𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Sunday, December 04, 2022
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Generated Mon 5 Dec 02:43:35 GMT 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
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Gemini index for the day: gemini://gemini.techrights.org/2022/12/04/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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QmW2j2ckzmovo3T5PVVEPyCDY6cxTKFEYB2dhVvwPkm1n7


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

⦿ When a Company Simply Refuses to Talk to Technical and Exerienced Staff Through Internal Avenues | Techrights

⦿ IRC Proceedings: Saturday, December 03, 2022 | Techrights

⦿ Sirius Open Source: The Home of Stress and Bullying by Management | Techrights

⦿ Office Manager in Company Without an Office | Techrights

⦿ [Meme] Kings Instead of Open Consultation Among Peers | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/12/04/ignoring-staff-concerns/#comments
		http://techrights.org/2022/12/04/irc-log-031222/#comments
		http://techrights.org/2022/12/04/misuse-of-power-against-employees/#comments
		http://techrights.org/2022/12/04/sirius-office-manager/#comments
		http://techrights.org/2022/12/04/sirius-open-source-has-kings/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/12/04/openindiana-hipster-2022-10/#comments
		http://techrights.org/2022/12/04/pgadmin-4-version-6-17/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 60

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/04/ignoring-staff-concerns/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/04/ignoring-staff-concerns/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.04.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ When_a_Company_Simply_Refuses_to_Talk_to_Technical_and_Exerienced_Staff
Through_Internal_Avenues⠀✐


Posted in Deception, Free/Libre_Software at 9:42 pm by Dr. Roy Schestowitz


Video_download_link | md5sum

Working in the Blind
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/sirius-blinded-to-reality.webm


Summary: When companies behave like monarchies where staff has no role at all
in decision-making and decisions are made in violation of those companies’
tenets (or mission statements) it is inevitable that staff will issue concerns,
first internally and — failing that — in other channels


THE company Sirius fancies the word “Open”, but it does not engage in open
debate. Staff is left in the dark about the company’s own affairs, never mind
clients and the general public. Everything is decided secretly by an inner
cabal; it wasn’t always like that!


“This is no way to run a company, except into the ground.”In the more recent
past, bad decisions were made like abandoning Open stuff in favour of
proprietary spyware such as Slack, Skype, Google, and Zoom. A decision
regarding mobile phones came much later, without any consultations at all with
those actually impacted by the decision. They say there were concerns about the
staff pushing back, but if staff isn’t being listened to, then key staff will
leave the company. This already happened before. Managers, for instance, were
making our infrastructure obsolete and driving out people who can maintain it,
leaving rotting foundations and massive bills for “Clown Computing” (the same
could be hosted for like 10 times less and be controlled directly).


The video above mentions taxes, addresses, and a pattern of misleading clients
while taking great risk. This is no way to run a company, except into the
ground. Its long-earned reputation (almost 25 years) cannot compensate for
recent bad karma. █



                    ䷩ 𝚕𝚒𝚗𝚎 120

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/04/irc-log-031222/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/04/irc-log-031222/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.04.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Saturday,_December_03,_2022⠀✐


Posted in IRC_Logs at 3:00 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-031222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-031222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-031222.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-031222.gmi
Over HTTP:


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


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


CID                                              Description     Object type


                                                 IRC log for
 QmTAwH3Y2zAWBYME5hKpA9hLgxUwmskXQqbFsewjmbjKy3 #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmSvzyQxL3tBkLPY6VPfidDzfi5LUXtEGM7LeGYqPRhwi6 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
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                                                 IRC log for
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 QmVTGRH4XcLm3kn48DYktesrBPBUNKUn4X9fznzU41p36F social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 IRC log for
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 QmVnKYy2wXPhXZEnLdDGRj7T5sZ4NWykjPY1UyFnxSuzW5 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
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                                                 IRC log for
 QmT77Kdwnv5SdX6mdbxg1xzanSR3T2FYnVJrPgSJSrMWSA #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmcYUSUobRdDKSqyFhBwSd62WcqLfwPx126ckvQbMfU2PR (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
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                                                 IRC log for
 QmTipMXZSVU3L6aZ9pThDdphGt7NmteCCrtwKbeoycrhDf #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
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                                                 IRC log for
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 QmcfmkydkMDjacPf27cKPNumqsWJFFFyWGYVBTkLMRMe85 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmW2j2ckzmovo3T5PVVEPyCDY6cxTKFEYB2dhVvwPkm1n7



                    ䷩ 𝚕𝚒𝚗𝚎 247

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/04/misuse-of-power-against-employees/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/04/misuse-of-power-against-employees/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.04.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Sirius_Open_Source:_The_Home_of_Stress_and_Bullying_by_Management⠀✐


Posted in Deception, Free/Libre_Software at 7:15 pm by Dr. Roy Schestowitz


             🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Sirius_Open_Source:_stress-free⦈_


Summary: Part 3 of a report regarding Sirius Open Source, which is imploding
after bad judgement and misuse of power against employees


THE signs of Sirius collapsing were all over the place. In Part_I and in Part
II (see index) we explained some of the earlier days of the company, which
turns 25 next year. It might not even reach this milestone at all. Prognosis is
negative.


People can understand that institutions are failing when people improperly
qualified are assigned jobs they are incapable of doing. This is where Sirius
is today. And now we come to Part 3, looking back a bit:


===============================================================================
§ The Open Source Era⠀➾


⚓  Humble Beginnings⠀⇛


Roy’s loyalty to the company is evident and easily provable considering how
long he has served the company. But now it is not the company he entered in
early February 2011; nor is this the company Rianne entered in 2013. Much
patience and tolerance were needed to justify staying in the company for so
long (in 2 months it’ll be full 12 years since Roy joined), especially after
unforgettable tirades from management that has since then been (apparently)
removed, albeit only after a lot of backlash from a lot of staff. 12 years is a
long, long time. Roy worked there from his 20s to his 40s. He had much better
job offers elsewhere. 12 years is also the longest any existing worker has
served the company. That’s very long by today’s standards, where employment
records are a lot shorter than back in the 1960s-1980s. A lot of people hop
between jobs only months or a few years apart. But not Roy.


Both Roy and Rianne have consistently and persistently demonstrated loyalty to
the company, sticking to it even when times were rough and people elsewhere
offered “better” jobs. This, as a matter of very simple fact, is why there’s a
benevolent fight for the company and its (original) core mission. It’s why
internal issues are escalated internally (not to publicly embarrass the
company) and misguided directions get highlighted without admonishing anyone.


It’s important not to derail core tenets of the company. It’s essential for
recruitment, which can beget better clients, in turn rewarding the staff, too.
People who don’t care about their employer simply keep quiet, blindly follow
instructions, and don’t care about long-term consequences. Those are typically
employees that just come and go. They don’t offer much value to the company
(training takes up a lot of time and it’s an investment which goes astray), so
they don’t fully develop familiarity, skills, personal connection etc. (among
colleagues and among clients, who learn to trust the company based on names of
long-serving people). Many of them cannot develop software, either.


⚓  A Fast-Rotting Apple⠀⇛


Companies succeed and perish based on what people they can attract and what
people they lose. In the case of Sirius, much was lost and almost nothing
gained in the “human capital” or “human resources” sense. It’s becoming a
crisis. More on that later.


Over the past decade or longer there has been a change of leadership and severe
brain drain. Morale has not been good, to put it politely. The Sirius
management figures rely far too much on credibility of a company that existed
well over a decade ago — a company that had a physical office (real location),
a clearer and more elaborate leadership structure, and a lot of office staff,
not just remote workers. The company had assets, certified professionals in
fields of operations (not just technical fields), and therefore it functioned a
lot more reliably, e.g. in the accountancy. There were cheques and balances.
There were actual domain-proficient departments and not self-appointed jacks of
all trades.


As we shall see later, there was also a_change_of_address_in_October: [sic]


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Registered_office_address_changed_from_The_Columbia_Centre
Station_Road_Bracknell_Berkshire_RG12_1LP_United_Kingdom_to_80-83_Long_Lane_80-
83_Long_Lane_London_EC1A_9ET_on_11_October_2022⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Registered_office_address_changed_from_The_Columbia_Centre
Station_Road_Bracknell_Berkshire_RG12_1LP_United_Kingdom_to_80-83_Long_Lane_80-
83_Long_Lane_London_EC1A_9ET_on_11_October_2022⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Change_address:_Registered_office_address_changed_from_The
Columbia_Centre_Station_Road_Bracknell_Berkshire_RG12_1LP_United_Kingdom_to_80-
83_Long_Lane_80-83_Long_Lane_London_EC1A_9ET_on_11_October_2022⦈_


There is not the Sirius address, it is the accountancy’s address.


Sadly, what we’re seeing or what ‘low-level’ employees have witnessed so far
this year is a growing level and ever-increasing frequency of cover-up (few
examples to come later) of what was/is really happening. Those who are
portrayed as troublemakers are in fact those who supposedly ‘threaten’ this
veil of secrecy or amicably challenge the company to improve (from within,
repeatedly if necessary, in order to spare otherwise-avoidable damage and save
face). As internal avenues of grievances are exhausted, people start speaking
to friends, even without naming any persons, companies etc. This is a well-
known high cost of failing to act upon internal suggestions or constructive
complaints, leaving little leeway and inevitably causing a sort of spill-over
of woes and gripes. This, suffice to say, is another example of managerial
failure. Being unable to listen (not just hear but actually listen) to workers
is a weakness. It’s not a strength, although it can be rather tempting to
simply ignore critics and impulsively alluring to reject criticism as
fundamentally “invalid”, “void”, “hostile”, “paranoid”, “ignorant” and so on.
Egocentric companies end up with no inflation in business, just inflation of
the self. That weakens teamwork. A cohesive working environment boils down to
collaboration and deep trust, not a bunch of superhero avatars in Slack
channels, which to an outsider may indicate that the company is immature,
unprofessional, and child-like.


In the past, the company known as “Sirius” (same name, very different people)
had more competent administrators (like a person associated with the Ubuntu
community back when Roy joined), i.e. folks who actually understood the
products and services that Sirius provided. It helps to have such people
onboard because of networking and links; they can bring business (around that
time Sirius had clients directly connected to Ubuntu; it was a gateway to a
flourishing network of other clients). Likewise, some world-class and well-
known PostgreSQL engineers were employed by the company; this is a sign of
solid corporate leadership, technical leadership, and also a lead to future
clientele. Of course almost all of those people have since then left the
company, leaving the company with a “skeleton crew”.


Having an administrator with no background in computing is not a good idea;
clients can sense they’re interacting (e.g. over the telephone) with people
whose skills are limited to “personal assistant” that soon got promoted to
management due to an unfilled vacuum. Potential of career leap may seem nice,
but that comes at a collective, company-wide cost. Another aspect of this
phenomenon was in recent years dubbed “imposter syndrome”. That can lead to
insecurity, which in turn causes backlash, outbursts, and paranoia. It makes
any workplace potentially toxic. Any time a company is hiring unskilled people
or promoting people in spite of a lack of relevant skills it causes issues on
several levels; clients lose respect, workers feel dissatisfied, and job roles
cannot be performed (maybe not by intention, but high forms of incompetence are
not distinguishable from malice). Due to (corporate) survival instincts, those
being scrutinised can turn aggressive very fast.


In the past 4 years staff casually witnessed tantrums (albeit staff was
subjected to divide-and-rule tactics, impeding communication between staff or
across teams); that typically came from above, not from below, e.g. managers
resorting to bullying. General consensus within workers’ circles is that at
least some of that stems from some people’s desperate desire to cover up their
lack of capabilities. This is very dangerous to any company, including those
who do the bullying (after all, without the company they too would be
unemployed). Those who stand to lose the most are long-serving staff, whose CV
is closely connected and long-connected to that one firm. Those who just come
and seed destruction can move on and repeat the same modus operandi. Short-term
workers have a different set of personal interests. That’s just how it is. █


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⣿⣿⠿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⣿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣯⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣿⣿⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⣛⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⢋⢙⣥⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣭⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣯⣷⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⣵⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠉⠀⠀⠀⠀
⣿⣐⣄⣉⣉⣙⣁⣡⣈⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣟⠏⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣾⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⢉⣡⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠙⢿⣿⣿⣿⣻⢽⡻⣿⣿⣿⢟⠭⣿⣿⣿⣿⣟⡯⢝⢿⣿⣿⡿⣫⣽⣻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣉⣉⣉⣉⣉⣉⣦⣤⣤⡄⠀⠀⠀⠀⠁⠀
⣿⣿⣇⠀⠀⣸⣿⣿⣧⡿⠥⣧⣿⣿⣿⡻⠤⢟⣿⣿⣿⣿⠎⠼⣽⣿⣿⣟⠷⠼⣻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀
⣿⣟⣛⣛⣛⣛⣻⣿⣿⣛⣛⣻⣿⣿⣿⣛⣛⣙⣿⣿⣿⣙⣛⣙⣻⣿⣿⣿⣙⣛⣻⣿⣿⣿⢸⢿⢹⣿⣿⢿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⢘⣭⣶⣿⣿⣿⣿⣿⣿⣿⡟⡛⢿⣿⠻⠷⠼⠻⡿⠿⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡾⣟⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠠⢾⠿⣾⠾⣶⡾⠾⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⠷⠛⢉⣿
⣿⡏⢹⣿⣿⣉⠍⣉⣹⢛⠛⣹⣻⢙⣛⢛⠛⡻⡿⢛⡋⢛⣋⡩⣽⣹⡉⣭⡿⣛⣙⣋⣿⣿⢸⡿⠟⠋⠁⢿⣿⣿⣿⣿⣿⣷⣴⣴⣶⣶⣶⣶⣶⣆⢡⣤⣤⣥⣤⣤⣤⣿⣿⣿⣿⣿⣿⡿⣟⣯⠷⠛⣁⣤⣶⢿⣻⣽
⣿⣿⣿⣿⣿⣉⣉⢉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣷⣿⣿⣿⣶⢿⣻⣿⣾⣿⡿⠟
⣿⣿⣻⣿⣿⡿⣿⢿⢿⠿⣿⢿⣿⣿⣿⡿⢿⢿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠅⣬⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣷⣿⣿⣿⣿⢿⣻⣽⣾⣿⡿⠟⠋⠁⠀⠀
⣿⣾⣲⣿⣿⣦⣤⣴⣴⣶⣾⣴⣶⣴⣴⣵⣶⣤⣤⣷⣴⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⡿⠗⠛⣹⣿⣿⢿⣻⣽⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀
⣿⠏⡙⣿⣿⠛⠿⠟⠿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⡽⠚⢋⣤⣴⣾⢿⣻⣽⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣴⣿⣿⣷⣶⣷⣷⣷⣾⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⣻⣽⣾⣿⣿⣿⣾⢿⣻⣽⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀
⣿⡏⣊⣿⣿⡋⡛⡛⡏⡋⢻⠻⣛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣻⣽⣾⣿⣿⣿⣿⢿⣻⣽⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣴⢾⣻⣽⠾⠛⣻⣿⣿⡿⠟⠉⠀⠹⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢄⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢀⣸⣀⣀⣀⡀⠂⣼⣿⣿⣿⣴⣦⡠⠀⣶⣶⢀⢺⠇⣷⠀⢲⢀⢀⡆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⣾⡇⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣌⢺⣿⣿⣿⣿⣿⢰⣏⠻⣿⣿⣿⣿⣿⣾⣯⠻⣾⣷⣙⣿⣸⣦⡽⣿⣻⣶⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡄⠀⢠⡀
⣿⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⡙⢿⣿⣿⣿⣿⣷⣬⡻⣿⣿⣿⣿⣿⣷⣾⢿⣿⣞⢿⣿⣷⣹⣷⡻⣿⣐⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣇⠠⢽⡒⠬⣷
⣾⡅⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣝⢶⣍⠫⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⣦⣹⣿⣿⡿⣿⣿⣾⢿⣿⣿⡴⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡌⣛⣯⢝⣻
⣟⡿⣿⣷⣮⣝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣳⣯⡙⢿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⢿⣿⣯⣿⣿⣿⣖⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣇⡒⢽⣐⡮
⠛⠿⣷⣯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣻⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣝⣿⣿⡿⣿⣷⣿⣿⢿⣜⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⠬⠍⣗⠩
⠀⠀⠀⠉⠙⠻⢷⣯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⢮⣝⢿⣿⣿⣷⣯⣙⢿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣽⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⡯⢐⣻⡬
⣀⡀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣯⡻⣿⣿⣿⣾⣝⢿⣿⣿⣿⣮⡿⣿⡿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⢹⣒⡚⣯
⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠉⠛⠷⣯⣟⣻⢿⣿⣝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣟⢿⣿⣿⣿⣝⣿⣿⣿⣷⣟⣿⣿⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣗⠊⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠉⠛⠿⣾⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡗⣾⡻⣿⣿⣷⣽⣿⣿⣿⣧⣿⣿⡿⣿⣿⢹⡷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢳⡠⢭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠈⠙⠻⢾⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣷⣿⣿⣿⣿⣾⣻⣿⣿⣸⣿⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⠣⠀
⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠉⠛⠾⢴⣨⢇⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣼⠻⣿⣿⣿⡻⣿⣷⣿⣯⣿⣟⣿⣇⡹⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡈⣄⠶⡝
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠈⠉⠛⠺⢶⣆⣿⢽⣻⣿⡇⣿⠇⡿⢿⠀⡇⡟⣿⣿⣯⣻⣿⣿⡿⣿⣿⣿⣶⢌⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢜⣩⣴⣾⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠈⠙⠻⢿⣏⡐⡯⠀⡇⢸⠀⡇⡇⡗⡎⡿⣿⣯⣻⡇⣟⣿⣿⣿⡈⠡⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠛⣋⣥⠞
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠉⠓⠶⣧⣺⠈⡇⣧⣷⡧⡇⣿⣝⣿⣷⣿⣿⣿⣿⡇⣀⠈⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡧⠟⠀⠀
⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡉⠙⠳⢿⣽⣿⡇⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⠀⢄⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠤⠀⠄⡀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣶⣦⣌⣙⠓⠿⣿⣿⣿⢸⣿⣿⣿⣿⢰⣦⣀⠀⢸⢸⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡳⢭⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⠿⢿⣿⣶⣦⡍⣽⣸⣿⣿⣿⣿⠀⠀⠉⠃⠈⠘⠛⣿⣿⣿⣿⣿⣯⠁⠀⠐⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⡁⠐⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⢟⡯⠿⣿⣿⣿⠀⠈⠉⠀⣀⡇⡌⢙⣼⠉⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣈⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⡆⠈⠉⠀⡄⠀⠀⡯⡄⠁⠀⠈⠁⠈⠈⠁⠀⠀⠀⢾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢡⣠⣥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇⣀⡀⡀⢀⣀⣠⣀⣀⡿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠁⠙⣞⡀⣀⡀⣀⣀⣀⡀⢀⣤⣤⡥⠀⠀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠤⠀⠿⠼⠿⠿⠿⢛⢚⠓⠒⡒⡨⠭⣭⣹⠭⢿⣴⣶⣼⣿⣿⡿⠗⠀⢠⣤⣤⣶⡶⣄⣾⠇⢩⣵⣷⣿⣿⣿⣿⣿⣷⠈⠘⠙⠛⠒⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣼⢋⣁⡴⣀⣥⣦⡀⠙⠏⢷⣴⠟⣽⣷⣿⣿⣿⣿⠿⠿⠛⠛⠉⣉⣤⣶⡇⡐⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣷⣤⣶⠄⠀
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡿⣻⣷⣻⡭⣯⠁⠂⠀⠐⡄⣀⣟⠛⠋⠉⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣷⣇⣿⣿⣿⡿⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣛⢷⣤
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡟⣰⠉⠸⠋⠺⠋⣀⣀⠀⠀⠀⠉⢻⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣯⠟⠁⢠⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣝⠿⠉⠀⠉
⠀⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠀⠀⠀⣿⢹⠀⢐⠀⢀⣤⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⠟⠁⠀⠈⠉⠁⠈⠀⠀⠁⠀⠻⣿⣟⢿⣧⠛⣻⣿⣗⡄⠠⠄
⠀⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣰⠀⢺⡄⢸⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠞⡫⠉⠀⠀⠀⢀⡞⠠⠄⢙⣛⣛⣻⣄⢢⠏⠈⢻⡂⠘⠿⢷⣶⡀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠉⠫⠕⢀⣈⣬⣾⣿⣿⣿⣿⣿⣟⣿⣿⡿⠟⣡⢞⠵⠌⠀⠀⠀⠀⠀⡼⠀⠀⠀⠶⢒⣚⣶⣮⣴⣅⣀⣠⣬⡂⠀⠈⠫⠙⠃
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⢀⣀⣤⣶⣂⣀⣤⣤⣶⣶⣶⣿⣿⣿⢧⣿⣟⠻⠿⠿⠞⢿⡿⠋⣠⣞⠑⠕⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠹⠯⠽⢟⣛⣋⠉⠓⠶⢤⣈⡀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⣛⣛⡛⠛⠛⠛⣛⠛⢀⣴⣬⣟⠿⠛⣋⣥⣴⣾⣿⣿⣿⣿⠿⠟⠓⠫⠙⠋⠉⠉⠉⠉⣀⣾⣿⣼⣼⣽⡯⠉⣠⠞⠣⠂⠊⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠯⠭⣉⣑⣦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⠻⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⢸⢉⠛⢛⢛⣏⠛⡟⡟⢛⡛⠛⢛⢛⣛⣟⣋⠹⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣁⣀⣑⣈⣀⣃⣈⣈⣀⣀⣙⣀⣈⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⢿⠿⠿⠿⢿⡿⡿⠿⢿⣿⠿⢿⠿⠿⡿⠿⠿⢿⢿⣿⠿⢿⡿⠿⡿⢿⠿⠿⠿⡿⠿⢿⠿⠿⣿⢿⡿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡗⠨⢸⢸⢨⠀⠀⡘⠇⡇⠬⢸⣇⠺⢂⠀⣥⡇⠭⠇⣄⢸⣿⠨⠀⡐⠗⣀⠸⢠⢨⡁⠇⠻⢺⠨⠽⣿⠸⠿⡇⣿⠸⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠻⠿⠿⠿⠿⠿⡿⠟⠿⢿⠛⠛⠟⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡷⠶⠶⠶⠶⠾⠶⠶⠷⠶⠾⠿⠶⠷⠾⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⢹⣶⡶⠶⣶⡶⣶⣶⣶⣶⣶⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣸⣿⣷⣤⣦⣤⣤⣦⣴⣼⣿⣇⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⠛⠻⠿⡟⠿⢿⠿⠿⠿⠿⡿⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠾⠶⢶⣶⣷⣦⣾⣶⣶⣶⣦⣷⣾⣼⣿⣿⣘⣛⣿⣧⣭⣭⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣸⣯⣤⣤⣬⣤⣤⣥⣥⣤⣭⣬⣥⣽⣦⣭⣭⣤⣤⣬⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣥⣭⣤⣬⣸⣈⣥⣿⣿⣿⣿⣿⠰⠶⣿⡏⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⢸⣿⠛⠛⠛⢛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢻⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣼⣷⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⣿⡟⠿⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⢿⡟⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣷⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⡿⠿⠟⠿⠟⣿⡇⠤⠠⠠⠤⡄⠇⠤⡤⢤⢠⡤⠤⠤⡤⠠⠤⠤⢼⠤⠤⠧⠄⣴⠤⢤⠦⠤⢤⠀⠄⢢⡧⠤⠤⡼⠤⣤⠼⠄⠤⣤⣤⣼⣿⠿⠿⠟⠿⢻⢿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣿⣇⣀⣀⣂⣀⣹⣓⣆⣱⣀⣛⣐⣒⣀⣉⣰⣶⣶⣾⣶⣶⣾⣶⣷⣶⣾⣶⣶⣾⣶⣷⣾⣶⣶⣶⣶⣷⣷⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠖⠶⢲⠶⡶⠶⠶⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣧⣤⣤⣤⣼⣿⣧⣤⣤⣥⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣼⣤⣧⣤⣤⣤⣼⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠒⠒⠒⠂⠀⠁⠰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 532

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    Gemini version at gemini://gemini.techrights.org/2022/12/04/sirius-office-manager/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.04.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Office_Manager_in_Company_Without_an_Office⠀✐


Posted in Deception, Free/Libre_Software at 12:07 am by Dr. Roy Schestowitz


Sirius ‘Open Source’, where managers do not use Open Source


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Louise Menezes, Office Manager at Sirius: Without any
 qualifications; Basically tick boxes on everything, then pay a fee/cert mill;
            All the qualified  managers left; There is no office⦈


Summary: Imagine having an “Office Manager” in a_company_that_does_not_even
have_an_office. Welcome to corporate posturing.


⣿⣿⣿⡿⠿⢿⡛⠛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢃⣸⠀⡁⣁⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣁⣍⣈⣀⣇⣠⣁⣗⣈⣹⣝⣁⣷⣈⣉⣉⣁⣇⣉⣗⣀⣲⣨⣘⣇⣀⣃⣿⣀⣉⠉⣏⣉⣹⣈⣧⣤⣹⣈⣹⣘⣎⣨⣗⣂⣀⣢⣻⣀⣎⣸⣳⣁⣁⣯⣉⣉⣁⣉⣈⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢛⠟⢟⡿⢿⠻⢿⢿⢟⣟⣟⢿⠻⠿⠿⠿⠿⠿⢿⠛⠻⢻⢻⠛⣻⢛⠛⠛⠿⠿⡟⡟⠿⠿⠿⠿⠿⢿⡿⡻⡛⠟⠿⠿⡿⠟⣻⠻⢻⠻⡟⢻⡿⠿⢻⠛⡟⣟⢟⢻⠛⠻⠻⠿⢿⣿⠛⣛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣶⣾⣷⣶⣾⣾⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣾⣶⣷⣾⣶⣶⣾⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣾⣤⣷⣶⣷⣶⣿⣾⣿⣾⣿⣷⣶⣶⣷⣿⣶⣾⣶⣾⣶⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣑⣑⣧⡾⣪⣈⣉⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠻⠟⠿⠿⢿⢿⠿⣿⠿⠿⢿⡿⠻⠿⡿⣻⢻⡛⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⠿⡿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⠿⠿⡿⠻⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⡟⠿⡟⠻⣻⠛⢻⠿⢿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣷⣷⣿⣷⣥⣷⣾⣿⣷⣷⣶⣶⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣿⣿⣷⣶⣶⣷⣶⣶⣿⣼⣶⣾⣧⣿⣶⣷⣷⣶⣿⣶⣶⣶⣶⣶⣾⣶⣼⣶⣶⣶⣷⣶⣷⣶⣾⣶⣾⣶⣷⣷⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣩⣩⣏⣭⣉⣩⣏⡉⣉⡍⢹⣭⣍⣉⡏⣩⣉⢈⣉⣉⣏⣉⣈⣨⣇⣍⣉⣭⣍⣉⣩⣉⣏⣉⣏⣉⣉⣉⣉⣉⣉⣥⣋⡩⢻⣉⣉⣨⣈⣉⣍⣹⣀⣈⣾⣗⣗⣖⣑⣡⣿⣹⣝⣅⣗⣁⣀⣸⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠿⠿⠟⠿⠿⡟⠿⢿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣶⣾⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣿⣷⣶⣷⣶⣾⣶⣴⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 611

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/12/04/sirius-open-source-has-kings/#comments
    Gemini version at gemini://gemini.techrights.org/2022/12/04/sirius-open-source-has-kings/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.04.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Kings_Instead_of_Open_Consultation_Among_Peers⠀✐


Posted in Deception, Free/Libre_Software at 7:30 pm by Dr. Roy Schestowitz


      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Sirius Open Source: I'm the boss, always right⦈


Summary: In Sirius there’s no room for debate, even among half a dozen or so
technical colleagues; decisions are made in the dark by a tightly-knit cabal
(with rather childish superhero cartoons as their avatars) and then imposed on
everybody else (hardly democratic, not sane)


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

                    ䷩ 𝚕𝚒𝚗𝚎 1696

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.04.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_04/12/2022:_Fosshost_Shudown_and_OpenIndiana_Hipster_2022.10⠀✐


Posted in News_Roundup at 6:44 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Kernel_Space
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o Reviews
          o New_Releases
          o Debian_Family
          o Canonical/Ubuntu_Family
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Health/Nutrition/Agriculture
          o Security
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o ⚓ H2S Media ☛ 5_Reasons,_why_Hackers_Use_Kali_Linux?_–_Linux
            Shout⠀⇛


                 Kali is the most popular and commonly used Linux by
                 hackers to perform penetration testing or hacking.
                 However, nowadays “hackers” term is not only used for the
                 wrong group of people to perform “Black hat hacking”.
                 There are ethical hackers those do white hat hacking to
                 find out the security loopholes and make our system more
                 secure and better.


                 Hence, Kali Linux distribution is widely used specialized
                 Linux for security and penetration testing of IT systems.
                 Out of the box, Kali Linux which is based on Debian
                 offers numerous tools to perform various hacking and
                 testing tasks.


                 For the Desktop interface by default, KALI uses XFCE,
                 however, GNOME & KDE are also available. It is an open-
                 source project, developed by Offensive Security, and is
                 aimed primarily at professional users but can also be
                 used by private individuals.


                 Earlier Kali Linux was known as BackTrack. It can be
                 booted into a virtual machine and installed on a 32-bit
                 or 64-bit x86 system as well as on computers with ARM
                 architecture.


                 Even the single-board computer Raspberry Pi can also be
                 operated with the Kali distribution. For some Android-
                 based devices, the penetration testing platform NetHunter
                 exists, which originated from Kali Linux.


          o ⚓ Bleeping Computer ☛ Open_source_software_host_Fosshost_shutting
            down_as_CEO_unreachable⠀⇛


          o ⚓ Linux Links ☛ Linux_Around_The_World:_USA_–_North_Dakota_–
            LinuxLinks⠀⇛


                 We cover events and user groups that are running in the
                 US state of North Dakota. This article forms part of our
                 Linux Around The World series.


          o ⚓ Linux Made Simple ☛ Linux_Weekly_Roundup_#212⠀⇛


                 Welcome to this week’s Linux Weekly Roundup. We had these
                 releases this week; NixOS 22.11, PCLinuxOS 2022.11.30,
                 ArcoLinux 22.12.02, OpenIndiana 2022.10, Linux Mint 21.1
                 Beta, and KDE neon 20221202.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ We_Should_Stop_Labeling_Linux_Distros_“Easy”_And
                  “Hard”⠀⇛


                       One of the things that bothers me is how the people
                       in the Linux community (including myself at times)
                       love to label distros as “easy” or “hard.” I think
                       those terms are not very descriptive.


                # ⚓ Video ☛ These_Webcams_Now_Slightly_Less_Broken_On_Linux_–
                  Invidious⠀⇛


                       A while back I did a video on new IPU6 cameras on
                       the Intel Alder Lake laptops that were completely
                       and still are useless on Linux out of the box and
                       they’re soon going to be slightly less annoying to
                       work with.


                # ⚓ Video ☛ Ubuntu_Unity_22.10_Review_|_Unity_is_back_from_the
                  DEAD!_(NEW)_–_Invidious⠀⇛


                       This is the all-new Ubuntu Unity 22.10. The newest
                       addition to the Official Ubuntu Flavors brings the
                       nostalgic unity desktop back and I’m thrilled. The
                       stunningly gorgeous looks, simple and sleek user
                       interface, quick and nimble performance.


                # ⚓ Video ☛ How_to_install_Synfig_Studio_on_Linux_Mint_21_–
                  Invidious⠀⇛


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


          o § Kernel Space⠀➾


                # ⚓ Linux ☛ Linux_6.1-rc8⠀⇛


                       So we've finally started calming down, and rc8 is
                       noticeably smaller
                       than previous release candidates.

                       So everything looks good, and while the calming
                       down may have happened
                       later than I wished for, it did happen. Let's hope
                       this upcoming week
                       is as quiet (or quieter).

                       The changes here are few enough that scanning
                       through the shortlog
                       below should give you an idea of what's been going
                       on, but it's
                       basically small changes spread all over. Nothing
                       particularly stands
                       out to me.

                       I'm also happy to see that I already have a few
                       pull requests
                       scheduled for when the 6.2 merge window opens up,
                       so some people are
                       being proactive and want to have everything already
                       lined up for a
                       calm holiday season. Hint, hint.

                                       Linus
          o § Instructionals/Technical⠀➾


                # ⚓ ID Root ☛ How_To_Install_Drupal_on_Rocky_Linux_9_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Drupal on Rocky Linux 9. For those of you who
                       didn’t know, Drupal is a powerful content
                       management system that can help you grow revenue
                       and establish long-term loyalty with your customers
                       by having a fast and reliable website. Drupal
                       provides a robust content management tool with
                       sophisticated APIs for multichannel publishing.


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


                # ⚓ Make Use Of ☛ How_to_Install_Ubuntu_on_VMware_Workstation⠀⇛


                       Ubuntu is one of the most popular Linux
                       distributions out there. Even if you are a Windows
                       user, you may have heard of Ubuntu and its features
                       from your peers. It has lower system requirements
                       than Windows and can help you re-purpose your old
                       PC.


                       But what if you don’t want to install it directly
                       on your machine? We understand your skepticism
                       about trying out a new operating system which is
                       why you can try Ubuntu on a virtual machine. Here’s
                       how you can install Ubuntu on VMware.


                # ⚓ Ubuntu Pit ☛ 17_Best_Tips_To_Speed_Up_Your_Ubuntu_Linux
                  [Ed: Not new but newly updated]⠀⇛


                       Ubuntu Linux is a polished Debian-based Linux
                       distro; however, you may start to experience some
                       system lag days after installation. There are many
                       reasons this might happen. If you want to speed up
                       your Ubuntu desktop performance, then follow these
                       simple tips and tweaks. These tips will help you
                       smooth out your system performance so that you can
                       do your regular tasks more easily. You don’t have
                       to follow all of the tips, but even just a few of
                       them will make a big difference in the overall
                       performance of your Ubuntu system.


                # ⚓ Linux Made Simple ☛ How_to_install_Jelly_Drift_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Jelly Drift
                       on a Chromebook.


                       If you have any questions, please contact us via a
                       Rumble comment and we would be happy to assist you!


                       This tutorial will only work on Chromebooks with an
                       Intel or AMD CPU (with Linux Apps Support) and not
                       those with an ARM64 architecture CPU.


                # ⚓ Ubuntu Handbook ☛ PyCharm_2022.3_Released!_How_to_Install
                  in_Ubuntu_22.04_|_20.04_|_UbuntuHandbook⠀⇛


                       PyCharm Python IDE 2022.3 was finally released a
                       few days ago. Here are the new features and how to
                       guide for installing it in Ubuntu Linux.


                # ⚓ Major Hayden ☛ Clocks_in_multiple_time_zones_with
                  i3status⠀⇛


                       Many of my coworkers are on Central European Time
                       (CET) and they’re seven hours ahead of me (most of
                       the time). Then there are those weird times of year
                       where they move their clocks for Daylight Savings
                       Time before we do in the USA.


                # ⚓ The New Stack ☛ Kubernetes_101:_Install_Kubernetes_on_Rocky
                  Linux_–_The_New_Stack⠀⇛


                       Kubernetes is an incredibly powerful container
                       orchestrator that can deploy and manage
                       containerized applications at scale with more power
                       and flexibility than any other tool on the market.


                       Thing is, Kubernetes is hard. Really hard. With so
                       many moving pieces, developing an application or
                       service to be deployed to a Kubernetes cluster can
                       be an overwhelming challenge. It takes a lot of
                       skill and patience to get this right.


                       Given that Kubernetes container development itself
                       is such a challenge, you probably don’t want to
                       have to deal with yet more obstacles to get things
                       up and running. Guess what, installing Kubernetes
                       on a Linux server isn’t exactly the easiest thing
                       either.


                       Once upon a time, it was much simpler, thanks to
                       distributions like Ubuntu and the Docker container
                       runtime. However, the Kubernetes team decided to
                       strip Docker support from Kubernetes, which makes
                       using it on some operating systems a bit more
                       challenging. Kubernetes is an open source project
                       of the Cloud Native Computing Foundation.


          o § Games⠀➾


                # ⚓ Boiling Steam ☛ Best_Steam_Deck_Games_Released_in_the_Past
                  Week_–_2022-12-05_Edition_–_Boiling_Steam⠀⇛


                       Between 2022-11-28 and 2022-12-05 there were 119
                       new games validated for the Steam Deck. We use
                       several criteria such as popularity, ratings, and
                       more to identify the Best Steam Deck Games released
                       recently.


    * § Distributions and Operating Systems⠀➾


          o § Reviews⠀➾


                # ⚓ Boiling Steam ☛ HP_Dev_One_Laptop_with_Pop!_OS:_The
                  Definitive_Review_–_Boiling_Steam⠀⇛


                       So I got this shiny new piece of hardware from HP,
                       the HP Dev One laptop. A mobile workstation that
                       ships directly with Linux, in this case Pop!_OS
                       (yes, this is the right spelling). I won’t do any
                       kind of unboxing because I care very little about
                       packaging that gets disposed anyway. What really
                       matters is how solid the product is, and if you can
                       use it to good effect. Let’s dive into it!


          o § New Releases⠀➾


                # ⚓ NomadBSD_131R-20221130_is_now_available!⠀⇛


                       We are pleased to present the release of NomadBSD
                       131R-20221130.


                # ⚓ OpenIndiana_Hipster_2022.10_is_here_–_openindiana⠀⇛


                       As you may already have noticed we have released
                       new ISO and USB images for OpenIndiana Hipster some
                       days ago. As usual we have received many updates
                       via illumos-gate, eg. the latest Intel and AMD CPU
                       microcode updates, the latest time zone changes and
                       lots of enhancements for BHyVe and the internal SMB
                       server.


          o § Debian Family⠀➾


                # ⚓ Daniel Pocock ☛ Incinerated_workers_&_Debian_unhealthy
                  culture⠀⇛


                       In June, a worker at the Caterpillar factory fell
                       into a tank of molten iron and was instantly
                       incinerated. Health and Safety inspectors were
                       quick to determine that the lack of guard rails was
                       an obvious factor in the death.


                       Earlier this year I explored the huge volumes of
                       email experienced by Frans Pop before the
                       Debian.Day suicide. Like the Caterpillar forge,
                       debian-private and Debian in general lacks guard
                       rails.


                       Thinking about the Shaya Potter incident in 1998, I
                       decided to do the same thing that I did for Frans
                       Pop and chart the email volumes on debian-private
                       in the twelve months leading up to Potter’s
                       mistakes.


                       Potter appears to be quite a brilliant developer.
                       Reading through his history, I could only empathize
                       with his story. Potter was selected for an elite
                       internship at the Naval Research Laboratory while
                       still in the middle of high school. Back in 1995,
                       the Royal Australian Air Force (RAAF) had selected
                       twenty high school students to spend a week at the
                       Australian Defence Force Academy (ADFA) in
                       Canberra. They gave us nice certificates.


                       I wanted to know more about Potter’s story: what
                       really happened here? So I did the same thing that
                       I did for Frans Pop. Here is the chart, it shows
                       that email volumes on debian-private were steadily
                       growing at the time that Potter made these
                       mistakes. There is a lack of guard rails.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ 9to5Linux ☛ First_Look_at_Linux_Mint_21.1_Beta_with_the
                  Cinnamon_5.6_Desktop_Environment_–_9to5Linux⠀⇛


                       The beta version of the upcoming Linux Mint 21.1
                       “Vera” distribution release is here and it comes
                       with the latest Cinnamon 5.6 desktop environment,
                       so I took it for a quick test drive to see what’s
                       new.


                       Linux Mint 21.1 “Vera” is the second release in the
                       Linux Mint 21 series, which is derived from the
                       upstream Ubuntu 22.04 LTS (Jammy Jellyfish)
                       operating system and powered by the long-term
                       supported Linux 5.15 LTS kernel. This series will
                       receive security updates until 2027.


                       Linux Mint 21.1 is slated for release this
                       Christmas, but we don’t have an official date set
                       in stone, so it will be out when it’s ready. For
                       now, all we have is the beta version, which started
                       appearing earlier today through various of Linux
                       Mint’s mirrors around the globe. An official
                       announcement for the beta release will be made by
                       the Linux Mint team when all mirrors are synced
                       with the main download server.


                # ⚓ OMG Ubuntu ☛ Linux_Mint_21.1_Beta_is_Available_to_Download
                  –_OMG!_Ubuntu!⠀⇛


                       A brand new beta build of Linux Mint 21.1 “Vera” is
                       available to download.


                       Linux Mint 21.1 beta builds are up on the Linux
                       Mint servers for download, though the milestone is
                       yet to be “officially” announced. This beta is in
                       advance of a planned stable release later this
                       month. It is still based on the Ubuntu 22.04 LTS
                       release, albeit with scores of home-grown software
                       on top.


                       As updates go, Linux Mint 21.1 isn’t the biggest
                       one Mint has put out. “Vera” is more of a
                       collection of iterative improvements rather than a
                       mass of major new ones — exactly as most point
                       releases are.


                       At the heart of Linux Mint 21.1 is Cinnamon 5.6.
                       This is the latest stable release of the nimble
                       (and rather traditional) Cinnamon desktop
                       environment. It offers a few new features,
                       including the new Corner Bar applet we wrote about
                       last month. Corner Bar is enabled by default, and
                       lets you click the end of the panel to instantly
                       hide all windows and show the desktop.


                # ⚓ DebugPoint ☛ Linux_Mint_21.1_beta_is_now_available_for
                  testing⠀⇛


                       Linux Mint 21.1 is the first point release of the
                       21 series and will be released before Christmas
                       this year. Codenamed “Vera”, which was announced a
                       few weeks back, is now available for beta testing.


                       The beta testing is expected to continue for at
                       least a week before the final release. Since it is
                       the first point, the feature list is not at that
                       higher end. But some significant updates are
                       arriving in the final release.


                       Here’s what’s new.


                # ⚓ OMG Ubuntu ☛ Xubuntu_23.04_Adds_PipeWire_&_Flatpak_to
                  Default_Install⠀⇛


                       Both PipeWire, the newer and less buggy multimedia
                       stack, and Flatpak, the sandboxed package
                       management, have been adopted by Ubuntu’s
                       lightweight sibling. Other Ubuntu flavours adopted
                       PipeWire during the 22.10 cycle, and Ubuntu MATE
                       added native Flatpak support in its 22.04 LTS
                       release.


                       In the December development update Xubuntu’s Sean
                       Davis explains: “PipeWire has been reported to
                       improve many of the issues users have with
                       PulseAudio, including high CPU usage and Bluetooth
                       connection issues. Xubuntu 23.04 adds PipeWire,
                       WirePlumber, and the Bluetooth connection
                       libraries.”


                       And having used the tech on Ubuntu (and other
                       distros) a fair bit I have to say, anecdotal though
                       it is, I’m yet to encounter any major hiccups,
                       drop-outs, or codec issues.


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


          o § Programming/Development⠀➾


                # ⚓ Jussi Pakkanen ☛ Nibble_Stew:_Color_management,_this_time
                  with_PDF⠀⇛


                       In previous posts the topic of color management in
                       Cairo was examined. Since then people have told me
                       a few things about the issue. According to them
                       (and who am I do to proper background research and
                       fact checking, I’m just someone writing on the
                       Internet) there are a few fundamental problems with
                       Cairo. The main one is that Cairo’s imaging model
                       is difficult to implement in GPU shaders. It also
                       is (again, according to Internet rumors) pretty
                       much impossible to make work with wide gamut and
                       HDR content.


                       Dealing with all that and printing (which is what I
                       was originally interested in) seems like a too
                       large a mouthful to swallow. One thing lead to
                       another and thus in the spirit of Bender, I wrote
                       my own color managed PDF generator library. It does
                       not try to do any imaging or such, just exposes the
                       functionality that is in the PDF image and document
                       model directly. This turned out to take
                       surprisingly little work because this is a
                       serialization/deserialization problem rather than
                       an image processing one. You just dump the draw
                       commands and pixels to a file and let the PDF
                       viewer take care of showing them.


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ TheWeeklyChallenge/TWC_193:_Evens_and
                        Oddballs⠀⇛


                             In which we revisit seventh grade, and sing
                             in the key of “A”.


                      # ⚓ Rakudo_compiler,_Release_#158_(2022.12)_–_Rakudo
                        Compiler_for_Raku_Programming_Language⠀⇛


                             On behalf of the Rakudo development team, I’m
                             very happy to announce the December 2022
                             release of Rakudo #158. Rakudo is an
                             implementation of the Raku1 language.


                             The source tarball for this release is
                             available from https://rakudo.org/files/
                             rakudo. Pre-compiled archives will be
                             available shortly.


    * § Leftovers⠀➾


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Ubuntu Pit ☛ How_To_Stop_Being_Addicted_To_My_Phone?⠀⇛


                       Being addicted to one’s smartphone has now become a
                       global problem. Eventually, psychologists have
                       tracked down a new psychological disorder named
                       nomophobia which refers to the fear of being
                       without a smartphone. This problem is mostly seen
                       in teenagers and young people. Eventually, most
                       adults nowadays face problems in their work and
                       productivity just for their smartphone addiction.
                       As a result, the question of how to stop being
                       addicted to my phone is now a global question.


                       However, there are many different ways you can
                       follow to get rid of your phone addiction. We will
                       talk about them briefly in this content. While most
                       solutions are regarding self-control, there is a
                       technical way to overcome it. And it’s all about
                       the apps that help overcome phone addiction. So,
                       our focus will be learning about those besides
                       getting some tips to get rid of this problem.


          o § Security⠀➾


                # ⚓ Eric Hameleers ☛ New_update_for_Chromium_to_address_0-day
                  exploit_|_Alien_Pastures⠀⇛


                       Earlier last week Google released 108.0.5359.71. On
                       friday, I had finally built and uploaded Slackware
                       packages for this, when they released a quick fix
                       to plug an already actively exploited hole (CVE-
                       2022-4262).


                       [...]


                       Chromium packages for Slackware 15.0 and -current
                       will of course keep coming.


                # ⚓ Qubes_Canary_033_|_Qubes_OS⠀⇛


                       We have published Qubes Canary 033. The text of
                       this canary is reproduced below.


                       This canary and its accompanying signatures will
                       always be available in the Qubes security pack
                       (qubes-secpack).


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Para-bishops_and_the_infinite-dimensional_chessboard⠀⇛


                       If you have learnt chess, you would have learnt
                       that bishops have a particular handicap that no
                       other piece has: it cannot visit every square on
                       the board. In particular, given that the board is
                       chequered as it is in a FIDE chessboard, a bishop
                       is limited to half the squares on a board: if it
                       started on a white square, it cannot move to a
                       black square, and vice-versa. It is because of this
                       that pieces that cannot see all the squares on a
                       board are called colourbound.


                # ⚓ 🔤SpellBinding:_AUILMTH_Wordo:_LULLS⠀⇛


                # ⚓ Planescape_is_in_your_head⠀⇛


                       The good kind of prep is when I start with a one
                       page dungeon or something similar, add monsters,
                       roll for treasure, get inspired, start scribbling,
                       run out of space, add more paper… let the dungeon
                       flow!


          o § Technical⠀➾


                # ⚓ Reinventing_How_We_Use_Computers⠀⇛


                       Nearly two years ago, I put into words the dream I
                       had for a durable computer. A computer that would
                       be built for a lifetime. A computer that would not
                       do everything but could do 80% of what I expect
                       from it. I called this idea the Forever Computer.


                # ⚓ Hey_Debian,_How_Can_I_Help?⠀⇛


                       I’m running Debian Testing on some computers here
                       at home, and I’m well aware that it means that
                       stuff breaks every now and then. That’s fine. I
                       just wish there was something I could do beyond
                       waiting for a fix.


                       My latest example is the Raspberry Pi I have
                       connected to my TV. With the latest update Xorg
                       broke because it depends on fbturbo, which is only
                       available in the stable repo with a version that in
                       turn depends on an older version of another
                       package. To clarify the dependency issue is
                       something like this: package P has been updated to
                       1.1, but package Q depends on the 1.0 version of P.


                # ⚓ What_happened_to_mobile_as_a_platform?_(A_Rant)⠀⇛


                       So my partner switched over to android after the
                       final straw of dealing with the Apple ecosystem.
                       (It was too difficult to do anything beyond
                       explicitly what they ask of you, and they moved to
                       Linux a few months prior which added to the
                       frustration). They were lying in bed when they
                       asked me “what are some fun mobile games?”


                # ⚓ Cutting_off_unnecessary_complexity⠀⇛


                       So I’ve been meaning to get Monica-CRM
                       (monicahq.com) up and running for a few months,
                       because I like the idea of a personal CRM and have
                       a way to nurture my relationships. However, I’ve
                       run out of patience with it this weekend.


                # ⚓ Re:_Gemini_and_the_Golden_Age_of_Air_Travel⠀⇛


                       My original narration was moved a bit. I was
                       writing about a barrier that in my opinion is set
                       by the knowledge required to participate in the
                       Geminispace. So reading could be easy because it is
                       possible to use a HTTP proxy. But every aspect
                       besides that could be a high cliff for an average
                       newcomer. In the world of the so-called modern
                       browser, which had rid of a protocol name from the
                       address bar, a gemini:// prefix could be
                       mysterious. The concept of certificates, despite
                       it’s explored also by big tech companies, could be
                       a question. Understanding the base idea of
                       publishing easiness, that it so a simple text
                       protocol and you put only a text file on the
                       Internet, sounds like black magic when people
                       publish every information in WWW by web
                       applications. And of course, most utilities are
                       outside the seen world of an average user, who
                       can’t operate on a text file through the net. So…
                       we don’t have many gemlogs of young mothers, who
                       are discussing children feeding. But we have many
                       gemlogs which are about programming. And probably
                       in the world are enough young mothers who would
                       want to join here, but? We are in the programmer’s
                       bubble. And it’s a barrier to joining here.


                # ⚓ My_new_fridge_choose_issue…⠀⇛


                       So, actually, I have an issue. I have an old fridge
                       (has about ten years, maybe more, it is a second-
                       hand fridge) with a frost issue in the freezer part
                       (too much frost, maybe I should defrost my fridge
                       more often 😅) and I should change this since about
                       some months (or years, but I have good pretexts to
                       postpone it). I try to do some search, but for the
                       moment, I don’t found the good fridge for me, take
                       time to decide, said “yes, but I have to be
                       organized and chose the right moment to do the
                       change”. More generally, I have two ways to buy
                       things :


                # § Internet/Gemini⠀➾


                      # ⚓ Server_move_and_new_certificates⠀⇛


                             I’ve moved gemini.locrian.zone and vath.click
                             from their home on a DigitalOcean droplet to…
                             a different DigitalOcean droplet, because I
                             realized I had WAY more space allocated than
                             I needed, and it was costing me an extra $24
                             a year. I mean, I can afford that, but why
                             pay it if I don’t need to?


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



                    ䷩ 𝚕𝚒𝚗𝚎 2515

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.04.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_03/12/2022:_pgAdmin_4_Version_6.17⠀✐


Posted in News_Roundup at 10:41 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o New_Releases
          o Debian_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o SaaS/Back_End/Databases
          o Programming/Development
                # Perl_/_Raku
                # Python
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Linux_Foundation
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ E92:_Tech_Talk_w/_@DistroTube_–_Linux_Enthusiast_–
                  Open_Source_Advocate_–_Invidious⠀⇛


          o § Applications⠀➾


                # ⚓ OpenSource.com ☛ Make_your_Linux_computer_feel_faster_with
                  the_Xfe_file_manager_|_Opensource.com⠀⇛


                       Computers are like filing cabinets, full of virtual
                       folders and files waiting to be referenced, cross-
                       referenced, edited, updated, saved, copied, moved,
                       renamed, and organized. In this article, I’ll look
                       at a file manager for your Linux system.


                       Back before NVMe drives and 12-core processors,
                       applications could take seconds to launch. While
                       that wait time is fine for a big application like
                       LibreOffice or Blender, it’s a little painful when
                       it’s a tiny application you use frequently. 2
                       seconds times 10 file manager windows in an hour,
                       times 12 hours a day, is 4 whole minutes of wasted
                       time. OK, I admit that’s actually not that much
                       when you do the math, but ask anybody and they’ll
                       tell you that it felt like 4 hours. One way to make
                       a computer, whether it’s last year’s model or
                       something hot off the shelf, feel faster is to use
                       “lightweight” applications. An application is
                       usually considered lightweight when it’s designed
                       around minimal code libraries that don’t demand
                       much from your system’s resources.


                       The X File Explorer (Xfe) file manager is one of
                       those applications. It’s quick to launch, it
                       doesn’t feature fancy animations or effects, and it
                       has few dependencies beyond some basic libraries,
                       most of which are probably already on your Linux
                       system.


          o § Instructionals/Technical⠀➾


                # ⚓ LinuxTechi ☛ How_to_Install_Docker_Desktop_on_Ubuntu
                  22.04⠀⇛


                       In this tutorial, we walk you through the
                       installation of Docker Desktop on Ubuntu 22.04.


                       The conventional way of running and managing Docker
                       container images is on the command line. However,
                       this can be a daunting prospect for beginners who
                       are just getting started out with learning Docker.
                       And this is where Docker Desktop comes in.


                       Developed by Docker, Docker Desktop is a free and
                       user-friendly GUI application that allows users to
                       easily run and manage Docker containers and images
                       from their Linux PC without the need for executing
                       commands on the CLI.


                       Docker Desktop is a cross-platform application
                       which means you can install it on Windows, Linux,
                       and Mac. It is free for companies of up to 250
                       employees beyond which you need a paid
                       subscription.


                # ⚓ URLs_with_//_at_the_beginning — mina86.com⠀⇛


                       Just a quick message to remained/inform everyone
                       that relative URLs can start with a double slash
                       and that it means something different than a single
                       slash at the beginning. Specifically, such relative
                       addresses are resolved by taking schema of the
                       website they are on (and keeping everything else as
                       is).


                # ⚓ It’s FOSS ☛ How_to_Install_Firefox_ESR_in_Ubuntu⠀⇛


                       The snap version of Ubuntu is not to your liking?
                       Don’t like constantly changing things with every
                       Firefox release? You can try the Firefox ESR
                       version if you value stability over features.


                # ⚓ SparkFun Electronics ☛ Send_Sensor_Data_Over_LoRa_With_Our
                  New_Tutorial!_–_News_–_SparkFun_Electronics⠀⇛


                       We are on mission here at SparkFun to demonstrate
                       the simplest ways to send sensor data using
                       different wireless solutions. So far together we
                       have explored sending sensor data over wifi, but
                       what about longer range projects?


                # ⚓ FOSSLinux ☛ Bash_tr_command_explained_with_examples_|_FOSS
                  Linux⠀⇛


                       There are a lot of basic functionalities that we
                       don’t think about twice in our daily life. For
                       example, it is straightforward if you are trying to
                       use the find and replace function in your word
                       document. But what about when you cannot have a
                       beautiful interface? What if you need to program it
                       into your script?


                       There is the simple solution of using an if-else
                       statement, but that is too long and requires too
                       much effort. A quicker method must be there for
                       something as commonplace as this, which is
                       precisely what Bash offers.


                       Today we look at the tr command, which translates
                       (replaces), squeezes (removes repetition), or
                       deletes elements from the standard input and
                       provides a standard output.


                # ⚓ Linux Nightly ☛ OpenLiteSpeed_Default_Password_–_Linux
                  Nightly⠀⇛


                       After installing OpenLiteSpeed or LiteSpeed web
                       server on Linux, you may be wondering how to log in
                       to the admin panel. In this tutorial, you will
                       learn how to generate a username and password and
                       log in to the admin panel of OpenLiteSpeed web
                       server.


                       There is no default password for the admin page of
                       OpenLiteSpeed. Instead, run the script below to
                       configure a username and password for the web
                       server.


                # ⚓ Linux Nightly ☛ Bash_Script_Read_Input_–_Linux_Nightly⠀⇛


                       The read function allows us to prompt users for
                       input and read that data from within a Bash script
                       on Linux. In this tutorial, you will see multiple
                       examples on how to read input from a Bash script.


                # ⚓ Linux Nightly ☛ Linux_stress_Command_–_Stress_Test_CPU_–
                  Linux_Nightly⠀⇛


                       A performance test will put load on your Linux
                       machine and stress test components like the CPU,
                       memory, and hard drive. The stress Linux command is
                       an ideal utility to put load on a computer and push
                       your hardware to its limits. In this tutorial, you
                       will learn how to install and use the stress and
                       stress-ng commands and their various options.


                # ⚓ Linux Nightly ☛ How_to_Install_Pip_on_Kali_Linux_–_Linux
                  Nightly⠀⇛


                       pip is the package installer for Python. On Linux,
                       pip allows for easy installation of Python programs
                       and dependencies. For Python developers, pip is an
                       essential tool.


                       In the context of Kali Linux, pip is mostly used
                       for hacking scripts or to download dependencies
                       that hacking scripts rely on. Even if you don’t
                       write Python scripts yourself, you may still find
                       it necessary to install pip. In this guide, you’ll
                       see how to install pip on Kali Linux.


                # ⚓ Linux Nightly ☛ How_to_Install_Python_3_on_Kali_Linux_–
                  Linux_Nightly⠀⇛


                       In this tutorial, you will learn how to get the
                       latest version of Python and pip installed on Kali
                       Linux.


                # ⚓ Linux Nightly ☛ Update_System_Time_From_Command_Line_in
                  Ubuntu⠀⇛


                       In this tutorial, we will learn how to update the
                       system time and time zone on Ubuntu Linux. This can
                       be done from the command line terminal with the
                       timedatectl command to synchronize your system’s
                       time with official time servers.


                # ⚓ Linux Nightly ☛ Download_File_With_wget_Command_on_Linux_–
                  Linux_Nightly⠀⇛


                       Learn how to update the system time and time zone
                       in Ubuntu Linux by using the timedatectl command to
                       stay in sync with time servers.


                # ⚓ Linux Nightly ☛ How_to_List_Installed_Packages_With_dnf_–
                  Linux_Nightly⠀⇛


                       dnf is a package management tool used for RPM-based
                       Linux distributions like Fedora, Red Hat, CentOS,
                       AlmaLinux, Rocky Linux, and others. In this
                       article, we will show the useful dnf commands that
                       allow us to list installed packages.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Steam_Deck_OS_3.4_Preview_adds_support_for
                  8BitDo_Ultimate_Wireless_controller_dongle⠀⇛


                       Valve put out a small and sweet update for Steam
                       Deck OS (SteamOS) 3.4 Preview, which adds in
                       support for the 8BitDo Ultimate Wireless controller
                       dongle.


                # ⚓ Björn Wärmedal ☛ How_I_Ran_an_RPG_Con_4_Times_a_Year_For_a
                  Decade⠀⇛


                       I promised ~dozens to write this, so here we are 😊️


                       A week or so ago I wrapped up the 40th instalment
                       of a small Old School RPG convention I’ve run four
                       times a year since 2012. A disclaimer here is that
                       I didn’t actually run the first one, though I was
                       present.


                       But what do I mean when I say I’ve been running
                       this convention? Basically I mean that I’ve done
                       the administration and economy. How did I do it? By
                       cheating, of course. The typical expenses for a
                       convention is 1) rent, and 2) other stuff that I
                       don’t really know or care about. Maybe marketing?


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ DebugPoint ☛ Trinity_Desktop_Environment_R14.0.13_is
                        now_out_with_updates!⠀⇛


                             If you are one of those users who miss the
                             good ol’ KDE (3.5) look, then you can get it
                             via Trinity Desktop Environment (TDE). The
                             TDE is a fork of the KDE 3.5 desktop
                             environment developed by a small team of
                             volunteers. It’s a continuation of the KDE 3
                             desktop methodology, providing updates and
                             bug fixes for those who appreciate its
                             features and design.


                             Despite being a small and independent
                             project, TDE is still actively developed and
                             maintained, offering users an alternative to
                             more mainstream desktop environments. And
                             following the prior R14.0.12 release, the
                             thirteenth minor release brings a few
                             goodies.


                             The new minor release of Trinity Desktop
                             Environment (TDE R14.0.13) brings a few new
                             features and bug fixes. This is a release
                             summary.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Trend Oceans ☛ Distrobox:_Try_Any_Linux_Distribution_Inside_Your
            Terminal⠀⇛


                 Have you ever thought to taste exclusive RHEL or Arch-
                 based distribution tools in your Ubuntu or Debian system
                 (or vice versa)? Distrobox is then here for you; it is an
                 open-source wrapper for Podman or Docker (depending on
                 your choice) to provide you with the ability to install
                 whatever Linux system you want…


          o § New Releases⠀➾


                # ⚓ DebugPoint ☛ 4MLinux_41.0_stable_is_now_available_with_SDL
                  games_+_More⠀⇛


                       MLinux is a decade-old small Linux distribution
                       that focuses on four main capabilities: maintenance
                       (e.g., as a system rescue live CD), multimedia
                       (e.g., playing video DVDs), miniserver (using the
                       inetd daemon), and mystery (small Linux games). It
                       is independently developed and comes with 32-bit
                       images as well. A perfect lightweight Linux
                       distribution for older hardware.


                       The 4MLinux 41.0 series have been updated to its
                       stable version. This version includes tools for
                       editing documents such as LibreOffice and GNOME
                       Office, file sharing with DropBox, web browsing
                       with Firefox and Chromium, email with Thunderbird,
                       and more. It also includes a LAMP server setup and
                       programming languages like Perl, Python, and Ruby.


                       Here’s a summary of the changes.


          o § Debian Family⠀➾


                # ⚓ Ben_Hutchings:_Debian_LTS_work,_November_2022⠀⇛


                       In November I was assigned 24 hours by Freexian’s
                       Debian LTS initiative. I worked 9 of those hours
                       and will carry over the remainder.


                       I updated the linux (4.19) package to the latest
                       stable update, but didn’t upload it. I attended the
                       monthly LTS team meeting.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Cool_Pi_4_Model_B_–_A_much_faster
                  alternative_to_Raspberry_Pi_4_SBC_–_CNX_Software⠀⇛


                       Cool Pi 4 Model B is a powerful alternative to
                       Raspberry Pi 4 SBC with mostly the same form factor
                       and interfaces but equipped with a Rockchip RK3588S
                       octa-core Cortex-A76/A55 processor that will run
                       circles around the Broadcom BCM2711 SoC found in
                       the Raspberry Pi board.


                       We’ve already reviewed Rockchip RK3588/RK3588S
                       single board computers and mini PC such as Rock 5B,
                       Khadas Edge2 Pro, and Mekotronics R58, and we were
                       impressed by the performance, but if you prefer to
                       have such a board in Raspberry Pi 4 form factor,
                       then the Cool Pi 4 Model B might be for you.


                # ⚓ Linux Gizmos ☛ $10.80_RISC-V_AIoT_module_supports_Linux⠀⇛


                       The Sipeed M1s is a compact module integrating the
                       Bouffalo Lab BL808 RISC-V SoC module along with a
                       NPU. The device also provides WiFi/BL, 802.15.4
                       Zigbee connectivity and support for interfaces such
                       as UART, I2C, SPI, etc.


          o § Open Hardware/Modding⠀➾


                # ⚓ Ken Shirriff ☛ How_the_8086_processor’s_microcode_engine
                  works⠀⇛


                       In brief, the microcode in the 8086 consists of 512
                       micro-instructions, each 21 bits wide. The
                       microcode engine has a 13-bit register that steps
                       through the microcode, along with a 13-bit
                       subroutine register to store the return address for
                       microcode subroutine calls. The microcode engine is
                       assisted by two smaller ROMs: the “Group Decode
                       ROM” to categorize machine instructions, and the
                       “Translation ROM” to branch to microcode
                       subroutines for address calculation and other
                       roles. Physically, the microcode is stored in a
                       128×84 array. It has a special address decoder that
                       optimizes the storage. The microcode circuitry is
                       visible in the die photo below.


                # ⚓ Raspberry Pi ☛ Raspberry_Pi_audio_boards_for_your_hi-fi
                  projects⠀⇛


                       Back in 2020, we welcomed the IQaudio family of hi-
                       fi audio products into the Raspberry Pi family.
                       This was the first, and so far only, time we’ve
                       acquired electronic products from someone else,
                       rather than developing them ourselves: that we made
                       an exception for IQaudio is a testament to what
                       Gordon, Sharon, and Andrew had built together.


                # ⚓ Robert Heaton ☛ Gameboy_Doctor:_debug_and_fix_your_gameboy
                  emulator⠀⇛


                       Gameboy Doctor is a tool that compares your
                       emulator to an example emulator that passes
                       Blargg’s test ROMs. It finds the exact tick where
                       your emulator’s state diverges from the example,
                       helping you isolate and fix your bugs. You don’t
                       need to have implemented an LCD in order to use it,
                       and you don’t even have to be able to successfully
                       get any kind of pass/fail message back from Blargg!
                       All you need is a minimally functional CPU and
                       motherboard.


                # ⚓ Erich Styger ☛ Advent_Calendar_2022⠀⇛


                       It is already December 1st, and time for a new
                       Advent Calendar. This year the design includes
                       birch plywood with PMMA, SK6812 RGBW LEDs running
                       with a Raspberry Pi Pico board, building a small
                       village.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ GSM Arena ☛ Android_TV_13_is_officially_out_–_GSMArena.com
                  news⠀⇛


                # ⚓ 9to5Google ☛ What_Google_apps_have_animated_Android_splash
                  screens_[Gallery]⠀⇛


                # ⚓ Express ☛ Check_your_Android_phone_immediately_and_delete
                  these_popular_apps_now_|_Express.co.uk⠀⇛


                # ⚓ Make Use Of ☛ How_to_Add_Custom_Shortcuts_to_Your_Android
                  Quick_Settings_Menu⠀⇛


                # ⚓ Make Use Of ☛ How_to_Use_TeamViewer_Remote_Control_to
                  Remotely_Troubleshoot_Android_Devices⠀⇛


                # ⚓ Make Tech Easier ☛ How_to_Find_Downloaded_Files_on_Any
                  Android_Device⠀⇛


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


          o ⚓ Leah Oswald ☛ Scaling_the_Mastodon⠀⇛


                 I was going to write an article for a while now, but
                 there was too much work to do with the latest influx.
                 Together with my co-admin @rixx we run the chaos.social
                 instance. As of writing this, we are one of the biggest
                 and most active instances on the fediverse and one of the
                 oldest mastodon instances, starting mid of April 2017.
                 For the last 5 years everything was simple, one VM with
                 10 cores, 500GB NVMe SSD Storage and 32GB RAM. This VM
                 did everything from the database to the webserving. Then
                 Musk happened.


                 The first time we really had to scale our setup was in
                 May 2022 after Musk announced to buy twitter. We rented
                 another server with 4TB NVMe in a RAID1, 16 Cores, 32
                 Thread, and 128 RAM and migrated the database to this
                 server. And then there was Friday the 27h October 2022
                 with the headline that Musk finally bought twitter all
                 over the news. With this date, everything became very
                 complicated very quickly. In only two days, the scaling
                 in work load on the fediverse network increased, and most
                 of the larger instances got very slow. We fixed this in
                 only a few days, and this article is a summary about what
                 we did until now. I will keep it up to date with future
                 changes.


          o § SaaS/Back End/Databases⠀➾


                # ⚓ PostgreSQL ☛ PostgreSQL:_pgAdmin_4_v6.17_Released⠀⇛


                       The pgAdmin Development Team is pleased to announce
                       pgAdmin 4 version 6.17. This release of pgAdmin 4
                       includes 10 bug fixes and new features. For more
                       details please see the release notes.


                       pgAdmin is the leading Open Source graphical
                       management tool for PostgreSQL. For more
                       information, please see the website.


          o § Programming/Development⠀➾


                # ⚓ Rlang ☛ Exact_integral_of_a_polynomial_on_a_simplex⠀⇛


                       The paper Simple formula for integration of
                       polynomials on a simplex by Jean B. Lasserre
                       provides a method to calculate the exact value of
                       the integral of a multivariate polynomial on a
                       simplex (i.e. a tetrahedron in dimension three). I
                       implemented it in Julia, Python, and R.


                       Integration on simplices is important, because any
                       convex polyhedron can be decomposed into simplices,
                       thanks to the Delaunay tessellation. Therefore one
                       can integrate over convex polyhedra once one can
                       integrate over simplices (I wrote an example of
                       doing so with R).


                # ⚓ [Old] Bob Alexander ☛ Re-creating_a_Byte_Magazine_Cover_as
                  a_Photograph⠀⇛


                       Byte magazine was the leading personal computer
                       magazine in the 1970s and 80s. Every month, its
                       cover was adorned with a beautiful, surrealistic
                       painting by Robert Tinney, showing a mash-up
                       between computers and unrelated objects. The July
                       1977 issue featured an article about controlling a
                       model railroad with a computer, and so Mr. Tinney
                       painted a cover integrating a train with a computer
                       board. According to Mr. Tinney, this “Computer
                       Engineering” image is one of his most popular
                       creations.


                       I wanted to create a piece of art that appeared to
                       be a photograph of a real-life scene that Mr.
                       Tinney might have painted. My first step was to
                       obtain the components pictured in Tinney’s
                       painting. Some of them are no longer manufactured –
                       like the resistor and the big blue potentiometer
                       with the black thumbwheel – or expensive to buy
                       new, like the red transistor socket. I got what I
                       could from eBay and compromised with a white
                       thumbwheel on the potentiometer. I mocked up the
                       component layout on a perfboard, designed the
                       “circuit” (there isn’t actually a complete
                       electrical circuit here) in DipTrace and sent it
                       off to China to be manufactured.


                       (Projects like this are the main reason I use
                       DipTrace or KiCad instead of Eagle Lite. The PCB I
                       made is 5.5″ × 6″. The free version of Eagle would
                       not have allowed me to make a board that big.)


                # ⚓ Abhinav Sarkar ☛ Solving_Rock-Paper-Scissors_in_Type-level
                  Haskell⠀⇛


                       Let’s solve part 1 of today’s Advent of Code
                       challenge “Rock Paper Scissors” in type-level
                       Haskell.


                       Instead of using term-level programming as we
                       usually do, we make Haskell’s type system do the
                       work of calculating the solution. So the solution
                       is be known right after we compile the program, and
                       we do not even need to run the compiled program.


                # ⚓ Rlang ☛ Gaussian_Process_Regression_for_FEA_Designed
                  Experiments_–_Building_the_Basics_in_R⠀⇛


                       Why would GPR be a good choice for modeling data
                       produced by FEA? Well FEA is a deterministic
                       modeling process – the prediction for any set of
                       inputs (boundary conditions) is unique and
                       repeatable. There is no noise or experimental
                       error. This means a transfer function that passes
                       through every point in the training data would be
                       preferred. With a traditional regression model, the
                       flexibility needed hit every data point would
                       require many high order terms, sabotaging the
                       model’s predictive ability on new data. But GPR has
                       the amazing ability to swerve gently and fluidly
                       between data points, meeting each one perfectly on
                       its way to the next. This allows GPR to make
                       perfect predictions on the training data while
                       providing sound predictions in the areas in between
                       the training points.


                # ⚓ [Old]_It’s_Time_For_‘Maximum_Viable_Product’_|_by_Clive
                  Thompson_|_Debugger⠀⇛


                       “Feature creep” messes up a lot of good software.


                       We’ve all seen it happen to our favorite apps. We
                       get an early version, we thrill to it; it does
                       exactly what we want. We’re in love.


                # ⚓ The_broken_bridge_between_biologists_and_statisticians_|
                  The_coefficient_of_determination:_is_it_the_R-squared_or_r-
                  squared?⠀⇛


                       We often use the coefficient of determination as a
                       swift ‘measure’ of goodness of fit for our
                       regression models. Unfortunately, there is no
                       unique symbol for such a coefficient and both \
                       (R^2\) and \(r^2\) are used in literature, almost
                       interchangeably. Such an interchangeability is also
                       endorsed by the Wikipedia (see at: https://
                       en.wikipedia.org/wiki/Coefficient_of_determination
                       ), where both symbols are reported as the
                       abbreviations for this statistical index.


                       As an editor of several International Journals, I
                       should not agree with such an approach; indeed, the
                       two symbols \(R^2\) and \(r^2\) mean two different
                       things, and they are not necessarily
                       interchangeable, because, depending on the setting,
                       either of the two may be wrong or ambiguous. Let’s
                       pay a little attention to such an issue.


                # ⚓ Version_0.13.0_of_NIMBLE_released_–_NIMBLE⠀⇛


                       We’ve released the newest version of NIMBLE on CRAN
                       and on our website. NIMBLE is a system for building
                       and sharing analysis methods for statistical
                       models, especially for hierarchical models and
                       computationally-intensive methods (such as MCMC and
                       SMC).


                # ⚓ Finnstats ☛ Matthews_Correlation_Coefficient_in_R_–
                  finnstats⠀⇛


                       Matthews Correlation Coefficient in R, We can
                       evaluate a classification model’s effectiveness
                       using a metric called the Matthews correlation
                       coefficient (MCC).


                # ⚓ rOpenSci_|_postdoc_1.0:_minimal_and_uncluttered_HTML
                  package_manuals⠀⇛


                       This post is part of a series of technotes about r-
                       universe, a new umbrella project by rOpenSci under
                       which we experiment with various ideas for
                       improving publication and discovery of research
                       software in R. As the project evolves, we will post
                       updates to document features and technical details.
                       For more information, visit the r-universe project
                       page.


                # ⚓ Geshan ☛ Using_Axios_timeout_to_make_your_application_more
                  efficient⠀⇛


                       Axios is one of the most popular JavaScript
                       libraries to do HTTP requests. It is an HTTP client
                       available for both the browser and Node.js. Setting
                       Axios timeout properly makes your application
                       perform efficiently even when the called API/URL is
                       not responding in a timely manner. In this post,
                       you will learn about Axios, its configs, and how to
                       set Axios timeout properly to not hamper your
                       application’s performance. Let’s get going.


                       [...]


                       In today’s world of highly interconnected services
                       and API economy, more often than not your
                       application will call either external HTTP APIs or
                       internal ones. Depending on how your company’s
                       applications and the communication between them is
                       architected, you are most likely calling some
                       internal HTTP APIs. In addition to that, your
                       applications might also be calling external APIs to
                       accomplish all sorts of tasks from some AI-related
                       calculation to creating shipments for a customer
                       order.


                       Imagine this, your shipment application is calling
                       the Auspost/DHL API to create a shipment and get an
                       Airway Bill (AWB) number to send to the customer.
                       Due to the last quarter of the year, the high
                       traffic season of Black Friday and Christmas sales
                       their API is responding extremely slowly. Usually,
                       the create AWB HTTP API would respond in under 200
                       milliseconds (ms) but due to the load and ongoing
                       issue at the time of calling it was responding in
                       around 3 seconds.


                       This means that your warehouse (fulfillment center)
                       staff are waiting for no direct benefit. In
                       addition, as the API responses are flaky it is
                       causing other issues too. This is where timeout on
                       HTTP requests comes in handy, which is what is
                       going to be discussed next.


                # ⚓ Paolo Melchiorre ☛ Paolo_Melchiorre_–_2022_Malcolm
                  Tredinnick_Memorial Prize⠀⇛


                       It is difficult to write what a great honor it is
                       for me that the Django Software Foundation has
                       awarded me the 2022 Malcolm Tredinnick Memorial
                       Prize, when it was announced to me via email by
                       Anna Makarudze I was not sure how this was
                       possible.


                       The two years leading up to this one were very
                       difficult for me, but this last one I’ve been
                       trying to make up for lost time and get back to
                       participating in the life of the Django community
                       in person. I have to admit that it was a reward
                       just that I was able to meet so many amazing
                       members of our community again, each of whom
                       deserves this award.


                # ⚓ Geshan ☛ A_beginner’s_guide_to_parse_and_create_XML_with
                  Node.js⠀⇛


                       Writing and parsing XML files with Node.js might
                       not be one of the first things that strike your
                       mind. On the contrary, the Fast XML parser has
                       millions of downloads per week on NPM. In this
                       post, you will learn how to validate and parse XML
                       with Node.js. You will also learn to generate an
                       XML file from JavaScript objects. Let’s get
                       started!


                # ⚓ Dave DeLong ☛ Adventures_in_Advent_of_Code⠀⇛


                       The nature of last night’s problem was that, when I
                       had a bunch of inputs, I could expect that there
                       was only a single common element between all of
                       them. After getting lucky and solving the problem
                       correctly, I started golfing my code to make it
                       terser. That’s when I started noticing something
                       odd.


                # ⚓ Hackaday ☛ Better_Coding_Through_Sketching⠀⇛


                       Back in the late 1970s and early 1980s, engineering
                       students would take a few semesters of drafting and
                       there would usually be a week or two of “computer-
                       aided drafting.” In those days, that meant punching
                       cards that said RECTANGLE 20,30 or something like
                       that and getting the results on a plotter. Then we
                       moved on to graphical  CAD packages, but lately,
                       some have gone back to describing rather than
                       drawing complex designs. Cornell University
                       researchers are trying to provide the same options
                       for coding. They’ve built a Juypter notebook
                       extension called Notate that allows you to sketch
                       and handwrite parts of programs that interact with
                       traditional computer code. You can see a video
                       about the work below.


                # § Perl / Raku⠀➾


                      # ⚓ Rakulang ☛ Day_4:_Give_the_gift_of_time_–_Raku_Advent
                        Calendar⠀⇛


                             Lately, Santa was getting lots of letters
                             that went a bit like this


                # § Python⠀➾


                      # ⚓ Martijn Braam ☛ Rewriting_my_blog_again⠀⇛


                             Since this is a fully standalone client side
                             webapp thing I can just host those four files
                             and then write a Python Flask application
                             that implements the same REST api that the
                             nodejs backend provided.


                             This is exactly what I did, the whole backend
                             is now a small Flask application that
                             implements the Ghost API in ~500 lines of
                             Python. It’s called Spook (since this is
                             dutch for ghost).


    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ This_Is_The_Future_Of_Waste_Management⠀⇛


                 Many of us have been asking for some time now “where are
                 our robot servants?” We were promised this dream life of
                 leisure and luxury, but we’re still waiting. Modern life
                 is a very wasteful one, with items delivered to our doors
                 with the click of a mouse, but the disposal of the
                 packaging is still a manual affair. Wouldn’t it be great
                 to be able to summon a robot to take the rubbish to the
                 recycling, ideally have it fetch a beer at the same time?
                 [James Bruton] shares this dream, and with his extensive
                 robotics skillset, came up with the perfect
                 solution; behold the Binbot 9000. (Video, embedded below
                 the break)


          o ⚓ Ruben Schade ☛ Demand_for_ads_on_the_receiving_end⠀⇛


                 But it’s Doc’s observation about the demand side that
                 piqued my interest. We’re so regularly told about the
                 supply side, from new tracking technologies to business
                 models. But if you ask someone on the proverbial street
                 if they like advertising, or even if they want it, you’ll
                 get the same answer.


          o ⚓ Ben Congdon ☛ On_Personal_Predictions⠀⇛


                 For the last couple years, I’ve maintained a spreadsheet
                 of personal predictions. It’s been a useful practice that
                 I would recommend. “Personal” in this context has 2
                 meanings: first, that I don’t preregister or publicly
                 publish these predictions; second, that the content of
                 some of the predictions is personal in nature.


                 I’ve had predictions & forecasting on my radar for
                 several years, but it really picked up during the
                 pandemic and 2020 elections. There was a plethora of
                 salient “in the world” things to predict, and in an
                 environment of heightened epistemic uncertainty, checking
                 your intuitions about how things “in the world” were
                 progressing felt quite valuable.


          o ⚓ Kev Quirk ☛ I’m_a_Fire_Starter!_–_Kev_Quirk⠀⇛


                 I recently moved to a house that has an open fire (my
                 first one), and I’ve quickly fallen in love with the
                 whole process of maintaining an open fire.


                 A little over a month ago my wife, 2 kids, 2 dogs, cat
                 and 4 fish tanks all upped sticks and moved to the Welsh
                 countryside. It’s a much bigger house than we had before,
                 with 2.5 acres of land, a double garage (for my
                 motorbikes) and a couple of outbuildings.


                 We’re hoping that it will be a much nicer way of life
                 down here. We intend to have a vegetable patch, more
                 animals and generally be closer to nature. A
                 smallholding, if you will.


                 This house has an open fire in the lounge, it’s actually
                 the first house I’ve ever lived in that has an open fire.
                 Lucky for us, my wife grew up with one, so she knows how
                 to lay it properly.


          o ⚓ Terence Eden ☛ Is_it_cheating_to_use_spell_check?⠀⇛


                 When I was a kid, our school had one computer per
                 classroom. Luxury!


                 Teachers had long-since given up on the state of my
                 handwriting. So I got special dispensation to write up
                 some of my work on whatever primitive word processor was
                 installed on the PC. With one caveat: no spell check!


                 Which, even as a ten year old, I thought was reasonable.
                 Learning to spell is an adult life skill. So using a
                 spell-checker was cheating.


                 Once I got to secondary school, it was assumed that I
                 knew how to spell. And there was no restriction on using
                 Wrd 2.0′s splel chek.


          o ⚓ Mark Dominus ☛ Whatever_became_of_the_Peanuts_kids?⠀⇛


                 One day I asked Lorrie if she thought that Schroeder
                 actually grew up to be a famous concert pianist. We
                 agreed that he probably did. Or at least Schroeder has as
                 good a chance as anyone does. To become a famous concert
                 pianist, you need to have talent and drive. Schroeder
                 clearly has talent (he can play all that Beethoven and
                 Mozart on a toy piano whose black keys are only painted
                 on) and he clearly has drive. Not everyone with talent
                 and drive does succeed, of course, but he might make it,
                 whereas some rando like me has no chance at all.


                 That led to a longer discussion about what became of the
                 other kids. Some are easier than others. Who knows what
                 happens to Violet, Sally, (non-Peppermint) Patty, and
                 Shermy? I imagine Violet going into realty for some
                 reason.


          o ⚓ The Washington Post ☛ It’s_not_your_imagination:_Shopping_on
            Amazon_has_gotten_worse [Ed: This Web site is owned by the owner of
            Amazon; it gets the facts wrong, issues "CORRECTION"]⠀⇛


                 A previous version of this article incorrectly reported
                 that the “Highly rated” label could be purchased. In
                 fact, Amazon selects who is featured under that label.
                 This article has been corrected.


          o ⚓ Slate ☛ How_the_Wordle_editor_is_ruining_wordle.⠀⇛


                 I realize, doctors, that technically that may not be
                 accurate. But as a 46-year-old with a toddler, I am often
                 propelled from my bed at 6 a.m. (or, God forbid, before)
                 with “Mommy, Mommy, Mommy, Mommygetup” and no room to lie
                 still and savor the warm covers. My body is awake and
                 moving around the apartment long before my brain has
                 caught up.


                 That’s where Wordle comes in. Once I have managed to sort
                 the child—or, more likely, my husband has taken over—I
                 like to slowly sip my morning tea while tapping the tiles
                 (dark, hard mode). The ritual lets my mind adjust to the
                 morning. I enjoy a tricky word—GLYPH, I see you. I find
                 double consonants sort of irritating (FOGGY???). But
                 mostly, I enjoy the random puzzle as a way to rev my
                 consciousness and prepare for the day.


                 When the New York Times announced, on November 7, that
                 Wordle would have an editor, I didn’t give it much
                 thought. How much could the mere presence of a person
                 really change it?


          o ⚓ Daniel Miessler ☛ Companies_as_Alaskan_Fishing_Boats⠀⇛


                 What if companies are supposed to be like Alaskan fishing
                 boats? You know, the kind on The Deadliest Catch.


                 So you have this tiny crew of total badasses. Everyone is
                 a superhero at their particular role because the crew
                 needs to stay extremely small to protect profits. The
                 captain is a dictator. The mission is clear. And bad
                 performances from anyone is immediately noticeable and
                 immediately dealt with.


                 You hurt your back? Sorry, you’re a great crew member,
                 but you’re not going out on this trip. You want to spent
                 more time with your brother who’s visiting? Cool, you’re
                 off the ship. This crew is for hardcore people only.
                 Remind you of anything?


                 [...]


                 So to me the question isn’t whether it’s an effective way
                 for people to run their businesses. The question is
                 whether it’s a model that we should pursue given the
                 effects on the people who work there.


          o ⚓ Terence Eden ☛ The_ethics_of_syndicating_comments_using
            WebMentions⠀⇛


                 This blog uses WebMention technology. If you write an
                 article on your website and mention one of my blog posts,
                 I get a notification. That notification can then be
                 published as a comment. It usually looks something like
                 this: [...]


          o ⚓ Roger Comply ☛ Joe_Nobody_declares_victory⠀⇛


                 In short, within 48 hours after I sent the first abuse
                 report, the phishing website was rendered useless, thanks
                 to actions taken by some of the notified service
                 providers. Based on my previous experiences with sending
                 abuse reports to service providers, I’ll admit that this
                 was not the outcome I expected.


          o ⚓ Hackaday ☛ Nixie_Display_Module_Is_Addressable_Via_SPI⠀⇛


                 There are plenty of SPI interface screens on the market,
                 but few of them have the charm of the good old Nixie
                 tube. [Tony] decided to whip up a simple three-Nixie
                 module that could be addressed via SPI. 


          o ⚓ Hackaday ☛ Build_Your_Own_Mini_Fogging_Cauldron⠀⇛


                 The best cauldrons are full of bubbling, steamy potions
                 of great magical potential. We don’t have many of those
                 in the real world, though, so sometimes we have to make
                 do with a simulacra. [wannabemadsci] has built just that,
                 with this fogging cauldron prop that uses no fog fluid or
                 dry ice, running solely with water instead.


          o § Science⠀➾


                # ⚓ Vice Media Group ☛ A_Huge_Satellite_Is_Now_One_of_the
                  Brightest_Objects_In_the_Sky,_Astronomers_Warn⠀⇛


                       The shiny glare of the 693-square-foot satellite,
                       as well as its voluminous radio activity, “could
                       severely hamper progress in our understanding of
                       the cosmos,” according to a statement released on
                       Monday by the International Astronomical Union.


                       Scientists involved with IAU’s Center for the
                       Protection of the Dark and Quiet Sky from Satellite
                       Constellation Interference (IAU CPS) also raised
                       alarms about AST SpaceMobile’s plan to deploy a
                       hundred satellites that are as big, or even larger,
                       than BlueWalker 3 (BW3) in order to build a
                       cellular broadband network designed to fill in
                       coverage gaps around the world.


                # ⚓ ACM ☛ AI_is_Solving_Classical_Computing’s_Quantum_Problem⠀⇛


                       Artificial intelligence (AI)—in particular, machine
                       learning (ML)— recently began to solve problems for
                       which quantum computers are targeted, according to
                       researchers at the California Institute of
                       Technology (CalTech), the Flatiron Institute (New
                       York City), and IBM (Yorktown Heights, NY).


                       “ML cannot emulate every quantum algorithm,” said
                       Hsin-Yuan Huang, a quantum information theorist at
                       CalTech, “but ML can emulate more quantum
                       algorithms than classical algorithms that do not
                       have learning abilities. For example, to solve the
                       problem of finding quantum ground states [lowest
                       energy levels], one typically wants to use
                       adiabatic [thermodynamic] quantum algorithms. But
                       we’ve proven that a classical ML model can learn
                       from data to predict these ground states
                       efficiently.”


                # ⚓ Sabine Hossenfelder ☛ Sabine_Hossenfelder:_Backreaction:
                  Consciousness_and_Quantum_Mechanics:_What’s_the_Links⠀⇛


                # ⚓ Freethink Media Inc ☛ Does_consciousness_change_the_rules
                  of_quantum_mechanics?_–_Big_Think⠀⇛


                       We can all agree that quantum entanglement is
                       weird. We don’t worry too much about it, though,
                       beyond some of its more practical applications.
                       After all, the phenomenon plays out on scales that
                       are vastly smaller than our everyday experiences.
                       But perhaps quantum mechanics and entanglement are
                       not limited to the ultra-small. Scientists have
                       shown that macroscopic (albeit small) objects can
                       be placed in entanglement. It begs the question: Is
                       there a size limit for quantum entanglement?
                       Carrying the idea further, could a person become
                       entangled, along with their consciousness?


                       Asking these questions not only lets us probe the
                       limits of quantum mechanics, but it could also lead
                       us to a unified theory of physics — one that works
                       equally well for anything from electrons to
                       planets.


          o § Education⠀➾


                # ⚓ uni Stanford ☛ Stanford_Law_School_will_no_longer
                  participate_in_U.S._News_Rankings,_joining_peer
                  institutions⠀⇛


                       Martinez also wrote that SLS believes the ranking
                       methodology “distorts incentives” and is “harmful
                       to legal education as a whole.” Specific concerns
                       included the discouragement of public interest
                       careers and inappropriate weight on student
                       expenditure and loan repayment programs. SLS
                       students who are also pursuing an MBA or a Ph.D.
                       are considered “unemployed” under the metrics of
                       the rankings, Martinez wrote.


                # ⚓ Vice Media Group ☛ ‘Most_Dangerous_Person_In_the_World’_Is
                  a_Teacher_Union_Leader,_Former_CIA_Director_Says⠀⇛


                       Weingarten has served as the president of the
                       American Federation of Teachers for the past 15
                       years, and is a well-known labor leader and
                       attorney in the United States. She has also been
                       the focus of targeted outrage from right-wing
                       pundits for the union’s position supporting COVID
                       mandates, for example. Fox News has smeared the
                       union and Weingarten specifically as being greedy
                       and attempted to paint a picture of kids failing
                       school due to unions. Weingarten has also been
                       vocal in supporting teachers against right-wing
                       attacks against teaching accurately on topics such
                       as race in schools.


                # ⚓ CER ☛ Doing_a_Little_Housekeeping_and_Rebranding⠀⇛


                       I have been reticent to post under a banner saying
                       “Computing Education Research” because this site
                       has pretty broad visibility now. There are many
                       more subscribers than the first few years.
                       Newcomers might come here with that title and
                       expect to read a newsletter or an authoritative
                       perspective on the field — that’s an overwhelming
                       responsibility. I recognize that I’m a senior
                       (read: “old”) voice in the field, but I am just one
                       of many voices in the field. Like any academic, I
                       want to share what we’re working on and what I’m
                       thinking about. I do not want to my posts here to
                       appear like I’m speaking for the field.


                       So, I have renamed the blog for a second time:
                       Computing Ed Research – Guzdial’s Take. This blog
                       represents my perspective. That’s how I’ve always
                       thought of the blog, but I want to make it
                       explicit.


          o § Hardware⠀➾


                # ⚓ Lionel Dricot ☛ Reinventing_How_We_Use_Computers⠀⇛


                       Unsurprisingly, most of the reactions I had from my
                       Forever Computer dream where about hardware. Every
                       idea, every project I saw could be summarised as
                       “How to make hardware we can repair while not
                       questioning what we do with this hardware?” The
                       (very interesting) Framework laptop is available
                       as… a Chromebook. This is like transitioning to
                       electric cars while having electricity generated
                       from coal and not questioning why we ride in the
                       first place. Oh, wait…


                # ⚓ Hackaday ☛ Bit-Banging_Bidirectional_Ethernet_On_A_Pi
                  Pico⠀⇛


                       These days, even really cheap microcontroller
                       boards have options that will give you Ethernet or
                       WiFi access. But what if you have a Raspberry Pi
                       Pico board and you really want to MacGyver yourself
                       a network connection? You could do worse than check
                       out this project by [holysnippet] that gives you a
                       bit-banged bidirectional Ethernet port using only
                       scrap passive components and software.


                # ⚓ Hackaday ☛ A_Cycle-Accurate_Intel_8088_Core_For_All_Your
                  Retro_PC_Needs⠀⇛


                       A problem faced increasingly by retrocomputer
                       enthusiasts everywhere is the supply of chips. Once
                       a piece of silicon goes out of production its
                       demand can be supplied for a time by old stock and
                       second hand parts, but as they become rare so the
                       cost of what can be dubious parts accelerates out
                       of reach. Happily for CPUs at least, there’s a ray
                       of hope in the form of FPGA-based cores which can
                       replace the real thing, and for early PC owners
                       there’s a new one from [Ted Fried]. MCL86 is a
                       cycle accurate Intel 8088 FPGA Core that can be
                       used within an FPGA design or as a standalone in-
                       circuit replacement for a real 8088. It even has a
                       full-speed mode that sacrifices cycle accuracy and
                       can accelerate those 8088 instructions by 400%.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ ABC ☛ FBI_director_raises_national_security_concerns_about
                  TikTok⠀⇛


                       Wray said the FBI was concerned that the Chinese
                       had the ability to control the app’s recommendation
                       algorithm, “which allows them to manipulate
                       content, and if they want to, to use it for
                       influence operations.” He also asserted that China
                       could use the app to collect data on its users that
                       could be used for traditional espionage operations.


                       “All of these things are in the hands of a
                       government that doesn’t share our values, and that
                       has a mission that’s very much at odds with what’s
                       in the best interests of the United States. That
                       should concern us,” Wray told an audience at the
                       University of Michigan’s Gerald R. Ford School of
                       Public Policy.


                       Those concerns are similar to ones he raised during
                       congressional appearances last month when the issue
                       came up. And they’re being voiced during ongoing
                       dialogue in Washington about the app.


                # ⚓ New York Times ☛ The_Next_Anti-Abortion_Tactic:_Attacking
                  the_Spread_of_Information⠀⇛


                       Now that abortion has been banned in more than a
                       dozen states, abortion opponents want to stoke
                       confusion about the legality of not just having an
                       abortion, but even of discussing the procedure. The
                       ultimate goal seems to be ensuring that women are
                       unclear about their options to obtain an abortion
                       or contraception, in their home state or elsewhere.


                       Signs of this trend can be found around the
                       country. In Nebraska, law enforcement obtained a
                       warrant to search a teenager’s private Facebook
                       messages, in which she told her mother of her
                       urgent desire to end her pregnancy. The mother is
                       now being prosecuted on charges of helping her
                       daughter abort the pregnancy by giving advice about
                       abortion pills.


                # ⚓ Michael West Media ☛ Dust_cloud_over_worker_safety:
                  asbestos_alarm_at_Sydney’s_first_skyscraper,_the_AMP_rebuild
                  –_Michael_West⠀⇛


                       Construction workers at Sydney landmark, the AMP
                       building have been exposed to asbestos. But those
                       responsible aren’t talking. Exclusive MWM report by
                       Callum Foote.


                       Construction workers refurbishing the AMP building
                       in Circular Quay have been exposed to asbestos. MWM
                       understands approximately 30 workers have so far
                       been required to undergo medical examinations.


                       Exposure to the deadly mineral appears to be a
                       significant failure of process, and has been
                       condemned by the construction union.


                       Other parties have not responded to questions by
                       MWM.


                # ⚓ Pro Publica ☛ The_Uranium_Industry_Continues_to_Poison_U.S.
                  Groundwater⠀⇛


                       In America’s rush to build the nuclear arsenal that
                       won the Cold War, safety was sacrificed for speed.


                       Uranium mills that helped fuel the weapons also
                       dumped radioactive and toxic waste into rivers like
                       the Cheyenne in South Dakota and the Animas in
                       Colorado. Thousands of sheep turned blue and died
                       after foraging on land tainted by processing sites
                       in North Dakota. And cancer wards across the West
                       swelled with sick uranium workers.


          o § Proprietary⠀➾


                # ⚓ Vincent Bernat ☛ Broken_commit_diff_on_Cisco_IOS_XR⠀⇛


                       Never trust show commit changes diff on Cisco IOS
                       XR.


          o § Linux Foundation⠀➾


                # ⚓ Future Car ☛ Electric_Automaker_XPeng_and_Bosch_Join_the
                  ‘ELISA_Project’_to_Promote_the_Use_of_Linux_in_Safety-
                  Critical_Automotive_Applications_–_FutureCar.com_–_via
                  @FutureCar_Media⠀⇛


                       Electric automaker and Tesla rival XPeng, along
                       with leading automotive component supplier Bosch,
                       have announce they have joined the ELISA Project to
                       promote the use of the Linux open-source software
                       in critical automotive safety applications of
                       electric and connected vehicles. The ELISA Project
                       was launched in Feb 2019 to create a shared set of
                       tools and processes to help companies build and
                       certify Linux-based, safety-critical applications.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ John Gruber ☛ Two_Weeks_Later_and_Twitter_Is_Still
                        Up⠀⇛


                             In the immediate aftermath of Twitter’s mass
                             layoffs and subsequent resignations, there
                             were widespread reports that the staffing
                             situation and collective brain drain were so
                             dire that the site would collapse. Two weeks
                             later — with World Cup soccer drama fueling
                             record usage — such concerns seem to have
                             been overblown.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Brr ☛ McMurdo’s_Automated_Teller_Machines⠀⇛


                             As of this writing, the McMurdo station store
                             accepts cash and cards. The post office
                             accepts only cards. Bars accept only cash.
                             Haircuts accept only cash. I know I’m going
                             to regret posting this, since it’ll likely
                             change in future years as technology evolves.


          o § Defence/Aggression⠀➾


                # ⚓ Scheerpost ☛ War_Is_a_Cancel_Culture_[VIDEO]⠀⇛


                       How Democrats, their pro-war Republican cohorts and
                       the media canceled the U.S. Senate campaign of ex-
                       Marine and US foreign policy official Matthew Hoh.


                # ⚓ Gustaf Erikson ☛ The_moral_bankruptcy_of_the_IR
                  “realists”⠀⇛


                       Only a so-called “international relations realist”
                       can present these demands for an end of the war in
                       Ukraine as “extremist”…


                       [...]


                       Note to conflation of two separate things here: the
                       supposition that NATO expansion caused Putin to
                       start the war and that the likely end of the war
                       will be a negotiated settlement or a frozen
                       conflict. I personally am a pessimist. I do believe
                       that a negotiated settlement is likely. But having
                       the ideal of a full Ukrainian victory in mind is
                       the morally correct one, not to try to aim for a
                       settlement a priori.


                       But it is not clear to me that NATO expansion left
                       Putin with only one option. Note that he himself
                       did not refer to NATO in the beginning of the war,
                       when he was sure he was going to force a regime
                       change in Ukraine within days. Now that Russia is
                       losing badly it’s “because of NATO”, but that’s
                       because he, like the author of this piece, cannot
                       see Ukrainians as a worthy foe.


                       By starting the war, Putin ensured that Finland and
                       Sweden applied to join NATO, suddenly increasing
                       Russia’s border with NATO by thousands of
                       kilometers. So Russia has now a worse position vis-
                       a-vis NATO than before the war, even discounting
                       the sanctions and the billions of treasure lost to
                       Ukrainian forces armed by NATO countries.


                # ⚓ Gatestone Institute ☛ Belgium’s_World_Cup_Football_Riots:_A
                  Symbol_of_the_Failure_of_the_Migration_Policy⠀⇛


                       In Brussels, Moroccans outnumber people of Belgian
                       origin in the under-18 age group; many schools are
                       attended exclusively by children of non-European
                       origin. In those public schools where parents have
                       the choice of religion classes, Islam is now
                       followed by a majority of pupils. Whether one
                       describes these changes as “diversity” or as a
                       “great replacement” is of little importance; over a
                       few decades the evolution has been considerable and
                       has modified the social fabric of Belgium’s cities.


                # ⚓ ABC ☛ More_charges_against_teen_for_ISIS-inspired_plot_show
                  threat_to_Chicago_may_have_been_more_serious⠀⇛


                       Investigators cited statements from other teenagers
                       allegedly involved in the plot, evidence that
                       Pelkey planned to bring guns and ammunition to
                       Chicago in addition to the explosive devices.


                       The homemade bombs, according to court records,
                       were cooked up and concocted out of easily
                       purchased items. That is the new ISIS MO: use what
                       you have and can find to maim and kill.


                # ⚓ New York Times ☛ Facebook_Failed_to_Stop_Ads_Threatening
                  Election_Workers⠀⇛


                       Facebook says it does not allow content that
                       threatens serious violence. But when researchers
                       submitted ads threatening to “lynch,” “murder” and
                       “execute” election workers around Election Day this
                       year, the company’s largely automated moderation
                       systems approved many of them.


                       Out of the 20 ads submitted by researchers
                       containing violent content, 15 were approved by
                       Facebook, according to a new test published by
                       Global Witness, a watchdog group, and New York
                       University’s Cybersecurity for Democracy.
                       Researchers deleted the approved ads before they
                       were published.


                # ⚓ Meduza ☛ ‘A_permanent_struggle’_Mayor_of_Kyiv_Vitali
                  Klitschko_spoke_to_RBC_Ukraine_about_the_aftermath_of_recent
                  attacks_on_the_city,_and_what_the_winter_months_hold_for_its
                  residents_—_Meduza⠀⇛


                # ⚓ Meduza ☛ ‘Packing_their_bags’_Russia_might_be_leaving_the
                  Zaporizhzhia_NPP_in_hopes_of_‘a_deal’_—_Meduza⠀⇛


                # ⚓ Hackaday ☛ Cargo_Culting_And_Buried_Treasure⠀⇛


                       I have no idea how true the stories are, but legend
                       has it that when supplies were dropped on some
                       Melanesian islands during WWII, some locals took to
                       replicating runway signs in order to further please
                       the “gods” that were dropping them. They reportedly
                       thought that making landing strips caused laden
                       airplanes to visit. Richard Feynman later turned
                       this into a metaphor about scientific theory – that
                       if you don’t understand what you’re doing deeply,
                       you may be fooling yourself.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Vice Media Group ☛ Sasha_Grey_Is_Not_Recruiting_Soldiers
                  for_the_Russian_Army⠀⇛


                       The image is a photoshop made from three separate
                       images. The original recruitment ad featured a
                       smiling soldier with the same message. The woman in
                       the uniform comes from a profile of a Russian
                       troop, and Grey’s face has just been layered on
                       top. This isn’t the first time Grey’s face has
                       appeared in weird Russian propaganda.


                # ⚓ Craig Murray ☛ Trains_(Mostly)_Planes_and_Automobiles_Part
                  2⠀⇛


                       When the papers were leaked of a law firm
                       representing many thousands of people and
                       enterprises hiding their assets in parliament, the
                       western media filtered the information and hid
                       everything connected to prominent western companies
                       and individuals. Instead they deliberately gave the
                       entirely false impression that the bulk of money
                       laundered through Panama is Russian, and made the
                       headlines entirely about Russian and Russian-linked
                       individuals, including a chef with tenuous
                       connections to Putin as an official caterer.


                       Out of 10 million documents leaked, about 120 were
                       actually made available as documents by the
                       journalists, and about a number 200 had their
                       contents referred to by mainstream media
                       journalists – how fully and how honestly we have no
                       way of knowing.


                       We live in a world of fake investigative
                       journalism. Access to the Panama Papers was
                       strictly controlled by a Washington-based entity,
                       the “International Consortium of Investigative
                       Journalists”. Their funders include [...]


          o § Environment⠀➾


                # ⚓ Counter Punch ☛ COP27_Continues_the_Climate_Summit_Ritual
                  of_Words_Without_Action⠀⇛


                       The 27th Conference of the Parties to the United
                       Nations Framework Convention on Climate Change, to
                       use the formal name for COP27, ended with what has
                       the appearance of a breakthrough: An agreement on
                       the establishment of a “loss and damage” fund for
                       Global South countries severely affected by weather
                       and environmental disasters triggered by global
                       warming, and for which they bear almost no
                       responsibility. This finally fulfills a pledge made
                       at the 2009 Climate Summit in Copenhagen. To read
                       this article, log in here or subscribe here. If you
                       are logged in but can’t read CP+ articles, check
                       the status of your access hereIn order to read CP+
                       articles, your web browser must be set to accept
                       cookies.


                # ⚓ Common Dreams ☛ ‘Turn_Off_the_Tap_on_Plastic,’_UN_Chief
                  Declares_Amid_Debate_Over_New_Global_Treaty⠀⇛


                       Hours before the first round of negotiations to
                       advance a global plastics treaty concluded Friday
                       in Punta Del Este, Uruguay, the leader of the
                       United Nations implored countries “to look beyond
                       waste and turn off the tap on plastic.”


                       “The push for an ambitious global plastics treaty
                       has only just begun.”


                # ⚓ Common Dreams ☛ Opinion_|_Rich_Countries_Have_an_Historic
                  Responsibility_to_Help_Global_South_Transition_to_Post-
                  Fossil-Fuel_Future⠀⇛


                       To keep the planet from overheating, there’s just
                       so much more carbon that humans can pump into the
                       atmosphere. From the onset of the Industrial
                       Revolution until today, humanity has used up
                       approximately 83 percent of its “carbon budget”—the
                       amount of carbon the atmosphere can absorb and not
                       exceed the Paris climate agreement’s aspirational
                       goal of a 1.5C degree increase in global
                       temperatures since the pre-industrial era. At the
                       current rate of emissions, the budget will be used
                       up within the next decade.


                # § Energy⠀➾


                      # ⚓ Erich Styger ☛ Energy_Crisis_in_Europe:_Optimizing_a
                        Building_from_4.5_to_2.4_MWh⠀⇛


                             Saving energy always makes a lot of sense,
                             now even more, both for the environment and
                             directly saving money. Luckily, I started
                             thinking about optimizing the electrical
                             energy used in my house back in 2021, and now
                             in 2022 it really pays off: The daily average
                             of 16 kWh/day (including heating and cooling)
                             came down to 7 kWh/day, or from 4.5 MWh/year
                             down to 2.4 MWh/year, or a reduction of 47%.


                             There were different areas contributing to
                             this very positive result: [...]


                # § Wildlife/Nature⠀➾


                      # ⚓ TruthOut ☛ EU’s_New_Climate_Plan_Will_Cause
                        Biodiversity_Loss_and_Deforestation⠀⇛


                      # ⚓ Meduza ☛ 700_dead_seals_wash_up_on_the_Caspian_shore
                        —_Meduza⠀⇛


                             650-700 dead seals were discovered in
                             Makhachkala, Dagestan, on the shores of the
                             Caspian Sea, reports the North Caucasus
                             department of the Russian Federal Agency for
                             Fishery.


          o § Finance⠀➾


                # ⚓ TruthOut ☛ With_No_Child_Tax_Credit,_Families_Are_Slipping
                  Back_Into_Poverty_Amid_Inflation⠀⇛


                # ⚓ TruthOut ☛ Pentagon_to_Spend_$200_Billion_on_New_Nuclear
                  Bomber_as_Millions_Live_in_Poverty⠀⇛


                # ⚓ TruthOut ☛ Railroad_Workers_Slam_Biden_for_Siding_With
                  Bosses_to_Avoid_Strike⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Once_Upon_a_Time_the_US_Taxed_the
                  Rich⠀⇛


                       Once upon a time, the United States seriously taxed
                       the nation’s rich. You remember that time? Probably
                       not. To have a personal memory of that tax-the-rich
                       era, you now have to be well into your seventies.


                # ⚓ Common Dreams ☛ Opinion_|_As_Millions_Face_Poverty,_Global
                  Food_Companies_Paid_Out_Nearly_15_Billion_to_Shareholders⠀⇛


                       The world’s biggest food companies have paid out
                       nearly £15bn to shareholders as spiralling prices
                       leave desperate families struggling to afford to
                       eat, openDemocracy can reveal.


                # ⚓ TechCrunch ☛ Kanye_West_isn’t_buying_Parler_after_all_–
                  TechCrunch⠀⇛


                       Despite a joint statement between Ye (fka Kanye
                       West) and Parler in October noting that the two had
                       reached an agreement for the rapper to buy the
                       social network, the purchase will not come to pass,
                       Parler-owner Parlement Technologies said today.


                       [...]


                       Well, there is the fact that earlier today West
                       praised Adolf Hitler and the Nazis during an
                       interview with none other than Alex Jones — himself
                       a person who was recently found liable for nearly
                       $1 billion in damages for spreading horrible lies
                       about the incredibly tragic Sandy Hook school
                       shooting.


                # ⚓ John Gruber ☛ Elon_Musk_Gets_Mail⠀⇛


                       And to be clear, Elon, you will lose, and you know
                       it.


                # ⚓ Michael West Media ☛ Google_Giggle:_Josh_Frydenberg’s
                  “world-first”_media_reform_a_hand-out_to_billionaire_mates_–
                  Michael_West⠀⇛


                       Josh Frydenberg’s “world-first” Media Code is a
                       world-first joke lapped up by a sycophantic media
                       enjoying secret cash payments from Google and
                       Facebook. Michael West reports on the hype and the
                       shameless Treasury review which endorses it.


                       Josh Frydenberg sallied forth with a fulsome pat on
                       the back this week … for himself.


                       “The Coalition’s ‘world-first’ Media Bargaining
                       Code was a ‘success’,” pronounced the former
                       Treasurer. A success indeed; a terrific success for
                       the Coalition’s media mates Rupert Murdoch, Peter
                       Costello and Kerry Stokes.


                       To be fair to Josh, he was only repeating what was
                       in the press. Josh’s “media reforms” had forced
                       Google and Facebook to pay millions in cash
                       (secretly) to Big Media. In return, the News Corp,
                       Nine, Guardian Australia and so forth sang the
                       praises of Josh’s “world-first”. Manufacturing
                       consent is a breeze, you just have to pay people.


                # ⚓ Michael West Media ☛ Qantas_profits_soar,_but_little_room
                  for_better_pay_for_staff_as_shareholders_re-Joyce⠀⇛


                       Qantas profit estimates just jumped again this week
                       when Alan Joyce threatened to axe regional routes,
                       ramping up pressure on politicians to stop the
                       looming industrial relations reforms. Michael
                       Sainsbury reports.


                       The priorities of Qantas chief executive Alan Joyce
                       and chairman Richard Goyder were on display again
                       this week, preferring the fortunes of shareholders
                       and executives over those on the front line of the
                       airline’s low altitude standards – staff and
                       customers. Joyce even reprised the age old Qantas
                       tactic of pressuring politicians by dangling the
                       idea he might shut down a regional route or two …
                       if industrial relations policy did not go his way.


                # ⚓ Financial Times ☛ Twitter’s_$5bn-a-year_business_hit_as
                  Elon_Musk_clashes_with_advertisers⠀⇛


                       Multiple top advertising agencies and media buyers
                       told the Financial Times that nearly all of the big
                       brands they represent have paused spending on the
                       social media platform, citing alarm at Musk’s ad
                       hoc approach to policing content and decision to
                       axe many of its ad sales team.


                       Musk, meanwhile, has sought to personally call
                       chief executives of some brands that have curbed
                       advertising in order to berate them, according to
                       one senior industry figure, leading others to
                       instead reduce their spend to the bare minimum
                       required so as to avoid further confrontation with
                       the billionaire entrepreneur.


                # ⚓ The Wall Street Journal ☛ Elon_Musk’s_Boring_Company_Ghosts
                  Cities_Across_America⠀⇛


                       The unsolicited proposal from Elon Musk’s tunnel-
                       building venture arrived in January 2020. To the
                       local transportation authority, it felt like
                       finding Willy Wonka’s golden ticket.


                # ⚓ A_ghost_to_most_–_Lawyers,_Guns_–_Money⠀⇛


                       While he brings his idiotic ideas to Twitter, it’s
                       worth noting that his hole-digging company is
                       basically vaporware that exists solely to undermine
                       actually potentially viable mass transit proposals…


                # ⚓ Common Dreams ☛ Protesting_Fuel_Poverty,_People_Tell_UK
                  Government_to_‘Keep_Everyone_Warm_This_Winter’⠀⇛


                       People in dozens of cities across the United
                       Kingdom hit the streets on Saturday to demand
                       immediate government action to prevent thousands of
                       struggling workers from freezing to death in their
                       homes this winter.


                       Demonstrators drew attention to the worsening
                       crisis of fuel poverty and called on lawmakers to
                       pick up more of the tab for skyrocketing bills,
                       fund home insulation, and accelerate clean energy
                       production—all of which would be made easier by
                       enacting a stronger tax on oil and gas
                       corporations’ windfall profits.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The_inside_story_of_Trump’s_explosive_dinner_with_Ye_and
                  Nick_Fuentes⠀⇛


                       “I wanted to show Trump the kind of talent that
                       he’s missing out on by allowing his terrible
                       handlers to dictate who he can and can’t hang out
                       with,” Yiannopoulos told NBC News. “I also wanted
                       to send a message to Trump that he has
                       systematically repeatedly neglected, ignored,
                       abused the people who love him the most, the people
                       who put him in office, and that kind of behavior
                       comes back to bite you in the end,” he added.


                       And, Yiannopoulos said, he arranged the dinner
                       “just to make Trump’s life miserable” because news
                       of the dinner would leak and Trump would mishandle
                       it.


                       Fuentes echoed the sentiment: “I hate to say it,
                       but the chickens are coming home to roost. You
                       know, this is the frustration with his base and
                       with his true loyalists.”


                       Trump fumed afterward that Ye had betrayed him by
                       ambushing him. “He tried to f[uck] me. He’s crazy.
                       He can’t beat me,” Trump said, according to one
                       confidant, who then relayed the conversation to NBC
                       News on the condition of anonymity to discuss
                       private conversations.


                       “Trump was totally blindsided,” the source said of
                       Fuentes’ presence. “It was a setup.”


                # ⚓ TruthOut ☛ Right-Wing_Extremist_Lauren_Boebert_to_Guide
                  Policy_on_House_GOP_Leadership_Team⠀⇛


                # ⚓ TruthOut ☛ Let’s_Honor_Kevin_Johnson_by_Dismantling_the
                  Systems_That_Failed_Him⠀⇛


                # ⚓ Maxim Tips ☛ Lies_about_Chatcontrol,_Part_1⠀⇛


                       Recently (2022-12-01), the European Commission
                       published an article about their planned
                       legislation (called chatcontrol by critics). While
                       the Commission has in the past cited statistics
                       which are wrong, the published article is so
                       stunningly bad in that almost every single sentence
                       is strongly misleading, a blatant lie or flat out
                       wrong. As it’s rather short, I’ll fully cite the
                       article and explain what’s wrong with each part. I
                       assume you have some familiarity with chatcontrol.
                       If not, you may want to read about what it is
                       before reading this post.


                # ⚓ The Verge ☛ Elon_Musk’s_promised_Twitter_exposé_on_the
                  Hunter_Biden_story_is_a_flop_that_doxxed_multiple_people⠀⇛


                       The emails show Twitter’s team struggling with how
                       to explain their handling of the New York Post
                       story that broke the news of Hunter’s leaked laptop
                       files — and whether they made the correct
                       moderation decision in the first place. At the
                       time, it was not clear if the materials were
                       genuine, and Twitter decided to ban links to or
                       images of the Post’s story, citing its policy on
                       the distribution of hacked materials. The move was
                       controversial even then, primarily among
                       Republicans but also with speech advocates worried
                       about Twitter’s decision to block a news outlet.


                       While Musk might be hoping we see documents showing
                       Twitter’s (largely former) staffers nefariously
                       deciding to act in a way that helped now-President
                       Joe Biden, the communications mostly show a team
                       debating how to finalize and communicate a
                       difficult moderation decision.


                # ⚓ The Spectator UK ☛ The_Taliban_and_Isis_are_in_a_battle_for
                  control⠀⇛


                       Isis and the Taliban both follow variations of
                       jihadist Sunni Islam, but they are ideological
                       enemies. The Taliban’s beliefs are drawn from the
                       Deobandi branch of Islam – which is less extreme
                       than the Wahhabi-Salafist form of Islam practised
                       by Isis (and also by al Qaeda). Many of the
                       Taliban’s beliefs come not only from Sunni Islam
                       but also the traditional Pashtun tribal way of life
                       in Afghanistan. Isis’s jihadi-Salafism places
                       greater emphasis on the ‘purity’ of anti-idolatry
                       than the Taliban. Crucially, the two groups also
                       disagree over nationalism: Isis rejects it, which
                       runs counter to the Afghan Taliban’s aims of ruling
                       Afghanistan.


                # ⚓ New York Times ☛ Twitter_Keeps_Missing_Its_Advertising
                  Targets_as_Woes_Mount⠀⇛


                       In tandem, Twitter was rapidly cutting its revenue
                       projections. The company previously forecast that
                       it would generate $1.4 billion in the last three
                       months of the year, down from $1.6 billion a year
                       ago because of the global economic downturn. But as
                       Twitter kept missing its weekly advertising
                       targets, that number slid to $1.3 billion, then to
                       $1.1 billion, two people said.


                       Elon Musk, Twitter’s new owner, has warned
                       repeatedly that his social media company faces dire
                       financial straits. Interviews with seven former
                       employees and internal documents seen by The New
                       York Times paint a fuller picture of Twitter’s
                       financial woes.


                # ⚓ Vice Media Group ☛ How_SBF_Created_the_New_Playbook_for
                  Manipulating_Washington,_D.C.⠀⇛


                       At the roundtable, Bankman-Fried—who,
                       characteristically, tweeted through the
                       event—played the role of the boy genius to an often
                       receptive crowd. “There were a lot of people there
                       who seemed to be taking some type of pleasure or
                       delight in the fact that they were in the same room
                       with him,” said Lee Reiners, a former financial
                       regulator and current policy director at the Duke
                       Financial Economics Center, who sat near the FTX
                       CEO at the roundtable. The few times Bankman-Fried
                       was attacked, he lashed out, saying at one point:
                       “Most of the traders on our platform know a lot
                       more about these contracts than many of the people
                       in this room.”


                # ⚓ Counter Punch ☛ Latin_America’s_New_Left⠀⇛


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ ABC ☛ Defeated_election_conspiracists_seek_to_lead
                        Michigan_GOP⠀⇛


                             All three candidates were endorsed by former
                             President Donald Trump and echoed his false
                             claims of a stolen election — although Dixon
                             pivoted away from her earlier statements
                             after she won the Republican primary for
                             governor.


                      # ⚓ Vice Media Group ☛ Anti-Vaxers_Celebrate_Twitter’s
                        New_COVID_Misinformation_Policy⠀⇛


                             Gold is the founder of America’s Frontline
                             Doctors, a pseudo-medical organization
                             devoted to spreading bad information about
                             COVID and vaccines. Her good mood was due to
                             a brief statement by Twitter that it will no
                             longer enforce its policy against misleading
                             information about COVID-19.


          o § Censorship/Free Speech⠀➾


                # ⚓ Meduza ☛ Moscow_libraries_pull_LGBT-themed_and_‘foreign
                  agent’_authored_books_—_Meduza⠀⇛


                       Moscow libraries are hiding books by authors who
                       have been declared “foreign agents,” or who are
                       critical of the war in Ukraine, as well as books
                       that authorities might consider “LGBT propaganda.”
                       Such books are being pulled from shelves, taken out
                       of circulation, and are not available to order
                       online, writes publication The Village, citing
                       sources in four Moscow libraries.


                # ⚓ Meduza ☛ Three_TV_Rain_employees_to_leave_network_over
                  firing_of_host_Alexey_Korostelev_—_Meduza⠀⇛


                       TV Rain hosts Margarita Lyutova (who also works as
                       a special correspondent for Meduza) and Vladimir
                       Romesky announced that they are leaving the network
                       after their colleague, Alexey Korostelev, was fired
                       over an on-air gaffe about the Russian army. 


                # ⚓ Meduza ☛ Chechen_blogger_and_Kadyrov_critic_Tumso
                  Abdurakhmanov_is_missing_in_Sweden_—_Meduza⠀⇛


                       Chechen opposition blogger Tumso Abdurakhmanov, who
                       lives in Sweden, has stopped communicating, reports
                       Vayfond, a Chechen human rights organization based
                       in Sweden.


                # ⚓ Michael Geist ☛ Freedom_of_Expression_for_a_Price:
                  Government_Confirms_Bill_C-18_Requires_Platform_Payment_for
                  User_Posts_That_Include_News_Quotes_and_Hyperlinks⠀⇛


                       The longstanding debate over whether Bill C-18, the
                       Online News Act, requires payment for linking came
                       to an end yesterday. Government officials admitted
                       that even basic quotes from news articles that
                       include a hyperlink to the original source would
                       scope user posts into the law and require platforms
                       such as Google and Facebook to negotiate payment
                       for the links. As noted below, even that position
                       may understate the impact of the bill, which
                       appears to also cover a user post of a news quote
                       without a link. In other words, merely quoting a
                       few sentences from a news article on an Internet
                       platform is treated as making news content
                       available, which triggers a requirement for the
                       platforms to negotiate payment. This position runs
                       counter to Canada’s copyright obligations under the
                       Berne Convention and has no place in a country
                       committed to freedom of expression.


                # ⚓ Dawn Media ☛ Iranian_killed_‘celebrating’_World_Cup_loss_to
                  US⠀⇛


                       An Iranian man was shot dead by the security forces
                       after celebrating when the United States eliminated
                       his country’s national team from the World Cup,
                       rights groups said on Wednesday.


                # ⚓ BBC ☛ World_Cup_2022:_Inside_the_‘secret_club’_of_Iranian
                  anti-government_football_fans⠀⇛


                       Many Iranians are boycotting the World Cup as they
                       feel the team has not done enough to support the
                       protest movement or criticise a regime which has
                       killed hundreds of people. But a group of expat
                       fans are trying to keep the protest flame alive
                       inside Qatar’s stadiums.


                # ⚓ Wired ☛ Security_News_This_Week:_China’s_Police_State
                  Targets_Zero-Covid_Protesters⠀⇛


                       The protests are stress-testing China’s
                       sophisticated censorship apparatus, and experts say
                       that the sheer volume of video clips has likely
                       overwhelmed China’s armies of censors. Leaked
                       documents from China’s Cyberspace Administration
                       called the protests a “Level I Internet Emergency
                       Response,” and authorities ordered ecommerce
                       platforms to limit the availability of VPNs and
                       firewall-circumventing routers. On Sunday, Chinese-
                       language Twitter accounts spammed the service with
                       links to escort services alongside city names where
                       protests were occurring to drown out information
                       about the protests.


                # ⚓ John Gruber ☛ Meanwhile,_in_‘Free_Speech’_Twitter_Utopia⠀⇛


                # ⚓ 9to5Mac ☛ Apple_to_restrict_‘Everyone’_option_in_AirDrop_to
                  10_minutes_in_China_with_iOS_16.1.1_[U]⠀⇛


                       Apple today released iOS 16.1.1 for all users.
                       While the release notes for the update say nothing
                       about new features or major changes, there’s a
                       significant one coming for users in China. There,
                       Apple is changing how the “Everyone” option in
                       AirDrop works, which will no longer be enabled for
                       more than 10 minutes.


                # ⚓ New York Times ☛ Hate_Speech’s_Rise_on_Twitter_Is
                  Unprecedented,_Researchers_Find⠀⇛


                       Problematic content and formerly barred accounts
                       have increased sharply in the short time since Elon
                       Musk took over, researchers said.


                # ⚓ John Gruber ☛ On_the_Prevalence_of_Hate_Speech_on_Twitter⠀⇛


                       Reactions on Twitter to this story all seemingly
                       take it at face value that Twitter now has a
                       problem with hate speech being tweeted. I suspect
                       my take is going to be unpopular with many of you,
                       but I’m not seeing it. Doubling the daily average
                       of racial and gay slurs and antisemitic posts is
                       obviously bad. That should go without saying. But
                       in absolute terms these numbers show just how rare
                       hate-speech tweets are. There are over 800 million
                       new tweets posted every day.


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


                # ⚓ Jerusalem Post ☛ Iran_intensifying_efforts_to_kidnap,_kill
                  officials,_activists_and_journalists_–_report⠀⇛


                       The report is based on government documents and
                       interviews with 15 officials in the US, Europe and
                       the Middle East officials.


                       The individuals being targeted include former
                       senior US government officials, Iranian dissidents
                       who fled to Western countries, media organizations
                       critical of the regime and Jewish individuals or
                       people linked to Israel.


                # ⚓ Declassified UK ☛ Minister_‘misled_parliament’_on_Foreign
                  Office_role_in_secret_Assange_operation⠀⇛


                       A British MP has accused a Foreign Office minister
                       of “misleading parliament” over his department’s
                       involvement in the secret operation to arrest
                       Julian Assange.


                       Kenny MacAskill MP, a former Scottish justice
                       secretary, asked the Foreign Office “whether any
                       people working on Operation Pelican were based
                       within [its] Department’s premises.”


                       Pelican was the secret Metropolitan Police-led
                       operation to seize Assange from his asylum at the
                       Ecuadorian embassy in London, which was mounted in
                       April 2019.


                       Junior foreign minister David Rutley told
                       parliament last week in answer: “No Foreign and
                       Commonwealth Office [FDCO] officials were directly
                       assigned to work on Operation Pelican.”


                       However, in response to a Freedom of Information
                       Act (FOI) request in July last year, the Foreign
                       Office had already admitted: “Three FCDO officials
                       did some work on Operation Pelican, the most senior
                       of which was Head of Latin America Department.”


          o § Civil Rights/Policing⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_Supreme_Court_Case_303_Creative
                  Is_About_Power,_Not_Religious_Liberty⠀⇛


                       The U.S. Supreme Court went after reproductive
                       autonomy in Dobbs v. Jackson Women’s Health
                       Organization, and recent oral arguments signal that
                       affirmative action could be next on the chopping
                       block. But there’s another landmark case being
                       heard this month that also deserves our attention
                       for its potential to not only roll back anti-
                       discrimination protections for millions of LGBTQ+
                       Americans but also gut civil rights laws
                       nationwide.


                # ⚓ Vice Media Group ☛ Amazon_Is_Refusing_to_Comply_with_a
                  Federal_Judge’s_Order,_Emails_Show⠀⇛


                       Amazon is refusing to fully comply with a
                       requirement to tell its employees that it was
                       ordered by a federal judge to stop retaliating
                       against unionizing employees, according to a motion
                       filed by the National Labor Relations Board.


                # ⚓ BBC ☛ Afghanistan:_Parks_become_latest_no-go_areas_for
                  women_in_Kabul⠀⇛


                       For many Afghan girls, though, it’s not about the
                       scale of the impact, but the symbolism of the move
                       – and what it reveals about the intent of the
                       Taliban since they seized power in August 2021.


                       “Every day, as girls in Afghanistan, we wake up to
                       new restrictions. It’s like we are just sitting and
                       waiting for the next one,” one female student says.
                       She’s not being named to protect her.


                       “I was lucky I finished secondary school before the
                       Taliban came. But I’m scared now that universities
                       might also be closed for women. My dreams will be
                       over.”


                # ⚓ JURIST ☛ Uvalde_elementary_school_shooting_survivors_file
                  $27B_class-action_lawsuit⠀⇛


                       Survivors of the mass shooting that killed 19
                       students and two teachers in May at elementary
                       school in Uvalde, Texas, filed a $27 billion class-
                       action lawsuit on Tuesday against various public
                       officials, including the school district, law
                       enforcement agencies and individual officers. The
                       lawsuit, filed in th US District Court for the
                       Western District of Texas, alleges that public
                       officials failed to follow active shooter protocols
                       and seeks damages for the emotional and
                       psychological wounds of survivors, including
                       parents whose children were killed, and students,
                       teachers and support staff who witnessed the
                       massacre.


                # ⚓ Associated Press ☛ UN:_Iraq_Christians_were_victims_of
                  Islamic_State_war_crimes⠀⇛


                       The report to the U.N. Security Council said crimes
                       included forcibly transferring and persecuting
                       Christians, seizing their property, engaging in
                       sexual violence, enslavement and other “inhumane
                       acts,” such as forced conversions and destruction
                       of cultural and religious sites.


                # ⚓ Gannett ☛ Disgraced_doc’s_evidence_sent_man_to_prison._No
                  one_knows_how_many_others_are_like_him.⠀⇛


                       Affected cases may be scattered across different
                       jurisdictions with a maze of deadlines and funding
                       limits. Courts can’t just toss every case an
                       unreliable witness touched — in some he may have
                       been accurate or his testimony wasn’t central to
                       the conviction. And it’s difficult to find detailed
                       case files to begin with.


                       “Those records just simply don’t exist. You’d think
                       they would, but they just don’t,” said Marissa
                       Bluestine, a former Innocence Project defense
                       attorney turned conviction review expert. “We
                       didn’t have databases. We didn’t have centralized
                       information intake. Maybe even now, frankly.”


                # ⚓ Psychology Today ☛ Child_Marriage_Links_to_Climate_Change⠀⇛


                       By 2050, UNICEF predicts the total number of child
                       brides in Africa, the continent most impacted by
                       climate change, could double to 310 million.


                # ⚓ RTL ☛ Iran’s_hijab_law_under_review:_attorney_general⠀⇛


                       Protesters have burned their head coverings and
                       shouted anti-government slogans. Since Amini’s
                       death a growing number of women are not observing
                       hijab, particularly in Tehran’s fashionable north.


                       The hijab headscarf became obligatory for all women
                       in Iran in April 1983, four years after the 1979
                       revolution that overthrew the US-backed monarchy.


                # ⚓ Meduza ☛ Moscow_Financial_University_students_arrested_and
                  sent_to_a_military_enlistment_office_—_Meduza⠀⇛


                       Several full-time students from the Financial
                       University under the Government of the Russian
                       Federation, in Moscow, were arrested in their
                       dormitory and taken to a military enlistment
                       office. Kirill Yudin, the brother of one of the
                       students, reported the events to publication
                       Kholod.


                # ⚓ Common Dreams ☛ Opinion_|_Right-Wing_Supreme_Court’s
                  Shredding_of_the_Voting_Rights_Act_Helped_GOP_Win_House⠀⇛


                       The Republicans have won a narrow majority in the
                       House of Representatives. Depending on the outcome
                       in the two seats that have not yet been called, a
                       swing of between three and five seats would have
                       left the House in Democratic hands.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Jamie Zawinski ☛ PSA:_Do_Not_Use_Services_That_Hate_The
                  Internet⠀⇛


                       As you look around for a new social media platform,
                       I implore you, only use one that is a part of the
                       World Wide Web.
                       tl;dr avoid Hive and Post.


                       If posts in a social media app do not have URLs
                       that can be linked to and viewed in an
                       unauthenticated browser, or if there is no way to
                       make a new post from a browser, then that program
                       is not a part of the World Wide Web in any
                       meaningful way.


                       Consign that app to oblivion.


                       Most social media services want to lock you in.
                       They love their walled gardens and they think that
                       so long as they tightly control their users and
                       make it hard for them to escape, they will rule the
                       world forever.


                       This was the business model of Compuserve. And AOL.
                       And then a little thing called The Internet got
                       popular for a minute in the mid 1990s, and that
                       plan suddenly didn’t work out so well for those
                       captains of industry.


                # ⚓ John Gruber ☛ Ooh.directory⠀⇛


                       Mastodon is — deservedly! — getting a lot of
                       attention as people re-evaluate their use of
                       Twitter. But what I’m digging more in our current
                       moment is renewed enthusiasm for blogging, and, on
                       the consumption side, RSS feed reading.


                # ⚓ CER ☛ Doing_a_Little_Housekeeping_and_Rebranding_|
                  Computing_Ed_Research_–_Guzdial’s_Take⠀⇛


                       I discovered today that I have written over 2,500
                       blog posts here on WordPress, starting in June
                       2009. There was a time when I was writing daily.
                       This is the first post I’ve written here since
                       June. From a pace of a new post every day, to once
                       every six months.


                       Our lives change so much from year to year.
                       Thirteen years feels like so many changes ago. I
                       live in a different state, working for a different
                       University. Even the name of the department where I
                       work has changed — I was in the School of
                       Interactive Computing at Georgia Tech. Now I’m in
                       the Division of Computer Science and Engineering in
                       the College of Engineering at the University of
                       Michigan and I direct the Program in Computing for
                       the Arts and Sciences.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ Reddit_Reports_Surge_in_Copyright
                        Takedown_Notices_and_User_Bans⠀⇛


                             Reddit has released a new transparency
                             report, revealing that the number of DMCA
                             takedown requests its receives has rapidly
                             increased. In the first half of this year,
                             738,010 pieces of content were flagged by
                             rightsholders, already exceeding the total
                             for 2021. In addition, the number of
                             copyright-related user bans has shot up as
                             well.


                      # ⚓ Creative Commons ☛ Our_Work_in_Policy_at_CC:
                        Artificial_Intelligence⠀⇛


                             As the year comes to a close, we’re
                             spotlighting Creative Commons’ public policy
                             work, recapping what we’ve done and looking
                             ahead to the new year. In this edition, we
                             turn to our work on artificial intelligence
                             (AI).


                      # ⚓ Michael Geist ☛ A_Tale_of_Two_Readouts:_U.S.
                        Escalates_Trade_Concerns_With_Canadian_Digital_Policy
                        as_Canada_Seeks_To_Downplay_the_Issue⠀⇛


                             Canadian International Trade Minister Mary Ng
                             and U.S. Trade Representative Katherine Tai
                             met yesterday to discuss Canada-U.S. Trade
                             issues and concerns regarding Canada’s
                             digital policy – most notably a proposed
                             digital sales tax and Bills C-11 and C-18 –
                             continue to mount. The U.S. raised digital
                             policy concern over the summer, specifically
                             citing Bill C-11 with a reference to “pending
                             legislation in the Canadian Parliament that
                             could impact digital streaming services.” The
                             latest readout suggests that the concerns are
                             growing, as the U.S. now cites both Bills C-
                             11 and C-18 by raising “pending legislation
                             in the Canadian Parliament that could impact
                             digital streaming services and online news
                             sharing and discriminate against U.S.
                             businesses.”


                             The U.S. concern is notable for several
                             reasons. First, the Canadian readout against
                             makes no reference to the issue, seemingly
                             hoping that it will simply go away if Canada
                             ignores it or pretends it doesn’t hear the
                             concerns (Canadian officials keep insisting
                             that the U.S. understands where Canada is
                             coming from as if that addresses the
                             concern). The government is clearly aware of
                             trade implications of its legislation – last
                             night it rejected a proposed amendment to
                             Bill C-11 during Senate hearings citing trade
                             obligations – but committees studying the
                             bills have barely scratched the surface on
                             trade related risks. As further discussed
                             below, the Canadian bills are vulnerable to
                             trade challenges with the prospect of
                             billions in retaliatory tariffs that could
                             hit some of Canada’s most important economic
                             sectors.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Dungeon_room_history,_done_right⠀⇛


                       I’ve often been annoyed by dungeon room
                       descriptions that have tons of history. Scarlet
                       Citadel and Arden Vul both have this problem; they
                       tell you what’s been there before, while as a DM I
                       need to know what’s there now.


                       It sucks when it says “this room was an alchemist’s
                       lab used by the great Garbanzo the Magnificent” etc
                       for two whole pages only to end on “anyway, now
                       only glass shards remain”.


                       So sometimes I’ve thought that all that history is
                       just in the way and shouldn’t be in the book, and
                       many reviewers have expressed something similar.


                       We would’ve wanted: “This room has glass shards”
                       and that’s it.


                       I“ve recently reconsidered that, especially as I
                       reread my old post about running mysteries.


          o § Technical⠀➾


                # ⚓ Void_Linux_Post-Install_and_1_month_later_notes⠀⇛


                       I’ve now been using Void for a bit over a month. I
                       really enjoy it and want to convert my last Ubuntu
                       computer to Void. I’m going to wait another few
                       weeks, just to confirm stability, and then make the
                       full switch, but mostly I think it’ll just be fine.
                       But Void isn’t a simple works-out-of-the-box
                       install, so this is a document of my own work in
                       order to be able to reproduce it.


                       Below are my notes and a collection of useful
                       snippets. To be honest, I don’t feel confident this
                       is a ‘final’ level of configuration. Maybe a first
                       step. For example, I didn’t try to set up a
                       printer, bluetooth, and the like, and I want to try
                       some machine learning work to later on with the
                       machine. At the end of this post I’ll link to some
                       info on others’ more extensive post-install scripts
                       and guides.


                # ⚓ qiudanz_tag⠀⇛


                       the idea of exploring tag systems with movement
                       sequences originated as danzasistemas-tag, and the
                       qiudanz technique was devised as a way to explore
                       it using the same language that could be used for
                       other types of abstract machines.


                # § Internet/Gemini⠀➾


                      # ⚓ Re:_Reinventing_How_We_Use_Computers⠀⇛


                             Uhh hi gemspace. It’s been /awhile/. A lot’s
                             happened. The rising tide of homophobia in my
                             country meant that continuing to work with
                             kids as an instructor wasn’t feasible
                             anymore. I changed careers. I got my
                             makerspace project taken from me. A lot has
                             happened.


                             On the other hand I now I have a job that
                             actually pays me a living wage and I have the
                             opportunity to create an actual curriculum
                             that addresses literacy around AI hype and
                             the limitations of this technology across
                             departments at a higher ed institution


                      # ⚓ RSS⠀⇛


                             I was recently listening to the Cortex
                             podcast on Relay.fm, a podcast hosted by the
                             YouTuber CGP Grey and Podcast Professional
                             Myke Hurley. On this they went into the apps
                             they’re using and ways they try and
                             streamline and improve their lives.


                             The podcast episode as a whole (State of the
                             Apps) rarely applies to me because of how
                             integrated into the Apple/iOS ecosystem they
                             are – but I have found some common cross-tech
                             struggles and adapted their solutions.


                      # ⚓ clubs,_corners,_and_correspondence_–_a_blog
                        renaissance(?),_and_a_smol_web_takes_shape⠀⇛


                             I joined `Ctrl-c.club` as of late. I made
                             mention of Midnight.pub, and Smol.pub, and
                             Write.as, and lo and behold, a member
                             mentioned that they, too, frequented some of
                             those/these establishments! 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽
                             ⦇:)⦈  I asked which one(s), but no response,
                             yet. This occurred on the CLI-based message
                             forum, Iris.


                             But in regards to a blog renaissance, I’ve
                             heard the term tossed around lately. Some on
                             Write.as, some from Gemini, some from
                             wherever, all over. It’s likely true, though
                             for the “knowledgeable”/ “tHinKfLuEnCeRs”,
                             they’re likely stuck on Substack in
                             Centralia. Because they have a snowball’s
                             chance in hell of actually monetizing that to
                             an extent where a bill (a whole bill!) can be
                             paid


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


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