𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, January 01, 2022
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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/2022/01/01/


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

⦿ My Year as a Digital Vegan — Part VIII — Who Teaches the Teachers? | Techrights

⦿ Schools Are Not Vendor Certification Mills, They’re Meant to Teach Pupils/Students | Techrights

⦿ 2021 Was a Fantastic Year for Gemini, 2022 Might be the Same | Techrights

⦿ In 2022 We Should Quit Calling it Google and Explain What It Has Really Become: Gulag (Goolag) | Techrights

⦿ IRC Proceedings: Friday, December 31, 2021 | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/01/01/article-on-digital-rights-in-2021-part-8/#comments
		http://techrights.org/2022/01/01/gafam-schools/#comments
		http://techrights.org/2022/01/01/gemini-2021-review/#comments
		http://techrights.org/2022/01/01/google-goolag-or-gulag/#comments
		http://techrights.org/2022/01/01/irc-log-311221/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/01/01/gnu-alive-2-0-4/#comments
		http://techrights.org/2022/01/01/happy-new-year-2022/#comments
		http://techrights.org/2022/01/01/septor-2022/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 61

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/01/article-on-digital-rights-in-2021-part-8/#comments
    Gemini version at gemini://gemini.techrights.org/2022/01/01/article-on-digital-rights-in-2021-part-8/

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Gemini_version_available_♊︎


✐ My_Year_as_a_Digital_Vegan_—_Part_VIII_—_Who_Teaches_the_Teachers?⠀✐


Posted in Free/Libre_Software, GNU/Linux, Google, Microsoft at 3:24 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. My_Year_as_a_Digital_Vegan_—_Part_V_—_Change_in_Societal_Norms_and
      Attitudes
   6. My_Year_as_a_Digital_Vegan_—_Part_VI_—_The_Right_Words
   7. My_Year_as_a_Digital_Vegan_—_Part_VII_—_Staying_the_Course_and_Fake_It
      Till_You_Make_It?
   8. YOU ARE HERE ☞ Who Teaches the Teachers?
                      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Some teachers⦈


Summary: Dr. Andy Farnell explains the oft-overlooked, oft-ignored, oft-
forgotten problems associated with outsourcing schools to tech monopolies and,
by doing so, giving unjust control to surveillance-centric firms (usually
foreign if not hostile to one’s country) over children’s lives and their future


Taking back tech in education is a major challenge for everyone in digital
rights.


Being a teacher, and also a parent, many of my battles for fair and ethical
technology are within educational institutions. I’ve been raising awareness of
digitally mediated abuse in schools and universities, such as invasive_student
monitoring and the degeneration of our schools’ privacy and integrity as Google
and Microsoft “infrastructure” intrudes into places it does not belong.


“Parents have a vague idea that “technology is good” because we “don’t
want kids left behind”. Both ill-formed sentiments are pernicious.”We all want
the best for our students and our own kids. But when it comes to understanding
whether educational technology (and the administrative technology we use) is
good or bad for them I think we are clueless, and we ought to admit that.


Parents have a vague idea that “technology is good” because we “don’t want kids
left behind”. Both ill-formed sentiments are pernicious. We should want our
children to learn about technology, not be taught by it. And “being left
behind” is not a warning, it’s a threat. Teachers think that all and any
technology is unquestionably good. The myth of digital literacy uber alles,
being an unqualified good for the economy, has remained unexamined since the
1980s. We conflate mere exposure to tech with understanding, and with life
value.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Free but restricted entry⦈ I’ve pushed back a lot against
the disgraceful_scam that is “Turnitin”, first criticised by Dutch technology
writer Hans_de_Zwart as the plagiarism monopolist, with onerous terms that
demand a “royalty-free, perpetual, worldwide, irrevocable license” to students’
works. Turnitin is the poster child for everything wrong with careless
application of “algorithms” to human trust problems.


For one thing, plagiarism detectors are like “lie_detectors”. Although the
theory looks impressive, in_reality they are merely intimidation devices, as
Bayesian Analysis with first order Markov chaining produces a laughable
avalanche of false positives. They are bad algorithms that effect a
disproportionately negative impact on the lives of young people, almost always
without their explicit consent.


“Digital Veganism is a family thing too.”Far from improving student behaviour
we encourage an assignment cheating arms-race that feeds essay_mills. I design
assignments such that we don’t need to worry about plagiarism, make sure that,
wherever possible, automatic submission is unchecked in Moodle systems, and
explicitly warn my students where I think their rights are being violated.


I’ve written about the flexibility, equality and low-bandwidth ecological
benefits of text_based teaching methods – amidst which came the unexpected
demise_of_Freenode.


Digital Veganism is a family thing too. This year a moment of great pride has
been watching my daughter log onto her Unix system with her username and non-
trivial password, then type on the command line to play her favourite music.
She’s also been helping me teach_some_classes, and chastising adults pawing
their_smartphones for “not paying attention to their children”.


Careful technological parenting makes its demands. Every letter from the school
about some new “Lunch monitor system” might require push-back and a little
explaining to a teacher about “why that doesn’t work for us”. On the other
hand, I’ve had overwhelming support from parents for kids “hacking classes”
(where we actually teach Python), so much that they badger me in the street and
home asking when the Covid subsides will I run them again? Demand for real
technological teaching feels insatiable.


I think the sociological interplay around technology and education is
fascinating. Most of us have no real idea what is good or dangerous technology
for young people in our care, but we have to muddle through and pretend we do.
Especially for teachers – why should they? Most will just uncritically use the
tools they are told to 3.


The way that technically disenfranchised adults vicariously shrug their
heteronomy via kids is astonishing. In some ways it’s heartwarming, in that we
still believe they can build a better future and be more courageous than us.
But it’s also pitiful. This happens when we say “Kids are whizzes, they know
all about technology”, or “Don’t worry they will just figure it out”. This is
dangerous romanticism and shrugging of responsibility. I wrote about this
complex psychology in Digital Vegan, citing real examples from social work in
which “role reversal” takes place and children are forced to “be the adult” in
a world where the actual grown-ups have given up 4.


“Teaching children to take control of technology, to master it, use it to
express their creative and intellectual energy, and to explore a library of
carefully curated knowledge is what we can achieve.”Because of Covid again this
year I was unable to attend ICICTE, the unbelievably cool Greek conference
where freethinking teachers, sysadmins and researchers come to share ideas on
using technology creatively for teaching. You’ll appreciate, I have a lot of
amazing arguments there with people who disagree with me. And then we get drunk
together until 4am. There’s a lot more work to do with advancing the idea of
“Digital_Self_Defence” as an approach for kids as young as five.


Teaching children to take control of technology, to master it, use it to
express their creative and intellectual energy, and to explore a library of
carefully curated knowledge is what we can achieve.


Luring children into a lifetime of helpless dependency on expensive products
that work as dark magic, over which they have no control, which expose them to
hostile entities and damaging ideas, all while allowing corporate data vampires
to juice their souls dry is what we have achieved. And it’s a deplorable
tragedy we should be ashamed of.


“Luring children into a lifetime of helpless dependency on expensive products
that work as dark magic, over which they have no control, which expose them to
hostile entities and damaging ideas, all while allowing corporate data vampires
to juice their souls dry is what we have achieved.”Parents nod mindlessly to
the platitudes and empty “assurances” given by heads or school boards, yet no-
one involved has the requisite technical knowledge to make or evaluate such
assurances.


Administrators literally say stuff like; “I can assure you this software is
absolutely safe.”


So ask them;


     “Do you have any knowledge of cybersecurity?”


     “No.”


     “Do you know who wrote the application?”


     “No.”


     “Do you know if it uses a client or server-side model?”


     “Err, No.”


     “Do you know where data is stored?”


     [embarrassing silence]


     “Have you read the source code?”


     [embarrassing silence]


     “Have you any basis whatsoever to feel you can sincerely
     offer me any assurances?”


     [long embarrassing silence]… “No.”


Here’s a little problem;


Anyone who has opened a newspaper in the past twenty years should have a little
enough knowledge of cybersecurity to know that applications written by
convicted criminals store your child’s data outside the school and that nobody
has ever seen the extremely-badly written source code, and so nobody can attest
to its safety.


So, with respect, one must say:


     “please don’t embarrass us both by claiming you can offer
      assurances”.


Most-times though, the conversation is more like;


     “I can give you assurances that this software is absolutely safe.”


     “Oh, assurances, why didn’t you say so. You’re obviously some kind of
     expert. Please sell my kid’s life to corporate monsters”


By tacit conspiracy of avoidance we construct a “theatre of fake
understanding”. It is a folly of overconfident negligence that puts our
children at risk. I am staggered that, other than parents who work in IT or
security, so few of the other parents at my child’s school are educated on the
issues. They are aware of the issues, but that isn’t the same. Strange
confusions of 5G virus or radiation risks are unhelpful.


All are made fools by the salesmen, Microsoft and Google lobbyists who want to
exploit the lives of our children. I believe more and more that corporate edu-
tech is utterly unfit for purpose, offers no substantial advantages, has no
useful place in education up to university level.


I think that for school ages 0 – 17 (primary and secondary):


    * Government mandate open-source Libre software
    * Software used in schools meet the general approval of PTA board
    * Any Parent, Teacher or Child5 may audit the code and raise concerns
    * Parents unsatisfied with the security or ethics of any code or data
      handling have an unchallengable right to require an alternative be used
      or to abstain their child from a system.
    * Compatability regarding “employability” or “industry standards” should
      not be a concern below the age of 17. █
_______


✐ Footnotes:⠀✐


3 Which I actually think is a problem. It’s telling that some sceptical
teachers might refuse to participate in organising vaccinations (which is their
– misguided in my opinion – prerogative), yet they would compliantly expose
children to insecure Microsoft software that can damage a kid’s whole life.


4 For example; this happens when a child (who speaks English) of immigrant
parents who do not speak English, intermediates with police, sometimes having
to translate traumatising crime details like rape. This inappropriate pre-
mature role is what is happening when we abdicate responsibility for technology
so that kids have to manage their own digital self-defence.


5 Children learning that they have a stake and agency in the machinery that
runs their lives is a cornerstone of Civic Cybersecurity. There is no age too
early to start.


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⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⡩⠁⠀⠀⢀⣤⠁⠀⢾⣿⡗⠀⠀⠀⠀⠀⠛⢣⡀⠀⠀⠀⠀⠈⠀⠀⢘⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣼⣬⣤⣼⣿⣧⣧⠉⠉⠓⠛⢉⠅⣰⣿⢁⣷⣾⣶⣶⣿⣿⣛⡏⠀⣞⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⣴⡿⡟⠹⠀⠈⠋⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⢀⣴⢰⣆⠀⢺⠻⠛⠝⢿⠧⢸⣴⣶⣿⣿⣷⣤⣤⣿⣿⣿⠹⠩⠉⣷⡆⠀⠦⠀⠨⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡏⠸⠁⠀⠀⠀⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⡏⣹⣼⡇⠀⣾⣠⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢠⡔⠀⠀⠀⠀⡄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣀⠀⡤⠀⠀⢀⣤⠨⣿⠿⠀⠀⣄⠀⣠⢻⣿⣽⣦⢀⠿⠛⢿⣿⠛⣿⣿⣿⡛⢻⣿⣉⢿⡿⣿⣿⣿⣿⣿⣿⠇⡀⠀⠀⡅⠰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣤⣿⣿⣥⠦⠤⠐⠀⠀⣧⣀⣽⣤⣀⣠⠀⡆⣰⣿⣬⢽⣷⡠⢾⣿⣦⣿⣿⣿⣾⣿⣦⡥⣿⣿⣿⡄⠚⠿⣧⣾⡯⣶⣿⣿⡟⠁⢻⠧⠲⣼⣶⣍⠘⣧⡄⠹⣷⣷⣷⣶⣶⣿⣶⣶
⠁⠀⣀⣀⡀⠀⠀⠀⣠⠤⣿⣿⣾⣯⣭⡍⠝⠀⠀⠀⠀⠐⡿⠫⠀⢿⠟⠁⠀⠽⠹⣖⡛⣹⣬⣻⠀⠀⣶⡂⢉⢨⡇⢀⣉⣿⠀⢀⡀⠁⢰⡿⠿⠺⡿⣇⣲⢿⢶⡿⡿⡇⡼⣾⡻⠃⠰⣽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣶⢰⠟⠛⣴⣿⣿⣗⠏⢹⣿⣿⣿⣿⣿⣿⡄⡀⠀⢠⣾⡥⡁⣀⣀⣸⣾⣧⣼⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡷⣿⣏⣫⣿⣾⡂⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣂⣸⠤⣿⣿⡿⣿⠄⠈⣿⣿⣿⣍⣿⣟⣷⡾⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣾⡔⢻⠀⠀⠈⢿⣿⣿⣿⡿⣿⡿⣯⣿⣿
⠢⠈⠈⢐⣈⣉⣥⣵⣶⣿⣿⣿⣿⣧⡼⣿⡿⠀⡀⢰⣿⡟⠿⣿⢟⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠃⠁⣿⣿⣿⣿⣛⠯⠿⢿⣿⣿⣿⣿⣾⣿⣿⠁⢀⣀⣤⣄⣼⣿⣿⣿⣿⣿⢾⣮⠏⢿
⣶⣾⣿⣿⣿⣿⣟⢿⣚⣻⣿⣿⣿⣿⡷⠂⠛⠀⡀⣘⠟⠇⠀⣻⣯⣷⡶⢛⣷⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠷⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣇⠸⢛⡻⢿⣿⣿⣿⣿⣿⣿⠇⣿⣻⣷⣼
⣿⣿⣿⣿⣿⣿⣿⣿⡖⣿⡟⣌⠋⠉⣄⡀⠀⠀⢻⠋⠼⠀⢀⣶⣞⣃⡴⠟⠁⢬⣷⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⢿⣟⣿⠿⢹⡸⠿⠿⢛⣩⣾⣿⣿⡿⢿⡿⣿⣟⡦⣵⣿⢖⠌⢙⣿⣶⠿⢿⣯⣤⣭⣴⣿
⣿⣿⣟⣿⢿⣿⣿⣿⠀⣿⣏⣽⡄⠀⢹⣿⡇⠀⠀⠀⠀⣀⠐⡲⠟⠉⠉⠀⠀⠀⢨⣴⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣧⣿⣛⢧⡌⠙⠒⠋⢿⣿⣿⣿⣿⡿⠙⠈⡿⠟⣺⣿⣏⡛⠗⠑⣥⣕⣾⣫⣤⣤⣤⣝⣷⣾⣷⣿
⣿⣿⣿⣿⣾⣸⣿⡟⠑⠻⣧⢹⢇⣀⣸⣛⡂⠀⠀⢱⠶⠿⠀⢄⣤⣤⣤⣤⣶⠖⢐⣿⣿⣷⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠃⢀⡳⠀⡀⢠⣿⣿⣿⣟⣅⣶⡠⢸⡊⣽⣿⣌⣙⣷⣶⠾⠟⢿⣷⣬⠉⣿⢜⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣻⣿⣥⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⢿⣻⣽⣾⣿⣧⣀⣉⣁⣉⣉⣤⣴⣶⡶⣶⣿⣿⣷⣿⠿⢿⣿⣯⣿⠋⠀⠀⠈⠀⠈⠀⠜⠻⠟⠯⠞⠫⠋⠀⢸⠖⢹⣿⣿⠟⠛⠓⠲⡀⡐⣤⣽⢳⡿⢠⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣯⣭⣭⣤⣤⣼⣿⣿⣶⣿⣷⣶⣄⣤⣤⣶⣶⣶⣶⣦⣤⣤⣶⣾⣿⣤⣸⣿⠇⣀⣄⡠⠤⣀⣭⣶⣭⣭⣤⣤⣬⣭⣭⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣟⣭⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⣍⣁⡀⠰⣕⣒⢀⢂⣠⣀⣉⡙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣀⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠠⠇⠋⠉⠍⡙⢉⢏⢭⠉⡉⢉⠹⠿⠷⠶⡉⡛⠉⢛⣿⣻⣿⣿⣿⠋⠣⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⣷⣶⣶⣶⣶⣷⣾⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡬⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠒⠐⡂⣐⣦⣢⣮⡴⣦⣦⣆⣈⣶⣃⣀⣓⣐⣬⣤⣴⣭⡍⠋⠙⠉⡉⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⡋⢹⣿⣿⣿⣧⣯⡟⣳⣴⢹⣿⣿⣿⣿⣿⣿⡟⣿⠠⡀⠀⠄⢘⠑⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢹⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⣿⣤⣮⣦⣦⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠉⠉⠉⣿⣿⣿⣿⣿⡿⡽⣿⣿⣿⣿⣿⣿⣿⣯⡫⠙⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠩⠑⣿⣿⣿⣧⣺⣿⣿⣿⣿⣿⡏⠑⣃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣅⣄⣈⣉⣁⣐⣬⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⣿⣿⠀⠀⢸⣿⠋⠀⠀⣀⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣀⣸⡇⠀⠀⠙⢿⣿⡗⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⢻⣄⠀⠈⢻⣿⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠘⢿⠀⠀⢸⠃⠀⠀⣾⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠛⠛⠛⢻⡇⠀⠀⠀⠀⠹⡇⠀⠀⢹⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠸⠿⠂⠀⢀⣿⣦⡀⠀⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣦⡀⠀⠀⠀⢸⡆⠀⠀⢿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣤⣤⣤⣼⡇⠀⠀⣷⣄⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⢠⡀⠀⠀⢿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣄⠀⠀⢸⣿⣤⡀⠀⠈⠁⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠉⢹⡇⠀⠀⣿⣿⣷⡄⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⢸⣿⡄⠀⠈⢻⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣶⣶⣿⣿⣿⣷⣶⣾⣿⣿⣶⣶⣾⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢹⣿⣿⠀⣿⣿⣿⡏⢹⣉⣉⠉⢉⣉⣉⠉⢹⣿⣿⡏⠉⣿⠟⠉⣉⡉⠙⢻⣿⠉⢉⡉⠙⣿⠉⢹⠟⢉⡉⢹⡏⠉⠉⠉⢹⡏⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤⠀⢻⣿⠀⣿⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⠀⠘⠛⠛⠃⠀⡏⠀⣾⣿⣿⣷⠀⢹⠀⠘⠋⢀⣿⠀⢸⣄⠈⠻⣿⡇⠀⠛⠛⢻⡇⠈⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣤⣤⠀⢻⠀⠹⠿⠿⠃⢸⣿⣿⠄⢸⣿⣿⠀⢸⣿⣿⡇⠀⣧⡀⠻⢿⡿⠟⠀⣼⠀⢰⣆⠈⢿⠀⢸⠻⢷⡆⠈⡇⠀⣶⣶⣾⡇⠀⣿⣿⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣧⣴⣿⣦⣤⣤⣶⣿⣿⣿⣧⣼⣿⣿⣦⣼⣿⣿⣧⣤⣿⣿⣦⣤⣤⣴⣾⣿⣤⣼⣿⣧⣤⣤⣼⣦⣤⣤⣴⣧⣤⣤⣤⣤⣧⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠿⠿⠿⠿⣿⠿⠿⠿⣿⣿⣿⠿⠿⣿⣿⣿⡿⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⠀⢹⠀⢠⣤⣤⣾⠀⢠⣤⠀⢻⠁⢠⣤⣸⡟⠁⣠⣤⣤⡀⠻⣧⠀⠘⢿⣿⡇⠀⣿⠀⠘⢿⣿⡇⠀⣿⠀⣤⣤⣤⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⣁⣠⣼⠀⢀⣉⣉⣽⠀⢈⠁⠠⣿⣦⣀⠉⠻⡁⢸⣿⣿⣿⡷⠀⢳⠀⣷⡀⠙⠇⠀⣿⠀⣷⡀⠙⠇⠀⣿⠀⣉⣉⣉⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⠘⠛⠛⢻⠀⢸⣷⡄⠙⠉⠛⠃⢀⣧⡀⠙⠛⠛⠁⣰⣿⠀⣿⣿⣦⡀⠀⣿⠀⣿⣿⣦⡀⠀⣿⠀⠛⠛⠛⣿⠀⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣶⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣾⣿⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⣿⠟⠛⢿⣿⣿⡟⠻⡿⠛⣿⣿⡟⠛⢿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣶⣿⣶⡄⠘⡇⠀⡈⠻⣿⡇⠈⡇⠀⣿⣿⣿⣦⡈⠛⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣿⣿⠇⠀⡇⠀⣿⣆⠈⠃⠀⣧⠀⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣉⣁⣠⣾⣇⣀⣿⣿⣷⣄⣀⣯⣀⣉⣉⣉⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 416

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/01/gafam-schools/#comments
    Gemini version at gemini://gemini.techrights.org/2022/01/01/gafam-schools/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Schools_Are_Not_Vendor_Certification_Mills,_They’re_Meant_to_Teach_Pupils/
Students⠀✐


Posted in Free/Libre_Software, GNU/Linux, Google, Microsoft at 7:47 pm by Dr.
Roy Schestowitz


Video_download_link | md5sum 13afb64f5bd01ca9289d8263f6ce0f73


http://techrights.org/videos/edu-tech.webm


Summary: Rather than teach students how to work with technology many schools
are training them to become subjects of technology giants, sometimes from
another country that has no respect for basic human rights


ALMOST 4 years ago the US passed_a_law — without any public debate! — that
would formally turn GAFAM into corporate eyes of Five Eyes (which is now Six
Eyes because Japan officially joined “the club”).


“We must protect not only the dignity of youngsters but also their families’;
they never explicitly consented to such abuse.”Many people somehow think — or
have managed to convince themselves — that it is perfectly normal to outsource
schools/universities and their data to spy agencies. Thankfully, the likes of
Dr. Andy Farnell stand_in_their_way and persistently explain why this status
quo should be rejected. Schools of all sorts should hire suitably trained
people who know how to manage stuff such as E-mail (not sign some paperwork
that sends it to spying companies) and can give students real skills, including
the use of freedom-respecting software that does not harvest data (e.g. LaTeX/
LyX/Kile and LibreOffice instead of Google and Microsoft stuff). We’ve long
argued that schools should also teach GemText or similar, not HTML, as the Web
is a monopolised and overly complicated platform with DRM. It’s not useful for
education.


The video above adds some thoughts to Dr. Farnell’s article. I’ve attempted to
merely add some things which merit a mention; there are ethical — not just
financial — considerations. We must protect not only the dignity of youngsters
but also their families’; they never explicitly consented to such abuse. █



                    ䷩ 𝚕𝚒𝚗𝚎 475

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/01/gemini-2021-review/#comments
    Gemini version at gemini://gemini.techrights.org/2022/01/01/gemini-2021-review/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ 2021_Was_a_Fantastic_Year_for_Gemini,_2022_Might_be_the_Same⠀✐


Posted in Site_News at 8:12 am by Dr. Roy Schestowitz


Video_download_link | md5sum 0ace1ff5c356d9e31fffcd3716e91e16


http://techrights.org/videos/gemini-2021-review.webm


Summary: A look back at 12 months of Gemini (or gemini://), which brings us
about half a million page requests each month


THE transport and presentation of pages in the Internet ought not be
monopolised by the World Wide Web, i.e. HTTP/S and HTML (though the latter is
nowadays mostly JavaScript frameworks, i.e. the ‘new Flash’ with DRM on top of
it).


“Let’s see if this year Gemini can double or triple in terms of adoption. In
recent months it enjoyed linear growth…”Gemini started less than 3 years ago
and last year was a highly successful year for it. The number of working
capsules grew sharply, many new services and capsules became available (without
stretching the standard), and nowadays it’s possible to get all sorts of
information without even opening a Web browser. I don’t use browsers all that
much anymore (RSS readers, terminals, text editors and Gemini clients cover
much ground already).


The video above presents some evidence of the growth and various use cases. We
showed many use cases in the past. Searching Gemini space isn’t hard, it’s not
monopolised (there are several potent options), and there’s plenty of code one
can (re)use to convert an existing Web site into a Gemini capsule. Not much
ought to be done from scratch and the learning curve/access barrier is low.
Let’s see if this year Gemini can double or triple in terms of adoption. In
recent months it enjoyed linear growth, so one can predict by extrapolation
that there will be 2,000 working capsules before spring and maybe 3,000+ by the
end of this year. We’ll try to keep track of the steady growth and point out
new capsules of interest (especially when they offer something unique).
Interpolation and extrapolation with statistics will help us assess the general
‘health’ of Geminispace. The good news is, this past year we see no corrupting
corporate forces, neither in the specifications nor in Gemini space. It’s 100%
genuine people; no spam, no advertising, no state/corporate propaganda. Unlike
social control media, there’s no censorship and it’s likely that none is need.
█



                    ䷩ 𝚕𝚒𝚗𝚎 539

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/01/google-goolag-or-gulag/#comments
    Gemini version at gemini://gemini.techrights.org/2022/01/01/google-goolag-or-gulag/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ In_2022_We_Should_Quit_Calling_it_Google_and_Explain_What_It_Has_Really
Become:_Gulag_(Goolag)⠀✐


Posted in Google at 9:18 pm by Dr. Roy Schestowitz


Related (Google-funded trolls in 2021): Professional_Troll_Matthew_Garrett
Spreads_Libel,_Defamation_and_Slander_About_the_Free_Software_Community_to
Entertain_Microsoft_and_Friends


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


Summary: Considering how Google treats people in sites like YouTube, it has
become clear that the company operates more like a forced_‘labour_camp’ for
“content” “creators” or “generators” or “users” (people who get used, and whose
sole purpose is to help Alphabet profit from ads and spy on everybody, with a
site that won’t even work without cookies and JavaScript)


⣿⡿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣛⢿⣿
⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽
⣿⣻⣿⡿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢟⣻⣿⣿
⣿⡿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣟⣿⣿
⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽
⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢟⣻⣿⣿
⣿⡿⣋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣩⣟⣿⣿
⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽
⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⢻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⢿⣿⢿⣿⡿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢟⣻⣿⣿
⣿⡿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣛⣿⣿
⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽
⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⣿⠾⠿⠿⡿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢟⣻⣿⣿
⣿⡿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⣟⣿⣿
⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣛⣋⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⡷⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣟⣿⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡯⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣺⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽
⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠻⠿⠟⣿⠽⠯⠾⠳⣿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⢻⡟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣻⣿⣿
⣿⡿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⣛⣿⣿
⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣽
⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⢿⠿⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠥⠿⠿⣿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣻⣿⣿
⣿⡿⣋⣹⣻⣿⣿⣿⣿⣟⣿⣿⣚⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣩⣟⢿⣿
⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣧⣽⣿⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⢸⢺⣿⣿⣿⣿⣿⣿⣽⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽
⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⢿⠪⠿⠿⠿⠿⠿⠿⣾⠾⠿⠿⠿⠿⠿⠾⣿⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠭⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢟⣻⣿⣿
⣿⡿⣋⢩⣾⣾⣿⣿⣟⢿⣏⣼⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣻⢿⣿
⣟⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢼⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣽
⣿⣿⣿⣿⠿⢿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠇⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢻⠸⠿⠿⠻⠽⠿⠿⠿⠿⢻⡟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢟⣻⣿⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⢿⣿
⡟⠀⠀⠀⠀⢠⣶⣶⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⠁⠀⠀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⡋⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠉⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⢼⣿⣿⣿⣿⣷⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠁⣿⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣰⣦⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⠏⠈⠛⠛⣫⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⠫⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠎⠏⠐⠉⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣾⣿⣿⣿⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⣿⣿⣿⣿⣿⠋⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⣿⣿⣿⡟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⣿⣿⣿⠿⢿⠷⠾⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠛⠛⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣤⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣶⣯⣄⡀⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢀⣺⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⢀⣼⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⣼⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣤⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠻⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠉⠙⠙⡿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠿⣿⣿⣿⣿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠰⠁⠀⢻⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡌⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣿⣿⣿⣿⡿⠉⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢀⣿⣿⣿⣿⠏⠀⠀⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣿⣿⠿⢿⣿⠾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠉⠙⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣾⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⣠⣴⣀⣠⣵⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣴⣦⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢨⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⢀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠿⢿⡏⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣦⣶⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠉⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠿⣿⡏⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⣿⣿⣿⣿⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣾⣿⣿⣿⡿⢹⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⡿⠋⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣿⣿⠿⢿⡷⠾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠉⠀⠀⠀⢸⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⣹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣀⣜⣿⣿⣿⣿⣿⣷⣷⣦⣶⠆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⢰⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⡟⠛⠿⡿⠟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣠⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⡿⣿⣿⣿⣿⠋⠻⣿⡟⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣤⣤⣤⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⡿⣿⡏⠀⢠⣿⣿⣿⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣶⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠋⢉⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣼⣿⣿⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠉⠻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⣿⣿⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠘⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⣿⣿⠿⠋⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣿⣿⠿⣿⠷⠾⠾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣾⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⡀⠀⠀⣤⡀⠀⠀⣀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡿⠿⠛⠋⣹⣿⣿⣿⡿⠀⠀⠀⠀⠀⣹⢀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣄⠀⢸
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⡻⡿⠏⠀⠙⠻⠿⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠄⢸
⠀⠀⠀⠀⣼⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣷⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⢿⣿⣿⣿⠀⠀⠈⠉⠉⠉⢹⠀⠀⠀⠀⢸
⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⢺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢸⠃⠀⠅⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⣤⣤⣤⣴⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁⣹⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸
⠀⠀⣿⣿⣿⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠋⢉⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⢹⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣿⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠈⣿⣿⣿⣿⣇⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠘⢻⣿⡧⠜⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣾⣿⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠟⣟⠏⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸
⣿⣾⣷⣾⠿⣷⠷⠼⠾⠷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⣶⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣙⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⢀⣀⣸⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⢹
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠿⠿⠛⠋⢡⣿⣿⣿⠟⠀⠀⣸⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⣿⠃⠀⢸
⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠐⠀⠈⠉⡍⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣤⣀⣤⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣇⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⣽⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⢿⣿⣿⣿⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⡏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠈⡇⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣤⣀⣀⣤⣾⣿⣿⣿⣿⡿⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸
⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠁⠀⠀⠈⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸
⣿⣾⣶⣶⠿⢷⡷⠸⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣠⣶⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡄⠀⠀⠀⠐⠲⢶⣾⣷⣧⣍⡙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣾⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠄⢹
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠿⠟⠛⠉⢠⣾⣿⣿⡿⠿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⠟⠀⢈
⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⢸⠉⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⠈⠛⠟⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⢈
⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡇⠀⠀⠀⢸⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⢻⣿⣿⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠀⣼⠀⢀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣀⣀⣿⣴⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣿⣿⣄⣀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢰
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣣⣤⡀⠀⠀⠀⠀⣠⣷⣦⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⢸
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡿⢁⣼⣿⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⢻⡟⠻⠿⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢨
⠀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠟⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⠶⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠹⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠇⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣷⣤⣀⣀⣀⣠⣴⣾⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈
⣆⠀⠀⠀⠀⠀⠀⠀⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠷⠰⢾⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣧⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡄⠀⠀⠘⢦⣤⣴⣶⣶⣦⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣷⣾⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠿⣿⣿⣿⣿⣿⣿⣧⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠿⠟⠛⠉⢡⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠏⠀⢀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀⢸⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⢸⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣐⣠⡄⠀⠀⠀⢠⣿⣿⡿⠛⢻⣿⣿⡧⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡆⠀⠀⢸⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠶⣶⣾⣿⣿⡿⠓⠒⠀⣼⣿⣿⠃⠀⢰⣿⣿⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣀⣸⣠⣤⣾⣿⣿⠏⠈⢆⣀⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⠿⠃⠀⠀⢰⣿⣿⡟⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠿⠿⠋⢹⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⠁⣼⣿⣿⣿⠟⠉⠹⡿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣿⣿⠇⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⣿⠏⠁⠀⠀⠀⣇⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢻⣿⣿⡆⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⢨⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⡀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣤⣀⣀⣀⣠⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠇⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠸⣿⡿⠟⠁⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠷⠰⠶⠶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⣦⣤⣤⣴⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⢰⣾⣿⣿⣿⣿⣿⣿⣦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠟⠛⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡒⠒⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⢹⠀⠀⠉⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠙⠉⠻⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⢸⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⣿⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⣼⣿⣿⠃⠀⢐⣿⣿⡿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⣿⣀⣀⣤⣾⣿⣿⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⠋⠀⠀⠀⢠⣿⣿⡗⠀⠀⢸⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠿⠿⠋⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⣿⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⣴⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⣿⣿⠃⠀⣸⣿⣿⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⣿⣿⠏⠁⠉⡇⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⡀⣰⣿⣿⡿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⣿⣿⡇⠀⠀⠀⣇⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣤⣀⣀⣀⣂⣤⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠷⠤⠀⠀⠀⠀⡇⠀⠘⣿⣿⣷⣤⣀⣀⣸⣆⣴⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⡅⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠟⢻⡟⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣶⣶⣧⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⢿⡿⠟⠁⠀⠙⣿⣿⣿⣿⠧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠖⠰⠶⠶⠶⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⣿⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢀⣠⣤⣴⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣶⣶⣤⣥⣤⣀⣀⡄⠀⠀⠀⠀⠈⢿⣿⣿⣦⣄⣠⣶⣿⣿⣿⣿⣿⣿⣦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠟⠛⠉⢹⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠄⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⠙⣿⣿⣿⠏⠃⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⣿⣿⡿⠛⢻⣿⣿⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⣿⡧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣀⣀⣠⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣴⣶⣶⣿⣿⣿⡏⠀⠀⠀⢠⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠿⠿⠋⢹⠇⠀⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⣿⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠁⣾⣿⣿⣿⣿⠿⠛⠛⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⣿⣿⠁⠀⢰⣿⣿⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⣿⣿⡿⣿⠀⠉⠁⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⡀⣰⣿⣿⡿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣀⢸⠀⠀⠀⢸⣿⣿⡏⠀⢻⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣄⣀⣀⢀⣀⣴⣾⣷⡌⠁⢸⠀⠀⠀⢸⣿⣿⡇⠀⢸⡀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢸⠀⠀⠀⠈⣿⣿⣷⣤⣀⣇⣀⣀⣴⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢹⢿⠀⠀⢸⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣦⣴⣶⣴⣴⣦⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⢟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⢿⡿⠟⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠟⠲⠄⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⢹⠀⠀⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢀⣠⣤⣴⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣣⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣀⣀⣴⣿⣿⣿⣿⣿⣿⣦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠛⠋⠉⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠤⠽⣿⣿⣿⡧⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⢠⣾⣿⡿⠛⢻⣿⣿⡇⠀⠉⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⡇⠀⠀⣼⣿⣿⠃⠀⠀⣿⣿⡯⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⣀⣀⣠⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⡏⠀⠀⠀⢠⣿⣿⡗⠀⠀⢸⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠿⠿⠋⠉⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⣿⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⢸⠀⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⣿⣿⠃⠀⣰⣿⣿⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠄⠀⠀⠀⣼⣿⣿⡿⢿⡁⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⡀⣰⣿⣿⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡗⠀⠀⠀⢸⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣄⣀⣀⣀⣀⣠⣾⣿⣿⣿⢷⡀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⢸⠀⠀⠀⠀⠈⣿⣿⣿⣧⣀⣀⣀⣀⣴⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢸⣷⣤⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠉⠀⠀⢸⢸⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣶⣤⣄⣤⣤⣾⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠸⢿⡿⠟⠁⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⣿⢸⠆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠩⣿⡀⠘⠁⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢀⣠⣤⣤⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣫⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠛⠛⠉⣹⣿⣿⣿⡿⠿⠿⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿⡄⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠙⣾⣿⣿⣿⡟⠁⠀⢠⣾⣿⡿⠛⢻⣿⣿⣿⠿⣿⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠓⢤⠀⣼⣿⣿⠃⠀⠀⣿⣿⡿⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣤⣶⣶⣿⣿⡿⡿⠀⠀⠀⢰⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣴⣶⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠿⠿⠋⠁⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⣿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⡖⠀⠉⠉⠉⢯⣾⣿⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣿⣿⠇⠀⣰⣿⣿⡏⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⠄⠀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⡀⣰⣿⣿⡿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣄⣀⣀⢀⣀⣠⣾⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡇⠀⡰⠄⠀⡞⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡟⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣿⣿⣿⣿⡅⠀⠀⠀⢀⣀⣧⣴⣿⣷⣄⣀⡀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠉⠀⠀⡇⢸⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣦⣤⣄⣤⣴⣿⣿⣿⣿⠟⠀⠉⠙⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡟⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⢿⡿⠛⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠟⢻⠇⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇⠀⢸⡀⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢀⣠⣤⣤⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⢃⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⢀⣴⣿⣿⣿⣿⣿⣿⣆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠛⠋⠙⣹⣿⣿⣿⡿⠿⠿⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠂⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠁⠀⣼⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⡻⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣴⣴⣶⣿⣿⣿⣿⡿⡿⠓⢰⣿⣿⡗⠀⠀⢸⣿⣿⡏⠉⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣴⣶⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠛⠿⠿⣿⡿⠿⠟⠋⠉⡟⠁⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⣿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⣿⣿⣿⠀⠀⠉⠉⠉⢁⣶⣿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣿⣿⠁⠀⢰⣿⣿⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⣿⣿⡆⠀⠀⠠⢤⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⡀⣰⣿⣿⡟⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⠇⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣄⣀⣀⢀⣀⣠⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡇⠀⢰⣠⡴⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣿⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⡟⢲⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣿⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣦⣤⣀⣤⣤⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⢀⠇⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠟⠋⡇⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠴⠰⠶⠶⠶⠀⠀⠀⠀⠀⡿⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡇⠀⠀⡇⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⠀⠀⠀⢀⣠⣤⣤⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⢃⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⢀⣴⣿⣿⣿⣿⣿⣿⣆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠛⠛⠉⣵⣾⣿⣿⡿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠿⠿⠿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣏⡀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣯⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⡅⠀⣼⣿⣿⠃⠀⠀⣿⣿⡿⠻⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢐⣄⣤⣀⠀⠀⠘⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿⣿⡿⠃⢰⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⠇⠀⠀⢶⡶⣿⣿⣿⣿⣿⣿⣶⣤⡈⣿⢿⣿⣿⣿⣿⣿⣿⣟⣣⣴⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⡿⠿⠿⡿⠛⡿⠉⠁⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠠⠖⠉⣿⡟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⢨⡿⣿⠿⠿⠿⣿⣿⣿⣿⠀⠀⠉⠉⠹⣭⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⠁⠀⢰⣿⣿⡇⠀⠀⠀⠀⡗⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⢠⣿⣿⣿⡿⠋⡀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⡀⣰⣿⣿⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡿⠉⠂⠀⠀⠀⠀⠀⢀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣄⣀⣇⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣷⣿⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣦⣤⣀⣤⣤⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⡏⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢶⠔⠰⠶⠶⠶⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡇⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⢃⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⢀⣴⣿⣿⣿⣿⣿⣿⣆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠿⢟⣯⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠀⠀⠀⠐⢲⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣯⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⣿⡿⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣀⣀⣀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣤⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠙⢿⣿⣿⣷⣧⡄⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡇⠀⢤⣷⣶⣾⣿⣿⣿⣷⣷⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⢟⣡⣤⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⠿⠿⠟⠛⣿⣿⣿⡀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠈⠽⠿⣿⡿⠇⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣷⠴⠛⢿⣿⡿⣿⠟⠛⠛⠻⢿⣿⣿⣿⠀⠀⠉⠉⠉⣡⣶⣿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⠀⠀⢸⣿⣿⠁⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣷⡀⠀⠈⡟⠀⠀⠁⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⠿⠄⠀⠠⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⢂⠀⢸⣿⣿⡀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢿⣿⣷⣄⠀⣷⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⠛⠆⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣄⣀⡀⢀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢆⣤⣴⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣾⣿⣿⣿⡅⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⡧⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣤⣾⣿⣿⣿⣿⣿⣦⣤⣀⣤⣤⣾⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⡇⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠔⠰⠶⢾⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⠰⡇⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⢃⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣤⡀⢀⣴⣿⣿⣿⣿⣿⣿⣆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠋⠉⣵⣿⣿⣿⣿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠿⠻⠿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠀⠀⠀⠀⠠⢾⣿⣿⣿⡟⠁⠀⠀⠀⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⣾⣿⡿⠛⢻⣿⣿⣯⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⣿⡿⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣴⣤⡆⠀
⠀⠀⢸⣿⣿⡟⣸⣤⣴⣶⣾⣿⣿⣿⣷⣷⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣟⣣⣴⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⡓⠺
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠁⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡇⠀⠀
⠀⠀⠘⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠘⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠸⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣄⣀⠀⢀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣿⣿⣿⣦⠴⠈⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢦⣤⣆⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⡿⠳⠀⢀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠙⡟⠏⠁⠀⣤⣾⣿⣿⣿⣿⣿⣦⣤⣀⣤⣤⣴⣿⣿⣿⠛⠉⠂⠀⡇⠀⠀
⣆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠋⢸⠀⠀⠀⠀⡇⠀⣸
⣿⣶⣶⣶⠿⢶⠔⢸⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣧⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠋⠉⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠟⠿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠁⠀⠀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣬⣦⣰
⠀⠀⢸⣿⣿⠇⠀⢀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠙⠿⢿⢿⡿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠉
⢄⡀⣼⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠈⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠘⠁⠀⢿⠉⠻⣿⣿⣷⣦⣄⣀⢀⢀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠂⣀⡀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⢸⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡶⠀⠀⠀⢸⠀
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⣠⢀⣤⣾⣿⣿⢿⣿⣿⣦⣄⣀⣀⣤⣴⣿⣿⣿⠋⠀⠂⠀⠀⢸⠀
⣆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠿⠻⠿⠈⠙⢿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⢸⣸
⣿⣶⣶⣶⡿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣼⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣣⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠋⠉⣽⣿⣿⣿⣿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠟⠻⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠈⢹⣿⣿⣿⠟⠳⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣯⡙⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣯⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠁⠀⠀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣤
⠀⠀⢸⣿⣿⠃⠀⢀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣟⣡⣤⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠙⠿⢿⢿⡿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⢈⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡏⠈⠂⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⠟⠛⠻⣿⣿⣷⣦⣄⣀⢀⢀⣀⣠⣴⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡐⠀⠀⠀⠀⠀
⠄⢹⡏⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⡗⠒⠀⠀⠀⠀
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⣿⣿⣿⠁⠀⠀⣤⣾⣿⣿⢿⣿⣿⣦⣄⣀⣠⣤⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⠟⠓⠀⠀⠐⢿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣷⣶⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢸⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⡀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠛⠉⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠟⠿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⠻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⣸⣿⣿⠃⠀⠀⣿⣿⡿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣄⣤
⠀⠀⢸⣿⣿⠇⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⢿⢿⡿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⢿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⠿⠛⠋⠛⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠋⠉⠻⣿⣿⣷⣦⣄⣀⢀⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⣁⡀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠘⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡁⠀⠀⠀⠀⠐⠂⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠠⢸⣾⣾⣾⣶⣶⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣀⣤⣴⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠐⠿⡿⠋⠁⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣉⠙⢿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣤⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⡀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠛⢉⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠟⠻⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⢐⣿⣿⣿⡏⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣯⡹⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⣸⣿⣿⠁⠀⠀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣠
⠀⠀⢸⣿⣿⠃⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠉⠉⠉⣹⣿⣿⣿⣿⡿⠛⠋⠛⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠻⣿⣿⣷⣦⣄⣀⢀⢀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠰⡄⠀⣰⠂⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡄⠀⣄⠀⡠⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⣤⣾⣿⣷⡀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠄⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⣿⣿⣿⣿⣶⣤⣤⣴⣿⣿⡿⠁⠀⠀⣤⣾⣿⣿⢿⣿⣿⣦⣄⣀⣠⣤⣴⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠞⢹⠉⠙⠻⢿⣿⣿⡿⠿⠋⠀⠀⠀⠘⢿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠋⢉⣽⣿⣿⣿⡿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠟⠻⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣯⡹⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⣸⣿⣿⠁⠀⠀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣠
⠀⠀⢸⣿⣿⠇⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠉⠉⠉⢡⣿⣿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠻⣿⣿⣷⣦⣄⣀⠀⠀⣀⣠⣴⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⣾⣶⣦⡤⠴⠆⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣆⠀⠀⠄⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠤⠴⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡦⠂⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⡿⠁⠀⠀⣤⣾⣿⣿⢿⣿⣿⣦⣄⣀⣀⣤⣶⣿⣿⣿⠛⠄⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠘⢿⠿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣉⠙⢿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣄⡀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⢛⣻⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠛⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⡙⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⠻⣿⣿⣯⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⣸⣿⣿⠁⠀⠀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣤⣀⣀⣀⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣄⣄⣠
⠀⠀⢸⣿⣿⠃⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣶⣾⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⢿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠉⠉⠉⣻⣿⣿⣿⣿⡿⠛⠋⠛⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⢠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠠⡰⣆⣠⠤⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡠⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠻⣿⣿⣷⣤⣄⣀⠀⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠙⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⣶⣶⣆⡄⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⡿⢿⣿⣿⣦⣤⣤⣴⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣀⣤⣴⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⡿⠿⠋⠀⠀⠀⠐⠿⠿⠋⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠯⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣉⠙⢿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠛⢉⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠛⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⡙⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⠻⣿⣿⣯⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⣸⣿⣿⠁⠀⠀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣤⣀⣀⣀⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠘⢿⣿⣿⣷⣦⣤⣤⣤⣄⣠
⠀⠀⢸⣿⣿⠃⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣟⣡⣤⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⢿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠉⠉⠉⣻⣿⣿⣿⣿⠿⠛⠋⠛⠻⢿⣿⣷⡀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⢀⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠘⣿⣿⣇⠀⢂⣴⣴⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡿⠳⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢨⣿⣿⣿⡇⠉⠁⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠻⣿⣿⣷⣤⣀⣀⠀⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠤⠀⠉⣦⣄⡀⢀⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣄⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠶⠀⠉⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⡟⢿⣿⣿⣦⣤⣤⣴⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣀⣤⣴⣿⣿⣿⠃⠀⠂⠀⣠⡀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⡿⠿⠋⠀⠀⠀⠘⠿⡿⠋⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠟⠋⢼⠀⠀⠉⠐⠛⠁⣸
⣿⣶⣶⣶⠿⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡉⠙⢿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠛⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠈⢹⣿⣿⣿⠿⠻⠋⠀⠀⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⡙⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⣀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⠻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⠻⠿⠃⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⣸⣿⣿⠁⠀⠀⣿⣿⡟⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣀⣀⣀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠘⢿⣿⣿⣷⣦⣤⣄⣀⣄⣠
⠀⠀⢸⣿⣿⠃⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣟⣡⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⢿⠿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⢿
⠀⠀⢸⣿⣿⣷⣾⣿⣿⠿⠟⠛⠛⠋⠛⠻⢿⣿⣿⣿⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⠿⠛⠋⠛⠻⢿⣿⣷⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⢈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⢸⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠻⣿⣿⣷⣤⣀⣀⠀⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣷⣤⣼⡓⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣄⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⢀⣾⣿⣿⣿⡀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⡟⢿⣿⣿⣦⣤⣤⣴⣿⣿⡟⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣤⣿⣿⣿⣿⣿⠟⠉⢁⠁⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⡿⠿⠋⠀⠀⠀⠐⠿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢹⠀⠀⠀⠀⠀⣤⣸
⣿⣶⣶⣶⠯⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣤⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠛⠋⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠻⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⢘⣿⣿⣿⠋⠀⠀⠈⠉⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⡙⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⠻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⣤⣶⣄⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⣸⣿⣿⠁⠀⠀⣿⣿⡟⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠙⢿⣿⣿⣶⣦⣤⣤⣀⣄⣠
⠀⠀⢸⣿⣿⠃⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣄⡈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣾⣿⣿⠿⠟⠛⠋⠙⠛⠻⢿⣿⣿⣿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠛⠋⠛⠻⢿⣿⣷⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠈⢹⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⢀⣴⣧⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⢸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠸⣿⣿⣷⣿⣿⡟⠀⠀⠀⢀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡿⠋⠉⠻⣿⣿⣷⣤⣀⣀⠀⠀⣀⣠⣴⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣅⡀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣄⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠐⢂⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⡟⢿⣿⣿⣦⣤⣤⣴⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣀⣠⣾⣿⣿⣿⡟⠉⠉⠛⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⠿⣿⣿⣿⠿⠋⠀⠀⠀⠐⠿⠿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠋⢻⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣉⠙⢿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣤⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠛⢉⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠟⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⡙⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⣀⣠⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⣸⣿⣿⠁⠀⠀⣿⣿⡿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣀⣀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠘⢿⣿⣿⣷⣦⣤⣤⣤⣄⣠
⠀⠀⢸⣿⣿⠇⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⢿⠿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⣼⣿⣿⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⢿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⡿⠛⠋⠛⠻⢿⣿⣷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⢸⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⢰⣿⣿⡟⠁⠀⠠⠀⠀⠀⠀⠀⣿⣿⡗⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠻⣿⣿⣷⣤⣄⣀⠀⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡄⢀⢄⠀⡠⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣄⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠄⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⡟⢿⣿⣿⣦⣤⣤⣴⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣠⣤⣾⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⡿⠿⠋⠀⠀⠀⠐⢿⡿⠋⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣇⣤⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⢛⣻⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠻⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠉⠀⠀⠀⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⡹⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⠻⣿⣿⣯⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠁⠀⠀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣄⣤⣠
⠀⠀⢸⣿⣿⠇⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠙⠿⢿⢿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⢿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⡿⠟⠋⠛⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⢠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⢀⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣀⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠻⣿⣿⣷⣤⣄⣀⠀⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⢄⠠⠀⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠂⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⡿⢿⣿⣿⣦⣤⣤⣴⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣤⣤⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⡿⠿⠋⠀⠀⠀⠘⠿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⡿⢃⣤⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠋⢉⣱⣾⣿⣿⣿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠻⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠠⢾⣿⣿⣿⡟⠁⠀⠀⠀⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⡙⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⣸⣿⣿⠁⠀⠀⣿⣿⡿⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣀⣀⣀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠘⢿⣿⣿⣷⣦⣤⣤⣤⣤⣠
⠀⠀⢸⣿⣿⠇⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣟⣡⣤⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⡿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⢿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠈⠉⠉⣻⣿⣿⣿⣿⡿⠛⠋⠛⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⢀⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠘⣿⣿⣇⠐⣄⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡿⠳⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠉⠻⣿⣿⣷⣤⣄⣀⢀⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⠂⠀⡀⠀⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣄⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢰⣶⣿⣷⠶⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⡟⢿⣿⣿⣦⣤⣤⣴⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣠⣤⣴⣿⣿⣿⠃⠀⠂⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⡿⠿⠋⠀⠀⠀⠘⠿⡿⠋⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠟⠋⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢶⠔⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⠿⢁⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠋⠁⢀⣴⣿⣿⡿⠿⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠟⠻⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⡙⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠁⠀⠀⣿⣿⡿⠺⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⣀⣀⣀⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢰⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣠⣄⣠
⠀⠀⢸⣿⣿⠇⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⡈⣿⠿⣿⣿⣿⣿⣿⣿⣟⣡⣤⣶⣾⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠙⠿⢿⠿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⢈⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⣿⣿⣧⠠⢤⣴⣔⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡏⠉⠂⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⣿⣿⣿⡧⢤⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡿⠋⠉⠻⣿⣿⣷⣤⣄⣀⠀⠀⣀⣠⣴⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⢄⡰⠐⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠒⣲⣾⣿⣷⠀⠒⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⡟⢿⣿⣷⣦⣤⣤⣴⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣠⣠⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⡿⠿⠋⠀⠀⠀⠘⠿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⠟⢁⣤⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠋⠉⢀⣼⣿⣿⡿⠿⠿⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠻⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣯⡹⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⣼⣿⣿⠁⠀⠀⣿⣿⡿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣀⣀⣀⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣠
⠀⠀⢸⣿⣿⠇⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⡈⣿⢿⣿⣿⣿⣿⣿⣿⣿⣣⣤⣶⣾⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠁⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⣀⣶⣴⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⢸⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⣾⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡿⠋⠉⠻⣿⣿⣷⣤⣄⣀⠀⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠐⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣤⣄⣁⡀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢹⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠐⠂⢰⣿⣿⣿⠂⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⡟⢿⣿⣷⣦⣤⣤⣴⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⢿⣿⣿⣦⣄⣀⣠⣤⣴⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⡿⠿⠋⠀⠀⠀⠘⠿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢶⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣉⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⠟⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠛⠋⠉⢀⣾⣿⣿⠿⠏⠀⠠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠘⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣮⡹⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠛⢻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣀⣀⣀⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣠
⠀⠀⢸⣿⣿⡃⠀⣀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⡀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣡⣴⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⠿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠀⠀⠉⠉⠉⠀⣵⣿⣿⣿⠿⠟⠛⠛⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠘⣿⣿⣧⠰⣄⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⡿⠋⠉⠻⣿⣿⣷⣦⣄⣀⠀⠀⣀⣠⣼⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⡄⠀⣄⠀⡠⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⠀⠀⠀⠀⠈⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⠏⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⢀⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠄⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⡿⣿⣿⣷⣶⣤⣤⣴⣿⣿⡿⠁⠀⠀⣤⣾⣿⣿⢿⣿⣿⣦⣄⣀⣠⣤⣾⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠘⠿⡿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠉⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⣾⣿⡿⠛⢻⣿⣿⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠃⠀⠀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣀⣀⣀⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣶⣶⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣠
⠀⠀⢸⣿⣿⡇⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⡀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⡿⠟⠛⠛⠛⠛⠿⣿⣿⣿⣧⠀⠀⠉⠉⠉⠉⣰⣿⣿⡿⠟⠉⠉⠛⠻⣿⣿⣷⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠁⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⢀⣤⣇⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡗⠠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⠋⠉⠻⣿⣿⣷⣦⣄⣀⢀⢀⣀⣠⣾⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣤⣆⡀⠀⠄⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠈⠀⠀⠀⠀⠀⢿⣿⣿⣄⣀⣀⣀⣀⣤⣾⣿⣿⠟⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡦⠂⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⡟⣿⣿⣿⣶⣤⣤⣴⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣄⣀⣠⣤⣶⣿⣿⣿⠛⠄⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠻⠿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠋⢸⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠔⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡀⣼⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⣾⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠃⠀⢀⣿⣿⡿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣀⣀⢀⣀⣾⣿⣿⣏⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣤⣶⣶⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡏⠀⠀⢸⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣤
⠀⠀⢸⣿⣿⡇⠀⣀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⡀⠙⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⣿⠁⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣷⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⣿⣿⣿⣇⠀⠈⠉⠉⠉⠁⠀⠀⠈⠛⠋⠉⠉⠙⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠃⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⣸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡗⠠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠋⠉⠻⣿⣿⣷⣦⣄⣀⣀⣀⣀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⢀⣦⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠐⢢⣤⡆⠀⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⢀⣠⣾⣿⣿⠏⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠻⣿⣿⣿⣶⣤⣤⣴⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⣀⣤⣤⣶⣿⣿⣿⠛⠉⠂⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿
⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣍⠙⢿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣵⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⣼⣿⣿⡿⠿⣿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⣾⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⣼⣿⣿⠃⠀⢀⣿⣿⡿⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣯⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡏⠀⠀⢸⣿⣿⡇⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣴
⠀⠀⢸⣿⣿⡇⠀⣀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠿⠟⠛⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⣿⠁⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⣿⣿⣿⣆⠀⠀⠀⠈⠉⠉⠙⢿⡿⠟⠋⠉⠉⠻⣿⣿⣿⣄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠃⠀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣸⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆⠀⣤⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢺⣿⣿⡀⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀
⣿⣿⣿⠋⠉⠻⣿⣿⣷⣦⣄⣀⣀⣀⣀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣤⣭⣂⣀⣤⡄⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠀⠀⠃⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣶⣤⣤⣴⣿⣿⡿⠁⠀⠀⠀⠀⠘⠻⢿⣿⣿⣦⣤⣀⣤⣤⣶⣿⣿⡿⠋⠀⠂⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⠿⢷⠶⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠛⣷⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⠿⠛⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠉⠛⠛⢷⣦⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡛⠉⠉⠉⠉⠻⢷⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⣀⣀⣀⣼⠟⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣷⣤⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⣀⣤⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡟⠋⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠿⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠁⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣉⣿⣿⡿⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⡉⠉⢙⣻⡿⠛⠉⠉⠉⠉⠀⠀⠙⠛⢿⣿⡋⠀⠀⠀⠉⣻⣿⡿⡛⠉⠉⠋⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠛⣷⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣙⠛⠛⠻⢷⣄⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡛⠉⠉⠉⠉⠛⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⣀⡀⠀⠀⠉⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣷⣠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⣀⣤⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡟⠋⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠿⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠁⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠟⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⡉⠉⢙⣻⡿⠛⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣻⣿⡿⠛⠃⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣛⣛⠛⠛⠻⣶⣄⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠛⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠈⠻⣧⣠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣧⣀⣤⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡟⠋⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠿⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠁⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⡉⠉⢙⣻⡿⠛⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣛⣿⡿⠟⠉⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣛⡛⠻⠷⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣂⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣇⣀⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡟⠋⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠿⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠁⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⡉⠉⢉⣻⡿⠛⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣛⣿⡿⠛⠉⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠰⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⣴⣾⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⣀⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣬⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡟⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠿⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠁⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣉⡉⠉⢉⣻⡿⠛⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣛⣿⡿⠟⠉⠩⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⣀⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡟⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⠿⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠁⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⡉⠉⢙⣻⡿⠛⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣛⣿⡿⡟⠉⠉⠋⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⠦⠄⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⣀⣤⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣽⣿⣿⣿⣿⠿⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⡉⠉⢙⣻⡿⠛⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣻⣿⡿⠛⠋⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⢀⣤⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠟⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣭⣽⣿⠟⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⡉⠉⢙⣻⡿⠛⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡉⠀⠀⠀⠉⣛⣿⡿⠟⠉⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⢀⣰⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠈⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣭⣄⠐⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠙⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⡉⠉⢉⣻⡿⠛⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣛⣿⡿⠛⠉⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⢿⣷⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣄⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣛⣿⡿⠛⠉⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠈⢿⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⣿⣋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣛⣿⡿⠛⠉⠉⠋⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣬⣭⣭⣥⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠻⢿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠛⢿⣿⡋⠀⠀⠀⠉⣻⣿⡿⡛⠉⠉⠋⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡧⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⣛⣿⡿⠛⠁⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⠛⢿⠿⠋⠁⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⡟⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠁⠀⠀⠀⠉⠙⠛⠛⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⠛⠛⠛⠋⠁⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⠙⠛⠛⠉⠀⠉⠉⠉⠁⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣦⣰⣠⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1535

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

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Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_December_31,_2021⠀✐


Posted in IRC_Logs at 2:14 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-311221.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-311221.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-311221.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-311221.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
 QmS3xPqAgetT8s7Csf1d5zCRmNsAmJW7v8nJw9f6P8BEeU #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmR4VM5B7PSynNHTGEeGjpvf547eq8HZCp7nHZeUcaHx6f (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmYBwZ3QrLfD7fvP82saqdsHnVcEAnGFypSVVTmK42nJaS social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmQrfTYuSW2JTxXpPdeQ8YfSLN1pYimTgA68ENQF7q5v61 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmRuffzhKassW2FfaH47P2py3SMMVnwhHGnLpyP8z1yc2r #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmTBp1BLfDiBNdXDvFiWWScxnPhUX7SiWdZGs1Xi2s1Lug (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmZxkSSANAbYCz1eHaXmY7WXL3THCBVSVGrt7Y6JvRteyW #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmSQLCgaf4W9LW5uj7tom9hvypEkbhUx1TiFqMxysbEbtw (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmVgY18p35Thp6aWh7cRUuoocqLYGYFW2QnLEJhuqn69Kw



                    ䷩ 𝚕𝚒𝚗𝚎 1662

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_2/1/2022:_GNU_Alive_2.0.4_and_FSF_Membership_Drive_Runs_Until_January
20th⠀✐


Posted in News_Roundup at 9:26 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Desktop/Laptop⠀➾


                # ⚓ Top_5_Best_Linux_Tablets_Recommended_For_Privacy_Lovers_
                  (2022)_–_DekiSoft⠀⇛


                       Over time Linux has had a lot of popularity all due
                       to the advantages that different distros bring to
                       the table, the best among all is security and
                       privacy. All thanks to them these OS are able to
                       secure your data from malware and other attacks. We
                       have picked the top 5 Linux tablets for privacy
                       users. This includes choices for different people
                       and has a variety of devices.


          o § Audiocasts/Shows⠀➾


                # ⚓ NEW_LINUX_DESKTOP,_Duck_Duck_Go_browser,_and_Libadwaita_1.0
                  –_Linux_and_Open_Source_News_–_December_–_Invidious⠀⇛


                # ⚓ Archfi:_So_Called_“Best”_Arch_Install_Script_–_Invidious⠀⇛


                       I’ve been trying out a bunch of Arch Linux install
                       scripts recently, like Arch Linux GUI and Anarchy
                       Linux but I’ve been getting requests for Archfi for
                       over a year now and I’m finally getting around to
                       checking it out.


                # ⚓ Ten_Linux_Predictions_For_2022_–_Invidious⠀⇛


                       Happy New Years, guys! This is a quick phone vlog
                       where I give you ten Linux predictions for 2022. By
                       the way, most of you know that COVID has hit
                       several members of my family over the holidays,
                       including myself, but I’m feeling much better now
                       that I did few days ago. Thank you to all that send
                       good thoughts and prayers!


                # ⚓ Who_should_use_Linux?_–_Invidious⠀⇛


                       After the Linux Challenge and various other videos
                       showing who should NOT use Linux, lets talk about
                       who SHOULD use Linux.


                # ⚓ Art_Livestream_(Mon_Jan_3rd,_2022)_›_Ken_Vermette⠀⇛


                       Hullo! On Monday January 3rd 5:00pm GMT (12:00pm
                       EST) I’m going to try livestreaming work on a
                       potential Plasma wallpaper, possibly some icon
                       work, and other potential tangential work. I’ll
                       also be answering questions, giving advice and tips
                       for software like Krita and Inkscape, and if
                       there’s time I may also show some terrible
                       unreleased design work from the bowels of my
                       storage drive. The stream will be of indeterminate
                       length; at least a couple hours but it might run
                       long.


                # ⚓ GNU_World_Order_441⠀⇛


                       **GNU Emacs** , the beginning and ending of the
                       **E** software series of Slackware.


          o § Applications⠀➾


                # ⚓ Pinta_2.0_Open-Source_Paint_Program_Is_Out_Now_as_a_Major
                  Update,_Ported_to_GTK_3 [Ed: Mono_danger]⠀⇛


                       Pinta 2.0 comes a little over a month after the
                       release of the Pinta 1.7.1 update, and it’s here to
                       finally port the paint program to the GTK+ 3 and
                       .NET 6 application frameworks for a more modern
                       look and new functionality.


                       The GTK+ 3 and .NET 6 porting means that Pinta not
                       only looks better and more moder, but it also
                       offers improved support for HiDPI displays, support
                       for platform-native file dialogs, as well as
                       support for GTK+ 3 themes.


                # ⚓ Pinta_2.0_Released,_Completes_Port_to_GTK3_&_.NET_6⠀⇛


                       With a new year starting you might be planning to
                       indulge your creativity side this year — and if so,
                       take a look at the latest stable release of open
                       source image editing app Pinta.


                       Pinta 2.0 is major new release that completes the
                       app’s transition to GTK3 and .NET 6. It’s a big
                       foundational uplift that results in some welcome
                       improvements. Pinta 2.0 now looks better on the
                       modern Linux desktop, with GTK dialogs, choosers,
                       pickers, and widgets all looking how they should.


          o § Instructionals/Technical⠀➾


                # ⚓ Finding_all_files_with_a_certain_extension_in_Linux?_–
                  Darryl_Dias⠀⇛


                       The example above is using the find command to
                       search files in the tmp folder for Python files,
                       that have the extension .py.


                       To get a list of all the files with the same
                       extension inside the current directory, for this
                       example looking for all the Python extension files.


                # ⚓ How_To_Install_Vivaldi_Browser_on_Fedora_35_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Vivaldi Browser on Fedora 35. For those of you who
                       didn’t know, Vivaldi is a freeware, cross-platform
                       web browser developed by Vivaldi Technologies. It
                       had grown from the downfall of Opera with many
                       disgruntled when it changed from the Presto layout
                       engine to a Chromium-based browser. Although it,
                       too, is based on Chromium, its minimalistic user
                       interface and features such as tab stacking and
                       tiling, built-in ad blocker and trackers, custom
                       themes, quick commands, etc., give it an edge over
                       the likes of Chrome, Edge, and Brave.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you through the step-by-
                       step installation of the Vivaldi Browser on a
                       Fedora 35.


          o § Distributions⠀➾


                # § New Releases⠀➾


                      # ⚓ MX_Linux_21_Is_The_Best_Linux_Distribution_Of_2021⠀⇛


                             So overall, all of these reasons were what
                             motivated us to choose MX Linux 21 as the
                             best desktop Linux distribution of 2021.
                             Combining hardware support, low resources
                             consumption and huge number of utility apps
                             and deep functionality options… It all
                             creates a wonderful Linux distribution for
                             the average user.


                             Perhaps the only thing that the developers
                             need to work on is the default UX and UI for
                             their default apps and overall system, as it
                             sounds too traditional and classical from the
                             first while, comparing to distributions like
                             elementaryOS 6 which feature more elegant
                             user interfaces.


                             But… That aside, MX Linux 21 is one of the
                             best Linux distributions out there to try,
                             and we recommend any new user thinking of
                             switching to Linux from Windows to test it
                             out.


                             Congratulations to MX Linux developers, and
                             everyone who has worked on creating this
                             great distribution! It truly paid off.


                      # ⚓ Neptune_7_“Faye”_released⠀⇛


                             This version comes with a new Debian base (11
                             “Bullseye”) that offers newer and better
                             hardware support as well as newer software
                             and apps.
                             KDE Plasma 5.20.5 ships with a new Neptune
                             specific theme that embraces the Breeze
                             widget style for maximum compatibility and
                             introduces a new subtle but modern flat look
                             and feel to Neptune. We also updated the Icon
                             theme to our own variation of the Tela Icon
                             theme to fit with the new look of the system.
                             The default panel has been modernized to
                             allow pinning more apps and tasks to it
                             aswell as offering a new bigger easier look
                             to the eyes.
                             Besides that Linux Kernel 5.10 offers modern
                             hardware support aswell as bugfixes.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ CentOS_Linux_8_Reached_End_of_Life,_It’s_Time_to
                        Migrate_to_an_Alternative_OS⠀⇛


                             The time has come to say goodbye to the
                             CentOS Linux 8 distribution as it reached end
                             of life on the last day of 2021, December
                             31st. As of today, the distribution is no
                             longer supported, which means that it will no
                             longer receive software and security updates,
                             making your installations vulnerable to
                             attacks, in time.


                             CentOS Linux is a GNU/Linux distribution
                             built using and compatible with the sources
                             of the commercial Red Hat Enterprise Linux
                             operating system. CentOS Linux 8 was
                             initially released only two years ago, on
                             September 24th, 20219, and it was supposed to
                             be maintained for 10 years, until the year
                             2029.


                # § Debian Family and Similar⠀➾


                      # ⚓ LiVES_problems_and_more_problems⠀⇛


                             Easy 3.1.17 has LiVES 3.0.2, which seems to
                             basically work.


                      # ⚓ rshift_internationalized_and_fr_updates⠀⇛


                             esmourguit (forum name) is maintaining the
                             French translations for EasyOS.


                      # ⚓ Sparky_news_2021/12⠀⇛


                             The 12th, and the last of 2021 year, monthly
                             Sparky project and donate report:
                             – Linux kernel updated up to 5.15.12 & 5.16-
                             rc7
                             – Added to repos: FinalCrypt, Firefox &
                             Firefox ESR Mozilla builds
                             – Sparky 2021.12 & 2021.12 Special Editions
                             of the rolling line released
                             – Lumina Desktop updated up to 1.6.2; debs
                             built for amd64, i386, armhf & arm64


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ Small_EInk_Phone⠀⇛


                             Happy new year! Would you be interested in
                             crowdfunding a small E Ink Open Phone? If
                             yes, check out the specs and fill out the
                             form below.


                             If I get 1000 interested people, I’ll
                             approach manufacturers. I plan to share the
                             results publicly in either case. I will never
                             share your information with manufacturers but
                             contact you by email if this goes forward.


                      # ⚓ Neat_little_hobby_kit:_CircuitMess_Ringo⠀⇛


                             My son is a tinkerer and creator. He is still
                             somewhat young and has expressed on multiple
                             occasions that he dreams of building his own
                             phones. Enter the CircuitMess Ringo. It is an
                             educational DIY kit to build a mobile phone
                             (that uses actual SIM cards). As soon as I
                             saw this, I knew it was perfect for him and
                             on Christmas morning, he was ecstatic when
                             realizing what this was. Anyway, I will be
                             guiding and assisting him with his project
                             very soon and may share more details as we
                             progress through it.


                      # ⚓ Cool_the_Shop_with_a_Thermal_Battery-Based_System⠀⇛


                             Having any kind of shop is pretty great, no
                             matter how large it may be or where it’s
                             located. If the shop is in an outbuilding,
                             you get to make more noise. On the other
                             hand, it will probably get pretty darn hot in
                             the summer without some kind of cooling
                             system, especially if you don’t have a window
                             for a breeze (or a window A/C unit).


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


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Oracle_OC4J_–
                  LinuxLinks⠀⇛


                       Oracle is a computer technology corporation best
                       known for its software products and services like
                       Java.


                       In 2020, Oracle was the second-largest software
                       company in the world by revenue and market
                       capitalization. They employ over 130,000 people,
                       and sell cloud-engineering services and systems and
                       database management systems.


                       Oracle has a fairly prominent position with open
                       source. They are a supporting member of the Linux
                       Foundation, Cloud Native Computing Foundation,
                       Eclipse Foundation, and the Java Community Process.


                       Through its acquisition of Sun Microsystems in
                       2010, Oracle also became the steward of many other
                       important and long-running open source projects
                       such as the Java programming language and the MySQL
                       relational database, introduced in 1995. The
                       acquisition of Sleepycat Software, brought the open
                       source Berkeley DB key/value store.


                       The company co-develops the OpenJDK, an open source
                       implementation of the Java Platform Standard
                       Edition, and Btrfs, a B-tree file system. They also
                       open source the Oracle Coherence Community Edition,
                       NetBeans, and produce Oracle Linux which is a Linux
                       distro compiled from Red Hat Enterprise Linux
                       source code.


                       While Oracle develops and distributes open source
                       software, they have many different business models.
                       The majority of their products are published under
                       a proprietary license. This series looks at free
                       and open source alternatives to Oracle’s products.


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Oracle’s_Products
                  –_LinuxLinks⠀⇛


                       Oracle is a computer technology corporation best
                       known for its software products and services like
                       Java.


                       In 2020, Oracle was the second-largest software
                       company in the world by revenue and market
                       capitalization. They employ over 130,000 people,
                       and sell cloud-engineering services and systems and
                       database management systems.


                       Oracle has a fairly prominent position with open
                       source. They are a supporting member of the Linux
                       Foundation, Cloud Native Computing Foundation,
                       Eclipse Foundation, and the Java Community Process.


                       Through its acquisition of Sun Microsystems in
                       2010, Oracle also became the steward of many other
                       important and long-running open source projects
                       such as the Java programming language and the MySQL
                       relational database, introduced in 1995. The
                       acquisition of Sleepycat Software, brought the open
                       source Berkeley DB key/value store.


                       The company co-develops the OpenJDK, an open source
                       implementation of the Java Platform Standard
                       Edition, and Btrfs, a B-tree file system. They also
                       open source the Oracle Coherence Community Edition,
                       NetBeans, and produce Oracle Linux which is a Linux
                       distro compiled from Red Hat Enterprise Linux
                       source code.


                       While Oracle develops and distributes open source
                       software, they have many different business models.
                       The majority of their products are published under
                       a proprietary license. This series looks at free
                       and open source alternatives to Oracle’s products.


                # ⚓ Best_Free_and_Open_Source_Alternatives_to_Cisco’s_Products
                  –_LinuxLinks⠀⇛


                       Cisco Systems, Inc. is an American multinational
                       technology corporation that focuses on networking
                       hardware and software. It has over 75,000 employees
                       with its headquarters in San Jose, California.


                       Cisco has been participating in open source
                       development for almost 30 years including founding
                       projects like OpenDaylight, FD.io, VPP, PNDA, SNAS,
                       and OpenH264, and contributing to projects like
                       OPNFV, Kubernetes, OpenStack, Ansible, Chef,
                       Puppet, Maven, and many others.


                       Cisco has also been a key contributor to the Linux
                       kernel over the years, accounting for about 0.5% of
                       total kernel commits, and is a Platinum Member of
                       the Linux Foundation and Premium Sponsor of the
                       Open Source Initiative.


                       From a software perspective, Cisco’s main focus is
                       developing proprietary programs. In this series we
                       look at free and open source alternatives to their
                       products.


                # § FSF⠀➾


                      # ⚓ Help_keep_the_end-of-year_momentum_going:_Membership
                        drive_extended_to_January_20th⠀⇛


                             We’ve been inspired by seeing the 262 new
                             associate members who have decided to help us
                             ring in the new year by joining the Free
                             Software Foundation (FSF). We’re sincerely
                             grateful for the way they’ve answered the
                             call by standing up for software freedom.
                             We’re just as grateful for all of the
                             donations and membership renewals we’ve had
                             during our year-end drive. Since we’ve seen a
                             strong show of support in the latter half of
                             our appeal, we’re extending the date to join
                             and still receive one of the special pins
                             we’re offering to January 20th.


                      # § GNU Projects⠀➾


                            # ⚓ GNU_Alive_2.0.4_available⠀⇛


                                   release notes:

                                     Maintenance release.  Happy new year.

                                   README excerpt:

                                     GNU Alive is a keep-alive program for
                                   internet connections.
                                     It repeatedly pings a series of user-
                                   specified hosts, thereby
                                     encouraging (one hopes) the involved
                                   networks to not disappear.

                                   NEWS for 2.0.4 (2022-01-01):

                                     - .tar.xz no longer distributed

                                       If you have GNU tar, you can use
                                   "tar xf" and it will DTRT.
                                       If not, you can use "lzip -dc
                                   TARBALL | tar xf -" to unpack.

                                     - https in URLs

                                       GNU and GNUVOLA URLs now say
                                   ‘https’ instead of ‘http’.  This
                                       shows up in the docs, and in ‘--
                                   help’ / ‘--version’ output.

                                     - bootstrap/maintenance tools

                                       upgraded:

                                        GNU texinfo 6.8
                                        GNU Automake 1.16.5
                                        GNU Autoconf 2.71
                                        GNU Guile 2.2.7
                                        Guile-BAUX 20211208.0839.a5245e7
                                        GNU gnulib 2021-12-10 21:54:54

                                       as before:

                                        (none)

                                   tarball and detached signature:

                                   https://ftp.gnu.org/gnu/alive/alive-
                                   2.0.4.tar.lz


                                   https://ftp.gnu.org/gnu/alive/alive-
                                   2.0.4.tar.lz.sig

                                   source code:

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

                                   homepage:

                                   https://www.gnu.org/software/alive/
    * § Leftovers⠀➾


          o ⚓ Attack_Of_The_Eighty-Foot_String_Shooter_|_Hackaday⠀⇛


                 String shooters are exciting because they adhere to the
                 laws of physics in that peculiar way that makes us ask,
                 “How?” and “Why?” After a bit of poking and prodding,
                 maybe some light rope burn, we probably have a few ideas
                 on how we’d make our own. [Nick Belsten] and [Joey Rain]
                 saw some desktop models and thought, “Let’s make that
                 puppy eighty feet long!” Video also embedded after the
                 break.


                 Instead of hobby motors, flashlight batteries, and toy
                 car wheels, they choose a washing machine motor and bike
                 tires, then plug into an extension cord. The three-minute
                 video isn’t a how-to build because once you start welding
                 this kind of hardware together, you are already flying by
                 the seat of your pants. You will see a front yard with
                 people delighting in the absurdity of launching rope
                 continuously over the treetops. There’s plenty of room
                 for observing a wave traveling along the cord or
                 polishing your fingernails in a hurry.


          o § Hardware⠀➾


                # ⚓ Ski_Lift_Design_Does_The_Impossible_|_Hackaday⠀⇛


                       Tis The Season, for those who are so inclined, to
                       loft themselves to the top of a steep snow-covered
                       hill and then go downhill, really fast. And if
                       something gets in their way, turn. Whether they be
                       on skis, a snowboard, or some other means, getting
                       down usually involves using gravity. Getting up, on
                       the other hand, usually involves a ski lift. And in
                       the video by [kalsan15] after the break, we learn
                       how technology has stepped in to make even the most
                       inaccessible slopes just a lift ride away.


                # ⚓ Virtual_Eurorack_Based_CPU_Computes_To_The_Beat_Of_A
                  Different_Drum_Module_|_Hackaday⠀⇛


                       In Arthur C. Clarke’s 1972 story “Dial F for
                       Frankenstein”, the worlds first global network of
                       phone exchanges was created by satellite link, and
                       events happened that caused the characters in the
                       story to wonder if the interconnected mesh of
                       machinery had somehow become sentient. And that’s
                       what we wondered when we saw this latest virtual
                       CPU construction built by GitHub user [katef] and
                       made from a virtual analog synthesizer software
                       called VCV Rack.


                       Analogous to a Redstone computer in Minecraft,
                       there’s no physical hardware involved. But instead
                       of making crazy synth sounds for a music project,
                       [katef] has built a functioning CPU complete with
                       an Arithmetic Logic Unit, an adder, and other
                       various things you’ll find in a real CPU such as
                       registers and a clock.


                # ⚓ Genius_or_Cursed,_This_USB-C_Connector_Is_Flexible⠀⇛


                       USB connectors have lent themselves to creative
                       interpretations of their mechanical specifications
                       ever since the first experimenter made a PCB fit
                       into a USB-A socket. The USB-C standard with its
                       smaller connector has so far mostly escaped this
                       trend, though this might be about to change thanks
                       to the work of [Sam Ettinger]. His own description
                       of his USB-C connector using a flexible PCB and a
                       BGA-packaged ATTiny84A microcontroller is “cursed”,
                       but we can’t decide whether or not it should also
                       be called “genius”.


                       Key to this inspired piece of connector fabrication
                       is the realization that the thickness of BGA and
                       flex PCB together comes to the required 0.7 mm. The
                       BGA provides the necessary stiffness, and though
                       it’s a one-sided connector it fits the space
                       perfectly. There are several demo boards as proofs-
                       of-concept, and the whole lot can be found in a
                       GitHub repository.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ Blackberry_Will_Run_Out_of_Juice_on_January_4th⠀⇛


                             Happy New Year, though it may not be for
                             Blackberry fans. The company that has so
                             often had their products compared to a
                             certain addictive substance recently
                             announced that they are ending support for
                             Blackberry OS and Blackberry 10 devices.


                             What does this mean? While they won’t be
                             bricking phones outright, they might as well
                             be. On January 4th, Blackberry will be
                             shutting off all the key services — data,
                             SMS, phone calls, and 911 support. In
                             official terms, they are ending network
                             provisioning for these older devices, meaning
                             that they won’t be able to join any cellular
                             or WiFi networks.


                      # ⚓ Alexa_Suggests_Dangerous_‘Outlet_Challenge’_to_10-
                        Year-Old⠀⇛


                      # § Security⠀➾


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Facial_Recognition_for_Covid-19_Tracking
                                    in_Seoul⠀⇛


                                         The city of Bucheon, population
                                         830,000, is a satellite city
                                         southwest of Seoul and part of
                                         the greater metropolitan area and
                                         the site of a pilot program to
                                         apply AI facial recognition and
                                         tracking technologies to aid
                                         Covid-19 epidemiological
                                         investigators. South Korea has
                                         been generally praised for its
                                         rapid response to coronavirus
                                         patient tracking since the
                                         beginning of the outbreak. People
                                         entering public facilities enter
                                         their information on a roster or
                                         scan a QR code. Epidemiologists
                                         tracking outbreaks use a variety
                                         of data available to them,
                                         including these logs, electronic
                                         transaction data, mobile phone
                                         location logs, CCTV footage, and
                                         interviews. But the workload can
                                         be overwhelming, and there are
                                         only a fixed number of workers
                                         with the required training
                                         available, despite efforts to
                                         hire more.


                                         As contract tracing has been done
                                         to-date, it takes one
                                         investigator up to an hour to
                                         trace the movements of one
                                         patient. When the system goes
                                         online in January, it should be
                                         able to trace one patient in less
                                         than a minute, handling up to ten
                                         traces simultaneously. Project
                                         officials say there is no plan
                                         for this system to expand to the
                                         rest of Seoul, nor nationwide.
                                         But with the growing virus
                                         caseloads and continued
                                         difficulties hiring and training
                                         investigators, it’s not
                                         unexpected that officials will be
                                         turning to these technologies
                                         more and more to keep up with the
                                         increasing workload.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ FOSS_Patents:_Alternative_app_store_with_improved
                        security_filed_antitrust_lawsuit_against_Apple_in
                        Florida,_simultaneously_alleging_infringement_of_patent
                        on_reverse_lookup_of_phone_numbers⠀⇛


                             With Ericsson still not having announced (by
                             the time I’m writing this) a renewal of its
                             patent cross-license agreement with Apple,
                             dozens of patent infringement complaints
                             against Apple–in multiple jurisdictions–may
                             be imminent as the license agreement is just
                             about to expire. And other major standard-
                             essential patent holders like Nokia and
                             InterDigital haven’t announced a renewal with
                             Apple in many years, so there may be even
                             more infringement actions to come in 2022.


                      # ⚓ European_Union:_EPO_Board_Of_Appeal_Refuses
                        Applications_With_Non-Human_Inventor [Ed: EPO
                        constantly_violates_the_EPC, which it does not even
                        care about, but this time it decided to pretend
                        otherwise]⠀⇛


                             Yesterday, 21 December 2021, the EPO’s Legal
                             Board of Appeal dismissed the applicant’s
                             appeal in respect of the two European patent
                             applications that attempted to name a
                             computer system as the sole inventor. This is
                             the latest decision in the long-running and
                             widespread attempts by Dr Stephen Thaler and
                             his legal team to gain recognition for
                             machines as inventors within the patent
                             system. The full reasons for the Board’s
                             decision will be published later, but a brief
                             Press Communiqué has been issued by the EPO.


                             It appears that the Board has substantively
                             agreed with the decisions of the EPO’s
                             Receiving Section (reported here) that, under
                             the EPC, the inventor has to be a person with
                             legal capacity and so the applicant’s main
                             request, naming the computer system DABUS as
                             the sole inventor, was not allowable.



                    ䷩ 𝚕𝚒𝚗𝚎 2489

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_1/1/2022:_Happy_New_Year_2022!⠀✐


Posted in News_Roundup at 5:18 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ Happy_New_Year,_Folks_—_Let’s_Fill_it_with_Linux,_Yeah?!_–_OMG!
            Ubuntu!⠀⇛


                 This is a short (and yes, rather predictable) post to
                 wish every single person reading this site a very
                 merry—wait, we’ve already had that one—a happy new year.


                 Yes, even those of you still sat in your pants (the
                 British kind).


                 It may feel like the world now exists in a dark timeline
                 but there are things to be hopeful about, especially
                 where Linux and open source software is concerned.


                 After all, despite the environment, 2021 was a
                 particularly buoyant year for Ubuntu on the desktop


                 Ubuntu 21.04 and 21.10 both made their way out with new
                 features, new kernels, and in the latter’s case, even a
                 new desktop. Strong foundations laid ahead of April 2022
                 release of Ubuntu 22.04 LTS.


          o § Linux Magazine⠀➾


                # ⚓ Visualize_your_network_with_Skydive⠀⇛


                # ⚓ Indoor_navigation_with_machine_learning⠀⇛


                # ⚓ Comparing_tools_for_an_easy_data_exchange⠀⇛


                # ⚓ Zack’s_Kernel_News⠀⇛


                # ⚓ Create_impressive_presentations_with_Kdenlive⠀⇛


                # ⚓ Fuzzing_and_the_quest_for_safer_software⠀⇛


                # ⚓ What_About_the_Cats?⠀⇛


                # ⚓ Distributed_programming_made_easy_with_Elixir⠀⇛


                # ⚓ EndeavorOS_21.4_Has_Arrived⠀⇛


                # ⚓ This_month_in_Linux_Voice.⠀⇛


                # ⚓ Sparkling_gems_and_new_releases_from_the_world_of_Free_and
                  Open_Source_Software⠀⇛


                # ⚓ Modern_PDF_security⠀⇛


                # ⚓ An_Amiga_emulator_for_the_Raspberry_Pi_400⠀⇛


                # ⚓ Creating_your_own_custom_maps⠀⇛


                # ⚓ Reviving_old_computers⠀⇛


                # ⚓ Pacstall_brings_the_freedom_of_the_AUR_to_Ubuntu⠀⇛


                # ⚓ The_sys_admin’s_daily_grind:_getnews.tech⠀⇛


                # ⚓ Game_development_with_Go_and_the_Fyne_framework⠀⇛


                # ⚓ A_security-conscious_OS⠀⇛


                # ⚓ On_the_DVD_»_Linux_Magazine⠀⇛


                       The Parrot Project is an Italian-based distribution
                       based on the Debian Testing repository with an
                       emphasis on security. Although regular releases are
                       made, Parrot OS is also a rolling release,
                       enhancing security with the latest updates.


                       Parrot OS is available in three editions: Security,
                       Home, and ARM. The Security Edition, which is set
                       up for everything from penetration testing to
                       digital forensics and reverse engineering, includes
                       a wide variety of programming tools. The Home
                       Edition on this month’s DVD includes many of the
                       security features found on the Security Edition.
                       The Home Edition features Tor (aka The Onion
                       Router), the well-known tool for anonymous web
                       browsing; OnionShare, which shares files of any
                       size over Tor; and AnonSurfer, which routes the
                       operating system’s communications over Tor. Other
                       tools include the Electrum Bitcoin Wallet for
                       secure trading of crypto currencies and the self-
                       explanatory metadata cleaner and secure file
                       deleter.


                       Parrot OS deals with many advanced security
                       concepts and tools. However, by placing the tools
                       on a desktop environment, Parrot makes privacy and
                       security accessible to users of all levels. If you
                       are a new user, Parrot is one of the best
                       distributions to teach you what you need to know to
                       keep your computing safe.


          o § Audiocasts/Shows⠀➾


                # ⚓ Noodlings_35_|_Light_for_Christmas⠀⇛


          o § Instructionals/Technical⠀➾


                # ⚓ How_To_Install_Cockpit_On_Rocky_Linux_8_Or_Alma_Linux_8_|
                  Tips_On_UNIX⠀⇛


                       Cockpit is a web-based server administration tool
                       sponsored by Red Hat and by using this tool you can
                       easily manage the server in a graphical way.


                       From Fedora 21 and RHEL 8 onwards Cockpit loaded
                       with default.


                       This tutorial will be helpful for beginners to
                       install cockpit on Rocky Linux 8 / Alma Linux 8.


                # ⚓ How_to_Install_and_Use_FFmpeg_on_CentOS_8.⠀⇛


                       FFmpeg is a free and open-source software project
                       consisting of a suite of libraries and programs for
                       handling video, audio, and other multimedia files
                       and streams. It contains a set of shared audio and
                       video libraries such as libavcodec, libavformat,
                       and libavutil. With FFmpeg, you can convert between
                       various video and audio formats, set sample rates,
                       capture streaming audio/video, and resize videos.


                # ⚓ Install_and_Configure_Virtualmin_on_Ubuntu_20.04⠀⇛


                       So, Virtualmin is an open-source web hosting and
                       cloud control panel. Virtualmin has the right
                       features and controls over managing all the
                       different domains at the same portal. It allows
                       access to the server via an SSL-encrypted HTTP
                       line. For example,. via a standard browser and
                       provides a clear user interface.


                # ⚓ Install_Miniconda_In_Linux⠀⇛


                       Miniconda is a minimal and stripped-down version of
                       Anaconda distribution. As the name implies,
                       Miniconda contains only Conda package manager,
                       Python and a small number of useful packages such
                       as pip, zlib including their dependencies.


                       Miniconda is suitable for those who don’t mind to
                       install each package individually. It saves you not
                       only the disk space but also avoids dumping a lots
                       of unnecessary applications that you don’t use
                       often in your hard drive. For those wondering,
                       Anaconda distribution automatically installs 1,500
                       packages that consumes around 3 GB disk space. If
                       you use only a handful of applications, miniconda
                       might be a good choice.


                # ⚓ How_to_set,_change_and_delete_music_tags_with_Mutagen⠀⇛


                       Tagging music files is a way of keeping a music
                       library well organized and let us search for songs
                       on the base of Artists, albums, genre and other
                       parameters. Many graphical and command line
                       applications exist on Linux to manage tags for
                       audio files, like Picard or Quodlibet. Most of
                       those applications are written in Python and use
                       the “mutagen” module at their core. In this
                       tutorial we learn how to use it directly.


                # ⚓ Top_Five_Chat_Apps_For_Ubuntu_Users⠀⇛


                       Here are the top five chat apps for Ubuntu users.
                       Having a decent chat application could help team
                       members to collaborate in an effective way. Team
                       members can collaborate effectively with a decent
                       chat app. Although there are many applications
                       available in the market, we will discuss only five
                       of them which are Ubuntu compatible. Click here to
                       refer to more similar topics.


                       As a result of the pandemic, collaboration tools
                       have become more important. Which utility to
                       choose? So, It varies from user to user because
                       sometimes the criteria are sharing data and other
                       times secure and encrypted communication. A decent
                       GUI, quick installation, and easy-to-use features
                       are important. Here, after going through multiple
                       utilities, we tried to opt top 05 tools. Hope they
                       will be as per your need. Let’s start.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ This_week_in_KDE:_Finally_root_file_operations_in
                        Dolphin_–_Adventures_in_Linux_and_KDE⠀⇛


                             This week the last piece of a major project
                             almost five years in the making was merged:
                             PolKit support in KIO! This allows Dolphin
                             and other KDE apps that use the KIO library
                             to to create, move, copy, trash, and delete
                             files in non-user-owned locations! It took a
                             long time but we finally got it. Thanks very
                             much to Jan Blackquill for pushing this over
                             the finish line and Chinmoy Ranjan Pradhan
                             for starting it and getting it very far those
                             years ago. Support will arrive in Frameworks
                             5.90 in a few weeks. Please test it out and
                             file bugs on frameworks-kio if things don’t
                             work right!


                      # ⚓ Highlights_from_2021_–_Adventures_in_Linux_and_KDE⠀⇛


                             The coronavirus pandemic frustratingly
                             continued to spread misery this year, but one
                             silver lining to this cloud was that keeping
                             people at home meant lots of contributions to
                             KDE! As a result this was an enormous year
                             for KDE and all who use its software. Like I
                             did last year, I’d like to mention some of my
                             favorite big features and improvements from
                             the past 12 months. Also like last year,
                             what’s written here is just the tip of the
                             tip of the iceberg, probably not even a tenth
                             of a percent, and also a very selective look
                             at just some of the software I use and follow
                             on a regular basis. There’s a whole lot more
                             at https://planet.kde.org!


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Best_Ubuntu_Themes_In_2022⠀⇛


                             Ubuntu is one of the most popular Linux
                             operating systems right now on the internet.
                             It is often considered as the first choice
                             for people using Linux for the first time.


                             In this post, we will be discussing the best
                             Ubuntu themes available on the internet. You
                             can install various Ubuntu themes to make
                             your distro more beautiful.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ New_year,_new_Opensource.com_community_manager_|
                        Opensource.com⠀⇛


                             I am privileged to be here at Opensource.com
                             as the new community manager. I’m looking
                             forward to working with existing
                             correspondents and contributors, and also
                             bringing in new contributors and increasing
                             the diversity of thoughts and ideas shared
                             here on Opensource.com.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ A_Tidy_Cyberdeck_That_You_Could_Take_Anywhere._|
                        Hackaday⠀⇛


                             The cyberdeck trend has evolved to a
                             relatively straightforward formula: take a
                             desktop computer and strip it to its barest
                             essentials of screen , PCB, and input device,
                             before clothing it in a suitably post-
                             apocalyptic or industrial exterior. Sometimes
                             these can result in a stylish prop straight
                             from a movie set, and happily for [Patrick De
                             Angelis] his Raspberry Pi based cyberdeck
                             (Italian, Google Translate link) fits this
                             description, taking the well-worn path of
                             putting a Raspberry Pi and screen into a
                             ruggedised flight case. Its very
                             unremarkability is the key to its success,
                             using a carefully-selected wired keyboard and
                             trackpad combo neatly dodges the usual
                             slightly messy arrangements of
                             microcontroller boards.


                      # ⚓ The_No-MCU_Fan_Controller_|_Hackaday⠀⇛


                             The default for any control project here in
                             2019 was to reach for a microcontroller. Such
                             are their low cost and ubiquity that they can
                             be used to replicate what might once have
                             needed some extra circuitry, with the minimum
                             of parts. But here we are at the end of 2021,
                             and of course microcontrollers are hard to
                             come by in a semiconductor shortage. [Hesam
                             Moshiri] has a project that takes us back to
                             a simpler time, a temperature controlled fan
                             the way they used to be made, without a
                             microcontroller in sight.


                      # ⚓ Customisable_Micro-Coded_Controller_Helps_With_In-
                        Circuit_Debugging_|_Hackaday⠀⇛


                             Over on Hackaday.io, [Zoltan Pekic] has been
                             busy building a stack of tools for assisting
                             with verifying and debugging retro computing
                             applications. He presents his take on using
                             Intel hex files for customised in-circuit
                             testing, which is based upon simple
                             microcoded sequencers, which are generated
                             automatically from a high level description.


                             The idea is that it is very useful to be able
                             to use an FPGA development board to emulate
                             the memory bus component of the CPU, allowing
                             direct memory access for design validation
                             purposes. This approach will also allow the
                             production of a test rig to perform board
                             level verification. The microcode compiler
                             (MCC) generates all the VHDL, and support
                             files needed to target a Xilinx FPGA based
                             dev board, but is generic enough to enable
                             targeting other platforms with a little
                             adaptation.


                      # ⚓ 3D_Printering:_Adding_A_Web_Interface_Where_There_Was
                        None_Before_|_Hackaday⠀⇛


                             [Renzo Mischianti] got himself a Chinese 3D
                             printer, specifically a FlyingBear Ghost 5.
                             (Cracking name, huh?) He was more than a
                             little irritated with the fact that whilst
                             the controller, an MKS Robin Nano, did have a
                             integrated Wi-FI module, it provided no web-
                             based interface for monitoring and control
                             purposes. This seemed a bit short-sighted in
                             this day and age, to say the least. Not being
                             at all happy with that situation, [Renzo]
                             proceeded to write dedicated Wi-Fi firmware
                             using websockets, but not without fully
                             documenting his journey in a detailed series
                             of the blog posts.


                             [...]


                             We’ve been covering 3D printer hacking since
                             the dinosaurs were roaming. This is the
                             oldest, and still one of the strangest, posts
                             that we could find in a quick search. Anyone
                             care to find something older?


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Some_Android_apps_on_the_Samsung_Galaxy_Store_could
                        infect_your_phone_with_malware,_so_delete_them⠀⇛


                      # ⚓ Nokia_G50_gets_Android_12_update_–_GSMArena.com
                        news⠀⇛


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


                      # ⚓ OP:_Pixel_handheld_could_start_Android_gaming
                        revolution_–_9to5Google⠀⇛


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


                # ⚓ 4_metrics_to_measure_sustainable_open_source_investments._–
                  Justin_W._Flory’s_blog⠀⇛


                       How do we understand value when we talk about
                       sustainability? What does investing in open source
                       mean? The meaning is different for many people
                       because of an implicit understanding of what open
                       source means.


                       This post is a reflection on the past year in my
                       work with the UNICEF Venture Fund. We integrated
                       new open source tools to capture metrics and data
                       about open source repositories connected to UNICEF
                       portfolio companies and created a shortlist of key
                       metrics that map to business sustainability
                       metrics. Now, we are better positioned to look back
                       on past, current, and upcoming portfolio companies
                       and mentor support programs.


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ Use_basegfx_to_convert_angle_unit_–_EasyHack⠀⇛


                             First, what is basegfx, how it is used for
                             converting angle units, and why we should
                             care?


                             If you look at the list of LibreOffice
                             modules in docs.libreoffice.org, you will see
                             that basegfx is one of the LibreOffice
                             modules. It contains the “algorithms and data
                             types for graphics“, and it provides useful
                             functions for LibreOffice graphics code. We
                             care because using these functions helps us
                             write cleaner code using well tested methods.


                      # ⚓ Happy_New_Year_2022!⠀⇛


                # § Programming/Development⠀➾


                      # ⚓ Header_Guards_C++⠀⇛


                             A header guard in C++ is a component that
                             proves to be your savior whenever you attempt
                             and make a mistake while writing your code by
                             defining a function more than once with the
                             same name. Every programmer needs to know
                             that it is never considered good practice to
                             include the function definitions in the
                             header files. However, at times, you need to
                             do so. In that case, you must know how to
                             properly use the header guards in C++.
                             Therefore, this article discusses the need to
                             use the header guards in C++, followed by
                             some examples to teach you their usage on the
                             Ubuntu 20.04 system.


                             Why Do We Need to Use the Header Guards in
                             C++?


                             While writing your code, you define certain
                             header files on your own, depending upon the
                             functionality you require. After creating
                             these header files, you can include them all
                             in your .cpp file that contains your actual
                             code. However, sometimes these header files
                             depend upon each other. So, you have to
                             include one header file into another. In that
                             case, when you include both these header
                             files into your .cpp file, the same functions
                             of one header file might be defined twice.
                             This leads to the generation of a compile-
                             time error since C++ strictly prohibits the
                             definition of the same function twice within
                             the same code. Therefore, we use the header
                             guards to protect your header files from
                             malfunctioning to resolve this dependency
                             issue.


                             These header guards can be implemented using
                             the four pre-processor directives: #ifndef,
                             #define, #ifdef, and #endif. For example,
                             whenever you enclose a piece of code within
                             the “#ifndef” directive, the compiler always
                             checks whether the following code has been
                             previously defined or not. If not, then the
                             statements following the “#define” directive
                             are executed. Otherwise, these statements are
                             simply ignored. This, in turn, ensures that
                             your program always compiles successfully and
                             the same functions are not defined more than
                             once within the same code. The “#ifdef”
                             directive works vice-versa. You will be able
                             to understand all this in a better way after
                             going through the following two examples.


    * § Leftovers⠀➾


          o ⚓ Movement_Music_After_the_Movement_Fades:_Reflections_on_Phil
            Ochs⠀⇛


                 Throughout Phil’s twenties — that is, throughout the
                 1960’s — social movement activity in the US (and much of
                 the rest of the world, for lots of different reasons)
                 grew.  It was a period of constant tumult and change of
                 all sorts, and Phil’s style of music was probably more
                 popular in the early Sixties than in the later part of
                 the decade, with louder, more electric instruments being
                 more dominant in the scene, and on the FM airwaves.  But
                 regardless of various career ups and downs — and despite
                 what was later demonstrated to be an organized campaign
                 conducted by the FBI against a variety of musicians,
                 including Phil — he continued to write, record, tour and
                 perform throughout the United States and occasionally
                 elsewhere, throughout the period.


                 In the early 1970’s a lot of things were happening that
                 were supposedly affecting the antiwar movement’s size and
                 scope, such as the massacres of protesters at Kent and
                 Jackson state universities, as well as the scaling back
                 of the presence of ground troops in Vietnam, since so
                 many of them were refusing to fight anyway, and fragging
                 their officers instead.  (If you don’t happen to know
                 what “fragging” means, please look it up, you’ll be glad
                 you did.)


          o ⚓ NYC_Officials_Denounced_for_Holding_New_Year’s_Celebration_Amid
            Omicron_Surge⠀⇛


                 Public health experts expressed shock Friday as New York
                 City went ahead with its plans to hold a scaled-back—but
                 still large—New Year’s Eve celebration in Times Square,
                 with 15,000 people expected to pack the landmark to ring
                 in 2022 as the city sets new records for Covid-19 cases.


                 Outgoing Democratic Mayor Bill de Blasio announced last
                 week that the traditional New Year’s ball drop will go
                 on, prompting epidemiologists to warn that the event will
                 carry risks for attendees and the city’s already-strained
                 healthcare facilities—as well as communities across the
                 country, since many of the attendees are likely to be
                 visiting from elsewhere.


          o ⚓ Intrepid_Trips,_Indeed⠀⇛


                 The next few years, as I dove deeper into the world of
                 the counterculture I learned that that book’s author Tom
                 Wolfe was a damn good observer, a pretty decent
                 journalist if you liked this stuff they called the New
                 Journalism, and anything but a hippie freak. I read that
                 book every summer in high school, the style and the story
                 imprinted in my brain. As the 1970s wore on, I watched as
                 the world of the grey flannel suits fought against the
                 world of blue jeans, long hair and marijuana. I knew
                 which side I was on. It wasn’t the ones wearing suits
                 (figuratively speaking). Unlike the political world of
                 the time—which ultimately put “if there’s going to be a
                 bloodbath, let’s get it over with” Ronald Reagan into the
                 White House in 1980—there were no clear cut victors in
                 the cultural struggle. Capitalists in both realms figured
                 out ways to sell the pieces of the counterculture that
                 were salable. And the people bought it.


                 As for me, I moved to the Bay Area, where the
                 counterculture was still hanging on. I began meeting some
                 of the people I had only read about. I played it cool,
                 listening to their stories while hanging out drinking
                 beer in People’s Park, crashing at the Hog Farm house, at
                 concerts big and small, the White Panther squats and the
                 parties I ended up at. The storytellers included acid
                 manufacturers recently out of prison, Black Panthers
                 tending bar, hippie women turned Christian, street
                 hustlers who fought the cops in the Haight uprisings and
                 then People’s Park, college professors, working musicians
                 and burnt out rock musicians whose bands had left them
                 behind. Every collection of freaks had their memories and
                 every freak had their own version of what went down.
                 Still, certain stories and storytellers were paramount.
                 Like the book of Genesis or the creation stories of the
                 Tlingit, those stories were origin stories. Those were
                 the ones I wanted to hear, to collect and remember. This
                 interest remained even as those who knew them left their
                 earthly existence, taking their tales with.


          o ⚓ A_Prescription_for_Resistance_to_the_Bully_of_Christmas:_Make
            Art⠀⇛


                 Given such evidence of where our public education has
                 gone, before alluding to a story from the Christian bible
                 which – for various reasons – may not be in every
                 reader’s wheelhouse, I’ll briefly fill in the details,
                 trusting I insult no one! Here goes:


                 In Matthew’s version of the Christmas story, Herod the
                 king feared the birth of a rival and so sent out his
                 soldiers to murder all the male babies in Bethlehem. An
                 angel warns Mary and Joseph, the new parents of baby
                 Jesus, to flee in order to save the child. Importantly,
                 the parents heeded the advice and got the hell out of
                 town (the flight into Egypt). They did not, that is,
                 declare the warning preposterous, did not protest but
                 people don’t do that kind of thing to little children! At
                 great personal expense, they exiled themselves, becoming
                 refugees.


          o ⚓ Macedonian_Ramble:_Hell’s_Foundations_at_Galliopoli⠀⇛


                 By my standards I splurged on my accommodation, the Hotel
                 des Etrangers in Çanakkale, wanting to have a room that
                 overlooked the Dardanelles so that from my window I could
                 watch the passage of ocean-going ships on their stately
                 procession to and from the Bosphorus and the Aegean.


                 At Çanakkale the strait (which separates Europe from
                 Asia) is only several kilometers wide, and in the course
                 of a few hours by the seafront everything from container
                 ships to destroyers passes before your eyes. Many ships
                 are headed to Istanbul; the rest ply the Black Sea.


          o ⚓ 2021_Latin_America_and_the_Caribbean_in_Review:_The_Pink_Tide
            Rises_Again⠀⇛


                 Central has been the struggle of the ALBA (Bolivarian
                 Alliance for the Peoples of our America) countries –
                 particularly Venezuela, Cuba, and Nicaragua – against the
                 asphyxiating US blockade and other regime-change
                 measures. Presidential candidate Biden pledged to review
                 Trump’s policy of US sanctions against a third of
                 humanity. The presumptive intention of the review was to
                 ameliorate the human suffering caused by these unilateral
                 coercive measures, considered illegal under international
                 law. Following the review, Biden has instead tightened
                 the screws, more effectively weaponizing the COVID
                 crisis.


                 Andean Nations


          o ⚓ Opinion_|_Top_3_Pieces_of_Good_News_in_2021—Because_Optimists_Are
            the_Problem_Solvers⠀⇛


                 News corporations think good news does not sell, which is
                 why you see so little of it on television or on the front
                 page of news websites. Executives at for-profit news
                 believe their corporations benefit, just as do social
                 media platforms, from provoking your fight or flight
                 reflexes — making you angry or afraid — since the
                 adrenaline rush keeps you reading and keeps you coming
                 back for more. They think bad news is addictive. It is to
                 the point that the editors and journalists seem to feel
                 they have to cast President Biden in a bad light unfairly
                 to keep their viewers.


          o ⚓ Yes,_There_Were_10_Good_Things_About_2021⠀⇛


                 It was, indeed, a disastrous year, but we do have some
                 reasons to cheer:


                 1. The U.S. survived its first major coup plot on January
                 6 and key right-wing groups are on the wane. With
                 participants in the insurrection being charged and some
                 facing significant jail time, new efforts to
                 mobilize–including September’s “Justice for J6”
                 rally–fizzled. As for Trump, let’s remember that in early
                 2021, he was impeached again, he lost his main
                 mouthpiece, Twitter, and his attempt to build a rival
                 social media service seems to have stalled. QAnon is in
                 decline—its major hashtags have evaporated and Twitter
                 shut down some 70,000 Q accounts. We may still see a
                 resurgence (including another Trump attempt to take the
                 White House), but so far the insurrection seems to have
                 peaked and is being rolled back.


          o ⚓ 2021_Year_in_Review:_EFF_Graphics⠀⇛


                 All the graphics we create are original, and free to the
                 public to use on a Creative Commons Attribution license.
                 That means that if you are fighting to stop police misuse
                 of surveillance technology in your community, promoting
                 free expression online, or simply looking for a way to
                 share your love for EFF and digital rights with the
                 world, you are free to download our graphics and use them
                 for your own purposes without permission. It’s our way of
                 seeding the Commons!


                 Below is a selection of graphics we produced this year.
                 We hope you enjoy perusing them! To learn more about each
                 project, go ahead and click the image. It will link you
                 to a page where you can learn more.


          o ⚓ Bright_Green_Lies_Torpedoes_Greens⠀⇛


                 According to Bright Green Lies authors Derrick Jensen,
                 Lierre Keith, and Max Wilbert: “We are writing this book
                 because we want our environmental movement back.” As
                 such, they charge ahead with daggers drawn, similar to
                 Planet of the Humans (2019-20), nobody spared.


                 As explained therein, Rachel Carson’s Silent Spring
                 (1962) brought on the environmental movement as well as
                 establishment of the EPA, the Clean Air Act, the Clean
                 Water Act, and the Endangered Species Act. She did not
                 call for “saving civilization,” which is the common
                 rallying cry today (“Civilizations Last Chance” by Bill
                 McKibben or Lester Brown, “The Race to Save
                 Civilization”). Rachel Carson called for “saving nature.”


          o ⚓ Looking_Up_From Don’t_Look_Up:_Adam_McKay_and_End_Times⠀⇛


          o ⚓ Who_Will_Guard_the_Guardians?⠀⇛


                 Quis custodiet ipsos custodes? (Juvenalis, Satires) — who
                 will guard over the guardians ? — when the mainstream
                 media no longer performs the function of the watchdog, no
                 longer alerts us to endemic — and punctual — governmental
                 abuses but act more like echo-chambers of the interests
                 of certain “elites” and transnational corporations…  who
                 will blow the whistle on governmental and private-sector
                 scams?  How can we defend our rights when our elected
                 officials, those who have the obligation to uphold the
                 law, are actually in the service of other, more powerful
                 and lucrative interests?  What can we do when the
                 executive, legislative and judiciary are progressively
                 corrupted, when institutions like the ICC discontinue
                 investigations into gross criminality by powerful states
                 while prosecuting the little fish, when the Organization
                 for the Prohibition of Chemical Weapons tampers with the
                 evidence of inspectors and suppresses crucial facts
                 (Douma “report” on Syria), when the OAS is complicit in a
                 coup d’état against an OAS member state (Bolivia), when
                 other supposedly objective organizations systematically
                 dis-inform the public, disseminate evidence-free news,
                 suppress dissent?


                 Only we can be the guardians — by reclaiming democracy
                 and our right to effective participation in public
                 affairs, as stipulated in article 25 of the International
                 Covenant on Civil and Political Rights. We must condemn
                 the politicization and “weaponization” of human rights,
                 especially when human entitlements are instrumentalized
                 to obliterate others.


          o ⚓ Bells_Tolling_for_Russian_Memory⠀⇛


                 Similar is the story of former prisoner Susanna Pechuro,
                 who as a teenager with her boyfriend tried to safeguard
                 revolutionary values from what they both considered the
                 ideological deviation of Stalin’s government. After their
                 arrest, the boyfriend was shot while Susanna was
                 sentenced to decades in the gulag. When, after Stalin’s
                 death, Khrushchev declared amnesty, Susanna became a
                 history teacher and later one of the founders of the
                 Memorial, institution fostered by Mikhail Gorbachev’s
                 perestroika. Her dress with the white schoolgirl’s collar
                 in which she was arrested and which she wore in prison
                 was deposited at the Memorial.


                 In the Memorial I also found books, which in the gulag
                 represented the most treasured possession, although
                 generally forbidden and therefore scarce. Books were the
                 salvation because reading made one forget the
                 wretchedness of the camp and provided the prisoners with
                 thoughts to occupy their minds while they worked up to
                 fourteen hours a day, not counting the long marches to
                 the place of work. In the reading, the prisoners found
                 surprising insights and unusual beauty, which helped them
                 to retain their dignity as human beings. Many people who
                 spent years or decades in the gulag deposited in the
                 Memorial those objects that had helped them most to
                 develop resilience.


          o ⚓ Who_Owns_the_Clouds?_The_Adventures_of_the_Chinese_and_Me_in
            Changing_the_Weather⠀⇛


                 An article in the Guardian on December 3 was about
                 climate change and it described the ways China is now
                 trying to increase rainfall to cope with present and
                 future water shortages. What really caught my eye was the
                 scope of China’s undertaking, which is immense. It also
                 caught my attention for personal reasons. The main method
                 the Chinese are using is of course cloud seeding and that
                 is something I have been involved in.


                 The article featured a photo of Chinese soldiers firing a
                 cannon aimed at the sky—which is certainly in keeping
                 with numerous articles about what is now described as
                 China’s aggressive behavior. If you only looked at the
                 headline and the photo you might think that now the
                 Chinese are attacking even the clouds. The Chinese were
                 firing rockets filled with either silver iodide or liquid
                 nitrogen into clouds. Either substance will cause the
                 cloud’s moisture to form water droplets. As it happens I
                 was involved in this same activity years ago, although I
                 did not use a cannon.


          o ⚓ Happy_New_Year,_It’s_Sure_Been_Weird⠀⇛


                 Whether the pandemic that’s swept the world started from
                 a bat or not, as 2021 ends, I think it’s safe to say that
                 we’re all far battier than we were when it began.


          o ⚓ Harry_Reid_Understood_Power⠀⇛


                 Former Senate Democratic leader Harry Reid died Tuesday
                 at 82. Effective, ruthless, and understated, Reid used
                 his position as head of the Senate’s Democratic caucus
                 from the end of the Bush years through the Obama
                 presidency to advance Democratic legislation and protect
                 programs like Social Security.


          o ⚓ Brazil,_Amazon,_World:_Sociopathy_vs_Democracy⠀⇛


                 Although it’s a monstrous form of conscious social
                 engineering aimed at concentrating wealth and power,
                 neoliberalism tends to be presented as a kind of evenly
                 spread biological law governed by a “market” that panders
                 to individuals turned into consumers whose democratic
                 choices are mainly limited to competitive buying and
                 selling. Those who can’t enter the competition drop or
                 are dropped by the wayside. When this sociopathic system
                 appears, full-blown, in a person who commits or
                 encourages these crimes, its malignity for all living
                 things is unmasked.


                 Take one of Bolsonaro’s more recent demonstrations of
                 this. After weeks of heavy rain in Brazil’s north-eastern
                 state of Bahia, the Igua dam on the Verruga River near
                 the city of Vitoria da Conquista collapsed on 25
                 December, and a second dam, the main source of potable
                 water in Jussiape, 100 kilometres to the north, burst on
                 26th. Twenty people have died as a result of the heavy
                 rains and flooding, more than 430,000 people have been
                 affected, 36,000 are homeless and thousands have been
                 evacuated from at least 72 towns facing emergency
                 situations, many of them without electricity. In the
                 state capital, Salvador, the December rainfall has been
                 six times higher than the average.


          o ⚓ New_Year’s_Message:_The_Arc_Of_The_Moral_Universe_Is_A_Twisty
            Path⠀⇛


                 As long term readers of Techdirt know, each year since
                 2008 my final post of the year has been a kind of
                 reflection on optimism. This tradition started after I
                 had a few people ask how come it seemed that I was so
                 optimistic when I seemed to spend all my time writing
                 about scary threats to innovation, the internet, and
                 civil liberties. And there is an odd contradiction in
                 there, but it’s one that shows up among many innovation
                 optimists. I’m reminded of Cory Doctorow’s eloquent
                 response to those who called internet dreamers like John
                 Perry Barlow “techno utopians.”


          o § Science⠀➾


                # ⚓ Biden_administration_will_continue_ISS_cooperation_through
                  2030⠀⇛


                       The ISS’s future was called into question in 2018,
                       when a draft budget proposal from President Donald
                       Trump’s administration had scheduled ending support
                       for the space station in 2025. More recently,
                       escalating tensions between the US and Russia have
                       threatened the cooperation required to work
                       together on the ISS. In November, Russia blew up a
                       satellite, creating a dangerous debris cloud in
                       Earth’s orbit.


          o § Education⠀➾


                # ⚓ The_Tutor⠀⇛


                       For Josephus, Pilate was an unreasonable tyrant.


                       During my thirty-five years at Cal., ninety-five
                       percent of my students were suburban whites. Long
                       before Andrew Hacker* and Charles Murray,** I
                       learned that “a tangle of pathologies” was
                       occurring in the suburbs, while Hollywood,
                       Television, and Think Tank intellectuals and
                       columnists were profiting by blaming social
                       problems on Black personal behavior. I’m not
                       surprised that life expectancy among whites is
                       diminishing because of Opioid addiction. Heroin
                       epidemics were occurring in the suburbs of
                       Philadelphia in the late nineties; the epidemics
                       were hidden in the back pages. They didn’t want to
                       embarrass those who supported their advertisers.
                       While the press divided races between powder
                       cocaine and crack cocaine users, the typical crack
                       addict was white. Jonathan Capehart says he just
                       found that out. I wrote about white crack addiction
                       ten years ago.* Even as the drug crisis among white
                       Americans is spreading, the media represents the
                       distribution of drugs and their consumption as
                       Black.


                # ⚓ Teacher_faces_probe_for_organizing_mixed-gender_forest_walk
                  for_students⠀⇛


                       The administration of a prestigious high school in
                       İstanbul has launched an investigation into a
                       teacher for organizing a walk in the woods with the
                       participation of both male and female students, the
                       Gerçek Gündem news website reported.


                       Gülay Hacısalihoğlu, the principal of the Beyoğlu
                       Anatolian High School, initiated the investigation
                       into teacher Engin Ulus for organizing a mixed-
                       gender walk in the Bentler Nature Park in İstanbul
                       on Oct. 23, Gerçek Gündem said.


                # ⚓ Conservative_Muslims_pressure_liberals_in_Berlin_schools:
                  study⠀⇛


                       Berlin schools in the multicultural Neukölln
                       district face growing religious intolerance.
                       Conservative Muslims pressure liberal students and
                       teachers to adapt their behavior to stricter
                       interpretations of Islam, according to a survey
                       conducted by the Association for Democracy and
                       Diversity in Schools established by the federal
                       government.


                       The research, supported by the Ministry for Federal
                       Ministry for Family Affairs, Senior Citizens,
                       Women, and Youth at the request of the Neukölln
                       district office, focused mainly on confrontational
                       manifestations of religion and lasted three months.


          o § Hardware⠀➾


                # ⚓ Threaded_Wires_Save_Phone_Numbers_|_Hackaday⠀⇛


                       If you thought programming your 1990s VCR was
                       rough, wait until you see this Russian telephone
                       autodialer that [Mike] took apart over on the
                       mikeselectricalstuff YouTube channel (video below
                       the break). [Mike] got this 1980s Soviet-era
                       machine a few years ago, and finally got around to
                       breaking into it to learning what makes it tick.
                       The autodialer plugs into the phone line, much like
                       an old-school answering machine. It provides the
                       user with 40 pre-set telephone numbers, arranged in
                       two banks of 20, and a speaker to monitor the
                       connection process. It uses pulse dialing — no
                       touch tones. What’s surprising is how you program
                       the numbers. Given that this was build in the 1980s
                       Soviet Union, he wasn’t expecting a
                       microcontroller. But he wasn’t expecting
                       transformer core “rope” memory, either.


                       [...]


                       Mike tries to decipher the schematics and pokes
                       around enough to get the gist of how it works. This
                       design is an interesting solution to the problem of
                       building an autodialer in that era. If you want to
                       learn more about core memory, here’s an article we
                       wrote about deciphering an Apollo rope memory
                       module, perhaps one of the most well-known examples
                       of this technology. We also covered a couple of
                       projects using rope memory techniques but on a
                       small scale, here and here.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Ending_a_Global_Pandemic_Should_Not_Rely_on_“Individual
                  Responsibility”⠀⇛


                # ⚓ Why_Leftists_are_Joining_Hands_With_the_Right_in_Opposing
                  Vaccine_Mandates⠀⇛


                       Most telling, archconservatives hated the mandates.
                       That’s always a good sign that you are on the side
                       of the angels.


                       But while many on the far right oppose the mandates
                       for idiotic reasons (whacky conspiracy theories,
                       quack science) and a few have gone so far as to
                       plot the assassination of a German governor, more
                       and more people on the far left are objecting to
                       vaccine mandates out of ideological concerns, i.e.,
                       how far government power can be exercised.


                # ⚓ On_Manhood_and_Vaccines⠀⇛


                       Beyond misinformation, the real reason for opposing
                       the vaccinations is simple defiance to the wishes
                       of people and institutions that anti-vaxxers don’t
                       like.  It is intransigence based on an intuitive
                       version of Napoleon’s Maxim XVI: “never do what the
                       enemy wishes you to do for this reason alone, that
                       he desires it.”2  In this petty, internalized form,
                       it is also related to the resentful slave morality
                       outlined by Nietzsche in On the Genealogy of Morals
                       and the idea of not giving others the satisfaction
                       of complying with their desires, even when they are
                       right.  In psychology, the doubling-down on being
                       wrong in this way is known as cognitive
                       dissonance.3  Those who still do not realize that
                       they are wrong are the victims of a mass
                       propaganda-driven cult-like phenomenon. The fact
                       that so many people would accept Internet rumors
                       over medical science is shocking but not
                       surprising.


                       But the implied justification for resisting
                       vaccination is moral staunchness and physical
                       toughness, and when manifested in a man, it harkens
                       back to older notions of manhood and manliness.  To
                       those of us who accept vaccines as safe and
                       effective products of modern science, the anti-
                       vaccine mindset appears to be a widespread instance
                       of noisy and occasionally violent yahooism, and a
                       kind of physical and moral cowardice—the opposite
                       of manliness.  It is the virtues of honorable
                       manhood honored in the breach.  It is dumb
                       braggadocio. Courage must have a higher purpose
                       than just courting personal risk and the anti-
                       vaxxers mistake recklessness for valor. And their
                       external bluster appears to mask squeamishness
                       about needles and well-tested medicine.


                # ⚓ Ideological_Struggle:_Language_in_the_Era_of_COVID-19⠀⇛


                       The abundant use of military metaphors is clearly
                       demonstrated by phrases such as “increasing our
                       armamentarium of weapons to combat COVID-19,” or
                       such as when Vice President Harris announced that
                       “the virus hit our shores” and when President Biden
                       announced plans to deploy 1,000 military medical
                       professionals to “support overburdened hospitals”
                       in US cities. A particularly vile instance was a
                       recent NY Daily News headline which announced that
                       “kids enter COVID-19 crosshairs”. These
                       announcements, and the words chosen to make them,
                       should prompt, among other things, increased
                       recognition of the adverse impact the use of
                       military metaphors, related terms and the frames
                       they evoke, and of the strategic value of their
                       avoidance or minimization. Both with respect to
                       COVID-19 and more generally, the strategic value of
                       utilizing metaphors and frames that better reflect
                       progressive goals of equitable public health,
                       community, solidarity and peace cannot be
                       understated.


                       Progressive struggle requires action through a
                       range of domains, including the ideological. A key
                       component of ideological struggle is the choice of
                       words used to promote and support important
                       positions–a strategy regressive extremist forces
                       have recognized and effectively exploit. For
                       example, Republican strategist Frank Luntz
                       emphasized that Republicans should never speak of a
                       “public health care option”, “oil drilling” or an
                       “estate tax”, but should instead only refer to a
                       “government mandate”, to “energy exploration” or to
                       a “death tax”; while promoting reactionary,
                       neoliberal positions, he has nonetheless correctly
                       stressed the strategic importance of using word
                       choices that make use of the conscious or
                       subconscious emotional content of words.


                # ⚓ Campaign_Urges_Biden_Admin_to_Mail_‘Continuous’_Supply_of
                  Masks,_Tests_to_All_US_Households⠀⇛


                       A new campaign led by public health experts and
                       grassroots activists—including the daughter of a
                       Covid-19 victim—is calling on the Biden
                       administration to deliver rapid tests and high-
                       quality masks to every household in the United
                       States as the nation faces a tsunami of new
                       infections.


                       “We are asking you to mail an ample and continuous
                       supply of free rapid at-home tests and N95-quality
                       masks to every household in America twice a month
                       through May 2022, with additional supplies sent to
                       first responders, healthcare workers, and public
                       centers in our most impacted communities,” reads
                       campaigners’ open letter to Jeffrey Zients, the
                       White House’s coronavirus response coordinator.


                # ⚓ My_APA_Resignation⠀⇛


                       I’ve been a member of the American Psychological
                       Association (APA) for years, and a fellow for the
                       past six or seven years. I sat on their Council of
                       Representatives, which theoretically sets policy
                       for the APA, for three years. I am just ending my
                       term as president of the APA’s Society for Media
                       and Technology, where I have met many wonderful
                       colleagues. Yet, at the end of 2021, I decided to
                       resign my membership in the APA. My concern is that
                       the APA no longer functions as an organization
                       dedicated to science and good clinical practice. As
                       a professional guild, perhaps it never did, but I
                       believe it is now advancing causes that are
                       actively harmful and I can no longer be a part of
                       it.


                # ⚓ Inside_psychogenic_death,_the_phenomenon_of_“thinking”
                  yourself_to_death⠀⇛


                       Yet until recently the idea that our beliefs, or
                       our fears, could kill us was not taken seriously in
                       Western medicinal circles, due to the lack of a
                       mechanical explanation for how something as
                       ephemeral as the mind could extinguish something as
                       tangible as the body. Now, thanks to the work of a
                       British psychologist and researcher named John
                       Leach, that may change, as he has mapped out at
                       least one road to this unfortunate end.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ 2021_in_review:_‘Right_to_Repair’_campaigners_claim
                        iPhone_victory⠀⇛


                             Manufacturers, including Apple, are still
                             introducing new features that appear intended
                             only to make repairs more difficult, says
                             Kevin Purdy at iFixit, a company that sells
                             spare parts and offers free how-to guides.
                             Components that are glued together or require
                             proprietary tools to remove are common and
                             can often be overcome using third-party kits
                             from such services, but a growing trend is
                             for companies to add software-coded serial
                             numbers to components, which alert the device
                             to any unauthorised repairs.


          o § Defence/Aggression⠀➾


                # ⚓ O_Lenderking,_the_Lies_You_Bring:_a_Look_at_Biden’s_Special
                  Envoy_for_Yemen⠀⇛


                       In the same speech, Biden announced, not without
                       fanfare, the appointment of “career foreign policy
                       officer” Tim Lenderking as special envoy to Yemen. 
                       Lenderking is attempting to forge peace between
                       Yemen’s Iran-backed Houthi rebels and the Saudi-led
                       coalition which is at war with the Houthis.


                       On December 16, Lenderking appeared on public
                       radio’s The World.  Lenderking told World host
                       Carol Hills, presumably with a straight face, that
                       one of the Biden Administration’s “first
                       principles” for ending the war “is to get outside
                       actors out of the conflict.”


                # ⚓ British_Colonialism_and_How_India_and_Pakistan_Lost
                  Freedom⠀⇛


                       Do nations and civilizations grow out of the moral
                       mire of military conquests, killings of innocent
                       people, political cruelty and subjugation by
                       imperialism? For more than 800 years, India as a
                       Moghul Empire was an economically well integrated
                       and politically viable entity and west European had
                       strong trade and political relationships. After
                       intrigued conspiracies and planned division,
                       British invaded India in 1857, committing cold
                       blooded massacres of two millions people mostly
                       Muslims opposing the military invasion described
                       just as a “Mutiny” in the British chronicle.
                       Bahadur Shah Zafar – the last Moghul emperor was
                       deposed over night in Delhi, his youngest son head
                       was chopped-off and put on a breakfast plate to
                       strangle the Shah and make him surrender
                       unconditionally. Shah was hurriedly taken to
                       Rangoon (Burma) and imprisoned in a garage and
                       later on died and buried only to write poems in
                       loss of his freedom and beloved country. Did the
                       British overtake India to be a free country for
                       democracy or to support the Hindu domination of
                       futuristic India? British robbed Moghul India and
                       became it became Great Britain and imagined India
                       as an absolute entity of the British Empire.


                       Leaders like Gandhi and Nehru, Dr. Mohammad Iqbal,
                       Mohammad Ali Jinnah and Liaquat Khan though
                       educated in British intellectual traditions but
                       articulated new mission and visions for national
                       freedom as a revulsion against the British colonial
                       political traditions and continuity of British Raj
                       in India. Was this violent and ruthless
                       indoctrination part of the British heritage or
                       history-making efforts to besiege India forever?
                       Lord Mountbatten, the last Viceroy made sure that
                       Indians will remain loyal and committed subservient
                       to the futuristic blending of so called celebrated
                       national freedom after the 1947 partition into
                       India and Pakistan. British failed to deliver the
                       truth of national freedom to both nations in a
                       universal spirit of political responsibility. Both
                       nations continued to engage in military warfare,
                       ethnic conflicts and hegemonic control to dominate
                       each other by undermining their own future.


                # ⚓ Opinion_|_The_Real_Lesson_of_Jan._6_Is_That_Trump-World’s
                  Coup_Effort_Is_Far_From_Over⠀⇛


                       January 6 will be remembered as one of the most
                       shameful days in American history. On that date in
                       2021, the United States Capitol was attacked by
                       thousands of armed loyalists to Donald Trump, some
                       intent on killing members of Congress. Roughly 140
                       officers were injured in the attack. Five people
                       died that day.


                # ⚓ Pentagon_Projected_to_Hand_$407_Billion_to_Private_Military
                  Contractors_This_Fiscal_Year⠀⇛


                       President Joe Biden signed a record-shattering
                       military budget earlier this week, and a new
                       analysis published Thursday predicted that if
                       recent contracting trends continue, the Pentagon
                       will funnel $407 billion worth of public funds to
                       private weapons makers this fiscal year—more than
                       the federal government spent when sending $1,400
                       relief checks to most Americans in 2021.


                       Stephen Semler, co-founder of the Security Policy
                       Reform Institute, found that “from fiscal year (FY)
                       2002 to FY2021, 55% of all Pentagon spending went
                       to private sector military contractors.”


                # ⚓ Pentagon_Fails_Audit_(Again!)⠀⇛


                       Instead, the story, which broke on November 17, was
                       largely ignored or buried. The nation’s two main
                       newspapers, the Washington Post and the New York
                       Times, have simply ignored it. Other news
                       organizations stenographically quoted Pentagon
                       officials as admitting that they “failed again” but
                       saw “progress,” and as promising that they would
                       achieve a “clean” audit by… get this … 2027.


                       The Pentagon, with some $3 trillion (give or take a
                       trillion but who’s counting?) in assets and a
                       record current 2021 budget of $738 billion, has for
                       the third year in a row failed its audit. An army
                       of 1400 auditors hired by us taxpayers for $230
                       million and borrowed from some of the biggest
                       auditing firms in the country, spent the past year
                       poring through the books and visiting hundreds of
                       operations of the government’s largest and
                       geographically vastest single agency, and came back
                       with word that they couldn’t give it a pass.


                # ⚓ Even_as_Crime_Declines,_Gun_Violence_Is_Rising⠀⇛


                # ⚓ JFK_Revisited:_Oliver_Stone_and_the_New_JFK_Fact_Pattern⠀⇛


                       Stone is the dogged veteran of a culture war that
                       has been going on for thirty years since the
                       release of his 1991 Oscar-winning feature film,
                       JFK, a struggle to define American history that
                       ripples through the culture with every new
                       development in the ever-evolving JFK story. He is
                       also a Vietnam veteran who did a dangerous tour of
                       combat duty, as depicted his 1987 film Platoon. The
                       man risked his life for his country, I thought, a
                       sacrifice that few of his harshest critics have
                       ever made.


                       When I shared that thought with Stone in a
                       telephone interview, he demurred. “Serving as a
                       soldier doesn’t give me any better political
                       insights than someone who did not,” he insisted,
                       with the modesty that has recurred in our
                       occasional conversations over the years. As film
                       critic Ann Hornaday observed in a recent Washington
                       Post piece that was actually fair to the Oscar-
                       winning director. “To spend time with Oliver Stone
                       is to enter a different kind of looking glass,”
                       Hornaday wrote, “A man often caricatured as wild-
                       eyed provocateur is thoughtful, easygoing and
                       generous even at his most contrarian.”


                # ⚓ One_Year_in,_Biden’s_Nuclear_Policies_Look_a_Lot_Like
                  Trump’s⠀⇛


                # ⚓ UN_Demands_‘Urgent_Protection’_of_Children_in_Conflict
                  Zones_in_2022⠀⇛


                       As a year in which millions of youth were caught up
                       in armed conflicts around the world came to a close
                       Friday, the United Nations Children’s Fund warned
                       that “grave violations against children” are on the
                       rise and called on all offending parties to work
                       for a more peaceful 2022.


                       “Year after year, parties to conflict continue to
                       demonstrate a dreadful disregard for the rights and
                       wellbeing of children.”


                # ⚓ How_CIA_Plots_Undermined_African_De-Colonization⠀⇛


                       The latest and most noxious of these colonial
                       iterations is the U.S. military’s AFRICOM, although
                       a French oligarch “controls 16 West African ports
                       through bribery and influence peddling,” as
                       Margaret Kimberley recounted in Black Agenda
                       Report, December 1. “Canadian companies control
                       gold mining in Burkina Faso, Mali and
                       D.R.C.…British soldiers are still stationed in
                       Kenya.” So the west never stopped strangling
                       African nations. In this effort, the vile 1961
                       assassination of Patrice Lumumba was key. Needless
                       to say, the CIA was involved up to its eyeballs.


                       As Congo’s first freely elected leader after the
                       Belgian rout, Lumumba made the honest mistake of
                       trusting western democratic ideals.  Then, when he
                       discovered they were phony, he tilted – very
                       slightly – toward the Soviets. That sealed his
                       fate. “President Eisenhower authorized the
                       assassination of Lumumba,” writes Susan Williams in
                       her newly published book, White Malice: the CIA and
                       the Covert Recolonization of Africa. The
                       consequences were ghastly. After Lumumba’s murder
                       and dismemberment, for well over three decades,
                       “the Congo was ruled with an iron fist by Mobutu –
                       a dictator chosen by the U.S. government and
                       installed by the CIA.”


                # ⚓ Using_and_abusing_Djibouti:_How_the_US_transformed_a_tiny
                  African_state_into_a_hub_of_imperial_aggression⠀⇛


                # ⚓ Beijing’s_Movie_War_Propaganda—and_Washington’s⠀⇛


                       To coincide with the 100th anniversary of the
                       founding of the ruling Communist Party, the
                       powerful Chinese Central Propaganda Department
                       commissioned a blockbuster film that depicts a US
                       defeat in the Korean War.


                # ⚓ Daniel_Pipes:_The_Challenge_to_Islam_It_Has_Never_Faced⠀⇛


                       You may have noticed much less news about violent
                       jihad in the United States. Two reasons explain
                       this. First, counterterrorism has become far more
                       effective, rendering a 9/11-style attack almost out
                       of the question. Second, what I call the 6Ps –
                       police, politicians, press, priests, professors and
                       prosecutors – have made it harder to find out about
                       jihad. When Islamist attacks take place, they tend
                       to be portrayed as mere violent episodes without
                       motive. Exceptions exist, such as Boston Marathon
                       and Fort Hood attacks, but most of what appear to
                       be jihadi attacks that are simply not reported,
                       although these seem to take place every few months.


                # ⚓ Sweden,_Gang_Violence_and_a_New_Prime_Minister⠀⇛


                       Sweden has the highest number of fatal shootings
                       per million inhabitants in Europe according to the
                       latest report by Brå on shooting, released in May.
                       Sweden, furthermore, is the only country in Europe
                       in which fatal shootings have increased since the
                       year 2005.


                       “The main underlying reason for the development
                       with shootings and explosions is the situation that
                       prevails in vulnerable [sic] areas, where residents
                       feel threatened by criminals, where there is open
                       drug trafficking and where criminals in some places
                       have created parallel social structures”, Swedish
                       police wrote in a recent press release.


                # ⚓ French-Syrian_man_arrested_in_France_over_chemical_weapons
                  parts_in_Syria⠀⇛


                       A French-Syrian man has been detained by French
                       police on suspicion of supplying components for the
                       manufacture of chemical weapons in Syria through
                       his shipping company, sources briefed on the case
                       told AFP Sunday.


                # ⚓ 70,000_New_Arabic_Teachers_Hired_To_Teach_Quran_In_Punjab
                  Schools⠀⇛


                       Earlier this year, the SED issued official guidance
                       requiring district education authorities to visit
                       all schools in their respective areas, including
                       public and private schools, as well as madrassahs,
                       to ensure that the Holy Quran was being taught as
                       its own subject. Following this directive, three
                       school principals in Nankana Sahib were recommended
                       for disciplinary action for improperly teaching the
                       Holy Quran.


          o § Environment⠀➾


                # ⚓ Roaming_Charges:_When_the_Old_Anomaly_Became_the_New
                  Normal–2021,_the_Year_in_Climate⠀⇛


                       + Through the first 10 months of 2020 there were no
                       regions on the planet which experienced near record
                       cold. When it came to heat, however…


                       + This satellite image, taken back on 9 September
                       2020, shows some of the wildfires over Oregon,
                       including the fire that drove us from our house.
                       The view on the right utilizes SWIR bands to
                       penetrate the smoke.


                # ⚓ Seasonal_insomniacs_in_Times_of_Climate_Chaos⠀⇛


                       Because of the human-wrought climate crisis, it
                       rained on Christmas Eve.


                       This is a fierce and fragile region, rugged and
                       imperiled all at once. Deserts endure an existence
                       one step closer to death’s scythe than other
                       regions. Their inhabitants are wily survivors. The
                       toads wear dragon’s spines. The cacti guard their
                       precious water with miniature swords. The junipers
                       twist upon themselves, the size of small children
                       despite being centuries old.


                # ⚓ Opinion_|_Seasonal_Insomniacs_in_Times_of_Climate_Chaos⠀⇛


                       It snowed, finally. We’ve been waiting for months,
                       restless and agitated. Have you ever seen your
                       child settle more deeply into slumber after you
                       tuck them under the blanket? That’s how it feels
                       here. I live in the high-altitude desert of
                       Northern New Mexico. Deserts often invoke images of
                       Saharan sands, but this desert sprawls atop black,
                       volcanic basalt. Perched at 7,000 feet, it snows
                       here in the winter. Or, it used to.


                # ⚓ ‘We_Are_in_a_Climate_Emergency’:_Late-December_Wildfires
                  Ravage_Colorado⠀⇛


                       Tens of thousands of Coloradans were forced to flee
                       their homes Thursday as two fast-moving
                       wildfires—whipped up by wind gusts reaching 110
                       mph—tore through communities just outside of
                       Denver, engulfing entire neighborhoods in flames
                       and destroying hundreds of buildings.


                       Colorado Gov. Jared Polis has declared a state of
                       emergency to help aid the disaster response as
                       officials characterized the late-December fire
                       event as among the worst in the state’s history.


                # § Energy⠀➾


                      # ⚓ Trump-Appointed_Judge_Sides_With_Cops_Who_Brutalized
                        DAPL_Protesters⠀⇛


                             Five years after police brutalized activists
                             opposed to the Dakota Access Pipeline, a
                             federal judge appointed by former President
                             Donald Trump has dismissed a lawsuit accusing
                             North Dakota law enforcement officers of
                             excessive use of force—a decision that
                             critics have characterized as a tacit
                             endorsement of the violent repression of
                             climate justice advocates.


                             Several peaceful protesters who gathered at
                             the Standing Rock Sioux Reservation to
                             struggle against the expansion of fossil fuel
                             infrastructure were assaulted by law
                             enforcement officers on November 20, 2016.
                             Police sprayed demonstrators with water
                             cannons amid sub-freezing temperatures that
                             night, and according to the plaintiffs’
                             lawyers, they also used tear gas and fired
                             rubber bullets and exploding munitions
                             “indiscriminately into the crowd.”


                      # ⚓ Germany_One_Step_Closer_to_Nuclear-Free_Future_as
                        Three_of_Six_Power_Plants_Go_Offline⠀⇛


                             Green groups on Friday celebrated as Germany
                             prepared to shut down three of its six
                             remaining nuclear power plants, part of that
                             country’s ambitious goal of transitioning to
                             mostly renewable energy by the end of the
                             decade.


                             “Wind, solar, geothermal, and hydropower are
                             forms of energy that protect the environment
                             and climate, are safe, and affordable. The
                             future lies in their use.”


                      # ⚓ The_US_Still_Doesn’t_Know_How_and_Where_It_Will_Store
                        Its_Growing_Nuclear_Waste⠀⇛


                      # ⚓ Plans_to_capture_CO2_from_coal_plants_wasted_federal
                        dollars,_watchdog_says⠀⇛


                             About $1.1 billion has flowed from the
                             Department of Energy to carbon capture and
                             storage (CCS) demonstration projects since
                             2009. Had they panned out, nine coal plants
                             and industrial facilities would have been
                             outfitted with devices that scrub most of the
                             CO2 out of their emissions. Once captured,
                             the CO2 can be sent via pipelines to
                             underground storage in geologic formations.


                             That’s not what happened. The DOE doled out
                             $684 million to coal six coal plants, but
                             only one of them actually got built and
                             started operating before shuttering in 2020.
                             Of the three separate industrial facilities
                             that received $438 million, just two got off
                             the ground. Without more accountability, “DOE
                             may risk expending significant taxpayer funds
                             on CCS demonstrations that have little
                             likelihood of success,” the GAO says.


                # § Wildlife/Nature⠀➾


                      # ⚓ 15_Things_Biodiversity_Protectors_Are_Watching_Out
                        for_in_2022⠀⇛


                      # ⚓ Climate_Crisis_Fuels_Late-December_Wildfires_Ravaging
                        Colorado⠀⇛


                      # ⚓ Behold,_the_Deepest-Dwelling_Squid_Known_to_Science_|
                        Hakai_Magazine⠀⇛


                             When a team of subsea explorers completed the
                             deepest ever dive to a shipwreck earlier this
                             year, the news was broadcast around the
                             world. A team from Caladan Oceanic found the
                             USS Johnston, which sank during an intense
                             naval battle in 1944, to be astoundingly
                             well-preserved, its guns still pointing in
                             the direction of the enemy. A few days before
                             making their record-setting trip, however,
                             the explorers had carried out another descent
                             to the seafloor, a dive that ended up being a
                             few kilometers off the mark.


                             Though they failed to find the wreck that
                             day, they did find something else.


                             Once footage from the excursion came in, Alan
                             Jamieson, a deep-sea researcher from the
                             University of Western Australia, sat in his
                             office aboard the expedition ship scrolling
                             through frame after uneventful frame,
                             searching for anything that might be of
                             interest.


          o § Finance⠀➾


                # ⚓ Opinion_|_‘Historic_Victory’:_Garment_Workers_Organize_to
                  End_Wage_Theft⠀⇛


                       Daisy Gonzalez’s mother emigrated to California
                       from Guatemala in the ’80s and landed a job as a
                       garment worker. “My mother was a trimmer and an
                       ironer. I learned how difficult this work was for
                       her body from her experience,” Gonzalez says.
                       Beyond the difficult conditions, the pay was
                       equally abysmal. She recounts her mother once
                       working for a week, and the employer paying her
                       just $30. Her mother’s struggles opened Gonzalez’s
                       eyes to the trenchant problem of “wage theft,” a
                       phenomenon she says is built into the very fabric
                       of the garment industry and its global supply
                       chain. 


                # ⚓ How_A_Boy_Called_Christmas_Converted_Me_to_the_Politics_of
                  Greed⠀⇛


                       Worse, as my daughter had grown older, the content
                       of the lie had become more obviously poisonous –
                       and not only because a childhood spent venerating
                       Father Christmas likely serves as one of the
                       pillars of the continuing patriarchy.


                       The degree to which to the Christmas story
                       reinforces our understanding of how society should
                       be organised – and at a time before we can think
                       critically – was driven home to me by a new Netflix
                       and Sky joint film production I watched with my
                       family on Christmas Day.


                # ⚓ Starbucks_Workers_in_Chicago_and_Colorado_File_Union
                  Petitions_With_NLRB⠀⇛


                       Capping off what organizers and other labor rights
                       advocates have dubbed “the year of the worker,”
                       employees at two more Starbucks stores are seeking
                       to unionize.


                       Workers at a pair of Starbucks locations in
                       Broomfield, Colorado and Chicago, Illinois filed
                       union petitions with the National Labor Relations
                       Board (NLRB), a Twitter account associated with
                       organizing efforts at the coffee giant announced
                       Thursday.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ A_Shuffling_of_the_Cards_in_Germany⠀⇛


                       Pious or not, they were faced by the old truism,
                       “Two’s company, three’s a crowd!” The SPD still
                       calls itself “left” and tries somehow to appeal to
                       workers, or at least union leaders. The Greens,
                       once the party of rebelliousness, still stand for
                       women`s rights, gay rights in all variations,
                       opposing neo-Nazis and far-right xenophobia. But
                       they have grown tamer and tamer. While still
                       playing their basic environment-ecology card they
                       often cozy up to monopolies who like to talk green
                       but always think first of their bank accounts.  In
                       southern Baden-Württemberg, the Greens’ one and
                       only state governor gets along fine with Daimler-
                       Benz, the giant which is centered there. In Hesse,
                       as junior coalition partners of the Christian
                       Democrats (CDU),  they have had no known run-ins
                       with the bank interests centered there in
                       Frankfurt/Main. All the same, the media still
                       classifies those two as “left” – or at least
                       “center-left”.


                       But that third Free Democratic Party (FDP) is
                       unabashedly right-wing pro-capitalist, at least in
                       all economic matters. Despite the  fewest popular
                       votes of the three its good-looking, well-spoken
                       one-man boss, Christian Lindner, has a loud voice,
                       and it is he who grabbed the powerful job of
                       Finance Minister and has taken a no-compromise
                       stand against raising taxes on the super-rich
                       (using the same leak-down arguments as in the USA
                       since Reagan). While SPD and Greens have ties with
                       the monopolies, they occasionally move them to
                       limited concessions, like raising minimum wages,
                       some aid to children and a few more euros to the
                       jobless. But Lindner and his FDP belong  outright
                       to the biggies. Whether the pandemic wanes or
                       worsens, working people, the jobless, the elderly,
                       and several millions with precarious, temp, gig,
                       part-time and unprotected jobs will have to exert
                       strong pressure “from below”  to hinder further
                       stagnation or worse.


                # ⚓ Biden_Congratulates_Leftist_Chilean_President-Elect_Gabriel
                  Boric⠀⇛


                       In a departure from previous administrations’
                       responses to left-wing victories in Latin America,
                       President Joe Biden on Thursday congratulated
                       Chilean President-elect Gabriel Boric, who beat his
                       right-wing opponent earlier this week after running
                       on a social-democratic platform.


                       Biden called the 35-year-old president-elect, who
                       will be sworn in as the country’s youngest leader
                       in March, to say his victory has set a “powerful
                       example to the region and the world,” according to
                       a White House statement.


                # ⚓ Democracy_with_United_States_Characteristics⠀⇛


                       The USA should be described as a democracy with
                       United States characteristics.


                       The U.S. government often expresses the idea that
                       its system is so desirable that leaders of other
                       countries should model their country after it.


                # ⚓ The_True_Problem_With_the_GOP’s_Patricia_Morgan⠀⇛


                       Some very good Black writers at websites like The
                       Root and The Grio have already dissected the racism
                       of this strange missive and I cannot commend those
                       readings enough.


                       Unfortunately, for whatever reason, there are two
                       issues that are important to put emphasis upon as
                       we move into the midterm elections, particularly
                       because of the manifest ineptitude and flaccidity
                       of the Democratic electoral strategy.


                # ⚓ J._Edgar_Hoover’s_Legacy:_Spying_On_Democracy⠀⇛


                       The FBI has been conducting domestic surveillance
                       operations since its inception in the 1920s,
                       marking nearly a hundred years of violating the
                       First Amendment of the Constitution.  Very few of
                       these operations involved the investigation and
                       gathering of evidence of a serious crime, the only
                       justification for FBI surveillance.  J. Edgar
                       Hoover, appointed director of the Bureau of
                       Investigation in1924, amassed illegal powers of
                       surveillance that enabled him to conduct extra-
                       legal tracking of activists, collect compromising
                       information, and even to threaten and intimidate
                       sitting presidents.


                       Hoover created the Counterintelligence Program
                       (COINTELPRO) in the 1950s to counter the activities
                       of the Communist Party in the United States, but it
                       morphed into a program of covert and illegal
                       activities to disrupt numerous political
                       organizations, particularly the anti-Vietnam war
                       and civil rights organizations of the 1960s and
                       1970s.  He exaggerated the threat of communism to
                       ensure financial and public support for the FBI. 
                       (The Pentagon similarly exaggerates the Russian and
                       Chinese threats to elicit greater defense spending,
                       such as the record-setting budget that President
                       Biden signed on Monday.)  When Supreme Court
                       decisions made it more difficult to prosecute
                       individuals for their political opinions, Hoover
                       formalized a covert “dirty tricks” program that
                       included illegal wiretaps, forged documents, and
                       burglaries.


                # ⚓ Want_an_answer_to_Trumpism?_Rewatch “It’s_a_Wonderful
                  Life”⠀⇛


                       When I first saw the movie in the late 1960s, I
                       thought it pure hokum. America was coming apart
                       over Vietnam and the assassinations of Martin
                       Luther King, Jr. and Robert F. Kennedy, and I
                       remember thinking the movie could have been
                       produced by some propaganda bureau of the
                       government that had been told to create a white-
                       washed (and white) version of the United States.


                # ⚓ In_‘Victory_for_Democracy’_and_‘Blow_to_Trumpism,’_FDIC
                  Chair_Resigns⠀⇛


                       What has been described as both “open lawlessness”
                       and a “partisan brawl” came to an end Friday when
                       Federal Deposit Insurance Corporation Chair Jelena
                       McWilliams—an appointee of former President Donald
                       Trump—revealed she is resigning, which will give
                       Democrats control of the agency.


                       In a letter to President Joe Biden published on the
                       FDIC’s website, McWilliams said she intends to step
                       down effective February 4, 2022. Politico pointed
                       out that her resignation “means that FDIC board
                       member Martin Gruenberg will become acting chair,
                       his third stint atop at the 88-year-old agency,
                       which insures trillions of dollars in deposits at
                       the nation’s banks.”


                # ⚓ Best_of_CounterSpin_2021⠀⇛


          o § Misinformation/Disinformation⠀➾


                # ⚓ Palestinian_COVID_conspiracy_theories_do_matter⠀⇛


                       If one isolated lunatic wrote those words, there
                       would be no reason to take him seriously. But the
                       publication of that conspiracy theory in the
                       official P.A. newspaper means that it reflects the
                       views of the P.A. leadership. And it means that
                       this is what the P.A. wants the Palestinian Arab
                       public to believe.


          o § Censorship/Free Speech⠀➾


                # ⚓ Belgium_refuses_extradition_of_fugitive_Spanish_rapper⠀⇛


                       Beltran was sentenced for lyrics in songs published
                       online in 2012 and 2013 at a time when he was a
                       little-known rapper in the Balearic Islands.


                       These included: “Let them be as frightened as a
                       police officer in the Basque Country” and “the king
                       has a rendezvous at the village square, with a
                       noose around his neck.”


                # ⚓ Afghanistan:_Taliban_‘sentences_TV_To_Death,’_Destroys
                  Scores_Of_Musical_Instruments⠀⇛


                       In the chilling video, the Taliban that has
                       enforced strict sharia law for governance after the
                       political takeover is seen forcing a man to take an
                       oath that he would never watch TV again. This is
                       purportedly due to the belief among the Islamist
                       extremists that it is not permissible in sharia
                       (Islamic law) to watch TV. The Taliban men are seen
                       smashing a television set and destroying scores of
                       musical instruments including harmonium as it is
                       “haram” [forbidden] in Islam. Pakistani journalist
                       Hamza Azhar Salam who first shared the footage
                       appeared to normalise the behaviour as he stressed
                       that “things can change in future.”


                # ⚓ Prominent_vaccine_scientist_banned_from_Twitter_for
                  spreading_anti-vaxx_content⠀⇛


                       Dr Robert Malone has amassed over 500,000 followers
                       but the scientist was removed from the platform
                       after sharing a video about supposed harmful
                       effects of the Pfizer vaccine.


                       Twitter has not commented on the decison and it’s
                       unclear whether the banning was automated or
                       actioned by a human.


                # ⚓ Who_is_Robert_Malone?_Twitter_Suspends_Account_of
                  Virologist_Who_Warns_Covid-19_Vaccine_is_‘NOT_SAFE’_for
                  Children⠀⇛


                       However, it is unclear if the suspension was
                       automatic or Twitter deliberately suspended his
                       account due to violation as the platform did not
                       make any comment regarding the same.


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


                # ⚓ Democracy_Now!_at_25:_Celebrating_a_Quarter-Century_of
                  Independent_News_on_the_Frontlines⠀⇛


                       Democracy Now! first aired on nine community radio
                       stations on February 19, 1996, on the eve of the
                       New Hampshire presidential primary. In the 25 years
                       since that initial broadcast, the program has
                       greatly expanded, airing today on more than 1,500
                       television and radio stations around the globe and
                       reaching millions of people online. We celebrate 25
                       years of The War and Peace Report with an hour-long
                       retrospective, including highlights from the show’s
                       early years, some of the most controversial
                       interviews, and groundbreaking reports from East
                       Timor, Standing Rock, Western Sahara and more.


                # ⚓ Dr._Oz_and_wife_thought_they’d_hung_up_—_got_caught_raging
                  against_“f**king_girl_reporter”⠀⇛


                       Dr. Mehmet Oz and his wife Lisa were overheard by a
                       journalist describing her as a “fucking girl
                       reporter” after they failed to hang up successfully
                       while trying to duck her phone calls.


                       New York Magazine reporter Olivia Nuzzi traveled to
                       Pennsylvania to profile Oz’s Republican Senate
                       campaign but had difficulty tracking down the
                       celebrity doctor or any signs of an actual
                       campaign. After contact with the campaign “proved
                       elusive,” she wrote, she showed up at Oz’s empty
                       campaign office and asked a nearby business owner
                       to connect her with Oz’s family. She was ultimately
                       able to reach Lisa Oz, who hung up on her. When
                       Nuzzi tried again, Lisa Oz presumably intended to
                       hang up again, but connected her phone to her car’s
                       sound system instead, allowing Nuzzi to hear her
                       conversation with her husband.


          o § Civil Rights/Policing⠀➾


                # ⚓ Creativity_in_Nonviolent_Resistance⠀⇛


                       We humans have studied war for perhaps 11,000 years
                       or more. We have colleges and massive industries
                       devoted to that destructive ability of our species.


                       What about the opposite, the creative ability, the
                       constructive conflict?


                # ⚓ In_2021,_the_Police_Took_a_Page_Out_of_the_NSA’s_Playbook:
                  2021_in_Review⠀⇛


                       While dragnet searches were once thought to be just
                       the province of the NSA, they are now easier than
                       ever for domestic law enforcement to conduct as
                       well. This is because of the massive amounts of
                       digital information we share—knowingly or not—with
                       companies and third parties. This data, including
                       information on where we’ve been, what we’ve
                       searched for, and even our genetic makeup, is
                       stored in vast databases of consumer-generated
                       information, and law enforcement has ready access
                       to it—frequently without any legal process. All of
                       this consumer data allows police to, essentially,
                       pluck a suspect out of thin air.


                       EFF has been challenging unconstitutional dragnet
                       searches for years, and we’re now seeing greater
                       awareness and pushback from other organizations,
                       judges, legislators, and even some companies. This
                       post will summarize developments in 2021 on one
                       type of dragnet suspicionless search—reverse
                       location data searches. 


                       Reverse location searches allow the police to
                       identify every device in a given geographic area
                       during a specific period of time in the past as
                       well as to track people’s paths of travel.
                       Geographic areas can include city blocks full of
                       people unconnected to the crime, including those
                       living in private residences and driving on busy
                       streets. 


                # ⚓ Opinion_|_Tutu’s_Courage_on_Israeli_Apartheid_Is_Played
                  Down_in_American_Media⠀⇛


                       The Guardian has published an important eulogy to
                       the late Desmond Tutu by Chris McGreal, saying what
                       so many in the Palestinian solidarity community are
                       saying: After fighting apartheid in South Africa,
                       Tutu used his stature to call out apartheid in
                       Israel and Palestine, and he paid a large price for
                       doing so.


                # ⚓ Remembering_My_Time_With_Bishop_Tutu⠀⇛


                       The following took place more than a quarter of a
                       century ago before the widespread use of the
                       Internet, and my memory may be a bit faulty
                       regarding some details. Be that as it may, to the
                       best of my recollection, after the worst excesses
                       of apartheid had been defeated and Nelson Mandela
                       had been elected South Africa’s President, Tutu
                       flew to Hawaii circa 1995. In Downtown, Honolulu
                       the Anglican Bishop made a speech at St. Andrew’s
                       Episcopal Cathedral, which was commissioned in the
                       19th century by a Hawaiian monarch before a white
                       settler- and U.S.-backed coup overthrew the
                       independent Polynesian kingdom.


                       Prior to his talk, the anti-apartheid leader agreed
                       to do an interview with me, I believe for the
                       Australian Broadcasting Corp. and/or its overseas
                       service, Radio Australia. The RA is the main source
                       of news for and about the Pacific Islands, and I
                       had been reporting as a stringer for this broadcast
                       outlet since the assassination of the President of
                       the Republic of Palau in 1985, where I’d lived at
                       the time. My interview with the much-in-demand,
                       extremely busy Bishop took place in a room that was
                       part of the rather large cathedral complex, where
                       there were a number of aides sitting with him (none
                       interfered with the Q&A, although it’s possible one
                       staffer may have informed us my allotted time was
                       up).


                # ⚓ Remembering_the_Real_Desmond_Tutu,_1931–2021⠀⇛


                       “It’s realpolitik, this forgiveness thing,” said
                       Archbishop Desmond Tutu to me in 1996 with
                       characteristically blunt eloquence, about the job
                       he had to do as chair of South Africa’s Truth and
                       Reconciliation Commission (TRC). “It’s not just
                       something in the realm of religion or the
                       spiritual. If justice is your last word, you’ve had
                       it. You’ve got to go beyond it.”


                # ⚓ The_Russian_Supreme_Court_Moves_to_Shut_Down_a_Prominent
                  Human_Rights_Group⠀⇛


                       On December 10, my father Dmitry Muratov, the 2021
                       Nobel Peace Prize co-laureate, proclaimed when he
                       received his award: “Memorial is not ‘an enemy of
                       the people,’ Memorial is a friend of the people.”
                       Russian-based human rights groups Memorial Human
                       Rights Center and Memorial International have
                       worked for decades to rehabilitate over a million
                       victims of Stalinist repression. On December 28, 18
                       days after Muratov’s speech, the Russian Supreme
                       Court ruled to shut down the organization.


                # ⚓ As_Many_as_1_in_3_Afghan_Refugee_Women_at_U.S._Bases_are
                  Pregnant⠀⇛


                       When thousands of Afghans first arrived at the
                       military base in rural Wisconsin, local residents
                       in Sparta, the “Bicycling Capital of America”, a
                       small city of less than 10,000, began warning that
                       the Afghans being housed at Fort McCoy were putting
                       a significant strain on their infrastructure and
                       their medical services. I was told that there were
                       as many as 800 pregnant refugees at the base. The
                       number seemed wildly implausible, but now the
                       official number is out.


                       According to military officials, there have been
                       500 pregnant Afghans at Fort McCoy and, according
                       to a local news report, “the numbers keep growing”.


                # ⚓ No_Trips_For_Afghan_Women_Unless_Escorted_By_Male_Relative:
                  Taliban⠀⇛


                       Afghanistan’s Taliban authorities said Sunday that
                       women seeking to travel anything other than short
                       distances should not be offered transport unless
                       they are accompanied by a close male relative.


                       The guidance, issued by the Ministry for the
                       Promotion of Virtue and Prevention of Vice, also
                       called on all vehicle owners to offer rides only to
                       those women wearing Islamic hijabs.


                # ⚓ Sexual_crimes_against_children_rampant_in_Turkey_–
                  reports⠀⇛


                       “This is the tip of the iceberg,” Aksay told
                       BirGün. “These numbers are from one hospital, and
                       cases that made it to the criminal unit.”


                # ⚓ Wiesenthal_Center_puts_BBC_3rd_–_after_only_Iran,_Hamas_–
                  on_antisemitism_list⠀⇛


                       “People might assume we would put neo-Nazi groups
                       on our list,” Hier told the paper, “but the BBC is
                       there because when a globally recognized
                       organization allows antisemitism to creep into its
                       reporting, it makes it all the more insidious and
                       dangerous.”


                       The full list is to be released on Tuesday.


                # ⚓ Women_Protesters_Injured_In_Stampede_After_Taliban
                  Militants_Fire_In_The_Air⠀⇛


                       Participants told RFE/RL that up to 130 women
                       attended the protest in Kabul, and shots fired in
                       the air by Taliban militants trying to disperse the
                       demonstration prompted fleeing protesters to fall
                       and trample one another. Several women sustained
                       injuries in the stampede, witnesses said.


                       It was not immediately clear how many women were
                       injured in the incident.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ A_new_coronavirus_vaccine_heading_to_India_was
                        developed_by_a_small_team_in_Texas._It_expects_nothing
                        in_return.⠀⇛


                             Unlike the vaccines of big-name manufacturers
                             such as Pfizer-BioNTech and Moderna, the
                             Texas Children’s Hospital vaccine, which is
                             called Corbevax, is being shared patent-free.
                             The Texas Children’s Hospital team is also
                             working with manufacturers like Biological E.
                             to ensure they have the know-how to make
                             doses.


                             The ambition is to create a low-cost, open-
                             source alternative to expensive and limited-
                             supply mRNA vaccines for developing and
                             under-vaccinated countries. And it won’t stop
                             at India: Hotez and Bottazzi are talking to
                             other manufacturers around the world and have
                             consulted with the World Health Organization
                             to see how they can share the vaccine
                             globally.


                # § Copyrights⠀➾


                      # ⚓ Do_Pirate_IPTV_Customers_“Support_Human_Trafficking_&
                        Arms_Trading”?⠀⇛


                             Over the years there have been frequent
                             claims by entertainment companies that by
                             using pirate services, users are helping to
                             finance other crimes. Just recently an
                             article appeared in Forbes warning that,
                             among other things, pirate IPTV providers are
                             also involved in people trafficking, arms
                             trading and drug shipments. Read on….


                      # ⚓ 6._Consumer_protection_for_digital_content_expands⠀⇛


                             In the past, there has been no clear
                             regulation for errors or delays within
                             digital content.



                    ䷩ 𝚕𝚒𝚗𝚎 4914

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_1/1/2022:_Slackel_7.5_and_Septor_2022⠀✐


Posted in News_Roundup at 1:30 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ Here_are_5_Stats_About_Linux_that_will_make_you_Proud⠀⇛


                 Cat command is used to read and print file content on a
                 terminal screen. While tac command is similar to a cat
                 command, but the difference is data will print in reverse
                 order.


          o § Kernel Space⠀➾


                # § Graphics Stack⠀➾


                      # ⚓ Mesa’s_RADV_Driver_Lands_Workaround_For_Flickering
                        Issue_With_F1_2021_–_Phoronix⠀⇛


                             For those wanting to enjoy the F1 2021 racing
                             game on Linux via Valve’s Steam Play, it’s
                             slowly getting into good shape. The latest
                             enhancement is on the Radeon Vulkan driver
                             side with Mesa’s RADV adding a workaround
                             targeting the game.


                             Samuel Pitoiset of Valve’s Linux graphics
                             driver team has landed a workaround in Mesa
                             22.0-devel Git (and also marked for back-
                             porting to Mesa 21.3 stable) for fixing
                             severe flickering issues exhibited by F1 2021
                             within the in-game menus.


          o § Benchmarks⠀➾


                # ⚓ OpenBenchmarking.org_In_2021_By_The_Numbers_–_Phoronix⠀⇛


                       Since we are all about performance and numbers,
                       here is a look at the 2021 statistics for
                       OpenBenchmarking.org itself as the online
                       complementary component to the Phoronix Test Suite.


                       Here are some year-end stats on
                       OpenBenchmarking.org for the health of open-source
                       benchmarking, which in 2021 marked ten years since
                       OpenBenchmarking.org went public alongside Phoronix
                       Test Suite 3.0.


          o § Applications⠀➾


                # ⚓ Best_Free_and_Open_Source_Software_–_December_2021
                  Updates⠀⇛


                       Here are the latest updates to our compilation of
                       recommended software.


                # ⚓ AviDemux_2.8.0_(64-bit)⠀⇛


                       Avidemux is a free video editor designed for simple
                       cutting, filtering and encoding tasks. It supports
                       many file types, including AVI, DVD compatible MPEG
                       files, MP4 and ASF, using a variety of codecs.
                       Tasks can be automated using projects, job queue
                       and powerful scripting capabilities. Avidemux is
                       available for Linux, BSD, Mac OS X and Microsoft
                       Windows under the GNU GPL license.


                # ⚓ Pinta_2.0_Drawing_App_Comes_Ported_to_GTK_3_and_.NET_6 [Ed:
                  This is helping Microsoft spread Mono. Not a good thing at
                  all.]⠀⇛


                       Now seemingly very stable, Pinta 2.0 is well on its
                       way to becoming one of Linux’s favorite painting
                       and editing applications out there.


                       Pinta is a free cross-platform graphics editor,
                       that means you can install it on Windows, macOS, or
                       Linux. It is a hassle-free tool for all Linux users
                       who do not want to struggle through documentation
                       to master a more complicated graphics tool.


                       The app is a perfect match for Viewers & Editors in
                       the Design & Photo category. It puts all the common
                       graphic editing and design tools at your disposal:
                       paintbrush, paint can, cloning stamp, gradient,
                       different selection types, etc.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_and_configure_Docker-CE_on_Ubuntu_20.04_–
                  NextGenTips⠀⇛


                       In this tutorial am going to show you how you can
                       install Docker-CE on Ubuntu 20.04.


                       Docker is a set of platform as a service product
                       that uses OS-level virtualization to deliver
                       software in packages called containers. Containers
                       are usually isolated from one another and bundled
                       their own software libraries and configuration
                       files, they can communicate with each other through
                       well-defined channels.


                       Docker makes it possible to get more apps running
                       on the same old servers and also makes it easy to
                       package and ship programs.


                # ⚓ PlaySMS_Kannel_SMS_Gateway_integration_on_NGINX+Debian⠀⇛


                       PlaySMS is a free and open source SMS management
                       software, a web interface for SMS gateways and bulk
                       SMS services. In this article we will configure
                       PlaySMS on Debian 10 with NGINX web server and
                       MariaDB Database. We will need PHP to run PlaySMS
                       web application and Kannel SMS Gateway. To install
                       Kannel SMS Gateway please check this article.


                # ⚓ How_to_install_MyBB_Forum_on_Ubuntu/Debian⠀⇛


                       MyBB is a open-source forum application which comes
                       with amazing unique features which gives your forum
                       a completely unbelievable look. It comes with many
                       pre-installed features and utilities to keep your
                       forum completely managed and solid. Since, It’s
                       open source, There are many themes developed by the
                       community members for you to use it freely, also
                       there are many plugins which gives you and your
                       forum users more accessibility to the forum.
                       Plugins like Social Login Integration, ShoutBox,
                       Arcade Gamers etc. It’s one of the most reliable
                       free forums software on the market. Many known
                       communities uses MyBB to this day


                # ⚓ PPLOG_personal_blog_fixed⠀⇛


                       PPLOG is a personal blog, a perl script, found in
                       the menu under “Personal” category. I received an
                       email that it doesn’t work.


                # ⚓ pa-applet_menu_modified⠀⇛


                       The right-click menu lists all possible outputs and
                       allows changing the default; however, that is
                       conflicting with Multiple Sound Card Wizard and
                       upsetting pavucontrol.


                # ⚓ What_Is_A_Linux_Shell?⠀⇛


                       What comes to your mind when you hear about Linux?
                       A hacker wearing a black hoodie and a Guy Fawkes
                       mask, typing gibberish in the terminal on one
                       screen, while the other screen flickers with code
                       no one understands. What if we told you that you
                       could do that too and “try” to look cool with your
                       friends?


                       All of that is done in a Shell program pre-
                       installed in all Linux distributions. In this
                       article, let’s look at what a Linux Shell is and
                       its use in Linux.


                # ⚓ How_to_use_cat_and_tac_command_in_Linux_–_TREND_OCEANS⠀⇛


                       Cat command is used to read and print file content
                       on a terminal screen. If you bifurcate
                       concatenation, you will get a cat in between, which
                       means you can combine multiple files at once. The
                       cat command is not limited to reading files, and it
                       can do more, let me show you how to leverage cat.


                # ⚓ How_to_Use_WhatsApp_on_a_Linux_Desktop⠀⇛


                       WhatsApp is a cross-platform messaging service
                       available for Android, iOS, Windows, and macOS. The
                       unavailability of an official WhatsApp client for
                       Linux has left users wondering whether or not they
                       can use WhatsApp on a Linux desktop.


                       The straightforward answer is yes. Although you
                       have the choice to run WhatsApp on an Android
                       emulator, there must be a better way, one not
                       involving emulation. Therefore, in this article, we
                       will discuss how you can use WhatsApp on Linux.


                # ⚓ How_to_Install_MX_Linux_21_Step_by_Step_with_Screenshots⠀⇛


                       Debian, which is a hugely popular Linux
                       distribution, has given rise to a wide selection of
                       popular Debian flavors. Among the most celebrated
                       and hugely popular Debian flavors is MX Linux,
                       which takes the first position in Distrowatch at
                       the time of penning down this tutorial.


                       MX Linux project is made possible by the
                       collaborative efforts of AntiX and former MEPIS
                       Linux communities. It is a desktop-oriented Linux
                       flavor that provides XFCE as the default desktop
                       environment – although you can get it in KDE Plasma
                       and Fluxbox.


                       MX Linux is a middleweight Linux distribution that
                       combines a colorful and efficient desktop with
                       rock-solid stability and superb performance. The
                       latest stable version of MX Linux is MX Linux 21,
                       codenamed Wildflower. It is based on Debian 11
                       Bullseye and ships with all the latest software
                       updates and goodness for an amazing and elegant
                       desktop distribution.


                       In this guide, we will show you how to install MX
                       Linux 21 step-by-step.


                # ⚓ Install_LibreOffice_7_on_Ubuntu_from_AppImage,_DEB,_Flatpak
                  and_Snap⠀⇛


                       This tutorial explains how you can install
                       LibreOffice version 7.0 and later on an Ubuntu
                       computer with several choices of installation
                       methods namely AppImage, DEB, PPA, Snap and Flatpak
                       sorted by difficulty from beginner to advanced.
                       Thanks to these choices, you who have computer with
                       GNU/Linux distros other than Ubuntu can also
                       practice this. Now let’s install it.


                # ⚓ How_to_install_OpenBox_on_minimal_Debian_11_Bullseye_–
                  Linux_Shout⠀⇛


                       If you are using a minimal Debian 11 Bullseye
                       server distro and want a lightweight Windows
                       manager along with a low resource consuming display
                       manager and desktop panel; then here is the
                       tutorial to install OpenBox Window manager on
                       minimal Debian 11 Linux distro using the command
                       line.


                # ⚓ How_To_Install_Apache_on_CentOS_9_Stream_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Apache on CentOS 9 Stream. For those of you who
                       didn’t know, Apache, also known as Apache HTTP
                       server is a free, open-source, and cross-platform
                       HTTP server, including powerful features, and can
                       be extended by a wide variety of modules. It is
                       part of the LAMP stack (Linux, Apache, MySQL, PHP)
                       that powers much of the internet.


                       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 Apache webserver on CentOS 9
                       Stream.


          o § Wine or Emulation⠀➾


                # ⚓ My_progress_in_porting_Wine⠀⇛


                # ⚓ Astounding_Progress_Made_In_Porting_Wine_To_Haiku_For
                  Running_Windows_Software_–_Phoronix⠀⇛


                       Haiku as the open-source operating system in
                       development for two decades as the inspirational
                       successor to BeOS is kicking off 2022 by….
                       beginning to be able to run Windows applications
                       via Wine. There is great progress being made in
                       porting Wine to running on Haiku.


                       Developer “X512″ who has achieved a lot of other
                       great Haiku development milestones from graphics
                       driver porting to other work has been tackling Wine
                       this week. He has been quickly making progress on
                       being able to run Windows programs on the BeOS-
                       inspired open-source operating system.


          o § Games⠀➾


                # ⚓ 80%_of_Steam’s_top_100_games_now_work_on_Linux_–_OSnews⠀⇛


                       I have long stopped even checking ProtonDB to see
                       if the games I’m interested in run well on Linux –
                       I just assume that the games I’m into belong to the
                       80%, with the remaining 20% being the massive
                       garbage pile that are abandoned indie games, anime
                       nonsense, and porn that have infested Steam over
                       the years.


                       Proton, and all the work Wine, Valve, and open
                       source developers have poured into it, is arguably
                       one of the biggest contributions to desktop Linux
                       in a long, long time, and with the Steam Deck on
                       the horizon, it’s only going to get even better
                       from here.


          o § Desktop Environments/WMs⠀➾


                # ⚓ LABWC_0.4_Stacking_Wayland_Compositor_Brings_Fullscreen
                  Mode,_Drag_&_Drop_–_Phoronix⠀⇛


                       Early in 2021 there was the inaugural release of
                       LABWC as a stacking Wayland compositor that
                       promoted itself as an alternative to Openbox. In
                       kicking off the new year, LABWC 0.4 is now
                       available.


                       The LABWC Wayland compositor is built off the
                       wlroots library and takes inspiration from Openbox
                       while being focused on simplicity and speed while
                       still having some nice window management features.


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


                      # ⚓ KDE_Ends_2021_With_More_Plasma_Wayland_Fixes,_Root
                        File_Operations_For_Dolphin_–_Phoronix⠀⇛


                             KDE developers ended out 2021 with more
                             Wayland session fixes coming for the Plasma
                             5.24 release. There was also nice user
                             feature work like KIO-using applications such
                             as Dolphin now properly dealing with non-
                             user-owned locations.


                             KDE developer Nate Graham this morning
                             published his usual weekly development
                             summary of all the interesting changes going
                             on in the KDE space. Some of the KDE changes
                             for the final week of 2021 included:


                             - The Dolphin file manager can now be
                             launched as root or other non-user-owned
                             locations. This is thanks to PolKit support
                             being merged in KIO. KDE applications making
                             use of KIO can now create/move/copy/trash/
                             delete files in non-user-owned locations as
                             of KDE Frameworks 5.90.


          o § Distributions⠀➾


                # § New Releases⠀➾


                      # ⚓ Slackel_7.5_“Openbox”⠀⇛


                             Slackel 7.5 Openbox has been released.
                             Slackel is based on Slackware and use
                             salixtools from Salix.


                             Includes the Linux kernel 5.15.12 and latest
                             updates from Slackware’s ‘Current’ tree.
                             Wicd has been removed. NetworkManager is the
                             default app for connecting to networks now.


                             The new version is available in 64-bit and
                             32-bit builds.


                             The 64-bit iso image support booting on UEFI
                             systems.
                             Iso images are isohybrid.
                             Iso images can be used as installation media.


                             It is good to read the Slackel Startup Guide
                             before install Slackel.


                      # ⚓ Septor_2022⠀⇛


                             Septor Linux is a operating system that
                             provides users with a perfect computing
                             environment for surfing the Internet
                             anonymously. Septor providing users with a
                             stable and reliable distribution that is
                             based on Debian GNU/Linux and works on a wide
                             range of computers. Distribution featuring a
                             customised KDE Plasma desktop.


                             Tor Browser, OnionShare (an anonymous file
                             sharing utility) and qTox (an instant
                             messaging client built on a “privacy goes
                             first” agenda). Thunderbird, HexChat and
                             QuiteRSS are all pre-configured to connect to
                             the Internet via the Tor network. The
                             distribution can be used in “live” mode or it
                             can be installed to hard disk via the
                             standard Debian installer.


                # § Arch Family⠀➾


                      # ⚓ 8_Things_You_Should_Know_Before_Installing_Arch
                        Linux⠀⇛


                             Arch Linux is no doubt one of the best
                             distros for Linux power users. But there are
                             some things you should know about Arch before
                             installing it.


                             When installing most Linux distros, you
                             simply download the ISO, create a bootable
                             media, and begin the installation process—no
                             research required.


                             But things are a little different with Arch
                             Linux. If you jump right into the
                             installation part without learning about the
                             distro first, you’ll be dumbfounded by the
                             complexity of the process. And that’s just
                             the installation to speak of.


          o § Devices/Embedded⠀➾


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ How_to_enhance_privacy_on_your_Android_phone⠀⇛


                      # ⚓ Android_patch_of_January_2022,_there_is_already_the
                        first:_it_is_Galaxy_A51_–_How_smart_Technology_changing
                        lives⠀⇛


                      # ⚓ Realme_UI_3.0_(Android_12)_update_tracker:_Eligible
                        devices,_release_date_…⠀⇛


                      # ⚓ Realme_GT_Master_Edition_gets_Android_12-based_Realme
                        UI_3.0_early_access_beta_–_GSMArena.com_news⠀⇛


                      # ⚓ 9_new_and_notable_Android_apps_from_the_last_three
                        weeks_including_Tracker_Detect,_DINA:_Personalized
                        Weather,_and_Matrix_Code_–_Live_Wallpaper_(12/11/21_–
                        01/01/22)⠀⇛


                      # ⚓ PinePhone_keyboard_now_available_(Wireless_charging,
                        fingerprint,_and_LoRa_cases_too)⠀⇛


                             The PinePhone is an inexpensive Linux-
                             friendly smartphone with a $150 starting
                             price. And now you can turn it into a tiny
                             Linux laptop thanks to a $50 keyboard
                             accessory.


                             It’s one of four new PinePhone accessories
                             that are now available from the Pine Store.


                             In addition to being able to run mobile Linux
                             distributions, the PinePhone has a few other
                             special features that are available when you
                             remove the back cover of the phone. There are
                             a set of hardware kill switches for disabling
                             the mic, camera, or wireless features. And
                             there are a set of pogo pins that allow you
                             to connect other hardware.


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


                # ⚓ A_Brief_History_of_Blender:_The_Invention_and_Evolution_of
                  the_3D_Graphics_Software⠀⇛


                       Blender was originally a product of a Dutch
                       animation studio by the name of NeoGeo. After
                       blazing his way through continental Europe, co-
                       founder Ton Roosendaal felt a need to raise the bar
                       on the software that he and his team used to carry
                       out their work.


                       One of the things that helped Roosendaal find so
                       much success at the helm of NeoGeo, even before
                       Blender’s official inception was the proprietary 3D
                       rendering and animation software that came before
                       it, crafted for the company in-house under
                       Roosendaal’s supervision.


                       He was the catalyst force driving this new mission
                       to totally revamp the platform that they were
                       already using at the time. They got the ball
                       rolling in 1995, but it took several years to
                       accomplish what they had set out to do.


                # ⚓ 2022_Outlook_–_Open_source,_OpenTelemetry,_&_emerging_tech
                  –_JAXenter⠀⇛


                       What does 2022 hold for open source and
                       OpenTelemetry? Which cutting-edge technologies
                       should you be paying attention to in 2022? We asked
                       the experts about their predictions for the coming
                       year. Stay ahead of the curve and learn how to plan
                       strategically in the new year.


                       [...]


                       With a focus on people from the UK Government we
                       will see two things. Firstly, there will be a shift
                       in education to embrace more on open source
                       software, open hardware and open data, particularly
                       around practical training. This will help the next
                       generation of developers and other professionals
                       enter the market with the right skills to
                       participate in how companies today build their
                       software and then manage it over time. This doesn’t
                       just mean code, but all the jobs that exist around
                       software development and that provide value to
                       users.


                       Secondly, there will be more focus on supporting
                       home grown businesses in the tech space worldwide,
                       which ultimately means those start-up and scale-up
                       companies working around open technology.


                       In the UK, this will manifest itself in increased
                       investment from the Financial Services sector, the
                       likes of Pension Funds which currently lag
                       significantly behind those in the US in terms of
                       investment in tech. There is increased
                       understanding in that market around how to value
                       companies and how they operate, which should
                       support more companies in growing and being
                       successful in the longer term.


                # ⚓ Trust_in_HiveOS_tarnished_as_open_source_miner_developers
                  come_forward_with_accusations_of_skimming_developer_fee⠀⇛


                       Open source developers of various open source
                       cryptocurrency miners show what they say as proof
                       that HiveOS modified code preventing compensation
                       for vital development work. It was described that
                       developers had previously implemented checks into a
                       cryptocurrency miner to signal any modifications to
                       the development address and to raise alarm. A
                       private investigation was then performed which
                       apparently shows proof that HiveOS is behind all of
                       it.


                # § FSF⠀➾


                      # § Licensing/Legal⠀➾


                            # ⚓ TikTok’s_Live_Studio_app_accused_of_violating
                              OBS_licensing_terms⠀⇛


                                   Last week, TikTok quietly released a
                                   game-changing tool for gamers and live
                                   streamers in the form of a desktop-
                                   based streaming app called TikTok Live
                                   Studio. Turns out, TikTok’s app that
                                   will allow gamers and TikTokers to
                                   stream high-quality content from their
                                   PCs to their TikTok accounts appears to
                                   be based on OBS’s open-source software.
                                   Unfortunately, TikTok has already been
                                   accused of breaking OBS’s GPL, or
                                   General Public License, by not
                                   releasing its open source code for
                                   TikTok Live Studio.


                                   OBS’s business development manager Ben
                                   Torell told Protocol that OBS has
                                   “clear evidence” that TikTok’s Live
                                   Studio allegedly violated licensing
                                   terms. OBS has reached out to TikTok
                                   and is waiting to hear back.


                # § Programming/Development⠀➾


                      # § Java⠀➾


                            # ⚓ [Older]_Open_source_security_leader_Brian
                              Behlendorf_discusses_the_impact_of_Log4j⠀⇛


                                   For the last few weeks, the world of
                                   computer security has been turned
                                   upside down as teams struggled to
                                   understand if they needed to worry
                                   about the Log4j vulnerability. The
                                   relatively small Java library didn’t do
                                   anything flashy, but it was a well-
                                   built open source tool for tracking
                                   software events, and that made it
                                   popular with Java developers. That
                                   meant it often found its way into
                                   corners that people didn’t expect.


                                   While the security teams will continue
                                   to debate the nature of the flaw itself
                                   and search for similar problems, many
                                   are wondering how this might change the
                                   industry’s reliance on open source
                                   practices. Everyone enjoys the free
                                   tools until a problem like this
                                   appears. Is there a deeper issue with
                                   open source development that brought
                                   this about? Can society continue to
                                   rely upon the bounty of open source
                                   without changing its expectations and
                                   responsibilities?


                                   VentureBeat talked to Brian Behlendorf
                                   to understand the depth of the problem
                                   and also try to make sense of how
                                   software developers can prevent another
                                   flaw like this from getting such wide
                                   distribution. Behlendorf was one of the
                                   original developers of the Apache web
                                   servers, and he’s long been a leader of
                                   open source development. He’s been
                                   working with the Linux Foundation and
                                   the Open Source Security Foundation
                                   (OpenSSF) to find better practices and
                                   support them throughout the open source
                                   ecosystem.


                            # ⚓ 7_Reasons_Java_is_Perfect_for_Enterprise
                              Software_–_Business_2_Community⠀⇛


                                   Java is the fifth most used programming
                                   language worldwide in 2021, with a
                                   market share of 35.35%. Today, there
                                   are thousands of companies that use
                                   Java software development services for
                                   digital products and solutions. Among
                                   these, enterprise software is one of
                                   the most in-demand services for
                                   companies – and Java has been a primary
                                   part of the technology stack for
                                   developing these applications.


                            # ⚓ Java_News_Roundup:_More_Log4Shell_Statements,
                              Spring_and_Quarkus_Updates,_New_Value_Objects
                              JEP⠀⇛


                                   This week’s Java roundup for December
                                   20th, 2021, features news from OpenJDK
                                   with a new draft on value objects, JDK
                                   18, JDK 19, Project Loom, additional
                                   statements from vendors on Log4Shell,
                                   numerous Spring and Quarkus updates,
                                   Hibernate ORM 6.0.0-M3, point releases
                                   from Apache Camel and Camel Quarkus,
                                   Apache Tika 2.2.1 and GraalVM Native
                                   Build Tools 0.9.9.


    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ How_Disgust_Explains_Everything_–_The_New_York_Times⠀⇛


                       For psychologists who study it, disgust is one of
                       the primal emotions that define — and explain —
                       humanity.


                # ⚓ Investigation_of_possible_underlying_mechanisms_behind
                  water-induced_glucose_reduction_in_adults_with_high
                  copeptin⠀⇛


          o § Hardware⠀➾


                # ⚓ Out_of_the_Box_3D_Printer_Tips_for_Beginners_|_Tom’s
                  Hardware⠀⇛


                       First, when we talk about “leveling the bed”
                       understand that what we really mean is tramming the
                       print surface. 3D printers have been tacked to the
                       walls or flipped upside down and still work fine.
                       Being level to a table has nothing to do with their
                       ability to print.


                       When you level the bed on a 3D printer, you’re
                       making sure that the nozzle is at the same height
                       across the entire print surface. This allows the
                       printer to lay down a perfect first layer and the
                       foundation for a good print.


                       If your printer didn’t come with a probe to auto
                       level the bed for you, have no fear. It’s really
                       not that hard.


                       First, heat the nozzle and bed as if you’re setting
                       up a print. Metal expands slightly when warm, so
                       never calibrate a cold machine. Allow the printer
                       to warm up for a few minutes.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ How_a_cancer_survivor_turned_a_bad_diagnosis_into_life-
                  changing_work⠀⇛


                       That dream started with cancer.


                       [...]


                       Specialists soon provided a name. The then-43-year-
                       old had multiple myeloma, a relatively rare form of
                       blood cancer that typically strikes people in their
                       70s. Back then, few lived longer than two years.


                       She spent the next six months in America undergoing
                       tandem stem cell transplants using her own healthy
                       cells, while family and friends rallied so Paul and
                       the kids could stay in Mexico. He traveled back and
                       forth to be with her when she was sickest. Then she
                       moved back to Mexico and traveled periodically to
                       Houston for treatments. After months of that, they
                       moved back to the United States.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Is_LastPass_Password_Manager_Hacked?_Users
                              Reveal_Possible_Compromise,_3_Ways_to_Protect
                              Your_Password⠀⇛


                                   The free and popular password manager
                                   LastPass might be compromised. Its
                                   members reported multiple attempted
                                   logins by malicious actors who used the
                                   correct LastPass master password.


                                   Members are advised to enable two-
                                   factor authentication to secure their
                                   accounts.


                                   LastPass is popularly known as a
                                   reliable password manager and web
                                   browser extension. Its service also
                                   extends to smartphones via an app.
                                   Unfortunately, its good reputation is
                                   now being tested after members reported
                                   concerning issues about its interface.


                            # ⚓ Top_10_Open_Source_Cybersecurity_Projects_to
                              Try_In_2022⠀⇛


                                   Cybersecurity is one of the important
                                   elements in the existing computer
                                   systems of all organizations in
                                   Industry 4.0. The rise in innovations
                                   of cutting-edge technologies like
                                   artificial intelligence, cloud
                                   computing, and machine learning has
                                   instigated organizations to adopt
                                   digital transformation to boost
                                   performance. But, this adoption can
                                   welcome a plethora of opportunities for
                                   cybercriminals to successfully achieve
                                   cyberattacks into the systems. Thus,
                                   aspiring techies, who want to join the
                                   cybersecurity field, have to try
                                   certain cybersecurity projects to gain
                                   sufficient knowledge of open source
                                   projects. There are innumerable open
                                   source projects on cybersecurity to
                                   gain confidence in this domain and earn
                                   a lucrative salary package per annum.
                                   Thus, let’s explore some of the top ten
                                   open source cybersecurity projects to
                                   try in 2022.


                                   [...]


                                   GNU Radio is one of the top ten open
                                   source projects on cybersecurity and
                                   software development toolkits to
                                   provide signal processing blocks for
                                   implementing software radios.
                                   Organizations can use this with
                                   readily-available low-cost external RF
                                   hardware for software-defined radio.


                                   [...]


                                   Google has launched the open-source
                                   cybersecurity project known as
                                   OpenTitan to secure chip design
                                   efficiently. This project will allow
                                   organizations to enhance the initial
                                   design and strengthen the security of
                                   the implementation of the chip. It can
                                   be used in data centres and
                                   infrastructures to build upon a
                                   trustworthy state.


                            # ⚓ T-Mobile_hit_with_a_data_breach_–
                              NotebookCheck.net_News⠀⇛


                                   T-Mobile has suffered a data breach
                                   according to The T-Mo Report. While
                                   this breach appears to be on a smaller
                                   scale, the mobile company was hit with
                                   another, much larger-scale attack in
                                   August.


                                   Documents show that bad actors targeted
                                   user accounts and engaged in
                                   ‘unauthorized activity’ in the form of
                                   SIM swapping or spying of the user’s
                                   customer proprietary network
                                   information (CPNI).


                            # ⚓ Getting_the_Most_Out_of_Sandboxing⠀⇛


                                   Chris Palmer discusses the nature and
                                   particulars of the OS limitations we
                                   face, what security gap they leave us
                                   with, and what we are doing to make
                                   Chromium’s large codebase less memory-
                                   unsafe.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Is_New_Orleans_Trading_Internet_Access
                                    for_Corporate_Surveillance?_|_The_New
                                    Republic⠀⇛


                                         The city’s plan to use smart
                                         streetlights to deliver free WiFi
                                         is causing alarm about who will
                                         own New Orleanians’s data.


          o § Defence/Aggression⠀➾


                # ⚓ Iraqi_Minister_Sacks_Babylon_Police_Chief_after_Deadly
                  Operation_|_Asharq_AL-awsat⠀⇛


                       Iraq’s interior minister dismissed Babylon
                       province’s police chief on Friday and several
                       officers were called for questioning following an
                       operation that reportedly led to the deaths of 20
                       members of the same family.


                       The operation, details of which remain unclear,
                       took place Thursday when rapid intervention units
                       and intelligence forces sought to storm a house in
                       the village of Al-Rashayed in the central Iraqi
                       province.


          o § Environment⠀➾


                # § Wildlife/Nature⠀➾


                      # ⚓ Man_Killed_in_Apparent_Shark_Attack_Off_California,
                        the_Authorities_Say⠀⇛


                             A man who had been on a boogie board off the
                             coast of central California died after he was
                             apparently attacked by a shark near Morro
                             Bay, the authorities said on Friday.


                             The man, who the authorities did not
                             identify, was found floating and unresponsive
                             off Morro Strand State Beach at about 10:40
                             a.m. and was pronounced dead at the scene,
                             according to a statement from California
                             State Parks.


                             [...]


                             There were 57 unprovoked shark attacks
                             worldwide in 2020 and 39 provoked attacks,
                             resulting in 13 fatalities, according to the
                             International Shark Attack File, another
                             organization that tracks shark data, which is
                             based at the Florida Museum of Natural
                             History at the University of Florida.


          o § Finance⠀➾


                # ⚓ Messy_NFT_drop_angers_infosec_pioneers_with_unauthorized
                  portraits⠀⇛


                # ⚓ What_Military_Budget_Expansion_Says_About_Our_Broken
                  Financial_System⠀⇛


                       The externalities of unfettered money printing are
                       extremely overweight to the negative side of the
                       spectrum. When the government has the ability to
                       work in conjunction with central banks to print
                       money ex-nihilo to fund an activity, those who are
                       in control of managing that activity are
                       incentivized to be extremely wasteful to justify
                       their budgets funded by the money printer. There is
                       no greater example of this than the US military,
                       which currently boasts an annual budget of $768.2B
                       for 2022.


                # ⚓ The_Richmond_Observer_–_N.C.’s_Apple_deal_named_worst_of
                  2021⠀⇛


                       The $846 million subsidy deal that North Carolina
                       struck with Apple just topped the “year’s worst”
                       list of a nonpartisan economic think tank. The
                       Center for Economic Accountability selected the 39-
                       year agreement to put Apple’s campus in Research
                       Triangle Park as the “Worst Economic Development
                       Deal of the Year,” saying that its annual $21
                       million cost to the state led the list of reasons.


                       “A billion dollars is a lot of money for North
                       Carolina’s taxpayers and communities, because
                       that’s $1 billion worth of public services not
                       being funded,” said John Mozena, CEA president.
                       “But for a company like Apple, which reported more
                       than $1 billion a day in revenues this past year,
                       it isn’t anywhere near enough money to move the
                       needle on a major site selection decision.”


                       CEA opposes economic development subsidies in
                       general, as a nonpartisan watchdog group promoting
                       government transparency and free-market principles.
                       In their report, researchers pointed out that North
                       Carolina’s anticipated $21 million in annual lost
                       tax revenue is more than the state spends on work
                       force building programs like community college
                       distance education.


                # ⚓ GOVERNMENT-IMPOSED_BITCOIN_ADOPTION_IS_CLASHING_WITH
                  COMMUNITY_EFFORTS_ON_THE_GROUND_IN_EL_SALVADORs⠀⇛


                       Embracing Bitcoin is a bold move and a great chance
                       for countries like El Salvador, but the end doesn’t
                       justify the means. Bitcoiners are being played for
                       President Nayib Bukele’s power fantasies of a new
                       Bitcoin City, whose original plans were downloaded
                       from the internet. Bitcoin is non-political,
                       therefore Bitcoiners shouldn’t get too close to
                       politics. Educational communities like Bitcoin
                       Beach and Bitcoin City SV are far more likely to
                       achieve sustainable Bitcoin adoption than airdrops
                       and the coercion to use custodial wallets.


                # ⚓ Strategic_industries_need_government_support [Ed: What they
                  mean to say is that they want grifting at taxpayers' expense
                  (e.g. national debt) for a patent cartel, or monopolies that
                  hurt the public two-fold]⠀⇛


                       The United States has lost two industries of
                       critical strategic importance: semiconductors and
                       communications-infrastructure equipment. Only about
                       9% of the world’s semiconductor devices are
                       currently produced in the US and no significant
                       telecom-equipment manufacturers remain in that
                       country.


                       Different reasons are responsible for these losses,
                       but government support will be required in both
                       cases if the United States is to keep its
                       industrial competitiveness.


                       Since these industries were largely pioneered in
                       the US, we should examine how this happened, and
                       ask further how valid are concerns about America’s
                       apparent loss of technological leadership.


          o § Civil Rights/Policing⠀➾


                # ⚓ [Older]_ISIS_Man_Who_Chained_a_Five-year-old_Yazidi_Girl_to
                  Die_Jailed_For_Life⠀⇛


                       An ISIS fanatic who chained up a five-year-old
                       Yazidi girl in the sun and let her die of thirst as
                       punishment for wetting the bed collapsed in a
                       German court today after he was jailed for life for
                       genocide.


          o § Monopolies⠀➾


                # ⚓ Big_Tech’s_Next_Monopoly_Game:_Building_the_Car_of_the
                  Future⠀⇛


                # § Patents⠀➾


                      # ⚓ European_Union:_Will_The_European_Patent_System
                        Embrace_Grace_Periods? [Ed: Convinced corrupt firm
                        Marks & Clerk does not want you to know about EPO
                        corruption, which it is abetting]⠀⇛


                             The European Patent Office is conducting a
                             survey of European patent applicants, to
                             assess the impact of the EPO’s strict novelty
                             requirement on applicants’ disclosure and
                             commercialisation strategies. In particular,
                             the EPO wishes to assess what impact
                             different grace period scenarios might have
                             on the commercial behaviour of patent
                             applicants. Other patent systems, notably
                             that in the US, allow for grace periods,
                             which proponents argue allow inventors to
                             test their inventions in the marketplace
                             before committing to the time and cost of
                             filing patent applications. On the other
                             hand, a strict novelty requirement for
                             patentability can provide greater certainty
                             to the patent granting process.


                      # ⚓ EPO_consults_on_patent_grace_periods_(again) [Ed:
                        Instead of tackling its_profound_corruption, EPO
                        management asks about “grace” periods”]⠀⇛


                             The EPO has launched a user consultation on
                             grace periods for patents, the results of
                             which will be published in early 2022 (EPO
                             press release). The EPC as it currently
                             stands does not permit a grace period in
                             which inventors may disclose their invention
                             without prejudicing a future patent filing.
                             Whilst this is not the first time the EPO has
                             considered whether there would be any
                             benefits to introducing a patent grace
                             period, so far widespread support for
                             introducing a grace period in Europe has
                             always been lacking. EPO users are set-up for
                             operating in a file-first, publish-after
                             system, and few would welcome the legal
                             uncertainty that a European grace period
                             would introduce. Nonetheless, the EPO clearly
                             believes that it is time once again time to
                             take the temperature on their no-grace period
                             approach.


                             Legal Background: Grace Periods


                             According to Article 54 EPC, the state of the
                             art for determining novelty constitutes
                             everything that was made available to the
                             public before the priority date of the patent
                             application, regardless of whether the
                             applicant/inventor was responsible for the
                             publication. By contrast, the US patent
                             system retains a grace period for patent
                             applications. In the US, disclosures made by
                             an inventor (or someone who obtained the
                             subject-matter from the inventor), up to 1
                             year from the priority date, do not
                             constitute prior art for the patent (AIA 35
                             U.S.C. 102(b)(1)(A)). If the inventor has
                             disclosed their invention during the grace
                             period, then further disclosures by third
                             parties also don’t constitute prior art (AIA
                             35 U.S.C. 102(b)(1)(B)).


                # § Copyrights⠀➾


                      # ⚓ Happy_Public_Domain_Day_2022!_–_The_Public_Domain
                        Review⠀⇛


                             Each January 1st is Public Domain Day, where
                             a new crop of works have their copyrights
                             expire and become free to enjoy, share, and
                             reuse for any purpose.


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