𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, October 13, 2021
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ No, JWZ, Discord is Not “IRC With Pictures” | Techrights

⦿ The EPO’s Overseer/Overseen Collusion — Part XI: “General Bock”  -  Battistelli’s Swiss Apprentice? | Techrights

⦿ GNOME (and Debian) Infringe Human Rights by Shipping Parental Control Software (Internally Called “Malcontent”) | Techrights

⦿ IRC Proceedings: Tuesday, October 12, 2021 | Techrights

⦿ Süddeutsche Zeitung Became a Propaganda Arm of EPO Management (and by Extension Software Patents/Patent Lobbyists) | Techrights

⦿ [Meme] [Teaser] Swiss Alexandre Benallas | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/10/13/discord-and-irc/#comments
		http://techrights.org/2021/10/13/general-bock-switzerland/#comments
		http://techrights.org/2021/10/13/human-rights-gnome/#comments
		http://techrights.org/2021/10/13/irc-log-121021/#comments
		http://techrights.org/2021/10/13/suddeutsche-zeitung-epo-fluff/#comments
		http://techrights.org/2021/10/13/swiss-armed-bullies/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/10/13/firefox-keylogger/#comments
		http://techrights.org/2021/10/13/sparky-2021-10/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 63

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/13/discord-and-irc/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/13/discord-and-irc/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.13.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ No,_JWZ,_Discord_is_Not_“IRC_With_Pictures”⠀✐


Posted in Free/Libre_Software at 7:36 pm by Guest Editorial Team


Guest post by Ryan, reprinted with permission from the_original


Jamie Zawinski made a comment about Discord basically being “IRC with pictures”
somewhere along the way, but it’s actually not.


What Discord does is way worse. It pretends to be IRC plus all of these neat
features, so that it can rope people in and centralize their communications,
and log everything they do.


They have this thing that they call “running a Discord Server”, which is bogus,
because you don’t run the server. They do.


This means that anything anyone ever does on Discord is subject to failure if
the company goes out of business or has downtime.


According to Wikipedia, once Discord got enough people used to the free
version, they started imposing artificial limits on what you could do, and then
selling you subscriptions to get the things you were doing before. This is
pretty typical of proprietary software, especially “web apps” like Microsoft
365.


When users got together as a community to make robot programs (like you could
always do on IRC) to play Youtube music, ad-free, Google sent DMCA attacks and
Discord removed the bots.


When people who had various political beliefs that were not popular among the
fascist woke “left” started gathering on Discord, Discord promised to Cancel
them.


(Did they, eventually do that? I don’t know, but the fact is that they can.)


We may disagree with other people’s opinions, but having opinions isn’t illegal
in a civilized society. Woke trolls use Big Tech to silence their opposition
and then again to whine and destroy them professionally.


Discord stepped in and disrupted Wall Street Bets, for making rich people look
stupid and causing them to lose some money.


This is just a small list of things they can do.


With IRC, we’ll still have it in 20 years and know how it works. Governments
won’t be able to tell the “IRC company” (there isn’t one) to ban end-to-end
encryption, which government officials themselves use to prevent leaks, or to
shut down servers that they don’t like. If they tried it, it could be hosted
somewhere else. If you get banned on one server, you can go somewhere else. If
your ISP or government tries to blockade it, you can use an obfuscated VPN or
Tor tunnel and use it anyway.


Most tech companies just end up doing whatever the government tells them to in
order to not have any of their own business activities suspended. In some
cases, this includes being unmasked in order to be executed.


The first step in avoiding a trap, is knowing of its existence.


Discord is not “IRC with pictures”. It’s a trap.


Zawinski seems to be more of a hipster who made good on the dotcom hysteria and
then went on to rest on his laurels, occasionally amusing himself by buying a
bar, and some Macs, which he swears up and down work fine even though they lock
him out of his computer.


(In a recent post, it wouldn’t even let him program software and compile it
because Apple didn’t sign those make and python binaries.)


The Macs are (still) more buggy than any GNU/Linux distro I’ve ever seen,
according to Zawinski himself. (Who goes on to quote problems in GNU/Linux that
were solved 13 _years_ ago as reasons for hating GNU/Linux.)


I think he shouldn’t be listened to for advice about software and using it.


IRC can do all of the important things you need it to do, and it hasn’t gotten
much fatter than it was in the 1990s, despite having a new version on the way.


How many things on your computer can you say that about? Remember how slow
Windows 98 was on the internet, on dial up? Remember progress bars taking
forever, and pulling down menus being painfully slow?


Why is it, today, that your laptop is thousands of times faster than your
desktop PC was then, and yet it feels like we’ve made no progress at all?


Windows has gotten morbidly obese to the point even a new computer feels slow
right out of the box, which is alarming, and something they use to drive
hardware sales, even though they’re like a shittier Apple now. Your PC is three
years old! Throw it away! Windows 11!


They throw parties for themselves. They pull a string and OMG MSFT! Joey,
Michael Larabel, and SJVN dance for them. It’s sad.


But a few things certainly don’t need to get much fatter and more horrible as
time goes on because they’re controlled by a community process (like some GNU/
Linux operating systems), and IRC is definitely one of those things. Leave IRC
alone! 😉



                    ䷩ 𝚕𝚒𝚗𝚎 202

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/13/general-bock-switzerland/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/13/general-bock-switzerland/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.13.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_–
Battistelli’s_Swiss_Apprentice?⠀✐


Posted in Europe, Patents at 4:51 pm by Dr. Roy Schestowitz


Series parts:


   1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In!
   2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous”
      Endorsement?
   3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes
   4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States
   5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja”
   6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch
      Courage
   7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity
   8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and
      Pusillanimous_Hibernia
   9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss
      Cheese
  10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the
      Controversial_Christian_Bock
  11. YOU ARE HERE ☞ “General Bock” – Battistelli’s Swiss Apprentice?
                🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Rambos_in_the_Swiss_State⦈_
“General Bock’s Rambos” were prominently featured in the February 2021 issue of
 K-ISOM, a German_magazine [PDF] which covers “the real world of modern elite
                              and special units”.


Summary: The António_Campinos-led EPO won’t be subjected to real oversight by
the Administrative Council, which ‘met’ (online) earlier today; so we look at
who in the Administrative Council did what; today we wrap up the parts about
Switzerland (third part of three)


In the last part we introduced the controversial Christian Bock and looked at
some of the critical media coverage which he has attracted in Switzerland
recently. More specifically, we saw how Bock has become the subject of
increasing public scrutiny due to his aggressive and confrontational management
style as director of the Federal Customs Administration (FCA).


“Like the preceding coverage in the print media, the SRF report referred to
Bock’s fondness for dressing up in a specially designed ceremonial uniform and
carrying a gun.”Amongst other things, it was mentioned that the Swiss TV
channel SRF produced a report on the situation at the FCA, entitled
“Zolldirektor_mit_Pistole:_Der_umstrittene_Christian_Bock” (“Customs Director
with a Pistol: the controversial Christian Bock”).


Like the preceding coverage in the print media, the SRF report referred to
Bock’s fondness for dressing up in a specially designed ceremonial uniform and
carrying a gun.


According to SRF, Bock’s fondness for wearing his dress uniform – despite the
fact that his job is essentially a civilian administrative position – has
earned him the derogatory nickname “General Bock”.


“The MEK Helvetia was originally set up in 2006, but prior to Bock’s arrival it
always operated in a low-key manner and stayed out of the public
spotlight.”Bock has also attracted a lot of criticism because of his over-
enthusiastic promotion of the Swiss Customs’ paramilitary mobile response unit,
known as the Mobiles Einsatzkommando Helvetia (MEK_Helvetia).


The MEK Helvetia was originally set up in 2006, but prior to Bock’s arrival it
always operated in a low-key manner and stayed out of the public spotlight.


However, Bock has ambitious plans to reshape the Federal Customs
Administration.


More specifically, he wants to transform it from its traditional role as a
predominantly civilian fiscal tax-collecting authority into a paramilitary
border security agency endowed with extensive powers of surveillance and
intervention.


“…he wants to transform it from its traditional role as a predominantly
civilian fiscal tax-collecting authority into a paramilitary border security
agency endowed with extensive powers of surveillance and intervention.”And so
it came to pass that – with Bock’s approval – the MEK Helvetia ended up posing
in a very public manner in a 20-page spread published in the February_2021
edition of Kommando – International Special Operations Magazine (K-ISOM). K-
ISOM is a magazine published in Germany which is dedicated to “the real world
of modern elite and special forces”.


The reaction in Switzerland was predominantly negative.


A former cantonal police commander did not object to the existence of such a
force but he took the view that it was “stupid and harmful to spread it over 20
pages in a magazine.”


An expert in the Swiss Ministry of Defence was quoted as saying “These are
General Bock’s Rambos”. The expert – who preferred to remain anonymous – noted
that not even Putin’s special forces would put themselves on public display in
such an ostentatious manner.


“It was even questioned whether there was an adequate legal basis for such a
special militarised unit under the control of the FCA.”Some representatives of
the Swiss cantons argued that the Federal Customs Administration did not need
“expensive Rambos to kick down doors” because there were already enough well-
trained special units in cantonal security forces and in other federal
government agencies. It was even questioned whether there was an adequate legal
basis for such a special militarised unit under the control of the FCA.


These doubts arose because Switzerland is a decentralized_federation with a
highly devolved system of government in which the cantons are sovereign to the
extent that their sovereignty is not limited by federal law. The competence of
the federal government is restricted to a limited number of areas. Public
security and law enforcement are primarily matters for the cantons.


This constitutional arrangement is a fundamental aspect of Swiss-style
democracy which has deep historical roots. Bock’s plans to restructure the FCA
as powerful federal police force in the style of the FBI run contrary to
Switzerland’s long-established constitutional traditions and have attracted
vigorous criticism from many quarters.


“This constitutional arrangement is a fundamental aspect of Swiss-style
democracy which has deep historical roots.”One of his most prominent critics is
Markus_Mohler, a former public prosecutor and retired Commissioner of Police in
Basel. Although now retired from public service, Mohler remains active as a
legal_consultant.


“From a legal perspective, measures of this kind which involve curtailments of
fundamental rights should be defined in a specific and concrete manner in order
to ensure their compatibility with the rule of law.”According_to_Mohler, the
legislative proposal drafted by Bock is not compatible with the Swiss
constitution because – amongst other things – it envisages the takeover of
cantonal security competencies by the Federal Customs Administration.


Mohler described Bock’s legislative proposal as “poorly drafted”. In
particular, he criticised numerous general clauses which are designed to grant
the customs authorities access to policing and surveillance powers which have
not been clearly defined.


From a legal perspective, measures of this kind which involve curtailments of
fundamental rights should be defined in a specific and concrete manner in order
to ensure their compatibility with the rule of law.


“By a curious coincidence, Markus Mohler also holds a part-time position at the
EPO where he is the Chairman of the Disciplinary Committee of the EPO’s
Administrative Council.”Mohler expressed surprise that, despite the manifold
deficiencies in Bock’s legislative draft, it still managed to pass muster at
the Federal Ministry of Justice, which is supposed to function as the “legal
conscience of the Federal_Council“.


By a curious coincidence, Markus Mohler also holds a part-time position at the
EPO where he is the Chairman of the Disciplinary Committee of the EPO’s
Administrative Council.


This is the body which is competent to conduct disciplinary procedures against
Council appointees such as the EPO President, Vice-President and members of the
Boards of Appeal. Mohler was appointed to this position at the 154th meeting of
the Council in December_2017. (warning: epo.org link)


“It is not known whether Mohler has ever expressed any opinion about the
serious breaches of the fundamental rights of EPO staff which occurred during
the Battistelli era with the complicity of the Swiss delegation. It would
certainly be interesting to hear his views on that topic.”The Administrative
Council’s Disciplinary Committee has only been called into action on one
occasion over the last 40 years, namely in the notorious_case concerning a
member of the Boards of Appeal who was unlawfully subjected to a “house ban” by
Benoît_Battistelli in December 2014. As far as can be determined, Mohler was
not involved in that case.


It is not known whether Mohler has ever expressed any opinion about the serious
breaches of the fundamental rights of EPO staff which occurred during the
Battistelli era with the complicity of the Swiss delegation. It would certainly
be interesting to hear his views on that topic.


             🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Swiss_legal_expert_Markus_Mohler⦈_
Swiss legal expert Markus Mohler is sharply critical of “General Bock” and his
attempted power grab at the Federal Customs Administration. Mohler also holds a
  part-time position at the EPO where he is the chairman of the Disciplinary
                   Committee of the Administrative Council.


In any event, the critical coverage of “General Bock” in the Swiss media
between April and June 2021 led to political_interventions by a number of Swiss
parliamentarians and other public figures, accompanied by calls for an
independent investigation into the_situation_at_the_Federal_Customs
Administration. [PDF]


At the beginning of May 2021, it was reported that Bock’s current political
boss, the Federal Finance Minister Ueli_Maurer, had rallied_to_his_defence.


“It was also reported that his “Twitter” account had been deleted.”Amongst
other things, Maurer denounced_the_critical_media_reports_about_Bock [PDF] – in
particular the series of articles authored by Henry_Habegger and published by
the CH media group in April 2021 – as a “one-sided and defamatory campaign.”


However, some weeks later in June 2021, it was reported that Maurer had failed
to secure the backing of his peers in the national government – the Federal
Council – for his efforts to defend his controversial Customs Director.


           🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Federal_Finance_Minister_Ueli_Maurer⦈_
Bock (left) was supported by Federal Finance Minister Ueli Maurer (right), but
 in June 2021 it was reported that Maurer had failed to obtain the backing of
          the Federal Council for his controversial Customs Director.


At around the same time, Bock disappeared_from_view both inside the FCA and in
public. It was also reported that his “Twitter” account had been deleted.
Nobody appeared to know what exactly was going on, but the impression was that
Bock had flounced off in a huff.


“Although the SFAO was fundamentally positive about the plans for the
digitisation of the Customs Administration, it identified a number of serious
problems in the ongoing implementation.”More recently in September 2021, Swiss
media reported that Bock had re-surfaced_but_that_he_was_now_conducting_himself
in_a_more_subdued_manner. [PDF]


At around the same time, it also became known that the Swiss Federal Audit
Office (SFAO) had published the results_of_an_intermediate_assessment of the
implementation of Bock’s_DaziT_programme. [PDF]


Although the SFAO was fundamentally positive about the plans for the
digitisation of the Customs Administration, it identified a number of serious
problems in the ongoing implementation.


“In its latest assessment, the SFAO confirmed that it lacked “a complete and
comprehensible view of the total costs.”
It remains to be seen how Bock will deal with the fallout from the latest SFAO
report and whether or not he will manage to survive much longer in his current
position as Director of the Federal Customs Administration.”Back in 2018, the
SFAO had recommended that mechanisms be created “to objectively assess results
or goal achievement.” However, in its most recent report it noted that these
control mechanisms are still under construction. This made it difficult to
perform “a robust assessment of progress” and had a negative impact on the
“reliability of the results assessment”.


According to media reports (see above PDF), insiders have long warned about the
danger of DaziT getting out of control financially. One criticism which has
been voiced repeatedly is that no one really has an overview, either of the
status of expenditures or of everything that is being developed and financed.


In its latest assessment, the SFAO confirmed that it lacked “a complete and
comprehensible view of the total costs.”


It remains to be seen how Bock will deal with the fallout from the latest SFAO
report and whether or not he will manage to survive much longer in his current
position as Director of the Federal Customs Administration.


“So far nobody in Switzerland appears to have noticed that – during his time as
deputy head of the Swiss delegation on the EPO’s Administrative Council from
June 2000 until the end of 2014 -Bock served his apprenticeship under the
malignant influence of Grossenbacher, Battistelli and their cronies.”Many
commentators have expressed surprise that an individual like Bock has been able
to rise to such a senior management position inside the Swiss civil service. In
particular, they have wondered where he acquired his authoritarian and
confrontational management style which is rather untypical for Switzerland.


So far nobody in Switzerland appears to have noticed that – during his time as
deputy head of the Swiss delegation on the EPO’s Administrative Council from
June 2000 until the end of 2014 -Bock served his apprenticeship under the
malignant influence of Grossenbacher, Battistelli and their cronies.


Perhaps it is nothing more than a coincidence, but in his current role as
Director of the Swiss Federal Customs Administration, Bock now seems to be
replicating a style of toxic management uncannily similar to that promoted by
Battistelli at the EPO between 2010 and 2018.


“Perhaps it is nothing more than a coincidence, but in his current role as
Director of the Swiss Federal Customs Administration, Bock now seems to be
replicating a style of toxic management uncannily similar to that promoted by
Battistelli at the EPO between 2010 and 2018.”That concludes our look at the
delegates representing the Swiss Confederation in June 2013 – namely, the
Administrative Council “alpha male” Roland Grossenbacher and his deputy, the
future “General Bock” – both of whom seem to have been whole-hearted and
enthusiastic supporters of Battistelli’s liberticidal project at the EPO.


In the next part we will turn our attention to the members of the French
delegation who likewise endorsed the Vichyite_"Strike_Regulations" proposed by
their compatriot Benoît Battistelli. █


⠀⠈⠐⠄⠀⢀⠤⠢⠠⠀⠀⠀⠀⠀⠄⠁⡄⢨⠐⠁⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣶⢖⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠠⣶⡦⠄⠠⠄⠤⠀⠄⠀⠄⠀⠄⠤⠠⠄⢐⣦⣷⣶⢰⡖⢰⣶⢠⡦⡆⣶⣰⡔⡆⡦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠐⠀⢆⠀⠃⠙⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿
⢐⣄⢥⣠⣀⣄⣠⣀⡀⡤⣄⣀⢀⠀⣠⣀⣀⣀⣀⣟⣋⢛⢘⠹⣜⢙⡈⣋⡃⠛⣙⣅⢃⢋⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠒⠇⠀⠐⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿
⠙⠃⡈⡍⠉⠉⠉⡉⢁⠥⡭⠉⠉⠔⠟⣉⡍⡩⠿⠏⠈⠈⡈⠈⠈⣉⠉⢵⠁⠉⠩⡫⠈⡈⠘⠀⠀⠐⠒⠲⠤⢤⣄⣐⡄⠀⠀⠴⠀⠂⠀⠀⠀⠁⡷⡦⡤⢤⣬⣤⡴⡴⠲⠖⠊⠉⠀⣀⣀⣀⣀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⢀⡛⣉⣛⣆⣙⠯⠈⠛⠙⠘⠉⠛⠉⡛⠘⢿⠿⠙⠁⢠⠒⠛⠘⠋⠠⠀⠀⠘⢆⠥⡈⠀⠀⢄⠀⠀⠀⠈⠀⠀⣍⠁⠀⠀⠀⠐⠀⠴⠄⢥⡄⠂⠀⠀⠁⠁⠈⠀⠀⠀⢀⣠⣴⡦⠤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠞⠒⠈⠁⠀⠋⡉⠀⣹⢌⡁⠉⠛⡉⡈⢀⠓⠈⢅⣀⠀⠀⠚⠀⡹⢿⡵⠀⠀⠀⠨⠤⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠠⣃⠥⢠⡀⠂⠠⠀⠐⠀⢈⠡⠀⣰⣶⣐⣲⣐⠶⣾⣓⣑⣺⣸⣷⡠⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠤⠀⠈⠀⠁⠀⠀⠆⢰⣶⡂⠀⢀⠀⠀⠀⠀⠀⢠⡉⡠⠒⡡⠴⡠⠄⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡡⠁⠁⠐⢸⠅⠠⠐⢀⠀⠀⠂⠐⠀⣛⠻⣛⠛⠉⠄⠉⠉⠛⠿⣺⢪⣉⡉⠁⠀⠀⠀⣿⣿⣿⣿⣿
⠔⣠⡤⢄⡀⠀⡤⠂⠍⠁⢁⣴⠇⠄⠀⡄⠠⠠⢬⣳⢿⡿⠞⣭⢿⡈⢽⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⡀⠀⠀⡀⢀⠀⠀⠉⢰⣿⣶⣲⣶⣦⣴⣷⣴⣦⣦⣞⣟⣷⣿⣿⣳⣶⣾⣿⣿⣿⣿⣿
⠌⠎⠙⠅⣿⡻⢳⣷⡠⠒⠳⣌⣤⡀⠀⠀⠀⠀⣸⣿⣿⢙⣛⡀⢙⢓⣤⡉⢛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠁⠀⠀⣀⠀⡀⠀⠸⣿⣏⣋⣫⣙⣉⣙⣩⣉⣹⣍⣻⣽⣊⣙⣹⣽⣿⣿⣿⣿⣿
⣠⠤⢤⡼⣯⡂⡲⡚⢦⠀⠆⠈⠈⢧⠀⠠⠄⢠⣿⠟⠛⠻⠋⠀⠈⠉⠑⣷⠀⠑⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⠖⣪⢨⡐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠩⡏⣛⣛⠛⡝⢛⢙⡩⠙⢙⡏⣉⢋⠛⡯⢾⣿⣿⣿⣿⣿
⡏⠀⠁⠘⠟⠺⠅⠀⠸⢀⢀⠀⠀⠘⣧⠤⠤⢬⣄⣀⡀⠀⠀⠀⠀⠀⢀⡸⠥⡩⡐⡀⠂⠀⠄⠀⠀⠀⠀⠀⠀⢢⡗⠀⡁⠁⠀⣇⠀⠀⡀⠄⡆⠀⠴⣣⠀⡿⢾⠿⠷⢿⠿⢿⡿⠿⠿⣿⡿⡿⠿⡿⢿⣿⣿⣿⣿⣿
⠀⢈⣼⣖⢦⠀⠀⠀⠰⣴⠀⠆⠰⢰⢎⣿⣯⣬⣭⣙⠃⠄⢒⣠⠠⣾⡿⠋⠉⠸⢜⠖⠠⠀⠤⡀⠀⠀⠀⠄⢀⢼⣀⠔⣃⠁⢓⠛⠀⠤⠤⠦⠮⠦⠰⠞⠂⣷⣿⣷⣲⣷⣶⣾⣿⣧⣺⣿⢶⣻⣶⣶⣷⣿⣿⣿⣿⣿
⠤⠼⡤⠤⣙⡀⠀⣀⠀⣻⠁⠀⠀⠁⣼⣿⣥⣤⣿⣷⠀⡉⡉⠀⠀⠈⠀⠀⠔⠈⠈⢀⢂⣉⣀⣀⣁⣀⡤⠀⢠⠄⠉⠊⠇⠂⠉⠁⠀⠀⠀⢦⡄⣀⡔⠁⠀⣧⣥⣫⣠⣥⣒⣢⣴⣤⣦⣵⣤⣮⣥⣢⣤⣿⣿⣿⣿⣿
⠰⠊⠒⠉⠙⠀⠋⠛⠀⠛⠁⠀⠂⠐⢈⠻⣿⣿⣟⠊⠁⠋⣙⠀⠀⠀⠀⠀⠀⢠⡄⡂⠾⣿⣿⠥⠭⠑⠃⠉⠛⢙⢑⣒⢤⡀⡀⠀⠀⠄⠀⡈⠩⡋⠀⣄⣀⣏⣝⣫⣛⢉⣋⡟⣙⣟⣙⣩⣋⢿⣍⣙⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠄⠀⢀⠄⢀⠀⠀⣸⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣾⠛⠟⠜⢯⠊⢌⣀⡡⠀⠋⠃⠈⠙⡀⠉⠉⠙⠁⣠⠀⠞⠉⠰⠁⠁⠁⠋⡟⢝⠟⡟⡛⠻⠿⠿⠿⢿⠿⠿⠿⠾⣽⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⣿⣗⠉⠀⢸⣻⣿⣤⠀⠀⠀⠀⠀⠄⠀⠀⠀⢶⠅⠠⠭⠈⠃⠈⣶⡂⣤⠋⠀⠀⠄⠁⠘⠛⠇⠀⠁⠐⠁⠀⢀⠀⠀⠀⠀⡷⡿⠿⠾⠷⢷⠷⢷⢿⠾⢶⢾⢿⠿⡷⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⢸⣿⠀⠄⣴⠀⠀⠠⠄⠀⠀⢺⡍⠤⠁⠁⠆⠀⠈⠠⢖⠂⢀⣴⡾⡧⠀⣆⡫⠐⠀⠀⠈⣘⠀⣀⠀⡀⡆⣷⣶⣷⣾⣶⣶⣶⢶⢷⣶⣴⣦⣷⣾⣼⣴⣿⣿⣿⣿⣿
⣶⠆⢤⣤⠠⠐⢀⢀⡀⡤⠴⡄⡀⡐⠀⠀⠀⠀⠀⢘⣵⡻⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣿⡏⣉⣋⡩⢂⠀⢸⡇⠈⣏⠀⡀⠈⠃⠀⣏⣉⣈⣡⣩⣤⣡⣫⣣⣾⣬⣆⣅⣈⣠⢕⣿⣿⣿⣿⣿
⢌⠽⣰⠳⠋⠐⢋⣥⡖⢿⣟⣶⣮⡐⢕⠄⠀⠀⢀⡶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢒⠚⣛⡁⠴⠗⠀⠀⠀⠐⡈⣀⣐⣐⣉⣆⣤⣤⣤⡟⣉⢩⣏⣙⡋⣋⣩⢙⣛⢋⡹⢏⣙⢩⢙⣿⣿⣿⣿⣿
⢉⣔⡓⠃⡬⢰⣿⢯⡑⡈⣵⢽⡝⣿⣆⠰⠀⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣸⣤⠠⢠⡀⠀⠀⠀⠀⠀⣼⣻⣦⣷⣶⣖⣶⣶⣾⡟⠟⠽⡿⢿⠟⠻⠿⢿⠟⠿⠿⠿⠻⠝⠛⣿⣿⣿⣿⣿
⠐⣮⢵⢀⠀⡟⣁⠀⡄⠾⡽⠽⡇⠙⢻⢸⠄⢐⠨⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣵⣆⢰⡷⠄⠗⠋⠙⠂⠘⢳⣦⣷⣤⣶⣦⣥⣿⡷⣿⢶⢾⡶⠶⡿⡷⠶⣷⡺⢿⢷⡶⢳⢶⣿⣿⣿⣿⣿
⡻⠨⠃⠀⢀⡹⣿⣦⣤⣔⡿⣏⠏⢤⡏⢼⠁⢈⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⡀⢀⠀⠐⠐⠻⡿⠷⠌⡢⠀⠀⠀⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⣷⣦⣤⣾⣾⣶⣷⣴⣴⣶⡦⣶⣶⣽⡿⣖⣿⣿⣿⣿⣿
⡣⢀⠩⠲⠀⠐⠈⠻⠿⣷⣿⡘⠋⣊⡔⢃⣄⣠⣴⡄⠀⢒⡄⢄⠄⠈⠄⡂⢠⢄⡠⢴⣆⣀⡂⠍⠄⢚⣛⡄⠀⠖⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢿⣿⣏⣫⣉⣱⣉⣉⣟⣻⣋⣍⣹⣊⣍⣏⣫⣯⣿⣿⣿⣿⣿
⠀⠠⢀⠼⢲⢀⢌⠑⠰⠴⠀⠄⢙⢠⠄⣕⡸⣿⣿⡇⣁⠤⠄⢀⣚⢡⠧⡏⡆⠰⠂⡈⠜⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠈⣽⡿⣿⣿⣿⢟⢟⣭⢁⣯⣽⣿⣽⣭⣭⣭⣿⣿⣵⣿⣽⣽⣯⣽⣭⣿⣿⣿⣿⣿
⣉⣑⣁⣐⣁⣄⣈⣮⣡⣀⣨⣀⣏⣀⣀⣃⣛⣍⣮⣯⣑⣜⣈⣝⣃⣒⣑⣄⣋⣐⣊⣈⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣚⣧⣀⣑⣁⣟⣹⣹⣯⣉⣋⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡦⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⡫⡻⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠥⣀⡀⠈⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠀⢀⣐⣿⣷⣼⣦⣽⣭⣿⣿⣷⣷⣶⣾⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠣⢀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡄⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣍⢂⣨⠛⢿⠏⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡜⠃⢐⣅⣆⣤⣄⣠⣍⣉⡹⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⣡⣿⣯⣄⠈⢋⠻⣿⣿⣿⣿⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⡀⢀⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇⢸⣐⣿⣿⣿⣿⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢸⣿⣿⣿⣾⡷⣶⣬⣙⣛⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⡇⠀⠀⠀⠀⠈⠟⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⣤⣩⡭⠙⠋⢹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣀⡀⠰⣄⡋⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠙⢶⡌⢳⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⣳⡆⠙⠈⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢠⡀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠎⣠⡾⠃⢀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠁⣾⠀⠀⠀⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢁⡴⠋⢀⣴⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠨⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⠀⡴⠋⢀⣴⠟⠁⣠⡞⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⡆⢀⣴⠟⠁⣠⡾⠋⢀⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣤⣖⣀⡄⢠⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣲⣀⠀⠀⠿⢿⣿⡿⠟⠛⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣷⣼⡇⠰⣿⣶⣤⠀⠀⢢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⠟⠛⠉⠁⠀⠀⣦⣮⡋⠁⠀⣿⣿⡿⠇⠐⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⢀⢤⣿⣿⣿⣿⣿⣿⣼⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠈⠛⠃⢠⠀⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⣘⢿⣿⣿⣿⣿⣿⣍⣥⡾⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠅⢄⡀⠀⠀⠀⠉⠈⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⠉⡌⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣞⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠛⠋⠈⠟⣛⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠈⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶
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                    ䷩ 𝚕𝚒𝚗𝚎 610

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

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    Gemini version at gemini://gemini.techrights.org/2021/10/13/human-rights-gnome/

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Gemini_version_available_♊︎


✐ GNOME_(and_Debian)_Infringe_Human_Rights_by_Shipping_Parental_Control
Software_(Internally_Called_“Malcontent”)⠀✐


Posted in Debian, GNOME, GNU/Linux at 7:50 pm by Dr. Roy Schestowitz


Guest post by Ryan, reprinted with permission from the_original


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


This isn’t easy to say, but it’s true, and I’ve been meaning to write about it
for several days now.


In the 1990s, when the Internet at home was becoming more of a thing,
Helicopter_Parents began to fret that there was a growing “information
superhighway” where their kids wouldn’t be “safe”.


In response to this, many corporations appeared on the scene such as Net Nanny
and Cybersitter to claim that they would safeguard the PC for parents, so their
children wouldn’t be able to access “inappropriate” content on the Web.


Unfortunately, for the stupid people who shelled out money for this crap,
Windows 9x/Me had no security mechanisms whatsoever, and a child with even
moderate levels of knowledge on how to reboot the machine into MS-DOS mode and
run the system from there could disable it, reboot into Windows, do whatever
they wanted, and then reboot back into DOS and configure it to turn back on to
make their parents think that it was on the entire time. Windows was even worse
then than it is now, because it didn’t even pretend at having access control
lists, security labels, multiple user accounts (not real ones).


At its core, it was a fancy DOS shell that happened to implement some of the
Windows NT APIs.


Most proprietary operating systems now have built-in “Parental Controls”
(censorship software).


I couldn’t tell you how well they work, but it’s funny that Microsoft has one,
since Bill Gates was palling around with one of the most prolific child rapists
of the century, Jeff Epstein.


(As if one affiliation wasn’t bad enough, an engineer named Rick Allen Jones
was arrested inside the Gates Mansion for possession of a child pornography
trove. And it only barely made the news, and the courts quickly covered it up
and the guy even had an illegal handgun, and somehow that went away, and he’s
not on the sex offender list, and he’s living in Flagstaff, Arizona with his
mother now.)


Even on a much better designed operating system than Windows, like GNU/Linux,
one with real security features, one where security vulnerabilities are fewer
and are legitimate mistakes in the code and not NSA backdoors like they are on
Windows and the Mac, it’s impossible to “secure” or lockdown a computer when a
person has physical access to it.


My guess is there will either be a misconfiguration somewhere or the child will
just figure out a way to boot into Tails or something, and then there goes
GNOME/FreeDesktop “Parental Controls”. (“Malcontent”)


In fact, putting this on the computer and then trying to remove the GNOME
metapackage and Flatpak if you get rid of it is an insult on the part of
Debian, which has already betrayed the ideals of Free Software by including
Firefox, which now has a Surveillance Capitalism Keylogger malware component.


In the United_Nations_Convention_on_the_Rights_of_the_Child, an international
law which along with (if I recall correctly) the prohibition on cluster bombs
and land mines, only the United States has refused to sign, “acknowledges that
children have the right to express their opinions and to have those opinions
heard and acted upon when appropriate, to be protected from abuse
or exploitation, and to have their privacy protected. It requires that their
lives not be subject to excessive interference.”.


So, what GNOME and Debian are doing flies in the face of this Treaty as well. I
wonder how the GNOME project feels in pushing this software that takes away
people’s voices.


Parents can be every bit as autocratic, corrupt, and evil as a rogue state. And
just saying “I pay the bills around here!” doesn’t give them an excuse to
commit endless offenses against human rights.


In fact, the Treaty has optional protocols that require signatories to crack
down hard on child abuse and to take measures to stop child prostitution.


Since the United States refuses to ratify it on account of some right-wing
Christian nutcases rambling on about how they won’t be able to have their
children “homeskeweled”, it can’t sign those protocols either.


If we, as a society, want to protect children, it needs to be tough punishment
for abusers and the enablers of abusers of children.


No more of this trip to namby pamby land that Epstein and Jones got because
they were rich, or Bill came to the rescue to avoid personal embarrassment.


But, you see, this is sort of what courts do. It’s not what you did, it’s who
you know, how much money you have to fight back with, can you afford a lawyer
that’s buddies with the judge.


For the most part, when I was a child, I had a tough time. I was bullied in
school. Right after I turned 9 years old, my parents had another child and
turned their focus to him, then I started to do poorly in school due to
organizational problems and mental illness (which is also the reason why
Michael O’Hare had to leave Babylon 5 after the first season…when it hits, it
can hit hard).


Then my parents drifted apart and my mother started cheating on my dad with a
truck driver.


They had each other in divorce court slinging mud back and forth. Between her
cheating and the weird religious cults my dad has been in over the years, and
me bouncing back and forth between their houses where my dad would
psychologically abuse me and blame me for my mother leaving him, and my mom’s
second husband’s house where he’d come home drunk and beat me to within an inch
of my life, I’d say it’s amazing I even went back and completed school and did
anything.


Was I exposed to Web pornography when I was a minor?


Yeah, I mean, I was curious and we had the internet in the house. My dad didn’t
even know we had the internet. I hid an entire web browser in the C:\Windows
subfolder mess and made a hidden folder in there where I shoved anything I
wanted to keep. I had “free” dial up ISPs where I figured out how to crash the
toolbars and then later to decipher my login credentials and use them ad-free
on the (Mandrake) Linux partition.


Dad caught me browsing the news or something (so could have been worse, I
guess) and reamed me out for getting the Internet without his permission, and
he wouldn’t believe me when I said it was a local telephone call and there
wouldn’t be any bills coming.


I guess that’s the long way of saying I was above average intelligence. I’d say
I still am. Not a genius, but above average.The average is going down, btw.


And I figured out how to thwart my parents, install GNU/Linux in the 90s on an
HP Pavilion from Walmart, freeload off some dotcom ISPs, find anything I wanted
to on the internet, and use “BitchX” for IRC, which while Mandrake was
installing, I said, “BitchX? What the hell is BitchX?”.


If it was still around, maybe Mitchell Baker would rename it BossX. Who knows.


Your kids, if you have them and you are reading this, are probably a lot
craftier than you give them credit for. Than society gives them credit for. If
I’ve learned a few things in life, one of those is that you underestimate
people at your own peril.


In Chicago, right after I moved here with my ex, I was mugged, and I had to go
to Juvenile Court to testify against my attacker. While I was waiting, I was
reading some Democrat tripe about how “children aren’t just small adults”,
except by the time they’re teenagers, they sort of kind of are.


The gangs in Chicago think they’re fine to use as child soldiers as soon as you
can shove a gun in their hand and tell them to steal someone’s cars and cell
phones and wallets.


The whole reason they can convince teenagers to start a life of crime is,
basically nothing happens once they get to court. And they learn that nothing
happens, and then they keep offending for life.


In closing, if anyone from GNOME, Debian, or FreeDesktop happens to read this,
“Parental Control” software isn’t the answer.


Free and Open Source Software should empower users, including children, who use
it.


We shouldn’t aspire to confine, deny information and ideas to, and help oppress
people like Microsoft and Apple do.


They say they want to go after child abusers, and I say it takes some to know
some. █


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                    ䷩ 𝚕𝚒𝚗𝚎 863

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/13/irc-log-121021/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/13/irc-log-121021/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.13.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Tuesday,_October_12,_2021⠀✐


Posted in IRC_Logs at 2:47 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      121021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-121021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-121021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      121021.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
 QmXBYdadY1YYznNYwzxkiqrCmPMudUKhsrdruDF8idiSFM #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmYHuJMtXR9aMW67pMbD6NCm1TChHXpRmaPvgU1ZwYokCo (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmZ7PKG53rhLzGXbgW2h4VJbUJQMz1SozXyhWpRi9RgiCa social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmW4cD3V5vx1ZeaYH9GvADzPgLevYnDQbLsWJ79tsZojnu social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmZFekJic8uY3WQBmdiWBGCdGVhu3oXbK5De4XNXSgdoZY #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


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§ Bulletin for Yesterday⠀➾


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                    ䷩ 𝚕𝚒𝚗𝚎 992

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/13/suddeutsche-zeitung-epo-fluff/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/13/suddeutsche-zeitung-epo-fluff/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.13.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Süddeutsche_Zeitung_Became_a_Propaganda_Arm_of_EPO_Management_(and_by
Extension_Software_Patents/Patent_Lobbyists)⠀✐


Posted in Deception, Europe, Patents at 8:20 pm by Dr. Roy Schestowitz


Maybe paid and defanged, co-opted like many other_German_publishers and EPO
“media partners”?


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Süddeutsche_Zeitung_on_Software_Patents_(from_PDF/JPEG)⦈_


Summary: EPO ‘genius’ António_Campinos enjoys shallow press coverage, which
echoes or resembles Benoît_Battistelli‘s corruption of the media (paid-for
fluff)


Hours ago the EPO published the above fluff (text below). A “sign of renewed
interest by the Süddeutsche Zeitung in the activities of the EPO”?


Sort of.


“Recently published on the EPO’s intranet,” as our source notes, was something
“[m]ore like using the SZ as a vehicle for pushing software_patents.”


So Süddeutsche Zeitung writes about the EPO again. “But not for critical
investigative reporting on breaches of fundamental rights,” our source adds.


Here’s the full text about “EPO’s approach to CII patenting”:


     Home → Organisation → DG 0 → PD Communication → Announcements → 2021


     13.10.2021


     Patents in a digitised finance sector


     SZ Finance Summit: President advocates greater support for innovative
     SMEs


     Invited as the first-ever EPO speaker to participate at the annual
     “Bayerische Finanzgipfel” President António Campinos, spoke last week
     on the EPO’s approach to patenting digital inventions, and the
     relevance of such inventions for the European economy.


     The event was organised by the publishing house SZ-Verlag
     (Süddeutsche Zeitung) under the auspices of the Bavarian State
     Ministry of the Economy. Held in a hybrid format with strict COVID
     measures, the Finanzgipfel attracted some 70 attendees to the
     congress venue in Munich, and some 250 finance and insurance experts
     following by video stream. The invitation to President Campinos to
     speak at the conference can also be seen as sign of renewed interest
     by the Süddeutsche Zeitung in the activities of the EPO.


     The central topic around which the conference presentations and
     podium discussion revolved was the need of the finance industry to
     re-invent itself after the pandemic with the help of digital
     technologies. Speakers from government institutions, leading banks,
     insurance groups and digital technology providers shared their
     business experience and discussed a wide range of new digital
     solutions to improve their services for clients.


     The President’s podium dialogue with Herbert Fromme, a leading
     journalist from Süddeutsche Zeitung’s economics pages, was dedicated
     to discussing the suitability of patents as appropriate instruments
     for supporting the digital technology evolution, and whether
     patentability of software should be legally acceptable in Europe.
     President Campinos responded by setting out the EPO’s approach to CII
     patenting, and explaining the role of the EPO’s examiners, as well as
     the value of our databases and systems, such as Ansera, when
     processing applications for digital inventions.


     President Campinos concluded by encouraging the sector to monitor
     more closely the development of new and promising inventions in the
     field, as they are often submitted by start-ups, SMEs and public
     research institutions. These enterprises need to be more effectively
     supported by investors if Europe is to catch up with its competitors
     in Asia and the US.


Süddeutsche Zeitung gave him a platform.


Notice the ridiculously promotional ending (makes one wonder who funded this
puff piece, soon to be ‘cited’ with pride by the EPO itself): “President
Campinos concluded by encouraging the sector to monitor more closely the
development of new and promising inventions in the field…”


Yes, THANK YOU! Thank you, Dr. Professor Sir Campinos! █


                🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Funeral de Jorge Campinos⦈


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⠟⠿⠿⠿⠛⠛⡟⠻⠿⠛⡻⢟⠻⠿⠿⠿⠿⠻⠿⠻⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⢿⠛⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣷⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣷⣾⣿⣿⣶⣷⣶⣶⣾⣶⣾⣶⣶⣶⣶⣾⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡅⠁⣿⢈⢎⠇⠄⠈⢨⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢑⡉⠙⢩⢉⡋⡙⢩⡉⣿⠈⡍⣿⠉⢻⡏⢸⠈⠍⢈⡍⣋⠍⡙⠩⢸⡅⢸⠉⠏⢹⠉⡋⠝⡉⣿⠉⠋⠙⡭⠉⠉⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣷⣷⣿⣿⣶⣾⣿⣾⣷⣿⣶⣿⣷⣾⣷⣴⣾⣾⣷⣿⣾⣶⣿⣿⣿⣿⣷⣾⣿⣷⣾⣶⣿⣶⣷⣾⣾⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠛⢛⣿⡟⠛⠛⢻⠻⠛⠟⠻⠻⣿⡟⠛⠛⠟⠛⠟⠛⠟⢛⢻⣿⡟⠛⠛⠛⠟⠛⠛⠟⠛⠻⢛⣿⡟⠻⠛⠻⠛⠻⠛⠛⠛⠟⠟⢻⣿⠟⠛⠻⠻⠛⠛⠟⠟⣿⣿⠛⢻⠛⠻⠛⢟⠟⠛⣻⣿⢛⠛⠟⣿⣿⣿
⣿⣿⢶⣶⣶⣿⣷⣷⣶⡶⡶⣶⣶⣶⡶⠿⡷⡶⢶⣶⣶⣶⣾⣶⣶⣾⣿⣷⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣷⣷⣶⣶⣶⣶⣶⣶⣾⣿⣦⣴⣷⣶⣶⣶⣶⣶⣿⣿⣶⣶⣦⣾⣴⣶⣶⣷⣾⣿⣾⣶⣶⣿⣿⣿
⣿⣿⣀⣀⣰⣀⣠⣀⣀⣀⣀⣀⣀⣸⣀⣀⣄⣇⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣿⣘⣀⣌⣠⣂⣀⣂⣿⣇⣀⣸⣿⣇⣰⣁⣸⣿⣰⣀⣀⣔⣭⣀⣄⣄⣁⣾⣿⣐⣠⣜⣸⣿⣇⡀⣀⣨⣀⣐⣀⣱⣿⣧⣂⣸⣿⣇⣀⣀⣆⣪⣂⣇⣀⣠⣂⣸⣿⣅⣀⣿⣿⣀⣬⣀⣿⣇⣸⣄⣀⣜⣀⣀⣿⣿⣿
⣿⣿⣉⠉⠟⠛⠛⠛⡋⠛⢛⢙⠟⢻⣏⡉⠛⠛⣟⠛⡛⠋⢛⠋⠙⢹⣹⡏⡙⡛⠛⠋⢛⠙⠛⠋⣻⠏⠛⠛⡛⠙⡛⠙⢻⡏⡽⠛⠛⠛⡛⠙⠛⡛⠛⢿⡟⠛⠛⠋⢛⠛⣿⠛⠛⠋⣻⠛⠛⠻⠛⠙⡿⡛⠛⣿⣿⣿
⣿⣿⢿⣶⣷⣷⠿⠾⠷⠶⢷⣾⣷⣾⣿⣿⣿⣶⣿⣷⣶⣾⡶⣿⣷⣿⣿⣿⢿⣷⣶⢶⣷⣷⣶⣿⡾⢿⡷⢿⣶⢾⡿⣷⣾⣿⣾⣾⠷⣷⣾⣿⣿⣾⣾⣾⣷⡷⣿⠾⣷⣶⣿⣷⣷⢷⣿⣿⣿⣾⣾⣷⣿⣾⡿⢿⣿⣿
⣿⣿⣔⣆⣄⣿⣔⣦⣦⣣⣆⣸⣧⣀⣢⣀⣴⣀⣄⣅⣦⣸⣧⣐⣼⣇⣠⣠⣠⣸⣆⣸⣴⣀⣸⣧⣪⣄⣠⣔⣀⣼⣧⣴⣥⣤⣠⣦⣠⣔⣥⣄⣘⣿⣅⣤⣤⣢⣷⣠⣾⣀⣿⣰⣀⣤⣰⣡⣠⣤⣔⣄⣾⣇⣤⣿⣿⣿
⣿⣿⠛⠛⢟⣛⢻⠙⡛⠛⠛⣟⠋⡟⡛⠛⠛⣿⠙⠛⣻⢛⠙⠛⢻⢉⢻⠛⢛⠛⠛⢛⠛⠛⣿⠛⢛⠛⢛⠛⠛⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣷⣷⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣿⣷⣿⣿⣾⣿⣷⣿⣷⣿⣶⣷⣿⣷⣷⣾⣾⣾⣿⣿⣶⣷⣷⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡍⢙⠛⢻⡟⠛⠛⠙⠛⠹⡟⡛⠋⡏⢿⠛⢛⠋⠏⠛⠋⠋⠋⠋⢹⠉⠛⢻⡏⢉⠋⢻⡋⠛⠋⢙⠉⠙⠙⠙⡙⠛⣿⡛⠛⠻⠛⠛⢻⡏⠩⠩⣛⠋⠋⠛⠹⠙⠙⣿⠉⠉⠉⠋⠙⠙⢹⠟⠙⠙⠙⡙⠋⣿⣿⣿
⣿⣿⠿⢿⡿⢿⣿⡿⡿⡿⣿⣿⣿⡿⣿⢿⢿⣿⣿⠶⠿⡿⣿⣿⣿⣿⣿⣿⡷⡿⡿⡿⣿⣿⣾⠿⣿⡿⢿⣿⣿⣿⡿⢶⢿⣿⢿⣿⠿⣿⢿⣿⡿⠿⢿⡿⣿⣿⣿⡿⠶⢿⡾⡿⢿⣿⣿⣿⣿⡿⢿⣿⢿⢿⣿⣿⣿⣿
⣿⣿⣥⣥⣤⣬⣤⣤⣄⣈⣿⣿⣤⣴⣤⣤⣴⣼⣿⣦⣤⣤⣼⣿⣤⣬⣤⣄⣤⣤⣤⣤⣽⣿⣤⣼⣿⣧⣴⣤⣼⣿⣧⣤⣴⣵⣤⣴⣤⣤⣮⣿⣧⣤⣤⣤⣥⣼⣿⣴⣾⣤⣤⣤⣬⣴⣰⣿⣧⣤⣿⣿⣬⣤⣤⣿⣿⣿
⣿⣿⠉⡫⠩⠉⠙⠝⠉⢩⢋⢿⣿⢙⠉⠉⡫⢹⣿⠉⢹⣿⠉⢻⣿⠉⡙⠩⠋⢙⠍⣿⡏⠩⡋⢩⠉⠉⠩⣿⡏⡉⠉⠍⢹⣿⠉⠩⡍⠫⠩⣿⡏⠏⠭⡉⡉⠏⢍⣿⡏⢩⠋⠉⠉⠉⠿⠙⠙⠹⢿⣿⠩⡉⠉⣿⣿⣿
⣿⣿⠿⠿⢿⠿⠿⡿⠿⠿⠾⠟⠿⢻⣿⡿⡿⠿⠿⢿⠿⢿⢿⠟⣿⡿⠾⢿⠿⢿⢿⣿⡿⠿⠿⣿⡿⠿⠿⠿⡿⠿⢻⢿⠿⠿⣿⡿⠿⣿⣿⠿⠿⠿⣿⣿⢿⢿⠿⡿⠿⠿⡿⠿⢿⣿⠿⠿⡿⠿⢿⢿⣿⡿⠿⣿⣿⣿
⣿⣿⣴⣤⣧⣤⣴⣥⣅⣠⣠⣿⣤⣼⣿⣤⣤⣬⣤⣤⣬⣤⣴⣥⣿⣧⣤⣼⣧⣤⣴⣿⣧⣦⣽⣿⣧⣤⣥⣤⣼⣤⣤⣤⣤⣤⣿⣧⣬⣼⣿⣬⣤⣤⣿⣿⣥⣥⣤⣌⣤⣦⣤⣤⣼⣿⣴⣤⣼⣤⣤⣼⣿⣧⣤⣿⣿⣿
⣿⣿⢉⠉⠏⠉⠙⠅⡝⢿⡏⠉⡝⠉⣿⠉⠫⡋⠉⠋⢻⡟⠉⢹⠉⣿⠉⢩⠋⠉⣙⠭⠉⣿⠉⢩⠫⢸⡏⠉⠋⡻⠉⡍⠉⠙⠝⠙⣟⠉⠉⠩⡋⠉⡍⠉⣿⠙⢝⠉⠉⡉⠋⢫⠉⢹⡇⢝⢋⣿⢉⠉⢹⠉⠉⣿⣿⣿
⣿⣿⠿⠻⠿⠿⠿⠿⠿⣾⣟⡛⠿⠿⣿⠻⠿⡿⠿⠿⠿⠻⢿⠿⣿⠻⢿⣿⠛⠿⠿⠿⠻⠻⢿⠿⠻⡿⣛⠿⠿⠿⠿⡟⠿⠿⡿⣿⠿⠿⣿⠾⠿⡿⠿⠟⢿⡿⠿⢿⡟⠻⠿⢿⡷⠾⢿⠿⠚⢿⠿⢿⠿⠿⠿⣿⣿⣿
⣿⣿⣤⣬⣷⣴⣤⣤⣷⣽⣿⣷⣧⣤⣿⣤⣼⣼⣤⣤⣦⣴⣽⣦⣿⣴⣵⣿⣾⣴⣤⣤⣤⣴⣴⣦⣬⣷⣭⣤⣾⣤⣬⣦⣦⣦⣧⣿⣮⣤⣿⣤⣬⣦⣤⣤⣾⣧⣴⣼⣧⣼⣤⣼⣧⣥⣼⣧⣴⣴⣶⣼⣦⣬⣤⣿⣿⣿
⣿⣿⡩⠉⣩⢹⡋⠁⠉⠉⣿⠈⡉⣿⠉⡉⡋⠉⢹⡏⠉⢹⡏⠁⠉⣩⢹⡫⡁⣾⢉⠉⠉⡉⡝⢉⠉⠉⣿⠈⣭⢉⢉⣍⢉⢉⢽⡏⡉⣹⡇⣨⠉⢹⡧⢈⠎⠁⡩⠈⠉⢩⠉⠉⠅⣙⠉⡷⠠⡉⣨⠍⢹⡍⠉⣿⣿⣿
⣿⣿⠻⢿⡟⠿⠿⢿⡿⠿⠟⠻⡿⠛⢻⠿⠿⡿⠿⢻⠻⠻⠿⣿⠛⢛⢟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⣿⣿⣤⣿⣧⣼⣤⣼⣧⣤⣥⣼⣴⣤⣶⣤⣴⣷⣵⣿⣮⣤⣦⣿⣬⣴⣦⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡛⡻⠿⢿⡿⠿⠿⠿⠻⠿⠟⣿⠻⠿⠿⠿⠿⡿⢿⠿⢿⠿⠿⠿⢻⡿⠿⠻⠻⠟⠿⣿⠛⢿⠿⣿⠿⠿⠿⡟⠿⠿⠿⠿⡿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠻⠿⠛⠿⠿⠿⢿⡿⠿⢿⠟⣿⠿⠿⠿⠛⢿⠿⠿⣿⣿⣿
⣿⣿⣷⣾⣶⣾⣷⣶⣶⣷⣶⣷⣶⣿⣶⣶⣴⣶⣾⣷⣶⣶⣶⣶⣾⣶⣾⣷⣶⣶⣶⣷⣷⣿⣶⣷⣶⣿⣶⣶⣶⣷⣶⣾⣶⣾⣶⣶⣾⣧⣶⣷⣶⣶⣶⣷⣶⣶⣶⣾⣶⣶⣾⣷⣶⣷⣶⣿⣴⣾⣶⣶⣶⣾⣶⣿⣿⣿
⣿⣿⣁⣨⣉⣉⣋⣉⣉⣈⣉⣍⣏⣍⣩⣋⣉⣈⣉⣩⣁⣯⣉⣉⣉⣹⣨⣈⣉⣹⣩⣉⣉⣉⣸⣏⣁⣼⣨⣈⣉⣿⣀⣩⣋⣉⣉⣍⣉⣇⣩⣋⣈⣉⣉⣉⡍⣽⣈⣉⣿⣉⣉⣅⣩⣉⣉⣹⣉⣸⣇⣨⣉⣉⣀⣿⣿⣿
⣿⣿⠛⢛⠻⠻⢿⡟⡛⠻⠻⣿⠛⠛⣟⠟⠻⠻⠻⠛⢟⣿⡿⠟⠛⢛⣿⡟⢛⠟⢿⡟⣻⠻⠛⢻⡿⡻⢻⡿⡛⠛⠛⢛⠛⢻⡟⡛⠻⡛⡻⡻⠟⠻⡻⠛⠻⠻⢻⣿⡟⠛⠛⠟⠟⠟⠻⠻⡛⢻⡟⢛⢟⢟⠟⣿⣿⣿
⣿⣿⣶⣾⣶⣶⣿⣷⣶⣶⣶⣿⣶⣶⣿⣶⣶⣶⣶⣶⣶⣾⣷⣾⣶⣾⣿⣷⣾⣶⣾⣷⣷⣶⣦⣾⣿⣶⣾⣷⣶⣦⣴⣶⣶⣾⣷⣶⣶⣶⣷⣷⣶⣶⣶⣤⣶⣶⣶⣿⣷⣶⣴⣶⣶⣶⣶⣶⣷⣾⣷⣾⣶⣾⣶⣿⣿⣿
⣿⣿⠁⣑⣉⣈⣈⣆⣎⣆⣈⣈⣀⣘⣿⣇⣀⣁⣐⣀⣘⣁⣈⣪⣀⣁⢻⣿⣇⣀⣀⣑⣀⣀⠑⣹⣿⣀⣀⣇⣁⣉⡘⣿⣿⣀⣈⣈⣋⣐⣈⣀⣑⣁⣽⣿⠀⣰⣈⣘⣑⣁⣸⣿⣀⣱⣁⣸⣿⣑⣀⠀⣀⣂⣀⣿⣿⣿
⣿⣿⠛⠻⢟⠛⢟⠟⠛⢟⢟⠛⢿⣿⠻⢛⡻⠻⠻⡛⠛⢛⠻⣿⠟⢛⠟⠟⠛⠟⢻⣿⠛⠻⠻⠛⣻⡟⠻⡿⠻⠛⠻⠻⠻⢻⣿⠛⡻⡟⠿⠛⡛⠟⢟⠟⡛⢻⣿⠻⠛⢟⢻⡟⠛⠟⢟⢿⠛⠛⠛⠻⡛⣿⠛⣿⣿⣿
⣿⣿⣶⡶⣶⣶⣾⣶⣶⣶⣧⣤⣾⣿⣶⢾⣶⣶⣶⣶⣶⣾⣶⡿⣶⣾⢶⣶⣷⡶⣾⣿⢶⣾⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⡶⣧⣶⢶⣷⣶⣾⣶⣶⢾⣷⣶⣶⡶⢾⣷⣶⣶⢶⣶⣶⣶⣶⣶⣶⣿⣶⣿⣿⣿
⣿⣿⣠⣀⣐⣀⣸⣰⣀⣰⡁⢀⣸⣇⣀⣾⣀⣅⣉⣠⣇⣺⡐⣀⣐⣀⣸⣀⣕⣁⣀⣐⣀⣀⣎⣀⣇⣐⣸⣀⣆⡀⣪⣆⣢⣡⣀⣷⣂⣮⣀⣃⣾⣀⣀⣰⣠⣀⣂⣘⣸⣇⣐⣵⣯⣒⣠⣀⣰⣔⣀⣻⣿⣿⣿⣿⣿⣿
⣿⣿⠿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣴⣀⣸⣿⣇⣄⣆⣀⣀⣕⣀⣀⣶⣰⣀⣿⣿⢀⣕⣕⣀⣘⣰⣀⣿⣿⣐⣸⣀⣀⣨⢂⣀⣀⣿⣿⣄⣡⣆⣀⣿⣿⣸⣀⣀⣆⣪⣀⣠⣺⣿⣇⣆⣆⣀⣴⣀⣰⣁⡘⣿⣿⣀⣿⣿⣀⣨⣀⣀⣀⣆⢀⣿⣿⣿
⣿⣿⠙⡛⠛⢛⠛⠛⡏⠙⠋⣿⠉⡛⠛⡛⢻⣏⠙⠝⠋⠋⠛⠛⠋⡛⠛⡋⠛⢻⡯⢩⠛⠉⡛⠛⠻⠛⡙⢻⡟⠛⡛⠛⡛⠛⠛⡛⠙⠛⢻⣟⠛⠛⠛⠛⠛⢿⡟⠛⠛⡛⢿⠋⠛⠛⠉⢛⠛⢛⠛⢛⢹⢙⠛⣿⣿⣿
⣿⣿⡾⢾⣶⣿⣾⣷⣿⢷⣷⣿⣾⡷⡾⣿⣿⣷⣿⣾⣶⠷⣷⢷⡾⠶⢷⣿⣿⣾⣷⢾⣶⣾⣶⡶⣿⣶⣷⣿⣷⣶⣾⣾⣿⣾⣿⣿⣶⣶⣿⣷⣷⣶⢾⡾⣾⣾⣿⢿⣶⣷⢿⣶⣷⣷⣶⣷⣷⢷⣷⣷⡿⢷⣶⣿⣿⣿
⣿⣿⣄⣴⣠⣲⣃⣀⣀⣀⣦⣀⣿⣧⣢⣤⣠⣿⣇⣠⣹⣄⣀⣔⣄⣠⣔⣰⣿⣧⣢⣼⣿⣇⣄⣠⣂⣠⣦⣀⣸⣿⣅⣄⣼⣿⣄⣅⣄⣠⣦⣢⣢⣰⣄⣄⣄⣼⣿⣤⣦⣠⣠⣆⣨⣦⣤⣠⣦⣰⣸⣿⣇⣔⣥⣿⣿⣿
⣿⣿⠛⠛⡟⠛⠛⡛⠋⡋⠛⠛⣻⡏⢙⠛⢻⡟⠋⠟⠋⠙⠛⢹⡏⠛⠛⡋⠛⡻⠛⠙⠛⠛⠛⣿⠛⡻⡛⠋⠛⡛⠙⠛⡛⢿⡟⠻⠛⠋⣿⡛⢛⠙⠛⢙⠙⠛⠛⣿⢛⠛⠋⠛⠛⠋⡛⠋⢻⠉⠉⡻⣻⢟⠋⣽⣿⣿
⣿⣿⡶⡷⠷⢷⣾⡾⣿⡾⣿⣷⢾⢷⡿⣷⡾⡿⣾⡷⢾⣾⣾⡿⡷⡷⡷⡿⢿⣿⣾⡿⡾⡶⣾⣿⠷⠷⡷⢷⢷⣷⣿⢾⢿⣾⠿⢾⣿⢷⣿⢿⢿⣿⣷⠷⢿⡷⡿⣿⠶⡷⡾⡷⣿⡿⠶⢾⡾⣿⡷⢷⢿⣷⡿⣿⣿⣿
⣿⣿⣤⣤⣴⣤⣤⣥⣤⣦⣼⣿⣬⣤⣤⣯⣤⣤⣿⣧⣤⣤⣿⣧⣤⣈⣤⣤⣴⣼⣿⣥⣤⣤⣤⣄⣴⣤⣤⣤⣤⣼⣿⣤⣼⣿⣤⣤⣤⣦⣄⣤⣤⣽⣿⣴⣦⣤⣤⣤⣤⣤⣴⣤⣿⣧⣭⣤⣴⣤⣠⣼⣦⣤⣤⣿⣿⣿
⣿⣿⢛⠛⠛⠋⡋⠛⠛⠍⠛⠋⣿⡏⠙⠛⣿⡟⠛⠉⠉⠙⡙⠛⣿⡟⢹⠛⠹⣿⡋⢉⠋⢻⣿⠉⢉⡩⢝⡏⢿⡿⠙⠋⠋⠛⠋⠋⠛⠉⡙⣿⡏⠛⣿⡟⠭⢩⢹⣿⠋⠋⠋⠋⠛⢋⠏⠛⠫⠻⣿⡟⠛⡙⠋⣿⣿⣿
⣿⣿⡿⣿⣿⡾⡿⣿⣿⢿⢿⢿⣿⠿⢿⣾⣿⣿⣿⢿⢿⣿⣿⠶⣿⠿⢿⢿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢾⣾⢿⣿⡿⣿⣿⣿⣿⡿⡿⣿⡿⣿⣿⡿⡿⣾⢿⣿⣿⢿⢿⣿⢿⣶⣷⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣥⣅⣤⣤⣤⣦⣤⣦⣀⣿⣤⣦⣤⣿⣴⣤⣤⣤⣿⣤⣼⣿⣤⣾⣤⣿⣤⣴⣦⣥⣧⣼⣧⣤⣬⣤⣤⣦⣥⣤⣤⣦⣌⣿⣧⣤⣼⣧⣦⣤⣧⣿⣧⣤⣼⣧⣥⣤⣼⣿⣴⣤⣤⣼⣤⣿⣤⣼⣿⣤⣬⣤⣿⣿⣿
⣿⣿⠉⠋⠋⠉⡏⠉⠙⠙⠙⠉⡏⠙⠉⠉⣿⠉⡙⠋⡩⠉⢩⠉⠉⢿⡏⠉⢛⠭⠉⣿⠉⠉⡿⡉⢩⠋⠉⠉⡍⠹⣿⣉⠁⡝⠉⠉⣿⠉⢩⠉⡫⠋⠋⠉⠉⠉⠫⢻⠉⠋⠉⠉⢛⠭⠉⠉⡫⠋⠙⢹⡏⠩⡋⣿⣿⣿
⣿⣿⠿⢿⠿⠿⠿⡟⡿⠿⣿⠿⠿⢿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣴⣡⣤⣥⣤⣧⣼⣤⣦⣤⣧⣤⣮⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⡿⣿⠿⠿⠿⡿⣿⢿⡿⡿⠿⡿⠿⠿⡿⡿⢿⡿⡿⡿⠿⠟⢿⡿⠿⢿⠿⡿⢿⡿⣿⠿⠿⡿⡿⣿⠿⠿⠿⠿⡿⠿⢿⡿⠿⡿⢿⡿⠿⠿⠿⠿⠿⢿⠿⠿⣿⠿⢿⢿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⣿⣿⣿
⣿⣿⣴⣼⣤⣤⣤⣥⣤⣼⣦⣿⣬⣤⣤⣤⣯⣤⣤⣬⣤⣼⣬⣬⣦⣤⣥⣬⣬⣤⣤⣥⣧⣵⣰⣷⣤⣤⣬⣬⣦⣤⣧⣄⣠⣼⣄⣸⣧⣼⣤⣼⣧⣤⣤⣥⣬⣤⣿⣬⣥⣿⣤⣤⣵⣤⣤⣬⣤⣿⣼⣤⣤⣼⣤⣿⣿⣿
⣿⣿⡩⢈⢍⢉⠉⠈⣹⡇⢭⠉⢹⡏⢍⠉⣉⡉⣉⢍⠉⢩⡉⠉⢩⠉⣿⠩⣡⣿⡉⠉⡉⢫⣏⢙⡉⠉⣿⠩⡉⡩⡉⢉⣏⢉⣏⠉⢹⣇⣩⢋⣉⠉⡍⠀⡫⡉⠉⢹⡇⢩⣻⡩⢈⡉⣹⣡⠈⠁⡩⡸⣿⠉⠉⣿⣿⣿
⣿⣿⠻⠿⠿⢿⢿⣿⠿⡿⠿⣿⣿⠿⠟⠻⠿⠿⣿⣿⠿⠿⠻⡿⠿⠻⠟⠿⠿⢻⣿⡟⠿⡿⣿⡿⠟⠿⠿⠿⣿⠿⠿⠿⢿⣿⣿⢛⠟⠻⠛⠿⣿⣿⠿⠿⡿⢻⣿⡿⠿⠿⠿⠛⠿⣿⣿⠿⢿⠿⠿⠿⠿⠿⠻⣿⣿⣿
⣿⣿⣬⣧⣤⣧⣿⣿⣤⣷⣦⣿⣿⣮⣶⣴⣴⣥⣿⣿⣴⣤⣬⣾⣤⣶⣥⣦⣤⣼⣿⣧⣼⣼⣿⣧⣤⣥⣤⣧⣶⣤⣬⣦⣮⣿⣿⣥⣶⣷⣬⣤⣿⣿⣤⣴⣮⣼⣿⣧⣤⣴⣵⣤⣬⣿⣿⣶⣼⣴⣤⣤⣼⣬⣤⣿⣿⣿
⣿⣿⣈⣍⣉⣁⣨⣉⣨⣈⣉⣍⣙⣻⣷⣰⣍⣉⣉⣉⣿⣉⣉⣁⣉⣉⡍⣉⣅⣉⣉⣉⣿⣩⣉⣉⣉⣁⣿⣈⣹⣇⣉⣉⣿⣩⣍⣉⣩⣉⣿⣉⣅⣀⣉⣉⣀⣉⣉⣁⢉⣿⣉⣙⢉⡉⣉⣍⣁⣍⣉⣸⣿⣈⢉⣿⣿⣿
⣿⣿⠻⠿⠿⠿⠿⠻⠿⠿⠿⡟⢛⡟⠻⡿⠿⠿⠿⠿⣿⠻⢿⠻⠿⣿⠿⠿⠻⠟⠿⡿⣿⠿⡿⠿⠟⠛⢿⡟⠻⢿⡿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⡟⠿⢿⠟⡿⠟⠿⣿⠿⠿⠿⢻⠻⠻⠿⣿⢻⠟⢻⣿⣿⣿⣿⣿
⣿⣿⣶⣿⣾⣶⣶⣾⣶⣾⣶⣷⣾⣷⣶⣶⣶⣷⣴⣶⣿⣶⣾⣾⣶⣷⣶⣶⣶⣷⣷⣷⣾⣴⣿⣶⣷⣶⣿⣷⣾⣶⣷⣶⣶⣷⣦⣶⣶⣶⣾⣶⣾⣶⣷⣾⣾⣶⣶⣶⣶⣷⣶⣶⣶⣾⣾⣶⣶⣿⣶⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠸⠯⠎⠟⠸⠭⠂⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡆⠠⠁⠳⠊⠠⠀⠠⠫⠄⠂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠤⠐⠒⠀⢀⡀⠀⠀⠀⡉⠉⠉⠘⠛⠛⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⢆⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣉⣒⣀⣲⣤⣠⠤⠤⠼⠤⠤⠬⠵⠖⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠙⠍⠁⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠑⠢⠤⠞⠂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠀⢀⣾⣷⣄⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡦⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠉⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠀
⢼⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣬⣉⢩⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠁⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠸⠀⠀⠀⠀⠛⠛⠴⠷⢿⠀
⠀⡾⠿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⡿⠛⠂⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⡅⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⣁⡑⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⠀⠀⠀⠀⠀⠸⣿⣿⣶⣄⡀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣷⡀⠀⠀⠠⠿⢄⢀⡀⣴⣷
⢸⣃⡾⠛⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡼⠀⠀⣀⣧⣤⣄⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠈⣟⡇⠀⠀⠀⠀⠸⢿⣟⣿⡇
⣿⣻⣿⣿⢿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⡇⠀⠓⠘⣿⣿⢻⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣯⠉⢲⣄⢀⣀⠻⠷⠓⠲⣤⡀⠐⣺⣿⣟⠀
⣿⣫⣿⣿⣼⡷⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⢀⢀⣿⢿⣻⣿⣿⣿⣿⣥⠀⠀⠀⠈⣿⣿⣿⣿⣧⣼⠿⣿⡿⠦⠀⠠⢄⡸⠿⣴⡿⣱⣿⣤
⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠁⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡞⠀⠰⠻⢿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠹⠟⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⢈⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⠉⠿⠓⠋⠁⠛⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠽⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠛⠻⢶⡶⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⣬⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠟⠟⠻⢿⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⠟⠓⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠙⠻⠋⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1211

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/13/swiss-armed-bullies/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/13/swiss-armed-bullies/

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Gemini_version_available_♊︎


✐ [Meme]_[Teaser]_Swiss_Alexandre_Benallas⠀✐


Posted in Europe, Patents at 4:46 am by Dr. Roy Schestowitz


The political right shifts Switzerland to thug culture like_in_New_Zealand


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Mathieu Bock-Côté: EPO needs “expensive Rambos to kick down
                                    doors⦈
   Mathieu Bock-Côté. Nothing like raiding a judge’s office, in the name of
                    judicial integrity and “independence”.


Summary: The EPO‘s French dictator, Benoît_‘Vichy’_Battistelli, might be
relieved to hear that his enabler in the adjacent Switzerland also enlisted
armed_bullies to keep the population down (the father of António_Campinos might
know a thing or two about those; it’s why he fled to France)


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

                    ䷩ 𝚕𝚒𝚗𝚎 2236

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.13.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_13/10/2021:_Firefox_Keylogger_on_(By_Default),_GNOME_Platform_Design
Discussed⠀✐


Posted in News_Roundup at 7:09 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Audiocasts/Shows⠀➾


                # ⚓ You_don’t_NEED_the_command_line_to_use_Linux,_but_you
                  SHOULD_use_it!_–_Invidious⠀⇛


                       This thing is often considered as much an argument
                       FOR the use of Linux, as an argument AGAINST it.
                       Power users can’t live without it, beginners are
                       scared of it, and people who never used Linux are
                       convinced it’s needed just to run a program. Let’s
                       see why most regular users don’t NEED the command
                       line, but why you can miss out if you don’t use it.


                # ⚓ Is_Firefox_Suggest_Stealing_Your_Key_Strokes?_–_Invidious⠀⇛


                       Recently Firefox updated Firefox suggest to add
                       sponsored advertisements into the search
                       suggestions in their browser and this can operate
                       with telemetry so some articles have thought this
                       means it defaults to enabled.


                # ⚓ Full_Circle_Weekly_News_#231⠀⇛


          o § Applications⠀➾


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Microsoft
                  Office⠀⇛


                       This series looks at the best free and open source
                       alternatives to products and services offered by
                       Microsoft. This article focuses on the best free
                       and open source alternatives to Microsoft Office.


                       What are the best open source alternatives to
                       Office 365? This article focuses on replacements
                       for only some of the components of Office 365.
                       We’ll explore other components in later articles in
                       this series.


          o § Instructionals/Technical⠀➾


                # ⚓ [Old] Useless_Use_Of_dd⠀⇛


                       dd can even end up doing a worse job. By
                       specification, its default 512 block size has had
                       to remain unchanged for decades. Today, this tiny
                       size makes it CPU bound by default. A script that
                       doesn’t specify a block size is very inefficient,
                       and any script that picks the current optimal value
                       may slowly become obsolete — or start obsolete if
                       it’s copied from


                       Meanwhile, cat is free to choose its buffer size
                       that best serves a modern system, and the GNU cat
                       buffer size has grown steadily over the years from
                       512 bytes in 1991 to 131072 bytes in 2014. ./src/
                       ioblksize.h in the coreutils source code has
                       benchmarks backing up this decision.


                       However, this does not mean that dd should
                       necessarily be categorically shunned! The reason
                       why people started using it in the first place is
                       that it does exactly what it’s told: no more and no
                       less.


                # ⚓ How_to_use_yt-dlp_instead_of_yt-dl_with_mpv_|_Hund⠀⇛


                       I interact with YouTube using the text-based client
                       pipe-viewer. I then watch any video using my
                       favourite media player mpv. This has always worked
                       perfectly fine thanks to mpv supporting youtube-dl,
                       which unfortunately, now seems to be an abandoned
                       project.


                # ⚓ How_to_install_Friday_Night_Funkin_Character_Test
                  Playground_Remake_2_on_a_Chromebook⠀⇛


                # ⚓ How_To_Upgrade_Debian_10_to_11_Desktop_Made_Simple⠀⇛


                       This tutorial will explain step by step to upgrade
                       Debian Desktop version 10 Buster to version 11
                       Bullseye for your computer. We do this to the GNOME
                       edition and the process downloads all the updates
                       using the internet not CDROM. We will use command
                       lines to proceed. We hope you can upgrade yours
                       successfully including if you use Debian desktop
                       choice other than ours. Let’s upgrade!


                # ⚓ How_to_Install_Java_17_(JDK_17)_on_Debian_11⠀⇛


                       The Java Development Kit (JDK) is the name of the
                       software development kit (SDK) for the Java
                       programming language, which enables anyone to
                       create both Java applications and applets for
                       running on many operating systems. This tutorials
                       shows how to install Java JDK on Debian 11.


                # ⚓ Beginner’s_Guide_to_Installing_Pop!_OS_Linux [Ed: Newly-
                  updated]⠀⇛


                # ⚓ How_to_Install_Virtualmin_on_Ubuntu_20.04_–_VITUX⠀⇛


                       Virtualmin is a web hosting control panel that
                       allows you to manage your virtual private servers
                       through an easy-to-use interface. You can use this
                       software to create and delete websites, install and
                       update server applications, and monitor resource
                       usage.


                       Virtualmin features a number of scripts that can
                       simplify the process of installing and maintaining
                       software on your servers. It comes with a script
                       installer for popular applications like Drupal,
                       Joomla, bbPress, Django… and many others.


                # ⚓ How_to_Install_and_Secure_MongoDB_on_Debian_11⠀⇛


                       MongoDB is an open-source, general-purpose,
                       document-based, and distributed database designed
                       for modern application developers. It is also
                       called a NoSQL database because it does not rely on
                       a traditional table-based relational database
                       structure. It stores data in JSON format instead of
                       the table style method. It can be integrated easily
                       with various programming languages. It is used by
                       many well-known companies including, Facebook,
                       Cisco, Forbes, Adobe, Nokia, etc.


                       In this post, we will show you how to install and
                       secure MongoDB NoSQL database on Debian 11.


                # ⚓ How_to_Install_and_Use_NVM_on_Debian_11⠀⇛


                       NVM is a version manager for Node.js used to
                       install and manage multiple Node.js versions in
                       Linux. It is a command-line utility and provides
                       several options for the easy installation of
                       Node.js. It allows you to download and install any
                       version of Node locally with a simple command.


                       In this post, we will show you how to install and
                       use NVM to manage Node.js on Debian 11.


                # ⚓ How_to_Shorten_Dock_Panel_&_Move_‘Show_Applications’_to_Top
                  in_Ubuntu_21.10_|_UbuntuHandbook⠀⇛


                       After installed the new Ubuntu 21.10, one of the
                       top things to do is tweaking the left dock panel.


                       Via “System Settings -> Appearance”, you may change
                       the panel position to bottom, adjust icon size, and
                       enable auto-hide. However, the 9 dots ‘Show
                       Applications’ icon sticks to the bottom which is
                       not movable.


                # ⚓ How_to_install_Apache_Kafka_on_Rocky_Linux_8_or_AlmaLinux_–
                  Linux_Shout⠀⇛


                       Here are the steps to install Apache Kafka on Rocky
                       Linux or AlmaLinux 8 server, of course, using
                       command terminal.


                       Apache Kafka is open-source software that enables
                       the storage and processing of data streams via a
                       distributed streaming platform. In simple words,
                       Apache Kafka is an event streaming platform that
                       acts as a messaging system between the sender and
                       the recipient with high fault tolerance and
                       scalability capabilities because it is based on a
                       distributed architecture that is optimized for the
                       same.


                # ⚓ How_to_install_Audacity_on_Linux_Lite_5.4_–_Invidious⠀⇛


                       In this video, we are looking at how to install
                       Audacity on Linux Lite 5.4.


                # ⚓ How_to_listen_to_podcasts_on_the_Linux_desktop_with_CPod⠀⇛


                       Are you in need of a good, elegant podcast client
                       for your Linux desktop? If so, you need to try out
                       CPod. It’s a friendly little app that makes
                       listening to your favorite shows fast and easy on
                       Linux. Here’s how to use it.


          o § Games⠀➾


                # ⚓ Monster_Crown_is_the_next-generation_of_retro_monster
                  catching_out_now_|_GamingOnLinux⠀⇛


                       Monster Crown takes the idea of the older Pokemon
                       games and blends in some fancy new ideas, along
                       with a darker story to make a game that will suit
                       fans of monster catching games nicely.


                       “Unravel Crown Island’s dark story as you create
                       your own monster legacy. With a history of sadistic
                       rulers and heroic saviors, the island faces another
                       threat in the form of a malicious young woman
                       seeking power. It’s up to you and the monsters you
                       make pacts with to prevent the return of tyranny.
                       Will your decisions make you a savior or a dark
                       messiah?”


                # ⚓ Wonderful_time-looping_adventure_Elsinore_got_a_big_price
                  drop_|_GamingOnLinux⠀⇛


                       Elsinore released back in 2019 and it’s actually
                       quite a wonderful adventure that sees you go
                       through a time-loop set in the world of
                       Shakespeare’s Hamlet.


                       Like a lot of games it went somewhat under the
                       radar for potential players, with it seeing less
                       than 200 reviews on Steam but it does have a Very
                       Positive user rating. With the price dropping from
                       £15.49 to £7.19 it’s hopefully going to allow more
                       people to try it who missed it.


                # ⚓ Warzone_2100_version_4.2.0_Beta_1_is_out,_gets_Spectators
                  and_Replays_support_|_GamingOnLinux⠀⇛


                       Looks like the next version of the free and open
                       source strategy game Warzone 2100 is going to be a
                       big one. Two new highlight features are coming to
                       the game with spectators and replays.


                       When it comes to being a spectator, this opens up
                       Warzone 2100 to allow people to watch a game in
                       progress. This could easily open up the game to
                       more competitive play, twitch livestreams, help
                       teach people to play and more. The way they’ve
                       explained that it will work is with dedicated
                       spectator spots, with them being able to chat
                       together and see the whole map.


                       Linking in with that is also a replay feature,
                       allowing you to play back an entire match. This
                       gives players the ability to capture fun moments,
                       figure out where you want wrong, share it with
                       others and also helps to show off bugs in the game
                       too and this feature was built on top of the
                       spectator support.


                # ⚓ GameCIH_APK_v3.0.4_Free_Download_for_Android_Latest_Version
                  –_DekiSoft⠀⇛


                       This is an original memory editor that was created
                       some 7-10 years back. It itself is quite old and
                       has been since 2006. GameCIH free download for
                       Android came out in Taiwan by a talented programmer
                       going by alias CIH<SoftwareMagician>, this standing
                       for the company/collective it is a part of. This is
                       not seemed to be the first of its kind but also
                       quite an easy tool to use. The best thing about
                       this one is that it has gained a lot of popularity
                       for money cheats.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Kubuntu_Focus_M2_Linux_laptop_gets_a_spec_bump_(and_a
                        smaller,_cheaper_sibling:_the_Kubuntu_Focus_XE)⠀⇛


                             The Kubuntu Focus family of Linux laptops is
                             growing.


                             A 3rd-gen Kubuntu Focus M2 laptop with a 15.6
                             inch display, 45-watt Intel Core i7-11800H
                             Tiger Lake processor, and NVIDIA GeForce RTX
                             30-series graphics is now available for $1945
                             and up. But if you’re in the market for
                             something smaller and/or cheaper, the Kubuntu
                             team also introduced the 14 inch Kubuntu
                             Focus Xe this summer. It sells for $895 and
                             up.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ GNOME:_Platform_Design_Goings_On⠀⇛


                             The GNOME design team has recently been
                             working on GNOME’s application development
                             platform, and I thought that it might be
                             interesting for people to hear about what
                             we’ve been up to.


                             The following is an overview of our recent
                             platform design activities, particularly
                             libadwaita. It will give an idea of what is
                             currently going into the GNOME platform from
                             a UXD perspective, as well as some of things
                             that people might expect from the platform in
                             the future.


                      # ⚓ GNOME’s_Platform_Design_Continues_Evolving_From_Dark
                        Mode_To_Toast⠀⇛


                             GNOME developer Allan Day has provided an
                             update on behalf of the GNOME design time
                             around some of their recent platform design
                             improvements and some of the changes they are
                             talking about in the near future.


                             Allan’s blog post today covers some of the
                             recent GNOME platform design work like:


                             - Ongoing improvements to the GNOME/GTK
                             application styling, especially around
                             libadwaita.


                             - The recent excitement around GNOME 42
                             adding a system-wide dark style preference.


                      # ⚓ Clapper_–_A_New_Gnome_Media_Player_for_Linux⠀⇛


                             Clapper is a free and open-source media
                             player. It was built for GNOME using GJS with
                             the GTK4 toolkit. For its media backend,
                             Clapper uses GStreamer, and it renders
                             everything via OpenGL. The app is built with
                             memory friendliness in mind.


                             It ships with all the features you expect in
                             a basic media player and more. This includes
                             windowed, floating, and full-screen viewing
                             modes. Other features include using playlists
                             from a file, floating mode, and hardware
                             acceleration.


                             Note that working with playlists is feature-
                             limited in Flatpak version to contents of
                             user “Videos” directory by default. Clapper
                             can only open playlist files with the .claps
                             file extension. There should be a single file
                             path per line which can be either relative or
                             absolute. Playlists can also contain HTTP
                             links instead of file paths.


          o § Distributions⠀➾


                # § Reviews⠀➾


                      # ⚓ Kubuntu_Focus_XE_is_the_perfect_laptop_for_Windows-
                        switchers_and_Linux_beginners_[Review]⠀⇛


                             Should you buy the Kubuntu Focus XE Linux
                             laptop? If you are looking to run a Linux-
                             based operating system and want a laptop that
                             is guaranteed to work, it should absolutely
                             be considered. Not only is the hardware
                             largely great, but arguably more importantly,
                             the included software is top-notch.


                             The Kubuntu operating system is wonderful, as
                             is all of the included curated apps. Not to
                             mention, the Kubuntu Focus enhancements
                             including the specialized apps, Welcome
                             Wizard, and welcome guide, will make things
                             much easier for Linux beginners. The Kubuntu
                             Focus team set out to deliver an excellent
                             user experience at an affordable price with
                             the XE laptop and they totally delivered.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Red_Hat_Is_Hiring_Another_Linux_Developer_To_Work_On
                        GPU_Hardware_Enablement_–_Phoronix⠀⇛


                             Red Hat already employs numerous open-source
                             graphics driver developers from DRM subsystem
                             maintainer David Airlie to numerous others on
                             his team working on areas from Mesa OpenCL
                             support to Heterogeneous Memory Management to
                             other user and kernel-space improvements for
                             open-source Linux graphics. Red Hat has now
                             put out a call to hire yet another
                             experienced Linux GPU driver developer.


                      # ⚓ IBM_Attempts_An_Uncrewed_Atlantic_Crossing_(Again)_|
                        Hackaday⠀⇛


                             IBM and a non-profit company, ProMare, failed
                             to send their 49-foot Mayflower autonomous
                             ship across the Atlantic back in June. Now
                             they are almost ready to try again. The
                             Mayflower will recreate the path of its more
                             famous namesake.


                             The total voyage is set to take a month, but
                             the last attempt developed mechanical
                             problems after three days. Now they are
                             running more sea trials closer to shore
                             before attempting another crossing in 2022.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ CAN_communication_on_the_Raspberry_PI_with
                        SocketCAN⠀⇛


                             Looking for a way to connect your Raspberry
                             PI to a Controller Area Network (CAN) bus?
                             With the help of the low-cost Waveshare
                             RS485/CAN hat, you can augment your Raspberry
                             PI such that it can communicate with the
                             traffic on the CAN bus. This article explains
                             how to configure the Waveshare RS485/CAN hat
                             as a SocketCAN interface on your Raspberry
                             PI.


                      # ⚓ Engaging_Black_students_in_computing_at_school_—
                        interview_with_Lynda_Chinaka⠀⇛


                      # ⚓ The_Beauty_Of_Dance,_Seen_Through_The_Power_Of_Touch
                        |_Hackaday⠀⇛


                             This platform, which is called Kinetic Soul,
                             uses Posenet computer vision to track a
                             dancer’s movements. Posenet detects the
                             dancer’s joints and creates a point map to
                             determine what body parts are moving where,
                             and at what speed. Then the system translates
                             and transmits the movements to the 32 pins on
                             the surface, creating a touchable picture of
                             what’s going on. Each 3D-printed pin is
                             controlled with a solenoid, all of which are
                             driven by a single Arduino.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ MUNBYN_Android_Barcode_Scanner_as_Your_Best_Business
                        Partner!_|_Tech_Times⠀⇛


                      # ⚓ Android_Auto_beta_update_introduces_two_crucial_new
                        features_|_T3⠀⇛


                      # ⚓ The_new_Nokia_G300_is_a_$199_5G_Android_phone_with_a
                        big_battery_|_Android_Central⠀⇛


                      # ⚓ Best_Android_app_deals_of_the_day:_Gunslugs_2,_more_–
                        9to5Toys⠀⇛


                      # ⚓ Smart_Lock_loses_UI_dating_back_to_Android_Lollipop_–
                        9to5Google⠀⇛


                      # ⚓ Digital_Car_Keys_Are_Coming_Soon_to_Android⠀⇛


                      # ⚓ GPD_XP:_Android_gaming_handheld_to_launch_on
                        Indiegogo_–_NotebookCheck.net_News⠀⇛


                      # ⚓ Android_Phones_Still_Track_You,_Even_When_You_Opt
                        Out⠀⇛


                      # ⚓ 5_Android_Development_Blunders_That_Can_Ruin_Your
                        Android_App⠀⇛


                      # ⚓ Alibaba_T-head_RVB-ICE_dual-core_RISC-V_SBC_supports
                        Android_10,_Debian_11_–_CNX_Software⠀⇛


                      # ⚓ Questions_You_Need_to_Ask_When_Using_Your_Android
                        Device_For_Trading_Bitcoin⠀⇛


                      # ⚓ Android_Phones_Can_Still_Track_You_Despite_Opting
                        Out–Study_|_Tech_Times⠀⇛


                      # ⚓ Realme_UI_3.0_Launch_Tomorrow:_Supported_Devices,
                        Rollout_Timeline,_Android_12_Support_–_Trak.in_–_Indian
                        Business_of_Tech,_Mobile_&_Startups⠀⇛


                      # ⚓ TECNO_CAMON_17_to_launch_the_all-new_Android_12
                        through_its_upcoming_HiOS_8.5_|_Africanews⠀⇛


                      # ⚓ How_to_Print_From_an_Android_Device_|_Tech_Times⠀⇛


                      # ⚓ How_to_send_a_group_text_message_on_Android_–
                        Phandroid⠀⇛


                      # ⚓ How_to_find_out_which_Android_apps_are_using_the_most
                        memory_–_TechRepublic⠀⇛


                      # ⚓ Update_your_Android!_Patch_fixes_security
                        vulnerabilities⠀⇛


                      # ⚓ You_Can_Now_Follow_RSS_Feeds_on_Chrome_for_Android⠀⇛


                      # ⚓ Nokia_T20_Android_tablet_features_an_all-day_battery
                        life_and_a_captivating_2K_display_»_Gadget_Flow⠀⇛


                      # ⚓ Nokia_G300_is_a_budget_5G_device_with_Android_11_for
                        $199_|_Pocketnow⠀⇛


                      # ⚓ Qualcomm_working_on_Android_console_to_rival_Nintendo
                        Switch:_Report_|_Technology_News,The_Indian_Express⠀⇛


                      # ⚓ Samsung_Galaxy_S21_Ultra_vs_Vivo_X70_Pro_Plus:
                        Android_Camera_Kings_go_for_a_Shootout⠀⇛


                      # ⚓ Z_Cam_Introduces_IPMAN_AMBR._A_Dual_HDMI_5.5”
                        Wireless_Android_Streaming_Device_–_Newsshooter⠀⇛


                      # ⚓ Best_music_widgets_for_Android_–_Phandroid⠀⇛


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


                # ⚓ Top_6_open-source_Self-hosted_Bookmark_Manager_Solution⠀⇛


                       Bookmarking is a great way to save documents that
                       you think may need to reference them in the future.


                       If you use paper bookmarks then, of course, you are
                       reading a book, It’s pretty great, to save your
                       spot using a bookmark to keep your place in the
                       book.


                       Let’s say, that you explore the internet every day,
                       and you like to keep an archive of you find, learn
                       to review it later. Your local browser is not
                       reliable, you need to keep them in the cloud to
                       access them from anywhere. So, this article is for
                       you.


                       Some services may help you to save and record your
                       bookmarks, back in the day we had Del.icio.us
                       (terminated), Digg, Stumbleupon (Mix), and
                       Pinterest which many people use it to save their
                       links.


                       I believe I had over than 19k bookmarks in my
                       Del.icio.us, when the website terminated, then I
                       created my own system to record my links which I
                       still use for years.


                # ⚓ 7_Open-Source_Software_Options_for_Architects⠀⇛


                       Open-source software is released under a specific
                       license that gives users the right to download,
                       use, or change the software and its source code.
                       Unlike commercial software, which typically has a
                       protected source code and proprietary file formats,
                       open-source software projects are not profit-driven
                       and encourage users to modify and share their code
                       with the wider community. Often the goal of these
                       projects is to develop applications that can
                       accommodate multiple viewpoints and ways of
                       working. Some well-known open-source projects
                       include the Linux operating system, the WordPress
                       web publishing platform, and the audio-editing
                       application Audacity.


                # § Funding⠀➾


                      # ⚓ Donation_campaign:_“Framasoft,_it’s_also…”⠀⇛


                             The campaign is named “Framasoft, it’s also…”
                             and communicate in a playful way (a card
                             game) their actions in the digital world, but
                             also in real-life. You can flip more than
                             thirty illustrated cards to discover the org.
                             You’ll probably be surprised by the amount of
                             what they manage.


                # § Programming/Development⠀➾


                      # ⚓ What_can_enterprises_do_about_soaring_technical
                        debts?⠀⇛


                             Over the last few decades, technical debts
                             for multiple organizations are witnessing
                             growth due to failed and non-planned tech
                             projects architecture. According to
                             OutSystem’s latest research, technical debt
                             is estimated to cost businesses $5 trillion
                             in the next ten years. Thus, the IT debts
                             have become the central focus, along with re-
                             directing the analysis criteria of every
                             project.


                             [...]


                             She says, “Refactoring code has to be a norm.
                             Every spring I have certain cycles that I
                             reserve for refactoring. The second thing
                             required is fearless developers who can fix
                             the bugs when necessary. Also, retiring
                             legacy systems needs to be addressed as they
                             can pose a threat to security. So, we make
                             sure to retire from the things which don’t
                             make sense anymore.”


                      # ⚓ Apple_II_Programming:_From_A_Cabin_In_The_Woods⠀⇛


                             Adam: Hello, and welcome to CoRecursive. I’m
                             Adam Gordon Bell. Each episode, a guest
                             shares the story behind a piece of software
                             being built. Today’s episode is about remote
                             work. Well, sort of. I’ve been working from
                             my home office for almost exactly 10 years
                             now. And when everyone started working from
                             home, I felt like I had some tips to share,
                             like to break up the Zoom meetings you can
                             just go for walking meetings. Just call in on
                             your phone. It makes a big difference. But
                             I’m not totally sure we figured out all that
                             remote work can be. So I found someone who
                             has something to teach me about remote work.
                             I think that he might be the original remote
                             software developer. He left California behind
                             for a lower cost of living in Oregon. And
                             from Oregon, he developed software for Apple.
                             But the kind of surprising thing is he did
                             this all in 1976. And he did it so well he
                             became rich and even briefly quite famous.


                             Paul: That’s 60s artist, whose name escapes
                             me, said everybody is famous for 15 seconds.
                             I was famous for slightly longer than that.
                             But during that time, it was nuts. People
                             would show up and try to ask for autographs
                             and stuff. It was weird. I mean, it never
                             occurred to me that people would want the
                             autographs of a computer programmer. I mean,
                             that’s just not like the normal, famous
                             person kind of an image I have in my mind.


                             Adam: That was Paul Lutus. He built Apple
                             Writer for the Apple II. And he thinks
                             there’s something that we, as a profession,
                             are missing, something that we’ve forgotten.
                             But to understand his story and how he got on
                             the front page of the Wall Street Journal,
                             how he got interviewed for national TV
                             programs and all for writing software, we
                             need a little background.


                      # ⚓ Tilde_expansion_in_Rust⠀⇛


                             In several of my personal projects I have a
                             need for tilde expansion, which means taking
                             a filename such as ~/foo and expanding the
                             tilde into the current user’s home directory.
                             For me, that would result in /home/liw/foo.
                             This is ubiquitous in Unix, and now unknown
                             elsewhere. The usual tilde syntax is a little
                             more complex than that: one can refer to
                             another user’s home directory as well.


    * § Leftovers⠀➾


          o ⚓ Parable_of_the_Magpie_and_the_Mirror⠀⇛


                 A certain scientist had a cage, and took a magpie, and
                 put the magpie in the cage.


                 And the magpie’s head and neck were black, and black were
                 its beak and eyes, but the breast and belly of the magpie
                 were white as paper.


          o ⚓ Slain_reporter’s_father_calls_for_action_against_Facebook_over
            video_of_daughter’s_death⠀⇛


                 The complaint also alleges that Facebook is engaging in
                 deceptive trade practices by violating its own terms of
                 service and misrepresenting the safety of the platform.


          o ⚓ Things_that_go_“Bump”_in_the_Night:_Non_HTTP_Requests_Hitting_Web
            Servers⠀⇛


                 If you are reviewing your web server logs periodically,
                 you may notice some odd requests that are not HTTP
                 requests in your logs. In particular if you have a web
                 server listening on a non standard port. I want to
                 quickly review some of the most common requests like
                 that, that I am seeing: [...]


          o § Education⠀➾


                # ⚓ ‘Threats_Are_Being_Made_Against_Teachers_Who_Are_Teaching
                  the_Truth’⠀⇛


                       Janine Jackson interviewed Stevana Sims about
                       defending anti-racist education for the October 8,
                       2021, episode of CounterSpin. This is a lightly
                       edited transcript.


                # ⚓ Taliban_won’t_commit_to_allowing_girls_to_return_to_high
                  school_in_Afghanistan⠀⇛


                       Girls in grades 6 and above can’t attend school
                       under new Taliban rule


          o § Hardware⠀➾


                # ⚓ Sinclair_Pocket_TV_Teardown_|_Hackaday⠀⇛


                       A pocket-sized TV is not a big deal today. But in
                       1983, cramming a CRT into your pocket was quite a
                       feat. Clive Sinclair’s TV80 or FTV1 did it with a
                       very unique CRT and [Dubious Engineering] has a
                       teardown video to show us how it was done.


                       A conventional CRT has an electron gun behind the
                       screen which is why monitors that use them are
                       typically pretty thick. The TV80’s tube has the
                       electron gun to the side to save space. It also
                       uses a fresnel lens to enlarge the tiny image.


                # ⚓ Bendable_Colour_EPaper_Display_Has_Touch_Input_Too_|
                  Hackaday⠀⇛


                       The Interactive Media Lab at Dresden Technical
                       University has been busy working on ideas for user
                       interfaces with wearable electronics, and presents
                       a nice project, that any of us could reproduce, to
                       create your very own wearable colour epaper display
                       device. They even figured out a tidy way to add
                       touch input as well. By sticking three linear
                       resistive touch strips, which are effectively touch
                       potentiometers, to a backing sheet and placing the
                       latter directly behind the Plastic Logic Legio 2.1″
                       flexible electrophoretic display (EPD), a
                       rudimentary touch interface was created. It does
                       look like it needs a fair bit of force to be
                       applied to the display, to be detectable at the
                       touch strips, but it should be able to take it.


          o § Health/Nutrition⠀➾


                # ⚓ Opinion_|_Our_Health_Depends_on_Indigenous_Botanical
                  Knowledge_and_Plants_That_Are_Rapidly_Being_Destroyed⠀⇛


                       Southwest Harbor, Maine (Special to Informed
                       Comment) – While mainstream media celebrate the
                       remarkable development in record time of vaccines
                       spectacularly effective against the Covid virus,
                       knowledge that might contribute to other medical
                       breakthroughs is being steadily undermined. This
                       decline is not the result of some dramatic lawsuit
                       or corporate takeover. It is one of the effects of
                       the industrial modernization that is supposed to
                       have brought increasing comfort, health and
                       advanced knowledge into our lives. Economic growth
                       has produced not only a climate emergency but a
                       less publicized decline in the many efficacious
                       forms of traditional knowledge and the biodiversity
                       they sustain and are sustained by. In an email
                       exchange I had with ethnobotanist Kirsten
                       Tripplett, Ph.D., she pointed out:


                # ⚓ Poll_Finds_88_Percent_Support_Sanders’s_Plan_to_Lower
                  Prescription_Drug_Prices⠀⇛


                # ⚓ ‘Therapeutics_Nationalism’?_Poor_at_Risk_of_Being_Left
                  Behind_as_Rich_Buy_Up_New_Covid_Drug⠀⇛


                       Public health experts are voicing increased concern
                       that poor countries—already denied adequate access
                       to coronavirus vaccines—could be left behind once
                       again as rich nations rush to buy up supplies of
                       Merck’s promising new Covid-19 drug before it has
                       even won regulatory approval.


                       “Merck’s intellectual property monopolies should
                       not be permitted to obstruct global treatment
                       access.”


                # ⚓ Nearly_42,000_Sources_of_Toxic_‘Forever_Chemicals’_Put_US
                  Drinking_Water_at_Risk:_Study⠀⇛


                       Bolstering calls for stronger PFAS regulations and
                       more testing, a new analysis released Tuesday finds
                       nearly 42,000 potential sources of toxic “forever
                       chemicals” that could contaminate drinking water in
                       communities throughout the United States.


                       “Every community in the U.S. is likely affected by
                       PFAS contamination, but those living near or
                       downstream from industrial facilities may be more
                       at risk.”


                # ⚓ Doctor_Who_Revealed_Flint_Lead_Crisis_Calls_Benton_Harbor
                  Emergency_More_‘Environmental_Injustice’⠀⇛


                       As the people of Benton Harbor, Michigan are being
                       advised to drink only bottled water due to lead
                       contamination in the city’s pipes, the doctor whose
                       research revealed Flint’s lead crisis described
                       similarities between the two emergencies, which she
                       called examples of “environmental injustice” in an
                       interview published Monday.


                       “There is lead in the water, and there’s been lead
                       in the water for too long… and it is absolutely not
                       safe for anyone to be drinking at this time.”


                # ⚓ Abbott_Issues_Executive_Order_Banning_Vaccine_Mandates_in
                  Texas⠀⇛


                # ⚓ Wisconsin_Mom_Sues_School_District_After_Her_Sons_Test
                  Positive_for_Coronavirus⠀⇛


                # ⚓ Sanders,_Jayapal_Say_Medicare_Expansion_in_Reconciliation
                  Package_‘Not_Negotiable’⠀⇛


                       As congressional progressives push back against
                       right-wing Democrats seeking to shrink the size and
                       scope of the Build Back Better Act, Sen. Bernie
                       Sanders and Rep. Pramila Jayapal on Tuesday
                       insisted that expanded Medicare benefits must
                       remain part of the $3.5 trillion budget
                       reconciliation package.


                       “I do understand that the healthcare industry does
                       not like this idea, but maybe, just maybe, we stand
                       with the American people.”


                # ⚓ Amid_Corporate_Dems’_Threats,_New_Poll_Shows_83%_of_Voters
                  Back_Drug_Pricing_Reform⠀⇛


                       “Even with PhRMA spending millions on scare tactics
                       and lies—voters know the truth.”


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Patch_Tuesday,_October_2021_Edition⠀⇛


                             Microsoft today issued updates to plug more
                             than 70 security holes in its Windows
                             operating systems and other software,
                             including one vulnerability that is already
                             being exploited. This month’s Patch Tuesday
                             also includes security fixes for the newly
                             released Windows 11 operating system.
                             Separately, Apple has released updates for
                             iOS and iPadOS to address a flaw that is
                             being actively attacked.


                      # ⚓ Office_365_Spy_Campaign_Targets_US_Military_Defense⠀⇛


                             A new threat actor, dubbed DEV-0343, has been
                             spotted attacking U.S. and Israeli defense
                             technology companies, Persian Gulf ports of
                             entry and global maritime transportation
                             companies with ties to the Middle East. The
                             threat actor’s goal is Microsoft Office 365
                             account takeovers.


                      # ⚓ Govt_to_force_businesses_with_$10m_annual_turnover_to
                        report_ransomware_attacks [iophk: Windows TCO]⠀⇛


                             In a statement on Wednesday, Andrews said the
                             reporting regime was part of a plan — called
                             the Ransomware Action Plan — to protect
                             Australians against ransomware.


                             The government will also introduce new
                             criminal offences and tougher penalties as
                             part of the plan. However, there is no date
                             given for the Plan to take effect.


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation⠀➾


                                        # ⚓ Nokia_says_PTC,_Linux_Foundation,
                                          Smart_Mobile_Labs_and_Taqtile_start
                                          running_on_MX_Industrial_Edge_–
                                          Telecompaper⠀⇛


                                               Nokia has announced the
                                               expansion of the Industry
                                               4.0 digitisation enabler
                                               application ecosystem
                                               running on its newly
                                               launched MX Industrial Edge
                                               (MXIE), to include PTC’s
                                               Kepware, the Linux
                                               Foundation’s Fledge, the
                                               Smart Mobile Labs Edge
                                               Video Orchestrator, and
                                               Taqtile’s Manifest
                                               platform.


                      # § Security⠀➾


                            # ⚓ Security_updates_for_Tuesday_[LWN.net]⠀⇛


                                   Security updates have been issued by
                                   Debian (firefox-esr, hiredis, and icu),
                                   Fedora (kernel), Mageia (libreoffice),
                                   openSUSE (chromium, firefox, git,
                                   go1.16, kernel, mbedtls, mupdf, and
                                   nodejs8), Oracle (firefox and kernel),
                                   Red Hat (firefox, grafana, kernel,
                                   kpatch-patch, and rh-mysql80-mysql),
                                   and SUSE (apache2, containerd, docker,
                                   runc, curl, firefox, kernel, libqt5-
                                   qtsvg, and squid).


                            # ⚓ Google_Releases_Security_Updates_for_Chrome_|
                              CISA⠀⇛


                                   Google has updated the Stable channel
                                   to 94.0.4606.81 for Windows, Mac and
                                   Linux. This version addresses
                                   vulnerabilities that an attacker could
                                   exploit to take control of an affected
                                   system.


                                   CISA encourages users and
                                   administrators to review the Chrome
                                   Release and apply the necessary
                                   updates.


                            # ⚓ Microsoft_Releases_October_2021_Security
                              Updates⠀⇛


                                   Microsoft has released updates to
                                   address multiple vulnerabilities in
                                   Microsoft software. An attacker can
                                   exploit some of these vulnerabilities
                                   to take control of an affected system.


                            # ⚓ Apple_Releases_Security_Update_to_Address_CVE-
                              2021-30883⠀⇛


                                   Apple has released a security update to
                                   address a vulnerability—CVE-2021-
                                   30883—in multiple products. An attacker
                                   could exploit this vulnerability to
                                   take control of an affected system.
                                   This vulnerability has been detected in
                                   exploits in the wild.


                            # ⚓ Apache_OpenOffice_users_should_upgrade_to
                              newest_security_release!⠀⇛


                                   The Apache Software Foundation (ASF)
                                   has released Apache OpenOffice 4.1.11,
                                   which fixes a handful of security
                                   vulnerabilities, including CVE-2021-
                                   33035, a recently revealed RCE
                                   vulnerability that could be triggered
                                   via a specially crafted document.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Most_People_Probably_Don’t_Need_A_VPN,
                                    Experts_Now_Advise⠀⇛


                                         Given the seemingly endless
                                         privacy scandals that now engulf
                                         the tech and telecom sectors on a
                                         near-daily basis, many consumers
                                         have flocked to virtual private
                                         networks (VPN) to protect and
                                         encrypt their data. One study
                                         found that VPN use quadrupled
                                         between 2016 and 2018 as
                                         consumers rushed to protect data
                                         in the wake of scandals,
                                         breaches, and hacks.


                                  # ⚓ Facebook_Banning_&_Threatening_People_For
                                    Making_Facebook_Better_Is_Everything_That’s
                                    Wrong_With_Facebook⠀⇛


                                         Regular readers know that I’m a
                                         believer in trying to get the big
                                         internet companies to embrace a
                                         more protocols over platforms
                                         approach, in which they’re
                                         building something that others
                                         can then build on as well, and
                                         improve in their own ways
                                         (without fear of having the rug
                                         pulled out from under them). It’s
                                         why I’m hopeful about Twitter
                                         working on just such a plan with
                                         its Bluesky project. Facebook,
                                         unfortunately, takes a very
                                         different view of the world.


                                  # ⚓ Open_Source_Intelligence_(OSINT)_is_Great
                                    for_Catching_Bad_Actors;_But_It_Can_Also_Be
                                    Used_Against_the_Good_Ones_–_You_and_Me⠀⇛


                                         Using this publicly-available
                                         information, Bellingcat have
                                         helped understand who shot down
                                         the MH17 passenger plane, and who
                                         poisoned the MI6 double agent
                                         Sergei Skripal and his daughter.
                                         Those are obviously valuable
                                         contributions to public
                                         understanding of important
                                         events. But there is a darker
                                         side to the use of OSINT tools.
                                         After all, it is not just bad
                                         actors who post huge amounts of
                                         personal information online: we
                                         all do. This means that
                                         potentially anyone with the right
                                         software can piece together this
                                         digital jigsaw puzzle to discover
                                         much about our daily lives.


                                  # ⚓ Coalition_Against_Stalkerware_Named_J.D.
                                    Falk_Award_Winner_for_Raising_Awareness
                                    About_and_Helping_Victims_of_Malicious
                                    Spying_Apps⠀⇛


                                         The award is being presented
                                         today by the Messaging, Malware
                                         and Mobile Anti-Abuse Working
                                         Group (M3AAWG), a global industry
                                         organization working against
                                         internet abuses including
                                         botnets, malware, spam, viruses,
                                         DDoS attacks and other online
                                         exploitation. The award honors
                                         the work of one of M3AAWG’s
                                         founding members, J.D. Falk, an
                                         antispam and email security
                                         pioneer. It recognizes
                                         individuals and organizations
                                         improving the internet experience
                                         and protecting end users.


                                         The Coalition Against Stalkerware
                                         was created in 2019 by ten
                                         founding partners in response to
                                         the growing threat of
                                         commercially available apps and
                                         devices that enable someone to
                                         covertly spy on another person’s
                                         electronic devices. Stalkerware
                                         enables abusers to remotely
                                         monitor victims’ web searches,
                                         text messages, geolocation,
                                         photos, voice calls, and more. It
                                         affects hundreds of thousands of
                                         victims around the world and is
                                         often used to facilitate partner
                                         surveillance, gender-based and
                                         domestic violence, harassment,
                                         and sexual abuse.


                                         The Coalition helps those
                                         targeted by stalkerware and works
                                         with antivirus makers to improve
                                         the detection of stalkerware on
                                         mobile phones, laptops, and other
                                         devices. The Stopstalkerware
                                         website, offered in seven
                                         different languages, has
                                         resources for victims to learn
                                         how to protect their devices, as
                                         well as find and remove
                                         stalkerware once it has been
                                         installed. It also offers a
                                         global directory of organizations
                                         for victims of stalking, domestic
                                         violence, online abuse, and more.


                                  # ⚓ Researchers_Find_Android_Phones_Still
                                    Track_You,_Even_When_You_Opt_Out⠀⇛


                                         A lot of the blame here, as the
                                         researchers point out, fall on
                                         so-called “system apps.” These
                                         are apps that come pre-installed
                                         by the hardware manufacturer on a
                                         certain device in order to offer
                                         a certain kind of functionality:
                                         a camera or messages app are
                                         examples. Android generally
                                         packages these apps into what’s
                                         known as the device’s “read only
                                         memory” (ROM), which means you
                                         can’t delete or modify these apps
                                         without, well, rooting your
                                         device. And until you do, the
                                         researchers found they were
                                         constantly sending device data
                                         back to their parent company and
                                         more than a few third
                                         parties—even if you never opened
                                         the app at all.


                                  # ⚓ The_European_Parliament_Voted_to_Ban
                                    Remote_Biometric_Surveillance⠀⇛


                                         It’s not actually banned in the
                                         EU yet — the legislative process
                                         is much more complicated than
                                         that — but it’s a step: a total
                                         ban on biometric mass
                                         surveillance.


                                  # ⚓ Cybersecurity:_EU_To_Ban_Anonymous
                                    Websites⠀⇛


                                         The EU is currently drafting
                                         legislation to increase cyber
                                         security (revised NIS Directive,
                                         in short “NIS 2”). According to
                                         this directive, the registration
                                         of internet domain names will in
                                         future require the correct
                                         identification of the owner in
                                         the Whois database, including
                                         name, address and telephone
                                         number. So far, registries such
                                         as denic do not register
                                         telephone numbers of the holders.
                                         The leading Industry Committee
                                         wants to additionally mandate
                                         „verification“ of the
                                         registration data. The plans
                                         could mean the end of “whois
                                         privacy” services for proxy
                                         registration of domains,
                                         threatening the safety of
                                         activists and whistleblowers. The
                                         Home Affairs Committee is voting
                                         on the issue this week. The lead
                                         committee ITRE is expected to
                                         take a position at the end of the
                                         month.


                                  # ⚓ Haugen_Isn’t_Really_a_‘Facebook
                                    Whistleblower’⠀⇛


                                         Haugen has brought to the surface
                                         a fuzziness in what many of us
                                         understand by the idea of
                                         whistleblowing.


                                         Even Russell Brand, a comedian
                                         turned soothsayer whose critical
                                         and compassionate thinking has
                                         been invaluable in clarifying our
                                         present moment, joined in the
                                         cheerleading of Haugen, calling
                                         her a “brave whistleblower”.


                                  # ⚓ Help_Us_Find_the_Apps_That_Sell_Your
                                    Location⠀⇛


                                         Last week we wrote about the
                                         estimated $12 billion market for
                                         your phone’s location data. We
                                         identified 47 companies that play
                                         one of the many roles in the
                                         location data pipeline:
                                         providers, buyers, sellers, and
                                         aggregators.


                                         Now we need your help finding a
                                         missing piece of the data
                                         pipeline: the mobile phone apps
                                         that harvest and share location
                                         data with the industry.


                                  # ⚓ Facebook_Banned_Me_for_Life_Because_I
                                    Help_People_Use_It_Less⠀⇛


                                         If someone built a tool that made
                                         Facebook less addictive—a tool
                                         that allowed users to benefit
                                         from Facebook’s positive features
                                         while limiting their exposure to
                                         its negative ones—how would
                                         Facebook respond?


                                         I know the answer, because I
                                         built the tool, and Facebook
                                         squashed it. This summer,
                                         Facebook sent me a cease-and-
                                         desist letter threatening legal
                                         action. It permanently disabled
                                         my Facebook and Instagram
                                         accounts. And it demanded that I
                                         agree to never again create tools
                                         that interact with Facebook or
                                         its other services.


          o § Defence/Aggression⠀➾


                # ⚓ Trump’s_Cryptic_Comment_From_2017_May_Have_Foreshadowed_His
                  Coup_Attempt⠀⇛


                # ⚓ ‘Profiteers_of_Armageddon’:_Report_Reveals_Who_Benefits
                  From_US_‘Nuclear_Modernization’_Plan⠀⇛


                       A short list of contractors that pour large sums of
                       money into campaign contributions, lobbying, and
                       industry-friendly think tanks benefits from the
                       U.S. government’s ongoing, decadeslong “nuclear
                       modernization” plan worth up to $2 trillion,
                       according to a report out Tuesday.


                       The issue brief—entitled Profiteers of Armageddon:
                       Producers of the next generation of nuclear
                       weapons—was authored by William Hartung, director
                       of the Arms and Security Program at the Center for
                       International Policy, who also outlined his report
                       in Inkstick.


                # ⚓ Report:_TSA_Is_Spending_$1_Billon_On_Bag_Scanners_That_‘May
                  Never_Meet_Operational_Needs’⠀⇛


                       Somehow, “TSA” stands for “The Terrorists Won.” In
                       exchange for endless inconveniences, inconsistently
                       deployed security measures, and a steady stream of
                       intrusive searches and rights violations, we’ve
                       obtained a theatrical form of security that’s more
                       performative than useful.


                # ⚓ Opinion_|_Life_in_the_Post-9/11_Military:_A_Navy_Wife’s
                  Perspective⠀⇛


                       I know what it means to be watched all too
                       carefully, a phenomenon that’s only grown worse in
                       the war-on-terror years. I’m a strange combination,
                       I suspect, being both a military spouse and an
                       anti-war-on-terror activist. As I’ve discovered,
                       the two sit uncomfortably in what still passes for
                       one life. In this country in these years, having
                       eyes on you has, sadly enough, become a common and
                       widespread phenomenon. When it’s the government
                       doing it, it’s called “surveillance.” When it’s
                       your peers or those above you in the world of the
                       military spouse, there’s no word for it at all.


                # ⚓ What_are_the_Prospects_For_Peace?_An_Interview_with_William
                  Astore⠀⇛


                       William J. Astore is a retired US Air Force
                       lieutenant colonel. He has taught at the Air Force
                       Academy and Naval Postgraduate School, and now
                       teaches history at the Pennsylvania College of
                       Technology. He is the author or co-author of three
                       books and numerous articles focusing on military
                       history as well as the history of science,
                       technology, and religion. We are extremely honored
                       that he took the time to talk to us and share his
                       views. His responses below are exactly as he
                       provided.


                       The questions here are not philosophical or
                       abstract. They focus on the realities of the
                       international power struggle unfolding in real
                       time. They directly address the role of the U.S. in
                       the escalating tensions and its capacity to reduce
                       them. We also probe the role of everyday citizens
                       in affecting the relationship the U.S. now has and
                       will have with the rest of the world community.


                # ⚓ As_CIA_Warns_China_“Most_Important”_Threat_to_U.S.,_Is
                  Biden_Pursuing_a_“New_Cold_War”?⠀⇛


                       We look at growing tensions between China and
                       Taiwan as China’s military said Monday it had
                       conducted beach landing and assault drills in the
                       province across from Taiwan. Taiwan’s president
                       responded on Sunday saying Taiwan would not bow to
                       pressure from China. This comes as The Wall Street
                       Journal has revealed a small team of U.S. special
                       operations forces and marines have been secretly
                       operating in Taiwan for at least a year to help
                       train Taiwanese military forces for a possible
                       conflict with China. We speak with Ethan Paul of
                       the Quincy Institute for Responsible Statecraft,
                       who warns U.S. interference could cause “a conflict
                       that could engulf the entire region.” His latest
                       article is “Biden doesn’t understand the ‘new Cold
                       War.’”


                # ⚓ Choosing_Its_“Gates”:_US_Punishes_Russia_but_is_Giving_UAE
                  a_Free_Pass⠀⇛


                       The Western corporate media peddled claims of
                       direct Russian interference in the 2016 U.S.
                       presidential election, but remains silent on the
                       seemingly provable interference of the United Arab
                       Emirates (UAE). Even worse is that the Biden
                       administration, armed with information about the
                       interference, is still selling weapons to Abu
                       Dhabi.


                # ⚓ US_Writes_Belarus_into_Its_Familiar_Regime-Change_Script⠀⇛


                       Quietly, the U.S. national security state is
                       turning up the heat on Belarus, hoping that the ex-
                       Soviet country of 9 million will be the next
                       casualty of its regime-change agenda. This
                       sentiment was made clear in President Joe Biden’s
                       recent speech at the United Nations General
                       Assembly. Biden announced that the U.S. would
                       pursue “relentless diplomacy” finding “new ways of
                       lifting people up around the world, of renewing and
                       defending democracy.” The 46th president was
                       explicit in whom he meant by this: “The democratic
                       world is everywhere. It lives in the anti-
                       corruption activists, the human rights defenders,
                       the journalists, the peace protestors on the
                       frontlines of this struggle in Belarus, Burma,
                       Syria, Cuba [and] Venezuela,” he said, putting
                       Belarus first on the list of states in desperate
                       need of a change in government.


                # ⚓ Belgium:_State_Security_links_mosque_to_extremism⠀⇛


                       According to Pano, the Belgian intelligence report
                       rated several mosques in Belgium, among them the
                       Sultan Ahmet Mosque in Heusden-Zolder, Limburg. The
                       facility is run by several members of the Üstün
                       family, including Mehmet Üstün, who has been
                       president of the EMB, the organisation representing
                       Muslims in Belgium, since May 2018.


                # ⚓ Violent_crimes_rise_in_Mexico;_94.8%_go_unpunished⠀⇛


                       The report found that 93.3 percent of cases aren’t
                       reported to authorities and that of the small
                       percentage that are, 95 percent go unpunished. The
                       attorney general’s office initiated 38,855
                       investigations last year, 60 percent fewer than in
                       2019.


                # ⚓ After_20_years_of_drone_strikes,_it’s_time_to_admit_they’ve
                  failed⠀⇛


                       More than 1,100 people in Pakistan and Yemen were
                       killed between 2004 and 2014 during the hunt for 41
                       targets, according to the British human rights
                       organization Reprieve. Most of those targets are
                       men who are still alive, like the Haqqanis, or Al-
                       Qaeda leader Ayman al-Zawahiri, who just published
                       another book while thousands of people have been
                       murdered by drones instead of him. As far back as
                       2014, the London-based Bureau of Investigative
                       Journalism revealed that only 4% of drone victims
                       in Pakistan were identified as militants linked to
                       Al-Qaeda. It also underlined that the CIA itself,
                       which was responsible for the strikes in the
                       country, did not know the affiliation of everyone
                       they killed. “They identified hundreds of those
                       killed as simply Afghan or Pakistani fighters,” or
                       as “unknown,” the report stated.


                       And yet many US military officials and politicians
                       continue to spin the drone narrative. Even the
                       targeted militant groups have joined in: for a
                       couple of years, the Taliban have been using armed
                       commercial drones to attack their enemies,
                       portraying drones as technologically superior—just
                       as American officials had done before them. “The
                       drone’s targeting system is very exact,” one member
                       of the Taliban’s drone unit recently told Afghan
                       journalist Fazelminallah Qazizai.


                # ⚓ Father_and_daughter_convicted_of_running_illegal_school
                  despite_previous_conviction_for_same_offence⠀⇛


                       Paul Goddard, from the CPS, said: “These defendants
                       continued to run an illegal school despite their
                       previous conviction for the same offence. Nadia
                       Ali’s determination to defy the law was made clear
                       by an interview she gave to the BBC, following her
                       first conviction, in which she vowed that the
                       school would remain open.


                # ⚓ Father_and_daughter_sentenced_for_running_illegal_south
                  London_school⠀⇛


                       “Unregistered schools pose a serious threat to
                       children. During one visit to the school inspectors
                       found a lack of evidence to indicate that all
                       teachers employed by the school were qualified to
                       teach, or that all had passed DBS checks.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Alabama_Supreme_Court_Rules_Law_Enforcement_Can_Withhold
                  Almost_All_Records_Indefinitely⠀⇛


                       Here’s what you need to know about Alabama and its
                       public records laws before we head to a depressing
                       state Supreme Court opinion that makes everything
                       worse:


                # ⚓ A_Drone_Whistleblower_Goes_to_Prison⠀⇛


                       A federal judge in August sentenced Daniel Hale to
                       45 months in federal prison for informing the
                       American public about secret drone killings by the
                       U.S. military.


                       Hale is a former Air Force intelligence analyst who
                       shared classified documents with reporter Jeremy
                       Scahill. Those documents, published in 2015 at The
                       Intercept and in a book called The Assassination
                       Complex (Simon & Schuster), revealed that secret
                       drone assassinations in Afghanistan, Yemen, and
                       Somalia had likely killed untold numbers of
                       innocent people, a fact the U.S. government had
                       concealed.


          o § Environment⠀➾


                # ⚓ See_how_climate_change_could_drown_landmarks_around_the
                  world⠀⇛


                       Just 3 degrees Celsius (5.4 degrees Fahrenheit) of
                       global warming stands between Cuba’s Plaza de La
                       Catedral looking typically dry or looking like
                       something straight out of the myth of Atlantis. The
                       iconic plaza in Old Havana is just one of many
                       landmarks that could face a watery grave in the
                       future if greenhouse gas emissions from burning
                       fossil fuels continue unabated.


                # ⚓ Why_Everything_is_Suddenly_Getting_More_Expensive_—_And_Why
                  It_Won’t_Stop⠀⇛


                       The “chip shortage” is something that the world
                       doesn’t really grasp yet, in its full importance
                       and magnitude. It is the first climate catastrophe
                       related shortage to hit us at a civilizational,
                       global level. In a world of stable temperatures,
                       guess what, we’d probably still have microchips to
                       power our cars and gadgets and AV studios, because
                       factories wouldn’t be losing power or be so parched
                       they don’t have enough water. But they are — and so
                       we do have a microchip shortage that has been
                       caused by climate change, aka global warming.


                       That’s the first such catastrophe, but it won’t be
                       the last. The chip shortage is just the tip of the
                       immense shockwave rolling down the volcano. It’s
                       just the first burning rock soaring through the
                       ash-filled sky. Today, it’s chips. Tomorrow? Well,
                       some of the things that are already becoming more
                       and more costly to produce are steel, food, and
                       water. That is because all those things rely on
                       energy, and energy is getting more expensive.


                # ⚓ When_global_warming_stops,_seas_will_still_rise⠀⇛


                       Even if humanity beats the odds and caps global
                       warming at 1.5 degrees Celsius above preindustrial
                       levels, seas will rise for centuries to come and
                       swamp cities currently home to half-a-billion
                       people, researchers warned Tuesday.


                       In a world that heats up another half-degree above
                       that benchmark, an additional 200 million of
                       today’s urban dwellers would regularly find
                       themselves knee-deep in sea water and more
                       vulnerable to devastating storm surges, they
                       reported in Environmental Research Letters.


                       Worst hit in any scenario will be Asia, which
                       accounts for nine of the ten mega-cities at highest
                       risk.


                # ⚓ Indigenous_leader_warns_Amazon_ruin_could_spark_global
                  ‘apocalypse’⠀⇛


                       There are two scenarios: (one is the) apocalypse,
                       with no return. People will run out of oxygen, the
                       planet will warm up in 50 years, by two or even
                       three degrees. Life on this planet will not be
                       possible if the Amazon disappears.


                       The other scenario (is) that our children can bathe
                       in this river, learn about what is here, see the
                       trees, the biodiversity, see this macaw fly. This
                       is the scenario we propose to the world if it helps
                       us protect 80 percent of the Amazon.


                       — Is the damage reversible? —


                       If Amazon deforestation reaches 20 percent, it will
                       be very difficult to go back. The desertification,
                       the lack of water, the fires will devastate the
                       Amazon. We are at a turning point.


                # ⚓ In_2021,_US_on_Pace_for_Most_Billion-Dollar_Weather
                  Disasters_Since_Records_Began⠀⇛


                       The National Oceanic and Atmospheric Administration
                       announced Tuesday in its latest monthly report that
                       the United States endured 18 “billion-dollar
                       weather and climate disasters” through the first
                       nine months of 2021, putting this year on pace to
                       be among the worst for such catastrophes.


                       For decades, scientists have sounded the alarm that
                       extreme weather would become more frequent and
                       intense amid the fossil fuel-driven climate
                       emergency. With 18 calamities costing at least $1
                       billion already on the books and three months to
                       go, 2021 is second only to 2020, when there were 22
                       such events. 


                # ⚓ Greta_Thunberg_Has_Zero_Expectations_From_World_Leaders_at
                  Climate_Summit⠀⇛


                # ⚓ Greta_Thunberg_Is_“Open”_to_Meeting_Biden_at_the_UN_Climate
                  Summit⠀⇛


                       This story originally appeared in The Nation and is
                       part of Covering Climate Now, a global media
                       collaboration strengthening coverage of the climate
                       story. The interview with Greta Thunberg was
                       conducted by CCNow partners NBC News, Reuters, and
                       The Nation.


                # ⚓ I_Was_Targeted_Under_Louisiana’s_Felony_Trespassing_Law_for
                  Reporting_on_Police_Working_for_a_Pipeline_Company⠀⇛


                       For the first time in nearly three years, I woke up
                       a few months ago without felony charges hanging
                       over my head. 


                       I’m an investigative journalist and I’d been
                       arrested twice in 2018, both times for allegedly
                       trespassing on what’s known as “critical
                       infrastructure,” a felony under a then-new
                       Louisiana law that — at the urging of the oil and
                       gas industry — redefined pipelines and their
                       construction sites as critical infrastructure. (In
                       the U.S., that term historically referred to
                       systems necessary for society to function, such as
                       power plants and communication lines.) 


                # ⚓ Harry_Potter_and_the_Secret_of_COP26⠀⇛


                       “Merlin’s pants!” Hermione Granger broke in,
                       closing The Complete List of Inscrutable
                       Contradictions in Magical Fiction with a look of
                       unbearable frustration. “If the Muggles are holding
                       another conference to put up a feable pretense of
                       forestalling the destruction of all life on earth,
                       and it’s the 26th one, and the 25 previous ones
                       have had the opposite result of what was needed,
                       then it actually follows,” — Hermione spoke slowly
                       and clearly as if to a three-year-old — “that we
                       can’t just let the Muggles worry about it, and it
                       just might have some relevance to our future too,
                       no matter what sort of imbecilic prats we decide to
                       act like.”


                       Harry knew he needed to say something, but before
                       he could, Ron was mumbling, with a mouth full of
                       chocolate frogs, something about how he was sure
                       Viktor Krum probably had the answer, considering
                       how many oil wells his family owned.


                # § Energy⠀➾


                      # ⚓ Code_Red_on_FacingFuture.TV⠀⇛


                             According to the Code Red interview, the IPCC
                             is taking off its ultra conservative facemask
                             of prior years to reveal a surly cantankerous
                             grim sneer on a darkened background. In
                             short, climate change is much worse than the
                             IPCC has previously been willing to admit.


                      # ⚓ Indigenous_Leaders_Among_the_136_Arrested_at_White
                        House_Fossil_Fuel_Protest⠀⇛


                             On October 11, Indigenous People’s Day, 136
                             people, including many Indigenous leaders
                             opposing fossil fuel projects, were arrested
                             in front of the White House in Washington,
                             D.C., while calling on President Biden to
                             declare a climate emergency and to stop
                             approving fossil fuel projects. The day
                             marked the first in a five-day-long series of
                             protests in the nation’s capitol organized by
                             the Build Back Fossil Free coalition, which
                             is made up of numerous environmental and
                             social justice advocacy groups. 


                             Over the course of five days, thousands are
                             expected to bring the message to Biden’s door
                             that he must do more to protect the planet,
                             and many demonstrators are coming prepared to
                             participate in acts of civil disobedience, to
                             make sure the President hears their message
                             before next month’s COP26 climate summit in
                             Glasgow, Scotland. These demonstrations,
                             labeled People vs. Fossil Fuels, are being
                             billed as a test for Biden. 


                      # ⚓ 155_More_Arrested_for_‘People_Vs._Fossil_Fuels’
                        Protest_at_White_House⠀⇛


                             At least 155 more protesters were arrested
                             outside the White House Tuesday as part of a
                             weeklong action pressuring President Joe
                             Biden to declare a climate emergency and end
                             all new fossil fuel projects.


                             “This is President Biden’s moment to keep his
                             word.”


                      # ⚓ Biden_Can_Block_Fossil_Fuel_Projects_With_Pollution
                        Equal_to_Over_400_Coal_Plants:_Report⠀⇛


                             Two dozen fossil fuel infrastructure projects
                             that President Joe Biden can block via
                             executive action would produce as much annual
                             greenhouse gas pollution as 404 coal-fired
                             power plants—or the equivalent of roughly 20%
                             of all 2019 U.S. emissions—according to a
                             report published Tuesday.


                             “Building new fossil fuel infrastructure and
                             increasing U.S. emissions at a time when we
                             must persuade other countries to reduce their
                             use of fossil fuels sends the wrong signal to
                             every nation.”


                      # ⚓ As_Tar_Sands_Flow_Through_Line_3,_Water_Protectors
                        Fight_Trumped-Up_Felonies⠀⇛


                      # ⚓ Opinion_|_FEMA_Ignores_Puerto_Rico’s_Once-in-a-
                        Lifetime_Chance_to_Build_a_Clean_Energy_Grid⠀⇛


                             The Biden Administration has a once-in-a-
                             lifetime opportunity to help Puerto Rico
                             transition to a greener and more resilient
                             energy future, but it’s on the verge of
                             making a multibillion-dollar mistake.


                      # ⚓ Oil_Pipeline_Protesters_Are_Building_Trauma_Support
                        Centers⠀⇛


                             While the resistance has led to a temporary
                             shutdown of the pipeline and triggered an
                             environmental review, many of those who came
                             to Standing Rock left traumatized, facing
                             large medical bills and lengthy court
                             battles.


                             Timothy Cominghay, an indigenous volunteer
                             who provided legal support for Standing Rock
                             defendants, said he witnessed the effects of
                             the trauma they had endured. “I’ve seen the
                             end of these campaigns. People go home and
                             die. People drink themselves to death. People
                             go home and kill themselves,” he told
                             Motherboard. “And, you know, on the other
                             side, instead of going home and dying, they
                             go to the next campaign. They carry all this
                             pain and fear and trauma that they
                             experienced with them and that just poisons
                             that campaign before it even begins.”


                      # ⚓ Inside_Africa’s_biggest_cryptocurrency_scams⠀⇛


                             Africa is home to the world’s smallest
                             cryptocurrency economies, but is also one of
                             the fastest-growing regions for crypto
                             adoption. Because cryptocurrencies promise a
                             swift, convenient, and efficient means of
                             investment, cross-border payments, and
                             remittances, they attract many adopters in
                             the continent.


                      # ⚓ Trans-Alaska_Pipeline_faces_increasing_threats_from
                        floods._Is_there_a_long-term_solution?⠀⇛


                             Flooding along the 800 miles of the Trans-
                             Alaska Pipeline has intensified as rising
                             temperatures hasten snowmelt and amplify
                             rainfall surges. Rivers paralleling the
                             pipeline are reaching higher levels for
                             longer periods, increasing their potential to
                             wash out the pipeline and touching off
                             frantic fights to prevent their churning
                             waters from reaching it.


                # § Wildlife/Nature⠀➾


                      # ⚓ Opinion_|_The_United_States_Must_Rejoin_the_Global
                        Biodiversity_Conservation_Community⠀⇛


                             After a long stretch of public inattention,
                             biodiversity conservation is a hot topic
                             again, as if we had suddenly been jolted into
                             awareness that our survival as a species,
                             too, depends on the flourishing of all the
                             other nonhuman beings who inhabit this Earth.
                             Articles and op-eds are now filling print and
                             online spaces. This, of course, is very
                             encouraging, but no one is speaking about the
                             elephant in the room or, rather, not in the
                             room: the United States federal government is
                             missing from the global biodiversity
                             conservation community.


                      # ⚓ Bolsonaro_Accused_of_Crimes_Against_Humanity_at_ICC
                        Over_Amazon_Destruction⠀⇛


                             “They are knowingly aiding and abetting the
                             perpetrators on the ground committing crimes
                             such as murder, persecution, and other
                             inhumane acts.”


                             “Bolsonaro will be brought to justice.”


                      # ⚓ World’s_oldest_white_rhino_dies_in_Italian_zoo_aged
                        54⠀⇛


                             White rhinos normally live up to 40 years
                             when held in captivity, and up to 30 years in
                             the wild, she said.


                      # ⚓ The_Industrial_Forestry_Paradigm_is_a_Threat_to_the
                        Forests_of_the_Northern_Rockies⠀⇛


                             For instance, the Forest Service’s
                             silviculturist interviewed for the article
                             suggests the reason for the project is to
                             promote “ForestHealth.” But, of course, the
                             timber industry and Forest Service have
                             defined what constitutes “health”
                             conveniently based on the Industrial Forestry
                             Paradigm, which favors logging as the
                             solution to any problem—real or imagined.


                             The irony of “forest health” as a
                             justification for logging is that much
                             science finds the second-highest biodiversity
                             occurs after significant bark beetle
                             outbreaks or wildfire. There are more bees,
                             birds, small mammals, flowers, fungi, and
                             shrubs. All of which contribute to
                             diversity—which ostensibly the Forest Service
                             suggests is the goal of the project.


                      # ⚓ Hundreds_of_giant_sequoias_may_have_burned_as_the
                        Complex_Fire_rages_in_California_–_CNN⠀⇛


                             The KNP Complex Fire has destroyed many of
                             California’s iconic sequoia trees and is only
                             11% contained, according to the National Park
                             Service.


                             On October 4, the high-intensity fire pushed
                             north and caused damage to Redwood Canyon,
                             the National Park Service told CNN in a
                             statement. The fire now covers over 85,000
                             acres.


                             Currently, the exact number of burned trees
                             is unknown because the fire is mostly
                             uncontained, but the NPS said it has been a
                             significant number — in the hundreds.


                # § Overpopulation⠀➾


                      # ⚓ Newsom_Asks_Urban_Users_to_Voluntarily_Reduce_Water
                        Use_As_Nut_Growers_Suck_Up_Water⠀⇛


                             On July 15, Governor Gavin Newsom added nine
                             counties to the regional drought state of
                             emergency and urged Californians to
                             voluntarily reduce their water use by 15
                             percent “with simple measures” to protect
                             water reserves if drought conditions
                             continue.


                             “The realities of climate change are nowhere
                             more apparent than in the increasingly
                             frequent and severe drought challenges we
                             face in the West and their devastating
                             impacts on our communities, businesses and
                             ecosystems,” said Governor Newsom.


          o § Finance⠀➾


                # ⚓ Opinion_|_The_US_Has_Become_a_Tax_Haven_for_the_Vile_and
                  the_Vicious⠀⇛


                       We’ve become accustomed, over recent decades, to
                       see Americans front and center whenever a
                       blockbuster new report spotlights the world’s super
                       rich.


                # ⚓ Extreme_Inequality_Fuels_the_Rigged_World_Economy_Shown_in
                  the_Pandora_Papers⠀⇛


                       The Pandora Papers—a treasure trove of nearly 12
                       million leaked financial records from 14 different
                       “offshore” wealth-service firms—expose the various
                       ways billionaires, corporations, drug traffickers
                       and con men secret their money in notorious tax
                       havens such as Belize, the Seychelles, the British
                       Virgin Islands and Sioux Falls, S.D.


                # ⚓ Biden_Wants_Tuition-Free_Community_College._What’s_Next?⠀⇛


                       Over the course of the Covid pandemic, we have seen
                       one of the largest upward shifts of wealth in
                       recent history. According to Forbes, there were 660
                       more billionaires in 2021 than the year before. At
                       the same time, enrollment in community colleges and
                       four-year universities plummeted in the United
                       States, with the student debt crisis creating a
                       situation in which low-income communities are
                       hesitant to pursue higher education because of the
                       likelihood of leaving with crippling debt.


                # ⚓ Building_Back_Better_and_the_September_Jobs_Report⠀⇛


                       But before getting to these issues, it’s first
                       important to dispel the idea that this was a bad
                       jobs report. The September data showed a 0.4
                       percentage point drop in the unemployment rate,
                       bringing it to 4.8 percent. Most analysts had
                       predicted a drop of just 0.1 or 0.2 percentage
                       points. We didn’t get the unemployment rate down to
                       4.8 percent following the Great Recession until
                       January of 2016. And, this decline was due to
                       workers getting jobs, not the unemployed dropping
                       out of the labor market. The number of employed in
                       the household survey increased by 526,000.


                       The negative view of the September report is based
                       on the weaker than expected job growth reported in
                       the establishment survey. The increase of 194,000
                       in payroll jobs was well below the 400,000 to
                       500,000 job gain most analysts had expected. While
                       that seems like a bad story, a closer look shows
                       otherwise.


                # ⚓ Tigard,_Oregon:_Ground_Zero_in_the_Fight_for_Affordable
                  Housing⠀⇛


                # ⚓ The_Latest_Bretton_Woods_Bean-Counting_Scandal_Nearly
                  Evicts_IMF_Director_Georgieva⠀⇛


                       After a major leadership crisis that further
                       degrades the Bretton Woods Institutions’ number-
                       crunching credibility by revealing a pro-corporate
                       bias – one that in 2017 was aimed at pleasing
                       Beijing’s “Communist” government – yet another
                       discredited managing director rules the
                       International Monetary Fund. But Kristalina
                       Georgieva was nearly fired, saved only with her
                       board’s grudging, divided affirmation on October
                       11, in spite of two imperialist powers – the U.S.
                       and Japan – threatening to swing the axe.


                       Georgieva is a Bulgarian neoliberal economist who
                       climbed the ranks at the World Bank and was chosen
                       by the European bloc to lead the International
                       Monetary Fund in 2019. In her prior job as Bank
                       operations chief, she was a capitalist spin-doctor
                       on behalf of China, with the permission of Bank
                       president Jim Yong Kim, an ex-leftist who in his
                       days as a public health advocate had favoured the
                       Bank’s “abolition” due to its staff’s relentless
                       harm-doing.


                # ⚓ How_“Terror_Capitalism”_Links_Uyghur_Oppression_to_the
                  Global_Economy⠀⇛


                       “Where is your ID!” the police contractor yelled at
                       me in Uyghur. I looked up in surprise. I had been
                       avoiding eye contact, trying to attract as little
                       attention as possible. In April 2018, in the
                       tourist areas of Kashgar—where there were
                       checkpoints every 200 yards—contractors usually
                       recognized a bespectacled white person as a
                       foreigner. But over the years that I had lived and
                       worked as an anthropologist in Xinjiang, a region
                       in Northwest China, I had often been mistaken for a
                       Uyghur. This essay is adapted from Darren Byler’s
                       new book, In the Camps: China’s High-Tech Penal
                       Colony, published by Columbia Global Reports.


                # ⚓ ‘Please_Help_Us’:_Essential,_Low-Wage_Workers_Share_Why
                  They_Need_Reconciliation_Package⠀⇛


                       Low-wage essential workers—joined by economists,
                       faith leaders, and a progressive lawmaker—gathered
                       outside the U.S. Capitol on Tuesday to share their
                       stories and encourage Congress to “look at the
                       people behind the numbers” in debates about the
                       Build Back Better budget reconciliation bill.


                       “We are literally starving. It’s time for Congress
                       to act.”


                # ⚓ Why_Is_PayPal_Denying_Service_to_Palestinians?⠀⇛


                       This is not the first time PayPal has denied
                       service to a vulnerable group; the company
                       routinely cuts off payments to those engaged in sex
                       work or the sale of sexually explicit content, and
                       last year, PayPal division Venmo was sued for
                       blocking payments associated with Islam or Arab
                       nationalities or ethnicities.


                       Just four months ago, EFF and 21 other rights
                       groups wrote to PayPal, taking the company to task
                       for censoring legal, legitimate transactions, and
                       calling on both PayPal and Venmo to provide more
                       transparency and accountability on account freezes
                       and closures. Our coalition’s demands included a
                       call for regular transparency reports, meaningful
                       notice to users, and a timely and meaningful
                       appeals process.  These recommendations align with
                       the Santa Clara Principles on Transparency and
                       Accountability in Content Moderation, developed by
                       free expression advocates and scholars to help
                       companies protect human rights when moderating
                       user-generated content and accounts.


                       It is unclear why PayPal chose to deny service to
                       Palestinians, they’re not unique. Many American
                       companies have taken an overly broad interpretation
                       of anti-terrorism statutes and sanctions, denying
                       service to entire groups or geographic areas—rather
                       than narrowly targeting those parties whom they are
                       legally obligated to block. This practice is deeply
                       troubling, causing serious harm to those who rely
                       on digital services for their basic needs.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Opinion_|_The_Media_Keeps_Getting_It_Wrong:_The_Democrats
                  Are_Not_Divided⠀⇛


                       Historians describe Franklin D. Roosevelt’s 1936
                       presidential victory (with 60.8% of the popular
                       vote), Lyndon Johnson’s 1964 triumph (61.1%), and
                       Ronald Reagan’s 1984 win (58.8%) as “landslide”
                       elections. Likewise, in 2018, the San Diego Union-
                       Tribune and many other news outlets described
                       Democrat Gavin Newsom’s defeat of Republican John
                       Cox for the California governorship by a 62% to 32%
                       margin as a “landslide.” When a recent poll found
                       that 65% of Americans support vote-by-mail during
                       the COVID pandemic, a USA Today headline proclaimed
                       that the support was “overwhelming.” Reporting on a
                       survey showing that 73% of American voters
                       supported President Biden’s plan to withdraw U.S.
                       troops from Afghanistan, another news outlet, The
                       Hill, described it as an “overwhelming majority.” A
                       news story reporting that 94% of American voters
                       embrace universal background checks for gun-buyers
                       called that support “near unanimous.” A few years
                       ago, another news story used the same phrase—”near
                       unanimous”—when 61 of 64 coaches (95.3%) ranked the
                       University of Alabama football team as the best in
                       the country.


                # ⚓ A_September_to_Remember⠀⇛


                # ⚓ America’s_Long_History_of_Mistreating_Haitian_Migrants⠀⇛


                       United States Border Patrol agents on horseback
                       swinging their reins as they charged at desperate
                       Haitian migrants on the banks of the Rio Grande
                       river in Del Rio, Tex. That’s the image that in
                       recent days blanketed the Internet, dominated
                       headlines, and drew sharp criticism from some
                       political figures and human rights advocates.


                # ⚓ AOC_Warns_Pelosi_and_Schumer:_‘We_Can’t_Negotiate
                  Reconciliation_Bill_Down_to_Nothing’⠀⇛


                       Rep. Alexandria Ocasio-Cortez joined seven of her
                       fellow New York Democrats on Tuesday in issuing a
                       warning to House Speaker Nancy Pelosi and Senate
                       Majority Leader Chuck Schumer: Don’t cut funding
                       for housing, transportation, or immigration reform
                       from the emerging reconciliation bill in an attempt
                       to appease right-wing lawmakers.


                       “We can’t let corporate interests, Big Pharma, and
                       a few conservative Democrats stand in our way of
                       delivering.”


                # ⚓ Who_Won_Germany’s_Election_in_2021?⠀⇛


                       All in all, 25.7% voted for the center-mildly-
                       progressive social-democratic party SPD. With that,
                       the SPD overtook Germany’s conservatives and
                       strong-state favoring CDU – Angela Merkel’s
                       political party – sitting at 24.1%.


                       The environmental Green party received less than
                       expected ending up with 14.8%. While Germany’s
                       truly neoliberal party, the FDP, did surprisingly
                       well with 11.5%.  Germany’s Neo-Nazi party, the AfD
                       lost a little bit of support arriving at 10.3%, but
                       has established itself as a 10%-party. Finally,
                       Germany’s socialist party, the Linke, received just
                       4.9% but entered the parliament because the party
                       managed to get three candidates elected in local
                       constituencies. This rule renders the 5% barrier
                       obsolete. And, with a raft of micro-parties shared
                       the remaining 8.7%.


                # ⚓ Anti-Social_Media:_Can_Our_Already_Volatile_Political
                  Culture_Transcend_a_Facebook_World?_–_The_Project_Censored
                  Show⠀⇛


                       Alan MacLeod is a media critic, a staff writer at
                       MintPress News, and a contributor to many other
                       publications. He’s also the author/editor two
                       books, including Propaganda in the Information Age:
                       Still Manufacturing Consent. Nolan Higdon lectures
                       in history and media studies at California State
                       University, East Bay and other colleges in CA. He’s
                       also the author of several books and academic
                       articles, including, United States of Distraction
                       and The Anatomy of Fake News.


                # ⚓ Trump_Won_the_County_in_a_Landslide._His_Supporters_Still
                  Hounded_the_Elections_Administrator_Until_She_Resigned.⠀⇛


                       An elections administrator in North Texas submitted
                       her resignation Friday, following a monthslong
                       effort by residents and officials loyal to former
                       President Donald Trump to force her out of office.


                       Michele Carew, who had overseen scores of elections
                       during her 14-year career, had found herself
                       transformed into the public face of an electoral
                       system that many in the heavily Republican Hood
                       County had come to mistrust, which ProPublica and
                       The Texas Tribune covered earlier this month.


                # ⚓ Voter_Turnout_in_Iraq_Hits_All-Time_Low_as_Faith_in
                  Democratic_Process_Falters⠀⇛


                # ⚓ Iraqi_Journalist:_Amid_Low_Election_Turnout,_“Iraq’s
                  Streets_Littered_with_the_Memories_of_Our_Dead”⠀⇛


                       Voter turnout at the fifth parliamentary election
                       in Iraq hit an all-time low, with many Iraqis
                       refusing to vote as widespread faith in the
                       democratic process and politics falters. Shiite
                       cleric Muqtada al-Sadr, who has been a vocal
                       opponent of foreign invasion, won the most seats.
                       He has also been accused of kidnapping and killing
                       his critics. “The election has more to do with
                       making this regime and this system look good than
                       responding to the demands of the people,” says
                       Nabil Salih, Iraqi journalist and photographer, who
                       also discusses protests that sped up the election
                       and conditions in Iraq’s hospitals. His latest
                       piece for Middle East Eye is “Iraq’s streets are
                       littered with the memories of our dead.”


                # ⚓ Facebook_Files:_MEPs_to_invite_whistleblower_Frances_Haugen
                  to_a_hearing⠀⇛


                       The decision to organise a public hearing in the
                       European Parliament on “Whistleblowers’ testimonies
                       on the negative impact of big tech companies’
                       products on users” was taken this afternoon by the
                       Chair and the coordinators of the political groups
                       in the committee. After the meeting, Chair Anna
                       Cavazzini (Greens/EFA, DE) said:


                       “Whistleblowers like Frances Haugen show the urgent
                       need to set democratic rules for the online world
                       in the interest of users. Her revelations lay bare
                       the inherent conflict between the platform’s
                       business model and users’ interests. It shows that
                       we need strong rules for content moderation and
                       far-reaching transparency obligations in Europe.


                # ⚓ Facebook_whistleblower_invited_to_speak_to_European
                  Parliament⠀⇛


                       The European Parliament has invited Facebook
                       whistleblower Frances Haugen to speak before a
                       committee that’s considering new social media
                       regulations.


                       Haugen, a data scientist and former employee of the
                       social media giant, has recently gone public with
                       criticism that Facebook has profited from stoking
                       political divisions, spreading disinformation and
                       harming the mental health of teenage girls. She
                       made the remarks last week during a 60 Minutes
                       segment and before a U.S. Senate panel.


                # ⚓ Facebook_Whistle-Blower_to_Speak_Out_at_U.K.,_EU
                  Parliaments⠀⇛


                       Whistle-blower Frances Haugen will give evidence on
                       Oct. 25 to a parliamentary committee examining the
                       U.K.’s draft Online Safety Bill and will also share
                       her ideas on how to regulate social media,
                       according to a government statement.


                # ⚓ Philanthropy_Is_a_Scam⠀⇛


                       By way of visions for the future of philanthropy,
                       many of the milder books offer up either a promise
                       of greater accountability for foundations or a
                       reinvention of the concept of taxation. At the end
                       of The Givers, his survey of contemporary
                       philanthropy, David Callahan concludes, “None of
                       the reforms I’ve suggested will substantially limit
                       the influence of wealthy philanthropy over public
                       life. Perhaps the best we can hope for is that
                       funders bring greater self-restraint and
                       mindfulness to giving that affects the lives of
                       their fellow citizens.” The neoliberal imagination
                       is nothing if not humble; all it can ask of us is
                       to share its faith that a culture of moderation and
                       transparency could in theory keep the
                       philanthropists’ sprawling networks of influence in
                       check. Accordingly, the purpose of these books is
                       not to imagine a changed world but to foster trust
                       that the billionaires will get us there.


          o § Misinformation/Disinformation⠀➾


                # ⚓ [Old] PH_remains_top_in_social_media,_[Internet]_usage
                  worldwide_–_report⠀⇛


                       Advertising firms We Are Social and Hootsuite on
                       Tuesday, January 27, released their annual report,
                       which gives insights into global social media usage
                       and digital trends for the past year.


                       The Philippines tops the world again for time spent
                       using social media this year, making it the 6th
                       straight year it has done so. According to the
                       report, Filipinos spend an average of 4 hours and
                       15 minutes each day on social media, which is 22
                       minutes higher than last year’s average of 3 hours
                       and 53 minutes, and 3 minutes higher than 2019’s
                       average of 4 hours and 12 minutes.


                       It’s also 30 minutes higher than this year’s
                       second-placer, Colombia, which has an average of 3
                       hours and 45 minutes.


          o § Censorship/Free Speech⠀➾


                # ⚓ Twitch,_Others,_Ban_Amouranth_Yet_Again,_Once_Again_With
                  Zero_Transparency⠀⇛


                       Regular readers here will by now likely be familiar
                       with Twitch streamer “Amouranth”. She has made it
                       onto our pages as part of the year-long mess that
                       Amazon’s Twitch platform appears to be making for
                       itself, during which it has demonstrated its
                       willingness to both treat its creative community
                       quite poorly and fail to properly communicate that
                       poor treatment to much of anyone at all. For
                       instance, Twitch has temporarily banned or kept
                       Amouranth from live-streaming several times, all
                       likely due to the content of her streams. That
                       content seems nearly perfectly designed to poke the
                       line on Twitch’s streaming guidelines, including
                       so-called “hot tub streaming” and ASMR streams.
                       Twitch has never been great about explaining the
                       reasons for bans like these, but in the past it has
                       at least linked to the offending content so that a
                       streamer knows which videos were objectionable. But
                       with some, including Amouranth, Twitch often times
                       doesn’t even bother doing that, such as when it
                       demonetized Amouranth’s videos without warning or
                       explanation.


                # ⚓ Records_Shed_New_Light_on_Trump_White_House_Officials’
                  Efforts_to_Punish_Social_Media⠀⇛


                       The records, released to EFF and the Center for
                       Democracy & Technology as part of a joint FOIA
                       lawsuit, add additional details to the timeline
                       before Trump issued his unconstitutional Executive
                       Order retaliating against online social media
                       services for moderating his posts. President Joseph
                       R. Biden revoked the order in May.


                       Although Trump’s Executive Order is no longer in
                       effect, the new documents show the lengths
                       officials within the Office of Management and
                       Budget (OMB) went to as part of an unconstitutional
                       effort to leverage the federal government’s
                       spending power to punish platforms for exercising
                       their First Amendment rights to moderate Trump’s
                       speech.


                       A day before Trump issued the order on May 28,
                       2020, OMB officials sought to learn whether the
                       government already had data that would show how
                       much money all federal agencies spent to advertise
                       on social media. In an email exchange on May 27,
                       2020, officials inquired whether it was possible to
                       use www.usaspending.gov to calculate the figure.


                # ⚓ EFF_to_Tenth_Circuit:_First_Amendment_Protects_Public
                  School_Students’_Off-Campus_Social_Media_Speech⠀⇛


                       In this case, C1.G. v. Siegfried, a student and
                       some friends visited a thrift shop on a Friday
                       night. The student took a picture of his friends
                       wearing wigs and hats, including one hat that
                       looked like a foreign military hat from World War
                       II. Intending to be funny, the student posted a
                       picture of his friends with an offensive caption
                       related to violence against Jews to Snapchat (and
                       deleted it a few hours later). The school suspended
                       and eventually expelled the student.


                       EFF’s brief argued in favor of the expelled
                       student, focusing on the Supreme Court’s strong
                       protection for student speech rights in its
                       decision from this summer in Mahanoy v. B.L. There,
                       the Court explained that three “features” of
                       students’ off-campus speech diminish a school’s
                       authority to regulate student expression. Most
                       powerfully, “from the student speaker’s
                       perspective, regulations of off-campus speech, when
                       coupled with regulations of on-campus speech,
                       include all the speech a student utters during the
                       full 24-hour day.” Mahanoy makes clear that
                       students’ longstanding right to speak on campus
                       except in narrow circumstances, as recognized by
                       the Supreme Court in its 1969 decision in Tinker v.
                       Des Moines, is even stronger off campus—and that
                       includes, as the Mahanoy Court said, “unpopular
                       expression.”


                       Our brief also urged the appellate court to reject
                       a special rule for social media. The school argued,
                       and the district court agreed, that the uniquely
                       shareable and accessible nature of speech on the
                       internet—that it can easily make its way onto
                       campus—justifies greater school authority over
                       students’ off-campus social media speech. Rejecting
                       this argument is particularly important given that
                       social media is a central means for young people to
                       express themselves, connect with others, and engage
                       in advocacy on issues they care about; and heeds
                       the Supreme Court’s concern about “full 24-hour
                       day” speech regulations.


                # ⚓ One_Time,_Pakistan_Accidentally_Brought_Down_YouTube
                  Worldwide⠀⇛


                       The video insulted Islam, claimed Pakistani
                       authorities. We don’t have access to the video now,
                       but it allegedly featured the 2005 Danish cartoons
                       of the prophet Muhammed, over which protesters
                       rioted and killed dozens of people. Pakistan didn’t
                       have the means to take down that video
                       specifically, and they refused to wait on YouTube
                       doing it themselves. So they figured the best
                       course of action was to block YouTube throughout
                       the country.


                # ⚓ Kathleen_Stock:_UCU_statement_‘ends_my_career’_at_Sussex⠀⇛


                       Vice-chancellor Adam Tickell said the university
                       was “investigating activity on our campus which
                       appears to have been designed to attack Professor
                       Kathleen Stock for exercising her academic
                       freedoms”.


                       “Disturbingly, this has included pressuring the
                       university to terminate her employment. Everyone at
                       the university has the right to be free from
                       harassment and intimidation.”


                # ⚓ LinkedIn’s_unanswered_questions_about_China_censorship⠀⇛


                       In early 2021, Chinese regulatory authorities
                       punished LinkedIn for lax censorship; three months
                       later, the company blocked the profiles of a spate
                       of researchers.


                       The big picture: U.S. internet companies once
                       claimed they could help make China more open and
                       free. But Beijing has instead brought them to heel.


                # ⚓ Whistleblower_testimony_launches_bipartisan_campaign_for
                  Facebook_censorship⠀⇛


                       The solution to “Facebook’s problems,” according to
                       Haugen and the Wall Street Journal, is government
                       control over what is said by Facebook’s users. A
                       review of Haugen’s testimony as well as the
                       response of both the Democrats and Republicans and
                       the corporate press reveals that a consensus is
                       developing within the capitalist ruling
                       establishment for government intervention that, far
                       from stopping the giant tech company from putting
                       “profits before people,” aims to gain control of
                       all of Facebook’s platforms and, in particular,
                       censor left-wing and socialist content.


                # ⚓ Netflix_defends_Chappelle,_suspends_staff_in_transgender
                  row⠀⇛


                       The stand-up star has courted controversy with “The
                       Closer” in which he asserts “gender is a fact,” and
                       criticises what he says is the thin skin of the
                       trans community.


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


                # ⚓ Julian_Assange_and_the_CIA-USA_Daily_Wars_Against
                  Humanity⠀⇛


                       Of the estimated 1.4 million top security clearance
                       U.S. personnel employed by one or another of the
                       government’s 18 braches of its $81 billion annually
                       budgeted “U.S. Intelligence Community,” perhaps one
                       or two individuals each year are designated as
                       “whistleblowers” and persecuted to the high
                       heavens. These include heroes like Edward Snowden
                       and Chelsea Manning today and Daniel Ellsberg, the
                       renowned Vietnam-era Pentagon Papers defendant of
                       yesteryear, whose revelations educated millions
                       about the U.S. horrors committed against the
                       Vietnamese people. Four million Vietnamese were
                       murdered in this ten-year genocide, begun with the
                       CIA’s lie that a U.S. destroyer was attacked in
                       Vietnam’s Tonkin Bay by the equivalent of a
                       Vietnamese sampan or small fishing boat.


                       Another handful of heroes, like WikiLeaks founder
                       and journalist/publisher Julian Assange, are
                       similarly persecuted when they exercise their right
                       to publish what the whistleblowers have revealed
                       about U.S. war crimes around the world. In addition
                       to the 1.4 million top secret U.S. government
                       spies, another 4.25 million “Intelligence
                       Community” employees have some type of special
                       clearance but don’t necessarily work in secure and
                       undisclosed locations. That’s a total approaching
                       some six million people in the U.S. spy business,
                       not to mention the tiny proportion in the business
                       of directly ordering and planning assassinations,
                       kidnappings, death squad wars, covert and overt
                       wars, drone wars, regime change military coups,
                       cyber wars, media disinformation wars, industrial
                       spying wars and all the rest.


                # ⚓ ShotSpotter_files_$300M_defamation_suit_against_Vice
                  Media⠀⇛


                       Vice’s technical vertical Motherboard has published
                       half a dozen articles on the controversial gun
                       detection technology, but Monday’s lawsuit
                       primarily focused on one in July alleging that
                       ShotSpotter had altered evidence for court cases at
                       the behest of police.


                       Vice’s article claims that the company has worked
                       to help support the police’s narrative of events in
                       several cases, sometimes even deleting evidence
                       that would clash with how law enforcement described
                       altercations.


                       The article is based on public court documents and
                       testimony from experts who have raised doubts about
                       the accuracy of ShotSpotter’s tech at identifying
                       gunshots.


                # ⚓ 3_nights_in_a_migrant_detention_center—for_the_crime_of_not
                  carrying_passport⠀⇛


                       What I didn’t know is that someone had been
                       fighting for my freedom from outside. By her own
                       intuition she had managed to get in touch with the
                       head of immigration in Chiapas, which seems to have
                       prompted my release.


                # ⚓ The_Daily’s_founding_producer,_Theo_Balcomb,_is_leaving_the
                  Times⠀⇛


                       A quick summary of Balcomb’s very busy audio life:
                       She started at NPR as an intern and rose the ranks
                       to become the youngest supervising producer on All
                       Things Considered. She joined the Times in 2016 as
                       senior producer for a soon-to-be-launched, unnamed
                       show, aka The Daily. Of course, The Daily went on
                       to be a smashing success that reaches millions of
                       people per day. In 2019, she was promoted to
                       executive producer of The Daily and News, where she
                       is today. All of which is to say: Congrats to Theo,
                       and we’re excited to hear what she gets up to next!


          o § Civil Rights/Policing⠀➾


                # ⚓ LA_Sheriff’s_Handpicked_‘Public_Integrity_Unit’_Doing
                  Little_More_Than_Harassing_And_Intimidating_The_Department’s
                  Critics⠀⇛


                       The Los Angeles Sheriff’s Department is apparently
                       incapable of being reformed. Over the years, the
                       LASD has run an illegal prison informant program,
                       one that culminated in an FBI investigation during
                       which the LASD threatened FBI agents and federal
                       witnesses.


                # ⚓ Women_Yell_Things_to_Me._But_They’re_All_Compliments.⠀⇛


                       I’m not brave for letting my hair go white. My hair
                       salon closed as the Covid pandemic lockdown began
                       in New York City, in March 2020, right when I was
                       due for my mandatory every-three-weeks color. They
                       were closed for a few months, which gave me enough
                       time to grow a solid two inches of pretty cool
                       white hair we suspected was there, but weren’t
                       sure.


                # ⚓ The_Legacy_of_Bani_Sadr⠀⇛


                       Bani Sadr’s political activism dates back to his
                       secondary school education. During this period, the
                       Tudeh (communist) Party was active in schools and
                       universities across Iran, and it was during this
                       time that Bani Sadr was introduced to the law of
                       dialectics. While Bani Sadr was in secondary
                       school, the movement to nationalise the Iranian oil
                       industry under Mohammad Mosaddegh was starting to
                       take hold. Through this movement and his family’s
                       interest in it, he developed a curiosity about the
                       concepts of independence and liberty, which
                       remained with him and were his guiding principles
                       right up until his death. He focussed much of his
                       research career to fully understanding these
                       principles, and devoted his life to ensuring their
                       realisation.


                       In the years following the 1953 coup against the
                       Mossadegh government, political groups in Iran had
                       differing priorities. The liberals prioritised
                       liberty, patriots prioritised independence from the
                       Eastern and Western Blocs, Marxists focussed on a
                       socialist revolution and seizing of power by the
                       proletariats, supporters of religious
                       authoritarianism gave precedence to Islam and the
                       supporters of the Pahlavi monarchy concentrated on
                       modernity. Bani Sadr argued that a fundamental
                       effort was needed to rid Iran and other such
                       societies of this destructive “war of priorities”,
                       which he maintained, had steered Iran towards
                       destruction for over half a century.


                # ⚓ Virginie_Despentes’s_Philosophy_of_Rage⠀⇛


                       In 2006, Virginie Despentes published a manifesto
                       called King Kong Theory, an origin story that
                       begins with her rape and the shame it caused. She
                       writes: “The moment you call your rape a rape, the
                       whole surveillance system roars into life: Do you
                       really want people to know what happened to you?”
                       Despentes’s skepticism toward disclosure comes from
                       her own experience, as a former sex worker turned
                       prominent writer, that trauma could become unmoored
                       from its specific context and commodifed by
                       prurient attention. Her reckoning with the public
                       and private aspects of both fame and violence feels
                       almost prescient now, in the shadow of the #MeToo
                       movement, which marked a shift in what could be
                       said about rape and assault in the public sphere.
                       And while the initial wave of anger that the
                       movement incited felt reparative, it was, like
                       Despentes’s own experience, also co-opted and
                       misrepresented.


                       Questions of power and consent were adjudicated
                       mostly in the narrow scope of the workplace. Yet,
                       as writers like Jacqueline Rose have pointed out,
                       #MeToo failed to address a more widespread
                       experience of sexual violence, one that is more
                       diffuse than what can be litigated in a white-
                       collar office, let alone in Hollywood. Somewhere
                       along the way, we lost the plot; after #MeToo, our
                       language around violence took on the sheen of HR
                       obfuscation. The residual dribbles of the movement
                       left something vital behind: the injustice of
                       rape—that it happens all the time, all over the
                       world, and is a universal historical event to be
                       reckoned with.


                # ⚓ Dayton_Police_Dragged_Paraplegic_Man_Clifford_Owensby_from
                  His_Car;_NAACP_Says_Arrest_Was_“Unlawful”⠀⇛


                       Clifford Owensby says Dayton police violently
                       arrested him last month even though he is
                       paraplegic and repeatedly told them he could not
                       use his legs to get out of the car during a traffic
                       stop. New police bodycam video shows the officers
                       dragging Owensby out of his car and yanking him by
                       his hair as he shouted for help. Owensby had his 3-
                       year-old child in the car at the time of arrest. He
                       has now filed a complaint with Dayton’s branch of
                       the NAACP. “The officers should be placed at least
                       on administrative leave,” says Derrick Foward,
                       president of the Dayon Unit NAACP. Foward says that
                       Owensby is expected to bring a case against Dayton
                       police once all the evidence is collected, and he
                       attributes the quick release of the bodycam video
                       to recent police reforms advocated for in the wake
                       of the murder of George Floyd.


                # ⚓ A_Grim_Winter_Looms._These_Activists_Are_Keeping_Spirits_Up
                  Through_Organizing.⠀⇛


                # ⚓ Boko_Haram_administers_marriage_for_Christians,_Muslims_in
                  LGA_occupied_in_Niger,_girls_under_pressure⠀⇛


                       In Shiroro LGA, Boko Haram insurgents in charge.


                       The terrorists are proving this by taking over
                       marriage administration in the LGA of Niger. They
                       settle disputes too, preventing locals from
                       reporting to police and courts.


                       It’s no doubt coercive, and hard on girls.


                # ⚓ ‘Are_We_Human?’_Modi’s_Use_of_Antiterror_Law_Draws_Scrutiny
                  From_Courts⠀⇛


                       India’s government under Prime Minister Narendra
                       Modi has jailed thousands of people through a
                       statute that critics say is aimed at silencing
                       dissent.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Why_Section_230_‘Reform’_Effectively_Means_Section_230
                  Repeal⠀⇛


                       Some lawmakers are candid about their desire to
                       repeal Section 230 entirely. Others, however,
                       express more of an interest to try to split this
                       baby, and “reform” it in some way to somehow
                       magically fix all the problems with the Internet,
                       without doing away with the whole thing and
                       therefore the whole Internet as well. This post
                       explores several of the types of ways they propose
                       to change the statute, ostensibly without outright
                       repealing it.


          o § Monopolies⠀➾


                # ⚓ ‘A_Huge_Deal’:_Amazon,_Google_Workers_Demand_Companies
                  Sever_Ties_With_Israeli_Military⠀⇛


                       Roughly 400 Amazon and Google workers on
                       Tuesday condemned their employers for contributing
                       to the surveillance and dispossession of
                       Palestinians by selling cloud services to the
                       Israeli military and government and urged both
                       companies to cut ties with the oppressive regime.


                       “We call on global technology workers and the
                       international community to join with us in building
                       a world where technology promotes safety and
                       dignity for all.”


                # § Patents⠀➾


                      # ⚓ OSE_Immunotherapeutics_Receives_New_European_Patent
                        Notice_of_Allowance_for_Tedopi [Ed: Is OSE
                        Immunotherapeutics aware of the_collapse_of_patent
                        quality_of_the_EPO? Has it been paying attention?]⠀⇛


                             OSE Immunotherapeutics SA (ISIN:
                             FR0012127173; Mnemo: OSE) announced today
                             that it has received notice of allowance from
                             the European Patent Office for a patent
                             application related to Tedopi®, a neoepitope
                             therapeutic vaccine, protecting a method for
                             manufacturing a ready-to-use peptide emulsion
                             for its use in the treatment of cancers in
                             HLA-A2 positive patients. This patent will
                             provide a protection until 2038.


                             This new patent notice of allowance granted
                             in Europe reinforces the patent protection
                             for Tedopi® and confirms an optimized
                             industrial manufacturing process using a
                             ready-to-use peptide emulsion.


                      # ⚓ Demonstrators_Call_on_Biden_to_Show_Leadership_on
                        Vaccine_Patent_Waivers⠀⇛


                      # ⚓ Protest_at_US_Embassy_in_South_Africa_Demands_Biden
                        ‘Walk_the_Talk’_on_Vaccine_Patent_Waiver⠀⇛


                             Public health campaigners rallied outside the
                             U.S. Embassy in South Africa on Tuesday to
                             criticize the Biden administration’s
                             passivity in ongoing negotiations over a
                             patent waiver for coronavirus vaccines, a
                             proposal that remains deadlocked at the World
                             Trade Organization more than five months
                             after the White House endorsed it.


                             “We don’t have time to waste. The U.S. must
                             deliver on its promise and ensure that the
                             TRIPS waiver is adopted.”


                # § Copyrights⠀➾


                      # ⚓ Lithographs_from_M._E._Descourtilz’s_*Atlas_des
                        Champignons*_(1827)_–_The_Public_Domain_Review⠀⇛


                             Set of prints which sort mushrooms found in
                             France and elsewhere into three classes:
                             edible, suspect, and poisonous.


                      # ⚓ Adobe_Uses_DMCA_to_Nuke_Project_That_Keeps_Flash
                        Alive,_Secure_&_Adware_Free⠀⇛


                             In January 2021, development and support for
                             Adobe Flash was discontinued. That marked the
                             end of an era but in reality, Flash wasn’t
                             quite dead. Flash Player is still available
                             in China, something that was exploited by the
                             Clean Flash project to continue making the
                             software more widely and safely available.
                             Adobe has now used the DMCA to shut the
                             project down.


                      # ⚓ Google_Opposes_‘Sweeping’_Popcorn_Time_Piracy
                        Blocking_Request⠀⇛


                             Google has asked a Virginia federal court for
                             permission to formally oppose the request for
                             a far-reaching anti-piracy injunction. The
                             contested anti-piracy measures, aimed at
                             shutting down a popular Popcorn Time app, are
                             proposed by a group of filmmakers. However,
                             Google fears that the proposed blocking
                             efforts go too far.


                      # ⚓ License_Stewardship_consultation⠀⇛


                             At this milestone of the 20th anniversary of
                             Creative Commons, we are embarking on a
                             public consultation around CC’s stewardship.
                             Specifically, we seek to collectively define
                             the principles and responsibilities that CC
                             should and will uphold in its role as
                             stewards of the CC legal tools. And we want
                             you to participate.



                    ䷩ 𝚕𝚒𝚗𝚎 5412

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.13.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_13/10/2021:_Sparky_2021.10_and_New_Archcraft⠀✐


Posted in News_Roundup at 10:13 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⠀➾


                # ⚓ Microsoft_and_CNET_confuse_users_with_fake_“This_PC_can’t
                  run_Windows_11”_errors._Suggest_buying_a_completely_new
                  computer.⠀⇛


                       Microsoft and CNET confuse users with fake “This PC
                       can’t run Windows 11” errors. Suggest buying a
                       completely new computer.


                       Mostly, if your machine doesn’t have “Security
                       Theater Boot” and the “Toilet Paper Module” (I
                       jest.) available to be turned on, you need to buy
                       another computer.


                       Except that you don’t. You could format Windows off
                       your computer entirely and go on happily using GNU/
                       Linux for many more years without fake
                       incompatibility messages from your pals at
                       Microsoft and Intel, where sales have been in the
                       dumps and they need fake error messages to drive
                       new sales.


                # ⚓ Framework_MarketPlace_lets_you_buy_replacement_parts,
                  expansion_cards_for_the_modular_Framework_Laptop⠀⇛


                       The Framework Laptop is a thin and light notebook
                       with a 13.5 inch display and an Intel Tiger Lake
                       processor. But what really makes the notebook stand
                       out is its modular design and emphasis on
                       repairability and customization.


                       When the Framework laptop went up for pre-order
                       earlier this year, customers could choose from a
                       couple of different configuration options. But now
                       Framework has launched a Marketplace, which were
                       you purchase Expansion Cards to further customize
                       the laptop, as well as replacement parts that let
                       you swap out keyboards, batteries, displays, and
                       even motherboards and processors.


          o § Audiocasts/Shows⠀➾


                # ⚓ Life_Changing_Virtualization_|_LINUX_Unplugged_427⠀⇛


                       Wimpy stops by with a new tool that will change
                       your virtualization game, and we share our thoughts
                       on Ubuntu 21.10 and take the flavor challenge.


                # ⚓ mintCast_371.5_–_Minus_One⠀⇛


                       1:37 Linux Innards
                       35:41 Vibrations from the Ether
                       50:04 Check This Out
                       53:53 Announcements & Outro


                # ⚓ LHS_Episode_#434:_Linux_Install_Media_Deep_Dive⠀⇛


                       Hello and welcome to the 434th installment of Linux
                       in the Ham Shack. In this episode, the hosts
                       discuss creating bootable images to start your
                       computer with Linux or install the operating
                       system. Discussion ranges from CDs to DVDS, USB
                       flash drives and Micro SD cards. Also touched on
                       are persistence, running distros from install
                       media, dual booting and more. We hope you enjoy
                       this episode and come back for the next one. Have a
                       great week.


          o § Kernel Space⠀➾


                # ⚓ 7.4M_IOPS_Achieved_Per-Core_With_Newest_Linux_Patches_–
                  Phoronix⠀⇛


                       Linux block subsystem maintainer and lead IO_uring
                       developer Jens Axboe had a goal of hitting 7M IOPS
                       per-core performance this week. On Monday he
                       managed to already hit 7.2M IOPS and today hit 7.4M
                       IOPS with his latest work-in-progress kernel
                       patches.


                       This month Jens Axboe has been making some
                       remarkable improvements to the Linux block code for
                       squeezing out every bit of I/O potential of the
                       system. Yesterday Jens Axboe was hitting 7.2M IOPS
                       with new persistent DMA map patches that also
                       shaved off around 10% of synchronization latency.


                # ⚓ Loongson_Volleys_Latest_Patches_For_LoongArch_Linux_Support
                  –_Phoronix⠀⇛


                       Chinese vendor Loongson continues working on their
                       Linux kernel patches enabling the LoongArch
                       processor ISA as their fork from MIPS. While early
                       on when copying existing MIPS open-source code they
                       were quick to call their new ISA “not MIPS”, in
                       these later patch series they continue to refer to
                       their ISA as “a bit like MIPS or RISC-V.”


                       LoongArch debuted this summer with their Loongson
                       3A5000 processors and since then their engineers
                       have been working to get the LoongArch support into
                       the mainline kernel. Loongson though has ruffled
                       some feathers of the upstream kernel developers
                       with in some areas just copying existing MIPS code.


                # ⚓ DAMON_Extended_To_Offer_Physical_Memory_Address_Space
                  Monitoring_–_Phoronix⠀⇛


                       One of many exciting additions with the forthcoming
                       Linux 5.15 kernel is DAMON landed as a data access
                       monitoring framework. DAMON opens up new
                       possibilities around proactive reclamation of
                       system memory and other interesting features.
                       Currently though it’s limited to monitoring the
                       virtual address space of the kernel but a new set
                       of patches out allow for physical address space
                       monitoring as well.


                # § Graphics Stack⠀➾


                      # ⚓ Portable_Computing_Language_1.8_Released_For_OpenCL
                        On_CPUs,_Other_Accelerators_–_Phoronix⠀⇛


                             PoCL is the open-source project implementing
                             OpenCL for CPU-based execution as well as
                             multi-device support by getting its Portable
                             Computing Language implementation working
                             atop NVIDIA GPUs via CUDA, AMD GPUs via HSA,
                             and other back-ends by way of LLVM. PoCL 1.8
                             is out today as the newest feature release.


                      # ⚓ Mesa_21.3_Fixes_Issue_Of_Some_Games_Having
                        Transparency_Issues_Under_Wayland_–_Phoronix⠀⇛


                             Landing in time for the imminent Mesa 21.3
                             feature freeze / code branching is support
                             for the EGL_EXT_present_opaque extension on
                             Wayland. While this EGL extension may not
                             sound too exciting, for some OpenGL games on
                             Wayland it will address some transparency
                             issues.


                             The issue stems from this issue ticket opened
                             during the summer by game porter Ethan Lee.
                             The issue is around needing an EGL equivalent
                             to VkCompositeAlphaFlagBitsKHR as “we’ve got
                             a whole lot of games that are unintentionally
                             translucent in Wayland.” Portal 2 is among
                             the games as a result having issues under
                             native Wayland.


                      # ⚓ Vulkan_1.2.196_Introduces_H.265_Encode_Extension_–
                        Phoronix⠀⇛


                             Arriving back in April were the initial
                             Vulkan Video extensions that included support
                             for video decode of H.264 and H.265 while the
                             initial video encode support was limited to
                             H.264. Out today with Vulkan 1.2.196 is the
                             new extension allowing for H.265 encoding
                             with this new industry-standard video API.


                             Vulkan 1.2.196 introduces the provisional
                             VK_EXT_video_encode_h265 extension. This
                             extension was worked on by AMD, Intel, and
                             NVIDIA but at least under Linux only the
                             NVIDIA proprietary driver currently exposes
                             Vulkan Video encode/decode support.
                             Presumably this morning NVIDIA will be
                             issuing a new Vulkan beta driver providing
                             timely support for this new H.265 encode
                             provisional extension.


          o § Benchmarks⠀➾


                # ⚓ AMD_Radeon_RX_6600_Linux_Performance⠀⇛


                       Today AMD is officially launching the Radeon RX
                       6600 graphics card as a trimmed down model from the
                       Radeon RX 6600 XT that launched back in August.
                       This new (non-XT) model has a suggested price of
                       $329 USD and here is a look at how well this RDNA2
                       graphics card is performing under Linux.


                       The AMD Radeon RX 6600 graphics card features 28
                       compute units, 1792 stream processors, a 2044MHz
                       game clock with up to 2491MHz boost clock, 8GB of
                       GDDR6 video memory, and 32MB infinity cache.


          o § Instructionals/Technical⠀➾


                # ⚓ How_To_Enable_Virtual_Emulated_Desktop_On_Proton_Steam_On
                  Ubuntu_Linux!_–_Fosslicious⠀⇛


                       Proton is an application released by Valve that is
                       used to run Windows Operating System Games on
                       Linux. We can install this application via Steam.


                       To see a list of games that can be run on Proton,
                       please visit ProtonDB. There are also some
                       discussions posted by users regarding problems when
                       running games using Proton.


                       Proton was developed from Wine. So, some features
                       of Wine can be used in this application. One of
                       them is Virtual Emulated Desktop.


                # ⚓ How_To_Install_Snap_on_Linux_Mint_20_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Snap on Linux Mint 20. For those of you who didn’t
                       know, Snap is a package management system for
                       installing and managing applications (called Snaps)
                       developed by Cananoical for Linux operating
                       systems. The system is designed to work for the
                       internet of things, cloud and desktop computing.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of Snap on a Linux Mint 20 (Ulyana).


                # ⚓ Install_Docker_and_Portainer_–_blackMORE_Ops⠀⇛


                       Docker is a set of platform as a service (PaaS)
                       products that use OS-level virtualization to
                       deliver software in packages called containers.
                       Containers are isolated from one another and bundle
                       their own software, libraries and configuration
                       files; they can communicate with each other through
                       well-defined channels. Because all of the
                       containers share the services of a single operating
                       system kernel, they use fewer resources than
                       virtual machines. The service has both free and
                       premium tiers. The software that hosts the
                       containers is called Docker Engine.


                       Portainer CE is a lightweight ‘universal’
                       management GUI that can be used to easily manage
                       Docker, Swarm, Kubernetes and ACI environments. It
                       is designed to be as simple to deploy as it is to
                       use. Portainer consists of a single container that
                       can run on any cluster. It can be deployed as a
                       Linux container or a Windows native container.
                       Portainer allows you to manage all your
                       orchestrator resources (containers, images,
                       volumes, networks and more) through a super-simple
                       graphical interface. A fully supported version of
                       Portainer is available for business use.


                # ⚓ Learn_Usage_of_chown_(Change_Ownership)_Command_in_Linux⠀⇛


                       Under Linux, the ownership of created or existing
                       files and directories is associated with a specific
                       Linux system user, group, or other (file/directory
                       permission access types).


                       However, files or directories ownership verdicts
                       are not final as it is possible to chown (Change
                       Ownership) of any file and/or directory within the
                       Linux operating system.


                # ⚓ Learn_Usage_of_chgrp_(Change_Group)_Command_in_Linux⠀⇛


                       If you are reading this article on the chgrp
                       command, there is a high chance you have explored
                       all the depths of Linux’s chown command and chmod
                       command.


                # ⚓ Linux_Essentials:_Background_(bg)_and_Foreground_(fg)_–
                  Invidious⠀⇛


                       In this episode of Linux Essentials, we’ll take a
                       look at how to send tasks to the background, and
                       then bring them to the foreground.


          o § Games⠀➾


                # ⚓ Space_sci-fi_point_and_click_adventure_Warp_Frontier
                  releases_for_Linux_in_November_|_GamingOnLinux⠀⇛


                       Developed Brawsome emailed to note that their space
                       sci-fi adventure Warp Frontier will be releasing
                       for Linux (and macOS) in November following the
                       Windows release in late September.


                       Warp Frontier is a 2D point and click adventure set
                       in the year 2215, in orbit around humanity’s newest
                       extrasolar colony. It follows the story of war hero
                       turned cop, Vincent Cassini, and his robot partner
                       Mac, as they investigate the cover-up of a war
                       crime by an old enemy that stole the lives of
                       thousands, including his wife and best friend. The
                       game has a particularly Australian flavour in both
                       the writing and the voice cast, including the
                       talents of Kevin Powe (Dead Static Drive), Aimee
                       Smith (Eastern Market Murder), and Angela Tran (The
                       Lake). The game also features an original
                       soundtrack by Thomas Regin (Unavowed).


                # ⚓ Space_Crew:_Legendary_Edition_releases_as_a_free_expansion
                  on_October_21_|_GamingOnLinux⠀⇛


                       Curve Digital and Runner Duck have together
                       announced that Space Crew: Legendary Edition will
                       arrive on October 21 as a free expansion to the
                       base game with a ton of new content.


                       Planned content includes a new “epic” Android
                       Ambush campaign, the ability to take crew off-ship
                       onto stations, outposts and new vessels in Away
                       Team missions. There will also be a new star-system
                       to explore with new missions as well as a range of
                       special features and gameplay experiences.


                # ⚓ Magical_realist_point_and_click_adventure_No_Longer_Home
                  now_on_Linux_|_GamingOnLinux⠀⇛


                       After the initial release back in July, No Longer
                       Home from Humble Grove and Fellow Traveller has
                       launched the Linux version. Funded on Kickstarter
                       back in 2018, the original plan was to have Linux
                       support so it’s good to see it land.


                       Based upon the real life experiences of the
                       developer, where they were forced apart so they
                       decided to stay in touch and make a game together.
                       Here’s what the story entails: “Bo and Ao are
                       graduating university and preparing to leave the
                       flat they’ve lived in together for a year. Thanks
                       to visa limitations, Ao is forced to return to
                       Japan, leaving Bo in England. Disillusioned by
                       post-educational life and shoved aside by a
                       government who doesn’t want them there, both are
                       trying to come to terms with their uncertain
                       futures. And deep under their South London flat,
                       something grows…”


                # ⚓ Doom_Fighters_turns_the_classic_Doom_II_into_a_beat_‘em_up
                  |_GamingOnLinux⠀⇛


                       Doom mods do a lot of things from small adjustments
                       to total conversions and Doom Fighters is one of
                       the most interesting I’ve seen recently that turns
                       Doom II into a beat ‘em up.


                       Released on October 10 is genuinely a surprise.
                       Giving you a 3D character model for Doomguy, you
                       run around and beat up monsters. You get to punch,
                       kick, grab enemies, fly away with them and more.
                       The developer mentioned they do plan to expand the
                       game to include powerful execution moves, alternate
                       deaths, weapons and destructible environments.
                       Sounds like multiplayer will be sorted eventually
                       too.


                # ⚓ Competitive_action-puzzler_Petal_Crash_Online_arrives_on
                  Steam_as_a_free_update_|_GamingOnLinux⠀⇛


                       Petal Crash Online is the free update to the
                       original Petal Crash, a block-matching game where
                       you push blocks around and smash them together to
                       score points. It’s pretty great actually. A genre
                       of games that isn’t overly popular on PC but this
                       is easily one of the best.


                       This new online mode was first launched on itch.io
                       as a separate game but folks on Steam now have it
                       free as an update download with it now giving you
                       the option to play the original or the online mode
                       when you launch it. The online client was built
                       ground the ground-up to support rollback net-code
                       for nicely synced matches.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ 25_ways_you_can_contribute_to_KDE⠀⇛


                             In honor of KDE’s impending 25th birthday
                             tomorrow, here are 25 ways you can get
                             involved to help make KDE software the best
                             in the world!


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Excuse_me,_your_memory_is_leaking._GNOME_Software
                        running_in_the_background,_taking_hundreds_of_MB_of
                        RAM.⠀⇛


                             So I noticed today that GNOME software is
                             constantly running in the background taking
                             up to 435 MB of RAM.


                             It does that (very) occasionally,
                             unpredictably. I can’t figure out why.
                             Usually, it’s only taking 30-60 MB.


                             Obviously that’s a bit much for a program
                             that’s only job is sitting there and telling
                             me when updates are available or waiting for
                             me to install a program, and obviously there
                             are leaks, and indeed, all you apparently
                             need to do is run valgrind on it and it will
                             find some.


          o § Distributions⠀➾


                # § New Releases⠀➾


                      # ⚓ Archcraft_October_Release_Available⠀⇛


                             New ISO of Archcraft is now available to
                             download.


                             Many users faced issues with the September
                             release, due to the bug in the installer.
                             However it was not a big issue and can be
                             fixed easily, But there are people who are
                             completely new to Linux in general. So, this
                             release belongs to them. This release fixes
                             every issue on the previous release.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ SUSE_Harvester:_Deploying_virtual_machines_with
                        Kubernetes⠀⇛


                             I use Kubernetes. You use Kubernetes. We all
                             use Kubernetes to manage containers. What you
                             couldn’t do, though, is use Kubernetes to
                             manage virtual machines (VM)s as well. That
                             was another ballgame. Until now. SUSE, the
                             European Linux giant with one foot in
                             containers and cloud computing, has released
                             the first production version of Harvester,
                             which along with Rancher, SUSE’s Kubernetes
                             as a Service offering, enables you to unify
                             the delivery of VMs and containers


                # § Slackware Family⠀➾


                      # ⚓ Un-Googled_Chromium_update_for_Slackware_14.2_and_-
                        current_|_Alien_Pastures⠀⇛


                             After nearly two weeks of pulling my hair out
                             I finally was able to build the newest
                             Chromium in its un-Googled variant. You can
                             find packages for Slackware 14.2 and -current
                             in my repository on slackware.nl.


                             It’s a jump from the 92 to the 94 release
                             (94.0.4606.81 to be precise) but I simply did
                             not have the opportunity to build a 93
                             release. In part because the un-googled
                             repository maintained by Eloston did not
                             offer release tarballs for a while. Extended
                             leave of absence of the maintainer seems to
                             be the issue which by now has been resolved
                             by giving more people commit access to that
                             repository.


                             The un-Googled version of Chromium is
                             incapable of “phoning home” to Google, by
                             altering the source code and stripping/
                             mangling all occurrences where that might
                             happen. This is basically what Eloston’s
                             project does.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Kube_by_Example_expands_training_curriculum_with_new
                        learning_paths_for_Kubernetes_developers⠀⇛


                             We see Kubernetes as the foundation for
                             hybrid cloud, and hybrid cloud as the future
                             of IT. The technology remains among both the
                             most loved and most wanted tools in this
                             year’s Stack Overflow Developer survey. Given
                             its prevalence and strategic importance, we
                             have also seen developers seeking out and
                             engaging with Kubernetes-focused training
                             resources like Kube by Example, an online
                             destination for free Kubernetes-focused
                             tutorials, news and community interaction.


                             As the company behind the industry’s leading
                             enterprise Kubernetes platform, Red Hat has
                             backed Kube by Example and is diligently
                             working to establish it as the premier
                             destination for developers and operators to
                             sharpen their Kubernetes skills in a hands-on
                             environment.


                      # ⚓ Celebrating_Ada_Lovelace_with_4_career_lessons_from
                        women_in_technology⠀⇛


                             Ada Lovelace is known as the first computer
                             programmer. Mainly known for her work with
                             Charles Babbage’s Analytical Engine in the
                             1800s, she was the first to recognize that
                             the machine could do more than simple
                             calculation — that it could follow a set of
                             instructions (a program) to perform tasks.
                             While Babbage’s computer was never built,
                             Lovelace is credited with writing up an
                             algorithm to be carried out by such a
                             machine. Now, every year in mid-October, we
                             celebrate women tech pioneers on Ada Lovelace
                             Day.


                      # ⚓ Igor_Seletskiy_Steps_Down_to_Assure_AlmaLinux
                        Independence_–_FOSS_Force⠀⇛


                             Today Igor Seletskiy, co-founder and CEO of
                             CloudLinux, announced that he’s stepped down
                             from his role as chairman of the board at the
                             AlmaLinux Foundation, and is also vacating
                             his seat on the board of directors.


                             The foundation, which he started earlier this
                             year, produces AlmaLinux, a drop-in
                             replacement for Red Hat’s CentOS Linux that
                             Seletskiy announced in December, shortly
                             after Red Hat said it was moving the Linux
                             distribution from its traditional role as a
                             downstream clone of Red Hat Enterprise Linux
                             to sit upstream as RHEL’s “nightly build.”


                             A replacement was needed because many
                             organizations, including many Fortune 500
                             enterprises, use CentOS in production as a
                             way to take advantage of RHEL’s stability
                             without having to pay for support contracts.


                             Both Seletskiy and the AlmaLinux Foundation
                             are very clear there’s no palace intrigue
                             behind this move. The new distro’s founder is
                             stepping down not because of some power
                             struggle within the organization, but because
                             he wants the distro he birthed to have a life
                             of its own as an independent project.


                      # ⚓ Why_can’t_I_use_sudo_with_rootless_Podman?⠀⇛


                             I was recently asked: Why can’t I run
                             rootless Podman containers when I log into a
                             user via sudo or su? The problem is a bit
                             complex to explain, so I’ll start with an
                             example.


                      # ⚓ Digital_transformation:_3_myths_the_pandemic_busted⠀⇛


                             When the pandemic struck, most organizations
                             had no choice but to accelerate their digital
                             technology adoption. Many condensed into a
                             matter of months what might otherwise have
                             been years of consideration, strategizing,
                             and change.


                             According to a survey by McKinsey, the
                             pandemic sparked a seven-year increase in the
                             rate at which companies developed digital or
                             digitally enhanced offerings. It accelerated
                             the digitization of their customer and
                             supply-chain interactions and internal
                             operations by three to four years.


                             This shift sparked a new reality for today’s
                             organizations to remain competitive and meet
                             customers’ changing needs. But while
                             enterprises have certainly dedicated more
                             resources to the process of digital
                             transformation, many misconceptions still
                             remain.


                # § Debian Family⠀➾


                      # ⚓ Sparky_2021.10⠀⇛


                             Sparky 2021.10 of the (semi-)rolling line is
                             out; it is based on Debian testing
                             “Bookworm”.


                             This iso update provides:
                             – all packages upgraded as of October 12,
                             2021
                             – Linux kernel 5.14.9
                             – Calamares 3.2.44.3
                             – i386 libs removed from amd64 iso images
                             – small improvements


                             No reinstallation is required if you
                             installed Sparky 2021.09, simply keep it up
                             to date.


          o § Devices/Embedded⠀➾


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Android_12-based_RealmeUI_3.0_debuts:_first_beta_to
                        come_to_Realme_GT_in_October_–_GSMArena.com_news⠀⇛


                      # ⚓ Samsung’s_still_on_track_for_a_stable_Android_12_/
                        One_UI_4_release_in_2021_–_SamMobile⠀⇛


                      # ⚓ Anker’s_new_Nebula_Android_TV_4K_streamer_is_on_sale
                        for_the_first_time_at_$75_(Reg._$90)_–_9to5Toys⠀⇛


                      # ⚓ Google_dismisses_claims_Android_smartphones_snoop_on
                        users_|_TechRadar⠀⇛


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


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ pg_partman_4.6.0_released⠀⇛


                             PostgreSQL Partition Manager (pg_partman)
                             v4.6.0 has been released.


                      # ⚓ PostgreSQL:_PGConf_NYC_2021_Sessions_Announced,_Last
                        Week_for_Early_Bird!⠀⇛


                             The first community PostgreSQL conference in
                             many months is coming to New York City in
                             less than two months! PGConf NYC is a non-
                             profit, community-run and PostgreSQL
                             community recognized conference being run by
                             the United States PostgreSQL Association
                             (PgUS).


                             PGConf NYC delivers two days packed with
                             presentations about PostgreSQL and related
                             technologies, as well as the usual hallway
                             and social track. PGConf NYC is being held
                             December 2nd and 3rd, 2021 in New York City.


                      # ⚓ Psycopg_3.0_released⠀⇛


                             I am extremely excited to announce the first
                             stable release of Psycopg 3!


                             Psycopg 3 is a complete rewrite based on the
                             experience accumulated with the development
                             and maintenance of psycopg2. Psycopg 3
                             targets all the current versions of Python
                             (3.6-3.10) and PostgreSQL (10-14) and allows
                             the use of modern Python development
                             techniques, such as async and statically
                             typed code. A list of the new features is
                             available in the documentation.


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ Tender_to_implement_C++_accessibility_tests_(#202110-
                        01)⠀⇛


                             The Document Foundation (TDF) is the
                             charitable entity behind the world’s leading
                             free/libre open source (FLOSS) office suite
                             LibreOffice.


                             We are looking for an individual or company
                             to implement C++ accessibility tests.


                             The work has to be developed on LibreOffice
                             master, so that it will be released in the
                             next major version.


                             The current accessibility tests are rather
                             incomplete and hard to maintain.
                             Additionally, they are written in Java.


                # § Programming/Development⠀➾


                      # ⚓ abs_function_in_C⠀⇛


                             Why is it necessary for programmers to use
                             the abs() function? It’s accessible in almost
                             every programming language; But how much good
                             is a function that just turns negative values
                             into positive ones? You may find yourself
                             wanting positive numbers occasionally, and
                             the abs() function ensures that you will get
                             them. The abs function is an abbreviation for
                             “Absolute Value” inside the C programming
                             language, and it specifies the distance of a
                             number just on a number line beginning from 0
                             without taking the direction into account.
                             The abs value of a number, or its absolute
                             value, has always been positive, implying
                             that a distance could never be negative.
                             The abs () method returns the absolute
                             appropriate value integers and is specified
                             in the stdlib.h header file. To return the
                             absolute value of a particular number, we
                             must include the stdlib.h header file in our
                             C application. Only positive values are
                             returned by the abs() function.


                             Consider the following scenario: If we have
                             an integer number -2 and wish to find the
                             absolute value, we may use the abs() method
                             to have the positive number 2. In addition,
                             when we have an integer number 2 and want to
                             determine the absolute value, we can use the
                             abs() method to return the very same value as
                             2. It gives the very same number if we
                             provide it with any positive number.


                      # § Python⠀➾


                            # ⚓ Printf-style_debugging_using_GDB,_Part_2⠀⇛


                                   The first article in this series
                                   introduced the GNU debugger, GDB, and
                                   in particular its dprintf command,
                                   which displays variables from programs
                                   in a fashion similar to C-language
                                   printf statements. This article expands
                                   on the rich capabilities of printf-
                                   style debugging by showing how to save
                                   commands for reuse and how to save the
                                   output from the program and GDB for
                                   later examination.


                            # ⚓ Python_Wrapper_to_find_all_primes_from_a_given
                              interval_via_sieve_of_Eratosthenes_released_as
                              C++_procedure⠀⇛


                            # ⚓ Intel_Contributes_AVX-512_Optimizations_To
                              Numpy,_Yields_Massive_Speedups_–_Phoronix⠀⇛


                                   Intel has contributed AVX-512
                                   optimizations to upstream Numpy. For
                                   those using Numpy as this leading
                                   Python library for numerical computing,
                                   newer Intel CPUs with AVX-512
                                   capabilities can enjoy major speed-ups
                                   in the range of 14~32x faster.


                                   This summer Intel volleyed their
                                   initial AVX-512 code for Numpy and
                                   finally this week the code was merged
                                   upstream. This open-source AVX-512 code
                                   originates from the Intel Short Vector
                                   Math Library (SVML) that they open-
                                   sourced the code from. Intel has also
                                   been working on allowing Numpy to be
                                   built against SVML as a separate
                                   improvement.


                      # § Shell/Bash/Zsh/Ksh⠀➾


                            # ⚓ TSV_to_CSV_on_the_CLI_(if_you_really_have_to)⠀⇛


                                   Regular visitors to this blog will know
                                   that I don’t like the CSV format. It’s
                                   awful. In my humble opinion, data
                                   workers should aim to use invisible
                                   tabs (TSV) or visible pipes (PSV) as
                                   field separators in delimited text
                                   tables. Sometimes, though, data workers
                                   are required to convert a perfectly
                                   good TSV or PSV to a CSV. What to do?


                                   I don’t recommend opening the TSV or
                                   PSV in spreadsheet software and saving
                                   the result as a CSV, unless there are
                                   no leading or trailing quotes in the
                                   data items, or umatched quotes
                                   generally. The original quotes might
                                   well disappear in the saved CSV.


                                   There are a number of TSV-to-CSV
                                   programs for the command line. One is
                                   in Haskell, for example, and there also
                                   routines to do the job in Perl and
                                   Python. But if the individual fields in
                                   the TSV don’t contain commas or quotes,
                                   the TSV-to-CSV conversion is simple —
                                   use tr:


                            # ⚓ Useful_Bash_Commands_You_May_Not_Know_About⠀⇛


                                   Bash is a fairly powerful language to
                                   program in, and is also quite easy to
                                   start off with.


                                   After all, it’s almost universally the
                                   shell you’re going to see when you open
                                   up your terminal. That makes it
                                   extremely useful to get accustomed to.


                                   There’s some powerful commands in Bash
                                   that you may not be aware of though,
                                   even if you’re fairly seasoned with
                                   using the language. All of these
                                   commands can serve quite useful
                                   purposes though, and can make the shell
                                   scripts you write cleaner, more
                                   maintainable, and just outright more
                                   powerful than they could’ve been
                                   before.


    * § Leftovers⠀➾


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Adobe_Gives_a_Free_PDF_Editor_for_Google_Chrome_and
                        Edge_Users⠀⇛


                             Adobe announced via a blog post that Acrobat
                             extension for Google Chrome and Microsoft
                             Edge now have basic PDF editing features,
                             right inside the browser.


                      # § Security⠀➾


                            # ⚓ Don’t_penalise_cybersecurity_researchers!⠀⇛


                                   We wrote to the Indian Computer
                                   Emergency Response Team regarding a
                                   provision in their new Responsible
                                   Vulnerability Disclosure and
                                   Coordination Policy that penalises
                                   cybersecurity researchers for
                                   vulnerability disclosures. In our
                                   representation, we highlighted how such
                                   provisions would create an atmosphere
                                   in which researchers would be reluctant
                                   about reporting vulnerabilities and
                                   recommended that a robust disclosure
                                   mechanism be implemented that protects
                                   researchers from harm.


                                   [...]


                                   Such provisions contribute to a
                                   disclosure regime in which security
                                   researchers would be liable under the
                                   Information Technology Act, 2000 (‘IT
                                   Act’), and are penalised for
                                   disclosures of genuine security
                                   vulnerabilities. Section 43 of the
                                   Information Technology Act, 2000
                                   penalizes anyone who gains unauthorized
                                   access to a computer resource without
                                   permission of the owner, and so fails
                                   to draw a distinction between malicious
                                   hackers and ethical security
                                   researchers. Thus, even when
                                   researchers have acted in good faith
                                   they may be charged under the IT Act.
                                   As we have mentioned earlier, companies
                                   have exploited this loophole in the
                                   said provision to press charges against
                                   cybersecurity researchers who expose
                                   data breaches in their companies. The
                                   Personal Data Protection Bill, 2019,
                                   currently being considered by a Joint
                                   Parliamentary Committee, also fails to
                                   protect security researchers and
                                   whistleblowers. All of this leads to
                                   situations in which researchers are
                                   reluctant to report vulnerabilities for
                                   fear of being sued.


                                   Clause 7 of the Policy is also in
                                   conflict with the Information
                                   Technology (The Indian Computer
                                   Emergency Response Team and Manner of
                                   Performing Functions and Duties) Rules,
                                   2013 (‘2013 IT Rules’) which adapts a
                                   cooperative and collaborative approach.
                                   Rule 10 requires CERT-IN to interact
                                   with stakeholders including research
                                   organisations and security experts for
                                   preventing cyber security incidents.
                                   Under Rule 11(2), CERT-IN is obligated
                                   to collaborate with, among others,
                                   organisations and individuals engaged
                                   in preventing and protecting against
                                   cyber security attacks. Thus, by
                                   imposing complete and sole
                                   responsibility on cyber security
                                   researchers for actions undertaken
                                   during the discovery of a
                                   vulnerability, the policy is in
                                   conflict with the collaborative spirit
                                   of the 2013 IT Rules and so is a
                                   genuine impediment to effective
                                   collaboration.


                            # ⚓ Airline_Passenger_Mistakes_Vintage_Camera_for_a
                              Bomb⠀⇛


                                   Back in 2007, I called this the “war on
                                   the unexpected.” It’s why “see
                                   something, say something” doesn’t work.
                                   If you put amateurs in the front lines
                                   of security, don’t be surprised when
                                   you get amateur security. I have lots
                                   of examples.


                            # ⚓ How_to_create_an_effective_security_policy:_6
                              tips⠀⇛


                                   Are your security policies boring? OK,
                                   that’s not entirely fair. Security
                                   policies are boring, especially to
                                   people outside of IT – in the way that
                                   children find their parents’ or
                                   teachers’ rules “boring.” There’s a
                                   limit to how interesting one can make
                                   “best practices for creating strong
                                   passwords” sound to the masses.


                                   The point of such policies is to
                                   educate people on organizational rules
                                   and the habits of good security
                                   hygiene. This is the administrative
                                   layer of security controls: all of the
                                   rules, standards, guidelines, and
                                   training an organization puts in place
                                   as part of its overall security
                                   program. It’s the human-focused
                                   component that rounds out the other two
                                   general categories of security
                                   controls, according to Terumi
                                   Laskowsky, an IT security consultant
                                   and cybersecurity instructor at
                                   DevelopIntelligence. The other two
                                   categories are technical/logical
                                   controls (your hardware and software
                                   tools) and physical controls (things
                                   like building or site access).


                                   Laskowsky notes that people tend to
                                   question the value of administrative
                                   controls. That’s partly because it can
                                   be difficult to measure or “see” their
                                   effectiveness, especially relative to
                                   technical or physical controls. But
                                   Laskowsky and other security experts
                                   generally agree that they are
                                   necessary. Security is not a steady-
                                   state affair – while our security
                                   tooling and processes are becoming more
                                   automated, a strong posture still
                                   requires human awareness, intelligence,
                                   and adaptability.


                                   “Raising our security awareness through
                                   administrative controls allows us to
                                   start seeing the patterns of unsafe
                                   behavior,” Laskowsky says. “We can then
                                   generalize and respond to new threats
                                   faster than security companies can come
                                   up with software to handle them.”


                            # ⚓ 10_Most_Commonly_Used_FOSS_Packages⠀⇛


                                   The Core Infrastructure Initiative
                                   Census Program II report released
                                   earlier this year identified the most
                                   commonly used FOSS components in
                                   production applications, with the goal
                                   of understanding potential
                                   vulnerabilities in these components and
                                   better securing the open source
                                   software supply chain.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Access_Now_report_holds_up_poster_child
                                    Aadhaar_as_‘Big_ID’_bugbear_|_Biometric
                                    Update⠀⇛


                                         A legal vacuum and vulnerable
                                         population allowed the creation
                                         of the world’s largest biometric
                                         digital ID project and built a
                                         myth which could be used by an
                                         entire industry to sell similar
                                         systems and dreams elsewhere, a
                                         new report argues.
                                         India’s Aadhaar biometric ID
                                         program is presented as a
                                         ‘cautionary tale’ for all the
                                         ills of ‘Big ID’ and its growing
                                         number of digital ID projects
                                         around the world in a new and in-
                                         depth report by campaign group
                                         Access Now.


                                         ‘Busting the Dangerous Myths of
                                         Big ID Programs: Cautionary
                                         Lessons from India’ attempts to
                                         knock the Unique Identification
                                         Authority of India project from
                                         its pedestal to ask why a digital
                                         ID is required in the first place
                                         and list what is wrong with
                                         “these centralized, ubiquitous,
                                         data-heavy forms of digital
                                         identification.”


                                  # ⚓ Is_Australia_becoming_a_surveillance
                                    state?_|_IT_PRO⠀⇛


                                         At the end of August, the
                                         Australian Parliament passed the
                                         Surveillance Legislation
                                         Amendment (Identify and Disrupt)
                                         Bill 2021 granting the Australian
                                         Federal Police (AFP) and
                                         Australian Criminal Intelligence
                                         Commission (ACIC) extensive new
                                         powers.


                                         Senator Lidia Thorpe, the
                                         Australian Greens spokesperson
                                         for Justice, said the bill
                                         enables both law enforcement
                                         agencies to be “judge, jury, and
                                         executioner”, adding there’s no
                                         explanation as to why these
                                         powers are necessary. She also
                                         highlighted that allies like
                                         Canada, New Zealand, the UK and
                                         US don’t grant their own law
                                         enforcement these rights.


                                         With this bill being brought into
                                         law with cross-party support, is
                                         Australia moving closer to being
                                         a surveillance state?


          o § Censorship/Free Speech⠀➾


                # ⚓ Facebook:_Insulting_the_Taliban_will_get_you_Talibanned.⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ Singapore:_Withdraw_“foreign_interference”_law_or_risk
                  violating_civic_freedoms⠀⇛


                       Today, Access Now and nine organizations are
                       calling on the Singapore government to withdraw the
                       Foreign Interference (Countermeasures) Bill (FICA)
                       — a law that contravenes international legal and
                       human rights principles, and will significantly
                       curtail already-limited civic space in the country.


                       “Protecting national security may be a legitimate
                       aim — but FICA is not the way to achieve it,” said
                       Raman Jit Singh Chima, Senior International Counsel
                       and Asia Pacific Director at Access Now. “It
                       unnecessarily expands the government’s already-wide
                       powers to control and censor online and offline
                       speech, and potentially allows for even legitimate
                       associations to be criminalized and monitored.
                       Civil society, journalists, academics, researchers,
                       artists, and writers who are often supported by
                       cross-border collaboration and funding will be
                       hardest hit.”


                       On October 4, Singapore’s parliament passed FICA,
                       three weeks after it was tabled on by the Ministry
                       of Home Affairs to purportedly “prevent, detect and
                       disrupt foreign interference in […] domestic
                       politics.” This move came despite serious red flags
                       raised by members of the public, civil society,
                       legal fraternity, independent media, political
                       opposition, academia, and industry in Singapore
                       that the law would undermine civic freedoms.


                # ⚓ Access_Now_to_Telenor’s_Board:_Stop_the_sale_in_Myanmar_–
                  Access_Now⠀⇛


                       Norway’s Telenor Group must not jeopardize the
                       human rights of people across Myanmar through the
                       “disposal” of its local enterprise. For months,
                       Telenor has ignored civil society’s ongoing
                       pressure to stop the sale of its Myanmar operations
                       to M1 Group — a telecoms conglomerate notorious for
                       extracting profits from conflict zones and
                       operating without appropriate human rights
                       safeguards. Access Now is urgently calling on
                       Telenor’s Board to immediately reverse their
                       decision, and stop the sale.


                       As Access Now’s letter to the Board outlines in
                       detail, M1 Group has demonstrated a complete
                       disregard for human rights in other high-risk
                       markets, and actively coordinates with oppressive
                       regimes. The company’s owners face serious
                       corruption allegations, and there is strong
                       evidence to suggest ties between M1 Group and the
                       Myanmar military.


                       “No rights-respecting Norwegian company should
                       operate with such disregard for the human rights of
                       others,” said Brett Solomon, Executive Director at
                       Access Now. “Leaving the people who depend on its
                       services in the hands of a company with such a
                       dubious history is an abandonment of Telenor’s
                       principles of transparency and respect for human
                       rights. Telenor’s subscribers, particularly those
                       most at risk of persecution by the Myanmar
                       military, deserve better.”


                       Telenor’s hasty decision in July, 2021, to hand
                       over its operations in Myanmar to M1 Group has
                       alarmed human rights activists, including a group
                       of over 400 Myanmar-based civil society
                       organizations who filed a complaint with the OECD
                       Norwegian National Contact Point, which has since
                       accepted it. In August, 2021, Access Now, along
                       with 44 organizations, laid out the potential
                       dangers of this sale to the Telenor Board, calling
                       for them to stop the sale and conduct human rights
                       due diligence in line with international standards.


                # ⚓ Singapore’s_anti-foreign_interference_law_will
                  ‘substantially_narrow’_civic_space,_rights_groups_say⠀⇛


                       Fica will allow Singapore to ‘expand curtailment of
                       civil freedoms to the detriment of its people’,
                       said 11 groups including Access Now, Human Rights
                       Watch and Article 19


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