𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, September 29, 2022
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Generated Fri 30 Sep 02:44:55 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
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Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
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Gemini index for the day: gemini://gemini.techrights.org/2022/09/29/


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

⦿ Facts About the European Patent Office and Why Recruiting/Retaining Capable Examiners Isn’t Possible Anymore | Techrights

⦿ EPO Management Plans to Further Accelerate Grants of Illegal, Invalid, Fake European Patents Next Year | Techrights

⦿ [Meme] EPO Would Probably Argue It’s Just a Coincidence That “Women Have Received, on Average, Only 0.88 Steps to Every 1 Step Awarded to Men” | Techrights

⦿ IRC Proceedings: Wednesday, September 28, 2022 | Techrights

⦿ No Protection for Linux Offered by the So-called ’Linux’ Foundation | Techrights

⦿ The Linux Foundation is in No Position to Lecture Us (or Anybody) on Diversity | Techrights

⦿ Software Freedom Conservancy (SFC) is Facilitating a Hostile Takeover by Corporations (Privatising Free Software) | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/09/29/capable-examiners-leaving/#comments
		http://techrights.org/2022/09/29/epo-bogus-patents/#comments
		http://techrights.org/2022/09/29/epo-misogyny/#comments
		http://techrights.org/2022/09/29/irc-log-280922/#comments
		http://techrights.org/2022/09/29/no-protection-for-linux-from-monopolies/#comments
		http://techrights.org/2022/09/29/the-linux-foundation-is-in-no-position-to-lecture-us-or-anybody-on-diversity/#comments
		http://techrights.org/2022/09/29/video-on-sourceware/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/09/29/avidemux-2-8-1/#comments
		http://techrights.org/2022/09/29/progress-on-gnome-43/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 66

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/29/capable-examiners-leaving/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/29/capable-examiners-leaving/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Facts_About_the_European_Patent_Office_and_Why_Recruiting/Retaining_Capable
Examiners_Isn’t_Possible_Anymore⠀✐


Posted in Europe, Patents at 4:13 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 7e85aabf781dae691a2e707de1787fb6
EPO by the Numbers
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-data-on-compensation.webm


Summary: A couple of new papers (or parts of a long paper) reveal an office
responsible for granting patents which intentionally fails to do the job
properly


THE video above shows that the EPO barely publishes anything anymore, except
maybe once a week. The latest fluff (warning: epo.org link) is just misleading
two-paragraph propaganda about an illegal and unconstitutional ploy called
Unified Patent Court (UPC). With many obstacles ahead, those words won’t age
well.


But much of the video then deals with Parts 3 and 4 of a multi-part paper (see
first_and_second_part) from the staff representatives. It’s shown in a hurry
(see this [PDF] and that [PDF]). It contains many charts and demonstrates the
appalling conditions, which discourage suitably-qualified people from joining
the EPO and even just staying at the EPO.


epo.org is still a parade of lies, but it has lost momentum. The EPO itself is
an_imploding_bubble, having granted far too many invalid patents, whose harm
will be seen in decades to come.


To quote the The Central Staff Committee’s message to staff:


     § Rewards Exercise 2022: Reduction of the budget and comparing
     populations⠀➾


     Dear colleagues,


     Every July the Office proudly announces the results of the yearly
     reward exercise. This year was no different, with the Office’s
     publication concerning the reward exercise of 2022 “Celebrating
     outstanding achievements with an inclusive approach”. In an effort to
     improve the transparency of the practice, the annual announcement is
     accompanied by a document containing the detailed statistics, which
     provide breakdowns of different divisions of our EPO population. We
     appreciate having access to the data, since it allows for an analysis
     of the distribution of the rewards despite being far from complete
     (i.e. lacking data on functional allowances).


     The staff representation has carefully examined the data provided
     this year and for previous years and has initiated a short series of
     publications (part 1, part 2) detailing our analysis. The next are:


     Part three: Reduction of the budget


     Part four: Comparing populations


     Over the coming weeks, subsequent editions in this series on the
     rewards exercise will be published that take a closer look at a
     number of topics that have given us cause for concern.


     Sincerely yours,


     The Central Staff Committee – CSC


In the next post we’ll show that António_Campinos is already being contacted
regarding the plan to grant loads of European Patents illegally. █



                    ䷩ 𝚕𝚒𝚗𝚎 167

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/29/epo-bogus-patents/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/29/epo-bogus-patents/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EPO_Management_Plans_to_Further_Accelerate_Grants_of_Illegal,_Invalid,_Fake
European_Patents_Next_Year⠀✐


Posted in Europe, Patents at 4:41 pm by Dr. Roy Schestowitz


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Unsustainable productivity increase of +10% for 2023⦈


Summary: The EPO has quit behaving like a patent office; it’s just issuing a
lot of bogus patents to meet pre-defined “targets” and then it_bullies
examiners_into_blind_compliance


AS noted earlier this evening, the EPO‘s “f***king president” (that’s what he
calls himself) António_Campinos plans to grant even more illegal patents. Why
is this being tolerated?


Well, examiners aren’t tolerating this. The Central Staff Committee (CSC) has
just told staff that “historically low compliance rate of granted patents
(73.3%) contrasts with the overall production plan for 2023″ (those plans are
just marketing and lies).


Here’s the message to staff:


     § Unsustainable productivity increase of +10% for 2023⠀➾


     Dear colleagues,


     In this open letter we urge the President to refrain from imposing
     yet another productivity increase of +10% on staff. A historically
     low compliance rate of granted patents (73.3%) contrasts with the
     overall production plan for 2023: more production, fewer staff,
     purely top-down planning.


     We appeal for common sense, in view of the future of the European
     patent system, the reputation of the EPO and, of course, in the
     interest of the staff.


And here’s the corresponding open letter:


     Reference: sc22124cl
     Date: 22.09.2022


     European Patent Office | 80298 MUNICH | GERMANY


     Mr António Campinos
     President of the EPO


     By email


     OPEN LETTER


     § Unsustainable productivity increase of +10% for 2023⠀➾


     Dear Mr President,
     In a speech held on 13 September 2022 in front of Master students at
     the University of Alicante, you stressed the importance of delivering
     high-quality patents for entrepreneurs, inventors and investors. The
     EPO is, however, currently far from its own high-quality objectives:
     the audit compliance rate for granted patents is historically low at
     73.7% (figures of end of June 2022), below the 2022 target of 85% and
     far below the target of 95% in the Strategic Plan 2023.


     The DG 1 overall production plan for 2023 recently announced at
     operational level will further worsen the situation: more production
     is to be achieved from fewer staff, the planning will be purely top-
     down and a steep increase in productivity of around +10% is
     requested.


     The steep increase in productivity is presented as justified by the
     need to catch-up with the current salary adjustment procedure – the
     result for the year 2022 will be around 10% because of the high
     Eurozone inflation. This argument is a misrepresentation of the
     financial bundle of measures (CA/18/20) approved by the Council on
     the basis of the Mercer Financial Study 2019 (CA/83/19). It is the
     biennial adjustment of the EPO fees (and not productivity) which
     shall be inflation based.


     Digitization and IT tools are also said to help to achieve this
     increase in productivity. The Central Staff Committee sincerely
     doubts in view of recurring complaints from staff on the lack of
     ergonomics of many tools, repetitive outages and automation not
     developing as expected.


     The Strategic Plan 2023 is coming to an end soon, which may tempt the
     Office to present positive results deriving from it to the
     Administrative Council. However, imposing yet another productivity
     increase of +10% is neither justified nor sustainable to improve the
     quality of EPO granted patents.


     The Central Staff Committee urges you to refrain from continuing in
     this direction – in the interest of the European patent system, the
     reputation of the EPO and its staff.


     Yours sincerely,


     Michael Sampels
     Acting Chairman of the Central Staff Committee


He’ll probably just ignore such letters; just like he ignores_demands_to_comply
with_a_court's_ruling. █


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⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 340

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/29/epo-misogyny/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/29/epo-misogyny/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_EPO_Would_Probably_Argue_It’s_Just_a_Coincidence_That_“Women_Have
Received,_on_Average,_Only_0.88_Steps_to_Every_1_Step_Awarded_to_Men”⠀✐


Posted in Europe, Patents at 4:24 pm by Dr. Roy Schestowitz


Maybe the EPO’s management has a very simplistic view of women’s technical
capabilities


           🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇People that the EPO isn't promoting⦈


Summary: Women barely_get_promotions at the EPO (“men are 54% more likely to
receive a double step compared to women”); the EPO keeps storytelling to
distract from these measurable facts


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⣀⢀⡀⣀⡀⠀⣀⡀⡀⢘⠙⢉⡃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣾⠹⠈⣐⠉⢉⠁⠉⢶⣴⢿⡿⠢⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠋⠛⠛⠋⠈⠙⠛⠙⠋⠛⠉⠉⠙⠛⠛⠉⠉⠈⠉⠃⠂⠘⠚⠀⠂⠀⠁⠁⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣤⣤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⢰⣜⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠜⠿⠒⢈⢨⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠨⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡟⠁⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⡻⠆⠀⠀⠀⢻⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠉⠁⠹⠿⣿⡏⠀⠀⠁⠀⠀⠀⢹⢷⡗⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣄⡀⠀⢀⠀⠛⢿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣶⣶⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠈⠁⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠀⠀⠀⣿⡿⠿⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⢀⣿⣿⣿⢿⣃⣀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⣘⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⢻⡇⠀⢸⣿⢹⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⣿⣧⣄⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣿⡟⢻⣿⠀⢸⣿⠀⠀⢀⡀⣿⡇⣀⢸⣿⢸⣿⠀⣿⣧⣿⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣹⣷⣶⡆⠀⠀⠀⢨⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⢈⣷⣿⣷⠀⠈⠀⠈⣿⠀⠀⣼⣷⣿⣷⡿⠾⡇⠀⠉⠀⣾⣿⣿⣾⣿⣿⣿⣤⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣜⠀⣿⣽⢹⡇⢠⡄⣤⣼⣿⣿⣿⣯⣤⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⣸⢠⣴⡿⢡⣴⡏⣟⣽⣿⣯⡋⣥⣤⣤⡄⣽⣯⡏⣿⡽⣽⡏⢟⣴⢶⣤⣻⡆
⣀⣀⣀⢸⣿⣀⣀⣿⣇⣸⣿⢸⣿⠀⣿⡇⣤⠀⣿⡇⢻⣧⣌⢩⣄⣿⣷⢸⡇⠈⠁⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⠟⣿⣿⠃⣿⡇⢸⡿⣷⣼⢻⡇⢿⣿⠀⣿⡟⠀⣿⡇⢰⢿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢻⡀
⣿⣿⣿⣿⣿⢩⣽⣿⣿⣭⣵⣾⣿⠀⣿⣿⣿⠀⣿⣷⣠⡍⣻⣷⢿⣿⣹⣿⡇⠀⠂⠀⣿⣿⣿⣿⣿⣿⠉⡍⠀⣿⡏⢹⣧⣿⣿⠀⣿⡇⢸⣧⣿⡿⣼⡇⣾⣿⠀⣿⣧⡆⣿⡇⣾⣼⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣷
⣿⣿⣿⣿⣿⣿⣏⣿⣟⣿⣿⣿⣿⠶⣟⣽⣿⠆⠿⡿⠘⠷⠾⣟⣿⠿⣡⠿⢇⠀⠀⠀⠿⣿⣿⣿⣿⡿⠀⠀⣆⣿⣇⣸⣿⣯⣿⠶⠟⠁⠸⢟⣸⣇⣿⣇⣯⡿⠶⣿⣽⡇⠿⠇⣿⣻⣿⣇⠿⣠⠿⢇⣞⠿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣛⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣭⣭⣭⣭⣭⣍⣉⣉⣩⣉⣩⣭⣭⣍⣉⣉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣽⣲⡔⣂⣜⣋⣝⣿⣞⡩⢏⣡⠙⢟⠑⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠧⡮⡀⣮⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⠙⠛⠛⠊⠉⠛⠋⠙⠛⠛⠋⠙⠙⠋⠙⠋⠉⠛⠃⠛⠛⠛⠁⠊⠉⠉⠀⠀⠈⠀⠀⠉⣂⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣲⣶⣾⣾⣲⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡯⡷⣿⣺⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢥⢿⣟⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠈⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢪⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⡗⠖⠀⠀⠈⢻⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠈⠁⠀⠹⠿⣿⡏⠀⠀⠁⠀⠀⠀⢹⣧⣣⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣄⡀⠀⢀⠀⠛⢿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣿⣦⣶⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠈⠃⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠀⠀⠀⠀⣿⠿⠿⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⢀⣿⣿⣿⠿⣋⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣀⣘⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣻⡇⠀⢸⣿⢹⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢿⡇⠀⢸⣿⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⣿⣧⣄⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣿⡟⢻⣿⠀⢸⣿⠀⠀⢀⡀⣿⡇⣀⢸⣿⢸⣿⠀⣿⣧⣿⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⣹⣷⣶⡆⠀⠀⠀⢨⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⢈⣷⣿⣷⠀⠈⠀⠈⣿⠀⠀⣼⣷⣿⣷⣿⡾⡇⠀⠁⠀⣾⣿⣿⣾⣿⣿⣷⣤⠀⠀⠀⠀⠀
⠁⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣴⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣜⠀⣿⣽⢹⡇⢠⡄⣤⣼⣿⣿⣿⣯⣤⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⣸⢠⣴⡿⢠⣴⡏⣟⣽⣿⣯⡋⣧⣤⣤⡄⣽⣯⡏⣿⡽⣽⡏⢟⣴⢶⣤⣻⡆
⣀⣀⣀⢸⣿⣀⣀⣿⣇⣸⣿⢸⣿⠀⣿⡇⣤⠀⣿⡇⢻⣧⣌⢩⣄⣿⣷⢸⡇⠈⠁⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⠇⣿⡇⢸⡿⣷⣼⢻⡇⢿⣿⠀⣿⡟⠂⣿⡇⢰⢿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢻⡀
⣿⣿⣿⣿⣿⢩⣽⣿⣿⣭⣵⣼⣿⠀⣿⣿⣿⠀⣿⣷⣠⡍⣻⣷⢿⣿⣹⣿⡇⠀⠂⠀⣿⣿⣿⣿⣿⣿⠉⡍⠀⣿⡏⢹⣧⣿⣿⠀⣿⡇⢸⣧⣿⡿⣼⡇⣾⣿⠀⣿⣧⡆⣿⡇⣾⣼⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣷
⣿⣿⣿⣿⣿⣿⣏⣿⣟⣿⣿⣿⣿⠶⣟⣽⣿⠆⠿⡿⠘⠷⠾⣟⣿⡿⣡⢿⢇⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⣆⣿⣗⣸⣿⣯⣿⠶⠟⠁⠸⣟⣸⣇⣿⣇⣯⡿⠶⣿⣽⡇⠿⠇⣿⣻⣿⣇⠿⣠⠿⢇⣞⠿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣭⣭⣭⣭⣭⣩⣩⣍⣉⣍⣉⣩⣍⣍⣉⣉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⡧⢨⢓⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡎⢇⣙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠙⠉⠙⠋⠛⠙⠛⠛⠋⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠻⠛⠛⠽⠙⠉⠛⠋⠁⠀⠀⠀⠈⣢⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣶⣤⣤⣴⣤⣶⣤⣤⣤⣤⣄⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⢷⣿⢚⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⡟⠁⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣏⡝⠀⠀⠈⢻⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠇⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠈⠉⠁⠹⢿⣿⡏⠀⠀⠉⠀⠀⠀⢻⣷⠧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⣠⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣄⡀⠀⢀⠀⠛⢿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣿⣶⣶⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠈⠃⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠀⠀⠀⠀⣿⠿⠿⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⢀⣿⣿⣿⠿⣋⣀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⣘⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠀⢸⣿⢹⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣸⡇⠀⢸⣿⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⣽⣧⣄⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣿⡟⢻⣿⠀⢸⣿⠀⠀⢀⡀⣿⡇⣀⢸⣿⢸⣿⠀⣿⣷⣿⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣹⣶⣶⡆⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⢈⣷⣿⣷⠀⠈⠀⠈⣿⠀⠀⣼⣷⣿⣷⣿⣾⡇⠀⠁⠀⣾⣿⣿⣾⣿⣿⣿⣤⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣴⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣜⠀⣿⣹⢹⡇⢠⡄⣤⣼⣿⣿⣿⣿⣤⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⣸⢠⣤⡿⢡⣤⡏⣟⣽⣿⣯⡋⣧⣤⣤⡌⣽⣯⡏⣿⡽⣽⡏⢟⣴⢶⣤⣻⡆
⣀⣀⣀⢸⣿⣀⣀⣿⣇⣸⣿⢸⣿⠀⣿⡇⣤⠀⣿⡇⢻⣧⣌⢩⣄⣿⣷⢸⡇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⠂⣿⡇⢸⡿⣷⣼⢻⡇⢿⣿⠀⣿⡟⠂⣿⡇⢸⢿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢻⡁
⣿⣿⣿⣿⣿⢩⣽⣿⣿⣭⣵⣾⣿⠀⣿⣿⣿⠀⣿⣷⣠⡍⣻⣷⢿⣿⣹⣿⡇⠀⠂⠀⣿⣿⣿⣿⣿⣿⠉⡍⠀⣿⡏⢹⣧⣿⣿⠀⣿⡇⢸⣧⣿⡿⣼⡇⣾⣿⠀⣿⣧⡆⣿⡇⣾⣼⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡏⣷
⣿⣿⣿⣿⣿⣿⣏⣿⣟⣿⣿⣿⣿⠶⣟⣽⣿⠆⠿⡿⠙⠷⠾⣟⣿⡿⣡⣿⣇⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⣆⣿⣇⣸⣿⣯⣿⠶⠟⠁⠸⣟⣸⣇⣿⣇⣯⣿⠾⣿⣽⡇⠿⠇⣿⣻⣿⣇⡿⣠⠿⢇⣞⠿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⣭⣍⣩⣍⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡾⢿⢷⣿⣿⣾⣾⣿⣿⣷⣴⣊⠓⣴⡔⣲⣒⠒⠄⠀⠀⠐⠐⣶⣮⣿⣐⣳⣻⣞⠐⠜⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣾⣻⣿⣶⣮⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣶⣊⡹⢯⣭⣑⣂⣿⣷⣿⣶⣂⢷⣾⢯⡼⢗⡟⣺⠵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠉⠉⠛⠛⠙⠛⠛⠋⠛⠛⠋⠛⠛⠋⠛⠛⠛⠉⠛⠓⠒⠎⠫⠩⠽⠙⠉⠀⠀⠀⠉⠉⠊⣀⡖⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣰⢶⣜⠓⣿⢵⣁⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣷⣿⣓⣪⣻⡆⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡱⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠉⠉⠙⢿⣿⣿⣶⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣯⣎⠈⠀⠈⢻⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⠀⠉⠉⠹⣿⣿⡟⠉⠉⠉⠀⠀⠀⢻⣿⢬⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠘⣿⣶⠀⠀⠀⢈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡄⠀⠀⡀⠀⠻⣿⣿⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⢀⣷⣤⣤⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡆⠈⠂⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠃⠀⠀⠀⠘⣿⣿⡟⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⢀⣾⣿⣿⣿⣃⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣀⣐⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⡇⠀⢸⣿⢩⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢺⡇⠀⢸⣿⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢼⣧⣄⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣿⡟⢻⣿⠀⢸⣿⠀⠀⢀⡀⣿⡇⣀⢸⣿⢸⣿⠀⣿⣧⣿⢻⣧⣄⡀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣩⣴⣶⡆⠀⠀⠀⢨⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⢈⣷⣿⣷⠀⠀⠀⠀⣿⠀⠀⣼⣷⣿⣷⣿⡾⡇⠀⠀⠀⣼⣿⣿⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣜⠀⣿⣹⢹⡇⢠⡄⣤⣼⣿⣿⣿⣯⣥⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⡠⢠⣤⡿⢠⣤⡏⣟⣽⣶⣯⡋⣧⣤⣤⡄⣽⣯⡏⣿⡽⣽⡏⢟⣴⢶⣤⣻⡆
⣀⣀⣀⢸⣿⣀⣀⣿⣇⣸⣿⢸⣿⠀⣿⡇⣄⠀⣿⡇⢻⣧⣌⢭⣀⣿⣷⢸⡇⠈⠁⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⠇⣿⡇⢸⡿⣷⣼⢻⡇⢿⣿⠀⣿⡿⠆⣿⡇⢰⢿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢫⠀
⣿⣿⣿⣿⣿⢩⣽⣿⡿⣭⣵⣼⣿⠀⣿⣿⣿⠀⣿⣧⣠⡍⣻⣷⢿⣿⣹⣿⡇⠀⠂⠀⣿⣿⣿⣿⣿⣿⠉⡍⠀⣿⡏⢹⣧⣿⣿⠀⣿⡇⢸⣧⣿⡿⣼⡇⣼⣿⠀⣿⣧⡄⣿⡇⣾⣸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣷
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⣿⣿⣿⠶⣟⣽⣿⠄⠿⡿⠘⠷⠾⣟⣿⡿⣡⣿⣇⠀⠀⠀⢿⣿⣿⣿⣿⡿⠈⠀⣆⣿⣇⣸⣿⣯⣿⠶⠟⠁⠸⢟⣸⣇⣿⣇⣯⡿⠶⢿⣽⡇⠿⠇⣿⣻⣿⣇⠿⣠⠿⢇⣞⠿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠘⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣛⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣒⣛⡛⠛⠛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣙⣙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣾⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣷⣶⡖⠄⡀⠀⠀⢀⡠⠀⠰⡴⣆⢐⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⢀⠀⠀⠀⡑⢰⣾⣦⠰⠛⠏⠁⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠻⠻⠟⠛⠿⠻⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠒⠠⠬⠂⠀⠀⠑⠛⠉⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠷⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢐⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⠄⠒⠀⢀⢠⡆⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢐⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⠋⠉⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢂⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡗⠀⠀⠈⠙⢻⡿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠘⠉⠁⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⠈⠛⠉⢻⣿⣿⡟⠉⠉⠛⠀⠀⠀⢻⢇⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠘⣶⣶⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⡀⠀⠀⠀⠀⠿⣿⣷⣶⣶⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣦⣀⡀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠘⠄⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠸⣿⣿⡇⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⢀⣾⣿⣿⡿⣃⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⢹⣷⢸⣿⠉⠁⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⡇⠀⢸⣿⠩⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⢷⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣄⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣿⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣿⢻⣇⡀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢉⣤⣤⡄⠀⠀⠀⢨⣿⣿⣶⣶⡀⠀⠁⠀⠀⠀⠀⢈⣷⣿⣷⠀⠀⠀⠀⣿⠀⠀⣼⣷⣿⣷⣿⣾⡇⠀⠀⠀⣸⣿⣿⣾⣿⣿⣦⣀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣄⠀⣽⣹⢹⡅⢠⡄⣤⣼⣿⣿⣿⣯⣥⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⡀⢠⣤⡿⢠⣤⡍⣟⣴⣶⣮⡊⣤⣤⣤⡄⣽⣯⡏⣿⡽⣽⡏⢟⣴⢶⣤⣺⡄
⣀⡀⠀⢸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⡀⠀⣿⡇⢻⣧⣌⢭⡀⣿⣷⢸⡇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡿⣷⣼⢻⡇⣿⣿⠀⣿⡿⠇⣿⡇⢸⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢻⠀
⣿⣿⣿⣾⣿⢩⣽⣿⡟⣭⣥⣼⣿⠀⣿⣷⣿⠀⣿⣇⣠⡍⣻⣷⣿⣿⣹⣿⡇⠀⠄⠀⣿⣿⣿⣿⣿⣿⠉⡍⠀⣿⡏⢹⣧⣿⣿⠀⣿⡇⢸⣧⣿⡿⣼⡇⣸⣿⠀⣿⣇⡀⣿⡇⣾⣸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣦
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⣿⣿⣿⠶⣟⣽⣿⠀⠿⣿⠘⡷⠾⣟⣿⣿⣡⣿⢇⠀⠀⠀⢿⣿⣿⣿⣿⡿⠘⠁⣆⣿⣇⣸⣿⣯⡿⠶⠟⠁⠸⢟⣸⣇⣿⣇⣯⡿⠶⢿⣽⡇⠿⢇⣿⣻⣿⣇⠿⣠⠿⢇⣞⠿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠾⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣋⣏⣿⣯⢩⣻⢿⢭⣿⣚⢼⣹⡫⠫⢫⠩⡘⠠⣛⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⡧⣽⣿⣛⡿⣽⣛⣻⣻⡇⠁⠀⠀⠀⠁⠀⠀⡀⠀⠁⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⡿⠿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⡿⢽⣿⣯⠭⠿⡿⡭⠍⠁⠨⠾⣶⢈⣫⡽⠿⠏⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⢶⣂⣶⣬⡤⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣽⣊⣗⣸⣿⣿⣷⣗⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡏⠀⠀⠀⠘⠛⠋⠬⠄⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠃⠀⠛⠛⢻⣿⣿⡿⠛⠛⠻⠁⠀⠀⢻⡿⡿⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠉⠻⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣾⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⢠⣤⠀⡀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣶⡄⠑⠆⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠀⠀⠀⢸⣿⣿⡇⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⠀⢀⣾⣿⣿⡿⣃⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣀⣘⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣈⣁⠀⠀⠀⠀⠐⠛⠛⠃⠀⠀
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢹⣷⢸⣿⠉⠉⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⡇⠀⢸⣿⢩⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⢷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣄⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣿⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣼⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣠⣤⡄⠀⠀⠀⢠⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⠀⠀⠀⠀⣿⠀⠀⣼⣷⣿⣷⣿⣾⡇⠀⠀⠀⣸⣿⣿⣾⣿⣷⣆⡀⠀⠀⠀⠀⠀
⠃⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣄⠀⣭⣹⢹⡅⢠⡄⣤⣼⣿⣿⣿⣯⣧⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⡀⢠⣤⡿⢠⣤⡍⣟⣵⣶⣮⡋⣥⣤⣤⡄⣽⣯⡏⣿⣽⣽⡍⢟⣴⢶⣤⣲⡆
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⡀⠀⣿⡇⢻⣧⣌⢭⠀⣿⣷⢸⡇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⡄⣿⡇⢸⡿⣷⣼⢻⡇⣿⣿⠀⣿⣿⡇⣿⡇⢸⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢫⠇
⣿⣿⣿⣾⣿⢩⣽⣿⡟⣭⣥⣸⣿⠀⣿⣷⣿⠀⣿⣇⣠⡍⣻⣷⣻⣿⣹⣿⡇⠀⠄⠀⣿⣿⣿⣿⣿⣿⠉⡉⠀⣿⡏⢹⣧⣿⣿⠀⣿⡇⢸⣇⣿⡟⣸⡇⣸⣿⠀⣿⣇⡀⣿⡇⣾⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣤
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⣿⣿⡿⠶⣟⣽⣿⡀⢿⣷⠘⡷⠾⣟⣿⣿⣣⣿⣇⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠁⣆⣿⣇⣸⣿⣯⣿⠶⠟⠁⠸⣟⣸⣇⣿⣇⣯⡿⠶⣟⣽⡇⠿⢇⣿⣻⣿⣇⠿⣠⠿⢇⣞⠿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠤⠴⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣋⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⡻⢇⣰⡗⠀⠑⢄⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⡇⣉⡪⠰⣀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣟⣿⣿⣿⣿⣿⣿⡿⠷⠒⠈⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠁⠀⠁⠉⠈⠈⠉⠉⠁⠀⠀⠈⠛⠉⠉⠀⠀⠀⠀⠈⠉⠋⣿⣿⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠷⠶⠿⠟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣶⣶⡿⣚⣾⡀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢰⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡏⠀⠀⠀⠹⠟⠛⠿⡁⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠃⠈⠿⠿⢿⣿⣿⡿⠛⠛⢿⠋⠀⠈⢿⣿⣿⠀⠀⠀⢸⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠈⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠈⠛⠿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⢽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⠀⣿⣿⣦⣀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⡀⠳⡄⠀⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠀⠀⠀⢸⣿⣿⡇⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⠀⢀⣼⣿⣿⣿⣃⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣀⣙⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣘⣉⠀⠀⠀⠀⠸⠿⠿⠃⠀⠀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢹⣷⢸⣿⠛⠙⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⡇⠀⢸⣿⢩⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⢷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣿⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢁⣀⣀⡀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⣴⠀⠀⣴⣶⣿⣷⣶⣾⣇⠀⠀⠀⢸⣿⣿⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀
⠟⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡴⢶⣄⠀⣭⣹⢹⡅⢠⡄⣤⣼⣿⣿⣿⣯⣧⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⡀⢠⣤⡿⢡⣤⡍⣟⣽⣶⣯⡉⣭⣤⣤⡄⣽⣯⡏⣿⣽⣽⡍⣗⣴⢶⣤⣰⡄
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⡀⠀⣿⡇⢻⣧⣌⢭⠀⣿⣷⢸⡇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⡇⣿⡇⢸⡿⣷⣼⢻⡇⣿⣿⠀⣿⣿⡇⣿⡇⢸⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢻⡇
⣿⣿⣿⣾⣿⢩⣽⣿⡟⣭⣥⣸⣿⠀⣿⣷⣷⠀⣿⡇⣠⡍⣻⣷⢻⣿⣹⣿⡇⠀⡄⠀⣿⣿⣿⣿⣿⣿⠉⠉⠀⣿⡏⢹⣯⣿⣿⠁⣿⡇⢸⣇⣿⡟⣸⡇⢹⣿⠀⣿⡇⡁⣿⡇⣾⢹⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣇⣄
⣿⣿⣿⣿⣿⣿⣏⣿⣏⣿⣿⣿⣿⠶⣟⣽⣿⡀⢿⣟⠘⡷⠾⣟⣿⣿⣣⣿⣇⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠁⣆⣿⣇⣸⣿⣯⣿⠶⠟⠁⠸⣟⣸⣇⣿⣇⣯⣿⠶⣿⣽⡇⠿⢇⣿⣻⣿⣇⣿⣠⠿⢇⣞⠿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣼⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢯⢿⡿⡟⠆⢙⠦⡙⠉⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠶⢣⢙⢂⠄⠄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⠟⠙⡄⢀⠿⠞⠒⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠋⠉⠋⠙⠛⠛⠛⠉⠁⠀⠉⠛⠛⠛⣿⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣴⣶⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣀⣴⣷⣿⣟⣟⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⠿⠿⣿⣓⡀⡀⡀⠀⢘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠏⠉⢿⣿⣿⣿⣿⡿⠿⠿⣿⠋⠉⠙⣿⣿⣿⠀⠀⠀⢹⡿⠋⠙⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣷⣀⠴⠂⠀⠀⠙⢻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠈⠿⣿⡇⠀⠀⠈⠀⠀⠀⢸⣿⣯⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⣀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠇⠀⠀⠀⡀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣤⠀⠦⡀⠉⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣶⡆⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⠃⢀⣿⣿⣿⣿⣃⣀⠀⠀⣀⣀⣀⠀⢀⡀⠀⢀⣀⣛⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣘⣛⠀⠀⠀⠀⢸⡿⠿⠇⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢹⣷⢸⣿⠻⠝⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⡇⠀⢸⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⢀⣀⡀⠀⠀⠀⢀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⣤⠀⠀⣴⣶⣿⣷⣶⣾⣇⠀⠀⠀⢨⣿⣿⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡴⢶⣄⠀⣬⣹⢩⡅⢠⡄⣤⣼⣿⣿⣿⣯⣧⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⡀⢠⣤⡟⢡⣤⡍⣟⣽⢿⣯⡋⣭⣤⣤⡄⣽⣯⡏⣿⣽⣽⡏⣆⣴⢶⣤⣠⡄
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⠀⠀⣿⡇⢻⣧⣌⢭⠀⣿⣷⢸⡇⠈⠁⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⠄⣿⡇⢸⡿⣷⣼⢻⡇⣿⣿⠀⣿⣿⡇⣿⡇⢰⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢻⡇
⣶⣶⣶⣼⣿⢩⣵⣿⡟⣍⣁⢸⣿⠀⣿⣧⣧⠀⣿⡇⣠⡍⣻⣷⢶⣿⢹⣿⡇⠀⡀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠀⣿⡏⢹⣯⣿⣿⠀⣿⡇⢸⡇⣿⡟⢸⡇⢻⣿⠀⣿⡏⠃⣿⡇⣼⢻⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡏⡀
⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣿⣿⣿⠶⣟⣽⣿⡀⢿⣇⠘⡷⠾⣟⣿⣿⣧⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣆⣿⣇⣸⣿⣯⣿⠶⠟⠁⠸⣿⣸⣇⣿⣇⣯⡿⠶⢿⣽⡇⠿⢇⣿⣺⣿⣇⡿⣠⠿⢇⣞⠿⠶⠻⢧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣠⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣼⣧⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣿⣿⣿⣦⣤⣤⣤⣬⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⣿⠋⣫⠇⠜⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⠃⠙⡆⠎⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣏⣓⠊⣿⢽⠹⡯⠽⠻⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠋⠋⠙⠙⠋⠛⠛⠻⠿⠟⠟⠉⠉⠙⠿⠿⠿⣿⣿⡟⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣋⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣠⣿⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠨⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠈⢻⣿⣿⣿⡷⠀⠀⠀⠀⠸⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡏⠙⣿⣿⣿⣿⣿⡿⠿⠿⣿⠋⠉⠛⣿⣿⡏⠀⠀⠀⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⢋⡁⠀⠁⠀⠈⠙⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠙⢿⣿⠁⠀⠀⠈⠀⠀⠀⢹⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⢠⡤⢄⣵⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣤⣄⠀⣆⡈⠙⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣿⡏⠀⠀⠀⣼⣧⣤⡄⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⣀⠁⢀⣿⣿⣿⡿⣃⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣀⣟⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣸⣟⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢹⣷⢸⣿⠻⠝⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⡇⠀⢸⣿⠋⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠷⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣬⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⢈⣉⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣨⣥⠀⠀⠀⠀⣤⠀⠀⣤⣤⣭⣥⣴⣾⡅⠀⠀⠀⢸⣿⣿⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀
⡗⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣄⠀⣭⣹⢩⡅⢠⡄⣤⣼⣿⣿⣿⣯⣤⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⡀⢠⣬⡟⢠⣤⡍⣟⣽⢿⣯⡋⣽⣤⣤⡄⣽⣯⡏⣿⣽⣭⡄⣄⣴⢶⣤⣠⡀
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⡿⢸⣿⠀⣿⡇⠀⠀⣿⡇⢻⣧⣌⠍⠀⣿⣷⢸⡇⠈⠁⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⡀⣿⡇⢸⡿⣷⣼⢻⡇⣿⣿⠀⣿⣿⡇⣿⡇⣸⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢻⠀
⣶⣶⣶⣼⣿⢩⣵⣿⡟⣍⣁⢸⣿⠀⣿⣧⡇⠀⣿⡇⣠⡍⣻⣷⢶⣿⢹⣿⡇⠀⡀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠀⣿⡏⢹⣯⣿⣿⠀⣿⡇⢸⡇⢿⡟⢸⡇⢻⣿⠀⣿⡟⡃⣿⡇⣿⢻⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠶⣟⣽⣿⠀⢿⡇⢘⡷⠾⣟⣿⣿⣷⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣇⣿⣇⣸⣿⣯⣿⠶⠟⠁⢸⣟⣸⣗⣿⣇⣮⡿⠶⣟⣵⡇⠿⢇⣿⣸⣿⣇⠿⣠⠿⢇⣜⠿⠶⡻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣬⣥⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡩⣻⣿⣿⡿⠗⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠻⠿⠻⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠻⠿⠿⢿⡿⢿⣿⠿⣿⡿⠿⠿⠛⠛⠟⠿⢶⢾⣦⡲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣦⣤⡄⠀⠀⣀⣴⣷⣿⣛⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠄⠀⠀⠀⠀⠀⠨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠉⠉⠙⢿⣿⣿⣿⠅⠀⠀⠀⠀⠨⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⡏⠁⠀⠈⣿⡿⠿⠯⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠉⠉⠛⠁⠁⠁⠂⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠁⠀⠉⠉⠹⣿⣿⠇⠀⠀⠙⠀⠀⠀⢹⣿⣧⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⣪⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⢀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠳⢠⣆⡀⠀⡄⠀⠻⣿⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠁⠀⠀⢠⣤⣀⡀⠀⠀
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⣈⠃⢀⣿⣿⣿⣿⣃⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣀⣿⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣈⣿⠏⠀⠀⠀⢸⣿⣿⠇⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⢹⣷⢸⣿⢻⡝⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⡇⠀⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡷⠾⠏⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠈⠁⠈⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⡀⣈⠀⠀⠀⠀⣸⣿⣿⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀
⡗⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⡀⠀⠀⣬⡄⣠⡶⢦⣄⠀⣤⣰⢠⡄⢠⡄⣤⣼⣿⣿⣿⣧⣤⢤⣤⠀⣤⡤⣤⡼⣟⣽⡿⣦⡀⢠⣼⡏⢠⣤⡍⣟⣽⢿⣯⡋⣥⣤⣤⣤⣽⣯⡏⣿⣽⣥⡄⢀⣴⢶⣤⠀⠀
⠁⠀⠀⢸⣿⣀⡀⣿⣇⣸⡿⢸⣿⠀⣿⡇⠀⠀⣿⡇⢻⣧⣌⠉⠸⣿⣷⢸⡇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⣟⣿⣿⡀⣿⡇⢸⡿⣷⣼⢻⡇⣾⣿⠀⣿⣷⡇⣿⡇⣿⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⢳⠀
⣤⣤⣤⣸⣿⢩⣥⣿⡟⡍⠁⢸⣿⠀⣿⣇⡆⠀⣿⡇⣠⡍⢻⣷⢠⣿⢹⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠀⣿⡏⢹⣯⣿⣿⠀⣿⡇⢸⣧⣿⡟⢸⡇⢿⣿⠀⣿⣿⡇⣿⡇⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⠶⢟⣽⣧⠀⢿⡇⢘⡷⠾⣿⣾⣿⣦⣿⣇⡇⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⣗⣿⠇⢸⣿⣯⣿⠶⢿⠁⠸⣇⣸⣇⣸⣇⣬⡿⠶⢟⣵⡆⠿⢇⣿⣻⣿⣇⠿⣠⠿⢇⡞⠿⠶⠻⢇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣂⣀⣘⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⣉⣍⣉⣉⣉⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠻⠿⢟⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠷⠿⠟⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⡀⠀⠀⢀⣤⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠄⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠋⠉⠻⣿⣿⣿⣟⠆⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⡏⠁⠀⢹⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠙⠉⠛⢿⠇⠘⠏⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠁⠀⠉⠉⢻⣿⣿⠁⠀⠈⠋⠀⠀⠀⢿⣿⡇⠀⠀⠘⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣈⣀⣄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠐⠆⢰⡀⠀⠀⡄⠘⢻⣿⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⣉⠀⢀⣿⣿⣿⡿⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣀⣏⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣘⣿⠃⠀⠀⠀⢸⡿⠾⠇⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢹⣷⢸⣿⢻⡝⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⡇⠀⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠋⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡷⠾⠏⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠷⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠁⠀⡈⠀⠀⠀⢀⣾⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⡀⠀⠀⣥⡄⣠⡶⢦⣄⠀⣤⣰⢠⡄⢠⡄⣤⣿⣿⣿⣿⣦⣤⢤⣤⠀⣤⡤⣤⡽⣟⣽⡶⣦⡀⢠⣼⡇⢠⣬⡍⣟⣽⢿⣯⡋⣤⣤⣤⣬⣽⣯⡏⣿⡽⣠⡄⢀⣴⢶⣤⠀⠀
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⡿⢸⣿⠀⣿⡇⠀⠀⣿⡇⢻⣧⣌⠉⢸⣿⣷⢸⡇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣀⣿⠀⣿⣇⣼⣟⣿⣿⠀⣿⡇⢸⡿⣧⣼⢻⡇⣼⣿⠀⣿⣷⠆⣿⡇⣿⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⠃⠀
⣤⣤⣤⣸⣿⢩⣥⣿⡟⡍⠁⢸⣿⠀⣿⣇⠀⠀⣿⡇⣠⡏⢻⣷⢸⣿⢹⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⡀⣿⡏⢹⣯⣿⣿⠃⣿⡇⢸⣧⣿⡟⢸⡇⣿⣿⠀⣿⣿⠀⣿⡇⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡿⠶⢟⣽⡆⠀⣿⠇⢘⡷⠾⣟⣾⣿⣤⣿⣇⠀⠀⣆⣿⣿⣿⣿⣿⡿⠀⢰⣇⡿⠇⢸⣿⣯⣿⠶⠟⠁⠸⣇⣸⣇⣸⣇⣌⡿⠶⣟⣱⠀⠿⢇⣿⣻⣿⣇⠿⣠⠿⢇⠘⠿⠶⠻⢇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣻⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡿⡿⠓⠒⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣉⣉⣉⣉⣉⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣸⢿⡦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⠽⣻⣿⣿⠿⣿⡤⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡷⠶⠿⠷⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣧⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⢠⢨⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⠩⠀⠀⠀⠀⠠⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⡿⠋⠉⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠛⠛⠿⡓⢀⣸⡀⠀⠀⠳⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠈⠉⠉⢿⣿⡏⠀⠈⠹⠃⠀⠀⠈⣿⣇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡅⢜⠗⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⢾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡀⠀⢀⡀⢸⣿⣶⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣀⣹⠀⢸⣿⣿⣿⡇⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣸⣇⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣙⣟⠃⠀⠀⠀⣿⣦⣴⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⢹⣷⢸⣿⢻⡝⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⡇⠀⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠩⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡷⠾⠏⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠉⠁⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⢀⠀⠀⠀⠀⣼⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣦⡀⠀⠀⣤⡄⣠⡶⢶⣄⡀⣤⣰⢠⡄⢠⡄⣤⣿⣿⣿⣷⢠⣤⢤⣤⠀⣤⡤⣤⡽⣟⣵⡶⣤⡀⢠⣶⡄⢠⣤⡍⣟⣽⢶⣯⡂⣤⣤⣼⣯⣽⣯⡏⣯⡴⢠⡄⢀⣴⢶⣤⠀⠀
⠀⠀⠀⢸⣿⣀⠀⣿⣇⣸⡿⢸⣿⠀⣿⡇⠀⠀⣿⡇⢻⣧⣌⠉⣿⣿⣷⢸⡇⠈⠀⠀⣿⣿⣿⣿⣼⣿⣀⣿⠆⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡿⣧⣼⢿⡇⣼⣿⠀⣿⡇⠀⣿⣷⣿⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⠃⡀
⣤⣤⣤⣸⣿⢩⣥⣿⡟⠉⠁⢸⣿⠀⣿⡇⠀⠀⣿⡇⣰⡏⢻⣷⢻⣿⢹⣿⡇⠀⠀⡧⣿⣿⣿⣿⣿⣿⠉⢉⡆⣿⡏⢹⣯⣿⣿⠀⣿⡇⢼⣧⢿⡟⢸⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⡇
⣿⣿⣿⣿⣿⣿⣟⣿⣇⣿⣿⣿⡿⠶⣟⡅⠀⣔⡿⠇⣝⡷⢾⣟⣾⣿⣦⣿⡇⠀⢠⣇⣿⣿⣿⣿⣿⠿⠀⣼⣇⡿⠇⣸⣿⣯⣿⠶⠟⠁⠸⣇⣸⣇⣸⣇⣌⡿⠶⣟⡁⠀⠿⢇⣿⣻⣿⡇⠿⣠⠿⠇⠘⠿⠶⠻⠇⢙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣾⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡂⠀⠀⠀⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣍⣉⣉⣉⣉⣉⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡚⡿⢻⠿⠛⠿⠿⠿⠂⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⡷⠁⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠁⠀⠉⠉⠁⠈⠁⠙⠹⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣻⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⢰⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠙⠛⠻⢿⣿⠅⣵⡀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠈⠉⠙⣿⣿⠏⠈⠉⢻⠁⠀⠀⠸⣿⡇⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣿⣯⡅⠀⠀⠀⠹⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⢀⠀⣼⣿⣄⣤⣴⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣈⣛⠈⢿⣿⣿⣿⡇⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢀⣸⣃⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣻⣟⠀⠀⠀⠀⣷⣤⣤⠀⠀⠀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⢹⣷⢸⣿⢻⡝⣾⡏⢹⣷⠀⣿⡏⣿⡇⢻⡇⠀⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⢀⣿⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⡷⠾⠟⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⢀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠉⠁⠊⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣦⡀⠀⠈⣤⡄⣠⡶⢶⣄⣦⣤⣰⢠⡄⢠⡄⣼⣿⣿⣿⣧⢠⣤⢤⣤⠀⣤⡤⣤⡴⣖⣴⡶⣤⡀⢰⣦⡄⢠⣤⡌⣟⣽⢶⣧⡀⣤⣤⣼⣯⣽⣯⡏⣿⡤⢠⡄⢀⣴⢶⣤⠀⠀
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⡿⢸⣿⠀⣿⡇⠀⠀⣿⡇⢿⣧⣌⠩⣿⣿⣷⢸⡇⠈⠀⡷⣿⣿⣿⣿⢸⣿⣀⣿⠄⣿⣇⣼⣟⣿⣿⡀⣿⡇⣸⡿⣧⣼⣿⡇⣼⣿⠀⣿⡇⠀⣿⣷⣿⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⠃⠀
⣤⣤⣤⣸⣿⢩⣥⣿⡟⠉⢡⢸⣿⠀⣿⡇⠀⡆⣿⡇⣷⡍⢻⣷⢿⣿⢹⣿⡇⠀⢠⡧⣿⣿⣿⣿⢸⣿⠉⢩⡆⣿⡏⢻⣯⣿⣿⠁⣿⡇⢿⡇⢿⡟⣾⡇⣿⣿⠀⣿⡇⠀⣿⡏⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⡇
⣿⣿⣿⣿⣿⣿⣧⣿⣇⣿⣿⣿⡿⠶⢟⠁⠀⣟⡿⢇⣝⡷⢾⣟⣾⣿⣦⣿⡇⠀⢸⣇⣿⣿⣿⣿⣿⠿⠀⣾⣇⠿⢇⣸⣿⣯⣿⠶⠟⠁⢸⣇⣸⣇⣸⣇⣌⡻⠶⣟⠁⠀⠿⢇⣿⣻⣿⣇⠿⣠⠿⠇⠘⠿⠶⠻⠇⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣉⣉⣉⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣂⣀⣀⣀⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢓⠆⣀⠻⠉⡻⣿⣿⣯⡟⠿⠟⢻⠛⠛⢿⠃⠘⠀⠀⠀⠀⠀⠒⠪⠿⢹⡿⣿⣿⣯⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⢿⢿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠈⠙⢻⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡶⡶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⣴⣾⣷⣿⣇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢐⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠠⡄⠠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡎⣍⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣥⣾⣀⡐⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⠭⡇⠚⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠈⠙⢻⣿⣿⠋⠉⠙⣿⠁⠀⠀⢹⣟⠁⠀⠀⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠀⠉⠙⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠙⠟⠀⠀⠀⠘⠀⠀⠀⠀⣿⡀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⢀⢀⣾⡇⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣦⣈⣛⠻⢿⣿⣿⣿⠏⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣿⣁⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡈⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣿⣟⠀⠀⠀⢰⣦⣠⡄⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢹⣷⢸⣿⢻⡝⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠀⢸⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⢸⡉⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡷⠾⢿⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠶⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠀⠀⠀⠀⠀⢩⣾⣾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣦⡀⠀⠆⣤⡄⣠⡶⢶⣄⣆⣤⣰⢠⡄⢠⡄⣽⣿⣿⣿⡄⢠⣤⢤⣤⠀⣤⡤⣭⡽⣟⣴⠶⣤⡀⢰⣦⡄⢠⣬⡍⢟⣽⢷⣦⡀⣤⣤⣿⣯⣽⣯⡏⣥⡄⢠⡄⢀⣴⢶⣤⠀⠀
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⡿⢸⣿⠀⣿⡇⠀⡀⣿⡇⢿⣧⣌⢩⣿⣿⣷⢸⡇⠈⢰⡇⣿⣿⣿⡇⢸⣿⣀⣿⠀⣿⣇⣼⣟⣿⣿⠀⣿⡇⣼⡟⣧⣼⣿⡇⣼⣿⠀⣿⡇⠀⣿⣷⣿⣿⣿⡇⣿⣷⣻⡇⢸⣿⠀⠛⠃⠀
⣶⣤⣤⣼⣿⢩⠁⣿⡟⠉⣡⢸⣿⠀⣿⡇⢠⡇⣿⡇⣷⡍⢻⣷⢿⣿⢹⣿⡇⠀⢸⡯⣿⣿⣿⣇⢸⣿⠉⣹⡆⣿⡏⢻⣯⣿⣿⠀⣿⣧⢿⡇⢿⡿⣾⡇⢿⣿⠀⣿⡇⠀⣿⡏⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣇⣿⣗⣿⣿⣿⡿⠶⠟⠁⢸⣏⠿⢷⣝⡷⠾⣟⣾⣿⣧⣿⠇⠀⣾⣇⣿⣿⣿⣿⡼⠿⢠⣿⡇⠿⢇⣸⣿⣯⣿⠶⠟⠁⣸⣇⣸⣇⣸⣇⣬⡿⠶⠟⠁⠀⠿⣇⣿⣹⡿⡇⠿⣠⠿⠇⠘⠿⠶⠻⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣶⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣟⣛⣃⣀⣀⣀⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⢷⣿⢿⣰⣝⠙⠈⣾⡃⡾⠝⣿⣛⢿⠹⠶⠿⠟⠲⠆⠂⠋⠉⠂⠀⠁⠀⠀⠌⠹⠜⣻⣿⡭⠶⠾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⠋⣽⡟⠊⣁⣆⣒⢭⡀⡀⡂⠈⡐⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣿⣟⣟⢂⣦⢴⢹⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣶⡋⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠁⠈⠛⠁⠋⠋⠋⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣶⣦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢿⣿⣿⣿⣯⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣦⣶⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⢀⡰⣷⣾⣷⠄⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠢⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠤⠀⠀⢀⠀⠀⢽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢅⠀⢰⡄⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣅⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⠃⠀⠀⠹⣿⣿⣿⣿⣟⣿⣽⣿⡿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠉⠛⣿⣿⡟⠛⠛⢿⡟⠁⠀⠈⢿⡋⠀⠀⠙⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢛⣪⣿⣿⡂⠂⠃⢿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠘⠛⡇⠀⠀⠀⠃⠀⠀⠀⠘⣧⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠿⣛⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣄⣹⣾⢿⢷⣾⣿⣿⠉⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢸⣿⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡉⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣐⣿⣁⠀⠀⠀⢶⣄⣠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⢹⣷⢸⣿⢻⡍⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠀⢸⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⣘⣛⠻⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡷⠾⣿⢸⣿⢿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⣼⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠈⠁⠁⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⣹⣶⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡶⢦⣄⡆⣤⡀⢠⡄⢠⡄⣿⣿⣿⣧⠀⢠⣤⢤⣤⠀⣤⡤⣭⡽⣟⣤⠶⣤⡀⢰⣤⡄⢠⣬⡍⣟⣽⢶⣦⡀⣤⣤⣿⣯⣽⣯⡏⣤⡄⢠⡄⢀⣴⢶⣤⠀⠀
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⡿⢸⣿⠀⣿⡇⠀⠀⣿⣷⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⢹⡇⣿⣿⣿⡆⢸⣿⣀⣿⠀⣿⣗⣼⣟⣿⣿⠀⣿⣇⣼⡟⣧⣼⢿⡇⣼⣿⠀⣿⡇⠀⣿⡗⣿⣿⣿⡇⣿⣷⣺⡇⢸⣿⠀⠛⠃⠀
⣤⣤⣤⣼⣿⠉⢡⣿⡟⠉⣡⢸⣿⠀⣿⡇⣾⡇⣿⣿⣧⡍⢻⣷⢿⣿⢹⣿⡇⠀⣿⡇⣿⣿⣿⡇⢸⣿⠉⣽⠀⣿⡏⢻⣯⣿⣿⠀⣿⣿⢿⡇⢿⡿⣾⡇⢿⣿⠀⣿⡇⠀⣿⡇⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣧⣿⣗⣿⣿⣿⠿⠶⠟⠁⣿⣇⠿⢿⣝⡷⠾⣟⣾⣿⣧⡿⠇⠀⣿⣇⣿⣿⣿⣧⠸⠿⢸⣿⡆⠿⣇⣸⣿⣯⡿⠶⠟⢱⣸⣇⣸⣇⣸⣇⣌⡿⠶⠟⠁⠀⠿⣇⣿⣻⡿⡇⠿⣠⠿⠇⠘⠿⠶⠻⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣀⣾⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣿⣿⣿⣿⣿⣿⣏⣛⣀⣀⣀⣀⣉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⢒⢵⠐⣀⣀⠂⡟⢿⢻⠟⡿⠸⠈⠔⠢⠋⡀⠒⠂⠈⠑⠂⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⢻⣀⣃⠀⢁⠦⠁⠤⠈⠁⠨⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣾⣿⡰⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠋⠀⠈⠉⠓⠉⠈⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣴⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠠⣿⣿⣿⣿⣏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⢀⣾⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠂⣘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠄⢄⠀⡁⠬⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡑⡷⣥⠂⢷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡯⣹⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡟⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠙⣿⣿⣿⠟⠛⠻⣿⡟⠁⠀⠙⣿⠁⠀⠀⢹⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡛⠑⠚⠉⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠈⠻⡟⠀⠀⠀⢹⡇⠀⠀⠀⢹⡆⠀⠀⠸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠐⢞⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢀⣼⣇⠀⢀⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⣀⣛⣻⢿⢿⣿⣿⠁⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢿⣇⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣈⡃⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣸⣟⣀⠀⠀⠀⣦⣀⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⢹⣷⢸⣿⢫⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠀⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⣟⠟⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⡷⠾⣿⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠶⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⣿⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠈⠈⠁⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣉⣠⣾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⡀⠆⠀⣤⡄⣠⡶⢶⣔⣦⣤⡀⢠⡄⢠⡌⣿⣿⣿⡆⠀⢠⣤⢤⣤⠀⣤⡴⣭⡽⣗⣤⠶⣤⣀⢠⣤⡄⢠⣬⡍⣗⣴⠶⣤⡀⣤⣤⣿⣯⣽⣯⡇⣤⡄⢠⡄⢀⣴⢶⣤⠀⠀
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⡿⢸⣿⠀⣿⡇⠀⠀⣿⣷⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣹⡇⣿⣿⣿⠀⢸⣿⣀⣿⠀⣿⣗⣼⣟⣿⣿⠀⣿⣇⣼⡟⣧⣼⣿⡇⣼⣿⠀⣿⡇⣀⣿⣷⣿⣿⣿⡇⣿⣷⣺⡇⢸⣿⠀⠛⠃⠀
⣤⣤⣤⣼⣿⠉⢱⣿⡟⢉⣥⢸⣿⠀⣿⣇⣿⡄⣿⣿⣧⡍⢻⣷⢿⣿⢹⣿⡇⠀⣿⣇⣿⣿⣿⠀⢸⣿⠉⣭⠀⣿⡏⢻⣯⣿⣿⠀⣿⣿⢿⡇⢿⡿⣾⡇⢿⣿⠀⣿⡇⠻⣿⡏⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⢀
⣿⣿⣿⣿⣿⣿⣇⣿⣗⣿⣿⣿⠻⠶⠟⢹⣿⡇⠿⣿⣝⡷⠾⣟⣾⣿⣦⠿⠇⠀⣿⣇⣿⣿⣿⡆⠸⠿⢸⣿⠀⠿⣧⣸⣿⣯⣿⠶⠟⣽⣸⣇⣸⣇⣸⣇⣬⡿⠶⠟⠁⢀⢿⣇⣿⣻⣿⡇⠿⣠⠿⠇⠘⡿⠶⠻⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⢸⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣀⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣦⣾⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣋⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣄⣀⣀⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣚⠴⣂⠈⡹⣿⣟⠻⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣯⡄⠤⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠉⠉⠉⠉⠋⠉⠛⠙⠙⠛⠛⠉⠉⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣅⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠅⡤⠀⠀⠀⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣧⣼⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠙⣿⣿⣿⠛⠛⠻⣿⡏⠀⠀⠙⣿⠀⠀⠀⣽⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠉⠉⠙⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠈⠿⡇⠀⠀⠀⢻⠇⠀⠀⠀⢻⡆⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣾⣄⣀⣤⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣦⣀⣛⣻⢿⢿⣿⣟⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⠀⢿⣇⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣈⡁⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣻⣏⣀⠀⠀⠀⣶⣤⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⢹⣷⢸⣿⠋⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣾⡇⠀⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⢀⣿⡿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⡷⠾⠟⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠶⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⣿⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠈⠈⠁⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣰⣾⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣔⣦⣤⡀⢠⡄⢠⡌⣿⣿⣿⡄⠀⢠⣤⢤⣤⠀⣤⡬⣭⡽⣗⣤⠶⣤⣀⢠⣤⡄⢠⣭⡍⣟⣵⠶⣤⡀⣤⣼⣿⣯⣽⣯⡇⣤⡄⢠⡄⢀⣴⢶⣤⠀⠀
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⡿⢸⣿⠀⣿⡇⠀⠀⣿⣷⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣹⡇⣿⣿⣿⠀⢸⣿⣀⣿⠀⣿⣗⣼⣟⣿⣿⠀⣿⡇⣼⡟⣧⣼⣿⡇⣾⣿⠀⣿⡇⠀⣿⣷⣿⣿⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣤⣤⣤⣼⣿⠉⢱⣿⡟⢉⣵⢸⣿⠀⣿⣇⣿⡀⣿⣿⣧⡍⢻⣷⢿⣿⢹⣿⡇⠀⣿⡏⣿⣿⣿⠀⢸⣿⠉⣍⠀⣿⡏⢻⣯⣿⣿⠀⣿⣿⢿⡇⢿⡿⣾⡇⢿⣿⠀⣿⡇⠀⣿⡏⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣇⣿⣗⣿⣿⣿⠻⠶⠟⢹⣿⡇⠿⣿⣝⡷⠾⣟⣿⣿⣦⠿⠇⠀⣿⣗⣿⣿⣿⡄⠸⠿⢰⣿⠀⢿⣇⣸⣿⣯⣿⠶⠟⣽⣸⣇⣸⣇⣼⣇⣬⡿⠶⠟⠁⢀⣿⣇⣿⣻⡿⡇⠿⣠⠿⠇⢘⡿⠶⠻⠇⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣤⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣦⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣍⣉⣉⣭⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣤⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⢴⠴⢆⣯⣠⣹⣿⢿⠽⡿⡛⢻⣿⡿⣯⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⡬⣴⣜⣿⣶⣿⣿⣿⣟⡇⠐⡓⣩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢀⣿⣿⣿⣿⣿⣿⣆⣨⣠⢰⠘⣭⣯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠶⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣴⣶⣶⣶⣶⣴⣦⣤⣴⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠀⠉⠙⠃⠉⠉⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⣴⣶⣷⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡂⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⠄⢀⢦⡀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣗⣷⣿⣿⣾⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡟⠋⠋⠻⣿⣿⡿⠿⢿⠂⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⠁⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⡿⡿⣛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⠏⠉⠉⢻⣿⠁⠀⠀⢹⡇⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢨⣱⡥⢿⡁⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠻⠀⠀⠀⠈⠿⠀⠀⠀⠈⡗⠀⠀⠘⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⣾⣷⣤⣴⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣀⣈⣿⢿⢿⣿⣃⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢸⢿⣃⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣿⣁⣀⠀⠀⢸⣷⣴⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⣽⣷⢸⣿⠋⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣼⡇⠘⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⢨⠈⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⡷⠾⠏⢸⣿⠷⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⣿⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⢠⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠈⠈⠁⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⣼⣾⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣜⣯⣥⡀⢠⡄⢠⡍⣿⣿⣿⡄⠀⢠⣤⢤⣤⠀⣤⡬⣭⡽⣟⣤⠶⣤⣠⢡⣤⡄⢠⣭⡍⢟⣵⠶⣤⡀⣤⣼⣿⣯⣽⣯⡇⣤⡄⢠⡄⢀⣴⠶⣤⠀⠀
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⠀⠀⣿⣷⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⣷⠀⢸⣿⣀⣿⠀⣿⣟⣼⣟⣿⣿⠀⣿⡇⣼⡟⣧⣼⢿⡇⣾⣿⠀⣿⡇⠀⣿⡧⣿⣿⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣤⣴⣶⣾⣿⠉⣹⣿⡟⣭⣵⢸⣿⠀⣿⣧⡄⠀⣿⣿⣤⡍⢻⣷⢿⣿⢹⣿⡇⠀⣿⡇⣿⣿⣿⠀⢸⣿⠉⡍⠀⣿⡏⢻⣯⣿⣿⠀⣿⡇⢻⡇⢿⡿⣼⡇⢿⣿⠀⣿⡇⠀⣿⡇⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣧⣿⣇⣿⣿⣿⠻⠶⠟⢹⣿⠀⢿⣿⣝⡷⠾⣟⣿⣿⣦⠿⠇⠀⣿⣇⣿⣿⣿⡄⠸⠿⢸⡇⠀⣿⣇⣸⣿⣯⣿⠶⠟⠁⣸⣇⡸⢇⠻⢇⣮⡿⠶⠟⠁⣄⣿⣇⣿⣻⠿⡇⠿⣀⠿⠇⣜⠿⠶⠻⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠼⠿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⡛⣛⣛⣛⣛⣛⣛⣛⣻⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠴⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠤⣤⣤⣀⢀⡠⡁⠠⢛⡚⠒⠪⡟⠎⢓⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⣽⣿⣾⣿⣥⡤⡦⣢⡕⠴⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢠⣾⣿⣿⣿⣿⣏⡄⣨⠠⠀⢀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠾⠿⢿⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣷⣶⣶⣶⣤⣤⣀⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠁⠁⠉⠀⠁⠁⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣴⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⢠⣷⣷⣷⡆⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠀⠠⣀⡀⡤⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠉⠉⠻⣿⣿⣿⣿⣿⣽⣯⣟⢼⣗⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⠋⠉⠉⢻⣿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⠟⡿⠿⠿⢿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⠁⠀⠈⢿⡟⠀⠀⠀⢹⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠻⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠛⠀⠀⠀⠘⠇⠀⠀⠀⢸⡃⠀⠀⣹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠰⢿⣷⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣀⣸⣿⢿⢿⣿⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢸⢿⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠸⣏⣀⣀⠀⠀⢸⣿⣾⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⣽⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣼⡇⢸⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠟⣿⡷⠾⠋⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠸⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⣿⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⢰⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣉⣁⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⢠⣿⣾⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⡀⠀⠀⣤⡄⣠⡶⢶⣝⣯⣥⡀⢠⡄⢠⡍⣿⣿⣿⡄⠀⢠⣤⢤⣤⠀⣤⡬⣭⡽⣟⣤⠶⣤⣰⢡⣤⡄⢨⣭⡍⢟⣵⠶⣤⡀⣤⣼⣿⣯⣽⣯⡇⣤⡄⢠⡄⢀⣴⠶⣤⠀⠀
⠀⠀⠀⢸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⠀⠀⣿⣷⢻⣧⣌⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⡇⠀⢸⣿⣀⣿⠀⣿⣟⣼⣟⣿⣿⠀⣿⡇⣾⡟⣧⣼⢿⡇⣾⣿⠀⣿⡇⠀⣿⡇⣿⣿⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣶⣶⣶⣾⣿⢉⣽⣿⡟⣭⣵⣸⣿⠀⣿⣇⠀⠀⣿⣿⣤⡏⣻⣷⢻⣿⢹⣿⡇⢠⣿⡇⣿⣿⣧⠀⢸⣿⢉⡍⠀⣿⡏⢻⣯⣿⣿⠀⣿⡇⢹⡇⢿⡟⣼⡇⢻⣿⠀⣿⡇⠀⣿⡇⣿⣿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣇⣿⣇⣿⣿⣟⠻⠶⠟⢹⡇⠀⣿⣿⣝⡷⠾⣟⣿⣿⣤⠿⠇⠈⣿⣇⣿⣿⣿⡄⠸⠿⢸⡇⢀⣿⣗⣸⣿⣯⣿⠶⠟⠁⠸⢇⡸⢇⠻⢇⣯⡿⠶⠟⠁⢀⣿⣇⣿⣺⠿⡇⠿⣀⠿⠇⠘⠿⠶⠻⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⣿⣿⣿⣿⣿⣷⠀⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣶⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣒⣒⣒⣒⣒⣒⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣯⣿⣾⣷⠀⡀⠀⠀⠀⢠⢉⢴⣶⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠲⢾⣷⣺⡟⠙⡩⠿⠿⠀⢀⢀⣀⣀⢨⣻⡷⠿⢿⣿⡿⣾⠯⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣩⢸⠀⠀⠰⢖⡃⠀⡀⢀⠀⠀⠸⢣⢤⣤⡦⡿⠁⠀⠉⠂⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠯⠿⢿⠿⢿⠿⠿⡿⣿⠿⣷⢿⡤⢿⣽⣷⣽⣧⣟⣤⣆⣐⣎⢖⣹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡷⠶⠿⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡷⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢺⣿⣿⣿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⣠⣖⡀⠭⡄⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠐⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠠⠠⣿⣿⣿⣿⡿⠁⠀⠀⠙⣿⣿⣿⣫⣛⣴⢄⣸⣽⢭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠏⠉⢿⣿⣿⠛⠛⢿⣿⡿⠉⠉⠙⢯⠀⠀⠀⣹⣿⡟⠉⠙⠁⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⢶⠉⠈⠉⠹⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⠃⠀⠀⠀⢿⡇⠀⠀⠀⠘⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢗⢿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⣶⣄⣀⣠⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⡀⠘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢰⣄⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣀⣿⣿⢿⢿⣇⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢺⢇⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠸⣁⣀⣀⠀⠀⢘⠛⠛⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡏⢹⡷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠸⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⡷⠾⠃⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⣻⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⢉⣀⣀⡀⠀⠀⠀⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣁⣀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣠⣤⡍⠀⠀⠀⠀⣼⣿⣾⣾⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⠀⠀⠀⣤⣄⣠⡶⢿⣝⣯⣭⡀⢠⡄⢹⡍⣿⣿⣿⡅⠀⢠⣤⢤⣤⠀⣤⡭⣭⡽⣟⣤⠶⣤⣸⢡⣤⡄⢨⣭⡍⣟⣵⠶⣤⡀⣤⣿⣿⣯⣽⣭⡇⣤⡄⢠⡄⢀⣴⠶⣤⡀⠀
⠀⠀⣀⢸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⢰⡇⣿⣿⢿⣧⣌⢭⣿⣿⣧⢸⡇⢸⣽⡇⣿⣿⣿⠀⢸⣿⣀⣿⠀⣿⣟⣼⣟⣿⣿⠀⣿⡏⣾⡟⣧⣼⢿⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⣿⣿⡇⣿⣷⢸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⠉⣁⣿⡟⣭⣵⣾⣿⠀⣿⡇⢸⡇⣿⣿⣤⡍⣻⣷⢿⣿⢹⣿⡇⣾⣿⣧⣿⣿⣿⠀⢸⣿⢩⠉⠀⣿⣏⢻⣯⣿⣿⠀⣿⣇⢹⡇⢿⡟⣸⡇⢹⣿⠀⣿⡇⠀⣿⡇⣿⣻⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣇⣿⣇⣿⣿⣿⡿⠶⠟⠁⣿⣏⣿⣿⣝⡷⠾⣟⣟⣿⣠⠿⠇⣿⣿⣇⣿⣿⣿⣆⠸⠿⢸⡀⠀⠿⣏⣸⣿⣯⣿⠶⠟⢹⡸⠇⡸⢇⣻⣇⣯⡿⠶⠟⠁⠀⢿⣇⣿⡸⠿⡇⠿⠀⠿⠇⡞⠿⠶⠻⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣧⣀⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣩⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣃⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣬⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣯⢝⣽⠿⣿⣾⠂⠀⢀⣀⠀⠀⠈⢀⣦⡿⣿⣿⣯⣭⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣻⢿⣿⣿⣿⠿⣿⢿⣿⡻⠾⢆⣆⠈⠛⠙⡙⠇⠀⠐⠈⠝⠠⢂⣤⡞⠊⣿⣿⣿⢿⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢏⣞⡚⢸⣾⢀⠀⠀⠸⠑⠂⠂⠀⠀⠀⠀⠄⢢⢄⢀⣴⡯⠁⠀⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠯⠿⠿⠿⠿⠿⠽⢿⠯⠮⠿⠯⣔⡦⣦⣼⣷⢯⣜⣰⣶⣆⢀⡪⣄⢽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡷⠶⠿⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡷⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⢠⣦⣀⣹⡁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠅⠀⡀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡿⠁⠀⠀⠙⣿⣿⣿⣯⣱⣶⢄⣀⣣⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠏⠉⢿⣿⡿⠛⠛⢿⣿⡿⠉⠉⠙⢿⠀⠀⠀⣹⣿⡟⠋⠙⠂⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠞⠉⠈⠀⠹⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⠃⠀⠀⠀⢿⡇⠀⠀⠀⠘⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠋⣽⡍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⣀⣠⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⡀⠘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⢰⣄⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣀⣿⣿⢿⢿⣇⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢿⢇⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠺⣀⣀⣀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡏⢹⡷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠸⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⡷⠾⠃⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢿⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⢉⣀⣀⡀⠀⠀⠀⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣈⣀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣤⡍⠀⠀⠀⠀⣼⣿⣾⣾⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣤⡄⢀⣤⠶⣤⠀⠀⠀⣤⣄⣠⡶⢿⣝⣯⣭⡀⢠⡄⢹⡍⣿⣿⣿⡇⠀⢠⣤⢤⣤⠀⣤⡭⣭⡽⣟⣤⠶⣤⣸⢡⣤⡄⢨⣭⡍⣟⣵⠶⣤⡀⣤⣿⣿⣯⣽⣭⡇⣤⡄⢠⡄⢀⣴⠶⣤⡀⠀
⠀⠀⣀⢸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⢰⡇⣿⣿⢿⣧⣌⢭⣿⣿⣧⢸⡇⢸⣽⡇⣿⣿⣿⠀⢸⣿⣀⣿⠀⣿⣟⣼⢟⣿⣿⠀⣿⡏⣺⡟⣧⣼⢿⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⣿⣿⡇⣿⣷⢸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⠉⣁⣿⡟⣭⣵⣾⣿⠀⣿⡇⢸⡇⣿⣿⣤⡍⣻⣷⢿⣿⢹⣿⡇⣾⣿⡇⣿⣿⣿⠀⢸⣿⢩⠉⠀⣿⣏⢹⣯⣿⣿⠀⣿⣇⢻⡇⢿⡟⣸⡇⢹⣿⠀⣿⡇⠀⣿⡇⣿⢻⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣇⣿⣇⣿⣿⣿⡿⠶⠟⠁⣿⣇⣿⣿⣝⡷⠾⣟⣟⣿⣠⠿⠇⣿⣿⣇⣿⣿⣿⣆⠸⠿⢸⡀⠀⠿⣏⣸⣿⣯⣿⠶⠟⢹⡸⠇⡸⢇⣻⣇⣯⡿⠶⠟⠁⠀⣿⣇⣿⡸⠿⡇⠿⠀⠿⠇⡞⠿⠶⠻⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣧⣀⣽⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣛⡛⢛⠛⠛⠛⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣩⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⡃⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢷⣿⣻⣿⣿⣿⣇⠀⢠⣨⣿⣶⢶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⠯⡿⠻⠷⢠⣑⢔⡾⡹⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠿⣿⣿⣻⣿⣿⣿⣿⣯⣿⣯⢀⠀⢠⠐⢨⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣭⣿⣻⠋⠯⣟⣻⠯⢴⣴⠡⠀⢀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠉⠉⠋⠋⠉⠃⠈⠈⠀⢨⣤⡖⠘⠀⠐⠌⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡷⠶⠿⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡷⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠚⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⢨⣿⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠠⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡀⠀⠀⠀⢀⠂⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡿⠋⠀⠈⠙⣿⣿⣿⣿⣣⣬⣗⣜⣮⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠉⠙⣿⣿⠛⠛⢻⣿⣿⠋⠉⠙⢿⠀⠀⠀⢸⣿⡿⠋⠙⠋⠀⠀⠀⠀⠀⠀⠳⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⢿⠁⠈⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡸⠇⠀⠀⠀⢿⡏⠀⠀⠀⠈⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡸⣾⣟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣴⣶⣄⣀⣠⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤⡀⠙⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⣠⣿⣿⢿⢿⣇⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⣿⢃⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠟⣃⣀⣀⠀⠀⢻⠿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡏⢹⡷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠈⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿⡷⠾⠃⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢛⠆⡞⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢉⣉⣀⣤⣄⠀⠀⠀⢠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⡀⠀⠀⢀⣤⣤⣦⣿⠀⠀⠀⠀⣸⣿⣾⣾⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⣤⣥⡄⢀⣤⠶⣤⠀⠀⠀⣤⣄⣠⡾⢿⣝⣯⣭⡀⢠⡄⢸⡍⣿⣿⣿⣧⠀⢠⣤⢤⣤⠀⣤⣭⣭⡽⣟⣥⠶⣤⡀⢡⣤⡄⢨⣭⡍⣟⣵⠶⣤⡀⣤⣿⣿⣯⣽⣭⡇⣤⡄⢠⡄⢀⣴⠶⣤⡀⠀
⠀⢀⣀⣸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⣾⡇⣿⣿⢻⣧⣌⢭⣿⣿⣧⢸⡇⢸⣽⡇⣿⣿⣿⠀⢸⣿⣀⣿⠀⣿⣟⣼⣟⣿⣿⠀⣿⡇⢿⡟⣧⣼⢿⡇⣿⣿⠀⣿⡇⠀⣿⡗⣿⣿⣿⡇⣿⣷⢸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢉⣡⣿⡟⣭⣵⣿⣿⠀⣿⡇⣿⡇⣿⣷⣶⡏⣻⣷⢿⣿⢹⣿⡇⣼⣿⡇⣿⣿⣿⡄⢸⣿⢩⠉⠀⣿⣏⢹⣧⣿⣿⠀⣿⣇⢸⡇⢿⡟⣸⡇⣸⣿⠀⣿⡇⠀⣿⡇⣿⣹⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⣿⣿⡿⠶⠟⠡⣿⣇⡿⢿⣝⡷⠾⣟⣟⣿⣠⠿⠇⣿⣿⣇⣿⣿⣿⣷⠸⠿⣸⣄⣀⣿⣟⣸⣿⣯⣿⠶⠟⣹⡸⢇⡸⣇⣿⣇⣯⡿⠶⠟⠁⢀⣿⣇⣿⡺⠿⡇⠿⠀⠿⠇⣞⠿⠶⠻⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⡄⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠭⠭⠽⠿⠿⠿⠿⠿⠿⣿⣶⣾⣿⣯⣯⣭⣭⣭⣭⣭⣭⣄⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⣷⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣿⣟⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣾⣷⡿⣽⣧⣷⠀⡒⣠⣷⢿⣿⣍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⠻⠶⢮⣏⠼⡿⠽⢛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⢿⢿⣟⣽⣿⣿⣿⣿⣶⣿⠾⠊⠉⡈⣁⣬⠻⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣼⣿⣿⣿⣧⣾⡻⡛⢻⢟⣿⢯⣵⢼⣆⣰⠰⠔⠀⠀⠀⠀⠀⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠈⠈⠈⠀⠉⠁⠉⠉⠋⠉⠉⠙⠉⠋⠃⠀⠀⠊⠑⠋⢪⣶⡞⠱⠟⢟⠙⡙⠐⡋⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⠶⠿⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡷⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀⣻⣿⣿⣿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⣴⡄⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⢨⣽⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢥⠀⢀⠠⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠨⢰⡶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠋⠉⠉⠛⣿⣿⣿⣟⣗⣶⣣⣿⣾⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠉⠙⢿⣿⠟⠛⢿⣿⣿⠟⠋⠛⢿⠁⠀⠀⢹⣿⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⠟⠉⠉⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠃⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⡽⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣴⣦⡀⠀⣀⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⠀⠹⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠀⣠⣿⣿⢿⢿⣇⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢻⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠻⣃⣀⣀⠀⠀⢿⣿⠾⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⡏⢽⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠀⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠻⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿⡷⠾⠃⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢸⣿⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠯⠥⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢉⣉⣤⣤⣤⠀⠀⠀⢠⣤⣤⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⡀⠀⠀⠀⡀⠀⠀⢀⣤⣤⣶⣯⠁⠀⠀⠀⢠⣿⣾⣾⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⡤⣥⡄⢀⣤⠶⣤⠀⠀⠀⣤⣄⣠⡾⢿⣝⣯⣭⡀⢠⡄⢸⡍⣿⣿⣿⣧⠀⢠⣤⢤⣤⠀⣤⣯⣭⡽⣟⣵⠶⣤⡀⢡⣤⡄⢨⣭⡍⣟⣵⠶⣤⡀⣤⣼⣿⣯⣽⣭⡇⣤⡄⢠⡄⢄⣴⠶⣤⡀⠀
⠀⢀⣠⣸⣿⣀⡀⣿⣇⣸⣿⢸⣿⠀⣿⡇⣶⡇⣿⡏⢻⣧⣌⢭⣿⣿⣧⢸⡇⢨⣽⡇⣿⣿⣿⠀⢸⣿⣀⣿⠀⣿⣟⣼⢟⣿⣿⠀⣿⡇⣿⡟⣧⣼⢿⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⢿⣿⡇⣿⣷⢸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣡⣿⡟⣭⣵⢸⣿⠀⣿⡇⣿⣧⣿⣧⣶⡏⣻⣷⢿⣿⢹⣿⡇⣼⣿⡇⣿⣿⣿⡄⢸⣿⠩⠉⠀⣿⣏⢻⣧⣿⣿⠀⣿⣇⢸⡇⢿⡟⣸⡇⣸⣿⠀⣿⡇⠀⣿⡇⣿⢹⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⣿⣎⡿⠶⠟⠁⣿⣇⡿⢿⣝⠷⠾⣟⣟⡿⣠⠿⠇⣿⣿⣇⣿⣿⣿⣷⠸⠿⣀⣀⣄⣿⣟⣸⣿⣯⣿⠶⠟⢹⡸⢇⡸⣇⣻⣇⣯⡿⠶⠟⠁⢀⣿⣇⣿⣺⠿⡇⠿⠀⠿⠇⣞⠿⠶⠻⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣇⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣅⢀⣨⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠾⠿⠿⠿⠿⠿⠭⠤⠀⠈⠉⠭⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⢉⣿⣿⣿⣿⣿⡏⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⠇⢰⠹⡿⠿⣟⠟⠖⠄⠥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⢇⠈⠤⣁⠃⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⣿⣷⣮⣮⡱⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠁⠁⠁⠀⠉⠈⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠋⠉⠋⠛⠋⢙⣬⣄⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡷⠶⠿⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡷⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⠷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡢⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⣼⡿⣷⣶⠄⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢭⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣥⣴⠄⢤⣿⣽⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠟⠉⢻⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⠋⠉⠉⢻⣿⣿⠟⠛⢻⠂⠀⠀⠀⠀⠀⢐⢿⣿⣿⣿⡟⠁⠀⠀⠀⠙⠋⠙⢻⣿⣿⣿⣿⠿⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡅⠀⠀⠀⠏⠀⠀⠈⢻⣿⠁⠀⠀⠈⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⠛⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⢀⣀⡀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⢺⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⢿⣿⣦⣤⣾⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⠀⣸⣿⣿⢿⢿⣅⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢿⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣘⠟⣁⣀⣀⠀⠀⢺⣷⡶⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⡏⣽⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣼⡇⠀⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠨⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠘⣿⡷⠾⠋⢸⣿⠷⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⢀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢻⣿⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡧⡦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢉⣩⣤⣤⣥⠀⠀⠀⢠⣿⣷⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣯⠀⠀⠀⠀⢠⣿⣾⣾⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⡤⣤⡄⢀⣤⠶⣤⠀⠀⠀⣤⣤⣠⡶⢿⣝⣯⣭⡁⢠⡄⢸⡍⣿⣿⣿⣧⠀⢠⣤⢤⣤⠀⣬⣭⣯⡽⣟⣵⠶⣤⡀⢡⣤⡄⢨⣭⡍⣟⣵⠶⣤⡀⣤⣼⣿⣯⣭⣭⡏⣥⡤⢠⡄⢄⣴⢶⣤⣀⠀
⠀⠀⣠⣸⣿⣐⡂⣿⣇⣸⣿⢸⣿⠀⣿⡇⣾⡇⣿⡏⢻⣧⣌⢭⣿⣿⣧⢸⡇⢨⣽⡇⣿⣿⣿⠀⢸⣿⣀⣿⠀⣿⣟⣼⢟⣿⣿⠀⣿⡇⢻⡟⣧⣼⢿⡇⢿⣿⠀⣿⡇⠀⣿⡇⣿⣿⣿⡇⣿⣷⢸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣥⣿⡟⣭⣵⢸⣿⠀⣿⡇⢿⡧⣿⣷⣶⡏⣻⣷⢿⣿⢹⣿⡇⣾⣿⡇⣿⣿⣿⡇⢸⣿⠉⠉⠀⣿⣯⢹⣧⣿⣿⠀⣿⣇⢸⡇⢿⡟⣼⡇⣼⣿⠀⣿⡇⠀⣿⡇⣿⣹⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣇⣿⣇⣿⣿⣈⡿⠶⢟⡁⢸⣇⡿⢿⣝⠷⠾⣟⣞⠿⣠⠿⠇⣿⣿⣇⣿⣿⣿⣿⠸⠿⢀⣠⣄⣿⣟⣸⣿⣯⣿⠶⠟⢹⣸⣇⣸⣇⣻⣇⣯⡿⠶⠟⠁⢀⣿⣇⣿⡹⠿⡇⠿⠀⠿⠇⣞⠿⠶⠻⢇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣧⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣦⡄⢀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣒⣒⣓⣛⣛⣓⣛⣛⣓⡒⠂⠀⠀⠒⠒⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣞⢿⣯⡿⡆⠀⠐⠐⠀⠀⠀⠈⠐⠄⣴⢒⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⡿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣟⣿⣿⣯⠦⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣯⣾⣿⣿⣿⡻⣿⣯⡟⣞⣤⣲⣐⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠈⠁⠈⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠙⠛⠋⠙⠙⠛⠉⠑⠉⠚⠘⣥⣧⠋⠉⠘⠝⡊⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⠶⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡷⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣾⣿⣿⣿⡗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⣤⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⢀⣼⣾⣹⣾⣆⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠀⡀⠈⢀⢘⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⢀⠀⠄⣐⡾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣏⣒⣀⣰⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠉⠹⣿⡿⠿⣿⣿⣿⣿⠿⠿⣿⠟⠉⠙⢿⣿⣿⠟⠛⢻⡇⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠙⠋⠙⢻⣿⣿⣧⣲⠽⠟⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠝⠀⠀⠈⢻⣿⠃⠀⠀⠈⠀⠀⠀⢸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⡏⡯⡟⠏⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣀⡀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢀⡀⠀⠀⠀⠀⠀⢡⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⢿⣿⣦⣤⣶⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠁⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠀⣸⣿⣿⢿⢿⣁⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢸⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠻⣋⣀⣀⠀⠀⠠⣿⣷⠾⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣾⡇⠀⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⣿⡷⠾⠋⢸⣿⠷⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢻⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢻⣧⣥⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠈⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⣉⣤⣤⣵⡀⠀⠀⢀⣾⣷⣾⣿⡅⠀⠀⠀⠀⠀⠀⠀⣼⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣯⠀⠀⠀⠀⠀⣽⣾⣾⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⡤⣤⡄⢀⣤⠶⣤⠀⠀⠀⣤⣤⣠⡶⢿⣝⣯⣭⡁⢠⡄⢸⡍⣿⣿⣿⣿⠀⢠⣤⢤⣤⠀⣤⡭⣭⡽⣟⣵⠶⣤⡀⢨⣤⡄⢠⣭⡍⣟⣵⡶⣤⡀⣤⣤⣿⣯⣽⣯⡏⣭⡴⢠⡄⢀⣴⢶⣤⣠⠀
⠀⠀⣀⣸⣿⣀⡢⣿⣇⣸⣿⢸⣿⠀⣿⡇⢼⡇⣿⣿⢻⣧⣌⢭⣿⣿⣧⢸⡇⢨⣽⡗⣿⣿⣿⡇⢸⣿⣀⣿⠀⣿⣟⣼⢟⣿⣿⠀⣿⡇⢸⡟⣧⣼⢿⡇⢿⣿⠀⣿⡇⠀⣿⡗⣿⣿⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣥⣿⡟⣭⣵⢸⣿⠀⣿⡇⢸⡇⣿⣷⣶⡏⣻⣷⢿⣿⢹⣿⡇⢸⣿⡗⣿⣿⣿⣇⢸⣿⠩⠉⠀⣿⣯⢹⣧⣿⣿⠀⣿⡇⢸⡇⢿⡟⣼⡇⣼⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣇⣿⣇⣿⣿⣈⡿⠶⠟⡁⠘⣇⣿⢿⣝⠷⠾⣟⣟⠿⣠⠿⠇⣿⣿⣇⣿⣿⣿⣿⡾⠿⠀⢠⣄⣿⣇⣸⣿⣯⣿⠶⠟⢱⡸⢇⣸⣇⣻⣇⣯⡿⠶⠟⠁⢀⣿⣇⣿⡸⠿⡇⠿⠀⠿⠇⣞⠿⠶⠻⢇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠘⠛⠻⠿⠿⠿⠿⠿⠿⠿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⠀⠸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆⠀⣼⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⠇⠀⣀⣉⣉⣛⣛⣛⣛⣋⣉⣛⣛⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⠒⠀⠀⠀⠒⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣬⣥⣤⣤⣬⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣵⣶⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⡿⣿⣿⠯⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣹⣹⣗⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⣿⣿⣷⣴⣳⣴⠔⠆⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠙⠉⠙⠉⠐⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡂⢶⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⡀⣠⣷⣾⣾⣷⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠐⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠠⡄⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠋⠉⠙⣿⣿⣿⣿⣅⣀⠀⠀⠡⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠏⠉⢿⡿⠿⢿⣿⣿⣿⠟⠛⢿⠋⠉⠉⢻⣿⣿⠟⠉⠛⠿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠉⠉⠙⣽⣽⣵⣤⠀⠋⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠘⠁⠀⠀⠹⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠰⣿⢾⠟⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⣤⣄⠀⠀⠀⣰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⢶⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠈⢻⣿⣷⣶⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⣸⣿⣿⢿⢿⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢸⢃⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠻⣋⣀⣀⠀⠀⠀⣿⡿⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡏⢽⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠈⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⡷⠾⠋⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣸⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢹⣧⣥⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⡻⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⣩⣤⣶⣿⡀⠀⠀⠀⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⣼⣶⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⣴⣴⣶⣿⡁⠀⠀⠀⠀⣸⣶⣾⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⡄⣤⡤⣤⡄⢀⣤⠶⣤⠀⠀⠀⣤⣤⣠⡶⢿⣝⣯⣭⡁⢠⡄⢨⡍⣿⣿⣿⣿⡄⢠⣤⢤⣤⠀⣤⡭⣭⡿⣟⣵⠶⣤⡀⢨⣤⡄⢠⣭⡍⣟⣽⠶⣤⡀⣤⣤⣽⣯⣽⣭⡏⣭⡽⢠⡄⢀⣴⢶⣤⠀⠀
⠀⢀⣀⣸⣿⣀⣲⣿⣇⣸⣿⢸⣿⠀⣿⡇⣾⡇⣿⣿⢿⣧⣌⢭⣿⣿⣧⢸⡇⢨⣽⡇⣿⣿⣿⡇⢸⣿⣀⣿⠀⣿⣟⣼⠟⣿⣿⠀⣿⡇⢸⡟⣧⣼⢿⡇⢻⣿⠀⣿⡇⠀⣿⡇⣿⢿⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣾⣿⣿⣿⣿⢩⣽⣿⡟⣭⣵⢻⣿⠀⣿⡇⢻⡧⣿⣿⣶⡏⣻⣷⢿⣿⢹⣿⡇⣼⣿⡇⣿⣿⣿⣧⢸⣿⠉⠉⠀⣿⣿⢻⣧⣿⣿⠀⣿⡇⢸⡇⢿⡟⣼⡇⣾⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⣿⣏⡻⠶⠟⡁⠘⣇⣿⢿⣝⠷⠾⣟⣞⠿⣠⠿⠇⣿⣿⣇⣿⣿⣿⣿⡾⠿⠀⣠⣆⣿⣇⣸⣿⣯⡿⠶⠟⣹⡸⢇⡸⣇⣿⣇⣯⣿⠶⠟⠁⢀⣿⣇⣿⡸⠿⡇⠿⣀⠿⠇⣞⠿⠶⠻⢇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠃⠠⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢀⣿⣿⣿⣿⣿⣿⣿⠃⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠙⠛⢛⠛⣻⣿⣿⣿⣿⡿⠁⠀⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡏⠀⣠⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⠀⠀⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠯⠽⢷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣝⣾⣾⡅⡀⢁⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⡿⣿⣽⣽⣷⣿⣿⡶⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠉⠉⠉⠉⠈⠁⠉⠈⠈⠉⠁⠙⠉⠙⠈⠉⠉⠁⠉⠈⠃⢡⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢘⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡂⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣾⣿⣷⣿⣷⣿⣿⣿⣿⣿⣶⣷⣶⣦⣀⣀⣠⣾⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠄⠀⠀⠀⠀⠂⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⢯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠉⠀⠈⢻⣿⣿⣿⣿⢄⣀⣀⢐⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠟⠀⠸⡿⠛⠿⣿⣿⣿⠛⠉⠻⠁⠀⠀⢹⣿⣿⡏⠉⠙⠻⠂⠀⠀⠀⠀⠀⢲⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⣻⣺⣿⣿⠖⠋⠉⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⢼⡿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣽⣯⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢠⣶⣶⡀⠀⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠹⡾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢹⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⢸⣆⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⣸⣿⣿⢿⢿⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⢸⢇⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠙⣃⣀⣀⠀⠀⠀⠸⠿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⠈⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣿⡷⠾⠃⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣸⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢢⢀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢹⣧⣄⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠨⠏⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⢩⣴⣶⣿⡀⠀⠀⠀⣸⣷⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣽⣶⣿⣷⣏⠀⠀⠀⠀⠀⠀⠀⣸⣾⣷⣿⡇⠀⠀⠀⠀⢸⣶⣼⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⡀⠀⡀⣤⣴⣢⡶⢾⣝⣯⣭⡁⢠⡄⢠⡍⣿⣿⣿⣿⡄⢠⣤⢤⣤⠀⣤⡭⣯⡿⣟⣽⠶⣤⡀⢠⣤⡄⢠⣭⡍⣟⣽⡶⣤⡀⣤⣤⣽⣯⣽⣯⡏⣭⡽⣭⡅⢀⣴⢶⣤⠀⠀
⠁⢀⣠⣸⣿⣀⣸⣿⣇⣸⣿⣸⣿⠀⣿⡇⣸⡇⣿⣿⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⣿⡇⢸⣿⣀⣿⠀⣿⣟⣼⠟⣿⣿⠀⣿⡇⢸⡟⣧⣼⢿⡇⢻⣿⠀⣿⡇⠀⣿⡇⣿⣹⣿⡇⣿⣷⣹⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⣵⣾⣿⠀⣿⡇⣿⡇⣿⣿⣷⡏⣻⣷⢿⣿⢹⣿⡇⢰⣿⡏⣿⣿⣿⣧⢸⣿⠉⠉⠀⣿⣿⢻⣯⣿⣿⠀⣿⡇⢸⡇⢿⡟⣼⡇⣾⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣯⣿⣇⣿⣿⣿⡻⠶⠟⠁⠸⣇⣿⢿⣝⠷⠾⣟⡞⠿⣠⠿⠇⢸⣿⣇⣿⣿⣿⣿⡿⠿⢀⣠⣇⣿⣏⣸⣿⣯⣿⠶⠟⣹⣸⣇⣸⣇⣻⣇⣯⡿⠶⠟⠁⢀⣿⣇⣿⡺⠿⡇⠿⣠⠿⠇⣘⠿⠶⠻⢇⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⠃⠀⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⠇⠀⣩⣭⣭⣭⣭⣭⣭⣭⣭⠁⠀⠙⠛⠛⣛⣛⣛⣛⣛⣛⣛⡀⠀⠘⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⢀⣠⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠌⣿⣿⣷⣿⣿⣿⣿⠹⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⠿⠿⢿⠿⠯⠱⠾⠿⡯⣟⣿⣽⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣖⣻⣼⣾⡀⡀⣀⣀⢏⡼⢛⠩⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⡿⣿⣿⣿⣷⣦⡶⣽⣿⣿⣿⣷⣶⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠉⠉⠉⠉⠉⠉⠙⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠸⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⣠⣼⣿⣾⣿⠀⠀⠀⠀⠀⠀⠰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢆⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⡄⠀⠄⢘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣧⢤⠀⠀⠠⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⠙⠛⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠙⠿⠛⠿⣿⣷⣿⣶⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⠛⠀⠈⠋⠉⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠹⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠊⠀⠀⠹⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⣀⠀⠀⠀⠀⢹⡛⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⣟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⣿⣷⣶⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡄⢹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣷⣤⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⣿⣿⢿⢿⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⢸⢇⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠈⣉⣀⣀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣿⡏⢹⡇⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⢿⡇⠘⢸⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠃⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣼⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⣳⡂⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢹⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⢠⣀⡀⣿⡇⠀⢸⣿⢸⣿⠀⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠷⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⢩⣶⣶⣿⠀⠀⠀⠀⣸⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣽⣶⣿⣷⣏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⡇⠀⠀⠀⠀⣽⣾⣾⣿⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⠀⢀⡀⣤⣴⣣⡶⢾⣝⣯⣿⡀⢠⡄⢠⡍⣿⣿⣿⣿⠀⢠⣤⢤⣤⠀⣤⣿⣿⡿⣟⣽⠶⣤⡀⢨⣥⡄⢠⣭⡍⣟⣽⠷⣤⡀⣤⣤⣿⡯⣽⣯⡏⣭⡽⣭⡍⢂⣴⢶⣤⠀⠀
⣃⣀⣤⣼⣿⣀⣀⣿⣇⣿⣿⣼⣿⠀⣿⡇⣸⣧⣿⣿⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⣿⠀⢸⣿⣀⣿⠀⣿⣏⣼⢟⣻⣿⠀⣿⡇⢸⡟⣧⣼⢿⡇⢹⣿⠀⣿⡇⠀⣿⡇⣿⢽⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⣷⣿⣿⠀⣿⡇⣿⡇⣿⣿⣷⡏⢻⣷⢿⣿⢹⣿⡇⢰⣿⡇⣿⣿⣿⡆⢸⣿⠉⠉⠀⣿⡿⢻⣯⣿⣿⠀⣿⡇⢸⡇⢿⡟⣼⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣯⣿⣇⣿⣿⣿⡿⠶⠟⢱⣿⣇⣿⢿⣝⠷⠾⣟⣞⠿⣠⠿⠇⢸⣿⣇⣿⣿⣿⡇⠸⠿⢠⣤⣇⣿⣇⣸⣿⣯⣿⠶⠟⣹⣸⣟⣸⣇⣿⣇⣯⣿⠶⠟⠁⢀⣿⣇⣿⣸⡿⡇⠿⣠⠿⠇⠘⠿⠶⠻⢇⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⢘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⡇⠀⠠⠶⠶⠶⠶⠶⠾⠿⠿⠿⠀⠀⠈⠉⠉⠉⠩⠭⠭⠭⠭⠭⠄⠀⠈⠭⠭⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⣯⣽⣟⠀⠠⢒⡌⠍⠁⠄⠄⠀⠐⠉⣁⡠⠌⢎⢿⡿⢟⢯⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⡿⣟⣧⣨⣀⣀⣀⣀⡀⣄⣀⡈⠼⣿⡗⡣⠂⠐⠽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣛⣿⣰⣤⡀⡀⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢿⠿⠿⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⠿⠿⠷⠒⠶⠽⣳⣲⣖⣤⣦⣿⣾⣿⣿⣾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠈⠉⠁⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠑⢿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡄⠤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⣠⣴⣷⣶⣿⡀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠀⠂⠀⠀⢈⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠋⠉⠛⢿⣿⣿⣿⣇⡄⡀⠀⠀⠽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠟⠛⠟⠁⠀⠙⣿⣿⣿⡿⠿⢿⣟⠅⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⠃⠀⠀⠀⠈⠛⠙⠻⣽⣾⣯⣶⡴⠾⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠛⠉⠀⠀⠉⠀⠉⢿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⢽⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡷⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⢀⣀⡀⠀⠀⢀⣹⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠻⣿⣿⣶⣾⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⢸⣿⡶⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⢿⢟⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⢸⢇⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡏⢹⡇⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⢿⡇⠘⢸⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠃⢸⣿⠶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣸⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣲⠂⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⠀⣿⡇⠀⠀⢹⣧⣤⢸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⠀⢸⣿⠀⢠⣤⡀⣿⡇⠀⢸⣿⢸⣿⢠⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⢩⣶⣷⣿⠀⠀⠀⠀⣽⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣽⣶⣿⣷⣯⠀⠀⠀⢠⠀⠀⠀⣾⣿⣷⣿⡇⠀⠀⠀⢀⣿⣾⣾⣿⣿⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀
⣄⠀⠀⢠⣤⣤⡄⣤⣤⣤⣄⣀⣤⠶⣤⡀⢀⡄⣤⣼⣣⡶⢾⣝⣯⣯⡀⢠⡄⢠⡍⣿⣿⣿⣿⠀⢠⣤⢤⣤⠀⣤⣿⣯⡿⣟⣽⠶⣤⡀⢨⣥⡄⢠⣭⡍⣟⣽⠷⣤⡀⣤⣬⣿⡯⣭⣯⡏⣭⡽⣭⡍⢇⣴⢶⣤⠀⠀
⣏⣀⣴⣾⣿⣀⣰⣿⣇⣿⣿⣾⣿⠀⣿⡇⣾⡇⣿⣿⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⣿⠀⢸⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡟⣧⣼⢿⡇⣸⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣹⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⣷⣿⣿⠀⣿⡇⣿⡇⣿⣿⣿⡏⢻⣷⢿⣿⢹⣿⡇⢰⣿⡇⣿⣿⣿⡄⢸⣿⠉⠉⠀⣿⡏⢻⣯⣿⣿⠀⣿⣇⢸⡇⢿⡟⣼⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡿⠶⠟⢱⣿⣇⣿⢿⣝⠷⠾⣟⣞⠿⣀⠿⠇⢸⣿⣇⣿⣿⣿⠃⠸⠿⢰⣴⣇⠿⢇⠸⠿⣯⡿⠶⠟⢹⣸⣟⣸⣇⠿⢇⣯⡿⠶⠟⠁⣀⣿⣇⣿⣹⠿⡇⠿⣠⠿⢇⡘⠿⠶⠻⢇⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⡅⠀⠀⢨⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣿⡇⠀⠀⠀⣒⣒⡒⢒⣒⣒⣒⣒⣒⣀⣀⣀⡀⠀⠀⠒⠒⠒⠲⠶⠶⠆⠀⠀⠀⠒⠛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿
⣿⣧⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣀⣆⠀⢿⡯⠴⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣗⣾⢯⡠⣀⢀⠀⡀⠀⡀⠀⠀⡈⢴⢿⢺⣣⢑⣛⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣫⣩⡽⣒⣄⣕⣪⣶⣟⣮⣤⣶⣿⣧⡷⠻⢆⣣⣪⡰⢀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠟⠳⠾⠿⠷⠶⠶⡶⡴⢿⣾⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠀⠸⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠰⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢀⠠⠠⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠟⠁⠀⠈⢻⣿⣿⣿⣷⣤⣄⡠⠀⣱⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠛⠿⠿⢿⣿⣿⡿⠋⠙⠁⠀⠀⠘⣿⣿⣿⡿⠛⢻⣿⡧⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠉⣿⣯⣞⡏⠏⠀⠉⢻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⣠⣴⣄⣀⣠⣤⣴⡏⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠼⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠙⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⢀⣦⠀⣠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⡿⠟⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣿⣿⣿⠿⢇⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⢸⢇⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⡇⢸⣿⠋⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⢹⡇⣸⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⣿⡷⠾⠃⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡇⠀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⠀⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⣿⡇⠀⠀⢸⣿⣬⡄⢿⣇⣸⡿⡀⣿⡇⠀⠀⢸⣧⣤⣸⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⢀⢸⣿⠀⣴⣦⡄⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡉⢉⣾⣷⣿⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣷⡏⠀⠀⠀⢸⡀⠀⢀⣿⣿⣷⣿⣷⠀⠀⠀⣸⣿⣾⣾⣿⣿⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀
⣤⡀⠀⢠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⠀⣠⣆⣭⣽⣠⡶⢾⣝⣯⣭⡀⢠⡄⢠⡍⣿⣿⣿⡯⠀⢠⣤⢤⣤⠀⣬⡿⣿⡿⣟⣵⠶⣦⡀⢸⣥⡄⢨⣯⡍⣟⣽⢿⣦⡀⣤⣽⣿⡯⣽⣭⡏⣭⡽⣩⡍⢇⣴⢶⣤⡀⠀
⣿⣦⣴⣿⣿⣀⣰⣿⣇⣿⣿⢸⣿⠀⣿⡇⣿⡇⣿⣧⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⡇⠀⢸⣿⣀⣿⠀⣿⣇⣼⣗⣿⣿⠀⣿⡇⢸⡟⣧⣼⢿⡇⣼⣿⠀⣿⡇⠀⣿⡇⣿⢽⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣽⣿⡿⣭⣷⣸⣿⠀⣿⡇⣿⡏⣿⣿⣷⡏⢻⣷⢻⣿⢹⣿⡇⠀⣿⡇⣿⣿⣷⠀⢸⣿⢉⠉⡀⣿⡯⢻⣯⣿⣿⠀⣿⣇⢸⣇⣿⡟⣼⡇⣿⣿⠀⣿⡇⡀⣿⡇⣿⢿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡿⠻⠶⠟⢱⣿⡇⠿⢿⣝⠷⠾⣟⣞⠿⡀⠿⠇⢀⣿⣇⣿⣿⣿⠀⠸⠿⢸⣟⡃⠿⠗⠸⠟⣋⠻⠶⠟⠹⠸⠟⠸⠇⠻⠇⣏⠻⠶⠟⠁⠇⠿⠇⣿⡻⠿⡇⠿⣠⠿⢇⣞⠿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⠀⡀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣭⣤⣭⣭⣭⣭⣭⣭⡀⠀⢀⣉⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿
⣻⣵⣆⣐⠒⠀⠀⠀⠀⠀⠀⣀⡀⢠⣥⣢⡴⢖⣻⣞⣉⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣫⣧⢦⣐⢀⢀⣀⡀⡀⢀⢄⡌⢬⣿⣽⡿⠼⡹⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣿⣾⣽⣭⣽⣿⣾⣿⣘⣿⣟⢪⣽⣿⣿⡖⣆⡕⠄⠀⠀⠀⠀⠀⠀⠠⣢⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠿⠻⠻⠛⠻⠿⠿⠿⠿⠿⠿⠿⠺⠍⠳⠓⠚⠛⠚⠓⠶⠴⢔⠂⢿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣴⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠰⣠⣖⢖⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠜⠂⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠔⠌⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⣯⣇⡧⣼⣔⢐⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣹⢿⢿⡿⠛⠿⠛⢿⣿⣿⠟⠉⠉⠀⠀⠀⠘⢿⣿⣿⠟⠛⢿⣿⠇⠀⠀⠀⠀⠘⢎⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⡟⠃⠀⠈⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠫⠃⠀⠀⠀⠀⠀⠀⠙⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⣶⣀⣀⣠⣶⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠲⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡙⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣷⣀⣠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⠿⢇⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⣸⢇⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⡇⢸⣿⠫⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⣾⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⠀⠀⣿⡷⠾⠃⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡏⠋⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⢀⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣾⠀⠀⣿⡇⠀⠀⢸⣿⣬⡄⢿⣇⣸⡿⡀⣿⡇⠀⠀⢸⣷⣶⣼⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡷⣾⡟⢻⣿⢠⢸⣿⠀⣶⣶⡄⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡀⠀⡍⢉⣾⣷⣿⠀⠀⠀⠀⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣷⡇⠀⠀⠀⢸⡄⠀⢀⣿⣿⣷⣿⣷⠀⠀⠀⣾⣿⣾⣾⣿⣿⣾⣷⣶⣶⣤⠀⠀⠀⠀⠀
⣤⠀⠀⣠⣤⣤⡄⣤⣤⣤⣄⢀⣤⠶⣤⡀⣴⡎⣭⡝⣠⡷⢾⣝⣯⣭⡀⢠⡄⢠⡍⣿⣿⣿⡏⠀⢠⣤⢤⣤⠀⣬⡿⣿⡿⣟⣵⠶⣦⡀⢹⣧⡄⢨⣿⡏⢟⣽⢿⣦⡀⣤⣿⣿⡯⢽⣭⡏⣭⡽⣭⡍⢏⣴⢶⣤⠀⠀
⣿⣷⣾⣿⣿⣐⡀⣿⣇⣿⣿⢸⣿⠀⣿⡇⣿⡇⣿⣧⢿⣧⣬⢭⣿⣿⣧⢸⡇⠈⣽⡧⣿⣿⡇⠀⢸⣿⣀⣿⠀⣿⣗⣼⢟⣿⣿⠀⣿⡇⢸⡟⣧⣼⢿⡇⣾⣿⠀⣿⡇⠀⣿⡇⣿⣾⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⣷⢸⣿⠀⣿⡇⣿⡇⣿⣿⣷⡏⢻⣷⢻⣿⢹⣿⡇⠀⣿⡇⣿⣿⣿⡀⢸⣿⢉⠉⡄⣿⡏⢻⣯⣿⣿⠀⣿⣇⣸⣧⣿⡟⣼⡇⣿⣿⠀⣿⡇⡆⣿⡇⣿⢿⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠿⠎⠻⠶⠟⠹⠿⠇⠿⢿⣝⠷⠾⣟⣞⠿⡀⠿⠇⢀⣿⣇⣿⣿⣿⡇⠸⠿⢸⣿⣇⠿⢏⡸⢟⣋⡻⠶⠟⠙⠹⠏⡸⢇⣻⣇⣋⡻⠶⠟⠁⠃⠿⠇⣿⠺⠿⡇⠿⣠⠿⢇⣞⡿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⡄⠀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣶⣶⣾⣿⣿⣿⣿⣿
⢝⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠂⠈⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠪⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢠⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠠⡂⢄⠀⡀⢠⣴⣏⣧⣀⡂⡀⠀⠰⠰⠠⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠋⠃⠉⠁⠙⠛⠛⠛⠛⠛⠒⠓⠐⠋⠚⠈⠀⠀⠘⠒⠂⠐⠰⠎⠕⠟⠙⠛⠋⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⠷⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢈⣿⣿⣿⡟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⡰⠂⣰⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣽⣿⣽⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣇⠄⣂⡀⠀⠀⡛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠙⠿⣿⣟⣻⣮⠷⡦⡤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡽⠿⠿⠿⠉⠙⠛⠻⣿⣿⠟⠉⠉⠀⠀⠀⠈⠿⣿⣿⠛⠛⠻⣿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⢿⣎⡛⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣄⠀⠀⣠⣤⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⣿⣿⣿⣿⡟⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣶⣄⣠⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢃⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⣼⢃⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⡇⢸⣿⢫⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⢿⣇⡟⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⢀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣿⡷⠾⠃⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⡏⠁⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⢸⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⢛⡇⠀⠀⣿⡇⠀⠀⢸⣿⣬⡄⢿⣇⣸⡿⡄⣿⡇⠀⠀⢸⣿⣿⣾⣿⣤⡄⢸⠀⢸⣿⠀⢸⣿⠀⣿⡗⣾⡟⢻⣿⢠⢸⣿⠀⣶⣤⡄⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣤⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣡⡄⢰⣿⠉⣾⣷⡏⠀⠀⠀⠈⣿⣷⣿⣿⡇⠀⢸⠀⠀⠀⠀⢀⣿⣶⣿⣷⡇⠀⠀⠀⣸⡆⠀⢠⣿⣿⣷⣿⣷⠀⠀⢀⣿⣿⣾⣾⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⣽⠀⢠⣤⣭⡄⣬⣭⣭⡄⢀⣤⠶⣤⠀⣿⡏⣭⡅⣨⡷⢶⣝⣯⣥⡀⢠⡄⢠⡍⣿⣿⣿⡇⠀⢠⣤⢤⣤⠀⣬⡭⣭⡝⣟⣵⠶⣦⡀⢹⣥⡄⢨⣭⡍⣟⣽⢿⣦⡀⣤⣭⣯⡏⢩⣭⡏⣭⡽⢩⡍⢇⣴⢶⣤⠀⠀
⣿⣿⣿⢺⣿⣘⣀⣿⣧⣿⡧⢸⣿⠀⣿⡇⣿⡇⣿⣧⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⡇⠀⢸⣿⣀⣿⠀⣿⣟⣼⣟⣿⣿⠀⣿⡇⢸⡟⣧⣼⢿⡇⢿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣽⣿⣟⣭⡁⢸⣿⠀⣿⡇⣿⡇⣿⣿⣷⡏⢻⣷⢻⣿⢹⣿⡇⠀⣿⡇⣿⣿⣿⡄⢸⣿⢉⢉⡀⣿⡏⢻⣯⣿⣿⠀⣿⣧⢸⡧⣿⡟⣼⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⣸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡇⠈⠿⠶⠟⠁⢩⡅⠿⢿⣝⠷⠾⣟⡞⠿⠀⠿⠇⣀⣿⣇⣿⣿⣿⣷⠸⠿⢐⣒⡂⠿⢇⠸⠟⠊⠻⠶⠟⠁⠸⠇⠸⠇⠺⠇⣊⡻⠶⠟⠁⠀⠿⠇⢻⠸⠿⡇⠿⣠⠿⢇⣞⡿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿
⣿⣿⣏⡝⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡨⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢈⠍⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⡠⠈⠄⠀⠃⣬⣮⣧⣄⣰⡁⠀⣄⠐⢄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠁⠀⠀⠙⠛⠋⠉⠋⠉⠃⠐⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠋⠙⠋⠁⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⢂⢐⣠⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣯⡇⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡃⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠁⠀⠀⠈⠻⠿⢿⣿⢉⠄⣭⣶⠠⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠔⠛⠿⡿⠁⠙⠛⠻⣿⣿⠟⠉⠉⠀⠀⠀⠙⠻⣿⣿⠋⠉⠻⡿⠃⠀⠀⠀⠀⠀⠐⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢞⢷⠆⠁⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣤⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣶⣾⣿⡏⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣶⣄⣠⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⢁⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⣾⢀⣀⣀⠀⠀⢀⣐⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡏⢹⡇⢸⣿⢋⠀⣾⡏⢹⣷⠀⣿⡏⣿⡇⣿⡇⡟⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⢀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⡄⠀⠀⣿⡷⠾⠃⢸⣿⠿⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⣇⣀⢸⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⢸⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠘⠃⠀⠀⣿⡇⠀⠀⢸⣿⣬⡄⢿⣇⣸⡿⡄⣿⡇⠀⠀⢸⣿⣿⣾⣿⣤⡄⢸⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⢠⢸⣿⠀⣶⣦⡆⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣧⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣁⣤⡄⢰⣿⠉⣾⣷⡏⠀⠀⠀⠈⣿⣷⣿⣿⡇⠀⠸⠀⠀⠀⠀⢠⣿⣶⣿⣷⡇⠀⠀⠀⣾⡆⠀⢸⣿⣿⣷⣿⣷⠀⠀⢀⣿⣿⣾⣾⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀
⢠⣿⠀⢠⣬⣭⡅⣬⣭⣥⡄⢀⣴⠶⣤⠀⣿⡏⣯⡅⣨⡷⢶⣝⣯⣥⡀⢠⡄⢠⡍⣿⣿⣿⡇⠀⢠⣤⢤⣤⠀⣬⡭⣭⡽⣟⣵⠶⣦⣀⢩⣥⡄⢨⣭⡍⣟⣽⢶⣦⡀⣤⣭⣭⡍⢩⣭⡏⣭⡽⢩⡍⢇⣴⢶⣤⠀⠀
⣿⣿⣿⢸⣿⣘⣢⣿⣇⣿⡇⢸⣿⠀⣿⡇⣿⡇⣿⣧⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⡇⠀⢸⣿⣀⣿⠀⣿⣟⣼⢟⣿⣿⠀⣿⡇⢸⡟⣧⣼⢿⡇⢿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⠁⢸⣿⠀⣿⡇⣿⡇⣿⣿⣷⡏⢻⣷⢻⣿⢹⣿⡇⠀⣿⡇⣿⣿⣿⡄⢸⣿⠉⠉⠄⣿⡏⢻⣯⢿⣿⠀⣿⡇⢸⡧⢿⡟⢼⡇⢿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣄
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⠇⠈⡿⠶⠟⠁⣩⣅⠿⢿⣝⠷⠾⣟⣎⠿⠀⠿⠇⣠⣿⣇⣿⣿⣿⣿⠸⠿⣨⣭⣅⣿⣇⣸⣟⣉⡻⠶⠟⣁⠸⠇⡸⢇⣹⣇⣉⣻⠶⠟⠁⠀⠿⠇⣹⠸⠿⡇⠿⣠⠿⢇⣞⡿⠶⠻⢧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠟⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣗⣎⠐⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⢿⠥⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢇⠈⡚⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠀⠀⠀⠘⠻⠿⠗⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⢿⡟⠀⠈⠙⠿⣿⡿⠉⠀⠀⠀⠈⠛⠿⢻⡟⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣠⣴⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⡿⠦⠞⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣋⠁⢀⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⡏⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⡷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⢿⡇⣿⡇⠁⢸⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⢀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠃⢸⣿⠷⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⣧⣤⢸⣿⠶⠀⡀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⢿⣿⢸⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⡄⣿⡇⠀⠀⢸⣿⣿⣿⣿⣤⡄⠃⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⢠⢸⣿⢰⣿⣿⡇⣿⡇⠀⢸⣿⣸⣿⢸⣿⣧⣿⢻⣶⣶⣦⠀⠀⠀⠀⠀⠀
⣠⣤⠀⠀⣠⣤⡄⢀⣤⡀⠀⠀⡀⠀⠀⠀⣤⣿⣿⡄⢰⡏⠉⣾⣷⠁⠀⠀⠀⠈⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣷⠀⠀⠀⠀⣾⡄⠀⣼⣿⣿⣷⣿⣷⠀⠀⢀⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣽⣿⣀⢠⣬⣭⡅⣬⣭⣥⡄⢀⣽⠶⣤⠀⣿⡏⣭⡅⣨⡷⢾⣝⣯⣤⡀⢠⡄⢠⡍⣯⣭⣿⡅⠀⢨⣤⢤⣤⠀⣤⡭⣭⡽⣟⣵⠶⣦⣸⢩⣥⡄⢩⣭⡍⣟⣽⢶⣦⡀⣬⣭⣭⡍⢩⣭⡏⣭⡽⢩⡍⢇⣴⢶⣤⠀⠀
⣿⣿⣿⣸⣿⣘⣳⣿⣇⣿⡇⢸⣿⠀⣿⡇⣼⡇⣿⣷⢿⣧⣌⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⡇⠀⢸⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⠀⣿⡏⢸⡟⣧⣼⢿⡇⣼⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⠀
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⠁⢸⣿⠀⣿⡇⠻⠇⣿⣿⣷⡏⢻⣷⠃⣿⢹⣿⡇⠀⣿⡇⣿⣿⣿⡄⢸⣿⠩⠭⠄⣿⡏⢹⣯⢽⣿⠀⣿⡇⢸⡇⢿⡟⢼⡇⢽⣿⠀⣿⡇⠀⣿⡇⢿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣶
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⠀⢈⡿⠶⠟⠁⣸⣇⠿⢿⣝⠷⠾⣟⡖⠿⠀⠿⢇⣿⣿⣇⣿⣿⣿⣿⠸⠿⣰⣶⣆⣿⣇⣸⣿⣮⡻⠶⠟⣱⠸⠇⡸⢇⣺⣇⣮⣿⠶⢟⡁⠀⠿⢇⣿⠸⠿⡇⠿⣠⠿⢇⣞⡿⠶⠻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡏⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢶⣷⡶⠤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢿⣿⣿⡧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣶⣶⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠎⣀⠨⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⡶⢶⣖⣴⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠻⣿⣿⣿⡧⡀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣾⣿⠟⠻⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠉⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠸⢑⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⢿⡏⠀⠀⠙⠿⣿⡏⠀⠀⠀⠀⠘⠿⠿⣿⡿⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⢀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⣶⣷⠶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠒⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣋⠀⢀⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⡅⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⢿⡇⢾⡇⠁⢸⣿⠉⠀⠀⠈⢻⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⢀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣿⡷⠾⠋⢸⣿⠷⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⣷⣶⣸⣿⠶⠀⡀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⠀⢸⣿⠀⢀⣀⡀⣿⡇⠀⢸⣿⢿⣿⢸⣿⡿⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣤⡄⢿⣇⣸⡿⡆⣿⡇⠀⠀⢸⣿⣿⣿⣿⣤⡄⠁⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⣰⢸⣿⢰⣿⣿⡇⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣿⢻⣿⣿⣶⠀⠀⠀⠀⠀⠀
⢰⣶⠀⠀⣴⣶⡦⠀⣶⡄⠀⠀⣆⠀⠀⢠⣾⣿⣿⡄⢰⡏⢉⣾⣷⠀⠀⠀⠀⠀⢿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣶⣿⣷⠀⠀⠀⢈⣾⡆⠀⢼⣿⣿⣷⣿⡇⠀⠀⠀⣿⣿⣾⣾⣿⣿⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀
⣾⣿⣤⢠⣬⣭⡅⣤⣭⣥⡄⢐⣽⠶⣤⠀⢿⡏⣭⡅⣨⡷⢾⣝⣯⣤⡀⢠⡄⢠⡌⣽⣭⣭⡅⠀⢨⣤⢤⣤⠀⣤⡭⣭⡿⣟⣵⠶⣦⣸⢩⣭⡄⢨⣭⡍⣟⣽⢷⣦⡀⣤⣭⣭⡍⢩⣭⡏⣭⡽⢩⡍⢇⣴⢶⣤⠀⠀
⣿⣿⣿⣼⣿⣘⣻⣿⣇⣿⡇⢸⣿⠀⣿⡇⢸⡇⣿⣿⢿⣧⣌⢭⡏⣿⣧⢸⡇⠈⢽⡇⣿⣿⣇⠀⢸⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⠀⣿⡏⢸⡟⣧⣼⢿⡇⣾⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⣀
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⠁⢸⣿⠀⣿⡇⠘⡃⣿⣿⣷⡏⢻⣷⠃⣿⢹⣿⡇⣀⣼⡇⣿⣿⣿⣆⢸⣿⢉⣉⡂⣿⡏⢹⣇⢺⣿⠀⣿⡇⢸⡇⢿⡟⢸⡇⢺⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⠀⠈⠿⠶⢟⣁⣸⣇⠿⢿⣝⠷⠾⣟⣆⠿⢀⠿⢇⣿⣿⣇⣿⣿⣿⣿⠸⠿⣸⣿⣇⢿⣇⣸⣿⣯⡻⠶⢟⣱⡸⢇⡸⢇⣻⣇⣯⣿⠶⣟⡁⠀⠿⠇⣿⠸⠿⡇⠿⣀⠿⢇⣞⡿⠶⡻⢇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠛⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠙⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡿⠉⠙⢿⣿⣿⠋⠉⠁⠀⠈⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⣠⣾⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠉⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢸⣦⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡐⠀⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⢻⡇⢿⡇⣀⢸⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⠀⠀⠉⣿⡏⠁⢸⣿⢸⣿⢠⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠏⢸⣿⠷⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣸⣿⣿⣼⣿⠶⠀⡀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣧⡄⢸⣿⢀⣿⣷⡆⣿⡇⠀⢸⣿⢿⣿⢸⣿⡿⣶⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠀⢀⣀⠀⢀⣀⠀⠀⠀⣿⡇⠀⣀⢸⣿⣤⡄⢿⣇⣸⡿⡆⣿⡇⠀⠀⢻⣿⣿⣿⣿⣤⡄⠃⠀⢸⣿⠀⢸⣿⠀⣿⡇⣼⡟⢻⣿⣰⢸⣿⢸⣿⣿⡇⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀
⢸⣿⣀⡀⢹⣿⡇⢸⣿⠀⠀⢸⡆⠀⠀⢿⣾⣿⣿⠆⢰⣯⣿⣾⡇⠀⠀⠀⡀⠈⣿⣷⣿⣿⡇⠀⠀⠀⠈⠀⠀⢸⣿⣶⣿⣷⠀⠀⠀⢹⣾⡆⠀⢸⣿⣿⣷⣿⡇⠀⠀⠀⢸⣿⣾⣾⣿⣿⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣡⣬⣭⣵⣬⣭⣤⡄⢘⣵⠶⣤⠈⣿⡏⣭⣤⣫⡿⢿⣝⡇⣤⡀⢠⡅⢠⡍⣭⣭⣭⡅⠀⢨⣤⢤⣤⠀⣬⡭⣭⡿⣟⣵⠶⣦⣸⢩⣥⡄⢩⣭⡍⣟⣽⢷⣤⡀⣤⣭⣭⡍⢩⣭⡏⣭⡽⢩⡍⢀⣴⢶⣤⠀⢠
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣻⡇⢸⣿⠀⣿⡇⠹⠇⣿⣿⢿⣧⣌⢭⡇⣿⣧⢸⡇⠈⢹⡇⣿⣿⣷⡀⢸⣿⣀⣿⠀⣿⣇⣼⢟⣻⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⢹⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⣾
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⡅⢸⣿⠀⣿⡇⢰⡇⣿⣿⣷⡏⢻⣷⠃⣿⢹⣿⡇⣿⣿⡇⣿⣿⣿⣷⢸⣿⢩⣭⡆⣿⡏⢹⣧⣾⣿⠀⣿⡇⢸⡇⢿⡟⣸⡇⣾⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⡇⠈⡿⠶⢟⣽⣿⣇⣿⣿⣝⡷⠾⣟⣖⣿⣠⠿⢇⣿⣿⣇⣿⣿⣿⣿⠸⠿⣸⣿⣇⣿⣇⣸⣿⣯⣻⠶⢿⣽⣸⣇⣸⣇⣻⣇⣯⣿⠶⢟⣅⠀⠿⢇⣿⡸⢿⣇⣿⣠⣿⣇⣞⡿⢶⡻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣉⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣤⣀⣠⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠻⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡘⠋⠀⠈⢻⣿⡟⠀⠀⠀⠀⠈⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⣤⣤⣤⣾⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⣿⣿⣿⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⠟⠒⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢄⣂⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⢻⡆⢿⡇⣀⢸⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡇⠈⢹⣿⠉⢀⣀⡉⣿⡏⠁⢸⣿⢸⣿⢰⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠏⢸⣿⠷⠀⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⣿⣿⣼⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣷⡆⢸⣿⢰⣿⣿⡇⣿⡇⠀⢸⣿⢿⣿⢸⣿⡿⣷⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⣤⣤⠀⢠⣤⠀⠀⠀⣿⡇⣠⣤⢸⣿⣴⡄⢿⣇⣸⡿⡆⣿⡇⠀⠀⣿⣿⣿⣿⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣼⡟⢻⣿⣠⢸⣿⢸⣿⣿⡇⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀
⢰⣷⣶⡆⢸⣿⠀⣾⣿⠀⠀⢸⡀⠀⠘⣿⣿⣿⣿⠂⢰⣿⣿⣾⣇⠀⠀⠀⡀⠈⣿⣷⣿⣿⠁⠀⠀⠀⠸⡀⠀⢸⣿⣶⣿⣷⡀⠀⠀⣹⣾⡆⠀⢸⣿⣿⣷⣿⡇⠀⠀⠀⢸⣿⣾⣾⣿⣿⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣡⣬⣭⣽⣭⣭⣥⡄⢘⣴⠶⣤⣸⣿⡏⣭⣵⣫⡿⢿⣝⡏⣤⡀⢠⡍⢠⡍⣭⣭⣭⡅⠀⢠⣤⢤⣥⠀⣬⡭⣭⡿⣟⣵⠶⣦⣸⢩⣥⡄⢨⣭⡍⣟⣽⢷⣦⡀⣤⣭⣭⡍⢩⣭⡏⣭⡽⢩⡍⢀⣴⢶⣤⠀⣴
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣿⡇⢸⣿⠀⣿⡇⠛⡃⣿⣿⢿⣧⣌⢭⡇⣿⣧⢸⡇⣈⣹⡇⣿⣿⣷⡄⢸⣿⣀⣿⠀⣿⣇⣼⢗⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⢸⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⣿
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⡅⢸⣿⠀⣿⣇⣿⡇⣿⣿⣷⡏⢻⣷⠃⣿⢹⣿⡇⣿⣿⡇⣿⣿⣿⣿⢸⣿⢩⣭⡆⣿⡏⢹⣧⣿⣿⠀⣿⡇⢸⡇⢿⡟⣼⡇⣾⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡇⢈⣿⠶⣟⣽⣿⣇⣿⣿⣝⡷⠾⣟⣞⣿⣠⣿⢇⣿⣿⣇⣿⣿⣿⣿⠸⠿⣸⣿⣇⣿⣇⣸⣿⣯⣻⠶⣿⣽⣸⣇⣸⣇⣻⣇⣯⣿⠶⣟⣥⣄⣿⣇⣿⣸⣿⣇⣿⣠⣿⣇⣞⡿⢶⡻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢐⣿⣿⡿⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠿⢗⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠡⡮⡔⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏⠀⠀⠀⠈⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠹⣿⣿⠏⠁⠀⠀⠀⢹⣿⣿⣿⡶⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠹⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠀⠁⠀⣠⣄⣀⣠⣾⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⡷⠦⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡅⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢿⣷⣀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⢀⠀⣀⣀⣀⡀⢀⣀⢀⣀⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣷⢸⣿⠉⠀⣾⡏⢹⣷⠀⣿⡏⢻⡆⣿⣧⣤⢸⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡟⡌⢹⣿⢩⣴⣤⡉⣿⡏⠁⢸⣿⢸⣿⢸⣿⡟⣭⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⢏⢸⣿⢶⠀⣿⡇⢸⣿⠀⣿⡷⠿⠳⣿⣿⣿⣿⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣷⡇⢸⣿⢸⣿⣿⡇⣿⡇⠀⢸⣿⢿⣿⢸⣿⡿⣷⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⣰⡆⠸⡆⢸⣿⣿⡆⠀⠀⣿⡇⣿⣿⢸⣿⣼⡇⢿⣇⣸⡿⡆⣿⡇⠀⠀⣿⣿⣿⣿⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣾⡟⢻⣿⢰⢸⣿⢸⣿⣿⡇⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣿⢻⣿⣿⡇⠀⠀⠀⠀⠃⠀
⣴⣿⣿⡇⢀⣇⣸⣿⣿⣇⠀⠀⠀⠀⢻⣿⣾⣿⣿⣦⣴⣿⣿⣾⣷⠀⠀⠀⡀⠸⣿⣷⣿⣿⡇⠀⠀⠀⠈⡇⠀⠈⣿⣶⣿⣷⣇⠀⠀⢹⣾⡆⠀⢸⣿⣿⣷⣿⣷⡀⠀⠀⢸⣿⣾⣾⣿⣿⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣭⡄⢀⣴⠶⣬⣻⣿⡏⣭⣽⣫⡿⢿⣝⡏⣥⡀⢠⡅⢠⡍⣭⣭⣭⣅⠀⢠⣤⢤⣥⠀⣬⡭⣭⡝⣟⣽⠶⣦⡘⢩⣥⡄⢩⣭⡍⣛⣽⢿⣦⡀⣤⣬⣭⡍⢩⣭⡏⣭⡽⢩⡍⢀⣴⢶⣤⣰⣿
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣿⣷⢸⣿⠀⣿⡇⣶⡆⣿⣿⢿⣧⣌⢭⡇⣿⣧⢸⡇⣬⣽⡇⣿⣿⣿⣷⢸⣿⣀⣿⠀⣿⣇⣼⢗⣼⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣼⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⢫⣿
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⣵⢸⣿⠀⣿⣇⣿⡇⣿⣿⣷⡏⣻⣷⢷⣿⢹⣿⡇⣿⣿⡇⣿⣿⣿⣿⢸⣿⠉⢩⡆⣿⣏⢻⣧⣿⣿⠀⣿⣇⢸⣧⣿⡟⣼⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣷⣬⣿⠶⣟⣽⣿⣇⣿⣿⣝⡷⢾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⣿⣿⡸⢿⣸⣿⣇⣿⣿⣸⣿⣯⣿⠶⣿⣽⣸⣿⣼⣧⣿⣇⣯⣿⠶⣿⣽⣧⣿⣇⣿⣺⣿⣇⣿⣠⣿⣇⣾⡿⢶⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠆⠦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣏⢽⣋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠨⠔⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠉⠙⢿⣿⣿⣟⡂⠀⠀⠀⠀⠀⠀⡀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣅⡵⣾⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⢃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠛⠛⠛⠀⢀⠀⠀⢀⠀⠒⠒⠮⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡈⠉⠁⠈⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢐⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠤⡄⠀⠀⠀⣠⣶⣦⣤⣶⣿⡿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠜⣿⣿⣿⣿⣿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡟⠓⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣿⣆⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣀⡀⠀⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡀⠀⣀⣀⣀⢀⣀⣀⣀⢶⠀⣀⣀⣀⡀⢀⣀⢀⣶⢶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣷⢸⣿⠋⠀⣾⡏⢹⣷⠀⣿⡏⢿⣧⣿⣿⣶⣼⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⡇⢠⣿⢹⡿⡌⢹⣿⢩⣼⣧⡍⣿⡏⠁⢸⣿⢸⣿⢸⣿⡟⣭⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣿⡷⠾⣏⢸⣿⢶⡀⣿⡇⢸⣿⠀⣿⡷⠿⠻⣿⣿⣿⣿⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⡇⢸⡟⢸⣷⣇⢸⣿⢸⣿⣿⡇⣿⡇⠀⢸⣿⢿⣿⢸⣿⡿⣷⣿⣿⣿⡇⠀⠀⠀⠀⣄⠀
⠀⢰⣿⣷⠀⠀⣿⣿⣿⣧⠀⠀⣿⡇⣿⣿⢾⣿⣼⡇⢿⣇⣼⡿⡆⣿⡇⠀⠀⣿⣿⣿⣿⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡧⣾⡟⢻⣿⣸⢸⣿⢸⣿⣿⡇⣿⡇⠀⢸⣿⢸⣿⢸⣿⣧⣿⢻⣿⣿⡇⠀⠀⠀⠀⢻⠀
⣶⣾⣿⣿⡀⠀⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣾⣿⣿⣷⣶⣿⣿⣾⣷⡇⠀⠀⠀⢺⣿⣷⣿⣿⣇⠀⠀⠀⢸⣇⠀⠀⢹⣶⣿⣷⣿⠀⠀⣿⣾⡂⠀⣸⣿⣿⣷⣿⣷⠀⠀⠀⠀⣿⣾⣾⣿⣿⣾⣿⣿⣧⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣭⣅⢀⣤⠶⣯⡻⠿⠏⣭⡽⣫⡿⢿⣝⡏⣭⡀⢠⡄⢨⡍⣭⣭⣭⣽⡄⢠⣤⢬⣥⠀⣤⡭⣭⡝⢟⣽⠶⣦⡘⢩⣭⡍⢩⣭⡍⢏⣽⠿⣦⡀⣤⣤⣭⡍⢩⣭⡏⣭⡽⢩⡍⢀⣴⢶⣬⣻⣿
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣿⣿⢸⣿⠀⣿⡏⣿⡇⣿⣿⢿⣧⣌⢭⡇⣿⣧⢸⡇⣬⣽⡇⣿⣿⣿⣿⢸⣿⣀⣿⠀⣿⣇⣼⢗⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣾⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⢫⣿
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⣵⢸⣿⠀⣿⣗⣿⡇⣿⣿⣷⡏⣻⣷⢿⣿⢹⣿⡇⣿⣿⡇⣿⣿⣿⣿⣸⣿⠉⢩⡆⣿⣯⢻⣧⣿⣿⠀⣿⣇⢸⣧⣿⡟⣼⡇⣿⣿⠀⣿⣇⡀⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣟⣽⣿⣇⣿⣿⣝⡷⢾⣟⣿⣿⣠⣿⣇⣿⣿⣇⣿⣿⣿⣿⣿⣿⣰⣾⣇⣿⣿⣸⣿⣯⣿⢶⣿⣽⣺⣿⣼⣧⣿⣇⣯⣿⠶⣿⣽⣷⣿⣇⣿⣻⣿⣇⣿⣠⣿⣇⣾⡿⢶⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⢀⠀⣀⡂⢀⠀⣁⣎⢀⠀⠀⢐⡂⠖⠲⣂⡀⠀⠀⠁⠀⢐⣤⣄⠐⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠈⠈⠁⠁⠈⠈⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡂⣤⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣚⡂⡵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠙⢿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⡥⢺⣾⣿⡿⠟⠁⠀⠈⢿⣿⣿⣿⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠁⠀⠢⡺⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⡟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠄⠀⠀⠀⣾⣿⣷⣶⣿⣿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⢰⣤⡀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⣀⣀⠀⢀⣿⣷⡀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣤⡄⠀⢠⣀⣀⠀⠀⢀⣀⣀⣀⢀⣠⠤⣤⡄⠀⣀⣀⡀⢀⣀⣀⣀⢶⡦⣤⣠⣀⡀⢀⣀⢀⣸⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⡷⢸⣿⠉⠀⣾⡏⢹⣷⠇⣿⡏⢻⣿⣿⣿⣿⣾⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⣧⢠⣿⢹⡟⣌⢹⣿⢩⣼⣧⡍⣿⡟⠁⢸⣿⢸⣿⢸⣿⡟⣭⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⣤⡄⠀⢠⣤⣤⣤⣦⠀⠀⣿⡷⣾⣇⢸⣿⢶⡀⣿⡇⢸⣿⡀⣿⡷⠿⢻⣿⣿⣿⣿⣿⠶⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⣿⢸⡟⢸⣷⣿⢸⣿⢸⣿⣿⡇⣿⡇⠀⢸⣿⢿⣿⢸⣿⡿⠷⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀
⠀⢸⣿⡟⠀⠘⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⣼⡇⢿⣇⣼⡿⡇⣿⡇⠀⠈⣿⣿⣿⢻⣿⣤⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡿⣿⡟⢻⣿⢸⢸⣿⢸⣿⣿⡇⣿⡇⡄⢸⣿⢸⣿⢸⣿⣧⣿⢻⣿⣿⡇⠀⠀⠀⠀⠘⠁
⣶⣿⣿⣇⣀⣠⣿⣿⣿⣿⡆⠀⠈⣷⣿⣿⣾⣿⣿⣷⣷⣿⣿⣾⣷⣿⡀⠀⢰⣾⣿⣷⣾⣿⣿⠀⠀⠀⢸⡷⠀⠀⣿⣶⣿⣷⣿⡇⠀⣿⣾⡎⠈⠘⠿⢿⣷⣿⣷⡇⠀⠀⠀⣹⣾⣾⣿⣿⣾⣿⣿⣷⠀⠀⠀⠀⢀⣤
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣭⡅⢀⣴⢿⣯⣛⣛⡋⣭⣍⣩⡷⢾⣝⡏⣭⡁⢠⡌⢩⡍⣭⣭⣭⣽⣷⢠⣤⢤⣤⠀⣤⡬⣭⡝⣛⣽⠷⣦⣹⢩⣭⡍⢩⣭⡍⣛⣽⣿⣯⡀⣤⣤⣭⡍⢩⣭⡏⣭⡽⢩⡍⢀⣴⢶⣬⣻⣿
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣿⣿⢸⣿⠀⣿⣯⣿⡇⣿⣿⢿⣧⣌⢭⣧⣿⣧⢸⡇⣬⣽⡇⣿⣿⣿⣿⣼⣿⣀⣿⠇⣿⣇⣼⢗⣿⣿⠀⣿⡏⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⢫⣿
⣿⣿⣿⣿⣿⢩⣽⣿⡟⣭⡅⢸⣿⠀⣿⣗⣿⡇⣿⣿⣷⡏⣻⣷⢿⣿⢹⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢩⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⢸⣧⣿⡟⣼⡇⣿⣿⠀⣿⣇⡄⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣮⣿⣶⣿⣽⣿⣗⣿⣿⣝⡷⢾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⣿⣿⡿⠿⣸⣿⣇⣿⣿⣸⣿⣯⣿⠶⣿⣽⣸⣿⣼⣧⣿⣇⣯⣿⠶⣿⣽⣧⣿⣇⣿⣸⣿⣇⣿⣠⣿⣇⣾⡿⢶⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠡⠾⢼⡻⣿⣿⠀⣀⡂⢐⣘⡷⣂⠰⣆⣠⢐⠠⢺⣶⣶⣦⣄⠤⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠁⠀⠃⠉⠛⠛⠃⠈⠀⠀⠁⠈⠀⠐⠘⠘⠉⠁⠈⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⠀⠀⠀⠀⠀⠄⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⡀⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠇⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠉⢿⣿⣿⡃⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⢠⡂⣿⣿⣿⠟⠁⠀⠈⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠁⠼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⣸⣿⣿⣿⣯⡁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠢⠄⠀⠀⠀⣿⣿⣷⣶⣾⣿⡿⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠇⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣻⣿⡀⠀⣀⣀⠀⠀⣀⣀⡀⠀⣤⣤⣤⢤⣀⣀⠀⠀⢀⣀⣀⣀⢀⣠⠴⣶⡄⠀⣀⣀⠀⢀⣀⣀⣀⢶⡴⣴⣄⣄⡀⢀⣀⢀⣀⢿⣿⣦⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⡷⢸⣿⠉⠁⣾⡏⢹⣷⠇⣿⡏⢻⣇⣿⣿⣿⣾⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⣷⣤⣿⢹⡇⣬⢹⣿⢩⣼⣧⡍⣿⡟⡁⢸⣿⢸⣿⢸⣿⡟⣭⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀
⠀⠀⣴⡄⠀⠀⣶⣶⣶⣦⠀⠀⣿⡷⣾⣯⢸⣿⢾⡀⣿⡇⢸⣿⠀⣿⡷⠿⠋⣿⣿⣿⣿⣿⢷⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⣿⢹⡟⢸⣷⣿⢸⣿⢸⣿⣿⡇⣿⡇⠁⢸⣿⢿⣿⢸⣿⡿⣷⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀
⡅⢀⣿⠃⢸⠀⢹⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⣼⡅⢿⣇⣼⡿⡇⣿⡇⠀⠀⣿⣿⣿⢻⣿⣼⡄⠀⠀⢸⣿⠀⢸⣿⠀⣿⡿⣿⡟⢻⣿⢸⢸⣿⢸⣿⣿⡇⣿⡇⡇⢸⣿⢸⣿⢸⣿⣧⣯⢻⣿⣿⡇⠀⠀⠀⠀⠘⠇
⣿⣿⣿⣀⣼⣤⣿⣿⣿⡇⠀⠀⠀⣷⣿⣿⣾⣿⣿⣶⣷⣿⣿⣾⣷⣉⡀⠀⢰⣾⣿⣷⣾⣿⣿⡄⠀⠀⢸⡿⠀⠀⣿⣶⣿⣷⣿⡇⠀⢹⣾⡆⠈⠚⠛⠻⠷⢿⢷⣷⠀⠀⠀⢸⣾⣾⣿⣿⣾⣿⣿⣷⠀⠀⠀⠀⣀⣠
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣥⡄⢀⣤⠾⣯⣩⣭⡍⣭⣭⣩⡿⢿⣝⡏⣭⡁⢠⡄⢩⡍⣭⣭⣭⣽⣿⢠⣤⢤⣤⠀⣤⡭⣭⡝⣝⣽⠶⣦⣸⢩⣭⡍⢩⣭⡍⣍⣽⣿⣯⡀⣤⣤⣬⡍⢩⣭⡏⣭⡽⢩⡍⢀⣴⠶⣤⣻⣿
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣻⡿⢸⣿⠀⣿⣿⣿⡇⣿⣿⢿⣧⣌⢭⡇⣿⣧⢸⡇⣬⣽⡇⣿⣿⣿⡿⢸⣿⣀⣿⠀⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⢣⣿
⣿⣿⣿⣿⣿⢩⣽⣿⡟⡍⠁⢸⣿⠀⣿⣇⣿⡇⣿⣿⣷⡏⣻⣷⢿⣿⢹⣿⡇⣿⣿⡇⣿⣿⣿⠇⢸⣿⢩⣽⡆⣿⣯⢹⣯⣿⣿⠀⣿⣇⢸⣇⣿⡟⣼⡇⣿⣿⠀⣿⣇⡄⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣶⣮⣿⣶⣿⣽⣿⣟⣿⣿⣝⡷⢾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⣿⡀⠸⣿⣸⣿⣇⣿⣿⣸⣿⣯⣿⠶⣿⣽⣺⣿⣼⣷⣿⣇⣯⣿⠶⣿⣽⣧⣿⣇⣿⣺⣿⣇⣿⣠⣿⣇⣞⡿⢶⣻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠼⠿⣺⣗⣿⣿⣿⣺⢀⣀⡀⡀⠰⢍⣲⡁⠄⢰⣠⢴⢄⣤⠢⠀⡐⡀⣀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠒⠈⠘⠛⠋⠀⠀⠈⠉⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠉⠀⠀⠀⣠⣄⠀⠀⠀⠀⠂⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢪⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠀⠀⠀⠀⠀⠚⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠉⠉⠙⢻⣿⣿⡯⠘⠀⠀⠀⠀⠀⠀⠀⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⢿⠿⣿⣿⠟⠁⠈⠙⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠘⠁⠀⠀⠀⠀⢈⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠤⡀⠀⠀⢠⣾⣿⣦⣀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠉⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠻⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣿⣇⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⣶⣶⢶⣆⣀⠀⠀⢀⣀⣀⣀⢀⣀⠶⣶⡦⠀⣀⣀⠀⢀⣀⣀⣀⢤⡤⣤⣶⣄⡀⢀⣀⢀⣀⠀⣿⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣗⢸⣿⠉⠁⣾⡏⢹⣷⠇⣿⡏⢻⡆⣿⣿⣿⣾⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⣷⣤⣿⢹⡇⣨⢹⣿⢩⣼⣧⡍⣿⡟⡅⢸⣿⢸⣿⢸⣿⡟⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄
⣤⠀⢠⡆⢀⣀⠰⣶⣶⡶⠀⠀⣿⡷⢾⣯⢸⣿⢿⡀⣿⡇⢸⣿⡀⣿⡷⠿⠃⣿⣿⣿⣿⣿⢷⠀⠀⠀⢸⣿⠀⢸⣿⠿⣿⣿⢹⡟⢸⣧⣿⢾⣿⢸⣿⣿⡇⣿⡇⡇⢸⣿⢿⣿⢸⣿⡿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇
⣿⣀⣰⠃⢸⣿⠀⣿⣿⡇⠀⠀⣿⡇⣿⣿⢸⣿⣼⡇⢿⣇⣸⡿⡇⣿⡇⠀⠀⣿⣿⣿⢹⣿⣼⡇⠀⠀⢸⣿⠀⢸⣿⠀⣿⡿⣿⡟⢻⣿⣸⢸⣿⢸⣿⣿⡇⣿⡇⣧⢸⣿⢸⣿⢸⣿⣧⣯⢻⣿⣿⣿⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣀⣾⣷⣤⣿⡏⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣶⣶⣿⣿⣾⣷⠁⠀⠀⠀⢾⣿⣷⣾⣿⣿⡆⠀⠀⢸⣿⠀⠀⢹⣶⣿⣷⣿⡷⠀⠈⢺⠀⠀⣈⣉⣙⣓⣿⣷⣿⡀⠀⠀⢈⣾⣾⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣭⣭⣽⣭⣥⣤⡄⢀⣴⠶⣮⣲⣶⡆⣤⣤⣢⡶⢾⣝⡏⣥⡀⢠⡄⢨⡍⣭⣭⣭⡍⣷⢠⣤⢬⣤⠀⣤⡤⣭⡝⣞⣵⠶⣦⡀⢠⣤⡄⢠⣤⡄⣖⣴⢶⣦⡀⣤⣤⣬⡍⢩⣭⡏⣭⡽⢩⡍⢀⣴⠶⣤⣻⣿
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣸⣿⢸⣿⠀⣿⡟⣿⡇⣿⣿⢿⣧⣌⢭⡇⣿⣧⢸⡇⣬⣵⡆⣿⣿⣿⠏⢸⣿⣀⣿⠆⣿⣇⣼⢗⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⢣⣿
⣿⣿⣿⣿⣿⢩⣽⣿⡏⢉⣵⢸⣿⠀⣿⣧⣿⡇⣿⣿⣷⡏⣻⣷⢿⣿⢹⣿⡇⣿⣿⡇⣿⣿⡏⠀⣾⣿⢩⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⢸⣇⣿⡟⣼⡇⣿⣿⠀⣿⣧⡆⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣮⣿⣶⣿⣽⣿⣟⣿⣿⣝⡷⠾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⡀⢀⣿⣿⣸⣿⣇⣿⣿⣸⣿⣯⣿⠶⣿⣽⣸⣟⣼⣧⣿⣇⣯⣿⠶⣿⣽⣧⣿⣇⣿⣸⣿⣇⣿⣠⣿⣇⣞⡿⢶⣻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣫⣵⣿⣿⡷⣿⣿⣟⣒⣢⣶⣾⣶⣯⣳⣾⣵⣾⣽⣾⣲⣷⣶⢀⢀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠠⠤⢤⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠒⠘⠛⠛⠛⠛⠛⠻⠟⠋⠛⠛⠉⠉⠙⠛⠛⠋⠁⠉⠉⠈⠅⠄⠀⡀⠀⠙⢛⠁⠀⠈⢂⣐⠰⢰⠲⠠⠆⠀⡝⣭⡟⣯⢃⠀⠀⠈⠉⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣏⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢾⣿⣿⣯⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠠⠉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠻⢿⣿⣿⣿⡏⠍⠀⠀⠀⠀⠘⠤⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡿⢿⣿⡿⠛⠉⠛⢿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠈⠠⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠁⠀⠋⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡄⠀⠀⢠⣴⣶⣄⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠈⠙⣿⣿⣿⣿⣿⠟⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣀⣀⠀⢀⣀⣻⣷⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⣴⣶⢦⣄⣀⠀⠀⢀⣀⣀⣀⢀⣀⠴⣶⡶⠀⣀⣀⠀⢀⣀⣀⣀⢤⡤⣀⣶⣄⡀⢀⣀⢀⣀⠀⣶⣶⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣗⢸⣿⠉⠁⣾⡏⢹⣷⠇⣿⡏⣻⡆⣿⣿⣿⣾⣿⠉⠀⠀⠈⢹⣿⠉⢸⣿⠀⣿⣿⣤⣿⢹⡇⢨⢹⣿⢩⣼⣧⡝⣿⡟⣥⢸⣿⢸⣿⢠⣿⡟⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀
⣤⡄⠀⣶⠀⣤⠀⣶⣶⡶⠀⠀⣿⡷⣾⣯⢸⣿⢿⣀⣿⡇⢸⣿⡄⣿⡷⠿⠃⣿⣿⣿⣿⣿⢿⡀⠀⠀⢸⣿⡆⢸⣿⠿⣿⣿⢹⡟⢸⣧⣿⣾⣿⢸⣿⣿⡇⣿⡇⣿⢸⣿⢿⣿⢸⣿⡿⡷⣿⣿⣿⣿⡆⠀⠀⠀⠀⣷
⣿⣧⢀⠋⢰⣿⠇⢸⣿⡇⠀⠀⣿⡇⢿⣿⢸⣿⣽⡇⢿⣇⣸⡿⡇⣿⡇⠀⠀⣿⣿⣿⢹⣿⣼⡇⠀⠀⢸⣿⠁⢸⣿⠀⣿⡿⣿⡟⢻⣿⢸⢻⣿⢸⣿⣿⡇⣿⡇⣿⢸⣿⢸⣿⢸⣿⣧⣿⢻⣿⣿⣿⠃⠀⡄⠀⠀⢿
⣿⣿⣿⢀⣼⣿⣤⣾⣿⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣶⣶⣿⣿⣾⣷⡏⠀⠀⠀⠘⣿⣷⣾⣿⣿⡆⠀⠀⣾⣿⠆⠀⢹⣶⣿⣷⣿⣷⠀⠈⢸⠈⠈⣈⣉⣉⣓⣿⣷⣿⡆⠀⠀⠈⣾⣾⣿⣿⣾⣿⣿⣿⡇⠀⠇⠀⠀⠀
⣿⣿⣿⣯⣭⣭⣽⣭⣥⣤⡄⢀⣵⠶⣤⣳⣶⡆⣤⣴⣢⡶⢾⣝⡏⣥⡀⢠⡄⢠⡍⣭⣭⣭⡝⣷⢠⣤⢬⣤⠂⣤⡤⣤⡴⣖⣴⡶⣦⡀⢨⣤⡄⢠⣤⡄⣖⣴⢶⣦⡂⣤⣤⣤⡍⢩⣭⡏⣭⡽⢩⡍⢀⣴⢶⣤⣺⣿
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣸⣿⢸⣿⠀⣿⣿⣿⡇⣿⣿⢿⣧⣌⢭⣧⣿⣧⢸⡇⣬⣽⡇⣿⣿⣿⠏⢸⣿⣀⣿⠇⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⢣⣿
⣿⣿⣿⣿⣿⢩⣽⣿⡟⠉⣱⢸⣿⠀⣿⣿⣿⡇⣿⣿⣷⡏⣻⣷⢿⣿⢹⣿⡇⣿⣿⡇⣿⣿⡟⠀⣼⣿⢩⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⢸⣧⣿⡿⣼⡇⣿⣿⠀⣿⣧⡇⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣿⣾⣿⠶⣿⣽⣿⣟⣿⣿⣝⡷⠾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⠃⠀⣿⣿⣸⣿⣇⣿⣿⣸⣿⣯⣿⠶⣿⣽⣺⣿⣼⣧⣿⣇⣯⣿⠶⣿⣽⣷⣿⣇⣿⣺⣿⣇⣿⣠⣿⣇⣾⡿⢶⣻⢿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣉⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢛⣿⢾⣯⣻⢽⣿⣿⣒⣀⣶⣶⡶⣤⣀⣤⣦⣤⣄⣬⣶⠲⢤⡀⠀⢀⡀⠁⣤⣀⡀⠀⠀⠠⠄⣀⡀⠀⠀⠀⠠⠄⠠⠤⠄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠚⠛⠛⠛⠛⠚⠛⠛⠟⠙⠉⠙⠒⠉⠛⠙⠿⠛⠋⠉⠉⠁⠄⠀⠂⠀⠙⠛⠃⠀⠀⢁⣀⡠⢒⡰⢒⠢⢞⢝⡔⡭⡔⠂⠀⠀⠈⠉⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠁⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢺⣿⣿⣿⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠐⠀⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠛⠻⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⠿⠛⠿⢿⣿⣿⣿⣿⣿⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠻⠿⠟⠓⠀⠀⠀⠀⠀⠀⠑⠚⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠁⠀⠘⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣄⠀⠀⢀⣴⣶⣄⠀⠀⣀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠈⠙⣿⣿⣷⣿⣿⠟⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⣦⣴⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣹⣿⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⣰⣶⢦⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠰⣶⡶⡀⣀⣀⠀⢀⣀⣀⣀⢠⡀⣀⣠⣄⡀⢀⣀⢀⣀⠀⣠⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣇⢸⣿⠉⠁⣾⡏⢹⣷⠇⣿⡏⢻⡆⣼⣿⣿⣾⣿⠉⠀⠀⠈⢹⣿⡍⢸⣿⠀⣿⣿⣧⣿⢹⡇⢈⢹⣿⢩⣼⣧⡍⣿⡟⣥⢸⣿⢸⣿⠀⣿⡟⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰
⣠⣄⠀⢰⠀⣠⡀⢰⣶⡷⠀⠀⣿⡷⢾⣯⢸⣿⢿⣠⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⣿⣿⣿⣿⢿⡀⠀⠀⢸⣿⡇⢸⣿⠿⣿⣿⢹⡟⢸⣧⢸⣿⣿⢸⣿⣿⡇⣿⡇⣿⢸⣿⢿⣿⢰⣿⡿⡷⣿⣿⣿⣿⡇⠀⡄⠀⠀⣸
⣿⣿⣀⡘⠀⣿⡇⢘⣿⡇⠀⠀⣿⡇⢻⣿⢸⣿⣼⣯⢿⣇⣸⡿⡆⣿⡇⠀⠀⣸⣿⣿⢹⣿⣼⡇⠀⠀⢸⣿⠃⢸⣿⠀⣿⡿⣿⡟⢻⣿⣸⢹⣿⢸⣿⣿⡇⣿⡇⣿⢸⣿⢸⣿⢸⣿⣧⣿⢻⣿⣿⣿⡇⠀⡇⠀⠀⢿
⣿⣿⣿⡇⣰⣿⣧⣼⣿⠁⠀⠀⠀⠀⠸⣿⣾⣿⣿⣶⣶⣿⣿⣾⣷⡟⠀⠀⠀⠈⢿⣷⣾⣿⣿⣾⠀⠀⢸⣿⠆⠀⠘⣶⣿⣷⣿⣷⠂⠀⢸⠊⠀⣈⣉⣙⣑⣻⣓⣿⡆⠀⠀⠀⢸⣾⣿⣿⣾⣿⣿⣿⡇⠀⡇⠀⠀⠀
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣤⡄⢀⣵⠶⣤⣳⣶⡆⣤⣴⣢⡶⢾⣝⡏⣭⡀⢠⡄⢠⡍⣭⣭⣭⣽⣿⢠⣤⢬⣥⠂⣤⡤⣤⡴⣖⣴⡶⣦⡀⢠⣤⡄⢠⣤⡄⣖⣴⣶⣦⡂⣤⣤⣤⡍⢩⣭⡏⣭⡽⢩⡍⢁⣴⢶⣤⣸⣿
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣸⣿⢸⣿⠀⣿⣟⣿⡇⣿⣿⢿⣧⣌⢭⣧⣿⣧⢸⡇⣬⣽⡇⣿⣿⣿⡟⢸⣿⣀⣿⠆⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⡇⠀⣿⡇⣿⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⢣⣿
⣿⣿⣿⣿⣿⢩⣽⣿⡟⠉⢱⢸⣿⠀⣿⣟⣿⡇⣿⣿⣷⡏⣻⣷⢿⣿⢹⣿⡇⣿⣿⡇⣿⣿⡿⠀⢸⣿⢉⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⢸⣇⣿⡟⣼⡇⣿⣿⠀⣿⣷⡇⣿⡇⣿⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⣮⣿⠶⣿⣽⣿⣟⣿⣿⣝⡷⠾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⠃⠀⣿⣿⣸⣿⣇⣿⣿⣸⣿⣯⣿⠶⣿⣽⣺⣟⣼⣧⣿⣇⣯⣿⠶⣿⣽⣷⣿⣇⣿⣺⣿⣇⣿⣠⣿⣇⣾⡿⢶⡻⢿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣴⣶⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣥⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠑⠊⢲⡗⢴⡐⠀⠀⠀⠀⠔⠀⠀⣀⠀⠄⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠁⠤⠰⠗⠠⠀⠸⠿⠗⠐⠀⠀⠐⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢽⣿⣿⣏⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣠⣠⣠⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠛⠛⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢾⠙⠿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⢻⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠁⠀⠀⠀⢹⣿⣿⣿⣿⣏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢤⡀⠀⠀⣴⣾⣦⡀⠀⢀⣤⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠈⣿⣿⣿⣿⣿⠿⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡤⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠧⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣀⣀⠀⢀⣀⣻⣧⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⣠⣤⢄⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣶⡶⡄⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣇⢸⣿⠉⠁⣾⡏⢹⣷⠆⣿⡏⢻⡆⢸⣿⣿⣸⣿⢋⠀⠀⠈⢹⣿⡍⢸⣿⠀⣿⣿⣷⣿⢹⡇⠈⢹⣿⠉⣼⣧⡍⣿⡟⣥⢸⣿⢸⣿⠀⣿⡟⣭⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⣤⠀⢰⣆⠀⡀⠸⣿⣿⡆⠀⣿⡷⢾⣯⢸⣿⢿⣰⣿⡇⢸⣿⠀⣿⡷⠿⠃⣿⣿⣿⣿⣿⢿⡀⠀⠀⢸⣿⣷⢸⣿⠿⣿⣿⢹⡟⢸⣧⠀⣼⣿⢰⣿⣿⡇⣿⡇⣿⢸⣿⢿⣿⠀⣿⡿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⢠⣿⣄⣰⠃⢸⣿⠀⣿⣿⡇⠀⣿⡇⢻⣿⢸⣿⣼⣯⢿⣇⣸⡿⡆⣿⡿⠀⠀⢹⣿⣿⢹⣿⣼⣗⠀⠀⢸⣿⣿⢸⣿⠀⣿⡿⣿⡟⢻⣿⢰⣽⣿⢸⣿⣿⡇⣿⡇⣿⢸⣿⢸⣿⠀⣿⣧⣿⢻⣿⣿⣿⣿⠀⢀⠀⠀⢠
⣿⣿⣿⣿⠀⣼⣿⣧⣿⡟⠀⠀⠀⠀⢸⡿⠾⠿⠿⠾⠷⠿⠿⣾⣷⣿⡇⠀⠀⠈⢹⣷⣾⣿⣿⣾⠀⠀⢸⣿⠿⠀⠀⢲⣿⣷⣿⣷⡇⠀⢺⠎⠈⠚⠛⠛⠓⠛⢓⣛⣎⠀⠀⠀⠀⣾⣿⣿⣾⣿⣿⣿⣿⠀⢸⠀⠀⠀
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣥⡄⢀⣴⠶⣤⣻⣿⡏⣭⣽⣫⡶⢶⣝⡏⣭⡱⢠⡄⢠⡌⣭⣭⣭⡝⣿⢠⣤⢬⣥⠂⣤⡤⣤⡔⣖⣴⡶⣦⡀⢠⣤⡄⢠⣤⡄⣖⣴⣶⣦⡂⣤⣤⣤⡌⢩⣭⡏⣭⡽⢩⡍⢏⣴⢶⣤⢠⣶
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣻⡷⢸⣿⠀⣿⣿⣿⡇⣿⣿⣿⣧⣌⢭⣇⣿⣧⢸⡇⣬⣵⡇⣿⣷⣿⣿⢸⣿⣀⣿⠄⣿⣇⣼⢗⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⣇⡀⣿⡇⣾⢸⣿⡇⣿⣷⢸⡇⢸⣿⠀⠛⠃⣿
⣿⣿⣿⣿⣿⢹⣽⣿⡟⡍⠁⢸⣿⠀⣿⣿⣿⡇⣿⣿⣿⡏⣻⣷⢿⣿⢹⣿⡇⣿⣿⡇⣿⣿⣿⠇⢸⣿⢩⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⢸⣧⣿⡟⣼⡇⣿⣿⠀⣿⣿⡇⣿⡇⣿⢸⣿⡁⣿⢹⣿⡇⢸⣿⠘⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣯⣿⣇⣧⣤⣮⣿⠶⣟⣽⣿⣗⣿⣿⣝⡷⠾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⡟⠀⠸⠿⢸⣿⣇⠿⢿⠸⠿⣯⡻⠶⢿⣽⡸⠟⡼⢇⠿⠇⣯⡿⠶⢿⣽⣷⠿⢇⣿⠸⠿⡇⠿⣠⣿⣇⣞⡿⢶⡻⢿⣿
⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠘⠿⡦⡀⠔⠀⠤⠀⡪⣗⠆⠀⠀⠤⠄⠠⢀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠿⠂⠦⠂⠂⠤⠰⠶⠷⠊⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣾⠿⢻⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢹⡿⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠴⡀⠀⠀⣴⣿⣷⣄⢀⣀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡦⠔⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⢸⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠛⠃⠀⠀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣿⣿⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⣤⢀⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣰⣶⡆⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⢀⣀⢀⣀⠀⣀⣀⣀⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣇⢸⣿⠉⠁⣾⡏⢹⣷⠄⣿⡏⢻⡆⢸⣿⣿⣼⣿⢋⠀⠀⠈⢹⣿⡍⢸⣿⠀⣿⣿⣷⣿⢹⡇⠈⢹⣿⠉⣼⣧⡍⣿⡟⣥⢸⣿⢸⣿⠀⣿⡟⣭⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⠀⢠⠀⢸⣧⠀⢀⠸⣿⣿⡆⠀⣿⡷⢾⣯⢸⣿⢿⣠⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⣿⣿⣿⣿⢿⡀⠀⠀⢸⣿⣷⢸⣿⠿⣿⣿⢹⡟⢸⣧⠀⢸⣿⢀⣿⣿⡇⣿⡇⣿⢸⣿⢿⣿⠀⣿⡿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⣼⣤⣴⡟⠀⣿⠀⣿⣿⡇⠀⣿⡇⢿⣿⢸⣿⣼⣯⢿⣇⣸⡿⡆⣿⣿⠄⠀⢸⣿⣿⢹⣿⣼⡇⠀⠀⢸⣿⣿⢸⣿⠀⣿⡿⣿⡟⢻⣿⢠⢿⣿⢸⣿⣿⡇⣿⡇⣿⢸⣿⢸⣿⠀⣿⣧⣿⢻⣿⣿⣿⣿⠀⠀⠀⠀⢀
⣿⣿⣿⣿⡇⢠⣿⣧⣽⣿⠁⠀⠀⠀⢸⡿⠾⠿⠿⠿⠷⠿⠿⣾⣷⣿⡿⠀⠀⠈⢻⣷⣾⣿⣿⣶⠀⠀⠈⣿⠿⠂⠀⢰⣿⣷⣿⣷⡇⠀⢸⠎⠁⠚⠛⠛⠓⠛⢓⣛⣺⠀⠀⠀⠀⣾⣿⣿⣾⣿⣿⣿⣿⠀⢐⠁⠀⠀
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣭⡄⢀⣴⠶⣬⣻⣿⡏⣭⣽⣫⡶⢶⣝⡏⣭⣹⢠⡄⢠⡌⣭⣭⣭⡝⣿⣧⣤⢤⣥⠂⣤⡤⣤⡔⣖⣴⡶⣦⣠⢠⣤⡄⢠⣤⡄⣖⣴⢶⣦⡂⣤⣤⣤⡄⢩⣭⡏⣭⡽⢩⡍⢟⣴⢶⣤⢀⣶
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣿⣿⢸⣿⠀⣿⣿⣿⡇⣿⣿⣿⣧⣌⢭⣷⣿⣧⢸⡇⣬⣵⡇⣿⣷⣿⣿⢸⣿⣀⣿⠂⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⣧⡄⣿⡇⣺⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⣿
⣿⣿⣿⣿⣿⢹⣽⣿⡿⣭⠁⢸⣿⠀⣿⣿⣿⡇⣿⣿⣿⡏⣻⣷⢿⣿⢹⣿⡇⣿⣿⡇⣿⣿⣿⡟⢸⣿⢩⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⢸⣇⣿⡿⣼⡇⣿⣿⠀⣿⣿⡇⣿⡇⢸⢸⣿⡁⣿⢹⣿⡇⢸⣿⠘⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⣤⣬⣿⠶⣟⣽⣿⣗⣿⣿⣝⡷⠾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⣿⠀⠸⠿⢸⠿⠇⠿⠿⠸⠿⣯⡿⠶⢿⣽⠸⠟⠸⠇⠿⠇⣯⡿⠶⢿⣽⣿⠿⢇⣿⠸⠿⡇⠿⣠⣿⣇⣞⡿⢶⡻⢿⣿
⣛⣋⣉⣙⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣦⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡔⠤⢢⠒⢠⡀⠀⠀⠀⠀⠘⠲⣖⠤⠤⢄⣀⠰⠖⠂⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠒⠱⠰⠧⠀⠀⠀⠀⠀⢰⣶⡶⠀⠃⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⣤⣤⣤⣀⣀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠉⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⡿⠋⠉⠉⠻⣿⣿⣿⣿⣿⣿⠂⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢹⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠐⠂⠀⠀⠘⢿⣿⣷⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠾⡃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣻⣿⣿⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢠⢄⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⣶⡴⣀⣀⠀⢀⣀⣀⣀⠀⠀⣠⣤⣤⡄⢀⣀⢀⣀⠀⣀⣀⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣇⢸⣿⠉⠁⣾⡏⢹⣷⠀⣿⡏⢻⡆⢸⣇⣿⣼⣿⢋⠀⠀⠈⢹⣿⣩⢸⣿⠀⣿⣿⣷⣿⢹⡇⠈⢹⣿⠉⢰⣧⡍⣿⡟⣥⢸⣿⢸⣿⠀⣿⡟⣯⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀
⡆⠀⢀⣾⣷⣄⠀⢸⣿⣷⠀⠀⣿⡷⢾⣿⢸⣿⢿⣠⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⣿⣿⣿⣿⢿⡀⠀⠀⢸⣿⣿⣸⣿⠿⣿⣿⢹⡿⢸⣧⠀⢸⣿⠀⣸⣿⡇⣿⡇⣿⢸⣿⢿⣿⠀⣿⡿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠇⠀⣾⣿⣿⡟⠀⣼⣿⣿⡀⠀⣿⡇⣿⣿⢸⣿⣼⣿⢿⣇⣸⡿⡆⣿⣷⡄⠀⢸⣿⣿⢹⣿⣼⡇⠀⠀⢸⣿⣿⣿⣿⠀⣿⡿⣿⡟⢻⣿⠀⢸⣿⢀⣿⣿⡇⣿⡇⣿⢸⣿⢸⣿⠀⣿⣧⣿⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣇⠀⠀⠀⣿⣿⣾⠿⠿⠿⠷⠿⠿⠾⣷⣿⣾⡇⠀⠀⣿⣷⣾⣿⣿⣆⠀⠀⠀⢸⡿⠏⠀⠀⣿⣷⣿⡗⠀⠀⠀⡾⠉⠘⠛⠛⠓⠛⢓⣛⣺⡇⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣭⣝⢀⣤⢶⣯⣻⣿⡏⣭⣽⣫⡷⢶⣝⡏⣭⣹⢡⡄⢨⡍⣭⣭⣭⡽⣿⣦⣤⢤⣬⠃⣤⡤⣤⡔⣖⣴⡶⣦⡀⢠⣤⡄⢠⣤⡄⣖⣴⢶⣦⡂⣤⣤⣤⡄⢩⣭⡏⣭⡽⢩⡍⢟⣵⢶⣤⠀⣤
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣿⣿⢸⣿⠀⣿⣿⣿⡇⣿⣿⣿⣧⣌⢭⣷⣿⣷⢸⡇⢨⣽⡇⣿⣿⣿⣿⢻⣿⣀⣿⠇⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⣿⡇⣿⡇⢰⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⣿
⣿⣿⣿⣿⣿⢹⣿⣿⡟⣭⣷⢸⣿⠀⣿⣿⣿⡇⣿⣿⣿⡏⣻⣷⢿⣿⢹⣿⡇⣾⣿⡇⣿⣿⣿⣿⢸⣿⢩⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⢸⣧⣿⡟⣼⡇⣿⣿⠀⣿⣿⡇⣿⡇⢸⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣿⣇⣿⣷⣬⣿⠶⣟⣽⣿⣇⣿⣿⣝⡷⠾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⣿⡏⠸⠿⠸⠿⠇⠿⠟⠸⠿⠯⠿⠶⠿⠽⠸⠟⠸⠇⠿⠇⠯⠿⠶⠿⠽⠿⠿⠇⠾⠸⠿⠇⠿⣠⣿⣇⣞⡿⢶⡻⢿⣿
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⡶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣦⡴⢼⢿⣿⢾⠤⠤⠄⠠⠳⣶⣶⡴⣆⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⡾⠿⠿⠾⠶⢽⠖⠔⢰⣷⣷⡦⠫⣀⠨⠅⠀⠠⠠⠦⠤⣁⠁⡀⠀⠀⠀⠀⠸⣷⣶⠁⠀⣀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡟⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣄⣀⣀⣀⣀⣀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠈⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠟⠉⠀⠀⠙⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⣀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠘⠂⠀⠀⠘⢿⣿⣷⣶⣶⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⣄⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⢸⣿⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢸⣗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣿⣿⣿⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⢠⢄⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⣦⡤⣀⣀⠀⢀⣀⣀⣀⠀⠀⣠⣴⣤⡀⢀⣀⢀⣀⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣇⢸⣿⠉⠁⣾⡏⢹⣷⠀⣿⡏⢻⡆⢸⣇⣿⣸⣿⠋⠀⠀⠈⢹⣿⣩⢸⣿⠀⣿⣿⣷⣿⢹⡇⠈⢹⣿⠉⢰⣧⡍⣿⡟⣥⢸⣿⢸⣿⠀⣿⡟⣯⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀
⡄⠀⢀⣾⣶⡄⠀⢰⣿⡇⠀⠀⣿⡷⢾⣯⢸⣿⢿⣰⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⣿⣿⣿⣿⢿⠀⠀⠀⢸⣿⣧⢸⣿⠿⣿⣿⢹⡿⢸⣧⠀⢸⣿⠀⣸⣿⡇⣿⡇⣿⢸⣿⢿⣿⠀⣿⡿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠇⠀⣾⣿⣿⡇⠀⣸⣿⡇⠀⠀⣿⡇⣿⣿⢸⣿⣼⣯⢿⣇⣸⡿⡆⣿⣇⠀⠀⢸⣿⣿⢹⣿⣼⡅⠀⠀⢸⣿⣿⢾⣿⠀⣿⡿⣿⡟⢻⣿⠀⢸⣿⢀⣿⣿⡇⣿⡇⣿⢸⣿⢸⣿⠀⣿⣧⣿⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣷⣾⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣾⠿⠿⠿⠷⠿⠿⠾⣷⣿⣿⡇⠀⠀⣼⣷⣾⣿⣿⠀⠀⠀⠀⢸⡿⠀⠀⠐⣿⣷⣿⡗⠀⠀⠀⠈⠉⠘⠛⠛⠓⠛⢓⣛⣞⡇⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣟⠀⠀⠀⠀
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣭⣅⢀⣤⢶⣯⣻⣿⡏⣭⣽⣫⡷⢾⣝⡏⣭⣹⢡⡄⢠⡍⣭⣭⣭⣽⣧⢠⣤⢤⣬⠃⣤⡤⣤⡴⣖⣴⠶⣦⡀⢠⣤⡄⢠⣤⡄⣖⣴⣶⣦⡂⣤⣤⣤⡄⢩⣭⡏⣭⡽⢩⡍⢟⣵⠶⣤⠀⣤
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣿⡿⢸⣿⠀⣿⣿⣿⡇⣿⣿⣿⣧⣌⢭⣿⣿⣷⢸⡇⢨⣽⡇⣿⣿⣿⡏⢸⣿⣀⣿⠇⣿⣇⣼⢗⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⣿⡇⣿⡇⢰⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⣿
⣿⣿⣿⣿⣿⢹⣿⣿⡟⣭⣧⢸⣿⠀⣿⣿⣿⡇⣿⣿⣿⡏⣻⣷⢿⣿⣹⣿⡇⣾⣿⡇⣿⣿⣿⠁⢸⣿⢩⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⢸⣧⣿⡿⣼⡇⣿⣿⠀⣿⣿⡇⣿⡇⢸⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⣿⣬⡿⠶⣟⣽⣿⣇⣿⣿⣝⡷⠾⣟⣟⣿⣠⣿⣇⣿⣿⣇⣿⣿⣿⡇⠸⠿⠸⠿⠇⠿⠟⠸⠿⠯⠻⠶⠿⠽⠹⠟⠸⠇⠿⠇⠯⠿⠶⠟⠽⠟⠿⠇⠾⠸⠿⠇⠿⢠⣿⣇⣞⡿⢶⡻⢿⣿
⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠾⠾⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⣿⣿⣻⣟⣟⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠀⢀⢐⢴⣠⢒⣿⡶⣴⣦⠒⠦⡄⠠⠖⢀⡰⠤⠀⠀⠀⡀⠄⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡾⣷⡩⠿⠟⠶⢷⡻⢿⢅⡀⣿⣶⣤⢉⢪⡿⠯⠃⢢⣦⣰⣵⡄⠀⠈⠀⠀⠀⠀⣰⣷⣦⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠒⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⠁⠀⠈⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⠃⠀⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠨⢻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣀⣀⠀⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠈⠃⠀⠀⠘⢻⣿⣷⣶⣿⡿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⣼⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢿⣿⣿⣿⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⣠⢄⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⣤⡶⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣄⣀⡀⢀⣀⢀⣀⠀⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣇⢸⣿⠉⠁⣾⡏⢹⣷⠀⣿⡏⢻⡇⢸⣧⣿⣼⣿⠋⠀⠀⠈⢹⣿⡍⢸⣿⠀⣿⣿⣷⣿⢹⡇⠈⢹⣿⠉⢰⣧⡍⣿⡟⣥⢸⣿⢸⣿⠀⣿⡟⣭⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀
⠀⠀⠀⣄⡀⠀⠀⢀⣿⠀⠀⠀⣿⡷⢾⣯⢼⣿⢿⣢⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⣿⣿⣿⣿⢿⠀⠀⠀⢸⣿⡇⢸⣿⠿⣿⣿⢹⡟⢸⣧⠀⢸⣿⠀⣼⣿⡇⣿⡇⣿⢸⣿⢿⣿⠀⣿⡿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⡀⠀⢀⣿⡇⠀⠁⢸⣿⠀⠀⢠⣿⡇⣿⣿⢸⣿⣼⣿⢿⣇⣸⡿⡆⣿⡇⠀⠀⢸⣿⣿⢹⣿⣼⡄⠀⠀⢸⣿⣷⢸⣿⠀⣿⡿⣿⡟⢻⣿⢀⣼⣿⢰⣿⣿⡇⣿⡇⣿⢸⣿⢸⣿⠀⣿⣧⣿⢻⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⣷⣿⣿⡇⠀⠀⢸⣿⠀⠀⢸⠀⠀⣿⣿⣾⠿⠿⠿⠷⠿⠿⠾⣷⣿⡦⠀⠀⠀⣽⣷⣾⣿⣿⠀⠀⠀⠀⢸⡿⠀⠀⠀⣿⣷⣿⡇⠀⠀⢸⠎⠁⠘⠻⠿⢷⣿⣷⣿⣾⣷⠀⠀⠀⣸⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⢸
⣿⣿⣿⣯⣭⣭⣽⣭⣭⣤⣄⣞⣤⠶⣯⣻⣿⡏⣭⣽⣫⡿⢿⣝⡏⣭⡁⢠⡄⢠⡍⣭⣭⣭⣭⠀⢠⣤⢤⣬⠃⣤⡤⣤⡴⣖⣴⡶⣦⡀⢠⣤⡄⢠⣤⡄⣖⣴⢶⣦⡂⣤⣤⣤⡄⢩⣭⡏⣭⡽⢩⡍⢟⣽⠶⣤⠀⣾
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣾⣿⣸⣿⠀⣿⣿⣿⡇⣿⣿⣿⣧⣬⢭⣿⣿⣷⢸⡇⠈⣽⡇⣿⣿⣿⠀⢸⣿⣀⣿⠇⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⣿⡇⣿⡇⢸⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⣿
⣿⣿⣿⣿⣿⢹⣿⣿⡟⠉⣱⣿⣿⠀⣿⣿⣿⡧⣿⣿⣿⡏⣻⣷⢿⣿⣹⣿⡇⣶⣿⡇⣿⣿⣿⠀⢸⣿⢩⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⢸⣧⣿⡿⣼⡇⣿⣿⠀⣿⣿⡇⣿⡇⢸⢸⣿⠇⣿⢹⣿⡇⢸⣿⠘⣿⣷⣿
⣿⣿⣿⣿⡿⣿⣿⣿⢇⣶⣿⣯⡿⠶⢟⣽⣿⣇⣿⣿⣝⡷⢾⣟⣿⣿⣠⣿⣇⣿⣿⣇⣿⣿⡏⠀⠸⠿⠸⠿⠇⠿⠟⠸⠟⠯⠻⠶⠿⠹⠸⠟⠸⠇⠻⠇⠯⠿⠶⠟⠽⠇⠿⠇⠤⠸⠿⠀⠿⢠⠿⢇⣞⡿⠶⡻⢿⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⠛⣿⣿⣻⣟⣟⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣀⡄⣐⣢⣶⣢⣷⣶⣶⣤⠠⠤⣴⣲⡖⣄⣴⣶⢀⠂⣀⢀⠒⠄⣀⠀⠀⡄⠀⠂⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⣽⠿⢻⡽⣿⠿⢞⣾⢟⡿⡐⢸⣿⣮⠛⠾⠿⢿⠩⢲⣶⣶⡮⣎⡄⢁⠪⠈⠅⠀⢣⣵⣦⡥⠀⠄⠀⡀⡀⠐⠀⠀⠌⠀⡀⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠷⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣺⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠒⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠈⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠀⠀⣀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⠀⢸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠀⠀⠀⠈⠃⠀⠀⠘⢿⣿⣶⣶⣿⡿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢿⣿⣿⣿⠀⣀⣀⠀⠀⣀⣀⡀⠀⢀⡀⣴⢄⣀⣀⠀⠀⢀⣀⣀⣀⢀⣀⠀⣀⡤⡦⣀⣀⠀⢀⣀⣀⣀⠀⠀⣀⣤⣀⡀⢀⣀⢀⣀⠀⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣇⢸⣿⠉⠁⣾⡏⢹⣷⠀⣿⡏⣿⡇⢸⣷⣿⣾⣿⠉⠀⠀⠈⢹⣿⡉⢸⣿⠀⣿⣿⣷⣿⢹⡇⠈⢹⣿⠉⢰⣧⡍⣿⡟⣥⢸⣿⢸⣿⠀⣿⡟⣭⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀
⠀⠀⠀⣄⠀⢠⡄⠀⣿⠀⠀⠀⣿⡷⢾⣿⢸⣿⢿⣲⣿⡇⢸⣿⠀⣿⡷⠿⠃⢸⣿⣿⣿⣿⢿⠀⠀⠀⢸⣿⡇⢸⣿⠿⣿⣿⢹⡟⢸⣧⠀⢸⣿⠀⣼⣿⡇⣿⡇⣿⢸⣿⢿⣿⠀⣿⡿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣠⠀⠀⣿⠀⢸⡇⠀⣿⠀⠀⠀⣿⡇⣿⣿⢹⣿⣼⣯⢿⣇⣸⡿⡄⣿⡇⠀⠀⢸⣿⣿⢹⣿⣼⡄⠀⠀⢸⣿⣧⢸⣿⠀⣿⡿⣿⡟⢻⣿⢀⣾⣿⢰⣿⣿⡇⣿⡇⣿⢸⣿⢸⣿⠀⣿⣧⣿⢻⣿⣿⣿⣿⣿⡇⠀⠀⢸
⣿⣷⣿⣿⠀⢸⡇⢀⡟⠀⠀⣶⠀⠀⣿⣿⣾⣿⣿⣿⢶⣿⠟⠚⣷⣿⡆⠀⠀⠀⣿⣷⣾⣿⡏⠀⠀⠀⠀⢸⡿⠀⠀⠀⢻⣷⣿⡇⠀⠀⢸⣾⠁⠈⠿⠿⡷⣿⣷⣿⣾⣷⠀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⢿
⣿⣿⣿⣯⣭⣭⣽⣭⣥⢤⣄⣟⣤⠶⣮⣻⣿⡏⣭⣽⣫⡿⢿⣝⣏⣭⡁⢠⡄⢠⡍⣭⣭⣭⣅⠀⢠⣤⢤⣬⠃⣤⡤⣤⡴⣟⣴⡶⣦⡀⢠⣤⡄⢠⣤⡄⣖⣴⢶⣦⡂⣤⣤⣤⡄⢩⣭⡏⣭⡽⢩⡍⢟⣽⢶⣤⠀⣾
⣿⣿⣿⣿⣿⣘⣻⣿⣇⣸⣿⣾⣿⠀⣿⣿⣿⡇⣿⣿⣿⣧⣬⢭⣿⣿⣧⢸⡇⠈⣽⡇⣿⣿⣿⡄⢸⣿⣀⣿⠇⣿⣇⣼⢟⣿⣿⠀⣿⡇⢸⡟⣷⣼⢿⡇⣿⣿⠀⣿⣿⡇⣿⡇⢸⢸⣿⡇⣿⣷⣸⡇⢸⣿⠀⠛⠃⣿
⣿⣿⣿⣿⣿⢹⣿⣿⡟⠉⣵⣿⣿⠀⣿⣿⣿⣇⣿⣿⣿⡏⣻⣷⢿⣿⣹⣿⡇⣶⣿⡇⣿⣿⣿⠄⢸⣿⢩⣽⡆⣿⣯⢻⣯⣿⣿⠀⣿⣇⣸⣧⣿⡿⣼⡇⣿⣿⠀⣿⣿⡇⣿⡇⠀⢸⣿⡇⣿⢹⣿⡇⢸⣿⠘⣿⣷⣿
⣿⣿⣿⡿⠿⠿⢿⠿⠇⠰⠿⠿⠿⠶⢟⣽⣿⣇⣿⣿⣝⡷⠾⣟⣟⣿⣢⣿⣇⣿⣿⣇⣿⣿⣿⠀⠸⠿⠘⢛⡃⠿⠟⠸⠟⠋⠻⠶⠟⠙⠸⠟⠸⠇⠻⠇⠋⠻⠶⠟⠹⠗⠿⠇⠀⠸⠿⠀⠿⢠⡿⢇⣞⡿⠶⡻⢿⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⠉⣿⣿⣻⣟⣟⣫⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2223

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/29/irc-log-280922/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/29/irc-log-280922/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Wednesday,_September_28,_2022⠀✐


Posted in IRC_Logs at 2:09 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-280922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-280922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-280922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-280922.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
 QmTaskbsDfCZgfvTJGfgDsaghpV85LXWCJudg4G2arMsab #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmX2D3iGKkn6yrg3jv2JoexwauSQsHW3tNVRTsUQRE2K7x (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmZZ5R8nMZR31x26RyeGNMDHWF8j6Koh4VLBHAWL62pPb2 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmTXn4MHz4Ye98nuZD9mTJ4424fNnaqU4uU8QF7FDuSTXN social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 Qmf843uvkRTQBASJYE7hcc1a62bUqxo68y8bU4a7SC7kb6 #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmfWVM84vVqBDDK8K9wT6FH1QCJKqLxCUKWyVJ8RhQkFpv (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 Qmd2s9Bq41iTvXbonhSxaz4HHaS9gcmCNjcYYoKzJrwMkc #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmWE8mVev8mgNXZSTm8r5FdU8XmR4rKQvRAA29SdHaABfg (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmenFrYXbGBu2iTqkM1ZVF7uotUuiMKBWQgMwjKRxvNmog



                    ䷩ 𝚕𝚒𝚗𝚎 2350

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/29/no-protection-for-linux-from-monopolies/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/29/no-protection-for-linux-from-monopolies/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ No_Protection_for_Linux_Offered_by_the_So-called_‘Linux’_Foundation⠀✐


Posted in Antitrust, Deception, GNU/Linux, IBM, Microsoft at 3:50 pm by Dr. Roy
Schestowitz


Video_download_link | md5sum bdfdd6fa693b45158f0e1cb63bb496ef
Protection Racket
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/lf-protecting-monopolies-only.webm


Summary: From a purely objective perspective, the so-called ‘Linux’ Foundation
spends far more time/money protecting monopolies than it spends protecting
Linux; hence, the organisation arguably does more harm than good to society


EARLIER today we said that the Linux_Foundation (LF) was claiming, in vain,
that it had protected women and minorities. It’s about rhetoric with almost
nothing to show for it. We said that "The_Linux_Foundation_is_in_No_Position_to
Lecture_Us_(or_Anybody)_on_Diversity" because it seemed like a typical
corporate ploy; they paint_communities_as_zealots_and_bigots, then demand
control of the projects of these communities. The Software Freedom Conservancy
(SFC) constantly_uses_such_issues_as_a_"wedge". SFC played a big role in the
coup against the FSF, even more than once. Someone has told us that “a reminder
about the anti-RMS petition tied to the unfounded smear campaign is needed. The
campaign was based on baldfaced lies which too many, out of apparent eagerness
to lynch RMS or destroy FOSS, did not examine.”


“It’s about rhetoric with almost nothing to show for it.”The video above
discusses that for a bit and then proceeds to pointing out how the LF does
nothing about ‘secure-core’ or ‘secure’_boot_blocking_Linux (back doors’
proponents and spy agencies like the NSA misframe security). In other words,
when it comes to pressing issues the LF is on the same side as Microsoft and
IBM, which even tried_to_deprecate_BIOS_support. Restrictions and lockdowns
like DRM and TPM are perfectly OK with the LF.


An associate of ours brought up “secure-core”, the “thicker part of the wedge,
long after the thin edge.”


“SFC played a big role in the coup against the FSF, even more than once.”The
associate said “secure-core has hardly been covered at all; remember 20+ years
ago when Microsoft tried to acquire Phoenix or AMI BIOS? I forget which. That
was when they laid out their strategy to also begin lock-in from the hardware
on up. Not just from the OS on down. I’m missing a few steps but secure-core
appears to be a certification programme where restricted boot is not just on by
default but on permanently in such a way as to prevent non-Microsoft systems
from booting.”


Recently, Microsoft_and_the_OEMs_stepped_this_agenda_up_a_little. Where was the
LF? What did it do to protect Linux from this? Absolutely nothing! Spending
endless_millions_on_vanity_offices. █



                    ䷩ 𝚕𝚒𝚗𝚎 2425

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/29/the-linux-foundation-is-in-no-position-to-lecture-us-or-anybody-on-diversity/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/29/the-linux-foundation-is-in-no-position-to-lecture-us-or-anybody-on-diversity/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_Linux_Foundation_is_in_No_Position_to_Lecture_Us_(or_Anybody)_on
Diversity⠀✐


Posted in Deception, GNU/Linux, IBM, Kernel, Red_Hat at 10:11 am by Dr. Roy
Schestowitz


Earlier this month the following photo was taken (all male); Original_in_LWN
(months ago LWN also became all male as ris had stepped down)


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


Summary: The Linux_Foundation cannot_define_support_and_cannot_understand_how
to_support_women so instead_it_trolls_people; it_also_hires_no_black_people and
just like IBM_it_then_accuses_the_community_of_being_an_impediment_to_diversity
(community projects actually have more such diversity)


A couple of years ago we said that “IBM (Red Hat) Lectured FSF That It Needed
More Diversity, But Was It Looking at the Mirror? IBM and Red Hat Are Even Less
Diverse.”


The new photo (above) shows that the so-called ‘Linux’ Foundation fails to
demonstrate to us how corporations are taking the lead (these men are
employees) or will tackle diversity woes.


We’ve been writing about this subject for years because destructive people in
Debian brought_the_same_disruptive_ideology_to_Debian, resulting in almost zero
women developers (they’re used as political props, which in turn puts them
off). So the ‘Linux’ Foundation’s psyche spreads and it’s not helping. It’s a
straw man. Identity politics distract from key issues like Software Freedom and
threats_such_as_corporate_takeovers. Corporations do not have genders and
races, they just have shareholders and they want to dominate everyone.


In a recent press release, the boasting_about_diversity_was_prominent. Many of
these LF pages keep boasting about diversity, but usually they assign women to
do clerical and low-paid work. It’s the same at Red Hat and IBM. They want us
to at least feel like they have lots of girls on tje payroll.


What is it that makes this relevant? We need to talk about it because IBM/Red
Hat and LF (the front group) keep weaponising this as a smear against
communities (for_3_years_already), i.e. projects not controlled by
corporations. In the case of Linux (the kernel), if all those salaried coders
are not female, what does that tell us about corporations as the ‘solution’?


As an associate explains, “many (most) don’t understand the weaponisation,
especially of the CoC. It’s “mean” to criticize a corporation for illegal,
unethical, and anti-competitive behavior especially if the corporation hurts
the kernel and the FOSS world in general.”


Jim Zemlin, who seems_to_idolise_Bill_Gates, kept insinuating that criticising
Microsoft is like_kicking_puppies. Criticising a company that attacks you is
“hatred” (we_did_a_video_about_this_less_than_a_day_ago) and very irrational,
apparently… and it’s akin to brutality against animals. He moreover insisted
that_"Open_Source_loves_Microsoft"… (i.e. Microsoft loves what it is
attacking!)


As an associate puts it, “Microsoft has worked hard to earn and stay the object
of any hate it receives.”


Not only does the LF hijack the narrative on diversity with so-called 'studies'
(marketing) [1, 2] and paid-for puff pieces to promote that narrative [1, 2];
GPL violators and Linux haters join_in_as_well.


It’s more of a siege than a genuine, sincere attempt to introduce more people
to Linux. See the photo above; it’s like playing “Where’s Waldo?” but in this
case don’t bother looking for a Waldo; there’s a total of zero women. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣢⣇⣟⣺⣓⣿⣋⣝⣩⣏⣏⣏⣽⣅⣿⣷⣕⣛⣝⣸⣑⣇⣋⣹⣸⣁⣏⣽⣹⣍⣿⣪⣍⣏⣿⣹⣋⣏⣹⣸⣺⡏⢻⣹⣽⣹⣋⡏⣹⡏⣏⣻⣩⣋⣗⣝⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⣿⣿⡿⣿⢿⠿⠿⠿⡿⢿⡿⣿⣿⠿⡿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣗⣒⣒⣚⣓⣲⣓⢒⣒⣲⣒⣒⣚⣒⣒⣒⣖⣓⣒⣒⣒⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⢿⣯⣽⣿⣿⣿⣽⣿⣿⣿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠲⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⡇⣿⡏⡏
⡿⣿⣿⣷⠖⢲⣾⣾⣿⣿⣟⣿⠟⣻⣿⣿⣿⡿⣛⢻⣿⣿⣿⣿⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣇⠀⣹⣿⣿⣿⣿⡿⢿⠀⠀⠀⠀⠀⢻⣿⣿⡿⡛⠹⢿⡟⠸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⢗⢷
⣿⣿⣿⣿⣎⢰⣿⣿⣿⣿⢟⣿⠐⢿⣿⣿⣿⢸⡍⠀⢻⣿⣿⣿⣟⣀⣿⠡⠤⠙⣿⣿⢿⣿⡒⠂⠸⠋⠻⠀⠙⠛⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⡅⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤
⣿⣿⡿⣿⡁⠀⠉⠉⠉⠀⠀⠉⠀⠀⠈⢻⠿⡸⢇⠀⠘⢿⠟⠋⠛⠈⠉⡋⠁⣰⣅⣳⣿⡿⢀⠀⠀⠀⠀⠀⢀⡄⠀⢻⠿⠀⠀⠀⠀⢰⣺⠀⠀⢍⠼⠁⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⠇⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣳⣎⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠘⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⣿⣿⣇⠹⣧⡄⠀⡀⠀⠀⠀⠀⠀⠀⢀⣷⠈⢶⠆⠀⡖⠀⠿⠀⠇⡄⠘⠀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⣶⣿⣮⣴⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣆⡈⠇⠼⣡⠀⠀⠀⠀⠀⠀⠀⢛⣤⡀⠀⠞⠀⠐⣿⢛⠀⡧⣰⣷⠀⣠⣤⡄⠀⠀⠀⠀⣴⣶⡛⣿⣿⣿⣿⣿⣡⣤⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⠿⠿⠿⡏⠁⣿⡿⠇⠀⠀⠀⠼⠃⢹⣿⠓⠀⠀⠀⠀⣿⡈⡸⠿⠀⠀⠀⣿⡏⡅⠀⠀⠀⠀⢻⣽⢁⣿⣿⣿⣿⡿⢿⣲⠂⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣶⡶⣷⣶⣿⣷⣶⣶⣶⣶⣶⣶⣷⣷⢶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣾⡿⣷⠂⠀⢠⣴⣾⠿⠺⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠩⢭⡉⣉⢉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠛⠛⠛⠚⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡂⠀⠀⠀⠀⠀⠠⢰⡆⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣦⣀⠀⡀⣠⠀⠀⠻⣄⠀⠀⢸⣿⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠻⡷⠇⠀⠀⠀⠘⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣛⣻⣟⣻⣙⣟⣟⣟⣟⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢸⣷⣶⡶⣶⣖⡟⣻⣏⣻⣿⢛⠛⠻⠛⡟⣿⣿⣏⣿⠛⠛⠛⣿⡟⡏⠻⢻⣿⠙⢛⡏⡉⠟⢻⣻⡇⠀⠀⠀⠀⠀
⣷⣶⣾⣿⣷⣿⣶⣶⣷⣿⣶⣶⣿⣶⣶⣾⣷⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠀⠀⢸⣿⣿⣟⡻⠿⣿⢿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡀⠀⠀⡖⠸⣿⣿⣷⣷⣶⣿⣾⣷⣶⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⣦⣶⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣯⣴⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣟⣹⣛⣿⣛⣟⣟⣋⣛⣻⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2543

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/29/video-on-sourceware/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/29/video-on-sourceware/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Software_Freedom_Conservancy_(SFC)_is_Facilitating_a_Hostile_Takeover_by
Corporations_(Privatising_Free_Software)⠀✐


Posted in Free/Libre_Software, FSF, GNU/Linux, Red_Hat at 3:05 pm by Dr. Roy
Schestowitz


Video_download_link | md5sum 989d6ee61c6398bf072bba30c65de7a2
Outsourcing GNU Piecewise
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/takeover-of-gnu.webm


Summary: The Software Freedom Conservancy (SFC), which is trying to take
‘business’ and funds away from the FSF (also from SFLC, which_sued_it_over
that), helps IBM/Red Hat and the corporate front groups take over important GNU
projects, typically under the guise of providing security and funds (financial
security)


THE MONEY tends to make things toxic in the Free software world.


James Bottomley (IBM) wrote_about_it_less_than_a_day_ago and we’ve already
witnessed how IBM uses its “donations” to the FSF as a form of blackmail (“do
what we say or lose money!”).


Lately, some awful things were done by awful people who had defamed the founder
of the Free software movement. They wanted to forcibly remove him and, failing
that, to forcibly remove projects they’re connected to from GNU and/or the FSF.
In the process they detached_copyrights and caused chaos, mostly benefiting
employers_such_as_IBM. IBM likes to behave as though it owns GNU! It’s all
about money to these people…


“Lately, some awful things were done by awful people who had defamed the
founder of the Free software movement.”Earlier this month there was a_shouting
match culminating in this_week's_message and about 18 hours ago LWN liberated
(outside the paywall today) last_week’s_article, which mentions what it was all
about and gave access to video. It says “yelling from the audience made it
clear that there was some disagreement at this point — disagreement that had
never been expressed during the month-long mailing-list discussion.”


There’s an unspoken-about conflict of interest, as the author is in the Linux
Foundation, which pockets or gains control over these projects. I mention this
in the video above. Similarly, many of the comments come from kernel
developers/enthusiasts, so there’s an inherent bias. At one point the author
and_editor_admits_“Funding_from_the_LF” when he writes: “Through the end of
2019, LWN received some travel sponsorship from the LF that enabled us to get
to events and was much appreciated. For some strange reason we stopped
travelling in 2020 and that sponsorship ended; we have received no funds from
the LF since that time. So the claim in the above comment is not really true.
We might see if they are willing to renew the travel money at some point, but
we have not even asked that question. The steady stream of “I got COVID”
reports coming in from the events of the last two weeks has not increased our
urgency on that point.”


The video above makes it clear that this account of events is tilted in favour
of the corporate allies.


“There’s an unspoken-about conflict of interest…”The modus operandi isn’t too
hard to grasp. First, small grassroots communities develop good software. Over
time it gains a lot in adoption, including corporate absorption (downstream and
upstream, it’s even in billions of products). But these corporations are then
tempted to take over the entire thing, not just hire the key developers.
They’re taking over the governance, copyrights, maybe even topping it with
obligatory software patents (obligatory to employees recruited from these
projects).


In 2018 we saw Linus Torvalds temporarily ousted (and brought back in a lower
position) from his own project and a year later Richard Stallman (rms) suffered
the same fate, albeit less temporarily. For corporations, kicking aside project
founders (like rms) and the FSF is the ‘natural’ next step. It’s like a process
of gradual privatisation, turning the Commons into “intellectual property”.


The author says “Red Hat could turn evil someday (though he sees no signs of
that now) and it is good to have a contingency plan.”


Saying there’s “no signs of that now” is missing the full picture; Red Hat is
just a drone of IBM and many managers at Red Hat came from Microsoft following
a massive and still-ongoing staff exodus.


“There are a lot of interesting comments, and almost 99% of them are from LWN
subscribers, i.e. people who pay LWN.”I’ve not watched the video of the
controversial “debate”, but this_comment notes: “Looking at the video of the
talk, that was egregiously unprofessional. I just cringed…”


There are a lot of interesting comments, and almost 99% of them are from LWN
subscribers, i.e. people who pay LWN. █



                    ䷩ 𝚕𝚒𝚗𝚎 2660

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_29/09/2022:_Avidemux_2.8.1_and_Pithos_1.6.0⠀✐


Posted in News_Roundup at 6:54 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o New_Releases
          o Red_Hat_/_IBM
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Productivity_Software/LibreOffice/Calligra
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                # Rust
    * Leftovers
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                # Privacy/Surveillance
          o Censorship/Free_Speech
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          o Internet_Policy/Net_Neutrality
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    * Gemini*_and_Gopher
          o Personal
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                # Programming
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ The Register UK ☛ IBM’s_‘bare_metal’_LinuxONE_push:_Did
                  somebody_say_OpenShift?⠀⇛


                       Red Hat has released betas of RHEL 8.7 and 9.1
                       while its parent company IBM is offering Linux
                       mainframe instances in the cloud, although only in
                       some regions.


                       If you’re looking for some particularly resilient
                       home in the cloud to run Linux workloads, Red Hat’s
                       parent company IBM has a new mainframe-based
                       Infrastructure-as-a-Service product out under the
                       LinuxONE umbrella, which it has dubbed “bare metal
                       servers.”


                       As we described a few years ago, IBM offers a whole
                       range of different hypervisors on mainframes,
                       including PR/SM (akin to a hypervisor in the
                       firmware) and the native Linux in-kernel hypervisor
                       KVM. One of the company’s flagship mainframe OSes,
                       z/VM, is perhaps more commonly used to manage VMs
                       on Z series, but it’s cheaper to rent LinuxONE
                       mainframes because they’ve been tweaked to only run
                       Linux, excluding any native IBM mainframe OSes.


                       It’s noticeable that the announcement specifically
                       mentions Red Hat’s container management platform
                       OpenShift – maybe not unrelated to Red Hat’s new
                       CEO Matt Hicks, who was one of the original
                       OpenShift team.


                # ⚓ CentOS ☛ CentOS_Hyperscale_SIG_conference_recap_–
                  Blog.CentOS.org⠀⇛


                       In the past couple of months members of the CentOS
                       Hyperscale SIG attended several conferences where
                       they were able to share the work the SIG is doing
                       and meet up in person, in some cases for the first
                       time.


                       We have a page tracking conference presentations
                       around Hyperscale-related topics. You can find
                       references there to all talks mentioned below,
                       including video recordings where available.


                       Conferences aren’t just about presentations though.
                       The “hallway track” provides a great opportunity
                       for serendipidous connection, and the various
                       social events are often a great venue for folks to
                       mingle and get to know each other in an informal
                       setting.


                       If you’d like to meet us in person at a future
                       event please reach out. We also generally cover
                       conferences we plan to attend in our quarterly
                       reports.


                # ⚓ Kubernetes Blog ☛ Enforce_CRD_Immutability_with_CEL
                  Transition_Rules⠀⇛


                       Immutable fields can be found in a few places in
                       the built-in Kubernetes types. For example, you
                       can’t change the .metadata.name of an object.
                       Specific objects have fields where changes to
                       existing objects are constrained; for example, the
                       .spec.selector of a Deployment.


                       Aside from simple immutability, there are other
                       common design patterns such as lists which are
                       append-only, or a map with mutable values and
                       immutable keys.


                       Until recently the best way to restrict field
                       mutability for CustomResourceDefinitions has been
                       to create a validating admission webhook: this
                       means a lot of complexity for the common case of
                       making a field immutable.


                       Beta since Kubernetes 1.25, CEL Validation Rules
                       allow CRD authors to express validation constraints
                       on their fields using a rich expression language,
                       CEL. This article explores how you can use
                       validation rules to implement a few common
                       immutability patterns directly in the manifest for
                       a CRD.


                # ⚓ Exploring_the_Benefits_of_Containerization_–_Container
                  Journal⠀⇛


                       As part of the effort to simplify application
                       development processes, many developers are
                       leveraging containerization. It is one way of
                       grouping the infrastructure of applications, making
                       it easier for developers to interact with and
                       manage. It’s not a new method and has been evolving
                       for several years now, allowing developers to
                       become more confident in using it. Containerization
                       also has many benefits for developers.


                # ⚓ The_Growing_Appreciation_for_Service_Mesh⠀⇛


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Fedora_Broke_H264_GPU_Acceleration_For_“Legal
                  Reasons”_–_Invidious⠀⇛


                       This Fedora video codec situation is a complete
                       mess, Fedora removed h264, h265 and vc1 support
                       from their mesa build basically breaking GPU
                       acceleration for these codecs on AMD based systems
                       and I hope that it doesn’t have a knock on effect
                       in other distros.


                # ⚓ Video ☛ Enterprise_Linux_Security_Episode_Episode_44_–_Is
                  Linux_less_of_a_Target?_–_Invidious⠀⇛


                       In this episode, Jay and Joao discuss how much of a
                       target Linux is, as well as some myths surrounding
                       Linux and security. Also, there will be some news
                       updates as well.


                # ⚓ Video ☛ Stadia,_Kindle,_‘Stream’_decks_and_more_–_A_Trendy
                  Talk_–_Invidious⠀⇛


                # ⚓ Video ☛ SpiralLinux_11.220925_overview_|_Linux,_faster_than
                  a_snail_–_Invidious⠀⇛


                       In this video, I am going to show an overview of
                       SpiralLinux 11.220925 and some of the applications
                       pre-installed.


                # ⚓ Linux_Action_News_260⠀⇛


                       The controversial change for the GNU Toolchain,
                       critical vulnerabilities in popular Matrix clients,
                       and the significant milestone for the Ingenuity
                       LinuxCopter this week.


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ The_2022_Linux_Kernel_Maintainers_Summit_[LWN.net]⠀⇛


                       After a two-year hiatus, the 2022 Linux Kernel
                       Maintainers Summit returned to an in-person format
                       in Dublin, Ireland on September 15. Around 30
                       kernel developers discussed a number of process-
                       related issues relating to the kernel community.
                       LWN had the privilege of being there and is able,
                       once again, to report from the event.


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


                       The first scheduled session at the 2022 Linux
                       Kernel Maintainers Summit was a half hour dedicated
                       to regression tracking led by Thorsten Leemhuis.
                       The actual discussion took rather longer than that
                       and covered a number of aspects of the problem of
                       delivering a kernel to users that does not break
                       their applications.
                       Leemhuis started by saying that, after a break of a
                       few years, he has managed to obtain funding to work
                       as the kernel’s regression tracker and is back at
                       the job. He has created a new bot intended to
                       minimize the amount of work required and to, he
                       hopes, enable effective regression tracking while
                       not creating additional overhead for developers. In
                       an ideal world, bug reporters will put bot-related
                       directives into their reports, after which the bot
                       will track replies. When it sees a patch with a
                       Link tag pointing back to the report, it will mark
                       the bug as resolved.


                       This application (called “regzbot”) is still young,
                       he said, and it has its share of warts and
                       deficiencies. It has reached a point of being
                       useful for Linus Torvalds, but it is not yet as
                       useful for subsystem maintainers. It is, in any
                       case, far better than trying to track bugs
                       manually. Regzbot has already caught regressions
                       that would have otherwise fallen through the
                       cracks. He thanked Meta for providing the funding
                       that makes this work possible.


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


                       The Rust for Linux project, which is working to
                       make it possible to write kernel code in the Rust
                       programming language, has been underway for a few
                       years, and there is a growing number of developers
                       who feel that it is time to merge this work into
                       the mainline. At the 2022 Linux Kernel Maintainers
                       Summit, Miguel Ojeda updated the group on the
                       status of the project with the goal of reaching a
                       conclusion on when this merge might happen. The
                       answer that came back was clear enough: Rust in the
                       kernel will be happening soon indeed.


                       There was little suspense on that front; Linus
                       Torvalds spoke up at the beginning of the session
                       to say that he plans to accept the Rust patches for
                       the 6.1 kernel (likely to be released in mid-
                       December) unless he hears strong objections. Ojeda
                       indicated that he would like to see that happen and
                       asked how the patches should be routed into the
                       mainline. Torvalds said that he would rather not
                       accept them directly, so it seems likely that Kees
                       Cook will be routing this work upstream.


                # ⚓ LWN ☛ How_far_do_we_want_to_go_with_BPF?⠀⇛


                       The BPF subsystem has come a long way in recent
                       years; what started as a mechanism for implementing
                       packet filters has become a way to load code into
                       the kernel for a wide variety of tasks. At the 2022
                       Linux Kernel Maintainers Summit, Jiri Kosina kicked
                       off a session by asking how far the transition to
                       BPF should go. The actual scope of the session
                       turned out to be rather more limited than that, and
                       no fundamental changes were considered.


                       Kosina started by saying that BPF has been highly
                       successful and it is increasingly being used by
                       user programs. But the kernel community has no
                       policies about out-of-tree BPF code and, in
                       particular, how to deal with associated bug
                       reports. What happens when a kernel change breaks
                       somebody’s BPF program? Ted Ts’o added that future
                       applications are increasingly likely to include BPF
                       scripts, and users may not be aware that they are
                       running something that is more like a kernel module
                       than an ordinary program. That can lead to
                       confusion and complaints to kernel developers when
                       things break.


                # ⚓ LWN ☛ Various_short_development-process_topics⠀⇛


                       The final part of the 2022 Linux Kernel Maintainers
                       Summit included a number of relatively short
                       discussions on a variety of topics. These included
                       testing of stable updates, compiler versions, test
                       suites, and the traditional session where Linus
                       Torvalds talks about his happiness (or lack
                       thereof) with the way the development process is
                       going.


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


                       The traditional mechanism for launching a program
                       in a new process on Unix systems—forking and
                       execing—has been with us for decades, but it is not
                       really the most efficient of operations. Various
                       alternatives have been tried along the way but have
                       not supplanted the traditional approach. A new
                       mechanism created by Josh Triplett adds process
                       creation to the io_uring asynchronous I/O API and
                       shows great promise; he came to the 2022 Linux
                       Plumbers Conference (LPC) to introduce
                       io_uring_spawn.


                       Triplett works in a variety of areas these days,
                       much of it using the Rust language, though he has
                       also been working on the kernel some of late. He is
                       currently working on build systems as well. Build
                       systems are notorious for spawning lots of
                       processes as part of their job, “so I care about
                       launching processes quickly”. As with others at
                       this year’s LPC, Triplett said that he was happy to
                       see a return to in-person conferences.


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


                       Nobody should need more memory than a 64-bit
                       pointer can address — or so developers tend to
                       think. The range covered by a pointer of that size
                       seems to be nearly infinite. During the Kernel
                       Summit track at the 2022 Linux Plumbers Conference,
                       Matthew Wilcox took the stage to make the point
                       that 64 bits may turn out to be too few — and
                       sooner than we think. It is not too early to start
                       planning for 128-bit Linux systems, which he termed
                       “ZettaLinux”, and we don’t want to find ourselves
                       wishing we’d started sooner.


                       The old-timers in the audience, he said, are likely
                       to have painful memories of the 32-bit to 64-bit
                       transition, which happened in the mid-1990s. The
                       driving factor at the time was file sizes, which
                       were growing beyond the 2GB that could be
                       represented with signed, 32-bit numbers. The Large
                       File Summit in 1995 worked out the mechanisms
                       (“lots of dreadful things”) for handling larger
                       files. Developers had to add the new lloff_t size
                       for 64-bit file sizes and the llseek() system call
                       to move around in large files. Wilcox said that he
                       would really prefer not to see an lllseek() for
                       128-bit offsets.


          o § Graphics Stack⠀➾


                # ⚓ Collabora ☛ Weston_11.0:_what’s_new,_what’s_next⠀⇛


                       Among those changes, this new version brings in
                       some optimization being done in the DRM-backend
                       that refactors and simplifies the handling of
                       buffers that can be scanned out by hardware planes,
                       as well as some changes to include preliminary work
                       towards having support for multiple GPUs.


                       Color management infrastructure code has landed
                       that allows HDR characteristics to be delivered to
                       an HDR-capable monitor by setting-up HDR metadata
                       in a weston.ini configuration file and delivering
                       that to KMS. Once Weston gains the ability to
                       produce HDR content in a future version, it will
                       come naturally supported.


                       This new version brings in multiple RDP
                       improvements, like clipboard pasting, various
                       keyboard language support, bumped support for a
                       newer version of FreeRDP library, and many more
                       other improvements and fixes.


                       With refactoring of the weston_buffer
                       infrastructure, support for
                       wp_single_pixel_buffer_v1 protocol has landed,
                       allowing for instance more optimal media playback.


                       Finally, as part of our re-architecture effort to
                       support multiple inputs, outputs, and back-ends
                       being active at the same time, the initial
                       groundwork has been laid to support multiple back-
                       ends with more incoming changes still in-flight.


                # ⚓ LWN ☛ Weston_11.0:_what’s_new,_what’s_next_(Collabora_blog)
                  [LWN.net]⠀⇛


                       Over on the Collabora blog, Marius Vlad writes
                       about the recent Weston 11.0.0 release. Weston is
                       the reference compositor for the Wayland display
                       server protocol. Vlad looks at features of the
                       release, including some things that are being
                       deprecated and removed, as well as features coming
                       in Weston 12.


          o § Applications⠀➾


                # ⚓ Ubuntu Handbook ☛ Avidemux_2.8.1_is_out_with_New_Filters_&
                  HiDPI_Improvements_|_UbuntuHandbook⠀⇛


                       Avidemux video editor released version 2.8.1 a few
                       days ago. Here’s the new features and how to
                       install instruction for Ubuntu 22.04 and Ubuntu
                       20.04.


                       The new release improved HiDPI displays support by
                       updating the icon set, and using OpenGL for
                       rendering on-the-fly preview in video filter
                       dialog.


                       Avidemux 2.8.1 also introduced new filters: 3D LUT,
                       Decimate, and Arbitrary Rotate, as well as new
                       video encoder: VideoToolbox HEVC for macOS users.


                       It also added support for decoding 8-bit VP9 on
                       Windows using DXVA2 and Linux using VDPAU with
                       graphics card that features a VP9 decoder.


                # ⚓ Ubuntu Handbook ☛ Pandora_Radio_Client_Pithos_1.6.0_Now
                  Uses_CSD_Header_bar_[Ubuntu_PPA]_|_UbuntuHandbook⠀⇛


                       Pithos, native Linux client for Pandora Radio, got
                       a new release update few days ago. Here’s how to
                       install it in Ubuntu 22.04, Ubuntu 20.04 & Ubuntu
                       18.04 via PPA.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Hint ☛ Configure_Lets_Encrypt_Digital_Ocean⠀⇛


                       A website’s domain must have SSL/TLS encryption if
                       it intends to get visitors. SSL/TLS certificates
                       provide a strong connection among web servers and
                       browsers. Earlier, security wasn’t a major concern.
                       It was relatively common for websites to deliver
                       data via the established HTTP protocol. Nowadays,
                       the channel used to communicate with the server
                       must be secured, though, because cybercrimes
                       including identity theft, credit card fraud, and
                       espionage are on the rise.


                       A Certificate Authority (CA) called Let’s Encrypt
                       offers free SSL/TLS certificates, enabling HTTPS
                       encryption on web servers. It is domain verified,
                       so a dedicated IP Address is not necessary. It is
                       usually advised to have an SSL certificate enabled
                       on your website to improve your SEO ranking,
                       particularly on Google.


                # ⚓ OSTechNix ☛ How_To_Configure_Mouse_Support_For_Linux
                  Virtual_Consoles_With_GPM [Ed: Last updated today]⠀⇛


                # ⚓ Make Use Of ☛ How_to_Manage_RSS_Feeds_With_Mozilla
                  Thunderbird_on_Linux⠀⇛


                       Thunderbird is one of the best desktop email
                       clients for Linux. It’s fast, easy to use, and
                       provides a range of features to simplify email
                       management on your desktop. In addition, Mozilla
                       also includes a few additional functionalities in
                       the Thunderbird Mail client: chat, newsgroups, and
                       syndication, which extend its scope of use further.


                       If you already use Mozilla Thunderbird for email
                       management on your machine, you can now also access
                       your latest news feeds and blogs within the same
                       program. Here’s how to use Thunderbird Mail as an
                       RSS feed reader on Linux.


                # ⚓ Make Use Of ☛ How_to_Live_Monitor_YouTube_Views_and_Google
                  Analytics_With_a_Raspberry_Pi⠀⇛


                       People who make YouTube videos or produce web
                       content often set up dedicated displays to monitor
                       performance statistics live, such as YouTube
                       Analytics and Google Analytics. The live analytics
                       data can give an insight of trending content, while
                       the statistics can be used to quickly tweak and
                       optimize related content.


                       In an ideal world, live monitoring should start at
                       the flip of a power switch or the push of a power
                       button on the television remote. A Raspberry Pi
                       connected to a television or a monitor is ideal for
                       this.


                # ⚓ HowTo Forge ☛ How_to_Install_Jekyll_Static_Website
                  Generator_on_Ubuntu_22.04⠀⇛


                       Jekyll is a free and open-source static file
                       generator written in Ruby.


                # ⚓ HowTo Forge ☛ How_to_Install_Graylog_4_on_Ubuntu_22.04⠀⇛


                       Graylog is a free and open-source log monitoring
                       tool used for capturing, storing, and enabling
                       real-time analysis of terabytes of machine data.


                # ⚓ Make Use Of ☛ How_to_Install_Flatpak_Packages_on_a
                  Chromebook⠀⇛


                       Flatpak offers newer versions of apps than what you
                       find by default on Chromebooks. Here’s how to run
                       the latest Linux software.


                       On most Chromebooks, you can install a complete
                       version of Debian Stable under the Linux
                       development environment. If you want access to
                       newer apps, many popular Linux apps are available
                       as Flatpak packages. It can be tricky to get such
                       apps running on a Chromebook, but the process is
                       easy when you know how.


                # ⚓ Linux Handbook ☛ How_to_Follow_Symbolic_Links_in_Linux⠀⇛


                       A symbolic link (also known as soft link) is a kind
                       of shortcut to another file. It’s heavily used in
                       Linux for shared libraries.


                       But how do you know to which original file the link
                       points to?


                # ⚓ Trend Oceans ☛ How_to_Fix_Error:_Failed_to_Download
                  Metadata_for_Repo_‘AppStream’_from_CentOS_8_–_TREND_OCEANS⠀⇛


                       If you are compelled to use CentOS 8 or have any
                       other reason to have it still running on your
                       system, Then I hope you know that CentOS 8 has died
                       and reached its End Of Life (EOL) on December 31st,
                       2021.


                # ⚓ ID Root ☛ How_To_Install_SonarQube_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       SonarQube on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, SonarQube or formerly Sonar is an
                       open-source platform for static code analysis and
                       code security. It can find the security
                       vulnerabilities in more than 20 programming
                       languages along with auto-analyzing code quality to
                       detect code bugs and smells. SonarQube also
                       provides reports such as duplicate code, coding
                       standards, code complexity, and security
                       recommendation.


                       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 SonarQube 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.


                # ⚓ AddictiveTips ☛ How_to_chat_on_Whatsapp_on_Linux_with
                  ZapZap⠀⇛


                       ZapZap is a beautiful, powerful Whatsapp client for
                       Linux. It is an unofficial app with improved
                       features like support for multiple users,
                       integrated spellcheck, notifications, etc. Here’s
                       how to chat on Whatsapp on Linux with ZapZap.


                # ⚓ TechRepublic ☛ How_to_install_Rancher_Desktop_on_Linux_and
                  macOS_|_TechRepublic⠀⇛


                       Docker Desktop is one of the more popular GUI tools
                       for developing and managing Docker containers.
                       However, it’s not alone in the world of Docker
                       GUIs. Although many Docker GUIs have come and gone,
                       some have stood the test of time. One such GUI tool
                       is Rancher Desktop.


                # ⚓ TechRepublic ☛ How_to_enable_Docker_command_completion_in
                  Linux_to_simplify_the_Docker_CLI_|_TechRepublic⠀⇛


                       For some, Docker is second nature. The commands
                       used are ingrained in their psyche. For others,
                       however, it can be a chore to have to remember all
                       those command line options. Is it docker image,
                       docker images, or docker import? Given how
                       complicated container deployment and management can
                       be, the last thing you want is to have to remember
                       every single command option available.


          o § Games⠀➾


                # ⚓ Godot Engine ☛ Godot_Engine_–_Dev_snapshot:_Godot_4.0_beta
                  2⠀⇛


                       We released Godot 4.0 beta 1 two weeks ago! That
                       was a big milestone on our journey to finalize our
                       next major release – be sure to check out that blog
                       post if you haven’t yet, for an overview of some of
                       the main highlight of Godot 4.0.


                       But the “1″ in beta 1 means that it’s only the
                       first step of the journey, and like for the alpha
                       phase, we’re going to release new beta snapshots
                       roughly every other week. So here’s beta 2!


                       The reception of beta 1 was surprisingly good –
                       we’re happy to see the community tinker with the
                       beta, report bugs and provide feedback on the new
                       features. Many bugs have been fixed in just two
                       weeks, with close to 250 PRs merged, many of which
                       fixed bugs reported by beta testers.


                # ⚓ Boiling Steam ☛ Did_the_TGS2022_Help_The_Steam_Deck_Gain
                  Awareness_in_Japan?_Apparently_Yes!_–_Boiling_Steam⠀⇛


                       As you know Valve and Komodo have partnered to have
                       a huge booth at the Tokyo Games Show 2022
                       (TGS2022), and while the show was much smaller than
                       usual, because of the post-COVID19 era, there were
                       still quite a few journalists covering the event,
                       almost as much as usual. But has the event managed
                       to increase the interest in the device locally?


                # ⚓ GamingOnLinux ☛ Google_gives_up_on_Stadia,_will_offer
                  refunds_on_games_and_hardware_|_GamingOnLinux⠀⇛


                       As expected for some time now, Google has decided
                       to call it quits on their cloud gaming service
                       Stadia. This was announced in a blog post today.


                       Written up by Phil Harrison, the Vice President and
                       General Manager at Stadia, the post mentions how
                       “it hasn’t gained the traction with users that we
                       expected so we’ve made the difficult decision to
                       begin winding down our Stadia streaming service”.


                       The wildest part about this, is that they’re going
                       to be refunding all Stadia hardware purchases made
                       through the main Google Store and they will also be
                       refunding all game and add-on content purchases
                       made through the Stadia store. Harrison said they
                       expect to have finished up the majority of refunds
                       by Mid-January, 2023. They will not be refunding
                       any Stadia Pro subscriptions though, only the full
                       purchases. More info on the process here but it
                       seems like it’s not ready yet.


                # ⚓ Google ☛ A_message_about_Stadia_and_our_long_term_streaming
                  strategy⠀⇛


                       For many years, Google has invested across multiple
                       aspects of the gaming industry. We help developers
                       build and distribute gaming apps on Google Play and
                       Google Play Games. Gaming creators are reaching
                       audiences around the world on YouTube through
                       videos, live streaming and Shorts. And our cloud
                       streaming technology delivers immersive gameplay at
                       massive scale.


                       A few years ago, we also launched a consumer gaming
                       service, Stadia. And while Stadia’s approach to
                       streaming games for consumers was built on a strong
                       technology foundation, it hasn’t gained the
                       traction with users that we expected so we’ve made
                       the difficult decision to begin winding down our
                       Stadia streaming service.


          o § Desktop Environments/WMs⠀➾


                # ⚓ DebugPoint ☛ Xfce_4.18_Arriving_on_Christmas,_After_Two
                  Long_Years⠀⇛


                       An early Christmas gift for Xfce desktop fans. Per
                       the new Xfce 4.18 announcement, the new release is
                       planned for later this year.


                # ⚓ Web Pro News ☛ Linux_Distro_Reviews:_Xfce⠀⇛


                       Xfce is one of the oldest desktop environments (DE)
                       available for Linux, but it is still going strong
                       as a top contender for modern users.


                       In the previous entry in this series, we explained
                       the role of DEs in the Linux world. Among those,
                       Xfce is a unique offering that threads the line
                       between functionality, stability, and performance,
                       making it a popular choice in the Linux and Unix
                       world.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Web Pro News ☛ Linux_Distro_Reviews:_Gnome⠀⇛


                             Gnome is the most popular desktop environment
                             (DE) available for Linux, but it is easily
                             the most controversial and the hardest to
                             rate.


                             In the previous entry in this series, we
                             explained the role of DEs in the Linux world.
                             Among those, Gnome is a study in
                             contradictions, simultaneously delighting and
                             angering its user base.


    * § Distributions and Operating Systems⠀➾


          o ⚓ 9to5Linux ☛ Security-Oriented_Distro_Parrot_5.1_Arrives_with
            AnonSurf_4,_Linux_Kernel_5.18,_and_More⠀⇛


                 Parrot 5.1 is here six months after Parrot 5.0 and it’s
                 powered by Linux kernel 5.18, which, unfortunately,
                 reached end of life in August. However, the new kernel
                 comes as a significant update from Linux kernel 5.16 used
                 in the previous release, so you should expect better
                 hardware support.


                 Parrot 5.1 also ships with the in-house built AnonSurf 4
                 anonymity tool that provides users with a solution to
                 automatically route all the system traffic through the
                 anonymous Tor network.


          o § New Releases⠀➾


                # ⚓ Linux Magazine ☛ ExTiX_22.9_Released_with_Support_for
                  Installing…_–_Linux_Magazine⠀⇛


                       The developers of the ExTiX Linux Distribution have
                       released a new version that includes added support
                       to make installing and using Android apps on the
                       desktop a breeze.


                       ExTiX is a KDE Plasma-based Linux distribution that
                       has recently enjoyed a new release, 22.9, which
                       adds something special into the mix…the ability to
                       easily install Android apps.


                       The ExTiX developers have added Anbox into the mix
                       with support for Google Play Services pre-
                       installed. Because this take on Anbox comes
                       complete with Google Play Store integration, not
                       only is the installation of Android apps simplified
                       on Linux, but the apps should run more dependably
                       and predictably.


          o § Red Hat / IBM⠀➾


                # ⚓ Red Hat Official ☛ Red_Hat_Satellite_6.11.3_has_been
                  released⠀⇛


                       We are pleased to announce that Red Hat Satellite
                       6.11.3 is generally available as of September 29,
                       2022.


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


                # ⚓ IBM Old Timer ☛ The_Importance_of_Open_Source_Digital
                  Wallets_to_the_Future_of_the_Internet [Ed: IBM promoting the
                  lie that “The LF was originally founded in 2000″ (no, not
                  really, but they_put_this_lie_in_Wikipedia)]⠀⇛


                       On September 13, the Linux Foundation (LF)
                       announced its intent to form the Open Wallet
                       Foundation (OWF) at its Open Source Summit Europe
                       in Dublin. The OWF aims to develop open source
                       software, key building blocks, and best practices
                       that anyone can use as a starting point to build
                       multi-platform, highly secure, privacy-protecting
                       digital wallets. In addition, the OWF will advocate
                       for the wide adoption of open source wallets that
                       can be used to support a wide variety of
                       applications, from payments to digital identities.


                       The LF was originally founded in 2000 as the Open
                       Source Development Labs to help set the standards
                       for the Linux operating system and support its
                       continued development and commercial adoption. It
                       grew over the years and assumed its current name,
                       Linux Foundation, in 2007. Over the past decade,
                       the LF has undergone a major expansion beyond its
                       original Linux mission. It now has over 1,260
                       company members and supports hundreds of open
                       source projects. Some of the projects are focused
                       on technology horizontals, – e.g., AI, blockchain,
                       security, cloud, – and others on industry
                       verticals, including energy, automative,
                       government, and health care.


                       Let me attempt to explain the importance of this
                       announcement by addressing three key questions:
                       what is a digital wallet?; what are digital
                       identities?; and why do we need standard-based,
                       open source digital wallets?


                # ⚓ LWN ☛ Two_visions_for_the_future_of_sourceware.org_
                  [LWN.net]⠀⇛


                       Public hosting systems for free software have come
                       and gone over the years but one of them,
                       Sourceware, has been supporting the development of
                       most of the GNU toolchain for nearly 25 years.
                       Recently, an application was made to bring
                       Sourceware under the umbrella of the Software
                       Freedom Conservancy (SFC), at least for fundraising
                       purposes. It turns out that there is a separate
                       initiative, developed in secret until now, with a
                       different vision for the future of Sourceware. The
                       2022 GNU Tools Cauldron was the site of an intense
                       discussion on how this important community resource
                       should be managed in the coming years.


                       The session in question was initially set up as a
                       birds-of-feather gathering where Sourceware
                       “overseer” Mark Wielaard would describe some of the
                       new services that are being developed for that
                       site. He did not get far before being interrupted
                       by David Edelsohn, who questioned whether it was
                       correct to describe Sourceware as a “software
                       project”. Wielaard tried to push on, noting that
                       there are currently two Red Hat employees, helped
                       by a number of volunteers, looking after the site.
                       Carlos O’Donell repeatedly broke in to describe
                       Sourceware as specifically a Red Hat system. The
                       site’s mission statement, he said, describes it as
                       “a Red Hat system providing services for open-
                       source projects for Red Hat” (which isn’t quite the
                       wording on the actual statement). The purpose of
                       these interjections was evidently (at a minimum) to
                       dispute the notion that Sourceware is a community
                       resource.


                # ⚓ Red Hat Official ☛ What_are_the_differences_between
                  absolute_and_relative_paths?_|_Enable_Sysadmin⠀⇛


                # ⚓ Red Hat Official ☛ Connecting_to_the_RHEL_web_console,_part
                  2:_Running_the_Cockpit_web_server⠀⇛


                       The Red Hat Enterprise Linux (RHEL) web console
                       provides a web-based graphical interface for
                       managing and monitoring systems. The web console
                       can be used to complete a wide variety of tasks,
                       such as managing storage, users, the firewall,
                       monitoring performance metrics, reviewing log
                       files, installing system updates and many others.
                       See the Managing systems using the RHEL 9 web
                       console documentation for more information.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Ubuntu_MATE_22.10_Release_Notes_|_Ubuntu_MATE⠀⇛


                       Ubuntu MATE 22.10 is a modest update by recent
                       standards and focused on “quality of life
                       improvements”. And there is good reason why this
                       release of Ubuntu MATE doesn’t feature the usual
                       bucket 🪣 list of changes you’d typically expect,
                       and that’s because I’ve been helping bring the full
                       Ubuntu MATE experience to Debian MATE 🧉


                # ⚓ Ubuntu ☛ Ubuntu_Blog:_Build_Ubuntu_Pro_Golden_Image_on
                  Google_Cloud⠀⇛


                       A Golden image is a base image that is used as a
                       template for your organization’s various virtual
                       machines either on-prem or in the public cloud. It
                       streamlines software development processes since
                       mission-critical applications are dependent on a
                       certified environment. Using Golden Images saves
                       numerous hours and resources as they create
                       consistent environments for your developers and
                       operation teams. Golden Images not only help
                       prevent human errors but also standardize VM
                       configurations.


                # ⚓ Beta News ☛ Ubuntu_desktop_comes_to_AWS⠀⇛


                       Until today Amazon WorkSpaces cloud desktop
                       solution simply offered the option of either
                       Windows or Amazon Linux machines. Now though
                       Canonical has announced the availability of Ubuntu
                       WorkSpaces on AWS.


                       This is a fully managed virtual desktop
                       infrastructure (VDI) on the public cloud and the
                       first third-party Linux OS to be available on the
                       platform. It gives developers access to a wide
                       choice of open source tools and libraries in
                       cutting-edge fields like data science, artificial
                       intelligence/machine learning, cloud and internet-
                       of-things.


                # ⚓ Ubuntu ☛ Ubuntu_Arrives_on_Amazon_WorkSpaces:_The_First
                  Fully_Managed_Ubuntu_VDI_on_a_Public_Cloud_|_Ubuntu⠀⇛


                       Canonical is proud to announce the availability of
                       Ubuntu WorkSpaces on AWS, a fully managed virtual
                       desktop infrastructure (VDI) on the public cloud
                       and the first third-party Linux OS available on the
                       platform. Ubuntu Desktop’s availability on Amazon
                       WorkSpaces was announced today at the AWS End User
                       Computing Innovation Day in Seattle, WA.


                       Amazon WorkSpaces offers a fully managed and highly
                       secure cloud desktop solution across a broad
                       hardware spectrum, without the upfront costs of
                       deployment and configuration. They enable remote
                       developers to access high-performance desktops from
                       any location, preserving security.


          o § Open Hardware/Modding⠀➾


                # ⚓ CNX Software ☛ ELLO_LC1_–_A_2mm_thin_DIY_“computer”_based
                  on_Microchip_PIC18_8-bit_MCU_–_CNX_Software⠀⇛


                       We often write about business card or credit card-
                       sized boards, but it’s only true for 2D dimensions,
                       as most boards are over a centimeter thick, with
                       possibly the thinnest we’ve covered being the
                       Khadas Edge2 SBC that’s just 7mm thick.


                # ⚓ Arduino ☛ Digitize_your_collection_of_35mm_slides_|_Arduino
                  Blog⠀⇛


                       Sharing photos used to be a difficult task. Even
                       after paying for someone to develop your photos and
                       waiting to get them back, you’d end up with small
                       prints that your friends would have to huddle
                       around. One common alternative was 35mm slide
                       projection. Photographers could snap images and
                       then have them developed as 35mm slides. They could
                       then pop those into a slide projector that would
                       blow up the image on a screen or wall where
                       everyone could see the photo. If your family has a
                       large collection of 35mm slides, this Instructables
                       tutorial will help you digitize them.


                       As great as 35mm slides were, they don’t have much
                       of a place in our modern world. Not many people
                       have working slide projectors these days and most
                       would prefer digital photos that they can share on
                       social media, store on their computer, or display
                       on a TV. There are 35mm slide digitizing services,
                       but those can cost more than 50 cents (USD) per
                       slide. That becomes very expensive if your slide
                       collection is large. If you have a slide projector,
                       even if its projection bulb is burnt out, this
                       tutorial will help you digitize the slides by
                       snapping photos with a modern DSLR camera.


                # ⚓ Arduino ☛ Add_ML-controlled_smart_suspension_adjustment_to
                  your_bicycle_|_Arduino_Blog⠀⇛


                       Some modern cars, trucks, and SUVs have smart
                       active suspension systems that can adjust to
                       different terrain conditions. They adjust in real-
                       time to maintain safety or performance. But they
                       tend to only come on high-end vehicles because
                       they’re expensive, complicated, and add weight.
                       That’s why it is so impressive that Jallson Suryo
                       was able to add a similar smart suspension
                       adjustment system to his bicycle.


                       This system will only work on specific bicycles
                       that have suspension forks that the user can adjust
                       with a knob. A servo-driven mechanism mounts onto
                       the fork and turns the knob to tweak the firmness
                       and rebound of the front suspension. Normally the
                       rider would need to stop and turn that knob by hand
                       when necessary, but this system can perform that
                       adjustment automatically in response to the current
                       conditions. It can recognize and accommodate five
                       different conditions: idle, medium, rough, smooth,
                       and sprint.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Linux Magazine ☛ ExTiX_22.9_Released_with_Support_for
                  Installing…_�_Linux_Magazine⠀⇛


                # ⚓ Android Headlines ☛ Best_Security_Apps_For_Android_In_2022-
                  23⠀⇛


                # ⚓ Make Use Of ☛ How_Often_Should_You_Buy_a_New_Android
                  Phone?⠀⇛


                # ⚓ Sportskeeda ☛ How_to_root_your_Android_phone_in_2022?⠀⇛


                # ⚓ Android Central ☛ How_to_set_up_Focus_Mode_in_Android_13_|
                  Android_Central⠀⇛


                # ⚓ 9to5Google ☛ The_Galaxy_S20_series_is_getting_Android_13
                  beta_in_Korea⠀⇛


                # ⚓ The Sun ☛ Android_owners_warned_of_hidden_risk_when
                  downloading_apps_on_holiday_–_The_US_Sun_|_The_US_Sun⠀⇛


                # ⚓ Qt ☛ Getting_Started_With_Qt_for_Android⠀⇛


                # ⚓ Verizon_pre-announces_Razer_Edge_5G_Android_gaming
                  handheld⠀⇛


                # ⚓ SamMobile ☛ Has_Verizon_really_released_stable_Android_13
                  update_to_the_Galaxy_S22?_–_SamMobile⠀⇛


                # ⚓ Google_Pixel_screen_freezing_on_Android_13_while_using
                  DoorDash⠀⇛


                # ⚓ TechRadar ☛ This_Android_phone_tries_to_follow_the_Samsung
                  Galaxy_S22_Ultra_but_with_one_problem_–_our_Vivo_X80_Pro
                  review_|_TechRadar⠀⇛


                # ⚓ Computer World ☛ 7_secrets_for_a_smarter_Android_Chrome
                  experience_|_Computerworld⠀⇛


                # ⚓ How_To_Remove_or_Replace_any_Image_Background_On_Android⠀⇛


                # ⚓ Make Use Of ☛ “XDA_Phone”_F(x)tec_Pro1X…_Is_a_Massive
                  Disappointment⠀⇛


                       The Pro1X is an unmitigated disaster that starkly
                       highlights the risks of backing electronics
                       projects on crowdfunding sites. If you’re looking
                       for a mobile phone with a physical keyboard built-
                       in, look instead for something more accomplished,
                       like the Planet Computers Cosmo Communicator or
                       even a second-hand Blackberry.


                       [...]


                       I wanted to be able to demonstrate the Ubuntu Touch
                       or PostmarketOS experience on the F(x)tec Pro1X.
                       Indeed, a key reason for backing the project was to
                       have a working, flexible Linux phone.
                       Unfortunately, there is no version of either (or
                       any other Linux-based phone OS) that will run on
                       the F(x)tec Pro1X without missing the most basic of
                       features (e.g. telephony, networking, camera).


                       Given how long the phone has been in development,
                       and the availability of the Pro1 and early releases
                       of the Pro1X, this seems like an unforgivable
                       oversight.


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


          o ⚓ Collabora ☛ Three_conferences_for_the_price_of_none!⠀⇛


                 This year’s X. Org Developer’s Conference (XDC) is
                 teaming up with WineConf and FOSS XR for a jam-packed
                 three day event in Minneapolis at the University of St.
                 Thomas’ Opus Hall. From October 4 to 6, XDC + WineConf +
                 FOSS XR attendees will be able to learn about the latest
                 developments in open sources graphics and XR, and attend
                 the annual technical meeting for the Wine Project. The
                 cherry on top – admission for this in-person event is
                 free!


          o ⚓ PR Newswire ☛ Cassandra_Summit_Returns_in_2023⠀⇛


          o ⚓ Cassandra_Summit_Returns_in_2023⠀⇛


          o ⚓ Venture Beat ☛ How_MLops_deployment_can_be_easier_with_open-
            source_versioning_|_VentureBeat⠀⇛


                 Modern software development typically follows a very
                 iterative approach known as continuous integration/
                 continuous development (CI/CD). The promise of CI/CD is
                 better software that is released quicker and it’s a
                 promise that ClearML now intends to bring to the world of
                 machine learning (ML).


                 ClearML today announced the general availability of its
                 enterprise MLops platform that extends the capabilities
                 of the company’s open-source edition. The ClearML
                 Enterprise platform provides organizations with security
                 controls and additional capabilities for rapidly
                 iterating and deploying ML workflows.


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ Document Foundation ☛ LibreOffice_Conference_2022:_Day_1⠀⇛


                       We’ve just wrapped up the first day of the
                       LibreOffice Conference 2022. You can check out the
                       video streams from room 1 and room 2 – and after
                       the conference, we’ll edit and upload individual
                       videos of the talks.


                # ⚓ Document Foundation ☛ Live_streams_from_the_opening_session
                  of_the_LibreOffice_Conference_2022⠀⇛


                       The LibreOffice Conference 2022 is go!


          o § Programming/Development⠀➾


                # ⚓ Linux Links ☛ Excellent_Free_Tutorials_to_Learn_GDScript_–
                  LinuxLinks⠀⇛


                       GDScript is Godot’s built-in language for scripting
                       and interacting with nodes. It evolved as a custom
                       scripting language to be used with the Godot
                       computer (and mobile device) Game engine, and it
                       also supports Virtual Reality.


                       GDScript is easy to learn with a syntax similar to
                       Python where the code is indented rather than using
                       lots of brackets and semicolons.


                       Unlike Python, GDScript is optimized for Godot’s
                       scene-based architecture and can specify strict
                       typing of variables.


                # ⚓ Qt ☛ Dialogs_in_Qt_Quick⠀⇛


                       The Qt Quick Dialogs module has undergone a lot of
                       changes in the last two years. Its purpose has
                       always been to make it simple for developers to add
                       dialogs to their applications. Native dialogs
                       should be used by default on platforms that have a
                       native dialog for a specific dialog type, and if
                       the system can’t provide one, then the module
                       should fall back to a suitable dialog that’s
                       implemented in Qt.


                # ⚓ Qt ☛ Getting_Started_With_Qt_for_Android⠀⇛


                       Ready to try out Qt’s Android toolchain and
                       leverage some of those fresh Qt 6 modules in your
                       Android app? Or perhaps you’re already using the Qt
                       API but want to see what Qt Creator can do?


                # ⚓ Qt ☛ Qt_6.4_Released⠀⇛


                       Today we have released Qt 6.4! The latest version
                       of Qt introduces support for a new platform, brings
                       lots of new functionality – some as technology
                       previews (TP) – and plenty of improvements under
                       the hood. Let’s start with the biggest highlight.


                # ⚓ Ubuntu Pit ☛ C_vs_C++_vs_C#_|_The_Key_Differences_To_Know⠀⇛


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


                       Parts of the Rust language may look familiar to C
                       programmers, but the two languages differ in
                       fundamental ways. One difference that turns out to
                       be problematic for kernel programming is the
                       stability of data in memory — or the lack thereof.
                       A challenging session at the 2022 Kangrejos
                       conference wrestled with ways to deal with objects
                       that should not be moved behind the programmer’s
                       back.


                       C programmers take full responsibility for the
                       allocation of memory and the placement of data
                       structures in that memory. Rust, instead, takes
                       most of that work — and the associated control —
                       out of the programmer’s hands. There are a number
                       of interesting behaviors that result from this
                       control, one of which being that the Rust compiler
                       will happily move objects in memory whenever that
                       seems like the thing to do. Since the compiler
                       knows where the references to an object are, it can
                       move that object safely — most of the time.


                # ⚓ SMB3_UNIX_Extensions_–_David_Mulder⠀⇛


                       One of the primary issues preventing the last few
                       holdouts from migrating away from SMB1 is a lack of
                       Posix/UNIX extensions in SMB2+. SMB1 is definitely
                       going away though in the near future.


                       To compensate, the community has been hard at work
                       creating a new UNIX extension standard for SMB3.
                       These have been in the works since as early as
                       2010, but have recently seen some renewed interest
                       in completion. The Linux ksmbd server and cifs
                       client both support SMB3 UNIX extensions. Several
                       third party servers also offer support. Support
                       from Samba server is nearing completion.


                # ⚓ syslog-ng_101:_how_to_get_started_with_learning_syslog-
                  ng?⠀⇛


                       How to get started with syslog-ng? There are two
                       main resources: the syslog-ng documentation and the
                       syslog-ng blogs. You should learn the concepts and
                       basics from the documentation. The blogs document
                       use cases and you can use the docs as a reference.


                # ⚓ Daniel Stenberg ☛ The_first_300_setopts_|_daniel.haxx.se⠀⇛


                       Already when the first version of curl shipped in
                       1998, I had plans and ideas in the back of my head
                       to turn it to a library at some point. I had
                       already before worked on providing libraries with
                       APIs for applications and I appreciated their
                       powers.


                       During the summer of 2000 I refactored the curl
                       internals so that it would become a library with an
                       exposed API that we could provide to the world and
                       then let applications get the same file transfer
                       capabilities that the curl command line tool has.


                       [...]


                       It took four years to double the amount of options
                       and ten years alter the official count was at 180.


                       Today, in September 2022, we recently merged code
                       that made the setopt counter reach 300 and this is
                       the number of options that will ship in the pending
                       7.86.0 release. After 22 years we’ve added 241 new
                       options, almost 11 new options per year on average.


                       Every new option comes with a cost: more code, more
                       tests, more documentation and an even larger forest
                       in which users can get lost when they try to figure
                       out how to tell libcurl to behave the way the want
                       it. The benefit of course being that libcurl gets
                       one more capability and new chances to fulfill
                       users’ wishes. New options certainly are both a
                       blessing and a curse.


                # § Rust⠀➾


                      # ⚓ Rust Blog ☛ Announcing_the_Rust_Style_Team⠀⇛


                             Rust has a standardized style, and an
                             implementation of that style in the rustfmt
                             tool. The standardized style helps Rust
                             developers feel comfortable and at home in
                             many different projects, and the tooling
                             support from rustfmt makes it easy to
                             maintain and to incorporate in continuous
                             integration. rustfmt also provides many
                             options to customize the style, but the style
                             guide defines the defaults, and most projects
                             use those defaults.


                             The standard Rust style resulted from
                             development and discussion within the Rust
                             style team, between 2016 and 2018. After
                             publishing the style guide, the Rust style
                             team concluded its active work, by design.


    * § Leftovers⠀➾


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ YLE ☛ Finland’s_Covid_cases_to_rise_again,_health_authority
                  predicts⠀⇛


                       There will be an increase in new Covid cases across
                       Finland as winter approaches, according to a
                       forecast from the National Institute for Health and
                       Welfare (THL).


                       The health authority presented an assessment of the
                       coronavirus situation at a joint press briefing
                       with the Ministry of Social Affairs and Health, on
                       Thursday morning.


                       The experts said vaccinations are not effective in
                       significantly reducing the spread of the virus at
                       this point. The best protection from severe Covid
                       symptoms comes from hybrid immunity, which people
                       gain from a combination of vaccinations and a
                       recent infection.


                       Finland is monitoring two Omicron subvariants of
                       the coronavirus that causes Covid-19 — BA.2 and
                       BA.4 — particularly closely.


          o § Security⠀➾


                # ⚓ IT Wire ☛ iTWire_–_Optus_breach:_Labor_pledge_to_update
                  laws_covering_security⠀⇛


                       Federal Attorney-General Mark Dreyfus says the laws
                       governing security have not kept pace with
                       technology, adding that the government would work
                       to update legislation to make it fit for purpose.


                       He told Channel 7′s Sunrise program on Thursday:
                       “We need everybody who has Australians’ data to
                       take care of it.


                       “We need to make sure that when there is a hack or
                       data breach, that they immediately notify people
                       that have been affected and notify financial
                       institutions and banks and government so that we
                       can take action and that banks and financial
                       institutions can take action to keep people safe
                       from the effects of the hack.


                       “So the laws haven’t kept pace. The prime minister
                       talked about this yesterday in the Parliament.
                       We’re going to make sure that our laws are brought
                       up to date and work to protect Australians.”


                       {loadposition sam08}Optus revealed on 22 September
                       it had suffered a massive data breach. The data
                       that has been stolen includes Medicare details,
                       drivers’ licence data and also passport data. The
                       government is insisting that the telco pay for
                       replacement of these forms of ID where it is
                       needed.


                       Regarding the Medicare data, the company said in a
                       statement on Wednesday: “Of the 9.8 million
                       customer records exposed, we have identified 14,900
                       valid Medicare ID numbers that have not expired.


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


                       Security updates have been issued by Debian
                       (chromium, lighttpd, and webkit2gtk), Fedora
                       (firefox, gajim, libofx, and python-nbxmpp), Gentoo
                       (bluez, chromium, expat, firefox, go,
                       graphicsmagick, kitty, php, poppler, redis,
                       thunderbird, and zutty), Oracle (firefox and
                       thunderbird), Red Hat (kernel), Slackware (xorg),
                       SUSE (expat, libostree, lighttpd, python3-lxml,
                       rust1.62, slurm, slurm_18_08, and vsftpd), and
                       Ubuntu (libxi, linux-gcp, postgresql-9.5, and
                       sqlite3).


                # ⚓ AccessNow ☛ Geneva_Declaration:_international_community
                  unites_to_end_spyware_abuse_–_Access_Now⠀⇛


                       It’s time to make a collective commitment to human
                       rights, and stop the dangerous, unchecked, and
                       proliferating use of spyware technology. Access
                       Now, the Government of Catalonia, the private
                       sector, and civil society from across the globe are
                       demanding concerted global change to this
                       uncontrolled industry through the Geneva
                       Declaration on Targeted Surveillance and Human
                       Rights.


                       “Digital technologies have the power to advance
                       human rights. Surveillance technology does the
                       opposite — it robs people and communities of
                       privacy, agency, and freedom,” said Laura O’Brien,
                       Senior UN Advocacy Officer at Access Now. “We must
                       put an end to the deployment of these treacherous
                       tools, and demand the immediate moratorium on the
                       export, sale, transfer, servicing of, and use of
                       digital surveillance tech. Collectively, we must
                       uphold the Geneva Declaration on Targeted
                       Surveillance and Human Rights.”


                       Members of the international community are calling
                       for an end to the proliferation of surveillance
                       technologies used to target individuals and
                       communities engaging in protected activities, such
                       as exercising their right to protest. They are also
                       pressuring governments, in coordination with civil
                       society and the private sector, to implement a
                       moratorium on the export, sale, transfer,
                       servicing, and use of targeted digital surveillance
                       technologies, until rigorous human rights
                       safeguards are put in place to regulate such
                       practices.


                # ⚓ Citizen Lab ☛ Statement_on_the_fatal_flaws_found_in_a
                  defunct_CIA_covert_communications_system_–_The_Citizen_Lab⠀⇛


                       In 2018, Jenna McLaughlin and Zach Dorfman of Yahoo
                       News reported that a system used by the CIA to
                       covertly communicate with its assets around the
                       world had been compromised by Iran and China around
                       2011. The compromise reportedly led to the death of
                       “more than two dozen sources” in China in 2011 and
                       2012, and also reportedly led Iran to execute some
                       CIA assets and imprison others.


                       Because the network was used by CIA assets around
                       the world, the compromise also reportedly enabled
                       Iran and China to track espionage activities
                       outside of their borders, related to other
                       countries.


                       While relevant oversight bodies reportedly
                       performed an investigation into the as-yet-
                       unreported compromise in 2013, Yahoo News reported
                       that those responsible for the intelligence
                       failures were never held accountable: “One of the
                       central concerns among those familiar with the
                       scope of the breakdown is the institutions
                       responsible for it were never held accountable.”


                # ⚓ Bleeping Computer ☛ New_malware_backdoors_VMware_ESXi
                  servers_to_hijack_virtual_machines⠀⇛


                       A modified level of trust is not enough for the
                       ESXi system to accept it by default but the
                       attacker also used the ‘–force’ flag to install the
                       malicious VIBs.


                # ⚓ Bruce Schneier ☛ Differences_in_App_Security/Privacy_Based
                  on_Country_–_Schneier_on_Security⠀⇛


                       Depending on where you are when you download your
                       Android apps, it might collect more or less data
                       about you.


                # ⚓ The Conversation ☛ The_same_app_can_pose_a_bigger_security
                  and_privacy_threat_depending_on_the_country_where_you
                  download_it,_study_finds⠀⇛


                       Google and Apple have removed hundreds of apps from
                       their app stores at the request of governments
                       around the world, creating regional disparities in
                       access to mobile apps at a time when many economies
                       are becoming increasingly dependent on them.


                       The mobile phone giants have removed over 200
                       Chinese apps, including widely downloaded apps like
                       TikTok, at the Indian government’s request in
                       recent years. Similarly, the companies removed
                       LinkedIn, an essential app for professional
                       networking, from Russian app stores at the Russian
                       government’s request.


                # ⚓ The Register UK ☛ Rust_is_eating_into_our_systems,_and_it’s
                  a_good_thing_•_The_Register⠀⇛


                       C++ first appeared in commercial form in 1985, the
                       year the Nintendo Entertainment System hit the US.
                       A generation of systems programmers have gone from
                       hip young codeslingers to senior management, and
                       they can say truthfully that the fundamental
                       underpinning of IT has been successfully built in
                       the older way. Everything Rust can do, the current
                       C++ can do too; it’s even insulting to suggest that
                       programmers need the extra help.


                # ⚓ USCERT ☛ CISA_Publishes_User_Guide_to_Prepare_for_Nov._1
                  Move_to_TLP_2.0⠀⇛


                       Managed by the Forum of Incident Response and
                       Security Teams (FIRST), TLP is a system of markings
                       that communicates information sharing permissions.
                       According to FIRST, the purpose of TLP is “to
                       facilitate greater sharing of potentially sensitive
                       information and more effective collaboration.”
                       Note: Unlike formal classification systems, TLP is
                       not legally binding.


                # ⚓ CISA ☛ CISA_Releases_Six_Industrial_Control_Systems
                  Advisories_|_CISA⠀⇛


                       CISA has released six (6) Industrial Control
                       Systems (ICS) advisories on September 29, 2022.
                       These advisories provide timely information about
                       current security issues, vulnerabilities, and
                       exploits surrounding ICS.


                # ⚓ Duo ☛ New_Chaos_Malware_Targets_Windows_and_Linux_Devices_|
                  Decipher⠀⇛


                       A threat actor possibly based in China is deploying
                       a new multiplatform piece of malware named Chaos
                       that is infecting SOHO routers, brute-forcing SSH
                       password, ising known vulnerabilities to propagate,
                       and launching DDoS attacks against a variety of
                       targets.


                # ⚓ FOSSLife ☛ Chaos_Malware_Targets_Home_Routers_with_DDoS
                  Attacks⠀⇛


                       Additionally, he notes, the recent shift to remote
                       work has made home routers and other devices
                       outside corporate networks particularly attractive
                       targets for attackers.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Middle East Eye ☛ ‘No_one_is_safe’:_As_UN_debates
                        spyware_threats,_rights_groups_say_ban_it⠀⇛


                             Human and digital rights advocates have
                             welcomed UN Secretary-General Antonio
                             Guterres’ recent recognition that spyware has
                             become a significant threat to the UN’s human
                             rights work.


                             But they say now is the time for member
                             states to finally enforce a global moratorium
                             on the sale and use of surveillance
                             technologies until regulations catch up with
                             technology.


                             “Digital surveillance is one of the biggest
                             threats facing activists and human rights
                             movements today,” said Marwa Fatafta, Middle
                             East policy manager at Access Now which
                             defends digital rights.


                             “We’ve reached the tipping point with the
                             proliferation of malicious spyware. No one,
                             no where is safe.”


                      # ⚓ AccessNow ☛ The_Geneva_Declaration_on_Targeted
                        Surveillance_–_Human_Rights⠀⇛


                             The Geneva Declaration on Targeted
                             Surveillance and Human Rights (the
                             Declaration) is a collective commitment to
                             human rights in the digital age. While
                             recognizing that digital technologies can
                             strengthen democracy and human rights, the
                             Declaration specifically condemns the
                             proliferating use of surveillance
                             technologies to target communities engaging
                             in protected activities, and calls on
                             governments, in coordination with civil
                             society and the private sector, to implement
                             a moratorium on the export, sale, transfer,
                             servicing and use of targeted digital
                             surveillance technologies developed by the
                             private industry, until rigorous human rights
                             safeguards are put in place to regulate such
                             practices.


                             Led by civil society organisation Access Now
                             and the Government of Catalonia, the
                             Declaration is set to officially launch on 29
                             September 2022 at the UN Human Rights
                             Council’s 51st session side event Spyware: A
                             Threat to Human Rights and Democracy
                             organised by Access Now and the Government of
                             Catalonia, in Geneva, Switzerland.


          o § Censorship/Free Speech⠀➾


                # ⚓ Reuters ☛ ‘The_internet_is_dead_in_Iran’:_Protests_targeted
                  by_shutdown⠀⇛


                       Saeed Souzangar, who runs a technology company in
                       Tehran, is adept at navigating frequent internet
                       disruptions to ensure his business can keep
                       operating, but even he has been thrown by
                       nationwide communications outages this month.


                       The death of Mahsa Amini, a 22-year-old woman who
                       died in custody after being arrested by the
                       country’s morality police, has triggered the
                       biggest street protests in years, prompting a
                       sweeping security crackdown and curbs on internet
                       and phones.


                # ⚓ Reuters ☛ Six_million_silenced:_A_two-year_internet_outage
                  in_Ethiopia⠀⇛


                       She had just been crowned world champion, but
                       Ethiopian marathon runner Gotytom Gebreslase broke
                       down in tears when asked if her family was
                       celebrating her win back home in war-torn Tigray.


                       “I haven’t spoken to my parents in months,” she
                       said, wiping her eyes as she spoke at a news
                       conference during the World Athletics Championships
                       in Eugene, in the northwestern U.S. state of
                       Oregon, in July.


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


                # ⚓ VOA News ☛ Cambodia’s_Press_Freedom_‘Under_Attack,’_Report
                  Finds⠀⇛


                       Independent media in Cambodia continue to come
                       under attack, with journalists harassed and
                       retaliated against, a new report found.


                       In its September report assessing the civic space
                       of Cambodia, the international nonprofit CIVICUS
                       rated the country as “repressed.”


                # ⚓ Reuters ☛ ‘Living_in_the_stone_age’:_Offline_for_18_months
                  in_Indian_Kashmir⠀⇛


                       For editors at The Kashmir Walla, fact-checking a
                       story used to involve a flurry of googling before
                       press time. So when an 18-month internet and phone
                       shutdown began in the Indian Himalayan region in
                       2019, they had to improvise.


                       “We used to leave blank spaces in news stories when
                       we couldn’t verify certain facts. Every week, a
                       team member would fly to Delhi and fill in the
                       blanks,” said Yash Raj Sharma, an editor with the
                       weekly magazine.


                       It was one of numerous headaches for the region’s
                       journalists. Unable to use his mobile, Sharma, 25,
                       recalled driving to a telephone booth at Srinagar
                       airport to dictate an 800-word news story to a
                       friend in Delhi.


                       “That incident will remain with me forever as a
                       memory of working during the longest communication
                       and internet shutdown,” said Sharma, who also used
                       to call friends in Delhi to ask them to read out
                       and respond to his emails.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ In_Myanmar’s_rebel_strongholds,_internet_can_mean_life_or
                  death⠀⇛


                       For Zaw Myint Thein, a farmer in northwestern
                       Myanmar, having no internet in the area for more
                       than a year causes many inconveniences – his son is
                       unable to study, he can no longer sell his
                       watermelon crops online, and he feels cut off.


                       “It’s like my eyes and ears are closed,” the 45-
                       year-old said by phone from the Sagaing region.


                       But in this stronghold of resistance to the
                       military junta that seized power in a coup early
                       last year, the army-ordered internet shutdown – and
                       sporadic cuts to mobile phone communications – puts
                       lives on the line, Zaw Myint Thein said.


                # ⚓ Public Knowledge ☛ FCC_Votes_To_Give_Disabled_Incarcerated
                  People_Access_to_Specialized_Communications_Services_–_Public
                  Knowledge⠀⇛


                       Today, the Federal Communications Commission voted
                       to approve a Report and Order and Further Notice of
                       Proposed Rulemaking to improve access to
                       communications for incarcerated people with
                       disabilities and to reduce the financial burdens
                       created by certain calling service charges and
                       practices.


          o § Monopolies⠀➾


                # ⚓ Public Knowledge ☛ Public_Knowledge_Applauds_House_for
                  Passing_Bill_Increasing_Funding_for_Antitrust_Enforcement_–
                  Public_Knowledge⠀⇛


                       Today, the U.S. House voted to pass the “Merger
                       Filing Fee Modernization Act,” a package of bills
                       introduced by Representatives Joe Neguse (D-CO) and
                       Ken Buck (R-CO) to increase funding for federal
                       antitrust enforcement agencies and support state
                       attorney general antitrust enforcement through more
                       favorable venue rules. The bill passed on a
                       bipartisan vote of 242-184.


                       Public Knowledge led a letter signed by more than
                       35 public interest, consumer advocacy, unions, and
                       civil society groups urging Congress to pass the
                       bill to enable these agencies to “properly fulfill
                       their role safeguarding the economy and consumers
                       from anticompetitive conduct and harmful mergers.”


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ EclipSmart_Binoculars_Arrived⠀⇛


                       I bought some Celestron EclipSmart binoculars,
                       which are basically just 10x42mm binoculars with
                       built-in continuum (a.k.a. white-light) filters, so
                       that they can be safely used for viewing the Sun.
                       Obviously, they are targetting people who want to
                       view eclipses, but they work just as well any other
                       time that you want to view the solar disc.


                       I gave them a quick test this morning and as
                       expected, I was able to see the solar disc, and I
                       saw one sunspot clearly. I compared what I saw with
                       the Intensitygram image from NASA, and the sunspot
                       was in the same location, though the NASA image
                       showed three additional small sunspots.


                # ⚓ Polyphia_–_Ego_Death_(feat._Steve_Pai)⠀⇛


                       I was actually hesitsting in sharing a Polyphia
                       track but then this new track came and I think I’d
                       just commit to it.


                       I’m not a guitar nerd, I’m not a music nerd, but I
                       like music, and that alone doesn’t stop me from
                       listening to whatever prog rock instrumentals that
                       they’re presenting.


                       What I like about this track is that there’s
                       basically no breathing room through the entire
                       almost 6 minutes of the track, and that I think
                       different parts of the piece added up together
                       makes it so that there’s always something new on
                       the table, while being rhythmetically and
                       melodically pleasing, without being out of place.


          o § Technical⠀➾


                # ⚓ Automatically_ban_ports_scanner_IPs_on_NixOS⠀⇛


                       Since I switched my server from OpenBSD to NixOS, I
                       was missing a feature. The previous server was
                       using iblock, a program I made to block IPs
                       connecting on a list of ports, I don’t like people
                       knocking randomly on ports.


                       iblock is simple, if you connect to any port on
                       which it’s listening, you get banned in the
                       firewall.


                # ⚓ Legend_of_Homebody_(PC)⠀⇛


                       For the last little bit I’ve been wanting to get
                       away from games where problems are solved through
                       acts of violence. They’ve been getting a bit
                       tiresome of late, so I’m exploring other avenues in
                       the medium at the moment. Lately, I’ve been playing
                       some Legend of Homebody. This is a game where you
                       stay in your apartment all day trying to make it in
                       one of four professions: visual artist, writer,
                       musician, or programmer.


                       There are a number of different game modes to
                       choose from that mostly effect how long you play.
                       There’s normal mode where the closest thing to a
                       story happens, followed by increasingly difficult
                       modes where the gameplay is similar but story
                       becomes less of a thing. There are also
                       increasingly long modes for people who want
                       extended sessions. Core activities stay the same in
                       each mode, but they add a bit more color to each
                       playthrough.


                # § Programming⠀➾


                      # ⚓ Forth_without_IF_THEN_ELSE_jumping_around⠀⇛


                             I crudely avoided the issue of how one would
                             implement what I tried to describe in my
                             previous post: a Forth in which decompiled
                             source looks like original source. Someone
                             called me on it, and I should clarify.


                             The problem is that we are trying to
                             linearize the unlinearizable. Code,
                             especially Forth code, is more of a tree. We
                             read and write code linearly – a function
                             consists of a bunch of tokens, and think of
                             it as an ordered sequence. But the threaded
                             code is executed as a depth-first tree walk,
                             down into definitions until the bottom CODE,
                             then up and down again, until the entire tree
                             is walked. It’s kind of awe-inspiring to
                             visualize execution.


                             So, whether IF jumps over some code or jumps
                             sideways to some code somewhere else makes
                             little difference. This opens the door for
                             if’s clauses to be elsewhere as anonymous
                             subroutines, os as Slava of Factor calls
                             them, quotations.


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



                    ䷩ 𝚕𝚒𝚗𝚎 4775

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.29.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_29/09/2022:_Linuxfx_11.2_and_Progress_on_GNOME_43⠀✐


Posted in News_Roundup at 7:46 am 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
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o New_Releases
          o Fedora_Family_/_Red_Hat_/_IBM
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers/Web_Servers
                # Mozilla
          o SaaS/Back_End/Databases
          o Education
          o Programming/Development
                # TeX
                # Python
                # Java
                # Rust
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Pseudo-Open_Source
                # Openwashing
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Politics
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o ⚓ Hacker Noon ☛ The_Linux_Writing_Contest_2022:_Final_Results
            Announced!_|_HackerNoon⠀⇛


                 The Linux Writing Contest by Linode and HackerNoon has
                 come to an end. It’s time to celebrate the final round
                 winners. This contest slowly took momentum, and we
                 received a good amount of high-quality stories in the
                 third (and final) round of the contest.


          o § Desktop/Laptop⠀➾


                # ⚓ GamingOnLinux ☛ System76_gives_the_Oryx_Pro_a_big_refresh
                  with_an_OLED_4k_display⠀⇛


                       The Linux flagship NVIDIA laptop from System76 has
                       been given a major overhaul, making it something of
                       a beast. Pricey though, with you needing to dig
                       deep into your wallets with a base price of $2,199.


                # ⚓ Unicorn Media ☛ System76_Upgrades_Its_Oryx_Pro_Linux
                  Laptops⠀⇛


                       The July upgrade also brought the option for
                       purchasers to configure Oryx Pro with either NVIDIA
                       RTX 3070 Ti with 6144 CUDA Cores or NVIDIA RTX 3080
                       Ti with 7424 CUDA Cores dedicated graphics cards,
                       configured so that users can switch between the
                       laptop’s integrated Intel GPU and the dedicated
                       NVIDIA graphics directly through the graphics
                       profiles in Pop!_OS, the Linux distribution that
                       System76 builds in-house, and which is installed by
                       default on its machines (although purchasers can
                       opt for the latest and greatest LTS Ubuntu release
                       if they wish).


                # ⚓ Real Linux User ☛ Coming_soon_–_my_book_Linux_for_the_rest
                  of_us_–_Real_Linux_User⠀⇛


                       In recent blog posts, I have hinted that I have
                       been writing my own book for quite some time. My
                       goal for this book has always been, much like
                       through this website, to bring Linux closer to
                       normal users by providing easy-to-understand
                       tutorials and background information in an
                       accessible way. Because of the many articles I have
                       written for reallinuxuser.com, I had a lot of
                       material at my disposal as a good foundation for
                       writing this book. And now it is almost time that,
                       after about 2 years of research and writing, I can
                       proudly share that I have completed my book.


                       In the coming weeks, my book “Linux for the rest of
                       us” will be available through Amazon KDP in
                       paperback and Kindle eBook format. I am now busy
                       with the final preparations and administrative
                       actions to be able to publish the book. In
                       approximately 370 pages in 6 by 9 inches format,
                       the book helps novice Linux users, doubters, and
                       potential switchers, to understand what Linux is,
                       what choices to make and how, to properly choose
                       the right distribution, where to find Linux
                       distributions, how to create a Linux live USB
                       media, how to make sure you have a secure download
                       to start with, how to install Linux, how to get the
                       system working optimally for different hardware
                       types, how to find and install beautiful
                       applications, and it also offers many more
                       interesting topics that will help you further in
                       your Linux journey. The book will help anyone who
                       is not really interested in the most in-depth
                       technical aspects but wants to use a computer for
                       productive purposes, to understand, set up, and use
                       their new Linux system in an effective way,
                       according to a logical step-by-step approach.


          o § Audiocasts/Shows⠀➾


                # ⚓ FLOSS_Weekly_700:_The_Linux_Kernel_Gets_Rusty_–_Jonathan
                  Corbet,_RUST_and_the_Linux_Kernal_[sic]_Development⠀⇛


                       Jonathan Corbet of LWN tells Doc Searls and Shawn
                       Powers what’s happening with the Linux Kernel,
                       including the ascendence of Rust, the role of
                       companies that employ developers and maintainers,
                       the needs for more maintainers, plus diversity, and
                       the growing role of the Linux Foundation. Great
                       discussion on FLOSS Weekly.


                # ⚓ Video ☛ GTA_6_Hacker_“Teapot”_Has_Been_Arrested_in_the_UK_–
                  Invidious⠀⇛


                       The teenage hacker most recently known as teapot
                       (also goes under other aliases like white, and
                       SigmA) was arrested in Oxford shire UK on suspicion
                       of hacking and is currently held in police custody.


                # ⚓ Video ☛ How_to_install_Notepadqq_on_Linux_Mint_21_–
                  Invidious⠀⇛


                       In this video, we are looking at how to install
                       Notepadqq on Linux Mint 21.


                # ⚓ Video ☛ Arch_Linux_Finally_Puts_An_End_To_Python_2!!_–
                  Invidious⠀⇛


                       Python 2 was put to rest by it’s developers all the
                       back in 2020 but it’s still been sticking around in
                       the FOSS world and distros like Arch linux still
                       had packages available in places like Debian and
                       RHEL it’s even still shipped by default.


                # ⚓ The BSD Now Podcast ☛ BSD_Now_474:_EuroBSDcon_2022⠀⇛


                       Deploying FreeBSD on Oracle Cloud, A Tale of
                       300,000 Imaginary Friends, EuroBSDcon 2022 recap,
                       OpenBSD Mastery: Filesystems” Status Report,
                       OpenBGPD 7.6 Released, immutable userland mappings,
                       Portable OpenSSH commits now SSH-signed, and more.


                # ⚓ Video ☛ Stellarium:_Using_a_Linux_Star_Chart_–_Invidious⠀⇛


                # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_973⠀⇛


                       Joe hates hunger games.


                # ⚓ Akademy_2022_Interview:_In_conversation_with_Hector_Martin
                  –_Kockatoo_Tube⠀⇛


                # ⚓ Akademy_2022_Interview:_In_conversation_with_Hector_Martin
                  –_Kockatoo_Tube [Ed: Another URL]⠀⇛


          o § Kernel Space⠀➾


                # ⚓ Linux_0.0.1_compiling_on_Ubuntu_64⠀⇛


                       You might need some packages first


                # ⚓ Data Swamp ☛ Avoid_Linux_locking_up_in_low_memory
                  situations_using_earlyoom⠀⇛


                       Within operating system kernels, at least for Linux
                       and the BSDs, there is a mechanism called “out of
                       memory killer” which is triggered when the system
                       is running out of memory and some room must be made
                       to make the system responsive again.


                       However, in practice this OOM mechanism doesn’t
                       work well. If the system is running out of memory,
                       it will become totally unresponsive, and sometimes
                       the OOM killer will help, but it may take like 30
                       minutes, but sometimes it may be stuck forever.


                       Today, I stumbled upon a nice project called
                       “earlyoom”, which is an OOM manager working in the
                       user land instead of inside the kernel, which gives
                       it a lot more flexibility about its actions and the
                       consequences.


          o § Graphics Stack⠀➾


                # ⚓ GamingOnLinux ☛ NVIDIA_put_out_new_Vulkan_Beta_Driver_with
                  Vulkan_Video_updates⠀⇛


                       NVIDIA has released a new version of their Vulkan
                       Beta Driver, with new extensions supported and
                       updates to their support of the newer Vulkan Video.
                       What is Vulkan Video? It’s the attempt to add in
                       hardware accelerated video compression and
                       decompression into the Vulkan API.


          o § Applications⠀➾


                # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to
                  Apple_Photo_Booth_–_LinuxLinks⠀⇛


                       Photo Booth is a software application for taking
                       photos and videos with an iSight camera. iSight is
                       a brand name used by Apple to refer to cameras on
                       various devices. The software offers live filters
                       and the ability to replace backgrounds.


                       Photo Booth is not available for Linux. We
                       recommend the best free and open source
                       alternatives.


          o § Instructionals/Technical⠀➾


                # ⚓ UNIX Cop ☛ How_To_Install_KeePassXC_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       In this guide, we will show you how to install
                       KeePassXC on Ubuntu systems.


                       KeePassXC is a free and open-source password
                       manager. It started as a community fork of KeePassX
                       (itself a cross-platform port of KeePass).


                # ⚓ Linux Capable ☛ How_to_Install_Code::Blocks_IDE_on_Fedora
                  36_Linux⠀⇛


                       Code::Blocks is free and open-source software
                       highly extensible Integrated Development
                       Environment (IDE) for the C, C++, and Fortran
                       programming languages. It features support for a
                       wide range of compilers, parallel builds, and
                       multi-target projects and also provides an
                       interface with GNU GDB. The code editor in Code::
                       Blocks features syntax highlighting, code folding,
                       a tabbed interface, code completion, a class
                       browser, and smart indenting.


                       In the following tutorial, you will learn how to
                       install Code::Blocks on Fedora 36 Linux desktop
                       with either DNF or Flatpak package manager using
                       the command line terminal and instructions on how
                       to update and remove the software in the future if
                       required.


                # ⚓ Citizix ☛ How_to_Setup_Metabase_and_Nginx_to_proxy_traffic
                  on_Rocky_Linux_9⠀⇛


                       Metabase is an open-source business intelligence
                       tool. Metabase lets you ask questions about your
                       data, and displays answers in formats that make
                       sense, whether that’s a bar chart or a detailed
                       table. You can save your questions, and group
                       questions into handsome dashboards.


                # ⚓ markaicode by Mark ☛ How_to_Modify_Ban_Time_Fail2ban_|_Mark
                  Ai_Code⠀⇛


                       Fail2ban is an open-source log parsing program that
                       guards against brute-force assaults on your system.
                       It parses log files and blacklists IP addresses
                       with a high number of authentication failures.


                       This commonly happens when a person tries to log in
                       through trial and error. Fail2ban then takes
                       action, such as modifying the firewall rules to ban
                       that IP address for a set amount of time, which is
                       usually 10 minutes or 600 seconds. To avoid locking
                       off innocent users who may have frequently mistyped
                       their passwords, the blocked IP address is
                       automatically unbanned after 10 minutes.


                       This post will teach you how to adjust the ban time
                       in fail2ban and, if desired, how to permanently ban
                       an IP address.


                # ⚓ UNIX Cop ☛ How_To_Install_OpenToonz_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       OpenToonz is a 2D Animation Program based off of
                       Toonz Developed by Digital Video in Italy. It’s
                       open source animation production software to
                       develop and create all together.


                       OpenToonz has been customized by Studio Ghibli, and
                       used for the creation of its works for many years.
                       Dwango has launched the OpenToonz project in
                       cooperation with Digital Video and Studio Ghibli.


                # ⚓ UNIX Cop ☛ How_To_Install_Peek_on_Ubuntu_20.04_|_22.04
                  LTS⠀⇛


                       In this tutorial, we will show you how to install
                       Peek in Ubuntu systems.


                       Peek is a computer software program for Linux to
                       create simple animated GIF file based on the GIF89a
                       file format. A screencast is created from a user-
                       defined screen area. Peek is optimized for
                       generating animated GIFs, but can also directly
                       record to WebM or MP4.


                       Peek is not a general purpose screencast app with
                       extended features but rather focuses on the single
                       task of creating small, silent screencasts of an
                       area of the screen for creating GIF animations or
                       silent WebM or MP4 videos.


                # ⚓ UNIX Cop ☛ How_To_Install_Code_Blocks_on_Ubuntu_20.04_|
                  22.04_LTS⠀⇛


                       Code::Blocks is a free, open-source cross-platform
                       IDE that supports multiple compilers including GCC,
                       Clang and Visual C++. It is developed in C++ using
                       wxWidgets as the GUI toolkit. Using a plugin
                       architecture, its capabilities and features are
                       defined by the provided plugins. Currently, Code::
                       Blocks is oriented towards C, C++, and Fortran. It
                       has a custom build system and optional Make
                       support.


                # ⚓ UNIX Cop ☛ Install_OpenShot_on_Ubuntu_20.04_|_22.04_LTS⠀⇛


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


                       OpenShot Video Editor is a free and open-source
                       video editor for Windows, macOS, Linux, and Chrome
                       OS. The project started in August 2008 by Jonathan
                       Thomas, with the objective of providing a stable,
                       free, and friendly to use video editor.


                       The program supports Windows, macOS, and Linux ever
                       since version 2.1.0 (released in 2016). OpenShot
                       added support for Chrome OS in version 2.6.0
                       (released in 2021). There is an unofficial portable
                       version beginning in 2020.


                # ⚓ Its FOSS ☛ How_to_Use_Picture_in_Picture_Mode_in_Brave
                  Browser⠀⇛


                       Brave is an excellent Chrome-like and yet Chrome
                       alternative web browser.


                       Firefox and Brave are two browsers I like using on
                       my Linux system. Both have different advantages.


                       There is one thing that Firefox does better than
                       Brave and it is the picture-in-picture (PIP) mode
                       that works on YouTube, Netflix and most streaming
                       sites.


                       Brave too has picture-in-picture mode but it’s so
                       hidden that you feel like there is no PIP support
                       at all.


                       The built-in picture-in-picture works on some
                       websites (like YouTube) but may not work on others
                       (like Prime Video). Worry not! you can use a
                       dedicated extension for that.


                       Let me show both methods in this tutorial.


                # ⚓ List_all_packages_in_Ubuntu/Debian_that_no_package_depends
                  on⠀⇛


                # ⚓ RoseHosting ☛ How_to_install_and_Secure_Redis_on_Ubuntu
                  22.04_–_RoseHosting⠀⇛


                       In this tutorial, we are going to explain in step-
                       by-step detail how to install and secure Redis on
                       Ubuntu 22.04.


                       Redis is a shortcut for a remote dictionary server
                       and an in-memory data structure store. It is used
                       as an option for a distributed in-memory key-value
                       database with durability. Redis server is written
                       in C language and supports a huge range of data
                       types such as strings, hashes, lists, and many
                       more.


                       Installing and securing Redis on Ubuntu 22.04 is a
                       straightforward process that may take up to 15
                       minutes. Let’s get things working!


                # ⚓ Jay Little ☛ The_Siren_Song_of_Set_It_and_Forget_It⠀⇛


                       The truth is I work with a lot of clients, many of
                       which should know better, whom rely almost
                       exclusively on legacy applications, operating
                       systems and platforms to handle their work on a day
                       to day basis. What makes matters worse is that
                       these legacy tools have been integrated into
                       workflows that they now consider to be sacrosanct
                       despite the fact that over the last decade or two,
                       far superior and far more efficient replacements
                       have been developed.


                       But replacing these tools generally requires that
                       end users change or adapt their workflows and they
                       really don’t want to do that as I discussed back in
                       2021′s post “Spock Was Wrong: In Tech is is Easier
                       to Create than to Destroy”: [...]


                # ⚓ uni Toronto ☛ Reaching_past_our_firewalls_with_WireGuard_
                  (some_thoughts)⠀⇛


                       The appeal of WireGuard for this is that it’s a
                       lightweight service that requires little
                       configuration or operation, and is now supported
                       across all of our Ubuntu fleet. This creates two
                       obvious options, depending on how much work we want
                       to do on these external machines. The first option
                       is to run WireGuard in a non-routed, “point to
                       point” mode on each of the internal machines that
                       have services we want to provide access to. The
                       internal machine would expose its service(s) on an
                       private WireGuard network as well as its normal IP
                       address (in many cases this requires no service
                       changes), and external machines would reach the
                       service by talking to the internal machine’s
                       private WireGuard IP address. The one drawback to
                       this is that it requires configuring each external
                       machine to use the appropriate magic WireGuard IPs
                       for these services, instead of the hostnames we
                       normally use.


                # ⚓ Manuel Matuzovic ☛ Day_2:_logical_properties⠀⇛


                       Logical properties are a new way of working with
                       directions and dimensions, one that allows you to
                       control layout through logical, rather than
                       physical mappings. This is especially useful, if
                       you’re dealing with websites that are presented in
                       different languages and writing modes, like right-
                       to-left.


                # ⚓ Manuel Matuzovic ☛ Day_3:_logical_property_shorthands⠀⇛


                       If you use a shorthand property like margin with
                       all 4 values, the properties will always be applied
                       in the direction top – right – bottom – left, no
                       matter the reading direction.


                # ⚓ Matt Rickard ☛ Simple_Group_Theory⠀⇛


                       The formal definition of a group and a short proof:
                       A group is a set G with a binary operation on G
                       that satisfies these four axioms1:


                       Associativity: For all a,b,c in G (a • b) • c = a •
                       (b • c)


                       Identity: There exists an element e in G such that,
                       for each a in G e • a = a and a • e = a


                       Inverse: For each a in G there exists an element b
                       in G such that a • b = e and b • a = e, where e is
                       the identity element.


                       Closure: For each a, b in G, a • b and b • a are
                       contained in G.


                # ⚓ Linux Handbook ☛ Getting_Started_With_Rootless_Container
                  Using_Podman⠀⇛


                       Are you deploying software using containers? Are
                       you using Podman? Do you want to up your security
                       game by running containers with as little privilege
                       as possible? Boy, do I have an article for you!


                # ⚓ ID Root ☛ How_To_Install_Audacity_on_Fedora_36_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Audacity on Fedora 36. For those of you who didn’t
                       know, Audacity is a free and open-source digital
                       audio editor and recording application. The
                       software includes many features that allow users to
                       edit and record quickly, mix audio files, and
                       support a variety of audio file formats, as well as
                       VST plug-ins. It is available for Windows, macOS,
                       Linux, and other Unix-like operating systems


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the Audacity audio editor on a
                       Fedora 36.


                # ⚓ HowTo Forge ☛ How_to_Install_Docker_Swarm_on_Debian_11⠀⇛


                       Docker Swarm is a container orchestration built on
                       Docker Engine. It allows you to create and deploy a
                       cluster of Docker nodes with multiple servers.


                # ⚓ ByteXD ☛ How_to_Transfer_Files_from_a_Remote_Server_to
                  Local_Machine_–_ByteXD⠀⇛


                       This tutorial walks you through transferring files
                       from a remote server to a local machine using…


                # ⚓ Linux Made Simple ☛ How_to_install_Scartchin’_Melodii_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Scartchin’
                       Melodii on a Chromebook. Please follow the video/
                       audio guide as a tutorial where we explain the
                       process step by step and use the commands below.


                # ⚓ Linux.org ☛ TCP/IP_Basics_by_Math_|_Linux.org⠀⇛


                       The TCP/IP Protocol is essential for accessing the
                       Internet. This is the only protocol used for the
                       Internet, so it is important to have some
                       understanding.


                       Before we get to the math, let’s look at some
                       basics.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Terraria:_Labor_of_Love_update_is_out_now⠀⇛


                       Terraria: Labor of Love, another major update for
                       the popular crafting and survival game is
                       officially out now. There’s a ridiculous amount (as
                       usual) that’s new, here’s the biggest stuff to look
                       out for.


                # ⚓ GamingOnLinux ☛ Free_evolution_sim_‘Thrive’_adds_a_new_part
                  to_let_organisms_spew_mucilage⠀⇛


                       What I can only describe as some form of
                       microscopic fart-cannon, the free and open source
                       evolution sim Thrive has added what they call a
                       Mucilage Jet for your creatures in version 0.5.10.


                # ⚓ GamingOnLinux ☛ Manage_games_and_people_in_Roller_Drama
                  with_full_Linux_/_Steam_Deck_support⠀⇛


                       Roller Drama is an upcoming hybrid of a sports team
                       management sim, along with visual novel elements
                       too and it sounds like a great idea for a game.
                       Just recently, the developer also noted it will
                       have full Native Linux support along with controls
                       nicely tweaked and set ready for the Steam Deck
                       directly.


                # ⚓ GamingOnLinux ☛ Steam_Deck_got_another_Beta_update_focused
                  on_Steam_Input_and_FlickStick⠀⇛


                       Seems Valve snuck out another Steam Deck Beta
                       update while I was asleep, this time focused on
                       improvements to Steam Input after the smaller bug
                       fix earlier.


                # ⚓ GamingOnLinux ☛ Valve_give_update_on_official_Steam_Deck
                  Dock,_Valve_excited_for_SteamOS_on_more_devices⠀⇛


                       In a new interview with IGN, Valve has given a few
                       more little details about their thoughts on how
                       things with the Steam Deck are going along with
                       notes on the official Steam Deck Dock and SteamOS
                       on more devices. The full interview is worth a read
                       but here’s a few choice notes for you.


                # ⚓ GamingOnLinux ☛ Steam_drops_the_Lunar_New_Year_Sale,_we’re
                  getting_a_big_Spring_sale_instead⠀⇛


                       Valve has announced some changes to their major
                       seasonal sales, along with the Lunar New Year Sale
                       being dropped.


                # ⚓ Trend Oceans ☛ Mazter_Game:_A_Maze_in_Your_Linux_Terminal⠀⇛


                       Mazter is a fun and interesting game, and the rules
                       are simple. On each level, it will put you in a
                       random maze and you need to find your way out of
                       this maze.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Nate Graham ☛ KDE:_Making_it_easier_to_submit_bug
                        reports⠀⇛


                             
                             A persistent complaint KDE faces is that it’s
                             too hard to submit bug reports. One obstacle
                             was the giant scary list of products at
                             https://bugs.kde.org/enter_bug.cgi. Well, no
                             longer! This page is now organized into
                             logical categories with user-friendly text,
                             so it should be much easier to find the right
                             place for your bug report if that’s your
                             entry point. This has been rolled out already
                             and is available immediately…


                             There are also other entry points; for
                             example all KDE apps have a “Report a bug”
                             menu item that will take you to the right
                             place automatically. However two prominent
                             ones did not: System Settings and Plasma. In
                             System Settings, the menu item took you to
                             the generic product, not the specific
                             component for the page you’re on. And Plasma
                             had no functionality like this at all.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Progress_Update_For_GNOME_43_–_Chris’s_Design_–
                        Development⠀⇛


                             GNOME 43 is out the door now, and I want to
                             use this post to share what I’ve done since
                             my post about my plans.


                             [...]


                             Since my post in April, Loupe has received
                             many changes. Allan Day provided a new set of
                             mockups for me to work from, and I’ve
                             implemented the new look and a sidebar for
                             the properties. There are some open questions
                             about how the properties should be shown on
                             mobile sizes, so for now Loupe doesn’t fit on
                             phones with the properties view open.


    * § Distributions and Operating Systems⠀➾


          o § New Releases⠀➾


                # ⚓ Linuxfx_11.2_22.04.3_LTS_WxDesktop_11.7⠀⇛


                       It is with great pleasure that we announce the
                       release of Linuxfx version 11.2 22.04.3. This
                       release is now based on Ubuntu 22.04.3 Jammy
                       Jellyfish. Support for .exe and .msi applications
                       has been improved with Wine 7.18, kernel 5.15 is
                       also present in this release, improving support for
                       more modern hardware. We updated KDE and the entire
                       application base, which is now downloaded directly
                       from the Neon repositories. WxDesktop, all its
                       tools and themes have also been updated. Support
                       for android games and apps has been improved. There
                       are several new features and improvements, so we
                       recommend downloading this version immediately!


          o § Fedora Family / Red Hat / IBM⠀➾


                # ⚓ Fedora Project ☛ Fedora_Community_Blog:_Contribute_to_the
                  Fedora_Project_during_Hacktoberfest_2022⠀⇛


                       Allow us to wake you up when September ends because
                       Hacktoberfest is (nearly) here. And you can
                       contribute to the Fedora Project while
                       participating in Hacktoberfest 2022! This event is
                       an excellent opportunity to advocate for free and
                       open-source software, all while giving back to the
                       community with the contribution of your choice.
                       Hacktoberfest includes low and non-code
                       contributions. You can diversify your contributions
                       to include writing docs, creating designs, running
                       tests, mentoring folks, and much more. This global
                       event is open for anyone, from students to
                       professionals. People of all backgrounds and skill
                       levels are encouraged to join us.


                # ⚓ OpenSource.com ☛ How_Podman_packaging_works_on_Linux_|
                  Opensource.com⠀⇛


                       Over the past few months, the Podman project has
                       been reworking its process for generating Debian
                       and Ubuntu packages. This article outlines the past
                       and present of the Debian packaging work done by
                       the Podman project team. Please note that this
                       article does not refer to the official Debian and
                       Ubuntu packages that Reinhard Tartler and team
                       created and maintain.


                # ⚓ Enterprisers Project ☛ New_Ebook:_10_resources_to_make_you
                  a_better_communicator_|_The_Enterprisers_Project⠀⇛


                       Are you desperate for advice on fostering healthy
                       conflict in your organization? Have you been
                       stressed out by the prospect of endless meetings
                       with a new remote workforce? What are the best ways
                       to enhance your EQ in the modern workplace?
                       Especially in this time of hybrid work, IT leaders
                       need to know how to make connections across the
                       globe.


                # ⚓ Enterprisers Project ☛ IT_talent:_6_tips_for_success_in_an
                  SRE_role⠀⇛


                       A career in Site Reliability Engineering (SRE) can
                       be very promising. LinkedIn named the Site
                       Reliability Engineer one of the 25 fastest-growing
                       job titles over the past five years. As the need
                       for more SRE professionals grows, so does the need
                       for specific skills.


                # ⚓ Using_a_GraphQL_endpoint_from_an_Ansible_playbook⠀⇛


                       I recently had to call a GraphQL API from an
                       Ansible playbook, and considering I had never done
                       that before and there is little to no documentation
                       about this online, it was a bit tricky.


                       In the end, I got everything working, and figured I
                       would share here for posterity (and myself, when I
                       have to do this again in the future!)


                       A GraphQ API call consists of either one or two
                       parts: the actual query or mutation and optionally
                       a set of variable as input to the query or
                       mutation.


                # ⚓ Red Hat ☛ The_benefits_and_limitations_of_flexible_array
                  members_|_Red_Hat_Developer⠀⇛


                       Discover how flexible array members offer
                       convenience and improve performance, and how
                       compiler complexities are mitigated.


          o § Devices/Embedded⠀➾


                # ⚓ Linux Gizmos ☛ Comet_Lake_based_PC_available_in_barebone
                  and_customizable_options⠀⇛


                       The Mitac E410-13CMI is an industrial grade
                       embedded system powered by the Intel Comet Lake
                       10th Gen processor. This fanless PC provides
                       support for dual 4K displays, up to 64GB RAM, 512GB
                       SSD, Wi-Fi 6/Bluetooth 5.1 and several other
                       peripherals.


                # ⚓ Purism ☛ Reclaiming_Digital_Privacy⠀⇛


                       The advancements of the digital age has gifted us
                       with the ability to search and access world’s
                       information sources within a few seconds. However,
                       Big Tech companies still make it hard for users to
                       control their own privacy when accessing digital
                       products and services.


                       The problem is deeper for our kids or elderly
                       parents, who are bombarded with all kinds of
                       content without the ability to control their
                       security preferences easily. It’s like driving a
                       car on the free way (or the highway) without its
                       brakes working properly. They need secure devices
                       that safeguard their privacy from the get-go.


                       When Founder and CEO, Todd Weaver, saw his kids
                       interact with digital devices, he was concerned
                       about their privacy online. He decided to start the
                       movement of respectful technologies for the next
                       generation. After a lifetime of work as an
                       engineer, developer, architect, and advocate for
                       Free and Open Software, it was his role as father
                       that solidified his next business mission. Purism
                       started in 2014, with the focused intent to build
                       secure products that respect digital freedom.


          o § Open Hardware/Modding⠀➾


                # ⚓ Adafruit ☛ When_the_Push_Button_Was_New,_People_Were
                  Freaked_@JSTOR_Daily⠀⇛


                       The doorbell. The intercom. The elevator. Once upon
                       a time, beginning in the late nineteenth century,
                       pushing the button that activated such devices was
                       a strange new experience. The electric push button,
                       the now mundane-seeming interface between human and
                       machine, was originally a spark for wonder,
                       anxiety, and social transformation.


                # ⚓ JSTOR ☛ When_the_Push_Button_Was_New,_People_Were_Freaked⠀⇛


                       Ultimately, the idea that electricity was a kind of
                       magic would triumph over a more hands-on,
                       demystifying approach.


                # ⚓ Arduino ☛ Crack_combination_locks_with_this_nifty_robot⠀⇛


                       This cracking process works thanks to the mechanics
                       of combination padlocks. While the combination lock
                       on something like a bank vault is very
                       sophisticated, these padlocks have limited space
                       for their mechanisms. They also tend to be cheap.
                       For those reasons, one can feel the mechanisms
                       engaging when stress is on the shackle.


                # ⚓ Adafruit_ENS160_MOX_Gas_Sensor⠀⇛


                       We’ve of course broken out all the pins to standard
                       headers and added a 3.3V voltage regulator and
                       level shifting to allow you to use it with either
                       3.3V or 5V systems such as the Arduino Uno, or
                       Feather M4.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ CNX Software ☛ Amlogic_POP1-G_octa-core_Cortex-A73/A53
                  processor_shows_up_in_Amazon_Fire_TV_Cube_2022_–_CNX
                  Software⠀⇛


                # ⚓ CNX Software ☛ Geniatech_unveils_SMARC_2.1_compliant
                  Rockchip_RK3568_system-on-module_–_CNX_Software⠀⇛


                # ⚓ Lifewire ☛ How_to_Set_an_SD_Card_as_Default_Storage_in
                  Android⠀⇛


                # ⚓ 9to5Google ☛ Square_working_on_iPhone-like_‘Tap_to_Pay’_for
                  Android_merchants⠀⇛


                # ⚓ 9to5Google ☛ Android_apps_getting_‘major’_Google_TTS
                  quality_upgrade⠀⇛


                # ⚓ New_Android_Games:_Best_New_Android_Games_This_Week⠀⇛


                # ⚓ Android Headlines ☛ Best_Security_Apps_For_Android_In_2022-
                  23⠀⇛


                # ⚓ 9_Ways_to_Fix_Android_Wi-Fi_Not_Turning_On_[2022]_–
                  TechPP⠀⇛


                # ⚓ Galaxy_S22_Ultra_Almost_Got_Android_13_From_Verizon,_But
                  Didn’t⠀⇛


                # ⚓ Giz China ☛ Android_12L_Issues_That_Google_Must_Fix_Now-
                  Gizchina.com⠀⇛


                # ⚓ XDA ☛ The_Razer_Edge_5G_is_a_new_handheld_Android_gaming
                  console_with_support_for_5G⠀⇛


                # ⚓ SamMobile ☛ Samsung’s_Galaxy_S22_is_the_first_Android_phone
                  to_get_October_2022_security_update_–_SamMobile⠀⇛


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


          o ⚓ Linuxiac ☛ 5_Best_Free_Self-Hosted_Music_Streaming_Software⠀⇛


                 This article shows you the five best music streaming
                 services you can install for free and fully control your
                 music collection.


                 If you’re a music lover looking for free and open-source
                 music server software to build your own self-hosted live
                 streaming audio server for your extensive music
                 collection, you’ve come to the right place.


                 Setting up your own music server with media server
                 software is simple. But services like Spotify already
                 offer similar functionality. So, why build your own?


          o ⚓ Jussi Pakkanen ☛ Nibble_Stew:_“Why_is_it_that_package_managers
            are_unnecessarily_hard?”_–_or_are_they?⠀⇛


                 At the moment the top rated post in In the C++ subreddit
                 is Why is it that package managers are unnecessarily
                 hard?. The poster wants to create an application that
                 uses fmt and SDL2. After writing a lengthy and
                 complicated (for the task) build file, installing a
                 package manager, integrating the two and then trying to
                 build their code the end result fails leaving only
                 incomprehensible error messages in its wake.


                 The poster is understandably frustrated about all this
                 and asks a reasonable question about the state of package
                 management. The obvious follow-up question, then, would
                 be whether they need to be hard. Let’s try to answer that
                 by implementing the thing they were trying to do from
                 absolute scratch using Meson. For extra challenge we’ll
                 do it on Windows to be entirely sure we are not using any
                 external dependency providers.


          o ⚓ James_Bottomley:_Paying_Maintainers_isn’t_a_Magic_Bullet⠀⇛


                 Open Source is often portrayed as a “disrupter” of the
                 market, but it’s not often appreciated that a huge part
                 of that disruption is value destruction. Consider one of
                 the older Open Source systems: Linux. As an operating
                 system (when coupled with GNU or other user space
                 software) it competed in the early days with proprietary
                 UNIX. However, it’s impossible to maintain your margin
                 competing against free and the net result was that one by
                 one the existing players were forced out of the market or
                 refocussed on other offerings and now, other than for
                 historical or niche markets, there’s really no
                 proprietary UNIX maker left … essentially the value
                 contained within the OS market was destroyed. This value
                 destruction effect was exploited brilliantly by Google
                 with Android: to enter and disrupt an existing lucrative
                 smart phone market, created and owned by Apple, with a
                 free OS based on Open Source successfully created a load
                 of undercutting handset manufacturers eager to be cheaper
                 than Apple who went on to carve out an 80% market share.
                 Here, the value isn’t completely destroyed, but it has
                 significantly reduced (smart phones going from a huge
                 margin business to a medium to low margin one).


                 All of this value destruction is achieved by the free (as
                 in beer) effect of open source: the innovator who uses it
                 doesn’t have to pay the full economic cost for developing
                 everything from scratch, they just have to pay the
                 innovation expense of adapting it (such adaptation being
                 made far easier by access to the source code). This
                 effect is also the reason why Microsoft and other
                 companies railed about Open Source being a cancer on
                 intellectual property: because it is. However, this view
                 is also the product of rigid and incorrect thinking: by
                 destroying value in existing markets, open source
                 presents far more varied and unique opportunities in
                 newly created ones. The cardinal economic benefit of
                 value destruction is that it lowers the barrier to entry
                 (as Google demonstrated with Android) thus opening the
                 market up to new and varied competition (or turning
                 monopoly markets into competitive ones).


          o ⚓ Diziet ☛ Hippotat_(IP_over_HTTP)_–_first_advertised_release⠀⇛


                 The result is that, in practice, currently Hippotat has
                 to be built with (a) a reasonably recent Rust toolchain
                 such as found in Debian unstable or obtained from Rust
                 upstream; (b) dependencies obtained from the upstream
                 Rust repository.


          o § Web Browsers/Web Servers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Tor ☛ New_Alpha_Release:_Tor_Browser_12.0a3_(Android,
                        Windows,_macOS,_Linux)⠀⇛


                             Tor Browser 12.0a3 updates Firefox on
                             Android, Windows, macOS, and Linux to
                             102.3.0esr.


          o § SaaS/Back End/Databases⠀➾


                # ⚓ PostgreSQL ☛ PostgreSQL:_PostgreSQL_Anonymizer_1.1:_Privacy
                  By_Default_For_Postgres⠀⇛


                       PostgreSQL Anonymizer is an extension that hides or
                       replaces personally identifiable information (PII)
                       or commercially sensitive data from a PostgreSQL
                       database.


                       The extension supports 3 different anonymization
                       strategies: Dynamic Masking, Static Masking and
                       Anonymous Dumps. It also offers a large choice of
                       Masking Functions such as Substitution,
                       Randomization, Faking, Pseudonymization, Partial
                       Scrambling, Shuffling, Noise Addition and
                       Generalization.


                # ⚓ Linux Hint ☛ Data_Visualization_Tools_for_SQL⠀⇛


                       SQL is a high-in-demand programming language used
                       in domains like business analytics to interact with
                       relational data. Professionals widely use it for
                       tasks such as data manipulation, data analysis, and
                       data visualization.


                       Interacting with data is one thing, but to be able
                       to translate that data into meaningful information
                       is a challenge in itself.


                       Data visualization is the art of converting
                       information from data into visual contexts to make
                       it easier and understandable for the human brain.
                       Data visualization may include creating maps,
                       graphs, and charts so that it is easy to pull
                       meaningful insights from the data.


                # ⚓ Stacey on IoT ☛ Surprise!_People_are_shelling_out_for_IoT
                  subscriptions⠀⇛


                       IFTTT, which lets users link connected devices and
                       web services to other connected devices and web
                       services, has achieved $6 million in annual
                       recurring revenue from 150,000 subscribers two
                       years after it announced a subscription plan.
                       Linden Tibbets, the CEO and co-founder of IFTTT,
                       told me the company has reached break even on its
                       revenue and that, going forward, it plans to focus
                       solely on paid subscriptions from users.


          o § Education⠀➾


                # ⚓ Walled Culture ☛ Walled_Culture,_the_book,_now_freely
                  available:_what_that_means,_and_how_you_can_help⠀⇛


                       Much of the book draws on the interviews that have
                       appeared on the blog over the last year, and on
                       blog posts. But it is supplemented by a huge array
                       of additional material. Testimony to that are the
                       book’s 750 references to further information
                       online. For all the digital versions, there are
                       live hyperlinks to allow readers to check details
                       and pursue further research on topics and ideas of
                       interest.


          o § Programming/Development⠀➾


                # ⚓ Linux Hint ☛ Break_Statement_in_C⠀⇛


                       “To remove the program control from the loop, we
                       utilize the C language term “break.”The loop’s
                       iterations cease as immediately after the break
                       statement is detected inside the loop, and control
                       is instantly handed onto the first statement
                       following the break.


                       In this tutorial, we will practically implement the
                       break statement to execute various example codes in
                       C.”


                # ⚓ Linux Hint ☛ How_to_Declare_Variables_in_C⠀⇛


                       “A variable is simply a name that is assigned to a
                       storage space so it will be easy for users to
                       access or read in the program. The size, layout of
                       a variable’s memory, and the range of values or set
                       of different operations that can be implemented on
                       the variable are all recognized by the type of
                       variable, and each variable is unique in C
                       programming language. It is understandable that the
                       variable declared in a program can be edited
                       anywhere in the code. You can assign the variable
                       names as any number, letter, or character. Because
                       C is a case-sensitive language, so the uppercase
                       and lowercase characters are separate.


                       C programming language allows us to define various
                       data types such as Integer, float, char, string,
                       etc., which we will learn with various examples.”


                # ⚓ Light Blue Touchpaper ☛ Talking_Trojan:_Analyzing_an
                  Industry-Wide_Disclosure⠀⇛


                       Talking Trojan: Analyzing an Industry-Wide
                       Disclosure tells the story of what happened after
                       we discovered the Trojan Source vulnerability,
                       which broke almost all computer languages, and the
                       Bad Characters vulnerability, which broke almost
                       all large NLP tools. This provided a unique
                       opportunity to measure software maintenance in
                       action. Who patched quickly, reluctantly, or not at
                       all? Who paid bug bounties, and who dodged
                       liability? What parts of the disclosure ecosystem
                       work well, which are limping along, and which are
                       broken?


                # § TeX⠀➾


                      # ⚓ Linux Hint ☛ How_to_Make_a_Multiline_Equation_in
                        LaTeX⠀⇛


                             Sometimes, we need to break some long
                             equations in a document into multiple lines
                             to make it easy to understand. In lengthy
                             derivations, breaking the equations is
                             essential to explain everything step by step.


                             That’s why LaTeX also provides some ways to
                             break the equations. Still, many new users
                             don’t know how to create multiline equations.
                             In this tutorial, we will give you a complete
                             information on how to write the multiline
                             equations in LaTeX.


                      # ⚓ Linux Hint ☛ How_to_Underline_a_Text_in_LaTeX⠀⇛


                             Underlining a text is not limited to only
                             showing a website hyperlink. We underline a
                             text to make the reader notice some specific
                             words in a document. Underlined text attracts
                             the reader’s attention to it. If you write
                             any technical paper, underlining a text can
                             highlight it for the readers.


                             That’s why LaTeX provides a simple way to
                             highlight the text. However, many users don’t
                             know the ways to underline a text. If you
                             want to learn the approach to underlining a
                             text, read this tutorial thoroughly.


                      # ⚓ Linux Hint ☛ How_to_Use_a_Box_Text_in_LaTeX⠀⇛


                             A text box can be useful when you want to
                             move a text around in the document. It can
                             emphasise the specific text on a research
                             paper. We can use the \makebox to create a
                             boxed text on a page in LaTeX.


                             However, many LaTeX users are still unaware
                             of the ways to add a boxed text in the
                             technical document. If you don’t know how to
                             do it, read this tutorial thoroughly. We will
                             explain the various ways to add and use a
                             boxed text in LaTeX.


                      # ⚓ Linux Hint ☛ How_to_Write_and_Use_a_Floor_Symbol_in
                        LaTeX⠀⇛


                             Mathematically, the floor function is denoted
                             by the floor ⌊x⌋ symbol and the floor (x).
                             The shape of the floor symbol looks like a
                             square bracket ⌊x⌋ with no tops. From
                             programming to mathematics, the floor symbol
                             plays a vital role in showing a specific
                             function.


                             Many users add the floor function while
                             creating the technical document in any
                             document processor. However, a floor function
                             requires the correct use of the source code
                             to create it. If you want to learn how to
                             write and use a floor symbol in LaTeX, this
                             tutorial is for you. Let’s get started!


                # § Python⠀➾


                      # ⚓ Linux Hint ☛ Fibonacci_Numbers_in_Python_Language⠀⇛


                             Fibonacci numbers are a particular sequence
                             where the first value is pre-declared as 0
                             and the second value is pre-declared as 1.
                             The rest of the numbers are produced from
                             these two by adding the previous two numbers.
                             All Fibonacci numbers are positive integers,
                             beginning from 0.


                      # ⚓ Adafruit ☛ ICYMI_Python_on_Microcontrollers
                        Newsletter:_Retrofitting_old_computers,_Pinguin_and
                        much_more!_#CircuitPython_#ICYMI_@micropython
                        @Raspberry_Pi⠀⇛


                             In about a month, there will be a new yearly
                             release of Python: version 3.11. The main
                             feature for this version is a significant
                             increase in speed. People are testing the new
                             version and their results are stunning.
                             Extrapolating keeping at this pace, Python
                             3.14 will be faster than C++. To be exact,
                             the loop time will be -0.232 seconds, so it
                             will be done just before you want to do the
                             calculation – Towards Data Science.


                      # ⚓ Nicholas Tietz-Sokolsky ☛ Rounding_in_Python⠀⇛


                             In software engineering, there are two
                             principles that often come into conflict. The
                             first one is the principal of least surprise.
                             The second one is doing the right thing.
                             These come into conflict when the usual thing
                             that people do is in fact the wrong thing. A
                             particular example of this is the behavior of
                             rounding.


                             In school we were taught that rounding is
                             always done in one particular way. When you
                             round a number it goes toward the nearest
                             hole number, but if it ends in 5, than it
                             goes toward the higher one. For example, 1.3
                             rounds to 1, and 1.7 rounds to 2. And we were
                             taught that 1.5 rounds to 2, and 2.5 goes to
                             3.


                             Because this is the way that we were taught
                             rounding works, it can be quite surprising
                             when rounding works differently. In fact,
                             there are a number of different ways to round
                             numbers. The Wikipedia article on rounding
                             gives no fewer than 14 different methods of
                             rounding. Fortunately, with computers, we
                             expect fewer: The IEEE 754 standard for
                             floating point numbers defines five rounding
                             rules.


                # § Java⠀➾


                      # ⚓ Alexandru Nedelcu ☛ The_Trouble_with_Checked
                        Exceptions:_Part_2⠀⇛


                             Java’s Checked Exceptions are problematic,
                             and it’s not due to their ergonomics, but
                             rather because they are in conflict with
                             abstraction and OOP. Also, few people care
                             about typed exceptions (unless they are happy
                             path results, not errors).


                # § Rust⠀➾


                      # ⚓ Rust Weekly Updates ☛ This_Week_In_Rust:_This_Week_in
                        Rust_462⠀⇛


    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Mining_And_Refining:_Sulfur⠀⇛


                 When you think of the periodic table, some elements just
                 have a vibe to them that’s completely unscientific, but
                 nonetheless undeniable. Precious metals like gold and
                 silver are obvious examples, associated as they always
                 have been with the wealth of kings. Copper and iron are
                 sturdy working-class metals, each worthy of having entire
                 ages of human industry named after them, with silicon now
                 forming the backbone of our current Information Age.
                 Carbon builds up the chemistry of life itself and fuels
                 almost all human endeavors, and none of us would get very
                 far without oxygen.


          o ⚓ Hackaday ☛ The_1337_PNG_Hashquine⠀⇛


                 A hashquine is a fun way to show off your crypto-tricks —
                 It’s a file that contains its own hash. In some file
                 types it’s trivial, you just pick the hash to hit, and
                 then put random data in a comment or other invisible
                 field till you get a collision. A Python script that
                 prints its own hash would be easy. But not every file
                 type is so easy. Take PNG for instance. these files are
                 split into chunks of data, and each chunk is both CRC-32
                 and adler32 checksummed. Make one change, and everything
                 changes, in three places at once. Good luck finding that
                 collision. So how exactly did [David Buchanan] generate
                 that beautiful PNG, which does in fact md5sum to the
                 value in the image? Very cleverly.


          o ⚓ Telex (Hungary) ☛ Hungarian_girl_completes_most_brutal_trail_in
            the_United_States⠀⇛


          o § Science⠀➾


                # ⚓ Hackaday ☛ AI_Dreaming_Of_Time_Travel⠀⇛


                       We love the intersection between art and
                       technology, and a video made by an AI (Stable
                       Diffusion) imagining a journey through time
                       (Nitter) is a lovely example. The project is
                       relatively straightforward, but as with most art
                       projects, there were endless hours of [Xander
                       Steenbrugge] tweaking and playing with different
                       parts of the process until it was just how he liked
                       it. He mentions trying thousands of different
                       prompts and seeds — an example of one of the
                       prompts is “a small tribal village with huts.” In
                       the video, each prompt got 72 frames, slowly
                       increasing in strength and then decreasing as the
                       following prompt came along.


                # ⚓ Democracy Now ☛ Asteroid_Diversion?_Earth_Is_Still
                  “Careening_Headlong_into_Climate_Catastrophe,”_Says_NASA
                  Scientist⠀⇛


                       NASA successfully crashed a robotic spacecraft into
                       an asteroid this week, a first-of-its-kind test of
                       technology that could prevent a comet or asteroid
                       from hitting the Earth, though the chances of such
                       a catastrophe are low. We speak with NASA climate
                       scientist Peter Kalmus, who calls the successful
                       mission “bittersweet.” “We’re doing these amazing
                       missions like redirecting asteroids, and yet with
                       all that technology, with all that knowledge,
                       somehow it’s not translating into stopping what is
                       clearly the biggest threat facing humanity, which
                       is global heating,” says Kalmus.


                # ⚓ Omicron Limited ☛ Artificial_intelligence_reduces_a
                  100,000-equation_quantum_physics_problem_to_only_four
                  equations⠀⇛


                       The formidable problem concerns how electrons
                       behave as they move on a gridlike lattice. When two
                       electrons occupy the same lattice site, they
                       interact. This setup, known as the Hubbard model,
                       is an idealization of several important classes of
                       materials and enables scientists to learn how
                       electron behavior gives rise to sought-after phases
                       of matter, such as superconductivity, in which
                       electrons flow through a material without
                       resistance. The model also serves as a testing
                       ground for new methods before they’re unleashed on
                       more complex quantum systems.


          o § Education⠀➾


                # ⚓ TruthOut ☛ Los_Angeles_Teachers_Are_Burned_Out_and_Priced
                  Out_of_Living_in_Their_City⠀⇛


                # ⚓ The Telegraph UK ☛ Inside_the_dark_world_of_student_sex
                  work⠀⇛


                       University students have been supporting their
                       studies with sex work for decades. Jay-Z rapped
                       about ‘chicks wishin’ they aint have to strip to
                       pay tuition’ in Hard Knock Life in 1998 (the year
                       tuition fees were first introduced in the UK).
                       Belle de Jour (Brooke Magnanti), a research
                       scientist, wrote a best-selling book, The Intimate
                       Adventures of a London Call Girl, in 2005, about
                       her secret life as an escort after she ran out of
                       money in the final stages of her PhD thesis at
                       Sheffield University.


                       But the subject really came to the fore last
                       November when Durham University was identified as
                       offering training sessions to support students
                       involved in sex work.


          o § Hardware⠀➾


                # ⚓ CNET ☛ What_Intel_Learned_When_an_Elevator_Smashed_Into_Its
                  Supercomputer_Chips⠀⇛


                       He didn’t say how many were ruined, but the loss
                       stung because they were initial samples used to
                       test performance and look for problems. “Every one
                       of them at that stage is expensive,” Koduri said in
                       an interview. With hundreds of manufacturing steps,
                       it takes months to make a single advanced chip.


                       The elevator door wasn’t just a one-off bummer. It
                       actually revealed a problem that stood in the way
                       of Intel’s effort to reclaim its processor
                       manufacturing leadership: human error.


                # ⚓ Andre Alves Garzia ☛ The_appeal_of_small_computers⠀⇛


                       I just read an article about the MNT Pocket Reform
                       at the IEEE Spectrum website and the comments about
                       it at HN. Often when I dive deep into threads about
                       small devices, my attention is drawn to bad
                       comments. People asking who would want such
                       device?, or $SOME_PAST_DEVICE did it first and
                       failed, etc. You get the gist: people projecting
                       their dislike about someone else’s vision disguised
                       as unquestionable facts.


                # ⚓ Hackaday ☛ Recycling_Junk_E-tags_Into_A_LoRaWAN_AQI
                  Sensor⠀⇛


                       [Aduecho] had seen those cheap eBay deals of e-
                       paper-based pricing tags, and was wondering if they
                       could be hacked to perform some other tasks. After
                       splitting the case open, the controller chip was
                       discovered to be a SEM9110, with some NFC hardware
                       support but little else. [aduecho] was hoping to
                       build some IoT-connected air quality indicator
                       (AQI) units but the lack of a datasheet for SEM9110
                       plus no sensors in place meant the only real course
                       of action was to junk the PCB and just keep the E-
                       paper display and the batteries. These units
                       appeared to be ‘new old’ stock, so there was a good
                       chance that both would be fresh and ripe for
                       picking.


                # ⚓ Hackaday ☛ The_First_Microcomputer:_The_Q1⠀⇛


                       Quiz time, what was the first commercially
                       available microcomputer? The Altair 8800? Something
                       obscure like the SCELBI? The Mark-8 kit? According
                       to [The Byte Attic], it was actually the Q1, based
                       on the Intel 8008 processor. The first Q1
                       microcomputer was delivered in December of 1972,
                       making it the first, as far as he can tell. Later
                       revisions used the Z80 processor, which is the
                       model pictured above that [The Byte Attic] has in
                       his possession. It’s a beautiful little machine,
                       with a striking orange plasma display.


                # ⚓ Hackaday ☛ A_Look_Inside_An_Old-School_Synchroscope⠀⇛


                       There’s nothing quite like old-school electrical
                       gear, especially the stuff associated with power
                       distribution. There’s something about the chunky,
                       heavy construction, the thick bakelite cases, and
                       the dials you can read from across the room. Double
                       points for something that started life behind the
                       Iron Curtain, as this delightful synchroscope
                       appears to have.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Salon ☛ Don’t_have_a_cow,_but_there’s_a_major_butter
                  shortage⠀⇛


                       According to a recent report from The Wall Street
                       Journal, the quantity of butter in cold storage
                       recently hit its lowest level since 2017, thanks to
                       a combination of worker shortages and lowered dairy
                       outputs across U.S. farms. As a result, the price
                       of butter has skyrocketed, climbing 24.6% in the
                       last 12 months. As the demand for butter increases
                       during the holiday baking season, these tight
                       supplies (and their accompanying costs) aren’t
                       going anywhere.


                # ⚓ Jelmer Vernooij ☛ Northcape_4000⠀⇛


                       The Northcape event has been held for several
                       years, and while it always ends on the North Cape,
                       the route there varies. Last years’ route went
                       through the Baltics, but this years’ was perhaps as
                       direct as possible – taking us through Italy,
                       Austria, Switzerland, Germany, the Czech republic,
                       Germany again, Sweden, Finland and finally Norway.


                # ⚓ TruthOut ☛ Kaiser_Permanente_Therapists_Keep_Striking,
                  Citing_Dangerous_Delays_for_Patients⠀⇛


                # ⚓ Common Dreams ☛ Experts_Sound_Alarm_Over_‘Growing_Threat’
                  of_Genetically_Engineered_Trees⠀⇛


                       “The convenience of trees that can survive
                       glyphosate will likely result in the use of more
                       glyphosate, more often.”


                # ⚓ The Nation ☛ Jackson_Mississippi’s_Poisoned_Water⠀⇛


                # ⚓ Scheerpost ☛ ‘Habitual_Offender’_Laws_Imprison_Thousands
                  for_Small_Crimes_—_Sometimes_for_Life⠀⇛


                       Data obtained by The Appeal show nearly 2,000
                       people in Mississippi and Louisiana are serving
                       long—and sometimes life—sentences after they were
                       labeled “habitual offenders.” But most are behind
                       bars for small crimes like drug possession.


          o § Pseudo-Open Source⠀➾


                # § Openwashing⠀➾


                      # ⚓ ZDNet ☛ Open_Source_Initiative_expands_its_role_to_AI
                        and_machine_learning [Ed: OSI_has_shifted_into_a
                        Microsoft_front_and_GPL_violations_enabler]⠀⇛


                             As part of this, the OSI is putting more
                             emphasis on its [Microsoft] ClearlyDefined
                             project.


          o § Security⠀➾


                # ⚓ Krita ☛ Only_Download_Krita_From_Trusted_Places⠀⇛


                       Third party download sites are outside our control,
                       and can be compromised!


                # ⚓ Never-before-seen_malware_has_infected_hundreds_of_Linux
                  and_Windows_devices [Ed: So the problem is bad passwords and
                  stolen keys, not "Linux"]⠀⇛


                       SSH infections using password brute-forcing and
                       stolen keys also allow Chaos to spread from machine
                       to machine inside an infected network.


                # ⚓ IT Wire ☛ Optus_CEO’s_spin_not_exactly_the_best_way_to
                  handle_breach⠀⇛


                       One wonders what exactly drove Optus chief
                       executive Kelly Bayer Rosmarin to front a media
                       session last Friday, in a bid to spin her way
                       through a damaging development at the telco.


                       Had she been proficient in the technical aspects of
                       data breaches and was willing to level with people,
                       then it may have done a world of good. Or she could
                       have brought along a technically competent person
                       and let him/her explain things correctly.


                       But Bayer Rosmarin tried to paint the breach as a
                       sophisticated attack, something that even a
                       politician like Home Affairs Minister Clare O’Neil
                       was able to shoot it down.


                # ⚓ The Hill ☛ [Crackers]_breach_tech_magazine,_send_racist
                  push_notifications_to_iPhones⠀⇛


                       [Attackers] breached the content management system
                       of Fast Company, a monthly business and tech
                       magazine, on Tuesday evening.


                       The [crackers] reportedly sent two obscene and
                       racist push notifications to followers of the
                       magazine in Apple News.


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ George ☛ Unique_Identifier⠀⇛


                             As more and more things are moving online,
                             two problems became apparent to our
                             collective consciousness:


                             1. How do you know someone is really a
                             person?


                             2. How do you know someone is who they say
                             they are?


                             Initially, the “person” thing wasn’t a big
                             issue, the [Internet] was used for low-stake
                             amicable activities, and impersonation, bots,
                             and alternative accounts weren’t a big deal.
                             As for the second issue, well, we used
                             usernames and passwords.


                # § Privacy/Surveillance⠀➾


                      # ⚓ AccessNow ☛ Digital_identity:_What_the_World_Bank
                        won’t_talk_about_–_Access_Now⠀⇛


                             On October 10, the World Bank and the
                             International Monetary Fund will hold an
                             annual summit to discuss the challenges and
                             opportunities that will determine the course
                             of their work on inclusivity and sustainable
                             development all over the world.
                             Unfortunately, this is the second year in a
                             row that they have kept digital identity
                             programs off the agenda, even as civil
                             society organizations continue to press for
                             answers about their responsibility in
                             developing systems that further human rights
                             abuse, exclusion, marginalization, and
                             surveillance.


                             The push to implement digital identification
                             systems remains a priority for the World Bank
                             and other international organizations, as it
                             is viewed as integral for reaching UN
                             Sustainable Development Goal (SDG) 16.9,
                             “legal identity for all.” However, attempting
                             to reach that goal this way is both short-
                             sighted and treacherous, as many different
                             digital identity programs the World Bank has
                             funded or promoted demonstrate.


                      # ⚓ AccessNow ☛ U.S._Congressional_briefing:_what
                        overturning_Roe_v._Wade_means_for_digital_rights_–
                        Access_Now⠀⇛


                             Today, September 28, Access Now hosted the
                             U.S. Congressional Briefing, Your body, your
                             data: data-veillance and reproductive rights
                             in a post-Roe world to unpack what the
                             Supreme Court ruling means for human rights
                             and digital safety, and what’s next for
                             collective action.


                             “When the U.S. Supreme Court reversed Roe v.
                             Wade, it didn’t only obliterate reliable
                             access to abortion services for women and
                             people who birth — and demolish any sense of
                             agency we had over our own bodies — it threw
                             the right to privacy of all people across the
                             country into jeopardy,” said Willmary Escoto,
                             U.S. Policy Analyst at Access Now. “The
                             threat to privacy is even more dangerous for
                             Black and Latina women, the disabled,
                             immigrants, LGBTQ+, low-income people, and
                             other communities that have been historically
                             discriminated against and exploited.”


                      # ⚓ India Times ☛ DoT_mandates_IMEI_registry_before_1st
                        sale_or_import_of_mobiles⠀⇛


                             The Department of Telecommunications (DoT)
                             has mandated smartphone manufacturers and
                             importers to register the IMEI number of
                             smartphones before the first sale or before
                             the import of the device on a new portal in
                             operation from 2020.


                             In a gazette notification, the DoT on Monday,
                             amended the prevention of tampering of the
                             Mobile Device Equipment Identification
                             Number, Rules, 2017 to enforce smartphone
                             manufacturers to register the IMEI number of
                             every mobile manufactured in India with the
                             Indian Counterfeited Device Restriction
                             Portal (ICDR) maintained by the DoT.


                      # ⚓ Site36 ☛ Plans_for_more_data_exchange:_EU_agreement
                        with_Interpol_delayed⠀⇛


                             So far, only EU states and Europol are
                             allowed to access databases at Interpol, but
                             soon Frontex and the new public prosecutor’s
                             office will be allowed to do so as well. The
                             EU Parliament has drawn red lines for the
                             negotiations.


                      # ⚓ Stacey on IoT ☛ Amazon_doesn’t_need_a_phone._Alexa
                        will_be_everywhere.⠀⇛


                             Amazon launched a profusion of sensor-filled
                             speakers, cameras, and televisions as well as
                             services from its Eero Wi-Fi business and
                             Ring security business on Wednesday as it
                             doubled down on its idea of ambient
                             intelligence. Basically, Amazon is making
                             sure everything it releases can act as a
                             sensor providing as much information about
                             the environment to Alexa, its digital
                             assistant.


                      # ⚓ YLE ☛ Prosecutors_charge_ex-CEO_of_[cracked]_therapy
                        firm_Vastaamo [iophk: Windows TCO]⠀⇛


                             The Helsinki-based company’s database was
                             breached on at least two separate occasions —
                             in November 2018 and March 2019 — leading to
                             extortionists demanding payment of nearly
                             half a million euros for the data’s return in
                             October 2020.


                             When the company refused to pay, the
                             sensitive patient information was leaked onto
                             the dark web.


                      # ⚓ [Old] The Hill ☛ DHS_planning_to_collect_social_media
                        info_on_all_immigrants⠀⇛


                             Homeland Security’s inspector general
                             published a report earlier this year
                             concluding that DHS pilot programs for using
                             social media to screen immigration applicants
                             “lack criteria for measuring performance to
                             ensure they meet their objectives.”


                      # ⚓ EFF ☛ Automated_License_Plate_Readers_Threaten
                        Abortion_Access._Here’s_How_Policymakers_Can_Mitigate
                        the_Risk⠀⇛


                             Police can also attach ALPRs to their patrol
                             cars, then capture all the cars they pass. In
                             some cities police are taught to do
                             “gridding,” where they drive up and down
                             every block of a neighborhood to capture data
                             on what cars are parked where. There is also
                             a private company called Digital Recognition
                             Network that has its own contractors driving
                             around, collecting plate data, and they sell
                             that data to law enforcement.


                      # ⚓ EFF ☛ EFF_Urges_FTC_to_Address_Security_and_Privacy
                        Problems_in_Daycare_and_Early_Education_Apps⠀⇛


                             “Parents find themselves in a bind: either
                             enroll children at a daycare and be forced to
                             share sensitive information with these apps,
                             or don’t enroll them at all,” EFF’s letter to
                             Khan said. “Paths for parents to opt a child
                             out of data sharing are, with rare exception,
                             completely absent.”


          o § Defence/Aggression⠀➾


                # ⚓ The Hill ☛ Iowa_man_who_was_one_of_the_first_Jan._6_
                  [insurrectionists]_to_enter_Capitol_found_guilty_on_7
                  charges⠀⇛


                       Doug Jensen was found guilty of all charges he
                       faced, according to the U.S. Attorney’s Office for
                       the District of Columbia, including felony charges
                       of assaulting, resisting or impeding a law
                       enforcement officer; obstruction of an official
                       proceeding; interfering with a law enforcement
                       officer during a civil disorder; entering and
                       remaining in a restricted building or grounds with
                       a dangerous weapon; and disorderly and disruptive
                       conduct in a restricted building or grounds with a
                       dangerous weapon.


                # ⚓ TruthOut ☛ Chomsky:_US_Must_Join_Global_Call_for
                  Negotiations_as_Russia_Escalates_Actions⠀⇛


                # ⚓ The Nation ☛ The_US_Military_Is_the_Enemy_of_Climate
                  Mitigation⠀⇛


                       On October 1, the US military will start spending
                       the more than $800 billion Congress is going to
                       provide it with in fiscal year 2023. And that
                       whopping sum will just be the beginning. According
                       to the calculations of Pentagon expert William
                       Hartung, funding for various intelligence agencies,
                       the Department of Homeland Security, and work on
                       nuclear weaponry at the Energy Department will add
                       another $600 billion to what you, the American
                       taxpayer, will be spending on national security.


                # ⚓ Meduza ☛ Russian_military_commissar_says_mistakenly_drafted
                  Russians_have_themselves_to_blame_—_Meduza⠀⇛


                       In a video address published Wednesday, Altai Krai
                       military commissar Marat Usmanov said that Russians
                       who are conscripted by mistake are themselves to
                       blame for the error.


                # ⚓ Meduza ☛ ‘Fighting_in_the_war_against_Ukraine_is_a_crime’
                  Philosopher_Arseny_Kumankov_on_why_Russians_have_a_moral_duty
                  to_evade_the_draft_—_Meduza⠀⇛


                       Participating in the war against Ukraine is a moral
                       crime. For this reason, we have an obligation to do
                       everything possible to avoid becoming complicit in
                       this aggressive, unjust war. There are a number of
                       reasons to regard Russia’s invasion of Ukraine and
                       its subsequent mobilization this way. The first
                       reason is that the Russian government has violated
                       its social contract with its people. The second
                       reason is that people are being sent to war by an
                       illegitimate power that is playing on a false sense
                       of patriotism. And the third reason is that the war
                       itself is a criminal act of aggression against the
                       citizens of Ukraine. The last reason is the primary
                       one. But I’ll begin with the points that apply
                       directly to Russians.


                # ⚓ Meduza ☛ Governor_reports_14_injured_by_munitions_accident
                  in_Belgorod_—_Meduza⠀⇛


                       Belgorod Regional Governor Vyacheslav Gladkov
                       reported Wednesday that “munitions were detonated”
                       in the city’s Valuysky District. The explosion,
                       which reportedly injured 14 people, was caused by
                       “the human factor,” Gladkov said. According to the
                       Telegram channel Mash, a grenade launcher was
                       unintentionally fired during military training.


                # ⚓ Meduza ☛ ‘The_model_of_“one_deciding_for_all”_isn’t
                  working’_Filmmaker_Andrey_Zvyagintsev_explains_his
                  resignation_from_the_Russian_Oscar_Committee_—_Meduza⠀⇛


                       On Sept. 26, Russia’s Oscar Committee announced
                       that it would not be nominating a feature film for
                       this year’s Academy Awards. Nikita Mikhalkov, head
                       of the Russian Cinematographers’ Union, said that
                       “it would be senseless” to submit a film under
                       current circumstances.


                # ⚓ Meduza ☛ ‘Honestly,_they’re_all_going_to_die’_What_Russian
                  soldiers_who_have_already_fought_in_Ukraine_think_about
                  Putin’s_mobilization_effort_—_Meduza⠀⇛


                # ⚓ Meduza ☛ Heads_of_the_self-proclaimed_‘LNR’_and_the
                  Russian-occupied_Kherson_region_appeal_to_‘join_Russia’
                  following_the_‘referendums’_—_Meduza⠀⇛


                       Vladimir Saldo, head of the Russian-installed
                       administration of the occupied Kherson region, has
                       appealed to Russia’s President Vladimir Putin,
                       requesting that the Kherson region be joined to
                       Russia. RIA Novosti reports that Saldo published
                       his appeal on Telegram.


                # ⚓ Meduza ☛ Russian_State_Duma_Speaker_says_border_guards
                  keeping_lists_of_draft_evaders_—_Meduza⠀⇛


                       Russian border authorities are keeping lists of
                       citizens who leave the country, State Duma Speaker
                       Vyacheslav Volodin said at a session of the body on
                       Wednesday, according to Interfax.


                # ⚓ Meduza ☛ Head_of_self-proclaimed_‘DNR’_‘promises_new_phase
                  of_combat_operations’_after_‘becoming_part_of_Russia’_—
                  Meduza⠀⇛


                       Denis Pushilin, who heads the self-proclaimed
                       “Donetsk People’s Republic,” has said that after
                       the “DNR” “becomes part of Russia” following a
                       “referendum,” a “new phase of combat operations”
                       will begin.


                # ⚓ Common Dreams ☛ Highland_Park_Victims_Sue_Gun-Maker,_Stores
                  Over_Negligence_and_Deceptive_Practices⠀⇛


                       Along with the company—which plaintiffs argue
                       violated a consumer protection law—the families and
                       victims sued online retailer Bud’s Gun Shop, local
                       gun store Red Dot Arms, shooting suspect Robert
                       Crimo III, and Robert Crimo, Jr., the suspect’s
                       father.


                # ⚓ Common Dreams ☛ NC_Dems_Plead_for_Cash_as_Beasley
                  Deadlocked_With_GOP_Opponent_in_Decisive_US_Senate_Race⠀⇛


                       “National Democrats are making a big mistake if
                       they’re not paying attention to North Carolina.”


                # ⚓ Common Dreams ☛ ‘Yeah,_Right’:_Pentagon_Report_Claiming_US
                  Military_Killed_Just_12_Civilians_Last_Year_Met_With
                  Skepticism⠀⇛


                       “They were targeting people. It was intentional.”


                # ⚓ Common Dreams ☛ Opinion_|_Poll_Shows_Majority_in_US_Want
                  Harder_Diplomatic_Push_to_End_Ukraine_War⠀⇛


                       Nearly 60 percent of Americans would support the
                       United States engaging in diplomatic efforts “as
                       soon as possible” to end the war in Ukraine, even
                       if that means Ukraine having to make concessions to
                       Russia, according to a new poll. 


                # ⚓ Common Dreams ☛ Opinion_|_The_Big_Lie,_Media_Complicity,
                  and_the_Science_of_Propaganda⠀⇛


                       Donald Trump is still insisting he won the 2020
                       election, despite having lost by about 7 million
                       votes and being wiped out in the Electoral College.


                # ⚓ Common Dreams ☛ Sanders,_Kaine_Hail_US_Senate’s_Passage_of
                  Brazil_Election_Resolution⠀⇛


                       “With this vote, the Senate sent a powerful
                       message.”


                # ⚓ The Nation ☛ Sanders,_Raskin_Want_Congress_to_Get_Serious
                  About_Averting_a_Coup_in_Brazil⠀⇛


                       Polls from Brazil show that President Jair
                       Bolsonaro, the Donald Trump–like authoritarian who
                       has run the country disastrously since his election
                       in 2018, is trailing far behind his leftist
                       challenger, former president Luiz Inácio Lula da
                       Silva, in the run-up to the first round of voting
                       on Sunday. But Bolsonaro is claiming that if he
                       doesn’t win by a landslide, it will be because
                       “something abnormal” happened with the voting
                       process—echoing Trump’s false narrative from before
                       he lost the 2020 election in the United States.


                # ⚓ The Nation ☛ Brittney_Griner_Gets_No_Support_From_Former
                  Coach_Kim_Mulkey⠀⇛


                       Sports coaches love military allegories, so here is
                       one for legendary LSU basketball coach Kim Mulkey:
                       Leave no person behind. But that’s exactly what the
                       three-time national champion did to Brittney
                       Griner, a player who brought Mulkey to a national
                       title when the coach was at Baylor. The superstar
                       led Mulkey’s Baylor squad to a 40-0 regular season
                       and championship in 2012.


                # ⚓ The Nation ☛ We_Like_the_Idea_of_Asylum_Seekers,_but_Not
                  the_Real_Thing⠀⇛


                       Little Amal, the 12-foot-tall puppet of a Syrian
                       refugee girl, went looking for her mother in
                       Brooklyn last week, as she has done all over the
                       world. She was greeted enthusiastically by crowds
                       of children and adults who were charmed by her
                       lifelike movements and huge, blinking eyes, and by
                       the grace with which the puppeteers made her move,
                       dance, peer into windows, and even reach out for a
                       hug.


                # ⚓ Scheerpost ☛ NYT_Op-Ed_Criticizes_Biden_for_Not_Being
                  Hawkish_Enough⠀⇛


                       You know you’re living in a profoundly sick society
                       when the world’s most influential newspaper runs
                       propaganda for World War III while voices pushing
                       for truth, transparency and peace are marginal…


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ The Dissenter ☛ Snowden’s_Russia_Citizenship:_Establishment
                  Response_Illustrates_Why_He_Hasn’t_Returned_Home⠀⇛


          o § Environment⠀➾


                # ⚓ The Atlantic ☛ The_Senate_Just_Quietly_Passed_a_Major
                  Climate_Treaty⠀⇛


                       What if the Senate passed an international climate
                       treaty—a pact so powerful that it could avert
                       nearly 1 degree Fahrenheit of global warming—and
                       nobody noticed?


                       That’s more or less what happened a week ago. Last
                       Wednesday, the Senate ratified the Kigali
                       Amendment, a treaty that will phase out the world’s
                       use of hydrofluorocarbons, or HFCs, a climate
                       pollutant used as an industrial refrigerant and in
                       sprayable consumer products. Because HFCs are
                       hundreds of thousands of times more potent at
                       capturing heat in the atmosphere than carbon
                       dioxide, the Kigali Amendment, which has already
                       been adopted by 137 countries, is the most
                       significant environmental treaty that the United
                       States has joined in at least a decade.


                # ⚓ NBC ☛ ‘I’ve_always_wanted_to_be_a_tree’:_Human_composting
                  starts_to_catch_on⠀⇛


                       California Gov. Gavin Newsom this month signed a
                       bill that requires state regulators to create a
                       program allowing “natural organic reduction” by
                       2027. It will become the fifth state to pass
                       legislation permitting what providers often call
                       “human composting” or “terramation.”


                       The process, which is essentially the controlled
                       decomposition of a human body by a funeral service
                       provider, takes about two months. Processing a
                       person’s remains creates 1-2 cubic yards of compost
                       — enough to nearly fill the bed of a pickup truck,
                       which can then be used in gardens or conservation
                       projects.


                # ⚓ TruthOut ☛ Manchin’s_Big_Oil_Deal_Scrapped_From_Budget_Bill
                  in_Victory_for_Climate_Movement⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Defeat_of_Manchin’s_Dirty_Deal_Is
                  a_Win_for_Environmental_Justice_and_Health_Equity⠀⇛


                       Facing fierce resistance from frontline communities
                       and concerned citizens across the country, Senator
                       Joe Manchin (D-W.Va.) withdrew his so called
                       “permitting reform” provision from the must-pass
                       government funding bill Tuesday.


                # ⚓ Common Dreams ☛ ‘We’ll_Beat_You_Again,’_Say_Climate
                  Advocates_as_Biden_Eyes_New_Path_for_Manchin’s_Dirty_Deal⠀⇛


                       In a statement after Manchin (D-W.Va.) asked Senate
                       Majority Leader Chuck Schumer (D-N.Y.) to remove
                       the permitting overhaul from the government funding
                       bill, White House Press Secretary Karine Jean-
                       Pierre made clear that President Joe Biden doesn’t
                       intend to let the measure die despite fresh
                       warnings over its potentially disastrous emissions
                       impacts.


                # ⚓ Scheerpost ☛ Ben_&_Jerry’s_Pilot_Project_Aims_to_Halve_Ice
                  Cream_Emissions_by_2024⠀⇛


                       Christopher Bonasia reports that the iconic ice
                       cream maker Ben & Jerry’s will work with 15 dairy
                       farms to halve greenhouse gas emissions by 2024.


                # ⚓ Common Dreams ☛ Fresh_Demands_for_‘Climate_Emergency
                  Declaration’_as_Monster_Hurricane_Ian_Comes_Ashore⠀⇛


                       The hurricane, which killed at least two people in
                       Cuba and left the entire country without power
                       before causing major flooding in the Florida Keys
                       Tuesday night, approached the state’s coast as a
                       Category 4 storm and was expected to strengthen to
                       a Category 5 before making landfall.


                # ⚓ Democracy Now ☛ Tampa_Update_on_Hurricane_Ian:_Millions
                  Prepare_for_Cat._5_Storm_Fueled_by_the_Climate_Crisis⠀⇛


                       As Hurricane Ian is set to strengthen into a
                       Category 4 or 5 storm and make landfall Wednesday
                       afternoon south of Tampa Bay, the storm already
                       knocked out power in Cuba and killed at least two
                       people Tuesday. Communities across Central Florida
                       are preparing for a “very strong storm,” says Seán
                       Kinane, news and public affairs director at Tampa
                       community radio station WMNF, and many acknowledge
                       the strength of the hurricane is “definitely
                       impacted by climate disruption.”


                # ⚓ DeSmog ☛ Hydrogen_Lobby_Targeting_Labour_Conference_with
                  ‘False_Solutions’,_Say_Campaigners⠀⇛


                       Labour has made climate and energy its central
                       policy agenda, and its conference in Liverpool this
                       week has touted the slogan “A Fairer, Greener
                       Future”. However, the hydrogen industry has had an
                       outsized presence at the event compared to cleaner
                       alternatives.


                # ⚓ Hackaday ☛ 2022_Hackaday_Prize:_Congratulations_To_The
                  Winners_Of_The_Climate-Resilient_Communities_Challenge⠀⇛


                       Holy humanitarian hacking, Batman! We asked you to
                       come up with your best climate-forward ideas, and
                       you knocked it out of the ionosphere! Once again,
                       the judges had a hard time narrowing down the field
                       to just ten winners, but they ultimately pulled it
                       off — and here are the prize-winning projects
                       without much further ado.


                # § Energy⠀➾


                      # ⚓ Cambridge_Bitcoin_Electricity_Consumption_Index⠀⇛


                             Note: monthly consumption figures are the sum
                             of daily consumption figures calculated by
                             assuming constant power usage over 24 hours
                             at the daily best-guess estimate of Bitcoin’s
                             network power demand. The cumulative
                             consumption is the sum of monthly totals
                             since the start of the model on July 18th
                             2010. A separate analysis that ignores
                             profitability considerations suggests that
                             the cumulative consumption for the period
                             between January 2009 and July 2010 has only
                             amounted to 4.74 megawatt-hours (MWh), or
                             0.00000474 TWh – a mere rounding error. It is
                             therefore safe to assume that the cumulative
                             consumption figure listed above provides a
                             robust estimate of Bitcoin’s total
                             consumption since its inception in 2009.


                      # ⚓ Variety ☛ Inside_the_Fight_Over_the_‘Pulp_Fiction’
                        NFT⠀⇛


                             January was a heady time for the Secret
                             Network. The two-year-old platform had
                             launched a cryptocurrency – SCRT – and was
                             preparing to make a big splash in Hollywood.
                             Teaming up with Quentin Tarantino, the
                             network was preparing to auction an NFT based
                             on the screenplay for “Pulp Fiction.”


                      # ⚓ Matt Rickard ☛ Is_Ethereum_a_Dumb_Pipe?⠀⇛


                             Commoditized protocols (especially
                             decentralized ones) often create value but
                             have a different entity capture most of it.
                             See examples of email (Gmail) or git
                             (GitHub). Who captures the value? Scaling
                             layers? On-ramps/off-ramps? Regulated
                             exchanges?


                      # ⚓ CS Monitor ☛ What_is_‘dead_pool’_and_what_does_it
                        mean_for_Colorado_River?⠀⇛


                             The Colorado River supports more than two
                             dozen tribes, seven U.S. states, and Mexico,
                             but Americans living outside the Western
                             region benefit, too. The river preserves
                             national parks and produces winter
                             vegetables, shipped countrywide.


                             Yet a long-term rise in demand – and
                             increasingly arid conditions linked to
                             climate change – have resulted in a dire
                             river reality. Lake Mead and Lake Powell,
                             major reservoirs, could reach “dead pool,”
                             with levels of water so low that the river
                             can’t flow below the dams.


                      # ⚓ Cory Doctorow ☛ Oil_is_Bankrupt_(If_We_Want_It)_:
                        Alberta’s_Oil_Companies_Are_the_Walking_Dead.⠀⇛


                             Albert’s oil-patch is a zombie, the walking
                             dead. The companies that extract oil there
                             owe more money than they can pay, more than
                             they can borrow, more than they can earn. If
                             they were made to pay their lawful debts,
                             they would all go bankrupt, and, in so doing,
                             would end the extraction of one of the
                             dirtiest, worst sources of oil…


                      # ⚓ TruthOut ☛ Bill_McKibben:_The_End_of_Manchin’s
                        Pipeline_Deal_Is_a_Grassroots_Victory⠀⇛


                      # ⚓ Democracy Now ☛ Bill_McKibben:_Victory_Over_Big_Oil
                        as_Sen._Manchin_Forced_to_Drop_“Hideous_Deal”_on
                        Energy⠀⇛


                             Democratic Senator Joe Manchin abandoned his
                             own energy permitting proposal Tuesday that
                             would have fast-tracked the federal review of
                             energy projects, including the contested
                             Mountain Valley Pipeline. Following intense
                             pressure from a range of climate justice and
                             Appalachian organizers, Manchin asked Senate
                             Majority Leader Chuck Schumer to drop the
                             permitting reforms from a funding bill after
                             it became clear he did not have the votes to
                             pass the proposal. 350.org founder Bill
                             McKibben says Manchin may try to partner with
                             the GOP to revive the proposal later this
                             year, but still says the news represents an
                             “impressive win by grassroots
                             environmentalism.”


                      # ⚓ Common Dreams ☛ Apparent_Sabotage_of_Nord_Stream
                        Pipelines_Risks_‘Unprecedented’_Climate_Nightmare⠀⇛


                             One early estimate from Jean-Francois
                             Gauthier, vice president of measurements at
                             the satellite firm GHGSat, indicates that the
                             Russian gas pipelines were unleashing more
                             than 500 metric tons of methane per hour when
                             they were first damaged.


                      # ⚓ Common Dreams ☛ 11_Million_Without_Electricity_in
                        Cuba_as_Hurricane_Ian_Knocks_Out_Power_Grid⠀⇛


                             Around a million people lost power Tuesday as
                             Hurricane Ian lashed the island with heavy
                             rain and wind, tearing off people’s roofs,
                             devastating farms, and reportedly killing at
                             least two people. By late Tuesday, Cuba’s
                             entire power grid had collapsed, leaving
                             roughly 11 million without electricity.


                      # ⚓ Scheerpost ☛ Explosions_Cause_Major_Damage_to_Both
                        Nord_Stream_Pipelines⠀⇛


                             A Polish member of European Parliament
                             suggested the US was responsible.


                      # ⚓ IT Wire ☛ iTWire_–_On_World_EV_Day,_Victoria_is
                        proudly_taxing_owners_of_EVs⠀⇛


                             On World Electric Vehicle Day, Victoria can
                             celebrate the fact that it charges people who
                             use EVs a tax. The same Victoria that calls
                             itself the education state. It also touts
                             itself as progressive.


                             When most of the world is trying to push the
                             use of electric vehicles, Victoria has its
                             foot firmly on the brake. No, make that both
                             feet on the brake.


                # § Wildlife/Nature⠀➾


                      # ⚓ Common Dreams ☛ Alarming_Report_Warns_1_in_8_Bird
                        Species_Now_Facing_Extinction⠀⇛


                             “If we give nature a chance, it can recover.”


                      # ⚓ The Revelator ☛ Countering_Anti-Science_Rhetoric_—
                        With_Squid_Facts⠀⇛


          o § Finance⠀➾


                # ⚓ IT Wire ☛ Apple_to_cut_back_on_iPhone_14_production_as
                  demand_drops:_claim⠀⇛


                       Apple has decided to drop its plans to increase
                       production of the iPhone 14 due to an anticipated
                       increase in demand not eventuating, a report
                       claims.


                       A Bloomberg report on Wednesday said the cutback
                       would amount to about six million units less being
                       produced in the second half of 2022.


                # ⚓ Aral Balkan ☛ Nlnet_Grant_Application_for_Domain_–_First
                  Update:_Questions_and_Answers⠀⇛


                       This is the first update to our NLnet Grant
                       Application for Domain.


                # ⚓ TruthOut ☛ 85%_of_the_World_Will_Likely_Live_Under_“Deadly”
                  Austerity_Measures_Next_Year⠀⇛


                # ⚓ Common Dreams ☛ Truss’_Tories_Plan_to_Slash_Public_Spending
                  While_Clinging_to_Chaos-Causing_Tax_Cuts⠀⇛


                       “What was intended as mere bribery has turned out
                       to be a gigantic financial bomb.”


                # ⚓ Common Dreams ☛ Top_Central_Banks_Told_to_Stop
                  ‘Bankrolling’_Deforestation⠀⇛


                       “It betrays the mission that all three central
                       banks have to act in the wider public good.”


                # ⚓ Common Dreams ☛ ‘Obscene,’_Says_Sanders_After_CBO_Reports
                  Richest_1%_Now_Owns_Over_1/3_of_US_Wealth⠀⇛


                       “A society cannot sustain itself when so few have
                       so much while so many have so little.”


                # ⚓ TruthOut ☛ “Billionaires_Cannot_Have_It_All”_–_Sanders
                  Calls_for_Redistribution_of_Wealth⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_California_AB_257_Is_Tip_of_the
                  Iceberg_When_It_Comes_to_‘Workplace_Fissure’⠀⇛


                       California Governor Gavin News has signed AB 257—a
                       bill championing workers’ rights in the fast food
                       industry—into law. Despite being a huge step
                       forward for workers, tens of millions of dollars
                       will be spent trying to kill it. Before anyone has
                       a chance to vote on it via a possible ballot
                       measure, it’s key that people understand the bigger
                       picture of just how damaging, pervasive, and
                       exploitative “workplace fissuring” is throughout
                       almost every industry.


                # ⚓ Common Dreams ☛ 85%_of_Global_Population_Set_to_Live_Under
                  ‘Deadly’_Austerity_Measures_Next_Year⠀⇛


                       With countries across the globe facing major costs-
                       of-living crises and looming recessions as prices
                       remain high and central banks rush to slow economic
                       demand, an analysis published Wednesday estimates
                       that 85% of the world population will be living
                       under austerity measures by next year as tens of
                       millions face hunger, homelessness, and health
                       crises.


                # ⚓ The Nation ☛ For_the_First_Time,_the_Federal_Government
                  Will_Help_Poor_Families_Get_Diapers⠀⇛


                       For the first time, the federal government is
                       directly addressing diaper need, which leaves one
                       in three American families struggling to afford
                       enough diapers for their children. To start
                       chipping away at the problem, the Department of
                       Health and Human Services just announced the
                       creation of the Diaper Distribution Pilot to hand
                       out diapers to low-income families. The
                       Administration for Children and Families will give
                       $8 million in grants to six states—Arizona, Iowa,
                       North Carolina, South Carolina, Washington, and
                       Virginia—and one tribal consortium, the South Puget
                       Intertribal Planning Agency, in Washington State.
                       Recipient agencies will work with existing diaper
                       banks and social service agencies to get diapers
                       into the hands of parents struggling to afford
                       them.


                # ⚓ Common Dreams ☛ New_Report_Reveals_How_13_US_States_‘Shield
                  the_Fortunes_of_the_World’s_Richest_People’⠀⇛


                       “The wealth of nations is hidden in states like
                       Wyoming, Delaware, Nevada, and South Dakota.”


                # ⚓ Scheerpost ☛ Imperialism_and_Capitalism_Are_‘Bleeding_the
                  World_Dry’:_At_UN,_Nicaragua_Calls_for_Global_Rebellion⠀⇛


                       At the United Nations General Assembly, Nicaragua’s
                       Sandinista government called for a global rebellion
                       against the “imperialist and capitalist system”
                       that is “bleeding the world dry.” Condemning …


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ MEMRI ☛ Palestinian_Islamic_Scholar_Issam_Amira:_Nurture_In
                  Your_Children_The_Hatred_Of_Britain_Like_Mothers_Breastfeed
                  Babies;_Britain_Is_Responsible_For_All_The_World’s_Crises⠀⇛


                       Palestinian Islamic scholar Issam Amira said in a
                       speech posted to the Al-Aqsa Call YouTube channel
                       on September 18, 2022 that Britain is the “mother
                       of all crimes and disasters.” He blamed Britain for
                       the Palestinian nakba, for the “humiliation” the
                       Palestinians are suffering, and for the world’s
                       crises throughout history. He criticized the
                       leaders of Muslim countries for offering their
                       condolences over the recent death of Queen
                       Elizabeth II, and recalled a visit to the British
                       Museum in which he realized that everything in the
                       museum had been stolen from nations. He added: “May
                       Allah curse Britain.” It is noteworthy that Amira
                       recently gave a recorded speech at the Hizb-ut
                       Tahrir conference in Britain (see MEMRI TV Clip No.
                       9749).


                # ⚓ Sahara Reporters ☛ EXCLUSIVE:_Amid_Alleged_Islamisation
                  Agenda,_Nigerian_Police_Academy_Commandant,_Ahmad_Accused_Of
                  Replacing_Christian_Personnel_With_Muslims⠀⇛


                       Ahmed was alleged to have illegally transferred
                       some Christian personnel out of the institution and
                       replaced them with Muslims.


                # ⚓ Freedom_of_speech_in_universities:_is_there_a_problem_and
                  does_the_Free_Speech_Bill_help?⠀⇛


                       Does the Bill present an opportunity for the Higher
                       Education sector to take reasonable steps to secure
                       freedom of speech on university campuses, is it
                       entirely unnecessary, or will it even make free
                       speech more difficult to maintain?


                # ⚓ CoryDoctorow ☛ Federalist_Society_v_Corporate_Personhood⠀⇛


                       When tech monopolies used their market power to sew
                       up all the public forums for discourse and then
                       kicked off Donald Trump, Milo Yiannopoulos and Alex
                       Jones, key figures on the right became highly
                       selective trustbusters, dedicated to curbing the
                       power of tech monopolies.


                       The ideological cover for this is thin to
                       nonexistent: diehard Federalist Society types like
                       Ted Cruz don’t even bother to try articulating a
                       theory of “good” monopolies and “bad” monopolies. A
                       “good” monopoly is one that helps Ted Cruz and his
                       pals. A “bad” monopoly is one that gets in their
                       way.


                       The latest ideological flipflop from the right
                       comes in its relationship to corporate personhood.
                       For a generation, the right has insisted that
                       corporations are people, and, more importantly,
                       corporations are the kinds of people who have free
                       expression rights under the First Amendment of the
                       US Constitution.


                # ⚓ Sabine Hossenfelder ☛ I’ve_said_it_all_before_but_here_we
                  go_again⠀⇛


                       But trying to get rid of me isn’t going to solve
                       their problem. For one thing, it’s not working.
                       More importantly, everyone can see that nothing
                       useful is coming out of particle physics, it’s just
                       a sink of money. Lots of money. And soon enough
                       governments are going to realize that particle
                       physics is a good place to save money that they
                       need for more urgent things. It would be in
                       particle physicists’ own interest to listen to what
                       I have to say.


                       And I have said this all many times before but I
                       hate long twitter threads, so let me just summarize
                       it in one blogpost: [...]


                # ⚓ TruthOut ☛ Poll:_Most_People_Want_Certification_Process
                  Updated_to_Prevent_Another_Jan._6⠀⇛


                # ⚓ Techdirt ☛ Indian_Legislators_Want_The_Government_To_Be
                  Able_To_Intercept_Encrypted_Messages⠀⇛


                       India is still a democracy. Or so it pretends. But
                       it’s becoming indistinguishable from autocratic
                       regimes, like those found in some of its nearby
                       neighbors, China, Turkey, and Pakistan.


                # ⚓ TruthOut ☛ Staffers_for_Andy_Levin_Unanimously_Vote_to_Form
                  First-Ever_Congressional_Union⠀⇛


                # ⚓ Pro Publica ☛ How_to_Vote_in_Person_or_by_Mail⠀⇛


                       First things first: Have you confirmed your voter
                       registration yet? You’ll need to be registered in
                       order to vote by mail or in person.


                # ⚓ Telex (Hungary) ☛ They_come_to_Hungary_for_work,_only_to
                  find_out_that_life_is_no_bed_of_roses_here_either⠀⇛


                # ⚓ Telex (Hungary) ☛ Russian_Patriarch_Kirill_awards_Hungarian
                  Deputy_Prime_Minister_Semjén⠀⇛


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ NPR ☛ Facebook_takes_down_Russian_network
                        impersonating_European_news_outlets⠀⇛


                             It involved more than 60 websites pretending
                             to be legitimate, high-profile European news
                             organizations, including the U.K.’s The
                             Guardian and Daily Mail, Germany’s Der
                             Spiegel and Bild, and Italian news agency
                             ANSA.


                             The spoofed websites were built with care,
                             Nimmo said, under the apparent theory that
                             imitating a big brand would draw a big
                             audience. They copied the layouts of outlets’
                             real sites and imitated their web addresses.
                             In some cases they used bylines and photos of
                             real journalists and included working links
                             to other news articles.


                      # ⚓ CS Monitor ☛ Russian_online_propaganda?_Meta_says
                        yes,_shuts_down_network.⠀⇛


                             The operation involved more than 60 websites
                             created to mimic legitimate news sites
                             including The Guardian newspaper in the
                             United Kingdom and Germany’s Der Spiegel.
                             Instead of the actual news reported by those
                             outlets, however, the fake sites contained
                             links to Russian propaganda and
                             disinformation about Ukraine. More than 1,600
                             fake Facebook accounts were used to spread
                             the propaganda to audiences in Germany,
                             Italy, France, the U.K., and Ukraine.


                             The findings highlighted both the promise of
                             social media companies to police their sites
                             and the peril that disinformation continues
                             to pose.


                      # ⚓ Craig Murray ☛ Twitter’s_Shoddy_Fakery⠀⇛


                             Watch these three clips very carefully,
                             focusing on the count on the retweet symbol.
                             Do you see what is wrong?


                      # ⚓ Robert Reich ☛ This_One_Thing_Made_Alex_Jones_Stop
                        Lying⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ RAIR Foundation ☛ Will_Muslims_Kill_More_Innocent_People
                  Because_Charlie_Hebdo’s_Latest_Cartoon_Hurt_Their_Feelings⠀⇛


                       On September 21, the French satirical weekly
                       magazine, Charle Hebdo, published its latest
                       cartoon, “230th anniversary of the proclamation of
                       the French republic”.


                # ⚓ Techdirt ☛ Kentucky_Court_Tells_Anonymous_Covington
                  Students_They_Can’t_Sue_For_Defamation_If_They’re_Anonymous⠀⇛


                       You all remember the media shit-storm around kids
                       from Covington Catholic High School and a run-in
                       with folks in Washington DC that became a sort of
                       Rorshach test demonstrating your political
                       viewpoints based on how you viewed the encounter.
                       The main character from Covington Catholic was Nick
                       Sandmann, who sued a bunch of media orgs over their
                       characterization of the events. While a few
                       publications settled — for what it seems was
                       clearly a tiny “nuisance fee” — Sandmann lost all
                       of his other cases against the media, because there
                       was no defamation at all.


                # ⚓ Scheerpost ☛ Tom_Engelhardt_on_the_Corporate_Equivalent_of
                  Book_Burning⠀⇛


                       Tom Engelhardt offers a deeply personal look at how
                       two progressive publishing houses where he worked
                       as an editor found that there simply was no place
                       for them in mainstream publishing.


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


                # ⚓ Common Dreams ☛ Opinion_|_Policies_That_Center_Community
                  Voices_Are_Key_to_Solving_the_Local-News_Crisis⠀⇛


                       Over the past 15 years, the United States has lost
                       more than half the newspaper reporters covering
                       state and local beats. Runaway media consolidation,
                       mismanagement, new technologies and changing
                       consumer habits have led to widespread job losses
                       and newsroom closings. The decimation of local news
                       has disproportionately harmed low-income
                       communities, people of color, rural communities,
                       and immigrants. And as news deserts expand,
                       disinformation proliferating online has filled the
                       void.


          o § Civil Rights/Policing⠀➾


                # ⚓ Ali Reza Hayati ☛ Nobody_survives_with_oppression⠀⇛


                       It has been more than ten days since my people in
                       Iran have started protesting against injustices
                       they are suffering from, triggered by the death of
                       Mahsa Amini, a young girl reportedly killed by
                       morality police.


                       The government has shut down the [Internet] again
                       and killed almost all messengers and communication
                       services people used and access to any server
                       located outside the country is very much
                       restricted. This has been a common way for the
                       regime to oppress protesters.


                # ⚓ VOA News ☛ Iran_Riot_Police_Confronting_Protesters_in
                  Tehran_Over_Death_of_Woman⠀⇛


                       The protests have spread to at least 80 cities and
                       towns throughout Iran. Security police have used
                       tear gas, clubs and, in some cases, live ammunition
                       to quell the protests calling for the end of the
                       Islamic establishment’s more than four decades in
                       power.


                # ⚓ The Nation ☛ Iran’s_Brutal_Crackdown_on_“Women,_Life,
                  Freedom”⠀⇛


                       Iran’s “morality police” murdered Jîna Emînî, a 22-
                       year-old Kurdish woman, for wearing an “improper
                       hijab.” They killed her because she was Kurdish and
                       because she was a woman. The hashtag #MahsaAmini is
                       trending, but we should address this injustice
                       appropriately: by the name Jîna’s family gave her.
                       Mahsa is the name imposed on her by the Islamic
                       Republic, a government that oppresses minority
                       groups such as the Kurds and bans the use of
                       Kurdish names in many cases. Jîna’s identity as a
                       Kurdish woman should not be erased. “Jin Jîyan
                       Azadî,” or “Women, Life, Freedom” in Kurdish, has
                       become the slogan of the movement in Iran, but
                       Western media has failed to honor its full
                       significance. It’s a demand for women’s liberation
                       emerging from the Kurdish Freedom Movement.


                # ⚓ Scheerpost ☛ In_Iran,_Women_Are_at_the_Vanguard_of
                  Transformative_Change_Once_Again⠀⇛


                       Vrinda Narain and Fatemeh Sadeghi unravel the roots
                       of women’s uprisings in Iran in the wake of Mahsa
                       Amini’s death.


                # ⚓ The Economist ☛ “I’m_the_same_as_Mahsa._And_I_want_my
                  freedom”:_anger_at_Iran’s_regime_spills_onto_the_streets⠀⇛


                       What happened to Mahsa has happened to many girls.
                       Often they come for girls who are alone in the
                       street and put them in their vans. Then no one
                       knows where they are. That has happened to so many
                       friends of mine. It doesn’t matter to the police if
                       your hijab is problematic or not. They just get you
                       and then ask you to pay them money. And you have to
                       pay them. If they catch me in the market, they can
                       ask me for 3m rial (about $70). If they question me
                       and I don’t answer, I’ll have to pay more. Once
                       they stopped me in Isfahan and asked me for my
                       phone number. They warned me that if they caught me
                       three times, I’d end up in prison. And I wasn’t
                       even wearing a “bad” hijab. I’d just come from
                       university where we have to wear a proper black
                       hijab.


                # ⚓ Frontpage Magazine ☛ The_Islamic_Republic:_Shaken_to_its
                  Core⠀⇛


                       The government has ended Internet service in parts
                       in Tehran, and ended access to WhatsApp and
                       Telegram. Despite this, the protesters still manage
                       somehow to meet up and come out in force, and in
                       ever larger numbers, across the country.


                # ⚓ Medforth ☛ France:_Islamists_spread_photos_of_Muslim_women
                  not_wearing_headscarves_in_schools_on_social_networks_to_put
                  them_under_social_pressure⠀⇛


                       Screenshots of these accounts and quotes from the
                       social networks support this finding. One user
                       wrote: “School is not a legitimate excuse for
                       taking off the veil and delaying prayer.” On August
                       23, 2022, an Islamist influencer with 47,500
                       followers posted a video on TikTok urging young
                       women of the Muslim faith to ” (…) put a sash over
                       the abaya [long dress worn over the regular dress,
                       note]”.[…]Le Point


                # ⚓ BBC ☛ Myanmar_OnlyFans_model_sentenced_to_six_years_jail⠀⇛


                       In such areas – and under state of emergency laws
                       renewed by the Myanmar junta government earlier
                       this year – those charged with crimes are tried in
                       a military court where they’re denied rights like
                       access to a lawyer.


                # ⚓ Common Dreams ☛ Demanding_Broad_Reforms,_Thousands_of
                  Inmate_Workers_on_Strike_at_Alabama_Prisons⠀⇛


                       The work stoppage began Monday after about three
                       months of planning and organizing by inmates, with
                       help from groups including Alabama Prison Advocacy
                       and Incarcerated Families United.


                # ⚓ Scheerpost ☛ The_U.S._Sees_an_Unprecedented_Investment_in
                  Policing_Alternatives⠀⇛


                       Since 2021, around $500 million in new federal,
                       state, and philanthropic funding has been directed
                       toward initiatives that fall under the umbrella of
                       so-called “community violence intervention,” or CVI


                # ⚓ Shadowproof ☛ In_Washington_State,_Incarcerated_Organizers
                  Build_Community_With_Youth_To_Fight_For_Releases⠀⇛


                       At Washington’s Stafford Creek Corrections Center,
                       a group of incarcerated organizers have built
                       community with local youths to fight for sentencing
                       reforms, grappling with what it means to organize
                       through an abolitionist lens from inside.


                # ⚓ Democracy Now ☛ “Lady_Justice”:_Dahlia_Lithwick_on_Women
                  Who_Used_the_Law_to_Fight_Racism,_Sexism_Under_Trump_&_Won⠀⇛


                       We speak with Dahlia Lithwick, who covers the
                       courts and the law for Slate, about women who
                       fought the racism, sexism and xenophobia of Trump’s
                       presidency. She profiles many of them in her new
                       book, “Lady Justice: Women, the Law, and the Battle
                       to Save America.” “Law is slow and takes a long
                       time, but at its best, it really can make us all
                       freer and safer and restore dignity to those that
                       have been harmed,” says Lithwick.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ The Nation ☛ Who_Owns_the_Internet?⠀⇛


                       What is the Internet, and who owns it? These are
                       not simple questions; their boundaries are muddy.
                       Most people would agree that the Internet
                       encompasses physical infrastructure and physical
                       networks—the satellites, radio towers, and fiber-
                       optic cables, aboveground and underwater, that
                       connect our devices—but does it not also refer to
                       the content they carry? And how can one
                       meaningfully distinguish between that content and
                       the servers that host it; the software that
                       translates it into legible form; the eyes and ears
                       that consume it; the hands that build and maintain
                       it? US Senator Ted Stevens was once mocked for
                       describing the Internet as “a series of tubes,” but
                       his metaphor was about as accurate as one could
                       hope for in so few words. The only trouble is that
                       it’s hard to say where the tubes begin and end.


                # ⚓ India Times ☛ Five_things_to_know_about_the_UN_telecoms
                  agency⠀⇛


                       Here is a look at the oldest agency in the United
                       Nations fold, which behind the scenes sets the
                       global standards underlying mobile phones,
                       television and the [Internet].


                # ⚓ Techdirt ☛ US_Treasury_Department_Moves_To_Protect_Internet
                  Access_For_Iranian_Citizens⠀⇛


                       Information wants to be free and it is never freer
                       than when it traverses the internet. That’s why so
                       many autocratic leaders strive to shut down this
                       essential connection. It allows governments to
                       control narrative and control citizens. Limiting
                       their communication options means it will be the
                       government’s view that prevails.


          o § Monopolies⠀➾


                # ⚓ Computer World ☛ Mozilla:_Apple,_Google,_and_Microsoft_lock
                  you_into_their_browsers⠀⇛


                       Mozilla researchers found each platform maker
                       “wants to keep people within its walled garden” by
                       steering mobile and desktop users to Apple Safari,
                       Google Chrome, or Microsoft Edge. “All five major
                       platforms today (Google, Apple, Meta, Amazon,
                       Microsoft) bundle their respective browsers with
                       their operating systems and set them as the
                       operating system default in the prime home screen
                       or dock position,” Mozilla wrote in a 66-page
                       report.


                # ⚓ Five_Walled_Gardens:_Why_Browsers_are_Essential_to_the
                  Internet_and_How_Operating_Systems_Are_Holding_Them_Back⠀⇛


                       Mozilla has published new research into how
                       consumers across a number of different countries
                       and continents install and use browsers. It shows
                       the importance of web browsers to consumers, with
                       the vast majority of people surveyed using them
                       each day. It also shows that although many people
                       report knowing how to install a browser in theory,
                       lots of people never actually install an
                       alternative browser in practice. A similar trend
                       can be seen between the number of people reporting
                       to know how to change their default browser versus
                       the number who do this in practice. Crucially,
                       people raise concerns about privacy and security,
                       but they similarly fail to act on these concerns.


                # ⚓ Five_Walled_Gardens:_Why_Browsers_are_Essential_to_the
                  Internet_and_How_Operating_Systems_are_Holding_Them_Back
                  [PDF]⠀⇛


                       This report has two purposes: first, to present
                       Mozilla’s research (both recent surveys and years
                       of knowledge) into consumer interaction with
                       browsers. Secondly, to highlight the foreclosure of
                       browser engines and independent browsers by
                       operating systems. Part 1 of the paper is about
                       operating systems, browsers, browser engines and
                       how consumers behave. Part 2 highlights the online
                       choice architecture practices by operating system
                       providers which we believe have shaped consumer
                       browser usage away from independent browsers.


                       The research we are releasing with this report
                       paints a complex picture with many paradoxes:
                       people say they know how to change their browser,
                       yet many never do. Many people believe they can
                       choose their browser, yet they have a bias towards
                       software which is pre-installed, set to default and
                       difficult to change. In fact, their browser choice
                       on desktop computers has been thwarted for many
                       years, and it has never truly existed on mobile
                       devices. Our research corroborates what many
                       regulators have already noticed: software can be
                       designed to influence or even manipulate consumer
                       outcomes. And operating systems are designed to
                       maximize usage of their affiliated browsers.


                # ⚓ Techdirt ☛ Rep._Ken_Buck’s_Irrational_Spite_Of_Tech
                  Companies_May_Have_Screwed_Up_Another_Antitrust_Bill⠀⇛


                       It’s kinda weird how the GOP’s pure hatred and
                       spite towards tech companies, and their desire to
                       exact maximum punishment rather than make good
                       policy, keeps blowing up bills that might otherwise
                       pass. We’ve talked plenty about how Republicans
                       have effectively torpedoed the big tech antitrust
                       bill by insisting that it must include provisions
                       that will be used to sue tech companies over
                       antitrust for… suppressing disinformation. And then
                       there was Ted Cruz (at least temporarily) blowing
                       up a (terrible) journalism antitrust bill by
                       bringing content moderation into it.


                # ⚓ Techdirt ☛ Google_Tries_To_Fend_Off_Telecom_Backed_‘Big
                  Tech_Tax’_In_EU⠀⇛


                       We just got done noting how the European Union,
                       prompted by regional telecom monopolies, has been
                       seriously pushing for a new tax on big tech to fund
                       broadband. For decades, telecom giants have
                       lustfully eyed big tech ad revenues. They’ve then
                       convinced politicians that the best way to fix the
                       “digital divide” (lack of broadband) is by taxing
                       tech giants, which telecom giants (falsely) claim
                       get a “free ride.”


                # § Copyrights⠀➾


                      # ⚓ The Atlantic ☛ Hollywood_Learned_All_the_Wrong
                        Lessons_From_Avatar⠀⇛


                             That is a myopic reaction considering the
                             fact that the biggest hit of all time was a
                             wholly original film. Sure, Avatar’s story of
                             a human interloper ingratiating himself with
                             an alien tribe is reminiscent of earthbound
                             epics like Dances With Wolves or The Last of
                             the Mohicans, but Cameron’s movie isn’t
                             directly adapted from any prior work. And yet
                             Hollywood has mined every avenue of
                             intellectual property imaginable over the
                             past decade-plus, surely thinking that the
                             better-known the title, the less risk there
                             is sinking hundreds of millions into making
                             and marketing it. I’ve always been amused at
                             the ironic notion that Avatar had no cultural
                             impact because nobody can name its main
                             character; maybe that’s because the story
                             hasn’t been crammed down viewers’ throats
                             year after year since its release.


                      # ⚓ Torrent Freak ☛ Teen’s_Destiny_2_Cheat_Strategy_Gifts
                        Bungie_Unlimited_Lawsuit_Ammo⠀⇛


                             A teenager who allegedly threatened staff at
                             Bungie and cheated in Destiny 2 is facing
                             fierce opposition as he attempts to dismiss a
                             lawsuit filed by the developer. Bungie says
                             the defendant doesn’t understand the scope of
                             the DMCA and by declaring Bungie’s software
                             license void due to his age, even more
                             copyright claims are on the way.


                      # ⚓ Torrent Freak ☛ Liverpool_and_Manchester_United_Team
                        Up_to_Beat_Counterfeiters⠀⇛


                             Liverpool and Manchester United are arch
                             rivals on the field but in U.S. federal court
                             they have teamed up to fight a common enemy.
                             Together with Tottenham Hotspur, the English
                             football clubs are taking a stand against
                             counterfeiters selling infringing products
                             through Alibaba, Amazon, eBay, Wish, and
                             other stores, seeking millions in damages.


                      # ⚓ Creative Commons ☛ UNESCO_MONDIACULT2022:_A_Starting
                        Point_for_Open_Culture⠀⇛


                             It was in 1982 that the Mexico City
                             Declaration on Cultural Policies defined a
                             path for culture to become a fundamental
                             pillar of development. 40 years on, culture
                             now underpins all 17 of the United Nations
                             Sustainable Development Goals (SDGs), and
                             calls are being made to make culture a
                             sustainable development goal in itself. We
                             agree with UNESCO that “culture is the bridge
                             between peoples and countries… and the key to
                             unlocking mutual understanding and
                             reinforcing global action based human rights
                             and respect for diversity.”


    * § Gemini* and Gopher⠀➾


          o § Politics⠀➾


                # ⚓ My_Chrissy_Teigen_Moment⠀⇛


                       I have no idea who Chrissy Teigen is and I’m not
                       interested to know. As Saayaa put it, it’s the
                       whole point of calling this kind of moment :
                        realizing you have missed some news and that you
                       are happy about it!


                       [...]


                       I’m a knowledge freak. I want to know it all about
                       everything. All the time. As soon as I learn about
                       a subject that I didn’t know previously, I will
                       spend at least one hour exploring it, reading
                       wikipedia pages about it just to get a big picture
                       of said subject, trying to find a reference book
                       and ordering it.


                # ⚓ The_Party_of_Fiscal_Responsibility⠀⇛


                       The GOP a.k.a. Republicans are lying about being
                       “small government” and “fiscally responsible”.


                       “Fiscal” means related to managing a country’s
                       financial resources.


                       The GOP is the party of enriching the ultra-rich at
                       the expense of the working poor and even the middle
                       class (and while, contrary to the “working class
                       MAGA” popular perception, GOP-voting households
                       average higher income than supposedly “elite”
                       Democrat voting households, the difference is only
                       around 15% meaning that these families are getting
                       just as exploited by the lobbyists and PACs).


          o § Technical⠀➾


                # ⚓ A_Mod_For_OpenTTD⠀⇛


                       Thankfully this can be amended by writing a mod of
                       a type called NewGRF (New Graphic Resource File).
                       There are several tools available for doing this.
                       The first I tried was TrueGRF, which is a web based
                       tool with a lovely and usable interface. It really
                       was a joy to work with.


                # § Internet/Gemini⠀➾


                      # ⚓ Re:_Re:_Sneakernets⠀⇛


                             I read ew0k’s post about Sneakernets and it
                             made me think about the wonderful time I
                             happened to grow up in.


                             In middle school I was connecting to a local
                             BBS (Cherryland BBS in Sturgeon Bay, Wi). I
                             had to sneak over to my grandfather’s
                             construction company at night to get access
                             to his better phone system, he had free long
                             distance while we did not. Dialed in, read
                             some posts, sent some messages and started
                             the download of a game or app and let the
                             system run through the night as it was
                             sloooooow.


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


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