𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, December 29, 2021
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Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2021/12/29/


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  Previous bulletins in IPFS (past 21 days, in chronological order):

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QmarLrYBMcbMFgab1qAkPGRjRr57niwUpd5PEPbMp8225S


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

⦿ My Year as a Digital Vegan — Part V — Change in Societal Norms and Attitudes | Techrights

⦿ End of 2021: Looking Back and Looking Ahead | Techrights

⦿ Associates and Enablers of Benoît Battistelli Are Commenting in IP Kat Today | Techrights

⦿ IRC Proceedings: Tuesday, December 28, 2021 | Techrights

⦿ OSI Might be Using COVID-19 to Report Their Critics to Twitter (for Suspension) | Techrights

⦿ Under the Leadership of Stefano Maffulli as Executive Director, the OSI is Still Controlled by Microsoft, Promoting Proprietary Software Like GitHub | Techrights

⦿ Response to Latest Call for EPO Strike Contains Lies From Campinos (and Another Warning That Quality of European Patents Has Collapsed) | Techrights

⦿ Criticising Microsoft and the OSI is “COVID-19 Misinformation” | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/12/29/article-on-digital-rights-in-2021-part-5/#comments
		http://techrights.org/2021/12/29/end-of-2021/#comments
		http://techrights.org/2021/12/29/ip-benoit-kat/#comments
		http://techrights.org/2021/12/29/irc-log-281221/#comments
		http://techrights.org/2021/12/29/osi-censorship/#comments
		http://techrights.org/2021/12/29/osi-sold/#comments
		http://techrights.org/2021/12/29/quality-of-european-patents-has-collapsed/#comments
		http://techrights.org/2021/12/29/straw-man-censorship/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/12/29/2021-roundups/#comments
		http://techrights.org/2021/12/29/gnu-serveez-0-3-1/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 69

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/29/article-on-digital-rights-in-2021-part-5/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/29/article-on-digital-rights-in-2021-part-5/

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Gemini_version_available_♊︎


✐ My_Year_as_a_Digital_Vegan_—_Part_V_—_Change_in_Societal_Norms_and
Attitudes⠀✐


Posted in Free/Libre_Software at 2:13 pm by Dr. Roy Schestowitz


By Dr. Andy Farnell


Series parts:


   1. My_Year_as_a_Digital_Vegan_—_Part_I_—_2021_in_Review
   2. My_Year_as_a_Digital_Vegan_—_Part_II_—_Impact_of_a_‘COVID_Year’
   3. My_Year_as_a_Digital_Vegan_—_Part_III_—_Lost_and_Found;_Losing_the_Mobile
      Phone_(Cellphone)
   4. My_Year_as_a_Digital_Vegan_—_Part_IV_—_Science_or_Scientism?
   5. YOU ARE HERE ☞ Change in Societal Norms and Attitudes
                          🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Alone⦈_


Summary: Dr. Andy Farnell shares his experiences from this past year; today’s
focus is his sense that there’s some new sort of enlightenment, for people
reach a high level of scepticism and fatigue over supposedly “smart”
technologies that do not improve lives


§ Problems shared⠀➾


Technology is about how we relate to each other. This year being a Digital
Vegan really hit home through encounters with others. Of course our stereotype
as techies is as basement dwellers. For everyone though, while we use words
like social media it is anything but, tending instead to enhance individualism
and our focus on ourselves.


“Is it cool to talk about tech-rights? Do you ask, “Hey mate, has your phone
ever been hacked?”, “What do you think of child labour in the factory where it
was made?”, “Do you trust contactless cards?””My grandmother said that it’s
impolite to talk about religion, money or politics over the dinner table. In
reality, being of Northern English descent, we’d talk about little else.
Talking is a vital part of understanding. Most of what we really believe gets
tested against others, so we hear ideas repeated back to us in a critical and
reflective way. I wonder whether we should add to that list a new item,
technology?


Sure, we will make small-talk by casually comparing features. “How much RAM
have you got in that iThing?”, “How many mega-widgets?” In that sense,
technology has joined the realm of traditional banter along with cars and
football. But is there an invisible boundary around that? Is it cool to talk
about tech-rights? Do you ask, “Hey mate, has your phone ever been hacked?”,
“What do you think of child labour in the factory where it was made?”, “Do you
trust contactless cards?”


It seemed common that many such conversations die early, with a sigh, a shrug
and a closing rhetorical platitude like “What_can_you_do?”. However, this year
I have noticed a growing enthusiasm to face-up to “awkward”. “What about those
kids that jump off the iPhone factory roof?”, “Aren’t you worried about having
a “Smart TV” in the bedroom?”


“As the psychologists predicted, the backlash to pandemic isolation was
enhanced proximity-seeking.”We are starting to overcome what psychologist John
Bowlby termed the “things we know we are not supposed to know” Bowlby79, to
break what sociologist Elisabeth Noelle-Neumann called the “Spiral of Silence”
Noelle-Neumann73, and what documentary maker Adam Curtis dubbed “Oh Dearism”
Curtis16. Turns out there is a good deal you can do (and should do), from just
saying no, to turning things off, buying alternatives, and changing the way you
relate to technology as a social construct. Indeed, the wealth and urgency of
alternative living is why I wrote a book on it.


As the psychologists predicted, the backlash to pandemic isolation was enhanced
proximity-seeking. Our human attachment needs burst back onto the scene, and it
feels like a more brotherly and sisterly world. Social thawing around tech-
difference helped me make a great many more meaningful inter-personal
connections with new people (including reaching out to people like Roy, the
editor of Techrights).


“In real life and online, digital sceptics, techno-realists or whatever you
want to call us, are popping out the woodwork…”I’ve spent more time out in the
open air, in the radical absence of technology, saying “hi” to strangers. To be
clear, this isn’t some wild-man escape into the woods to feed on grubs and
berries, as those mocking_individual_efforts to live healthier technological
lives might entail. It is neither romantic folly nor “white-male privilege” to
make space to rebuild relationships with humanity and the wider nature of which
we are a part.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Ocean_turtle⦈_


If anything it’s a subtle change in the tone of conversations I have and hear
around me. Once open to the possibility, strangers happily initiate, and
candidly share concerns about digital living and our technological society. In
real life and online, digital sceptics, techno-realists or whatever you want to
call us, are popping out the woodwork like in that Was_(Not_Was) song.


For once in a long time I feel recognised, heard and less alone. Vibrant
conversations happen with other parents and teachers who are deeply concerned
for the digital health of our kids. When I say “I don’t have a phone”, others
visibly relax. Once, they used to tense up, on “weirdo alert!”. Something’s
changed. Now I get more of an apologetic note – “Oh yes, I’m thinking of
‘downgrading’ too!” Now I feel a little too righteous, like I “tech-shamed”
them.


“When I say “I don’t have a phone”, others visibly relax. Once, they used to
tense up, on “weirdo alert!”. Something’s changed.”Some people even offer “wait
a moment while I switch mine off… so we can have a private
conversation”. Just… WOW! Symbolically, cellphones are a concealed carry
weapon. We all know this in our hearts and yearn to disarm. Conspicuously
switching off your phone or indicating you don’t have one might now be the most
powerful non-verbal signal of interest in another person.


My advanced social network system – called “walking up to people and asking
them stuff”, fills life with cool encounters, synchronicity, fortunate
happenstance and feelings of mental well-being. Theoretically the density of
potential connections in your real neighbourhood is much greater than those
mediated through Menlo Park or Mountain View. Folks who knew your grandparents,
or future lovers and business partners walk near you every day. The question
is, if the universe wants to connect you, do you want to take the risk of
reaching out to them?


“Modern etiquette seems to be that if more than two or three aren’t using App-
X or trying to pay by iCash then it’s rude to press the matter.”Being Digital
Vegan can still lead to some uneasy social situations. Just like for real
Vegans, a group vote for BBQ ribs at the steak-house could create a…
sticky situation. Modern etiquette seems to be that if more than two or three
aren’t using App-X or trying to pay by iCash then it’s rude to press the
matter. So it’s nice to go with at least one other Digital Vegan on a night
out.


§ Funny Money⠀➾


Even though my income has gone down I’ve felt more inclined to tip waiters,
give to charity and put an extra few coins in the church collection. There was
that awful time when, having enjoyed a pizza, and the staff refused to take a
generous cash payment plus tip, I had to walk out of a restaurant with a free
meal in my belly.


The hardest part was insisting that friends not “pay digitally for me” like I
have a “disability”. The manager waiving the bill may have been genuine
munificence. If it was supposed to make me feel bad, I pointed out that I
actually felt a little embarrassed for the staff who had been made to look
foolish by “just following orders” not to even let me leave cash on the table.


“The hardest part was insisting that friends not “pay digitally for me” like I
have a “disability”.”That day I learned that for some people, actual reality,
including hard economics, does not exist outside of their fantasy of how a
“digital world” should work. A few weeks later I was interviewed for a
documentary called “Cash-tastrophy”, pondering the insanity of a “cashless
society”. My faith in human beings means I am not convinced people are really
so stupid around this, rather there are hidden pressures operating behind the
scenes.


“A few weeks later I was interviewed for a documentary called “Cash-tastrophy”,
pondering the insanity of a “cashless society”. My faith in human beings means
I am not convinced people are really so stupid around this, rather there are
hidden pressures operating behind the scenes.”Face it, cash (anonymous street
money) is here to stay. Two years ago we thought Coronavirus might be spread by
contact with money. We now know that fomite_transmission_doesn’t_happen. Some
people didn’t get that memo, because the messaging, insofar as it’s influenced
by private banks, is against cash. As far as I can see much of the discussion
is mired in junk-science and specious theories around the costs and benefits of
various systems. Stores that stopped handling cash in the pandemic must now
concede, if they continue to do so, that it is for financial gain, and they are
acting in a prejudicial and exclusionary manner. Wise_economists have warned of
the extreme dangers of removing stabilising state-backed physical currencies
from circulation.


Surprising myself, I’ve gone from a Bitcoin disciple to a crypto-dissident.
Yes, we need a way to divorce human affairs from the wickedness of the banking
elites, but this isn’t it. Sometimes you just need the courage to say, oops I
made a mistake, back to the drawing board.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Biker⦈_


“…if tomorrow we built enough fusion reactors to eliminate all fossil fuels and
provide a surplus of electricity, Bitcoin would adjust its value and expand its
activity to burn-off the entire surplus.”Pondering the trap that is “proof of
waste” is depressing. It’s one of those tragedies where we think we can solve
it by “pushing through”. There’s some truth in the argument that, despite
mining disincentives of diminishing returns, these technologies are lethally
expansive. In other words, if tomorrow we built enough fusion reactors to
eliminate all fossil fuels and provide a surplus of electricity, Bitcoin would
adjust its value and expand its activity to burn-off the entire surplus. Have
we have created a monstrous non-intelligent paperclip_maximiser? I wonder why
we didn’t see this coming; that combining unfettered greed with a boundless
appetite for energy might
create a Godel Sentence for humanity already on the precipice of climate
catastrophe.


My underlying enthusiasm for digital currencies is not spoiled though.
Hopefully bitcoin and “proof of waste” Ponzi_schemes will be usurped by taxable
yet_anonymous_low-energy_e-currency. Despite the El-Salvadorian false start
(fail?), some kinds of non-corporate non-fiat electronic cash may become
practical, useful and popular. Finding the sweet-spot of decentralised
ownership without proof of work will be hard.


“To avoid economic fragmentation there should be no place for companies or
governments to enact Method-X-Only enclaves and we may even need new laws to
protect common cash currencies.”We may have to live for a long time with
different kinds of money, some more fungible, some more private, some very
volatile, and people may find it hard to understand the advantages and risks of
each. To progress, we will need to go through a period of diversity and
tolerance around payment, perhaps even resurrecting electronic barter systems.
To avoid economic fragmentation there should be no place for companies or
governments to enact Method-X-Only enclaves and we may even need new laws to
protect common cash currencies.


§ Digital Vegan: Is it a thing?⠀➾


Finally for this part I’d like to talk about Digital (tech) Veganism as an
identity. I dislike identity politics and have said in radio interviews that I
don’t see it as being an identity. In the same way that non-smoker isn’t a
cultural identity, it’s a disposition or stance, because we’d hope for the
best, non-malevolent technology for everyone.


Unavoidably though there is labelling and self-labelling at play. The past 10
years have sometimes been alienating for one without social media or a
smartphone and no single word to explain that to others. Nipping at the heels
of my self-assured confidence in taking a different life-path with computers,
has always been a note of stigma and exclusion. So adopting the epithet, and
“coming out as openly Digital Vegan” has been transformative.


“The past 10 years have sometimes been alienating for one without social media
or a smartphone and no single word to explain that to others.”In reality there
are a dozen banners to stand beneath; I am a Linux User (and BSD these days). I
am a Classical Liberal. I am a Philosopher of Science and Tech(ne) Critique
(which goes back beyond Aristotle). I’m an Advocate for Human Rights. And so
on… Most of all, as a Scientist, I object to much we’ve discussed in
these essays as an affront to reason, the rise of Cargo Cultism, and
celebration of ignorance of technical magic. And as non-secular Humanist, I
lament the obvious corrosion of social bonds, love and human values.


Can Digital Veganism be a thing?, I think not. It was a cool title for a book
of essays, and a borrowed fun snark that Cody Brown coined for his annoying
mates who, like me, were probably causing an awkward moment with their “wrong
phones”.


Practically what it does do, is throw back into the faces of various non-
thinkers, authoritarians, post/anti-humanist cyborgs and techno-fascists, the
absurdity of their assumptions about how we should all just roll over and get-
with their unexamined, parochial conceit of “progress”.


“Practically what it does do, is throw back into the faces of various non-
thinkers, authoritarians, post/anti-humanist cyborgs and techno-fascists, the
absurdity of their assumptions about how we should all just roll over and get-
with their unexamined, parochial conceit of “progress”.”Anyway, I have started
to feel (not just sympathise) with other minorities who provoke fearfulness and
ridicule from others by merely being themselves. I’ve finally understood why
the only practical choice is to wear it proudly.


I see also that “Identity” is at once liberating and constraining. I understand
identity politics better because I can see the lure of it. Feeling empowered
rather than a little worried, embarrassed and defensive is… well…
empowering. For example; during those occasional acts of group techno-worship
(when everyone gets out their phones in unison), I have some fun, smile and
ride out the “awkward” moment by raising and tickling my own palm. Hopefully
people think I just have a very small phone, but somehow, suddenly the
awkwardness is no longer mine to hold.


“…during those occasional acts of group techno-worship (when everyone gets out
their phones in unison), I have some fun, smile and ride out the “awkward”
moment by raising and tickling my own palm.”Another thought that occurred to me
is that, in terms of identity, I have not changed, but the world has. It occurs
to me that barring a period of geek-chic in the first decade of this century,
for nerds, our otherliness never really changed. Sometime between that eternal
September and Snowden we flipped from being gushing advocates of ubiquitous
technology, to cautious advisers against it.


Perhaps writing my own book on the subject sensitised me to the plight of
others less able to manage or understand tech, and why those people become
dependent on technology. The pandemic, and the CompSci Masters students I’ve
taught through 2021 (who have done amazing projects on digital rights and
personal cyber-security) helped me see further. I get why we fall victim to
bullying by employers, peers or even our own family, and are pressured into
making technological choices that are bad for us, bad for others and for the
planet. It is this psychology that has illuminated how we can most effectively
mount resistance. █


_______


✐ Bibliography⠀✐


    * [Bowlby79] John Bowlby, On knowing what you are not supposed to know and
      feeling what you are not supposed to feel, Canadian Journal of
      Psychiatry, (5), 403-408 (1979).
    * [Noelle-Neumann73] Noelle-Neumann, The spiral of silence: Public opinion,
      our social skin, University of Chicago Press (1973).
    * [Curtis16] Adam Curtis, HyperNormalisation, BBC documentary, (2016).
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⠀⠀⠀⠀⠀⠀⠨⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣇⢷⢳⠘⠀⠀⢸⣽⣿⣿⡇⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⡾⢣⣠⣱⣿⣿⠆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠁⠀⠙⠀⠀⠀⠀⠀⠄⠀⠊⠅⠉⠘⡞⠀⠀⢇⢹⣏⣿⣿⡇⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⢳⢧⡟⣵⣿⣿⣿⠠⠀⠀⠀⠀⠠⠀⠀⡐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡄⠀⠀⠀⠀⠀⢱⠄⠇⢱⢹⠄⠀⠬⣰⣿⣯⣷⠑⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣺⣿⣿⣿⣧⠏⠀⣰⠆⠀⠀⠀⠄⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⡄⠀⠀⢈⠀⡀⢎⣇⡠⠀⡀⢹⣿⣿⣥⠁⣾⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠟⢇⣿⣿⡟⡿⣿⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢨⠀⠁⠀⠀⢠⠄⢰⠘⡌⠁⡂⠀⠀⣿⣿⣟⠀⣿⢻⣿⣿⡟⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⡟⡱⡀⣝⣿⠀⡀⠀⢀⠄⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠈⢸⠘⡇⠗⠀⢀⠈⣆⡿⠇⣻⠀⣿⣻⣿⣿⡇⣡⢸⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⡿⣯⣿⣿⣷⣿⣿⣻⣏⣾⣿⡏⢔⠇⠀⠃⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⢈⢷⠑⡆⠘⠘⠀⡼⡿⣿⢛⢰⡿⣻⣿⣿⣿⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⢯⡇⡳⣹⣳⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣆⢰⡡⠀⠀⠸⡸⣿⡿⣻⢸⣷⣽⣿⣿⣏⣾⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢻⣾⢟⣞⣕⣯⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⣌⠇⠀⠀⠁⢳⣳⣏⣻⣿⡗⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⢂⣿⣿⢸⣿⠏⡌⡤⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠂⠀
⠇⠀⠀⠀⠀⠀⠀⠀⡇⣶⣄⠀⠀⠀⠀⠀⠀⠀⠐⣇⢹⢾⠀⠀⠧⠈⣯⠟⡙⠀⠀⢀⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⢏⢼⣶⣿⣾⢏⣾⢏⠸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡏⢢⠀⠀⠀⠀⠀⠀⢀⠠⣡⠀⠀⠀⣂⣶⢿⡟⡁⣤⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢟⣾⣵⣟⡅⡿⣣⠆⢈⣷⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣆⢠⣌⠂⢸⡀⠀⠀⠀⡂⠀⠈⠔⡜⠀⠀⠠⢝⢿⣯⣿⡉⣿⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠏⢯⣇⣾⢝⣽⣍⢴⣿⢔⣿⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢤⡀⠘⠟⠸⣿⠆⠀⡃⠀⠀⠀⠁⠀⠀⠀⢿⢔⠀⠀⠉⣜⣞⠾⠁⡾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⡟⢡⢏⡞⣧⣺⣗⡟⣨⣿⠛⣡⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠈⢻⣳⡀⠀⠋⡁⠀⣿⡀⠀⠁⠀⠀⠀⠀⡦⠀⠐⡆⠂⡿⡜⡼⢸⡞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⢪⠏⠀⡗⣿⢃⢸⡇⡢⣾⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠌⠀⠀⠀⠀⠉⠻⠂⣽⣶⡄⠀⠘⠁⡀⢀⠀⠀⠀⢠⠓⡀⠀⠘⢰⣵⡹⡼⡜⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠃⡁⡀⡁⢢⠙⣷⣾⢇⣻⣾⢣⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠡⠀⠄⠀⠀⠀⢃⣿⠇⡅⣷⣤⠀⠓⠂⠀⠀⠙⡏⠁⠀⠀⣀⢣⡻⡝⠽⡦⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡇⡴⢙⠇⠘⠀⣠⢨⢟⡟⠈⡿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠠⢀⠁⢰⣿⠑⢹⣆⠀⠈⢳⢰⡄⢰⠄⠐⠈⣯⣳⡝⠔⠧⠡⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⠐⡄⣸⠁⠀⠸⠀⠉⣿⠗⢈⣜⣝⣆⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢆⠀⠘⠢⡄⠰⡃⠀⢠⠈⠘⠋⠀⡀⢠⡘⠇⣄⡀⠀⠀⣮⣳⡝⣜⠎⢖⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣇⢶⡿⠀⠀⠀⠀⡸⣌⡧⣼⡻⢿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡤⢨⣦⡀⠀⠀⠓⠋⠇⠀⠀⠐⢲⣶⣄⡀⠸⢿⣦⡀⠌⠀⡈⣜⠟⡍⣮⠐⡻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣸⣿⣿⣷⣿⣿⠂⠂⠀⠀⡀⠹⢉⣈⣶⢇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠸⣿⡿⣠⠀⠀⠀⠀⠀⠀⠈⠂⠿⡿⣿⠰⣦⡇⠀⠁⣄⠳⠟⠷⢀⠦⠘⢩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⢀⣿⣿⡄⡶⠀⠄⠀⠀⡘⡾⠋⣦⡦⡀⠀⠀⠀⠀⠀⠠⠄⠔⠒⠉⠀⠀
⠀⠀⠀⠠⠈⠃⠉⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠁⠀⠹⠀⠐⠀⠁⠈⡈⠳⠬⣷⠀⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣹⡯⣿⣿⣿⣿⣿⣿⣥⡆⠀⠀⠀⢥⠶⣪⣽⡿⠻⡇⡄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠢⠄⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠢⢠⣤⡁⡀⠀⡾⡆⠀⠀⠀⠁⡛⠒⢦⡿⠈⣮⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⡟⣿⣿⣿⣷⢿⣿⣵⡇⠀⠀⠀⡀⠉⢭⡵⣾⣿⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠐⠹⠟⠀⠈⢻⡄⠈⠀⠀⠀⠀⢂⣑⠿⢶⡍⠠⣽⣿⣿⢺⣿⣿⣿⣿⡿⠟⠿⢿⣿⣿⣿⠀⢈⣼⣿⣫⣿⢾⣟⣿⣷⡇⠀⠀⡠⠟⠀⣠⣁⠋⡄⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⡀⠀⠁⠸⣟⡘⠙⠷⢦⢠⣿⣿⣿⢸⣿⣿⣿⣿⣧⠄⠀⣼⣿⣿⣿⠀⢘⣀⣿⣟⣟⣿⣿⣭⠫⡗⠀⠀⠀⣦⢲⡟⢹⢻⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠤⠀⠀⠤⠄⠠⠰⡖⠗⠈⠀⠀⠀⠀⠀⢸⢠⡈⣿⠂⠀⠀⠀⢐⡿⠟⠻⢣⠲⣺⣿⣿⢸⣿⣿⣿⣿⠟⠊⠁⠛⢿⣿⣿⠀⢸⢎⣿⡗⠧⣽⣯⢯⢼⠁⠀⠀⠠⣡⡤⣁⢨⠨⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠘⠈⢿⣿⠲⠀⠀⠀⠱⣿⣟⣛⠻⢸⢽⣟⣿⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⢼⣿⡟⣋⡿⡶⡶⠒⠀⠄⠀⢐⡽⢈⡞⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⢤⠀⠸⠈⠀⠀⠀⠀⠺⣈⣹⣽⡞⢱⣿⣿⡟⣿⣿⣿⣥⡀⠀⠀⠀⠀⢀⢀⣾⠀⠘⢻⣿⣷⠒⣝⠋⢱⠂⠀⢀⠀⠂⠄⢺⢳⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⣠⡤⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⡀⠀⢸⢟⡬⡷⡇⢸⣼⣿⣷⣿⣿⣿⣿⡀⠀⠀⢀⢤⢸⣟⣿⠀⠀⣻⣿⡯⠄⠞⡄⠿⠂⠠⡀⠀⠀⡚⡷⣦⢰⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠇⠀⠀⠄⡜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⡄⠀⠄⠀⢀⠩⢹⣷⣞⡤⣨⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠂⠸⣿⣿⠀⠀⣸⡾⢟⠆⠡⡅⠀⠀⠀⠀⠀⠛⢣⣃⠸⠸⡈⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠐⠁⠀⠀⢀⣠⠀⠀⠀⠀⠀⣠⢰⣄⠃⠀⠇⠀⠀⠀⣨⠴⣻⡷⡧⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣮⠀⡰⣹⡏⢔⡵⣼⢠⠀⠀⠀⠀⠀⢀⡄⠍⢷⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠠⢠⠒⠋⠈⠀⠀⠀⠀⠀⠈⣻⢾⣿⡴⠀⠈⠀⠀⠀⠐⠀⡿⢋⢰⡀⢸⣆⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⢸⣤⠀⢀⣿⡏⣿⣋⠀⠇⢮⠯⠃⠀⠀⠀⠀⠘⢿⣿⣹⡍⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡨⠏⢣⠀⡀⠀⠀⠀⠀⢈⣂⠛⡼⢧⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⡟⣿⠞⣀⠄⡁⡗⠀⠀⠀⠀⠀⠀⠙⢹⡿⣿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⢠⣤⣤⠀⠀⠀⠀⠀⠈⠃⠘⠄⢸⠨⠀⣀⣖⣆⢏⠀⠀⡇⣗⢫⣯⡿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⡟⢬⣾⡽⠡⠀⠐⠅⠀⠠⠀⠀⠀⠀⠠⠸⡇⠗⠨⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⢀
⠀⠀⢀⠠⢤⣽⣿⡾⠿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠸⡠⠈⢈⠷⡇⠀⠀⣴⡋⢿⢰⡙⣿⣶⣿⣿⣿⣿⣿⣇⣶⣼⣿⣿⣿⡿⣫⣿⣿⣷⢃⠁⢀⠀⢈⠀⠀⠠⣶⣶⢀⠀⡅⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠔⠊⠁⠀⢀⠈⠔⠁⣠⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠡⡀⠀⠀⠧⢀⡶⠛⡋⢁⣿⡿⣤⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣏⠆⢀⠀⠀⠀⡡⣱⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢄⠠⠔⠀⠀⠀⢀⠈⠀⠄⠀⠀⠀⠀⣿⠃⠀⠀⢡⢠⣧⡦⣱⣾⣿⣻⣿⣿⣮⣝⡿⢿⣿⣿⠿⣟⣫⣷⣿⣿⣿⣿⡿⢻⣷⡿⠂⠀⠂⠀⠀⠙⢡⠙⡛⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⠀⢠⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣫⣥⡬⡀⠀⠀⠂⠀⠀⢩⠀⠈⣴⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠉⠀⠀⠀⠀⢠⡄⠂⠀⠖⣀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠁⠐⢻⣟⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠁⠀⠀⠀⣠⣼⡿⠃⠉⢀⣼⣿⣗⠀⠀⠀⠀⠀⠀⠀⢠⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢇⠀⠈⠄⠀⠀⠀⠀⠀⠂⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠊⠠⢀⡤⠒⡉⠛⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡏⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡰⠋⠀⠀⠀⠀⢠⣾⣿⡿⠆⠀⠀⠀⠈⠀⠀⠀⡆⣴⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣻⣿⣿⣯⣽⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠠⢠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡰⠠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⢀⠀⠀⠀
⢠⢆⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣅⡀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢸⠆⠀⠙⢿⣿⢯⠛⢿⣟⣛⣛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠙⠒⠀⠪⠍⢩⢉⠛⣭⣼⡿⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⠛⠁⠀⠊⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣂⢀⣿⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠟⠛⠛⢛⡻⢿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⣿⢧⣤⢀⣤⢴⢖⣶⠾⠋⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⡡⣼⣿⣿⣿⣿⣿⣷⣦⣶⢭⣄⣄⣨⠤⠒⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣽⣿⣿⢿⠿⠿⣿⣿⣿⣿⣦⡉⢁⡌⢿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⣶⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣽⡿⢓⡏⠋⠠⣄⣀⡀⠀⠈⠙⠻⠿⠿⢿⢿⡇⠈⢻⡛⢿⣿⠛⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣶⡮⢿⣿⢿⡿⠿⢿⠿⠿⠛⠛⣿⣿⡿⣿⣿⡿⠛⠉⢀⠸⣵⣴⣾⣿⣯⣷⣥⣤⣄⣀⠀⠀⡀⠀⠃⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⡟⠛⢋⠻⠛⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠗⠀⠀
⣿⣿⣿⣿⡉⡈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢶⣽⠯⣻⠝⠒⠁⠀⠀⠀⠈⠉⠉⠋⢉⠉⠛⠛⠂⠄⠀⠀⠑⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣄⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣛⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣶⣈⣛⣿⠿⣽⡾⠿⠙⠿⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀
⢻⣿⠷⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠒⠉⠉⠉⠛⠛⠢⡾⠛⠋⢁⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⢁⣒⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢀⣴⠶⢖⣉⠋⠙⣉⣁⢁⣤⠤⠄⠀⠀⠀⠀⠀⠀⠙⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠁⠀⠀⠀⠉⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠤⠿⢷⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣟⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠤⠀⠄⠀⠈⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀
⠀⠀⠀⠠⣀⣂⠹⢓⣶⣿⢿⣿⣿⣿⣿⣟⣿⣿⣥⣤⣽⣿⣶⣿⣿⡿⡿⡟⠛⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿
⠀⣀⣠⣤⡤⡿⠄⠂⠛⠿⠿⣟⡉⠉⠻⣿⣿⣿⣿⣭⣟⣹⣿⣿⡷⠖⠿⠻⠿⣏⣋⢓⠓⠻⢯⣩⣯⣤⠍⠈⣿⠎⠈⠈⠂⠈⠉⠙⣿⣋⢹⢛⣻⣿⣿⡟⠌⣵⣿⣿⣏⠿⢿⣿⣻⡻⠿⢻⣄⣍⠩⠋⠛⡿⠇⡀⠀⠙
⠀⠉⠀⠈⠦⠄⠆⠒⠤⠀⠄⠀⠒⠄⠀⢈⠉⠩⠉⠙⠿⣻⣤⣤⣀⣀⣀⣀⠀⢀⣀⣊⠀⢀⣴⠟⠓⢟⠏⣶⡇⢨⠄⠀⠀⠀⠀⠘⢻⣮⣽⡿⢫⣥⣽⣶⡖⠛⠶⠈⠙⠑⠀⠴⣶⣤⣥⠶⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠀⠀⠀⠀⠀⠀⢽⠋⠓⠋⢏⠉⠁⢀⠀⠈⡛⠐⠊⠇⠀⠀⠂⠲⠟⠓⠈⠂⠐⠉⠀⠀⠀⠀⠉⠙⠀⠚⠛⠿⠛⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⣶⡲⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⢀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣁⣀⣐⡀⠀⠀⠀⢀⠀⠀⠀⠐⠀⢘⣿⣿⠷⠄⠀⠀⠀⠀⠐⢺⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠈⠀⠀⠁⢈⢥⣤⣶⣶⣤⣠⣄⣀⣠⣤⣤⣠⣠⣴⣶⣦⣤⣦⣀⣀⠀⠄⠀
⣿⣿⣿⣿⣶⣦⢥⣿⣿⠷⠶⢶⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⠋⠉⠉⠛⠙⠛⠿⣿⣿⣿⣿⡄⠂⠀⠀⠀⠠⡿⠯⠿⡿⠟⠋⠁⠀⠀⠈⠈⠈⠉⠛⠛⠿⣿⣿⣿⣃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡯⠀⠀⠀⠀⠀⠛⠲⢄⠠⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣄⠀⠀⠁⠉⠉⠉⠀⠀⠀
⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⢀⠈⣉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢾⣿⣷⣦⣤⣤⣤⣤⣶⣿⣿⣷⣦⣀⣀⣀⣠⣴⡾⠋⠜⠂⠀⠀⠀⠀⠀⠀⠀⠈⠅⠹⣿⣿⡿⠿⠛⠛⠋⠉⠙⠛⠠⠤⠀⠀⠀⠀⠀⠀⠀
⠿⠋⠛⠋⠀⠀⠐⣾⣿⠿⡿⠁⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡏⣉⣉⡟⠁⠐⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣷⡂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣤⣤⣀⣀⣀⣈⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⢻⣿⣿⣿⠇⠀⠀⠀⠀⠘⠙⠫⠛⠛⠙⠋⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠛⠛⣻⣟⣀⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⡯⢇⠀⣀⠀⢀⠨⠣⣬⣿⣥⣶⣦⣤⣄⣀⣤⣤⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣼⠋⠈⠋⠀⢠⣼⠿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣿⣿⣿⣿⣿⣿⣛
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⡞⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠢⠉⠟⡿⣿⣿⣿⣿⢿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡽⣷⣏⢚⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⢂⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠿⠿⡻⢿⣿⣾⣱⣿⣸⣿⡇⠀⣤⡄⣀⣀⡤⠄⠀⠀⠀⠀⠀⢠⣾⢻⡻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⡢⠤⠤⠬⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣀⣠⣤⣤⣤⣤⡀⠀⣶⡗⠱⣿⣿⢻⣿⣿⠀⠙⠟⠛⠉⠀⠀⢀⣥⣄⠀⣰⣿⡿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠀⠁⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⣾⣫⡀⠀⠘⢟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢨⠙⣡⣾⠟⠉⠀⣴⣷⡮⢐⠀⢄⡠⠄⡀⢀⣴⠅⠀⠀⠊⠙⠻⣦⣄⠐⢄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⠿⢛⣉⣉⣱⡿⡱⣿⣿⠀⠀⠘⣷⣄⡐⠀⠀⠀⠀⠀⠀⠀⠤⠞⠋⠉⢀⡄⢀⠠⠈⣀⠀⠸⣿⠏⠀⢉⠛⠋⠀⠀⢍⠔⢿⣿⡍⣝⢧⠀⢡⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⡏⣴⣿⢿⣿⢏⡖⡆⢹⣵⣿⠀⠀⣿⣿⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣀⣀⣤⠞⣻⣟⣻⡶⠀⠀⣼⠀⢰⠸⡔⡆⢀⠈⠙⡻⣿⣇⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⡿⢿⣿⣾⣷⣿⡟⣲⣾⣿⢿⠀⠀⣿⣿⣿⣇⠀⠀⠀⢀⠀⠀⠰⣀⣴⣿⣿⣿⡟⣿⣎⣟⣿⣿⡆⣤⠀⠃⢀⠸⢀⠀⠟⠇⠀⢠⣴⣿⣧⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢿⣿⣿⣿⣍⡙⠛⠛⣋⣴⣿⣿⢯⠃⢀⣸⣿⣿⣿⣿⣤⡀⠀⠀⠀⠠⠟⣿⣻⣿⣿⣿⣷⡿⠿⣿⣿⡿⠃⠀⠀⡀⠈⢦⠀⠁⠠⠶⠶⣿⡿⠟⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣄⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣭⣤⡀⠀⠀⠒⠤⠴⠶⠶⠞⠊⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠉⠛⠛⠛⠛⠛⠉⢀⣠⣶⣿⣿⣿⣿⢿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣈⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣍⣉⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 513

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/29/end-of-2021/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/29/end-of-2021/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.29.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ End_of_2021:_Looking_Back_and_Looking_Ahead⠀✐


Posted in Site_News at 9:09 am by Dr. Roy Schestowitz


Video_download_link | md5sum ea91aa0599935dc0b4acb38e36805ecf


http://techrights.org/videos/end-of-year.webm


Summary: 2021 was probably one of our best years; with over 3,000 blog posts in
total (for_the_first_time_since_2010) and many bits of leaked material we’ve
grown our trove of information, which is moreover replicated fully in gemini:/
/ (fully self-hosted)


THE year is nearly over (2.5 days before the end) and we’ve had an
exceptionally productive year. We made a big splash at the start of the year
with Raspberry Pi revelations and Intel_leaks. Then we started a number of in-
depth investigations of the EPO; many people are still reading these in an
effort to better understand their home countries. At the middle of this year we
had major IRC scandals as Freenode was in a state of flux and we ended up
setting up our own IRC network, as we had already wanted or planned in prior
years, especially in 2020. IPFS and Gemini adoption increased (1,543_live
capsules and persistent_linear_growth); a lot of people now read Techrights
using protocols other than HTTP/S, in formats other than HTML. Our Git
repository finally_went_public and it is discoverable_through_Geminispace-wide
search. More and more projects now choose to present Git over_Gemini_Protocol —
an encouraging trend we expect to carry on.


“IPFS and Gemini adoption increased; a lot of people now read Techrights using
protocols other than HTTP/S, in formats other than HTML.”The informal video
above explains what’s to come next. We have a number of internal document to
put out there and we have a lot of stuff to show about Team Mono (Microsoft
GitHub Exposé — Part XIII is due Monday).


Means for communicating with us securely have further expanded, from self-
hosted IRC to E2EE for voice. We hope it will encourage more people to send
tips and documents our way. █



                    ䷩ 𝚕𝚒𝚗𝚎 572

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/29/ip-benoit-kat/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/29/ip-benoit-kat/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.29.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Associates_and_Enablers_of_Benoît_Battistelli_Are_Commenting_in_IP_Kat
Today⠀✐


Posted in Deception, Europe, Patents at 7:02 pm by Dr. Roy Schestowitz


Summary: Daniel_X._Thomas can be seen in today’s comments about the EPO; we’re
meant to think this is perfectly OK while the ‘Kat’ censors critics of António
Campinos


THE FOLLOWING has just been noticed:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇I_would_like_to_draw_the_attention_to_T_1399/17_which_came
to_a_different_conclusion._As_the_claims_amended_during_the_OP_before_the_OD
which_lead_to_maintenance_in_amended_form_were_not_adapted_to_the_description
and_hence_left_doubts_about_the_scope_of_protection,_the_MR_was_not_allowable.
https://www.epo.org/law-practice/case-law-appeals/recent/t171399eu1.html_See
Point_2_of_the_reasons⦈_


Yes, Benoît_Battistelli has bossed him in more than one institution:


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


So Team Battistelli is leaving comments in IP Kat, whereas many critics of
theirs get banned/censored. █


Elsewhere today:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Given_the_absence_of_any_adjustment_to_the_rules_for_oral
proceedings_in_the_light_of_G_1/21,_it_seems_that_the_EPO_intends_to_conduct
oral_proceedings_by_relying_upon_provisions_that_are_clearly_unlawful._It_is
not_hard_to_see_how_this_could_lead_to_some_very_messy_situations._However,
this_will_only_come_back_to_bite_the_EPO_if_the_EBA_truly_does_represent_an
independent_'judiciary'._Given_the_EBA's_performance_in_G_3/19_and,_in_parts,
in_G_1/21,_it_would_be_reasonable_to_have_at_least_some_doubts_on_that_point.⦈_


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

                    ䷩ 𝚕𝚒𝚗𝚎 751

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/29/irc-log-281221/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/29/irc-log-281221/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.29.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Tuesday,_December_28,_2021⠀✐


Posted in IRC_Logs at 2:46 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-281221.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-281221.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-281221.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-281221.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
 QmNsavfo6HsPVdnoYmq23SGSV9zf4GnrodMiD5iD6Kta2t #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmfZx1HdUrp9z2RFQM9H4Vhr8pqYdEQ28Bno8D1fbZQ4zx (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmRk3jh6bfNZGwXsmaBaPDPNfPBBSC2geYDdcNJcqaYaBW social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmeuDzcxbnrFFzvAyEhKfb7rLbwveYRoacWd5w4oc7aWm9 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmQYPHGaqpiUCQkQoM1wTGreJpCgvwMQvd21T5GtCTyd31 #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmWMKfwc78rg8DHuwvH8LMCAYDUBmFxsGFiDrVtxnF3RR8 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmazBX52qxZFPkdSvsFCcTKC5MMV5EWEe1mUFQj67qWKkM #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmRk1hX9NizYeqK4nUnGNASkPd8Piv1AWzRGQ8yxefV1W4 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmarLrYBMcbMFgab1qAkPGRjRr57niwUpd5PEPbMp8225S



                    ䷩ 𝚕𝚒𝚗𝚎 878

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/29/osi-censorship/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/29/osi-censorship/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.29.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ OSI_Might_be_Using_COVID-19_to_Report_Their_Critics_to_Twitter_(for
Suspension)⠀✐


Posted in Deception, Microsoft, OSI at 8:15 pm by Dr. Roy Schestowitz


I wonder, who could possibly have reported me for this? The OSI keeps_doing
this…


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇OSI_censorship⦈_


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


Summary: A week after the_FSFE_misused_Twitter_rules in an effort to censor
critics it seems like the OSI is doing the same, by weaponising rules that are
completely not related; this_article must have struck a nerve and they don’t
want people to see it…


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢉⠙⠿⠻⠉⠟⠿⠛⠿⠻⣿⣉⢉⢹⠻⠻⠟⢿⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣈⣡⣄⣀⣀⣀⣀⣀⣄⣀⣿⣿⣸⣆⣄⣸⣀⣠⣀⣸⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣀⣠⣠⣠⣸⣸⣇⣄⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⢋⠛⠛⠛⠋⡛⠛⡏⢙⠛⡟⠛⠛⠙⠛⢻⠟⠛⢻⠛⠛⠛⠛⠛⠋⠛⠛⢻⠛⠋⠛⠙⠛⠛⠉⠛⠛⡟⠛⡛⠋⡟⠛⠋⠛⠛⠙⠛⠋⠛⡏⡛⠛⡛⠛⠙⠛⡏⢛⠋⠛⠛⠛⠛⠉⠛⠟⢻⠛⠋⠛⠙⠛⢹⣿⣿
⣿⡿⠾⡶⠳⠖⠶⠓⠲⣷⢾⠶⣷⣾⣾⣿⣾⣾⣷⣿⣾⣶⣶⣾⣶⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣿⣶⣷⣷⣶⣶⣶⣷⣷⣶⣶⣷⣷⣶⣷⣶⣶⣾⣷⣾⣾⣾⣶⣶⣶⣶⣷⣿⣾⣶⣶⣶⣶⣶⣾⣿⣿
⣿⣧⣤⣷⣥⣬⣦⣧⣤⣶⣼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣈⡉⣏⣋⣉⣈⣉⣉⣈⣉⣉⣸⣀⡉⡁⡏⡘⣉⣈⡉⢹⢉⣭⡉⡉⣏⣁⣏⣉⡈⣉⢹⣉⣉⣁⣇⣍⢉⡉⡉⣁⡀⠉⣇⣸⡈⣻⢁⣠⣈⡉⣩⣩⡉⣿⣉⣉⣉⣉⣏⣁⣍⣁⣇⣉⣏⣉⣹⣈⣹⣈⢉⢉⢙⣿⣿
⣿⡟⢛⢻⢛⠻⠛⣻⠛⢛⢛⣟⠛⠛⠛⡏⠛⠟⠻⣻⣟⢟⠟⠛⡟⠛⠋⠛⣿⠻⢛⠛⠛⢻⠋⡋⠛⡟⢛⠋⢛⠛⣿⠻⠛⡟⠛⠛⠻⠙⠛⡏⠙⠛⡟⠛⠛⠛⠛⠛⣿⢟⢻⠛⠛⠛⠙⢛⠛⡟⠙⠛⢻⣛⠛⠻⣿⣿
⣿⡷⠷⠷⡾⣾⢶⡿⡶⢾⡶⡷⡶⢶⠶⡷⠶⢾⡾⡾⢷⠿⠶⠶⣷⡶⢾⠾⠿⠶⠾⡶⢶⢾⢷⠷⡶⠷⢷⠷⢶⠾⣿⢶⢶⠷⣶⠶⡶⢶⠶⠷⣶⠶⠷⢶⠶⡶⢾⡷⢾⢷⢿⠷⠶⡶⣶⠾⢶⠷⢶⣶⣾⣿⣶⣶⣿⣿
⣿⣇⣤⣤⣤⣼⣬⣷⣤⣤⣧⣤⣇⣤⣤⣄⣤⣤⣤⣧⣦⣤⣤⣴⣬⣧⣦⣤⣤⣤⣤⣄⣼⣤⣤⣦⣤⣴⣼⣦⣦⣤⣇⣠⣤⣤⣼⣤⣴⣤⣤⣔⣼⣤⣀⣤⣴⣤⣬⣆⣬⣤⣤⣤⣤⣤⣼⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣉⣁⣈⣉⣁⡈⣉⣝⣉⣏⣉⣉⣉⣉⣉⢙⣏⣡⡏⣉⣁⢉⣁⣏⣉⣉⣸⣈⡉⣉⣹⢉⣉⣈⣀⢹⣨⡉⣉⣁⣈⣇⣉⣈⣩⣍⡉⣁⡈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠻⠿⡿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⡿⢿⠟⠟⠿⠟⠛⢿⢿⠿⣿⠿⢿⣿⡿⠟⣿⠿⢿⡿⣿⠿⠿⠿⠿⠿⣿⠻⠿⠿⢿⠿⡿⠿⠿⠿⢿⠿⠻⠿⠿⠿⡿⡿⡿⠿⠻⡿⠿⡿⠻⠿⠿⠿⠿⢿⣿⣿⣿
⣿⣧⣦⣤⣧⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣦⣯⣤⣼⣬⣮⣴⣤⣬⣶⣿⣤⣽⣤⣤⣧⣤⣤⣿⣤⣼⣌⣬⣤⣤⣤⣤⣤⣼⣷⣤⣦⣼⣤⣤⣬⣤⣇⣸⣀⣤⣤⣤⣤⣿⣤⣤⣤⣴⣧⣤⣤⣼⣤⣤⣤⣤⣤⣿⣿⣿
⣿⡇⣀⣈⣈⣈⣸⣧⣈⣀⣡⣇⣈⣇⣌⣸⣌⣀⣈⣉⣡⣠⠁⣇⣠⣉⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠝⠛⡛⢛⠛⠻⠙⠻⠛⡟⠉⠛⠛⠛⠛⢻⠛⠍⠩⠙⡉⠩⠻⢹⢩⢿⠛⠋⠟⠛⠛⡏⠛⢻⠉⠛⢻⠛⠛⠙⠙⢻⠙⠛⢛⣻⠉⡛⢻⡙⢋⡋⠩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⡺⠾⡻⠿⡷⠿⡿⢿⠿⡟⠻⡺⠾⠚⢺⡾⡿⢿⠳⠿⠿⢿⠿⠿⣾⠟⠞⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣦⣦⣥⣤⣧⣬⣮⣮⣬⣯⣴⣵⣶⣤⣵⣾⣧⣾⣼⣤⣤⣼⣼⣤⣾⣴⣦⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢋⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⡟⠉⠉⠉⠉⠉⠙⣿⠛⠿⣿⠛⠿⠿⡿⢻⠿⠻⠿⠿⠻⠿⠿⠛⠿⡟⠛⠻⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⡇⠀⠀⠀⠀⠀⠈⣿⠤⢾⠼⡤⡦⡦⠷⢴⡴⠤⣤⣤⣤⣤⣴⣤⣤⣯⣤⣾⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣴⣤⣤⣤⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣧⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⡿⠛⠛⠿⠟⠛⡟⠻⠿⠟⣟⠛⠟⠻⠏⠿⢻⣿⠛⢛⠛⢻⢻⣛⡛⠻⠻⢻⣟⣛⣛⠛⢟⢛⢛⠻⡟⡟⢻⡛⠛⠿⠿⠹⠛⠻⠟⠟⡿⠟⢿⠛⠻⠿⠛⠿⠿⠻⢻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣷⣶⣾⣾⣯⣮⣼⣦⣶⣾⣿⣾⣴⣵⣷⣶⣴⣿⣶⣮⣶⣵⣾⣷⣶⣴⣽⣼⣷⣵⣮⣾⣼⣾⣴⣶⣷⣯⣾⣿⣧⣿⣶⣶⣵⣿⣶⣮⣷⣯⣾⣾⣿⣶⣾⣷⣶⣶⣽⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣏⢀⠜⠴⠈⠍⡩⡉⡩⡁⡬⡏⠉⠉⢸⡶⠈⢹⠉⡀⡌⡭⡉⠉⡽⠉⠘⠉⠍⡁⢘⢍⢀⠍⣩⠉⢩⢹⡷⠎⡍⠍⠉⣻⢃⠫⡄⠉⢩⡷⠎⠁⠩⠭⠉⢹⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣟⢻⠻⠿⠿⠿⠿⣿⡛⠛⠿⡛⠿⠿⠟⣟⠛⠿⠿⠿⢿⡟⠗⣻⠿⠿⠿⠿⠷⠛⢿⠿⠿⠟⣟⠛⠿⡟⣛⠿⠿⠷⠿⠿⠿⠻⠿⠿⡟⠟⠿⠿⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣯⣵⣤⣥⣥⣤⣰⣿⣡⣥⣬⣥⣤⣤⣤⣿⣵⣼⣵⣤⣽⣧⣤⣭⣬⣴⣵⣴⣵⣴⣽⠬⣥⣤⣯⣥⣤⣷⣥⣊⣎⣤⣦⣤⣤⣼⣼⣴⣧⣦⣤⣶⣾⣿⣿⣿⣿⠿⠿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣷⠰⠉⠉⠈⠉⠽⠏⠉⣻⢄⠆⠭⠁⡅⡩⡯⡱⣿⣹⡆⡎⠉⠅⠉⠽⠉⠨⠩⢹⡏⠠⣹⠨⠩⠉⢍⠉⢣⡄⢋⠍⠝⡌⠅⡰⢆⠈⠴⠩⣈⢡⢀⠀⠩⠉⢹⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⠻⠻⠿⠿⠿⢿⠻⡿⠿⢿⡛⢛⠛⠛⡛⢛⡻⢛⢻⢛⠛⣛⢻⢲⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣼⣼⣤⣬⣍⣤⣤⣤⣯⣤⣥⣤⣧⣭⣤⣬⣤⣬⣴⣤⣥⣬⣤⣬⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⡻⠻⢿⠛⢻⡟⢛⠛⢻⣟⣟⠟⠛⢿⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣶⣶⣾⣶⣶⣷⣶⣶⣾⣿⣷⣶⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣌⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠻⣿⠿⠻⠟⠿⠿⠿⡟⠿⠿⠿⠿⢿⣿⠿⢿⣿⢿⠟⠿⠿⠿⠿⡿⠿⠿⡿⡿⠻⠿⢿⠿⢿⣿⢿⠛⣿⠿⡿⢿⠿⠿⠿⠿⠿⠿⡿⠻⡿⡟⠻⠿⠿⠿⢿⡟⠿⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣼⣤⣤⣥⣤⣦⣡⣧⣵⣤⣤⣤⣬⣇⣮⣬⣿⣤⣥⣤⣤⣤⣴⣤⣤⣀⣤⣧⣴⣤⣼⣰⣥⣽⣾⣿⣤⣤⣤⣼⣶⣬⣤⣬⣤⣬⣿⣼⣤⣿⣤⣴⣤⣤⣼⣷⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⢹⢉⠙⢿⡏⡙⢉⠙⡏⢉⠙⡙⠙⡏⠙⠙⠉⠙⡏⢻⡉⠛⠉⠋⠉⠙⢿⠙⢿⠙⣉⠋⡟⠉⢹⠋⠉⠉⠋⠋⢹⠉⢻⠟⠹⣿⣉⠉⠋⠋⠋⡏⡙⠉⠋⡏⠉⠉⢹⠙⡙⠙⠏⠋⣏⠛⠋⢹⠋⠉⡏⠋⢻⣿⣿⣿
⣿⡟⠛⠺⢛⡟⠛⠛⠛⢻⢛⢻⠛⠋⢹⠛⠛⠛⠛⠙⢻⠙⠛⠛⠛⠋⡟⠛⡛⡙⢻⠛⠛⢻⡛⠻⡛⠛⠚⡾⠛⢻⢛⡟⠛⠛⠛⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣷⣷⣾⣷⣶⣷⣷⣷⣿⣿⣿⣷⣾⣾⣶⣾⣶⣶⣾⣶⣷⣾⣶⣶⣷⣿⣿⣿⣾⣷⣷⣿⣷⣷⣿⣾⣿⣷⣷⣷⣾⣷⣶⣶⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⡏⢹⡹⣛⢯⡟⡟⡟⡻⣿⡋⡿⡻⡟⡻⡛⡟⡛⡿⣛⢿⢟⣟⢻⢻⡏⡏⡿⣟⣿⣿⢿⢻⠻⡻⣿⣛⣟⡻⢟⡋⣿⡟⣻⡟⡻⡟⡛⡛⡿⡻⣿⡿⡻⡏⣹⡟⡿⡿⣛⡟⣿⢻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⣧⣷⣭⣿⣿⣵⣧⣭⣿⣧⣧⣭⣧⣧⣧⣇⣭⣷⣭⣾⣿⣬⣼⣼⣧⣧⣧⣼⣿⣿⣼⣼⣿⣧⣿⣯⣯⣽⣮⣥⣿⣯⣤⣯⣥⣧⣧⣧⣧⣭⣿⣧⣥⣧⣿⣿⣰⣧⣭⣷⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠎⡏⠮⡏⠮⡏⠎⡇⠇⡇⣷⢱⢸⣿⢸⠱⢽⠳⢹⢸⠸⢹⢸⡏⠮⡯⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⣿⣆⠙⠿⣒⣿⣧⣿⣿⣧⣬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣾⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠈⣿⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣀⣹⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣭⣙⣟⣻⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⢻⣿⠿⢿⣿⡿⣿⠿⣿⣟⢿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⣷⣶⣾⣼⣶⣿⣶⣿⣶⣾⣷⣾⣾⣿⣿⣶⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 999

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/29/osi-sold/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/29/osi-sold/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.29.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Under_the_Leadership_of_Stefano_Maffulli_as_Executive_Director,_the_OSI_is
Still_Controlled_by_Microsoft,_Promoting_Proprietary_Software_Like_GitHub⠀✐


Posted in Microsoft, OSI at 4:54 pm by Dr. Roy Schestowitz


Maffulli’s grace_period did not last long…


                    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Clearly Microsoft⦈


Minutes ago:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇ClearlyDefined_Update:_December_2021⦈_


As explained and covered before, ClearlyDefined is like a Microsoft front and
it receives most of the financial resources of the OSI:


    * Meet_the_People_Behind_ClearlyDefined_(Mostly_or_Clearly_‘Microsoft
      Proxy’),_Where_Most_of_the_OSI’s_Budget_Nowadays_Goes_and_Flows
    * ClearlyDefined_is_Just_Microsoft_Land_Grab_(Which_the_OSI_Now_Actively
      Participates_in)
    * ‘It’s_Dead,_Jim’:_OSI_Controlled_(Partly)_by_Microsoft_and_Promotes
      Microsoft_Proprietary_Software_After_Taking_Microsoft_Bribes
    * Clear_Linux_is_to_GNU/Linux_What_Clearly_Defined_is_to_Open_Source
    * Free_Software_Institutions_Are_Only_as_Good_or_as_Valuable_as_Their
      Credibility
    * The_OSI_Song
    * Entryism_Works:_OSI_Uses_COVID-19_Pandemic_to_Promote_Microsoft_and_Its
      Proprietary_Software_Traps_After_Taking_Money_(Bribes)_From_Microsoft_and
      Its_Oppressive_New_Tentacles_(GitHub)
    * Passive-Aggressive_Hypocrisy_Defined:_CommitChange_Seemingly_Committed_to
      Corporate_Takeover_in_the_Name_of_Tolerance_(Not_of_Everyone)
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⢰⣶⣆⠀⠀⢰⣶⣶⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢡⣤⣤⡜⠛⠋⣤⣶⣾⣿⣿⣿⣶⣾⣿⣿⣤⣤⡄⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⠿⠿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢃⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠉⠱⣶⣾⡏⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢀⣤⡄⠛⠛⢡⣤⣼⠛⠛⣿⣿⣿⡟⠛⢻⣿⣿⠛⠛⠋⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠸⠿⠿⢀⣀⡸⠿⠿⣀⣀⡘⠿⠿⠀⣀⡀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⢿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡾⠋⠁⠈⠉⠃⠀⣿⠀⠀⣀⣠⣄⡀⠀⠀⣀⣠⣀⠀⠀⢀⡄⣀⡄⢸⡇⢀⡀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣆⠀⢠⣿⠀⣛⠀⣀⣀⢀⡀⡀⢀⣀⡀⠀⣀⡀⠀⣀⣀⠀⣸⣏⣱⣆⠀⠀⠀⠀
⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⠀⣰⣿⣿⣿⣿⡄⠈⢁⣀⣈⣷⠀⢸⡏⠀⠀⢸⡇⠀⢳⡀⠀⣼⠃⠀⢸⣿⣿⣿⣯⣿⣿⣿⡧⠀⠀⡏⠹⣤⡟⢸⠀⣿⢸⠋⠈⢸⡏⠁⣿⣿⣿⡆⠧⣄⢼⣿⣿⣷⢹⡏⢹⡏⠀⠀⠀⠀
⠀⠈⢧⣀⠀⠀⢀⡄⠀⣿⠀⠹⣅⠀⠀⣀⠀⢼⣿⣿⣿⣿⠀⢸⡇⠀⠀⢸⡇⠀⠀⢷⣰⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠓⠀⠛⠀⠘⠀⠛⠈⠓⠒⠘⠃⠀⠛⠛⠋⠀⠒⠋⠈⠛⠛⠃⠘⠃⠘⠓⠀⠀⠀⠀
⠀⠀⠀⠉⠙⠋⠉⠀⠀⠉⠀⠀⠈⠉⠋⠉⠀⠀⠉⠋⠁⠉⠀⠈⠁⠀⠀⠈⠁⠀⠀⣸⠏⠀⠀⠀⠘⠛⠛⠛⠉⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣶⠀⢰⣶⠀⢀⣀⠀⠀⣶⢀⣀⣀⡀⠐⣓⢀⣀⣀⡀⠀⢀⣀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡄⠀⡼⣿⢨⡅⢀⣤⡄⣠⣠⣄⣠⣤⡀⢀⣤⡄⢀⣤⣄⢠⣾⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⠒⢺⣿⢰⡿⠿⠷⠀⣿⢸⣿⣿⣿⠄⣿⢸⡏⠉⣿⢰⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣾⣿⣿⣿⡆⠀⢸⡇⢳⣼⠁⣿⢸⡇⣿⠀⠀⣿⠁⢸⣿⣿⣿⠘⢶⡄⣿⣿⣿⡇⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠛⠀⠘⠛⠀⠙⠛⠃⠀⠛⢸⡟⠛⠋⠀⠛⠘⠃⠀⠛⠀⣍⣋⣽⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠁⠈⠁⠀⠉⠈⠁⠈⠉⠁⠉⠀⠀⠉⠉⠁⠈⠉⠁⠈⠉⠉⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⡀⣴⣶⣦⡀⠀⠀⣶⠶⣦⡶⢶⡄⣠⣶⣶⡄⢰⡶⠆⣴⣶⣦⡀⠀⢠⣖⠲⠀⣶⠀⢰⡆⣠⠶⠶⠄⣤⠶⠶⢀⣴⣶⣦⢠⣶⠲⠆⣴⡖⠖⢾⡷⠆⣶⠀⢰⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⢿⣭⡭⠁⠀⠀⣿⠀⣿⠀⢸⡇⠻⣿⣿⠏⢸⡇⠀⢿⣭⡭⠁⠀⠠⣍⣽⠆⢻⣤⣼⡇⠻⣦⣤⠄⠿⣤⡤⠘⢿⣭⡭⠠⣭⣽⠇⢬⣭⡷⢸⡇⠀⢻⣤⣼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣯⣝⣉⣍⣩⣽⢉⣹⣉⣹⣏⣍⣉⣭⣹⣿⣉⣹⣁⣉⣭⣁⣿⣍⣸⣟⣹⣿⣁⣩⣍⣏⣽⣹⣁⣿⣲⡈⣿⣩⣹⣿⣄⣹⣉⣻⣭⣿⣭⣯⣋⣏⣠⣏⣍⣫⣏⣏⣽⣋⣯⣉⣇⣏⣙⣽⣉⣿⣁⣯⣍⣏⣍⣿⣿⣿⣿
⣿⢿⠿⠻⡿⠟⣿⠻⠿⠿⣿⡟⠿⠿⠿⠿⠿⢿⣿⠿⡿⡿⡟⣿⠿⠻⠿⡿⠿⡿⣿⠿⢿⣿⠿⢿⠿⠿⢿⠿⠟⠿⡿⠿⢿⠟⡿⠟⢿⠿⠿⠿⡿⡿⠿⠿⠿⢿⡿⢿⠿⠿⠿⢿⡿⡿⠿⣿⢿⠿⠿⠿⣿⡿⢿⣿⣿⣿
⣿⣧⣶⣼⣧⣴⣿⣼⣧⣦⣿⣷⣬⣦⣾⣬⣴⣼⣧⣶⣦⣧⣦⣿⣿⣦⣼⣼⣤⣗⣼⣵⣮⣿⣦⣧⣦⣤⣿⣼⣴⣧⣿⣴⣼⣥⣿⣥⣷⣤⣼⣦⣿⣴⣶⣴⣷⣼⣧⣼⣧⣶⣤⣣⣿⣼⣬⣯⣼⣮⣮⣶⣽⣦⣼⣿⣿⣿
⣿⡽⡍⠉⡅⢠⢋⡏⢭⠉⢙⡇⠈⠍⢙⡍⠉⡋⡗⣽⠰⡉⢽⡟⡉⢽⠏⣿⡍⠋⡝⡉⢹⡫⡫⠉⣭⠉⢝⠀⠉⣯⢙⢝⢙⡏⡽⢹⡋⠉⢹⠈⡍⡏⢽⠈⢙⢝⠉⡏⢹⡍⠩⢸⢩⡋⠉⢙⠅⣏⠍⢽⣿⣿⣿⣿⣿⣿
⣿⢿⠿⡿⠿⠗⡾⡿⠿⢿⢿⡿⢿⢿⢿⠿⡿⡿⣿⢿⢿⠿⣿⢷⢿⢿⣿⢿⠿⢿⢿⠿⣿⢿⡿⡿⣿⢷⢿⢿⡿⢿⢿⠻⢿⢿⡿⡿⡿⣿⣿⡿⡿⣷⣿⣿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣦⣤⣧⣼⣱⣧⣽⣤⣴⣧⣤⣥⣴⣧⣤⣤⣿⣴⣥⣼⣧⣼⣧⣢⣿⣭⣆⣵⣤⣼⣿⣤⣬⣤⣽⣧⣥⣤⣧⣥⣽⣤⣥⣦⣥⣷⣦⣼⣠⣬⣤⣽⣯⣥⣼⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡍⡍⣻⠛⢛⢿⠛⢛⠟⢻⣟⠛⠻⠛⢛⣿⢫⣿⠛⠟⡟⣿⢟⢩⠛⢻⡉⢛⡟⠻⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣷⣿⣶⣾⣾⣼⣶⣷⣾⣿⣾⣾⣶⣶⣿⣷⣿⣶⣷⣿⣿⣼⣶⣿⣾⣷⣾⣷⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣗⣆⣩⣝⣉⣇⡍⣵⣺⣩⣸⣏⣉⣭⣁⣿⣩⣻⣋⣿⣽⣩⣹⣅⣹⣋⣿⣿⣹⣹⣏⣿⣁⣯⣍⣽⣏⣸⣏⣘⣏⣯⣃⣏⣉⣍⣽⣇⣹⣉⣿⣰⡈⣏⣩⣹⣹⣤⣫⣉⣏⣹⣹⣩⣷⣜⣉⣵⣨⣉⣝⣉⣏⣽⣿⣿⣿
⣿⣿⡿⠿⢿⠿⠿⠿⠿⣿⡟⠻⠻⢿⣿⠿⠿⠿⡿⠿⠿⣿⠟⢿⠿⠻⢿⡿⠿⠿⢿⠿⠿⡟⠿⡿⢿⠿⠿⡿⠟⠿⣿⠿⠿⡿⠿⢿⢿⠿⣿⢿⡿⢿⠿⠿⠻⡿⠿⢿⠿⠻⢿⠿⡿⠿⣿⢿⢿⠿⣿⢿⠿⠿⢻⣿⣿⣿
⣿⣿⣧⣥⣼⣧⣥⣦⣧⣿⣷⣦⣧⣼⣯⣬⣴⣼⣧⣿⣤⣽⣧⣿⣥⣴⣼⣧⣤⣥⣼⣧⣼⣧⣼⣏⣸⣯⣮⣮⣤⣧⣿⣴⣵⣧⣴⣥⣼⣧⣿⣼⣇⣽⣤⣮⣴⣧⣄⣹⣤⣯⣼⣥⣮⣦⣽⣾⣽⣤⣧⣼⣧⣮⣼⣿⣿⣿
⣿⡯⢿⠉⠋⣯⣭⢫⡏⢝⠉⢠⡏⢙⢙⡟⡙⣭⠉⢩⢽⢸⡫⡏⠉⣽⠹⠉⡟⢹⠩⡫⠁⢘⠙⠉⡏⠭⢹⡩⢨⡏⢹⠉⡫⠃⡬⢉⠻⠙⢩⠉⡏⣿⡍⡫⣿⠏⠫⠀⢩⡏⢹⡝⢉⢨⡏⠉⢽⠩⠏⠋⡍⠉⣟⠍⢡⣿
⣿⡿⠿⣿⣿⡿⡷⡾⡿⣿⣿⢿⡿⣿⢿⣿⠿⡿⠿⡿⣿⢿⣿⢿⣿⡿⣿⣿⢿⢿⡾⣿⡿⣿⡿⡿⡿⢿⡿⢿⢿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⡿⡿⠿⡿⡿⡿⣿⢿⢿⢷⡾⣿⣿⢿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣼⣤⣼⣤⣭⣤⣯⣤⣬⣤⣼⣤⣫⣿⣴⣴⣼⣧⣤⣯⣧⣼⣿⣬⣥⣤⣧⣬⣤⣿⣧⣽⣼⣯⣤⣿⣬⣤⣼⣤⣼⣽⣬⣬⣽⣿⣿⣧⣬⣼⣤⣯⣤⣯⣤⣤⣿⣥⣼⣤⣼⣦⣷⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣟⠛⡟⢹⡋⢙⠛⡟⠙⡟⢻⡻⡟⣛⠻⢻⡛⢻⠛⢻⣟⢟⡟⡟⣿⣻⡛⠹⣛⡻⡏⡏⠻⣛⡏⠙⡟⣛⠛⡛⢟⣻⢹⠛⢛⠿⣛⠋⣿⠛⢻⢻⠟⡻⡛⠋⡿⡟⢙⣿⢛⡏⢛⠋⣟⠛⡟⣛⠻⢻⡋⢻⠛⣻⣿⣿
⣿⣷⡷⣿⣿⣿⣿⣷⡿⣾⣿⣾⣿⣾⡿⣿⣿⣿⣿⣷⣷⣿⣿⣾⣿⣿⣿⣿⣾⣿⣾⣾⣿⣿⣿⣾⣿⣿⣾⣾⣿⣷⣷⣿⣷⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿
⣿⣇⣀⣪⣂⣜⣀⣿⣀⣆⣀⣿⣨⣂⣶⣠⣈⣆⣀⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⡛⠿⢿⠿⡟⠿⢛⣻⠿⢻⡿⠿⠿⠟⣿⠿⢿⠿⡿⠿⣿⠿⢿⠿⢿⢻⠻⡿⣟⢻⡛⡛⣟⢻⡿⡿⠿⡟⣿⢿⣿⠿⢿⠿⢿⢻⠿⠿⠿⢿⣿⡿⠿⢿⡟⢿⠿⠿⠿⣿⠿⠿⡿⠻⠿⠟⣿⠿⢿⠟⢻⠿⣿⢿⣿⣿
⣿⣷⣷⣾⣷⣶⣷⣧⣿⣾⣾⣾⣷⣶⣿⣶⣿⣴⣾⣾⣿⣾⣿⣾⣾⣾⣿⣾⣶⣷⣷⣾⣶⣷⣷⣿⣾⣷⣶⣷⣽⣷⣿⣷⣾⣾⣿⣾⣷⣾⣷⣮⣿⣶⣶⣿⣷⣶⣿⣾⣾⣿⣷⣶⣷⣶⣿⣶⣿⣦⣾⣶⣾⣾⣷⣿⣿⣿
⣿⡯⠁⡭⣏⢽⢸⣡⠉⣯⢉⢍⠅⡩⣯⢙⢹⡀⢨⢫⢿⢐⠏⢉⢍⢹⣉⡭⢈⢻⡝⣉⠉⣿⠉⠩⡯⢈⢹⠅⣯⢹⠏⡯⡉⢝⠍⣩⢸⡇⡩⡉⣽⡰⢊⢽⡏⠍⢽⡍⣽⠍⡩⡉⣝⠉⢩⡏⠍⣿⣻⡇⢰⡝⡭⢹⠏⣿
⣿⣿⠿⢿⢿⡿⣻⠿⣿⠿⢿⠿⡿⠻⡿⠻⢿⢿⣷⡿⠿⡿⢿⡿⡿⠿⢿⡿⢷⠿⠿⡿⡿⠿⠿⡿⢿⠿⡿⠿⣿⠟⢿⠿⣷⢿⣿⡿⠿⠿⠿⠿⠿⣿⠟⡿⡟⢻⠿⠻⠟⠿⡿⠿⢿⣿⠿⠟⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿
⣿⣯⣤⣴⣴⣧⣥⣬⣾⣤⣧⣬⣮⣤⣥⣤⣬⣼⣿⣰⣬⣦⣼⣯⣧⣤⣿⣧⣿⣥⣶⣼⣧⣦⣤⣿⣴⣤⣴⣤⣿⣤⣧⣤⣿⣿⣿⣮⣥⣤⣧⣤⣤⣿⣥⣦⣧⣤⣧⣴⣥⣬⣿⣤⣼⣯⣤⣤⣼⣄⣹⣿⣿⣿⣿⣿⣿⣿
⣿⡯⠏⡋⡋⠙⡅⡙⡽⢝⠙⢱⡏⠙⢙⠉⣿⡏⡛⢝⢻⣏⢩⡏⢻⡝⢹⡟⢩⣧⠫⣟⣯⢫⡏⠋⣿⠙⢫⢻⠏⡯⠛⠝⠿⡯⡏⡝⠫⡟⠋⡏⡏⢹⡫⠘⢝⡏⣯⠋⠋⣿⡟⠉⡋⠋⠙⠙⢙⡏⠝⢹⠙⡟⢽⠛⣯⣿
⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣀⣋⣘⣘⣓⣘⣓⣂⣛⣈⣛⣘⣛⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⡻⡟⢿⢙⠟⠛⠿⠻⡟⢻⡟⣟⢻⣟⠻⠻⠛⢛⢿⠟⠿⡻⢛⢛⠛⡻⢛⣿⠛⢛⢿⠟⣿⢻⠻⢛⡟⠛⠛⢟⠛⣻⡟⢛⣹⢛⠛⠟⣿⢻⣿⠛⡟⡟⣛⠟⢻⠛⢛⡙⢛⡟⠻⡋⡟⣿⢻⠛⢛⣿⣿⣿⣿⣿⣿⣿
⢿⣷⣷⣷⣾⣾⣶⣾⣾⣶⣷⣾⣷⣶⣾⣷⣶⣾⣶⣾⣾⣾⣶⣶⣾⣶⣶⣷⣤⣿⣶⣾⣾⣶⣿⣾⣶⣶⣷⣶⣶⣦⣴⣿⣷⣾⣿⣶⣷⣶⣿⣶⣿⣶⣶⣷⣿⣼⣶⣷⣾⣷⣾⣷⣶⣶⣷⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣍⣼⣩⣿⣼⣍⣹⣩⣿⣩⣁⣸⣨⣿⣉⣧⣏⣉⣯⣏⣝⣏⣏⣹⣿⣙⣭⣯⣁⣿⣁⣀⡏⣽⣋⣯⣉⣇⣟⣉⣿⣿⣭⣝⣝⣸⣏⣀⣨⡏⣹⣷⣡⣹⣭⣏⣽⣹⢉⣏⣍⣇⣿⣈⣏⣏⣿⣩⢹⣁⣹⡝⣽⣿⣿⣿
⣿⠿⠻⡟⠿⡿⠿⠿⠟⠿⠿⣿⠿⠿⢿⠻⠿⠿⠻⢿⠿⢿⡟⠿⠿⢿⡿⠿⢿⠿⣿⠿⠟⣟⠻⡻⡛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣼⣶⣵⣧⣷⣴⣥⣦⣧⣿⣁⣾⣼⣬⣶⣼⣧⣼⣷⣼⣧⣿⣴⣼⣧⣤⣷⣤⣿⣵⣿⣧⣵⣵⣬⣧⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡯⠝⠝⢫⡝⢫⡝⠻⡟⠛⡯⡛⣟⠛⡋⠻⠋⣿⡟⡛⠋⣻⠻⠫⣟⠋⡏⢫⡿⠛⢙⡏⡫⢻⣯⠻⢛⢿⠙⡿⢹⣟⣻⠟⢫⡛⠩⠛⠛⣽⠫⠋⣿⢽⠟⢫⠏⡯⠙⠝⢫⡏⣿⠛⢫⠛⢹⡟⡟⠛⡿⢹⠝⠝⢻⡹⣿
⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⡿⢿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣷⣔⣦⣤⣔⣮⣤⣤⣦⢀⣿⣢⣦⣔⣴⣤⣯⣲⣠⣕⣷⣼⣔⣄⡴⣱⣿⣤⣤⣴⣿⣤⣺⣖⣴⣥⣺⣔⣔⣤⣶⣤⣶⣤⣣⣴⣿⡰⣹⣇⣔⣼⣕⣿⣴⣴⣦⣔⣽⣔⣿⣦⣠⣆⣿⣤⣔⣦⣢⣦⣧⣺⣩⣿⣰⣼⣿
⣿⣟⠙⡟⠛⣟⡛⡻⡟⣟⠛⢻⡏⠻⡛⠉⢛⠙⠛⢟⢻⣿⠛⠟⠻⡟⢛⢿⠛⠟⠛⡛⣿⡛⣟⠟⠋⠉⣿⡛⠙⡋⢻⣿⢻⡛⡟⢻⡛⠟⡏⢛⣿⡟⣻⣟⢙⠛⢻⣟⠛⢛⠟⢻⠻⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡷⣶⣶⣶⣿⣶⣾⣷⣾⣶⣾⣿⣾⡾⣶⣷⣶⣮⣾⣾⣿⣾⣾⣾⣷⣶⣷⢴⣷⣷⣶⣿⣷⣿⣶⣷⣶⣿⣶⡶⣶⣿⣷⣾⣶⣷⣾⣤⠶⣷⣾⣿⣷⣿⣷⣾⣶⣾⣿⣾⣾⣾⣿⣵⣷⣶⣶⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣯⣈⣨⣒⣀⣰⣁⡲⢡⣻⣠⣡⣈⣇⣎⣀⣌⣅⣹⣀⣿⣘⣂⣿⣆⣁⣗⣸⣗⣕⣉⣺⣀⣯⣺⣊⣰⣁⣱⣀⣊⣘⣗⣈⣊⣰⣇⣻⣰⣎⣪⣀⣎⣇⣊⣪⣀⣎⣠⣾⣘⣷⣀⣔⢁⣇⣆⣨⣈⣠⣾⣐⣇⣁⣆⣺⣿
⣿⣿⠿⢿⢻⡿⢿⡟⢿⡿⢿⣿⢻⣿⢿⡿⣿⠿⣿⢿⢻⡿⡿⢿⡿⡟⣟⣿⠿⣿⢿⡟⣿⠿⡿⠟⣿⡿⢿⢿⠿⣿⣿⠿⠟⡿⠻⡟⡿⡟⣿⠿⠿⢿⢻⡿⣿⠻⣿⠿⢿⢿⢿⢻⠿⢿⠿⢿⡿⠿⡿⡟⢿⠿⣿⠿⢿⣿
⣿⣿⣷⣾⣾⣶⣾⣷⣾⣷⣼⣭⣬⣭⣥⣥⣭⣥⣭⣭⣬⣭⣥⣬⣥⣥⣥⣭⣥⣭⣬⣥⣭⣤⣭⣤⣭⣥⣥⣬⣤⣽⣿⣾⣾⣷⣶⣷⣷⣷⣿⣶⣾⣿⣾⣾⣿⣶⣾⣷⣾⣼⣷⣾⣷⣾⣶⣾⣿⣶⣧⣷⣷⣷⣾⣶⣿⣿
⣿⡝⣉⢀⣯⣹⡯⣯⢙⢹⣝⢉⡩⢸⠉⢩⢉⡇⢩⣹⢠⡝⡅⣬⣿⢁⡋⡅⣸⡍⢨⢅⡩⣯⣹⡯⡫⣉⢍⣹⠅⣸⡍⠉⡯⡉⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⢿⣿⡿⡿⣿⢿⢿⢿⣿⡿⣿⢿⢿⢿⢿⡿⡿⢿⢿⣿⢿⢿⣿⣿⣿⢿⢿⢿⣿⣿⡿⣿⢿⣿⢿⣿⡿⡿⣿⠿⣿⢿⢿⣿⢿⡿⣿⢿⣿⢿⡿⡿⡿⣿⣿⠿⢿⡿⢿⢿⢟⣿⢿⢿⡿⣿⣿⢿⡿⡿⢿⣿⣿⣿⣿
⣿⣵⣤⣼⣧⣴⣤⣿⣧⣷⣥⣦⣦⣼⣤⣧⣤⣥⣧⣷⣦⣴⣧⣧⣤⣤⣽⣇⣦⣬⣤⣼⣿⣴⣤⣴⣧⣬⣼⣠⣤⣦⣥⣿⣥⣵⣇⣽⣥⣤⣧⣯⣼⣯⣥⣤⣦⣤⣧⣊⣯⣵⣤⣼⣧⣤⣴⣤⣿⣴⣥⣥⣮⣼⣿⣿⣿⣿
⣿⣟⢛⢟⠛⣻⡟⢻⡛⢛⣿⠛⡛⢟⡛⣿⡻⢹⡛⢛⠙⣛⣻⡏⢻⠛⣿⢉⡛⢛⣿⠛⣟⡛⡛⣟⢟⢛⠟⣟⣿⡏⢛⢿⡻⠛⢛⣿⡋⣟⠟⣏⢹⡏⢙⠛⣛⢿⣛⣿⠛⢛⢛⡟⠛⡋⠉⡏⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣷⣾⣷⣿⣿⣿⣿⣿⣷⢷⣿⣿⣾⠿⣾⣿⣿⢾⣾⢿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣾⣿⣿⣷⣿⣾⣿⣿⣿⣿⣷⣿⣿⣾⠾⣾⢾⣿⣿⣿⣿⣿⣿⣿⡿⡾⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣄⣅⢸⣃⣄⣇⣖⣿⣆⠐⣿⣨⣨⣀⣔⣀⣪⣀⣐⣠⣿⣀⣆⣺⣆⣾⣗⣸⣃⣰⣇⣂⣺⣀⣎⣀⣎⣀⣷⣀⣔⢤⣧⣸⣡⣀⣷⢌⣿⣸⣠⣸⣀⣯⣂⣰⣇⣰⣀⣸⣎⣤⣀⢎⣾⣇⣶⡧⣤⣪⣘⣿⣀⣰⣀⣿
⣿⣿⠛⣛⠛⣟⠟⠟⣟⠟⢟⢹⣿⣛⣿⠻⠛⡟⡟⢿⠻⡻⠟⣻⡿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣷⣶⣿⣶⣷⣶⣶⣷⣶⣿⣴⣿⣶⣶⣷⣷⣯⣴⣾⣶⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣧⣛⠉⢸⣿⢔⢨⡋⠉⣭⠉⣍⢹⣟⡃⡅⡋⡏⣯⣽⡍⡩⠁⡫⡉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⡛⡿⡿⠿⠟⢿⢟⢿⠿⠛⡿⢿⢿⠿⣿⢛⠿⡿⢿⡿⢷⢿⠿⠿⠻⢿⠿⣿⣿⠿⡿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣥⣦⣦⣤⣧⣢⣯⣵⣤⣼⣧⣴⣤⣬⣿⣬⣼⣎⣸⣿⣤⣴⣤⣼⣤⣿⣀⣿⣭⣤⣤⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⡉⡍⢩⡏⠍⠩⠏⠃⡯⠻⠉⣥⢉⠛⡉⠙⡝⢹⡏⠋⡝⠉⣿⡉⠋⡋⠋⣽⠏⡯⡏⡙⠉⡫⢫⠫⠋⠟⢽⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1146

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

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✐ Response_to_Latest_Call_for_EPO_Strike_Contains_Lies_From_Campinos_(and
Another_Warning_That_Quality_of_European_Patents_Has_Collapsed)⠀✐


Posted in Deception, Europe, Patents at 12:59 pm by Dr. Roy Schestowitz


                        🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Dogfooding⦈_
                  Choking on his own lies. Lies, lies, lies.


Summary: Before the unlawful "Strike_Regulations"_were_thrown_out_by_ILO-AT_in
Geneva Campinos tried to talk down a strike that would happen the following
year. Today we look at the response to that talk…


THE EPO has long had illegal “Strike Regulations”, made up by Benoît
Battistelli with complicity of many states. We still have a couple more parts
to publish in a_series_about_this_complicity.


In the meantime, consider the time Campinos (who had already enjoyed these
unlawful “Strike Regulations” for 1.5 years) said: “I appreciate that for some
of you, things may not be changing as quickly as you would like.”


Another couple of years have passed since then. Nothing has improved. In the
response below, published 25 months ago, we can clearly see the “Message from
the President”, who lied to the staff while crushing_the_staff. As the union
put it back then, “in response to the call for strike from SUEPO, President
Campinos raised several points. We have now carried out a fact-checking
exercise. Financial study, social dialogue, production pressure, disciplinary
cases, career progression, ballot for a strike…”


Incredibly enough, all this time later many of the same points remain valid. We
thus reproduce the publication below.


     27.11.2019
     su19028mp – 0.2.1/0.3.2


     § President: “I appreciate that for some of you, things may not be
     changing as quickly as you would like.”⠀➾


     In his recent “Message from the President”, in response to the call
     for strike from SUEPO, President Campinos raised several points. We
     have now carried out a fact-checking exercise. Our report is below.


     President: “Financial Study, we want to assess which levers are most
     appropriate”


     Fact: The President presented a heavily-biased Financial Study
     without the involvement of Staff Representation. His call for
     feedback, asking staff to choose between the Measures, is divisive
     and a psychological trick to feign respect, community and
     cooperation. The President has repeatedly stated that the_most
     important_conclusion,_that_we_have_to_fill_a_€5.8_billion_gap,_is_not
     open_for_discussion.


     President: “There have been 89 meetings so far between the Office and
     Staff Representation”


     Fact: The President’s delegates who participated in the various
     meetings were never given the mandate to properly negotiate. We_must
     conclude_that_the_purpose_for_most_meetings_was_simply_to_buy_time.
     Again and again, Staff Representatives and SUEPO filed both proposals
     and critical analysis. On their part, management never entered into
     any real dialogue. The high number of meetings is now being used for
     marketing purposes with the Administrative Council. So much has gone
     wrong at the Office: from a human perspective, from a patent quality
     perspective, from a perspective of fairness and openness. We are
     eager to renew the EPO and move away from the past. The President,
     however, sticks to the past and the same management.


     President: “We decided to lower the original production target for
     2018 and for 2019”


     Fact: This is very true. Unfortunately, the production target is not
     the problem, it is the productivity target. And there they are again,
     the frequent half-truths of management. In_fact,_overall_productivity
     and_production_pressure_has_increased_in_recent_years. An Examiner
     has 20 minutes’ less time to complete a product in 2019 compared to
     2018 (2 hours less than in 2014). The target for 2019 is 1.77 days
     per product. As of today, 1.79 days per product has been reached.


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


     President: “Disciplinary cases (…) One has been resolved and the
     other is pending. Seven cases have been settled”


     Fact: The President has taken 14 months to settle just one urgent
     case concerning dismissal. Another similarly outrageous case in The
     Hague is still pending. But there are other Battistelli-era cases the
     President does not even want to speak about. And then, of course, all
     managers responsible for these years of unbearable pressure and false
     accusations are still in place. We_still_have_a_long_way_to_go_before
     being_able_to_close_the_dark_chapter_of_the_past.


     President: “Career progression (…) we are pursuing a policy of “no
     one should be left behind”


     Fact: This is perhaps the most hypocritical statement of all. For
     years we have denounced the harmful consequences of the New Career
     System such as rewarding quantity over quality, and penalising staff
     members on parental leave and maternity leave. Newcomers have been
     systematically discriminated against during the Reward Exercise.
     Older colleagues have been put under extreme production pressure. In
     the meantime, patent quality has degraded dramatically, as has the
     reputation of the Office. An authoritarian management style blocks
     innovation and open discussion. Many colleagues are frustrated and
     demotivated. On his first day in the Office Staff Representation
     presented the new President with proposals for a new, fairer career
     system. After_15_months_nothing_has_changed.


     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_growth_in_granted_patents_is_accompanied_by_a
     drop_in_patent_quality._Number_of_granted_patents_per_year_(blue)_and
     quality_of_granted_patents_according_to_DQA_(red).⦈_


     President: “I personally don’t believe that we’re at the stage of
     last resort (…) strikes.”


     Fact: Unsustainable production pressure. Falling patent quality.
     Outrageous legal fights. An increasingly arbitrary career system.
     Five-year contracts. Threats and pressure. Although it is true that
     the communication-style of management has become gentler and
     seemingly more understanding, this is merely marketing. Indeed, only
     the_marketing_has_changed. The new President, after 18 months in the
     Office, remains surrounded by mostly the same faces as the old
     President. The autocratic management-style of President Battistelli
     clings on. And yet there is so much potential at the EPO. So many
     clever and highly-trained professionals eager to innovate, to involve
     themselves, to discuss, to try new things and produce the best
     patents with the highest quality. This potential just has to be
     unleashed. We_are_ready_for_real_change!_What_are_you_still_waiting
     for,_Mr_President?


     SUEPO Munich


Things have only gotten worse since then. Where’s the media coverage? Where’s
the journalism on these matters? The bribed operatives from IAM tell us that
EPO “quality” is top-notch while bagging EPO money from the EPO’s PR agency,
FTI Consulting. Shouldn’t the media be covering the bribery of the media? Maybe
not, the media does not wish to discredit itself; the EPO is meanwhile hiring
more_people_to_manipulate_the_media. █


⠉⠤⠀⠙⠲⠯⠝⠃⢀⣀⣀⠀⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⡀⠀⠘⠛⠖⠛⠲⠤⠤⠿⠦⠄⠶⣿⣿⣿⣿⣿⣿⠿⠟⠫⣽⡿⠛⠉⢻⣏⣩⣿⣧⡶⠎⠏⠉⠛
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⠛⠛⠛⠃⠻⢿⣿⣿⡿⠥⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡄⠠⠀⠀⠀⠉⠐⠲⠶⠀⠀⠀⠈⠉⠛⠛⠓⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠛
⠀⠀⣸⣧⣤⠄⠘⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢀⠼⠷⠆⠈⠉⠁⠾⠷⣤⣄⠀⢛⠀⠀⠠⣶⡄⠀⢠⠄⠁⠀
⣤⣀⣀⣀⠀⢀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠒⠒⠦⠀⠀⠀⠼⠟⣋⣩⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣈⣀⡀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢐⣊⣠⡤⢀⣀⣠⣠⣤⣤⣤⣤⣤
⠿⠂⠈⠉⠿⠍⠙⠷⠈⠭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢩⣧⠀⠀⠻⠷⠄⠀⠈⠻⠭⠥⢄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣖⠛⠛⠉
⣦⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⣠⣤⣈⣉⠉⠁⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠘⠿⢿⣿⣿⣏⡛⠛⠛⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⠿⣷⣄⠀⠙⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠎⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⣀⣀⣀⠀⠁⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣧⣤⣀⡀⠠⠞⠛⠛⠑⠰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⡈⠿⠿⠿⠿⣿⡏⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⣺⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠠⠷⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡀⠀⣸⣿⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠈⠁⢨⣿⣿⣿⡆⠀⠀⠀⠙⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⣀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠟⠛⠉⠉⠙⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⡉⠀⠀⠀⠀⠀⠈⠑⠖⠛⠛⠛⠋⠉⠉⢹⣷⣿⣿⣿⣿⣿⣇⣀⣤⣬⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠩⢿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣀⠀⠀⠀⠀⠀⠰⢶⠚⠓⠀⠀⠀⠀⢀⣀⠀⠠⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣽⣿⣿⣿⠀⠀⠀⠀⢀⣤⣾⣻⣿⣀⣘⡿⠉⡁⠀⠀⠀⠀⣀⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀
⣄⣀⣈⠉⠉⠀⠀⠀⠀⠈⠛⢿⡛⠻⠟⣋⣹⣛⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢾⣿⣿⣿⣿⣿⣿⣷⣦⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢩⣍⠃⠀⠀⠀⢲⣿⣿⣶⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠾⠿⠷⠖⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠈⣵⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠤⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣷⣾⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠂⠘⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣠⣄⣀⣀⣀⣀⣀⣶⣶⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣉⣉⣀⣀⣀⣈⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣷⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠉⠤⠀⠙⠲⠮⠝⠃⢀⣠⠤⠀⠘⠂⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⡀⠀⠚⠛⠄⠛⠲⠤⠤⠿⠦⠄⠶⣿⣿⣿⣿⣿⡿⠿⠟⠫⢽⡿⠛⠉⢻⣏⣩⣿⣷⡶⠆⠏⠉⠛
⣷⠶⢇⣠⣤⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣟⠯⠙⠛⠧⣤⣤⡀⠀⠤⣤⣉⠶⠒⠉⠉⠉⠉⣀⣀⣨⣁⠀⠀⢠⣤⣤⣰⡿⢿⢿⣷⣶⣶⣶⢤⡀
⢾⣷⣖⣰⣶⣄⠲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⣶⡭⠿⠟⠛⢋⡉⠐⠒⠒⠀⠀⠀⠀⣼⣿⣿⣷⣛⠀⠒⠟⠉⠀⠀⣐⣛⣻⣯⣭⡭⢁
⣻⣻⣿⢿⣿⣛⠋⠲⠆⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠐⠒⢢⣽⡗⠀⠀⠀⠀⢀⣠⣂⡀⠈⠙⠻⠛⠒⠒⠺⠟⠋⢋⣉⡈⠁⠀⢩⡍
⠛⠛⠛⠉⠻⠿⣿⣿⠿⠥⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠐⠲⠶⠀⠀⠀⠈⣉⠙⢛⡓⠀⠀⠀⡀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠙
⠀⠀⢬⣷⣤⠤⠈⠉⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠲⠀⢀⠼⠷⠆⠈⠉⠁⠾⠷⢶⡤⠀⢛⣀⣀⢐⣶⡆⠀⠠⠆⠁⠈
⣤⣄⣀⣀⡀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢗⠒⠦⠀⠄⠀⠼⠟⣋⡥⠀⠠⠀⠀⠀⠀⠀
⣤⣤⣘⣀⣀⠈⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠛⠿⠋⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢉⣁⠀⠀⣐⣃⣤⡤⢀⣠⣤⣤⣤⣤⣴⣦⣤
⠿⠂⠈⠉⠿⠏⠙⠻⠊⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣩⣷⠀⠀⠻⠷⢆⠀⠈⠛⠻⠦⠄⣀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣖⡋⠉⠉
⣶⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠴⣦⣄⣈⠉⠉⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠈⠻⠿⣿⣿⣯⣍⠉⠉⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⣦⡀⠉⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠲⠎⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣄⣀⣀⠀⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠞⠛⠋⠁⠲⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⣀⠛⠿⠿⠿⢿⡟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠤⠀⠀⣺⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠗⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣿⡿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢀⡀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠉⠈⣿⣿⣿⣷⠀⠀⠀⠈⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣠⣤⣾⣿⠟⢿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠛⠛⠉⠉⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢏⠁⠀⠀⠀⠀⠀⠀⠒⠙⠛⠛⠛⠉⠉⠈⠹⣿⣿⣿⣿⣿⣏⣀⣤⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠟⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣀⠀⠀⠀⠀⠀⠰⢷⠛⠓⠀⠀⠀⠀⢀⣀⠀⠠⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣾⣻⣿⣀⣩⡯⠈⣁⠀⠀⠀⢀⣸⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠒⠀⠀⠀
⣄⣀⣀⠉⠉⠀⠀⠀⠀⠈⠛⢿⡛⠻⠿⢉⣩⣛⣻⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣌⣁⣀⣀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⣿⣿⣿⣿⣿⣿⣷⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢩⣍⠋⠀⠀⠀⢲⣿⣿⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡛⠛⠛⠛⠛⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠛⠛⠖⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢵⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠤⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠤⠒⠂⠘⠛⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣠⣔⣀⣀⣀⣀⣀⣶⣶⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣦⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠉⠤⠀⠙⠲⠮⠝⠃⢀⣠⠄⠀⠘⠂⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⡀⠀⠚⠛⠄⠛⠲⠤⠤⠿⠦⠄⠶⣿⣿⣿⣿⣿⡿⠿⠟⠫⢽⡿⠛⠉⢻⣏⣩⣿⣧⡶⠆⠏⠉⠛
⣷⠶⢏⣠⣤⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣟⠭⠙⠛⠧⣤⣤⡀⠀⠤⣤⣉⠶⠒⠉⠉⠉⠉⣀⣀⣠⣁⠀⠀⢤⣤⣄⣰⡿⢿⢿⣿⣶⣷⣶⢤⡀
⢾⣷⣖⣰⣶⣄⠲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⣶⡭⠿⠟⠛⢋⡉⠒⠒⠒⠀⠀⠀⠀⣼⣿⣿⣷⣋⠀⠒⠟⠉⠀⢀⣐⣛⣻⣯⣭⡍⢁
⣻⣻⣿⢿⣿⣛⠛⠲⠆⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠐⠒⢢⣽⡓⠀⠀⠀⠀⠀⣠⣂⡀⠈⠙⠻⠛⠂⠒⠺⠟⠋⢋⣉⡈⠁⠀⢩⡍
⠛⠛⠛⠉⠻⠿⣿⣿⠿⠥⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠐⠲⠶⠀⠀⠀⠈⣉⠙⢛⡛⠀⠀⠀⡀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠙
⠀⠀⢬⣧⣤⠬⠈⠉⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠲⠀⢀⠼⠷⠂⠈⠉⠁⠺⠷⢶⡤⠀⢛⣀⣀⠐⣶⡆⠀⠰⠆⠁⠈
⢤⣄⣀⣀⡀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⢗⠒⠦⠀⠄⠀⠼⠟⣋⡥⠀⠠⠀⠀⠀⠀⠀
⣤⣤⣘⣀⣀⠈⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠛⠿⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢉⣁⠀⠀⣐⣃⣤⡤⢀⣀⣤⣤⣤⣤⣶⣦⣤
⠿⠂⠈⠉⠿⠏⠙⠻⠊⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣩⣷⠀⠀⠻⠿⢆⠀⠈⠛⠻⠦⠄⣀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣖⡋⠉⠉
⣶⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⡤⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⢴⣤⣀⣈⠉⠉⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠈⠻⠿⣿⣿⣯⣍⠉⠉⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⣦⡀⠉⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠲⠎⣁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⠀⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠚⠛⠋⠁⠺⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⣀⠛⠿⠿⠿⢿⡟⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠤⠀⠀⣺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠗⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣿⡟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢀⡀⣾⣿⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠁⠀⠀⠉⠀⣿⣿⣿⣷⠀⠀⠀⠈⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣠⣤⣾⣿⠿⢟⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠛⠛⠉⠉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢏⠁⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠉⠀⠹⣿⣿⣿⣿⣿⣏⣀⣤⣶⣾⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⣀⠀⠀⠀⠀⠀⠠⣿⠛⠒⠀⠀⠀⠀⢀⣀⠀⠠⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣾⣻⣿⣀⣩⡯⢈⣁⠀⠀⠀⢀⣨⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀
⣄⣀⣀⠉⠉⠀⠀⠀⠀⠈⠛⢻⡛⠻⠿⢉⣩⣛⣻⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣌⣁⣀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⣿⣿⣿⣿⣿⣿⣷⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢩⣝⠋⠀⠀⠀⢲⣿⣿⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡛⠛⠛⠛⠛⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠛⠛⠗⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢵⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠤⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠤⠒⠂⠘⠛⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣠⣄⣀⣀⣀⣀⣀⣶⣶⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣦⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠤⠈⠛⠲⠭⠝⠃⢀⣀⣀⠀⠛⠒⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣀⡀⠀⠘⠛⠔⠛⠲⡤⠤⠷⠦⠠⢶⣿⣿⣿⣿⣿⣿⢿⡛⠫⣽⡿⠛⠉⢿⣏⣩⣿⣯⡶⠮⠏⠉⠻⠿
⠶⢗⣀⣤⡤⠤⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡔⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢼⣟⠟⠛⠓⢦⣄⣀⡀⠠⠤⣤⣵⠶⠒⠋⠉⠉⢛⣉⣀⣤⡁⠀⠀⣤⣤⣄⣰⣿⣿⣿⣾⣦⣦⣤⢤⣀⣀
⣶⣞⣰⣦⡤⠤⠬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⣶⣭⡿⠞⠛⣛⡛⠐⠒⠒⠀⠀⠀⠀⣼⣿⣿⣶⡒⠂⠲⠟⠉⠀⠀⣐⣛⣿⣟⣭⡉⣁⣀
⣿⣿⣿⣷⣛⠓⠲⠆⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠖⢬⣿⠆⣀⡀⠀⠀⢀⣨⠧⠈⠉⠛⢿⠒⠒⠒⠶⠷⠛⠋⠉⠉⠉⠀⢉⡙⢻
⠻⠟⠙⠻⢿⣿⣿⠿⠤⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢠⡀⠠⠀⠀⠀⠉⠀⠶⠦⠀⠀⠀⠙⠛⠻⠷⠖⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⠀⠀⠀⠛⣿
⢀⣸⣧⣤⠄⠛⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢀⠿⠦⠀⠚⠓⠠⢿⡦⣤⡀⠐⠗⠀⠀⢰⣶⡄⠀⢠⠂⠁⠘⠋
⣀⣀⣀⠀⣀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠰⠦⠤⠄⣀⠀⠀⠿⢟⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣙⣀⡀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠋⠀⠀⠀⣒⣁⣤⠄⢀⣀⣤⣄⣤⣤⣮⣤⣤⣤
⠊⠉⠙⠿⠍⠻⠷⠈⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣩⣥⠀⠀⠻⠷⠄⠀⠈⠿⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⣿⣿⣤⣽⣿⣿⣿⣿⣿⣿⡞⠛⠋⠉⠙
⣤⣤⣤⣤⣄⣀⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠐⠒⠂⢀⣤⣄⣉⡉⠙⠒⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠛⠿⢿⣿⣿⣝⡛⠛⠋⠉⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⠿⣷⡄⠈⠓⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣀⣔⣛⠛⠛⠙⢲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠘⠿⠿⠿⠿⣿⡏⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⢐⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸⠷⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠉⠉⣿⣿⣿⣿⡄⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢋⣿⠿⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⠛⠋⠙⠛⠻⠛⠿⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠛⠁⠀⠀⠀⠀⠙⠠⠘⠻⠛⠛⠛⠛⠉⠉⠉⡟⣀⣠⣠⣤⣶⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰⠖⠶⠎⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⣿⠀⠀⠀⠀⠀⣠⣶⣺⣶⣀⣚⡿⠙⡁⠀⠀⠀⠀⣙⡶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀
⣀⡈⠉⠉⠀⠀⠀⠀⠀⠛⢻⠟⢻⡟⣋⣱⣻⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⢀⠀⠀⠀⠀⣌⢁⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⣿⣿⣿⣿⣷⣦⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣚⣛⠃⠀⠀⠀⢲⣾⣿⣶⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠈⢩⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⣀⠀⠀⠉⠉⠉⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⣶⣾⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠀⠀⠀⠤⠴⠀⠚⠛⠀⠀⠀⡀⠠⠤⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠻⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣀⣀⣀⣀⣠⣴⣶⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣉⣉⣀⣀⣀⣁⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣹⣷⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠟⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⣛⡻⠏⠁⠀⠀⠁⠶⠤⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠻⠦⣠⠶⢄⣀⣘⣷⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⣿⠿⢿⣿⣟⣍⢹⠿⢿⣿⣿⣿⣿⣿⣿
⣀⣠⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣷⠄⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⣿⡷⠶⠤⣄⡀⠀⠀⢩⣉⣉⣣⣤⡭⠿⠟⠿⠿⠟⠉⠻⠀⠉⠛⠀⣀⠈⣿⣾⣿⣿⣟⣡⣌⣀⡀⠈⢁⣀⣿⣿⣿
⣀⣠⣅⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢀⠀⠈⣩⣛⣷⣤⣾⣿⠾⢡⣤⣄⠀⠀⠐⢛⣾⣷⣦⣤⣜⣛⣻⡿⠛⠉⠛⣿⣿⣿⠿⠿⠿⠓⠶⠶⢾⣿⣿
⠿⠦⢤⡄⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠯⠭⠤⣤⣶⣦⡀⠀⠀⠀⠀⠀⣸⡟⠛⠿⣷⣦⣄⣭⣡⣴⣴⣶⡿⠟⠿⠛⡿⠷⣶⣾⣤⣬⣥⣤
⣿⣶⣶⣶⣂⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡀⢀⠀⠀⠀⠛⢂⣭⣁⠀⠐⠺⠷⢦⣤⣤⡈⠃⠀⠀⠈⠉⠄⠀⠶⠖⠀⠀⠘⢯⣴⣿⣿⣿⣟⡀
⣈⠿⠛⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⣄⠈⢀⣤⣀⠠⢤⠄⣠⣯⣀⠀⠀⢰⣆⠀⠀⣠⣄⡀⠀⡠⠆⣠⡿⠋⠛⠛⠛⠓
⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⠈⠉⠁⠀⠀⢠⣌⣻⡽⡋⠀⢰⣶⡶⠶⠛⠋⠀⠘⠁⠠⠀⠀⠀⠀⠶⠒⠖
⠛⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠬⠉⠉⠙⢃⠤⠊⠁⠚⠛⠁⠀⠀⠀⣠⠆⠀⠀⠀⢀⣀⣈⣙
⡖⠲⣦⣔⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣂⠈⠀⣷⣄⡉⠁⢐⣒⣒⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀⣤⡭⠴⣖⣠⣴⣶⣶⣶⡶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣀⣐⡙⠃⠀⠀⠈⠙⠒⢤⣤⡀⠈⣉⠑⠒⠶⠤⠤⠀⠀⠀⠈⠉⠙⠛⠻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣭⡄⠀⠀⠈⠉⠉⠉⠀⠀
⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠦⠄⠀⠀⠘⠋⠉⠁⠀⠀⠀⠀⠙⠛⢻⣿⣷⣶⣄⠀⠠⢤⡀⠀⠀⠀⠀⠀⠙⠃
⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠄⠀⠉⠀⢀⣠⣀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢈⣰⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⢶⣶⣤⣤⣤⣀⡴⢾⣿⠍⠉⠛⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣈⣉⠁⠀⠘⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⢤⡌⠉⠛⠛⠛⢿⡁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣯⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠟⠁⠻⠿⠛⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢽⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠙⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠷⠶⠂⠀⠉⠁⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⢦⣤⠀⠠⣄⠀⠀⠀⠀⠀⠉⠳⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⣿⣿⣿⣿⣶⠿⢯⣴⣶⡦⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠦⠀⠀⠀⠀⠀⠀⠀⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡐⠂⠘⠂⠈⠩⠴⠿⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣧⣤⣤⣤⣄⣀⡀⠀⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣴⣷⣒⡒⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⣯⣥⠀⠁⠀⠀⠘⠧⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠛⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⣀⣈⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠀⠀⣀⠀⢤⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠠⡀⠉⠙⠛⢿⣿⣿⡛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣂⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣒⣀⣁⣀⣀⣀⣀⣀⣒⣤⣤⣄⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣻⣷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⣛⡻⠏⠁⠀⠀⠁⠶⠤⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠹⠦⣠⠶⢄⣀⣘⣷⣀⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⣿⠿⢿⣿⣟⣍⢹⠿⢿⣿⣿⣿⣿⣿⣿
⣀⣠⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣷⠄⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⣿⡶⠶⠤⣤⡀⠀⠀⢩⣉⣉⣢⣤⡭⠿⠟⠿⠿⠛⠉⡻⠀⠉⠛⠀⣀⠈⣻⣾⣿⣿⣟⣡⣌⣀⡀⠈⢁⣐⣻⣿⣿
⣀⣠⣅⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢀⠀⠈⣩⣛⣷⣤⣾⡿⠾⢡⣤⣄⠀⠀⠐⢛⣿⣷⣦⣤⣜⣛⣻⡿⠛⠉⠛⣻⣿⣿⡿⠿⠿⠓⠶⠶⢷⣿⣿
⠿⠦⢤⡄⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠯⠭⠤⣤⣶⣦⡀⠀⠀⠀⠀⠀⣸⡋⠛⠿⣷⣦⣄⣭⣡⣴⣴⣶⡿⠟⠿⠛⡿⠷⣶⣾⣤⣤⣥⣤
⣿⣶⣶⣶⣂⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡀⢀⠀⠀⠐⠛⢂⣭⣁⠀⠀⠺⠷⢦⣤⣤⡈⠃⠐⠀⠈⠉⠄⠀⠶⠖⠀⠀⠘⢯⣴⣾⣿⣿⣟⡀
⣘⠿⠛⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⣄⠈⢁⣤⣀⠠⢤⠄⣠⣯⣀⠀⠀⢠⣆⠀⠀⣠⣄⡀⢀⡠⠆⢠⡿⠋⠛⠛⠛⠓
⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠉⠁⠀⠀⢠⣌⣻⡽⡋⠀⢰⣶⡶⠶⠛⠋⠀⠘⠁⠠⠀⠀⠀⠀⠶⠖⠖
⠛⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠬⠍⠉⠉⢃⠤⠊⠁⠚⠛⠁⠀⠁⠀⣠⠆⠀⠀⠀⢀⣀⣈⣙
⡖⠲⣦⣔⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡂⠈⠀⣷⣄⠉⠀⢐⣒⣒⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀⣤⡥⠴⣖⣠⣤⣶⣶⣶⡶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣀⣐⡛⠋⠀⠀⠈⠙⠓⢤⣤⡀⠈⣉⠑⠒⠲⠤⠤⠀⠀⠀⠈⠉⠙⠛⠻⢿⣶⣿⣿⣿⣿⣿⣿⣿⣭⡄⠀⠀⠈⠉⠉⠉⠁⠀
⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠦⠄⠀⠀⠐⠋⠉⠁⠀⠀⠀⠀⠙⠛⢻⣿⣷⣦⣄⠀⠠⢤⡀⠀⠀⠀⠀⠀⠙⠃
⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠄⠀⠉⠀⢀⣠⣀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡆⠐⠂⠀⠀⠀⠀⠰⠆⠀⠀⠀⢈⣲⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⢶⣦⣤⣤⣤⣀⡴⢾⣿⠍⠉⠙⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣈⣉⠁⠀⠘⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⢤⡌⠉⠛⠛⠛⢿⡁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣯⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⠟⠁⠻⠿⠻⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣹⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠙⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠷⠶⠂⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣐⢶⣤⠀⢠⣄⠀⠀⠀⠀⠀⠉⠳⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⣿⣿⣿⣿⣶⠿⢯⣶⣶⡦⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠦⠀⠀⠀⠀⠀⠀⠀⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡠⠂⠘⠂⠈⠩⠶⠿⠷⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣧⣤⣤⣤⣄⣀⡀⠀⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣴⣷⣒⡒⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⣯⣧⠀⠁⠀⠀⠘⠧⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠛⠿⠿⠿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⣀⣈⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠀⠀⣀⠀⢤⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⡀⠉⠙⠛⢿⣿⣿⡛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣂⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣒⣀⣁⣀⣀⣀⣀⣀⣒⣤⣤⣤⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣻⣷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⣀⣈⠲⠦⢤⡄⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢦⣄⠀⠀⠐⢻⣶⣤⣶⣄⣀⣙⣧⣀⢀⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣸⣷⡄⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢻⣿⣷⣦⣤⣤⡀⠀⠈⢩⣉⣉⣯⣬⡽⠿⠿⢿⡿⠟⢻⡿⠛⠛⠃⢀⡠⣻⣿⣾⣿⣿⣿⣭⣉⣀⠀⠙⢛⣻⣿⣿⣿⣿⣟⣻⣿
⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠤⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠅⠀⢉⣩⣟⣷⣾⣿⣿⣏⣁⣀⣀⠂⠀⠚⣿⣿⣶⣦⣔⣛⣛⣿⡿⠟⠟⠻⣿⣿⣿⣿⡿⠿⠶⣬⣿⣿⣿⣿⠟⠛⠉⠀
⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠿⢿⣭⢤⣶⣿⣀⡀⠠⠥⠀⠀⢰⣿⡟⠿⢿⣶⣌⣸⣟⣱⣦⣴⣾⡿⠿⠿⢓⡾⢷⣶⣾⣤⣭⣥⣤⣤⣶⣮⠇
⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠛⠒⠠⠀⠀⠀⢀⡀⠂⠀⠉⡠⣄⡀⠀⠙⠛⣲⣍⡁⠀⠐⠾⠿⣦⣤⣶⡛⠂⠚⠋⠉⠩⠄⠼⠶⠆⠈⠉⣿⣯⣽⣿⣿⣿⡋⠁⠀⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⡈⠁⠀⠀⠠⣌⣩⣄⣄⢀⣀⡀⠀⢹⣯⡀⠀⠀⢰⡦⠀⠀⣠⣄⠀⢀⣤⣀⣿⠿⠛⠻⠿⠿⠆⠀⠶⠶⠀
⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠶⠏⠛⠋⠉⠉⣀⣿⣿⣿⡛⠂⣼⣿⡶⠾⠛⠃⠘⠋⠩⠿⠃⠀⠀⢰⡶⠶⠄⠠⠤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⠈⠀⣤⣽⢟⠛⢛⣫⡼⠋⠙⠒⠛⠂⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠓⠚⠒⠒⠰⠶
⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⣀⡁⣿⣦⣀⠉⠁⣒⣖⣂⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣁⡭⣴⣖⣢⣤⣴⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣉⣒⡘⠛⠐⠀⠉⠉⠻⠦⣤⣀⠉⢉⡙⠲⠶⠤⠤⠀⠈⠉⠉⠙⠻⠿⠿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣉⡉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢳⠶⠄⠀⠠⠞⠋⠉⠁⠀⠀⠀⠙⠛⠿⣿⣿⣯⣍⡉⠉⠁⣀⡀⠀⠐⠒⠀⠊⠛⠂⠀⠀⠀⠀⠀
⣿⣶⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣶⡄⠈⠓⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡤⠒⠀⠀⠀⠀⠀⢶⡆⠀⠀⠈⣛⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢴⣦⣤⣤⣀⣀⣈⣶⣶⣿⡏⠉⠿⠇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣦⣄⣋⣉⠉⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠦⣤⣻⠿⠿⠿⠿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢀⣽⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⠋⠸⣿⡿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠟⠛⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠉⠻⠿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⢻⣷⡆⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠳⣟⣟⠟⠛⠋⠂⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣷⣿⣶⣶⣾⣮⣴⣤⡄⠀⠀⠲⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠫⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠭⠽⠯⢙⣛⣂⣒⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠤⠤⠄⠀⠘⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣿⣿⣿⣿⣿⣿⣿⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡛⠛⠛⠛⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠛⠿⠿⠗⠀⠀⠐⠒⠈⠙⠛⠛⠂⠀⠀⠀⠀⣠⣿⣷⣦⡀⠀⠠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠔⠊⠁⠀⠀⠛⠶⠦⡀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⣃⣈⣉⣁⣀⣀⣤⣀⣚⣂⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣁⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣛⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⣿
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⣿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿
⠛⠓⠀⠀⠀⠀⠀⠉⠉⣅⠰⠐⢲⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣦⣀⠀⠚⠛⠿⠶⢿⣦⣤⣽⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣽⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠀⠐⠛⠓⢶⡿⣿⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣽⣿⣿⠿⠷⣶⣦⣤⣄⡹⣤⣬⡷⠞⠛⠛⠛⠿⣿⣩⣿⠋⠈⢩⣤⣤⣾⣿⣿⣿⣿⣿⣿⣾⣯⣄⡀⠨⣽⣭⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉
⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠐⢠⡀⠠⣾⣿⡿⢿⣿⣿⡶⠶⣶⡾⠀⠀⢹⣿⣿⣿⣿⡟⠩⣽⣿⡟⢙⡏⣩⣿⣿⣿⣿⣛⡟⠛⠿⣿⣿⠿⠛⠉⠀⣤⡄⠀⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀⠀⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⠀⠀⠀⠀⠀⠂⠀⠈⠙⡛⠿⠶⠶⠿⢿⣧⠰⣿⠏⠀⣀⣽⣿⡍⣛⣿⣿⠶⣾⣷⣿⡿⠿⢿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣶⡶⠶⠾⠻⠛⠃⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⢶⡄⠀⠀⠀⠀⠀⠈⠉⠉⠒⠂⠀⣀⣤⠌⠁⠀⢠⣔⣤⣄⠀⠈⠙⢯⠤⠀⠋⡉⠙⠛⠻⡿⠗⠈⠁⠉⢀⡐⠒⠒⠛⠛⠛⠀⠸⣿⣿⣿⣿⣿⣿⣄⠀⠀⠞⠂⠀⢀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⢆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠈⠡⡀⢀⡀⠀⠒⢶⡟⣿⡶⣝⠛⠃⢠⣿⣷⣤⣤⡀⣾⣇⠀⣤⣶⡦⣤⣴⣷⣾⠟⠋⠉⠉⠛⠛⠂⠘⠛⠃⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠥⣙⣛⠉⠒⠄⠀⣰⣿⣿⣿⣿⣄⣹⣿⡿⢛⣋⠉⡀⠉⠀⠛⠋⠀⠀⠀⠻⢛⣣⣶⡖⠂⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠁⠀⠀⠀⢐⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⢲⣿⡟⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠘⠿⢿⣷⣤⣥⣶⡋⠀⠈⣉⣽⣀⣀⣀⣾⣷⣤⣤⣤⣤⣤⣤⣭⣭⣭⣥⣼⣟⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣀⣨⣿⣖⠤⢿⣿⣦⡤⠸⠿⠿⢭⣤⡀⠀⠀⠀⠀⠺⠿⠿⢶⣶⣾⣿⣿⣛⣯⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣦⡄⢌⠀⢀⠀⠉⠙⠲⠶⠆⣤⣤⣉⣉⠙⠒⢄⣤⡤⠤⠤⠀⠉⠉⢿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠖⠀⠀⢀⣀⡉⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠛⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⢀⠀⠉⢽⣿⣿⣿⣦⣀⠐⢲⣦⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⣤⣤⣼⡟
⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣎⣑⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⡀⠉⠛⠛⠳⢤⡉⠀⢀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣋⣀⣀⣀⠀⢨⡿⠃⣀⣤⣴⡾⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⢿⣿⣿⣶⣶⣤⣼⠿⠿⠿⠂⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⡌⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⢾⣿⠻⠟⠛⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢡⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢿⣿⣿⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣛⣛⡛⠛⠋⠀⠻⠿⠿⣟⣿⣿⣿⡋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⢿⣿⣿⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠗⠀⠀⠀⠹⣿⠙⠉⠁⠀⠘⠛⠛⠉⠁⠹⣿⡿⠋⠈⠻⠿⠿⠿⣿⠛⠗⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣾⡦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠻⣯⣀⠀⠀⠀⠀⠀⢀⣄⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⣾⣿⣿⣿⣷⣶⠀⠀⠐⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠱⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⢤⣤⠀⠀⠈⠉⠀⠀⠰⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉
⣯⣭⣿⣋⡑⠂⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣃⣀⣀⣀⣀⣀⠀⠀⢈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠛⠙⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢿⣿⣿⣿⣿⣿⣿⣿⣷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣴⣿⣿⣟⠛⠛⠉⠉⠿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠟⠀⠀⠀⠒⠈⠛⠛⠛⠓⠀⠀⠀⠀⢠⣾⣿⣶⣄⡀⠐⢒⣒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⡖⠉⡁⠀⠀⠛⠿⢶⣦⠀⠀⠀⠀⢉⡙⠛⠿⢿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡶⢦⣤⣀
⣀⣤⣀⣛⣃⣀⣀⣀⣀⣀⣀⣉⣉⣉⣁⣰⣁⣈⣉⣉⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣈⣇⣀⣀⣀⣙⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣇⣀⣈⣙
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠷⠶⣶⠿⣿⣿⠴⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣤⣀⣐⣶⡄⠀⡂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠹⣷⣦⣄⣉⣉⡙⠛⠛⢿⣶⠾⢿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡟⠉⢹⣿⣿⣿⣿⣿⣿⣶⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠀⠰⠀⠀⠀⠀⠀⢠⠈⠛⠛⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡟⡛⠉⠛⠿⣶⣶⣶⣾⣶⣶⠛⠋⠉⠫⠉⠙⣿⣴⣿⣏⣀⣰⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣠⣾⠶⢿⣿⣿⣿⡿⠿⠋⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⣻⣿⣿⠋⠩⣿⣿⡍⠉⣻⣟⠀⠐⣾⣿⣿⣿⣿⣏⠀⢾⡿⢯⣤⣇⣰⣿⣿⣿⣟⣩⣉⣉⣛⣿⠿⠛⠋⠀⢀⣶⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠦⢠⡈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠻⠿⢧⣀⠀⠁⠀⠀⠀⢀⠀⠨⠙⠛⠋⠛⠛⣿⣧⡭⠿⣃⣀⣤⣿⠶⣶⣬⣿⣿⡛⣿⠿⠿⠟⠛⣿⠋⠛⠛⢿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠶⠒⠀⠀⠀⡶⠷⠶⠂⠀⠀⠘⠛⠓⠘⣿⢯⠛⠛⠓⢚⣽⡉⠀⠀⢀⠉⠉⠉⠉⠉⠁⠀⣈⢿⣿⣿⣿⣿⣿⣦⡀⠀⣙⣃⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠦⠀⠄⠀⠀⢹⣖⣣⠴⣾⡀⠀⠀⢀⣿⣿⣿⠶⢶⣿⣦⣄⣲⣿⣦⣶⡾⣿⣾⠟⠉⠀⣀⡉⠉⠃⠀⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣃⣀⡂⠀⠀⠀⠀⠂⠀⠀⠐⠂⠉⠽⣶⠀⠀⢠⣼⣿⣿⡿⡿⠷⣴⠿⣛⣫⣥⠀⠄⠀⢀⡉⠁⠀⠀⠀⠙⣉⣉⣒⣓⡂⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡯⢹⣿⣋⠀⠤⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⢈⣁⣀⣀⠛⢛⣿⣿⣾⣿⡯⢀⣀⣤⣶⣤⣤⣤⣿⣿⣤⣤⣤⣴⣶⣶⣶⣬⣭⣥⣼⣿⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣀⣊⠛⠿⠁⠙⢻⣿⣆⡈⢀⣉⣉⡻⠦⣤⣄⡀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠻⢿⣿⠿⠛⠛⠻⠿⠿⠿⠯⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠉⠉⠀⠂⠐⠲⠀⠀⠈⠉⠉⠉⠛⠛⠿⡦⠀⠉⠓⣶⣖⠒⠒⠀⠀⠀⠈⠻⢿⣿⣿⣿⣟⣛⠛⠛⠛⠃⠀⠤⠤⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣴⣒⣂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠐⠿⠿⢿⣿⣶⣄⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣼
⣶⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣇⠀⣠⠀⠀⠀⠀⠀⣀⣤⠀⠀⠙⢿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣦⣀⣠⣀⡈⠉⠙⠲⢄⣀⣠⣴⡿⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣄⣀⡀⠀⠻⠉⣐⠶⠶⠿⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠈⢻⣿⣿⣿⣿⣷⡾⠻⠿⠟⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠛⠉⣉⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠙⠟⠻⣿⣿⣿⡍⠉⠙⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣯⣤⣶⣿⣟⣻⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⠏⠀⠀⠀⠻⣿⠉⠁⠀⠀⠈⠋⠋⠉⠁⠀⠉⠉⠈⠉⠉⠉⠻⠿⠛⠉⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣶⣶⣀⠀⠀⠀⠀⣀⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⠤⠤⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀
⡿⢿⣿⠿⠿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠒⠶⠄⠀⠀⠀⠀⠀⠈⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉
⢿⣿⡷⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣯⣥⣤⣤⣤⣤⣤⣄⠀⣀⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⡦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣀⠀⠀⠀⠀⢺⣿⣿⣿⣉⠁⠀⠀⠘⠧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡉⠁⢀⣀⠠⠉⢀⣉⣉⠉⠁⠀⠀⠀⠀⣠⣿⣿⣿⣦⣀⣈⣙⣓⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠉⡿⢋⣤⣀⡀⠀⠈⠛⠳⡦⠀⠀⠀⠀⢉⡉⠙⠛⠿⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡖⢶⣤⣄
⣘⣃⣀⣀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣠⣬⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣃⣀⣀⣀⣈⣻⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣏⣀⣀⣙
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⠀⠀⣶⡆⠀⢴⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠷⠶⣶⠿⣿⣿⠴⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿
⠤⢤⡄⠀⠀⠀⠀⠐⠻⠛⣶⣾⣿⡆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣹⣿⣷⣶⣶⣤⣬⣉⣉⣿⣏⣙⣻⣿⠿⠿⢿⡛⢿⣿⢿⣿⣿⠟⢉⣿⣃⡀⢘⣿⣷⣿⣿⣿⣿⠿⠉⠛⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠀⠀⠀⠀⠐⠃⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠫⠅⠀⣙⣻⣿⣿⣿⣿⣿⡿⠶⢶⣶⡾⠍⣰⢶⣾⣿⣷⣶⣬⣟⣛⣿⣿⠟⣿⢿⣿⣿⣿⣿⣶⣶⣤⣾⣻⣻⣿⣿⡿⠟⠛⠉
⣒⠒⠀⠀⠀⠀⠀⠀⠀⢤⡀⢈⡀⠈⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⠀⠀⠀⠀⠀⠄⠈⠉⠶⢿⣿⣏⣭⣽⣿⣧⣤⣼⣿⠃⠀⠀⣾⡟⠻⢿⣿⣧⣄⣽⣟⣫⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣟⡛⢉⣁⣀⣠⣾⣷
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠲⢄⣈⣡⣤⡀⠀⠀⠀⠀⠈⠙⠛⠲⠤⠄⠀⠀⣀⠐⠂⠀⢙⣠⡄⠀⠉⠙⠿⣇⣛⡓⢶⡾⣿⡿⠙⠛⠛⠿⠿⣿⣿⣛⣟⣭⣉⣭⣥⡬⠙⢹⣿⣿⣿⣿⣿⣿⠟⠛⠉⣉⡉⠀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠄⢀⠀⠘⠋⠙⡋⠁⠀⢤⣉⣩⠄⢘⣷⡀⠀⠀⢁⣀⡤⣴⣏⣩⣇⠀⠀⢀⡀⠀⠀⣠⣬⣿⣿⡿⢿⣿⣿⣧⡀⠀⣭⡥⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⠓⠈⠁⠀⠂⠹⣿⣾⣿⠍⠀⠀⣠⣾⣿⣷⣾⣿⠟⣿⣶⣶⣿⡿⢷⠿⢿⣿⡿⠋⠀⠀⣄⣀⣉⢁⡀⠉⠀⠀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣅⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣭⡭⣀⣀⣀⡐⠀⠀⠀⠀⠈⠈⢙⠛⠀⣀⣴⣾⣿⣿⣿⣿⣋⣱⠟⠻⠿⠶⢶⠐⠀⠀⣠⡅⠀⠀⠀⠀⠩⠤⠤⣯⣭⠉⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡰⠿⣿⣿⢿⣯⣤⣠⣭⣭⣽⣷⣦⣤⡀⠀⠀⠤⠄⣭⣭⣭⣬⣭⣽⣭⣭⣽⣷⣒⣤⣤⣶⣷⣶⣶⣾⣿⣷⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢋⠁⣀⣠⣤⣬⠹⣧⣜⠛⠛⠋⠉⠙⠻⢿⣯⡛⠛⠿⠛⠂⠀⠀⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠉⠉⠛⠛⠿⠿⠛⠛⠛⠛⠛⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠻⣿⣿⣤⣄⣴⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠼⢿⣍⡉⠉⠀⠀⠀⠈⠛⠿⢿⣿⣿⣭⣍⠉⢉⣉⡀⠀⠒⠒⠠⠤⠶⢶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠋⠉⠁⠀⠀⠀⠓⠒⠿⠉⠁⠀⠀⠀⠈⠉⠉⠛⠓⠃⠀⠀⠒⠀⠀⠙⠛⠛⠿⣿⣷⣄⠙⠿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣧⡄⠀⠀⠀⠀⢰⣶⣶⡶⠖⠀⠀⢀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣤⣤⣄⣀⣉⣙⠓⣤⣤⣴⡿⠷⣶⣶⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠈⠻⠋⠁⠘⠛⠛⠉⠙⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⣙⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⠀⠀⢀⣼⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠛⠛⠫⢍⣭⠿⠶⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣿⣿⡟⠛⠛⠛⠉⢹⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠉⢹⣯⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠙⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣾⣿⣧⣤⣤⡀⠀⠠⠶⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠾⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠰⠦⠤⠤⠤⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀
⣿⣛⣿⠟⠻⡟⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠛⠹⠟⠀⠀⠀⠀⠀⠀⠀⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠛⠿⠿⠟⠓⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣶⣶⣶⣶⣶⣶⣦⣄⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣲⡦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣴⣶⣶⣤⠄⠀⠀⣀⣙⣿⣿⣿⣧⡀⠀⠀⠀⠛⠦⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⠤⠄⠀⠁⣤⣤⣄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⣬⣭⣭⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡄⠲⠶⠋⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⣀⠿⠳⠶⠤⠄⠀⠀⠉⠛⠷⠆⠀⠀⠀⠠⣤⠉⠙⠛⢿⣿⣿⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡶⢦⣤
⣀⣀⣀⣀⣀⣀⣀⣚⣓⣶⣶⣦⣤⣤⣤⣾⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣙⣻⣿⣷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣇⣀⣈
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠷⠶⣶⠿⣿⣿⠴⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿
⠒⠒⠚⣷⣤⡀⠀⠀⠈⢉⣋⠽⠿⠿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣿⣿⣿⠿⢿⣷⣶⣶⣽⣿⣥⣭⣿⠟⠛⠻⣯⡙⠿⠿⣿⣿⠟⠩⣽⣯⣤⣌⣿⣿⣿⣿⣿⣿⣿⠁⠬⠟⠋⣹⣿⣿⣿⣿⣿⣿
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠉⠒⣤⠤⣽⣿⣿⣿⣿⣿⣿⠿⠛⣿⡿⠛⢡⢿⣿⣿⣿⣿⣷⣿⣭⣽⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛
⣭⠿⠍⠀⠀⠀⠀⠀⠀⠀⠒⠶⠀⣭⣄⡉⠻⢦⡄⠀⠀⠀⠀⠀⠀⠸⣷⣶⡄⠀⠀⠂⠀⠒⠀⠀⠙⣛⡿⠯⠶⣾⣿⣿⣷⣾⣿⡿⠀⣾⣿⣟⡻⣻⣿⣿⣦⣴⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣤⣤⣤⣬
⡛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣴⣷⣆⡀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠀⣀⣤⠌⠉⠀⢠⣴⣦⣀⡀⠀⠛⢻⣬⡭⠻⣿⢿⡿⢉⣬⡭⠉⠉⢻⣿⣿⠯⠭⠥⢼⣷⡤⠞⠿⣿⣿⣿⣿⣿⣿⡟⠉⠉⣠⣖
⣤⠀⠶⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣧⡀⠀⠀⠀⠀⠀⣤⠀⠄⠀⠀⠁⠒⠠⠄⠈⢩⡉⢭⡀⠀⠲⣦⣤⣖⣬⣿⠷⠀⠀⢀⣤⣜⣻⣿⣵⣶⡀⠀⢀⣤⣀⢀⣠⣶⣿⣿⡿⠿⠿⣿⣷⣄⠀⣭⣥
⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠚⡗⠤⡀⠀⠀⠀⠀⠀⠀⠸⢤⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠⣤⣀⢀⣀⡀⠀⠚⢉⡀⠀⠀⢉⣈⣿⡿⠟⠁⣠⣤⣶⣿⣿⣿⡿⠟⣻⣿⣿⡿⠿⠟⠻⠿⠛⣿⡿⠋⠀⠀⣶⣤⣬⣉⣀⣀⡀
⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣷⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣴⣶⣴⣿⣷⣤⣭⣿⣻⣿⣗⡀⠀⠀⣀⣤⣽⠿⠟⠉⠭⠽⣿⢿⡿⠿⠿⠿⠭⠽⠶⠶⣂⠞⠃⠀⣤⣦⠀⠀⠀⠀⠀⠲⠶⠿⠷⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡓⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⣍⡛⠛⢿⣿⣿⢷⣦⣾⣶⡤⠀⠠⣤⣤⣤⣤⣴⣶⣤⣴⣾⣟⣥⣴⣶⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣇⠉⠱⣿⣿⣣⡀⣀⣈⣛⠶⠶⠿⠿⢧⣀⠀⠀⣀⣈⡉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⠉⠉⠙⠻⠿⠛⠉⠉⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠬⠙⠛⠀⠀⠉⠀⣤⣾⠟⠛⢀⣍⡀⠀⣀⡤⠟⠁⠀⠾⠛⠛⠉⠁⠀⠀⣀⠀⠉⠛⢿⣿⣿⣿⣭⡉⠉⣁⣀⠀⠘⠓⠒⠒⠿⠿⠆⠀⠀⠀⠀
⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣄⣀⣰⡀⢀⣡⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠛⠛⠲⠖⠚⠙⠒⠂⠉⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠈⠛⠛⠻⢿⣿⣶⣘⡻⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡞⠻⣿⣿⣿⣿⣿⠟⣃⣀⣀⣤⣤⣦⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣶⣤⣤⣉⣉⡛⢳⣤⣴⣿⣛⣿⣶⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣍⠉⠉⠿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠉⠉⠙⠀⠀⢠⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠽⠥⠿⠷⠂⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢤⡘⣻⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠙⠙⠛⣷⡄⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣄⠀⠀⠀⠀⠀⣀⡀⢠⣤⣤⣶⣿⣿⠉⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣀⣤⣤⣶⣿⠿⣿⣿⣾⠃⠈⢿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠿⣿⣿⣿⡋⠀⠀⠀⠙⠛⡛⢁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠂⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠆⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠠⠯⠀⠀⢄⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠒⠒⠶⠤⠤⠤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀
⣿⣯⣽⣿⣉⡙⠋⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠛⠋⠭⠙⠛⠀⠀⠀⠀⠀⠀⠀⠻⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠥⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠙⠛⠛⠉⠉⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠒⠂⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠿⠿⠿⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⠷⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠿⠿⢿⡶⠂⠐⠠⠤⡼⡿⠿⠿⠷⠆⠀⠀⠀⠉⢓⣶⣤⣀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⡴⠒⠊⠁⠐⢷⣶⣦⣄⠀⠀⠀⠀⠰⠿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠶⠆⠉⠉⠀⠀⠀⣀⣀⠀⠐⠒⠚⠛⢲⣴⠛⠿⠿⠗⠂⠀⠀⠈⠙⠻⠷⠀⠀⠀⠐⣶⠀⠉⠉⢻⣿⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠳⢶
⣀⣀⣀⣀⣀⣀⣤⣤⣉⣙⣿⣿⣿⣒⣒⣛⣛⣒⣦⣤⣤⣀⣙⣃⣀⣀⣀⣀⣀⣀⣀⣀⣈⣂⣀⣀⣀⣉⣛⣿⣿⣦⣄⣠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣁⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠈⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣶⠀⠀⣶⣦⠀⣴⣶⡄⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠰⠷⠶⣶⠿⣿⣿⠶⢶⣿⣿⠀⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⡍⠀⠙⣛⣿⣿⣧⣿⣿⣿⣿⣿⡿⠻⢿⡋⠻⠿⣷⣿⣿⣦⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣤⣭⣿⣿⣿⣿
⣂⠀⣒⣒⡛⠀⠀⠀⠀⠀⠀⠀⢤⣄⠈⣓⠘⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⠀⠀⢀⡀⠀⢀⠀⠙⢥⣽⣿⣟⣉⣻⣿⣿⣿⣇⢠⡤⣤⣈⠳⢾⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿
⠿⠿⢿⡮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⣄⣉⣡⣤⡄⠀⠀⠀⠀⠈⠙⠿⠦⢤⣀⡀⠀⠀⠠⠤⠀⠒⢉⡉⠉⠙⠻⢿⣿⠿⠿⣧⣼⣿⣿⡿⠂⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⣛⠛⣛⣿⠿⣻⡿⣿⣿⣿⣿⣿⣿
⣛⣋⡁⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣉⡁⠀⠸⠟⠻⡟⠂⠀⣀⡉⣛⣛⣩⣭⣿⠋⠀⠲⠿⠿⢿⣷⣤⣿⡟⠉⠉⠛⠛⠋⠉⠁⢀⣹⣿⣿⣿⣿⣿⣿⣷
⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣄⡀⠀⠀⠀⠀⠀⠀⠈⢹⡛⠂⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠈⠁⠀⠘⠆⠑⠂⠠⠄⠻⣿⣵⣿⣿⠟⠀⠀⣠⣿⣿⣾⣿⣿⣿⣷⣄⣠⣶⣶⣤⣴⣶⣿⣿⣿⠛⠉⣀⣉⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠨⣇⠹⡆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣙⣔⣒⡂⠀⠀⠀⠐⠀⠀⠀⠑⠒⠛⠿⠉⠁⠲⢶⣾⣿⣿⣿⣿⣿⣿⣿⢟⣛⣫⣍⣩⡌⠈⠁⠹⠛⠁⠀⠀⠛⣛⣋⣵
⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣼⣿⣿⣿⣿⣿⠷⠶⠤⠶⢶⣦⣄⡀⠀⠀⡐⠀⠀⠀⣀⣈⣛⣛⣿⠏⣉⣈⣁⣨⣭⠌⣀⣶⣁⣀⣀⣼⣿⣤⣤⣤⣤⣤⣬⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⡶⠶⢭⡶⢉⣹⣿⣿⡶⠦⠤⣴⣶⣼⣿⡛⠿⠶⢶⣶⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡉⣅⡄⠸⠷⠀⢈⣉⠠⡄⠀⠀⠀⠀⠈⠉⠛⠓⠢⠀⠐⣢⣴⡶⠒⠒⠂⠀⠀⠈⠻⢿⣿⣿⣿⣟⡿⠿⠿⠛⠒⠀⢠⣄⣈⣉⣤⣤⡀
⣿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⣶⣶⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⢻⣿⣿⣄⠀⢀⡀⠀⠀⠠⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠄⠀⠸⠿⣿⣿⣿⣧⣄⢻⣶⡄⠀⠀⠀⠀⠉⠙⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣄⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣥⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⢠⣦⣤⣀⣀⡈⠙⠿⠿⢶⣏⢀⣠⣴⣦⣄⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠲⠶⠶⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡝⢿⣿⣿⣿⣶⣶⣴⡾⣿⣿⠿⠚⠛⠛⠀⠀
⣿⣿⣿⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣿⠆⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⠿⠿⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⢤
⣿⣿⣿⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠘⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣾⣿⣦⠀⠀⠀⠀⣠⣿⣿⡿⠿⠿⢿⣷⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣴⣽⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠻⠟⠛⠁⠈⠉⠉⠣⣴⣶⡖⠀⣰⠿⠟⠛⠛⠉⣻⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣭⣬⣿⣿⣿⣿⣶⡶⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⣷⡴⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⢠⣼⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣢⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⡀⠀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣟⣻⡿⠿⣿⡷⠀⠀⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣶⣄⠛⠛⠓⠒⠀⠀⠀⠀⣀⣤⣶⠶⠶⣶⠆⠀⠀⠉⠁⠀⠀⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠽⠶⠶⠒⠀⠀⠄⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⡿⠛⠓⠢⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣷⣤⣤⣤⣤⣤⣄⠀⣀⡉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀
⣿⡗⠀⣭⣀⠀⠀⠀⠀⠐⠀⠶⠤⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠱⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣴⣶⣶⣤⣄⠀⠀⣀⣐⣿⣿⣿⣿⣍⡀⠀⠀⠘⠷⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠫⠍⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣉⣉⠁⠀⠀⢀⣀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣁⣠⠤⠔⠈⣭⣭⣍⡉⠉⠀⠀⠀⠀⣴⣿⣿⣿⣦⣀⣛⣛⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⡶⠾⠿⠋⠁⠀⠀⠀⠀⠀⠤⠤⢶⠦⣈⡽⣿⣥⣴⣄⠀⠀⠙⠻⢿⡦⡀⠀⠀⠀⣭⠉⠛⠻⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⡿⠛⠉⠁⠀⠀⠀⠀⢀⣀⠐⠒⢶⣶⣶⡤⠤⣴⣿⢧⣤⣀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠈⠻⢿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿
⣀⣤⣀⣀⣀⣀⣀⣐⣾⣿⣿⣟⣊⣁⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣶⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣚⣻⣿⣿⣿
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠈⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣶⠀⢠⣶⣶⠀⣶⣶⡄⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠰⠷⠶⣶⠿⣿⣿⠶⢾⣿⣿⠀⣿⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠽⠟⠛⠻⢿⣿⣷⠦⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿
⣶⣶⣶⣶⣚⠛⠛⠛⠛⠋⠁⠀⠀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⣿⠿⠛⠛⠛⠛⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠰⡶⡛⠛⠉⠀⠀⠀⠀⠀⢠⣤⣶⣿⣷⣿⣿
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⣾⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣍⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡾⠿⠿⠿⢻⣤⣀⣀⣀⢛⣻⡿⢷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠛⠋⠁⠀⠈⠙⠛⠛⠛⠋⠙⠿⢿⣿⣿⣿⡟⠛⠛⠓⠂⠀⠀⠀⠀⠀⠤⠴⠶⠶⠒⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠽⠶⠶⠶⠾⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠀⢀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⣶⣄⣀⣀⠀⠀⠀⣠⣼⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠈⠛⢻⣿⡧⠄⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠉⠁⠀⠀⠀⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣻⣷⣤⣤⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄⠀⠘⠛⠃⠂⠀⠀⠀⠀⠀⢤⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⡛⠻⡿⠃⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠙⢻⣿⣟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⡍⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣄⣀⣀⣀⠀⠀⠀⠀⠐⠾⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠛⠛⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀
⠿⣿⣿⣷⣦⣤⣤⣽⡿⠿⡿⠿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⣀⠀⠀⠈⠋⠉⠉⠉⠀⠀⠀⠀⠀⣤⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠈⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢉⣉⣁⡀⠀⠀⠈⠛⢃⡀⠀⠀⠀⠀⠀⠚⠻⣿⣿⣿⣿⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⢲⣶⣦⣤⣄⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⣀⣀⣠⠠⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⢧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠛⠛⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣉⣉⣉⣿⣿⣿⣿⣿⣿⣛⣋⣉⣉⣉⣙⣻⣵⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠶⣶⠏⢿⣿⠰⠶⣿⡗⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣈⣻⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠹⠛⠛⠻⠿⣷⣷⠦⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿
⣶⣶⣶⣶⣞⠛⠛⠛⠛⠋⠀⠀⠀⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⣿⠿⠛⠛⠛⠛⢶⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠰⡾⣛⠛⠋⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣾⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣏⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡾⠿⠿⠿⢻⣤⣀⣀⣀⢛⣻⡿⢷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⠿⠿⠛⠋⠀⠀⠈⠙⠛⠛⠛⠛⠙⠿⢿⣿⣿⣿⡟⠛⠛⠒⠂⠀⠀⠀⠀⠀⠤⠴⠶⠶⠒⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠶⠶⠶⠾⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠀⢀⣀⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⢤⢶⣶⣄⣀⣀⠀⠀⠀⣠⣼⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠈⠛⣻⣿⠷⠄⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠉⠁⠀⠀⠐⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣻⣷⣤⣤⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄⠀⠚⠛⠓⠀⠀⠀⠀⠀⠀⢤⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⡟⠿⡿⠋⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠙⢻⣿⣟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⡍⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣯⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆⣀⣀⣀⠀⠀⠀⠀⠐⠾⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠛⠛⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀
⠿⣿⣿⣶⣤⣤⣤⣽⡿⠿⡿⠿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⣀⠀⠀⠈⠋⠉⠋⠉⠀⠀⠀⠀⠀⣤⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢉⣉⣁⠀⠀⠀⠈⠛⢃⡀⠀⠀⠀⠀⠀⠚⠻⣿⣿⣿⣿⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⢀⣀⣲⣶⣦⣤⣄⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢀⣀⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠛⠛⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣉⣉⣉⣿⣿⣿⣿⣿⣿⣛⣋⣉⣉⣉⣛⣺⣷⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠶⣶⠏⢿⣿⠰⠶⣿⡗⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣶⡎⠀⠀⠀⠀⠀⢀⣴⣿⣧⣄⡀⠀⠉⠉⠀⠀⠀⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⢄⣘⠁⠀⠀⠀⣀⣤⣤⣄⣀⡀⠀⠦⠀⠀⠁⠀⠀⠀⠀⠀⠚⠻⠋⠈⠉⠙⠛⠀⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠉⠀⠠⠀⣀⣀⣤⣬⣭⣥⣤⣤⣄⣠⣤⠙⠻⢷⣦⣴⣤⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⣶⡦⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣶⣾⣿⣶⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠘⠿⠿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⡟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⠿⠿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡷⠶⠿⠿⠿⠟⠋⠉⢀⡀⣤⣀⡀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀
⠀⢀⠀⠀⢘⣯⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⣿⣿⣿⣿⣿⣾⣿⠷⢶⡿⠛⠻⣶⣶⣂⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⣀⠀⢀⣿⣿⣿⣿⣿⣉⣙⡻⠻⡍⡁⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠠⠂⠀⠒⠀⠀⣿⣿⣿⣟⠻⠥⠈⢹⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠤⠤⠤⠓⠁⠀⣠⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠉⢉⣀⠉⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠉⠩⠀⣀⣀⣠⣤⣭⣭⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⢠⣄⠀⠀⠀⠀⠩⣄⣀⠀⠐⠂⠀⠀⣨⣯⣭⡀⠉⣉⣉⣁⠲⠞⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⢸⣟⡀⠀⠀⠀⠀⢀⣶⣤⣮⠀⢀⠠⠀⠻⠏⠁⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠰⣶⣶⡆⠀⠄⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣧⡤⢀⡀⠁⠀⠀⠶⠶⠆⠉⠃⠀⢠⣿⣿⡯⠉⠀⠠⠀⠀⠀⠀⠐⢲⣦⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣟⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠄⠀⠀⠀⠈⠉⠀⢦⠀⠀⠁⠀⠂⠀⠀⠈⠛⠃⠀⠐⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠠⣤⣤⠀⠀⠀⠐⢲⣄⣀⡀⠒⠀⠀⠀⠀⠉⠿⢷⣤⣤⣤⣤⣤⡀⠀⠤⠿⠷⠂⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣀⣀⣀⣐⣲⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣄⣈⣻⣷⣦⣤⣀⣀⣬⣿⣷⣤⣄⣈⣀⣀⣀⣀⣀⣀⣀⣀⣙⣢⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠶⣶⠏⢿⣿⠰⠶⣿⡗⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣶⡎⠀⠀⠀⠀⠀⢀⣴⣿⣧⣄⡀⠀⠉⠉⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⢄⣘⠁⠀⠀⠀⣀⣤⣤⣄⣀⡀⠀⠦⠀⠀⠁⠀⠀⠀⠀⠀⠚⠻⠋⠉⠉⠙⠛⠂⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠉⠀⠠⠀⣀⣀⣤⣬⣭⣥⣤⣤⣄⣠⣤⠙⠻⢷⣦⣴⣤⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⣶⡦⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣶⣶⣿⣷⣶⣶⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠁⠀⠀⠘⠿⠿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣏⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠟⠿⠿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡷⠶⠿⠿⠿⠟⠋⠉⢀⡀⣤⣄⡀⠀⠿⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀
⠀⣀⠀⠀⢘⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⣿⣿⣿⣿⣿⣾⣿⠷⢶⡿⠛⢻⣶⣶⣂⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠁⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⣀⠀⢠⣿⣿⣿⣿⣿⣉⣙⡛⠻⡍⡁⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠂⠀⠒⠀⠀⣿⣿⣿⣟⠻⠥⠈⢹⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠤⠤⠤⠒⠃⠀⣠⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠉⢁⣈⠉⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⢾⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠀⡀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠉⠩⢀⣀⣀⣠⣤⣭⣭⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⢠⣄⠀⠀⠀⠀⠩⣄⣀⠀⠐⠂⠀⠀⣠⣭⣭⡀⠉⣉⣉⣁⠲⠞⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⢸⣟⡀⠀⠀⠀⠀⠀⣶⣤⣮⠀⢀⠠⠀⠻⠏⠁⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠲⣾⣶⡆⠀⠄⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣧⡤⢀⡀⠀⠀⠀⠶⠶⠆⠉⠃⠀⢠⣿⣿⡯⠉⠀⠠⠀⠀⠀⠀⠒⢲⣦⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣟⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡄⠀⠀⠀⠈⠉⢀⢦⠀⠀⠀⠀⠂⠀⠀⠈⠛⠃⠀⠐⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠁⠀⠠⣤⣤⡀⠀⠀⠐⢲⣄⣀⡀⠒⠀⠀⠀⠀⠉⠿⢷⣤⣤⣤⣤⣤⡀⠀⠤⠿⠗⠂⠉⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣂⣀⣀⣐⣒⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣈⣻⣷⣦⣤⣈⣀⣼⣿⣷⣤⣄⣉⣀⣀⣀⣀⣀⣀⣀⣀⣙⣢⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠶⣶⠏⢿⣿⠰⠶⣿⡗⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠿⢶⣶⠖⠀⢀⣤⠀⢠⣤⣶⣶⣆⡀⠈⠉⠛⠉⠁⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣈⣙⣿⠃⠀⠀⠐⣂⣀⣀⠀⠀⠀⢠⡈⠉⠙⠃⡰⠊⠉⠀⠤⠿⠿⠋⠋⠛⠳⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠲⠆⠀⠀⠉⠙⠛⠐⠖⠂⠈⠉⠙⠛⠛⠛⠂⢤⣁⠀⠀⠀⣒⣒⣒⣀⣀⣀⣀⣨⣽⠷⢶⣦⣤⣬⣍⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠛⠋⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠀⠶
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠛⠟⢿⣏⡁⠀⠈⠛⠛⢉⣉⣀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⠖⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠂⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣛⠛⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣵⠒⠐⠂⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣍⠉⠉⠀⠀⠀⠀⠨⠭⠥⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠙⠻⠿⣿⣿⣿⢿⣿⣿⠿⠟⠋⠉⣉⣀⣀⡀⢰⣶⡯⢉⡛⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠂⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠂⠀⢠⣶⣿⣿⣿⣶⣿⣿⣾⣶⡶⢾⣷⣦⣽⠛⠓⠀⠀⠀⠺⠗⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠻⣿⣟⣿⣿⣿⣿⡿⠿⠋⠉⠒⠂⠀⠀⠀⠀⠀⣰⣿⣿⣅⠓⢒⠛⠀⠰⠶⠶⠾⠿⢿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⡟⢛⣿⣿⣿⡛⠃⠈⠉⠉⠙⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠈⠉⠛⠛⠏⠀⠈⠁⠀⠀⠀⣠⡿⢶⣦⡄⠈⠩⠅⠀⢸⣿⣿⣿⣿⣿⣿⢛⣷⣿⡿⠇⠀⠀⠀⠀⠈⠁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠙⠿⠋⢀⣭⣭⡰⠶⠆⠀⣼⣿⣿⣏⣉⠒⢦⣤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠂⠐⠛⠒⠶⠖⠀⠀⠀⠲⠶⠄⠁⠒⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠏⢀⠉⢉⣓⡒⣒⣒⡀⠀⠉⣉⣙⣛⡋⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠁⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠐⢲⣆⠀⣩⣠⠭⠷⠄⠀⣿⣛⡋⠙⠛⠛⠿⣭⣵⣷⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⠀⠀⠀⠀⢸⣿⡗⠀⢀⠐⠠⠭⢽⣭⣿⣋⠠⢄⡉⢿⣿⠟⠙⠋⠻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠢⠤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠀⠈⠽⢿⣿⣷⡾⠉⣀⡀⣤⣄⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⠀
⣛⣋⡙⠛⠀⠀⠂⠀⠀⠀⠘⠿⣶⣿⣗⣤⠀⠐⠒⠒⠂⣠⣤⣬⠛⠷⠄⢠⣶⣶⣶⡖⠒⢉⡙⠿⠛⠛⠭⢤⣤⡄⢂⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⢀⣀⣶⣷⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠠⢤⣤⣀⠀⠠⠈⠛⠛⠡⣤⠀⠐⠒⠲⠤⠄⠀⠸⠿⣿⠀⠨⠥⠀⠐⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠤⠾⠛⠙⢯⣭⣅⡀⠀⠀⠰⣦⣄⠀⠀⠦⢤⡀⠈⠁⠒⣾⣿⣭⣴⣆⣀⣀⠀⠈⣉⣷⣶⡴⠖⠒⣀⡉⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣡⣤⣤⣤⣄⣩⣿⣯⣄⣀⣀⣉⣋⣉⣉⣀⣀⣀⣰⣶⣶⣥⣈⣻⣟⣻⣿⣿⣍⣈⣵⣶⣄⣄⣀⣀⣈⣉⣰⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⣿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠿⢶⣶⡖⠀⢀⣤⠀⢁⣤⣴⣶⣆⡀⠈⠉⠛⠋⠁⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣈⣹⣿⠃⠀⠀⠐⣂⣀⣀⠀⠀⠀⢠⡈⢉⠙⠃⡰⠊⠉⠀⠤⠿⠿⠋⠋⠛⠳⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠲⠆⠀⠀⠉⠙⠛⠒⠖⠂⠈⠉⠙⠛⠛⠛⠂⢤⣁⠀⠀⠀⣒⣒⣒⣀⣀⣀⢀⣨⣽⠷⢶⣦⣤⣬⣍⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠚⠋⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠀⠶
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠿⠟⢿⣏⠀⠀⠈⠛⠛⢉⣉⣀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣶⣤⣤⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠒⠂⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣛⡛⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣵⡖⠐⠂⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⣿⣿⣿⣿⣍⠉⠉⠀⠀⠀⠀⠨⠭⠥⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠙⠛⠿⣿⣿⡿⢿⣿⣿⠿⠛⠋⠉⣉⣀⣀⡀⢰⣶⡯⢉⡛⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠂⠀⠀⠀⠀⠐
⣀⡀⠀⠀⠀⠀⠳⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⣀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠂⠀⢠⣶⣿⣿⣿⣶⣿⣿⣶⣶⡶⠾⣿⣦⣭⠟⡃⠀⠀⠀⠿⠗⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠻⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠒⠂⠀⠀⠀⠀⠀⣰⣿⣿⣅⠓⢒⠛⠀⠰⠶⠶⠾⠿⢿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⡟⢛⣿⣿⣿⡛⠃⠈⠉⠉⠙⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠭⠁⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠈⠉⠛⠛⠯⠀⠈⠁⠀⠀⠀⣠⡿⢶⣦⡀⠈⠩⠅⠀⢸⣿⣿⣿⣿⣿⣟⢛⣷⣿⡿⠃⠀⠀⠀⠀⠈⠁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠙⠻⠏⢀⣭⣍⡴⠶⠆⠀⣼⣿⣿⣏⣉⠒⢶⣤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠒⠒⠛⠒⠶⠖⠀⠀⠀⠲⠶⠄⠁⠒⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠏⢀⠉⢉⣓⠒⣒⣒⡀⠀⠉⣉⣙⣛⡋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠁⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⢐⢲⣆⠀⣬⡤⠭⠷⠄⢀⣿⣟⡋⠙⠛⠛⠻⣭⣵⣷⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⠀⠀⠀⠀⢸⣿⡗⠂⠀⠐⠠⠭⣽⣭⣿⣋⠠⢀⣉⢻⣿⠟⠙⠋⠻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠈⠉⠙⠓⠁⠀⠀⠘⠿⢿⣿⣷⡾⠋⣀⡀⣤⣄⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣄⠀
⣛⣋⡙⠛⠀⠀⠀⠀⠀⠀⠚⠿⣾⣿⣗⣤⠀⠐⠒⠒⠂⣠⣤⣬⠛⠷⢄⣠⣶⣶⣶⡖⠂⣉⡙⠿⠚⠛⠭⢤⣤⡄⣢⣤⣤⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⢀⣀⣶⣾⡄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠠⢤⣥⣀⠀⠠⠌⠛⠛⠡⣤⠀⠐⠒⠢⠤⠤⠀⠸⠿⣿⡀⠨⠥⠀⠐⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠤⠾⠛⠛⢯⣭⣅⡁⠀⠀⠰⣦⣄⠀⠀⠦⢤⡀⠉⠁⠒⣾⣿⣭⣴⣆⣀⣀⠀⠈⣉⣷⣶⡴⠖⠒⣚⡉⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣡⣤⣤⣤⣄⣩⣿⣯⣄⣀⣀⣉⣉⣉⣉⣀⣀⣀⣰⣶⣶⣥⣈⣻⣟⣿⣿⣿⣍⣈⣱⣦⣄⣄⣀⣀⣉⣉⣰⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⣿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣶⣤⣭⠥⠀⢀⡀⠉⣀⣠⣤⣶⡄⠀⠘⠛⠛⠋⠁⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢳⡶⠃⠀⠀⠠⠄⠀⠀⠁⠀⠀⣀⠚⠛⠿⢄⣀⠛⠃⢀⣨⣿⣿⠛⠛⠓⢶⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀
⠀⠀⠲⢤⠀⠀⠉⠛⠻⠧⠤⠤⠀⠒⠛⠛⠿⠷⠶⢄⣘⣀⠁⠀⠀⠤⠤⠤⠀⠀⠀⠀⣀⣶⢶⣶⣤⣀⣙⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣥⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠤⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⢠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠘⠉⠀⣤⡅⠀⠀⠀⠉⠉⢉⣀⣀⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣰⣶⣶⣿⣿⣶⣶⣶⣤⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣤⡄⠐⠂⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⡃⠀⠀⠈⠉⠉⠛⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠀⠀⠀⠀⢩⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠾⠿⡿⠿⡿⠿⣿⣿⠿⠟⠋⠛⣓⣀⢀⠀⢴⣶⠋⢉⠛⠃⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⢀⡀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⣋⠀⢀⣠⣤⣶⣶⣤⣾⣿⣿⣶⡶⢶⣶⣭⣽⠛⠁⠈⠉⠐⠿⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠿⠿⣷⣶⣶⣶⣶⣿⣿⡿⠛⠛⠳⠀⠀⠀⠀⠀⠀⣰⣿⣿⡐⠒⠒⠒⠀⠰⠦⣤⣴⣶⣶⣶⣶⣿⡅⠀⢸⣿⣿⣿⣿⡟⠻⣿⣿⣿⠓⠀⠉⠉⠉⠓⣤⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⡀⠈⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠘⠛⠻⠿⠷⠀⠙⠁⠀⠀⠀⢠⣶⣦⣤⠀⠉⢹⡅⠀⢸⣿⣿⣿⢿⣿⡿⠿⣷⣿⡿⠅⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⣀⣙⣁⢲⣶⠀⠀⣾⣿⣿⣋⡉⠊⢥⣈⣉⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠀⠀⠀⠀⠂⠰⠶⠠⠶⠆⠀⠐⠀⠴⠯⠍⠀⠤⠀⢸⣿⣿⣿⣿⣿⡁⠈⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠀⡄⠐⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣬⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⠍⠉⠉⠒⢂⠤⠶⠄⠀⠉⠙⣛⣛⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠛⠛⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠈⠀⢨⡭⠤⠍⠩⣿⡻⠛⠻⠿⠿⢿⣓⣺⣭⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠐⠀⠀⠀⠀
⠂⠀⠂⠠⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⣒⠈⠉⠀⠀⢹⣿⠧⠀⠀⠂⢌⣙⣟⣉⣿⠃⠤⢈⠛⣿⣿⠗⠺⠟⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠙⠏⠐⠒⠃⠀⠀⠰⠿⣿⣿⣥⡔⠋⠀⠀⢍⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀
⠿⢛⠲⠶⠀⠀⠈⠁⠀⠀⠶⢶⣶⣶⣦⣄⠀⠐⠰⠶⠄⣠⣀⡐⠲⣤⠈⢀⣤⣶⣶⠶⠈⠉⠻⠳⠶⠭⣅⣉⣉⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀
⠻⠛⠃⠀⠀⣤⣶⠀⠀⠀⠀⠀⡉⠛⠉⠉⠈⠛⠂⠂⠀⠭⣩⣁⡀⠀⣀⡛⠻⠿⢉⣁⠀⠹⠒⢀⣀⠀⠀⠺⣿⣆⡉⣙⣁⠀⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⡶⠛⠛⣟⣛⡉⠃⠀⠀⢤⣤⠀⠀⠠⣤⣀⠀⠙⠠⢴⣾⣟⣃⣤⡀⠀⠀⠀⠐⠛⣦⣤⡠⠤⠄⠐⠂⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣃⣀⣀⣀⣈⣻⣿⣃⣀⣀⣀⣛⣛⣛⣂⣀⣀⣀⣤⣤⣬⣍⣙⣿⣿⣿⣿⣿⣀⣈⣭⣍⣉⣀⣀⣈⣉⣃⣤⣤⣄⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⣿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢺⣶⣤⣭⠥⠀⢀⡀⠉⣀⣠⣤⣶⡄⠀⠘⠛⠛⠋⠁⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢳⡶⠃⠀⠀⠠⠄⠀⠀⠉⠀⠀⣀⠚⠛⠿⢄⣀⠛⠃⢀⣨⣿⣿⠛⠛⠓⢶⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀
⠀⠀⠲⢤⠀⠀⠉⠛⠿⠧⠤⠤⠀⠒⠛⠛⠿⠷⠶⢄⣙⣀⠁⠀⠀⠤⠤⠤⠀⠀⠀⠀⣀⣶⢶⣶⣤⣀⣙⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣥⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠞⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠤⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠟⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠚⠉⠀⣬⡄⠀⠀⠀⠉⠉⢉⣀⣀⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣰⣶⣶⣿⣿⣶⣶⣦⣤⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠛⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⠖⠐⠂⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⡃⠀⠀⠈⠉⠉⠛⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠀⠀⠀⠀⠩⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠾⢿⡿⠿⡿⠿⣿⣿⡿⠟⠋⠙⣓⣀⢀⠀⢴⣶⠋⢉⠛⠃⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⢀⡀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠛⠋⠀⢀⣠⣤⣶⣶⣤⣾⣿⣿⣶⡶⢶⣾⣭⣽⠛⠁⠈⠉⠀⠿⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠟⠛⢷⣶⣶⣶⣶⣿⣿⡿⠛⠛⠳⠀⠀⠀⠀⠀⠀⣰⣿⣿⡐⠒⠒⠒⠀⠰⠦⣤⣴⣶⣶⣶⣶⣿⡅⠀⢸⣿⣿⣿⣿⡟⠻⣿⣿⣿⠓⠀⠉⠉⠉⠓⣤⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⡀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠘⠛⠻⠿⠧⠀⠙⠁⠀⠀⠀⢠⣶⣦⣤⠀⠉⢹⡅⠀⢸⣿⣿⣿⢿⣿⡿⠿⣷⣿⡿⠅⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃⣈⣙⣁⢲⣶⠀⠀⣼⣿⣿⣋⡙⠘⢥⣈⣉⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠂⠐⠶⠠⠶⠄⠀⠐⠀⠴⡯⠍⠀⠤⠀⢸⣿⣿⣿⣿⣿⡁⠈⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠀⡀⠐⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣬⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⠍⠉⠁⠒⢂⡤⠶⠄⠀⠉⠙⣛⣛⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠛⠛⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠈⠀⢨⡭⠤⠍⠩⣿⡻⠛⠻⠿⠿⢿⣓⣪⣭⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠐⠀⠀⠀⠀
⠂⠀⠂⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣒⠈⠉⠀⠀⢹⣿⠧⠀⠀⠂⢌⣙⣟⣉⣿⠃⠤⢈⠛⣿⣿⠿⠺⠟⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠙⠟⠐⠒⠃⠀⠀⠠⠿⢿⣿⣥⡔⠋⠀⠀⢍⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀
⠟⢛⠲⠶⠀⠀⠈⠁⠀⠀⠲⢶⣶⣶⣦⣄⠀⠐⠰⠶⠄⣠⣀⡐⠲⣦⠈⢀⣤⣶⣶⠶⠈⠉⠻⠷⠦⠭⢍⣉⣉⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀
⠛⠛⠃⠀⠀⣤⣦⠀⠀⠀⠀⠀⡉⠛⠉⠉⠈⠛⠂⠂⠀⠩⣩⣅⡀⠀⣀⡙⠻⠿⢉⣁⠀⠙⠂⢀⣀⡀⠀⢺⣿⣇⠉⣙⣁⠀⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣠⡶⠛⠛⣟⣛⡉⠃⠀⠀⢤⣤⠀⠀⠠⣤⡀⠀⠙⠠⢴⣿⣟⣃⣤⡀⠀⠀⠀⠐⠛⣦⣤⡠⠤⠀⠐⠂⠀⠀⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣃⣀⣀⣀⣈⣻⣿⣃⣀⣀⣀⣛⣛⣛⣂⣀⣀⣀⣤⣤⣬⣍⣙⣿⣿⣿⣿⣿⣀⣈⣭⣍⣉⣀⣀⣈⣉⣃⣤⣤⣄⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠷⠚⠋⢈⠛⠓⠀⠀⠀⠈⠁⠀⠈⢭⡍⠹⣿⣿⣟⣙⢉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣦⡄⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⠚⠀⠀
⠀⠀⠀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣦⣈⣛⣒⠀⢀⡉⠒⢦⣀⣤⣤⣄⠀⠒⠻⠿⠗⠓⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠓⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠴⢶⣶⠆⠠⠀⢠⣤⠀⠀⠓⠀⠀⡈⠿⠟⢿⡤⢤⡼⠛⢀⣽⣿⣿⠟⠟⠷⢶⣤⢤⣔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀
⢤⣀⡀⠀⠲⠶⢾⣏⣀⣀⡀⠰⠶⠶⠶⠶⣦⣄⠘⠃⡐⠀⠈⢭⡤⠤⠌⠁⢀⡁⢐⣶⣶⣶⣦⣀⣙⣛⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠈⠀⠀⠑⢤
⠀⠈⠁⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣥⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣟⣒⠸⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣄⣀⠺
⠤⠤⠄⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⢄⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠋⣤⣾⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠤⠠⠀⠀⠀⣀⣀⡄⠀⠀⣰⣿⣿⣿⠿⢿⣿⣦⠀⠈⠙⠛⠿⢿⣿⡛⠉⠉⠉⢁⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣻⣷⣶⣶⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠗⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠀⠀⠀⠀⠀⠻⠿⠟⠃⠀⠀⠋⠻⣿⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⢐⡒⠒⠒⠀⠀⠀⠐⠚⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣚⠛⠃⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠃⠘⠛⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⣀⣖⠂⠀⠀⠀⠀⠀⠀⠀⠛⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣯⠈⠁⠀⠀⠀⠉⠐⠿⠧⠀⠀⠀⠂⠀⠀⠀⢐⠛⢑
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢤⣀⣀⣀⣠⣶⣆⠛⠛⢋⣙⣥⣄⣀⣀⣿⣿⠁⣘⠛⠀⠄⠀⠀⠀⠀⠀⠀⠀⠴⠟⢂⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢤⣶⣶⣷⣶⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⡀⠀⠀⠀⠀⣠⣤⣤⣤⣦⡄⠀⠀⠀⠀⣀⡀⢀⣀⣠⣾⣿⣷⡿⢿⣿⣶⣿⠋⠉⠀⠀⣉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣾⣿⣿⣿⠟⠛⠿⠄⠀⠀⣀⠀⠀⣰⣿⣿⣟⠓⠒⠚⠀⠶⠶⣶⣿⡿⢿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⡟⣛⣿⡿⣿⣋⠀⠀⠉⠉⢻⣴⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀
⡿⡿⠿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⣰⣿⡆⠘⠋⠻⠿⠻⠄⠙⠃⠀⠀⠀⣠⣶⣦⣤⡄⠈⠹⠅⠀⣿⣿⣿⣿⣿⣿⣟⢛⣿⣿⡟⠇⠀⠀⠀⠓⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⣤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠙⠻⡇⣈⣉⣉⡰⠶⠆⢀⣿⣿⣿⣉⣋⠓⢲⣦⣅⡀⠈⠀⠀⠀⠄⠉⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⠀⠀⠒⠐⠶⠦⠶⠶⠀⠀⠒⠰⠶⠬⠁⠒⠊⠸⣿⣿⣿⣿⣿⠅⣈⡐⠀⠁⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢈⠁⣄⠐⠂⠀⠀⠀⠻⣿⣿⣿⣿⣷⣾⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠒⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⡯⠉⠉⠑⣒⣠⠶⡦⢀⠈⠉⢉⣙⣛⡋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠃⠀⠀⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠛⠛⠋⠀⠀⠀⢀⡁⠀⠀⠀⠄⠀⠀⠠⠴⣆⠈⢭⠨⠭⠥⠬⠉⣾⣟⡛⠛⠛⠻⢻⢯⣵⣿⣶⠦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠓⠆⠊⠉⠀⠀⠀⠛⢦
⠀⠠⢤⣀⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣒⠈⠉⠁⠀⢸⣿⡧⠤⠀⠘⢄⣙⣻⣛⣻⡟⠢⢄⣙⣿⣿⡿⠒⠟⠻⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢤⣄⣀⠈⠀⢀⣀⠀⠀⠈⠉⠙⠢⠀⠀⠀
⠤⠀⠀⠉⠁⠀⠀⠀⠀⠀⠠⡤⠄⠀⠀⠀⢙⡉⠁⠀⠀⠀⠙⠿⠛⠶⠛⠀⠀⠰⠾⢿⣿⣯⣴⠛⣁⡀⢬⣁⠀⠀⠀⠐⠦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⢦⣤⣀⠀⠀⠀
⠾⠧⣤⡄⠀⠍⠛⠂⠀⠠⣶⣴⣶⣤⣄⡀⠨⠭⢭⠤⢀⣀⣀⠶⣦⡄⠀⣠⣤⣤⡴⠦⢩⠛⢿⠶⠭⢭⣍⣉⡅⣤⣤⣤⣤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀
⠿⠗⠀⠀⣠⣤⣄⠐⠂⠀⠐⢈⣛⡛⠛⠓⠊⠀⠐⠂⠈⣉⣉⠁⠀⢈⡘⠿⠿⠟⣉⡀⠈⠷⠢⣄⣁⡄⠐⢿⣷⣈⣙⣏⡁⠤⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣶⣶⣿⣿⣛⣒⣀⣀⣐⣄⣀⣀⣀⣠⣀⣀⣐⣆⣠⣼⣿⣟⣠⣄⣀⣁⣀⣐⣛⣷⣤⣄⣤⣄⣠⣖⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⣿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠗⠒⠁⠀⠙⠃⠀⠀⠀⠀⠁⠀⠀⢠⡈⠉⢛⣿⣟⡉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣤⣈⣑⣂⠀⠀⡉⠒⢀⢀⣠⣤⡄⠀⠐⠚⠻⠓⠂⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⢤⣴⠄⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠹⠚⠿⠀⠀⠘⠃⠀⢙⣿⣿⠛⠛⠳⢶⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀
⠄⣀⡀⠀⠒⠶⢶⡇⢀⣀⡀⠰⠶⠶⠶⠶⣦⡄⠈⠃⠀⠀⠈⢡⠤⠤⠀⠀⠀⠀⢀⣲⠶⣦⣤⣀⣈⡋⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣥⣤⣶⣶⣶⣶⣶⣶⣶⣯⣿⣟⡂⠀⠸⠟⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠸
⠠⠤⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠾⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢰⣿⣿⣿⠿⢿⣷⣦⠀⠈⠉⠙⠻⠿⠿⠛⠉⠉⠉⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣻⣷⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠘⠻⠛⠁⠀⠀⠈⠉⠉⠀⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⠀⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⣻⣯⠍⠋⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⠔⡒⠚⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣒⠂⠀⠀⠀⠀⠀⠀⠀⠛⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠾⠦⠀⠀⠀⠀⠀⠀⠀⠐⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡴⡆⠛⠛⠉⣉⣠⣀⣀⠀⣿⡮⠁⣘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠀⠀⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠤⣴⣶⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡀⠀⠀⠀⠀⣀⡀⠀⢀⣠⣶⠿⣶⠾⠿⣷⣶⡿⠉⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠲⠶⣶⣶⣤⣴⣿⣿⡿⠟⠛⠳⠀⠀⠀⠀⠀⠀⣰⣿⣿⣀⠒⠂⠒⠀⠰⠶⠦⢾⡷⢾⣿⣿⣿⠀⠀⢸⣿⣿⣟⣿⡇⢛⣻⡿⢟⢋⠀⠀⠈⠉⠋⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀
⠀⠉⠻⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⡄⠐⠋⠻⠟⠛⠀⠈⠁⠀⠀⠀⢠⡶⠦⣤⠀⠈⠩⠅⠀⢸⣿⣿⣟⠛⣿⡟⢛⣷⢿⡟⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣤⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⢀⣈⣁⠰⠶⠀⠀⣸⣿⣿⣀⣈⠀⠢⡄⢁⡀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠂⠐⠒⠀⠴⠆⠀⠀⠀⠰⠶⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⢀⠀⡀⠀⠂⠀⠀⠀⠻⣿⣿⣿⣿⣷⣦⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠒⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠬⠀⠉⠐⣒⠠⠶⠦⢀⠀⠉⢉⣉⣛⡋⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠭⠠⠌⠁⢼⣛⠛⠙⠛⠛⠋⢉⣀⠡⡴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠀⢸⡿⠿⠶⣾⠿⠿⣿⠿⠿⣿⠿⢿⠿⠿⣿⠿⠿⣿⠿⠿⣿⠿⡿⢿⠷⡶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠈⡉⠀⠀⠀⠀⢸⣷⠀⡆⢸⠀⡇⠈⠀⠦⣿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠘⠀⡇⠸⠤⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀
⠾⠧⠤⠄⠀⠈⠑⠀⠀⠠⢦⣤⣤⡤⢀⠀⠠⠍⠡⠄⢀⣀⣸⣟⣀⣁⣼⣀⣃⣴⣀⣁⣻⣀⣿⣀⣃⣼⣀⣃⣼⣀⣃⣼⣀⣇⣠⣀⣇⣘⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠾⠗⠀⠀⢠⣤⡄⠀⠂⠀⠀⠈⡛⠛⠛⠃⠀⠀⠀⠀⠈⢉⣉⠉⠉⢉⠙⠻⠿⠟⣉⡉⠙⠿⠉⢍⠉⠉⠙⢿⣿⡋⢙⣋⡉⠩⠿⠛⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣴⣶⣾⣟⣃⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣐⣂⣀⣤⣿⣛⣀⣄⣀⣀⣀⣀⣚⣷⣤⣄⣀⣀⣀⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠟⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⣛⣧⣤⣸⣋⡛⠁⠀⠀⠀⠀⠶⠀⠀⠀⣀⢸⣿⣷⣿⣿⣿⣦⣤⣭⠤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⠀⣀⠀⠀⠀⠀⠀⠤⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⠇⠒⠋⠈⠛⠂⠀⠀⠀⠉⠀⠀⠈⣥⠈⠻⣿⣿⣟⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀
⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⣤⣐⣒⣂⠀⠈⠉⠒⠀⢀⣠⣤⠀⠀⠒⠛⠛⠒⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⣤⣤⠄⠀⠀⢀⡄⠀⠀⠃⠀⠀⠈⠿⠛⢿⠀⠀⠚⠃⢀⣹⣿⣿⠛⠛⠲⢶⠤⢄⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠠⠤⣼⡏⣀⣀⡀⠠⠶⠶⠶⢶⣤⡄⠙⠂⠐⠀⠈⢡⠤⠤⠀⠀⠀⠀⣰⡶⢶⣶⣤⣄⣽⣃⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢤⣤
⠀⠈⠁⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣥⣴⣶⣶⣶⣶⣶⣶⣾⣯⣝⣛⠂⠒⠚⠋⠙⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⠛
⠤⠤⠄⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠠⠾⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠋⢙⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣤⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢰⣾⡏⠉⠁⠀⠀⠀⠘⠛⠋⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠈⠹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡿⣿⣿⣿⣿⣿⠋⠉⠉⠙⠛⠛⠛⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣷⣾⢩⠀⠈⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠐⠒⠂⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠙⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣖⣊⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⠤⠾⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⣀⡀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠛⠿⠟⠛⣛⢛⣿⢿⡇⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣿⣿⡿⠿⢿⣿⡿⠛⠉⣀⡨⢭⣤⣤⡀⡿⠯⢀⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⢴⣾⣶⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣷⣞⡡⠄⠀⠀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣦⣤⣾⣿⣿⠿⠛⠛⠓⠀⠀⠀⠀⠀⠀⣠⣿⣿⡍⠓⣀⡈⠀⠸⠶⠶⠾⠷⠻⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣇⣙⣿⠟⣿⣉⡀⠀⠀⠈⡉⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠋⠛⠋⠁⠀⠈⠁⠀⠀⠀⢠⡿⠶⣦⡀⠀⠩⠅⠀⢸⣿⣿⣿⣻⠿⠯⠙⣿⠿⡟⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣭⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⠃⢀⣤⣅⡴⠷⠀⠀⣼⣿⣿⣤⣤⠁⠹⡤⢀⡀⠀⠀⠀⠀⠀⠛⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠂⠐⠒⠂⠲⠖⠀⠀⠀⠒⠶⠂⠀⠒⠀⠀⣿⣿⣿⣿⣽⡆⢀⣀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠒⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠎⠀⠉⠈⣓⠐⠒⡒⠀⠀⠈⢉⣉⣛⡋⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠟⠛⠛⠋⠀⠀⠀⢀⠀⠀⢠⡶⠾⠿⣷⠶⠾⣶⠿⠿⣿⠿⢿⠿⠿⣿⠿⠿⣿⠿⠿⣿⠿⡿⢿⠿⡿⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠢⠀⠂⠀⠀⠀⠐⠶⢄
⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⣿⠀⡆⢸⠀⡆⠈⠀⠦⣿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠘⠀⡇⠸⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠈
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠘⡉⠁⠀⠀⠀⢸⣟⣀⣁⣼⣀⣃⣴⣀⣁⣻⣀⣿⣀⣃⣼⣀⣃⣼⣀⣃⣼⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀
⡶⠦⣤⡄⠀⠀⠒⠀⠀⠠⢤⣤⣤⣤⣄⠀⠨⠍⠩⡤⢀⣀⣀⠿⣯⡍⠋⣩⣿⣭⡽⠏⠛⠛⠛⠻⠿⠭⣋⣉⡉⠹⣍⣉⠉⠙⠋⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀
⣶⣶⣀⣀⣀⣤⣀⣀⣀⣀⣀⣈⣛⣓⣛⣃⣂⣀⣀⣀⣘⣉⣉⣁⣀⣈⣘⣿⣿⣟⣉⣀⣈⣥⣄⣄⣀⣀⣀⣿⣷⣄⣉⣋⣁⣀⣤⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⣛⣧⣤⣴⣋⡛⠁⠀⠀⠀⠀⠶⠀⠀⠀⣀⢸⣿⣷⣿⣿⣿⣦⣤⣭⠤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⠀⣀⠀⠀⠀⠀⠀⠤⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠸⠇⠒⠋⠈⠛⠂⠀⠀⠀⠉⠀⠀⠉⣥⠈⠻⣿⣿⣟⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀
⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⣤⣐⣒⣂⠀⠈⠉⠒⠀⢀⣠⣤⠀⠀⠒⠛⠛⠂⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⣤⣤⠄⠀⠀⢀⡄⠀⠀⠃⠀⠀⠈⠿⠛⢿⠀⠀⠚⠃⢀⣹⣾⣿⠛⠛⠲⢦⠤⢄⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠠⠤⣼⣏⣀⣀⡀⠠⠶⠶⠶⢶⣤⡄⠙⠂⠒⠀⠈⢡⠤⠤⠀⠀⠀⠀⣰⡶⢶⣶⣤⣄⣽⣃⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢤⣤
⠀⠈⠁⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣥⣴⣶⣶⣶⣶⣶⣶⣾⣯⣝⣓⠂⠒⠚⠋⠙⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⠛
⠤⠤⠄⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⢠⠾⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠋⢙⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣤⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢰⣾⡏⠉⠁⠀⠀⠀⠘⠛⠉⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠈⠹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⡿⣿⣿⣿⣿⣿⠋⠉⠉⠙⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣷⣾⢉⠈⠉⠁⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠐⠒⠂⠀⠀⠀⠀⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠙⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣖⣪⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠾⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⣀⡠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠛⠿⠟⠛⣛⢛⣿⢿⡇⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡈
⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣿⣿⡿⠿⢿⣿⡿⠛⠉⣀⡈⢭⣤⣤⠀⡿⠯⢀⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⢴⣾⣾⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⠻⣿⣷⣟⣡⠄⠀⠀⠄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣦⣤⣾⣿⣿⠿⠛⠛⠓⠂⠀⠀⡀⠀⠀⣠⣿⣿⣍⠓⣀⡈⠀⠸⠶⠶⠾⠷⠻⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣇⣙⣿⠟⣿⣍⡀⠀⠀⠈⡉⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠋⠛⠋⠁⠀⠈⠁⠀⠀⠀⢠⡾⠶⣦⡀⠀⠩⠅⠀⢸⣿⣿⣿⣛⠿⠯⠉⣿⠿⠟⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣩⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⠃⢀⣤⣅⡴⠷⠂⠀⣼⣿⣿⣤⣤⠁⠹⡤⢀⡀⠀⠀⠀⠀⠀⠛⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠂⠐⠒⠂⠴⠖⠀⠀⠀⠒⠶⠂⠀⠒⠀⠀⣿⣿⣿⣿⣽⡆⠀⣀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠒⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠎⠀⠉⠈⣓⠐⠒⡖⠀⠀⠈⢉⣉⣛⡋⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⢠⡶⠾⠿⣷⠶⠾⣶⠿⠿⣿⠿⢿⠿⠿⣿⠿⠿⣿⠿⠿⣿⠿⡿⢿⠿⡿⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠢⠄⠂⠀⠀⠀⠐⠶⢄
⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⠀⡆⢸⠀⡆⠈⠀⠦⣿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠘⠀⡇⠸⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠈
⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠈⡉⠁⠀⠀⠀⢸⣟⣀⣁⣼⣀⣃⣴⣀⣁⣻⣀⣿⣀⣃⣼⣀⣃⣼⣀⣃⣼⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀
⡶⠦⣤⡄⠀⠀⠒⠀⠀⠠⢤⣤⣤⣤⣄⠀⠨⠍⢩⡤⢀⣀⣀⠿⣯⡍⠉⣩⣿⣭⡽⠏⠛⠛⠛⠻⠿⠭⣋⣉⡉⠹⣭⣉⠉⠙⠋⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀
⣶⣶⣀⣀⣀⣤⣀⣀⣀⣀⣀⣈⣛⣛⣛⣃⣂⣀⣀⣀⣘⣉⣉⣁⣀⣈⣘⣿⣿⣟⣉⣀⣈⣥⣄⣄⣀⣀⣐⣿⣷⣄⣉⣋⣁⣀⣤⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠟⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠿⢿⣯⣤⣠⣟⣛⠋⠀⠀⠀⠀⡶⠀⠀⠀⢀⠸⣿⣿⣿⣿⣿⣧⣠⣍⡥⢀⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢄⣀⠀⠀⠀⠀⠀⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠸⠇⠐⠋⠀⠛⠒⠀⠀⠀⠉⠁⠈⠉⣡⠘⢻⣿⣿⣟⠛⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠖⠂⠀⠀
⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣤⣐⣒⣂⠀⠈⠙⠒⢠⣀⣠⣤⡀⠀⠐⠻⠿⠒⠃⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⢀⣀⠀⠀⠃⠀⠀⠈⠽⠿⢿⠀⠀⠼⠃⢀⣻⣾⣿⠛⠛⠷⢦⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀
⢀⣀⠀⠀⠠⠤⣤⣏⣀⣀⡀⠠⠴⠶⠶⢶⣤⡄⠙⠃⠐⠀⠈⢁⠤⠤⠀⠉⢉⠉⢰⣶⢶⣦⣤⣄⣘⣋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠉⠀⠈⢡⣤
⠀⠈⠁⠀⠀⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣡⣤⣶⣶⣶⣶⣶⣶⣾⣯⣝⣛⠐⠒⠚⠛⠙⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠰⠿
⠤⠤⠄⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⢀⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠊⣡⣾⡿⠿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠋⣻⣿⠿⠟⠛⠋⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣭⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠀⠀⠀⠀⣀⣀⡀⠀⠀⢰⡞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠚⠛⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⣿⣾⢏⡉⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠒⠒⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣯⣒⣀⡉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣀⡀⠟⠂⠀⠀⠀⠀⠀⠀⠀⠁⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⣿⣷⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⡻⠾⣿⣿⡧⠈⠁⠀⠀⠀⠀⠙⠶⠀⠀⠀⠀⠀⠀⠀⠀⣚⣉⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⢿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣤⣤⣤⣶⡿⠿⢿⣿⣿⠛⠋⢉⡉⢥⣤⣀⠈⣿⡯⢁⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢴⣶⣶⣿⣾⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣍⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣶⣞⡉⠄⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣤⣼⣿⣿⡿⠛⠛⠛⠆⠀⠀⢀⠀⠀⣠⣿⣿⡝⠒⣒⠀⠀⠲⠶⠶⠾⠿⠿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⡗⣛⣿⡿⣿⣉⠀⠀⠀⠉⢉⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⠿⠿⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠋⠻⠟⠃⠀⠙⠁⠀⠀⠀⢠⡶⢶⣤⡀⠀⠩⠅⠀⢸⣿⣿⣿⣛⣿⣟⠛⣿⠿⣟⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠛⠃⢀⣉⣉⡴⠶⠂⠀⣸⣿⣿⣄⣈⡉⢲⡤⢄⡀⠀⠀⠀⠀⠀⠛⠓⠒⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠂⠐⠒⠀⠶⠆⠀⠀⠀⠐⠶⠍⠀⠐⠀⠀⣿⣿⣿⣿⣽⠄⢀⡀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠀⡀⠐⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣦⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠒⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠮⠁⠉⠐⣒⠠⠶⠦⠀⠀⠉⢉⡙⣛⡋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⢠⡶⠾⠿⣶⠿⠿⣶⠿⠿⣾⠿⢿⠿⠿⣿⠿⠿⣿⠿⠿⣿⠿⡿⢿⠿⡿⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠦⠀⠒⠀⠀⠀⠀⠶⣄
⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠤⠀⠉⠁⠀⢸⣿⠀⡆⢸⠀⡇⠈⠀⠦⣿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠘⠀⡇⠸⠤⣿⠀⠄⠀⠀⠀⠀⠀⠠⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠈
⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⢺⣟⣀⣁⣼⣀⣃⣴⣀⣁⣻⣀⣿⣀⣃⣼⣀⣃⣼⣀⣃⣼⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠈⠉⠉⠀⠀⠀⠈⠀⠀⢠⣄⡀⠀⠀⠀⠀
⡶⢦⣤⠀⠀⠐⠂⠀⠀⢠⣤⣤⣤⣤⡀⠀⠨⠍⣩⡄⢀⣀⠀⠽⣭⡉⠋⣉⣯⣭⡽⠟⠛⠛⠛⠿⠟⣛⣛⣛⠉⠭⣍⣉⠉⠙⠋⠉⠩⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀
⣶⣆⣀⣀⣀⣄⣀⣀⣀⣀⣠⣙⣻⣗⣛⣀⣂⣀⣀⣀⣛⣛⣋⣀⣀⣉⣸⣿⣿⣟⣃⣀⣈⣥⣄⣀⣀⣀⣐⣿⣷⣈⣉⣋⣀⣠⣤⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠶⠶⣶⠿⢿⣿⠰⠶⣿⡷⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠟⠁⠀⣘⡙⠛⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⣤⢤⣍⣻⣷⣀⣈⣁⠀⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠒⠀⠐⠂⠀⠀⠀⠀⠁⠀⠉⢀⡀⠙⠛⣻⣟⠓⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠒⣂⠀⠀⠀⠂⠀⠀⢀⣠⡀⠀⠀⠺⠶⠖⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠩⠍⠹⠅⠀⠀⠀⠀⠈⣀⣘⠏⠻⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡀⠀⠀⠤⢤⡼⠀⠀⠀⠀⠤⠤⠶⠤⣤⡄⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠀⣰⠤⣤⣤⣀⣈⣛⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣠⣤⣶⣶⣶⣶⣶⣦⣤⣘⡛⠀⠀⠈⠟⠉⠛⠓⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⠶⢖⣲⣶⣶⣶⣶⣶⣶⣄⠽⣿⣷⣿⣿⣿⣿⣶⣾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠛⠛⠉⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⡿⣤⣶⣿⣿⣿⡿⣿⣯⡄⠀⢁⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⠿⣿⣇⡐⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣄⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣟⢻⣿⣿⣟⡻⠛⠿⠿⠿⠻⠶⣿⣿⡅⠉⠁⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠁⠀⠉⠙⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⠿⠿⢿⡿⠛⠋⠉⠉⢀⣀⡀⠀⢻⡏⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⡿⠶⠚⡷⠶⠶⠞⠻⣷⣶⠆⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢤⣤⣤⣿⣿⠿⠛⠋⠓⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣟⣻⠃⢐⣒⠈⠛⠋⠀⠀⠈⠉⠉⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠈⠀⠀⠀⠀⠠⠄⠀⣀⠀⠀⠠⠄⠀⢹⣿⣿⣻⠙⢹⡏⠉⡶⢿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⢀⣀⣀⠠⠒⠀⠀⢀⣿⣿⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡧⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠀⠀⠀⠀⠤⠉⠀⠀⠀⠀⣿⣿⣿⣿⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠀⠁⠐⠂⠀⠤⠄⠀⠀⠉⠉⠛⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠷⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⢀⡶⠾⠶⣶⠷⠶⣶⠿⠷⣾⠿⢷⠿⠿⣶⠿⠿⣿⠿⠿⣿⠿⡾⢿⠷⡶⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡇⠀⠀⢸⠀⡆⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⢸⣇⣀⣀⣼⣀⣁⣴⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⡀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢬⣉⠉⠉⢉⣭⣭⡭⠙⠛⠛⠋⠙⠛⠋⡙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣻⣒⣃⣀⣀⣀⣀⣀⣙⣋⣁⣀⣀⣀⣸⣿⣧⣓⣂⣀⣀⣀⣀⣀⣀⣀⣀⣽⣤⣀⣉⣁⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠲⣶⠎⢿⣿⠰⠶⣿⡗⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠃⠀⣀⣋⠛⠃⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⣴⣤⣯⣻⣿⣄⣀⣉⡀⢀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠸⠀⠔⠀⠀⠒⠀⠀⠀⠀⠉⠀⠉⠉⡀⠙⠛⣻⣿⡛⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠴⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠒⢒⠀⠀⠀⠒⠂⠀⢀⣀⣄⠀⠀⠰⠷⠶⠒⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠭⠹⡇⠀⠀⠒⠀⠀⣃⣾⡿⠹⠷⠦⡤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀
⠀⢀⡀⠀⠀⠠⢤⣼⡃⠀⣀⠀⠤⠴⠶⠶⢤⣤⠀⠙⠀⠂⠀⠀⣀⠠⠄⠀⠉⠉⠁⣰⣦⣤⣤⣄⣀⣛⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠁⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣠⣤⣶⣶⣶⣶⣶⣶⣼⣦⣛⡃⠀⠈⠿⠉⠛⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠤⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢀⣀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣀⣴⣿⣷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢰⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣽⣿⣷⣿⣿⣿⣿⣶⣶⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠉⠁⠀⠀⠸⣷⡾⠿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣟⠓⢻⣭⡉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡗⠋⣤⣀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⠋⠉⠉⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣟⣿⠛⠿⠿⠿⠿⠿⣿⣿⡍⠉⠉⠀⠀⠀⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠿⣿⣿⠛⠋⠉⠉⣀⣀⡀⠀⢻⡎⠉⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠈⠉⠀
⠀⠀⠀⠀⢤⣶⣶⣶⣶⣶⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡶⢿⣷⠶⢶⠞⠻⣿⣶⡞⠉⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⡶⣶⣤⣤⣼⣿⣿⠿⠛⠛⠓⠀⠀⠀⠀⠀⠀⢠⣾⣷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣟⣿⠇⢚⣳⠞⢛⠋⠀⠀⠈⠉⠋⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⠏⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢻⣿⣿⡿⠛⣿⡏⠛⡶⢿⠖⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠖⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⢀⣀⣀⡠⠦⠀⠀⢨⣿⣿⣈⡀⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠶⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡷⠀⠀⠀⠀⠀⠐⠒⠀⠴⠄⠀⠀⠀⠠⠬⠉⠀⠀⠀⠀⣿⣿⣿⣿⣭⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠂⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠍⠈⠁⠐⠂⠠⠤⠄⠀⠈⠉⠙⠛⣛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠺⠶⠶⠶⡤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⢠⡶⠾⠷⣶⠿⠿⣶⠿⠷⣿⠿⢿⠿⠿⣿⠿⠿⣿⠿⠿⣿⠿⡿⢿⠷⡶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⢀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⡇⠀⡆⢸⠀⡇⠈⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⢺⣇⣀⣁⣼⣀⣁⣴⣀⣁⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣼⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠀⠀⠐⠆⠀⠀⠈⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⢠⡄⠀⠀⠐⠀⠀⠀⢤⣤⣤⣤⡀⠀⠀⠈⠈⣀⠀⠀⠀⠠⢬⡉⠙⠉⣩⣭⣭⡭⠛⠛⠛⠋⠙⢛⣛⡛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠀⠀⠀
⣶⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣒⣃⣀⣀⣀⣀⣀⣛⣋⣁⣀⣀⣀⣾⣿⣥⣓⣀⣀⣡⣄⣀⣀⣀⣀⣩⣿⣄⣈⣙⣁⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣷
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠶⣶⠏⢿⣿⠰⠶⣿⡗⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⣿⣿⠿⠀⠀⠙⠳⠦⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⢉⠻⣯⡍⠁⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠓⠶⠭⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡒⣲⠀⠀⠀⠀⠀⠀⠀⠈⠉⠤⢄⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠐⠄⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣀⣀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠂⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⠸⠇⠀⠉⠹⠇⠙⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠤⠤⠤⠤⢤⡤⠄⢠⠤⠄⠀⠐⢦⠄⠀⡴⠦⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠉⡉⢛⣁⠘⠇⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣂⣐⡂⠲⣦⡀⠀⠴⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣾⣿⣿⣿⣿⣓⠿⠾⣦⣤⣙⣓⡀⣠⣳⣶⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠿⢿⣿⣿⢻⣶⣾⡗⠛⢿⣿⡛⠿⠟⢿⢛⣿⠿⣩⣿⣿⡋⠙⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠥⠤⠄⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⡿⢿⣿⣿⠻⣽⣶⠶⠟⠃⠐⠀⠀⠀⠀⠲⡄⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⣦⡤⠰⠦⢤⣤⡤⠶⢢⣤⡉⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⡿⠿⠛⠉⠄⠀⠀⠀⠀⢀⣤⣤⣴⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⡿⠶⠆⠀⠀⠀⠒⠒⠀⠈⠉⠓⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⡆⣼⣿⡿⠂⠀⠐⠛⠠⣤⡤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠋⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⢀⡀⠀⠈⠛⠛⠻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⣶⠶⠶⣶⠶⠶⣶⠶⢶⠶⠶⣶⠶⠶⣶⠷⠿⣷⠶⡶⢷⠶⡶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠸⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠉⠉⠉⣉⣉⣉⠉⠻⠿⠋⠉⠛⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣿⣥⣄⣀⣀⣀⣀⣀⣐⣒⣂⣀⣉⣀⣠⣶⣍⣩⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠲⣶⠂⢿⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⣶⣴⣶⡦⠀⠘⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⣿⣂⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠠⠤⠤⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠓⠐⣿⡶⠤⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⡄⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠉⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⠙⠓⡖⠐⢦⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠚⠂⠀⠶⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⣶⠄⠠⠠⢤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠦⢴⣶⣦⣀⡐⠲⠄⠀⡐⣤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉⠙⣿⣟⣿⠿⢺⣿⠶⡖⢾⣿⣛⣻⣿⡿⠛⠋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢾⣶⣤⠿⠀⠄⠀⠁⠈⠁⣤⠠⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣀⣠⣴⣿⡿⠿⣡⣾⣇⡀⢠⣌⣁⣀⣀⡄⣀⡐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⢲⣤⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢰⣿⣿⡍⠀⠀⠀⠈⠭⠄⠀⠑⠛⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣸⣿⡷⠈⠀⠰⠆⢀⣀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⠇⠁⠀⠀⢻⡏⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠟⠛⠛⠋⠁⠀⠀⠀⣠⣼⣿⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠀⠀⢀⡴⠶⠶⣶⠶⠶⣶⠷⠶⣶⠶⢶⠾⠿⣷⠶⠶⣶⠶⠶⢶⠶⡶⢶⠶⡶⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠋⠙⢏⣉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣒⣖⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣂⣀⣀⣤⣑⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠆⠲⣶⠂⢿⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⣀⣀⣀⡀⠀⢠⣀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠠⣤⣦⣌⠀⠈⢉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠛⠃⠀⠀⡉⠛⠂⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠍⣿⣦⣀⡈⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⣭⣉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠈⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡒⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠚⠛⠂⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⢀⣀⠀⠚⠓⠢⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⠌⠀⠀⠀⠀⠴⠶⠶⠶⠤⠀⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⣔⠲⠦⢤⡄⢨⣁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣮⣭⣀⡀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠰⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠈⠩⢯⡅⠰⡍⠀⠀⠀⠉⠗⠀⠠⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⣀⢐⣄⠀⠀⠀⣀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣨⣥⣄⡈⠱⢤⡀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢙⣿⣿⡿⢷⣶⣮⡭⣽⣿⠷⢶⣶⣶⠷⠿⡋⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠠⣿⣯⣶⠈⣍⠀⠁⠈⠋⣉⠉⡍⠛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣈⣩⣿⣿⣿⣯⣤⡆⠀⠀⠀⠊⠉⢀⡀⠀⠀⠤⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣲⣤⣤⠤⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠀⠀⣼⣿⣗⠀⠀⠀⠙⣛⣋⠁⠫⠿⢅⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠛⠉⠁⠀⠀⠀⠀⠀⢹⠿⢿⡿⠿⠟⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣯⡝⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⣿⣿⣿⣿⣿⡿⠟⠀⠀⠒⠀⠀⠸⣿⠋⠀⠀⠀⠀⠨⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋⠉⠁⠤⠤⠀⠀⠀⠀⠀⣠⣿⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡇⠀⠀⢀⡴⠶⠶⣶⠶⠶⣶⠾⠶⣶⠶⢶⠿⠿⣶⠾⠷⣶⠶⠶⣶⠿⡿⢿⠶⡶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠓⠒⠒⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠁⠀⠀⠀⢰⡇⠀⠀⢸⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣠⣤⣤⣄⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠲⣶⠂⢿⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⢉⠀⣀⠂⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢷⣾⡿⠆⠀⠈⠓⠦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣈⠻⣦⡀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠒⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢤⣀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣘⡃⠀⠀⠈⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡒⠀⠀⠠⢄⠀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡥⢤⣄⡀⢙⣂⡀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣭⢤⣌⡉⣹⣷⣦⠤⣤⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠻⢿⠿⣿⠏⠀⠚⠁⠀⠙⠈⠀⠈⠛⠒⠒⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⡀⠀⠀⠀⠛⠉⠁⠀⠀⠀⢄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣉⣽⣿⣿⣟⠛⠋⠀⠀⠀⣸⡿⠂⠈⠓⠒⠒⠂⠂⠐⢲⡂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠋⠉⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⣴⣶⠀⠀⠀⠀⣿⡉⠀⠀⣀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄⠀⠀⠀⠩⠀⠀⠀⣺⡟⠁⠀⠀⠀⠀⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⣸⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣿⣿⣿⠁⡴⠶⠶⣶⠶⠶⣶⠶⠶⣾⠶⢶⠿⠾⣶⠶⠶⣶⠶⠶⢶⠾⡿⢿⠿⡿⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠦⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠛⠉⢀⡇⠀⠀⢘⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠋⠙⠙⠋⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠀⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠆⠲⣶⠀⢾⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡁⠀⠀⠀⠀⠀⠚⠀⠐⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣦⣤⣶⡄⠀⠐⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠻⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠤⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠟⠒⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣄⣀⡘⠂⠀⠈⠩⠁⠙⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠐⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡠⠀⠀⠑⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣋⣁⣘⣛⢛⣲⣤⣤⣠⣀⣠⡼⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠅⠀⠚⠉⠁⠉⠛⠃⠰⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠻⢿⠟⠛⠁⣀⠈⠁⠀⠚⠙⠃⠀⠀⠀⢀⡀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⣼⣿⠄⠀⠒⠀⠤⠔⠂⠀⢂⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢤⣾⣿⣿⣿⣷⣦⣿⣏⠀⠀⠀⠈⠉⠉⠛⣻⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⣿⡛⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⡿⠁⠀⠀⠉⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⡿⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⣀⣤⡶⠿⠶⣶⠶⠶⣶⠶⠶⣶⠶⢶⠶⠶⣶⠶⠷⣶⠶⠶⢶⠶⡶⢾⠿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠻⡇⠀⠀⠈⠀⠀⠀⠀⠤⢼⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣴⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠀⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠆⠲⣶⠀⢾⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠐⠃⠀⠦⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣤⣤⣤⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⢧⡈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠤⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠘⠿⠖⠤⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠡⠄⣀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠶⠀⠉⠉⠇⠀⠳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⣀⠀⠀⠐⠂⠀⠀⠐⠂⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠀⠀⠀⠀⠀⢉⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⠀⠘⠢⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣟⣉⣀⠛⠛⢲⣤⣌⣁⣀⣠⣬⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠩⠏⠉⠑⠋⠋⠉⠻⠿⠤⠾⠛⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠉⠛⠿⠉⠉⢈⠉⠉⠁⠲⠷⠚⠁⠀⠁⠀⡀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⠋⠉⠙⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⢠⣿⡧⠀⠰⠤⠤⠤⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⠀⣀⣤⣦⣀⣀⣀⠀⠀⠈⠉⣉⣽⣿⡿⠌⠁⠛⠋⣀⣴⡆⠀⠀⠀⠀⣼⡿⠒⠀⠀⠀⠀⠒⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⡿⠿⣛⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠀⠀⣿⡿⠀⢀⠈⠁⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣶⣿⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡾⠿⠿⣷⠶⠶⣶⠶⠶⣶⠶⢶⠶⠶⣶⠶⠶⣶⠶⠶⢶⠶⡶⢶⠾⡿⠿⢿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⢿⡇⠀⠀⢸⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⡿⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⠍⠉⠉⠉⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠆⠲⣶⠀⢾⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠀⠀⠀⠀⠀⠒⠂⠀⠤⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⣤⣤⣤⠀⠀⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠤⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠻⠷⠒⠤⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠰⠆⠀⠉⠩⠄⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠃⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠀⢀⣀⣀⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣀⡀⠀⠓⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡛⣀⡘⠛⠳⣦⣄⣉⣑⣀⣤⣥⠶⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡟⠿⠿⢿⣿⣿⣿⣿⡟⠉⠿⢋⠉⠺⠛⠋⠙⠿⠯⠥⠾⠛⠫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⡉⠹⠉⠐⡶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠉⠀⠀⠈⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠄⠐⠦⠤⠤⠀⠀⠀⢤⡬⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⢀⣤⣀⣀⣀⣀⣀⣀⣀⣨⣽⡿⠷⠓⠀⠀⠀⠀⣀⠀⢀⣦⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠐⠒⠂⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⡿⠛⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡁⠀⠀⢸⣿⠇⠀⡀⠙⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣾⣿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡾⠿⠿⣿⠶⠶⣶⠶⠶⣶⠶⢶⠶⠶⣶⠶⠶⣶⠶⠶⢶⠶⡶⢶⠶⡿⠿⢿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⡇⠀⠀⢸⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⣿⠀⠀⠀⠘⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠯⠉⠉⠉⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠀⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠆⠲⣶⠀⢾⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠈⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠴⠀⢠⡄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣄⣀⣤⡄⠀⠠⢤⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠒⠠⢖⣂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⣀⡄⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠑⠒⢿⡶⠤⠄⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠠⠄⠀⠀⠀⠀⠀⠀⠐⠀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠴⠀⠉⠛⢒⠀⠲⠤⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠐⠒⠀⠀⠀⠐⠂⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣷⠒⠀⠸⠲⠶⣤⣈⣋⣀⠀⣄⣤⠆⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠻⡟⠛⢿⣿⣿⣿⣿⣿⣿⠏⠙⠟⡉⠩⠝⠛⠁⢻⡿⠭⠩⠿⠛⢍⠁⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⢴⡶⠶⠂⠀⠐⠀⠀⠀⠀⠠⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣴⣾⡿⠗⠀⠃⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣧⠀⠠⠤⠤⣀⠠⠀⠠⢀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄⠀⠀⠀⣸⣿⠧⠀⠀⠀⠀⠐⠒⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⠀⠀⠀⣽⣿⠀⠀⠐⠒⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠟⠛⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⣴⣾⣷⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠿⣿⠿⠶⣶⠶⠶⣶⠶⢶⠶⠶⣶⠶⠶⣶⠶⠶⢶⠶⡶⢶⠶⡾⠿⢿⡿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠘⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⣿⠀⠀⠀⠀⠐⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠛⢉⠹⠍⠉⠉⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠆⠲⣶⠀⢾⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠀⠀⠀⠀⠛⠛⠂⠀⠀⠀⠀⠠⠤⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⡀⠀⢠⣀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠄⢤⡮⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⣀⡈⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠽⣷⣤⣀⣐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣈⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠄⠀⠉⠉⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠛⠒⡂⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠆⠀⠶⢶⣤⣀⡛⠂⠄⢀⣐⣠⠤⠀⠀⠀⠀⠀⠀
⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⠉⠙⢛⣿⣿⣿⣿⣿⡟⢻⣿⠛⠻⡿⠶⠒⢾⣿⣛⣹⡿⠟⣋⠁⠀⠀⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠲⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠋⢤⣶⡤⠇⠀⠂⠀⠀⠀⠀⠠⠄⠂⠀⠌⠅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠁⠀⠀⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡀⢠⣌⣁⣀⠀⠀⢀⣀⡒⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⡀⣀⣴⣶⣤⣤⣤⣤⣤⣤⣶⣿⠟⠉⠀⠀⠀⠀⣰⣄⣀⡀⠀⠀⠀⢼⣿⣯⠀⠀⠀⠀⠠⠤⠀⠀⠛⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠙⠻⠿⠀⠀⠀⣼⣿⠆⠀⠐⠆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⢠⣼⣷⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠾⣿⠿⠿⣶⠶⠶⣶⠶⢶⠶⠶⣶⠶⠶⣶⠶⠶⢶⠶⡶⢶⠶⡶⠿⢿⣿⠿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⢸⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⢠⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⣿⠀⠀⠀⠀⠀⠠⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠙⠋⠉⠉⠉⠉⠉⠉⠉⢉⣏⠉⠉⠉⠉⠻⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠆⠲⣶⠀⢾⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠦⠀⠀⠀⠀⠾⠶⠦⠀⠀⠀⠀⠀⣀⣀⠉⠉⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣠⣀⣬⡃⠄⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠗⠀⠀⠉⠓⠂⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠤⢙⣷⣄⣀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠌⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠖⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠛⠓⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠅⠀⠀⠀⠀⠀⢀⡀⠀⠉⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠒⠦⢤⠀⢤⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣬⣤⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠈⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⣀⣀⠀⢀⡀⠀⠀⠠⣄⡀⠀⠤⠤⠤⠄⠀⠤⠤⠀⠀
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠛⠳⠄⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣡⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠨⢄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⡧⠤⢠⣤⣤⣀⡐⠲⢤⠀⣀⢀⣤⠤⠀⠀⠀⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⠉⠉⠉⣿⣿⣿⣿⣿⠿⣿⠿⢶⣶⠶⡖⢴⣿⣟⢛⣺⡷⣟⠛⠁⠔⠒⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠈⠛⠻⢿⠿⢣⣤⣬⡽⠂⠠⠄⠀⠀⠉⠀⣀⠥⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣠⣴⡈⢁⣉⡛⡁⠀⡀⠀⡀⠒⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠙⢛⣩⣿⡿⠛⠁⠀⢠⣤⣀⣀⠀⠀⠀⢈⣿⣿⡉⠀⠉⠉⢉⣡⠀⠀⠚⠧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⢰⣿⠆⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠀⠀⠀⠘⠛⠿⠿⡇⠀⠀⢸⣿⣧⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢸⣿⠁⠀⠒⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⢀⣠⣿⡤⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⣿⠿⠿⣶⠶⠶⣶⠶⢶⠶⠶⣶⠶⠶⣶⠶⠶⢶⠾⡷⢶⠶⡶⠾⢿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⢸⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠀⣀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⣿⠁⠉⠁⠀⠁⠠⡄⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠙⠟⠉⠉⠉⠉⠉⠉⠋⠉⢙⠉⠉⠉⠙⠻⡝⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠆⠲⣶⠂⢿⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠶⠦⢤⡄⠀⠀⠀⢴⣶⣆⡄⢀⠀⠀⠁⠀⡉⠑⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢉⣩⣈⣓⣈⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⢶⣾⡷⠀⠀⠙⠲⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢨⣙⣾⣄⡀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠋⢉⡉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠒⠂⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠏⠀⠀⠀⠀⠀⠀⣐⠂⠒⠒⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⡤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⣤⡀⢈⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣤⣬⣍⣀⠀⠀⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠘⠛⠁⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⣀⡀⠀⣠⣀⣀⣀⢀⢀⣄⠀⠀
⠋⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠂⠚⠻⠄⠀⠄⠀⠀⠀⠈⠑⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠉⣥⡀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣲⣶⡤⢤⣭⣤⣀⠀⠶⢄⡀⠀⠤⣀⣀⠀⠀⠀⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⡿⣿⡿⠷⣶⣶⡿⢭⣽⣿⠷⢲⣶⣯⠟⠏⢀⠢⠄⠀⠀⠀
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣧⠀⠀⠐⠿⢿⣿⢿⣠⣭⣱⡂⠩⣁⠀⠀⠈⠉⣉⣩⠅⢘⣛⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢀⣠⡆⠁⣈⠛⠋⠁⠀⠀⠀⠀⠤⠀⠀⠈⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠿⣿⣿⠿⠿⠛⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣠⣄⠀⠀⠀⠈⣿⣿⡏⠀⠉⠉⠙⣛⣉⠀⠩⠿⢀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠛⣛⣿⣿⠒⠐⠻⠿⣿⣧⠀⠀⢠⣿⣿⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⣿⠛⠓⠀⠂⠀⠀⠀⠒⠀⠀⠸⣿⡟⠀⠠⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠉⠀⠀⠤⠄⠀⠀⠀⠀⠀⣀⣿⣧⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⣶⠶⠶⣶⠶⠶⣶⠿⢶⠶⠶⣷⠶⠶⣶⠶⠶⣶⠶⡶⢶⠶⡶⠾⢿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠀⠈⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⣿⠃⠙⠛⠀⠉⠁⣀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣟⠉⠉⠉⠉⠉⠙⣛⠛⠙⠋⠉⠉⠙⠛⣛⠓⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣚⣃⣀⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠲⣶⠂⢿⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠈⠉⠍⠉⠃⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣈⠀⠀⠁⠀⠀⠘⡋⣐⡶⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⣦⣴⣶⡆⠀⠐⠶⡤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢉⡻⣿⣍⠀⠈⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠒⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣙⠓⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠼⠶⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡒⢒⠀⠀⠀⠀⠀⠀⠈⠅⠰⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠄⠀⠀⠀⢀⣀⠀⠀⠀⠉⠁⠀⠤⣤⣀⣀⢀⡋⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣛⡀⠀⠀⠓⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⡄⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀
⠛⠁⠀⠀⠀⢈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠙⢿⣄⠀⠀⠀⠀⠀⠈⠁⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢺⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠐⣂⠀⠀⠀⢀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢶⣶⣀⣄⣭⣀⡀⠀⢥⣄⠀⠀⠄⢀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣦⣭⣭⣽⣿⠶⢾⣷⣼⠷⣟⣉⡤⠄⠀⠀⠀
⠈⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⢹⣿⡿⣁⣈⣛⡆⠉⡉⠉⠈⠛⠛⠓⢛⡏⠉⠛⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠧⠀⠀⢀⣄⠛⠐⠻⠟⠋⠀⠀⠀⠠⡤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢺⣿⡿⠂⠙⠛⠓⠒⠉⠀⠘⣶⣂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠋⠀⠀⠀⠀⣿⣿⠟⠋⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣴⣦⠀⠀⠀⣿⣿⡛⠀⢀⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠻⠿⣿⣿⡿⠍⠀⠀⠈⠭⠀⠀⠀⣿⡿⠃⠠⠄⠈⢀⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⠃⠀⣀⣀⠀⠀⠀⠀⠀⠀⣹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⢾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⣶⠶⠶⣶⠶⠶⣶⠾⢿⠿⠿⣿⠷⠶⣶⠶⠷⣶⠶⡶⢶⠶⡶⠶⢿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⠀⠀⠀⠀⠤⢿⠀⢻⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⠈⠀⡇⠸⠤⣿⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⣼⣀⣀⣤⣀⣀⣸⣀⣿⣀⣃⣼⣀⣃⣼⣀⣁⣸⣀⣇⣠⣀⣇⣘⣀⣿⠖⠘⠿⠆⠐⠂⣀⠈⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠙⢻⠋⠉⠉⠉⠉⠛⠻⠟⠋⠙⠉⠉⠙⠻⠿⠶⠀⠐⠀⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣐⣗⣀⣠⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧
⠈⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣶⠀⠀⣶⡆⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠖⠲⣶⠂⢿⣿⠰⠶⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⢻⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣛⣻⢻⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠿⠻⠛⠟⠻⣿
⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⢿⣿⠛⠛⢹⣿⣀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⢰⣤⣤⣤⣤⣤⣤⣿
⣿⣇⡀⣀⣀⣨⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠋⠉⣀⡀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⢁⣠⣼⣿⣠⣶⣾⣿⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠟⠛⠛⠀⠀⣠⣴⣶⣾⣿⣿⣿⣷⣧⠄⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣠⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⠛⣿⣿⣿⣿⣿⣿⠸⡛⠛⠛⠛⠛⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢉⣀⣄⣴⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠈⢻⣿⣿⣿⣿⣿⡛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠉⠉⠀⣠⢀⣠⣿⣿⣿⣿⣿⣿⢸⣶⣶⣶⣶⣶⣶⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 2610

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/12/29/straw-man-censorship/#comments
    Gemini version at gemini://gemini.techrights.org/2021/12/29/straw-man-censorship/

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Gemini_version_available_♊︎


✐ Criticising_Microsoft_and_the_OSI_is_“COVID-19_Misinformation”⠀✐


Posted in Deception, Microsoft, OSI at 9:32 pm by Dr. Roy Schestowitz


Once you control the media the prospect of controlling social control media as
well becomes seductive


“You want to infiltrate those. Again, there’s two categories. There’s those
that are controlled by vendors; like MSJ; we control that. And there’s those
that are independent. [...] So that’s how you use journals that we control. The
ones that third parties control, like the WinTech Journal, you want to
infiltrate.”


                                                  –Microsoft's_chief_evangelist


Summary: Social control media has become the instrument_of_dictators; shortly
after publishing this_short_and_factual_post_about_Microsoft_and_the_OSI the
OSI has, once_again, apparently resorted to unjust censorship of its critics;
we have good reasons to suspect OSI itself is responsible for a false report to
Twitter, based on the timing


As noted earlier, Twitter had_just_suspended_my_account_for_7_days_for
criticising_Microsoft_and_the_OSI without even contacting me first (it offered
no due process). Of course the OSI or its allies would not be frank and upfront
about the true motivations; they prefer to falsely pretend it’s about COVID-19
and use that to flag criticism of theirs. If this isn’t the worse censorship
attempt, I don’t know what is.


I’m astounded. Not exactly surprised, however, knowing how poor Twitter can be
at “moderation”.


So I accused them of using/exploiting the pandemic (COVID-19) to promote
something harmful from Microsoft. That was many months ago. And now that I
criticise them for something totally unrelated they latch onto COVID-19 to
silence me for one week or more. I cannot even respond to anyone.


We suggest that readers of Techrights should contact OSI, and maybe Twitter to
the extent feasible. Minutes after my account was suspended (about 10 minutes
afterwards) the chief of the OSI tweeted this to me:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Tweet_of_OSI⦈_


I could not even reply to him! And he responded to me hours after I had posted
this, or minutes after my account had been suspended. It makes one wonder who
exactly reported me. I contacted Simon Phipps on this matter and responded to
Stefano Maffulli via E-mail


     My reply: you give them a majority of your budget, in effect
     promoting proprietary software vendor lock-in.


     I cannot even respond because you folks appear to have reported me to
     suspend my account. Which one of you misused COVID-19 to suppress a
     voice critical of Microsoft?


Clear and obvious misuse of “report” to suppress perfectly-factual criticism of
an unpopular institution.


I’ve filed a (counter) report to Twitter:


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


They say it can take days to assess. Yes, days.


If not trusting Microsoft is “COVID-19 misinformation”, then we’re in seriously
trouble in social control media, which I’ve warned about all along.


Twitter sent only an automated reply by E-mail:


     Hello,


     We’ve received your appeal request.


     Our support team will take a look at the information you provided for
     your appeal. We will respond via email as soon as possible. Please
     note that while we review your appeal, you’ll be unable to access
     your Twitter account.


     If you would prefer, you may instead choose to cancel your appeal
     request and resolve the violations by proceeding to Twitter and
     following the on-screen instructions to restore your account to full
     functionality.


     Thanks,
     Twitter


The suspension (00:54) was about 20 minutes before the reply from Mr. Maffulli.
So the correlation in times may highlight who’s responsible for it.


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


Remember, kids. Don’t criticise Microsoft and their facilitators (like Linux
Foundation) or they will ‘vanish’ you digitally… like in China. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⠉⢻⣿⣿⣿⣻⡟⢿⣿⠿⢿⣿⣿⡻⢻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⡌⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡁⠑⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⢿⢿⢿⣿⡿⣿⣿⢻⣿⡟⣿⢿⢻⣿⡿⡿⣻⢻⣿⡿⡿⣿⢿⡿⣿⢿⡿⣿⢿⢿⡿⡿⡿⣿⢿⡿⣿⣿⢿⡿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⣿⢿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣲⣿⣿⣼⣼⣭⣧⣧⣾⣼⣽⣧⣿⣾⣼⣭⣧⣧⣿⣼⣿⣿⣯⣷⣶⣶⣿⣯⣯⣷⣾⣼⣧⣷⣿⣿⣭⣯⣷⣿⣼⣴⣿⣿⣨⣻⣯⣯⣽⣿⣧⣯⣽⣽⣧⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⢻⢿⣟⣟⣿⢹⡿⡿⣻⡟⡿⣿⣻⣿⣯⢯⢿⣻⣿⣯⣟⣿⢻⣟⢿⢿⠻⡟⣿⢻⢻⡟⣿⣻⡿⡟⣿⣻⢹⢻⢻⢿⣿⢹⣻⡿⣿⣻⢿⣟⣿⣻⢿⣿⣟⣟⡿⢻⣿⢿⣿⣟⡿⣿⣻⣟⡟⡿⣟⣿⣻⢻⣿⣿⣿
⣿⣷⣿⣾⣾⣿⣷⣿⣾⣷⣿⣾⣷⣷⣿⣿⣾⣿⣾⣿⣾⣾⣿⣿⣿⣿⣷⣷⣿⣾⣷⣿⣾⣮⣿⣿⣾⣿⣷⣿⣿⣾⣾⣾⣿⣿⣾⣾⣼⣿⣾⣾⣷⣿⣾⣿⣿⣷⣷⣿⣾⣾⣾⣿⣷⣿⣿⣿⣿⣷⣿⣷⣿⣿⣾⣿⣿⣿
⣿⣯⣽⣿⣯⡇⣫⣽⣭⣿⣯⣽⢭⡛⡽⣭⣿⢭⣛⢯⣿⡍⣿⣽⣿⣭⡏⡝⣫⣹⣯⣿⣯⢝⣭⡿⣿⢩⢫⢟⣝⣿⢩⢻⣽⣭⣿⢫⣛⣭⡯⣿⣭⢫⢿⣿⣏⢟⣻⣯⡗⣫⢿⣯⣿⣱⡷⡧⡗⣿⣿⣏⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣯⣿⣱⣟⣎⣿⣿⣟⢹⣿⣿⣏⣏⣿⣋⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⢰⣶⡇⣋⠙⡟⣉⠙⡟⢋⡙⣿⠸⢛⡟⣉⠻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⣿⡇⣿⠀⡇⠤⠀⡇⢸⡇⣿⢰⡈⠗⠠⢈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠟⠿⠿⠿⡿⠿⡿⠿⣿⠿⠿⢻⠻⡿⠿⢿⠻⡿⠿⠿⢿⡿⠿⣿⠿⠿⠟⠻⠿⠿⢿⠿⠿⣟⠛⢿⠿⠿⠿⢿⣟⠟⡟⢿⡿⠿⠿⢿⢿⠿⢿⠿⠟⠻⣿⡿⠟⠟⡿⣿⠻⢿⡿⠿⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⣿⣿
⣿⣿⣼⣥⣤⣼⣧⣤⣮⣠⣵⣤⣤⣼⣼⣤⣤⣼⣬⣦⣤⣤⣧⣧⣤⣽⣵⣤⣤⣬⣤⣤⣽⣧⣥⣿⣼⣤⣾⣥⣤⣬⣿⣼⣴⣴⣧⣤⣧⣼⣬⣤⣮⣤⣤⣜⣼⣧⣤⣥⣦⣿⣤⣼⣿⣤⣤⣨⣬⣤⣧⣥⣿⣿⣿⣿⣿⣿
⣿⣏⠉⠈⢭⣿⡉⡏⢹⡇⠉⢉⢻⠫⠈⠉⠉⠹⣿⠍⠉⣽⡏⠉⠉⣭⠋⢹⠈⠙⠉⠏⠉⠉⣿⣍⠉⢉⢻⡭⠉⠈⠉⣻⠋⠉⡝⢝⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⢉⠙⠛⠛⠻⠛⡟⡛⡛⠛⢛⠙⣿⠟⡛⠛⣟⡟⢻⣛⠛⢫⢹⣽⡛⡛⠛⡛⣟⢙⠛⣿⠛⢛⣿⠛⠛⡻⠛⣿⡏⠛⡛⠛⣻⡏⡽⠛⡉⠙⠛⣻⠉⠙⠟⡛⡛⠛⢟⢹⣿⣋⡟⠛⡛⣿⡟⠛⡛⡛⡉⣿⣿⣿⣿⣿
⣿⣷⣿⣶⣶⣶⣾⣶⣿⣾⣷⣶⣶⣾⡿⣾⣶⣶⣿⢷⣾⣿⣶⣶⣾⣿⣷⣶⣶⣾⣿⠷⢶⣿⣶⣾⣿⣶⣶⣿⣶⣿⣷⢾⢾⣶⣿⡷⣷⡿⣷⢶⣾⣿⣶⣶⣦⣾⣶⣶⣿⣶⣿⣿⣧⣷⣾⣾⣷⣾⣾⣷⣷⣿⣿⣿⣿⣿
⣿⣇⣀⣨⣀⣇⣪⣆⣀⢻⣗⡤⣹⣗⣀⣀⣨⣂⣔⣰⡀⢺⡎⣔⣀⣻⣾⣀⣰⣆⣀⣀⣆⣸⣀⢐⣀⣀⣶⣿⣀⣰⣑⣸⣀⣆⣀⣀⣾⣇⣂⣀⣂⣀⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⠛⢻⣿⡅⠈⡋⠉⡍⠉⠍⠋⠩⡝⡩⠉⠉⡍⠝⠁⠉⠉⠉⠫⣧⠀⠉⠏⡉⠁⠉⢩⠈⠈⠫⠁⡝⠉⢹⠈⠈⠉⠅⠍⠉⢸⢉⠙⠉⠉⠉⠉⢛⠉⠍⡍⠉⠉⠉⢝⢩⠋⠅⠁⠉⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣇⣀⣈⣿⠟⠻⠳⠛⠻⠻⠻⠻⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠾⠶⠶⠶⠶⣦⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠲⢲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠘⠃⡇⢸⣿⢠⡌⡟⢋⣿⣿⠀⠈⡟⡙⢛⠛⢻⣿⡁⠠⠟⣙⡇⡛⡟⠉⠛⠉⠋⢘⠛⡙⡟⠟⠟⡇⡃⣙⠛⢻⣿⠁⡧⠀⠀⣜⠀⠀⢈⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣧⣧⣼⣿⣤⣴⣧⣿⣼⣿⣤⣦⣵⣤⣾⣀⣿⣿⣤⣴⣦⣤⣧⣧⣷⣤⣤⣤⣶⣤⣦⣤⣧⣼⣴⣧⣧⣤⣤⣼⣿⣄⣯⣥⣶⣿⣬⣼⣾⣡⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡈⣠⢉⠙⠉⠏⡏⣉⣿⠉⠙⠋⣉⠋⣉⠋⡉⡏⡏⠉⢉⢙⠀⣹⣿⣿⠁⡀⠙⠉⠹⠋⣹⢈⡉⠋⠉⠋⠉⡁⣉⢉⠙⠙⠉⠉⠀⡁⣉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣶⣦⣶⣷⣿⣿⣦⣶⣷⣴⣶⣴⣶⣴⣷⣶⣶⣾⣾⣶⣦⣾⣿⣤⣀⣼⣦⣶⣶⣼⣾⣷⣷⣴⣷⣴⣷⣶⣦⣶⣷⣶⣾⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢈⠙⠍⠉⡋⠉⣿⡇⡍⠙⠉⠙⠉⠙⠉⡉⣿⡇⡏⢩⠙⢩⡅⠈⠉⠉⠙⠉⠀⣿⡇⠀⢩⠙⢉⣽⣏⠙⢹⢸⠉⠉⠀⠏⠉⡇⢨⢸⠉⡍⡏⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⡶⣶⣶⣷⣶⣿⣷⣶⣾⣶⣾⢶⣾⣶⣷⣿⣷⣷⣶⣾⣶⣶⣶⣶⣶⢾⣶⣶⣿⣷⣾⣶⣾⣾⣿⣿⣶⣿⣾⣶⣶⣶⣶⣶⣷⣶⣾⣶⣷⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⠨⡅⡍⠉⠉⢹⣷⡆⣶⠙⡙⣹⢨⠨⡅⢭⢉⡙⠉⣽⣿⢐⠠⡏⡏⡇⠘⢉⢹⣉⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣷⣷⣾⣶⣾⣿⣷⣿⣶⣷⣿⣾⣶⣷⣾⣶⣾⣶⣿⣿⣾⣷⣷⣶⣷⣾⣶⣾⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⡋⢩⠛⣹⣭⢩⣽⢫⢏⠋⣟⢏⡏⡍⣹⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣾⣿⣿⣿⣷⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⠛⡋⢟⠏⡟⢛⢻⠙⡻⢛⢻⡟⡋⡻⠛⢿⡟⠻⠛⠏⠹⣛⠻⣿⢟⠟⡛⣿⠛⡟⠻⢛⠛⠟⢻⢛⠋⢛⠻⡛⣿⢛⠟⡟⠛⡏⠟⠟⠻⢟⠉⡟⢻⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣷⣾⣾⣶⣷⣤⣼⣷⣶⣷⣶⣿⣧⣶⣶⣷⣶⣶⣴⣿⣶⣶⣷⣿⣶⣧⣶⣾⣶⣷⣾⣶⣶⣾⣶⣤⣿⣾⣷⣷⣶⣷⣶⣶⣶⣶⣶⣷⣾⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⠉⡏⢙⠅⣿⠩⢉⠍⡨⡋⢹⡍⡭⡇⠉⡇⣨⡉⣿⢨⠉⠉⢩⢩⢩⡇⡌⠏⢸⡇⢩⢩⣌⠍⢩⡍⢩⠉⠉⡨⣘⠉⡏⣹⣟⣭⠉⡇⠉⡇⢍⠉⠩⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠾⠿⡿⠿⠿⢿⣿⠿⡿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣼⣤⣿⣬⣽⣬⣼⣤⣧⣬⣵⣾⣥⣧⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⢋⡉⢹⡿⠉⣽⠍⠉⣯⠉⠉⠙⠉⠫⢹⠩⡝⠉⠩⡯⠈⢿⡍⣯⠋⢹⡭⠉⢩⡋⠉⢹⠫⣧⡏⢽⡅⠉⠈⢹⠉⣯⠋⢹⣿⡍⠉⠉⠙⠩⣿⣯⢍⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢛⡏⠛⡟⠻⡋⠋⣟⣿⠋⢛⡟⠛⣿⢟⠛⢟⠿⠛⡿⠛⠙⠟⡟⡗⣚⢻⢛⡟⢻⢛⡛⡏⠻⠻⠛⢛⢿⠟⠛⣿⠛⠛⠟⠏⢻⡟⠟⠻⡛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⡷⠷⢶⡷⡞⡷⣶⠷⢶⠖⡶⢷⠶⠿⡷⣶⢶⢷⠺⢷⣿⢶⠶⠷⢷⠶⠾⡶⠳⣾⢶⡶⠷⢶⠾⠶⠴⣿⢼⣶⢷⡶⠶⠶⢶⡾⠲⠶⢾⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣗⣴⣥⣤⣼⣧⣬⣦⣦⣴⣥⢧⣴⣧⣤⣥⣿⣤⣼⣤⣼⣽⣬⣾⣤⣵⣤⣼⣧⣼⣼⣬⣇⣤⣵⣤⣬⣲⣽⣧⣴⣤⣧⣧⣤⣽⣥⣤⣧⣼⣬⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣆⣨⣦⣀⣺⣡⣀⣿⣗⣀⣿⣚⣂⣰⣗⣀⣵⣀⣷⣢⣀⣸⣺⣠⣆⣀⡎⣼⣀⣐⣇⣀⣸⣀⣿⣴⣇⣨⣺⣂⣺⣇⣀⣨⣂⢐⣽⣀⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⡝⠉⠉⡇⠁⡝⢿⠈⢙⠽⠹⠉⢽⠉⠉⢝⡏⠍⠙⡝⠉⠙⠉⠩⡏⢨⡋⠉⣿⠍⠉⡋⠋⢹⠁⠙⡍⢙⠭⠅⡙⣿⠙⠉⡏⡇⠉⡏⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⡛⠟⠹⡋⠛⢛⢟⡛⢻⣋⢛⡛⠛⣻⡟⢺⣟⠋⣻⡛⢛⠙⠛⣟⠙⢿⠻⡟⠛⠚⣿⠛⣻⠛⠛⡟⣛⣹⠛⡿⡚⢙⠟⠆⡟⢻⡛⢛⣿⠟⠛⡻⠻⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠴⡶⠺⡖⠲⢾⠲⡶⠾⢿⠾⠲⣶⠻⠷⠺⠾⠶⠿⡶⡾⢲⢶⠷⣾⣾⣾⣷⣶⣾⣾⣾⣾⣶⣶⣷⣾⣿⣤⣾⣶⣶⣷⣶⣷⣾⣷⣶⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣥⣤⣬⣦⣤⣽⣼⣤⣤⣼⣤⣼⣿⣤⣼⣯⣤⣿⣼⣧⣤⣼⣵⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⣌⢍⢹⣯⢩⡫⡉⡍⢹⠈⣭⡌⢹⡍⣩⡏⢉⠅⠍⢩⢻⠉⢩⢹⠰⡇⢦⢁⢸⠆⣛⠾⠕⡹⡏⢹⢹⡍⢋⠉⠀⡏⢹⢹⡯⠉⢿⡯⠈⢹⡍⠩⡉⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⡙⢛⢟⢛⣿⡟⠛⢻⠋⠙⣻⠛⡟⣻⠙⢻⡛⠛⢹⣟⠛⠻⠻⠉⣛⣿⠛⣿⡋⢙⡟⠛⡋⠉⡟⠟⢻⡟⡛⡟⠛⢻⠛⠻⡗⠛⠋⠙⠛⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠗⠷⢿⡞⠿⣷⠺⠾⠶⠲⠿⠶⡟⢾⠶⠺⠾⣶⣾⣿⣶⣾⣶⣶⣾⣿⣶⣷⣷⣾⣷⣶⣷⣶⣷⣷⣶⣷⣾⣷⣶⣶⣾⣾⣷⣷⣶⣷⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠵⣴⣼⣧⣦⣾⣦⣴⣦⣴⣧⣤⣷⣾⣧⣴⣤⣿⣿⣿⣿⠿⡿⣿⣿⡿⢿⣿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣻⣔⣷⣔⣷⣤⣼⣵⣧⣞⣄⣼⣴⣿⣨⣸⣠⣇⣅⣿⣠⣻⣜⣴⣽⣇⣿⣽⣸⣡⣻⣇⣥⣾⣱⣧⣦⣸⣷⣤⣷⣧⣶⣤⣸⣗⣤⣿⣢⣤⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣬⡩⣯⣩⣿⣅⣽⢉⣧⣙⣄⣍⡱⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡹⠹⢩⢛⢻⠛⣟⠟⢻⣿⢻⢫⡝⡝⡻⣿⢩⡻⡏⣯⢻⣫⡛⣻⡛⢻⣟⢙⢟⣿⢉⢯⢙⡯⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣛⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⡿⢿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢻⠒⢸⡏⣿⣿⣘⣀⣆⣿⣠⣈⣀⡄⣸⣇⣈⣐⣂⣈⣀⣅⣰⣀⣀⣇⣀⣆⣀⣀⣺⣇⣁⣠⣆⣠⣜⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣾⣿⠿⣿⣿⣿⠀⢨⣉⣹⣈⣉⣍⣛⣉⣍⣉⣝⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡋⣸⠰⠉⡩⢩⢫⠉⠉⠉⣿⢃⠉⢽⢩⡩⢹⣿⠉⣉⠎⠕⡏⡇⢏⢙⠉⠉⡏⠾⠰⡉⣹⡱⢜⡳⢯⢊⡇⡈⢹⡍⠉⡋⠋⢩⡇⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢛⡛⡏⠝⡛⢻⣛⠛⣛⡛⢻⡟⢛⠹⠉⢛⣟⠛⡟⢟⠏⢙⡟⠛⡻⡋⡏⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡖⢲⠳⠷⢷⠾⠿⠲⠾⠶⠾⠷⠞⣺⠶⠓⢿⠶⠶⠷⠷⣖⠓⠶⠿⢶⢷⡶⠾⠻⠿⡿⣟⠛⢿⡿⡿⠿⢿⡟⠟⠿⡿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡦⠾⣾⠷⣽⣥⣼⢤⡼⣥⣤⣇⣮⡴⡵⣼⣥⣴⣤⣼⣤⡿⣤⣧⣤⣵⣴⣷⣮⣯⡤⣾⣿⣤⣼⣮⣧⣴⢹⣧⣦⡬⣿⣤⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣼⣀⣰⣀⣪⣀⣀⣺⣴⣰⣀⣴⣆⣇⣤⣿⣒⣠⣢⣀⣀⣶⣺⣀⣷⣀⣸⣷⣀⣸⣜⣄⣺⣢⣰⣀⣀⣀⣠⣤⣸⣷⣡⣨⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡆⠈⣯⠁⠉⡋⠅⡉⡏⣿⢄⢖⠀⢭⢸⠏⠈⣏⣏⣹⣶⠈⡫⣯⠉⡅⠉⣯⡃⠉⣟⠌⣿⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣥⣈⣨⣀⣇⣂⣸⣇⣾⣐⣗⣁⣽⣖⣰⣇⣰⣺⣷⣁⡁⣪⣀⣇⣰⣂⣸⣂⣿⣡⣏⣊⣀⣸⣸⣗⣸⣆⣀⣿⣄⣎⣀⡏⣹⣿⣀⣇⣈⣂⣷⣂⣺⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣵⣿⣴⣮⣷⣧⣿⣴⣵⣼⣧⣽⣧⣯⣯⣼⣥⣥⣯⣶⣽⣾⣯⣾⣬⣿⣾⣧⣼⣿⣧⣷⣽⣤⣿⣿⣤⣯⣵⣵⣵⣮⣧⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣢⢩⠩⡯⠍⢙⠉⡯⢸⡯⡭⣻⡆⡞⢩⢨⠭⡏⢹⣽⣯⢉⢝⣉⢻⡇⡯⢹⡇⠸⡫⣯⠅⣽⠉⣿⡏⠉⢉⠏⠉⣿⣉⢻⡯⣯⢹⡟⡉⢽⠏⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠿⡿⠿⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠀⠉⠀⠁⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⢻⢻⡟⠛⠛⢛⡟⢿⠛⡟⠟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

                    ䷩ 𝚕𝚒𝚗𝚎 2866

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.29.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_29/12/2021:_Linux_5.17_Work_and_2021_Roundups⠀✐


Posted in News_Roundup at 4:40 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Audiocasts/Shows⠀➾


                # ⚓ Million-Dollar_Predictions_|_LINUX_Unplugged_438⠀⇛


                       We do our best to predict what will happen in 2022,
                       and own up to what we thought might happen in 2021.


          o § Kernel Space⠀➾


                # ⚓ Linux_5.17_Prepares_To_Finally_Support_The_Adreno_506,
                  Other_MSM_DRM_Changes_–_Phoronix⠀⇛


                       The MSM Direct Rendering Manager driver providing
                       the open-source kernel display/graphics support for
                       Qualcomm Adreno hardware has ready its batch of
                       changes for DRM-Next to appear in Linux 5.17.


                       The MSM DRM driver updates for Linux 5.17 includes
                       support for the Qualcomm Adreno 506. The Adreno 506
                       is an aging Qualcomm 5xx design used by the
                       Snapdragon 450, 625, 626, and 632 SoCs. There was
                       previously some A506 display preparations in Linux
                       5.16 while now for 5.17 the support appears to be
                       ready to go in full. Separately, this pull request
                       also includes DisplayPort support introduced for
                       Snapdragon SC7280 Chromebook boards.


                # ⚓ Intel_Readies_“PFRUT”_For_Linux_5.17_To_Allow_Updating
                  System_Firmware_Without_Rebooting_–_Phoronix⠀⇛


                       Intel open-source engineers have prepared “PFRUT”
                       support for Platform Firmware Runtime Updates for
                       allowing (U)EFI capsule updates to be performed on
                       capable systems without rebooting the system in
                       order to eliminate downtime.


                       Intel has worked on PFRUT that is now part of the
                       ACPI specification for allowing platform firmware
                       components to be updated on-the-fly without the
                       need to restart the system. The intent of this is
                       for servers where they need to be “available 100%
                       of the time” and other cases where downtime must be
                       kept to an aboslute minimum. This “pfr_update”
                       driver set for Linux 5.17 introduction seems to be
                       primarily geared for being able to update system
                       firmware in cases of critical bugs or security
                       issues in a timely manner while not introducing any
                       new downtime.


          o § Benchmarks⠀➾


                # ⚓ AMD_Ryzen_APUs_Get_A_Free_Performance_Boost_With_Linux
                  5.16,_Up_To_28%_Improvement⠀⇛


                       This is definitely great news for AMD Ryzen APU
                       notebook owners and it looks like it is definitely
                       worth upgrading to the latest Linux 5.16 Kernel as
                       there are only gains to be made. There are
                       benchmarks that don’t see a huge performance jump
                       but they also don’t have a performance regression
                       over the previous Linux Kernels so overall, it’s a
                       win-win situation for Ryzen owners. A stable
                       release of the Linux 5.16 Kernel is expected to be
                       released on the 9th of January.


                # ⚓ OS_and_Memory_Impact_on_Mini_PC_Gaming_Performance_–_CNX
                  Software⠀⇛


                       Gaming performance may differ between Windows and
                       Linux so the choice of OS will likely depend on
                       whether the desired games have ‘native’ versions or
                       are supported by an appropriate compatibility
                       layer.


                       However, increasing the memory appears to improve
                       gaming performance on AMD mini PCs with notable FPS
                       increments especially under Windows whereas no
                       perceptible improvements were observed on Intel
                       mini PCs. Whether these findings justify the extra
                       expense of purchasing more memory is debatable.
                       However, if you have it available it makes sense to
                       use it.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_Install_or_Enable_Cockpit_on_CentOS_8_Stream_–
                  LinuxCapable⠀⇛


                       Cockpit is a free remote server manager that is
                       lightweight and easy to use for GNU/Linux servers.
                       Cockpit is a web-based graphical interface for
                       servers intended for people new to Linux to the
                       experts such as sysadmins. Cockpit makes Linux
                       discoverable, allowing anyone using the software to
                       perform tasks such as start containers, administer
                       storage, configure networks, and inspect logs.


                       In the following tutorial, you will learn how to
                       install or enable Cockpit on CentOS 8 Stream.


                # ⚓ How_to_Install_Rust_on_CentOS_8_Stream_–_LinuxCapable⠀⇛


                       Rust is an open-source programming language that
                       focuses on speed, memory safety, and parallelism.
                       Developers use Rust to create a wide range of new
                       software applications, such as game engines,
                       operating systems, file systems, browser
                       components, and simulation engines for virtual
                       reality. Rust is syntactically similar to C++ but
                       can guarantee memory safety by using a borrow
                       checker for validating references.


                       For users, especially developers wanting to try out
                       Rust Programming language, you will know how to
                       install Rust Programming Language on CentOS 8
                       Stream.


                # ⚓ Fix_“Starting_full_system_upgrade._there_is_nothing_to_do”
                  Issue_In_Arch_Linux_–_OSTechNix⠀⇛


                       I recently noticed that my Arch Linux desktop
                       system will not update/upgrade to the latest
                       version. I thought there wasn’t any new updates
                       yet. I visited Arch Linux website and noticed that
                       there are plenty of updates are already available.
                       But, whenever I try to update my Arch Linux system,
                       I keep getting the following message every time.


                # ⚓ How_to_Install_Git_on_CentOS_8_Stream_–_LinuxCapable⠀⇛


                       Git is a mature, actively maintained open source
                       project initially developed in 2005 by Linus
                       Torvalds, the famous Linux operating system kernel
                       creator. Git is designed for developers that need a
                       pretty straightforward version control system. Most
                       software is collaborative efforts and sometimes can
                       have hundreds of people with commits working on
                       software development projects. It is essential to
                       track these commits customarily done in branches in
                       most projects before being merged into the master
                       for release. It is easy to review and track down
                       any incorrect commits and revert, leading to a much
                       easier development if anything goes wrong.


                       In the following tutorial, you will learn how to
                       install Git on CentOS 8 Stream in various methods.


                # ⚓ Enable_PowerTools_Repository_on_CentOS_8_Stream_–
                  LinuxCapable⠀⇛


                       The PowerTools repository is a container that
                       contains many packages, libraries, and developer
                       tools for either creating from source or installing
                       applications. Most repositories rely on the
                       PowerTools to be enabled, including the most
                       popular Extra packages for the Enterprise Linux
                       repository.


                       In the following tutorial, you will quickly install
                       the EPEL repository and enable PowerTools on your
                       CentOS 8 Stream system.


                # ⚓ How_To_Install_MongoDB_on_Fedora_35_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       MongoDB on Fedora 35. For those of you who didn’t
                       know, MongoDB is a free and open-source document
                       database designed for ease of application
                       development and scaling. It is classified as a
                       NoSQL database and thus it stores data in flexible,
                       JSON-like documents, meaning fields can vary from
                       document to document and data structure can be
                       changed over time.


                       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 MongoDB NoSQL database program
                       on a Fedora 35.


                # ⚓ How_to_install_NGINX_on_NetBSD?_|_LibreByte⠀⇛


                       NGINX is a web server with excellent performance
                       and low memory footprint. NGINX can also be used as
                       a reverse proxy (FastCGI, Apache, uWSGI), as a
                       proxy for mail protocols (IMAP, POP3) and as a load
                       balancer.


                # ⚓ How_to_Install_WordPress_on_AlmaLinux_–_ThisHosting.Rocks⠀⇛


                       In this tutorial, we’ll show you how to install
                       WordPress on AlmaLinux with a LEMP stack.


                       AlmaLinux is a relatively new Linux distro – an
                       alternative to the old CentOS. It’s an RHEL clone,
                       a downstream build, run by the community, and it’s
                       free. You can easily migrate from CentOS to
                       AlmaLinux using their tools. You can already get an
                       AlmaLinux VPS at some hosting providers like Linode
                       and Vultr.


                # ⚓ How_to_Install_Apache_(HTTPD)_on_openSUSE_Leap_15⠀⇛


                       Apache, also known as Apache HTTP server, has been
                       one of the most widely used web server applications
                       globally for the past few decades. It is a free and
                       open-source web application software maintained by
                       the Apache Software Foundation. Apache provides
                       some powerful features with dynamically loadable
                       modules, easy integration with other software, and
                       handling of static files, among other popular
                       features.


                       In the tutorial, you will learn how to install and
                       configure Apache (HTTPD) on openSUSE Leap 15 with a
                       free TLS/SSL certificate from Let’s Encrypt.


                # ⚓ How_To_Install_pgAdmin_4_On_Debian_11_–_Citizix⠀⇛


                       PGAdmin is a web-based GUI tool used to interact
                       with the Postgres database sessions, both locally
                       and remote servers as well. It is an open-source,
                       powerful, and feature-rich graphical user interface
                       (GUI) administration and management tool for the
                       PostgreSQL database. It provides a powerful user
                       interface that enables you to easily create,
                       manage, maintain and use database objects, by both
                       beginners and experienced Postgres users alike.


                       pgAdmin 4 supports PostgreSQL 9.2 or later, and
                       runs on Unix and its variants such as Linux, Mac OS
                       X as well as Windows operating systems.


                       In this article, we will learn how to install
                       pgadmin 4 on Debian 11 server. This guide assumes
                       that you already have Postgres 9.2 installed and
                       set up. If not checkout How to Install and
                       Configure Postgres 14 on Debian 11


                # ⚓ Getting_Started_with_Flutter_on_Linux_Desktop⠀⇛


                       Software development is moving to better milestones
                       thanks to Google’s effort in creating open-source
                       UI software applications like Flutter. Flutter’s
                       footprints are applicable in the development of
                       numerous cross-platform applications by referencing
                       a single codebase.


                       So whether your apps target Windows, Linux, Mac,
                       iOS, and Android users or those used to web
                       platforms, Flutter will natively compile and build
                       the perfect app for your target audience.


                # ⚓ How_to_install_EmulationStation_on_Linux_|_FOSS_Linux⠀⇛


                       EmulationStation is a frontend for emulators that
                       gives a GUI (Graphical User Interface) to access
                       all favorite games. It is the frontend for the
                       widely known RetroPie projects that comes pre-
                       configured with more than 30 different emulators
                       for distinct platforms.


                       In this article guide, we shall cover the
                       installation process of the EmulationStation on
                       your Linux OS.


                # ⚓ How_to_Install_Open_VM_Tools_on_Debian_10_/_11_–
                  LinuxCapable⠀⇛


                       Sometimes you may want to install Debian desktop or
                       server on a virtual machine. However, you may have
                       realized that communication between the host and
                       the VM machine doesn’t exist. Luckily, many
                       distributions now carry the open-source VM tools
                       that can be used for many of the most popular
                       Virtual Machine products such as VMware.


                       In the following small tutorial, you will learn how
                       to install these tools on your Debian 10 Buster or
                       Debian 11 Bullseye server or desktop environment.


                # ⚓ How_to_install_TimescaleDB_on_Ubuntu_20.04_–_VITUX⠀⇛


                       If you are looking for a database for analyzing
                       time series data, TimescaleDB might be the best
                       option. TimescaleDB is based on PostgreSQL, but is
                       tuned for speed and scalability when it comes to
                       analyze time series data. It is an open source and
                       free database system provided by the PostgreSQL
                       developers. This database system is very useful
                       when using a real-time monitoring system and a
                       system that requires time series data. In this
                       article we will learn how to install and configure
                       TimescaleDB with PostgreSQL on Ubuntu 20.04.


                # ⚓ [Updated]_Install_LXC_(Linux_Containers)_in_RHEL,_Rocky_&
                  AlmaLinux⠀⇛


                       LXD is described as the next-generation container
                       and virtual machine manager that offers an
                       immersive for Linux systems running inside
                       containers or as virtual machines.


                       It provides images for an inordinate number of
                       Linux distributions with support for a wide
                       selection of storage backends and network types. It
                       also provides the option of installing the images
                       on an individual PC/laptop and even on a cloud
                       instance.


                       LXD allows you to manage containers and VMs using
                       three ways. You can leverage the lxc client or
                       command-line tool, a REST API, or even third-party
                       integrations.


                # ⚓ How_to_install_and_use_the_Exa_command_on_Ubuntu_20.04_–
                  Unixcop_the_Unix_/_Linux_the_admins_deams⠀⇛


                       Hello, friends. In this post, you will learn how to
                       install the Exa command on Ubuntu 20.04. This
                       command adds functionality to another command known
                       throughout Linux as ls So, let’s get started.


                # ⚓ How_to_install_Kdenlive_18.12_on_a_Chromebook⠀⇛


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


                # ⚓ How_to_install_MEGAsync_on_Elementary_OS_6.0_–_Invidious⠀⇛


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


                # ⚓ Arch_Linux:_Always_install_software_without_asking⠀⇛


                # ⚓ How_to_get_the_most_out_of_a_3D_printer_on_Linux_with
                  SuperSlicer⠀⇛


                       SuperSlicer is an open-source fork of the
                       PrusaSlicer application. It works quickly and
                       efficiently and can help you get the most out of
                       your 3D printer. Here’s how to use SuperSlicer on
                       your Linux PC.


                # ⚓ How_to_prepare_a_3D_model_for_printing_on_Linux_with_Cura⠀⇛


                       SuperSlicer is an open-source fork of the
                       PrusaSlicer application. It works quickly and
                       efficiently and can help you get the most out of
                       your 3D printer.


          o § Games⠀➾


                # ⚓ Our_Game_Picks_on_Linux_for_2021_(including_VR)_–_Boiling
                  Steam⠀⇛


                       As is customary every year for us here at Boiling
                       Steam, we got together to list our game picks of
                       2021 on Linux. Note that most of these games are
                       available on Steam and as such, will likely be on
                       sale during the Steam Winter Sale. If it is, we
                       will add a link to the Steam store page and mention
                       the percentage off (we’ll also let you know if
                       there’s a native Linux version available).


          o § Devices/Embedded⠀➾


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ How_to_See_Your_Android_Phone’s_Processor_and_Speed⠀⇛


                      # ⚓ How_to_control_Chromecast_volume_in_Android_12⠀⇛


                      # ⚓ Samsung_resumes_Android_12_rollout,_updates_some
                        foldables,_and_more_S21s_–_The_Verge⠀⇛


                      # ⚓ Google_is_making_sure_future_Android_phones_offer
                        users_these_safety_and_emergency_options⠀⇛


                      # ⚓ Xiaomi_12_Pro:_New_Android_flagship_to_beat_launches
                        with_Sony_IMX707_camera_sensor,_120_W_charging_and_a
                        Snapdragon_8_Gen_1_chipset_–_NotebookCheck.net_News⠀⇛


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


                # ⚓ Twelve_Months_of_Open_Source_in_2021_–_Copyleft_Currents⠀⇛


                       With year two of the COVID era drawing to a close,
                       here is a look back on some of the most interesting
                       open source developments of 2021. Let’s hope the
                       new Omicron wave of working from home creates some
                       amazing new projects — and ends soon.


                # § Funding⠀➾


                      # ⚓ Lunduke’s_‘Tux_on_Tour’_NFT_Campaign_for_Funding_Open
                        Source_Projects⠀⇛


                             Brian Lunduke, the “Linux Sucks” guy who was
                             once known as “The Linux Tycoon” (a moniker
                             he swears wasn’t his idea), has come up with
                             a way to harness the non-fungible token craze
                             for the good of Linux and open source.


                             With tongue only partly in cheek, he
                             announced on The Lunduke Journal of
                             Technology on Monday that he has launched a
                             “Tux on Tour” campaign to raise money for
                             Linux and open source projects.


                # § Programming/Development⠀➾


                      # ⚓ glibc_is_still_not_Y2038_compliant_by_default_–
                        Ariadne’s_Space⠀⇛


                             Most of my readers are probably aware of the
                             Y2038 issue by now. If not, it refers to 3:
                             14:07 UTC on January 19, 2038, when 32-bit
                             time_t will overflow. The Linux kernel has
                             internally switched to 64-bit timekeeping
                             several years ago, and Alpine made the jump
                             to 64-bit time_t with the release of Alpine
                             3.13.


                             In the GNU/Linux world, the GNU libc started
                             to support 64-bit time_t in version 2.34.
                             Unfortunately for the rest of us, the
                             approach they have used to support 64-bit
                             time_t is technically deficient, following in
                             the footsteps of other never-fully-completed
                             transitions.


                      # § Perl/Raku⠀➾


                            # ⚓ Draft:_Dancer2_Deprecation_Policy⠀⇛


                                   The Dancer Core Team has done our best
                                   to look at this every which way and
                                   cover all potential issues and use
                                   cases, but we’re sure to have missed
                                   something here or there. So take a look
                                   and let us know. Your feedback is
                                   welcome – please add comments,
                                   feedback, and suggestions on the issue.


                      # § Shell/Bash/Zsh/Ksh⠀➾


                            # ⚓ A_Guide_to_Zsh_Expansion_with_Examples⠀⇛


                                   Zsh is particularly powerful when you
                                   need some good old expansions. It
                                   supports common ones used by Bash too,
                                   and add many flags and modifiers on
                                   top. It comes in handy to manipulate
                                   quickly your commands without writing
                                   boring shell scripts.


                                   We’ll see, in this article, what we can
                                   do with Zsh expansions, and more
                                   specifically:


                                   How to use glob operators and globbing
                                   flags.


                                   What glob qualifiers we can use to
                                   expand filenames.


                                   How to expand the Zsh history and how
                                   to modify these expansions.


                                   How to expand parameters, using
                                   modifiers and flags.


                      # § Java⠀➾


                            # ⚓ Check_for_Log4j_vulnerabilities_with_this
                              simple-to-use_script⠀⇛


                                   One great thing about Linux and the
                                   open source community is that as soon
                                   as a vulnerability is detected,
                                   developers are hard at work releasing
                                   tools to mitigate the problem. Such is
                                   the case with the Log4j vulnerability.


    * § Leftovers⠀➾


          o ⚓ A_Grope_In_Meta’s_Space⠀⇛


                 Horizon Worlds is a VR (virtual reality) social space and
                 world building game created by Facebook. In early
                 December, a beta tester wrote about being virtually
                 groped by another Horizon Worlds user. A few weeks later,
                 The Verge and other outlets published stories about the
                 incident. However, their coverage omits key details from
                 the victim’s account. As a result, it presents the
                 assault as a failure of user operated moderation tools
                 rather than the limits of top-down moderation.
                 Nevertheless, this VR groping illustrates the difficulty
                 of moderating VR, and the enduring value of tools that
                 let users solve problems for themselves.


          o ⚓ Ruralist_Lament:_A_Cold_Reality⠀⇛


                 That’s changed. Vanishingly small numbers of people still
                 farm, and whatever relative security or independence
                 citizens can attain is now based on the whim of fickle
                 employers. Workers are supposed to gain “skills” which
                 can produce profits for hedge-funders single-mindedly
                 focused on “efficiency.” That means getting the
                 “workforce” to do more for less.


                 Kids in our downwardly-mobile society are encouraged to
                 become “employable” and even at the collegiate level the
                 idea of exploring the world of ideas, history and
                 philosophy——still common through the mid-20th century ——
                 is increasingly outmoded.


          o ⚓ Opinion_|_Yes,_There_Were_10_Good_Things_About_2021⠀⇛


                 This year, 2021, began with a huge sense of relief as
                 Trump left office. We hoped to emerge from the ravages of
                 COVID, pass a hefty Build Back Better (BBB) bill, and
                 make significant cuts to the Pentagon budget. But, alas,
                 we faced a January 6 white nationalist insurrection, two
                 new COVID mutations, a sliced-and-diced BBB bill that
                 didn’t pass, and a Pentagon budget that actually
                 INCREASED! 


          o ⚓ Forever_Homeless⠀⇛


                 Before my long travel, I pack my suitcases, stuff them
                 with some sand from our land, some scent from my mother’s
                 kitchen and sounds of birds in the morning.


                 And in my pockets, I put the four directions. My hands
                 are the compass.


          o ⚓ Another_Name_for_America_Is_Time⠀⇛


          o ⚓ Yes,_There_Were_10_Good_Things_About_2021⠀⇛


                 This year, 2021, began with a huge sense of relief as
                 Trump left office. We hoped to emerge from the ravages of
                 COVID, pass a hefty Build Back Better (BBB) bill, and
                 make significant cuts to the Pentagon budget. But, alas,
                 we faced a January 6 white nationalist insurrection, two
                 new COVID mutations, a sliced-and-diced BBB bill that
                 didn’t pass, and a Pentagon budget that actually
                 INCREASED!


          o ⚓ “People_Have_the_Power”:_Poet_&_Singer_Patti_Smith_Awarded_Key_to
            New_York_City⠀⇛


                 Legendary poet, singer, author and activist Patti Smith
                 has been awarded a key to New York City. Smith’s music
                 has inspired countless bands and helped earn her the
                 title of the queen of punk. Her song “People Have the
                 Power” has become an anthem at protests across the globe.
                 Patti Smith has also been a longtime activist, performing
                 regularly at antiwar rallies and political benefits. She
                 gave an emotional acceptance speech during a ceremony
                 Monday with outgoing New York City Mayor Bill de Blasio.
                 We also air a clip of her live performance with singer
                 Michael Stipe at Democracy Now!’s 20th anniversary
                 celebration in 2016.


          o ⚓ Bing_stops_accepting_Sitemap_pings,_switch_to_IndexNow_instead⠀⇛


                 The Microsoft Bing search engine has quietly stopped
                 accepting XML Sitemap pings over the holiday break. XML
                 Sitemaps are a structured data format that contains a
                 list of a website’s primary pages. Websites can
                 proactively ping search engines when they publish changes
                 to request that the search engine come and index their
                 new pages.


                 Sometime between December 14th and 22nd, Bing stopped
                 accepting new ping submissions to its XML Sitemap Ping
                 service. The API endpoint at bing.com/ping now returns an
                 HTTP 410 Gone error message. The error message suggests
                 deliberation and permanence (as opposed to an
                 intermittent problem (HTTP 500) or an HTTP 404 Not
                 Found).


          o § Hardware⠀➾


                # ⚓ 1950s_Vacuum_Tube_Computer_Replica_Communicates_Through_USB
                  |_Hackaday⠀⇛


                       When we talk about a “computer” today, we generally
                       picture an electronic machine that can perform
                       various kinds of mathematical operations, manage
                       its program flow, move data from one place to
                       another, and string all these functions together to
                       perform some useful task. But once upon a time
                       there were machines that could perform only a
                       subset of these functions; these might be
                       classified somewhere between computers and
                       calculators.


                       One such machine was the Elektronensaldierer ES 24,
                       built in 1955 by German computer pioneer Heinz
                       Nixdorf. Its name translates as “electronic
                       balancer”, with “balance” in the accounting sense
                       meaning the difference of assets and liabilities.
                       Designed to interface with a punch card machine
                       from French manufacturer Bull, it contained several
                       hundred vacuum tubes and could be used to add and
                       subtract numbers stored on those punch cards.


                # ⚓ Clear_Off_The_Coffee_Table,_It’s_Pinball_Time_|_Hackaday⠀⇛


                       [BuildXYZ] started by building a pintisserie, which
                       is exactly what it sounds like — a rotating
                       barbecue spit for a pinball machine’s guts that
                       makes it a breeze to work on. This maintenance-
                       friendliness reappears in the new cabinet design,
                       where the circuit boards are screwed to a pair of
                       drawers.


                       No, you don’t have to play it flat. But you do have
                       to clear off the top before pressing Start, because
                       a pair of mini industrial linear actuators raise
                       the back end by 5-7° depending on the setting. We
                       were a little sad about the lack of plunger, but
                       [BuildXYZ] is right — it would knock at your
                       kneecaps. On the bright side, [BuildXYZ] reused the
                       ‘free ball’ solenoid as the ball launcher, which is
                       driven by that shiny metal button. Again, be sure
                       to check it out after the break.


                # ⚓ Enter_The_Matrix_With_This_Custom_PC_Side_Panel_|
                  Hackaday⠀⇛


                       All of the LEDs are connected to a NodeMCU ESP8266
                       by way of a 74AHCT125 level-shifter, though [Will]
                       notes you could certainly use a different
                       microcontroller with some tweaks to the code. As it
                       stands, the user selects from various lighting
                       patterns using two potentiometers and a button that
                       have been mounted next to the panel. But if you
                       were so inclined, it certainly wouldn’t take much
                       to adapt the firmware so that the lighting effects
                       could be triggered from the PC.


                # ⚓ UV_Printing_PCBs_|_Hackaday⠀⇛


                       We always enjoy [Thomas Sanladerer’s] 3D printing
                       videos. But his latest isn’t only about 3D
                       printing. He shows how he uses a DLP printer —
                       which has UV light, after all — to expose PC board
                       blanks with great results. Honestly, once we heard
                       the idea, we immediately saw how that could work it
                       is surprising more people aren’t taking advantage
                       of their DLP printers like that. Of course,
                       [Thomas] does his usual thorough treatment of the
                       topic.


                       Really, this isn’t exactly 3D printing even though
                       it uses a 3D printer. Exposing boards with UV light
                       and artwork is an old process that has been around
                       for years, usually using transparency film and a UV
                       light source. With a printer, you can create
                       artwork digitally and the UV light source is
                       already there.


                       We liked his test strip method for dialing in the
                       exposure time. Reminded us of our old darkroom
                       days. He also tried using resin as a resist on a
                       bare copper board but that didn’t seem to work as
                       well as you would hope.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Plague_Doctors’_Bacchanal⠀⇛


                # ⚓ A_Socialist_Defense_of_Vaccine_Mandates⠀⇛


                       The reason I support vaccine mandates is that all
                       policies are in a vacuum. It may very well be a
                       violation of certain freedom to mandate vaccines
                       and in a socialist utopia on our horizon we would
                       not have a profit making machine that creates
                       pandemics nor would we have an authoritarian state
                       to mandate treatment for them by profit-making
                       companies. But in our world, where our immediate
                       choices are capitalism with vaccines and capitalism
                       without vaccines I’ll take the former.


                       Our lives aren’t free under the current tyranny of
                       the employer-employee relationship, according to
                       Mr. Wolff. He’s correct. What’s one more unfreedom
                       to add to the list when it saves the lives of the
                       working class?


                # ⚓ They_Were_the_Pandemic’s_Perfect_Victims⠀⇛


                       By the time Cheryl Cosey learned she had COVID-19,
                       she had gone three days without dialysis — a day
                       and a half more than she usually waited between
                       appointments. She worried how much longer she could
                       wait before going without her life-saving
                       treatments would kill her.


                       The 58-year-old Cosey was a dialysis technician for
                       years before she herself was diagnosed with end-
                       stage renal disease. After that, she usually took a
                       medical transport van to a dialysis facility three
                       days a week. There, she sat with other patients for
                       hours in the same kind of cushioned chairs where
                       she’d prepped her own patients, connected to
                       machines that drew out their blood, filtered it for
                       toxins, then pumped it back into their fatigued
                       bodies.


                # ⚓ Your_Free-Range_Organic_Chicken_May_Have_Been_Processed_at
                  a_Large_Industrial_Poultry_Plant⠀⇛


                       Americans who want to buy the safest chicken and
                       turkey have had little to go on beyond brand names
                       and labels.


                       But those don’t tell the whole story, as we learned
                       from the readers who’ve used our Chicken Checker
                       app.


                # ⚓ ‘Alarming’_Levels_of_‘Forever_Chemicals’_Found_in_Water
                  Near_US_Bases_in_Okinawa⠀⇛


                       As the U.S. military continues construction of a
                       controversial new base at Henoko Bay, Okinawa, the
                       recent discovery of extreme levels of highly toxic
                       “forever chemicals” in local waterways and
                       groundwater has renewed long-standing opposition to
                       the American occupation of large portions of the
                       Japanese archipelago.


                       “Imagine the uproar if China were responsible for
                       this PFOS contamination. But since the U.S. is to
                       blame, it will be swept under the rug.”


                # ⚓ Opinion_|_Dangerous_Petroleum-Contaminated_Water_Threatens
                  Thousands_in_Hawai’i⠀⇛


                       On Friday, December 24, I went to Aliamanu Military
                       Reservation at Red Hill housing area which is
                       located above the entryway into the main tunnel
                       that leads into the U.S. Navy’s deep, massive,
                       leaking 80-year-old Red Hill underground jet fuel
                       storage tanks complex. These tanks are only 100
                       feet above the main aquifer of drinking water for
                       400,000, half the population of the island of
                       O’ahu, Hawai’i.


                # ⚓ New_Business-Friendly_CDC_Guidance_on_Isolation_for_People
                  With_Covid-19_Is_‘Reckless,’_Experts_Say⠀⇛


                       Workers’ rights advocates accused the Centers for
                       Disease Control and Prevention of putting business
                       interests ahead of public health Tuesday after the
                       agency released new guidelines for asymptomatic
                       Americans with Covid-19, while experts expressed
                       concern that the guidance will result in confusion
                       and more transmission of the disease.


                       The CDC announced late Monday that instead of
                       isolating at home for 10 days, people who contract
                       the coronavirus will be advised to isolate for five
                       days immediately after testing positive. If the
                       person is asymptomatic after five days f, they may
                       return to work, school, and other activities but
                       should wear a mask everywhere, including at home if
                       they live with others, for five more days.


                # ⚓ CDC’s_Covid-19_Vaccine_Push_Threatens_Americans_With
                  Exorbitant_Hospital_Bills⠀⇛


                       The latest push by the U.S. government to encourage
                       Americans to get vaccinated against Covid-19 took
                       on a “dark and dystopian” appearance, healthcare
                       advocates said Tuesday, after the Centers for
                       Disease Control and Prevention released an ad
                       warning those who are hospitalized could face
                       exorbitant medical bills.


                       “Only in the United States could the government run
                       a public health campaign centered on fears of
                       large, unexpected medical bills,” tweeted Sarah
                       Kliff, a health policy reporter for the New York
                       Times.


                # ⚓ There’s_a_giant,_mysterious_gap_in_the_omicron_variant’s
                  family_tree⠀⇛


                       First, note that mutations are, to some degree,
                       expected of a virus. As the novel coronavirus began
                       to lose battle after battle to human immune systems
                       and due to human ingenuity (vaccines), the
                       “survivor” viruses tended to be the ones that
                       mutated to effectively ward off human efforts at
                       immunity. Those survivors then pass those traits to
                       the offspring viruses it creates through
                       replication. Thanks to genetic technology,
                       researchers have been able to study those mutant
                       strains and learn about SARS-CoV-2′s “family tree,”
                       so to speak — that is, the relationship between all
                       the variants that stemmed from one another.


                       Here’s where it gets weird. There is a big gap in
                       the omicron variant’s timeline.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Alexa_tells_10-year-old_girl_to_touch_live_plug_with
                        penny⠀⇛


                             The dangerous activity, known as “the penny
                             challenge”, began circulating on TikTok and
                             other social media websites about a year ago.


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ In_2021,_We_Told_Apple:_Don’t_Scan_Our
                                    Phones⠀⇛


                                         In August, Apple made a startling
                                         announcement: the company would
                                         be installing scanning software
                                         on all of its devices, which
                                         would inspect users’ private
                                         photos in iCloud and iMessage. 


                                         This scanning software, intended
                                         to protect children online,
                                         effectively abandoned Apple’s
                                         once-famous commitment to
                                         security and privacy. Apple has
                                         historically been a champion of
                                         encryption, a feature that would
                                         have been undermined by its
                                         proposed scanning software. But
                                         after years of pressure from law
                                         enforcement agencies in the U.S.
                                         and abroad, it appears that Apple
                                         was ready to cave and provide a
                                         backdoor to users’ private data,
                                         at least when it comes to photos
                                         stored on their phones. 


                                         At EFF, we called out the danger
                                         of this plan the same day it was
                                         made public. There is simply no
                                         way to apply something like
                                         “client-side scanning” and still
                                         meet promises to users regarding
                                         privacy. 


                                  # ⚓ AT&T_Exits_The_Ad_Business_As_Merger
                                    Ambitions_Continue_To_Unravel⠀⇛


                                         We’ve noted for years how U.S.
                                         telecom giants aren’t
                                         particularly competent when it
                                         comes to wandering outside of
                                         their core competencies (building
                                         and running networks, lobbying
                                         the government to hamstring
                                         competitors). As government
                                         pampered regional monopolies who
                                         haven’t had to try particularly
                                         hard for decades, stuff like
                                         competition, innovation,
                                         adaptation, and creativity are
                                         often alien constructs.


          o § Defence/Aggression⠀➾


                # ⚓ USAID_Is_Running_Out_of_Money_for_COVID_Vaccines_While
                  Pentagon_Got_$778_Billion⠀⇛


                # ⚓ Ukrainians_Are_Far_From_Unified_on_NATO._Let_Them_Decide
                  for_Themselves.⠀⇛


                # ⚓ Daunte_Wright’s_Family_Gets_Accountability,_if_Not
                  Justice⠀⇛


                       Brooklyn Center, Minn.—It was a typical Sunday
                       afternoon, and Daunte Wright was driving with his
                       girlfriend, Alayna Albrecht-Payton, in this
                       Minneapolis suburb to get his white Buick LaCrosse
                       cleaned. The 20-year-old Black man had just left
                       his parents’ house after his mother, Katie Bryant,
                       gave him $50 for gas and a car wash.


                # ⚓ LAPD_Releases_Footage_From_Police_Killing_of_Valentina
                  Orellana-Peralta⠀⇛


                # ⚓ The_LAPD_Murder_of_a_14-Year-Old_Girl⠀⇛


                       I don’t care what kinds of excuses are made by the
                       cop or cops who fired shots, one of which tore away
                       this young girl’s life as her horrified mother had
                       to watch and desperately try to save her. There is
                       simply no possible justification for firing police
                       guns in a crowded store.


                       I cannot even bear to try and imagine the agony her
                       family is now suffering, especially listening to
                       the tired police excuses and lame platitudes that
                       always accompany such all too frequent monstrous
                       acts by America’s centurions.


                # ⚓ LAPD_Releases_Footage_From_Police_Killing_of_14-Year-Old
                  Girl⠀⇛


                       The Los Angeles Police Department released video
                       footage Monday showing the moment when an officer
                       fatally shot 14-year-old Valentina Orellana-Peralta
                       while firing three rifle rounds at an assault
                       suspect inside a Burlington Coat Factory store in
                       North Hollywood.


                       Orellana-Peralta was with her mother trying on
                       clothes in a Burlington dressing room on Thursday
                       when she was shot and killed by an officer whose
                       name has yet to be released by the LAPD. Police
                       said Monday that a bullet bounced off the floor and
                       went through the wall of the dressing room.


                # ⚓ Former_US_Intelligence_Analysts_Sued_For_Hacking_A_Saudi
                  Activist’s_Phone_On_Behalf_Of_The_United_Arab_Emirates⠀⇛


                       In early 2019, a whistleblower revealed some
                       ugliness emanating from the United Arab Emirates:
                       former NSA analysts working for a private company
                       hired to perform counterterrorism work for the
                       government were spying on journalists, activists,
                       and the occasional American citizen on behalf of
                       their royal benefactors.


                # ⚓ UN_Envoy_Warns_‘Threat_to_Civilian_Lives_Is_Increasing’_in
                  Yemen⠀⇛


                       A United Nations special envoy on Tuesday raised
                       alarm about the safety of civilians in war-torn
                       Yemen given escalating violence, including
                       airstrikes by the Saudi-led coalition.


                       “Airstrikes on Sanaa have resulted in loss of
                       civilian lives, and damaged civilian infrastructure
                       and residential areas.”


                # ⚓ Fox_News_host’s_‘kill_shot’_comment_about_Dr._Fauci_was_not
                  harmless⠀⇛


                       We are all far too accustomed to the crude tone and
                       tenor of public discourse. Many media experts will
                       tell you that there is an emphasis on sound bites
                       and clickbait — the more odd and ostentatious the
                       better. That’s nothing new.


                       In that ocntext, one may be almost tempted to
                       dismiss Fox News host Jesse Watters and his
                       comments offered up at the expense of Dr. Anthony
                       Fauci as one of the latest examples of such
                       crudeness in our culture war.


                # ⚓ Afghan_women_protest_against_‘Taliban_killings’_of_ex-
                  soldiers⠀⇛


                       Around 30 women gathered near a mosque in the
                       centre of Kabul and marched a few hundred metres
                       chanting “justice, justice” before they were
                       stopped by Taliban forces, an AFP correspondent
                       saw.


                       The Taliban also tried to prevent journalists from
                       covering the march, organised against the
                       “mysterious murders of young people, particularly
                       the country’s former soldiers”, according to social
                       media invitations.


                       Taliban fighters briefly detained a group of
                       reporters and confiscated equipment from some
                       photographers, deleting images from their cameras
                       before returning them.


          o § Environment⠀➾


                # ⚓ Opinion_|_Biden_Owes_Voters_Climate_Action_on_Auto
                  Pollution⠀⇛


                       President Biden was right when he said global
                       warming is an existential threat. That’s why it’s
                       so disappointing that his administration produced
                       auto-pollution rules that are a speed bump on the
                       road to the climate precipice, right when we need a
                       U-turn.


                # ⚓ It_Is_‘Strange,’_Says_Greta_Thunberg,_That_Biden_Is_Seen_as
                  a_Climate_Leader⠀⇛


                       In an interview published in The Washington Post
                       Magazine on Monday, Swedish activist Greta Thunberg
                       said it is “strange” that some consider U.S.
                       President Joe Biden a climate leader even as his
                       administration fails to take the ambitious steps
                       necessary to tackle the intensifying planetary
                       crisis.


                       When asked whether she is “inspired” by Biden or
                       other world leaders, Thunberg pointed out that “the
                       U.S. is actually expanding fossil fuel
                       infrastructure” under the current administration.


                # ⚓ Russian_Green_Deal:_Light_at_the_End_of_the_Tunnel?⠀⇛


                       “Before this year, Russia was rather skeptical
                       about climate change and the role of people in
                       climate change,” reports Tatiana Lanshina. “But
                       this year, the official rhetoric actually changed a
                       bit.”


                       One reason for that shift in rhetoric was the very
                       real impact of climate change on Russia over the
                       last year. Flames consumed huge stretches of
                       Siberian forest over the summer in what turned out
                       to be a record year for wildfires. Flooding in
                       southern agricultural regions disrupted farming
                       which, combined with droughts elsewhere, has
                       threatened the country’s food security.


                # § Energy⠀➾


                      # ⚓ ‘Big_Win’_as_Shell_Ordered_to_Stop_Seismic_Blasting
                        Along_South_African_Coast⠀⇛


                             Conservationists and impacted communities
                             celebrated Tuesday after a South African
                             court blocked Shell’s seismic exploration for
                             oil and gas along the country’s Wild Coast,
                             which critics argued endangered marine life
                             and the livelihoods of local fishers.


                             “The case has huge significance in that it
                             shows that no matter how big a company is, it
                             ignores local communities at its peril.”


          o § Finance⠀➾


                # ⚓ There_Was_No_Union._There_Was_No_Plan.⠀⇛


                       Although questions remain about the deaths of six
                       workers at the Amazon warehouse in Edwardsville,
                       Ill., we do know one thing: While extreme weather
                       events are rare (although becoming increasingly
                       less so), safety problems at Amazon are terribly
                       common. Its facilities are massive, the pace of the
                       order fulfillment process is punishing, and many
                       buildings are not climate-controlled. Turnover and
                       injury rates are high. According to OSHA data from
                       2020, for every 200,000 hours worked at an Amazon
                       warehouse in the United States, there were 5.9
                       serious accidents, which is close to double the
                       rate of non-Amazon warehouses—higher than
                       construction, coal mining, and most manufacturing.
                       A 2020 study by Reveal, based on three years of
                       weekly data, found that the Edwardsville warehouse
                       had an injury rate of 9.5 in 2018 and 6.6 in 2019.


                # ⚓ ‘Let’s_Win_This_Thing!’:_Major_Philly_Union_Endorses_PA
                  State_Senate_Candidate_Paul_Prescod⠀⇛


                       One of Philadelphia’s biggest unions has endorsed
                       Paul Prescod, a progressive Democratic candidate
                       for Pennsylvania’s 8th Senate District, joining a
                       growing list of working-class advocates backing
                       the campaign of the educator and longtime labor
                       movement organizer.


                       “I will be willing to take on the wealthy interests
                       that are getting in the way of the future we
                       deserve.”


                # ⚓ How_Can_Workers_in_“The_Great_Resignation”_Harness_Leverage
                  Long-Term?⠀⇛


                # ⚓ Why_Democrats_Started_Fixating_on_Inflation⠀⇛


                       Republicans, along with some prominent right-wing
                       Democrats, have been hammering the Biden
                       administration over rising food and gas prices for
                       months. In November, when the Labor Department
                       announced that consumer prices had risen 6.2
                       percent from October 2020 to October 2021, the
                       Republican National Committee tweeted,
                       “Bidenflation is hurting working Americans all over
                       the country.” Corporate media outlets are boosting
                       this line of attack, from a viral CNN segment about
                       a family that buys 12 gallons of milk a week to the
                       downright false claims that inflation is being
                       driven by the Covid-19 stimulus package that passed
                       in March or by rising wages for the working class.


                # ⚓ The_Real_Antidote_to_Inflation⠀⇛


                       Even more at risk are the small and medium-sized
                       enterprises (SMEs) that are the backbone of the
                       productive economy, companies that need bank credit
                       to survive. In 2020, 200,000 more U.S. businesses
                       closed than in normal pre-pandemic years. SMEs
                       targeted as “nonessential” were restricted in their
                       ability to conduct business, while the large
                       international corporations remained open. Raising
                       interest rates on the surviving SMEs could be the
                       final blow.


                       Cut Demand or Increase Supply?


                # ⚓ Proposed_EU_directive_targets_shell_companies_after_Pandora
                  Papers_exposed_offshore_system_abuses⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ A_Way_Out⠀⇛


                       In July 2016, Hillary Clinton’s presidential
                       campaign released an ad titled “Role Models.” It
                       starts off with what appear to be exterior shots of
                       a single-family home in the rural Midwest and then
                       of an inner-city rowhouse. Next we see children,
                       representing numerous target demographics, watching
                       TV inside dimly lit living rooms as candidate
                       Donald Trump’s voice emanates from a bright screen.
                       Some of his greatest hits ensue: “I could stand in
                       the middle of Fifth Avenue and shoot somebody and
                       not lose any voters, OK?


                       It’s like incredible!” and “Blood coming out of
                       her… wherever.” As the children’s innocent faces
                       are illuminated by the on-screen Trump mid-sound-
                       bite, we are meant to be aghast, worried about
                       their moral development (and maybe also their
                       eyesight). However, by the time “You can tell them
                       to go [bleep] themselves” rolled around, I remember
                       thinking to myself, “This is a terrible commercial,
                       at least if it’s meant as an attack ad. Everyone I
                       know has someone they want to tell to go fuck
                       themselves. What stops us? We need the job, the
                       favor, the reference, the free babysitting from the
                       in-laws.” Trump—encased by wealth and
                       shamelessness—needed none of those things. He was
                       bound by nothing. For some, a vote for Trump was a
                       chance to inhabit that boundlessness, to tell the
                       rest of the world to go fuck ourselves.


                # ⚓ These_Progressives_Fought_the_Good_Fight_in_2021—and_Gave
                  Us_Hope_for_2022⠀⇛


                       The year 2021 demanded every bit as much from
                       progressives as the difficult years that preceded
                       it. Joe Biden replaced Donald Trump only after the
                       outgoing president urged on a coup attempt and was
                       impeached for the second time. In the face of an
                       ongoing pandemic and the economic uncertainty
                       extending from it, Biden found himself struggling
                       not just with Republicans but also with corporate-
                       aligned “centrist” Democrats who were disinclined
                       to govern boldly. That set the stage for a year
                       that saw progress come slowly and presidential
                       approval ratings decline. Progressives had to fight
                       to keep the administration from missing historic
                       opportunities, while at the same time they
                       championed an urgent racial justice agenda that
                       faced a growing backlash, defended abortion rights,
                       and struggled to save the planet. It wasn’t an easy
                       year, but these leaders fought the good fight—and
                       gave us hope for 2022.  John Nichols1


                # ⚓ How_Canceling_Student_Loan_Debt_Would_Be_Strategically
                  Smart_for_Biden⠀⇛


                       As rising coronavirus cases and the derailing of
                       the Build Back Better bill dampened holiday cheer,
                       the Biden administration made an announcement last
                       week that inspired some hope for the new year.
                       After sustained public pressure, it extended until
                       May the moratorium on student loan repayments that
                       was scheduled to end in January. With 89 percent of
                       borrowers reporting that they are not “financially
                       secure” enough to resume payments in the immediate
                       future, the extension will provide vital relief.


                # ⚓ Retroactive_repression_Five_former_team_Navalny_activists
                  arrested_in_cities_across_Russia⠀⇛


                       Russian police reportedly detained as many as five
                       former activists from Alexey Navalny’s disbanded
                       political network on Tuesday, December 28.
                       According to various reports, arrests were carried
                       out in the cities of Tomsk, Irkutsk, Arkhangelsk,
                       Barnaul, and Saratov (though not all of the
                       detentions have been confirmed). Following
                       interrogations, investigators brought criminal
                       charges against two of the detained activists
                       — former regional coordinators Ksenia Fadeeva and
                       Zakhar Sarapulov — for involvement in an extremist
                       group and participation in a nonprofit organization
                       that infringes on the rights of citizens. Both
                       Fadeeva and Sarapulov were arraigned on Tuesday and
                       placed under restrictions pending trial. 


                # ⚓ Rand_Paul_Says_Legal_Campaign_Methods_Are_How_Dems_“Steal”
                  Elections⠀⇛


                # ⚓ A_National_Network_of_Election_Deniers_will_Oversee_the
                  2024_Election⠀⇛


                       The liberal press has covered this effort with
                       Barton Gellman’s article in the Atlantic Trump’s
                       Next Coup Has Already Begun, leading the charge.
                       But as Gellman immediately notes, Trump’s attempt
                       wouldn’t be an armed uprising.


                       Nevertheless, violence like the January 6 offense
                       on the Capitol could be repeated in the future by
                       right-wing groups like the Oath Keepers, 1st
                       Amendment Praetorian and the Proud Boys. There is
                       no other word than “violence” to describe what
                       happened. At a congressional hearing last week,
                       four officers testified before congress that crowds
                       of people, many wielding weapons, attacked and
                       threatened them. Over one hundred were seriously
                       wounded in protecting our nation’s Capitol.


                # ⚓ Donald_Trump_Has_Spent_the_Last_Two_Weeks_Offending_His
                  Closest_Allies⠀⇛


                # ⚓ Democracy_is_as_Fragile_Now_as_it_was_During_My_Father’s
                  Time_in_Weimar_Germany⠀⇛


                       After leaving university, Claud had won a
                       travelling fellowship from Queen’s College, Oxford,
                       which he believed would give him just enough money,
                       when supplemented by meagre journalistic earnings,
                       to live in Berlin for a couple of years. But as
                       Christmas approached at the end of the first year,
                       he realised that he had miscalculated and,
                       moreover, he had to feed not only himself but a dog
                       left in his care by his girlfriend Berta who had
                       gone to Vienna for the holiday period.


                       “It was a horrible Christmas for the dog,” Claud
                       wrote later in his memoir In Time of Trouble,
                       “because just at that time I had run entirely out
                       of money and was living chiefly on expectations of
                       a cheque from the United States that never came. To
                       begin with, the dog fed fairly well because the
                       butcher round the corner always had a pile of
                       scraps – offal, bacon rind and the like – which he
                       gave me free when I bought meat for myself.”


          o § Misinformation/Disinformation⠀➾


                # ⚓ GA_Inquiry_Into_“Dead_People”_Voting_Reaffirms_That_Trump’s
                  Claims_Were_Bogus⠀⇛


                # ⚓ Retailers_Are_Blaming_The_Internet_For_A_Retail_Theft_Surge
                  That_Might_Not_Be_Happening;_Media_Is_Helping_Them_Out⠀⇛


                       It’s becoming quite a theme: basically every
                       industry is blaming the internet for anything wrong
                       happening in their industry and the legacy media is
                       more than willing to help out. The latest is the
                       supposed “surge” in shoplifting and retail crime.
                       You’ve probably seen the stories, and maybe the
                       shaky video coverage of the big smash and grab runs
                       at some big San Francisco stores. This is being
                       leveraged by those retailers in a variety of ways,
                       including in a push to roll back policing reforms,
                       but also to attack the internet. We’ve talked about
                       the problems of the INFORM Act, which is being
                       pushed heavily by large retailers. If you read that
                       letter (sent to Congressional leaders by a bunch of
                       big retailers), it uses those stories of theft to
                       say we need to pass new regulations about internet
                       sales:


          o § Censorship/Free Speech⠀➾


                # ⚓ Chinese_Gov’t_Inflicts_Its_Selective_Amnesia_On_Hong_Kong,
                  Forcing_The_Removal_Of_Tiananmen_Square_Massacre_Monuments⠀⇛


                       To be subservient to the Chinese government is to
                       be in a constant state of (mandated) denial. The
                       government has a narrative to project. No, that’s
                       not an accurate depiction. The state has a
                       narrative to enforce.


                # ⚓ Weeks_After_Blasting_Twitter_For_‘Strangling_Free
                  Expression’_GETTR_Bans_The_Term_‘Groyper’_In_Effort_To_Stop
                  White_Nationalist_Spam⠀⇛


                       It’s always fun to watch each new entrant into the
                       social media market that rushes in claiming that it
                       is the “true” supporter of “free speech” learn
                       about the necessity of some level of content
                       moderation. We watched it happen with Parler, the
                       site set up by Trump benefactor Rebekah Mercer. And
                       now we’re watching it happen with former Trump
                       spokesperson Jason Miller — who is so supportive of
                       “free speech” that he once sued a news org for
                       reporting on something he didn’t want public (he
                       lost badly and was told to pay legal fees). GETTR
                       has already had some fun learning that content
                       moderation is necessary (and not a necessary “evil”
                       — just necessary). But now it’s gone up a level.


                # ⚓ ‘We_never_counted_on_love_from_the_state’_Meduza_talks_to
                  Memorial’s_Yan_Rachinsky_immediately_after_Russia’s_Supreme
                  Court_shuttered_this_prominent_rights_organization⠀⇛


                       In a ruling on Tuesday, December 28, Russia’s
                       Supreme Court shut down the country’s oldest and
                       most authoritative human rights organization — the
                       “Memorial” International Historical Educational
                       Charitable and Human Rights Society. The ruling
                       granted a petition filed by the Attorney General’s
                       Office, which maintains that International Memorial
                       repeatedly violated Russia’s “foreign agent”
                       legislation (without presenting convincing evidence
                       to support this claim). Moscow prosecutors filed a
                       similar lawsuit against Memorial’s human rights
                       branch — the next hearing is scheduled for
                       Wednesday, December 29. To find out what today’s
                       ruling means for the future of International
                       Memorial, Meduza spoke to the chairman of the
                       organization’s board, Yan Rachinsky. 


                # ⚓ Russia’s_Supreme_Court_dissolves_historical_research_branch
                  of_prominent_group_Memorial⠀⇛


                       In a ruling on Tuesday, Russia’s Supreme Court
                       dissolved the “Memorial” International Historical
                       Educational Charitable and Human Rights Society,
                       granting a petition by the Attorney General’s
                       Office, which argues that the organization
                       repeatedly violated Russia’s laws on “foreign
                       agents” by failing to disclose its “agent” status
                       in content shared on social media.


          o § Civil Rights/Policing⠀➾


                # ⚓ Intelligence,_Artificial_and_Otherwise:_Our_Ruling_Class⠀⇛


                       The Council on Foreign Relations is usually
                       regarded as a peak institution of the US ruling
                       class. Its fellows design policy and its members,
                       drawn from Wall Street, academia, and elite
                       journalism, hobnob with government ministers and
                       even the occasional president. But its star has
                       fallen with the demise of the old WASP
                       establishment and the replacement of its bipartisan
                       deliberative style with the crude bombast of the
                       present.


                # ⚓ With_Abortion_Access_in_Peril,_States_Move_to_Protect
                  Reproductive_Rights_in_2022⠀⇛


                       As the future of reproductive rights in the United
                       States is threatened by the U.S. Supreme Court’s
                       right-wing supermajority and a wave of anti-choice
                       laws passed by states across the nation, some
                       Democrat-led states are taking proactive steps to
                       safeguard the right to choose in ways that go above
                       and beyond affirmative legislation.


                       “In my mind, there should be no question where
                       Vermont stands with regard to its core values and
                       fundamental rights… they need to be enshrined in
                       our state constitution.”


                # ⚓ Opinion_|_Adoption_Does_Not_Remove_the_Need_for_Access_to
                  Abortion⠀⇛


                       I was born on Jan. 11, 1973, 11 days before Roe v.
                       Wade decriminalized abortion across the United
                       States. As a self-described politically aware,
                       adopted teenage girl, this was a chilling factoid
                       for me. Phew, I always thought. Made it. Of course,
                       it was also insignificant, because I was born,
                       adopted and raised in New York, where abortion up
                       to the 24th week of pregnancy had been legalized in
                       1970, long before I was conceived.


                # ⚓ Dallas_PD_Brags_About_Stealing_Money_From_A_Woman_At_An
                  Airport,_Is_Now_Facing_Scrutiny_From_Its_Oversight_Board⠀⇛


                       In a spectacular bit of self-ownership, the Dallas
                       Police Department (DPD) took to Facebook to brag
                       about stealing money from a person at Love Field
                       Airport.


                # ⚓ “Our_Deadline_is_Victory”:_Rev._William_Barber’s_Vow⠀⇛


                       “Senator Manchin is playing a Caesar or at least a
                       King Herod in today’s Christmas story,” said Rev.
                       Dr. Liz Theoharis, a co-chair of the Poor People’s
                       Campaign. “He’s saying there’s no room in this
                       democracy for the 140 million poor and low-income
                       Americans, including the 700,000 West Virginians
                       who’ve been locked into poverty and low wages under
                       his watch. He wants to limit poor children’s lives
                       just so he can hold on to his power and wealth. On
                       Christmas Eve, doesn’t this indeed sound like
                       Herod?”


                       The Poor People’s Campaign has held numerous
                       rallies and acts of civil disobedience over the
                       past year in support of the Build Back Better Act,
                       while acknowledging that the legislation would be
                       just a first step towards a moral economy.


                # ⚓ Capitalists_are_Dispensable,_Laborers_Are_Not⠀⇛


                       This thesis flows from a neglected asymmetry
                       between capitalists and laborers. The capitalist
                       does not stand in the same relation to capital and
                       the services of capital as a laborer does with
                       respect to his laboring capacities and the services
                       of these capacities. This distinction goes
                       unacknowledged by neoclassical economists as well
                       as economists of other persuasions. If this is
                       because they have concluded that this is of no
                       consequence, we offer some arguments to the
                       contrary.


                       There is irony in this thesis even as capitalism
                       threatens to render laborers ‘useless,’ that is,
                       replace them with intelligent machines faster than
                       it creates new jobs. But this is not the place to
                       address this irony.


                # ⚓ Opinion_|_Honoring_the_Reverend_Desmond_Tutu⠀⇛


                       The death of Desmond Tutu has been a tragic loss to
                       human rights, justice and development in Africa.
                       Many words will be said in his honor. However, the
                       best way to honor his memory is for leaders of
                       industrialized countries to provide increased
                       public health and socio-economic support to the
                       African people to whom Desmond Tutu devoted his
                       life and work.


                # ⚓ Fifth_Circuit_Agrees_to_Hold_Hearing_on_Texas_Abortion_Law
                  in_January⠀⇛


                # ⚓ “His_Spirit_Reflected_a_Giant”:_Mumia_Abu-Jamal_Remembers
                  Archbishop_Desmond_Tutu’s_Visit_on_Death_Row⠀⇛


                       Mumia Abu-Jamal remembers South African Archbishop
                       Desmond Tutu, who died on Sunday at the age of 90.
                       Tutu was awarded the Nobel Peace Prize for fighting
                       to end apartheid in South Africa. In 2007, Tutu
                       visited Mumia when he was still on death row. “His
                       spirit reflected a giant,” says Abu-Jamal. “He
                       struggled for change with his prophetic voice, his
                       sweet humor, his deep love and his boundless sense
                       of compassion.”


                # ⚓ Angela_Davis_Speaks_on_Abolition,_Justice_for_Palestine_and
                  Critical_Race_Theory⠀⇛


                # ⚓ Scholar_Angela_Davis_on_Prison_Abolition,_Justice_for
                  Palestine,_Critical_Race_Theory_&_More⠀⇛


                       World-renowned author, activist and professor
                       Angela Davis talks about the prison abolition
                       movement from her time as a Black Panther leader to
                       today. In her tireless efforts as an abolitionist
                       and a teacher, Davis continues to be a fierce
                       advocate of education and the interconnected
                       struggles of oppressed peoples. Davis talks about
                       Indigenous genocide, Palestine, critical race
                       theory and the role of independent media.
                       “Democracy Now! helps us to place our own domestic
                       issues and struggles within the context of global
                       battles against fascism,” says Davis.


                # ⚓ Angela_Davis_on_Imagining_New_Worlds,_the_Campaign_to_Free
                  Mumia_and_the_Biden_Presidency⠀⇛


                       World-renowned author, activist and professor
                       Angela Davis talks about navigating the pandemic
                       and an inadequate two-party political system during
                       a time of racial uprising in the United States. She
                       also talks about imprisoned journalist Mumia Abu-
                       Jamal, the Biden presidential campaign and the
                       protests that erupted from the police killing of
                       George Floyd and Breonna Taylor.


                # ⚓ American_Gulag:_Inside_the_U.S.’_Massive_Prison_System,
                  with_Chris_Hedges⠀⇛


                # ⚓ Archbishop_Desmond_Tutu:_Father_of_South_Africa’s_‘Rainbow
                  Nation’⠀⇛


                       Archbishop Tutu earned the respect and love of
                       millions of South Africans and the world. He carved
                       out a permanent place in their hearts and minds,
                       becoming known affectionately as “The Arch”.


                       When South Africans woke up on the morning of 7
                       April, 2017 to protest against then President Jacob
                       Zuma’s removal of the respected Finance Minister
                       Pravin Gordhan, Archbishop Tutuleft his Hermanus
                       retirement home to join the protests. He was 86
                       years old at the time, and his health was frail.
                       But protest was in his blood. In his view, no
                       government was legitimate unless it represented all
                       its people well.


                # ⚓ Honoring_the_Reverend_Desmond_Tutu⠀⇛


                       Today the coronavirus pandemic has resulted in
                       hundreds of thousands of deaths in Africa that
                       could have been avoided. Having sufficient vaccines
                       available to all will help curtail the coronavirus
                       pandemic in Africa. And, by stalling the
                       development of new mutations, in the rest of the
                       world.


                       Health problems in Africa still require
                       considerable technical and financial assistance.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Where_Net_Neutrality_Is_Today_and_What_Comes_Next:_2021_in
                  Review⠀⇛


                       With President Biden’s appointments of Chairwoman
                       Jessica Rosenworcel and Gigi Sohn, a net neutrality
                       pioneer, to staff the FCC’s leadership team, we can
                       usher in a better era. Both appointees made clear
                       their support for the 2015 Open Internet Order and
                       belief that the FCC should begin a process to re-
                       establish federal authority over broadband
                       carriers, including network neutrality rules. More
                       fights lie ahead when the new federal rules are
                       established but let’s review what’s happened so far
                       and what they mean for protecting your access to
                       the Internet.


                       At its core, the necessity for net neutrality
                       protections rests on one simple fact: people don’t
                       want their broadband provider to dictate their
                       experience online. It’s a need that only grew
                       during the pandemic.


                       As the country rapidly transitions education,
                       social activities, and jobs to rely on a
                       persistent, open, and non-discriminatory connection
                       to the world, views of access have shifted. Today,
                       an eye-popping 76% of American Internet users
                       consider internet service to be as important as
                       water and electricity in their daily life. But
                       unlike those utility services, internet access is
                       subject to the whims of private carriers for a
                       large number of American users.


                # ⚓ NordVPN_doesn’t_really_have_enough_bandwidth_to_handle
                  BitTorrent,_so_they_throttle_it._–_BaronHK’s_Rants⠀⇛


                       Pretty much every software update makes the client
                       software buggier than before, but they’ve really
                       been stepping on the hose with BitTorrent traffic.


                       Much of the time, you can’t get any real bandwidth
                       at all and you’re stuck downloading at 20-30 KB per
                       second regardless of how fast everything else
                       works. Direct downloads over HTTP(S) work just
                       fine, but BitTorrent traffic is being throttled by
                       some sort of QoS system.


                # ⚓ 2021:_Bringing_public_policy_closer_to_the_public⠀⇛


                       Throughout 2021, we have tried to respond to the
                       various policy initiatives and projects launched by
                       the Central and State governments with meaningful
                       and privacy-respecting policy analysis. We have
                       also utilized the Right to Information Act, 2005 to
                       bring accountability in the working of every public
                       authority.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Unpatented_Shot_Dubbed_‘The_World’s_Covid-19_Vaccine’
                        Wins_Emergency_Approval_in_India⠀⇛


                             An unpatented Covid-19 vaccine developed by
                             the Texas Children’s Hospital, Baylor College
                             of Medicine, and the pharmaceutical firm
                             Biological E. Limited received emergency-use
                             authorization from Indian regulators on
                             Tuesday—news that the jab’s creators hailed
                             as a potential turning point in the push to
                             broaden global vaccine access.


                             “Our Texas Children’s Center does not plan to
                             make money on this, it’s a gift to the
                             world.”


                      # ⚓ Opinion_|_The_Vaccine_Monopolies_Must_Be_Broken⠀⇛


                             This month, the world could have been
                             celebrating the waning of the COVID-19
                             pandemic. Instead, vaccine apartheid and
                             restricted production continue to fuel the
                             spread of the coronavirus.


                # § Trademarks⠀➾


                      # ⚓ TTABlog_Test:_Is_ZERO_MEAT_Merely_Descriptive_of
                        Animal,_Fish,_and_Poultry_Certification_Services?⠀⇛


                             The USPTO refused to register the proposed
                             mark ZERO MEAT for “Testing, analysis and
                             evaluation of the goods and services of
                             others to determine conformity with
                             certification standards; testing, analysis
                             and evaluation of the food products of others
                             to determine conformity with certification
                             standards relating to animal, fish or
                             poultry,” on the ground of mere
                             descriptiveness. Applicant Equity argued that
                             the proposed mark is a coined phrase, and
                             that other terms like “contains no …”, or
                             free of …” or “vegan” or “vegetarian” would
                             be used to indicate the absence of animal,
                             fish, or poultry content in foods. How do you
                             think this came out? In re Equity IP
                             Holdings, LLC, Serial No. 88517758 (December
                             16, 2021) [not precedential] (Opinion by
                             Judge George C. Pologeorgis).


                      # ⚓ The_TTABlog®:_Precedential_No._35:_TTAB_Grants_MIRAGE
                        BRANDS_Cancellation_Petition_Due_To_Likelihood_of
                        Reverse_Confusion⠀⇛


                             In an otherwise straightforward Section 2(d)
                             analysis, the Board ruled that confusion is
                             likely between Respondent’s registered marks
                             MIRAGE BRANDS (standard form) and MIRAGE
                             BRANDS & Design [BRANDS disclaimed], and
                             Petitioner Mahender Sabhnani’s previously
                             used and registered mark ROYAL MIRAGE &
                             Design, all for perfume. Finding that
                             “Respondent’s presence in the marketplace is
                             considerably greater than that of
                             Petitioner,” the Board saw “a circumstance of
                             reverse confusion in which consumers exposed
                             to Respondent’s marks for perfumes who
                             encounter Petitioner’s mark for perfume are
                             likely to believe mistakenly that
                             Petitioner’s goods originate with
                             Respondent.” Mahender Sabhnani v. Mirage
                             Brands, LLC, 2021 USPQ2d 1241 (TTAB 2021)
                             [precedential] (Opinion by Judge Christopher
                             Larkin).


                # § Copyrights⠀➾


                      # ⚓ Court_Orders_WhatsApp_To_Block_Groups_Sharing_Pirated
                        Newspapers⠀⇛


                             India’s largest newspaper publishing group
                             has filed a complaint at the Delhi High Court
                             against dozens of defendants said to have
                             illegally offered its copyrighted
                             publications via WhatsApp. The full case will
                             be heard next year but in the interim,
                             WhatsApp is required to take down or block
                             the infringing groups.


                      # ⚓ Startup_Uses_Blockchain_and_Pirate_Sites_to_Pay
                        Filmmakers_Directly⠀⇛


                             Movie industry startup White Rabbit allows
                             people to pay for the films they watch on
                             pirate sites. The service compensates
                             filmmakers directly while sharing revenue
                             pirate sites in the process. Add in a
                             blockchain distribution model and it’s clear
                             that the service is up with the times. Or is
                             there such as thing as too much innovation?



                    ䷩ 𝚕𝚒𝚗𝚎 4923

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 12.29.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_29/12/2021:_GNU_Serveez_0.3.1_and_postmarketOS_21.12⠀✐


Posted in News_Roundup at 3:48 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Audiocasts/Shows⠀➾


                # ⚓ Destination_Linux_258:_Linux_in_2021:_Year_In_Review!⠀⇛


                       This week’s episode of Destination Linux, we’re
                       going to take a look back at this year in Linux.
                       There are so many amazing things that happened with
                       Linux and we’re going to cover all the highlights.
                       Then we’re going to discuss the future of the Linux
                       Desktop in Virtual Reality! Plus we’ve also got our
                       famous tips, tricks and software picks. All of this
                       and so much more this week on Destination Linux. So
                       whether you’re brand new to Linux and open source
                       or a guru of sudo. This is the podcast for you.


                # ⚓ How_Does_KDE_Think?_–_Kockatoo_Tube⠀⇛


          o § Kernel Space⠀➾


                # ⚓ Linux_5.15.12⠀⇛


                       I'm announcing the release of the 5.15.12 kernel.

                       All users of the 5.15 kernel series must upgrade.

                       The updated 5.15.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.15.y
                       and can be browsed at the normal kernel.org git web
                       browser:

                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s...

                       thanks,

                       greg k-h
                # ⚓ Linux_5.10.89⠀⇛


                # ⚓ Linux_5.4.169⠀⇛


                # ⚓ Linux_4.19.223⠀⇛


                # ⚓ Linux_4.14.260⠀⇛


                # ⚓ Linux_4.9.295⠀⇛


                # ⚓ Linux_4.4.297⠀⇛


                # ⚓ Improved_Thermal/Power_Management_For_Intel_“Titan_Ridge”
                  Thunderbolt_Coming_To_Linux_–_Phoronix⠀⇛


                       For those with systems making use of an Intel
                       “Titan Ridge” Thunderbolt 3 controller, a Linux
                       kernel driver improvement working its way to
                       mainline should yield thermal/power benefits.


                       Intel’s Titan Ridge are the JHL7440 / JHL7540 /
                       JHL7340 controllers providing Thunderbolt 3 in some
                       desktop motherboards. Titan Ridge was launched back
                       in 2018 and has been supported in the mainline
                       Linux kernel since that point.


                # § Graphics Stack⠀➾


                      # ⚓ Mesa_22.0_Zink_Lands_macOS_Build_Fix_For_OpenGL_On
                        Vulkan_Via_MoltenVK_On_Metal_–_Phoronix⠀⇛


                             Last year there was some work for getting
                             Gallium3D Zink working on macOS for this
                             OpenGL-on-Vulkan implementation to in turn
                             run it atop the MoltenVK library for
                             translating the Vulkan calls to Apple’s Metal
                             graphics/compute API. That work fell into
                             disrepair but now the fixed up code for
                             allowing Zink to build on Apple’s operating
                             system has been merged into Mesa 22.0.


          o § Benchmarks⠀➾


                # ⚓ AMD_AOCC_3.2_vs._GCC_vs._Clang_Compiler_Performance_On_Zen
                  3_–_Phoronix⠀⇛


                       Earlier this month AMD released AOCC 3.2 as the
                       newest version of their LLVM/Clang-based compiler
                       focused on delivering optimized Zen performance.
                       With our initial AMD AOCC 3.2 benchmarks on Zen 3,
                       there is nice incremental improvement compared to
                       the prior 3.x releases. But how does this AMD-
                       optimized compiler stack up against the upstream
                       LLVM Clang and GCC compilers? Here is a look at the
                       AMD AOCC performance against the current Clang and
                       GCC C/C++ compilers.


                       This round of compiler testing was carried out on
                       the frequency-oprimized AMD EPYC 72F3 (Zen 3)
                       server processor with Supermicro H12SSL-
                       i motherboard, 8 x 16GB DDR4-3200 memory, and
                       running Ubuntu 21.04 with the Linux 5.14 kernel.
                       Following the AOCC 3.0 / 3.1 / 3.2 compiler
                       benchmarks, the comparison was extended to include
                       LLVM Clang 12.0.1, LLVM Clang 13.0.1, GCC 10.3, GCC
                       11.2, and GCC 12.0 in its current development form.


                       While testing all of these compilers with their
                       release builds, the CFLAGS/CXXFLAGS were set to “-
                       O3 -march=native” throughout. The main focus of
                       this testing is seeing how AMD’s in-house AOCC
                       downstream of LLVM/Clang is performing against the
                       common GCC and Clang releases for the performance
                       of the resulting binaries from these compilers.
                       AOCC has also been maturing its Fortran support
                       with the FLANG front-end and comparison tests that
                       will come in due course with the LLVM FLANG support
                       still maturing.


          o § Applications⠀➾


                # ⚓ Gamestonk_Terminal_–_investment_research_tool⠀⇛


                       Python is one of the finest open source languages
                       for data scientists mainly because of its
                       incredibly powerful ecosystem with its huge array
                       of machine learning/deep learning libraries, and
                       powerful visualization software. To get a flavour
                       of the ecosystem, check out our recommended Python
                       Deep Learning and Python Visualization software.


                       One of the many use cases for the Python ecosystem
                       is in the field of investment research. Can’t see
                       the wood from the trees? Are you uncertain of the
                       next investment decision to make? Step forward
                       Gamestonk Terminal.


                       Gamestonk Terminal provides a modern Python-based
                       integrated environment for financial investment
                       research. It aims to provide a comprehensive tool
                       to help make better investment decisions. This
                       terminal-based tool is free and open source
                       software written in Python.


                # ⚓ Fun_with_Telescopesu⠀⇛


                       Recently I purchased a small telescope to look at
                       solar spots. When choosing a mount, I checked
                       whether it can be controlled with OSS.


                       In this context INDI is mentioned everywhere and my
                       desired mount was supported. indi and kstars are
                       already part of Debian, so “apt install”, selecting
                       my mount, …. oh, wait, the menu shows it, but I can
                       not select it.


                       Ok, that was the time when I learned about the
                       difference of indi and indi-3rdparty. The indi
                       package just contains a few drivers and others are
                       available from a different repository. This split
                       has been done either due to different release
                       cycles of the driver, a different OSS license of
                       it, or just due to binary blobs without source
                       being part of some drivers.


                       Fine, there are already packages of the 3rdparty-
                       repository available from an Ubuntu PPA, so it
                       should be no problem to add them do Debian as well.


          o § Instructionals/Technical⠀➾


                # ⚓ How_To_Connect_QEMU_Host-Guest_Networks_Made_Easy⠀⇛


                       This tutorial will explain for QEMU virtual machine
                       users how you can make two-ways network connection
                       between host and guest on Ubuntu Desktop. This
                       enables internet access automatically for the guest
                       if available on the host. This tutorial gives you
                       an example exercise, that is, to remote login with
                       SSH from host to guest and reversely from guest to
                       host. Now let’s start!


                # ⚓ How_To_Install_Icinga_on_Linux_Mint_20_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Icinga on Linux Mint 20. For those of you who
                       didn’t know, Icinga is an open-source computer
                       system and network monitoring application. It is
                       one of the most popular monitoring tools on the
                       internet that provides high availability and
                       distributed monitoring. Icinga 2 has a user-
                       friendly web interface, but it also comes with a
                       command-line interface that can be used for
                       monitoring.


                       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 Icinga 2 monitoring tool on a
                       Linux Mint 20 (Ulyana).


                # ⚓ How_to_install_Manjaro_21.2.0_–_Invidious⠀⇛


                       In this video, I am going to show how to install
                       Manjaro 21.2.0.


                # ⚓ How_to_Find_Vulnerabilities_In_Containers_and_Files_With
                  Grype_–_CloudSavvy_IT⠀⇛


                       Grype is an open-source vulnerability scanner that
                       finds weaknesses within container images and
                       filesystem directories. Grype is developed by
                       Anchore but works as a standalone binary that’s
                       easier to get to grips with than the Anchore
                       Engine.


                       Known vulnerabilities make their way into your
                       software via outdated operating system packages,
                       compromised programming language dependencies, and
                       insecure base images. Actively scanning your
                       artifacts keeps you informed of issues before
                       malicious actors find them. Here’s how to use Grype
                       to find problems in your code and containers.


                # ⚓ How_to_Install_and_Test_Parrot_OS_in_VirtualBox⠀⇛


                       Parrot OS lays a heavy focus on providing extensive
                       security and penetration testing capabilities to
                       the end-users. Even though most advanced users
                       might only use Kali Linux for their pen testing
                       needs, the reality is that Parrot OS is an equally
                       efficient operating system that is useful as a
                       privacy-focused distro.


                       Since Parrot OS draws its inspiration from Debian,
                       the Linux distro continues to be easy to install
                       for users. It inherits some intelligent features
                       from its counterparts, including the APT package
                       manager and a full-fledged suite of penetration
                       testing and privacy tools.


                       To test Parrot OS, you can install the distro on
                       Oracle’s VirtualBox.


                # ⚓ How_to_install_memcached_on_OpenSUSE_/_SUSE_Linux_–
                  nixCraft⠀⇛


                       While working with the client’s system, I noticed
                       that the database would come under load due to
                       increased demand. After reviewing the code, the
                       developer and I conclude that something like
                       memcached will improve performance by caching
                       queries. This page explains how to install a
                       memcached server on OpenSUSE or SUSE enterprise
                       Linux server using the ssh command.


                # ⚓ Still_working_with_gnome_boxes_—_Unixcop⠀⇛


                       A couple of weeks ago, I’ve wrote an article about
                       how I’m (kinda) in love with gnome boxes. Well, I’m
                       still working with gnome boxes every day. And that
                       simpleness I’m kinda in love to comes with a cost:
                       to do some things are the exact opposite to simple.


                       Here’s a small list of things that annoyed me and
                       how I’ve solved it.


                # ⚓ Run_Distrobox_on_Fedora_Linux_–_Fedora_Magazine⠀⇛


                       Distrobox is a tool that allows you to create and
                       manage container-based development environments
                       without root privileges.


                       Distrobox can use either podman or docker to create
                       containers using the Linux distribution of your
                       choice.


                       The created container will be tightly integrated
                       with the host, allowing sharing of the HOME
                       directory of the user, external storage, external
                       USB devices, graphical apps (X11/Wayland), and
                       audio.


                       As a project, it is inspired by Container Toolbx
                       (all the props to them!), but it aims to have
                       broader compatibility with hosts and containers,
                       without having to require a dedicated image to use
                       in Distrobox.


                # ⚓ How_to_Determine_the_File_System_Type_in_Linux_(Ext2,_Ext3,
                  or_Ext4)?_–_TREND_OCEANS⠀⇛


                       Linux is an ocean of different kinds of file
                       systems. Some distributions ship Ext4 as the
                       default file system, while distributions like
                       RedHat stick with an XFS.


                       Besides Ext4 and XFS, there are around 10+ file
                       systems in Linux with unique features and few
                       drawbacks. To know, your Linux system is running in
                       which type of file system use the below method.


                # ⚓ How_To_Install_RStudio_IDE_on_Fedora_35_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       RStudio IDE on Fedora 35. For those of you who
                       didn’t know, RStudio provides free and open-source
                       tools for R and enterprise-ready professional
                       software for data science teams to develop and
                       share their work at scale. RStudio makes it easier
                       to write Python, Shell, SQL scripts with syntax
                       highlighting, code completion, and smart
                       indentation.


                       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 RStudio IDE on a Fedora 35.


                # ⚓ How_to_install_Mongodb_Server_on_Linux_mint_18_|_19_|_20_–
                  Linux_Shout⠀⇛


                       Steps and commands to install the latest version of
                       MongoDB server and client on Linux Mint 18, 19, and
                       20 using the command terminal.


                       What is MongoDB? MongoDB is an open-source database
                       that is different from Oracle MySQL, Microsoft SQL,
                       and other popular SQL database servers. Because
                       this one is based on a non-relational document
                       model. That’s why we called NoSQL database (NoSQL =
                       Not-only-SQL) and makes it differs fundamentally
                       from conventional relational databases. The meaning
                       of its name is “humongous” founded by developer
                       Eliot Horowitz in 2009.


                       MongoDB is available in both community and
                       Enterprise editions. The community version is good
                       for SMBs, developers, individuals for testing and
                       learning; whereas the enterprises with a heavy
                       workload and require large-scale implementation
                       should go for the Enterprise version. In the
                       enterprise version, the user will get Technical
                       support, Kubernetes Integration, advanced access
                       control, and data security, LDAP Proxy
                       Authentication, Encryption at Rest, Auditing,
                       Kerberos Authentication, and other features…


          o § Games⠀➾


                # ⚓ Rats_Learn_To_Play_DOOM_In_This_Automated_VR_Arena_|
                  Hackaday⠀⇛


                       When we run an article with “DOOM” in the title,
                       it’s typically another example of getting the
                       venerable game running on some minimalist platform.
                       This DOOM-based VR rig for rats, though, is less
                       about hacking DOOM, and more about hacking the
                       rats.


                       What started as a side project for [Viktor Tóth]
                       has evolved into quite a complex apparatus. At the
                       center of the rig is an omnidirectional treadmill
                       comprised of a polystyrene ball about the size of a
                       bowling ball. The ball is free to rotate, with
                       sensors detecting rotation in two axes — it’s
                       basically a big electromechanical mouse upside
                       down. The rat rides at the top of the ball, wearing
                       a harness to keep it from slipping off. A large
                       curved monitor sits right in front of the rat to
                       display the virtual environment, which is a custom
                       DOOM map.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Better_Adaptive_Icons_for_2022!_›_Ken_Vermette⠀⇛


                             Some new CSS classes are coming to icons
                             courtesy Janet Blackquill, and I’m excited to
                             cover what exactly this will let icon artists
                             do in 2022! This post is part tutorial and
                             part news. For those looking for a quick
                             TLDR; icons are going to get even better. I’m
                             also going to clear up some inaccuracies in
                             existing documentation (which I plan on
                             updating at some point later)


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ The_icon_view_is_dead,_long_live_the_icon_view!_–
                        Blog_about_what_I_do⠀⇛


                             Porting Files to GTK 4 has been helping me
                             learn and appreciate even more the legacy of
                             the nautilus software package. Its two-
                             decades-long history is closely entangled
                             with the history of the GNOME project.


                             As I prepare to merge the removal of more
                             than 20 thousand lines of code, I’ve decided
                             to stop and pay some tribute to the legacy
                             widget that’s about to be decommissioned.


                             [...]


                             At some point renamed/forked to FooCanvas and
                             later EelCanvas, this base widget continued
                             to serve as the fundamental base for the
                             GNOME desktop files and file browser’s icon
                             view across major versions.


                             However, as GNOME 3 no longer featured icons
                             on desktop, a free-position canvas was no
                             longer required. Various efforts were made to
                             implement a less complex grid view, but the
                             canvas refused to be dethroned easily.


          o § Distributions⠀➾


                # ⚓ XeroLinux_is_a_refreshingly_cool_desktop_in_desperate_need
                  of_some_polish⠀⇛


                       Clearly, XeroLinux isn’t for the new user. Anyone
                       who prefers their desktops work with a certain
                       level of reliability will want to steer clear of
                       this entry. But if you love eye candy and you don’t
                       mind spending a bit of extra time getting things to
                       work, XeroLinux might be just the sidetrack from
                       the standard-issue desktop.


                       This is one of those distributions that I sincerely
                       hope continues growing. Even with the issues, what
                       Anindo Neel Dutta has done is impressive. XeroLinux
                       has the makings of what could be the most beautiful
                       Linux desktop on the market. If he can work out
                       some of the quirks, he’ll have something special on
                       his hands.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Fedora_36_Looking_To_Change_Its_Default_Fonts_–
                        Phoronix⠀⇛


                             Fedora is often on the bleeding-edge of
                             changes for tier-one Linux distributions but
                             not all of them are very technical in nature
                             but sometimes just cosmetic alterations.
                             Among the latest batch of change proposals
                             for next spring’s Fedora 36 is to change the
                             default font.


                             Currently Fedora relies on the DejaVu fonts
                             for European and other language scripts. But
                             not all languages are covered by DejaVu so
                             there are also other fonts involved.


                      # ⚓ 10_networking_guides_for_sysadmin_success_|_Enable
                        Sysadmin⠀⇛


                             Of the many changes created by the pandemic,
                             one of the more enduring is that remote work
                             is still the norm. Networking makes this
                             possible. Understanding and appreciating how
                             networks work and are designed is a needed
                             skill, especially in this digital world.


                      # ⚓ Open_source_tools_for_running_a_small_business_in
                        2022⠀⇛


                             This year, Opensource.com ran several great
                             articles focusing on open source in business.
                             These articles show the power of open source
                             in business as tools, platforms, or
                             integration points. Let’s review some of the
                             top open source business stories from 2021:


                      # ⚓ Hybrid_work:_5_resolutions_to_help_leaders_support
                        teams⠀⇛


                             The hybrid work model is here to stay, and
                             the way organizations shape their new work
                             models in early 2022 will influence the
                             structure of the workforce for many years to
                             come. It’s becoming clear that the most
                             practical approach for larger companies is a
                             combination of remote and in-person
                             structure, focused on high engagement,
                             connection, and collaboration.


                             Your goal for the first quarter of 2022
                             should be to create a work environment that
                             is valuable for both those working in the
                             office and those working remotely, while
                             recognizing that the two experiences will
                             never be the same. Your office structure 2.0
                             must also address pain points created by the
                             pandemic, like video meeting fatigue and
                             feeling disconnected from colleagues.


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Ubuntu_Touch_OTA-21_Arrives_on_January_5th,_2022,
                        with_Redesigned_Greeter,_More_Fixes⠀⇛


                             Still based on the Ubuntu 16.04 LTS (Xenial
                             Xerus) operating system series, the Ubuntu
                             Touch OTA-21 update is yet another bugfix
                             release that fixes various issues reported by
                             users from previous OTA updates.


                             For example, it fixes support for setting up
                             a Google account, it fixes microphone access
                             in the default web browser, and fixes a weird
                             animation issue in Clock app’s timer mode
                             that occurred when the clock hands were moved
                             across the 12-hour clock position.


                      # ⚓ What’s_New_in_Linux_Mint_20.3_“Una”⠀⇛


                             Linux Mint’s final point release in the 20
                             series, nicknamed “Una,” is now in beta. It
                             builds on version 20.2 “Uma” with some new
                             features and refinements. Are those changes
                             more substantial than the name change? Let’s
                             find out.


          o § Devices/Embedded⠀➾


                # ⚓ Raspberry_Pi_UPS_HAT_takes_two_18650_batteries_
                  (Crowdfunding)⠀⇛


                       Raspberry Pi UPS solutions have been available for
                       years with products like PiJuice Zero, PiVoyager,
                       or LiFePO4wered/Pi+. But the team at SB Components
                       has designed another UPS HAT for Raspberry Pi with
                       a holder for two 18650 batteries.


                       The HAT is designed for 5V operation up to 2.5A,
                       connects with the Raspberry Pi SBC through the I2C
                       bus from the 40-pin GPIO header, and is equipped
                       with a 0.91-inch OLED for information display.


                # § Open Hardware/Modding⠀➾


                      # ⚓ postmarketOS_//_Release:_v21.12⠀⇛


                             It’s the end of another year, and we’re happy
                             to announce the v21.12 release of
                             postmarketOS, based on Alpine Linux 3.15!


                             Thanks to our amazing contributors, the
                             amount of supported devices has been
                             increased to 23 (from 15 in v21.06). As in
                             previous releases, we ship pre-built images
                             for phones and tablets with the mobile-
                             optimized Phosh, Plasma Mobile and Sxmo
                             interfaces. Other form factors, such as the
                             PineBook Pro get images with different
                             interfaces as it makes sense. In the picture
                             above it runs Plasma Desktop, and besides
                             that we have Gnome, Sway, Phosh and Console.
                             Find all images at the download page.


                             v21.12, like previous releases, is geared
                             mainly towards Linux enthusiasts; it may be a
                             bit rough around the edges so expect some
                             bugs. Help identifying and resolving issues
                             is always greatly appreciated.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ 40_of_Our_Best_Android_Hacks_of_2021⠀⇛


                      # ⚓ Digital_Turbine_Inks_Strategic_Deal_with_Google_to
                        Support_the_Android_Ecosystem⠀⇛


                      # ⚓ Hidden_Android_12_features_you_got_to_try_on_Pixel_6
                        –_CNET⠀⇛


                      # ⚓ OPPO_Reno_5_and_Reno_6_starts_receiving_stable
                        ColorOS_12_update_with_Android_12⠀⇛


                      # ⚓ From_Android_12_to_Oculus:_Here_are_some_of_our
                        biggest_news_stories_of_2021_|_Android_Central⠀⇛


                      # ⚓ Android_12_Update_for_ASUS_ZenFone_8_Rolling_Out_|
                        Finally_Stable?_|_Tech_Times⠀⇛


                      # ⚓ Tecno_Spark_Go_2022_With_Dual_Rear_Cameras,_Android
                        11_(Go_Edition)_Launched_in_India:_Price,
                        Specifications_|_Technology_News⠀⇛


                      # ⚓ How_you_can_clear_your_Android_phone’s_browser
                        cookies_and_cache_–_CNET⠀⇛


                      # ⚓ How_to_easily_back_up_all_your_Android_phone_data_–
                        Technology_News⠀⇛


                      # ⚓ How_Google_is_trying_to_ensure_future_Android_phones
                        offer_important_safety_and_emergency_options_–_Times_of
                        India⠀⇛


                      # ⚓ Realme_Fastest_Growing_5G_Android_Smartphone_Brand
                        Globally_in_Q3_2021:_Counterpoint_Research_|_Technology
                        News⠀⇛


                      # ⚓ Sony’s_latest_Xperia_Android_smartphones_are_now_$100
                        off_at_the_best_prices_of_the_year_–_9to5Toys⠀⇛


                      # ⚓ Chrome_for_Android:_so_you_can_see_when_you_last
                        visited_a_website_and_its_history_–_How_smart
                        Technology_changing_lives⠀⇛


                      # ⚓ New_app_for_Britbox_Australia_on_Android_TV_and
                        Google_TV_finally_available_–_Ausdroid⠀⇛


                      # ⚓ Android_12_is_coming_to_these_Samsung_phones,_but_you
                        should_probably_wait_–_SlashGear⠀⇛


                      # ⚓ Google_Pixel_Android_12_bugs,_problems,_&_issues
                        tracker⠀⇛


                      # ⚓ Android_12_stable_update_for_the_ASUS_ZenFone_8_is
                        now_rolling_out⠀⇛


                      # ⚓ Samsung_resumes_stable_Android_12_update_on_its
                        Galaxy_S20,_Fold_devices_|_Technology_News,The_Indian
                        Express⠀⇛


                      # ⚓ What_is_Google_Play_Protect_and_what_makes_it_the
                        most_important_part_of_your_Android_phone_–_Times_of
                        India⠀⇛


                      # ⚓ Split_Screen_on_Android:_How_to_Use_Split_Screen_on
                        OnePlus,_Samsung,_Vivo,_OPPO,_Realme_and_Xiaomi_Android
                        Mobile_Phones?_–_MySmartPrice⠀⇛


                      # ⚓ Android_Auto_bugs,_issues_&_problems_tracker:_Here’s
                        the_current_status⠀⇛


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


                # ⚓ Top_13_open-source_WebRTC_projects_to_build_Video
                  conferencing_and_calling_apps⠀⇛


                       WebRTC is an open-source framework that enables
                       real-time communications for the web through your
                       web browser.


                       In contrast, it is the basic protocol that allows
                       web apps and websites to capture and stream videos
                       and audio and exchange data between web browsers.


                       WebRTC is created first by Google to make peer-to-
                       peer communication possible for web browsers and
                       mobile apps, leading to dozens of video and audio
                       communication apps that we use every day.


                       It is a free and open-source project, which means
                       it does not require any cost to run and use it


                       Another Advantage for WebRTC is it is fast, and
                       because, unlike UDP-based apps, it does not require
                       any handshake between the client and the server.


                # ⚓ Ghislaine_Maxwell_conviction,_Silva_Arapi,_Nafi_Shehu,_Elio
                  Qoshi_&_Ubuntu_underage_girl⠀⇛


                       Many people are holding their breath waiting for a
                       jury to decide whether to convict Ghislaine
                       Maxwell, sidekick of Jeffrey Epstein.


                       It appears strange for a woman to be involved in
                       crimes against women and children but it is not
                       uncommon. Here at Debian Community News we recently
                       covered the similarities between Debian and the
                       NXIVM sex cult.


                       Debian is a combination of the names Debra and Ian,
                       Ian being the founder of Debian and Debra his
                       girlfriend at the time Debian was conceived. The
                       name Debian is now being used to brand volunteers
                       in much the same way that NXIVM convicted criminals
                       branded their initials on slaves genital skin. It
                       is a tragic coincidence. Debra and Ian would not
                       condone this, yet this is what eventuated under the
                       cult-like regime of Chris Lamb and Molly de Blanc.


                # ⚓ 9_Open_Source_Tech_Careers_to_Consider⠀⇛


                       As we close out this challenging year, we look back
                       at the most popular FOSSlife articles of 2021 and
                       look ahead to the opportunities that 2022 may hold.


                       In the coming year, we will continue to provide
                       news and features to keep you informed of the
                       latest open source trends and technologies and
                       continue to build a collection of resources to help
                       you understand the array of opportunities that open
                       source has to offer.


                # § FSF⠀➾


                      # § GNU Projects⠀➾


                            # ⚓ GNU_Serveez_0.3.1_available⠀⇛


                                   release notes:

                                     Quick-fix release.

                                   README excerpt:

                                     GNU Serveez is a server framework.
                                   It provides routines and help
                                     for implementing IP-based servers
                                   (currently TCP, UDP and ICMP).
                                     It supports named pipes for all
                                   connection-oriented protocols.

                                     We think it is worth the effort
                                   because many people need server
                                     functionality within their
                                   applications.  However, many people
                                     experience problems with select(2) or
                                   poll(2) loops, and with
                                     non-blocking operations.

                                     GNU Serveez demonstrates various
                                   aspects of advanced network
                                     programming in a portable manner.  It
                                   is known to compile and
                                     run on GNU/Linux systems, as well as
                                   on other 32-bit and 64-bit
                                     flavours of Unix and on Microsoft
                                   Windows (9x/ME/NT/2000/XP).

                                     You can use it for implementing your
                                   own servers or for
                                     understanding how certain network
                                   services and operations work.

                                   NEWS for 0.3.1 (2021-12-11):

                                     - build regression fixed

                                       Part of the documentation build
                                   process uses programs to scan
                                       both Scheme and C files for "doc
                                   strings" (actually, comments).
                                       The Serveez 0.3.0 (2021-12-06)
                                   release introduced a bug whereby
                                       the Scheme-scanning program was
                                   passed a flag that is only valid
                                       for the C-scanning program.
                                   Result: FTBFS (sometimes).

                                     - URLs now predominantly https

                                       The world is less trusting, alas.
                                   Docs and ‘--version’ output
                                       updated, as well as all the
                                   copyright notices in the source (of
                                       course).  URLs found in ChangeLog
                                   files are the same.

                                     - bootstrap/maintenance tools

                                       upgraded:

                                        Guile-BAUX 20211208.0839.a5245e7
                                        GNU gnulib 2021-12-10 21:54:54

                                       as before:

                                        GNU Texinfo 6.8
                                        GNU Autoconf 2.71
                                        GNU Automake 1.16.5
                                        GNU Libtool 2.4.6

                                   tarballs and detached signature:

                                   https://ftpmirror.gnu.org/serveez/
                                   serveez-0.3.1.tar.lz


                                   https://ftpmirror.gnu.org/serveez/
                                   serveez-0.3.1.tar.lz.sig

                                   source code:

                                   https://git.savannah.gnu.org/cgit/
                                   serveez.git?h=p

                                   homepage:

                                   https://www.gnu.org/software/serveez/

                                   --
                                   Thien-Thi Nguyen ----------------------
                                   -------------------------
                                    (defun responsep (query)
                                   ; (2021) Software Libero
                                      (pcase (context query)
                                   ;       = Dissenso Etico
                                        (`(technical ,ml) (correctp ml))
                                        ...))
                                   748E A0E8 1CB8 A748 9BFA
                                   --------------------------------------
                                   - 6CE4 6703 2224 4C80 7502
                # § Programming/Development⠀➾


                      # ⚓ Automatic_detection_of_audio_device⠀⇛


                             What I want is when plugin a USB audio
                             device, that it will be detected, and if it
                             is a sink device launch the Multiple Sound
                             Card Wizard. Yes, I will explain that, but
                             also want to point out a serious potential
                             bug that still exists in woof-CE built pups.


                      # ⚓ Qt_6.2_Web_Assembly_What’s_New⠀⇛


                             You may have seen the news that we released
                             Web Assembly as Tech Preview in Qt 6.2 LTS a
                             while ago (please find the latest Qt here).
                             This blog post is a Qt6 refresh of a similar
                             post done earlier for Qt 5, starting a series
                             of Qt Web Assembly posts discussing the
                             recent developments on Qt6 side.


                      # § Perl/Raku⠀➾


                            # ⚓ My_new_modules_in_2021_|_Leon_Timmermans_
                              [blogs.perl.org]⠀⇛


                                   I had a reasonably productive year,
                                   releasing several modules that I think/
                                   hope are useful for the wider
                                   ecosystem.


                            # ⚓ Perl_Weekly_Challenge_145:_Palindromes⠀⇛


    * § Leftovers⠀➾


          o ⚓ Why_Does_“Natural_Scrolling”_Exist,_Anyway?⠀⇛


                 Perhaps you don’t think of it this way, but the way that
                 we interact with the objects we own is not necessarily a
                 given. And this is proven when those not-a-given things
                 change unexpectedly out of the blue. I wanted to talk
                 about one of those things, a small but confusing shift to
                 the way we use computers, a default that befuddles many,
                 but others don’t mind. When it comes to “natural
                 scrolling,” I fall deeply into the befuddled camp.
                 Released with version 10.7 of Mac OS X just over a decade
                 ago, the attempt to reinvent the way our mice and
                 trackpads work felt like an unnecessary flip, but it’s
                 still around a decade later, and most other operating
                 systems now do it as well. Apple convinced people that
                 its way of scrolling was “natural.” Now, while I missed
                 the 10th anniversary of this subtle-but-not-so-subtle
                 change by about five months, I still wanted to get my
                 thoughts about it down way before the 15th anniversary.
                 While the embers of 2021 are still emitting light,
                 today’s Tedium looks back at the moment Apple flipped the
                 way we scroll through things on our computers on its
                 head.


          o ⚓ Foam_Surfboard_From_Scratch⠀⇛


                 Have you ever wanted to make your own surfboard, but felt
                 held back by a lack of tools, materials, or the cost of
                 it? Drawing almost entirely from what can be found at a
                 well-known home improvement retailer, [AndrewW1997]
                 details the steps needed to craft your board.


                 In his guide, he details the difference between XPS
                 (expanded polystyrene) and EPS (extruded polystyrene) and
                 how each product’s closed cell and open cell nature
                 affects the final board. Starting with two pink sheets of
                 XPS, he laminated them together with glue to form his
                 blank. A stringer is a long piece of wood in the middle
                 of the surfboard that provides additional flex and
                 strength. Some flooring plywood curved with a jigsaw
                 provides the shape needed. Unfortunately, the blank needs
                 to be split in half to install the stringer. However, he
                 has a trick for gluing the blank back together without it
                 buckling, and that trick is ratchet straps.


          o § Science⠀➾


                # ⚓ The_Current_State_Of_Play_In_Autonomous_Cars_|_Hackaday⠀⇛


                       Bluster around the advent of self-driving cars has
                       become a constant in the automotive world in recent
                       years. Much is promised by all comers, but real-
                       world results – and customer-ready technologies –
                       remain scarce on the street.


                       Today, we’ll dive in and take a look at the current
                       state of play. What makes a self-driving car, how
                       close are the main players, and what can we expect
                       to come around the corner?


          o § Hardware⠀➾


                # ⚓ The_Three_Cent_Motor_Controller⠀⇛


                       If you follow the world of small microcontrollers
                       you will certainly be familiar with the usual fare
                       of Atmel, ARM Cortex, PIC, and others. But these
                       aren’t the smallest or cheapest devices, below them
                       is an entire category of grain-of-dust
                       microcontrollers with minimal capabilities and at
                       rock bottom prices. Maybe the most well known are
                       the Padauk series of chips, whose PIC12-like
                       architecture can be had for literal pennies. These
                       are the famous 3 cent microcontrollers, but despite
                       their fame they have a bit of a reputation in our
                       community for being difficult to work with. [Ben
                       Lim] dispels some of those ideas, by Padauk-
                       enabling a motor and encoder from a printer to make
                       a three cent motor controller.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Astronaut_Food_Is_Light_Years_Beyond_Tang_And_Freeze-Dried
                  Ice_Cream_|_Hackaday⠀⇛


                       When it comes down to it, we humans have two major
                       concerns when venturing away from home for an
                       extended period of time: what we’ll eat, and where
                       we will sleep. Depending on the mode of travel, you
                       might take some snacks along, or else rely on
                       restaurants and/or the pantry of your possible
                       hosts. Until the day we can reliably grow many
                       types of food in space, or that Milliways, that
                       five-star eatery at the end of the universe is
                       operational, astronauts and other space-bound
                       travelers will have to bring most of their food
                       with them.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Security_updates_for_Wednesday⠀⇛


                                   Security updates have been issued by
                                   Debian (firefox-esr, python-gnupg,
                                   resiprocate, and ruby-haml), Fedora
                                   (mod_auth_mellon), openSUSE
                                   (thunderbird), Slackware
                                   (wpa_supplicant), and SUSE (gegl).


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ Modern_Toilet_Generates_Energy⠀⇛


                             Environmental Engineering [Prof Jaeweon Cho]
                             at South Korea’s Ulsan National Institute of
                             Science and Technology specializes in water
                             and waste management. He has developed an
                             energy-generating toilet called BeeVi
                             (pronounced beevee) that recycles your waste
                             in three ways. Liquid waste is processed in a
                             microbial reaction tank to make a liquid
                             fertilizer. Solid waste is pumped into an
                             anaerobic digestion tank, which results in
                             methane gas used to power a silicone oxide
                             fuel cell to make electricity. The remaining
                             solids are composted to make fertilizer. The
                             daily waste from one person is about 500 g,
                             which can generate about 50 L of methane.


          o § Finance⠀➾


                # ⚓ How_Education_International_is_Pushing_Teachers’_Unions
                  into_the_4th_Industrial_Revolution⠀⇛


                       or nearly a hundred years, the American Federation
                       of Teachers (AFT) and the National Education
                       Association (NEA) – the two largest teachers’
                       unions in the United States – have cozied up to
                       corporate foundations, such as the Rockefeller
                       philanthropies and the Bill and Melinda Gates
                       Foundation, along with multinational technology
                       companies, including IBM and Microsoft. After
                       almost a century of cutting side deals with Robber
                       Barons and Tech Barons alike, the AFT and the NEA
                       are now parroting the Gates Foundation’s “Reimagine
                       Education” campaign, which is being buoyed by the
                       World Economic Forum (WEF) and the United Nations
                       Educational, Scientific, and Cultural Organization
                       (UNESCO). Altogether, the AFT, the NEA, the WEF,
                       and UNESCO are all “reimagining” a new post-human
                       education system as they simultaneously push for
                       ed-tech overhauls. As documented in my
                       investigative series, “Teachnocracy,” these
                       overhauls seek to privatize public schools through
                       partnerships with Big Tech corporations that
                       facilitate online “distance learning” to
                       accommodate indefinite classroom health
                       restrictions in a post-COVID world.


                       In fact, the AFT and the NEA are tethered to the
                       WEF and UNESCO through an entity known as Education
                       International (EI). EI is a Global Union Federation
                       (GUF) that combines “383 member organisations,”
                       including the AFT and the NEA, and collaborates
                       with the WEF and UNESCO. As the intermediary
                       between America’s teachers’ unions and the WEF and
                       UNESCO, EI has been galvanizing the AFT and the NEA
                       into conformity with the “reimagine” ed-tech
                       agendas of these global governance institutions. To
                       put it bluntly, EI puppeteers the AFT and the NEA
                       using marionette strings that are tied to the WEF
                       and UNESCO. In turn, the AFT and the NEA, along
                       with the other 381 member organizations belonging
                       to EI, are being spurred to “reimagine” schools
                       through corporate ed-tech innovations geared
                       towards advancing the Fourth Industrial Revolution
                       (4IR) that is being accelerated by the WEF and the
                       United Nations (UN) through the policy agendas
                       collectively known as the “Great Reset.”


          o § Monopolies⠀➾


                # ⚓ UKIPO_unveils_report_highlighting_influence_of_social_media
                  influencers_(also)_on_the_purchase_of_counterfeits⠀⇛


                       Last week, the UK Intellectual Property Office
                       (UKIPO) released an intriguing report measuring and
                       analyzing (apparently for the first time) the
                       influence that social media influencers exert on
                       consumers also when it comes to purchasing
                       counterfeits.


                       [...]


                       The UKIPO’s findings are based on a quantitative
                       survey of 1,000 female (studies suggest that
                       influencer marketing is “highly gendered”)
                       consumers in the UK, aged 16 to 60 and who use
                       social media at least once per week.


                       In addition, the notion of ‘counterfeit’ was taken
                       to refer to “items that look identical to a genuine
                       product with or without the official branding/logo,
                       but are not made by the brand and may be of lower
                       quality, for example, a handbag of identical design
                       to a “Chanel” with or without the Chanel logo.”


                       While the majority (70%) of those who have
                       knowingly purchased a counterfeit (17% of the
                       surveyed consumers) are aged 16 to 33, 13% of the
                       surveyed persons have their purchasing behaviour
                       relating to counterfeits influenced by social media
                       endorsements and 10% are prompted to buy
                       counterfeits by social media endorsements. The most
                       popular product categories for counterfeit shopping
                       are fashion, accessories, jewellery, and beauty.


                # § Patents⠀➾


                      # ⚓ XIAOMI_Case:_Paris,_the_“New_World”_of_FRAND_–_Kluwer
                        Patent_Blog [Ed: Patent extremist Matthieu Dhenne
                        (Ipsilon), who keeps promoting a crime and a violation
                        of European constitutions (UPC) by peddling fake news,
                        is now pushing the FRAND scam, basically_a_patent
                        fraud; it has been extremely easy to demonstrate the
                        overlap between cheerleaders of EPO corruption,
                        proponents and representatives of patent trolls, Team
                        UPC, and ‘Team FRAND/SEP’]⠀⇛


                             I have already mentioned on many occasions on
                             this blog the difficulties that FRANDs were
                             causing regarding the choice of jurisdiction
                             and the increasingly favorable position of
                             French Courts to SEPs holders. The two
                             decisions rendered by the Paris High Court in
                             the XIAOMI vs. PHILIPS case confirm this
                             trend by holding that the Paris High Court
                             has jurisdiction to set a global FRAND rate,
                             as ETSI is in Nice, France (December 7, 2021,
                             [RG 20/12558] and [RG 20/12558]). I will
                             return below to the context of this decision,
                             before referring to the decision itself and
                             giving my comments on it.


                      # ⚓ The_IPKat_EPO_Enlarged_Board_of_Appeal_(EBA)_Year_in
                        Review_2021 [Ed: The EPO’s_very_own_kangaroo_court,
                        which has not only harmed Europe but also the
                        perception of patent justice and respect for
                        constitutions]⠀⇛


                             2021 has been year brimmed full with juicy
                             case law from the Enlarged Board of Appeal
                             (EBA). The biggest (or at least the most
                             controversial) story of the year was the
                             referral to the EBA on the legality of
                             mandatory ViCo oral proceedings (G 1/21).
                             This year also saw release of the EBA
                             decision on double-patenting and a new
                             referral on the thorny issue of plausibility
                             and post-published evidence. As the year
                             draws to a close, we also have news of a new
                             referral to the EBA on the EPO’s co-applicant
                             approach to priority.


                      # ⚓ The_IPKat_EPO_Boards_of_Appeal_(BA)_Year_in_Review
                        2021 [Ed: Even_the_EPO’s_former_officials_have_blasted
                        these_tribunals, as they’re controlled by the very
                        people whose illegal actions they’re meant to decide
                        on]⠀⇛


                             Following on from our IPKat EBA 2021 Year in
                             Review, here is some more festive holiday
                             reading on some of the important decisions to
                             come out of the EPO Boards of Appeal this
                             year. 2021 saw key decisions on claim
                             supremacy, types of antibody claims, the data
                             threshold for second medical use inventions
                             and the AI inventor debate.


                      # ⚓ University_of_South_Florida_Research_Foundation,_Inc.
                        v._Fujifilm_Medical_Systems_U.S.A.,_Inc._(Fed._Cir.
                        2021) [Ed: The taxpayers pay for it, then it gets
                        privatised with patents]⠀⇛


                             The issue of standing can be outcome-
                             determinative: without it, no matter how
                             worthy a party’s position or arguments, a
                             court will not consider them without
                             standing. The vagaries of standing and its
                             importance were illustrated this fall in the
                             Federal Circuit’s opinion in University of
                             South Florida Research Foundation, Inc. v.
                             Fujifilm Medical Systems U.S.A., Inc.*


                             The action arose over a dispute involving an
                             invention described in the opinion as
                             “Workstation-User Interface for Digital
                             Mammography.” This invention was initially
                             disclosed by faculty at the University of
                             South Florida who assigned their rights to
                             the University. A later assignment of what is
                             presumably a “new and improved” version of
                             the invention was assigned by these inventors
                             five years later, leading to filing an
                             application resulting in U.S. Patent No.
                             6,630,937, entitled “Workstation Interface
                             for Use in Digital Mammography and Associated
                             Methods.”


                             The details of the relationship between the
                             University and University of South Florida
                             Research Foundation (USFRF) are obscured by
                             redactions, but under a nunc pro tunc license
                             agreement (putatively) relating to the ’937
                             patent between these Florida entities, the
                             USFRF filed suit against Fujifilm for
                             infringement.


                      # ⚓ SPC_trends_to_watch_in_2022:_an_EU_review,_the
                        waiver,_Article_3c [Ed: Imagine Managing IP actually
                        asking for the opinions from people outside this price-
                        fixing cartel (but those people are sponsoring this
                        propaganda mill, which isn't a source of journalism but
                        lobbying, with occasional fake news)]⠀⇛


                             Pharma-focused in-house and law firm counsel
                             highlight the most important supplementary
                             protection certificate issues for next year


                      # ⚓ At_the_Drop-Bottom:_Sanford_v._Kepner,_344_U.S._13_
                        (1952).⠀⇛


                             The USPTO interference sided with the first-
                             filer Kepner and so Sanford took the case to
                             Federal Court. Sanford argued (1) that
                             Sanford should have priority as the first-to-
                             invent and thus get the patent; and (2) even
                             if Kepner gets priority, Kepner’s patent
                             should still be invalidated based upon the
                             prior art. (“Void for lack of invention.”)
                             The Pennsylvania district court sided with
                             the first-filer Kepner on priority grounds,
                             and refused to decide the question of
                             patentability. Sanford v. Kepner, 99 F. Supp.
                             221, 222 (M.D. Pa. 1951). On appeal, Sanford
                             argued that the district court should have
                             decided the validity question also, but the
                             appellate court affirmed. Sanford v. Kepner,
                             195 F.2d 387, 390 (3d Cir. 1952). In
                             particular, the 3rd Circuit explained that
                             once the priority issues are decided, the
                             plaintiff would need some additional
                             justification to maintain standing: “some
                             manifest threat … or interference with the
                             activities of the petitioner beyond the
                             issuance of a patent to another is required
                             to create a controversy justiciable under the
                             Declaratory Judgment Act.” Id. The Supreme
                             Court then took up the case and again
                             affirmed, with Justice Black writing a short
                             opinion for a unanimous court. Sanford v.
                             Kepner, 344 U.S. 13 (1952).


                      # ⚓ FOSS_Patents:_Daimler_takes_Avanci_patent_license–all
                        major_German_car_makers_now_Avanci-licensed,_but
                        Volkswagen_only_up_to_3G⠀⇛


                             Germany’s leading business weekly,
                             Wirtschaftswoche, has just been first (and I
                             might still be second) to report that Daimler
                             has finally taken a standard-essential patent
                             (SEP) license from the Avanci pool, whose
                             licensors include Qualcomm, Nokia, Ericsson
                             as well as dozens of other companies from
                             around the globe.


                             If you can’t beat’em, join’em.


                             It was actually Avanci’s approach of
                             licensing the end product–the vehicle as
                             opposed to a component thereof–which Daimler
                             had originally rejected. As a result, the
                             Nokia v. Daimler patent infringement dispute
                             lasted more than two years and ended in a
                             bilateral (just Nokia and Daimler) license
                             agreement that was announced on June 1, 2021.
                             Daimler had also brought an EU antitrust
                             complaint (over Nokia’s refusal to grant
                             Daimler’s suppliers an exhaustive SEP
                             license) that it withdrew after the
                             settlement.


                             Prior to settling with Nokia, Daimler had
                             already taken bilateral licenses from
                             Japanese electronics giant Sharp and non-
                             practicing entity Conversant Wireless. All
                             those companies–plus Japan’s IP Bridge–had
                             sued Daimler in Germany over patent
                             infringements. And all of them are among the
                             Avanci pool’s more than three dozen
                             licensors.


                             [...]


                             C-level interest in IP differs greatly
                             between the automotive industry and Big Tech.
                             Big Tech CEOs have subscribed to this blog
                             and the related Twitter account, but I’m not
                             aware of the top brass of automotive
                             companies ever having subscribed to FOSS
                             Patents.


                             As Daimler’s Avanci license shows, the
                             automotive industry has to come to terms with
                             the fact that major wireless companies are
                             now in the position to impose their preferred
                             business models on car makers, no matter how
                             much the auto industry may point to century-
                             old traditions regarding their supply chains
                             and what have you.


                             The battle over the business model is
                             practically over. Daimler’s legal fees are a
                             sunk cost, and its financial controllers will
                             be crying tears. What all car makers–above
                             all, Volkswagen–need to reflect on now is how
                             to achieve the best results possible under a
                             framework that wasn’t their first choice, but
                             which has simply prevailed. They’ve all
                             learned a few lessons in recent years–and
                             they’ve paid their tuition fees. The problem
                             they face is that the world around them is
                             changing faster than their organizations can
                             adjust. Increasingly they’re going to face
                             competition from companies that hold SEPs,
                             such as Apple, Google, or Xiaomi. In times of
                             transformation, leadership from the very top
                             of those organizations is needed. Otherwise
                             the only beneficiaries will continue to be
                             patent litigation firms.


                      # ⚓ European_Patent_Office_ruling_on_indoor_farming
                        patent_published [Ed: EPO once again admitting that it
                        granted fake patents for_the_sake_of_faking_growth.
                        This has profound impact on everybody.]⠀⇛


                             The European Patent Office this week
                             published its decision revoking a previously
                             granted patent on indoor farming. PlantLab,
                             which owned patent EP2348841, and Certhon
                             together with partner Signify have been
                             fighting a legal battle over the patent for
                             years.


                             Last month, when the decision was made, both
                             parties responded.


                             John van der Sande, Chief Innovation Officer
                             at Certhon, commented, “The fact that the
                             European patent on indoor farming is not
                             valid is, as we indicated earlier, a victory
                             for the entire industry.”


                      # § Software Patents⠀➾


                            # ⚓ E-Mail_Read_Status_Indication:_Non-Technical
                              [Ed: Preston Richard from the software_patents
                              boosters at Bardehle Pagenberg (promoting illegal
                              agenda at the EPO)]⠀⇛


                                   This decision relates to a European
                                   patent application that concerns
                                   displaying e-mail messages with E-mail
                                   read status indication. The Board
                                   decided that the rule defining when the
                                   flag is to be switched is not based on
                                   any technical considerations as it
                                   reflects an administrative choice or
                                   the user’s subjective preferences. Here
                                   are the practical takeaways from the
                                   decision T 1227/17 (E-mail read status
                                   indication/UNIFY) of November 19, 2021,
                                   of Technical Board of Appeal 3.5.01:


                # § Trademarks⠀➾


                      # ⚓ On_Remand_from_the_CAFC,_TTAB_Denies_Petition_for
                        Cancellation_of_“NAKED”_Registration_for_Condoms⠀⇛


                             The NAKED condom case returned to the TTAB
                             after a CAFC reversal [TTABlogged here] and
                             the Supreme Court’s denial of the
                             registrant’s petition for writ of certiorari
                             (September 2021). The CAFC ruled that the
                             Board erred in concluding that Petitioner
                             Australian Therapeutic lacked “standing” to
                             bring its petition for cancellation, pointing
                             out that a petitioner need not have a
                             proprietary interest in a mark to have
                             standing. On remand, the Board has denied all
                             three of Australian’s claims: Section 2(d)
                             likelihood of confusion (due to lack of
                             proprietary rights in its purported marks
                             NAKED and NAKED CONDOMS), lack of bona fide
                             intent, and Section 2(a) false suggestion of
                             a connection. Australian Therapeutic Supplies
                             Pty. Ltd. v. Naked TM, LLC, Cancellation No.
                             92056381 (December 16, 2021) [not
                             precedential] (Opinion by Judge Marc A.
                             Bergsman).


                # § Copyrights⠀➾


                      # ⚓ Misbeliefs_must_not_derail_Hong_Kong_SAR_copyright
                        reform [Ed: Stop calling copyright law "IP regime" and
                        other such nonsense; also, stop suggesting that
                        rejection of patent and copyright maximalists/
                        extremists means you "fall behind other major
                        jurisdictions" (this 'domino bricks' strategy, which
                        relies on blackmail by shaming, is used by malicious
                        cartels]⠀⇛


                             Sources say proposed amendments to the
                             region’s copyright law are necessary to
                             ensure that its IP regime doesn’t fall behind
                             other major jurisdictions


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