⢸⡿⠟⠿⣷⣤
⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠀⠀⠀⠀⠀⠀⣸⠇⠠⠀⠙⣿
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⣀⣴⣿⡀⠀⣠⣅⣼
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⡿⠋⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠘⣿⢿⠋⠉⠙⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿
⠀⠀⠛⠻⢿⣿⡇⠀⠀⠀⠀⠀⣸⣿⠟⠛⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣠⡾⢷⣿⡄⠀⠀⠀⢸⣿⠂⢀⣀⣠⣤⣤⣤⣴⣶⣾⣶⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠁⠀⠀
⠀⠀⠂⢸⣿⣿⣷⣤⣤⣴⣶⡿⠛⢿⡀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⣿⣿⣁⣠⣿⣷⣤⣴⣶⣾⡟⢛⣿⠉⣿⡥⣶⣾⣿⣿⣿⣿⡿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠷⣷⣿
⠀⠂⠀⢈⡿⠋⠙⣿⣿⣿⣏⠀⠀⢸⣧⣤⡴⠂⠀⠀⣀⣤⣤⣄⣀⣀⣤⣤⠴⢾⠾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠿⣿⣾⣿⡀⢹⣿⣿⣷⣾⡿⢿⣿⣿⠀⢙⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿
⠄⠀⢀⣾⠁⠀⠈⠺⣻⣿⣿⣿⣷⣿⣿⠿⠇⠀⠀⣸⣿⣿⣿⣿⢿⣧⠀⣶⡿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣿⡇⢘⣿⢹⣿⣿⢶⣿⣿⣿⡶⢿⣿⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠠⢀⠀⠁⠄⠙⠛⡿⠿⠟⠀⠀⠀⠀⠀⠀⠸⣦⣾⣿⣾⣿⢷⣿⡇⠙⣿⣿⣷⣤⣿⣯⣿⣯⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣤⣤⠴⠾⠿⠛⢻⣿⡏⠀⠀⠀⠀⢰⣿⣿⣿⢿⣷⣴⣦⣄⣠⣴⡶⠖⠒⠒
⠐⠦⠘⠿⣿⣾⣿⣶⡄⣀⣰⠀⠀⠀⣶⣶⠀⣶⣶⠘⣿⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡖⣿⣿⡟⢩⣿⣿⣶⣦⠀⣶⣶⡄⣾⣷⠖⡀⠀⠀⢀⣿⣿⣿⣿⣄⠈⢻⣿⣿⣿⠃⠀⠐⠚⠛
⠀⠀⠠⣤⣽⣿⣿⣿⣿⠟⠁⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⢤⣿⡿⣿⣿⠞⣿⣿⣟⣿⣿⣿⣅⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣷⣿⣿⡺⢁⠀⠀⠀⢿⣿⣿⣿⣷⣤⠀⣿⣿⣿⠶⣶⣶⣶⣶
⣿⣶⣤⣁⠀⠉⠉⠉⠛⢶⣤⣾⣷⡀⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣭⣤⢸⣿⡇⣿⣿⠀⣿⣿⣿⣿⣷⡿⠒⣿⣿⣷⣄⣿⣿⣇⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⠀⠤⠈⠉⣠⣼⣿⣿⡟⠟⠛⠀⣿⣿⡍⢰⣿⣿⣿⣿
⠛⠿⣿⣿⣿⣶⣤⣤⣾⣿⠏⢻⣥⣷⣿⣟⢻⣿⣿⣿⣿⣿⣸⣿⡿⠈⠙⣿⣿⣿⣿⣿⡇⣿⣿⣶⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣟⣿⣿⣿⣿⣿⣹⣿⣿⢠⣤⣴⣒⣉⣸⣿⣟⣁⠀⢀⠞⡨⢻⣷⡌⠛⢿⣿⣿
⠀⠀⠀⠉⠛⠛⢻⣿⣿⡿⠖⢾⣿⣿⡟⠛⣟⣻⣿⣿⣿⡟⠛⠛⠁⢀⠀⣿⣟⠛⠛⠛⣻⣿⣿⣿⣿⣿⣶⣿⡿⠟⠛⢻⣿⡟⠃⠈⠛⢛⣿⣿⣿⣿⠛⠸⣻⡟⠘⠛⠛⢻⣟⣿⣿⣟⣻⣦⣾⠀⠀⠀⠙⠻⡆⠈⠙⠁
⠀⠀⠀⢀⣀⡐⢨⣿⣿⣆⡀⠀⣿⣿⠀⠀⢿⣿⣿⠟⠉⠀⠀⠀⣸⡇⠀⠘⠻⣷⣦⣤⣿⠿⠿⣿⣿⡿⠋⠀⠀⢀⣠⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⣿⠒⢦⣤⡄⠃⠛⠋⠉⣹⣿⡿⣸⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⣿⣶
⠛⠟⠿⣿⠿⢿⣿⣿⣿⡿⠿⣿⢿⣿⣇⡄⢸⣿⡟⠒⠊⠁⠀⠀⢻⣷⣄⠀⠀⠈⠉⠻⣿⣴⣶⣶⣤⣤⣤⡶⠾⠛⠛⠉⢻⣧⠀⢠⠞⠉⢼⣿⣿⣿⣤⠤⣭⣄⠰⠶⠶⠶⣿⣿⡿⢿⣦⢻⣿⣿⢿⣿⣿⣿⣿⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠉⠈⠉⢿⣿⣭⣽⡀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⣿⡟⠁⠀⠀⠀⠀⠈⣿⠿⠻⣷⣦
⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⢠⡿⠀⠄⠈⢻
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⢀⣠⣾⣇⠀⢀⣌⣼
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣿⠛⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⣿⡿⡟⠉⠙⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣿⣿⣿⣿⢿
⡇⠀⠘⠻⠿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⠛⠻⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⢀⣴⠿⣿⣧⠀⠀⠀⠈⣿⡆⢀⣀⣠⣤⣤⣤⣴⣶⣾⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡉⠉⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣶⣾⠟⠻⣇⠀⠀⠀⢹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣶⣾⣿⣏⣠⣼⣿⣤⣴⣶⣶⣿⢛⣿⠉⣽⡥⣶⣶⣿⣿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⢻⣾
⠀⠰⠀⠀⣿⠟⠋⢿⣿⣿⣿⡁⠀⠀⣿⣤⣤⠖⠀⠀⢀⣠⣤⣤⣀⣀⣤⣤⠴⠶⡿⢿⣿⣿⣭⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡂⢹⣿⣿⣿⣾⡿⠿⣿⣿⠀⠈⡟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿
⠠⠀⠀⣰⡏⠀⠀⠑⢿⣿⣿⣿⣿⣾⣿⡿⠿⠀⠀⢀⣿⣿⣿⣿⢿⣧⠀⣶⡿⢿⣷⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡇⢘⣿⢹⣿⡽⡾⣾⣿⣿⣶⠾⣷⣸⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⠀⡀⠈⠠⠈⠛⢻⠿⠿⠃⠀⠀⠀⠀⠀⠸⣄⣾⣿⣾⣿⢷⣿⡇⠈⣿⣿⣧⣦⣿⣯⣿⣯⣿⣿⣿⡇⠸⣿⠝⠿⠿⣛⣙⣛⣭⣤⠴⠶⠿⠛⠛⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⡿⣿⣶⣶⣤⣀⣤⡶⠶⠒⠒
⠐⠢⠄⠻⣿⣿⣿⣷⣤⢀⣀⡇⠀⠀⣶⣶⠀⣶⣶⠀⣽⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣿⣵⢂⠀⠀⠀⣼⣿⣿⣿⣧⡄⠙⣿⣿⣿⡟⠀⠐⠒⠛
⡀⠀⠀⢤⣬⣿⣿⣿⣿⡿⠋⠀⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣟⣋⣤⣿⣿⣿⣷⠚⣿⣿⣟⣿⣿⣷⣯⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⣲⠏⡀⠀⠀⠸⣿⣿⣿⣿⣦⡄⣼⣿⣿⡷⢶⣶⣶⣶
⣿⣷⣤⣈⠁⠉⠉⠉⠛⠳⣤⣴⣾⣆⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣯⣤⣸⣿⡇⣿⣿⠀⣿⣿⣷⣾⣿⣾⠗⣿⣿⣷⣦⣿⣿⣇⣿⣿⣧⣿⣿⣇⣿⣿⣿⣿⣿⠀⠠⠄⠉⢁⣤⣿⣿⣿⠿⠛⠁⢸⣿⣯⢡⣾⣿⣿⣿
⠙⠻⣿⣿⣿⣷⣦⣤⣴⣿⡟⠙⣯⣽⣿⣿⢻⣿⣿⣿⣿⣿⣸⣿⡿⠈⠉⣻⣿⣿⣿⣿⡇⣿⣿⣦⣿⣿⣿⠄⣿⣿⣧⣿⣿⣿⡿⢿⣿⣏⣿⣿⣿⣿⣿⢹⣿⣿⢠⣤⣤⣖⣋⣀⣿⣿⣃⡀⠀⡰⢁⠹⣿⣦⠙⢻⣿⣿
⠀⠀⠀⠉⠛⠛⠻⣿⣿⣿⠷⠲⣿⣿⣿⠛⢸⣛⣿⣿⣿⡿⠛⠛⠁⠀⠀⢻⣟⡋⠛⠛⢓⣿⣿⣿⣿⣿⣷⣾⣿⡿⠛⢛⣿⣿⠃⠈⠛⠛⣻⣿⣿⣿⡟⠈⢛⡿⠛⠛⠛⢛⣿⣻⣿⣟⣻⣷⣴⡇⠀⠀⠈⠻⢧⠀⠉⠋
⠀⠀⠀⠀⢀⣀⢂⣹⣿⣷⡀⠀⢸⣿⡇⠀⢸⣿⣿⡿⠛⠁⠀⠀⢀⣾⠁⠀⠻⢷⣦⣤⣼⡿⠿⢿⣿⣿⠟⠉⠀⠀⣀⣼⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠗⠶⣤⣥⠐⠘⠛⠉⢉⣿⣿⢃⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣷
⠛⠟⠿⣿⠿⢿⣿⣿⣿⣿⠿⢿⡿⣿⣷⣰⠀⣿⣿⠓⠒⠁⠀⠀⠘⣿⣦⡀⠀⠀⠉⠹⢿⣧⣶⣶⣬⣤⣤⣴⠶⠟⠛⠋⠹⣿⡄⢀⡴⠋⢹⣿⣿⣿⣧⡤⢬⣥⡀⠲⠶⠶⣾⣿⣿⠿⣷⡜⣿⣿⡿⣿⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⢿⣯⣭⣽⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⠟⠛⣷
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⢰⡏⠐⠄⠈
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⢤⣿⣇⡀⢠⣬
⠀⠀⠀⣸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿
⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿
⣧⠀⠀⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠈⣿⣿⠏⠉⠙⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠛⣿⣿⣭⣿
⣿⡆⠀⠸⠿⣿⣿⣿⠀⠀⠀⠀⠀⢨⣿⡿⠟⠻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⢀⣾⠏⣿⣆⠀⠀⠀⠈⣿⢆⣀⣠⣤⣤⣤⠴⢶⣾⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡉⠁⠀
⣿⠀⠀⠀⠀⣶⣿⣿⣤⣤⣤⣶⣶⠿⠿⡇⠀⠀⠀⢻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣶⣿⣣⣄⣽⣿⣴⣶⣶⣿⣿⣿⠉⣿⡥⣶⣶⣶⣾⣿⣿⡿⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⢻
⠏⠀⠰⠀⠀⣿⠟⠝⢿⣿⣿⣿⠁⠀⠀⣿⣄⣠⠔⠀⠀⢀⣀⣤⣄⣀⣤⣤⠴⠶⢾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡂⢹⣿⣿⣷⣿⡿⠜⢿⣿⡀⠈⡏⡏⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿
⠀⠀⠀⠀⣰⡏⠀⠀⠁⢿⣿⣿⣿⣷⣾⣿⣿⠿⠀⠀⢺⣿⣿⣿⣿⣿⣦⣶⡿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢘⣿⢹⣿⠥⡼⡾⣾⣿⣿⣶⢿⣧⣺⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠀⠀⠰⣿⡇⠄⠀⠑⠬⠉⠛⢿⠿⠿⠃⠀⠀⠀⠀⢸⡆⣾⣿⣾⣿⣿⣿⡇⠈⣻⣿⣧⣆⣿⣯⣿⣯⣿⣿⣿⣿⢸⣿⠝⠿⠿⣛⣙⣛⣴⣬⢤⠶⠿⠛⠛⠙⣷⡿⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣶⣶⣤⣠⣴⡶⠾⠛
⠀⠐⠤⠄⠻⣿⣿⣿⣷⣤⠀⠀⡅⠀⣶⣶⠀⣶⣶⠀⣴⣿⣿⣿⣿⣿⡿⢿⣷⣶⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⣯⡵⢂⠀⠀⠀⣼⣿⣿⣿⣧⡁⠙⣿⣿⣿⡏⠀⠀⠚
⣀⠀⠀⠀⢤⣽⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣏⣤⣿⣿⣿⣷⠒⣿⣿⡿⣿⣿⣧⣶⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⣟⡻⢋⠀⠀⠀⠹⣿⣿⣿⣿⣷⡄⣼⣿⣿⡷⢾⣿⣶
⣿⣿⣶⣤⣈⠉⠉⠉⠉⠛⠳⣤⣴⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣧⣼⣿⣇⣿⣿⠀⣿⣿⡷⣶⣾⣿⣿⣿⣿⡗⢶⣿⣿⡇⣿⣿⣧⣿⣿⣧⣿⣿⣿⣿⣿⠓⠀⠠⠄⠈⢁⣤⣿⣿⣿⠻⠋⠁⢸⣿⣿⠡⣿⣿⣿
⠉⠙⠿⣿⣿⣿⣷⣤⣤⣤⣿⡿⠛⣿⣿⣿⢻⣿⣿⣾⣿⣿⣸⣿⡿⠀⠈⣹⣿⡿⣿⣿⡇⣿⣿⣦⣿⣿⣷⣾⣿⣿⣇⣤⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⢹⣿⣿⣄⣠⣤⣤⣖⣋⣠⣿⣿⣏⡀⠀⡰⠁⠙⣿⣧⠙⢻⣿
⡄⠀⠀⠀⠙⠛⠛⠻⣿⣿⣿⠷⠴⣿⣿⣿⠘⢛⣻⣿⣿⣿⣿⠛⠁⠀⠀⠛⢻⣧⠙⠛⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠟⢛⣿⣷⠈⠛⠛⠛⣻⣿⣿⣿⡆⠛⢛⡿⠛⠛⠛⢛⣿⣻⣿⣿⣿⣷⣼⡇⠀⠀⠈⠛⣷⡀⠉
⠀⠀⠀⠀⠀⠀⢀⠂⣹⣿⣧⠀⠀⢸⣿⡇⠀⢸⣿⣿⡿⠛⠁⠀⠀⢀⣾⠁⠀⠻⢷⣦⣤⣼⡿⠿⢿⣿⣿⠟⠉⠀⠀⣀⣾⣿⡏⠀⠀⠀⢐⣿⣿⣿⣿⠗⠶⣦⣦⠘⠉⠛⠉⢡⣿⣿⢇⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿
⠛⠟⠿⣿⠿⢿⠿⣿⣿⣿⣿⠿⣿⡿⣿⣷⣰⠈⣿⣿⠓⠒⠃⠀⠀⠸⣿⣦⡀⠀⠀⠉⠻⢿⣧⣶⣶⣬⣤⣤⣶⠶⠟⠛⠋⠹⣿⡄⠀⡴⠋⢹⣿⣿⣿⣧⠤⢬⣥⡀⠒⠶⠶⣿⣿⣿⠿⣷⡜⣿⣿⡿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠈⠹⣿⣽⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⢿⣿⡿⠁⠀⠀⠀⠀⠀⢹⡟⠛⠻
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⢠⣼⣿⣀⢀⣤
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿
⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⣿⣿
⣿⡆⠀⢸⣿⣿⣿⣿⡿⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⢹⡿⠿⠉⠉⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣯⣽
⣿⣷⠀⠈⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⣹⣿⡿⠛⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⣠⡿⢼⣷⡀⠀⠀⠀⢹⣧⣀⣠⣤⣤⣤⠴⠶⣾⣶⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠈⠀
⣿⡏⠀⠀⠀⢰⣾⣿⣧⣄⣤⣤⣶⣾⠿⢿⠀⠀⠀⠘⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣾⣿⣄⣬⣿⣷⣶⣶⣶⣿⣿⠉⣿⡥⣶⣶⢶⣾⣿⣿⣿⠿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡟
⠻⠁⠀⠄⠀⢸⣿⠯⠹⣿⣿⣿⡏⠁⠀⢸⣧⣀⡤⠂⠀⠀⣀⣠⣤⣀⣤⣤⠴⠶⠖⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡂⢹⣿⣿⣷⣾⡿⠠⢻⣿⣆⠈⡇⢹⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺
⠀⠀⠀⠀⠀⣾⠁⠀⠘⠸⣿⣿⣿⣿⣶⣿⣿⡿⠇⠀⢺⣹⣿⣿⣿⣿⣷⣶⡿⢿⣦⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢘⣿⢹⣿⠡⢴⢗⢿⣿⣿⣷⣿⢿⣔⣿⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠂⠀⠀⢸⣿⠀⠀⠈⠢⠌⠛⠻⡿⠿⠟⠀⠀⠀⠀⠸⡇⣾⣿⣾⣿⣷⣿⡇⠈⣻⣿⣿⣴⣿⣯⣿⣯⣿⣿⣿⣿⢿⣿⠝⠿⠿⣛⣙⣛⣤⣦⢥⠶⠖⠛⠛⠛⢻⣾⠇⠀⠀⠀⠀⢸⣿⣿⣿⠿⣷⣶⣶⣤⣤⣶⠿⠛
⠀⠀⠢⠤⠜⢿⣷⣿⣿⣤⡄⠀⢨⠀⣶⣶⠀⣶⣶⠀⣴⣿⣿⣿⡿⣿⣿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⣸⣭⠖⡀⠀⠀⢠⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⠃⠀⠀
⣄⡀⠀⠀⢠⣤⣿⣿⣿⣿⣿⡟⠉⠀⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣘⣻⣤⣿⣿⣿⣷⠒⣿⣿⡿⣿⣿⣯⣴⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⣿⣛⠿⣁⢀⡀⠀⢿⣿⣿⣿⣿⣦⠀⣿⣿⣿⠿⣿⣿
⣿⣿⣷⣦⣄⠉⠉⠉⠉⠛⠻⢦⣠⣶⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣇⣿⣿⠀⣿⣿⠿⣶⣶⣾⣿⣿⣿⡗⠲⣿⣿⡇⣿⣿⣇⣿⣿⣧⣿⣿⣿⣿⣿⠟⠂⠀⠤⠀⠀⣠⣼⣿⣿⡿⠟⠉⠀⣿⣿⡏⢸⣿⣿
⠉⠉⠻⢿⣿⣿⣿⣦⣤⣤⣼⣿⠟⢻⣿⣿⣻⣿⣿⣼⣿⣿⣾⣿⡿⠀⠀⣹⣿⡿⣿⣿⣇⣿⣿⣦⣿⣿⣧⣶⣿⣿⣇⣠⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣻⣿⣿⣤⣀⣤⣤⣴⣚⣁⣼⣿⣿⣀⠀⢀⠎⠘⢻⣿⣌⠙⢿
⣄⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⡿⠤⢾⣿⣿⡟⠛⣛⣿⣿⣿⣿⡟⠁⠀⠀⠛⠛⣷⡜⠛⠻⠿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠿⠛⢻⣿⡎⠛⠛⠛⢋⣿⣿⣿⣿⠛⠛⣿⠟⠛⠛⠛⣻⣟⣿⣿⢿⣿⣦⣿⠀⠀⠀⠉⣛⣆⡈
⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣇⠀⠀⣿⣿⠃⠀⣿⣿⣿⠟⠋⠀⠀⠀⣰⡏⠀⠘⠿⣶⣤⣄⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣰⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⣿⠒⢶⣶⡄⠋⠙⠉⠉⣸⣿⣿⣰⡿⣿⣿⣷⣦⣶⣿⣿⣿⣿
⠙⠟⠿⣷⠿⢿⠿⢿⣾⣿⣿⡿⢿⣿⢿⣿⣇⣄⢸⣿⡿⠐⠒⠁⠀⠀⢿⣷⣄⠀⠀⠈⠙⠿⣿⣴⣶⣦⣥⣤⣤⡶⠾⠻⠛⠉⢻⣧⠀⢠⠞⠉⢸⣿⣿⣿⡤⠤⣭⣆⠐⠲⠶⠿⣿⣿⡿⢿⣦⢻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⢿⣯⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠹⣿⣿⠋⠀⠀⠀⠀⠀⢈⡿⠛⠛
⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⣸⡇⠐⠀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⣴⣿⣇⣀⣠
⠀⠀⠀⠀⣰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣶⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿
⣿⣧⠀⠀⣿⣿⣿⣿⣿⠟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⠀⠀⠈⣿⣿⠏⠉⠙⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣯
⣿⣿⡄⠀⠻⠿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠟⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢠⣾⠯⣿⡆⠀⠀⠀⠘⣿⣀⣠⣤⣤⣤⠴⠶⢾⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠁
⣿⣿⠀⠀⠀⠀⣶⣿⣿⣄⣀⣤⣴⣶⠿⠿⡇⠀⠀⠈⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣶⣿⣇⣤⣿⣿⣶⣶⣶⣿⣿⠉⣿⡥⣶⣶⢶⣾⣿⣿⣿⡿⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻
⠻⠏⠀⠠⠀⠀⣿⡿⠝⣿⣿⣿⣿⠉⠀⠀⣿⣀⣠⠔⠀⠀⣀⣀⣀⣀⣤⣤⠴⠶⠖⢻⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡂⢹⣿⣿⣷⣾⡿⢀⢼⣿⣧⡈⡇⠈⡏⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠇⠀⢀⠀⠀⢰⡏⠀⠀⠣⢿⣿⣿⣷⣶⣾⣿⣿⠿⠀⢸⢹⣿⣿⣿⣿⣿⣶⡿⢿⣦⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢘⣿⢹⣿⠁⠤⡾⡺⣿⣿⣿⣷⠿⣧⣺⡇⠀⠀⠀⠀⢀⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠀⠀⠠⣿⡇⠀⠀⠑⠌⠙⠻⢿⠿⠿⠋⠀⠀⠀⠸⡎⣾⣿⣾⣿⣷⣿⡇⠈⣻⣿⣿⣦⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⠝⠿⠿⣛⣙⣛⣤⣴⢴⠶⠖⠛⠛⠛⠙⣷⡿⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣶⣶⣦⣤⣴⠾⠟
⠀⠀⠀⠤⠤⢿⣷⣾⣷⣦⣄⠀⠀⡅⣶⣶⠀⣶⣶⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⢰⣯⡴⢀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠙⢿⣿⣿⡏⠀⠀
⣤⣀⠀⠀⠀⣤⣹⣿⣿⣿⣿⡿⠛⠁⣿⣿⣇⣿⣿⢸⣿⣿⣸⣿⣿⣘⣋⣧⣿⡿⣿⣷⠒⣿⣿⡿⣿⣿⣿⣥⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⣿⣟⡻⢋⠀⣀⠀⠹⣿⣿⣿⣿⣷⡄⣼⣿⣿⡿⠿⣿
⣿⣿⣿⣦⣄⡘⠉⠉⠋⠙⠛⢧⣄⣴⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⣿⣿⠿⣶⣶⣾⣿⣿⣿⡗⠒⣿⣿⡇⣿⣿⣇⣿⣿⣧⣿⣿⣿⣿⣿⡿⠓⠀⠠⠄⠀⢀⣤⣿⣿⣿⠿⠋⠁⢹⣿⣿⠡⣿⣿
⠉⠉⠙⠿⣿⣿⣿⣶⣤⣤⣤⣿⡿⠛⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡟⠀⠀⣹⣿⡿⣿⣿⣇⣿⣿⣦⣿⣿⣧⣴⣿⣿⣇⣀⣿⣿⣿⣿⣿⣟⣿⣿⠿⣿⣿⣿⣿⣿⣤⣄⣠⣤⣴⣒⣋⣠⣿⣿⣇⡀⠀⡴⠁⠛⣻⣧⡈⠻
⢄⣀⠀⠀⠈⠙⠛⠛⠻⣿⣿⣿⡧⠴⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⠁⠀⠀⠛⠛⢻⣞⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣿⣿⠛⠛⠛⠋⣸⣿⣿⣿⡛⠛⢿⡿⠛⠛⠛⢛⣿⣻⣿⣿⣿⣷⣼⡇⠀⠀⠈⢙⣳⣀
⣀⠀⠀⠀⠀⠀⠀⠀⠂⣻⣿⣯⠀⠀⢸⣿⡏⠀⢸⣿⣿⡿⠛⠁⠀⠀⢀⣾⠁⠀⠻⢷⣦⣤⣸⡿⠿⢿⣿⣿⠟⠉⠀⠀⣀⣼⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⠗⠲⣶⣦⠘⠉⠋⠉⢀⣿⣿⢃⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿
⠙⠟⠷⣷⠿⢿⠿⠿⣷⣿⣿⣿⠿⣿⡿⣿⣷⣠⠈⣿⣿⠃⠖⠂⠀⠀⠸⣿⣦⡀⠀⠀⠉⠻⢿⣧⣶⣶⣬⣤⣤⣴⡶⠟⠟⠋⠹⣿⡄⠀⡴⠋⢰⣿⣿⣿⡧⠤⢬⣴⡀⠒⠶⠾⣿⣿⣿⠿⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠹⣿⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢿⣻⡟⠁⠀⠀⠀⠀⠀⣿⠟⠛
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⢠⡿⠀⠂
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⠀⣤⣾⣧⣀⢀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣾⣿⣿⣿⣿⣿
⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣿⣿⣿⣿
⣿⣿⡄⠀⢸⣿⣿⣿⣿⡿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⢻⢿⡟⠉⠙⠻⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⢻⣿⣯
⣿⣿⡇⠀⠘⠿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⢀⣴⡿⣿⣧⠀⠀⠀⠀⣻⣇⣠⣤⣤⣤⠴⠶⠾⣶⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠈
⣿⣿⡇⠀⠀⠀⢰⣿⣿⣦⣀⣀⣤⣶⡾⠿⣯⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣶⣶⣿⣏⣤⣼⣿⣶⣶⣖⣿⣿⡏⣿⡥⣶⣶⢶⣾⣿⣿⣿⣿⠿⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟
⡟⠿⠁⠀⡄⠀⢸⣿⠯⢿⣿⣿⣿⡏⠀⠀⢸⣆⣀⡤⠀⠀⣀⣀⣀⣀⣤⣤⠴⠶⠖⢛⣿⣿⣿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⡃⢹⣿⣿⣷⣾⡿⠀⣸⣿⣿⣌⡇⠀⣹⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠀⠀⡀⠀⠀⣾⠁⠀⠑⠽⣿⣿⣿⣶⣶⣿⣿⡿⠇⢺⠉⣿⣿⣿⣿⣿⣿⡿⢿⣦⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢘⣿⢹⣿⠁⠠⢴⢿⣿⣿⣿⣷⡾⣿⣴⡿⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠥⠤⠄⠀⠀⣼⣿⢠⠀⠈⠢⠉⠻⠿⡿⠿⠟⠁⠀⠀⠸⡆⣿⣿⣾⣿⣷⣿⡇⠈⣻⣿⣿⣷⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠝⠿⠿⣛⣙⣛⣤⣤⢶⠶⠖⠛⠛⠛⠃⢿⣾⠃⠀⠀⠀⠀⣸⣿⣿⣿⢿⣷⣶⣶⣤⣤⡶⠿
⠀⠀⠀⠠⣄⠸⣿⣷⣿⣶⣤⡀⠀⢸⣶⣶⠀⣶⣶⠀⣴⣷⣿⣿⣿⣿⡿⣿⣷⣶⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⠀⣿⣥⢆⡀⠀⠀⢰⣿⣿⣿⣿⡤⠈⠻⣿⣿⣿⠁⠀
⣤⣄⠀⠀⠀⢠⣈⣿⣿⣿⣿⣿⠟⠋⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⣼⣿⣿⣿⣷⠒⣿⣿⣟⣿⣿⣟⣯⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣧⣿⣿⢸⣿⡛⠟⡠⢀⡀⠈⢿⣿⣿⣿⣯⣆⢰⣿⣿⣿⠻⣿
⣿⣿⣿⣶⣤⣀⠋⠉⠛⠙⠛⠻⣄⣠⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣇⣿⣿⠀⣿⣿⠚⣶⣶⣾⣿⣿⣿⡗⠒⣿⣿⣇⣿⣿⣇⣿⣿⣧⣿⣿⣿⣿⣿⣿⠟⠂⠠⠤⠀⠀⣠⢼⣿⣿⡿⠏⠉⠈⣿⣿⡇⢼⣿
⠉⠉⠙⠿⣿⣿⣿⣶⣤⣄⣀⣴⣿⠟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠀⠀⣸⣿⡿⢿⣿⣇⣿⣿⣀⣿⣿⣧⣤⣿⣿⡇⣀⣿⣿⣿⣿⣿⣟⣿⣿⠟⣿⣿⣿⣿⣿⣡⣤⣀⣤⣤⣖⣊⣁⣼⣿⣟⣅⠀⢠⠎⠜⢛⣿⣄⠙
⠀⣀⡀⠀⠀⠉⠛⠿⠟⣿⣿⣿⣿⠤⢿⣻⣿⡟⠛⣿⣿⣿⣿⣿⠅⠀⠀⠛⠛⠃⣿⡛⠛⠿⠟⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⠛⣻⣿⡟⠛⠛⠋⢠⣿⣿⣿⡟⠛⠙⣻⠟⠛⠛⠛⣻⣟⣿⣿⣿⣿⣦⣿⠀⠀⠀⠉⣛⣆
⣀⠀⠀⠀⠀⠀⠀⠀⠐⢘⣿⣿⡅⠀⠈⣿⣿⠀⠀⣿⣿⣿⠟⠋⠀⠀⠀⣰⡍⠀⠹⢿⣦⣤⣀⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣰⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡟⠒⢶⣴⡀⠋⠉⠉⠁⣼⣿⡟⣸⡿⣿⣿⣿⣶⣶⣿⣿⣿
⠙⠟⠷⣶⠿⢶⠿⠿⢷⣾⣿⣿⡿⣿⣿⣿⣿⣆⡄⢸⣿⡿⠰⠒⠀⠀⠀⢿⣷⡀⠀⠀⠉⠛⠿⣿⣴⣶⣭⣥⣤⣴⣶⠾⠛⠛⠉⢿⣇⠀⣠⠞⠁⣾⣾⣿⣿⡤⠤⣥⣆⠐⠲⠶⢿⣿⣿⡿⢿⣦⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣿⣿⡿⠋⠀⠀⠀⢹⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣻⣻⡏⠀⠀⠀⠀⠀⠀⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⢠⡟⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⢠⣴⣿⣷⣄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣿⣿⣿⣿⣿
⣦⣄⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢿⣿⣿⣿
⣿⣿⣷⡀⠀⢹⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⣿⢿⡟⠉⠙⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⢻⣿
⣿⣿⣿⡇⠀⠸⢷⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⣴⡿⣿⣧⠀⠀⠀⢈⣿⣷⣤⣤⣤⠴⠶⠾⣖⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⡇⠀⠠⠀⣸⣿⣿⣆⣀⣀⣤⣴⣾⠿⣏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⣶⣿⣯⣤⡼⣿⣶⣖⣛⣿⣿⣿⡧⣶⣶⢶⣾⢿⣿⣿⣿⣿⠿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⣿⠁⠀⡄⠀⢸⣿⢿⢿⣿⣿⣿⡏⠀⠀⢸⣄⣀⡤⠀⣀⣀⣀⣀⣤⣤⠴⠶⠖⢛⣛⣟⣿⣿⣿⣶⣦⣻⣿⣿⣿⣿⣿⡋⢹⣿⣿⣷⣾⡿⠊⢸⣿⠻⣿⣇⠀⠀⡹⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⣿⠀⠀⡀⠀⠀⣾⠁⠀⠙⠿⣿⣿⣷⣶⣶⣿⣿⣿⢿⠉⣩⣿⣿⣿⣿⣿⣿⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⢹⣿⠁⠀⠠⡼⣿⡿⣿⣿⣷⡾⣷⣼⡟⠀⠀⠀⠀⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀
⡾⠥⠤⠄⠀⠀⣼⣿⢠⠀⠘⠀⠙⠻⠿⣿⣿⠟⠉⠀⠸⡆⣾⣿⣾⣿⢿⣿⣧⠋⣻⣿⣯⢻⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⡟⠿⠿⣛⣙⣛⣤⣤⢤⠷⠗⠛⠛⠙⠛⠃⣿⣾⠁⠀⠀⠀⠀⣸⣿⣿⣟⠿⣿⣾⣶⣤⣴⡾
⠁⠀⠀⠀⠤⣀⠸⣿⣶⣿⣶⣄⡀⠀⣶⣶⠀⣶⣶⠀⣴⣷⣿⣿⣿⣿⡿⢿⣿⣷⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⠀⠀⣿⣴⢇⡀⠀⠀⢰⣿⣿⣿⣿⡤⠈⠻⣿⣿⣿⠁
⣶⣤⣀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⡿⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⣤⣿⣿⣿⣷⠒⣿⣿⠙⣿⣿⣟⣛⣿⣿⣿⡉⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣷⣿⣿⠀⣸⣿⠛⢟⡠⢀⣀⠈⢿⣿⣿⣿⣿⣦⢰⣿⣿⣿⠟
⢿⣿⣿⣿⣶⣄⡀⠛⠛⠛⠛⠛⠯⣤⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⣿⣶⣾⣿⣇⣿⣿⡀⣿⣿⠁⣐⣷⣶⣾⣿⣿⡗⠒⣿⣿⣷⣿⣿⡇⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⠟⠂⠠⠔⠀⠀⣴⢾⣿⣿⡿⠋⠉⠈⢿⣿⡆⢸
⠀⠙⠛⠛⠿⣿⣿⣷⣶⣤⣀⣀⣴⣿⣿⣿⢻⣿⣿⠸⣿⣿⣾⣿⣿⠀⠀⣸⣿⡿⢿⣿⣧⣿⣿⣀⣿⣿⣧⣤⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⢈⣡⣦⣀⣤⣤⣖⣋⣥⣾⣿⣿⣤⠀⢠⠎⠐⠛⣿⣆
⠀⠀⣀⡀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡄⠀⠛⠛⠃⠘⣿⡋⠛⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠛⣿⣿⡟⠛⠋⠀⢛⣿⣿⣿⡟⠘⠛⣻⠟⠛⠛⢛⣻⣿⣿⣿⢿⣿⣧⣿⠀⠀⠀⢈⣛
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⢘⣿⣿⡅⠀⠈⣿⣿⠀⢀⣿⣿⣿⠟⠛⠀⠀⠀⣰⡏⠀⠹⠿⣶⣤⣀⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣴⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣟⠒⢶⣶⡄⠋⠉⠉⠁⣼⣿⣿⣸⡿⣿⣿⣿⣷⣾⣿⣿
⠉⠟⠻⣶⠿⢶⠶⠾⠿⢷⣾⣿⣿⡿⣿⣾⣿⣿⣆⡄⢹⣿⡿⠤⠒⠀⠀⠀⢿⣷⣄⠀⠀⠉⠛⠿⣿⣴⣶⣬⣥⣤⣴⣶⠾⠛⠛⠉⢿⣧⠀⣠⠟⠁⣾⣿⣿⣿⠤⠤⣴⣆⡐⠚⠿⢿⣿⣿⡿⠿⣧⢹⣿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣿⣿⡿⠋⠀⠀⠀⢹⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⣽⡏⠀⠀⠀⠀⠀⠀⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⢠⡟⠀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⢠⣴⣿⣷⣄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣿⣿⣿⣿⣿
⣦⣄⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢻⣿⣿⣿
⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⣻⢿⡟⠉⠙⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⢻⣿
⣿⣿⣿⡇⠀⠸⢿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⣴⡿⣿⣧⠀⠀⠀⢈⣿⣷⣤⣤⣤⠴⠶⠾⣖⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⣿⣿⣿⡇⠀⠠⠀⢼⣿⣿⣆⣀⣀⣤⣴⣾⢿⣏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⣶⣿⣯⣤⡼⣿⣶⣖⣛⣿⣿⣿⡧⣶⣶⢶⣾⢿⣿⣿⣿⣿⠿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⣿⠁⠀⡄⠀⢸⣿⢿⣿⣿⣿⣿⡏⠁⠀⢸⣄⣀⡤⠀⣀⣀⣀⣀⣤⣤⠴⠶⠖⢛⣛⣟⣿⣿⣿⣶⣦⣻⣿⣿⣿⣿⣿⡋⢹⣿⣿⣷⣾⡿⠊⢸⣿⠻⣿⣇⠀⠀⡹⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⣿⠀⠀⡀⠀⢀⣾⠁⠀⠘⠿⣿⣿⣷⣶⣶⣿⣿⣿⢿⠉⣩⣿⣿⣿⣿⣿⣿⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⢹⣿⠁⠀⠠⣼⣿⡿⣿⣿⣷⡾⣷⣼⡟⠀⠀⠀⠀⢀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀
⡾⠥⠤⠄⠀⠀⣼⣿⢠⠀⠘⠀⠙⠻⠿⣿⣿⠟⠉⠀⠸⡆⣾⣿⣾⣿⢿⣿⣧⠋⣻⣿⣯⢻⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⡟⠿⠿⣛⣙⣛⣤⣤⢤⠷⠗⠛⠛⠙⠛⠃⢿⣾⠁⠀⠀⠀⠀⣸⣿⣿⣟⠿⣿⣾⣶⣤⣴⡾
⠁⠀⠀⠀⠤⣀⠸⣿⣶⣿⣶⣄⡐⠀⣶⣶⠀⣶⣶⠀⣴⣷⣿⣿⣿⣿⡿⢿⣿⣷⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⡟⣩⣿⣿⣶⣦⠀⣶⣶⡄⣶⣶⠀⠀⣿⣴⢇⡀⠀⠀⢰⣿⣿⣿⣿⡤⠈⠻⣿⣿⣿⠁
⣶⣤⣀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⡿⣿⣿⣇⣿⣿⢸⣿⣿⢸⣿⣿⣘⣋⣤⣿⣿⣿⣷⠒⣿⣿⠛⣿⣿⣟⣛⣿⣿⣿⡉⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣷⣿⣿⠀⣸⣿⠛⢟⡠⢀⣀⠈⢿⣿⣿⣿⣷⣦⢰⣿⣿⣿⠟
⢿⣿⣿⣿⣶⣄⡀⠛⠛⠛⠛⠛⠯⣤⣿⣿⣿⣿⣿⢸⣿⣿⢻⣿⣿⣿⣶⣾⣿⣇⣿⣿⡀⣿⣿⠁⣐⣷⣶⣿⣿⣿⡗⠒⣿⣿⣧⣿⣿⡇⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⠟⠂⠠⠔⠀⠀⣴⢾⣿⣿⡿⠋⠉⠈⢿⣿⡆⢼
⠀⠉⠛⠛⠿⣿⣿⣷⣶⣤⣀⣀⣴⣿⣿⣿⢿⣿⣿⠸⣿⣿⣾⣿⣿⠀⠀⣸⣿⡿⢿⣿⣧⣿⣿⣀⣿⣿⣧⣤⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⢈⣡⣦⣀⣤⣤⣖⣋⣥⣾⣿⣿⣤⠀⢠⠎⠐⠙⣿⣆
⠀⠀⣀⡀⠀⠈⠉⠻⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠠⣿⣿⣿⣿⣿⡄⠀⠛⠛⠃⠘⣿⡋⠛⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠛⣿⣿⡟⠛⠋⠀⢛⣿⣿⣿⡟⠘⠛⣻⠟⠛⠛⢛⣻⣿⣿⣿⢿⣿⣷⣿⠀⠀⠀⢈⣛
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⢘⣿⣿⡅⠀⠈⣿⣿⠀⠀⣿⣿⣿⠟⠛⠀⠀⠀⣰⡏⠀⠹⠿⣶⣤⣀⣿⠿⠿⣿⣿⡿⠋⠁⠀⢀⣴⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣟⠒⢶⣶⡄⠋⠉⠉⠁⣼⣿⣿⣸⡿⣿⣿⣿⣷⣾⣿⣿
⠉⠟⠻⣶⠿⢶⠶⠶⠿⢷⣾⣿⣿⡿⣿⣾⣿⣿⣆⣌⢸⣿⡿⠤⠒⠀⠀⠀⢿⣷⣄⠀⠀⠉⠛⠿⣿⣴⣶⣬⣥⣤⣴⣶⠾⠛⠛⠉⢿⣧⠀⣠⠟⠁⣾⣿⣿⣿⡤⠤⣴⣆⡐⠚⠿⢿⣿⣿⡿⠿⣷⢹⣿⣿⣻⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2781

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/irc-log-260523/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/irc-log-260523/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_May_26,_2023⠀✐


Posted in IRC_Logs at 2:06 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-260523.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-260523.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-260523.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-260523.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
 Qmf3Ey2afxYusRQPgHcYn54SY3RySaL1z49BFyKH6xxQsv #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmSEdTzpBG847PCMzfFiaEwrEtV4V6n1TUT82EGerdjfiZ (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 Qmc673N3qocgnALqt6wWL9L2onWe5hDN3c3eQg3n3jhF4t social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmeXYx9cXMZ153JhxpyEMJqb96aj1dyz2kngTmrAcD19ud social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmcCxrrVumz6u7g3G2GBrePq8pU1qhutngqV641AVQeJsF #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmZpDMgRgVQMrT2eEbv6ijjF9rdstDcKHDiGXpeyAmEEee (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmX5i9soierb1iQKYtLzoDNxy4dMrX9y3NEzKT5DdB9oxP #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmZz6ob1zdcu6v3HNwzKSQZ4aUTxVZMFgqdTHp77sGWogu (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmX2VFCGCawxbCCUo2h1FKvHmTmxLRFAdDLmVDjFaZoLpw



                    ䷩ 𝚕𝚒𝚗𝚎 2908

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/social-control-networks-need-to-be-purged/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/social-control-networks-need-to-be-purged/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Social_Control_Media_Needs_to_be_Purged_and_We_Need_to_Convince_Others_to
Quit_It_Too_(to_Protect_Ourselves_as_Individuals_and_as_a_Society)⠀✐


Posted in Deception, Free/Libre_Software at 7:57 am by Dr. Roy Schestowitz


Video_download_link | md5sum 58fe869dbe56783f7f1ce90f27458ef6
Collective Risk From Social Control Networks
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/social-control-media-harms-everybody.webm


Summary: With the Tux Machines anniversary (19_years) just days away we
seriously consider abandoning all social control media accounts of that site,
including Mastodon and Diaspora; social control networks do far more harm than
good and they’ve gotten a lot worse over time


AMONG the potential topics for today we’ve included the impact of social
control media ‘by peer’, e.g. within families (dinner table, sleep) or inside
workplaces. I’ve meanwhile noticed, as stated in the above video, that
Mastodon’s largest instance does not like GNU/Linux sites. It does_not_like
GNU/Linux_users,_either. Tux Machines (username tuxmachines) has been delisted
and demoted; it’s not visible, even if it’s still there, and nothing gets
imported into the account.


“Tux Machines (username tuxmachines) has been delisted and demoted; it’s not
visible, even if it’s still there, and nothing gets imported into the
account.”For now I’ve decided not to even ‘fix’ the tuxmachines social control
media accounts. It’s just not worth the trouble and as early as next week Tux
Machines might quit social control media altogether. It’s a total catastrophe
and nobody deserves to have to deal with such crap.


The video above focuses on this_new_article_from_YLE. It talks about how
children’s use of crap_like_Fentanylware/TikTok_harms_health; those are topics
that we did not cover or barely covered before.


To make society better off and more secured/protected from harm — both domestic
and foreign — we need to convince peers/family/friends to abandon social
control media, including federated/Free software/decentralised derivatives/
copycats of the same behavioural machines. “Free (as in Freedom) platforms
would not drive “engagement” nor aim for other aspects of addiction and harm,”
an associate noted. █



                    ䷩ 𝚕𝚒𝚗𝚎 2973

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/some-privacy-still-feasible/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/some-privacy-still-feasible/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Anonymously_Travelling:_Still_Feasible?⠀✐


Posted in Free/Libre_Software at 6:57 am by Dr. Roy Schestowitz


Video_download_link | md5sum 6f335d84226615033fae0b1049d476d8
Anonymous Travel as a Right
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/travel-dignity.webm


Summary: The short story is that in the UK it’s still possible to travel
anonymously by bus, tram, and train (even with shades, hat and mask/s on), but
how long for? Or how much longer have we got before this too gets banned under
the false guise of “protecting us” (or “smart”/”modern”)?


THE element of “curious Roy” has long motivated and led me to “testing” all
sorts of stores and businesses, sometimes even government departments. I did
assessments and surveys, then published the outcomes in my personal site. Back
in the days there were media/societal watchdogs that did this routinely and
reported their latest-found outcomes.


“Surveillance states mostly punish law-abiding people.”The other day I decided
to check the experience of travelling by train anonymously. In a nutshell, it’s
still possible to purchase train tickets and travel anonymously. It’s also
possible to do this with an actual human and the queue was short even at 8:
30AM. Yes, actual humans are available! And they talk back at you with advice
and stuff…


Of course not every train station still has humans available. In some countries
the regime and the corporations (graft) try to herd people into “smart” “apps”
and other such nonsense. Those should not be needed. More of that is covered in
the video above, including why in a free society anonymous travel is still very
important. In some parts of the world it’s already impossible to travel
privately in a car, unless it’s a stolen car. Does this prevent crime? Hardly.
Many criminals already exercise special caution and steal cars, from which
crimes get committed. Surveillance states mostly punish law-abiding people. █



                    ䷩ 𝚕𝚒𝚗𝚎 3032

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/stuttgarter-zeitung-epo/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/stuttgarter-zeitung-epo/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ German_Media_About_Industry_Patent_Quality_Charter_(IPQC)_and_the_European
Patent_Office_(EPO)⠀✐


Posted in Europe, Law, Patents at 5:16 am by Dr. Roy Schestowitz


More translations (with more languages) available in the site of the EPO‘s
union, SUEPO


                         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_shot⦈_
    Siemens is one of the largest applicants at the European Patent Office.
                           Source: Matthias Balk/dpa


Summary: SUEPO has just released 3 translations of new articles in German; this
is the first of the three (“Industrie_kritisiert_Europäisches_Patentamt”)


THE following was translated by staff of the EPO. The staff wants to general
public to know this:


     § Industry criticises European Patent Office⠀➾


     An initiative of several large companies is concerned about the
     quality of patent examinations at the European Patent Office. There,
     speed comes before accuracy, they say. The office sees things
     differently.


     The European Patent Office (EPO) has come in for criticism from
     industry. An initiative of now 21 companies is concerned about the
     quality of patent examination. “We have the impression that the EPO
     is primarily concerned with processing as many patents as possible,”
     says Beat Weibel, head of patents at Siemens, who initiated the
     Industry Patent Quality Charter (IPQC), in an interview with the
     Deutsche Presse-Agentur. Examiners, he says, are exposed to ever-
     increasing production pressure and are therefore no longer in a
     position to examine thoroughly enough. “While in our case we see that
     the amount of work required for a patent application on average is
     always bigger, things have to move faster and faster at the EPO,”
     explains Weibel. “That worries us because the quality of the
     examination suffers as a result. He does not receive exact figures
     from the EPO on the time budget of the examiners, he says. “But if
     you look at the number of examiners and the number of examinations
     patents, the result is roughly a halving over the past ten years.”


     Jörg Thomaier, head of patents at Bayer, which is also a member of
     the IPQC, shares Weibel’s
     concerns.


     “The EPO used to be known for taking a long time to test. In recent
     years, we have the impression that more attention is paid to speed
     and that examinations are no longer as thorough,” he says. “Things
     are faster now, but the revocation rate in the patent appeal process
     has gone up.”


     Such a revocation is extremely unfavourable for the patent
     applicants. “Patents are extremely important for a company like
     Bayer,” Thomaier emphasises. “It’s not so much the quantity that
     matters, but that I can enforce them – if necessary – and that they
     don’t fall over at the first gust of wind of a review.” The Swiss
     company Roche, which has also joined the IPQC, says: “As an industry,
     we depend on reliable patents. That is the basis for investing in our
     research.”


     Siemens is one of the largest applicants at the European Patent
     Office. Last year, the Munich-based company was number six among
     applicants at the EPO, and number two among European companies –
     behind Ericsson. The Swedes are also members of the IPQC.
     “We would like the auditors to have more time to do their job,
     because the Patents are becoming more and more complex,” says
     Gabriele Mohsler, Vice President Patent Development there. “In
     individual cases, we have also seen that the searches were not
     sufficiently thorough.”


     Overall, however, her assessment is not quite as critical:
     “Basically, I think the quality at the EPO is good. But we don’t want
     it to drop and in some areas it could be higher,” says Mohsler.


     Thomaier from Bayer also says: “In a global comparison, the quality
     of the EPO is not bad. But it is a long way from what it once was:
     the clear gold standard. And that’s where we as an industry want to
     get back to.” A key solution in his eyes: more staff.
     “More applications also require more examiners,” he emphasises. “At
     the moment, we have the
     impression that the capacity is not sufficient.


     The EPO, on the other hand, emphasises on request that the quality of
     patent searches “always has top priority”. Many countries regard its
     work “as a global benchmark for patent quality”. This is also
     reflected in surveys by “leading intellectual property journals”, in
     which the EPO “consistently ranks first among patent professionals”.
     Some of the figures used by the IPQC, however, are inaccurate.


     In addition, the Patent Office points out that it has its own working
     group on quality in its Standing Consultative Committee with 74
     members from 40 countries. Last October, it also published a new
     Quality Charter, “in which our commitment to high quality and
     excellence at every stage of the patent granting process is set out”.


There are two more English translations that we wish to reproduce for plain
text and Gem(ini)Text. Then comes a new video. █


⠈⠻⢷⣦⡀⠐⠤⠀⠐⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣷⠀⣠⣾⠿⠋⠑⣇⡀⠀⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⢀⣠⣾⣿⠟⠋⣠⣴⣿
⠀⠀⠀⠉⠻⢷⡄⠈⠒⠀⠙⠻⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⠿⠋⣿⡄⣀⣴⢿⠋⠀⠀⠛⣤⣶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢁⣠⣾⣿⣿⣿
⣦⣀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢸⣿⣿⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣿⠀⣹⣿⡟⠃⠀⢸⣀⣴⣾⣿⣿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿
⠈⠙⠧⣤⡀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢰⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢀⡀⣿⠛⠁⠀⡇⣠⣴⣿⣿⣿⠿⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠁⠃⣤⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⠈⠁⢸⠀⢰⣾⣿⣿⡿⠟⡏⠀⠀⠀⠍⠠⠀⠀⠀⠀⠀⢠⡀⠆⢀⠀⠀⠀⢀⠀⠀⣠⣾⣿⠟⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠳⠶⠶⠶⠶⠶⠶⣿⣾⣶⣤⣤⣤⣤⣤⣽⣟⠀⠀⢸⣿⣿⣿⢿⣿⢿⣿⣿⣿⢻⠀⢴⣸⣿⣿⠿⣏⠁⠀⢀⣧⠶⠀⠀⢠⠀⠀⠀⣤⡀⡄⢨⣟⣼⠇⠀⠀⠀⢉⣠⣾⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠉⠩⠍⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣴⡿⢻⡍⠀⢀⣿⠴⠈⠉⢱⠀⣄⣤⣤⣞⡄⠟⠻⣤⠛⡻⡻⠋⠀⠀⢀⣴⣿⠟⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣤⣤⡄⠀⢸⣧⣤⣤⣈⣽⣉⡉⣉⢙⢹⠀⠀⠘⡇⠀⠈⢹⠀⣠⣤⣼⣿⣿⣿⣿⡯⣣⢿⣿⠋⠀⠀⠀⠀⢀⣴⣿⠟⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣦⡖⠁⠀⠀⠀⠀⠛⢿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⡇⠀⣤⣾⣾⣿⣿⣿⣿⣿⣿⡇⠂⠋⠀⠀⠀⠀⠀⣠⣶⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣅⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢰⢾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠐⢂⣀⡇⠰⣿⣿⣿⣿⣿⡿⡟⠛⠉⠀⠀⣀⠀⠀⠋⣠⣾⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢐⣴⢟⡁⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⠀⣿⣷⣼⣿⠿⡟⠋⠱⢐⠃⡤⠔⠀⠀⠀⢀⣴⡿⠛⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡴⠋⠁⠈⠀⠀⠆⠀⠀⠀⠀⠀⡄⣼⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣹⣼⡿⠿⣏⠉⠀⢀⡇⠤⠽⠋⢡⢀⣘⡁⢀⣴⠿⠋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢹⠀⠀⠀⣇⣀⣤⣶⣾⣿⣿⠟⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⢀⡀⠀⢀⣸⢀⣴⣾⣿⣿⣿⣿⣿⡫⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢐⣿⣏⠹⣿⣿⣿⣿⠟⠏⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⡿⠦⠙⠉⠉⠁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣾⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣭⣽⣿⠛⠛⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡾⠂⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢛⣛⣛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣧⠀⠄⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠆⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠄⠀⠀⢠⣄⣀⣀⠀⣤⣀⣤⣄⣤⣤⣤⣤⣄⠀⠀⣀⣤⣜⣧⣤⢰⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠿⠷⠾⠿⠿⠿⠾⠀⠀⢻⣿⣿⣿⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠂⠠⠀⠰⠶⠆⢰⠶⠶⠆⢶⣾⣿⡿⣿⣿⣿⡦⠀⠈⢿⣿⣿⣿⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠻⠛⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠛⠛⠛⢛⣛⠛⢛⣛⣛⢛⣛⣛⣛⣛⣋⣛⣛⣛⣁⠀⢀⣠⡦⣤⡤⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣤⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠄⠴⠶⠶⠾⠿⠿⠶⠿⠿⠷⠿⢿⣿⡿⣿⣟⢀⠀⢼⡧⠤⠤⢸⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠨⡿⢫⣿⡿⢿⡿⠿⠿⠛⠻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠀⠒⠒⠒⠒⠒⠿⠟⠺⠟⢓⡚⢻⣗⡛⣻⣛⡃⠘⣇⣄⣀⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠷⠀⠀⠀⠀⠀⠈⠉⠉⠩⠭⠭⠭⠭⠭⠭⠭⠭⠭⡯⡇⠀⣿⣿⣿⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⡿⠇⠀⣿⣿⣿⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⣴⠄⠀⡀⠀⠀⠀⠒⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡅⠀⠙⢛⠋⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡴⢦⢰⣯⣼⡅⣭⢠⡶⠆⣾⣻⡆⠀⢺⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿
⡄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡿⡇⢀⣄⣌⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣇⢸⠇⡇⢸⡆⢻⠸⣧⣤⢿⣭⡅⠀⠈⠻⣶⡶⠈⠻⠿⠿⠇⠘⠛⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⡟⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢁⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⣼⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡻⡇⣯⣷⢸⣍⠀⠀⣿⠻⣆⢹⡟⢰⣟⣻⣎⢿⣆⣾⡇⣼⣟⣿⣦⠻
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠛⠃⠛⠶⠰⠾⠂⠀⠹⣴⠟⠸⣇⠈⢿⣭⣭⠈⢿⣿⠃⢹⣿⣙⣛⡀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⠉⠛⠛⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3202

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/stuttgarter-zeitung-thomas-magenheim-on-epo/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/stuttgarter-zeitung-thomas-magenheim-on-epo/

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Gemini_version_available_♊︎


✐ EPO_Applicants_Complain_That_Patent_Quality_Sank_and_EPO_Management_Isn’t
Listening_(Nor_Caring)⠀✐


Posted in Deception, Europe, Patents at 5:36 am by Dr. Roy Schestowitz


More translations (with more languages) available in the site of the EPO‘s
union, SUEPO


Summary: SUEPO has just released 3 translations of new articles in German (here
is the_first_of_the_batch); the following is the second of the three (“Kritik
am_Europäischen_Patentamt_–_Patente_ohne_Wert?”)


THIS is an article from yesterday, composed by Thomas Magenheim, who
understands_these_matters. The following is at least partly machine-generated:


     § Criticism of the European Patent Office Patents without value?⠀➾


     26.05.2023 – 00:00 hrs
     Photo: imago/STL


     To increase its revenues, the European Patent Office grants
     questionable patents, say critics. Transparency International sees
     structures that favour corruption.


     Thomas Magenheim


     The example described by the Munich patent attorney makes it clear
     what is at stake. A pharmaceutical company developed a pill against
     infertility, had it protected at the European Patent Office (EPO) and
     invested in its marketing. Then a rival entered the market with an
     alleged plagiarism. The patent holder went to court and lost. The
     alleged imitator was able to show a US patent that Epa examiners had
     overlooked. This rendered their property right worthless. “In extreme
     cases, this can cause millions in damages,” explains the patent
     attorney, who wishes to remain anonymous. He works for one of the
     largest patent law firms in Europe. Patenting for several countries
     alone consumes a six-figure sum and many times that amount is
     invested in production in reliance on the patent. There is a system
     of meagre returns, the expert complains. Examiners are encouraged to
     grant more and more patents because this maximises the office’s
     income. Quality research falls by the wayside.


     Michael Heisel hangs the grievances even higher. “We see structural
     problems at the Epa that facilitate corruption,” says the Bavarian
     head of the anti-corruption organisation Transparency International.
     An element of this, he says, is the Epa Board of Directors, in which
     39 European countries are represented and which is supposed to
     control the management of the office. But this is called into
     question by a conflict of interests, warns Heisel. On the one hand,
     the office takes over the patent examination for many countries. On
     the other hand, the states receive a share of the Office’s income for
     granted patents. “The supervisory authorityThe administrative board
     is not independent of the person being controlled, and that can’t
     work,” Heisel criticises. Epa service instructions support this view.
     “Productivity has to improve, very soon, . …because productivity is
     the only thing that guarantees that our payroll will be paid on 26.
     of each month,” writes an Epa director. The clarity of a patent is
     not a priority, the inventive step is not to be examined in depth, it
     continues. It is to be examined quickly, decided positively and
     recognised a lot, it means.


     ⚓  Siemens is also among the critics⠀⇛


     This practice is also a thorn in the side of Siemens patent chief
     Beat Weibel. His company is the largest German patent applicant and
     initiator of an industry initiative with the abbreviation IPQC. 20
     major international corporations such as Siemens, Bayer or Nokia, but
     also smaller companies, have united because they fear for effective
     patent protection. “We have nothing in our hands if patent examiners
     can’t find the state of the art and can only do incomplete research
     due to internal time pressure,” complains Weibel. Siemens, too, has
     had similar experiences with Epa patents. Representatives of IPQC and
     Office 2023 have met twice to discuss and resolve problems. But that
     already fails in terms of awareness. “The Management of the office
     has denied quality deficiencies,” regrets the Siemensian. The
     Critics, meanwhile, remain silent. “We ask for your understanding
     that Epa does not wish to comment on this,” a spokesperson explains
     succinctly when asked.


     The data speak a clear language. For example, Siemens has documented
     an increase in the time spent on patent applications by one third in
     the past decade. At the same time, according to internal Epa
     statistics, the time available to examiners per patent search has
     almost halved, i.e. the opposite development has taken place. As a
     result, those who challenge patents are becoming more successful.
     From 2015 to 2021, the revocation rate climbed from 41 to 46 per
     cent, according to Siemens. For 2022, a study by the Chair of
     Intellectual Property at the University of Osnabrück has determined a
     revocation rate of almost 50 per cent at the Epa Board of Appeal.
     Another almost 40 per cent of contested patents were marginally to
     substantially restricted. It is striking that not even one in ten
     revocations is based on documents that could not be found in the Epa
     patent database, the study authors write. This means that in nine out
     of ten contested cases, the patent should not have been granted in
     the first place if a precise search had been carried out.


     ⚓  Internal complaints have gone unheard⠀⇛


     “We need reliable patents, and for that examiners need enough time
     and experience,” emphasises a patent expert from the pharmaceutical
     company Roche in Switzerland. He too is a member of the IPQC. Epa –
     Staff representatives support the accusations from industry and
     research. To the outside world, the office management claims that
     everything is fine and plays down quality deficiencies or ignores
     them altogether, they explain. Only four out of five exiting auditors
     are replaced, despite an increase in work. Internal complaints that
     this is at the expense of the quality of research have gone unheard.


     “The Office must provide more examiners and more examination time,”
     the Munich patent attorney also demands. A few years ago, several
     large patent law firms sent a fire letter to the Office. which
     criticised the declining quality of patents. This has been negated on
     the part of the office. “Nothing happened,” regrets the expert. Like
     Transparency International, he sees the Epa Board of Directors as
     problematic.


     ⚓  Aiming for patent fees⠀⇛


     “There are states for which this is a significant source of income,”
     says Weibel, criticising the control body’s actions and its focus on
     patent fees. Patent trolls have also recognised this and are taking
     advantage of it. These are applicants who apply for superficial
     patents, which are granted if the examination is poor, explains
     Heisel. These patents then block competitors. “China in particular
     applies for a large number of patents, and if they are not carefully
     examined, German companies can lose innovation opportunities.
     [sic] take,” warns Heisel. This is another reason why the IPQC
     remains persistent. “We will not give up,” promises Weibel in the
     fight for patent quality.


     ⚓  European Patent Office⠀⇛


     Organisation
     The European Patent Office (EPO), with its headquarters in Munich, is
     a supranational organisation, not an EU organisation, which is only
     subject to very limited state jurisdiction in the German country
     where it has its headquarters. The management of the Office, under
     President Antonio Campinos, is controlled by the Epa Administrative
     Council. It is made up of representatives of the 39 European states
     that are members of the European Union.


     Patent Convention have acceded to. These representatives are usually
     the heads of the national patent offices. For Germany, there is a
     Secretary of State for Justice.


     Patents
     In particular, patent applications from China have been on the rise
     at the European Patent Office for years. In 2022, the increase on
     this basis was a good 15 percent to more than 19,000 requests for
     protection by Chinese inventors. By comparison, applications from the
     USA grew by only three percent to a good 48,000 requests, while those
     from Germany fell by almost five percent to 24,684 inventions.
     However, these figures say nothing about their quality.


EPO managers redefined quality as speed of granting. That’s not quality at all.
Remember that the EPO hired people from Transparency International (noted
above). That helped silence them about EPO corruption for a while. █



                    ䷩ 𝚕𝚒𝚗𝚎 3398

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/27/suepo-and-epo-articles/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/27/suepo-and-epo-articles/

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Gemini_version_available_♊︎


✐ With_EUIPO_in_Focus,_and_Even_an_EU_Kangaroo_Tribunal,_EPO_Corruption_(and
Cross-Pollination_With_This_EU_Agency)_Becomes_a_Major_Liability/Risk_to_the
EU⠀✐


Posted in Europe, Patents at 6:25 am by Dr. Roy Schestowitz


Video_download_link | md5sum 17b91cbac42af9980f77f07a77c03d7d
EPO Under Scrutiny, But Will EU Listen?
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-backlash-2023.webm


Summary: With the UPC days away (an illegal and unconstitutional kangaroo court
system, tied to the European Union in spite of critical deficiencies) it’s
curious to see EPO scandals of corruption spilling over to the European Union
already


THE EU is about to get contaminated with the EPO cancer (EPO staff compares the
administration to a cancer). Will that doom the union? Well, it certainly won’t
help.


“To get promoted in these institutions one must be profoundly corrupt or
participate in profound corruption.”In past years we covered EUIPO corruption
that had come from (or via) the EPO. Does the EU really want to go on with
this? Will_EUIPO_replace_the_EPO? The European Commission does not seem to
understand what it’s doing; it’s a puppet on strings for corporate lobbyists —
even actors working on behalf of foreign countries.


SUEPO has just taken note of the following article, which was put behind a
paywall except this_part:


     We provide a rundown of Managing IP’s news and analysis coverage from
     the week, and review what’s been happening elsewhere in IP


     French govt complained to EPO over EUIPO election conduct


     French finance minister Bruno Le Maire wrote to António Campinos,
     president of the EPO, to complain over the timing of an event that
     will be held in Lisbon one week before the EUIPO leadership vote,
     Managing revealed this week.


     Le Maire, minister for the economy and finance since 2017, suggested
     the event could be seen as interfering with the process to select a
     new EUIPO executive director.


     Managing IP can also reveal that the incumbent executive director,
     Christian Archambeau, hinted at interference “from Munich” in the
     decision to remove him last November.


We previously saw more coverage related to this; that too was behind a paywall,
so only the patent microcosm can see it. Remember that António Campinos is in
fact French and he’s only using the Portuguese government to forge his
political career of corruption, coercion, and suppression. António Campinos is
using EPO budget to bribe governments and officials, mimicking exactly what
Benoît_Battistelli did before him (same modus operandi). António was born to a
well-known father (already dead while António was a teenager) who fought to
bury people like his son, António. As for Archambeau, he’s just another_EPO
opportunist who is still reviled by some EPO longtimers. To get promoted in
these institutions one must be profoundly corrupt or participate in profound
corruption.


More in the video above… █



                    ䷩ 𝚕𝚒𝚗𝚎 3490

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Gemini_version_available_♊︎


✐ Links_27/05/2023:_Plans_Made_for_GNU’s_40th_Anniversary⠀✐


Posted in News_Roundup at 11:33 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Education
          o Programming/Development
                # Python
    * Leftovers
          o Education
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Wildlife/Nature
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Trademarks
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o § Applications⠀➾


                # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to
                  Apple_Activity_Monitor⠀⇛


                       Activity Monitor displays a variety of resources in
                       use on a system in real time. These include
                       processes, disk activity, memory usage, and more to
                       provide a sort of dashboard.


                       Activity Monitor is proprietary software and not
                       available for Linux. We recommend the best free and
                       open source alternatives.


                # ⚓ DebugPoint ☛ Top_10_Debian-Based_Linux_Distributions_for
                  Everyone⠀⇛


                       Debian is a Linux operating system that has been
                       around for a long time and is known for its
                       universal compatibility. It is well known for long-
                       term support, stability, security, and critical
                       business use cases.


                       The Debian stable version is one of the sought-
                       after Linux distributions because its support spans
                       multiple years. This helps if you are running older
                       versions of applications or packages which are
                       critical.


                       We review ten Debian-based Linux distributions,
                       which you may want to try out for all use cases.


                # ⚓ TecMint ☛ 10_Most_Popular_Download_Managers_for_Linux_in
                  2023⠀⇛


                       Download managers on Windows are one of the most
                       needed tools that are missed by every newcomer to
                       the Linux world, programs like Internet Download
                       Manager Download Accelerator Plus and Free Download
                       Manager are very wanted, but these tools are not
                       available under Linux or Unix-like systems.


                       No, to worry, you will find several alternate
                       download managers for Linux that can help you
                       manage and accelerate your file downloads on a
                       Linux desktop.


          o § Instructionals/Technical⠀➾


                # ⚓ Ubuntubuzz ☛ What_To_Do_After_Installing_elementary_OS_7⠀⇛


                # ⚓ OSTechNix ☛ 15_Essential_Linux_Commands_Every_Beginner
                  Should_Know⠀⇛


                # ⚓ Herman Õunapuu ☛ I_held_a_talk_about_my_self-hosting
                  adventure!⠀⇛


                       The talk took place on May 25th 2023 at k-space, a
                       hackerspace in Tallinn, Estonia.


                # ⚓ Adriaan Roselli ☛ Brief_Note_on_Popovers_with_Dialogs⠀⇛


                       The fake page is meant to mimic the stress of
                       filling out a complex multi-step form while working
                       against the clock. As the user hits a toggle-tip to
                       get more information on a field, a dialog appears
                       telling the user they will be logged out unless
                       they hit the button.


                # ⚓ University of Toronto ☛ In_practice,_Grafana_has_not_been
                  great_at_backward_compatibility⠀⇛


                       We started our Prometheus and Grafana based metrics
                       setup in late 2018. Although many of our Grafana
                       dashboards weren’t created immediately, the
                       majority of them were probably built by the middle
                       of 2019. Based on release history, we probably
                       started somewhere around v6.4.0 and had many
                       dashboards done by the time v7.0.0 came out. We’re
                       currently frozen on v8.3.11, having tried v8.4.0
                       and rejected it and all subsequent versions. The
                       reason for this is fairly straightforward; from
                       v8.4.0 onward, Grafana broke too many of our
                       dashboards. The breakage didn’t start in 8.4, to be
                       honest. For us, things started to degrade from the
                       change between the 7.x series and 8.0, but 8.4 was
                       the breaking point where too much was off or not
                       working.


                # ⚓ Jim Nielsen ☛ Link_Preload_as_Image⠀⇛


                       I’ve been playing with these fancy new view
                       transitions and my experience thus far is that they
                       work ok on localhost, but as soon as I push code to
                       a preview branch on a remote server, the image
                       loads between transitions are janky because of
                       image loading.


                # ⚓ How_to_install_the_AWS_CLI_on_Linux_using_PIP_of_Python⠀⇛


                       The AWS Command Line Interface (CLI) is a free tool
                       provided by the Amazon web service, a cloud
                       computing platform. It allows users to interact and
                       manage the various AWS services directly from their
                       system’s command terminal. Well, if you are a
                       Ubuntu Linux user then can install AWS CLI directly
                       using the APT package manager, however, for other
                       distro users who want to get the latest AWSL CLI
                       version but using the PIP, this article is for
                       them. PIP is a popular package manager developed to
                       install libraries and other dependencies for a
                       Python project.


                # ⚓ Network World ☛ Resizing_images_on_the_Linux_command_line_|
                  Network_World⠀⇛


                       The convert command from the ImageMagick suite of
                       tools provides ways to make all sorts of changes to
                       image files. Among these is an option to change the
                       resolution of images. The syntax is simple, and the
                       command runs extremely quickly. It can also convert
                       a image from one format to another (e.g., jpg to
                       png) as well as blur, crop, despeckle, dither, flip
                       and join images and more.


                       Although the commands and scripts in this post
                       mostly focus on jpg files, the convert command also
                       works with a large variety of other image files,
                       including png, bmp, svg, tiff, gif and such.


                # ⚓ Beebom ☛ 10+_Ways_to_Use_the_find_Command_in_Linux_|
                  Beebom⠀⇛


                       Have you ever found yourself frantically searching
                       for an important file, only to realize that you
                       wasted many hours trying to look in every directory
                       but the file is nowhere to be found? Well, this is
                       a common problem that most Linux users face,
                       especially new users with a huge number of
                       disorganized files and directories. In this
                       article, we explain how you can search for files
                       and directories in different ways using the find
                       command in Linux.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Warhammer_40,000:_Gladius_–_Relics_of_War
                  is_free_to_keep_until_June_1st⠀⇛


                       Get your 4x Warhammer strategy gaming on, as
                       Warhammer 40,000: Gladius – Relics of War from
                       Proxy Studios and Slitherine Ltd is free to claim
                       and keep until June 1st. It has Native Linux
                       support and is Steam Deck Playable.


                # ⚓ GamingOnLinux ☛ Highly_rated_colour-changing_puzzle
                  adventure_‘Hue’_free_to_keep_until_June_8th⠀⇛


                       Need a free game? You’re in luck as Hue from
                       Fiddlesticks Games and Curve Games is currently
                       free to keep on Steam until June 8th. Released
                       originally back in 2016, it has a Native Linux
                       version available and is rated Steam Deck Playable.


                # ⚓ GamingOnLinux ☛ Many_years_later_Neverwinter_Nights:
                  Enhanced_Edition_is_still_getting_better⠀⇛


                       Originally released in 2002 and then later as
                       Neverwinter Nights: Enhanced Edition from Beamdog,
                       many years on it’s still getting major upgrades
                       including a new Toon shader and loading speed
                       improvements.


                # ⚓ GamingOnLinux ☛ Nintendo_hits_Valve_with_DMCA_against_the
                  Dolphin_emulator_release⠀⇛


                       Back in March the plan was announced for the Wii
                       and GameCube emulator Dolphin to release on Steam,
                       along with some useful Steam features but now that
                       seems unlikely to happen.


                # ⚓ GamingOnLinux ☛ Stone_Age_farming_life-sim_Roots_of_Pacha
                  has_returned_to_Steam⠀⇛


                       After a messy situation with their publisher, Soda
                       Den has now split from Crytivo and Roots of Pacha
                       has returned for sale on Steam.


                # ⚓ GamingOnLinux ☛ Valve_upgrades_Proton_Experimental_with_a
                  number_of_bug_fixes⠀⇛


                       Today there’s a new build of Proton Experimental
                       available for Steam Deck and desktop Linux gamers,
                       with it Valve has given us a bunch of bug fixes.
                       With there now being many different Proton versions
                       it can get a bit confusing, so head on over to
                       my beginner’s guide on Steam Play and Proton for
                       more info.


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ Nate Graham ☛ This_week_in_KDE:_Night_color_on
                        Wayland_with_NVIDIA⠀⇛


                             This week probably the biggest news is that
                             in Plasma 6, the Night Color feature will
                             work as expected on Wayland when you’re using
                             an NVIDIA GPU! Because NVIDIA’s drivers don’t
                             support the necessary Gamma LUT features to
                             make it work in an optimal way as on Intel
                             and AMD GPUs, we had to use a slightly
                             different approach that isn’t quite as
                             efficient. But hopefully that’s better than
                             not having the feature work at all, and if
                             you care about the increased resource usage,
                             you’re welcome to not use the feature.


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ HPC Wire ☛ CIQ_Extends_Enterprise-Grade_Support_for_Rocky
                  Linux_9.2_and_8.8⠀⇛


                       CIQ, the company supporting enterprises with the
                       next generation of software infrastructure built
                       atop the Rocky Linux enterprise Linux distribution,
                       announced today that it has certified its suite of
                       software products on recently released Rocky Linux
                       9.2 and Rocky Linux 8.8. Certified CIQ products
                       include Warewulf and Apptainer as well as the newly
                       launched Fuzzball and images available in the
                       Mountain repo as a service offering. CIQ also
                       announced enterprise grade professional support on
                       both of the new versions of Rocky Linux.


                       [...]


                       Additionally, CIQ is announcing long term support
                       (LTS) for Rocky 9.2 which will include support for
                       the Federal Information Processing Standards
                       (FIPS). The addition of LTS brings support to CIQ
                       customers for Rocky Linux 9.2 for an additional 18
                       months, providing support beyond the community
                       edition for customers who need assurance that a
                       trusted partner will be there to support them for a
                       guaranteed time frame.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Ubuntu ☛ Ubuntu_Summit_2023⠀⇛


                       After the success of last year’s Ubuntu Summit in
                       Prague, the organizers at Canonical set a goal to
                       make this year’s Summit bigger, better and bolder.
                       With this goal in mind, we are all extremely
                       excited to announce that this year’s Ubuntu Summit
                       will be hosted in the beautiful city of Riga,
                       Latvia!


                       The Ubuntu Summit is more than just a conference;
                       it’s an annual celebration of the most compelling
                       and groundbreaking innovations from the open source
                       ecosystem. Produced and hosted by Canonical, the
                       publishers of Ubuntu, the Summit offers a unique
                       opportunity to experience first-hand the cutting-
                       edge innovations and pioneering technologies that
                       are transforming our world.


                # ⚓ Ubuntu ☛ Time_to_prepare_for_Ubuntu_18.04_LTS_end_of
                  standard_support_on_31_May_2023_–_Options_for_Google_Cloud
                  users⠀⇛


                       In accordance with the information shared in our
                       latest blog post, it is important to note that
                       Ubuntu 18.04 LTS, codenamed ‘Bionic Beaver,’ is
                       approaching the end of its standard five-year
                       maintenance period on 31 May 2023. Consequently,
                       unless you hold an Ubuntu Pro subscription, updates
                       for Ubuntu 18.04 LTS servers will cease to be
                       available.


                       By subscribing to Ubuntu Pro, you can ensure that
                       your Ubuntu 18.04 LTS deployment remains fully
                       supported until 2028. This extended support period
                       provides you with continued assistance and
                       maintenance for your workloads running on Google
                       Compute Engine (GCE).


          o § Devices/Embedded⠀➾


                # ⚓ ZimaBoard_832_Single_Board_Server_Review_for_All_Creators⠀⇛


                       The ZimaBoard 832 Single Board Server is a compact
                       and powerful solution that caters to a wide range
                       of server applications. In this comprehensive
                       review, we will explore its design, features, and
                       capabilities, highlighting its potential as a
                       versatile and efficient server platform.


                       [...]


                       Once the hardware setup is complete, the next step
                       is to install the operating system (OS) on the
                       ZimaBoard 832. The board supports a range of OS
                       options, including Linux distributions such as
                       Ubuntu, Debian, or Fedora.


                # ⚓ Linux Gizmos ☛ Debix_Model_B_SBC_targets_industrial
                  embedded_applications⠀⇛


                       The Debix Model B is a single board computer
                       integrating the NXP i.MX8M Plus processor with 2.3
                       TOPs NPU and with extended operating temperature
                       range. The new embedded device comes in a Raspberry
                       Pi form-factor and offers similar peripherals.  


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Analyze_the_ambient_sound_around_you_with_this
                  Arduino_setup⠀⇛


                       Like the visualizer of the equalizer on an old
                       stereo receiver, this displays the levels of
                       several frequency bands within the audio it
                       monitors. In this case, that audio is the sound
                       around the device collected by an onboard
                       microphone. It shows the levels for seven different
                       frequencies: 63Hz, 160Hz, 400Hz, 1kHz, 2.5kHz,
                       6.3kHz, and 16kHz. Most devices like this use LEDs
                       to show the levels, but this shows them on a OLED
                       screen instead and that allows for more
                       flexibility.


                # ⚓ Olimex ☛ New_Open_Source_Hardware_design_is_verified:
                  ESP32-SBC-FabGL_single_board_computer_based_on_FabGL_library
                  with_PS2_keyboard,_mouse_and_VGA_display_with_many_retro
                  computer_emulators⠀⇛


                       This is how the idea for ESP32-SBC-FabGL was born.
                       I wanted to create a board that could be used as a
                       graphics/sound/IO co-processor for other retro
                       computers based on different processors.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ India Today ☛ New_virus_targets_Android_phone,_steals_call
                  records,_passwords_and_other_sensitive_data_of_users_–_India
                  Today⠀⇛


                # ⚓ The Register UK ☛ Predator_may_have_more_spyware
                  capabilities_than_we_know_•_The_Register⠀⇛


                # ⚓ SlashGear ☛ Android_TV’s_Live_Tab:_What_It_Is_And_How_To
                  Use_It⠀⇛


                # ⚓ 9to5Google ☛ Google_gives_tips_for_how_to_buy_Android_TV
                  box_without_malware⠀⇛


                # ⚓ The Sun ☛ Billions_of_Android_phone_owners_must_beware
                  ‘masquerade’_call_that_steals_your_money_–_sinister_sign
                  you’re_a_victim_|_The_US_Sun⠀⇛


                # ⚓ Make Use Of ☛ Is_GM_Ditching_Android_Auto_and_Apple_CarPlay
                  a_Sign_of_Things_to_Come?⠀⇛


                # ⚓ Phone Arena ☛ Inexpensive_tool_can_be_used_to_easily_break
                  into_Android_phones_–_PhoneArena⠀⇛


                # ⚓ Android Authority ☛ How_to_turn_off_your_Android_phone_–
                  Android_Authority⠀⇛


                # ⚓ Lifewire ☛ How_to_Add_Apps_to_Android_Auto⠀⇛


                # ⚓ XDA ☛ Android_14_Beta_2.1_arrives_with_a_whole_bunch_of
                  stability_improvements⠀⇛


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


          o ⚓ The Register UK ☛ Why_you_might_want_an_email_client_in_the_era
            of_webmail⠀⇛


                 A rather nice feature for Linux and BSD users is that now
                 you can use the middle-click function, which pastes
                 whatever text is currently selected, to create a new tab.
                 Google Chrome has done this for years, so it’s welcome to
                 see it come to Firefox. It works for URLs and for plain
                 text — if what you’re pasting doesn’t look like a web
                 address, then Firefox will search for it.


          o § Education⠀➾


                # ⚓ GNU ☛ GNU_40th_Anniversary⠀⇛


                       Join us to celebrate the GNU Project’s freedom-
                       spreading accomplishments with presentations in
                       English about various GNU packages, hacking on free
                       software and making new releases! The 40th
                       anniversary hacker meeting is open to all who want
                       to celebrate, work on, or learn about free
                       software. We are putting together an appropriate
                       schedule, if you have something to contribute,
                       please contact <gnu40@gnu.org> with an informal
                       proposal. We hope to put together a diverse
                       selection of presentations, discussions and
                       announcements all day long.


          o § Programming/Development⠀➾


                # ⚓ Daniel Lemire ☛ Expected_performance_of_a_Bloom_filter⠀⇛


                       A Bloom filter is a standard data structure in
                       computer science to approximate a set. Basically,
                       you start with a large array of bits, all
                       initialized at zero. Each time you want to add an
                       element to the set, you compute k different hash
                       values and you set the bits at the k corresponding
                       locations to one.


                # ⚓ Daniel Pocock ☛ JSON_CEE_structured_logging_for_WebRTC,_SIP
                  and_XMPP⠀⇛


                       I’ve recently added JSON CEE structured logging to
                       reSIProcate and submitted pull requests for
                       identical functionality in some related projects.


                       The use case for structured logging is quite
                       compelling in the RTC world, which includes WebRTC,
                       SIP and XMPP software. In the early days, we would
                       do everything with a single process like Asterisk
                       and we would only have to deal with a single log
                       file. Today, especially with WebRTC, we often have
                       multiple processes involved in a single phone call
                       or video meeting. When something goes wrong, we
                       need to be able to look at the logs from all of
                       these processes. Structured logging provides a
                       convenient way to combine and analyze the log
                       files.


                # ⚓ Earthly ☛ CI/CD_Security:_Challenges_and_Best_Practices⠀⇛


                       This article will delve into the challenges and
                       risks associated with CI/CD security, best
                       practices for securing the pipeline, code, and
                       infrastructure, and an overview of the tools and
                       technologies available to organizations to ensure
                       their CI/CD process is secure. By the end of this
                       article, you will have a better understanding of
                       the importance of CI/CD security, and the steps
                       necessary to mitigate the risks associated with it.


                # ⚓ PR Newswire ☛ The_Linux_Foundation_Announces_WasmCon_Event
                  Focused_on_WebAssembly_Technologies⠀⇛


                # § Python⠀➾


                      # ⚓ Earthly ☛ Querying_Relational_Databases_With
                        SQLAlchemy_in_Python⠀⇛


                             If you are interested in working with
                             relational databases in Python, then you need
                             to know what SQLAlchemy is. It is a Python
                             library that provides a high-level, SQL
                             abstraction layer for relational databases.
                             With SQLAlchemy, you can interact with
                             databases using Python objects and methods,
                             rather than writing raw SQL queries. In this
                             tutorial, you will learn how to get started
                             with SQLAlchemy and also learn how to
                             interact with and query an SQLite relational
                             database with the SQLAlchemy library.


    * § Leftovers⠀➾


          o ⚓ Telex (Hungary) ☛ ‘Life_shouldn’t_be_taken_too_seriously,_you
            must_be_able_to_smile_about_it’⠀⇛


                 It is very rare for an athlete to become an Olympic
                 champion without first having won an individual gold
                 medal at a European or World Championship, or even at a
                 Hungarian championship. Valéria Gyenge won a gold medal
                 at the most successful Olympics for Hungary, the 1952
                 Helsinki Olympics without having been a national champion
                 before. Her victory was a surprise even though she had
                 won the 400 freestyle at a smaller event a month before
                 the Olympics, having set a good time. The Hungarian
                 swimmers were at their best then, and the team was by far
                 the strongest ever, with four of the five gold medals
                 going to Hungary.


          o ⚓ The Nation ☛ When_Tina_Turner_Rocked_Out_for_George_McGovern⠀⇛


                 Tina Turner, a native of Tennessee who lived much of her
                 life in Europe, only rarely waded into American politics.
                 The “Queen of Rock and Roll,” who died Wednesday at age
                 83, quietly supported Barack Obama for the presidency in
                 2008, with the encouragement of Oprah Winfrey and some
                 inspiration from Caroline Kennedy. But Turner’s one high-
                 profile political performance came decades earlier, as
                 part of a remarkable show of women’s solidarity with the
                 anti–Vietnam War campaign of 1972 Democratic presidential
                 nominee George McGovern.


          o ⚓ Scheerpost ☛ What’s_Your_Sign⠀⇛


          o § Education⠀➾


                # ⚓ BIA Net ☛ Erdoğan_makes_fun_of_intellectuals_his_government
                  included_in_the_Peace_Process⠀⇛


                       Erdoğan used the term “entel-dantel” to name these
                       people who were included in the process to
                       strengthen public support for it..


                       While “entel” is short for “entellektüel,”
                       (intellectual in Turkish), dantel means lace. The
                       term is used to mock those who are either well-
                       educated or who write or express their opinions in
                       different ways, especially on political or social
                       issues and problems.


                # ⚓ Democracy Now ☛ “Education_Leads_to_Liberation”:_Nikole
                  Hannah-Jones_on_The_1619_Project_&_Teaching_Black_History⠀⇛


                       As attacks on the teaching of Black history
                       escalate in Florida and other states, we hear from
                       The New York Times journalist Nikole Hannah-Jones,
                       who won a Pulitzer Prize for her work on “The 1619
                       Project.” She spoke on May 19 at the Malcolm X and
                       Dr. Betty Shabazz Memorial and Educational Center,
                       which is housed in the former Audubon Ballroom in
                       New York where Malcolm X was assassinated in 1965,
                       and talked about the impact Malcolm X’s writing had
                       on her life, as well as the importance of teaching
                       the full history of the United States. “What we
                       commonly call history is actually memory, and that
                       memory in the United States has been shaped too
                       often by white men in power who want us to remember
                       the history of a country that never existed,” she
                       said.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ YLE ☛ Telia_prohibits_employees’_TikTok_use_on_company
                  devices⠀⇛


                       The new rules will go into effect at the end of
                       this month, affecting its operations in Finland and
                       six other countries in which it operates.


                       The Swedish company based its decision on data
                       security concerns related to the social media
                       platform that have been raised by authorities,
                       according to the firm’s quality and security
                       management chief in Finland, Kalle Kaasalainen.


                # ⚓ New York Times ☛ The_Surgeon_General’s_Social_Media_Warning
                  and_A.I.’s_Existential_Risks⠀⇛


                       The U.S. surgeon general, Dr. Vivek Murthy, says
                       social media poses a “profound risk of harm” to
                       young people. Why do some in the tech industry
                       disagree?


                # ⚓ Variability_≠_“We_don’t_know”_how_COVID_vaccines_work⠀⇛


                       It’s been a while since I’ve written about a basic
                       science paper misinterpreted and/or misused by
                       antivaxxers. It’s also been a while since I’ve
                       encountered an antivax influencer or blogger with
                       whom I was unfamiliar when first seeing their
                       blather. So when I came across a post by someone
                       going by the ‘nym of Joomi entitled, New study
                       shows how little we know about how mRNA vaccines
                       “work”—along with a blurb claiming that “Vastly
                       different levels of spike protein depending on cell
                       type”—I knew I had my topic for today. I have no
                       idea who “Joomi” is other than this description
                       from the Substack Let’s Be Clear:


          o § Proprietary⠀➾


                # ⚓ Ars Technica ☛ Green_hills_forever:_Windows_XP_activation
                  algorithm_cracked_after_21_years⠀⇛


                       On the blog of tinyapps.org (first spotted by The
                       Register), which provides micro-scale, minimalist
                       utilities for constrained Windows installations, a
                       blog post appropriately titled “Windows XP
                       Activation: GAME OVER” runs down the semi-recent
                       history of folks looking to activate Windows XP
                       more than 20 years after it debuted, nine years
                       after its end of life, and, crucially, some years
                       after Microsoft turned off its online activation
                       servers (or maybe they just swapped certificates).


                # ⚓ The Register UK ☛ Microsoft_has_made_Azure_Linux_generally
                  available._Repeat,_Azure_Linux [Ed: The Register pushing
                  Microsoft agenda; this isn't support of GNU/Linux but an
                  attack on it]⠀⇛


                # ⚓ Dev Class ☛ Azure_Linux_released_at_Build_–_where_Microsoft
                  revealed_why_it_did_not_fork_Fedora [Ed: Microsoft mole Tim
                  Anderson moved from The Register to this other site, in which
                  he continues to actively attack and tarnish the Linux brand
                  for Microsoft]⠀⇛


                # § Windows TCO⠀➾


                      # ⚓ Security Week ☛ Organizations_Worldwide_Targeted_in
                        Rapidly_Evolving_Buhti_Ransomware_Operation⠀⇛


                             In a recent attack, the Buhti operators used
                             a minimally modified version of the LockBit
                             3.0 (LockBit Black) ransomware to target
                             Windows machines. The builder for LockBit
                             leaked online in September 2022.


          o § Security⠀➾


                # ⚓ Bleeping Computer ☛ New_Buhti_ransomware_gang_uses_leaked
                  Windows,_Linux_encryptors [Ed: Ransomware is about 95%
                  Windows; when Microsoft puts back doors in Windows, it blames
                  "China"; when it's something like WordPress extensions,
                  Microsoft media blames "Linux". The pinnacle of one's nerve
                  is attributing holes in proprietary software of VMware to
                  "Linux". Defective software can be installed on any system,
                  but that's like saying cars are unsafe because you can drive
                  them down a cliff.]⠀⇛


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


                       Security updates have been issued by Debian
                       (sniproxy), Fedora (c-ares), Oracle (apr-util,
                       curl, emacs, git, go-toolset and golang, go-
                       toolset:ol8, gssntlmssp, libreswan, mysql:8.0,
                       thunderbird, and webkit2gtk3), Red Hat (go-toolset-
                       1.19 and go-toolset-1.19-golang and go-toolset:
                       rhel8), Slackware (ntfs), SUSE (rmt-server), and
                       Ubuntu (linux-raspi, linux-raspi-5.4 and python-
                       django).


                # ⚓ ABC ☛ Patients_told_to_contact_NT_Health_following_privacy
                  breach_of_identifiable_medical_records⠀⇛


                       Northern Territory Health says the onus is on
                       individuals to check if the privacy of their
                       medical records has been breached by the
                       government.


                # ⚓ Data Breaches ☛ NT_Health_throws_breach_notification
                  obligations_out_the_window;_says_patients_should_call_them_to
                  find_out_if_they_were_affected?!⠀⇛


                       According to Northern Territory Health’s website,
                       the Australian government agency manages the
                       Northern Territory public health system, operating
                       across five service delivery regions, six
                       hospitals, 74 health clinics, and seven corporate
                       offices.


                # ⚓ Data Breaches ☛ Tennessee_Orthopaedic_Clinics_notifies_HHS
                  of_breach;_has_yet_to_notify_patients⠀⇛


                       An undated message on the Tennessee Orthopaedic
                       Clinics website states that TOC recently responded
                       to a security incident. They don’t say when they
                       discovered it, but their investigation determined
                       “that an unauthorized party accessed some of our
                       systems between March 20, 2023, and March 24, 2023,
                       and may have accessed or acquired certain files.”


                # ⚓ Data Breaches ☛ Two_ransomware_groups_claimed_to_have
                  attacked_Albany_ENT_&_Allergy_Services_and_leaked_data,_but
                  AENT_doesn’t_mention_that_at_all_in_their_notification?
                  ⠀⇛


                       On April 28, DataBreaches reported that two
                       different ransomware groups claimed to have
                       attacked Albany ENT & Allergy Services, P.C. in
                       Albany, New York. This week, Albany ENT & Allergy
                       Services notified regulators and 224,486 affected
                       employees and patients about a breach. Their
                       notification is stunning, however, for its lack of
                       certain details.


                # ⚓ NYSDFS_Fines_Lender_and_Mortgage_Servicer_$4.25M_for
                  Cybersecurity_Failures_Including_Vendor_Management⠀⇛


                       Yesterday, New York’s Department of Financial
                       Services (“DFS”) announced another enforcement
                       action under the state’s Cybersecurity Requirements
                       for Financial Services Companies, 23 N.Y.C.R.R.
                       Part 500 (“Reg 500”). According to the press
                       release, OneMain Financial Group LLC (“OneMain”)
                       will pay a $4.25 million penalty to New York State
                       for alleged violations of Reg 500.


                # ⚓ Security Week ☛ Google_Cloud_Users_Can_Now_Automate_TLS
                  Certificate_Lifecycle⠀⇛


                       Google makes ACME API available to all Google Cloud
                       users to allow them to automatically acquire and
                       renew TLS certificates for free.


                # ⚓ Krebs On Security ☛ Phishing_Domains_Tanked_After_Meta_Sued
                  Freenom⠀⇛


                       The number of phishing websites tied to domain name
                       registrar Freenom dropped precipitously in the
                       months surrounding a recent lawsuit from social
                       networking giant Meta, which alleged the free
                       domain name provider has a long history of ignoring
                       abuse complaints about phishing websites while
                       monetizing traffic to those abusive domains.


                # ⚓ Security Week ☛ Zyxel_Firewalls_Hacked_by_Mirai_Botnet⠀⇛


                       A Mirai botnet has been exploiting a recently
                       patched vulnerability tracked as CVE-2023-28771 to
                       hack many Zyxel firewalls.


                # ⚓ Ubuntu ☛ How_to_secure_your_MLOps_tooling?⠀⇛


                       Production-grade AI initiatives are not an easy
                       task. Organisations need to go through different
                       stages to prepare data, develop the model and
                       deploy it. Reproducibility and portability are
                       essential for such projects. This is where machine
                       learning operations (MLOps) can help. 


                # § Privacy/Surveillance⠀➾


                      # ⚓ The Register UK ☛ Subpoenaed_PyPI_says_bye-bye_to_as
                        much_IP_address_data_as_it_can⠀⇛


                             But now that the code repository has
                             disclosed receiving three subpoenas for data
                             on five users earlier this year, the Python
                             community package registry wants developers
                             to understand that it’s working to minimize
                             the user data that it stores.


                      # ⚓ Techdirt ☛ Leaked_Document_Shows_Spain_Is_Fully_On
                        Board_With_The_EU_Commission’s_Plan_To_Criminalize
                        Encryption⠀⇛


                             For a few years now, the EU Commission has
                             been pushing legislation that would
                             undermine, if not actually criminalize, end-
                             to-end encryption. It’s “for the children,”
                             as they say. To prevent the distribution of
                             CSAM (child sexual abuse material), the EU
                             wants to mandate client-side scanning by tech
                             companies — a move that would necessitate the
                             removal of one end of the end-to-end
                             encryption these companies offer to their
                             users.


          o § Defence/Aggression⠀➾


                # ⚓ Scheerpost ☛ ‘There_Is_No_Safe_Place_in_Gaza’:_Palestinians
                  Speak_Out_During_Israeli_Assault⠀⇛


                       In a vicious five-day assault, Israeli occupying
                       forces killed 33 Palestinians in Gaza.


                # ⚓ Scheerpost ☛ How_a_Small_Activist_Sailing_Ship_Successfully
                  Challenged_the_Nuclear_Arms_Race⠀⇛


                       The 1958 voyage of the Golden Rule offers important
                       strategic lessons on how to confront an
                       overwhelming evil and win.


                # ⚓ Democracy Now ☛ Seditious_Conspiracy:_Oath_Keepers_Founder
                  Stewart_Rhodes_Gets_18_Years_in_Prison_for_Jan._6⠀⇛


                       Stewart Rhodes, founder of the far-right Oath
                       Keepers group, has been sentenced to 18 years in
                       prison for his role in the attack on the U.S.
                       Capitol. It is the longest sentence handed down so
                       far to any participant in the January 6
                       insurrection, when thousands of Trump supporters
                       stormed the halls of Congress to stop the
                       certification of Joe Biden’s 2020 presidential
                       victory. One of Rhodes’s associates, Kelly Meggs,
                       who led the Florida chapter of the Oath Keepers,
                       was sentenced Thursday to 12 years in prison. A
                       jury had convicted both men of seditious conspiracy
                       in November. The sentences are a “substantial win
                       for democracy,” says Kristen Doerer, who reports on
                       right-wing extremism and followed the case.


                # ⚓ The Nation ☛ What_We_Can_Learn_From_the_Surge_of_Far-Right
                  Violence_in_India⠀⇛


                       Are you worried about the rising political power of
                       violent white nationalists in America? Well, you’ve
                       got plenty of company, including US national
                       security and counterterrorism officials. And we’re
                       worried, too—worried enough, in fact, to feel that
                       it’s time to take a look at the experience of
                       India, where Hindu supremacist dogma has
                       increasingly been enforced through violent means.
                       While there are striking parallels between both
                       countries, India appears to have ventured further
                       down the road of far-right violence. Its experience
                       could potentially offer Americans some valuable, if
                       grim, lessons.


                # § War in Ukraine⠀➾


                      # ⚓ Scheerpost ☛ Ukraine:_Why_Negotiations_Are_the_Only
                        Rational_Option_in_the_Face_of_Climate_Chaos_and
                        Nuclear_Dangers⠀⇛


                             The Pentagon Leaks have shown that, from the
                             U.S. military’s perspective, the
                             confrontation between Russia and Ukraine has
                             reached a stalemate. Neither side can win in
                             the foreseeable future, according to the
                             assessment.


                      # ⚓ Meduza ☛ Medvedev_says_‘conflict_in_Ukraine’_could_be
                        ‘going_on_for_decades’_—_Meduza⠀⇛


                             During an official visit to Vietnam on
                             Friday, Russian Security Council Deputy Chair
                             (and former President) Dmitry Medvedev told
                             journalists that the “military conflict” in
                             Ukraine will be “long-lasting.”


                      # ⚓ Meduza ☛ Russia_carries_out_deadly_missile_strike_on
                        Dnipro_medical_center_—_Meduza⠀⇛


                             A Russian missile has struck a medical center
                             in Dnipro, killing at least one person and
                             injuring at least 15, according to Ukrainian
                             President Volodymyr Zelensky.


                      # ⚓ Meduza ☛ ‘I_prayed_I_wouldn’t_be_next’_The_secretive
                        prisons_where_Russia_hides_and_tortures_Ukrainian
                        civilians⠀⇛


                             Over the last 14 months, Russia has abducted
                             thousands of Ukrainian civilians, from
                             volunteers and journalists to former soldiers
                             and officials, and locked them in Russian
                             prisons. The victims don’t have POW status,
                             they’re not allowed to see their lawyers or
                             loved ones, and most of them are impossible
                             to communicate with from outside. Those who
                             have managed to get out often still don’t
                             know the official reasons for their
                             incarceration or their release. In Simferopol
                             alone, more than 100 civilian hostages (as
                             they’re called by human rights advocates) are
                             currently in captivity. Meduza special
                             correspondent Lilia Yapparova spoke with
                             Ukrainians who have been released from the
                             facilities, as well as with their relatives
                             and lawyers, to find out how this clandestine
                             prison system works.


                      # ⚓ Latvia ☛ Police_car_convoy_heads_from_Latvia_to
                        Ukraine_Friday⠀⇛


                             On Friday, May 26, a convoy with technical
                             aid was sent by the Latvian State Police to
                             soldiers in Ukraine. In cooperation with the
                             Ministry of Defense and the Entrepreneurs for
                             Peace Fund, a 12-vehicle convoy has been
                             launched today, but there are more cars in
                             the aid package, as well as unmanned
                             aircraft, generators, mobile power stations
                             and uniforms.


                      # ⚓ Meduza ☛ The_second_drone_war_How_Ukraine_and_Russia
                        are_trying_to_use_drones_to_their_advantage_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_intelligence_ship_returns_to
                        Sevastopol_following_naval_drone_attack_—_Meduza⠀⇛


                             The Russian intelligence ship Ivan Khurs,
                             part of Russia’s Black Sea Fleet, has
                             returned to Sevastopol. Video footage of the
                             ship circulated on Telegram, and Russian news
                             outlet Kommersant confirmed that the Ivan
                             Khurs had returned to Sevastopol Bay.


                      # ⚓ Meduza ☛ Georgian_President_Salome_Zourabichvili
                        criticizes_government_for_appeasing_Russia_and_drifting
                        away_from_Europe_—_Meduza⠀⇛


                             In her Independence Day address, Georgian
                             President Salome Zourabichvili criticized the
                             government for its policies with regard to
                             Russia and Russian immigrants.


                      # ⚓ Latvia ☛ Baltic_states_and_Germany_pledge_long-term
                        support_for_Ukraine⠀⇛


                             The Prime Ministers of the Baltic
                             states gathered in Tallinn, Estonia May 26 to
                             meet with German Chancellor Olaf Scholz.


                      # ⚓ Latvia ☛ LTRK_President:_Latvians_should_help
                        Ukrainians_into_the_European_market⠀⇛


                             The revival of Ukraine’s economy will also be
                             an opportunity for Latvian entrepreneurs, who
                             should help Ukrainians to break into the
                             European market, Aigars Rostovskis, president
                             of the Latvian Chamber of Commerce and
                             Industry, said in an interview to Latvian
                             Television on May 26.


                      # ⚓ AntiWar ☛ Trying_To_Build_Peace_One_BRICS_at_a_Time⠀⇛


                             In the early days of the war in Ukraine,
                             Ukrainian President Volodymyr Zelensky was
                             open to negotiating a peace. The United
                             States was not.


                      # ⚓ The Strategist ☛ Putin_may_lose_it_all_by_going_all-
                        in_for_Ukraine⠀⇛


                             Russia’s continued isolation from the G7, and
                             the expansion of sanctions against Moscow,
                             have made the severe consequences of
                             President Vladimir Putin’s invasion of
                             Ukraine clearer than ever.


                      # ⚓ France24 ☛ Deadly_Russian_strike_on_hospital,_Kremlin
                        talks_with_China_and_Brazil⠀⇛


                             A hospital in the eastern Ukrainian city of
                             Dnipro was hit Friday morning in a Russian
                             missile attack, regional governor Serhiy
                             Lysak said. This comes as Russia held
                             separate talks with China and Brazil on the
                             war in Ukraine. Follow our blog to see how
                             the day’s events unfolded. All times are
                             Paris time (GMT+2).


                      # ⚓ France24 ☛ In_Ukraine’s_Avdiivka,_divided_loyalties
                        after_nearly_a_year_of_Russian_assault⠀⇛


                             Russian forces have for months been
                             concentrating their offensive on eastern
                             Ukraine with the aim of capturing the Donetsk
                             region. Avdiivka, a town located on the
                             outskirts of the occupied regional capital,
                             is one of the most dangerous places on the
                             front line. It has resisted Russian assaults
                             for nearly a year of continuous siege, and
                             Russian aircraft and missiles have been
                             ravaging what remains of the town for weeks.
                             FRANCE 24 reporters Catherine Norris Trent,
                             Johan Bodin and Dymitro Kovalchuk went in to
                             speak with the people there.


                      # ⚓ Hong Kong Free Press ☛ EU_urges_China_to_push_Russia
                        to_withdraw_from_Ukraine⠀⇛


                             The European Union told China’s envoy on
                             Thursday that it expects Beijing to help push
                             Russia to stop the bloodshed in Ukraine and
                             withdraw from the country. Senior EU foreign
                             policy official Enrique Mora met China’s Li
                             Hui in Brussels on the latest leg of
                             Beijing’s special representative for Eurasian
                             affairs’ European tour. Li has received
                             coordinated […]


                      # ⚓ Meduza ☛ Peskov_confirms_plans_to_move_Andrey
                        Rublev’s_fragile_‘Holy_Trinity’_icon_to_cathedral,
                        despite_conservators’_fears_—_Meduza⠀⇛


                             The Kremlin Press Secretary Dmitry Peskov
                             says that plans for transporting Andrey
                             Rublev’s “Holy Trinity” icon from the
                             Tretyakov Gallery to Moscow’s Christ the
                             Savior cathedral have been finalized and
                             approved by stakeholders.


                      # ⚓ LRT ☛ Lithuania_presents_next_military_aid_package
                        for_Ukraine⠀⇛


                             Lithuania’s next military assistance package
                             for Ukraine will include drone jamming
                             equipment, ammunition, military rations and
                             other support, Defence Minister Arvydas
                             Anušauskas has said.


                      # ⚓ RFERL ☛ Russian_Arms_Maker_Kalashnikov_Boosts_Output
                        Of_Kamikaze_Drones⠀⇛


                             Russian arms producer Kalashnikov, maker of
                             the world’s most widely used assault rifle,
                             said on May 26 it was launching a new
                             division for the production of kamikaze
                             drones — one of the key weapons used in the
                             Ukraine war.


                      # ⚓ RFERL ☛ German_Chancellor_Warns_Putin_Against_Frozen
                        Conflict_In_Ukraine⠀⇛


                             German Chancellor Olaf Scholz warned
                             President Vladimir Putin against creating a
                             frozen conflict along the borders of the
                             Ukrainian territories seized by Russia, in
                             remarks published on May 26 in the Koelner
                             Stadt-Anzeiger newspaper.


                      # ⚓ RFERL ☛ Blinken_To_Travel_To_Sweden,_Norway,_Finland,
                        As_Stockholm_Reiterates_NATO_Aspirations⠀⇛


                             U.S. Secretary of State Antony Blinken is set
                             to visit to Sweden, Norway, and Finland from
                             May 29 to June 2 as Washington seeks to
                             deepen transatlantic cooperation amid
                             Russia’s ongoing invasion of Ukraine.


                      # ⚓ RFERL ☛ EU’s_Former_Top_Diplomat_Concedes_Ukraine
                        Oversights,_Saying_‘Hindsight_Is_Always_Difficult’⠀⇛


                             The European Union’s former high
                             representative for foreign affairs and
                             security policy, Catherine Ashton, has
                             defended the bloc’s initial response after
                             Russia occupied Crimea in 2014, but
                             acknowledged “we did not know then what we
                             know now.”


                      # ⚓ RFERL ☛ Protesters_Condemn_Screening_Of_Russian
                        Azovstal_‘Propaganda’_In_Bulgaria⠀⇛


                             Dozens of people protested the screening at a
                             Russian cultural center in Sofia on May 25 of
                             a Russian film casting the capture last year
                             of the Azovstal steel plant in southern
                             Ukraine as a “liberation” from “neo-Nazis.”


                      # ⚓ teleSUR ☛ Moscow_Rejects_Sullivan’s_Remarks_About
                        Strikes_on_Russia⠀⇛


                             “We have not placed limitations on Ukraine
                             being able to strike on its territory within
                             its internationally recognized borders,” U.S.
                             Security Adviser said.


                      # ⚓ The Atlantic ☛ The_Russian_Red_Line_Washington_Won’t
                        Cross—Yet⠀⇛


                             Ukraine wants long-range missiles in order to
                             regain Crimea and end the war. Why won’t
                             Washington supply them?


                      # ⚓ YLE ☛ Migri_opening_17_new_reception_centres⠀⇛


                             Most reception system clients have come to
                             Finland from Ukraine, according to the
                             Finnish Immigration Service.


                      # ⚓ New York Times ☛ Russian_Missile_Strike_Hits
                        Ukrainian_Hospital⠀⇛


                             A Russian missile killed at least two people
                             and wounded dozens more at a hospital, while
                             apparent Ukrainian strikes hit occupied
                             cities in the south.


                      # ⚓ New York Times ☛ For_Ukraine_Military,_Far-Right
                        Russian_Volunteers_Make_for_Worrisome_Allies⠀⇛


                             Some fighters who led an incursion into
                             Russian territory this week have neo-Nazi
                             ties. “I worry that something like this could
                             backfire on Ukraine because these are not
                             ambiguous people.”


                      # ⚓ New York Times ☛ Anti-Kremlin_Group_Involved_in
                        Border_Raid_Is_Led_by_a_Neo-Nazi⠀⇛


                             The leader of the Russian Volunteer Corps,
                             one of the two insurgent groups responsible
                             for an armed incursion into Russia this week,
                             is a far-right extremist, German officials
                             and humanitarian groups say.


                      # ⚓ New York Times ☛ Ukraine_NATO_Bid_Mirrors_West
                        Germany’s_During_Cold_War⠀⇛


                             West Germany joined NATO in 1955, choosing
                             security over immediate territorial
                             integrity. Some suggest the same path could
                             be the best guarantee for Ukraine.


                      # ⚓ New York Times ☛ Russian_Public_Appears_to_Be_Souring
                        on_War_Casualties,_Analysis_Shows⠀⇛


                             Support for the war in Ukraine remains high
                             but could potentially turn if concern over
                             the high numbers of casualties persists,
                             according to FilterLabs AI.


                      # ⚓ Reason ☛ Eli_Lake:_Trump,_Russiagate,_and_the_End_of
                        FBI_Credibility⠀⇛


                             The Durham report is a “black eye” for the
                             FBI, leading Democrats, and the media, says
                             Lake.


                      # ⚓ New York Times ☛ The_Counteroffensive_Is_Coming⠀⇛


                             We preview what is next in the war in
                             Ukraine.


                      # ⚓ Defence Web ☛ Arms-to-Russia_row_raises_doubt_about
                        South_Africa’s_compliance,_which_could_face_tougher
                        scrutiny⠀⇛


                             The recent furore over accusations by the US
                             ambassador to South Africa, Reuben Brigety,
                             that South Africa was supplying arms to
                             Russia despite its declared policy of non-
                             alignment, has sparked a debate on whether
                             the country’s arms control is lax, non-
                             compliant and lacks oversight.


                      # ⚓ LRT ☛ Russia_moves_ahead_with_deployment_of_tactical
                        nuclear_weapons_in_Belarus⠀⇛


                             Russia moved ahead on Thursday with a plan to
                             deploy tactical nuclear weapons in Belarus,
                             whose leader said the warheads were already
                             on the move, in the Kremlin’s first
                             deployment of such bombs outside Russia since
                             the 1991 fall of the Soviet Union.


                      # ⚓ LRT ☛ Lithuanian_language_commission_sceptical_about
                        renaming_Kaliningrad⠀⇛


                             The State Commission of the Lithuanian
                             Language (VLKK) has rejected a proposal by
                             several MPs to stop calling the Russian
                             exclave wedged between Lithuania and Poland
                             ‘Kaliningrad’.


                      # ⚓ LRT ☛ Lithuania_hosts_9th_Vilnius_Russia_Forum⠀⇛


                             The Lithuanian capital is hosting the 9th
                             Vilnius Russia Forum on Friday.


                      # ⚓ RFA ☛ Malaysia’s_Mahathir_says_Russia_may_take
                        nuclear_option⠀⇛


                             The former prime minister also told Asia not
                             to take sides in U.S.-China disputes


                      # ⚓ RFERL ☛ Kazakhstan_Says_It_Has_No_Plans_To_Join_Any
                        Union_States⠀⇛


                             Kazakh presidential spokesman Ruslan
                             Zheldybai told journalists on May 26 that the
                             energy-rich Central Asian country has no
                             plans to join any union states, adding that
                             the integration process within the Russian-
                             led Eurasian Economic Union should only be in
                             the sphere of economics.


                      # ⚓ The Atlantic ☛ What_Happens_if_Russia_Stashes_Nukes
                        in_Belarus⠀⇛


                             And some news about that Kremlin drone strike


                      # ⚓ YLE ☛ No_reply_from_Russia_about_freezing_Finnish
                        embassy,_consulate_accounts⠀⇛


                             The bank accounts of the Finnish Embassy in
                             Moscow and the Consulate General’s office in
                             St Petersburg were frozen at the end of last
                             month.


                      # ⚓ New York Times ☛ Evan_Gershkovich_Appeals_Russia’s
                        Extension_of_His_Detention⠀⇛


                             Already jailed for two months on charges for
                             which Russia has provided no evidence, Mr.
                             Gershkovich has been ordered to remain in
                             prison for three more.


                      # ⚓ Meduza ☛ RIA_Novosti_source_threatens_‘consequences’
                        for_journalist_Evan_Gershkovich_if_WSJ_continues_to
                        publish_‘disinformation’_about_Russia_—_Meduza⠀⇛


                             Russia’s state news agency, RIA Novosti,
                             published a message from an “informed source
                             in Moscow,” warning The Wall Street Journal
                             (WSJ) of “consequences” for Evan Gershkovich,
                             a WSJ journalist who was arrested in Russia
                             in March 2023.


                      # ⚓ New York Times ☛ U.S._Condemns_Deal_Allowing_Russia
                        to_Deploy_Nuclear_Weapons_in_Belarus⠀⇛


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Techdirt ☛ Twitter_Demands_Academics_Who_Won’t_Pay_$42k/
                  Month_Delete_Any_Twitter_Data_They_Currently_Have⠀⇛


                       Elon Musk has insisted that “transparency is the
                       key to trust” in rebuilding Twitter in his image.
                       He says it all the time. But, of course, under
                       Musk, Twitter has been significantly less
                       transparent, choosing to skip its transparency
                       reports, and generally close itself off. But one of
                       the key methods for transparency on Twitter has
                       long been its willingness to allow academic
                       researchers to access its API and do research
                       around Twitter and its users.


                # ⚓ The Dissenter ☛ Kissinger_Vs._‘The_Most_Dangerous_Man_In
                  America’⠀⇛


          o § Environment⠀➾


                # ⚓ The Nation ☛ Warning_Signs_Are_Everywhere⠀⇛


                # ⚓ ANF News ☛ Ecologists_call_on_people_not_to_vote_for_those
                  who_destroy_nature_and_history⠀⇛


                       Ecocide is one of the most disastrous acts
                       perpetrated by the AKP government during its 22-
                       year rule. The AKP government has deliberately
                       plundered the nature of Kurdistan, not only through
                       construction, but also through dams and power
                       plants.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Nation ☛ Should_We_Bring_Species_Back_From
                        Extinction?⠀⇛


                             If you had a chance to save a species from
                             extinction, would you take it? I would—and I
                             am.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ FAIR ☛ Montana_TikTok_Ban_a_Sign_of_Intensified_Cold_War
                  With_China⠀⇛


                       Republicans see this as momentum to push other
                       state bans. Lawmakers of both major parties are
                       pushing legislation that “would block all
                       transactions from any social media company in or
                       under the influence of a ‘country of concern,’ like
                       China and Russia,” a move that would ban TikTok in
                       the US (USA Today, 12/13/22). Such a sweeping ban
                       is popular among voters, especially among
                       Republicans (Pew, 3/31/23; Wall Street Journal, 4/
                       24/23).


                # ⚓ Common Dreams ☛ Show_Don’t_Tell:_Josh_Hawley’s_Manly,
                  Rancid,_Ludicrous_Log_of_Suet⠀⇛


                       Improbably – is there enough irony left in the
                       world to contain it? – “spineless chicken man,”
                       “sniveling li’l bitch,” liar, coward and “coifed,
                       soft, seditionist” Josh Hawley, famed for his “wee
                       scamper of fear” from Jan. 6 rioters he abetted,
                       has written a book about…manhood. Predictably, it’s
                       been shredded by the former Marine and Democrat
                       seeking his Senate seat and most of the known world
                       for banalities like, “Every man is called to be a
                       warrior.” Most cogent review: “As if.”


                # ⚓ Insight Hungary ☛ EU_Commissioner:_Long_way_to_go_for
                  Hungary_to_receive_EU_funds⠀⇛


                       EU Budget Commissioner Johannes Hahn says there is
                       no specific deadline for the ongoing procedure
                       against Hungary, Euronews reports. It is also
                       possible that the closure of the case will slip
                       into the next Commission’s tasks in 2024. “There
                       are still major issues to be resolved, so we are
                       nowhere near the finish line,” said Hahn during a
                       hearing at the European Parliament. The Austrian
                       politician called the setting up the Integrity
                       Authority a step forward but said the Hungarian
                       government had not yet met the conditions. 


                       He also denied that the Commission was blocking the
                       deal. The Commission is interested in a solution
                       that serves the interests of Hungarian citizens, he
                       added. Hahn also said that since the rule of law
                       procedure has no time limit, the process could be
                       completed after the next European Commission is in
                       place. He suggested that it might be worth changing
                       the rules of the procedure in the future.


                # ⚓ Telex (Hungary) ☛ Three_upcoming_national_elections_could
                  bring_about_Orbán’s_veto_coalition_and_a_turnaround_in
                  Europe,_think_tank_expects⠀⇛


                       Nézőpont Institute, the government-affiliated think
                       tank, isn’t expecting any major changes at the 2024
                       EP elections. Speaking at an event organised by the
                       institute on Thursday at the headquarters of
                       Polgári Magyarországért Alapítvány (Foundation for
                       a Civic Hungary, the party foundation of Fidesz) on
                       Stefánia út, Ágoston Sámuel Mráz said that
                       according to their latest analysis, Fidesz could
                       win as big a victory on 9 June 2024 as it did at
                       the last EP elections or five years before.


                # ⚓ The Nation ☛ Biden_Must_Remake_His_Candidacy⠀⇛


                       Joe Biden’s reelection campaign isn’t going well.
                       Since announcing his bid for a second term in
                       April, the president’s poll numbers have remained
                       dismal. RealClearPolitics’ average of recent polls
                       gives him a 41.4 percent approval rating among
                       likely voters, while 53.8 percent disapprove. And
                       it won’t necessarily get better when Biden is in a
                       two-person race against a MAGA Republican. The
                       overall RCP average of recent polls currently has
                       Biden trailing former president Donald Trump by 1.4
                       points, while a mid-May Harvard CAPS/Harris survey
                       put the incumbent down by seven points against the
                       indicted Republican. An early May ABC News/
                       Washington Post poll had Florida Governor Ron
                       DeSantis leading Biden by five points.1


                # ⚓ The Nation ☛ Fox’s_Lies_Are_the_Folklore_of_Racial
                  Capitalism⠀⇛


                       It’s been a rough couple of weeks for the handful
                       of indefatigable optimists who took a Susan
                       Collins–like posture on the prospects that Fox News
                       might have learned some newsgathering lessons from
                       its $787.5 million settlement with Dominion News
                       over the election lies it aired in the wake of the
                       2020 presidential balloting. Yes, Fox cut ties with
                       white nationalist hate merchant Tucker Carlson,
                       purportedly over a private text communication in
                       which he remained a bit too true to the bit even
                       for the jaded and Caligulan Fox executive class.
                       But there’s been no broader institutional reckoning
                       with the network’s flagrant mendacity—indeed,
                       without missing a beat, the network that has aired
                       endless variations on the War on Christmas and a
                       steady stream of James O’Keefe–grade election-
                       season agitprop has resumed fabulizing about
                       virtually every facet of public life in the United
                       States.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Deutsche Welle ☛ EU:_Twitter_leaves_voluntary_pact_on
                        fighting_disinformation⠀⇛


                             Twitter has withdrawn from a voluntary
                             European Union agreement to stamp out
                             disinformation online, a top EU official said
                             late Friday.


                             “Twitter leaves EU voluntary Code of Practice
                             against disinformation. But obligations
                             remain,” EU Internal Market Commissioner
                             Thierry Breton wrote on Twitter.


                      # ⚓ The Revelator ☛ The_Perils_of_Capitalism_and
                        Disinformation:_4_Critical_New_Books⠀⇛


                      # ⚓ DeSmog ☛ Revealed:_1_in_3_GB_News_Hosts_Spread
                        Climate_Denial_On_Air_in_2022⠀⇛


                             A majority of GB News hosts attacked climate
                             action on the channel in 2022, while one in
                             three spread climate science denial, a DeSmog
                             analysis can reveal. 


                             Opponents of green policies have seized on
                             the energy crisis sparked by Russia’s
                             invasion of Ukraine to denounce the UK’s net
                             zero target and push for new,
                             environmentally-damaging fossil fuel
                             extraction. 


          o § Censorship/Free Speech⠀➾


                # ⚓ RFA ☛ Tiananmen_Mothers_calls_on_China’s_Xi_to_‘take
                  responsibility’_for_1989_massacre⠀⇛


                       Tiananmen Mothers, a group representing victims of
                       the June 4 massacre that ended weeks of pro-
                       democracy protests in 1989 has called on Chinese
                       leader Xi Jinping to take responsibility for the
                       actions of the government ahead of this year’s 34th
                       anniversary.


                # ⚓ Techdirt ☛ The_Supreme_Court_May_Not_Have_Read_Our_Brief
                  About_The_First_Amendment_And_Copyright,_But_You_Can⠀⇛


                       Technically we’ve posted this analysis before, when
                       we posted our entire amicus brief submitted to the
                       Supreme Court in the Andy Warhol Foundation v.
                       Goldsmith case, along with a summary of what we had
                       written in it. But that summary also included other
                       arguments, and a very condensed version of this
                       one, that the First Amendment requires copyright
                       law to be interpreted in a way that doesn’t harm
                       future free expression. It is an idea important
                       enough to be worth more attention – especially
                       given that it seems the Supreme Court itself
                       overlooked it.


                # ⚓ Meduza ☛ Alexey_Navalny’s_new_felony_trial_scheduled_to
                  begin_May_31._Prosecution_may_seek_30-year_sentence_for
                  jailed_politician.⠀⇛


                       The first hearing in a new criminal case against
                       the imprisoned Russian politician Alexey Navalny
                       has been scheduled for May 31, according to
                       Navalny’s social media accounts.


                # ⚓ Meduza ☛ Russian_journalist_hit_with_misdemeanor_charges
                  for_sharing_Meduza’s_reporting⠀⇛


                       The St. Petersburg authorities have opened a
                       misdemeanor case against journalist Valery Nechay,
                       the former head of the radio station Echo of St.
                       Petersburg, for participating in the activities of
                       an “undesirable” organization, according to the
                       human rights organization First Department.


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


                # ⚓ RFA ☛ Burmese_journalist_sentenced_to_10_years_in_jail_by
                  military_junta_court⠀⇛


                       A Burmese journalist was sentenced on Friday to 10
                       years in prison with hard labor for violating
                       Myanmar’s counterterrorism law, in addition to a
                       three-year sentence she received in December 2022
                       for defamation, an attorney working on her case
                       said.


                # ⚓ ANF News ☛ Journalist_who_exposed_rape_to_stand_trial_while
                  alleged_rapists_walk_free⠀⇛


                       Journalist Oktay Candemir covered the rape case in
                       Bêgirî (Muradiye) district last January. He
                       described how the “girl, studying at Muradiye
                       Nizamettin Aktaş High School, was made to use drugs
                       since 2019, and then was systematically sexually
                       assaulted. She was suspended from school on the
                       grounds that she was a drug addict. The people who
                       took pictures of Y., including police and officers,
                       raped Y. for years, using the pictures to blackmail
                       her.”


          o § Civil Rights/Policing⠀➾


                # ⚓ Amnesty International ☛ Afghanistan:_The_Taliban’s_war_on
                  women:_The_crime_against_humanity_of_gender_persecution_in
                  Afghanistan⠀⇛


                       After the Taliban seized control of Kabul in August
                       2021, the human rights situation of women and girls
                       in Afghanistan deteriorated severely, despite the
                       Taliban’s initial promise to respect women’s and
                       girls’ rights. The Taliban have been increasingly
                       introducing new restrictions with the apparent aim
                       of completely erasing women’s and girls’ presence
                       from public arenas. Taliban policies have been
                       further oppressing women and girls in almost all
                       aspects of their lives. The widespread and
                       systematic subjugation of girls and women in
                       Afghanistan is a flagrant violation of their human
                       rights and fundamental freedoms.


                # ⚓ [Repeat] New York Times ☛ Minnesota_Governor_Vetoes_Gig
                  Worker_Pay_Bill⠀⇛


                       Gov. Tim Walz of Minnesota on Thursday vetoed a
                       bill that would have guaranteed a minimum wage and
                       other protections for Uber and Lyft drivers.


                # ⚓ EFF ☛ EFF_at_RightsCon_2023⠀⇛


                       RightsCon provides an opportunity for human rights
                       experts, technologists, government representatives,
                       and activists to discuss pressing human rights
                       challenges and their potential solutions. 


                       We’re excited that many EFFers are heading to Costa
                       Rica and will be actively participating in this
                       year’s event – both online and in person. Several
                       members will be leading sessions and contributing
                       as speakers, as well as being available for
                       networking.


                # ⚓ Pro Publica ☛ How_We_Reached_Dairy_Farm_Workers_to_Write
                  About_Them⠀⇛


                       Spanish-speaking dairy farm workers in Wisconsin,
                       many of them undocumented immigrants, are not
                       regular readers of our website. Most have never
                       heard of ProPublica, let alone formed a trusting
                       relationship with us. Some have low levels of
                       literacy and poor internet connections because the
                       farms they work on are remote. Connecting with
                       them, both to conduct our reporting and to share
                       our findings, is a challenge.


                       For months, Melissa Sanchez and Maryam Jameel have
                       been reporting on conditions at these farms. But
                       one of their earliest missions was crucial. They
                       needed to find out how the workers got their news
                       and make sure ProPublica’s reporting reached them
                       and their communities. The reporters’ process
                       underscores one of our central beliefs at
                       ProPublica: Publishing a story about injustice
                       isn’t enough if we don’t reach the people who are
                       directly affected.


                # ⚓ Pro Publica ☛ Colorado_Limits_Court_Use_of_Family
                  Reunification_Camps⠀⇛


                       A bill signed into law this week in Colorado
                       prohibits family courts from ordering children to
                       participate in reunification programs that isolate
                       them from a trusted caregiver. Many of these
                       programs purport to offer treatments for parental
                       alienation, a psychological disorder that has been
                       rejected by mainstream scientific circles but
                       continues to influence custody decisions.


                       The new law, which takes effect immediately, also
                       requires experts who advise the court on custody
                       cases to have training in working with victims of
                       domestic violence and child abuse.


                # ⚓ Democracy Now ☛ Spike_Lee_on_“Malcolm_X”_&_How_Hollywood
                  Almost_Prevented_Landmark_Film_from_Being_Made⠀⇛


                       May 19 marked what would have been the 98th
                       birthday of Malcolm X. The director Spike Lee gave
                       the keynote address at an event marking the day at
                       the Malcolm X and Dr. Betty Shabazz Memorial and
                       Educational Center, which is housed in the former
                       Audubon Ballroom in New York where Malcolm X was
                       assassinated in 1965. Lee discussed the challenges
                       of making his acclaimed 1992 biopic of Malcolm
                       starring Denzel Washington, and how he overcame
                       funding shortfalls and studio indifference to get
                       the film made. “We knew that we had to keep going,”
                       Lee said.


                # ⚓ Democracy Now ☛ Memorial_Day_Massacre:_Chicago_Cops_Killed
                  10_During_1937_Steel_Strike,_Then_the_Media_Covered_It_Up⠀⇛


                       We look at the largely forgotten 1937 Memorial Day
                       Massacre, when police in Chicago shot at and gassed
                       a peaceful gathering of striking steelworkers and
                       their supporters, killing 10 people, most of them
                       shot in the back. It was a time like today, when
                       unions were growing stronger. The workers were on
                       strike against Republic Steel, and the police
                       attacked them with weapons supplied by the company.
                       The tragic story is told in a new PBS documentary.
                       “The mass media, right up to The New York Times,
                       was supporting the police story that they had no
                       choice but to open fire on this mob,” says Greg
                       Mitchell, who directed the new PBS documentary,
                       Memorial Day Massacre: Workers Die, Film Buried,
                       and edited a companion book that is the first oral
                       history on the tragedy. The film can be viewed at
                       PBS.org and was produced by Lyn Goldfarb.


                # ⚓ The Nation ☛ What_the_Brutal_Death_of_Gabriella_Gonzalez
                  Tells_Us_About_Domestic_Violence_Post-Roe⠀⇛


                       In early May, Texas resident Gabriella Gonzalez
                       traveled to Colorado for abortion care. The journey
                       out of state is a familiar one for Texans, who have
                       lived under a draconian six-week abortion ban since
                       2021, long before the US Supreme Court overturned
                       Roe v. Wade last year, and a criminal “trigger law”
                       that imposes up to life in prison for providers,
                       since August. Like so many Texans, the 26-year-old
                       mother of three was forced out of her home state
                       for health care. Upon her return, Harold Thompson,
                       her 22-year-old ex-boyfriend who is believed to
                       have impregnated her and who did not approve of her
                       abortion—sought revenge. During an argument at a
                       gas station in Dallas the morning after she
                       returned, Thompson placed Gonzalez in a choke hold
                       and then fatally shot her once in the head and
                       several times thereafter.


                # ⚓ The Nation ☛ Unions_Are_Stepping_Up_to_Find_a_Solution_to
                  California’s_Housing_Crisis⠀⇛


                       Today, Friday, May 26, unions in Los Angeles are
                       pushing some big new ideas into the public sphere.
                       Negotiators with UNITE HERE Local 11, the radical
                       trade union that represents thousands of
                       hospitality workers in restaurants, hotels, sports
                       arenas, and airports around the region, are
                       advancing a set of proposals for an updated
                       contract with 100 employers, replacing those
                       contracts that are expiring at the end of June.


                # ⚓ The Nation ☛ Fascism_by_Default⠀⇛


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Techdirt ☛ Hugely_Profitable_And_Consolidated_Streaming
                  Platforms_Suddenly_Too_Cheap_To_Pay_Residuals_And_Writers,_Or
                  Keep_Niche_Shows_Online⠀⇛


                       We’ve noted repeatedly that as the streaming sector
                       grows and consolidates, it’s revealing many of the
                       same problems we saw inherent in traditional,
                       shitty, cable TV. As in the need to provide Wall
                       Street improved quarterly returns at any cost has
                       them doing the sort of things common in the
                       traditional cable sector they used to criticize and
                       disrupt (see Netflix’s password sharing cash grab).


          o § Monopolies⠀➾


                # § Trademarks⠀➾


                      # ⚓ Techdirt ☛ Monster_Energy_Opposes_A_Fitness_Trainer’s
                        Trademark_Because_Of_Course_It_Did⠀⇛


                             Ah, Monster Energy. For regular readers of
                             Techdirt, the name of the company alone is
                             enough to get your eyes rolling harder than a
                             teenager at a rave. Posts on the company’s
                             trademark bullying ways are so legion that I
                             dare not even begin listing them; if you’re
                             unfamiliar with them, click the link and be
                             sure you have a pillow on your desk or you’re
                             going to suffer a concussion.


                # § Copyrights⠀➾


                      # ⚓ Walled Culture ☛ Top_EU_court_to_issue_definitive
                        ruling_on_whether_copyright_is_more_important_than
                        privacy⠀⇛


                             This is an important case, because it will
                             clarify whether copyright infringement can be
                             considered a “serious crime” that trumps
                             privacy concerns and allows general online
                             surveillance of the public despite the
                             region’s privacy laws. In bringing the case,
                             La Quadrature du Net naturally hopes that
                             data protection laws will not be trampled
                             upon so easily, and that the EU’s top court
                             will affirm copyright’s relative lack of
                             importance in the grand scheme of things, but
                             nothing is certain. Euractiv writes: [...]


                      # ⚓ Torrent Freak ☛ 2.5_Billion_Visits:_ACE_Targets
                        9anime_Among_Several_Pirate_Anime_Sites⠀⇛


                             Despite offering only one type of content,
                             9anime is one of the most-visited sites in
                             the world, period. Since that amounts to over
                             2.5 billion visits per year, it was no
                             surprise to see anti-piracy coalition ACE
                             back in court this week hoping to obtain
                             information on the site’s operators. Other
                             anime piracy sites are under the spotlight
                             too, including some that appear to have no
                             traffic at all.


                      # ⚓ Torrent Freak ☛ Court_Orders_Instagram_to_Expose
                        Pirates,_Boot_Their_Accounts,_and_Purge_URLs⠀⇛


                             The High Court in Bombay, India, has ordered
                             Instagram to share the personal details of
                             copyright-infringing users with a media
                             company. Through a broad dynamic injunction,
                             the social media giant is further required to
                             terminate associated accounts and purge
                             infringing URLs they shared from its
                             platform.


                      # ⚓ Techdirt ☛ Studies_Suggest_That_Rather_Than_Killing
                        Jobs,_AI_Could_Revive_The_Middle_Class⠀⇛


                             We’ve certainly been talking a lot about the
                             “AI Doomers” who insist that AI is all too
                             likely to destroy humanity. However, even
                             people who aren’t fully on board with the
                             existential threat of AI do often say that,
                             at the very least, it’s going to destroy jobs
                             for most people, potentially creating huge
                             problems. For years now, people have been
                             arguing for universal basic income, in large
                             part, because they think that automation and
                             AI will take away everyone’s jobs. I mean, it
                             was a core plank of Andrew Yang’s silly run
                             for President.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ 🔤SpellBinding:_AHLMNOR_Wordo:_TIDED⠀⇛


                # ⚓ PMBOK_Guide_7,_Underneath_the_Surface_(book)⠀⇛


                       I’ve written a new book on PMBOK 7 (the well-known
                       project management standard). I aimed to go
                       underneath the surface and explain what it really
                       means. It’s about appreciating its true value
                       without dogmatism.


          o § Technical⠀➾


                # ⚓ May_CLI_additions⠀⇛


                       I added a commandline cheatsheet for mutt (my mail
                       client) and updated the one for amforai (gemini
                       space browser).


                       The mutt cheatsheet is not a full step-by-step
                       tutorial, they aren’t meant to be. I’ve done my
                       best to give a structured outline of what I
                       tweaked.


                # § Internet/Gemini⠀➾


                      # ⚓ From_my_bubble_about_Bubble⠀⇛


                             There is much buzz about [Skyjake's project
                             called Bubble] on the Geminispace. There was
                             a long thread on Cosmos, which I can’t locate
                             now. A good start of discussion is
                             Bacardi55′s second gemlog article. So there
                             are many points of view, as usual in today’s
                             world.


                             It’s something like the plot of /Silo/ (a TV
                             series, according to Wikipedia: based on the
                             /Wool/ series of novels by author Hugh
                             Howey). /Silo/ is about the last ten thousand
                             people living in the underground concrete
                             bunker formed in a silo-shaped hole. They
                             live according to the rules called the Pact,
                             which origin is unclear. One of the Pact
                             regulations forbade the installation of
                             elevators. So they walk up and down the
                             stairs. There are hundreds of floors, so such
                             travels last all day.


                      # ⚓ From_my_bubble_about_Bubble⠀⇛


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



                    ䷩ 𝚕𝚒𝚗𝚎 5678

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_27/05/2023:_Goodbyes_to_Tina_Turner⠀✐


Posted in News_Roundup at 3:36 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Games
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
    * Leftovers
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Patents
                # Trademarks
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o § Games⠀➾


                # ⚓ Godot Engine ☛ Dev_snapshot:_Godot_4.1_dev_3⠀⇛


                       The end of May means the approach of the feature
                       freeze for Godot 4.1, and this dev snapshot aims to
                       give you as many new features to test as possible.


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ Packit_Team:_Handling_of_Release_field_in
                  propose_downstream_job⠀⇛


                       Handling of Release field in propose_downstream job
                       # We have recently made some fixes to the process
                       of handling the Release field regarding the
                       %autorelease macro, so let’s take that opportunity
                       to explain how it works.


                       You can maintain the Release field manually, you
                       can use a dummy value or you can take advantage of
                       the %autorelease macro.


                       Maintaining Release manually # You can maintain the
                       Release field manually as you would do downstream,
                       for example you could bump the value every time you
                       make changes to the spec file and reset it to 1
                       when you release a new version.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ This_cheap_robot_arm_can_follow_recorded
                  movements⠀⇛


                       There are many ways to control a robot arm, with
                       the simplest being a sequential list of rotation
                       commands for the motors. But that method is very
                       inefficient when the robot needs to do anything
                       complex in the real world.


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Updates_1980′s_Omnibot_with
                  AI_and_Machine_Learning⠀⇛


                       Matt from Viam Robotics has upgraded an old 1980s
                       Omnibot with a Raspberry Pi to give it new modern
                       features.


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Brings_Ghostly_Betta_Fish_to
                  Life⠀⇛


                       N4MI0 is using a Raspberry Pi to power a Pepper’s
                       Ghost effect betta fish project that looks like a
                       fish in a bowl.


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Helps_Research_Team_Monitor
                  Glaciers_in_Peru⠀⇛


                       This research team is using Raspberry Pis to
                       monitor glacier calving in Peru and Iceland using
                       cameras to make 3D renders of glaciers.


                # ⚓ Tom’s Hardware ☛ Milk-V_Offers_a_Trio_of_RISC-V_Raspberry
                  Pi_Alternatives⠀⇛


                       With models starting from $9, Milk-V is offering an
                       enticing trio of Raspberry Pi alternatives — all of
                       which are powered by a RISC-V CPU


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


          o § Programming/Development⠀➾


                # ⚓ Rlang ☛ What_is_the_sink()_function?_Capturing_Output_to
                  External_Files⠀⇛


                       The sink() function in R is used to divert R output
                       to an external connection. This can be useful for a
                       variety of purposes, such as exporting data to a
                       file, logging R output, or debugging R code.


                # ⚓ Rlang ☛ R_Programming_and_Pharmaceutical_Data_Analysis_
                  (Packages_for_Clinical_Trial_Data)⠀⇛


                       In the clinical trials reporting industry, there is
                       an incorrect assumption that SAS software is ideal
                       as regulatory agencies “require” it. Regulatory
                       agencies generally do not mandate the use of
                       specific software for clinical trials reporting.
                       They primarily focus on the accuracy, integrity,
                       and compliance of the reported data.


    * § Leftovers⠀➾


          o ⚓ RTE ☛ Cruinniú_na_nÓg_2023_is_back_–_Supported_by_RTÉ⠀⇛


                 WATCH our promo here. Cruinniú na nÓg takes place on
                 Saturday 10th June, and this year more than 500 free
                 creative events are planned for thousands of young people
                 throughout the country, including Forest Bathing in
                 Castlefreke, Celestial Mechanics at the Dunsink
                 Observatory, a recreation of Clones Town in ceramics,
                 Hula hooping in Waterford…


          o ⚓ New York Times ☛ Rolf_Harris,_Disgraced_British_Entertainer,_Dies
            at_93⠀⇛


                 His career as a musician and a painter over six decades
                 ended abruptly when he was convicted of sexually abusing
                 teenage girls.


          o ⚓ The Atlantic ☛ Push_Notifications_Are_Out_of_Control⠀⇛


                 There must be better ways of opting out.


          o § Education⠀➾


                # ⚓ Helsinki Times ☛ Massive_education_budget_cuts_proposed_in
                  government_negotiations_–_Could_lead_to_closure_of_over_100
                  educational_institutions⠀⇛


                       According to information made public, government
                       negotiators are considering a drastic 50 percent
                       cut in funding for adult education based on a
                       proposal by the Ministry of Finance. Such a
                       decision would have severe consequences for
                       employment, continuous learning, public well-being,
                       and regional equality. A joint statement from 14
                       organizations warns that numerous educational
                       institutions would be forced to shut down as a
                       result of these budget cuts.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ Ultrawide_8.8-inch_HDMI_and_USB_information
                  display_is_offered_with_optional_touchscreen_support⠀⇛


                       Last year, I wrote about the Turing Smart Screen
                       low-cost 3.5-inch display based on a WCH CH552T 8-
                       bit E8051 core microcontroller that connects to a
                       PC or other device through a USB Type-C cable in
                       order to display system or other information using
                       AIDA64 software or an open-source Python software.


                # ⚓ CNX Software ☛ FireBeetle_2_ESP32-S3_camera_board_ships
                  16MB_flash,_8MB_PSRAM,_PCB_or_external_antenna⠀⇛


                       DFRobot “FireBeetle 2 ESP32-S3” is a 2MP camera
                       board with ESP32-S3N16R8 dual-core WiFi and
                       Bluetooth microcontroller fitted with 16MB flash
                       and 8MB PSRAM, and offered in two versions: a more
                       compact variant with a PCB antenna, and one with an
                       external antenna offering a better signal quality.


                # ⚓ CNX Software ☛ SONOFF_TX_Ultimate_Review_–_A_smart_touch
                  wall_switch_with_innovative_features⠀⇛


                       SONOFF has been producing a wide range of new
                       products over the years, and since the beginning of
                       the year, the company introduced various new
                       products and features including the iHost Smart
                       Home Hub local hub which no longer requires cloud
                       connectivity. The one we are going to review is the
                       Ultimate Smart Touch Wall Switch (also known as the
                       SONOFF TX Ultimate).


                # ⚓ CNX Software ☛ AMD_Ryzen_and_Athlon_7020-C_processors_to
                  power_Chromebooks_with_up_to_19.5_hours_of_battery_life⠀⇛


                       AMD has just unveiled the Ryzen and Athlon 7020-
                       C series processor family designed for Chromebooks,
                       with up to four “Zen 2” cores clocked at up to 4.3
                       GHz, AMD RDNA 2 graphics, and promises of high
                       power efficiency with Chromebook based on the
                       entry-level Athlon Silver 7120C processor lasting
                       up to an estimated 19.5 hours on a charge.


                # ⚓ CNX Software ☛ Zotac_PI430AJ_Pico_mini_PC_features_Airjet
                  solid-state_active_cooling_chips⠀⇛


                       ZOTAC PI430AJ Pico is the first mini PC equipped
                       with (two) Airjet solid-state active cooling chips
                       introduced at CES 2023, doing without the metal
                       case required by typical fanless systems, and
                       instead relying on a plastic case. The PI430AJ Pico
                       is powered by a recent 7W Intel Core i3-N300 octa-
                       core Alder Lake-N processor coupled with up to 16GB
                       LPDDR5 RAM and an M.2 NVMe SSD up to 1TB capacity.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ The Atlantic ☛ Think_About_Your_Death_and_Live_Better⠀⇛


                       Contemplating your mortality might sound morbid,
                       but it’s actually a key to happiness.


                # ⚓ The Atlantic ☛ Tina_Turner’s_Cosmic_Life⠀⇛


                       The late singer stretched human expression to its
                       fraying limits—and then her story became a
                       folktale.


                # ⚓ TwinCities Pioneer Press ☛ DEA’s_failure_to_punish
                  distributor_blamed_in_opioid_crisis_raises_revolving_door
                  questions⠀⇛


                       It has allowed one distributor to keep shipping
                       painkillers despite a judge’s recommendation to
                       strip its license.


                # ⚓ Science Alert ☛ 1st_Plastics_Pollution_Weather_Forecast
                  Predicts_88_Pounds_of_Microplastic_Over_Paris⠀⇛


                       Hope your umbrella’s sturdy.


                # ⚓ teleSUR ☛ +300_Unprotected_Level_Crossings_to_Be_Secured_in
                  Sri_Lanka⠀⇛


                       “…the modifications to secure the level crossings
                       will be completed in two months…”


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Vice Media Group ☛ Captcha_Is_Asking_Users_to
                        Identify_Objects_That_Don’t_Exist⠀⇛


                             Discord’s captcha asked users to identify a
                             ‘Yoko,’ a snail-like object that does not
                             exist and was created by AI.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Bruce Schneier ☛ Indiana,_Iowa,_and_Tennessee_Pass
                        Comprehensive_Privacy_Laws⠀⇛


                             It’s been a big month for US data privacy.
                             Indiana, Iowa, and Tennessee all passed state
                             privacy laws, bringing the total number of
                             states with a privacy law up_to_eight. No
                             private right of action in any of those,
                             which means it’s up to the states to enforce
                             the laws.


          o § Defence/Aggression⠀➾


                # ⚓ The Strategist ☛ Israel_at_75⠀⇛


                       Religion and miracles often go hand in hand, so it
                       should come as little surprise that Israel, which
                       just marked its 75th birthday, is something of a
                       miracle.


                # ⚓ The Strategist ☛ Parliamentary_scrutiny_is_essential_for
                  effective_national_defence⠀⇛


                       Our dangerous times are driving an unprecedented
                       tempo of strategy writing in Canberra.


                # ⚓ New York Times ☛ A_Year_in_Uvalde⠀⇛


                       How grief has warped the lives of the Uvalde
                       shooting victims’ families and friends.


                # ⚓ New York Times ☛ USS_Mannert_L._Abele,_Navy_Ship_Sunk_in
                  World_War_II,_Is_Found⠀⇛


                       The U.S.S. Mannert L. Abele was broken in half by
                       two kamikaze attacks and sank in 4,500 feet of
                       water, killing 84 sailors.


                # ⚓ New York Times ☛ Biden_to_Nominate_Gen._Charles_Q._Brown_to
                  Be_Joint_Chiefs_Chairman⠀⇛


                       If confirmed by the Senate, the Air Force chief of
                       staff would become the senior military adviser to
                       the president.


                # ⚓ New York Times ☛ Nashville_Parents_Can_Have_Say_in_Case
                  Over_Shooter’s_Writings,_Judge_Rules⠀⇛


                       A group of about 100 families will now have the
                       chance to argue in court against releasing the
                       writings of the assailant who killed six people at
                       a Christian school.


                # ⚓ New York Times ☛ A_Look_at_the_Fight_for_Gun_Control_Since
                  the_Uvalde_Shooting⠀⇛


                       After the Supreme Court ruled last year that people
                       could carry guns outside their homes, legal
                       challenges and legislative debates have been
                       playing out across the country.


                # ⚓ CS Monitor ☛ One_year_after_Uvalde,_three_activists_share
                  their_stories⠀⇛


                       The crucible of grief after school shootings has
                       spurred some people to push for change. One year
                       after Uvalde, three activists share their stories.


                # ⚓ YLE ☛ Finland_joins_Nato’s_Brunssum_HQ_in_the_Netherlands⠀⇛


                       As Nato is in a period of transition and
                       reorganisation, Finland’s time at the Netherlands’
                       headquarters may be temporary.


                # ⚓ RFERL ☛ In_Belgrade,_U.S._Senator_Urges_Quick
                  Implementation_Of_Serbia-Kosovo_Agreement⠀⇛


                       U.S. Senator Chris Murphy told reporters during a
                       visit to Belgrade on May 25 that Serbia and Kosovo
                       should quickly implement an EU-brokered agreement
                       to normalize ties, calling it a step forward that
                       both sides should be proud of.


                # ⚓ teleSUR ☛ Putin_Calls_for_Enhanced_Eurasian_Union-LATAM
                  Cooperation⠀⇛


                       “Our association is constantly asserting itself as
                       one of the independent and self-sufficient centers
                       of the emerging multipolar world,” he stressed.


                # ⚓ Latvia ☛ Stoltenberg:_“NATO_can_count_on_Latvia._And_Latvia
                  can_count_on_NATO”⠀⇛


                       NATO Secretary General Jens Stoltenberg welcomed
                       Latvian Prime Minister Krišjānis Kariņš to NATO
                       Headquarters in Brussels on May 24, thanking
                       him for Latvia’s contributions to the Alliance,
                       including leadership on defense spending, and
                       deployments to maritime operations and missions in
                       Kosovo and Iraq.


                # ⚓ teleSUR ☛ Armenia_And_Azerbaijan_Move_To_Normalize
                  Bilateral_Relations⠀⇛


                       Nagorno-Karabakh, an Armenian-populated enclave
                       within Azerbaijan, has been a source of conflict in
                       recent years.


                # ⚓ The Atlantic ☛ A_Chinese_American_Show_That_Doesn’t_Bother
                  to_Explain_Itself⠀⇛


                       Disney+’s American Born Chinese, based on the best-
                       selling graphic novel, offers a confident take on
                       the second-generation experience.


                # ⚓ LRT ☛ Lack_of_training_facilities_‘showstopper‘_for
                  Baltics,_says_German_general⠀⇛


                       The lack of military training facilities is a
                       “showstopper” for the Baltic states’ better
                       interoperability with allies, Harald Gante,
                       Commander of Germany’s Field Army, has said.


                # ⚓ teleSUR ☛ A_Fugitive_Wanted_for_Rwandan_Genocide_is
                  Arrested⠀⇛


                       In 1994, Fulgence Kayishema, together with other
                       co-perpetrators, murdered over 2,000 men, women,
                       elderly and children refugees in Kivumu commune.


                # ⚓ JURIST ☛ DRC_files_ICC_complaint_against_Rwanda_over
                  alleged_theft_of_natural_resources⠀⇛


                       Democratic Republic of the Congo (DRC) Minister of
                       Justice Rose Mutombo filed an International
                       Criminal Court (ICC) complaint against Rwanda on
                       Tuesday over Rwanda’s alleged involvement in the
                       theft of natural resources in the DRC.


                # ⚓ Vice Media Group ☛ A_New_Uber_Clone_With_Armed_Drivers_Is
                  the_App_for_a_Violent_and_Paranoid_America⠀⇛


                       “What I’m creating is a necessary evil,” the app’s
                       founder claims while operating in a city with
                       falling crime rates.


                # ⚓ RFERL ☛ Bodies_Of_Migrants_Who_Died_In_Bulgaria_Returned_To
                  Afghanistan,_Taliban_Says⠀⇛


                       Afghanistan’s Taliban-controlled Foreign Ministry
                       says the bodies of 18 Afghan migrants who died of
                       suffocation while attempting to cross into Bulgaria
                       have been transferred to Kabul.


                # ⚓ teleSUR ☛ Over_1_Mln_Are_Internally_Displaced_in_Somalia_in
                  Four_Months⠀⇛


                       Currently, 3.8 million people are now displaced in
                       Somalia, exacerbating a dire humanitarian situation
                       where some 6.7 million people are struggling to
                       meet their food needs.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Lumen_Researcher_Interview_Series:_Professor_Jon_Penney⠀⇛


                       the Lumen teamn chats with Professor Jon Penney
                       about how Lumen has been part of his work.


          o § Environment⠀➾


                # ⚓ New York Times ☛ Mawar_Becomes_a_Super_Typhoon_After
                  Lashing_Guam:_Latest_Storm_Updates⠀⇛


                       Island residents experienced howling winds and
                       periods of intense rainfall, which left most of
                       Guam without power. Officials had yet to assess the
                       damage, but typhoon warnings remained in effect.


                # ⚓ teleSUR ☛ UN:_8.5_Mln_USD_for_Cyclone_Victims_in
                  Madagascar⠀⇛


                       “We launched humanitarian projects to support
                       335,000 people in the most vulnerable areas”


                # ⚓ teleSUR ☛ Italy:_Massive_Emergency_Aid_Package_Approved,
                  Flood-Hit_Region⠀⇛


                       “…it has an estimated value in excess of 2 billion
                       euros…”


                # ⚓ Federal News Network ☛ Guam_‘very_blessed’_with_no_early
                  reports_of_major_damage_in_the_messy_aftermath_of_Typhoon
                  Mawar⠀⇛


                       Residents of Guam are cleaning up after Typhoon
                       Mawar tore through the remote U.S. Pacific
                       territory and ripped roofs off homes, flipped
                       vehicles and shredded trees. Officials say there
                       were minor injuries reported but no fatalities. The
                       typhoon is the strongest to hit the territory of
                       roughly 150,000 people since 2002. It briefly made
                       landfall Wednesday night as a Category 4 storm. The
                       island’s international airport flooded and the
                       swirling typhoon churned up a storm surge and waves
                       that crashed through coastal reefs and flooded
                       homes. A police sergeant says Guam has been “very
                       blessed” without any deaths or major damage.


                # § Energy/Transportation⠀➾


                      # ⚓ New York Times ☛ France_Bans_Short_Domestic_Flights,
                        But_Not_Much_Changes⠀⇛


                             A decree formalizing the measure, which was
                             passed in 2021, is riddled with exceptions.
                             Critics call its effect symbolic, at best.


                      # ⚓ YLE ☛ Finland’s_average_electricity_price_slips_into
                        negative_territory⠀⇛


                             The oversupply of virtually emissions-free
                             electricity is mainly due to spring flooding,
                             which is super-charging hydropower
                             production.


                      # ⚓ Vice Media Group ☛ Scientists_Working_to_Generate
                        Electricity_From_Thin_Air_Make_Breakthrough⠀⇛


                             Scientists making the “Air-gen” device have
                             discovered that any material can be used to
                             generate electricity from the air.


                      # ⚓ Federal News Network ☛ California_unlikely_to_run
                        short_of_electricity_this_summer_thanks_to_storms,_new
                        power_sources⠀⇛


                             California regulators say the state is
                             unlikely to run short of electricity this
                             summer, thanks to new power sources and a wet
                             winter that filled reservoirs to restart
                             hydroelectric power plants shuttered during
                             the drought. Officials say more than 8,000
                             megawatts of new wind, solar and battery
                             power will come online by September. One
                             megawatt of electricity is enough to power
                             about 750 homes. California normally has more
                             than enough electricity to power the homes
                             and businesses of its more than 39 million
                             people. But the electrical grid has trouble
                             when it gets really hot and everyone turns on
                             their air conditioners at the same time.
                             California ran short of power in 2020. That
                             caused brief blackouts for hundreds of
                             thousands of households.


                # § Wildlife/Nature⠀➾


                      # ⚓ IDA ☛ IDSW_2023_Wrap-Up!⠀⇛


                             We at DarkSky International want to express
                             our sincerest thank you and congratulations
                             to dark sky advocates around the world for
                             making International Dark Sky Week 2023 a
                             resounding success!/blockquote>


                      # ⚓ New York Times ☛ Orcas_Have_Sunk_3_Boats_in_Southern
                        Europe,_Scientists_Say⠀⇛


                             A small group of orcas is ramming into
                             sailboats in waters off the Iberian
                             Peninsula. Researchers say they do not know
                             what is driving the unusual behavior toward
                             boats.


                      # ⚓ YLE ☛ Helsinki_zoo_opens_wildlife_emergency_help
                        line⠀⇛


                             Helsinki’s Korkeasaari Zoo has opened an
                             emergency number to provide advice to people
                             who find wild animals in urgent need of help.


                      # ⚓ Science Alert ☛ Study_Confirms_That_You_Can_Really
                        Communicate_With_Your_Cat_By_Doing_This⠀⇛


                             It really works.


                      # ⚓ Latvia ☛ Orphan_bear_to_move_to_France⠀⇛


                             On Thursday, May 25, the bear cub which was
                             delivered to the Rīga National Zoo in April
                             after being found alone next to a highway is
                             heading to her new home at the La Taniere zoo
                             in France, the Nature Conservation Agency
                             said.


                # § Overpopulation⠀➾


                      # ⚓ The Straits Times ☛ 1_out_of_10_paediatric_clinics_in
                        Seoul_shut_since_2017_amid_low_fertility_and_profits⠀⇛


                             While clinics face ultra-low birth rates, the
                             government has also frozen doctor appointment
                             fees.


          o § Finance⠀➾


                # ⚓ CNBC ☛ Tech_layoffs_ravage_the_teams_that_fight_online
                  misinformation_and_hate_speech⠀⇛


                       Meta, Amazon, Alphabet and Twitter have all
                       drastically reduced the size of their teams focused
                       on internet trust and safety as well as ethics as
                       the companies focus on cost cuts.


                # ⚓ Atlantic Council ☛ There_is_no_alternative_to_US
                  Treasuries⠀⇛


                       In the wake of a US default, investors searching
                       for safe assets may have no viable alternative to
                       US Treasuries.


                # ⚓ Axios ☛ The_gender_confidence_gap_in_investing⠀⇛


                       Note: Among non-retirees with self-directed
                       retirement savings. Data: Federal_Reserve; Chart:
                       Axios Visuals


Men are far more comfortable investing their own retirement money than women, a
new Fed survey shows.


⚓ CS Monitor ☛ How_much_would_debt_default_damage_US?_History_offers_clues.⠀⇛


     In U.S. debt limit talks, even going to the brink of default can harm
     investor confidence. Yet the nation has survived past cases of mini
     default.


⚓ The Atlantic ☛ The_Case_for_Debt-Ceiling_Optimism⠀⇛


     All of the public feuding is good, actually.


⚓ teleSUR ☛ Fitch_Places_US_AAA_Rating_on_Negative_Watch⠀⇛


     Despite reaching the US$31.4 trillion debt limit in January,
     discussions between the White House and congressional leaders only
     began on May 9.


⚓ teleSUR ☛ Eurasian_Economic_Union-BRICS_Turnover_Increases_by_60_Pct⠀⇛


     Policymakers from various countries meet in Moscow to discuss the
     issue of Eurasian integration in a multipolar world.


⚓ Latvia ☛ Latvia’s_unemployment_rate_slightly_above_EU_average_in_Q1⠀⇛


     Results of the Labour Force Survey (LFS) published on May 25 by the
     Central Statistical Bureau of Latvia (CSB) show that in Q1 2023
     Latvian unemployment rate constituted 6.4 %. Over the quarter it fell
     by 0.3 percentage points and over the year by 0.9 percentage points.


⚓ YLE ☛ European_Commission_says_Finland’s_debt_is_exceptional,_proposes_4_ways
to_cut_it⠀⇛


     PM-apparent Petteri Orpo (NCP) said that the latest EU comparison
     confirms the urgency of major fiscal reforms. Finland was the only EU
     state where the debt ratio of public finances rose last year.


⚓ Helsinki Times ☛ Limited_impact_of_tax_credit_for_household_expenses_on
shadow_economy_among_businesses⠀⇛


     A recent study conducted by the Grey Economy Information Unit of the
     Finnish Tax Administration has found that the tax credit for
     household expenses has a limited impact on reducing shadow economy
     activities among businesses. While there is a lower risk of engaging
     in shadow economy practices for companies that provide services
     eligible for the tax credit, the overall average risks of shadow
     economy activity do not differ significantly between sectors eligible
     for the credit and other sectors.


⚓ Michael West Media ☛ Greens_seek_to_release_list_of_names_in_PwC_tax_leak⠀⇛


     The Greens have sought to publicly release a list of names of PwC
     employees allegedly involved in the tax advice scandal. But the
     finance committee on Friday decided instead to refer the tabling of
     the document to Senate Clerk Richard Pye after concerns were raised
     it could jeopardise an Australian Federal Police investigation.


⚓ The Atlantic ☛ Why_the_GOP_Wants_to_Rob_Gen_Z_to_Pay_the_Boomers⠀⇛


     The budget clash, in many ways, represents the fiscal equivalent to
     the battle over cultural issues raging through Republican-controlled
     states.


⚓ The Atlantic ☛ Colorado’s_Ingenious_Idea_for_Solving_the_Housing_Crisis⠀⇛


     And why local governments hate it


⚓ Vice Media Group ☛ Tenants_Shut_Down_Brooklyn_Bridge_to_Protest_Predatory
Landlords⠀⇛


     Over a thousand tenants holding signs like “Cap the Rent” and “The
     Rent is Too Damn High” marched in one of NYC’s biggest tenant
     protests in years.


⚓ Quartz ☛ Gautam_Adani_has_scraped_his_way_back_into_the_world’s_top
billionaires’_list⠀⇛


     Gautam Adani has found his way back into the world’s top 20
     billionaires list as his conglomerate makes a stellar recovery after
     bleeding for weeks on the stock exchange.


⚓ Quartz ☛ Airbnb_is_encouraging_neighbors_to_complain_about_parties_at_its
rentals⠀⇛


     Summer revelers be warned—Airbnb is embarking on an anti-party
     crackdown.


§ AstroTurf/Lobbying/Politics⠀➾


    * ⚓ Anger_most_dominant_emotion_prior_to_May_14′s_dual_election,_survey
      reveals⠀⇛


           A new report by Politus Analytics shows relatively similar
           emotional trends among Erdoğan and Kılıçdaroğlu supporters,
           with the February 6 earthquakes evoking large spikes in various
           emotions in both constituencies.


    * ⚓ teleSUR ☛ Early_Voting_Ends_at_Turkish_Diplomatic_Missions_Abroad⠀⇛


           In the first round, Recep Tayyip Erdogan had earned 49.52
           percent of the vote while Kemal Kilicdaroglu received 44.88
           percent.


    * ⚓ New York Times ☛ They_Cuddled_a_Kiwi._New_Zealand_Said,_‘Stop_That.’⠀⇛


           Video of the national bird being handled by Miami zoo visitors
           caused an outcry in New Zealand. Even the prime minister
           weighed in.


    * ⚓ New York Times ☛ Why_the_‘Rules’_of_Politics_Don’t_Always_Stymie
      Outsiders_to_the_System⠀⇛


           For decades, many voters grew accustomed to a certain set of
           norms that seemed to govern political systems like rules. But
           elite groups have lost the power they once had to enforce those
           norms, or decided to change their own behavior.


    * ⚓ New York Times ☛ Netanyahu_Budget_May_Risk_His_Economic_Legacy_in
      Israel⠀⇛


           Israel’s prime minister has long advocated a small state, free
           markets and benefit cuts. But his new budget is heavy on
           subsidies for the ultra-Orthodox community, whose political
           support he needs.


    * ⚓ New York Times ☛ For_Senator_Feinstein,_There’s_No_Time_Like_the
      Present_to_Resign⠀⇛


           The country shouldn’t discriminate against older workers, and
           older workers shouldn’t insist on staying in jobs they can no
           longer really carry out.


    * ⚓ The Straits Times ☛ Opposition_parties_to_boycott_new_Parliament
      inauguration_by_India’s_Modi⠀⇛


           Mr Modi has chosen to dedicate the building without the Indian
           President’s participation.


    * ⚓ The Straits Times ☛ De-risking,_taken_too_far,_will_lead_to_fragmented
      and_decoupled_world_economy:_Lawrence_Wong⠀⇛


           The DPM was taking on the latest language that had emerged at
           the recently concluded Group of Seven summit.


    * ⚓ The Straits Times ☛ Bangladesh_says_will_take_steps_to_address
      election-meddling_after_visa_threat_from_US⠀⇛


           The country is set to hold elections in January amid large
           protests.


    * ⚓ LRT ☛ Lithuanian_president_could_call_snap_elections_in_case_of_no-
      confidence_in_cabinet_–_PM⠀⇛


           Lithuanian President Gitanas Nausėda could call an early
           general election if the parliament passed a motion of no
           confidence in the government, Prime Minister Ingrida Šimonytė
           said on Thursday.


    * ⚓ The Atlantic ☛ DeSantis’s_Campaign_of_Trolling⠀⇛


           The Florida governor seems to understand that in today’s GOP
           primary, serious people need not apply.


    * § Misinformation/Disinformation/Propaganda⠀➾


          o ⚓ ‘Shamelessness’⠀⇛


                 The attitude that Erdoğan and his closest companions have
                 in the face of the “fabricated video” scandal, that the
                 state is addressing the public with lies and with
                 falsifications, risks a total attack on society’s sense
                 of reality. The near and serious threat is this.


          o ⚓ Marcy Wheeler ☛ ABC_Reports_that_Sources_Familiar_Say_2_+_2_=_5⠀⇛


                 Trump milked grievance on his social media platform
                 yesterday in advance of being indicted. ABC did him the
                 favor of claiming he was doing something else.


§ Censorship/Free Speech⠀➾


    * ⚓ Musicians_detained_on_‘terror’_charges_for_participating_in_Green_Left
      Party_events⠀⇛


           The musicians had participated in the opening events for the
           party’s election campaign offices in İzmir.


    * ⚓ CS Monitor ☛ Picking_books_for_public_schools⠀⇛


           The push to restrict or place controversial books in public
           schools has prompted many local communities to seek greater
           empathy and civic engagement.


    * ⚓ New Yorker ☛ The_Discovery_of_a_Forgotten_and_Banned_Nuremberg_Film⠀⇛


           “Filmmakers for the Prosecution” tells the story of how two
           scions of Hollywood contributed crucial evidence and made a
           documentary that was suppressed by the U.S. Army.


    * ⚓ The Atlantic ☛ The_Israeli_Minister_Who_Is_Defending_Elon_Musk⠀⇛


           Amichai Chikli championed the billionaire when his tweets were
           criticized for anti-Semitic overtones. I asked Chikli why.


    * ⚓ New Yorker ☛ Here_at_the_War-Poison_Factory,_We_Want_to_Run_a
      Progressive_Workplace⠀⇛


           Please, sleep easy knowing that you’re making war poison for a
           company that cares.


    * ⚓ The Atlantic ☛ You_Hurt_My_Feelings_Is_a_Hilarious_Anxiety_Spiral⠀⇛


           The film traces a betrayal that’s trivial, comical, and also
           completely devastating.


§ Freedom of Information / Freedom of the Press⠀➾


    * ⚓ Victory_Party_members_obstruct_Kurdistan24_journalists_covering
      Kılıçdaroğlu-Özdağ_presser⠀⇛


           The party members did not allow the K24 microphone on the
           lectern during the press conference of the two leaders.


§ Civil Rights/Policing⠀➾


    * ⚓ Gezi_prisoners_granted_human_rights_award_in_İstanbul⠀⇛


           In the name of the eight prisoners, their family members
           received the award named after Sevinç Özgüner, a socialist
           politician assassinated in 1980.


    * ⚓ What_Kılıçdaroğlu-Özdağ_deal_implies_about_removal_of_elected_mayors_in
      Kurdish_cities⠀⇛


           The government has replaced all but a few of the HDP mayors in
           Kurdish-majority regions since the 2019 local election. The
           Kılıçdaroğlu-Özdağ protocol pledges to maintain this practice,
           but exclusively for individuals with “proven connections to
           terrorism.”


    * ⚓ Kılıçdaroğlu_pledges_to_expel_refugees_‘without_being_racist’_in_Hatay
      visit⠀⇛


           Ahead of the crucial presidential runoff on May 28, the main
           opposition leader repeated his claims to send all refugees back
           to their own county.


    * ⚓ Crackdown_on_Kurdish-linked_groups_continues_as_18_detained_in_house
      raids⠀⇛


           Green Left Party and HDP members are among the detained in the
           raids that took place early in the morning.


    * ⚓ New York Times ☛ 95-Year-Old_Australian_Woman_Dies_Days_After_Police
      Used_a_Taser_on_Her⠀⇛


           Hours before Clare Nowland died, the police announced charges
           against the officer who used the stun gun on her in the care
           facility where she lived.


    * ⚓ The Straits Times ☛ Family_pays_tribute_to_Australian_woman,_95,_who
      died_after_police_taser⠀⇛


           Ms Nowland’s family said she died “surrounded by the love and
           support of her family”.


    * ⚓ JURIST ☛ Bolivia_Catholic_Church_leaders_admit_failure_to_protect
      victims_of_sexual_abuse⠀⇛


           Bolivian Roman Catholic Church leaders Wednesday admitted that
           the Church had been “deaf” to the persistent sexual abuse which
           has occurred within its schools as outrage over recent reports
           of child sexual abuse by priests continues to grow.


    * ⚓ LRT ☛ Vilnius_priest_accused_of_sexual_relations_with_minor_–_media⠀⇛


           The chancellor of the Vilnius Archdiocese has been convicted of
           the acquisition and possession of pornographic material. He was
           also accused of having sexual relations with a minor, but the
           investigation was later dropped, the Delfi news website
           reported.


    * ⚓ RFA ☛ Court_in_Myanmar’s_Mandalay_imprisons_3_monks_for_funding
      terrorism⠀⇛


           They were accused of supporting People’s Defense Force members
           sheltering in a monastery.


    * ⚓ teleSUR ☛ Major_Raid_on_Last_Generation_Members_by_German_Police⠀⇛


           “…preliminary proceedings initiated against seven individuals…”


    * ⚓ JURIST ☛ New_UK_student_visa_reform_restricts_international_students’
      ability_to_bring_family_with_them⠀⇛


           The UK Home Office announced new reforms on Tuesday regarding
           international students and their ability to bring their
           families with them into the country. The move is seen as an
           attempt to control the UK’s rising immigration numbers. In
           2022, alone, the UK reportedly issued half a million student
           visas to international students.


    * ⚓ LRT ☛ Opposition_party’s_no-confidence_initiative_against_Lithuanian
      cabinet_falls_through⠀⇛


           The Lithuanian Farmers and Greens Union’s initiative for a vote
           of no-confidence in the government has failed to get the
           backing of other opposition MPs.


    * ⚓ The Atlantic ☛ The_Problem_With_How_the_Census_Classifies_White
      People⠀⇛


           Being an unspecified “white” person has allowed many Americans
           to blend in. In this era of identity-driven polarization, we
           should acknowledge all the ways we are different.


    * ⚓ Federal News Network ☛ Texas_lawmakers_issue_20_articles_of_impeachment
      against_state_Attorney_General_Ken_Paxton⠀⇛


           Texas lawmakers have issued 20 articles of impeachment against
           state Attorney General Ken Paxton, ranging from bribery to
           abuse of public trust as state Republicans surged toward a
           swift and sudden vote that could remove him from office. The
           charges were released Thursday night, hours after a Republican-
           led House investigative committee recommended impeaching the
           state’s top lawyer. The House could vote on the recommendation
           as soon as Friday. If it impeaches Paxton, he would be forced
           to leave office immediately.


    * ⚓ The Straits Times ☛ Cathay_CEO_says_Hong_Kong’s_image_damaged_by_cabin
      crew_discrimination_incident⠀⇛


           A passenger had recorded flight attendants joking about a
           Mandarin-speaking customer’s English-language ability.


    * ⚓ RFERL ☛ Belarusian_Educator,_Family,_Friends_Handed_Parole-Like
      Sentences_Over_2020_Protests⠀⇛


           A court in Minsk on May 25 handed parole-like sentences to
           noted Belarusian educator Yauhen Livyant, his wife Yulia,
           daughters Halina and Hanna, son-in-law Mikita Drozd, and his
           associates Alyaksey Ivanov and Alyaksandra Ensayn (aka
           Vilchytskaya).


    * ⚓ RFERL ☛ Iranian_Bill_Before_Parliament_Increases_Penalties_For_Defiance
      Of_Hijab⠀⇛


           A bill containing Iran’s Chastity and Hijab law has been
           presented to parliament, legislation that many see as a
           continuation of the government’s oppression of women and human
           rights.


    * ⚓ Vice Media Group ☛ Drivers_Sue_Amazon_Over_‘Inhumane’_Conditions,
      Having_to_Pee_in_Bottles⠀⇛


           A proposed class action in Colorado alleges that Amazon broke
           state wage and anti-discrimination laws by not letting drivers
           take breaks to use the bathroom.


§ Internet Policy/Net Neutrality⠀➾


    * ⚓ APNIC ☛ [Podcast]_A_look_back_at_notable_root_zone_changes⠀⇛


           How the DNS root zone has changed over the years and what’s
           coming next.


§ Monopolies⠀➾


    * § Patents⠀➾


          o ⚓ This_week_on_MIP:_France_v_EPO_spat,_Med-El_loss⠀⇛


                 We provide a rundown of Managing IP’s news and analysis
                 coverage from the week, and review what’s been happening
                 elsewhere in IP


                 French govt complained to EPO over EUIPO election conduct


                 French finance minister Bruno Le Maire wrote to António
                 Campinos, president of the EPO, to complain over the
                 timing of an event that will be held in Lisbon one week
                 before the EUIPO leadership vote, Managing revealed this
                 week.


                 Le Maire, minister for the economy and finance since
                 2017, suggested the event could be seen as interfering
                 with the process to select a new EUIPO executive
                 director.


                 Managing IP can also reveal that the incumbent executive
                 director, Christian Archambeau, hinted at interference
                 “from Munich” in the decision to remove him last
                 November.


    * § Trademarks⠀➾


          o ⚓ TTAB Blog ☛ Sustaining_Tumblr’s_Opposition,_TTAB_Finds_“TUMBLOG”
            Generic_for_…._Guess_What?⠀⇛


                 In a rare opposition based on genericness, the Board
                 sustained Tumblr’s challenge to an application to
                 register TUMBLOG for “[p]roviding customized on-line web
                 pages and data feeds featuring user-defined information,
                 which includes blog posts, new media content, other on-
                 line content, and on-line web links to other websites,”
                 deeming the proposed mark to be generic for the recited
                 services. The Board, without explanation, applied a
                 “preponderance of the evidence” standard, ignoring CAFC
                 case law requiring “clear evidence” of genericness.
                 Tumblr, Inc. v. Mark David-Dale Kindy, Opposition No.
                 91252639 (May 19, 2023) [not precedential] (Opinion by
                 Judge Jonathan Hudis).


    * § Copyrights⠀➾


          o ⚓ New York Times ☛ Tina_Turner,_Magnetic_Singer_of_Explosive_Power,
            Is_Dead_at_83⠀⇛


                 Hailed in the 1960s for her dynamic performances with her
                 first husband, Ike, she became a sensation as a recording
                 artist, often echoing her personal struggles in her
                 songs.


          o ⚓ CS Monitor ☛ ‘Simply_the_Best’:_Icon_Tina_Turner_defined_survivor
            in_epic_career⠀⇛


                 Beloved entertainer Tina Turner lived a storied life of
                 strength, overcoming horrific abuse and a stalled solo
                 career to become one of the most popular singers of her
                 era.


          o ⚓ Marcy Wheeler ☛ RIP_Riverboat_Queen⠀⇛


                 As you may have heard, Tina turner has passed at the age
                 of 83. It is pretty hard to describe how incredible, and
                 important, she was over so many decades.


§ Gemini* and Gopher⠀➾


    * § Personal⠀➾


          o ⚓ Vegetation_map_of_Bicuar_National_Park_–_Teixeira_1968⠀⇛


                 I’ve been searching around for a long time for a copy of
                 a vegetation map of Bicuar National Park, Angola,
                 produced in 1968 by J. B. Teixeira. A number of
                 contemporary publications looking at the ecology of
                 Bicuar reference this map, but I realised I have never
                 seen it. To my knowledge, it remains the only vegetation
                 map of Bicuar National Park. I would like to see if I can
                 geo-reference this map and overlay it on a new vegetation
                 map we are producing, to see how they line up.


    * § Technical⠀➾


          o ⚓ Games_Showcase:_Half-Life_Alyx⠀⇛


                 What happens when one of the most influential game
                 developers of all time writes a love letter to Virtual
                 Reality?


          o § Internet/Gemini⠀➾


                # ⚓ An_email_about_estimating_productivity⠀⇛


                       In our lab group we use a lot of repeat inventory
                       tree growth data, from plots in forests, savannas,
                       and woodlands, to understand rates of biomass
                       dynamics and land-atmosphere carbon exchange.


          o § Programming⠀➾


                # ⚓ R_functions_to_download_data_from_KoboToolbox⠀⇛


                       I have created a couple of R functions to download
                       data from a KoboToolbox[1] server, using their API.
                       The functions sometimes fail with a 502 bad gateway
                       error, so it might be worth wrapping them in a try
                       () statement to get them to fail nicely.


                # ⚓ Pair_Reviewing⠀⇛


                       The world of programming offers countless paths to
                       learning, from online tutorials and forums to
                       extensive documentation. But one rich avenue for
                       learning and development often goes unheralded:
                       pair reviewing. By pairing up to review code,
                       developers can sharpen their skills, learn from
                       their peers, and contribute to a culture of
                       continuous learning.


                       [...]


                       Pair reviewing not only fosters individual growth
                       but also strengthens the team as a unit. The
                       process encourages open communication, mutual
                       respect, and shared ownership of code. It nurtures
                       a sense of camaraderie and mutual respect within
                       the team, contributing to an overall healthier,
                       more productive work environment.


                       The shared learning experience also helps equalize
                       knowledge across the team, reducing the risk
                       associated with knowledge silos or ‘bus factors’.
                       As each developer has the opportunity to both learn
                       and teach, the team becomes more balanced and
                       resilient. As the renowned software engineer Grady
                       Booch once said, “The function of good software is
                       to make the complex appear to be simple.” Through
                       pair reviewing, developers not only work towards
                       creating good, simplifying software but also engage
                       in the enriching process of continuous learning and
                       knowledge exchange.


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



                    ䷩ 𝚕𝚒𝚗𝚎 7117

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.27.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_28/05/2023:_New_Wine_and_More⠀✐


Posted in News_Roundup at 8:48 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Instructionals/Technical
          o WINE_or_Emulation
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o SUSE/OpenSUSE
          o Slackware_Family
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Productivity_Software/LibreOffice/Calligra
          o Programming/Development
                # Python
    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Patents
                # Trademarks
    * Gemini*_and_Gopher
          o Personal
          o Politics
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o § Instructionals/Technical⠀➾


                # ⚓ TecAdmin ☛ Setting_Up_Permissions_in_Home_Directory_on
                  Linux⠀⇛


                       One of the fundamental aspects of system security
                       and user privacy in any Linux or Unix-based
                       operating system (OS) is the proper management of
                       permissions. In these systems, a home directory is
                       the default location for a user’s personal files,
                       documents, and configuration settings.


                # ⚓ TecAdmin ☛ Configuring_Apache_Userdir_on_Ubuntu_and_Debian:
                  A_Simplified_Guide⠀⇛


                       Apache is a versatile, open-source HTTP server for
                       modern operating systems including UNIX and
                       Windows. It provides a secure, efficient, and
                       extensible server that provides HTTP services in
                       sync with the current HTTP standards.


                # ⚓ TecAdmin ☛ How_to_Install_Apache_CouchDB_on_Ubuntu_&
                  Debian⠀⇛


                       Apache CouchDB is a database management system that
                       seamlessly takes the data to the edge and then back
                       again. It’s known for its ease of replication and
                       setup. If you want to install Apache CouchDB on
                       your Ubuntu or Debian system, you’re at the right
                       place.


                # ⚓ Ubuntu Handbook ☛ How_to_Install_Python_3.12_(Beta_so_far)
                  in_Ubuntu_22.04_|_20.04_|_23.04⠀⇛


                       For developers who want to prepare their project
                       for the latest Python releases, here’s how to
                       install Python 3.12 in all current Ubuntu releases.
                       Python 3.12 now is in Beta development stage.


                # ⚓ Make Tech Easier ☛ How_to_Concatenate_Files_in_Linux⠀⇛


                       Being able to combine various files together into
                       one can be very helpful. You can arrange and sort
                       out your desktop and combine several related
                       documents into one. In Linux, there are several
                       ways to concatenate files together.


                # ⚓ Adam_Young:_Opening_the_perf_file_descriptor⠀⇛


                       A couple months back I recorded this line on my
                       blog as part of investigating perf:


                # ⚓ TecAdmin ☛ What_is_the_“/etc/profile.d/”_Directory’s_Role
                  in_Linux⠀⇛


                       In the vast landscape of the Linux operating
                       system, understanding the intricacies of various
                       system directories is key to effective system
                       administration. The Linux directory structure holds
                       a set of directories, each with a unique purpose,
                       and among these is the “/etc/profile.d/” directory.


                # ⚓ TecAdmin ☛ How_to_Add_a_Directory_to_Your_$PATH_Variable_in
                  Linux⠀⇛


                       The $PATH variable in Linux is an environment
                       variable that determines where the shell looks for
                       executable files. By adding directories to this
                       variable, you make it easier to run your scripts
                       from anywhere without having to specify the full
                       path to the script’s location.


                # ⚓ Policy_Power:_Using_Network_Policies_Effectively_in
                  Kubernetes⠀⇛


                       Introduction With the increasing adoption of
                       containerization technology, Kubernetes has become
                       one of the most popular platforms for running and
                       managing containers.


                # ⚓ Xe’s Blog ☛ Syncing_my_emulator_saves_with_Syncthing⠀⇛


                       One of the most common upsells in gaming is “cloud
                       saves”, or some encrypted storage space with your
                       console/platform manufacturer to store the save
                       files that games make. Normally Steam, PlayStation,
                       Xbox, Nintendo, and probably EA offer this as a
                       service to customers because it makes for a much
                       better customer experience as the customer migrates
                       between machines. Recently I started playing Dead
                       Space 2 on Steam again on a lark and I got to open
                       my old Dead Space 2 save from college. It’s magic
                       when it works.


                       [...]


                       I own these two games on cartridge and I have
                       dumped my copy of them from cartridge using a
                       hackable Switch.


          o § WINE or Emulation⠀➾


                # ⚓ WINE Project (Official) ☛ WineHQ_–_Wine_Announcement_–_The
                  Wine_development_release_8.9_is_now_available.⠀⇛


                       The Wine development release 8.9 is now available.

                       What's new in this release:
                         - Mono engine updated to version 8.0.0.
                         - Completion of PE conversion in the PostScript
                       driver.
                         - Doppler shift support in DirectSound.
                         - GdiPlus performance improvements.
                         - Various bug fixes.

                       The source is available at:

                       https://dl.winehq.org/wine/source/8.x/wine-
                       8.9.tar.xz

                       Binary packages for various distributions will be
                       available from:

                       https://www.winehq.org/download

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

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

                       Wine is available thanks to the work of many
                       people. See the file
                       AUTHORS in the distribution for the complete list.
          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ This Week in GNOME ☛ Felix_Häcker:_#97_GNOME_Latam
                        2023⠀⇛


                             Update on what happened across the GNOME
                             project in the week from May 19 to May 26.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Barry Kauler ☛ Little_Flapi,_Appi_and_pupX_fixes⠀⇛


                 Caramel reported a problem, sometimes Flapi (the Flatpak
                 Installer) did not detect when an app is already
                 installed.


                 I found that the OpenShot AppImage can now be updated.
                 Previously Appi installed version 3.0.0 and the next
                 release didn’t work. However, the latest, 3.1.1 does
                 work.


          o § SUSE/OpenSUSE⠀➾


                # ⚓ William ☛ William_Brown:_Starting_with_Rage_on_OpenSUSE⠀⇛


                       Rage is a rust implementation of Age, a modern,
                       simple and secure file encryption tool. It is
                       easier to use than other tools like GPG, and being
                       written in a memory safe language it avoids many of
                       the exploits that may occur in C based tools.


                       § Installing Rage


                       You can install rage on leap or tumbleweed from
                       zypper


          o § Slackware Family⠀➾


                # ⚓ Eric Hameleers ☛ Chromium_114_Early_Release_on_Slackware⠀⇛


                       An “early release” of Chromium 114 source code was
                       published a few days ago, the release notes are on
                       the developer blog. Since Chromium 110, Google
                       rolls out new major releases to a small sub-set of
                       its users to monitor any potential breakage and
                       apply fixes before the majority of users get
                       upgraded. The formal release of Chromium will be on
                       May 30th, but I decided to go along with the early
                       release this time, and offer this version to
                       Slackware users already this weekend, to celebrate
                       the Pentecost.


                       Looking at the new stuff in Chromium 114, there’s
                       two things you might want to play with, since they
                       are already contained in the browser and mostly
                       usable in Chromium 114, but not yet enabled by
                       default.


          o § Fedora Family / IBM⠀➾


                # ⚓ Remi Collet ☛ Remi_Collet:_PHP_version_8.1.20RC1_and
                  8.2.7RC1⠀⇛


                       Release Candidate versions are available in testing
                       repository for Fedora and Enterprise Linux (RHEL /
                       CentOS / Alma / Rocky and other clones) to allow
                       more people to test them. They are available as
                       Software Collections, for a parallel installation,
                       perfect solution for such tests, and also as base
                       packages.


                       RPM of PHP version 8.2.7RC1 are available


                # ⚓ Red Hat Official ☛ Save_the_date_for_Red_Hat_Summit_2024⠀⇛


                       As we close out the last day of this year’s Red Hat
                       Summit, it’s time to mark your calendar for next
                       year’s event. We’re headed to the Mile High City –
                       Denver, CO – for Red Hat Summit and AnsibleFest
                       2024! Join us at the Colorado Convention Center,
                       May 6-9, 2024, as we bring together thousands of
                       customers, partners and technology industry leaders
                       and open source community members from around the
                       world for another high-energy week of innovation,
                       education and collaboration.


                # ⚓ CRN ☛ Red_Hat_CEO_Keynote:_5_Boldest_Remarks_On_AI,_New
                  Products⠀⇛


                       Red Hat CEO Matt Hicks kicked off Red Hat Summit
                       2023 on Tuesday in Boston by explaining his
                       company’s artificial intelligence, open-source
                       vision and new products to thousands in attendance.


                       “We’re in one of those [game-changing] moments
                       right now. It’s the moment of AI,” said Hicks
                       during his keynote at the Boston Convention Center
                       today. “AI has moved from the obscurity of academia
                       to the ubiquity of ChatGPT. But it’s also moved
                       from the power of few, to the power of many.”


                       Several of Red Hat’s key product launches include
                       generative AI for Ansible, an enterprise-grade open
                       developer hub and new services in the Red Hat
                       Trusted Software Supply Chain suite.


                # ⚓ TechCrunch ☛ Red_Hat_brings_generative_AI_to_IT_automation
                  with_Ansible_Lightspeed⠀⇛


                       Red Hat is holding its annual customer summit in
                       Boston this week, and today it announced a couple
                       of enhancements to Ansible, its open source IT
                       automation tool, including the new AI-fueled
                       Lightspeed.


                       Automation at its core is about distilling complex
                       processes into a playbook or recipe of actions. The
                       next step is building low-code and no-code
                       workflows. The recent rise of generative AI could
                       strip that process down even more to simply
                       describing the process and letting the tool do the
                       rest, creating a set of steps and providing the
                       necessary code and tools to move it through a work
                       process without much further human intervention
                       required (at least in theory).


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ FOSSLinux ☛ The_20_Best_Themes_for_Ubuntu_[2023_Edition]⠀⇛


                       In the world of Linux, customization is king. One
                       of the easiest ways to give your Ubuntu system a
                       personal touch is by changing its theme. From sleek
                       and modern to quirky and colorful, there’s a theme
                       to match every taste. As we step into 2023, a whole
                       new lineup of eye-catching and feature-rich themes
                       are available to add a touch of flair to your
                       Ubuntu desktop.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Notebook Check ☛ T30_Pro,_Doogee’s_third_Android_tablet,
                  set_to_arrive_next_month_–_NotebookCheck.net_News⠀⇛


                # ⚓ TechRadar ☛ Google’s_Pixel_8_Pro_needs_to_beat_this_Android
                  phone_to_win_me_back_|_TechRadar⠀⇛


                # ⚓ SlashGear ☛ How_Use_Your_Android_Phone_As_A_Webcam_For_Your
                  Computer⠀⇛


                # ⚓ Giz China ☛ How_to_Block_YouTube_Ads_on_Android_TV_–
                  Gizchina.com⠀⇛


                # ⚓ SlashGear ☛ 14_Coolest_Android_Phones_You_Can’t_Buy_In_The
                  United_States⠀⇛


                # ⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss_this
                  week_–_Android_Apps_Weekly⠀⇛


                # ⚓ SlashGear ☛ 5_Of_The_Best_Money-Saving_Apps_You_Can_Use_On
                  Android⠀⇛


                # ⚓ Tom’s Guide ☛ Android_AI_text_suggestions_are_here_—_but
                  there’s_a_catch_|_Tom’s_Guide⠀⇛


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


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ LibreOffice_Community_at_Events_in_Italy,_Spring_2023⠀⇛


                       Emiliano Vavassori, Deputy Chairperson in The
                       Document Foundation’s Board of Directors, give us
                       an update on recent events in Italy: Linux Arena at
                       Fiera del Radioamatore — Pordenone, April 23rd and
                       24th As in every spring, the Pordenone Linux Users
                       Group (PNlug) organizes an internal event inside
                       the local ham radio/electronics fair, «Fiera del
                       Radioamatore»…


          o § Programming/Development⠀➾


                # ⚓ Qt ☛ May_26th,_2023:_Qt_5.15_Standard_Support_for_Legacy
                  License_Holders_Ends_Today⠀⇛


                       Standard support for the last release of the Qt 5
                       series ends for term and perpetual license holders
                       today. Customers distributing applications and
                       embedded devices using Qt 5 series software should
                       evaluate how to access technical support and
                       maintenance releases which may include security and
                       major bug fixes.


                # § Python⠀➾


                      # ⚓ TecAdmin ☛ Understanding_Python’s_Underscore_(___):_A
                        Comprehensive_Guide⠀⇛


                             Python, as a flexible and intuitive language,
                             introduces many constructs that enable the
                             ease of coding. One such construct is the
                             underscore ( _ ), a special character with
                             multiple uses, ranging from variable naming
                             to interpreter purposes, and more. For novice
                             programmers, underscores might appear
                             confusing, but understanding their purpose
                             can significantly enhance your [...]


                      # ⚓ Linux Hint ☛ Seaborn_Theme⠀⇛


                             In Python, the “sns.set_theme()” method can
                             be used along with the “style” parameter and
                             its value to customize the seaborn theme.


                      # ⚓ Linux Hint ☛ Seaborn_Legend_Location⠀⇛


                             To set the seaborn legend location in Python,
                             the “plt.legend()” method can be used along
                             with the “loc= ‘value’” parameter.


                      # ⚓ Linux Hint ☛ Remove_Substring_from_String_in_Python⠀⇛


                             To remove the substring from a string, the
                             “replace()”, “for” loop with “replace()”,
                             “translate()”, and the “Index” methods are
                             used in Python.


    * § Leftovers⠀➾


          o ⚓ Valhalla’s_Things:_Correspondence_Book⠀⇛


                 I write letters. The kind that are written on paper with
                 a dip pen 1 and ink, stamped and sent through the post,
                 spend a few days or weeks maturing like good wine in a
                 depot somewhere2, and then get delivered to the
                 recipient.


                 Some of them (mostly cards) are to people who will
                 receive them and thank me via xmpp (that sounds odd, but
                 actually works out nicely), but others are proper letters
                 with long texts that I exchange with penpals.


                 Most of those are fountain pen frea^Wenthusiasts, so I
                 usually use a different ink each time, and try to vary
                 the paper, and I need to keep track of what I’ve used.


          o ⚓ Valhalla’s_Things:_Late_Victorian_Combinations⠀⇛


                 Some time ago, on an early Friday afternoon our internet
                 connection died. After a reasonable time had passed we
                 called the customer service, they told us that they would
                 look into it and then call us back.


                 On Friday evening we had not heard from them, and I was
                 starting to get worried. At the time in the evening when
                 I would have been relaxing online I grabbed the first
                 Victorian sewing-related book I found on my hard disk and
                 started to read it.


          o § Science⠀➾


                # ⚓ New York Times ☛ Brain_Implants_Allow_Paralyzed_Man_to_Walk
                  Using_His_Thoughts⠀⇛


                       In a new study, researchers describe a device that
                       connects the intentions of a paralyzed patient to
                       his physical movements.


                # ⚓ Science Alert ☛ A_New_Type_of_Brain_Cell_Found_in_Mice_May
                  Trigger_Overactive_Appetites⠀⇛


                       It’s been overlooked until now.


                # ⚓ Science Alert ☛ Earth-Like_World_Covered_in_Raging
                  Volcanoes_May_Have_Been_Found⠀⇛


                       Hell on Earth?


                # ⚓ Science Alert ☛ Up_to_30%_of_Published_Neuroscience_Papers
                  May_Be_Faked_–_And_That’s_Before_ChatGPT⠀⇛


                       Something is seriously wrong here.


                # ⚓ Science Alert ☛ For_The_First_Time,_Scientists_Have
                  Detected_a_Cyclone_on_The_North_Pole_of_Uranus⠀⇛


                       “It isn’t just a plain blue ball of gas.”


                # ⚓ Science Alert ☛ Reactivated_Genes_From_Stone_Age_Dental
                  Plaque_Reveal_Lost_Mouth_Microbes⠀⇛


                       Welcome back!


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Nice_Try,_But_It’s_Not_Aperture_Synthesis⠀⇛


                       Some of the world’s largest radio telescopes are
                       not in fact as physically large as they claim to
                       be, but instead are a group of telescopes spread
                       over a wide area whose outputs are combined to
                       produce a virtual telescope equal in size to the
                       maximum distance between the constituents of the
                       array. Can this be done on the cheap with an array
                       of satellite dishes? It’s possible, but as
                       [saveitforparts] found out when combining a set of
                       Tailgater portable dishes, not simply by linking
                       together the outputs from a bunch of LNBs.


                # ⚓ The Straits Times ☛ Washington_and_Tokyo_vow_closer_chip
                  cooperation⠀⇛


                       The move comes as both the US and Japan reduce
                       exposure to China.


                # ⚓ Hackaday ☛ Nokia_N-Gage_QD_Becomes_Universal_Bluetooth
                  Gamepad⠀⇛


                       The Nokia N-Gage might not have put up much of a
                       fight against Nintendo’s handheld dynasty, but you
                       can’t say it didn’t have some pretty impressive
                       technology for the time. [BeardoGuy] happens to
                       have a perfectly functional N-Gage QD, which he
                       turned into a universal Bluetooth gamepad.


                # ⚓ Hackaday ☛ Learning_3D_Printing_Best_Practices_From_A_Pro⠀⇛


                       It might seem like 3D printing is a thoroughly
                       modern technology, but the fact is, it’s been used
                       in the industry for decades. The only thing that’s
                       really new is that the printers have become cheap
                       and small enough for folks like us to buy one and
                       plop it on our workbench. So why not take advantage
                       of all that knowledge accumulated by those who’ve
                       been working in the 3D printing field, more
                       accurately referred to as additive manufacturing,
                       since before MakerBot stopped making wooden
                       printers?


                # ⚓ Hackaday ☛ Restoring_Dot_Matrix_Printer_Cartridges_For
                  2023⠀⇛


                       The noise of a dot matrix printer is probably as
                       synonymous with 1980s computing as the modem
                       handshake would become with the desktop experience
                       a decade or more later. But unlike the computers
                       that would have driven it, a dot matrix printer can
                       still be a very useful device here in 2023. And why
                       not? They’re cheap to operate and can produce
                       surprisingly good quality when paired with suitable
                       drivers. There is a snag though; while cartridges
                       for popular models can still be found, there are
                       plenty whose consumables are long gone. [Drygol]
                       had an Apple ImageWriter II with exactly that
                       problem, and after finding all his cartridges were
                       non-functional, took a look at how to bring them
                       back.


                # ⚓ Ruben Schade ☛ A_new_old-stock_floppy_drive⠀⇛


                       This will be a quick post in my Am386 board
                       adventures today, but I received my new old stock
                       Panasonic 3.5-inch high density floppy drive today
                       this week, and it’s beautiful!


                       [...]


                       I’ve had Mitsumi, Sony, Mitsubishi, and Samsung
                       3.5-inch drives growing up, but this is my first
                       Panasonic that isn’t a 5.25-inch unit. One little
                       Easter Egg that doesn’t come up well on camera is
                       that the eject button is glossly! Maybe they
                       figured the matt beige plastic doesn’t stand up to
                       the rigours of regular pressing, so they buffed it
                       to a shine to make it look deliberate.


                # ⚓ Ruben Schade ☛ A_cool_Adaptec_AHA-1542CP_ISA_SCSI_card⠀⇛


                       All the parts I ordered months ago for my impromptu
                       Am386 build have stared arriving at once. Hot on
                       the heels of the Panasonic floppy drive last week,
                       we have another awesome new-old stock device, this
                       time a classic 16-bit ISA SCSI controller.


                       View_all_posts_in_the_Am386_series


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Hackaday ☛ Generating_Hydrogen_Peroxide_For_Disinfecting
                  Water_Using_A_Solar-Driven_Catalyst⠀⇛


                       Ensuring that water is safe to use and consume can
                       be a real chore, especially for those who live in
                       impoverished areas without access to safe drinking
                       water. Here is where researchers at Stanford
                       University hope that their recently developed low-
                       cost catalyst can make a difference. This catalyst
                       comes in the form of nano-sized particles
                       (nanoflakes) consisting out aluminium oxide,
                       molybdenum sulfide, copper and iron oxide. When
                       exposed to sunlight,  the catalyst performs like a
                       photon-sensitive semiconductor/metal junction (Cu-
                       MoS2), with the dislodged electrons going on to
                       react with the surrounding water, resulting in the
                       formation of hydrogen peroxide (H2O2) and hydroxy
                       radicals.


                # ⚓ The Straits Times ☛ Vietnam_to_cut_annual_rice_exports_by
                  44%_to_4_million_tonnes_by_2030⠀⇛


                       The move is aimed at boosting exports of high-
                       quality rice, ensuring domestic food security,
                       protecting the environment and adapting to climate
                       change.


                # ⚓ Science Alert ☛ Exertion_Headaches_Can_Make_Exercise_a_Real
                  Pain._Here’s_What_to_Do_About_Them⠀⇛


                       Mitigate the pain for your gain.


                # ⚓ Science Alert ☛ Fungal_Infections_Could_Obliterate_Our_Food
                  Supply,_Scientists_Warn⠀⇛


                       The future is blight.


                # ⚓ uni Stanford ☛ ‘The_difference_water_can_make’:_Matt_Damon
                  and_Gary_White_discuss_clean_water_access⠀⇛


                       Matt Damon and Gary White, co-founders of
                       WaterEquity and Water.org, spoke with students
                       about the economic and equity implications of water
                       scarcity around the world. The event was hosted by
                       the course SUSTAIN 345: Global Leaders and
                       Innovators in Human and Planetary Health:
                       Sustainable Societies Lab.


                # ⚓ Helsinki Times ☛ The_unrestricted_sale_of_nicotine_pouches
                  poses_a_significant_threat_to_the_health_of_young_people_in
                  particular⠀⇛


                       The sale of nicotine pouches was deregulated at the
                       beginning of April. Nicotine pouches, which fall
                       under the scope of the Medicines Act, are now
                       subject to tobacco and chemical regulations.
                       Nicotine pouches with high nicotine concentrations
                       are harmful to health, and young people are
                       particularly at risk. Nicotine pouches should be
                       subjected to stricter regulations promptly.


                # ⚓ Mexico News Daily ☛ Seized_psychiatric_medications_released
                  by_health_regulator⠀⇛


                       Regulators have released medication seized from
                       manufacturer Psicofarma, to address a shortage of
                       mental health drugs in the country.


                # ⚓ Axios ☛ Sorry,_stevia:_Artificial_sweeteners_get_more_bad
                  PR⠀⇛


                       The World Health Organization isn’t sweet on non-
                       sugar sweeteners, the_agency_announced.


                       Driving the news: It advised against using sugar
                       substitutes like Splenda, stevia and Sweet’n Low
                       for weight loss — and warned about potential long-
                       term health risks of too much intake.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Reason ☛ European_Union_Fines_Meta_$1.3_Billion
                        Because_of_NSA_Spying_Programs⠀⇛


                             The record penalty seems to be based less on
                             the Facebook parent company’s lax data
                             practices than the U.S. intelligence
                             community’s data-collection programs.


                      # ⚓ Quartz ☛ Tesla_could_face_a_$3.3_billion_fine_over_a
                        massive_data_leak⠀⇛


                             A whistleblower leaked a massive trove of
                             data about the electric carmaker Tesla to the
                             German publication Handelsblatt.


          o § Defence/Aggression⠀➾


                # ⚓ New York Times ☛ Sedition_Sentence_for_Oath_Keepers’
                  Stewart_Rhodes_Marks_Moment_of_Accountability⠀⇛


                       The 18 years in prison given to Stewart Rhodes for
                       a rarely charged crime underscored the lengths to
                       which the Justice Department and the courts have
                       gone in addressing the assault on the Capitol.


                # ⚓ France24 ☛ Suspect_arrested_in_Japan_gun_and_knife_attack
                  that_killed_four⠀⇛


                       Japanese police on Friday detained a man who had
                       holed up in a building after allegedly killing four
                       people, including two police officers, in a gun and
                       knife attack.


                # ⚓ France24 ☛ Over_a_dozen_‘innocent’_Westerners_still
                  detained_in_Iran⠀⇛


                       Over a dozen Western passport-holders are detained
                       in Iran, even after the release on Friday of
                       Belgian aid worker Olivier Vandecasteele in an
                       exchange deal between Belgium and Iran brokered by
                       Oman.


                # ⚓ Reason ☛ A_Georgia_Woman_Died_After_Falling_Out_of_a_Moving
                  Patrol_Car._Now,_Her_Family_Is_Suing_the_Cops_Responsible.⠀⇛


                       Brianna Grier was having a mental health crisis.
                       She needed an ambulance. She got two cops instead.


                # ⚓ Hong Kong Free Press ☛ Caught_in_the_crossfire:_Chinese
                  diaspora_bears_brunt_of_Canada-Beijing_tensions⠀⇛


                       The Chinese diaspora has been caught in the
                       crossfire of Ottawa’s row with Beijing over its
                       alleged meddling in Canada’s affairs — facing both
                       intimidation from Chinese operatives and rising
                       stigmatization.


                # ⚓ France24 ☛ Saudi_and_US_report_improved_ceasefire
                  conditions_in_Sudan⠀⇛


                       Saudi Arabia and the United States said Friday the
                       warring sides in Sudan’s conflict are adhering
                       better to a new, weeklong cease-fire following days
                       of sporadic fighting.


                # ⚓ France24 ☛ Investigation:_The_deadly_attacks_on_Syrian
                  truffle_hunters_by_the_Islamic_State_group⠀⇛


                       The Bedouin communities living in the unforgiving
                       Badia, or the Syrian desert, are facing a surge in
                       armed attacks. The violence reaches a peak each
                       year between February and April: the truffle
                       season. As tribes go out to hunt truffles, they
                       risk being ambushed by sleeper cells of the Islamic
                       State group, which has taken refuge in the Badia
                       since 2019. This exclusive investigation from
                       FRANCE 24′s Observers team exposes the horrific
                       abuses being carried out deep in the desert.


                # ⚓ Latvia ☛ Latvia’s_healthcare_provision_for_children_has
                  huge_room_for_improvement⠀⇛


                       Eurostat data published May 26 shows Latvia with
                       some of the least comprehensive healthcare
                       provision for children in the European Union.


                # ⚓ Latvia ☛ One_in_four_ticks_found_to_carry_Lyme_this_year_in
                  Latvia⠀⇛


                       More than 20% of the ticks analyzed in all Latvian
                       laboratories have been tested positive for Lyme
                       borrelia this year. Borrelia can cause Lyme disease
                       against which there are no vaccines. The other
                       dangerous tick-borne illness – encephalitis – has
                       only been found in a few ticks, Latvian Television
                       reported on May 26.


                # ⚓ New York Times ☛ Passenger_Arrested_on_Suspicion_of_Forcing
                  Open_Plane_Door_Mid-Flight⠀⇛


                       A man was arrested on suspicion of unlocking an
                       emergency exit on an Asiana Airlines flight in
                       South Korea when it was about 700 feet off the
                       ground.


                # ⚓ The Straits Times ☛ North_Korea_spent_the_pandemic_building
                  a_huge_border_wall⠀⇛


                       It has enabled the regime to tighten the flow of
                       information and goods into the country and keep
                       foreign elements out.


                # ⚓ teleSUR ☛ Rwandan_Genocide_Fugitive_Appears_In_South
                  African_Court⠀⇛


                       Fulgence Kayishema was arrested two days ago in
                       South Africa after more than two decades on the
                       run.


                # ⚓ JURIST ☛ UN_tribunal_arrests_man_wanted_for_Rwanda_genocide
                  since_1994⠀⇛


                       A special tribunal established by the UN, known as
                       the International Residual Mechanism for Criminal
                       Tribunals (IRMCT), announced Thursday that fugitive
                       Fulgence Kayishema has been arrested in Paarl,
                       South Africa after 22 years on the run. Kayishema,
                       a police officer accused of orchestrating the
                       killing of more than 2,000 Tutsi refugees at Nyange
                       Catholic Church…


                # ⚓ France24 ☛ Rwanda_genocide_fugitive_Kayishema_appears_in
                  South_Africa_court⠀⇛


                       Fulgence Kayishema, one of the last fugitives
                       sought over the 1994 Rwanda genocide, appeared
                       before a court in the South African city of Cape
                       Town on Friday, two days after being arrested
                       following 22 years on the run.


                # ⚓ Defence Web ☛ Measures_in_place_to_address_SANDF_sexual
                  exploitation_–_Cabinet⠀⇛


                       South Africa’s Cabinet has commended a set of
                       measures that have been put in place to address the
                       incidents of sexual exploitation and abuse (SEA)
                       within peace keeping missions the South African
                       National Defence Force (SANDF) takes part in.


                # ⚓ DOD_sends_new_cyber_strategy_to_Congress,_releases
                  unclassified_fact_sheet⠀⇛


                       The highly anticipated strategy is the first since
                       2018 and follows the release of the National
                       Cybersecurity Strategy in March.


                # ⚓ Defence Web ☛ Rwandan_fugitive_wanted_for_genocide_nabbed
                  in_SA⠀⇛


                       A Rwandan fugitive, wanted in connection with the
                       1994 Rwandan genocide, has been arrested in Paarl
                       in the Western Cape by a South African Operational
                       Task Team (OTT).


                # ⚓ LRT ☛ ‘Historic_opportunity.’_Lithuania’s_airports_prepare
                  for_challenges_during_Vilnius_NATO_summit⠀⇛


                       As Vilnius looks to host the NATO summit in July,
                       preparations are underway at Lithuania’s airports,
                       with aircraft service companies looking for extra
                       staff and airports coordinating security
                       procedures.


                # ⚓ Defence Web ☛ Top_UN_award_for_Ghanaian_female
                  peacekeeper⠀⇛


                       Ghana’s position as the largest contributor of
                       female military personnel to United Nations (UN)
                       peacekeeping efforts received another boost when
                       Captain Cecilia Erzuah was named the world body’s
                       Military Gender Advocate of the Year.


          o § Environment⠀➾


                # ⚓ France24 ☛ Paris_to_ban_single-use_plastic_from_the_2024
                  Olympic_Games⠀⇛


                       Paris Mayor Anne Hidalgo said on Friday the city
                       planned to ban single-use plastic when it holds the
                       2024 Olympic Games as part of efforts to tackle a
                       global plastic pollution crisis.


                # ⚓ Mexico News Daily ☛ New_plastic_recycling_collection_center
                  opens_in_Tijuana⠀⇛


                       The center looks to increase Mexico’s recycling by
                       processing PET bottles from both Mexico and the
                       United States.


                # ⚓ CS Monitor ☛ Women_in_Guyana_plant_mangroves_to_battle
                  rising_seas⠀⇛


                       Indigenous women use drones, scientific data, and
                       the replanting of mangroves to slow the progression
                       of rising seas in the South American nation of
                       Guyana.


                # ⚓ Mexico News Daily ☛ Drone_video_footage_shows_smoking
                  Popocatépetl_crater⠀⇛


                       Footage obtained by the Mexican Navy shows the
                       first images of the crater, which has been
                       experiencing increased activity for two weeks.


                # ⚓ CS Monitor ☛ ‘Uncharted_territory’:_How_Asia_is_coping_with
                  extreme_heat⠀⇛


                       When it comes to beating rising heats, there’s no
                       one-size-fits-all solution. Across Asia,
                       communities are adapting to extreme temperatures,
                       showcasing both human resilience and the far-
                       reaching costs of climate change.


                # § Energy/Transportation⠀➾


                      # ⚓ Hackaday ☛ Fly_Like_You_Drive_With_This_Flying_RC
                        Drift_Car⠀⇛


                             So it’s 2023, and you really feel like we
                             should have flying cars by now, right? Well,
                             as long as you ignore the problem of scale
                             presented by [Nick Rehm]’s flying RC drift
                             car, we pretty much do.


                      # ⚓ Ruben Schade ☛ Evolving_use_patterns_of_the_NYC
                        subway⠀⇛


                             The pandemic subway is a different system
                             than what cities have known in the past. The
                             same numbers of people aren’t flooding into
                             central business districts every weekday, but
                             ridership for many agencies has surged on
                             afternoons and weekends.


                      # ⚓ New York Times ☛ Gasoline_Prices,_a_Source_of_Pain
                        Last_Year,_Have_Come_Way_Down⠀⇛


                             Reasons include a stronger supply of oil and
                             weaker-than-expected demand, energy experts
                             say. Some people are saving hundreds of
                             dollars on fuel.


                      # ⚓ RFA ☛ Global_solar_investment_set_to_surpass_oil
                        spending,_report_says⠀⇛


                             China leads the way, according to the
                             International Energy Agency.


                      # ⚓ Science Alert ☛ Scientists_Find_a_Way_to_Harvest
                        Clean_Energy_From_Nothing_But_Air⠀⇛


                             “The air contains an enormous amount of
                             electricity.”


                # § Wildlife/Nature⠀➾


                      # ⚓ Science Alert ☛ Research_Reveals_The_Creepy_Way
                        Greedy_Gulls_Decide_What_to_Eat⠀⇛


                             Mine. Mine. Mine. Mine. Mine.


                      # ⚓ Axios ☛ Drones_go_out_on_shark_patrol⠀⇛


                             Lifeguards and beachgoers are getting a new
                             ally this summer in the fight to prevent
                             potentially dangerous shark encounters:
                             drones.


                             Why it matters: While actual shark-on-human
                             attacks are vanishingly rare, a spate of
                             sightings near shore has been raising alarms
                             from Massachusetts to Hawaii recently.


          o § Finance⠀➾


                # ⚓ RFERL ☛ Georgian_Billionaire_Wins_$926_Million_From_Credit
                  Suisse_After_Fraud⠀⇛


                       Credit Suisse was ordered to pay $926 million to
                       Georgia’s former prime minister on May 26 for
                       losing part of his fortune, in a Singapore court
                       ruling that represents one of the biggest legal
                       awards made against the bank.


                # ⚓ YLE ☛ Specialty_shops_closing_in_Finnish_city_centres⠀⇛


                       The most successful shops in recent years sell
                       sporting goods, hardware, home electronics and
                       eyeglasses while the least successful offer books,
                       watches, jewellery and clothes.


                # ⚓ New Yorker ☛ Affirmations_for_the_Landlord_Facing
                  Adversity⠀⇛


                       I am a landlord, not a charity. Eviction is a
                       healthy boundary-setting practice.


                # ⚓ Helsinki Times ☛ Expensive_food_often_leads_to_unhealthy
                  choices_according_to_survey⠀⇛


                       Rising food prices have had an impact on consumer
                       behavior, resulting in new choices being made in
                       grocery stores. Vaasan has examined changes in
                       purchasing habits over the past year, and the
                       results reveal a concerning trend. An increasing
                       number of Finns are forced to carefully consider
                       their food purchases, which, for some, leads to
                       unhealthy choices. However, by choosing nutritious
                       alternatives, consumers can get the best value for
                       their money.


                # ⚓ The Straits Times ☛ Economic_development_in_Asia_still
                  faces_many_challenges,_says_China’s_commerce_minister⠀⇛


                       China, as a major developing country, is willing to
                       make due contributions, Mr Wang said.


                # ⚓ Quartz ☛ Biden_and_Republicans_are_$70_billion_away_from
                  settling_their_debt_ceiling_squabbles⠀⇛


                       >


                       US debt ceiling talks appear to have overcome an
                       impasse and are now close to finding a resolution.


                # ⚓ Axios ☛ U.S._economy_hotter_than_policymakers_would_like⠀⇛


                       Economic data released on Friday show a pickup in
                       consumer spending, alongside persistent inflation,
                       which suggests the Federal Reserve might not yet be
                       done with its rate-hiking campaign.


                       Why it matters: Demand across the economy is still
                       hotter than policymakers would like.


                       ===================================================
                # ⚓ Quartz ☛ New_York_City_is_withholding_new_deposits_at_five
                  banks_accused_of_inaction_on_discrimination⠀⇛


                       >New York City is taking its business away from
                       banks that lack anti-discrimination plans.


                # ⚓ RFA ☛ US_debt_deal_nears,_but_Asia_will_look_on_warily⠀⇛


                       Lawmakers say they’re near a deal to pay America’s
                       debts, but the fight to get there has aired much
                       dirty laundry.


                # ⚓ YLE ☛ Statistics_Finland:_Wages_not_rising_in_line_with
                  inflation⠀⇛


                       Real earnings dropped by nearly five percent
                       compared to early 2022.


                # ⚓ Vice Media Group ☛ Minnesota_Governor_Vetoes_Minimum_Pay
                  for_Ridehail_Drivers_After_Uber_Threatens_to_Leave⠀⇛


                       The bill would have set minimum payouts for drivers
                       indexed to inflation.


                # ⚓ Axios ☛ U.S._will_run_out_of_money_on_June_5:_Yellen⠀⇛


                       Treasury Secretary Janet_Yellen has given Congress
                       a more precise date — June 5 — for when the U.S.
                       government will hit the debt ceiling and run out of
                       money to pay its bills.


                # ⚓ New York Times ☛ Will_Lawmakers_Sacrifice_Our_Health_and
                  Safety_to_Get_a_Debt_Ceiling_Deal?⠀⇛


                       A crucial part of the clean energy transition is
                       swept up in the high-pressure negotiations
                       happening in Washington.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Kurdish_politician_Aysel_Tuğluk’s_sentence_suspended_for
                  one_year_for_health_reasons⠀⇛


                       Diagnosed with dementia, Tuğluk was released from
                       prison in October last year. The prosecutors
                       concluded that her health condition is not suitable
                       for a return to the prison.


                # ⚓ The Straits Times ☛ ‘Wang_hong’_culture_booms_in_China_as
                  more_young_people_dream_of_becoming_influencers⠀⇛


                       But many underestimate the difficulties in having
                       to constantly come up with new content.


                # ⚓ Ruben Schade ☛ No_more_@Rubenerd_Blog_Twitter_posts⠀⇛


                       With changes to Twitter’s API, it’s no longer
                       feasible for me to auto-post new entries to the
                       @Rubenerd_blog account. I apologise if that’s how
                       you tracked stuff here.


                       As an alternative, I’d recommend opening an account
                       with one of the RSS reader services below, and
                       adding my feed so you don’t miss a post: [...]


                # ⚓ New York Times ☛ Alberta_Election_Tests_Conservatives’_Far-
                  Right_Shift⠀⇛


                       The pandemic took the conservative party in the
                       oil-rich province of Alberta far to the right. An
                       election on Monday will test if voters,
                       traditionally among Canada’s most conservative,
                       will follow.


                # ⚓ RSF_attests_media_system_is_rigged,_denounces_biased
                  coverage_of_Turkey’s_election⠀⇛


                       The campaign of opposition candidate Kemal
                       Kılıçdaroğlu has been significantly impeded by an
                       unjust distribution of airtime and editorial
                       control, while the incumbent Erdoğan has utilized
                       tactics like intimidating and detaining independent
                       journalists, as well as acquiring around 85% of the
                       media.


                # ⚓ Turkey_elections:_Latest_polls_ahead_of_second_round⠀⇛


                       While AREA research predicts a win for the
                       oppositional contender on May 28, two other polling
                       companies foresee a win for the incumbent.


                # ⚓ New York Times ☛ Burhan_Sönmez_on_the_Tensions_Between
                  Politics_and_Art_in_Turkey⠀⇛


                       Burhan Sönmez, who is president of PEN
                       international, discusses the tension between
                       politics and art and the role of literature in
                       authoritarian societies.


                # ⚓ New York Times ☛ Turkey’s_Presidential_Runoff_Election_on
                  Sunday:_What_to_Know⠀⇛


                       President Recep Tayyip Erdogan led his main
                       challenger, Kemal Kilicdaroglu, by a comfortable
                       margin after the first round of voting.


                # ⚓ New York Times ☛ How_Turkey’s_Erdogan_Rose_to_Power⠀⇛


                       Turkey’s leader faced a criminal conviction, mass
                       protests and a coup. Instead of hurting or ending
                       his political career, they helped him accumulate
                       ever more control.


                # ⚓ New York Times ☛ Turkey’s_Erdogan_Woos_Voters_in_Re-
                  Election_Campaign⠀⇛


                       President Recep Tayyip Erdogan has rock star appeal
                       at his election rallies, promising to lead Turkey
                       to claim its rightful place as a global power if he
                       is re-elected in a runoff on Sunday.


                # ⚓ CS Monitor ☛ Why_quakes_that_razed_homes_may_raise_up
                  Turkey’s_Erdoğan⠀⇛


                       Expectations that a weak response to earthquakes
                       would cost the Turkish government votes proved
                       false. Political preferences have become
                       identities.


                # ⚓ The Atlantic ☛ Photos_From_Turkey’s_Convulsive_Decade⠀⇛


                       The photographer Emin Özmen has spent his career
                       documenting life in Erdoğan’s shadow, watching his
                       country transform from an aspiring democracy to a
                       vision of the dystopian autocratic future.


                # ⚓ RFERL ☛ Georgian_President_Criticizes_Government_In
                  Independence_Day_Speech⠀⇛


                       Georgian President Salome Zurabishvili has used a
                       speech during the South Caucasus nation’s
                       Independence Day celebrations to criticize the
                       government over fears it is backsliding on
                       democratic reforms.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Michael West Media ☛ Twitter_abandons_EU_pact_against
                        disinformation⠀⇛


                             Twitter has dropped out of a voluntary
                             European Union agreement to combat online
                             disinformation, a top EU official says.
                             European Commissioner Thierry Breton tweeted
                             that Twitter had pulled out of the EU’s
                             disinformation “code of practice” that other
                             major social media platforms have pledged to
                             support.


          o § Censorship/Free Speech⠀➾


                # ⚓ Meduza ☛ Russia’s_Justice_Ministry_adds_lead_singer_of_rock
                  group_Bi-2,_journalists,_and_scholars_to_its_list_of_‘foreign
                  agents’_—_Meduza⠀⇛


                       Russia’s Justice Ministry updated its registry of
                       “foreign agents.” New additions include Lyova Bi-2
                       (real name Yegor Bortnik), lead singer of the band
                       Bi-2, and other individuals and organizations:


                # ⚓ China_deletes_1.4_million_social_media_posts_in_crack_down
                  on_‘self-media’_accounts
                  ⠀⇛


                       China’s cyberspace regulator said 1.4 million
                       social media posts have been deleted following a
                       two-month probe into alleged misinformation,
                       illegal profiteering, and impersonation of state
                       officials, among other “pronounced problems.”
                       The Cyberspace Administration of China (CAC) said
                       in a statement on Friday it had closed 67,000
                       social media accounts and deleted hundreds of
                       thousands of posts between March 10 and May 22 as
                       part of a broader “rectification” campaign.
                       Since 2021, China has targeted billions of social
                       media accounts in a bid to “clean” its cyberspace
                       and make it easier for authorities to control.
                       The latest crackdown targeted accounts on popular
                       Chinese social media apps including WeChat, Douyin,
                       and Weibo that fall under the category of “self
                       media,” a term that broadly refers to accounts that
                       publish news and information but are not
                       government-run or state-approved.


          o § Civil Rights/Policing⠀➾


                # ⚓ RFERL ☛ Kosovar_Police_Clash_With_Protesters_In_Serb-
                  Majority_Northern_Towns,_Drawing_U.S.,_EU_Rebukes⠀⇛


                       Police in northern Kosovo used tear gas and stun
                       grenades to disperse crowds in three Serb-majority
                       towns and enter municipal buildings in support of
                       recently elected ethnic Albanian mayors — security
                       actions that drew quick rebukes from Pristina’s
                       Western allies, who urged dialogue.


                # ⚓ Axios ☛ Judge_temporarily_blocks_South_Carolina’s_6-week
                  abortion_ban⠀⇛


                       A state judge on Friday temporarily blocked South
                       Carolina’s_recently_enacted_six-week_abortion_ban
                       until the state supreme court has a chance to
                       review it, Axios has confirmed.


                # ⚓ Neritam ☛ This_Labor_Day,_Remember_That_Martin_Luther
                  King’s_Last_Campaign_Was_for_Workers’_Rights⠀⇛


                       Most Americans today know that Reverend Martin
                       Luther King Jr. was killed in Memphis, Tennessee in
                       1968, but few know why he was there.


                # ⚓ France24 ☛ Tear_gas_fills_the_air_as_TotalEnergies_AGM
                  rejects_climate_activist_resolution⠀⇛


                       TotalEnergies shareholders rejected an activist
                       resolution on Friday urging faster cuts to the oil
                       major’s greenhouse gas emissions programme after
                       police intervened to stop climate protesters
                       disrupting its annual general meeting.


                # ⚓ RFERL ☛ Iranian_Lawyers_Say_Courts_Issuing_Them_Dozens_Of
                  Summonses_With_No_Charges⠀⇛


                       A leading member of one of Iran’s legal
                       associations says more than 100 lawyers from across
                       the country have been summoned to Tehran’s security
                       court, even though there is no mention of any
                       charges against them.


                # ⚓ RFA ☛ Childhood_friend_of_North_Korea’s_Kim_Jong_Un_says_he
                  has_never_heard_about_Kim’s_son⠀⇛


                       Focus on daughter Ju Ae seems to undermine South
                       Korean claims that Kim has a son


                # ⚓ Mexico News Daily ☛ Girls_develop_phone_apps_to_solve
                  problems_in_their_community [Ed: Well, phone apps, however,
                  create rather than solve problems]⠀⇛


                       The nonprofit Technovation is teaching young
                       Mexican girls to develop technology to help others
                       and also see a better future for themselves.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Hackaday ☛ Where_Exactly_Did_That_Network_Packet_Come
                  From?⠀⇛


                       Have you ever noticed that some websites can figure
                       out, at least roughly, where you are? Sometimes
                       they use it to find you a closer content provider.
                       Or they might block you from seeing certain things
                       while offering you other things specific to your
                       location. This is possible because there are
                       databases that map IPs to locations. [Mark
                       Litwintschik] looks at using those databases from
                       an API or downloading them into your own database.
                       He also shows some very large database queries,
                       which is interesting, too. He uses IPInfo, although
                       there are other providers. Some only provide a
                       limited number of lookups, but there are plenty of
                       free tiers for low-volume usage.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ USPTO’s_ANPRM_Has_Major_Problems⠀⇛


                             Throughout my 26 years in Congress, including
                             three terms as Chairman of the House
                             Judiciary Committee, there was a clear need
                             to strengthen our patent system in order to
                             protect the rights of innovators and
                             entrepreneurs.


                      # ⚓ Europe_embarks_on_a_new_era_of_patent_protection [Ed:
                        EPO is celebrating illegal and unconstitutional
                        program. Europe embarks on a new era of criminality and
                        law-breaking -- all this to appease lobbyists with
                        their moles running the EPO.]⠀⇛


                             The Unitary Patent system enters into
                             operation


                      # ⚓ JUVE ☛ Top_ten_most-read_UPC_articles [Ed: Those "UPC
                        articles" are sponsored by Team UPC. JUVE got paid to
                        promote crimes, and is now taking stock of fake "news"
                        is produced for a fee. We nowadays have a press
                        apparatus sponsored to promote crime on behalf of
                        criminals, including reputation-laundering PR. There's
                        money in that.]⠀⇛


                             With the Unified Patent Court just days away
                             from launch, JUVE Patent has rounded up the
                             top ten most-read articles concerning the
                             pan-European court published on the site
                             since 2018.


                      # ⚓ Unified Patents ☛ Mel_NavIP_automobile_speech
                        recognition_patent_likely_invalid⠀⇛


                             On May 23, 2023, the Patent Trial and Appeal
                             Board (PTAB) instituted trial on all
                             challenged claims in an IPR filed by Unified
                             against U.S._Patent_8,060,368, owned and
                             asserted by Mel NavIP, LLC. The ’368 patent
                             is generally directed to navigation and
                             speech recognition for a vehicle. The patent
                             had been asserted against Toyota and is
                             currently asserted against GM and Hyundai.


                      # ⚓ Dennis Crouch/Patently-O ☛ The_Silent_Echo:_Supreme
                        Court’s_Non-Engagement_with_the_Federal_Circuit_in
                        Amgen_v._Sanofi⠀⇛


                             Prof. Chris Holman recently characterized
                             Amgen v. Sanofi as an “endorsement of the
                             Federal Circuit’s current interpretation and
                             application of the enablement requirement,
                             and maintenance of the status quo.”  Although
                             I largely align with Holman’s views, I note
                             that the Supreme Court did not explicitly
                             engage with Federal Circuit precedent. More
                             specifically, the Court neither cited nor
                             discussed any Federal Circuit or CCPA
                             decision outside of case-specific historical
                             documents.


                # § Trademarks⠀➾


                      # ⚓ TTAB Blog ☛ TTABlog_Test:_How_Did_These_Three_Appeals
                        from_Section_2(d)_Refusals_Turn_Out?⠀⇛


                             By my count, the TTAB has affirmed about 83%
                             of the Section 2(d) refusals it has reviewed
                             on appeal this year. How do you think these
                             latest three appeals came out? Results will
                             be found in the first comment.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Birotam_emi⠀⇛


                       Two weeks ago I finally bought a bicycle. I went to
                       a bike shop where
                       they do measure you and based on your criteria that
                       you gave them
                       beforehand, they propose a bike that should fit
                       your needs. They also
                       mount everything based on your sizes.


                       Of course it costs more than buying in a shopping
                       mall, but as I have
                       no idea about bicycles it was a safe choice. This
                       way I also do not
                       have to worry about maintenance, they do everything
                       and I just have to
                       reserve a time slot online and drop off the bike in
                       the shop. They
                       also have a bike wash.


          o § Politics⠀➾


                # ⚓ End_the_slaughter_age⠀⇛


                       EU citizens: there is time until 5th June to sign
                       the ECI petition to close animal farms and
                       slaughterhouses.


          o § Technical⠀➾


                # ⚓ Love_is_all_I_need⠀⇛


                       The trouble with so fantastic a read/review is now
                       I’d rather read CircaDian than play Half-Life Alyx.


                # § Internet/Gemini⠀➾


                      # ⚓ About_the_Domain_“Geminispace.org”⠀⇛


                             I have encountered a few complaints that the
                             domain name of this site, Geminispace.org, is
                             problematic because it can be somewhat
                             ambiguous and misleading: it may be unclear
                             whether one means just this capsule or
                             Geminispace as a whole — a collection of
                             Gemini capsules and the people who maintain
                             them. One might react to this dismissively
                             and think that a name is just a name, but I
                             want to give this topic some serious
                             consideration.


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


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