𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, July 19, 2022
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Generated Wed 20 Jul 02:39:51 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2022/07/19/


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⦿ When Criminals Make It a Crime to Speak About Their Crimes | Techrights

⦿ [Meme] EPO Ignorance is Bliss | Techrights

⦿ [Meme] Bubble Schwabble | Techrights

⦿ Microsoft GitHub Exposé — Part XXIV — Using Microsoft Money as ’Get Out of Jail’ Card After Suffocating Women | Techrights

⦿ IRC Proceedings: Monday, July 18, 2022 | Techrights

⦿ The EPO Bubble — Part VII — A Multifaceted Man of Letters | Techrights

⦿ Site Migration Has Begun | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/07/19/epo-non-disclosure-agreements/#comments
		http://techrights.org/2022/07/19/epo-quiets-down-reps/#comments
		http://techrights.org/2022/07/19/epo-terminator-meme/#comments
		http://techrights.org/2022/07/19/get-out-of-jail-with-microsoft/#comments
		http://techrights.org/2022/07/19/irc-log-180722/#comments
		http://techrights.org/2022/07/19/razik-the-man-of-letters/#comments
		http://techrights.org/2022/07/19/site-migration-alpine/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/07/19/microsoft-offline-again/#comments
		http://techrights.org/2022/07/19/rip-thomas-lord/#comments
		http://techrights.org/2022/07/19/ubuntu-21-10-end-of-life/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 67

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/19/epo-non-disclosure-agreements/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/19/epo-non-disclosure-agreements/

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Gemini_version_available_♊︎


✐ When_Criminals_Make_It_a_Crime_to_Speak_About_Their_Crimes⠀✐


Posted in Deception, Europe, Patents at 5:47 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 0ec5420818157c7113ab4c89811b739c
New Levels of Censorship at EPO
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/gagging-epo-reps-nda-style.webm


Summary: Gag orders or something akin to NDAs (non-disclosure agreements) are
the latest attack on free speech at the EPO; to make matters worse, this is
designed to make corruption and crime in the management ranks impermissible to
speak about (they make it a taboo or a ‘crime’ to talk about crime)


THE EPO bribes_media_and_academia and today it openly_bragged_about_it.
(warning: epo.org link)


What does it mean for the media when staff representation at the EPO is also
being gagged, preventing media from even finding out what’s going on inside the
EPO?


“What does it mean for the media when staff representation at the EPO is also
being gagged, preventing media from even finding out what’s going on inside the
EPO?”That’s the subject of the video above. Based on publications in
circulation this week, the censorship has reached new heights. As far as we can
recall, even Benoît_Battistelli did not do this and this is what António
Campinos resorts to after securing (buying) another term.


This is what a report now looks like (just to make a point):


     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇The Central Staff Committee's (CSC) empty letter⦈
      The Central Staff Committee (CSC) posts an empty letter in protest


Worry not, however, as there’s a canary in this coalmine. Why can the CSC not
speak?


In new ommunications entitled “Reward Exercises 2022: “Full transparency” in
the Harmonisation Committee” the CSC says: “Our full report on the meeting of
the Harmonisation Committee of 27 June 2022 can be found here. It complies with
the official instructions given to our observer.”


Here’s the gag order:


     We note that the Office allows the CSC to appoint an observer in the
     Harmonisation Committee (HC) – even though this is not foreseen in
     the regulations – to contribute to a transparent rewards exercise. To
     ensure this transparency, in your capacity of observer, you were
     invited to attend the HC and were given access to the same
     confidential information the HC’s statutory members have.


     As an observer to the HC, you are also free to report at any time in
     general terms to the CSC what you observed, including by raising any
     issue of a general nature. Nevertheless, this capacity of observer
     does not allow you to share any confidential documents (which served
     as a basis for the discussion) nor any confidential information with
     anyone outside the HC (incl. the CSC), neither before nor after the
     President has taken a decision. In that respect, the obligation of
     confidentiality applicable to the HC’s statutory members, applies
     equally to you.
     Finally, as specifically concerns the rewards statistics report, it
     is noted that the confidentiality thereof was duly specified
     beforehand, and not challenged by you either before or during the
     meeting. This report can therefore not be shared with the CSC.


We saw similar rules when people entered a room to hear the “hearing” about
Judge Corcoran. That was a very long time ago.


“We disagree that, under the restrictions set out, the observer is able to
ensure any transparency in the procedure at all,” the CSC notes. “In this open
letter to the President we request reconsideration of his decision to disallow
a nominated staff representative to share documents and details of discussions
held in said meeting with the rest of the staff representation.”


Campinos may be experimenting with a new oppressive approach — one that ILOAT
cannot squash quickly enough, as the video above notes.


Here’s what the letter to Campinos says:


     European Patent Office
     80298 Munich
     Germany


     Central Staff Committee
     Comité central du personnel
     Zentraler Personalausschuss


     centralSTCOM@epo.org


     Reference: sc22097cl
     Date: 14.07.2022


     European Patent Office | 80298 MUNICH | GERMANY
     Mr António Campinos
     President of the EPO


     By email


     § OPEN LETTER⠀➾


     ⚓  Information sharing within Staff Representation⠀⇛


     Dear Mr President,


     The CSC has been permitted to appoint a single observer to the
     Harmonisation Committee. In advance of the last meeting of this
     Committee, our observer was provided with the relevant documentation,
     along with a statement explicitly forbidding the sharing of the
     document with the other members of the CSC. In reply to a query from
     our observer, your services reiterated their position, and stated
     that the “role [of] an observer is to ensure transparency but does
     not allow [the observer] to disclose any documents or discussions
     from the meeting”, and further that the observer is “free to report
     at any time in general terms to the CSC what [was] observed,
     including by raising any issue of a general nature”.


     In light of this exchange we note the following:


     • We disagree that, under the restrictions set out, the observer is
     able to ensure any transparency in the procedure at all, since the
     observer is obstructed from effectively informing the CSC.
     • We question what information would be considered “general” by the
     administration.
     • We object to our observer being put in the difficult position of
     potentially disclosing information that the administration later
     deems to not fit the “general” requirement, and being sanctioned for
     it.


     =====================================================================
     • We have not been given any justification as to why the documents
     are not suitable to be shared among the elected staff
     representatives, especially since they contain merely anonymised
     statistics rather than any personal or identifying information of
     individuals.


     We are of the opinion that the role of the observer is to report to
     the CSC the events of the Harmonisation Committee meetings. To
     effectively do so, the observer must not be impeded with undue
     barriers. Should any irregularities be identified (for example,
     unaccounted for funds are identified or disproportionately large
     bonuses are awarded to a particular subset of staff) the CSC can take
     appropriate action. Alone, the observer is powerless to act on any
     findings.


     Therefore, we request that the decision to disallow a nominated staff
     representative to share documents and details of discussions held in
     said meeting with the rest of the CSC be reconsidered.


     Yours sincerely,


     Michael Sampels
     Acting Chairman of the Central Staff Committee


It’s clear that Tony ‘the f***ing president’ (in his own words) Campinos is
only getting worse. He gets more oppressive over time. We certainly hope that
staff will stand up and oppose this before it escalates further. What next?
Banning calls for strike? Remember he’s thus far refusing to obey the_ILOAT
ruling from a fortnight ago. He has not lifted mass-mail restrictions. █


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⣿⣿⣷⣯⣼⣷⣿⣿⣷⣿⣿⣷⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⣿
⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⣿⣿⣿⣿
⣿⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢻⣿⣿⣿
⣿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿
⣿⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿
⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿
⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢿⣿⣿⣿
⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿
⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⣿⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿
⣿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢿⣿⣿⣿
⣿⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿
⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿
⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 335

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/19/epo-quiets-down-reps/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/19/epo-quiets-down-reps/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.19.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_EPO_Ignorance_is_Bliss⠀✐


Posted in Europe, Patents at 5:55 pm by Dr. Roy Schestowitz


           🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Everyone happy at EPO; Nobody speaks⦈
                            No comment, no dissent?


Summary: The EPO‘s ban_on_sharing_of_"general"_information (even between staff
representatives and people who elect them) is a sign of the urgency to take
action


⣤⣤⣤⣤⣄⣤⣤⣤⣤⠤⣤⣤⣤⣤⠀⣀⢀⣤⡄⠀⠀⠀⢠⡄⣄⠀⢀⠀⠀⠀⢠⣤⣤⣤⣄⡄⠀⢠⡄⠀⡀⢠⢤⡤⠀⠄⢠⠀⣤⣤⡄⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣀
⣿⠿⢿⣻⡷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣄⠠⢈⢻⣧⣴⢀⣈⡿⠷⠀⡀⠠⠀⠀⠀⢸⣿⡝⣿⣛⡇⠀⢸⡇⢀⣅⣬⣼⣤⣤⣤⣴⣀⣾⣷⡆⢀⠀⡀⣿⠐⠁⠸⠆⠛⠀⠗⠸⠇⠘⠀⠈⠃⠀⠀⡇⢸⣿⠛⠛⠛⠿⢛
⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠈⡱⡍⣠⣾⢛⡟⠸⠃⣶⢾⠛⠀⠀⢸⣿⡿⣿⣿⡇⢀⣼⣿⢿⠟⠟⠋⠈⠁⠚⠿⣿⣿⣷⣦⡐⠀⡀⣿⢰⡆⢰⠆⠆⠀⠃⠘⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢠⡀⠀⠀
⠛⠻⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠃⠀⠠⡷⡇⢒⣠⣄⠂⣶⣗⠛⣛⡗⠀⠀⠺⣟⣳⡿⢿⣷⠾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣟⣛⣟⣆⠀⣿⠀⠀⠐⠀⠀⠀⠀⠰⠂⢀⠀⢸⠀⠀⠀⠃⢰⣿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣼⣷⣶⣾⣿⣏⣿⣿⣿⡆⢶⡶⢋⡄⠫⣯⠝⠁⣋⣩⣀⣚⡃⠀⠀⠐⠻⠋⠀⢻⠃⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⠈⠉⢉⡛⠃⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠠⣵⠀⠠⠀⠑⠂
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠉⠀⠀⢐⢂⣤⣿⡏⢻⣿⣿⣷⣆⠀⠀⠀⠀⠁⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠈⠨⢉⣣⣤⣤⣤⡤⣤⡤⠄⠠⠄⠀⠀⠐⠀⠀⠀⠄⠐⠉⠀⠶⠶⠶⠠
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠨⣾⣿⣧⣿⣿⣣⡈⠻⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣾⣶⣶⣾⣶⢶⢤⠀⠀⠀⠀⠀⠀⠄⠄⠀⢀⠀⢈⠀⠀⠀
⣸⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣇⢠⣀⠀⠀⠀⠀⠀⢉⡻⣿⣿⣿⠘⠀⠀⢀⡄⣠⣠⡄⠀⠀⣿⣿⡿⠿⢿⣿⣿⡏⠉⢉⣛⣿⣿⣿⣦⠀⣰⣦⣿⣿⣿⣿⣿⣿⣾⣾⡆⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⣷⠀⠀⠀
⠙⢻⣿⣿⣷⣤⣼⣿⣿⣿⡇⢸⣿⣿⣗⣼⣿⣿⡆⠀⡜⠀⢾⡇⢿⣿⣧⠀⢀⣠⣟⠃⣹⣛⡇⠀⠀⢛⠁⠀⢀⠀⢹⣿⣧⣄⢤⣶⣿⣿⣿⣿⣼⣽⣿⠙⠛⢻⣿⣿⠿⣿⠹⠀⠀⠀⠀⠃⠀⠐⠀⢸⡇⢼⣿⣴⣶⣾
⣷⣜⣿⣿⣿⣿⣯⣯⣭⣭⣿⣪⣭⣽⣯⡍⣭⣭⣭⡉⣽⢩⣭⣽⣭⢭⡿⣻⣟⢻⡟⣶⣿⡟⣛⣓⣂⢸⣴⣶⣺⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⢁⣀⣀⣀⣀⠀⢀⣤⣤⣤⣤⣄⣤⣤⣀⣠⣀⣀⣀
⣽⠻⣿⣿⠻⢟⢹⣿⣿⣿⣿⣹⣧⣿⣿⡝⣿⣧⣿⢧⣹⣾⣏⣹⣿⢸⡇⢸⣿⣼⡇⣽⣧⡄⠋⣿⣇⢺⣿⣿⣿⢷⠛⠿⣫⣽⣿⣿⣿⣿⣿⣿⣿⠹⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⠀⢼⣿⣿⡿⣿⣿⡧⣿⣿⣿⣿⣿⣿
⣿⣷⣬⣿⠆⠀⢸⣿⣀⠙⣿⣿⣿⣿⣿⣲⣿⡇⣿⡷⣿⣿⣾⣽⣿⣹⣏⣿⣏⣿⣿⣿⣟⣻⣿⣻⡏⠘⢿⢻⣿⣿⡷⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣦⣶⣶⣶⡦⣤⣿⣿⢠⣄⣯⣭⠤⣬⣥⢰⣠⣿⣏⣀⣀⣀
⠿⠿⠋⠁⠐⣿⣾⣿⣿⣇⣭⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⠿⣿⡿⠇⠀⠀⣾⣿⣏⢄⢀⣬⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡟⠛⠧⠛⣈⣿⣿⣿⣿⣟⠀⠋⠏⣠⢙⣿⣿⣿⣿⣿
⠀⢠⡆⢱⣆⣿⣿⣿⢈⣿⣿⣽⢻⣿⢦⡄⣶⢀⣶⢨⣩⣽⣿⣿⣿⣿⣿⣧⡉⣿⣿⠿⣿⡷⣽⢡⣴⢶⡜⠉⢿⣻⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⡛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿
⠀⢸⣿⣾⡟⢹⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣥⣿⣧⣿⢸⣿⢸⡇⠀⠀⡀⠈⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡟⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣾⠏
⠀⢸⣿⣽⡿⣿⡷⣿⡆⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢰⣿⢾⣷⠀⣿⡏⠉⠙⣿⣿⡿⣿⣿⡟⢻⣿⣸⡇⠀⠀⢻⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠈⠁⠙⠓⠢⠄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠿⠋⠀⠀
⡀⠈⣿⣿⣷⣿⣿⣿⣥⣭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠑⠿⣿⠷⠛⠉⠉⠀⠀⠀⢸⣿⣷⣄⠂⠹⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣾⣦⣄⣀⡀⠀⠀⠀⠀⠒⠂⠀⠀⠀
⣿⣶⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠒⠩⠻⣿⣿⣿⣿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠳⠤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⡇⠸⣿⣿⡮⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢁⡀⠀⢀⣴⣾⣶⣾⣿⠇⠀⠿⠿⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣶⣿⢀⣴⠟⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠁⠀⠈⠻⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠃⠀
⣤⣤⣤⣤⣄⣤⣤⣤⣤⠤⣤⣤⣤⣤⠀⣀⢀⣤⡄⠀⠀⠀⢠⡄⣄⠀⣀⠀⠀⠀⢠⣤⣤⣤⣄⡄⠀⢠⡄⠀⡀⢠⢤⡤⠀⠄⢠⠀⣤⣤⡄⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣀
⣿⠿⢿⣻⡷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣤⠀⢈⢻⣷⣴⢀⣈⡿⠷⠀⡀⠠⠀⠀⠀⢸⣿⡿⣿⣛⡇⠀⢸⡇⢀⣁⣬⣼⣤⣤⣤⣴⣀⣾⣷⡆⢀⠀⡀⣿⠰⠁⠸⠇⠛⠀⠇⠸⠇⠘⠀⠘⠃⠀⠀⡇⢸⣿⠛⠛⠛⠿⢛
⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠈⡳⡍⣠⣼⣛⡟⠼⠃⣶⣾⠙⠀⠀⢨⣿⡿⣿⣿⡇⢀⣼⣿⣿⠟⠿⠋⠈⠁⠚⠿⣿⣿⣷⣦⡐⠀⡀⣿⠰⡆⢰⠆⠆⠀⠃⠘⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢠⡀⠀⠀
⠛⠻⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠃⠀⠠⡷⡇⢂⣠⣄⠂⣾⣗⠛⣛⡓⠀⠐⠺⣿⣳⠿⢿⣷⠾⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣛⣟⣆⠀⣿⠀⠀⠰⠀⡀⠀⡀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢸⣿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣾⣿⣯⣿⣿⣿⡄⢶⡶⢋⡄⠋⣿⠝⠁⣋⣩⣁⣛⡃⠀⠀⠀⠻⠋⠛⢿⠃⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⠈⠉⢉⡛⠃⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⢨⣽⠀⠠⠀⠁⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠰⠂⣤⣿⡏⢻⣿⣿⣿⣆⠀⠀⠀⠀⠁⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠈⠨⢍⣣⣤⣤⣤⡤⣤⡄⠄⠠⠄⠀⠀⠐⠀⠀⠀⠄⠐⠉⠀⠶⠶⠶⠤
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠨⣾⣿⣧⣾⣿⣣⠈⠻⠀⠀⠀⠀⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣾⣷⣶⣾⣶⢦⢄⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⢰⠀⠀⠀
⣼⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣇⢠⣀⠀⠀⠀⠀⠀⢉⡻⣿⣿⣿⠘⠀⠀⢀⡀⣠⣠⡄⠀⠀⣿⣿⡿⠿⢿⣿⣿⡏⠉⠉⣛⣿⣿⣿⣦⠀⣰⣦⣿⣿⣿⣿⣿⣿⣾⣾⡆⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⣷⠀⠀⠀
⠙⢻⣿⣿⣧⣤⣼⣿⣿⣿⡇⢸⣿⣿⣇⣼⣿⣿⡆⠀⡔⠀⢾⡇⢿⣿⣧⠀⢀⣠⣟⠃⣹⣛⡇⠀⠀⢛⠁⠀⢀⠀⢹⣿⣧⣄⢤⣶⣿⣿⣿⣿⣾⣽⣿⠙⠛⢻⣿⣿⠿⣿⠹⠀⠀⠀⠀⠃⠀⠘⠀⢸⡇⢾⣿⣴⣶⣾
⣷⣜⣿⣿⣿⣿⣯⣯⣭⣭⣿⣪⣭⣽⣭⡍⣭⣭⣭⡉⣽⢩⣭⣽⣭⢭⡿⣻⣟⢻⡟⣶⣿⡟⣛⣓⡂⢸⣴⣶⣺⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⣁⣀⣀⣀⣀⠀⢀⣤⣄⣄⣤⣄⣠⣤⣤⣤⣀⣀⣀
⣽⠻⣿⣿⠻⢟⢹⣿⣿⣿⣿⣹⣧⣿⣿⡝⣿⣧⣿⢧⣹⣾⣏⣹⣿⢸⡇⢸⣿⣼⡇⣽⣧⡄⠋⣿⣯⢾⣿⣿⣿⢳⠛⠿⣯⣽⣿⣿⣿⣿⣿⣿⣿⠹⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⢼⣿⣿⡿⣿⣿⡧⣿⣿⣿⣿⣿⣿
⣿⣷⣬⣿⠆⠂⢸⣿⣀⠙⣿⣿⣿⣿⣿⣲⣿⡇⣿⡷⣿⣿⣾⣿⣿⣹⣏⣽⣏⣿⣟⣿⣟⣻⣿⣻⡏⠘⢿⢻⣿⣿⡧⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣦⣶⣶⣶⡦⣤⣿⣿⢠⣄⣯⣭⠤⣬⣤⢰⣠⣿⣏⣀⣀⣀
⠿⠿⠋⠁⠐⣿⣾⣿⣿⣇⣭⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡾⣿⣿⣿⣿⣿⠯⣿⡿⠇⠀⠀⣾⣿⣋⣠⣄⣬⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡟⠛⠧⠛⣈⣿⣿⣿⣿⣟⠀⠋⠋⣠⢘⣿⣿⣿⣿⣿
⠀⢠⡄⢱⣦⣿⣿⣿⢈⣿⣿⣽⢻⣿⢦⡄⣶⢀⣶⢨⣩⣽⣿⣿⣿⣿⣿⣧⡉⣿⣿⠿⣿⡧⣽⢡⣴⢶⡜⠉⢿⡻⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⡛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿
⠀⢸⣿⣾⡟⢹⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣥⣿⣧⣿⢸⣿⢸⡇⠀⠀⡀⠘⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣾⠏
⠀⢸⣿⣽⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠙⣿⣿⡿⣿⣿⡟⢻⣿⣸⡇⠀⠀⢻⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠘⠉⠙⠓⠠⠄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠿⠋⠀⠀
⡀⠈⣿⣿⣷⣿⣿⣿⣥⣭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠁⠿⣿⠷⠛⠉⠉⠀⠀⠀⢸⣿⣷⣄⠀⠹⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣾⣦⣤⣀⡀⠀⠀⠀⠀⠒⠂⠀⠀⠀
⣿⣶⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠒⠩⡻⣿⣿⣿⣿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠳⠤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⡇⠸⣿⣿⡮⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢁⡀⠀⢀⣤⣶⣶⣾⣿⠇⠀⠿⠿⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣶⣿⢀⣴⠟⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠉⠁⠀⠈⠿⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠃⠀
⣤⣤⣤⣤⣄⣤⣤⣤⣤⠤⡤⣤⣤⣤⠀⣀⢠⣤⡄⠀⠀⠀⢠⡄⣄⠀⣀⠀⠀⠀⢠⣤⣤⣤⢤⡄⠀⢠⡄⠀⡀⢠⢤⡤⠀⠄⢠⠀⣤⣤⡄⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⢤⣀
⣿⠿⢿⣻⡷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣤⠠⢊⢻⣧⣴⢀⣈⡿⠷⠂⡀⠤⠀⠀⠀⢸⣿⣽⣿⣝⡇⠀⢸⠆⢀⣁⣬⣼⣤⣤⣦⣴⣀⣾⣷⡆⣄⠀⡀⣿⠰⠁⠸⠆⠛⠀⠇⠸⠇⠘⠀⠈⠃⠀⠀⡇⢸⣿⠛⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠈⡳⡍⣡⣾⣛⡟⠸⠃⣶⣾⠻⠀⠀⢨⣿⣿⣿⣾⡇⢀⣼⣿⢿⠿⠿⠋⠊⠀⠛⠿⣿⣿⣷⣦⡐⠀⡀⣿⢰⡆⢰⠆⠆⠀⠃⠘⠃⠀⠀⢐⠀⠀⠀⡃⢸⣿⠀⢠⡀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠃⠀⠠⡷⡇⢖⣠⣄⠃⣾⣗⠛⣛⠓⠀⠀⠺⣿⣳⢿⢿⣷⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣛⣛⣟⣦⠀⣿⠀⠀⠰⠀⠀⠀⠀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢸⡿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣾⣿⣏⣿⣿⣿⡆⢶⡶⢋⡄⠫⣻⠻⠁⣋⣩⣀⣚⡁⠀⠀⠀⠛⠋⠚⢻⠃⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⠈⠉⣉⡛⠃⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⢸⣽⠀⠠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠀⠀⢐⠂⣤⣿⡏⢻⣿⣿⣷⣆⠀⠀⠀⠀⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⠨⠍⢣⣤⣤⣤⡤⣤⡄⠄⠠⠄⠀⠀⠐⠀⠀⠀⠄⠘⠉⠀⠶⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠨⣾⣿⣧⣾⣿⣣⡘⢻⠀⠀⠀⢀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣾⣶⣶⣾⣶⣶⢤⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⡇⢠⣀⡀⠀⠀⠀⠀⢉⡻⣿⣿⣿⠘⠃⠀⢀⡀⣀⣄⡅⠀⠀⣿⣿⠿⠿⢿⣿⣿⡋⠉⢉⣿⣿⣿⣿⣦⠀⣰⣦⣿⣿⣿⣿⣿⣿⣾⣾⡆⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣷⠀⠀⢐
⠛⢻⣿⣿⣧⣤⣼⣿⣿⣿⡇⢸⣿⣿⣇⣼⣿⣿⡆⠀⣔⠀⣼⡇⢿⣿⣇⠀⢀⣠⣟⠃⣹⣛⡇⠀⠀⢛⠀⠀⢀⠀⣺⣿⣧⣄⣴⣾⣿⣿⣿⣿⣼⣿⣿⠙⠛⠻⣿⣿⠿⣿⠹⠀⠀⠀⠀⠃⠀⠘⠀⢸⠇⢾⣿⣴⣶⣾
⣷⣜⣿⣿⣿⣿⣿⣯⣭⣭⣿⢪⣭⣽⣯⡍⣭⣭⣭⡉⣽⢩⣭⣽⣭⢬⡿⣻⣟⢻⡟⣶⣿⡟⣛⣓⢂⢸⣶⣶⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⣁⣀⣀⣀⣀⠀⢠⣤⣤⣄⣤⣄⣄⣀⣄⣠⣀⣀⣀
⣽⠻⣿⣿⠻⢟⢹⣿⣿⣿⣿⣹⣧⣿⣿⡝⣿⣧⣿⢧⢹⣾⣏⣹⣿⢸⡇⢸⣿⣼⡇⣽⣧⡄⠋⡿⢨⣿⣿⣿⣿⣛⠛⠻⣭⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⢿⣿⣿⡯⣼⣿⣿⣿⣿⣿
⣿⣷⣼⣿⠆⠂⢸⣿⣀⠙⣿⣿⣿⣿⣿⣲⣿⡇⣿⡷⣿⣿⣾⣿⣿⣸⣏⣿⣏⣿⣿⣿⣟⣛⣿⠃⠀⠚⢿⢻⣿⣿⠧⠻⠿⢿⢿⣻⣿⣿⣿⣿⣿⣰⣿⣿⣶⣶⣶⣶⡦⣤⣿⣿⢠⣍⣯⣭⢠⣭⣥⠐⣤⣿⣏⣀⣀⣀
⠿⠿⠋⠀⢰⣿⣾⣿⣿⣇⣽⣙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡾⣿⣿⣿⣿⣿⠿⣿⡄⠀⠀⠈⢿⣿⣇⠤⢬⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡟⠛⠇⢛⣈⣿⣿⣿⣿⡏⠀⠋⡟⢠⡈⣿⣿⣿⣿⣿
⠀⢠⡄⢱⣦⣿⣿⣿⠈⣿⣿⣽⢻⣿⢦⡄⣶⢠⣶⢨⣩⣽⣿⣿⣿⣿⣿⣧⡉⣿⣿⠿⣿⡧⣽⢣⣴⢾⡅⠈⢿⡿⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⡛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿
⠀⢸⣷⣾⡟⢹⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣥⣿⣧⣿⢸⣿⢸⡇⠀⠀⠀⠘⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣾⣯
⠀⢸⣿⣼⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠙⣿⣿⡿⣿⣿⡟⢸⣿⣸⡇⠀⠀⢻⣄⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡿⠘⠁⠙⠓⠠⢄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠿⠛⠛⠛
⡀⠈⣿⣿⣷⣿⣿⣿⣥⣭⡀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠀⠀⠀⠉⠉⠑⠿⣿⠇⠀⠈⠉⠀⠀⠀⢸⣿⣷⣄⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⠳⢾⣤⣄⣀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀
⣿⣶⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠒⠩⠻⣿⣿⣿⣿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠷⠤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⡇⠸⣿⣿⡮⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢁⡀⠀⢀⣴⣾⣶⣾⣿⠇⠀⠿⠿⠇⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣾⡿⢀⣴⠟⢹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀
⠟⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠉⠁⠀⠈⠿⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠶⠖
⣤⣤⣤⣤⣄⣤⣤⣤⣤⠤⢤⣤⣤⣤⠀⣀⣠⣤⡄⠀⠀⠀⠠⡄⣄⠀⢀⠀⠀⠀⢠⣤⣤⣤⢀⡄⠀⢠⡄⠀⡄⢠⢤⡤⠀⠄⢠⠀⣤⣤⡄⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣀
⣿⠿⢿⣻⡷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣄⠠⢊⢻⣇⣰⢀⣀⡿⠷⠀⡀⠠⠀⠀⠀⢸⣿⡽⣿⣛⡇⠀⢸⠇⢀⣁⣬⣼⣤⣤⣤⣴⣀⣾⣷⡆⣄⠀⡀⣿⠐⠁⠸⠆⠛⠠⠇⠸⠇⠘⠀⠘⠃⠀⠀⡇⢸⣿⢛⠛⠛⠿⢛
⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠉⠀⠈⠱⡍⣡⣾⢛⡟⠸⠃⣶⢾⠛⠀⠀⢸⣿⡿⣿⣿⡇⢀⣼⣿⣿⠿⠟⠋⠊⠀⠛⠿⣿⣿⣷⣦⡐⠀⡀⣿⢰⡆⢰⠆⠆⠀⠃⠘⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢠⡀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⣿⣿⣇⣿⣿⣿⠁⠀⠠⡷⠃⢒⣠⣄⠃⣶⣗⡛⢛⠒⠀⠀⠺⣟⣳⡻⢿⣷⠿⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢩⣍⣿⣟⣦⠀⣷⠀⠀⠐⠀⡀⠀⡀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢠⣿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣾⣿⣏⣿⣿⣿⣆⢶⡶⢋⡄⠫⢿⠻⠁⣋⣩⣀⣚⡀⠀⠀⠀⠚⠋⠀⢻⠃⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣀⠀⠉⣙⡛⡃⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⢨⣽⠀⠠⠀⠁⠚
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠉⠀⠀⠰⢂⣤⣿⡏⢿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⠨⠍⢣⣤⣤⣤⡤⣤⡤⠄⠠⠄⠀⠀⠐⠀⠀⠀⠄⠐⠉⠀⠶⠶⠶⠴
⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠨⣶⣿⣧⣾⣿⢣⠈⠻⠀⠀⠀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣷⣶⣾⣶⢶⢤⠀⠀⠀⠀⠀⠀⠄⠅⠀⢀⠀⢰⠀⠀⠀
⣹⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⡇⢠⣀⠀⠀⠀⠀⠀⢉⡻⣿⣿⣿⠚⠃⠀⢀⡄⣐⣀⡅⠀⠀⣿⣿⠿⠿⢿⣿⣿⠉⠉⠩⣽⣿⣿⣿⣦⠀⣰⣦⢿⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣷⠀⠀⠀
⡛⢻⣿⣿⣷⣤⣼⣿⣿⣿⡇⢸⣿⣿⣇⣼⣿⣿⡆⠀⣐⠀⢼⡏⢿⣿⣇⠀⢀⣠⣟⠃⣹⣛⡇⠀⠀⢋⠀⠀⠀⠀⣿⣿⣤⣄⣴⣾⣿⣿⣿⣿⣼⣽⣿⠘⠛⢻⣿⣿⠿⣿⠹⠀⠀⠀⠀⠃⠀⠘⠀⢸⠇⢾⣿⣴⣶⣾
⣷⣄⣿⣿⣿⣿⣿⣯⣭⣭⣿⣪⣭⣽⣯⡍⣭⣭⣭⡉⣿⢩⣭⣽⣭⢬⡿⣿⣟⢻⡟⣶⣿⡟⣛⠓⣄⣸⣶⣶⣮⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⣁⣀⣀⣀⣀⠀⣠⣤⣤⣤⣤⣤⣄⣀⣄⣠⣀⣀⣀
⣽⠻⣿⣿⠻⢿⢹⣿⣿⣿⣿⣹⣧⣿⣿⡝⣿⣧⣿⠧⣹⣾⣏⣹⣿⢸⡇⢸⣿⣼⡇⣽⣧⡄⠋⠀⣿⣿⣿⣿⡿⣛⠛⢛⣭⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⢿⣿⣿⣿⢼⣿⣿⣿⣿⣿
⣿⣷⣼⣿⠆⠂⢸⣿⣀⠘⣿⣿⣿⣿⣿⣲⣿⡇⣿⡧⣿⣿⣾⣿⣿⣼⣏⣿⣏⣿⣿⣿⣟⣛⡇⠀⠚⠋⢿⢻⣿⣿⠿⠻⠿⣿⢿⣻⣿⣿⣿⣿⣿⣠⣿⣿⣦⣶⣶⣶⡦⣤⣿⣿⢠⣩⣧⣬⢤⣭⣥⡄⣆⣿⣯⣀⣀⣀
⠿⠿⠋⠀⢐⣿⣾⣿⣿⣇⣽⣙⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⠿⡧⠀⠀⡀⠀⢿⣿⣇⡤⢬⠤⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡟⠛⠧⢛⣈⣿⣿⣿⣿⡃⠀⢹⣿⢁⡀⣻⣿⣿⣿⣿
⠀⢠⡄⢱⣆⣿⣿⣿⢈⣿⣿⣽⣻⣿⢦⡄⣶⢀⣶⢨⣩⣽⣿⣿⣿⣿⣿⣧⡈⣿⣿⠿⣿⡧⣭⢠⣴⢿⡄⠈⠻⡿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣅⣿⣧⡿⢸⣿⢸⡇⠀⠀⢀⠈⠛⠻⠿⠟⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣾⣯
⠀⢸⣿⣾⡿⣿⡷⣿⡆⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⡿⣿⡿⠀⢸⣿⣸⡇⠀⠀⢸⣄⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⡿⠈⠋⠙⠓⠠⠄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠻
⡀⠈⣿⣿⣷⣿⣿⣿⣥⣭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠁⠿⠁⠀⠀⠈⠉⠀⠀⠀⢸⣿⣷⣄⡀⠙⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⣼⣤⣄⣀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠌
⣿⣾⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⠩⠻⣿⣿⣿⣿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠶⠤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠈⢿⣿⡇⠸⣿⣿⡎⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢁⡀⠀⢀⣶⣾⣶⣾⣿⠃⠀⠿⠿⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣾⡿⢀⣴⠟⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠈⠁⠀⠈⠻⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠄
⣤⣤⣤⣤⣄⣤⣤⣤⣤⠤⠤⣤⣤⣤⠀⣀⣠⣤⡄⠀⠀⠀⢠⡄⣄⠀⣀⠀⠀⠀⢠⣤⣤⣤⣀⡄⠀⢠⡄⠀⡀⢠⢤⡤⠀⠄⢠⠀⣤⣤⡀⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣠⣀
⣿⠿⢿⣻⡷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣄⠰⢈⢻⣇⣴⢀⣈⡿⠷⠀⡀⠠⠀⠀⠀⢸⣿⡝⣿⣟⡇⠀⢸⠆⢀⣁⣬⣼⣤⣤⣤⣴⣀⣾⣷⡆⢀⠀⡀⣿⠐⠁⠸⠆⠛⠐⠇⠸⠇⠘⠀⠘⠃⠀⠀⡇⢸⣿⠟⠛⠛⠿⢛
⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠈⠱⡍⣠⣼⢛⡟⠰⠁⣶⢾⠙⠀⠀⢸⣿⡿⣿⣾⡇⢀⣼⣿⣿⠿⠟⠋⠋⠀⠛⠿⣿⣿⣷⣦⡐⠀⡀⣿⢰⡆⢰⠆⠆⠀⠃⠘⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢠⠀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠁⠀⢀⡷⠃⢂⣠⣄⠃⣾⣗⠛⢛⠒⠀⠐⠺⣟⣳⡿⣿⣷⠿⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣽⣿⣦⠀⣷⠀⠀⠐⠀⡀⠀⠀⠠⠂⢀⠀⢸⠀⠀⠀⠃⢠⡿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣾⣿⣯⣿⣿⣿⡆⢶⡶⢋⡄⠫⣺⠘⠁⣋⣭⣀⣘⡂⡀⠀⠀⠛⠋⠀⢻⠃⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣦⣄⠀⠈⣝⣛⣃⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠠⣵⠀⠠⠀⠀⠚
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠀⠀⠰⢂⣤⣿⡏⢻⣿⣿⣿⣆⠀⠀⠀⠀⠈⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠬⢡⣤⣤⣤⡤⣤⡄⠄⠠⠄⠀⠀⠐⠀⠀⠀⠄⠐⠉⠀⠶⠶⠶⠤
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠨⣾⣿⣧⣿⣿⣣⠈⠳⠀⠀⠀⣄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⣿⣿⣷⣶⣾⣶⢶⢤⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣸⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣇⢠⣀⠀⠀⠀⠀⠀⢉⡹⣿⣿⣿⠘⠀⠀⢀⡄⣠⣠⡄⠀⠀⣿⡿⠟⠛⢿⣿⣟⠁⠀⠬⢽⣿⣿⣿⣦⢀⣴⣶⢿⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⣷⠀⠀⠀
⡛⢻⣿⣿⣧⣤⣼⣿⣿⣿⡇⢸⣿⣿⣗⣼⣿⣿⡆⠀⣰⠀⢼⡇⢿⣿⣇⠀⢀⣠⣟⠃⣹⣛⡇⠀⠀⢋⠀⠀⢀⠀⣿⣿⣦⣄⣶⣿⣿⣿⣿⣿⣼⣽⣿⠘⠛⢻⣿⣿⠿⣿⠹⠀⠀⠀⠀⠃⠀⠘⠀⢸⠇⢾⣿⣴⣶⣾
⣷⣄⣿⣿⣿⣿⣯⣯⣭⣭⡿⣪⣭⣽⣯⡍⣭⣭⣭⡉⣯⢩⣭⣽⣭⢬⡿⣻⣟⢻⡟⣶⣿⡟⠛⣵⡄⢸⣶⣶⣽⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⣁⣀⣀⣀⡀⠀⣠⣤⣤⣤⣤⣤⣀⣄⣀⣠⣀⣀⣀
⣽⠻⣿⣿⠻⠟⢹⣿⣿⣿⣿⣹⣇⣿⣿⡟⣿⣧⣿⠇⣹⣾⣏⣹⣿⢸⡇⢸⣿⣼⡇⣽⣧⡄⠀⢷⣿⢻⣿⣿⡿⣫⠙⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣼⡿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⡿⢿⣿⣿⣿⠤⣿⣿⣿⣿⣿
⣿⣷⣼⣿⠆⠂⢸⣿⣀⠘⣿⣿⣿⣿⣿⣲⣿⡇⣿⡧⡿⣿⣾⣿⣿⣸⣏⣿⣏⣿⣿⣿⣟⡃⠀⠘⠁⠀⠻⢹⣿⣿⠗⠛⣛⠻⣻⣿⣿⣿⣿⣿⣿⣠⣿⣿⣦⣶⣶⣶⡶⣤⣿⣷⢠⣥⣧⡅⣬⣭⣥⡄⢠⣾⣯⣀⣀⣀
⠿⠿⠋⠀⢒⣿⣾⣿⣿⣇⣽⣙⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⠇⠀⠀⣀⠀⠀⢷⣿⣅⠦⠤⡴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢉⣹⡟⠛⠇⢛⣈⣿⣿⣿⣿⡁⢘⢹⣿⡇⣀⢹⣿⣿⣿⣿
⠀⢠⡄⢱⣆⣿⣿⣿⢈⣿⣿⣽⢻⣿⢦⡄⣶⢠⣶⢨⣩⣽⣿⣿⣿⣿⣿⣧⡈⣿⣿⠟⣿⡧⣤⢠⣿⢶⡄⠈⠛⠝⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢹⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣥⣿⣧⡿⢸⣿⢸⡇⠀⠀⢠⠈⠙⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣾⣯
⠀⢸⣿⣾⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⡿⣿⡇⠀⢸⣿⣸⡇⠀⠀⢸⣆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠈⠋⠙⠓⠠⢄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠿⠛⠚⠿
⡀⠈⣿⣿⣷⣿⣿⣿⣧⣭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠈⠉⠀⠉⠁⠀⠀⠉⠉⠁⠉⠀⠀⠀⠈⠉⠀⠀⠀⠸⣿⣷⣤⡀⠙⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⠳⣼⣤⣀⣀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠬
⣿⣾⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠉⠙⢿⣿⣿⣿⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠲⠤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⡇⠸⣿⣿⡌⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣁⠀⠀⢀⣶⣿⣷⣾⣿⠃⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣾⡿⣠⣶⠏⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠈⠀⠀⠈⠿⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣄⣤⣤⣤⣤⠤⣤⣤⣤⣤⠀⡀⢠⣤⡄⠀⠀⠀⠠⡄⣄⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⡄⠀⡄⢠⢤⡤⠀⠄⢠⠀⣤⣤⠄⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣀
⣿⠿⢿⣻⡷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣤⠠⢘⢻⣇⣰⢀⣈⡿⠗⠀⡀⠀⠀⠀⠀⢸⣿⡝⣿⣙⡇⠀⢸⡇⢀⣅⣤⣼⣤⣴⣦⣴⣄⣾⣷⡆⣄⠀⡀⣿⠰⠁⠸⠆⠛⠐⠇⠸⠇⠘⠀⠈⠃⠀⠀⡇⢸⣿⠛⠛⠛⠿⠛
⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠈⠱⡍⣠⣾⣛⡟⠼⠃⣶⢾⠙⠀⠀⢨⣿⡿⣿⣿⡇⢀⣼⣿⡿⠿⠟⠁⠁⠈⠛⠻⢿⣿⣷⣦⡀⠀⡀⣿⢰⡆⢰⠆⠆⠀⠃⠘⠃⠀⠀⢐⠀⠀⠠⡁⢸⣿⠀⢠⠀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠁⠀⠠⡷⠃⢂⣠⣄⠂⣷⣗⠛⢛⠖⠀⠐⠺⣟⣳⡿⢿⣷⠿⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣽⣯⣦⠀⡧⠀⠀⠐⠀⡀⠀⡀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢰⡿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣾⣿⣯⣿⣿⣿⡆⢶⡶⢋⡄⠋⢯⠹⠁⣋⣭⣁⣚⡓⡀⠀⠀⠛⠋⠉⢻⠃⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣷⣶⣄⠀⠀⣍⣛⣃⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⢠⣵⠀⠠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠀⠀⠐⢂⣤⣿⡏⢻⣿⣿⣿⣦⠀⠀⠀⠀⠈⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠁⠒⠬⠡⣤⣤⣤⡤⣤⡤⠄⠠⠄⠀⠀⠐⠀⠀⠀⠄⠐⠉⠀⠶⠶⠶⠦
⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠨⣾⣿⣧⣿⣿⣣⠈⠻⠀⠀⠀⣄⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣷⣶⣾⣶⢶⢄⠀⠀⠀⠀⠀⠀⠄⡅⠀⢀⠀⢸⠀⠀⠀
⣨⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣇⢠⣀⡀⠀⠀⠀⠀⢉⡻⣿⣿⣿⠙⠁⠀⢀⡄⣠⣠⡄⠀⠀⣿⠿⠛⠛⠻⣿⣿⠀⠀⠰⢿⣿⣿⣿⣦⢀⣴⣶⢹⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⣷⠀⠀⠐
⡛⢻⣿⣿⣧⣤⣼⣿⣿⣿⡇⢸⣿⣿⣇⣼⣿⣿⡆⠀⣔⠀⢼⡏⢿⣿⣇⠀⢀⣠⣟⠃⣹⣛⡇⠀⠀⢩⠀⠀⢀⢀⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣼⣿⣿⠘⠛⢹⣿⣿⠿⢿⠹⠀⠀⠀⠀⠃⠀⠐⠀⢸⠇⢼⣿⣴⣶⣾
⣿⣄⣿⣿⣿⣿⣿⣯⣭⣭⡿⣮⣭⣽⣯⡍⣭⣭⣭⡉⣯⢭⣭⣽⣭⢭⡿⣻⣟⢻⡟⣶⣿⡏⣷⡄⠀⢸⣿⣿⣷⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢉⣁⣀⣀⣀⡀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣀⣀
⣽⠻⣿⣿⠻⠿⢹⣿⣿⣿⣿⣹⣧⣾⣿⡝⣿⣧⣿⠇⣹⣾⣏⣹⣿⢸⡇⢸⣿⣼⡇⣽⣧⡄⢶⣾⠀⠸⣿⣿⡟⣭⣉⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⡿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿
⣿⣷⣬⣿⠆⠂⢸⣿⣀⠘⣿⣿⣿⣿⣿⣲⣿⡇⣿⡷⣿⣿⣾⣽⣿⣸⣏⣿⣯⣿⣿⣿⣇⡀⠘⠁⠀⠀⠻⣹⣿⡿⠀⢙⠛⠟⣻⣽⣿⣿⣿⣿⣿⣠⣿⣿⣦⣶⣶⣶⡶⣤⣿⣷⢈⣭⣧⡄⣬⣭⣥⣤⢰⣸⣧⣀⣀⣀
⠿⠟⠋⠀⢲⣿⣾⣿⣿⣗⣽⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⠁⠀⣀⠀⠀⠀⢻⣿⣥⣒⠶⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡟⠛⠇⢛⣈⣿⣿⣿⣿⠀⠈⢹⣿⡿⢈⢸⣿⣿⣿⣿
⠀⢠⣄⢱⣦⣿⣿⣿⢈⣿⣿⣽⢻⣿⢦⡄⣶⢠⣶⢸⣹⣽⣿⣿⣿⣿⣿⣧⡈⣿⣿⠟⣿⡤⣤⢫⣴⢶⡄⠀⠻⠝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⠅⣿⣧⡿⢸⣿⢸⡇⠀⠀⢰⠈⠉⠙⠛⠉⢙⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣾⣯
⠀⢸⣿⣾⡿⣿⡷⣿⡆⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣟⡀⣿⡇⠀⢸⣿⣸⡇⠀⠀⢸⣦⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠀⠃⠙⠓⠠⠄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠻
⡀⠈⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠁⠉⠀⠀⠀⠈⠉⠀⠀⠀⠘⣿⣿⣦⣀⠈⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⣼⣤⣀⣀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠬
⣿⣾⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠑⠝⢿⣿⣿⣿⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠶⠤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⡇⠸⣿⣿⡎⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣁⠀⠀⣠⣶⣿⣿⣾⣿⠁⠀⠿⠿⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⡟⢤⡾⠋⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀
⠋⠖⠲⣶⠏⢶⠌⠱⠷⠶⠆⠻⠿⠿⠻⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣄⣤⣤⣤⣤⠤⢤⣤⣤⣤⠀⡀⣠⣤⡄⠀⠀⠀⠠⡄⡄⠀⡀⠀⠀⠀⢠⣤⣤⣤⣀⡄⠀⢠⡄⠀⡄⢠⢤⡤⠀⠄⢠⠀⣤⣤⠄⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣀
⣿⠿⢿⣻⡷⣿⣿⣿⣿⡟⡛⣻⣿⣿⣤⠸⢊⢻⣷⣴⢀⣈⡿⠷⠂⡀⠤⠀⠀⠀⢸⣿⣽⣿⣙⡇⠀⢸⡇⣀⣅⣬⣾⣶⡶⣶⣶⣤⣾⣷⡆⢀⠀⡀⣿⠰⠁⠸⠇⠛⠰⠇⠸⠇⠘⠀⠈⠃⠀⠀⡇⢸⣿⠛⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠈⡱⡏⣡⣾⣟⡟⠼⠃⣶⢿⠛⠀⠀⢨⣿⡿⣿⣿⡇⢀⣼⣿⡿⠻⠟⠁⠃⠈⠙⠛⢿⣿⣿⣦⡔⠀⡀⣿⠰⡆⢰⠆⠆⠀⠃⠘⠃⠀⠀⠐⠀⠀⠀⡁⢸⣿⠀⢠⡀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠃⠀⢠⡷⠇⢒⣠⣔⠃⣿⣗⠛⣛⠖⠀⠀⠺⣟⣳⡿⢿⣷⡟⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⣭⣯⣧⡀⣇⠀⠀⠐⠀⡀⠀⠀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢰⡿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣾⣿⣏⣿⣿⣿⡆⣾⡾⢋⡄⠫⣿⠛⠁⣋⣭⣀⣚⣃⡀⠀⠀⠛⠛⠙⠛⠏⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣤⡀⠀⣬⣝⣃⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⢈⠀⠀⠀⠀⢠⣵⠀⠠⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠀⠀⠰⢂⣤⣿⡏⢻⣿⣿⣿⣆⠀⠀⠀⠀⠈⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠈⠒⠂⠁⣤⣤⣤⡤⣤⡤⠄⠠⠄⠀⠀⠐⠀⠀⠀⠄⠘⠉⠀⠶⠶⠶⠶
⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠬⣾⣿⣧⣿⣿⣣⠉⠻⠀⠀⠀⢄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣆⠀⠀⠀⠘⢿⣿⣶⣶⣾⣶⢶⢄⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣹⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣇⢠⣀⠀⠀⠀⠀⠀⢩⡻⣿⣿⣿⠙⠃⠀⢀⡄⣠⣠⡅⠀⠀⢿⠟⠋⠉⠻⣿⣿⠂⠀⠒⣺⣿⣿⣿⣷⢀⣼⣷⢸⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣷⠀⠀⠐
⡛⢻⣿⣿⣷⣤⣼⣿⣿⣿⡇⢸⣿⣿⣇⣼⣿⣿⡆⠀⣔⠀⢼⡏⢿⣿⣧⠀⢀⣠⣟⠃⣹⣛⡇⠀⠀⢸⠀⠀⣠⢀⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣾⣿⣿⠘⠛⠹⣿⣿⠿⣿⠹⠀⠠⠀⠀⠃⠀⠘⠀⢸⠇⢾⣿⣶⣶⣾
⣿⣄⣿⣿⣿⣿⣿⣯⣭⣭⡿⢪⣭⣽⣯⡍⣭⣭⣭⡙⣯⢭⣭⣽⣭⢭⡿⣻⣟⢻⡟⣶⣯⡅⡄⠀⠐⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⣁⣀⣀⣀⡀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⣽⠻⣿⣿⠻⠟⢸⣿⣿⣿⣿⣹⣇⣿⣿⡟⣿⣧⣿⠇⣹⣾⣏⣹⣿⢸⡇⢸⣿⣼⡇⣿⣧⡖⡾⠀⠀⠘⣿⣿⣟⣷⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⠿⣿⣿⣿⣿⡿⢼⣿⣿⣿⣿
⣿⣷⣬⣿⠆⠂⢸⣿⣀⠘⣿⣿⣿⣿⣿⣲⣿⡇⣿⣷⣿⣿⣾⣽⣿⣹⣏⣿⣯⣿⣿⣿⣇⡐⠃⠀⠀⠀⠻⣽⣿⡿⠋⠉⠭⣉⣽⣿⣿⣿⣿⣿⣿⣀⣿⣿⣦⣶⣶⣶⡶⣤⣿⣷⢨⣯⣯⠤⣬⣭⣥⣤⡀⣼⣧⣀⣀⣀
⠿⠟⠋⠀⢲⣿⣿⣿⣿⣷⣩⣍⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⣿⣿⣷⣿⠉⠁⣀⠀⠀⠀⠀⢻⣿⣤⣓⠲⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡏⠛⠇⢛⣈⣿⣿⣿⣏⠀⡋⣿⣿⣿⠃⠈⣿⣿⣿⣿
⠀⢠⣄⢱⣦⣿⣿⣿⢈⣿⣿⣽⢻⣿⢦⡄⣶⢠⣶⢸⣹⣽⣿⣿⣿⣿⣿⣧⡈⣿⣿⠇⣤⡶⣭⢀⣴⢶⡄⠀⠹⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⡛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⡿⠻⣿⣿⣧⠀⣿⣧⡿⢸⣿⢸⡇⠀⠀⢰⠀⠉⠉⠋⠉⢩⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣯
⠀⢸⣿⣾⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡇⠀⠀⣿⣇⡀⣿⡇⠀⢸⣿⣸⡇⠀⠀⢸⣧⡀⡀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠈⠃⠉⠓⠢⠄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠹⠛⠛⠿
⡄⠈⣿⣿⣷⣿⣿⣿⣧⣭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠈⣿⣿⣦⣆⠈⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⠳⣴⣤⣀⣀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠬
⣿⣾⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠐⠙⢿⣿⣿⡿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⢤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢀⠈⢿⣿⡇⠸⣿⣿⡌⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣠⠀⠀⣠⣿⣿⣿⣿⣿⠁⠀⠿⠿⠇⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣏⢴⠟⠁⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀
⠋⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣄⣤⣤⣤⣤⠤⢤⣤⣤⣤⠀⡀⣠⣤⡄⠀⠀⠀⢠⡄⣄⠀⠀⠀⠀⠀⢠⣤⣤⣤⣠⡄⠀⢠⡄⠀⡄⢠⢤⡤⠀⡄⢠⠀⣤⣤⡄⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣀
⣿⠿⢿⣻⡷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣤⠰⢚⢻⣟⣴⢀⣌⡿⠷⡂⡀⠤⠀⠀⠀⢸⣿⣽⣿⣙⡇⠀⢸⠏⣀⣅⣬⣾⣶⡶⣶⣶⣤⣾⣷⡆⢄⠀⡀⣿⠰⠁⠸⠆⠛⠐⠇⠸⠇⠘⠀⠈⠃⠀⠀⡇⢸⣿⢛⠛⠛⠿⢛
⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠈⡳⡏⣠⣾⣛⡟⠼⣁⣶⢿⠙⠀⠀⢸⣿⡿⣿⣿⡇⢀⣼⣿⣿⠻⠛⠁⠃⠀⠉⠛⠻⣿⣿⣦⣔⠀⡀⣿⢰⡆⢰⠆⠂⠀⠃⠘⠃⠀⠀⢐⠀⠀⠠⡁⢸⣿⠀⢠⡀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠁⢀⠠⠷⡇⢂⣠⣄⠃⣟⣗⡛⣟⡗⠀⠐⠺⣟⣳⠻⣿⣷⡾⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣾⣯⣷⡀⣷⠠⠀⠐⠀⡀⠀⠀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢰⡿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣿⣿⣏⣿⣿⣿⡆⣶⡾⢋⡄⠫⢮⠙⠁⣋⣭⣄⣚⣓⡀⠀⠀⠞⠁⠂⠃⡏⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀⣮⢍⣗⡇⠠⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠄⢸⣽⠀⠠⠀⠀⠊
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠉⠀⠀⡰⢂⣤⣿⡏⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠈⠐⠒⠁⣤⣤⣤⡤⣤⡤⠄⠠⠄⠀⠀⠐⠀⠀⠀⠄⠘⠉⠀⠶⠶⠶⠶
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠼⣾⣿⣧⣿⣿⣣⠈⠙⠀⠀⠠⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠐⢿⣿⣷⣶⣾⣶⢶⢤⠀⠀⠀⠀⠀⠀⠄⡅⠀⢀⠀⢸⠀⠀⠀
⣹⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣇⢠⣀⠀⠀⠀⠀⠀⢉⡻⣿⣿⣿⠈⠃⠀⢀⡆⣀⣤⡄⠀⠀⢻⠛⠉⠉⠹⣿⣿⠀⠀⢚⣻⣿⣿⣿⣷⢀⣼⣷⣼⣿⣿⣿⣿⣿⣾⣾⡆⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⣷⠀⠀⢀
⡛⢻⣿⣿⣧⣤⣼⣿⣿⣿⡇⢸⣿⣿⣗⣼⣿⣿⡂⠀⣔⠀⣾⡏⣿⣿⣇⠀⢀⣠⣟⠃⣹⣛⡇⠀⠀⢰⢀⣀⡠⣠⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⠘⠛⢹⣿⣿⠿⣿⠹⠀⠠⠀⠀⠃⠀⠘⠀⢸⠅⢾⣿⣶⣶⣾
⣿⣄⣿⣿⣿⣿⣿⣯⣭⣭⡿⢫⣭⣽⣯⡍⣭⣭⣭⡙⣭⢭⣭⣽⣥⢭⡿⣹⣟⢻⡟⣦⣭⡄⠀⠙⠓⢸⣿⣿⣿⡯⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀⠉⣁⣀⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣄⣠⣀⣀
⣽⠻⣿⣿⠻⢟⢹⣿⣿⣿⣿⣸⣇⣿⣿⡟⣿⣧⣿⢇⣹⣾⣏⣹⣿⢸⡇⢸⣿⣼⡇⣽⣧⡄⡀⠀⢀⡈⣿⣿⣯⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣼⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⢿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿
⣿⣷⣬⣿⠆⠂⢸⣿⣀⠘⣿⣿⣿⣿⣿⣲⣿⡇⣿⣷⣿⣿⣾⣾⣿⣸⣏⣿⣯⣿⡏⣿⣗⡂⠀⠀⠀⢷⣿⣽⣿⡟⠁⠌⠙⣃⣵⣾⣿⣿⣿⣿⣿⢀⣿⣿⣦⣶⣶⣶⡶⣤⣿⣧⣸⣧⣯⢤⣭⣭⣥⣤⡄⣼⣯⣀⣀⣀
⠿⠟⠋⠀⢲⣿⣿⣿⣿⣷⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣷⠈⠉⠁⠀⠀⠀⠈⠁⠻⣿⣾⣛⡚⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡏⠛⠇⢛⣈⣿⣿⣿⣇⠀⡋⣿⣿⣿⡷⠈⣿⣿⣿⣿
⠀⢠⣄⢱⣦⣿⣿⣿⢈⣿⣿⣽⢻⣿⢦⡄⣶⢀⣶⢨⣩⣽⣿⣿⣿⣿⣿⣧⡈⣿⣷⠀⣴⡿⣤⢀⣴⢶⡄⠰⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⡇⠈⠉⣿⣧⠀⣿⣧⡿⢸⣿⢸⡇⠀⠰⢿⠈⠉⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣾⣯
⠀⢸⣿⣿⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠁⠀⣿⣇⡀⣿⡇⠀⢸⣿⣸⡇⠀⠀⢸⣧⡀⠀⡀⢾⣿⣿⣿⣿⣿⣿⡿⠈⠋⠉⠳⠢⠄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠿
⡅⠈⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⣿⣦⣄⣹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⣴⣤⣀⣀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠬
⣿⣾⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠉⠁⠐⠙⢿⣿⣿⡿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠶⢄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⣀⠈⢿⣿⡇⠸⣿⣿⡎⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⣠⠀⢀⣤⣿⣿⣿⣿⣿⠁⠀⠿⠿⠃⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣏⢴⠟⠁⢹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣄⣤⣤⣤⣤⠤⣤⣤⣤⣤⠀⣀⣠⣤⡄⠀⠀⡀⠠⡄⣄⠀⠀⠀⠀⠀⢠⣤⣤⣤⢀⡄⠀⢠⡄⠀⡄⢠⢤⡤⠀⡄⢠⠀⣤⣤⡄⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣀
⣿⠿⣿⣻⡷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣄⠰⢉⢻⣿⣴⢀⣜⡿⠷⡀⡀⠤⠀⠀⠀⢸⣿⣝⣿⣝⡇⠀⢸⡏⣀⣅⣬⣾⣶⡶⣶⣶⣤⣾⣷⡆⣄⠀⡀⣿⠰⠃⠸⠆⠛⠐⠇⠸⠇⠘⠀⠈⠃⠀⠀⡇⢸⣿⠛⠛⠛⠿⢛
⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟⠈⠈⡳⡅⣡⣾⣟⡟⠼⠁⣶⣿⠹⠀⠀⢨⣿⡿⣿⣾⡇⢀⣼⣿⣿⠻⠛⠁⠃⠀⠉⠛⠻⣿⣿⣶⣔⠀⡀⡿⢰⡆⢰⠆⠆⠀⠃⠘⠃⠀⠀⠐⠀⠀⠀⡁⢸⣿⠀⢠⡀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠃⠀⢠⣷⡇⢂⣠⣴⠃⣿⡗⡛⣟⡓⠀⠀⠺⣟⣳⡿⣿⣷⡾⠛⠉⠈⠀⠀⠀⢀⣀⣀⠀⠀⠐⠶⢾⣯⣷⡀⣧⠀⠂⠐⠀⡀⠀⠀⠰⠂⢀⠀⢸⠀⠀⠀⠃⢰⣿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣿⣿⣏⣿⣿⣿⡆⣾⡾⢋⡄⠫⣯⠿⠁⣋⣭⣁⣚⣃⡀⠀⠀⠛⠋⠊⠛⡏⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⢬⠽⣕⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⢸⣽⠀⠠⠁⠐⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠀⠀⠰⢂⣤⣿⡏⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠑⠒⠅⣤⣤⣤⡤⣤⡄⠄⠠⠀⠀⠀⠐⠀⠀⠀⠄⠘⠉⠀⠶⠶⠶⠴
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢬⣾⣿⣧⣿⣿⣣⠉⠻⠀⠀⠀⢄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⣷⣶⣾⣶⣶⢤⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣾⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣇⢠⣀⡀⠀⠀⠀⠀⢉⡹⣿⣿⣿⠙⠃⠀⢀⡂⣐⣤⡅⠀⠀⢹⠛⠉⠉⠙⣿⣿⠁⠀⣈⣿⣿⣿⣿⣷⢀⣼⣿⣼⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣷⠀⠀⠘
⡛⢻⣿⣿⣷⣤⣾⣿⣿⣿⡇⢸⣿⣿⣇⣼⣿⣿⡆⠀⣔⠀⢾⡏⣿⣿⣇⠀⢀⣠⣟⠃⣹⣛⡇⠀⠀⢸⣀⣀⣠⣠⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠛⢻⣿⣿⠿⣿⠹⠀⠠⠀⠀⠃⠀⠘⠀⢸⠇⢾⣿⣶⣶⣾
⣿⣄⣿⣿⣿⣿⣿⣯⣭⣭⣿⢫⣭⣽⣯⡍⣭⣭⣭⡛⣭⣭⣭⣽⣥⢭⡿⣻⣟⢻⡟⣤⣤⡍⠛⢛⡓⢸⣿⣿⣿⠿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣷⠀⠀⠉⣁⣀⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣄⣀⣀
⣽⠻⣿⣿⠻⠟⢹⣿⣿⣿⣿⣸⣧⣿⣿⡟⣿⣧⣿⢇⣹⣾⣏⣹⣿⢸⡇⢸⣿⣼⡇⣿⣧⡄⠀⢸⣧⡈⣿⣿⣯⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣼⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⣿⢿⣿⣿⣿⣿⣿⠦⣿⣿⣿⣿
⣿⣷⣬⣿⠆⠂⢸⣿⣀⠘⣿⣿⣿⣿⣿⣲⣿⡇⣿⡷⣿⣿⣾⣿⣿⣸⣏⣿⣏⣿⡇⢿⣇⡀⠀⠀⢿⣷⣿⣼⣿⠏⠀⠐⠒⣠⣶⣾⣿⣿⣿⣿⣿⢀⣾⣿⣦⣶⣶⣶⡶⣤⣿⣆⣸⣯⡧⣤⣭⣭⣥⣤⡄⣦⣯⣀⣀⣀
⠿⠟⠋⠀⢲⣿⣿⣿⣿⣷⣯⣉⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠙⠋⡞⢳⣿⠁⠈⠉⠁⠀⠀⠈⠿⠏⠹⣿⣶⣉⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢉⣹⡟⡛⠧⢛⣈⣿⣿⣿⡇⢨⠉⣿⣿⣿⣿⠄⣿⣿⣿⣿
⠀⢠⣄⢱⣦⣿⣿⣿⢈⣿⣿⣽⢻⣿⢦⡄⣶⢠⣶⢸⣽⣽⣿⣿⣿⣦⣴⣧⠈⣧⣤⠄⣶⡦⣤⢀⣴⢶⡄⠀⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢹⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⡇⠀⠀⣿⣧⠀⣿⣧⡿⢸⣿⢸⡇⠀⢿⣷⠀⠉⠉⠉⢉⣩⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣾⣯
⠀⢸⣿⣿⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡇⠉⠉⣿⣇⡀⣿⡇⠀⢸⣿⣸⡇⠀⠈⢸⣧⡀⠀⡀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠉⠓⠠⠄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠻
⡄⠈⣿⣿⣷⣿⣿⣿⣧⣭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⣿⣶⣄⣝⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⣼⣤⣀⣀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠬
⣿⣾⣿⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠁⠐⠙⢿⣿⣿⡿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠶⣄⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢀⠈⢿⣿⡇⠸⣿⣿⡎⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⣠⠀⢀⣤⣿⣿⣿⣿⣿⠀⠀⠿⠿⠇⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⣴⠟⠁⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⠀⡀⣠⣤⡄⠀⠀⡀⢠⡄⣄⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⡄⠀⡄⢠⢤⡤⠀⡄⢠⠀⣤⣤⡄⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣠⣀
⣿⠿⣿⣻⡷⣿⣿⣿⣿⡟⡛⣻⣿⣿⣤⡰⢈⢻⣷⣴⢀⣈⡿⠷⡀⡀⠠⠀⠀⠀⢸⣿⣽⣿⣝⡇⠀⢸⡌⢀⣅⣬⣾⣷⡶⣶⣶⣤⣾⣷⡄⢀⠀⡀⣿⠰⠃⠸⠇⠟⠘⠇⠸⠇⠘⠀⠈⠃⠀⠀⡇⢸⣿⢛⠛⠛⠿⠛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟⠀⠈⡳⡏⣠⣾⣛⡟⠼⡁⣶⢿⠹⠀⠀⢸⣿⡿⣿⣾⡇⢀⣸⣿⣿⠿⠟⠁⠃⠀⠉⠛⠻⣿⣿⣶⣔⠀⡀⣿⠰⡆⢸⠆⠎⠀⠃⠘⠃⠀⠀⢐⠀⠀⠠⡃⢸⣿⠀⢠⡀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠓⢀⢠⡷⡃⢂⣠⣔⠃⣿⣗⡛⣛⡓⠀⠐⠺⣟⣳⡛⣿⣷⡾⠛⠉⠈⠀⠀⠀⢀⣀⣀⡀⠀⠐⠶⢾⣿⣷⡄⣗⢠⠀⠐⠀⡀⠀⠀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢠⡿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣿⣿⣏⣿⣿⣿⣆⢶⡶⢋⡄⠫⣫⠿⠁⣋⣭⣅⣚⣃⡀⠀⠐⠛⠉⠈⠛⡾⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⢮⠽⣝⡇⠀⠀⠀⠀⡀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⢠⣽⠀⠠⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠀⠀⠐⢂⣤⣿⡏⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠈⠁⠒⠅⣤⣤⣤⡤⣤⡤⠀⠠⠀⠀⠀⠀⠀⠀⠠⠄⠘⠉⠀⠶⠶⠶⠴
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣾⣿⣧⣿⣿⣣⠉⠹⠀⠀⠀⢄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⣷⣶⣶⣶⢶⢤⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣹⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣇⢠⣀⡀⠀⠀⠀⠀⢩⡹⣿⣿⣿⠙⠃⠀⣀⡆⣀⣤⡄⠀⠀⢹⠛⠉⠈⠙⣿⣿⠇⠀⣉⣿⣿⣿⣿⣷⣀⣼⣷⡾⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣷⠀⠀⠐
⡛⠻⣿⣿⣷⣤⣾⣿⣿⣿⡇⢸⣿⣿⣇⣼⣿⣿⡆⠀⣔⠀⣼⡏⣿⣿⣇⠀⢀⣰⣟⠃⣹⣛⡇⠀⠀⢸⣄⣀⣤⣠⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢹⣿⣿⠿⣿⠹⠀⠀⠀⠀⠃⠀⠐⠀⢸⠇⢾⣿⣴⣶⣿
⣿⣄⣿⣿⣿⣿⣿⣯⣭⣭⣿⢫⣭⣽⣯⡍⣭⣭⣭⡛⣭⢭⣭⣽⣭⢭⡿⣹⣝⢻⣏⣤⣭⡟⣛⣛⡛⢺⣿⣿⣿⡿⠿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣷⠀⠀⢉⣁⣀⣀⣀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀
⣿⠻⣿⣿⠻⠿⢹⣿⣿⣿⣿⣸⣧⣿⣿⡟⣿⣧⣿⢇⣹⣾⣏⣹⣿⣸⣇⢸⣿⣼⡏⣿⣧⡄⠈⣻⣧⡀⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢼⣼⣿⣿⣿⣿⣿⣿⣿⠂⢸⣿⡿⣿⣿⣿⣿⣿⣿⠧⣿⣿⣿⣿
⣿⣷⣬⣿⠆⠀⢸⣿⣀⠘⣿⣿⢷⣿⣿⣺⣿⡇⣿⡷⣿⣿⣾⣿⣿⣸⡏⢿⡏⣿⡧⣿⣇⡀⠈⢻⣿⣷⣾⣼⣿⠏⣁⢀⣂⣵⣾⣿⣿⣿⣿⣿⣿⢀⣼⣿⣶⣶⣶⣶⡶⣤⣿⣄⣸⣯⡧⣬⣭⣭⣤⣤⣄⢠⣧⣀⣀⣀
⠿⠟⠋⠀⢲⣿⣿⣿⣿⣷⣿⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢰⡞⢳⠈⠁⠈⠉⠁⠀⠸⣿⣿⠿⠹⣿⣷⣬⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢉⣹⡏⡛⠇⢛⣈⣿⣿⣿⡁⢸⢹⣿⣿⣿⣿⡆⣸⣿⣿⣿
⠀⢠⣄⢱⣦⣿⣿⣿⢈⣿⣿⣽⣻⣿⢦⡄⣶⢠⣶⢸⣽⣽⣿⣿⣷⣤⣿⠇⠀⣤⣤⠄⣦⡤⣤⢀⣴⢿⡌⠀⢼⡗⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣇⣀⣀⣿⣧⠀⣿⣧⡿⢸⣿⢸⡷⠀⢸⣷⠀⠀⠉⠉⢉⣹⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣾⣯
⠀⢸⣿⣿⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣇⡀⣿⡇⠀⢸⣿⣸⡇⠀⠀⠸⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠋⠙⠓⠠⢄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠿
⡀⠈⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠁⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⣿⣶⣔⣽⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠑⠣⣴⣤⣀⣀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠨
⣿⣾⣿⣿⣿⣿⣿⣥⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠁⠐⠙⢿⣿⣿⡿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⣀⠈⢿⣿⡇⠸⣿⣿⡎⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⣤⠀⢀⣤⣿⣿⣿⣿⣿⠀⠀⠿⠿⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢏⣴⠟⠁⢻⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀
⠋⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⣤⣤⠀⡀⢠⣤⠄⠀⠀⡀⢠⠄⣄⠀⠀⠀⠀⠀⢠⣤⣤⣤⢠⡄⠀⢠⡄⠀⡄⢠⢤⡤⠀⡄⢠⠀⣤⣤⡀⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣀
⣿⠿⣿⣻⡷⣿⣿⣿⣿⡟⡛⣻⣿⣿⣄⠐⣈⢻⣇⣠⢀⣌⡿⠗⡀⡀⠠⠀⠀⠀⢸⣿⣽⣿⣙⡇⠀⢸⠁⢀⣄⣬⣾⣶⡶⣶⣶⣤⣾⣷⡄⣄⠀⡀⡿⠸⠁⠸⠃⠛⠐⠇⠸⠇⠘⠀⠘⠃⠀⠀⡇⢸⣿⠛⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠈⡳⡍⢠⣾⣛⡟⠜⡁⣶⢭⠩⠀⠀⢼⣿⡿⣿⣾⡇⢀⣸⣿⣿⠻⠟⠁⠃⠀⠉⠛⠻⣿⣿⣶⣔⠀⡀⣿⠰⡆⢸⠆⠆⠀⠃⠘⠃⠀⠀⠐⠀⠀⠀⡁⢸⣿⠀⢠⠀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠁⠀⠠⡷⡃⢂⣠⣄⠃⣿⡗⡛⢛⠓⠀⠐⠺⣟⣓⠻⡿⣷⡾⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢾⢿⣵⡄⣇⢐⠀⠐⠀⡀⠀⠀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢰⡿⠀⠈⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣾⣿⣏⣿⣿⣿⣄⣶⡶⢋⡄⠫⢿⠼⠁⣋⣭⣁⣘⣁⡀⠀⠐⠘⠋⠊⠃⡾⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀⢮⠽⣝⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠨⣵⠀⠠⠀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠀⠀⠐⢀⣴⣿⡏⢻⣿⣿⣷⣆⠀⠀⠀⠀⠀⡁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠈⠁⠒⠅⣤⣤⣤⡤⣤⡄⠀⠠⠀⠀⠀⠐⠀⠀⠠⠄⠘⠉⠀⠶⠶⠶⠴
⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠬⣾⣿⣧⣿⣿⣣⡉⠛⠀⠀⠀⢄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⣷⣶⣶⣶⢶⢤⠀⠀⠀⠀⠀⠀⠄⠄⠀⢀⠀⢸⠀⠀⠀
⣸⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⡇⢠⣀⡀⠀⠀⠀⠀⢩⡻⣿⣿⣿⠙⠀⠀⢀⡢⣀⣤⡄⠀⠀⢹⠛⠉⠉⠙⣿⣿⠅⠀⣚⣻⣿⣿⣿⣷⡄⣼⣷⡞⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣷⠀⠀⠀
⡋⠻⣿⣿⣷⣤⣾⣿⣿⣿⡇⢸⣿⣿⣇⣼⣿⣿⡇⠀⣔⠀⢼⡏⢿⣿⣇⡀⢀⣰⣟⠃⣹⣛⡇⠀⡀⢸⣀⣀⣠⣠⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢹⣿⣿⠿⣿⠹⠀⠀⠀⠀⠃⠀⠐⠀⢸⠇⢾⣿⣶⣶⣾
⣿⣄⣿⣿⣿⣿⣿⣯⣭⣭⣿⢫⣭⣭⣯⡍⣭⣭⣭⡋⣭⢭⣭⣽⣭⢭⡿⣽⣝⢻⡏⢼⣯⡏⣛⣛⡛⢺⣿⣿⣿⡿⢿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣷⠀⠀⣉⣁⣀⣀⣀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣀
⣾⠻⣿⣿⠛⠟⢸⣿⣿⣿⣿⣸⡇⣾⣿⡝⣿⣧⣿⠇⣹⣾⣏⣹⣿⢸⡷⢸⣿⣼⡇⣼⣧⡌⢉⣿⣧⡀⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣼⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡷⢼⣿⣿⣿
⣿⣷⣬⣿⠆⠂⢸⣿⣀⠘⣿⣿⢧⣿⣿⣲⣿⡇⣿⡷⣿⣿⣾⣽⣿⣸⡇⢹⡏⣿⡗⢻⣇⡈⣿⣻⣿⣷⣾⣼⣿⢏⣀⣬⣵⣶⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⣦⣶⣶⣶⡶⣤⣿⣠⣸⣧⢥⣬⣭⣭⣥⣤⣤⢰⣴⣄⣀⣀
⠿⠟⠋⠀⢲⣿⣿⣿⣿⣷⣿⣍⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠉⢉⣾⡎⠁⠈⠁⠈⠉⠁⠸⣿⣿⣿⡿⠻⣿⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢉⣹⡇⡛⠧⢛⣈⣿⣿⣿⠀⠏⢹⣿⣿⣿⣿⡆⢘⣿⣿⣿
⠀⢠⣄⢱⣦⣿⣿⣿⢈⣿⣿⣽⢻⣿⢦⡄⣶⢠⣶⢸⣹⣽⣿⡏⢤⣼⣯⠀⠀⣤⣶⠄⣤⡤⣤⢨⣿⢿⡅⠀⠸⡿⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡷⣦⣿⣧⣄⠀⣿⣧⠀⣿⣧⡿⢸⣿⢸⣿⠀⠸⣷⡀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⡟⣿⣿⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣯
⠀⢸⣿⣿⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠀⣿⣇⡀⣿⡇⠀⢸⣿⣸⡏⠀⠀⠘⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠉⠓⠠⢄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠻
⡄⠘⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⣿⣶⣔⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠑⠣⣴⣄⣀⡀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠨
⣿⣾⣿⣿⣿⣿⣿⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠉⠁⠐⠙⢿⣿⣿⡿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠶⢄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⣀⠈⢿⣿⡇⠸⣿⣿⡎⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⣠⠀⢀⣤⣿⣿⣿⣿⣿⠁⠀⠿⠿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⣴⠟⠁⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀
⠋⠖⠲⣶⠏⢶⠜⠱⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⣤⣤⠀⣀⣠⣤⡄⠀⠀⡀⢠⡄⡄⠀⠀⠀⠀⠀⢠⣤⣤⣤⢠⡄⠀⢠⡄⠀⡄⢠⢤⡤⠀⡄⢠⠀⣤⣤⡀⢤⠀⡀⣤⠠⠄⠀⠀⠤⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣀
⣿⢿⣿⣻⡷⣿⣿⣿⣿⡟⡛⣻⣿⣿⣤⠰⢊⢻⣗⣴⢀⣌⡿⠷⡀⡀⠠⠀⠀⠀⢸⣿⡭⣿⣙⡇⠀⢸⡉⢀⣅⣬⣾⣶⡶⣶⣶⣤⣾⣷⡆⢀⠀⡀⣿⠸⠃⠸⠃⠟⠐⠇⠸⠇⠘⠀⠘⠃⠀⠀⡇⢸⣿⠛⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠈⡱⡏⢠⣾⣿⡟⠜⡁⣶⢿⠹⠀⠀⢼⣿⡿⣿⣿⡇⢀⣸⣿⣿⠿⠿⠁⠃⠀⠉⠛⠻⣿⣿⣶⣔⠀⡀⣿⠰⡆⢸⠆⠇⠐⠃⠸⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢠⡄⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠑⠀⠠⣷⡃⢒⣠⣔⠃⣿⣗⡛⢛⠓⠀⠐⠺⣟⣳⣛⣻⣷⡾⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣾⣿⣷⡄⣧⠠⠀⠐⠀⡀⠀⠀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢰⡿⠀⠘⣠⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣿⣿⣯⣿⣿⣿⡆⢾⡶⢋⡄⠫⢿⠻⠁⣋⣭⣄⣛⣑⡀⠀⠐⠛⠋⠘⠫⡾⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣷⣦⡀⠀⢮⢽⣝⡃⠠⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢨⣽⠀⠠⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠀⠀⠰⢂⣤⣿⡏⣻⣿⣿⣿⣇⠀⠀⠀⠀⠀⡃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠈⠑⠒⠅⣤⣤⣤⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠉⠀⠶⠶⠶⠶
⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢸⣾⣿⣧⣿⣿⣣⠉⠻⠀⠀⠀⢄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠀⠀⠄⡅⠀⢀⠀⢸⠀⠀⠀
⣹⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⡇⢠⣄⡀⠀⠀⠀⠀⢩⡻⣿⣿⣿⠙⠃⠀⢀⡦⣠⣤⡅⠀⠀⢹⠟⠋⠉⠹⣿⣿⠆⠀⠒⣻⣿⣿⣿⣷⡄⣼⣿⡎⣿⣿⣿⣿⣿⣾⣾⡆⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣷⠀⠀⠀
⡛⠻⣿⣿⣷⣴⣾⣿⣿⣿⡇⢸⣿⣿⣇⣼⣿⣿⡆⠀⣖⠀⢼⡏⣿⣿⣇⡀⣀⣰⣟⠃⣹⣉⡇⠀⡀⢸⡀⣀⣀⢀⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢹⣿⣿⠿⣿⠹⠄⠀⠀⠀⠃⠀⠐⠀⢸⠇⢾⣿⣶⣶⣾
⣿⣄⣿⣿⣿⣿⣯⣯⣭⣯⣿⢫⣭⣭⣯⡍⣭⣭⣭⡋⣭⢭⣭⣽⣬⣭⡿⣭⣝⢩⡟⣬⣭⡏⣛⣛⡛⢺⣿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⣉⣀⣀⣀⣀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣄
⣾⠻⣿⣟⠻⠿⢸⣿⣿⣿⣿⣸⡇⣿⣿⡟⣿⣧⣿⢧⣹⣾⣏⣹⣿⢸⡏⢹⣿⣼⡇⢸⣧⡌⢉⣿⣧⡀⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣼⡿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠿⣿⣿⣿⣿⣿⣿⡿⢼⣿⣿⣿
⣿⣷⣬⣿⠆⠂⢸⣿⣀⠘⣿⣿⠇⣿⣿⣺⣿⡇⣿⣷⣿⣿⣾⣾⣯⣸⡇⢸⣏⣿⡇⢸⣇⣛⣿⣻⣿⣷⣾⣼⣿⠟⣉⣈⣭⣿⣷⣿⣿⣿⣿⣿⣿⢁⣼⣿⣦⣶⣶⣶⡶⣤⣏⣤⣸⣧⢠⣬⣭⣭⣥⣤⣤⠀⣼⣦⣀⣀
⠿⠟⠋⠀⢶⣿⣿⣿⣿⣷⣿⣍⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢩⣿⠿⠈⠁⠈⠁⠈⠉⠙⣿⣿⣿⣿⣿⠿⣿⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢉⣹⡏⡛⠧⣛⣈⣿⣿⣏⠘⡏⣿⣿⣿⣿⣿⡆⡀⣿⣿⣿
⠀⢠⣄⢱⣦⣿⣿⣿⢨⣿⣿⣿⢻⣿⢦⡄⣶⢠⣶⢸⣹⣽⣷⡀⢤⣤⣤⠀⠀⣶⣶⠀⣤⡤⣬⢿⣿⢿⡇⠀⠘⣟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠠⠀⣿⢹⡿⣷⣿⣧⠀⠀⣿⣧⠀⣿⣧⡿⢸⣿⢸⣿⠃⠀⠿⡄⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣿⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣯
⠀⢸⣿⣿⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠀⠀⣿⣇⡀⣿⡇⠀⢸⣿⣸⡏⠀⠂⠈⣷⣄⡀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠙⠓⠠⢄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠹⠛⠛⠿
⡄⠘⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠀⠉⢀⠀⠀⠈⠉⠀⠀⠀⠀⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠑⠣⣴⣄⣀⡀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠨
⣿⣾⣿⣿⣿⣿⣿⣥⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠁⠐⠈⢿⣿⣿⣿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⢀⠀⢿⣿⡇⠸⣿⣿⡎⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢟⣠⠀⢀⣠⣿⣿⣿⣿⣿⠁⠀⠿⠿⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⢴⠟⠁⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⠀⣀⣠⣤⡄⠀⠀⣀⢠⡄⣄⠀⠀⠀⠀⠀⢠⣤⣤⣤⢠⡄⠀⢠⠄⠀⡄⢠⢤⡤⢀⡀⣠⠀⣤⣤⡀⢤⠀⠀⣄⠠⠄⠠⠀⠤⠀⠄⠀⠀⢀⠀⢤⡄⠀⢀⡤⢤⣤⠀⠀⡄⣤⣠
⣿⢿⣿⣻⡷⣿⣿⣿⣿⡟⡛⣻⣿⣿⣄⠒⣚⢻⣇⣶⢀⣜⡿⠗⠀⡀⠤⠀⠀⠀⢸⣿⣿⣿⣙⡇⠀⢸⠈⢀⣅⣠⣼⣦⣴⣶⣶⣤⣾⣷⡆⣄⠀⡁⡿⠸⠃⠸⠂⠟⠰⠇⠸⠇⠘⠀⠘⠃⠀⠀⡇⢸⣿⢛⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠈⠈⡲⡍⢡⣾⣟⡟⠜⣁⣶⣿⠩⠀⠀⢸⣿⡿⣿⣿⡇⢀⣸⣾⣿⠿⠿⠋⠊⠀⠙⠻⢿⣿⣿⣶⣔⠀⡀⡧⢰⡆⢸⠆⠏⠀⠃⠘⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢠⠀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣇⣿⣿⣿⠁⠀⢤⡷⡃⣂⣠⣔⠃⣿⣗⡛⣛⠓⠀⠐⠺⣟⣛⠛⡟⣷⡾⠛⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣭⣯⣷⣄⡇⢰⠀⠐⠀⡀⠀⡀⠐⠂⠀⠀⢸⠀⠀⠀⠃⢸⡿⠀⠈⣤⣤⣤
⣶⣾⣿⣿⣆⣿⣷⣶⣿⣿⣯⣿⣿⣿⣆⣶⡶⢋⡆⠫⢫⠿⠀⣫⣭⣄⣛⣓⡀⠀⠘⠛⠉⠘⠣⡟⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣷⣶⣤⠀⠀⢩⣝⣛⡃⠠⠀⠀⠀⡄⠀⠀⢀⠀⢠⠀⠈⠀⠀⠀⠀⢸⣵⠀⠠⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠴⢂⣴⣿⡏⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⡃⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠒⠲⠍⢤⣤⣤⣤⣤⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠘⠉⠀⠾⠶⠶⠔
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡰⣾⣿⣧⣿⣿⣧⠘⢻⠀⠀⠀⢄⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠻⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣇⢠⣄⠀⠀⠀⠀⠀⢩⡻⣿⣿⣿⠉⠂⠀⣀⡧⣠⣤⡅⡀⠀⢹⡿⠟⠛⠻⣿⣿⡅⠀⠤⠿⣿⣿⣿⣷⡄⣰⣾⡆⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣷⠀⠀⢀
⡛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡇⢸⣿⣿⣇⣾⣿⣿⡂⠀⣞⠀⢼⡏⣿⣿⣇⡀⣀⣰⣟⠃⣹⣛⡇⠀⡀⢸⡀⠀⠀⠀⣽⣿⣷⣤⣾⣿⣿⣿⣿⣿⣷⣿⣿⡇⠛⢹⣿⣿⠻⣿⠹⠀⠠⠀⠀⠃⠀⠐⠀⢸⠂⢿⣿⣶⣶⣾
⣿⣄⣿⣿⣿⣿⣿⣯⣭⣭⣿⢫⣭⣭⣭⡍⣭⣭⣽⡋⣭⢭⣭⣍⣬⣭⣟⢩⣝⢹⡝⣼⣿⡏⣛⣛⡛⢺⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⣉⣀⣀⣀⡀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣾⠹⣿⣟⠛⠟⢹⣿⣿⣿⣿⣿⡇⣿⣿⡟⣿⣧⣿⢧⣹⣾⡏⢹⡿⢸⡏⢸⣿⣼⡇⣿⣧⡌⢉⣿⣧⡈⢿⣿⣿⣯⣉⣹⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣼⡿⣿⣿⣿⣿⣿⡟⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠧⣿⣿⣿
⣟⣷⣼⣿⠆⠀⢸⣿⣀⠘⣿⣿⡇⣼⣿⣲⣿⡇⣿⡿⡿⣿⠀⢸⣿⣸⡇⢼⡏⣿⡇⣿⣟⣛⣿⣿⣿⣷⣾⣽⣿⡿⠓⠙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣦⣶⣶⣶⡶⣤⢣⣦⣹⡇⣤⣬⣭⣭⣤⣤⣤⡌⢠⣐⣄⣀
⠷⠟⠋⠀⢳⣿⣿⣿⣿⣗⣿⣍⣆⣿⣿⣿⣿⣿⣿⣿⡇⠉⠀⠛⠋⠉⠀⠈⠁⠈⠁⠈⣿⠏⣿⣿⣿⣿⣿⣿⣿⣧⣌⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡏⡛⠯⢛⣈⣿⣿⡀⠺⣹⣿⣿⣿⣿⣿⡗⣀⢹⣿⣿
⠀⢠⣄⣱⣦⣿⣿⣿⢈⣿⣿⣽⢻⣷⢦⡄⣶⢀⣶⠰⣱⣴⣤⣀⢤⣤⣤⡴⠀⣤⣤⠀⣿⡧⣽⢿⣿⢿⣿⠃⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢹⡏⣿⠀⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣷⣿⡇⠀⠀⣿⣧⠀⣿⣧⣿⣸⣿⢸⣿⡖⠀⠐⡆⠀⠀⠉⠈⢉⣿⣿⣿⣿⣿⣿⡟⣿⣿⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣯
⠀⢸⣿⣿⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡇⠀⠀⣿⣇⡀⣿⡇⠙⢻⣿⣼⡿⠁⠀⠀⣷⣔⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⠃⠙⠈⠓⠤⢄⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠿
⡅⠸⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠁⠉⠀⠀⠐⠋⠉⠀⠀⠀⠀⣿⣿⣷⣄⡽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠒⠣⣴⣄⣀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠨
⣿⣾⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋⠉⠐⠈⢻⣿⣿⣿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⡏⠸⣿⣿⡎⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣡⠄⠀⣠⣾⣿⣿⣿⣿⠃⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢴⠿⠋⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠈⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⠀⣀⣠⣤⡄⠀⠀⣀⢠⡄⣄⠀⡀⠀⠀⠀⢠⣤⣤⣤⢤⡄⠀⢠⠄⠀⡄⢠⣤⡤⢀⡀⣠⠀⣤⣤⡀⢤⠀⠀⣤⠠⠄⠠⠀⠤⠀⠄⠀⠀⢀⠀⢤⡄⠀⢀⡤⣤⣤⠀⠀⡄⣤⣠
⣿⢿⣿⣻⡷⣿⣿⣿⣿⡟⡛⣻⣿⣿⣤⡻⣊⢿⣗⣶⢀⣼⡿⠷⠂⡀⠵⠀⠀⠀⢸⣿⣿⣿⢛⡇⠀⢸⡄⠀⣅⣨⣼⣦⣴⣶⣶⣴⣾⣷⡆⣆⠀⡀⡿⠸⠃⠸⠆⠟⠰⠇⠸⠇⠙⠀⠘⠃⠀⠀⡇⢸⣿⢛⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⡳⡏⢡⣾⣿⡟⠜⡁⣶⣿⠹⠀⠠⢼⣿⣿⣿⣾⡇⠀⣸⣾⣿⠿⠿⠋⠈⠀⠛⠻⢿⣿⣿⣶⣶⠀⡀⡿⢰⡆⢸⠆⠏⠐⠃⠘⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢠⠀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣧⣿⣿⣿⠑⣀⢤⣷⡃⣂⣠⣴⠣⣿⣟⡛⣟⡓⠀⠒⠺⣿⣻⣻⣿⣷⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣭⣿⣽⣆⡇⢰⠀⢐⠀⡀⠀⡀⠰⠂⢀⠀⢸⠀⠀⠀⠃⢸⣿⠀⠈⣤⣤⣤
⣶⣾⣿⣿⣇⣿⣷⣶⣿⣿⣯⣿⣿⣿⣦⣾⡾⢋⡆⠫⢿⠿⠀⣫⣭⣅⣛⣃⡀⠀⠘⠛⠟⠛⠃⣾⠁⠀⠀⠀⣀⣤⣶⣾⣿⣿⣷⣶⣤⡀⠀⢩⣝⣛⡃⠠⠀⠀⠀⣄⠀⠀⢀⠀⢠⠀⠈⠀⠀⠀⠀⢸⣷⠀⠠⠀⠐⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⡉⠀⠀⡴⢂⣴⣿⡏⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠐⠢⠍⢠⣤⣤⣤⣤⡄⠀⠠⠀⠀⠀⠐⠀⠀⠠⠄⠘⠉⠀⠾⠶⠶⠴
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣾⣿⣧⣿⣿⣷⡝⢻⡀⠀⠠⣄⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠻⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣽⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⣧⢠⣀⡀⠀⠀⢀⠀⢩⡻⣿⣿⣿⠙⠃⠀⣤⡦⣸⣤⡅⡀⠀⢹⡿⠟⠛⠻⣿⣿⡇⠀⠤⠿⣿⣿⣿⣷⡄⣠⣶⡆⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣷⠀⠀⢀
⡛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡇⢸⣿⣿⣗⣿⣿⣿⡂⠀⣞⠀⣼⡏⣿⣿⣇⡀⣀⣰⣟⠃⣽⣛⡇⠁⡀⢸⡀⠀⠀⠀⣸⣿⣷⣦⣶⣿⣿⣿⣿⣿⣷⣿⣿⡇⠛⢹⣿⣿⠿⣿⠹⠀⠠⠀⠀⠃⠀⠚⠀⢸⠄⢿⣿⣶⣶⣿
⣿⣄⣿⣿⣿⣿⣿⣯⣭⣭⣿⢫⣭⣭⣭⡍⣭⣭⣽⡉⣭⣭⣭⣭⣬⣭⡍⢩⣟⢻⡟⣼⣿⡟⣛⣛⡛⢺⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣉⣀⣀⣀⡀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠹⣿⣟⠻⠿⢹⣿⣿⣿⣿⣿⡇⢿⣿⡟⣿⣧⣿⢧⣹⣾⠇⢸⣿⣸⡇⢸⣿⣼⡇⣿⣧⡌⢉⣿⣧⡀⢿⣿⣿⣿⣉⣹⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣼⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡧⢼⣿⣿
⣿⣷⣼⣿⠆⠀⢸⣿⣀⠘⣿⣿⡇⣼⣿⣺⣿⡇⣿⡷⠋⣿⢠⣸⣿⣸⡏⢸⡏⣿⡿⣿⣟⣻⣿⣿⣿⣷⣾⣿⣿⡿⠛⠛⣛⣻⣿⣽⣿⣿⣿⣿⣿⣇⣼⣿⣦⣶⣶⣶⡶⣤⢣⣦⣿⡇⣶⣭⣭⣭⣤⣤⣤⡼⢰⣔⣤⣀
⠿⠟⠋⠀⢷⣿⣿⣿⣿⣷⣿⣍⣶⣸⣿⣿⣿⣿⣿⣇⠀⠉⠉⠁⠉⠉⠀⠈⠁⠈⠁⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡟⡛⠯⣛⣈⣿⣿⠀⢉⣹⣿⣿⣿⣿⣿⣷⢀⡘⣿⣿
⠀⢠⣆⣱⣦⣿⣿⣿⢨⣿⣿⣽⢻⣷⢦⡄⣶⢀⣶⠠⣵⣴⣤⡀⢤⣤⣶⠄⠀⣤⣴⠍⣿⡧⣽⢿⣿⢿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠠⠀⣿⢹⡿⠂⣿⡇⠀⠀⣿⣧⠀⣿⣧⣿⣼⣿⣾⣿⣷⠂⠀⡎⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣯
⠀⢸⣿⣿⡿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡇⠀⠀⣿⣇⡀⣿⡿⡟⢻⣿⣽⡿⠏⠀⠀⣷⣄⣄⢖⣶⣿⣿⣿⣿⣿⣿⣿⠃⠋⠈⠗⡤⢄⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠿
⡅⠸⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠁⠉⢹⠷⠗⠋⠉⠀⠀⠀⠀⣿⣿⣷⣅⡹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠒⠧⣴⣄⣀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠨
⣿⣾⣿⣿⣿⣿⣿⣦⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋⠉⠑⠙⢻⣿⣿⣿⠁⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⡟⠸⣿⣿⡮⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣡⠄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠿⠿⠇⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢴⡾⠋⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠁⠀⠀⠀⠿⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢤⣤⣤⣤⠀⣀⣠⣤⡄⠀⠀⡀⢠⡄⣤⠀⡀⠄⠀⠀⢠⣤⣤⣤⢠⡄⠀⢠⡄⠀⡄⢠⢤⡤⢀⡄⣠⠀⣤⣤⡀⢤⠀⠄⡤⠠⠄⠀⠀⠤⠀⠄⠀⠀⢀⠀⢤⡄⠀⠀⡤⣤⣤⠀⠀⡄⣤⣠
⣿⢿⣿⣻⠷⣿⣿⣿⣿⡟⡛⣻⣿⣿⣤⡻⣊⢿⣷⣶⢀⣼⡿⠗⡀⡀⠵⠀⠀⠀⢸⣿⣿⣿⢙⡇⠀⢸⠈⢀⣅⣨⣽⣦⣴⣶⣶⣴⣾⣷⡆⣆⠀⡀⡇⠸⠃⠸⠂⠟⠸⠇⠸⠇⠙⠀⠘⠃⠀⠀⡇⢸⣿⢛⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠈⡳⡏⢡⣾⣿⡟⠜⡁⣶⣿⠸⠀⠠⢼⣿⣿⣿⣾⡇⠀⣸⣾⣿⡿⠿⠋⠈⠀⠙⠻⠿⣿⣿⣷⣶⠀⡀⡇⢰⡆⢸⠆⠏⠐⠃⠸⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢰⠀⠀⠀
⠛⠛⣿⣾⡏⣿⡿⠿⢿⣿⣧⣿⣿⣿⠙⢀⢤⣷⡃⣂⣠⣔⠃⣿⣗⡻⣿⠓⠀⠒⠺⣟⣻⣿⣿⣷⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣭⣿⣽⣆⡇⢰⠀⢐⠀⡀⠀⡀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢸⡿⠀⠈⣤⣤⣤
⣶⣾⣿⣿⣄⣿⣷⣶⣿⣿⣯⣿⣿⣿⣦⣿⡾⢋⡆⠫⣿⠿⠀⣫⣥⣅⣛⣐⡀⠀⠘⠛⠙⠛⠣⣾⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣶⣤⡀⠀⢩⣝⣛⡃⠠⠀⠀⠀⡄⠀⠀⢠⠀⢠⠀⠈⠀⠀⠀⠀⢸⣿⠀⠰⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠀⠀⡶⢂⣴⣿⡏⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⠒⠲⠍⢠⣴⣤⣤⣤⡄⠀⠠⠀⠀⠀⠐⠀⠀⠠⠄⠘⠉⠀⠾⠶⠶⠶
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⣼⣾⣿⣧⣿⣿⣧⡝⢻⡀⠀⠠⣤⠄⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠻⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⡇⢸⣿⣿⡇⢠⣀⡀⠀⠀⠀⠀⢩⡿⣿⣿⣿⠙⠃⠀⣠⡦⣸⣤⡅⡀⠀⢹⡿⠟⠛⠻⣿⣿⡇⠀⠤⠿⣿⣿⣿⣷⡄⣠⣶⡆⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⣸⡆⢸⣷⠀⠀⢀
⡛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡇⢸⣿⣿⣇⣿⣿⣿⡀⠀⣞⠀⣼⡟⣿⣿⣇⡀⣀⣰⣿⠃⣽⣛⡇⠁⡀⢸⡀⠀⠀⠀⣸⣿⣷⣦⣶⣿⣿⣿⣿⣿⣷⣿⣿⡇⠛⢹⣿⣿⠿⣿⠹⠠⠠⠀⠀⠃⠀⠚⠀⢺⠄⢿⣿⣶⣶⣿
⣿⣄⣿⣿⣿⣿⣿⣯⣽⣭⣿⢫⣭⣭⣭⡍⣭⣭⣽⡉⣭⢭⣭⢿⣯⣬⡍⢹⣝⢻⡝⣼⣯⡟⣛⣻⡛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣉⣁⣀⣀⡀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣾⡹⣿⣟⠿⠿⢹⣿⣿⣿⣿⣿⡇⢻⣿⡟⣿⣧⣿⠧⢹⣾⠇⢸⣿⢸⡇⢸⣿⣼⡇⣿⣧⡌⢉⣿⣧⡀⢿⣿⣿⣻⣉⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣼⡿⣿⣿⣿⣿⣿⡇⠠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣿⣿
⣟⣷⣼⡿⠆⠀⢸⣿⣀⠘⣿⣿⡇⣼⣿⣺⣿⡇⣿⡇⠀⣿⣾⢸⣿⣸⡇⢸⡏⣿⣿⣿⣿⣻⣿⣿⣿⣷⣾⣽⣿⡿⠛⢛⣻⢿⣻⣭⣿⣿⣿⣿⣿⣇⣼⣿⣦⣶⣶⣶⡶⣤⢡⣦⣿⠗⣦⣭⣭⣭⣥⣤⣤⣿⠁⣔⣢⣀
⠿⠟⠉⠀⢿⣿⣿⣿⣿⣷⣿⣍⣾⣘⣿⣿⣿⣿⣯⣁⠀⠉⠀⠀⠉⠉⠀⠈⠁⠈⣹⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡏⡛⠯⣛⣈⣿⣿⠀⣃⣿⣿⣿⣿⣿⣿⣿⢂⡌⣿⣿
⠀⢠⣄⣱⣦⣿⣿⣿⢨⣿⣿⣽⢻⣷⢦⡄⣶⢠⣶⠠⣵⣴⣤⡀⢤⣶⣦⠀⠀⣤⣿⠟⣿⡧⣽⢿⣿⢿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠈⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡇⠀⣿⡇⠀⠀⣿⣧⠀⣿⣧⣿⣸⣿⢾⣿⣿⡖⠀⡌⠉⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡇⠀⠀⣿⣇⡀⣿⣿⡟⢻⣿⣽⡿⠟⠀⠀⣷⣔⡠⠒⣶⣿⣿⣿⣿⣿⣿⣿⠃⠛⠙⠓⠤⢄⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠿
⡅⢸⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠁⠉⣿⠷⠖⠋⠉⠀⠀⠀⠀⣿⣿⣷⣅⠹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠒⠧⣴⣄⣀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠨
⣿⣾⣿⣿⣿⣿⣿⣦⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠉⠑⠉⢻⣿⣿⣿⠁⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⡟⠸⣿⣿⡮⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣡⡄⠀⣠⣶⣿⣿⣿⣿⠇⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣠⡾⠋⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠻⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⠀⣀⣠⣤⣄⠀⠀⣀⢠⡤⣤⠀⡀⠀⠀⠀⢠⣤⣤⣤⢠⡄⠀⢠⠄⠀⡄⢠⢤⡤⢠⡀⣤⠀⣤⣤⡀⢤⠀⠀⡄⠠⠄⠀⠀⠤⠀⠀⠀⠀⢀⠀⢠⡄⠀⠀⡤⢤⣤⠀⠀⡄⣤⣠
⣿⢿⣿⣻⡷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣦⡿⢊⢿⣗⣶⢀⣼⡿⠷⠀⡀⠵⠀⠀⠀⢸⣿⣿⣿⣛⡇⠀⢸⠈⢀⣅⣨⣿⣦⣴⣶⣶⣤⣾⣷⡆⣆⠀⡀⡇⠸⠃⠺⠂⠟⠸⠇⠸⠇⠙⠀⠘⠃⠀⠀⡇⢸⣿⢛⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠈⠈⡳⡏⢡⣾⣿⡟⠜⡁⣶⣿⠹⠀⠠⢼⣿⣿⣿⣾⡇⠀⣸⣾⣿⡿⠿⠋⠈⠀⠙⠻⠿⣿⣿⣷⣶⠀⡀⡧⢰⡆⢸⠆⠏⠐⠃⠸⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢠⠀⠀⠀
⠛⠛⣿⣾⠏⣿⠿⠿⢿⣿⣇⣿⣿⣿⠑⣀⢤⣷⡇⣂⣠⣔⢣⣿⣗⡛⣻⠓⠂⠒⠺⣿⣻⣿⣿⣷⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣭⣿⣽⣆⡇⢰⠀⢐⠀⡀⠀⡀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢸⣿⠀⠘⣤⣤⣤
⣷⣾⣿⣿⣄⣿⣷⣶⣿⣿⣯⣿⣿⣿⣶⣾⡾⢋⡆⠫⣿⢿⠀⣫⣥⣅⣛⣐⡀⠀⠘⠟⠛⠛⠣⣾⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣶⣤⡀⠀⢨⣽⣛⡃⠠⠀⠐⠀⡄⠀⠀⢀⠀⢠⠀⢈⠀⠀⠀⠀⢸⣿⠀⠰⠀⠀⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⡉⠀⠀⡰⢀⣴⣿⡏⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠓⠲⠍⢠⣴⣤⣤⣤⡤⠀⠠⠀⠀⠀⠐⠀⠀⠠⠄⠘⠉⠀⠾⠶⠶⠖
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣾⣿⣧⣿⣿⣧⠝⢻⡀⠀⠠⣄⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠻⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣯⣿⣿⣿⡟⠛⢻⣿⣿⣿⡄⢸⣿⣿⡇⢠⣠⡀⠀⠀⢀⠀⢩⡻⣿⣿⣿⠛⠃⠠⣀⡧⣰⣤⡅⡀⠀⢹⡿⠛⠛⠻⣿⣿⡇⠀⠰⢿⣿⣿⣿⣷⡄⣠⣷⡆⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⣸⡆⢸⣷⠀⠀⢀
⡛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡇⢸⣿⣿⣇⣿⣿⣿⠃⠀⣞⠀⣸⡟⣿⣿⣇⡀⣀⣰⣿⠃⣽⣋⡇⡃⡀⢸⡅⠀⠀⢀⣸⣿⣷⣦⣾⣿⣿⣿⣿⣿⣷⣿⣿⡇⠛⢹⣿⣿⠿⣿⠹⠁⠠⠀⠀⠃⠀⠒⠀⢻⠆⢿⣿⣶⣶⣿
⣿⣄⣿⣿⣿⣿⣿⣯⣽⣭⣿⢫⣭⣽⣯⡍⣭⣭⣿⡉⣭⢹⣿⣿⣤⢭⡝⢹⣝⢻⡝⣼⣽⡟⣛⣻⡛⢲⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⣉⣀⣀⣀⡀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣾⡹⣿⣟⠻⠟⢹⣿⣿⣿⣿⣿⡏⢻⣿⡟⣿⣧⣿⠃⢹⣾⣧⣼⣿⢸⡇⢸⣿⣼⡇⣿⣧⡌⢉⣿⣇⡀⢿⣿⣿⣻⣉⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣼⡿⣿⣿⣿⣿⣿⡇⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⣿⣿
⡟⣷⣼⣿⠀⠀⢸⣿⣀⠘⣿⣿⡇⢸⣟⣺⣿⡇⣿⡇⠼⣿⠀⢸⣿⣸⡇⢸⡏⣿⣿⣿⣿⣻⣿⣿⣿⣷⣾⣿⣿⡿⠋⣛⡻⠿⣛⣭⣿⣿⣿⣿⣿⣇⣼⣿⣦⣶⣶⣶⡶⣤⢠⣆⣿⠲⣦⣭⣭⣭⣥⣤⣤⣿⡇⢄⣢⣀
⠿⠟⠋⠀⢿⣿⣿⣿⣿⣷⣿⣏⣾⣈⣿⣿⣿⣷⣍⡁⠀⠉⠀⠀⠉⠉⠀⠈⠁⣹⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢉⣹⡏⡛⠏⣛⣈⣿⡇⠀⣉⣿⣿⣿⣿⣿⣿⣿⠇⣀⢻⣿
⠀⢠⣄⣱⣦⣿⣿⣿⢨⣿⣿⣽⢻⣷⢦⡄⣶⢠⣶⠈⡴⣤⣤⡀⢶⣦⣤⠀⠀⣿⣿⠟⣿⡷⣽⢿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣹⠛⠛⠛⠛⡛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠉⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡇⠀⣿⡇⠀⠀⣿⣧⠀⣿⣧⣿⣼⣿⣺⣿⣿⡖⠀⡌⠉⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡇⠀⠀⣿⣇⡀⣿⣿⡟⢻⣿⣽⡿⠟⠁⠀⣷⣄⣆⢶⣶⣿⣿⣿⣿⣿⣿⣿⠃⠏⠙⠳⠤⢄⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⠿
⡅⠸⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠁⢹⣿⠷⠓⠉⠉⠀⠀⠀⠀⣿⣿⣷⣍⠹⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠒⠧⣵⣄⣀⡀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠨
⣿⣾⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠉⠑⠉⢻⣿⣿⣿⠁⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⡟⠸⣿⣿⡬⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⡄⠀⣠⣶⣿⣿⣷⣿⡇⠀⠿⠿⠇⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣠⡾⠋⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠻⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⡤⣤⣤⣤⢀⣀⣠⣤⡄⠀⠀⣀⢠⡀⣄⠀⣀⠄⠀⠀⢠⣤⣤⣤⢠⡄⠀⢠⠀⠀⡄⢠⣤⡤⢠⡀⣤⢀⣤⣤⡀⣤⠀⠄⡄⠠⠄⠀⠀⠤⠀⠄⠀⠀⢀⠀⢤⡄⠀⢀⡤⣤⣤⠀⠀⡄⣤⣠
⣿⢿⣿⣻⠷⣿⣿⣿⣿⡟⡛⣿⣿⣿⣤⣟⣙⢿⣗⣷⢀⣼⡿⠗⡂⡀⠽⠈⠀⠀⢸⣿⣿⣿⣛⡇⠀⢸⠈⢀⣅⣨⣿⣶⣴⣶⣶⣤⣾⣷⡆⣆⠀⡀⡇⠸⠃⠾⠂⠛⠸⠇⠸⠇⠙⠀⠘⠃⠀⠀⡇⢸⣿⢛⠛⠛⠿⢟
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠈⡳⡍⢥⣾⣿⡟⠜⡁⣶⣿⠹⠀⠀⢼⣿⣿⣿⣾⡇⠀⣸⣾⣿⠿⠿⠋⠈⠀⠉⠻⠿⣿⣿⣶⣶⠀⡀⡧⢰⡆⢸⠆⠋⠐⠃⠸⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢰⠀⠀⠀
⠛⠛⣿⣾⠏⣿⡿⠿⢿⣿⣧⣿⣿⣿⠑⣀⢤⣿⡃⣂⣠⣴⢣⣿⣗⡛⣻⠓⠀⠐⠺⣿⣻⣿⡿⣷⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣭⣿⣽⣆⡇⢰⠀⢐⠀⡀⠀⠀⠐⠂⠀⠀⢸⠀⠀⠀⠃⢸⡿⠀⠘⣤⣤⣤
⣶⣾⣿⣿⣄⣿⣷⣶⣿⣿⣯⣿⣿⣿⣤⣾⡾⢋⡆⢫⣿⠿⠀⣫⣥⣅⣛⣐⡀⠀⠐⠝⠛⠛⠃⣾⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣶⣦⡀⠀⢠⣽⣛⡃⠠⠀⠀⠀⡄⠀⠀⢀⠀⢠⠀⢈⠀⠀⠀⠀⢸⣿⠀⠰⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠂⡉⠀⠀⡴⢀⣼⣿⡏⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⡃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠑⠲⠍⢤⣴⣤⣤⣤⡤⠀⠠⠀⠀⠀⠐⠀⠀⠠⠄⠘⠁⠀⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⣾⣾⣿⣧⣿⣿⣧⡝⢻⡀⠀⠠⣄⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠻⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠠⠀⠄⡄⠀⢀⠀⢸⠀⠀⠀
⣽⣿⣿⣿⡟⠛⢻⣿⣿⣿⡄⢸⣿⣿⣇⢠⣤⡀⠀⠀⢀⠀⢩⡻⣿⣿⣿⠙⠃⠠⣠⡦⣰⣤⡅⡀⠀⢹⡿⠛⠛⠻⣿⣿⡇⠀⠰⢿⣿⣿⣿⣷⡄⣠⣿⡆⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⣼⡆⣸⣷⠀⠀⢀
⡛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡇⢸⣿⣿⣇⣿⣿⣿⠁⠀⣞⠀⣸⡟⣿⣿⣇⡀⣀⣰⣿⠃⣿⣛⡇⡃⡀⢸⡅⠀⠀⢀⣼⣿⣷⣦⣾⣿⣿⣿⣿⣿⣷⣿⣿⡇⠛⢹⣿⣿⠿⣿⠹⠡⠠⠀⠀⠃⠀⠒⠀⢻⠀⢿⣿⣶⣶⣿
⣷⣐⣿⣿⣿⣿⣿⣯⣽⣭⣿⢩⣭⣽⣭⡍⣭⣭⣯⡉⣽⢻⣯⢀⣭⣭⡿⣽⣝⢻⡟⣼⣽⡟⣻⣻⡛⢲⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⣉⣀⣀⣀⡀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⢹⣿⣟⠻⠟⢹⣿⣿⣿⣿⣿⡏⢹⣿⡟⣿⣧⣿⠃⣹⣾⣏⢸⣿⢸⡇⢸⣿⣼⡇⣿⣧⡌⢉⣿⣇⡀⣿⣿⣿⣿⣉⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣼⣿⣿⣿⣿⣿⣿⠂⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣾⣿
⡟⣷⣽⡿⠀⠀⢸⣿⣀⠘⣿⣿⢇⢸⣿⣺⣿⡇⣿⡇⠏⣿⠚⢸⣿⣸⡇⢸⣯⣿⣿⣿⣿⣻⣿⣿⣿⣷⣾⣿⣿⡿⠋⣛⠻⠽⣛⣯⣿⣿⣿⣿⣿⣇⣼⣿⣦⣶⣶⣶⡶⣤⢠⣌⡿⢲⣿⣭⣭⣭⣤⣤⣤⣿⡇⢠⣢⣀
⠿⠟⠉⠀⢿⣿⣿⣿⣿⣷⣿⣏⣼⣈⣿⣿⣿⣧⣍⠁⠀⠉⠀⠀⠉⠉⠀⠈⢹⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣹⡏⡛⠏⣛⣘⣿⡇⠀⣈⣿⣿⣿⣿⣿⣿⣿⡷⢈⢹⣿
⠀⢠⣦⣱⣮⣿⣿⣿⢨⣿⣿⣿⢻⣷⢦⡄⣶⢠⣶⠀⡄⣤⣴⡄⢤⣤⣤⠀⠈⣿⣿⡟⣿⡧⣽⢿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠉⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠠⠀⣿⢸⡇⠀⣿⡇⠀⠀⣿⣯⣤⣿⣧⣿⣼⣿⣾⣿⣿⣷⢂⡌⠉⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡇⠀⠀⣿⣇⡿⣿⣿⡟⢻⣿⣽⡿⠟⠃⠈⣷⡄⠴⠶⣶⣿⣿⣿⣿⣿⣿⣿⠃⠏⠉⠗⠤⢄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠛⠛⢿
⡅⠸⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠑⢻⣿⠷⠓⠉⠉⠀⠀⠀⠀⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⣵⣄⣀⡀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠨
⣿⣾⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠉⠑⠉⢻⣿⣿⣿⠁⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⡟⠸⣿⣿⡮⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⡄⠀⣠⣴⣿⣿⣷⣿⡇⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣠⡾⠋⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠾⠖⠻⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠻⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⢀⣀⣠⣤⣄⡀⠀⣀⢠⡤⣄⠀⡀⠄⠀⠀⢠⣤⣤⣤⣠⡄⠀⢠⠀⠀⡄⢠⣤⡤⢠⡀⣤⢠⣤⣤⡀⣤⠀⠀⡄⠠⠄⠠⠀⠤⠀⠄⠀⠀⢀⠀⣤⠄⠀⢀⡤⣤⣤⠀⠀⡄⣤⣠
⣿⢿⣿⣻⠷⣿⣿⣿⣿⣟⡛⣿⣿⣿⣶⣿⣺⣿⣿⣷⢀⣼⡿⢷⡂⡢⠿⠀⠀⠀⢸⣿⣿⣿⣛⡇⠀⢸⠈⢀⣅⣨⣿⣦⣴⣶⣶⣴⣾⣷⡆⣆⠀⣁⡇⠸⠃⠾⠀⠛⠸⠇⠸⠇⠙⠀⠘⠃⠁⠉⡇⢻⣿⢻⠛⠛⠿⢟
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠈⣷⡏⣥⣾⣿⡟⠜⣁⣾⣿⡽⠀⠤⢼⣿⣿⣿⣾⡇⢀⣸⣾⣿⠿⠿⠋⠈⠀⠙⠻⢿⣿⣿⣶⣆⠀⡀⡇⢰⡆⢾⠀⠟⠐⠃⠘⠃⠀⠀⢐⠀⠀⠠⡃⢸⣿⠀⢰⠀⠀⠀
⠛⢛⣿⣾⠏⣿⠿⠿⢿⣿⣷⣿⣿⣿⠙⣔⢦⣿⡇⣒⣤⣼⢡⣿⣟⡻⣿⠓⠐⠒⢺⣿⣻⣟⣿⣷⡾⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣭⣿⣷⣆⡇⢰⠀⢐⠀⡄⠀⡀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢸⡿⠀⠘⣤⣤⣤
⣶⣾⣿⣿⣄⣿⣷⣶⣿⣿⣿⣿⣿⣿⣲⣿⡾⢫⡆⢯⣿⢿⠈⣫⣭⣅⣛⣓⡀⠀⢘⠿⠟⠿⠧⡟⠀⠀⠀⢀⣀⣴⣶⣾⣿⣿⣿⣶⣤⡀⠀⢬⣽⣛⡃⠠⠀⠐⠀⡄⠀⠂⢐⠀⢠⠀⠈⠀⠀⠀⠀⢸⣿⠀⢸⠀⠑⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠊⣉⠀⠐⡶⢀⣼⣿⡏⣿⣿⣿⣿⣧⠀⠀⠈⠄⠀⡁⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠓⠲⢍⣤⣴⣤⣤⣤⡤⠄⠠⠀⠀⠀⠐⠀⠀⠠⠀⠘⠁⠀⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠈⠈⠀⠀⠀⣾⣾⣿⣧⣿⣿⣯⠝⢿⡀⠀⠠⣤⡄⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠠⠀⠄⡄⠀⢄⠀⣼⠀⠀⠈
⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⡀⢸⣿⣿⡧⢠⣠⡀⠀⠀⠀⠀⢩⡻⣿⣿⣿⠛⠃⠠⣶⣧⣠⣤⡅⡀⠀⢹⡿⠟⠛⠻⣿⣿⡇⠀⠴⢿⣿⣿⣿⣷⡄⣸⣿⡎⣿⣿⣿⣿⣿⣾⣾⡆⠀⠀⠀⠁⠀⠀⠀⣾⡆⣸⣷⠀⠀⣠
⡛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡇⢸⣿⣿⣇⣿⣿⣿⠁⠀⣞⢈⣸⡟⣿⣿⣇⡀⣀⣰⣿⠃⣿⣫⡇⣃⡀⢸⡅⠀⠀⢀⣽⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⢹⣿⣿⠿⣿⠹⠠⠠⠀⠀⠃⠀⠒⠀⢿⠀⣿⣿⣷⣶⣿
⣿⣰⣿⣿⣿⣿⣿⣯⣽⣭⣿⢩⣭⣽⣭⡍⣭⣭⣭⣛⣿⢋⣭⢁⣭⣭⣿⣯⣝⢻⡟⣼⣿⡟⣻⣛⡓⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣉⣀⣀⣀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⢻⣿⣟⠿⠟⢹⣿⣿⣿⣿⣿⡇⢻⣿⡟⣿⣧⣿⢿⣻⣾⠇⢸⣿⣸⣇⣸⣿⣼⡇⣿⣧⡌⣉⣿⣇⡈⣿⣿⣿⣿⣍⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣼⣿⣿⣿⣿⣿⣿⠀⣼⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣿
⣿⣷⣽⡿⠀⠀⢸⣿⣀⠘⣿⣿⡇⣸⣏⡀⣿⡇⣿⡏⠟⣿⠀⢸⣿⣸⣿⣿⣯⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⠋⣛⣻⠿⣛⣯⣿⣿⣿⣿⣿⣇⣼⣿⣷⣶⣶⣶⡶⣤⢰⣽⡗⣶⣷⣯⣭⣭⣤⣤⣤⣿⣧⡀⣤⣀
⠿⠟⠋⠀⣿⣿⣿⣿⣿⣷⣿⣏⣼⣍⣿⣧⣌⠁⠉⠁⠀⠉⠀⠀⠉⠉⢹⡞⣻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣿⡟⡛⠯⣛⣘⣿⠀⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⠷⢘⣿
⠀⢰⣮⣱⣮⣿⣿⣿⢨⣿⣿⣿⢻⣷⢦⡆⣶⢠⣦⠀⠀⣴⣤⡀⢴⣶⣾⣦⡉⣿⣿⡟⣿⡷⣽⢿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⣟⢻⡏⣿⠉⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢸⡇⠀⣿⡇⠈⢻⣿⣯⣤⣿⣧⣿⣼⣿⣺⣿⣿⣿⣾⡉⠛⠛⠻⠛⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⡟⢻⣿⣿⡿⠟⠋⠸⣷⡴⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁⠟⠙⠳⠤⢄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⡛⠛⢿
⡅⢸⣿⣿⣷⣿⣿⣿⣧⣭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠑⢿⣿⠷⠒⠉⠉⠀⠀⠀⠀⣿⣿⣷⣝⡻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠁⠀⠁⠀⠀⠉⠛⠧⣷⣄⣀⣀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠛⠉⠑⠉⠻⣿⣿⣿⠁⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⡀⢻⣿⡟⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣡⡄⠀⢠⣼⣿⣿⣿⣿⡇⠀⠿⠿⠇⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣠⡾⠋⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠛⠖⠶⣶⠏⢶⠜⠳⠷⠾⠖⠻⠿⠿⠿⠿⠃⠀⠀⠀⠚⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⢀⣀⣠⣤⣄⠀⠀⣀⣠⣠⣄⠀⡀⡀⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠀⡄⢠⣤⡤⢠⡀⣤⢠⣤⣤⠀⣤⠀⡄⡄⠠⠄⠠⠀⠤⠀⠄⠀⠀⢀⠀⣤⠄⠀⢀⡤⣤⣤⠀⠀⡄⣤⣠
⣿⢿⣿⣻⠶⣿⣿⣿⣿⣟⡛⣿⣿⣿⣶⣟⣏⣿⣟⣷⢐⣼⡿⢗⡀⡤⠽⠈⠀⠀⢸⣿⣿⣿⣟⡇⠀⢸⠈⢀⣅⣼⣿⣦⣴⣶⣶⣴⣾⣷⡄⣆⠀⣈⡇⠸⠃⠾⠀⠛⠸⠇⠸⠅⠙⠀⠘⠁⠅⠁⡇⢿⣿⢛⠛⠛⠿⢟
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠉⣷⡍⢥⣾⣿⡟⠜⣁⣶⣿⠽⠀⠤⢼⣿⣿⣿⣾⡇⢀⣸⣿⣿⠿⠿⠋⠋⠀⠛⠻⢿⣿⣿⣶⣆⠀⡀⡇⢰⡆⢾⠀⠟⠘⠃⠸⠃⠀⠀⢐⠀⠀⠀⡅⢸⣿⠀⢰⠀⠀⠀
⠛⢛⣿⣾⠏⣿⠿⠿⢿⣿⣿⣿⣿⣿⠙⣔⢬⣿⠃⣃⣤⣜⢡⣿⡗⡻⣿⠓⠐⠐⠺⣟⣛⣿⡿⣷⡾⠛⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣭⣯⣷⣄⡇⢰⠀⢖⠀⡀⠀⡀⠐⠂⢀⠀⢸⠀⠀⠀⠃⢸⡿⠀⠘⣤⣤⣤
⣶⣾⣿⣿⣄⣿⣷⣶⣿⣿⣿⣿⣿⣿⣲⣿⠾⢫⡆⢫⣿⢿⠈⣫⣥⣅⣛⣐⡀⠀⠘⠟⣛⠛⠣⡏⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣷⣶⣤⡀⠀⢭⣿⣟⠇⠰⠀⠄⠀⡄⠀⠀⢀⠀⢠⠀⢈⠀⠀⠀⠀⢸⣿⠀⢸⠀⠁⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠊⣉⠀⠀⡶⢀⣼⣿⡏⣿⣿⣿⣿⣧⠀⠀⠀⠄⠈⠁⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠒⠢⠅⣤⣴⣤⣤⣤⡤⠄⠠⠀⠀⠀⠐⠀⠀⠠⠀⠘⠁⠐⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠈⠀⠀⠀⣶⣾⣿⣧⣿⣿⣧⠝⢻⡀⠀⠠⣄⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠀⠀⠄⡄⠀⢀⠀⣸⠀⠀⠈
⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⠀⢸⣿⣿⡇⢠⣠⡀⠀⠀⢀⠀⢩⡻⣿⣿⡿⠙⠃⠨⣴⡧⣰⣤⡅⡀⠀⢻⡿⠟⠛⢻⣿⣿⡇⠀⠤⠿⣿⣿⣿⣷⡄⣸⣶⡞⣿⣿⣿⣿⣿⣾⣾⡆⠀⠀⠀⠀⠀⠀⠀⣾⠆⣸⣷⠀⠀⢀
⡛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡇⢸⣿⣿⣇⣿⣿⣿⡁⠀⣞⠀⢸⡟⣿⣿⣇⡀⣀⣰⣿⠃⣿⣫⡇⣃⠀⢸⡄⠀⠀⠀⣽⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⢹⣿⣿⠿⣿⠹⠠⠤⠀⠀⠃⠀⠒⠀⢿⠀⣿⣿⣶⣶⣿
⣿⣰⣿⣿⣿⣿⣿⣯⣽⣭⣿⢩⣭⣭⣭⡍⣭⣭⣿⡛⣯⢩⣭⢁⣭⣭⡿⣭⣝⢫⡝⣬⣿⡟⣻⣻⡓⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢈⣉⣀⣀⣀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣻⣿⣟⠿⠟⢻⣿⣿⣿⣿⣿⡇⢹⣿⡄⣿⣧⣿⢿⣽⣾⠇⢸⣿⣸⣇⣸⣿⣼⡇⣿⣧⡌⣉⣿⣇⡈⣿⣿⣿⣯⣉⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⣾⣿⣿⣿⣿⣿⡿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣿
⣿⣷⣽⡿⠀⠀⢸⣿⣀⠘⣿⣿⡇⣸⣇⡀⣿⡇⣿⡿⠋⣿⠀⢸⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠟⣛⣻⠿⣟⣯⣿⣿⣿⣿⣿⣃⣼⣿⣷⣶⣶⣶⡶⣤⢠⣽⠷⣦⣷⣿⣯⣭⣤⣤⣤⣿⣧⣄⢤⣀
⠿⠟⠋⠀⣿⣿⣿⣿⣿⣗⣿⣏⣴⣏⣯⣁⠈⠁⠉⠁⠀⠉⠀⠀⠉⢹⣿⡞⣻⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣿⡟⡛⠏⣛⣘⣟⠀⣅⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿
⠀⢰⣎⣰⣾⣿⣿⣿⢨⣿⣿⣽⢻⣷⢦⡆⣶⢀⣤⠀⠀⣤⣴⡄⢴⣾⣿⣦⣉⣿⣿⠟⣿⡧⣽⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣺⠛⠛⠛⠛⡛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠉⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢸⡇⠀⣿⡟⢿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣾⣿⣿⣿⢿⡉⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢰⣿⢾⣷⠀⣿⡇⠈⠉⣿⣿⣿⣿⡿⡟⢻⣿⣽⡿⠟⠋⠸⣷⡦⠦⢴⣶⣿⣿⣿⣿⣿⣿⣿⠁⡿⠙⠳⠠⠄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠟⠛⠛⢿
⡅⢸⣿⣿⣷⣿⣿⣿⣧⣭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠑⢻⣿⠷⠒⠉⠉⠀⠀⠀⠀⣿⣿⣿⣅⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠉⠙⠧⣷⣤⣀⣀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠩
⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣄⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠛⠉⠑⠈⠻⣿⣿⣿⠁⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠻⣿⡟⠸⣿⣿⡮⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣡⡄⠀⣠⣾⣿⣿⣿⣿⡇⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣠⣆⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣠⡾⠋⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠿⠿⠟⠀⠀⠀⠰⠛⠿⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⢀⣀⣠⣤⣄⠀⠀⣀⣠⣤⣄⠀⡀⡀⠀⠀⢠⣤⣤⣤⢤⡄⠀⢠⠀⠀⡄⢠⣤⡤⢠⠀⣤⢠⣤⣤⠀⣤⠀⢀⡄⠠⠄⠠⠀⠤⠀⠀⠀⠀⢀⠀⣤⠄⠀⢀⡤⣤⣤⠀⠀⡄⣤⣠
⣿⢿⣿⣻⠶⣿⣿⣿⣿⣟⡛⣿⣿⣿⣤⡿⣜⣿⣿⣷⢀⣼⡿⢷⡄⡤⢽⠈⠀⠀⢸⣿⣿⣿⣟⡇⠀⢸⠈⢀⣅⣤⣿⣦⣴⣶⣶⣴⣾⣷⡄⣆⠀⡈⡇⠸⠃⠿⠀⠟⠸⠇⠸⠅⠹⠀⠘⠀⠁⠀⡇⢿⣿⢻⠛⠛⠿⢟
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⡷⡍⢥⣿⣿⡟⠜⣡⣾⣿⡭⠀⠤⢼⣿⣿⣿⣾⡇⢀⣸⣿⣿⠿⠿⠋⠋⠀⠛⠿⢿⣿⣿⣶⣆⢀⡀⡇⢸⡆⢾⠀⠋⠘⠃⠸⠃⠀⠀⢐⠀⠀⠠⡅⢸⣿⠀⢰⠀⠀⠀
⠛⢛⣿⣾⠍⣿⠿⠿⢿⣿⣿⣿⣿⣿⠛⣔⢾⣿⠃⣳⣤⣜⢡⣿⡟⡻⣿⠒⠒⠒⢺⣟⣛⣟⣿⣷⡾⠛⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣽⣯⣷⣄⡇⢰⠀⢔⠀⡀⠀⡀⠐⠀⠄⠀⢸⠀⠀⠀⠃⢸⡿⠀⠘⣤⣤⣤
⣷⣿⣿⣿⣄⣿⣷⣶⣿⣿⣿⣿⣿⣿⣰⣿⠞⢫⡆⢫⢿⠿⠘⣫⣭⣅⣟⣃⡀⠀⢐⠝⡙⠏⠣⡏⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣷⣶⣤⠀⠈⣭⣽⣛⠇⠰⠀⠀⠀⡄⠠⠀⢀⠀⢤⠀⢈⠀⠀⠀⠀⢸⣷⠀⠸⠈⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠊⢁⠀⠐⡖⢀⣾⣿⡏⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠉⠒⠢⢅⣤⣴⣤⣤⣤⡤⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠘⠁⠐⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⡶⣾⣿⣧⣿⣿⣧⠙⢻⠀⠀⠠⢤⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⢿⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠀⠀⠄⡄⠀⢄⠀⢼⠀⠀⠈
⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⠀⢸⣿⣿⡧⢠⣠⡀⠀⠀⠀⠀⢩⡻⣿⣿⡿⠙⠃⠠⣰⡧⣠⣤⡅⡀⠀⢻⡿⠟⠛⢿⣿⣿⡇⠀⠤⠿⣿⣿⣿⣷⡀⣸⣾⣾⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠁⠀⠄⠀⣾⠀⣼⣷⠀⠀⣂
⡛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡄⢸⣿⣿⣗⣿⣿⣿⡁⢀⣞⢈⢸⡟⣿⣿⣇⡀⣀⣰⣿⠃⣿⣫⡇⣃⠀⢸⡄⠀⢀⠀⣽⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢹⣿⡿⠿⣿⠹⠠⠠⠀⠀⠃⠀⠓⠀⢿⠀⣿⣿⣶⣶⣿
⣿⣸⣿⣿⣿⣿⣿⣯⣽⣭⣿⢩⣭⣽⣭⡍⣭⣿⣿⡛⣭⢭⣭⢈⣭⣭⡿⣭⣍⢩⡏⣬⣭⡏⣻⣻⡓⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣈⣁⣀⣀⡀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⢻⣿⡟⠿⠿⢹⣿⣿⣿⣿⣿⡇⢹⣧⡄⣿⣯⣿⠇⢹⣾⣏⢸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣇⡈⣿⣿⣿⣯⣙⣹⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⣿⡿⣿⣿⣿⣿⡇⢠⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣾
⣿⣷⣽⡿⠀⠀⢸⣿⣀⠘⣿⣿⡇⢸⣇⣐⣿⡧⣿⡇⠈⣿⠈⢻⣿⣽⣏⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠛⣛⣻⠿⢟⣭⣿⣿⣿⣿⣿⣁⣾⣿⣷⣶⣶⣶⡶⣄⢠⣿⢢⣷⣿⣮⣯⣭⣤⣤⣤⣿⣧⣄⢰⣀
⠿⠟⠋⠀⣿⣿⣿⣿⣿⣷⣿⣿⣠⣌⡉⠁⠉⠁⠉⠁⠀⠉⠀⠐⣿⣿⣿⡞⣻⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣿⡛⡛⢏⣛⣘⡇⠀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣹
⠀⢰⣮⣰⣮⣿⣿⣿⢨⣿⣿⣽⢿⣷⢦⡄⣤⢀⣴⠀⠀⣴⣶⡄⣿⣿⣿⣦⣉⣿⣿⠿⣿⡧⣽⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣻⠛⠛⠛⠛⡛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠉⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢸⡇⠈⣿⣿⣿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣾⣿⣿⣿⢿⡈⠛⠻⠿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢰⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⡟⢻⣿⣽⡿⠟⠋⢸⣿⡴⠤⣤⣴⣿⣿⣿⣿⣿⣿⣿⠉⡿⠛⠳⠠⠄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠟⠛⠛⢿
⡅⢸⣿⣿⣷⣿⣿⣿⣧⡭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠑⢻⡿⠷⠒⠉⠉⠀⠀⠀⠀⣿⣿⣾⣅⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠉⠙⠧⣷⣤⣀⣀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠩
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠑⠈⢻⣿⣿⣿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⡀⢻⣿⡟⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠿⠿⠇⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣠⡾⠋⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠟⠟⠀⠀⠀⠀⠿⠗⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⢀⣀⣠⣤⡄⠀⠀⣀⢠⣤⣄⠀⣀⡄⠀⠀⢠⣤⣤⣤⢤⡄⠀⢠⠀⠀⡄⢠⣤⡤⢠⠀⣤⢠⣤⣤⠀⣤⠀⢀⡄⠠⠄⠠⠀⠤⠀⠄⠀⠀⢀⠀⣤⠄⠀⢀⡤⣤⣤⠀⠀⡄⣤⣠
⣿⢿⣿⣻⠶⣿⣿⣿⣿⣟⠛⣿⣿⣿⣤⣟⣘⣿⣗⣷⢀⣼⡻⢗⡀⡄⠽⠈⠀⠀⢸⣿⣿⣿⣟⡇⠀⢸⠈⢀⣅⣤⣿⣦⣴⣶⣶⣴⣾⣷⡄⣆⠀⣉⡇⠸⠃⠿⠀⠟⠸⠇⠸⠅⠙⠀⠘⠀⠅⠃⡇⢿⣿⢻⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠉⡷⠍⢥⣾⣿⡟⠜⡡⣾⣿⠭⠀⠤⢼⣿⣿⣿⣾⡇⢀⣸⣿⣿⢿⠿⠋⠋⠀⠛⠿⢿⣿⣿⣶⣆⠀⡀⡇⢰⡆⢾⠀⠋⠘⠃⠸⠃⠀⠀⠐⠀⠀⠀⡁⢸⣿⠀⢰⠀⠀⠀
⠛⢛⣿⣾⠍⣿⠿⠿⢿⣿⣿⣿⣿⣿⠛⣔⢼⣷⠃⣢⣤⣜⢡⣿⡗⡿⣻⠓⠐⠒⠺⣟⣛⣛⣿⣷⡾⠛⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣽⣯⣷⣀⡇⢰⠀⢖⠀⡀⠀⠀⠐⠂⠄⠀⢼⠀⠀⠀⠃⢸⡿⠀⠘⣤⣤⣤
⣶⣾⣿⣿⣄⣿⣷⣶⣿⣿⣿⣿⣿⣿⣰⣿⠞⣫⡆⠫⣿⠿⢈⣫⣥⣥⣛⣀⡀⠀⠘⠟⣟⠍⠣⡏⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣷⣦⣄⠀⠈⣭⣿⣛⠇⠰⠀⠀⠀⡄⠀⠀⢀⠀⢤⠀⢈⠀⠀⠀⠀⢸⣗⠀⢸⠈⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠂⠁⠀⠐⡖⢠⣾⣿⡏⣿⣿⣿⣿⣦⠀⠀⠈⠄⠈⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⠉⠒⠦⠅⣤⣴⣤⣤⣤⡄⠄⠠⠀⠀⠀⠀⠀⠀⠠⠀⠘⠁⠐⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⣷⣾⣿⣧⣿⣿⣧⠝⢿⡀⠀⠠⢄⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⢿⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠀⠀⠄⡄⠀⢄⠀⣨⠀⠀⠈
⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⠀⢸⣿⣿⡧⣤⣠⡀⠀⠀⢀⠀⢩⡻⣿⣿⡟⠙⠃⠐⣲⡧⣠⣤⡅⡀⠀⢿⡿⠟⠛⢿⣿⣿⡇⠀⠤⠿⣿⣿⣿⣷⡀⣰⣿⣼⣿⣿⣿⣿⣿⣾⣾⡀⠀⠀⠀⠁⠀⠀⠀⣾⠀⣼⣷⠀⠀⣀
⠛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡄⢸⣿⣿⣇⣿⣿⣿⡁⢀⣞⢈⢸⡟⣿⣿⣇⡀⣀⣰⣿⠃⣿⣫⡇⣃⠀⢸⡀⠀⢀⠀⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹⣿⡿⠿⣿⠹⠠⠤⠀⠀⠃⠀⠓⠀⢿⠀⣿⣿⣶⣶⣿
⣿⣸⣿⣿⣿⣿⣿⣯⣽⣭⣿⢩⣭⢭⣭⡍⣽⣿⣯⡉⣭⢭⣭⢈⣭⣭⡽⣭⣝⢹⡍⣬⣽⡏⣻⣻⣓⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣈⣁⣀⣀⡀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⢿⣿⡟⠻⢿⢹⣿⣿⣿⣿⣿⡇⢸⣧⡜⣿⣧⣿⠃⢹⣾⣏⢸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣇⡈⣿⣿⣿⣯⣙⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇⢾⣾⡿⣿⣿⣿⣿⡇⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢼
⣿⣷⣽⡿⠀⠀⢸⣿⣀⠘⣿⣿⠇⢸⣇⣈⣿⡇⣿⡇⠈⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⠟⣛⣻⠿⢟⣭⣿⣿⣿⣿⣿⣀⣿⣿⣷⣶⣶⣶⡶⣄⢨⡟⣦⣷⣷⣷⣭⣭⣤⣤⣤⣿⣧⣤⠐⣄
⠿⠟⠉⠀⣿⣿⣿⣿⣿⣷⣿⣯⡀⠈⠉⠁⠉⠁⠉⠁⠀⠉⢻⣿⣿⣿⣿⡞⣻⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣿⣛⡛⠏⣛⣘⡅⠪⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢉
⠀⢰⣮⣰⣮⣿⣿⣿⢈⣿⣿⣽⢿⣷⢦⡄⣤⢀⣦⠀⠀⣴⣾⣿⣿⣿⣿⣦⣉⣿⣿⠟⣿⡧⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣺⠛⠛⠛⠛⡛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢹⡏⣿⠉⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢸⡟⢿⣿⣿⣿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣺⣿⣿⣿⢿⡈⠛⠻⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣶⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢰⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⡟⢻⣿⣾⡿⠟⠋⢸⣧⡰⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⠈⡟⠛⠷⠠⢄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠟⠛⠛⢿
⡅⢸⣿⣿⣷⣿⣿⣿⣧⢭⣀⡀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠑⢻⡿⠷⠒⠉⠉⠀⠀⠀⠈⣿⣿⣶⣅⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠉⠛⠧⣷⣤⣀⣀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠩
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣇⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠑⠉⢻⣿⣿⣿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢶⢄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⡏⠸⣿⣿⡯⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠿⠿⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣠⡾⠋⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠛⠖⠶⣶⠏⢶⠜⠳⠷⠾⠖⠻⠿⠛⠀⠀⠀⠰⠿⠂⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠻⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⢀⣀⣠⣤⣄⠀⠀⣀⣠⣠⣄⠀⡀⡀⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠀⡄⢠⣤⡄⢠⠀⣤⢠⣤⣤⠀⣤⠀⢤⡄⠠⠄⠤⠀⠄⠀⠄⠀⠀⢀⠀⣤⠄⠀⣀⡤⣤⣤⠀⢀⡄⣤⣠
⣿⢿⣿⣻⠶⣿⣿⣿⣿⣟⠛⣿⣿⣿⣶⣗⣝⣿⣿⣷⢐⣼⡿⢟⡄⡄⢽⠈⠀⠀⢸⣿⣿⣿⣛⡇⠀⢸⠈⢀⣅⣬⣿⣦⣴⣦⣶⣴⣾⣷⠄⣆⠀⣘⡇⠘⠃⠿⠀⠛⠸⠇⠸⠁⠙⠀⠘⠀⠃⠁⡇⢿⣿⢻⠛⠛⠿⢟
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠉⡷⠍⢥⣿⣿⡟⠜⡡⣾⣿⡽⠀⠤⢼⣿⣿⣿⣾⡇⢀⣼⣾⣿⠿⠿⠉⠋⠀⠛⠿⢿⣿⣿⣦⣆⠀⡰⡇⢰⡆⢾⠀⠃⠘⠃⠸⠃⠀⠀⢐⠀⠀⠀⡁⢸⣿⠀⢰⠀⠀⠀
⠛⢛⣿⣾⠍⣿⠿⠿⢿⣿⣿⣿⣿⣿⠙⣔⢮⣿⠃⣣⣤⣜⢡⣿⡿⡿⣿⠒⠐⠒⢺⣟⣛⣟⣿⣷⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣽⣯⣷⣀⡇⢰⠀⢖⠀⡀⠀⠀⠐⠀⠄⠀⢼⠀⠀⠀⠃⢸⡿⠀⠈⣤⣤⣤
⣶⣾⣿⣿⣄⣿⣿⣶⣿⣿⣿⣿⣿⣿⣰⣿⠞⣫⡆⠫⣿⠿⠈⣯⣵⣅⣛⣁⡀⠀⢘⠟⡟⠛⢳⡏⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣷⣦⣄⠀⠈⣭⣿⣛⠇⠰⠀⠄⠀⡄⠠⠀⢀⠀⢤⠀⠨⠀⠀⠀⠀⢸⡗⠀⢸⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠂⣁⠀⠀⡖⢀⣾⣿⡏⣿⣿⣿⣿⣇⠀⠀⠈⠄⠈⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠒⠦⠁⣤⣶⣤⣤⣤⡤⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠙⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠈⠀⠄⠀⠀⣷⣾⣿⣧⣿⣿⣧⠙⢿⠀⠀⠠⢄⠌⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⢿⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠄⠀⠄⡄⠀⢄⠀⣼⠀⠀⠈
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⢸⣿⣿⡇⣤⣠⡀⠀⠀⢀⠀⢩⣻⣿⣿⡟⠙⠃⠀⣰⡧⣠⣤⡅⠀⠀⣿⡿⠟⠛⢿⣿⣿⡅⠀⠴⠿⣿⣿⣿⣶⢀⣼⣶⣼⣿⣿⣿⣿⣿⣾⣾⡄⠀⠀⠀⠁⠀⠀⠀⣾⠀⣼⣷⠀⠀⣤
⠛⢻⣿⣿⣷⣶⣾⣿⣿⣿⡀⢸⣿⣿⣇⣿⣿⣿⡁⢀⣞⢈⢸⡟⣿⣿⣇⡀⣀⣰⣿⠁⣿⣫⡇⣃⠀⢸⡀⠀⢀⠀⣿⣿⣷⣔⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⣿⡿⠿⣿⠹⠀⠤⠀⠀⠃⠀⠓⠀⢿⠀⣿⣿⣶⣶⣿
⣷⣸⣿⣿⣿⣿⣿⣯⣽⣭⣿⢩⣭⢭⣭⡝⣿⣯⣭⡋⣭⢭⣭⢈⣭⣭⡿⣭⣝⢽⡍⣭⣭⡏⣻⣻⣓⢸⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣈⣁⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⢿⣿⡟⠻⠟⢹⣿⣿⣿⣿⣿⡇⢸⣿⡟⣿⣧⣿⢧⣹⣾⣏⣸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣇⡘⣿⣿⡿⣯⣙⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⢿⣾⡿⣿⣿⣿⣿⡇⢰⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢴
⣿⣷⣽⡿⠀⠀⢸⣿⣀⠘⣿⣿⠇⣸⣟⣿⣿⡇⣿⡇⢿⣿⣾⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠛⣛⣻⠿⢟⣭⣿⣿⣿⣿⣿⣀⣿⣿⣷⣶⣶⣶⡶⣄⢸⡗⣾⣷⣷⣷⣯⣭⣤⣤⣤⣿⣧⣤⡀⣆
⠿⠟⠉⠀⣿⣿⣿⣿⣿⣷⣯⡉⠀⠈⠉⠁⠉⠁⠉⠁⠨⣿⣿⣿⣿⣿⣿⡞⣻⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣿⣛⡛⠏⣛⣘⠀⢋⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢠⣮⣰⣮⣿⣿⣿⢨⣿⣿⣽⢴⣤⢤⡄⣶⢀⣴⠀⠀⣼⣿⣿⣿⣿⣿⣦⣉⣿⣿⡿⣿⡧⣽⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣺⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢹⡏⣿⠉⣿⣯⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣺⣿⣿⣿⢿⠈⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢰⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⡟⢻⣿⣾⡿⠟⠋⢸⣧⡠⣆⣤⣴⣿⣿⣿⣿⣿⣿⣿⠈⡿⠛⠳⠠⢄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠝⠛⠛⠿
⡅⢸⣿⣿⣷⣿⣿⣿⣧⣭⡀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠑⢻⡿⠷⠒⠉⠉⠀⠀⠀⠘⣿⣿⣮⣄⡹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠉⠛⠧⣷⣤⣀⣀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠩
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠉⠑⠉⢻⣿⣿⣿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢶⢄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⡏⠸⣿⣿⡮⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠿⠿⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣠⡾⠋⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠛⠖⠶⣶⠏⢶⠜⠳⠷⠶⠖⠻⠃⠀⠀⠀⠸⠇⠀⠀⠀⠘⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠁⠀⠀⠀⠻⠟⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢀⣀⣠⣤⣄⠀⢀⡀⣠⣤⣄⠀⣀⡄⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠀⠄⢠⣤⡄⢠⡀⣄⢠⣤⣤⠀⣤⠀⢤⡄⠠⠄⠤⠀⠄⠀⠀⢀⠀⣀⠀⣤⠀⠄⣠⡤⣤⣤⠀⢠⡄⣤⣠
⣿⢿⣿⣻⠾⣿⣿⣿⣿⣟⠛⣿⣿⣿⣶⣗⣝⣿⣿⣷⢰⣼⡿⢟⡄⡄⢽⠀⠀⠀⢸⣿⣿⣿⣟⡇⠀⢸⠈⢀⣅⣴⣿⣦⣴⣦⣶⣴⣾⣷⠄⣆⠀⣹⡇⠘⠃⠿⠀⠛⠸⠇⠸⠁⠩⠀⠸⠀⠇⠉⠃⣿⣿⢻⠛⠛⠿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⣷⠍⢥⣿⣿⡏⠞⡡⣿⣿⡭⠀⠤⢼⣿⢿⣿⣾⡇⢀⣼⣿⣿⠿⠿⠁⠁⠈⠛⠿⢿⣿⣷⣦⡆⢀⣸⡇⢸⠆⠿⠀⠋⠘⠃⠘⠃⠀⠀⡐⠀⠀⠈⠅⢽⣿⠀⢰⠀⠀⠠
⠛⢛⣿⣿⠭⣿⠿⠿⣿⣿⣿⣿⣿⣿⠙⣔⣾⣿⠃⣳⣤⣾⢰⣿⡿⡿⣻⠒⠒⠒⢺⣟⣾⣻⣿⣷⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⢭⣽⣿⣷⣸⡇⢰⠀⢖⠀⡀⠀⠀⠘⠀⠄⠀⣽⠀⠀⠐⠁⢸⡟⠀⢘⣤⣤⣤
⣶⣿⣿⣿⣀⣿⣿⣶⣿⣿⣿⣿⣿⣿⢰⣿⠞⣫⡆⠻⣿⠿⢘⣭⣵⣅⣛⣑⡀⠀⢘⠿⡛⠛⢳⡏⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣶⣄⠀⠀⣭⣟⣛⡇⠰⠀⡆⠀⡀⠐⠀⢀⠀⣤⠀⠨⠀⠀⠀⠀⢸⡗⠀⢸⠈⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠊⢁⠀⠰⡞⢠⣾⣿⡏⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⠒⠮⠁⣤⣶⣤⣤⣤⡤⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠙⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⢷⣾⣿⣧⣿⣿⣯⠙⢿⠄⠀⠠⣄⠌⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠄⠀⠄⡀⡀⢄⠀⡼⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⢸⣿⣿⡧⣤⣠⡀⠀⠀⢀⢀⢩⡻⣿⣿⡟⠙⠃⠰⣴⣧⣤⣤⡅⠀⠀⣿⠿⠛⠛⢻⣿⣿⡂⠀⠶⣿⣿⣿⣿⣷⢀⣼⣷⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢁⠀⠅⠀⣿⠀⣾⣷⠀⠀⣟
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢸⣿⣿⣇⣿⣿⣿⡁⢀⣎⢘⢸⡟⣿⣿⣇⡀⣀⣵⡹⠁⣿⣻⡇⣃⠀⢹⠀⠀⢀⢀⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⠘⠋⢻⣿⡿⠿⡿⠹⠀⠠⠀⠀⠃⠀⠓⠀⢿⠀⣿⣿⣶⣶⣿
⣷⣘⣿⣿⣿⣿⣿⣯⣽⣭⡿⢩⣭⣽⣯⡍⣽⣯⣭⡋⣭⣭⣭⢙⣭⣭⣿⣭⣝⢭⡍⣭⣭⡍⣻⣻⡓⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣈⣁⣀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣟⢿⣿⡟⠻⠿⢹⣿⣿⢹⣿⣾⣯⣿⣧⡄⣿⣧⣿⢧⢹⣾⡏⣸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣇⡘⣿⣿⣿⣯⣉⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⣿⣿⣿⣿⠂⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧
⣿⣷⣽⡿⠀⠀⢸⣿⣀⠘⣿⣿⡿⣿⣇⡀⣿⡇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠛⣛⠻⢟⣻⣽⣿⣿⣿⣿⣿⣠⣿⣿⣷⣶⣶⣶⡶⣄⣿⢳⣿⣷⣷⣿⣿⣭⣤⣤⣼⣿⣧⣤⣀⢰
⠿⠋⠁⠀⣿⣿⣿⣭⠉⠀⠉⠉⠀⠈⠉⠁⠉⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣷⣖⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣿⣛⡛⢏⣋⡀⠘⢁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⢠⣮⣰⣾⣿⣿⣿⣽⣶⡤⣤⢠⣶⢦⡄⣶⢀⣶⠄⡿⣿⣿⣿⣿⣿⣿⣦⣉⣿⣿⡟⣿⡷⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣺⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢹⡏⣿⠉⣿⣧⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣺⣿⣿⣿⢻⠈⠉⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⡟⣻⣿⣿⡿⠟⠁⢸⣯⡢⣤⠦⣾⣿⣿⣿⣿⣿⣿⡿⠸⡿⠛⡷⠠⢄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠛⠛⠛⢿
⡄⢸⣿⣿⣷⣿⣿⣿⣧⠭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠈⠉⠀⠉⠁⠀⠀⠉⠉⠑⢻⡿⠿⠒⠉⠉⠀⠀⠀⠸⣿⣿⣮⣏⣻⣿⣿⣿⣿⣿⣿⠇⠀⠁⠁⠀⠀⠀⠈⠉⠛⠧⣷⣤⣀⣀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠉
⣿⣿⣿⣿⣿⣿⣿⣧⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠐⠙⢿⣿⣿⣿⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢶⣤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⣀⠀⢿⣿⡇⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣤⠄⠀⣠⣾⣿⣿⣿⣿⠃⠀⠿⠿⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⣴⠿⠋⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠟⠖⠶⣶⠏⢶⠜⠳⠷⠶⠖⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠿⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⡤⣤⣤⢀⣀⣠⣤⣄⠀⠀⣀⣠⡤⣄⠀⣀⡄⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠀⠄⢠⣤⡄⢠⡀⣄⢠⣠⣤⠀⡤⠠⢤⡄⠠⠄⠤⠀⠄⠀⠀⢀⠀⣀⠀⣤⠀⠀⣠⡤⣤⣤⠀⢠⡄⣤⣠
⣿⢿⣿⣻⠶⣿⣿⣿⣿⣟⠛⣿⣿⣿⣶⣷⣝⣿⣷⣷⢰⣼⡿⢟⡄⡴⢽⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢸⠈⣀⣄⣴⣿⣶⡶⣶⣶⣴⣾⣷⠄⣆⠀⣸⡇⠘⠃⠿⠀⠋⠸⠇⠸⠁⠩⠀⠘⠀⠃⠉⠃⣿⣿⢛⠛⠛⠟⢟
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⣷⠍⢤⣿⣿⡏⠞⣡⣿⣯⡭⠀⠤⢼⣿⢿⣿⣾⡇⢀⣼⣿⡿⠻⠟⠁⠁⠈⠙⠛⢿⣿⣷⣦⣆⢀⣸⡇⢸⠆⠿⠀⠋⠘⠃⠘⠂⠀⠀⡐⠀⠀⠈⠁⢽⣿⠀⢰⠀⠀⠠
⠛⢛⣿⣾⠭⣿⠿⠿⣿⣿⣿⣿⣿⣿⠛⣔⢾⣷⠃⣣⣴⣾⢠⣿⡟⡿⣿⠒⠐⠒⢺⣟⣺⣻⣿⣷⡿⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣯⣶⣸⡇⢰⠀⣒⠀⡀⠀⠀⠘⠀⠀⠀⣿⠀⠀⠀⠀⣸⡟⠀⠘⣤⣤⣤
⣶⣿⣿⣿⣀⣿⣷⣶⣿⣿⣿⣿⣿⣿⢰⣿⠟⣣⡆⢯⣿⠿⢘⣭⣵⣥⣟⣂⡀⠀⢘⢿⡛⠛⢳⠏⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣦⡀⠀⢮⣽⣟⡇⠰⠀⡆⠀⡄⠀⠀⢀⠀⣤⠀⠨⠀⠀⠀⠀⢸⡗⠀⢸⠈⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⡁⠀⠠⡞⢠⣾⣿⡏⣿⣿⣿⣿⣧⠀⠀⠀⠀⢈⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠒⠢⠡⣦⣶⣤⣤⣤⡤⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠙⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢷⣾⣿⣧⣿⣿⣥⠙⢿⠄⠀⠠⢄⠌⠀⠰⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣆⠀⠀⠀⠘⣿⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠄⠀⠄⡀⡀⢄⠀⢼⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⢸⣿⣿⡇⣤⣠⡀⠀⠀⢀⠀⢩⡻⣿⣿⡟⠙⠃⠠⣴⡧⣤⣤⡅⠀⠀⣿⠟⠋⠉⠻⣿⣿⠆⠀⠚⣻⣿⣿⣿⣷⢀⣼⣷⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢁⠀⠄⠀⣿⠀⣼⣷⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢸⣿⣿⣇⣿⣿⣿⡀⢀⣏⢈⢸⡟⣿⣿⣇⡀⣀⣶⡹⠁⣿⣫⡇⣁⠀⢸⡀⠀⣀⣠⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣾⣿⣿⠘⠋⢹⣿⡿⠿⡿⠹⠠⠠⠀⠀⠊⠀⠓⠀⢿⠀⣿⣿⣶⣶⡿
⣿⣸⣿⣿⣿⣿⣿⣯⣽⣭⣿⣭⣭⣭⣭⡍⣽⣭⣭⡋⣭⣭⣭⢙⣭⣭⡿⣭⣝⢭⡍⣭⣭⡍⣻⣻⠳⣸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣁⣀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣟⢿⣿⡟⠻⠿⢹⣿⣥⢸⣿⣿⣇⣼⣧⡝⣿⣧⣿⢧⢹⣾⡇⣸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣇⡘⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⢿⣿⣿⣿⠀⣼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⣿⣷⣽⡿⠀⠀⢸⣿⣀⠘⣿⣿⡏⢹⣇⡐⣿⡇⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣷⣶⣶⣶⡶⣄⡿⢶⣿⣷⣷⣿⣯⣭⣤⣤⣼⣿⣧⣤⣄⠰
⠿⠋⠁⠀⣿⣷⣌⠉⠉⠀⠉⠉⠀⠈⠉⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣻⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣿⣛⡛⢏⣋⡀⠈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠
⠀⢠⣮⣰⣾⣿⣿⣷⣀⣤⡤⣤⢰⣤⢤⡄⣶⢀⣶⠄⡿⣿⣿⣿⣿⣿⣿⣦⣉⣿⣿⡟⣿⡷⣽⢿⣿⣿⣿⣿⣿⣯⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠉⣿⣧⡿⢸⣿⣼⡇⢹⣿⠇⠀⠄⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣸⣿⣿⣿⢿⡀⠀⠂⠉⢉⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣮
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⠟⣻⣿⣾⡿⠟⠁⢸⣧⡂⣼⣷⣿⣿⣿⣿⣿⣿⣿⡿⠸⣟⠛⣷⠠⢄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠛⠛⠛⢿
⡄⢸⣿⣿⣷⣿⣿⣿⣧⠭⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠙⢻⡿⠾⠒⠉⠉⠀⠀⠀⠸⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠁⠀⠀⠀⠈⠉⠛⠧⣷⣤⣀⣀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠉
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋⠉⠐⠈⢿⣿⣿⡿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢶⢤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⣀⠀⢿⣿⡇⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣤⠄⠀⣠⣿⣿⣿⣿⣿⠃⠀⠿⠿⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣴⠿⠃⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠖⠀⠀⠀⠀⠀⠸⠿⠿⠿⠛⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠿⠟⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⢀⣀⣠⣤⣄⠀⢀⣀⢠⡤⣄⠀⡀⠄⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠀⠄⠠⣤⡄⢠⡀⣄⢠⣠⣤⠀⡤⠀⢤⡄⠠⠄⠤⠀⠄⠀⠀⢀⠀⣀⠀⣤⠀⠀⣠⡤⣤⣤⠀⢠⡄⣤⣠
⣿⢿⣿⣻⠺⣿⣿⣿⣿⣟⠛⣿⣿⣿⣦⠗⢝⣿⣗⣧⢰⣽⡿⢗⡀⡠⢽⠀⠀⠀⢸⣿⣿⣿⣛⡇⠀⢸⠈⣀⣄⣴⣿⣶⢶⣶⣶⣴⣾⣷⠄⡆⠀⣸⡇⠘⠃⠿⠀⠋⠸⠇⠸⠁⠉⠀⠘⠀⠃⢉⠃⣿⣿⢛⠛⠛⠿⢛
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠉⣷⠍⢤⣿⣿⡏⠞⡡⣿⣿⠍⠀⠤⢸⣿⢿⣿⣾⡇⢀⣼⣿⣿⠻⠛⠁⠁⠀⠉⠛⠻⣿⣷⣦⡆⢀⣸⡇⢸⠆⠿⠀⠃⠘⠃⠸⠃⠀⠀⡐⠀⠀⠈⠀⢿⣿⠀⢰⠀⠀⠠
⠛⢛⣿⣾⠭⣿⠿⠿⣿⣿⣽⣿⣿⣿⠉⣔⢾⣿⠂⣣⣤⣼⢠⣿⡟⡛⣻⠒⠀⠐⢺⣟⣛⣻⡿⣷⠟⠋⠁⠈⠀⠀⠀⣀⣀⣀⡀⠀⠐⠶⢾⣯⣦⣰⡇⢰⠀⢖⠀⡀⠀⠀⠘⠀⠄⠀⣽⠀⠀⠀⠀⢸⡏⠀⠈⣤⣤⣤
⣶⣿⣿⣿⣄⣿⣷⣾⣿⣿⣿⣿⣿⣿⢰⣿⠞⣣⡆⠻⣿⠿⢘⣭⣵⣥⣛⣁⡀⠀⢘⠟⡛⠙⢳⠇⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣦⡀⢀⣮⢯⣿⡇⠐⠀⠆⠀⡀⠀⠀⢀⠀⣤⠀⠉⠀⠀⠀⠀⢸⡗⠀⢸⠀⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠁⠀⠠⡞⢠⣾⣿⡏⣿⣿⢿⣿⣆⠀⠀⠀⠀⠈⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⠈⠙⠒⢡⣦⣶⣤⣤⣤⡄⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠙⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡷⣿⣿⣧⣿⣿⣧⠝⢿⡄⠀⠠⣄⠄⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣇⠀⠀⠀⠘⣿⣿⣿⣶⣶⣶⣶⢦⠀⠀⠀⠀⠄⠀⠄⡀⠀⢀⠀⡬⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⢸⣿⣿⡇⣤⣠⡀⠀⠀⢀⠀⢩⡻⣿⣿⡏⠙⠁⠐⣴⡧⣴⣤⡅⠀⠀⣿⠛⠉⠉⠙⣿⣿⡇⢀⣉⣿⣿⣿⣿⣷⢠⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢁⠀⠄⠀⣿⠀⣾⣷⠀⠀⣆
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢸⣿⣿⣇⣿⣿⣿⡀⢀⣎⢈⢸⡟⣿⣿⣇⡀⣀⣵⡹⠁⣿⣫⡇⣁⠀⢸⣀⣀⣠⣤⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⠘⠋⢻⣿⡿⠿⡿⠹⠀⠤⠀⠀⠋⠐⠓⠀⢿⠀⢿⣿⣶⣶⡿
⣿⣘⣿⣿⣿⣿⣿⣯⣽⣽⣏⢩⣭⣭⣭⡍⣽⣭⣭⡋⣭⣭⣥⢙⣭⣭⡽⣭⣍⢭⡍⣭⣭⡍⣻⣻⠳⣸⣿⣿⣿⡿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⣀⣁⣀⣀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣟⢿⣿⡟⠛⠟⢹⣿⣤⢿⣿⣿⡇⢸⣧⡟⣿⣧⣿⣧⢹⣾⡇⢸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣇⡸⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠿⢿⣿⣿⣿⠀⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣷⣽⡿⠀⠀⢸⣿⣀⠘⣿⣿⠇⢸⣇⣰⣿⡇⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣯⣿⣿⣿⣟⣻⣿⣿⣿⣷⣿⣿⣿⣏⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣷⣶⣶⣶⡖⣄⠟⣶⣿⣷⣷⣶⣧⣭⣤⣤⣼⣿⣧⣤⣠⡀
⠿⠋⠁⠀⣄⡀⠈⠉⠉⠀⠉⠉⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣻⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣿⣛⡛⢋⣋⡀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃
⠀⢠⣮⣰⣮⣿⣶⣦⠀⣤⡶⣤⢠⣤⢤⡄⣶⢀⣶⠄⡿⣿⣿⣿⣿⣿⣿⣦⡉⣿⣿⡿⣿⡷⣽⢿⣿⢿⣿⣿⣿⡟⠛⠛⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⣟⢹⡏⣿⠀⣿⣧⡿⢸⣿⣼⡇⢹⣿⠇⠀⠀⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣿⣿⣿⣿⢻⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣮
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⠟⢻⣿⣾⡿⠟⠁⢸⣧⡸⡽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⣟⠙⠗⠠⢄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠛⠛⠛⢿
⡄⢸⣿⣿⣷⣿⣿⣿⡧⠉⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠙⢻⡿⠟⠂⠉⠉⠀⠀⠀⢸⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠁⠀⠀⠀⠀⠉⠙⠧⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠉
⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠉⠁⠐⠈⢿⣿⣿⡿⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠶⢤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⣀⡀⢿⣿⡇⠸⣿⣿⡮⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣤⠀⢀⣤⣿⣿⣿⣿⣿⠁⠀⠿⠿⠇⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⣴⠟⠁⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠟⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠀⠀⠀⠐⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⢀⣀⣠⣤⣄⠀⠀⣀⢠⣄⣄⠀⡠⠄⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠀⠄⠠⣤⡄⢠⠀⣄⢠⣠⣤⠀⠤⠀⢠⡄⠠⠄⠤⠀⠄⠀⠀⠀⠀⣀⠀⣤⠀⠀⣠⡤⣤⣤⠀⢠⡄⣤⣠
⣿⢿⣿⣻⠺⣿⣿⣿⣿⣟⠛⣿⣿⣿⣔⠗⣝⣿⣗⡧⢠⣼⡿⢗⡄⡴⢽⠀⠀⠀⢸⣿⣿⣿⣻⡇⠀⢸⠀⣀⣄⣴⣿⣶⢶⣶⣶⣴⣾⣷⠄⣇⠀⣸⡇⠘⠃⠿⠐⠏⠸⠇⠸⠁⠉⠀⠘⠀⠃⠉⠃⣿⣿⢛⠛⠛⠿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⡷⠍⢤⣿⣿⡏⠞⣡⣿⣿⠍⠀⠤⢸⣿⢿⣿⣾⡇⢠⣼⣿⣿⠻⠛⠁⠃⠀⠈⠙⠻⢿⣷⣦⡆⢀⣸⡇⢰⠆⠿⠀⠃⠘⠃⠘⠂⠀⠀⡐⠀⠀⠀⠀⢿⣿⠀⢰⠀⠀⠨
⠛⢛⣿⣿⠭⣿⠿⠿⣿⣿⣼⣿⣿⣿⠁⡔⢾⣿⠂⣃⣤⣼⢰⣿⡟⡿⣻⠓⠀⠒⠺⣟⣾⣛⡟⣷⠟⠋⠁⠈⠀⠀⢀⣀⣀⣀⣀⠀⠘⠳⠾⣿⣦⢸⡇⢰⠀⣒⠀⡀⠠⠀⠘⠀⠄⠀⣽⠀⠀⠀⠀⢸⡟⠀⢈⣤⣤⣤
⣶⣿⣿⣿⣀⣿⣷⣶⣿⣿⣿⣿⣿⣿⢰⣿⠞⣣⠆⠡⣿⠿⢘⣭⣵⣤⣛⣁⡀⠀⢘⠟⡋⠛⢣⠇⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⡀⢀⣾⠯⣿⡇⠰⠀⠆⠀⡄⠀⠀⢀⠀⣤⠀⠉⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⡁⠀⠰⡞⢠⣾⣿⡏⣿⣿⢿⣿⣆⠀⠀⠀⠀⠈⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡢⠈⠙⠒⢡⣦⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⢷⣿⣿⣷⣿⣿⣧⠝⢿⠀⠀⠠⢄⠄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣛⠛⣻⣿⣿⣿⣧⡀⠀⠀⠘⣿⣿⣿⣶⣶⣶⢶⢦⠀⠀⠀⠀⠀⠀⠄⡀⠀⢀⢀⡬⠀⠀⠈
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⢸⣿⣿⡇⣤⣠⡀⠀⠀⢀⢀⢩⣻⣿⣿⡏⠙⠃⠐⣴⡥⣵⣤⡄⠀⠀⣿⠋⠀⠀⠙⣿⣿⣇⢈⣩⣿⣿⣿⣿⣿⢠⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢁⠀⠄⠀⣿⠀⣾⣷⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢸⣿⣿⣇⣿⣿⣿⡀⢀⣎⠸⢸⡚⣿⣿⣇⡀⣀⣷⡹⠁⣿⣫⡇⣅⠀⢸⣠⣤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠋⢻⣿⡿⠿⡿⠹⠀⠠⠀⠀⠈⠀⠓⠀⢿⠀⣿⣿⣶⣶⡿
⣷⣘⣿⣿⣿⣿⣿⣿⣿⣦⡄⢩⣭⣽⣭⡍⣽⣭⣭⡋⣭⢭⣥⢹⣭⣭⡿⣭⣍⢭⡍⣭⣭⡍⣻⣻⠓⣸⣿⣿⣿⡟⠻⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⠀⣈⣁⣀⣀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣟⢿⣿⡟⠋⠉⢸⣿⣿⣿⣿⣼⡇⣿⣧⡟⣿⣧⣿⢧⢹⣾⡇⣸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣇⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⣿⠿⢿⣿⣿⡿⠀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⠝⠁⠀⠀⢸⣿⣘⠛⣿⣿⠇⢻⣇⣐⣿⡇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣫⠶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣷⣶⣶⣶⠆⣄⠑⣾⣿⣿⣷⣷⣯⣬⣤⣤⣼⣿⣧⣤⣄⡀
⠿⠋⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣻⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣉⣿⣛⡛⢏⣋⡀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⢠⣮⣴⣦⣦⣤⣤⠀⣾⡦⣤⢠⣴⢦⡄⣶⢀⣶⠄⡟⣿⣿⣿⣿⣿⣿⣦⡉⣿⣿⡿⣿⡶⣽⢿⣿⣿⣿⣿⣿⡟⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣺⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢻⡏⣿⠀⣿⣧⡿⢸⣿⣼⡇⢹⣿⠇⠠⠄⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣺⣿⣿⣿⣷⠀⡀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡏⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⠟⢻⣿⣿⡿⠛⠁⢹⣯⡳⣽⣺⣿⣿⣿⣿⣿⣿⣿⡟⠸⣟⠻⢖⠠⢄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠛⠛⠛⢿
⡄⢸⣿⣿⣷⣿⣿⡏⠁⠉⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠉⠉⠙⢻⡿⠞⠒⠉⠉⠀⠀⠀⢸⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠀⠀⠀⠀⠀⠉⠙⠷⣷⣤⣄⣀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠉
⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠉⠁⠐⠈⢿⣿⣿⡟⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⡤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⢀⣀⡀⢿⣿⡇⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣋⣤⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠿⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡗⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢏⣴⠟⠁⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠜⠳⠶⠶⠆⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⢀⣀⣠⣤⡄⠀⠀⣀⣠⣄⣄⠀⡠⠄⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠀⠄⠠⣤⡄⢠⠀⣄⢠⣠⣤⠀⡤⠀⢠⡄⠠⠄⠤⠀⠄⠀⠀⢀⠀⣀⠀⣤⠀⠀⣠⡤⣤⣤⠀⢠⡄⣤⣠
⣿⢿⣿⣻⠺⣿⣿⣿⣿⣟⠛⣿⣿⣿⣦⠟⣝⣿⣯⡷⢰⣼⡿⢞⡄⡰⢽⠀⠀⠀⢸⣿⣿⣿⣻⡇⠀⢸⠀⣀⣤⣴⣿⣶⢶⣶⣶⣴⣾⣷⠄⡇⠀⢸⡇⠘⠃⠿⠐⠃⠸⠇⠸⠁⠉⠀⠘⠀⠆⠉⠁⣿⣿⢛⠛⡛⠟⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠈⠉⣷⠉⢤⣿⣿⡇⠞⣡⣿⣯⠍⠀⠤⢼⣿⢿⣿⣾⡇⢠⣼⣿⣿⠻⠛⠁⠁⠀⠈⠉⠻⢿⣷⣦⡆⢀⣸⡇⢸⠆⠿⠐⠃⠘⠃⠘⠂⠀⠀⡐⠀⠀⠈⠀⢿⣯⠀⢰⠀⠀⠠
⠛⢛⣿⣿⠭⣿⠿⠿⣿⣿⣼⣿⣿⣿⠉⡔⢼⣿⠂⣣⣴⣜⢰⣿⡟⡿⣿⠓⠀⠐⠺⣿⣟⣛⣟⣷⠟⠉⠉⠈⠀⠀⣀⣀⣀⣀⣀⠀⠘⠛⠾⣿⣦⢸⡇⢰⠀⣖⠀⡀⠀⠀⠘⠀⠄⠀⣿⠀⠀⠀⠀⣸⡟⠀⢘⣤⣤⣤
⣶⣿⣿⣿⣀⣿⣿⣾⣿⣿⣿⣿⣿⣿⢰⣷⠞⣣⠆⠹⣿⠿⢘⣭⣵⣥⣛⣂⡀⠀⠘⠻⠉⠛⢓⠇⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠐⣷⠯⣿⡇⠰⠀⡂⠀⡄⠀⠀⢀⠀⡤⠀⠉⠀⠀⠀⠀⢹⡇⠀⢰⠈⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⡁⠀⠠⡖⢠⣾⣿⡏⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠉⠒⢡⣦⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢷⣿⣿⣷⣿⣿⣥⠙⢻⠀⠀⠠⢄⠄⠀⠈⣿⣿⡿⢿⣿⣿⣿⣏⠉⣽⣿⣿⣿⣧⡀⠀⠀⠙⣿⣿⣿⣶⣶⣶⣶⢦⠀⠀⠀⠀⠄⠀⠄⡀⠀⢄⢀⡮⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⢸⣿⣿⡇⣤⣠⡀⠀⠀⢀⢀⢩⣻⣿⣿⡏⠙⠀⠀⣴⡥⣥⣤⡄⠀⠀⣿⠉⠀⠀⠈⣿⣿⣇⡀⣤⣿⣿⣿⣿⣿⢠⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⠀⠄⠀⣿⠀⣾⣷⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⡿⣿⡀⢸⣿⣿⣇⣿⣿⣿⡀⢀⣇⢸⢸⠘⣿⣿⣇⡀⣀⣶⡹⠀⣿⣫⡇⣁⠀⢸⣤⣤⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠋⢹⣿⡿⠿⡟⠩⠀⠄⠀⠀⠈⠀⠓⠀⠿⠀⡿⣿⣶⣶⡿
⣿⣘⣿⣿⣿⠿⢿⣿⣦⢤⡝⢩⣭⣭⣭⡍⣯⣭⣭⡋⣭⢭⣥⢹⣭⣭⡿⣭⣍⢭⡍⣭⣭⡍⣟⣻⠓⣸⣿⣿⣿⣟⠛⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣗⠀⣈⣁⣀⡀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣏⢿⡿⠉⠁⠀⢸⣿⣿⢸⣿⣼⣇⣿⣧⡝⣿⣧⣿⢧⢹⣾⡇⣸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣇⣸⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣧⣿⠿⢿⣿⣿⡗⠀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠂⠀⠀⠀⠀⢸⣿⣁⠈⣿⣿⠿⣿⣇⣐⣿⡇⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣥⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣿⣿⣷⣶⣶⣶⢢⣄⠱⣾⣿⣷⣷⣶⣮⣥⣤⣤⣴⣿⣧⣤⣠⡀
⠆⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠀⢉⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣈⣿⣛⡛⢏⣋⠀⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣦⣰⣆⢠⣤⣤⠆⣤⡤⣤⢰⣶⢦⡄⣶⢀⣶⠄⡿⣿⣿⣿⣿⣿⣿⣦⡉⣿⣿⣟⣿⡶⣽⢿⣿⣿⣿⣿⣿⡟⠛⠛⠻⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣺⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⢹⡇⣿⠀⣿⣧⡿⢸⣿⣼⡇⢹⣿⠇⠀⠄⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣺⣿⣿⡿⣿⢄⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣯
⠀⢸⣿⣿⣿⣿⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⠛⣻⣿⣿⡿⠛⠁⢻⣦⡹⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⡟⠙⢖⠠⠄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠛⠛⠛⢿
⡄⢸⣿⣿⣷⣿⡇⠈⠁⠉⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠈⠉⠀⠉⠁⠀⠀⠉⠉⠙⢻⡿⠞⠂⠉⠉⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠉⠙⠷⣷⣤⣄⣀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠉
⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠀⠐⠘⢿⣿⣿⡏⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⡤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⢀⣀⡈⢿⣿⠃⠸⣿⣿⡯⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣫⣤⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢇⡶⠟⠁⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠌⠰⠶⠶⠖⠸⠿⠟⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⢀⣀⣠⣤⣄⠀⢀⣀⣠⣤⣄⠀⡀⡄⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠠⠄⡤⣤⡄⢠⠀⣄⢠⣠⣄⠀⠤⠠⢤⡄⠠⠄⠄⠀⠄⠀⠀⢀⠀⣀⠀⣤⠀⠄⣠⡤⣤⣤⠀⢠⡄⣤⣠
⣿⢿⣿⣻⢺⣿⣿⣿⣿⣟⠛⣿⣿⣿⣶⣿⣝⣿⣷⡧⢱⣼⡿⢟⡄⡴⢽⠀⠀⠀⢸⣯⣿⣿⣿⡇⠀⢸⢀⣀⣤⣴⡿⡶⢾⣶⣶⣶⣾⣷⠄⡇⠈⢹⡇⠘⠃⠿⠐⠇⠸⠇⠻⠁⠉⠀⠘⠀⠇⢹⠁⣿⣿⢻⠛⠛⠿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠈⠉⣷⠍⢴⣿⣿⠇⠞⣡⣿⣯⠍⠀⠤⢸⣿⢿⣿⣾⡇⢠⣾⣿⣿⠻⠛⠀⠁⠀⠈⠉⠻⢿⣷⣦⡆⢀⣸⡇⢸⠆⠿⠐⠃⠘⠃⠛⠀⠀⠀⡑⠐⠀⠌⠀⣿⣏⠀⢰⠀⠀⠸
⠛⢛⣿⣿⠭⣿⠿⠿⣿⣿⣼⣿⣿⣿⠛⣔⢾⣿⠂⣣⣤⣾⢸⣿⡿⡿⣻⠒⠐⠒⢺⣿⣾⣻⡿⣿⠟⠉⠁⠀⠀⢀⣀⣀⣄⣄⣀⡀⠘⠛⠿⣿⣦⢸⡇⢐⠀⡒⠀⡀⢀⠀⠘⠀⠄⠀⣿⠀⠀⠘⠀⣸⡇⠀⢨⣤⣤⣤
⣶⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣷⠞⣣⠄⠫⣿⠟⢘⣭⣵⣥⣟⣃⡀⠀⢘⠿⠛⠟⢳⠇⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠰⣷⠯⣾⡇⠰⠀⡆⠀⡄⠀⠀⢀⠀⡤⠀⠉⠀⠀⠀⠀⢹⡇⠀⢸⠈⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠉⠁⠀⠰⡞⢠⣼⣿⡏⣿⣿⣿⣿⣆⠠⠀⠀⠠⢈⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⠈⠉⠒⢡⣦⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠉⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⠀⠀⢷⣿⣿⣷⣿⣿⣧⠙⢿⠄⠀⠠⢄⠀⠀⠸⣿⣿⡿⢿⣿⣿⣿⣧⢼⣿⣿⣿⣿⣧⡀⠀⠀⠙⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠄⠀⠠⠀⡀⠄⢀⢮⠀⠀⢀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣼⣿⣿⡇⣤⣠⡀⠀⠀⢀⢈⢩⣻⣿⣿⡏⠙⠁⠑⣴⡥⣵⣤⡄⠀⠀⣿⠁⠀⠀⠙⣿⣿⣇⣠⣤⣿⣿⣿⣿⣿⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢁⠀⡄⠀⣿⠀⣾⣷⠀⠀⣗
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢸⣿⣿⣇⣿⣿⣿⡀⢀⣏⢸⢸⠘⣿⣿⣇⣀⣀⣿⡹⠀⣿⣻⡇⣀⠀⢸⣤⣤⣼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⢻⣿⡿⠿⡟⠽⠀⠤⠀⠀⠈⠐⠓⠀⠿⠀⢿⣿⣶⣶⡿
⣿⣘⣿⢿⣾⣷⢠⣤⣽⢭⣟⢩⣭⣽⣭⡝⣭⣭⣭⡋⣭⣭⣬⣹⣭⣭⣿⣭⣍⢭⡍⣭⣭⡍⣿⣻⠃⣾⣿⣿⣿⣟⠛⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⡗⢀⣈⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡏⠉⠉⠠⢿⣿⣿⣿⣤⢸⣿⣾⡇⣿⣯⡝⣿⣧⣿⢧⢹⣾⡏⣸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣆⣹⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠰⣧⣿⡿⢿⣿⣿⡇⢰⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⣤⠀⠛⠋⢸⣿⣀⠘⣿⣿⣿⣿⣇⣀⣿⡇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣋⡤⣤⣵⣶⣿⣿⣿⣿⣿⣿⡇⣰⣿⣿⣷⣶⣶⣶⢰⡄⢶⣿⣿⣿⣷⣷⣮⣯⣤⣤⣼⣿⣧⣤⣤⣀
⠘⠋⠀⠀⠀⠀⠈⠉⠉⠀⠉⢿⣿⣏⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣈⣿⣛⡛⢋⡃⠘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⡄⢠⡄⣤⣶⣤⠀⣤⡶⣽⢽⣷⢦⡦⣶⢠⣶⠄⡟⣿⣿⣿⣿⣿⣿⣦⡉⣿⣿⣟⣿⡶⣽⢿⣿⢿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣻⠓⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣾⡇⢸⡇⣿⠀⣿⣧⡿⢸⣿⣼⡇⢹⣿⠇⠠⠄⣿⢹⡿⣿⣿⣿⣿⣷⣿⣯⣤⣿⣧⣿⣼⣿⣺⣿⣿⡿⣿⣄⣀⢀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣞
⠀⢸⣿⣿⡇⣾⡷⣿⡆⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⠟⣻⣿⣿⡿⠛⠁⢿⣦⡻⣴⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣏⡛⢖⠠⠄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠛⠛⠛⢿
⡄⢸⣿⣮⠁⠉⠁⠈⠁⠉⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠈⠉⠀⠉⠁⠀⠀⠉⠉⠙⢻⡿⠾⠒⠉⠉⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠀⠀⠀⠀⠉⠛⠷⣷⣤⣄⣀⡀⠀⠀⠀⠀⠐⠒⠒⠒⠉
⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⠀⠐⠈⢿⣿⣿⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⡤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⢀⣀⣈⢿⣿⠃⠸⣿⣿⡏⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣾⡄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣫⣤⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢧⡾⠟⠁⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠟⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢀⣀⣠⣤⣄⠀⢀⣀⣠⣤⣄⠀⡀⠄⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠠⠄⡤⣤⡄⢠⠀⡄⢠⣤⣄⠀⠤⠠⢤⡄⠠⠀⠤⠀⠄⢀⠀⢀⠀⣀⠀⣤⠀⠀⣠⡤⣤⣤⠀⢠⣄⣤⣠
⣿⣿⣿⣻⠺⣿⣿⣿⣿⣟⢛⣿⣿⣿⣶⣷⣝⣿⣷⡧⣠⣼⡻⢗⡄⡰⢽⡀⠀⠀⢸⣿⣿⣿⣻⡇⠀⢸⢀⣠⣤⣴⡿⣶⢶⣶⣶⣴⣾⣷⠄⡇⠈⢸⡇⠘⠃⠿⠐⠏⠸⠇⠻⠁⠉⠀⡸⠀⠆⠹⠁⣿⣿⢻⠛⠛⠿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⣷⠉⢴⣿⣿⠇⠟⣡⣿⣿⡍⠀⠠⢺⣿⢿⣿⣿⡃⢠⣾⣿⣿⠻⠛⠈⠁⠈⠈⠙⠻⢿⣷⣦⡆⢀⣸⡇⢸⠆⠿⠐⠃⠘⠃⠛⠀⠀⠀⡑⠀⠀⠌⠀⣿⣏⠀⢸⠀⠀⠸
⠛⢛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠛⡔⢾⣿⠀⣣⣤⣾⢸⣿⡟⣿⣻⠓⠒⠒⢺⣿⣾⣻⣿⣿⠟⠉⠑⠀⠀⠀⣀⣀⣀⣀⣀⠀⠙⠳⠾⣿⣆⢸⡇⢠⠀⣖⠀⡀⠀⠀⠘⠀⠄⠀⣽⠀⠀⠘⠀⣸⡇⠀⢈⣤⣤⣴
⣶⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣷⠞⣣⠀⢭⣿⠿⢘⣭⣵⣤⣛⣃⡀⠀⢘⡿⡛⠿⢻⠃⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀⢰⣿⠯⣾⡇⠰⠀⡆⠀⡀⠀⠀⢀⠀⠤⠀⠉⠀⠀⠀⠀⢹⡇⠀⢸⠈⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢈⡁⠀⠰⡞⢠⣾⣿⡏⣿⣿⣿⣿⡇⠀⠀⠠⠄⢈⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡢⠈⠙⠚⢱⣦⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⠀⠀⣷⣾⣿⣷⣿⣿⣧⠙⢿⠆⠀⠠⣤⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⣯⢾⣿⣿⣿⣿⣧⡀⠀⠀⠙⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠄⠀⠠⠀⡀⠄⢀⡯⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣼⣿⣿⡇⣤⣠⡀⠀⠀⢀⢀⢩⢻⣿⣿⡏⠙⠁⠘⣴⡥⣵⣴⡄⠀⠀⣿⠁⢀⡀⠛⣿⣿⣃⣈⣩⣿⣿⣿⣿⣷⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⠀⡄⠀⣿⠀⣾⣷⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢸⣿⣿⣇⣿⣿⣿⡀⢀⣏⢸⢸⠘⣿⣿⣇⡀⣀⣿⡹⠀⣿⣻⡇⣀⠀⢹⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⢻⣿⡿⠿⡟⠽⠀⠄⠀⠀⠈⠐⠓⠀⠿⠀⢿⣿⣶⣾⠿
⣿⣘⣫⣷⣦⠀⢩⣯⣽⣩⣟⢩⣭⣽⣭⡝⣭⣭⣭⡋⣭⣭⣬⣹⣭⣭⣿⣭⣍⢭⡍⣭⣭⡍⣿⣻⢣⣿⣿⣿⣿⡿⠿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⡗⢀⣈⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠛⠁⢸⣿⣿⡀⢸⣿⣽⣿⣿⣾⡧⣾⣧⡅⣿⣧⣿⢧⢹⣾⡏⣸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣆⣹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠰⣧⣿⡿⢿⣿⣿⠇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠐⠿⠋⠀⢸⣿⣀⠘⣿⣿⣿⣿⣇⣀⣿⡇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡥⣼⣾⣿⣿⣿⣿⣿⣿⣿⡇⣰⣿⣿⣷⣶⣶⣶⢰⡄⣾⣿⣿⣷⣷⣿⣾⣬⣤⣤⣼⣿⣧⣤⣤⣀
⠛⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣿⣏⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣈⣿⣛⡛⢋⡁⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⡄⢰⡇⢠⣤⣤⠀⣾⡿⣽⢿⣷⢦⡆⣷⢠⣶⡄⡟⣿⣿⣿⣿⣿⣿⣦⡉⣿⣿⣟⣿⡶⣽⢿⣿⢿⣿⣿⣿⣿⢿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣻⠓⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿
⠀⢸⣷⣾⡇⢸⡇⣿⠀⣿⣧⡿⢸⣿⣼⡇⢹⣿⠇⠠⠄⣿⢹⡿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣧⣿⣼⣿⣺⣿⣿⡿⣷⣀⡈⠀⢈⣩⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣞
⠀⢸⣿⢸⡇⣾⡷⣿⡆⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⠟⣹⣿⣿⡿⠛⠁⢻⣮⡻⣿⣽⣿⣿⣿⣿⣿⣿⣿⡏⠸⡯⢙⢶⠠⢄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠛⠛⠛⢿
⡄⢸⡅⠈⠁⠉⠁⠈⠁⠉⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠈⠉⠀⠉⠁⠀⠀⠉⠉⠙⢻⡿⠞⠒⠉⠉⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠉⠛⠷⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠒⠒⠒⠉
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠀⠐⠈⢿⣿⣿⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⡤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⢀⣀⣈⣿⣿⠇⠸⣿⣿⡏⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣶⣾⣆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣫⣤⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢧⡾⠟⠁⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⢀⣀⣠⣤⣄⠀⢀⣀⣠⣀⣄⠀⡀⠄⠀⠀⢠⣤⣤⣤⣤⡄⠀⢠⠀⠀⠄⡤⣤⡄⢠⠀⡄⢠⣠⣄⠀⠤⠠⢠⡄⠠⠀⠄⠀⠄⠀⠀⢀⠀⣀⠀⣤⠀⠀⣠⡤⣤⣤⠀⢠⣀⣤⣠
⣿⢿⣿⣿⣺⣿⣿⣿⣿⣟⢛⣿⣿⣿⣶⣟⣝⣿⣇⡧⣰⣼⡿⢟⡄⡴⢽⡀⠀⠀⢸⣿⣿⣿⣻⡇⠀⢹⢀⣠⣤⣶⣿⣶⢶⣶⣶⣴⣾⣷⠄⡇⠨⢸⡇⠘⠃⠿⠐⠇⠸⠇⠻⠁⠉⠀⠸⠠⠇⠛⠁⣿⣿⢛⠛⠛⠟⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⠙⣷⠉⢴⣿⣿⠇⠟⣡⣿⣯⠍⠀⠠⢾⣿⢿⣿⣾⡇⣠⣾⣿⡿⠟⠛⠀⠁⠈⠙⠛⠿⣿⣷⣦⡂⢀⣸⡇⢸⠇⠿⠐⠃⠘⠃⠚⠀⠀⠀⡑⠀⠀⠌⠀⣿⣏⠀⢰⠀⠀⠸
⠛⢛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠉⡖⢾⣿⠀⣣⣤⣾⢸⣿⡿⡟⣻⠓⠐⠂⣺⣟⣞⣛⣿⣿⠟⠋⠁⠁⠀⠀⠀⢀⣀⣀⠀⠀⠘⠶⣿⣿⣆⢸⡇⢐⠀⡖⠀⡀⢀⠀⠘⠀⠄⠀⣿⠀⠀⠘⠀⣸⡇⠀⢨⣤⣤⣴
⣶⣿⣿⣿⣤⣿⣷⣾⣿⣿⣿⣿⣿⣿⢰⣿⠟⣣⠄⠷⢿⠿⢘⣭⣵⣤⣟⣃⠀⠀⢙⠟⣛⠟⢻⠁⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣦⡀⢰⡯⢯⣾⡇⠰⠀⡆⠀⡀⠐⠀⢀⠀⡤⠀⠉⠀⠀⠀⠀⢹⡇⠀⢸⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠈⡁⠀⢰⡞⢠⣾⣿⡏⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⠈⠙⠪⢡⣦⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠄⠀⠀⣷⣿⣿⣷⣿⣿⣧⠙⢿⠄⠀⠠⢄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⡽⣿⣿⣿⣿⣆⠀⠀⠀⠙⣿⣿⣿⣿⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠠⠀⡀⠄⢀⡯⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣠⡀⠀⠀⢀⢀⢩⢻⣿⣿⡏⠙⠁⠌⣴⡥⣤⣤⡄⠀⠈⡿⠉⠀⠘⠻⣿⣿⡋⠚⣛⣿⣿⣿⣿⣷⢠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⠀⡄⠀⣿⠀⣾⣷⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢸⣿⣿⣇⣿⣿⣿⡀⢀⣏⢸⢸⠘⣿⣿⣇⡀⣀⣿⡹⠀⣿⣻⡇⡀⠀⢻⣀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⢻⣿⡿⠿⡟⠭⠀⠄⠀⠀⠈⠐⠓⠀⠿⠀⢿⣿⣶⣾⠿
⣿⣪⣯⡍⠉⠛⢿⣯⣽⣭⣟⢩⣭⣭⣭⡝⣭⣭⣭⡋⣭⣭⣬⣽⣭⣭⣿⣭⣍⢭⡍⣭⣭⡍⣟⣿⢣⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡗⢀⣀⣀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠛⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣾⣧⣿⣧⡄⣿⣧⣿⢧⢹⣾⡏⣹⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣆⣹⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⣧⣿⠿⢿⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢽⡿⠃⠀⠀⢸⣿⣀⠘⣿⣿⣿⣿⣇⣀⣿⡇⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⣭⣽⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣷⣶⣶⣶⢰⠐⣾⣿⣿⣷⣷⣷⣶⣼⣤⣤⣼⣿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣿⣿⣿⣏⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣈⣿⣛⡛⢏⠀⢁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣦⣴⡄⢠⣶⣦⠈⣿⣿⣽⢽⣷⢦⡎⣷⢀⣶⡄⡟⣿⣿⣿⣿⣿⣿⣦⡉⣿⣿⣿⣿⡶⣽⢿⣿⢿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣺⠒⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿
⠀⢸⣿⣿⡇⢸⡇⣿⠀⣿⣧⡿⢸⣿⣼⡇⢹⣿⠇⠠⠄⣿⢹⡿⣿⣿⣿⣿⣷⣿⣯⣤⣿⣧⣿⣼⣿⣾⣿⣿⣿⣯⢄⡀⠀⠉⣩⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣞
⠀⢸⡿⢸⡇⣾⡷⣿⡆⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⠛⢹⣿⣿⡿⠟⠁⢻⣮⡳⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⠯⢹⢶⠠⢄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠛⠛⠛⢿
⡄⠈⠁⠈⠁⠉⠁⠈⠁⠉⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠈⠉⠀⠉⠁⠀⠀⠉⠉⠙⢻⡿⠞⠒⠉⠉⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⠀⠀⠀⠀⠀⠉⠛⠷⣷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠒⠒⠒⠉
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠀⠐⠈⢿⣿⣿⡏⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⡤⠄⠀⠀⠀⠀⠀⠀
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⢀⣀⣈⢿⣿⠇⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣫⣤⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢯⡾⠟⠁⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠟⠖⠲⣶⠏⢶⠄⠰⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⢀⣀⣠⣤⣄⠀⢀⣀⣠⣄⣄⠀⠠⠄⠀⠀⣠⣤⣤⣤⣤⡄⠀⢠⠀⠠⠀⢤⣤⡄⢠⠀⣄⢠⣤⣄⠀⠤⠠⢤⡄⠠⠄⠄⠀⠄⠀⠀⢀⠀⣀⠀⣤⠀⠄⣠⡤⣤⣤⠀⢠⣄⣤⣠
⣿⣿⣿⣿⡺⣿⣿⣿⣿⣿⢛⣿⣿⣿⣖⣿⣝⣿⣯⡧⣰⣽⡿⢟⡄⡴⢽⠈⠀⠀⢸⣿⣿⣿⣿⡇⠀⢸⢀⣀⣤⣶⣿⣶⣶⣶⣶⣴⣾⣷⠀⡇⠈⢸⡇⠘⠃⠿⠐⠇⠸⠇⠻⠀⠉⠀⡸⠀⠃⢹⠁⣿⣿⢻⠛⠛⠿⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠈⢉⣷⠉⢴⣿⣿⠇⢟⣡⣿⣯⡍⠀⠤⢽⣿⢿⣿⣿⡇⣀⣾⣿⡿⠿⠟⠑⠁⠈⠛⠻⢿⣿⣷⣦⡆⢀⣸⡇⢸⠇⠿⠐⠃⠘⠃⠻⠀⠀⠀⡑⠀⠀⢌⠀⣿⡯⠀⢰⠀⠀⠸
⠛⢛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠛⡔⢾⣿⠀⣣⣤⣾⢸⣿⣿⡛⣻⠓⠐⠒⢺⣿⣾⣟⣿⣷⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣽⣿⣆⢸⡇⢀⠀⣒⠀⡀⠰⠀⠘⠀⠄⠀⣿⠀⠀⠘⠀⣸⡇⠀⢨⣤⣤⣴
⣶⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⠟⣣⠀⠵⣯⠟⢘⣭⣵⣤⣛⣃⡀⠀⢘⠛⡛⠙⢻⠃⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣄⠀⠠⣭⣯⣺⡇⠐⠀⡆⠀⡀⠀⠀⢀⠀⡤⠀⠉⠀⠀⠀⠀⢹⡇⠀⢸⠈⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⡁⠀⢰⡞⢠⣼⣿⡏⣿⣿⣿⣿⡆⠀⠀⠠⠀⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⠉⠒⠪⣡⣦⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠉⠁⠰⠾⠶⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄⠀⠀⣷⣿⣿⣷⣿⣿⣧⠙⢿⠆⠀⠠⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣄⠀⠀⠀⠘⣿⣿⣿⣿⡶⣶⡶⣦⠀⠀⠀⠀⠄⠀⠠⠀⡄⠄⢀⡯⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣾⣿⣿⡇⣤⣠⡀⠀⠀⢀⢀⢩⢻⣿⣿⡏⠙⠁⠜⣴⣥⣥⣤⡄⠀⠈⣿⠛⠉⠹⢿⣿⣿⠟⠑⠛⣿⣿⣿⣿⣧⢠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢀⠀⡅⠀⣿⠀⣾⣷⠀⠀⣗
⠛⢿⣿⣿⣷⣶⣿⣿⣿⣿⡀⢻⣿⣿⣇⣿⣿⣿⡀⢀⣏⢸⣼⠘⣿⣿⣇⣀⣀⣿⡹⠀⣯⣻⡇⡀⠀⢿⠀⠀⣠⣠⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⢻⣿⡟⢿⡟⠽⠐⠀⠀⠀⠈⠐⠓⠀⠿⠀⠿⣿⣶⣾⠿
⣧⣌⠙⠛⢿⣿⣿⣯⣽⣭⣟⢩⣭⣭⣭⡍⣭⣭⣭⡋⣭⣭⣬⣽⣭⣭⣿⣭⣍⢭⡍⣭⣭⡍⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢀⣈⣀⣀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡀⠀⠀⠘⢹⣿⣿⣿⣿⣾⣷⣿⣧⡅⣿⣧⣿⢧⢹⣾⣯⣸⣿⣸⣇⣸⣿⣼⣇⣿⣧⡌⣉⣿⣆⣹⣿⣿⣿⣿⣉⣽⣶⣿⣿⣿⣿⣿⣿⣿⡿⠸⣧⣿⡿⢿⣿⣿⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠀⠀⠀⠀⢸⣿⣀⠘⣿⣿⣿⣿⣇⣀⣿⡇⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣷⣶⣶⣶⠰⢰⣿⣿⣿⣷⣷⣶⣶⣬⣤⣤⣼⣿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣿⣛⡛⢃⠀⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⡦⢰⡆⢠⣾⣿⣯⣿⣿⣽⢿⣷⢦⡎⣶⢀⣶⡄⡟⣿⣿⣿⣿⣿⣿⣦⡉⣿⣿⣿⣿⡶⣽⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣿⠒⠛⠛⢛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿
⠠⢸⣷⣾⡇⢸⡇⣿⠀⣿⣧⡿⢸⣿⣼⡇⢹⣿⠇⠀⠄⣿⢹⡿⣿⣿⣿⣿⣷⣿⣯⣤⣿⣧⣿⣼⣿⣺⣿⣿⣿⣯⡈⠉⠉⠙⢛⣻⣿⣿⣿⣿⣿⣿⢻⣿⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾
⠀⢸⡇⢸⡇⣾⡷⣿⡇⣿⡇⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⣿⢾⣷⠀⣿⡏⠉⠉⣿⣿⣿⣿⣿⠛⣹⣿⣿⡿⠟⠁⢻⣦⡳⣠⣶⣿⣿⣿⣿⣿⣿⣿⡏⠸⢯⡙⢶⠠⢄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠛⠛⠛⢿
⠀⠈⠁⠈⠁⠉⠁⠈⠁⠉⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠈⠉⠈⠉⠀⠉⠁⠀⠀⠉⠉⠙⢻⡿⠾⠒⠉⠉⠀⠀⠀⢸⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠁⠀⠀⠀⠀⠉⠛⠷⣷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠒⠒⠚⠉
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠉⠀⠐⠈⢿⣿⣿⡏⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠤⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⢀⣀⣈⢿⣿⠇⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡆⠀⠀⠐⠀⠀⢀⣀⣠⣴⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣫⣤⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠿⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢏⡾⠟⠁⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠋⠖⠲⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⠀⢠⣄⣤⣤⣤⠄⡤⡄⠀⠀⣤⣤⣤⣤⣤⡄⠀⣤⠀⢠⠄⣤⣤⡄⢠⠀⣄⢠⣤⣤⠀⡤⠠⢤⡄⠠⠄⠤⠀⠄⢠⡄⢀⡀⣀⠀⣤⠄⠄⣤⡤⣤⣤⠀⢠⣄⣤⣤
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢛⣿⣿⣿⣾⣿⣟⣿⣿⡧⣹⣽⡿⢟⡄⡾⣿⡈⠀⠀⣿⣿⣿⣿⣿⡇⠀⣿⠈⣠⣤⣶⣿⣦⣶⣶⣶⣼⣿⣿⠄⣗⢨⢹⡇⠺⠃⠿⠸⠯⠸⠇⠿⠃⠋⠀⡻⠠⠇⢻⠉⣿⣿⢿⢟⡿⠿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⣻⣿⠉⢴⣿⣿⡧⢟⣵⣿⣿⡿⠤⠼⣿⣿⣿⣿⣿⡇⣀⣿⣿⣿⠿⠟⠹⠋⠘⠻⠿⣿⣿⣷⣦⡆⢀⣸⡇⢸⠇⠿⠸⠓⠸⠃⠿⠃⠄⠀⡻⠐⠀⢼⠏⣿⣿⠀⣼⠀⠀⢸
⠛⢛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⢿⣶⣿⣿⠒⣧⣼⣿⢸⣿⣿⣿⣿⡓⠒⠒⣿⣿⣿⣿⣿⣷⡿⠟⠏⠃⠀⠀⠀⠀⠀⠀⠀⠈⠽⣽⣿⣿⣶⢸⡇⢰⡀⣖⠀⡄⢰⠀⠞⠀⠤⠀⣿⠀⠀⠘⠂⣽⡟⠀⢸⣤⣴⣼
⣷⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢟⣫⠆⢿⣿⡟⢘⣭⣵⣭⣿⣓⡀⠀⣽⣿⣿⢿⢿⠃⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣷⣦⣄⠀⢹⣿⣿⣺⡇⠰⠀⡖⢀⡄⢐⠀⢠⠀⣦⠀⣭⠀⠀⠀⠀⣿⡗⠀⢼⠈⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠑⣋⣥⠀⢰⡟⣠⣾⣿⡟⣿⣿⣿⣿⣧⡽⡒⠽⣥⠁⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢎⠙⠒⠯⣳⣶⣶⣶⣦⣶⡶⠒⠲⠀⠀⠀⠏⠂⠀⠠⠀⠙⠅⠰⡿⠶⠶⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠉⠉⡄⠄⢠⣷⣿⣿⣿⣿⣿⣯⡿⣿⡧⠀⠾⣭⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠺⣿⣿⣿⣿⣷⣶⣶⣶⠀⠀⠀⠀⠄⠠⡤⡀⡔⠄⢀⣿⠄⠈⣙
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡧⣤⣤⡀⠀⠀⣴⢛⣹⣻⣿⣿⡟⠙⠇⡽⣿⣧⣷⣾⡇⠀⠘⣿⠟⠛⢻⣿⣿⣿⡿⠹⠿⣿⣿⣿⣿⣦⢠⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢑⠀⡅⢤⣿⠀⣿⣷⠀⠀⣿
⠛⢿⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣿⣿⡁⢀⣏⢹⣿⡝⣿⣿⣇⣀⣀⣿⡽⢈⣿⣻⣇⡀⠀⣿⠄⠒⢂⢈⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⢻⣿⡿⣿⡿⠿⠵⠤⠀⠘⠉⠘⠓⠀⢿⠀⣿⣿⣷⣾⢿
⡛⠚⠻⣿⣿⣿⣿⣏⣹⣙⣿⡿⢿⡿⡿⣿⣹⣿⡿⢿⢿⡇⢙⡿⣿⣿⣿⣿⣿⢿⣿⣻⡛⣻⣿⣿⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣈⣁⣀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣇⠀⠀⠈⠻⢿⢿⣿⣿⣿⣿⣾⣶⣶⠂⠁⣿⣭⣥⣤⢠⢠⣾⣥⣬⣍⣀⣈⣁⣠⣃⣀⣀⣈⣙⣿⣇⣹⣿⣿⣿⣿⣛⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⡿⣿⣿⣿⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠀⠀⠀⠀⠀⠄⠀⠀⣰⣾⣿⣿⣿⣃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣇⣼⣿⣿⣷⣶⣶⣶⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣧⣤⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣈⣿⣛⡛⢇⠘⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢟⣵⢠⣾⣿⡂⠐⣦⡿⢻⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⠟⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣿⠒⠛⠛⢛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠁⠈⠁⠀⠀⠀⠤⠤⠌⠹⣿⣿⣿⣿⣿⣿⣾⣿⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⣿⣿⣿⡟⡫⣿⣿⠿⠟⠁⢻⣷⡷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣷⠠⢄⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠍⢿⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠿⠒⠉⠀⠀⠀⠀⢸⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⠁⠘⡻⠛⠙⠂⠀⠈⠉⠛⢷⣿⣤⣤⣀⠀⠀⠀⠀⠁⠀⠒⠒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠉⠀⠐⠚⢿⣿⣿⡟⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠀⠀⠀⢀⣠⣬⣿⣿⡇⠸⣿⣿⡯⠽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⣴⠂⢀⣴⣿⣿⣿⣿⣿⠀⠀⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢯⡾⠟⠁⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠖⠶⣶⠏⢶⠜⠳⠿⠾⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠈⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⠀⢠⣄⣤⣤⣤⠄⣤⡄⠀⠀⣤⣤⣤⣤⣤⡄⠀⣤⠀⢠⠄⣤⣤⡄⢠⠀⣄⢠⣤⣄⠀⠤⠠⢤⡄⠠⠄⠄⠀⠄⢀⡀⢀⡀⣀⠀⣤⢀⠄⣠⣤⣤⣤⠀⢠⣄⣤⣤
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢛⣿⣿⣿⣷⣿⣟⣿⣿⡧⣱⣿⡿⣟⣄⡿⣿⡁⠀⠀⣿⣿⣿⣿⣿⡇⠀⣿⠈⣀⣤⣶⣿⣶⣶⣶⣶⣴⣿⣿⠤⡗⠸⢹⡇⠺⠃⠿⠸⠟⠸⠇⠿⠁⠉⠀⡻⠠⠇⢻⠁⣿⣿⢿⢛⡿⠿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠹⢙⣿⠉⢴⣿⣿⡧⢟⣵⣿⣯⡯⠠⠬⢿⣿⣿⣿⣿⡇⣀⣿⣿⣿⠿⠟⠁⠁⠘⠛⠿⢿⣿⣷⣦⡆⢀⣸⡇⢺⠇⠿⠸⠃⠘⠃⠿⠃⠄⠀⡳⠐⠀⢞⠏⣿⣯⠀⢼⠀⠀⢸
⠛⣛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⢟⣶⣿⣿⠐⣣⣴⣿⢸⣿⣿⣿⣿⡓⠒⠒⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢽⣿⣿⣦⢸⡇⢐⠀⣖⠀⡀⠰⠀⠚⠀⠥⠀⣿⠀⠀⠘⠂⣿⡟⠀⢨⣴⣴⣼
⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⢟⣻⠂⢿⣿⡟⢘⣭⣵⣥⣿⣃⡀⠠⣽⣿⣿⠿⢿⠃⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣤⡀⡰⣯⣿⣺⡇⠰⠀⡖⢠⡄⢀⠀⢠⠀⡦⠀⠭⠀⠀⠀⠀⣿⡇⠀⢼⠈⠉⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⣉⣁⠀⢺⡟⣠⣾⣿⡟⣿⣿⣿⣿⣧⠸⠉⠩⣤⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠉⠒⠮⣳⣶⣶⣦⣶⣶⡖⠒⠒⠐⠀⠀⠇⠂⠀⠰⠀⠙⠁⠰⠿⠶⠶⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠈⠈⡄⠀⢠⣿⣿⣿⣿⣿⣿⣯⠿⣿⡧⠀⠾⣧⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠺⣿⣿⣿⣿⣷⣶⣶⣶⠀⠀⠀⠀⠄⠀⠤⠀⡔⠄⢀⡿⠄⠀⣝
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡧⣤⣤⡀⠀⠀⣀⢚⣹⢿⣿⣿⡟⠙⠅⡽⣾⣥⣷⣾⡇⠀⠈⣿⠟⠋⠹⢿⣿⣿⡟⠵⠛⣿⣿⣿⣿⣷⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⢑⠀⡅⠄⣿⠀⣿⣷⠀⠀⣿
⠛⢿⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣷⣿⣿⣿⡀⢀⣏⢸⣿⠙⣿⣿⣇⣀⣀⣿⡹⢈⣿⣻⣇⡄⠀⣿⠄⠀⢠⣠⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⢻⣿⡿⢿⡿⠿⠐⠤⠀⠘⠉⠐⠓⠀⢿⠀⣿⣿⣷⣾⢿
⣿⣺⠛⣿⣿⣿⣿⣏⣹⣙⣿⠿⠿⠿⣿⢯⣽⣿⡿⢿⢽⠁⢹⡿⣿⣿⣿⣿⣿⢿⣿⣻⡛⣻⣿⣿⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣈⣀⡀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠈⢿⣧⡘⠻⢿⢿⣿⣿⣿⣿⣾⣶⣶⡆⠈⢹⣭⣥⣤⢠⢰⣭⣥⣤⣝⣀⣈⣀⣠⣃⣀⣀⣈⣙⣿⣆⣹⣿⣿⣿⣿⣭⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⣿⡿⣿⣿⡗⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⠇⠀⠀⠄⠀⠀⣰⣾⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡿⠟⣛⣽⣿⣿⣿⣿⣏⣼⣿⣿⣷⣶⣶⣶⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣧⣤⣤⣄
⠀⠀⠁⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣈⣿⣛⡛⢀⢳⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⢰⣾⣿⡂⠐⡆⡟⢻⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⠟⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣿⠚⠛⠛⢛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿
⠀⠀⠈⠛⣿⣿⡏⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠠⠤⠍⠹⣿⣿⣿⣿⣿⣿⣾⣿⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠈⢻⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⣿⣿⣿⠟⡫⣿⣿⡿⠟⠁⢻⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣶⠠⢄⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢛⠛⠻⣿
⠀⠀⠀⠀⠀⠈⣿⣷⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠿⠒⠉⠀⠀⠀⠀⢸⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⠁⠈⠛⠛⠀⠀⠀⠈⠉⠛⢷⣷⣤⣄⣀⠀⠀⠀⠀⠁⠀⠒⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠉⠁⠐⠙⢿⣿⣿⡟⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⢀⣀⡈⢿⣿⡇⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⣦⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣤⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠿⠿⠗⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣶⠟⠁⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠖⠶⣶⠏⢶⠜⠳⠷⠾⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠈⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⡤⡤⣤⣤⢀⡀⣠⣤⡄⠀⢀⣀⣠⣠⡄⠀⠠⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⣤⠀⢀⠄⡤⣤⡄⢀⠀⡄⢠⣤⡄⠀⠤⠠⢠⡄⠠⠀⠄⠀⠄⠀⠀⢀⠀⣀⠀⣤⠀⠀⣠⡤⣤⣤⠀⢠⣀⣤⣠
⣿⣿⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⣶⡳⣍⢿⣇⡇⣰⣽⡻⢗⠀⠤⢽⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣸⢀⣀⣤⣴⣿⣶⠶⣶⣶⣴⣾⣷⠀⡇⠀⢸⡇⠘⠀⠿⠘⠅⠸⠇⠻⠁⠉⠀⠘⠀⠂⢹⠀⣿⣿⢛⠛⠛⠟⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⢘⢷⠉⠴⣿⣿⠃⠏⣱⣿⣯⠍⠀⠀⢽⣿⢿⣿⣿⡃⣠⣾⣿⡿⠻⠛⠁⠁⠈⠙⠛⠿⣿⣿⣦⡂⢀⢸⡇⠸⠂⠿⠘⠃⠘⠃⠛⠀⠀⠀⡐⠀⠀⢈⠀⣿⡇⠀⢼⠀⠀⠰
⠛⢛⣿⣿⠽⣿⠿⠿⢿⣿⣼⣿⣿⣿⠀⡔⣾⣿⠀⣣⣤⣞⢸⣿⡿⡟⣻⠒⠀⠀⢺⣟⣚⣛⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠘⠷⣿⣯⣦⢸⡇⢀⠀⡂⠀⠀⠀⠀⠘⠀⠄⠀⣿⠀⠀⠘⠀⣼⡇⠀⢨⣤⣤⣴
⣶⣿⣿⣿⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⢰⣷⠞⣣⠀⠱⢯⠏⢘⣭⣵⣤⣟⣁⡀⠀⠘⠚⠛⠋⢻⠃⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⣮⢯⣾⡇⠐⠀⡄⠀⡀⠀⠀⠀⠀⡤⠀⠉⠀⠀⠀⠀⢻⡇⠀⠸⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⡁⠀⠀⡞⢠⣾⣿⡏⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠈⠑⠪⢡⢦⣶⣤⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠰⠾⠲⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢷⣿⣿⣷⣿⣿⣧⠙⢿⠀⠀⠠⢄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⡭⣿⣿⣿⣿⣆⠀⠀⠀⠘⣿⣿⣿⣿⣶⣶⡶⣆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀⠧⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣤⡀⠀⠀⢀⢀⢩⢻⣿⣿⡏⠙⠁⠔⣴⣤⣥⣤⡄⠀⠀⣿⠋⠁⠈⠻⣿⣿⡋⠘⢛⣿⣿⣿⣿⣷⢠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠄⠀⣿⠀⣾⣗⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢿⣿⣿⣇⣿⣿⣿⡀⢀⡇⢸⣺⠘⣿⣿⣇⣀⣀⣿⡙⠀⣏⣻⡇⣄⠀⢹⣀⣀⣠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⢻⣿⡟⠿⡟⠭⠀⠀⠀⠀⠈⠐⠓⠀⠿⠀⠿⢿⣶⣾⢿
⣧⣸⠋⢿⣿⣿⣿⣏⣹⣭⣿⣿⡿⣻⣿⣏⡝⣯⣭⣟⠭⣡⣭⣟⢽⣿⣿⣏⢩⣏⣫⡍⡉⣛⣿⣿⠣⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢀⣀⣀⡀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣏⢿⣧⡈⠛⠟⢛⣿⣿⣿⣿⣿⣷⣿⡇⣿⠁⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣈⣉⣿⣆⣹⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣧⣿⠿⠿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣦⣿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣇⣿⠀⣿⣿⣿⢿⣿⣸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠉⠤⢙⣣⣿⣾⣿⣿⣿⣿⣏⣸⣿⣿⣷⣶⣶⣶⠰⣾⣿⣿⣿⣿⣷⣿⣶⣦⣤⣤⣼⣿⣤⣤⣤⣄
⠘⠉⠁⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣿⣛⠛⢀⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣯⣭⣝⣵⣤⣶⡖⣤⣤⡆⣮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⣿⠟⠀⠙⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣸⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿
⠀⠈⢻⣛⣛⣿⡋⠉⠉⠉⢿⣬⡉⢹⣿⣸⡇⣿⣧⡄⣼⡟⣿⠿⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣗⡀⠀⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⠀⠈⢻⣿⣿⡁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣯⢹⣿⣹⡿⣿⣿⣿⠛⡉⣽⣿⠿⠛⠁⢻⣦⣰⣲⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⡋⠙⠲⠠⠄⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢿
⠀⠀⠀⠀⢻⣿⣿⣷⣦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⢻⡿⠖⠒⠉⠀⠀⠀⠀⢸⣿⣿⣦⣎⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠉⠙⠳⣷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠒⠒⠒⠉
⠀⠀⠀⠀⠘⣿⣿⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠉⠁⠐⠙⢿⣿⣿⡏⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⢀⣀⠈⢿⣿⠇⠸⣿⣿⡎⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣋⣤⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣤⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢏⡶⠟⠁⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⡤⣤⣤⠀⡀⣠⣤⡄⠀⢀⣀⣠⢀⡄⠀⠠⠀⠀⠀⢤⣤⣤⣤⣤⡄⠀⣤⠀⠀⠄⣤⣤⡄⢀⠀⡄⠠⣠⡄⠀⠤⠠⢠⡄⠠⠀⠀⠀⠄⠀⠀⢀⠀⣀⠀⣤⠀⠀⣠⠤⣤⣤⠀⢠⣀⣤⣠
⣿⣿⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⣆⠓⣍⢿⣇⡇⣠⣽⡻⢂⠀⠀⢜⠀⠀⠀⢸⣿⣽⣯⣿⡇⠀⢸⢀⣠⣤⣴⡿⡶⢾⣶⣶⣶⣾⣧⠀⡃⠀⢸⡇⠘⠀⠿⠘⠅⠸⠇⠫⠀⠉⠀⠘⠀⠂⠹⠀⣿⣿⢛⠛⠛⠟⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢘⠧⠁⠴⡿⣽⠣⠋⣠⣿⣯⠅⠀⠀⢽⣿⢿⣿⣿⡃⢠⣾⡿⣿⠛⠛⠀⠁⠀⠈⠙⠻⢿⣿⣦⡂⢀⢸⡇⠸⠆⠿⠐⠃⠘⠃⠛⠀⠀⠀⡐⠀⠀⢈⠀⣿⡇⠀⢰⠀⠀⠸
⠛⢛⣻⣿⠽⣿⠿⠿⢿⣿⣼⣿⣿⣿⠀⡔⣼⣿⠀⣣⣤⣞⢸⣿⡿⡛⣻⠂⠀⠀⢺⣟⣛⣛⡿⣿⠟⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠘⠲⠾⣿⣦⢸⡇⢀⠀⠂⠀⠀⠀⠀⠘⠀⠄⠀⣿⠀⠀⠘⠀⣼⡇⠀⢨⣤⣤⣴
⣶⣿⣿⣿⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⢰⡾⠟⣣⠀⠑⠯⠋⢘⣭⣵⣤⣟⣃⡀⠀⠙⠛⠙⠙⢃⠃⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣶⠯⢽⡇⠐⠀⠀⠀⡀⠀⠀⠀⠀⡤⠀⠉⠀⠀⠀⠀⢳⡇⠀⠰⠀⠈⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠁⠀⢀⠞⣠⣾⣿⡋⣿⣿⣿⣿⡆⠀⠀⠀⠀⢈⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠉⠒⢰⣦⣶⣤⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠰⠾⠲⠶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢶⣿⣿⣷⣿⣿⣧⠙⢧⠀⠀⠠⢄⠀⠀⠘⣿⣿⣿⢿⣿⣿⣿⣿⠼⣿⣿⣿⣿⣧⡀⠀⠀⠙⣿⣿⣿⣿⣶⣶⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠧⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣠⡀⠀⠀⠀⠀⢩⢻⣿⣿⡏⠙⠀⠔⣴⣤⣥⣤⡄⠀⠀⣿⠉⠀⠀⠛⣿⣿⣇⢈⣉⣿⣿⣿⣿⣿⢠⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⡅⠀⣿⠀⣿⣗⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢿⣿⣿⣇⣿⣟⣿⡀⢀⡇⠸⣸⠘⣿⣿⣇⣀⣀⣾⡙⠀⣏⣻⡃⣁⠀⢸⣀⣠⣴⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⢻⣿⡟⠿⠏⠩⠀⠀⠀⠀⠈⠀⠓⠀⠿⠀⠿⠿⣶⡾⢿
⣷⣸⡟⢿⣿⣿⣿⣏⣹⣭⣿⣽⡿⣻⣽⣏⡏⣭⣭⣝⠭⣨⣭⣟⢽⣭⣯⣏⢩⣍⣩⡍⡉⣉⣿⣿⠃⣾⣿⣿⣿⡿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡗⢀⣀⣀⡀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣏⢿⣧⡀⠛⠟⢛⣿⣿⣿⣿⣿⣷⣿⡇⣿⠀⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣈⣉⣿⣆⣸⣿⣿⣿⣿⣶⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⠰⣧⣿⠿⠿⢿⠇⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣦⣿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣟⣿⣇⣿⠀⣿⣏⣿⢾⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠏⠠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⣿⣷⣶⣶⡶⢰⡾⣿⣿⣿⣷⣷⣶⣶⣦⣤⣤⣼⣿⣥⣤⣤⣄
⠿⠉⠁⠀⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣿⣛⠃⢈⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣯⣭⣝⣵⣤⣼⡗⣤⣤⡄⣮⣽⣿⣿⣿⣿⣿⣦⣭⣿⣿⣿⠟⠀⠙⣿⣿⣿⣿⣿⣿⡯⠻⠻⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿
⠀⣈⣻⣛⣛⣻⡋⠉⠉⠉⢿⣬⡉⢹⣿⣸⡇⣿⣧⡄⣼⡟⣿⠿⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣼⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⠈⢿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣯⢹⣿⣹⡿⢿⣿⣿⠛⠉⣿⡿⠿⠛⠁⢻⣦⡀⠶⢻⣿⣿⣿⣿⣿⣿⣿⡏⠘⠉⠙⠷⠂⠤⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠛⢿
⠀⠀⠈⣿⣿⣿⣿⣷⡦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⢻⡿⠖⠂⠁⠀⠀⠀⠀⢸⣿⣿⣾⣵⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠐⠒⠒⠉
⠀⠀⠀⠘⣿⣿⣷⣦⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠀⠐⠈⢿⣿⣿⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠤⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⢀⣀⡈⢿⣿⠃⠸⣿⣿⡎⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣋⣤⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⡶⠟⠁⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠟⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⣤⣤⢀⡀⣠⣤⡄⠀⢀⡀⣠⣀⡄⠀⠠⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⢤⠀⠀⠄⣤⣤⡄⢠⠀⡄⢠⢠⡄⠀⠤⠠⢠⡄⠠⠀⠄⠀⠀⠀⠀⢀⠀⣀⠀⣤⠀⠀⣠⡤⣤⣤⠀⢠⣀⣤⣠
⣿⣿⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⣖⠷⣍⣿⣇⠇⣠⣼⡻⢃⠀⠠⢱⡀⠀⠀⢸⣯⢽⣯⣿⡇⠀⢸⢀⣠⣤⣶⡿⡶⢿⣷⣶⣶⣾⣧⠀⠇⠈⢸⡇⠘⠀⠿⠐⠅⠸⠇⠫⠀⠉⠀⠘⠀⠂⢹⠀⣿⣿⢛⠛⠛⠏⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠷⠁⠴⡿⣽⠣⢏⣰⡿⣭⠅⠀⠀⢼⣿⢿⣿⣿⡃⢠⣾⡿⣿⠻⠛⠀⠁⠀⠈⠙⠻⢿⣿⣦⣆⠀⢸⡇⠸⠂⠿⠀⠃⠘⠃⠛⠀⠀⠀⡐⠀⠀⢈⠀⣿⡇⠀⢰⠀⠀⠸
⠛⢛⣿⣿⠽⣿⠿⠿⢿⣿⣼⣿⣿⣿⠀⠀⢼⣿⠀⣣⣤⣞⢸⣿⡟⡛⣻⠀⠀⠀⠺⣟⣞⣛⣟⣿⠟⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠘⠳⠾⢿⣧⣸⡇⢀⠀⠒⠀⠀⠀⠀⠘⠀⠄⠀⣿⠀⠀⠈⠀⣼⡇⠀⢈⣤⡤⣴
⣶⣿⣿⣿⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⢰⠷⠞⣡⠀⠱⠯⠏⢘⣭⣵⣤⣟⣁⡀⠀⠙⠛⠑⠘⢃⠃⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⣶⠯⢽⡇⠐⠀⠄⠀⡀⠀⠀⢀⠀⠤⠀⠉⠀⠀⠀⠀⢳⡇⠀⠸⠀⠈⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠁⠀⠀⠞⣠⣾⣿⡋⣿⣿⢿⣿⡄⠀⠀⠀⠀⢀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠉⠒⢰⠶⣶⣤⢠⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠰⠾⠶⠶⠲
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢶⣿⣿⣷⣿⣿⣧⠉⠇⠀⠀⠠⢄⠀⠀⠈⣿⣿⣿⢿⣿⣿⣿⣿⠶⣿⣿⣿⣿⣧⡀⠀⠀⠙⣿⣿⣿⣿⣶⣶⡶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠇⠀⠀⠀
⣽⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣠⡀⠀⠀⢀⠀⢨⢻⣿⣿⡏⠙⠁⠔⣴⡤⣥⣤⡄⠀⠀⢿⠉⠀⠀⠙⣿⣿⣇⢈⣩⣿⣿⣿⣿⣿⢠⣾⣷⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⡄⠀⣿⠀⣾⣇⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢽⣿⣿⣇⣿⣟⣿⡀⢀⡇⢸⣸⠘⣿⣿⣇⣀⣀⣾⡙⠀⣯⣻⣇⣁⠀⢸⣄⣤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠉⢻⣿⡟⠿⠏⠭⠀⠀⠀⠀⠀⠀⠓⠀⠿⠀⠿⠷⢶⡾⠿
⣧⣸⡟⢻⣿⣿⣿⣏⣹⣭⣿⣽⡿⣻⣿⣍⡟⣯⣭⣟⠭⣨⣭⣟⢭⣿⣭⣍⢩⣍⣩⡍⡉⣉⣝⣽⠓⣸⣿⣿⣿⡿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣗⣀⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣏⢿⣧⡀⠛⠟⢛⣿⣿⣿⣷⣿⡷⣿⡇⣿⠁⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣈⣉⣿⣆⣸⣿⣿⣿⣿⡶⠿⣿⡿⡿⣿⣿⣿⣿⣿⣿⠐⣧⣿⠿⠿⢿⠃⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣦⣿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣟⣿⣇⣿⠀⣿⣯⣿⠾⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣽⣿⢋⠤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣏⣰⣿⣿⣷⣶⣶⡶⢰⣼⣿⣿⣿⣷⣿⣶⣶⣾⣤⣤⣼⣿⣧⣤⣤⣤
⠛⠉⠀⠀⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣭⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣿⣛⠁⢈⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣯⣭⣝⣵⣤⣾⡗⣤⣤⡆⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⡿⣿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣺⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿
⠀⣈⣟⣛⣛⣻⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠟⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣼⣿⣿⣿⣿⣿⡿⣷⠀⠀⠀⡀⣠⣼⣿⣿⣿⣿⣿⣿⢻⣿⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⢹⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣯⢹⣿⣹⡿⣿⣿⣿⠛⠉⣿⡿⠿⠛⠁⢻⣮⡨⢨⢻⣿⣿⣿⣿⣿⣿⣿⡏⠸⠏⠙⠓⠂⠤⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠙⢿
⠀⠘⣿⣿⣿⣿⣿⣷⣦⠤⠈⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⢻⠿⠖⠂⠁⠀⠀⠀⠀⢸⣿⣿⣶⣵⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠐⠒⠒⠉
⠀⠀⠈⣿⣿⣿⣷⣦⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠀⠐⠈⢿⣿⣿⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠤⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⢀⣀⡈⢿⣿⠃⠸⣿⣿⡎⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣫⣤⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⡾⠟⠁⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠋⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⣤⠤⠤⠤⣤⣤⠀⢀⣠⣤⡄⠀⢀⡀⣠⢀⡄⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⢤⠀⠀⠄⡤⣤⡄⢠⠀⡄⢠⢠⡄⠀⠤⠠⢠⡄⠠⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣤⠀⠀⣠⡤⣤⣤⠀⢠⣀⣤⣠
⣿⣿⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⣖⡓⣍⢿⣇⡇⣠⣼⡻⢃⠀⠐⢵⡀⠀⠀⢸⣯⢹⣯⣿⡇⠀⢸⢀⣠⣤⣶⡿⡶⢾⣷⣶⣶⣾⣷⠀⠇⠨⢸⡇⠘⠀⠿⠘⠅⠸⠇⠫⠀⠉⠀⠘⠀⠂⢸⠀⣿⣿⢛⠛⠛⠏⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠧⠁⠴⡿⣿⠃⢋⣠⣿⣭⠍⠀⠀⢿⣿⢿⣿⣾⡃⢠⣾⡿⣿⠛⠛⠀⠁⠀⠈⠉⠻⢿⣿⣦⣆⠀⢸⡇⠸⠆⠿⠀⠃⠘⠃⠛⠀⠀⠀⡐⠀⠀⠌⠀⢿⡇⠀⢰⠀⠀⠰
⠛⢛⣿⣿⠽⣿⠿⠿⢿⣿⣸⣿⣿⣿⠀⡀⢼⣿⠀⣣⣤⣞⢸⣿⡽⡟⣻⠀⠀⠀⠻⣿⣞⣛⡟⣿⠟⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠘⠳⠾⣿⣧⣸⡇⢀⠀⠒⠀⠀⠀⠀⠘⠀⠄⠀⣿⠀⠀⠘⠀⣼⡇⠀⢈⣤⡤⣴
⣶⣿⣿⣿⣤⣿⣷⣾⣿⣿⣿⣿⣿⣿⢰⡷⠞⣡⠀⠑⠯⠏⢈⣭⣵⣤⣟⣀⠀⠀⠘⠛⠙⠘⢳⠃⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⣶⠯⢽⡇⠐⠀⡄⠀⡀⠀⠀⢀⠀⡤⠀⠈⠀⠀⠀⠀⢻⡇⠀⠰⠀⠈⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠁⠀⠠⠟⢠⣾⣿⡏⣿⣿⣿⣿⡇⠀⠀⠀⠀⢈⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠒⢰⠦⣶⣤⢠⣤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠰⠾⠶⠶⠲
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢶⣿⣿⣷⣿⣿⣦⠉⠏⠀⠀⠠⢄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠽⣿⣿⣿⣿⣧⡀⠀⠀⠘⣿⣿⣿⣿⡶⣶⡶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠧⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣠⡀⠀⠀⢀⢀⢨⢻⣿⣿⡏⠙⠀⠔⣴⠤⣥⣤⡄⠀⠀⢿⠉⠀⠀⠙⣿⣿⣏⢈⣉⣽⣿⣿⣿⣿⢠⣾⣷⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⡄⠀⣿⠀⣾⡇⠀⠀⣆
⠙⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢹⣿⣿⣇⣿⣟⣿⡀⢀⡇⢸⣸⠘⣿⣿⣇⣀⣀⣾⡙⠀⣏⣹⡃⣁⠀⢸⣀⣀⣴⣤⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠉⢻⣿⡟⠿⠯⠫⠀⠀⠀⠀⠀⠀⠓⠀⠿⠀⠿⠷⢶⡾⠿
⣧⣸⡟⢻⣿⣿⣿⣏⣹⣭⣿⣭⡿⣻⣿⣍⠟⣭⣭⣟⠍⣨⣭⣟⢽⣽⣯⣍⢩⣍⣩⡍⡉⣉⣽⣿⠓⢼⣿⣿⣿⡿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣗⣀⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣏⢿⣧⡀⠛⠟⢋⣿⣿⣿⣷⣿⡷⣿⡇⣿⠁⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣈⣿⣾⣁⣀⣈⣉⣿⣆⣸⣿⣿⣿⣿⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⠐⣧⣿⠿⠿⠿⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣦⣿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣟⣿⣇⣿⡀⣿⣏⣿⠿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣽⣿⢋⣁⣒⣲⣽⣿⣿⣿⣿⣿⣿⣏⣰⣿⣿⣷⣶⣶⡆⢶⣼⣿⣿⣿⣷⣷⣶⣶⣶⣤⣤⣼⣿⣥⣤⣤⣄
⠿⠉⠀⠠⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣭⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣿⣛⠀⢲⣌⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣯⣭⣝⣥⣤⣾⡗⣤⣤⡄⣮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⣿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿
⠀⣈⣿⣛⣛⣻⡋⠉⠉⠉⢿⣬⡉⢹⣿⣸⡇⣿⣧⡄⣼⡟⣿⠟⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣴⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⢻⣿⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⢹⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣯⢹⣿⣹⡿⣿⣿⣿⠛⠉⣿⡿⠿⠛⠁⢻⣦⡠⢘⣾⣿⣿⣿⣿⣿⣿⣿⡏⠘⠉⠉⠗⠂⠤⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠙⢿
⠀⢸⣿⣿⣿⣿⣿⣷⠦⠤⠈⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⢻⡿⠖⠂⠁⠀⠀⠀⠀⢸⣿⣿⣾⣵⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠐⠒⠒⠉
⠀⠀⣿⣿⣿⣿⣿⣦⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠀⠐⠈⢿⣿⣿⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠤⠄⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⢀⣀⡈⢿⣿⠃⠸⣿⣿⡮⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣫⣤⠀⢀⡴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⡾⠟⠁⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠘⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⣄⠤⢤⠤⣤⣤⢀⠀⣠⣤⡀⠀⢀⡀⣠⢀⡀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⣠⠀⠀⠄⡤⣤⡄⢀⠀⡀⢠⢠⡄⠀⠤⠠⢠⡄⠠⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣤⠀⠀⢠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⡆⠓⣝⢿⡆⡆⣠⣜⡻⠃⠀⠠⢐⠀⠀⠀⢸⣯⣹⣭⣹⡃⠀⢸⢀⣠⣤⣶⣿⣶⠶⣶⣶⣴⣾⣦⠀⠅⠀⢸⡇⠘⠀⠟⠘⠁⠸⠇⠋⠀⠉⠀⠘⠀⠂⠹⠀⣿⡿⢛⠛⠛⠏⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠧⠀⠴⡿⣭⠡⢋⣠⣿⣭⠅⠀⠀⢸⣿⢿⣿⣿⡃⣠⣾⣿⡿⠛⠋⠁⠁⠈⠙⠛⢿⣿⣿⣦⣂⠀⢸⡇⠸⠀⠿⠐⠁⠘⠂⠛⠀⠀⠀⡐⠀⠀⢈⠀⢿⡇⠀⢰⠀⠀⠰
⠛⢛⣛⣿⠽⣿⠿⠿⢿⣿⣸⣿⣿⣿⠀⠀⢸⣿⠀⣡⣤⣞⢸⣿⡽⡛⣻⠀⠀⠀⠻⣟⣛⣛⣻⣿⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⣽⣯⣦⢸⡇⢀⠀⠂⠀⠀⠀⠀⠘⠀⠄⠀⡯⠀⠀⠈⠀⣼⡇⠀⢀⣤⡴⣴
⣶⣿⣿⣿⣤⣿⣷⣾⣿⣿⣿⣿⣿⣿⠰⠶⠞⣡⠀⠑⠯⠋⢈⣭⣵⣤⣛⣁⠀⠀⠈⠊⠁⠈⠻⠁⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣄⠀⠀⡬⢍⣻⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢢⡇⠀⠸⠀⠈⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠖⣠⣼⣿⡋⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⠒⠢⠱⠶⣶⣤⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠰⠞⠲⠶⠰
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢶⣿⣿⣷⣿⣿⣦⠉⠆⠀⠀⠠⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⣄⠀⠀⠀⠘⣿⣿⣿⣿⡶⣶⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀
⣾⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣠⡀⠀⠀⠀⠀⣨⢻⣿⣿⡏⠉⠀⠀⣴⠤⣤⣴⡄⠀⠀⣿⠟⠉⠉⠻⣿⣿⠟⠐⠚⣿⣿⣿⣿⣷⢠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⣾⡇⠀⠀⣆
⠙⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⢿⣿⣿⣃⣿⣟⣿⡀⢀⡇⢸⣻⠘⣿⣿⣇⣀⣀⣾⡙⠀⣏⣹⣃⡀⠀⢣⠀⠀⣀⣀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⢻⣿⡟⠿⠏⠡⠀⠀⠀⠀⠀⠀⠃⠀⠿⠀⠿⠷⠶⠾⠿
⣧⣸⡿⠻⣿⣿⣿⣇⣹⣭⣿⣭⡿⣹⣯⣝⠟⣭⣭⣟⠍⣨⣭⣟⢽⣽⣭⣍⢩⣍⢩⡍⡉⣉⣝⣽⠃⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣟⢿⣧⠀⠘⠟⢋⣿⣿⣿⣷⣿⡷⣿⡇⣿⠀⣿⣧⡿⢠⣿⢸⣿⣬⣿⣸⣿⣀⣿⣾⣁⣀⣈⣉⣿⣆⣸⣿⣿⣿⣯⣉⣽⣾⣿⣿⣿⣿⣿⣿⣿⡟⠸⣧⣿⠿⠿⠿⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣦⣿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣟⣿⣇⣿⠀⣿⣏⣿⠾⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⠋⣉⡯⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣷⣶⣶⠐⣷⣼⣿⣿⣿⣷⣷⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣄
⠟⠉⠀⠠⣼⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣭⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣦⣙⣺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣿⡃⠈⢂⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣇⣿⣿⣯⣭⣝⣥⣤⣤⡖⣤⣤⡄⣮⣽⣿⣿⣿⣿⣿⣦⣭⣽⡿⣿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢠⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿
⠀⣈⣿⣛⣛⣻⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠟⣿⣿⣿⣿⣿⣼⣧⣶⣤⣤⣴⣿⣿⣿⣿⣿⡿⣇⠀⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⢻⣿⣿⠃⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⢹⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣻⣿⣿⠛⠉⣿⡿⠟⠛⠁⢿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⠉⠒⠢⠤⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠙⢿
⡀⢸⣿⣿⣿⣿⣿⣷⣦⠤⠈⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⢻⠿⠖⠂⠁⠀⠀⠀⠀⢸⣿⣿⣦⣄⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⣤⣤⣀⡀⠀⠀⠀⠁⠀⠐⠒⠒⠉
⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠀⠐⠙⢿⣿⣿⡇⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠳⠤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⢀⣀⠈⢿⣿⠃⠸⣿⣿⡎⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣋⣤⠀⢀⡴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠧⡾⠟⠁⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣚⣀⣀
⠛⠖⠲⣶⠏⢶⠌⠱⠷⠶⠆⠻⠿⠟⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠘⠿⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⡄⡤⠤⢤⣤⣤⢀⣀⣠⣤⡀⠀⢀⡀⣠⣠⡄⠀⠠⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⣤⠀⢀⠄⡤⣤⡄⢀⠀⡀⠠⢤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⢀⠀⣀⠀⣤⠀⠀⣠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⣖⠓⣝⢿⡆⡆⣠⣜⡻⢓⠀⠀⢔⠀⠀⠀⣸⣿⢿⣯⣽⠂⠀⣹⢀⣠⣤⣶⣷⣶⣶⣶⣦⣴⣻⣮⠀⠅⠠⢸⡇⠘⠀⠿⠘⠅⠸⠇⠋⠀⠉⠀⠘⠀⠂⢸⠀⣿⡿⢛⠛⠛⠏⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠧⠀⠴⡿⣭⠣⢋⣰⣿⣭⠅⠀⠀⢼⣿⢿⣿⣿⡃⣠⣿⣿⠿⠛⠟⠁⠁⠈⠛⠿⢿⣿⣿⣦⡂⠀⢸⡇⠸⠂⠿⠐⠁⠘⠃⠛⠀⠀⠀⡐⠀⠀⢈⠀⣿⡇⠀⢴⠀⠀⠸
⠛⢛⣻⣿⠽⣿⠿⠿⢿⣿⣼⣿⣿⣿⠀⠀⣼⣿⠀⣁⣤⣞⢸⣿⡽⠛⣻⠀⠀⠀⢻⣟⣛⣛⣻⣿⠟⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣽⣿⣦⢸⡇⢀⠀⡂⠀⠀⠀⠀⠘⠀⠄⠀⡿⠀⠀⠘⠀⣼⡇⠀⢠⣤⡴⣴
⣶⣿⣿⣿⣤⣿⣷⣾⣿⣿⣿⣿⣿⣿⢰⠶⠚⣡⠀⠑⠷⠋⢘⣭⣵⣤⣟⣁⠀⠀⠈⠋⠉⠙⡹⠁⠀⠀⠀⣀⣠⣶⣶⣿⣿⣿⣷⣦⣄⠀⠀⣍⣍⣺⠇⠐⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢹⡇⠀⠸⠀⠈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠁⠀⠀⠟⣠⣼⣿⡋⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠁⠒⠬⠰⠶⣶⣤⢠⣤⡐⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠰⠞⠲⠶⠲
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢶⣿⣿⣷⣿⣿⣦⠉⠇⠀⠀⠠⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣶⣶⡶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠧⠀⠀⠀
⣽⣿⣿⣿⡛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣠⡀⠀⠀⠀⠀⣨⢻⣿⣿⡏⠙⠀⠄⣴⠤⣤⣴⡀⠀⠘⣿⠿⠛⠛⢿⣿⣿⠟⠩⠿⣿⣿⣿⣿⣦⢀⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⣾⡇⠀⠀⣂
⠙⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣇⣿⣟⣿⡀⢀⡇⢸⢾⠘⣿⣿⣇⣀⣀⣾⡙⢀⣏⣹⣃⡀⠀⣇⠀⠀⢀⢀⣿⣿⣦⣔⣾⣿⣿⣿⣿⣿⣿⣿⡿⠙⠉⢻⣿⡟⠿⠏⠧⠀⠀⠀⠀⠀⠀⠃⠀⠿⠀⠿⠷⠶⠾⠿
⣧⣸⣿⠻⣿⣿⣿⣏⣹⣭⣿⣽⡿⣻⣯⣝⠏⣭⣭⣟⠁⣨⣽⣟⢿⣽⣯⣍⢩⣍⣩⡍⡉⣉⣝⣿⠂⣿⣿⣯⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣟⢿⣧⠀⠘⠟⢋⣿⣿⣿⣷⣿⡷⣿⡇⣿⠀⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣈⣙⣿⣆⣹⣿⣿⣟⣍⢙⣫⣶⣿⣿⣿⣿⣿⣿⣿⡏⢸⣧⣿⠿⠿⠿⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣦⣿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣇⣿⠀⣿⣿⣿⠾⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠛⣛⣛⡿⣯⣽⣿⣿⣿⣿⡇⣼⣿⣿⣷⣶⡆⠘⢶⣼⣿⣿⣿⣷⣷⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣤
⠟⠉⠀⠠⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣖⡲⠷⣶⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣀⣈⣿⡃⠀⢈⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣧⣿⣿⣯⣭⣝⣴⣤⣼⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⡿⣿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠇⢶⣼⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿
⠀⣌⣿⣛⣛⣿⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠟⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣴⣿⣿⣿⣿⣿⡿⣇⠀⠉⠙⠛⢛⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⢻⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣿⣿⣿⠛⠉⣿⡿⠿⠛⠁⢿⣦⡀⡒⡰⣿⣿⣿⣿⣿⣿⣿⡇⠸⡉⠙⠒⠠⠄⣀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠙⢿
⡀⢸⣿⣿⣿⣿⣿⣷⡦⠤⠈⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⢻⡿⠖⠂⠁⠀⠀⠀⠀⢸⣿⣿⣦⣄⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⣤⣤⣀⠀⠀⠀⠀⠁⠀⠐⠒⠒⠋
⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠟⠉⠁⠐⠙⢿⣿⣿⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⢀⣀⠘⣿⣿⠃⠸⣿⣿⡎⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣋⡤⠀⢀⡴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠃⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠧⡶⠟⠁⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠘⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⡄⡤⠤⠤⣤⣤⠀⠀⣠⡤⡀⠀⢀⡀⣠⣀⡄⠀⠠⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⣤⠀⢀⠄⡤⣤⡄⢀⠀⡀⢠⢠⡄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⢀⠀⣀⠀⣤⠀⠀⢠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⡖⠖⣝⢿⣆⠆⣠⣼⡻⢃⠀⠀⢔⡀⠀⠀⢸⣿⣿⣭⣻⠆⠀⢹⢀⣠⣤⣶⣿⣶⣶⣶⣦⣴⣾⣮⠀⠅⠀⢸⡇⠘⠀⠿⠘⠁⠸⠃⠋⠀⠉⠀⠘⠀⠂⢹⠀⣿⡿⢛⠛⠛⠏⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠧⠀⠴⡿⣽⠣⢋⣰⣿⣭⠅⠀⠀⢾⣿⢿⣿⣿⡂⣠⣿⣿⠿⠛⠟⠁⠁⠈⠛⠿⢿⣿⣿⣦⡂⠀⢸⡇⠸⠀⠿⠐⠁⠘⠂⠛⠀⠀⠀⡐⠀⠀⢈⠀⣿⡇⠀⢰⠀⠀⢸
⠛⢛⣻⣿⠽⣿⠿⠿⢿⣿⣸⣿⣿⣿⠀⠐⢾⣿⠐⣁⣴⣞⢸⣿⡽⠛⣻⠁⠀⠀⢻⣟⣟⣛⣻⣿⠟⠋⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣽⣿⣦⢸⡇⢀⠀⠂⠀⠀⠀⠀⠘⠀⠄⠀⡿⠀⠀⠈⠀⣸⡇⠀⢠⣤⡴⣴
⣶⣿⣿⣿⣤⣿⣷⣾⣿⣿⣿⣿⣿⣿⢰⠶⠛⣡⠀⠑⠯⠋⢈⣭⣵⣤⣟⣁⠀⠀⠈⠋⠁⠙⠺⠁⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣄⠀⠀⣬⣙⣺⡇⠐⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢳⡇⠀⠰⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠟⣠⣾⣿⡋⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠐⠒⠬⠰⠶⣶⣤⢠⣤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠰⠞⠲⠖⠰
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢶⣿⣿⣷⣿⣿⣦⠉⠏⠀⠀⠠⢄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣶⣶⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠇⠀⠀⠀
⣿⣿⣿⣿⡛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣠⡀⠀⠀⠀⠀⣨⢻⣿⣿⡏⠙⠀⠀⣴⠤⣥⣴⡀⠀⠘⣿⠿⠛⠛⢿⣿⣿⠟⠩⠿⣯⣿⣿⣿⣦⢀⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⣿⡇⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣇⣿⣟⣿⡀⢀⡇⢸⣸⠘⣿⣿⣇⣀⣀⣾⡙⠀⣏⣹⣃⡀⠀⣇⠀⠀⠀⢀⣿⣿⣦⣔⣾⣿⣿⣿⣿⣿⣿⣿⡿⠙⠉⢻⣿⡟⠿⠏⠧⠀⠀⠀⠀⠀⠀⠃⠀⠿⠀⠿⠷⢶⠾⠿
⣧⣸⣿⠛⢿⣿⣿⣇⣹⣭⣿⣭⡿⣻⣯⣝⠟⣭⣭⣟⠁⣩⣭⣟⢿⣿⣿⣍⢩⣍⢩⡍⡉⣉⣝⣟⠂⣿⣾⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣟⢿⣿⠀⠈⠏⢋⣿⣿⣿⣷⣿⡷⣿⡇⣿⠀⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣈⣙⣿⣆⣹⣿⣿⣟⣏⢙⣫⣶⣿⣿⣾⣿⣿⣿⣿⡏⢸⣧⣿⠿⠿⠟⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣦⣿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣟⣿⣇⣿⠀⣿⣏⣿⢾⣿⢸⣿⢸⣿⣽⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠛⣛⣻⡿⢿⣽⣿⣿⣿⣿⣇⢼⣿⣿⣷⣶⡆⢸⢲⣼⣿⣿⣿⣷⣷⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣤
⠛⠉⡀⠠⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣄⠬⢥⢴⣿⣿⣿⣿⣿⣿⣿⣏⢼⣿⣀⣈⣿⠃⠀⢈⣋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣇⣿⣿⣯⣭⣝⣴⣤⣬⡗⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⡿⠛⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠱⢧⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿
⠀⣌⣿⣛⣛⣻⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡟⣿⠟⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣴⣿⣿⣿⣿⣿⡿⡇⠙⠛⠻⠛⠛⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⢻⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣻⣿⣿⠛⠉⣽⣿⠿⠛⠁⣿⣄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠨⠈⠙⠒⠠⠄⣀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠙⣷
⡀⢸⣿⣿⣿⣿⣿⣷⠦⠤⠈⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⢻⠿⠖⠂⠁⠀⠀⠀⠀⢸⣿⣿⣦⣀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣶⣤⣄⣀⠀⠀⠀⠀⠁⠀⠐⠒⠒⠉
⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⠁⠐⠙⣿⣿⣿⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠲⠤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⡀⠘⣿⣿⠃⠸⣿⣿⡎⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢋⣤⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠿⠿⠇⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢇⣴⠟⠁⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠋⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠘⠿⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⣄⡤⠤⡤⣤⣤⠀⠀⢠⣤⡀⠀⢀⡀⣠⣀⡄⠀⠠⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⣤⠀⢀⠄⡤⣤⡄⢀⠀⡄⢠⣠⠄⠀⠤⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⣤⠀⠀⣠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⣆⠗⣝⣿⣆⡇⣠⣼⡻⢃⠀⠠⣔⡀⠀⠀⣽⣿⣿⣯⣻⠁⠀⣿⢀⣠⣤⣶⣷⣶⠶⣶⣦⣴⣻⣮⠀⠇⠨⢸⡇⠘⠀⠿⠘⠁⠸⠇⠋⠀⠉⠀⠘⠀⠂⢹⠀⣿⡿⢛⠛⠛⠏⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢘⢧⠡⠴⣿⣽⠣⢋⣴⣿⣯⠅⠀⠀⢿⣿⢿⣿⣿⠂⣠⣿⣿⡿⠛⠛⠀⠁⠈⠙⠻⢿⣿⣿⣦⡂⠀⢸⡇⠸⠂⠿⠘⠁⠘⠃⠻⠀⠀⠀⡑⠀⠀⢨⠁⣿⡇⠀⢰⠀⠀⢸
⠛⢛⣛⣿⠽⣿⠿⠿⢿⣿⣸⣿⣿⣿⠁⡔⢾⣿⠀⣁⣤⣞⢸⣿⡽⡛⣻⠁⠀⠀⢻⣿⣛⣛⣻⡿⠟⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⢭⣽⣿⣦⢸⡇⠀⠀⡂⠀⠀⠀⠀⠘⠀⠄⠀⣿⠀⠀⠈⠀⣾⡇⠀⢠⣤⡴⣴
⣶⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡷⠞⣡⠀⠱⠿⠏⢈⣭⣵⣤⣟⣁⠀⠀⠙⠋⠙⠙⡹⠁⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣷⣶⣄⠀⠀⣭⣍⣺⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠁⠀⠀⠀⠀⢳⡇⠀⠰⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠰⠟⣠⣾⣿⡋⣿⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⠒⠬⠰⠶⣶⣦⢠⣤⡒⠀⠐⠀⠀⠀⠁⠀⠀⠠⠀⠁⠀⠰⠟⠲⠶⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢶⣿⣿⣷⣿⣿⣦⠉⢋⠀⠀⠠⢄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠇⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣤⡀⠀⠀⠀⠀⣨⢻⣿⣿⡏⠉⠀⠔⣴⠤⣥⣴⡀⠀⠘⣿⠟⠋⠛⢿⣿⣿⠏⠱⠚⣿⣿⣿⣿⣦⢠⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⡄⠀⣿⠀⣿⡇⠀⠀⣅
⠛⢿⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣇⣿⣟⣿⡀⢠⡇⢸⣿⠘⣿⣿⣇⣀⣀⣾⡙⢀⣏⣹⣃⡀⠀⣇⠀⠀⡀⢀⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠉⢻⣿⡟⠿⠏⠥⠐⠀⠀⠀⠀⠀⠃⠀⠿⠀⠿⠷⠶⠿⠿
⣧⣸⣿⠛⢿⣿⣿⣇⣹⣭⣿⣭⡿⣻⣥⣝⡟⣭⣭⣟⠁⣩⣽⣟⢿⣿⣯⣍⢩⣭⣩⡍⡉⣉⣽⣟⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⡀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣟⢿⣿⠀⠈⠟⢋⣿⣿⣿⣷⣿⡷⣿⡇⣿⠀⣿⣧⡿⢀⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣈⣉⣿⣆⣹⣿⣿⣯⣯⣉⣽⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣧⣿⠿⠿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣮⣿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣇⣿⠀⣿⣏⣿⠾⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⢋⣙⣿⠿⢻⣭⣿⣿⣿⣿⣇⡼⣿⣿⣷⣶⡂⢶⢲⣼⣿⣿⣿⣷⣷⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣤
⠛⠉⡀⠠⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠯⣴⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⠻⣷⣿⣿⣿⣿⣿⣿⣴⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣟⠠⣯⣀⣈⣿⠀⠁⢈⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣧⣿⣿⣯⣭⣝⣴⣤⣼⡿⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⡿⠛⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡏⠴⢦⣼⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿
⠀⣬⣿⣛⣛⣻⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠟⣿⣿⣿⣿⣿⣼⣧⣶⣤⣤⣼⣿⣿⣿⣿⣿⡿⡇⠉⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⢻⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣻⣿⣿⠛⠉⣿⡿⠿⠛⠀⣿⣄⢄⣀⣠⣾⣿⣿⣿⣿⣿⣿⠇⠸⠈⠙⠒⠠⠄⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠉⠙⣷
⡀⢺⣿⣿⣿⣿⣿⣷⠦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⢻⠿⠖⠂⠁⠀⠀⠀⠀⢻⣿⣷⣮⣠⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣶⣤⣄⣀⠀⠀⠀⠀⠁⠀⠐⠒⠒⠋
⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⠁⠂⠙⣿⣿⣿⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⢀⡀⠘⣿⣿⠁⠸⣿⣿⡎⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣃⡤⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢣⣶⠟⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠟⠖⠲⣶⠏⢶⠌⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⠀⠀⠀⠘⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⣤⠤⠤⢤⣤⣤⠀⠀⣠⣤⡀⠀⠀⡀⣠⢀⡄⠀⠠⠀⠀⠀⣤⣤⣤⣤⣤⠄⠀⣤⠀⢀⠀⡤⣤⡀⢀⠀⡀⢠⣠⠄⠀⠤⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⣤⠀⠀⣠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⣆⠗⣝⢿⣖⡇⣠⣼⡻⢂⠀⠀⣔⡀⠀⠀⢻⣿⣽⣯⣻⠂⠀⣿⣀⣠⣤⣶⡿⡶⠶⣶⣶⣴⣾⡯⠀⠇⠠⢸⡇⠘⠀⠿⠘⠁⠸⠃⠋⠀⠉⠀⡘⠀⠂⢹⠀⣿⡿⠛⠛⠛⠯⢉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢈⢧⠁⠴⣿⣽⠣⢋⣰⣿⣯⠁⠀⠀⢿⣿⢿⣿⣿⠂⣤⣿⣿⡿⠛⠋⠀⠀⠈⠙⠛⠿⣿⣿⣦⡂⠀⢸⡇⠸⠀⠿⠘⠁⠘⠂⠟⠀⠀⠀⡑⠀⠀⢈⠀⣿⡇⠀⢰⠀⠀⢸
⠛⢛⣛⣿⠽⣿⠿⠿⢿⣿⣸⣿⣿⣿⠀⡔⢾⣿⠐⣁⣤⣞⢸⣿⡝⠟⣻⠁⠀⠀⠻⣿⡿⣟⣻⡿⠛⠉⠁⠁⠀⠀⠀⠀⡀⡀⠀⠀⠸⠶⣾⣿⣦⢸⡇⠀⠀⡂⠀⠀⠀⠀⠘⠀⠄⠀⡿⠀⠀⠈⠀⣾⡇⠀⢠⣤⡴⣴
⣶⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠷⠟⣡⠀⠑⠧⠋⢈⣭⣵⣤⣟⣁⠀⠀⠙⠛⠉⠙⡸⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣆⠀⠀⠮⢯⣾⠇⠀⠀⡀⠀⡀⠀⠀⠀⠀⠤⠀⠁⠀⠀⠀⠀⢻⡇⠀⠠⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠁⠀⠀⠰⠟⣠⣾⣿⡋⣟⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⠐⠊⠰⠶⣶⣶⢠⣴⡐⠂⠒⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠰⠟⠲⠖⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢶⣿⣿⣷⣿⣿⣦⠉⠃⠀⠀⠠⢄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⣄⠀⠀⠀⠘⣿⣿⣿⣿⣶⣶⡶⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀⠇⠀⠀⠀
⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣠⡀⠀⠀⠀⠀⣬⢻⣿⣿⡏⠉⠀⠄⣴⢤⣥⣴⡀⠀⠘⡿⠛⠉⠉⠻⣿⣿⠏⠐⠛⣿⣿⣿⣿⣧⢠⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⡄⠀⣿⠀⣿⡇⠀⠀⣇
⠛⢻⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⢠⡇⢸⣿⠘⣿⣿⣇⣀⣀⣾⡙⢀⣏⣹⣃⡀⠀⣧⠀⢀⣀⣠⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠉⢻⣿⡟⠿⠏⠇⠐⠀⠀⠀⠀⠀⠃⠀⠿⠀⠿⠷⠷⠿⠿
⣧⣸⣿⠟⢿⣿⣿⣇⣹⣭⣿⣭⡿⣻⣭⣞⡟⣭⣭⣏⠁⣩⣽⣟⢿⣿⣽⣍⢩⣍⢩⡍⡉⣩⣭⣝⠣⣿⣿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⡀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣟⢿⣿⠀⠀⠟⢋⣿⣿⣿⣷⣿⡷⣿⡇⣿⠁⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣈⣙⣿⣆⣹⣿⣿⣯⣦⣨⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣧⣿⠿⠿⠇⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣮⣿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣟⣿⣇⣿⡃⣿⣟⣿⢿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⢉⡬⠽⢛⣻⣾⣿⣿⣿⣿⣇⣼⢿⣿⣷⣶⠂⡆⢲⣼⣿⣿⣿⣷⣷⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣤
⠛⠉⡀⠠⣼⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⡿⣤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣦⡒⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣀⣈⣟⠀⠀⢈⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⢀⣴⣿⣿⣿⣇⣿⣿⣯⣭⣝⣴⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⡋⠼⢦⣾⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿
⠀⣌⣿⣛⣛⣛⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠿⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣴⣿⣿⣿⣿⣿⡿⡇⠈⠉⠛⠛⢉⣹⣿⣿⣿⣿⣿⡿⣿⣿⣿⠃⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣜
⠀⢻⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡟⣻⣿⣿⠛⠉⣽⡿⠟⠋⠀⣿⣄⡄⠀⢴⣿⣿⣿⣿⣿⣿⣿⠇⠘⠈⠙⠒⠢⠄⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠙⣷
⡀⢺⣿⣿⣿⣿⣿⣷⠦⠤⠈⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⢻⠿⠖⠂⠁⠀⠀⠀⠀⢻⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⣤⣤⣀⡀⠀⠀⠀⠉⠀⠐⠒⠚⠋
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⠀⠒⠙⣿⣿⣿⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⢀⣀⠘⣿⣿⠀⠸⣿⣿⡎⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣃⡤⠀⢀⡴⣿⣿⣿⣿⡿⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠣⡶⠟⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⠀⠀⠀⠘⠿⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⠤⢤⣤⡤⢀⣠⣤⣤⣀⠀⢀⣀⣤⣀⡄⠀⠤⠀⠀⠀⣤⣤⣤⣤⣤⠄⠀⣤⠀⢠⠀⡤⣤⡄⢀⠀⡀⠠⢤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⣤⠀⠀⢠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⡶⡒⣝⢿⣶⡇⣰⣼⡻⢂⠀⠀⣔⡀⠀⠀⣿⣿⣽⣯⣽⠀⠀⣿⣀⣤⣤⣶⡿⡶⢿⣷⣷⣾⣿⡯⠀⠇⠨⢸⡇⠸⠀⠿⠘⠁⠸⠃⠋⠀⠉⠀⠙⠀⠂⢹⠀⣿⡟⠛⢛⠙⠫⢉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⢧⠠⠴⡿⣽⠡⢋⣴⣿⣭⡅⠀⠀⣿⣿⢿⣿⣿⠂⣤⣿⡿⡟⠙⠋⠀⠀⠈⠈⠛⠻⢿⣿⣦⣂⢀⢸⡇⠸⠀⠿⠘⠃⠘⠃⠻⠀⠀⠀⡑⠀⠀⢈⠀⣿⡇⠀⢤⠀⠀⢸
⠛⢛⣿⣿⠽⣿⠿⠿⢿⣿⣼⣿⣿⣿⠀⡔⢼⣿⠐⣥⣴⣞⢸⣿⣯⠛⣻⠁⠀⠀⢻⣟⣟⣛⣿⡿⠛⠉⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠐⠲⠾⣿⣦⢸⡇⠀⠀⠒⠀⠀⠀⠀⠚⠀⠄⠀⡷⠀⠀⠘⠀⣾⡇⠀⢠⣤⣶⣼
⣾⣿⣿⣿⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⠸⡿⢛⣱⠀⠑⠧⠍⢨⣭⣤⣤⣯⣃⡀⠀⠘⠟⠙⠉⡹⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⡦⠯⢽⠇⠐⠀⡀⠠⡀⠀⠀⠀⠀⠦⠀⠁⠀⠀⠀⠀⢷⡇⠀⠌⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⡀⠀⢰⠟⣠⢾⣿⡉⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠂⠰⠶⣶⣶⢢⣶⡒⠂⠒⠀⠀⠀⠁⠀⠀⠰⠀⠉⠀⠰⠟⠲⠶⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⢶⣿⣿⣿⣿⣿⣧⠉⢗⠀⠀⠰⢄⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⡩⣿⣿⣿⣿⣆⠀⠀⠀⠙⣿⣿⣿⣿⣷⣶⡶⡆⠀⠀⠀⠀⠀⠀⠠⠀⡀⠄⢀⠇⠀⠀⠀
⣿⣿⣿⣿⡛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡇⣤⣤⠀⠀⠀⠀⠀⣼⢻⣿⣿⡏⠙⠀⢔⣴⢤⣥⣶⠁⠀⠀⡿⠋⠁⠉⠻⣿⣿⠏⠈⣉⣿⣿⣿⣿⣷⢠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⡀⠀⣿⠀⣿⡧⠀⣤⡄
⠛⣿⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⢠⡇⢸⣿⠘⣿⣿⣇⣀⣀⣾⡙⢀⣯⣽⣃⣀⠀⣿⣀⣀⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠉⢻⣿⡟⠿⠇⠧⠐⠀⠀⠐⠀⠀⠃⠀⠿⠰⠿⠷⣷⣄⠀
⣧⣾⣿⡟⢻⣿⣿⣇⣹⣭⣿⣽⡿⣫⣴⣟⡟⣭⣭⣏⠀⣩⣽⣟⢿⣽⣭⣍⢩⣭⣩⡍⡉⣉⣭⣝⠣⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⡀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀
⣟⢿⣿⠀⠀⠙⢋⣿⣿⣿⣿⣿⡷⣿⡷⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣆⣹⣿⣿⣷⣷⣴⣾⣿⣿⡿⢿⣿⣿⣿⣿⡇⢸⣧⣿⠿⠿⠃⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀
⣿⣮⡿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣇⣿⣇⣿⣏⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠋⠠⠶⣖⣯⣿⣿⣿⣿⣿⣿⣇⣼⡿⢿⣵⡶⢸⠆⢲⣼⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣤
⠛⠉⣀⠠⣼⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⠿⣧⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣍⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣚⣈⡇⠈⠀⢊⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⢀⣀⣴⣿⣿⣿⣇⣿⣿⣯⣭⣍⣶⣤⣽⡟⣤⣤⡄⣮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⠃⠷⢢⣼⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠻⠿⢿⠿⣿⡿⣿
⠀⣼⣿⣻⣛⣻⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠟⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⡟⡇⠀⠀⠉⠉⣨⣽⣿⣿⣿⣿⣿⡿⣷⣿⣿⠃⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⡟
⠀⢿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡟⣿⣿⣿⠛⠉⣿⡿⠟⠋⠀⣿⣦⣧⡘⠺⣿⣿⣿⣿⣿⣿⣿⠃⠹⠉⠙⠒⠢⠤⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠁⠀⠀
⡀⢺⣿⣿⣿⣿⣿⣷⡦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠘⣻⠿⠒⠀⠁⠀⠀⠀⠀⢻⣿⣿⣮⣬⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢶⣤⣤⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠉⠀⠐⠙⣿⣿⣿⠇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⢀⣀⠘⣿⣿⠀⠸⣿⣿⡎⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣣⡤⠀⣀⣼⣿⣿⣿⣿⡏⠀⠀⠻⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡣⡾⠏⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠶⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠸⠿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⠤⣤⣤⣤⢀⣀⣤⣤⣀⠀⢀⣀⣤⣠⡄⠀⠤⠄⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⡤⣤⡄⢀⠀⡀⠠⣤⠄⠀⠤⠠⢠⡄⠠⠀⠀⠀⡀⢀⡀⣀⠀⣀⠀⣤⠀⠀⢠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⣶⡟⣝⢿⣷⡆⣠⣽⡻⢓⠀⠀⣕⡀⠀⠀⣿⣿⣽⣯⣽⠀⠀⣿⣀⣤⣦⣶⡿⡶⢾⣶⣶⣾⣿⡯⠀⠅⠨⢸⡇⠺⠀⠿⠘⠁⠸⠃⠋⠀⠉⠀⠙⠀⠂⢹⠀⣿⡿⠛⠛⠛⠏⢙
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢉⢧⠠⠴⣿⣽⠣⢋⣴⣿⣭⡅⠀⠀⣿⣿⢿⣿⣿⡀⣤⣿⡿⡟⠛⠋⠀⠀⠈⠉⠛⠻⣿⣿⣶⣂⠀⢸⡇⠸⠀⠿⠘⠁⠘⠃⠟⠀⠀⠀⡑⠀⠀⢌⠀⣿⡇⠀⢴⠀⠀⢸
⠛⣛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠃⡔⣾⣿⠐⣥⣴⣞⢸⣿⣯⠿⣿⡁⠀⠀⢻⣿⣟⣟⣿⡿⠛⠉⠁⠀⠀⠀⠀⣀⣀⣀⡀⠀⠐⠶⢾⣿⣦⢸⡇⠀⠀⠂⠀⠀⠀⠀⠚⠀⠄⠀⡿⠀⠀⠘⠀⣾⡇⠀⢠⣤⣶⣼
⣾⣿⣿⣿⣤⣿⣿⣾⣿⣿⣽⣿⣿⣿⢸⡿⠛⣱⠀⠙⠷⠍⢨⣭⣴⣤⣯⣃⡀⠀⠉⠛⠉⠉⡻⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⢐⡮⠯⣽⠇⠐⠀⠀⠠⡀⠀⠀⠀⠀⠦⠀⠁⠀⠀⠀⠀⣿⡇⠀⠔⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠰⠟⣠⣾⣿⡋⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠑⠒⢰⠶⣶⣶⢲⣶⡒⠂⠒⠀⠀⠀⠀⠀⠀⠰⠀⠉⠀⠰⠟⠲⣶⣺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠄⠀⢶⣿⣿⣷⣿⣿⣦⠉⠇⠀⠀⠰⢤⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣆⠀⠀⠀⠙⣿⣿⣿⣿⣷⣶⡶⡆⠀⠀⠀⠀⠀⠀⠠⠀⡀⠄⠀⠀⠀⠙⠻
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡆⣤⣤⡀⠀⠀⠀⠀⣼⢻⣿⣿⡏⠙⠀⡔⣼⢤⣧⣴⡀⠀⠈⡿⠛⠉⠉⠻⣿⣿⠏⠘⢛⣿⣿⣿⣿⣷⢠⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⢀⠀⡄⠀⣿⠀⡿⠶⠆⠀⠀
⠛⣿⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⢠⡇⢸⣿⠘⣿⣿⣇⣀⣀⣿⡝⢀⣯⣽⣃⣀⠀⣯⣀⣀⣄⣠⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠉⢻⣿⡟⠿⠇⠇⠐⠀⠀⠘⠈⠀⠃⠀⠿⠀⠿⠤⠤⠀⠀
⣧⣾⣿⡟⠹⣿⣿⣏⣹⣭⣿⣽⡿⣫⣴⣟⡟⣭⣯⣏⠈⣹⣽⣟⢿⣽⣿⣍⢩⣭⣩⡍⡉⣉⣭⣽⠣⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀
⣟⣿⣿⠀⠀⠹⢋⣿⣿⣿⣷⣿⣷⣿⡷⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣆⣹⣿⣿⣷⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣧⣿⠿⠟⠁⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀
⣿⣮⡿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣗⣿⣇⣿⣇⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⠋⠡⠬⢿⣻⣿⣾⣿⣿⣿⣿⣇⣼⣿⣿⣷⡆⢷⢆⢶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣾⣿⣤⣤⣄⣀
⠛⠉⡀⠸⣼⣿⣿⡿⣿⣿⣽⣿⣿⣿⡿⠿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣘⣉⡁⠀⡄⢊⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⢀⣀⣴⣿⣿⣿⣇⣿⣿⣯⣭⣏⣶⣤⣽⡟⣤⣤⡄⢯⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠈⣿⠣⠷⢠⣿⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⠋⠀
⠀⣬⣿⣻⣛⣟⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠟⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣼⣿⣿⣿⣿⣿⡟⡇⡀⠈⠉⠉⣩⣿⣿⣿⣿⣿⣿⡿⣷⣼⣿⠃⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠋⠀⠀
⠀⢿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡟⣿⣿⣿⠛⠉⣿⡿⠟⠋⠀⣿⣮⣤⡽⢾⣿⣿⣿⣿⣿⣿⣿⠃⠹⠈⠙⠒⠢⠄⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⡀⢺⣿⣿⣿⣿⣿⣷⡦⠤⠈⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⣻⠿⠒⠀⠁⠀⠀⠀⠀⢻⣿⣿⣮⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣶⣤⣤⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠉⠀⠐⠙⣿⣿⣿⠇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⢀⣀⠘⣿⣿⠀⠸⣿⣿⡎⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣣⡤⠀⣀⣼⣿⣿⣿⣿⡏⠀⠀⠿⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣣⡾⠟⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠸⠿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⠤⢤⣤⣤⢠⡀⣤⣤⣀⠀⢀⣀⣤⣠⡄⠀⠤⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⡤⣤⡄⢀⠀⡀⠠⣤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⡀⣀⠀⣀⠀⣤⠀⠀⢠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣻⣿⣿⣿⣿⣻⢛⣿⣿⣿⡶⣏⣝⢿⣷⡆⣠⣿⡻⢓⠀⠐⣕⡀⠀⠀⣿⣿⣿⣯⣽⠀⠀⣿⣀⣤⣤⣶⡿⡶⢶⣶⣷⣼⣿⣯⠠⠇⠨⢸⡇⠪⠀⠿⠸⠁⠸⠃⠋⠀⠉⠀⠛⠀⠂⢹⠀⣿⡟⠻⠛⠙⠫⢉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢘⢷⠠⠴⣿⣽⠣⢋⣴⣿⣯⡅⠀⠀⣿⣿⢿⣿⣿⠀⣤⣿⣿⡟⠛⠋⠀⠀⠈⠙⠛⢿⣿⣿⣶⡂⢀⢸⡇⠼⠀⠿⠘⠃⠘⠃⠟⠀⠀⠀⡑⠀⠀⢌⠀⣿⡇⠀⢴⠀⠀⢸
⠛⣛⣻⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠃⡔⣼⣿⠐⣥⣴⣞⢸⣿⣭⡛⣻⠁⠀⠀⢻⣿⣿⣛⣿⡿⠛⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⣿⣿⣦⢸⡇⠄⠀⠂⠀⠀⠀⠀⠚⠀⠄⠀⡧⠀⠀⠘⠀⣾⡇⠀⢠⣤⣶⣼
⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⢛⣱⠀⠝⠿⠏⢨⣭⣴⣬⣯⣃⡀⠀⠙⠛⠉⠙⡻⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣄⠀⢰⡯⢯⣾⠇⠐⠀⡀⢠⡀⠀⠀⠄⠀⠦⠀⠅⠀⠀⠀⠀⢿⡇⠀⠜⠀⠈⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⡀⠀⢰⠟⣠⣾⣿⣙⣿⣿⣿⣿⡄⠀⠀⠀⠀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⠒⠪⡰⠶⣶⣶⢢⣶⡒⠒⠒⠀⠀⠀⠁⠀⠀⠰⠀⠉⠀⠰⣿⡷⠶⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠄⠠⢶⣿⣿⣿⣿⣿⣧⠉⠗⠂⠀⠰⢤⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣄⠀⠀⠀⠹⣿⣿⣿⣿⣷⣶⡶⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠛⠀⠀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡂⣤⣤⡀⠀⠀⠀⠀⣼⢻⣿⣿⡏⠙⠄⢔⣾⢤⣥⣴⠀⠀⠘⡿⠛⠉⠙⢿⣿⣿⠏⠐⠛⣿⣿⣿⣿⣧⣠⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⡄⠀⡿⠛⠇⠀⠀⠀⠀
⠛⣿⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⢠⡇⢸⣿⠘⣿⣿⣇⣀⣀⣾⡙⢀⣏⣽⣁⡀⠀⣿⠀⠀⣀⣠⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠉⢻⣿⡟⠿⠟⠇⠐⠀⠀⠘⠀⠀⠃⠀⠛⠒⠂⠀⠀⠀⠀
⣧⣿⣿⡟⠹⣿⣿⣇⣹⣭⣿⣽⡿⣫⣽⣟⡟⣯⣭⣏⠈⣹⣽⣟⣿⣿⣿⣏⢩⣭⣩⡍⡉⣉⣭⣿⠣⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣀⠀
⣟⣿⣿⠁⠀⠸⢫⣿⣿⣿⣷⣿⡗⣿⡷⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣆⣹⣿⣿⣯⣧⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣧⡿⠿⠟⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⢐⣿⣿
⣿⣮⡿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣇⣿⣇⣿⣅⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⢋⣭⠽⣟⣷⣾⣿⣿⣿⣿⣧⣼⣿⣿⣷⠆⣷⢶⢶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣾⣿⣷⡬⠟⠋
⠛⠉⡀⠸⣴⣿⣿⡿⣿⣿⣽⣿⣿⣿⡿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣶⣖⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⣻⠀⢡⡘⢊⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢀⣀⣴⣿⣿⣿⣧⣿⣿⣯⣭⣏⣶⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠹⠀⣽⠡⠦⢡⣼⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠻⠿⣿⠁⠀⠀⠀
⠀⣼⣿⣻⣛⣟⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠿⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⡟⡇⠈⠉⠛⠋⣉⣿⣿⣿⣿⣿⣿⡿⣷⣄⣻⠃⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣿⣿⣿⠛⠩⣿⡿⠟⠋⠀⣿⣜⣧⣶⢺⣿⣿⣿⣿⣿⣿⣿⠃⢹⡉⠙⠒⠢⠄⣀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢿⣿⣿⣿⣿⣿⣷⡦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠁⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⣻⠿⠒⠊⠁⠀⠀⠀⠀⢿⣿⣷⣾⣺⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠉⠀⠂⠹⣿⣿⣿⠇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠦⠤⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⢀⣀⠸⣿⣿⠀⠸⣿⣿⡏⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣣⡤⠀⢀⣼⣿⣿⣿⣿⡏⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣣⡾⠟⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠸⠿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⢤⢤⣤⣤⢀⡤⣤⣤⣀⠀⢀⣀⣤⣠⡄⠀⠤⡀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⡤⣤⡄⢀⠀⡀⢠⣤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⡀⣀⠀⡀⠀⣤⠀⠀⢠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⣶⡛⣝⢿⣷⡆⣰⣽⡻⢃⢀⠐⣕⡀⠀⠀⣿⣿⣽⣯⣽⠀⠀⣿⣀⣠⣤⣶⣷⣶⢶⣶⣦⣼⣿⣿⠠⠇⠨⢸⡇⠺⠀⠿⠘⠁⠸⠃⠋⠀⠉⠀⡙⠀⠂⢹⠀⣿⡟⠛⠛⠙⠯⢍
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢘⢧⠠⠴⣿⣽⠡⢋⣴⣿⣯⡅⠀⠀⣿⣿⢿⣿⣿⠀⣤⣿⣿⡿⠝⠋⠘⠀⠈⠛⠿⣿⣿⣿⣦⡂⢀⢸⡇⠾⠀⠿⠘⠁⠘⠃⠿⠀⠀⠀⡑⠀⠀⢈⠀⣿⡇⠀⢴⠀⠀⢸
⠛⣛⣻⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠁⡔⢾⣿⠐⣅⣤⣞⢸⣿⣝⠿⣿⠁⠀⠀⢿⣿⣿⣛⣿⡿⠟⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣭⣽⣽⣆⢸⡇⠄⠀⠂⠠⠀⠀⠀⠚⠀⠄⠀⡧⠀⠀⠘⠀⣾⡇⠀⢠⣤⣴⣼
⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠿⢛⣱⠀⠝⠷⠏⢨⣭⣵⣬⣭⣃⡀⠀⠙⠋⠋⠝⡟⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣷⣦⣄⠀⠠⣭⣯⣺⠇⠐⠀⡀⢠⡀⠀⠀⠄⠀⠆⠀⠅⠀⠀⠀⠀⣿⡇⠀⠌⠈⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⡀⠀⢰⠟⣠⣾⣿⡙⣿⣿⣿⣿⡄⠀⠀⠀⠀⡁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠑⠒⠪⡴⠶⣶⣶⢰⣶⡒⠂⠒⠐⠀⠀⠁⠂⠀⠠⠀⢡⣤⡔⠛⠳⠶⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠄⠀⣶⣿⣿⣿⣿⣿⣧⠉⢏⠂⠀⠢⢤⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡄⣤⣤⡀⠀⠀⠀⠀⣼⢻⣿⣿⡏⠙⠀⢔⣼⢤⣥⣴⠀⠀⢸⣿⠿⠛⠛⣿⣿⣿⠗⠩⠿⣯⣿⣿⣿⣦⣠⣿⡆⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⡘⠛⠃⠀⠀⠀⠀⠀⠀
⠛⣿⣿⣿⣷⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⢠⠇⢸⣿⠙⣿⣿⣇⣀⣀⣾⡝⢨⣏⣽⣀⡀⠀⣇⠀⠀⡄⢀⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠙⠉⢻⣿⡟⠿⠇⠇⠐⠀⠀⠘⠀⠐⠛⠒⠃⠀⠀⠀⠀⠀⠀
⣧⣿⣿⡿⠻⣿⣿⣇⣹⣭⣿⣽⡿⣫⣿⣟⡟⣿⣭⣏⠈⣻⣽⣟⣿⣿⣿⣯⢩⣭⣩⡍⡉⣩⣭⣝⢂⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⢀⣄⠀⠀⣐
⣟⢿⣿⡃⠀⠸⢋⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣆⣿⣿⣿⣿⣏⣙⣫⣶⣿⣿⣿⣿⣿⣿⣿⡇⢺⣧⡿⠿⠛⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠰⣿⣿⣿⣿
⣿⣮⡿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣗⣿⣇⣿⣇⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣵⠚⡷⣴⢶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣬⠶⠛⠁⠀⠒
⠛⠉⡀⠸⣴⣿⣿⡿⣿⣿⣽⣿⣿⣿⡿⡿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣶⡲⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣘⠀⢠⠙⢈⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠄⠀⠀⠘
⠀⢀⣀⣴⣿⣿⣿⡇⣿⣿⣯⣭⣏⣶⣤⣽⡿⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⡿⠛⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠆⢨⠰⠎⢣⣼⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⣿⠁⠀⠀⠀⠀⠀
⠀⣼⣿⣿⣛⣛⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠿⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⡿⡇⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⡿⣷⣄⠘⠃⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀
⠀⢿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣿⣿⣿⠛⠉⣿⡿⠟⠋⠀⣿⣕⢳⣴⣺⣿⣿⣿⣿⣿⣿⣿⠃⢹⠉⠙⠒⠠⢄⣀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢿⣿⣿⣿⣿⣿⣷⣦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠁⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⣻⠿⠒⠂⠁⠀⠀⠀⠀⢿⣿⣷⣼⣪⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠉⠀⠊⠻⣿⣿⣿⠇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠦⠤⠀⠀⠀⠠⡾⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⢀⡀⠸⣿⣿⠀⠸⣿⣿⡮⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣣⡄⠀⢀⣼⣿⣿⣿⣿⡏⠀⠀⠿⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡣⡾⠟⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀
⠟⠖⠶⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠹⠿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⢤⣤⡤⢀⡀⣤⣤⣀⠀⢀⡀⣤⢤⡄⠀⠤⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⣤⣤⡄⢀⠀⡀⢠⣤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⡀⣀⠀⡀⠀⣤⠀⠀⣠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣻⣿⣿⣿⣿⣻⢛⣿⣿⣿⡖⠚⣝⣿⣷⡆⣠⣽⡻⢓⢀⠀⣐⡀⠀⠀⣿⣿⣽⣯⣽⠀⠀⣿⢀⣠⣤⣶⣷⣶⣶⣶⣦⣼⣿⡿⠀⠇⠨⢸⡇⠺⠀⠿⠘⠅⠸⠃⠋⠀⠉⠀⠙⠀⠆⢹⠀⣿⡿⠛⠛⠙⠯⢙
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⢯⠠⠴⣿⣽⠡⢋⣴⣿⣯⡅⠀⠀⢿⣿⢿⣿⣿⠀⣠⣿⣿⠿⠟⠋⠘⠀⠘⠻⠿⣿⣿⣷⣦⡂⢀⢸⡇⠾⠀⠿⠘⠁⠘⠃⠟⠀⠀⠀⡑⠀⠀⢊⠀⣿⡇⠀⣴⠀⠀⢸
⠛⣛⣻⣿⠽⣿⠿⠿⢿⣿⣼⣿⣿⣟⠀⡀⢸⣻⠐⣅⣴⣞⢸⣿⣭⠟⣿⠁⠀⠀⢻⣟⣛⢛⣿⡿⠟⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣽⣽⣆⢸⡇⠄⠀⠂⠀⠀⠀⠀⠚⠀⠄⠀⡷⠀⠀⠘⠀⣿⡇⠀⢡⣤⣶⣼
⣾⣿⣿⣿⣴⣿⣿⣿⣿⣿⣽⣿⣿⣿⢠⠿⢛⣱⠀⠝⠧⠇⢨⣭⣵⣬⣭⣃⠀⠀⠙⠉⠈⠙⡟⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣶⣦⡀⠀⢠⣽⣛⣸⠇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠆⠀⠅⠀⠀⠀⠀⣿⡇⠀⠌⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠰⠟⣰⣾⣿⣙⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠑⠒⠬⡴⠶⣶⢶⢰⣶⡒⠂⠒⠀⠀⠀⠁⠂⠀⢠⣤⡁⠀⠰⠟⠳⠖⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣆⠉⠇⠀⠀⠢⠄⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡶⡶⡆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡄⣤⣤⡀⠀⠀⠀⠀⣬⢻⣿⣿⡏⠙⠀⣔⣼⢤⣧⣴⠀⠀⢸⣿⠿⠛⠻⢿⣿⣿⠗⠩⠿⣿⣿⣿⣿⣆⣠⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠛⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⢠⡇⢸⣿⠘⣿⣿⣇⣀⣀⣾⡙⢀⣏⣽⣁⡀⠀⣇⠀⠀⡀⠈⣿⣿⣦⣐⣾⣿⣿⣿⣿⣿⣿⣿⡇⠙⠉⢻⣿⡟⠿⠇⠇⠀⠀⠀⠘⠓⠒⠂⠀⠀⠀⠀⠀⢀⠀⠀
⣧⣿⣿⡿⠛⣿⣿⣇⣹⣭⣿⣽⡿⣩⣧⣟⡟⣿⣭⣏⠈⣿⣿⣟⣿⣿⣿⣭⢩⣭⣩⡍⠉⣉⣝⣟⢀⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⣀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⢀⣄⡀⣀⡌⠀⠀
⣝⢿⣿⡃⠀⠘⢋⣿⣿⣿⣷⣿⡇⣿⡗⣿⡇⣿⣧⡿⢀⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣆⣿⣿⣿⣟⣏⠛⣫⣽⣿⣿⣿⣿⣿⣿⣿⡇⢺⣧⡿⠿⠛⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠜⣿⣿⡿⠿⣶⡀
⣿⣮⡿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣗⣿⣇⣿⣇⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⠟⠻⢿⣿⣯⣿⣿⣿⣿⣿⣧⣾⣿⣿⡴⢸⠶⣴⢶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣮⠖⠊⠁⠈⣉⣿⣿
⠛⠉⡀⠸⣼⣾⣿⡿⣿⣿⣽⣿⣿⣿⡿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣴⡒⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢀⠋⣤⠙⢈⣁⣸⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⠀⠀⠉⠉⠀
⠀⢀⣀⣴⣿⣿⣿⡇⣿⣿⣯⣭⣏⣶⣤⣽⡟⣤⣤⡄⣮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⡿⠛⠀⠙⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠱⠀⠠⠝⢳⣼⠛⠛⠛⢛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⣻⣛⣟⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠟⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣼⣿⣿⣿⣿⣿⡿⡇⠈⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⡿⣷⣄⠀⠁⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣿⣿⣿⠛⠉⣿⡿⠟⠋⠀⣷⣌⡢⢄⣴⣿⣿⣿⣿⣿⣿⣿⠃⠻⠁⠛⠖⠠⢄⣀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⣿⣿⣿⣿⣿⣿⣷⠦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠁⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⣻⠿⠒⠂⠁⠀⠀⠀⠀⢿⣿⣷⣬⣺⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣤⣄⣀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠉⠀⠊⠻⣿⣿⣿⠇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⡤⠀⣾⠋⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⢀⡀⠹⣿⣿⠀⠸⣿⣿⡮⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣃⡤⠀⢀⣼⣿⣿⣿⣿⡏⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⡣⡾⠟⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠈⠀⠀⠀⠹⠿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⢠⣄⣤⣤⣤⠀⢠⣀⣤⣤⡄⠀⠤⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⣤⣤⡄⢀⠀⡀⢠⣤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⡀⣀⠀⣀⠀⣤⢀⠀⢠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣻⣿⣿⣿⣿⣻⢛⣿⣿⣿⣶⣻⣝⣿⣶⡆⣰⣿⡻⢋⢀⠰⣕⡀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣿⣀⣠⣴⣶⣷⡶⢶⣶⣦⣼⣿⡿⠠⠇⠨⢸⡇⠫⠀⠿⠸⠁⠸⠃⠋⠀⠉⠀⠙⠀⠆⢹⠀⣿⡟⠻⢛⠙⠯⢍
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢘⢧⠠⠴⣿⣽⠣⢋⣴⣿⣯⡅⠀⠄⣿⣿⢿⣿⣿⢀⣤⣿⣿⡟⠟⠋⠘⠀⠉⠛⠻⣿⣿⣷⣦⡂⢀⢸⡇⠾⠀⠿⠘⠁⠘⠃⠿⠀⠀⠀⡑⠀⠀⢌⠁⣿⡇⠀⣶⠀⠀⢸
⠛⣛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠓⡖⣺⣿⢘⣅⣴⣞⢸⣿⣽⠟⣻⠃⠀⠀⢻⣟⣿⣟⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢽⣿⣽⣆⢸⡇⢆⠀⠂⠀⠀⠀⠀⠛⠀⠄⠀⡿⠀⠀⠘⠀⣿⡇⠀⢠⣤⡶⣼
⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣽⣿⣿⣿⣸⡿⢛⣱⠀⠟⠿⠏⢨⣭⣴⣬⣯⣃⡀⠀⠙⠯⡋⠟⡟⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣄⠀⢠⣭⣭⣸⠃⠐⠀⡀⢠⡀⠀⠀⠀⠀⠦⠀⠅⠀⠀⠀⠀⣿⡇⠀⠔⠀⠉⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡁⡀⠀⢰⠏⣰⣾⣿⣙⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠁⠒⠪⡶⠶⣶⣶⢲⣶⡒⠒⠒⠀⠀⠀⡁⠀⠀⠰⠀⠉⠀⠰⠟⠶⠶⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠄⠠⢶⣿⣿⣿⣿⣿⣧⠙⠟⠀⠀⠢⢤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⡶⡆⠀⠀⠙⠿⠀⠀⠀⠀⣀⠤⠶⠟⠷⠶⠞
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡆⣤⣤⡀⠀⠀⠀⠀⣼⢻⣿⣿⡏⠙⠀⢔⣼⢤⣥⣴⠀⠀⢸⡿⠟⠛⠛⣿⣿⣿⠋⠔⢻⣿⣿⣿⣿⡆⣠⣿⡞⣿⣿⣿⣿⣿⣿⣿⣷⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⠠⡇⢸⣿⠙⣿⣿⣇⣀⣀⣾⡝⢈⣏⣽⣃⡀⠈⡇⠀⠀⡄⣨⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠉⢻⣿⡟⠿⠏⢧⣤⠤⠆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀
⣧⣿⣿⣿⠛⣿⣿⣇⣹⣭⣿⣽⡟⣹⣿⣟⡟⣿⣿⣅⠉⣿⣿⣟⣿⣿⣿⣏⢩⣭⣩⡍⡉⣩⣭⣽⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⡀⠀⣀⣤⣤⣤⡀⠃⠀⠀⢡⡀⣀⣴⣄⡀⠀⠀⠀⠀⠀
⣟⢿⣿⡛⠀⠈⢏⣿⣿⣿⣿⣿⣗⣿⡧⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣆⣿⣿⣿⣿⣭⣉⣵⣾⣿⣿⣿⣿⣿⣿⣿⡇⢺⣧⣿⠟⠃⠰⠿⢿⣿⣿⣧⣤⣄⠀⣸⣿⣿⡯⣿⣿⣄⠀⠀⠀⠀
⣿⣮⡿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣗⣿⣇⣿⣇⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠿⠋⢙⣛⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⡅⠿⣠⣶⢶⣾⣿⣿⣿⣾⣿⡭⠟⠙⠿⠿⠟⠛⠀⠀⠀⠀
⠛⠉⡀⠸⣼⣾⣿⡿⣿⣿⣽⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣼⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡀⢀⣏⠙⢈⣁⣸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣴⣿⣿⣿⣧⣿⣿⣯⣭⣍⣶⣤⣿⡟⣤⣤⡄⢦⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡅⠀⠿⢣⣾⠛⠛⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⣿⣛⣿⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠿⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠉⣛⣿⣿⣿⣿⣿⣿⡟⣿⣤⠄⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠
⠀⣿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣿⣿⣿⠛⠉⣿⡿⠟⠋⠈⣷⣴⣳⣬⣿⣿⣿⣿⣿⣿⣿⣿⠃⢙⡉⠛⠒⠠⢄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠁⠀⠁
⡀⣿⣿⣿⣿⣿⣿⣷⠦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⣻⠿⠓⠈⠁⠀⠀⠀⠀⣿⣿⣷⣼⣺⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣤⣤⣄⣀⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠉⠀⠪⠻⣿⣿⣿⠃⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠦⡤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⢀⡀⠹⣿⣿⠀⠸⣿⣿⡮⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣡⡄⠀⢀⣼⣿⣿⣿⣿⡏⠀⠀⠿⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣡⡾⠟⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠖⠶⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠈⠀⠀⠀⠻⠿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⢤⣤⣤⢀⣄⣤⣤⣠⠀⢀⣀⣤⣠⡄⠀⠤⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠄⣤⣤⡄⢀⠀⡀⠀⣤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⡀⣀⠀⣀⠀⣤⠀⠀⢠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣻⣿⣿⣿⣿⣻⢛⣿⣿⣿⣶⠻⣝⣿⣷⡆⣰⣿⡻⢓⢀⠰⣟⡀⠀⠀⣿⣿⣽⣯⣿⠀⠀⣿⣀⣤⣴⣶⣷⡶⢶⣶⣦⣼⣿⠿⠠⠇⠨⢸⡇⠹⠀⠿⠘⠅⠸⠃⠋⠀⠉⠀⠙⠀⠂⢹⠀⣿⡿⠛⠛⠙⠯⢉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢙⢯⠠⠴⣿⣽⠣⢋⣴⣿⣯⡅⠀⠀⣿⣿⢿⣿⣿⢀⣤⣿⣿⠟⠛⠋⠈⠀⠈⠙⠛⢿⣿⣿⣦⡂⢀⢸⡇⠾⠀⠿⠘⠁⠘⠃⠿⠀⠀⠀⡑⠀⠀⢈⠀⣿⡇⠀⣶⠀⠀⢸
⠛⣛⣻⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠀⡔⣼⣿⠘⣥⣴⣞⢸⣿⣽⠿⣿⠃⠀⠀⢻⣿⣿⣟⣿⡿⠛⠉⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠺⢶⣿⣽⣆⢸⡇⢄⠀⠂⠀⠀⠀⠀⠛⠀⠄⠀⡷⠀⠀⠘⠀⣿⡇⠀⢡⣤⣶⣼
⣶⣿⣿⣿⣤⣿⣿⣿⣿⣿⣽⣿⣿⣿⡸⠿⢛⣱⠀⠛⠷⠏⢨⣭⣴⣬⣭⣃⡀⠀⠙⠛⠛⠚⡏⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠰⡭⣭⣸⠇⠐⠀⠀⢠⡀⠀⠀⠀⠀⠆⠀⠅⠀⠀⠀⠀⢿⡇⠀⠌⠀⠉⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢰⠟⣰⣾⣿⣙⣿⣿⣿⣿⡄⠀⠀⠀⠀⡁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⠒⠊⡶⠶⣶⢶⢲⣶⡒⠒⠒⠀⠀⠀⠁⠂⠀⠰⠀⠉⠀⠰⡟⠳⠶⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠄⠠⢶⣿⣿⣿⣿⣿⣦⠉⠏⠀⠀⠲⢤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡶⠒⠀⢶⣦⠀⠀⠀⠰⠴⠶⠿⠛⠛⠓⠒⠦⢄
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡄⣤⣤⡀⠀⠀⠀⠀⣼⢻⣿⣿⡏⠙⠀⣔⣾⢤⣧⣴⠄⠀⢸⡿⠛⠉⠙⢿⣿⣿⠃⠒⢛⣻⣿⣿⣿⡆⣬⣿⡞⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⠠⡇⢸⣿⠘⣿⣿⣇⣀⣀⣿⡙⢈⣏⣽⣁⡀⠈⡇⢀⢀⣄⣸⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣷⣿⡇⠙⠉⢻⣿⡟⢿⡏⢙⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⣿⣿⣿⠟⣿⣿⣇⣹⣭⣿⣭⡏⣹⣷⣿⡟⣿⣯⣅⠩⣿⣿⣟⣿⣿⣿⣯⢩⣭⣩⡍⡉⣩⣭⣽⢢⣿⣿⣷⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⡀⠀⣀⣌⠉⠅⠀⠐⠀⠀⢴⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀
⣟⢿⣿⡛⠀⠈⢩⣿⣿⣿⣷⣿⡧⣿⡷⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣆⣿⣿⣿⣿⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣧⡿⠟⠃⠰⠿⢿⡆⣀⠀⠀⣼⣶⣶⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀
⣿⣮⡿⠇⠀⠀⠀⠀⢀⣿⣹⣿⣿⣿⣗⣿⣇⣿⣇⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⡩⢽⣿⣷⣿⣿⣿⣿⣿⣧⣾⣿⣿⠉⡇⢰⣶⢶⣾⣿⣷⡶⢺⡿⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠛⠉⣀⠸⣼⣾⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⣿⣑⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡀⠀⣙⠙⢈⣁⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣴⣿⣿⣿⡧⣿⣿⣯⣭⣏⣶⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢰⠀⠸⢧⣼⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⣼⣿⣿⣛⣿⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠿⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⢿⣄⠈⠉⠙⠛⣛⣿⣿⣿⣿⣿⣿⡟⣿⣧⡼⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠠⡶⠟⠻
⠀⣿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡟⣻⣿⣿⢛⠉⣿⡿⠟⠋⠘⣿⣜⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⠁⢉⠉⠛⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⠉⠀⠀⠀⠀⢀
⡀⣻⣿⣿⣿⣿⣿⣷⠦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⣻⠿⠒⠀⠀⠀⠀⠀⠀⣿⣿⣷⣽⣯⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠉⠓⢶⣤⣤⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠉⠀⠊⠻⣿⣿⣿⠁⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠦⠤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⣀⡀⠹⣿⡿⠀⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣡⡾⠋⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠟⠖⠲⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⡤⢤⣤⡤⢠⡠⣤⣤⣠⠀⢀⣀⣤⣠⡄⠀⠤⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⡤⣤⡄⢀⠀⡀⠠⣤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⡀⣀⠀⣀⠀⣤⠀⠀⣠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣻⣿⣿⣿⣿⣻⢛⣿⣿⣿⡶⡚⣝⣿⣷⡆⣰⣿⡻⢋⠀⠰⣖⡀⠀⠀⣿⣿⣿⣯⣿⠀⠀⣿⣀⣤⣴⣶⣷⡶⢶⣶⣦⣼⣿⠿⠀⠇⠨⢸⡇⠻⠀⠿⠘⠁⠸⠃⠋⠀⠉⠀⡛⠀⠂⢹⠀⣿⡟⠛⠛⠙⠋⢉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠙⢧⠠⠴⣿⣽⠡⢋⣴⣿⣯⡅⠀⠀⣿⣿⢿⣿⣿⢀⣴⣿⢿⠟⠛⠋⠈⠀⠈⠙⠛⢿⣿⣿⣴⡂⢀⢸⡇⠾⠀⠿⠘⠁⠘⠃⠿⠀⠀⠀⡑⠀⠀⢈⠀⣿⡇⠀⣴⠀⠀⢸
⠛⣛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠁⡐⣾⣿⢘⣅⣴⣞⢸⣿⣭⢿⣿⠁⠀⠀⢻⣟⣿⣟⣿⡿⠛⠉⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠲⠶⡿⣿⣆⢸⡇⠄⠀⠂⠀⠀⠀⠀⠛⠀⠄⠀⡷⠀⠀⠘⠀⣿⡇⠀⢣⣤⣶⣼
⣶⣿⣿⣿⣤⣿⣿⣿⣿⣿⣽⣿⣿⣿⣸⡿⢛⣱⠀⠝⠧⠏⢨⣭⣴⣬⣭⣃⡀⠀⠙⠻⠉⠙⡟⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⡰⡭⢭⣸⠇⠐⠀⠀⢠⡀⠀⠀⠄⠀⠆⠀⠅⠀⠀⠀⠀⢿⡇⠀⠜⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢰⠏⣰⣾⣿⣙⣿⣿⣿⣿⡄⠀⠀⠀⠀⡁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⠒⠊⡶⠶⣶⣶⢲⣶⡒⠂⠒⠀⠀⠀⠁⠂⠀⢰⣀⠉⠀⠰⠟⠷⠖⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣧⠉⠃⠀⠀⠢⢄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⡷⢶⣶⡆⠀⠀⠀⠀⠒⠚⠛⠉⠛⠉⠑⠳⠀⠀⠀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡆⣤⣤⡀⠀⠀⠀⠀⣬⢻⣿⣿⡏⠙⠀⢔⣾⢤⣧⣴⠀⠀⢸⡿⠛⠉⠙⢿⣿⣿⠃⠚⢛⣻⣿⣿⣿⡆⣼⣿⡾⣿⣿⣿⣇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗
⠛⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⠠⡇⢸⣿⠘⣿⣿⣇⣀⣀⣿⡝⢨⣏⣽⣃⡀⠈⣇⢀⣀⣄⣼⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠉⢻⣿⠛⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿
⣧⣿⣿⣿⠟⢿⣿⣇⣹⣭⣿⣽⡏⣹⣷⣿⡟⣿⣿⣅⠹⣿⣿⣟⣿⣿⣿⣏⢩⣍⣩⡍⡉⣩⣭⣽⢂⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⡀⠐⠒⠘⠀⠠⠄⠀⠾⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣟⢿⣿⡋⠀⠀⢩⣿⣿⣿⣷⣿⣧⣿⡇⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣆⣿⣿⣿⣿⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣧⡿⠛⠃⠰⠀⠀⠀⠀⣷⣄⣘⣻⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣿
⣿⣮⡿⠇⠀⠀⠀⠀⢀⣿⣹⣿⣿⣿⣗⣿⣇⣿⣇⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠛⠁⠬⢽⣻⣷⣿⣿⣿⣿⣿⣥⣾⣿⣿⠘⡧⠴⣶⢶⣴⡄⣿⣿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠛⠉⡀⠸⣼⣾⣿⡿⣿⣿⣽⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣟⣓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠁⣈⠙⢈⣁⡰⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⣸⣿
⠀⢀⣀⣴⣿⣿⣿⣧⣿⣿⣯⣭⣍⣶⣤⣽⡟⣤⣤⡆⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠇⠀⢧⣾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⣼⣿⣿⣛⣟⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡟⣿⠿⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣼⣿⣿⣿⣿⣿⢿⡤⠈⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⡟⣿⣷⡤⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⠀⠰⠟⠛⠛⠛⠿
⠀⣿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣻⣿⣿⠛⠉⣿⡿⠟⠋⠘⣷⣵⢣⣷⢾⣿⣿⣿⣿⣿⣿⣿⠁⠓⠉⠋⠐⠠⢄⣀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⠤⢤
⡀⣿⣿⣿⣿⣿⣿⣷⠦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⣻⠿⠒⠀⠁⠀⠀⠀⠀⣿⣿⣷⣼⣫⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣿⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠉⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠦⠤⠀⠀⠀⠀⠀⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⣀⡀⠹⣿⡿⠀⠸⣿⣿⡏⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣡⡾⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠈
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⢤⢤⣤⣤⢀⡀⣠⣤⣀⠀⢀⣀⣤⣤⡄⠀⠤⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⡤⣤⡄⢀⠀⡀⠠⣤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⡀⣀⠀⡀⠀⣤⠀⠀⢠⠤⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣻⣿⣿⣿⣿⣻⢛⣿⣿⣿⡶⠛⣝⢿⣷⠆⣠⣼⡻⢃⠀⠀⣔⡀⠀⠀⣿⣿⣽⣯⣿⠀⠀⣿⣀⣠⣴⣶⣷⡶⢶⣶⣦⣼⣿⠿⠀⠇⠨⢸⡇⠯⠀⠿⠘⠁⠸⠃⠋⠀⠉⠀⡙⠀⠆⢹⠀⣿⡟⠛⠛⠻⠯⢉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢧⠠⠴⣿⣽⠡⢋⣴⣿⣯⡅⠀⠀⣿⣿⢿⣿⣿⢀⣤⣿⢿⠟⠟⠋⠈⠀⠈⠙⠻⢿⣿⣷⣤⡀⠀⢸⡇⠾⠀⠿⠘⠁⠘⠂⠟⠀⠀⠀⡑⠀⠀⢈⠀⣿⡇⠀⣴⠀⠀⢸
⠛⣛⣛⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣟⠃⡐⣾⣿⢐⣅⣴⣞⢸⣿⣭⠟⣿⠁⠀⠀⢻⣿⣿⣛⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣵⣄⢸⡇⠄⠀⠂⠀⠀⠀⠀⠚⠀⠄⠀⡇⠀⠀⠘⠀⣿⡇⠀⢡⣤⡴⣼
⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣽⣿⣿⣿⢸⡿⢛⣱⠀⠝⠧⠏⢨⣭⣴⣬⣭⣃⡀⠀⠙⠛⠋⠛⡏⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣄⠀⠰⠭⢭⣸⠇⠐⠀⠀⢠⡀⠀⠀⠀⠀⠆⠀⠅⠀⠀⠀⠀⣯⡇⠀⠄⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⠀⢰⠏⣠⣾⣿⡙⣿⣿⣿⣿⡄⠀⠀⠀⠀⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠁⠐⠊⡶⠶⣶⣶⢰⣶⡒⠂⠒⠀⠀⠀⠁⠀⡀⠠⠀⠉⠀⠰⠟⠷⠖⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣧⠉⢧⠀⠀⠰⢄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣷⡀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡶⠶⠆⠀⠀⠐⠛⠋⠉⠋⠁⠓⠀⠀⠇⠀⠀⠀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡆⣤⣄⡀⠀⠀⠀⠀⣼⢻⣿⣿⠏⠙⠀⣜⣼⢤⣧⣴⠀⠀⢸⡿⠛⠉⠙⢿⣿⣿⠋⠐⢛⣿⣿⣿⣿⡆⣼⣿⣾⣿⡏⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣓
⠛⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⢠⡇⢸⣿⠙⣿⣿⣇⣀⣀⣾⡝⢨⣏⣽⣀⡀⠈⡇⠀⢀⣄⣸⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠉⠶⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢿⠿
⣧⣿⣿⣿⡟⢻⣿⣇⣹⣭⣿⣽⡏⣹⣿⣟⡟⣿⣯⣄⠹⣿⣿⣟⣿⣿⣿⣏⢩⣭⣩⡍⡉⣩⣽⣝⢀⣿⣿⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠴⠦⠖⠀⣀⡀⠠⠾⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤
⣟⢿⣿⠋⠁⠀⢩⣿⣿⣿⣷⣿⡇⣿⡇⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣆⣿⣿⣿⣿⣥⣩⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣧⡿⠛⠀⠀⠀⠀⣄⡀⢹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣿⣮⡿⠇⠀⠀⠀⠀⢀⣿⣹⣿⣿⣿⣇⣿⣇⣿⣇⣿⡾⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⡭⢽⣿⣷⣾⣿⣿⣿⣿⣤⣿⣿⣿⢸⡆⠴⣄⡀⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤
⠛⠉⡀⠸⣴⣾⣿⡿⣿⣿⣽⣿⣿⣿⠿⠿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣷⣿⣿⣿⣿⣿⣷⣞⣓⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠈⠥⢀⠛⡥⠋⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⣽⣿⣿⣿
⠀⢀⣀⣴⣿⣿⣿⣇⣿⣿⣯⣭⣏⣶⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⡿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠂⠐⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⣼⣿⣿⣛⣟⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠿⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⢿⣄⠀⠉⠉⠉⣉⣿⣿⣿⣿⣿⣿⡟⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠰⠟⠋⠙⠛⠻⢷⣞
⠀⣿⣿⣿⣿⣯⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡟⣿⣿⣿⠛⠉⣿⡿⠟⠋⠘⣷⣕⢔⣼⢾⣿⣿⣿⣿⣿⣿⣿⠁⠁⠈⠉⠒⠠⢄⣀⠀⢀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⡲⠦⡀⠀
⡀⣿⣿⣿⣿⣿⣿⣷⠦⠤⠈⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠁⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⣻⠿⠒⠈⠁⠀⠀⠀⠀⣿⣿⣷⣼⣪⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣄
⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠉⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠤⠀⠀⠀⢻⣿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⣀⡀⠹⣿⡟⠀⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠙⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠇⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣡⡾⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣄⣿⠀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠑⠋⠀
⣤⣤⣤⣤⢤⣤⣤⣤⣄⣤⣤⢤⣤⡤⢀⡀⣤⣤⣀⠀⢀⣀⣤⢠⡄⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⡤⣤⡄⢀⠀⡀⠠⣤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⣤⠀⠀⢠⠠⣤⣤⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣿⡖⡳⣝⢿⡿⡆⣰⣽⡻⢃⢀⠸⣕⡀⠀⠀⣿⣿⣽⣯⣽⠀⠀⣿⣀⣠⣴⣶⣷⡶⢶⣶⣦⣼⣿⡯⠀⠇⠨⢸⡇⠎⠀⠿⠘⠅⠸⠃⠋⠀⠉⠀⠙⠀⠄⢹⠀⣿⡟⠛⢛⠙⠫⠉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠐⢧⠠⠴⣿⣽⠡⢋⣴⣿⣭⡅⠀⠀⣿⣿⣿⣿⣿⢀⣤⣿⣿⠟⠛⠋⠈⠀⠉⠛⠻⣿⣿⣷⣔⡂⠀⢸⡇⠾⠀⠿⠘⠁⠘⠃⠿⠀⠀⠀⡑⠀⠀⢈⠀⣿⡇⠀⣴⠀⠀⢸
⠛⣛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣟⠃⡔⣺⣿⠐⣥⣴⣞⢸⣿⣽⠛⣻⠁⠀⠀⢻⣟⣿⣛⣿⡿⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣯⣿⣷⣄⢸⡇⠄⠀⠂⠀⠀⠀⠀⠛⠀⠄⠀⡷⠀⠀⠘⠀⣿⡇⠀⢢⣤⣶⣼
⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣽⣿⣿⣿⢸⡿⢛⣱⠀⠝⠧⠏⢨⣭⣴⣬⣭⣃⡀⠀⠙⠛⠋⠙⠏⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣶⣦⡄⠀⢨⢽⣽⣸⠃⠐⠀⡀⢠⡀⠀⠀⠀⠀⠆⠀⠅⠀⠀⠀⠀⣿⡇⠀⠌⠀⠉⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠰⠏⣰⢾⣿⡙⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠐⠒⠍⡶⠶⣶⣶⢰⣶⡒⠒⠒⠀⠀⠀⠁⠂⠀⠠⠀⠁⠀⠰⠟⠷⠖⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣧⠉⡇⠀⠀⠢⢄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡶⣶⡶⠖⠛⠛⠛⠁⠐⠲⠀⡀⠄⢀⠧⠀⠀⠀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡄⣤⣤⡀⠀⠀⠀⠀⣼⢻⣿⣿⡏⠙⠀⢔⣾⢤⣧⣴⠀⠀⢹⡿⠟⠛⠛⣿⣿⣿⠂⠴⢿⣿⣿⣿⣿⡆⣼⣿⡎⠈⠉⠻⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⡇⠀⠀⣓
⠛⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣧⣿⣟⣿⡀⢠⡅⢸⣿⠙⣿⣿⣇⣀⣀⣾⡝⢨⣏⣽⣀⠀⢸⡅⠀⠀⡀⣸⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠶⡄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⣿⠿
⣧⣿⣿⣿⡟⢻⣿⣇⣹⣭⣿⣽⡏⣹⣿⣿⡟⣿⣭⣄⠹⣿⣿⣟⣿⣿⣿⣏⢩⣭⣩⡍⡉⣉⣽⣝⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠄⠀⠀⠀⢤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤
⣟⣿⣿⠙⠃⠀⢩⣿⣿⣿⣷⣿⡗⣿⡗⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣎⣿⣿⣿⣿⣍⣉⣵⣾⣿⣿⣿⣿⣿⣿⣿⠃⢿⣧⠁⠀⠀⢀⡀⠐⣒⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⣿⣮⡿⠇⠀⠀⠀⠀⢀⣿⣹⣿⣟⣿⣇⣿⣇⣿⣇⣿⣾⣿⣸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠟⢉⣙⡿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⡆⢀⠀⢸⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣤⣿⣤⣤⣤⣤
⠟⠉⡀⠸⣽⣾⣿⡿⣿⣿⣽⣿⣿⣿⠿⠿⢿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⣔⠲⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⣤⠿⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣴⣿⣿⣿⣇⣿⣿⣯⣭⣏⣶⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⡗⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⠿⣿⣿⣿
⠀⣼⣿⣻⣛⣿⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠟⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⢿⡀⠉⠉⠙⠛⣛⣿⣿⣿⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠰⠟⠛⠛⠛⠿⣿⣿⣷⣜
⠀⣿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣿⣿⣿⢋⠉⣿⡿⠟⠋⠸⣷⣖⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⢻⡉⠛⠒⠠⢀⣀⣀⠀⠀⠈⠀⠁⠀⠀⠀⢀⣤⠴⢤⡀⠉⠙⣿
⡀⢿⣿⣿⣿⣿⣿⣷⠦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⣻⠿⠒⠀⠁⠀⠀⠀⠀⣿⣿⣷⣼⣫⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⣤⣤⣄⣀⠀⠀⠀⠉⣿⣷⣧⡀⠀⠉
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠉⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠦⠤⠀⢿⣿⣯⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⣀⡀⠹⣿⡟⠀⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣡⡾⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀
⠛⠖⠲⣶⠏⢶⠜⠳⠷⠶⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⢤⣤⣤⣤⢠⢄⣤⣤⣀⠀⢀⣀⣤⢤⡄⠀⠤⠄⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⣤⣤⡄⢀⠀⡄⠠⣤⠄⠠⠄⠠⢠⡄⠠⠀⠀⠀⡀⢀⠀⣀⠀⣀⠀⣤⠀⠀⢠⠠⣤⡄⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣻⣿⣿⣿⣿⣻⢛⣿⣿⣿⡖⡳⣝⣿⣶⡆⣰⣽⡻⢃⠀⠠⣗⡀⠀⠀⣿⣿⣿⣯⣽⠀⠀⣿⣀⣠⣤⣶⣷⣦⣶⣶⣆⣼⣿⡿⠠⠅⠨⢸⡇⠪⠀⠿⠸⠁⠸⠃⠋⠀⠉⠀⡛⠀⠂⢹⠀⣿⡿⠛⠛⠻⠫⠏
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢘⢮⠠⠴⣿⣿⠡⢋⢴⣿⣯⠅⠀⠀⣿⣿⢿⣿⣿⢀⣤⣿⣿⠿⠿⠋⠎⠀⠛⠿⢿⣿⣿⣶⣔⡂⠈⢸⡇⠾⠀⠿⠘⠁⠘⠂⠿⠀⠀⠀⡓⠀⠀⢌⠁⣿⡇⠀⣦⠀⠀⢸
⠙⣛⣿⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⣿⠁⡐⣸⣿⢘⣥⣶⣞⢸⣿⣽⢻⣿⠁⠀⠀⢿⣿⣿⣻⣿⡿⠛⠃⠑⠀⠀⠀⠀⠀⠀⠀⠀⠩⣯⣭⣯⣷⣀⢸⡇⠄⠀⠂⠀⠀⠀⠀⠛⠀⠄⠀⡇⠀⠀⠘⠀⣿⡇⠀⢣⣤⣶⣼
⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣽⣿⣿⣿⢸⠿⢛⣱⠀⠝⠷⠇⢨⣭⣬⣬⣯⣁⡀⠀⠙⠛⠉⢙⠏⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣄⠀⠈⣭⣿⣓⢸⠁⠐⠀⡀⢠⡀⠀⠀⠀⠀⠆⠀⠅⠀⠀⠀⠀⣿⡇⠀⠄⠈⠉⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠠⠏⣰⣾⣿⣙⣿⣿⣿⣿⡆⠀⠀⠀⢈⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠁⠒⠦⠝⡶⠶⣶⣶⢢⣶⡒⠒⠒⠂⠀⠀⠁⠂⠀⠠⠀⠁⠀⠰⠟⠳⠶⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣧⠁⠗⠀⠀⠢⢄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡶⠶⠦⠤⡀⠀⠀⠀⠐⠰⠀⡀⠄⢀⠧⠀⠀⢀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡆⣤⣤⠀⠀⠀⠀⠀⣼⢻⣿⣿⡏⠙⠀⢔⣼⢤⣥⣴⠀⠀⢻⣿⠿⠿⠿⣿⣿⣿⠄⠬⢿⣿⣿⣿⣷⡄⣸⣶⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⣿⠀⣿⡇⠀⠀⣗
⠛⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣷⣿⣟⣿⡀⢠⡇⢸⣿⠙⣿⣿⣆⣀⣀⣾⡝⢨⣏⣽⣁⠀⢸⡁⠀⠀⠀⢹⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠿⠸⠿⠿⠿⡿⡿
⣧⣿⣿⣿⡿⠻⣿⣏⣹⣭⣿⣽⡍⣹⣿⣞⡟⣿⣯⣌⠹⣿⣿⣟⣿⣿⣿⣯⢩⣍⣩⡍⠉⣩⣽⣷⢸⣷⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣛⣿⣿⠛⠃⠀⢨⣿⣿⣿⣷⣿⡷⣿⡇⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣎⣿⣿⣿⣿⡛⠟⣫⣽⣿⣷⣿⣿⣿⣿⣿⠀⠏⣴⣞⣛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣮⡿⠇⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣇⣿⣇⣿⣇⣿⣼⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣤
⠟⠉⡀⠸⣽⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⡤⣈⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣴⣿⣿⣿⡇⣿⣿⣯⣭⣏⣶⣤⣽⡟⣤⣤⡄⣮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡛⠛⠛⠛⠻⠿⢿⢿⣿⣿⣿
⠀⣼⣿⣿⣛⣻⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠿⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⢿⡌⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣦⡀⠀⠀⠀⠀⢀⡀⠀⢀⣴⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⣿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣿⣿⣿⢛⢉⣿⡿⠟⠋⢸⣯⣲⡆⣀⣴⣿⣿⣿⣿⣿⣿⣿⠈⠛⠙⠳⠂⠤⣀⣘⠀⠂⠀⠉⠀⠀⣀⡀⠀⠀⠀⠘⠛⠛⠉⠙⣿
⡀⣿⣿⣿⣿⣿⣿⣷⡦⠦⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⢿⠿⠖⠊⠁⠀⠀⠀⠀⣿⣿⣷⣜⡿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠈⠀⠀⠀⠀⠈⠉⠳⢦⣤⣤⣾⣿⣭⣷⡀⠀⠉⠀⠐⠒⠚⠋
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠋⠉⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⣀⡀⢻⣿⡟⠀⠸⣿⣿⡯⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣡⡄⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣡⡾⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠖⠲⣶⠏⢶⠜⠳⠷⠾⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⢤⣤⡤⢠⣤⣤⣤⣀⠀⢀⣀⣤⣤⡄⠀⠄⠄⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⡤⣤⡄⢀⠀⡀⠀⣤⠄⠠⠄⠠⢠⡄⠠⠀⠀⠀⡀⢀⠀⣀⠀⡀⠀⣤⠀⠀⢠⠤⣤⡄⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣻⣿⣿⣿⣿⣻⢛⣿⣿⣷⡶⡳⣝⢿⣶⡆⣰⣽⡻⢋⢀⠰⣖⡀⠀⠀⣿⣿⣿⣯⣽⠀⠀⣿⣀⣠⣤⣶⣷⣦⣶⣶⣆⣼⣿⠯⠠⠅⠨⢸⡇⠯⠀⠿⠸⠁⠸⠃⠋⠀⠉⠀⠙⠀⠄⢸⠀⣿⡟⠛⢛⠹⠯⠋
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⢷⠠⠴⡿⣽⠡⢋⢴⣿⣯⠅⠀⠀⣿⣿⢿⣷⣿⢀⣤⣿⣿⠿⠿⠋⠎⠀⠛⠿⢿⣿⣿⣶⣐⡂⠀⢸⡇⠾⠀⠿⠘⠃⠘⠂⠟⠀⠀⠀⡓⠀⠀⢈⠁⣿⡇⠀⣦⠀⠀⢸
⠛⣛⣟⣿⢽⣿⠿⠿⣿⣿⣼⣿⣿⣟⠁⡔⣼⣟⢘⣥⣴⣞⢸⣿⣭⢻⣿⠁⠀⠀⢿⣿⣿⣻⣿⡿⠛⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠩⣯⣽⣯⣷⣀⢸⡇⢄⠀⠂⠀⠀⠀⠀⠛⠀⠄⠀⡇⠀⠀⠘⠀⣿⡇⠀⢣⣴⣶⣼
⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⢛⣱⠀⠟⠷⠃⢨⣭⣼⣬⣯⣃⠀⠀⠙⠛⠛⠛⠏⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣄⠀⠈⣭⣟⣓⢸⠃⠐⠀⡀⢠⡀⠀⠀⠀⠀⠆⠀⠅⠀⠀⠀⠀⢿⡇⠀⠎⠀⠉⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠁⡀⠀⠰⠟⣰⣾⣿⣙⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠉⠒⠮⢹⠶⠶⣶⢶⢠⣶⡒⠒⠒⠒⠀⠀⠁⠀⠀⠠⠀⠉⠀⠰⠟⠳⠶⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠂⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣧⠉⠯⠂⠀⠲⢤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣶⡶⡆⠀⠀⠀⠀⠀⠐⠰⠀⡀⠄⢀⠧⠀⠀⣀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡄⣤⣤⡀⠀⠀⢀⠀⣼⢻⣿⣿⠏⠙⠀⢔⣼⢤⣧⣴⠀⠀⢿⣿⠿⠿⠿⣿⣿⣿⠀⠭⢿⣿⣿⣿⣷⡄⣼⣶⠀⠛⠉⠉⠀⠀⠀⠈⠑⠂⠀⠀⢀⢀⠀⠀⠀⣿⠀⣿⣇⠀⠀⣓
⠙⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣱⣿⣟⣿⡀⢠⡇⢸⣿⠙⣿⣿⣆⣀⣀⣾⡝⢨⣏⣽⣀⠀⢸⡃⠀⠀⠀⢹⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠿⠸⠿⠿⠿⣿⠿
⣧⣿⣿⣿⡿⠛⣿⣇⣹⣭⣿⣿⡍⣻⣷⣟⡟⣿⣯⣌⠹⣿⣿⣟⣿⣿⣿⣏⢩⣍⣩⡍⠉⣩⣽⣗⢸⣷⣶⣾⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡛⣿⣿⠋⠃⠀⢈⣿⣿⣿⣷⣿⡷⣿⡷⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣞⣿⣿⣿⣿⡛⠛⣫⣽⣿⣿⣿⣿⣿⣿⣿⠀⣶⢷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣮⡿⠇⠀⠀⠀⠀⢀⣿⣹⣿⣿⣿⣇⣿⣇⣿⣇⣿⠼⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠟⠻⣿⣿⣯⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠰⣾⣶⣶⣶⣶⣤⣤⣿⣿⣤⣤⣤⣤
⠟⠉⡀⠸⣽⣶⣿⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣤⠭⠭⣶⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣴⣿⣿⣿⣇⣿⣿⣯⣭⣏⣾⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣎⠛⠛⠛⠛⠛⠛⠻⠿⢿⠿⣿⣿⣿
⠀⣼⣿⣿⣟⣿⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠿⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⢷⢌⠛⠛⠻⠿⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⣿⣿⣿⣿⣿⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣿⣿⣿⢛⢉⣿⡿⠟⠋⢸⣯⣲⣠⣔⣴⣿⣿⣿⣿⣿⣿⣿⠈⢟⠙⠳⡂⠼⣤⣐⠛⠋⠉⠉⠉⠃⠀⠀⠀⠀⠀⠘⠛⠛⠉⠙⣿
⡀⣻⣿⣿⣿⣿⣿⣷⡦⠦⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⢻⠿⠗⠊⠁⠀⠀⠀⠈⣿⣿⣷⣍⡻⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠉⠲⠶⣶⣾⣦⣄⠀⠀⠀⠈⠉⠀⠐⠒⠚⠋
⣿⣿⣿⣿⣿⣿⣷⣷⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠉⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢦⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⣀⡀⢻⣿⡟⠀⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣁⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣡⡾⠋⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠟⠖⠲⣶⠏⢶⠜⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⢤⢤⣤⡤⢀⣀⣤⣤⣀⠀⢀⣀⣤⢠⡄⠀⠄⠄⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⣤⣤⡀⢀⠀⡀⠀⣤⠄⠠⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⣤⢀⠀⢠⠤⣤⡄⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣷⣶⣪⣝⢿⣿⡆⣠⣼⡻⢃⢀⠰⣕⡀⠀⠀⣿⣯⣿⣯⣿⠀⠀⣿⣀⣠⣤⣶⣷⣶⣶⣤⣆⣼⣿⡯⠠⠅⠨⢸⡇⠿⠀⠿⠘⠁⠹⠁⠋⠀⠉⠀⠙⠀⠀⢹⠀⣿⡟⠛⠛⠹⠫⠉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⢧⠠⠴⣿⣽⠡⢋⢴⣿⣯⠅⠀⠀⣿⣿⢿⣿⣿⢀⣤⣿⣿⠿⠟⠋⠊⠀⠛⠿⢿⣿⣿⣶⣐⠂⠀⢸⡇⠾⠀⠿⠘⠁⠘⠀⠟⠀⠀⠀⡁⠀⠀⢨⠀⣿⡇⠀⣦⠀⠀⢸
⠛⣛⣛⣿⢽⣿⠿⠿⣿⣿⣼⣿⣿⡟⠁⡐⣺⣿⢘⣥⣴⣞⢸⣿⣭⠿⣻⠁⠀⠀⢻⣿⡿⢿⣿⡿⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣽⣯⣷⣀⢸⡇⠄⠀⠂⠀⠀⠀⠀⠛⠀⠄⠀⡇⠀⠀⠘⠀⣿⡇⠀⢢⣤⣶⣼
⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣰⡿⢛⣵⠀⠝⠷⠃⢨⣥⣴⣬⣭⣀⠀⠀⠙⠋⠉⠙⠏⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣶⣶⣤⡀⠀⢬⣝⣓⢸⠁⠐⠀⠀⢠⡀⠀⠀⠀⠀⠆⠀⠁⠀⠀⠀⠀⢷⡇⠀⠄⠀⠉⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠰⠏⣰⣾⣿⣙⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠒⠢⢽⡶⠶⣶⢶⢠⣶⡒⠒⠒⠀⠀⠀⠁⠀⠀⠠⠀⠁⠀⠰⠟⠳⠶⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣦⠉⠏⠀⠀⠢⢄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡶⡶⡆⠀⠀⠀⠀⠀⠐⠰⠀⡀⠄⢀⠇⠀⠀⡀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡄⣤⣤⠀⠀⠀⠀⠀⣼⢻⣿⣿⡏⠙⠀⢔⣾⢤⣧⣴⠀⠀⢻⣿⠿⠛⠿⣿⣿⡿⠀⠭⢿⣿⣿⣿⣷⡀⣼⣶⠘⠋⠉⠉⠉⠛⠿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⣿⡇⠀⠀⣒
⠙⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣳⣿⣟⣿⡀⢠⡇⢰⣿⠙⣿⣿⣆⣀⣀⣾⡝⢨⣏⣽⣀⠀⢸⡀⠀⠀⠀⢹⣿⣷⣤⣲⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠘⠀⠀⠃⠀⠿⠸⠿⠷⠿⠿⠿
⣧⣿⣿⣿⣿⠛⣿⣇⣹⣭⣿⣿⡍⣻⣷⣟⡟⣿⣥⣌⠹⣿⣽⣟⣿⣿⣿⣏⢩⣍⣩⡍⠉⣩⣽⣵⣸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡙⣿⣿⠋⠋⠀⢈⣿⣿⣿⣷⣿⡷⣿⡧⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣞⣿⣿⣿⣿⡙⢛⣯⣾⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣮⡿⠇⠀⠀⠀⠀⢀⣿⣹⣿⣿⣿⣇⣿⣇⣿⣏⣿⠸⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠿⠛⢟⣻⣿⣭⣿⣿⣿⣿⣿⣠⣿⣦⡀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣾⣶⣶⣶⣶⣤⣤⣾⣿⣤⣤⣤⣤
⠛⠉⡀⠸⣽⣾⣾⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣷⣿⣿⣿⣿⣿⣧⣔⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣴⣿⣿⣿⣇⣿⣿⣯⣭⣏⣾⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⡿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢠⣤⠈⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⠿⣿⣿⣿
⠀⣼⣿⣿⣛⣻⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠿⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⢿⠄⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⢿⣦⣀⠀⠀⠀⢀⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣜
⠀⣿⣿⣿⣿⣏⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡟⣿⣿⣿⢛⠉⣿⡿⠟⠋⢸⣧⣢⣴⣔⣴⣿⣿⣿⣿⣿⣿⡿⠈⢇⠙⠓⠒⠶⢿⣛⠛⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠉⠙⣿
⡀⣿⣿⣿⣿⣿⣿⣷⡦⠦⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠁⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⢻⠿⠖⠂⠁⠀⠀⠀⠈⣿⣿⣶⣄⡹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢶⣤⣤⣄⣀⠀⠀⠀⠈⠁⠀⠐⠒⠚⠋
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠦⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⣀⡀⢻⣿⡟⠀⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣠⡾⠋⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠟⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⣄⣤⢤⢤⣤⡤⢠⣀⣤⣤⡀⠀⠀⣀⣤⢠⡄⠀⠄⠀⠀⠀⣤⣤⣤⣄⣤⠀⠀⣤⠀⢠⠀⡤⣤⡀⢀⠀⡀⠀⢤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⣤⠀⠀⢠⠠⣤⡄⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣷⡴⢢⡝⢿⣶⡆⣠⣼⡻⢂⠀⠀⣐⡀⠀⠀⣿⣿⣹⣯⣽⠀⠀⣿⣀⣠⣤⣶⣷⣶⣶⣦⣦⣜⣿⠯⠠⠅⠨⢸⡇⠋⠀⠿⠘⠁⠸⠁⠋⠀⠉⠀⠙⠀⠀⢸⠀⣿⡟⠛⠛⠹⠫⠉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢈⢦⠠⠴⢿⣽⠡⢋⢴⣿⣭⠅⠀⠀⣿⣿⢿⣷⣿⢀⣤⣿⣿⠿⠟⠁⠊⠀⠙⠛⢿⣿⣿⣷⣄⠂⠀⢸⡇⠾⠀⠿⠘⠁⠘⠀⠟⠀⠀⠀⡃⠀⠀⢈⠀⣿⡇⠀⣦⠀⠀⢸
⠛⣛⣛⣿⢽⣿⠿⠿⣿⣿⣼⣿⣿⣟⠁⡀⢼⣟⢘⣥⣴⣞⢸⣿⣭⠻⣻⠁⠀⠀⢻⣟⣛⣻⣿⠿⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣭⣯⣷⣀⢸⡇⠀⠀⠂⠀⠀⠀⠀⠛⠀⠄⠀⡇⠀⠀⠘⠀⣿⡇⠀⢣⣤⣶⣼
⣾⣿⣿⣿⣴⣿⣿⣿⣿⣿⣽⣿⣿⣿⢸⡷⢛⣱⠀⠝⠇⠅⢨⣭⣤⣬⣭⣁⠀⠀⠙⠛⠉⢙⠏⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣶⣤⡀⠀⢬⣍⣕⢸⠀⠐⠀⡀⢠⡀⠀⠀⠀⠀⠆⠀⠅⠀⠀⠀⠀⢿⡇⠀⠄⠈⠉⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠰⠏⣰⣾⣿⣙⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠐⠢⢹⠶⠶⣶⢶⢠⣶⠒⠒⠒⠀⠀⠀⠁⠀⠀⠠⠀⠁⠀⠰⠟⠳⠶⠺
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠠⢶⣿⣿⣷⣿⣿⣦⠉⠧⠀⠀⠢⢄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⡶⡶⡆⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⢀⠇⠀⠀⠀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡄⣤⣄⠀⠀⠀⠀⠀⣬⢻⣿⣿⠏⠙⠀⢔⣼⢤⣥⣴⠀⠀⢻⡿⠟⠛⠻⣿⣿⡿⠂⠽⢿⣽⣿⣿⣷⡄⣼⣿⠘⠉⠛⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⣿⡇⠀⠀⣒
⠙⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣱⣿⣟⣿⡀⢠⡇⢠⣿⠙⣿⣿⣆⣀⣀⣾⡙⢨⣏⣽⣀⠀⢸⡀⠀⠀⠀⣸⣿⣷⣦⣲⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠻⠇⠇⠐⠀⠀⠘⠀⠀⠃⠀⠿⠰⠿⠷⠿⠿⠿
⣧⣿⣿⣿⣿⠛⣿⣇⣹⣭⣿⣯⡽⣻⣷⣞⡟⣿⣥⣍⡽⣿⣿⣟⣿⣿⣿⣏⢩⣍⣩⡍⠉⣩⣭⣕⢸⣷⣿⣽⣷⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡙⣿⣿⠙⠛⠀⠈⣿⣿⣿⣷⣿⣷⣿⡇⣿⡇⣿⣧⡿⢠⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣌⣿⣿⣿⣿⣍⢛⣷⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣮⡿⠇⠀⠀⠀⠀⢀⣿⣹⣿⣿⣿⣇⣿⣇⣿⣏⣿⠀⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠟⠛⣙⣻⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⣿⣿⣾⣷⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣤
⠛⠉⡀⠸⣽⣾⣧⡿⣿⣿⣽⣿⣿⣿⠿⠿⢿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣧⣬⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⢈⢰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣴⣿⣿⣿⡇⣿⣿⣯⣭⣏⣶⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣀⣜⠛⠋⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⠿⣿⣿⣿
⠀⣼⣿⣿⣛⣻⡋⠉⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠻⣿⣿⣿⣿⣿⣼⣷⣷⣤⣤⣼⣿⣿⣿⣿⣿⢷⠀⠀⠉⠉⠙⣉⣿⣿⣿⣿⣿⣿⢿⣦⣀⠀⢰⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞
⠀⣿⣿⣿⣿⣏⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡟⣿⣿⣿⢛⠉⣿⡿⠟⠋⢸⣧⣲⠀⠄⣶⣿⣿⣿⣿⣿⣿⡿⠀⢏⠙⠹⠛⠿⢿⣿⡧⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠙⣷
⡀⢿⣿⣿⣿⣿⣿⣷⡦⠤⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⢻⠿⠒⠈⠁⠀⠀⠀⠈⣿⣿⣷⣝⣙⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣦⣤⣄⣀⠀⠀⠀⠀⠉⠀⠐⠒⠚⠋
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠦⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⣀⡀⢻⣿⡏⠀⠸⣿⣿⡯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠃⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣠⡾⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠖⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⣄⡤⠤⢤⣤⡤⢀⠀⢠⣤⣀⠀⠀⣀⣤⢠⡄⠀⠄⠀⠀⠀⣤⣤⣤⡄⣤⠀⠀⣤⠀⢠⠀⡤⣤⡀⢀⠀⡀⠀⣤⠄⠀⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⣤⠀⠀⢠⠠⣤⡄⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣷⡶⠢⣝⢿⡷⠆⣠⣼⡛⢂⠀⠀⣐⠀⠀⠀⣿⣿⣿⣭⣹⠀⠀⣿⣀⣠⣤⣶⣷⡶⣶⣶⣦⣼⣿⠯⠠⠁⠨⢸⡇⠫⠀⠿⠘⠁⠸⠃⠋⠀⠉⠀⠙⠀⠄⢸⠀⣿⡟⠛⠛⠙⠋⠉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⢦⠠⠴⢿⣽⠡⢋⢴⣿⣭⠅⠀⠀⣿⣿⢿⣷⣿⢀⣤⣿⡿⠟⠛⠃⠊⠀⠉⠛⠿⣿⣿⣷⣔⠀⠀⢸⡇⠾⠀⠿⠘⠁⠘⠀⠟⠀⠀⠀⡁⠀⠀⢈⠀⣿⡇⠀⡦⠀⠀⢸
⠙⣛⣛⣿⠽⣿⠿⠿⣿⣿⣼⣿⣿⡟⠂⡀⢸⣟⢘⣥⣶⣞⢸⣿⣍⠛⣻⠁⠀⠀⢻⣟⣿⢻⣿⠟⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⢭⣭⣯⣷⣀⢸⡇⠀⠀⠂⠀⠀⠀⠀⠚⠀⠄⠀⡇⠀⠀⠘⠀⣿⡇⠀⢡⣤⣴⣼
⣶⣿⣿⣿⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⠰⡿⢛⣱⠀⠑⠗⠃⢨⣭⣤⣬⣭⣁⠀⠀⠙⠊⠈⢙⠏⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣶⣤⡀⠀⢬⣭⣕⢸⠀⠐⠀⠀⢠⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢷⡇⠀⠄⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠠⠏⣰⣾⣿⢙⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠐⠂⢙⠶⠶⣶⢶⢠⣶⡒⠒⠒⠂⠀⠀⠁⠀⠀⠠⠀⠁⠀⠰⠛⠲⠖⠺
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⢶⣿⣿⣾⣿⣿⣦⠉⠇⠀⠀⠠⢄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⡶⡶⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠄⢀⠇⠀⠀⠀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡄⣤⣤⡀⠀⠀⠀⠀⣼⢻⣿⣿⠇⠙⠀⢔⣼⢤⣥⣴⠀⠀⢻⡿⠟⠛⠻⢿⣿⡿⠂⠼⢿⣽⣿⣿⣿⡄⣼⣿⠘⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⣿⡇⠀⠀⣐
⠙⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣳⣿⣟⣯⠀⣠⡅⢠⣿⠙⣿⣿⣆⣀⣀⣾⡝⢨⣏⣽⣀⠀⢸⡀⠀⢀⠀⣸⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⢿⣿⡟⠟⠇⠇⠀⠀⠀⠘⠀⠀⠃⠀⠿⠰⠿⠷⠿⠿⠿
⣧⣿⣿⣿⣿⠟⣿⣅⣹⣭⣿⣯⡽⣻⣷⣞⡟⣿⣥⣍⡽⣿⣽⣟⣿⣽⣯⣍⢩⣍⣩⡍⠉⣩⣭⣅⢸⣿⣿⣽⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡙⣿⣯⠙⠛⠀⠀⣿⣿⣿⣷⣿⡷⣿⡇⣿⡇⣿⣧⡿⠀⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣎⣿⣿⣿⣿⣍⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣮⡿⠃⠀⠀⠀⠀⢀⣿⣹⣿⣿⣿⣇⣿⣇⣿⣏⣿⠀⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⡿⠛⠉⣙⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣶⣶⢶⡾⣿⣿⣿⣾⣶⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣤
⠟⠁⡀⠸⣽⣾⣷⡿⣿⣿⣽⣿⣿⣿⠿⠿⢿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣧⣬⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣉⠙⢈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣴⣿⣿⣿⡇⣿⣿⣯⣭⣏⣾⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⡿⡿⠛⠀⠹⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣀⡸⠿⢇⣟⠚⠛⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⠿⣿⣿⣿
⠀⣼⣿⣿⣛⣛⡋⠀⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠻⣿⣿⣿⣿⣿⣼⣷⣶⣤⣤⣼⣿⣿⣿⣿⣿⢷⠀⠀⠈⠉⠉⣉⣿⣿⣿⣿⣿⣿⢿⣦⣼⣿⣷⡄⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣜
⠀⣿⣿⣿⣿⣏⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡿⣿⣿⣿⢛⠉⣿⡿⠟⠋⢸⣯⡲⡠⠄⣾⣿⣿⣿⣿⣿⣿⡿⠀⠁⠉⠉⠛⠳⢄⣀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠙⣷
⡀⣻⣿⣿⣿⣿⣿⣷⡦⠦⠈⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⢻⠿⠒⠀⠁⠀⠀⠀⠈⣿⣿⣶⣕⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣤⣄⣀⠀⠀⠀⠀⠉⠀⠐⠒⠚⠋
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠢⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⣀⡀⢻⣿⡏⠀⠸⣿⣿⡮⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠇⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣠⡾⠋⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀
⠛⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⣄⣤⠤⢤⣤⡄⢀⠀⣤⣤⡀⠀⢀⣀⣤⢀⡄⠀⠄⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⡤⣤⡀⢀⠀⡀⠀⣤⠄⠠⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⣤⠀⠀⢠⠠⣤⡄⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣷⡖⠂⡝⢿⣶⠆⣠⣼⡛⢃⠀⠀⣔⡀⠀⠀⣿⣿⣻⣯⣽⠀⠀⣿⣀⣠⣤⣶⣷⣶⣶⣦⣦⣜⣿⠯⠠⠁⠨⢸⡇⠋⠀⠟⠘⠁⠹⠁⠋⠈⠉⠀⠙⠀⠀⢸⠀⣿⡟⠛⠛⠙⠋⠉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⢦⠠⠴⠟⣽⠡⢋⢴⣿⣭⠅⠀⠀⣿⣿⢿⣷⣿⢀⣤⣿⡿⠿⠛⠋⠊⠀⠙⠻⢿⣿⣿⣷⣄⠀⠀⢸⡇⠾⠀⠿⠘⠁⠘⠀⠟⠀⠀⠀⡁⠀⠀⢈⠀⣿⡇⠀⠦⠀⠀⢸
⠙⣛⣛⣿⢽⣿⠿⠿⣿⣿⣼⣿⣿⡏⠀⠀⣸⣞⢘⣥⣴⣎⢸⣿⡭⠛⣻⠁⠀⠀⢻⣟⡻⣻⣿⡿⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣭⣯⣷⡀⢸⡇⠄⠀⠂⠠⠀⠀⠀⠛⠀⠄⠀⡇⠀⠀⠘⠀⣾⠇⠀⢠⣤⡴⣼
⣶⣿⣿⣿⣬⣿⣶⣿⣿⣿⣽⣿⣿⣿⠰⡷⢛⣱⠀⠙⠆⠃⢨⣥⣤⣬⣍⣀⠀⠀⠙⠋⠈⢘⠏⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣶⣶⣤⡀⠀⢬⣝⣕⢸⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠆⠀⠄⠀⠀⠀⠀⣷⡇⠀⠄⠀⠈⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠐⠏⣰⣾⣿⢙⣿⣿⣿⣿⠄⠀⠀⠀⠈⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠐⠒⢍⠶⠶⣶⢶⢲⣶⠒⠂⠒⠀⠀⠀⠁⠀⠀⠠⠀⠁⠀⠰⠟⠳⠖⠺
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣯⣦⠁⠧⠀⠀⠠⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣧⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⡶⡶⡆⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⢀⠇⠀⠀⠀
⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⡀⣤⣄⠀⠀⠀⠀⠀⣼⢻⣿⣿⠇⠙⠀⢐⣼⢤⣥⣴⠀⠀⢻⡿⠿⠛⠿⣿⣿⡿⠀⠬⠿⣽⣿⣿⣷⡄⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⣿⡇⠀⠀⣁
⠙⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣰⣿⣟⣯⠀⢠⡅⢠⣿⠙⣿⣿⣆⣀⣀⣾⡙⢠⣏⣽⣀⠀⢸⡀⠀⠀⠀⢸⣿⣧⣄⣒⣾⣿⣿⣿⣿⣿⣿⣿⠉⠙⠉⣿⣿⡟⠟⠇⠇⠐⠀⠀⠘⠀⠀⠃⠀⠿⠸⠿⠧⠿⠿⠿
⣧⣿⣿⣿⣿⡟⢻⣅⣹⣭⡿⣭⡯⣻⣷⣞⡟⣭⣤⣍⢹⣯⣿⣟⣿⣯⣯⣏⢩⣍⣩⡍⠉⣩⣭⣕⢸⣷⣶⣮⣷⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡹⣿⣯⠉⠙⠁⠀⣿⣿⣿⣷⣿⡷⣿⡇⣿⡇⣿⣧⡿⠀⣿⢸⣿⣬⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣎⣿⣿⣿⣿⡙⢛⣫⣾⣿⣿⣿⣿⣿⣿⣿⠀⣿⠁⡿⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⡿⠃⠀⠀⠀⠀⢀⣿⣹⣿⣿⣿⣇⣿⣇⣿⣏⣿⠀⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡩⣿⣿⠟⠚⠛⣻⣿⣿⣿⣿⣿⣿⣿⠠⡿⠘⢿⣴⣆⣶⣶⢖⡾⣿⣿⣿⣾⣶⣶⣶⣶⣤⣤⣼⣿⣤⣤⣤⣤
⠛⠁⡀⠸⣽⣶⣷⡼⣿⣿⣽⣿⣿⣿⠿⠿⠿⢿⣿⣯⣧⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣧⣌⣙⣟⣿⣿⣿⣿⣿⣿⣿⣿⡀⣧⠀⣶⣨⣿⣉⠙⢈⡁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣶⣿⣿⣿⡇⣿⣿⣯⣭⣏⣾⣤⣽⡟⣤⣤⡄⢮⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⡿⠛⠀⠙⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⡿⠿⢇⣟⠛⠋⠉⠋⠛⠛⠛⠛⠛⠛⠻⠿⢿⠿⣿⣿⣿
⠀⣼⣿⣿⣛⣻⡋⠀⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠛⣿⣿⣿⣿⣿⣼⣷⣷⣴⣤⣴⣿⣿⣿⣿⣿⢱⠀⠀⠈⠉⠉⣙⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠁⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣜
⠀⣿⣿⣿⣿⣏⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡟⣿⣿⣿⠋⠉⣿⠿⠟⠁⢸⣧⣠⠀⠄⣶⣿⣿⣿⣿⣿⣿⡿⠀⠁⠈⠉⠒⠠⢄⣀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠋⠉⠙⣷
⠀⢿⣿⣿⣿⣿⣿⣷⠶⠦⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⡻⠿⠒⠀⠀⠀⠀⠀⠈⣿⣿⣶⣅⣘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣤⣄⣀⠀⠀⠀⠀⠉⠀⠀⠒⠚⠋
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠁⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⣀⡀⠻⣿⡏⠀⠸⣿⣿⡎⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣡⡄⠀⣠⢾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠃⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢠⡾⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀
⠋⠖⠲⣶⠏⢶⠌⠳⠷⠶⠆⠻⠿⠟⠿⠿⠿⠿⠿⠿⠿⠛⠛⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠻⠟⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿
⣤⣤⣤⣤⢤⣤⣤⣤⣄⣤⠤⢤⣤⡄⢀⠀⣤⣤⡀⠀⠀⣀⣤⢀⡄⠀⠄⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⢠⠀⣄⣤⡀⢀⠀⡀⠀⢤⠄⠠⠄⠠⢠⡄⠠⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⣤⠀⠀⢠⠠⣤⡄⠀⢠⣀⣤⣤
⣟⣻⣿⣿⣺⣿⣿⣿⣿⣻⢛⣿⣿⣷⣖⠢⡝⢿⣶⠆⣠⣼⡛⢃⠀⠠⣐⡀⠀⠀⣿⣿⣹⣯⣽⠀⠀⣿⣀⣠⣤⣶⣷⣶⣶⣶⣧⣜⣿⠯⠠⠁⠨⢸⡇⠫⠀⠟⠘⠁⠸⠁⠋⠀⠉⠀⠙⠀⠂⢸⠀⣿⡟⠛⠛⠹⠫⠉
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⢦⠠⠴⠟⣽⠡⢋⢴⣿⣭⠁⠀⠀⣿⣿⣿⣷⣿⢀⣤⣿⣿⠿⠟⠋⠊⠀⠛⠿⢿⣿⣿⣷⣔⡀⠀⢸⡇⠾⠀⠿⠘⠁⠘⠀⠟⠀⠀⠀⡁⠀⠀⢈⠀⣿⡇⠀⣦⠀⠀⢸
⠙⣛⣛⣿⢽⣿⠿⠿⣿⣿⣼⣿⣿⣏⠂⡐⣼⣟⢘⣥⣴⣎⢸⣿⡭⠛⣻⠁⠀⠀⢻⣿⣻⢛⣿⠿⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⣯⣭⣯⣷⣀⢸⡇⠀⠀⠂⠠⠀⠀⠀⠚⠀⠄⠀⡇⠀⠀⠘⠀⣿⡇⠀⢠⣤⡶⣼
⣶⣿⣿⣿⣼⣿⣾⣾⣿⣿⣽⣿⣿⣿⠸⡷⢛⣱⠈⠕⠷⠇⢨⣥⣤⣬⣭⣀⠀⠀⠙⠋⠙⢙⠏⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣄⠀⠈⣬⣝⣕⢸⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠆⠀⠅⠀⠀⠀⠀⣷⡇⠀⠄⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠠⠏⣰⣾⣿⢙⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠒⠢⢝⠶⠶⣶⢶⢢⣶⠒⠒⠒⠀⠀⠀⠁⠀⠀⠠⠀⠁⠀⠰⠟⠳⠶⠺
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠠⢾⣿⣿⣾⣿⣯⣦⠉⠇⠀⠀⠠⢄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⡶⡶⡆⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢀⠧⠀⠀⠀
⣽⣿⣿⣿⠛⠛⣿⣿⣿⣿⠀⣿⣿⣿⠄⣤⣠⠀⠀⠀⠀⠀⣼⢻⣿⣿⠏⠙⠀⢔⣴⢤⣥⣴⠀⠀⢻⣿⠿⠿⠿⣿⣿⣿⠄⣨⣿⣿⣿⣿⣷⡄⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⢀⠀⠀⠀⣿⢀⣿⡇⠀⠀⣀
⠙⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⣿⣿⣿⣱⣿⣟⣿⠀⣠⡅⢰⣿⠙⣿⣿⣆⣀⣀⣾⡙⢨⣏⣽⣀⠀⢸⠁⠀⠀⠀⢹⣿⣧⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⠉⠙⠉⣿⣿⡟⠟⠇⠇⠀⠀⠀⠘⠀⠀⠃⠀⠿⠸⠿⠷⠿⠿⠿
⣧⣿⣿⣿⣿⡿⢻⣅⣹⣭⡿⣭⡯⣻⣷⣞⡟⣭⣤⣍⢹⣿⣿⣟⣿⣿⣯⣍⢩⣍⣩⡍⠉⣩⣭⣕⢸⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡹⣿⣿⠛⠛⠃⠀⣿⣿⣿⣷⣿⣷⣿⡇⣿⡇⣿⣧⡿⠀⣿⢸⣿⣼⣿⣸⣿⣀⣿⣾⣁⣀⣉⣙⣿⣌⣿⣿⣿⣿⠛⠿⣯⣽⣿⣷⣿⣿⣿⣿⣿⠀⣿⢡⡿⠀⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⡿⠃⠀⠀⠀⠀⢀⣿⣹⣿⣟⣿⣇⣿⣇⣿⣏⣿⠀⣿⢸⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⠞⠻⢿⣻⣿⣟⣿⣿⣿⣿⣴⡟⢹⢿⣴⣴⣶⣶⢖⡾⣿⣿⣿⣾⣶⣶⣶⣶⣤⣤⣾⣿⣤⣤⣤⣤
⠛⠁⡀⠸⣽⣷⣷⡼⣿⣿⣽⣿⣿⣿⠿⠿⢿⢿⣿⣯⣿⣽⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣧⣐⡒⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣦⣨⣿⣉⠙⢈⣁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⣠⣶⣿⣿⣿⡇⣿⣿⣯⣭⣏⣾⣤⣽⡟⣤⣤⡄⢦⣽⣿⣿⣿⣿⣿⣦⣭⣽⣿⡿⠛⠀⠹⣿⣿⣿⡿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⡿⠿⢇⣞⠛⠋⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⠿⣿⣿⣿
⠀⣹⣿⣿⣛⣿⡋⠀⠉⠉⢿⣬⡉⢸⣿⣸⡇⣿⣧⡄⣼⡏⣿⠛⣿⣿⣿⣿⣿⣼⣷⣷⣴⣤⣼⣿⣿⣿⠁⠀⢰⠀⠉⠉⠛⠛⠛⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠁⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣜
⠀⣿⣿⣿⣿⣏⣁⠀⠀⠀⣶⣹⣿⢸⣿⠀⠀⣿⣇⡀⣿⡷⣿⡀⣿⢹⣧⢹⣿⣹⡟⣻⣿⣿⢋⠉⣿⠏⠀⠀⢸⣧⣲⡢⠄⣶⣿⣿⣿⣿⣿⣿⡿⠈⠍⠉⠙⠒⠠⢄⣀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠙⣷
⠀⣿⣿⣿⣿⣿⣿⣷⠦⠦⠉⠉⠁⠈⠉⠀⠀⠉⠉⠁⠉⠀⠉⠁⠉⠀⠉⠀⠉⠉⠁⠙⡻⠿⠒⠈⠀⠀⠀⠀⠈⣿⣿⣷⣕⣙⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣤⣄⣀⠀⠀⠀⠀⠉⠀⠐⠒⠚⠋
⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠀⠊⠻⣿⣿⣿⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⣀⡀⠹⣿⡏⠀⠸⣿⣿⡮⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣡⡄⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠿⠃⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣠⡾⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀
⠋⠖⠲⣶⠏⢶⠌⠳⠷⠶⠖⠻⠿⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠻⠟⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿

                    ䷩ 𝚕𝚒𝚗𝚎 1662

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/19/epo-terminator-meme/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/19/epo-terminator-meme/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.19.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Bubble_Schwabble⠀✐


Posted in Europe, Patents at 3:38 am by Dr. Roy Schestowitz


Terminating the EPO in only_a_few_years


              🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_is_fine,_EPO_doing_great!⦈_
Don’t listen to evil, malicious tongues. EPO management has done a great job!
                              (For its own good)


Summary: The den of nepotism and despotism, led by Benoît_Battistelli and
António_Campinos (shown above), is in denial about the direction in which it’s
heading (burning laws, constitutions and treaties for a short-term money-
grebbing expedition)


⠀⠀⠀⠀⠀⠀⣶⣦⢠⡦⢤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠄⠠⣤⣤
⡀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣀⡄⠙⢻⣿⣿⣿⣿⣿⣵⣾⣿⣿
⡷⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣼⣿⡷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⡻⣿⣷⡄⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⠿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣠⣾⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢸⣿⣿⣿⣿⣇⣼⣿⠇⠀⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠿⠛⠁⠀⠀⠁⠈⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢈⣽⣿⠏⠈⠉⢉⠁⠀⢸⣿⠏⠉⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢤⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿⠋⣀⡀⠀⠈⠁⢰⣿⠋⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣽
⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢰⣿⠇⢰⣿⣿⣷⣶⣷⡏⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣤⣤⠈⠹⣿⣿⣿⣿⣿⣼⠿⡿⢛
⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⠠⢾⣿⠿⠟⣽⠋⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣶⣾⣿⠀⠀⢿⡟⠛⠿⠙⠛⠈⢠⠌
⣤⠀⠀⠀⠀⠀⠀⠘⠋⠀⢰⣾⣿⣿⣿⡉⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠿⠛⠻⠆⠀⣼⢯⠠⠀⠀⠀⠀⢰⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠈⠻⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⣴⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠁⠀⠀⢀⣴⣿⡁⠀⢀⡀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡂⠀⣛⠛⠉⠁⠐⣾⣗⠀⠀⠈⠁
⣶⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⠑⢓⣚⡃⠀⣀⣀⣴⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠸⣇⣀⢁⡀⠀⣀⣀⠠⣁⣀⣀⣀⣀
⣿⣧⣄⣠⣤⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣇⠀⢻⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣧⡴⣿⣿⣿⣿⣿⣿⢷⣦⣹⣿⠀⣿⡀⠈⢿⠇⠿⠿⠯⠻⠟
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣿⣟⣼⢨⠉⠁⠉⠁⠙⠀⠁⠀⠈⠉⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⠘⠀⠘⢻⡆⠈⠄⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠋⠉⠉⠉⠛⠛⠉⠈⠙⠛⠿⣿⣿⣦⢠⠀⠀⠀⠀⢻⣿⡿⢸⠀⠀⠀⠀⠀⠠⠀⣀⢀⣴⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⣀⣯⡧⠤⠤⠤⠤⠤⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠀⠀⠀⣀⣸⣿⣿⣾⡀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣤⠀⠉⠉⠉⠀⠀⠀⠛⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⢷⣻⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⡞⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀
⠀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢃⣽⡿⣿⠛⢿⣿⡿⣝⢿⣿⣿⣿⣧⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣍⣶⣿⣿⡇⣿⣇⣀⣾⣿⣿⡀⣹⣿⣿⣿⠚⣿⣿⠀⠀⠀⠀⠀⠀⠐⡶⠊⢹⣿⣿⣿⡆⠀⠀
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⡿⢻⠻⣿⣿⣿⣽⣿⣷⣾⣿⣛⠛⣧⠘⠻⣿⡿⡂⣿⡏⠀⣀⣠⣤⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⣿⡇⢸⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣻⣷⣶⣬⣥⣬⣾⣷⣿⡿⠟⠈⠁⠀⢀⣴⣾⣿⣿⣿⣷⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⡇⢸⠀⠀⠀⣼⠲⢼⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣴⣦⣤⣤⣤⣤⣶⣦⣤⣴⣦⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣄⠠⠀⡤⣤
⠀⠀⠸⠿⠀⠀⢿⡿⢿⠿⣿⣿⣿⣿⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⣠⡄⠘⢻⣿⣿⣿⡟⠏⢴⠈⣽⣿
⠀⠀⠀⠀⠀⢀⣾⣷⡄⣰⣿⣿⣿⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣤⣿⡇⠀⠀⣿⣿⣿⣿⣾⣷⣶⣿⣿
⠀⠀⠀⣀⠀⠠⣻⣿⣶⣿⡿⠿⠩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⡇⣽⣿⡿⣿⣿⡌⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⡿⠿⠇⠀⠀⣿⣿⣿⣿⣿⣿⠟⠿⣿
⠀⠀⠘⢿⣷⢰⣿⡿⣿⣿⣷⣄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣀⠀⢸⣿⡇⣸⣿⣇⣼⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠋⢀⡀⠈⠻⢿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⢉⣽⣿⠋⠉⠉⠁⠀⠀⢸⣿⡿⠉⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⠄⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⢿⣿⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠙⠀⣴⣿⠏⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀
⣀⠀⠀⢸⣿⠇⠀⠈⠛⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⠁⣸⣿⣿⣶⣶⣶⠏⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣤⣤⠀⠙⣿⠯⠅⠉⠀⠀⠀⠠⡤
⢿⠂⠀⢀⣄⠀⣶⣾⣿⡆⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠟⠃⠠⣿⡿⠿⢛⡿⠋⠀⠀⠀⠀⠀⢀⣼⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣶⣶⣿⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠂
⣼⣷⠀⠈⠁⠀⠛⠛⠉⢰⣿⣿⣿⣿⣿⣏⠁⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠐⠙⠁⠀⠈⠁⠀⠀⠀⠀⠀⣰⠟⠋⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠟⠛⠻⠆⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀
⡈⠉⢴⡆⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠃⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠁⠀⠀⢀⣴⣷⠄⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡂⠀⣟⠛⠉⠀⠀⠴⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⠓⢶⣶⡏⠀⣀⣶⣤⣶⡿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠸⣇⣀⢁⡀⠀⣀⣀⠠⣇⣀⣀⣀⣾
⣿⣶⣦⡄⠀⣠⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣿⠿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣇⠀⢹⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⢷⣦⣹⣿⠀⣿⡀⠈⢿⠧⠿⠿⠿⠿⠟
⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⣿⣟⣾⢺⠉⠉⠉⠁⠀⠀⠉⠀⠉⠋⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠘⢩⡄⠈⠄⠀⠀⠀⠀⠀
⠿⢿⣿⡿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠙⠛⠋⠁⠈⠙⠛⢿⣿⣿⣷⣴⡄⠀⠀⠀⢻⣿⡿⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⣀⣮⡥⠤⠤⠤⠤⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⡁⠀⠀⣀⣸⣿⣷⣾⡀⠀⠀⠀⠀⠄⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡿⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣾⣿⣷⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠉⠉⠁⠁⠀⠀⠛⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⡍⠹⣿⣿⣿⣿⡾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀
⠀⠀⡀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⡟⢿⣿⣳⣝⢿⣿⣿⣿⣧⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣧⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⡇⢿⣿⣿⣿⠻⣿⣿⠀⠀⠀⠀⠀⠀⠐⣶⠟⢿⣿⣿⣿⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⢄⣄⠀⠀⣠⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣧⠘⠿⣿⡿⠇⢿⡏⠀⣀⣠⣤⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣆⢰⣿⡇⠀⠀⠀⣿⡟⢻⠇⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣥⣴⣿⣷⣿⡿⠇⠀⠁⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠉⠬⢿⣿⡄⠉⠁⠀⠀⠀⣿⡇⢸⠀⠀⠀⣼⠢⢾⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢠⣤⠀⣴⡄⠀⡀⠀⣀⡀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡄⠄⠤⡤⣤
⠀⠀⢀⣘⡿⠇⠉⠁⠀⣠⣾⢶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⡄⠈⠻⣿⣿⣿⣿⡁⠀⠄⢸⣿
⠀⠀⣸⣿⠇⠀⣰⣦⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣴⣿⡗⠀⠀⣿⣿⣿⣿⣶⣶⣶⣿⣿
⣦⠀⠘⠃⠀⠀⠙⠛⢶⡎⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⢀⣈⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠟⠛⠃⠀⠀⣿⣿⣿⣿⣿⡿⠋⠁⠀
⠁⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⢸⣿⡇⠸⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣴⡆⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠉⠁⣰⣿⡟⠉⠁⠀⠀⠀⠉⣿⡿⠛⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⠀⠀⠀⠘⠃⠀⠀⠈⠉⠉⠁⠀⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠐⠂⢀⣴⡟⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⠀⠈⠙⠛⠿⠙⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⠃⢰⣿⣷⣦⣴⣦⡾⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣷⣺⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠐⠛⠃⠠⣿⣿⡿⢟⡿⠋⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⣿⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⡇⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠁⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠉⠙⠃⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠘⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠉⠻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣀⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⡀⢀⣾⣷⡆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠐⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⣏⠉⠀⠀⠀⠋⠆⠀⠀⠀⣰
⣿⣿⣿⣶⣿⣿⣥⣤⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠚⢂⣶⡶⠃⣀⣀⣀⣠⠶⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣟⠛⠘⣃⣀⢁⡀⠀⢀⣀⠀⣑⣀⣀⣀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⣿⠛⣿⣿⣿⣿⣿⣿⡄⢸⣿⣇⠀⢸⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⢷⣦⣹⣿⠀⣿⣀⠈⢿⠇⠿⠿⠏⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⣿⣟⣾⢸⠉⠁⠉⠁⠀⠀⠈⣿⠙⠉⠀⡈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠘⢨⡀⠈⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠉⠉⠉⠉⠀⠀⠈⠙⣻⣿⣿⣿⣶⡆⠀⠀⠀⢻⣿⡿⢸⠀⠀⠀⠀⠀⠀⠀⣹⣧⣴⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⣀⣮⣤⡤⠤⠤⠤⠤⠀⠀
⣿⣿⣿⡿⠿⠏⠀⠀⠀⣠⣤⣶⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣸⣿⣿⣾⡀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡿⠃⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⡀⡀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠁⠻⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣻⡞⣿⣿⣿⡏⠀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⢿⣿⣿⣾⣇⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡈⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⠿⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡟⢿⣿⣿⣿⡼⣿⣿⠀⠀⠀⠀⠀⠀⠀⢶⠿⢿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠁⠆⠄⠉⠻⣿⠀⠀⢀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡛⣿⣿⣿⡫⢿⡏⠀⣀⣠⣤⣦⠀⠀⠈⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⠀⠀⠀⠀⠀⢀⣾⣿⡇⢀⣿⣿⢿⠃⠈⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣯⣾⣽⣿⣿⡿⠇⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⢀⣸⡿⠿⠃⢾⣿⡇⢸⠀⠀⠀⣼⠢⢾⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣀⣤⣶⣶⠀⠀⠀⣴⣦⢶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⢀⠄⠀⠉⠯⠷⠳⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠸⠿⠉⢿⣿⠉⠀⠀⠈⠿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣿⣧⣭⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣤⣾⠃⠀⠀⣿⣦⣶⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣄⠈⠁⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣈⣻⣿⣿⡿⠟⠛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠋⠉⠁⠀⠀⣿⣿⣿⣧⣤⡀⠀⠀⠀
⠀⠀⠀⣀⡙⠋⢀⡀⠀⢠⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⡇⠸⣿⣯⣿⣿⠇⠀⠀⣿⣿⡄⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣀⣼⣽⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠸⣿⠇⠀⠀⠁⠀⠀⠉⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠉⠁⢀⣼⣿⠏⠁⠀⠀⠀⠉⠉⣿⠿⠎⠉⠱⢿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⠛⠉⠙⠛⠉⠀⠀⠀⠀⠀
⠿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⡛⠺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠇⠀⠀⠀⢠⣤⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⣿⠏⠀⣶⡛⠒⣠⣤⣤⠟⠁⠀⠀⠀⠀⢀⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣦⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠚⠋⠀⢼⣿⡿⠿⢫⠝⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⣰⡿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠘⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠚⠁⠀⠀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣦⣤⠀⣶⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠨⡇⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⢀⣀⣀⣀⣀⣀⣀⣈⠿⢧⣴⡴⠀⣀⣀⣀⣀⠠⣾⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣆⠛⠀⣃⣀⢀⡀⠀⢀⣀⠀⣀⣀⣀⣀⡻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⡍⣼⠋⣿⣿⣿⣿⣿⣿⡄⢸⣿⣇⠀⢸⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⢷⣦⣹⣿⠀⣷⡄⠈⠻⠆⠟⠛⠋⠛⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⣿⣟⣾⢲⠉⠁⠉⠀⠀⠙⠋⠉⠟⠉⠀⡈⣹⣯⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠈⢰⡄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣧⣤⣬⣽⣿⣿⣿⣿⣦⣄⡀⣀⠀⢻⣿⡿⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⣿⣿⣿⣿⡿⠋⠈⠛⠙⠛⠋⢈⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣮⣥⣤⠤⠤⠤⠄⠀⠀
⣿⣿⣿⣯⣠⣤⣴⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣾⡄⡀⠀⠀⠀⠄⠰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣍⠹⣿⣯⡀⠠⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠛⠀⣿⣿⠿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣳⡕⠏⣿⠊⢠⡀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⣿⣿⣿⣯⣿⣿⣿⡯⣿⣷⣬⣿⣿⣿⠂⢸⣇⠴⠧⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠊⢹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣽⣿⣿⣿⣿⣛⠛⣇⠀⠙⢻⠄⠀⢿⡏⠀⣀⠀⠤⠄⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⢠⣤⡀⠀⠄⠀⠀⠀⠀⠀⣿⡟⢸⠀⠉⠉⠉⠙⢿⣿⣿⣿⣿⡿⠿⣷⣶⣬⣥⣤⣼⣷⣿⡿⠇⠀⠀⠀⢀⣴⣾⣿⣿⣿⢷⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⣿⡇⢸⠀⠀⠀⣼⠢⢌⢿⣿⣿⣿⡯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠠⣤⠄⠀⠀⠤⠀⠀⢠⣶⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢤⣤⣤⣤⡤⢀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢠⠆⠀⠘⠿⠃⠓⠁⠀⢀⣀⠀⠀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣶⣾⡇⠀⠀⣾⣮⣤⣴⣶⣿⣿⣇⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣈⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⢹⣿⣿⣿⣇⠀⠀⠋⠉⠁⠀⢀⠁⠀⠀⠊⠛⠋⠛⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣇⣼⣿⣿⡿⠏⣿⣿⡇⠉⢻⣿⡇⢸⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣄⡀⠀⠀⠀⣴⣮⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠁⠀⠈⢉⣽⣿⠟⠀⠀⠉⠉⠀⢠⣬⣭⣵⣮⡍⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣀⢀⣤⡿⠇⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⢀⣿⠿⠛⠿⢿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⡗⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣾⡟⠁⢠⡲⠦⠄⣀⣀⣴⠟⠁⠀⠀⠀⢀⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⢘⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠺⠛⠀⢠⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢼⣷⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠁⠀⠈⠁⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢾⣦⡈⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⡀⠀⣴⢿⣶⡄⠀⠀⠀⠀⠀⠀⢀
⣠⣄⠀⠘⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠻⠟⠀⣤⣤⣤⣠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢐⣠⡤⠬⣁⣀⣀⣀⠀⣴⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠋⠈⣁⣰⢟⡿⡿⣷⣷⠆⣀⣀⣀⣀⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡄⠘⣿⣇⠀⢸⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⢷⣦⣹⣿⠀⣿⣶⣿⣿⠧⠿⠛⠋⠻⠃
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⠀⣿⣟⣿⣿⠉⠉⠉⠁⠀⠀⠁⠀⠈⠉⢀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⢽⡇⡏⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⠆⠄⠀⠀⠀⠀⠀⣀⢀⣾⣿⣿⣿⣿⣿⠿⢿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣀⣿⣧⣥⣼⣤⣤⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣶⣶⣤⣴⢖⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡿⠃⠀⠈⠻⠛⠛⠋⠉⠉⠈⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣷⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⢶⠚⢿⣿⣿⣿⣇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⣿⣧⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⠠⠠⠦⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋⠀⠈⠭⢁⠀⠻⠿⠻⠿⣿⡿⢿⡿⠈⠀⣾⠷⢾⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠄⠀⢠⣦⠀⢠⣶⠀⢤⣤⡄⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⠀⠀⠁⠀⢀⢉⡁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⠁⠀⠀⠀⠤⡆⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠟⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⡀⠀⠀⣶⣿⠇⠀⠀⠇⠀⠀⠀⠐⠒⠒⠂⠈
⠀⠘⠃⠀⢀⠀⠀⠀⡈⠉⠿⠃⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡍⠁⣼⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣦⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣇⠀⢸⣿⣶⠀⠀⢰⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣇⣼⣿⠇⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣧⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠈⠋⠀⢸⣿⠉⠀⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⠉⠉⠁⢀⣴⣿⠏⠉⠉⠉⠉⢹⣿⣿⣍⠁⣈⣩⣽⠮⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠧⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣶⣿⠟⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⣾⣿⣿⣍⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣴⠟⠉⠀⢄⡀⠀⠀⠀⢠⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠛⢿⡟⠋⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠠⠞⠁⠀⣰⣶⣶⣤⠶⠟⠒⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⣿⠟⢿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⣼⣿⣤⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠻⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢠⡀⠀⣾⣿⣶⣦⣀⣀⣤⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⠀⠀⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡆⠀⣿⣿⣿⣿⣿⣼⣿⣧⠀⠀⠀
⠀⠀⠀⠀⢠⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⢀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⡀⠴⣟⣀⣀⣀⠀⢨⣽⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣟⠉⠀⣀⣴⢏⡻⡿⣿⣿⡿⣯⣁⣀⣀⡀
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡄⢸⣿⣇⠀⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⢷⣦⣽⣿⠀⣿⣾⣿⣿⣧⡿⠿⠯⠾⠇
⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠙⠋⠉⠉⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠘⣸⡏⡯⡇⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣆⡆⠀⢴⣦⣰⢾⣿⣯⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣀⣿⣧⣥⣼⣤⣤⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡤⠤⣴⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡿⠃⠀⠈⡙⠛⠉⠉⠉⠀⠉⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠋⠿⠿⣿⡟⠋⠉⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣾⡌⣿⣿⣿⡏⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀
⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠚⠀⠀⠀⠀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⡟⢿⣿⣿⣟⢿⣿⣿⣿⡇⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⢠⣾⣷⠀⠀⠀
⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷⣿⣷⣌⣿⣿⣿⠋⢻⣿⣿⣯⠞⣿⣿⠀⠀⠄⠀⠀⠀⠀⠶⠚⢿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠆⠀⠀⠀⢀⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣛⢛⣧⢸⣿⣿⣿⣯⢿⡟⠀⣀⠀⠀⠤⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⣀⣿⡿⡿⠁⠀⠀⣿⡟⢸⠁⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⡿⠷⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠀⠀⣿⣯⡛⠁⠀⠀⠀⣿⡇⢸⠀⠀⠀⣼⠣⢜⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⡤⢦⢄⡀⠀⠀⣴⣶⣦⣴⣦⠠⠤⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠠⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠈⠁⠀⠀⠉⠉⡀⠉⠉⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⢴⡄⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀
⣦⠀⢠⣶⠀⠀⣀⡀⠋⣀⡀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⢺⣿⣿⣿⠀⠀⠰⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀
⠀⠀⠈⠉⠀⠀⠛⠃⠀⠻⠟⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣷⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⢿⣿⣧⣸⣿⣿⣿⣿⣦⡀⠀⠀⠀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠆⠀⠀⠀⠀⠀⢸⣿⣿⣷⣴⣶⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⠁⠀⠀⣸⣿⡿⠿⠿⣿⣿⣿⣿⣯⣵⣮⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠿⠀⠀⣿⡿⠟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣴⠟⠋⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⢸⣿⣿⣿⣧⣿⣟⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡴⠛⠀⢀⣤⣤⣬⣠⣶⠶⠐⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣿⠿⢿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢠⡀⠀⣾⣿⣿⣶⣶⣶⣔⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡆⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀
⠀⠀⠀⠀⢐⣄⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡄⡈⢀⣠⣀⣀⣀⣠⣴⣶⣦⣀⣀⣀⣀⠀⢤⣤⡴⠶⣿⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣟⠁⠀⣠⣴⢏⡻⣿⣿⣿⡿⣿⣿⣄⣀⣤
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣇⣀⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⢷⣦⣽⣿⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠘⣽⣿⣿⡏⠀⠀⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠁⠀⠈⢻⣿⠟⣿⢉⣿⣿⣿⣿⣿⡿⠛⠛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣀⣿⣧⣥⣼⣤⣤⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣶⣶⠖⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡿⠃⠀⢉⡟⠛⠋⠉⠉⠁⠈⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⢿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣞⣿⣿⣿⡏⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣼⣿⠟⠁⠀⠀⣿⣿⣿⣿⡿⣫⣿⣿⣿⡛⢿⣿⣷⣟⢿⣿⣿⣿⣯⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣶⣤⣄⣠⣀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⢹⣿⣿⣍⣾⣿⣿⣇⣿⣷⣬⣿⣿⣿⡞⣿⣿⣿⣿⣟⣿⣿⠀⠀⡄⠀⡄⠀⠀⠶⠚⢹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⢸⡿⢻⠟⣿⣿⣿⣽⣿⣿⣿⣿⣛⢟⣯⣿⣿⣿⣿⣿⢿⡟⠀⣀⠀⠀⠆⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⣾⡇⢸⠀⠈⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠀⠀⠀⠨⣿⣿⠇⠀⠀⠀⣿⡇⢸⠀⠀⠀⡼⠣⢼⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢠⣤⠀⠀⠀⠀⣶⠄⠀⢴⣶⠄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣴⣶⣦⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠠⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢿⣿⡿⢸⣿⣿⣿⠀⠀⠀⡀⣶⠄⠀⠈⠍⠁⠀⠀⠀⠀⠀⠀⠀
⣦⠀⠀⠀⠀⠀⣶⣿⠆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣼⣿⡇⢸⣿⣿⣿⠀⠀⠸⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢰⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣤⣄⠀⠀⠀⠀⢿⣷⡀⠰⣾⣷⣾⢉⠁⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣷⢸⣿⣿⣿⣿⣦⡄⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠓⠀⠀⠀⢈⣿⣶⢫⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠁⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣯⣽⣿⣭⣿⣮⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠘⠿⠛⢸⣿⣿⣿⣿⠏⠉⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠃⠀⠙⠃⠀⢀⣤⠀⠀⣰⣾⣽⣿⣁⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠤⠚⠉⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣼⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠉⣸⣿⣿⣿⣿⣿⡏⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠐⣿⠿⣿⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⢰⡆⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⡿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣴⣿⣾⣶⣀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣤⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠃⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠐⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴
⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⢾⣿⡶⠿⣿⣿⣷⣀⠀⢴⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣏⠁⠀⣤⣴⢏⡻⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⠿⠏⠉⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣇⠀⢿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⠉⠁⠀⠀⠀⠀⠙⠉⠀⡉⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠏⠀⠘⣿⡏⣿⡏⠀⠀⡌⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⣀⠀⣴⣾⣿⣿⣿⡿⠛⠛⠛⠻⠻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣠⣿⣧⣥⣼⣤⣤⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⡀⠀⠀⢠⠄⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢩⢹⣿⣿⣿⣿⡿⠃⠀⢈⣿⠛⠉⠉⠀⠀⠈⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠙⢿⣿⣿⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣏⠹⣿⣿⡯⢸⠈⣿⣿⣿⡏⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⡛⢿⣿⣳⣝⢯⣿⡞⣰⡇⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⣠⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⠀⠀⠀⢹⣿⣴⣦⡄⠀⣿⣿⣿⣭⣾⣿⣿⡧⣿⣷⣌⣿⣿⣿⠃⢹⣿⡾⣧⡜⣿⣿⠀⠀⠄⠀⠄⠀⠀⠶⠚⢹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⢤⣤⣼⡧⠸⣿⠇⠀⣿⣿⢿⠿⣿⣿⢻⣽⣿⣿⣿⣿⣟⠛⣷⣽⣿⣿⡿⣯⣿⡏⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⠀⠀⠉⠛⠛⠀⠀⢹⡇⠀⣿⡇⢸⠀⠈⠁⠙⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⣿⡇⠸⠀⠀⠀⡼⠀⢈⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣶⣶⣶⣴⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠹⡇⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠙⠻⠻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢸⣿⣿⣿⠀⠀⢠⣬⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣟⠀⠀⠸⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⣀⡀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠈⠴⣾⣿⣿⡆⣿⣿⣬⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⢺⣿⣿⣿⣿⣷⠀⠀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣦⠉⢿⣟⣁⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⢁⣼⣿⣿⣿⣯⣭⣽⣮⣭⣽⠮⣽⣿⣿⣿⣿⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡰⣿⠀⠀⠀⠀⠘⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠃⠀⠻⠃⠁⠀⣀⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢰⣶⣾⣷⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣀⠀⢀⣶⣿⣿⣿⣿⣿⡇⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⠟⠛⠿⠀⢰⣿⣧⣤⣤⣤⡄⠀⠀⠀
⠀⠀⠒⠺⠇⠀⠀⠀⠹⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣶⣦⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢲⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣷⠀⠰⡆⠀⠀⣀⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠘⠇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠹⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢖⣿⣿⡟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⣀⢀⣀⠀⢀⣈⡿⠿⣿⣿⣿⣟⠁⢴⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣁⠀⠀⣶⣾⢀⡻⣿⣿⣿⡿⣿⣿⣿⣿⣿
⡆⠀⠀⠀⠀⣀⣀⣈⠋⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡝⣿⠛⣿⣿⣿⣿⣼⣹⡄⠘⣿⣇⠀⢻⣿⣿⣿⣷⣨⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠛⢳⣿⡿⠿⠟⠂⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣗⣾⢠⠉⠁⠉⠀⠀⠀⠀⠀⠈⠉⠀⠈⠙⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⠉⠀⢸⣿⡏⣿⡏⠀⠀⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⡿⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣾⣿⣿⣿⡿⠛⠛⠛⠻⠻⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣀⣸⣿⣧⣥⣼⣤⣤⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠿⣿⣿⡿⣿⣿⣿⣿⣿⣂⣸⣿⣷⣾⡌⡀⠀⠀⣤⠄⣰⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⢹⣿⣿⣿⣿⡿⠃⠀⢸⡟⠛⠉⠉⠉⠀⠀⡀⠀⠀⠀
⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⡏⠈⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣯⡻⣿⣿⣷⣾⡈⣿⣿⣿⠏⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠁⣀⡀⠀⠁⠀⢀⣽⣿⣿⣆⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣧⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣄⣠⣄⣾⣿⣿⣿⠟⠁⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡇⣿⣿⣿⣿⡜⣿⣿⠀⠀⠀⠀⠀⠀⠐⠖⠊⢹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠃⢸⣿⣿⣿⣿⣿⡿⠀⠀⢾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣷⢿⡏⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⠀⠈⢿⣿⣿⢿⣿⠃⠀⠀⣾⡇⢸⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠈⠉⠀⠀⠈⣯⣍⠸⠿⠄⠀⠀⣿⡇⠸⠀⠀⠀⡼⠠⢀⢿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣤⣤⣄⣤⣤⣤⣤⣤⣶⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⣀⡀⣄⠀⣶⠀⠀⠀⠀⠀⠀⠘⠿⠓⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣏⢸⣿⣿⣿⠀⠀⢠⣬⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⣿⡇⠀⠀⠟⠀⠀⠀⠀⠺⠆⠀⣀⠀⣿⣿⣚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡏⢸⣿⣿⣛⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣷⠈⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢸⣿⣿⣿⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠋⣿⣿⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⢺⣿⣿⣿⣿⣿⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣄⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⣹⣿⣿⣿⣿⣯⣽⣾⣭⣽⢮⣽⣿⣿⣿⡿⠀⠀⠀⠐⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡏⠀⠀⠀⣤⡄⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢰⣶⣿⣇⠀⢰⣿⣆⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⢀⡀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣇⡀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⠛⠛⠿⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀
⢰⡆⠀⢠⣄⢿⡷⣀⡀⢀⡀⠛⠻⣿⣿⣿⣿⣿⣿⣷⣴⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠸⠿⠀⠀⠈⣡⣿⡇⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣲⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⣶⠀⠀⣴⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⡄⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠘⠀⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠺⣿⡟⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⢀⣀⡀⠈⣹⣟⣛⣉⠉⣽⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣀⠀⠀⣻⣿⢀⣹⣿⣿⣿⡿⣿⣿⣿⣿⣿
⢠⣶⡆⢠⣶⣰⡷⢿⡗⠀⠸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⡍⣿⠟⣿⣿⣿⣿⣾⣽⡄⢸⣿⣇⠀⢻⣿⣿⣿⣷⣈⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠉⠀⠀⠁⠉⠁⠛⠁⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡁⠀⣿⣗⣾⢠⠉⠁⠉⠀⠀⠀⠀⠈⠈⠉⠀⡈⢙⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⠉⠀⢸⣿⡏⣿⡏⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠿⣿⡿⠀⠹⣿⣿⣿⣿⠀⢻⣿⣿⣿⠄⣤⠀⠀⠀⠀⠀⣀⠀⣴⣾⣿⣿⣿⡿⠛⠛⠛⠻⠻⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣀⣸⣿⣧⣥⣼⣤⣤⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⣄⣠⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⡤⢤⣴⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⢹⣿⣿⣿⣿⡿⠁⠀⢹⡿⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣯⣹⣿⣿⣷⢸⡈⣿⣿⣿⠏⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⠋⠉⠙⣿⡿⣿⣿⣿⣿⣿⣟⠃⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⣿⣿⣝⢿⣿⣿⣿⡇⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣭⣻⣿⣿⣿⣿⣿⠋⠀⣿⣿⣿⣭⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⡇⢿⣿⣿⣿⠘⣿⣿⠀⠀⠀⠀⠀⠀⠐⠖⠈⢹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⡏⣿⣿⣿⡄⠀⢹⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⠿⣧⠻⢿⣿⡿⠄⢿⡇⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⢰⣿⣿⠟⢁⣿⡟⠻⣷⠀⣾⡇⢸⠀⠈⠉⠛⠹⣿⣿⣿⣿⣿⣿⠿⣿⣾⣭⣽⣭⣼⣿⣿⡿⠇⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠈⠸⢿⠉⠀⠀⠋⠀⠀⠈⠀⣿⡇⢸⠀⠀⠀⢼⠢⢌⢛⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣀⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢠⣤⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⡇⢸⣿⣿⣿⠀⠀⢰⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⢸⣿⣿⣣⡀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣧⣀⠀⠀⠀⢀⣴⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⣽⣿⣿⡿⠟⠀⠀⠀⠘⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⠀⣠⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣀⣻⡆⠀⢹⣿⣿⣿⣷⣤⣤⣀⠀⠀
⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤
⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠁⠈⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⠃⢰⣶⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢤⠀⠀⠀⠀⠀⠀⠀⣤⣄⣤⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣾⣦⠸⣿⡇⠀⠀⣰⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠋⠀⠀⢠⣠⣾⣿⣿⠖⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠉⣀⣼⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠻⠙⠙⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⡀⠀⣀⣁⣦⣚⠛⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣇⣀⡀⢠⣿⣿⢀⡹⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⢀⣶⡆⢰⡿⠾⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣇⠀⢿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠛⠻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠙⠋⠉⠙⢿⡿⣿⣿⣿⣟⢀⡈⠙⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⢈⠁⠀⢸⣿⡏⡿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣧⣷⣤⣠⣾⣶⣿⣿⣫⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⠻⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣀⣸⣿⣧⣥⣼⣤⣤⠤⠀⠀
⣀⣀⣀⣴⣶⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢽⢹⣿⣿⣿⣿⡿⠁⠀⢹⡿⠛⠋⠉⠉⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⡏⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡌⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣦⢨⣿⣿⣿⠀⠀⣿⣿⣿⣿⡿⣻⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣯⢿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠀⠛⠻⣿⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣭⣼⣿⣿⣿⣿⣿⣼⣿⣿⣿⣟⣿⣿⣿⣿⡼⣿⣿⠀⠀⠚⠁⠀⠀⠰⠶⠚⢹⣿⣿⣿⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢘⣿⣿⣿⡇⠀⠀⠀⠀⢸⡿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣹⣿⣿⣿⡟⢿⡏⢀⣀⠀⠀⠀⠀⣀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⠀⣾⣿⠟⢿⡇⠀⠀⠀⠀⣸⡇⢸⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠷⠀⠀⣺⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⡇⠸⠀⠀⠀⣼⠠⢼⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⢹⣿⣯⢿⣿⡟⢸⣿⣿⣿⠀⠀⠾⠿⠗⠀⠀⢰⣆⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣼⣿⡇⢸⣿⣿⣻⡀⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⣰⣶⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣿⠏⠁⠀⢀⣠⡀⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠈⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⣤⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠹⠿⠿⡧⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⠁⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀⠀⠱⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⢤⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣾⣿⣿⠁⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠋⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣦⠀⠀⠀⠀⠻⣿⡇⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣴⣾⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⣗⣀⣠⣼⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣇⣀⣴⢶⣿⣷⢀⡸⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡤⠴⠤⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣇⠀⢿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⢿⣾⢻⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⡈⠙⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⢐⠀⢀⣿⣿⡟⣿⡏⠀⠀⡄⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣤⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⠿⠿⠙⠀⣈⠀⣴⣿⣿⣿⣿⡿⠛⠟⠛⠻⠻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣈⣾⣿⣿⣭⣼⣤⣤⠤⠄⠀
⣀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⣸⣿⣿⣿⣿⣧⡤⠠⢤⠀⠠⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡿⠁⠀⢹⢿⠿⡛⠙⠉⠉⠉⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣾⡈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢋⣿⣿⣿⡟⢿⣿⣿⣟⢿⣿⣿⣿⡇⢿⣿⣿⠀⠠⣤⡶⠀⠀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣍⣴⣿⣿⡧⣿⣷⣬⣿⣿⣿⡃⢹⣿⣿⣿⠘⣿⣿⠀⠈⠋⠁⠀⠀⠰⡶⠚⢹⣿⣿⣿⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⠧⣿⣿⢻⣿⣿⣷⣿⣿⣟⠛⣧⠘⠿⣿⣿⠅⢿⡟⢀⣀⠀⠀⠀⣠⢦⠀⢠⣿⣿⣿⣿⣿⡀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠉⠁⠙⢿⣿⣿⣿⣿⡿⢿⣿⣷⣭⣭⣦⣽⣿⣿⡿⠷⠀⠈⢋⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠁⠀⠈⠿⣤⠀⠀⠀⠀⠀⣿⡇⠸⠀⠀⠀⢼⠢⢌⢷⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⣤⣤⣤⣤⣦⣤⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣀⣠⣄⣀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣏⢳⣿⡇⢸⣿⣿⣿⠀⠀⠸⠛⠃⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⡇⢸⣿⣿⣟⣄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡷⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀
⠀⠀⢠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣽⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤
⠀⣠⡈⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⠁⠀⠀⠠⣤⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣶⣷⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⠛⠻⠇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣷⣄⣀⣀⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠲⣿⣿⣶⣤⣤⣄⣀⣀⡀⢀⢀⣠⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣿⠟⠈⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠛⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣉⡈⠙⠛⠛⢻⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣶⡿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣴⡂⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡆⠀⣂⣀⣀⣼⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣇⣀⣾⢿⣿⣟⢀⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣇⠀⢹⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⢿⠦⢹⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉⠉⠀⠈⠉⣇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠐⠀⢰⣿⣿⡏⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣆⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡏⠀⠀⠀⠀⠀⣀⠀⣴⣾⣿⣿⣿⡞⠈⠈⠛⠻⠻⢛⣛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⢀⣰⣼⣿⣧⣥⣼⣤⣤⠤⠀⠀
⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⡄⠀⠀⢠⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⢹⣿⣿⣿⣿⡿⠃⠀⠙⠻⠟⠋⠉⠉⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢷⣺⣿⣿⣿⣿⣏⡹⣿⣿⣿⣸⡌⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢋⢸⡿⣿⠛⢿⣿⣷⣝⠿⣿⡿⣾⡇⢻⣿⣿⠀⠀⠠⡟⠀⠀⠀⠀⢀⠀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡍⣴⣾⣿⡇⣿⣷⣈⣿⣿⣿⠂⢹⣿⣼⡷⠘⣿⣿⠀⠀⠀⠀⠀⠀⠰⠶⠚⢹⣿⣿⣿⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣷⣄⠀⠀⠀⠀⠀⢸⡟⢻⠇⢿⡿⠙⣰⣽⣷⣿⣿⣛⠛⣦⠐⠻⢿⠗⠀⢿⡏⢀⣀⠀⠀⠀⣴⡦⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠉⠛⠿⣧⡀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠈⢿⡿⣭⣿⣿⠟⠻⣷⣶⣬⣥⣤⣼⣿⣿⡿⠷⠀⠀⠋⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠹⠿⠷⠄⠀⣿⡇⠸⠀⠀⠀⣼⠢⠌⢁⣿⣿⣿⡋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⣀⣠⡄⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣠⣄⣀⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⣿⣿⣇⠀⠀⠹⠛⠃⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⢻⡿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣂⣀⣿⣿⣿⣆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀
⠀⠀⣠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⠀⣤⡈⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣴⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣶⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⣿⣿⣿⣿⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠹⠛⠻⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⢾⣿⣿⣿⣿⣿⣷⣦⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢲⣿⣿⣿⣦⣤⣤⣤⣀⣀⣤⣀⣤⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠛⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠛⠻⠛⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡟⠻⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⣆⣀⣀⣼⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣇⣀⣾⢿⣿⣟⢀⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠼⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣇⠀⢿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡮⣻⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠙⠋⠀⡈⡙⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⢰⠀⣰⣿⣿⣿⣿⡟⠉⠉⡏⠁⠀
⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣶⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠃⠀⠀⠀⠀⣀⠀⣴⣿⣿⣿⣿⡿⠛⠙⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣐⣿⣿⣿⣿⣯⣼⣤⣤⡤⠄⠀
⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡤⠀⠀⣤⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡿⠃⠀⢻⠿⣿⣟⠛⠉⠉⠉⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠿⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠉⠀⠀⠀⠈⠀⠸⠉⠀⢸⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣴⡿⠀⠀⠀⠀⢀⡈⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣍⣼⣿⣿⣧⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⣰⣾⡟⢿⣿⣿⣿⣇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠏⢻⣿⣷⣄⠀⠀⠀⠀⠀⢸⡿⢻⠿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⢠⣴⣿⣿⣶⣿⣿⣿⣿⣿⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠙⠻⢿⣧⡀⠀⠀⠀⢸⡇⢸⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠻⠿⠿⠄⠀⣿⡇⠸⠀⠀⠀⣼⠳⢾⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⢠⡄⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⡄⠀⠀⡤⠤⠄⠀⠀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀
⠀⠀⠀⣿⣿⠿⠏⢻⣿⠿⣶⡆⢠⣾⡟⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡿⣿⣮⣇⣿⣿⠿⠆⢠⣿⣿⣷⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⡀⠰⠷⣿⣿⣀⠀⢸⣿⣆⣿⣇⣸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⡀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⢰⣤⣤
⠁⠀⠀⣿⣿⠉⠀⢸⣿⠛⠉⠉⢹⣿⡇⣿⣿⠘⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣼⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣶⡆⣼⣿⠀⠀⠀⠸⣿⣧⣿⡿⠀⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠿⠇⠀⠀⠀⠀⠀⠀⢀⣠⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⣠⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡆⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣴⡄⠀⠀⠀⠀⢰⣷⡀⢀⣼⣿⣿⣇⡀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⣈⣉⠁⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⡟⠉⠃⠀⠀⠀⠀⠈⠛⠀⣸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣿⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⡀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⢄⡎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣤⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⢠⣢⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣉⣀⠀⢀⣀⡀⠀⣀⣀⣀⣿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣄⣀⠿⠿⣿⣇⢀⣾⠿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠻⠿⠻⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡄⠈⣽⣇⠀⢸⣿⣿⣿⣷⣘⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⠷⠄⢸⠁⠀⣿⣦⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⢠⣄⣃⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⣿⣟⣿⣻⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⡃⠀⠉⠉⠙⠛⢿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⢂⠀⠀⣿⢻⣿⡇⡯⠇⠀⠀⠀⠀⠀
⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣤⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⣀⠀⣰⣾⣿⣿⣿⡄⠀⠀⠀⠐⠀⠀⢈⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⢀⣀⣸⣿⣧⣤⣼⣤⣤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣸⣿⣿⣿⡖⠀⠄⠀⠀⠀⠀⣿⣴⣿⣿⣿⣿⣿⢿⣵⣶⣾⣿⣿⣿⣿⡿⠛⠁⢸⣿⣿⣿⣿⡽⠁⠀⠉⠙⠉⠉⠉⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠋⠉⠙⠋⠛⠋⢙⣿⣚⣦⣿⣿⣿⣿⣿⣿⠗⣺⣿⣿⣿⣻⠁⠙⣿⣧⠁⠀⠈⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠟⠋⣿⣿⣿⣿⡿⠃⢀⡘⣿⠛⢿⣿⠁⡀⠋⣿⠀⢀⠂⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣱⢿⠿⠃⠀⠀⢹⣿⣿⡍⣰⣾⡴⠇⣿⣷⢄⣯⣷⣟⠀⠰⣷⡐⡁⠘⣿⣿⠀⠀⠀⠀⠀⠀⡰⡶⠞⢻⣿⣿⣿⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⢸⡟⢻⠃⠻⠏⠀⠐⣽⣷⣿⣿⣙⠛⢆⠀⠘⠹⠄⠀⢿⡟⢀⣀⠀⠀⠠⣶⡆⠁⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⢲⠭⢭⣿⣿⠗⠛⣷⣶⣬⣥⣤⣼⣿⣿⠿⠇⠀⠀⠈⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣴⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⡇⠸⠀⠀⠀⣼⠲⠀⢀⣽⣿⣟⡂⠛⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⢀⠀⠀⠀⢀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡄⠈⠀⣿⣿⠿⠇⢸⣿⠿⣿⣿⣦⣾⡟⣿⣦⢿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⡇⣿⣿⠿⠆⢠⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⣿⣿⣀⠀⢼⣿⣈⣿⡏⢸⣿⡇⣿⣿⠘⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⠉⠀⢸⣿⠋⠉⠁⢸⣿⣧⣿⣿⠀⠘⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⣼⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⣿⣿⣶⡆⣼⣿⠀⠀⠀⠸⣿⣯⣿⡿⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⡆⣿⣿⡍⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣷⣶⡄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣶⣶⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣤⣶⡃⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠛⠻⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⣿⡄⠀⠘⠃⠀⢰⣶⠀⣴⣿⣿⣿⣿⣷⣤⣦⣤⡈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⠈⠙⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠃⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⢿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣶⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠁⠀⠀⠀⠀⠀⠘⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠛⠁⣀⣀⠀⢀⣀⣀⣀⣀⣀⢀⣈⠛⢀⣀⡀⠀⣀⣀⣀⣿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣇⣀⠙⠉⣛⣃⢀⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣀⣠⢻⣿⡌⢿⠻⣿⡿⣿⣿⣾⣸⡄⠈⣽⣇⠀⢸⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⡷⠄⢸⣧⠀⣿⣆⣿⣿⣷⣿⠿⠿⠿⠿
⡀⠀⠀⠀⡀⠀⠀⢀⣀⡀⢀⣠⣿⣿⣾⣧⣤⣄⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⠀⣿⡏⣸⠠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠃⠀⠈⠉⠉⠉⠙⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⠀⠈⠟⢻⢳⡆⡏⠆⠀⠀⠀⠀⠀
⣿⣷⣦⣤⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠹⢠⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣈⣯⣧⣤⣤⣤⣤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⣸⣏⣀⣼⡀⠀⠀⠠⣤⠀⠀⣿⣴⣿⣿⣿⣿⣿⢷⣴⣶⣶⣿⣿⣿⡿⠟⠋⠀⢸⣿⣿⡿⣿⡍⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠄⠀⠛⣿⣝⠋⠈⠀⣿⣿⣿⣿⣿⣿⢷⣺⣿⢿⣆⠂⠁⠀⠀⠀⠀⠀⠈⣿⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⣿⠃⢠⡄⠀⣽⣿⣿⣿⡿⠃⠀⡿⣿⠛⠛⣶⠀⡀⠀⢄⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢸⠀⠀⠀⢨⣿⣦⣼⠟⠀⢸⠁⠀⢹⣿⣿⡅⣰⣶⢶⠃⣿⡧⢀⡮⣷⣞⠀⠸⣦⡄⡄⠘⣿⣿⠀⠀⠀⠀⠀⢀⡴⢶⠚⢿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡄⠈⠀⠀⠀⠀⢉⣿⣿⡆⠀⠈⠀⠀⢸⡟⢹⠁⠹⠋⠀⠁⣹⡷⢾⣿⣙⠛⢆⠀⠘⢻⠉⠀⢿⡟⠀⣀⠀⠀⠀⣶⠆⠀⢠⣿⣿⣿⣿⣿⡀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⢠⡭⢭⣽⣿⠟⠛⣷⣶⣤⣥⣤⣼⣿⣿⡿⠇⠀⠀⠁⣀⣴⣾⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢤⡿⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⣿⡇⠸⠀⠀⠀⣼⠳⠀⠀⣽⣿⣟⡂⠛⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⣿⣿⠿⠆⣸⣿⠿⣷⡾⣿⣿⡟⣿⣦⢹⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣿⣿⡿⠆⢠⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣀⡀⢸⣿⣀⣿⡇⢿⣿⡇⣿⣿⠸⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⠙⠁⢸⣿⠛⠉⠁⢸⣿⡇⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣼⣿⣈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⠀⠀⣿⣿⣶⡆⢸⣿⠀⠸⢃⣼⣿⣧⣿⡿⠰⠇⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣿⣿⣍⣿⣷⢿⣿⣿⣿⣿⢹⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⣀⣠⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣾⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⣿⣿⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠉⠙⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣶⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠂⠀⢼⣿⠀⠀⠀⠀⠀⢤⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠻⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠁⠀⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠈⠉⠀⢠⣶⡀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⣂⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣷⣀⣤⣄⣀⠀⠀⣀⣀⣀⣀⣀⣠⣶⠆⢀⣀⡀⠀⢀⣀⣀⣿⠿⢿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣅⣀⠉⠁⣉⣃⢀⡿⠿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⢀⣤⣿⣿⣿⣿⣿⣿⡿⠻⣿⡀⢦⠉⣿⣿⣿⣿⣿⣿⡆⠈⣿⣇⠀⢸⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⠷⠄⢸⣿⠀⣿⡆⢪⣿⣷⠿⠿⠿⠿⠿
⣿⣿⣵⡿⣿⠤⢤⣤⣤⣤⡄⠀⢀⢠⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡯⠀⠀⣿⡇⣸⠠⠀⠀⠀⠀⠀⠈⠋⠀⠈⠉⠀⠈⠉⠃⠀⠀⠀⠀⠉⠉⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⢐⠈⠛⢻⢳⡆⠏⠆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣴⣶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢸⣿⡹⣰⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣈⣯⣧⣤⣤⣤⣤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣀⣸⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⣿⣴⣿⣿⣿⣿⣿⢿⣴⣶⣶⣿⣿⣿⡿⠛⠋⠀⢸⣿⣿⣷⣿⡿⠁⠀⠉⠈⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠙⣿⣿⣿⠿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢷⣺⣿⣿⣟⡏⠁⠀⢲⡀⠀⠀⠈⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠹⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢃⠸⡿⣿⠛⠿⣷⡀⠀⠨⢄⠀⣀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⡄⠀⠀⠄⠀⣠⣿⣷⣄⠀⠀⠀⢹⣿⣿⡍⣰⣾⡿⠇⣿⡷⢀⣯⣷⣏⠀⠸⣶⡀⢄⠘⣿⣿⠀⠀⠀⠀⠀⣀⡷⣶⠾⢿⣿⣿⣿⣇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⡄⠀⠀⠀⢹⣿⣿⠈⠀⠀⠀⢸⡟⢹⠁⠛⠟⠈⡙⣽⡷⣾⣿⣙⠛⢆⠀⠚⠿⠁⠀⢿⡿⠀⣀⠀⠀⠀⣶⠆⠁⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣤⣾⡿⠁⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⢰⡭⢭⣿⣿⠟⠛⣷⣶⣬⣥⣤⣼⣿⣿⠿⠇⠀⠀⠈⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡽⠭⡁⠀⠀⠀⠀⠀⣿⡇⠘⠀⠀⠀⣼⠳⠀⢀⣽⣿⣟⡂⠛⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣠⠀⠀⣿⣿⠿⠆⢸⣿⠿⣷⡆⢠⣾⡟⣿⣦⠀⠀⠋⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣀⠀⢸⣿⣀⣿⣷⣾⣿⣿⣿⣿⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⢹⣿⢽⣿⣿
⠀⠀⠀⣿⣿⢉⡀⢸⣿⠋⠉⠁⢸⣿⡟⣿⣿⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠋⠀⣼⣿⣸⣿⡟⣿⣿⣿⣿⣿⣾⣿⣸⣿⣿
⠀⠀⠀⣿⣿⣾⡇⢸⣿⢰⣶⠀⠸⣿⣧⣿⡿⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣿⣿⣭⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢿⠿⢿⡆⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣤⡆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣴⣶⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣤⣤⣤⣤⣄⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠿⠿⢿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣀⣀⣿⣷⣦⣀⣀⣀⢀⢀⠀⢀⣀⡀⠀⢀⣀⣀⣻⠿⢿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣀⢴⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⡆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣸⡄⠈⣹⣇⠀⢸⣿⣿⡿⣷⡈⢻⣿⣿⣿⣿⣧⡤⣿⣿⣿⣿⣿⣿⠷⡤⢸⣿⠀⣿⡆⢨⣿⠧⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣓⣦⣤⣠⣴⣆⡀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⠙⠁⠁⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⣿⣿⣿⣿⣿⣿⣶⢂⢐⠈⠛⢻⣻⡄⡏⠆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⢿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣀⠀⣰⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣷⣧⢞⣿⣿⡿⣿⣿⣿⠇⠀⣀⣈⣿⣧⣤⣤⣤⣤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣀⣸⣿⣿⣿⡜⣤⣤⣤⣦⠀⠀⣿⣴⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢸⣿⣿⣿⣿⣿⠃⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⣠⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⢷⣺⣿⣿⣿⣿⡅⠙⢧⡄⠀⠀⠈⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡿⠋⣼⣿⣿⠛⢿⣿⡃⣘⠺⣿⡜⢰⡀⢹⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢹⣿⣿⣍⣼⣾⣿⡧⣿⡧⢀⣯⣿⣿⠀⢹⣿⣾⣯⠘⣿⣿⠀⠀⠀⠀⠀⢾⣷⡾⠟⢿⣿⣿⣿⣇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡯⠉⠀⠀⠀⢸⡟⢹⠀⠙⠛⠙⢹⣿⣿⣾⣿⣙⠛⣦⠐⠿⣿⡿⠀⢿⡿⠀⣀⠀⠀⠀⢶⣆⠀⢠⣿⣿⣿⣿⣿⡀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⢶⡿⢭⣿⣿⠟⠻⣷⣶⣬⣥⣤⣼⣷⣿⡿⠇⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠩⠭⠁⠀⠀⠀⠀⠀⣿⡇⠘⠀⠀⠀⣼⠳⠌⢁⣿⣿⣿⡂⠛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡦⠀⠀⢠⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣄⣤⣀⣤⣤⣤⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣿⣿⠿⣷⣾⣿⠿⣷⣆⣠⣾⡟⣿⣿⢣⣾⡿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⢿⣿⡿⠇⢿⣿⣷⣾⣿
⠀⠀⠀⣿⣿⣤⣶⣿⣿⣀⣿⡟⢻⣿⡇⣿⣿⣸⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿
⠀⠀⠶⣿⣿⠉⠁⢹⣿⣿⡟⠁⣸⣿⡇⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⣼⣿⣸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣶⡆⢸⣿⠉⠀⠈⠿⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⠉⠙⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⣀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠁⠀⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢸⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠰⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣷⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣦⣥⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠉⠉⠙⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⠉⠀⠘⢫⣿⣿⡟⣿⣦⡀⣀⣀⣠⣬⣿⣿⣷⣀⣀⢀⣀⠀⢀⣀⡀⠀⢀⣀⣀⣉⠟⢿⣿⣿⣻⣿⣻⠿⠿⣿⣿⣿⣿⣿⣧⠀⠀⣀⣠⢼⡿⠿⢿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡄⠈⣭⣇⠀⢸⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⣧⡄⣿⣿⣿⣿⣿⣿⠷⠄⢸⣿⠀⣿⡆⢈⣻⠧⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠈⠉⠀⠈⠉⠃⠀⠉⠉⠉⠀⠀⠀⠹⣿⡇⣿⣿⣿⣿⣿⣿⣶⢂⣰⠈⠉⢹⠀⠀⠉⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⠃⣀⠀⣰⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⢞⣿⣿⡿⣿⣿⣿⠏⠀⣀⣀⣧⣤⣤⣤⡤⣤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢸⣿⣿⣷⣿⡿⠯⢉⠉⠀⠈⠈⠁⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⣿⣿⣿⣿⣿⣿⢷⣻⣿⣿⣿⣿⠁⠙⢻⡀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⡿⠃⢸⡿⣿⠛⢿⣿⡳⡑⠪⣎⠀⢀⠀⢹⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⢸⣿⢿⠅⣴⣾⣿⠇⣿⣇⢀⣯⣷⣟⠀⠹⣷⡼⠇⠘⣿⣿⠀⠀⠀⠀⠀⢈⡷⣶⠛⢿⣿⣿⣿⣇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠏⠌⠁⣹⣿⡧⠘⠇⠀⠀⢸⡟⢸⠀⠈⠉⠀⠀⣽⡷⣾⣿⡙⠛⣆⠀⠈⠻⠃⠀⢿⡟⠀⢀⠀⠀⠀⠀⠆⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⡩⢭⣽⣿⠟⠚⣷⣶⣤⣥⣤⣼⣷⣿⡿⠇⠀⠀⠀⢀⣴⣾⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠀⠀⠀⣼⠳⠀⢀⣽⣿⣟⡂⠛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠠⡄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣤⣤⣤⣄⡀⠀⠀⠀⢀⣤⣤⣄⠄⠀⠀⠀⠀⠀⣴⣤
⠀⠀⠀⣿⣿⠿⠆⢸⣿⠿⣶⡦⢦⣾⡟⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⢿⣿⡿⠇⢺⣿⣷⣽⣿
⠀⠀⠀⣿⣿⣀⠀⢸⣿⣀⣿⡟⣼⣿⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⢸⣿⡻⣿⣿⣿⣿⣿⣻⣿⣼⣿⣿
⠆⠀⠀⣿⣿⠉⢀⣼⣿⢻⣯⠁⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⣼⣿⣸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣶⡿⣿⣿⠀⠋⠀⠾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠆⠀⠐⣿⠇⠀⠀⣠⡀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡅⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡄⣿⡿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣠⣼⣿⣿⣿⣧⣀⣀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣿⡅⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠛⠛⠻⠟⠻⠛⠿⠿⠿⢿⣷⣄⣀⡀⠀⠀⢀⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⢀⣀⡀⠀⢀⣀⣀⣉⠍⢿⣿⣿⣿⣥⣦⠨⠽⢿⢿⣿⣿⣿⣧⠀⠀⢀⣰⢿⡿⠿⢿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣇⠀⢸⣿⣿⣿⣷⣈⢿⣿⣿⣿⣿⣧⡄⡿⣼⣿⣿⣿⣿⠶⠄⢸⣿⠀⣿⡀⠈⣻⠧⠿⠿⠿⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠉⠀⠀⠉⠃⠀⠉⠉⠉⠉⠙⠁⢹⣿⡇⣿⣾⣿⣿⣿⣿⣶⢂⣰⠀⠀⢹⠀⠀⠉⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠟⢫⣴⠆⣀⠀⣰⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⢞⣿⣿⡿⢿⣿⣿⠏⠀⢀⣀⣧⣤⣤⣤⢤⣤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣶⣤⣤⣶⣶⣶⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⠟⠃⠀⢸⣿⣿⣷⣿⡿⠋⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⣿⣿⣿⣿⣿⣿⢷⣺⣿⣿⣿⣿⠁⠉⢳⣀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⡿⠻⢟⢿⣿⣏⠀⠀⠀⢹⣿⣿⣿⡿⠃⠐⡿⣿⠛⢿⣿⡀⡐⠈⣨⡄⣀⡀⢹⣿⣿⠀⠀⠀⠀⠀⢄⠀⠀⢀⡈⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠙⠿⣿⡂⠀⠀⢸⣿⠋⠁⣰⣾⠴⠆⣿⡧⢀⡮⣷⣏⠀⠨⣆⠔⠂⠘⣿⣿⠀⠀⠀⠀⠀⢀⡵⡶⠺⢻⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⠀⠀⠀⠀⠀⢡⡷⢾⢽⡉⠛⢆⠀⠈⠛⠁⠀⢿⡏⠀⢀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠩⢭⣽⣿⠓⠚⣷⣶⣤⣤⣄⣼⣷⣿⡿⠧⠀⠀⠀⢀⣴⣾⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠈⠀⠀⠀⣼⠳⠀⠀⣽⣿⣟⡂⠙⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⡀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⣿⡄⢸⣿⠿⣶⡄⢸⣾⡟⣿⣮⢿⣿⡿⣿⣿⣿⣷⡟⣏⣾⣿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠠⣤⣿⣿⣉⠁⢸⣿⣀⣿⡇⢸⣿⣷⣿⣿⢸⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣏⠀⢸⣿⢸⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠂⣿⡟⠉⠀⢸⣿⠉⠉⠁⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠉⠀⣾⣿⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣿⣷⣶⡆⢸⣿⠀⢀⠀⠘⣿⣯⣿⣿⣿⣿⡟⣿⣿⣿⣿⠏⠙⢿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣶⡆⣿⡿⠙⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⢀⡄⠀⠀⠀⠉⠀⢿⠇⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⣶⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠃⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣆⠀⠀⣠⣴⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣤⣤⣀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣶⣿⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠃⠀⠘⠛⠛⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣷⣤⡀⡀⢸⣿⣧⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣇⡀⠀⢀⣀⣀⣀⠰⢿⣿⣿⣿⣿⣿⠿⠿⣿⢾⣿⣿⣿⣏⠀⠀⢀⣸⢿⡿⠿⢿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣇⠀⠀⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⣧⡄⣿⣾⣿⣿⣿⡿⠢⠄⢘⡏⠀⣷⠀⠀⢻⠇⠿⠛⠏⠻⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⠹⣿⡿⢻⣿⣿⣿⣷⠈⠉⠀⠀⠉⠃⠈⠉⠉⠉⠉⠉⠁⠹⣿⡇⣿⣿⣿⣿⡷⣴⣔⠀⢰⠀⠀⠹⠀⠀⠈⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⡿⠃⠀⠉⠱⠃⣨⠀⣰⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣥⢞⣿⣿⡧⢿⣿⣿⠏⠀⠀⣀⣦⣤⣤⠤⠤⠤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⡿⡤⠤⣤⣶⠔⠐⣿⣷⣿⣿⣿⣿⣿⢿⣴⣷⣾⣿⣿⣿⡿⠛⠁⠀⢸⣿⣿⣷⡟⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⠟⢻⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⠷⣺⣿⣿⣏⡭⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢻⡻⡟⠀⠘⡿⠀⠀⠀⢹⣿⣿⣿⡿⠃⠀⠙⣿⠛⢛⣾⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣨⡷⠀⠀⠀⠁⠀⠀⠀⢸⣿⠀⠀⡐⠂⠀⠀⢿⡇⠀⠬⢷⡄⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠰⠖⠚⢹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⠀⠀⠀⠀⠀⠀⠳⠎⢤⡀⠙⢆⠀⠀⠀⠀⠀⢻⡇⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠀⠀⢀⣼⠅⣼⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢁⣬⣝⠂⠐⣳⣦⣤⣤⣄⣼⣷⣿⠿⠷⠀⠀⠀⢀⣰⣾⣿⣿⣟⢷⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠘⠯⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾⡇⠘⠀⠀⠀⣾⠃⠀⠀⣼⣿⣟⡀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⡿⠿⢿⣿⣿⣯⣭⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⣿⡶⠿⠀⢰⣿⢷⣶⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⠿⠇⢀⣿⣿⣷⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣧⣀⣠⣼⣿⣀⣿⡇⢸⣿⣿⣿⣿⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣁⠀⢸⣿⣸⣿⠀⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿
⠀⠀⠀⣿⡏⠉⠈⢻⣿⠉⠉⠁⢸⣿⡏⣿⣿⢸⣿⡇⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⡍⠀⣼⣿⣿⣿⡇⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣷⣶⡆⢸⣿⠀⠀⠀⠘⣿⣧⣿⡿⣼⣿⡟⣿⣿⣿⣿⠇⠀⢿⣯⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⡆⣿⡟⠉⣿⣧⣸⣿⣿⣿⣿⢽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⣀⣀⣀⣤⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⠉⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣤⣬⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⡿⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢇⣀⡀⠀⢀⣀⣀⣀⠸⢿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣈⢿⡹⠀⢐⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣇⠀⠀⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣧⡄⣿⣿⣿⣿⠿⡛⠢⠄⢸⡇⠀⣿⠀⠀⢻⠆⠿⠿⠟⠿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣟⣾⣾⠈⠀⠉⠉⠁⠁⠀⠀⠈⠁⠀⠀⠉⠃⠀⠈⠉⠉⠉⠉⠉⠹⣿⡇⣿⣻⣿⣿⣧⣴⣶⣆⣰⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⣀⠀⣰⣾⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⢞⣿⣿⣿⢿⣿⡿⠋⠀⠀⣀⣦⣤⣤⠤⠤⠤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⠿⠛⠉⣀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣴⣿⣿⣿⣿⣿⢿⣷⣿⣾⣿⣿⣿⡿⠟⠁⠀⢸⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⢿⡿⠉⠀⠀⢿⣿⣿⣯⠀⠀⣿⣿⣿⣿⣿⣿⠷⣺⣿⣿⣿⣿⠁⠈⠡⠀⠀⠀⠈⣿⣿⣿⡅⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⢀⠀⢸⣿⣶⠀⠀⠀⢿⣿⣿⠀⠀⢹⣿⢿⣿⡿⠃⠀⡙⣿⠛⢿⣿⠀⠀⠈⠁⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠀⠏⣿⣿⡂⠀⠀⠈⢻⠁⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⢿⠇⠀⠈⢳⡄⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠐⠖⠚⢻⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣹⣿⡇⠀⠠⠀⠀⠀⠀⠀⢸⡏⢰⠀⠀⠀⠀⠀⢀⠗⠎⢤⡀⠙⢆⠀⠀⠀⠀⠀⢻⡇⠀⢀⡀⢀⠄⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣾⣿⠧⠄⠀⠀⠀⠀⠀⠀⣾⡇⢸⠀⠀⠀⠀⠀⠀⠈⠁⣬⣟⠃⠐⣳⣦⣤⣤⣄⣼⣷⣿⠿⠗⠀⠀⠀⢀⣰⣾⣿⣻⣟⢿⢽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠿⡿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⠀⠀⠀⣾⠣⠀⠀⣼⣿⣟⡀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⠿⢿⣿⣿⣿⣭⣿⣿⣿⡟
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠟⠀⠀⣾⣾⠿⠀⢸⣿⠷⣶⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⢀⣿⣿⣷⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣆⠀⣾⣿⣀⣿⡇⢸⣿⣿⣿⣿⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣅⠀⢸⣿⣸⣿⠀⠈⣿⣿⣿⣿⣻⣿⣿⣿⣿
⠀⠀⠀⣿⡏⠉⠀⢹⣿⠙⡯⠁⢸⣿⡇⣿⣿⢨⣿⣇⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡍⠀⣼⣿⣻⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣷⣶⡆⣼⣿⠀⠀⠀⠘⣿⣧⣿⣿⣼⣿⡏⣿⣿⣿⣿⣇⣀⢿⣧⣽⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⡆⣿⡟⠉⣿⣧⣼⣿⣿⣿⣿⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢠⣶⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⡀⠀⠀⣠⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣦⣴⣷⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠟⠻⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⢿⠋⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣘⣿⣿⣿⣏⣛⠀⢀⣀⡀⠀⠀⣀⣠⣀⠸⢿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⢿⡌⠀⢀⣀⠼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣙⣿⠿⣿⣿⣿⣿⣿⣹⡄⠈⢙⣇⠀⠀⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣧⡄⣿⣿⣿⣿⠿⡛⠢⠄⢸⠇⠀⣷⠀⠀⢹⠅⠿⠿⠯⠿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡟⣺⠠⠀⠉⠙⠋⠁⠀⠀⠀⠈⠉⠀⠀⠉⠃⠀⠁⠉⠉⠉⠙⠊⢹⣿⡇⣿⣿⣿⣿⣶⣴⣶⣦⣴⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢋⠀⢸⣿⡿⣸⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡅⢞⣿⣿⣿⢿⣿⡟⠋⠀⠀⣀⣦⣤⣤⠤⠤⡤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣠⣿⣂⣸⣿⣿⣿⣞⣤⣤⣤⡴⠀⠀⣿⣴⣿⣿⣿⣿⣿⢿⣷⣶⣾⣿⣿⣿⡿⠟⠃⠀⢸⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣿⣿⣿⣿⣿⢷⣺⣿⣿⣿⣿⠁⠉⢃⡀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⡿⡿⠈⢿⡇⠀⠀⠀⣿⣿⢿⣿⡿⠃⠀⠝⣿⠛⢿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠛⠀⠀⠙⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⢿⠇⠀⠈⠷⡄⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠐⠶⠚⢹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠏⠀⠀⠀⠀⠀⠄⠀⠀⢸⡟⢸⠀⠀⠀⠀⠀⢠⠳⠞⢥⡀⠛⢆⠀⠀⠀⠀⠀⢻⡇⠀⢀⡀⣀⠄⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠈⠁⣬⣟⠂⠐⣳⣦⣤⣤⣄⣼⣷⣿⠿⠇⠀⠀⠀⢀⣰⣾⣿⣿⣟⢷⢽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠀⠀⠀⣾⠣⠀⠀⣼⣿⣟⡀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⣭⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠒⣿⡶⠶⠀⢰⣶⠲⣶⡄⢠⣾⠟⢿⣮⠻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠿⠀⢀⣾⢿⣷⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣇⣀⠀⢸⣿⣀⣼⣇⣸⣿⠀⢸⣿⠀⢙⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣀⠀⢸⣿⣾⣿⠀⠀⣿⣿⣿⣿⢻⣿⢽⣿⣿
⠀⠀⢀⣿⣿⣯⠀⢸⣿⠉⠉⠙⢻⣿⠀⢸⣿⠀⠘⡇⣿⣿⣿⣿⡟⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡏⠀⣸⣿⣉⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⠻⣿⣿⣿⡄⢸⣿⠀⠀⠀⠘⢿⣧⣿⡿⠀⢀⡄⣿⣿⣿⣿⣇⠀⢿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⡇⣿⣿⣿⡆⣿⡟⠉⣿⣷⣾⣿⣿⣿⣿⢹⣿⢽⣿⣿
⣿⣄⣀⣀⣀⡀⠀⠀⠀⠀⢀⣶⣦⣶⣶⣶⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠉⠉⠉⠉⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠁⠀⢀⣿⠿⠿⠿⠛⠛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢠⡼⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⠟⠃⠀⠀⠀⠀⠀⣾⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣀⣠⣄⡀⢀⣤⡀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠠⢦⣤⣂⣼⣿⣿⠿⠿⣿⣿⣿⣿⣿⣁⠀⠀⢀⣀⠈⡀⠀⢀⣀⠀⣀⢀⡽⣿⡷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢉⣇⠀⠀⣾⣿⡧⣷⡈⢻⣿⣿⣿⣿⣧⡄⣿⣹⣿⣿⠽⡛⠢⡄⢸⠇⠀⣷⠀⠀⠹⠀⠛⠘⠃⠚⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⠹⡿⠟⠉⠀⠀⠀⠀⠀⠁⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣿⢹⣿⣿⣤⣤⣾⣗⣸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⢻⣿⡿⣿⠆⠇⠀⠀⠀⠀⠀⡀⠀⢰⣾⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡄⢞⣿⣿⣿⣿⣿⠋⠀⠀⠀⣀⣦⡠⠤⠤⠤⠤⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⣸⣿⣿⣿⡜⣤⠀⠀⠀⠀⠀⣿⣴⣿⣿⣿⣿⣿⢿⣴⣶⣶⣿⣿⣿⡿⠛⠁⠀⢸⣿⣿⣿⣿⡍⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⢻⡿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠷⣺⣿⣿⣿⠿⠁⠈⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠁⢀⡀⠀⠀⠀⠀⠀⢹⣟⢻⣿⠿⠃⠀⠘⣿⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⢻⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠊⢹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⠀⠀⢤⣿⡇⠀⠀⠀⠀⠀⢸⡟⢸⠀⠀⠀⠀⠀⠀⠐⠊⠄⠀⠙⢆⠀⠀⠀⠀⠀⢻⡇⠀⣀⠀⠀⠄⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⣸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣤⡉⠂⠐⣳⣤⣤⣤⣀⣼⣷⣿⠿⠇⠀⠀⠀⢀⣠⣾⣿⣻⣟⢷⢽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⠀⠀⠀⣼⠃⠀⠀⣼⣿⣟⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⢿⣿⣿⣧⣬⣵⣿⣿⠟
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡆⠀⠀⣿⡷⠶⠀⢰⣶⠷⣶⡆⢠⣶⣟⣿⣦⠀⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠿⠀⢠⣿⣿⣷⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠀⣿⣇⣀⠀⢸⣿⣀⣿⡇⢸⣿⡿⣿⣿⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⠀⢸⣿⢿⣿⠀⠀⣾⣿⣿⣿⢻⣿⢸⣿⣿
⣼⣿⠀⣿⡏⠉⠀⢸⣿⠉⠉⠀⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡏⠙⣿⡟⢻⣿⣿⣸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⢻⣿⣯⣻⣿⣿⢻⣿⣿⣿⣿⡇⣿⣿⣯⠀⣼⣿⣀⣿⡇⣠⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣇⣿⣷⣶⡆⢸⣿⠀⠀⢛⡼⣿⣿⣿⣿⣴⣶⡆⣿⣿⣿⣿⣧⣄⢿⣧⣼⡿⢻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣿⣯⡿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣿⣷⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⢹⣿⢽⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣿⣿⣿⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠠⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣠⣤⡀⠹⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣤⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠿⠿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠛⠁⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⢁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣾⡯⠋⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠉⠙⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣀⠀⣀⣀⢀⢈⠉⢁⣀⡀⠀⢀⣀⣀⣒⠼⢿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣟⣀⠀⠀⣀⣠⠀⡹⠾⢂⣀⠀⣀⢀⣔⣋⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣯⣿⣴⣿⣿⡄⢸⡄⠈⣿⣇⠀⢸⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣧⡄⣿⣿⣿⣿⢿⡛⢶⣦⣸⡏⠀⣷⠀⠀⠹⠀⠟⠘⠃⠺⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠩⡉⠉⠀⠀⠀⠀⠀⠈⠉⠀⡈⣙⡇⠈⠉⠉⠉⠙⠛⠋⢹⣿⡇⣿⣿⣿⣿⣿⣷⣾⠛⠹⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⣀⢀⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⣷⣧⢞⣿⣿⣿⣿⣿⡆⠀⠀⣀⣀⣦⣤⣤⣤⣤⣤⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡟⣤⣤⣤⣤⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢸⣿⣿⣿⣿⡿⠁⠀⠈⠛⠉⠉⠁⠀⠀⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⢷⣻⣿⣿⣿⡿⠉⠉⢹⠃⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠩⠃⠀⠈⡿⡇⠀⠀⠀⣿⣿⣿⣿⡿⠃⠈⠙⣿⠛⠛⣿⠀⠀⠈⠁⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢄⠀⡀⠀⠀⠀⢻⠃⠀⠈⢷⡄⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠚⢹⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⣿⢻⠀⠀⠀⠀⠀⠀⠒⠎⠁⡀⠙⢆⠀⠀⠀⠀⠀⢻⡏⠀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠁⣬⣟⠂⠐⣳⣤⣤⣤⣀⣼⣷⣿⡿⠇⠀⠀⠀⢀⣰⣾⣿⣻⣟⢷⢽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⠀⠀⠀⣼⠃⠀⠀⣼⣿⣟⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣭⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠀⠀⣾⡷⠶⠀⢰⣶⠲⣶⡄⢠⣶⡟⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⣿⣿⠿⠀⢠⣾⣿⣷⠀⠸⢿⣿⣿⣷⣿⣿⣿⣿⣿
⣤⡀⠀⣿⣧⣀⠀⢸⣿⣀⣿⡇⢸⣿⣷⣿⣿⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⠿⠿⢿⢹⣿⣿⣿⣿⡇⣿⣿⣇⠀⢸⣿⠻⣿⠀⠀⣿⣿⣿⣿⢹⣿⢸⣿⣿
⣿⣿⣦⣿⣿⠉⠀⢸⣿⠉⠉⠁⢸⣿⣏⣿⣿⠀⠀⠀⣿⣿⣿⣿⡇⠈⣿⡇⢹⣿⣿⢼⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢹⣿⡇⢻⣿⣿⢼⣿⣿⣿⣿⡇⣿⣿⣯⡀⣼⣿⣀⣿⡇⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣾⣿⣿⡄⢸⡄⠈⢉⣇⠀⠀⣾⣿⡿⣷⡈⢿⣿⣿⣿⣿⣧⡄⣿⣿⣿⣿⢿⡛⢶⣦⣸⡏⠀⣷⠀⠀⢹⠀⠿⠘⠃⠻⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⣿⣿⣿⣿⠹⣟⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠃⠀⠀⠉⠉⠉⠉⠈⠹⣿⡇⣿⣿⣿⣿⣿⣿⣾⢋⠙⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⠿⢿⡿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⠷⣻⣿⢿⣿⠻⠁⠉⢡⠅⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⠀⠀⠀⠀⠀⠀⠐⠎⠤⡀⠙⢆⠀⠀⠀⠀⠀⢻⡏⠀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 2294

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/19/get-out-of-jail-with-microsoft/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/19/get-out-of-jail-with-microsoft/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.19.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Microsoft_GitHub_Exposé_—_Part_XXIV_—_Using_Microsoft_Money_as_‘Get_Out_of
Jail’_Card_After_Suffocating_Women⠀✐


Posted in Microsoft at 6:54 am by Dr. Roy Schestowitz


Series parts:


   1. Microsoft_GitHub_Exposé_—_Part_I_—_Inside_a_Den_of_Corruption_and
      Misogynists
   2. Microsoft_GitHub_Exposé_—_Part_II_—_The_Campaign_Against_GPL_Compliance
      and_War_on_Copyleft_Enforcement
   3. Microsoft_GitHub_Exposé_—_Part_III_—_A_Story_of_Plagiarism_and_Likely
      Securities_Fraud
   4. Microsoft_GitHub_Exposé_—_Part_IV_—_Mr._MobileCoin:_From_Mono_to
      Plagiarism…_and_to_Unprecedented_GPL_Violations_at_GitHub_(Microsoft)
   5. Microsoft_GitHub_Exposé_—_Part_V_—_Why_Nat_Friedman_is_Leaving_GitHub
   6. Microsoft_GitHub_Exposé_—_Part_VI_—_The_Media_Has_Mischaracterised_Nat
      Friedman’s_Departure_(Effective_Now)
   7. Microsoft_GitHub_Exposé_—_Part_VII_—_Nat_Friedman,_as_GitHub_CEO,_Had_a
      Plan_of_Defrauding_Microsoft_Shareholders
   8. Microsoft_GitHub_Exposé_—_Part_VIII_—_Mr._Graveley’s_Long_Career_Serving
      Microsoft’s_Agenda_(Before_Hiring_by_Microsoft_to_Work_on_GitHub’s_GPL
      Violations_Machine)
   9. Microsoft_GitHub_Exposé_—_Part_IX_—_Microsoft’s_Chief_Architect_of_GitHub
      Copilot_Sought_to_be_Arrested_One_Day_After_Techrights_Article_About_Him
  10. Microsoft_GitHub_Exposé_—_Part_X_—_Connections_to_the_Mass_Surveillance
      Industry_(and_the_Surveillance_State)
  11. Microsoft_GitHub_Exposé_—_Part_XI_—_Violence_Against_Women
  12. Microsoft_GitHub_Exposé_—_Part_XII_—_Life_of_Disorderly_Conduct_and_Lust
  13. Microsoft_GitHub_Exposé_—_Part_XIII_—_Nihilistic_Death_Cults_With
      Substance_Abuse_and_Sick_Kinks
  14. Microsoft_GitHub_Exposé_—_Part_XIV_—_Gaslighting_Victims_of_Sexual_Abuse
      and_Violence
  15. Microsoft_GitHub_Exposé_—_Part_XV_—_Cover-Up_and_Defamation
  16. Microsoft_GitHub_Exposé_—_Part_XVI_—_The_Attack_on_the_Autonomy_of_Free
      Software_Carries_on
  17. Microsoft_GitHub_Exposé_—_Part_XVII_—_Backsliding_Into_1990s-Style
      Digital_Slavery_by_Microsoft
  18. Microsoft_GitHub_Exposé_—_Part_XVIII_—_The_Story_of_NPM
  19. Microsoft_GitHub_Exposé_—_Part_XIX_—_The_Collapse_of_Team_Mono
  20. Microsoft_GitHub_Exposé_—_Part_XX_—_Entering_Phase_II
  21. Microsoft_GitHub_Exposé_—_Part_XXI_—_Rumours_About_How_Microsoft_Plans_to
      Actually_Make_Money_(Not_Losses)_From_GitHub
  22. Microsoft_GitHub_Exposé_—_Part_XXII_—_‘Mr._GitHub_Copilot’_Balabhadra_
      (Alex)_Graveley_Pleads_Guilty_After_Assaulting_Women
  23. Microsoft_GitHub_Exposé_—_Part_XXIII_—_CoPlagiarist:_Microsoft’s_GPL
      Violations_and_Plagiarism_Tool_Created_by_Serial_Plagiarists
  24. YOU ARE HERE ☞ Using Microsoft Money as ‘Get Out of Jail’ Card After
      Suffocating Women
          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GitHub: Where everything comes to die⦈


Summary: The person behind Copilot is a highly_perverted strangler and he was
supported_by_Microsoft despite Microsoft knowing what he had done. Today we
merely present some more evidence and we shall soon show how Microsoft handled
the situation (it dealt with this as a routine, not a crisis, and kept paying
the mobster/monster).


A few months ago we published the arrest_record_of_Balabhadra_(Alex)_Graveley
and around that time these documents were floating ‘behind the scenes’. This
was after Nat Friedman had left (we’re told both he and Miguel_de_Icaza got
pushed out, but we need more hard evidence) and months after our series began.


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

  A loophole for rich people; this is how Bill Gates got out of jail at least
                          twice following his arrests


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

                              $25,000 or $50,000


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




And the receipt


Meanwhile, Graveley’s lawyer is trying_to_cover_things_up. At a later point we
shall show how Microsoft-connected media also played a role in covering up
these affairs.


Stay tuned. This series can last a very long time, going well into next year.
It helps show a pattern of the media failing women, Microsoft gaslighting
victims of crimes (while Microsoft itself commits a lot of crime), and
separately we shall run a series about how Microsoft’s media operatives think.
That’s aside from our EPO series (not the same “EPO” mentioned in the paperwork
above).


As Bill Gates put_it_this_year, “well, he’s dead…” (the mindset of killing
people who know something incriminating about you) █


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣀⡀⠀⠀⠀⠘⠛⠓⠐⠿⠿⣿⣷⣶⣦⣤⣤⣤⠀⠀⣤⣄⠤⢄⣀⡄⠈⢻⣿⣿⠋⢁⣀⣀⣽⡏⢙⣿⠛⢻⣿⠉⢹⣯⡄⠀⣠⣤⣤⣤⣤⡄⠀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣿⣿⣿⣿⣿⣷⠀⠈⣿⡇⠀⣾⡟⠛⢻⡏⠉⣏⠀⢈⣹⡀⠘⠛⠃⠀⡏⠉⣿⡏⠉⡇⠀⣉⡉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⣿⣿⣿⣿⠟⠀⢰⣿⣧⠀⢿⣷⡆⢸⡇⠀⣿⠀⢸⣿⠂⢸⣿⡇⠀⡗⠀⣿⡇⠀⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠦⢼⣿⣿⠀⠀⣠⣿⣿⣿⣶⣤⣤⣤⣼⣧⣤⣿⣦⣤⣼⣤⣼⣿⣧⣤⣿⣤⣤⣤⣤⣧⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡿⠿⡿
⠷⣿⣷⣷⣯⣄⣍⠻⣿⣿⣿⣯⣽⡽⢿⣿⣿⣿⣿⡿⡿⢿⣿⣟⠛⠻⢿⢿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⣷⣶⢶⣿⣿⣿⣷⣷⣬⣵⣶⣷⣴⣲⣆⣌
⠞⢅⣵⣒⣾⣬⠺⡟⣿⣾⣿⡯⣷⣽⣗⣿⣗⣝⣿⣯⣮⣿⡞⣿⢭⣓⣿⣏⡿⡈⣿⢿⢷⣿⠏⣿⢿⣿⣻⡿⣽⣿⣿⢯⣿⣿⣫⣿⣟⣯⣿⣿⢻⡿⢷⣿⣿⣿⣟⢹⣟⢻⢿⡯⣿⣿⢻⣯⣻⣿⣿⢿⠿⠙⠯⠿⠿⠛
⠋⠃⠀⠈⠚⡁⠓⠱⠿⠆⠘⠛⠑⠮⠿⠡⠿⠹⣿⡧⣪⠿⠡⠿⣭⣏⣿⣭⣿⣤⣿⣤⣆⣼⣠⠿⣬⣆⠫⠿⠷⠸⢿⣶⣶⣿⣌⠷⣯⠿⢿⠖⠼⢧⠶⣿⡄⣼⣧⣼⣧⡼⣴⡿⢇⡝⢧⠼⠫⠏⠍⠛⢻⡂⠄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⣀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⣴⠒⣲⢨⡖⠺⣍⢻⣿⠩⣵⡟⢻⡟⡻⣻⣷⡺⡙⠲⠖⢺⣞⢏⡷⠒⣮⢳⣄⣲⡞⢲⡌⣲⣖⢲⡖⣲⣄⠉⠌⠉⠁⠁⠒⣁⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⠀⠐⠀⠀⠈⢿⣩⡢⡸⣇⣢⡟⣸⡘⠟⣸⣇⣸⣏⣅⣠⣉⣻⠆⠈⠐⣸⡟⢘⣯⣖⡿⠀⠋⣹⣏⣹⠇⣸⡏⣸⣏⣫⠀⠀⠀⠈⠀⠉⠁⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃
⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀
⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

                    ䷩ 𝚕𝚒𝚗𝚎 2528

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/19/irc-log-180722/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/19/irc-log-180722/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.19.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Monday,_July_18,_2022⠀✐


Posted in IRC_Logs at 2:10 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-180722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-180722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-180722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-180722.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
 QmeQvC8eeJpWNKypTBvP29iF1iGrJCAFZHc2kJ6ftWsA7B #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmUcXFtpAQGMS1HaEGpbjG1MJK9pS1Ps17PUTnBsJeL6c2 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmYEsCMWEywd2yDGTErNe9GZPGTYnFYtoCmXqBoM33Lb7x social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmZC428dQVHsABt9N2qgsQo1ARa2qr1467ZQaF5hR22xWW social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmQ5VVycqqn3cjWkJb3XqtFNPo2EznT4gfPQGYQgNyEfey #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmSuo7YAhj7W5hKUDbmpjzUUNyp9x6MtNVoPMm7mWThUCz (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmRtqcw3omDY8JQMX4SkxA9gj89KDoxqGWz8U93bWvUKCo #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmRDuhjj5PLzE2cythNsaRL2amP47vgwn32ChN5uwpjjig (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmYTKahqtmH46iM3ZthdPvDKojc39tpTCiyk2GGs8Y29DU



                    ䷩ 𝚕𝚒𝚗𝚎 2655

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/19/razik-the-man-of-letters/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/19/razik-the-man-of-letters/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.19.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_EPO_Bubble_—_Part_VII_—_A_Multifaceted_Man_of_Letters⠀✐


Posted in Europe, Patents at 3:13 am by Dr. Roy Schestowitz


Overview: [Teaser]_The_EPO’s_Deflating_Patent_Bubble_and_Pursuit_of_Illegal
Software_Patents_(With_Kangaroo_Courts,_UPC,_and_Bullied_Examiners)


Series parts:


   1. The_EPO_Bubble_—_Part_I_—_An_“Unprecedented_Surge”
   2. The_EPO_Bubble_—_Part_II_—_Signs_of_a_Deflating_Bubble?
   3. The_EPO_Bubble_—_Part_III_—_Dividing_Up_the_Spoils…
   4. The_EPO_Bubble_—_Part_IV_—_A_Cashflow_Problem_Looming_on_the_Horizon?
   5. The_EPO_Bubble_—_Part_V_—_Propping_Up_the_Bubble?
   6. The_EPO_Bubble_—_Part_VI_—_From_Humble_Examiner_to_CO³
   7. YOU ARE HERE ☞ A Multifaceted Man of Letters
                    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇razik-baby-sitter⦈_
  In his spare time Razik Menidjel is something of a “man of letters”. He has
  published a number of books including poetry, drama and a novel co-authored
                        with his brother Méki Menidjel.


Summary: The Benoît_Battistelli- and António_Campinos-elevated Frenchman, who
insiders believe will push illegal software_patents to make anther bubble, has
a parallel ‘career’


A casual observer could be forgiven for assuming that Razik’s Menidjel’s
written output is limited to dry-as-dust technical subject-matter, patent
search and examination reports, articles about patent searching in the area of
biomaterials and polymers, and scientific tracts such as his doctoral
dissertation “Novel_Syntheses_for_Precursors_of_Unusual_Nitrogen-Heterocycles
and_Polyketides”.


However, if one takes the trouble to scratch below the surface a more
multifaceted individual emerges.


It soon becomes clear that, in his spare time, Razik is something of a “man of
letters”, an aspiring belletrist in fact.


“The book is full of extravagant and inflated assertions about the military
exploits of the “Turcos”, in particular their contribution to Allied efforts
during World War II.”Over the course of the last three decades, despite his
busy schedule at the European Patent Office Razik has managed to churn out
several volumes of poetry, along with an occasional theatre_play and a novel
for good measure.


As far as can be determined, his literary début was a now out-of-print volume
of poetry entitled “Plein Couer” published in 1991 by the Parisian publishing
house Éditions_Saint-Germain-des-Prés which folded up in 1997.


His recent literary oeuvres have been distributed by Publibook, a small
publishing house founded in June 2000. Publibook is located in Saint-Denis, a
commune in the northern suburbs of Paris, and is reportedly one of the leaders
in the French Internet publishing market.


Razik’s most recent literary undertaking is a racy criminal thriller entitled
“Baby-Sitter” which he co-authored with his brother Méki in 2018. In his day
job Méki is a French civil servant, a senior administrator with the Regional
Health Agency of Île-de-France.


                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Meki_Menidjel⦈_
Razik’s brother and sometime literary “collaborateur”, Méki Menidjel, a French
civil servant and senior administrator with the Regional Health Agency of Île-
                                  de-France.


The following promotional blurb gives a taste of what the reader can expect:


     “Cindy’s scream catches the leader’s attention. His eyes meet the
     children’s. Cindy and Bruce rush to their room, frightened by the
     stranger. Julio, hiding by the door, grabs his knife and slashes the
     arm of the chief, who, wounded, retreats outside, cutting off the
     entrance to his three henchmen who accompany him. Julio violently
     closes the door and pushes the chest of drawers to the side in front
     of it before rushing towards Juliana.”


     Written by two brothers who show their taste for muscular films,
     “Baby-Sitter” pits Julio, a man with a dark past and two children
     whose lives he is trying to save, against a murderous commando ready
     for anything… and the worst. A confrontation that hides even greater
     stakes, since the father of the children is none other than the
     assistant of a senator himself in danger.


     Manipulations and blackmail, fights and chases, tensions and notes of
     humour…


     The Menidjel brothers brilliantly arrange and choreograph these
     elements throughout this text that ignores dead time and hides
     nothing of its references. Catchy and intense, a script-tribute to
     action cinema.


In 2007 Razik made his first and only venture into the realms of amateur
military historiography with a publication entitled “Les_Tirailleurs
algériens”.


                🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Les_Tirailleurs_algeriens⦈_
 “Les Tirailleurs algériens” is a bombastic tribalistic rant dedicated to the
   French colonial troops recruited from the Arab and Berber communities of
                                   Algeria.


This is a book dedicated to the “Algerian Skirmishers”, French colonial troops
of Algerian extraction who acquired the nickname “Les Turcos” during the
Crimean War.


These soldiers were regiments of indigenous infantry recruited from the Arab
and Berber communities of Algeria who were used as cannon-fodder to serve
French imperial interests during the 19th and 20th centuries.


                        🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Les_Turcos⦈_
     The “Tirailleurs algériens”, nicknamed “Les Turcos” were regiments of
 indigenous infantry recruited from the Arab and Berber communities of Algeria
 and were used as cannon-fodder to serve French imperial interests during the
                           19th and 20th centuries.


The “Turcos” were deployed under French command in both World Wars and also
during the interwar period to assist Spanish forces in the brutal suppression
of the Abd-el-Krim_insurgency between 1921 and 1926 (known as the “Rif_War”).
After World War II they were used during the 1950s and 1960s to prop up the
remnants of France’s colonial empire in Africa (including Algeria itself) and
in “Indochina” (Vietnam).


“Les Tirailleurs algériens” may be described as a 451-page tribalistic rant in
which the author begins by paying his respects to family members who “died_for
France”.


The list starts with Bou Menidjel el Amara who died at sea on 4 November 1915
(presumably on board the military transport ship “Le_Calvados” sunk by a German
submarine in the vicinity of Gibraltar) and ending with Bouguerra ben Ain
Bouati who died in action on 13 March 1954 at Điện_Biên_Phủ (Vietnam) defending
the last vestiges of European imperialism in “French_Indochina”.


“In the next part, our focus will shift back to EPO affairs and we shall see
how the intrepid “Algerian Skirmisher” made further advances in his primary
career when he replaced the “British Grenadier” Grant Philpott as Chief
Operating Office in charge of ICT towards the end of 2019.”The book is full of
extravagant and inflated assertions about the military exploits of the
“Turcos”, in particular their contribution to Allied efforts during World War
II.


Amongst other things, the author boldly claims that the losses inflicted on the
Axis armies by these French colonial troops during the North_African_campaign
were more decisive for the outcome of the war than the losses inflicted on the
Wehrmacht by the Soviet Red Army on the Eastern Front.


It’s difficult to believe that the purveyor of such bombastic and jingoistic
“ballyhoo” could rise to occupy a prominent position in an international
organisation like the EPO. But given the levels of Francophone_cronyism
prevailing during the Battistelli era perhaps it’s not altogether surprising.


Before concluding this part, it seems appropriate to give a brief mention to
Razik’s wife Nicola_Kipper, another student of chemistry with artistic
inclinations.


Nicola acquired a Ph.D. in natural substances chemistry (“Naturstoffchemie”)
from the University of Göttingen in 1997 with a dissertation about the
structure and synthesis of dioxolides entitled “Struktur_und_Biosynthese_der
Dioxolide:_Ein_neuer_Abzweig_des_Shikimisäureweges”.


Nicola comes from Varel in Northern Germany and is more an aficionado of the
visual_beaux-arts rather than belles lettres. She exhibits her artworks
regularly in the South-Holland region, including at the_EPO’s_annual_Artists’
Exhibition_“ArtEx”, and won second_place in the “Groene_Hart”_Art_Awards in
2015.


                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Nicola_Kipper⦈_
 Nicola Kipper won second_place in the “Groene_Hart”_Art_Awards in 2015 (l.).
           Relaxing on the beach at Scheveningen near Rijswijk (r.).


As we shall see in a later part of the series, when Razik and Nicola feel like
escaping the windy and rainy maritime climate of Leidschendam in South-Holland,
they enjoy travelling to sunnier spots, such as the island of Crete where they
obtained planning permission for constructing a holiday home in 2018.


That concludes our exploration of Razik Menidjel’s parallel career as a “man of
letters”.


In the next part, our focus will shift back to EPO affairs and we shall see how
the intrepid “Algerian Skirmisher” made further advances in his primary career
when he replaced the “British Grenadier” Grant Philpott as Chief Operating
Office in charge of ICT towards the end of 2019. █


⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⡇⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣶⣶⣶⣶⣶⣧⣷⣾⣿⣧⣿⣿⣿⢿⢿⣿⢿⣿⣿⣿⢿⢿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣸⣁⣘⣰⢳⣿⣗⣻⣿⣨⣓⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠙⠛⠛⠛⠛⠛⠛⠛⠛⠟⠟⠿⠿⠿⡿⢿⣿⣿⣿⣛⣛⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠤⠄⠖⠂⠀⠀⠀⠐⠀⠀⠀⠐⠲⡾⢾⣶⠶⠿⠛⠛⠛⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣝⠿⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠮⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠐⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢽⠗⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠁⠀⠀⠀⠺⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣤⣴⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠤⢾⣿⣿⣿⣷⠹⠁⠸⣿⣿⣿⣿⠉⠩⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠿⠏⠀⠀⠈⣿⣿⣿⣿⠀⠀⠠⠿⠿⠿⣿⢉⣿⡉⠉⢩⡍⠉⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⢹⣐⣒⣒⠀⠀⢀⡈⠈⠀⠉⠖⡀⠀⠆⣀⣀⣿⢈⢀⡘⡇⣕⣁⣛⣈⣡⣁⡱⡀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⠅⠀⢸⠛⢮⣁⠀⣨⡟⣧⠀⠀⠘⢁⣈⠁⠀⠀⣿⢼⣼⣯⣤⣿⣥⣼⣤⣤⣴⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠀⠀⣿⡳⠀⠭⠃⠏⢣⠘⠄⠀⢀⠉⢀⠀⢀⣀⣿⢐⣊⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠠⡄⠀⠀⠉⠠⠃⠀⠀⠢⠀⠀⠀⠀⠀⠀⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⡏⣉⠙⣿⢿⡿⣿⢉⡏⣽⡿⠿⡿⠛⢿⢩⡿⡿⢿⣿⣿⠿⠿⡿⠋⠭⠋⢽⢩⡿⠿⣿⢩⡿⠿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⠀⠀⢀⠉⠄⠠⠂⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣤⠈⡇⡼⠁⡏⢸⢀⡇⣈⣤⡇⢰⡇⣸⢀⡖⢸⣿⡇⣼⠆⡷⢰⡖⢰⡆⣸⢰⡶⡇⡜⢀⣡⡼⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⡄⢸⡆⠀⠀⠀⠀⠀⢠⠄⣀⠂⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣾⣷⣿⣾⣷⣶⣾⣷⣶⣷⣿⣾⣷⣾⣿⣷⣶⣾⣃⣜⣃⣾⣷⣿⣶⣾⣶⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⠀⡇⢸⡇⠀⠀⠀⠀⠀⠈⠼⠿⡇⠀⢺⠀⠘⣿⣿⣝⣩⣹⣍⣛⣉⣹⣋⣏⣏⣉⣋⣹⣻⣙⣍⣋⣝⣟⣹⣉⣉⣙⣉⣋⣍⣙⣍⣏⣩⣩⣟⣉⣟⣋⣏⣻⣙⣏⣙⣉⣿⣏⣉⣉⣻⣻⣙⣏⣿⣻⣋⣋⣙⣩⣻⣻
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠿⣿⣯⣭⣽⣯⣭⣭⣿⣿⣵⣭⣯⣽⣽⣯⣯⣭⣯⣭⣿⣿⣭⣽⣯⣽⣽⣭⣽⣯⣽⣭⣯⣽⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⠤⠤⠤⠤⠶⠒⠒⠒⠒⠂⠉⠉⠉⠀⠀⠀⠀⣿⣧⣥⣼⣦⣤⣬⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣤⣿⣿⣿⣿⣿⣿⣯⣅⣵⣮⣧⣷⣌⣯⣵⣭⣵⣧⣽⣭⣥⣬⣧⣬⣯⣤⣥⣷⣤⣵⣽⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠿⡟⢿⡿⠟⠿⠿⠻⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣥⣐⣥⣺⣬⣬⣠⣬⣥⣩⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⣾⣷⣾⣶⣶⣦⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠟⢻⠛⣿⣿⢹⢹⢛⡟⢻⢺⢸⢸⠛⠟⡟⡟⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⢦⣽⣥⡿⣿⡼⣾⣾⣮⣾⣼⣼⣼⣬⣷⣥⣧⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⢸⠑⢉⠊⡏⡏⡏⠪⢹⢹⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⣿⡿⠿⡿⢿⣿⡉⢩⢽⠿⠿⠿⡯⡏⡏⣿⠿⡿⡿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣛⣇⣒⣓⣹⣿⣇⣸⣸⣀⣏⣂⣇⣇⣇⣃⣒⣆⣃⣇⣿⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⡍⡿⠿⠟⢽⠿⡯⡿⠻⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣕⣘⣃⢆⡑⣔⣲⣸⣇⣇⣒⣃⣇⣗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠻⡟⠛⢻⢻⣛⡛⡟⠟⠿⠿⣟⠛⠿⢿⢻⠻⠿⠿⡟⠻⠿⠿⠛⠿⡟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠬⡬⠍⠭⠭⠬⠽⠭⠬⡭⠭⠽⠭⠩⠭⢧⢭⠍⡩⠬⠯⢯⠭⠭⢭⢭⠭⣿⣿⣿⣿
⠛⢛⣟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⡿⢻⣿⣿⣿⣿⣿⣿⣿⣟⣚⣛⣛⣞⣓⣟⣻⣛⣙⣃⣳⣓⣛⣳⣚⣻⣚⣚⣑⣒⣓⣚⣒⣛⣻⣚⣚⣿⣿⣿⣿
⠀⠀⣀⠐⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠩⠋⢸⣿⣿⣿⣿⣿⣿⣿⡗⠖⠺⠒⠦⠲⢰⠒⢲⠒⠛⠛⠛⡟⡟⠻⠛⢻⠻⢿⠻⠛⠻⣻⠛⠛⠛⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣀⣀⣀⣀⣤⣮⣼⣿⣿⣿⣿⣿⣿⣿⡧⠭⠽⠭⡽⠭⢭⠭⠭⣭⠭⠭⠯⢥⡭⠯⠬⠽⠭⡭⠭⠭⠭⠭⠭⠭⠭⠭⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠙⠻⢻⣿⣿⣿⠿⠛⠛⡉⢀⣠⡃⢀⠀⠀⠈⠉⢉⣉⠥⠠⠖⠖⣿⠟⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣝⣛⣚⣋⣛⣛⣋⣹⣛⣋⣛⣋⣻⣛⣛⣙⣙⣛⣛⣻⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿
⠄⠂⠠⠄⠐⠤⢀⠂⠀⠉⠉⢀⠀⡀⠈⠀⠐⠂⠀⠄⢁⠀⠀⢀⠘⠃⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠹⣟⢻⣿⣿⣿⣿⣿⣿⣿⣗⡖⠒⢒⠒⡓⡒⣲⢚⢲⡒⡗⡒⢲⠒⡚⡖⠒⠒⢒⡒⡖⠒⣖⢲⠒⢒⢒⣿⣿⣿⣿
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⢿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⢿⠿⢿⠿⠿⡿⠿⠿⢿⠿⠿⣿⣿⣿⣿
⡏⡦⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢁⢸⣿⣿⣿⣿⣿⣿⣿⣏⣝⣋⣋⣙⣻⣛⣙⣉⣉⣯⢉⣙⡙⣎⡙⣉⣏⣻⡻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣚⣲⣒⣒⣒⣺⣒⡓⣒⣲⡓⣒⣖⡒⣗⢒⣒⣒⣓⣺⣒⣲⣖⣳⢒⣒⣒⣿⣿⣿⣿
⠀⠄⡤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡯⠭⠭⠥⠭⠯⠭⠭⠭⢽⠭⠭⠯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣶⣾⣷⡿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢹⣉⣉⣉⣉⣍⣏⣹⣉⣋⣏⣍⣉⣉⣏⣏⣉⡹⣩⣉⡩⣙⣹⢹⣙⣹⣉⣿⣿⣿⣿
⠛⠍⠉⣽⣿⣯⣥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣓⣒⣒⣖⣒⢒⣒⣒⣒⣓⣒⣒⣺⣒⣲⣲⣚⣒⣒⣖⣒⣒⣓⡒⣒⣛⣛⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⡟⢖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡯⢩⠥⠭⠭⢼⠸⡬⢭⠬⢭⠣⢬⠥⠽⢿⡿⢿⠻⢿⡿⠿⠿⡿⠿⠻⠿⠿⣿⣿⣿⣿
⢤⣾⣿⣿⣿⣿⣶⢳⢞⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣌⣹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣻⣛⡧⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⠿⡿⠿⠿⡿⣟⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⣉⣙⣉⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣒⣓⣒⣒⣓⣒⣓⣒⣒⣒⣳⣶⣷⣶⣿⣿⣿⣛⣛⣋⣛⣿⡟⠇⢀⠄⠄⠐⠀⢼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⢻⣿⡛⡿⣿⣿⣿⠿⣿⢿⡟⡟⡟⡟⡻⡟⣿⠿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣾⣿⣷⣿⣿⠀⠌⡀⣿⣾⣶⣿⣿⣿⣾⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡭⡓⣿⣿⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣠⣀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣮⣫⢺⣿⣿⣿⣿⣿⣷⡌⡃⢡⣿⣗⢒⡖⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⣾⠟⠀⢀⢠⠾⣿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣏⡁⢿⡆⢦⠤⢿⣿⣿⣿⣿⣿⡟⢰⠁⠀⣿⡏⣻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠘⠁⠀⡉⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣤⡴⣿⢎⠴⢶⡏⠘⣊⣸⢙⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⡀⠆⢥⣝⣿⣿⣿⣿⢠⠅⠀⢀⠸⡧⠛⠘⠉⠘⢻⣿⠿⣿⠿⣿⣿⣿⣿⡿⡠⡠⡤⢊⢿⠮⠀⠛⠛⠫⣿⣿⣿⣟⠃⡐⡟⠂⢉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢫⠆⡼⢁⡀⠈⠛⠢⠀⠀⠘⣿⣿⣿⣿⣿⡟⢋⣒⢠⣧⠊⡠⠈⠹⢿⣿⣿⠇⠀⢠⣮⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⣾⣴⣿⣿⣿⢯⢰⢡⠀⡠⠊⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧⢳⠙⠿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⡆⡇⠊⠀⠰⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣤⢂⡟⢊⣧⢠⣠⡤⢴⠶⢻⣿⠀⣸⠸⢿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⣿⣿⣀⡆⠘⠀⠇⠑⠒⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠙⠋⡡⠖⡀⠈⣿⣿⣿⣿
⣿⣿⣿⠃⡰⠁⡇⠢⠠⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⡍⢛⠳⣻⣷⣫⣣⠅⠈⠡⢸⣿⣷⣿⡄⣾⢧⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡟⢻⣿⣿⣢⠀⠀⠀⠸⠒⠖⢒⠀⠀⠀⢸⣿⣿⣿⠁⡧⢀⠀⣨⢬⠊⠈⠊⢿⣿⣿
⣿⣿⡿⣰⠀⠀⢰⠄⡔⠁⠄⠀⠀⠀⢠⣿⣿⣿⣿⣺⠀⣨⠞⠁⢟⣒⢿⡁⠀⠀⢸⣿⣿⣿⠗⠁⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⢸⣷⢸⣿⡏⢹⠀⠀⠀⠀⢣⠉⣁⠀⠀⢀⣼⣿⣿⠃⠀⠢⠀⠘⢡⡛⠲⠀⠀⠈⣿⣿
⣿⣿⠁⠀⢀⣆⣈⠂⠒⠋⠀⢀⢸⣿⣿⣿⣿⣿⣗⣫⠞⠁⠈⠀⠹⣽⣏⡧⡰⡂⢸⣿⡿⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠀⠀⢸⣿⢖⣿⠀⠈⠀⠀⠀⠀⠀⠉⠈⠇⡀⢸⣿⣿⠁⠀⡌⠀⠀⠀⢋⠁⠉⢰⡆⠀⠘⣿
⣿⣿⠠⠀⠈⠹⠛⠀⢀⠀⠀⠹⢸⣿⣿⣿⡿⠟⡽⣥⠃⠀⠀⠀⠀⠀⠀⢀⠄⠀⣾⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⡟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠔⢇⣾⣿⡷⠂⣜⠶⠋⠀⠀⠀⠀⠘⠏⢉⣠⣾⣿
⡿⣧⡄⠀⠀⠀⠂⡴⣶⣤⡂⢀⡈⣿⣿⣿⣿⣷⣢⡟⠀⠀⠀⠀⠀⣠⣤⡈⠀⡞⣿⣿⣠⢆⠀⠀⡐⡅⠀⠀⠀⠀⠀⢰⣦⠈⣿⣿⢰⣜⡇⠀⠀⠀⠀⠀⠀⠀⡰⣧⢸⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⢾⡇⡐⡙⢿⣿⣿
⣥⣥⡄⠀⠈⢀⡜⢿⣶⣭⡿⣙⡀⢈⠙⢳⢰⣾⣿⠁⠀⠀⠀⠀⠀⠊⠉⠐⠋⢇⢻⣿⡿⢾⣶⣷⣎⠀⠀⠀⠀⠀⢀⡷⠙⠂⣸⣿⠓⢸⡇⠀⠀⠀⠀⠀⠀⠀⢡⠇⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢻⣿
⣿⣿⠀⠀⢠⠻⢿⣶⣝⡟⣙⠊⠠⠀⢰⠈⡏⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⠃⣿⣿⣼⣎⣿⣟⣿⠀⠀⠀⠀⠀⡸⠀⢀⢨⢿⣿⡀⡚⣇⠀⠀⠀⠀⠀⠀⠀⡋⡃⠀⢿⡟⠑⠠⠤⢀⡄⡀⢠⡀⣠⡀⠀⠘⠀⠀⢿
⣿⣿⠀⠀⠈⠓⠦⡼⠏⣻⠎⠀⢈⣠⣿⠀⣿⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢃⣼⠀⣳⣿⣿⣿⣿⢝⡣⠀⠀⠀⠀⢠⠃⠀⠘⣨⣼⣿⡅⡇⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢘⢐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢘
⣿⡇⠀⠀⠀⠀⠈⠓⠙⠊⠠⣴⠅⣿⣿⢠⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⡌⠀⠀⠀⣿⣿⣿⡇⡅⢙⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣾⣿⣤⡄⠀⠐⠀⠀⠀⠀⠀⠈⢁⣤⣴⣾⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠅⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⢰⠁⠀⠀⢰⣿⣿⣿⡄⡟⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣶⠆⠘⣿⣿⣿⣿
⣿⣿⣦⠀⠀⠀⠀⠀⠀⢐⠀⣀⣑⣿⣣⣾⣿⣿⣄⣀⣀⠀⠀⠀⡀⢠⠟⠀⣀⣤⣿⣿⣿⣿⡿⠀⠀⠀⠀⣼⠏⠀⠀⠀⣼⣿⣿⣿⣧⡁⣿⣷⣄⡀⢀⡀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣆⣀⡀⠀⠀⠀⢟⣡⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣤⣔⣚⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⠋⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⡿⠀⠀⠀⣸⣿⣿⣿⣿⣽⡇⣿⣿⣿⣿⣤⣤⣦⣤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⠘⠃⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⣿⣿⠀⠀⢰⣿⣿⣿⣿⣧⣿⠀⣿⣿⣿⣿⣿⣟⢿⡏⣿⣿⡿⠿⠿⢿⣿⣽⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⠉⠁⢙⣿⠿⣿⠪⠍⠉⢉⣉⣽⣿⣿⣿⣿⡛⠉⢀⣀⣀⠛⠀⢀⠩⠍⠉⠀⡰⠿⠟⠁⠀⢰⡿⠿⠟⠀⢀⠘⠛⢛⣻⣿⣬⣽⣤⣽⣏⣉⣈⣩⠏⠻⠷⠀⣀⣤⣴⣶⣿⣿⣿⠟⠛⠾⠇⠛⠻⠍⢉⣉⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣁⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣠⣤⣤⣶⣶⣿⣿⣿⣶⣶⣿⣷⣶⣾⡋⠀⠤⠴⠶⠿⠿⠿⠿⠿⠿⣿⣿⡿⣿⣿⣯⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣒⣒⣚⣛⣛⣻⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣭⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡝⢳⡆⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣟⣟⣿⣿⣿⣟⡿⣝⣿⣟⣿⣿⡇⠀⠀⡀⠈⢩⣏⣿⣿⣯
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⠀⠁⢀⣼⣿⣿⣿⣿
⣿⡇⡻⢿⣿⣟⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠹⠼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠁⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢆⡠⠄⠀⠉⢿⣿⣿⣿⣿
⣿⡇⠚⠳⣶⣭⣙⡻⠿⣶⣾⣭⣽⣛⣿⡿⠁⠰⢸⣿⣗⣶⠭⣽⣉⣛⣛⡛⠃⠀⠀⠀⣿⣿⠁⠀⠀⢀⢹⣤⣥⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⣼⣿⣿⣿⣿
⣿⡇⢑⢖⣈⡋⠫⠻⠷⠦⢭⣛⡃⠿⡯⡇⢰⣷⡄⢽⣿⣿⣻⣿⣶⣶⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠸⣷⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠸⡿⡿⠿⠿⠛
⣿⡇⠀⠀⠀⠀⠀⠂⠁⢑⣿⣭⡻⢿⣮⠀⠉⠋⠓⠘⠻⠿⢿⢿⣶⢥⣍⠀⠀⠀⠀⠀⡟⠛⡂⠀⠀⠀⠈⣽⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠂⢲⣷⣾⡡⣎⠙⠂⢻⣷⣲⣦⣄⣠⣤⣈⡀⢤⢒⠉⠁⠀⠀⠀⠀⠀⡶⣦⣷⣦⠄⢀⣤⣹⡟⢡⣶⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠘⠿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠈⠀⠀⠤⢤⠀⠜⠀⡼⠁⠀⠈⠹⠫⢟⣻⠛⢴⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⣀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠉⠙⠛⠉⠀⠀⢠⡄⠤⡄⠀⠂⡀⠀⠀⠀⠀⠀⣀⡠⣀⠀⠀⠀⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠸⠀⠘⠀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⡟⠘⠃⠀⠍⠀⠹⡃⠀⠀⠀⠀⠀⠠⢳⠅⠋⢻⣿⠿⠿⣿⠛⠋⠀⠀⠀⠀⢐⠀⠀⠸⡁⢀⣸⠀⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡷⣴
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⣀⣀⣠⣤⣤⣬⣿⣶⣶⡾⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠺⠋⠀⠀⠁⠀⠀⠀⠀⡀⠀⡀⠡⠀⢐⢁⠘⡧⠘⣡⣤⡄⠀⠀⠀⠀⢘⡿⢻⠯⠶⠟⡉
⣿⣿⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠴⡀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠸⡳⡍⢪⢼⠋⢠⠷⠀⠀⠀⠀⠂⠀⠁⠀⠀⢀⣩⣤

                    ䷩ 𝚕𝚒𝚗𝚎 2986

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/19/site-migration-alpine/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/19/site-migration-alpine/

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Gemini_version_available_♊︎


✐ Site_Migration_Has_Begun⠀✐


Posted in Site_News at 5:09 am by Dr. Roy Schestowitz


                 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇CentOS,_here,_try_alpine⦈_


Summary: CentOS, which IBM does not want anymore (except as another Fedora), is
being left behind as we move everything to Alpine


A couple of nights ago the new target OS for Techrights was instantiated. The
migration will be slow but non-lossy, starting with Tux Machines and ending
with Techrights. The OS is Alpine, which had a new release yesterday (and does
not have systemd). We’re creating two Git servers, one for each site, and the
plan is to offer full encryption as well as Gemini for both sites.


“We need to deny revisionists and their harmful distortions of what’s going
on.”The process can take several months (due to remaining_work_obligations),
but at least we got the ball rolling. The CMS will be custom-made (built from
scratch) and we’re still working on it. We’re probably weeks away from a public
beta; testing is done privately for now.


Tux Machines is about 170,000 pages, 3 times as many as Techrights, and
preserving all the information entirely is utmost priority. Revisionism always
relies on old information going out of existence/print. We need to deny
revisionists and their harmful distortions_of_what's_going_on. █


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠹⢿⣿⣟⡁⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣉⠛⢿⣿⣿⣿⣿⣿⣶⡄⠉⠻⣿⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢈⣉⡛⠛⢿⣿⣷⠈⢻⣷⣽⣿⣿⣿⣿⣄⠀⠙⣿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠉⢻⣿⣶⣿⣿⡆⠈⠿⢿⣿⣿⣿⣿⣿⣿⣦⣌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠃⠀⠀⠀⣙⣿⣿⣿⠇⠀⠀⠙⠛⢿⣿⣿⣿⡌⠻⠿⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇⠉⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠉⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣷⡴⣶⣶⣤⣀⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⠟⠁⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⣿⣿⣿⣿⠁⢠⣿⣿⣿⣿⠏⠀⣾⣿⣿⣿⣿⣷⢽⣿⣿⣿⣷⡝⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣥⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠁⠀⢸⣿⣿⣿⡟⠀⠀⠙⢿⣿⣿⣿⣿⠀⠉⠻⣿⣿⣿⠀⠹⢿⣿⣆⠀⠀⠀⢀⣴⣶⣷⣶⡄⢰⣶⣶⣶⡆⣶⣶⡄⣶⣶⢰⣶⣶⣶⣶⡆⣰⣶⣿⣶⣆⢈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠈⠛⢿⣿⠁⠀⠀⠀⠀⠙⠻⣿⡟⠀⠀⠀⠈⢻⣿⠀⠀⠀⣿⡟⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠈⣿⣿⠁⠀⣿⣿⠈⣿⣿⢼⣿⣿⣝⠻⠿⡿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⢀⣀⣿⣿⠀⢤⣿⣿⢀⣿⣿⠀⠙⠻⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣸⣿⣟⣸⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⠸⣿⣿⣹⣿⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠹⢿⣿⣟⡁⠈⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡉⠛⢿⣿⡿⣿⣿⣿⣶⡄⠉⠻⣿⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣉⡙⠛⢿⣿⣷⡄⢻⣷⣽⣿⣿⣿⣿⣄⠀⠘⢿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡀⠀⠉⠻⣿⣶⣿⣿⡆⠈⠿⢿⣿⣿⣿⣿⣿⣿⣦⣌⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠃⠀⠀⠀⢈⣿⣿⣿⡗⠀⠀⠙⠛⢿⣿⣿⣿⡌⠛⠛⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇⠉⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠉⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠖⠲⣶⠊⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣶⣶⡤⠀⢰⣶⣦⣤⡠⣤⣤⣄⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠁⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠛⠉⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣷⠘⣿⣿⣿⣦⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣿⣿⣁⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⠀⢰⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⡆⢿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡄⣶⣶⢰⣶⣶⣶⣶⡆⣰⣶⣷⣶⣆⢈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡙⠃⠀⠀⣨⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠈⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣙⠻⢿⣿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠁⠀⠀⠀⢿⣿⡏⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠈⠛⢿⣿⣿⠀⠀⠙⢿⣿⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⢀⣿⣿⠀⣿⣿⠀⠙⠿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣸⣿⣟⣸⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⠸⣿⣿⣹⣿⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠹⣿⣿⣛⠁⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡉⠛⢿⣿⣿⣿⣿⣿⣶⡀⠙⠻⣿⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢘⠛⠛⢿⣿⣷⡄⢻⣧⣸⣿⣿⣿⣿⣄⠀⠙⢿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠻⣷⣶⣽⣿⡆⠈⠻⢿⣿⣿⣿⣿⣿⣷⣦⣌⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠓⠀⠀⠀⠈⣿⣿⣿⡗⠀⠀⠘⠻⢿⣿⣿⣿⡄⠻⠿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡏⠉⠻⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠈⠙⢿⣿⣿⡇⠀⠀⠀⠙⠻⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠖⠲⣶⠊⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀⠚⢿⣿⣶⣄⠚⣿⣿⣿⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⠟⠁⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠋⠻⣿⣿⣟⢻⠁⠀⢸⣿⣿⣿⣇⠈⣿⣿⣿⣟⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣿⣟⣁⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠁⠀⠀⣿⣿⡟⠀⠀⠀⣼⣿⣿⣿⡇⠀⢻⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡄⣶⣶⢰⣶⣶⣶⣶⡆⣰⣶⣷⣶⣆⢈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⠛⢛⠛⠻⠿⠃⠀⠀⠀⠿⠟⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠈⣿⣿⠁⠀⣿⣿⠈⣿⣿⢸⣿⣿⣙⠻⢿⣿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⡇⠘⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⡀⢀⣿⣿⢀⣿⣿⠈⠙⢿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠈⢻⣿⣿⠃⠀⠈⠹⣿⡇⠀⠀⠀⠀⢸⣿⣿⣸⣿⣟⣸⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⠸⣿⣿⣹⣿⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠀⠀⠙⡟⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠹⣿⣿⣛⠁⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡉⠛⢿⣿⣿⣿⣿⣿⣦⡀⠙⠿⣿⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣈⠛⠻⢿⣿⣷⡄⢻⣯⣸⣿⣿⣿⣿⣄⠀⠙⢿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠻⣷⣾⣿⣿⡆⠈⠻⢿⣿⣿⣿⣿⣿⣷⣦⣌⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠓⠀⠀⠀⠘⣿⣿⣿⡗⠀⠀⠚⠻⢿⣿⣿⣿⡄⠻⠿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡏⠉⠻⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠈⠛⢿⣿⣿⡇⠀⠀⠀⠙⠻⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠖⠲⣶⠊⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⠟⠁⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠀⠉⠉⢲⠄⠀⠰⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣟⣉⣀⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⢸⣿⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⡄⢰⣶⣶⣶⡆⣶⣶⡄⣶⣶⢰⣶⣶⣶⣶⡆⣰⣶⣿⣶⣆⢈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠀⠀⠀⠀⢸⣿⠏⠻⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣈⠀⣿⣿⣷⣿⣿⠀⠈⣿⣿⠉⠀⣿⣿⢸⣿⣿⣼⣿⣿⣙⠻⢿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠃⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⢀⣿⣿⢸⣿⣿⠈⠙⢿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣟⣸⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⠸⣿⣿⣹⣿⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠹⣿⣿⣛⠁⠉⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⣿⡆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡉⠛⢿⣿⣿⣿⣿⣿⣶⣄⠙⠿⣿⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⢻⡿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⡘⠛⠛⢿⣿⣷⡄⢹⣿⣜⣿⣿⣿⣿⣆⠀⠙⢿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠻⣿⣶⣽⣿⣧⠀⠻⢿⣿⣿⣿⣿⣿⣷⣤⣌⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠘⠻⠿⣿⣿⣿⣇⠹⠿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠙⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠈⠙⢿⣿⣿⣿⠀⠀⠀⠙⠻⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡷⠀⠘⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⠟⠁⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⠒⠲⠶⣦⣤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢘⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⣙⣀⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠁⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣶⡄⢰⣶⣶⣶⡆⣶⣶⡄⣶⣶⢰⣶⣶⣶⣶⡆⣴⣶⣿⣶⣆⢈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢻⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣉⠀⣿⣿⣷⣿⣿⠀⠉⣿⣿⠉⠁⣿⣿⢹⣿⣿⢼⣿⣿⣝⠻⢿⣿⠏⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠃⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⢄⣿⣿⢸⣿⣿⠈⠙⢿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣟⣸⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⠸⣿⣿⣹⣿⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣿⣿⣛⠁⠉⠙⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⠙⠻⣿⣿⣿⣿⣿⣷⣄⠙⠿⣿⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⡿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢘⡛⠛⢿⣿⣿⣆⠙⣿⣌⣿⣿⣿⣿⣧⠀⠙⢿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠹⣿⣶⣿⣿⣷⠀⠹⠿⣿⣿⣿⣿⣿⣷⣦⣌⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⠀⠀⠀⠈⣻⣿⣿⣿⠀⠀⠘⠛⠿⣿⣿⣿⣧⠹⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠉⠙⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠙⠻⣿⣿⣿⠃⠀⠀⠈⠛⠿⢿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠖⠲⣶⠎⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⠿⠋⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣦⣤⣤⣀⠀⠀⠀⠈⠻⠿⠗⠀⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣛⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠋⠉⠙⠛⠻⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⡄⢰⣶⣶⣶⡆⣶⣶⡄⣶⣶⢰⣶⣶⣶⣶⡆⣰⣶⣿⣶⣆⢈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣀⠀⣿⣿⣷⣿⣿⠀⠈⣿⣿⠁⠀⣿⣿⢸⣿⣿⣼⣿⣿⣝⠿⢿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠙⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠃⣿⣿⣿⣿⣿⠀⠀⣿⣿⡀⣤⣿⣿⢸⣿⣿⠈⠙⢿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣟⣸⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⠸⣿⣿⣹⣿⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠺⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠹⣿⣿⣛⠁⠉⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣄⣉⠙⠻⣿⣿⣿⣿⣿⣷⣄⠙⠿⣿⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣘⣛⠛⠿⣿⣿⣦⠘⣿⣯⣿⣿⣿⣿⣧⠀⠙⢿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢹⡟⠁⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⠀⠈⠙⢿⣷⣾⣿⣷⠀⠹⠿⣿⣿⣿⣿⣿⣷⣦⣌⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⠃⠀⠀⠈⢻⣿⣿⣿⠆⠀⠘⠛⠻⣿⣿⣿⣷⠹⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠛⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠈⠛⠿⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⠿⠋⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣤⣀⠀⠀⠀⠈⠻⠿⠗⠀⠻⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣛⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠋⠉⠙⠛⠻⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⡄⢰⣶⣶⣶⡆⣶⣶⡄⣶⣶⢰⣶⣶⣶⣶⡆⣰⣶⣿⣶⣆⢈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣀⠀⣿⣿⣷⣿⣿⠀⠈⣿⣿⠁⠀⣿⣿⢨⣿⣿⣼⣿⣿⣝⠻⢿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠉⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⡀⣀⣿⣿⢨⣿⣿⠈⠙⢿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣟⣸⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⠸⣿⣿⣹⣿⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠺⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠹⣿⣿⣛⠁⠉⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣄⣈⠙⠻⣿⣿⣿⣿⣿⣷⣄⠙⠿⣿⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢠⣤⡄⢠⣤⣤⣤⢠⣤⣤⣤⣄⠀⣤⣤⣴⠃⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣈⡛⠛⠿⣿⣿⣦⠘⣿⣯⣿⣿⣿⣿⣧⠀⠙⢿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⡇⢸⣿⣏⡁⢸⣿⣇⣿⣿⠀⣿⣿⣙⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⠀⠈⠙⢿⣷⣾⣿⣷⠀⠹⠿⣿⣿⣿⣿⣿⣷⣦⣌⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⢸⣿⡟⠛⢸⣿⡟⣿⣧⠀⣿⣿⠛⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⠃⠀⠀⠀⣻⣿⣿⣿⠂⠀⠘⠛⠻⣿⣿⣿⣷⠹⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⢸⣿⣧⣤⢸⣿⡇⣿⣿⠀⣿⣿⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠈⠉⠉⠉⠈⠉⠁⠈⠉⠀⠉⠉⠉⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⢀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠀⠀⣤⣤⣤⠀⢠⣤⡄⠀⣤⣤⣤⣤⡀⣤⣤⠀⣤⣄⢠⣤⡄⣤⣤⣤⡄⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⣿⣿⠁⠀⣿⣿⣸⣿⠇⢹⣿⣾⡟⠀⠀⢠⣿⣿⣿⡄⢸⣿⡇⠀⣿⣿⢈⣿⡇⣿⣿⠀⣿⣿⣼⣿⡇⣿⣿⣁⠀⠀⠀⠉⠻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡏⠙⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠘⢿
⠀⠀⣿⣿⠀⠀⣿⣿⢻⣷⡄⠈⣿⣿⠁⠀⠀⢸⣿⣉⣿⡇⢸⣿⡇⠀⣿⣿⠟⠛⠁⣿⣿⠀⣿⡿⣿⣿⡇⣿⣿⠛⠃⠀⠀⠀⠀⠀⠹⠟⠋⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠈⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣾⣿⠛⣿⣷⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢿⣿⡇⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⠉⠀⠀⠉⠉⠈⠉⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠉⠉⠈⠉⠉⠁⠈⠉⠀⠀⠀⠉⠉⠀⠉⠁⠈⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⠿⠃⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣿⣿⣋⣀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⡄⢰⣶⣶⣶⡆⣶⣶⡄⣶⣶⢰⣶⣶⣶⣶⡆⣰⣶⣿⣶⣆⢈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠿⢿⣿⣿⣿⡿⠃⠀⠈⠛⢿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠈⣿⣿⠁⠀⣿⣿⠀⣿⣿⣸⣿⣿⣛⠿⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠏⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠈⠉⠀⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⣀⣿⣿⠀⣿⣿⠈⠙⢿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⠸⣿⣿⣹⣿⣿⣤⡀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣛⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠹⣿⣟⣛⠉⠉⠓⠀
⠀⠀⠀⠀⠀⠀⠹⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠙⠻⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣦⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢠⣤⡄⢠⣤⣤⣤⢠⣤⣤⣤⣄⠀⣤⣤⣴⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣦⠘⣿⣧⣻⣿⣿⣿⣷⠀⠙⢿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⡇⢸⣿⣏⠀⢸⣿⣇⣿⣿⠀⣿⣿⣉⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⢿⣶⣾⣿⣿⡄⠘⠿⣿⣿⣿⣿⣿⣷⣤⣈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⢸⣿⡟⠛⢸⣿⡟⣿⣧⠀⣿⣿⠛⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠃⠀⠀⠀⢙⣿⣿⣿⡇⠀⠀⠛⠻⢿⣿⣿⣿⡹⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⢸⣿⣧⣤⢸⣿⡇⣿⣿⠀⣿⣿⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠈⠉⠉⠉⠈⠉⠁⠈⠉⠀⠉⠉⠉⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⢀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠀⠀⣤⣤⣤⠀⢠⣤⡄⠀⣤⣤⣤⣤⡀⣤⣤⠀⣤⣄⢠⣤⡄⣤⣤⣤⡄⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⣿⣿⠁⠀⣿⣿⣸⣿⠇⢹⣿⣾⡟⠀⠀⢠⣿⣿⣿⡄⢸⣿⡇⠀⣿⣿⢈⣿⡇⣿⣿⠀⣿⣿⣼⣿⡇⣿⣿⣀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿
⠀⠀⣾⣿⠀⠀⣿⣿⢻⣷⡀⠈⣿⣿⠁⠀⠀⢸⣿⣉⣿⡇⢸⣿⡇⠀⣿⣿⠟⠛⠁⣿⣿⠀⣿⡿⣿⣿⡇⣿⣿⠛⠃⠀⠀⠀⠀⠀⠙⠿⠛⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⠈⠙⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⣿⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢿⣿⡇⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠉⠀⠀⠉⠁⠈⠉⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠉⠉⠈⠉⠉⠁⠈⠉⠀⠀⠀⠉⠉⠀⠉⠁⠈⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾
⠀⠖⠲⣶⠎⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠟⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁⢀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡄⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣀⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⢿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⢀⣿⣿⠀⣿⣿⠈⠙⢿⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠸⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⣄⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣿⠰⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠋⠀⠀⠀⠙⠿⡿⠋⠀⠀⠙⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠙⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠹⣿⣟⡛⠁⠉⠁⠀
⠀⠀⠀⠀⠀⢻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠉⠛⢿⣿⡿⣿⣿⣷⣄⠙⠿⣷⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⠀⣤⣤⠀⣤⡄⢠⣤⣤⣤⢠⣤⣤⣤⣄⠀⣤⣤⣽⠛⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠒⠛⠻⣿⣿⣦⠈⢻⣧⣹⣿⣿⣿⣷⠀⠘⢿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣨⣿⡇⢸⣿⡇⠀⢸⣿⡇⣿⣿⠀⣿⣏⠈⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠉⢻⣶⣮⣿⣿⡄⠈⠿⢿⣿⣿⣿⣿⣷⣄⡈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⣿⡇⢸⣿⡟⠃⢸⣿⡟⣿⣧⠀⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠃⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠘⠛⢿⣿⣿⣿⡽⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠰⣿⡇⢸⣿⣧⣤⢸⣿⡇⣿⣿⠀⣿⣧⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠈⠉⠉⠉⠈⠉⠁⠈⠉⠀⠉⠉⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⢀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠀⠀⣤⣤⣤⠀⢠⣤⡄⠀⣤⣤⣤⣤⡀⣤⣤⠀⣤⡄⢠⣤⠀⣤⣤⣤⡄⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠂⢹⣷⣾⡏⠀⠀⢀⣿⣿⣿⡀⢸⣿⡇⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⣸⣿⠀⣿⣿⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠉⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⡀⠀⣿⣿⠁⠀⠀⢸⣿⣁⣿⡇⢸⣿⡇⠀⣿⣿⠛⠛⠁⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠙⠻⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠉⠉⠈⠁⠉⠁⠈⠉⠀⠀⠀⠈⠉⠀⠉⠀⠀⠉⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠆⠲⣶⠊⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠋⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⢀⣤⡖⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠀⠙⢿⣿⣷⡆⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡀⠛⠉⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⣄⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⣴⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡇⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠹⣿⣟⡛⠁⠉⠁⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⣋⠉⠟⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠛⢿⣿⡿⣿⣿⣷⣦⡙⠿⣷⣤⡀⠀
⠀⠀⠀⠀⠈⢿⣿⣿⡿⠋⠀⠀⣤⣿⢿⣿⡿⢿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣶⡀⢻⣧⣸⣿⣿⣿⣷⡀⠙⢿⣧⠀
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⣿⣿⣘⣿⡇⢸⣿⡏⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣽⣿⡆⠈⠻⠿⣿⣿⣿⣿⣷⣄⡈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⣿⡇⢸⣿⡟⠛⢸⣿⡟⣿⣧⠈⣿⣿⣿⠻⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢻⣿⣿⣿⣿⣿⡳⣄⠀⠀⠀⠃⠀⠀⠀⠈⣻⣿⣿⡇⠀⠀⠀⠙⠛⣿⣿⣿⡟⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⢸⣿⣧⣤⢸⣿⡇⣿⣿⠀⣿⣿⣤⢠⣤⠉⠛⠋⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣾⣿⣶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠈⠉⠉⠉⠀⠉⠁⠈⠉⠀⠉⠉⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠀⠀⣤⣤⣤⠀⢠⣤⡄⠀⣤⣤⣤⣤⡀⣤⣤⠀⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠙⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠂⢹⣷⣾⡏⠀⠀⢀⣿⣿⣿⡀⢸⣿⡇⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⣸⣿⠀⣿⣿⡀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣏⠉⠙⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⡀⠀⣿⣿⠁⠀⠀⢸⣿⣀⣿⡇⢸⣿⡇⠀⣿⣿⠛⠛⠁⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠻⣿⣿⣿⠀⠀⠀⠈⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠃⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠀⠙⢿⣿⣷⡆⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣿⣿⣾⣿⣧⠀⠏⠉⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⣄⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⣤⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣻⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠹⣿⣟⠛⠁⠉⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠛⢿⣿⡿⣿⣿⣷⣦⡙⢿⣷⣤⡀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣶⡀⢻⣧⣘⣿⣿⣿⣷⡀⠙⢿⣧⠀
⠀⠀⠀⠀⠀⠈⠿⠟⠋⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣽⣿⡆⠈⠻⠿⣿⣿⣿⣿⣷⣄⡈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⣿⡇⢸⣿⡿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠻⣿⣿⣿⣿⣿⡳⣄⠀⠀⠀⠃⠀⠀⠀⠈⣻⣿⣿⡗⠀⠀⠀⠉⠛⢿⣿⣿⡟⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⢸⣿⣧⣬⢹⣿⡇⢿⣿⠻⣿⣿⣿⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⣙⣿⣿⣿⣿⣿⣾⣿⣶⣴⣿⣿⣶⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠈⠉⠉⠉⠀⠉⠁⠈⠉⠀⠉⠉⠉⠈⠋⠉⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠀⠀⣤⣤⣤⠀⢠⣤⡄⠀⣤⣤⣤⣤⡀⣤⣤⠀⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠙⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠂⢹⣷⣾⡏⠀⠀⢀⣿⣿⣿⡀⢸⣿⡇⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⣸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⣟⠉⠙⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⠀⠀⣿⣿⠁⠀⠀⢸⣿⣀⣿⡇⢸⣿⡇⠀⣿⣿⠛⠛⠁⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠘⠻⣿⣿⣿⠀⠀⠀⠈⠛⠿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠟⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠈⠙⢿⣿⣷⡆⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣿⣷⣾⣿⡅⠘⠙⠉⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⣄⣿⣿⣼⣿⣿⣶⣾⣿⣿⣿⣶⣿⣿⣤⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣻⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠹⣿⣟⠛⠁⠉⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢣⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠛⢿⣿⡿⣿⣿⣷⣮⡙⢿⣷⣤⡀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠄⣿⣿⣻⣿⣿⣿⣿⣯⣥⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣷⡄⢻⣧⣘⣿⣿⣿⣷⡄⠙⢿⣧⠀
⠀⠀⠀⠀⠀⠻⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣽⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣽⣿⡆⠈⠹⠿⣿⣿⣿⣿⣷⣄⡈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢻⣿⣿⣿⣿⣯⡷⣄⠀⠀⠀⠓⠀⠀⠀⠈⢻⣿⣿⡗⠀⠀⠀⠉⠛⢿⣿⣿⡟⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⣿⡇⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⢙⣿⣿⣿⣿⣿⣾⣿⣶⣴⣿⣿⣶⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠈⠉⠉⠙⠿⠉⠁⠉⠙⢿⣿⣿⡏⠙⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠀⠀⣤⣤⣤⠀⢠⣤⡄⠀⣤⣼⣭⣤⡀⣤⣼⠉⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠙⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠂⢹⣷⣾⡏⠀⠀⢀⣿⣿⣿⡀⢸⣿⡇⠀⣿⣿⠀⣿⡇⣿⣿⠀⣿⣿⣸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣟⠉⠙⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⡀⠀⣿⣿⠁⠀⠀⢸⣿⣀⣿⡇⢸⣿⡇⠀⣿⣿⠛⠛⠁⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠙⠻⣿⣿⣿⠀⠀⠀⠈⠛⠿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠟⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⣠⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠈⠛⢿⣿⣿⡆⠁⠀⠀
⠀⠀⠀⠀⠀⣠⣶⣠⣼⣇⠀⠋⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⣄⣿⣿⣼⣿⣿⣶⣾⣿⣿⣿⣶⣿⣿⣤⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡆⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣻⣿⣷⣿⣿⣿⣿⣿⠟⠛⠉⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠹⣿⣛⠛⠉⠉⠁⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠛⠿⣿⣿⢿⣿⣿⣮⡙⢿⣶⣤⡀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣬⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠚⠛⢻⣿⣷⡄⠙⣿⣌⣿⣿⣿⣿⡄⠙⣿⣷⠀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠹⣷⣶⣽⣿⣧⠀⠹⠿⣿⣿⣿⣿⣷⣄⡈⢷⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠙⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠉⠛⢿⣿⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣉⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣷⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠻⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠀⠈⣿⣿⣿⠁⢻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠙⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠀⢹⣷⣾⡏⠀⠀⢀⣿⣿⣿⡀⢸⣿⡟⢿⣿⣿⠈⣿⡟⣿⣿⠃⣿⣿⣸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠉⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⡀⠀⣿⣿⠁⠀⠀⢸⣿⣀⣿⡇⢸⣿⡇⠀⣿⣿⠛⠛⠁⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠈⠻⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣧⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠟⠁⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠁⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠈⠛⢿⣿⣿⡆⠁⠀⠀
⠀⠀⠀⠀⠀⣠⣦⣀⣼⠃⠈⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⡄⣿⣿⣼⣿⣿⣶⣾⣿⣿⣿⣶⣿⣿⣤⣿⣿⠀⣿⣿⣻⣿⣿⣄⠀⠀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣻⣿⣷⣿⣿⣿⣿⣿⠟⠛⠉⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠹⣿⣛⠛⠉⠉⠁⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠛⠿⣿⣿⢿⣿⣷⣮⡙⢿⣶⣤⡀⠀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⢤⠠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣤⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠐⠚⠛⠻⣿⣷⡄⠘⣿⣌⣿⣿⣿⣿⡆⠙⢿⣷⠀
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠈⠙⣷⣶⣬⣿⣧⠀⠙⠿⢿⣿⣿⣿⣷⣄⡈⢷⣄
⠀⠀⠀⠀⠀⠘⠉⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠙⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠉⠛⢿⣿⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣈⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣷⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠙⢿⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠻⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠈⠻⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠙⠟⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠂⢹⣷⣾⡏⠀⠀⢀⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⠈⣿⡿⣿⣿⠇⣿⣿⣸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠋⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⠀⠀⣿⣿⠁⠀⠀⢸⣿⣁⣿⡇⢸⣿⡇⠙⣿⣿⠛⠛⠁⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠙⢿⣿⣿⣿⡆⠀⠀⠈⠻⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡄⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣧⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠰⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠛⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⠀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠀⠙⢿⣿⣷⡆⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡄⢀⣹⠃⠈⠻⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⡄⣿⣿⣼⣿⣿⣶⣾⣿⣿⣿⣶⣿⣿⣤⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣶⡀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣛⣿⣷⣿⣿⣿⣿⣿⡟⠛⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡹⣿⣟⠛⠁⠉⠁⠀
⠀⠀⠀⢨⣿⣿⣿⣿⣿⡿⠃⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠙⠻⣿⣿⢿⣿⣿⣦⣝⠿⣷⣤⡀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⣀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣤⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣦⠘⣿⣄⣻⣿⣿⣿⣆⠘⢿⣷⠀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠙⢿⣶⣮⣿⣷⠀⠙⠿⢿⣿⣿⣿⣿⣄⡈⢻⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⠀⠀⠀⠀⢙⣿⣿⣿⠂⠀⠀⠈⠙⠻⣿⣿⣿⡿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣷⣌⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢻⣿⡅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠙⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠙⠛⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠂⢹⣷⣾⡏⠀⠀⢀⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⢈⣿⡿⣿⣿⠃⣿⣿⣸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡋⠙⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⠀⠀⣿⣿⠁⠀⠀⢸⣿⣁⣿⡇⢸⣿⡏⠛⣿⣿⠛⠛⠁⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠙⠿⠛⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠈⠛⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠛⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠁⠀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠀⠙⢿⣿⣷⡆⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡄⢀⣹⠃⠘⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⡄⣿⣿⣼⣿⣿⣶⣾⣿⣿⣿⣶⣿⣿⣤⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⡀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣛⣿⣷⣿⣿⣿⣿⣿⡟⠛⠉⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣄⡹⣿⣟⠛⠁⠉⠁⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠙⠛⢿⣿⢿⣿⣿⣶⣝⠿⣶⣤⡀⠀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⣀⠠⣿⣿⢿⣿⣿⣿⣿⣿⣯⣡⣤⣼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⠘⣿⣄⣻⣿⣿⣿⣆⠘⢿⣷⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠉⢿⣶⣦⣽⣷⠀⠈⠿⢿⣿⣿⣿⣿⣄⡀⢻⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠟⢿⣿⣿⣿⣿⣟⣦⣀⠀⠀⠈⠂⠀⠀⠀⢙⣿⣿⣿⠆⠀⠀⠈⠙⠻⣿⣿⣿⡿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣄⣽⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠀⠙⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠈⠛⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠂⢹⣷⣾⡏⠀⠀⢀⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⠃⣿⣿⣸⣿⠀⣿⣿⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡋⠙⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⡀⠀⣿⣿⠁⠀⠀⢸⣿⣁⣿⡇⢸⣿⡏⠻⣿⣿⠛⠛⠁⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠈⠙⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠟⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠁⠀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠈⠛⢿⣿⣿⡆⠁⠀⠀
⠀⠀⠀⠀⠀⢀⡄⢀⣹⠇⠘⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⡄⣿⣿⣼⣿⣿⣶⣶⣿⣿⣿⣶⣿⣿⣤⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⡀⠀⠀⣀⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣛⣿⣷⣿⣿⣿⣿⣿⡿⠛⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡹⣿⣟⠛⠉⠉⠁⠀
⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠇⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⠙⠻⣿⣿⢿⣿⣿⣾⣝⠿⣶⣤⡀⠀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣤⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣦⠘⣿⣄⣻⣿⣿⣿⣆⠙⢿⣷⠀
⠀⠀⠀⠀⠹⢿⣿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠉⢿⣶⣮⣿⣷⠀⠉⠿⢿⣿⣿⣿⣿⣄⡈⢿⣄
⠀⠀⠀⠀⠀⠈⠛⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⠂⠀⠀⠀⢙⣿⣿⣿⠆⠀⠀⠈⠛⠻⣿⣿⣿⡿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣌⣽⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⢿⣿⡅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠈⠻⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠙⠛⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠂⢹⣷⣾⡏⠀⠀⢸⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⢘⣿⣿⣿⣿⡇⣿⣿⣸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡋⠛⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⡀⠀⣿⣿⠁⠀⠀⢸⣿⣉⣿⡇⢸⣿⡿⣿⣿⣿⠛⠛⠉⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠈⠛⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣧⢸⣿⣧⡄⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠴⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠟⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠁⠀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠈⠛⢿⣿⣿⡆⠁⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⣹⠇⠸⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⡄⣿⣿⣼⣿⣿⣶⣾⣿⣿⣿⣷⣿⣿⣤⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⡀⠀⠀⢀⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣛⣿⣷⣿⣿⣿⣿⣿⡟⠛⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡹⣿⣟⠛⠉⠉⠁⠀
⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⠙⠻⣿⣿⢿⣿⣿⣶⣝⢿⣶⣤⡀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⡉⠙⠻⣿⣿⣦⠘⣿⣄⣻⣿⣿⣿⣆⠙⢿⣷⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣷⣮⣿⣷⠀⠉⠿⢿⣿⣿⣿⣿⣄⡈⢻⣄
⠀⠀⠀⠀⠀⠈⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⠀⠀⠀⠀⢙⣿⣿⣿⠂⠀⠀⠉⠙⠻⣿⣿⣿⡿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣆⣽⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠙⢿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠙⠛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠂⢹⣷⣾⡏⠀⠀⢹⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡋⠙⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⠀⠀⣿⣿⠁⠀⠀⢸⣿⣛⣿⡇⢸⣿⡿⣿⣿⣿⠛⠛⠉⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠈⠛⠿⠟⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠈⠛⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣧⡌⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠰⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠟⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠁⠀⣠⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠈⠛⢿⣿⣷⡆⠁⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⢹⠇⠸⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⡄⣿⣿⣼⣿⣿⣶⣾⣿⣿⣿⣷⣿⣿⣴⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣾⣿⣤⡀⠀⠀⠀⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣛⣿⣷⣿⣿⣿⣿⣿⡟⠛⠉⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣄⡹⣿⣟⠛⠉⠉⠃⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⠉⠻⣿⣿⢿⣿⣿⣶⣝⠿⣶⣤⡀⠀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⡉⠙⠻⢿⣿⣦⠘⣿⣤⣿⣿⣿⣿⣆⠙⢿⣷⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣾⣿⣷⠀⠉⠿⢿⣿⣿⣿⣿⣄⡈⢻⣄
⠀⠀⠀⠀⠀⠈⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠈⠀⠀⠀⠀⢙⣿⣿⣿⠂⠀⠀⠀⠙⠻⣿⣿⣿⡿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣆⣽⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢠⣤⠟⢿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠘⠛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠀⢹⣷⣾⡏⠀⠈⢻⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡋⠙⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⠀⠀⣿⣿⠁⠀⠀⢸⣿⣛⣿⡇⢸⣿⣿⣿⣿⣿⠛⠛⠛⣿⣿⠀⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠈⠙⠿⠋⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠈⠛⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡆⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣧⡏⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠟⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⣠⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⢰⣶⣶⣶⡆⣶⣶⡀⣶⣶⢰⣶⣶⣶⣶⡆⣠⣶⣶⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣷⢸⣿⣿⣀⠀⣿⣿⣧⣿⣿⠀⠀⣿⣿⠁⠀⣿⣿⠀⣿⣿⢸⣿⣿⣛⠿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣀⣀⢸⣿⣿⠿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠈⠛⢿⣿⣷⡆⠁⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⢹⡇⠹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡟⢸⣿⣿⣤⡄⣿⣿⣼⣿⣿⣶⣾⣿⣿⣿⣷⣿⣿⣴⣿⣿⠀⣿⣿⣹⣿⣿⣄⠀⠀
⠀⠀⠀⠀⣠⣾⣷⣾⣿⣤⠀⠀⠀⠀⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣛⣿⣷⣿⣿⣿⣿⣿⡟⠛⠉⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣤⡹⣿⣟⠛⠉⠉⠃⠀
⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠉⠛⣿⣿⢿⣿⣿⣷⣝⠿⣷⣤⡀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣉⠉⠛⢿⣿⣦⠘⣿⣆⣻⣿⣿⣿⣇⠙⢿⣷⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⢀⠀⠀⠈⠿⣷⣶⣿⣷⠀⠉⠻⢿⣿⣿⣿⣿⣄⡈⢻⣄
⠀⠀⠀⠀⠀⠙⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠈⡀⠀⠀⠀⣙⣿⣿⣿⠂⠀⠀⠈⠙⠻⣿⣿⣿⡿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣆⣽⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⡍⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀
⠀⣤⣤⣤⣤⡄⣤⣤⣤⣤⠀⣤⡄⢩⣽⠿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⣤⡄⢠⣤⠀⣤⣤⣤⡄⠀⠈⠛⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢹⣿⠀⠀⣿⣿⣸⣿⠀⢹⣷⣾⡏⠀⠘⢿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡋⠙⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢸⣿⠀⠀⣿⣿⢻⣷⠀⠀⣿⣿⠁⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠛⠛⠛⣿⣿⠁⣿⡿⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠈⠙⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠀⠀⣿⣿⢸⣿⡃⠀⣿⣿⠀⠀⠀⣼⣿⠛⣿⣷⢸⣿⣿⡟⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⢻⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠰⠰⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3432

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.19.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_19/07/2022:_Microsoft_is_Offline_Again⠀✐


Posted in News_Roundup at 9:50 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
    * Canonical/Ubuntu_Family
    * Devices/Embedded
    * Open_Hardware/Modding
    * Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Events
          o Programming/Development
                # Python
    * Leftovers
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Pseudo-Open_Source
                # Openwashing
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy
                # 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 Digital_Restrictions_(DRM)
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Science
    * § GNU/Linux⠀➾


          o § Applications⠀➾


                # ⚓ Linux Links ☛ 6_Best_Free_and_Open_Source_C++_Static_Site
                  Generators⠀⇛


                       
                       LinuxLinks, like most modern websites, is dynamic
                       in that content is stored in a database and
                       converted into presentation-ready HTML when readers
                       access the site.


                       While we employ built-in server caching which
                       creates static versions of the site, we don’t
                       generate a full, static HTML website based on raw
                       data and a set of templates. However, sometimes a
                       full, static HTML website is desirable. Because
                       HTML pages are all prebuilt, they load extremely
                       quickly in web browsers.


                       There are lots of other advantages of running a
                       full, static HTML website.


                # ⚓ Linux Links ☛ 14_Best_Free_and_Open_Source_Linux_System
                  Monitoring_Tools⠀⇛


                       
                       These types of systems gather data relating to CPU,
                       memory, network, disk utilization, response time of
                       network services, and much more.


                       To provide an insight into the quality of software
                       that is available, we have compiled a list of 14
                       Linux system monitoring tools. Hopefully, there
                       will be something of interest here for anyone who
                       wants to monitor a specific service or situation.


          o § Instructionals/Technical⠀➾


                # ⚓ OpenSource.com ☛ Event-driven_architecture_explained_in_a
                  coloring_book⠀⇛


                       “Explain it to me like I’m five.”


                       When you want someone to get to the point as
                       efficiently and as clearly as possible, that’s what
                       you say. Following that logic, you might be
                       compelled to ponder the most powerful tool the
                       average, everyday 5-year old wields: coloring
                       books. What better way than a coloring book to
                       transform a droll slideshow presentation into a fun
                       and educational journey?


                       That’s what artists Máirín Duffy and Madeline Peck
                       thought, anyway, and it has turned out to be
                       accurate. In the past, Máirín has helped produce
                       five open source coloring books to help explain
                       advanced topics including SELinux, Containers,
                       Ansible, and more. It’s a fun and easy way to learn
                       about emerging technology, and you can either color
                       your lessons yourself or hand it over to a resident
                       specialist (an actual 5-year old) for project
                       completion.


                       The latest coloring book in the series is all about
                       event driven architecture (EDA). As with all the
                       previous coloring books, this one’s not only free
                       to download, but it’s also open source. You can
                       download the sources and assemble it yourself, or
                       learn from the files so you can build your own
                       about topics important to you.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Exanima_gets_vastly_improved_Linux_and
                  Steam_Deck_support⠀⇛


                       Exanima is an unforgiving 3D isometric RPG set in
                       an original dark, low fantasy world. Currently in
                       Early Access, it seems the developers have been
                       paying attention to user requests for better Linux
                       and Steam Deck support with Proton.


                # ⚓ GamingOnLinux ☛ Tesla_to_demo_Steam_for_more_in-car_gaming
                  soon_using_Linux_&_Proton⠀⇛


                       Tesla and Steam? It’s coming and it sounds like
                       it’s progressing nicely with a demo to come soon to
                       show it off.


                # ⚓ GamingOnLinux ☛ Dead_Cells_has_an_exciting_roadmap_ahead_as
                  it’s_far_from_finished⠀⇛


                       Dead Cells is the absolutely brilliant game from
                       Motion Twin and Evil Empire. A rogue-lite,
                       metroidvania inspired, action-platformer and it’s
                       not finished, far from it. The developers have just
                       recently revealed a roadmap, that mentions how 2023
                       will be the “most exciting year in Dead Cells’
                       history” which is a pretty bold claim.


                # ⚓ GamingOnLinux ☛ Hot_swapping_SD_Cards_on_Steam_Deck_is_okay
                  but_Valve_plans_improvements⠀⇛


                       There’s been a lot of talk about the Steam Deck and
                       SD Cards lately around hot swapping and apparently
                       bricked SD Cards but Valve say it’s fine, although
                       improvements are coming.


                # ⚓ GamingOnLinux ☛ Relive_memories_of_going_to_the_arcade_in
                  Point_Rescue_Arcade⠀⇛


                       Point Rescue Arcade is a game that very much leans
                       into the experience you might have had when going
                       to a real Arcade, grabbing a big gun and sticking
                       in some coins.


                # ⚓ GamingOnLinux ☛ fheroes2_game_engine_for_Heroes_of_Might
                  and_Magic_II_gets_even_more_AI_upgrades⠀⇛


                       Fully playable but they’re not done yet. The team
                       behind the Heroes of Might and Magic II game engine
                       reimplementation continue to improve it even
                       further for playing it on modern platforms. This
                       free and open source reimplementation is simply
                       awesome, the best way to play the classic.


                # ⚓ GamingOnLinux ☛ Swirl_W@tch_is_a_blindly-vibrant_upcoming
                  stealth-action_rogue-lite⠀⇛


                       Sleeper Games have revealed their latest game with
                       Swirl W@tch, a very colourful and bright stealth-
                       action rogue-lite that will release later this
                       year.


                # ⚓ GamingOnLinux ☛ iFixit_have_the_Steam_Deck_Fan_in_stock_if
                  you’re_in_the_U.S.⠀⇛


                       Want to get rid of the whine that certain models of
                       Steam Deck have with their fan? Good news, at least
                       if you’re in the USA, as iFixit have fans in stock.


                # ⚓ GamingOnLinux ☛ Souls-like_game_Hellpoint:_Blue_Sun_major
                  expansion_DLC_is_out_now⠀⇛


                       The thoroughly challenging Souls-like game
                       Hellpoint has expanded with the Hellpoint: Blue Sun
                       major expansion DLC. With the DLC you will end up
                       getting some answers, as they said it reveals the
                       full story “for those who can understand it”.


                # ⚓ GamingOnLinux ☛ Open_source_evolution_sim_Thrive_gets
                  procedural_maps,_better_gameplay⠀⇛


                       Thrive is a free and open source science-based game
                       about evolution, currently allowing you to swim
                       around as a little cell and attempt to survive. The
                       latest release brings in some major improvements.
                       It’s in Early Access and they have a long way to go
                       before it’s a complete game but it’s still a really
                       interesting idea, very much like an expanded early-
                       stage version of Spore.


                # ⚓ GamingOnLinux ☛ Heroic_Games_Launcher_adds_GOG_Cloud_Saves,
                  Epic_Overlay_support,_anti-cheat_helpers⠀⇛


                       The Heroic Games Launcher for Epic Games and GOG on
                       Linux has a huge new Beta release (plus a bug fixes
                       for the stable build) with loads of fancy new
                       features.


                # ⚓ GamingOnLinux ☛ Wine_7.13_rolled_out_recently_continuing
                  the_PE_conversion⠀⇛


                       Fashionably late on this one. Wine 7.13 rolled out
                       just before the weekend rolled in, so here’s a
                       quick run down of what’s new in this Windows
                       compatibility layer.


                # ⚓ Hackaday ☛ The_Commodore_64_Smartwatch_Can_Now_Sync_With
                  Your_Commodore_64_Desktop⠀⇛


                       If you’ve got a smartwatch on your wrist, chances
                       are you’ve also got a device nearby that links up
                       with it. Most modern watches will happily sync with
                       Android devices or iPhones, and some will also talk
                       to Windows PCs. But what if you’re running an
                       alternative OS? Something like, say, Commodore
                       BASIC? In that case, you might want to check out
                       [Nick Bild]’s latest project, which lets you to
                       sync your smartwatch to your Commodore 64.


    * § Distributions and Operating Systems⠀➾


          o ⚓ South Africa ☛ Asahi_Linux_runs_on_Apple_M2_machines⠀⇛


                 The team behind Asahi Linux have announced that the
                 distribution runs on the M1 Ultra and Mac Studio without
                 needing a virtual machine.


    * § Canonical/Ubuntu Family⠀➾


          o ⚓ DebugPoint ☛ Top_10_Features_of_Linux_Mint_21_“Vanessa”_
            [Featured]⠀⇛


                 A list of top 10 features of Linux Mint 21 “Vanessa”
                 across Cinnamon, Xfce and MATE desktop environments and
                 more.


          o ⚓ Its FOSS ☛ Ubuntu_21.10_Has_Reached_End-of-Life,_Upgrade_Now!⠀⇛


                 
                 Ubuntu 21.10 has reached end-of-life on 14th of July.
                 Backup your files before starting an upgrade!


                 While Ubuntu 21.10 was the only way to experience GNOME
                 40 back then, it brought a newer kernel and high-quality
                 Bluetooth codecs.


                 Unfortunately, it reached end-of-life on the 14th of
                 July, meaning you will no longer receive any updates for
                 it.


                 So it’s time to upgrade!


    * § Devices/Embedded⠀➾


          o ⚓ Linux Gizmos ☛ Geniatech’s_SBC_taps_Rockchip_SoC_and_runs_on
            Android_11_&_Debian⠀⇛


                 The XPI-3566 is the latest Single Board Computer
                 developed by Geniatech. This SBC is powered by the
                 Rockchip RK3566 System on Chip (SoC) and it comes in a
                 Raspberry Pi 4 form factor. The company expects to target
                 smart retail and similar interactive applications.


                 This SBC implements the Rockchip RK3566 which is a four
                 core Cortex-A55 processor with a maximum frequency of
                 1.8GHz. In addition, there is a Mali-G52-2EE GPU and a
                 Neural Process Unit (NPU) with processing performance up
                 to 1.0 TOPS (according to the Rockchip datasheet).


    * § Open Hardware/Modding⠀➾


          o ⚓ Hackaday ☛ Hacker_Liberates_Hyundai_Head_Unit,_Writes_Custom
            Apps⠀⇛


                 [greenluigi1] bought a Hyundai Ioniq car, and then, to
                 our astonishment, absolutely demolished the Linux-based
                 head unit firmware. By that, we mean that he bypassed all
                 of the firmware update authentication mechanisms,
                 reverse-engineered the firmware updates, and created
                 subversive update files that gave him a root shell on his
                 own unit. Then, he reverse-engineered the app framework
                 running the dash and created his own app. Not just for
                 show – after hooking into the APIs available to the dash
                 and accessible through header files, he was able to
                 monitor car state from his app, and even lock/unlock
                 doors. In the end, the dash got completely conquered –
                 and he even wrote a tutorial showing how anyone can
                 compile their own apps for the Hyundai Ionic D-Audio 2V
                 dash.


    * § Mobile Systems/Mobile Applications⠀➾


          o ⚓ Auto_Rotate_Not_Working_On_Android?_Here’s_How_To_Fix_It⠀⇛


          o ⚓ Android Police ☛ Google_has_a_new_home_on_Amazon_and_doesn’t_want
            to_talk_about_Android⠀⇛


          o ⚓ TechRadar ☛ Surprise_Android_phone_update_brings_Android_13
            feature_early_|_TechRadar⠀⇛


          o ⚓ PR Newswire ☛ Headwolf_Releases_WPad1,_the_First_Android_12
            tablet⠀⇛


          o ⚓ Pocket Lint ☛ When_is_Android_13_coming_to_my_phone?⠀⇛


          o ⚓ Notebook Check ☛ Ulefone_Armor_X6_Pro:_a_new_budget_rugged
            smartphone_with_an_upgrade_to_Android_12_–_NotebookCheck.net_News⠀⇛


          o ⚓ Business Insider ☛ Acer_launches_new_Android_11-powered_budget
            smart_TVs_in_India_starting_at_₹14,999_|_Business_Insider_India⠀⇛


          o ⚓ HowTo Geek ☛ How_to_Make_a_Song_Your_Ringtone_on_Android⠀⇛


          o ⚓ SlashGear ☛ How_To_Fix_An_Android_Phone_That_Keeps_Crashing⠀⇛


          o ⚓ SlashGear ☛ Why_You_Need_To_Turn_Your_Android’s_Bluetooth_Off
            When_You’re_Not_Using_It⠀⇛


          o ⚓ GSM Arena ☛ Google_Wallet_update_starts_rolling_out_to_Android
            users_–_GSMArena.com_news⠀⇛


          o ⚓ Phone Arena ☛ Google_promotes_its_apps_on_Amazon_page_without
            using_the_Android_name_–_PhoneArena⠀⇛


          o ⚓ Express ☛ Nothing_Phone_(1):_Android_fans_get_blockbuster_FREE
            bonus_when_buying_one_|_Express.co.uk⠀⇛


          o ⚓ Android_Auto_issue_gets_acknowledged_by_Google_|_T3⠀⇛


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


          o ⚓ Hackaday ☛ Ortur_Laser_Will_Go_Open-Source⠀⇛


                 Well, that was fast! Last week, we wrote about a video by
                 [Norbert Heinz] where he called out the Ortur laser
                 engravers for apparently using the GPL-licensed grbl
                 firmware without providing the source code and their
                 modifications to it, as required by the license. Because
                 open source and grbl are dear to our hearts and CNC
                 machines, we wrote again about Norbert’s efforts over the
                 weekend, speculating that it might just be unfamiliarity
                 with the open source license requirements on Ortur’s
                 part.


          o § Events⠀➾


                # ⚓ Unicorn Media ☛ SCaLE_Returns_to_Celebrate_Its_20th
                  Birthday_July_28-31⠀⇛


                       This year SCALE, the community-focused Southern
                       California Linux Expo, is back — live and in-person
                       — on July 28-31. The lineup is great, and will
                       include a closing keynote address by Vint Cerf,
                       who’s regarded as one of the “fathers’ of the
                       internet.”


          o § Programming/Development⠀➾


                # ⚓ OpenSource.com ☛ Code_your_first_React_UI_app⠀⇛


                       Who wants to create their first UI app? I do, and
                       if you’re reading this article, I assume you do,
                       too. In today’s example, I’ll use some JavaScript
                       and the API with Express I demonstrated in my
                       previous article. First, let me explain some of the
                       tech you’re about to use.


                # § Python⠀➾


                      # ⚓ OpenSource.com ☛ Turn_your_Python_script_into_a
                        command-line_application⠀⇛


                             I’ve written, used, and seen a lot of loose
                             scripts in my career. They start with someone
                             that needs to semi-automate some task. After
                             a while, they grow. They can change hands
                             many times in their lifetime. I’ve often
                             wished for a more command-line tool-like
                             feeling in those scripts. But how hard is it
                             really to bump the quality level from a one-
                             off script to a proper tool? It turns out
                             it’s not that hard in Python.


    * § Leftovers⠀➾


          o ⚓ Quillette ☛ Cognitive_Distortions⠀⇛


                 Damaging as they may be, hoaxes by individual pranksters
                 are usually removed from Wikipedia as soon as they are
                 discovered. Something far more potentially harmful, both
                 to Wikipedia and to public knowledge as a whole, is when
                 several users work together across multiple Wikipedia
                 articles to discredit a body of scientific research, and
                 do not allow their misrepresentations to be corrected by
                 any of the site’s other users. This is what has occurred
                 over the past two years on Wikipedia’s articles related
                 to human intelligence.


          o ⚓ Counter Punch ☛ The_Shallow_End⠀⇛


                 The bottom now is actually miles below our feet, in water
                 so deep it looks dark at noon. This thought is so
                 frightening we push it aside when it comes up.


                 We’ve stupidly drifted out to sea, far away from the pool
                 of American mythology, taking undue comfort in the belief
                 we could get right back to it in the next election if
                 only we all get out the vote.


          o ⚓ Techdirt ☛ The_Metaverse_Could_Change_The_World,_If_We_Could_Stop
            Getting_In_Its_Way⠀⇛


                 Beyond the overproduced marketing videos and janky
                 product prototypes closely associated today with “the
                 metaverse” lies a bright and boundless future. In a
                 pandemic-stricken world that imposes more and stronger
                 barriers at every turn—whether they be medical, social,
                 legal, economic, or geopolitical—there is magic in
                 transposing the spirit of a global free and open internet
                 into a more immersive technological utopia. But many
                 obstacles stand in the way of that dream, including the
                 companies trying to build it and the governments who will
                 regulate it.


          o ⚓ Pro Publica ☛ Journalist_Patrick_Radden_Keefe_Explains_His
            Craft⠀⇛


                 In the years since his byline first appeared in The New
                 Yorker in 2006, Patrick Radden Keefe has become known for
                 his revealing portraits of powerful people who refuse to
                 speak to him. It is a testament to Keefe’s prowess that
                 his subjects end up feeling more lifelike in his stories
                 — more brazen, vulnerable, even sympathetic — than they
                 do in their own memoirs and authorized biographies. This
                 might explain why El Chapo, the Mexican drug lord and the
                 focus of two of Keefe’s articles, wanted him to
                 ghostwrite a book about his life — an assignment that
                 Keefe politely declined.


                 Keefe’s recent output has cemented his reputation as one
                 of the most popular and thrilling journalists at work
                 today. In 2018, he published “Say Nothing,” a rigorously
                 psychological account of the Troubles in Northern
                 Ireland. A bestseller, it was followed by the hit podcast
                 “Wind of Change,” a picaresque tour of the Cold War’s
                 cultural front, and last year’s “Empire of Pain,” a
                 meticulous investigation of the Sackler family’s role in
                 the opioid crisis.


          o § Education⠀➾


                # ⚓ Internet Archive ☛ Internet_Archive_Seeks_Summary_Judgment
                  in_Federal_Lawsuit_Filed_By_Publishing_Companies⠀⇛


                       The motion for summary judgment, filed Thursday in
                       the U.S. District Court for the Southern District
                       of New York by the Electronic Frontier Foundation
                       (EFF) and Durie Tangri LLP, explains that our
                       Controlled Digital Lending (CDL) program is a
                       lawful fair use that preserves traditional library
                       lending in the digital world.


                       The brief explains how the Internet Archive is
                       advancing the purposes of copyright law by
                       furthering public access to knowledge and
                       facilitating the creation of new creative and
                       scholarly works. The Internet Archive’s digital
                       lending hasn’t cost the publishers one penny in
                       revenues; in fact, concrete evidence shows that the
                       Archive’s digital lending does not and will not
                       harm the market for books.


                # ⚓ Raspberry Pi ☛ How_to_create_great_educational_video
                  content_for_computing_and_beyond⠀⇛


                       Over the past five years, we’ve made lots of online
                       educational video content for our online courses,
                       for our Isaac Computer Science platform for GCSE
                       and A level, and for our remote lessons based on
                       our Teach Computing Curriculum hosted on Oak
                       National Academy.


                # ⚓ TruthOut ☛ Students_Like_Me_Can_Target_School_Boards_to_Get
                  Police_Out_of_Schools⠀⇛


                # ⚓ Scheerpost ☛ Will_Our_Children_Be_Able_to_Read?⠀⇛


                       The sharp attack on education during this past
                       decade forces us to consider the kind of future
                       that young people will inherit, writes Vijay
                       Prashad.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Quick_Hack:_The_Phone_To_Stream_Deck
                  Conversion⠀⇛


                       What do you do with those old Android or iPhone
                       phones and tablets? You have plenty of options, but
                       it is pretty easy to build your own stream deck
                       with a little off-the-shelf software. What’s a
                       stream deck, you ask? The name comes from its use
                       as a controller for a live-streaming setup, but
                       essentially, it’s an LCD touchscreen that can
                       trigger things on your computer.


                # ⚓ Hackaday ☛ How_To_Become_A_Lego_Submariner⠀⇛


                       A submarine is by necessity a complex and safety-
                       critical machine, but the principle upon which it
                       depends is quite simple. The buoyancy is variable
                       by means of pumping water in and out of tanks,
                       allowing the craft to control the depth at which it
                       sits. The [Brick Experiment Channel] has a series
                       of posts describing in detail the construction of a
                       working submarine, with a hull made from a plastic
                       tube and mechanics made from Lego.


                # ⚓ Hackaday ☛ Modular_Z80_Really_Racks_Up_The_Retrocomputer
                  Cred⠀⇛


                       Very few retrocomputing projects are anything other
                       than a labor of love. There’s really no practical
                       reason to build a computer that is woefully
                       inadequate for just about any task compared to even
                       an entry-level PC today. But the lack of a
                       practical reason to do something rarely stops a
                       hacker, as with this nifty modular Z80-based rack
                       computer.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ Boost_Now_or_Wait_for_New_Vaccine?_Many_Wonder
                  How_to_Face_COVID’s_Next_Wave⠀⇛


          o § Pseudo-Open Source⠀➾


                # § Openwashing⠀➾


                      # ⚓ AIM ☛ Is_Microsoft’s_VS_Code_really_open_source?⠀⇛


                             As stated, Microsoft follows an open-core
                             model for VS code. Therefore, developers who
                             want access to the full open source code that
                             is MIT licensed will have to download the
                             code from the repository and then build the
                             VS code on their own.


                             The task is cumbersome for most users. This
                             is where VS Codium comes into play. VS Codium
                             is fully open-source software binaries of VS
                             Code licensed under the MIT license. With VS
                             Codium, developers do not need to download
                             and build from the source. Instead, the VS
                             Codium team builds VS Code from the source
                             repository and uploads the binaries to
                             GitHub. “VS Codium is a clone of Microsoft’s
                             Visual Studio Code. This project’s sole aim
                             is to provide you with ready-to-use binaries
                             without Microsoft’s telemetry code,”
                             mentioned Abhishek Prakash, creator of It’s
                             FOSS (a web portal focused on open source),
                             in a blog.


          o § Security⠀➾


                # ⚓ Bleeping Computer ☛ Microsoft_investigates_ongoing_Exchange
                  Online,_Outlook_outage⠀⇛


                       Microsoft is investigating an ongoing outage
                       impacting Microsoft 365 services after customers
                       have reported experiencing issues while trying to
                       sign into, access, and receive emails on the
                       outlook.com portal and via Exchange Online.


                # ⚓ TechRadar ☛ Microsoft_Patch_Tuesday_update_has_broken
                  another_really_important_software⠀⇛


                       It seems some updates that came as part of this
                       month’s Patch Tuesday (opens in new tab) broke MS
                       Access runtime applications. Multiple users have
                       reported having this issue to Microsoft, saying MS
                       Access 2016 (opens in new tab) and MS Access 2013
                       are having issues, post KB5002112 and KB5002121
                       updates.


                # ⚓ Krebs On Security ☛ A_Deep_Dive_Into_the_Residential_Proxy
                  Service_‘911’⠀⇛


                       For the past seven years, an online service known
                       as 911 has sold access to hundreds of thousands of
                       Microsoft Windows computers daily, allowing
                       customers to route their Internet traffic through
                       PCs in virtually any country or city around the
                       globe — but predominantly in the United States. 911
                       says its network is made up entirely of users who
                       voluntarily install its “free VPN” software. But
                       new research shows the proxy service has a long
                       history of purchasing installations via shady “pay-
                       per-install” affiliate marketing schemes, some of
                       which 911 operated on its own.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Rolling Stone ☛ ICE_Is_Buying_Up_Massive_Troves_of
                        Cell_Phone_Location_Data…_For_Some_Reason⠀⇛


                             The Department of Homeland Security is
                             purchasing cell phone location data on a
                             massive scale, according to documents
                             released by the American Civil Liberties
                             Union.


                             Per the documents, hundreds of thousands of
                             location points across North America have
                             been attained by DHS. Purchasing the
                             information from private businesses would
                             help circumvent legal requirements to obtain
                             a warrant.


                      # ⚓ The Hill ☛ Growing_support_for_political_violence
                        raises_alarms⠀⇛


                             The chilling incident is among a series of
                             violent threats recently that have targeted
                             political figures and comes amid a shifting
                             landscape in which the share of partisans who
                             think violence is sometimes justified to
                             achieve political ends has grown
                             significantly.


                      # ⚓ Salon ☛ Joe_Walsh’s_MAGA_warning:_If_Trump_is
                        indicted,_expect_“major_violence”⠀⇛


                             As the country becomes more racially diverse,
                             younger, forward thinking and pluralistic,
                             the American right wing is attempting to
                             force the country back to the 19th century
                             and the Gilded Age. Such moves are generally
                             unpopular with the American people en masse.
                             The Republican Party and the larger right
                             wing movement dismiss such protests because
                             they reject the basic principle of a true “We
                             the People” democracy and are earnestly
                             working to create a herrenvolk, apartheid,
                             plutocratic, Christian fascist new America
                             that will be ruled by a small number of white
                             men and their allies.


                             As seen on Jan. 6 with Trump’s coup attempt
                             and the terrorist attack on the Capitol by
                             his followers, such political violence will
                             become the norm as the Republican-fascists
                             expand and consolidate their power and target
                             the Democratic Party (and liberals and
                             progressives more generally) as illegitimate.


                      # ⚓ EFF ☛ EFF_and_Partners_Urge_the_Indian_Government_to
                        Keep_End-to-End_Encryption_Alive⠀⇛


                             End-to-end encryption is vital for private
                             and secure communications. And while the
                             Indian Supreme Court introduced a necessity
                             and proportionality test when it recognized
                             that the right to privacy as a fundamental
                             right, the traceability requirement, in fact,
                             is a disproportionate measure: it breaks
                             encryption; threatens freedom of speech,
                             privacy and national security of Indian
                             people and businesses. Therefore, it is
                             imperative to withdraw the traceability
                             requirements under the Indian 2021 IT Rules. 


                             The full text of the letter and list of
                             signatories are below. 


                      # ⚓ Techdirt ☛ Ring:_Cops_Can_Still_Obtain_Recordings
                        Without_Warrants_Or_User_Consent⠀⇛


                             Welcome back to the negative news cycle,
                             Ring! It’s been awhile.


          o § Defence/Aggression⠀➾


                # ⚓ Counter Punch ☛ Can_the_System_Be_Saved?⠀⇛


                       Now, those hearings are offering the country (and
                       the Justice Department) what could be a last chance
                       to begin restoring the kind of governance that once
                       underlay a functioning democracy. There is,
                       however, a deeply worrisome trend lurking just
                       under this moment’s attempt to garner
                       accountability — namely, the way loyalty to
                       institutional Washington (even outside the law)
                       perpetuates a flight from accountability that’s
                       become a crucial part of American political life.


                       So far, the January 6th hearings have inspired a
                       cascade of takeaways. With each televised session,
                       new evidence about the acts of Donald Trump and
                       crew have come to light, among them that the former
                       president was all too tight with the far right and
                       that he knew the crowd approaching the Capitol on
                       January 6, 2021, was armed and dangerous. So, too,
                       those watching have learned about witness
                       tampering and also the lengths White House lawyers
                       and others went to in trying to restrain the former
                       president’s engagement with the January 6th
                       rioters. Overall, many Americans (though not so
                       many Republicans) have learned that January 6th was
                       part of a far larger Trumpian effort to negate the
                       results of the 2020 presidential election, no
                       matter the facts or the law.


                # ⚓ Common Dreams ☛ Opinion_|_The_State_of_US_‘Democracy’_Is
                  Grim._Can_It_Be_Saved?⠀⇛


                       Well before the House select committee’s January
                       6th investigation began, trust in the classic
                       American system of checks and balances as reliable
                       protection against executive (or, more recently,
                       Supreme Court) abuses of power had already fallen
                       into a state of disgrace. A domestically shackled
                       Biden presidency, a Congress unable to act, and a
                       Supreme Court that seems ever more like an
                       autocratic governing body has left American
                       “democracy” looking grim indeed.


                # ⚓ Common Dreams ☛ Opinion_|_Don’t_Normalize_Trump’s
                  Enablers⠀⇛


                       The historic House Select Committee’s hearings on
                       the insurrection of Jan. 6, 2021, are a necessary
                       undertaking for the health of our democracy. The
                       fact that most of the witnesses are Republican—and
                       many are former members of Donald Trump’s own inner
                       circle—greatly bolsters the committee’s
                       credibility. In our hyper-partisan reality, this
                       fact can also lead to a temptation to hail the
                       witnesses as courageous, honorable figures putting
                       their consciences above ideology.


                # ⚓ Counter Punch ☛ Night_Raids_and_Executions:_the_SAS_in
                  Afghanistan⠀⇛


                       A senior officer who worked at UK Special Forces
                       headquarters told the BBC there was “real concern”
                       over the squadron’s reports.


                       “Too many people were being killed on night raids
                       and the explanations didn’t make sense,” he said.
                       “Once somebody is detained, they shouldn’t end up
                       dead. For it to happen over and over again was
                       causing alarm at HQ. It was clear at the time that
                       something was wrong.”


                # ⚓ Counter Punch ☛ An_Iron_Curtain_is_Descending_on_America
                  and_We_Were_Warned⠀⇛


                       “Every gun that is made, every warship launched,
                       every rocket fired signifies, in the final sense, a
                       theft from those who hunger and are not fed, those
                       who are cold and are not clothed.


                       “This world in arms is not spending money alone. It
                       is spending the sweat of its laborers, the genius
                       of its scientists, the hopes of its children. The
                       cost of one modern heavy bomber is this: a modern
                       brick school in more than 30 cities. It is two
                       electric power plants, each serving a town of
                       60,000 population. It is two fine, fully equipped
                       hospitals. It is some fifty miles of concrete
                       pavement. We pay for a single fighter plane with a
                       half million bushels of wheat. We pay for a single
                       destroyer with new homes that could have housed
                       more than 8,000 people.” [Note: the numbers are
                       from 1953 and are more unfair today.]


                # ⚓ Common Dreams ☛ Opinion_|_The_House_Military_Spending_Bill
                  Is_a_Massive_Giveaway_to_the_Weapons_Industry⠀⇛


                       On Thursday, the House of Representatives passed
                       its version of the National Defense Authorization
                       Act, which sets policy goals and recommends a
                       number for total Pentagon spending. The final
                       version of the bill will be determined later this
                       year.


                # ⚓ TruthOut ☛ The_Coup_Allegations_Against_the_Secret_Service
                  Are_Astonishing⠀⇛


                # ⚓ TruthOut ☛ Steve_Bannon’s_Contempt_of_Congress_Trial
                  Formally_Began_Today⠀⇛


                # ⚓ The Nation ☛ Threading_Violence⠀⇛


                # ⚓ Meduza ☛ Deceased_Russian_soldier’s_family_uses
                  compensation_payment_to_buy_new_car_‘in_his_memory’_—
                  Meduza⠀⇛


                       On July 17, the state-owned television channel
                       Russia-1 ran a story about Staff Sergeant Alexey
                       Malov, a tank commander who died on the third day
                       of the war in Ukraine. According to the report,
                       Malov’s relatives have already spent the
                       compensation money they received from the
                       government for his death. “In memory of our son,”
                       Malov’s father told reporters, the family bought “a
                       brand new car.”


                # ⚓ Meduza ☛ Fear_and_hardship_in_the_Donbas_After_years_of
                  frozen_conflict,_Donetsk_residents_describe_life_under
                  constant_shelling_—_Meduza⠀⇛


                       Before Russia began its full-scale invasion of
                       Ukraine, the intensity of the hostilities in the
                       Donbas had been declining steadily since 2014. In
                       2021, the United Nations recorded 36 civilian
                       casualties in eastern Ukraine, most of which were
                       caused by landmines and the mishandling of
                       unexploded ordinances. Since mid-June 2022,
                       however, regular explosions have plagued the city
                       of Donetsk. Ukraine has either refrained from
                       commenting on the blasts or reported the
                       destruction of Russian ammunition depots in the
                       region. In response, the authorities in Donetsk,
                       Luhansk, and Moscow have accused Ukrainian forces
                       of deliberately targeting civilians. (Meanwhile,
                       Russia’s constant attacks on civilian areas across
                       Ukraine have claimed thousands of lives). For
                       insight into what everyday life is like in wartime
                       Donetsk, Meduza turned to local residents.


                # ⚓ Meduza ☛ ‘I_have_no_moral_right_to_joke_about_Ukraine’
                  Standup_comic_Denis_Chuzhoy_discusses_threats,_emigration,
                  and_how_war_shattered_Russian_comedy_—_Meduza⠀⇛


                       Standup comic Denis Chuzhoy denounced the war
                       against Ukraine on the first day of Russia’s full-
                       scale invasion in February 2022. In return for
                       speaking out, he started receiving death threats on
                       the phone, and audience members at a show in
                       Vologda approached the stage and presented him with
                       a funeral wreath. Chuzhoy left the country more
                       than two months ago, but he’s returned to Russia
                       several times for performances that he scheduled
                       before February, donating part of the proceeds to
                       charities helping Ukrainian refugees. Meduza spoke
                       to him about threats, emigration, and what kind of
                       career in comedy is even possible today for
                       Russians.


          o § Environment⠀➾


                # ⚓ The Economist ☛ The_danger_posed_by_heatwaves_deserves_to
                  be_taken_more_seriously⠀⇛


                       Heatwaves may generate headlines, but less
                       attention is paid to them than they deserve. In
                       2018 roughly 300,000 people over the age of 65 died
                       as a result of extreme heat, mainly in India and
                       China, a 54% increase since 2000, according to a
                       report in the Lancet, a medical journal. Unlike
                       storms and floods, heat does not lead to dramatic
                       before-and-after pictures or widespread damage to
                       property. It is a silent killer, its victims often
                       apparent only in retrospect, as statisticians tot
                       up excess deaths and hospital admissions. (The fact
                       that as many as 70,000 people died as a result of a
                       heatwave in Europe in 2003, for example, became
                       apparent only in 2008.) Heat also kills by
                       exacerbating conditions such as heart problems, so
                       not all the deaths it causes may be directly
                       attributed to it.


                # ⚓ Counter Punch ☛ Greenland_Threatens⠀⇛


                       Greenland is sending signals to coastal
                       metropolises around the world that it’s never too
                       early to start building seawalls. These are not
                       mixed signals from the big ice island. Rather, they
                       are straightforward signals indicative of rapid
                       breakdown of average ice thickness of 5,000 feet
                       sooner than ever thought possible.


                       Stating the obvious, it’s horrible news.


                # ⚓ Common Dreams ☛ Biden_Considers_Declaring_Climate_Emergency
                  Amid_‘Heat_Apocalypse’⠀⇛


                       With large swaths of the planet currently in the
                       grips of hellish, record-shattering heatwaves and
                       devastating wildfires, U.S. President Joe Biden is
                       reportedly considering declaring a national climate
                       emergency this week as a senator with deep ties to
                       the fossil fuel industry continues to obstruct
                       much-needed renewable energy spending.


                       Biden’s plans for a possible emergency declaration,
                       first reported late Monday by the Washington Post,
                       come as the White House is facing mounting pressure
                       to take unilateral climate action as its agenda
                       remains stalled in the upper chamber of Congress,
                       hampering U.S. efforts to rein in planet-warming
                       carbon emissions as temperatures soar worldwide.


                # ⚓ TruthOut ☛ Bill_McKibben:_“Appalling”_European_Heat_Wave
                  Demands_Massive_Climate_Action⠀⇛


                # ⚓ Democracy Now ☛ Bill_McKibben:_Record_Heat_Wave_in_Europe
                  Is_Latest_Warning_That_Action_on_Climate_Can’t_Wait⠀⇛


                       A scorching heat wave continues to fuel wildfires
                       across southern Europe and parts of North Africa,
                       resulting in hundreds of heat-related deaths and
                       forcing thousands to evacuate their homes. The
                       record-breaking temperatures come as Senator Joe
                       Manchin of West Virginia has effectively killed
                       President Biden’s Build Back Better climate
                       legislation after stringing Biden along for 18
                       months. “It’s appalling, but it’s not unexpected.
                       It’s why we have to keep building movements
                       bigger,” says Bill McKibben, climate author,
                       educator, environmentalist and founder of the
                       organizations Third Act and 350.org.


                # § Energy⠀➾


                      # ⚓ Common Dreams ☛ ‘Collective_Action_or_Collective
                        Suicide’:_UN_Chief_Pleads_for_Real_Climate_Response⠀⇛


                             Governments can either come up with a
                             collaborative and urgent plan to tackle the
                             fossil fuel-driven climate emergency that is
                             already wreaking deadly havoc across the
                             globe or keep allowing corporations to
                             pollute the atmosphere without limit, thereby
                             condemning humanity to a grim future.


                             That stark warning comes from United Nations
                             Secretary-General António Guterres, who said
                             Monday: “We have a choice. Collective action
                             or collective suicide.”


                      # ⚓ Counter Punch ☛ Nuclear_Power_is_Racist,_Sexist_and
                        Ageist:_So_Why_Do_Some_Progressives_Support_It?⠀⇛


                             Nuclear power is all three of these things,
                             yet Booker, Whitehouse and a number of others
                             on the Democratic left, support nuclear power
                             with almost fervent evangelism.


                             Let’s start with racism. The fuel for nuclear
                             power plants comes from uranium, which must
                             be mined. The majority of those who have
                             mined it in this country — and would again
                             under new bills such as the ‘International
                             Nuclear Energy Act of 2022’ forwarded by not-
                             so-progressive “Democrat”, Senator Joe
                             Manchin (D-WV) — are Native Americans.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ Salmon_Farming’s_Dirty_Business⠀⇛


                # § Overpopulation⠀➾


                      # ⚓ Mexico News Daily ☛ Water_situation_is_critical_in_4
                        states:_Conagua⠀⇛


                             Related to the La Niña climate pattern, the
                             lack of rainfall is also reflected by the
                             scarcity of water in dams. The newspaper El
                             País reported Monday that Mexico’s 210 main
                             dams are only 45% full on average, a level
                             that is 10% lower than normal. Some dams are
                             completely dry or close to it.


                      # ⚓ Los Angeles Times ☛ Tracking_the_California_drought⠀⇛


                             Since 2000, the U.S West. has grown warmer
                             and drier. Data from the U.S. Drought Monitor
                             shows that the region has plunged deeper into
                             extreme drought over the past several years.
                             Scientists have increasingly said the West is
                             experiencing “aridification” driven by human-
                             caused climate change, and they have called
                             for the region to prepare for drier
                             conditions in the long term as temperatures
                             continue to rise.


                      # ⚓ Bloomberg ☛ California’s_Idle_Crop_Land_May_Double_as
                        Water_Crisis_Deepens⠀⇛


                             California’s historic drought may leave the
                             state with the largest amount of empty
                             farmland in recent memory as farmers face
                             unprecedented cuts to crucial water supplies.


                      # ⚓ ABC ☛ Texas_residents_asked_to_‘immediately’_conserve
                        water_amid_drought,_extreme_heat⠀⇛


                             The utility company, which serves about 2
                             million people in northern Texas, including
                             the city of Plano and North Dallas County,
                             was forced to cease water production at one
                             of its four treatment plants unexpectedly on
                             Saturday to perform critical maintenance “to
                             return the plant back to full water
                             purification capacity,” according to the
                             alert.


                      # ⚓ NPR ☛ Arizona_cities_respond_to_the_worst_drought_in
                        over_a_thousand_years_with_a_new_plan⠀⇛


                             The Colorado River supplies water to about 40
                             million people across the southwest, but it
                             is facing catastrophically dry conditions.
                             The last two decades have been the driest in
                             1,200 years. At least six cities in Arizona,
                             including Phoenix, have now declared water
                             shortages. But as Katherine Davis-Young at
                             member station KJZZ reports, one of the first
                             to start cutting back was Scottsdale.


          o § Finance⠀➾


                # ⚓ Common Dreams ☛ Just_Two_Weeks_of_Food_Billionaire_Wealth
                  Gains_Could_Fund_Anti-Hunger_Effort_in_East_Africa⠀⇛


                       The aid group Oxfam International estimated Monday
                       that a mere two weeks of wealth gains recently
                       secured by global food billionaires would be enough
                       to fully fund the United Nations’ multibillion-
                       dollar effort to combat hunger in East Africa,
                       where soaring commodity prices are intensifying
                       food insecurity and pushing poverty to new
                       extremes.


                       “A monstrous amount of wealth is being captured at
                       the top of our global food supply chains.”


                # ⚓ Common Dreams ☛ Opinion_|_Structuring_the_Economy_to_Give
                  Money_to_the_Rich_Is_Inflationary⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_The_Federal_Reserve_Thinks_the
                  Answer_to_Inflation_Is_Imposing_Class_War⠀⇛


                # ⚓ Common Dreams ☛ Just_27_Billionaires_Have_Spent_$90_Million
                  to_Buy_GOP_Congress:_Report⠀⇛


                       A few dozen billionaires are spending tens of
                       millions of dollars on the 2022 midterm
                       elections—mostly to support Republican candidates,
                       including many who have parroted the dangerous lie
                       that the 2020 presidential election was stolen—in a
                       bid to ensure that Congress is full of lawmakers
                       willing “to make their wealthy benefactors even
                       richer,” according to a fresh analysis.


                       “What’s good for billionaires—including cutting
                       taxes on the rich and corporations—is bad for
                       working families.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Computer World ☛ Why_Tim_Cook_is_concerned_about_coding
                  skills⠀⇛


                       Demand and supply. In theory, when demand
                       increases, supply emerges to meet it. Except it
                       doesn’t always work out that way and as the world
                       gets more digitized, the need for coders is growing
                       faster than the world can keep up.


                # ⚓ The Hill ☛ CISA_announces_launch_of_London_bureau⠀⇛


                       The Cybersecurity and Infrastructure Security
                       Agency (CISA) announced on Monday that it will open
                       its first attaché office in London later this
                       month.


                       The London bureau will serve as a focal point for
                       international collaboration between U.S. and U.K.
                       government officials, the agency said. It will also
                       help advance CISA’s objectives in cybersecurity,
                       critical infrastructure protection and emergency
                       communications.


                # ⚓ TruthOut ☛ Sanders_Denounces_Manchin_for_“Intentionally
                  Sabotaging”_Democratic_Agenda⠀⇛


                # ⚓ TruthOut ☛ Omar_Calls_for_Manchin_to_Be_Removed_From_Role
                  as_Chair_of_Energy_Committee⠀⇛


                # ⚓ Common Dreams ☛ Sanders_Rips_Manchin:_He_‘Represents_the
                  Very_Wealthiest_People_in_This_Country’⠀⇛


                       Sen. Bernie Sanders lambasted fellow Sen. Joe
                       Manchin on Sunday for sinking the Democratic
                       Party’s latest effort to pass renewable energy
                       funding, accusing the West Virginia Democrat of
                       acting on behalf of his corporate and billionaire
                       donors instead of the working class of his home
                       state.


                       Rejecting the notion that Manchin “abruptly pulled
                       the plug” on the majority party’s revived push for
                       a scaled-back reconciliation package ahead of the
                       November midterms, Sanders told ABC’s Martha
                       Raddatz that there was “nothing new” about the West
                       Virginia senator’s move last week, when he
                       reportedly told the Democratic leadership that he
                       wouldn’t support new climate spending or taxes on
                       the wealthy.


                # ⚓ Common Dreams ☛ After_Visit,_Palestinians_Say_Biden
                  Presidency_Is_‘Like_the_Trump_Years_With_a_Smile’⠀⇛


                       Palestinians offered a dour assessment of U.S.
                       President Joe Biden’s policy agenda and track
                       record thus far in the wake of his brief visit to
                       Israeli-occupied territory last week, with one
                       official describing the administration as “like the
                       Trump years with a smile.”


                       Biden’s trips to East Jerusalem and Bethlehem on
                       Friday were met with protests from rights groups
                       and ordinary Palestinians who decried the
                       administration’s refusal to break substantively
                       from its predecessors and condemn Israel’s deadly
                       military aggression and unlawful occupation of
                       Palestinian land.


                # ⚓ Scheerpost ☛ After_Visit,_Palestinians_Say_Biden_Presidency
                  Is_‘Like_the_Trump_Years_With_a_Smile’⠀⇛


                       “There must immediately be a settlement freeze, in
                       accordance with international law and resolutions
                       to preserve the right of the Palestinian people to
                       their independent state,” said on…


                # ⚓ Democracy Now ☛ Bill_McKibben:_Egypt_U.N._Climate_Summit
                  Must_Demand_Freedom_for_Jailed_Activist_Alaa_Abd_El-Fattah⠀⇛


                       We speak with climate author and activist Bill
                       McKibben, who is pushing for the climate movement
                       to demand the release of Egyptian prisoner and
                       human rights activist Alaa Abd El-Fattah ahead of
                       the next U.N. climate conference, which will be
                       hosted in Egypt. McKibben says releasing El-Fattah
                       to the U.K., which has agreed to house him, would
                       be “the easiest of gestures” by Egypt, whose
                       authoritarian leader met Saturday with President
                       Biden. “The spread of authoritarian governments
                       around the world is one of the things that’s making
                       it difficult to deal with the existential challenge
                       that climate change [presents],” says McKibben.


                # ⚓ Democracy Now ☛ Biden_Fails_to_Hold_Saudi_Arabia
                  Accountable_for_Khashoggi_Murder._Now_UAE_Arrests_His
                  Lawyer.⠀⇛


                       President Biden met with Saudi Crown Prince
                       Mohammed bin Salman Friday, as the Saudis agreed to
                       increase oil production as well as open their
                       airspace to Israeli commercial flights. Biden says
                       he told the crown prince he held him responsible
                       for the murder of Saudi journalist Jamal Khashoggi,
                       who was a U.S. resident, though Biden’s claims were
                       later contradicted by a top Saudi official. We
                       speak with Sarah Leah Whitson, executive director
                       of Democracy for the Arab World Now, who says
                       Biden’s friendly fist bump with the crown prince
                       will become the “legacy of President Biden as a man
                       who broke his promises” on holding Saudi Arabia
                       accountable and sends a troubling message to other
                       wealthy oil-producing countries. Whitson also calls
                       for the UAE to give civil rights lawyer Asim
                       Ghafoor, who represented Khashoggi, “due process”
                       after he was detained by officials while traveling
                       through Dubai’s airport and sentenced to three
                       years in prison for fraud charges he denies.


                # ⚓ Counter Punch ☛ The_Rise_and_Fall_of_the_Megamachine⠀⇛


                       That is the case Fabian Scheidler makes in his
                       recent work, The End of the Megamachine: A Brief
                       History of a Failing Civilization. He begins by
                       looking back to the first military-industrial
                       complex, when around five to six thousand years ago
                       in the Middle East humanity learned to make bronze
                       by smelting copper and tin with wood-stoked fires.
                       Before that time, human settlements evidenced
                       relative equality in terms of dwellings, food and
                       burial rites. Then the hardness of bronze made
                       possible weapons and armor that allowed rulers and
                       empires to emerge. Temples and palaces appeared.
                       Some people ate better than others, and had more
                       elaborate burial rites.


                       Rulers forced farmers to pay taxes in the form of
                       grain, accumulating the currency of food in
                       temples, controlling distribution. Around 2500 BC
                       came the first evidence of land ownership in the
                       early empire of Sumer. Writing and the first legal
                       codes came about to record and enforce tax
                       obligations and property ownership. With failure to
                       pay taxes and debts came enslavement. Around this
                       time also came the first religions with a singular,
                       dominating god.


                # ⚓ Counter Punch ☛ Lula’s_Next_Visit_to_Pernambuco⠀⇛


                       Lula in Pernambuco is a movie that never stops
                       playing. It is the cinema of Recife, where the
                       people enter the screen and participate in the
                       action. But what films, what epics of political
                       love awaken and pass their presence among us? Do we
                       see Os Companheiros or Eles não usam black-tie? If
                       so, the film would be more related to the story of
                       the worker Luiz Inácio Lula da Silva. But I think
                       Lula’s film, which keeps on playing in these dark
                       times, is Charlie Chaplin’s The Great Dictator. And
                       why is that? In the film, Chaplin gives a speech of
                       hope, which projects the end of fascism to crowds
                       who are in anguish and despair:


                       The Great Dictator may be the movie, because the
                       above words are worthy of Lula and of these hours.
                       But first, in greeting the future president, what
                       collective chant could be sung by the crowd? For
                       the people of Recife, it could and will be a frevo,
                       or frevos. But by whom, Capiba or Nelson Ferreira?


                # ⚓ Telex (Hungary) ☛ Parliament_passes_proposal_which
                  recommends_dismantling_the_EP_in_its_current_form⠀⇛


                # ⚓ Telex (Hungary) ☛ Serbia_purchased_250_million_euros_worth
                  of_gas_from_Hungary⠀⇛


                # ⚓ Telex (Hungary) ☛ Protesters_spot_and_question_government’s
                  Communications_Commissioner⠀⇛


                       At one point during this morning’s demonstrations
                       in Budapest, the police was blocking the way of a
                       few hundred demonstrators at the House of
                       Representatives without justification, citing
                       security reasons, and started to stop pedestrians
                       in the area of the nearby Olympic Park. At the same
                       time István Hollik, the Government’s Commissioner
                       for Communication made his way on foot to the
                       parliamentary session starting at 13:00. In the
                       end, he almost had to make a run for it and needed
                       a rather large police escort, although people only
                       wanted to consult him about the new tax law.


                # ⚓ Telex (Hungary) ☛ President_Novák_signs_new_tax_law⠀⇛


                       The President of Hungary, Katalin Novák has signed
                       the amended tax law, thus it is final: beginning in
                       September, hundreds of thousands of Hungarians who
                       have been using this form of paying their taxes
                       will be forced to change to another tax category or
                       give up their business altogether. Earlier, both
                       MSZP and Jobbik had asked Novák to send the bill
                       back to parliament, but she did not exercise this
                       right.


                # ⚓ Common Dreams ☛ ‘Historic_Day’_as_Staff_of_8_House
                  Democrats_File_for_Union_Elections⠀⇛


                       Staffers of eight Democrats in the U.S. House of
                       Representatives on Monday took a key step toward
                       unionizing by filing petitions for representation
                       at the Office of Congressional Workplace Rights.


                       “We are bringing worker power and equitable
                       conditions to one of the most powerful institutions
                       in the world.”


                # ⚓ Common Dreams ☛ Opinion_|_The_Great_Crisis_of_the_21st
                  Century:_Hijacked_Democracies,_Propaganda,_and_Rebellions⠀⇛


                       Professor Walter Scheidel, in his book The Great
                       Leveler, showed, more than convincingly, that from
                       prehistory to the present day, all the
                       socioeconomic systems known to humanity tended
                       towards inequality and ended in global
                       catastrophes. The first is quite obvious and we are
                       seeing it today: those who have financial and
                       economic power have inflamed political power, which
                       produces a snowball effect. The rich and their
                       corporations are the big donors to the political
                       parties and then write the laws at their
                       convenience. In 1971, a classic of political
                       comics, The Wizard of Id summed it up best: “The
                       golden rule is that he who has the gold makes the
                       rules.”


                # ⚓ Counter Punch ☛ White_Supremacists_Want_‘Their’_Country
                  Back⠀⇛


                       One thing I notice as I read the growing warnings
                       that this is the case is the assumption that
                       suddenly the USA has become a divided nation, a
                       splintered democracy, when, in point of fact, it
                       has always been deeply – and for much of its
                       history, good God, legally – divided.


                       Indeed, Jim Crow America was the prime model for a
                       certain would-be European dictator.


                # ⚓ Counter Punch ☛ The_Rise_of_BRICS:_The_Economic_Giant_that
                  is_Taking_on_the_West⠀⇛


                       As was the case since the start of the Russia-
                       Ukraine war, the West attempted to display unity,
                       though it has become repeatedly obvious that no
                       such unity exists. While France, Germany and Italy
                       are paying a heavy price for the energy crisis
                       resulting from the war, Britain’s Boris Johnson is
                       adding fuel to the fire in the hope of making his
                       country relevant on the global stage following the
                       humiliation of Brexit. Meanwhile, the Biden
                       Administration is exploiting the war to restore
                       Washington’s credibility and leadership over NATO –
                       especially following the disastrous term of Donald
                       Trump, which nearly broke up the historic alliance.


                       Even the fact that several African countries are
                       becoming vulnerable to famines  – as a result of
                       the disruption of food supplies originating from
                       the Black Sea and the subsequent rising prices –
                       did not seem to perturb the leaders of some of the
                       richest countries in the world. They still insist
                       on not interfering in the global food market,
                       though the skyrocketing prices have already pushed
                       tens of millions of people below the poverty line.


                # ⚓ TruthOut ☛ Constitutional_Law_Prof_Tells_Dems:_Use_14th
                  Amendment_to_Block_Trump_2024_Run⠀⇛


                # ⚓ The Nation ☛ Joe_Biden’s_Age_Isn’t_the_Problem⠀⇛


                       In politics, age is not just a number—it’s a
                       weapon. Recently, we’ve seen it wielded in a spate
                       of articles, from The New York Times to The
                       Atlantic, seeking to attack President Biden’s
                       potential reelection campaign. But such attacks are
                       hardly new, with Biden enduring an avalanche of
                       them in both the 2020 Democratic primary and
                       general elections. In fact, criticizing elderly
                       politicians for lacking sufficient “fight” is among
                       the oldest—and dirtiest—campaign tricks in American
                       politics.


                # ⚓ Scheerpost ☛ The_Age_of_Weird_Men:_Gonzo_Politicians_From
                  Berlusconi_to_BoJo⠀⇛


                       Students 50 years from now may be asked by their
                       teachers to write an essay on the importance of the
                       fall of Boris Johnson……


                # ⚓ Techdirt ☛ Elon_Musk’s_Response_To_Twitter’s_Legal_Filing
                  May_Impress_His_Fans_On_Twitter,_But_Is_Not_A_Good_Legal
                  Argument⠀⇛


                       Last week, I wrote about Twitter’s opening legal
                       salvo in its case to try to force Elon Musk to pay
                       the $44 billion he agreed to pay for Twitter (or,
                       more likely, to try to force him to pay a very
                       large settlement to walk away). As we noted, it was
                       a very strongly argued filing, and Musk’s lawyers
                       had their work cut out for them. Nothing is certain
                       in court, and getting the Delaware Chancery Court
                       to order “specific performance” (i.e., complete the
                       agreement you signed) may still be a long shot, but
                       Twitter’s lawyers had a very strong opening. I
                       expected that Musk would have a strong comeback,
                       but many of the points Twitter raised would be
                       difficult to refute.


                # ⚓ Counter Punch ☛ Shared_Values_and_Fist_Bump_Geopolitics:
                  Biden’s_Blurred_Vision_of_Human_Rights⠀⇛


                       I mention China’s effort to enhance its image as a
                       legitimate state as a positive development not
                       deserving the hostile reaction that it received in
                       many sectors of the West, but especially in those
                       quarters that were intent on a new cold war to
                       counter the competitive edge that China was
                       gaining, especially in the world economy and on
                       many technological frontiers of special relevance
                       in the digital age. To seize upon this Chinese
                       initiative, even granting that it was partly
                       motivated by quite legitimate soft power ambitions,
                       is to denigrate efforts to develop an international
                       culture of respect for human rights as an essential
                       foundation for indispensable cooperation in a
                       variety of functional areas ranging from trade to
                       climate change and migration. And let us not
                       overlook American arrogance in relation to human
                       rights, given its refusal to accord economic and
                       social rights the normative status they deserve,
                       and of which China is justly proud of its
                       remarkable record. This acute societal shortcoming
                       in the United States is exhibited to the world by
                       highly visible urban homelessness in the cities of
                       the United States coupled with the unavailability
                       of affordable health care to millions of its own
                       citizens; as well, constitutionally validated gross
                       violations of the right to life due to promiscuous
                       access to assault weaponry for anyone with the cash
                       to make the purchase, and despite a rash on mass
                       school and mall shooting the governing institutions
                       turn their heads away from the carnage.


                       It is with these considerations in the background
                       that we should assess the Biden mid-July visit to
                       Israel and Saudi Arabia. If the critical reaction
                       to Bachelet’s visit reflected establishment
                       resentment as a breach in the geopolitical wall of
                       hostility that had been mobilized to justify
                       coercive diplomacy directed at China. In contrast,
                       Biden’s visit to the Middle East dramatized the
                       extent to which human rights are buried far
                       underground when perceived to clash with strategic
                       interests being pursued in foreign policy as
                       abetted by the domestic incentives to treat the
                       most flagrant violators of human rights as if they
                       are behaving as a model democracy. Of course, it is
                       of relevance to note that overlooking Saudi Arabia
                       dreadful record, which includes blood dripping from
                       the hands of the de facto head of state, Crown
                       Prince Mohammed bin Salmon (MBS), did bring Biden
                       and the normally compliant media visible discomfort
                       and some steps back from fist bump amicability in
                       Saudi Arabia. Biden made clear that only national
                       security interests prevented him from fulfilling
                       his 2020 campaign pledge to treat Saudi Arabia as a
                       ‘pariah’ state, he continued to believe that it was
                       when it came to human rights and even more
                       pointedly he rejected MBS’s insistence that he had
                       nothing to do with the murder of Jamal Khashoggi
                       back in 2018. Awkwardly, Biden made himself
                       vulnerable to MBS’s clever taunt—you seem to care
                       much more about Jamal Khashoggi than Shireen Abu
                       Akleh. Rather than implicate Israel, the U.S.
                       investigation of the murder of its own citizen,
                       seems prepared to share the grief of Akleh’s
                       surviving family instead of seeking accountability
                       of the sort that might protect journalists covering
                       dangerous hotspots in the future.


          o § Censorship/Free Speech⠀➾


                # ⚓ Variety ☛ Stephen_Colbert’s_Team_Has_Charges_Dropped_for
                  Filming_Insult_Dog_Segment_at_Capitol_Without_Escort⠀⇛


                       The U.S. Attorney’s Office for the District of
                       Columbia has decided to drop charges against the
                       members of “The Late Show With Stephen Colbert”
                       production team that were arrested at the U.S.
                       Capitol on June 16. The group had been filming a
                       Triumph the Insult Dog segment for the talk show.


                       The decision to decline prosecution on the case was
                       confirmed in a statement made by U.S. Capitol
                       Police on Monday.


                # ⚓ The Nation ☛ You_Can’t_Buy_These_Books⠀⇛


                       In a remarkable brief filed on July 7 in their
                       ongoing lawsuit, four titans of corporate
                       publishing (Hachette, Penguin Random House,
                       HarperCollins, and Wiley) accused the Internet
                       Archive of stealing, “mass-scale copyright
                       infringement,” and “[distributing] full-text
                       digital bootlegs for free.” Those are pretty wild
                       allegations—especially considering that the
                       Internet Archive’s Open Library operates on the
                       traditional terms that libraries in this country
                       have abided by for centuries. The Open Library
                       loans books, which it owns, to one patron at a
                       time, for a fixed period—just like any other
                       library. Like any public library, the Open Library
                       doesn’t charge money for this service. The main
                       difference is that the Open Library loans e-books
                       online. Each e-book is scanned from a paper copy,
                       and the paper copy is stored away and doesn’t
                       circulate; this practice is called Controlled
                       Digital Lending, or CDL.


                # ⚓ BBC ☛ Jafar_Panahi:_Acclaimed_Iran_film_maker_ordered_to
                  serve_six_years_in_jail⠀⇛


                       Iranian media said Mr Panahi was held after going
                       to Evin prison to ask about one of two fellow
                       directors arrested for supporting protests.


                # ⚓ Scheerpost ☛ Meet_the_Ex-CIA_Agents_Deciding_Facebook’s
                  Content_Policy⠀⇛


                       It is an uncomfortable job for anyone trying to
                       draw the line between “harmful content and
                       protecting freedom of speech. It’s a balance”…


                # ⚓ Meduza ☛ A_new_stage_of_repression_Three_experts_weigh_in
                  on_the_Kremlin’s_changing_approach_to_silencing_dissent_—
                  Meduza⠀⇛


                       On July 15, a judge in Komsomolsk-on-Amur acquitted
                       artist and LGBT activist Yulia Tsvetkova after
                       three years of legal proceedings. Tsvetkova was
                       accused of “distributing pornography” after she
                       published drawings of vulvas on a social media page
                       called the “Vagina Monologues.” Since Russia
                       launched its war against Ukraine, the number of
                       absurd cases like Tsvetkova’s has only grown;
                       Russians can now be charged for as little as
                       putting quotation marks around the phrase “special
                       [military] operation.” For insight into how the
                       authorities’ censorship methods are evolving,
                       Meduza asked a human rights advocate, a political
                       scientist, and a state repression historian about
                       the purpose of cases like Tsvetkova’s.


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


                # ⚓ VOA News ☛ Russian_Journalist_Released_After_Brief
                  Detention⠀⇛


                       Her lawyer, Dmitri Zakhvatov, said she was detained
                       because she was suspected of having “discredited”
                       the army in remarks outside a Moscow court last
                       week in support of opposition activist Ilya Yashin,
                       who is accused of spreading false information about
                       the army.


                       After sending troops to Ukraine, Moscow adopted
                       laws imposing sentences of up to 15 years for
                       spreading information about the military deemed
                       false by authorities.


                # ⚓ Scheerpost ☛ Assange_Fights_Extradition_To_US_With_Two
                  Appeals⠀⇛


                       Attorneys for WikiLeaks founder Julian Assange
                       separately appealed decisions by Home Office
                       Secretary Priti Patel and a United Kingdom…


          o § Civil Rights/Policing⠀➾


                # ⚓ TMZ ☛ Drake_Okay,_Fine_…_I_Did_Have_a_Run-In_w/_Swedish
                  Cops⠀⇛


                       In any case, he seems to have had an easier go than
                       A$AP Rocky did. Thank goodness for that.


                # ⚓ The Hill ☛ Uber_to_pay_millions_to_settle_lawsuit_for
                  overcharging_customers_with_disabilities⠀⇛


                       In a news release, the DOJ said Uber has committed
                       to waiving wait time fees for customers who need
                       more time to get into a car due to their disability
                       or refund disabled customers who don’t get a waiver
                       beforehand.


                       The company will also pay back some 65,000 eligible
                       riders for double the amount they were charged in
                       wait time fees, which the DOJ said could add up to
                       millions of dollars.


                # ⚓ The Verge ☛ Uber_will_pay_over_$2_million_to_disabled
                  riders_after_federal_settlement⠀⇛


                       Uber has settled with the Department of Justice
                       over allegations that it discriminated against
                       disabled passengers, the DOJ announced in a press
                       release on Monday. As part of the agreement, Uber
                       will credit double the total wait fees issued to
                       the 65,000 disabled riders already identified by
                       Uber’s programs and commit more than $2 million to
                       funds for other affected individuals.


                       The claims center on Uber’s wait fee policy, which
                       adds additional fees when a passenger takes more
                       than two minutes to board the car. Disabled riders
                       have long objected to the policy, claiming the fees
                       disproportionately affect riders with physical
                       disabilities.


                # ⚓ Counter Punch ☛ White_Riot⠀⇛


                       The Clash’s lead singer Joe Strummer strenuously
                       denied charges that the song was racist. It was, he
                       said, explicitly anti-racist. The song approvingly
                       cites the uprising of Black youth in British cities
                       against poverty and racism. The lyrics urge White
                       youth to rise up in solidarity since, after all,


                       The events of January 6, 2021 are an eerie, fun-
                       house reflection of these lyrics. In what turned
                       into a White riot, the insurrectionists effectively
                       wanted a “riot of my own” after observing the
                       BlackLivesMatter protests that broke out in the
                       wake of George Floyd’s killing half a year earlier.
                       But this was hardly a demonstration of solidarity.
                       Even though the January 6 riot ended up being far
                       more antagonistic and violent toward the police
                       than any #BLM demonstration, it was a direct
                       repudiation of the efforts by African Americans and
                       others against police brutality, political
                       disenfranchisement, and economic inequality.


                # ⚓ Common Dreams ☛ Opinion_|_Cruelty_Is_Still_the_Point,_But
                  Will_It_Make_a_Difference_in_November?⠀⇛


                       Since the Supreme Court’s overturning of Roe v.
                       Wade on June 24, the Republican party has doubled
                       down on its utter contempt for women’s rights and
                       civil rights more generally.


                # ⚓ Democracy Now ☛ 10-Year-Old_Ohio_Rape_Survivor_Shows_U.S.
                  Not_Ready_for_Post-Roe_“Unimaginable_Abortion_Stories”⠀⇛


                       We speak with Harvard journalism analyst Laura
                       Hazard Owen, who says reporters will have to
                       abandon “conventional journalism wisdom” to cover
                       abortion stories following the overturning of Roe
                       v. Wade. “Reporters are going to need to accept
                       that it’s going to be really hard to sort of do the
                       things that they’ve been trained to do when they’re
                       writing about these cases,” says Hazard Owen,
                       explaining why privacy laws and the criminalization
                       of doctors will make it harder to identify pregnant
                       people and fact-check different abortion stories
                       that involve young victims or occur in Republican-
                       controlled states. Her latest piece is titled
                       “Unimaginable abortion stories will become more
                       common. Is American journalism ready?”


                # ⚓ FAIR ☛ WaPo_Joined_Right_in_Casting_Doubt_on_10-Year-Old’s
                  Post-Roe_Nightmare⠀⇛


                       Fox News‘ Tucker Carlson (Mediaite, 7/13/22)
                       accused Biden of “lying,” insisting the story was
                       “not true”; a New York Post op-ed headline (7/12/
                       22) declared it “looks like a lie”; and Fox
                       contributor Charlie Hunt (7/12/22) opined:


                # ⚓ Common Dreams ☛ Lawmakers_Answer_Supreme_Court_Threat_to
                  LGBTQ+_Equality_With_Respect_for_Marriage_Act⠀⇛


                       Members of Congress alarmed by the U.S. Supreme
                       Court’s recent reversal on abortion rights and
                       threats to other basic freedoms on Monday
                       introduced legislation intended to ensure
                       protections for LGBTQ+ and interracial marriages.


                       “The far-right Supreme Court is waging war on the
                       freedoms of the American people, including the
                       rights of the LGBTQ+ community.”


                # ⚓ Common Dreams ☛ ‘We_Need_to_Fight’:_Cori_Bush,_Tina_Smith
                  Unveil_Bill_to_Bolster_Access_to_Medication_Abortion⠀⇛


                       Rep. Cori Bush and Sen. Tina Smith introduced
                       bicameral legislation Monday aimed at bolstering
                       access to medication abortion as Republican-led
                       states across the U.S. attempt to restrict
                       distribution of the pills in their drive to ban
                       abortion entirely.


                       If passed, the Protecting Access to Medication
                       Abortion Act would codify into federal law the Food
                       and Drug Administration’s Risk Evaluation and
                       Mitigation Strategy (REMS) for mifepristone, one of
                       two medications commonly used in tandem to end a
                       pregnancy. In December, the FDA permanently lifted
                       its requirement that mifepristone be administered
                       in person, allowing patients to receive the
                       medication through the mail.


                # ⚓ Counter Punch ☛ We_Need_Honest_Debate,_Not_Unprincipled
                  Attacks:_A_Further_Response_to_the_Attacks_On_Rise_Up_4
                  Abortion_Rights⠀⇛


                       Never mind that Rise Up 4 Abortion Rights already
                       thoroughly rebutted the dishonest claims against it
                       that Sommers elevated and attempted to legitimize.
                       Never mind that, from their own perspective, the
                       Revcoms rebutted the attacks on them and their
                       leader, Bob Avakian, as well.


                       It is necessary for organizations and individuals
                       to substantively debate differences of analysis and
                       strategy. This is a process that everyone can learn
                       from and which serves to forge unity in the fight
                       against injustice. But it is something else
                       entirely to traffic in lies, slanders, and libel,
                       as do the attacks Sommers is legitimizing.


                # ⚓ TruthOut ☛ Idaho_GOP_Sets_Party_Line_Against_Life-Saving
                  Exception_for_Abortions⠀⇛


                # ⚓ TruthOut ☛ House_Staffers_in_8_Offices_File_to_Form_First-
                  Ever_Congressional_Unions⠀⇛


                # ⚓ Scheerpost ☛ Starbucks_and_Other_Companies_Escalate_War_on
                  Unions_With_Store_Closures⠀⇛


                       Workers at “progressive” companies like Starbucks
                       and Heine Brothers’ Coffee exercised their right to
                       form a union. Now the companies are closing their
                       stores.


                # ⚓ Scheerpost ☛ What_Is_Class_Struggle_Unionism?⠀⇛


                       Joe Burns’ new Class Struggle Unionism comes at a
                       key time. That’s because the long-slumbering union
                       movement looks like it could be starting to stir
                       again.


                # ⚓ The Nation ☛ “The_Worst_Abuser_You_Could_Ever_Have”⠀⇛


                       Tracy McCarter did everything that society tells
                       domestic violence survivors to do. She separated
                       from her husband, Jim Murray, and moved on with her
                       life. She continued working full-time as a nurse at
                       NewYork-Presbyterian Hospital, was enrolled in a
                       master’s program at Columbia University, and was
                       looking forward to celebrating her graduation with
                       her four grown children. In the seven months since
                       she had separated from her husband, she had rented
                       her own apartment in Manhattan and was in the
                       process of buying one in Queens, far enough away
                       from Murray, whose alcoholism had been spiraling
                       out of control, to minimize his intrusions.
                       Although she still loved her husband, McCarter was
                       preparing to enter a new chapter in her life—one in
                       which she would welcome her first grandchild into
                       the world, purchase and renovate a co-op, and
                       advance her career.1


                # ⚓ The Nation ☛ The_Fight_Over_Berlin’s_Comfort_Woman_Statue⠀⇛


                       On the second Monday of each month, Jim-Bob
                       Heimberg walks across the street from his family’s
                       flower shop café to a park in the quiet Berlin
                       neighborhood of Moabit. There, Heimberg, a tall,
                       27-year-old German, places a crown of flowers atop
                       a statue of a small Korean girl.


                # ⚓ The Nation ☛ Edafe_Okporo’s_Manifesto_for_the_Migrant⠀⇛


                       When Edafe Okporo was released from a New Jersey
                       immigration detention center in 2017, he had
                       nowhere to go. He spent a few nights wandering in
                       Newark Penn Station, dozing on benches and in
                       corners, and then found shelter at a nearby YMCA.
                       He had no money, no phone, knew nobody, and,
                       besides a few hours in a back room of JFK airport,
                       had never been in the United States as a free man.
                       A year later, he was the director of a homeless
                       shelter in Harlem, offering refuge to people who
                       were facing the same displacement and homelessness
                       he had barely overcome.


                # ⚓ Pro Publica ☛ Two_Cities_Took_Different_Approaches_to
                  Pandemic_Court_Closures._They_Got_Different_Results.⠀⇛


                       On Dec. 31, 2020, a 40-year-old man named Leon
                       Casiquito walked into Kelly Liquors on Route 66 in
                       Albuquerque and tried to shoplift a bottle of
                       tequila. When one of the owners, Danny Choi, tried
                       to stop him, Casiquito flashed a small pocketknife.
                       Choi told police he knocked the bottle out of
                       Casiquito’s hand with a stick and Casiquito left
                       the store.


                       Choi locked the door, but Casiquito hung around in
                       the parking lot, shouting that he was going to beat
                       up the store’s employees. One of them called the
                       police, and soon four officers arrived and wrestled
                       Casiquito to the ground. He was charged with armed
                       robbery and aggravated assault with a deadly weapon
                       — despite not actually attacking anyone with the
                       pocketknife — and held without bail at the
                       Metropolitan Detention Center in Albuquerque.


                # ⚓ Techdirt ☛ Federal_Court_Allows_Protesters’_First_Amendment
                  Suit_Against_Violent_Boston_Cops_To_Continue⠀⇛


                       A lawsuit filed by four protesters against three
                       Boston police officers can move forward, following
                       a federal judge’s determination that the cops’
                       counterarguments were too ridiculous to be granted
                       credence.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Common Dreams ☛ Advocates_Welcome_New_Push_for_‘Incredibly
                  Important’_Net_Neutrality_Bill⠀⇛


                       Open internet advocates on Monday celebrated news
                       of soon-to-be-unveiled legislation that “would
                       reclassify broadband as a telecommunications
                       service,” exposing industry giants to stricter
                       federal oversight.


                       “Broadband internet is a necessity, not a luxury.”


                # ⚓ India Times ☛ U.S._Senate_Democrats_plan_bill_aiming_to
                  restore_‘net_neutrality’⠀⇛


                       Two U.S. Senate Democrats active in internet issues
                       are working on a bill to restore landmark “net
                       neutrality” rules that would bar telecommunications
                       companies from blocking or throttling traffic or
                       offering paid fast lanes. Senators Edward Markey
                       and Ron Wyden plan to introduce a bill this summer
                       that would put broadband under the umbrella of a
                       telecommunications service, which means that
                       providers would be subject to stricter Federal
                       Communications Commision (FCC) oversight, a source
                       briefed on the matter told Reuters. Representative
                       Doris Matsui is working on a companion House
                       version.


                # ⚓ The Verge ☛ Democrats_prepare_bill_that_would_codify_net
                  neutrality⠀⇛


                       The Net Neutrality and Broadband Justice Act —
                       spearheaded by longtime Senate internet advocates
                       Ed Markey (D-MA) and Ron Wyden (D-OR) — would
                       reclassify broadband as a telecommunications
                       service under Title II. This would give the Federal
                       Communications Commission new enforcement powers
                       over the internet, including the power to set rules
                       against throttling, blocking, or paid
                       prioritization.


                # ⚓ The Washington Post ☛ Democrats_plan_sweeping_net
                  neutrality_bill_as_FCC_majority_stalls⠀⇛


                       While the two-page bill is seemingly simple in
                       scope, it would have massive implications in
                       addition to reinstating net neutrality, the rules
                       that bar internet service providers from blocking
                       or throttling content. It would shift how
                       aggressively the FCC can regulate issues like
                       internet pricing, consumer privacy and competition
                       in the broadband market.


                       Lawmakers plan to introduce the bill in coming
                       weeks, likely before the August recess, according
                       to two people familiar with the negotiations, who
                       spoke on the condition of anonymity to discuss
                       private talks.


                # ⚓ Internet Freedom Foundation ☛ Legislative_Brief_on_Digital
                  Rights_for_Monsoon_Session_2022⠀⇛


                       We have prepared our legislative brief on digital
                       rights for the Monsoon Session 2022 of the Indian
                       Parliament. In our brief, we highlight some of the
                       focus areas within the larger issues of digital
                       rights, data governance, increased digitalisation
                       in the absence of robust rights-based policies, and
                       other concerns that call for extensive deliberation
                       in the Houses of Parliament.


                       [...]


                       The Monsoon Session of the Indian Parliament
                       commenced on July 18, and as per bulletins by the
                       Lok Sabha and Rajya Sabha secretariats, it will end
                       on August 18.


                       The previous Budget Session of the Parliament saw
                       several key issues being taken up as part of the
                       budget deliberations in both the Houses. Even
                       though the House was adjourned sine die a day ahead
                       of schedule, the Lok Sabha worked for 123% of its
                       scheduled time and Rajya Sabha for 90%. In our
                       review of the Budget Session, we had previously
                       analysed the budgetary allocations for the Ministry
                       of Home Affairs, Ministry of Information and
                       Broadcasting, and Ministry of Electronics and
                       Information Technology (“MeitY”).


                       Though the Prime Minister called for the Members to
                       put aside party politics, this session is expected
                       to be a confrontational one, as issues like the
                       agnipath scheme, demolitions drives, raids on
                       members of the opposition, allegations of use of
                       spyware and planting of evidence, rising inflation
                       and unemployment are expected to come to the fore.
                       While there is speculation that the Draft Data
                       Protection Bill, 2021 and new legislation to
                       replace the Information Technology Act, 2000 might
                       be tabled in the House this time, they have not
                       been included in the Lok Sabha List of Business as
                       of July 15, 2022.


                # ⚓ Techdirt ☛ U.S._Consumers_Pay_$1,600_Annually_For_Cable_TV
                  Channels_They_Don’t_Watch⠀⇛


                       One of the reasons that propaganda mills like Fox
                       News don’t take a bigger hit from advertising
                       boycotts is because U.S. consumers pay billions of
                       dollars annually for the channel, even if they
                       don’t watch it. More specifically, Fox rakes in
                       $1.8 billion in carriage fees to include the
                       channel in bloated cable bundles, despite the fact
                       that just 3 million of the nation’s 90 million
                       cable TV subscribers actively watch.


                # ⚓ Techdirt ☛ Brief_Reprieve:_UK_Puts_Online_Safety_Bill_On
                  Hold_While_It_Sorts_Out_Its_Boris_Johnson-Shaped_Mess⠀⇛


                       I guess it’s only natural that the UK’s Online
                       Safety Bill — brilliantly dubbed the bill to Brexit
                       the internet by Heather Burns — is getting delayed,
                       just like the regular Brexit. And, no surprise,
                       Boris Johnson is part of the issue again. As you’ll
                       have likely heard, if you haven’t been under a
                       rock, Johnson is on his way out and is currently in
                       the lamest of lame ducks periods as we wait to
                       figure out what other nutty character will replace
                       him (don’t worry, none of the choices are good).


                # ⚓ Techdirt ☛ Just_A_Click_Away:_How_To_Improve_Broadband
                  Competition⠀⇛


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ The Hill ☛ Netflix_braces_for_critical_earnings_call_after
                  challenging_year⠀⇛


                       Netflix will share its earnings information and
                       outlook going forward on Tuesday after a rocky year
                       in which it faced falling subscription rates and
                       increasing competition.


                       Tuesday’s call will be the streaming service
                       giant’s first briefing on its quarterly earnings
                       since sharing in April that the company lost
                       200,000 subscribers — its first subscriber loss in
                       more than 10 years.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ US_Lawmakers_Want_FTC_to_Crack_Down
                        on_Overpromising_and_Dishonest_VPNs⠀⇛


                             Senator Ron Wyden and Representative Anna
                             Eshoo are urging the Federal Trade Commission
                             (FTC) to take action against abusive and
                             deceptive practices in the VPN industry. They
                             note that many Americans benefit from the
                             increased privacy and security that VPNs
                             offer, but some VPN providers can overpromise
                             or be dishonest with their subscribers.


                      # ⚓ Torrent Freak ☛ Court_Orders_Cloudflare’s_DNS
                        Resolver_1.1.1.1_to_Block_Pirate_Sites_in_Italy⠀⇛


                             An Italian court has ordered Cloudflare to
                             block three torrent sites on its public DNS
                             resolver 1.1.1.1. The anti-piracy measures
                             were requested by local music industry group
                             FIMI and anti-piracy group FPM. This is the
                             first time that Cloudflare DNS must block
                             pirate sites and, with this injunction in
                             hand, Google and OpenDNS could be next.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Dimanĉo⠀⇛


                       I had no trouble waking up for Liturgy this
                       morning, in fact I had an excellent sleep. It was
                       the local bishop’s namesday and so we greeted him
                       after liturgy. The weather has been clear and
                       unseasonably chilly, though I would rather it be a
                       too cold than too warm.


                       At lunch I met 3 Polish-speaking young women, one
                       from Germany, one from somewhere else in Poland,
                       and one from Białystok. They seem very nice if a
                       little insular, i.e. they are more comfortable
                       speaking Polish to each other rather than English
                       to the rest of us, and I can’t blame them. Ili
                       estas agrablaj, kaj mi antaŭĝojas paroli pli kun
                       ili.


                       I’m excited for the conference; it technically
                       starts tomorrow. Meeting people from around the
                       world and sharing ideas and time will be great.


          o § Technical⠀➾


                # § Science⠀➾


                      # ⚓ Observing_Sound_Waves_Up_Close⠀⇛


                             I never really thought about the intricacy of
                             sound waves before, the minute variations
                             they possess. However, given that I am
                             entering the field of audio design, gradually
                             creating more intricate songs, I decided
                             today to view, firsthand, the microscopic
                             pattern of a waveform, courtesy of a piece of
                             software I have installed which allows for a
                             comprehensive visualization.


                             The results were stunning, as well as being
                             visually appealing on their own merits. The
                             amount of variation present within
                             microseconds of audio spans a wide range of
                             strange and unique patterns. Given that I am
                             also involved in the visual field, I see
                             something captivating in these whorls of
                             invisible force.


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



                    ䷩ 𝚕𝚒𝚗𝚎 5871

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.19.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_19/07/2022:_RIP,_Thomas_Lord,_We’ll_Miss_You!⠀✐


Posted in News_Roundup at 3:38 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o SUSE/OpenSUSE
          o Fedora_/_Red_Hat
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o GNU_Projects
          o Programming/Development
                # JS
                # Rust
    * Leftovers
          o Privatisation/Privateering
          o Security
          o Civil_Rights/Policing
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ The Register UK ☛ You_can_liquid_cool_this_Linux_laptop_to
                  let_the_GPU_soar⠀⇛


                       Computer chips are getting so hot these days, some
                       companies are starting to put liquid cooling into
                       laptops so that they can run faster — or quieter
                       and less hot to the touch.


                       Just look at Germany-based Tuxedo Computers, which
                       released a 15-inch high-performance laptop earlier
                       this year that supports an external liquid-cooling
                       module. After initially running Windows, the Tuxedo
                       Stellaris 15 – Gen4 now plays nice with Linux, the
                       vendor recently announced.


                       The laptop can be configured with some of the
                       fastest CPUs out there, letting users choose
                       between an Intel Core i7-12700H, Intel Core i9-
                       12900H, or AMD Ryzen 9 6900HX. For GPU, the laptop
                       supports a wider range of options, from Nvidia’s
                       GeForce RTX 3060 to the RTX 3080 Ti.


                       Tuxedo’s liquid-cooling module, called Aquaris, is
                       offered as a €199 ($201 based on current exchange
                       rates) add-on for the laptop, which varies in price
                       based on configuration but starts at around €2,000
                       ($2,028) for the hardware.


          o § Audiocasts/Shows⠀➾


                # ⚓ MakuluLinux_GameR_Build_Preview_–_MakuluLinux⠀⇛


                       In this video we take a closer look at the upcoming
                       MakuluLinux “GameR” Build, due in the next few
                       weeks…


                # ⚓ Video ☛ openSUSE_15.4_Quick_overview_#linux_#openSUSE
                  #Shorts_–_Invidious⠀⇛


                       A Quick overview of openSUSE 15.4.


                # ⚓ Video ☛ Zorin_OS_16.1_Lite_Review_–_Lightweight_Linux_ep._2
                  –_Invidious⠀⇛


                       In episode 2 of exploring lightweight Linux
                       distributions that can run on older hardware, we
                       have Zorin OS Lite 16.1.


          o § Kernel Space⠀➾


                # ⚓ Geeky Gadgets ☛ Asahi_Linux_now_supports_M2_Apple_Macs_–
                  Geeky_Gadgets⠀⇛


                       The community and element team responsible for
                       creating Asahi Linux have released a new update
                       supporting the latest Apple Mac computers powered
                       by the M2 Apple silicon chips. As well as
                       supporting the Mac Studio range of computers and
                       Bluetooth connectivity. “The end result is that
                       existing reference distro users can simply upgrade
                       their packages, reboot, and Bluetooth should just
                       work without any further configuration or changes!”


                # ⚓ Mac Observer ☛ Asahi_Linux_Now_Supports_Mac_Studio_and_M2
                  MacBooks⠀⇛


                # ⚓ AppleInsider ☛ Apple_Silicon_Linux_project_gets_initial_Mac
                  Studio_&_M2_support_|_AppleInsider⠀⇛


                       The Asahi Linux for Mac project has made some
                       improvements, with the latest version adding
                       initial support for M2 chips as well as the Mac
                       Studio, along with Bluetooth.


                # ⚓ Linux_Memory_Statistics_–_Dropbear⠀⇛


                       Memory sits in the first row after the headers then
                       we have the swap statistics. Most of the numbers
                       are directly fetched from the procfs file /proc/
                       meminfo which are scaled and presented to the user.
                       A good example of a “simple” stat is total, which
                       is just the MemTotal row located in that file. For
                       the rest of this post, I’ll make the rows from /
                       proc/meminfo have an amber background.


          o § Graphics Stack⠀➾


                # ⚓ An_introduction_to_the_Linux_graphics_stack⠀⇛


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


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


                       All of those abstraction layers come with a history
                       of their own1, and it’s kinda amazing that we can
                       even have such a smooth experience with all of
                       those, community-powered, beautifully thought-out,
                       moving pieces, twisting and turning in a life of
                       their own.


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


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


          o § Applications⠀➾


                # ⚓ Make Use Of ☛ The_6_Best_Linux_Camera_Apps_to_Get_the_Most
                  Out_of_Your_Webcam⠀⇛


                       
                       It’s one thing for your computer to have a webcam,
                       but it doesn’t work without the right software.
                       Here are several of the top options for Linux.


                       Most laptops these days feature a built-in webcam
                       that lets you make video calls, do live streams, or
                       take photos of yourself. However, unlike Mac or
                       Windows, some Linux distros don’t come with a
                       built-in camera app.


                       As a result, if you want to use your webcam
                       effectively, you need a third-party camera app on
                       your computer. Linux has several options in this
                       regard. Unfortunately, not all of them are as good
                       and have the necessary webcam features.


                # ⚓ A_look_back_in_celebration_of_Inkscape_contributors_&
                  milestones_in_2021⠀⇛


                       Yes, we’re over halfway through 2022. That won’t
                       stop us from celebrating our volunteers and the
                       work accomplished during 2021. It’s always a good
                       time to look back at how we have arrived here this
                       year. Enjoy the read!


                       The Inkscape project is composed of a global team
                       of volunteer contributors who collaborate to
                       maintain, develop, translate, design, document,
                       promote and use this free and open source (FOSS)
                       professional vector-editing software.


                       Without our volunteers, Inkscape simply would not
                       exist!


                       This diversely-skilled team of contributors spend
                       their time and energy serving Inkscape users and
                       mentoring each other and summer students through
                       our chat groups and the forum, meeting to plan
                       launches, organize activities, participate in
                       external events, and connecting with followers
                       across multiple social media platforms. There was
                       even an opportunity to connect for one
                       international conference via a virtual room from
                       continents around the planet.


          o § Instructionals/Technical⠀➾


                # ⚓ HowTo Forge ☛ Resolving_Domain_Names_with_dig_Command_on
                  Linux⠀⇛


                       This tutorial shows how to resolve domain names on
                       the Linux shell and how to query a name server for
                       various kinds of DNS records like A, MX and NS
                       records. To resolve a domain name on the shell, we
                       will use the command dig.


                # ⚓ Daniel_P._Berrangé_»_Blog_Archive_»_Trying_sd-boot_and
                  unified_kernel_images_in_a_KVM_virtual_machine⠀⇛


                       A recent thread on the Fedora development list
                       about unified kernel images co-incided with work
                       I’m involved in wrt confidential computing (AMD SEV
                       [-SNP], Intel TDX, etc). In exploring the different
                       options for booting virtual machines in a
                       confidential computing environment, one of the
                       problems that keeps coming up is that of validating
                       the boot measurements of the initrd and kernel
                       command line. The initrd is currently generated on
                       the fly at the time the kernel is installed on a
                       host, while the command line typically contains
                       host specific UUIDs for filesystems or LUKS
                       volumes. Before even dealing with those problems,
                       grub2‘s support for TPMs causes pain due to its
                       need to measure every single grub.conf
                       configuration line that is executed into a PCR.
                       Even with the most minimal grub.conf using
                       autodiscovery based on the boot loader spec, the
                       grub.conf boot measurements are horribly cumbersome
                       to deal with.


                       With this in mind, in working on confidential
                       virtualization, we’re exploring options for
                       simplifying the boot process by eliminating any
                       per-host variable measurements. A promising way of
                       achieving this is to make use of sd-boot instead of
                       grub2, and using unified kernel images pre-built
                       and signed by the OS vendor. I don’t have enough
                       familiarity with this area of Linux, so I’ve been
                       spending time trying out the different options
                       available to better understand their operation.
                       What follows is a short description of how i took
                       an existing Fedora 36 virtual machine and converted
                       it to sd-boot with a unified kernel image.


                       First of all, I’m assuming that the virtual machine
                       has been installed using UEFI (EDK2’s OOVMF build)
                       as the firmware, rather than legacy BIOS (aka
                       SeaBIOS). This is not the default with virt-
                       manager/virt-install, but an opt-in is possible at
                       time of provisioning the guest. Similarly it is
                       possible to opt-in to adding a virtual TPM to the
                       guest, for the purpose of receiving boot
                       measurements. Latest upstream code for virt-
                       manager/virt-install will always add a vTPM if UEFI
                       is requested.


                # ⚓ Russell Coker ☛ DDC_as_a_KVM_Switch_«_etbe_–_Russell
                  Coker⠀⇛


                       With the recent resurgence in Covid19 I’ve been
                       working from home a lot and using both my work
                       laptop and personal PC on the same monitor. HDMI
                       KVM switches start at $150 and I didn’t feel like
                       buying one. So I wrote a script to change inputs on
                       my monitor. The following script locks the session
                       on the local machine and switches the monitor’s
                       input to the other machine. I ran the command
                       “ddcutil vcpinfo| grep Input” which shows that (on
                       my monitor at least) 60 is the VCP for input. Then
                       I ran the command “ddcutil getvcp 60” to get the
                       current value and tried setting values sequentially
                       to find the value for the other port.


                # ⚓ Red Hat ☛ Secure_Kubernetes_certificates_with_cert-manager
                  and_Dekorate_|_Red_Hat_Developer⠀⇛


                       Cert-manager is a cloud-native certificate
                       management service for Kubernetes and Red Hat
                       OpenShift. To configure cert-manager, you need to
                       install several resources using custom resource
                       definitions (CRDs). Depending on the issuer type
                       and the certificate you need, creating these custom
                       resources can become complex. This article
                       introduces Dekorate as an easier way to generate
                       the cert-manager custom resources. We will also
                       provide an example Java application based on Spring
                       Boot that uses the certificate generated by cert-
                       manager.


                # ⚓ ID Root ☛ How_To_Create_Apache_Virtual_Host_on_Ubuntu_22.04
                  LTS_–_idroot⠀⇛


                       In this tutorial, we will show you how to create
                       Apache Virtual Host on Ubuntu 22.04 LTS. For those
                       of you who didn’t know, The term “Virtual Hosting”
                       refers to the hosting of many domains on a single
                       server. The virtual hosting concept is used by
                       companies to host multiple websites using a single
                       machine. It can be achieved either by an ‘IP-based’
                       method or a ‘domain-name-based’ approach. In ‘IP-
                       based’ hosting we have distinct IP addresses for
                       each website. In the case of ‘name-based’ hosting,
                       we have multiple names running on each IP address.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step set up
                       Apache Virtual Host on Ubuntu 22.04 (Jammy
                       Jellyfish). You can follow the same instructions
                       for Ubuntu 22.04 and any other Debian-based
                       distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ Install_VirtualBox_Guest_Additions_on_Rocky_Linux_9_–
                  kifarunix.com⠀⇛


                       Follow through this tutorial to learn how to
                       install VirtualBox guest additions on Rocky Linux
                       9. We are installing the VirtualBox Guest additions
                       on Rocky Linux 9 Desktop.


                # ⚓ Make Use Of ☛ How_to_Set_Up_and_Configure_an_NFS_Server_on
                  Linux⠀⇛


                       An NFS server allows multiple systems to share a
                       file system deployed over a network. Here’s how you
                       can install and set up an NFS server on Linux.


                       Sun Microsystems’ NFS (Network File System) is an
                       RPC-based distributed file system structure that
                       allows networked devices to use servers running NFS
                       over a network as their local drives.


                       Here’s a step-by-step guide to setting up and
                       configuring an NFS server on a Linux machine.


                # ⚓ HowTo Forge ☛ How_to_Install_Moodle_with_Nginx_and_Free
                  Let’s_Encrypt_SSL_on_Ubuntu_22.04⠀⇛


                       Moodle is a free and open-source Learning
                       Management System and CMS written in PHP. It allows
                       tutors and instructors to create courses for their
                       students and provides long-distance education and
                       other online learning programs more accessible.
                       This tutorial will show you how to install Moodle
                       with Nginx and Let’s Encrypt SSL on Ubuntu 22.04.


                # ⚓ H2S Media ☛ Install_Emacs_27_text_editor_Ubuntu_22.04_LTS
                  Jammy_–_Linux_Shout⠀⇛


                       Learn the steps to install GNU Emacs 27 text editor
                       on Ubuntu 22.04 Focal Fossa using the command
                       terminal.


                       GNU Emacs is a programmable text editor suitable
                       for development. Emacs make it easier to write
                       source code through syntax highlighting and can be
                       customized by the user. Help is available for the
                       tool as well as support for multiple languages. GNU
                       Emacs can also be used to create text documents
                       based on LaTeX.


                       Apart from that, it is a very comprehensive and
                       platform-independent editor that is extensible by
                       its own Lisp dialect (Emacs Lisp). Since its
                       control is mainly based on keyboard shortcuts, it
                       requires some training in order to be able to use
                       all its possibilities intensively. Due to a high
                       number of plugins, the editor can be used in almost
                       all areas. For example, there are extensions for
                       file management, email and news, IRC, compilations,
                       web surfing, and much more.


                # ⚓ H2S Media ☛ How_to_install_Emacs_28_on_Ubuntu_20.04_LTS
                  Focal_Fossa⠀⇛


                       Learn the steps to install GNU Emacs 28 text editor
                       on Ubuntu 20.04 Focal Fossa using the command
                       terminal.


                       GNU Emacs is a programmable text editor suitable
                       for development. Emacs make it easier to write
                       source code through syntax highlighting and can be
                       customized by the user. Help is available for the
                       tool as well as support for multiple languages. GNU
                       Emacs can also be used to create text documents
                       based on LaTeX.


                       Apart from that, it is a very comprehensive and
                       platform-independent editor that is extensible by
                       its own Lisp dialect (Emacs Lisp). Since its
                       control is mainly based on keyboard shortcuts, it
                       requires some training in order to be able to use
                       all its possibilities intensively. Due to a high
                       number of plugins, the editor can be used in almost
                       all areas. For example, there are extensions for
                       file management, email and news, IRC, compilations,
                       web surfing, and much more.


                # ⚓ Install_Rocky_Linux_9_on_VirtualBox_–_kifarunix.com⠀⇛


                       In this tutorial, you will learn on how to simply
                       install Rocky Linux 9 on VirtualBox. With Rocky
                       Linux 9 now being available, you might want to try
                       it out and the best way out is through installing
                       it as a virtual machine.


                # ⚓ ByteXD ☛ EasyEngine:_Install_WordPress_Automatically_on
                  Ubuntu_22.04⠀⇛


                       EasyEngine is a free and open-source Linux command
                       line tool for managing WordPress sites on Ubuntu
                       and Debian servers. It enables you to deploy single
                       or multisite WordPress installations with various
                       configurations, such as caching, SSL with different
                       configs, different WordPress versions, database
                       configurations, different PHP versions, and more.
                       You can check out the full configuration options
                       for WordPress here.


                       It’s a Python based tool that can be used to manage
                       WordPress, MariaDB, Nginx, and PHP using the
                       command line.


                       EasyEngine can be installed on all Debian-based
                       distributions.


                # ⚓ TecMint ☛ How_to_Install_Latest_Wine_in_Ubuntu_Linux⠀⇛


                       Wine is a nifty utility that allows users to run
                       Windows applications and games inside a Linux
                       environment. Wine 7.0 is finally out, and it ships
                       with an array of numerous improvements and a total
                       of 40 bug fixes.


                # ⚓ Linux Capable ☛ How_to_Install_Node.js_on_Rocky_Linux_9⠀⇛


                       Node.js is a versatile platform for building
                       server-side applications. Built on Chrome’s V8
                       JavaScript engine, Node.js is fast and scalable. It
                       uses an event-driven, non-blocking IO model that
                       makes it lightweight and efficient. Node.js is an
                       ideal platform for building data-intensive real-
                       time applications across distributed devices. With
                       its wide range of features, Node.js provides
                       developers with everything they need to build high-
                       performance network applications. Node.js is also
                       highly extensible as an open-source platform,
                       making it easy to add new functionality as
                       required. Whether you’re looking to build a simple
                       API or a complex web application, Node.js is an
                       excellent choice for your back-end development
                       needs.


                       In the following tutorial, you will learn various
                       methods of installNode.js on Rocky Linux 9 desktop
                       or server with three methods.


                # ⚓ Its FOSS ☛ How_to_Uninstall_Deb_Packages_in_Ubuntu_Linux⠀⇛


                       Installing applications from a deb file is quite
                       simple. You double click on it and it opens in the
                       Software Center application and you install it from
                       there.


                       But what about uninstalling a .deb package in
                       Ubuntu or Debian? How do you remove the package you
                       installed some time back.


                       While there are several ifs and buts around it, the
                       simplest and most reliable way of deleting a deb
                       file is by using the apt remove command.


                # ⚓ TechRepublic ☛ How_to_install_a_Minecraft_server_on_Ubuntu
                  Server_22.04 [Ed: Jack Wallen, why are you promoting
                  Microsoft proprietary stuff?]⠀⇛


                # ⚓ Detailed_Guide_on_how_to_Set_Up_SSH_2FA_on_Ubuntu_Server
                  22.04 [Ed: This might be a plagiarism domain. Maybe not.]⠀⇛


                # ⚓ H2S Media ☛ How_to_install_Emacs_27_text_editor_Ubuntu
                  20.04_–_Linux_Shout⠀⇛


                       Learn the steps to install GNU Emacs 27 on Ubuntu
                       22.04 Focal Fossa using the command terminal. You
                       can also install Emacs 28/26/25 versions as well.


                       GNU Emacs is a programmable text editor suitable
                       for development. Emacs makes it easier to write
                       source code through syntax highlighting and can be
                       customized by the user. Help is available for the
                       tool as well as support for multiple languages. GNU
                       Emacs can also be used to create text documents
                       based on LaTeX.


                       Apart from that, it is a very comprehensive and
                       platform-independent editor that is extensible by
                       its own Lisp dialect (Emacs Lisp). Since its
                       control is mainly based on keyboard shortcuts, it
                       requires some training in order to be able to use
                       all its possibilities intensively. Due to a high
                       number of plugins, the editor can be used in almost
                       all areas. For example, there are extensions for
                       file management, email and news, IRC, compilations,
                       web surfing, and much more.


                # ⚓ Hands-on_installation_of_PipeWire_–_Bootlin’s_blog⠀⇛


                       Let’s jump right in! In the previous article, we
                       went through a theoretical overview of PipeWire.
                       Our goal will now be to install and configure a
                       minimal Linux-based system that runs PipeWire in
                       order to output audio to an ALSA sink. The hardware
                       for this demo will be a SAMA5D3 Xplained board and
                       a generic USB sound card (a Logitech USB Headset
                       H340 in our case, as reported by /sys/bus/usb/
                       devices/MAJOR-MINOR/product).


                       We won’t bother with the bootloader setup (in our
                       case U-Boot) as this is out of scope of our topic;
                       if needed, Bootlin has training sessions for
                       embedded Linux system development for which the
                       training materials are freely available.


                # ⚓ ID Root ☛ How_To_Install_PostgreSQL_on_Rocky_Linux_9_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       PostgreSQL on Rocky Linux 9. For those of you who
                       didn’t know, PostgreSQL is an immensely popular
                       open-source relational database management system
                       (RDBMS). Generally, it is used as the primary data
                       store for many web, mobile, geospatial, and
                       analytics applications. PostgreSQL can store
                       structured and unstructured data in a single
                       product. In addition, PostgreSQL is open source
                       software, meaning it can be freely used, modified,
                       and distributed.


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


                # ⚓ Red Hat Official ☛ Linux_essentials:_How_to_create_and
                  delete_files_and_directories_|_Enable_Sysadmin⠀⇛


                       Creating and deleting files and directories are
                       standard operations for a sysadmin. Depending on
                       your operating system and filesystem, there may be
                       different ways to perform these tasks. The most
                       efficient way is to use the shell (for instance,
                       Bash). This article assumes you already understand
                       how to enter commands into a Linux terminal. (Read
                       Nathan Lager’s What sysadmins need to know about
                       using Bash if you want a refresher.)


                # ⚓ TechRepublic ☛ 5_tips_for_securing_SSH_on_your_Linux
                  servers⠀⇛


                       
                       SSH is a tool I use every single day to log into
                       remote Linux servers and take care of my admin
                       tasks. Without SSH, my days would be more
                       complicated and less secure. That doesn’t mean,
                       however, that SSH is configured to your liking
                       right out of the box. There are a few weaknesses in
                       the default configuration and the way you’re
                       probably using the tool.


                       Let’s fix that.


                       Here are my five most straightforward tips for
                       securing SSH on your Linux machines. These tips
                       shouldn’t take you more than five minutes to handle
                       and, in the end, you’ll be glad you took the time
                       to do so.


          o § Games⠀➾


                # ⚓ Boiling Steam ☛ The_Steam_Deck_Reaches_a_New_Milestone_with
                  4000_Games_(Playable_or_Verified)_–_Boiling_Steam⠀⇛


                       Another milestone with 4000 games on the Steam Deck
                       as Playable or Verified – Well not exactly 4000
                       games as there were only 3999 games at the time of
                       writing but I hope you can allow us to round this
                       up a little! If we split the games in two
                       categories…


    * § Distributions and Operating Systems⠀➾


          o § SUSE/OpenSUSE⠀➾


                # ⚓ MicroOS_Desktop_Use_to_Help_with_ALP_Feedback_–_openSUSE
                  News⠀⇛


                       Participants from the openSUSE community working on
                       the upcoming release of the Adaptable Linux
                       Platform (ALP) encourage people to try openSUSE
                       MicroOS Desktop to gain user perspectives on its
                       applicability.


                       Users are encouraged to try out MicroOS Desktop by
                       installing it and using it on a laptop or
                       workstation for a week or so. By doing this, users
                       develop a frame of reference for how ALP can
                       progress; the community wants to gain feedback
                       about what users think about ALP’s usability, how
                       it fits user workflows and more. The community
                       would like to see critiques and evaluations that
                       work for users. People are encouraged to send
                       feedback to the ALP-community-wg mailing list.


                       The temporary use of the MicroOS Desktop will help
                       developers assess how to move forward with ALP’s
                       Proof of Concept (PoC).


                       Currently MicroOS Desktop has both GNOME and KDE’s
                       Plasma as an option.


                # ⚓ YaST_Development_Report_–_Chapter_5_of_2022_|_YaST⠀⇛


                       We have been a bit silent lately in this blog, but
                       there are good reasons for it. As you know, the
                       YaST Team is currently involved in many projects
                       and that implies we had to constantly adapt the way
                       we work. That left us little time for blogging. But
                       now we have reached enough stability and we hope to
                       recover a more predictable and regular cadence of
                       publications.


                       [...]


                       As you know, SUSE is developing the next generation
                       of the SUSE Linux family under the code-name ALP
                       (Adaptable Linux Platform). If you are following
                       the activity in that front, you also know several
                       so-called work groups has been constituted to work
                       on different areas.


                       The YaST Team is deeply involved on two of those
                       work groups, the ones named “1:1 System Management”
                       and “Installation / Deployment”. You can read more
                       details about the mission of each group and the
                       technologies we are developing in the wiki page
                       linked at the previous paragraph.


                       Since this blog is a well-established communication
                       channel with the (open)SUSE users, we decided we
                       will use it to report the progress on all the
                       projects related to those work groups. That goes
                       beyond the scope of YaST itself and even beyond the
                       scope of the YaST Team, since the mentioned work
                       groups also include other SUSE and openSUSE
                       colleages. But we are sure our readers will equally
                       enjoy the content.


          o § Fedora / Red Hat⠀➾


                # ⚓ FOSSLife ☛ Rocky_Linux_9_and_Rocky_Linux_8_Optimized_for
                  Google_Cloud_Now_Available⠀⇛


                       Rocky Linux 9 has been released, featuring various
                       security and performance updates as well as a new
                       build system called Peridot.


                       According to Gregory Kurtzer, CEO of CIQ and
                       founder of the Rocky Enterprise Software Foundation
                       (RESF), with Rocky Linux 9, “CIQ has created a
                       completely cloud-native build stack called Peridot,
                       which we have given to the RESF and released as
                       open source to the world.”


                       The Peridot build system was used to build Rocky
                       Linux 9 for the x86_64, aarch64, s390x and ppc64le
                       architectures, says the announcement. “A primary
                       goal in developing the new build system was
                       assuring that new versions of Rocky can be released
                       within one week after each Red Hat Enterprise Linux
                       new version release.” And, says Kurtzer, “Peridot
                       allows anyone to recreate, build, enhance and
                       manage Rocky Linux as we do.”


                # ⚓ Rocky_Linux_9_Comes_With_New_Security,_Application_And
                  Networking_Features_–_TFiR⠀⇛


                       Rocky Linux 9, codenamed “Blue Onyx”, is here with
                       a host of new security, application and networking
                       features. The capability in version 9 taking center
                       stage is the availability of all the build chain
                       infrastructure tools that developers would need to
                       pick up Rocky Linux to extend or reproduce the
                       operating system, should they desire to do
                       something independently of the community or any
                       upstream supporting organization. As a result,
                       Rocky Linux v9 delivers a supported enterprise
                       Linux platform for the next decade.


                # ⚓ Video ☛ How_to_install_Rocky_Linux_9.0_–_Invidious⠀⇛


                       In this video, I am going to show how to install
                       Rocky Linux 9.0.


                # ⚓ Enterprisers Project ☛ Digital_transformation:_4
                  initiatives_to_start_this_week_|_The_Enterprisers_Project⠀⇛


                       Most organizations struggle with digital
                       transformation (DX) and never achieve it. An
                       Everest Group study concluded that 73 percent of
                       companies were unsuccessful at providing any value
                       from their digital transformation process. Poor
                       planning and employee resistance are the most
                       common reasons for high failure rates.


                       The pursuit of DX does not have to commence with
                       large-scale initiatives; smaller projects can
                       increase the likelihood of a successful kickoff.
                       Short-term digital transformation efforts can have
                       immediate effects on business and offer positive
                       customer benefits.


                # ⚓ Enterprisers Project ☛ 3_infrastructure_principles_every_IT
                  leader_should_follow_|_The_Enterprisers_Project⠀⇛


                       In my experience building and training cross-
                       functional teams, I’ve identified three main
                       principles that apply to both engineering and IT.
                       These principles should be taught to all new hires
                       and adopted by IT leaders everywhere.


                # ⚓ Fedora Project ☛ Fedora_Explorer_Day_–_Panamá!_–_Fedora
                  Community_Blog⠀⇛


                       The Fedora Community in Panama recently celebrated
                       the release of Fedora Linux 36. Our last in-person
                       event was back in December 2019. Thank you to all
                       the organizers, participants, and attendees who
                       made the Fedora Explorer Day 36 event possible.


                       We had six sessions in total, four in person and
                       two online sessions with friends from Mexico and
                       Venezuela, with the addition of an hour of Fedora
                       networking on YouTube and Twitch.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Nano-U12P_–_An_8K_digital_signage_player
                  powered_by_an_Intel_Alder_Lake_processor_–_CNX_Software⠀⇛


                       Alder Lake processors were first formally announced
                       at the end of 2021 with the most powerful H-Series,
                       followed by a range of Alder Lake Edge IoT
                       processors, and in February, Intel officially
                       launched Alder Lake P-Series and U-Series mobile
                       hybrid processors which I had expected to find in
                       several mini PCs by now.


                       But apart from ASRock iBOX 1200 Series
                       announcement, and leaks of the NUC 12 Studio Pro, I
                       had not really seen any. But today, I found what
                       looks like a mini PC with the Polywell Nano-U12P,
                       but it’s instead marketed as an 8K digital signage
                       player with a choice of Alder Lake P-series and U-
                       series processors.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Touch-sensitive_steering_for_a_RatCar_|_Arduino
                  Blog⠀⇛


                       Bears on tricycles aside, animals are not very good
                       at piloting vehicles. But maybe that is because we
                       haven’t given them controls that suit their
                       thumbless bodies. If a vehicle had controls adapted
                       to a particular animal’s anatomy, could they drive?
                       Back in 2019, researchers at the University of
                       Richmond found that rats could. Inspired by that
                       study, this Instructables user built their own
                       RatCar with touch-sensitive steering.


                       This RatCar relies on classic behavioral principles
                       established by B.F. Skinner throughout the mid-20th
                       century. Through positive reinforcement, many
                       animals can learn to perform simple tasks. In the
                       case of the RatCar, the tasks are touching one of
                       three touch-sensitive copper meshes that cause the
                       vehicle to move forward, turn right, or turn left.
                       A rat can learn to operate the vehicle through
                       reinforcement training as they receive treats for
                       their actions.


                # ⚓ Arduino ☛ Get_connected_to_your_Nano_with_the_Screw
                  Terminal_Adapter⠀⇛


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ SamMobile ☛ Why_the_Galaxy_S10_Lite_will_get_Android_13_but
                  not_other_Galaxy_S10s_–_SamMobile⠀⇛


                # ⚓ XDA ☛ Android_13_Beta_2_is_now_available_for_the_Lenovo_P12
                  Pro⠀⇛


                # ⚓ CNBC ☛ Google_will_let_Android_developers_use_rival
                  payments_systems_in_Europe⠀⇛


                # ⚓ Make Use Of ☛ 5_Android_Phone_Settings_That_Protect_Your
                  Privacy_From_Other_Users⠀⇛


                # ⚓ Hindustan Times ☛ Best_Android_smartwatches_boast_of_sharp
                  display_and_interesting_features⠀⇛


                # ⚓ Digital Trends ☛ The_Snapdragon_W5_Gen_1_might_save_Android
                  smartwatches_|_Digital_Trends⠀⇛


                # ⚓ 9to5Google ☛ Google_Photos_gets_screenshots_shortcut_on
                  Android_–_9to5Google⠀⇛


                # ⚓ Notebook Check ☛ Transpeed_P10_projector_is_a_cheaper
                  Android-powered_model_with_up_to_200-in_wide_image_–
                  NotebookCheck.net_News⠀⇛


                # ⚓ 9to5Google ☛ Android_launcher,_Lawnchair,_takes_code_from
                  Pixel_Launcher_–_9to5Google⠀⇛


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


          o ⚓ Google ☛ Cirq_Turns_1.0_|_Google_Open_Source_Blog⠀⇛


                 Today we are excited to announce the first full version
                 release of the open source quantum programming framework
                 Cirq: Cirq 1.0. Cirq is a Python framework for writing,
                 running, and analyzing the results of quantum computer
                 programs. It was designed for near-term quantum
                 computers, those with a few hundred qubits and few
                 thousands of quantum gates. The significance of the 1.0
                 release is that Cirq has support for the vast majority of
                 workflows for these systems and is considered to be a
                 stable API that we will only update with breaking changes
                 at major version numbers.


          o ⚓ Paul Schaub ☛ Creating_a_Web-of-Trust_Implementation:_Certify
            Keys_with_PGPainless_–_vanitasvitae’s_blog⠀⇛


                 Currently I am working on a Web-of-Trust implementation
                 for the OpenPGP library PGPainless. This work will be
                 funded by the awesome NLnet foundation through NGI
                 Assure. Check them out! NGI Assure is made possible with
                 financial support from the European Commission’s Next
                 Generation Internet programme.


          o ⚓ The Register UK ☛ Microsoft_tweaks_Store_policy_for_open_source
            once_again [Ed: Not because Microsoft has changes, only due to
            massive blowback]⠀⇛


                 There was some backpedaling from Microsoft overnight as
                 the company tweaked its Store policy to allow the sale of
                 open-source apps that are otherwise available for free.


                 The news was delivered by Giorgio Sardo, general manager
                 of the Microsoft Store, that the policy changes have
                 undergone some substantial rewording. Gone is the
                 reference to open-source and free software in section
                 10.8.7 and, as if to emphasize Microsoft’s actual
                 intentions, a link to Microsoft’s online infringement
                 reporting form was added in section 11.2.


          o ⚓ syslog-ng_Store_Box_SQL_source_–_Blog_–_syslog-ng_Community_–
            syslog-ng_Community⠀⇛


                 The syslog-ng Store Box (SSB) is an appliance built on
                 syslog-ng Premium Edition (PE). SSB inherits most of
                 syslog-ng PE’s features and makes them available with an
                 easy-to-use graphical user interface. One of these
                 features is the SQL source. Many applications log their
                 messages to SQL databases. The SQL source of syslog-ng PE
                 and SSB allows you to collect these log messages in real-
                 time and process and store them with the rest of your
                 logs.


                 The syslog-ng Store Box appliance can collect log
                 messages from many different log sources and in many
                 formats. These include UNIX / Linux / Windows system
                 logs, firewall and router logs, various application logs,
                 and now also SQL sources. SSB can parse, rewrite, filter
                 and store log messages. In addition to the traditional
                 syslog-ng features, the SSB appliance provides an
                 interface to search log messages, and does complete log
                 life cycle management, including archival and backup.
                 Finally, it can also forward events to various on-prem
                 and cloud destinations. It allows you to optimize your
                 SIEM installations both for resources and licensing, as
                 you can collect log messages only once, store them on
                 SSB, and only forward a reduced subset of logs to various
                 analytics tools.


          o ⚓ GSM Arena ☛ Huawei_to_introduce_HarmonyOS_3.0_on_July_27_–
            GSMArena.com_news⠀⇛


                 Huawei will launch HarmonyOS 3.0 on July 27, the company
                 revealed on Weibo. A post on the Chinese social media
                 said “the future” and the “evolution” of Huawei is coming
                 next Wednesday, and the event is scheduled for 19:30
                 local time.


                 Minutes later, the company tweeted that a new Smart
                 Office launch party is taking place on the very same day
                 at the very same time, revealing the announcement is not
                 just a local event, it is a big deal for the brand across
                 the world.


          o § GNU Projects⠀➾


                # ⚓ LWN ☛ Tom_Lord_RIP⠀⇛


                       From Berkeley comes the sad news of the passing of
                       Tom Lord, a longtime free-software developer and
                       the original author of GNU arch. He will be missed.


                       [...]


                       I worked a bit with Tom on GNU Arch, back in the
                       day. He was a great mind, precise and dedicated. He
                       was always supporting and caring with contributors.


                       If we have distributed version control systems such
                       as Bazaar (first) and git (later), we owe it in no
                       small part to him.


                       Rest in peace Tom, I will miss you.


                # ⚓ Thomas_Lord⠀⇛


                       In 1995 he first moved to Berkeley and began
                       spending time in People’s Park, a place and a
                       society that held great meaning for him.


                       He returned to Pittsburgh PA in 1998, then came
                       back to the Bay Area in 2001 and relocated
                       permanently to Berkeley in 2004.


                       In 2007 he married Trina Pundurs, his life partner
                       since 1992.


                       Upon settling in Berkeley, he began engaging with
                       city politics and policymaking. His interest led
                       him to contribute to the Berkeley Daily Planet, and
                       his work with Planet editor Becky O’Malley drew him
                       further into city and regional issues, especially
                       housing, displacement, and homelessness. In 2016 he
                       was appointed by then-Councilmember Cheryl Davila
                       to serve on the City Housing Advisory Commission.


                       In 2018 he was profoundly moved by a news report
                       about scientists weeping in the aisles at COP 24,
                       where the IPCC presented its Special Report on the
                       impact of global warming of 1.5° C (“IPCC SR15”).
                       Upon studying SR15, and following the work of Greta
                       Thunberg, he became a tireless advocate of speaking
                       the truth about the climate emergency and treating
                       it as an actual emergency.


                       In addition to his climate and housing activism, he
                       spent several years volunteering with students at
                       Longfellow Middle School as part of the Writer
                       Coach Connection program.


                       He died unexpectedly this week of a massive brain
                       hemorrhage.


          o § Programming/Development⠀➾


                # ⚓ Perl ☛ Perl_Weekly_Challenge_174:_Disarium_Numbers_and
                  Permutation_Rankings⠀⇛


                # ⚓ The_Sustainability_Impact_of_Technical_Debt⠀⇛


                       ITOps teams can improve sustainability by reducing
                       their technical debt. One way to do that is to run
                       apps inside containers instead of VMs.


                # ⚓ Qt ☛ Commercial_LTS_Qt_6.2.5_Released⠀⇛


                       We have released Qt 6.2.5 LTS for commercial
                       license holders today. Compared to Qt 6.2.4, Qt
                       6.2.5 contains close to 700 bug fixes. As a patch
                       release, Qt 6.2.5 does not add any new
                       functionality.


                # § JS⠀➾


                      # ⚓ TecAdmin ☛ How_to_Generate_Random_String_In
                        JavaScript_–_TecAdmin⠀⇛


                             Random strings are used for various purposes
                             in software development. For example, they
                             can be used to code user IDs, generate
                             passwords, and construct tokens in
                             applications. If you’re developing a
                             JavaScript-based program that needs random
                             strings — or any other type of pseudo-random
                             data — then this article is for you! You see,
                             generating random characters (or strings) is
                             easy with the right tools and techniques.
                             Luckily, this article covers exactly that.
                             Let’s get started…


                # § Rust⠀➾


                      # ⚓ Rust Blog ☛ Announcing_Rust_1.62.1_|_Rust_Blog⠀⇛


                             The Rust team has published a new point
                             release of Rust, 1.62.1. Rust is a
                             programming language that is empowering
                             everyone to build reliable and efficient
                             software.


    * § Leftovers⠀➾


          o § Privatisation/Privateering⠀➾


                # ⚓ Bruce Schneier ☛ NSO_Group’s_Pegasus_Spyware_Used_against
                  Thailand_Pro-Democracy_Activists_and_Leaders⠀⇛


          o § Security⠀➾


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


                       Security updates have been issued by Fedora
                       (buildah), SUSE (dovecot23 and nodejs12), and
                       Ubuntu (harfbuzz, libhttp-daemon-perl, tiff, and
                       webkit2gtk).


                # ⚓ USCERT ☛ CISA_released_Security_Advisory_on_MiCODUS_MV720
                  Global_Positioning_System_(GPS)_Tracker⠀⇛


                       CISA has released an Industrial Controls Systems
                       Advisory (ICSA) detailing six vulnerabilities that
                       were discovered in MiCODUS MV720 Global Positioning
                       System Tracker. Successful exploitation of these
                       vulnerabilities may allow a remote actor to exploit
                       access and gain control the global positioning
                       system tracker. These vulnerabilities could impact
                       access to a vehicle fuel supply, vehicle control,
                       or allow locational surveillance of vehicles in
                       which the device is installed.


                # ⚓ CISA ☛ MiCODUS_MV720_GPS_tracker_|_CISA⠀⇛


                       This advisory contains mitigations for Use of Hard-
                       coded Credentials, Improper Authentication, Cross-
                       site Scripting, and Authorization Bypass Through
                       User-controlled Key vulnerabilities in the MiCODUS
                       MV720 GPS tracker.


          o § Civil Rights/Policing⠀➾


                # ⚓ Public Knowledge ☛ Public_Knowledge_Urges_Committee_To
                  Support_American_Data_Privacy_and_Protection_Act_–_Public
                  Knowledge⠀⇛


                       Last night, the House Energy and Commerce Committee
                       announced a markup for the “American Data Privacy
                       and Protection Act,” a bipartisan, bicameral bill
                       introduced by Frank Pallone, Jr., (D-NJ), Cathy
                       McMorris Rodgers (R-WA), Jan Schakowsky (D-IL), and
                       Gus Bilirakis (R-FL) to establish a national
                       standard to protect consumer data privacy.


                       As written, the bill would impose restrictions on
                       how businesses (and not just Facebook or Google)
                       can collect, use, and share consumer data, as well
                       as allow for federal, state, and individual
                       enforcement to protect consumers’ rights. Public
                       Knowledge urges the committee to report this bill
                       favorably to the House for a floor vote.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Public Domain Review ☛ Visualising_Bubbles_
                        (1500–1922)_–_The_Public_Domain_Review⠀⇛


                             Like the substance itself, which binds to all
                             kinds of grime, soap bubbles make for sticky
                             symbols, assuming disparate associations —
                             from innocence to vanitas, physics to
                             politics — in the history of visual art.


                             We have entered the dog days of July in the
                             Northern Hemisphere, with a heat wave
                             bringing Europe to a rolling boil, and
                             thoughts of sea, shade, or cooler climes to
                             many people’s minds. Writing of a shadowed
                             garden, Spanish poet Luis Cernuda (in Stephen
                             Kessler’s translation) captures the lethargy
                             of this weather and the pleasures of relief:
                             how the summer atmosphere can feel “light,
                             afloat; the world turning slowly, like a soap
                             bubble, delicate, iridescent, unreal”. While
                             soap froth has existed since at least the
                             time of Mesopotamia, the fragility,
                             iridescence, and impermanence that Cernuda
                             describes started to bubble into the West’s
                             visual imagination during the sixteenth
                             century. Like the substance itself, which
                             binds to all kinds of grime, soap bubbles
                             make for sticky symbols, assuming disparate
                             associations — from innocence to vanitas,
                             physics to politics — in the artist’s eye.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ SpellBinding:_ABPKNOE_Wordo:_CHAFF⠀⇛


          o § Technical⠀➾


                # ⚓ How_to_use_Docker_from_a_Linux_host_system_to_escalate_to
                  root⠀⇛


                       It’s often said Docker is not very good with regard
                       to security, let me illustrate a simple way to get
                       root access to your Linux system through a docker
                       container. This may be useful for people who would
                       have docker available to their user, but whose
                       company doesn’t give them root access.


                       This is not a Docker vulnerability being exploited,
                       just plain Docker by design. It is not a way to
                       become root from *within* the container, you need
                       to be able to run docker on the host system.


                       If you use this to break against your employer
                       internal rules, this is your problem, not mine. I
                       do write this to raise awareness about why Docker
                       for systems users could be dangerous.


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



                    ䷩ 𝚕𝚒𝚗𝚎 7278

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.19.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_19/07/2022:_Qubes_OS_4.1.1_and_Ubuntu_21.10_End_of_Life⠀✐


Posted in News_Roundup at 4:20 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o New_Releases
          o Arch_Family
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o Programming/Development
    * Leftovers
          o Monopolies
                # Patents
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ Linux Handbook ☛ 9_Best_Free_Website_Downtime_Monitoring
                  Services [Ed: One can set up one's own instead of
                  outsourcing]⠀⇛


                       It is crucial to monitor the availability of your
                       website if you do not want your readers/customers
                       to go away.


                       Whether it is an online business or a blog, website
                       downtime can hurt your website’s online presence.


                       It is also helpful to know if you picked the right
                       server for your website if you are aware of the
                       downtime. If your server is down for a long time at
                       regular intervals, you need to identify what’s
                       wrong with the server (or the configuration).


                       Honestly, it is not always a malicious actor or an
                       issue with a technology that you use; sometimes,
                       it’s just the server that’s at fault.


          o § Audiocasts/Shows⠀➾


                # ⚓ Tux Digital ☛ 287:_Customizing_Your_Terminal_to_be_a_1337
                  h@x0r_–_Destination_Linux_–_TuxDigital⠀⇛


                       This week’s episode of Destination Linux, we’re
                       going to be pimping out our terminals. We’re going
                       to give you all the tips you need to look like an
                       elite hacker even if you only know apt update and
                       apt upgrade. Then we will be discussing water
                       cooling your Linux laptop. Plus, we have our tips/
                       tricks and software picks. All this and more coming
                       up right now on Destination Linux to keep those
                       penguins marching!


          o § Applications⠀➾


                # ⚓ OMG Ubuntu ☛ Curtail_is_an_Awesome_Image_Compressor_Tool
                  for_Linux_–_OMG!_Ubuntu!⠀⇛


                       Running a blog like this means I need to keep one
                       eye on the size of screenshots I use in posts — the
                       smaller the images I upload the faster the page
                       loads for you.


                       Thus having access to a good image compressor tool
                       is a must.


                       Thankfully for those of us being mindful of
                       bandwidth we are spoilt for choice. Not only is
                       there a broad range of image compression apps for
                       Linux, from powerful CLI type through to noob-proof
                       GUI ones, there’s also a veritable surfeit of
                       online compressors (including superbly useful
                       Squoosh, which can work offline).


                       Thing is, I prefer desktop apps where possible.


          o § Instructionals/Technical⠀➾


                # ⚓ FOSSLinux ☛ How_to_use_systemd_in_Debian_|_FOSS_Linux⠀⇛


                       Systemd is a well-known Linux system and service
                       manager. Since Debian 8, systemd has been the
                       default init system. It is compatible with both
                       SysV and LSB init scripts. Therefore it can take
                       the place of sysvinit in some situations.


                # ⚓ FOSSLinux ☛ How_to_start_GNOME_desktop_from_command_line_in
                  Debian_|_FOSS_Linux⠀⇛


                       GNOME, an acronym for the GNU Network Object Model
                       Environment, is a graphical user interface and set
                       of computer desktop apps for Linux OS users. It is
                       aimed at making Linux OS an easy-to-use OS for non-
                       programmers. With GNOME, you can set the interface
                       to look like Windows or macOS. GNOME is a free and
                       non-proprietary desktop environment for all the
                       major Linux distros, including Fedora Linux,
                       Debian, Ubuntu, Enterprise Linux, Red Hat, SUSE,
                       and others.


                       On the other hand, a command-line alias cmd, CLI,
                       prompt, console, or terminal refers to a text-based
                       user interface (UI) utilized in viewing,
                       manipulating, handling, running programs, and
                       managing comp files as interacting with the
                       computer. It is much like Windows Explorer or
                       Finder on the macOS but without the graphical
                       interface.


                       GNOME has emerged as the most efficient, reliable,
                       and stable of all the available desktop
                       environments for Linux while retaining its user-
                       friendliness features. GNOME began as a free and
                       open desktop alternative to proprietary options
                       like KDE at the time, and it has been going strong
                       ever since.


                # ⚓ UNIX Cop ☛ How_To_Install_Sublime_Merge_on_Ubuntu_20.04_|
                  22.04_LTS⠀⇛


                       In this guide, we will show you how to install
                       Sublime Merge on Ubuntu systems


                       Sublime Merge is a git client. It allows to read a
                       git repository in order to display the differential
                       of the last modifications, the list of submissions
                       (commits) and the branches, among other things.


                       It is possible to submit (push) and retrieve (pull)
                       modifications from the interface


                       Sublime Merge includes a command line tool, smerge,
                       to work with repositories on the command line. This
                       can be used to open repositories, search, and merge
                       files.


                # ⚓ UNIX Cop ☛ How_to_Install_Strawberry_on_Ubuntu_20.04_|
                  22.04_LTS⠀⇛


                       In this guide, we will show you how to install
                       Strawberry in Ubuntu systems.


                       Strawberry is a free audio player for Linux , macOS
                       and Windows. Strawberry has now been ported to Qt 6
                       and is therefore available for the three major
                       desktop operating systems. It is a music player and
                       collection organizer focused on cataloging your
                       music collection.


                # ⚓ UNIX Cop ☛ How_to_Install_Zim_Desktop_Wiki_on_Ubuntu_20.04
                  |_22.04_LTS⠀⇛


                       In this article, we will illustrate how to install
                       Zim Desktop wiki on Ubuntu Systems.


                       Zim is a graphical text editor used to maintain a
                       collection of wiki pages. Each page can contain
                       links to other pages, simple formatting and images.
                       Pages are stored in a folder structure, like in an
                       outliner, and can have attachments. Creating a new
                       page is as easy as linking to a nonexistent page.
                       All data is stored in plain text files with wiki
                       formatting. Various plugins provide additional
                       functionality, like a task list manager, an
                       equation editor, a tray icon, and support for
                       version control.


                # ⚓ UNIX Cop ☛ How_to_Install_WoeUSB_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       In this guide, we will install WoeUSB on Ubuntu
                       systems


                       WoeUSB is a free, open-source simple tool that
                       enables you to create your own USB stick windows
                       installer from an iso image or an actual DVD. I
                       have used it myself to create bootable USB sticks
                       for installing Windows from ISO images, and it has
                       worked flawlessly every time. The interface is
                       straightforward to use.


                       It is a simple tool that enable you to create your
                       own usb stick windows installer from an iso image
                       or a real DVD.


                # ⚓ UNIX Cop ☛ How_to_Install_DeaDBeeF_Player_on_Ubuntu_20.04_|
                  22.04_LTS⠀⇛


                       In this article, we will illustrate how to install
                       DeaDBeef player on Ubuntu systems


                       DeaDBeeF (as in 0xDEADBEEF) is a modular cross-
                       platform audio player which runs on GNU/Linux
                       distributions, macOS, Windows, *BSD, OpenSolaris,
                       and other UNIX-like systems.


                       DeaDBeeF plays a variety of audio formats, converts
                       between them, lets you customize the UI in almost
                       any way you want, and use many additional plugins
                       which can extend it even more.


                # ⚓ Linux Capable ☛ How_to_Install_Arduino_IDE_on_Ubuntu_22.04
                  LTS⠀⇛


                       The Arduino IDE is free and open-source software to
                       write and upload your programming code. It consists
                       of an editor with features like assisted editing
                       enabled by the compiler so you can do everything
                       from within one program without switching between
                       files or windows as often – it does help streamline
                       things! The tool also enables better compiling
                       because errors will be noticed before uploading.
                       This means less time wasted on coding and more time
                       spent on the project.


                       In the following tutorial, you will learn how to
                       install Arduino IDE on Ubuntu 22.04 LTS Jammy
                       Jellyfish desktop with APT, Snap, or Flatpak method
                       using the command line terminal along with
                       instructions on how to update and remove the
                       software in the future if required.


                # ⚓ Linux Capable ☛ How_to_Install/Enable_FirewallD_GUI_on
                  Rocky_Linux_9⠀⇛


                       Rocky Linux is a security-focused distribution that
                       offers users a robust firewall feature with
                       FirewallD. For users accustomed to a Graphical User
                       Interface (GUI), the command line may seem daunting
                       because there is no visual representation. However,
                       for those willing to learn the commands, FirewallD
                       provides an easy way to control the firewall and
                       disable or enable access to ports, services, or
                       protocols. The software is also highly customizable
                       so that users can tailor the firewall to their
                       specific needs.


                       The following tutorial will teach you how to
                       install and enable FirewallD and install FirewallD
                       GUI on Rocky Linux 9 using the command line
                       terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Vivaldi_Browser_on_Rocky
                  Linux_9⠀⇛


                       Vivaldi is a freeware, cross-platform web browser
                       developed by Vivaldi Technologies. It was created
                       in response to the decline of Opera, as many users
                       were disgruntled when it switched from the Presto
                       layout engine to a Chromium-based browser. Vivaldi
                       is built on the Chromium platform and shares many
                       features with Google Chrome, but it also has some
                       unique features that set it apart. These include
                       built-in email and calendar functionality and
                       advanced tab management options. Vivaldi is also
                       highly customizable, allowing users to change the
                       look and feel of the browser to suit their
                       preferences. As a result of its unique features and
                       user-friendly interface, the browser has become one
                       of the most popular alternative web browsers on the
                       market.


                       In the following tutorial, you will learn how to
                       install Vivaldi Browser on Rocky Linux 9 using the
                       command line terminal and the option of Vivaldi
                       stable or Vivaldi snapshot browser versions and how
                       to maintain and remove it in the future.


                # ⚓ Linux Shell Tips ☛ How_to_Find_If_My_Linux_System_Runs_on
                  SSD_or_HDD⠀⇛


                       So why would you want to find out whether your
                       Linux system is running on SSD or HDD? There are
                       various valid reasons for this question.


                       Firstly, you might not be tech-savvy enough to
                       understand the hardware infrastructure associated
                       with your Linux system. Secondly, knowing whether
                       your Linux system runs on SSD or HDD helps set
                       reasonable performance expectations for your Linux
                       machine.


                # ⚓ Trend Oceans ☛ How_to_Restrict_Script/Application
                  Permission_using_AppArmor_on_Ubuntu/Debian_–_TREND_OCEANS⠀⇛


                       AppArmor is a Debian-based Mandatory Access Control
                       (MAC) system alternative to SELinux (for RedHat,
                       Fedora, CentOS, AlmaLinux, etc.), allowing you the
                       ability to restrict certain applications or scripts
                       from doing certain things or allowing access to
                       certain resources.


                # ⚓ Linux Shell Tips ☛ How_to_Copy_Directory_Structure_Without
                  Files_in_Linux⠀⇛


                       In this article you’ll learn about AppArmor and how
                       to create a profile for a user-generated script or
                       application, and modify or update permissions for
                       an already existing profile.


                       [...]


                       However, in some scenarios, you might want to mimic
                       a certain directory structure that already exists
                       maybe for your personal projects or for a files
                       storage system just because that directory
                       structure makes perfect sense and might require a
                       lot of time to completely recreate it from scratch.


                       This article will walk us through valid approaches
                       to copying an empty directory structure from
                       already populated directory files in Linux.


                # ⚓ Linux Capable ☛ How_to_Install_PostgreSQL_14_on_Rocky_Linux
                  9⠀⇛


                       PostgreSQL is a robust, stable, and reliable open-
                       source database management system that has been in
                       use for over 20 years. It’s backed by an active
                       community of developers who contribute their time
                       and expertise to its development, resulting in
                       higher levels of resilience, integrity, and
                       correctness. PostgreSQL powers many web
                       applications, including those from Google Earth
                       Engine Geospatial datastore for analytics software
                       like Tableau. Its features include horizontal
                       scalability, robust SQL compliance, and advanced
                       data types such as JSON and XML support. In
                       addition, PostgreSQL is open source software,
                       meaning it can be freely used, modified, and
                       distributed. As a result, it’s an attractive option
                       for powering large-scale web applications.


                       The following tutorial will teach you how to
                       install PostgreSQL 14 on Rocky Linux using the
                       command line terminal and some basic configuration
                       and setup tips.


                # ⚓ Its FOSS ☛ How_to_Install_Discord_on_Manjaro_and_Arch
                  Linux⠀⇛


                       Discord is a cross-platform application that can be
                       used for voice calling, video calling, text
                       messaging, and sharing media and files.


                       It is extremely popular among gamers and streamers.
                       Although, many open source projects have started
                       using it for hosting their community discussion.
                       You can find official Discord servers for such open
                       source communities.


                       Discord can be accessed straight from your web
                       browser. Installing the official desktop client
                       gives you system notifications and focused
                       communication rather than fumbling for the Discord
                       tab among multiple opened tabs.


                # ⚓ Linux Shell Tips ☛ What’s_the_Difference_Between_Grep,_Sed,
                  and_Awk_Commands⠀⇛


                       We cannot confidently call ourselves Linux file
                       management experts without the mastery of text
                       processing. Three known command-line tools (grep,
                       sed, and awk) have built their reputation as Linux
                       text processors. They come pre-installed on all
                       major Linux operating system distributions hence no
                       need to query their existence via a Linux package
                       manager.


                       Despite grep, sed, and awk commands being uniquely
                       attributed in their text processing
                       functionalities, some simple scenarios force their
                       functionalities to slightly overlap.


                       For instance, all these three commands can
                       comfortably query the possibility of a file pattern
                       match and forward the query results to standard
                       output.


                # ⚓ Linux Capable ☛ How_to_Install_Microsoft_Edge_Browser_on
                  Rocky_Linux_9 [Ed: Bad idea. It’s spyware and a passwords
                  stealer.]⠀⇛


                # ⚓ TecAdmin ☛ How_to_Install_Grunt_on_Ubuntu_22.04_&_20.04_–
                  TecAdmin⠀⇛


                       Grunt is a node-based task runner that helps
                       developers automate common tasks during the
                       software development process. It can be used to
                       compile code, run tests, and more. grunt is easy to
                       install and configure, and it can be used with any
                       programming language.


                       Grunt is available as a free, open-source tool,
                       that is typically used in conjunction with other
                       tools, such as Git and npm. A grunt is a powerful
                       tool that can help developers save time and improve
                       their workflow.


                       In this blog post, you will learn to install Grunt
                       on Ubuntu systems.


                # ⚓ H2S Media ☛ Fix_error:_Unable_to_parse_package_file_/var/
                  lib/dpkg/status⠀⇛


                       Linux distros come with lots of possibilities to
                       develop new innovative ideas, however, while doing
                       that you may face some errors, especially the
                       newbies, who are yet developing skills to become a
                       proficient Linux user… Out of hundreds of errors
                       that may appear in Linux OS due to any bug or
                       because of our mistakes, recently I faced the one:
                       here is that:


                       W: Unable to parse package file /var/lib/dpkg/
                       status (1)
                       E: The package lists or status file could not be
                       parsed or opened.
                       W: _cache->open() failed, please report.


                       I got this error because, by mistake, I deleted the
                       Status file, the reason for this error in your case
                       might be different.


                # ⚓ HowTo Forge ☛ How_to_Install_OpenLDAP_on_Ubuntu_22.04⠀⇛


                       OpenLDAP is a software implementation of the
                       Lightweight Directory Access Protocol (LDAP). This
                       guide will teach you how to set up LDAP Server with
                       OpenLDAP and LDAP Account Manager on the Ubuntu
                       22.04 server. This guide also will teach how to set
                       up LDAP users and how to set up an LDAP Account
                       Manager for managing the OpenLDAP server.


    * § Distributions and Operating Systems⠀➾


          o § New Releases⠀➾


                # ⚓ Qubes_OS_4.1.1_has_been_released!_|_Qubes_OS⠀⇛


                       We’re pleased to announce the stable release of
                       Qubes 4.1.1! This release aims to consolidate all
                       the security patches, bug fixes, and upstream
                       template OS upgrades that have occurred since the
                       initial Qubes 4.1.0 release in February. Our goal
                       is to provide a secure and convenient way for users
                       to install (or reinstall) the latest stable Qubes
                       release with an up-to-date ISO.


          o § Arch Family⠀➾


                # ⚓ [nonsystemd]_NetworkManager,_dbus_and_display_managers
                  require_manual_intervention⠀⇛


                       We have recently began a repackaging of
                       [nonsystemd] packages (see #3290). The
                       displaymanager-openrc package has been removed and
                       specific init scripts have been added for their
                       respective display manager (e.g. sddm-openrc for
                       sddm, gdm-openrc for gdm and so on with lxdm, xdm
                       and lightdm)


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Ubuntu_Fridge_|_Ubuntu_21.10_(Impish_Indri)_End_of_Life
                  reached_on_July_14_2022⠀⇛


                       This is a follow-up to the End of Life warning sent
                       earlier to confirm that as of July 14, 2022, Ubuntu
                       21.10 is no longer supported. No more package
                       updates will be accepted to 21.10, and it will be
                       archived to old-releases.ubuntu.com in the coming
                       weeks.


                       The original End of Life warning follows, with
                       upgrade instructions:


                       Ubuntu announced its 21.10 (Impish Indri) release
                       almost 9 months ago, on October 14, 2021, and its
                       support period is now nearing its end. Ubuntu 21.10
                       will reach end of life on July 14, 2022.


                # ⚓ Ubuntu_21.10_(Impish_Indri)_End_of_Life_reached_on_July_14
                  2022⠀⇛


                # ⚓ LWN ☛ Ubuntu_21.10_is_no_longer_supported_[LWN.net]⠀⇛


                       The Ubuntu 21.10 (“Impish Indri”) release is no
                       longer supported as of July 14; users who are on
                       that version will want to look into upgrading soon.


                # ⚓ Ubuntu_Fridge_|_Ubuntu_Weekly_Newsletter_Issue_744⠀⇛


                       Welcome to the Ubuntu Weekly Newsletter, Issue 744
                       for the week of July 10 – 16, 2022.


                # ⚓ Ubuntu_Weekly_Newsletter_Issue_744⠀⇛


          o § Open Hardware/Modding⠀➾


                # ⚓ CNX Software ☛ CrowPi_L_Raspberry_Pi_4_laptop_review_–_Part
                  1:_Unboxing_and_teardown_–_CNX_Software⠀⇛


                       Elecrow CrowPi L is an 11.6-inch laptop shell based
                       on Raspberry Pi 4 designed for STEM education with
                       optional electronics modules and tutorials. That’s
                       an evolution of the CrowPi 2 laptop I reviewed in
                       2020 with a thinner design and more flexible since
                       the electronics modules are optional, so it can
                       serve the market of people just wanting a Raspberry
                       Pi 4 laptop.


                       The company has sent me a full “CrowPi L Advanced
                       Kit” for review with the CrowPi L laptop fitted
                       with a Raspberry Pi 4, as well as the Crowtail
                       Starter Kit for Raspberry Pi.


                # ⚓ Arduino ☛ Move_this_custom_robotic_arm_through_a
                  touchscreen_interface_|_Arduino_Blog⠀⇛


                       Normally, robotic arms are controlled by a GUI
                       running on a host PC, or with some kind of analog
                       system that maps human inputs to various degrees of
                       rotation. However, Instructables user Maurizio
                       Miscio was able to build a custom robotic arm that
                       is completely self-contained — thanks to companion
                       mobile app that resides on an old smartphone housed
                       inside a control box.


                       Miscio started his project by making 3D models of
                       each piece, most of which were 3D-printed. These
                       included the gripper, various joints that each give
                       a single axis of rotation, and a large circular
                       base that acts as a stable platform on which the
                       arm can spin. He then set to work attaching five
                       servo motors onto each rotational axis, along with
                       a single SG90 micro servo motor for the gripper.
                       These motors were connected to an Arduino Uno that
                       also had an HC-05 Bluetooth® serial module for
                       external communication.


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


          o ⚓ Trend Oceans ☛ What_is_Open_Source_and_why_should_you_support
            them_–_TREND_OCEANS⠀⇛


                 Consider what would happen if you were using one of the
                 software applications that you have purchased by paying a
                 hefty amount to the company and which you have been using
                 for a decade without any issues.


                 Although you know, this was the only application that
                 could do specific work, and there was no alternative
                 option to this application available on the market.
                 Therefore, you couldn’t even imagine your life without
                 that software.


                 But unfortunately, one day, the company announced that we
                 will not provide further updates or support to this
                 particular application because they are shutting down
                 their company due to some internal conflict.
                 You will be under immense stress after hearing the
                 announcement and finding a way out of this situation but
                 you can’t do that because you don’t have the necessary
                 resources to update an application.


                 Now you are stuck in the middle of nowhere.


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ These_Weeks_In_Firefox:_Issue_120_–_Firefox_Nightly
                        News⠀⇛


                             Dale Harvey implemented an experimental Quick
                             Actions feature in the Address Bar


          o § Programming/Development⠀➾


                # ⚓ Qt ☛ The_Ability_to_Modify_the_Qt_Source_Code_–_Does_it
                  Matter? [Ed: Qt is now misframing the subject of software
                  freedom by pretending it's about "Ability to Modify... Source
                  Code"]⠀⇛


                       Yes, you can modify the source code of the Qt
                       framework. You can also distribute products using
                       the modified source code, as long it is in object
                       form. You can also share the modified source code
                       with the Qt Company for possible inclusion in
                       upcoming releases.


                # ⚓ DEV Community ☛ Afshan_Ahmed_Khan:_Outreachy:_Mid_way_blog
                  post⠀⇛


                       Time flies ! Now I have reached to middle of my
                       outreachy internship. This blog post will throw
                       some light on my journey till now .


    * § Leftovers⠀➾


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ IT Wire ☛ Sales_of_some_Oppo,_OnePlus_models_in
                        Germany_hit_by_lawsuit⠀⇛


                             Some models of Oppo and OnePlus mobile phones
                             will not be sold in Germany following a
                             ruling by a Mannheim court in favour of
                             Finnish telecommunications equipment vendor
                             Nokia over a patent.


                             The ruling, by a regional court in the
                             southwestern German city, was the second in
                             as many months and said Oppo’s use of some 5G
                             and 4G technologies infringed Nokia’s
                             patents, according to a report in the South
                             China Morning Post, which cited a statement
                             from the Finnish firm.


                             The first ruling was issued in June. Oppo and
                             OnePlus are both owned by Chinese firm B.B.K.
                             Electronics which also owns the vivo, realme
                             and iQoo brands.


                             Oppo constantly ranks as the fourth selling
                             smartphone brand after Apple, Samsung and
                             Xiaomi. Neither Nokia nor Oppo’s owners have
                             issued a public statement about the case.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Prefiguring_community⠀⇛


                       I’ve been calling myself an anarchist for all these
                       years, and I feel like a colossal hypocrite for
                       putting so much of my energy into fighting
                       (occasionally viscous fights) to make “leftist”
                       spaces “more prefigurative”¹ while I neglected
                       building more of the kinds of relationships that
                       are going to get me through the coming decades.


          o § Technical⠀➾


                # ⚓ A_screed_against_modern_consumer_electronics⠀⇛


                       So I’m watching this video on a mouse/scanner combo
                       thing when at the very end, Cathode Ray Dude [1]
                       goes on a rant about the companies that make modern
                       consumer electronics [2] that I found amusing. I
                       also think it’s a sad state of affairs that I agree
                       with his sentiment that most consumer electronic
                       companies exist just to get bought out and not to
                       sell a viable product.


                # § Internet/Gemini⠀➾


                      # ⚓ BBS_with_Gemtext_Frontend_(idea)⠀⇛


                             I run a BBS (Bulletin Board System) on the
                             Mystic BBS software which I find fun because
                             it brings back memories of connecting to BBS
                             when I was much younger before the Internet
                             was popular.


                             It is nostalgic to see the chuncky text and
                             ansi graphics when I connect using a client
                             like Netrunner or Syncterm however most of
                             the time, I am not interested in the
                             nostalgia but just to connect quickly to
                             check for messages or any new activity.


                             Since discovering gemini, this has stolen
                             some of the time that I previously would have
                             spent working on the BBS or chatting there or
                             other improvements.


                      # ⚓ Update_on_Squid’s_World⠀⇛


                             I want to increase the amount that I interact
                             in a positive way with others in the
                             Geminispace, which includes promoting more of
                             what other people are working on, and
                             understanding and respecting the motivations
                             for those others who are using this tech


                      # ⚓ Re:_Thoughts_on_RSS⠀⇛


                             Even the negatives on his list seem like huge
                             positives.


                             Technically, he’s wrong here; there’s nothing
                             stopping an RSS feed from getting slathered
                             in JavaScript and CSS and there are many
                             reading apps that will display that.


                             But culturally, that practice isn’t very
                             widespread, thankfully, and RSS (including
                             Atom) has been a readers’ bastion similar to
                             what we have here on Gemini. This is a good
                             thing, not a bad.


                             I’ve always seen Gemini as kind of similar to
                             RSS; another way to publish your stuff,
                             that’s more reader-friendly. Friendlier to
                             mashups, ebook exports, tours, offline, your
                             own styling, your own font choices, a clean
                             and consistent typography that goes across
                             sites, not just your own.


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


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