𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, November 12, 2021
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Generated Sat 13 Nov 02:40:37 GMT 2021
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2021/11/12/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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QmT9Hh5LgzS2eg26pkvFLpdGLNAEURRLod8DffDCczhxy1
QmdEutfCAc7HzKtnLt7k7b2dajGSqfBSGnEPAuD2bontJM
QmSuWrcnwPk5e1gVWiJbTq7uxUkNn8DzRVm659JmGTFR5W


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

⦿ EPO Dictatorship Coming Home to Roost | Techrights

⦿ IRC Proceedings: Thursday, November 11, 2021 | Techrights

⦿ Microsoft Updates Windows 11 to Stop People From Escaping Edge with EdgeDeflector | Techrights

⦿ Archiving Web Sites to Ensure They Last Decades, Not Years, Outliving or Outlasting Various Disruptive Events | Techrights

⦿ [Meme] Need New Hardware to Work for EPO | Techrights

⦿ The Central Staff Committee of the EPO Has Just Alleged That EPO Management Discarded All Input From Staff Representatives While Monetising the Pandemic | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/11/12/epo-telemetry-dictatorship/#comments
		http://techrights.org/2021/11/12/irc-log-111121/#comments
		http://techrights.org/2021/11/12/microsoft-abuses-linger-on/#comments
		http://techrights.org/2021/11/12/preserving-information/#comments
		http://techrights.org/2021/11/12/spyware-from-the-epo-and-microsoft/#comments
		http://techrights.org/2021/11/12/staff-representatives-and-ignorant-management/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/11/12/alpine-3-14-3/#comments
		http://techrights.org/2021/11/12/freebsd-12-3-rc1/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 63

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/12/epo-telemetry-dictatorship/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/12/epo-telemetry-dictatorship/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EPO_Dictatorship_Coming_Home_to_Roost⠀✐


Posted in Europe, Patents at 12:30 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 09e423c77322b2113b6910f966c5a67a


http://techrights.org/videos/epo-telework-tyranny.webm


Summary: Team Battistelli continues to crush EPO staff, having chased the staff
to their own homes where the oppression is nowadays done remotely and digitally
and is worse than ever before; the video above explains my personal views on
the current situation, which EPO management wants to ‘normalise’ by purely
political means, not_legal_means


HAVING just_published a new document, which circulates today among EPO staff,
we thought we should take a moment to explain what António_Campinos is really
doing. I speak a lot from personal experience.


“All in all, the experience can be severely worsened by a pandemic, but the
media and corporations (which own much of the media) like to paint home working
as a gift and casually frame it as an act of generosity.”Perhaps by sheer
coincidence, I have a story to tell that’s as recent as last night. I went to
sleep at 4:50AM instead of 1:30AM, so I’m very tired today, to the point where
I ended up taking a short nap on the chair a few hours ago. As explained in the
video above, a colleague did not show up (for me to hand over to) and I could
not reach the line manager or the CEO, who are in different time zones. With
many phones turned off, it’s even worse when there’s no 9-to-5 window. On top
of this, I needed to cope with obnoxious spam callers from the US, dealing with
clerical work because there’s nobody at the office (we closed it in July last
year due to the pandemic). Those calls typically get redirected to lesser-
technical or non-technical people who are no longer employed by us. All in all,
the experience can be severely worsened by a pandemic, but the media and
corporations (which own much of the media) like to paint home working as a gift
and casually frame it as an act of generosity. It might, at least at first,
seem that way; later on cuts can follow (sick leave, increments, access to
meals/canteens, car/petrol allowances), so it’s clearly just a passage of
capital to the “management class”, it’s hardly about anyone being generous,
except perhaps workers, who are still willing to work without prior benefits.


“ILO-AT will never be able to respond to such abuses in a timely fashion.”Weeks
ago we published other videos and more lengthy articles about what it means to
work from home [1, 2, 3]. It’s not a picnic and the management likes to exploit
the changes to bypass workers’ rights or labour regulations, filling up legal
vacuums with abuses that are convenient to the managers (including imposing
malicious technology on all staff). ILO-AT will never_be_able_to_respond_to
such_abuses_in_a_timely_fashion. █



                    ䷩ 𝚕𝚒𝚗𝚎 132

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/12/irc-log-111121/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/12/irc-log-111121/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Thursday,_November_11,_2021⠀✐


Posted in IRC_Logs at 11:22 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      111121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-111121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-111121.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      111121.txt
Over HTTP:


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


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


CID                                              Description     Object type


                                                 IRC log for
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                                                 IRC log for
 QmWfrfGHE8JULJuJEsy3HQY6LnKUJsJzZNLAT3z6i78ApB #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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 Qmei4aNScyC62cPdFS3JgeyeAB6ont1ELQT568uk7g1svz (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
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                                                 IRC log for
 QmNqAv6SAQe5SFFdrKvLEysN7TM2Nx8erFQDNpNHbeAxhp #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 IRC log for
                                                 #techrights
 QmdLPsXcLabzPbUHb251rcqTpSDRWUxGjg9L5ppuSwkm3u (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmRDvU3Bb1mJHK7qGvaLg5kKvJ9tXx4qDntaaZU2EPXgnr



                    ䷩ 𝚕𝚒𝚗𝚎 261

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/12/microsoft-abuses-linger-on/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/12/microsoft-abuses-linger-on/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Microsoft_Updates_Windows_11_to_Stop_People_From_Escaping_Edge_with
EdgeDeflector⠀✐


Posted in Antitrust, Microsoft at 8:26 pm by Guest Editorial Team


Guest post by Ryan, reprinted with permission from the_original


Enough people wanted to ignore Microsoft Edge, a browser so weak that only
about 4% of the web uses it despite being the default in Windows, that
Microsoft now resorts to dirtier tricks than ever.


Microsoft tried telling you Firefox and Chrome are dangerous.


They tried having Edge “accidentally” steal back default browser status.


Now they make you manually specify your default browser in dozens of places,
and then hard code Windows 11 to ignore it anyway and open stuff in Edge.


A guy named Daniel Aleksandersen wrote a program called EdgeDeflector to deal
with this annoyance from a former monopolist that can’t come to terms with
being an also-ran in the current consumer and professional OS market place
(having lost to Linux, Android, Chromebooks, and Macs….Windows is still big,
but the bathtub drain stopper has been unplugged and they now panic).


If you don’t count mobile devices, Microsoft has, at most, an_80%_market_share
in_PCs(even if you’re willing to accept the friendliest turf to Microsoft I
could find, as of late last year, even IDC and a Windows blog that doesn’t
mention desktop GNU/Linux can’t save them, and the article mentions a dead
project that was picked over to create “Windows 11”), but can’t manage to
convince 5% of the web to use Edge.


They went from being a juggernaut that you could barely escape, with 98% for
both categories, to this, and it’s not getting better for them.


Even Windows users (who often got stuck with the check for it as part of the
computer even though it is unreliable, horrendously bloated, and nasty) don’t
want it. And they’ve gotten used to using Microsoft’s browser once to download
something else, and then paying it no mind ever again.


It seems that enough people installed EdgeDeflector that it caught Microsoft’s
attention, so they_changed_how_the_OS_works_so_there’s_no_way_to_redirect_URLs
that_they_force-open_in_Edge_anymore.


At least not without ripping out Edge itself and putting in a “fake Edge” that
intercepts things that way, and Aleksandersen says he’s not prepared to go
there.


Remember that if you use GNU/Linux, you can install any browser you want and
there’s one setting that makes anything you want to use the default.


For some reason, the Micro-softies think you’ll install their keylogging
spyware, Edge, in “Linux”… Hard pass.


They_might_have_Mozilla_too_captured_to_do_anything_about_this, but hopefully
their real competitors (Jon_von_Tetzchner_of_Vivaldi_isn’t_happy) raise hell
and file lawsuits. Even if not, perhaps it will finally piss people off enough
that they go chill out on an OS that doesn’t treat them like livestock.


On GNU/Linux I think I have like 9 web browsers, and none of them have food
fights, and Debian certainly doesn’t steal my defaults and give them to
something I can’t even remove. █


                      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Ryan's Debian⦈
                   *Laughs in “Doesn’t need EdgeDeflector”*


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡴⣶⣤⣦⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 380

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/12/preserving-information/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/12/preserving-information/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Archiving_Web_Sites_to_Ensure_They_Last_Decades,_Not_Years,_Outliving_or
Outlasting_Various_Disruptive_Events⠀✐


Posted in Site_News at 3:04 pm by Dr. Roy Schestowitz


Video_download_link | md5sum b29da11a5ae25c7597c459e8e4c320b2


http://techrights.org/videos/archiving-techrights-site.webm


Summary: Today we upload 15 years’ worth of blog posts to the Internet Archive
(IA), or close to 32,000 stories along with Daily Links; we suggest that other
sites do the same in order to tackle ‘Internet rot’ and preserve information
(otherwise there’s room for obscene revisionism)


THE INTERNET won’t stay around forever. The Soviets, back in the old days,
tried to develop something similar to it. The Internet will probably survive
the next decade or two, but fifty years is a stretch; as for the World Wide
Web, it has already devolved into a transport layer for JavaScript and DRM,
having been rendered bloated and malicious in practice (albeit not in theory;
one can still produce elegant Web sites).


Earlier this year we moved to Gemini and more than a year ago we adopted IPFS,
which is used to circulate daily bulletins and IRC logs in a decentralised
fashion. Our IRC channels all became self-hosted (in our network) earlier this
year — an ambition that we’ve had for years but didn’t get around to until
Freenode collapsed.


Archiving a Web site isn’t the same as format changes and protocol changes.
It’s also not about making more copies, especially if those copies are as
vulnerable to censorship as one another. Here in this site we have some public
domain (PD) works that are of relevance to us and can be accessed in gemini://.
Most of the works, however, use a Creative Commons licence. We are not a
curation site per se, but it helps to keep copies of historical material, such
as antitrust material demonstrating Microsoft’s crimes (as tactics barely
change over time). Well, by Internet standards we have enjoyed a long span of
15 years (articles and daily links) and we remain active on the daily basis.
The same is true for Tux Machines, which turns 18 this coming summer, so a lot
of the material we have here is no longer available anywhere else, except the
Internet Archive (IA).


A few years ago we started making site archives in IA and we also recommended
the site to people, dubbing it the most important site on the Web. It’s no
eternal site however; as an associate of ours explains, “the IA is very
important but it will succumb as the WWW is phased out in favor of obfuscated,
proprietary JavaScript.”


IA can barely cope with (e.g. spider/index/save/navigate) many of the “modern”
Web. When you add DRM to the mix (EME), then it’s not a “format-shifting’” task
as that too becomes an impossibility. Sites need to evolve or perish, which may
mean getting off the Web and one day planning for the demise of the Internet as
a whole. Like IA, our associate explains, “archive.is is interesting, but it’ll
die one day. In the long run they will all pass away. In formal archives, one
of the initial decisions the institution has to make about any given artifact
is that of how long it shall be preserved for. Nothing lasts forever, but there
are ways of stretching things out and the duration determines the methods of
preservation.”


For a site such as ours it makes sense to keep the material available for 50
years, which is maybe how much longer I can live (if I’m lucky).


“Media shifting will obviously be involved,” the associate notes, “but at a
loss for some items. The plan pre-dates AWA by a great many years.”


Last weekend we turned 15. “Already in 15 short years,” our associate remarks,
“many whole sites are gone. And of the sites that remain, many have lost all
their old articles in clumsy reorgs. Of that which is left, some of those have
purged documents with “inconvenient” messages or themes… even Groklaw purged
its comments. I suppose few to none of the Groklaw comments made it into the
Library of Congress archives.”


At the time of writing I’m still uploading 205_MB_of_archives (as shown in the
video above). We hope it can inspire other sites to think ahead and do the
same. It’s not a big task and it’s better done before it’s “too late”…


Our associate concludes by saying that “many programmers and even engineers are
conscientious in erasing anything “old” even important records. Now with
electronic media, there is often only a single copy of anything any more and
that introduces, obviously, a single point of failure. So in the old days, one
could maintain a relevant personal or professional archive. Now those are all
centralized and continue to exist only at the whim of participant consensus.
Anyone with administrative privileges, can “tidy” up and easily erases the
world’s last copy of a standard or other evidence or similar material.”


We are going to add more material to IA and it_can_be_found_here_as_that_piles
up along with some material that isn’t ours. █



                    ䷩ 𝚕𝚒𝚗𝚎 496

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/12/spyware-from-the-epo-and-microsoft/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/12/spyware-from-the-epo-and-microsoft/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Need_New_Hardware_to_Work_for_EPO⠀✐


Posted in Deception, Europe, Microsoft, Patents at 10:08 am by Dr. Roy
Schestowitz


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇I need more RAM to run all this spyware from the EPO and
                                  Microsoft⦈
                          This is no laughing matter


Summary: Under the stewardship of Chairman Josef Kratochvíl (Czech Republic)
and his deputy Borghildur Erlingsdóttir (Iceland) serious_violations_of_privacy
(if not espionage) occur at the EPO and instead of tackling the issue they’ve
been working hard on covering the whole thing up


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⢿⢟⡛⣛⣛⣛⣛⣛⣛⡛⣛⣛⡻⣿⣛⣛⢛⣛⠻⣛⣛⠟⣛⣛⡻⣛⣛⣻⣟⣛⣛⠿⢛⣛⠻⣛⡛⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⢸⣿⢸⢸⣷⣿⢸⣿⣉⢾⣏⡁⣿⢹⡇⣿⢹⣿⣼⣿⢸⣿⣿⡇⣿⣹⡇⣿⣏⢹⠇⣿⣹⠇⣾⢿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⡀⠀⠀⠀⢀⠂⡦⡀⠀⠀⠀⠠⠄⠀⠀⠀⢸⣿⠀⢸⡟⣿⢸⣿⣁⢺⣏⡀⣿⣸⡇⠀⢸⣿⡟⣿⠸⣿⣿⡇⣿⢸⡇⣿⣏⡘⠂⣿⢸⡇⣿⢾⣇⣿⢸⡇⣿⢨⣿⣭⣽⣭⣽⠛⠛⠛⠛⠒⠀⠈⠹⣛⣿⣿⣿⣿
⣿⡇⣖⠀⠀⠀⠈⠀⠈⠁⢀⠀⡂⠠⠀⠀⠀⠀⠀⠉⠰⠈⠁⠉⠀⠉⠉⠈⠍⠁⠉⠉⠀⠀⠈⢥⠁⠉⠀⠈⠁⠀⠉⠨⠁⠈⠉⠀⠀⠉⠈⠅⠉⠈⠉⠉⠈⠡⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠀⣸⣿⣿⣿⣿⣿
⣿⡷⠿⠦⠤⠤⠤⣤⡄⣠⣤⡄⡁⠉⠁⠀⠀⠀⠉⠉⠉⠙⠉⠭⣥⣤⠉⠉⠹⠋⠩⢭⣭⣭⡉⣻⠙⠉⠩⠉⡍⠉⢙⠘⠉⠉⠉⠉⠉⠉⠋⡏⣙⣹⣯⣿⣍⣙⠁⢹⡟⣿⣿⣿⢋⠘⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿
⣿⡇⠈⠛⠉⠉⠁⠀⠙⠉⠉⠩⡧⡠⠀⠀⠀⠀⠀⠀⠐⣀⠀⠈⠉⠉⠀⠀⣠⠃⠀⠀⠀⠀⠀⣿⡀⣀⡀⢀⣀⣀⣸⣠⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⢀⣀⣀⣰⣀⣀⣀⣀⣀⣀⣀⣠⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿
⣿⣿⡏⠀⠉⠉⢁⡤⣀⠉⠀⢈⡁⡂⠈⠉⠁⡉⠉⠉⠉⢹⣻⣿⣿⣿⣟⣟⠈⣿⣿⣿⣿⣿⣻⣏⢘⣞⣿⣾⣿⣿⡂⢹⣱⣶⣶⣶⣶⣴⠉⡏⢻⣿⣿⣿⣿⡿⠁⠸⣷⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿
⣿⣿⡧⠀⠀⠀⠚⠒⠙⠀⠀⢸⡎⣄⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣘⢆⣃⣀⣀⣀⣀⣀⣿⢄⣀⣂⣐⣀⣂⣠⢸⣅⣐⡀⣀⣀⣀⣠⢇⢐⣂⣒⡐⣂⢼⡤⠤⣤⠤⡤⢤⠤⡦⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣠⠀⠀⠀⠀⡀⠀⠀⠀⢹⡇⠉⠁⠨⠿⠯⣈⡅⠁⢻⣿⣿⣿⣿⣿⡯⠸⣿⣿⣿⣿⣿⣿⣿⠈⠿⠿⠿⠿⠿⢾⠈⣽⣿⣿⣿⣿⡿⡇⠀⠸⠿⠿⠿⠿⠷⠁⠀⠿⠿⠿⠿⠯⠇⠀⠸⠿⠿⠿⠿⠽⣿⣿⣿⣿⣿
⣿⢽⠓⠿⠿⠿⠓⠃⠀⠿⠿⢿⡧⣦⡤⠤⡄⠀⢀⠠⠶⣬⡤⣤⣤⡤⣤⠼⣦⣧⣤⣤⡤⣤⠤⡽⣤⣤⣥⣬⣤⣥⣼⡶⣥⣤⣤⣤⣤⣤⡷⣦⢤⣤⣤⣤⣤⣴⣧⠤⣤⣤⣤⣤⣤⣤⠆⢤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿
⣿⣸⠒⠒⠒⠒⠂⠀⠐⠒⠐⢺⡅⡀⠿⠿⠿⠿⠿⠇⡀⠻⠿⠿⠿⠿⠯⠇⢸⡿⠿⠿⠿⠿⠽⡁⢹⠿⠿⠿⠿⠿⢿⡇⠸⠿⠿⠿⠿⠿⠇⢻⠸⠿⠿⠿⠿⠿⡇⠀⠿⠿⠿⠿⠿⠟⠀⠸⠿⠿⠿⠿⠷⣿⣿⣿⣿⣿
⣿⣿⢠⠀⠀⠀⣾⡳⣆⠀⠀⢤⡷⢷⢬⢤⣥⣬⣤⡥⣽⣶⣤⡥⣠⣤⣤⡜⢿⣧⣬⣤⣥⣬⣤⡷⢾⣾⢷⠿⡾⢵⢿⡗⡶⢶⠶⣶⣖⣲⠖⢿⠒⣒⣒⣒⣒⡒⡧⠐⠖⢒⣒⣒⠒⠺⢲⠒⣒⣒⣒⣒⣒⣿⣿⣿⣿⣿
⣿⣿⠘⠠⠀⠀⠀⠀⠀⠀⠀⢤⠉⠄⠯⠿⠿⠿⠿⠇⠀⠻⠿⠿⠿⠿⠯⠇⢸⡿⠿⠛⠻⠿⠿⢇⢸⠋⠛⠛⠛⠋⠙⡇⠀⠉⠐⠚⠓⠂⠀⠸⠘⠛⠛⠛⠛⠓⡇⠀⠀⠀⠒⠓⠀⠀⠀⠂⠓⠛⠛⠛⠓⢻⣿⣿⣿⣿
⣿⡿⢀⡄⠠⠤⠀⠀⢠⠴⠦⢤⠺⠾⣒⣒⣀⣀⣀⡒⠶⣔⣖⣒⣒⣒⣲⠺⢿⠗⠒⠒⠒⠒⠒⢿⢾⠒⠒⠒⠒⠒⠒⠏⡗⣒⣒⣖⣲⠒⠺⢿⢲⣖⣤⣤⣤⣶⡍⠐⢲⣦⣤⣤⣴⣦⠍⠂⠒⠀⠀⠠⠀⢼⣿⣿⣿⣿
⡇⣇⣀⣀⣀⣀⠀⠀⢈⣀⣀⡜⠀⠄⠿⠿⠿⠿⠷⠇⠄⠀⠘⠛⠛⠛⠒⠀⠸⠁⠀⠐⠊⠐⠀⢹⠈⠀⠀⠀⠂⠀⠀⡁⡃⠚⠛⠛⠛⠒⠂⠈⠀⠛⠛⠛⠛⠛⣃⠀⠘⠉⠛⠛⠋⢉⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿
⡇⡇⠀⠀⠀⠀⠀⣄⡀⠀⠀⠁⠈⠊⠒⠒⠀⠐⠒⠒⠋⠔⠒⠒⠒⠒⠒⠂⢨⡑⠖⠒⠒⠒⠖⠊⢅⢒⣻⣀⠄⠰⠒⡛⠋⠩⠋⠍⠍⠋⠓⢚⢩⣭⣤⣬⣭⣭⡛⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠀⠀⠀⠈⠀⣿⣿⣿⣿
⡇⠃⠀⠀⠀⠘⠗⠊⠃⠀⢀⣈⣀⢀⣤⣀⠀⢀⣀⣀⢀⡀⣀⢀⡀⣀⠀⠀⣀⡁⢀⡀⢀⣀⠀⢀⣈⣁⢉⡋⣀⢀⡀⢃⣤⡀⠀⣀⣤⡀⣀⣀⡈⣙⢋⣉⡙⣉⡁⣀⢀⣀⡀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⡇⣿⠀⢸⣧⣿⢸⡇⣿⢸⣿⣿⠀⢸⡟⣷⢸⡇⢸⣿⢐⠂⢹⡇⢸⣧⣿⢸⡇⠻⣯⡉⠀⠿⣮⡁⣿⣼⡇⢿⡿⢸⣇⣿⣿⡿⣼⢿⡇⣿⣿⡇⣿⣧⠈⠉⠉⠉⠉⠀⣽⣿⣿⣿
⡇⠀⠖⠂⠚⠒⠈⠀⠚⠛⠃⣿⠇⠸⣧⡿⠀⢸⡇⣿⠸⣧⡿⢸⡏⣿⠀⢸⡟⣿⢸⣧⣼⣿⡌⠀⢸⡇⢸⡇⣿⢸⡇⠻⣿⡿⠀⢿⣼⠇⣿⠀⠀⢸⡇⠘⣿⡇⣿⡇⣿⢻⣧⣿⢿⡇⣿⣧⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿
⠇⠀⠀⠀⠀⢠⣤⣄⣬⣄⠀⣠⣤⡀⣤⡌⣬⡔⠀⣤⣤⣤⣬⣥⡄⣤⡌⠒⣤⣤⢠⣤⣔⢒⣤⣔⢳⠎⣥⡔⢢⡄⣤⢡⣤⣌⠻⢡⣤⢠⣤⢈⣭⢁⣤⣅⢠⣤⣄⢀⣤⣄⢂⣤⣄⢀⣤⣄⠀⣤⣤⣤⣤⡄⣸⣿⣿⣿
⡀⠀⠀⠀⠀⢸⣧⣼⣿⣿⣻⣿⣿⡇⣿⣷⣿⡇⡀⢸⡇⢸⣿⣿⡇⣿⡄⠃⣿⣧⢸⣧⡿⢸⡇⣿⠀⢰⡟⣿⢸⣿⣿⢸⡇⣿⠀⢸⣿⣿⣿⢸⣿⢸⡇⠛⢸⣧⣿⢸⡇⣿⠘⢷⣭⢸⣿⣿⡇⣿⡄⢸⡇⣐⣛⣻⣿⣿
⣿⣿⣿⣿⣿⠸⠇⡸⠿⠸⠏⢿⡿⠃⠿⠻⠹⠇⠇⠸⠇⠸⠿⠿⠇⠿⠬⠀⠿⠷⠸⠷⢰⡸⢧⠿⢀⠸⠟⠿⠸⠏⠿⠸⠧⠿⢀⠸⠇⠿⠿⠸⠿⠸⢧⠿⠸⠇⠿⠘⢧⡿⡘⢿⡿⠛⢿⡿⠃⠿⣸⡸⠇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 551

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/11/12/staff-representatives-and-ignorant-management/#comments
    Gemini version at gemini://gemini.techrights.org/2021/11/12/staff-representatives-and-ignorant-management/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_Central_Staff_Committee_of_the_EPO_Has_Just_Alleged_That_EPO_Management
Discarded_All_Input_From_Staff_Representatives_While_Monetising_the_Pandemic⠀✐


Posted in Deception, Europe, Finance, Patents at 7:49 am by Dr. Roy Schestowitz


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


Summary: The EPO, which grants lucrative ‘pandemic monopolies’, is saving costs
(reducing expenses) by lowering salaries while turning people’s homes into
improvised ‘offices’; in other words, the pandemic is being exploited by EPO
raiders; they’re using it to increase profits and reduce Office expenses (at
staff’s expense) in defiance of staff’s wishes


The subject was mentioned here several times earlier this month (at least
thrice [1, 2, 3]). We don’t want to risk repeating what was already said.
“Despite our submissions,” says the Central Staff Committee (CSC), “the
administration has not brought any of the proposed amendments to the Circular.”
The document [PDF] is dated yesterday and it’s 11 pages in length. As usual,
the meeting with Staff Representatives (SRs) is intended to only give a false
illusion — fiction to put it another way — that there’s staff involvement in
decision-making. There’s no dialogue, it’s just theatrics. The document
contains quite a few tables, so we’re not converting the PDF into simplified
HTML this time around.


A video will soon follow (it takes hours to transcode and upload). █


“Staff at the European Patent Office went on strike accusing the organization
of corruption: specifically, stretching the standards for patents in order to
make more money.


“One of the ways that the EPO has done this is by issuing software patents in
defiance of the treaty that set it up.”


                                                              –Richard_Stallman


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

                    ䷩ 𝚕𝚒𝚗𝚎 1709

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_12/11/2021:_AlmaLinux_8.5_and_Alpine_3.14.3⠀✐


Posted in News_Roundup at 9:39 pm by Dr. Roy Schestowitz


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    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ Kubernets_Blog:_Dockershim_removal_is_coming._Are_you
                  ready?⠀⇛


                       Last year we announced that Dockershim is being
                       deprecated: Dockershim Deprecation FAQ. Our current
                       plan is to remove dockershim from the Kubernetes
                       codebase soon. We are looking for feedback from you
                       whether you are ready for dockershim removal and to
                       ensure that you are ready when the time comes.
                       Please fill out this survey: https://forms.gle/
                       svCJmhvTv78jGdSx8.


                       The dockershim component that enables Docker as a
                       Kubernetes container runtime is being deprecated in
                       favor of runtimes that directly use the Container
                       Runtime Interface created for Kubernetes. Many
                       Kubernetes users have migrated to other container
                       runtimes without problems. However we see that
                       dockershim is still very popular. You may see some
                       public numbers in recent Container Report from
                       DataDog. Some Kubernetes hosting vendors just
                       recently enabled other runtimes support (especially
                       for Windows nodes). And we know that many third
                       party tools vendors are still not ready: migrating
                       telemetry and security agents.


                # ⚓ Pull_container_images_faster_with_partial_pulls_|_Enable
                  Sysadmin⠀⇛


                       Have you ever wondered why it takes so long to pull
                       a container image from a container registry with a
                       container tool like Podman?


                # ⚓ What_you_need_to_know_about_cluster_logging_in_Kubernetes⠀⇛


                       Server and application logging is an important
                       facility for developers, operators, and security
                       teams to understand an application’s state running
                       in their production environment.


                       Logging allows operators to determine if the
                       applications and the required components are
                       running smoothly and detect if something unusual is
                       happening so they can react to the situation.


                       For developers, logging gives visibility to
                       troubleshoot the code during and after development.
                       In a production setting, the developer usually
                       relies on a logging facility without debugging
                       tools. Coupled with logging from the systems,
                       developers can work hand in hand with operators to
                       effectively troubleshoot issues.


                       The most important beneficiary of logging
                       facilities is the security team, especially in a
                       cloud-native environment. Having the ability to
                       collect information from applications and system
                       logs enables the security team to analyze the data
                       from authentication, application access to malware
                       activities where they can respond to them if
                       needed.


                       Kubernetes is the leading container platform where
                       more and more applications get deployed in
                       production. I believe that understanding the
                       logging architecture of Kubernetes is a very
                       important endeavor that every Dev, Ops, and
                       Security team needs to take seriously.


          o § Audiocasts/Shows⠀➾


                # ⚓ Hackaday_Podcast_144:_Jigs_Jigs_Jigs,_Fabergé_Mic,
                  Paranomal_Electronics,_And_A_60-Tube_Nixie_Clock_|_Hackaday⠀⇛


                       Hackaday editors Elliot Williams and Mike Szczys
                       get caught up on the week that was. Two builds are
                       turning some heads this week; one uses 60 Nixie
                       tube bar graphs to make a clock that looks like the
                       sun’s rays, the other is a 4096 RGB LED Cube
                       (that’s 12,288 total diodes for those counting at
                       home) that leverages a ton of engineering to
                       achieve perfection. Speaking of perfection, there’s
                       a high-end microphone built on a budget but you’d
                       never know from the look and the performance — no
                       wonder the world is now sold out of the microphone
                       elements used in the design. After perusing a CNC
                       build, printer filament dryer, and cardboard pulp
                       molds, we wrap the episode talking about electronic
                       miniaturization, radionic analyzers, and Weird Al’s
                       computer.


                # ⚓ How_To_Downgrade_Packages_In_Debian_And_Arch_Linux_–
                  Invidious⠀⇛


                       In this video, I will show you how to downgrade
                       packages in Debian-based and Arch-based Linux
                       distributions. I will be using Ubuntu and Manjaro
                       as examples. Downgrading a package is not something
                       that you will need to do very often (hopefully
                       never), but if the need arises, here’s how to do
                       it.


                # ⚓ Linux_From_Scratch:_Will_You_Compile_Or_Be_Compiled!!_–
                  Invidious⠀⇛


                       We’re in the middle of chapter 8 right now so that
                       means all we’re doing to do is compiling compiling
                       and more compiling.


                # ⚓ Gnome_Vs_System76_Scandle:_Outsiders_Perspective_#shorts_–
                  Invidious⠀⇛


          o § Kernel Space⠀➾


                # ⚓ Linux_5.15.2⠀⇛


                # ⚓ Linux_5.14.18⠀⇛


                # ⚓ Linux_5.10.79⠀⇛


                # ⚓ Linux_5.4.159⠀⇛


                # ⚓ Linux_4.19.217⠀⇛


                # ⚓ Linux_4.14.255⠀⇛


                # ⚓ Linux_4.9.290⠀⇛


                # ⚓ Linux_4.4.292⠀⇛


                # ⚓ Linux_To_Start_Seeing_Enablement_Patches_For_Intel_“Raptor
                  Lake”_–_Phoronix⠀⇛


                       Following today’s inaugural patch, over the coming
                       weeks we are expected to see Intel Raptor Lake
                       patches beginning to make it out onto the public
                       kernel mailing list for review.


                       Raptor Lake is anticipated to be the 13th Gen Core
                       processors and successor to the recently launched
                       Alder Lake processors. Previous leaks around Raptor
                       Lake have pointed to the new “Raptor Cove”
                       performance core and an improved Gracemont power
                       efficiency core. Leaks have also suggested Raptor
                       Lake S could top out at a 24 core / 32 thread
                       design. The launch of Raptor Lake is expected in
                       2022.


                # ⚓ Faster_Ceph_With_Linux_5.16_Now_That_Async_Dirops_Have_Been
                  Flipped_On_–_Phoronix⠀⇛


                       The Ceph open-source distributed storage system can
                       now enjoy better performance out-of-the-box with
                       Linux 5.16.


                       Last year with Linux 5.7 the Ceph file-system
                       driver added the feature of async directory
                       operations “dirops” and now finally with Linux 5.16
                       that is being enabled by default. After lots of
                       testing this summer on Ceph’s async dirops code,
                       the developers are comfortable enabling it by
                       default rather than requiring the “nowsync” mount
                       option.


                # § Graphics Stack⠀➾


                      # ⚓ The_Future_Is_Nowish⠀⇛


                             Zink can now run all display platform flavors
                             of Weston (and possibly other compositors?).
                             Expect it in zink-wip later today once it
                             passes another round of my local CI.


                      # ⚓ Experimental_Mesa_Zink_Code_Managing_To_Run_Wayland’s
                        Weston_Compositor_–_Phoronix⠀⇛


                             Following Mesa’s Zink OpenGL-on-Vulkan
                             translation driver finally running “glxgears”
                             in a correct and performant manner, the
                             newest milestone acheived by lead Zink
                             developer Mike Blumenkrantz is managing to
                             run Wayland’s Weston compositor.


                             With experimental, yet-to-be-merged or even
                             MR’ed code for Zink, Blumenkrantz can now get
                             the Wayland reference compositor running on
                             Zink which in turn is then running off the
                             native Vulkan driver.


                      # ⚓ Intel_Posts_Linux_Graphics_Driver_Patches_For_Raptor
                        Lake_–_Same_As_Alder_Lake_–_Phoronix⠀⇛


                             When writing this morning about intel “Raptor
                             Lake” Linux enablement to begin, I didn’t
                             expect that to bear fruit so quickly in just
                             a matter of hours… As predicted, that Linux
                             bring-up for the Alder Lake successor is
                             beginning now — and doing so at full-speed
                             with the initial Raptor Lake S (RPL-S)
                             graphics support being posted.


                             Following that early indicator today of the
                             Raptor Lake model ID being posted, Intel’s
                             graphics driver team has posted their initial
                             patches bringing up Raptor Lake S graphics
                             for their “i915″ kernel graphics driver. As
                             of writing, the Mesa Vulkan/OpenGL driver
                             user-space patches haven’t been posted but
                             are likely coming out soon.


                      # ⚓ Radeon_Software_21.40.1_Linux_Driver_Unifies_ROCm,
                        Uses_New_Driver_Distribution_Model_–_Phoronix⠀⇛


                             AMD this week quietly released Radeon
                             Software for Linux 21.40.1 as a fundamentally
                             big update for this packaged driver stack
                             targeting enterprise Linux distributions.


                             The Radeon Software for Linux 21.40.1
                             packaged driver release is their first that
                             usess unified ROCm (Radeon Open eCosystem)
                             and graphics drivers. This packaged driver
                             has integrated/unified their compute stack
                             with what is offered by ROCm compared to
                             prior releases also having still shipped
                             their legacy OpenCL/compute components.
                             Moving forward it’s all the ROCm-based
                             approach for OpenCL/compute. However, machine
                             learning users for now at least are
                             encoutaged to use the upstream ROCm packages
                             as the v21.40.1 point release hasn’t been
                             formally validated for that use-case yet.


                      # ⚓ Zink_OpenGL-On-Vulkan_Can_Finally_Render_glxgears
                        With_Great_Speed_–_Phoronix⠀⇛


                             While the Zink OpenGL-on-Vulkan code within
                             Mesa is close to OpenGL 4.6 conformant and
                             running many OpenGL games at good
                             performance, it’s taken until now to see good
                             performance out of the glxgears benchmark.


                             It took a long time for glxgears to even
                             render correctly on Zink even when it was on
                             to running various demanding OpenGL Linux
                             games… It was just earlier this year Zink
                             correctly rendered glxgears but was doing so
                             incredibly slow.


                      # ⚓ AMDGPU_Linux_Driver_Preparing_To_Enable_DSC-Over-eDP
                        For_More_Power-Savings_–_Phoronix⠀⇛


                             While the AMD Radeon “AMDGPU” Linux kernel
                             graphics driver has supported VESA Display
                             Stream Compression (DSC) over DisplayPort
                             connections, until now it hasn’t supported
                             the power-savings feature for eDP panels.


                             Since Display Stream Compression 1.1 the
                             specification has supported Embedded
                             DisplayPort for reducing the amount of data
                             transferred and in turn reducing system power
                             consumption and helping battery life on
                             laptops.


                             Finally the AMDGPU Linux kernel driver is
                             preparing to enable Display Stream
                             Compression for the eDP interface.


          o § Applications⠀➾


                # ⚓ Linux_users:_These_text-based_file_managers_are_overlooked
                  gems⠀⇛


                       Terminal-based file managers may seem like relics
                       of ancient times, but even in this age of
                       touchscreens, nothing can handle hundreds of files
                       more efficiently. Besides, a terminal may still be
                       your only option to work on remote servers or
                       recover your files after a system crash.


                       Two file managers for Linux that deserve more
                       coverage are nnn and ranger. These file managers
                       are made for terminals, but they’re also usable
                       with a mouse and available as binary packages for
                       most Linux distributions.


          o § Instructionals/Technical⠀➾


                # ⚓ What’s_the_difference_between_a_desktop_environment_and_a
                  window_manager_in_Linux?⠀⇛


                # ⚓ Zabbix_5.4_–_MariaDB_–_Centos_8⠀⇛


                # ⚓ Install_TaskBoard_with_Apache_and_let’s_Encrypt_SSL_on
                  Debian_11⠀⇛


                       TaskBoard is a free and open-source Kanban
                       application used to keep track of things that need
                       to get done. It is a PHP-based and self-hosted
                       application that helps you to keep track of all
                       tasks. It provides a simple and user-friendly web
                       interface for managing all your tasks. It is used
                       by teams or organizations to represent work and its
                       path towards completion.


                # ⚓ How_To_Upgrade_Ubuntu_21.04_to_21.10_via_Command_Lines⠀⇛


                       This tutorial explains step by step to upgrade an
                       Ubuntu desktop from version 21.04 Hirsute Hippo to
                       21.10 Impish Indri with command lines. You will
                       need to prepare a good internet access, enough disk
                       space, and some patience to work with it. Good
                       luck!


                # ⚓ How_To_Install_OpenNMS_on_Debian_11_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       OpenNMS on Debian 11. For those of you who didn’t
                       know, OpenNMS is an open-source and enterprise-
                       grade network monitoring and management solution.
                       It is a network monitoring application that gathers
                       critical information from local and network hosts
                       using the SNPM protocol. It can be installed on
                       Linux and Windows operating systems and provides a
                       web-based interface to monitor network traffics
                       through a web browser.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you through the step-by-
                       step installation of the OpenNMS Network Monitoring
                       Solution on a Debian 11 (Bullseye).


                # ⚓ How_To_Install_FreeIPA_Client_on_Rocky_Linux/Alma_Linux/
                  CentOS_8⠀⇛


                       In this article, we will learn how too install
                       freeipa client on Rocky Linux/Alma Linux/CentOS 8.
                       This guide will also work on other RHEL 8 based
                       systems.


                       This integrations allow a System Administrator to
                       conveniently configure the server centrally, on the
                       FreeIPA server. When a management command is
                       executed on the Client machine, the FreeIPA client
                       sends it to the server where it is executed.


                # ⚓ How_to_Setup_Anonymous_FTP_in_Rocky_Linux_8.4⠀⇛


                       FTP servers are commonly known to facilitate file
                       transfers between clients and servers. Typically,
                       ftp servers offer two types of access levels:
                       Authenticated and Anonymous. The first method
                       (Authenticated) requires a valid username and
                       password in order to access the files and
                       directories. The second method ( Anonymous) being
                       anonymous, we can download files without
                       restrictions. You can download files directly by
                       using the default user “FTP” or “anonymous”;


                       Linux has many FTP packages, but only a few have a
                       good design and provide even the most basic level
                       of security, and vsftpd is among the most secure.
                       This guide will teach you how to configure the
                       VSFTPD server to allow anonymous FTP downloads
                       without any restrictions. As part of this exercise,
                       we’ll install an FTP server on Rocky Linux 8.4.
                       However, these instructions can be adapted for
                       RHEL, CentOS, Fedora, Ubuntu, and Debian with a few
                       changes.


                # ⚓ How_to_install_Erlang_on_Fedora_35_–_Citizix⠀⇛


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


                       In this guide, we will install Erlang/OTP in a
                       Fedora 35 Server/Workstation.


                # ⚓ How_to_install_RabbitMQ_in_Fedora_35_–_Citizix⠀⇛


                       In this guide we will explore how to install the
                       latest release of RabbitMQ in Fedora 35 server or
                       Workstation


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


                # ⚓ How_to_install_Xubuntu_21.10⠀⇛


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


                # ⚓ How_to_play_911_Operator_on_Linux⠀⇛


                       911 Operator puts the player in the role of a 911
                       dispatcher for emergency lines and services. It is
                       a fun and challenging video game. It was developed
                       by Jutsu Games and published by Games Operators.
                       Here’s how you can play 911 Operator on Linux.


                # ⚓ How_to_run_Windows_11_in_a_KVM_virtual_machine_|
                  MontanaLinux.org⠀⇛


                       First of all… “What!?! An article about Microsoft
                       Windows on this Linux oriented website?!?!” Yes.
                       Hey, I’m running Windows 11 as a KVM virtual
                       machine on my Dell Latitude E6440 laptop that is 6+
                       years old… using Fedora 35 as my VM Host. I don’t
                       think Windows 11 would want to run on the physical
                       hardware either… but the method I mention should
                       make it work in many places that it would refuse to
                       because of hardware requirements enforced by the
                       installer.


                # ⚓ Arch_Linux_Install_Guide_with_GNOME_41.1_–_If_Not_True_Then
                  False⠀⇛


                       Many may think that installing Arch Linux is
                       difficult. In reality, the process is not much
                       different from installing any Linux, except that
                       the installation is done on the command line. Arch
                       Linux own installation guide is excellent, but I’m
                       trying here to explain in a little more detail how
                       the whole process goes. This is my own command list
                       for installing Arch Linux with GNOME Desktop.


                       Following this guide you can install Arch Linux
                       with GNOME 41.1 desktop, networkmanager, systemd-
                       boot, btrfs, man pages and basic devel packages. I
                       assume that you are using Linux when you create
                       your installation iso. If you use Windows, then use
                       Windows tools to create bootable USB Media.


                # ⚓ 16_Practical_and_Useful_Examples_of_Echo_Command_in_Linux⠀⇛


                       The shell commands have always been a crucial tool
                       in Linux. So learning about them gives a user fine-
                       grained control over the Linux machine. Such a
                       command of Linux bash shell is echo command.
                       However, the echo command seems to be a pretty
                       straightforward and easy one. It has a unique job
                       that cannot be done with other commands, especially
                       while writing a bash script. The echo command in
                       Linux is mainly used for printing text in the
                       console. It can show messages for the user while a
                       bash script is executing.


                # ⚓ How_to_Install_Chromium_Browser_on_Fedora_35_–
                  LinuxCapable⠀⇛


                       Chromium is an open-source browser project that
                       aims to build a safer, faster, and more stable way
                       for all users to experience the web. The Chromium
                       codebase is widely used. Microsoft Edge, Opera, and
                       many other browsers are based on the code.


                # ⚓ How_to_Install_OpenLiteSpeed_on_Rocky_Linux/AlmaLinux_–⠀⇛


                       In this tutorial guide we will learn how to install
                       Openlitespeed server on Rocky Linux/Alma Linux


                       Openlitespeed is an easy to use open source web
                       server. It offers unbeatable features and
                       performance to your website along with top notch
                       security. The server understands all the Apache
                       rewrite rules and has intelligent cache
                       acceleration features that let you implement the
                       fastest caching on your server.


                # ⚓ How_to_SSH_into_a_Docker_Container_and_Run_Commands_–
                  Unixcop_the_Unix_/_Linux_the_admins_deams⠀⇛


                       Docker is a set of platform as a service (PaaS)
                       products that use OS-level virtualization to
                       deliver software in packages called containers.


                       Docker is a utility that lets you create a
                       container for running applications. A Docker
                       container is a fully-contained virtual machine.


                       This guide will show you three methods to SSH into
                       a Docker container and run commands.


                # ⚓ How_to_Turn_Off_directory_browsing_on_Apache_and_Nginx_–
                  Unixcop_the_Unix_/_Linux_the_admins_deams⠀⇛


                       The directory content listing enabled by default
                       when you install Apache web server, This may_be a
                       desirable features in some scenarios, but it’s a
                       potential security hole in others. It’s easy enough
                       to turn this setting on or off for each website
                       (virtual host) that you have set up.


                       In this guide, we’ll show you how to turn off
                       directory browsing on Apache & Nginx web servers.


                # ⚓ How_to_install_and_Configure_Mariadb_10_in_Debian_11_–
                  Citizix⠀⇛


                       MariaDB is an open-source one of the most popular
                       relational database management system (RDBMS) that
                       is a highly compatible drop-in replacement of
                       MySQL. It is built upon the values of performance,
                       stability, and openness, and MariaDB Foundation
                       ensures contributions will be accepted on technical
                       merit.


                       MariaDB was developed as a software fork of MySQL
                       in 2009 in response to Oracle’s acquisition of
                       MySQL. MariaDB intends to remain free and open-
                       source software under the GNU General Public
                       License. It is part of most cloud offerings and the
                       default in most Linux distributions.


                       In this guide we will learn how to install and
                       configure MariaDB in Debian 11.


          o § Games⠀➾


                # ⚓ Relaxing_jelly-taming_RPG_Alchemic_Cutie_is_out_now_on
                  Steam_|_GamingOnLinux⠀⇛


                       Fancy exploring a cute pixel-art land filled with
                       wild bouncing jellies? Alchemic Cutie is a very
                       sweet casual RPG and it’s officially out now on
                       Steam. Note: key provided by the developer.


                       Developed by Viridian Software / Vakio is another
                       entry in the colourful and casual market, a very
                       welcome addition too as it’s properly wholesome.
                       Wimba Island, the place you live, is a magical land
                       filled with wild jellies. These strange creatures
                       roam the lands and your family has made a living
                       out of breeding them.


                # ⚓ Ryan_Gordon_gets_an_Epic_MegaGrant_to_further_improve_SDL,
                  helping_with_next-gen_APIs_|_GamingOnLinux⠀⇛


                       Looks like cross-platform game development with SDL
                       is going to get easier, as Ryan Gordon (also known
                       as Icculus) has confirmed an Epic MegaGrant and
                       details what it will be used for.


                       What is SDL? Simple DirectMedia Layer (SDL) is a
                       cross-platform development library designed to
                       provide low level access to audio, keyboard, mouse,
                       joystick, and graphics hardware. It is used by
                       video playback software, emulators, popular games
                       and some game engines.


                       Ryan Gordon is one of the people responsible for
                       its development, and Gordon has also ported plenty
                       of games to Linux, macOS and other platforms over
                       many years. In a new post on Patreon, a fun
                       announcement was detailed about an approved Epic
                       MegaGrant and how it’s going to be used to improve
                       SDL.


                # ⚓ Megaquarium:_Architect’s_Collection_is_out_now_with_15_new
                  animals_|_GamingOnLinux⠀⇛


                       Megaquarium: Architect’s Collection is a new and
                       exciting sounds expansion pack for the impressive
                       aquarium building game that’s now available.


                       Developed by solo-studio Twice Circled from Tim
                       Wicksteed, released originally in 2018 Megaquarium
                       is their second game following on from Big Pharma
                       in 2015. You can pick from tons of different
                       species to house in your exhibits, satisfy their
                       needs and don’t let them die, all while you try to
                       keep your guests happy and busy. This new expansion
                       gives players new ways to build up your aquarium
                       spaces with bridges, archways, tunnels and more
                       along with new creatures.


                # ⚓ Valve_Shares_New_Steam_Deck_Details,_Proton_Update
                  Available_For_Testing_–_Phoronix⠀⇛


                       Valve today hosted the much anticipated Steam Deck
                       Development Livestream where they and their
                       partners at AMD talked more about the forthcoming
                       Steam Deck’s hardware and software.


                       The recording from the livestream is embedded below
                       for those interested, but some of the key takeaways
                       from today’s developer-focused Steam Deck event
                       included…


                # ⚓ Halloween_Game_Lets_You_Shoot_Zombies_With_A_Laser-Powered
                  Crossbow_|_Hackaday⠀⇛


                       Suppose you were looking for all the essential
                       elements to make a great Halloween-themed shooting
                       game. Zombies? Check. Giant “lasers”? Check.
                       Crossbows shooting forks? We’ve got you covered.
                       Check out “Fork The Zombies“, which was set up by
                       [piles.of.spam] to entertain the neighborhood kids
                       this Halloween.


                       The game is played on a big screen, which shows a
                       horde of angry zombies marching toward the player,
                       who has to shoot as many as possible before they
                       reach the front of the screen. The weapon provided
                       is a crossbow; when the trigger is pulled, a fork
                       is launched and hopefully skewers one of the
                       ghouls. The game was written using an open-source
                       engine called Urho3D, which takes care of all the
                       hard-core 3D and physics work, allowing the user to
                       focus on designing the gameplay and visuals.


                # ⚓ Valve_Says_SteamOS_3.0_Will_Be_Available_for_Everyone_to
                  Download_and_Install⠀⇛


                       SteamOS was available to download for free, like
                       many other GNU/Linux distributions out there, and
                       you were able to install it on any machine if you
                       wanted to turn it into a full gaming computer. I
                       personally followed its development, and the latest
                       version ever released was SteamOS 2.195, more than
                       two years ago.


                       Apparently, during this time, Valve rebased their
                       SteamOS distro on Arch Linux, a powerful and
                       flexible rolling-release distribution, most
                       probably to provide users with the latest security
                       and software updates as soon as their are available
                       upstream.


                # ⚓ Forza_Horizon_5_now_runs_on_Linux,_sort_of⠀⇛


                       Forza Horizon 5 is one of the biggest games of the
                       year and has seen unprecedented player numbers and
                       rave reviews. The PC version it’s fair to say has
                       had some issues, but the fact it’s available
                       through Steam also opened up the possibility of
                       playing on Linux, and therefore Steam Deck, thanks
                       to Valve’s Proton.


                       Initially, it was a bust, but these folks don’t sit
                       still for long and already there have been some
                       positive developments. Improvements in the bleeding
                       edge versions of Proton Experimental have enabled
                       Forza Horizon 5 to be played on Linux with some
                       positive reports.


                # ⚓ Forza_Horizon_5_on_Linux?_Yeah_okay_fine,_Proton
                  Experimental_was_updated_|_GamingOnLinux⠀⇛


                       So it wasn’t enough that Age of Empires 4 from Xbox
                       Game Studios was now playable on Linux, Proton
                       Experimental has once again been upgraded to get
                       Forza Horizon 5 off the starting line. That’s
                       right, you can now play the latest (and greatest?)
                       from Playground Games and Xbox Game Studios on
                       Linux.


                       That was the single change noted in the update
                       notes from Valve for Proton Experimental for
                       November 11. It should work across both AMD and
                       NVIDIA GPUs now too, although it’s all still
                       experimental of course. Buy at your own peril for
                       now but hey — a couple days from release is pretty
                       damn good for the latest title to begin working.
                       Have to hand it to the developers at Valve and
                       CodeWeavers working on Proton, they certainly know
                       their stuff.


                # ⚓ Steam_Deck_and_Proton:_Good_&_Bad_Times_Ahead_–_Boiling
                  Steam⠀⇛


                       Steam was released as a beta for Linux nine years
                       ago. While Linux gaming was a niche within a niche
                       before that time, in the years since, gaming on
                       Linux has been only getting better and more
                       convenient. Valve released their own console-like
                       distro SteamOS in 2013, and while it was a mess,
                       distros like ChimeraOS have drastically improved
                       the quality-of-life experience of PC gaming in the
                       living room.


                       Valve brought most of their game catalog to Linux,
                       while many Linux gamers were begging developers to
                       port their games over. Some did, most of whom were
                       indie developers, and porting was made easier
                       thanks to engines like Unity and Unreal offering
                       one-click export options. Companies like Feral
                       Interactive, Aspyr, and Virtual Programming did the
                       AAA stuff, bringing titles like Borderlands 2,
                       Bioshock Infinite, the Tomb Raider reboot series,
                       the F1 series, and many more hits to our beloved
                       platform. While some of the ports were hit or miss,
                       it was awesome just seeing the splash screen for
                       GRID Autosport back in 2015 as the game was booting
                       up.


                       As it stands today, there are over 60k titles
                       available on Steam. Just a little over 9k (15% of
                       the entire catalog) are available natively for
                       Linux. In late 2017, a few months prior to the
                       announcement of Proton — a collection of tools
                       combined to create the best Windows gaming
                       experience on Linux — the number of Linux titles
                       was at its peak. Slowly over time, however, the
                       number of native titles dropped, as Proton was
                       proving to not only play many titles out-of-the-
                       box, but now game developers didn’t have to spend
                       the time and extra resources to support a secondary
                       platform when Proton took care of most things for
                       them.


                # ⚓ Live_–_Building_Gaming_Server…_for_everything!_–
                  Invidious⠀⇛


                # ⚓ Barotrauma_gets_its_biggest_discount_yet_and_a_Steam_Free
                  Weekend_|_GamingOnLinux⠀⇛


                       2D co-op submarine death simulator Barotrauma will
                       be having a big sale and a Steam Free Weekend
                       starting later today. Your chance to buddy up with
                       some friends and watch the chaos unfold.


                       Barotrauma sends up to 16 players on an underwater
                       journey in a sci-fi submarine in the oceanic depths
                       of Jupiter’s moon Europa. The crew discovers alien
                       wonders and horrors, commands various submarine
                       systems, and fights to survive dangers from both
                       outside and within. The game is continuously being
                       updated and improved.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Telegrand_is_a_Modern_GTK4_Telegram_Client_for_GNOME
                        in_Development⠀⇛


                             For Ubuntu, Fedora, and other Linux with
                             GNOME desktop, a modern GTK4 Telegram app
                             “Telegrand” is under development.


                             Telegrand is the free open-source client
                             written in Rust programming language. By
                             using libadwaita library, it has an adaptive
                             user interface to fit all screen sized.


                             Though Telegram has official app for Linux,
                             this new app is worth expecting for GNOME
                             users. As an in-development project, it isn’t
                             considered stable software yet. So far, it
                             supports log in via phone number or using QR
                             code.


          o § Distributions⠀➾


                # ⚓ 5_Lightweight_Linux_Distributions_to_Revive_Old_Computers⠀⇛


                       Many users may have a set of old computers laying
                       around, which they have accumulated over the years.
                       Instead of throwing them at the trash, you should
                       know that you can revive these old computers with
                       lightweight Linux distributions.


                       [...]


                       Now a lot of other people and websites may
                       recommend a totally different set of lightweight
                       distributions for you, but in our selection, we
                       didn’t just care for resources usage and the
                       distribution’s ability to work on old hardware.


                       Instead, we also cared for the ease of use and your
                       ability as a user to deal with the distribution on
                       daily basis to do your tasks. At the end, the goal
                       is not simply to get an old computer to just work –
                       the goal is to get an old computer to work and do
                       things that you need as someone living in 2021.


                       Remember that the definition of an “old computer”
                       varies a lot. A 2014 laptop can almost run any
                       Linux distribution released today, but a 2009 old
                       laptop? Not much. Here, we are talking about
                       hardware which is at most 10 years old.


                       So let’s end chatting… Here are our 5 most
                       recommended lightweight Linux distributions for
                       you.


                # § New Releases⠀➾


                      # ⚓ Alpine_3.14.3_released⠀⇛


                             The Alpine Linux project is pleased to
                             announce the immediate availability of
                             version 3.14.3 of its Alpine Linux operating
                             system.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ The_future_driving_is_software,_the_future_of
                        software_is_open_source⠀⇛


                             ith new entrants and incumbents enlivened by
                             technology, competition is fierce in the auto
                             industry. Yet, it’s how carmakers respond to
                             the digitization, electrification and
                             automation of how we move that will define
                             whether they still exist in a decade’s time.


                             Automakers can no longer afford to ignore the
                             reality of CASE – Connected, Autonomous,
                             Shared and Electric driving – and the way
                             it’s already reengineering the competitor
                             landscape. The pace of change is only going
                             accelerate.


                      # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2021/45_–
                        Dominique_a.k.a._DimStar_(Dim*)⠀⇛


                             Tumbleweed keeps being predictable when it
                             comes to the update cadence. This week, we
                             could publish 5 fully tested snapshots (1104,
                             1105, 1106, 1107, and 1110).


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Red_Hat_Enterprise_Linux_8.5_is_Heavily_Focused_on
                        Developers⠀⇛


                             Red Hat Enterprise Linux (RHEL) 8.5 brings
                             new features and improvements to help
                             deployments, optimize performance and help
                             risk mitigation.


                             Red Hat announced a few days ago the release
                             of the new version of Red Hat Enterprise
                             Linux 8.5. The 8.x branch, which will be
                             supported until at least 2029, is evolving
                             according to a new predictable development
                             cycle, which involves the formation of
                             releases every six months at a predetermined
                             time.


                      # ⚓ RHEL_8.5_delivers_key_container_improvements_|
                        ZDNet⠀⇛


                             Returning to RHEL basics, its web console,
                             which is based on the open-source Cockpit
                             project, now enables you to live patch the
                             kernel from it. Previously, you could only
                             keep your Linux running while updating the
                             kernel in real-time by using the shell.


                             The updated web console also includes an
                             enhanced-performance metrics page. With this,
                             you can more easily identify high CPU,
                             memory, disk, and network resource usage
                             spikes and their causes. In addition, you can
                             also more easily export metrics to a Grafana
                             server for a deeper look at what’s going on
                             in your servers.


                             Red Hat is also continuing to integrate its
                             Ansible DevOps program into RHEL. RHEL’s
                             system roles now use Ansible roles and
                             modules to configure, automate, and manage
                             RHEL services.


                      # ⚓ AlmaLinux_8.5_is_Here_for_Those_Who_Want_to_Leave
                        CentOS_Behind⠀⇛


                             AlmaLinux, the Linux distribution designed
                             specifically as a CentOS replacement, just
                             released version 8.5 as its third stable
                             release.


                             AlmaLinux OS is an open source, community-
                             governed and forever-free enterprise Linux
                             distribution. It is focused on long-term
                             stability and delivering a robust production-
                             grade platform. It is a production-ready
                             drop-in replacement for the CentOS Linux
                             distribution that will cease to be supported
                             at the end of this year.


                             AlmaLinux OS Foundation, the nonprofit that
                             stewards the community owned and governed
                             open source CentOS alternative, today
                             announced delivery of its third stable
                             release within 48 hours of general
                             availability of the upstream Red Hat
                             Enterprise Linux 8.5 release.


                      # ⚓ AlmaLinux_8.5_Is_Out,_Less_Than_48_Hours_After_Latest
                        RHEL_Release⠀⇛


                             Less than 48 hours after the release of Red
                             Hat Enterprise Linux 8.5, developers at the
                             RHEL clone, AlmaLinux, pushed their own 8.5
                             version out the door. This means there’s
                             already a drop in replacement for Red Hat’s
                             latest and greatest, ready for production use
                             without a subscription from Red Hat or anyone
                             else.


                      # ⚓ AlmaLinux_OS_8.5_Released_with_New_Repositories_and
                        SCAP_Profiles,_Updated_Components⠀⇛


                             AlmaLinux OS 8.5 builds on the changes that
                             Red Hat implemented in their Red Hat
                             Enterprise Linux 8.5 release, and also adds
                             two new repositories, including
                             ResilientStorage and Plus, as well as new
                             OpenSCAP Security Guide profiles, including a
                             new profile aligned with the Australian Cyber
                             Security Centre Information Security Manual
                             (ACSC ISM), a new STIG profile compatible
                             with server with GUI installations, and a new
                             French National Security Agency (ANSSI) high
                             level profile.


                      # ⚓ David_Cantrell:_rpminspect-1.7_released⠀⇛


                             rpminspect 1.7 is now available. This release
                             includes a lot of fine tuning and bug fixing
                             as more projects and workflows adopt
                             rpminspect.


                             The main feature present in the 1.7 release
                             is the unicode inspection. This inspection
                             has been added in response to the Trojan
                             Source vulnerabilities that were recently
                             disclosed to the public. The inspection
                             checks text files in source RPMs as well as
                             extract source archives for any files
                             containing forbidden Unicode code points. The
                             forbidden code points have to be defined in
                             the rpminspect configuration file. See the
                             data/generic.yaml file for an example
                             configuration block for the unicode
                             inspection. The code points defined there are
                             the bidirectional code points the Trojan
                             Source vulnerability discusses.


                      # ⚓ IBus_1.5.25_is_released_|_DesktopI18N’s_Blog⠀⇛


                             IBus 1.5.25 is now released and available in
                             Fedora 35.


                             # dnf update ibus


                             This release changes the default Emoji
                             shortcut key to Ctrl-period, which was Ctrl-
                             Shift-e previously, to follow GTK shortcut
                             keys. MS-Windows provides Super-period
                             shortcut key for Emoji typing and MacOS does
                             Command-Shift-space shortcut key currently.


                      # ⚓ IT_careers:_5_steps_to_get_hired_before_the_holidays
                        [Ed: IBM says, create an account with Microsoft to get
                        a job. Red Hat under IBM is not what it once was...]⠀⇛


                             One of the biggest misconceptions about job
                             searching is that hiring stops during the
                             holiday period. Job seekers often wait until
                             the beginning of the year to restart their
                             job application process, but there’s no need
                             to take a break.


                             Organizations are looking to fill open spots
                             before they close the budget for the end of
                             the year. Many are desperately looking for
                             candidates. By strategically applying for
                             opportunities during the holiday period, you
                             can increase your chances of landing a job
                             even before the start of the next year.


                      # ⚓ Video:_The_right_features_make_technology_more
                        adaptable_&_adoptable,_says_Red_Hat’s_Phil_Andrews [Ed:
                        Mostly fluff, maybe Red Hat paid for it too (IBM)]⠀⇛


                             Phil Andrews, VP and General Manager, CEMEA
                             Region, Red Hat, shares insights into the
                             findings of the latest ‘The State of
                             Enterprise Open Source’ report and calls on
                             organisations to work with the right vendors
                             to fully maximise the opportunities and
                             innovations within open source communities.


                      # ⚓ Linux_and_Cloud_Native_Security:_Red_Hat’s
                        Perspective [Ed: Red Hat is buying puff pieces (see
                        disclosure at the bottom), just like Microsoft does]⠀⇛


                             The Linux Foundation and Red Hat are sponsors
                             of The New Stack.


                # § Devuan Family⠀➾


                      # ⚓ Devuan_Chimaera_–_Back_to_the_future,_forward_to_the
                        past⠀⇛


                             The most frustrating thing about this whole
                             deal is that I wasn’t able to get to the
                             point where init matters, to see how it fares
                             and compares to systemd. But then, the live
                             system started in only about 20 seconds from
                             an ancient USB2.0 stick, not different from
                             any other distro. It was blazing fast in the
                             live session. Ugly but fast. Then, I
                             remembered. MX Linux. There’s a Debian-based
                             distro, which is fast, simple, elegant AND
                             uses init. And it boots fast and true. So I
                             can relax.


                             Back to Devuan. The experience is quite
                             similar to Debian. It’s not meant for home
                             use unless you’re willing to invest a lot of
                             energy getting everything sorted out nicely.
                             But then, at that point, you might as well
                             use a derivative distro that has been
                             polished, tweaked and made practical by
                             someone else. On top of that, Devuan wouldn’t
                             even boot after the installation, so there’s
                             very little else for me to say. Until the
                             next time.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Snapcraft_offline_mode_–_Build_snaps_while_saving
                        data⠀⇛


                             As part of the snap creation cycle, the
                             Snapcraft tool creates isolated build
                             instances inside which all of the necessary
                             work – download of sources, compilation,
                             packaging, etc. – is done in a safe manner,
                             without touching the host system. While there
                             are many advantages to the use of the virtual
                             machines (via Multipass) or containers (via
                             LXD) for these tasks, the downside is a
                             fairly liberal use of the network bandwidth
                             to setup and configure the Snapcraft work
                             environment.


                             In some scenarios, you may be constrained in
                             your available network throughput or data. To
                             help with that, the latest build of Snapcraft
                             comes with a new, experimental offline mode,
                             designed to minimize the reliance on online
                             sources, and allow you to continue working
                             and building snaps even if you have no access
                             to the network.


          o § Devices/Embedded⠀➾


                # ⚓ First_Look:_You_Can_Now_Run_Android_12_on_Your_Raspberry_Pi
                  4_Computer⠀⇛


                       Created by renowned XDA member KonstaT
                       (KonstaKANG), there’s now an unofficial LineageOS
                       19.0 build for Raspberry Pi 4 Model B, Raspberry P
                       400, and Raspberry P Compute Module 4 (CM4)
                       computers, based on the Android 12 mobile operating
                       system and, to my surprise, it runs quite well.


                       The image is distributed in the same format as any
                       other Raspberry Pi operating system, which means
                       that after you’ve downloaded the image (see direct
                       download link at the end of the article), you’ll be
                       able to easily write it on a microSD card with the
                       official Raspberry Pi Imager utility or a similar
                       tool.


                # ⚓ Rough,_tough_vehicle-mount_computer_runs_Linux_on_i.MX8M⠀⇛


                       Nexcom’s rugged, IP65 protected “VMC-220” in-
                       vehicle computer runs Linux on an i.MX8M with an 8-
                       inch, 1K-nits touchscreen, 80 dB speakers, GPS, 2x
                       M.2, M12 ports for GbE, USB, GPIO, CAN, and COM,
                       and battery and RFID options.


                       Nexcom announced a rugged vehicle mount computer
                       with an 8-inch touchscreen for vehicle fleets, port
                       warehouse management, vehicle control in mines, and
                       indoor and outdoor stacker storage vehicles used
                       for smart warehousing and logistics management. The
                       VMC-220, which follows earlier 8- and 10.4-inch
                       Nexcom VMC vehicle mount systems based on Intel’s
                       Apollo Lake, runs Linux on a quad-core, Cortex-A53
                       i.MX8M clocked at 1.3GHz. Android is available by
                       request.


                # ⚓ GL.inet_GL-S10_–_A_compact_BLE_to_MQTT_IoT_Gateway_–_CNX
                  Software⠀⇛


                # ⚓ Portwell_COM_Express_Tiger_Lake-H_module_supports_2.5GbE,
                  PCIe_Gen_4,_8K,_up_to_64GB_DDR4_–_CNX_Software⠀⇛


                       Portwell PCOM-B657VGL joins other COM Express and
                       COM HPC modules based on Intel Tiger Lake-H Xeon,
                       Core, and Celeron embeddded processors such as
                       ADLINK Express-TL and Congatec conga-HPC/cTLH.


                       Just like its competitors, the Portwell COM Express
                       Type 6 Basic module offers 8K video output, PCIe
                       x16 Gen 4, up to 64GB DDR4, USB 3.2 Gen 2, and
                       2.5GbE networking for a wide range of higher-end
                       embedded applications such as industrial
                       automation, medical equipment, graphics-intensive
                       applications, and artificial intelligence.


                # ⚓ M5Paper_Gets_Open_Source_Weather_Display_Firmware_|
                  Hackaday⠀⇛


                       We know you like soldering irons, we’re quite fond
                       of them ourselves. But the reality is, modular
                       components and highly capable development boards
                       allow the modern hardware hacker to get things done
                       with far less solder smoke then ever before. In
                       fact, sometimes all you need to finish your project
                       is the right code.


                       Case in point, check out the slick electronic paper
                       weather display that [Danko Bertović] shows off in
                       the video below. While it certainly fits the
                       description of a DIY project, he didn’t have to put
                       any of the hardware together himself. The M5Paper
                       is an ESP32 development kit designed around a crisp
                       4.7″, 960 x 540 e-paper panel that includes
                       everything from environmental sensors to an
                       internal 1150 mAh battery. To make your handheld e-
                       paper dreams come true, the only thing you need to
                       provide is the software.


                # ⚓ Palm_OS:_Reincarnate_|_Hackaday⠀⇛


                       [pmig96] loves PalmOS and has set about on the
                       arduous task of reimplementing PalmOS from scratch,
                       dubbing it Pumpkin OS. Pumpkin OS can run on x86
                       and ARM at native speed as it is not an emulator.
                       System calls are trapped and intercepted by Pumpkin
                       OS. Because it doesn’t emulate, Palm apps currently
                       need to be recompiled for x86, though it’s hoped to
                       support apps that use ARMlets soon. Since there are
                       over 800 different system traps in PalmOS, he
                       hasn’t implemented them all yet.


                       Generally speaking, his saving grace is that 80% of
                       the apps only use 20% of the API. His starting
                       point was a script that took the headers from the
                       PalmOS SDK and converted them into functions with
                       just a debug message letting him know that it isn’t
                       implemented yet and a default return value.
                       Additionally, [pmig96] is taking away some of the
                       restrictions on the old PalmOS, such as being
                       limited to only one running app at a time.


                # ⚓ Issue_#376_–_Bullseye!⠀⇛


                       My regular greeting is *finally* appropriate, as we
                       announce the latest version of Raspberry Pi OS,
                       named Bullseye. (Get it? Bullseye is the horse
                       owned by Woody in Toy Story, who is a cowboy and
                       says “howdy” all the time? Never mind.)


                       We also gave Japan the good news that a Raspberry
                       Pi 400 variant with a Japanese keyboard layout is
                       now available to buy.


                # ⚓ Arduino_Certification_Explained⠀⇛


                       It’s aimed at educators who use (or want to use)
                       Arduino kits in their middle school or high school
                       classrooms. Arduino Certification is an online exam
                       that tests your knowledge of electronics and
                       programming. Students, makers, professionals and
                       everyone in between can take the exam, too.


                # ⚓ Video:_Raspberry_Pi_OS_Update⠀⇛


                       Here’s a new video from the Raspberry Pi Foundation
                       regarding the upgraded Raspberry Pi OS that is now
                       based on Debian 11. See also the blog post on the
                       update.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Realme_announces_Android-12_based_public_beta_for
                        Realme_GT_Master_Explorer_Edition_–_Times_of_India⠀⇛


                      # ⚓ Google_Pixel_6_update_brings_fitness_features
                        unavailable_on_most_Android_phones_|_TechRadar⠀⇛


                      # ⚓ Samsung_Galaxy_S21′s_One_UI_4_(Android_12)_update
                        could_be_right_around_the_corner_|_Android_Central⠀⇛


                      # ⚓ Developer_ports_Android_12_to_the_Raspberry_Pi_4_B,
                        Pi_400,_and_Compute_Module_4⠀⇛


                      # ⚓ OnePlus_8_Android_12_beta_program_opens_up_–_Android
                        Authority⠀⇛


                      # ⚓ A_Dimensity_2000-powered_phone_is_the_first_Android
                        to_score_over_1_million_AnTuTu_points_–_GSMArena.com
                        news⠀⇛


                      # ⚓ 5_Android_settings_you_should_want_to_change_on_your
                        phone_right_now_–_CNET⠀⇛


                      # ⚓ Google_Pixel_6_Pro_deal_knocks_up_to_$800_off_the
                        Android_phone_of_the_year_|_Tom’s_Guide⠀⇛


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


                # ⚓ Top_5_Open-Source_Project_Management_Tools_for_Linux⠀⇛


                       Different project management software tools come in
                       all shapes and sizes, vary in functionality and
                       deployment models (SaaS or on-premises) but they
                       are always used to collaborate and delegate tasks
                       based on the needs of a team.


                       No matter the size of the team and its field of
                       activity, the goal remains the same – assigning
                       project roles and responsibilities to team members,
                       monitoring their progress, and managing the project
                       budget to achieve some valuable results.


                # ⚓ 16000_curl_commmits [Ed: Daniel Stenberg has let Microsoft
                  proprietary software manage his software, which is bad
                  because GitHub is run by people from the NSA]⠀⇛


                       Almost 14 months since I celebrated 15,000 commits
                       in curl’s source code repository I have now passed
                       16,000 commits.


                       My commit number 16,000 was a minor man page fix.


                       The official gitstats page shows that I’ve
                       committed changes on almost 4,600 separate days
                       since the year 2000.


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ Odyssey_1.2_released⠀⇛


                             Odyssey team is pleased to announce the
                             release of Odyssey 1.2, a scalable multi-
                             threaded connection pooler for
                             PostgreSQL\GreenplumDB designed for the
                             cloud.


                      # ⚓ PgBouncer_1.16.1_released⠀⇛


                             PgBouncer 1.16.1 has been released. This is a
                             minor release with a security fix.


                # § Public Services/Government⠀➾


                      # ⚓ In_the_spirit_of_open_government,_France_dumps_9,067
                        repos_online_to_show_off_its_FOSS_credentials⠀⇛


                             Le Gouvernement de la République française –
                             the government of France for Anglophones –
                             has published a website containing 9,067
                             repositories of FOSS software created by
                             1,022 organisations and groups in the French
                             public sector.


                             After two years of work, the site hit version
                             1.0 on Wednesday.


                             Helpfully for non-Francophones, the homepage
                             and much of the info is in English – although
                             saying that, just to warn you, the same isn’t
                             true of all the background information and
                             the various organisational pages we’re about
                             to link to.


                             The site is run by Etalab [Fr], which is a
                             department of DINUM [Fr], the
                             Interministerial Digital Directorate, and the
                             software is released under Etalab’s Open
                             License 2.0 – defined in English in this PDF
                             file.


                             The release happened as a result of a decree
                             [Fr] of Open Government [Fr] from 30 October
                             2019 after the French government joined the
                             Open Government Partnership in April 2014.


                      # ⚓ Applying_EU_Open_Source_Policy_in_the_United_States⠀⇛


                             As we reported previously, a study from the
                             European Commission investigating the impact
                             of open source software (OSS) and hardware
                             estimated that a €1 billion investment in
                             open source software resulted in an impact of
                             between €65 and €95 billion on the European
                             economy. The report also outlined extensive
                             recommendations for enabling future EU growth
                             of open source hardware and software.


                             A recent article by Frank Nagle for the
                             Brookings Institution further examines the
                             study in terms of U.S. digital infrastructure
                             and in light of the bipartisan infrastructure
                             bill.


                # § Programming/Development⠀➾


                      # ⚓ Qt_Online_Installer_4.2.0_released⠀⇛


                             We are happy to announce that Qt Installer
                             Framework, Qt Online Installer and Qt
                             Maintenance Tool 4.2.0 have been released.


                      # § Perl/Raku⠀➾


                            # ⚓ Perl_Weekly_Challenge_138:_Workdays_and_Split
                              Number⠀⇛


                            # ⚓ The_Ephemeral_Miniconf⠀⇛


                                   The Ephemeral Miniconf is planned on
                                   thursday 18th of november 2021!


                                   Have you heard about The Ephemeral
                                   Miniconf ?


                                   It’s a Perl/Raku free and online
                                   miniconf that will take place on Zoom!
                                   Think “TPRCiC” but smaller with only
                                   one track 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈


                            # ⚓ Util::H2O_~_Iterative_Refinement_of_Existing
                              Perl_Code⠀⇛


                                   Util::H2O is an incredibly powerful
                                   tool for managing HASH references in a
                                   more natural way.


                                   This post is the first of several that
                                   will explore this awesome module. I’ve
                                   started using it quite a bit in both
                                   new code and in existing code. There
                                   are several imporant cases where it
                                   really shines. Here we explore the
                                   power it has to iteratively refine
                                   existing code. It’s also fun and easy
                                   to introduce into existing code.


                                   Util::H2O provides a method called h2o
                                   that provides a very powerful way for
                                   turning a hash reference to an object.
                                   Generally speaking, this means I get
                                   accessors with as few keystrokes as
                                   possible.


    * § Leftovers⠀➾


          o § Education⠀➾


                # ⚓ Educational_Gag_Orders⠀⇛


                       Between January and September 2021, 24 legislatures
                       across the United States introduced 54 separate
                       bills intended to restrict teaching and training in
                       K-12 schools, higher education, and state agencies
                       and institutions. The majority of these bills
                       target discussions of race, racism, gender, and
                       American history, banning a series of “prohibited”
                       or “divisive” concepts for teachers and trainers
                       operating in K-12 schools, public universities, and
                       workplace settings. These bills appear designed to
                       chill academic and educational discussions and
                       impose government dictates on teaching and
                       learning. In short: They are educational gag
                       orders.


                       Collectively, these bills are illiberal in their
                       attempt to legislate that certain ideas and
                       concepts be out of bounds, even, in many cases, in
                       college classrooms among adults. Their adoption
                       demonstrates a disregard for academic freedom,
                       liberal education, and the values of free speech
                       and open inquiry that are enshrined in the First
                       Amendment and that anchor a democratic society.
                       Legislators who support these bills appear
                       determined to use state power to exert ideological
                       control over public educational institutions.
                       Further, in seeking to silence race- or gender-
                       based critiques of U.S. society and history that
                       those behind them deem to be “divisive,” these
                       bills are likely to disproportionately affect the
                       free speech rights of students, educators, and
                       trainers who are women, people of color, and
                       LGBTQ+. The bills’ vague and sweeping language
                       means that they will be applied broadly and
                       arbitrarily, threatening to effectively ban a wide
                       swath of literature, curriculum, historical
                       materials, and other media, and casting a chilling
                       effect over how educators and educational
                       institutions discharge their primary obligations.
                       It must also be recognized that the movement behind
                       these bills has brought a single-minded focus to
                       bear on suppressing content and narratives by and
                       about people of color specifically–something which
                       cannot be separated from the role that race and
                       racism still plays in our society and politics. As
                       such, these bills not only pose a risk to the U.S.
                       education system but also threaten to silence vital
                       societal discourse on racism and sexism.


          o § Hardware⠀➾


                # ⚓ Three-Dimensional_Design_Yields_Compact_Seven-Segment_Hex
                  Displays_|_Hackaday⠀⇛


                       Computers, from the simplest to the most complex,
                       aren’t very useful if they can’t provide feedback
                       to a user. Whether that interface takes the form of
                       a monitor, a speaker, or a simple LED, there’s
                       almost always some kind of output. One of the most
                       ubiquitous is the ever-present seven-segment
                       display. They’re small, they’re easy to use, and,
                       perhaps most important, they’re cheap.


                # ⚓ Is_This_12-layer_PCB_Coil_The_Next_Step_In_Ferrofluid
                  Displays?_|_Hackaday⠀⇛


                       [Applied Procrastination] is in the business of
                       vertical ferrofluid displays, but struggles
                       somewhat with the electromagnets available off the
                       shelf and the proliferation of wiring that results.
                       [Carl Bugeja] is in the business of making PCB
                       coils, both with rigid and flex PCB substrates, so
                       when the opportunity for a collaboration arose,
                       [AP] jumped at the opportunity.


                # ⚓ The_Scrolling_Orb⠀⇛


                       The evolution of the trackball, which is more than
                       an upside-down mouse. It’s the Royal Canadian
                       Navy’s greatest gift to modern-day computing.
                       Really.


                       Ever find yourself in a bar with a single arcade
                       machine, and the machine is inevitably not
                       targeting gamers? Like, rather than, say, a
                       fighting game or something iconic like NBA Jam or
                       even Donkey Kong, it’s either a variation of Big
                       Buck Hunter, a bowling game like Silver Strike
                       Bowling, or a golf game like Golden Tee. These
                       games, of course, aim for a wide audience, quite
                       literally in the case of Big Buck Hunter. But the
                       golf and bowling games are notable, really, because
                       of their control method—they don’t use a joystick;
                       they use a massive trackball. As far as input
                       devices go, the trackball is perhaps the nerdiest,
                       and therefore the most interesting. It’s also older
                       than you might expect. Today’s Tedium is gonna tell
                       you all about it—and why it’s not just a glorified
                       mouse. — Ernie @ Tedium


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Reasons_to_use_WSL2_on_Windows_11.⠀⇛


                             (From a joke I made on IRC. I bet I get
                             banned from #windows on Libera Chat shortly.)


                      # ⚓ Forbes:_‘Desperate’_Microsoft_Making_It_Harder_To
                        Switch_Windows_11_Browser⠀⇛


                      # § Security⠀➾


                            # ⚓ This_Week_in_Security:_Unicode_Strikes,_NPM
                              Again,_and_First_Steps_to_PS5_Crack [Ed:
                              Microsoft keeps serving malware through NPM and
                              the media keeps blaming the victims, who
                              basically receive malicious software because of
                              Microsoft]⠀⇛


                                   Maybe we really were better off with
                                   ASCII. Back in my day, we had space for
                                   256 characters, didn’t even use 128 of
                                   them, and we took what we got. Unicode
                                   opened up computers to the languages of
                                   the world, but also opened an invisible
                                   backdoor. This is a similar technique
                                   to last week’s Trojan Source story.
                                   While Trojan Source used right-to-left
                                   encoding to manipulate benign-looking
                                   code, this hack from Certitude uses
                                   Unicode characters that appear to be
                                   whitespace, but are recognized as valid
                                   variable names.


                                   [...]


                                   Last week, the coa and rc packages
                                   temporarily updated to versions
                                   containing malicious code. The timing,
                                   and nearly identical added code,
                                   indicates that it was the same
                                   individual or group behind both
                                   packages. While the malware seemed to
                                   be non-functional on some systems, it
                                   should be assumed that anywhere these
                                   malicious versions were deployed is
                                   compromised. At a combined 20 million
                                   weekly downloads for these two
                                   packages, there are sure to be many
                                   compromises, even given the short time
                                   the malicious packages were available
                                   on the 4th. NPM was hosting the
                                   malicious version of coa for one hour
                                   and twelve minutes. The rc package
                                   pushed the malicious update a couple
                                   hours later, and it’s unclear how long
                                   that version was available.


                                   The malicious code was run using a
                                   preinstall script, which seems to be
                                   the common vector for these hacks.
                                   There have been suggestions that
                                   install scripts should be disabled by
                                   default. While that would prevent these
                                   very simple attacks, it wouldn’t
                                   actually protect against the underlying
                                   problem. Supply chain attacks are a
                                   growing problem, but they seem to be
                                   particularly problematic in the world
                                   of full-stack JavaScript. If the
                                   popularity of node.js and npm are to
                                   continue, we will need a better
                                   solution to this pernicious problem.


                            # ⚓ Security_updates_for_Friday⠀⇛


                                   Security updates have been issued by
                                   Debian (node-tar, postgresql-11,
                                   postgresql-13, and postgresql-9.6),
                                   Fedora (autotrace, botan2, chafa,
                                   converseen, digikam, dmtx-utils,
                                   dvdauthor, eom, kxstitch, pfstools,
                                   php-pecl-imagick, psiconv, q, R-magick,
                                   radeontop, rss-glx, rubygem-rmagick,
                                   synfig, synfigstudio, vdr-scraper2vdr,
                                   vdr-skinelchihd, vdr-skinnopacity, vdr-
                                   tvguide, and WindowMaker), Mageia
                                   (kernel, kernel-linus, and openafs),
                                   openSUSE (kernel), Red Hat (freerdp),
                                   SUSE (bind and kernel), and Ubuntu
                                   (openexr, postgresql-10, postgresql-12,
                                   postgresql-13, and samba).


                            # ⚓ CISA_Releases_Advisory_on_Vulnerabilities_in
                              Multiple_Data_Distribution_Service
                              Implementations⠀⇛


                                   CISA has released an Industrial Control
                                   Systems Advisory (ICSA) related to a
                                   public report detailing vulnerabilities
                                   found in multiple open-source and
                                   proprietary Object Management Group
                                   (OMG) Data-Distribution Service (DDS)
                                   implementations. Successful
                                   exploitation of these vulnerabilities
                                   could result in denial-of-service or
                                   buffer-overflow conditions, which may
                                   lead to remote code execution or
                                   information exposure.


                                   CISA encourages users and
                                   administrators to review ICSA-21-315-
                                   02: Multiple Data Distribution Service
                                   (DDS) Implementations and apply the
                                   necessary updates as quickly as
                                   possible.


                            # ⚓ MacOS_Zero-Day_Used_against_Hong-Kong
                              Activists⠀⇛


                                   Google researchers discovered a MacOS
                                   zero-day exploit being used against
                                   Hong Kong activists. It was a “watering
                                   hole” attack, which means the malware
                                   was hidden in a legitimate website.
                                   Users visiting that website would get
                                   infected.


                            # ⚓ Google_Caught_Hackers_Using_a_Mac_Zero-Day
                              Against_Hong_Kong_Users⠀⇛


                                   Google researchers caught hackers
                                   targeting users in Hong Kong exploiting
                                   what were at the time unknown
                                   vulnerabilities in Apple’s Mac
                                   operating system. According to the
                                   researchers, the attacks have the
                                   hallmarks of government-backed hackers.


                                   On Thursday, Google’s Threat Analysis
                                   Group (TAG), the company’s elite team
                                   of hacker hunters, published a report
                                   detailing the hacking campaign. The
                                   researchers didn’t go as far as
                                   pointing the finger at a specific
                                   hacking group or country, but they said
                                   it was “a well resourced group, likely
                                   state backed.”


                                   “We do not have enough technical
                                   evidence to provide attribution and we
                                   do not speculate about attribution,”
                                   the head of TAG Shane Huntley told
                                   Motherboard in an email. “However, the
                                   nature of the activity and targeting is
                                   consistent with a government backed
                                   actor.”


                            # ⚓ Reproducible_Builds_(diffoscope):_diffoscope
                              191_released⠀⇛


                                   The diffoscope maintainers are pleased
                                   to announce the release of diffoscope
                                   version 191. This version includes the
                                   following changes:


                                   [ Chris Lamb ]
                                   * Detect XML files as XML files if
                                   either file(1) claims if they are XML
                                     files, or if they are named .xml.
                                     (Closes: #999438, reproducible-
                                   builds/diffoscope#287)
                                   * Don't reject Debian .changes files if
                                   they contain non-printable
                                     characters. (Closes: reproducible-
                                   builds/diffoscope#286)
                                   * Continue loading a .changes file even
                                   if the referenced files inside it do
                                     not exist, but include a comment in
                                   the diff as a result.
                                   * Log the reason if we cannot load a
                                   Debian .changes file.

                                   [ Zbigniew Jędrzejewski-Szmek ]
                                   * Fix inverted logic in the
                                   assert_diff_startswith() utility.
⚓ diffoscope_192_released⠀⇛


⚓ SSH_through_host_in_the_middle⠀⇛


     Following command will ssh through host in the middle.
     Unreachable_host is unavailable from local network, but it’s
     available from reachable_host’s network. This command creates a
     connection to unreachable_host through “hidden” connection to
     reachable_host.


⚓ Microsoft:_New_security_updates_trigger_Windows_Server_auth_issues⠀⇛


⚓ Open_Source_Project_Aims_to_Detect_Living-Off-the-Land_Attacks⠀⇛


⚓ Microsoft_Intune_bug_forces_Samsung_devices_into_non-compliant_state⠀⇛


⚓ ‘Lyceum’_Threat_Group_Broadens_Focus_to_ISPs⠀⇛


⚓ ClusterFuzzLite:_Continuous_fuzzing_for_all⠀⇛


     In recent years, continuous fuzzing has become an essential part of
     the software development lifecycle. By feeding unexpected or random
     data into a program, fuzzing catches bugs that would otherwise slip
     through the most thorough manual checks and provides coverage that
     would take staggering human effort to replicate. NIST’s guidelines
     for software verification, recently released in response to the White
     House Executive Order on Improving the Nation’s Cybersecurity,
     specify fuzzing among the minimum standard requirements for code
     verification.


⚓ ClusterFuzzLite:_Continuous_fuzzing_for_all_(Google_Security_blog)⠀⇛


     Over on the Google Security blog, Jonathan Metzman announced the
     release of ClusterFuzzLite, which is “a continuous fuzzing solution
     that runs as part of CI/CD workflows to find vulnerabilities faster
     than ever before”. ClusterFuzzLite is a descendant of OSS-Fuzz, which
     we looked at in 2017.


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


    * ⚓ Abcbot_—_A_New_Evolving_Wormable_Botnet_Malware_Targeting_Linux⠀⇛


§ Privacy/Surveillance⠀➾


    * ⚓ 1.8_TB_of_Police_Helicopter_Surveillance_Footage_Leaks_Online⠀⇛


           LAW ENFORCEMENT USE of surveillance drones has proliferated
           across the United States in recent years, sparking backlash
           from privacy advocates. But newly leaked aerial surveillance
           footage from the Dallas Police Department in Texas and what
           appears to be Georgia’s State Patrol underscore the breadth and
           sophistication of footage captured by another type of aerial
           police vehicle: helicopters.


           [...]


           The footage the group released Friday, samples of which were
           viewed by WIRED, shows helicopters operating during the day and
           at night, capturing everything from vistas high overhead to
           cars lined up at a McDonald’s drive-through, and individuals
           standing in their yards or on local streets. The leak
           illustrates the inherent risk of collecting and retaining
           sensitive footage that could be breached.


           “This is exactly one of the things that people are constantly
           warning about, especially when it comes to government
           surveillance and corporate data mining,” Best told WIRED in a
           text message interview. “Not only is the surveillance itself
           problematic and worrisome, but the data is not handled in the
           ideal conditions we’re always promised.”


           The vast majority of the leaked footage appears to come from
           the Dallas Police Department. In response to three screenshots
           from the leak, DPD public information officer Brian Martinez
           wrote in an email that “the pictures show screenshots of video
           from the department helicopter.” He declined to comment about
           DPD’s data storage practices, including how long the department
           retains helicopter surveillance videos. “Due to security
           measures, we are not able to discuss data storage,” he wrote.
           “All video from the helicopter is available to any person
           requesting the video through the Open Records Act.”


§ Defence/Aggression⠀➾


    * ⚓ To_Avoid_Armageddon,_Don’t_Modernize_Missiles—Eliminate_Them⠀⇛


           The single best option for reducing the risk of nuclear war is
           hidden in plain sight. News outlets don’t mention it. Pundits
           ignore it. Even progressive and peace-oriented members of
           Congress tiptoe around it. And yet, for many years, experts
           have been calling for this act of sanity that could save
           humanity: Shutting down all of the nation’s intercontinental
           ballistic missiles.


           Four hundred ICBMs dot the rural landscapes of Colorado,
           Montana, Nebraska, North Dakota, and Wyoming. Loaded in silos,
           these missiles are uniquely—and dangerously—on hair-trigger
           alert. Unlike the nuclear weapons on submarines or bombers, the
           land-based missiles are vulnerable to attack and could present
           the commander in chief with a sudden use-them-or-lose-them
           choice. “If our sensors indicate that enemy missiles are en
           route to the United States, the president would have to
           consider launching ICBMs before the enemy missiles could
           destroy them. Once they are launched, they cannot be recalled,”
           former Defense Secretary William Perry warns. “The president
           would have less than 30 minutes to make that terrible
           decision.”


§ Environment⠀➾


    * ⚓ Fake_Fake_Exposes_Real_Fakes_–_Tricksters_in_an_age_of_dirty_tricks⠀⇛


           In what would have been a monumental first for the group, the
           Yes Men supposedly got an absurd fake company — “YASAVA,”
           producing “bespoke airplane couture” for private corporate
           fleets — accepted into two official COP26 “Net Zero” programs:
           the Race to Zero and Science-Based Targets initiatives (which
           also, incidentally, include Maersk, Chevron, Halliburton,
           Delta, United, American, DL Piper, Edelman, JP Morgan, Hitachi,
           Iberdrola, Unilever, and thousands more climate luminaries from
           the transport, mining, and fossil energy sectors).


           The “fake” Yes Men release went out at 8am GMT Monday, Nov. 8
           and was soon followed up with a (fake) “reveal” from our
           partners in crime, Glasgow Calls Out Polluters (GCOP), who
           simultaneously released their (very real) report, “Race to Zero
           (credibility),” about the same two COP26 “net zero”
           initiatives.


§ Finance⠀➾


    * ⚓ How_the_Super_Rich_Changed_a_City,_For_Better_or_Worse_|_Time⠀⇛


           On the steps of city hall, Mayor David Anderson hollered a
           guttural “Wahhh!!!” and shot his arms into the sky to
           celebrate, looking like an inflatable air dancer blowing in the
           wind.


           “Four! Hundred! Million! Dollars!” he shouted, in July, to city
           residents in Bronson Park, a leafy plaza adorned with bronze
           busts and plaques honoring pioneers and philanthropists.


           Anonymous donors had just given what is thought to be the
           largest-ever gift to support a municipality, and for city
           officials, it felt like winning the lottery. It was also a win
           for two of Kalamazoo’s richest men, philanthropists William
           Parfet and William Johnston, who created the foundation that
           received the money and that will determine how most of it is
           spent.


    * ⚓ What_the_Hell_Is_‘Right-Clicker_Mentality’?⠀⇛


           Every new subculture eventually develops its own language, and
           the people buying and selling NFTs are no different.


           The blockchain scene is full of crypto-heads spouting phrases
           like WAGMI (we are going to make it), cope, and GM (good
           morning). Sometimes a subculture will produce a new phrase or
           buzzword so beautiful it gets adopted by the wider culture. So
           it is with “right-clicker mentality.”


           An NFT-bro using the phrase “right-clicker mentality” went
           viral on October 26 on Twitter while talking about Salt Bae. If
           you aren’t familiar, Salt Bae is a Turkish chef named Nusret
           Gökçe who went viral in 2017 for the way he sprinkles salt on
           meals. His restaurants boomed on the back of his internet
           success and now he charges tens of thousands of dollars for
           gold-encrusted steaks at his London location.


           A popular genre of post online right now teaches you how to
           make Salt Bae-quality meals at bargain prices. In one video, a
           man recreated one of Salt Bae’s $2,000 steaks for about $90. A
           NFT fan apparently felt that this was an example of what they
           called a “right-clicker mentality” and took to Twitter to share
           their frustration.


           “This is a great example of right-clicker mentality,” Midwit
           Milhouse said on Twitter. “Sure, you can make your own gold-
           coated steak for 65GBP, but then you don’t have the
           satisfaction, flex, clout that comes from having eaten at Salt
           Bae’s restaurant. The value is not in the cost of the steak. Go
           ahead, make yourself a gold-coated steak at home. Post a
           picture of it on Instagram. See how much clout it gets you.
           Salt Bae’s dish costs around 1500GBP because people want to pay
           1500 GBP to show off that they can afford to pay that much.
           It’s all about the flex.”


    * ⚓ A_mainnet_swap_and_its_subsequent_domino_effects_led_the_price_of_this
      token_to_5x_in_a_month⠀⇛


           A system modeled after Linux operations strives to improve
           institutional adoption, the next step in the technology’s
           mainstream usage.


           [...]


           aelf is designed as a customizable OS, the equivalent of a
           “Linux system” for blockchain. Considering Linux as an example,
           the Linux Kernel and other Linux versions make up a greater
           Linux family. The Linux Kernel addresses the critical parts
           within this family, while other developers can address the
           customized systems. aelf operates with a similar system, where
           the whole network is built in the platform’s innovative multi-
           library selection structure, enabling unlimited scalability and
           lower costs.


§ AstroTurf/Lobbying/Politics⠀➾


    * ⚓ Cory_Doctorow:_The_Unimaginable⠀⇛


           Margaret Thatcher was the least science-fictional world leader
           in modern history.


           Her motto was “There is no alternative,” a phrase she repeated
           so often it became an acronym: “TINA.”


           She was referring to capitalism, asserting that there is no
           conceivable alternative. It was a cheap but remarkably
           effective rhetorical device, treat­ing a demand as an
           observation. The true meaning of TINA isn’t “No alternative is
           possible,” but rather, “Stop trying to think of an
           alternative.”


           I mean, thinking of alternatives is literally my job.


           TINA is part of a philosophy, “capitalist realism,” a phrase
           coined by Mark Fischer in the early 2000s. Fischer said that
           capitalist realism is best captured in the quote “It is easier
           to imagine an end to the world than an end to capitalism” (this
           quote has been vari­ously attributed to the philosopher Slavoj
           Žižek and the literary critic Fredric Jameson).


           Žižek (or possibly Jameson) got a lot closer to the problem
           than Thatcher ever did. For while it’s easy to imagine
           something after capitalism, imagining capitalism’s sunset is
           far harder.



                    ䷩ 𝚕𝚒𝚗𝚎 4005

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 11.12.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_12/11/2021:_PipeWire_0.3.40_and_FreeBSD_12.3_RC1⠀✐


Posted in News_Roundup at 7:14 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Librem_14_EC_Upgrade_Hardware_Method⠀⇛


                       Librem 14s shipping today are already running the
                       latest and greatest EC firmware. For those that
                       already have their Librem 14, keeping your Librem
                       EC firmware updated is simple with our ISO upgrade
                       method. Still, for those needing to recover or test
                       development EC builds, this video will explain how
                       to upgrade your EC with a chip programmer.


                # ⚓ System76_is_developing_its_own_Pop_OS_desktop_in_Rust_–
                  itsfoss.net⠀⇛


                       System76 seems to want to become the Apple of
                       Linux, with all the differences that being based on
                       open source software supposes … more or less,
                       because there is everything. Thus, while on the one
                       hand it is announced that the company is developing
                       its own desk , on the other it is denounced


                       But let’s start at the beginning: System76, the
                       Apple of Linux? It is a way of speaking. They were
                       one of the first brands to sell Linux computers;
                       they later promoted their own Ubuntu-based
                       distribution, Pop! _OS ; They adapted GNOME to
                       their demands, modifying it and renaming it COSMIC
                       … Which did not take shape until recently , it
                       should be noted … And now they announce the
                       intention of developing their own desktop.


                # ⚓ System76_is_a_toxic_collaborator,_denounced_from_GNOME⠀⇛


                       And what does GNOME say about System76’s plans to
                       create its own desktop ? Any. He says it about
                       something else, although it is not exactly GNOME as
                       an organization – although it could well be – the
                       one that raises its voice, but Chris Davis, one of
                       its developers in an extensive article entitled
                       “System76: a case study on how not to collaborate
                       with the upstream «.


                       «The following post was written in the context of
                       the events that occurred in September. […] I waited
                       hoping that we could come to a happy ending with
                       System76. As time passes, that hope has faded.
                       Attempts to connect to System76 have not been
                       productive, and I think we’ve let the impression
                       that GNOME has been given to the tech community
                       linger too long, ”Davis begins.


                       Davis accuses System76 of launching FUD ( fear,
                       uncertainty and doubt , as is) against GNOME , but
                       also against specific people in the GNOME
                       environment as a result of the debates about the
                       future of the project that led to the noted GNOME
                       Way article. It is also not the first time that
                       System76 acts like this, according to Davis, who
                       has lost his confidence in the company correcting
                       its ways.


                # ⚓ Open_Up:_Contributions_and_Collaborations⠀⇛


                       Hello fellow space travelers! It’s been a while
                       since we catalogued all of our goings on here on
                       Starship Pop!_OS, so we thought it might be a good
                       time to highlight what our upstream contributions
                       have looked like over the last couple of years.
                       We’ve been logging some major light years! Have a
                       look.


                # ⚓ The_Chrome_OS_virtual_keyboard_is_joining_the_dark_side,
                  adding_Linux_app_support,_and_more [Ed: Google 'reinventing'
                  the same thing it took away when it chopped down Gentoo to
                  make its spyware]⠀⇛


                       The Chrome OS virtual keyboard – the on-screen
                       typing experience – has undergone plenty of changes
                       for the better over the past year. In Chrome 85, it
                       got a major facelift featuring key borders (love it
                       or hate it) and even became resizable. While we
                       knew it was going to receive light and dark mode at
                       some point, the most we knew for sure is that it
                       would coincide with the release of light and dark
                       mode for the entire operating system.


          o § Server⠀➾


                # ⚓ Huawei_hands_its_cloud_Linux_to_China’s_only_open_source
                  foundation⠀⇛


                       Huawei has donated the cut of Linux it created to
                       run on its cloud, and silicon, to China’s only open
                       source foundation.


                       The Chinese giant’s OS is called EulerOS and is
                       derived from CentOS. EulerOS runs on x86 silicon
                       but is tuned for top performance on the Arm64
                       architecture – which is what Huawei uses in the
                       Kunpeng 920 CPUs it designed to power its own
                       servers, cloud, and even the occasional laptop.


                       Huawei’s list of the operating system’s features
                       and benefits states it includes KVM virtualization,
                       ext4, the GFS2 cluster file system, systemd, Linux
                       containers, and can manage user identities across
                       Linux, UNIX, and Windows domains to help with your
                       SSO needs.


                       EulerOS also comes in an edition called OpenEuler
                       that’s maintained by a community said to comprise
                       7,233 contributors, 274,993 users, and 10 vendors
                       that package the OS.


          o § Audiocasts/Shows⠀➾


                # ⚓ JingPad_Roadmap_and_updates,_installing_other_distros,_open
                  source_status,_pen_latency,_and_more_–_Invidious⠀⇛


          o § Kernel Space⠀➾


                # ⚓ DAMON-Based_Memory_Reclamation_Merged_For_Linux_5.16_–
                  Phoronix⠀⇛


                       Following Amazon’s DAMON being merged in Linux 5.15
                       as a data monitoring access framework, being merged
                       for Linux 5.16 is an addition building on top of
                       that for memory reclamation when experiencing
                       system RAM pressure.


                       Merged as part of Andrew Morton’s patch series for
                       Linux 5.16 is DAMON-based memory reclamation that
                       has been under review on the kernel mailing list
                       the past few months.


                       This proactive reclamation of memory pages can help
                       under light memory pressure and makes use of
                       Amazon’s DAMON framework for determining the cold
                       pages on the system to reclaim.


                # § Graphics Stack⠀➾


                      # ⚓ David_Airlie_Hacking_On_Intel_Vulkan_Video_Decode,
                        Crocus_Gallium3D_VA-API_–_Phoronix⠀⇛


                             Red Hat’s David Airlie has been working on
                             early support for Vulkan Video API support
                             with Mesa’s Radeon “RADV” driver while the
                             past week he spent time working on similar
                             treatment for Intel’s open-source “ANV”
                             Vulkan driver and also resurrecting some
                             unfinished VA-API video acceleration code he
                             was working on for the Intel Crocus Gallium3D
                             driver.


                             Airlie was able to make some progress getting
                             Intel Vulkan Video API acceleration working
                             for the open-source Mesa Vulkan driver. With
                             H.264 video decoding he is seeing some
                             success now but still battling issues.


                      # ⚓ Dave_Airlie_(blogspot):_h264_video_decoding:_i-frames
                        strike_back⠀⇛


                             Last week I mentioned I had the basics of
                             h264 decode using the proposed vulkan video
                             on radv. This week I attempted to do the same
                             thing with Intel’s Mesa vulkan driver “anv”.


                             Now I’d previously unsuccessfully tried to
                             get vaapi on crocus working but got
                             sidetracked back into other projects. The
                             Intel h264 decoder hasn’t changed a lot
                             between ivb/hsw/gen8/gen9 era. I ported what
                             I had from crocus to anv and started trying
                             to get something to decode on my WhiskeyLake.


                             I wrote the code pretty early on, figured out
                             all the things I had to send the hardware.


                             The first anv side bridge to cross was Vulkan
                             is doing H264 Picture level decode API, so it
                             means you get handed the encoded slice data.
                             However to program the Intel hw you need to
                             decode the slice header. I wrote a slice
                             header decoder in some common code. The other
                             thing you need to give the intel hw is a
                             number of bits of slice header, which in some
                             encoding schemes is rounded to bytes and in
                             some isn’t. Slice headers also have a 3-byte
                             header on them, which Intel hardware wants
                             you to discard or skip before handing it to
                             it.


                             Once I’d fixed up that sort of thing in anv +
                             crocus, I started getting grey I-frames
                             decoded with later B/P frames using the grey
                             frames as references so you’d see this kinda
                             wierd motion.


                      # ⚓ Mike_Blumenkrantz:_Real_Benchmarking⠀⇛


                             That the one true benchmark for graphics is
                             glxgears. It’s been the standard for 20+
                             years, and it’s going to remain the standard
                             for a long time to come.


          o § Applications⠀➾


                # ⚓ age_–_simple_file_encryption_tool_by_Google⠀⇛


                       Encryption software is an important consideration
                       when it comes to protecting your files and folders.
                       Hack attempts and privacy intrusions mean that it’s
                       sensible to ensure that complete strangers don’t
                       gain access to your most personal details stored on
                       your computer.


                       There are a number of different approaches you can
                       take to protect your valuable data. For example,
                       disk encryption uses disk encryption software to
                       encrypt the entire hard disk. The onus is therefore
                       not on the user to determine what data should be
                       encrypted, or to remember to manually encrypt
                       files. By encrypting the entire disk, temporary
                       files, which may reveal important confidential
                       data, are also protected. Security is enhanced
                       further when disk encryption is combined with
                       filesystem-level encryption.


                # ⚓ PipeWire_0.3.40_Released_With_Better_JACK_Compatibility⠀⇛


                       PipeWire 0.3.40 is out today with various bug fixes
                       but also a number of improvements.


                       PipeWire 0.3.40 continues work on enhancing its
                       JACK compatibility with better matching that sound
                       server’s behavior and reworking other code. There
                       are also a number of fixes to its PulseAudio server
                       code.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_run_Mariadb_with_Docker_and_Docker-Compose⠀⇛


                       In this guide we are going to explore how to run
                       Mariadb 10 locally with docker and docker compose.
                       This can be helpful if you want to run Mariadb 10
                       locally without installing it in your machine or if
                       you want to run multiple versions of Mariadb
                       seamlessly.


                # ⚓ How_to_install_and_use_Podman_in_Debian_11⠀⇛


                       Podman is a container engine that’s compatible with
                       the OCI Containers specification. It is part of
                       RedHat Linux, but can also be installed on other
                       distributions. As it’s OCI-compliant, Podman can be
                       used as a drop-in replacement for the better-known
                       Docker runtime. Most Docker commands can be
                       directly translated to Podman commands. Podman
                       implements almost all the Docker CLI commands
                       (apart from the ones related to Docker Swarm).


                       Podman complements Buildah and Skopeo by offering
                       an experience similar to the Docker command line:
                       allowing users to run standalone (non-orchestrated)
                       containers. And Podman doesn’t require a daemon to
                       run containers and pods, so we can easily say
                       goodbye to big fat daemons. There are no daemons in
                       the background doing stuff, and this means that
                       Podman can be integrated into system services
                       through systemd.


                # ⚓ Update_Docker_Container_Automatically_When_Updating
                  Services⠀⇛


                       Imagine this scenario. You host a few web services
                       running in Docker containers. When the web service
                       has a new version release, you fetch the Docker
                       image and update the containers to update the
                       service.


                       I have discussed updating Docker containers without
                       downtime earlier but this article is not about
                       upgrading the web apps. This one is about updating
                       the operating system containers themselves.


                       Upgrading the OS running in the container manually
                       can be a daunting task from time to time. You must
                       run the relevant upgrade commands yourself on a
                       running container separately to make that happen.


                       How about eliminating this extra step and combine
                       the updating of OS along with the updating of the
                       service?


                # ⚓ How_to_install_Erlang_on_Rocky_Linux/Alma_Linux/CentOS_8⠀⇛


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


                # ⚓ How_to_Install_LEMP_Stack_with_PhpMyAdmin_in_Arch_Linux⠀⇛


                       Generally, the term LEMP stack can be broken down
                       to Linux, Nginx, MySQL/MariaDB, and PHP modules.
                       All these listed components have a priceless
                       contribution in mimicking the behavior of a
                       production server.


                       We have a hosting environment (Linux), a web server
                       (Nginx), a database engine/server (MySQL/MariaDB),
                       and a scripting language (PHP).


                # ⚓ How_to_Install_Spotify_on_Debian_11_Bullseye_–
                  LinuxCapable⠀⇛


                       Spotify is a digital music streaming service with
                       both free and paid features. It is the world’s
                       largest music streaming service provider, with over
                       381 million monthly active users, including 172
                       million paying subscribers, as of September 2021.
                       Spotify can give you instant access to a vast
                       online library of music and podcasts, which is very
                       popular as you can listen to the content of your
                       choice whenever you feel like it.


                       In the following tutorial, you will learn how to
                       install the Spotify application on your Debian 11
                       Bullseye desktop using three different methods.


                # ⚓ How_To_Find_A_Package_Version_In_Linux_–_OSTechNix⠀⇛


                       Even though package management has become easier
                       with the help of graphical package managers, some
                       users always prefer the command line way. There are
                       different commands to find out the package version
                       in different flavors of Linux. Today, in this
                       tutorial, we will be seeing how to find a package
                       version in some popular Linux distributions such as
                       Alpine Linux, Arch Linux and its derivatives,
                       Debian and its derivatives, RHEL and its
                       derivatives.


                # ⚓ Switch_to_Dark_Mode_in_Fedora_Linux_With_GNOME_Desktop⠀⇛


                       Unlike Ubuntu, Fedora offers the actual, vanilla
                       GNOME experience. And that works pretty well. The
                       horizontal layout, the three finger swipe, it’s all
                       good.


                       The one thing I don’t like is the default standard
                       theme which is a mix of Adwaita Light (default)
                       theme and the dark shell.


                       So, while the notifications and notification area
                       are dark, rest of the system and applications have
                       light theme. And quite honestly, it looks dull for
                       my taste.


                # ⚓ 8_Different_Ways_to_Know_Linux_OS_Version_–_Linux_Shout⠀⇛


                       It’s always crucial to know the Linux version and
                       distribution you’re working with, whether you’re
                       using Linux for personal or business reasons. That
                       way, you’ll know which package manager to use to
                       get new tools and upgrades, as well as which Linux
                       forum to visit if you have any concerns or
                       problems.


                       Having the information about the Linux version can
                       help you install the correct security patches and
                       identify the available features in the OS. There
                       are various methods for determining what
                       distribution and version to install on a system. In
                       this tutorial, we will explain different ways to
                       know the Linux os version.


                # ⚓ Install_the_Arduino_IDE_on_Linux_–_PragmaticLinux⠀⇛


                       Interested in developing software for your Arduino
                       board in Linux? The Arduino IDE is the recommended
                       tool for developing software and uploading the
                       resulting firmware to your Arduino board. Luckily,
                       the Arduino IDE is developed as a cross-platform
                       solution, meaning that you can also install it on
                       your Linux system. This article explains in detail
                       how you install the Arduino IDE on your Linux PC.


                # ⚓ How_to_install_Funkin’_Miku_Mod_on_a_Chromebook⠀⇛


                       Today we are looking at how to install Funkin’ Miku
                       Mod 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.


                # ⚓ How_to_install_Natron_on_Elementary_OS_6.0_–_Invidious⠀⇛


                       In this video, we are looking at how to install
                       Natron on Elementary OS 6.0.


                # ⚓ ‘IP_configuration_was_unavailable’:_a_laptop_cannot_connect
                  wirelessly_to_a_router_|_Fitzcarraldo’s_Blog⠀⇛


                       I recently switched my ISP from BT to Virgin Media
                       because the speed and reliability of the broadband
                       connection were low. A Virgin Media Hub 3 was
                       supplied as part of the package, and the TV,
                       laptops (Gentoo Linux, Windows 10 and macOS),
                       desktops (Lubuntu and Windows 10), tablets and
                       phones (Android and iOS) could connect to the Hub 3
                       without any trouble. A few weeks later Virgin Media
                       offered to upgrade the hub to a Hub 4. I don’t look
                       a gift horse in the mouth, so I accepted the offer.
                       The Hub 4 does indeed improve on the already
                       excellent broadband speeds I was getting with the
                       Hub 3. On the downside the Hub 4’s configuration
                       software has a couple of bugs, but I was able to
                       live with them.


                       In addition to the above-mentioned hub
                       configuration bugs, one of my laptops (a Compal
                       NBLB2 with Intel Wireless WiFi Link 5300 AGN
                       adapter) running Linux could not connect to the hub
                       via Wi-Fi, even though it had no trouble connecting
                       to the Hub 3. All other devices so far can connect
                       to the Hub 4, so I was scratching my head. The
                       laptop has no trouble connecting to the Hub 4 via
                       Ethernet cable.


                # ⚓ A_sane_vim_configuration_for_Fedora_–_Lukáš_Zapletal⠀⇛


                       I use vim on everyday basis from 1997 or something
                       like that. My configuration is quite old, clunky,
                       contains things for DOS and Windows even and I
                       should have totally cleaned it up. It still works
                       fine, however, recent reinstallation of my Fedora
                       laptop brought me to the idea to start a new Vim
                       configuration from scratch.


                       I am not huge fan of heavily-customized Vim
                       configs. Those configurations you can find in many
                       blogposts, youtube videos or github config
                       repositories. Thing is, when you login to a server
                       that has a “vanilla” vim, things can be hard for
                       people who got used to the custom plugins and other
                       fancy stuff.


                       For this reason, I’ve decided to come up with a
                       “sane” Vim configuration. Minimum possible
                       configuration changes and only plugins which ship
                       with Fedora 34+. Here it is.


                # ⚓ Nginx_Performance_Tuning_–_VITUX⠀⇛


                       Nginx is a free open source high performing and
                       lightweight web server that is used as the load
                       balancer, reverse proxy, HTTP cache, and mail
                       proxy. Although Nginx is quite new as compared to
                       other web servers, its popularity is rising due to
                       its high performance. With your default Nginx
                       configuration, you might get fast performance but
                       we can boost the Nginx performance at its best by
                       changing some configurations.


                       In this article, you will get to know 8 different
                       best ways to boost Nginx for better performance. To
                       demonstrate the example in this article I have
                       installed Nginx on the Ubuntu 20.04 LTS system.


          o § Games⠀➾


                # ⚓ LEDBOY_Is_A_Retro-Modern_Handheld_Game_|_Hackaday⠀⇛


                       Back in the 1970s, there were a few LED-based games
                       on the market that were quickly superseded by the
                       rise of LCDs and other fancier technologies.
                       However, [grossofabian] wanted to recreate that
                       classic style of game but with more modern
                       hardware. The result is the LEDBOY, a colorful
                       handheld game built in tribute to that era.


                       The handheld is based around the ATtiny 1614
                       microcontroller, driving a 10×10 array of NeoPixel
                       Nano 2427 LEDs, named for their small 2.4 mm x 2.7
                       mm form factor. They’re RGB, too, so there’s lots
                       of wonderful colors to play with.


                # ⚓ Steam_Deck_vs._Nintendo_Switch:_Is_it_a_fair_fight?⠀⇛


                       Ever since the Steam Deck was announced, people
                       have been trying to compare it to the Nintendo
                       Switch. “Is the Deck a Switch Killer?” “Will it
                       satisfy Nintendo fans who’ve been patiently waiting
                       a Switch Pro?” “Will we ever get a third edition of
                       the Deck?” In reality, these two devices serve
                       quite different markets.


                # ⚓ Valve’s_Steam_Deck_developer_event_is_open_to_all_to_watch
                  today_at_6PM_UTC_|_GamingOnLinux⠀⇛


                       Today (November 12) at 10am PST / 6PM UTC, Valve
                       are hosting the Steamworks Virtual Conference:
                       Steam Deck and you will actually be able to watch.
                       As a reminder, the Steam Deck has been delayed.


                       Originally, the announcement made it seem like you
                       had to be a registered Steamworks developer to
                       attend. However, Valve has sent out an email to
                       confirm that “anyone can watch the event, only
                       those signed in with a Steamworks developer account
                       can participate in the live Q&A and chat”. If you
                       will miss it, the sessions will be available
                       archived afterwards. Additionally, Valve said they
                       will release localized versions of the content next
                       week.


                # ⚓ Godot_3.4,_new_version_of_the_open_source_game_engine_–
                  LinuxStoney⠀⇛


                       Godot 3.4 has been published as stable to continue
                       with the development and consolidation of this Open
                       Source graphics engine oriented to video games.
                       Apart from the new features and improvements it
                       brings, we can also highlight the emergence of the
                       project itself, which is gradually making a dent in
                       the scene mainstream after having gone unnoticed
                       during its first years of life.


                       For starters, and as far as the kernel is
                       concerned, Godot 3.4 has brought in the validity
                       checks of objects for release builds. Another
                       interesting novelty is that the File API is now
                       capable of manipulating files of more than 2GiB,
                       something that has been introduced with the
                       intention of breaking limitations when dealing with
                       large projects and that has been achieved thanks to
                       the fact that everything has been refactored to use
                       64-bit unsigned integers, so Godot, as of launch,
                       is capable of loading files up to 8.4TiB .


                       Keyboard input support has been improved to more
                       effectively handle different keyboard layouts other
                       than Anglo-QWERTY, for example causing movement key
                       mapping to automatically switch from WASD to ZQSD
                       on AZERTY keyboards. used in France and other
                       French-speaking areas.


                       To finish off the kernel, the have been ported back
                       AES-ECB and AES-CBC encryption and decryption
                       methods to add cryptographic features , so “Godot
                       can now save and load public keys, sign and verify
                       a hash with an RSA key. and encrypt and decrypt RSA
                       keys ”.


                # ⚓ Valve_adds_documentation_for_Steam_Deck_development,
                  suggests_Manjaro_Linux_for_now_|_GamingOnLinux⠀⇛


                       With the Steam Deck delayed until February 2022,
                       Valve has produced new developer documentation
                       giving a helping hand to devs interested in testing
                       ready for it using Linux.


                       They’re not quite ready to put out SteamOS 3 Linux
                       just yet (which is what the Steam Deck uses), or
                       even an official developer image to install but
                       “soon” something should be available in that way.
                       Until then, they’ve come up with a way for
                       developers to test everything on Linux a little
                       easier.


                       It starts by going over the already expected
                       essential things like gamepad input and resolution
                       support but this time there’s more detail on
                       actually testing it on a Linux system.
                       Specifically, Valve are now suggesting developers
                       go for Manjaro KDE, as it’s also based on Arch
                       Linux and has the same Plasma desktop as you will
                       find in the desktop mode with SteamOS 3 on the
                       Steam Deck.


                # ⚓ Baba_Is_You_gets_a_level_editor_in_a_free_update_this_month
                  |_GamingOnLinux⠀⇛


                       Baba Is You, one of my most favourite puzzle games
                       ever, is set to finally see the big level editor
                       update on November 17 as a free upgrade for all
                       owners.


          o § Distributions⠀➾


                # ⚓ [Old] In_His_Own_Words:_Gary_KIldall⠀⇛


                       There is more, however. In 1993, the year before
                       his untimely death, Gary wrote a draft of a memoir
                       titled Computer Connections: People, Places, and
                       Events in the Evolution of the Personal Computer
                       Industry. He distributed bound copies to family and
                       friends, with a note that it “will go to print in
                       final form early next year.” It never did.


                # ⚓ [Old] Kildall_Manuscript [incomplete]⠀⇛


                       Of course, CP/M went through many “versions” like
                       the major and minor ones that I already talked
                       about. In 1978, there was a lot of pressure to make
                       a new one. The pressure came from manufacturers
                       that were using the smaller 5-1/4″ disks, like the
                       ones that were introduced with Woz’s Apple II. And,
                       our OEMs were pushing for a new standard BIOS for
                       the small disks.


                # § BSD⠀➾


                      # ⚓ FreeBSD_12.3-RC1_Now_Available⠀⇛


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

                             Installation images are available for:

                             o 12.3-RC1 amd64 GENERIC
                             o 12.3-RC1 i386 GENERIC
                             o 12.3-RC1 powerpc GENERIC
                             o 12.3-RC1 powerpc64 GENERIC64
                             o 12.3-RC1 powerpcspe MPC85XXSPE
                             o 12.3-RC1 sparc64 GENERIC
                             o 12.3-RC1 armv6 RPI-B
                             o 12.3-RC1 armv7 BANANAPI
                             o 12.3-RC1 armv7 BEAGLEBONE
                             o 12.3-RC1 armv7 CUBIEBOARD
                             o 12.3-RC1 armv7 CUBIEBOARD2
                             o 12.3-RC1 armv7 CUBOX-HUMMINGBOARD
                             o 12.3-RC1 armv7 RPI2
                             o 12.3-RC1 armv7 WANDBOARD
                             o 12.3-RC1 armv7 GENERICSD
                             o 12.3-RC1 aarch64 GENERIC
                             o 12.3-RC1 aarch64 RPI3
                             o 12.3-RC1 aarch64 PINE64
                             o 12.3-RC1 aarch64 PINE64-LTS

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

                             Installer images and memory stick images are
                             available here:

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

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

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

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

                             A summary of changes since 12.3-BETA3
                             includes:

                             o A fix to the cd(4) driver to improve TOC
                             access validation.

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

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

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

                             === Virtual Machine Disk Images ===

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

                             https://download.freebsd.org/ftp/releases/VM-
                             IMAGES/12.3-RC1/

                             The partition layout is:

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

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

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

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

                             To boot the VM image, run:

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

                             Be sure to replace "VMDISK" with the path to
                             the virtual machine image.
                      # ⚓ What_every_IT_person_needs_to_know_about_OpenBSD_Part
                        3:_That_packet_filter⠀⇛


                             ‘Functional, free and secure by default’,
                             OpenBSD remains a crucial yet largely
                             unacknowledged player in the open-source
                             field.


                             This series aims to highlight the project’s
                             signature security features and development
                             practices — razor-sharp focus on correct and
                             secure code coupled with continuing code
                             audit — as well as the project’s role as a
                             source of innovation in security practices
                             and an ‘upstream’ source for numerous widely-
                             used components such as OpenSSH, PF, LibreSSL
                             and others. Part 1 focused on the history,
                             Part 2 focused on usage and user experience,
                             and this final part will looks at that packet
                             filter (PF).


                             I mentioned PF, the OpenBSD packet filter,
                             earlier. I must confess that PF has been an
                             important part of my life in various contexts
                             since the early 2000s. Over the years, things
                             I have written have contributed to creating
                             the popular but wrong perception that OpenBSD
                             was primarily a firewall operating system.
                             There are a lot of useful and fun features
                             that turned up in or in connection with PF
                             over the years and were pioneered by OpenBSD.
                             Some features were ported to or imitated in
                             other systems, while others remain stubbornly
                             OpenBSD only.


                             So I will touch on some of my favourite PF
                             and PF-attached features, in quasi-random but
                             almost chronological order.


                # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾


                      # ⚓ Audacity_»_PCLinuxO⠀⇛


                             Audacity is a program that lets you
                             manipulate digital audio waveforms. In
                             addition to letting you record sounds
                             directly from within the program, it imports
                             many sound file formats, including WAV, AIFF,
                             MP3 and Ogg/Vorbis. It supports all common
                             editing operations such as Cut, Copy, and
                             Paste, plus it will mix tracks and let you
                             apply plug-in effects to any part of a sound.
                             Updated to 3.1.1.


                      # ⚓ Vivaldi_Browser_»_PCLinuxOS⠀⇛


                             Vivaldi is a new web browser based on
                             Chromium that is built by an Opera founder.
                             Updated to 4.3.2439.65.


                      # ⚓ Signal_Desktop_»_PCLinuxOS⠀⇛


                             Signal Desktop is a private messaging
                             application you can use right from your
                             desktop. Updated to 5.23.1.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ OpenSUSE_is_Looking_for_Candidates_to_Run_for_Its
                        Board⠀⇛


                             There’s not likely to be anything sexy, like
                             televised debates or nation state cracker
                             hackers attempting to steal emails to
                             influence the outcome, but the openSUSE
                             Project is going to have a board election and
                             they’re looking for a few good candidates to
                             step up to the plate.


                             In case you’re new to Linux, openSUSE is the
                             mostly autonomous organization responsible
                             for two Linux distributions based on SUSE,
                             the commercial Linux distribution that’s
                             vying for the “largest independent Linux
                             vendor by revenue” category, now that Red
                             Hat’s technically no longer an independent
                             open source vendor.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Red_Hat_8.5_released_with_SQL_Server_and_.NET_6_…
                        this_is_Linux,_right? [Ed: Tim Anderson is now painting
                        the RHEL release as if Microsoft owns the whole thing.
                        The Register is a loo, not journalism, and Microsoft
                        Tim is showing his true colours again.]⠀⇛


                             Version 8.5 of Red Hat’s Enterprise Linux
                             operating system (RHEL) is out, with updates
                             including .NET 6 and a system role for
                             Microsoft SQL Server, as well as improved
                             container support.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ New_software_for_old_phones:_Pixel_2_gets_Android_12
                        and_Ubuntu_Touch_ports_–_Liliputing⠀⇛


                             The Google Pixel 2 and Pixel 2 XL smartphones
                             were released in 2017 and they were pretty
                             great phones with good performance and
                             excellent cameras. But Google rolled out the
                             last official update for the phones at the
                             end of 2020, which means there’s no official
                             Android 12 build for the Pixel 2 series and
                             the phones no longer receives security
                             updates.


                             But independent developers are keeping
                             Google’s hardware alive even after Google has
                             abandoned it. You can now run Android 12 on
                             the Pixel 2 XL thanks to a custom ROM. And if
                             you’d rather try something quite different,
                             Pixel 2 support is coming to the Linux-based
                             Ubuntu Touch operating system. But you should
                             be aware that some features may not be
                             working yet.


                      # ⚓ Free_Ubuntu_Support_Comes_To_M1_Macs_With_Multipass
                        Update⠀⇛


                             Ubuntu developer Canonical has announced the
                             rollout of an update to its cross-platform VM
                             manager Multipass, adding a free and fast way
                             of running Linux on an M1-powered Mac. The
                             news comes a month after Linux became
                             available to run on Apple silicon ‘as a basic
                             desktop,’ and merely days after reports
                             suggested that Linux kernel 5.16 will include
                             mainline support for the Apple M1 chip’s PCIe
                             controller. Parallels Desktop 17 also offers
                             Ubuntu support on M1 Macs, but the price
                             starts at $79.99. Multipass is free.


                             Apart from the aforementioned software, M1
                             users do not currently have many options to
                             run Linux on their machines. While VirtualBox
                             does not support the M1′s underlying ARM
                             architecture, VMWare Fusion’s Linux support
                             for Apple silicon is still in the preview
                             stage. That makes Multipass a great option
                             for developers interested in running Linux on
                             their M1-powered MacBooks.


                      # ⚓ You’ll_float_too…_If_you_don’t_listen_to_your_IT⠀⇛


                             Here’s yet another hint Pennywise was trying
                             to signal – IT has a scary face that we
                             should all dread! If you don’t know who
                             Pennywise is, then you are missing out
                             watching the horrifying clown from the horror
                             movie series It – not IT (Eye-Tee). No wonder
                             it has become the highest-grossing horror
                             film of all time, especially as Pennywise is
                             giving us more scary life aspects to reflect
                             the movie on (like this one)!


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ So._What’s_Up_With_All_These_Crazy_Event_Networks
                        Then?_|_Hackaday⠀⇛


                             There no doubt comes a point in every
                             traveling hacker’s life when a small
                             annoyance becomes a major one and a rant
                             boils up from within, and perhaps it’s ETH0’s
                             misfortune that it’s at their event that
                             something has finally boiled over. I’m
                             speaking of course about wireless networks.


                             While on the road I connect to a lot of them,
                             the normal commercial hotspots, hackerspaces,
                             and of course at hacker camps. Connecting to
                             a wireless network is a simple experience,
                             with a level of security provided by WPA2 and
                             access credentials being a password. Find the
                             SSID, bang in the password, and you’re in.
                             I’m as securely connected as I reasonably can
                             be, and can get on with whatever I need to
                             do. At hacker camps though, for some reason
                             it never seems to be so simple.


                             Instead of a simple password field you are
                             presented with a complex dialogue with a load
                             of fields that make little sense, and someone
                             breezily saying “Just enter hacker and
                             hacker!” doesn’t cut it when that simply
                             doesn’t work. When you have to publish an app
                             just so that attendees can hook up their
                             phones to a network, perhaps it’s time to
                             take another look .


                      # ⚓ Motorcycle_Rally_Computer_Goes_Open_Source_|
                        Hackaday⠀⇛


                             Motorcycle rally racing is a high-speed,
                             exciting, off-road motorsport that involves
                             zipping across all types of terrain on two
                             wheels. While riding, it’s extremely
                             important for riders to know what’s coming up
                             next — turns, straightaways, stream
                             crossings, the list goes on. Generally, this
                             is handled by a roadbook — a paper scroll
                             that has diagrams of each turn or course
                             checkpoint, along with the distances between
                             them and any other pertinent information. Of
                             course, this needs to be paired with a
                             readout that tells you how far you’ve
                             traveled since the last waypoint so you’re
                             not just guessing. This readout usually takes
                             the form of a rally computer, a device that
                             can display speed, distance traveled, and
                             course heading (and some of the fancier ones
                             have even more data available).


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Stable_Android_12_update_for_Galaxy_S21_is_around_the
                        corner_–_9to5Google⠀⇛


                      # ⚓ Pixel_2_Android_12_ROM_reminds_us_of_one_key_Android
                        strength_–_SlashGear⠀⇛


                      # ⚓ Android_12_update_tracker:_Early_info_we_know_so
                        far⠀⇛


                      # ⚓ How_to_lock_apps_on_Android_–_Phandroid⠀⇛


                      # ⚓ Chrome_for_Android_banner_replaces_snackbar
                        notification_–_9to5Google⠀⇛


                      # ⚓ Most_powerful_Android_in_October_revealed,_it’s_not
                        ROG_Phone_5⠀⇛


                      # ⚓ Nokia_T20_Android_tablet_is_now_on_sale_and_here_are
                        three_features_that_make_it_a_good_option_–_Technology
                        News⠀⇛


                      # ⚓ Want_to_Disable_Ads_in_Your_Android_Games?_These
                        Tricks_Might_Help⠀⇛


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


                # ⚓ Sponsor_Success_at_Apache:_Exploration_and_Practice_of_the
                  Apache_Way_in_Tencent⠀⇛


                       The Apache Software Foundation (ASF) manages more
                       than 227 million lines of code, has 206 project
                       management committees, leads more than 350 Apache
                       projects and operates through a merit system, with
                       more than 850 members, 8,100+ committers, and tens
                       of thousands of contributors.


                       Previously the Apache Group, the ASF has grown to
                       one of the largest open source foundations in the
                       world today. It has built the well-known “Apache
                       Way” through its leadership, sound community, and
                       merit thinking, resulting in a set of schemes that
                       promote the sustainable development of open source
                       communities and guide the practice of open source
                       projects.projects.


                       Since Tencent Open Source was created 11 years ago,
                       a large number of Tencent engineers have formed a
                       deep connection with the Apache community by
                       participating and contributing to Apache projects.
                       Furthermore, by learning from the Apache Way,
                       Tencent is going through its open source journey.


                # § cURL Releases and Raves by Daniel Stenberg⠀➾


                      # ⚓ curl_7.80.0_post_quantum⠀⇛


                      # ⚓ The_curl_v8_plan⠀⇛


                             For a long time I have been wanting to avoid
                             us to ever reach curl version 7.100.0. I
                             strongly suspect that going three-digits in
                             the minor number will cause misunderstandings
                             and possibly even glitches in people’s
                             comparison scripts etc. If nothing else, it
                             is just a very high number to use in a
                             version string and I believe we would be
                             better off by starting over. Reset the clock
                             so to speak.


                             Given that, a curl version 8.0.0 is
                             inevitably going to have to happen and since
                             we do releases every 8 weeks and we basically
                             bump the version number in just about every
                             release, there is a limited amount of time
                             left to avoid the minor number to reach 100.
                             We just shipped curl 7.80.0, so we have less
                             than 20 release cycles in the worst case; a
                             few years.


                             A while ago it struck me that we have a
                             rather big anniversary coming up, also within
                             a few years, and that is curl’s 25th
                             birthday.


                      # ⚓ The_most_used_software_components_in_the_world⠀⇛


                             We can’t know for sure which products are on
                             the top list of the most widely deployed
                             software components. There’s no method for us
                             to count or estimate these numbers with a
                             decent degree of certainty. We can only guess
                             and make rough estimates – and it also
                             depends on exactly what we count. And quite
                             probably also depending on who‘s doing the
                             counting.


                             First, let’s acknowledge that SQLite already
                             hosts a page for mostly deployed software
                             module, where they speculate on this topic
                             (and which doesn’t even mention curl). Also,
                             does this count number of devices running the
                             code or number of installs? If we count
                             devices, does virtual machines count? Is it
                             the number of currently used installations or
                             total number of installations done over the
                             years?


                      # ⚓ My_first_25_years_of_HTTP⠀⇛


                             I like figuring out even or somehow
                             particularly aligned numbers and dates to
                             celebrate. Here’s another one: today marks
                             the day when httpget 0.1 was released in
                             1996.


                             httpget 0.1 was a tiny command line tool
                             written by Rafael Sagula. It was less than
                             300 lines of C code. (Today, the product code
                             is 173,000 lines!)


                             I found httpget just days after it was
                             released when I was searching for a tool to
                             use for downloading currency rates with from
                             an HTTP site. This was the time before Google
                             existed so I assume I used Altavista or
                             something. I can’t remember actually.


                      # ⚓ Hackad:_curl_use_on_TV⠀⇛


                             There’s this new TV-show on Swedish
                             Television (SVT) called Hackad (“hacked” in
                             English), which is about a team of white hat
                             hackers showing the audience exactly how
                             vulnerable lots of things, people and
                             companies are and how they can be hacked
                             using various means. In the show the hackers
                             show how they hack into peoples accounts,
                             their homes and their devices.


                             Generally this is done in a rather non-techy
                             way as they mostly describe what they do in
                             generic terms and not very specifically or
                             with technical details. But in some short
                             sequences the camera glances over a screen
                             where source code or command lines are shown.


                      # ⚓ curl_installations_per_capita⠀⇛


                             I’ve joked with friends and said that we
                             should have a competition to see whom among
                             us have the largest number of curl
                             installations in their homes. This is of
                             course somewhat based on that I claim that
                             there are more than ten billion curl
                             installations in the world. That’s more
                             installations than humans. How many curl
                             installations does an average person have?


                             Amusingly, someone also asked me this
                             question at curl presentation I did recently.


                             I decided I would count my own installations
                             to see what number I could possibly come up
                             with, ignoring the discussion if I’m actually
                             could be considered “average” in this regard
                             or not. This counting includes a few
                             assumptions and estimates, but this isn’t a
                             game we can play with complete knowledge. But
                             no crazy estimates, just reasonable ones!


                      # ⚓ One_new_contributor_every_3.4_days⠀⇛


                             In the curl project we keep track of and say
                             thanks to every single contributor. That
                             includes persons who report bugs or security
                             problems, who run infrastructure for us, who
                             assist in debugging or fixing problems as
                             well as those who author code or edit the
                             website. Those who have contributed to make
                             curl to what it is.


                             Exactly today October 4th 2021, we reached
                             2,500 names in this list of contributors for
                             the first time. 2,500 persons since the day
                             curl was created back in March 1998. 2,500
                             contributors in 8599 days. This means that on
                             average we’ve seen one new contributor
                             helping out in the project every 3.44 days
                             for almost twenty-four years. Not bad at all.


                # § Web Browsers⠀➾


                      # ⚓ Old_Microsoft_is_back:_If_the_latest_Windows_11
                        really_wants_to_use_Edge,_it_will_use_Edge_no_matter
                        what⠀⇛


                             Microsoft Windows 11 build 22494 appears to
                             prevent links associated with the Microsoft
                             Edge browser from being handled by third-
                             party applications, a change one developer
                             argues is anticompetitive.


                             Back in 2017, Daniel Aleksandersen created a
                             free helper application called EdgeDeflector
                             to counter behavioral changes Microsoft made
                             in the way Windows handles mouse clicks on
                             certain web links.


                             Typically, https:// links get handled by
                             whatever default browser is set for the
                             system in question. But there are ways to
                             register a custom protocol handler, for
                             operating systems and web browsers, that
                             defines the scheme to access a given resource
                             (URI).


                      # § Mozilla⠀➾


                            # ⚓ A_Firefox_mobile_product_manager_on_her
                              favorite_corners_of_the_internet⠀⇛


                                   Here at Mozilla, we are the first to
                                   admit the internet isn’t perfect, but
                                   we are also quick to point out that the
                                   internet is pretty darn magical. The
                                   internet opens up doors and
                                   opportunities, allows for people to
                                   connect with others, and lets everyone
                                   find where they belong — their corners
                                   of the internet. We all have an
                                   internet story worth sharing. In My
                                   Corner Of The Internet, we talk with
                                   people about the online spaces they
                                   can’t get enough of, what we should
                                   save in Pocket to read later, and what
                                   sites and forums shaped them.


                                   First up is Vesta Ware, a staff product
                                   manager at Firefox Mobile here at
                                   Mozilla on the parts of the internet
                                   she can’t stop talking about (and, yes,
                                   that includes Firefox).


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ MongoDB_5.1_for_DBaaS_arrives_amid_questions_over_on-
                        prem_release_stability⠀⇛


                             MongoDB, the company behind the document non-
                             relational database of the same name, has
                             released its 5.1 update but only as a managed
                             service.


                             While critics voice concerns that bugs from
                             5.0 have still not been fixed, the NoSQL
                             poster child has pushed on with efforts to
                             accommodate time series data and better
                             support analytics on operational systems.


                             The result could be good for users already
                             requiring these features, but is unlikely to
                             usurp rival databases with these performance
                             specialisms.


                             MongoDB 5.1 is the first in an “accelerated
                             release cadence” and will only be fully
                             supported on MongoDB Atlas, the company’s
                             database as a service, while being also
                             available to download as a “development
                             release.”


                             It features support for globally distributed
                             time series applications through MongoDB’s
                             native sharding to horizontally distribute
                             massive data sets and co-locate nodes.


                      # ⚓ What_if_…_MySQL’s_repeatable_reads_cause_you_to_lose
                        money?⠀⇛


                             Well, let me say if that happens because
                             there is a logic mistake in your application.
                             But you need to know and understand what
                             happens in MySQL to be able to avoid the
                             problem.


                             In short the WHY of this article is to inform
                             you about possible pitfalls and how to
                             prevent that to cause you damage. pitfalls1


                             Let us start by having a short introduction
                             to what Repeatable reads are about. Given I
                             am extremely lazy, I am going to use (a lot)
                             existing documentation from MySQL
                             documentation.


                # § Content Management Systems (CMS)<⠀➾


                      # ⚓ Take_the_2021_WordPress_Annual_Survey_(and_view_the
                        2020_results)!⠀⇛


                             Each year, members of the WordPress community
                             (users, site builders, extenders, and
                             contributors) provide their valuable feedback
                             through an annual survey. Key takeaways and
                             trends that emerge from this survey often
                             find their way into the annual State of the
                             Word address, are shared in the public
                             project blogs, and can influence the
                             direction and strategy for the WordPress
                             Project.


                             Simply put: this survey helps those who build
                             WordPress understand more about how the
                             software is used, and by whom. The survey
                             also helps leaders in the WordPress open
                             source project learn more about our
                             contributors’ experiences.


                      # ⚓ Bogus_“Unsupported_Browser”_errors_on_WordPress.com⠀⇛


                             Logging in to WordPress.com in GNOME Web 41
                             from Flatpak results in a page called “Browse
                             Happy” that says I need a different browser.


                             This made me unhappy.


                             The options are to continue anyway, or learn
                             about supported browsers on https://
                             browsehappy.com/ which implies that not using
                             a “GAFAM” browser puts you at risk on the
                             web.


                             I filed a bug report on GNOME Web in the
                             hopes they can add a UA quirk for WordPress
                             that makes it think I use another browser.


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ 8_New_Features_&_Improvements_to_Expect_in_GIMP
                              3.0_Release⠀⇛


                                   GIMP is one of the best free image
                                   editors available for Linux. Not just
                                   for users who want a free alternative
                                   to Adobe suite, but many professionals
                                   use GIMP for artwork, design, and photo
                                   editing.


                                   Even though GIMP offers many essential
                                   features and options to work with, many
                                   modern alternatives (irrespective of
                                   the platform) have popped up that
                                   outshine GIMP in several ways.


                                   And, GIMP 3.0 could be the release that
                                   turns the table by putting GIMP as one
                                   of the best modern offerings to compete
                                   with commercial options available out
                                   there.


                                   This article will discuss the expected
                                   features to arrive with GIMP 3.0
                                   release.


                # § Programming/Development⠀➾


                      # ⚓ Managing_a_Node_Applications_using_PM2⠀⇛


                             Hello, friends. In this post, you will learn
                             how to manage Node applications using PM2.
                             Although many developers should already know
                             that thanks to PM2 we will be able to control
                             the application we have already made using
                             NodeJS.


                      # ⚓ Easy!Appointments:_A_free_Self-hosted_Appointment
                        Scheduler⠀⇛


                             Easy!Appointments is an open-source, free,
                             web-based, self-hosted, event scheduler and
                             appointment manager. It is created by Alex
                             Tselegidis, a software developer from Greece.


                             Easy!Appointments syncs events with Google
                             Calendar, and similar calendar services.


                             It is a highly customizable, easy-to-use
                             system, written with PHP and uses MySQL. It
                             uses Full-Calendar which is a rich JavaScript
                             calendar library, Moment.js to manipulate
                             time, jQuery, and Bootstrap CSS framework.


                      # § Python⠀➾


                            # ⚓ How_to_manipulate_Excel_spreadsheets_with
                              Python_and_openpyxl⠀⇛


                                   Python is a general purpose programming
                                   language that needs no presentations.
                                   It was originally written by Guido Van
                                   Rossum, and saw its first release in
                                   the year 1991. At the moment of
                                   writing, the latest stable version of
                                   the language is 3.10. In this tutorial
                                   we see how to use it together with the
                                   openpyxl library to manipulate Excel
                                   spreadsheets.


    * § Leftovers⠀➾


          o ⚓ The_American_Dilemma⠀⇛


                 Religious mythology, from the Greeks on down, has been
                 utilized to provide easily interpreted moral imperatives
                 for the guidance of vulnerable, credulous humans. Gog and
                 Magog embodied the power of evil, as symbols of all that
                 was corrupt, perverse, and destructive in human nature,
                 and were dreaded as such.


                 Americans are short on mythology now, except for the
                 sleazy, dirty joke of Exceptionalist bullshit, but the
                 Gog/Magog model will serve well in describing one aspect
                 of the waning days of this despicable, moribund empire:
                 its governing political parties.


          o ⚓ Joanna_Hogg_and_the_Art_of_Life⠀⇛


                 When does a life become a story, a narrative legible to
                 those outside it? This question trills at the heart of
                 Joanna Hogg’s The Souvenir (2019) and the new The
                 Souvenir Part II, a two-part film à clef constructed like
                 a precarious house of cards: memories, texts, and
                 ephemera from a life, stacked carefully one upon another
                 in the hope that they hold their shape. The films take
                 their names from Jean-Honoré Fragonard’s rococo 18th-
                 century painting The Souvenir, which shows a woman in a
                 lustrous pink gown carving an initial into a tree; a
                 letter, presumably from her lover, lies on the ground by
                 her feet. It’s an image of willful alchemy—of turning a
                 memory, a feeling, into an object and event in the
                 exterior world. The painting itself reifies a scene in
                 Jean-Jacques Rousseau’s epistolary 1761 novel Julie; or,
                 The New Heloise, about the mercurial passions between a
                 married woman and her former flame—which in turn draws on
                 the medieval tale of the French nun Héloïse d’Argenteuil
                 and, likely, Rousseau’s own romantic entanglements. To
                 this series of artistic transfigurations, Hogg adds her
                 own, constellating personal references as she
                 reconstructs her youth: the 1938 song “A Souvenir of
                 Love” by Jessie Matthews, the films of Powell and
                 Pressburger, period fashion from Manolo Blahnik and Yohji
                 Yamamoto, letters from Hogg’s former lover, 16-millimeter
                 pictures she took in the 1980s. Together, all these
                 objects and invocations comprise a life of the mind, an
                 intellectual history assembled in the hope that it might
                 represent something more than just that: the haphazard
                 accumulations of one’s time on earth.


          o ⚓ 25_scenes_in_which_the_circumstances_did_not_apply⠀⇛


                 N1.in the light of a lamppost, a black fence in the
                 background, wearing a long, fabulously well-cut black
                 coat, feet in leather boots, 6’4” over me, he is a pylon


                 in his eyes all princesses locked behind heavy-lidded
                 eyes he turns to catchthe silent moonlight so i can
                 shudder at how dark they stayhe tells me his name is meat
                 because he eats meat because he’s from the mountainshe
                 calls me lola he predicts i will regret everything i
                 don’t dohe can’t know that i tell himmy name is dolores
                 and i’m not thinking of anybody


          o § Science⠀➾


                # ⚓ IFF_submits_its_comments_on_the_Draft_Approach_Paper_for
                  creating_a_Digital_Address_Code⠀⇛


                       We have provided our comments on the Draft Approach
                       Paper for creating a Digital Address Code. In our
                       comments, we have tried to highlight the governance
                       issues around geospatial data, data protection
                       issues around the use of geospatial data, and
                       potential surveillance and function creep
                       challenges which will arise from DAC. Finally, we
                       recommend that a comprehensive grievance redressal
                       mechanism be provided for complaints against
                       geospatial mapping, that robust security standards
                       and user rights be specified for the DAC database,
                       and that the principle of purpose limitation be
                       followed.


                       [...]


                       The latter approach is rather detailed and includes
                       using an algorithm which would allocate the
                       subsequent digits on the basis of habitation
                       density after assessing the population density and
                       designing a geospatial workflow. The DAC would be
                       allotted based on the division of areas into a
                       grid, each of which will comprise of around 300
                       addresses. Out of the 12 digits, the last digit
                       would be a ‘check digit’ and the immediately
                       preceding four would be identifiers within the
                       neighbourhood. Upto the neighbourhood level, the
                       DAC would be automated but for the final four
                       identifier digits at the neighbourhood level, a
                       ‘system driven consent process’ is proposed.


          o § Education⠀➾


                # ⚓ Would_You_Manage_70_Children_And_A_15-Ton_Vehicle_For_$18
                  An_Hour?⠀⇛


                       At year-round, full-time hours — the way the U.S.
                       Bureau of Labor Statistics calculates an annual
                       wage — the average school bus driver makes more
                       than $39,000 a year. But school bus drivers don’t
                       work year-round, full-time hours. “We’re only
                       guaranteed four hours of pay a day,” Steele said.


                       There are no paid holidays or sick days, she and
                       other bus industry experts say. Benefits vary from
                       company to company, and there’s no guaranteed work
                       at all in summer. “Spring break is all unpaid.
                       Every teacher-compensatory day, every snow day, any
                       time they cannot pay us they will,” Steele said.
                       She added that a recent, failed unionization effort
                       among the Robbinsdale bus drivers started in part
                       as a fight for snow-day pay.


          o § Hardware⠀➾


                # ⚓ How_To_Make_A_CPU_–_A_Simple_Picture_Based_Explanation⠀⇛


                       The purpose of this article is to explain how to
                       make a CPU out of rocks and sand as fast as
                       possible without using too many words. As the world
                       of proprietary hardware and software crushes in
                       around us, we risk losing the ability to make
                       things for ourselves as individuals. It is for this
                       reason that I felt compelled to learn how one could
                       hypothetically make their own integrated circuits
                       by themself. Skip to the end of this article for a
                       few more words on this subject and a disclaimer.


                # ⚓ Build_Your_Own_HV_Capacitors_|_Hackaday⠀⇛


                       Finding high voltage capacitors can be tricky.
                       Sure, you can buy these capacitors, but they are
                       often expensive and hard to find exactly what you
                       want. [RachelAnne] needed some low-value variable
                       capacitors that would work at 100 kV. So she made
                       some.


                       Instead of fabricating the plates directly, these
                       capacitors use laminations from a scrap power
                       transformer. These usually have two types of
                       plates, one of which looks like a letter “E” and
                       the other just like a straight bar. For dielectric,
                       the capacitors use common transparency film.


                # ⚓ Rolling_Your_Own_Long-Range_IoT_Sensor_Network_|_Hackaday⠀⇛


                       Homebrew wireless sensors are nothing new around
                       these parts: grab an ESP8266, hang a BME280 from
                       the I2C pins, and you’re just a few lines of code
                       away from joining the Internet of Things on your
                       own terms. Builds like this are so cheap and easy
                       that they make an excellent first project for folks
                       looking to get into the electronics game, but what
                       if you’re looking for something a bit more bespoke?


                       In that case, you could follow in the footsteps of
                       [Discreet Mayor] and put together a custom modular
                       architecture for long-range wireless sensors. The
                       core of the system is a breakout board for the
                       Texas Instruments SimpleLink CC1312 wireless MCU
                       which features a simple 2×11 header connector. This
                       allows the module to either be plugged into a
                       larger board or have a small sensor PCB attached
                       directly to it.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Hog_Futures_Soar_After_Biden_Moves_to_Speed_Up_Slaughter-
                  Lines,_Ignoring_Safety_Fears⠀⇛


                       The Biden administration’s Wednesday announcement
                       allowing several pork processing plants to speed up
                       production was well-received by livestock
                       traders—pleased to see an immediate spike in hog
                       futures—but progressive critics warned that the
                       move will make slaughterhouses, and the nation’s
                       food supply, more dangerous.


                       “The Biden administration is caving to industry
                       pressure.”


                # ⚓ Drug_Price_Negotiation_Is_A_Second-Best_Fix._Here’s_What
                  Will_Really_Work⠀⇛


                       As Democrats struggle to bring together 50 votes to
                       pass the Build Back Better Act, a major sticking
                       point with the legislation has emerged. That is,
                       whether it should include provisions changing the
                       law to allow Medicare to negotiate drug prices,
                       with caps on payments set based on prices paid by
                       other wealthy nations.


                # ⚓ How_You_Can_Report_on_the_Toxic_Hot_Spots_Near_You⠀⇛


                       Is the community you cover located in or near a hot
                       spot of cancer-causing industrial air pollution?
                       The ProPublica reporters who built the most
                       detailed map of toxic hot spots have created this
                       guide to help journalists across the country
                       illuminate the risks readers face and the remedies
                       they might have to hold government and industry
                       accountable. (For more background, you can learn
                       more about air toxics and read our national
                       overview story.)


                       As part of our effort to empower journalists to use
                       this new tool, ProPublica is also hosting a virtual
                       event geared toward journalists where our reporters
                       can answer questions about the map, the underlying
                       data and the shoe-leather reporting techniques
                       they’ve employed. This event will be held on
                       Monday, Nov. 22, 2021, at 3 p.m. Eastern time.
                       Register here. (There will be a separate virtual
                       event for the general public.)


                # ⚓ NIH_Praised_for_Standing_Up_to_Moderna_in_Vaccine_Patent
                  Fight⠀⇛


                # ⚓ Democrats_in_Statehouses_Aim_to_Secure_Abortion_Rights_as
                  “Roe”_Faces_Threats⠀⇛


                # ⚓ Federal_Judge_Overturns_Greg_Abbott’s_Ban_on_Mask_Mandates
                  in_Texas_Schools⠀⇛


                       A federal judge late Wednesday overturned Texas
                       Gov. Greg Abbott’s executive order prohibiting mask
                       mandates in the state’s public schools, arguing the
                       ban violates the Americans With Disabilities Act.


                       “The spread of Covid-19 poses an even greater risk
                       for children with special health needs,” U.S. Judge
                       Lee Yeakel of the Western District of Texas, a
                       George W. Bush appointee, wrote in his 29-page
                       ruling. “Children with certain underlying
                       conditions who contract Covid-19 are more likely to
                       experience severe acute biological effects and to
                       require admission to a hospital and the hospital’s
                       intensive-care unit.”


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Apple_will_let_users_pass_on_iCloud_data_when_they
                        die⠀⇛


                      # ⚓ Attacker_undetected_by_Qld_regional_water_supplier
                        for_nine_months⠀⇛


                             “The story here is typical: a legacy, more
                             vulnerable system was targeted first. Whilst
                             no critical data was stolen in this instance,
                             with the attackers simply redirecting Web
                             traffic, perhaps a more sophisticated bad
                             actor would have exploited the weakness
                             further.


                      # ⚓ Queensland_water_supplier_Sunwater_targeted_by
                        hackers_in_months-long_undetected_cyber_security
                        breach⠀⇛


                             Sunwater admitted the cyber breach after the
                             tabling of a Queensland’s Audit Office report
                             into the state’s water authorities, which
                             mentioned the incident but did not say which
                             authority was targeted.


                             x Following questions from the ABC, Sunwater
                             confirmed it was the authority affected by
                             the breach revealed in the Audit Office’s
                             report.


                      # ⚓ Judge_denies_Apple’s_request_to_delay_App_Store
                        changes.⠀⇛


                             A federal judge ruled on Tuesday that Apple
                             could not delay making changes to its App
                             Store, a move that could soon allow app
                             developers to directly communicate with
                             customers about ways to pay for services
                             outside Apple’s ecosystem.


                             Calling Apple’s request for a delay
                             “fundamentally flawed,” Judge Yvonne Gonzalez
                             Rogers of U.S. District Court for the
                             Northern District of California warned in her
                             ruling that the company’s strict App Store
                             rules were building toward “antitrust
                             conduct.”


                      # ⚓ Judge_orders_Apple_to_allow_external_payment_options
                        for_App_Store_by_December_9th,_denying_stay⠀⇛


                             Epic v. Apple judge Yvonne Gonzalez Rogers
                             says Apple must comply with an order to let
                             developers add links and buttons to external
                             payment options, denying the company’s motion
                             for a stay. “Apple’s motion is based on a
                             selective reading of this Court’s findings
                             and ignores all of the findings which
                             supported the injunction,” her new order
                             reads.


                             Judge Gonzalez Rogers issued her order after
                             a Tuesday hearing concerning the blockbuster
                             antitrust lawsuit, which Fortnite publisher
                             Epic Games filed in 2020 and which went to
                             trial this year. During the hearing, Apple
                             said it needed more time to rewrite its anti-
                             steering policies — rules that bar app
                             developers from linking to payment methods
                             besides the iOS App Store.


                      # ⚓ [Old] Epic_v_Apple_explained:_What_the_trial_is_about
                        and_what_happened_in_court⠀⇛


                             Last year, Epic Games intentionally broke
                             Apple’s rules by putting its own payment
                             processing system in the iPhone version of
                             Fortnite, bypassing Apple’s 30% fee and
                             giving players a V-bucks discount. Apple
                             responded by kicking Fortnite off the iOS App
                             Store, while Epic launched a lawsuit and PR
                             campaign declaring the iPhone maker “anti-
                             competitive.”


                             The companies have jabbed at each other for
                             the past year, building their cases. (Epic
                             CEO Tim Sweeney practices his ripostes on
                             Twitter weekly.) Now the time has come to
                             square off in person: The Epic and Apple
                             trial has begun.


                             Here’s what to expect from the trial, and
                             what it’s all about in the first place.


                      # ⚓ Judge_denies_Apple’s_request_for_a_stay_after_Epic
                        trial⠀⇛


                             Judge Yvonne Gonzalez Rogers has denied
                             Apple’s request for a stay of the injunction
                             ordering it to let app developers link to
                             non-Apple payment options. The company has 90
                             days from the verdict to comply.


                             As part of the Epic v Apple case that went to
                             court this year, Apple was found to be in
                             violation of California’s Unfair Competition
                             Law. A permanent injunction declared that,
                             “Apple Inc. [...] are hereby permanently
                             restrained and enjoined from prohibiting
                             developers from (i) including in their apps
                             and their metadata buttons, external links,
                             or other calls to action that direct
                             customers to purchasing mechanisms, in
                             addition to In-App Purchasing and (ii)
                             communicating with customers through points
                             of contact obtained voluntarily from
                             customers through account registration within
                             the app.”


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ The_Delhi_High_Court_directs_the_CIC_to
                                    provide_a_time_frame_within_which_our
                                    second_appeal_for_information_on
                                    surveillance_orders_will_be_decided⠀⇛


                                         We have been pursuing information
                                         relating to the scope and scale
                                         of e-surveillance conducted by
                                         the Ministry of Home Affairs
                                         since December 2018. The Ministry
                                         of Home Affairs (‘MHA’) had
                                         originally claimed that the
                                         information is exempt for
                                         national security, but the
                                         Central Information Commissioner
                                         (‘CIC’) said that this doesn’t
                                         apply – and directed the MHA to
                                         hear the matter again. When the
                                         MHA heard the matter again, it
                                         now claimed that it cannot
                                         provide the information anyway,
                                         because it has destroyed it! We
                                         filed another appeal before the
                                         CIC, and also filed a writ
                                         petition in the Delhi High Court
                                         to protect against further
                                         destruction of data in the
                                         meanwhile, and highlighting the
                                         immense delays faced in the CIC.
                                         The Delhi High Court has now
                                         directed the CIC to tell the High
                                         Court a timeline within which our
                                         appeal will be decided.


                                  # ⚓ Meta_Isn’t_Just_About_Rebranding
                                    Facebook:_Could_It_Bring_a_Dystopian
                                    Future?⠀⇛


                                         Is the launch of Meta merely an
                                         attempt at rebranding Facebook
                                         after the considerable hit its
                                         image has taken with the
                                         revelations of Facebook
                                         whistleblowers Frances
                                         Haugen and Sophie Zhang? Is it to
                                         move away from its sullied past
                                         and present to an alternate
                                         universe, the metaverse that
                                         Facebook will create in the
                                         future? Does the company want its
                                         users to forget about its hate-
                                         filled Facebook pages, which fuel
                                         the company’s ad-driven business
                                         empire, by moving the focus away
                                         from the Facebook brand? Or is
                                         this move aimed at winning back
                                         the young viewers that it is
                                         “losing traction” with?


                                         Facebook’s internal documents,
                                         made public by Haugen, reflect
                                         this desperation to win back the
                                         young users, and they even talk
                                         about focusing Facebook’s
                                         attention on preteens—children in
                                         the age group of 10 to 12—who are
                                         viewed as a “valuable but
                                         untapped audience.” More
                                         importantly, Facebook seems to
                                         follow the same logic as
                                         the cigarette companies do by
                                         targeting children and getting
                                         them hooked on smoking. Both
                                         Facebook and these cigarette
                                         companies seem to believe that
                                         once they hook these children
                                         onto their products, they stay
                                         hooked for life, providing these
                                         companies with captive, lifelong
                                         customers. Or, in the case of
                                         Facebook, this means selling
                                         the data of their users, those
                                         hooked on Facebook, to
                                         advertisers for the lifetime of
                                         these users.


                                  # ⚓ Lawmakers_Choose_the_Wrong_Path,_Again,
                                    With_New_Anti-Algorithm_Bill⠀⇛


                                         We need a strong privacy law. We
                                         need laws that will restore real
                                         competition and data
                                         interoperability. And then, we
                                         need to have a serious discussion
                                         about breaking Facebook up into
                                         its component parts. In other
                                         words, the federal government
                                         should go back and do the
                                         rigorous merger review that it
                                         should have done in the first
                                         place, before the Instagram and
                                         WhatsApp purchases.


                                         It’s unfortunate that lawmakers
                                         are, by and large, declining to
                                         pursue these solutions. As they
                                         express shock and rage at
                                         Haugen’s testimony, we continue
                                         to see them promote legislation
                                         that will entrench the power of
                                         existing tech giants and do
                                         grievous harm to users’ right to
                                         free expression.


                                         The most recent effort is a bill
                                         called the “Justice Against
                                         Malicious Algorithms Act” (JAMA
                                         Act, H.R. 5596). This proposed
                                         law, sponsored by House Energy
                                         and Commerce Committee Chairman
                                         Frank Pallone (D-NJ) and three
                                         others, is yet another misguided
                                         attack on internet users in the
                                         name of attacking Big Tech.


                                  # ⚓ Clearview_Officially_Kicked_Out_Of
                                    Australia_For_Violation_Country’s_Privacy
                                    Laws⠀⇛


                                         Clearview — the facial
                                         recognition tech company whose
                                         unproven AI runs searches on 10
                                         billion images scraped from the
                                         web — has been booted from
                                         another country.


                                  # ⚓ Belgium,_GDPR_Superpower,_About_to_Rule
                                    Leading_Ad_Tracking_Framework_is_Illegal⠀⇛


                                         Back in 2017, Belgium was one of
                                         three EU countries that ruled
                                         Facebook was breaking their
                                         privacy laws. Last year it
                                         emerged that Beligum was
                                         investigating the real-time
                                         bidding (RTB) process that lies
                                         at the heart of most online
                                         advertising today. The focus of
                                         that investigation was something
                                         called the Transparency and
                                         Consent Framework (TCF) from the
                                         leading digital advertising group
                                         IAB Europe, which describes its
                                         mission as “to lead political
                                         representation and promote
                                         industry collaboration to deliver
                                         frameworks, standards and
                                         industry programmes that enable
                                         business to thrive in the
                                         European market”.


                                  # ⚓ Supreme_Court_to_hear_‘secrets’_in_case
                                    over_Muslim_surveillance⠀⇛


                                         Ultimately Monteilh‘s handlers
                                         told him to ask about jihad and
                                         express a willingness to engage
                                         in violence. Those questions
                                         caused members of the community
                                         to report him to the FBI and
                                         other authorities and seek a
                                         restraining order against him.


                                         The FBI has acknowledged Monteilh
                                         was an informant, and the story
                                         was covered in the news media
                                         including on the National Public
                                         Radio show “This American Life.”


                                  # ⚓ Startpage_harasses_VPN_users….._So_much
                                    for_their_privacy_claims.⠀⇛


                                         So that’s nice. “Your access to
                                         Startpage has been suspended at
                                         this time.”.


                                         I’ve gotten this a few times
                                         while using NordVPN, but it’s
                                         happening more and more.


                                         Why do they want me to drop my
                                         VPN if they’re all about privacy?


          o § Defence/Aggression⠀➾


                # ⚓ Let’s_Turn_Rising_Generations_Into_War_Resisters_Rather
                  Than_Veterans⠀⇛


                # ⚓ A_Soldiers_Home_Companion⠀⇛


                       “My father lives there,” she said. “The food is
                       great. The rent is cheap. They take care of
                       everything.”


                       I’m on two housing lists but figured why not? I
                       filled out an application; two months later I had
                       an interview at the Chelsea Soldiers’ Home in
                       Boston.


                # ⚓ Day_of_the_Dead⠀⇛


                       Eventually everything is doomed. The sun will go
                       Red Giant and devour the Earth. All the stars will
                       eventually flame out and die. Why care? Why not
                       succumb to hedonism and excess, live it up and suck
                       it up. Who gives a flying fuck about some tweety
                       birds, posies and varmints.


                       Why? Because the Earth, the stars, the Universe,
                       somehow managed to bring forth these marvelous
                       organic inventions that live and breathe and frolic
                       and mate and fight and eat and hunt and fly and run
                       and howl and sing. Because we are all refugees
                       stranded on one blue marble in the vast cold
                       emptiness, possibly (but unlikely) the only life in
                       all the terrifying wilderness of space. Surely we
                       should look after one another.


                # ⚓ A_Real_Day_for_Veterans⠀⇛


                       There are 40,000 homeless veterans in this country.
                       A real day for veterans would address their
                       physical and emotional needs and help them access
                       permanent housing.


                       One of every 10 post 9/11 veterans has been
                       diagnosed with a substance abuse problem. A real
                       day for veterans would help them get treatment
                       without stigmatization or shame.


                # ⚓ Human_Rights_Advocates_Condemn_‘Intolerable’_Abuse_of
                  Refugees_Trapped_at_Poland-Belarus_Border⠀⇛


                       “Vulnerable people are not chess pawns to be used
                       in a geopolitical struggle… European values are
                       dangerously under threat when people are allowed to
                       die from hypothermia at its external border.”


                # ⚓ Veterans_Group_on_Annual_Mission_to_Reclaim_November_11_as
                  Day_for_Peace⠀⇛


                       As countries across the globe mark Armistice Day
                       Thursday, advocacy group Veterans for Peace is on
                       its annual campaign to bring the focus in the U.S.
                       back to the day’s original intent of a celebration
                       of peace.


                       “We want to be part of a society that acknowledges
                       peace as the ideal.”


                # ⚓ Why_Did_the_DoD_Abandon_a_Report_Tracking_139_Military
                  Mental_Health_Programs?⠀⇛


                # ⚓ Opinion_|_Honor_Armistice_Day_on_November_11th_as_a_Day_of
                  Peace⠀⇛


                       The first Armistice Day was a celebration of the
                       moment—the 11th hour of the 11th day of the 11th
                       month in 1918—that the brutality of that first
                       industrial war, which robbed 40 million soldiers
                       and civilians of life, ended and peace began.


                # ⚓ Nuclear_Weapons_Ban_Treaty_Tied_to_‘Historic_Shift’_Away
                  From_‘Perilous_Profiteering’⠀⇛


                       The latest Don’t Bank on the Bomb report, released
                       Thursday, sheds light on the early impacts of a
                       global treaty banning nuclear weapons worldwide
                       while also exposing the companies and financial
                       institutions responsible for continuing to build up
                       governments’ arsenals.


                       “This report looks at those with vested interests
                       to keep a nuclear arms race going.”


                # ⚓ Class_Warfare_and_Socialist_Resistance: Nicaragua,_Cuba,
                  Venezuela_as_Existential_Threats_to_the_US⠀⇛


                       One of the extreme ironies of the latest attack by
                       the settler-colonial regime of the United States
                       against the national democratic project of
                       Nicaragua is that in Nicaragua, the second poorest
                       nation in the Americas, universal healthcare and
                       education are guaranteed to the population as a
                       human right, while in the U.S. those kinds of basic
                       human rights are distant dreams.


                       The day after the so-called progressive block of
                       legislators in the U.S. House of Representatives
                       surrendered to President Joe Biden and the right-
                       wing corporate wing of the party on the Build Back
                       Better legislation that offered some minor and
                       temporary relief for workers and the poor, many of
                       those same “progressives” voted for the RENACER
                       Act. The RENACER Act is a vicious piece of
                       legislation meant to undermine the ability of the
                       Nicaragua government to protect the human rights of
                       its people and to punish the people for having the
                       temerity to support their government and their
                       anti-colonial project.


                # ⚓ Opinion_|_American_History:_Let’s_Face_the_Truth⠀⇛


                       When you’re losing the game, summon the commies!


                # ⚓ ATF_Goes_On_Tour_To_Teach_Journalists_That_Cops_Are_Usually
                  Right_When_They_Kill_Someone⠀⇛


                       The ATF (the accepted not-actually-an-acronym for
                       the Bureau of Alcohol, Tobacco, Firearms and
                       Explosives) is back on its periodic charm
                       offensive. This time the charm seems a bit more
                       forced, as citizens and governments all over the
                       nation are aggressively questioning force use by
                       law enforcement officers.


                # ⚓ Expel_Paul_Gosar_From_Congress⠀⇛


                       Arizona Republican Representative Paul Gosar’s
                       posting of an altered anime video that depicted him
                       killing a colleague, New York Democrat Alexandria
                       Ocasio-Cortez, should be the last straw for the
                       most dangerously delusional member of the US House
                       of Representatives.


                # ⚓ World_and_Regional_Powers_Shape_the_Horn_of_Africa,
                  Ethiopia_Bites_the_Dust⠀⇛


                # ⚓ Kurt_Vonnegut’s_Prescient_Insight_Into_Veterans’_Trauma⠀⇛


                       In The Writer’s Crusade: Kurt Vonnegut and the Many
                       Lives of Slaughterhouse-Five (Abrams, 2021), I
                       examine Vonnegut’s masterpiece by going on a
                       biographical and literary journey into the author’s
                       life, from the trauma he experienced in World War
                       II through his career and up to his final years as
                       an ornery New Yorker. I also talk with contemporary
                       authors, such as Tim O’Brien, to shed light on how
                       Vonnegut integrated his experiences and was able to
                       write a “true” war story. The excerpt below is
                       adapted from the book.1


                # ⚓ ‘Arrogant_Insensitivity’:_Defense_Lawyer_in_Arbery_Murder
                  Trial_Ripped_for_Bid_to_Bar_Black_Pastors⠀⇛


                       An attorney for one of the three men accused of
                       murdering unarmed Black runner Ahmaud Arbery in
                       Brunswick, Georgia last year raised eyebrows and
                       ire Thursday after asking the presiding judge in
                       the case to exclude Black faith leaders from the
                       courtroom because he believes their presence is
                       “political” and could sway the nearly all-white
                       jury.


                       “Asking a judge to bar me or any minister of the
                       family’s choice underscores the disregard for the
                       value of the human life lost and the grieving of a
                       family in need of spiritual and community support.”


                # ⚓ White_Supremacy_on_Trial:_From_Rittenhouse_in_Kenosha_to
                  Killers_of_Ahmaud_Arbery,_Will_They_Go_Free?⠀⇛


                       Kyle Rittenhouse took to the stand on Wednesday
                       before his defense team asked for a mistrial with
                       prejudice in the case. If a mistrial is granted,
                       Rittenhouse cannot be tried again, though the judge
                       did not immediately rule on the request and said
                       jury deliberations could begin on Monday. Now 18
                       years old, Rittenhouse was 17 when he fatally shot
                       two men and injured one with a semiautomatic rifle
                       during racial justice protests last year in
                       Kenosha, Wisconsin. Rittenhouse is pleading not
                       guilty to six charges, including homicide. While
                       questioned, Rittenhouse broke down in tears,
                       admitting to using deadly force but denying intent
                       to kill his victims, and Judge Bruce Schroeder
                       seemed to side with the defense at a handful of
                       different points during Rittenhouse’s testimony.
                       Meanwhile, the judge’s cellphone went off while the
                       court was in session and played a ringtone for the
                       song “God Bless the U.S.A.” by Lee Greenwood, the
                       opening song played at Donald Trump’s rallies. For
                       more on the Rittenhouse trial, as well as the
                       murder trial for the three men who killed Black
                       jogger Ahmaud Arbery in Georgia, we speak with Elie
                       Mystal, justice correspondent for The Nation, and
                       antiracist activist Bree Newsome Bass. Mystal says
                       Judge Schroeder “has pre-judged the trial in favor
                       of Rittenhouse,” and “that was obvious before the
                       trial.” Newsome Bass says, irrespective of the
                       trials’ outcomes, “the legal system itself is an
                       affront to the notion of justice.” She adds, “What
                       does justice even mean in a system that was
                       established to strip Black people of their humanity
                       and for the greater part of its history has never
                       really held white people accountable for murdering
                       Black people?”


                # ⚓ Six_War_Poems_by_Vietnam_Vets⠀⇛


                       Our medic works on a young soldier,
                       tails of battle dressings tangle around him
                       like intestines. On the bulldozers steel track,
                       linked like rosary beads,
                       a man sits, minus his arm, both legs. Someone’s
                       hands,
                       no–my hands–
                       pitch the smoke grenade. Through a squall of dust
                       and smoke,
                       the chopper’s open door
                       beckons. We carry litters,
                       all hunched over
                       like men in a hailstorm. Gentle cuffs against my
                       thigh.
                       A leg…
                       from knee to boot, dangles by a strand of flesh.
                       It taps to remind me
                       of my undeserved wholeness.


                       Gary Rafferty served with A Battery, 2nd Battalion,
                       94th Artillery, Vietnam 1970-71. His fortcoming
                       memoir is Nothing Left to Drag Home: The Siege at
                       Lao Bao During Operation Dewey Canyon II–Lam Son
                       719, as Told by an Artilleryman Who Survived It.
                       Email: Maddog7337@yahoo.com.


                # ⚓ Muslim_Mafia:_Migrant_Clans_Conquer_Sweden_–_Arab_War_Zone_
                  (Videos)⠀⇛


                       The clans control large zones of Swedish cities and
                       towns, effectively lawless areas which police
                       increasingly fear to approach. The crime families,
                       which have thousands of foot soldiers, have been
                       allowed to operate with virtual impunity for years.
                       Swedish judges and prosecutors have been unable or
                       unwilling to stop them, apparently out of fear of
                       retribution. Furthermore, police are terrorized by
                       them and often pressured by the state to remain
                       silent.


                # ⚓ History_accelerates_on_the_banks_of_the_Rhine,_the_river
                  that_waters_the_heart_of_Europe._as_Islam_moves_forward.⠀⇛


                       When Pastor Klemens Müller looked out the window
                       last week, he couldn’t believe his eyes. A young
                       Afghan was literally emptying his Frauenberg church
                       in Nordhausen. The Afghan, who has lived in Germany
                       for five years, dragged chairs out, emptied the
                       altar, tore up religious and organ music books and
                       did not stop at the cross, which he mutilated. The
                       shattered symbol, Die Welt says, had been saved
                       from the rubble after the bombing of Nordhausen in
                       World War II. It resisted the bombs, not Europe’s
                       masochism.


          o § Environment⠀➾


                # ⚓ 200+_Global_Scientists_Urge_Immediate_Large-Scale_Action_to
                  Limit_Global_Warming⠀⇛


                # ⚓ Over_84_Million_People_Forcibly_Displaced_by_Climate
                  Emergency,_Insecurity,_and_Violence⠀⇛


                       A United Nations agency revealed Thursday that a
                       rising number of people worldwide are fleeing
                       violence, insecurity, and the effects of the
                       climate emergency, with over 84 million relocating
                       within and beyond their home countries during the
                       first half of this year.


                       “It is the communities and countries with the
                       fewest resources that continue to shoulder the
                       greatest burden in protecting and caring for the
                       forcibly displaced.”


                # ⚓ Denmark_and_Costa_Rica_Launch_Anti-Oil_and_Gas_Alliance_at
                  COP26⠀⇛


                       A group of countries and regions led by Denmark and
                       Costa Rica have pledged to phase out oil and gas
                       production in a new initiative launched today at
                       the COP26 climate talks in Glasgow.


                       Wales, Ireland, France, Greenland, Québec and
                       Sweden have joined the Beyond Oil and Gas Alliance
                       (BOGA) as “core” members, which requires winding
                       down any existing projects by a Paris Agreement-
                       aligned date and not issuing new licences.


                # ⚓ Anti-Net_Zero_Activist’s_Claim_She_Was_‘Evicted’_from_COP26
                  Rejected_by_Organisers⠀⇛


                       The head of a new UK climate science denial group
                       calling for a referendum on the country’s net zero
                       goal falsely claimed to have been evicted from
                       COP26 and forced to hide in a toilet earlier this
                       week, according to organisers. 


                       Lois Perry, director of CAR26 – which questions
                       whether carbon dioxide has a “significant role in
                       global warming” – appeared on talkRADIO on Monday
                       claiming security tried to “bundle” her out of the
                       press area at the UN climate summit in Glasgow
                       because “they don’t want free speech”. 


                # ⚓ Iberdrola_Criticised_for_COP26_‘Greenwash_Gimmicks’_While
                  Expanding_Gas-Fired_Power⠀⇛


                       GLASGOW, SCOTLAND — A Spanish energy giant has been
                       criticised for touting its green credentials at
                       COP26 with free solar-powered WiFi booths and a
                       “cycling expedition”, while remaining involved in
                       multiple gas power projects in Mexico.


                       Iberdrola helps run an annual cycle ride to UN
                       climate summits backed by the International Energy
                       Agency, which recently called for an end to new
                       fossil fuel developments if the Paris Agreement
                       goals are to be met.


                # ⚓ ‘Shame_On_You’:_Indigenous_Campaigners_Demand_JPMorgan_End
                  Fossil_Fuel_Finance⠀⇛


                       Indigenous activists on Wednesday staged a protest
                       outside JPMorgan Chase headquarters in central
                       Glasgow as pressure on banks to halt oil and gas
                       extraction grows.


                       A crowd of over a hundred chanted “enough is
                       enough” and “shame on you” outside the American
                       multinational bank’s office building, just over a
                       mile from where crucial talks at the COP26 climate
                       conference are currently taking place.


                # ⚓ Opinion_|_Bill_Gates_Should_Know_Better:_How_the_Israeli
                  Occupation_Ravages_the_Environment_in_Palestine⠀⇛


                       Those who are not familiar with how Israel,
                       particularly the Israeli military occupation of
                       Palestine, is actively and irreversibly damaging
                       the environment might reach the erroneous
                       conclusion that Tel Aviv is at the forefront of the
                       global fight against climate change. The reality is
                       the exact opposite.


                # ⚓ Global_Alliance_Launches_With_the_Goal_of_Bringing_About
                  the_‘End_of_Oil_and_Gas’⠀⇛


                       In what environmentalists hope will mark a “turning
                       point” in the global climate fight, a coalition of
                       nations led by Costa Rica and Denmark formally
                       launched the Beyond Oil and Gas Alliance on
                       Thursday with the stated goal of halting all new
                       drilling and ultimately phasing out fossil fuel
                       production for good.


                       Announced at the tail end of the COP26 summit in
                       Glasgow, Scotland, BOGA represents the world’s
                       first coordinated diplomatic initiative aimed at
                       keeping planet-warming fossil fuels in the ground,
                       advocates said.


                # ⚓ Climate_Crisis_Cannot_Be_Solved_Without_Addressing_US
                  Military_Emissions,_Says_Ocasio-Cortez⠀⇛


                       U.S. Rep. Alexandria Ocasio-Cortez on Wednesday
                       denounced the exclusion of military emissions from
                       national decarbonization pledges, arguing—in
                       concert with scores of climate justice
                       advocates—that ignoring a key source of greenhouse
                       gas pollution makes it impossible to fully
                       understand and tackle the planetary emergency.


                       “When we have global conferences about cutting
                       emissions, to omit conversations about military
                       investment is to omit measuring our CO2 emissions,”
                       Ocasio-Cortez (D-N.Y.) told Abby Martin, host of
                       “The Empire Files,” in response to the journalist’s
                       question about whether greenhouse gases (GHG)
                       emitted by the U.S. armed forces should be included
                       in President Joe Biden’s vow to cut carbon
                       pollution in half from 2005 levels by the end of
                       the decade.


                # ⚓ Wealth_Inequality_Is_Fueling_the_Climate_Emergency⠀⇛


                # ⚓ Opinion_|_The_Big_Lie_Known_as_‘Net_Zero’_Will_Lead_Us_to
                  Climate_Disaster⠀⇛


                       Last week, at the UN climate negotiations, the
                       International Energy Agency announced that pledges
                       made thus far could hold warming to 1.8 or 1.9°C.
                       Yet an investigation published on Sunday by The
                       Washington Post found that countries’ pledges are
                       based on faulty data. And a report released on
                       Tuesday by Climate Action Tracker, a research group
                       that monitors action on greenhouse gas emissions
                       reductions, found that the targets will, at best,
                       keep temperatures to 2.7°C (5°F). That same day,
                       the United Nations Environmental Programme (UNEP)
                       published its annual Emissions Gap report, which
                       matched the Climate Action Tracker’s findings:
                       current pledges will lead to 2.7°C.


                # ⚓ 200+_Global_Scientists_Say_Urgent_and_‘Large-Scale_Actions’
                  Mandatory_to_Keep_1.5°C_Goal_Alive⠀⇛


                       As a global group of hundreds of scientists urged
                       negotiators at COP26 to acknowledge the latest
                       climate science by committing to “immediate,
                       strong, rapid, sustained, and large-scale actions,”
                       the head of the United Nations expressed pessimism
                       Thursday that the talks will end with an agreement
                       limiting warming to the key threshold of 1.5°C.


                       In an interview with The Associated Press a day
                       before the summit is scheduled to end on Friday,
                       U.N. Secretary-General António Guterres said the
                       goal of capping temperature rise to 1.5 by the end
                       of the century “is still on reach but on life
                       support.”


                # § Energy⠀➾


                      # ⚓ French_Poll:_Two-Thirds_Believe_Christians
                        ‘Threatened_with_Extinction’_by_Mass_Muslim_Migration⠀⇛


                             According to the Roman Catholic Archbishop of
                             Izmir, Turkey, Giuseppe Bernardini, in Europe
                             “the ‘dominion’ has already begun.” He notes
                             that Saudi “petro-dollars” have been used
                             “not to create work in the poor North African
                             or Middle Eastern countries, but to build
                             mosques and cultural centers in Christian
                             countries with Islamic immigration, including
                             Rome, the center of Christianity….How can we
                             ignore in all this a program of expansion and
                             re-conquest?”


                # § Wildlife/Nature⠀➾


                      # ⚓ The_Pitfalls_of_Collaboration_Strike_Again⠀⇛


                             And why are they so upset? Well, because
                             Montana’s other U.S. Senator, Steve Daines,
                             has decided the bill isn’t going anywhere
                             unless hundreds of thousands of already-
                             designated Wilderness Study Areas are
                             released to development.


                             They say “the once burnt child fears the
                             fire,” but apparently that doesn’t apply to
                             the adults who continue to believe if they
                             cut some kind of local deal chopping up the
                             remaining wilderness-quality public lands
                             among their select interests that it will
                             remain untouched and simply magically pass
                             into law unchanged.


          o § Finance⠀➾


                # ⚓ Opinion_|_The_Worst_Instincts_at_the_Very_Wrong_Time:_Fed
                  Chair_Jerome_Powell_Must_Go⠀⇛


                       US President Joe Biden faces a critical decision:
                       whom to appoint as chair of the Federal
                       Reserve—arguably the most powerful position in the
                       global economy.


                # ⚓ Opinion_|_Putting_Current_Inflation_in_the_Proper
                  Perspective⠀⇛


                       The October Consumer Price Index data has gotten
                       the inflation hawks into a frenzy. And, there is no
                       doubt it is bad news. The overall index was up 0.9
                       percent in the month, while the core index, which
                       excludes food and energy, rose by 0.6 percent. Over
                       the last year, they are up 6.2 percent and 4.6
                       percent, respectively. This eats into purchasing
                       power, leaving people able to buy less with their
                       paychecks or Social Security benefits.


                # ⚓ Right-Wing_Attacks_on_Native_Child_Welfare_Law_Should
                  Frighten_Us_All⠀⇛


                # ⚓ Opinion_|_It’s_Time_to_Expose_and_Upend_That_Damaging_Myth
                  About_Spending⠀⇛


                       The drama over the Build Back Better Act has
                       revealed the power of narrative in our political
                       landscape.


                # ⚓ Is_the_US_Beyond_Repair?⠀⇛


                       The Missouri Compromise kept the balance by
                       admitting Maine, which had been part of
                       Massachusetts, as a free state, and limiting the
                       spread of slavery below 36° 30´ latitude, parallel
                       to the southern border of Missouri. Said Jefferson,
                       “. . . this is a reprieve only, not a final
                       sentence.” When the compromise broke down in the
                       1850s, and the entire west was opened to slavery by
                       the 1854 Kansas-Nebraska Act and the Supreme
                       Court’s 1857 Dred Scott decision, Jefferson’s worst
                       fears were realized in a bloody Civil War.


                       Today, it seems we are heading in a similar
                       direction. Polls show broad support for secession
                       across the political spectrum. A University of
                       Virginia poll found support for breaking blue and
                       red states into two separate countries at 52% among
                       Trump voters and 41% among Biden voters. Asked if
                       leaders from the other party are “a clear and
                       present danger to democracy,” 80% of Biden voters
                       and 84% of Trump voters responded yes.


                # ⚓ The_Rich_Already_Have_Paid_Leave._Meet_Ruth_Martin,_One_of
                  the_Activists_Trying_to_Make_It_Universal⠀⇛


                # ⚓ How_Wealth_Inequality_Fuels_the_Climate_Emergency:_George
                  Monbiot_&_Scientist_Kevin_Anderson_on_COP26⠀⇛


                       The United States and China made a surprise
                       announcement on Wednesday at the U.N. climate
                       summit in Glasgow on a joint pledge to reduce
                       methane emissions and slow deforestation. The
                       United States is the largest historical emitter of
                       carbon emissions, while China has been the largest
                       emitter in recent years. As negotiations continue,
                       we speak with British journalist George Monbiot and
                       British climate scientist Kevin Anderson about how
                       world leaders and even some climate scientists are
                       downplaying the climate emergency. “Everything
                       we’ve been hearing here and at the previous 25
                       summits is basically distraction,” says Monbiot,
                       adding that global leaders could “fix” the worst
                       impacts of the climate crisis “in no time at all if
                       they wanted to.” Both guests highlight the role of
                       extreme wealth in fueling the climate crisis, with
                       Anderson noting it’s unfair to penalize nations
                       like China, whose rising emissions correlate to the
                       production of goods transported to wealthier
                       countries. “Equity has to be a key part of our
                       responses,” says Anderson.


                # ⚓ Vehicle_Residency:_Homelessness_We_Struggle_to_Talk_About⠀⇛


                       Their voices shatter when Sara Kuust and Jake
                       Blackburn talk about Kuust’s miscarriage while
                       residing in a Chevy Blazer. A red-light camera
                       flashing in the dark night, in a big box parking
                       lot near Portland. Four tiny kittens gamboling as a
                       winter storm approached. The worldly possessions of
                       three humans packed in “like Tetris,” litter box
                       perched. Electrical problems randomly triggering
                       door locks. The pain and metallic smell hitting.
                       Kuust losing it. Her cleaning up with a wet rag. No
                       security, no police coming through in the wee hours
                       of February 12. She hadn’t sought prenatal care,
                       didn’t go to a hospital. Blackburn and their
                       roommate cleaning with water and towels—and
                       favorite T-shirts—until dawn.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ How_to_Stop_Progressives_From_Losing_the_Working_Class⠀⇛


                       Republican victories in Virginia and New Jersey
                       last week are an ominous reminder of what is at
                       stake for Democrats. Glenn Youngkin’s victory over
                       Terry McAuliffe in the Virginia gubernatorial race
                       is a clear indication that Joe Biden’s victory,
                       particularly in such hotly contested purple states,
                       was in large part a reflection of the fact that
                       Donald Trump underperformed compared to more
                       generic, establishment Republicans. Perhaps the
                       most staggering difference was among non-college
                       educated voters—who Youngkin won by a significant
                       margin.


                # ⚓ Debunking_myths_about_Nicaragua’s_2021_elections,_under
                  attack_by_USA/EU/OAS⠀⇛


                # ⚓ Warren_Calls_for_Stricter_Enforcement_After_Trump_Team
                  Found_Violating_Hatch_Act⠀⇛


                # ⚓ Starbucks_Anti-Union_Blitz_in_High_Gear_as_Buffalo
                  Employees_Begin_Historic_Vote⠀⇛


                       “Starbucks will do everything it can to stop
                       Workers United’s organizing drive in Buffalo.”


                # ⚓ Republican_Who_Voted_for_Infrastructure_Bill_Got_Death
                  Threat_Over_Vote,_He_Says⠀⇛


                # ⚓ How_Buffalo_News_Helped_Keep_a_Socialist_out_of_City_Hall⠀⇛


                       Incumbent Buffalo Mayor Byron Brown’s seemingly
                       quixotic write-in campaign for re-election,
                       launched after losing the Democratic primary to
                       democratic socialist activist India Walton, turned
                       out to be successful. He had a lot of help in his
                       corner, such as unions with whom he had long-
                       standing relationships (WIVB, 9/6/21), Republicans
                       who worried about a left-wing mayor (WGRZ, 8/19/21)
                       and high-ranking New York state Democrats who
                       withheld their endorsement of the nominee (City and
                       State, 10/25/21).


                # ⚓ Virginia_Republicans_Perfected_the_Post-Trump_Dog_Whistle⠀⇛


                       Suburban Fleece Daddy Glenn Youngkin led Virginia
                       Republicans out of the wilderness in early
                       November, winning back white suburban voters to
                       take the governorship. But he did even more: He
                       helped the GOP win back the lieutenant governor and
                       attorney general offices and flip the House of
                       Delegates from blue to red. As I write, Democrats
                       have gone from a 55-45 edge there to a probable 48-
                       52 deficit, with two races in recount territory.


                # ⚓ Campaigners_warn_95_percent_of_Arabic_hate-speech_ignored
                  on_Facebook⠀⇛


                       Facebook deletes only a tiny fraction of Arabic
                       hate speech posted on its platforms because its
                       systems are heavily skewed towards monitoring
                       English language content, campaigners have warned.


                       Jonathan Greenblatt of the US-based Anti-Defamation
                       League said the social media giant’s AI or
                       artificial intelligence filter – which is designed
                       to automatically remove content that is offensive
                       or illegal – was deeply deficient in most regions
                       where English is not the main language.


                # ⚓ Indonesia,_UK_discuss_future_technology_and_cybersecurity⠀⇛


                       Indonesia, the world’s fourth most populous
                       country, is Truss’s last stop in a weeklong visit
                       to Southeast Asia to deepen economic and security
                       relations. She earlier visited Malaysia and
                       Thailand.


          o § Censorship/Free Speech⠀➾


                # ⚓ Chinese_Internet_Companies_Are_Censoring_People_Who_Write
                  Or_Speak_Tibetan_Or_Uyghur,_Lending_A_Hand_To_China’s
                  Cultural_Genocides⠀⇛


                       Techdirt has reported on the oppression of Tibetans
                       by the Chinese authorities for 15 years now. More
                       recently, the Turkic-speaking Uyghurs in Xinjiang
                       have come in for the same treatment, with the
                       apparent aim of breaking their spirit and imposing
                       total obedience. But alongside the hundreds of
                       prisons and physical repression — sometimes leading
                       to deaths — the Chinese authorities have been
                       making it increasingly hard for Tibetans and
                       Uyghurs to preserve their distinctive, non-Han
                       cultures. Now Chinese Internet companies are
                       lending a hand to these cultural genocides,
                       reported here by Protocol:


                # ⚓ Rupert_Murdoch_Spreads_False_Claim_Biden_FCC_Nom_Wants_To
                  ‘Censor_Conservatives.’_NewsMax_&_OAN_Immediately_Prove_Him
                  Wrong.⠀⇛


                       We’d already noted how telecom and media giants are
                       hard at work trying to scuttle the nomination of
                       consumer advocate Gigi Sohn to the FCC. Sohn is
                       broadly popular on both sides of the aisle in
                       telecom and media circles, so companies like AT&T
                       and News Corporation are working overtime to come
                       up with talking points politicians can use to
                       oppose her nomination. This week, that included
                       prodding Lindsey Graham to frame Sohn (who has
                       decades of telecom policy experience) as an
                       unqualified radical extremist looking to censor
                       conservatives:


                # ⚓ Censorship_is_the_Last_Gasp_of_the_Liberal_Class⠀⇛


                       On November 8, 2021, Twitter locked my account for
                       a period of one day for responding to corporate
                       media darling and Russiagate fanatic Keith
                       Olbermann’s slanderous reply to journalist Wyatt
                       Reed’s coverage of the Nicaraguan election. The
                       flagged tweet simply restated Olbermann’s question,
                       replacing “whore for a dictator” with “whoring for
                       the American oligarchy.” Twitter demanded that I
                       delete the tweet or send a time-consuming, lengthy
                       appeal with no assurances as to if or when my
                       sentence in “Twitter jail” would end. This prompted
                       me to delete the tweet and wait for the 12-hour
                       suspension to end. Keith Olbermann’s account went
                       unscathed.


                # ⚓ iOS_15.2_beta_can_censor_nudity_in_Messages_app⠀⇛


                       Apple released its iOS 15.2 beta earlier this week,
                       adding its “Communication Safety” feature to
                       messages.


                       MacRumors reported that the feature aims to protect
                       children from sexually explicit materials sent or
                       received through the messages app.


                       The messages app will automatically blur images in
                       which it detects nudity and warn the user of the
                       content.


                # ⚓ Experts_Caution_Against_One_Size_Fits_All_Approach_to
                  Content_Moderation⠀⇛


                       Some experts say they are concerned about a lack of
                       diversity in content moderation practices across
                       the technology industry because some companies may
                       not be well-served – and could be negatively
                       affected – by uniform policies.


                       Many say following what other influential platforms
                       do, like banning accounts, could do more harm than
                       good when it comes to protecting free speech on the
                       [Internet].


                # ⚓ Terror?_What_Terror?⠀⇛


                       But that’s one issue. Here’s another – one that
                       most of the Norwegian media have chosen not to
                       mention. The knife-wielder, a native of Chechnya
                       (which is 96% Muslim, and which was the site of one
                       of the most horrific terrorist acts of the post-9/
                       11 era, the Beslan school siege, in which 186
                       children were murdered), shouted “Allahu akbar!”
                       several times while storming down Theresesgate.


                       This detail, which according to journalist
                       Christian Skaug was first reported in the newspaper
                       VG and then scrubbed within hours (or less) from
                       its website, might in another time and place have
                       been considered by the authorities as a clue as to
                       the man’s motives. But not in Europe in 2021.


                # ⚓ Editor-in-chief_of_a_major_German_daily_newspaper_accuses
                  the_churches_of_concealing_or_downplaying_crimes_against
                  church_institutions_–_“They_shy_away_from_the_conflict_with
                  Muslim_contempt_for_Christians_and_left-wing_anti-Semitism”⠀⇛


                       Poschardt complains that the Protestant Church in
                       Germany (EKD) speaks out “unasked about the moral
                       challenges of the world” but remains “outrageously
                       silent” when it comes to “denouncing obvious
                       things” that affect them. “Statues of saints are
                       spat upon, crosses are desecrated, people urinate
                       in holy water basins. There is little to be heard
                       about this from the EKD’s otherwise so talk-show-
                       suitable permanent moral announcements. Even after
                       the outrageous event in the southern Harz region,
                       it remained rather quiet.”


          o § Civil Rights/Policing⠀➾


                # ⚓ Why_Voters_Rejected_Plans_to_Replace_the_Minneapolis_Police
                  Department⠀⇛


                       By a 56% to 44% margin, voters said “no” to a
                       charter amendment that would have replaced the
                       Minneapolis Police Department with a new Department
                       of Public Safety focused on public health
                       solutions.


                       Michelle Phelps at the University of Minnesota
                       leads a project looking at attitudes toward
                       policing in the city. The Conversation asked her to
                       explain what happened in the Nov. 2, 2021, vote and
                       where it leaves both Minneapolis’ beleaguered
                       police department and police reform movements
                       nationwide. An edited version of her responses are
                       below.


                # ⚓ John_Deere_Workers_Remain_on_Strike_and_Reject_Two-Tier
                  Pay⠀⇛


                       Davenport, Iowa—In October the United Auto Workers
                       and Iowa’s labor movement were on the march.


                # ⚓ October_Facts⠀⇛


                # ⚓ Rhetoric_is_Not_the_Answer!⠀⇛


                       The explanation that respected leaders and
                       governments were not prepared for this is not the
                       answer. Discrimination faced by Covid-patients on
                       account of their economic as well as social (race,
                       religion and so forth) background even in so-called
                       democratic countries remains a stark indicator of
                       helplessness faced by people when their own leaders
                       are at a loss for what to do. It is paradoxical
                       indeed, leaders and key power-holders supposed to
                       be in command of all “services” have been cornered
                       by socio-economic distress led to by impact of a
                       virus. Perhaps, more pathetic is almost dead
                       silence maintained by most leaders regarding
                       discrimination displayed in medical services
                       provided to affected people. Letting discrimination
                       take place and/or failing to check the same seems
                       to be a gross indicator of power-holders’ apparent
                       apathy towards such a “crime”.


                       The preceding point is probably just a mild
                       indicator of social illness still prevalent in most
                       countries, including the ones hailed as most
                       progressive as well as developed, expecting rest of
                       the world to toe their line.  What also cannot be
                       explained is failure to take timely action against
                       this virus in its initial phase. Importance began
                       being given to lockdown, etc after the virus had
                       already struck in its first phase. Ironically,
                       though reports suggest that its third phase is soon
                       expected, practically the whole world is applying a
                       reverse gear to tackle this. What else is suggested
                       by lifting of lockdowns, re-opening of national and
                       international travel? And pray what has happened to
                       key government heads no longer giving the same
                       importance to holding virtual meetings? The noise
                       made earlier about social distancing appears to
                       have been thrown to winds. What else can one
                       understand by Indian Prime Minister Modi trying to
                       use his “hug-diplomacy” at the recently held summit
                       in Glasgow? “Not all leaders wore masks. The same
                       “diplomacy” was displayed by Modi during his
                       meeting with Pope Francis in the Vatican.


                # ⚓ Afghan_women_desperate_to_escape_Taliban_rule:_‘We_don’t
                  know_how_long_we_can_hide’⠀⇛


                       She fled after six years with her three young
                       children — a newborn, 2 and 4 at the time — moving
                       from place to place to hide from her spouse. But
                       when the Taliban took power in Afghanistan last
                       summer, her fears skyrocketed; now she feared not
                       just being beaten but being killed. A woman who
                       left her husband, she says, would be executed by
                       the Taliban if discovered.


                # ⚓ Afghanistan:_Four_women_killed_following_phone_call_to
                  evacuate⠀⇛


                       Local sources told AFP that one of the women that
                       were killed was Frozan Safi, a known women’s rights
                       activist and university lecturer. According to the
                       sources, the women received a phone call that they
                       thought was an invitation to join an evacuation
                       flight, and they were picked up by a car, only to
                       be found dead later.


                       One of the sources said that three weeks prior,
                       they had also received a phone call from someone
                       who was pretending to offer assistance to flee
                       Afghanistan and seek refuge overseas. The source
                       said that the caller knew their information and
                       asked her to send documents and fill out a
                       questionnaire, pretending to be an official for the
                       office in charge of handing over information to the
                       US.


                # ⚓ Kelantan’s_new_syariah_laws_criminalises_tattooing_and
                  plastic_surgery⠀⇛


                       Attempts of converting out of Islam, distortion of
                       Islamic teachings, disrespecting the month of
                       Ramadan, destroying houses of worship, tattooing
                       and undergoing plastic surgery are among the
                       offences that will be punished under Kelantan’s
                       Syariah Criminal Code (I) Enactment 2019 which came
                       into effect on Monday (Nov 1).


                # ⚓ Malaysian_State’s_Latest_Enforcement_of_Sharia_Laws_Makes
                  Conversion_Criminal⠀⇛


                       The 24 offenses that will be punished include
                       attempting to convert out of Islam, distortion of
                       Islamic teachings, disrespecting the month of
                       Ramadan, destroying houses of worship, disobeying
                       parents, tattooing, and undergoing plastic surgery.


                # ⚓ Antisemitism_In_Sermons_In_U.S._Mosques⠀⇛


                       In Islam, imams serve not only as prayer and faith
                       leaders, but as pillars of the Muslim community.
                       They have the ability to inspire their community
                       members and to shape their religious outlook. Thus,
                       speeches and statements made by American imams may
                       provide valuable insight into what they preach to
                       the members of their communities.


                       To explore the views preached by imams in the
                       United States, I used the rich archives of the
                       Middle East Media Research Institute (MEMRI) –
                       which contain over 300 sermons and speeches made by
                       imams and Islamic figures in the West – to collect
                       a sample of statements made by Islamic scholars and
                       imams in America. As it turns out, these imams’
                       statements make it evident that antisemitism –
                       often in the form of anti-Zionism or anti-Israel
                       sentiment – is very present in some of America’s
                       mosques, and this might reflect a worrying reality
                       about the presence of antisemitism in some of
                       America’s Muslim communities.


                       In this article, I shall present some of the themes
                       I have found in statements made by American imams
                       and Islamic scholars, and I shall give an example
                       of each theme.[1]


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ The_Broadband_Plan_Will_Not_End_the_Digital_Divide⠀⇛


                       When Biden first proposed his infrastructure plan,
                       he famously proclaimed, “Broadband internet is the
                       new electricity.”  And he noted, “Yet, by one
                       definition, more than 30 million Americans live in
                       areas where there is no broadband infrastructure
                       that provides minimally acceptable speeds.”  This
                       is what is known as the “digital divide,” the gulf
                       between those who have ready access to computers
                       and online access, and those who do not.


                       Unfortunately, Biden’s original proposal called for
                       $100 billion for broadband but it was cut to $65
                       billion.  Equally troubling, it originally called
                       to “prioritize support for broadband networks
                       owned, operated by, or affiliated with local
                       governments, non-profits, and co-operatives.” This
                       was dropped as was his call to override laws in
                       18 states that block community broadband.


                # ⚓ Why_the_Internet_Is_Turning_Into_QVC⠀⇛


                       Yes, America’s [Internet] is turning into QVC.
                       (People under 30: Email me for an explanation of
                       home shopping TV.)


                       This is happening for three reasons: greed, fear
                       and China. And the growing mania for digital
                       shopping options is another example of how our
                       experiences online are shaped just as much by
                       corporations’ interests as by our desires.


                # ⚓ Commerce_Secretary_Raimondo_Emphasizes_Affordability,_Fiber
                  in_Infrastructure_Bill_Press_Briefing⠀⇛


                       Raimondo, who’s press conference represented
                       another victory lap for the administration since
                       the passage of the measure on Friday night, gave an
                       idea of what her department expects to see from the
                       bill, which had already passed the Senate in August
                       and is now on President Joe Biden‘s desk for
                       signing: a relatively quick turnaround on broadband
                       affordability and job creation, but a longer
                       timeline for fiber buildouts.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Denuvo_Games_Once_Again_Broken_For_Paying_Customers_Thanks
                  To_DRM_Mishap⠀⇛


                       It’s been a while since we’ve mentioned Denuvo, the
                       once-vaunted anti-piracy video game DRM that
                       subsequently became an industry punchline. Once
                       touted as “uncrackable”, Denuvo went from there to
                       becoming indeed crackable, then crackable shortly
                       after release of games, to then being crackable the
                       same day, to then being cracked in some cases hours
                       after a game’s release. As a result, plenty of
                       publishers have taken to patching Denuvo out of
                       their games, while Denuvo did a mini-pivot to
                       create anti-cheat software for online games. While
                       all that was going on, plenty of paying customers
                       of games protected by Denuvo complained about
                       various issues: authentication issues
                       intermittently preventing the customer from playing
                       the game they bought, performance issues that are
                       linked back to how Denuvo runs and behaves, or
                       Denuvo simply breaking games.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ The_Public_Should_Know_Who_Profits_From_Patent_Troll
                        Lawsuits⠀⇛


                             Even people who get sued over patents often
                             can’t figure out who is demanding money from
                             them. That’s even more true when the lawsuit
                             comes from a patent troll wielding a vague
                             software patent, something that is all too
                             common.


                             That’s why we’re glad to see the issue of
                             patent transparency come back to Congress, in
                             the form of a recently introduced bill called
                             the “Pride in Patent Ownership” Act, S. 2774,
                             sponsored by Senators Patrick Leahy (D-VT)
                             and Thom Tillis (R-NC). The Senate’s IP
                             Subcommittee held a hearing on the bill last
                             month.


                             Since 2013, EFF has supported efforts to make
                             it clear to the public who owns patents.
                             We’re pleased to see the issue come back to
                             Congress, because it will once more bring
                             attention to the lack of transparency in the
                             patent system. We support the Pride in Patent
                             Ownership Act as a modest step towards
                             shining some light on the opaque operations
                             of the U.S. patent system. However, because
                             the bill lacks a strong enforcement
                             mechanism, it falls short of being a bill
                             that will truly shed the sunlight that the
                             public needs.


                      # ⚓ NIH_Praised_for_Finally_Showing_‘Modicum_of_Verve’_in
                        Vaccine_Patent_Fight_With_Moderna⠀⇛


                             Public health campaigners applauded the
                             National Institutes of Health on Wednesday
                             for standing its ground in a patent fight
                             with Moderna, which claimed in a recent
                             filing that U.S. government scientists did
                             not co-invent technology at the heart of the
                             pharmaceutical giant’s shot.


                             Dr. Francis Collins, the director of the NIH,
                             told Reuters Wednesday that contrary to
                             Moderna’s assertion, government scientists
                             “played a major role in the development of
                             the vaccine” that the Massachusetts-based
                             corporation is “now making a fair amount of
                             money off of.”


                      # ⚓ Pfizer_Misleading_World_With_False_Claims_of
                        Equitable_Vaccine_Distribution:_Amnesty⠀⇛


                             A briefing published Thursday by Amnesty
                             International accused pharma giant Pfizer of
                             making misleading claims about its efforts to
                             provide Covid-19 vaccines to low-income
                             countries, while reserving most doses of the
                             inoculations for wealthier nations.


                             “Pfizer says it is committed to supplying
                             doses to low- and middle-income countries,
                             but the numbers just don’t bear this out. The
                             fact is that this company is still putting
                             profits first.”


                # § Copyrights⠀➾


                      # ⚓ Thousands_of_Pirate_Sites_are_Listed_on_WIPO’s
                        Advertising_Blacklist⠀⇛


                             The pirate site blocklist maintained by the
                             World Intellectual Property Organization
                             (WIPO) has grown to include well over 5,000
                             domain names. The list is maintained by
                             reporters from various countries and is used
                             by various major advertising companies to
                             prevent money from flowing to pirate sites.
                             Full details on this blocklist remain a
                             mystery, for now.


                      # ⚓ MPA/ACE_Attempt_to_Hunt_Down_Pirate_Site_Operators
                        via_US_Court⠀⇛


                             The Motion Picture Association has filed a
                             flurry of DMCA subpoena applications at a
                             California court. The aim is to compel Tonic
                             Domains and CDN provider Cloudflare to hand
                             over all information they hold relating to
                             dozens of pirate site operators. These
                             include major torrent site RARBG, the popular
                             Oha addon for the Watched app, streaming
                             portal Primewire, and a pair of IPTV sellers


                      # ⚓ The_Curious_Case_Of_Billionaire_Brian_Sheth,_An
                        Anonymous_Tweeter,_Copyright_Law,_Twitter,_And_Some
                        Company_That_Barely_Seems_To_Exist⠀⇛


                             Techdirt regular John Roddy highlighted a
                             truly bizarre fight happening in a California
                             court that may or may not involve billionaire
                             Brian Sheth. Sheth was a cofounder of the
                             high-flying Vista Equity Partners, and left
                             it a year ago in a high profile exit, after
                             the firm’s other cofounder, Robert Smith,
                             entered into a non-prosecution agreement with
                             the DOJ and agreed to pay $139 million and
                             “abandon” $182 million in deductions, related
                             to charges of tax fraud. In the Forbes link
                             above, Sheth claims he sought to have Smith
                             leave Vista following this revelation, but
                             “Smith prevailed” and so Sheth left. Nothing
                             in that article makes Sheth look particularly
                             bad.


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